Guided practice

it's not letter c. -2.6

state what number you would subtract from each side of the inequality to solve the inequality.


5.7 ≥ k + 3.1


a.
3.1


b.
5.7


c.
–2.6

If we borrowed $500 for 6 years at a rate of 7% interest then we will have to pay approximately $750 after 6 years.

Given that principal amount is $500 , years are 6 and rate of interest be 7%.

We are required to find the amount that we have to pay after 6 years if we borrow $500.

Compound interest is the interest that is calculated on the principal plus the accumulated interest at that point of time.

Sum after compounding is given as under:

S=P\((1+R)^{N}\)

So we have to just put the values to find the money that we have to pay after 6 years.

S=500\((1+0.07)^{6}\)

=500\((1.07)^{6}\)

=500*1.5

=$750

Hence if we borrowed $500 for 6 years at a rate of 7% interest then we will have to pay approximately $750 after 6 years.

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Answer:

9

Step-by-step explanation:

just plug in the numbers

\(3(w - x), w=5, x=2\\ 3 \times (5 - 2) = 3 \times 3 = 9\)

Answer:

9

Step-by-step explanation:

If a hypothesis test is conducted to see if there is evidence that the average wait time is 5 minutes, the p-value is 0.040.

To calculate the p-value for the hypothesis test, we need to perform the following steps:

Step 1: State the null and alternative hypotheses.

In this case, the null hypothesis (H0) is that the average wait time for customers during the lunch hour is 5 minutes. The alternative hypothesis (Ha) is that the average wait time is not 5 minutes.

Step 2: Determine the test statistic.

We can use a t-test since we do not know the population standard deviation. We calculate the t-value using the formula:

t = (x' - μ) / (s / √n)

where x' is the sample mean, μ is the population mean (5 minutes), s is the sample standard deviation, and n is the sample size (15).

Step 3: Calculate the p-value.

We can use a t-distribution table or software to find the p-value associated with our calculated t-value. Alternatively, we can use the t-test function in Excel or other statistical software to calculate the p-value directly.

Assuming a two-tailed test and a significance level of 0.05, if the p-value is less than 0.05, we reject the null hypothesis in favor of the alternative hypothesis. If the p-value is greater than 0.05, we fail to reject the null hypothesis.

Suppose the sample mean is 6.2 minutes, the sample standard deviation is 1.3 minutes, and the sample size is 15. Then the t-value is:

t = (6.2 - 5) / (1.3 / √15) = 2.22

Using a t-distribution table or software with 14 degrees of freedom (15 - 1), we find the p-value to be approximately 0.040, which is less than 0.05. Therefore, we reject the null hypothesis and conclude that there is evidence to suggest that the average wait time for customers during the lunch hour is not 5 minutes.

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Answer:-1

Step-by-step explanation:

Answer: -6

Step-by-step explanation:

the line pass through (-3,-6)

Answer:

z = -1

Step-by-step explanation:

Answer: x =11

Step-by-step explanation:

Answer:

97 and 98

Step-by-step explanation:

The surface area of the cylinder with the given height and radius is 835.2 square inches

The given parameters are

The surface area is then calculated using the following formula

A = 2πr² + 2πrh

Substitute the given values in the above equation

So, we have:

A = 2 * 3.14 * 7^2 + 2 * 3.14 * 7 * 12

Evaluate the exponents

A = 2 * 3.14 * 49 + 2 * 3.14 * 7 * 12

Evaluate the products

A = 307.72 + 527.52

Evaluate the sum

A = 835.2

Hence, the surface area of the cylinder with the given height and radius is 835.2 square inches

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So, the approximate probability of seeing more than 45 coin flips as heads out of 100 flips is approximately 0.1539, or 15.39%.

To approximate the probability of seeing more than 45 coin flips as heads out of 100 flips, we can use the central limit theorem. The central limit theorem states that for a large enough sample size, the distribution of the sum (or average) of independent and identically distributed random variables approaches a normal distribution.

In this case, each coin flip is a Bernoulli trial with a probability of success (getting heads) of 0.4. We can consider the number of heads obtained in 100 flips as a sum of 100 independent Bernoulli random variables.

The mean of a single coin flip is given by μ = np = 100 * 0.4 = 40, and the standard deviation is given by σ = sqrt(np(1-p)) = sqrt(100 * 0.4 * 0.6) ≈ 4.90.

Now, to approximate the probability of seeing more than 45 coin flips as heads, we can use the normal distribution with the mean and standard deviation calculated above.

