Eight times the difference of 2 and a number.

The function f(x) is given by (x + 5)² , and the derivative f'(a) is evaluated at a = -5.

To find f(x) and a, we need to simplify the given limit expression and identify the function and the value at which the derivative is taken.

Expanding the expression (5 + h)²  - 25h, we get:

(25 + 10h + h² ) - 25h

25 + 10h + h²  - 25h

h²  - 15h + 25

Now, we can recognize this expression as the square of the binomial (h - 5)² .

Therefore, f(x) = (x + 5)v, where x represents the variable in the function.

To determine a, we consider the limit expression again, which tends to zero as h approaches 0. This indicates that the derivative is evaluated at a point where the function is defined. Since the expression (x + 5)²  represents the square of a binomial, it is symmetric around x = -5. Hence, a = -5.

In summary, the function f(x) is given by (x + 5)² , and the derivative f'(a) is evaluated at a = -5.

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Hank can feed his dog for 40 days with one bag of dog food.

A fraction represents a part of a whole or a ratio between two quantities. It is a mathematical expression that consists of a numerator and a denominator separated by a horizontal line, also called a fraction bar or a vinculum.  

To solve the problem, we need to find how many scoops of dog food are in the bag and divide that by the number of scoops used per day:

Number of scoops in bag = 5 cups ÷ 1/8 cup/scoop = 40 scoops

Number of days he can feed his dog = 40 scoops ÷ 1 scoop/day = 40 days

Therefore, Hank can feed his dog for 40 days with one bag of dog food.

Statement: Hank can feed his dog for 40 days with one bag of dog food.

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\(\huge\text{Hey there!}\)

\(\huge\textbf{Equation:}\)

\(\mathbf{1 \dfrac{1}{5} \times \dfrac{x}{3} = \dfrac{9}{10}}\)

\(\huge\textbf{Solve:}\)

\(\mathbf{1 \dfrac{1}{5} \times \dfrac{x}{3} = \dfrac{9}{10}}\)

\(\mathbf{\rightarrow \dfrac{1\times5+1}{5} \times \dfrac{x}{3} = \dfrac{9}{10}}\)

\(\mathbf{\rightarrow \dfrac{5 + 1}{5} \times \dfrac{x}{3} = \dfrac{9}{10}}\)

\(\mathbf{\rightarrow \dfrac{6}{5} \times \dfrac{x}{3} = \dfrac{9}{10}}\)

\(\huge\textbf{Simplify it:}\)

\(\mathbf{\rightarrow \dfrac{2}{5}x = \dfrac{9}{10}}\)

\(\huge\textbf{Multiply \boxed{\bf \dfrac{5}{2}} to both sides:}\)

\(\mathbf{\rightarrow \dfrac{5}{2}\times \dfrac{2}{5}x = \dfrac{5}{2}\times \dfrac{9}{10}}\)

\(\huge\textbf{Simplify it:}\)

\(\mathbf{\rightarrow x = \dfrac{5}{2}\times \dfrac{9}{10}}\)

\(\mathbf{\rightarrow x = \dfrac{5\times9}{2\times10}}\)

\(\mathbf{\rightarrow x = \dfrac{45}{20}}\)

\(\mathbf{\rightarrow x = \dfrac{45\div5}{20\div5}}\)

\(\mathbf{\rightarrow x = \dfrac{9}{4}}\)

\(\mathbf{x \approx 2 \dfrac{1}{4}}\)

\(\huge\textbf{Therefore, your answer should be:}\)

\(\huge\boxed{\mathsf{x = }\frak{2 \dfrac{1}{4}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

Question :

Solution :

>> (5 × 1 + 1 / 5) × (x / 3) = 9 / 10

>> (5 + 1 / 5) × (x / 3) = 9 / 10

>> (6 / 5) × (x / 3) = 9 / 10

>> 6 × x / 5 × 3 = 9 / 10

>> 6x / 15 = 9 / 10

>> 2x / 5 = 9 / 10

>> 2x × 10 = 5 × 9

>> 20x = 45

>> x = 45 / 20

>> x = 9 / 4

Therefore,

Answer: the plant has grown 8x inches

Step-by-step explanation:

The plant has grown 8 times more than it's height last week so,

8 x \(x\) = 8x

Answer:

8x

Step-by-step explanation:

Plant inches: x

Amount it has grown: 8 times x (original height)

8 times x

simplify as

8x

Each x-value is paired with its corresponding y-value, which is calculated by multiplying the x-value by 8 and adding 2. For example, when x = 1, y= 8(1) + 2 = 10.

