A 20-foot ladder is placed against a building. If the top of the ladder will lean against the building 15-feet high, how far away from the base of the building is the bottom of the ladder located? Include a sketch that shows all known information and clearly shows what you need to find. Show all work and give the exact answer.

Answer:

£1.53 per litre

Step-by-step explanation:

original = 1.02

if it is increased by 2/3 then we do 1.02 / (2/3) =£1.53 per litre

Answer:

The answer is option 3.

Step-by-step explanation:

In order to solve the equation, you have to add 0.2 to both sides to eliminate -0.2 on the left side and make x the subject :

[tex]4x - 0.2 = 1.9[/tex]

[tex]4x - 0.2 + 0.2 = 1.9 + 0.2[/tex]

[tex]4x = 2.1[/tex]

Answer:

Add 0.2 to both sides of the equation

Step-by-step explanation:

4x-0.2=1.9

+0.2   +  0.2

4x=2.1

:4     :4

x=2.1/4

Answer:

Tan<C=2.4

Step-by-step explanation:

Opp=36

Adj=15

Tan<C=opp/adj

Tan<C=36/15

Tan<C=2.4

Hope this helps :) ❤

Answer:

11 and one fourth.

or

[tex]11\dfrac{1}{4}[/tex]

Step-by-step explanation:

Given the expression to be solved:

8 and one-half minus 2 + 4 and three-fourths

Let us solve them step by step:

8 and one-half can be represented as:

[tex]8\dfrac{1}{2}[/tex]

Method to solve a mixed fraction of the form [tex]p\frac{q}{r}[/tex] is:

[tex]p\dfrac{q}{r} = \dfrac{p\times r+q}{r}[/tex]

[tex]8\dfrac{1}{2}= \dfrac{8 \times 2+1}{2} = \dfrac{17}{2}[/tex]

Similarly, solving 4 and three-fourths:

[tex]4\dfrac{3}{4} = \dfrac{4 \times 4+3}{4} = \dfrac{19}{3}[/tex]

Now, the given expression:

[tex]8\dfrac{1}{2}-2+4\dfrac{3}{4}[/tex]

[tex]\Rightarrow \dfrac{17}{2} -2+\dfrac{19}{4}\\\Rightarrow \dfrac{17 \times 2-2 \times 4+19\times 1}{4}\\\Rightarrow \dfrac{34-8+19}{4}\\\Rightarrow \dfrac{45}{4}\\\Rightarrow 11\dfrac{1}{4}[/tex]

So, the answer is 11 and one fourth.

Answer:

11 and 1/4 on edge or B

Step-by-step explanation:

Answer:

cot(A-B) = 3/19

Step-by-step explanation:

The formula for cot(A-B) = (Cot A Cot B + 1 ) / (Cot B - Cot A)

we know that cot A = 1/ Tan A

Given

tan A=2/3

therefore cot A = 1/ tan A = 1/2/3 = 3/2

tan B= -3/5  

cot B = 1/ tan B = 1/-3/5 = -5/3

Thus,

(Cot A Cot B + 1 ) = (3/2)*(-5/3 )+ 1 = -5/2 +1 = (-5+2)/2 = -3/2

(Cot B - Cot A) = -5/3 -3/2 = (-5*2) + (-3*3) / 2 = -10 -9/2 = -19/2

Thus,

cot(A-B) = (Cot A Cot B + 1 ) / (Cot B - Cot A) = -3/2  / -19/2 = 3/19

Thus,

cot(A-B) = 3/19

This question is incomplete, here is the complete question:

Suppose in the next year, 2007, College D's expenses and enrollment remain about the same, but in addition to their current revenues, they receive an additional $50,000,000 grant. This would allow them to reduce average tuition by how much?

A) $1388.89

B) $3571.43

C) $5555.56

D) $9500.00

E) $25888.89

number of students = 36,000

Answer: A) $

1388.89

Step-by-step explanation:

the college received additional grant which is $50,000,000

and the number of students is 36,000,

and we also know that expenses and enrollment remained the same.

So if we have more money (grants) and nothing changed (expenses remain the same)

dividing the grant by the number of students will show just how much the average tuition fee would be reduced

therefore R = G/n

R = 50,000,000 / 36000

R = 1,388.888 ≈  $1388.89

Answer:

1057

Step-by-step explanation:

tower is 60 feet high.

angle of 3.25 degrees.

