0
Determine whether the curve is the graph of a function of x.
OYes, it is a function.
O No, it is not a function.
If it is, state the domain and range of the function. (Enter your answers in interval notation. If the curve is not the graph of a function of x, enter DNE.)
domain
range

Answer:

A) [tex]x = \dfrac{\log_6(46) + 6}{4}[/tex]

B) [tex]x = \dfrac{\ln(11)}{2}[/tex]

C) [tex]x = \dfrac{11}{5}[/tex]

Step-by-step explanation:

A) We can solve for x by taking log base 6 of both sides.

[tex]\log_6(6^{4x-6}) = \log_6(46)[/tex]

[tex]4x - 6 = \log_6(46)[/tex]

[tex]4x = \log_6(46) + 6[/tex]

[tex]\boxed{x = \dfrac{\log_6(46) + 6}{4}}[/tex]

B) First, we have to divide both sides by 2.

[tex]2e^{2x} / 2= 22 / 2[/tex]

[tex]e^{2x} = 11[/tex]

Then, we can solve for x by taking the natural log (log base e) of both sides.

[tex]\ln(e^{2x})= \ln(11)[/tex]

[tex]2x= \ln(11)[/tex]

[tex]\boxed{x = \dfrac{\ln(11)}{2}}[/tex]

C) We can solve for x by raising 2 to the power of each side.

[tex]2^{\log_2(5x + 5)} = 2^4[/tex]

This cancels the log base 2 on the left.

[tex]5x + 5 = 16[/tex]

[tex]5x = 11[/tex]

[tex]\boxed{x = \dfrac{11}{5}}[/tex]

The time taken to reach a population of 500 is gotten from  500=50e^0.55t

Exponential growth is a process that increases quantity over time as in the bacterial culture here.

We know that from the question, we have;

P(t)=Poe^rt

P(t) = population at time t

Po= Initial population

r = growth rate

t = time taken

Then we have that;

150 = 50e^2r

3=e^2r

ln3 = 2r

r = ln3/2

r = 0.55

If the rate of growth is 0.55, then to reach a population  of 500;

500=50e^0.55t

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The Exponential model is y = 0.74 (1.79)ˣ

We have,

(10, 160) and (11, 250)

Using the Exponential model

y = abˣ

where a is the initial amount and be is the constant.

Now, the value of b is

= 250/ 140

= 1.79

Now, y = abˣ

140 = a (1.79)⁹

a = 0.74

So, the Exponential model is y = 0.74 (1.79)ˣ

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Answer: B: cone with a height of 4 units and a radius of 3 units

Step-by-step explanation:

Surface Area: 9pi + 15pi = 24pi square units

Volume: 9pi x 4 x 1/3 = 12pi cubic units

Answer:

The amount of money spent on tickets and snacks will be $39 and $20. And the total amount is $59.

Step-by-step explanation:

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Ellie is going to see a movie and is taking her 2 kids. Each movie ticket costs $13 and there are an assortment of snacks available to purchase for $5 each.

The amount of tickets is given as,

Ticket's amount = 3 x $13

Ticket's amount = $39

Then the amount spent on snacks is given as,

Snack's amount = 4 x $5

Snack's amount = $20

Then the total amount is given as,

Total amount = $39 + $20

Total amount = $59

The amount of money spent on tickets and snacks will be $39 and $20. And the total amount is $59.

Answer:

The given equation is:

det [a 10 e b d 0] = [2 10 3 6 -1 0]

The determinant of a 3x3 matrix is calculated as follows:

|a b c|

|d e f| = a(ei - fh) - b(di - fg) + c(dh - eg)

Applying this formula to the given matrix, we get:

det [a 10 e b d 0] = a(d0 - b-1) - 10(ed - b0) + e(10*-1 - d*3)

= ab + 10b - 10ed - 3e

Substituting the given values, we get:

ab + 10b - 10ed - 3e = 2(6-0) - 10(3-(-1)) + 3(10-(-1))

ab + 10b - 10ed - 3e = 12 + 40 + 33

ab + 10b - 10ed - 3e = 85

We can simplify this equation by factoring out b and e:

b(a + 10) - e(10d + 3) = 85 - 10b

We can solve for a, d, and e by setting up a system of equations using the given values of the determinant:

ab + 10b - 10ed - 3e = 85

From this equation, we can solve for b:

b(a + 10) - e(10d + 3) = 85 - 10b

Substituting the value of b from the determinant equation, we get:

(a+10)(-1) - e(10d+3) = -8.5

Simplifying, we get:

-a - 10e - 3.3d = -8.5 ...(1)

Also, from the determinant equation, we have:

6a + 10d + 3e = 29

Solving for e in terms of a and d, we get:

e = (29 - 6a - 10d)/3 ...(2)

Substituting equation (2) into equation (1), we get:

-a - 10[(29 - 6a - 10d)/3] - 3.3d = -8.5

Simplifying and multiplying both sides by -3, we get:

3a + 20d - 29e = 25.5

Substituting equation (2) into this equation, we get:

3a + 20d - 29[(29 - 6a - 10d)/3] = 25.5

Simplifying, we get:

a + 6d - 29 = 1.5

a + 6d = 30.5

We have two equations in two variables:

-a - 10e - 3.3d = -8.5

a + 6d = 30.5

Solving for a and d using any method (substitution, elimination, etc.), we get:

a = 7

d = 4

Substituting these values into equation (2), we get:

e = (29 - 6a - 10d)/3 = (29 - 6(7) - 10(4))/3 = -3

Therefore, a = 7, d = 4, and e = -3.

Step-by-step explanation:

The base area of the cylinder is 78.54 ft².

The height of the cylinder is 2 ft.

The cylinder has a volume of 157.08 ft cube and the radius of the cylinder is 5 ft.

Therefore, the area of the base of the cylinder can be found as follows:

base area of the cylinder = πr²

base area of the cylinder = 3.1416 × 5²

base area of the cylinder = 3.1416 × 25

base area of the cylinder = 78.54 ft²

Therefore, let's find the height of the cylinder.

volume of the cylinder = πr²h

where

157.08 = 78.54 h

divide both sides by 78.54

h = 157.08 / 78.54

h = 2 ft

Therefore,

height of the cylinder = 2 ft

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If three squares are placed to form a right triangle as shown. The statement that must be true is: C .The difference of the areas of the smaller squares is always equal to the area of the largest square.

Let's use the letters a, b, and c to denote the side lengths of the squares, with c standing for the hypotenuse of the right triangle. Assuming that an is the shortest side length to preserve generality a2 is the area of the smallest square. The largest square has a surface area of c2 whereas the medium square has a surface area of b2.

The Pythagorean theorem demonstrates that a + b equals c. If we rewrite this equation, we obtain:

c^2 - b^2 = a^2

c^2 - a^2 = b^2

This means that the size of the largest square is equal to the difference between the areas of the two smaller squares, which is either a2 or b2.

Therefore the correct option is C.

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Expression for -16x squared +36 in factored form is [tex]-4(2x - 3)(2x + 3).[/tex]

The given equation is [tex]-16x^{2} +36[/tex]

simplifying the equation,

[tex]-16x^2 + 36 = 4(-4x^2 + 9)[/tex]

[tex]=-4x^2 + 9\\ = -(2x)^2 + 3^2 \\= -(2x - 3)(2x + 3)[/tex]

when compared together,

[tex]-16x^2 + 36 = 4(-4x^2 + 9) = 4(-(2x - 3)(2x + 3)) = -4(2x - 3)(2x + 3)[/tex]

The expression for the equation in factored form is -4(2x - 3)(2x + 3).

The question is incomplete. complete question will be "which of these expression is equivalent to [tex]-16x^{2} +36[/tex] in factored form?

options- 4(x+2)(3-2x) , -4(2x - 3)(2x + 3) or (4x+2x)(9x-2x)"

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Answer:

THE ANSWER OF 7×4=28 !!!!!!!

Answer:

A. V = 81π(7.25) = 1,844.90 cubic inches

V = 81(3.14)(7.25) = 1,843.97 cubic inches

B. Let p be the number of cans of paint.

1,843.97p = 10,000, so p = 5.42

Jessie will need 6 cans of paint.

C. Area of each storage area = π(9.5^2) = 283.53 square inches. Using 3.14 for π, this area is (3.14)(9.5^2) = 283.385 square inches. The base area of each paint can is 81π = 254.46 square inches (254.34 square inches if we use 3.14 for π). Jessie can't use the carrier because the area of each storage area exceeds the base area of each paint can.

a) The probability that the student was female is 43/76

b) The probability that the student was female AND got a "C" is 9/38

c) The probability that the student was female OR got a "C" is 45/76

We have,

             A   B   C  

Male     16  15  2  33

Female 14  11  18  43

Total     30 26 20 76

a) The probability that the student was female

= 43/76

b) The probability that the student was female AND got a "C"

= 18/76

= 9/38

c) The probability that the student was female OR got a "C"

= 43 /76 + 20/76 - 18/76

= 45/76

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The estimated population of the city after 3 years would be 8,537 people.

To find the population of the city after 3 years, we can use the formula for compound interest;

A = P ×[tex](1+r)^{t}[/tex]

where;

A = the final amount (population after 3 years)

P = the initial amount (initial population of the city) = 5,741

r = the annual growth rate (as a decimal) = 14% = 0.14

t = the number of years = 3

Plugging in the values, we get

A = 5,741 × (1 + 0.14)³

Simplifying the expression inside the parentheses first;

A = 5,741 × (1.14)³

Then, raising 1.14 to the power of 3;

A = 5,741 × 1.485136

A ≈ 8,536.98

So, the estimated population of the city after 3 years would be approximately 8,536.98 people. Since population cannot be in decimal numbers, we can round it to the nearest whole number;

A ≈ 8,537

Therefore, the estimated population of the city after 3 years would be 8,537 people.

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"Data are collected about a population," is not a characteristic of both experiments and surveys. Option A

A survey is a technique for gathering data about a study variable from the respondents of the population. An experiment is a technique used in science to isolate the problem being examined and test a theory.

Options B, C, and D are characteristics obtained in the case of the  experiments and surveys. In both types of research, subjects may be randomly selected (option B), the data collected may be studied for patterns (option C).

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Answer:

  cylinder

Step-by-step explanation:

You want to know which of two popcorn containers is a better value:

The volume formulas for the two shapes are ...

  V = 1/3πr²h . . . . . cone

  V = r²h . . . . . . . . . cylinder

For r = d/2, the ratio of these two volumes is ...

  [tex]\dfrac{V_{con}}{V_{cyl}}=\dfrac{\dfrac{1}{3}\pi\left(\dfrac{d_{con}}{2}\right)^2h_{con}}{\pi\left(\dfrac{d_{cyl}}{2}\right)^2h_{cyl}}=\dfrac{d_{con}^2\cdot h_{con}}{3\cdot d_{cyl}^2\cdot h_{cyl}}=\dfrac{12^2\cdot19}{3\cdot 8^2\cdot 15}=\dfrac{2736}{2880}=0.95[/tex]

The cone has less volume and costs more, so the cylindrical container is the better value.

If the Lions in their "seventh-game" scored 14 runs, then the true statement is (b) The mean increases and the median remains the same.

To determine how the additional 14 runs affect the mean and median, we need to calculate the original mean and median.

The mean is the sum of all the runs divided by the number of games:

So, Mean = (5 + 8 + 1 + 5 + 2 + 7)/6 = 28/6 = 4.67,

The median is defined as "middle-value" when data is arranged in order. In this case, the data in order is : 1, 2, 5, 5, 7, 8

So, the median is 5.

If the Lions scored 14 runs in their seventh game, the total number of runs for seven games is:

⇒ 5 + 8 + 1 + 5 + 2 + 7 + 14 = 42,

The new mean is the sum of all the runs for seven games divided by the number of games:

⇒ Mean = 42/7 = 6,

The new data in order is : 1, 2, 5, 5, 7, 8, 14,

So, the new median is also 5.

Comparing the original mean and median to the new mean and median, we can see that:

⇒ The median remains the same.

⇒ The mean increases from 4.67 to 6.

Therefore, the correct option is (b).

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The True statement is An equilateral triangle is always an isosceles triangle.

An equilateral triangle is always an isosceles triangle is True because isosceles triangle have two sides equal and equilateral have three sides equal.

A right triangle is never an isosceles triangle is False statement.

An obtuse triangle is sometimes an acute triangle is False statement.

An isosceles triangle is always a scalene triangle is False statement.

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It takes A. 5 months to pay off (Mini) the highest interest card.

To determine the number of months it takes to pay off the credit card debt, we shall calculate the monthly payment to pay off the highest interest card first.

First, calculate interest accrued on each card per month:

Murk: (5.6/100)/12 * $675.49 = $2.98 per month

Mini: (9.85/100)/12 * $902.43 = $7.42 per month

Next, we determine the order in which to pay off the cards, which is highest interest card first, we can allocate the entire $375 to Mini and leave a minimum for interest accrued on Murk.

This should be a percentage of the balance.

Assuming it's 2% of the balance, which is $13.51.

So, in month 1, we will pay:

Mini: $375

Murk: $13.51

Leaving these balances:

Murk: $675.49 + $2.98 - $13.51 = $664.96

Mini: $902.43 - $375 + $7.42 = $534.85

In month 2:

Mini: $534.85 + $7.42 = $542.27

Murk: $13.51 + $2.98 = $16.49

Balances:

Murk: $664.96 + $2.98 - $16.49 = $651.45

Mini: $542.27 - $375 + $7.42 = $174.69

month 3:

Mini: $174.69 + $7.42 = $182.11

Murk: $13.51 + $2.98 = $16.49

Balances:

Murk: $651.45 + $2.98 - $16.49 = $638.94

Mini: $182.11 - $174.69 + $5.52 = $12.94

month4:

Mini: $12.94 + $7.42 = $20.36

Murk: $13.51 + $2.98 = $16.49

Balances:

Murk: $638.94 + $2.98 - $16.49 = $625.43

Mini: $20.36 - $12.94 + $0.54 = $8.96

month 5:

Mini: $8.96 + $7.42 = $16.38

Murk: $13.51 + $2.98 = $16.49

Balances:

Murk: $625.43 + $2.98 - $16.49 = $612.92

Mini: $16.38 - $8.96 = $7.42

So, Mini's balance is paid off here.

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Note:

And we can allocate the entire $375 budget to Murk.

This means we will pay off Murk in month 6:

Murk: $612.92 + $2.98 + $375 - $13.51 = $977.39

Answer: 16* 2

Step-by-step explanation:

Answer:

x = -31 maybe

Step-by-step explanation:

We will conduct a one-sample t-test to determine if the mean length of the particular size of dress is significantly different from 29 inches.

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We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.005 level of significance that the mean length of the particular size of the dress is found to be significantly longer or shorter than 29 inches and the machines must be adjusted.

What is the null hypothesis?

The null hypothesis is the assertion that there is no association between the two sets of data or variables being investigated in a scientific study. The term "null" refers to the idea that any empirically observed difference is entirely attributable to chance and that no underlying causal relationship exists.

Here, we have

Given: A children's clothing company sells hand-smocked dresses for girls. The length of one particular size of the dress is designed to be 29 inches. The most recent simple random sample of 22 dresses had a mean length of 31.53 inches with a standard deviation of 8.24 inches.

We will conduct a one-sample t-test to determine if the mean length of the particular size of the dress is significantly different from 29 inches.

In the null hypothesis, the mean length of the particular size of the dress is equal to 29 inches.

In the alternative hypothesis, the mean length of the particular size of the dress is significantly longer or shorter than 29 inches.

We will use a 0.005 level of significance, which corresponds to a critical value of ±2.807 for a two-tailed test with 21 degrees of freedom.

Our test statistic is: t = (31.53 - 29) / (8.24 / sqrt(22)) = 1.774

Since our test statistic (1.774) is not greater than the critical value (2.807) or less than the negative of the critical value (-2.807), we fail to reject the null hypothesis.

Hence, We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.005 level of significance that the mean length of the particular size of the dress is found to be significantly longer or shorter than 29 inches and the machines must be adjusted.

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Answer:21y -78

Step-by-step explanation: Distribute the 7 to 3y and -10 to get 21y and -70.

Then combine like terms so the equation would be 21y -78

Step-by-step explanation:

-8+7(3y-10)

-8+21y-70

21y-70+8

21y-78

Last step because there is no more like terms to combine

Hope this helps

The value of the composite function t(s (2)) is 8

From the question, we have the following parameters that can be used in our computation:

s(x) = -x + 5

t(x) = 2x + 2

The composite function t(s(x)) is calculated as

t(s(x)) = 2s(x) + 2

Substitute the known values in the above equation, so, we have the following representation

t(s(x)) = 2(-x + 5) + 2

Again, substitute the known values in the above equation, so, we have the following representation

t(s(2)) = 2(-2 + 5) + 2

Evaluate

t(s(2)) = 8

Hence, the value of t(s(2)) is 8

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Answer:Assuming that the number on the end of the number line is a 1 (I cant read it too clearly), this number line goes to 7/7ths so that means A would be 1/7th and B would be 4/7th

Step-by-step explanation: thats how Number lines work

The y-intercept of the line of best fit is: y = 20

The formula for equation of a line of best fit is:

y = mx + c

where:

m is slope

c is y-intercept

Now, the y-intercept is simply defined as the point where the line crosses the y-axis.

In this case, the line crosses the y-axis at y = 20.

Thus, we can conclude that it is the y-intercept

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The order will be $50.4 with the price increase

From the question, we have the following parameters that can be used in our computation:

Order = $45

Percentage increase = 12%

Using the above as a guide, we have the following:

New order = Order * (1 + Percentage increase)

Substitute the known values in the above equation, so, we have the following representation

New order = 45* (1 + 12%)

Evaluate

New order = 50.4

Hence, the new order is $50.4

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The function that represents in the table is y = 0.5(2^x)

Option C is the correct answer.

We have,

Looking at the table,

We can observe that as the value of x increases, the value of f(x) doubles.

This doubling of f(x) indicates that the base of the exponential function is 2.

Also, when x = 0, the value of f(x) is 0.5, which means that the y-intercept of the exponential function is 0.5.

Thus,

The function can be represented as y = 0.5(2^x).

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