Answer:
d Because I just took the test and got it right
Surface area of Rectangular pyramid
The surface area of the rectangular pyramid is 75 m².
What is surface area?Surface area is the sum of all the surfaces on each side of a three-dimensional shape.
To calculate the surface area of the rectangular pyramid, we use the formula below
Formula:
S.A = 2lh+l²............................. Equation 1Where:
S.A = Surface area of the rectangular pyramidl = Length of the base of the pyramidh = Slope height of the pyramidFrom the question,
Given:
l = 5 mh = 5 mSubstitute these values into equaation 1
S.A = 2×5×5+5²S.A = 50+25S.A = 75 m²Learn more about Surface area here: https://brainly.com/question/1297098
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Line Segment BD and Line Segment CK are diameters of ⊙ A. Line Segment BP and Line Segment QP are tangents to ⊙ A. Find each of the following. Show your work.
11.) m∠ABP=_________
12.) m∠BAK=_________
13.) m∠AQP=_________
14.) m∠QAK=_________
15.) Measure of Arc BK=__________
16.) Measure of Arc BQ=__________
17.) m∠CAD=_________
18.) m∠CAB=_________
19.) Measure of Arc CB= __________
20.) m∠CDA=_________
The measure of angle ABP from the given circle is 90°.
From the given figure,
11) Measure of angle ABP is 90°.
12) Measure of angle BAK is 180°-(90°+25°)
= 180°-115°
= 65°
13) Measure of angle AQP is 90°.
14) Measure of angle QAK is 180°-(90°+25°) (Because ∠BPA=∠QPA=25°)
15) Measure of Arc BK = Measure of angle BAK = 65°
16) Measure of Arc BQ = Measure of angle BAQ = 65°×2
= 130°
17) m∠CAD=m∠BAK=65°
Therefore, the measure of angle ABP from the given circle is 90°.
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In a game, you can get 20 points, 10 points, 2 points. You calculated the expected value of the game; expected value = 5.6. If you play the game many times, how many points can you get on average?
On average, you can expect to get about 4.24 points per game if you play many times.
How to calculate how many points can you get on averageTo find the average number of points you can get by playing the game many times, you can use the expected value as a guide.
The expected value of the game is calculated as follows:
(20 points x probability of getting 20) + (10 points x probability of getting 10) + (2 points x probability of getting 2) = 5.6
Let's use the variables p20, p10, and p2 to represent the probabilities of getting 20 points, 10 points, and 2 points, respectively. Then we can set up the equation:
(20p20) + (10p10) + (2p2) = 5.6
We also know that the sum of the probabilities must equal 1:
p20 + p10 + p2 = 1
Now we have two equations and three variables. We need one more equation to solve for the variables. One way to do this is to assume that the probabilities of getting 20 points, 10 points, and 2 points are proportional to the point values themselves.
In other words, let's assume that:
p20 : p10 : p2 = 20 : 10 : 2
We can then use this proportion to write p20 and p2 in terms of p10:
p20 = 2p10
p2 = 4p10
Now we can substitute these expressions into the two equations we have:
(20p20) + (10p10) + (2p2) = 5.6
p20 + p10 + p2 = 1
Substituting the first equation gives:
(20(2p10)) + (10p10) + (2(4p10)) = 5.6
Simplifying:
80p10 + 10p10 = 5.6
90p10 = 5.6
p10 = 5.6/90
p10 = 0.062
Now we can use the proportions to find p20 and p2:
p20 = 2p10 = 2(0.062) = 0.124
p2 = 4p10 = 4(0.062) = 0.248
Finally, we can calculate the average number of points:
(20 points x 0.124) + (10 points x 0.062) + (2 points x 0.248) = 3.12 + 0.62 + 0.496 = 4.236
So, on average, you can expect to get about 4.24 points per game if you play many times.
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A group of friends wanted to rent a cabin for the fourth of July.
The total cost to rent the cabin was $960. However, 4 of the
friends decided not to go. The remaining friends decided to
divide the $960 cost equally, which therefore increased each
share by $120. How many friends were originally in the group?
Show all your work!
If a group of friends wanted to rent a cabin for the fourth of July. The number of friends that were originally in the group is 8.
