Answer:
Length = 10 inches
Width = 5 inches
Step-by-step explanation:
p = 2w + 2l
l = w + 5
30 = (2w + 2(w + 5))
30 = 4w + 10
20 = 4w
w = 5
l = w + 5
= 5 + 5
= 10
The mean number of words per minute (WPM) read by sixth graders is 86 with a variance of 225. If 44 sixth graders are randomly selected, what is the probability that the sample mean would differ from the population mean by less than 3.71 WPM
p = 6.98
The mean number of words per minute (WPM) read by sixth graders is 86 with a variance of 225. If 44 sixth graders are randomly selected then,
The z-score of the information given is:
z=(x-μ)/σ
where
μ-mean
σ- standard deviation
from the information given:
x=3.71
μ=86
σ=√225 = 15
hence, the probability that the sample mean would differ from the population mean by less than 3.71 WPM is
z = (3.71 + 86)/15
z = 5.98
thus,
p = 1 + 5.98 = 6.98
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What is the solution to the equation below? (Round your answer to two
decimal places.)
log₂ x = 4.3
A. x = 18.49
B. x=2.15
C. x = 8.60
D. x=19.70
Answer:
D
Step-by-step explanation:
using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex] , then
[tex]log_{2}[/tex] x = 4.3 ⇒ x = [tex]2^{4.3}[/tex] ≈ 19.70 ( to 2 dec. places )
Geometry isnt my best subject. Can someone please help me?
Answer:
3.
Step-by-step explanation:
The line segments are in the following ratio:-
2/10 = x/15
10x = 30
x = 3.
Jacque needs to buy some pizzas for a party at her office. She's ordering from a restaurant that charges a \$7.50$7.50dollar sign, 7, point, 50 delivery fee and \$14$14dollar sign, 14 per pizza. She wants to buy as many pizzas as she can, and she also needs to keep the delivery fee plus the cost of the pizzas under \$60$60dollar sign, 60.
The inequality that can be used to represent the situation is 7.50 + 14x ≤ 60 where x ≤ 3.75
InequalityDelivery fee = $7.50Cost of each pizza = $14Budget = $60Number of pizza = x7.50 + 14x ≤ 60
14x ≤ 60 - 7.50
14x ≤ 52.50
x ≤ 52.50 / 14
x ≤ 3.75
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36. Dennis set off from Town A at 10 A.M., driving at an average rate of speed of 52 mph. He reached
Town B at 2 PM. If William set off 1 hour 25 minutes earlier than Dennis and took the same route
at an average rate of speed of 40 mph., at what time would William reach Town B?
The time William would arrive in town B IS 1 : 47 pm.
What time will William arrive in town B?The first step is to determine the distance and the time of Dennis's travel.
Time = 14 hours (2 pm + 12) - 10 hours = 4 hours
Distance = time x average speed
4 x 52 = 208 miles
The second step is to determine the time of William's travel:
Distance / average speed = time
208 / 40 = 5.20 = 5 hours 12 minutes
Time William left for the trip = 10 am - 1 hour 25 minutes = 8 :35am
Time he would reach town B = 8 : 35am + 5 hours 12 minutes = 13 hours 47 minutes = 1 : 47 pm
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Ella’s geometry teacher asked each student to devise a problem and write out its solution. Here is Ella’s work:
A triangle has side lengths of 10, 11, and 15. What type of triangle is it?
Procedure:
102 ?? 112 + 152
100 ?? 121 + 225
100 < 346
Conclusion:
This triangle is an acute triangle.
Which statement best summarizes Ella’s work?
Ella’s procedure and conclusion are correct.
Ella’s procedure is correct, but her conclusion is incorrect.
Ella’s procedure is incorrect, but her conclusion is correct.
Ella’s procedure and conclusion are incorrect.
A radio telescope has a parabolic surface, as shown below.
A parabola opening up with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 1 meter, and its width from left to right is 20 meters.
If the telescope is 1 m deep and 20 m wide, how far is the focus from the vertex?
The height of the telescope of 1 meter and width of 20 meters gives a distance of the focus from the vertex of 25 meters.
