The number of lighter boards and heavier boards in the truck is 216 and 192 boards respectively.
EquationLight board = 9 poundsHeavy board = 15 poundsTotal weight = 408 poundslet
Light board = x
Heavy board = y
x = y + 24
x + y = 408
(y + 24) + y = 408
y + 24 + y = 408
2y = 408 - 24
2y = 384
y = 384 / 2
y = 192 boards
So,
x = y + 24
= 192 + 24
x = 216 boards
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Devin Gallagher purchased home entertainment equipment for $4,020.19 using the store's credit plan. He made
a 20% down payment.
Answer:
The answer will be $3216.152
Step-by-step explanation:
If you do the 20% of $4020.19 then the answer will came $804.038 and then subtract the result from $4020.19 then it will came $3216.152 and it is the result only.
The graph shows the cube root parent function.
Which statement is true?
A. (0, 0) is the x- and y-intercept of the function.
B. The function has no intercepts.
C. (0, 1) is the x- and y-intercept of the function.
D. (1, 1) is the x- and y-intercept of the function.
Answer:
A)
Step-by-step explanation:
The cube root parent function is [tex]y=x^3[/tex]
When y=0, x=0, hence (0,0) is the x and y-intercept of the function.
Hope I helped!
Two sides of a 90 degree triangle measure 6cm and 8cm, what is the length of the
hypotenuse?
10cm
3.7cm
100cm
14cm
24cm
please help!!!!!
Answer:
10 cm
Step-by-step explanation:
Hyp = [tex]\sqrt{6^{2}+8^{2} } =\sqrt{36+64} =\sqrt{100} =10[/tex]
Hope this helps
Solve for the remaining angles
By knowing the length of the three sides of the triangle and applying the law of the cosine, we find that the measure of the three angles are 33.544°, 114.998° and 31.458°.
How to find the missing angles of a triangle
In this question we know the length of the three sides of a triangle, we can find the measure of all angles by using the law of the cosine. So, we know that:
a = 270, b = 442.85, c = 255
Then, by the law of the cosine:
[tex]\cos A = \frac{270^{2}-255^{2}-442.85^{2}}{-2\cdot (442.85)\cdot (255)}[/tex]
A ≈ 33.544°
[tex]\cos B = \frac{442.85^{2}-270^{2}-255^{2}}{-2\cdot (270)\cdot (255)}[/tex]
B ≈ 114.998°
[tex]\cos C = \frac{255^{2}-270^{2}-442.85^{2}}{-2\cdot (270)\cdot (442.85)}[/tex]
C ≈ 31.458°
By knowing the length of the three sides of the triangle and applying the law of the cosine, we find that the measure of the three angles are 33.544°, 114.998° and 31.458°.
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The final exam test scores were: 62, 66, 71, 75, 75, 78, 81, 83, 84, 85, 85, 87, 89, 89, 91, 92, 93, 94, 95, 99. Find the percentile rank for a score of 85 on this test.
Using it's concept, the percentile rank for a score of 85 on this test is the 50th percentile.
What is the percentile of a measure?When a measure is in the xth percentile of a data-set, it is greater or equal than x% of the measures and lesser than (100 - x)%.
In this problem, there are 20 scores, and 85 corresponds to the 10th highest score, hence the percentile is given by:
p = 10/20 = 0.5 x 100% = 50th percentile.
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x =x=x, equals
^\circ
∘
degrees
Step-by-step explanation:
x = 145°
we don't even need the upper parallel line with the 35° angle.
it is simply based on the fact that the angles on both sides of 2 intersecting lines have to be the same (just left-right mirrored).
On a 8.5 x 11 inches (or larger) paper, create a carnival game (for example it could be: throwing a dart at a target, ball through a hoop, ball in cup, etc).
Provide a written description of your game.
Your game must use at least two different geometric shapes.
Label the dimensions of the shapes with the measurements in real life. Draw on the paper using a scale factor.
For example, if the game has a 3 feet diameter, label 3 feet on the image, but draw it to scale, so that the model game is similar to the actual dimensions. If the scale is 1 foot = 2 inches, then 3 feet = 6 inches.
Find the probability of winning your game. Include the calculations to show the probability.
Determine the type of prize a winner would deserve and the cost of playing your game.
The probability of winning the game is 0.065
The description of the gameThe game involves throwing two darts at two targets.
