The table shows the number of hours spent practicingsinging each week in three samples of 10 randomlyselected chorus members.Time spent practicing singing each week (hours)Sample 1 45873 56 579 Mean = 5.9Sample 2 68 74 5 4 8 4 5 7 Mean = 5.8Sample 3 8 4 6 5 6 4 7 5 93 Mean = 5.7Which statement is most accurate based on the data?O A. A prediction based on the data is not completely reliable, becausethe means are not the same.B. A prediction based on the data is reliable, because the means ofthe samples are close together.O C. A prediction based on the data is reliable, because each samplehas 10 data points.D. A prediction based on the data is not completely reliable, becausethe means are too close together.

Question:

Solution:

Answer:

Step-by-step explanation:

one dollar of the first day = 3^0

three dollars on the second day = 3^1

nine dollars on the third day = 3^2

twenty-seven dollars on the fourth day = 3^3

Numbers increase 3 times a day, it is an exponential function, powers of 3

The function is going to be:

Given: The equation below

To Determine: The slope, the vertical and horizontal intercept, and the graph of the equation

Solution

The general slope-intercept form of a straight line is as shown below

Let us compare the general slope-intercept form of a straight line to the given

The vertical intercept is the point where the x values is zero

The vertical intercept is y = 5, with coordinate (0, 5)

The horizontal intercept is the point where the y value is zero

The horizontal intercept is x = 5/2, with coordinate (5/2, 0)

The graph of the equation is as shown below

Answer Summary

(a) slope = -2

(b) Vertical intercept, y = 5

(c) Horizontal intercept, x = 5/2

Answer:

Explanation:

Given A = (4, 6) B = (2, 8) C = (5, 10)

SImilarly, for A' = (2, 3) B' = (1, 4) C' = (2.5, 5)

Since it is a dilation, AB/A'B' should be the same as BC/B'C', but that is not the case here.

We have four numbers. We have to know that negative numbers are "smaller" than positive numbers, and when numbers are far away from zero are even "bigger".

The least number is -27/36. It is a negative number.

We can also see that we have some fractions. A fraction is a part of "a whole".

So, as we can see 6 is not a fraction. Therefore, 6 is the greatest number from this list.

So we have the least and the greatest: -27/36 and 6, respectively.

We also need to compare 18/40 and 5/20. What fraction is bigger?

In order to compare them, we need to have two fractions with the same denominator. Then, the fraction with the greatest numerator is "bigger" than the other fraction.

Let us see:

If we divide the numerator and the denominator of 18/40 by 2, we have:

18/2 = 9

40/2 = 20

Then, the equivalent fraction is 9/20 (or 9/20 is equivalent to 18/40). Now, we can compare them:

9/20 and 5/20. So, which one is the greatest? The one with the greatest numerator: 9/20.

Our final list is this way, from least to the greatest as follows:

-27/36, 5/20, 18/40 (9/20), 6.

The total distance that Kim walked in 3 days is 6 2/3 miles. We would convert this distance to mixed numbers. To do this, we would multiply 6 by 3 and add 2. The denominator would still be 3. It becomes

20/3 miles

If she walked 20/3 miles in 3 days, the number of miles that she walked per day would be

total distance/number of days

It becomes

(20/3) / 3

If we change the division sign to multiplication, it means that we would flip 3 such that it becomes 1/3. Thus, we have

20/3 * 1/3 = 20/9

= By converting to mixed numbers, we would find how many 9's are in 20. It is 2. The remainder is 20 - 18 = 2

Thus, the answer is

2 2/9 miles per day

Given:

The point is (-2,3).

The parallel line is y=4x+2.

This is of the form

where slope m=4.

We know that the slope of the parallel lines is equal.

Thus we get the slope m =4 for the required line.

Consider the line equaiton

Substitute x= -2,y=3, and m =4 in the equation to find the value of b.

Adding 8 on both sides of the equation, we get

We get b=11.

Substitute m=4 and b=11 in the equation, we get

Hence the line equation that passes through the point (-2,3) and parallel to y=4x+2 is

start expanding the squared expression using the square of a binomial,

then,

replace in the original function

apply distributive and simplify

Answer:

Obtuse angles (90°–180°) are those that fall within this range. Right angles are those that have a 90 degree angle ( = 90°). Straight angles are those that have a 180 degree ( = 180°) angle.

Any angle more than 90 degrees is deemed obtuse: A straight angle is one with a 180° measurement. A zero angle is one with a measurement of 0°: Angles with measures that add up to 90 degrees are said to be complementary angles: Angles with measures that add up to 180° are referred to as supplementary angles.

We now understand that an obtuse angle is one that is greater than 90 degrees but less than 180 degrees. Obtuse angle examples include 110°, 135°, 150°, 179°, 91°, and more. As a result, all angles between 90° and 180° are obtuse angles.

Hence obtuse angle is one of the angle which is not correct 100 degree angle

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Given

AD = 6.4

BD = 3.6

Find

AC,BC and DC

Explanation

Using Pythogoras theorem in triangle ADC

Using PT in triangle BDC

Adding equation (1) and (2)

Using PT in triangle ABC

Equating above 2 equations

Putting this value of DC in equation (2)

Final Answer

AC = 8

BC = 6

DC = 4.8

the answer is:

Student G earns less money per hour than student F

(a)Recall that the circumference of a circle is given by the following formula:

Where d is the diameter of the circle.

Substituting d=14 ft in the above formula, we get:

(b) Recall that the area of a circle is given by the following formula:

Substituting d=14 ft in the above formula, we get:

Answer:

(a)

Exact solution:

Approximation:

(b) Exact solution:

Approximation:

Answer:

y=5x

Explanation:

The slope-intercept form of the equation of a line is:

First, we find the slope of the line by picking two points from the line.

• The points are (0,0) and (3,15).

Next, the line crosses the y-axis at y=0.

Therefore, the y-intercept, b=0.

Substitute m=5 and b=0 into the slope-intercept form:

The equation that gives the proportional relationship of the graph is y=5x.

We know the equation of a line is given by:

where m is its slope and b its interpcetion with y - axis.

We know the slope equation is

If (x₁, y₁) = (-2, -9) and (x₂, y₂) = (2, 11) then replacing in the slope equation

we are asked to determine the area of a circle with a diameter of 6 cm. To do that we will use the following formula for the area of a circle:

Replacing the value of the radius:

Replacing the value of pi:

Solving the operations:

Sidney will use 57 cups of soda for 19 cups of ice cream.

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

From the table,

The ratio of cups of ice cream to cups of soda.

3.5 cups ice cream = 10.5 cups of soda

Divide both sides by 3.5.

1 cup of ice cream = 3 cups of soda

Multiply 19 on both sides.

19 cup of ice cream = 57 cups of soda

Thus,

57 cups of soda.

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ANSWER :

EXPLANATION :

The resulting rational number is √100

Rational numbers:

A rational number is a number that can be represented a/b where a and b are integers and b is not equal to 0.

Given,

Here we have the following list of numbers

√75, -√25, 2√7, √100, √0.36, √0.0144, √3/7 , -√36/49

Now, we need to identify whether these are the rational numbers or not.

AS per the definition of rational number,

When we take the  root for the value √75, we get 8.660 that is a non-whole square root, 8.660 is not a rational number.

The value -√25 takes the negative value so it is not a rational number.

The number 2√7, this one also produce on-whole square root, so this one is not a rational number.

The value of √100 is 10, and it is a rational number.

The value of √0.36 is 0.6 which is less than 0, so it is not a rational number.

The value of √0.0144 is 0.012 which is less than 0, so it is not a rational number.

The value of √3/7 this one also produce on-whole square root, so this one is not a rational number.

The value -√36/49 takes the negative value so it is not a rational number.

Therefore, the rational number is √100.

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In order to sketch the graph we need to find the vertex and two more points to connect with the vertex.

To do so set the inside of absolute value to zero:

The y-coordinate of same is:

So the vertex is (- 3, - 1).

Since the coefficient of the absolute value is positive, the graph opens up, and the vertex is below the x-axis as we found above.

Find the x-intercepts by setting the function equal to zero:

We have two x-intercepts (-4, 0) and (-2, 0).

Now plot all three points and connect the vertex with both x-intercepts.

Now, from the graph we see there is no domain restrictions but the range is restricted to y-coordinate of the vertex.

