Review of logarithms (logs)
For each of the following equations, write down the
name of the operation that occurs in the equation and
the name of the inverse operation that helps you
solve the equation.
Equation
x+10=25
2x=28
4²=64
Name of operation
Name of inverse
operation

Answer:

6*3 + 6*2

6*5

6(3+2)

Step-by-step explanation:

All of these equations lead to the same answer which is 30.

The two diagrams are basically the same but they are just separated apart. When you look for the area of both diagrams, it leads to the same answer.

Answer:

Step6x3 = 18. And. 2x6 = 12. Then you add the amounts, 18+12 = 30-by-step explanation:

The product of a,b and c from the fraction is 6/125

The product is the result of the multiplication of the numbers

From the given exponential fractions, we have

=(3x³y²/³)÷(125³*¹/³y³*¹/³

Simplifying the expression to have

(3x³y²/³)(125)(1)

⇒3/125x³y²/³

The expressed form is [tex]ax^{b} y^{c}[/tex]

a=3/125 b=3 c 2/3

Simplify further to have

⇒3/125*3/1*2/3

Simplify further to get your final answer as

=6/125

Therefore, the product of the fractional exponents is 6/125

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Answer:

37609

Step-by-step explanation:

You'd put the 3,419 inside the box and 11 outside the box.

But you'd need around 4 spaces inside the box for each number to be on top. And you'd need 2 spaces on the side. (Hopefully that makes sense)
Your answer should be 37609

Answer:

Answer:

Below

Step-by-step explanation:

Domain is the set of values x can be for a function .....it looks like this one goes from -2 to 2 with asymptopes at these values:

-2< x < 2  

Range is the 'y' values a graph can have...this one goes from -1.5 -ish to 5.5 ish    

-1.5 <= y <= 5.5

Here is the graph with some lines on it:

Answer: Its the same number with the sign changed..

Step-by-step explanation:

5 multiplied by negative 1 would be -5

And

negative 5 multiplied by negative 1 would be 5

The width of the rectangle is 6 inches and length of rectangle is 12 inches

We have given the perimeter of the rectangle and the length of a rectangle is 6 inches longer than its width.

Let x be the width of the rectangle and x+6 be the length of the rectangle.

Perimeter = p = 36 inches

We have to find the values of width and length of rectangle.

The formula to find the Perimeter is:

p = 2l+2w

36 = 2(x+6)+2(x)

36 = 2x+12+2x

36 = 4x+12

36-12= 4x

24 = 4x

x = 6 inches.

Hence, the width of the rectangle is 6 inches and length of rectangle is 12 inches.

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Answer:can you copy and paste it?

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

y-4 = -3(x-2)

y - 4 = -3x + 6

y = -3x + 6 + 4

y = -3x + 10

Answer:

y = -3x+10

Step-by-step explanation:

Using the slope-intercept equation of a line

y = mx+b  where m is the slope and b is the y intercept

y = -3x+b

Substitute the point into the equation

4 = -3(2) +b

4 = -6+b

10 =b

y = -3x+10

The exact answer to the definite integral ∫16^1^3/π of x dx using the fundamental theorem is 8/π^2.

The fundamental theorem of calculus states that if f(x) is a continuous function on the interval [a, b] and F(x) is an antiderivative of f(x), then:

∫a^bf(x)dx = F(b) - F(a)

To use the fundamental theorem to evaluate the definite integral ∫16^1^3/π of x dx, we need to find an antiderivative of x. The antiderivative of x is x^2/2 + C, where C is an arbitrary constant.

Therefore, the definite integral ∫16^1^3/π of x dx can be written as:

∫16^1^3/π x dx = (x^2/2 + C) |16^1^3/π

Evaluating this expression gives us:

(3/π)^2/2 + C - (1/π)^2/2 + C = (9/π^2 - 1/π^2)/2 + 2C

Since C is an arbitrary constant, it cancels out when we take the difference between the upper and lower limits of integration. Therefore, the definite integral ∫16^1^3/π of x dx is equal to:

(9/π^2 - 1/π^2)/2 = 8/π^2

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The value of missing angles in the given figure are as follow:

m∠1= 56  ,m∠2= 56 and m∠3= 74.

As given in the question,

In the figure, MPQ is a triangle

We know that sum of the angles in the triangle is 180.

m∠ MPQ + m∠ PMQ + m∠1 =180

⇒58 + 66 + m∠1=180

⇒124 + m∠1= 180

⇒m∠1= 180 - 124

⇒m∠1=56

so m∠1=56.

∠1 and ∠2 are vertically opposite angles so ,

⇒m∠1= m∠2

therefore, m∠2=56.

Now in triangle QNO

∠QON + m∠2 + m∠3 =180

⇒50 + 56 +m∠ 3=180

⇒106 + m∠3= 180

⇒m∠3= 180 - 106

⇒m∠3=74

Therefore, the measure of the angles in the given figure are m∠1= 56  ,m∠2= 56 and m∠3= 74.

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For the study about cholestrol levels of people was taken by medical researcher.

a) Null and Alternative hypothesis for study is

H₀ : μd ≥0

Hₐ : μd <0

where μd --> average

b) The value of t-statistic is 3.78118

c) The critical value for t-test is - 2.015.

d) We fail to reject null hypothesis, H₀

e) There is sufficient evidence to support the claim of researcher that cholesterol level decreases on average.

The above table represents the patients and their cholesterol levels before and after they showed the film about the effect of high cholesterol levels. The "d" column shows the difference in their cholesterol levels.

Singnificance level, α =0.05

∑d = 122, n = 6 , ∑d² = 3348

Xd -bar = 122/6 = 20.33

Standard deviations, σ = √(∑d² - ∑d/n)/(n-1)

σ = √(3348 - 20.33)/5 = 13.170

a) The Null and Alternative hypothesis are

H₀ : μd ≥0

Hₐ : μd <0

b) test- statistic,

t - value = (Xd-bar - μd)/σ /√n

=> t = (20.33 - 0)/13.17/√6

=> t = 20.33/5.37662

=> t = 3.78118

c) degree of freedom, df = n-1 = 5

The critical t-value for a given confidence level c and sample size n is obtained by computing the quantity tα/2 for t-distribution with (n-1) degrees of freedom.

α = 0.05 , α/2 = 0.25 , df = 5

t(₀.₂₅, ₅) = - 2.015

d) Decision: As we seen t-value= 3.781 and t-critical value = - 2.015

so, t -value > critical value. Therefore, we fail to reject null hypothesis.

e) Conclusion: There is sufficient evidence to claim that the cholesterol level decrease on average.

Hence, we got all required answers.

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Complete question:

Cholesterol Levels A medical researcher wishes to see if he can lower the cholesterol levels through diet in 6 people by showing a film about the effects of high cholesterol levels. The data are shown. At =α0.05 , did the cholesterol level decrease on average? Use the P -value method and tables. Patient 1 2 3 4 5 6 Before 250 219 218 224 209 223 After 216 203 192 190 207 213 State the hypotheses and identify the claim with the correct hypothesis. H0 : ▼(Choose one) H1 : ▼(Choose one) This hypothesis test is a ▼(Choose one) test. Compute the test value. Always round t score values to three decimal places. t= Find the interval for the P -value. The correct interval is Make the decision. ▼(Choose one) the null hypothesis. Summarize the results. There is ▼(Choose one) that the mean heights are different

To compare the sampling distribution, first I would simulate the machine by randomly generating n number of samples between 8 and 10 oz with a uniform distribution and calculate the 4th spread for each sample size. I would then repeat this experiment multiple times and take the average of the fourth spread values for each sample size to compare the sampling distributions.

To compare the sampling distributions of the fourth spread for sample sizes n = 5, 10, 20, and 30, I would simulate the machine by randomly generating samples between 8 and 10 oz with a uniform distribution. For each sample size, I would calculate the fourth spread for each sample and then repeat the experiment multiple times. Finally, I would take the average of the fourth spread values for each sample size to compare the sampling distributions. This way, I would be able to see how the fourth spread changes as the sample size changes. It would also allow me to see how the fourth spread is affected by the uniform distribution of the machine's output.

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6 + 12^2

12 squared would be 12 to the second power

since the directions say "the sum"

you would use addition to add 6 and 12^2

The required sample size of the given value is 577.

What is margin of error?

The formula to calculate the sample size  :-

n = (p(1-p)((Zα/₂)/E)²

Given :  Estimated proportion  p = 0.60

Margin of error : E = 0.04

Significance level : α = 1-0.95 = 0.05

Critical value : Zα/₂ = 1.96

Now, the required sample size will be :-

n = (0.60)(0.11)(1.96/0.04)²

= 6.6 * (0.0784)²

= 0.57744

Hence, the required minimum sample size of the given is 577.

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The biomass a year later is [tex]& \ y \approx 3.23 \times 10^7 \mathrm{~kg}[/tex]  and t=1.58 years to reach 4 times 107 kg of biomass.

The following differential equation: [tex]& \Rightarrow \frac{d y}{d t}=k y\left(1-\frac{y}{M}\right) \\[/tex]

[tex]& \Rightarrow \frac{d y}{d t}=k y\left(\frac{M-y}{M}\right)[/tex]

Using variable separable method:

[tex]$$\Rightarrow \frac{d y}{y(M-y)}=\left(\frac{k}{M}\right) d t$$[/tex]

Integrate both sides:

[tex]$$\begin{gathered}\Rightarrow-\int \frac{d y}{y(y-M)}=\int\left(\frac{k}{M}\right) d t \\\\\Rightarrow-\frac{1}{M} \int \frac{M}{y(y-M)} d y=\int\left(\frac{k}{M}\right) d t \\\\\Rightarrow-\frac{1}{M} \int \frac{y-(y-M)}{y(y-M)} d y=\int\left(\frac{k}{M}\right) d t \\\\\Rightarrow-\frac{1}{M} \int\left(\frac{1}{y-M}-\frac{1}{y}\right) d y=\int\left(\frac{k}{M}\right) d t\end{gathered}$$[/tex]

[tex]\Rightarrow-\frac{1}{M}(\ln (y-M)-\ln y)=\frac{k t}{M}+C \\[/tex]

Let C1 be a constant such that C1 = MC, therefore,

[tex]$$\begin{gathered}\Rightarrow-\ln (y-M)+\ln y=k t+C_1 \\\Rightarrow \ln \frac{y}{y-M}=k t+C_1 \\\Rightarrow \frac{y}{y-M}=e^{k t+C_1} \\\\\Rightarrow y=y e^{k t+C_1}-M e^{k t+C_1} \\\\\Rightarrow y e^{k t+C_1}-y=M e^{k t+C_1} \\\\\Rightarrow y=\frac{M e^{k t+C_1}}{e^{k t+C_1}-1} \\\\\Rightarrow y=\frac{M}{1-e^{-k t-C_1}} \\\Rightarrow y=\frac{M}{1-e^{-k t} e^{C_1}}\end{gathered}$$[/tex]

Let A be a new constant such that:

[tex]\Rightarrow y=\frac{M}{1-A e^{-k t}}[/tex]

Substitute the values of M and k, we'll get:

[tex]\Rightarrow y=\frac{7 \times 10^7}{1-A e^{-0.76 t}}[/tex]

Substituting the given initial condition:[tex]\Rightarrow y(0)=2 \times 10^7[/tex]

[tex]\Rightarrow 2 \times 10^7=\frac{7 \times 10^7}{1-A e^{-0.76(0)}} \\\\\\Rightarrow 2=\frac{7}{1-A} \\[/tex]

=2-2A=7

=A=-2.5

Therefore, [tex]\Rightarrow y=\frac{7 \times 10^7}{1+2.5 e^{-0.76 t}}[/tex]

On simplification, we'll get:

[tex]$$\begin{aligned}& \Rightarrow y \approx 32270466.08 \mathrm{~kg} \\& \Rightarrow y \approx 3.23 \times 10^7 \mathrm{~kg}\end{aligned}$$[/tex]

(b). Substitute the given value in the equation

[tex]$$\begin{gathered}\Rightarrow 4 \times 10^7=\frac{7 \times 10^7}{1+2.5 e^{-0.76 t}} \\\Rightarrow 4=\frac{7}{1+2.5 e^{-0.76 t}} \\\Rightarrow 4+10 e^{-0.76 t}=7\end{gathered}$$[/tex]

On simplification, we'll get t=1.58 years

Therefore, it will take for the biomass to reach 4 times 107 kg is 1.58 years.

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Answer:

False.  They would form 4 right angles (90)

Step-by-step explanation:

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1A) To find out how much the hot air balloon rose each minute, we need to find the rate at which it rose. The rate can be calculated by dividing the change in altitude by the change in time. In this case, the change in altitude is 70 meters - 44 meters = 26 meters, and the change in time is 2 minutes - 3 minutes = -1 minute (since the time is decreasing). The rate is therefore 26 meters/-1 minute = -26 meters/minute.

1B) The hot air balloon started at an altitude of 44 meters - (-26 meters/minute) * 3 minutes = 44 meters - (-78 meters) = 122 meters.

1C) To find the equation that describes the relationship between the altitude of the hot air balloon and the elapsed time, we can use the information that we have. The altitude at time t=0 is 122 meters, and the rate at which the altitude changes is -26 meters/minute. The equation is therefore A = -26t + 122.

The hot air balloon rise 13 m each minute.

The hot air balloon was 5 m above the ground at start.

The equation that describes the relationship between the altitude of the hot air balloon in meters is A = 13t + 5.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

We have, After 3 minutes, the balloon was 44 meters above the ground.

After 2 minutes later, the hot air balloon had risen to 70 meters above the ground.

1. The rate of change

= (70-44)/ (5-3)

= 26/ 2

= 13 m / min

2. At start the hot air balloon is

= (44-13 x 3)

= 5 m above the ground

3. The equation that describes the relationship between the altitude of the hot air balloon in meters is

A = 13t + 5.

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Answer:

The correct answer is A. No, because 3(2) + 3 ≠ 15.

Step-by-step explanation:

because the total number of goals scored by Skylar and Wyatt was 15, and if Skylar scored 3 goals, then Wyatt would have scored 3 * 2 = 6 goals. Since the total number of goals scored by both players is 15, this scenario is not possible. Therefore, Skylar could not have scored 3 goals.

Answer:

To write the equation in standard form, we need to isolate the variables on one side of the equation and the constants on the other side. We can do this by combining like terms and using the distributive property.

First, we distribute the 3 on the right side of the equation:

4y - 5x = 12x - 6y + 3

Then, we combine like terms:

4y - 5x = 12x - 6y + 3

= -x + 6y + 3

Finally, we move all the constants to the right side of the equation and all the variables to the left side:

x - 6y = -3

This is the standard form of the equation. In standard form, the equation has the form ax + by = c, where a and b are coefficients, and c is a constant. In this case, the coefficients are 1 and -6, and the constant is -3.

Answer:

17x - 10y = - 3

Step-by-step explanation:

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

4y - 5x = 3(4x - 2y + 1) ← distribute parenthesis

4y - 5x = 12x - 6y + 3 ( subtract 4y - 5x from both sides )

0 = 17x - 10y + 3 ( subtract 3 from both sides )

- 3 = 17x - 10y , that is

17x - 10y = - 3 ← in standard form

For a 90% confidence interval the upper and lower bound is 11.50 and 9.56 respectively.

Confidence interval means the probability that a population parameter will fall between a set of values.

The formula for confidence interval is C.I = u ± z (sd/[tex]\sqrt{n\\}[/tex] ) where u is the mean, sd is the standard deviation and z is the confidence level value. For an area of 90% around the mean, which makes 45% on each side, for the confidence level we will find the z-score at 0.45+0.5 = 0.95 area, and then double it since we need for both sides. At 0.95, the z-score is approximately 1.64. Thus, z is 3.28.

Plugging the values in the formula for C.I gives the upper bound as 10.53 + 0.968 = 11.50 and the lower bound as 10.53 - 0.968 = 9.56

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Answer:

answer on the picture......

The correct statement is-number of students in the data set

In research and data collecting, something that is being measured and whose values can change is referred to as a variable.

Given that we have a range of alternatives from January to December, the aforementioned example demonstrates how the student birth month is a variable. The student's ability to indicate whether they support particular political parties or not makes their political affiliation another variable. Since they are college students, the age of the student is another variable, with replies falling within a range of 20 to 25.

Since students will give different answers, whether they live at the same address or a different one, student address is also a variable.

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To solve this inequality, we can start by converting the mixed numbers to improper fractions. The mixed numbers in this inequality are 1/3 and -2 1/4. The negative sign in front of 2 1/4 indicates that the resulting fraction will be negative. To convert 1/3 to an improper fraction, we can multiply the denominator (3) by the whole number (1) and add the result to the numerator (1). This gives us 1/3 = 4/3. To convert -2 1/4 to an improper fraction, we can multiply the denominator (4) by the whole number (-2) and add the result to the numerator (1). This gives us -2 1/4 = -9/4.

Next, we can combine the two fractions on the left side of the inequality by adding their numerators and denominators. This gives us m + 4/3 + -9/4. We can then simplify this expression by combining like terms. This gives us m - 9/12 + 4/3. We can further simplify this expression by adding the fractions with unlike denominators. To do this, we can find a common denominator by multiplying the two denominators together, which gives us 12 * 3 = 36. We can then convert the fractions to have this common denominator by multiplying the numerator and denominator of each fraction by the appropriate value. For m - 9/12 + 4/3, we have m - (9 * 3)/(12 * 3) + (4 * 12)/(3 * 12), which simplifies to m - 27/36 + 48/36. We can then combine like terms to get m + 21/36.

Finally, we can solve for m by moving all of the terms with m to one side of the inequality and all of the other terms to the other side. To do this, we can subtract 21/36 from both sides of the inequality, which gives us m + 21/36 - 21/36 < -2 1/4 - 21/36. This simplifies to m < -2 1/4 - 21/36, which we can further simplify by converting -2 1/4 - 21/36 to an improper fraction. To do this, we can multiply the denominator (4) by the whole number (-2) and add the result to the numerator (1), which gives us -2 1/4 = -9/4. We can then add -9/4 and -21/36 to get -9/4 - 21/36 = -105/36. Finally, we can convert this to a mixed number by dividing the numerator (-105) by the denominator (36) and taking the quotient (-2) as the whole number and the remainder (27) as the numerator of the fraction. This gives us -105/36 =

The number of bags filled by the pet shop is 879 and the number of treats they gave to the groomer is 4.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the data given in the question,

Total number of dog treats in the shop = 6157

Number of treats per bag = 7

Extra treats will be given to the groomer.

Then, the number of bags will be,

6157/7 = 879.57

This means that a total of 879 bags are there, with 7 pieces of treats per bag.

So, the total number of treats in 879 bags will be,

879 × 7 = 6153

So, the amount of treats left for the groomer is,

6157 - 6153 = 4 treats.

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This is one way we can represent a linear equation:

[tex]y-y_1=m(x-x_1)[/tex]

We're given:

These functions give us information on two points, as they are represented as [tex]f(x)=y[/tex]:

First, solve for the slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

⇒ Plug in the two points:

[tex]m=\dfrac{-6-(-7)}{3-(-1)}\\\\m=\dfrac{-6+7}{3+1}\\\\m=\dfrac{1}{4}[/tex]

⇒ Plug this into [tex]y_2-y_1=m(x_2-x_1)[/tex]:

[tex]y-y_1=\dfrac{1}{4}(x-x_1)[/tex]

Now, there are two ways we can write this equation, as we are given two points:

(-1, -7)

⇒ [tex]y-(-7)=\dfrac{1}{4}(x-(-1))\\y+7=\dfrac{1}{4}(x+1)[/tex]

(3,-6)

⇒ [tex]y-(-6)=\dfrac{1}{4}(x-(3))\\y+6=\dfrac{1}{4}(x-3)[/tex]

[tex]y+7=\dfrac{1}{4}(x+1)[/tex] or [tex]y+6=\dfrac{1}{4}(x-3)[/tex]

The table with constant of proportionality between x and y is table A

We should be able to know that constant of proportionality shows a type of relationship between two variables that shows a constant relationship or same ratio.

The given fraction is 8/5

Rewrite 8/5 as a ratio of two numbers

8:5

Constant of proportionality is written as

y=k/x

Making k the subject, k=y/x

Where k is a constant.

From table A,

The constant  (K) is 4/1 = 4:1

Now multiply 4*8=32

8*1=5

Therefore 32/5 is a proportion of 8/5

Also using the constant k=10

⇒10:1   Then 10*8=80

And 1*5=5

⇒ 80/5=16

Also in the last constant K=11, we have 11:1

⇒[tex]\frac{11*8}{1*5}[/tex] =88/5

In conclusion option A gives the table that has constant of proportionality to 8/5

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Answer:

a : c = 3 : 20

Step-by-step explanation:

Given ratios:

The value of b is 3 and 5.

The lowest common multiple of 3 and 5 is 15.

Multiply each ratio by a factor of 15 so that b is 15.

Multiply ratio a : b by 3:

⇒ a : b = 6 : 15

Multiply ratio b : c by 5:

⇒ b : c = 15 : 40

Therefore:

⇒ a : b : c = 6 : 15 : 40

So a : c is:

⇒ a : c = 6 : 40

Simplest form:

⇒ a : c = 3 : 20

The value of x in the equation, 3/4x + 6 - 1/4x = 2/4x + 9, is: x = -2.

Solving an equation involves finding the value of the variable in the equation. The value, when plugged into the equation would make it true.

The equation given is, 3/4x + 6 - 1/4x = 2/4x + 9, to solve for the value of x, follow the steps below:

3/4x + 6 - 1/4x = 2/4x + 9 [given]

Combine like terms:

3/4x - 2/4x - 1/4x = 9 - 6

(3 - 2 - 1)/4x = 3

-6/4x = 3

Simplify

-3/2x = 3

Multiply both sides by -2/3:

-3/2x × -2/3 = 3 × -2/3

x = -6/3

x = -2

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Answer:

Step-by-step explanation:

If a sample mean is 32, the range of possible values that best describes an estimate for the population mean is most likely (30, 38).

The sample mean is a statistic that is used to estimate the population mean. In general, the sample mean is a good estimate of the population mean, but it is not always perfectly accurate. There is always some degree of uncertainty or variability associated with any estimate, and this is especially true when the sample size is small.

One way to quantify this uncertainty is to use a confidence interval, which is a range of values that is likely to contain the population mean with a certain level of confidence. For example, a 95% confidence interval is a range of values that is likely to contain the population mean with 95% confidence.

In this case, if a sample mean is 32, a 95% confidence interval for the population mean would likely be a range of values centered around 32 and extending approximately 2 standard errors in either direction. For a sample mean of 32, a range of values extending 2 standard errors in either direction would be approximately (30, 38). Therefore, the range of possible values that best describes an estimate for the population mean is most likely (30, 38).

If a sample mean is 32, (30, 38) is most likely the range of possible values that best describes an estimate for the population mean. the correct option is option D.

Range serves as a statistical measure of dispersion in mathematics, or how widely spaced a particular data collection is from smallest to biggest. The range in a piece of data is the distinction between the highest and lowest number. The confidence interval of 95% for the population mean in this scenario, assuming the sample mean is 32, is likely to include a range of values centred around 32.

Extending around 2 standard errors in each direction. A range of results spanning two standard deviations in either way would result in around (30, 38) for a sample mean of 32. Thus, the range of potential values that most accurately captures an estimate of the population mean is (30, 38).

Therefore, the correct option is option D.

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