If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to x from the first equation is substituted into the second equation.

x + 4y = −9
2x + 5y = −6

2x + 5(4y − 9) = −6
2x + 5(−4y − 9) = −6
2(4y − 9) + 5y = −6
2(−4y − 9) + 5y = −6

The volume of the cylinder generated by rotating the region bounded by y = x³ , y = 8 , x = 0 and x = 9 be, 1608.25 cubic units.

Given, a cylinder generated by rotating the region bounded by the given curves about the specified axis

y = x³ , y = 8 , x = 0 and x = 9

we have to find the volume of the cylinder generated by the given region,

So, using the concept of integration, we get

Volume of the cylinder =  Integrating y from x³ to 8 then integrating x from 0 to 9.

Volume of the cylinder = ∫∫dy dx

Volume of the cylinder = ∫(x³ - 8) dx

Volume of the cylinder = x^4/4 - 8x

Volume of the cylinder = (9)^4/4 - 8(4)

Volume of the cylinder = 1640.25 - 32

Volume of the cylinder = 1608.25

So, the volume of the cylinder be 1608.25 cubic units.

Hence, volume of the cylinder be 1608.25 cubic units.

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Answer: 8/1 = 6/48

Step-by-step explanation: um thats the answer bye

The relationship between the number of students to tables or the ratio of students to number of tables is 8 to 1.

According to question,

We have the following information:

In an art classroom, 8 students can sit around 1 table, and 48 students can sit around 6 tables.

Now, we will find the relationship between the number of students and the number of tables or in simple words, ratio.

So, we have:

8 students = 1 table

48 students = 6 tables

It can be rewritten by dividing both the sides by 6 as 8 students to 1 table.

It means that there are 8 students for 1 table.

Hence, the relationship between the number of students to the number of tables is 8 to 1.

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Answer:

Step-by-step explanation:

Step 1:First Make 3/4 and 5/6 into like fractions.Find the L.C.M of 4 and  

            6,which is 12.

            3*3/4*3=9/12

             5*2/6*2=10/12

Step 2:Subtract 9/12 from 10/12,which is 1/12.

Answer:

neither

Step-by-step explanation:

using (y2-y1)/(x2-x1) you get the actual slopes which are JK = 3/2 and LM = -3/2

since they are neither the same (parallel), opposite reciprocals (perpendicular), they are neither parallel nor perpendicular

Answer:

We use the binomial distribution to describe this situation.

The mean number of phone sales is 749.7 with a standard deviation of 15.

Step-by-step explanation:

For each shopper, there are only two possible outcomes. Either they plan to purchase the newly released smart phone, or they do not. Each customer is independent of other customers. So we use the binomial distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

\(E(X) = np\)

The standard deviation of the binomial distribution is:

\(\sqrt{V(X)} = \sqrt{np(1-p)}\)

Fifty random shoppers at an electronics store have been interviewed and 35 of them intend to purchase a newly released smart phone.

This means that \(p = \frac{35}{50} = 0.7\)

What are its mean and standard deviation of phone sales if we are concerned about 1071 shoppers that day

1071 shoppers, so \(n = 1071\)

Mean

\(E(X) = 1071*0.7 = 749.7\)

Standard deviation

\(\sqrt{V(X)} = \sqrt{1071*0.7*0.3} = 15\)

The mean number of phone sales is 749.7 with a standard deviation of 15.

From the question given,

The formula to find the test statistics mean is given below as,

Where,

Given the values of the above below,

Substituting the values into the formula of test statistics t above,

Hence, the test statistics, t = -3.24 ( two decimal places)

Answer:

Approximately \(0.157\).

Step-by-step explanation:

Let \(X\) denote the speed of a car. The question is asking for \(P(60 \le X \le 70)\).

That probability is equal to \(P(X \le 70)- P(X \le 60)\).

Find each of \(P(X \le 60)\) and \(P(X \le 70)\) using a \(Z\)-table.

Calculate the \(Z\) value for \(x = 70\) and \(x = 60\):

At \(x = 70\), \(\displaystyle z = \frac{x - \mu}{\sigma} = \frac{60 - 55}{5} = 3\).

At \(x = 60\), \(\displaystyle z = \frac{x - \mu}{\sigma} = \frac{70 - 55}{5} = 1\).

In other words: \(P(X \le 70) = P(Z \le 3)\) whereas \(P(X \le 60) = P(Z \le 1)\).

Look up \(P(Z \le 3)\) and \(P(Z \le 1)\) on a \(Z\)-table. The question is asking that the answer be rounded to the nearest thousandth. Therefore, keep at least more decimal places than that in intermediate values.

\(P(Z \le 3) \approx 0.9987\) and \(P(Z \le 1) \approx 0.8413\).

Therefore:

\(\begin{aligned}P(60 \le X \le 70) &= P(X \le 70)- P(X \le 60) \\ &= P(Z \le 3) - P(Z \le 1) \approx 0.157\end{aligned}\).

Answer:1000

Step-by-step explanation:

Yes

By using compound interest formula, we conclude that Sophie deposited $16,638 (rounded to the nearest whole number) into the account.

Compound interest is a method of calculating interest on a principal amount of money, where the interest earned on the initial principal is added to the principal at the end of each compounding period (usually monthly, quarterly, or annually).

We can use the formula for compound interest to solve this problem. The formula is:

\(A = P(1 + r/n)^{(nt)\)

Where:

A = the total amount in the account

P = the principal (initial deposit)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

We know the values for A, r, n, and t, so we can solve for P:

\(A = P(1 + r/n)^{(nt)\)

\(22,099.87 = P(1 + 0.022/2)^{(2*13)\)

\(22,099.87 = P(1.011)^{26\)

22,099.87 = 1.329P

P = 22,099.87 / 1.329

P = 16,637.55

Therefore, Sophie deposited $16,638 (rounded to the nearest whole number) into the account.

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Answer:

170°

Step-by-step explanation:

180 - 10 = 170

The volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis is 51π cubic units.

To find the volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis, we can use the method of cylindrical shells.

The formula for the volume using cylindrical shells is:

V = 2π ∫ [a, b] x * h(x) dx

Where:

- V is the volume of the solid

- π represents the mathematical constant pi

- [a, b] is the interval over which we are integrating

- x is the variable representing the x-axis

- h(x) is the height of the cylindrical shell at a given x-value

In this case, we need to solve for x in terms of y to express the equation in terms of y.

Rearranging the given equation:

x = 5 ± √(1 - y)

Since we are only interested in the region in the first quadrant, we take the positive square root:

x = 5 + √(1 - y)

Now we can rewrite the volume formula with respect to y:

V = 2π ∫ [c, d] x * h(y) dy

Where:

- [c, d] is the interval of y-values that correspond to the region in the first quadrant

To determine the interval [c, d], we set the equation equal to zero and solve for y:

1 - (x - 5)² = 0

Expanding and rearranging the equation:

(x - 5)² = 1

x - 5 = ±√1

x = 5 ± 1

Since we are only interested in the region in the first quadrant, we take the value x = 6:

x = 6

Now we can evaluate the integral to find the volume:

V = 2π ∫ [0, 1] x * h(y) dy

Where h(y) represents the height of the cylindrical shell at a given y-value.

Integrating the expression:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * h(y) dy

To find h(y), we need to determine the distance between the y-axis and the curve at a given y-value. Since the curve is symmetric, h(y) is simply the x-coordinate at that point:

h(y) = 5 + √(1 - y)

Substituting this expression back into the integral:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

Now, we can evaluate this integral to find the volume

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

To simplify the integral, let's expand the expression:

V = 2π ∫ [0, 1] (25 + 10√(1 - y) + 1 - y) dy

V = 2π ∫ [0, 1] (26 + 10√(1 - y) - y) dy

Now, let's integrate term by term:

\(V = 2\pi [26y + 10/3 * (1 - y)^\frac{3}{2} - 1/2 * y^2]\)] evaluated from 0 to 1

V = \(2\pi [(26 + 10/3 * (1 - 1)^\frac{3}{2} - 1/2 * 1^2) - (26 * 0 + 10/3 * (1 - 0)^\frac{3}{2} - 1/2 * 0^2)]\)

V = 2π [(26 + 0 - 1/2) - (0 + 10/3 - 0)]

V = 2π (25.5)

V = 51π cubic units

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Therefore, Paxton will need to invest her money for approximately 21.62 years to increase her investment from $4850 to $8000 at a simple interest rate of 7.6% per year.

To determine how long Paxton needs to invest her money in order for it to increase to $8000, we can use the formula for simple interest:

I = P * r * t

Where:

I = Interest earned

P = Principal (initial investment)

r = Interest rate per year (expressed as a decimal)

t = Time (in years)

Given that Paxton invests $4850 at an interest rate of 7.6% per year, we have:

4850 * 0.076 * t = 8000

Simplifying the equation:

369.8t = 8000

To find t, we divide both sides of the equation by 369.8:

t ≈ 8000 / 369.8 ≈ 21.62 years

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Let the function in which "y" varies directly with "x" be y = kx where "k" is the proportionality constant and y ∝ x

As per the question statement, We are supposed to write any function in which "y" varies directly with "x" i.e., y ∝ x

Let's say y = kx be the function where "k" is the proportionality constant and y ∝ x.

Now let x = 3 and y = 6, so 6 = k*3

or k = 3

Hence for any value of "x" value of "y" would be k times the value of x and this is called the direct proportion relationship.

Hence,  the function in which "y" varies directly with "x" be y = kx where "k" is the proportionality constant and y ∝ x

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Answer:

1. 1. The constraints are as follows -

a) Limited weekly budgets

b) Limited ads requiring that there should be at least 15 and at least 2 ads of each type (Radio and  newspaper)

c) Newspaper ad being costly reach larger population segment as compared to the radio ads which is cheaper than newspaper ad but reaches only a small portion of population

2. 6 newspaper adds and 9 radio adds

Step-by-step explanation:

1. The constraints are as follows -

a) Limited weekly budgets

b) Limited ads requiring that there should be at least 15 and at least 2 ads of each type (Radio and  newspaper)

c) Newspaper ad being costly reach larger population segment as compared to the radio ads which is cheaper than newspaper ad but reaches only a small portion of population

The objective function

Maximum number of people per week = 6000  * number of newspapaer ads + 2000 * number of radio ads

b) $7,200

Minimum radio adds = 3 this will cost 3 * $400 = $1200

Remaining money = $7200 - $1200 = $6000

Cost of one add of news paper  = $ 6000/$600 = 10

But the minimum ads need to be 15

So, If Newspaper adds are reduced to 6, the radio adds will be 9 giving a sum of 15

The percentage is 26%, so the number is 26.

Here we know that the x% of the number 800,000 is equal to 208,000.

Remember that the x% of a number N, is given by the product:

(x%/100%)*N

So in this case we can solve the equation:

(x%/100%)*800,000 = 208,000

Solving that equation for the percentage, we will get:

x% = 100%*(208,000/800,000)

x% = 26%

That is the missing number.

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To find the slope of the curve, first differentiate the equation of the curve and substitute the value of x in the result

The slope of the curve is the change in y coordinates with respect to the change in x coordinates of the line

To find the slope of the curve at a given point

First differentiate the given equation of the curve with respect to x

That is dy / dx.

The derivative of the equation of the curve  is the slope of the curve.

In next step substitute the value of x in the slope of the curve

The result will be the slope of the curve at a given point

Therefore, these are the steps to find the slope of the curve

I have answered the question in general, as the given question is incomplete

The complete question is:

How to find the slope of a curve at a given point?

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Answer:

linear function

Step-by-step explanation:

straight line then add up

3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.

Let's start by breaking down the information given:

- Three-fourths of the yard is covered with grass.

- One-fourth of the yard is used as a garden.

- The sprinkler could only water 1/5 of the yard.

To find out how much of the grass died, we need to determine the portion of the grass that was not watered by the sprinkler.

Let's assume the total area of the yard is represented by the value 1. Therefore, we can calculate the area of the grass as 3/4 of the total yard, which is (3/4) * 1 = 3/4.

The sprinkler can only water 1/5 of the yard, so the portion of the grass that was watered is (1/5) * (3/4) = 3/20.

To find the portion of the grass that died, we subtract the watered portion from the total grass area:

Portion of grass that died = (3/4) - (3/20) = 15/20 - 3/20 = 12/20.

Simplifying, we get:

Portion of grass that died = 3/5.

Therefore, 3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.

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The true statements about column vector from the list are the product a.*b^2, a'*b, a.*b and a'.*b gives error and a.*b' is equal to a'.*b that is all are true.

The product a.*b^2 gives an error because the element-wise product requires that the two operands have the same size. In this case, a and b^2 do not have the same size, so an error is produced.

The product a'*b gives an error because the matrix product requires that the number of columns in the first operand (a') is equal to the number of rows in the second operand (b). In this case, a' and b do not have compatible dimensions, so an error is produced.

The product a'.*b' gives an error because the element-wise product requires that the two operands have the same size. In this case, a' and b' do not have the same size, so an error is produced.

The product a.*b' is equal to a'.*b because the element-wise product is commutative, meaning that the order of the operands does not matter. In this case, a.*b' is equivalent to b'.*a, which is equal.

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Answer:

c. A cost benefit analysis

Step-by-step explanation:

Answer:

-12

Step-by-step explanation:

Order of operations:

PEMDAS

First, do parenthesis, 2 x 2.2 = 4.4 then do -7.6 - 4.4 = -12

Therefore, the interest portion of the seventh payment is:7,000 x (1 + r + r2 + r3 + r4 + r5 + r6) / r7 - 7,000.

We have the following payments and their corresponding times of payment:At the end of year 1: $1,000At the end of year 2: $2,000At the end of year 3: $3,000At the end of year 4: $4,000At the end of year 5: $5,000At the end of year 6: $6,000At the end of year 7: $7,000

At the end of year 8: $8,000At the end of year 9: $9,000At the end of year 10: $10,000The present value of these payments is:PMT x [(1 - (1 + r)-n) / r]where PMT is the payment, r is the interest rate per year, and n is the number of years till payment.

For the first payment (end of year 1), the present value is:1,000 x [(1 - (1 + r)-1) / r]which equals

1,000 x (1 - 1 / (1 + r)) / r = 1,000 x ((1 + r - 1) / r) = 1,000

For the second payment (end of year 2), the present value is:2,000 x [(1 - (1 + r)-2) / r]which equals 2,000 x (1 - 1 / (1 + r)2) / r = 2,000 x ((1 + r - 1 / (1 + r)2) / r) = 2,000 x (1 + r) / r2

For the seventh payment (end of year 7), the present value is:

7,000 x [(1 - (1 + r)-7) / r]

which equals

7,000 x (1 - 1 / (1 + r)7) / r = 7,000 x ((1 + r - 1 / (1 + r)7) / r) = 7,000 x (1 + r + r2 + r3 + r4 + r5 + r6) / r7

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Answer:

x=45

Step-by-step explanation:

i hope its right good luck :)

i think im wrong

The name which is given to the practice which Hometown Bank and Trust practised by refusing to lend money to people trying to purchase property in a predominantly Hispanic neighborhood is:

Based on the given question, we need to show the name of the practice of segregating people based on their race by refusing to give them loans to purchase property in an area dominated by Hispanics.

This practise is known as redlining as the property agent tries to prevent people from getting property in a community dominated by a particular race.

Therefore, the correct answer is Redlining

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Step-by-step explanation:

I hope it will help man and also what's the answer please mention ?

Answer:

In ΔABC and Δ DEC:

∠ABC = ∠DEC (both angles are 90 degrees )

We can see that the angles, ∠ABC and ∠DEC are corresponding angles

Since the corresponding angles are equal, we can say that:  AB || DE

In ΔABC and Δ DEC:

∠ABC = ∠DEC  (Both are 90 degrees)

∠ACB = ∠ECD  (Common angle)

Hence, by the AA criterion, we can say that ΔABC ≈ Δ DEC

Finding the Ratio of Similarity:

From the triangle, we see that:

BC = 12 units

EC = 7 units

Since the triangles are similar, they have a constant ratio between their sides

Ratio of sides of  ΔABC and Δ DEC = BC / EC

Ratio = 12 / 7

Finding h:

We can see that the sides AB and DE are similar, we also know the ratio of similarity between the sides

We can say that:

h * ratio of similarity = AB

h * 12/7 = 9

h = 63 / 12

h = 5.25 units

Answer: 83.7

Step-by-step explanation: Do 0.3 x 279 to get 83.7.

Answer: 90,000

Step-by-step explanation:

Answer:

The circle is increasing at a rate of 1.76π or about 5.5292 square centimeters per second.

Step-by-step explanation:

We want to determine the rate at which a circle's area is increasing given that its radius is increasing at a rate of 0.02 cm/s at the instant when its radius is 44 cm.

In other words, we want to find dA/dt when dr/dt = 0.02 cm/s and r = 44.

Recall that the equation of a circle is given by:

\(\displaystyle A = \pi r^2\)

Take the derivative of both sides with respect to t:

\(\displaystyle \frac{d}{dt}\left[ A\right] = \frac{d}{dt}\left[ \pi r^2\right]\)

Implicitly differentiate:

\(\displaystyle \frac{dA}{dt} = 2\pi r \frac{dr}{dt}\)

dr/dt = 0.02 and r = 44. Substitute and evaluate:

\(\displaystyle \begin{aligned} \frac{dA}{dt} & = 2\pi (44\text{ cm})\left(0.02\text{ cm/s}\right) \\ \\ & =1.76\pi \text{ cm$^2$/s} \\ \\ &\approx 5.5292 \text{ cm$^2$/s} \end{aligned}\)

In conclusion, the circle is increasing at a rate of 1.76π or about 5.5292 square centimeters per second.