A group of 4 people go to a restaurant and the bill without tax comes to $105.73. Tax is 6%. Remember to round to the nearest hundredth because this is money. After tax is added, you want to leave a 20% tip on the new total. The group of 4 people decides to split the total cost equally. How much will each person pay?

Completely random design is used in this experiment.

In the given question,

A business wants to investigate the efficacy of a novel painkiller.

100 participants who suffer from chronic discomfort are enlisted.

Each participant takes the brand-new painkiller for two weeks before switching to a placebo for an additional two weeks.

The order of the tablets is chosen at random for each participant, and the subjects are unaware of which pill contains the actual medication.

Each subject's variance in total pain will be measured by researchers.

We have to check what type of experiment design is this.

As we can see in the question that they recruit 100 volunteers with chronic pain and each subject they use new pain relief medicine for a 2-week period and a placebo for another 2-week period.

They assign each subject randomly.

As we know that in a completely random design, treatments are randomly assigned to sampling material. The usual method for doing this is to make a list of the treatments and give each one a random number.

So we can see that completely random design is used in this experiment.

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The equation of the graph in vertex form is: y = 1x – 3| + 5.

The graph in the diagram above is a graph of an absolute value equation. The equation can be expressed as y = a|x – h| + k (vertex form), where the vertex is represented as (h, k).

The vertex of the graph is the coordinate of the point where the two straight lines meet.

Given the graph above, the vertex is at point (3, 5). Therefore:

h = 3

k = 5

The graph opens up, so the value of a = 1.

Substitute h = 3 and k = 5 into y = a|x – h| + k:

y = 1|x – 3| + 5

y = 1x – 3| + 5

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The difference of the given fractions is 9/20.

The given fractions are 3/4 and 3/10.

Subtracting fractions include the subtraction of two or more fractions with the same or different denominators. Like fractions can be subtracted directly but for unlike fractions we need to make the denominators same first and then subtract them.

The difference of the given fractions is

3/4 - 3/10

= 15/20 - 6/20

= 9/20

Therefore, the difference of the given fractions is 9/20.

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The equation of the line that is perpendicular to y = 5 and that passes through the point (-7, -5) is x = -7.

We have to find the equation of a line that is perpendicular to y = 5 and that passes through the point (-7, -5).

y = 5 is a line that is parallel to the x-axis hence, the line perpendicular to it will be parallel to the y-axis.

Also, the line touches (-7,-5) hence, it will touch the line y = 5 at (-7,5).

Hence, the line perpendicular  to y = 5 and that passes through the point (-7, -5)  is x = -7.

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Answer:

5

Step-by-step explanation:

Answer: θ≈18,553°

Step-by-step explanation:

[tex]\displaystyle\\sin\theta=\frac{7\ cm}{22\ cm} \\\\sin\theta=\frac{7}{22}\\\\\theta=arcsin\frac{7}{22} \\\\\theta\approx18.553^0[/tex]

The sale price of a basketball backboard set that sold for $79 is discounted by 15% is $67.15.

We will use the method of percentage to solve the given question.

We are given:

A basketball backboard set that sold for $79 is discounted by 15%.

We need to find the sale price after the discount is given.

We will subtract the discount from the marked price.

Let us solve this;

Sale price = marked price - discount

Sale price =  $79 - $79 * 15%

Sale price =  $79 - $79 * 15 / 100

Sale price =  $79 - $11.85

Sale price = $67.15

So, the sale price will be $67.15.

Thus, the sale price of a basketball backboard set that sold for $79 is discounted by 15% is $67.15.

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The probability will be 0.9940.

The provided parameters are

p = 0.05  (the true proportion or the mean )

n = 269   ( sample size )

we can calculate standard deviation as follows

σ = [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]

σ = 0.0132

Now the values that 'x' can take are

x = [tex]x_{1}[/tex] ±  [tex]x_{2}[/tex]

x = 0.05 + 0.03, 0.05 - 0.03

x = 0.08 , 0.02

Also the z-score is

z = (x - μ)/σ

z = [tex]\frac{0.08-0.05}{0.0132}[/tex]  , [tex]\frac{0.02-0.05}{0.0132}[/tex]

z = 2.27 , -2.27

we now find the p-values for the z-scores

p values are = 0.9970 , 0.0030

The difference in these values will give the probability

∴ P = 0.9970 - 0.0030

P =  0.9940

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The equation that are equivalent to the equation 1/4 (8x + 56) = 20 are 56 + 8x = 80 and 2x = 6

The equation is

1/4 (8x + 56) = 20

Solve the equation

8x + 56 = 80

8x = 80 - 56

8x = 24

x = 24/8

x = 3

The first equation is

56 + 8x = 80

8x = 80 - 56

8x = 24

x = 24/8

x = 3

The second equation is

14 = 20 - 8x

8x = 20 - 14

8x = 6

x = 6/8

x = 3/4

The third equation is

2x + 14 = 5

2x = 5 - 14

2x = -9

x = -9/2

The fourth equation is

2x = 6

x = 6/2

x = 3

Hence, the equation that are equivalent to the equation 1/4 (8x + 56) = 20 are 56 + 8x = 80 and 2x = 6

The complete question is:

Which equations are equal to this equation? Select all that apply.

1/4 (8x + 56) = 20

a. 56 + 8x = 80

b. 14 = 20 - 8x

c. 2x + 14 = 5

d. 2x = 6

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The equation that could be used to find q is q = 110-0.15(110) where q equal the price of a quarter-page ad after the markdown.

According to the question,

We have the following information:

Cost of a quarter-page ad cost = $110

Mark down in the price = 15%

Now, q represents the price of a quarter-page ad after the markdown.

(Note that when we remove the sign of % means that the number has to be divided by 100.)

So, the equation will be the difference of the markdown price from the original price:

q = 110-(15/100)110

q = 110-0.15*110

q = 110-0.15(110)

Hence, the correct option is the third one.

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The composite figure has a total area of 12 square centimeters.

In this problem we find the area of a composite figure, which is the result of subtracting the areas of four triangles of same dimensions from the area of the entire square. Now we proceed to determine the area:

A = (6 cm)² - 4 · 0.5 · (2 cm) · (3 cm)

A = 36 cm² - 2 · (12 cm²)

A = 36 cm² - 24 cm²

A = 12 cm²

The area of the composite figure is 12 square centimeters.

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Answer:$ 17.28

Step-by-step explanation:

Answer:

x=27 I think

Step-by-step explanation:

1 = 3x + 15

2 = 6x + 3

We can solve by putting both equations together.

Let's multiple the top equation by -2

-2(1 = 3x + 15)

-2 = -6x - 30

2 = 6x + 3

0=x - 27

27=x

Answer:

3

Step-by-step explanation:

what it means by generator is the continuance of the multiplication process so 1x3=3 and then 3x3=9 and so on.

Linear Regression analysis has three key applications:

(1) evaluating predictor strength, (2) anticipating an effect, and as well (3) trend forecasting.

Linear regression is a fundamental and widely used method of predictive analysis. The overall goal of regression is to investigate two things:

Regression analysis has three key applications:

The formula y = c + b*x defines the simplest form of the regression equation with one dependent so one independent variable,

where,

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1. An exponential equation modeling the skateboard's value, y, in x years is y = 380 x 1.07ˣ.

2. The value of the skateboard will be worth $610.28 in seven years.

An exponential equation is a mathematical function that depicts an equation with variable exponents.

The exponential function is always written in the form of y = abˣ.

Where a = the constant or initial value, b = the continuous growth rate, and x  or t = the time variable.

Y represents the value that we are looking for after the growth rate has been applied for several (t) years.

The current worth of the skateboard = $380

Annual increase = 7% = 0.07

Number of years = 7 years

Y = 380 x 1.07⁷

= 380 x 1.606

= 610.28

= $610.28

Thus, in seven years, using the exponential equation, the skateboard will be worth $610.28.

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Step-by-step explanation:

X-intercept is where the line crosses the x-axis or where y = 0

So, put y = 0 in the given equation

4x + 2(0) = 12

4x = 12

x = 12/4

x = 3

⇒ ∠AOC+∠AOE+∠EOD=180°(angles on a straight line are supplementary)

16°+90°+2y=180°

[tex]106+2y=180\\2y=180-106\\2y=74\\\frac{2y}{2} =\frac{74}{2} \\y=37[/tex]

∴y=37°

∠AOC+∠COF∠BOF=180°(angles on a straight line are supplementary)

16°+90°+4x=180

[tex]106+4x=180\\4x=180-106\\4x=74\\\frac{4x}{4} =\frac{74}{4} \\x=18.5[/tex]

∴x=18.5°

The equation for the absolute value function is y = -2lx-4l + 2

An absolute value function is what?

A function that surrounds an algebraic expression in absolute value symbols is called as an absolute value function. Remember that a number's distance from 0 on the number line represents its absolute value. The definition of the absolute value parent function is given as follows: f(x)=x if x>00 if x=0 if x0.

Y=a| x+h |+k is the form of the equation for an absolute value function. Also:

The graph's vertex is (h,k).

The range of the graph is y≥k for a>0 and its domain is a set of all real numbers.

The range of the graph is y≤k when a0, and its domain is a set of all real numbers.

X=h is the symmetry axis.

If a>0, it opens up; if a0, it opens down.

The graph of y=a| xh |+k can be created by translating the line graph y=| x | by h units horizontally and k units vertically.

If | a | 1 and if | a | >1, the graph of y=a| x | is wider than the graph of y=| x | and narrower.

So here (h,k)=(4,2)
range of y≤2

and its narrower so a≥1
hence the equation is y = -2 l x-4 l +2


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Answer:

-22 1/3

Step-by-step explanation:

We should start by subtracting both sides of the equality by 21.

After doing this, we get that -67=3m.

Furthermore, we can divide both sides by 3 and get -67/3=m.

However, this is an improper fraction, not a mixed number.

If we divide -67 by 3, we get -22 1/3.

Therefore, m= -22 1/3

Answer:

y = -5/3 - 3

Step-by-step explanation:

Since it's given a graph, we can use rise over run to figure it out

We pick 2 points that are integers on the graph , which means two points on the graph that the line goes through

Example- I picked (-3, 2) and (0, -3), you can indicate them so you don't forget or anything

We now draw a triangle formed by those two points (a line that goes from (-3, 2) to (-3, -3) and a line from (0, -3) to (-3, -3)

Rise (Which is the height of the triangle you just drew) is 5 units, but it's going down, so -5

The base (Run) is 3 units. Using rise/run, the slope is -5/3

The y-intercept, which is at the point where the graph crosses the y-axis, is -3.

The slope intercept form is y=mx+b, where m = slope and b = y-intercept, so the equation of the graph is y = -5/3x -3

64 is the standard deviation and the width of the confidence interval are both doubled .

What is standard deviation in math?

Margin of error(E)=0.5

Standard deviation(σ)=1.55

Significance level(α)=100%-99%=1% or 0.01

From Z distribution Critical value table

the Critical value(Zc)=2.58 at significance level=0.01

we know formula for the Margin of error

 E = Zc  * σ/√n

0.5 = 2.58 * 1.55/√n

√n = 2.58 *  1.55/0.5

 √n = 3.999/0.5

  √n = 7.998

  n = ( 7.998)²

 n = 63.968004

Aproximately

  n = 64

the realtionship between the sample size and margin of error is inversly proportional.

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Answer:

y+3=2x+4

Step-by-step explanation:

Answer:

2.12

Step-by-step explanation:

Discussion

The answer is given in the graph I've made for you. The distance you want is a contained in a line that is perpendicular to the given line and goes through (2,-1). If I have not interpreted this correctly please leave a comment under the question and I will edit it. I have ignored the 4.

The steps needed are

Givens

line y = -x + 4

point (2,-1)

Solution

The slope of the second line is

m1 * m2 = - 1

m1=  -1                From the given equation

m2 = ?

-1 * m2 = - 1

m2 = 1

Find the equation of the new line

x = 2

y = - 1 from the given point

-1 = 2 + b             Subtract 2 from both sides

-1 - 2 = 2-2 + b    Combine

-3 = b

Equation of the new line

y = x - 3

Intersection point of the two lines

y = -x + 4

y = x - 3              Add The xs cancel

2y = 1                  Divide by 2

y = 1/2

1/2 = -x + 4          Subtract 4 from both sides

1/2 - 4 = -x + 4 -4 Combine        

-3 1/2  = -x            Multiply both sides by - 1

3 1/2 = x

So the intersection point is (3.5, 0.5)

Find the distance between (2,-1) and (3.5,0.5)

d = sqrt( (2 - 3.5)^2 + (-1 - 0.5)^2 )

d = sqrt( (-1.5)^2 + (-1.5)^2 )

d = ( 1..5 * sqrt(2) )

d = 2.12

The likelihood that the measured distance will be shorter than the actual distance is equal to 0.3085.

In this case, the chance that the measured distance will be less than the true distance will be determined using the z-score formula. The z score is a normal score that adheres to a normal distribution with a mean and standard deviation of 0 and 1, respectively.

Given that,

Mean, μ = 50

Standard deviation, σ = 100

Less than 0% of the time, the overestimation is likely.

Consequently, the necessary probability is P (X ≤ 0)

Now,

P (X ≤ 0) = P [(X − μ) / σ ≤ (0 − μ) / σ]

P (X ≤ 0) = P [Z ≤ (0 − 50) / 100]

P (X ≤ 0) = P [Z ≤ − 0.5]

Excel formula for the probability mentioned above:

=NORMDIST(-0.5,0,1,1)

P (X ≤ 0) = 0.3085

0.3085 is the likelihood that the measured distance will be shorter than the actual distance.

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Answer

it’s because of the amplitude the value in the front controls the height

Step-by-step explanation:

A.

The length of AD in the parallelogram is 143 cm.

A parallelogram is a quadrilateral with opposite sides parallel to each other. The opposite angles of a parallelogram are equal. Two adjacent or consecutive angles of a parallelogram are supplementary.

Hence,

2x + 72 + 2x - 20 = 180

4x + 52 = 180

4x = 180 - 52

4x = 128

divide both sides by 4

4x / 4 = 128 / 4

x = 32

Therefore,

∠A = 2(32) + 72 = 64 + 72 = 136 degrees

z = 136°

Therefore,

AC = BC = BD = AD

AC = z + 7

AC = 136 + 7

AC = 143 cm

Hence,

AD = 143 cm

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