Without determining the derivative, use your understanding of calculus and rates of change to explain one observation that proves y = e^x and its derivative are equivalent.

Answer:

the answer is true

hope this gives you your answer!

:)

Answer:

True

Step-by-step explanation:

Both Jacob and Genesis have a constant of variation of 2 pages per minute

Jacob

90/45= 2

Genesis

120(2 hs.)/60= 2

Step-by-step explanation:

When the relationship between the regression line and the data points is weak, it indicates a lack of strong association and highlights the need for further investigation and consideration of alternative explanations to better understand the underlying dynamics of the variables being studied.

When the relationship is weak, it implies that the data points are scattered and do not follow a clear pattern or trend. The variability in the data is high, making it difficult to establish a strong linear relationship. This could be due to various reasons, such as the presence of outliers, measurement errors, or the existence of other unaccounted factors influencing the variables.

The weak relationship between the regression line and the data points suggests that the predictive power of the regression model is limited. The regression line may not effectively explain or predict the values of the dependent variable based on the independent variable(s). Consequently, relying solely on the regression analysis to make accurate predictions or draw conclusions may be unreliable.

It is important to interpret the results cautiously and consider alternative explanations or additional variables that might contribute to the observed variability in the data. Further exploration and analysis may be needed to identify other potential factors that influence the relationship between the variables and to determine whether a different model or approach is more appropriate.

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Answer:

22,566

Step-by-step explanation:

the answer can be determined by subtracting 90486 from 113052

113052 - 90486 = 22,566

Answer: m = 2/3

Step-by-step explanation: Use the slope formula to find the slope m.

: m = slope :

: slope of a line : m = rise/run = y2-y1/x2-x1 :

: (x1,y1) : coordinates of first point in the line :

: (x2,y2) : coordinates of second point in the line :

I hope this helps you out.

Answer:

Slope = 2 / 3

Step-by-step explanation:

Slope = (y2-y1) / (x2-x1)

y2 is the y coordinate of the second ordered pair and y1 is the y coordinate of the first ordered pair. x2 is the x coordinate of the second ordered pair and x1 is the x coordinate of the first ordered pair.

          =(8-2) / (5+4)

          = 6 / 9

Slope = 2 / 3

Answer:

1

Step-by-step explanation:

LOL

Answer:

1+1-1=1

Step-by-step explanation:

1+1=2

2-1=1

your answer is 1

By taking the quotients between the areas, we see that:

First we need to find the areas of the 3 shapes.

For the triangle, the area is:

T = 3*5/2 = 7.5

For the blue square, the area is:

S = 3*3 = 9

For the rectangle, the area is:

R = 10*6 = 60

Now, what is the probability that a random point lies on the triangle or in the square?

It is equal to the quotient between the areas of the two shapes and the total area of the rectangle, this is:

P= (7.5 + 9)/60 = 0.275

b) The area of the rectangle that is not the square is:

A = 60 - 9 = 51

Then the probability of not landing on the square is:

P' = 51/60 = 0.85

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Step-by-step explanation:

he sold the house for 180000, which is 24% more than the amount he paid.

180000 = x + 0.24x

Simplifying this equation, we get:

1.24x = 180000

x = 180000 / 1.24

x ≈ 145161.29

Chengbo paid approximately 145161.29 yuan for the house.

Answer: 2 pies

Step-by-step explanation: 18/6 = 2

Answer:

a. \(\mathbf{P(Y \leq 60) = 0.3333}\)

b. P(Y>50) = 0.8889

c. E(y) = 67.5 and  Standard deviation \(\sigma\) = 12.99

Step-by-step explanation:

From the information given :

an automobile body paint shop, has determined that the painting time of automobiles is uniformly distributed and that the required time ranges between 45 minutes to \(1\frac{1}{2}\)hours.

The objective is to determine  the probability that the painting time will be less than or equal to an hour?

since 60 minutes make an hour;

\(1\frac{1}{2}\)hours = 60 +30 minutes = 90 minutes

Let Y be the painting time of the automobile; then,

the probability that  the painting time will be less than or equal to an hour ca be  computed as :

\(P(Y \leq 60) = \int ^{60}_{45} f(y) dy \\ \\ \\ P(Y \leq 60) = \int ^{60}_{45} \dfrac{1}{45} dy \\ \\ \\ P(Y \leq 60) = \dfrac{1}{45} \begin {pmatrix} x\end {pmatrix}^{60}_{45} \\ \\ \\ P(Y \leq 60) = \dfrac{60-45}{45 } \\ \\ \\ P(Y \leq 60) = \dfrac{15}{45} \\ \\ \\ P(Y \leq 60) = \dfrac{1}{3} \\ \\ \\ P(Y \leq 60) = 0.3333\)

What is the probability that the painting time will be more than 50 minutes?

