The ratios in an equivalent ratio table are 3:12, 4:16, and 5:20. If the first number in the ratio is 10, what is the second number?

Answer:

52 tickets cost $10 and 18 tickets cost $12

Step-by-step explanation:

10x+12y=804. (1)

x+y=70. (2)

From (2)

x=70-y

Substitute x=70-y into (1)

10x+12y=804

10(70-y)+12y=804

700-10y+12y=804

700+2y=804

2y=804-700

2y=104

y=104/2

y=52

Recall

x+y=70

x+52=70

x=70-52

x=18

52 tickets cost $10 and 18 tickets cost $12

By solving a system of equations we will see that the correct option is A.

First, let's define the variables:

First, we know that 70 tickets were sold, so:

x + y = 70

And we know that they reached $804, then we have:

x*$10 + y*$12 = $804

Then our system is:

x + y = 70

x*$10 + y*$12 = $804

To solve this, we first need to isolate one of the variables in one of the equations, I will isolate x on the first equation:

x = 70 - y

Now we can replace that in the other equation to get:

(70 - y)*$10 + y*$12 = $804

$700 - y*$10 + y*$12 = $804

$700 + y*$2 = $804

y*$2 = $804 - $700 = $104

y = $104/$2 = 52

So, 52 $12 tickets were sold, then the other 18 tickets were $12, so the correct option is A.

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To calculate the present value of a zero-coupon bond, we can use the formula: Present Value = Future Value / (1 + Interest Rate)^n

where Future Value is the par value of the bond, Interest Rate is the annual market interest rate, and n is the number of years. In this case, the Future Value is $2,000, the Interest Rate is 10% (or 0.10), and the number of years is 5. Using Excel, we can calculate the present value as follows:
1. In cell A1, enter the Future Value: 2000
2. In cell A2, enter the Interest Rate: 0.10
3. In cell A3, enter the number of years: 5
4. In cell A4, enter the formula for calculating the present value: =A1 / (1 + A2)^A3
5. Press Enter to get the result.

The present value of the 5-year zero-coupon bond with a $2,000 par value and an annual market interest rate of 10% is $1,620.97.

The formula for present value calculates the current worth of a future amount by discounting it back to the present using the interest rate. In this case, the future value is $2,000, and we divide it by (1 + 0.10)^5 to account for the effect of compounding over 5 years. The result is the present value of $1,620.97, which represents the amount that is considered equivalent to receiving $2,000 in 5 years at a 10% interest rate.

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The TRE score of 4532 is relatively better than the LSVT score of 35.

Calculate the z-score for the TRE score of 4532:

z_TRE = (4532 - 5277) / 324 ≈ -0.23

Subtract the mean TRE score (5277) from the individual score (4532), and divide it by the standard deviation of the TRE scores (324).

Calculate the z-score for the LSVT score of 35:

z_LSVT = (35 - 44.2) / 4 ≈ -2.30

Subtract the mean LSVT score (44.2) from the individual score (35), and divide it by the standard deviation of the LSVT scores (4).

Compare the z-scores:

The z-score tells us how many standard deviations a particular score is away from the mean. A higher z-score indicates a better relative score.

In this case, the z-score for the TRE score of 4532 is approximately -0.23, while the z-score for the LSVT score of 35 is approximately -2.30.

Determine the relatively better score:

Since the z-score for the TRE score (-0.23) is closer to zero compared to the z-score for the LSVT score (-2.30), the TRE score of 4532 is relatively better than the LSVT score of 35.

Therefore, based on the z-scores, the TRE score of 4532 is relatively better than the LSVT score of 35.

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Step-by-step explanation:

The inequality that would result in the shaded solution on the unit circle to the right is and this can be determined by using the trigonometric properties.

Given :

The unit circle is given.

The following steps can be used in order to determine the inequality that would result in the shaded solution on the unit circle to the right:

Step 1 - First determine the value of cosine function when the angle is

Step 2 - Now, determine the value of the cosine function when the angle is .

Answer:

A triangle's total sum of angles is 180 °

19x + 66 = 180

19x = 114

x = 6

Answer:

25 people

Step-by-step explanation:

So, you're trying to find how many she needs to invite since only 92% show up. With this problem, you need to figure out 92% of what number is 23. An equation for this is:

92/100 = 23/x

1. Cross multiply to get 92x=2300

2. Divide both sides to get x by itself. You should get x= 25

3. So, she should invite 25 people

The nicotine content in cigarettes of a certain brand is normally distributed with a standard deviation of σ (sigma) representing the amount of variability in the data.

The term "normally distributed" means that the nicotine content follows a normal distribution, which is a bell-shaped curve. The standard deviation (σ) is a measure of how spread out the data is.

In this case, it tells us how much the nicotine content values vary from the average value.

Therefore, the nicotine content in cigarettes of a certain brand is normally distributed, with the standard deviation (σ) representing the amount of variability in the data.

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Answer:

x=16 degrees

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

85 - 21 = 64

64/4 = 16

this is assuming they are same length

After the evaluation of integral I = Sπ/6 0 2sin2x/cosx the result is -2 [Si(1) - Si(√3/2)], under the condition that the given integral is a form of infinite integral.

The  given integral I = ∫(π/6)0 2sin2x/cosx

can be evaluated by performing the principles of substitution method.

Then Let us consider u = cos(x),

then du/dx = -sin(x)

dx = -du/sin(x).

Staging these values in the integral

I = ∫(π/6)0 2sin2x/cosx dx

 = ∫(π/6)0 2sin2x/u (-du/sin(x))

 = -2 ∫u=cos(π/6)u=cos(0) sin(u)²/u du

 = -2 ∫u=√3/2u=1 sin(u)²/u du

 = -2 [Si(1) - Si(√3/2)]

here Si is the sine integral function.

After the evaluation of integral I = Sπ/6 0 2sin2x/cosx the result is -2 [Si(1) - Si(√3/2)], under the condition that the given integral is a form of infinite integral.

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Answer:

Step-by-step explanation:

(0+2)/(0-10)= 2/-10 = -1/5

y - 0 = -1/5(x - 0)

y = -1/5x

solution is D

The expression "x - y + z" can be simplified and rearranged using the associative property and commutative property of addition. Let's break it down step by step:

1. x - y + z

According to the associative property of addition, the grouping of terms does not affect the result when only addition and subtraction are involved. Therefore, we can choose to group "y" and "z" together:

2. x + (-y + z)

Next, using the commutative property of addition, we can rearrange the terms "-y + z" as "z + (-y)":

3. x + (z + (-y))

Now, we have the expression "x + (z + (-y))". According to the associative property of addition, we can group "x" and "z + (-y)" together:

4. (x + z) + (-y)

Finally, we can rewrite the expression as "(x + z) - y", which is equivalent to "(x - y) + z":

5. (x + z) + (-y) = (x - y) + z

Therefore, "x - y + z" is indeed the same as both "x - (y + z)" and "(x - y) + z" due to the associative and commutative properties of addition.

Answer:

- 16.2

Step-by-step explanation:

You can just divide it XD

-8.1 ÷ 0.5

= - 16.2

Answer:

\(x=\sqrt{153}\)

Step-by-step explanation:

\((\overline{BC})^2 = (\overline{AB})^2 + (\overline{AC})^2\\\\(13)^2=(x)^2+(4)^2\\\\169 = x^2+16\\\\169-16=x^2\\\\153=x^2\\\\\sqrt{x^2} = \sqrt{153}\\\\x=\sqrt{153}\)

Answer:

90.8

Step-by-step explanation:

20/13 = x/59

13x = 1180

x=90.76

x=90.8

Answer:

The value is \(E = \$ 1310.8\)

Step-by-step explanation:

From the question we are told that

   The principle is \(P = \$ 175,000\)

    The rate is  \(R = 0.0325\)

    The period is  \(t = 30 \ years\)

Generally the formula to calculate the  is mathematically represented as

       \(E = P * R * [\frac{(1 - R)^n}{ (1 + R)^n - 1} ]\)

=>    \(E = 175000 * 0.0325 * [\frac{(1 - 0.0325 )^{30}}{ (1 + 0.0325)^{30} - 1} ]\)

=>    \(E = \$ 1310.8\)

Solution:

Given:

A person can go up to 10 rides.

This means the maximum number of rides the person can go is 10.

Therefore, the description that best represents the number of rides a person can go is;

Any value less than or equal to 10.

Hence, representing this as inequality, if r is the number of rides a person could go, then the inequality statement is;

Answer:

5m/s²

Step-by-step explanation:

Given :-

To Find :-

Solution :-

We know that the rate of change of velocity is called acceleration. Therefore ,

\(\sf\implies a = v - u / t \\ \)

\(\sf\implies a = 60m/s - 40m/s/ 4 \\ \)

\(\sf\implies a = 20m/s \div 4 \\\)

\(\bf\implies a = 5m/s^2\)

Answer:

c

Because...

It has the same slope.

12 gallons of 90% orange juice drink is needed to be mixed with 16 gallons of 20% orange juice drink to obtain a mixture that is 50%.

Let's first use V to represent the volume in gallons of the 90% orange juice drink that we need to mix with 16 gallons of 20% orange juice drink.

The problem is asking for the amount of the 90% orange juice drink that is required to be mixed.

Let's determine the equation for this problem.

It is given that 90% orange juice is to be mixed with 20% orange juice to obtain 50% orange juice.

