D
Two friends rent an apartment together.
They agree that one person will
рау 1.5
times what the other person pays. If the rent
is $850, how much will each friend pay?

Answer:

the answer is 90

Step-by-step explanation:

Answer:

y=7x

Step-by-step explanation:

When finding the slope intercept form using 2 points, we do the following.

y=mx+b (Slope intercept from)

y=7x+b (7 is slope)

Substitute the point

7=7(1)+b

7=7+b

b=0

y=7x

The slope intercept equation is y = 7x

We are asked to find the degree 5 term and the degree 1 term in the expansion of the expression (4z²z+2) (102² – 5z - 4) (5z² – 5z - 4).

To find the degree 5 term in the expansion, we need to identify the term that contains z raised to the power of 5. Similarly, to find the degree 1 term, we look for the term with z raised to the power of 1.

Expanding the given expression using the distributive property and simplifying, we obtain a polynomial expression. By comparing the exponents of z in each term, we can determine the degree of each term. The term with z raised to the power of 5 is the degree 5 term, and the term with z raised to the power of 1 is the degree 1 term.

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Answer:

no solution

Step-by-step explanation:

2(x + 2) = 2x -8

2x+4 = 2x-8

2x - 2x =-8 - 4

0 = -12

if the numbers r not the same on both right and left side it have no solution.

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Answer:

3 miles

Step-by-step explanation:

1/8*24=3

Answer:

Step-by-step explanation:

He ran 24 times around the track1

Circumfrence of track=1/8 Mile

Total distance he covered=1/8*24

Distance = 3 miles

Answer:

0.1

Step-by-step explanation:

Answer:

0.4 ÷ 4 = 0.1

Explanation:

Answer:

Fraction form:

\(\frac{3}{4}\)

For every 3 dollars, there are 4 cookies

Step-by-step explanation:

To find the constant, find the rise (y-direction) and the run (x-direction). Of the two points on the line, the rise is 3 and the run 4. The constant is rise over run. So, it’s \(\frac{3}{4}\). This means that for every 3 dollars, there are 4 cookies.

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Each installment will be approximately $15,280.55.

To calculate the equal six-monthly installment, we can use the formula for the present value of an annuity.

Principal amount (P) = $500,000

Interest rate (r) = 12% per annum = 12/100 = 0.12 (compounded monthly)

Number of periods (n) = 20 (since there are 20 equal six-monthly installments)

The formula for the present value of an annuity is:

\(P = A * (1 - (1 + r)^(-n)) / r\)

Where:

P = Principal amount

A = Equal installment amount

r = Interest rate per period

n = Number of periods

Substituting the given values into the formula, we have:

$500,000 = \(A * (1 - (1 + 0.12/12)^(-20)) / (0.12/12)\)

Simplifying the equation:

$500,000 = A * (1 - (1.01)^(-20)) / (0.01)

$500,000 = A * (1 - 0.6726) / 0.01

$500,000 = A * 0.3274 / 0.01

$500,000 = A * 32.74

Dividing both sides by 32.74:

A = $500,000 / 32.74

A ≈ $15,280.55

Therefore, each installment will be approximately $15,280.55.

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The maximum number of vectors in set S can be determined by the dimension of the vector space R3, which is three.

If S is a set of vectors in R3 that are linearly independent, but do not span R3, it implies that S is a proper subset of R3. Since the dimension of R3 is three, S cannot contain more than three vectors.

To understand this, we need to consider the definition of spanning. A set of vectors spans a vector space if every vector in that space can be written as a linear combination of the vectors in the set. Since S does not span R3, there must be at least one vector in R3 that cannot be expressed as a linear combination of the vectors in S.

If we add another vector to S, it would increase the span of S and potentially allow it to span R3. Therefore, the maximum number of vectors in S is three, as adding a fourth vector would exceed the dimension of R3 and allow S to span R3.

To understand why, let's break down the options and their implications:

(A) If S contains only one vector, it cannot span R3 since a single vector can only represent a line in R3, not the entire three-dimensional space.

(B) If S contains two vectors, it still cannot span R3. Two vectors can at most span a plane within R3, but they will not cover the entire space.

(C) If S contains three vectors, it is possible for them to be linearly independent and span R3. Three linearly independent vectors can form a basis for R3, meaning any vector in R3 can be expressed as a linear combination of these three vectors.

(D) This option is incorrect because S cannot contain any number of vectors. It must be limited to a maximum of three vectors in order to meet the given conditions.

Thus, the correct answer is (C) three.

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The value of p for which V(X) is maximized is 0.5. If the variance of a binomial random variable is equal to 0, it indicates that all trials will yield the same result. The value of p for which V(X) is maximized is 0.5.

(a) There are no p values for which V(X) = 0. When every trial is a failure, there is no variability in X. Also, when every trial is a success, there is no variability in X. When the probability of success is the same as the probability of failure, there is no variability in X. Hence, if the variance of a binomial random variable is equal to 0, it indicates that all trials will yield the same result. It implies that the probability of success is 0 or 1.

In other words, the binomial experiment is not random, and every trial has an identical outcome. As a result, there is no variability in X.

(b) The value of p for which V(X) is maximized is 0.5. The variance of a binomial distribution is given by V(X) = npq, where p is the probability of success, q is the probability of failure, and n is the number of trials. V(X) is maximized when the product npq is maximum.

Now, p + q = 1.

Therefore,

q = 1 - p.

Hence,

V(X) = np(1 - p).

Taking the derivative of V(X) to p and equating it to zero, we get

dV(X)/dp = n - 2np = 0.

Thus,

p = 0.5.

Hence, V(X) is maximized when p = 0.5.

The variance of a binomial distribution depends on the probability of success, failure, and the number of trials. If the variance of a binomial random variable is equal to 0, it indicates that all trials will yield the same result. The value of p for which V(X) is maximized is 0.5.

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The values of h and k would be =2 and 2 respectively.

The value of x would be = 5.2

A horizontal distance is the distance that is be covered by a moving object through a horizontal pathway.

y = h + kx - 0.5x^2

When X = 2 and y = 5 is the centre of the hoop.

To calculate for y;

X max = -k/2× (-0.5)

X max = k = 2

y max = 5

Substitute the given variables into the equation and make h the subject of formula.

5 = (h + 2×2) - (0.5x^2)

5= (h + 4)- 1

h +4 = 5+1

h +4 = 6

h = 6-4

h = 2

Also from the graph, the value for x as the ball hits the ground would be = 5.2

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9514 1404 393

Answer:

  [-4, ∞)

Step-by-step explanation:

The vertical extent (range) of the graph is from -4 (at x=0) to +∞ (as x → ±∞).

In interval notation, this is ...

  [-4, ∞)

Stated as an inequality, the range is ...

  y ≥ -4

So first, we're gonna split these into their own little sections.

If Duncan drove 30 mph for 20 minutes, we need to think about the time for now. One hour is 60 minutes, and 20 minutes is 1/3 of an hour. If it's 30 miles per hour, then we'd need to split that into thirds to give it the twenty minute value, so in twenty minutes he drove 10 miles.

For the second part, we're gonna do the same thing. 40 mph in twelve minutes. 60 divided by 12 is 5. Then split the 40 mph into fifths. 40 / 5 = 8. Every twelve minutes, he drove 8 miles.

Add 10 and 8, and he drove a total of 18 miles to get home.

The value of the given expression [\(87^3+ 13^3/87^2 -87 * 13 + 13^2\)] by simplifying the numerator and denominator using suitable identities is 100.

We will first calculate the numerator:

As  (\(a^3\) + \(b^3\)) = (a + b)(\(a^2\) - ab + \(b^2\)) :

\(87^3\) + \(13^3\) = (87 + 13)(\(87^2\) - \(87 * 13\) + \(13^2\))

= 100(\(87^2\) - 87 * 13 + \(13^2\))

Now, calculate the denominator:

\(87^2 - 87 * 13 + 13^2\)

As,(\(a^2 -2ab +b^2\)) =\((a - b)^2\):

\(87^2 - 87 * 13 + 13^2 = (87 - 13)^2\)

\(= 74^2\)

So by solving the equation further:

\((87^3+13^3) / (87^2- 87 * 13+13^2) = 100*(87^2- 87 *13 + 13^2)/(87^2 - 87 * 13 + 13^2)\)

As we can see the numerator and denominator are the same expressions (\(87^2 - 87 * 13 + 13^2\)). so, they cancel each other:

\((87^3 + 13^3) / (87^2 - 87 * 13 + 13^2) = 100\)

So, the value of the given expression is 100.

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Answer:

3.357

Step-by-step explanation:

18.8 / 5.6 = 3.357

Answer:

110°

Step-by-step explanation:

The path in the inscribed polygon walked by Ellen is shown in the diagram attached. Let the degrees in which Ellen must turn to get back to her starting point be T. Therefore to calculate T we use the theorem "An inscribed quadrilateral whose vertices all lie on a circle, the opposite angles of such a quadrilateral are in fact supplements for each other i.e their sum is 180 degrees."

Therefore: T + 70° = 180°

T = 180° - 70°

T = 110°

To get back to the starting point, Ellen must turn 110°

Answer:

3, 5, -54, and -7 are like terms while -2x stays alone.

Step-by-step explanation:

3+5-2x-54-7=0

3+5-2x-61=0

5-2x=61-3

5-2x=59

-2x=59-5

-2x=54

(-x)=54/2

(-x)=27

x=-27

Answer:

519.90

Step-by-step explanation:

(64.94x2)+6(5x13) = 519.90

∫[3, 8] f(x) dx equals approximately 1683.17.

∫[3, 8] g(x) dx equals approximately 1932.5

To evaluate the given integrals, let's first identify the functions f(x) and g(x) and their respective intervals.

f(x) = 4x^2 - 3x + 2

g(x) = 2x^3 - 5x + 1

Interval: [3, 8]

Now, let's evaluate the integrals step by step.

∫[3, 8] f(x) dx:

We integrate the function f(x) over the interval [3, 8].

∫[3, 8] (4x^2 - 3x + 2) dx

To find the integral, we can use the power rule for integration. For each term, we increase the exponent by 1 and divide by the new exponent.

= [4 * (x^3/3) - 3 * (x^2/2) + 2x] evaluated from 3 to 8

Now we substitute the upper and lower limits into the integral expression:

= [(4 * (8^3/3) - 3 * (8^2/2) + 2 * 8) - (4 * (3^3/3) - 3 * (3^2/2) + 2 * 3)]

Simplifying further:

= [(4 * 512/3) - (3 * 16/2) + 16 - (4 * 27/3) + (3 * 9/2) + 6]

= [(1706.67) - (24) + 16 - (36) + (13.5) + 6]

= 1683.17

Therefore, ∫[3, 8] f(x) dx equals approximately 1683.17.

∫[3, 8] g(x) dx:

We integrate the function g(x) over the interval [3, 8].

∫[3, 8] (2x^3 - 5x + 1) dx

Using the power rule for integration:

= [(2 * (x^4/4)) - (5 * (x^2/2)) + x] evaluated from 3 to 8

Substituting the upper and lower limits:

= [(2 * (8^4/4)) - (5 * (8^2/2)) + 8 - (2 * (3^4/4)) + (5 * (3^2/2)) + 3]

Simplifying further:

= [(2 * 4096/4) - (5 * 64/2) + 8 - (2 * 81/4) + (5 * 9/2) + 3]

= [(2048) - (160) + 8 - (162/2) + (45/2) + 3]

= 1932.5

Therefore, ∫[3, 8] g(x) dx equals approximately 1932.5

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Answer:

\(h=\frac{1}{3} \pi r^{2} v\)

Step-by-step explanation:

height is equal to one third times pi times radius squared times volume

The expression of the volume of the cone in terms of height H will be as H = 3V/(πR²).

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

An expression is a mathematical proof of the equality of two mathematical expressions.

As per the given volume of the cone,

V=(1/3)πR²H

Manipulate the above formula as,

[V (3/1)]/(πR²) = H

H = 3V/(πR²)

Hence "The expression of the volume of the cone in terms of height H will be as H = 3V/(πR²)".

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Answer:

f(8)=69

Step-by-step explanation:

f(X)= -3 (-3x) -3

f(8)= -3 (-3(8)) -3

= -3 (-24) -3

= 72-3

=69

Given:

Total amount = $115

Amount spent = $90

Cost of each pair of socks = $5

To find:

The inequality to represent the greatest number of pairs of socks he can buy.

Solution:

Let x be the number of pairs of socks he can buy.

Cost of 1 pair of socks = $5

Cost of x pair of socks = $5x

Sum of amount spent and cost of x pair of socks must be less than or equal to the total amount he has.

\(90+5x\leq 115\)

\(5x\leq 115-90\)

\(5x\leq 25\)

Divide both sides by 5.

\(x\leq \dfrac{25}{5}\)

\(x\leq 5\)

The maximum value of x is 5. So, the maximum number of pair of socks is 5.

Therefore, the inequality of the given situation is \(90+5x\leq 115\) and \(x\leq 5\) represent the greatest number of pairs of socks he can buy.

Answer:

Moved the graph down by 4.

Step-by-step explanation:

By subtracting by 4 on the outside, you are moving it down 4.

The angle L is congruent to angle T ∠L ≅ ∠T and the reason is that  opposite angles of a parallelogram are congruent.

We are given the parallelograms GHLJ and GSTU in such a manner that the parallelogram GSTU is inscribed right inside parallelogram GHLJ with angle G coinciding on the two parallelograms.

Now, we can remember that property of parallelogram states that the opposite angles of a parallelogram are congruent.

Thus, angle G is congruent to angle T and angle L .

Therefore, ∠L ≅ ∠T

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Answer:

By the parallelogram angle theorem, opposite angles of a parallelogram are congruent. Therefore, angle T must be congruent to angle G, and angle G must be congruent to angle L. By the transitive property of congruence, angle T is congruent to angle L.

Step-by-step explanation:

got it right on edge2

The  grade would raise the grade to 58.76%.

To calculate the impact of a 50-point assignment on a 67.0% overall grade, we first need to know the weight of the assignment in the calculation of the overall grade. Let's assume that the assignment is worth 20% of the final grade for the class.

If the overall grade is 67.0%, then the weight of the remaining work in the calculation is 100% - 67.0% = 33.0%. Therefore, the current score for the final piece of work is:

(67.0% x 33.0%) = 22.11%

Adding the score for the 50-point assignment to this gives us the new score for the final piece of work:

22.11% + (50 / 100) x 20% = 32.11%

Since this is the score for the final piece of work, we can now calculate the new overall grade for the class using the updated weightings:

(67.0% x 80%) + (32.11% x 20%) = 58.76%

If the 50-point assignment is worth 20% of the final grade, adding it to a 67.0%.

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Yes, the sample size would be large enough if the population is school-aged children and young adults in the United States as this is a simple random sampling.

Simple random sampling is used for randomly selecting the sample size for research. No member in the population has a higher chance in comparison to others for selection in sampling. Every individual has an equal chance to be a part of the sample for the study. This is a type of probability sampling method.

The probability sampling method states that every individual has a fair and equal chance to be selected as a research sample. It includes simple random sampling, stratified sampling, systematic sampling, and cluster sampling. Here the researchers have picked around 150 students and young adults which is an appropriate amount of simple random sample for the study.

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Answer:

Step-by-step explanation:

Since the cost is $100 for deposit and $200 per hour, the function rule to find the total cost of renting the theatre for 'n' hours will be:

= 100 + 200(n)

= 100 + 200n

The total cost if you rented the theatre for 4 hours will be gotten by replacing n with 4. This will be:

= 100 + 200n

= 100 + 200(4)

= 100 + 800

= $900

Answer:The solution is in the attached file

Step-by-step explanation: