Answers
Answer:
See below ↓
Step-by-step explanation:
We need to check the different time intervals to find the max. height
t = 0 or 1 [both give same result]f(1) = -16(1) + 16(1) + 12 = 12 feet2. t = 2
f(2) = -16(2)² + 16(2) + 12 = -20 feet⇒ Clearly as she is diving, her maximum height will be her initial height which is 12 feet
⇒ To achieve this, it takes her 0 seconds [initial height = no time needed]
Taking f(x) = 0 [surface of water → just touching/hit the water]
0 = -16x² + 16x + 124x² - 4x - 3 = 04x² - 6x + 2x - 3 = 02x(2x - 3) + 1(2x - 3) = 0(2x + 1)(2x - 3) = 0x is positivex = 3/2 = 1.5 seconds⇒ After 1 second, she is 12 feet above the water
⇒ The diving board is 12 feet above the water
Related Questions
What is the value of x?
Answers
Answer:
19
Step-by-step explanation:
(5x+37)+(3x-9)=180
8x= 152
x=19
Find A and the reason
Answers
We see that Triangle ABC is an isosceles triangle which means:
Sides BA and BC are equal in lengthAngle BAC and BCA are equalWe see that Angle BCD and Angle BCA are on a straight line, which means that both of the angles' measures are equal to 180 degrees
--> in equation form:
Angle BCD + Angle BCA = 180
118 + Angle BCA = 180
Angle BCA = 62 degrees
Since Angle BCA and BAC are equal, then Angle BAC or Angle A in this case is 62 degrees
Hope that helps!
I need help first answer gets brainliest
Answers
To find which fractions are equal to each other, we must simplify or multiply to both denominator and numerator:
[tex]\frac{2}{6} =\frac{1*2}{3*2} =\frac{1}{3}*\frac{2}{2}=\frac{1}{3}*1= \frac{1}{3} \\\\\frac{8}{1}=8\\ \\\frac{2}{4} =\frac{1*2}{2*2} =\frac{1}{2}*\frac{2}{2} =\frac{1}{2} *1= \frac{1}{2} =\frac{1}{2}*1 =\frac{1}{2}*\frac{4}{4} =\frac{1*4}{2*4}=\frac{4}{8} \\\\\frac{2}{8} =\frac{1*2}{4*2}=\frac{1}{4}*\frac{2}{2} =\frac{1}{4} *1 =\frac{1}{4} \\\\\frac{4}{4} =1[/tex]
Hope that helps!
Answer:
2/6 = 1/3
8/1 = 8
2/4 = 4/8
2/8 = 1/4
4/4 = 1
Step-by-step explanation:
2/2 = 1 and 6/2 = 3 so that would make the equivalent fraction 1/3
for 8/1 it is the same as just 8
2*2 = 4 and 4*2 = 8 so that would make the equivalent fraction 4/8
and 2/8 is 1/4
and 4/4 is just 1
PLEASE RATE!! I hope this helps!!
If you have any questions let me know
While pushing a shovel into the ground with a force of 555 newtons ant an angle of 44 ∘ 44 ∘ to the ground. Find the magnitudes of the horizontal and vertical components of the force to the nearest whole newton.
Answers
The Horizontal component is 554.889N and the vertical component is
9.8235 Newton
Resolution of ForcesGiven Data
Force = 555 NewtonAngle of Applied force = 44°Fx = Horizontal component of the applied forceFy = the vertical component of the applied forceResolving the vertical force
Fy = 555 sin44°
Fy = 555 *0.01770
Fy = 9.8235 Newton
Resolving the horizontal force
Fx = 555 cos 44°
Fx = 555 *0.9998
Fx = 554.889 Newton
Learn more about forces here:
https://brainly.com/question/25997968
can someone help meeeeee
Answers
Answer:
Area of shaded rectangle = 42 cm²
55%
Step-by-step explanation:
The length of the shaded area is equal to the length of the white rectangle.
Therefore, length of shaded rectangle = 7 cm
The width of the shaded rectangle is equal to the length of the white rectangle minus two widths of the white rectangle.
Therefore, width = 7 - (2 x 0.5) = 6 cm
Area of shaded rectangle = width x length
= 6 x 7
= 42 cm²
----------------------------------------------------------------------------------------------
Perimeter of a square = 4 × side length
If the perimeter of the square is 40 cm,
then the side length = 40 ÷ 4 = 10 cm
Area of a square = side length x side length
⇒ area of this square = 10 x 10 = 100 cm²
To determine the shaded area, calculate the areas of the 2 white triangles and subtract these from the area of the square.
Area of a triangle = 1/2 x base x height
⇒ area of left triangle = 1/2 x (10 - 7) x 10 = 15 cm²
⇒ area of right triangle = 1/2 x 10 x (10 - 4) = 30 cm²
Therefore, shaded area = 100 - 15 - 30 = 55 cm²
To calculate the percentage, divide the shaded area by the area of the square and multiply by 100:
(55 ÷ 100) × 100% = 55%
the measures of the angles in a triangle are in a ratio 1:5:6. find the measures of the angles
Answers
Answer:
The required angles are 15, 75 and 90
Step-by-step explanation:
1x + 5x+ 6x = 180
or 12x = 180
180 ÷ 12 = 15
hence,
15, 75, 90.
Pete's Pottery observes the heights of the vases in inventory. The results are represented by the box plot shown below.
Select all of the true statements.
The data recorded must have been for 24 vases.
The box plot also gives data on the heights of mugs in inventory.
The heights are measured in centimeters.
The box plot gives data on the heights of vases in inventory.
There must be between 6 and 12 vases in inventory.
The heights are measured in inches.
Answers
Answer:
The box plot gives data on the heights of vases in inventory.The heights are measured in inches.Step-by-step explanation:
Given the question and the image, the following are the solution steps to answer the question.
STEP 1: Define box plot.
In descriptive statistics, a box plot or boxplot is a method for graphically demonstrating the locality, spread, and skewness groups of numerical data through their quartiles.
STEP 2: Choose the correct statement
The box plot shows the minimum height, maximum height, first and third quartiles, and the median.
Therefore,
The box plot does not show the number of vases recorded
The box plot does not show the heights of mugs, just vases.
The height is measured in inches, not centimeters.
A local outdoor equipment store is being sold. The buyers are trying to estimate the percentage of items that are outdated. They will randomly sample among its 100,000 items in order to determine the proportion of merchandise that is outdated. The current owners have never determined their outdated percentage and can not help the buyers. Approximately how large a sample do the buyers need in order to insure that they are 98 % confident that the margin of error is within 3%
Answers
Using the z-distribution, as we are working with a proportion, it is found that the buyers need a sample of 1505.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In this problem, we have a 98% confidence level, hence[tex]\alpha = 0.98[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.98}{2} = 0.99[/tex], so the critical value is z = 2.327.
There is no estimate of the percentage, hence [tex]\pi = 0.5[/tex], and the margin of error is of M = 0.03, hence we solve for n to find the desired sample size.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 2.327\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.03\sqrt{n} = 2.327(0.5)[/tex]
[tex]\sqrt{n} = \frac{2.327(0.5)}{0.03}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{2.327(0.5)}{0.03}\right)^2[/tex]
[tex]n = 1504.2[/tex]
Rounding up, the buyers need a sample of 1505.
More can be learned about the z-distribution at https://brainly.com/question/25890103
Does anyone know the answer to these?
Answers
Given one of the interior angles of the hanger, find the measures of angles A and B.
Answers
Answer:
A= 130
B= 25
Step-by-step explanation:
A is 130 because the amount of degrees that are in a triangle is 180 degrees. From that we can substract 25 from 180 and get 155.
Since B is congruent with 25, B is also 25 degrees. Therefore, A is 130 because 180 - 50 is 130.
Hope this helps.
Triangle ABC was transformed to create triangle DEF.
2 triangles are shown. Triangle A B C has point A at the top, B on the bottom right, and point C on the bottom left. Triangle D E F has point D at the top, E on the bottom right, and F on the bottom left. The triangles are identical.
Which statement is true regarding the side in the image that corresponds to Side length B A?
Side length B C corresponds to Side length B A because they are about the same length.
Side length E D corresponds to Side length B A because they are in the same position.
Side length E F corresponds to Side length B A because the transformation is isometric.
Side length F D corresponds to Side length B A because the length is not preserved.
Answers
Answer: Side length E D corresponds to Side length B A because they are in the same position.
Step-by-step explanation:
Answer: b
Step-by-step explanation:
Answer the questions about the following polynomial. 1- x³/8
Answers
the expression represents a quadratic polynomial with 2 terms.The constant term is 1, the leading tern is x and the leading coefficient is 1
How much interest is earned on a $5,000 loan at 10% interest for 3 years?
A $125
B $1,500
C $150,000
D $15,000
Answers
Answer: $1500
Step-by-step explanation:
Did the quiz on this hope you have a great day.
The costs for a new publishing company can be classified as fixed costs, such as rent and insurance, or variable costs, such as materials and labor. Fixed costs are constant, while variable costs change as the number of items produced changes. The graph shows the weekly variable costs based on the number of books produced.
a. If weekly fixed costs are $300, sketch a graph showing total expenses for the week.
b. Find the total cost of producing 75 books in a week.
Answers
Answer:
a) As weekly costs are fixed at $300, we simply need to shift the function up 300 units. (the new function is shown in blue on the attached graph).
b) Reading from the (blue) graph, the total cost of producing 75 books in a week is $600.
fixed cost + variable cost = $300 + $300 = $600
A week before an election 100 ople were asked who they planned to vote for or the people asked 45 said they planned to vote for
candidate and they planned to vote for candidate. The rest and they had not yet decided How many of the people that were asked
weet yetece who they plan tovorfor?
Answers
Answer:
the answer is c
Step-by-step explanation:
45% of 1500=675
38% of 1500=570
675+570=1245
1500-1245=255
Find an ordered pair (x,y) that is a solution to the equation -x+6y=1
Answers
Answer:
(5,1)
is one of infinitely many possible order pairs.
Step-by-step explanation:
There are an infinite amount of x values that give you an answer to this question. You get to choose. But first let's start off with isolating y.
[tex]-x + 6y = 1\\6y = 1 + x\\y = \frac{1+x}{6}[/tex]
Now the equation is easier to interpret. [tex]y = \frac{1+x}{6}[/tex]
Now here's the part where you actually get to choose. Take any x, value, I'll choose 5.
I'll sub it into the equation and get my y value, [tex]y = \frac{1 + (5)}{6}= 1[/tex]
Okay, we get that y = 1, when x = 5. That's an ordered pair:
(5,1)
Remember you could follow this same procedure for any x value you choose.
7. A study was done to determine the relationship between a person's screen time and their age.
A group of participants was asked to record their average daily screen time, in minutes, and
their age. The line of best fit for the data had the equation y=-3.2x + 273.4, where x was
the person's age and y was their screen time in minutes. Which of the following is the correct
interpretation based on this model?
For every year a person gets older, their screen time increases by 273.4 minutes.
(2) For every 3.2 years a person gets older, their screen time decreases by one minute.
(3) For every 3.2 years a person gets older, their screen time increases by 273.4 minutes.
(4) For every year a person gets older, their screen time decreases by, 3.2 minutes.
x=age
SC mins= -3.2 laget 273.
Answers
The true statement about the equation of the line of best fit (d) For every year a person gets older, their screen time decreases by 3.2 minutes
How to interpret the line of best fit?The equation of the line of best fit is given as:
y = -3.2x + 274.4
Where:
x represents the persons agey represents the average daily screen timeA linear equation is represented as:
y = mx + b
Where:
m represents the slopeb represents the y-interceptBy comparison, we have:
m = -3.2 and b = 274.4
This means that:
For every year a person gets older, the average screen time decreases by 3.2 minutes
Hence, the true statement is (d)
Read more about line of best fit at:
https://brainly.com/question/17261411
What is the measure of angle x? Show work.
Answers
Answer:
x = 67° (nearest whole degree)
Step-by-step explanation:
Sine Rule
[tex]\sf \dfrac{sin(A)}{a}= \dfrac{sin(B)}{b}= \dfrac{sin(C)}{c}[/tex]
where A, B and C are the angles, and a, b and c are the sides opposite the angles
Given information
From inspection of the triangle:
A = 38°a = 12B = x°b = 18Finding x:
Substitute given values into the formula and solve for x:
[tex]\sf \implies \dfrac{sin(38)}{12}= \dfrac{sin(x)}{18}[/tex]
[tex]\sf \implies 18\cdot\dfrac{sin(38)}{12}= sin(x)[/tex]
[tex]\sf \implies sin(x)=\dfrac32sin(38)[/tex]
[tex]\sf \implies x=sin^{-1}\left(\dfrac32sin(38)\right)[/tex]
[tex]\sf \implies x=67.44208077...[/tex]
Final Solution
x = 67° (nearest whole degree)
Answer:
∠x = 67°
Step-by-step explanation:
From the Law of Sines,
we know that :
sin(A) / a = sin(B) / aHere we have :
a = 12b = 18∠A = 38°∠B = x°On substituting,
sin38° / 12 = sinx° / 18sinx° = 3/2 x sin38°x = 3/2sin38° x sin⁻¹∠x = 67°Solve the inequality and write the solution in set-builder notation. 8 <r-14
Answers
Answer:
22<rStep-by-step explanation:
soln8<r-148+14<r22<r answer.The perimeter of a rectangle is 168 m. Its length is five times its width. Find the length and width.
Answers
Answer:
Length of rectangle = 63 mWidth of rectangle = 21 mStep-by-step explanation:
Given:
Perimeter of rectangle = 168 mLength of rectangle is five times the widthTo Find:
Length and WidthSolution:
Let's assume width of rectangle x m and length of rectangle be 3x m. To calculate the dimensions of the rectangle we will use the formula of Perimeter of the rectangle
Perimeter of rectangle = 2(L + B)
Substituting the required values:
→ 168 = 2(3x + x)
→ 168 = 2(4x)
→ 168/2 = 4x
→ 84 = 4x
→ 84/4 = x
→ 21 = x
Hence,
Length of the Rectangle = 3x = 3(21) = 63 mWdith of the rectangle = x = 21 mAnswer:
Length = 70 metreWidth = 14 metre⠀
Step-by-step explanation :
⠀
As, it is given that, the perimeter of a rectangle is 168 m and its length is five times its width and we are to find the length and width of the rectangle. So,
⠀
Let us assume the width of the rectangle as w metre and therefore, the length will be 5w metre .
⠀
Now, According to the Question :
⠀
[tex]{\longrightarrow \qquad { \pmb{\frak {2 ( Length + Breadth )= Perimeter_{(Rectangle)} }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad { {\sf{2 (5 w + w )= 168 }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad { {\sf{2 (6 w )= 168 }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad { {\sf{12 w = 168 }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad { {\sf \: w = \dfrac{168}{12} }}}[/tex]
⠀
[tex]{\longrightarrow \qquad { \underline{ \boxed{ \pmb {\frak{ w = 14 }}}}}} \: \: \bigstar[/tex]
⠀
Therefore,
The width of the rectangle 14 metre .⠀
Now, we are to find the length of the rectangle :
⠀
[tex]{\longrightarrow \qquad { { { \pmb {\frak{ Length = 5w }}}}}} \: \: [/tex]
⠀
[tex]{\longrightarrow \qquad { { { \pmb {\frak{ Length = 5 \times 14 }}}}}} \: \: [/tex]
⠀
[tex]{\longrightarrow \qquad { \underline{ \boxed{ \pmb {\frak{ Length = 70 }}}}}} \: \: \bigstar[/tex]
⠀
Therefore,
The length of the rectangle is 70 metreAmy and Tina each by a coffee.
Amy gets 15p change from £2
Tina gets £2.45 change from £5
How much more does Tina pay than Amy?
Give your answer in pence.
Answers
Answer:
70p
Step-by-step explanation:
Amy-
£2.00 - £0.15 = £1.85
so Amy payed £1.85
Tina-
£5.00 - £2.45 = £2.55
so Tina payed £2.55
£2.55 - £1.85 = £0.70
which means tina payed 70p more
solve the equation f'(x) = 0:
Answers
Break it down gently
f(x) = 1 - sin⁴3x + cos6x/6
let's break ( - sin⁴3x) and (Cos6x/6) and 1 separately
the derivative of ( -sin⁴3x) = 12cos3xsin³3x
the derivative of (cos6x/6) = -sin6x
the derivative of (1) = 0
f'(x) = 0
12cos3xsin³3x - sin6x = 0
Multiply the following fractions. Reduce your answer to lowest terms.
1/8 x 1/9 =
Answers
Answer:
1/72
Step-by-step explanation:
multiple the numerators and denominators by each other so 1*1 = 1 and 8*9 = 72
The median weekly income for someone with a high school diploma was $678.00. If they continued their education and obtained a bachelor's degree, their median weekly income increased about 67.7%. Determine the median weekly income for someone with a bachelor's degree. (2 points) $218.99 $568.51 $799.45 $1,137.01
Answers
Write a story problem to go with the multiplication problem 3 x
7
8
. Then, solve the problem.
Answers
Answer:
Each order of rings comes with 3 rings. There are 78 order to pack how many rings is there going to be?
Step-by-step explanation:
PLEASE HELP ASAP 30 POINTS!!!!!!!!!
Answers
Answer:
$11.25
Step-by-step explanation:
multiply 15 by 25% which is .25
15 * 0.25 = 3.75
minus 3.75 from 15
15 - 3.75 = 11.25
Describe what happens to a figure when the given sequence of transformations is applied
to it: (x, y) → (-x, y); (x, y) → (0.5x, 0.5y); (x, y) → (x - 2, y + 2)
(If you answer this you will get 100 points for answering in brainly)
Answers
Answer:
After the sequencing of transformations, reflection over the y-axis.
dilation with a scale factor of 0.5
translation 2 units left and 2 units up
Step-by-step explanation:
HELP PLEASEE, ILL BRAINLIST!!
Answers
Answer:
(a) To find the missing angle, we would do inverse tan.
[tex]angle =tan^{-1}\frac{opp}{adj}[/tex]
[tex]angle = tan^{-1}\frac{17}{21}[/tex]
angle= 39.0 degrees or 0.7 radians
(b) To find the missing angle, we would do inverse sin.
[tex]angle= sin^{-1}\frac{opp}{hyp}[/tex]
[tex]angle= sin^{-1}\frac{12.7}{22.1}[/tex]
angle= 35.1 degrees or 0.6 radians
How many solutions are there?
Answers
Answer:
no solution
Step-by-step explanation:
Solve:
6(2k + 1) = 12k + 1
Expand brackets:
⇒ 12k + 6 = 12k + 1
Subtract 12k from both sides:
⇒ 6 = 1
As 6 ≠ 1 there is no solution
Answer:
No solution
Step-by-step explanation:
Simplify the L.H.S and the R.H.S
⇒ [tex]6(2k + 1) = 12k + 1[/tex]
⇒ [tex]12k + 6 = 12k + 1[/tex]
Cancel out the "12k"
⇒ [tex]12k + 6 = 12k + 1[/tex]
⇒ [tex]6 = 1 (\text{False})[/tex]
Henceforth, this equation has no solution.
Click all the questions that are considered statistical questions. No links please.
Answers
Answer:
The first three are not statistical, the last three are.