the basketball court will be similar to an NCAA basketball court, which has a length of 94 feet and a width of 50 feet. the school plans to make the width of the new court 45 feet. find the perimeters of an NCAA court and the new court in the school

Answer:

y=2 is the correct ans.

here, tge equn of st line passing through the point (3,2) and is also parallel to y axis.

we have, equn of st line parallel to y xaus is y= b

so , the equn of st line passing through the point (3,2) is y= 2 (where 2 is likely to b).

The 90% Confidence interval will be (56.84  - 83.16).

The value of the sample is 30 and

the value of sample mean (X) = 70

The standard error(SE) = 8

for 90% CI in normal distribution ,  we have the z-value = 1.645

and the margin of error will be = ± SE x z-value

                                                = ± 8 x 1.645

                                                = ±  13.16

The confidence interval is given by  = mean ±  Margin of error

∴ The lower limit will  be =  mean - margin of error

                                          = 70 - 13.16

                                          = 56.84

The upper limit will be = mean + margin of  error

                                     =  70 + 13.16

                                     =  83.16

∴ 90% CI of normal distribution is ( 56.84  -   83.16 )

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Step-by-step explanation: To show that T is invertible, we need to show that T is both injective and surjective.

First, to show that T is injective, we need to show that if T(x1, x2) = T(y1, y2), then (x1, x2) = (y1, y2). So:

T(x1, x2) = T(y1, y2)

(6x1 - 8x2, -5x1 + 7x2) = (6y1 - 8y2, -5y1 + 7y2)

This gives us two equations:

6x1 - 8x2 = 6y1 - 8y2

-5x1 + 7x2 = -5y1 + 7y2

We can rewrite these equations as a matrix equation:

[6 -8; -5 7] [x1; x2] = [y1; y2]

This is a linear system of equations with the coefficient matrix [6 -8; -5 7], which we can row-reduce to get:

[1 0; 0 1] [x1; x2] = [(7/29)y1 + (8/29)y2; (5/29)y1 + (6/29)y2]

Since the coefficient matrix reduces to the identity matrix, we can see that the system has a unique solution for any given (y1, y2), which means that T is injective.

Next, to show that T is surjective, we need to show that for any (y1, y2) in R^2, there exists (x1, x2) in R^2 such that T(x1, x2) = (y1, y2). So we need to solve the equation T(x1, x2) = (y1, y2):

(6x1 - 8x2, -5x1 + 7x2) = (y1, y2)

This gives us two equations:

6x1 - 8x2 = y1

-5x1 + 7x2 = y2

We can rewrite these equations as a matrix equation:

[6 -8; -5 7] [x1; x2] = [y1; y2]

Since we showed earlier that the coefficient matrix [6 -8; -5 7] is invertible, we can solve for [x1; x2] using the formula:

[x1; x2] = [6 -8; -5 7]^-1 [y1; y2]

We can compute the inverse of [6 -8; -5 7] as follows:

[6 -8; -5 7]^-1 = (1/74) [7 8; 5 6]

Therefore, we have:

[x1; x2] = (1/74) [7 8; 5 6] [y1; y2]

= [(7/74)y1 + (8/74)y2; (5/74)y1 + (6/74)y2]

This shows that for any (y1, y2) in R^2, there exists (x1, x2) in R^2 such that T(x1, x2) = (y1, y2), which means that T is surjective.

Since T is both injective and surjective, we know that T is invertible. To find a formula for T^-1, we can use the formula for the inverse of a 2x2

0.0912   is the probability that the score will be 120 or higher .

What is probability explain with an example?

Zlower = X₁ - μ/σ  = 120 - 100/15  = 1.33

the probability is compared as

                    Pr ( X ≥ 120 ) = Pr(X - 100/15 ≥ 120 - 100/15)

                                         = Pr(Z ≥ 120 - 100/15

                                          = Pr( Z ≥ 1.33)

                                          = 0.0912

Since 0.0912 > 0.05 i.e. this IQ score is not unusual and hence I can believe the claim.

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Answer:

180 cm³

Step-by-step explanation:

2 x 5 x 6 = 30 x 2 = 60

3 x 8 x 5 = 40 x 3 = 120

120 + 60 = 180

Answer:

Irrational

Step-by-step explanation:

If we evaluate the square root, we realize that the number will not be a perfect square.

Since it is not a perfect square, it will be an unending, never-repeating, decimal.

Therefore, it will be irrational.

Answer:

She's  3 years old.

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

12/4=3

Answer:

\( \frac{4}{9} \)

Step-by-step explanation:

First add the two values

=⅓+⅑

LCM=9

=⅓x3+⅑

=

\( \frac{3}{9} + \frac{1}{9 } = \frac{4}{9} \)

50 mg be the expected mass of the sample in the year 2002, to the nearest whole number

In 1990, a sample of a radioactive isotope had an initial mass of 110 mg and decayed exponentially over time.

A measurement in 1993 revealed that the sample's mass had decayed to 90

110 mg - 90 mg = 20 mg (amount decayed in the 3 total years)

20 mg ÷ 3 years = 6.6 mg decayed per year

6.6 × 9 years (years between 1993 and 2002) = 60 mg

110 mg - 60 mg = 50 mg, rounded to 50 mg

50 mg be the expected mass of the sample in the year 2002, to the nearest whole number

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Answer:

48

Step-by-step explanation:

there are 16 cups in a gallon therefore you would multiply 16 times the number of gallons she uses which is 3 so 16 times 3 or you could do 16+16+16 which both would get you 48 so she would need 48 cups to make 3 gallons. hope this helps have a good rest of your night :)❤

Step-by-step explanation:

so, 80 L can get out of the tank every minute.

how long for 4800 L ?

that simply means "how many minutes for 4800 L ?"

and this we get by dividing 4800 by 80 (to see how often 80 fits into 4800) :

4800 / 80 = 60 minutes

so, it takes 60 minutes or 1 hour to discharge 4800 L.

Answer:

  a.  one solution (x = -8)

Step-by-step explanation:

You want to know how many solutions there are for the equation 2x -48 = 8x.

This is a 2-step linear equation.

Step 1: subtract 2x from both sides.

  -48 = 6x

Step 2: divide by the coefficient of x.

  -48/6 = -8 = x

There is one solution: x = -8.

__

Additional comment

When x terms are on both sides of the equal sign, there will be one solution if their coefficients are different.

If the coefficients are the same, the number of solutions may be 0 or infinite, depending on the constant value(s).

Answer:

Using the standard form of an equation we can easily find the intercepts.

To find the x-intercept, we set y=0 and solve for x.

To find the y-intercept, we set x=0 and solve for y.

Step-by-step explanation:

Answer:

432

Step-by-step explanation:

Answer:

432

Step-by-step explanation:

\(\frac{(14-3^{2}+1 )^{2} }{1/3.\frac{1}{4} }\)

Now, at first, we solve the numerator:

\((14-3^{2}+1 )^{2}\)

=\((14-9+1)^{2}\)

=\((15-9)^{2}\)

= \(6^{2}\)

= 36

Now let's solve the denominator:

1 ÷ 3 ×  \(\frac{1}{4}\)

=\(\frac{1}{3} . \frac{1}{4}\)

=\(\frac{1}{12}\)

Hence,

\(\frac{(14-3^{2}+1 )^{2} }{1/3.\frac{1}{4} }\)

=  \(\frac{36}{1/12}\)

= 36 x 12

= 432

Answer:

(5,0)

Step-by-step explanation:

Let y=0. Then, x=5.

The main goal of data democratization is to make data accessible to all users. Option (a) is correct.

Given the primary goal of data democratization.

Data democratization is the ability to make information in a digital format accessible to the average end user. The goal of data democratization is to allow non-professionals to collect and analyze data without the need for outside help. This requires us to support access with an easy way for people to understand data, so they can use it to accelerate decision-making and uncover opportunities for a business. The goal is for everyone to be able to use the data at any time to make decisions without barriers of access or understanding.

Therefore, the main goal of data democratization is to make data accessible to all users.

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Answer:

y = 2x - 8

Step-by-step explanation:

Note that in the point:

(x , y) = (6 , 4) ∴ (x = 6 , y = 4)

slope = m = 2

The equation of a line is:

y = mx + b

Plug in the corresponding numbers to the corresponding variables:

4 = (2)(6) + b

Simplify. Multiply 2 with 6:

4 = (2 * 6) + b

4 = 12 + b

Isolate the variable, b. Note the equal sign, what you do to one side, you do to the other. Subtract 12 from both sides:

4 (-12) = 12 (-12) + b

b = 4 - 12

b = -8

Plug in -8 for b:

y = 2x - 8 is your answer.

~

Answer:

The largest interior angle of ΔCDF is ∠F

Step-by-step explanation:

The bearings of the vertices of the triangle are given as follows;

The bearing of C from D = 056°

The bearing of F from D = 115°

The bearing of F from C = 184°

By angle addition property, we have;

The bearing of F from D = The bearing of C from D + ∠D

∴ ∠D = The bearing of F from D - The bearing of C from D

By plugging in the values, we have;

∠D = 115° - 056° = 59°

∠D in triangle ΔCDF = 59°

∠D = 59°

By alternate interior angles, we have;

The bearing of C from D = 056° = ∠BCD

Also, we have;

The bearing of F from C = ∠BCF + ∠ACB

∠ACB = 180°

∴ ∠BCF = The bearing of F from C - ∠ACB

∠BCF = 184 - 180° = 4°

∠C in ΔCDF = ∠BCD - ∠BCF

∴ ∠C = 056° - 4° = 52°

∠C = 52°

From angle sum property of ΔCDF, we have; ∠F = 180° - ∠C - ∠D

Therefore; ∠F = 180° - 52° - 59° = 69°

We have; ∠C = 52°, ∠D = 59°, ∠F = 69°, therefore;

∠F in triangle ΔCDF, has the largest interior angle.

Answer:

38.1%

Step-by-step explanation:

Increase = 29 - 21 = 8

Increase % = increase/original x 100

                  =  8/21 x 100

                  = 0.381 x 100

                  = 38.1%

The number of calories that Darrell will burn in 1 minute while kayaking is given as follows:

4 calories.

The number of calories that Darrell will burn in 1 minute while kayaking is obtained applying the proportions in the context of the problem.

For each input-output pair in the table, the constant of proportionality is of 4, hence the number of calories that Darrell will burn in 1 minute while kayaking is given as follows:

4 calories.

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Answer: (1) C. 65 + 28H < 250

(2) 6

Step-by-step explanation:

Here is the correct question:

Anand needs to hire a plumber. He's considering a plumber that charges an initial fee of $65 along with an

hourly rate of $28. The plumber only charges for a whole number of hours. Anand would like to spend no more than $250, and he wonders how many hours of work he can afford.

Let H represent the whole number of hours that the plumber works.

1) Which inequality describes this scenario?

Choose 1 answer:

A. 28 + 65H < 250

B. 28 + 65H > 250

C. 65 + 28H < 250

D. 65 +28H > 250

2) What is the largest whole number of hours that Anand can afford?​

Since the initial fee charged by the plumber is $65 and an hourly rate of $28, and Anand would like to spend no more than $250. This means that the addition of the initial fee plus the hourly fee based on number of hours worked will have to be less than $250. This can be mathematically expressed as:

= 65 + 28H < 250

That means option C is the correct answer.

Option B and D are incorrect because the greater sign was used but Anand doesn't want to spend more than $250 but the options denoted that he spent more than $250 which isn't correct.

2)'The largest whole number of hours that Anand can afford goes thus:

65 + 28H < 250

28H < 250 - 65

28H < 185

H < 185/28

H < 6.6

Therefore, the largest whole number of hours that Anand can afford is 6.

Answer: The Answer is 65+28H < 250 and the largest amount of hours is 6

Step-by-step explanation:

Mean of the sampling distribution of X is 180 and the standard deviation is approximately 4.96, which represents the average variability in sample proportions. The sampling distribution of X is approximately normal due to the Central Limit Theorem. The probability that an SRS of 1500 American adults will contain between 155 and 205 African Americans can be calculated using the normal approximation to the binomial distribution. A polling organization can compare the observed proportion of African Americans in the sample with the known proportion to check for undercovering and other sources of bias, helping identify potential issues and improve sampling methodology.

To calculate the mean and standard deviation of the sampling distribution of X, we need to use the properties of a simple random sample (SRS). In an SRS, each individual has an equal chance of being selected.

Mean of the sampling distribution of X:

The mean of the sampling distribution of X is equal to the population proportion. In this case, the proportion of African Americans in the population is 0.12.

Mean = population proportion * sample size

Mean = 0.12 * 1500

Mean = 180

Therefore, the mean of the sampling distribution of X is 180.

