The length of a rectangle is fourteen less than two and a half times its width. The perimeter of the
rectangle is fifty-six feet. Write an equation that can be used to find the length and width of the
rectangle described above. Solve the equation.

Using the normal distribution calculator, the probability that the mean salary of random sample of 100 workers is no more than $54,215 is  0.5171 or 51.71%.

Probability refers to the chance or likelihood that an expected event occurs out of many possible events.

Probability gives a value that lies between 0 and 1, depending on the degree of certainty.

Mean annual salary = $54,000

Standard deviation = $5,000

Sample size = 100 workers

Mean not above $54,215

Thus, the probability that the mean salary of random sample of 100 workers is no more than $54,215 is 0.5171.

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The annual salary for a certain job has a normal distribution with a mean of $54,000 and a standard deviation of $5000. What is the probability that the mean salary of a random sample of 100 workers is no more than $54,215?

Answer:

what is your question?

Lynne can buy 5 apples and 6 oranges with her $8.00.

The first thing to do is determine how much money Lynne spends on the apples. Since she is buying 5 apples,

we can multiply the price of each apple ($0.65) by 5: $5 * 0.65 = $3.25

Therefore, Lynne has $8 - $3.25 = $4.75 to spend on oranges.

Now we need to determine the maximum number of whole oranges that she can buy with $4.75. We can do this by dividing $4.75 by the price of each orange ($0.75): $4.75 ÷ $0.75 = 6.33.

Since we can't buy a fraction of an orange, the maximum number of whole oranges Lynne can buy is 6. Therefore, Lynne can buy 5 apples and 6 oranges with her $8.00.

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Yes, the rhombus is also a parallelogram

The area of the rhombus is 77 ft²

The formula for calculating the area of a rhombus is expressed as;

A = bh

Such that the parameters of the equation are verbally as;

From the information given, we have that;

base = 7ft

Height = 11 ft

Substitute the values, we get;

Area = 7(11)

Multiply the values, we have;

Area = 77 ft²

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The length of BC in the scale drawing should be approximately 9.6 feet.

We can use the Law of Cosines to solve for the actual length of BC in the roof truss, and then use the scale factor to find the corresponding length in the scale drawing.

Let c be the length of BC in the roof truss. Then we have:

c^2 = 38^2 + 22^2 - 2(38)(22)cos(115°)

c^2 ≈ 1708.07

c ≈ 41.3

The scale factor is given by the ratio of the length in the scale drawing to the actual length:

scale factor = BC in scale drawing / c

We can solve for BC in the scale drawing by multiplying both sides by c:

BC in scale drawing = scale factor × c

The scale factor is not given, but we can find it if we know the length of BC in the scale drawing. Let x be the length of BC in the scale drawing. Then we have:

scale factor = x / 22

Substituting this into the equation for BC in the scale drawing, we get:

BC in scale drawing = (x / 22) × 41.3

We want the scale drawing to be correct, which means that the length of BC in the scale drawing should be equal to x. So we set up the equation:

x = (x / 22) × 41.3

Simplifying and solving for x, we get:

x ≈ 9.6

Therefore, the length of BC in the scale drawing should be approximately 9.6 feet.

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Answer:

115 lbs = 52.16 kilograms

Step-by-step explanation:

115 pounds is a little over 52kg

Answer:

The probability is 0.933

Step-by-step explanation:

We start by calculating the z-score

Mathematically;

z-score = (x-mean)/SD

x = 4

mean = 5.5

SD = 1

z-score = (4-5.5)/1 = -1.5

So we proceed to get the probability

This is;

P( z > -1.5)

we can get this from the standard normal distribution table

That will be

P(z > -1.5) = 0.93319

To the nearest thousandth, this is 0.933

The number of 4-letter words that can be formed without any condition imposed is 8,064.

To determine the number of 4-letter words that can be formed without any conditions, we can use the concept of permutations. Since we have 8 options (a, b, c, d, e, f, g) for each letter position, we can multiply the number of options for each position to find the total number of possibilities.

For the first letter position, we have 8 options to choose from. Similarly, for the second, third, and fourth positions, we also have 8 options each. Therefore, the total number of possibilities is:

8 options for the first position × 8 options for the second position × 8 options for the third position × 8 options for the fourth position = 8 × 8 × 8 × 8 = 8,064.

Hence, there are 8,064 possible 4-letter words that can be formed without any conditions imposed.

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Answer:

SA: 456

V: 408

Step-by-step explanation:

To find the volume of this prism, you first need to find the area of the triangular base. The base has dimensions 6 by 8, and since it's a triangle, the area of the base is 6*8/2=24. Multiplying this by the length of the prism, you get a volume of 24*17=408. For the surface area, you need to find and add together the areas of all of the surfaces. We have already determined that the area of the two triangular bases are 24. The rectangle formed by the leg with length 6 has area 6*17=102, the one with length 8 has area 136, and the hypotenuse has area 170. Adding all of this together, you get a surface area of 24+24+102+136+170=456 square centimeters. Hope this helps!

Answer:

hgfdfghhgfd

Step-by-step explanation:

68.18% is the right answer

Answer: 60 minutes

Step-by-step explanation: 450 divide by 10 = 45

45+15=60

Answer:

x=43

Step-by-step explanation:

since we know already two values (90 which is the right angle and 47)

we can do 90+47 =137

180(angles in a triangle)- 137= 43

Answer:

There are 10,560 yards in 3 mile or miles in 3 yard. Both yards and miles are units of length in the US customary and imperial systems of measurement.

Answer:

1) 4 1/5 is the simplest mixed number form

2) 2.182

The value of x in the expression  (-8/15)x = 2.24 is - 4.2.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, An expression (-8/15)x = 2.24.

- 8x = 2.24×15.

- 8x = 33.6.

x =  - 4.2

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The radius of convergence (r) for the given series is 0.

To determine the radius of convergence for the given series, we need to consider the convergence of the series expansion of the function f(x) = ln(2 - x) around a specific point. The radius of convergence (r) is the distance from this point to the nearest singularity of the function.

In this case, the series expansion is centered around x = 2 since ln(2 - x) is not defined for x = 2. Therefore, the radius of convergence (r) is the distance from x = 2 to the nearest singularity.

Since the function ln(2 - x) is not defined for x = 2, we can say that the nearest singularity is located at x = 2. Hence, the distance from x = 2 to the nearest singularity is 0.

Therefore, the radius of convergence (r) for the given series is 0.

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Each row of a unitary matrix is orthogonal to every other row, and each row has a norm of 1, by the properties of unitary matrices.

In a unitary matrix, each row is orthogonal to every other row, and each row has a norm of 1 due to the properties of unitary matrices. A unitary matrix is a square matrix whose conjugate transpose (also known as the adjoint or Hermitian transpose) is equal to its inverse. Mathematically, if U is a unitary matrix, then \(U^H * U = U * U^H = I\), where \(U^H\) represents the conjugate transpose of U, and I is the identity matrix. To understand why each row of a unitary matrix is orthogonal to every other row, consider the product of two rows, say row i and row j, of the unitary matrix U. This product can be expressed as the dot product of the two rows:

\(= row_i * row{_j^H\)

Since U is unitary, the product \(U^H * U\) is equal to the identity matrix I. Therefore, we have:

\(row_i * row_j^H = (U * U^H)_{ij\)

\(= I_{ij \\= δ_{ij\)

Here, δij is the Kronecker delta, which is 1 if i = j and 0 otherwise. This implies that the dot product of row i and row j is 1 if i = j (for the same row) and 0 otherwise. Hence, the rows of a unitary matrix are orthogonal to each other. Additionally, the norm of a vector is defined as the square root of the dot product of the vector with itself. Considering a row of a unitary matrix as a vector, the dot product of a row with itself will be:

dot product(i, i) \(= row_i * row_i^H\)

=\((U * U^H)_{ii\)

=\(I_ii\)

= 1

This shows that the norm of each row of a unitary matrix is equal to 1. Therefore, each row of a unitary matrix is orthogonal to every other row, and each row has a norm of 1 due to the properties of unitary matrices.

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Answer:

Step-by-step explanation:

\(4-2b^2 +3c\\b =2\\c = -1\\4-2(2)^2 +3(-1)\\4- 2(4) -3\\4-8-3\\= -7\)

Answer:

-7

Step-by-step explanation:

Sub in the numbers

4 - 2(2)2+ 3(-1)

4 - 8 + (-3)

 = -7

Suppose a person lost 10 pounds in a month. This z-score tells you that x = 10 is 2.5  standard deviations to the right of the mean 5 pounds.

To verify that the z-score when x = 10 pounds is z = 2.5, we can use the formula:

z = (x - μ) / σ

where x is the value of the random variable, μ is the mean, and σ is the standard deviation.

Plugging in the given values, we have:

z = (10 - 5) / 2 = 2.5

This confirms that the z-score when x = 10 pounds is z = 2.5.

To determine what the z-score tells us about the location of x = 10 pounds relative to the mean, we can use the definition of a z-score:

z = (x - μ) / σ

Rearranging the formula, we have:

x = μ + zσ

So, when z = 2.5 and σ = 2, we have:

x = μ + 2.5(2) = μ + 5

This tells us that x = 10 pounds is 5 pounds above the mean. Since the z-score is positive, x = 10 pounds is to the right of the mean.

Therefore, the z-score tells us that x = 10 is 2.5 standard deviations to the right of the mean of 5 pounds.

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The area of the sector is evaluated to be equal to 9π square meters

The area of a sector is calculated by multiplying the fraction of the angle for the sector divided by 360° and πr², where r is the radius.

For the area of circle 72π m²;

πr² = 72π m²

r² = 72 m²

hence the area of the sector is calculated as follows:

area of the sector = (45°/360°) × π × 72 m²

we simplify by multiplication and division

area of the sector = 1/8 × π × 72 m²

area of the sector = π × 9 m²

area of the sector = 9π m².

Therefore, the area of the sector is evaluated to be equal to 9π square meters

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\(5-10x ~~ > ~~ 215+4x\implies 5~~ > ~~215+14x \\\\\\ -210~~ > ~~14x\implies \cfrac{-210}{14}~~ > ~~x\implies \boxed{-15~~ > ~~x} \\\\[-0.35em] ~\dotfill\\\\ 2(5+6x)~~\geqslant ~~-237-7x\implies 10+12x~~\geqslant ~~-237-7x \\\\\\ 10+19x~~\geqslant ~~-237\implies 19x~~\geqslant ~~-247 \\\\\\ x~~\geqslant ~~\cfrac{-247}{19}\implies \boxed{x~~\geqslant ~~-13}\)

Check the picture below.

Answer:

42 minutes

Step-by-step explanation:

6x7=42

Answer:

1) 3 people do 4 walls in 32 minutes

We make the assumptions that all people work at the same rate and each person starts and finishes at the same time. Since there are 3 people, each person does 1/3 of the total work. Therefore each person finishes their portion of the job in 32 minutes

2) 3 * 1/3 = 1 person does 4 * 1/3 = 4/3 walls in 32 minutes

The unit rate (the rate for 1 person to do 1 wall) is as follows

3) 1 person does 4/3 * 3/4 = 1 wall in 32 * 3/4 = 24 minutes

Since we need 4 people to do 7 walls then 1 person needs to do 1/4 of the work. So the following is true

4) 4 * 1/4 = 1 person does 7 * 1/4 = 7/4 wall

As we said before in #3

1 person does 1 wall in 24 minutes

So we conclude

5) 1 person does 1 * 7/4 = 7/4 walls in 24 * 7/4 = 42 minutes

And finally

6) 1 * 4 = 4 people do 7/4 * 4 = 7 walls in 42 minutes

Answer:

120

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

12 minutes is 1/5 of an hour.

She can blow up 5 balloons, so she can blow 25 balloons per hour.

Multiply 25 by 3 you get 75.

1.1) The volume of the cube is 27 cubic centimeters. 1.2)the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).

1.3) the mass of the water cube is 27 grams. 1.4) the weight of the water and the ice would be the same under the same conditions. 1.5)In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.

1.1) The volume of the cube can be calculated using the equation: Volume = width x height x length. In this case, the cube measures 3 cm wide, 3 cm tall, and 3 cm long, so the volume is:

Volume = 3 cm x 3 cm x 3 cm = 27 cm³.

Therefore, the volume of the cube is 27 cubic centimeters.

1.2) Density is defined as mass divided by volume. The mass of the ice cube is given as 24.76 grams, and we already determined the volume to be 27 cm³. Therefore, the density of the ice cube is:

Density = Mass / Volume = 24.76 g / 27 cm³ ≈ 0.917 g/cm³.

Therefore, the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).

1.3) The volume of the water cube is the same as the ice cube, which is 27 cm³. Given the density of liquid water as 1.00 g/cm³, we can calculate the mass of the water cube using the equation:

Mass = Density x Volume = 1.00 g/cm³ x 27 cm³ = 27 grams.

Therefore, the mass of the water cube is 27 grams.

1.4) The weight of an object depends on both its mass and the acceleration due to gravity. Since the volume of the water cube and the ice cube is the same (27 cm³), and the mass of the water cube (27 grams) is equal to the mass of the ice cube (24.76 grams), their weights would also be equal when measured in the same gravitational field.

Therefore, the weight of the water and the ice would be the same under the same conditions.

1.5) Ice floats on water because it is less dense than liquid water. The density of ice is lower than the density of water because the water molecules in the solid ice are arranged in a specific lattice structure with open spaces. This arrangement causes ice to have a lower density compared to liquid water, where the molecules are closer together.

When ice is placed in water, the denser water molecules exert an upward buoyant force on the less dense ice, causing it to float. The buoyant force is the result of the pressure difference between the top and bottom surfaces of the submerged object.

In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.

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Answer:

I can't able to understand this question plz check this question if it is right or not

Answer:

Step-by-step explanation:

One way you could do this is to put a vertical line at x = 6. Let that line have the properties of a mirror. Enlarge this and check out the lowest point which is at x = 2 y = 4,5

The same point for B is at x = 10 and y = 4.5

The x value in both cases is 4 units from the reflective line.

Answer:

x = 8

Step-by-step explanation:

Take x as 8:

8 - 1 = 7

I hope that's right :)

Answer:

The quotient will be -1

Step-by-step explanation:

2.6 ÷ -2.6

= 2.6/-2.6

= 1/-1

= -1

Hope it helps

Answer:

-1

Step-by-step explanation:

 2.6

-------- = -1

-2.6