what is the answer to -4(r+2)=4(2−2r)

Answer:

a.divide the amount by the percentage.

$2700× 25%

Ans:$675

subtract the selling price from the profit.

$2700 - $675

Ans:$2025

b.divide the 15% from selling price.

$2700 × 15%

Ans: 405

deduct the selling from from the discount given.

$2700 - $405

Ans: $2,295

The amount Marcia saved in interest by consolidating the two balances will be $105

It is given that

For Card A = 1,879.58 ; APR 14%; monthly = 43.73

For Card B = 861.00 ; APR 10% ; monthly = 18.29

Now \(\rm 5\ Years \times\ 12\ months =60\ months\)

For Card \(A=43.73\times60=2623.80\)

For Card \(B=18.29\times60=1097.40\)

Now the \(\rm Total=2623.80+1097.40=3721.20\)

Since Lowest APR is 10%. monthly rate: 0.83%

So the Total Card balance  \(1879.58+861=2740.58\)

\(A=\dfrac{P\times r(1+r)^n}{(1+r)^n} -1\)

\(A=\dfrac{2740.58\times(0.0083(1.0083)^{60}}{1.0083^{60}}-1\)

\(A=2740.58\times0.022\)

So monthly payment.

\(A=60.29\)  

\(60.29\times60=3617.40\)

For Separate cards: 3,721.20

For Consolidated:     3,617.40

The Difference: 103.80

Thus the amount Marcia saved in interest by consolidating the two balances will be $105

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Answer:

∠ a & ∠ d

∠ b & ∠

Answer:

∠ A and ∠ D

∠ B and ∠ E

Step-by-step explanation:

An individual's BMR decreases approximately 3 to 5 percent per decade on an average after the age of option C. 30.

Therefore, on an average individuals BMR is approximately decreases by round about 3 to 5 percent per decade after the age of option c. 30.

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The sample size when four marbles are selected at random without replacement from the marble bag, is 73,815.

The total number of marbles in the bag is:

10 (orange marbles) + 9 (yellow marbles) + 11 (black marbles) + 8 (red marbles) = 38 marbles.

the number of combinations of 4 marbles chosen from the 38 marbles.

The formula for calculating combinations is given by

C(n, r) = n! / (r! × (n - r)!),

where n is the total number of items and r is the number of items chosen.

Substituting the values into the formula, we have

C(38, 4) = 38! / (4! × (38 - 4)!)

Simplifying the expression

C(38, 4) = 38! / (4! × 34!)

Using factorials:

C(38, 4) = (38 × 37 × 36 × 35) / (4 × 3 × 2 × 1)

Calculating the expression

C(38, 4) = 73,815.

Therefore, the sample size, when four marbles are selected at random without replacement from the marble bag, is 73,815.

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Answer:

0.82

Step-by-step explanation:

A： area =2( 0.8*0.6*+0.6*1+0.8*1) =2(0.48+0.6+0.8)=2*1.88 =3.76

B：area = 2(1.4*0.5+0.5*1.2+1.4+1.2) =2(0.7+0.6+1.68)=2*2.98=5.96

total 9.72

cost = $6.79* 9.72/80 =$0.82

Answer:

the answer is 1.33333333333

Answer:

18

Step-by-step explanation:

original 3:4

now 18:24

Multiply by 6

Answer:

2nd option

Step-by-step explanation:

Given x = a is a root of a polynomial function then (x - a) is a factor

Given roots are x = 0, x = - 2, x = 7 , then corresponding factors are

(x - 0) , (x - (- 2) ) , (x - 7) , that is

x , (x + 2) , (x - 7)

The polynomial function f(x) is then the product of the factors, so

f(x) = x(x + 2)(x - 7)

Answer:

C, He got that answer by thinking that the question was asking how much Mr.McClary's class made

Step-by-step explanation:

Mrs.Shen Raised $120

Mr. McClary raised $60 (50% of 120)

120

+60

180

Answer:

its blarred, but in generally take the sum 90 and solve it

The solution to the mathematical expression \( 35.00 - 4.30 \times 10.00 \) is 0. The calculation involves multiplying 4.30 by 10.00, which gives 43.00, and then subtracting 43.00 from 35.00, resulting in 0.

To further explain the solution, let's break down the steps involved. In the expression, we first perform the multiplication operation, which involves multiplying 4.30 by 10.00. The product of these two values is 43.00.

Next, we subtract 43.00 from 35.00. Since the subtraction operation involves subtracting a larger value (43.00) from a smaller value (35.00), the result will be negative. Therefore, the final answer is 0.

It's important to follow the order of operations in mathematical expressions to arrive at the correct solution. In this case, the multiplication operation is performed first, and then the subtraction operation is carried out. By understanding the rules of arithmetic and executing the calculations correctly, we determine that the expression evaluates to 0.

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There can be 90% confident that the population mean salary of college graduates who took a statistics course is between $60,947.78 and $66,652.22.

To construct a 90% confidence interval for estimating the population means μ of salaries for college graduates who took a statistics course, we can use the formula:

Confidence interval = sample mean ± (critical value) x (standard error)

First, we need to find the critical value from the t-distribution table with a degree of freedom of n-1. Since we have 49 college graduates, our degrees of freedom are 48. Looking at the table, the critical value for a 90% confidence level is 1.677.

Next, we need to find the standard error, which is calculated by dividing the standard deviation by the square root of the sample size. In this case, the standard error is $11,936/sqrt(49) = $1703.05.

Substituting these values into the formula, we get:

Confidence interval = $63,800 ± 1.677 x $1703.05
Confidence interval = $63,800 ± $2852.22

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Therefore, the answer is option C: theta = pi/2 and theta = 3pi/2.

To determine when tan(theta) is undefined on the unit circle, we need to remember the definition of the tangent function.
Tangent is defined as the ratio of the sine and cosine of an angle. Specifically, tan(theta) = sin(theta)/cos(theta).

Now, we know that cosine can never be equal to zero on the unit circle, since it represents the x-coordinate of a point on the circle and the circle never crosses the x-axis. Therefore, the only way for tan(theta) to be undefined is if the cosine of theta is equal to zero.
There are two values of theta on the unit circle where cosine is equal to zero: pi/2 and 3pi/2.

At theta = pi/2, we have cos(pi/2) = 0, which means that tan(pi/2) = sin(pi/2)/cos(pi/2) is undefined.
Similarly, at theta = 3pi/2, we have cos(3pi/2) = 0, which means that tan(3pi/2) = sin(3pi/2)/cos(3pi/2) is also undefined.
Therefore, the answer is option C: theta = pi/2 and theta = 3pi/2.

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a) The line integral over C is:

∫C F dr = ∫r1 F dr + ∫r2 F dr = 2/5 + 1 = 7/5.

b) The potential function at (-1,1) and (1,1) yields:

∫C F dr = f(1,1) - f(-1,1) = 2.

Parametrize the first segment of C from (-1,1) to (0,0) as r1(t) = (-1+t, 1-t) for 0 ≤ t ≤ 1.

Then the line integral over this segment is:

\(\int r1 F dr = \int_0^1 F(r1(t)) \times r1'(t) dt\)

=\(\int_0^1 (3(-1+t)^2(1-t)^2, -2(-1+t)^3(1-t)) \times (1,-1)\) dt

=\(\int_0^1 [6(t-1)^2(t^2-t+1)]\)dt

= 2/5

Similarly, parametrize the second segment of C from (0,0) to (1,1) as r2(t) = (t,t) for 0 ≤ t ≤ 1.

Then the line integral over this segment is:

∫r2 F dr = \(\int_0^1 F(r2(t)) \times r2'(t)\) dt

= \(\int_0^1(3t^4, 2t^3) \times (1,1) dt\)

= \(\int_0^1 [5t^4] dt\)

= 1

The line integral over C is:

∫C F dr = ∫r1 F dr + ∫r2 F dr = 2/5 + 1 = 7/5.

Let f(x,y) = \(x^3 y^2\).

Then the gradient of f is:

∇f = ⟨∂f/∂x, ∂f/∂y⟩ = \((3x^2 y^2, 2x^3 y)\).

∇f = F, so F is a conservative vector field and the line integral over any path from (-1,1) to (1,1) is simply the difference in the potential function values at the endpoints.

Evaluating the potential function at (-1,1) and (1,1) yields:

f(1,1) - f(-1,1)

= \((1)^3 (1)^2 - (-1)^3 (1)^2\) = 2

∫C F dr = f(1,1) - f(-1,1) = 2.

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Answer: He has earned $200 interest and the balance of his account is $1,200.

Step-by-step explanation:

Given: Principal : P = $1,000

Simple interest rate : r = 5% = 0.05

Time: t = 4 years

Simple interest = \(Prt\)

\(=1000\times0.05\times4=200\)

i.e. Simple interest = $200

Balance of account = Principal + Simple interest

=  $1,000 + $200

= $1,200

Hence, he has earned $200 interest and the balance of his account is $1,200.

Answer:

Midpoint = (2,2.5)

Step-by-step explanation:

Midpoint = \((\frac{5 + -1}{2} , \frac{7 + -2}{2} ) = (2,2.5)\)

Answer:

The sum of 25 and 16 is 41.

Step-by-step explanation:

The sum of two numbers, 25 and 16, you can break apart the addends and add them separately to simplify the process. Here's how you can do it:

Break apart the numbers into their place values: For 25, you have 20 and 5, and for 16, you have 10 and 6. This step helps you work with the place values individually.

Add the tens place: In this case, you have 20 (from 25) and 10 (from 16). Adding them gives you 30.

Add the ones place: Now you add the ones place, which is 5 (from 25) and 6 (from 16). Adding them gives you 11.

Combine the sum of the tens place and the sum of the ones place: Take the sum of 30 (from step 2) and 11 (from step 3). Adding them together gives you 41.

So, the sun is 41.

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Answer:

I believe the answer would be 30 people.

Step-by-step explanation:

To calculate the percentage out of a group of people or items, you just multiply the percent (in decimal form) by the amount of people you want it out of. For example: A 0.1% chance out of 1,000 people would be a chance and expectancy of 1 person out of those 1,000 people. In this case it's 3% for every person. 0.03 • 1,000 is 30.

Answer:

200

Step-by-step explanation:

1cm=50m

1*4=50*4

4=200 miles

Step-by-step explanation:

principal=1000

rate=7.5

time=30 moths

interest= principal multiplied to rate multiplied to time by 100

which give 100multiplied to 7.t multiplied to 30 by 10p

which gives 22500by 100

which gives 225

amount= interest plus principal

= 225+1000

=1225

Average Auction Price is 0.9925the noncompetitive bidders will receive $750 million at a price of $0.9925 per $1 of par value.

To determine who will receive T-bills, what quantity, and at what price, we need to rank the bidders based on the bid prices and allocate the T-bills in descending order of bid prices until the entire $2.5 billion par value has been allocated. The bid prices listed are quoted as a percentage of par value, so we need to calculate the dollar amount bid for each bidder as follows:

Bid Amount = Bid Price × Par Value

For Bidder A:

Bid Amount = 0.9940 × 500 million

Bid Amount = $497 million

For Bidder B:

Bid Amount = 0.9901 × 750 million

Bid Amount = $742.6 million

For Bidder C:

Bid Amount = 0.9925 × 1.5 billion

Bid Amount = $1.48875 billion

For Bidder D:

Bid Amount = 0.9936 × 1 billion

Bid Amount = $993.6 million

For Bidder E:

Bid Amount = 0.9939 × 600 million

Bid Amount = $596.34 million

Total Bid Amount = $3.31874 billion

Since the total bid amount exceeds the $2.5 billion par value of the T-bills being auctioned, we need to allocate the T-bills to the highest bidders until the entire $2.5 billion has been allocated.

Ranking the bidders in descending order of bid prices, we have:

Bidder B with a bid price of $0.9901

Bidder C with a bid price of $0.9925

Bidder D with a bid price of $0.9936

Bidder E with a bid price of $0.9939

Bidder A with a bid price of $0.9940

Allocating T-bills to the highest bidders until the entire $2.5 billion par value has been allocated, we have:

Bidder B will receive $750 million at a price of $0.9901 per $1 of par value.

Bidder C will receive $750 million at a price of $0.9925 per $1 of par value.

Bidder D will receive $500 million at a price of $0.9936 per $1 of par value.

Bidder E will receive $250 million at a price of $0.9939 per $1 of par value.

The noncompetitive bids of $750 million will be allocated at the average auction price, which is calculated as the simple average of the four highest accepted bid prices:

Average Auction Price = (0.9901 + 0.9925 + 0.9936 + 0.9939) / 4

Average Auction Price = 0.9925

Therefore, the noncompetitive bidders will receive $750 million at a price of $0.9925 per $1 of par value.

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The theorem that proves that the two triangles are similar is the SAS Similarity Theorem. The theorem states that if two sides of one triangle are proportional to two sides of another triangle, and the included angle between these sides is the same in both triangles, then the two triangles are similar.

In this case, the ratio of the corresponding sides of the two triangles are:

AB/DE = 3/18 = 1/6

BC/EF = 7/42 = 1/6

Since the ratio of corresponding sides is equal, and the included angle between them (angle B and angle E) is the same, the two triangles are similar by the SAS Similarity Theorem.

Answer:

36°; 108°

Step-by-step explanation:

The measure of each interior angle of a regular pentagon is 108°.a) Two consecutive radii are joined to form an angle. The sum of these two angles is equal to 360° as a full rotation. Therefore, each angle formed by two consecutive radii measures (360°/5)/2 = 36°.b) A radius and a side of the polygon form an isosceles triangle with two base angles of equal measure. The sum of the angles of this triangle is 180°. Therefore, the measure of the angle formed by a radius and a side is (180° - 108°)/2 = 36°. Thus, the angle formed by the radius and the side plus two consecutive radii angles equals 180°. Hence, the angle formed by a radius and a side measures (180° - 36° - 36°) = 108°.Therefore, the measures of the angles formed by two consecutive radii and a radius, and a side of the polygon are 36° and 108°, respectively. Thus, the answer is 36°; 108°.

Answer:

Step-by-step explanation:

m n

A) The number of possible access codes is: 343

B) The probability of randomly selecting the correct access code is: 0.003

C) The probability of not selecting the correct access code is :  0.997

Permutations are used when order/order of placement is required. Combinations are used when you only need to search for the number of possible groups and not the order/order of locations. Permutations are used for things of different nature. Combinations are used for things of a similar nature.

a) The access code for a garage door consists of three digits. Each digit can be 2 through 8 and each digit can be repeated.

Thus, the number of possible access codes is:

7³ = 343

b) The probability of randomly selecting the correct access code is:

1/343 = 0.003

c) The probability of not selecting the correct access code is :

P = 1 - (1/343)

P = 0.997

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Complete question is:

The access code for a garage door consists of three digits. Each digit can be 2 through 8 and each digit can be repeated. Complete parts​ (a) through​ (c).

a) The number of possible access codes is?

b) The probability of randomly selecting the correct access code is (rounded to the nearest thousandth)?

c) The probability of not selecting the correct access code is (round to the nearest thousandth)?

The street can be represented in slope intercept form as follows:

y = x + 4

Linear equation can be represented in slope intercept form as follows:

y = mx + b

where

Parallel lines have the same slope.

The street goes by the name y = x + 17.

The slope of the street is 1.

Therefore, the street parallel to that one should have the same slope.

The street can be represented in slope intercept form is as follows:

y = x + 4

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Answer:

684 π

Step-by-step explanation:

volume of a sphere = (4/3) x (n) x (r^3)

n = 22/7

r = radius

volume of larger sphere

4/3 x n x 9³ = 972 n

4/3 x n x 6³ =288n

972n - 288n = 684n

The probability of getting exactly 2 tails in 7 flips of a coin with a probability of tails being 3/4 is 189/16384 or approximately 0.0115.

We can use the binomial distribution formula to solve this problem. Let X be the number of tails that come up in 7 flips of the coin. Then X follows a binomial distribution with n = 7 and p = 3/4 (since the probability of tails is 3/4).

The probability of getting exactly 2 tails is given by:

P(X = 2) = (7 choose 2) * (3/4)^2 * (1/4)^5

= (21 * 9/16 * 1/1024)

= 189/16384

So the probability that George flips exactly 2 tails is 189/16384, or approximately 0.0115.

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(a) n+3......................

seventh term is 19

eight term is 22

nine term is 25