Mid topic checkpoint chapter 4 for questions 3,and 4

The average rate of change of the function  f(x) = 7x from x1 = 0 to x2 = 4 is solved to be 7

The rate of change is solved using the formula

= change in y / change in x

In the problem, the function is  f(x) = 7x from x1 = 0 to x2 = 4

hence y = f(x) =

For x = 0, y = 7 * 0 = 0

For x = 4, y = 7 * 4 = 28

rate of change

= 28 - 0 / 4 - 0

= 28 / 4

= 7

the rate of change is 7

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Answer: √6/8 x √6/18

Step-by-step explanation: The square root of A over B is the same as the squared of A, so it's important to know that before I start with this product. To go over the square.

I can do that if I combine the two square roots under the exact square root. This is only for multiplication.

I could take the square root of the term separately

Since I'm using fractions, I'll add the tops and bottoms to the equation.

The square root is eight times 18 and the squared root is six times six. It is the square to 36 over. It's eight times 18. There are 44 items.

The square to 36 is a question. I don't know what time it gives me. There were 36. 36 times six is 6. Six Over would be this. What time gives me 1 44?

Twelve times. 6/12 would be the day. It doesn't want me to reduce that, but I could.

The answer would be 6/12.

The biggest angle in the triangle is opposite the largest side, which is how they actually relate to one another. The right answer is D.

A triangle's characteristics are:

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Part (a)

[tex]42^{\circ}[/tex] since the angle intercepted by a central angle is the same as the measure of the arc.

Part (b)

[tex]21^{\circ}[/tex] by the inscribed angle theorem.

Answer:

b

Step-by-step explanation:

b. There is 5% probability that a true null hypothesis will be rejected.

A p-value of 0.05 represents the probability of obtaining a test statistic as extreme or more extreme than the one observed under the assumption that the null hypothesis is true. In other words, it is the probability of observing the data or more extreme data assuming the null hypothesis is true. It is also the threshold level of significance beyond which the null hypothesis is rejected in favor of the alternative hypothesis. A p-value of 0.05 means that there is a 5% probability that the observed results occurred by chance under the null hypothesis and that there is a 95% probability that the observed results occurred due to a real effect.

Answer:

10

Step-by-step explanation:

The meaning of (p⋅c)(2) for the horse-drawn carriage tour company is: A. the horse-drawn carriage tour company can expect to take in $5760 when the charge per customer is $60.

In this scenario, a function which represents the price charged per customer c(x) is given by this mathematical expression;

c(x) = 50 + 5x.

where:

x represents the number of $5 increases they charge over a rate of $50 per person.

When x = 2, the price charged per customer c(x) is given by;

c(2) = 50 + 5(2)

c(2) = $60.

Furthermore, a function which represents the number of customers expected for the day is given by:

p(x) = 100 - 2x

where:

x represents the number of $5 increases they charge over a rate of $50 per person.

When x = 2, the number of customers expected for the day is:

p(2) = 100 - 2(2)

p(2) = 96.

Now, (p⋅c) can be calculated as follows;

(p⋅c) = p(2) × c(2)

(p⋅c) = 96 × 60

(p⋅c) = $5760.

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our function v(t) is differentiable in the interval 0 to 40, by mean value theorem a(t)=0 at least two value of t. it can be t=0 and t=5, which is smallest.

A test plane files in a straight line with positive velocity v(t), v is a differentiable function of t.

selected value of v(t) for 0≤ t≤ 40are shown in the table.

We have to justify that what is that smallest number of instances at which the acceleration of plane could equal to zero on the interval (0,40).

We are aware about mean value theorem.

somewhere between t=0 , t=5, v'(t) =0

because v(t) is a differentiable function.

also, t=25 and t=30

v'(t)=0 because

[tex]\frac{v(30)-v(25)}{30-25} =0[/tex],

this means a(t) =0 for at least two value of t.

So, our function is differentiable in the interval 0 to 40, by mean value theorem a(t)=0 at least two value of t. it can be t=0 and t=5.

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Answer:

y=3x+4

slope is the slope obviously and insert the point into the y=3x+b

itll be 7=3(1)+b

so itll be 4=b

The smallest four-digit number with one digit used twice is 2236.

What is Digit?

A positional numeral system uses a single symbol, the numerical digit, either individually or in combination to represent numbers. The term "digit" refers to the ten symbols of the conventional base-10 numeral system, or decimal digits, which the ten digits of the hands correspond to.

A number is a numerical unit of measurement and labeling in mathematics. The natural numbers 1, 2, 3, 4, and so on are the first examples. Number words are a linguistic way to express numbers.

Given digit is ;

3629

Digits are   3  6  2  9

Digits in ascending order

2  3   6  9

Minimal 4 digit number

We can employ a number Twice

So, we'll use the smallest digit, 2, twice.

at positions 1000th and 100th.

The smallest four-digit number with one digit used twice is 2236.

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The correct option B) x= 0,-3, are the values of x make the given quadratic equation true 3x = -x^2.

