A stainless steel patio heater is shaped like a square pyramid. The length of one side of the base is 10 inches. The slant height is 11 inches. What is the height of the heater? Round to the nearest tenth of an inch.

The probability of a home for sale having a garage but no pool is 0.42.

To do this, we need to use some probability rules. One useful rule is the formula for calculating the probability of an event not occurring. This is given by:

P(not A) = 1 - P(A)

where A is the event we are interested in, and not A is the event of A not occurring.

In this case, we are interested in the probability of a home having a garage but no pool. Let's call this event GNP (short for garage no pool). Using the information given, we know that 60% of homes have garages and 18% have both garages and pools. We can use this information to calculate the probability of a home having a garage but no pool as follows:

P(GNP) = P(G) - P(G and P)

where G is the event of a home having a garage and P is the event of a home having a pool.

Substituting the values we have:

P(GNP) = 0.6 - 0.18

P(GNP) = 0.42

To know more about probability here

https://brainly.com/question/11234923

#SPJ4

Answer:

GRAPH OF 3x + y = 3 (written on attachment)

GRAPH OF 2y = 10 - 6x (written on attachment)

The hospital must cut the number of overtime hours by approximately 2.91% in order to stay within budget.

To determine the required percentage reduction in overtime hours, we need to consider the impact of the nurses' hourly rate increase and the limited budget increase for overtime wages.

Let's assume the current budget for nurses' overtime wages is denoted by B, and the total number of overtime hours worked is denoted by H. The current overtime rate per hour is R.

With the 5% hourly rate increase, the new overtime rate per hour becomes 1.05R. Considering the limited budget increase of 3%, the new budget for overtime wages is 1.03B.

To calculate the required percentage reduction in overtime hours, we can set up the following equation:

(1.05R) * (1 - x) * H = 1.03B

where x represents the required percentage reduction in overtime hours.

Simplifying the equation, we have:

(1 - x) * H = (1.03B) / (1.05R)

Now, let's solve for x:

1 - x = (1.03B) / (1.05R * H)

x = 1 - [(1.03B) / (1.05R * H)]

Here, we can see that the required percentage reduction in overtime hours, represented by x, depends on the values of B, R, and H.

It's important to note that without knowing the specific values of B, R, and H, we cannot calculate the exact percentage reduction. However, based on the provided information, we can determine the maximum percentage reduction that the hospital must make to stay within budget.

By assuming that B, R, and H are constant, we can use the given constraints to calculate an approximate percentage reduction. Based on the constraints of a 3% budget increase and a 5% hourly rate increase, the hospital would need to reduce the number of overtime hours by approximately 2.91% to maintain a balanced budget.

Please keep in mind that this approximation may vary depending on the specific values of B, R, and H.

Learn more about budget here

https://brainly.com/question/29154668

#SPJ11

A 95% confidence interval for the difference in mean revenue at the box office for drama and comedy movies is (7.44, 72.56).

We have given that,

Sample mean of peoples who like drama , x₁-bar = 190

Sample mean of peoples who like comedy,x₂-bar = 150

Sample size for darama sample, n₁ = 17

Sample size for comedy sample, n₂ = 14

Standard deviations, s₁ = 60

Standard deviations, s₂ = 30

Confidence level = 0.95 or 95%

Using Z-table , Z-score for 95% confidence level is 1.96..

We have to calculate a 95% confidence interval for the difference in mean revenue at the box office for drama and comedy movies.

It is given by following Confidence interval formula,

x₁-bar - x₂-bar ± Z ( √(s₁²/n₁ + s₂²/n₂))

= 190 - 150 ± 1.96(√(60²/17 + 30²/14))

= 40 ± 1.96(√3600/17 + 900/14))

= 40 ± 32.56

= (7.44, 72.56)

Hence, the required 95% confidence interval is

(7.44, 72.56) .

To learn more about Confidence interval, refer:

https://brainly.com/question/17212516

#SPJ4

Complete question:

A Hollywood studio believes that a movie that is considered a drama will draw a larger crowd on average than a movie that is considered a comedy. To test this theory. the studio randomy selects several movies that are classified as dramas and several movies that are classified as comedies and determines the box office revenue for. each movie. The results of the survey are as follows. Assurne that the population variances are approximately equal, Calculate a

95%

confidence interval for the difference in mean revenue at the box office for drama and comedy movies: Let dramas be Population-1 and comedies be Population 2. Write your answer using interval notation and round the interval endpoints to two decimal places

Answer:

The answer is 12

Step-by-step explanation:

Trust me, kay? Please mark Brainliest!!!!

Answer:

12.8

Step-by-step explanation:

16% of 80

\(\frac{16}{100}\) × 80

\(\frac{16}{10}\) × 8

\(\frac{16}{5}\) × \(\frac{4}{1}\)

16 × 4

5

12\(\frac{4}{5}\) = 12.8

The conclusion in the argument is "the good, according to Plato, is that which furthers a person's real interests." which it is the correct answer.

In a well-structured argument, the conclusion is what the argument aims to prove.

The conclusion can be located at the beginning or end of the argument, and it should always be precise, clear, and understandable.

The conclusion in the argument above is that "the good, according to Plato, is that which furthers a person's real interests."

The argument tries to explain that the good in Plato's philosophical teachings is a thing that advances a person's genuine interests.

The statement "it follows that" is the premise that links the argument with the conclusion.

The premise and the conclusion have a relationship of cause and effect, and this implies that the argument's conclusion is "the good, according to Plato, is that which furthers a person's real interests."

Therefore, the right option is: the good, according to Plato, is that which furthers a person's real interests.

Learn more about premise here

https://brainly.com/question/28918493

#SPJ11

The possible change in volume of the spherical golf ball is approximately 5.24 cubic millimeters with a relative error of 0.05%.

The volume of a sphere can be calculated using the formula V = (4/3)πr^3, where r is the radius of the sphere.

Given that the radius of the golf ball is 5 mm, with a possible measurement error of 0.1 mm, we can write:

r = 5 ± 0.1 mm

Using differentials, we can find the change in volume ΔV caused by a change in radius Δr:

ΔV = dV/dr * Δr

Taking the differential of the volume formula with respect to r, we get:

dV/dr = 4πr^2

Substituting r = 5 mm, we get:

dV/dr = 4π(5)^2 = 100π mm^2

Therefore, the possible change in volume is:

ΔV = (100π mm^2) * (0.1 mm) = 10π mm^3 ≈ 31.42 mm^3

The original volume of the golf ball is:

V = (4/3)π(5)^3 = 523.6 mm^3

Hence, the relative error in the volume calculation is:

ΔV/V * 100% = (31.42/523.6) * 100% ≈ 0.05%

For more questions like Volume click the link below:

https://brainly.com/question/1578538

#SPJ11

The cost of 7 bags is $52.78

At the produce store, the cost of 4 bags is $30.16

The first step is to calculate the cost of one bag

4= 30.16

1= x

Cross multiply both sides

4x= 30.16

x= 30.16/4

x= 7.54

Therefore the cost of 7 bags can be calculated as follows

1= 7.54

7= y

y= 7.54 × 7

= 52.78

Hence the cost of 7 bags is $52.78

Read more on cost here

https://brainly.com/question/29204000

#SPJ1

Answer:

25

Step-by-step explanation:

Answer:

N=1

Step-by-step explanation:

Move all terms containing  n

to the left side of the equation.

− 3 n − 7 = − 10

Move all terms not containing  n

to the right side of the equation.

− 3 n=− 3

Divide each term by  −3

and simplify.

n = 1

Answer:

If you were look for the cords for the blue one. It will be (-5,4) for O (-2,1) for W and (-7,-3) for N

If it was for the Green one. It will be (-5,-2) for 'O (-1,-2) for 'W and (-5,-7) for 'N

Hope This Helped

The two triangles are similar If they have the same shape, but their sizes are different.

Similar triangles are triangles that have the same shape, but their sizes may be same or different. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion. The similarity of triangles are denoted by ‘~’ symbol

AA (or AAA) or Angle-Angle Similarity

If any two angles of a triangle are equal to any two angles of another triangle, then those two triangles are similar to each other.

SAS or Side-Angle-Side Similarity

If the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed between those two sides in both the triangle are equal, then two triangles are said to be similar.

