A clothing store sells T-shirts, t, for $8 a shirt; shorts, s, for $12; and hats, h, for $10 each. The store earned $406 in revenue last month. The store sold three times as many T-shirts than hats, and twice as many shorts as hats. Using the substitution method, how many T-shirts, shorts, and hats did the store sell?

Answer:

538,650

Step-by-step explanation:

We must first find how many errors there will be if filed manually and if filed electronically

Manually: 2,700,000*20% or 2,700,000*.2

Answer: 540,000 errors

Electronically: 2,700,000*.05% or 2,700,000*.0005

Answer: 1,350 errors

We must then find the difference; 540,000-1,350=538,650

Answer:

538,650.

Step-by-step explanation:

Number of erroneous manual returns = 20% of 2.7 million

= 0.20 * 2,700,00 = 540,000.

Number for electronically returned =  2,700,000 * 0.0005 = 1350.

Difference = 540,00 - 1350 = 538,650.

Answer:

The equation of the parabola is (x - 4)² = 8(y - 4)

Step-by-step explanation:

* Lets revise the equation of a parabola

- If the equation is in the form (x − h)² = 4p(y − k), then:  

• Use the given equation to identify h and k for the vertex, (h , k)

• Use the value of h to determine the axis of symmetry, x = h

• Use h , k and p to find the coordinates of the focus, (h , k + p)  

• Use k and p to find the equation of the directrix, y = k − p

* Now lets solve the problem

∵ The directrix is y = 2

∴ The equation is (x - h)² = 4p(y - k)

∴ The focus is (h , k + p)

∵ The focus is (4 , 6)

∴ h = 4

∵ k + p = 6 ⇒ (1)

∵ The directrix is y = k - p

∴ k - p = 2 ⇒ (2)

* Add (1) and(2) to find k

∴ 2k = 8 ⇒ ÷ 2 for both sides

∴ k = 4

* Substitute the value of k in (1) to find p

∵ 4 + p = 6 ⇒ subtract 4 from both sides

∴ p = 2

* Now lets write the equation

∴ (x - 4)² = 4(2)(y - 4) ⇒ simplify

∴ (x - 4)² = 8(y - 4)

* The equation of the parabola is (x - 4)² = 8(y - 4)

Answer:

g(x)=7x-3

Step-by-step explanation:

the y axis becomes -3 because 6-9=-3

ANSWER

B.

[tex] 4n + 2[/tex]

EXPLANATION

The given pattern is:

6, 10, 14, 18, 22, ...

The first term if the pattern is a=6.

The common difference among the terms is

[tex]d = 10 - 6 = 4[/tex]

The general pattern can be found using the formula:

[tex]f(n)=a+d(n-1)[/tex]

We substitute the values to get,

[tex]f(n)=6+4(n-1)[/tex]

Expand to get;

[tex]f(n)=6+4n-4[/tex]

[tex]f(n) = 4n + 2[/tex]

The correct answer is B.

Answer:

Sum of the interior angles = (n-2) x 180°

where

n is the number of sides of the polygon

Step-by-step explanation:

The formula for the sum of the interior angles of a polygon is:

[tex]sum=(n-2)*180[/tex]

where

[tex]sum[/tex] is the sum of the interior angle of the polygon

[tex]n[/tex] is the number of polygons

Let's check the formula using an example:

We want to find the sum of the interior angles of a square, we know that a square has 4 sides, so [tex]n=4[/tex].

Replacing values

[tex]sum=(4-2)*180[/tex]

[tex]sum=(2)*180[/tex]

[tex]sum=360[/tex]

We can apply the same procedure to any convex polygon with n sides.

Answer:

         Sum of the interior angles = (n - 2) × 180°.

         Where n is the number of sides of the polygon.

Explanation:

The formula (n - 2) × 180° is valid for any convex polygon.

A convex polygon is one whose interior angles (every interior angle) measure less than 180°.

You can prove and remember that formula following this reasoning:

For example, for a pentagon, a polygon with 5 sides, you can can draw 5 - 2 = 3 diagonals from one vertex, and so obtain 3 triangles. Then the sum of the interior angles shall be (n - 2) × 180° = (5 - 2) × 180° = 3 × 180° = 540°.

Answer:

[tex]P(B | A)=0.4=40\%[/tex]

Step-by-step explanation:

Call A to the event in which there are electrical storms.

Call B the event in which there is hail.

Then, by definition.

The Probability of B given A is:

[tex]P(B | A)=\frac{P(B\ and\ A)}{P(A)}[/tex]

We know that:

[tex]P(B\ and\ A)= 10\%=0.1\\\\P(A) = 25\%=0.25[/tex]

Therefore

[tex]P(B | A)=\frac{0.1}{0.25}[/tex]

[tex]P(B | A)=0.4=40\%[/tex]

The conditional probability of hail given thunderstorms is calculated using the formula P(Hail | Thunderstorms) = P(Thunderstorms and Hail) / P(Thunderstorms). Given the probabilities of 10% for thunderstorms with hail and 25% for thunderstorms, the result is a 40% probability of hail when thunderstorms are present.

The student is asking to find the conditional probability of hail occurring, given that thunderstorms are already happening. This is a probability question that involves understanding and applying the concept of conditional probability.

The probability of thunderstorms is given as 25% (or 0.25 in decimal form), and the probability of thunderstorms with hail is given as 10% (or 0.10 in decimal form). To find the probability of hail given thunderstorms, you use the formula for conditional probability which is P(Hail | Thunderstorms) = P(Thunderstorms and Hail) / P(Thunderstorms). The 'given' part is represented by the condition after the vertical bar '|', and the numerator is the probability of both thunderstorms and hail occurring.

Substituting the given values into the formula, we get P(Hail | Thunderstorms) = 0.10 / 0.25 = 0.40 or 40%. Therefore, if thunderstorms are occurring, there is a 40% probability that there is also hail.

Answer:

x(x-3)(x+2)

Step-by-step explanation:

x^3-x^2-6x

First subsitute out x:

x(x^2-x-6)

Find the multiples of the x's:

x(x-3)(x+2)

Answer:

x(x-3)(x+2)

Step-by-step explanation:

x^3-x^2-6x

First subsitute out x:

x(x^2-x-6)

Find the multiples of the x's:

x(x-3)(x+2)

Step-by-step explanation:

Answer:

110.9 sq ft

Step-by-step explanation:

split the equilateral triangle into two right triangles. use pythagorean theorem to discover that the height is about 13.86 ft. use the area formula, A= (1/2)bh

A=(1/2)(8)(13.86)= 110.9

Answer:

A =  64√2 ft² = approx. 90.5 ft²

Step-by-step explanation:

Because this is an equilateral triangle, the interior angles are also equal and are 60° each.  We'll use the area-of-a-triangle formula, A = (1/2)(b)(h), to find the area of this particular triangle.  We see from the diagram that the base is 16 ft.  

Drawing an imaginary line representing the height of this triangle, and letting h represent this height, we get

sin 60° = opp / hyp = h / (16 ft) = 1/√2, so that

 h        1

----- = -----

16      √2                              16

and so √2*h = 16, and h = -------

                                              √2

                                                                                        1      16     16

Then the area of this blue triangle is A = (1/2)(b)(h) = ---- * ----- * -------

                                                                                         2      1       √2

           128           128√2

or A = -------     = ------------ = 64√2 ft² = approx. 90.5 ft²

            √2               2

Answer: OPTION B

Step-by-step explanation:

Let be "x" the acceptable lengths for the rod.

You know that the ideal length of the metal rod is 30.5 centimeters and the measured length may vary from the ideal length by at most 0.015 centimeters.

