In your lab, a substance's temperature has been observed to follow the function T(x) = (x + 5)3 + 7. The turning point of the graph is where the substance changes from a liquid to a solid. Explain to your fellow scientists how to find the turning point of this function?

Final answer:

The value of n in the equation –(2n + 4) + 6 = –9 + 4(2n + 1) is -2. This is determined by simplifying and solving the given expression for n.

Explanation:

To find the value of n in the equation –(2n + 4) + 6 = –9 + 4(2n + 1), we need to simplify and solve for n. First, we distribute the negative sign and the 4 into the parentheses and then combine like terms:

-2n - 4 + 6 = -9 + 8n + 4

Now, we combine the constants:

-2n + 2 = -5 + 8n

To isolate n, we move all the terms involving n to one side and the constants to the other:

-2n - 8n = -5 - 2

-10n = -7

Finally, we divide by -10 to solve for n:

n = ⅔

Thus, the value of n is -2.

Answer:

multiplicative inverse

Step-by-step explanation:

hope it helps

The slope of the red line is -4/3. Therefore, option C is the correct answer.

Given that, the green line has a slope of 3/4.

We need to find the slope of the red line.

The formula for the slope of perpendicular lines is m1.m2 = -1. The product of the slopes of perpendicular lines is equal to -1.

Since, m1=3/4.

Now, 3/4.m2 = -1

⇒m2 =-4/3

The slope of the red line is -4/3. Therefore, option C is the correct answer.

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Answer:

Option B.

Step-by-step explanation:

Bruce had an EKG to measure his heartbeat rate. After conversion, the function produced was modeled by a cosine function.

Now we will form this function.

Function will be in the form of f(x) = a cos(Bx) + d

Amplitude [tex]a=\frac{Maximum-minimum}{2}[/tex]

[tex]a=\frac{4+2}{2}=3[/tex]

Period = π/2

And [tex]Period=\frac{2\pi }{B}[/tex]

⇒[tex]\frac{\pi }{2}=\frac{2\pi }{B}[/tex]

⇒ B = 4

Since minimum is (-2) and maximum is (4), means cosine graph was shifted upwards.

Mid line of the graph is [tex]x=\frac{4+2}{2}=3[/tex] which shows graph is shifted by one unit above the x-axis.

Now the function we get is f(x) = 3 cos4x + 1

Therefore option B is the answer.

Answer:

it is by similarity transformations

Step-by-step explanation:

so like it would be a rigid transformation then a dilation

EX- A translation then a dilation of R/r

Part A. To solve for the distance travelled during the interval, all we have to do is to plug in values of t = 3 and t = 3.5 in the equation and the difference would be the answer:

when t = 3: s = 16 (3)^2 = 144 m

when t = 3.5: s = 16 (3.5)^2 = 196 m

Therefore the distance travelled within the interval is:

196 m – 144 m = 52 m

Part B. The velocity is calculated by taking the 1st derivative of the equation. v = ds / dt

s = 16 t^2

ds / dt = 32 t = v

when t = 3: v = 32 (3) = 96 m / s

when t = 3.5: v = 32 (3.5) = 112 m / s

Therefore the average velocity is:

(96 + 112) /2 = 104 m / s

Part C. We can still use the formula v = 32 t and plug in the value of t = 3

v = 32 t = 32 (3)

v = 96 m / s

To calculate the distance and velocities for the ball in question, we use the formula s(t)=16t^2, calculate differences, and use limits as the intervals approach an instant.

The formula s(t)=16t2 gives the distance s(t) in feet that a ball has traveled after t seconds when dropped from a state of rest. To find the distance during the time interval [3,3.5], we calculate s(3.5) and s(3), and then find the difference: s(3.5) = 16 × (3.5)2 and s(3) = 16 × (3)2.

The average velocity over the interval [3,3.5] is the change in distance divided by the change in time, which is computed as ∆ s/ ∆ t.

For the instantaneous velocity at t=3, we compute the average velocities over smaller and smaller intervals approaching the instant t=3. As these intervals become smaller, the average velocity approaches the instantaneous velocity.

It's better to describe the center of distribution in Bakery A using the mean because the data is symmetric, while for Bakery B, the median is preferred due to asymmetric data.

To determine whether it's better to describe the centers of distribution in terms of the mean or the median for each bakery, we need to consider the shape of the data distribution.

For Bakery A:

- The data appears to be relatively symmetric, with values ranging from 34 to 61.

- There are no extreme outliers that significantly skew the data.

For Bakery B:

- The data is not symmetric; there is a wide range of values from 10 to 57.

- There is a notable outlier (10) that is much lower than the rest of the data.

Given these observations:

- For Bakery A, since the data is symmetric and there are no significant outliers, the mean (average) would be an appropriate measure of the center.

- For Bakery B, because the distribution is not symmetric and there is a significant outlier, the median (middle value) would be a more robust measure of the center.

So, the correct answer is:

C) Mean for Bakery B because the data is symmetric; median for Bakery A because the data is not symmetric.

Complete Question:

The number of bagels sold daily for two bakeries is shown in the table:

Bakery A 45 52 51 48 61 34 55 46

Bakery B 48 42 25 45 57 10 43 46

Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Explain.