How to find the number of friend?Let x represent the number of friends in the group
Cost per person =960/x
After the 4 friends dropped out the remaining number of friends was = x - 4
New cost per person =960/x + 120
New total cost of the cabin rental = (x - 4) * (960/x + 120)
Set the two expressions equal to each other
960 = (x - 4) * (960/x + 120)
960 = 960 - (3840/x) + 120(x - 4)
Simplifying
3840/x = 120x - 480
Multiplying both sides by x
3840 = 120x^2 - 480x
Rearranging
120x^2 - 480x - 3840 = 0
Dividing both sides by 120
x^2 - 4x - 32 = 0
Quadratic equation
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where:
a = 1, b = -4, and c = -32.
Plugin the formula
x = (4 ± √(16 + 128)) / 2
x = (4 ± √(144)) / 2
x = (4 ± 12) / 2
x = 8 or x = -4
Therefore the number of friends is 8.
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Consider the graph of a function, f(x), which represents the number of cars on a busy road x hours after midnight. What is the approximate average rate of change, in cars per hour, of the function from x=0 to x =12 ?
On average, the number of cars on the busy road increases by 25 cars per hour from midnight to 12:00pm
What is the average rate of change of the functionThe average rate of change of a function from x=a to x=b is given by the formula:
average rate of change = (f(b) - f(a)) / (b - a)
Using this formula, we can calculate the average rate of change of the function f(x) from x=0 to x=12 as follows:
average rate of change = (f(12) - f(0)) / (12 - 0)
Where
f(0) = 0 and f(12) = 300 -- from the graph
So, we have
Rate = (300 - 0) / 12
Rate = 25
Therefore, the approximate average rate of change of the function from x=0 to x=12 is 25 cars per hour.
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Which of the following are like radicals? Check all
of the boxes that apply.
3x√x²y
O -12x√√x³y
O-2x√xy³²
Ox√yx²
-x√x²y
O 2√xy
The like radicals are 3x√x²y and x√yx², and the answer is:
3x√x²y, -2x√xy³², x√yx², 2√xy
What is expression?An expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division. It does not have an equal sign and can be simplified or evaluated by applying the appropriate rules of arithmetic.
According to the given information:
The like radicals have the same radicand (expression under the radical sign) and the same index (the number outside the radical sign). Checking each expression:
3x√x²y: The radicand is x²y and the index is 2.-12x√√x³y: The expression can be simplified as -12x√(x√(x^2 * y)) = -12x√x³√y, which has a different index than the first expression, so it is not a like radical.-2x√xy³²: The radicand is xy³² and the index is 2.x√yx²: The expression can be simplified as x√(y*x²) = x√(x²y), which has the same radicand and index as the first expression, so it is a like radical.-x√x²y: The expression can be simplified as -x√(x²y) = -x|x|√y, which has a different coefficient and a different index than the first expression, so it is not a like radical.2√xy: The radicand is xy and the index is 2.Therefore, the like radicals are 3x√x²y and x√yx², and the answer is:
3x√x²y, -2x√xy³², x√yx², 2√xy
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calculate the work done required to drag a stone if mass 30kg on the ground through a distance of 50m.(Take acceleration due to gravity = 10m/s²).
Answer: Work done= F.d
= 15000 J
Step-by-step explanation:
Work done= Force*distance
where
Force= mass*acceleration
mass=30kg, acceleration= 10 m/s^2, distance
=30*10
=300 N
then by formula of work done
Work done= F.d
= 300*50
=15000J
Translate the phrase into a variable expression. Use the letter c to name th
variable. If necessary, use the asterisk (*) for multiplication and the slash
(/) for division.
...
the value of the company divided by 96884 shares...
Nathan is making lemonade to sell at a school fundraiser. His recipe requires $4 times as much water as sugar and twice as much sugar as lemon juice. He uses $3 cups of lemon juice. How many cups of water does he need
Nathan needs 24 cups of water to make his lemonade recipe.
Let's call the amount of lemon juice Nathan uses "x".
We know that Nathan uses 3 cups of lemon juice, so we can substitute x = 3 into the problem.
According to the recipe, the amount of sugar Nathan needs is twice the amount of lemon juice, so he needs 2x cups of sugar.
Substituting x = 3, we get that Nathan needs 2(3) = 6 cups of sugar.