Therefore, knowing this, you can say that the acceptable lengths must be:

[tex]30.5cm-0.015cm\leq x\\\\30.485\leq x[/tex]

[tex]x \leq 30.5cm+0.015cm\\\\x\leq 30.515[/tex]

Therefore, the range of acceptable lengths for the rod is the following:

[tex]30.485\leq x\leq 30.515[/tex]

This range matches with the one shown in the option B.

Answer:

The man should not buy the policy.

Step-by-step explanation:

A life insurance policy is a contract that pays a sum assured to a policy holder upon death, either immediately or at the end of year of death. The policy holder pays a premium amount in advance to cater for the future benefits (sum assured).

In the scenario presented, the man is 30 years old with a probability of 0.994 of survival with respect to mortality. The high probability of being alive through the year implies that the man is very unlikely to die and thus the probability of receiving the coverage amount is too minimal

Answer: The expected value is $400, so the man should buy the insurance policy.

Step-by-step explanation:

(150,000-500)(.006)-500(.994)=400

We want (x - h)^2 + (y - k)^2 = r^2.

This circle is not centered at the origin.

The point we want is in the form

(h, k).

We are given that h = -4 and k = 2.

We also know that the radius is 9.

Let r = 9 leading to (9)^2 or 81.

We know substitute in the form given above for circles not centered at the origin.

(x - (-4)^2 + (y - 2)^2 = 81

(x + 4)^2 + (y - 2)^2 = 81

Answer: Choice C

Answer:

The missing number is 8

Step-by-step explanation:

Hope this helps (3

it will be 297,088 as the answer

Answer:

it is 1/6 because there is 6 colors and the probability of getting 3 which is 1 number is 1 out of 6

Step-by-step explanation:

Answer:

A. how much of the students time is spent on social media during school hours.

B. By using some kind of selection technique Like Having students draw number from a hat, who ever have the specific numbers will take her survey.

C. The population for Sofies research would be a rate of 5/2. For every 5 people who take the survey only 2 turned it in.

D. She would conclude that 1 out of every 2 or 50 percent of students use social media while doing school work.

Step-by-step explanation:

The percent of all high school students who use social media while doing schoolwork, if Sofie uses only the completed surveys, is 50%.

Random sample is the way to choose a number or sample in such a manner that each of the sample of the group has an equal probability to be chosen.

For a research project, students are asked to study how often students at an online high school look at social media while doing schoolwork.

Sofie can use the question as, how many times a student look at social media while doing schoolwork?

Sofie can use a simple random sampling technique to select a simple random sample of students to take her survey.

As Sofie gives out 80 surveys but receives only 32 completed surveys. Thus, the sample is data of 32 completed surveys and the population is total 80 surveys.

Of the 32 students who completed surveys, 16 said they use social media while doing schoolwork. Thus, the percentage is,

[tex]P=\dfrac{16}{32}\times100\\P=50\%[/tex]

Hence, the percent of all high school students who use social media while doing schoolwork if Sofie uses only the completed surveys, is 50%.

Learn more about the random sample here;

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Answer:

[tex]\large\boxed{D.\ D(0,\ -4)}[/tex]

Step-by-step explanation:

The formula of a midpoint of the segment"

[tex]\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)[/tex]

We have the points X(3, -4) and Y(-3 -4).

Substitute:

[tex]x=\dfrac{3+(-3)}{2}=\dfrac{0}{2}=0\\\\y=\dfrac{-4+(-4)}{2}=\dfrac{-8}{2}=-4[/tex]

Answer:

x = 17

Step-by-step explanation:

For the parallelogram to be a rhombus then then the diagonal must bisect the given angle, thus

3x - 11 = x + 23 ( subtract x from both sides )

2x - 11 = 23 ( add 1 to both sides )

2x = 34 ( divide both sides by 2 )

x = 17

ANSWER

A.

It satisfies the top equation but not the bottom equation.

EXPLANATION

The given equations are;

2x-3y=18

5x+3y=3

When we substitute x=6 and y=-2 into the top equation we get,

2(6)-3(-2)=18

12+6=18

18=18

This is true. Hence the point satisfy the top equation.

But when we substitute x=6 and y=-2 into the bottom equation we get,

5(6)+3(-2)=3

30-6=3

24=3

Hence the bottom equation is not satisfied.

The first choice is correct.

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A scatter plot has a good fit when data points cluster near the line of best fit and show a clear positive or negative correlation, suggesting a strong relationship between variables. A bad fit is characterized by scattered data points with no apparent pattern and large residuals between the points and the line, indicating a weak or no correlation.

When a scatter plot has a good fit, it means that the line of best fit accurately represents the trend in the data. This line minimizes the distances, or residuals, between itself and all the points on the graph. You can tell if a scatter plot has a good fit if the data points form a pattern that closely follows the line of best fit, indicating that the variables have a strong correlation. Conversely, a bad fit is evident when the data points are widely scattered and do not follow a distinct pattern, suggesting a weak or no correlation between the variables.

Signs of a Good Fit in Scatter Plots

Signs of a Bad Fit in Scatter Plots

Whether the X and Y variables in a scatter plot are good candidates for linear regression depends on the aforementioned signs. If there is a clear positive or negative correlation and data points approximate a linear trend, they are good candidates for linear regression.

1 - 8

2 - 16

3 - 32

x - +200

Each lemonade has a profit of $1, so the number of cups of lemonade he sells is the same as the amount of dollars he has. You just need to add each previous day's total to the next day's, doubling the amount of cups from the previous day's for each new day.

4 - (32 x 2 = ) 64

8 + 16 + 32 + 64 = 120. We need at least $80 dollars more, so we continue.

5 - (64 x 2 = ) 128

120 + 128 = $248.00 That's more than enough, so Tom will have enough money for his bike after the fifth day of selling lemonade.

Answer:

(0, 1)

Step-by-step explanation:

all of the points are the same number away: 2√5

Answer:

  (0, 1)

Step-by-step explanation:

A, B, and C are points on a circle. You are being asked to find the center of the circle. You can do that any of several ways.

I find it useful to plot the points on a graph. Doing so reveals that AB is perpendicular to BC, so ABC is a right triangle, and the center you want is the midpoint of the hypotenuse (AC).

  (A+C)/2 = ((2, -3) +(-2, 5))/2 = (2-2, -3+5)/2 = (0, 1) . . . . . coordinates of center

___

From a construction point of view, the center of the circle is the point of intersection of the perpendicular bisectors of the chords. In the attached, we have used a geometry program to draw the perpendicular bisectors of AB and BC. They meet at (0, 1).

___

From an algebra point of view, the points on the circle with center (h, k) and radius r satisfy the equation ...

  (x -h)^2 +(y -k)^2 = r^2

Filling in the point values, you get three equations in the three unknowns (h, k, r):

Finding the difference between any two pairs of these will result in two linear equations in h and k, so are easily solved.

  First - second: (4 -4h +h^2) +(9 +6k +k^2) -(16 -8h +h^2) -(9 -6k +k^2) = r^2 -r^2

  -12 +4h +12k = 0 . . . simplify

  h +3k = 3 . . . . . . . . . put in standard form

  Second -third: (16 -8h +h^2) +(9 -6k +k^2) -(4 +4h +h^2) -(25 -10k +k^2) = r^2 -r^2

  -4 -12h +4k = 0 . . . . simplify

  3h -k = -1 . . . . . . . . . put in standard form

Now, we can add 3 times the second of these equations to the first to find h:

  (h +3k) +3(3h -k) = (3) +3(-1)

  10h = 0

  h = 0

Then either of the equations can be used to find k = 1.

The center is (h, k) = (0, 1).

Answer:

  216

Step-by-step explanation:

Each of the three digit positions can have any of 6 values, so there are ...

  6^3 = 216

possible numbers that can be formed.

The equation that has (-2, -1) as a solution is, C. 4x - y = -7.

To determine if an ordered pair is a solution to an equation, plug in the values of the coordinates of the pair into the equation to check if it will make it true

If it makes it true, it is a solution, otherwise, it is not if it does not make the equation true.

Given the ordered pair, (-2, -1) substitute the values to check which will be true:

-4(-2) - (-1) = 7

9 = 7 [not true].

4x + y = -7

4(-2) + (-1) = -7

-9 = -7 [not true]

4x - y = -7

4(-2) - (-1) = -7

-7 = -7

Therefore, the equation is: C. 4x - y = -7.

Learn more about the solution of an equation on:

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Complete Question:

The ordered pair (-2,-1) is a solution to which

of the following equations?

A.-4x - y = 7

B. 4x+y=-7

C. 4x - y = -7

D. -4x + y = -7

The degree of a polynomial is the highest exponent.

The highest exponent in this equation is 17x^4

The degree is 4.

Answer:

x = 11

Step-by-step explanation:

If a radius bisects a chord ( as in the lower chord )then it is perpendicular to the chord.

Thus both chords are equidistant from the centre ( both 12 ) and are therefore congruent.

Hence x = 11

Multiply the price before the tip by .20

[tex]45 * .20 = 9[/tex]

Add 9 to the total:

[tex]45 + 9 = $54[/tex]

So, the total cost for Thom's meal is $54

The total cost for Thom's meal is $54.

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct," "pct," and occasionally "pc" are also used, the percent sign, " percent ", is frequently used to signify it. A % is a number without dimensions and without a standard measurement.

Given

Thom's restaurant bill is $45

20 percent tip = 20 % of 45 = 20/100*45 = 9

Total cost =  Thom's restaurant bill + 20 percent tip

                = 45+ 9 = 54

Therefore, The total cost for Thom's meal is $54.

To know more about percentages refer to :

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Answer:

2. simplifying multiplication property of equality

3. x - 2 = 8

5. x = 10 , addition property of equality

Step-by-step explanation:

* Lets explain how to solve the problem

- The equation is [tex]\frac{x-2}{4}=2[/tex]

- The value of x is 10

- We want to a statement reason to each step to complete the proof

* Lets write each step with statement reason

1. [tex]\frac{x-2}{4}=2[/tex]  ⇒ Given

2. [tex]4(\frac{x-2}{4})=4*2[/tex]  ⇒ simplifying multiplication property of equality

3. x - 2 = 8  ⇒ Simplifying

4. x - 2 + 2 = 8 + 2                      

5. x = 10  ⇒  addition property of equality

- In step 2 we multiply both sides by 4 to cancel the denominator of

 the left hand side (simplifying multiplication property of equality)

- Then we simplify the two sides to get (x - 2 = 8)

- Then we add two to both sides to cancel -2 in the left hand side

- Then after adding we find (x = 10) , (addition property of equality)

* The answer is:

2. simplifying multiplication property of equality

3. x - 2 = 8

5. x = 10 , addition property of equality

x = 180° - 67° - 52°

x = 61°

So, the value of x is 61°

Answer:

  x = 30°

Step-by-step explanation:

x° is the other acute angle of the right triangle with 60° as the acute angle at the center of the circle. (The tangent line makes a right angle with the radius at the point of tangency.)

(x+4)(x-3)=30

x^2 +x -12 =30

x^2 +x =42

x^2 +x -42 =0

(i solved it by factorising: _x^2 × -42)

x^2 -6x +7x -42 =0

x(x-6) +7(x-6) 0

(x-6)(x+7)=0

x=6; x=-7

since it's a length, x can't be a negative number, so it must be 6

Answer:

The answer is 62208

Step-by-step explanation:

The reason is because 18*2=36 12*2=24 and 36*2=72

36*24*72=62208

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