Compound interest is a method of calculating interest where the interest earned on an investment is added to the principal amount, and the interest on the new total is calculated for the next period. This process continues over time, resulting in the gradual growth of the investment.

Given by the question.

There is only one table that can represent the function y = 8x + 2, which is as follows:

x      y

0     2

1    10

2    18

3    26

4    34

5    42

6    50

7    58

8    66

9    74

10    82

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Given :

Three trolley tours leave from the same stop at 9:00 am.

Tour A returns to the stop every 75 minutes, Tour B returns every 60 minutes, and Tour C returns every 40 minutes.

To Find :

In how many hours will all three tours return to the stop at the same time.

Solution :

We know, they will return to the stop at the same time is the L.C.M of three i.e 75, 60 and 40 minutes.

So, their L.C.M is :

L.C.M = 600 minutes.

Now, 600 minutes = 600÷60 hours = 10 hours.

Therefore, they will all meet at stop in 10 hours.

Hence, this is the required solution.

Answer:

Step-by-step explanation:

150 90x 100/60

By using Chebyshev's Inequality with K=3, we can determine that at least 88.89% of the days had temperatures between "F and "F, where "F represents the mean temperature of 76.4°F.

Chebyshev's Inequality provides a lower bound on the proportion of data that falls within a certain number of standard deviations from the mean. In this case, K=3 means that we are considering a range of three standard deviations from the mean.

The inequality states that for any dataset, the proportion of data falling within K standard deviations of the mean is at least 1 - (1/K^2). So, for K=3, we have 1 - (1/3^2) = 1 - (1/9) = 8/9 ≈ 0.8889. Therefore, at least 88.89% of the data falls within three standard deviations of the mean.

In the context of the temperature data, we can conclude that at least 88.89% of the days had temperatures between the mean temperature of 76.4°F minus three standard deviations (76.4 - 3 * 7.3) and the mean temperature plus three standard deviations (76.4 + 3 * 7.3). This range represents a relatively high proportion of the dataset, indicating that the temperature observations are fairly concentrated around the mean with limited extreme values.

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The inequality represents a number no more than 5 is n < 5.

What is inequality?

In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.

We have to find which inequality represents a number no more than 5.

Consider, the first inequality n ≤ 5.

This inequality contain 5 and less numbers.

Consider the second inequality n ≥ 25

This inequality contain numbers 5 and more

For n > 5  

This inequality contain numbers more than 5.

For n < 5

This inequality does not contain number more than 5.

Hence, the inequality represents a number no more than 5 is n < 5.

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The null hypothesis is formulated as a statement of equality to represent the assumption of no effect, no difference, or no relationship between variables in hypothesis testing.

The null hypothesis is typically formulated as a statement of equality because it represents the assumption or claim of no effect, no difference, or no relationship between variables in the context of statistical hypothesis testing.

When conducting hypothesis tests, we start with the assumption that there is no significant difference or relationship between variables, and any observed differences or relationships are merely due to random chance or sampling variability. The null hypothesis serves as a benchmark or reference point against which we compare the observed data.

Formulating the null hypothesis as a statement of equality allows for a clear and specific claim to be tested statistically. It sets the baseline or default position that is assumed to be true unless there is sufficient evidence to reject it in favor of an alternative hypothesis.

For example, in a study comparing the mean scores of two groups, the null hypothesis might state that the population means are equal (μ1 = μ2). This implies that any observed difference in sample means is due to chance, rather than a true difference in the population means.