The amount of water Nathan needs is four times the amount of sugar he needs, so he needs 4 times 6 cups of water, which is equal to 24 cups of water.
Therefore, Nathan needs 24 cups of water to make his lemonade recipe.
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Use the distributive property and inverse operations to solve the two-step equation.
-8(0.5x-3)=3
Answer:
5.25 or 5 1/4
Step-by-step explanation:
-8(0.5x-3)=3
first, just multiply -8 by 0.5x and -8 by -3 and you'll get:
-4x+24=3
next, subtract 24 on both sides, meaning subtract 24 by 24 on the left side and subtract 24 by 3 on the ride side:
-4x=-21
the final thing you have to do is divide -4 on both sides to get the x by itself:
x=5.25 or 5 1/4
The answer please thank uu
Answer:
1. is (18,4)
2. is (8,10)
3. (-9,-8)
4. (9,-8)
Step-by-step explanation:
i promise its right please give brainliest
imma be giving brainliest if you help me!!!???!!??
using trignometric ratio of sine thee measure of the angle x to the nearest degree is 28 degrees
What is Trignometric ratio?Trigonometric ratios are ratios of the sides of a right triangle, such as sine, cosine, and tangent, that are used to find missing side lengths or angles.
What is angle?An angle is a geometric figure formed by two rays or line segments that share a common endpoint, known as the vertex. It is typically measured in degrees or radians.
According the given information:
We can use the trigonometric ratio of sine to find the measure of the angle x.
sin(x) = opposite/hypotenuse
In this case, the opposite side is the height of the triangle, which is 13, and the hypotenuse is the length of the diagonal line connecting the base and the top of the triangle. We can use the Pythagorean theorem to find the length of the hypotenuse.
hypotenuse² = base² + height²
hypotenuse² = 22² + 13²
hypotenuse² = 769
hypotenuse ≈ 27.73
Now we can substitute the values into the sine ratio:
sin(x) = 13/27.73
x ≈ 28 degrees
Therefore, the measure of the angle x to the nearest degree is 28 degrees.
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Which line is represented by y=3/2x-3 ? A. B. C. D.
Answer:
B
Step-by-step explanation:
the equation y=3/2x-3 has a slope of 3/2 and a y intercept of -3
So, first find the graph(s) that have the y intercept of -3. The only options would be B and C.
Next, from the y-intercept of -3, go UP 3, and to the RIGHT 2 to find your next point. This eliminates option C for the slope. The slope of option C is 2/3, not 3/2.
So, option B is correct. Hope this helps ;)
Answer:
B
Step-by-step explanation:
y = mx + b
y = mx (slope) + b (y-intercept)
The y-intercept of y = 3/2x - 3 is -3, so the graph needs to have a point at (0, -3). The slope is 3/2, if you go up 3 times and to the right twice from the point (0, -3), it will point (2, 0).
a probability distribution of the claim sizes for an auto insurance policy is given in the table below: claim size 20 30 40 50 60 70 80 probability 0.10 0.10 0.10 0.20 0.15 0.10 0.25 what percentage of the claims are within one standard deviation of the mean claim size?
55% of the claims are within one standard deviation of the mean claim size.
To find the percentage of claims that are within one standard deviation of the mean claim size, we first need to calculate the mean and standard deviation of the distribution.
The mean claim size is:
u = (20 × 0.10) + (30 × 0.10) + (40 × 0.10) + (50 × 0.20) + (60 × 0.15) + (70 × 0.10) + (80 × 0.25) = 54
The variance can be calculated as follows:
s^2 = [[tex](20-54)^{2}[/tex] × 0.10] + [[tex](30-54)^{2}[/tex] × 0.10] + [[tex](40-54)^{2}[/tex] × 0.10] + [[tex](50-54)^{2}[/tex] × 0.20] + [[tex](60-54)^{2}[/tex] × 0.15] + [[tex](70-54)^{2}[/tex] × 0.10] + [[tex](80-54)^{2}[/tex] × 0.25] = 340
The standard deviation is the square root of the variance:
s = √340 ≈ 18.44
To find the percentage of claims that are within one standard deviation of the mean claim size, we need to find the range of claim sizes that fall within the interval (u - s, u + s).