It can be shown as:

Answer:

Step-by-step explanation:

Given absolute value function:

[tex]f(x)=|x+3|-1[/tex]

The parent function of the given function is:

[tex]f(x)=|x|[/tex]

Graph of the parent absolute function:

Translations

[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}.[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}.[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}.[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}.[/tex]

Therefore, the given function is the parent function translated 3 units left and 1 unit down.

If the vertex of the parent function is (0, 0) then the vertex of the given function is:

⇒ Vertex = (0 - 3, 0 - 1) = (-3, -1)

To find the y-intercept, substitute x = 0 into the given function:

[tex]\implies \textsf{$y$-intercept}=|0+3|-1=2[/tex]

To find the x-intercepts, set the function to zero and solve for x:

[tex]\implies |x+3|-1=0[/tex]

[tex]\implies |x+3|=1[/tex]

Therefore:

[tex]\implies x+3=1 \implies x=-2[/tex]

[tex]\implies x+3=-1 \implies x=-4[/tex]

Therefore, the x-intercepts are (-2, 0) and (-4, 0).

To sketch the graph:

Note: When sketching a graph, be sure to label all points where the line crosses the axes.

The domain of a function is the set of all possible input values (x-values).

The domain of the given function is unrestricted and therefore (-∞, ∞).

The range of a function is the set of all possible output values (y-values).

The minimum of the function is the y-value of the vertex:  y = -1.

Therefore, the range of the given function is:  [-1, ∞).

Answer:

a. The total weight

b. 2 times the weight of Jet

c. The weight of Fido

d. The total weight

Explanation:

We know that Fido weighs 10 pounds more than Jet and together they weigh 46 pounds. So, if j represents Jet's weight, the bar model is:

Now, we can answer each part as:

a. 46 represents the total weight of the small dogs

b. 2j represents 2 times the weight of Jet

c. j + 10 represents the weight of Fido because its weight is the weight of Jet j added to 10.

d. 2j + 10 also represents the sum of the weights of the small dogs.

So, the answers are:

a. The total weight

b. 2 times the weight of Jet

c. The weight of Fido

d. The total weight

If two lines are parallel, it means that they have the same slope. The given lines are

y = 2x - 4 and y = x - 4

The slope intercept form of a straight line is expressed as

y = mx + c

Where

m represents slope

c represents y intercept

By comparing both equations with the slope intercept form,

For y = 2x - 4

Slope, m = 2

For y = x - 4

Slope, m = 1

We can see that the slopes are not eaual. Thus, the lines are not parallel.

Also, we can conclude that there is no line that passes through the point (3,5) that is parallel to both lines

There is no line that passes through the point (3,5) that is parallel to both lines.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

If two lines are parallel, it means that they have the same slope. The given lines are

y = 2x - 4 and y = x - 4

By comparing both equations with the slope-intercept form,

For y = 2x - 4

Slope, m = 2

For y = x - 4

Slope, m = 1

We can see that the slopes are not equal. Thus, the lines are not parallel.

Also, we can conclude that there is no line that passes through the point (3,5) that is parallel to both lines.

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The equations that are equivalent to the formula PV = nRT are  V = nRT/P,  n = PV/RT and R = PVnT. Option B, C and D

From the information given, we have that;

The Ideal Gas law is represented as;

PV = nRT

Given that;

Subject of formula is described as the variable expressed in terms of other variables in an equation.

It is made to stand on its own on one end of the equality sign.

Let's make 'V' the subject of formula

Divide both sides by the coefficient of V which is the variable 'P', we have;

V = nRT/P

Making 'R' the subject of formula, we have

R = PV/ nT

Making 'n' the subject of formula, we have;

n = PV/RT

Hence, the equations are options B, C and D

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The complete question:

In physics, the Ideal Gas Law describes the relationship among the pressure, volume, and temperature of a gas sample. This law is represented by the formula PV = nRT, where P is the pressure, V is the volume, T is the temperature, n is the amount of gas, and R is a physical constant. Which of the equations below are equivalent to the formula PV = nRT? Select all that apply. A. P = VnRT B. V = nRT/P C. n = PV/RT D. R = PVnT E. T = nR/PV

Answer:Pv=NRT

Step-by-step explanation:

Given:

Cost of a CD = $14.50

Markup =30%

If markup 30% then:

