Can I please get some help it would mean the world if u guys helped me and also can u show ur work and how u did it thanks! <3 =) have a nice day!

Answer:

-3.73

Step-by-step explanation:

solution:

Given:

Angle between two lines=60⁰

slope of first line=1

Or, tanA=1

Or, A= tan inverse (1)

so, A=45⁰

so, angle of inclination of first line=45⁰

Now,

angle of inclination of second line= A+ 60⁰

= 45⁰+60⁰

=105⁰

so, slope of second line = tan105.

= -3.73

Answer:

The 15th term is 160

Step-by-step explanation:

The details are not clear. So, I will make the following assumptions

[tex]d = 10[/tex] ---- common difference

[tex]a_1 = 20[/tex] ---- first term

Required

The 15th term

This is calculated as:

[tex]a_{n} = a + (n - 1) * d[/tex]

Substitute 15 for n

[tex]a_{15} = a + (15 - 1) * d[/tex]

[tex]a_{15} = a + 14 * d[/tex]

Substitute values for d and a

[tex]a_{15} = 20 + 14 * 10[/tex]

[tex]a_{15} = 20 + 140[/tex]

[tex]a_{15} = 160[/tex]

Answer:

a)

The null hypothesis is: [tex]H_0: p_M - p_W = 0[/tex]

The alternative hypothesis is: [tex]H_1: p_M - p_W > 0[/tex]

b) For men is of 0.49 and for women is of 0.36.

c) The p-value of the test is 0.0039 < 0.01, which means that the results are statistically significant so that you can conclude a greater proportion of men expect to get a raise or a promotion this year.

Step-by-step explanation:

Before solving this question, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes 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 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]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Men:

98 out of 200, so:

[tex]p_M = \frac{98}{200} = 0.49[/tex]

[tex]s_M = \sqrt{\frac{0.49*0.51}{200}} = 0.0353[/tex]

Women:

72 out of 200, so:

[tex]p_W = \frac{72}{200} = 0.36[/tex]

[tex]s_W = \sqrt{\frac{0.36*0.64}{200}} = 0.0339[/tex]

a. State the hypothesis test in terms of the population proportion of men and the population proportion of women.

At the null hypothesis, we test if the proportion are similar, that is, if the subtraction of the proportions is 0, so:

[tex]H_0: p_M - p_W = 0[/tex]

At the alternative hypothesis, we test if the proportion of men is greater, that is, the subtraction is greater than 0, so:

[tex]H_1: p_M - p_W > 0[/tex]

b. What is the sample proportion for men? For women?

For men is of 0.49 and for women is of 0.36.

c. Use α= 0.01 level of significance. What is the p-value and what is your conclusion?

From the sample, we have that:

[tex]X = p_M - p_W = 0.49 - 0.36 = 0.13[/tex]

[tex]s = \sqrt{s_M^2+s_W^2} = \sqrt{0.0353^2 + 0.0339^2} = 0.0489[/tex]

The test statistic is:

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

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error, so:

[tex]z = \frac{0.13 - 0}{0.0489}[/tex]

[tex]z = 2.66[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a difference above 0.13, which is the p-value of z = 2.66.

Looking at the z-table, z = 2.66 has a p-value of 0.9961.

1 - 0.9961 = 0.0039.

The p-value of the test is 0.0039 < 0.01, which means that the results are statistically significant so that you can conclude a greater proportion of men expect to get a raise or a promotion this year.

Answer:

i) 0.1969 = 19.69% probability that there will be no defective fuse.

ii) 0.8031 = 80.31% probability that there will be at least one defective fuse.

iii) 0.2759 = 27.59% probability that there will be exactly two defective fuses.

iv) 0.5443 = 54.43% probability that there will be at most one defective fuse.

Step-by-step explanation:

For each fuse, there are only two possible outcomes. Either it is defective, or it is not. The probability of a fuse being defective is independent of any other fuse, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

15% are defective.

This means that [tex]p = 0.15[/tex]

We also have:

[tex]n = 10[/tex]

(i) No defective fuse

This is [tex]P(X = 0)[/tex]. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{10,0}.(0.15)^{0}.(0.85)^{10} = 0.1969[/tex]

0.1969 = 19.69% probability that there will be no defective fuse.

(ii) At least one defective fuse

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

We already have P(X = 0) = 0.1969, so:

[tex]P(X \geq 1) = 1 - 0.1969 = 0.8031[/tex]

0.8031 = 80.31% probability that there will be at least one defective fuse.

(iii) Exactly two defective fuses

This is P(X = 2). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{10,2}.(0.15)^{2}.(0.85)^{8} = 0.2759[/tex]

0.2759 = 27.59% probability that there will be exactly two defective fuses.

(iv) At most one defective fuse

This is:

[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{10,0}.(0.15)^{0}.(0.85)^{10} = 0.1969[/tex]

[tex]P(X = 1) = C_{10,1}.(0.15)^{1}.(0.85)^{9} = 0.3474[/tex]

Then

[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.1969 + 0.3474 = 0.5443[/tex]

0.5443 = 54.43% probability that there will be at most one defective fuse.

Answer:

The speed of the plane is 150 miles per hour, while the speed of the car is 50 miles per hour.

Step-by-step explanation:

Since a plane can fly 450 miles in the same time it takes a car to go 150 miles, if the car travels 100 mph slower than the plane, to find the speed (in mph) of the plane the following calculation must be performed:

450 to 150 is equal to 3: 1, that is, the plane travels three times the distance of the car.

Therefore, since 100/2 x 3 equals 150, the speed of the plane is 150 miles per hour, while the speed of the car is 50 miles per hour.

Answer:

k = 54

Step-by-step explanation:

k + (-12) = 42

Remove parenthesis and addition sign

k - 12 = 42

Add 12 to both sides

K = 54

[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]

Answer:

The first equation should be multiplied by 9 and the second equation by −4

Step-by-step explanation:

Given the simultaneous equation

First Equation: 5x − 4y = 28

Second equation: 3x - 9y = 30

In order to eliminate y, we must make the coefficient of x in both expression to be equal.

To do that the first equation should be multiplied by 9 (negative value of the coefficient of y in equation 2)and the second equation by -4( (coefficient of y in equation 1)

Answer:

Face validity

Step-by-step explanation:

In quantitative research in mathematics, we have four major types of validity namely;

- Content Validity

- Construct validity

- Criterion validity

- Face validity.

Now;

> Construct validity seeks to find out if the tool used in measurement is a true representation of what is really going to be measured.

> Content Validity seeks to find out whether a test covers every part of a particular subject being tested.

> Face validity seeks to find out how true a test is by looking at it on the surface.

> Criterion validity seeks to find out the relationship of a particular test to that of another test.

Now, in this question, we are told that The survey seems like a good representation of measuring dietary habits after just asking questions about each meal and snack they consumed for the week. Thus, it is a face validity because it just appears true on the surface to be a good representation but we don't know if it is effective until we go deep like content validity

Answer:

a) Mean blood pressure for people in China, which has mean 128 and standard deviation 23.

b) 0.3821 = 38.21% probability that a person in China has blood pressure of 135 mmHg or more.

c) 0.714 = 71.4% probability that a person in China has blood pressure of 141 mmHg or less.

d) 0.0851 = 8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.

e) Since |Z| = 0.3 < 2, it is not unusual for a person in China to have a blood pressure of 135 mmHg.

f) 90% of all people in China have a blood pressure of less than 157.44 mmHg.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

The mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg

This means that [tex]\mu = 128, \sigma = 23[/tex]

a.) State the random variable.

Mean blood pressure for people in China, which has mean 128 and standard deviation 23.

b.) Find the probability that a person in China has blood pressure of 135 mmHg or more.

This is 1 subtracted by the p-value of Z when X = 135, so:

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

[tex]Z = \frac{135 - 128}{23}[/tex]

[tex]Z = 0.3[/tex]

[tex]Z = 0.3[/tex] has a p-value of 0.6179.

1 - 0.6179 = 0.3821

0.3821 = 38.21% probability that a person in China has blood pressure of 135 mmHg or more.

c.) Find the probability that a person in China has blood pressure of 141 mmHg or less.

This is the p-value of Z when X = 141, so:

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

[tex]Z = \frac{141 - 128}{23}[/tex]

[tex]Z = 0.565[/tex]

[tex]Z = 0.565[/tex] has a p-value of 0.7140.

0.714 = 71.4% probability that a person in China has blood pressure of 141 mmHg or less.

d.) Find the probability that a person in China has blood pressure between 120 and 125 mmHg.

This is the p-value of Z when X = 125 subtracted by the p-value of Z when X = 120, so:

X = 125

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

[tex]Z = \frac{125 - 128}{23}[/tex]

[tex]Z = -0.13[/tex]

[tex]Z = -0.13[/tex] has a p-value of 0.4483.

X = 120

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

[tex]Z = \frac{120 - 128}{23}[/tex]

[tex]Z = -0.35[/tex]

[tex]Z = -0.35[/tex] has a p-value of 0.3632.

0.4483 - 0.3632 = 0.0851

0.0851 = 8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.

e.) Is it unusual for a person in China to have a blood pressure of 135 mmHg? Why or why not?

From item b, when X = 135, Z = 0.3.

Since |Z| = 0.3 < 2, it is not unusual for a person in China to have a blood pressure of 135 mmHg.

f.) What blood pressure do 90% of all people in China have less than?

The 90th percentile, which is X when Z has a p-value of 0.9, so X when Z = 1.28.

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

[tex]1.28 = \frac{X - 128}{23}[/tex]

[tex]X - 128 = 1.28*23[/tex]

[tex]X = 157.44[/tex]

90% of all people in China have a blood pressure of less than 157.44 mmHg.

Answer:

the market value of all final goods and services produced within the United States in a given period of time.

Answer:

Cos y = t / 8

Step-by-step explanation:

Using the hints given in the question, the omitted tribagke will look like the triangle attached on the picture ;

From trigonometry :

Sin y = opposite / hypotenus

Sin y = s / 8

Opposite side = s ; hypotenus = 8

Tan y = opposite / Adjacent

Tan y = s / t

Adjacent side = t

Then ;

Cos y = Adjacent / hypotenus

Hence,

Cos y = t / 8

Answer:

the answer is :

cos y°= t / 8

Step-by-step explanation:

I promise! I got this right, and.....you are welcome.

Tanθ =sin /cos

tan θ = 5/2 / y

tan (30°) = 5/2 /y

[tex]y = \frac{5 \sqrt{3} }{2} [/tex]

y=4.33

.Answer:

The answer is below

Step-by-step explanation:

The patient loses 1 kg every week for 5 weeks.

1 kg = 2.2 lbs

Therefore the patient loses 2.2 lbs every week for 5 weeks.

a) The weight of the patient after 5 weeks = 245 lbs. - (5 weeks)(2.2 lbs per week)

The weight of the patient after 5 weeks = 245 lbs. - 11 lbs. = 234 lbs.

b) The weight of the patient after 5 weeks = 245 lbs. - 11 lbs. = 234 lbs.

1 kg = 2.2 lbs.

234 lbs. = 234 lbs. * 1 kg per 2.2 lbs. = 106.36 kg

Answer:

0.31311311131111....

Step-by-step explanation:

We need to tell a number which when adds to 0.4 makes it a Irrational Number . We know that ,

Rational number :- The number in the form of p/q where p and q are integers and q is not equal to zero is called a Rational number .

Irrational number :- Non terminating and non repeating decimals are called irrational number .

Recall the property that :-

Property :- Sum of a Rational Number and a Irrational number is Irrational .

So basically here we can add any Irrational number to 0.4 to make it Irrational . One Irrational number is ,

[tex] \rm\implies Irrational\ Number = 0.31311311131111... [/tex]

So when we add this to 0.4 , the result will be Irrational . That is ,

[tex] \rm\implies 0.4 + 0.31311311131111 ... = 0.731311311131111 .. [/tex]

Answer:

12

Step-by-step explanation:

Scale factor of 4

CD = 3

3 · 4 = 12

Length of C'D' is 12 units

Answer:

12 units

Step-by-step explanation:

The original segment CD = 3 units

Scale factor is 4.

3 x 4 = 12

Answer:

12000 bacteria

Step-by-step explanation:

Recall that

60 minutes = 1 hour

Given that the rate of growth of the bacterial population is proportional to the number present.

If there were 3000 bacteria in the initial population and the number doubled after the first 60 minutes

Then after 60 minutes, the number of bacteria present would be

= 3000 * 2

= 6000

In another 60 minutes, the number would have doubled again, thus the number present then would be

= 6000 * 2

= 12000

Hence after 120 minutes, the number of bacteria present is 12000. 120 minutes is same as 2 hours

Answer:

Here we need to solve:

[tex]\frac{2}{y - 3} + \frac{6}{y + 3 } = \frac{\frac{2}{y-3}}{\frac{6}{y + 3} }[/tex]

The sum of the fractions is equal to the quotient between the fractions.

Notice that the two values:

y = 3

y = -3

make the denominator equal to zero, so those values are restricted.

We can simplify the right side to get:

[tex]\frac{2}{y - 3} + \frac{6}{y + 3 } = \frac{\frac{2}{y-3}}{\frac{6}{y + 3} } = \frac{2*(y + 3)}{6*(y - 3)} = 3*\frac{y + 3}{y - 3}[/tex]

Now we can multiply both sides by (y - 3)

[tex](y - 3)*(\frac{2}{y - 3} + \frac{6}{y + 3 }) = 3*(y + 3)\\2 + 6*\frac{y -3}{y + 3} = 3*(y + 3)[/tex]

Now we can multiply both sides by (y + 3)

[tex](2 + 6*\frac{y -3}{y + 3})*(y + 3) = 3*(y + 3)*(y + 3)[/tex]

[tex]2*(y + 3) + 6*(y - 3) = 3*(y + 3)*(y + 3)\\\\2*y + 6 + 6*y - 18 = 3*(y^2 + 2*y*3 + 9)\\\\8*y - 12 = 3*y^2 + 6*y + 33\\\\0 = 3*y^2 + 6*y + 33 - 8*y + 12\\\\0 = 3*y^2 - 2*y + 45[/tex]

First, let's see the determinant of that quadratic equation:

[tex]D = (-2)^2 - 4*3*45 = -536[/tex]

We can see that it is negative, thus, there are no real solutions of the equation.

Thus, there is no value of y such that the origina equation is true,

Answer:

y=15

Step-by-step explanation:

Answer:

Option C

Step-by-step explanation:

thankful that there are graphing tools. see screenshot

[tex]\huge❥︎\underbrace\mathfrak\red {SoLuTiOn}✈︎[/tex]

1)

[tex] £7 \: of \: £20 \\ \\ \fbox{considering as x} \\ \\ x\%of \: 20 = 7 \\ \\ x\% = \frac{7}{20} \times 100 \\ \\ x\% = \frac{7}{ \cancel{20}} \times \cancel{ 100} \\ \\ x\% = 7 \times 5 \\ \\ x\% = 35\%[/tex]

2)

[tex]28 \: kg \: of \: 40 \: kg \\ \\ \fbox{considering as x} \\ \\ x\% 40 = 28 \\ \\ x\% = \frac{28}{40} \times 100 \\ \\ x\% = \cancel \frac{28}{4 \cancel0} \times 10 \cancel0 \\ \\ x\% = 7 \times 10 \\ \\ x\% = 70\%[/tex]

Answer:

c. infinitely many solutions

General Formulas and Concepts:

Pre-Algebra

Distributive Properties

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

2(h - 8) - h = h - 16

Step 2: Solve for h

Hello from  MrBillDoesMath!

Answer:    c  (infinitely many solutions)

Steps:

1) Simplify  the original  equation

       2(h-8)- h= h - 16

2.As 2 (h-8) = 2h- 16,  the equation in 1) is equivalent to  

      (2h-16) -h  = h - 16

 or

      (2h-h) - 16 = h - 16

or

      h - 16 = h -16

which is true for all values of h.

Regards,  MrB

9514 1404 393

Answer:

  x = -2/5 or -1

Step-by-step explanation:

The last two terms of the expression on the left can be factored also.

  (5x+2)² +3(5x+2) = 0

And the common factor can be factored out:

  (5x+2)(5x +2+3) = 0

  5(5x +2)(x +1) = 0

Solutions to the equation make the factors zero:

  5x +2 = 0   ⇒   x = -2/5

  x +1 = 0   ⇒   x = -1

The values of x that are solutions to the equation are x = -2/5 and x = -1.

_____

Once you realize that (5x+2) is a factor, you know one solution is x = -2/5. The rest is just fluff to find the second solution. It is not required in order to answer the question.

Answer:

Range y≤-1

Domain all reals

Step-by-step explanation:

The range is the output values (y)

Y is less than or equal to -1

y≤-1

The domain is the values that the input can take

the arrows on the ends of the graph tells us x can take all real numbers

The range is the span of y-values. What is the smallest possible y-value and what is the largest possible y-value?

For this problem, the y-values start at -1 and decrease infinitely. Therefore, the range is y <= -1.

The domain is the span of x-values. What is the smallest possible x-value and what is the largest possible x-value?

For this problem, the parabola will keep expanding horizontally (or to the left and right). Therefore, the range is all real numbers.

Hope this helps!

9514 1404 393

Answer:

  1750 = 2 · 5³ · 7

Step-by-step explanation:

It is often helpful to start with divisibility rules when finding prime factors of a small composite number.

The least-significant digit is even, so we know 2 is a factor.

  1750/2 = 875

The least significant digit is 5, so we know 5 is a factor.

  875/5 = 175

  175/5 = 35

  35/5 = 7

7 is a prime number, so we're done.

The factorization is ...

  1750 = 2 · 5³ · 7

Answer:

[tex]{ \tt{ \frac{1}{24} m - \frac{2}{3} = \frac{3}{4} }} \\ \\ { \tt{ \frac{1}{24} m = \frac{17}{12} }} \\ m = 34[/tex]

Step 1: Find a common denominator

---The common denominator here is 24. So, we need to transform all of the fractions to have a denominator of 24.

1/24m - 16/24 = 18/24

Step 2: Solve

1/24m - 16/24 = 18/24

1/24m = 34/24

m = 34/24 x 24/1

m = 34

Hope this helps!

Answer:

(2, 79) (12, 24)

24-79/12-2=-55/10

m=-0.55

24=-6,6+b

30.6=b

y=-0.55x+30.6

Step-by-step explanation:

you multiply

using the equation to represent your answer

Step-by-step explanation:

When x = 0,

3x + 7

= 3 ( 0 ) + 7

= 0 + 7

= 7

When x = 4,

3x + 7

= 3 ( 4 ) + 7

= 12 + 7

= 19

When x = 8,

3x + 7

= 3 ( 8 ) + 7

= 24 + 7

= 31

When x = 14,

3x + 14

= 3 ( 14 ) + 14

= 14 ( 3 + 1 )

= 14 ( 4 )

= 56

Answer:

The 95% confidence interval for the true difference between the mean home prices in the two areas is (-$29156.52, $1956.52).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes 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.

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

First area:

33 homes, mean of $168,300, standard deviation of $37,825. Thus:

[tex]\mu_1 = 168300[/tex]

[tex]s_1 = \frac{37825}{\sqrt{33}} = 6584.5[/tex]

Second area:

33 homes, mean of $181,900, standard deviation of $25,070. Thus:

[tex]\mu_2 = 1819000[/tex]

[tex]s_2 = \frac{25070}{\sqrt{32}} = 4431.8[/tex]

Distribution of the difference:

[tex]\mu = \mu_1 - \mu_2 = 168300 - 181900 = -13600[/tex]

[tex]s = \sqrt{s_1^2+s_2^2} = \sqt{6584.5^2 + 4431.8^2} = 7937[/tex]

Confidence interval:

[tex]\mu \pm zs[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].  

The lower bound of the interval is:

[tex]\mu - zs = -13600 - 1.96*7937 = -29156.52 [/tex]

The upper bound of the interval is:

[tex]\mu + zs = -13600 + 1.96*7937 = 1956.52[/tex]

The 95% confidence interval for the true difference between the mean home prices in the two areas is (-$29156.52, $1956.52).