A 25-ft ladder leans against a building so that the angle between the ground and the ladder is 51 degrees. How high does the ladder reach up the side of the building? Please round your answer to 2 decimal places.

Answer:

[tex]P(X>8)=e^{-1}[/tex]

Step-by-step explanation:

The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:

[tex]P(X=x)=\lambda e^{-\lambda x}, x>0[/tex]

And 0 for other case. Let X the random variable that represent "The number of years a radio functions" and we know that the distribution is given by:

[tex]X \sim Exp(\lambda=\frac{1}{8})[/tex]

We can assume that the random variable t represent the number of years that the radio is already here. So the interest is find this probability:

[tex]P(X>8|X>t)[/tex]

We have an important property on the exponential distribution called "Memoryless" property and says this:

[tex]P(X>a+t| X>t)=P(X>a)[/tex]

Where a represent a shift and t the time of interest.

On this case then [tex]P(X>8|X>t)=P(X>8+t|X>t)=P(X>8)[/tex]

We can use the definition of the density function and find this probability:

[tex]P(X>8)=\int_{8}^{\infty} \frac{1}{8}e^{-\frac{1}{8}x}dx[/tex]

[tex]=\frac{1}{8} \int_{8}^{\infty} e^{-\frac{1}{8}x}dx[/tex]

[tex]=[lim_{x\to\infty} (-e^{-\frac{1}{8}x})+e^{-1}]=0+e^{-1}=e^{-1}[/tex]

Answer:

P = 68/552 = 0.123 or 12.3%

Step-by-step explanation:

First, let's calculate the probability of getting a lemon donut. We have only 4 lemon donut among 24 donuts, so probability is:

P(A) = 4/24

Next, as we already ate the lemon donut, we only have 23 donuts now, and among these 23, 17 are custard filled, so probability of choosing one of those is:

P(B) = 17/23

But we want to know the probability that the custard filled donut is choosen after you eat the lemon one so:

P(B|A) = P(A) * P(B)

Replacing:

P(B|A) = 4/24 * 17/23

P(B|A) = 68/552 = 0.123 or 12.3%

Answer:

  see below

Step-by-step explanation:

The signs on the bottom line alternate, so the value of k is, indeed, a lower bound.

_____

Comment on lower bound for this cubic

The signs of the coefficients alternate, so Descartes' rule of signs will tell you there are zero negative real roots. That is, 0 is a lower bound for real roots. No synthetic division is needed.

Answer:

Equation: 5t² − 10t + 13 = 0

Answer: No

Step-by-step explanation:

h(t) = -5t² + 10t + 22

When h(t) = 35:

35 = -5t² + 10t + 22

5t² − 10t + 13 = 0

This equation must have at least one real solution if the ball is to reach a height of 35 meters.  Which means the discriminant can't be negative.

b² − 4ac

(-10)² − 4(5)(13)

100 − 260

-160

The ball does not reach a height of 35 meters.

Answer:

Equation: 5t² − 10t + 13 = 0

Answer: No

Answer:

  > 6 cm

Step-by-step explanation:

Let b represent the length of the base in cm. Then the perimeter is ...

  b + (b -2) + (b +3) > 19

  3b +1 > 19 . . . . . . collect terms

  3b > 18 . . . . . . . . subtract 1

  b > 6  . . . . . . . . . divide by 3

The length of the base is greater than 6 cm.

The length of the base of the triangle is greater than 6 cm.

To find the length of the base of the triangle, let's assume that the base is x cm. According to the question, one side is 2 cm shorter than the base, so its length would be (x - 2) cm. The other side is 3 cm longer than the base, so its length would be (x + 3) cm. The perimeter of a triangle is the sum of all its sides, so we can set up an equation: x + (x - 2) + (x + 3) > 19. Solving this inequality will give us the value of x, which is the length of the base.

Therefore, the length of the base of the triangle is greater than 6 cm.

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Answer:it will take the two plants 6 weeks before the heights are the same

Step-by-step explanation:

Jill planted two flowers in her garden.

The first flower is 2 inches tall, and it is growing 2.25 inches each week. Since the growth rate is in an arithmetic progression, we will apply the formula for finding the nth term of the series

Tn = a + (n - 1)d

Tn = the nth height of the first flower

a = the initial height of the first flower

d = the common difference in height of the first flower weekly

n = number of weeks

From the information given,

For the first flower,

a = 2

d = 2.25

Tn ?

n ?

Tn = 2 + (n - 1)2.25

For the second flower,

a = 5.75

d = 1.5

Tn ?

n ?

