MATHEMATICS COLLEGE

Two sides of a triangle have lengths 9 and 15. What must be true about the length of the third side? less than 6 less than 15 less than 9 less than 24

Answers

Answer 1

Answer:

Answer:

D. 6<x<24.

Step-by-step explanation:

Let x be the length of third side of our triangle.

We have been given that two sides of a triangle have lengths 9 and 15.

To find the possible length for 3rd side of our triangle we will use triangle inequality theorem.

Triangle inequality theorem states that the sum of the lengths of any two sides of a triangle should be greater than the length of the third side.

Using triangle inequality theorem we will get:

$x+9-9>15-9$

$x>6$

$x<9+15$

$x<24$

Therefore, the third side of triangle must be greater than 6 and less than 24 and option D is the correct choice.

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The map shows the intersection of three roads. Malcom Way intersects Sydney Street at an angle of 162°. Park Road intersects Sydney Street at an angle of 87°. Find the angle at which Malcom Way intersects Park Road.

Answers

Answer:

Step-by-step explanation:

Write the prime factorization of 16. Use exponents when appropriate and order the factors from least to greatest (for example, 2.2.3.5). 23
hlp plz this is really hard

Answers

Answer:

16 =2^4

Step-by-step explanation:

16 = 4*4

but 4 is not prime

4 = 2*2

16 = 2*2*2*2

Rewriting with exponents

16 =2^4

Answer:

→ Prime factorization of 16 :

16 = 2 × 2 × 2 × 2
16 = 2⁴; in the form b = aⁿ
here, n = 4 is the exponent and a = 2 is the prime factor
16 = 2⁴ is the right answer.

You read that a study is planned for which a test of hypothesis will be done at significance level α = 0.10. Statisticians have calculated that for a certain effect size, the power is 0.7. What are the probabilities of Type I and Type II errors for this test?

Answers

Answer:

The probabilities of Type I is 0.10.

The probability of type II error is 0.3

Step-by-step explanation:

Consider the provided information.

Type I error: If we reject the null hypothesis when null hypothesis is true then it is called type I error.

The type I error is denoted by α.

Type II error: If we fail to reject the null hypothesis when null hypothesis is false then it is called type II error.

The type II error is denoted by β.

It is given that significance level α = 0.10.

Thus, the probabilities of Type I is 0.10.

The power of the test is: $Power=1-\beta$

It is given that power is 0.7.

Therefore,

$0.7=1-\beta$

$\beta=1-0.7=0.3$

Hence, the probability of type II error is 0.3

Which of the following objects most closely resembles a Golden Rectangle? 3x 5 inch index card, 8.5x11 inch paper, 11x14 inch paper, or 11x17 inch paper

Answers

did you learn about it

Julio's dad owns a restaurant. He bought 9 dozen potatoes to make french fries. He needs 7 potatoes for a large order of fries. How many large orders of fires will he be able to make?I multiplied 9x12=108
then divided 108/7
I got 15 with 3 left over. Is this right?

Answers

Answer:

yes, your math is correct

15 large orders of fries can be made

Step-by-step explanation:

There are two questions here: one in the question you're trying to answer, and one that you have asked about your math. Hence, there are two answers here.

9 dozen divided by 7 is ...

9·12/7 = 15 3/7

Julio's dad will be able to make 15 large orders of fries.

_____

Your math is correct, but you need to be sure you answer the question asked, preferably in at least one complete sentence. Pay attention to the question wording.

Find the greatest common factor of 108d^2 and 216d

Answers

Answer:

$\boxed{108d}$

Step-by-step explanation:

Part 1: Find GCF of variables

The equation gives d ² and d as variables. The GCF rules for variables are:

The variables must have the same base.
If one variable is raised to a power and the other is not, the GCF is the variable that does not have a power.
If one variable is raised to a power and the other is raised to a power of lesser value, the GCF is the variable with the lesser value power.

The GCF for the variables is d.

Part 2: Find GCF of bases (Method #1)

The equation gives 108 and 216 as coefficients. To check for a GCF, use prime factorization trees to find common factors in between the values.

Key: If a number is in bold, it is marked this way because it cannot be divided further AND is a prime number!

Prime Factorization of 108

108 ⇒ 54 & 2

54 ⇒ 27 & 2

27 ⇒ 9 & 3

9 ⇒ 3 & 3

Therefore, the prime factorization of 108 is 2 * 2 * 3 * 3 * 3, or simplified as 2² * 3³.

Prime Factorization of 216

216 ⇒ 108 & 2

108 ⇒ 54 & 2

54 ⇒ 27 & 2

27 ⇒ 9 & 3

9 ⇒ 3 & 3

Therefore, the prime factorization of 216 is 2 * 2 * 2 * 3 * 3 * 3, or simplified as 2³ * 3³.

After completing the prime factorization trees, check for the common factors in between the two values.

The prime factorization of 216 is 2³ * 3³ and the prime factorization of 108 is 2² * 3³. Follow the same rules for GCFs of variables listed above and declare that the common factor is the factor of 108.

Therefore, the greatest common factor (combining both the coefficient and the variable) is $\boxed{108d}$ .

Part 3: Find GCF of bases (Method #2)

This is the quicker method of the two. Simply divide the two coefficients and see if the result is 2. If so, the lesser number is immediately the coefficient.

$(216)/(108)=2$