A) Mean for both bakeries because the data is symmetric

B) Median because the distribution is not symmetric for both bakeries

C) Mean for Bakery B because the data is symmetric; median for Bakery A because the data is not symmetric

D) Mean for Bakery A because the data is symmetric; median for Bakery B because the data is not symmetric

The correct answer is B): Median because the distribution is not symmetric for both bakeries.

Let's first calculate the mean and median for each bakery:

Bakery A:

Data: 45, 52, 51, 48, 61, 34, 55, 46

Mean (average):

[tex]\[ \text{Mean} = \frac{45 + 52 + 51 + 48 + 61 + 34 + 55 + 46}{8} = \frac{392}{8} = 49 \][/tex]

Median (middle value):

Arrange the data in ascending order: 34, 45, 46, 48, 51, 52, 55, 61

[tex]\[ \text{Median} = \frac{48 + 51}{2} = 49.5 \][/tex]

For Bakery A, the mean is 49 and the median is 49.5. The median (49.5) is slightly higher than the mean (49), indicating a slight right skew in the data.

Bakery B:

Data: 48, 42, 25, 45, 57, 10, 43, 46

Mean (average):

[tex]\[ \text{Mean} = \frac{48 + 42 + 25 + 45 + 57 + 10 + 43 + 46}{8} = \frac{316}{8} = 39.5 \][/tex]

Median (middle value):

Arrange the data in ascending order: 10, 25, 42, 43, 45, 46, 48, 57

[tex]\[ \text{Median} = \frac{43 + 45}{2} = 44 \][/tex]

For Bakery B, the mean is 39.5 and the median is 44. The mean (39.5) is lower than the median (44), indicating a left skew in the data.

Bakery A: The median (49.5) is slightly higher than the mean (49), suggesting a slight right skew. Given this slight skewness, the  median might be a better measure of central tendency for Bakery A.

Bakery B: The mean (39.5) is noticeably lower than the median (44), indicating a left skew. Therefore, the median would likely be a better measure of central tendency for Bakery B.

Based on this analysis, the correct answer is B): Median because the distribution is not symmetric for both bakeries.

Complete Question:

The number of bagels sold daily for two bakeries is shown in the table:

Bakery A 45 52 51 48 61 34 55 46

Bakery B 48 42 25 45 57 10 43 46

Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Explain.

A) Mean for both bakeries because the data is symmetric

B) Median because the distribution is not symmetric for both bakeries

C) Mean for Bakery B because the data is symmetric; median for Bakery A because the data is not symmetric

D) Mean for Bakery A because the data is symmetric; median for Bakery B because the data is not symmetric

-375/3 = -125

-125-2 =-127

-125+2 = -123

-123 + -125 + -127 = -375

Final answer:

To calculate school taxes for a household earning an annual income of $80,000 at a tax rate of 2.5%, multiply the income by the rate. The household would pay $2,000 in school taxes.

Explanation:

If a household earns an annual income of $80,000 and the school taxes are 2.5% of the income, the amount paid in school taxes can be calculated by multiplying the income by the tax rate. Here's the calculation:

Tax Amount = Income × Tax Rate

Tax Amount = $80,000 × 0.025

Tax Amount = $2,000

Therefore, a household that earns $80,000 per year would pay $2,000 in school taxes.

Step-by-step explanation:

The equation of a moving object in physics is given by :

[tex]s=at^2+v_ot+s_o[/tex]...........(1)

Where

s₀ is the starting position of an object

a is the acceleration of the object

v₀ is the initial velocity of the object

t is the time taken

We need to find the value of acceleration by rearranging equation (1). Subtract [tex](v_ot+s_o)[/tex] on both sides of equation (1) as :

[tex]s-v_ot-s_o=at^2[/tex]

Divide both sides of above equation by t² as :

[tex]a=\dfrac{s-v_ot-s_o}{t^2}[/tex]

So, the value of acceleration is [tex]\dfrac{s-v_ot-s_o}{t^2}[/tex]. Hence, this is the required solution.

The total surface area of the soup can would be equivalent to the sum of the surface area of the 2 covers plus the surface area of the side.

Surface area of the 2 covers = 2 π r^2

Surface area of the 2 covers = 2 π (2.5 cm)^2

Surface area of the 2 covers = 39.27 cm^2

Surface area of the side = 2 π r h

Surface area of the side = 2 π (2.5 cm) (9 cm)

Surface area of the side = 141.37 cm^2

Total surface area = 39.27 cm^2 + 141.37 cm^2

Total surface area = 180.64 cm^2

The number of fish caught in a fishing tournament is a discrete variable, as it can only take specific or separate values which are whole numbers, not fractions or decimals.

The number of fish caught during a fishing tournament would be considered a discrete variable in mathematics. This is because discrete variables are variables that can only take specific or separate values.

In this case, you can't catch half a fish or 2.3 fish in a tournament, you can only catch whole fish. This makes the number of fish caught a discrete variable because the count can only be in whole numbers. This is different from a continuous variable, such as the amount of time spent fishing or the weight of the fish caught, which could take on any value within a given range.

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