(u - s) = 54 - 18.44 = 35.56
(u + s) = 54 + 18.44 = 72.44
We can see from the table that the claim sizes 40, 50, 60, and 70 fall within this range, and their probabilities add up to:
0.10 + 0.20 + 0.15 + 0.10 = 0.55
Therefore, 55 percentage of the claims are within one standard deviation of the mean claim size.
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Difference between problem with median nerve (C6-C8, T1) and with Klumpke's palsy (C7, C8, T1)
The median nerve and Klumpke's palsy are both related to nerve injuries in the arm, but they involve different nerve pathways and result in different symptoms.
The median nerve runs from the brachial plexus in the neck through the arm to the hand, and controls movement and sensation in the thumb, index, middle, and part of the ring fingers. Damage to the median nerve can result in symptoms such as weakness, numbness, and tingling in these fingers, as well as muscle wasting in the thumb.
Klumpke's palsy, on the other hand, involves damage to the lower brachial plexus nerves, specifically the C7, C8, and T1 nerve roots. This can result in weakness or paralysis in the hand and wrist, with symptoms such as a claw-like deformity, decreased grip strength, and loss of sensation in the affected areas.
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2. Given: MNOP is a rectangle.
Show: The diagonals bisect each other, and the diagonals are congruent.
M
-5
N
The answer of the given question based on the rectangle is , The MNOP congruence is shown by Side-Angle-Side (SAS) and the steps are given below.
What is Diagonal?In geometry, a diagonal is a straight line that connects two non-adjacent vertices of a polygon or a polyhedron. In other words, a diagonal is a line segment that joins two corners or vertices of a shape that are not next to each other. For example, in a rectangle, the diagonals are the line segments that connect opposite corners of the rectangle.
To show that the diagonals of a rectangle bisect each other and are congruent, we can use the following steps:
Draw the diagonal MO and the diagonal NP.Since MNOP is a rectangle, we know that angles M and N, as well as angles O and P, are right angles. Therefore, we have four right triangles: triangle MNO, triangle NOP, triangle OPM, and triangle PMN.Since each of these triangles shares side OP, we can use the Side-Angle-Side (SAS) congruence criterion to show that triangles MNO and OPM are congruent, and triangles NOP and PMN are congruent.Since these triangles are congruent, we know that their corresponding sides are congruent. In particular, we know that segment MP is congruent to segment NO.Since MO and NP intersect at point Q, we know that Q is the midpoint of both segments MO and NP. Therefore, the diagonals of rectangle MNOP bisect each other.Therefore, we have shown that the diagonals of a rectangle bisect each other and are congruent.
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Ann fills her water bottle with 1 liter of water before school. She sets a goal to drink all of the water by the end of the school day. To stay on track, she drinks the same amount of water each hour for 8 hours. How many milliliters of water does Ann drink each hour?
Ann drinks 125 milliliters of water each hour to stay on track and finish her 1-liter water bottle by the end of the school day.
To solve this problem, we first need to convert the given volume of water from liters to milliliters since milliliters are a more appropriate unit of measurement for the amount of water that Ann drinks each hour.
1 liter = 1000 milliliters
Therefore, Ann drinks 1000 milliliters of water in total for the day.
To find out how many milliliters of water Ann drinks each hour, we can divide the total amount of water by the number of hours she drinks it for.
1000 milliliters / 8 hours = 125 milliliters per hour
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Question 6
Hannah has $14,975 in an IRA. If she deposits $3,000 this year and then increases those deposits by $750 each following year, what rate does she need to earn to reach $1,000,000 in twenty-five years?
Hannah needs to earn an annual interest rate of approximately 5.88% to reach $1,000,000 in 25 years.
To determine the rate Hannah needs to earn to reach $1,000,000 in 25 years, we can use the future value formula for an annuity:
[tex]FV = Pmt * [(1 + r)^n - 1] / r[/tex]
where:
FV = future value (in this case, $1,000,000)
Pmt = periodic payment (in this case, Hannah's annual contribution)
r = annual interest rate
n = number of periods (in this case, 25 years)
Hannah will deposit $3,000 this year and increase her deposits by $750 each following year. So her annual contributions will be:
Year 1: $3,000
Year 2: $3,750
Year 3: $4,500
...
Year 25: $21,750
To simplify the calculation, we can use the average annual contribution over the 25-year period, which is:
[tex][(3,000 + 21,750) / 2] = $12,375[/tex]
Now we can plug in the values into the formula and solve for r:
[tex]1,000,000 = 12,375 * [(1 + r)^25 - 1] / r[/tex]
Multiplying both sides by r and dividing both sides by 12,375, we get:
[tex]r x (1 + r)^25 = 120.75[/tex]
We can solve for r using trial and error, or using a financial calculator or spreadsheet. Using trial and error, we can try different interest rates until we find the one that makes the equation true. One possible method is to start with a reasonable guess, such as 6%, and adjust up or down until we get close to 120.75. After a few iterations, we find that:
r = 5.88%
Therefore, Hannah needs to earn an annual interest rate of approximately 5.88% to reach $1,000,000 in 25 years, assuming she deposits $3,000 this year and increases those deposits by $750 each following year.
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May you please go over step by step of how to do this
The missing lengths of a geometric system are listed below: AC = 114, BC = 96, BE = 3
How to determine missing lengths of two similar triangles
In this problem we find a geometric system formed by two similar triangles. Two triangles are similar if every pair of corresponding sides have the same proportion. Then, the system is described by this proportion formula:
AB / AC = AE / AD = BE / CD
18 / AC = 15 / 95 = BE / 19
Then,
18 / AC = 15 / 95
AC = 18 × (95 / 15)
AC = 114
15 / 95 = BE / 19
BE = 19 × (15 / 95)
BE = 3
Now, we determine the length of side BC:
BC = AC - AB
BC = 114 - 18
BC = 96
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Use the trading data for Friday, October 20 and Friday, October 27 to answer the questions. ( in the picture)
A) what was the difference between the high and low prices on October 20?
B) on October 27, what was the actual volume of discovery group shares posted? Write the volume in numerals.
C) at what price did discovery group clothes on October 19?
D) use the October 19 closing price from above and the October 20 opening price to find the difference in the prices as a percent increase. Round to the nearest hundredth place.
E) on October 21 discovery group announced that they would close one of their manufacturing plants. This resulted in a drop in their stock price. It closed at $32 express the number change from October 20 to October 21 as a percent rounded to the nearest tenth of a percent.
F) on October 28 discovery group announce that they would not be closing the plant this news cause the price of the stock to rise. It closed at $48.20 express the net change from October 27 to October 28 as a percent, rounded to the nearest tenth of a percent.
G) explain why 52 week high and 52 week low numbers are the same in both charts ?
H) examine the closing price of discover group on October 27 one year earlier one share closed at 30% higher than that amount, what was the closing price one year earlier?
The difference between the high and low prices on October 20 is $3.33
On October 27, the actual volume of discovery group shares posted is 2360000
How to explain the valueThe price that Discovery group clothes on October 19 is $36.94
The difference in the prices as a percent increase is 0.76%
The number change from October 20 to October 21 as a percent rounded to the nearest tenth of a percentage is -16.9%
The net change from October 27 to October 28 as a percent, rounded to the nearest tenth of a percent is 14.8%
The reason why 52 week high and 52 week low numbers are the same in both charts is that there was no price higher than $76.19 or lower than $22.78 for those weeks.
The closing price one year earlier is $54.60
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Mrs. Ades places tiles numbered 1 through 10 in a bag and assigns numbers 1-6 to Elias and tiles 7-10 to Maha. Each day, she draws a tile, and the person whose tile is drawn has to do chores. Is Mrs. Ades being fair? Explain.
Answer:
Mrs. Ades is not being fair. The probability of Elias and Maha getting chosen should be equal, but Elias has a 6/10 chance of being chosen, while Maha only has a 4/10 chance of being chosen. This is because Elias has 6 tiles assigned to him, while Maha only has 4 tiles assigned to her.
Explanation:
To make it fair, Mrs. Ades should assign each person an equal number of tiles, or draw from a bag with the tiles numbered 1 through 5 twice, assigning one to Elias and one to Maha each time, and then draw from a bag with tiles numbered 6 through 10 twice, assigning one to Elias and one to Maha each time.
A figure which has a sphare and cylinder. The total height of figure is 102mm and the height of cylinder is 76mm. Find Volume and Surface Area of the figure
The volume of the figure is approximately 50101mm^3 and the surface area is approximately 8253mm^2.
The figure consists of a sphere and a cylinder. We can find the volume and surface area of the figure by calculating the volume and surface area of each component separately and adding them together.
The height of the cylinder is given as 76mm, which means the remaining height of the figure must be occupied by the sphere. Thus, the radius of the sphere can be calculated as half the difference between the total height of the figure and the height of the cylinder:
Radius of sphere = (102mm - 76mm)/2 = 13mm
Now we can calculate the volume and surface area of each component:
Volume of cylinder = πr^2h = π(13mm)^2(76mm) ≈ 40899mm^3
Surface area of cylinder = 2πrh + 2πr^2 = 2π(13mm)(76mm) + 2π(13mm)^2 ≈ 6128mm^2
Volume of sphere = (4/3)πr^3 = (4/3)π(13mm)^3 ≈ 9202mm^3
Surface area of sphere = 4πr^2 = 4π(13mm)^2 ≈ 2125mm^2
Finally, we can find the total volume and surface area of the figure by adding the values for the cylinder and sphere:
Total volume = Volume of cylinder + Volume of sphere ≈ 50101mm^3
Total surface area = Surface area of cylinder + Surface area of sphere ≈ 8253mm^2
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the hypothesis statement h: μ < 60 is an example of an alternative hypothesis in a one-tail test. is true or false
The hypothesis statement h: μ < 60 is an example of an alternative hypothesis in a one-tail test is true
Define hypothesisA hypothesis is a proposed explanation or prediction for an observation or phenomenon that is based on limited evidence or data. It is a tentative statement or idea that can be tested through further observation, experimentation, or data analysis. Hypotheses are often used in scientific research as a starting point to investigate a research question or problem.
The hypothesis statement "μ < 60" is an example of an alternative hypothesis in a one-tailed test.
In a one-tailed test, the alternative hypothesis is directional and states that the population parameter is either greater than or less than the null hypothesis value.
In this case, the alternative hypothesis states that the population mean is less than 60.
The null hypothesis, in contrast, is typically a statement of "no effect" or "no difference" and is often denoted by H0.
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A deck of standard playing cards holds 52 unique cards.
36 of these cards are numbered cards (numbered 2-9), 4
of these cards are aces, and 12 of these cards are face
cards (jack, queen, and king). If you play a card game and
draw half of the face cards, one ace, and one fourth of the
numbered cards, how many cards do you have? How
many of each card type of card do you have? Cite
evidence from the problem.
PLS HELP
The total number of cards drawn is 16 and As a result, we have the following:
6 face cards, Aces 1, 9 numbered cards
How to determine the type of each card?Because there are 12 face cards, half of them are 6 face cards.
There are 4 aces, so we draw 1.
There are 36 numbered cards in total, therefore one-fourth of them are 9 numbered cards.
We draw a total of 6 + 1 + 9 = 16 cards.
We may use the information provided in the problem to determine how many of each card type we have. We chose:
6 face cards make up half of the deck.
1 ace: 1 ace
9 numbered cards are one-fourth of the numbered cards.
As a result, we have:
6 face cards
Aces: 1
9 numbered cards
We can also ensure that the total number of cards drawn (16) corresponds to the number of cards in a regular deck by subtracting the cards we drew from the total number of cards: a deck of playing cards (52)
There are 52 - 16 = 36 cards left.
This means that there are 36 - 6 - 1 - 9 = 20 undrawn cards in the deck.
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1. Find volume, show work round to 2 decimal places
*cylinder*
in this case since it's a cylinder always have to do is multiply the two given measurements dancing that she gets all you need to do is run it off to the nearest two decimal places when you say to the nearest two decimal places while trying to say they are two numbers after the coma
1. Triangles
B = 4in, H = 5in
B = 6ft, H= 10ft
B = 12m, H = 15m
Application: Sandy is making tablecloths in the shape of triangles. She needs to make two triangle tablecloths for one table. The triangles have base of 2 ft and a height of 4 ft. What is the total area of the triangle tablecloths for one table?
2. Parallelogram (H = height) and (B = base)
H = 9in, B = 6in
H = 5 ft, B = 2ft
H = 7yds, B = 3yds
Application: If a parallelogram has a base of 13 mm and an area of 78 mm2 what is the height?
Hint: Use the formula. Substitute the given values and then solve as an equation.
3. Rectangle (L = length) and (w = width)
rect. DKIF with L = 8 ft and w = 6 ft
rect. AOPU with L = 13 ft and w = 5 ft
Application: Charles is paining the den. Two walls are 9 ft high and 15 ft long. The other two walls are 8 ft high and 10 ft long. Charles bought one gallon of paint that will cover 440 square feet of wall space. Does he have enough paint? Explain.
4. Rhombus ( d1 = diagonal 1) (d2 = diagonal 2)
rhombus with d1 = 12 yds and d2 = 12 yds
rhombus with d1 = 10 ft and d2 = 25 ft
rhombus with d1 = 16 in and d2 = 22 in
Application: a rhombus as an area of 72 ft and the product of the diagonals is 144. What is the length of each diagonal?
5. Trapezoid ( b1 = base 1) (b2 = base 2) (H = height)
b1 = 6 ft, b2 = 7 ft, H = 10 ft
b1 = 5 yds, b2 = 8 yds, H = 4 yds
c. b1 = 9 in, b2 = 11 in, H = 13 in
d. Application: The two bases of a trapezoid = 16 km and its area = 32 km2. What is its height?
The answers are:
1) The area of a triangle is given by the formula A = (1/2)bh, where b is the base and h is the height. For the given triangles:
Triangle 1: A = (1/2)(2ft)(4ft) = 4 sq ft (for one tablecloth), so for two tablecloths, the total area is 8 sq ft.
Triangle 2: A = (1/2)(6ft)(10ft) = 30 sq ft, so for two tablecloths, the total area is 60 sq ft.
Triangle 3: A = (1/2)(12m)(15m) = 90 sq m, so for two tablecloths, the total area is 180 sq m.
2) The area of a parallelogram is given by the formula A = Bh, where B is the base and h is the height. Rearranging this formula, we get h = A/B. For the given parallelogram:
A = 78 mm2 and B = 13 mm, so h = 78/13 = 6 mm.
3) The area of a rectangle is given by the formula A = LW, where L is the length and W is the width. For Charles' den:
The total wall space to be painted is (2 x 9 x 15) + (2 x 8 x 10) = 342 sq ft. One gallon of paint covers 440 sq ft, so Charles needs (342/440) = 0.7778 gallons of paint. Therefore, he does not have enough paint.
4) To calculate the total area of the walls to be painted, we can calculate the area of each wall and add them together.
The area of the two walls that are 9 ft high and 15 ft long is (9 x 15) = 135 sq ft each, for a total of 270 sq ft. The area of the other two walls that are 8 ft high and 10 ft long is (8 x 10) = 80 sq ft each, for a total of 160 sq ft. Adding them together, we get a total of 430 sq ft.
Since one gallon of paint covers 440 sq ft of wall space, Charles has enough paint to cover the den walls.
5) The area of a trapezoid is given by the formula A = (1/2)(b1 + b2)h, where b1 and b2 are the bases and h is the height. Rearranging this formula, we get h = 2A/(b1 + b2). For the given trapezoids:
A = (1/2)(6ft + 7ft)(10ft) = 65 sq ft and h = 2(65)/(6ft + 7ft) = 5 ft.
A = (1/2)(5yds + 8yds)(4yds) = 26 sq yds and h = 2(26)/(5yds + 8yds) = 2 sq yds.
A = (1/2)(9in + 11in)(13in) = 143.5 sq in and h = 2(143.5)/(9in + 11in) = 13.05 in.
For the application in part (d), we are given A = 32 km2 and (b1 + b2) = 16 km.
Rearranging the formula for A, we get h = 2A/(b1 + b2). Substituting the given values, we get h = 4
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help pleasejhdfjg THIS ASSIGNMENT IS LIKE 2 WEEKS OVERDUE
a) A 2*2 area model would not work to multiply (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) because this expression has 5 terms, and a 2*2 area model can only accommodate 4 smaller areas (b) The area model for (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) with the correct lengths and widths labeled has been attached below. (c) The final total area is 2x² - 10x - 15.
What is an area model?An area model is a way to visualize multiplication by breaking up the larger rectangle into smaller rectangles whose areas represent the products of the terms being multiplied. To determine the correct rows and columns for the area model, we count the number of terms in each factor and use that as a guide. For example, if one factor has 3 terms and the other has 4 terms, we would use a 3x⁴ area model, with 3 rows and 4 columns.
a) A 2*2 area model would not work to multiply (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) because this expression has 5 terms, and a 2*2 area model can only accommodate 4 smaller areas.
b) The area model for (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) with the correct lengths and widths labeled has been attached below.
2x⁴ − 3x³ − 2x² − 4x − 1
+---------------------------------------
x | 2x⁵ -3x⁴ -2x³ -4x² -x
|
3 | 6x⁴ -9x³ -6x² -12x -3
+---------------------------------------
c) To find the total area of a rectangle with length (x + 8) and width (x − 5), we can use an area model with 2 rows and 2 columns. The length (x + 8) corresponds to one dimension of the rectangle, while the width (x − 5) corresponds to the other dimension. The area of each smaller rectangle in the model represents the product of one term from each factor.
x + 8 x - 5
+--------------------
x | x² + 8x x² - 5x
|
-5 | -5x + -40 -5x + 25
+--------------------
The final total area can be found by adding up the areas of the smaller rectangles:
Total area = x² + 8x + x² - 5x - 5x - 40 + 25
= 2x² - 10x - 15
= 2x² - 10x - 15.
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show that the boundary of a generalized rectangle is the union of finitely many closed generalized rectangles with volume zero.
We have shown that the boundary of a generalized rectangle is the union of finitely many closed generalized rectangles with volume zero.
What is rectangle?The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.
Let A and B be two sets in a generalized rectangle R, i.e., R = A x B. The boundary of R, denoted by bd(R), is defined as the closure of the set of points that are not in the interior of R. In other words, bd(R) = cl(R) \ int(R), where cl(R) is the closure of R and int(R) is the interior of R.
To show that bd(R) is the union of finitely many closed generalized rectangles with volume zero, we first note that the closure of R can be expressed as the union of R and its boundary, i.e., cl(R) = R ∪ bd(R). Therefore, it suffices to show that R can be expressed as the union of finitely many closed generalized rectangles with volume zero and that bd(R) can also be expressed as the union of finitely many closed generalized rectangles with volume zero.
Let (a,b) be a point in R. Then there exists an open ball B((a,b), r) around (a,b) that is contained in R, where r > 0. Without loss of generality, we can assume that r is small enough so that B((a,b), r) is a generalized rectangle. Since B((a,b), r) is open, it follows that int(R) is the union of all such generalized rectangles. Therefore, R can be expressed as the union of finitely many closed generalized rectangles with volume zero, namely the closures of all such generalized rectangles.
Next, we show that bd(R) can be expressed as the union of finitely many closed generalized rectangles with volume zero. Let (a,b) be a point in bd(R). Then every open ball B((a,b), r) around (a,b) contains points both in R and in the complement of R. By definition of bd(R), the closure of B((a,b), r) intersects both R and the complement of R. Therefore, B((a,b), r) can be expressed as the union of two closed generalized rectangles, one contained in R and one contained in the complement of R. It follows that bd(R) can be expressed as the union of finitely many closed generalized rectangles with volume zero, namely the closures of all such balls B((a,b), r) and their decompositions into closed generalized rectangles.
Therefore, we have shown that the boundary of a generalized rectangle is the union of finitely many closed generalized rectangles with volume zero.
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PLEASE HELP ASAP‼️Solve the triangle MNO (find m
m and n).
n =
M
34°
12 cm
m=
N
4
2 fractions with different denominators that add up to 6 1/3
The two fractions with denominators of 2 and 6 that add up to 19/3 are 3/6 and 29/3, respectively.
First, let's break down what that mixed number means in terms of fractions. 6 1/3 is the same as 19/3.
Now, we need to find two fractions with different denominators that add up to 19/3. One way to do this is to use a common denominator. To find a common denominator, we need to find the least common multiple (LCM) of the two denominators.
Let's say we want to find two fractions that add up to 19/3, with denominators of 2 and 6. The LCM of 2 and 6 is 6. So, we can rewrite the fractions with a denominator of 6:
1/2 = 3/6
x/6
Now we need to find the value of x that makes the sum of the fractions equal to 19/3:
3/6 + x/6 = 19/3
To solve for x, we can multiply both sides by 6:
3 + x = 38/3
Then, we can subtract 3 from both sides:
x = 29/3
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