SSS or Side-Side-Side Similarity

If all the three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar.

Therefore, two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

To learn more about similarity refer here

https://brainly.com/question/25631497

#SPJ4

a. The probability that the network crashes on both Monday and Tuesday is 0.1024; b. The probability that the network crashes for the first time on Thursday is 0.1389 ; c. The probability that the network crashes every day is 0.0001; d. The probability that the network crashes on at least one day is 0.3222.

We can approach this problem using the binomial distribution. Let X be the number of days in a week that the network crashes. Then X follows a binomial distribution with parameters n = 5 (number of days in a workweek) and p = 0.16 (probability of a crash on any given day).

a. The probability that the network crashes on both Monday and Tuesday is:

P(X = 2) = (5 choose 2) * (0.16)² * (1-0.16)³

= 0.1024

b. The probability that the network crashes for the first time on Thursday is the probability that it does not crash on Monday, Tuesday, or Wednesday, but does crash on Thursday and/or Friday. So:

P(X = 1) * P(no crashes on Monday, Tuesday, Wednesday) = (5 choose 1) * (0.16) * (1-0.16)⁴ * (0.84)³

= 0.3808 * 0.3652

= 0.1389

c. The probability that the network crashes every day is:

P(X = 5) = (5 choose 5) * (0.16)⁵ * (1-0.16)⁰

= 0.0001

d. The probability that the network crashes on at least one day is the complement of the probability that it does not crash at all during the week:

P(X >= 1) = 1 - P(X = 0)

= 1 - (5 choose 0) * (0.16)⁰ * (1-0.16)⁵

= 1 - 0.6778

= 0.3222

Therefore, a. The probability that the network crashes on both Monday and Tuesday is 0.1024; b. The probability that the network crashes for the first time on Thursday is 0.1389 ; c. The probability that the network crashes every day is 0.0001; d. The probability that the network crashes on at least one day is 0.3222.

To know more about probability check the below link:

https://brainly.com/question/251701

#SPJ4

\(7x - 2 = 4 \\ 7x = 4 + 2 \\ 7x = 6 \\ x = \frac{6}{7} \)

\(2x + 7y = 28 \\ This \: has \: infinetly \: many \: solutions \: as \: i \: is \: linear \: equation.\)

Answer:

The amount invested at 7% is $12,000 while the amount invested at 10% is $8,000

Step-by-step explanation:

The given parameters are;

The total amount Hank invested = $20,000

The interest earned in one year = $1640

Hank invested part of the $20,000 at 7% interest and part of the $20,000 at 10%

Let the part invested at 7% = X and the part invested at 10% = Y, we have;

7% of X + 10% of Y = $1640 which gives;

0.07×X + 0.1×Y = $1640.....................(1)

X + Y = $20,000.................................(2)

Multiply equation (1) by 10 and subtract equation (1) from equation (2) to get;

X + Y - 10×(0.07×X + 0.1×Y) = $20,000 - 10×$1640

X - 0.7·X - Y - Y = $20,000 - $16,400 = $3,600

0.3·X = $3,600

X = $3,600/0.3 = $12,000

X = $12,000

Y = $20,000 - X = $20,000 - $12,000 = $8,000

Y = $8,000

Therefore, the amount invested at 7% = $12,000 and the amount invested at 10% = $8,000.

Answer:

$8,000 at 10%

$12,000 at 7%

Step-by-step explanation:

Let the part invested at 10% = x

Let the part invested at 7% = $20,000 - x

7% = 0.07

10% = 0.10

Hank invested a total of $20,000, part at 7%

0.07(20000 - x)

And part at 10%

0.10(x)

Hence, we have:

0.10x + 0.07(20000 - x) = 1640

0.10x + 1400 - 0.07x = 1640

0.10x - 0.07x = 1640 - 1400

0.03x = 240

x = 240/0.03

x = 8000

Hence, the amount he invested at 10% = $8,000

The amount he invested at 7% =

$20,000 - x

= $20,000 - $8,000

= $12,000

By probability, she will not receive a phone call from any of her grandchildren after 146 days

In those circumstances, probability helps in assessing the likelihood of an event. Probability plays a significant role in daily life. political strategy analysis, blood type determination, sports and gaming strategies, insurance buying or selling, online shopping, and online gaming.

