The graph below shows the solution set of which inequality?

1.

What do you know?

the troposphere extends 8 to 20 km above the Earth's surface. The surface temperature is 15°C and decreases at a rate of 6.5°C per kilometer away.

What do you want to find out?

The temperature at any point of the troposphere

What kind of answer do you expect?

Any value below 15°C

2. Define variables,

T is for temperature, and

d is the distance away from the surface

3. What is the b -value

b = 15

which is the Earth's surface temperature or the initial temperature for our problem

4. What is the slope

the slope 'm' equals -6.5

which means that the temperature decreases 6.5°C per km

5. write the equation

the general form for this equations is y = b + mx

thus, for our problem, the equation is: T = 15 - 6.5*d

6.

a) the slope represents the rate of change of temperature with respect to distance, since m = -6.5 °C/km , this means the troposphere is getting 6.5 °C colder per km away from Earth's surface

b) the y-intercept represents the Earth's surface temperature

Graph:

7. identify 3 points

when d = 0 then T = 15, so our first point is (0,15)

when d = 1 then T = 15 - 6.5 = 8.5 , so our second point is (1,8.5)

when d = 2 then T = 15 - 13 = 2 so our third point is (2,2)

8. calculate the slope

let's use this equation and this set of points,

let's replace and solve

We can see that it does match the slope from our model, which is -6.5

9. graph the line and the points,

10. Complete the sentence

... ends between 8 km and 20 km above Earth.

11. temperature at the farthest point

when d = 20 then,

... the temperature is -115°C

12. Temperature range,

from... 15 °C to -115 °C

Answer:

x = 2

z = 85°

Step-by-step explanation:

95° + z = 180°

z = 180 - 95

z = 85°

z + (11x + 73) = 180°

85 + (11x + 73) = 180°

11x + 85 + 73 = 180°

11x + 158 = 180°

11x = 180 - 158

11x = 22

x = 22/11

x = 2

Answer:

Number of quarters → 15

Number of dimes → 2

Step-by-step explanation:

Let the number of dimes I have = y

And number of quarters = x

Since, I have amount in my pocket = $2

Therefore, 0.10y + 0.25x = 2

100(0.10y + 0.25x) = 100×2

25x + 10y = 200

5x + 2y = 40

2y = -5x + 40

y = -2.5x + 20 ---------(1)

Total number of coins in my pocket = 17

x + y = 17

y = -x + 17 ---------(2)  

By using a graphing calculator we can graph these two lines (As attached)

Solution of the given system of equations will be the point of intersection of these lines.

Solution → (2, 15)

Number of quarters → 15

Number of dimes → 2

Answer:

Your slope would be -1/10

Step-by-step explanation:

To find the slope from two points, you would use the formula y2-y1/x2-x1

In this case, the equation would look like -4-(-3)/5-(-5)

-4 - (-3) = -1

5 - (-5) = 10

-1/10 = -1/10

Answer: each soda costs $1.5 and each hotdog costs $3.

Step-by-step explanation:

If H is the price for one hotdog and S is the price for one soda, we have the equations:

for Jack.

3*H + 2*S = $12

For Angie.

1*H + 4*S = $9

Now we can isolate one of the variables in one of the equations and then replace it in the other equation, let's isolate H in the second equation:

H = $9 - 4*S

now we replace it in the first eq

3*H + 2*S = $12

3*($9 - 4*S) + 2*S = $12

$27 - 12*S + 2*S = $12

-10*S = $12 - $27 = -$15

S = $15/10 = $1.5

Now we can replace it in the equation for H and get:

H = $9 - 4*$1.5 = $3

So each soda costs $1.5 and each hotdog costs $3.

Answer: One hotdog cost $3 and One soda costs $1.5

Step-by-step explanation:

Let hotdogs be denoted by h

Let sodas be denoted as s

Jack bought 3 hotdogs and 2 sodas for a total of $12. This can be written as:

3h + 2s = 12

Angie bought 1 hotdog and 4 sodas for $9. This can be written as:

h + 4s = 9

3h + 2s = 12

h + 4s = 9

1 × (3h + 2s = 12)

3 × (h + 4s = 9)

3h + 2s = 12

3h + 12s = 27

Subtract the equation

-10s = -15

s = -15/-10

s = 1.5

One soda cost $1.5

Since h + 4s = 9

h + 4(1.5) = 9

h = 9 - 6

h = 3

One hotdog costs $3

Answer:

x=8

this is because you do 57+89=146

and then you do 180-146 because a triangle adds up to 180.

this gives you 34

so the value of 5x-6=34

add the 6 onto 34 which gets rid of the -6 ans fives you the answer of 40

After that yoy divide 40 by 5 which gives you the value of x which is 8

The equation in standard form for the circle with center (5,0) passing through (5, 9/2) is 4x² + 4y² - 40x + 19 = 0

Given that

Center = (5, 0)

Point on the circle = (5. 9/2)

The equation of a circle can be expressed as

(x - a)² + (y - b)² = r²

Where

Center = (a, b)

Radius = r

So, we have

(x - 5)² + (y - 0)² = r²

Calculating the radius, we have

(5 - 5)² + (9/2 - 0)² = r²

Evaluate

r = 9/2

So, we have

(x - 5)² + (y - 0)² = (9/2)²

Expand

x² - 10x + 25 + y² = 81/4

Multiply through by 4

4x² - 40x + 100 + 4y² = 81

So, we have

4x² + 4y² - 40x + 19 = 0

Hence, the equation is 4x² + 4y² - 40x + 19 = 0

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Answer:

{F, O, U, R} in the word 'FOUR'

the discrepancy between the sample mean and the claimed protein content is due to chance error in the measurements

To determine whether the discrepancy between the sample mean and the claimed protein content of 4 grams can be due to chance error in the measurements, we can perform a hypothesis test.

The null hypothesis, H0, is that the true mean protein content is equal to 4 grams. The alternative hypothesis, Ha, is that the true mean protein content is less than 4 grams.

Using a one-tailed t-test with a significance level of 0.05 and four degrees of freedom (n-1=5-1=4), we calculate the t-value to be -1.386. The critical t-value for a one-tailed test at a significance level of 0.05 and four degrees of freedom is -2.132.

Since our calculated t-value of -1.386 is greater than the critical t-value of -2.132, we fail to reject the null hypothesis. This means that we do not have enough evidence to conclude that the true mean protein content is less than 4 grams. Therefore, it is possible that the discrepancy between the sample mean and the claimed protein content is due to chance error in the measurements.

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Answer: You have to use a calculator

Step-by-step explanation:

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To calculate the present value of $51,270 payments to be made at the end of each period for 17 periods at a 9% interest rate, we need to find the discounted value of each payment and sum them up.

The present value (PV) is calculated by discounting each future payment back to its current value using the interest rate. The formula to calculate the present value of a series of payments is:

PV = Payment × [1 - (1 + interest rate)^(-number of periods)] / interest rate.

In this case, the payment is $51,270, the interest rate is 9% (or 0.09 as a decimal), and the number of periods is 17.

Using the provided formula and rounding the factor values to 5 decimal places, we can calculate the present value as follows:

PV = $51,270 × [1 - (1 + 0.09)^(-17)] / 0.09.

Evaluating this expression will give us the present value of the payments. It's important to round the final answer to 0 decimal places, as stated in the question.

By substituting the values and calculating the expression, we can determine the present value of the $51,270 payments made over 17 periods at a 9% interest rate.

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Step-by-step explanation:

Your question isn't complete.

But if you are asking for finding the value of variable then, you should follow these things

x+2=6

x+2-2=6-2

x=4

Hence, positive number is cancelled

x-3=1

x-3+3=1+3

x=1

Hence, negative number is cancelled

3x=6

3x/3=6/3

x=2

Hence, the number in product form is cancelled

y÷3=1

y÷3×3=1×3

y=3

Hence, the number in divide form is cancelled

The value of the probability of choosing a green lollipop and a purple lollipop is, 8 / 45

We have to given that;

One bag contains 3 red lollipops and 2 green lollipops.

And, The other bag contains four purple lollipops and five blue lollipops.

Hence, The probability of choosing a green lollipop is,

P₁ = 2 / 5

And, The probability of choosing a purple lollipop is,

P₂ = 4 / 9

Thus, The value of the probability of choosing a green lollipop and a purple lollipop is,

P = P₁ ×  P₂

P = 2/5 × 4/9

P = 8/45

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Answer:

A

Step-by-step explanation:

There is a 50% chance of this correct

Jutin chooses a function J(x) = 3x - 1 that when he uses the number 7 as an input, then the output is 20.

As per the given data, Jutin chooses a function in which he uses the number 7 as an input, then the output is 20.

Here we have to determine which function Jutin has to use.

Now we have to substitute the value that x = 7 in all the given functions.

First function:

F(x) = 2\(x^{5}\)

F(7) = 2 \((7)^{5}\)

F(7) = 2 (16807)

F(7) = 33614 which is not equal to 20.

Second function:

G(x) = \(x^{2}\) - 19

F(7) = \((7)^{2}\) - 19

F(7) = 49 - 19

F(7) = 30 which is not equal to 20.

Third function:

H(x) = 13 - x

H(7) = 13 - 7

H(7) = 6 which is not equal to 20.

Fourth function:

J(x) = 3x - 1

J(7) = 3(7) - 1

J(7) = 21 - 1

J(7) = 20

The correct function is J(x) = 3x - 1

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Answer:

8y(y-4)(y+1)

Step-by-step explanation:

First find the GCF of the three terms, in this case its 8y

8y(y^2-3y-4)

factor y^2-3y-4 by finding two numbers that multiply to -4 and add to -3, in this case, its -4 and 1.

8y(y-4)(y+1)

Answer:

Well Circumference = πr^2, but I don't know what you're asking for?

Answer:

i) around 41.7 kg

ii) 72 books

Step-by-step explanation:

i) if 108 books are 30 kg then how much is the mass for 150? You cross multiply so 150 multiply by 30 and 108 multiply by x (the unknown mass). you will get 4500=108x and then 4500/108 is the unknown mass.

ii) use the same way as above.

Step-by-step explanation:

the time difference between 11:05 and 12:10 is 1hour 5minutes

Answer:

12

36'7;"&$',7:&7#&"^$//&

We were told that the salary, t years after 2015 is given by the function,

S(t) = 3100t + 56000

When considering 2017, the number of years, t from 2015 is 2017 - 2015 = 2

We would substitute t = 2 into the function and find S(2)

Thus,

S(2) = 3100 x 2 + 56000 = 6200 + 56000 = 62200

When considering 2020, the number of years, t from 2015 is 2020 - 2015 = 5

We would substitute t = 2 into the function and find S(2)

Thus,

S(5) = 3100 x 5 + 56000 = 15500 + 56000 = 71500

Thus, we can say that

when

x1 = 2, y1 = 62200

when x2 = 5, y2 = 71500

Recall,

slope or average rate of change = (y2 - y1)/(x2 - x1)

average rate of change = (71500 - 62200)/(5 - 2) = 9300/3

average rate of change = 3100

The last option is correct

Answer:

The answers are in the picture also with steps

Step-by-step explanation:

Answer:

After 10 hours, Jared is the most expensive sitter

Explanation:

Given that Kathy babysits for $7.25 an hour, plus $5.75 in transport cost, and

Jared babysits $7.50 an hour, plus $3.25 in transport cost.

We want to know after how many hours is Jared the most expensive sitter.

In an equation form, we write the cost of babysitting for x hours for

Kathy as: 7.25x + 5.75

Jared as 7.50x + 3.25

We want to know at what value of x is

7.50x + 3.25 > 7.25x + 5.75

Solving for x in the above inequality

Subract 7.25x from both sides:

7.50x + 3.25 - 7.25x > 5.75

0.25x + 3.25 > 5.75

Subtract 3.25 from both sides

0.25x > 5.75 - 3.25

0.25x > 2.5

Divide both sides by 0.25

x > 2.5/0.25 = 10

x > 10

Therefore, after 10 hours, Jared is the more expensive sitter.

The polynomial -3x^3 + 2 has only one turning point.

A turning point is a point on a curve where the curve changes direction, either from going up to going down or vice versa. In other words, it is a point where the first derivative of the curve changes sign.

For the polynomial -3x^3 + 2, the first derivative is given by:

d/dx (-3x^3 + 2) = -9x^2

Since the first derivative is a monotonically decreasing function (that is, its slope is always negative), the polynomial -3x^3 + 2 has only one turning point.

Slope of first derivative

d²(-3x^3 + 2)/dx² = -18x

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Answer:

  36.4%

Step-by-step explanation:

You want the percentage change from $22 to $30.

The percentage change is given by the formula ...

  percent change = ((new value)/(old value) -1) × 100%

  = (30/22 -1)(100%) ≈ 36.4%

The stock increased in value by about 36.4%.

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The probability of getting at least one head is 15/16.

What is probability?

The ratio of positive outcomes to all possible outcomes of an event is known as the probability.

Formula for probability = favourable outcomes/ total outcomes

Main body:

if 4 coins are tossed , total no. of outcomes = 2⁴ = 16

In a toss there are 2 outcomes T or H

so, Probability of getting Head = 1/2

The probability of getting at least 1 head = 1- probability of getting no heads

⇒1 - Probability of getting tail in 4 tosses

⇒ 1 - (1/2)⁴

⇒ 1 - 1/16

⇒ 15/16

So the probability of getting at least one head is 15/16.

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Answer:

Step-by-step explanation:

Part A:

The system of inequalities 4x + 2y ≤ 16 and x + y ≥ 4 can be graphed on a coordinate plane. To graph 4x + 2y ≤ 16, we can first graph the line 4x + 2y = 16. We can do this by finding the intercepts:

When x = 0, 4(0) + 2y = 16, so y = 8.

When y = 0, 4x + 2(0) = 16, so x = 4.

So, the intercepts are (0, 8) and (4, 0). We can connect these two points to graph the line.

To determine which side of the line to shade, we can test a point that is not on the line. For example, we can test the point (0, 0):

4(0) + 2(0) = 0 ≤ 16, so (0, 0) is in the shaded region.

Next, we can graph the line x + y = 4. This line passes through the points (0, 4) and (4, 0). To determine which side of the line to shade, we can test a point that is not on the line, such as (0, 0):

0 + 0 = 0 < 4, so (0, 0) is not in the shaded region. Therefore, we shade the region above the line.

The solution set for the system is the region that is shaded by both lines, which is the triangular region in the upper-left corner of the graph.

Part B:

To determine if the point (2, 3) is included in the solution area for the system, we can substitute x = 2 and y = 3 into both inequalities:

4(2) + 2(3) = 14 ≤ 16, so (2, 3) satisfies 4x + 2y ≤ 16.

2 + 3 = 5 ≥ 4, so (2, 3) satisfies x + y ≥ 4.

Therefore, the point (2, 3) is included in the solution area for the system.

Part C:

Let's choose the point (1, 3) as another point in the solution set. This means that Michael can buy 1 cupcake and 3 pieces of fudge, which would cost him:

1 cupcake * $4/cupcake + 3 pieces of fudge * $2/piece of fudge = $10

Since $10 is less than the $16 he has, he can afford to buy this combination of cupcakes and fudge. Therefore, the point (1, 3) represents a valid solution in which Michael buys 1 cupcake and 3 pieces of fudge to feed his siblings.

In this case, there are two unique factors: 2 and 3. The expression can be rewritten as (2^2) x 3, showing that the number 2 is raised to the power of 2 and then multiplied by 3. Since there are only two unique factors involved in this expression, the correct answer is: d. 2

The answer is d. 2. In a factorial combination, independent variables refer to the factors or variables that are being manipulated or varied. In the combination 2x2x3, there are two independent variables: the first variable has two levels or options, the second variable also has two levels or options, and the third variable has three levels or options. Therefore, the number of independent variables in this factorial combination is two.
 The given expression is 2x2x3, which is a product of three numbers. To determine the number of independent variables in this factorial combination, let's identify how many unique variables or factors are involved in the product.
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Answer:

6/7

Step-by-step explanation:

3x2/7 in the same as 3/1x2/7, which is 6/7

(simply multiply the denominator and numerator of the fraction)

Answer: hii <3

Exact Form:

6/7

Decimal Form:

0.857142

Step-by-step explanation:

Simplify the expression.

Hopefully this helps you

- Matthew

(a) ( x_{t+1}=\frac{1}{2} x_{t}+3 ), the solution to this difference equation is x_t = 2^t + 3, The difference equations in this problem are both linear difference equations with constant coefficients.

This can be found by solving the equation recursively. For example, the first few terms of the solution are

t | x_t

--- | ---

0 | 3

1 | 7

2 | 15

3 | 31

The general term of the solution can be found by noting that

x_{t+1} = \frac{1}{2} x_t + 3 = \frac{1}{2} (2^t + 3) + 3 = 2^t + 3

(b) ( x_{t+1}=-3 x_{t}+4 )

The solution to this difference equation is

x_t = 4 \cdot \left( \frac{1}{3} \right)^t + 4

This can be found by solving the equation recursively. For example, the first few terms of the solution are

t | x_t

--- | ---

0 | 4

1 | 5

2 | 2

3 | 1

The general term of the solution can be found by noting that

x_{t+1} = -3 x_t + 4 = -3 \left( 4 \cdot \left( \frac{1}{3} \right)^t + 4 \right) + 4 = 4 \cdot \left( \frac{1}{3} \right)^t + 4

The difference equations in this problem are both linear difference equations with constant coefficients. This means that they can be solved using a technique called back substitution.

Back substitution involves solving the equation recursively, starting with the last term and working backwards to the first term.

In the first problem, the equation can be solved recursively as follows:

x_{t+1} = \frac{1}{2} x_t + 3

x_t = \frac{1}{2} x_{t-1} + 3

x_{t-1} = \frac{1}{2} x_{t-2} + 3

...

x_0 = \frac{1}{2} x_{-1} + 3

The general term of the solution can be found by noting that

x_{t+1} = \frac{1}{2} x_t + 3 = \frac{1}{2} (2^t + 3) + 3 = 2^t + 3

The second problem can be solved recursively as follows:

x_{t+1} = -3 x_t + 4

x_t = -3 x_{t-1} + 4

x_{t-1} = -3 x_{t-2} + 4

...

x_0 = -3 x_{-1} + 4

The general term of the solution can be found by noting that

x_{t+1} = -3 x_t + 4 = -3 \left( 4 \cdot \left( \frac{1}{3} \right)^t + 4 \right) + 4 = 4 \cdot \left( \frac{1}{3} \right)^t + 4

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