You don't have a driver's license yet, so you have to walk to the store. You can walk 1.5 miles in 24 minutes. If it
took you 32 minutes to walk to the store, how far away is the grocery store?
Answer:
Units:
Blank 1:
Blank 2:

Answer:

1.1. 3(2a-7)

1.2. 3x(2x+3)

Step-by-step explanation:

Put the common factor on the outside of the parentheses.

1.1. 6a-21

The lowest common factor for 6a and -21 is 3.

     3(2a-7)

1.2. \(6x^{2} +9x\)

The lowest common factor for \(6x^{2}\) and 9x is 3x.

      3x(2x+3)

The correct unit of measure for the mean of the sampling distribution of I is A. Dollars.

The original distribution of prices for the car model is given in dollars, and the mean of the sampling distribution represents the average price of a random sample of 4 cars from that distribution. Hence, the correct unit of measure should be in dollars also.

In statistics, the mean is a measure of central tendency that represents the average value of a dataset. It is calculated by adding up all the values in a dataset and dividing by the number of observations. The formula for the mean of a dataset is:

mean = (sum of observations) / (number of observations)

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Answer:

3x+9

Step-by-step explanation:

If it’s multiple choice the other one is

x +1+1+1+x +1+1+1+ x +1+1+1

I hope this helps!

Answer: option D. B = 59.6° or B' = 120.4°

Step-by-step explanation:

Since the law is a/sinA = b/sinB = c/sinC you can try and verify each of them, by

10/sin(B)=......

and only B = 59.6° or B' = 120.4° give you the closed to 8.2/sin(45)= 11.59655121 which was 11.59401915.

(why the closed? because the question said it is "approximated")

The values of angles B and B' will be 59.6° and 120.4°, i.e. option C is the correct answer.

Triangle is a three sides two dimensional surface having three angles.

We have,

A triangle in which,

One of the angle is 45°, and the side opposite to angle 45° is 8.2 with corresponding angle B.

And the side opposite to angle B is 10.

Now,

Using the law of sine,

i.e.

\(\frac{SinA}{a} =\frac{SinB}{b} =\frac{Sin c}{c}\)

So,

According to the given triangle,

We get,

\(\frac{Sin 45^0}{8.2} = \frac{Sin B}{10}\)

We get,

\(Sin B=\frac{Sin 45^0}{8.2} *10\)

On solving we get,

⇒

\(SinB= 59.58^0\ \ or\ \ SinB= 120.42\)

i.e.

\(SinB= 59.6^0 \ \ or\ \ SinB'= 120.40\)

So,

The option C is the correct answer.

Hence, we can say that the values of angles B and B' will be 59.6° and 120.4°, i.e. option C is the correct answer.

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The probability of concluding that the row variable is independent of the column variable will be unaffected.

In a chi-square test of independence, we compare the observed frequencies in a contingency table with the frequencies that would be expected if the row and column variables were independent.

The test helps determine whether there is a relationship between the two variables.

When the observed and expected frequencies are close to each other, it suggests that the variables are independent. In this case, the chi-square statistic will be small, indicating less evidence against the null hypothesis of independence.

As a result, the probability of concluding that the row variable is independent of the column variable may decrease.

However, the probability can also be influenced by the number of rows and columns in the contingency table. If there are many rows and columns, the chi-square statistic tends to increase with larger sample sizes, making it more likely to reject the null hypothesis of independence. In such cases, the probability of concluding independence may increase.

On the other hand, if the differences between observed and expected frequencies are small and the sample size is small with fewer rows and columns, the chi-square statistic may not provide enough evidence to reject the null hypothesis, and the probability of concluding independence may be unaffected.

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The simplified value of the expression 5 + (2/3) × 2 is 19/3. we perform the operations correctly and obtain the accurate result.

The expression 5 + (2/3) × 2 can be simplified using the order of operations.

The order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right), helps us determine the sequence in which mathematical operations should be performed.

Let's simplify the expression step by step:

Step 1: First, we evaluate the multiplication within the parentheses.

(2/3) × 2 = 4/3

Step 2: Now, we add 5 to the result from Step 1.

5 + (4/3) = (15/3) + (4/3) = 19/3

Therefore, the simplified value of the expression 5 + (2/3) × 2 is 19/3.

Applying the order of operations ensures that we perform the operations correctly and obtain the accurate result.

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Answer:

36π mm

Step-by-step explanation:

The arc length formula is s = rФ, where Ф is the central angle (in radians).

If r = 48 mm and Ф = 3π/4, then the arc length is:

s = rФ = (48 mm)(3π/4) = 36π mm

Answer:

36π

Step-by-step explanation:

The estimate of the life expectancy of a child in 1950 is 59 years

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the linear equation is represented by the graph

The life expectancies are given as:

52 years = 1900

66 years = 2000.

Using the midpoint formula, the estimate of the life expectancy of a child in 1950 is calculated as:

Life expectancy = (Year 1950 + Year 2000)/2

This gives

Life expectancy = (52 + 66)/2

Evaluate

Life expectancy = 59

Hence, the estimate of the life expectancy of a child in 1950 is 59 years

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There are 27 elements in set B but not in set A.

Given:

Total number of elements in the universal set S = 69

Number of elements in set A = 10

Number of elements in set B = 36

Total number of elements in either A or B = 37

To find the number of elements in B but not in A, we can use the principle of inclusion-exclusion. The formula is:

|A ∪ B| = |A| + |B| - |A ∩ B|

In this case, |A ∪ B| represents the total number of elements in either A or B, which is given as 37.

|A| represents the number of elements in A, which is 10.

|B| represents the number of elements in B, which is 36.

Plugging these values into the formula, we get:

37 = 10 + 36 - |A ∩ B|

To find |A ∩ B|, we rearrange the equation:

|A ∩ B| = 10 + 36 - 37

|A ∩ B| = 9

Since |A ∩ B| represents the number of elements that are common to both A and B, and we need to find the number of elements in B but not in A, we subtract |A ∩ B| from the number of elements in B:

Number of elements in B but not in A = |B| - |A ∩ B|

Number of elements in B but not in A = 36 - 9

Number of elements in B but not in A = 27

There are 27 elements in set B but not in set A.

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The following are the missing proof of opposite sides of a parallelogram are equal;

5) Δ AEB ≅ Δ CED and Δ AED ≅ Δ CEB

Reason:

Angle-side-angle

Statement:

6) AE ≅ CE and DE ≅ EB

Statement:

1) AB CD and AD BC

Reason:

Given

Statement:

2) ∠ 1 = ∠ 3

Reason:

When a transversal crosses parallel lines, alternate interior angles are congruent

Statement:

3) ∠ 2 = ∠ 4

Reason:

When a transversal crosses parallel lines, alternate interior angles are congruent.

Statement:

4) AB = CD

Reason:

Opposite sides of a parallelogram are congruent

Statement:

5) Δ AEB ≅ Δ CED and Δ AED ≅ Δ CEB

Reason:

Angle-side-angle

Statement:

6) AE ≅ CE and DE ≅ EB

Reason:

Corresponding parts of congruent triangles are congruent,

Statement:

7) Point E bisects both AC and BD

Reason:

Definition of bisector

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The addition of two given expressions, -2.4\(n^{3}\) and -7.8m+2, is -2.4\(n^{3}\)-7.8m+2.

According to the question,

We have the following two expressions:

-2.4\(n^{3}\) and -7.8m+2

Now, we will add these two expressions:

-2.4\(n^{3}\)-7.8m+2

Now, this expression can not be solved further because any of the term in this expression can not be further added because they do not have the same variable.

We know that only terms with the same variables can be added or subtracted from each other. For example, 4x can only be added 5x but it can not be added to 5y because the variables are different.

Hence, the addition of two given expressions, -2.4\(n^{3}\) and -7.8m+2, is -2.4\(n^{3}\)-7.8m+2.

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The circumference of circle with radius 9.7inch is 60.916 inch.

The perimeter of a circle is known as its circumference. It is the length of the circle's whole perimeter. The diameter of a circle and the constant are multiplied to get the circumference of the circle. This measurement of a circle's circumference is necessary for someone to cross a circular park or for a circle-shaped table to have a border. The units of the circumference are the same as the units of length and it is a linear value.

A circle is a closed round object whose border points are all equally spaced apart from the center, which is a fixed point.

Given that :the circle with a radius of 9.7 inches

Circumference of a circle is \(2\pi r\)

2 ×3.14×9.7 = 60.916

The circumference of circle with radius 9.7inch is 60.916 inch.

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The maximum volume of the largest rectangular box that can be inscribed in the ellipsoid can be calculated by finding the x, y, and z coordinates in the first octant that satisfy the equation (x^2/4) + (y^2/64) + (z^2/49) = 1.

Since the box must have edges parallel to the axes, the coordinates will also be the lengths of the box's edges. From the equation, we get the x coordinate to be 2, the y coordinate to be 8, and the z coordinate to be 7.

The volume of the box is the product of its edges, so the maximum volume of the box is V = 8xyz = 8 * 2 * 8 * 7 = 896.

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Answer:

let cost of one banana be x and cost of one apple be y.

so,   2x+y=1.16 --> a

      x  + y = 0.71 -->b

   now subtracting b from a , we get the result as,  

      x =  0.45

so , y will be   0.71 - 0.45=  0.26  (from b)

so, cost of one apple will be (i.e y) = £0.26

Hope this helps:)

When looking at the results of a 90% confidence interval, we can predict the results of a two-sided significance test as follows: if the confidence interval does not include the null hypothesis value, then the two-sided significance test will reject the null hypothesis at the 10% significance level.

Conversely, if the confidence interval includes the null hypothesis value, then the two-sided significance test will fail to reject the null hypothesis at the 10% significance level. This is because the confidence interval provides a range of plausible values for the true population parameter, and if the null hypothesis value is not within this range, then it is unlikely to be true, leading to rejection of the null hypothesis.

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Answer:

Given for big triangle:

Given for small triangle:

setting up proportionality:

\(\hookrightarrow \sf \dfrac{36}{3x+24} = \dfrac{27}{3x+9}\)

\(\hookrightarrow \sf 36(3x+9) = 27(3x+24)\)

\(\hookrightarrow \sf 108x+324 = 81x+648\)

\(\hookrightarrow \sf 108x-81x = 648-324\)

\(\hookrightarrow \sf 27x = 324\)

\(\hookrightarrow \sf x = 12\)

Perimeter of the triangle:

36 + 17 + 15 + 3x + 9

36 + 17 + 15 + 3(12) + 9

113 units

Answer:

x = 12

perimeter = 113 units

Step-by-step explanation:

Triangle Proportionality Theorem states that if a line parallel to one side of the triangle intersects the other two sides, then it divides the sides into proportional corresponding segments.

\(\implies 3x+9 : 15 = (36-9) : 9\)

\(\implies 3x+9 : 15 = 27 : 9\)

\(\implies \dfrac{3x+9}{15}= \dfrac{27}{9}\)

\(\implies 3x+9 = 45\)

\(\implies 3x = 36\)

\(\implies x = 12\)

Perimeter = \(3x+9 + 15 + 17 + 36\)

Substituting \(x = 12\):

⇒ perimeter = 3(12) + 9 + 15 + 17 + 36

                     = 113

Answer:

If you end up with the exact opposite of what you started with (that is, if f (–x) = –f (x), so all of the signs are switched), then the function is odd.

Step-by-step explanation:

Work Shown:

(3.4^17)^4

3.4^(17*4)

3.4^68

The general rule is (a^b)^c = a^(b*c)

answer:

(1/y)^3(1/z)^4

step-by-step explanation:

negative exponents just move the number to the denominator. so all you have to do is move the y & z to the denominator to change the exponents to positive. hope that helps!