Tn = 5.75 + (n - 1)1.5

To determine the number of weeks that it will take until the two plants are the same height, we would equate Tn for both flowers. It becomes

2 + (n - 1)2.25 = 5.75 + (n - 1)1.5

2 + 2.25n - 2.25 = 5.75 + 1.5n - 1.5

Collecting like terms

2.25n - 1.5n = 5.75 - 1.5 - 2 + 2.25

0.75n = 4.5

n = 4.5/0.75

n = 6 weeks

To find out how many weeks it will be until the two plants are the same height, set up an equation and solve for x. The plants will be the same height after 5 weeks.

To find out how many weeks it will be until the two plants are the same height, we need to set up an equation. Let the number of weeks be represented by x. The height of the first plant can be represented as 2 + 2.25x, and the height of the second plant can be represented as 5.75 + 1.5x. Set these two expressions equal to each other: 2 + 2.25x = 5.75 + 1.5x.

To solve for x, subtract 1.5x from both sides: 2 + 0.75x = 5.75.

Then, subtract 2 from both sides: 0.75x = 3.75.

Finally, divide both sides by 0.75 to solve for x: x = 5.

Answer:

  {A, H, M, O, P, R, S, T} = {1, 7, 5, 0, 8, 6, 4, 9}

or

  {O, A, S, M, R, H, P, T} = {0, 1, 4, 5, 6, 7, 8, 9}

Step-by-step explanation:

Starting in the thousands column, we see the sum P+M+A mod 10 = M, so P + A = 10 or 11. That is, there is a carry to the next column of 1, meaning T + 1 = O, and that sum must also create a carry of 1, so S + 1 = M.

In order for T + 1 to generate a carry, we must have T = 9 and O = 0.

Now, consider the 10s column. This has 36 +A +(carry in) mod 10 = 9. So, A+(carry in) = 3.

Considering the 1s column, we have 9+0+2H+S = H+10 or H+20. We know H+S+9 cannot be 10, so it must be 20. That means H+S = 11, and (carry in) to the 10s column must be 2. Since A = 3 - (carry in), we must have A=1.

At this point, we have ... A=1, T=9, O=0, S+H=11, S+1=M.

Now, consider the 100s column. We know the carry in from the 10s column is 3, so we have 3+2A+R=A+10. Since we know A=1, this means 5+R=11, or R=6.

The carry in to the 1000s column is 1, so we have P+A+1 = 10, or P=8.

__

Our assignments so far are ...

  0 = O, 1 = A, 6 = R, 8 = P, 9 = T.

and we need to find S, M, and H such that M=S+1 and S+H=11. We know S and H cannot be 2, 3, or 5, because the 11's complement of those digits is already assigned. That leaves 4 and 7 for S and H, but we also need an unassigned value that is 1 more than S. These considerations make it necessary that S=4, M=5, H=7.

Then the addition problem is ...

  8197 + 90 + 5197 +491694 +19 = 505197

_____

Final assignments are ...

  O = 0, A = 1, S = 4, M = 5, R = 6, H = 7, P = 8, T = 9

Answer:

The worth of 375 Croatian Kuna  = $ 55.54

Step-by-step explanation:

Here, given:

The worth of  121.32 Croatian Kuna   = $18

Now, let us assume the worth of 375 Croatian Kuna  = $ m

As, both have same units in conversion at the same rate,

So, by the RATIO OF PROPORTION:

[tex]\frac{18}{121.32 }   = \frac{m}{375}[/tex]

Solving for the value of m, we get:

[tex]m = \frac{18}{121.32}  \times 375  = 55.64[/tex]

or, m = $55.64

Hence, the worth of 375 Croatian Kuna  = $ 55.54

Answer: Robert's present age is 10 years

Robert father's present age is 40 years

Step-by-step explanation:

Let r = Robert's current age

Let y = Robert father's current age

Robert's father is 4 times as old as robert. This means that

y = 4x

After 5 years, Robert's father will be three times as old as Robert. This means that

y + 5 = 3(x+5)

y + 5 = 3x + 15 - - - - - - - ;1

We will substitute y = 4x into equation 1. It becomes

4x + 5 = 3x + 15

Collecting like terms,

4x - 3x = 15 - 5

x = 10

y = 4x

Substituting x = 10,

y = 4× 10 = 40 years

The system of equations that represents the number of each vehicle rented is: x + y + z = 155, x = 9y, and y = 3z.

The question represents a system of linear equations. With the agreed notations: Let x represent cars, let y represent vans and let z represent trucks. We are given that:

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Answer:

Step-by-step explanation:

Refer to attached graph

Parent function:

Transformations

1. Reflection over x-axis: f(x) →  -f(x)

2. Horizontal shift 4 units to the right: g(x) → g(x - 4)

3. Vertical shift 3 units up: h(x)  → h(x) + 3

This is the final function

Answer:

Their intercepts are unique.

Explanation:

[tex]\displaystyle x^3 - 24x^2 + 192x - 508 = (x - 8)^3 + 4[/tex]

This graph's x-intercept is located at approximately [6,41259894, 0], and the y-intercept located at [0, −508].

[tex]\displaystyle g(x) = x^3[/tex]

The parent graph here, has both an x-intercept and y-intercept located at the origin.

I am joyous to assist you anytime.

What is the question?

Answer:

The answer is in the explanation.

Step-by-step explanation:

450x2=900 167x2=334 Then you add those together and you get 1,234 then you do 234x2=468 156x2=312 then you add those two, and you get 780 then you add 1,234+780= 2014. For his brother you do 254x2=508 and 56x2=112 then you add them and you get 620. Then you subtract 2014-620= 1394. That is the final answer. Hope it helps!

Answer:

Each container contains [tex]2.5 \ pounds \ \ OR \ \ \frac{11}{4} \ pounds \ \ OR \ \ 2 \frac{3}{4} \ pounds[/tex] of cat food.

Step-by-step explanation:

Given:

Amount of cat food = 8 1\4 pounds.

Also 8 1\4 can be rewritten as 8.25 pounds

Number of containers =3

We need to find the amount of cat food in each container.

Amount of cat food in each container can be calculated by Dividing Amount of cat food she has with number of Containers.

Amount of cat food in each container = [tex]\frac{8.25}{3}= 2.75 \ pounds[/tex]

2.75 pounds ca be rewritten as [tex]\frac{11}{4} \ pounds \ \ OR \ \ 2 \frac{3}{4} \ pounds[/tex]

Hence Each container contains [tex]2.5 \ pounds \ \ OR \ \ \frac{11}{4} \ pounds \ \ OR \ \ 2 \frac{3}{4} \ pounds[/tex] of cat food.

The circumference of circle with radius 18 inches in terms of pi is 36π inches

From the given figure, radius "r" = 18 inches

We have to find circumference of circle

circumference would be the length of the circle if it were opened up and straightened out to a line segment.

The circumference of circle is given as:

[tex]\text {circumference of circle }=2 \pi r[/tex]

Where "r" is the radius of circle

Substituting the value r = 18 inches in above formula,

[tex]\text {circumference of circle }=2 \times \pi \times 18=36 \pi[/tex]

Thus circumference of circle in terms of pi is 36π inches

Answer:

Step-by-step explanation:

Mae king earns a weekly salary of $305 plus a 7.5% commission on sales at a gift shop. This means that the total amount that she can earn in a week is not fixed. If in a week, she sold 4,300 worth of merchandise, her commission on this amount of sales will be 7.5 % of 4,300

Commission on sales = 7.5/100× 4300 = 0.075×4300= $332.25

Amount of money made for the week will be the sum of her weekly salary and the commission earned on sales. It becomes

305 + 332.25 = $627.5

Answer: Norm Alpina did better with z-score 0.79

Step-by-step explanation:

Z score formula = (raw score - mean) / standard deviation

For Jack Hartig,

score = 4; mean = 2.9; standard deviation = 2.1

Hence, Z score = (4 - 2.9) /2.1

= 1.1/2.1

= 0.52

For Norm Alpina,

score = 8; mean = 6.5; standard deviation = 1.9

Hence, Z score = (8 - 6.5) /1.9

= 1.5/1.9

= 0.79

Relatively, Norm Alpina did better for having Z score 0.79

By calculating z-scores for both students, which represent the number of standard deviations their scores are from the mean, Norm Alpina has a higher z-score and hence performed relatively better compared to Jack Hartig on their respective quizzes.

In order to determine which student did relatively better on their quizzes, we need to calculate the z-scores for each student. A z-score indicates how many standard deviations an observation is above or below the mean. The formula for a z-score is Z = (X - μ) / σ, where X is the score, μ(mu) is the mean, and σ(sigma) is the standard deviation.

For Jack Hartig:

Z = (4 - 2.9) / 2.1
 = 1.1 / 2.1
 = 0.524

For Norm Alpina:

Z = (8 - 6.5) / 1.9
 = 1.5 / 1.9
 = 0.789

Norm Alpina's z-score is higher, indicating that, relatively speaking, he performed better than Jack Hartig on the quiz based on how their scores relate to their respective class means and standard deviations.

Answer:

The value of x is [tex]\frac{10}{3}[/tex] hours.

Step-by-step explanation:

Machine A = 5 hours

Machine B = x hours

Machine A and B = 2 hours

Using the formula: [tex]\frac{T}{A}  + \frac{T}{B} = 1[/tex]

where:

T is the time spend by both machine

A is the time spend by machine A

B is the time spend by machine B

[tex]\frac{2}{5}  + \frac{2}{x}  = 1[/tex]

Let multiply the entire problem by the common denominator (5B)

[tex]5x(\frac{2}{5}  + \frac{2}{x} = 1)[/tex]

2x + 10 = 5x

Collect the like terms

10 = 5x - 2x

10 = 3x

3x = 10

Divide both side by the coefficient of x (3)

[tex]\frac{3x}{3}  = \frac{10}{3}[/tex]

[tex]x = \frac{10}{3}[/tex] hours.

Therefore, Machine B will fill the same lot in [tex]\frac{10}{3}[/tex] hours.

Answer:

-12

Step-by-step explanation:

Answer:

The first One

Step-by-step explanation:

I just got 100% on My Quiz

Answer:

  23°

Step-by-step explanation:

Let the interior angles of ΔABC be referenced by A, B, and C. The definition of point D means that ΔDAB is an isosceles triangle, so we have the relations ...

  A + B + 118 = 180 . . . . interior angles of ΔABC

  A = B +16 . . . . . . . . . . base angles of ΔDAB

Using the expression for A in the second equation to substitute into the first equation, we get ...

  (B+16) +B +118 = 180

  2B + 134 = 180 . . . . . collect terms

  2B = 46 . . . . . . . . . . . subtract 134

  B = 23 . . . . . . . . . . . . divide by 2

m∠ABC = 23°

Answer:

[tex]6^{14}[/tex]

Step-by-step explanation:

Use the "Power Law" of exponents that tells us that when you have a base to a power "n" and all that raised to a power "m", it is the same as writing the original base to the single exponent which is the product of n time m:

[tex](b^n)^m=b^{n*m}[/tex]

therefore in your case, the base "b" is 6, the exponent "n" is 2, and the exponent "m" is 7. Then:

[tex](6^2)^7=6^{2*7}=6^{14}[/tex]

Final answer:

To simplify the expression [tex](6^2)^7[/tex] using a single exponent, multiply the inner exponent 2 by the outer exponent 7, which yields 6¹⁴.

Explanation:

To write the expression [tex](6^2)^7[/tex] using a single exponent, you need to apply the rule for raising a power to a power. This rule states that you multiply the exponents together. So for our expression, we have the base number 6 raised to the power of 2, and this result is then raised to the power of 7. To combine them into a single exponent, you multiply 2 by 7, which gives you 14.

Therefore,[tex](6^2)^7[/tex] can be simplified to 6¹⁴. This is because when you raise a power to another power, the powers are multiplied: for example, (a^b)^c = a^(b*c).

Answer:

Open circle to the right of 4

x > 4

Step-by-step explanation:

Add 7 to both sides

2x > 8

x > 4

Open circle to the right of 4

Answer:

The length of the longer side is 4.48 inches.

Step-by-step explanation:

Given,

Length of diagonal = 6 in

Length of Short side = 4 in

Solution,

Let the length of long side be x.

Since the card is in the shape of rectangle. On drawing the diagonal the rectangle divides into two equal triangle.

So for find out the length of other side we use the Pythagoras theorem, which states that;

"In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides."

[tex]Hypotenuse^2=(Short\ side)^2+(Long\ side)^2[/tex]

[tex]\therefore 6^2=4^2+x^2\\36=16+x^2\\x^2=36-16=20\\x=\sqrt{20} =2\sqrt{5}[/tex]

[tex]x=2\times2.24=4.48\ in[/tex]

Thus the length of the longer side is 4.48 inches.

Answer:

d b f

Step-by-step explanation:

Answer with Step-by-step explanation:

We have to prove that

[tex]sin 2\theta=2sin\theta cos\theta[/tex] by using Euler's formula

Euler's formula :[tex]e^{i\theta}=cos\theta+isin\theta[/tex]

[tex]e^{i(2\theta)}=(e^{i\theta})^2[/tex]

By using Euler's identity, we get

[tex]cos2\theta+isin2\theta=(cos\theta+isin\theta)^2[/tex]

[tex]cos2\theta+isin2\theta=(cos^2\theta-sin^2\theta+2isin\theta cos\theta)[/tex]

[tex](a+b)^2=a^2+b^2+2ab, i^2=-1[/tex]

[tex]cos2\theta+isin2\theta=cos2\theta+i(2sin\theta cos\theta)[/tex]

[tex]cos2\theta=cos^2\theta-sin^2\theta[/tex]

Comparing imaginary part on both sides

Then, we get

[tex]sin2\theta=2sin\theta cos\theta[/tex]

Hence, proved.

Answer:

1740%.

Step-by-step explanation:

We have been given that the pawnbroker loans you ​$600. One month​ later, you get the guitar back by paying the pawnbroker ​$1470.

We will use simple interest formula to solve our given problem.

[tex]A=P(1+rt)[/tex], where,

A = Final amount after t years,

P = Principal amount,

r = Annual interest rate in decimal form,

t = Time in years.

1 month = 1/12 year

[tex]1470=600(1+r*\frac{1}{12})[/tex]

[tex]1470=600+\frac{600}{12}*r[/tex]

[tex]1470=600+50*r[/tex]

[tex]1470-600=600-600+50*r[/tex]

[tex]870=50*r[/tex]

[tex]50r=870=[/tex]

[tex]\frac{50r}{50}=\frac{870}{50}[/tex]

[tex]r=17.4[/tex]

Since our interest rate is in decimal form, so we will convert it into percentage by multiplying by 100 as:

[tex]17.4\times 100\%=1740\%[/tex]

Therefore, you paid an annual interest rate of 1740%.

Answer:

Step-by-step explanation:

280 cubit

Answer:

Step-by-step explanation:

The formula for the volume,V of the square base pyramid is

V = 1/3(lwh)

Where

l = length of one side of the base of the pyramid.

w = length of the other side of the base of the pyramid.

h = the perpendicular height of the pyramid. Since the base of the pyramid is a square, l = w

The Volume, V is given as 18069333.3333 cubits^3

l = 440 cubits

w = 440 cubits

18069333.3333 = 1/3 × 440 × 440 × h

18069333.3333 = 64533.33h

h = 18069333.3333/64533.33

h = 280 cubits

Answer:

12.5 cm

Step-by-step explanation:

16 - 9 = 7

7 (1/2) = 3.5

9 + 3.5 = 12.5

15 - 3.5 = 12.5

Answer: 5.1667 gallons of coffee had been dispensed

Step-by-step explanation:

Let x represent the number of gallons of coffee that had been dispensed.

By the end of each day, the coffee urn, which had started out with 7 1/4 gallons of coffee, was left with 2 1/12 gallons. This means that the initial number of gallons of coffee was 7 1/4 = 7.25 gallons

The amount left after dispense x gallons is 2 1/12 = 2.0833 gallons.

Therefore,

x +2.0833 = 7.25

x = 7.25 - 2.0833 = 5.1667 gallons

[tex]\boxed{(r-s)(x)=-3x-1} \\ \\ \boxed{(r\cdot s)(x)=10x^2-5x} \\ \\ \boxed{(r+s)(-2)=-15}[/tex]

In this exercise, we have the following functions:

[tex]r(x)=2x-1 \\ \\ s(x)=5x[/tex]

And they are defined for all real numbers x. So we have to write the following expressions:

First expression:

[tex](r-s)(x)[/tex]

That is, we subtract s(x) from r(x):

[tex](r-s)(x)=2x-1-5x \\ \\ Combine \ like \ terms: \\ \\ (r-s)(x)=(2x-5x)-1 \\ \\ \boxed{(r-s)(x)=-3x-1}[/tex]

Second expression:

[tex](r\cdot s)(x)[/tex]

That is, we get the product of s(x) and r(x):

[tex](r\cdot s)(x)=(2x-1)(5x) \\ \\ By \ distributive \ property: \\ \\ (r\cdot s)(x)=(2x)(5x)-(1)(5x) \\ \\ \boxed{(r\cdot s)(x)=10x^2-5x}[/tex]

Third expression:

Here we need to evaluate:

[tex](r+s)(-2)[/tex]

First of all, we find the sum of functions r(x) and s(x):

[tex](r+s)(x)=2x-1+5x \\ \\ Combine \ like \ terms: \\ \\ (r+s)(x)=(2x+5x)-1 \\ \\ (r+s)(x)=7x-1[/tex]

Finally, substituting x = -2:

[tex](r+s)(-2)=7(-2)-1 \\ \\ (r+s)(-2)=-14-1 \\ \\ \boxed{(r+s)(-2)=-15}[/tex]

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