By specifying the null hypothesis as a statement of equality, statistical tests provide a framework to assess the likelihood of observing the obtained data under the assumption of no effect or no difference, allowing us to make inference and draw conclusions about the population parameters based on the evidence from the sample.

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Answer:

6

Step-by-step explanation:

(4) The series diverges by the Comparison Test. Each term is greater than that of a divergent geometric series.

To determine whether the series converges or diverges, we can use the Comparison Test.
First, we can simplify the series by dividing both the numerator and denominator by n:
[Infinity] (4 + 1/n) / (3 - 5/n)

As n approaches infinity, both the numerator and denominator approach 4/3, so we can write:
[Infinity] (4 + 1/n) / (3 - 5/n) = [Infinity] 4/3

Since the harmonic series [Infinity] 1/n diverges, we can conclude that the original series diverges as well.
Therefore, the correct answer is:
4. The series diverges by the Comparison Test. Each term is greater than that of a divergent geometric series.

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Yes, we can conclude that there is a positive correlation between the success of college students (measured by cumulative grade point average) and the income of their respective families.

For testing whether there is a significant correlation between two variables, we need to calculate the correlation coefficient r.

Given that the sample size (n) is 20, and the correlation coefficient (r) is 0.40. The test statistic value, t can be calculated using the formula:

(\(t = (r * \sqrt{n - 2} /\sqrt{1 - r^2} )\))

Therefore, substituting the values,

(\(t = (0.40 *\sqrt{20 - 2} / \sqrt{1 - 0.4^2} )\))

= 2.53

Using the t-table with 18 degrees of freedom (df = n - 2 = 20 - 2 = 18) at a significance level of 0.01, we find that the critical value of t is 2.878.

Since the calculated value of t is less than the critical value of t, we fail to reject the null hypothesis.

Therefore, we can conclude that there is a positive correlation between the success of college students (measured by cumulative grade point average) and the income of their respective families.

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Answer:

4.75

graph picture is attached.

press or click on the picture to see the whole graph

Step-by-step explanation:

put 1 where x is

y = 4 + (0.75*1)

y = 4 + .75

y = 4.75

number next to x is the SLOPE

The value of the yakubu and bello business is N80,000.

Let's start by determining the original value of Yakubu and Bello's shares in the business before the sale took place.

The ratio of their shares is given as 3:5, which means Yakubu owns 3 parts and Bello owns 5 parts out of a total of 3+5 = 8 parts.

Now, let's assume the value of the business is represented by "V" (to be determined).

Since Yakubu later sold 3/4 of his share to Bello, this means he sold 3/4 * 3 = 9/4 parts of the business to Bello.

The value of 9/4 parts of the business is N180,000, so we can set up the following equation:

(9/4) * V = N180,000

To solve for V, we multiply both sides of the equation by 4/9:

V = (4/9) * N180,000

V = N80,000

Therefore, the value of the business is N80,000.

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To graphically solve the system of equations, we can represent the number of small boxes sent as x and the number of large boxes sent as y.

The system of equations is:

Equation 1: x + y = 9

Equation 2: 20x + 30y = 240

To solve graphically, we plot the lines representing these equations on a graph and find the point where they intersect. The x-coordinate of the intersection point represents the number of small boxes sent (x), and the y-coordinate represents the number of large boxes sent (y).

After graphing the lines, we find that the intersection point is (4, 5).

Therefore, the number of small boxes sent is 4, and the number of large boxes sent is 5.

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Answer:

Step-by-step explanation:

You had the first part of the first question correct. The answer is 100:64

The sides of the squares

Area of e = 69% more than area of area of f

e^2: f^2 = ( 1 + 69/100 ) / 1

e^2 : f^2 = (1.69)/1            Take the square root of both sides

e:f  = 1.3:1

The probability that the insurance representative will sell a policy to three out of four prospective clients is 0.0256.

The probability that the insurance representative sells to more than two prospective clients is 0.0272.

To calculate the probability that the insurance representative will sell a policy to a specific number of prospective clients out of four, we can use the binomial probability formula.

The binomial probability formula is given by:

P(X = k) = \((n C k) * p^k * (1 - p)^(n - k)\)

Where:

P(X = k) is the probability of exactly k successes (selling a policy) out of n trials (appointments).

(n C k) represents the combination or "n choose k" which calculates the number of ways to choose k successes out of n trials.

p is the probability of success on a single trial (probability of making a sale).

(1 - p) is the probability of failure on a single trial (probability of not making a sale).

Using this formula, we can calculate the probability of selling a policy to three out of four prospective clients.

Probability of selling a policy to three clients:

P(X = 3) = (4 C 3) * (0.20)^3 * (1 - 0.20)^(4 - 3)

Calculating:

P(X = 3) = 4 * 0.008 * 0.80

P(X = 3) = 0.0256

To calculate the probability that she sells to more than two clients, we need to sum the probabilities of selling to three clients and selling to all four clients.

Probability of selling to more than two clients:

P(X > 2) = P(X = 3) + P(X = 4)

Substituting the values:

P(X > 2) = \(0.0256 + (4 C 4) * (0.20)^4 * (1 - 0.20)^(4 - 4)\)

Calculating:

P(X > 2) = 0.0256 + 1 × 0.0016 × 1

P(X > 2) = 0.0272

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Answer:

We consider:

T1 = 2s

T2 = 3s

T3 = 5s

We calculate the least common multiple of the Ts:

Ttot = 30 s.

During a seven minute dance the lights will come on at the same time:

7*60 s / 30 = 14 times.

In a span of 7 minutes, the lights will blink together 14 times.

LCM of two or more than two given numbers is the smallest common multiple that is divisible by two or more than two given numbers.

Given, Joe was in charge of lights for a dance.

The red light blinks every two seconds, the yellow light every three seconds, and the blue light every five seconds.

∴ LCM of 2, 3, and 5 is 30 so the lights blink together after every 30 seconds.

So, in 7 minutes or (7×60) = 420 seconds the lights will blink together

(420/30) = (42/3) = 14 times.

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The probability that x is less than 5 = 0.45

Discrete probability distribution:

It is a type of probability distribution that displays all the possible values of a discrete random variable accompanying the affiliated probabilities. We can also say that a discrete probability distribution provides the chance of occurrence of every possible value of a discrete random variable.

Discrete probability distribution:

x          = -10      0       10        20

P(X=x) = 0.35  0.10   0.15     0.40

The probability that x is less than 5:

P(X<5) = 1 - P (X = 10) - P(X= 20)

1 - 0.15 - 0.40 = 0.45

The probability that x is less than 5 is = 0.45

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Answer:

first option

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

\(\frac{f(b)-f(a)}{b-a} \)

Here [ a, b ] = [ 1, 5 ]

f(b) = f(5) = 17 - 5² = 17 - 25 = - 8

f(a) = f(1) = 17 - 1² = 17 - 1 = 16 , then

average rate of change = \(\frac{-8-16}{5-1} \) = \(\frac{-24}{4} \) = - 6

Answer:

answer is -6

Step-by-step explanation:

Here,

Let [1,5] be[a,b]

f(x)=17-x²

f(a)=17-a²=17-1²=17-1 = 16

f(b) = 17-b² = 17-5² = 17-25 = -8

now, using formula,

{f(b)-f(a)}/(b-a)

(-8-16)/(5-1)

-24/4

=-6

Step-by-step explanation:

6×(2.5)+1.5

15+1.5

16.5

or

f(x)= 6x+1.5

f(2.5)= 6(2.5)+15

f(2.5)=16.5

You're welcome please add me as ur friend and brainiest please

The kind of sample that is described in the scenario is a lottery sample.

The lottery sample is the kind of sample that is described in the scenario in which 500 people attend a charity event, and each of them buys a raffle ticket.

The ticket stubs are placed in a drum and mixed thoroughly, and out of them, a few are drawn.