The probability that the painting will be more than 50 minutes is P(Y>50)

So;

\(P(Y>50) = \int \limits ^{90}_{50} f(y) dy\)

\(P(Y>50) = \int \limits ^{90}_{50} \dfrac {1}{45} dy\)

\(P(Y>50) = \dfrac{1}{45}[x]^{90}_{50}\)

\(P(Y>50) = (\dfrac{90-50}{45})\)

\(P(Y>50) = \dfrac{40}{45}\)

P(Y>50) = 0.8889

Determine the expected painting time and its standard deviation.

Let consider E to be the expected painting time

Then :

\(E(y) = \int \limits ^{90}_{45} y f(y) dy \\ \\ \\ E(y) = \int \limits ^{90}_{45} y \dfrac{1}{45} dy \\ \\ \\ E(y) = \dfrac{1}{45} [\dfrac{y^2}{2}]^{90}_{45} \\ \\ \\ E(y) = \dfrac{1}{45}[\dfrac{(90^2-45^2)}{2}] \\ \\ \\ E(y) = \dfrac{1}{45} (\dfrac{6075}{2}) \\ \\ \\ E(y) = \dfrac{1}{45} \times 3037.8 \\ \\ \\ \mathbf{E(y) = 67.5}\)

\(E(y^2) = \int \limits ^{90}_{45} y^2 f(y) dy \\ \\ \\ E(y^2) = \int \limits ^{90}_{45} y^2 \dfrac{1}{45} dy \\ \\ \\ E(y^2) = \dfrac{1}{45} [\dfrac{y^3}{3}]^{90}_{45} \\ \\ \\ E(y^2) = \dfrac{1}{45}[\dfrac{(90^3-45^3)}{3}] \\ \\ \\ E(y^2) = \dfrac{1}{45} (\dfrac{637875}{3}) \\ \\ \\ E(y^2) = \dfrac{1}{45} \times 2126.25 \\ \\ \\ \mathbf{E(y^2) = 4725}\)

To determine the standard deviation, we need to first know what is the value of our variance,

So:

Variance \(\sigma^2\) = E(x²) - [E(x)]²

Variance \(\sigma^2\) = 4725 - (67.5)²

Variance \(\sigma^2\) = 4725 - 4556.25

Variance \(\sigma^2\) = 168.75

Standard deviation \(\sigma\) = \(\sqrt{variance}\)

Standard deviation \(\sigma\) = \(\sqrt{168.75}\)

Standard deviation \(\sigma\) = 12.99

The number of possible ways to select two vehicles = 55

Let m represents the number of cars and n represents the number of trucks.

An auto dealer has 5 different cars and 6 different trucks.

This means that m = 5 and n = 6

so, the total number of vehicles (t) would be,

t = m + n

t = 5 + 6

t = 11

Let us assume that p represents the number of possible ways to select two vehicles.

We use the combination formula.

\(^{n}C_r=\frac{n!}{r!(n-r)!}\)

here, n = 11 and r = 2

Using combination formula,

p = \(^{11}C_2\)

p = \(\frac{11!}{2!\times (11-2)!}\)

p = 55

Therefore, the number of possible ways = 55

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Answer is 4 because

(-2)-(4)=2

Answer:  2.25

Step-by-step explanation:

3x - 4 = 5 - x

+x             +x

4x - 4 = 5

    +4     +4

     4x = 9

       x = 9/4

       x = 2.25

Answer:

Step-by-step explanation:

3x - 4 = 5 - x

4x = 5 + 4

4x = 9

x = 9 : 4

x = 2.25

--------------------------

check

3 *  2.25 - 4 = 5 - 2.25

6.75 - 4 = 2.75

2.75 = 2.75

the answer is good

9514 1404 393

Answer:

  195 ft

Step-by-step explanation:

The relationship between the horizontal distance, angle, and vertical height is given by ...

  Tan = Opposite/Adjacent

Referring to the attached diagram, we have ...

  tan(16°) = BT/MB

  tan(25°) = BK/MB

Solving for BT and BK, we can describe their difference as ...

  BT = MB·tan(16°)

  BK = MB·tan(25°)

  BK -BT = 35 = MB(tan(25°) -tan(16°))

Dividing by the coefficient of MB gives ...

  MB = 35/(tan(25°) -tan(16°)) = 35/0.179562

  MB = 195 . . . feet

Marcos is standing 195 feet from the base of the tree.

(a) To find the scalar projection of u onto v, we can use the formula:

Scalar Projection = |u| * cos(theta)

where |u| is the magnitude of vector u and theta is the angle between u and v. Since |u| = √(1^2 + 2^2 + 3^2) = √14 and the angle between u and v is 180 degrees (since they are opposite vectors), we have:

Scalar Projection = √14 * cos(180) = -√14

(b) To find the vector projection of u onto v, we can use the formula:

Vector Projection = (Scalar Projection) * (Unit Vector of v)

Since we already found the scalar projection as -√14 and the unit vector of v is v/|v| = (3, 2, 1)/√14, we have:

Vector Projection = -√14 * (3, 2, 1)/√14 = (-3, -2, -1)

(c) To find a unit vector perpendicular to u and v, we can take their cross product:

Cross Product = u x v

Cross Product = (1, 2, 3) x (3, 2, 1) = (-4, 8, -4)

To find the unit vector perpendicular, we divide the cross product by its magnitude:

Unit Vector = (-4, 8, -4)/√(16 + 64 + 16) = (-1/3, 2/3, -1/3)

(d) The area of the parallelogram spanned by u and v is equal to the magnitude of their cross product:

Area = |Cross Product|

Area = |(-4, 8, -4)| = √(16 + 64 + 16) = √96 = 4√6

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1. If you have collected data on all persons living in the apartment building, it is considered a census. A census is a complete collection of data from every individual or unit in a population.

2. If you have collected data only on people who were home during your visits to the building, it is considered a sample. A sample is a subset of the population from which data is collected. In this case, it would be a convenience sample, as you are only collecting data from those who happened to be present during your visits.

3. If you asked people to give their age and collected it as age categories (e.g., <5, 6-10, 11-15, etc.), this is an example of a categorical variable. Categorical variables are qualitative and represent characteristics or attributes that fall into distinct categories or groups.

4. If you asked people to give their ages in years, this is an example of a continuous variable. Continuous variables are quantitative and can take any numerical value within a certain range. Age in years can be measured on a continuous scale.

5. If you found that apartments with older water heaters had worse health outcomes, this would be considered observational evidence. It suggests a correlation between the age of water heaters and health outcomes, but it does not prove a causal relationship. Further research would be needed to establish causality.

6. If you observed that health was getting worse throughout your visits, this would also be considered observational evidence. It indicates a trend or pattern, but again, it does not prove causation. Other factors could be influencing the observed change in health.

7. If you found differences in health outcomes by age, this would be considered associative evidence. It suggests a relationship between age and health outcomes, but it does not imply causality. Other factors could be influencing the observed differences.

8. If you found that younger people in the building had worse outcomes and offered an intervention to help improve their health, the decision would be supported by associative evidence. The observed association between age and health outcomes suggests that targeting younger individuals with interventions may be beneficial. However, further research would be needed to confirm the effectiveness of the intervention.

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The firm's cash coverage ratio can be calculated using the formula:

Cash Coverage Ratio = (Operating Income + Depreciation) / Interest Expense.  Therefore, the firm's cash coverage ratio is approximately 6.93.

The cash coverage ratio is a financial metric used to assess a company's ability to cover its interest expenses with its operating income. It provides insight into the company's ability to generate enough cash flow to meet its interest obligations.

In this case, we first calculated the operating income by subtracting the cost of goods sold (COGS) and selling, general, and administrative expenses (SG&A) from the sales revenue. The resulting operating income was $143,106.

Since the question didn't provide information about the depreciation expenses, we assumed it to be zero. If depreciation expenses were given, we would have added them to the operating income.

The interest expense was given as $20,650, which we used to calculate the cash coverage ratio.

By dividing the operating income by the interest expense, we found the cash coverage ratio to be approximately 6.93. This means that the company's operating income is about 6.93 times higher than its interest expenses, indicating a favorable position in terms of covering its interest obligations.

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Answer:

78 degrees

Step-by-step explanation:

this is a situation where you have a right triangle and know the hypotenuse and adjacent side lengths, so you can use cos⁻¹

cos⁻¹(8.5/42) = 78.3 degrees

According to the question, the closing balance for quarter 2 is £82,750.

A quarter is one fourth of a year. It is typically a three month period, usually consisting of January, February, and March; April, May, and June; July, August, and September; or October, November, and December. The terms of a quarter can vary depending on the context. For example, in the United States, quarters are commonly referred to as “fiscal quarters,” and begin on the first day of October, January, April, and July. In this case, each quarter covers a three-month period.

Inflows for quarter 2: 540,000 x 1.075 = £581,000

Outflows for quarter 2: 495,000 x 1.05 = £519,250

Closing balance for quarter 2:

Opening balance + Inflows - Outflows =

20,000 + 581,000 - 519,250 = £82,750

Therefore, the closing balance for quarter 2 is £82,750.

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Answer:

8n-12p+24

Step-by-step explanation:

\(4 \times 2n = 8n\)

\(4 \times 3p = 12p\)

\(4 \times 6 = 24\)

put it together and you have 8n-12p+24

I hope this helps

Answer:

13 3/7

Step-by-step explanation:

94÷7=13 r3

13 and 3 over 7

Based on the chi-square test, there is no significant evidence to suggest that the die is not balanced.