The stated quadratic equation is-

3x = -x^2

x^2 + 3x = 0

Taking x common.

x(x + 3) = 0

x = 0, -3

Thus, the values of x that makes the equation true are  0, -3.

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The price for the Suite room for check-in on Friday and Saturday is given as follows:

$278.75.

The price for the room is obtained applying the proportions in the context of this problem.

The price for the room on the period from Sunday until Thursday is given as follows

$223.

The price for the room on Friday and Saturday is 25% higher than from Sunday until Thursday, hence the price is given as follows:

1.25 x 223 = $278.75.

(as an increase of 25% is equivalent to a proportion of 1.25).

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The number of countries ever visited is a discrete variable. Discrete variables are variables that can only take specific values, rather than any value within a range. The number of countries ever visited can only be a whole number, such as 0, 1, 2, 3, and so on, and not a fraction or decimal.

Pounds of chocolate consumed in the past year is a continuous variable. Continuous variables are variables that can take any value within a range. Pounds of chocolate consumed in the past year can be any value between 0 and a maximum value, such as 0.5, 1.5, 2.7, and so on.

Shoe size is a discrete variable. Shoe size is typically measured in whole numbers, such as 5, 6, 7, 8, and so on, and not in fractions or decimals.

Height in inches is a continuous variable. Height in inches can take any value within a range, such as 60, 61, 62, and so on.

The number of pets currently living in the household is a discrete variable. The number of pets can only be a whole number, such as 0, 1, 2, 3, and so on, and not a fraction or decimal.

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The graph of g(x) is represented by the equation g(x) = Root Index 3 Start Root x EndRoot-1.

Hence, the correct option is D) g(x) = RootIndex 3 Start Root x End Root–1

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Here x = 5, The two angles are ∠B = 41° and ∠C=  63°.

A pentagon is a 2D polygon with five sides and five angles.

Pentagon is formed from three triangles, so the sum of angles in a pentagon = 3 × 180° = 540°.

We are given in the figure , following information about a pentagon:

3 angles are 90 degrees, one angle is (6x+1) degrees, and the other angle is (8x-11) degrees.

To solve for x, we need to add all of the angles together.

The sum of the angles in any polygon is always equal to (n-2)*180, where n is the number of sides in the polygon.

In this case, n=5, so the sum of the angles is (5-2)*180 = 540 degrees.

We can now solve for x by substituting our known values into the equation.

540 = 90 + (6x + 1) + (8x - 11)

540 = 14x

x = 540/14

x = 5

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Answer:

C. Pulling a blue sock from a drawer of only blue socks

Step-by-step explanation:

If there is no other color in the drawer, only that color can be pulled certainly.

The values of the following are:

Sin A = 0.71

Cos A = 0.71

Sin B = 0.71

Cos B = 0.71

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

Right triangle ABC.

∠C = 90

The other two sides are a = 8 and b = 8

This means,

The angle opposite to the side a = 8 and b = 8 are equal.

Now,

∠A = ∠C

∠C + ∠A + ∠B = 180

90 + ∠A + ∠B = 180

2∠A = 180 - 90

∠A = 90/2

∠A = 45

∠B = 45

Now,

c² = a² + b²

c² = 64 + 64

c² = 128

c = √128

c = 11.31

Thus,

Sin A = a/c = 8/11.31 = 0.71

Cos A = b/c = 8/11.31 = 0.71

Sin B = b/c = 8/11.31 = 0.71

Cos B = a/c = 8/11.31 = 0.71

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Based on the graph of the general solution to the differential equation dy/dx = 2x + y, the option C: The slopes are all positive in Quadrant 1, is true.

What is a differential equation?

A differential equation is an equation that contains at least one derivative of an unknown function, either a normal differential equation or a partial differential equation.

The given the differential equation is dy/dx=2x+y.

The graph for the function is drawn.

dy/dx=2x+y

Now slope=2x+y

Along x-axis, y=0.

So, slope=2x≠0.

Since it depends upon x hence the slope along the y-axis are not horizontal.

Along y-axis, x=0.

So, slope=y≠0.

Since  it depends upon y the slope along the x-axis are also not horizontal.

In quadrant I -

x,y≥0

So, dy/dx≥0

Hence the slopes are all positive in quadrant I.

In quadrant IV -

x≥0,y≤0

So, dy/dx is not always positive.

Therefore, the slopes are not all positive in quadrant IV.

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Based on the graph of the general solution to the differential equation dy over dx equals 2 times x plus y comma which of the following statements is true? The slopes along the y-axis are horizontal. The slopes along the x-axis are horizontal. The slopes are all positive in Quadrant 1. The slopes are all positive in Quadrant 4.

Answer: Answers vary…

Step-by-step explanation:

Equivalent fractions can be written by multiplying or dividing both the numerator and the denominator by the same number. Some fractions equivalent to 1/2 are: 2/4, 3/6, 4/8, 5/10, 6/12, etc. This is because equivalent fractions have the same value in reduced form.

Given System of equation has multiple solution.

Simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.

Given a system of equation:

-1 = 2x - y and  8x - 4y = -4​

From equation 1

-1 = 2x - y

y = 2x + 1

Substitute this value on equation 2

8x - 4y = -4​

8x - 4(2x + 1) = -4

-4 = -4

An equation can have infinitely many solutions when it should satisfy some conditions. The system of an equation has infinitely many solutions when the lines are coincident, and they have the same y-intercept. If the two lines have the same y-intercept and the slope, they are actually in the same exact line.

Thus, Given System of equation has multiple solution.

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Answer:

  5.1% increase

Step-by-step explanation:

You want the percentage change in price per load when the price of detergent went from $16.99 for 52 loads to $16.49 for 48 loads.

The percentage change is given by the formula ...

  ((new price)/(old price) -1) × 100%

The price per load is found by dividing the price of the bottle of detergent by the number of loads it will wash.

  old price per load = $16.99/52 ≈ $0.32673

  new price per load = $16.49/48 ≈ $0.34354

Then the percentage change is ...

  (0.34354/0.32673 -1) × 100% ≈ 0.05145 × 100% ≈ 5.1%

The price per load has increased by about 5.1%.

Answer:

see i have a same solution not exactly though

Step-by-step explanation:

so check and solve good luck

Answer:

Step-by-step explanation:

y = 1x + 2

y = 3x + 3

y = 1/2x + 2

y = -3x + 12

Answer:

a) To determine the monthly mortgage payment, we first need to calculate the amount of the loan, which is equal to the purchase price of the house minus the down payment. In this case, the loan amount is 250,000 * 0.8 = 200,000. Next, we need to calculate the monthly interest rate, which is equal to the annual interest rate divided by 12. In this case, the monthly interest rate is 0.12/12 = 0.01. Using the formula for the monthly mortgage payment (P = L[i(1+i)^n]/[(1+i)^n-1]), where P is the monthly payment, L is the loan amount, i is the monthly interest rate, and n is the number of payments (in this case, 30 years * 12 = 360), we can calculate the monthly payment as:

P = 200,000[0.01(1+0.01)^360]/[(1+0.01)^360-1] = 1326.91

b) To calculate the total amount of interest Ato Liku will pay over the life of the mortgage, we can subtract the original loan amount from the total amount of payments made over the life of the mortgage. In this case, that would be 360 * 1326.91 - 200,000 = 480,596.

c) To determine the amount of the mortgage Ato Liku will have paid after 10 years, we can multiply the monthly mortgage payment by the number of payments made in 10 years (10 years * 12 = 120). In this case, that would be 120 * 1326.91 = 159,223.20.

Based on the information provided, it can be concluded that the vaccine trials most likely did not cause children to get polio as these are independent variables.

This type of bias implies people believe two events are related as a cause or effect. This often happens when one event follows another, and therefore people believe one event causes the other.

In this case, people are likely to believe the vaccine caused higher polio rates just because after the vaccine, polio rates seemed to increase. However, these two variables are independent as vaccines produce immunization against polio.

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Put the decimal point to the right to make the divisor a full number if it isn't already. The dividend's decimal point should likewise be moved the same number of spaces to the right (adding some extra zeros if necessary.)

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The fundamental frequency of the flute of length 49.0 cm and with its one end closed is 175 hertz.

Given,

           Length of flute = 49.0 cm

           Speed of sound in air = 343 m/s

The flute closed from one end and is open from the other exhibits a standing wave pattern.

We know that,

                        [tex]f =\frac{v}{4L}[/tex]

Now substituting values in the above equation:

                       [tex]f = \frac{343}{4* (0.49)}[/tex]

                       [tex]f = 175 hz[/tex]

Thus, the fundamental frequency of the flute is 175 hertz.

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In Amanda's case, an example of a parameter is the national average income for mechanical engineers.

As a mechanical engineer, Amanda is now seeking employment. Additionally, she is paid in line with both the national average for Mechanical engineers as well as the average for Mechanical engineers in our community. In Amanda's instance, a parameter example is needed, thus that is what the question asks for. The population's traits are referred to as a parameter, whereas the sample's characteristics are referred to as statistics.

Due to its gifts and the information it provided that was close to the average population slurry, it constitutes a parameter here. A representative sample of mechanical engineers is Amanda's city. In Amanda's city, the slurry from a sample is the mechanical engineers' average annual pay. They have therefore taken a representative sample of all the mechanical engineers in the city from the larger population.

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The purple line would be plotted at the level of output $60 billion, and the orange line segments would be plotted at 90, 95, 100, 105, and 110 respectively.

1. Plot the purple line at the level of output $60 billion.

2. Plot the orange line segments at 90, 95, 100, 105, and 110 respectively.

The long-run aggregate supply (RAS) curve is used to represent the natural level of output for an economy. In this case, the natural level of output is $60 billion of real GDP with a price level of 100. Therefore, the purple line should be plotted at the level of output $60 billion on the graph. The short-run aggregate supply (AS) curve is used to show how the level of output reacts to the price level. Therefore, the orange line segments should be plotted at 90, 95, 100, 105, and 110 respectively. This will show how the level of output changes when the price level is different from the natural level. This will help to illustrate how the economy may react when the price level is different than expected.

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