3.25/360 * 2 * pi * r = the arc length of this angle.

that would be equal to 0.0567232007* r

if we assume the arc length and the height of the tower are approximately equal, then 0.0567232007 * r = 60

solving for r, we get r = 60/0.0567232007 = 1057.768237 feet.

that's about how far the tower is from the observer.

since the arc length is going to be a little longer than the length of the chord formed by the flagpole, this means that the distance of 1057.768237 meters is going to be a little less than the actual distance.

Answer:

≈ 1058 ft

Step-by-step explanation:

Use of arc formula: s=rθ

Given:

r= s/θ= 60/0.0567 ≈ 1058 ft

Think about this. If we were to align the coefficients with their solutions to form this matrix, it would be the following -

[tex]\begin{bmatrix}2&-6&-2&|&1\\ 0&3&-2&|&-5\\ 0&2&2&|&-3\end{bmatrix}[/tex]

Now this is one way to assign the coefficients. As you can see, 2, - 6, - 2 are present as the coefficients for the first row. Similarly 0, 3, - 2 are present as the coefficients for the second row - ( as one term is missing from this row, it is replaced with a " 0 " ). The same applies for the third row. The end values of the system of equation is present as the last column.

The options are assigned in a manner with which the coefficients and variables are present in two columns, while the end values of the system of equation given, is present as the last column. Knowing the arrangement of both the coefficients and the end values of the system of equation, all we have to do is add these " variables " as one column -

Solution = Option B

Answer: C. y ≤ 2/3x + 1/5

Step-by-step explanation: From 1/5 on the y coordinate plane go up 2 and right 3 and it perfectly matches, so it would be C. 100% on Edge2020.

Answer:

C

Step-by-step explanation:

just did the test.

[tex]50/20=20/x\implies50x=400\implies\boxed{x=8\mathrm{ft}}[/tex]

Hope this helps.

The length of the shadow cast by the flag pole is 6.4 feet.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

We are given that;

Height of building= 50 foot

Shadow= 20foot

Now,

Let x be the length of the shadow cast by the flag pole. Then we have:

2050​=x20​

Cross-multiplying, we get:

50x=20×20

Dividing both sides by 50, we get:

x=5020×20​

Simplifying, we get:

x=58​×4

Multiplying, we get:

x=6.4

Therefore, by the proportion the answer will be 6.4 feet.

More can be learned about proportions at;

brainly.com/question/24372153

#SPJ2

They got 5 yards on 3 plays. For total yards multiply the 3 plays by 5 yards. The first play was negative, so add the negative value.  The answer is A.

Answer:

A

Step-by-step explanation:

Answer:

the minimum sample size n = 11.03

Step-by-step explanation:

Given that:

approximate value of the population standard deviation [tex]\sigma[/tex] = 49

level of significance ∝ = 0.01

population mean = 38

the minimum sample size n = ?

The minimum sample size required can be determined by calculating the margin of error which can be re[resented by the equation ;

Margin of error = [tex]Z_{ \alpha /2}} \times \dfrac{\sigma}{\sqrt{n}}[/tex]

[tex]38 = \dfrac{2.576 \times 49}{\sqrt{n}}[/tex]

[tex]\sqrt{n} = \dfrac{2.576 \times 49}{38}[/tex]

[tex]\sqrt{n} = \dfrac{126.224}{38}[/tex]

[tex]\sqrt{n} = 3.321684211[/tex]

[tex]n= (3.321684211)^2[/tex]

n ≅ 11.03

Thus; the minimum sample size n = 11.03

Answer:

C.  (x - 9)(x^2 + 9x + 81).

Step-by-step explanation:

The cube identities are

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

a^3 + b^3 = (a + b)(a^2 - ab + b^2)

Checking against the list the one that fits is the difference formula:

x^2 - 9^2 = (x - 9)(x^2 + 9x + 81).

a=1, b = 9, ab = 1 *9 = 9.

Answer:

The probability is 0.4647

Step-by-step explanation:

The variable X is the life of an electric component in years.

X follows a exponential distribution, it means that the probability that the life of an electric component is less than x years is calculated as:

[tex]P(X<x)=1-e^{\frac{-x}{\beta } }[/tex]

Where [tex]x\geq0[/tex] and [tex]\beta[/tex] is the mean life of the electric component.

