The length of a rectangle exceeds its width by 5 inches. The
area of the rectangle is 84 square inches. Find its dimensions.

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

Cost of large candle (a) = 25 each

Cost of small candles (y) = 10 each

Amount needed = $600

Number of each that must be sold to raise needed amount:

25a + 10y = 600.

Here a = number of large candles that must be sold at the price

y = number of small candles that must be sold at the price

Summing the revenue both should result in the required amount.

Answer:

m∠RQS = 102

m∠TQS = 78

Step-by-step explanation:

m∠RQS = (20x + 2)°

m∠TQS = (15x + 3)°

m∠RQS + m∠TQS = 180°

20x + 2 + 15x + 3 = 180

35x + 5 = 180

35x = 175

x = 5

m∠RQS = 20(5) + 2 = 100 + 2 = 102

m∠TQS = 15(5) + 3 = 75 + 3 = 78

Answer:

m∠RQS = 102°

m∠SQT = 78°

General Formulas and Concepts:

Definition of a Line: A line is 180°

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Set up equation

m∠RQS and m∠SQT must add up to m∠RQT.

m∠RQS + m∠SQT = m∠RQT

(20x + 2) + (15x + 3) = 180

Step 2: Solve for x

Step 3: Find m∠RQS

Step 4: Find m∠SQT

Approximately 99.7% of employees in the company earn between $5.40 and $24.60 per hour.

To find the interval within which 99.7% of employees' salaries fall, we can use the properties of the normal distribution.

Given:

Mean (μ) = $15.00 per hour

Standard deviation (σ) = $3.20

In a normal distribution, approximately 99.7% of the data falls within three standard deviations of the mean. So, we can calculate the interval as follows:

Lower bound = μ - 3σ

Upper bound = μ + 3σ

Lower bound = $15.00 - 3 * $3.20

= $15.00 - $9.60

= $5.40

Upper bound = $15.00 + 3 * $3.20

= $15.00 + $9.60

= $24.60

Therefore, approximately 99.7% of employees in the company earn between $5.40 and $24.60 per hour.

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Answer:

x=20

Step-by-step explanation:

3x-1+31+90=180

Combine like terms

3x+120=180

Subtract by 120 on both sides

3x=60

x=20

Answer:

59 degrees

Step-by-step explanation:

so first things first you have the tringle it has a right angle meaning that this triangle will equal 90 degrees so here is what our equation would look like:

90=31+(3x-1)

So in order to solve this equation you must subtract add and divide.

First Rule in doing these equations: what you do to one side of the equal sign you do to the other side.

so we subtract 31 from 90 to equal 59 so the equation looks like this:

59=(3x -1)

you then add a one to the negative one and the 59 to get 60 making the equation look like this

60= 3x

we then divide 60 by 3 to get 20

so 20= x

But this is not our answer this is simply the solvation for x in (3x - 1)

so the equation now looks like this (3(20) - 1) and this equals 59 degrees

now to check our work!

31 + 59 = 90 or 90- 31 = 59

                                       [tex]\left[\begin{array}{ccc}Your\;Answer\;is\;1.\end{array}\right][/tex]

[tex]Explanation[/tex] \/

Find the prime factorization of 6

[tex]6=2*3[/tex]

Find the prime factorization of 35

[tex]35 = 5 * 7[/tex]

To find the GCF, multiply all the prime factors common to both numbers:

Therefore, [tex]GCF = 1[/tex]

1 is the largest positive integer that divides both 6 and 35 without leaving a remainder.

The greatest common factor (GCF), also known as the greatest common divisor (GCD), of two numbers is the largest positive integer that divides both of the numbers without leaving a remainder.

Step 1: Prime factorization of 6

The prime factors of 6 are 2 and 3.

So, 6 = 2 * 3.

Step 2: Prime factorization of 35

The prime factors of 35 are 5 and 7.

So, 35 = 5 * 7.

Step 3: Determine the common prime factors

The common prime factors of 6 and 35 are 1.

Step 4: Multiply the common prime factors

Multiplying the common prime factors gives us 1.

Therefore, the GCF of 6 and 35 is 1.

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Answer:

Given that 5 pounds of rice at a store cost $6.50.

Then 1 pounds of rice at a store cost = $6.50/5= $1.3

So the equation for the cost can be written as:

C=1.3P just like we write equation y=mx

Now we have to graph the cost C, vs pounds of rice.

Variable for Pounds of rice is not given so let it be "P"

So let's make a table for number of pounds (P) and cost (C) the we can graph the points from that table to get the final graph.

Attached graph is the final graph.

Answer:

2x^2+x-6

Step-by-step explanation:

Use the F.O.I.L method

2x^2+4x-3x-6

Answer:

[tex]x=3[/tex]

Step-by-step explanation:

[tex]x+3=6[/tex]

Subtract 3 from both sides:

[tex]x+3-3=6-3\\x=3[/tex]

Hope this helps!

TestedHyperr

Answer:

a

Step-by-step explanation:

The expression that represent the new price is p(0.5 + 1).

Lora bought a house for a price of p dollars. After 1 year the value of the house increased by 50%.

Therefore, the expression that can be used to represent the new value of the house can be represented as follows:

Hence,

increased price = 50% of p

increased price = 50 / 100 p

increased price = 0.5p

Hence, the expression that represent the new price is as follows;

expression for the new price = 0.5p + p

expression for the new price = p(0.5 + 1)

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Answer:

1. 24

2. [tex]10+2n[/tex] where n denotes number of days.

3. 70

Step-by-step explanation:

1.

Consider the sequence: [tex]12,14,16,18,...[/tex]

Here,

[tex]14-12=2\\16-14=2\\18-16=2[/tex]

Take the common difference as d = 2 and the first term as a = 12

Use the formula: [tex]a_n=a+(n-1)d[/tex]

To find expected gain at the end of the week, find [tex]a_7[/tex]

[tex]a_7=12+(7-1)2\\=12+6(2)\\=12+12\\=24[/tex]

2.

Yes, the gain shows the pattern.

Put [tex]a=12,d=2[/tex] in [tex]a_n=a+(n-1)d[/tex]

[tex]a_n=12+(n-1)2\\=12+2n-2\\=10+2n[/tex]

Here, n denotes number of days.

3.

To find expected gain at the end of 30  days, put [tex]n=30[/tex] in [tex]a_n=10+2n[/tex]

[tex]a_{30}=10+2(30)\\ =10+60\\=70[/tex]

The statement "1,024 is the smallest 4-digit number that is a perfect square" is statement.

Yes, the given sentence "1,024 is the smallest 4-digit number that is a perfect square" is a statement. A statement is a sentence that conveys some information, idea, or proposition. It can either be true or false and is usually based on facts or opinions.

In this case, the statement is true as 1024 is the smallest four-digit number that is a perfect square. A perfect square is a number that is obtained by multiplying a number by itself. 1024 is a perfect square since it is equal to 32 * 32 (or 2^10).

The given statement, therefore, is a true statement since it conveys a factual and accurate piece of information.

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The closest answer is 80 cupcakes per minute, so the correct option is .8. The closest answer is 165 minutes, so the correct option is 165.

The throughput capacity of the icing stage can be calculated by dividing the number of cupcakes in a batch (100) by the time required to process each cupcake (1.25 minutes).

Throughput capacity = Number of cupcakes in a batch / Time to process each cupcake

Throughput capacity = 100 cupcakes / 1.25 minutes

Throughput capacity = 80 cupcakes per minute

The closest answer is 80 cupcakes per minute, so the correct option is .8.

The throughput time for a batch of cupcakes is the time required to process the entire batch, including the setup time.

Throughput time = Time for setup + (Number of cupcakes in a batch * Time to process each cupcake)

Throughput time = 40 minutes + (100 cupcakes * 1.25 minutes per cupcake)

Throughput time = 40 minutes + 125 minutes

Throughput time = 165 minutes

The closest answer is 165 minutes, so the correct option is 165.

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Answer:

1.

Step-by-step explanation:

The rearranged equation for V is V = 25 / (14.475 + 2.625g). This expression represents the value of V in terms of the given equation and the variable g.

To rearrange the equation (0.75V * 19.3) + (0.25V * 10.5) * g = 25 for V, we can start by expanding and simplifying the terms on the left side of the equation. The equation becomes (14.475V) + (2.625V * g) = 25.

Next, we can combine like terms by adding the coefficients of V. This gives us (14.475 + 2.625g)V = 25.

To isolate V, we divide both sides of the equation by the coefficient (14.475 + 2.625g). This results in V = 25 / (14.475 + 2.625g).

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Answer:

Step-by-step explanation:

Area of a circle = πr²

where

r is the radius of the circle

From the question

r = 58 cm

The area of the circle is

A = 58²π

= 3364π

= 10568.3176866761...

We have the final answer as

Hope this helps you

Here we are given with the radius of a circle and we have to find the area using formula.

✤ Formula for finding area of a circle:

[tex] \large{ \boxed{ \sf{\red{Area \: of \: \circ = \pi {r}^{2} }}}}[/tex]

Where r is the radius of the circle. So let's plug in the values for finding the area of the circle:

➝ Area = π(58 cm)²

➝ Area = 3.14 × 58 cm × 58 cm

➝ Area = 10562.96 cm²

Now let's round off upto 3 significant figures: 10600 cm² (Answer)

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Answer:

2135

Step-by-step explanation:

610 divided by to is 305 so the half of the hours the plane flys 305 miles.

610 times three equals 1830.

1830 plus 305 equals

Answer:

2135 miles

Step-by-step explanation:

ok so the plane is going at a speed of 610 mph

1 hour = 610 miles

this is a whole break down of what goes on in my head

610 x 3.5 = ?

600 x 3 = 1800

600 x .5 = 300

10 x 3 = 30

10 x .5 = 5

1800 + 300 + 30 + 5 = 2135

the plane will fly 2135 miles in 3.5 hours

Answer:

lw

Step-by-step explanation:

The formula to find the area of a rectangle is A = lw

A = Area

l = length

w = width

a.  MUx = ∂u/∂x1 = 1 - x1

And MUy = ∂u/∂x2 = 1 - x2

b. This suggests that Elena's utility function does not satisfy monotonicity or strict monotonicity.

c. MRSx,y = MUx / MUy = (1 - x1) / (1 - x2)

d. We also have the budget constraint:

Px * x1 + Py * x2 = I

4x1 + 10x2 = 1200

(a) To find the marginal utilities (MUx and MUy), we need to differentiate the utility function with respect to each variable.

Given:

u(x1​,x2​) = (x1​−21​x12​)+(x2​−21​x22​)

Differentiating with respect to x1:

∂u/∂x1 = 1 - 2x1/2 = 1 - x1

Differentiating with respect to x2:

∂u/∂x2 = 1 - 2x2/2 = 1 - x2

So, MUx = ∂u/∂x1 = 1 - x1

And MUy = ∂u/∂x2 = 1 - x2

(b) Monotonicity requires that if x increases, then utility should increase as well. Strict monotonicity requires that utility strictly increases as x increases.

In this case, since MUx = 1 - x1 and MUy = 1 - x2, we can see that both marginal utilities decrease as their respective goods' quantities increase. This suggests that Elena's utility function does not satisfy monotonicity or strict monotonicity.

(c) The Marginal Rate of Substitution (MRS) between two goods, x and y, is given by the ratio of their marginal utilities:

MRSx,y = MUx / MUy = (1 - x1) / (1 - x2)

(d) To find the equilibrium quantities for goods x and y, we need to set the MRS equal to the price ratio Px / Py and solve for x1 and x2.

MRSx,y = (1 - x1) / (1 - x2) = Px / Py = 4 / 10 = 2 / 5

Now we can solve for x1 and x2. Rearranging the equation:

(1 - x1) / (1 - x2) = 2 / 5

Cross-multiplying:

5(1 - x1) = 2(1 - x2)

Expanding:

5 - 5x1 = 2 - 2x2

Rearranging terms:

5x1 - 2x2 = 3

We also have the budget constraint:

Px * x1 + Py * x2 = I

4x1 + 10x2 = 1200

Now we have a system of two equations with two variables. Solving this system will give us the equilibrium quantities for goods x and y.

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Answer:

125

Step-by-step explanation:

i did it too

Answer:

see below

Step-by-step explanation:

1.  The inverse means take the not of both sides

If it is Saturday, then there is no school.

 Inverse     If it is not Saturday, then there is school.

The converse flips the then and the if

If there is no school, then it is Saturday.

2.) The first given part is the if, what will happen is the then part

If you are a freshman, then you are required to attend orientation.

3.)

Given: 3x+1=-14 Prove: x=-5

Statements    Reasons

1. 3x+1=-14     Given

2. 3x=-15          Subtraction Property of equality  ( since we subtract 1 from                         each side)

3. X=-5          Division Property  ( since we divide each side by 3)

The length of JL is 9 units. The length of KM is also 9 units. Yes, JL equals KM. Parallelogram JKLM is a rectangle.

To determine if parallelogram JKLM is a rectangle, we need to compare the lengths of its diagonals JL and KM.

Using the distance formula, we can calculate the length of JL:

JL = [tex]√[(x2 - x1)^2 + (y2 - y1)^2][/tex]

JL = [tex]√[(4 - (-8))^2 + (0 - 1)^2][/tex]

JL = [tex]√[12^2 + (-1)^2][/tex]

JL = √[144 + 1]

JL ≈ √145 ≈ 12.04 (rounded to two decimal places)

Using the distance formula, we can calculate the length of KM:

KM = [tex]√[(x2 - x1)^2 + (y2 - y1)^2][/tex]

KM = √[tex][(-6 - 2)^2 + (-4 - 5)^2][/tex]

KM = √[tex][(-8)^2 + (-9)^2][/tex]

KM = √[64 + 81]

KM ≈ √145 ≈ 12.04 (rounded to two decimal places)

Since JL = KM, the lengths of the diagonals are equal. This indicates that the opposite sides of parallelogram JKLM are congruent, which is a characteristic of a rectangle. Therefore, parallelogram JKLM is a rectangle.

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Answer:

2 2/3 miles

Step-by-step explanation:

so you take 2/3 and times it by 4/1

you now have 8/3

then you simply and come up with 2 2/3

the answer also just might be 2 depends on what they want, the full mile or the partial also.

Answer:

so every 6 cups there you can make 96 cookies

Step-by-step explanation:

Answer:

10.2%

Step-by-step explanation:

Prediction of the broadcaster = 88 points

Actual score scored = 98points

% error = actual score-predicted score/actual score × 100℅

Substitute the given scores into the formula;

%error = 98-88/98 × 100

%error = 10/98 × 100

%error = 1000/98

%error = 10.2%

Hence the broadcaster percentage error is approximately 10.2%