\(~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ (4)^{\frac{-4}{2}} \implies (4)^{-2}\implies 4^{-2}\implies \cfrac{1}{4^2}\implies \cfrac{1}{16}\)

Answer: is 2.5

Step-by-step explanation:

I looked it up

The equation of the line that intersects the x-axis at point (3, 0) and intersects the y-axis at point (0, 5) is y = (-5/3)x + 5.

To find the equation of a line that intersects the x-axis at point (3, 0) and intersects the y-axis at point (0, 5), we can use the slope-intercept form of a linear equation, which is y = mx + b. Given the point (3, 0) on the x-axis, we know that when x = 3, y = 0. This gives us one point on the line, and we can use it to calculate the slope (m).

Using the slope formula: m = (y2 - y1) / (x2 - x1)

Substituting the values (0 - 5) / (3 - 0) = -5 / 3

So, the slope (m) is -5/3. Now, we can substitute the slope and one of the given points (0, 5) into the slope-intercept form (y = mx + b) to find the y-intercept (b).

Using the point (0, 5):

5 = (-5/3) * 0 + b

5 = b

The y-intercept (b) is 5. Therefore, the equation of the line that intersects the x-axis at point (3, 0) and intersects the y-axis at point (0, 5) is:

y = (-5/3)x + 5

To sketch the diagram, plot the points (3, 0) and (0, 5) on the x-y plane and draw a straight line passing through these two points. This line represents the graph of the equation y = (-5/3)x + 5.

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Answer: k= -10x+12

Step-by-step explanation:

For function y =x² , slope of the line tangent at x=1 is 2, the unknown values of the table is equal to 2.01.

As given in the question,

Given function :

y =x²

Slope is dy/dx = 2x

Slope of the line tangent at x=1

dy/dx =2(1)

        =2

Values given in the table:

Δx                                      Δy= f(x +Δx) -f(x)                                 Δy/Δx

1                            f(2)-f(1) =2² -1² =3                                 3/1 =3

0.5                         f(1.5) -f(1) = 1.5²-1² =1.25                    1.25/0.5=2.5

0.1                         f(1.1)-f(1)=1.1²-1² =0.21                        0.21/0.1=2.1

0.01                     f(0.01) -f(1) =0.01² -1² =0.0201        0.0201/0.01=2.01

Therefore, for function y =x² , slope of the line tangent at x=1 is 2, the unknown values of the table is equal to 2.01.

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The appropriate sample size formula on the TI-84 calculator, you can determine the sample size needed to achieve your desired margin of error for estimating population parameters.

To find the sample size with a desired margin of error on a TI-84 calculator, you can use the following steps:

1. Determine the desired margin of error: Decide on the maximum allowable difference between the sample estimate and the true population parameter. For example, if you want a margin of error of ±2%, your desired margin of error would be 0.02.

2. Determine the confidence level: Choose the desired level of confidence for your interval estimate. Common choices include 90%, 95%, or 99%.

Convert the confidence level to a corresponding z-score. For instance, a 95% confidence level corresponds to a z-score of approximately 1.96.

3. Calculate the estimated standard deviation: If you have an estimate of the population standard deviation, use that value. Otherwise, you can use a conservative estimate or a pilot study's standard deviation as a substitute.

4. Use the formula: The sample size formula for estimating a population mean is n = (z^2 * s^2) / E^2, where n represents the sample size, z is the z-score, s is the estimated standard deviation, and E is the desired margin of error.

5. Plug in the values: Input the values of the z-score, estimated standard deviation, and desired margin of error into the formula. Use parentheses and proper order of operations to ensure accurate calculations.

6. Calculate the sample size: Perform the calculations using the calculator, making sure to include the appropriate multiplication and division symbols. The result will be the recommended sample size to achieve the desired margin of error.

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Answer:

x = 17

Step-by-step explanation:

Assuming you require to find x

4x - 3 and 115 are same- side interior angles and supplementary, sum to 180°

4x - 3 + 115 = 180

4x + 112 = 180 ( subtract 112 from both sides )

4x = 68 ( divide both sides by 4 )

x = 17