Match the correct equation with the proportional relationship X 4 8 12Y 1 2 3

Answer:

According to the local weather report, the probability of rain in Boston on February 24 is 0.13

Step-by-step explanation:

% means "out of a hundred", so 50% is 50 out of a hundred, so 50/100, so 1/2 - a half.

That means, if we want to convert from a percentage to a decimal fraction, we just need to multiply the number before % by 1/100 (or divide by 100 I guess).

13% = 13*(1/100) = 13/100 = 0.13

Answer:

\(54\)

Step-by-step explanation:

Formula for average A of two numbers m and n is:

\(A=\frac{m+n}{2}\)

Substitute the value m=36 and n=72

\(A=\frac{36+72}{2}\)

This is equivalent to:

\(A=\frac{108}{2}\)

The average is:

\(A=54\)

Answer:

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C. n/90 rad/sec.

Fractions represent divisions, when the numerator (number on top) and the denominator (number on the bottom) have different signs it means that the quotient between both numbers is negative.

For example

-When the numerator is negative:

The quotient is negative, you can directly write it as a negative fraction

- When the denominator is negative:

The quotient will also be negative, so the fraction can be expressed as a negative fraction too

- When both values have the same sign, then the quotient is positive:

Answer:

  a)  V = (8 -4/3π)r³

  b)  2048(2 -π/3) cm³ ≈ 1951.34 cm³

Step-by-step explanation:

When a sphere is placed in a box the empty space volume is the difference between the box volume and the sphere volume. Here, the box is a cube with the same outside dimensions as the sphere.

__

The side length of the cube is 2r, where r is the radius of the sphere. So, the volume of the cube is ...

  V = s³ = (2r)³ = 8r³

The volume of the sphere is given by the formula ...

  V = 4/3πr³

The volume of the empty space is the difference of these:

  V = (8r³) -(4/3πr³)

  V = (8 -4/3π)r³ . . . . . . . formula for the empty volume

__

For r=8 cm, the empty volume is ...

  V = (8 -4/3π)(8 cm)³ = 4(2 -π/3)(512 cm³)

  V = 2048(2 -π/3) cm³ ≈ 1951.34 cm³ . . . . empty volume

The slope of the given lines are representing that these lines are perpendicular.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given, the pair of the equation are parallel, perpendicular, or neither y=-7/8x-1, 32x-28y=-36

Slope intercept form of both equations of a line

1)  y = -7/8x - 1

it is already in a slope intercept form

2) 32x - 28y = -36

-28y = -32x -36

y = 8/7x + 9/7

Since their slope is inverse and had a negative constant.

The slope of a perpendicular line from the slope of a given line is obtained by taking the negative reciprocal of the slope of the given line. If the slope of the given line is m1 and the slope of a perpendicular line is m2 then we have m2 = -1/m1.

Therefore, The slope of the given lines are representing that these lines are perpendicular.

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Step-by-step explanation:

First, we need to find the unit rate for both. We do this by dividing the price they paid by the number of tickets they got.

47 / 3 = $15.66, which is the unit rate for Diego.

141 / 9 = $15.66, which is the unit rate for Andre.

They did pay at the same rate.

Now do the same thing buy with their gas.

15.12 / 8 = 1.89, which is the rate for Diego.

9.95 / 5 = 1.99, which is the rate for Andre.

They did not pay the same rate, Andre paid more by 10 cents per gallon.

Answer:

4x-2=14

4x=14+2

x=16/4=4

Answer:

10.6

Step-by-step explanation:

53/5

Answer:

\(10\frac{3}{5}\)

Step-by-step explanation:

We divide 53 by 5 which we get 10 3/5

Answer:

17/15

Step-by-step explanation:

Answer:x=7,1

Step-by-step explanation:

Answer:

(A) There is enough evidence to suggest that the proportion of traffic accidents is not same for each day of the week.

(B) Saturday has the highest percentage of traffic accidents.

Step-by-step explanation:

(A)

The Chi-square goodness of fit test would be used to determine if the proportion of traffic accidents is the same for each day of the week.

The hypothesis for the test can be defined as follows:

H₀: The proportion of traffic accidents is the same for each day of the week.

Hₐ: The proportion of traffic accidents is not same for each day of the week.

Assume that the significance level of the test is, α = 0.05.

The Chi-square test statistic is given by:

\(\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}\)

Compute the values in Excel.

The expected frequency for all the days is 60.

The Chi-square test statistic value is, 14.333.

Compute the p-value using the Excel function "=CHISQ.DIST.RT(14.33,6)".

p-value = 0.0262

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected.

The p-value is less than 0.05.

The null hypothesis will be rejected.

Conclusion:

There is enough evidence to suggest that the proportion of traffic accidents is not same for each day of the week.

(B)

Compute the percentage of traffic accidents occurring on each day of the week as follows:

\(\text{Sunday}=\frac{66}{420}\times 100\approx 16\%\\\\\text{Monday}=\frac{50}{420}\times 100\approx 12\%\\\\\text{Tuesday}=\frac{53}{420}\times 100\approx 13\%\\\\\text{Wednesday}=\frac{47}{420}\times 100\approx 11\%\\\\\text{Thursday}=\frac{55}{420}\times 100\approx 13\%\\\\\text{Friday}=\frac{69}{420}\times 100\approx 16\%\\\\\text{Saturday}=\frac{80}{420}\times 100\approx 19\%\)

Saturday has the highest percentage of traffic accidents.

The value of the inequality equation is x ≤ 7

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

4x ≤ 28   be equation (1)

Now , on simplifying the equation , we get

Divide by 4 on both sides of the inequality equation , we get

x ≤ 7

Therefore , the value of x is less than or equal to 7

All the numbers less than or equal to 7 satisfies the condition for x

The value of the equation x ≤ 7 is shown in the graph below

Hence , The value of the inequality equation is x ≤ 7

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Answer:

45⁰

Step-by-step explanation:

We need to find n first.

we are given that GQH is 90⁰ which means that the sum of GQL and LQK should 90⁰ because these are angles on a straight line which adds up to 180⁰.

so,

(4n-15) + 3n = 90⁰

Take the -15 to the other side after opening the brackets.

4n + 3n = 90⁰ + 15

7n = 105⁰

Divide it by 7 for both sides.

n = 15⁰

Now substitute n=15⁰ in you LQK equation.

4n -15

(4×15) -15

60⁰ - 15

45⁰

Answer:

b) y=3

Step-by-step explanation:

Answer:

y = 1 , x = - 1

Step-by-step explanation:

2x - 3y = - 5 → (1)

y = 2 + x ( subtract 2 from both sides )

y - 2 = x or x = y - 2

substitute x = y - 2 into (1)

2(y - 2) - 3y = - 5

2y - 4 - 3y = - 5

- y - 4 = - 5 ( add 4 to both sides )

- y = - 1 ( multiply both sides by - 1 )

y = 1

---------------------------------------------

substitute y = 1 into y = 2 + x

1 = 2 + x ( subtract 2 from both sides )

- 1 = x

The amount invested at 3% is $400, the amount invested at 4% is $700, and the amount invested at 5% is $1000.

Let's assume the amount invested at 4% is x dollars.

According to the given information, the amount invested at 5% is $1000 more than the amount invested at 4%.

So, the amount invested at 5% is (x + $1000).

The total amount invested is the sum of the amounts invested at each rate, which is $2100.

Therefore, we can write the equation:

x + (x + $1000) + (amount invested at 3%) = $2100

Now, we can calculate the amount invested at 3%.

We subtract the sum of the amounts invested at 4% and 5% from the total investment:

(amount invested at 3%) = $2100 - (x + x + $1000) = $2100 - (2x + $1000)

Given that Elena receives $95 per year in simple interest from the investments, we can use the formula for simple interest:

Simple Interest = Principal × Interest Rate

The interest earned from the investment at 3% is (amount invested at 3%) × 0.03, the interest earned from the investment at 4% is (amount invested at 4%) × 0.04, and the interest earned from the investment at 5% is (amount invested at 5%) × 0.05.

According to the problem, the total interest earned is $95.

So we can write the equation:

(amount invested at 3%) × 0.03 + (amount invested at 4%) × 0.04 + (amount invested at 5%) × 0.05 = $95

Now we can substitute the expression for (amount invested at 3%) and solve for x.

Once we have the value of x, we can calculate the amounts invested at 3%, 4%, and 5% using the given information.

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Answer:

her down payment is her down payment.........

Step-by-step explanation:

B sus

Answer:

D. 8​

Step-by-step explanation:

y varies jointly as x and z

y = k(xz)

-------------------------

Find k, the constant of variation

y = 12 when x = -2 and z=3

12 = k(-2 * 3)

12 = k(-6)

k = -2

-------------------------

find y when x is 4 and z is -1

using k = -2

y = -2(4 * -1)

y = -2(-4)

y = 8

If the dimension of the rectangle will be 8 cm by 13 cm. Then the area of the rectangle will be 104 square cm.

It is a polygon with four sides. The total interior angle is 360 degrees. A rectangle's opposite sides are parallel and equal, and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.

The length of a rectangle is 5 cm longer than it’s width if the perimeter of the rectangle is 42 cm.

Let w be the width. Then the length will be (w + 5).

Then we have

Perimeter = 2 (L + w)

           42 = 2 (w + 5 + w)

            21 = 2w + 5

          2w = 16

            w = 8 cm

Then the length will be

L = w + 5

L = 8 + 5

L = 13 cm

Then the area of the rectangle will be

Area = L x w

Area = 13 x 8

Area = 104 square cm

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The scatter plot shows negative correlation because as the plotted values of x increase, the values of y generally decrease.

When two variables are said to have negative correlation, it means that they move in the opposite direction from each other. When one variable is increasing, the other variable is decreasing.

The values of x and y in order of x are:

x  3     4    5   6   7   8   9  

y   6     7    5   4   3    4   2

As shown above, when x increases, y generally decreases and when x decreases, y generally increases. This is therefore a negative correlation relationship.

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Answer:

ther is 33 shepp in the zooo

Step-by-step explanation:

25 +8 =33

The coordinate of point W should be -4 or point C such that the ratio of AW to WF is 1:3

Given data

ratio 1:3

the ratio implies every unit WF is equal to 3 x AW.

hence every unit of AW multiplied by 3 gives WF

using equivalent of fractions in the comparison as follows

1 : 3 = 2 : 6 = 3 : 9

comparing  3 : 9 gives

For point A

Point A = - 7

point A + 3 = -7 + 3 = - 4 = point C

For point F

point F = 5

point F - 9 = 5 - 9 = - 4 = point C

\(\frac{AW}{WF} = \frac{|+3|}{|-9|} = \frac{AC}{FC}\)

Hence the coordinate of point W should be -4 or point C such that the ratio of AW to WF is equal to 1:3

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The lines with a slope larger than f(x) are:

option 4) y = (25/3)*x - 1/2

option 5) (4/5)*y - 16x = -1/2

A general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

First, you can see that the line crosses the y-axis at y = -4, so the line is something like:

y = a*x - 4

And we can see that it crosses the x-axis at x = 2, then we can write the equation:

0 = a*2 - 4

4 = a*2

4/2 = a

2 = a

So the linear equation on the graph is:

y = 2*x - 4

The slope is 2, the linear equations with a slope larger than that are:

option 4) y = (25/3)*x - 1/2

option 5) (4/5)*y - 16x = -1/2

Which can be rewritten as:

y = (5/4)*16x - (5/4)*(1/2)

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The operation used to find out how many choices there are is multiplication.

When you have n choices for one decision and m choices for another decision, the total number of possible combinations of the two decisions is n x m.

This is known as the multiplication principle, which states that the total number of outcomes is equal to the product of the number of choices for each decision.

For example, if you have 3 shirt options and 4 pant options, the total number of possible outfits you can create is 3 x 4 = 12.

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Answer:

y>5

Step-by-step explanation:

i did some but that rest i dont get sorry

The probability that a gorilla in this particular zoo will live between 14.3 and 19.4 years is 86% (or 0.86)

From the Empirical Rule, for a Normal Distribution, approximately:

68% of the data falls within one standard deviation of the mean

95% of the data falls within two standard deviations of the mean

99.7% of the data falls within three standard deviations of the mean

To estimate the probability of a gorilla living between 14.3 and 19.4 years, we first need to standardize these values by subtracting the mean and dividing by the standard deviation:

For 14.3 years: (14.3 - 16) / 1.7 = -1.18

For 19.4 years: (19.4 - 16) / 1.7 = 2

Now we can use a standard normal distribution table to find the probabilities associated with these z-scores:

The probability of a gorilla living less than 14.3 years is approximately the same as the probability of a standard normal variable being less than -1.18, which is about 0.12.

The probability of a gorilla living less than 19.4 years is approximately the same as the probability of a standard normal variable being less than 2, which is about 0.98.

Therefore, the probability of a gorilla living between 14.3 and 19.4 years is approximately the difference between these two probabilities: 0.98 - 0.12 = 0.86.

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Answer:

\((x-4)(x^2+1)\)

Step-by-step explanation:

The correct answer is:

a = 43%

b = 88%

To determine the values of a and b in the relative frequency table, we need to analyze the information provided in the Venn diagram and the given table.

From the Venn diagram, we can gather the following information:

The circle labeled "satellite" has a value of 55.

The circle labeled "cable" has a value of 75.

The overlap between the two circles is labeled as 12.

Using this information, we can complete the table:

First column - "Satellite":

Entries: Satellite, Not satellite, Total

Total: 55 (as given in the Venn diagram)

Second column - "Cable":

Entries: Blank, 51%, Blank

To find the value for the "Cable" entry, we need to subtract the overlap (12) from the total number of cable users (75).

Cable: 75 - 12 = 63

Therefore, the entry becomes: Blank, 51%, Blank

Third column - "Not Cable":

Entries: a, b, Blank

To find the value for "a," we subtract the overlap (12) from the total number of satellite users (55).

a: 55 - 12 = 43

To find the value for "b," we subtract the overlap (12) from the total number of households (100).

b: 100 - 12 = 88

Therefore, the entries become: 43, 88, Blank

Fourth column - "Total":

Entries: Blank, Blank, 100%

The total number of households is given as 100% (as stated in the question).

Therefore, the values of a and b in the relative frequency table are:

a = 43% (rounded to the nearest percent)

b = 88% (rounded to the nearest percent)

Hence, the correct answer is:

a = 43%

b = 88%

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Answer:

a

Step-by-step explanation: