A 12 ft ladder leans against the side of a house. The top of the ladder is 10ft off the ground. Find x, the angle of elevation of the ladder.
1. Remember to address each of the critical elements of the prompt:
Articulate your overall approach to solving this problem before tackling the details. In other words, think about what the question is actually asking, which pieces of information are relevant, and how you can use what you have learned to fill in the missing pieces.
2. Apply the mathematical process to solve the problem:
Interpret the word problem to identify any missing information.
Translate the word problem into an equation.
Appropriately use the order of operations and law of sines and cosines to determine the solution.
Check your work by ensuring that the known properties of triangles are met.

Answer:

[tex] \frac{1}{2} [/tex]

Step-by-step explanation:

[tex]scale \: factor = \frac{5}{10} = \frac{1}{2} \\ [/tex]

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

An insurance company examines its pool of auto insurance customers and gathers the following information: (i) All customers insure at least one car. (ii) 70% of the customers insure more than one car. (iii) 20% of the customers insure a sports car. (iv) Of those customers who insure more than one car, 15% insure a sports car. Calculate the probability that a randomly selected customer insures exactly one car, and that car is not a sports car?

Answer:

P( X' ∩ Y' ) = 0.205

Step-by-step explanation:

Let X is the event that the customer insures more than one car.

Let X' is the event that the customer insures exactly one car.

Let Y is the event that customer insures a sport car.

Let Y' is the event that customer insures not a sport car.

From the given information we have

70% of customers insure more than one car.

P(X) = 0.70

20% of customers insure a sports car.

P(Y) = 0.20

Of those customers who insure more than one car, 15% insure a sports car.

P(Y | X) = 0.15

We want to find out the probability that a randomly selected customer insures exactly one car, and that car is not a sports car.

P( X' ∩ Y' ) = ?

Which can be found by

P( X' ∩ Y' ) = 1 - P( X ∪ Y )

From the rules of probability we know that,

P( X ∪ Y ) = P(X) + P(Y) - P( X ∩ Y )    (Additive Law)

First, we have to find out P( X ∩ Y )

From the rules of probability we know that,

P( X ∩ Y ) = P(Y | X) × P(X)       (Multiplicative law)

P( X ∩ Y ) = 0.15 × 0.70

P( X ∩ Y ) = 0.105

So,

P( X ∪ Y ) = P(X) + P(Y) - P( X ∩ Y )

P( X ∪ Y ) = 0.70 + 0.20 - 0.105

P( X ∪ Y ) = 0.795

Finally,

P( X' ∩ Y' ) = 1 - P( X ∪ Y )

P( X' ∩ Y' ) = 1 - 0.795

P( X' ∩ Y' ) = 0.205

Therefore, there is 0.205 probability that a randomly selected customer insures exactly one car, and that car is not a sports car.

Answer:

probability of the event E = 1/5

Step-by-step explanation:

We are given;

Sample space, S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10},

Number of terms in sample S is;

n(S) = 10

We are given the event; E = {1, 2}

Thus, number of terms in event E is;

n(E) = 2

Now, Probability = favorable outcomes/total outcomes

Thus, the probability of the event E is;

P(E) = n(E)/n(S)

P(E) = 2/10

P(E) = 1/5

Answer:

A,D and E

Step-by-step explanation:

We are given that a function

[tex]f(x)=49(\frac{1}{7})^x[/tex]

The given function is exponential function .

The exponential function is defined for all real values of x.

Therefore, domain of f=Set of  all real numbers

Substitute x=0

[tex]y=f(0)=49>0[/tex]

Range of f is greater than 0.

x=1

[tex]y(1)=\frac{49}{7}[/tex]

x=2

[tex]y=49(\frac{1}{7})^2=\frac{1}{7}y(1)[/tex]

As x increases by 1, each value of y is one-seventh of the previous y-value.

Therefore, option A,D and E are true.

Answer:

A D E

Step-by-step explanation:

Edge2020 quiz

Answer:8.2 x 10^5

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

y = -sqrt(x) +1

We know that the domain is from 0 to infinity

The range is from 1 to negative infinity

Answer:

b

Step-by-step explanation:

e2020

Answer:

7

Step-by-step explanation:

hh

ht

th

tt

so it's a 1/4 chance

1/4 * 28 = 7

Answer:

7

Step-by-step explanation:

The probability of both coins landing on heads is:

1/2 × 1/2 = 1/4

Multiply by 28.