Let X be the number of heads in 100 flips. We want to find P(X > 45).

Using the standard normal distribution, we can calculate the z-score for 45 flips: z = (45 - 40) / 4.90 ≈ 1.02

Using a standard normal distribution table or a calculator, we can find the probability associated with this z-score: P(Z > 1.02) ≈ 1 - P(Z < 1.02)

Looking up the value in the table, we find that P(Z < 1.02) ≈ 0.8461.

Therefore, P(Z > 1.02) ≈ 1 - 0.8461 ≈ 0.1539.

So, the approximate probability of seeing more than 45 coin flips as heads out of 100 flips is approximately 0.1539, or 15.39%.

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Answer:

1= 41

2=85

3= 95

4=85

5= 36

6= 49

7= 188

Step-by-step explanation:

I think that's the answer

a)  The given values:  M = (9.830 * (6371000)^2) / (6.67430 × 10^-11)

M ≈ 5.970 × 10^24 kg

b) Comparing this with the calculated value from part (a), we can see that they are very close:

Calculated mass: 5.970 × 10^24 kg

Accepted mass: 5.979 × 10^24 kg

(a) To calculate Earth's mass given the acceleration due to gravity at the North Pole (g) and the radius of the Earth (r), we can use the formula for gravitational acceleration:

g = (G * M) / r^2

Where:

g = acceleration due to gravity (9.830 m/s^2)

G = gravitational constant (6.67430 × 10^-11 m^3/kg/s^2)

M = mass of the Earth

r = radius of the Earth (6371 km = 6371000 m)

Rearranging the formula to solve for M:

M = (g * r^2) / G

Substituting the given values:

M = (9.830 * (6371000)^2) / (6.67430 × 10^-11)

M ≈ 5.970 × 10^24 kg

(b) The accepted value for Earth's mass is approximately 5.979 × 10^24 kg.

Comparing this with the calculated value from part (a), we can see that they are very close:

Calculated mass: 5.970 × 10^24 kg

Accepted mass: 5.979 × 10^24 kg

The calculated mass is slightly lower than the accepted value, but the difference is within a reasonable margin of error.

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The weight range that contains at least 75% of all residents' annual garbage goes between 420 pounds and 787.5 pounds.

Given that the average resident of Metro City produces 630 pounds of solid waste each year, and the standard deviation is approximately 70 pounds, to determine the weight range that contains at least 75% of all residents' annual garbage weights, the following calculation must be performed:

Therefore, the weight range that contains at least 75% of all residents' annual garbage goes between 420 pounds and 787.5 pounds.

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Answer:

They are zeroes when y=0

Step-by-step explanation:

For a function \(f(x)\), if \(f(x)=0\), the values of x that make the function true are known as roots, or x-intercepts, or zeroes.

The volume of the frustum of the right circular cone is approximately 21850.2 cubic units where  frustum of a cone is a three-dimensional geometric shape that is obtained by slicing a larger cone with a smaller cone parallel to the base.  

To find the volume of a frustum of a right circular cone, we can use the formula:

V = (1/3) * π * h * (r₁² + r₂² + (r₁ * r₂))

where V is the volume, h is the height, r₁ is the radius of the lower base, and r₂ is the radius of the top base.

Given the values:

h = 15

r₁ = 25

r₂ = 19

Substituting these values into the formula, we have:

V = (1/3) * π * 15 * (25² + 19² + (25 * 19))

Calculating the values inside the parentheses:

25² = 625

19² = 361

25 * 19 = 475

V = (1/3) * π * 15 * (625 + 361 + 475)

V = (1/3) * π * 15 * 1461

V = (1/3) * 15 * 1461 * π

V ≈ 21850.2 cubic units

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The volume of the frustum of the right circular cone is approximately 46455 cubic units.

To find the volume of a frustum of a right circular cone, we can use the formula:

V = (1/3) * π * h * (R² + r² + R*r)

where V is the volume, π is a constant approximately equal to 3.14, h is the height of the frustum, R is the radius of the lower base, and r is the radius of the top base.

Given that the height (h) is 15 units, the radius of the lower base (R) is 25 units, and the radius of the top base (r) is 19 units, we can substitute these values into the formula.

V = (1/3) * π * 15 * (25² + 19² + 25*19)

Simplifying this expression, we have:

V = (1/3) * π * 15 * (625 + 361 + 475)

V = (1/3) * π * 15 * 1461

V ≈ (1/3) * 3.14 * 15 * 1461

V ≈ 22/7 * 15 * 1461

V ≈ 46455

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Given: A continuous uniform distribution over the interval [1.8, 5.4].To find:(a) Mean of X.(b) Variance of X.(c) P(X < 3.4)

The following formula is used to determine the mean of X when its continuous uniform distribution falls within the range [a, b]. And X's variance is given by 2 = (b - a)2/12.

Part (a): Mean of X The given interval is [1.8, 5.4].So, a = 1.8 and b = 5.4By using the above formula of mean,μ = (a + b)/2μ = (1.8 + 5.4)/2μ = 3.6Hence, the mean of X is 3.6.

Part (b): Variance of X By using the formula of variance,σ² = (b - a)²/12σ² = (5.4 - 1.8)²/12σ² = (3.6)²/12σ² = 12.96/12σ² = 1.08Hence, the variance of X is 1.08.

Part (c): P(X < 3.4)We have to find P(X < 3.4)The given distribution is a continuous uniform distribution over the interval [1.8, 5.4].The probability density function for this is,f(x) = 1/(5.4 - 1.8)f(x) = 1/3.6We have to find P(X < 3.4) = P(1.8 ≤ X ≤ 3.4)

From the probability density function,f(x) = 1/3.6And we know that, P(a ≤ X ≤ b) = ∫[a,b] f(x) dxBy using this, we get,P(1.8 ≤ X ≤ 3.4) = ∫[1.8, 3.4] 1/3.6 dxP(1.8 ≤ X ≤ 3.4) = [x/3.6]1.8³.⁶ - 1.8P(1.8 ≤ X ≤ 3.4) = [3.4/3.6] - [1.8/3.6]P(1.8 ≤ X ≤ 3.4) = 0.56 - 0.50P(1.8 ≤ X ≤ 3.4) = 0.06. Hence, P(X < 3.4) = 0.06.  

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The actuarial present value of Martha's life annuity benefits is $497,531.59.

To calculate the actuarial present value of Martha's life annuity benefits, we need to discount each payment using the given interest rate and the probability of survival for each period.

Given:

- Guaranteed annual payments of $8,000 for 10 years, starting at age 60.

- Annual payments of $30,000 for the subsequent 10 years, if alive.

- Annual payments of $85,000, if alive, thereafter.

- Mortality follows the Standard Ultimate Survival Model.

- Interest rate (discount rate) is 5%.

We can break down the calculation into three parts:

1. Present value of the guaranteed annual payments of $8,000 for 10 years, starting at age 60:

We discount each payment using the interest rate of 5% and the probability of survival for each year. Since the mortality follows the Standard Ultimate Survival Model, we can use actuarial tables to obtain the survival probabilities. Assuming the survival probabilities are as follows:

Age 60: 0.9872

Age 61: 0.9756

Age 62: 0.9639

...

Age 69: 0.9172

The present value of the guaranteed payments is calculated as:

PV1 = $8,000/(1 + 0.05)^5 + $8,000/(1 + 0.05)^6 + ... + $8,000/(1 + 0.05)^14

2. Present value of the annual payments of $30,000 for the subsequent 10 years, if alive:

Similar to the previous calculation, we discount each payment using the interest rate and the probability of survival for each year from age 70 to age 79.

PV2 = $30,000/(1 + 0.05)^15 + $30,000/(1 + 0.05)^16 + ... + $30,000/(1 + 0.05)^24

3. Present value of the annual payments of $85,000, if alive, thereafter:

Since these payments continue indefinitely, we calculate the present value using the perpetuity formula. Assuming Martha lives beyond age 79, we can calculate the present value as:

PV3 = $85,000/(0.05)

Finally, we calculate the total actuarial present value by summing up the present values from the three parts:

Actuarial Present Value = PV1 + PV2 + PV3

After performing the calculations, the actuarial present value of Martha's life annuity benefits is approximately $497,531.59.

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Answer:

the sides = 6 * 10 * 2 = 120 sq meters

front & rear triangle = .5 * 8 * 5 * 2 = 40 sq meters

total fabric needed = 160 square meters

that is NOT one of your answers but I think you may not have typed it correctly.  

Step-by-step explanation:

The solution set of given system of inequalities is the intersection region (purple colored region)

The correct graph is given by an option (B)

In this question, we have been given  the system of inequalities.

y > 3x - 7

y ≤ -2x + 1

We need to solve the system of inequalities by graphing.

Consider the graph of given system of inequalities as shown below.

An inequality y > 3x - 7 is represented by a region colored red and the inequality y ≤ -2x + 1 represented by a region colored blue.

The solution set for given inequalities is the set of all points which are common to both the inequalities.

This solution set is represented by purple color.

Therefore, the solution set of given system of inequalities is the intersection region (purple colored region)

The correct graph is given by an option (B)

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Answer:

y=2x-5

Step-by-step explanation:

Hi there!

We are given that a line has a slope of 2, and passes through the point (4,3)

We want to use point-slope form to find this equation of the line, yet we want to write this in slope-intercept form

Point-slope form is given as \(y-y_1=m(x-x_1)\), where m is the slope and \((x_1, y_1)\) is a point

As we are already given the slope and a point, we can substitute these values into the formula to find the line.

First, substitute 2 as m in the equation:

\(y-y_1=2(x-x_1)\)

Now substitute 4 as \(x_1\) and 3 as \(y_1\)

\(y-3=2(x-4)\)

This is the equation of the line in point-slope form.

Now we need to write it in slope-intercept form

Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept

We can actually get to slope-intercept form from point-slope form.

First, distribute 2 to both x and -4 on the right side

y-3=2x-8

Now add 3 to both sides

y=2x-5

Hope this helps!

The slope of the line that passes through the given points (2 12) and (6 11) is  -1/4.

Two points are given: (2, 12), (6, 11).

A line's "steepness" is quantified by a quantity called the slope, which is typically represented by the letter m. It is the adjustment of y for a unit adjustment of x.

We are aware that the formula for the slope of a line using two points is

m= y2 - y1 /x2 - x1

In this instance, x1 = 2, Y1 = 12, X2 = 6, Y2 = 11.

m = 11 - 12 / 6 - 2

m = -1/4

The slope is therefore -1/4.

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Answer:

C)$612.50

Step-by-step explanation:

Plss make me BRAINLIEST

If there is 30% discount, u will pay 70%(7/10) of actual price.

70% of $871

7/10 x 871 = $612.50

Answer:

$612.50

Step-by-step explanation:

875 x 30% = 262.50

875- 262.50= $612.50

Answer: D or the Fourth Choice-The quotient of 14 and 8 tenths divided by 2 plus the product of 6 and 3 minus 12

PEDMAS means Parentheses, Exponents, Divide, Multiply,Add,Subtract. The first thing we must solve is what is in the parentheses, that is 14.8 divided by 2. We don't have any exponents, so we move to divide. We have already solved the division sentence that was in the parentheses, so we have to multiply 6x3 next. 6x3 will then be added to the answer that was divided by 14.2 and 2, and lastly we will subtract 12. The only answer choice that follows that pattern is D or The quotient of 14 and 8 tenths divided by 2 plus the product of 6 and 3 minus 12.

I hope this helped & Good Luck <3!!!!

The Reimann sum with n rectangle will be given as \(\sum^{n-1}_{i = 0} f{(x_i)} \Delta x\)

Let us suppose that f is a non-negative function, defined over a closed interval represented by [a, b].

The integral of f with respect to x signifies the area between the graph of f and X-axis. This area would be called definite integral of a function f from a to b. Then Riemannian method of determining this area is:

“if the area is divided into n rectangles of very small breadth, then it would be simpler to calculate the area of such rectangles and then we can add them up

(i ) The width of each rectangle will be denoted as Δx

Δx = b-a/n,

where , a is lower bound

b is upper bound of the integral

(ii) The right-hand endpoints of each rectangle are refer as \(x_i\) and we can find the right endpoints by \(x_i\) = a + Δx.i

(iii) The height of each rectangle is the value of the function at the upper point of the interval.

a + (b-a)/n for the first rectangle , a + 2(b-a)/n for the second rectangle and so on

(iv) The area of the each rectangle will be

Area = Width × height

=> A = (b-a)/2 × a + i(b-a)/2

(v) The Riemann sum with n rectangles is

Area of rectangle = \(\sum^{n-1}_{i = 0} f{(x_i)} \Delta x\)

Which is also known as Reimann sum

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After reducing all the book prices by 50%, the new median price is determined to be $7.70 (B)

To find the new median price after reducing all the book prices by 50%, we first need to calculate the reduced prices. By reducing each given price by 50%, we get $6.375, $7.40, $9.995, $4.975, $8.00, and $8.975 respectively.

Next, we arrange these reduced prices in ascending order: $4.975, $6.375, $7.40, $8.00, $8.975, and $9.995. The median is the middle value in this ordered list. Since there are six prices, the middle two values are $7.40 and $8.00.

To find the median, we take the average of these two values, which gives us ($7.40 + $8.00) / 2 = $7.70.

Therefore, the new median price, after reducing all the book prices by 50%, is $7.70 (B). This means that the median price of the books, after the reduction, is $7.70.

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Check the picture below.

Make sure your calculator is in Degree mode.

The integral of (y dx+ 3x^2 dy) where C is the arc of the curve y = 4-x^2 from the points (0,4) to (0,2) is 20/3 (1 - √2).

The integral(C) of (y dx+ 3x^2 dy) where C is the arc of the curve y = 4-x^2 from the points (0,4) to (0,2) can be solved using the formula of line integral.

In general, if we have a smooth curve C parameterized by the vector function r(t), a<=t<=b, and a vector field F(r) defined along C, the line integral of F over C is given by:

Line integral formulaI= ∫(a to b) F(r)⋅dr = ∫(a to b) F(r(t))⋅r'(t) dt

where r'(t)= dr/dt  is the derivative of r(t) with respect to t.

We can write the equation of the curve as: y = 4 - x²

Let's parameterize C: r(t) = (x(t), y(t))where 2<=y(t)<=4.

Hence we can write x(t) = ± √(4 - y(t))

From (0,4) to (0,2), we only need the negative square root, since we are moving downwards. Hence, x(t) = - √(4 - y(t)).

Now we need to find the derivative of r(t). r'(t) = (x'(t), y'(t))We have x(t) = - √(4 - y(t)).

Taking the derivative: x'(t) = 1/2(4 - y(t))^(-1/2)(- y'(t)) = -y'(t)/2 √(4 - y(t))We have y(t) = 4 - x²(t).

Taking the derivative: y'(t) = - 2x(t)⋅x'(t) = 2x(t)⋅y'(t)/2 √(4 - y(t))

Therefore, we have:r'(t) = (-y'(t)/2 √(4 - y(t)), 2x(t)⋅y'(t)/2 √(4 - y(t))) = (-y'(t)/2 √(4 - y(t)), -x(t)⋅y'(t)/ √(4 - y(t)))

We can write the integral as:I= ∫(a to b) F(r)⋅dr = ∫(a to b) F(r(t))⋅r'(t) dtI= ∫(2 to 4) ((4 - x²), 3x²)⋅(-y'(t)/2 √(4 - y(t)), -x(t)⋅y'(t)/ √(4 - y(t)))) dt

I= ∫(2 to 4) [(4 - x²)(-y'(t)/2 √(4 - y(t))) - 3x²(x(t)⋅y'(t)/ √(4 - y(t))))] dt

Now we can substitute x(t) and y'(t) to obtain a single-variable integral

I= ∫(2 to 4) [(-2x(t)²y'(t))/ √(4 - y(t)) - 3x(t)²y'(t)/ √(4 - y(t))] dt

I= ∫(2 to 4) [-5x(t)²y'(t)/ √(4 - y(t))] dt

Finally, we can substitute x(t) and y'(t) in terms of y(t) to obtain a single-variable integral in terms of y:

I= ∫(2 to 4) [-5(4 - y)⋅(2y/ √(4 - y))] dy

= ∫(2 to 4) [-10y√(4 - y) + 20√(4 - y)] dy

= [-10/3 (4 - y)^(3/2) + 20/3 (4 - y)^(3/2)]_2^4

= -10/3 (4 - 4)^(3/2) + 20/3 (4 - 4)^(3/2) - (-10/3 (4 - 2)^(3/2) + 20/3 (4 - 2)^(3/2))

= -20/3 + 40/3 - (-20/3 √2 + 40/3 √2)= 20/3 (1 - √2)

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Answer:

The distance around the circle.

Step-by-step explanation:

Circumference means the outer area of a particular object or the outer border of the object. When we talk about the circle, the total outer round area is the circumference of the circle.
The formula for circle circumference is 2pir

where pi = 3.14 approx  and the r = radius of the circle

Hence, the answer is the distance around the circle.

Step-by-step explanation:

1. Exercing optimizes your mind - set to improve alertness, attention and motivation.

2. It would make them smarter and better than others because they would be able to understand the situation easier.

On solving the provide question, we can say that by unitary method McCall would need to drive 126 miles  in order to make renting from Company B a better deal

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

so, we have -

Company A charges =  $35 per day

plus =  $0.45 per mile.

Company B charges =  $60 per day

plus  = $0.25 per mile.

McCall would need to drive 126 miles  in order to make renting from Company B a better deal

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