Mary, Kevin, and Ahmad served a total of 126
 orders Monday at the school cafeteria. Kevin served 6
 more orders than Mary. Ahmad served 4
 times as many orders as Kevin. How many orders did they each serve? 

Answer:

Yes. These outcomes are mutually exclusive; they cannot occur simultaneously in one spin of the wheel.

Step-by-step explanation:

It's the answer trust

Answer:

6.

Step-by-step explanation:

14x=84

x=84÷14

x=6

Hope this helps!

Answer:

x=6

Step-by-step explanation:

14x = 84

Divide each side by 14

14x/14 = 84/14

x =6

Answer:

$104,000

The probability that the average salary between two groups is the same, is actually low. It could be close, but it's quite difficult to get the same exact amount.

Answer:

8n=20+6(n-2)

Step-by-step explanation:

n is the number of GB

Plan A has no initial fee and charges 8$ per each GB

So A has an equation that is y=0+8n or just y=8n.

Plan B has 20 for the first 2 GB and $6 for each addition GB after the first 2.

So B has an equation  that is y=0+20+6(n-2) assuming n is 2 are greater.

So the two equations are y=8n and y=20+6(n-2).

We want Plan A to be the same as Plan B.

So we need to solve:

8n=20+6(n-2).

Let's check our equation:

Distribute:

8n=20+6n-12

Subtract 6n on both sides:

2n=20-12

2n=8

Divide both sides by 2:

n=4

Plan A charges 8 dollars ber GB, so plan A charges 4(8)=32 dollars.

Plan B charges 20 dollars for the first 2GB and 6 dollars for each GB after so we used 4 which means we are spending 20+6(2)=20+12=32 dollars.

They are the amount so n=4 is right.

I am very late to answer this, but I want to help others who struggle on this question! The answer and explanation is in the picture, thank me later! :)

For this case we have that[tex]\frac {1} {4}[/tex]of the songs are jazz.

The total songs are 100.

So:

[tex]\frac {1} {4} = 0.25\\\frac {3} {4} = 0.75[/tex]

This tells us that 25% of the songs are jazz and 75% of the songs are pop.

[tex]\frac {1} {4} + \frac {3} {4} = \frac {4} {4} = 1[/tex]

So, the correct option is option D.

Answer:

Option D

Answer:

4names: z3, zt, zstu, zuts

Answer:

c. 19.73

Step-by-step explanation:

The Cosine rule shows states that:

a²=b²+c²-2bcCos A, where a, b and c are the sides of the triangle and A is the angle at vertex A.

A=108°

b=9

c=15

Substituting with the values above gives:

a²=9²+15²-(2×9×15 Cos 108)

a²=389.4346

a=19.73

Answer:

[tex]M=-\frac{d^2F}{kn}[/tex]

Please look at what I assumed your equation was:  [tex]F=-\frac{kMn}{d^2}[/tex].

Step-by-step explanation:

I'm going to pretend that says:

[tex]F=-\frac{kMn}{d^2}[/tex].

Please correct me if I'm wrong.

We want to solve for M.

The very first thing I'm going to do is multiply both sides by [tex]d^2[/tex].

[tex]d^2F=-kMn[/tex]

Now I'm going to divide both sides by -kn:

[tex]\frac{d^2F}{-kn}=\frac{-kMn}{-kn}[/tex]

Simplifying:

[tex]\frac{d^2F}{-kn}=M[/tex]

Sometimes people don't like the negative on bottom; just move it to the center:

[tex]-\frac{d^2F}{kn}=M[/tex]

[tex]M=-\frac{d^2F}{kn}[/tex]

Answer:

11.84 feet

Step-by-step explanation:

The given scenario will form a right angled triangle where the distance and the point from where the angle of elevation is measured will be the base of the triangle.

We know

Angle of elevation = x = 28 °

Height of pole = p = 6.3 feet

Distance from pole = d= ?

So,

[tex]tan\ x = \frac{p}{b}\\ tan\ 28 = \frac{6.3}{b} \\0.5317 = \frac{6.3}{b}\\b = \frac{6.3}{0.5317}\\b=11.84\ feet[/tex]

Therefore, the distance from the pole is 11.84 feet ..

Answer:

-10 is the answer

Step-by-step explanation:

Diving 10 feet below sea level increases the pressure by 1 atmosphere (ATA), causing the body's air pockets to compress. Divers must equalize the pressure by adding air to these airspaces on the descent.

When diving 10 feet below sea level, the pressure increases by 1 atmosphere (ATA). According to Boyle's law, the volume of gases decreases as pressure increases. The increase in pressure can compress the body's air pockets, such as those in the ears and lungs, which can cause discomfort or injury. Divers must equalize the pressure by adding air to these airspaces on the descent.

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Answer:

Step-by-step explanation:

The equation is in vertex form ...

  y = a(x -h)² +k . . . . . . . . vertex (h, k) and vertical scale factor "a"

  y = (x +2)² -1

so, you can read the vertex coordinates directly from the equation:

  (h, k) = (-2, -1)

__

The line of symmetry is the vertical line through the vertex, so has equation ...

  x = h

  x = -2 . . . . for this parabola

__

The vertex is always a point on the graph.

At x-values ±1 either side of the vertex, the vertical distance from the vertex is "a". Here, that is 1 unit, so the points (-3, 0) and (-1, 0) are on the graph.

At x-values ±2 either side of the vertex, the vertical distance from the vertex is a·2². Here that is 4 units, so the points (-4, 3) and (0, 3) are on the graph.

This is basically what the vertex form of the equation is telling you.

Lisa must swim 30 laps to cover the distance of 450 meters, by dividing the total distance she wants to swim by the length of one lap.

To calculate how many laps Lisa must swim to cover a distance of 450 meters, we divide the total distance she wants to swim by the length of one lap. Since the length of one lap is 15 meters, we perform the following calculation:

Therefore, Lisa needs to swim 30 laps to reach her goal of swimming 450 meters this week.

Answer:

12 hours

Step-by-step explanation:

If you divide 168 by 8, you get 21 which is the rate that Austin receives for every hour of work. Then divide 252 by 21 to find how many hours he worked and you get the answer, 12.

Answer:

[tex]\large\boxed{f^{-1}(x)=\dfrac{1}{3}x+5}[/tex]

Step-by-step explanation:

[tex]f(x)=3x-15\to y=3x-15\\\\\text{exchange x to y and vice versa:}\ x=3y-15\\\\\text{solve for}\ y:\\\\3y-15=x\qquad\text{add 15 to both sides}\\\\3y=x+15\qquad\text{divide both sides by 3}\\\\y=\dfrac{x}{3}+5\\\\y=\dfrac{1}{3}x+5[/tex]

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}x+5y=10\\3x+y=1&\text{multiply both sides by (-5)}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}x+5y=10\\-15x-5y=-5\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-14x=5\qquad\text{divide both sides by (-14)}\\.\qquad x=-\dfrac{5}{14}\to x\approx-0.357\\\\\text{Put it to the equation}\ 3x+y=1:\\\\3(-0.357)+y=1\\-1.071+y=1\qquad\text{add 1.071 to both sides}\\y=2.071[/tex]

Answer:

[tex]\large\boxed{(f-g)(x)=4^x+x+5}[/tex]

Step-by-step explanation:

[tex](f-g)(x)=f(x)-g(x)\\\\f(x)=4^x+3x,\ g(x)=2x-5\\\\(f-g)(x)=(4^x+3x)-(2x-5)=4^x+3x-2x+5=4^x+x+5[/tex]

Answer:

[tex]8.33\%[/tex]

Step-by-step explanation:

we know that

The total removed by milling is equal to (3.00"-2.75")=0.25"

In this problem 3.00" represent the 100%

so

using proportion

Find out how much percentage represent the total removed by milling

[tex]\frac{3.00}{100}=\frac{0.25}{x}\\\\x=100*0.25/3.00\\\\x=8.33\%[/tex]

Final answer:

To find the percentage of the block removed by milling, subtract the final size from the original size, divide by the original size, and multiply by 100. A 0.25" reduction from a 3.00" block represents an 8.33% decrease.

Explanation:

The question asks us to calculate the percentage of material removed from a block through the milling process. To find the percentage reduction, we start by determining the difference in size before and after the milling, which is 3.00" - 2.75" = 0.25". The next step is to divide the amount removed by the original size and then multiply by 100 to get the percentage. The calculation is as follows:

Find the difference: 3.00" - 2.75" = 0.25" (amount removed)

Calculate the percentage: (0.25" / 3.00") × 100 = 8.33%

Therefore, 8.33% of the original block is removed by milling.

Answer:

B., D., E.

Step-by-step explanation:

[tex] \sqrt{9} \cdot \sqrt{100} = [/tex]

[tex] = \sqrt{9 \cdot 100} [/tex]      This is choice B.

[tex] = \sqrt{900} [/tex]          This is choice E.

[tex] = 30 [/tex]              This is choice D.

Answer:

x+3y=14

Step-by-step explanation:

Standard form for an equation of a line is ax+by=c . Some books have restrictions on a,b, and c.

So first thing I'm going to do is state the equation I'm going to use to get there.

I'm going to use the point-slope form because we are given a point (2 really) and we can find the slope using two points (we have).

Line up points and subtract. You will then put second difference over the first difference.  This will give you the slope. You could just use (y2-y1)/(x2-x1).

( -1 , 5)

-(  2, 4)

-----------

-3     1

So the slope is 1/-3 or -1/3 .

So the equation in point-slope form, y-y1=m(x-x1), is y-4=-1/3 (x-2) .

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

First step: I'm going to get rid of the fraction by multiplying both sides by 3.

3y-12=-1(x-2)

Second step: Distribute

3y-12=-x+2

Third step: add x on both sidfes

x+3y-12=2

Fourth step: add 12 on both sides

x+3y=14.

[tex]\huge{\boxed{\text{vertical}}}[/tex]

[tex]\text{A vertical line is a line where all of the x values are the same.}[/tex]

[tex]\text{In this case, both of the points have an x value of -3, so this is a vertical line.}[/tex]

Answer:$96.75

Step-by-step explanation:

Answer: $64.5

Step-by-step explanation:

First let’s do 40% of 150 (40%=4/10): 4/10*150=60

The price of the bike is $60

7.5%=7.5/100, however we cannot have a decimal in a fraction so we multiply by 2/2 and get 15/200.

Next let’s multiply 60 by 15/200: 6*15/200=4.5

Then we add 60 which is the price of the bike, with 4.5, which is the tax to get the total of $64.5

Answer:

C.

Step-by-step explanation:

The remote exterior angles are angle x and y

The sum of two  interior angles (x +y) is equal to the value of exterior angle (z)

m∠x=(5n-19)°

m∠y=(n+7)°

m∠z=(144-6n)°

Equate as

∠x+∠y=∠z

(5n-19)° +(n+7)°=(144-6n)°

5n-19+n+7=144-6n----------------------collect like terms

5n+n+6n=144+19-7

12n=156---------------------divide both sides by 12 to get value of n

n=156/12= 13°

substitute value of n is equations

∠x=(5n-19)° =(5×13)-19 =65-19=46°

∠y=(n+7)°= (13+7)=20°

Measure of remote exterior angle will be 20°+46°=66° (From the theorem of interior angles and exterior angles)

Answer:

To simplify the expression let's multiply and divide by (8+5i) as follows:

[tex]\frac{(11+19i)(8+5i)}{(8-5i)(8+5i)}= \frac{207i-7}{89}= 2.32i - 0.08[/tex]'

Now, we have successfully removed the imaginary number from the denominator.

Answer:

6 and x

Step-by-step explanation:

h(-4)

=|-4-2|

=|-6|

=6

.

h(-x+2)

=|-x+2-2|

=|-x|

=x

Answer:

See below.

Step-by-stepexplanation:

The slope = rise/run

= (7- -5)/(-3-1)

=  12/-4

= -3

In point slope form:

y - y1 = -3(x - x1)

y - (-5) = -3(x - 1)

y + 5 = -3(x - 1) <--------- Point slope form.

y + 5 = -3x + 3

y = -3x - 2. <----------Slope-intercept form.

Answer:

y = -3x - 2

Step-by-step explanation:

If a line passes through (1.-5) and (-3, 7), the appropriate equation for the line in point-slope form is, y = -3x - 2.

Answer:

2(x - 3) = 7

Step-by-step explanation:

Set up the difference part first.

x - 3

Now deal with the "Twice."

2(x - 3)

Next equals

2(x - 3) =

And finally what it equals

2(x - 3) = 7

Answer:

2(x-3)=7

Step-by-step explanation:

Dont take my word for it double check with someone else.

Answer:

The average absolute deviation (or mean absolute deviation (MAD)) about any certain point (or 'avg. absolute deviation' only) of a data set is the average of the absolute deviations or the positive difference of the given data and that certain value (generally central values). It is a summary statistic of statistical dispersion or variability. In the general form, the central point can be the mean, median, mode, or the result of any other measure of central tendency or any random data point related to the given data set. The absolute values of the difference, between the data points and their central tendency, are totaled and divided by the number of data points.

Measures of dispersion

Edit

Several measures of statistical dispersion are defined in terms of the absolute deviation. The term "average absolute deviation" does not uniquely identify a measure of statistical dispersion, as there are several measures that can be used to measure absolute deviations, and there are several measures of central tendency that can be used as well. Thus, to uniquely identify the absolute deviation it is necessary to specify both the measure of deviation and the measure of central tendency. Unfortunately, the statistical literature has not yet adopted a standard notation, as both the mean absolute deviation around the mean and the median absolute deviation around the median have been denoted by their initials "MAD" in the literature, which may lead to confusion, since in general, they may have values considerably different from each other.

Mean absolute deviation around a central point

Edit

For arbitrary differences (not around a central point), see Mean absolute difference.

The mean absolute deviation of a set {x1, x2, ..., xn} is

{\displaystyle {\frac {1}{n}}\sum _{i=1}^{n}|x_{i}-m(X)|.} \frac{1}{n}\sum_{i=1}^n |x_i-m(X)|.

The choice of measure of central tendency, {\displaystyle m(X)} m(X), has a marked effect on the value of the mean deviation. For example, for the data set {2, 2, 3, 4, 14}:

Mean Absolute Deviation (MAD) is a measure of the average distance between each data point and the mean of the dataset. It is calculated by finding the absolute value of the difference between each data point and the mean, and then averaging those differences. MAD is a robust statistic, less sensitive to outliers compared to standard deviation.

Mean Absolute Deviation (MAD) is a statistical measure used to quantify the average deviation of data points from the mean or average of the dataset. To calculate MAD, you follow these steps:

The mean is the sum of all data divided by the number of data points, while the median is the middle value of an ordered dataset. MAD is more robust than standard deviation as it is not affected as much by extreme values. For example, if we have a dataset of exam scores, the standard deviation tells us how scores are spread out from the mean, which could be influenced by extremely high or low scores. On the other hand, MAD gives us a measure of spread that is more resilient to outliers in the data.

Relative Average Deviation (RAD) is similar to MAD, but it expresses the deviation as a percentage of the mean and hence provides a relative measure of spread.

The Inverse of the function f(x) = (1/3)^x is derived by swapping x and y and solving for y, resulting in f^-1(x) = log base (1/3) of x.

To find the Inverse of a function in the form f(x) = (1/3)^x, you need to interchange x and y and solve for y.

So, the Inverse of the function f(x) = (1/3)^x is first represented as x = (1/3)^y. However, we need to isolate y. We can do this by taking a logarithmic function on both sides. It turns out that y = log base (1/3) of x.

In other words, the inverse of f(x) = (1/3)^x is f^-1(x) = log base (1/3) of x.

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Answer:

c

Step-by-step explanation: