Find cos θ for θ = 60°

Answer:

Step-by-step explanation:

Additive inverse ⇒ sum of numbers is zero:

Multiplicative inverse ⇒ product of numbers is 1:

Step-by-step explanation:

the additive inverse and multiplicative inverse for the following number -3/4=-4/3

Answer:

Step-by-step explanation:

x is a midsegment of a given triangle as it connects the midpoints of the two sides.

Midsegment is parallel to the third side and equals to half of its measure:

Answer:

p = 1/2y - 3

Step-by-step explanation:

p=x/3 and x=1/2y [replace the "x" to solve]

p = (1/2y)/3

Answer:

(0,5) will be linear equation

Answer:

Step-by-step explanation:

3x -8 = 2x + 5

x - 8 = 5

x = 13

3(13) - 8 + 2(13) + 5

39 - 8 + 26 + 5

31 + 31 = 62

Answer:

25

Step-by-step explanation do 5 five times

Answer:

$9

Step-by-step explanation:

This means the cost of the item to you is $9. You will pay $9 for a item with original price of $10 when discounted 10%. In this example, if you buy an item at $10 with 10% discount, you will pay 10 - 1 = 9 dollars.

Answer:

27

Step-by-step explanation:

1 mile took 9 min to run, so 3 miles will be:

3 x 9 =

27

1/4s

Step-by-step explanation:

Multiply 1/4 with s

Answer:

1/4s

Step-by-step explanation:

x 1/4 by s

Answer:

her language arts hw takes longer and it takes 2/9 hr longer

Step-by-step explanation:

first of all, 4/9 > 2/9

4/9-2/9=2/9

Answer:

The first five terms are -1,4,9,14 and 19.

Step-by-step explanation:

The arithmetic sequence is :

[tex]T_n=5n-6[/tex]

We need to find the first five terms of the sequence.

Put n = 1 for first term.

[tex]T_1=5(1)-6=-1[/tex]

Put n = 2 for second term.

[tex]T_2=5(2)-6=\\\\=10-6\\\\=4[/tex]

Put n = 3 for third term.

[tex]T_3=5(3)-6=\\\\=15-6\\\\=9[/tex]

Put n = 4 for fourth term.

[tex]T_4=5(4)-6=\\\\=20-6\\\\=14[/tex]

Put n = 5 for fifth term.

[tex]T_3=5(5)-6=\\\\=25-6\\\\=19[/tex]

Hence, the first five terms are -1,4,9,14 and 19.

Answer:

B, 18.44 miles

Answer:

64 o/o

Step-by-step explanation: 50 times 2 is 100 and 32 x 2 is 64

Answer:

Reason SAS postulate

Step-by-step explanation:

The two triangles must be congruent.

Reason: SAS postulate

Answer: See explanation

Step-by-step explanation:

6 sacks of potatoes weigh 122.4 kg

1 sack would weigh 122.4 kg ÷ 6

122.4 ÷ 6 = 20.4

1 sack of potatoes weighs 20.4 kg

4 sacks of onions weigh 50 kg

1 sack would weigh 50 kg ÷ 4

50 ÷ 4 = 12.5

1 sack of onions weighs 12.5 kg

Answer:

a) 0.9207 = 92.07% probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes

b) 0.8907 = 89.07% probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes

c) 0.8114 = 81.14% probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For sum of n normally distributed variables, the mean is [tex]\mu*n[/tex] and the standard deviation is [tex]s = \sigma\sqrt{n}[/tex].

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question, we have that:

For a single commercial jet:

[tex]\mu = 8, \sigma = 2.8[/tex]

For the 37 jets combined:

[tex]\mu = 37*8 = 296, s = 2.8\sqrt{37} = 17.03[/tex]

(a) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes?

This is the pvalue of Z when X = 320. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{320 - 296}{17.03}[/tex]

[tex]Z = 1.41[/tex]

[tex]Z = 1.41[/tex] has a pvalue of 0.9207

0.9207 = 92.07% probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes.

(b) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes?

This is 1 subtracted by the pvalue of Z when [tex]X = 275[/tex]. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{275 - 296}{17.03}[/tex]

[tex]Z = -1.23[/tex]

[tex]Z = -1.23[/tex] has a pvalue of 0.1093

1 - 0.1093 = 0.8907

0.8907 = 89.07% probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes.

(c) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes?

This is the pvalue of Z when [tex]X = 320[/tex] subtracted by the pvalue of | when [tex]X = 275[/tex]

From a and b

0.9207 - 0.1093 = 0.8114

0.8114 = 81.14% probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes

Answer:

NIO

Step-by-step explanation:

a

Answer:

105

Step-by-step explanation:

7 (7x7) + 7 is the same as 7 x 14 + 7 so that would equal 105

Answer:

[tex]\theta \approx 82.34^\circ[/tex]

Step-by-step explanation:

Please refer to the attached diagram. (Apologies if the shading or resolution is a bit off.)

So, we want to find θ.

Since we formed a right triangle, we can use right triangle ratios.

We know the measure of the adjacent side to θ and the hypotenuse.

Therefore, we will use the cosine ratio:

[tex]\displaystyle \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}[/tex]

The adjacent side is 2 and the hypotenuse is 15. By substitution:

[tex]\displaystyle \cos(\theta)=\frac{2}{15}[/tex]

Now, we will take the inverse cosine of both sides. So:

[tex]\displaystyle \theta=\cos^{-1}\Big(\frac{2}{15}\Big)[/tex]

Use a calculator. Hence:

[tex]\theta \approx 82.34^\circ[/tex]

The angle between the ground and the ladder is about 82.34°.

Step-by-step explanation:

For every 2 hours across, the line graph goes up by 15 songs.

Therefore the slope of the line is 15/2. (D)

Answer:

6x + 3

General Formulas and Concepts:

Pre-Algebra

Distributive Property

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

3(2x + 1)

Step 2: Expand

Answer:

answer A is correct because the formula of equation in point slope is

y-y1=m(x-x1)

where,(x1,y1)point is given that is (6,-2)

slope=m=3

equation in point-slope form of the line that passes through the point (6, −2) and has a slope of 3 is  y + 2 = 3(x − 6)

statement of equality between two expressions consisting of variables and/or numbers.

As, equation line is:

y-y1=m(x-x1)

We have,

coordinates (6, −2) and slope=3

So,

y+2=3(x-6)

y+2=3x-18

y-3x= -20

Hence,  equation in point-slope form of the line that passes through the point (6, −2) and has a slope of 3 is y+2=3(x-6).

Learn more about equation here:

https://brainly.com/question/21511618

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Answer:

Step-by-step explanation:

Step 1 is incorrect. It should be:

Correct answer option is B