Then the equation for the problem can be written as:

0.9V + 0.2(16) = 0.5(V + 16)0.9V + 3.2 = 0.5V + 8

On solving the above equation we get,

0.9V - 0.5V = 8 - 3.20.4V = 4.8V = 12 gallons

Therefore, 12 gallons of 90% orange juice drink is needed to be mixed with 16 gallons of 20% orange juice drink to obtain a mixture that is 50%.

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Answer: 5/4

Step-by-step explanation:3/4 * 2 * 5/6=5/4 so 5/4 is our answer

The missing Value, x, that when multiplied by 5/3^4 gives the result of 5^4 is 13125.

The missing value that, when multiplied by 5/3^4, gives the result of 5^4, we can set up the equation:

(5/3^4) * x = 5^4

To solve for x, we can simplify both sides of the equation. First, let's simplify the right side:

5^4 = 5 * 5 * 5 * 5 = 625

Now, let's simplify the left side:

5/3^4 = 5/(3 * 3 * 3 * 3) = 5/81

Now we have:

(5/81) * x = 625

To solve for x, we can multiply both sides of the equation by the reciprocal of 5/81, which is 81/5:

(81/5) * (5/81) * x = (81/5) * 625

On the left side, the fraction (81/5) * (5/81) simplifies to 1, leaving us with:

1 * x = (81/5) * 625

Simplifying the right side:

(81/5) * 625 = 13125

Therefore, the missing value, x, that when multiplied by 5/3^4 gives the result of 5^4 is 13125.

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The statement that could be true for g is g(-4) = -11.

What is a function?

A function is a mathematical relationship between a set of inputs (called the domain) and a set of outputs (called the range), where each input has a unique output. In other words, for every value of x in the domain, there is exactly one corresponding value of g(x) in the range.

For the given function g, the domain is -20 ≤ x ≤ 5 and the range is -5 ≤ g(x) ≤ 45. We also know that g(0) = -2 and g(-9) = 6.

To determine which statement could be true for g, we can check each option against the given domain and range, as well as the known values of g(0) and g(-9):

g(7) = -1: This statement is not necessarily true, as g(7) may fall outside the given range of -5 ≤ g(x) ≤ 45.

g(-13) = 20: This statement is not necessarily true, as g(-13) may fall outside the given domain of -20 ≤ x ≤ 5.

g(-4) = -11: This statement could be true, as -20 ≤ -4 ≤ 5 and -5 ≤ -11 ≤ 45. However, we cannot confirm this without additional information.

g(0) = 2: This statement is not true, as g(0) is known to be -2.

Therefore, the statement that could be true for g is g(-4) = -11.

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Edward started his hike at an elevation of 115 feet below sea level. Throughout the hike he ascended 3,200 feet and then descended 676 feet. How much did his elevation change?

115+676=791

3200-791= 2409

his elevation changed by 2409 ft

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Answer:

Step-by-step explanation:

Write in y = mx +c form

2x + 3y + 1 = 0

3y = -2x - 1

Divide the entire equation by 3

\(y =\dfrac{-2}{3}x-\dfrac{1}{3}\)

\(m = \dfrac{-2}{3}\\\\\\c=\dfrac{-1}{3}\)

Using confidence interval concepts, it is found that the margin of error is of 7.

\(M = \frac{b - a}{2}\)

In this problem, the interval is (32, 46), hence \(b = 46, a = 32\), and the margin of error is:

\(M = \frac{46 - 32}{2} = 7\)

The margin of error is of 7.

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Answer:

Step-by-step explanation:

its 7 just did it

The 98% confidence interval for the difference in proportions of tails side up for a penny and a dime would lie between -0.2 and 0.6.

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, and presentation of data. It is used to summarize, analyze, and compare data in order to draw conclusions and make decisions. Statistical methods are used in a wide variety of fields, including economics, finance, business, engineering, medicine, psychology, social sciences, and many others.

Statistics helps us to understand the behavior of a large number of variables by studying their distributions, relationships, and other patterns. Statistical methods are used to describe and summarize the data, estimate parameters of the population, test hypotheses, and make predictions. Statistical analysis can be used to draw conclusions about the population based on sample data and to determine the probability of certain events occurring. Statistical techniques are used to identify trends and patterns in data, as well as to assess relationships between variables.


This confidence interval can be calculated using the formula for a confidence interval for two proportions, which is: CI = p1 - p2 ± (1.96 x √[(p1(1-p1)/n1) + (p2(1-p2)/n2)]).

In this case, p1 is the proportion of times a spinning penny lands with tails up (18/30 = 0.6), p2 is the proportion of times a spinning dime lands with tails up (20/30 = 0.67), n1 is the number of times the penny was spun (30) and n2 is the number of times the dime was spun (30). Plugging these values into the formula yields a confidence interval of -0.2 and 0.6.

This means that we can be 98% confident that the difference in proportions of tails side up for a penny and a dime lies between -0.2 and 0.6.

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Answer:

4

Step-by-step explanation:

have a nice day