Photo attached please help

The height of the stump is 3 ft.

The given equation represents the height of the frog, h(t), as a function of time, t. To find the height of the stump, we need to determine the height when the time, t, is equal to 0.

In the equation h(t) = -16t² + 64t + 3, we substitute t = 0:

h(0) = -16(0)² + 64(0) + 3

Since any term multiplied by zero is zero, we can simplify further:

h(0) = 0 + 0 + 3

Therefore, the height of the stump, at time t = 0, is 3 ft. This means that when the frog initially leaps from the stump, the height of the stump itself is 3 ft.

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In given fractions 8/9 is 1/36 large than 31/36

Finding the larger and smallest fraction in between two or more fractions is known as comparing fractions.

We need to change fractions with unlike denominators into fractions with similar denominators in order to compare them. For this, we will find the denominators' Least Common Multiple (LCM).    

If the denominators are the same then it is easy to compare the fractions.

Here we have

31/36 and 8/9

To find the largest fraction convert both denominators into the same  

Here LCM(36, 9) = 36  

Now multiply both numerator and denominators of fractions with a number to change the denominators  

=> \(\frac{31}{36} \times \frac{1}{1} = \frac{31}{36}\)  

=> \(\frac{8}{9} \times \frac{4}{4} = \frac{32}{36}\)  

From the above calculations given fractions are 31/36 and 32/36

Difference = \(\frac{32}{36} - \frac{31}{36} = \frac{1}{36}\)  

Therefore,

In given fractions 8/9 is 1/36 large than 31/36

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Answer:

Here are the steps for conducting a survey in your school to find out which mode of transportation students prefer the most, arranged in order from start to finish:

1) Define the objective: Clearly define the objective of the survey, which is to determine the preferred mode of transportation among students in your school.

2) Determine the sample size: Decide on the number of students you want to include in your survey. This will depend on factors such as the size of your school and the resources available for conducting the survey.

3) Design the survey questionnaire: Create a well-designed survey questionnaire that includes relevant questions about different modes of transportation. Ensure that the questions are clear, unbiased, and cover all the necessary aspects.

4) Seek necessary permissions: If required, seek permission from school authorities or relevant individuals to conduct the survey on school premises and to involve students.

5) Pre-test the survey: Before distributing the survey to the entire student population, pre-test the questionnaire on a small group of students to identify any potential issues or areas for improvement.

6) Distribute the survey: Once the questionnaire has been finalized and pre-tested, distribute it to the selected sample of students. Ensure that the survey is distributed in a fair and unbiased manner, taking into account the diversity of the student population.

7) Collect the survey responses: Set a specific timeframe for students to complete the survey and collect the responses. Consider using a combination of online platforms and physical collection methods to maximize participation.

8) Analyze the data: Once you have collected all the survey responses, analyze the data to determine the preferred mode of transportation among students. Use appropriate statistical tools and techniques to interpret the results accurately.

9) Present the findings: Prepare a report or presentation summarizing the survey findings. Include key insights, trends, and any significant findings related to the preferred mode of transportation among students.

10) Share the results: Share the survey results with the school community, including students, teachers, and administrators. This can be done through presentations, newsletters, or other suitable communication channels.

By following these steps, you will be able to conduct a comprehensive survey to determine the preferred mode of transportation among students in your school.

Hope this helps!

I can not do it for you but I can give you what you should do

Explanation: take a survey

If a skid mark with a length of 82.5 feet was found, then the speed of the car is 13.59 miles per hour

The function is

l(s) = 0.46s^2 - 0.199s + 0.264

Where l is the length of a skid mark measured in feet at an accident scene

s is the speed of the car in miles per hour

Given that the skid mark length = 82.5 feet

Then the equation will be

0.46s^2 - 0.199s + 0.264 = 82.5

Rearrange the terms

0.46s^2 - 0.199s + 0.264 - 82.5 = 0

0.46s^2 - 0.199s - 82.236 = 0

Use the quadratic equation

= \(\frac{-b+/-\sqrt{b^2-4ac} }{2a}\)

Substitute the values in the equation

= \(\frac{0.199+/-\sqrt{(-0.199)^2-4(0.46)(-82.236)} }{2(0.46)}\)

= (0.199 ± 12.30) / 0.92

Then

(0.199 + 12.30) / 0.92 = 13.59

(0.199 - 12.30) / 0.92 = -13.15

Therefore, the speed of the car is 13.59 miles per hour

The complete question is:

The function l(s) = 0.46s^2 - 0.199s + 0.264 relates the length of a skid mark measured in feet at an accident scene to the speed of the car in miles per hour. that means an accident reconstructionist can measure the length of a skid mark and find the speed the car was traveling. if a skid mark with a length of 82.5 ft was found, find the speed of the car. round your answer to the nearest tenth.

