a group of people are waiting in line for a movie premier. every 14th person in line will win a free movie ticket . every 10th person will receive a gift card of 30 dollars. which person is the first to win both prizes.if there are 200 people in line how many will receive both prizes?

Answer: 4/5 × 10/16 = 1/2

Step-by-step explanation:

Multiply the numerators and then multiply the denominators to get: 4/5 * 10/16 = 40/80

Simplify with the GCF (40): 40/80 / 40/40 = 1/2

And that's your simplified answer :)

The dimensions of the rectangular poster are:

Width = 3 inches.

Length = 9 inches.

A rectangle usually has a long side called the length, and a shorter side called the width.

The area of the rectangle is calculated by multiplying the length and the width together. Therefore, formula for the area of a rectangle is:

Area = (length)(width).

The rectangular poster has the following parameters:

Let x represent the width of the rectangular poster.

Width of the rectangular poster = x

Length of the rectangular poster = 3x

Area of the rectangular poster = 27 in.².

Plug in the values

(x)(3x) = 27

3x² = 27

Divide both sides by 3

3x²/3 = 27/3 [division property of equality]

x² = 9

Take the square root of both sides

√x² = √9

x = 3

Width of the rectangular poster = x = 3 inches.

Length of the rectangular poster = 3x = 3(3) = 9 inches.

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The coordinates of vertices U(1 , -3) , V(4 , -3) , T(1 , -4) , W(4 , -4) becomes

U' (1, 3) , V'(4 , 3) , T'(1 , 4) , W'(5 , 4) after the reflection across x-axis occurs.

In the question given 4 coordinates,

U(1 , -3)

V(4 , -3)

T(1 , -4)

W(5 , -4)

the reflection across x-axis

U(1 , -3) →U' (1, 3)

V(4 , -3) → V'(4 , 3)

T(1 , -4) → T'(1 , 4)

W(5 , -4) → W'(5 , 4)

so  after the reflection across the x axis the coordinates of the vertices becomes ,

U' (1, 3) , V'(4 , 3) , T'(1 , 4) , W'(5 , 4)

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Answer:

take the LCM of the three numbers. Since 2 is a multiple of 4, you can ignore the two and just take the LCM of 4 and 3.5. Since 3.5 is a decimal, the LCM is just 3.5*4 which is 14. That is how many minutes after 8:00 they will flash together again.

Step-by-step explanation:

Because the prisms are stacked onto one another, they have a total volume of 320 cubic units

The possible question is added at the end of the solution and as an attachment

From the attached figure, we have the following parameters

The volume of a prism is the prodict of its dimensions

This means that

Cube = Length^2

Cuboid = Base area * Height

So, we have the following equations

Shape 1 = a^3

Shape 2 =a^2b

Shape 3 =a^2c

Substitute the known values in the above equation

So, we have

Shape 1 = a^3 = 4^3 = 64

Shape 2 =a^2b = 4^2 * 6 = 96

Shape 3 =a^2c = 4^2 * 10 = 160

Add the above values

Prism volume =64 + 96 + 160

Evaluate the sum

So, we have

Prism volume = 320

Hence, the volume of the three prisms is 320 cubic units

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To graph an inequality, treat the <, ≤, >, or ≥ sign as an = sign, and graph the equation.

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Statistics can be misleading by faulty sampling and inaccurate graphs

The gathering, characterization, analysis, and drawing of inferences from quantitative data are all tasks that fall under the purview of statistics, a subfield of applied mathematics. Probability theory, linear algebra, and differential and integral calculus play major roles in the mathematical theories underlying statistics.

Given Data

Statistics can be misleading.

Statistics is quite powerful. So much so that some of the most significant decisions made by individuals and organizations were based on statistics. The adage that "statistics don't lie" may actually be true. However, statistics can occasionally be deceptive, and depending on how they are used, the same type of data can demonstrate the opposite tendency.

Sometimes inaccurate information is purposefully supplied in order to influence individuals and forward a goal. Similarly, it can also occur as a result of negligence or just failing to comprehend the data.

Knowing the various ways statistics can be abused will help you spot them and avoid making decisions based on skewed or inaccurate information.

1)Faulty sampling

The info can due to the sampling strategy employed to gather the data, be deceptive. For instance, the size and kind of the sample used in any statistics has a big impact. Since many surveys and polls are directed at specific groups of people who give particular answers, the sample sizes tend to be tiny and skewed.

2)Inaccurate graphs

Data manipulation can be done in a variety of ways, not just by using descriptive statistics incorrectly. You can identify them if you are aware of them.

3)Chooser Data Display

This type of data visualization might be perplexing and exaggerate differences. If you look at the data and consider how much variety there is in the numbers, you can spot false graphs in the media.

4)Absence of Baseline

Checking to see if the start-at-zero criteria has been adhered to is another approach to spot a deceptive graph. In a graph, The New York Times demonstrated that its sales are double those of The Daily Telegraph. However, if you look at the scale, you can see that the sales difference is just about 10%.

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The product of the numbers 758 and 93 is 70494

The numbers are given as

758 x 93

By using the standard algorithm i.e. the partial product method, we have the following equation

758 x 93 = 758 x (90 + 3)

Open the bracket

So, we have the following equation

758 x 93 = 758 x 90 + 758 x 3

Evaluate the products

758 x 93 = 68220 + 2274

Next, we evaluate the sum

758 x 93 = 70494

This means that the final product is 70494

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Answer:  The correct answer is:

Addition and multiplication are operations you can use to join equal groups.

Step-by-step explanation: Confirmed correct.

Answer:

The answer would be 36.

Step-by-step explanation:

I linked the steps I used to get this answer in the image, I hope this helps :)

A rational number is a number that can be written in the form:

Where p and q are coprimes. We are asked for finite sets, we can rule out options 3 and 4. In the set in option 2 the first element is:

This number cannot be written a ratio. We can rule out option 2.

All the elements in the set from option 1 can be written in the form p/q.Thus, the answer is the first option.

The cost of a t-shirt is $25, the cap costs $20 and the stuffed animal costs $15

Let t-shirts be represented by x, the cap is represented by y and stuffed animals are represented by z

Items purchased by family:

4 t-shirts + 1 cap + 1 stuffed animal

The total cost of the items was = $135

Equation: 4x+y+z=135--------(1)

Items purchased by couple 1:

2 t-shirts + 1 cap + 3 stuffed animals

The total cost of the items was = $115

Equation: 2x+y+3z=115------(2)

Items purchased by couple 2:

2 t-shirts + 1 cap + 1 stuffed animals = $85

Equation: 2x+y+z=85------(3)

Subtracting equation (3) from (2) we get:

2z = 30

z = 15

Substituting the value of z=15 in equations (1) and (3) we get the following equations:

4x+y+15=135

4x+y=120------(4)

And, 2x+y+15=85

2x+y=70-------(5)

Multiplying equation (5) with 2 and subtracting equation (4) we get:

4x+2y=140

4x+y=120

y = 20

So, x = 25

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Answer: maturity value = $17816.67

Explanation:

The formula for calculating simple interest is expressed as

I = PRT

where

I is the interest

P is the principal or initial amount

R is the interest rate

T is the time in years

From the information given,

P = 17104

R = 12.5% = 12.5/100 = 0.125

We would convert 4 months to years. Recall

12 months = 1 year

4 months = 4/12 = 1/3

Thus, the interest is calculated as follows

I = 17104 x 0.125 x 1/3 = 712.67

maturity value = principal + interest

maturity value = 17104 + 712.67

maturity value = $17816.67

The polynomial area of the framed picture is (27 + 2x) * (15 + 2x) and the value is 693 square units

The area of a shape is the amount of space on the shape

For most regular quadrilaterals, you multiply the side lengths to determine the area

The given parameters are

Width = 15

Length = 27

Also, we have

Length of the frame = x

This means that the area of the framed picture is

Area = (Length + 2 * Length of the frame) * (Width + 2 * Length of the frame)

Substitute the known values in the above equation

Area = (27 + 2x) * (15 + 2x)

In (a), we have

Area = (27 + 2x) * (15 + 2x)

When x = 3, we have

Area = (27 + 2 x 3) * (15 + 2 x 3)

Evaluate

Area = 693

Hence, the area is 693 square units

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Answer:

In ten year you will be 10 years older than you are now and so will your brother. The 6 years difference will remain if no one dies.

Step-by-step explanation:

You are z years old

Your brother is 6 years younger than z years; z - 6 years

In 10 years time, you will be z + 10 years

Your brother will be z - 6 years + 10 years = z + 4 years

OR

In 10 years time, you will be z + 10 years

You brother is still 6 years younger than you, so is z + 10 years - 6 years = z + 4 years

Answer:

Tom is currently 5 and Bill is currently 11

Step-by-step explanation:

Let b = Bill's current age

Let t = Tom's current age

We have 2 unknowns so we need to equations to solve for this.

b = t + 6  

(b-3) = 4(t-3)  We have to subtract 3 from both Tom and Bill's current age

b- 3 = 4t - 12  Distribute the 4 and then substitute in t + 6 for b.

t + 6 -3 = 4t -12  Combine like terms

t + 3 = 4t -12  Subtract t from both sides of the equation

3 = 3t - 12  Add 12 to both sides of the equation

15 = 3t  Divide both sides by 3

5 = t  Tom is 5.  Since Bill is 6 years old, her is 11.

Check:

11 = 5+ 6

Three years ago, Tom would have been 2 and Bill would have been 8.  Bill is four times older than Tom.  2x4 = 8.

The water pressure on the submerged object is given by d = P ÷ 64

Pressure is the force applied perpendicularly to an object's surface in relation to the area across which it is applied (symbol: p or P).  

a. The given formula is is P=64d

or , d = P ÷ 64

b. at a pressure of 672

d = 672  ÷ 64

or, d = 10.5 feet

Hence the pressure is 672 pounds per square foot at a depth of 10.5 feet.

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Answer: 2 million is 2,000 thousands.

Step-by-step explanation:

2,000,000 = 2 million

1,000 = 1 thousand

2,000 thousands = 2 million

Solution:

iven the figure below:

Where

Using the secant-secant theorem expressed as

Given that th e satellite signal reaches Bora-Bora at 38,000 km and Greenland which is an additional 20,000km, this implies that

If the distance from the satellite to Rapa Nui is 45,000 km, this implies that

The total distance from the satelite to St. Helen is expressed as

From equation 1,

Substituting the values, we have

divide both sides by 45000,

Hence, the signal will travel a distance of 48977.77777 km from the satellite to St. Helen.

The factored expression of the expression given as 12b - 30 is 6(2b - 5)

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

12b - 30

Factor out the common factor from the expression

So, we have

12b - 30 = 3 * 4b - 3 * 10

Factor out 3 from the expression

So, we have

12b - 30 = 3(4b - 10)

Factor out 3 from the expression

So, we have

12b - 30 = 6(2b - 5)

The expression above cannot be further simplified

This means that the expression has been completely factored and cannot be further factored

Hence, the equivalent expression of the expression given as 12b - 30 when it is factored by grouping is 6(2b - 5)

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A) The intersection of subsets A and B is; A ∩ B = {E3, E7, E9}

B)  The union of subsets A and B is; A ∪ B = {E1, E2, E3, E7, E9}

C) No, the union of A & B is not collectively exhaustive

We are given;

Sample space;

S = [E1, E2, E3, E4, E5, E6, E7, E8, E9, E10]

A = [E1, E3, E7, E9]

B = [E2. E3, E, E9]

A) Now, the intersection of subsets A and B would be the values that are common to both sets. This gives us;

A ∩ B = {E3, E7, E9}

B) The union of the subsets A and B with be the combination of all terms in both subsets and this gives us;

A ∪ B = {E1, E2, E3, E7, E9}

C) The union of A & B is not collectively exhaustive because it does not contain all the data available in the sample space.

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Accordig to the given line, City P is above sea level, and City R is below sea level because they are above and below zero, respectively.

The net cost equivalent is the price the customer pays after deducting all the discounts. To find the net cost equivalent given an amount n of discounts, we use the following formula

Where d is the discount written as a decimal.

In our problem, we have a series discount of 20/10/10/20, therefore, the net cost equivalent is

Answer:

9

Step-by-step explanation:

→ Multiply by every value to see

735 - ( 24.99 × 9 ) = 510.09

∴ He has to add money in the 9th month otherwise he will be charged

Answer:

9

Step-by-step explanation:

24.99 x 9 = 224.91

735 - 224.91 = 510.09

The choice that can be used to find the expression (three times the number increased by six is twenty-four) is (C) 3m + 6 = 24.

So,  three times the number increased by six is twenty-four:

Therefore, the choice that can be used to find the expression (three times the number increased by six is twenty-four) is (C) 3m + 6 = 24.

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The correct question is given below:

Grace is thinking of a number. She states that three times the number increased by six is twenty-four. Which choice can be used to find

(A) 3(2-6) = 24

(B)3-6=24

(C) 3m + 6 = 24

(D) 9x2=18+6=2

The first 3 pair of opposite integers are (-1,1),(-2,2) and (-3,3).

Given that,

We have to find the first 3 pairs of opposite integers.

Opposite integers means the "counting numbers" (sometimes known as integers), as well as zero, are integers. The pairs of integers known as opposite integers share the same absolute value, or, to put it another way, are equally spaced from zero. The numbers 10 and -10 are the opposites. The numbers 43 and -43 are the opposites.

So,

Keep in mind that our whole numbers are our integers. The negative and positive iterations of a number together are called a pair of opposite integers.

We get, the first 3 pair of opposite integers are (-1,1),(-2,2) and (-3,3).

Therefore, the first 3 pair of opposite integers are (-1,1),(-2,2) and (-3,3).

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Answer:

(-2,-7)

Step-by-step explanation:

Rewrite in vertex form and use this form to find the vertex (h,k).

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-15}x^2\stackrel{\stackrel{b}{\downarrow }}{-60}x\stackrel{\stackrel{c}{\downarrow }}{-67} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ -60}{2(-15)}~~~~ ,~~~~ -67-\cfrac{ (-60)^2}{4(-15)}\right) \implies \left( - \cfrac{ -60 }{ -30 }~~,~~-67 - \cfrac{ 3600 }{ -60 } \right) \\\\\\ (-2~~,~~-67+60)\implies {\Large \begin{array}{llll} (-2~~,~~-7) \end{array}}[/tex]

If you select four socks at random, the probability that at most three are blue is 42.9%.

Probability is the likelihood of an expected outcome occurring when many possible events can happen.

Probability is represented in percentages, fractions, and decimals to show that it describes what is likely from many outcomes.

The total number of socks in the drawer = 14

The number of blue socks = 8

The number of black socks = 6

The probability of getting a blue sock = 8/14

The probability of getting 3 out of 4 = 3/4

The combined probability = 8/14 x 3/4

= 42.86%

= 42.9%

Thus, when you randomly select four socks, you can probably get blue socks 42.9% of the time.

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Answer:

(x+3) (x+5)

Step-by-step explanation:

1) When factorising a quadratic like this the first step is to put x in front of two brackets:

(x ) (x )

2) Next check if all numbers in your question is positive (+). In this case it is so we put + after both x in bracket.

(x+ ) (x+ )

3) now the last number in your question is 15 so we find all factors of 15:

1 and 15

3 and 5

4) to know which pair of factors to use we look at owr second number in the question which is 8x. The factors that add up to 8 is 3 and 5.

Voilà