Evaluate ( (dx-4) dx 16 S (WX - 4) dx = ( (Type an exact answer in simplified form) 9

Number of sodas sold = 80

Number of hot dogs sold = 23

Let th number of sodas be xs

Let the number of hot dogs be h

The vendor sold a combined total of 103 sodas and hot dogs

s + h = 103............(1)

The nmber of soda sold was 57 more tha n the number of hot dogs sold

s = h + 57........()

Subtitute equation (2) into equation (1)

h + 57 + h = 103

2h = 103 - 57

2h = 46

h = 46/2

h = 23

Substitute h = 23 into equation (2)

s = 23 + 57

s = 80

Number of sodas sold = 80

Number of hot dogs sold = 23

ANSWER

EXPLANATION

The graph of the parent function f(x) = [x] is

The function has the value of x until the next integer. So we have:

f(x) = 0 when x = 0 until x = 1, and then it changes to f(x) = 1. This is for all values of x. We can say that the function "jumps" on each integer and then keeps its value.

If we do a vertical shift of 2 units we have to add 2 to each value of the parent function. This way the shifted function is f(x) = 2 when x = 0 until x = 1, and then it jumps to f(x) = 3:

Question 2

Answer:

Explanation:

Let x be a random variable representing the mean amount of time it takes a mechanic to rebuild the transmission for a 2010 Chevrolet Colorado. Given that it is normally distributed, we would calculate the z score by applying the formula,

z = (x - μ)/σ/√n

where

μ is the population mean

x is the sample mean

σ is the population standard deviation

n is the sample size

From the information given,

n = 40

x = 8.9

μ = 8.4

σ = 1.8

Thus,

z = (8.9 - 8.4)/(1.8/√40) = 1.76

We want to calculate P(x < 8.9). The probability value corresponding to z = 1.76 from the normal distribution table is 0.9608

Thus, the probability that their mean rebuild time is less than 8.9 hours is 0.9608

Solution:

Given:

Graphs showing lines through different points.

To get the line of best fit for the data.

The line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points.

It is the line that touches most points or passes through most of the points.

From the four graphs given, the line that touches or passes through most points is;

Therefore, the graph above is the line of best fit.

The second graph is the correct answer.

Marissa can plant 10 seeds in 1/5 hour

Then averagely, she will plant 1 seed in

Answer

Option B is correct.

Initial velocity = 32 ft/s

Initial height = 24 ft.

Explanation

The function gives us the function that models the height, h, in feet for the ball as a function of time, t, in seconds.

h(t) = -16t (t - 2) + 24

We are then asked to find the initial velocity and the initial height of the ball.

This means we find the velocity and the height of the ball at t = 0

Velocity is given as the first derivative of the height function

v = (dh/dt)

h(t) = -16t (t - 2) + 24

h(t) = -16t² + 32t + 24

v = (dh/dt) = -32t + 32

When t = 0

v = -32t + 32 = -32 (0) + 32 = 0 + 32 = 32 ft/s

Initial velocity = 32 ft/s

For the initial height, t = 0

h(t) = -16t (t - 2) + 24

h(t) = -16t² + 32t + 24

h(0) = -16(0²) + 32(0) + 24

h(0) = 0 + 0 + 24

h(0) = 24 ft

Initial height = 24 ft.

Hope this Helps!!!

Given:

Number of baseball points = 45 points

Number of basketball points = 14 points

Number of football points = 21 points

number of soccer points = 20 points.

To find the ratio of soccer to baseball points, we have:

soccer : baseball = 20 : 45

in simplest form, divide both sides by 5 which is the Greatest Common Factor (GCF) of both numbers.

Thus, we have:

20÷5 : 45÷5 = 4:9

Therefore, the ratio of soccer to baseball in simplest form is = 4 : 9

ANSWER:

4 : 9

First, we need to find 45% of $12

45% of $12 = 45/100 x12 = $5.4

He bought the shirt : $12 - $5.4 = $6.6

Therefore he saved $5.40

Volume of a cylinder = base area x heigth

Volume = 603.2 in3

Height = 12 in

Replacing:

603.2 = base area x 12

603.2/12 = base area

Base area = 50.26 in2

FiThe radius, in inches, grows as a function of time in minutes according to:

We know that the area of a circle is given by:

Where r is the radius of the circle. Then, using r(t) in this equation:

Finally, we evaluate this function for t = 2:

Given the function:

As the coefficeint of x = 1

So, the given function represents a parent function

Answer:

1/4 x 1/2 =1/8

Step-by-step explanation:

The circle is split into four parts (1/4)

Then one of the parts is split in half (1/2)

So the equation represented by the model is 1/4 x 1/2 = 1/8

Answer:

1/4x1/2=1/8

Step-by-step explanation:

this is because it has 4 pieces and then it shows 1/2 of a 1/4 piece

Answer:

4 cups

Explanation:

First, we calculate the volume of the regular size popcorn:

Given that:

Thus, if each pair of 2 students share one regular-size popcorn, each student will get approximately 4 cups.

Here, we want to simplify the expression

To do this, we shall use the term outside the bracket to multiply the terms inside the brackets before we proceed to add them together

We have this as follows;

From the question we're told that the sum of two consecutive numbers is 85,

Let the 1st number by y,

And the consecutive number be y+1

So, the sum of these two numbers will be equal to 85;

Let's go ahead and solve for y in the above equation;

So the first number is 42.

Let's find the consecutive number;

Therefore, the "first number = 42" and "consecutive number = 43"

Given:

There are given the statement:

The angle of elevation and the angle of depression are congruent:

Explanation:

According to the concept:

The angle of elevation and the angle of depression are congruent because they belong from an alternate interior angle.

Final answer:

Hence, the correct option is B.

The initial price of the computer was $X.

The current price is $0.36X

Thus, the current value is X-0.36X.

By taking the common factor, this can also be expressed as:

X(1-0.36).

Hence, the two(2) expressions that represent the value of the laptop today are options B and option D.

b: When x increases by 1, y increases 1 unit.

c. Apply the slope formula (m)

Replace with 2 points form the table:

For example:

Point 1 = (x1,y1)= (0,3)

Point 2= (x2,y2)= (1,4)

Replacing:

Slope = 1

It doesn't need to be written because x multiplied by 1 is equal to x.

Graph.

y=mx+b

y=x+3

Where :

b= y-intercept = 3( where the line crosses the y-axis)

m= slope=1

We have the following:

Bob's earnings can be calculated with the following equation

where x is the number of hours, they tell us that he made a profit of $ 207.50, we replace and solve for x

Therefore, Bob worked a total of 5 hours

Answer:

Step-by-step explanation:

The population means is an average of a group characteristic. A characteristic is just an item of interest.

Then, for the population mean and standard deviation of the age for males;

Total of population: 266

Given:

Two bags have a total weight of 8 3/4 pounds.

What could be their individual weights?

To answer the question, we will select the option that gives a sum of 8 3/4

We will check the options:

A. 7 pounds and 3/4 pounds

The sum = 7 + 3/4 = 7 3/4 pounds

So, option A is wrong

B. 3 1/4 pounds and 5 1/2 pounds

The sum = 3 1/4 + 5 1/2 = 8 3/4

So, option B is correct

C. 4 3/4 pounds and 4 pounds

The sum = 4 3/4 + 4 pounds = 8 3/4 pounds

So, option C is correct

D. 8 pounds and 1/4 pounds

The sum = 8 + 1/4 = 8 1/4

So, option D is wrong

E. 6 pounds and 2 3/4 pounds

The sum = 8 3/4

So, E is correct

The answer will be: B and C and E

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

264 + 638

Step 02:

place value blocks

264

+ 638

_______

902

That is the full solution.

we have the exponential function

For t=7 hours

substitute

To find the answer to this question, find the difference between the old television weight and the new television weight. Substract 32 to 81:

The old television weighs 49 pounds more than the new one.

x³ + 2x² - 9x - 18 is the polynomial function of least degree with integral coefficients that had the zeros -3 , 3 , -2.

Given, the zeros of a polynomial be,

-3 , 3 and -2

As, the polynomial has 3 zeros then the degree of the polynomial is also be , 3.

Let the polynomial be,

p(x) = (x - (-3))(x - 3)(x - (-2))

p(x) = (x + 3)(x - 3)(x + 2)

On multiplying the factors, we get

p(x) = (x² - 3²)(x + 2)

p(x) = (x² - 9)(x + 2)

p(x) = (x³ - 9x + 2x² - 18)

p(x) = x³ + 2x² - 9x - 18

So, x³ + 2x² - 9x - 18 is the polynomial function of least degree with integral coefficients that had the zeros -3 , 3 , -2.

Hence, x³ + 2x² - 9x - 18 is the polynomial function of least degree with integral coefficients that had the zeros -3 , 3 , -2.

Learn more about Polynomials here https://brainly.com/question/23974386

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In this problem we have a quadratic function (vertical parabola open upward)

the domain is all real numbers

therefore

The sum of angle 3x and 45 is equal to 72. So equation for x is,

Simplify the equation to obtain the value of x.

Determine the measure of angle 3x.

So value of x is 9 and measure of angle 3x is 27 degree.

Explanation:

Martin's age = 6 years old

Casandra's age = 3 years old

Difference in their age = 6 - 3

Difference in their age = 3

Since all the sides of the figure have the same length, then the figure is a rhombus. Then, its diagonals intersect at an angle of 90°.

Let O be the intersection of the diagonals of the rhombus. Notice that the triangle EOA is a right triangle. Since the side EA is the hypotenuse of the triangle, then, recalling the trigonometric functions:

Use this information to solve for the segments EO and OA:

Since the diagonal EM is twice the segment EO and the diagonal BA is twice the segment OA, then the lengths of the diagonals are:

Therefore, the answer is: