Raul is y years old. Kayla is 6 years older than raul and isaac is 4 years younger than raul what is kayla's age?

Answer:

(x+5)² + (y-2)² =58

Step-by-step explanation:

"Your answer needs to be at least 20 characters long"

The equation of circle C will be;

⇒ (x + 5)² + (y - 2)² = 7.61²

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The points j(-8,9) and k(-2,-5) are endpoints of a diameter of circle C.

Now,

Since, The points j(-8,9) and k(-2,-5) are endpoints of a diameter of circle C.

Hence, The diameter of circle = √(- 2 - (-8))² + (- 5 - 9)²

                                               = √ 6² + 14²

                                               = √36 + 196

                                               = √232

                                               = 15.23

Thus, The radius of circle = 15.23 / 2

                                        = 7.61

And, The center of the circle = (- 8 + (-2)) / 2 , (9 + (-5))/2

                                             = (- 5, 2)

So, The equation circle C is,

⇒ (x - (-5))² + (y - 2)² = 7.61²

⇒ (x + 5)² + (y - 2)² = 7.61²

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Answer:

the box can hold a volume of 1024 inches ^3

Step-by-step explanation:

The volume of the given box is 1024 in.3.

Suppose the base of the pyramid has length = l units, and width = w units.

Suppose that the height of the pyramid is of h units, then:

[tex]v = \dfrac{l \times w \times h}{3} \: \rm unit^3[/tex]

is the volume of that pyramid.

The base is a rectangle with length = L units, and width = W units, so its area is:

[tex]b = l \times w\: \rm unit^2[/tex]

We are given that;

Dimension= 16*8*8 inches

Now,

To find the area of the base, we need to use the formula:

B=lw

where l is the length and w is the width. Substituting the given values, we get:

B=16×8

B=128

So, the area of the base of the box is 128 in.2.

To find the volume of the box, we substitute the values of B and h into the formula:

V=Bh

V=128×8

V=1024

Therefore, by the given prism the answer will be 1024 in.3.

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Answer:

The area of the car tire = 254.57 in²

el área de la goma en pulgadas cuadradas = 254.57 in²

Step-by-step explanation:

English Translation

A car tire has a diameter of 18 inches which is the area of ​​the tire in square inches?

A car tire is circular in nature, the area of a circle (car tire) is given as

A = πr²

where

π = pi (a constant) = (22/7)

r = radius of the circle = (diameter/2) = (18/2) = 9 inches

Area of the car tire = π×9² = 254.57 in²

Hence, the area of the car tire = 254.57 in²

Hope this Helps!!!

Answer:

-6 ÷ -2 and  (-1)(-3)

Step-by-step explanation:

To find which expressions have a value of 3, set each expression equal to 3 and solve for the variable. The expressions that have a value of 3 when the variable is substituted are the ones that apply.

To find which expressions have a value of 3, we can set each expression equal to 3 and solve for the variable. The expressions that have a value of 3 when the variable is substituted are the ones that apply. Let's go through each expression:

So, the only expression that has a value of 3 is 2x - 1 = 3 when x = 2.

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Answer:

i hope that helps......

For the given equation, the value of [tex]x[/tex] is [tex]2[/tex].

[tex]8^{\frac{1}{6}} \times 2^{x} = 32^{\frac{1}{2}}[/tex]

[tex](2^{3})^{\frac{1}{6}} \times 2^{x} = (2^{5})^{\frac{1}{2}}[/tex]

[tex]2^{\frac{1}{2}} \times 2^{x} = 2^{\frac{5}{2}}[/tex]

[tex]2^{\frac{1}{2}+x}=2^{\frac{5}{2}}[/tex]

Since, the bases are equal, we can compare the powers.

[tex]\frac{1}{2}+x=\frac{5}{2}[/tex]

[tex]x=\frac{5}{2}-\frac{1}{2}[/tex]

[tex]x=\frac{5-1}{2}[/tex]

[tex]x=\frac{4}{2}[/tex]

[tex]x=2[/tex]

So, the value of [tex]x[/tex] is [tex]2[/tex].