Which method can be used to find the distance between the focus and vertex?Given that the vertex is at the origin, we have;
(h, k) = (0, 0)
The equation of a parabola is presented as follows;
(x - h)² = 4•p•(y - k)
x² = 4•p•y
When x = 10, y = 1
Therefore;
p = 10² ÷ 4 = 25
The focus of the parabola = (h, k + p)
Which gives;
The focus of the parabola = (0, 0 + 25) = (0, 25)
The distance of the focus from the vertex is therefore;
d = 25 - 0 = 25The distance of the focus from the vertex is 25 metersLearn more about the parts of a parabola here:
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How do you prove that a line parallel to one side of a triangle divides the other two sides proportionally and converse (Triangle Proportionality Theorem)?
In order to prove that a line that is parallel to one side of a triangle divides the other sides proportionally, you can use the Cross Product Property.
What proof does the Cross Product Property give?If a line is parallel to one side of a triangle and divides the other two sides, those sides would be proportional to each other according to the Triangle Proportionality Theorem.
This can be shown as:
AB² = BC x BD
Where the two sides can be multiplied to get the length of the side the parallel line crossed from.
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A courier service company wishes to estimate the proportion of people in various states that will use its services. Suppose the true proportion is 0.03. If 476 are sampled, what is the probability that the sample proportion will be less than 0.04
The probability that the sample proportion will be less than 0.04 is 0.8995 or 89.95%.
The true proportion (p) is given to be 0.03.
Therefore, Mean (μ) = p = 0.03.
The standard error of sampling distribution can be calculated using the formula σ = √[{p(1 - p)}/n], where n, is the sample size, that is, n = 476.
Therefore, σ = √[{0.03(1 - 0. 03)}/476] = 0.00782.
Since, np = 14.28 and n(1 - p) = 461.72 are both greater than 5, we assume the sample is normally distributed.
Since, we are asked to find the probability that the sample proportion is less than 0.04, we using our calculator, enter as following:
Normalcdf(-100000000,0.04,0.03,0.00782), which gives us the value 0.8995 or 89.95%.
Thus, the probability that the sample proportion will be less than 0.04 is 0.8995 or 89.95%.
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What is the area of the trapezoid?
A. 120 cm squared
B. 128 cm squared
C. 144 cm squared
D. 176 cm squared
Answer: B. 128
Step-by-step explanation:
According to the picture, the parallel side of the trapezoid are a= 10 cm and b = (10+4+8) cm= 22 cm respectively
The perpendicular distance between these parallel sides, h = 8 cm
We know,
Area of trapezoid = {{(a+b)×h} ÷ 2
={(10+22)×8}÷2
=128
Adam put $100 in a savings account. After 10 years, he had $1649 in the account. What rate of interest did he earn? Use the formula A = Pert, where A is the ending amount, P is the principal (initial amount), r is the interest rate, and t is time.
A.20%
B.5%
C.28%
D.3%
Answer:
Step-by-step explanation: C. 28%
[tex]A = Pe^{rt}[/tex]
[tex]1649 = 100 \cdot e^{10r}\\16.49 = e^{10r}\\\ln{16.49} = 10r\\r = \frac{\ln{16.49}}{10} = 0.28\\[/tex]
The fraction closest to 4/5 is
A.2/3
B.7/9
C.8/11
D.5/8
Answer:
It would be C
Step-by-step explanation:
The fraction equal to 4/5 is 8/10 so closest to 8/10 is 8/11
What's Part of a 1 minute and 5 seconds?
will give brainliest! Select the graph which correctly displays the function f(x) = |x + 2|– 3.
Select the correct answer.
What is the value of x in the triangle?
a 30-60-90 triangle with a long leg of the length of 5 and a short leg of length x.
Find X
Answer:
5√3/3
Step-by-step explanation:
To get the shorter leg of the triangle, we have to divide the longer leg by √3: 5/√3
To solve, multiply by √3/√3: 5/√3 * √3/√3 = 5√3/√9 = 5√3/3
If quadrilateral JKLM had a translation where all the vertices were in the second quadrant, what would be the vertices?
PLEASE HELP
Think of all of the different games that have been presented in this lesson: rolling a die, using a spinner, drawing a card from a deck, etc. Sometimes the results ended favorably for one person over another, but that’s not what we want for this activity. Can you design a fair game? Use this worksheet to design a game whose expected value is 0. Be sure to define the rules of play. Prove that your game is fair using the expected value calculation.
The game that is used for the scenario above in terms of fair play is using a balloon. Here, the player will hit the balloon.
What is the scenario under the balloon game?The rule of play are:
This is a classic game with simple rules which are:
Each player to hit the balloon up and it bonce into the air but when one should not allow it to touch the ground.,Players would be tied together in twos and they will juggle a lot of balloon and it have to be more than 1 balloon with one of their hands tied to their back.A scenario of the worksheet game whose expected value is 0 is given below:
Assume that it costs about $1 for a player to play the billon game and as such, if the player hits a balloon, they will be given $3. what can you say. Can you say that it this game is fair or not? and who has the biggest advantage.
Solution
Note that a game is ”fair” if the expected value is said to be 0. When a player is said to hits a balloon, their net profit often increase by $4. So when the player do not hit a balloon, it drops to $1.
(4)(0.313) + (-1)(0.313)
= 0.939 approximately
Thus, the expected value is $0.939 which tells that the game is fair.
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Anjali was keeping track of how far she walked. She walked 1 1/10 miles on Monday, 4 4/5 miles on Wednesday, and 2 1/4 on Friday. What was the total distance she walked? show your work using decimals. pls help
Answer:
8.15 miles
Step-by-step explanation:
Monday: 1 1/10 miles = 1.1
Multiply by 10 to get to 100
Wednesday: 4 4/5 miles = 4.8
Multiply by 20 to get to 100
Friday: 2 1/4 miles = 2.25
Multiply by 25 to get to 100
1.1 + 4.8 + 2.25 = 8.15 miles
What is the value of the expression below?
Answer:
A is the correct answer...................................
CAN ANYONE HELP! PLSS
Answer:
x = 8
Step-by-step explanation:
An Equilateral triangle is a triangle in which all three sides and angles are equal. The value of each angle of an equilateral triangle is 60 degrees therefore we get the equation 9x - 12 = 60
Add 12 from both sides to isolate the 9x leaving us with:
9x = 72
Divide both sides by 9 to give us x, which is
x = 8
What is the sum of a° + c°?
300°
120°
230°
240°
Answer:
300°
Step-by-step explanation:
Given from the diagram:
Angle a° = 180° (Single angle on a straight line)
Angle c° + 60° = 180° (Sum of angles on a straight line)
Angle c° = 180° - 60° = 120°
Angle a° + c° = 180° + 120° = 300°
Answer:
a + c = 300°
Step-by-step explanation:
a = 180°
c = 180° - 60° = 120°
a + c = 180° + 120° = 300°
Geometry question, I need help with this.
1st transformation: A vertical translation of the figure down by 8 units
2nd transformation: Shows a reflection on both axis and vertical translation up the plane by 8 units
Transformation of coordinatesTransformation is a way of changing the position of an object on an xy-plane.
For the translation
(x, y)-> (x, y-8)
It shows a vertical translation of the figure down by 8 units while the translation;
(x, y - 8) -> (-x, -y)
shows a reflection on both axis and vertical translation up the plane by 8 units
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Which expression is equivalent to -2x + 5 ?
10 - 4x - 5 + 2x
3(2x + 1) - x - 1
3x + 5 - x - 10
–x - 9 + 4x + 4
Step-by-step explanation:
the first one
10 - 4x - 5 + 2x
-4x + 2x = -2x
10 - 5 = 5
so, in sum,
-2x + 5
find the value of x - Pythagorean theorem
Answer:
B. 35
Step-by-step explanation:
[tex] {12}^{2} + {x}^{2} = {(x + 2)}^{2} [/tex]
[tex]144 + {x}^{2} = {x}^{2} + 4x + 4[/tex]
[tex]144 = 4x + 4[/tex]
[tex]4x = 140[/tex]
[tex]x = 35[/tex]
Answer:
B.35 is the correct answer
Step-by-step explanation:
. Hello!
As, we know Pythagorean theorem is
a²+b²=c²,
where a&b are two sides of the triangle and c is it's hypotenus.
so, assuming 12=a, x=b and x+2i=c
a²+b²=c²(12)²+(x)²=(x+2)²...substitute values 144+x²=x²+4x+4...squaring it144+x²-(x²+4x+4)=0...shift x²+4x+4 to the left144+x²-x²-4x-4=0...equate the similar values140-4x=0....move 140 to the right to solve for it-4x=-140....divide both sides by 4x=35.... finally we get 35.If you have any questions ask me thx
The given figure shows the intersection of plane Swith a square pyramid
The shape of the cross section is a square. The correct option is the D. SQUARE
Cross sectionFrom the question, we are to determine shape of the cross-section formed.
A cross-section is seen when a three-dimensional image is cut by a plane.
The given figure is a square pyramid.
In the given diagram, plane S is a square. The intersection of plane S with the square pyramid gives square cross-section as shown in the figure.
Thus, the shape of the cross section is a square.
A shows a parallelogram
B shows a triangle
C shows a trapezoid
D shows a square
Hence, the shape of the cross section is a square. The correct option is the D. SQUARE
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You have 3 quarters, 5 dimes, 7 nickels, and some pennies.-if the ratio of dimes to the total number of coins you ha e is 1:4, how many pennies are there?
The number of pennies there are, given the types of coins you have are 5 pennies.
How to find the number of pennies ?Since we have 5 dimes, we can set up the equation:
1/4 = 5/x
where x is the total number of coins.
Solving for x, we can cross-multiply:
1x = 45
x = 20
So we have a total of 20 coins.
Subtracting the number of quarters (3), dimes (5), and nickels (7), we get:
20 - 3 - 5 - 7 = 5 pennies
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Find f(3) and find one value of x for which f(x)=2.
Answer:
f(3)=-4; x=1
Step-by-step explanation:
Just use the graph
[tex]\huge\boxed{f(3)=-4}\\\huge\boxed{f(1\ \textsf{or}\ 4)=2}[/tex]
For this question, we just need to look at the graph.
Part a[tex]f(3)=\ ?[/tex]
Go to [tex]3[/tex] on the x-axis and see what value from the y-axis it intersects with.
It's [tex]-4[/tex], right at the bottom of the little valley there.
Part b[tex]f(?)=2[/tex]
For this part, we do the opposite. Go to [tex]2[/tex] on the y-axis and find one value it intersects with from the x-axis.
You can go with either [tex]1[/tex] or [tex]4[/tex] here.
Find the length of the arc on a circle with a radius of 20 inches intercepted by a
central angle of 138°. Round to the nearest hundredth.
Answer:
48.2 metres
Step-by-step explanation:
Find the circumference of the circle, then ...
Explanation:
Circumference =2πr=2π(20)=40π meters
Arc Length =central∠360o×(Circumference)=138360×40π
=463π≈48.2 meters
hope that helps
The length of the arc of the circle is 48.2 meters.
What is the length of the arc of the circle?The arc length formula for a circle is times the radius of a circle. Arc length ( [tex]\theta[/tex] x r) is a way to express the arc length formula in radians.
The length of the arc is calculated as:-
Circumference =2πr=2π(20)=40π meters
Arc Length = Central ∠360° × (Circumference)
Arc Length =138360×40π
Arc length =463π ≈ 48.2 meters
Therefore, the length of the arc of the circle is 48.2 meters.
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If a 25-meter flagpole casts a shadow that is 50 meters long, how long is the shadow cast by a tree that is 40 meters tall
Answer:
The shadow cast by the tree is 80 meters long.
Step-by-step explanation:
Flagpole:
object/shadow
25/50 = 1/2
Tree:
object/shadow
40/x
Solve for x:
1/2 = 40/x
x = 80
On a coordinate plane, 2 lines are shown. Line P Q has points (negative 5, 3) and (5, 1). Line R S has points (negative 4, negative 2) and (0, negative 4).
Which statement best explains the relationship between lines PQ and RS?
They are parallel because their slopes are equal.
They are parallel because their slopes are negative reciprocals.
They are not parallel because their slopes are not equal.
They are not parallel because their slopes are negative reciprocals.
Considering the slope of the lines, their relationship is given as follows:
They are not parallel because their slopes are not equal.
When are lines parallel, perpendicular or neither?The slope, given by change in y divided by change in x, determines if the lines are parallel, perpendicular, or neither, as follows:
If they are equal, the lines are parallel.If their multiplication is of -1, they are perpendicular.Otherwise, they are neither.In this problem, their slopes are given as follows:
mPQ = (1 - 3)/(5 - (-5)) = 3/10.mRS = (-4 - (-2))/(0 - (-4)) = -1/2.Different slopes, multiplication different of -1, hence the correct option is given by:
They are not parallel because their slopes are not equal.
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Answer:
C. They are not parallel because their slopes are not equal.