People whose tickets are drawn are declared winners of a prize. It is a type of probability sampling that depends on the element of chance.

In this type of sample, the probability of selecting an element is unknown and cannot be measured. I

t is a random process in which the probability of winning or being selected for the sample is entirely based on chance.

Hence, the lottery sampling technique is the appropriate one in the scenario.

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1. AABBCCDD: The probability of this happening is \(1/16\), since each parent would need to contribute a dominant allele for each gene.

2. AABBCcDD:  This genotype can be produced in two ways:

a) If both parents are homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D.

The probability of this happening is  = 1/128.

b) If one parent is homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A and B, homozygous dominant for C, and heterozygous for D.

3. The probability of this happening is 1/32.

AaBbCcDd : The probability of this happening is  1/256.

4. aaBBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D. The probability of this happening is  1/128.

b) If one parent is homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A, homozygous dominant for B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is  1/32.

To solve this problem, we need to use the principles of probability and Punnett squares.

For a tetrahybrid cross, we need to consider the four genes independently and combine the probabilities of each gene's alleles.

Assuming that A, B, C, and D are dominant alleles, and a, b, c, and d are recessive alleles, we can create a Punnett square for each gene, which would look like this:

A  |  A  |  a  |  a  

---|-----|-----|----

B  |  B  |  b  |  b  

---|-----|-----|----

C  |  C  |  c  |  c  

---|-----|-----|----

D  |  D  |  d  |  d  

Each box in the Punnett square represents a possible combination of alleles from the two parents.

For example, the top-left box represents offspring that inherit an A allele from the mother and an A allele from the father.

We can use these Punnett squares to calculate the probabilities of each genotype in the F2 offspring.

AABBCCDD - This genotype can only be produced if both parents are homozygous dominant for all four genes.

The probability of this happening is \((1/2)^4 = 1/16\) , since each parent would need to contribute a dominant allele for each gene.

AABBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D.

The probability of this happening is\((1/2)^4 * 1/2 * (1/2)^3 = 1/128\)

b) If one parent is homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A and B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is\(2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32\)

AaBbCcDd - This genotype can be produced in 16 ways, since each gene can be inherited in two different ways (dominant or recessive).

The probability of this happening is \((1/2)^8 = 1/256.\)

aaBBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D. The probability of this happening is\((1/2)^4 * 1/2 * (1/2)^3 = 1/128.\)

b) If one parent is homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A, homozygous dominant for B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is \(2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32.\)

Note that we have assumed independent assortment of the four genes, which means that the inheritance of one gene does not affect the inheritance of another gene.

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Using the power rule for differentiation, the first derivative of

\(f(x) = -x^{\frac12}\)

is

\(f'(x) = -\dfrac12 \cdot x^{\frac12-1} = -\dfrac12 x^{-\frac12}\)

and the second derivative is

\(f''(x) = -\dfrac12 \cdot \left(-\dfrac12 \cdot x^{-\frac12 - 1}\right) = \dfrac14 x^{-\frac32}\)

which makes E the correct choice.

Answer The answer will be 0.125

Step-by-step explanation:

To achieve a 99% confidence level with a margin of error of 0.75 points, the professor would need a sample size of approximately 112 scores, assuming a normal distribution for the exam scores and a population standard deviation of four points.

In order to determine the sample size needed, we can use the formula for the margin of error in a confidence interval:

Margin of Error = \(Z * (Standard\ Deviation /\sqrt{Sample\ size} )\)

Since the population standard deviation is known (4 points) and the desired margin of error is 0.75 points, we can rearrange the formula to solve for the sample size:

Sample Size = \((Z^2 * Standard\ Deviation^2) / Margin\ of\ Error^2\)

The Z-value for a 99% confidence level is approximately 2.576 (obtained from a standard normal distribution table). Plugging in the values, we have:

Sample Size = \((2.576^2 * 4^2) / 0.75^2\)
Sample Size = 112

Therefore, the professor would need a sample size of approximately 112 scores in order to achieve a 99% confidence level with a margin of error of 0.75 points.

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