We have,

To determine if the die is balanced, we can perform a chi-square test of goodness of fit.

The null hypothesis is that the die is balanced, and the alternative hypothesis is that the die is not balanced.

First, let's calculate the expected frequencies for each outcome assuming the die is balanced. Since there are 180 tosses in total, each outcome is expected to have an equal probability of 1/6.

Expected frequency for each outcome

= (Total tosses) x (Probability of each outcome)

Expected frequency for each outcome = (180) x (1/6)

Expected frequency for each outcome = 30

Now, we can calculate the chi-square test statistic using the formula:

χ² = Σ [(Observed frequency - Expected frequency)² / Expected frequency]

Let's calculate the chi-square test statistic:

χ² = [(28 - 30)² / 30] + [(36 - 30)² / 30] + [(36 - 30)² / 30] + [(30 - 30)² / 30] + [(27 - 30)² / 30] + [(23 - 30)² / 30]

χ² = [(-2)² / 30] + [(6)² / 30] + [(6)² / 30] + [(0)² / 30] + [(-3)² / 30] + [(7)² / 30]

χ² = 4/30 + 36/30 + 36/30 + 0/30 + 9/30 + 49/30

χ² = 134/30

χ² ≈ 4.467

Next, we need to compare the calculated chi-square value to the critical chi-square value at a significance level of 0.01 and degrees of freedom equal to the number of outcomes minus 1 (6 - 1 = 5).

Looking up the critical chi-square value in a chi-square distribution table with 5 degrees of freedom and a significance level of 0.01, we find it to be approximately 15.086.

Since the calculated chi-square value (4.467) is less than the critical chi-square value (15.086), we fail to reject the null hypothesis.

Therefore, we do not have sufficient evidence to conclude that the die is not balanced at a 0.01 level of significance.

Thus,

Based on the chi-square test, there is no significant evidence to suggest that the die is not balanced.

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The 64 fluid ounces of water, as suggested by Kamryn's doctor to drink everyday, will be equal to 1920 millilitres.

Writing the equation as per the relation between millilitres and fluid ounces -

1 fluid ounce = 30 millilitres

Now, we will perform multiplication to find the number of milliliters in 64 fluid ounces. Writing the expression representing relation between millilitres and fluid ounces

Number of milliliters = 30×64

Performing multiplication between the numbers 30 and 64

Number of milliliters = 1920

Therefore, on drinking 64 fluid ounces by Kamryn on her doctor's recommendation will drink 1920 millilitres of water everyday.

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Answer:

9 miles

Step-by-step explanation:

The answer is 9 miles because if you divide 0.6 mile by 4 minutes, you will have an answer of 9 miles an hour, as 0.6x15=9. In a full hour, Mike would walk 9 miles.

Step-by-step explanation:

Probability that Dan chooses a Green card = 0.2

Probability that Esther chooses a Green card = 0.2 (same set of cards = same probability)

Since they are independent events,

total probability = 0.2 * 0.2 = 0.04.

Answer:

I think b

bye have a great day

Answer:

They are the same

Step-by-step explanation:

LA cyl =

\(2\pi \: rh\)

SA sphere =

\(4\pi {r}^{2} \)

If the sphere is inscribed in the cylinder, they have the same radius. The height of the cylinder is the diameter (Or 2× radius) of the sphere.

If you substitute 2r for h, then both formulas are

\( 4\pi{r}^{2} \)

The volume of the right rectangular prism is the amount of cubes in it

The formula to determine the volume of the right rectangular prism is V(n) = n

The question is incomplete; as the figure is not given.

So, I will provide a general solution

The volume of a one inch cube is:

\(V = 1^3\)

\(V = 1\)

Assume the number of one inch cubes used to fill the right rectangular prism is n.

Then the volume of the right rectangular prism would be:

\(V(n) = n * 1\)

This gives

\(V(n) = n\)

Hence, the general formula to determine the volume of the right rectangular prism is V(n) = n

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Answer:

45

Step-by-step explanation:

Given that :

Voucher awarded (x) :

Repair = $50

Lose or destroy = $200

P(x):

Replacement voucher = 5%

Repair voucher = 10%

X ______ 50 ______ 200

P(x) ____ 0.1 _______ 0.05

Expected variance Var(X) :

ΣX²p(x) - E(x) ;

E(x) = Σx*p(x) = (50*0.1) + (200*0.05) = 15

ΣX²p(x) = Σ[(50^2 * 0. 1) + (200^2 * 0.05)] = 250 + 2000 = 2250

Var(X) = 2250 - 15^2 = 2025

Standard deviation = √Var(x)

Standard deviation = √2025

Standard deviation = $45