To win the game, the darts must hit anywhere in the following shapes
Rectangle: 5 by 4 inchesCircle: Radius, r = 3 inchesThe probability of winningThe area of the paper is:
Area = 8.5 inches * 11 inches
Area = 93.5 square inches
The area of the rectangle on the paper is:
Area = 5 inches * 4 inches
Area = 20 square inches
The area of the circle on the paper is:
Area = π * (3 inches)²
Area = 28.3 square inches
The probability of landing on both shapes is
P(Both) = 20/93.5 * 28.3/93.5
Evaluate
P(Both) = 0.065
Hence, the probability of winning the game is 0.065
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y ( x + w ) = c ( x + z )
The formula for x in terms of other terms in the equation is; x = (cz-yw)/(y-c).
What is the formular for x in term of other terms in the equation?According to the task content, it follows that the variable X is to be made the subject of the formula;
Hence, it follows that;
y ( x + w ) = c ( x + z )
yx +yw = cx +cz
x(y-c) = (cz-yw)
x = (cz-yw)/(y-c)
Remarks: The complete question requires that x be made the subject of the formula.
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A cat gave birth to 11 calico kittens and 16 non-calico kittens. What is the ratio of calico kittens to non-calico kittens?
Answer:
11:16
Step-by-step explanation:
Let theta be an angle in quadrant 2 such that cos theta =-3/4. Find the exact values of csc theta and cot theta.
Step-by-step explanation:
Since [tex]cos(\theta) = -\frac{3}{4}[/tex] we can get some information from this. First of all [tex]cos(\theta)[/tex] is defined as [tex]\frac{adjacent}{hypotenuse}[/tex]. So the adjacent side is 3 and the hypotenuse is 4. Using this we can find the opposite side to find [tex]sin(\theta)[/tex] to calculate csc and cot of theta. So using the Pythagorean Theorem we can solve for the missing side. Also I forget to mention we have to calculate the sign of the adjacent side and the hypotenuse. Since you're given that the angle is in quadrant 2, that means the x-value is going to be negative, and the y-value is going to be negative. And the x really represents the adjacent side and the y represents the opposite. So the adjacent side is what's negative. and the opposite is positive
Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex]
[tex](-3)^2 + b^2 = 4^2[/tex]
[tex]9 + b^2 = 16[/tex]
[tex]b^2 = 7[/tex]
[tex]b = \sqrt{7}[/tex]
So now we can calculate [tex]sin(\theta)[/tex].
[tex]sin(\theta) = \frac{\sqrt{7}}{4}[/tex]
Now to calculate the exact value of csc you simply take the inverse. This gives you [tex]csc(\theta)=\frac{4}{\sqrt{7}}[/tex]. Multiplying both sides by sqrt(7) to rational the denominator gives you [tex]\frac{4\sqrt7}{7}[/tex].
Now to calculate cot(theta) you find the inverse of tan. Tan is defined as [tex]tan(\theta) = \frac{sin(\theta)}{cos(\theta)}[/tex]. So all you do is take the inverse which is [tex]cot(\theta) = \frac{cos(\theta)}{sin(\theta)}[/tex].
Plug values in
[tex]cot(\theta) = \frac{-\frac{3}{4}}{\frac{4\sqrt{7}}{7}}[/tex]
Keep, change, flip
[tex]-\frac{3}{4} * \frac{7}{4\sqrt7}[/tex]
Multiply:
[tex]-\frac{21}{16\sqrt7}[/tex]
Multiply both sides by sqrt(7)
[tex]-\frac{21\sqrt7}{112}[/tex]
This is the value of cot(theta)
Joy read 1/3 of the book in the morning and she reads some more at night by the end of the day she still had 2/5 of the book to read how much of the book did joy read at night?
Answer:
4/15
Step-by-step explanation:
Lets find a common denominator in order to find the total amount. There is a common denominator of 15 among 3 and 5. Therefore we will convert the fraction so they have the same denominator.
1/3 > 5/15
2/5 > 6/15
If Joy had read 5/15 of the book before reading at night, she already had the progress of being at 10/15 way through the book. At the end of the day, Joy had only 6/15 left of the book. To find the remainder, we subtract 10-6=4. This helps find the answer that Joy only read 4/15 of the book towards the end of the day.
What type of reaction is HCl + AgNO3?
Answer:
Double-displacement reaction
Step-by-step explanation:
In double-displacement reaction, aka. double-replacement reaction, the cation of one compound is swapped with the cation of another. They have the general structure:
AB + CD ---> AD + CB
In this case, the silver cation (Ag⁺) from AgNO₃ is swapped with the hydrogen cation (H⁺) of HCl.
