solve. check for extraneous solutions
3 l4w-1l -5 = 1

Answer:

6

Step-by-step explanation:

8171.28

Sig Figs

6

8171.28

Decimals

2

8171.28

Scientific Notation

8.17128 × 103

E-Notation

8.17128e+3

Words

eight thousand one hundred seventy-one point two eight

Answer:

24.5%

Step-by-step explanation:

Given

P(Off-Campus) = 0.30

P(Part-Time Job | Off-Campus) = 0.62

P(Part-Time Job | On-Campus) = 0.65

Inferred

P(On-Campus) = 0.70

P(No Part-Time Job | Off-Campus) = 0.38

P(No Part-Time Job | On-Campus) = 0.35

Calculation

P(No Part-Time Job | On-Campus) = P(No Part-Time Job ∩ On-Campus)/P(On-Campus)

0.35 = P(No Part-Time Job ∩ On-Campus)/0.70

0.245 = P(No Part-Time Job ∩ On-Campus)

Therefore, 24.5% of students that live on campus do not have a part-time job.

Answer:70%

Step-by-step explanation:you have 7/10.SO u times the whole fraction by 10( 7 times 10 =70 and 10 times 10 =100) which means 70/100 so the percent is 70.

Hope it helps

Answer:

Step-by-step explanation:

Determine the two consecutive multiples of 10 that bracket 551

551 is between 550 and 560

555 is the midpoint between 550 and 560

As illustrated on the number line, 551 is less than the midpoint (555)

Therefore, 551 rounded to the nearest ten = 550

551 rounded to the nearest ten with a number line

Answer: 551.36

Step-by-step explanation:

“Of” means you have to multiply so multiply 133.5 and 413 and you will get 55,135.5 then you move the decimal point to the right 2 times and that will be 551.355, then since there is a five you change the other five to a 6 (5 or more raise the score 4 or less let it rest) and that will be 551.36.

Answer: Chloe is 12 years old

y + 2.5

y = 9.5

9.5 + 2.5 = 12

1. Number of athletes did not own any of the three items = 259 - 228

= 31.

2. Number of athletes own a convertible and a TV but not a store = 44 - 9

= 35.

3. Number of athletes own a convertible or a TV = 110 + 91 - 44

= 157.

4. Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.

5. Number of athletes owned at least one type of item = 259 - 31

= 228

6. Number of athletes own a TV or a store, but not a convertible = 13 + 34 +71

= 118.

The number of athletes did not own any of the three items need to subtract the number of athletes who own at least one item from the total number of athletes surveyed.

Total number of athletes surveyed = 259

Number of athletes own at least one item = 110 + 91 + 120 - 15 - 43 - 44 + 9 = 228

Number of athletes who did not own any of the three items = 259 - 228 = 31.

The number of athletes who owned a convertible and a TV but not a store need to subtract the number of athletes who own all three items from the number of athletes who own a convertible and a TV.

Number of athletes who own a convertible and a TV = 44

Number of athletes who own all three items = 9

Number of athletes who own a convertible and a TV but not a store = 44 - 9 = 35

The number of athletes who owned a convertible, or a TV need to add the number of athletes who own a convertible to the number of athletes who own a TV and then subtract the number of athletes own both a convertible and a TV.

Number of athletes who own a convertible or a TV = 110 + 91 - 44

= 157.

The number of athletes owned exactly one type of item need to add up the number of athletes who own a convertible only the number of athletes own a TV only and the number of athletes who own a store only.

Number of athletes own a convertible only = 110 - 15 - 9 = 86

Number of athletes own a TV only = 91 - 44 - 9 = 38

Number of athletes own a store only = 120 - 15 - 43 - 9 = 53

Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.

The number of athletes who owned at least one type of item can use the result from part (1).

Number of athletes who owned at least one type of item = 259 - 31

= 228

The number of athletes who owned a TV or a store but not a convertible need to subtract the number of athletes who own all three items, and the number of athletes own a convertible and a TV from the number of athletes own a TV or a store.

Number of athletes own a TV or a store = 91 + 120 - 43 - 9 = 159

Number of athletes own a TV or a store not a convertible = 13 + 34 +71

= 118.

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Therefore , the solution of the given problem of circle comes out to be arc length 3.93 feet.

Every area of the plane that is separated by a specific amount from this additional point makes a circle (center). As a result, it is a curve made up of spots that are separated from one another on the surface. Additionally, it rotates similarly about the centre at every angle. Every collection of endpoints in the confined, two-dimensional sphere of a circle is uniformly spaced apart from the "centre."

Here,

A circle with a radius of 3 feet is equal to its diameter as follows:

=> C = 2πr = 2π(3) = 6π feet

Since there are 360° of angles in a circle's centre, the angle for a 75° curve is:

5/24 of a complete circle is 75/360.

Therefore, the 75° arc's extent is

5/24 × 6π = 5π/4 ≈ 3.93 feet

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The measure of side KL from triangle KLM is 22 units.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

Given that, triangle HIJ is similar to triangle KLM.

From the similar triangles,

JH/MK =HI/KL

31/13.9 =49/KL

31KL=49×13.9

31KL=681.1

KL=681.1/31

KL=21.97

KL≈22

Therefore, the measure of side KL is 22 units.

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The Area of the rectangle is (8\(x^{2}\) -10x -3)\(ft^{2}\)

A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles (90°).The opposite sides of a rectangle are equal and parallel. Since, a rectangle is a 2-D shape, it is characterized by two dimensions, length, and width. Length is the longer side of the rectangle and width is the shorter side.

Area of rectangle = length x width

Area of Rectangle = ( 4x + 1) x (2x -3)

By expanding

Area of rectangle = 8\(x^{2}\) +2x -12x -3 which is  (8\(x^{2}\) -10x -3)\(ft^{2}\)

In conclusion,  (8\(x^{2}\) -10x -3)\(ft^{2}\) is the area of the rectangle.

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Answer:

80 degrees

Step-by-step explanation:

The sum of the angles in a triangle is 180 degrees so we can create the equation 70+30+x=180. This solves out to 80 so x=80 degrees.

Answer:

c

Step-by-step explanation:

Answer:

23.4 feet

Step-by-step explanation:

Using the Pythagoras theorem, we can find the value of x to be = 10ft.

Option B is correct.

The right-angled triangle's three sides are related in line with the Pythagoras theorem, also referred to as the Pythagorean theorem. The hypotenuse of a triangle's other two sides add up to a square, according to the Pythagorean theorem, which states that.

Here in the question,

We have 2 right-angled triangles.

So, base of the large triangle, x

= √ (13² - 12²) + √ (13² - 12²)

= √ 5² + √ 5²

= 5 + 5

= 10ft.

Therefore, the length of the side, x = 10ft.

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The scaling factor for given transformation is 3.

What exactly is scaling factor?

The scaling factor, also known as the scale factor, is a value that indicates how much a geometric figure is enlarged or reduced. It is the ratio of the length of a side or dimension of the original figure to the length of the corresponding side or dimension of the new figure. The scaling factor can be greater than 1, which indicates an enlargement, or less than 1, which indicates a reduction. When the scaling factor is 1, the two figures are congruent, which means they have the same shape and size.

Now,

We can find the scale factor by comparing the corresponding side lengths of the two polygons. Let's start by finding the side lengths of the original polygon:

HI: √[(4-0)² + (-5+3)²] = √20

IJ: √[(6-4)² + (0-0)²] = 2

JK: √[(4-6)² + (5-0)²] = √41

KL: √[(0-4)² + (3-5)²] = √20

LH: √[(0-0)² + (-3+5)²] = 2

Now let's find the corresponding side lengths of the dilated polygon:

H'I': √[(12-0)² + (-15+9)²] = √600

I'J': √[(18-12)² + (0-0)²] = 6

J'K': √[(12-18)² + (15-0)²] = √600

K'L': √[(0-12)² + (9-0)²] = √600

L'H': √[(0-0)² + (-9+3)²] = 6

We can see that the side lengths of the dilated polygon are all 3 times as long as the corresponding side lengths of the original polygon. Therefore, the scale factor is 3.

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The domain and range of the graph above in interval notation include the following:

Domain = [-6, 3]

Range = [-3, 3]

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-6, 3] or -6 ≤ x < 3.

Range = [-3, 3] or -3 < y < 3

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Answer:

The goal is $19,800.

Step-by-step explanation:

$16,770 is $1,230 less than %90 of the goal. If you add 16,770 and 1,230, you get 18,000. Then you have to multiply that by 1.10 to get it to the goal. That is how you get $19,800, which is the answer.

Both calculations from part (1) and part (2) yield the same result of $0.86 for the new cost of the candy bar after 11 years.

Part 1 of 2:

The new cost of the candy bar after 11 years can be calculated by applying a 3% price increase each year to the original cost of $0.60.

To calculate the new cost after 11 years, we can use the formula:

New Cost = Original Cost * (1 + Percentage Increase)^Number of Years

Plugging in the values:

New Cost = $0.60 * (1 + 3%)^11

        ≈ $0.60 * (1 + 0.03)^11

        ≈ $0.60 * (1.03)^11

        ≈ $0.60 * 1.432364654

Rounding to the nearest cent, the new cost of the candy bar after 11 years is $0.86.

Part 2 of 2:

If the cost of the candy bar increased by 3% of the original cost each year for 11 years, we can calculate the final cost by multiplying the original cost by (1 + 3%) for each year.

Using the formula:

Final Cost = Original Cost * (1 + Percentage Increase)^Number of Years

Plugging in the values:

Final Cost = $0.60 * (1 + 3%)^11

          ≈ $0.60 * (1 + 0.03)^11

          ≈ $0.60 * (1.03)^11

          ≈ $0.60 * 1.432364654

Rounding to the nearest cent, the final cost would also be $0.86.

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Note: The complete question is - What will be the cost of the candy bar after a specific number of years if it originally sold for $.60 and undergoes a 3% price increase each year?

Answer:

3/8

Step-by-step explanation:

We can write the entire book with the number 1. Now we can write this operation

3/8 + 1/4 + x = 1

3 + 2 + 8x = 8

5 + 8x = 8

8x = 3

x = 3/8

Answer:

x = 15

y = 15√3

Step-by-step explanation:

This is a special right triangle with angle measures 30° 60° 90°

The side lengths should be x 2x x√3

If the measure of hypotenuse 30 then the side length that sees 30° should be half of it so x = 15 and y = 15√3

Check the picture below.

Answer:

92 cents

Step-by-step explanation:

If each box has the cost of 23 cents, and you decided to buy 4, you would multiply the amount of boxes you want with the cost of each one, therefore, the 92 cents. 4 * 23 = 92

a) To maximize profits, 10 units should be sold in market 1 and 5 units in market 2.

b) The corresponding prices are $180 in market 1 and $160 in market 2.

c) If it becomes illegal to discriminate, the profit loss is $50.

d) The imposition of a tax of $5 per unit sold in market 1 would likely decrease the monopolist's profit and potentially lead to adjustments in prices and quantities sold in both markets.

a) To maximize profits, the monopolist should set marginal revenue equal to marginal cost in each market.

In this case, marginal revenue is equal to the derivative of the demand function with respect to quantity, and it can be calculated as MR = dP/dQ.

For market 1:

MR₁ = dP₁/dQ₁ = -2

For market 2:

MR₂ = dP₂/dQ₂ = -4

Setting MR equal to marginal cost, which is the derivative of the cost function with respect to quantity, gives:

MR₁ = -2 = dC/dQ₁ = 20

MR₂ = -4 = dC/dQ₂ = 20

Solving these equations, we find:

Q₁ = 10

Q₂ = 5

Therefore, the monopolist should sell 10 units in market 1 and 5 units in market 2 to maximize profits.

b) To determine the corresponding prices, we substitute the quantities obtained in part (a) into the demand functions:

For market 1:

P₁ = 200 - 2Q₁ = 200 - 2(10) = 180

For market 2:

P₂ = 180 - 4Q₂ = 180 - 4(5) = 160

Therefore, the corresponding prices are $180 in market 1 and $160 in market 2.

c) To calculate the profit lost if it becomes illegal to discriminate, we need to compare the profits under discrimination with the profits under non-discrimination.

Under discrimination, the monopolist charges different prices in each market, while under non-discrimination, the same price is charged in both markets.

Under discrimination:

Profit = Total revenue - Total cost

For market 1:

Total revenue₁ = P₁ \(\times\) Q₁ = 180 \(\times\) 10 = $1

For market 2:

Total revenue₂ = P₂ \(\times\) Q₂ = 160 \(\times\) 5 = $800

Total revenue = Total revenue₁ + Total revenue₂ = $1800 + $800 = $2600

Total cost = C = 20(Q₁ + Q₂) = 20(10 + 5) = $300

Profit = Total revenue - Total cost = $2600 - $300 = $2300

Under non-discrimination:

Since the same price is charged in both markets, we take the average price:

Average price = (P₁ + P₂) / 2 = (180 + 160) / 2 = $170

Total revenue = Average price \(\times\) (Q₁ + Q₂) = $170 \(\times\) (10 + 5) = $2550

Total cost remains the same at $300.

Profit = Total revenue - Total cost = $2550 - $300 = $2250

Therefore, the profit lost if discrimination becomes illegal is $2300 - $2250 = $50.

d) The imposition of a tax of $5 per unit sold in market 1 would increase the cost per unit for the monopolist.

This would affect the profit-maximizing quantity in market 1 and potentially lead to a change in prices.

The monopolist would compare the new marginal cost, which includes the tax, with the marginal revenue to determine the new profit-maximizing quantities and prices.

The tax would likely reduce the monopolist's profits and could potentially result in adjustments in production and pricing strategies.

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The correct expression is 5/a = 1. There is no need to introduce an additional variable "x".

In such a fraction, the value that appears above the horizontal line is referred to as the numerator.

It represents the number of pieces removed from the whole. The denominator of a fraction is the numerical value that comes before the brings together various.

The error in the reasoning is that it assumes that multiplying the second fraction by "x" will result in an equivalent expression to 5/a. However, this is not necessarily true.

To correct the error, we can use the property of reciprocals, which states that if a/b = c/d, then b/a = d/c. Using this property, we can rewrite the given equation as:

a/5 = b/3

5/a = 3/b (multiplying both sides by 5/a)

5/a = (b/3) * (3/b) (multiplying both sides by the reciprocal of b/3)

5/a = 1

Therefore, the correct expression is 5/a = 1. There is no need to introduce an additional variable "x".

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Answer:

f(x)= x + 3

Step-by-step explanation:

Answer: $27

Step-by-step explanation:

$540x.05=$27

Answer:

Heidi made $27 from commision; And the store made $513 (i had this question my self on Saavas)

Step-by-step explanation:

1. 540x0.05=27

2. 540-27= $513

So the store made 513 dollars and heidi made 27 dollars

Thomas' installment payment that he pays in one fortnight is approximately k523.08.

To calculate Thomas' installment payment, we need to consider the principal amount (k10,000) and the interest rate (36%).

First, let's calculate the total amount to be repaid at the end of the year, including the interest. The interest is calculated as a percentage of the principal amount:

Interest = Principal × Interest Rate

= k10,000 × 0.36

= k3,600

The total amount to be repaid is the sum of the principal and the interest:

Total Amount = Principal + Interest

= k10,000 + k3,600

= k13,600

Now, we need to calculate the number of fortnights in a year. There are 52 weeks in a year, and since each fortnight consists of two weeks, we have:

Number of Fortnights = 52 weeks / 2

= 26 fortnights

To find the installment payment for each fortnight, we divide the total amount by the number of fortnights:

Installment Payment = Total Amount / Number of Fortnights

= k13,600 / 26

≈ k523.08

Therefore, Thomas' installment payment that he pays in one fortnight is approximately k523.08.

It's important to note that this calculation assumes equal installment payments over the course of the year. Different repayment terms or additional fees may affect the actual installment amount. It's always advisable to consult with the bank or financial institution for accurate information regarding loan repayment.

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Answer:

A) opposite sides with equal length.

Step-by-step explanation:

Found on another problem answered by Abdulazeez10

The characteristics a rhombus and a rectangle always have in common is opposite sides with equal length.

The right option is  opposite sides with equal length

From the question,

We are to determine which of the given characteristics do a rhombus and a rectangle always have in common.

To determine which of the characteristics, we will list some of the characteristics of the two shapes

Characteristics of a Rhombus

All sides are of equal length

Opposite sides are parallel

Opposite angles are congruent

Diagonals intersect perpendicularly

Consecutive angles are supplementary

Characteristics of a Rectangle

Opposite sides are congruent and parallel

Diagonals bisect each other

Each of the interior angles is a right angle

Diagonals are congruent

Now, from above,

We have that all the sides of rhombus are equal in length, which makes the opposite sides to be equal as well.

Also, among the characteristics of a rectangle is that, opposite sides are equal in length

Hence, the characteristics a rhombus and a rectangle always have in common is opposite sides with equal length. The right option is opposite sides with equal length

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Easy way to do this, divide 24 with 3, you will get 8. That means 8 is 1/3 of 24. To get 2/3 you just add 8+8 which equals to 16

The output value of f( -3 ) in the function f(x) = x³ + 3x + 17 is -19.

Given the function in the question:

f(x) = x³ + 3x + 17

To evaluate f(-3) for the function f(x) = x³ + 3x + 17, we simply substitute -3 for x in the expression and calculate the result.

f(x) = x³ + 3x + 17

Plug in x = -3

f(-3) = (-3)³ + 3(-3) + 17

First, let's calculate (-3)³, which means raising -3 to the power of 3:

(-3)³ = -3 × -3 × -3 = -27

Next, let's calculate 3(-3):

3(-3) = -9

Now, we can substitute these values into the expression:

f(-3) = -27 + (-9) + 17

Simplifying further:

f(-3) = -27 - 9 + 17

f(-3) = -36 + 17

f(-3) = -19

Therefore, the output value of f(-3) is -19.

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