So the cost is:

markup cost is 18.85

new uniforms = 3

Total amount spent = $486

Amount spent per player = $486 /3 = $162

=====================================================

Explanation:

mu = 500 = mean

sigma = 100 = standard deviation

We'll need the z score for x = 620

z = (x - mu)/sigma

z = (620-500)/100

z = 1.20

The task of finding P(x > 620) is equivalent to P(z > 1.20)

Use a Z table or a Z calculator to find that

P(Z < 1.20) = 0.88493

which leads to

P(Z > 1.20) = 1 - P(Z < 1.20)

P(Z > 1.20) = 1 - 0.88493

P(Z > 1.20) = 0.11507

This converts to 11.507% and rounds to 11.5%

About 11.5% of the students score higher than a 620 on the SAT.

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

Another approach:

Open your favorite spreadsheet program. The command we'll be using is called NORMDIST. The template is this

NORMDIST(x, mu, sigma, 1)

If you were to type in [tex]\text{=NORMDIST(620,500,100,1)}[/tex] then you'll get the area under the normal distribution to the left of x = 620

This means [tex]\text{=1-NORMDIST(620,500,100,1)}[/tex] will get us the area to the right of 620. The result of that calculation is approximately 0.11507 which leads to the same answer of 11.5% as found earlier.

When using a spreadsheet, don't forget about the equal sign up front. Otherwise, the spreadsheet will treat the input as text and won't evaluate the command.

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

Another option is to use a TI83 or TI84 calculator.

Press the button labeled "2nd" in the top left corner. Then press the VARS key. Scroll down to "normalcdf"

The template is

normalcdf(L, U, mu, sigma)

The mu and sigma values aren't anything new here. But the L and U are. In this case L = 620 is the lower boundary and technically there isn't an upper boundary since it's infinity. Unfortunately the calculator wants a number here, so we just pick something very large. You could go for U = 99999 as the stand in for "infinity". The key is to make sure it's more than 3 standard deviations away from the mean.  

So if you were to type in [tex]\text{normalcdf(620,99999,500,100)}[/tex] then the calculator will display roughly 0.11507, which is in line with the other answers mentioned earlier.

As you can see, there are many options to pick from. Searching out "normal distribution calculator" or "z calculator" will yield many free options. Feel free to pick your favorite.

Explanation

Step 1

we have a perpendicular line, its slope is

two lines are perpendicular if

replace

so, our slope is 3/2

Step 2

using slope=3/2 and P(-5,2) find the equation of the line

Answer:

5x+3

Step-by-step explanation:

Three more than means we add 3

The product of 5 and a number means some number multiplied by 5 call it 5x

so three more than 5x is 5x+3.

The greatest number of bags of lunches Mr. Edmonds can make = 40, And , in each bag there will be one apple and one banana chips bag.

In the above question, the following information is given :

Mr. Edmonds wants to pack lunches for the schools field trip where he wants to put the same number of apples and the same number of bananas in each bag of lunches

We are given that,

Number of available bananas chips packs = 40

Number of available apples = 50

We need to find the greatest number of bags of lunches Mr. Edmonds can make

As the pair should be an even number and we have less number of banana chips bags than apples. So the number of lunches which can be packed with equal number of apples and banana chips bags depend on banana chips bags

Therefore, the greatest number of bags of lunches Mr. Edmonds can make = 40

And , in each bag there will be one apple and one banana chips bag.

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If the amount of time spent is lesser than or equal to 250, so the price is $29, so we have the first part of the piecewise equation:

Then, for an amount of time greater than 250, the extra minutes are charged by 0.35 per minute, and this extra cost will add the fixed cost of $29, so the second part of the equation is:

The option that shows the correct piecewise equation is option A.

We have the next given set for distances (in miles) to the nearest for 13airport families:

10, 13, 15, 15, 20, 26, 27, 28, 30, 32, 34, 37, 39

The minimum is the least number value. Then:

Minimum =10

In this case, we have 13 data, so :

- The middle number is the median:

10, 13, 15, 15, 20, 26, 27, 28, 30, 32, 34, 37, 39

Now, the lower quartile is given by the next equation:

Replacing:

The lower quartile is in the fourth position:

Lower quartile = 15

The upper quartile is given by the next equation:

The upper quartile is located in the 11th position:

Upper quartile = 34

The interquartile range is given by:

IQR=upper quartile - lower quartile

IQR=34-15

The interquartile range =19