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Answer:

can you please post the pyramid

Step-by-step explanation:

The statements that are true concerning the rectangular pyramids include the following:

What are the properties of a rectangular pyramid?

The properties of a rectangular pyramid include the following:

From the given rectangular pyramid, The area of the base is 24 cm² because, 6*4= 24cm²

There are four lateral faces which are triangular in shape.

Answer:

Explanation:

Answer:

Explanation:

Answer:

99% confidence interval for [tex]\mu = 73220 \pm 565.4[/tex]

Step-by-step explanation:

Sample mean = [tex]\bar{x} =73220[/tex]

Standard deviation = s = 4400

Z at 99%  confidence level = 2.57

Sample = n = 400

Formula of confidence interval :[tex]\bar{x} \pm Z \times \frac{s}{\sqrt{n}}[/tex]

Substitute the values in the formula :

So,99% confidence interval for [tex]\mu = 73220 \pm 2.57 (\frac{4400}{\sqrt{400}})[/tex]

99% confidence interval for [tex]\mu = 73220 \pm 565.4[/tex]

Answer:

1/3

Step-by-step explanation:

Let the probability of selecting all coloured chips in the bag be 1.

If the probability of randomly selecting a red chip from the bag is 1/8 and the probability of selecting a blue chip from the bag is 13/24, then the probability of selecting both will be 1/8+13/24

1/8+13/24

= (3+13)/24

= 16/24

= 2/3

If the probability of selecting both ted and blue chip is 2/3, then the probability that there are other colors in the bag too will be expressed as 1-2/3 which is equivalent to 1/3

Final answer:

To find the probability of picking a chip that is neither red nor blue from the bag, we subtract the probabilities of picking a red or blue chip from 1. The calculation shows that the probability of selecting a different color chip is 1/3.

Explanation:

The student's question pertains to the calculation of probabilities when selecting poker chips of different colors from a bag. We are given that the probability of selecting a red chip is 1/8, and the probability of selecting a blue chip is 13/24. The aim here is to find the probability of selecting a chip of a different color. Since probabilities sum up to 1 for all possible outcomes, we would subtract the given probabilities from 1 to find the probability of selecting a chip that's neither red nor blue.

The total probability for all colors in the bag is always 1 (or 100%), which can be mathematically expressed as:

P(red) + P(blue) + P(other colors) = 1

Given P(red) = 1/8 and P(blue) = 13/24, we can substitute to find P(other colors):

P(other colors) = 1 - (P(red) + P(blue))

P(other colors) = 1 - (1/8 + 13/24)

First, we need to find a common denominator to combine the fractions:

P(other colors) = 1 - (3/24 + 13/24)

P(other colors) = 1 - 16/24

P(other colors) = 1 - 2/3

P(other colors) = 1/3

Therefore, the probability of selecting a chip that is neither red nor blue is 1/3.

Answer:

System utilization = 0.7 or 70%

Step-by-step explanation:

Given arrival rate of customer = 15 customer/Hour

Servie rate = [tex] \dfrac{60}{2.8} customer/Hour [/tex]

Now, use the below formula to find the system utilization.

System utilization = [tex] \dfrac{\text{ Arrival rate of customer }}{\text{ Servie rate}}[/tex]

System utilization = [tex] \dfrac{15}{ \dfrac{60}{2.8}}[/tex]

System utilization = [tex] \dfrac{15}{ \dfrac{60}{2.8}}[/tex]

System utilization = 0.7 or 70%

Answer: 36 cubic inches

Step-by-step explanation:

The husband is correct; the probability of the first child being a girl is higher than the probability of the first two being girls.

Let's list the sample space of possible outcomes for the genders of three children:

1. BBB (all boys)

2. BBG (two boys, one girl)

3. BGB (one boy, one girl, one boy)

4. BGG (one boy, two girls)

5. GBB (one girl, two boys)

6. GBG (two girls, one boy)

7. GGB (two girls, one boy)

8. GGG (all girls)

Now, let's examine the probabilities the husband and wife are discussing:

1. Husband's claim: Probability of the first child being a girl is greater than the probability of the first two children being girls.

  Probability of the first child being a girl: [tex]\( \frac{4}{8} = \frac{1}{2} \)[/tex]

  Probability of the first two children being girls: [tex]\( \frac{2}{8} = \frac{1}{4} \)[/tex]

  The husband is correct.

2. Wife's claim: Probability of the first child being a girl is equal to the probability of the first two children being girls.

  Both probabilities are [tex]\( \frac{1}{2} \)[/tex].

  The wife is incorrect.

Therefore, the husband is correct in this scenario.

Answer:

1. less likely

2. more likely

Step-by-step explanation:

test took

Answer:

1. less likely

2. more likely

Step-by-step explanation:

Answer:

Move all the terms to the left and set equal to zero.

Then set each factor equal to zero.

Step-by-step explanation:

I hope this helps

The correct answer is that the expression [tex]\(a^2 + 2ab + b^2\)[/tex]  equals 44.

To solve the given mathematical expression [tex]\(a^2 + 2ab + b^2\),[/tex] we recognize that it is a perfect square trinomial. The perfect square trinomial can be factored into the square of a binomial:

[tex]\[ (a + b)^2 = a^2 + 2ab + b^2 \][/tex]

Given that this expression equals 44, we can set the factored form equal to 44:

[tex]\[ (a + b)^2 = 44 \][/tex]

To find the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex], we take the square root of both sides of the equation. Remembering that the square root of 44 is not a whole number, we can express it as the product of prime factors:

[tex]\[ \sqrt{44} = \sqrt{4 \cdot 11} = \sqrt{2^2 \cdot 11} = 2\sqrt{11} \][/tex]

 Therefore, we have:

[tex]\[ a + b = \pm 2\sqrt{11} \][/tex]

This equation tells us that the sum of [tex]\(a\)[/tex] and [tex]\(b\)[/tex] is either [tex]\(2\sqrt{11}\) or \(-2\sqrt{11}\).[/tex] Without additional information about [tex]\(a\)[/tex] and [tex]\(b\)[/tex], we cannot determine unique values for [tex]\(a\)[/tex] and [tex]\(b\)[/tex], but we know that their sum must equal one of these two values.

The expression [tex]\(a^2 + 2ab + b^2\)[/tex] is indeed equal to 44, and the relationship between [tex]\(a\)[/tex]  and [tex]\(b\)[/tex] is given by [tex]\(a + b = \pm 2\sqrt{11}\).[/tex]

Answer:

The larger the p value, the less evidence the data provide against the null hypothesis and in favour of the alternative hypothesis

Step-by-step explanation:

P Value is the probability of obtaining extreme observed results in a statistical hypothesis test, assuming that null hypothesis is correct.

High p value implies evidence in favour of null hypothesis, against alternate hypothesis.

Low p value implies evidence against null hypothesis, in favour of alternate hypothesis

The incorrect statement about hypothesis testing is that a smaller p-value indicates less evidence against the null hypothesis.

A small p-value actually provides strong evidence against the null hypothesis, prompting its rejection.

The p-value measures how unlikely the observed data is under the null hypothesis, but does not indicate the truth of the null hypothesis itself.

The statement in hypothesis testing that is not true is The smaller the p-value, the less evidence the data provides against the null hypothesis and in favor of the alternative hypothesis.

A small p-value indicates that the observed test statistic is very unlikely if the null hypothesis is true, which provides stronger evidence against the null hypothesis and in favor of the alternative hypothesis.

In fact, we generally use a significance level (commonly < 0.05) to determine if we should reject the null hypothesis. On the contrary, a larger p-value suggests less evidence against the null hypothesis, implying that we are less likely to reject it.

It's important to remember that the p-value is the probability of obtaining the observed data, or more extreme, given that the null hypothesis is true.

It does not, however, describe the probability that the null hypothesis itself is true, thus a small p-value means that the data is unlikely under the null hypothesis, leading to its potential rejection.

Answer: D-On a coordinate plane, a line with positive slope goes through points (0, negative 1) and (2, 0). plz mark me brainliest.

Step-by-step explanation:

Option D. is correct. On a coordinate plane, a line with positive slope goes through points (0, negative 1) and (2, 0).

Which graph represents a function with a rate of change of 0.5?

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is independent variable while Y is dependent variable.

since
given rate of change = 0.5
slope of curve = rate of change
slope = [tex]\frac{Y_2-Y_1}{X_2-X_1}[/tex]
we have (0,-1) and (2, 0)
slope = 0+1/2-0
= 1/5
=0.5
=rate of change

Thus, On a coordinate plane, a line with positive slope goes through points (0, negative 1) and (2, 0).

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Answer:

[tex]I'(t)=12I-0.004I^2, I_o=500[/tex]

Step-by-step explanation:

Population of the Community=3000

Let the number of infected=I

The number of uninfected=3000-I

The rate at which disease is spreading is proportional to the product of number of people infected and the number of people not yet infected.

[tex]\frac{dI}{dt}\propto I(3000-I) \\\frac{dI}{dt}=k I(3000-I)\\\frac{dI}{dt}=0.004 I(3000-I)\\$Let I_o$=Initial Number of Infected=500\\Therefore, the initial value problem is given as:\\I'(t)=12I-0.004I^2, I_o=500[/tex]

Answer:

Step-by-step explanation:

The null hypothesis is the statement or claim that is believed or assumed to be true. In this case, the null hypothesis is "They believe that 40% of first-time borrowers take out smaller loans than other borrowers". Since we are dealing with proportion, we will denote it with p. The null hypothesis would be

p = 0.4

The alternative hypothesis is what the researcher expects or predicts. It is the statement that is believed to be true if the null hypothesis is rejected. The alternative hypothesis is "They perform a hypothesis test to determine if the percentage is the same or different from 40%". It would be written as

p ≠ 0.4

Answer:

a

Step-by-step explanation:

good luck :)

Answer:

[tex]14.2-2.03\frac{6.4}{\sqrt{35}}=12.004[/tex]    

[tex]14.2+2.03\frac{6.4}{\sqrt{35}}=16.396[/tex]    

We are 95% confidence that the true mean for the delay time is between (12.004 and 16.396)

Step-by-step explanation:

Information given

[tex]\bar X=14.2[/tex] represent the sample mean for the delay time

[tex]\mu[/tex] population mean

s=6.4 represent the sample standard deviation

n=35 represent the sample size  

Confidence interval

The confidence interval for the true parameter of interest is given by:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The degrees of freedom, given by:

[tex]df=n-1=35-1=34[/tex]

The Confidence level is 0.95 or 95%,and the significance is [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical value for this case is [tex]t_{\alpha/2}=2.03[/tex]

And replacing we got:

[tex]14.2-2.03\frac{6.4}{\sqrt{35}}=12.004[/tex]    

[tex]14.2+2.03\frac{6.4}{\sqrt{35}}=16.396[/tex]    

We are 95% confidence that the true mean for the delay time is between (12.004 and 16.396)

The traveler is disputing the claim about the variance. The hypothesis test is a right-tailed test. The result of the test does not provide enough evidence to dispute the airline's claim.

109. The traveller is disputing the claim about the variance.

110. A sample standard deviation of 15 minutes is the same as a sample variance of 225 minutes.

112. H-o: The variance is 150 minutes or less.

113. d-f = 24

114. chi-square test statistic = 35.172

115. p-value = 0.082

116. Graph the situation:

117. Let a = 0.05

Decision: Fail to reject the null hypothesis

Conclusion: There is not enough evidence to dispute the airline's claim about the variance being 150 minutes or less.

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Answer:

[tex]t=\frac{70.5-68.7}{\sqrt{\frac{5.3^2}{360}+\frac{4.3^2}{329}}}}=4.913[/tex]  

Since we conduct a bilateral test we have the p value given by:

[tex]p_v =2*P(z>4.913)=8.97x10^{-7}[/tex]

Since the p value is very low compared to the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true means for girls and boys are different at 1% of significance

Step-by-step explanation:

Information given

[tex]\bar X_{boys}=70.5[/tex] represent the mean weigth for ten year boys

[tex]\bar X_{girls}=68.7[/tex] represent the mean weigth for ten year girls

[tex]s_{boys}=5.3[/tex] represent the sample deviation for 10 year boys

[tex]s_{girls}=4.3[/tex] represent the sample standard deviation for 10 year girls

[tex]n_{boys}=360[/tex] sample size for boys

[tex]n_{girls}=329[/tex] sample size for girls

t would represent the statistic

[tex]\alpha=0.01[/tex] significance level assumed

System of hypothesis to check

We need to conduct a hypothesis in order to check if the true means are different for boys and girls, the system of hypothesis would be:

Null hypothesis:[tex]\mu_{boys}=\mu_{girls}[/tex]

Alternative hypothesis:[tex]\mu_{boys} \neq \mu_{girls}[/tex]

The statistic for this case would be given by:

[tex]t=\frac{\bar X_{boys}-\bar X_{girls}}{\sqrt{\frac{s^2_{boys}}{n_{boys}}+\frac{s^2_{girls}}{n_{girsl}}}}[/tex] (1)

Replacing we got:

[tex]t=\frac{70.5-68.7}{\sqrt{\frac{5.3^2}{360}+\frac{4.3^2}{329}}}}=4.913[/tex]  

P value

We can assume that the degrees of freedom for this case are large enough to assume that the t distribution is approximately the normal distribution.

Since we conduct a bilateral test we have the p value given by:

[tex]p_v =2*P(z>4.913)=8.97x10^{-7}[/tex]

Since the p value is very low compared to the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true means for girls and boys are different at 1% of significance

Answer:

S1 = {∅, {t}, {u}, {v}, {t,u}, {t,v}, {u,v}, {t,u,v} }

Step-by-step explanation:

Given:

A = {t, u, v, w}

S1 = set of all subsets of A that do not contain w.

S2 = set of all subsets of A that contains w.

Therefore S1 & S2 in set roster notation will be given as:

S1 = {∅, {t}, {u}, {v}, {t,u}, {t,v}, {u,v}, {t,u,v} }

S2 = { {w}, {t,w}, {u,w}, {v,w}, {t,u,w}, {t,v,w}, {u,v,w}, {t,u,v,w} }

a) We can see that,

S1 = {∅, {t}, {u}, {v}, {t,u}, {t,v}, {u,v}, {t,u,v} }

The problem involves finding subsets of a given set. The set S1, which includes subsets of the original set A that do not contain the element 'w', includes eight such subsets.

The given set A contains the elements {t, u, v, w}. The set S1 consists of all the subsets of A that do not contain the element 'w'. Similarly, the set S2 consists of all the subsets of A that do contain the element 'w'.

To find S1, we can start by listing out each possible subset of A without the element 'w'. These include {}, {t}, {u}, {v}, {t, u}, {t, v}, {u, v}, and {t, u, v}. So, S1 = {{}, {t}, {u}, {v}, {t, u}, {t, v}, {u, v}, {t, u, v}}.

We ignore S2 as it's not relevant to the question asked.

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Answer:

It would take 15.3846 minutes to stock the shelf if the two clerks worked together

Step-by-step explanation:

The first grocery clerk can stock a shelf in 40 minutes, it means that he can do  1/40 shelf per minute. At the same way, the second clerk requires 25 minutes, it means that he can do 1/25 shelf per minute

Then, if they worked together, they can stock 13 shelfs in 200 minutes, and it is calculated as:

[tex]\frac{1}{40}+\frac{1}{25} = \frac{13}{200}[/tex]

Now, using the rule of three, we need to find the minutes required to stock 1 shelf if they work at a rate of 13 shelf in 200 minutes as:

13 shelfs --------------   200 minutes

1 shelf    ---------------    X minutes

Where X are the minutes required to stock 1 shelf.

So, solving for X, we have:

[tex]X=\frac{1*200}{13}=15.3846[/tex]

Finally, it would take 15.3846 minutes to stock the shelf if the two clerks worked together

Final answer:

The circumference of the outer circle is approximately 18.86 feet greater than the circumference of the inner circle, which has a circumference of 88 feet.

Explanation:

The circumference (C) of a circle is calculated using the formula C = 2πr, where π is Pi and r is the radius of the circle. Given that the circumference of the inner circle is 88 ft and the distance between the inner and outer circle is 3 ft, we deduce that the radius of the outer circle is 3 ft greater than the radius of the inner circle. Using the given approximation of π as 22/7, we can find the new circumference.

First, let's find the radius of the inner circle. Rearrange the formula to r = C / (2π) and substitute π with 22/7:

r = 88 / ((2 × 22)/7) = 88 / (44/7) = 88 / (6.2857) ≈ 14 ft

Now, the radius of the outer circle is r + 3 ft, which equals 17 ft. The circumference of the outer circle is then:

C = 2πr = 2 × 22/7 × 17 = 2 × 22 × 17 / 7 = 34 × 22 / 7 = 748 / 7 ≈ 106.86 ft

To find by how many feet the circumference of the outer circle is greater than the inner circle, subtract the circumference of the inner circle from that of the outer circle:

106.86 ft - 88 ft = 18.86 ft

Therefore, the circumference of the outer circle is approximately 18.86 ft greater than the circumference of the inner circle.

Answer:

  see below for a graph

  x = 4

Step-by-step explanation:

The perimeter is given by the formula ...

  P = 2(L +W)

The area is given by the formula ...

  A = LW

We want these two values to be equal. Using "y" for both perimeter and area, and substituting the given values for L and W, we have the equations ...

  y = 2(4 +x)

  y = 4x

The graph of these equations (below) shows the value of x is 4.

Answer:

Parasite

Step-by-step explanation:

It feeds off of other organisms by living on or in the animal.

Answer:

a) The function, f(x) is increasing at the intervals (x < -1.45) and (x > 3.45)

Written in interval form

(-∞, -1.45) and (3.45, ∞)

- The function, f(x) is decreasing at the interval (-1.45 < x < 3.45)

(-1.45, 3.45)

b) Local minimum value of f(x) = -78.1, occurring at x = 3.45

Local maximum value of f(x) = 10.1, occurring at x = -1.45

c) Inflection point = (x, y) = (1, -16)

Interval where the function is concave up

= (x > 1), written in interval form, (1, ∞)

Interval where the function is concave down

= (x < 1), written in interval form, (-∞, 1)

Step-by-step explanation:

f(x) = x³ - 6x² - 15x + 4

a) Find the interval on which f is increasing.

A function is said to be increasing in any interval where f'(x) > 0

f(x) = x³ - 6x² - 15x + 4

f'(x) = 3x² - 6x - 15

the function is increasing at the points where

f'(x) = 3x² - 6x - 15 > 0

x² - 2x - 5 > 0

(x - 3.45)(x + 1.45) > 0

we then do the inequality check to see which intervals where f'(x) is greater than 0

Function | x < -1.45 | -1.45 < x < 3.45 | x > 3.45

(x - 3.45) | negative | negative | positive

(x + 1.45) | negative | positive | positive

(x - 3.45)(x + 1.45) | +ve | -ve | +ve

So, the function (x - 3.45)(x + 1.45) is positive (+ve) at the intervals (x < -1.45) and (x > 3.45).

Hence, the function, f(x) is increasing at the intervals (x < -1.45) and (x > 3.45)

Find the interval on which f is decreasing.

At the interval where f(x) is decreasing, f'(x) < 0

from above,

f'(x) = 3x² - 6x - 15

the function is decreasing at the points where

f'(x) = 3x² - 6x - 15 < 0

x² - 2x - 5 < 0

(x - 3.45)(x + 1.45) < 0

With the similar inequality check for where f'(x) is less than 0

Function | x < -1.45 | -1.45 < x < 3.45 | x > 3.45

(x - 3.45) | negative | negative | positive

(x + 1.45) | negative | positive | positive

(x - 3.45)(x + 1.45) | +ve | -ve | +ve

Hence, the function, f(x) is decreasing at the intervals (-1.45 < x < 3.45)

b) Find the local minimum and maximum values of f.

For the local maximum and minimum points,

f'(x) = 0

but f"(x) < 0 for a local maximum

And f"(x) > 0 for a local minimum

From (a) above

f'(x) = 3x² - 6x - 15

f'(x) = 3x² - 6x - 15 = 0

(x - 3.45)(x + 1.45) = 0

x = 3.45 or x = -1.45

To now investigate the points that corresponds to a minimum and a maximum point, we need f"(x)

f"(x) = 6x - 6

At x = -1.45,

f"(x) = (6×-1.45) - 6 = -14.7 < 0

Hence, x = -1.45 corresponds to a maximum point

At x = 3.45

f"(x) = (6×3.45) - 6 = 14.7 > 0

Hence, x = 3.45 corresponds to a minimum point.

So, at minimum point, x = 3.45

f(x) = x³ - 6x² - 15x + 4

f(3.45) = 3.45³ - 6(3.45²) - 15(3.45) + 4

= -78.101375 = -78.1

At maximum point, x = -1.45

f(x) = x³ - 6x² - 15x + 4

f(-1.45) = (-1.45)³ - 6(-1.45)² - 15(-1.45) + 4

= 10.086375 = 10.1

c) Find the inflection point.

The inflection point is the point where the curve changes from concave up to concave down and vice versa.

This occurs at the point f"(x) = 0

f(x) = x³ - 6x² - 15x + 4

f'(x) = 3x² - 6x - 15

f"(x) = 6x - 6

At inflection point, f"(x) = 0

f"(x) = 6x - 6 = 0

6x = 6

x = 1

At this point where x = 1, f(x) will be

f(x) = x³ - 6x² - 15x + 4

f(1) = 1³ - 6(1²) - 15(1) + 4 = -16

Hence, the inflection point is at (x, y) = (1, -16)

- Find the interval on which f is concave up.

The curve is said to be concave up when on a given interval, the graph of the function always lies above its tangent lines on that interval. In other words, if you draw a tangent line at any given point, then the graph seems to curve upwards, away from the line.

At the interval where the curve is concave up, f"(x) > 0

f"(x) = 6x - 6 > 0

6x > 6

x > 1

- Find the interval on which f is concave down.

A curve/function is said to be concave down on an interval if, on that interval, the graph of the function always lies below its tangent lines on that interval. That is the graph seems to curve downwards, away from its tangent line at any given point.

At the interval where the curve is concave down, f"(x) < 0

f"(x) = 6x - 6 < 0

6x < 6

x < 1

Hope this Helps!!!

This question involves finding the increasing and decreasing intervals, local maximum and minimum values, and concavity of a cubic function f(x) = x3 – 6x2 – 15x + 4. These are found by taking the first and second derivative and applying various tests.

The subject of this question is Calculus, more specifically, regarding the properties of the function f(x) = x3 – 6x2 – 15x + 4. To find the intervals where the function is increasing or decreasing, we need to find the derivative of f(x), set it to zero and solve for x to find critical points. Then we set up a number line with these critical numbers and analyze the sign of f'(x) in each interval.

The local maximum and minimum values can also be found from the critical numbers. To find where the function is concave up or down, we find the second derivative (f''(x)) and perform a similar process we did with the first derivative.

The inflection points, where the function changes its concavity, can also be found from evaluating the second derivative.

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Answer:

35 square units.

Step-by-step explanation:

To find the area of a parallelogram, the formula is the exact same as finding the area of a rectangle. So 7 x 5 is 35.

Answer:

Step-by-step explanation:

Socratic had the answer on there I think

Answer:

1. x-2y

2. 2(13a-5)

Step-by-step explanation:

1. it's asking to expand the equation, so you should distribute the -1/2. -1/2*-2x becomes 1x or just x and -1/2*4y becomes -2y, so the answer is x-2y.

2. it's asking to factor, so you should find the greatest common factor of 26a and 10, which is 2. (a isn't on both terms, but if it was, then you would factor out the a also.) 26a/2 is 13a and -10/2 is -5, so the answer is 2(13a-5).

hope this helped!

Answer:

  salary

Step-by-step explanation:

Salary is the term generally used to refer to the annual amount of wages.

_____

tuition is the amount paid to an educational institution for the classes they offer.

hourly wage refers to the amount earned in an hour, not a year.

expense is the name given to any expenditure, not an amount earned.

Answer:

C. Salary

Step-by-step explanation:

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