Standard deviation of the sampling distribution of X:

The standard deviation of the sampling distribution of X is given by the formula:

Standard deviation = sqrt((population proportion * (1 - population proportion)) / sample size)

Standard deviation = sqrt((0.12 * (1 - 0.12)) / 1500)

Standard deviation ≈ 4.96

Interpretation of the standard deviation:

The standard deviation of the sampling distribution of X represents the average amount of variability or dispersion in the sample proportions that we would expect to see across different samples of the same size.

The sampling distribution of X is approximately normal due to the Central Limit Theorem (CLT). The CLT states that for a large enough sample size, regardless of the shape of the population distribution, the sampling distribution of the sample mean or proportion tends to follow a normal distribution.

To calculate the probability that an SRS of 1500 American adults will contain between 155 and 205 African Americans, we can use the normal approximation to the binomial distribution.

P(155 ≤ X ≤ 205) = P(X ≤ 205) - P(X ≤ 155)

Using the normal approximation, we can calculate the probability using the mean and standard deviation of the sampling distribution of X:

P(X ≤ 205) = P(Z ≤ (205 - 180) / 4.96)

P(X ≤ 205) ≈ P(Z ≤ 5.04)

Similarly, calculate P(X ≤ 155) using the same formula.

A polling organization can use the results from the previous question to check for undercoverage and other sources of bias by comparing the observed proportion of African Americans in the sample (based on the calculated probability) with the known proportion of 12% in the population. If the observed proportion significantly differs from 12%, it suggests the possibility of undercoverage or bias in the sample, indicating that certain groups might be underrepresented or overrepresented. This information can help identify potential sources of bias and improve the sampling methodology to obtain a more representative sample.

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Delilah drove from her house to the football game at a rate of 40 mph. she returned using the same route, but she drove at a rate of 30 mph. if the round trip took 90 minutes,the distance between Delilah's house and the football game is approximately 25.71 miles.

To find the distance between Delilah's house and the football game, we can use the formula: distance = rate × time.

Let's assume the distance between her house and the football game is "d" miles.

On her way to the game, Delilah drove at a rate of 40 mph. So, the time it took for her to reach the game can be calculated using the equation: time = distance / rate.

Since the distance is "d" miles and the rate is 40 mph, the time is d / 40 hours.

On her return journey, Delilah drove at a rate of 30 mph. The time it took for her to return can be calculated using the equation: time = distance / rate.

Since the distance is still "d" miles and the rate is 30 mph, the time is d / 30 hours.

The total round trip time is given as 90 minutes, which is equal to 1.5 hours.

We can set up the equation: d / 40 + d / 30 = 1.5.

To solve for "d," we can multiply both sides of the equation by the least common multiple of 40 and 30, which is 120. This gives us: 3d + 4d = 180.

Simplifying, we get: 7d = 180.

Dividing both sides by 7, we find that d = 25.71.

Therefore, the approximate distance from Delilah's home to the football game is 25.71 miles.

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It is important to re-evaluate financial goals periodically, in a situation, you fell sharply behind your expected schedule with regard to saving. Option A

This is further explained below.

Generally, Targets for your savings, investments, or expenditures that you want to accomplish over a certain amount of time are examples of financial objectives. The phase of life you are now in will almost always influence the kinds of accomplishments you have your sights set on.

Personal financial goals are long-term objectives that you establish for yourself on how you will save and spend money in the future. It's up to you if these are things you want to do in the near future or later down the line. In any case, setting your objectives in advance will almost always make it simpler to achieve them.

In conclusion, In case you've fallen far behind your intended saving timeline, it's a good idea to reevaluate your financial objectives on a regular basis. Plan A

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a) Equation for length and width of the rectangular rug be \(x^{2}\) + 8x - 42 = 0

b) Width of the rectangular rug be 3.5 feet

c) Diagonal of the rectangle is 12.5 feet

What is the area of the rectangle?

The area of ​​a rectangle is the area occupied by the rectangle within its four sides or boundaries.

The area of ​​a rectangle depends on its sides. Basically, the formula for area is equal to the product of the length and width of a rectangle. The perimeter of a rectangle is equal to the sum of all its four sides

It is given that area of a rectangular rug id 42 square feet. The rug is 8 feet longer than its wide

a) Let the width of the rectangular rug be x feet

Length of the rectangular rug = (x+8) feet

area of rectangular rug = Length × width = x × (x + 8) = \(x^{2}\) + 8x

area of rectangular rug = 42

\(x^{2}\) + 8x = 42

\(x^{2}\) + 8x - 42 = 0

Therefore, equation for length and width of the rectangular rug be \(x^{2}\) + 8x - 42 = 0

b) If the length of the rectangle is 12 feet

Area of rectangle = 42 square feet

length × width = 42 square feet

12 × width = 42 square feet

width = 42/12 = 3.5

Therefore, width of the rectangular rug be 3.5 feet

c) Length of the diagonal of the rectangle = \(\sqrt{length^2+width^2}\)

= \(\sqrt{12^2+3.5^2}=\sqrt{144+12.25}=\sqrt{156.25}= 12.5\)

Therefore, diagonal of the rectangle is 12.5 feet

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Answer:

$245

Step-by-step explanation:

350× 0.30 = 105 dollars off

350-105 = 245

Answer:

245

Step-by-step explanation:

350/10=35

35=10%

35x3=105

105=30%

350-105=245

Therefore, it would take approximately 10.246 hours for the satellite to fly 82000 miles.

We can use the concept of unit rate to solve this problem.

Given that the satellite flies 73680 miles in 9.21 hours, we can calculate the unit rate of the satellite's speed:

Unit Rate = Distance / Time

= 73680 miles / 9.21 hours

≈ 8004.55 miles/hour

Now, to find out how long it would take for the satellite to fly 82000 miles, we can use the unit rate:

Time = Distance / Unit Rate

= 82000 miles / 8004.55 miles/hour

Calculating this value:

Time ≈ 10.246 hours

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Answer:

C. I and II

Step-by-step explanation:

In q1, all trig functions are positive. q2, sin and csc is positve. hope this helps!!

The price we have to pay for the disc after 10% discount is 1467 dollars.

Percentage is the value per hundredth.

According to the given question we bought a disc which costs 1630 dollars there's a 10% discount we have to find how much i have to pay.

10% of 1630 dollars will be

= (10/100) × 1630 dollars.

= 16300/100 dollars.

= 163 dollars.

So, the price we have to pay for the disc after 10% discount is

= (Total amount - Discount amount)

= ( 1630 - 163 ) dollars.

= 1467 dollars.

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(a) Objective function: Maximize Z = x1 + 2x2

Functional constraints:

x1 + x2 ≤ 5 (a constraint on resource 1)

x1 + 3x2 ≤ 9 (a constraint on resource 2)

Nonnegativity constraints:

x1 ≥ 0

x2 ≥ 0

(b) Incorporate this model into a spreadsheet, and create a table with columns for x1, x2, and Z.

Enter the objective function in the Z column as "=x1+2*x2".

Enter the constraint on resource 1 as "x1+x2<=5" and the constraint on resource 2 as "x1+3*x2<=9".

Enter the nonnegativity constraints as "x1>=0" and "x2>=0".

(c) Check if (x1, x2) = (3, 1) is a feasible solution, substitute these values into the constraints, and check if they are satisfied:

x1 + x2 ≤ 5: 3 + 1 ≤ 5, so this constraint is satisfied.

x1 + 3x2 ≤ 9: 3 + 3 ≤ 9, so this constraint is also satisfied.

Therefore, (x1, x2) = (3, 1) is a feasible solution.

(d) Check if (x1, x2) = (1, 3) is a feasible solution, substitute these values into the constraints and check if they are satisfied:

x1 + x2 ≤ 5: 1 + 3 ≤ 5, so this constraint is satisfied.

x1 + 3x2 ≤ 9: 1 + 3*3 = 10, which violates this constraint.

Therefore, (x1, x2) = (1, 3) is not a feasible solution.

(e) Solve this model using Solver in Excel, follow these steps:

Click on the "Data" tab and select "Solver" from the "Analysis" group.

In the Solver Parameters dialog box, set the objective function to "Z" and select "Max" as the optimization goal.

Enter the cell range for the decision variables (x1 and x2).

Enter the cell range for the constraints (resource 1 and resource 2).

Select "Add" to add the nonnegativity constraints for x1 and x2.

Click "OK" to solve the model.

The Solver should output the optimal values of x1 = 2 and x2 = 3/2, with a maximum value of Z = 5.

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