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1. In 60 weeks, both Zac and Jon will earn the same amount, equating to their different earnings.

2. The student's claim that the solution to the equation 200 + 20w = -100 + 25w is w = 50 is false as the solution shows that w = 60.

3. The two correct justifications for the given steps used in solving w are:

The fixed earnings of Zac = $200

Zac's earnings per week = $20

The total earnings of Zac in w weeks = 200 + 20w

Jon's fixed debt so far = $100

Jon's earnings per week = $25

The total earnings of Jon in w weeks = -100 + 25w

To determine the weeks when the total earnings of Zac and Jon will be equal, we can equate the two expressions above as follows and solve for w:

200 + 20w = -100 + 25w

20w - 25w = -300

-5w = - 300

w = -300/-5

w = 60

Thus, we can conclude that in 60 weeks, the earnings of Zac and Jon will become equal.

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Answer:

2100 meters

Step-by-step explanation:

REMEMBER: 1 km = 1000 m

2.1 km x 1000= 2100 meters

hope this helps ;)

Answer:

m is 4 or -12.

Step-by-step explanation:

y = 2x^2 - 4x + 8.

To find the slope of the tangent at the point (x, y) we find the derivative.

y' = 4x - 4.

So m = 4x - 4.

Now our straight line is y = mx and m = 4x - 4 so

When y = mx meets the curve

mx = 2x^2 - 4x + 8

x(4x - 4) = 2x^2 - 4x + 8

4x^2 - 4x = 2x^2 - 4x + 8

2x^2 = 8

x^2 = 4

x = ±2.

So the line meets the curve and is tangent to it at the points where x = 2 and x = -2.

So the value of m   4(2) - 4 = 4

or 4(-2) - 4 = -12.

(A) The required down payment is $48,000.

(B) The amount of the mortgage is $192,000.

(C) Monthly payment = $192,000 * (0.085/12) * (1 + (0.085/12))^(3012) / (((1 + (0.085/12))^(3012)) - 1)

(a) To find the required down payment, we need to calculate 20% of the house price.

Down payment = 20% of $240,000

Down payment = 0.2 * $240,000

Down payment = $48,000

The required down payment is $48,000.

(b) The amount of the mortgage is equal to the total cost of the house minus the down payment.

Mortgage amount = Total cost of the house - Down payment

Mortgage amount = $240,000 - $48,000

Mortgage amount = $192,000

The amount of the mortgage is $192,000.

(c) To find the monthly payment for the mortgage, we can use the formula for the monthly payment on a fixed-rate mortgage:

Monthly payment = P * r * (1 + r)^n / ((1 + r)^n - 1)

Where:

P = Principal amount (mortgage amount)

r = Monthly interest rate (8.5% annual interest divided by 12 months and converted to a decimal)

n = Total number of monthly payments (30 years multiplied by 12 months)

Monthly payment = $192,000 * (0.085/12) * (1 + (0.085/12))^(3012) / (((1 + (0.085/12))^(3012)) - 1)

Using this formula and performing the calculation will give you the monthly payment amount.

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Answer:

92

Step-by-step explanation:

they must sell at least 92 because 92 times 5 equals 460 and so 460 is more than 455 so they made a profit

Answer:

\( \boxed{ \bold{ \boxed{ \sf{f( - 4) = 1}}}}\)

Step-by-step explanation:

Given, f ( x ) = - x - 3

Let's find the value of f ( - 4 )

\( \sf{f( - 4) = - ( - 4) - 3}\)

We know that , \(( - ) \times ( - ) = ( + )\)

⇒\( \sf{ 4 - 3}\)

Subtract 3 from 4

⇒\( \sf{1}\)

Hope I helped!

Best regards!!

Answer:

A=Minimum value

             B=Lower quartile

             C=Median

             D=Upper quartile

             E=Maximum value

Step-by-step explanation:

Answer:

answer above.

Step-by-step explanation:

your welcome

Answer:

Step-by-step explanation:

π as a value is \(\frac{22}{7}\). Expresssing \(\frac{22}{7}\) as decimal will give;

π = \(\frac{22}{7}\) = 3.142857 142857 142857 1...

It can be seen that the values after the decimal point goes indefinitely by continually imputing the value 142857 based on the segregation. Therefore an expansion to 5dp is the only approximate value for π since the remaining values are mere repetition.