The complete balanced equation is:
HCl + AgNO₃ ---> AgCl + HNO₃
help me please!!!!!!!! 20 points
Answer:
14 in^2
Step-by-step explanation:
Break the figure up into two rectangles (vertical line down the middle). Use the formula area = length x width for the Rectangle A (2 in x 4 in = 8 in^2) and Rectangle B (3 in x 2 in = 6 in^2) Add 8 in^2 and 6 in^2 for a total area of 14 in^2
HELP please, last question!
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
Fig. D is correct[tex]\textsf{ \underline{\underline{Explanation } }:}[/tex]
" when rays parallel to optical axis/ principal axis fall on a concave mirror it passes through focus of mirror after reflection "
[tex] \qquad \large \sf {Conclusion} : [/tex]
Fig. D is correctPaladin furnishings generated $4 million in sales during 2021, and its year end total assets were $3.2 million. also, at year end 2021 current liabilities were $500,000, consisting of $200,000 of notes payable, $200,000 of accounts payable, and $100,000 of accrued liabilities. looking ahead to 2022 the company estimates taht its assets must increase by $.80 for every $1.00 increase in sales. paladin's profit margin is 3% and its retention ratio is 50%. how large of a sales increase can the company achieve without having to raise funds externally?
Without having to raise funds externally sales could increase by $84,507.04.
Given that $4 million sales in 2021 and in end of the year total assets are $3.2, current liabilities are $500,000, payable notes are $200,000, accounts payable is $200,000 and accrued liabilities are $100,000 and in 2022 assets must increase by $.80 for every $1.00 increase in sales.
The amount of sales increase that the company can achieve without having to raise funds externally is calculated by multiplying the current year sales with the self-supporting growth rate.
Current Year Sales = $4,000,000
Profit Margin = 3.00%
Dividend Payout Ratio = 50%
Therefore, the Retention Ratio = 50%
Total Spontaneous Liabilities is, $200,000 + $100,000=$300,000
Last Year Total Assets = $3,200,000
Therefore, the Self-supporting Growth Rate=Addition to Retained Earnings÷[Total Assets–Total Spontaneous Liabilities-Addition to Retained Earnings]
= [Last year sales×Profit Margin×(1-Dividend Payout Ratio)]÷[Total Assets-Total Spontaneous Liabilities-Addition to Retained Earnings]
= [$4,000,000×0.03×(1–0.50)]÷[$3,200,000-$300,000–{[$4,000,000×0.04×(1–0.050)}]
= $60,000÷[$3,200,000-$300,000-$60,000]
= $80,000÷$2,840,000
= 0.02112676 or 2.112676%
Therefore, the increase in sales that the company can achieve without having to raise funds externally = Last Year Sales×Self-supporting Growth Rate
= $4,000,000×2.112676%
= $84,507.04
Hence, the Increase in Sales so the company achieve without having to raise funds externally $84,507.04”
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end behavior of f(x)= 10/x^2-7x-30
By applying definition of limits, the end behavior of the rational function f(x) = 10/(x² - 7 · x - 30) is represented for the horizontal asymptote x = 0.
What is the end behavior of a rational function
The end behavior of a rational functions is the horizontal asymptote of the rational function when x tends to ± ∞. Then, we find the end behavior by applying limits:
[tex]\lim_{x \to \pm \infty} \frac{10}{x^{2}-7\cdot x - 30}[/tex]
[tex]\lim_{n \to \infty} \frac{10}{x^{2}-7\cdot x - 30}\cdot \frac{x^{2}}{x^{2}}[/tex]
[tex]\lim_{x \to \pm \infty} \frac{\frac{10}{x^{2}} }{1 - \frac{7}{x}-\frac{30}{x^{2}}}[/tex]
[tex]\lim_{x \to \pm \infty} 0[/tex]
0
By applying definition of limits, the end behavior of the rational function f(x) = 10/(x² - 7 · x - 30) is represented for the horizontal asymptote x = 0.
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A school survey asked students which candidate they supported for class president. The survey data are shown in the relative frequency table. What percentage of females polled supported Martinez?
A:30%
B:58%
C: about 56%
D:about 54%
Answer:
About 56%
Step-by-step explanation:
KM=
What is the measure of KM?
Help please
A napkin is folded into an isosceles triangle, triangle ABC, and placed on a plate, as shown. The napkin has a perimeter of 38 centimeters.
Isosceles triangle A B C is shown. The length of A C is 8 centimeters and the lengths of sides A B and B C are congruent. Side A B has length c and side B C has length a. Angle A B C is 30 degrees.
Trigonometric area formula: Area = One-half a b sine (C)
To the nearest square centimeter, how many square centimeters of the plate are covered by the napkin?
16 square centimeters
30 square centimeters
56 square centimeters
60 square centimeters
The napkin covered approximately 56 square centimeters of the plate. The third option is correct.
What is the area of an isosceles triangle?The area of an isosceles triangle can be estimated by using the trigonometric function:
[tex]\mathbf{=\dfrac{1}{2} \times a \times b\times sin (C)}[/tex]
From the given information:
The base angle and sides of an Isosceles triangle are equal.The perimeter of the triangle:
P = a + b + c
38 = a + 8 + c
where;
a = c (base sides)So;
38 = 8 + 2a
38 - 8 = 2a
2a = 30
a = c = 15
Similarly, ∠ABC = 30
∠A + ∠B + ∠C = 180 (sum of angles in a triangle)
∠A + 30 + ∠C = 180
∠A = ∠C = x
2x = 180 - 30
2x = 150
x = 150/2
∠A = ∠C = x = 75°
Using the trigonometric function:
[tex]\mathbf{=\dfrac{1}{2} \times (15) \times (8) \times sin (75)}[/tex]
= 56 square centimeters.
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Answer: Option C
Step-by-step explanation:
Edge 2020
Determine the intercepts of the line.
Do not round your answers.
-4x + 7y = 3
The x and y-intercepts are (-3/4, 0) and (0, 7/3) respectively
How to determine the intercepts of a lineThe y-intercept is the point where the value of x is zero while the x-intercept is the point where the value of y is zero
Given the function below;
-4x + 7y = 3
For the x-intercept
-4x = 3
x = -3/4
The x-intercept is (-3/4, 0)
For the y-intercept
7y = 3
y = 3/7
The y-intercept is (0, 7/3)
Hence the x and y-intercepts are (-3/4, 0) and (0, 7/3) respectively
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Please help ill give whoever answers the best the brainliest answer :0
Answer:
The bottom graph
Step-by-step explanation:
It shows that the kid starts 4 meters away and slowly decreases the distance for 8 seconds, pauses for 3, and moves back for 4.
Answer:
the 4th answer option
Step-by-step explanation:
the first one is looking good too, but the difference is to start at 4 meters away.
and the first graph starts at 9 meets away.
so, it is the 4th graph :
starting 4 meters away the person is coming slowly closer and closer for 8 seconds, then stands still for 3 seconds, and then walks away quickly for 4 seconds.
remember, the passing time is on the x-axis moving to the right (bigger and bigger numbers).
while the distance to the person is on the y-axis. and that value can get bigger and smaller.
Isaiah sketches a model of a skateboard ramp. The model has two surfaces on which to skate, represented by sides AB and AD in the diagram.
Triangle A B D is shown. A perpendicular bisector cuts angle B A D to form triangle A B C. Triangle A B C has angle measures 45, 45, and 90 degrees. Triangle A C D has angle measures 60, 30, and 90 degrees.
The steepest side of the model, AB, measures 4 inches. What is the length of the other skating surface, AD?
2 StartRoot 2 EndRoot in.
2 StartRoot 3 EndRoot in.
4 StartRoot 2 EndRoot in.
4 StartRoot 3 EndRoot in.
The length of the other skating surface AD of the ramp is 4√2 inches
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Sine rule shows the relationship between the sides and angles of a triangle.
Using sine rule:
AB / sinD = AD / sinB
4/sin(30) = AD / sin(45)
AD = 4√2 inches
The length of the other skating surface AD of the ramp is 4√2 inches
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(C.) 4√2
________
I got it wrong, the correct answer was revealed <3
A local school district requires all fourth graders to complete a 20-minute test containing 200 multiple-choice mathematics problems. Students are not expected to complete all of the questions, but are graded on the number they are able to get correct in the time limit. What component of mathematics fluency is most likely the goal of this type of assessment
The component of mathematics fluency is most likely the goal of this type of assessment is Rate.
GIven,
A local school district requires all fourth graders to complete a 20-minute test containing 200 multiple-choice mathematics problems.
The component of mathematics fluency is most likely the goal of this type of assessment is Rate.
The school district is assessing the rate because they are seeing how many questions students can answer in a given time frame.
Hence, The component of mathematics fluency is most likely the goal of this type of assessment is Rate.
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In the diagram below, AB and TC are tangent to 0. Which equation could be solved to find x, the measure of AC?
A.1/2(238+58)=x
B.1/2(238-58)=x
C.1/2(238+x)=58
D.1/2(238-x)=58
The equation that could be solved to find x, the measure of AC is 58 = 1/2(238 -x)
Circle theoremThe given diagram shows two intersecting lines tangential to a circle at points A and C.
Using the theorem that states, the measure of the angle at the vertex is equal to the half of the difference of the measure of the intercepted arcs.
Mathematically;
<B = 1/2(arcADC - arcAC)
58 = 1/2(238 -x)
Hence the equation that could be solved to find x, the measure of AC is 58 = 1/2(238 -x)
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You enter a room. 2 dogs, 4 horses, 1 giraffe and a duck lie on the bed. 3 hens fly over a chair. How many legs are there on the floor
Answer:
10
Step-by-step explanation:
2 legs because you walked into the room and 4 legs of the bed and 4 legs of the chair.
here is the histogram of a data distribution. all class widths are 1. which of the following is the closest to the median of this distribution
The value of the median of the distribution is closest to 5.
What is the median?
A histogram is used to represent data graphically. the histogram is made up of rectangles whose area is equal to the frequency of the data and whose width is equal to the class interval.
The median is the number at the center of a dataset when the dataset is arranged in either ascending or descending order.
The numbers arranged in ascending order is : 2, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 9
Median = 5
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Answer:
Step-by-step explanation:
Please help! Which of the following is a solution to the system of two equations y = 3x - 7 and 4x - 5y = -20?
a.) (5,8)
b.) (10,12)
c.) 2,-1)
d.) 9,20)
Answer:
a
Step-by-step explanation:
y = 3x - 7 → (1)
4x - 5y = - 20 → (2)
substitute y = 3x - 7 into (2)
4x - 5(3x - 7) = - 20
4x - 15x + 35 = - 20
- 11x + 35 = - 20 ( subtract 35 from both sides )
- 11x = - 55 ( divide both sides by - 11 )
x = 5
substitute x = 5 into (1)
y = 3(5) - 7 = 15 - 7 = 8
solution is (5, 8 )
A quarter of farmland is too rought to use if two fifth is kept for poultry farms and this leaves 221 areas for planting cash crop.what is the area of farm too rough to use
The area of the farm that is too rough to use is 157.86
What is the area?An object's area is how much space it takes up in two dimensions. In other terms, it's the measurement of the number of unit squares that are completely around the surface of a closed shape.
Let the total area of the farm be x.
Area of the farm, too rough to use=x/4
Area of farm kept for poultry farms=2x/5
Remaining Area=221
Thus,
[tex]x-(\frac{x}{4}+\frac{2}{5}x)=221[/tex]
[tex]\\ x-\frac{13}{20}x=221\\[/tex]
[tex]\frac{7}{20}x=221\\[/tex]
x=631.43
Area of the farm too rough to use= 631.43/4
=157.86
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Geometric probability
Answer:
71.4%
Step-by-step explanation:
7+3+8+3=21 total fish
7+8=15 healthy fish
15÷21=0.7142=71.4%
Jane wants to buys some lollipops. If she buys 2 lollipops, she will have 3 dollars left. If she wants to buy 3 lollipops, she will need 2 more dollars. Jane has ___ dollars.
Since Jane wants to buys some lollipops, Jane has $13 dollars.
To answer the question, we need to solve simultaneous equations
What are simultaneous equations?Simultaneous equations are pairs of equations that contain two unknowns
How to calculate how much Jane has using simultaneous equationsLet
x = price per lollipop and y = total amount Jane hasWe know that If she buys 2 lollipops, she will have 3 dollars left, so we have that
y - 2x = 3 (1)
Also, If she wants to buy 3 lollipops, she will need 2 more dollars. So, we have that
y + 2 = 3x (2)
The required simultaneous equationsSo, the required simultaneous equations are
y - 2x = 3 (1)
y + 2 = 3x (2)
From (1), x = (y - 3)/2
Substituting x into (2), we have
y + 2 = 3x (2)
y + 2 = 3(y - 3)/2
2(y + 2) = 3(y - 3)
2y + 4 = 3y - 9
2y - 3y = -9 - 4
-y = -13
y = -13/-1
y = 13
So, Jane has $13 dollars.
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