1/4 × 28

= 7

Work Shown:

log(200) = log(2^3*5^2)

log(200) = log(2^3) + log(5^2)

log(200) = 3*log(2) + 2*log(5)

log(200) = 3*q + 2*p

log(200) = 2p + 3q

The log rules I used were

log(A*B) = log(A)+log(B)

log(A^B) = B*log(A)

The equivalent expression of log(200) is 2p + 3q

The logarithmic expression is given as:

[tex]\mathbf{log 200}[/tex]

Rewrite as:

[tex]\mathbf{log(200) = log (25 \times 8)}[/tex]

Express as exponents

[tex]\mathbf{log(200) = log (5^2 \times 2^3)}[/tex]

Split

[tex]\mathbf{log(200) = log (5^2) +log(2^3)}[/tex]

Apply law of logarithms

[tex]\mathbf{log(200) = 2log (5) +3log(2)}[/tex]

From the question;

log(5) = p and log(2) = q

So, we have:

[tex]\mathbf{log(200) = 2p +3q}[/tex]

Hence, the equivalent expression of log(200) is 2p + 3q

Read more about logarithmic expressions at:

https://brainly.com/question/9665281

Answer:

0.989

Step-by-step explanation:

For each graduate, there are only two possible outcomes. Either they find a job in their chosen field within a year after graduation, or they do not. The probability of a graduate finding a job is independent of other graduates. So we use the binomial probability distribution 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.

A study conducted at a certain college shows that "53%" of the school's graduates find a job in their chosen field within a year after graduation.

This means that [tex]p = 0.53[/tex]

6 randomly selected graduates

This means that [tex]n = 6[/tex]

Probability that at least one finds a job in his or her chosen field within a year of graduating:

Either none find a job, or at least one does. The sum of the probabilities of these outcomes is 1. So

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

We want [tex]P(X \geq 1)[/tex]

So

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

In which

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

[tex]P(X = 0) = C_{6,0}.(0.53)^{0}.(0.47)^{6} = 0.011[/tex]

So

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.011 = 0.989[/tex]

Answer:

X is 3 units.

Step-by-step explanation:

Volume of prism is cross sectional area multiplied by length. So 1/2 ×2× x ×2 into 3x, which is equal to 6x^2. So, 6x^2=54. Therefore, x=3.

Answer:

  5.03

Step-by-step explanation:

Answer:

5.03 = AC

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp/ adj

tan 40 = AC /6

6 tan 40 = AC

5.034597787 = AC

To the nearest hundredth

5.03 = AC

Answer:

13-n=4

Subtract both sides by 13

-n=-9

n=9

Step-by-step explanation:

13 less means - and a number means n that you don’t know. is means = sign. And so we get the answer that I gave you. Thank you

Answer:

[tex]solution \\ 3(5x) + 8(2x) \\ = 3 \times 5x + 8 \times 2x \\ = 15x + 16x \\ = 31x[/tex]

hope this helps...

Good luck on your assignment...

The expression  [tex]3(5x) + 8(2x)[/tex] in simplest form is 31x.

To simplify the expression [tex]3(5x) + 8(2x)[/tex], we can apply the distributive property:

[tex]3(5x) + 8(2x)[/tex]

[tex]= 15x + 16x[/tex]

Combining like terms, we have:

[tex]15x + 16x = 31x[/tex]

Therefore, the expression [tex]3(5x) + 8(2x)[/tex] simplifies to [tex]31x.[/tex]

To learn more on Expressions click:

https://brainly.com/question/14083225

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Question:

You are interested in estimating the the mean age of the citizens living in your community. In order to do this, you plan on constructing a confidence interval; however, you are not sure how many citizens should be included in the sample. If you want your sample estimate to be within 5 years of the actual mean with a confidence level of 97% , how many citizens should be included in your sample? Assume that the standard deviation of the ages of all the citizens in this community is 18 years.

Answer:

61.03

Step-by-step explanation:

Given:

Standard deviation = 18

Sample estimate = 5

Confidence level = 97%

Required:

Find sample size, n.

First find the Z value. Using zscore table

Z-value at a confidence level of 97% = 2.17

To find the sample size, use the formula below:

[tex] n = (Z * \frac{\sigma}{E})^2[/tex]

[tex] n = ( 2.17 * \frac{18}{5})^2 [/tex]

[tex] n = (2.17 * 3.6)^2 [/tex]

[tex] n = (7.812)^2 [/tex]

[tex] n = 61.03 [/tex]

Sample size = 61.03

Answer:

7.5* 10^8

Step-by-step explanation:

(1.5 x 10^5)(5 x 10^3)

Multiply the numbers

1.5*5=7.5

Add the exponents

10 ^(5+3) = 10^8

Put back together

7.5* 10^8

This is in scientific notation

Answer:

A. The E(Y) is 0.80

B. The expected amount of the surcharges is $165

Step-by-step explanation:

A. In order to calculate the E(Y), we would have to calculate the following formula:

E(Y)=∑yp(y)

E(Y)=(0*0.5)+(1*0.25)+(2*0.20)+(3*0.05)

E(Y)=0+0.25+0.40+0.15

E(Y)=0.80

B. In order to calculate the expected amount of the surcharges we would have to calculate the following formula:

E($110Y∧2)=110E(Y∧2)

=110∑y∧2p(y)

=110((0∧2*0.5)+(1∧2*0.25)+(2∧2*0.20)+(3∧2*0.05))

110(0+0.25+0.80+0.45)

=$165

Answer:

The full name of the place is the "Danat Jebel Dhanna".  The Jebel Dhanna is currently located in the Abu Dhabi.  It is said that it is one of the most best beach in the UAE, they also say that it is the biggest resort, of course, with a bunch of hotels.

hope this helps ;)

best regards,

`FL°°F~` (floof)

Answer:

y = 2x+4

Step-by-step explanation:

First we need to find the slope using two points

(-2,0) and (0,4)

m = (y2-y1)/(x2-x1)

m = (4-0)/(0--2)

   = 4/+2

   = 2

we have the y intercept  which is 4

Using the slope intercept form of the line

y = mx+b where m is the slope and b is the y intercept

y = 2x+4

Answer:

each bag of candy is $6.00

Step-by-step explanation:

1 bag would cost $6.00

1×$6.00=$6.00

6 bags × $6.00 = $36.00

Answer:

the constant of proportionally is 6

the prices of 6 bags of candy is 36

Step-by-step explanation:

to find the constant u divide 6 by 1 to find how they multiplying it by

the prices for six bags is 36 bc u can do 6 times 6 or look at the graph and see that it lands on 36

hope this helps

Answer:

Step-by-step explanation:

The question is in complete. Here is the complete question.

"The dimensions of a triangular pyramid are shown below. The height of

the pyramid is 6 inches. What is the volume in cubic inches?

Base of triangle = 1in

height of triangle = 5in"

Given the dimension of the triangular base of base 1 inch and height 5inches with the height of the pyramid to be 6inches, the volume of the triangular pyramid is expressed as [tex]V = \frac{1}{3}BH[/tex] where;\

B = Base area

H = Height of the pyramid

Base area  B = area of the triangular base = [tex]\frac{1}{2}bh[/tex]

b = base of the triangle

h = height of the triangle

B = [tex]\frac{1}{2} * 5 * 1\\[/tex]

[tex]B = 2.5in^{2}[/tex]

Since H = 6inches

Volume of the triangular pyramid = [tex]\frac{1}{3} * 2.5 * 6\\[/tex]

[tex]V = 2.5*2\\V =5in^{3}[/tex]

Answer:

{-1, -8}

Step-by-step explanation:

Please enclose "1 - 3x" inside parentheses so the reader will know that you want the square root of all of "1 - 3x".

Squaring both sides of the given equation, we get:

1 - 3x = x^2 + 6x + 9, or  x^2 + 6x + 8 + 3x, or

x^2 + 9x + 8 = 0.  Factoring, we get:  (x + 8)(x + 1) = 0, so that the solutions are {-1, -8}.

Answer:

I hope the given equation is :

{-1, -8}

First step to solve this equation to remove square root from the left side. So, take square on each sides of the equation. Therefore,

1 - 3x = (x + 3)²

1 - 3x = (x + 3)*(x + 3) Since a² = a * a

1 - 3x = x² + 3x + 3x + 3² By multiplication.

1 - 3x = x² + 6x + 9 Combine the like terms.

x² + 6x + 9 - 1 + 3x = 0 Subtract 1 and add 3x from each sides of equation

x² + 9x + 8 = 0 Combine the like terms.

Next step is to factor the trinomial to solve the above equation for x.

For that break downn the constant 8 into two multiples so that the addition of the multiples will result the coefficient of x = 9.

So, 8 = 1 * 8

Addition of 1 and 8 will give 9. So, next step is to replace 9x with 1x + 8x. So,

x² + 1x + 8x + 8 = 0

(x² + 1x) + (8x + 8) = 0 Group the terms.

x ( x + 1) + 8 (x + 1 ) = 0 Take out the common factor from each group.

(x +1 ) ( x + 8 ) = 0 Take out the common factor (x + 1).

So, x + 1 = 0 and x + 8 = 0 Set up each factor equal to 0.

Hence, x = -1 and - 8.

Next step is to plug in -1 and -8 in the original equation to cross check the solutions.

For x = -1,

Simplify each sides separately.

2 = 2

2 = 2 is correct. So, x = -1 satisfy the equation.

Hence, x = -1 is the real solution of the given equation.

Similarly let's plug in x = -8 now. So,

Simplify each sides separately.

5 = 2

5 = 2 is not true. So, x = -8 is the extraneous solution.

Therefore, the only solution is x = -1.

Hence, the correct choice is C.

Hope this helps you!

Step-by-step explanation:

mark brainlies plssssssssss

Answer:

Step-by-step explanation:

a. The data should be analyzed using paired samples because the economist made two measurements (samples) drawn from the same pair of identical cards. Each data point in one sample is uniquely paired to a data point in the second sample.

b. A pair is made up of two identical cards where one would go into Dutch auction and the other to the first-price sealed bid auction.

c. The explanatory variables are the types of online auction which are the Dutch auction and the first price sealed bid auction. The explanation variable here is categorical: the Dutch auction and the first price sealed bid auction.

d. The response variable which is also known as the outcome variable is prices for the 2 different auction for each pair of identical cards. This variable is quantitative.

e. Null Hypothesis in words: There is no difference in the prices obtained in the two different online auction.

Alternative hypothesis: There is a difference in the prices obtained in the two different online auction.

f. The parameter of interest in this case is the mean prices of pairs of identical cards for both auction and is assigned p.

g. Null hypothesis: p(dutch) = p(first-price sealed auction)

Alternative hypothesis: p(dutch) =/ p(first-price sealed auction)

h. Assuming the p-value is 0.17 at an assed standard 0.05 significance level, our conclusion would be to fail to reject the null hypothesis as 0.17 is greater than 0.05 or even 0.01 and we can conclude that, there is no statistically significant evidence to prove that there is a difference in the prices obtained in the two different online auction.

Answer

value of x is 34 degrees  

Step-by-step explanation:

Answer:

a) P(x > 43) = 0.9599

b) P(x < 42) = 0.0228

c) P(x > 57.5) = 0.03

d) P(x = 42) = 0.

e) P(x<40 or x>55) = 0.1118

f) 43.42

g) Between 46.64 and 53.36.

h) Above 45.852.

Step-by-step explanation:

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.

In this question, we have that:

[tex]\mu = 50, \sigma = 4[/tex]

a) x>43

This is 1 subtracted by the pvalue of Z when X = 43. So

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

[tex]Z = \frac{43 - 50}{4}[/tex]

[tex]Z = -1.75[/tex]

[tex]Z = -1.75[/tex] has a pvalue of 0.0401

1 - 0.0401 = 0.9599

P(x > 43) = 0.9599

b) x<42

This is the pvalue of Z when X = 42.

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

[tex]Z = \frac{42 - 50}{4}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a pvalue of 0.0228

P(x < 42) = 0.0228

c) x>57.5

This is 1 subtracted by the pvalue of Z when X = 57.5. So

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

[tex]Z = \frac{57.5 - 50}{4}[/tex]

[tex]Z = 1.88[/tex]

[tex]Z = 1.88[/tex] has a pvalue of 0.97

1 - 0.97 = 0.03

P(x > 57.5) = 0.03

d) P(x = 42)

In the normal distribution, the probability of an exact value is 0. So

P(x = 42) = 0.

e) x<40 or x>55

x < 40 is the pvalue of Z when X = 40. So

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

[tex]Z = \frac{40 - 50}{4}[/tex]

[tex]Z = -2.5[/tex]

[tex]Z = -2.5[/tex] has a pvalue of 0.0062

x > 55 is 1 subtracted by the pvalue of Z when X = 55. So

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

[tex]Z = \frac{55 - 50}{4}[/tex]

[tex]Z = 1.25[/tex]

[tex]Z = 1.25[/tex] has a pvalue of 0.8944

1 - 0.8944 = 0.1056

0.0062 + 0.1056 = 0.1118

P(x<40 or x>55) = 0.1118

f) 5% of the values are less than what X value?

X is the 5th percentile, which is X when Z has a pvalue of 0.05, so X when Z = -1.645.

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

[tex]-1.645 = \frac{X - 50}{4}[/tex]

[tex]X - 50 = -1.645*4[/tex]

[tex]X = 43.42[/tex]

43.42 is the answer.

g) 60% of the values are between what two X values (symmetrically distributed around the mean)?

Between the 50 - (60/2) = 20th percentile and the 50 + (60/2) = 80th percentile.

20th percentile:

X when Z has a pvalue of 0.2. So X when Z = -0.84.

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

[tex]-0.84 = \frac{X - 50}{4}[/tex]

[tex]X - 50 = -0.84*4[/tex]

[tex]X = 46.64[/tex]

80th percentile:

X when Z has a pvalue of 0.8. So X when Z = 0.84.

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

[tex]0.84 = \frac{X - 50}{4}[/tex]

[tex]X - 50 = 0.84*4[/tex]

[tex]X = 53.36[/tex]

Between 46.64 and 53.36.

h) 85% of the values will be above what X value?

Above the 100 - 85 = 15th percentile, which is X when Z has a pvalue of 0.15. So X when Z = -1.037.

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

[tex]-1.037 = \frac{X - 50}{4}[/tex]

[tex]X - 50 = -1.037*4[/tex]

[tex]X = 45.852[/tex]

Above 45.852.

Answer:  55.6 days

Step-by-step explanation:

[tex]P=P_oe^{kt}\\\\\bullet \quad P=\dfrac{1}{2}P_0\\\bullet \quad k=-0.1247\\\bullet \quad t = unknown\\\\\\\dfrac{1}{2}P_o=P_oe^{-0.1247t}\\\\\\\dfrac{1}{2}=e^{-0.1247t}\\\\\\ln\bigg(\dfrac{1}{2}\bigg)=-0.1247t\\\\\\\dfrac{ln\dfrac{1}{2}}{-0.1247}= t\\\\\\\large\boxed{55.6=t}[/tex]

Answer:

x^2 - 10x

Step-by-step explanation:

2x^2 - 4x - x^2 +6x

You subtract x^2 from 2x^2 and you get x^2

Then you add 6x and 4x together and get 10x

So then you have x^2 - 10x

(plus I took the test and this was the correct answer.)

Answer: -1

Step-by-step explanation:

to calculate f(-1), you know that x = -1. so all you have to do is substitute:

f(-1) = (-1)2 + 1

f(-1) = -2 + 1

f(-1) = -1

Answer:

0

Step-by-step explanation:

Answer:

[tex]\boxed{\sf \ \ \ k = 1 \ \ \ }[/tex]

Step-by-step explanation:

hello,

saying that p-1 is a factor of [tex]p^4+p^2-p-k[/tex]

means that 1 is a root of this expression, so it comes

1+1-1-k=0

<=> 1-k=0

<=> k = 1

Answer:

B) 92.03 < μ < 97.97

99% confidence interval for the mean score of all students.

92.03 < μ < 97.97

Step-by-step explanation:

Step(i):-

Given sample mean (x⁻) = 95

standard deviation of the sample (s) = 6.6

Random sample size 'n' = 30

99% confidence interval for the mean score of all students.

[tex]((x^{-} - Z_{0.01} \frac{S}{\sqrt{n} } , (x^{-} + Z_{0.01} \frac{S}{\sqrt{n} })[/tex]

step(ii):-

Degrees of freedom

ν =   n-1 = 30-1 =29

[tex]t_{0.01} = 2.462[/tex]

99% confidence interval for the mean score of all students.

[tex]((95 - 2.462 \frac{6.6}{\sqrt{30} } , 95 + 2.462\frac{6.6}{\sqrt{30} } )[/tex]

( 95 - 2.966 , 95 + 2.966)

(92.03 , 97.97)

Final answer:-

99% confidence interval for the mean score of all students.

92.03 < μ < 97.97

Answer:

  22 m

Step-by-step explanation:

Use the formula for the area of a triangle. Fill in the known values and solve for the unknown.

  A = (1/2)bh

  594 m^2 = (1/2)(54 m)h

  h = (594 m^2)/(27 m) = 22 m

The height of the window is 22 meters.