Converting to 5 decimal places means having just 5 values after the decimal point as shown;

\(\pi = \frac{22}{7} = 3.14286\)

The last value is rounded up to 6 because the succeeding value is 7(which is more than 5). In this case 1 will be added to the fifth place value in the figure rounding it up to 6.  

Answer:

5,4,6,7

Step-by-step explanation:

The digits 4​, 5​, 6​, 7​, and 8 are randomly arranged to form a​ five-digit number. Complete parts​ (a) and​ (b) below.

​(a) Find the probability that the number is odd.

The probability that the number is odd

​(Type an integer or a simplified​ fraction.)

​(b) Find the probability that the first and last digits of the number both are odd.

The probability that the first and last digits of the number both are odd is  

.

​(Type an integer or a simplified​ fraction.)

Answer:

181.24

Step-by-step explanation:

The total surface area of the Trapezoidal Prism to be covered is: 181.24 cm².

Surface Area = 2(area of trapezoid) + area of the 4 rectangular faces.

Area of Rectangle 1 = length × width = 9 × 4 = 36 cm²

Area of Rectangle 2 = length × width = 9 × 5 1/4 = 47.25 cm²

Area of Rectangle 3 = length × width = 9 × 4 1/5 = 37.8 cm²

Area of Rectangle 2 = length × width = 9 × 6 1/2 = 58.5 cm²

Area of the two trapezoids = 2[1/2(a + b)h] = 2[1/2(6½ + 5¼)4] = 47 cm²

Surface area = 36 + 47.25 + 37.8 + 58.5 + 47 = 226.55 cm²

Total surface that will be covered = 4/5(226.55) = 181.24 cm²

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Answer:

X=18.0

Step-by-step explanation:

It says round to the nearest tenth, which is 1 digit after the . Even though 18.02 is correct it wants you to round so X= 18.0

Final answer is X=18.0

The value of x is 18.0 rounded to nearest tenth.

Cosine law is a formula relating the length of the sides of a triangle to the cosine of one angle of the triangle.

u² = s² + t² - 2(s)(t)·cos U

We are Given Triangle with sides, 16, 30, and x, and a measure of an angle corresponding to x = 30°

Required: Value of x to the nearest tenth

Using the Cosine rule:

c² = a² + b² - 2abcos(C)

Let c = x, a = 16, b = 30

C = 30°

Thus,

c² = 16² + 30² - 2 x 16 x 30 x cos 30°

c² = 256 + 900 - 960 x 0.8660

c² = 1,156 - 831.36

c² = 324.64

c = √324.64

c = 18.017769

x ≈ 18.0 (rounded to nearest tenth)

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A 95% confidence interval for the difference of the meantime that the customers stayed for lunch and for dinner the correct option is option a (3.35, 16.65).

Given:

The number of random customers n1 = 25

The number of random customers n2 = 30

x1 = 45, x2 = 55

σx1 = 10, σx2 = 15

Zα12 = Z0.025 = 1.96

95% confidence interval,

= {(x2-x1) ± Zα12 [(σx1)^2/n1 + (σx2)^2/n2]^0.5}

= {(55-45)  ± 1.96 [\(10^{2}\)/25 + \(15^{2}\)/30]^0.5}

= {10 ± 1.96(4 + 7.5)^0.5}

= {10 ± 1.96(11.5^0.5)}

= {10 ± 1.96(3.3911)}

= {10 ± 6.6466}

=> (10-6.6466, 10 + 6.6466)

=> (3.35, 16.65)

So, the correct option is a (3.35, 16.65) for the difference of the meantime.

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The range of the equation f(x) = 3ˣ ⁻ ¹ - 2 is  y > -2

From the question, we have the following parameters that can be used in our computation:

f(x) = 3ˣ ⁻ ¹ - 2

The above equation is an exponential function

The rule of an exponential function is that

In this case, it is -2

So, the range is y > -2

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Answer:2,440,000,000

Step-by-step explanation:

Answer:

\(\frac{8-\sqrt{6} }{2}\)

Step-by-step explanation:

To rationalize the denominator, we need to multiply both the numerator and denominator by the conjugate of the denominator, which in this is 2 - √6.

We can write the expression:

\(\frac{3\sqrt{6}+5 }{2+\sqrt{6}} *\frac{2-\sqrt{6}}{2-\sqrt{6} }\)

We can use the special product of the difference of squares to simplify the denominator:

\((2 + \sqrt{6})(2-\sqrt{6}) = 2^2 - (\sqrt{6})^2 =4 - 6 = -2\)

We can use distributive for the numerator:

\((3\sqrt{6}+5)(2-\sqrt{6})=6\sqrt{6} -18+ 10-5\sqrt{6} =\sqrt{6} -8\)

Now we can rewrite the fraction:

\(\frac{\sqrt{6}-8 }{-2} =\frac{8-\sqrt{6} }{2}\)

Answer:

\(4 {x}^{2} - 4x - 8 - (2 {x}^{2} + 3x - 6) = 4 {x}^{2} - 4x - 8 - 2 {x}^{2} - 3x + 6 = 2 {x}^{2} - 7x - 2\)

The coordinates of the fourth vertex is (1,-8).

As three of a parallelogram's vertices, we were given:

(3,-2), (-1,-4), (5,-6). (5,-6).

We see that (3,-2) and (-1,-4) form a diagonal after charting the points as in the attachment.

The midpoint formula determines what point on this diagonal is in the middle.

Keep in mind that both diagonals' midpoints are identical.

Specify the coordinates of the fourth point (x,y).

As a result of once more applying the midpoint formula to (3, -2), we get:

x=1 and y=-8

The fourth point's locational details are as follows:

(1,-8).

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The complete question is,

A good can be produced for a total cost of 600 or 850 when making 100 units and 150 units, respectively. Discover an equation for TC in terms of Q, the number of generated units, presuming that the total cost function is linear.

Neither of the equation represent the a line that passes through (0, 5) and (4, 15)

The equation of a line can be represented in slope intercept form and point slope form as follows:

slope intercept form:

y = mx + b

where

Therefore,

m = 15 - 5 / 4 - 0

m = 10 / 4

m = 5 / 2

let's find y-intercept using (0, 5)

y = 5 / 2 x + b

5 = 5 / 2(0) + b

b = 5

Hence,

y = 5 / 2 x + 5

Let's find the equation in point slope form:

(0, 5)

y - y₁ = m(x - x₁)

y - 15 = 5 / 2(x - 4)

Therefore, neither of the equation represent the line.

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Based on the analysis it will be less expensive to get the new fridge, hence buying the new fridge is worth it.

Given that the current fridge

electricity charges= $60 monthly,

maintenance costs=$ 170

let the number of months be = x

and the total cost is y

the expression for the cost of the old fridge is

y=170+60x       ...say (1)

new fridge

electricity charges=$5

costs= $1140

let the number of months be x,

and the total cost be y'

the expression for the cost of the new fridge is

y'=1140+5x,       ... say(2)

For 10 year , there are 12*10=120 months

put x=120 in both equations,

y=170+60x  

y=170+60*120

y=170+7200

y=$7370

y'=1140+5*120

y'=1140+600

y'=$1740

Based on the analysis it will be less expensive to get the new fridge, hence buying the new fridge is worth it.

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Answer: x=4

Step-by-step explanation:

5x+2=3x+4(2x-1)

5x+2=3x+6x-4

-2 -2

5x=3x+6x-2

-3x -3x

2x=6x-2

+6x +6x

8x=2

Divide

X=4

According to the information given, it is found that she has 15 minutes left for question C.

The sum of the time for each question is the total time, which can be at most 30, hence:

\(10 + 5 + x \leq 30\)

\(15 + x \leq 30\)

\(x \leq 15\)

She has 15 minutes left for question C.

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From the information in the question, 15 minutes was spent on question C.

An equation is used in mathematics to describe problems. Typically, a problem is solved when sentences can be translated into equations.

From the question, we can see that;

The time spent on question C is obtained from;

10 + 5 + x = 30

x = 30 - (10 + 5)

x = 15

Hence, 15 minutes was spent on question C.

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Answer:

-11

Step-by-step explanation:

Notice how

\(f(x)=x^{2} +8x+1\)

So when we have

\(f(-6)=(-6)^{2} +8(-6)+1= 36-48+1=-11\)

The answer is:

f(-6) = -11

Step-by-step explanation:

Plug in -6 for x:

\(\sf{f(x)=x^2+8x+1}\)

\(\sf{f(-6)=(-6)^2+8(-6)+1}\)

Simplify this:

\(\sf{f(-6)=36-48+1}\)

\(\sf{f(-6)=-12+1}\)

\(\sf{f(-6)=-11}\)

The multiplicative inverse of 5/6 as required to be determined in the given task content is 6/5.

It follows from the task content that the multiplicative inverse of the given number; 5/6 is required to be determined.

By definition; it follows that the Multiplicative inverse of an expression refers to its reciprocal. It is the value that, when multiplied by the original, give a product of 1 (the multiplicative identity element).

So,

5/6 × 6/5

= 30/30

= 1

Hence, 6/5 is the multiplicative inverse of 5/6

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