There is a \(\frac{2}{3}\) chance that the first child won't call, a \(\frac{3}{4}\) chance that the second child won't call, and a \(\frac{4}{5}\) chance that the third child won't call on any given day. There is a \(\frac{2}{3} *\frac{3}{4} * \frac{4}{5} = \frac{2}{5}\) chance that no child calls her on a randomly selected day.

When we consider a sample of 360 days, in particular, this "unrigorous" reasoning becomes rigorous due to linearity of expectation; over the first 360 days, 360 * 2/5 = 144 days will pass without a phone call. Now, we just check the remaining days. On days $361 and $362, no one calls her. On days 363 and 364, she receives calls from children every three and four days, respectively. On day 365, she receives calls every five days. Therefore, to get our answer of 146, we two more days in  144.

To know more about probability visit:-

brainly.com/question/11234923

#SPJ4

The probability that a homebuilder takes 200 days or less to complete a house is approximately 0.8238, or 82.38%.

Explanation :

To answer this question, we can use the concept of the z-score. The z-score tells us how many standard deviations a data point is from the mean.

Let's calculate the z-score for a completion time of 200 days:
z = (x - μ) / σ
where x is the completion time, μ is the mean, and σ is the standard deviation.
Plugging in the values, we get:
z = (200 - 176.7) / 24.8 = 0.93

To find the probability associated with this z-score, we can use a z-table or a calculator. In this case, the probability is 0.8238.

This means that there is an 82.38% chance that the completion time of a house will be 200 days or less, given that the completion time follows a normal distribution with a mean of 176.7 days and a standard deviation of 24.8 days.

Learn more about probability from a given link :

https://brainly.com/question/23417919

#SPJ11

Answer:

D is the correct answer!

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

A function is a process or a relation that associates each element x of a set X, the domain of the function, to a single element y of another set Y (possibly the same set), the codomain of the function.

The requried Burger Quick is able to estimate its wait time more consistently because it has a smaller IQR. Option A is correct.

A straightforward method of expressing statistical data on a plot in which a rectangle is drawn to represent the second and third quartiles, with a vertical line inside to indicate the median value.

Here,
Burger Quick is able to estimate its wait time more consistently because it has a smaller interquartile range (IQR). The IQR is a measure of the spread of the middle 50% of the data and is calculated as the difference between the third quartile (Q3) and the first quartile (Q1). The smaller the IQR, the more consistent the data is around the median, which is represented by the line within the box in the box plot.

In this case, Burger Quick has a smaller IQR (8.0) compared to Super Fast Food (7.0), indicating that the wait times at Burger Quick are more consistent around the median. The range, which is the difference between the maximum and minimum values, is not a good measure of consistency as it is affected by outliers.

Therefore, based on the given information, Burger Quick is able to estimate its wait time more consistently because it has a smaller IQR.

Learn more about box plots here:

brainly.com/question/1523909

#SPJ1

the value of F(9) is approximately 23.308.

To find the value of F(9) given that F(x) is an antiderivative of (ln x)^3/x and F(1) = 0, we can use the fundamental theorem of calculus.

According to the fundamental theorem of calculus, if F(x) is an antiderivative of a function f(x), then:

∫[a,b] f(x) dx = F(b) - F(a)

Since F(1) = 0, we can write:

∫[1,9] (ln x)^3/x dx = F(9) - F(1)

To evaluate the integral, we can make a substitution:

Let u = ln x, then du = (1/x) dx

The integral becomes:

∫[ln 1, ln 9] u^3 du

Integrating u^3 with respect to u:

[(1/4)u^4] | [ln 1, ln 9] = (1/4)(ln 9)^4 - (1/4)(ln 1)^4

Since ln 1 = 0, we have:

(1/4)(ln 9)^4 - (1/4)(ln 1)^4 = (1/4)(ln 9)^4

Therefore, F(9) - F(1) = (1/4)(ln 9)^4

Since F(1) = 0, we can conclude that F(9) = (1/4)(ln 9)^4.