So, replacing x by 5 and [tex]\beta[/tex] by 8, we get that the probability that a randomly selected component has a life less than 5 years is:

[tex]P(X<5)=1-e^{\frac{-5}{8 } }=0.4647[/tex]

Answer:

Option (4)

Step-by-step explanation:

Surface area of a prism = 2B + P×h

where B = Area of the triangular base

P = perimeter of the triangular base

h = height of the prism

B = [tex]\frac{1}{2}(\text{leg 1})(\text{leg 2})[/tex]

Since, (Hypotenuse)² + (Leg 1)² + (Leg 2)² [Pythagoras theorem]

(20)² = (12)² + (Leg 2)²

Leg 2 = [tex]\sqrt{400-144}[/tex]

          = 16 units

Therefore, B = [tex]\frac{1}{2}\times 12\times 16[/tex]

                     = 96 units²

P = 12 + 16 + 20

P = 48 units

h = 7.5 units

Surface area of the prism = 2(96) + (48×7.5)

                                           = 192 + 360

                                           = 552 units²

Therefore, surface area of the given triangular prism = 552 units²

Option (4) will be the answer.

Answer:

Yes

Step-by-step explanation:

You see that angle D and angle A are congruent, and you see that angle C and angle F are congruent. In addition, line AC is congruent to DF. This means that yes, those triangles are congruent because of the ASA postulate.

Answer:

E

Step-by-step explanation:

(x+8)×8=12²=144

x+8=144/8=18

x=18-8=10

The value of x is 10.

When a tangent and secant share a common endpoint outside the circle the product of the secant and the external part of the secant is equal to the square of the tangent.

internal part of the secant = (x+8),

external part of the secant = 8,

tangent = 12,

[tex](x+8)\times 8 = 12^2\\8x+64 = 144\\8x = 144-64\\8x = 80\\x = \dfrac{80}{8}\\x=10[/tex]

Hence, the value of x is 10.

Learn more about tangent-secant theorem:

https://brainly.com/question/10732273

Answer:

7

Step-by-step explanation:

Answer: The box with three shaded squares and one non-shaded square

Step-by-step explanation:

You are trying to find the representation of the shaded region.

The scale shows point A at 0.75, and the scale can range from 0 to 1.

0.75 is equal to 3/4 of 1

3 of the 4 squares are shaded

So, the common ratio is 3:4 or 3/4

(8cm×5cm)+(1/2×5×5)cm^2

=40cm^2+12.5cm^2

=52.5cm^2

Answer:

b

Step-by-step explanation:

Answer:

Assuming that the null hypothesis is true and that the new cancer drug shrinks tumors by the same amount as the gold-standard drug, the probability that the test will lead the researcher to this decision = 95%

Step-by-step explanation:

The nulll hypothesis is correct and we are not rejecting it, which means we are making the correct decision.

P(not rejecting the null | null hypothesis is true)

= 1 - P(rejecting null hypothesis | null hypothesis is true)

= 1 - P(type I error)

P(type I error) = significance level of the test = 0.05

P(not rejecting the null | null hypothesis is true)

= 1 - 0.05

= 0.95

= 95%

Hope this Helps!!!

Answer:

Step-by-step explanation:

Since 15 liters of water flow through a water pipe and enter a tank within 4.5 minutes, the same amount of water would flow through a similar pipe at the same time. Therefore, if two similar water pipes are used, the volume of water that would flow into the tank in 4.5 minutes is 15 × 2 = 30 liters

Therefore, the time it will take to pump 727.5 liters of water into a water tank using 2 similar water pipes is

(727.5 × 4.5)/30 = 109.125 minutes

Answer:

(1) A Normal approximation to binomial can be applied for population 1, if n = 100.

(2) A Normal approximation to binomial can be applied for population 2, if n = 100, 50 and 40.

(3) A Normal approximation to binomial can be applied for population 2, if n = 100, 50, 40 and 20.

Step-by-step explanation:

Consider a random variable X following a Binomial distribution with parameters n and p.

If the sample selected is too large and the probability of success is close to 0.50 a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:

The three populations has the following proportions:

p₁ = 0.10

p₂ = 0.30

p₃ = 0.50

(1)

Check the Normal approximation conditions for population 1, for all the provided n as follows:

[tex]n_{a}p_{1}=10\times 0.10=1<10\\\\n_{b}p_{1}=100\times 0.10=10=10\\\\n_{c}p_{1}=50\times 0.10=5<10\\\\n_{d}p_{1}=40\times 0.10=4<10\\\\n_{e}p_{1}=20\times 0.10=2<10[/tex]

Thus, a Normal approximation to binomial can be applied for population 1, if n = 100.

(2)

Check the Normal approximation conditions for population 2, for all the provided n as follows:

[tex]n_{a}p_{1}=10\times 0.30=3<10\\\\n_{b}p_{1}=100\times 0.30=30>10\\\\n_{c}p_{1}=50\times 0.30=15>10\\\\n_{d}p_{1}=40\times 0.10=12>10\\\\n_{e}p_{1}=20\times 0.10=6<10[/tex]

Thus, a Normal approximation to binomial can be applied for population 2, if n = 100, 50 and 40.

(3)

Check the Normal approximation conditions for population 3, for all the provided n as follows:

[tex]n_{a}p_{1}=10\times 0.50=5<10\\\\n_{b}p_{1}=100\times 0.50=50>10\\\\n_{c}p_{1}=50\times 0.50=25>10\\\\n_{d}p_{1}=40\times 0.50=20>10\\\\n_{e}p_{1}=20\times 0.10=10=10[/tex]

Thus, a Normal approximation to binomial can be applied for population 2, if n = 100, 50, 40 and 20.

Answer:

a. A point estimate of the BMI for adults in the United States can be calculated from the sample mean, which has a value M=44.57.

b. The sample standard deviation is s=79.9507.

c. The 95% confidence interval for the BMI of adults in the United States is (26.18, 62.96).

Step-by-step explanation:

We start by calculating the sample mean and standard deviation of the BMI data:

[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{75}(16.2+31.1+24.8+. . .+22.9)\\\\\\M=\dfrac{3343}{75}\\\\\\M=44.57\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{74}((16.2-44.57)^2+(31.1-44.57)^2+(24.8-44.57)^2+. . . +(22.9-44.57)^2)}\\\\\\s=\sqrt{\dfrac{473016.8667}{74}}\\\\\\s=\sqrt{6392.1198}=79.9507\\\\\\[/tex]

We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=44.57.

The sample size is N=75.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{79.9507}{\sqrt{75}}=\dfrac{79.9507}{8.66}=9.232[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=75-1=74[/tex]

The t-value for a 95% confidence interval and 74 degrees of freedom is t=1.993.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=1.993 \cdot 9.232=18.39[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 44.57-18.39=26.18\\\\UL=M+t \cdot s_M = 44.57+18.39=62.96[/tex]

The 95% confidence interval for the BMI of adults in the United States is (26.18, 62.96).

Answer:

Step-by-step explanation:

Confidence interval measures the degree of uncertainty and certainty and comprises a range of values that might contain an unknown population parameter. A 99% confidence interval means we can expect that 99% of the 18 samples taken contains the parameter mean values between the upper and the lower bound values from the data collected from the 18 CEOs.

Answer:

50% chance.

Step-by-step explanation:

There are 3 numbers that are either greater than 4 or less than 2. They are 1, 5, and 6. There is a 3/6 chance you roll one of them or 50% chance.

Hey there! :)

Answer:

P(greater than or less than 2) = 50%.

Step-by-step explanation:

Numbers greater than 4: 5, 6

Numbers less than 2: 1

Total of 3 numbers that fit the criteria. Therefore:

P(greater than 4 or less than 2) = # of numbers / total

P(greater than 4 or less than 2) = 3 / 6 = 1 / 2

Convert fraction to percent:

1/2 × 100 = 50%

Answer:

[tex]g\left(x\right)=-2x^{2}-3[/tex]

Step-by-step explanation:

I graphed both of the functions on the graph below to find the equation for g(x).

Answer:

t = 16.3 s

Step-by-step explanation:

The equation to determine the time it will take to get to the canyon floor is.

H = ut - 1/2(gt²)

In this case

U = initial velocity= 0

H = 1300 metres

g = -9.8 ms^-2

1300= 0 - 1/2(-9.8t²)

1300= 9.8t²/2

1300*2= 9.8t²

2600= 9.8t²

2600/9.8= t²

265.306= t²

√265.306 = t

16.288 =t

To one decimal place

t = 16.3 s

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▹ Answer

1. x = -7

2. y = 7

▹ Step-by-Step Explanation

x - y = -7

x - 0 =7

x = -7

x - y = -7

0 - y = -7

y = 7

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

x-int: (-7,0)

y-int: (0,7)

Step-by-step explanation:

Hope it helps <3