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zepelin [54]
3 years ago
3

A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is

the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation.
x + y = 24

3x + 5y = 100

What does the solution of this system indicate about the questions on the test?

A. The test contains 4 three-point questions and 20 five-point questions.
B. The test contains 10 three-point questions and 14 five-point questions.
C. The test contains 14 three-point questions and 10 five-point questions.
D. The test contains 20 three-point questions and 8 five-point questions.
Mathematics
1 answer:
Sergio [31]3 years ago
3 0

Answer:

B

Step-by-step explanation:

To solve this system, solve by substitution.

Rewrite x + y = 24 as x = 24 - y. Substitute it into 3x + 5y = 100.

3(24 - y) + 5y = 100

72 - 3y + 5y = 100

2y = 28

y = 14 5-point questions

Substitute y = 14 back into x = 24 - y and solve for x.

x = 24 - 14

x = 10 3-point questions

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According to the graph, what is the value of the constant in the equation
Tomtit [17]

\sf  \dag \: \red{Answer :-}

Let us consider point A,

We are given that,

\sf :  \implies \: height =  \frac{constant}{width} \:  \:  \:  \:  \:  \:   \\  \therefore \sf constant = height \:   \times width

Now, we can simply put the given values at Point A,

\sf  \: constant = 30 \times 2 = 60

To verify, let's move on to next point, i.e. point B,

\sf \: costant = 10 \times 6 = 60

Hence, verified, the constant is \sf \red{60}.

Hope it helps you :)

7 0
3 years ago
A random sample of 20 items is selected from a population. When computing a confidence interval for the population mean, what nu
kumpel [21]

Answer:

For this case since the sample size is lower than 30 , n =20<30, is not appropiate use the normal standard distribution to calculate the confidence interval for the mean, and then for this case is better use the t distribution since takes in count the correction factor to approximate the distribution of the true parameter.

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

\bar X represent the sample mean for the sample  

\mu population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size  

Solution to the problem

For this case since the sample size is lower than 30 , n =20<30, is not appropiate use the normal standard distribution to calculate the confidence interval for the mean, and then for this case is better use the t distribution since takes in count the correction factor to approximate the distribution of the true parameter.

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

8 0
4 years ago
Describe how to transform the quantity of the third root of x to the fourth power, to the fifth power into an expression with a
Novosadov [1.4K]

Answer:

x^{\frac{20}{3} }

Step-by-step explanation:

To write: third root of x to the fourth power, to the fifth power into an expression with a rational exponent

Solution:

Exponent refers to the number of times a number is multiplied to itself.

Exponent is sometimes also known as power.

Third roots of x=x^{\frac{1}{3} }

Third root of x to the fourth power(x^{\frac{1}{3} })^4 =x^{\frac{4}{3} }

Third root of x to the fourth power, to the fifth power=(x^{\frac{4}{3} })^5= x^{\frac{20}{3} }

8 0
4 years ago
Solve for L.........
cupoosta [38]

Answer:

L = P/2 - W

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Equality Properties

Step-by-step explanation:

<u>Step 1: Define</u>

P = 2L + 2W

<u>Step 2: Solve for </u><em><u>L</u></em>

  1. Subtract 2W on both sides:                    P - 2W = 2L
  2. Divide 2 on both sides:                           (P - 2W)/2 = L
  3. Distribute division:                                   P/2 - W = L
  4. Rewrite:                                                    L = P/2 - W
7 0
3 years ago
22. Chris bought a new car for $12,500. He made a $3,000 down payment and financed the rest at an annual interest rate of 14.5%
Tatiana [17]

Answer:

Step-by-step explanation:

Purchase price (A) : $12,500

Down Payment (B): $3,000

Loan Taken (C = A - B):  $9500

D :  Interest calculation for $9,500 for 3 years P(1 + rt)

= 9500(1 + (14.5/100) * 3)

= 9500(1 + 0.145 * 3)

= 9500 * 1.435

= $13632.5

E : Interest calculation for $9,500 for 2 years P(1 + rt)

= 9500(1 + (14.5/100) * 2)

= 9500(1 + 0.145 * 2)

= 9500 * 1.29

= $12,255

Difference between D - E

= $13632.5 - $12,255

= $1377.5

Hence the answer is B i.e. $1377.5 less interest for same amount of load for 2 years vs 3 years

4 0
2 years ago
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