Calculating this value:

F(9) = (1/4)(ln 9)^4 ≈ 23.308

to know more about calculus visit:

brainly.com/question/29097043

#SPJ11

Therefore, when the number of copies made in a month is above 4000, company A's charges are higher than company B's charges in the given equation.

Let's start by setting up an equation to represent the cost of renting a copier from each company:

Cost for company A = 0.10x + 200

Cost for company B = 0.05x + 400

where x is the number of copies made in a month.

To find the number of copies above which company A's charges are higher than company B's charges, we need to set the two equations equal to each other and solve for x:

0.10x + 200 = 0.05x + 400

0.05x = 200

x = 4000

To know more about equation,

https://brainly.com/question/28243079

#SPJ11

The difference between the largest and smallest number of dimes that could be in the bank is 100.

Let's assume the number of nickels in the piggy bank is N, the number of dimes is D, and the number of quarters is Q.

From the given information, we can form two equations based on the number of coins and the total value:

Equation 1: N + D + Q = 100 (total number of coins)

Equation 2: 0.05N + 0.10D + 0.25Q = 8.35 (total value in dollars)

Now, let's determine the range for the number of dimes, D.

To find the smallest number of dimes, we maximize the number of nickels and quarters, which minimizes the number of dimes. Let's assume all remaining coins (100 - D) are nickels:

Equation 1: D + Q = 100 - N

Equation 2: 0.10D + 0.25Q = 8.35 - 0.05N

Since we want to minimize D, let's consider the maximum values for N and Q. Assuming all remaining coins are nickels, we have N = 100 - D - Q.

Plugging in these values, we get:

0.10D + 0.25Q = 8.35 - 0.05(100 - D - Q)

0.10D + 0.25Q = 8.35 - 5 + 0.05D + 0.05Q

0.05D + 0.20Q = 3.35

To simplify, we multiply the equation by 20:

D + 4Q = 67

The largest value for Q would be when D = 0. Therefore, if we assume all remaining coins are quarters, we have:

D = 0

Q = (100 - D) = 100

So, the largest number of quarters is 100, and the largest number of dimes is 0.

To find the largest value for D, we maximize the number of dimes. Assuming all remaining coins are nickels:

N = 100 - D - Q

Plugging this into Equation 2:

0.10D + 0.25Q = 8.35 - 0.05(100 - D - Q)

0.10D + 0.25Q = 8.35 - 5 + 0.05D + 0.05Q

0.05D + 0.20Q = 3.35

Multiplying by 20:

D + 4Q = 67

The smallest value for Q would be when D = 100. Therefore, if we assume all remaining coins are quarters, we have:

D = 100

Q = (100 - D) = 0

So, the smallest number of quarters is 0, and the smallest number of dimes is 100.

The difference between the largest and smallest number of dimes is:

100 (largest) - 0 (smallest) = 100.

Therefore, the difference between the largest and smallest number of dimes that could be in the bank is 100.

To learn more about piggy banks:

https://brainly.com/question/29624113

#SPJ11

The point (-10, 1) in Cartesian-Coordinates can be represented in polar coordinates as approximately (10.05, 3.0416 radians).

To convert the point (-10, 1) from Cartesian-Coordinates to polar coordinates, we can use the formulas:

r = √(x² + y²)

θ = arctan(y / x)

We know that, the point is (-10, 1), we substitute the values into the formulas:

We get,

r = √((-10)² + 1²) = √(100 + 1) = √101 ≈ 10.05, and

The point lies in second-quadrant, so, the angle is measured counterclockwise from the positive x-axis, which means it is between π/2 and π radians.

Therefore, The adjusted θ is : θ = π + arctan(1/-10) ≈ 3.0416 radians.

Learn more about Polar Coordinates here

https://brainly.com/question/105227

#SPJ4

Answer:

186

Step-by-step explanation:

Divide 4 and 6.0 get 86 add 100 = 86 + 100 = 186

100% right. Kinda confusing ..

Step-by-step explanation:

\( f(x) = - 3 {x}^{2} + 9x - 2\)

A) f(-2) + f(1) = -32 + 4 = -28

B) f(-2) - f(1) = -32 - 4 = -36

Answer: 3

Step-by-step explanation:

1: 3x-y+3=0

2: y=3x+3

y-intercept: (0,3) y value = 3

plug in and check: 3x-3+3=0 x=0

Answer:

y = -14

Step-by-step explanation:

3y = -42

Divide both sides by 3:

y = -14

Answer:

-14

Step-by-step explanation:

-42 divided by 3 =-14

The turntable turns through a 45.0 degree angle, the radial line also rotates by 45.0 degrees. Therefore, the direction of the ladybug's displacement vector is 45.0 degrees counterclockwise from the positive x-axis.

Part A:
The radius of the turntable is half of the diameter, which is 6.0 in. The ladybug crawls in a straight radial line to the edge, which means its displacement vector is equal to the radius of the turntable. Therefore, the magnitude of the ladybug's displacement vector is 6.0 in.

Part B:
The direction of the ladybug's displacement vector is the same as the direction of the radial line from the center of the turntable to the edge. This direction can be described by the angle between the positive x-axis and the radial line.

Since the turntable turns through a 45.0 degree angle, the radial line also rotates by 45.0 degrees. Therefore, the direction of the ladybug's displacement vector is 45.0 degrees counterclockwise from the positive x-axis.

Visit here to learn more about displacement vector  :  https://brainly.com/question/30466999
#SPJ11

The system of linear equation which can be used to find the number of nickles n, and quarters q Anatoily has are n + q = 104  and 1/20(104 - q) + (1/4)q = 22there are total 20 nickels and 84 quarters Anatoily has.

According to the given question.

Total number of nickles and quarters Anatoily have is 104.

'n' represents the total numbers of nickles and 'q' represents total number of quarters. So, the linear equation which represents the given condition

⇒ n + q = 104

Since, 20nickles = 1 dollar

⇒ 1 nickle = 1/20 dollar

And, 4 quarters = 1 dollar

⇒ 1quarter = 1/4 dollar

Here, it is also given that combination of 104 nickels and quarters totaling $22.

So, we have an other linear equation $(1/20)n + $(1/4)q = $22

Form

n + q = 104

We can write

n = 104 - q

Substitute the value of n in $(1/20)n + $(1/4)q = $22

Therefore,

$1/20(104 - q) + $(1/4)q = $22

⇒ 5.2 - q/20 + q/4 = 22

⇒ 5.2 +  (-q + 5q)/20 = 22

⇒ 5.2 + 4q/20 = 22

⇒ 5.2 + q/5 = 22

⇒ q/5 = 22 - 5.2

⇒ q/5 = 16.8

⇒ q = 16.8 × 5

⇒ q = 84

Therefore,

n = 104 - 84

⇒ n = 20

Hence,  the system of linear equation which can be used to find the number of nickles n, and quarters q Anatoily has are n + q = 104  and 1/20(104 - q) + (1/4)q = 22there are total 20 nickels and 84 quarters Anatoily has.

Find out more information about system of linear equations here:

https://brainly.com/question/19549073

#SPJ4

To solve the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0, we can use algebraic methods and the unit circle to determine the values of x that satisfy the equation.

1. Start by rearranging the equation to a quadratic form: \(6sin^2(x)\) + 6sin(x) + 1 = 0.

2. Notice that the equation resembles a quadratic equation in terms of sin(x). Let's substitute sin(x) with a variable, such as u: \(6u^2\) + 6u + 1 = 0.

3. Solve this quadratic equation for u. You can use the quadratic formula or factorization methods to find the values of u. The solutions are u = (-3 ± √3) / 6.

4. Since sin(x) = u, substitute back the values of u into sin(x) to obtain the values for sin(x): sin(x) = (-3 ± √3) / 6.

5. To find the values of x, we can use the inverse sine function. Take the inverse sine of both sides: x = arcsin[(-3 ± √3) / 6].

6. The arcsin function has a range of [-π/2, π/2], so the values of x lie within that range. Use a calculator to find the approximate values of x based on the values obtained in step 5.

7. Plot the obtained x-values on the graph to show the solutions of the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0. The graph will illustrate the points where the curve intersects the x-axis.

For more such questions on algebraic, click on:

https://brainly.com/question/4344214

#SPJ8