Math please help


An insurance company sells a 20-year term life insurance policy with a face value of $200,000 to a 45-year -old woman. Her annual premium is $990. If the woman dies after paying premiums for 6 years, what is the insurance company’s gain or loss?


Loss of $200,990


Loss of $194,060


Gain of $205,940


Gain of $199,010

Answers

Answer 1

The company will have a Loss of $194,060

The lady paid premiums for 6 years, which amounts to a total premium of$ 5,940($ 990 * 6).

Still, the insurance company will pay the face value of the policy, which is   $ 00, If she dies.

Thus, the company's total payout would be $200,000, while their total income would be $ 5,940 in premiums.

The loss for the company would be the difference between the payout and the income

200,000-$ 5,940 = $ 194,060

Thus, the insurance company's loss in this scenario would be $194,060.

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Related Questions

The velocity function is v(t)=−t2+5t−4 for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [-2,5].
displacement =
distance traveled =

Answers

Integrate the absolute value of the velocity function over each subinterval, and sum up the results to find the distance traveled.

Remember, displacement is the net change in position, while distance traveled is the total length of the path the particle moves along.

Hi! To find the displacement and distance traveled during the time interval [-2, 5], we need to integrate the velocity function v(t) = -t^2 + 5t - 4 over the given interval.

First, let's find the antiderivative of v(t) which gives us the position function s(t):
s(t) = ∫(-t^2 + 5t - 4) dt = (-1/3)t^3 + (5/2)t^2 - 4t + C

For displacement, we simply need to find the difference in the position function at the endpoints of the interval:
displacement = s(5) - s(-2)

For distance traveled, we need to consider both the positive and negative parts of the velocity function. Find the time when v(t) = 0 to determine when the particle changes direction:
-t^2 + 5t - 4 = 0

Solve this quadratic equation for t. Next, divide the interval [-2, 5] into subintervals based on the values of t where the particle changes direction. Integrate the absolute value of the velocity function over each subinterval, and sum up the results to find the distance traveled.

Remember, displacement is the net change in position, while distance traveled is the total length of the path the particle moves along.

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If the circumference of a circle is 50. 4 ft, what is its area? (Use π = 3. 14) *


2 points


50. 24 sq ft


113. 04 sq ft


202. 24 sq ft


314 sq ft

Answers

If the circumference of a circle is 50. 4 ft, its area is 202.24 sq ft. Correct  option is C: 202.24 sq ft.

The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle. We are given that the circumference is 50.4 ft, so we can solve for the radius:

50.4 = 2πr

r = 50.4 / (2π)

r ≈ 8.02 ft

Now we can use the formula for the area of a circle: A = πr²

A = 3.14 * (8.02)²

A ≈ 202.24 sq ft

Therefore, the answer is option C: 202.24 sq ft.

Alternatively, to find the area of a circle with a circumference of 50.4 ft, we will first find the radius using the formula for circumference (C = 2πr) and then use the formula for the area of a circle (A = πr²). Using π = 3.14:

Solve for the radius (r):
C = 2πr
50.4 = 2(3.14)r
r = 50.4 / (2 * 3.14)
r ≈ 8 ft

Calculate the area (A):
A = πr²
A = 3.14 * (8²)
A = 3.14 * 64
A ≈ 201.06 sq ft

The closest answer among the options provided is 202.24 sq ft. Correct  option is C: 202.24 sq ft.

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ANEXO 2


Identifica los objetos con los que se mide la masa y el volumen, y escribe en donde corresponda.


Manómetro


VOLUMEN


MASA


Pipetas


Fórmula de densidad,


Probetas


Báscula.


Matraz


Balanzas


Fórmula volumen


Vaso de precipitación

Answers

The objects used to measure mass are Balances and Scales. The objects used to measure Volume are Manometer, Pipettes, Graduated cylinders, Flasks, Volumetric flasks and Beakers. Here Density formula can be used to measure both mass and volume.

The problem is asking to match different measuring tools with the measurements they are used for, i.e., mass or volume.

The first tool is a manometer. A manometer is used to measure pressure and not mass or volume, so it does not belong in either category.

The next set of tools are pipettes, graduated cylinders, and volumetric flasks. These tools are all used to measure volume, so they belong in the volume category.

The next set of tools are scales and balances. These tools are used to measure mass, so they belong in the mass category.

The formula for density can be used to calculate the mass of an object given its volume and density, or the volume of an object given its mass and density, so it belongs in both categories.

Finally, a beaker or a graduated cylinder can be used to measure volume, so it belongs in the volume category.

Therefore, the correct categorization of the measuring tools are as follows

Volume

Pipettes

Graduated cylinders

Volumetric flasks

Beaker or graduated cylinder

Mass

Scales

balances

Both

Formula for density

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Afia visits the shopping mall on tuesday to purchase some groceries. if she goes back after 295 days, what day did she visit the shopping mall again​

Answers

Afia visits the shopping mall on Tuesday to purchase some groceries. if she goes back after 295 days, she visits the shopping mall again​ on a Wednesday.

To find out what day Afia visited the shopping mall again, we can divide  295 by 7  because there are 7 days in a week. we need to find out how many full weeks have passed and how many days.

= 295/ 7 = 42.1

The 295 divided by 7 is 42 with a remainder of 1 or we can write as that 42 full weeks and 1 day have passed.

When 42 weeks have passed that day will be Tuesday and the 1 day after Tuesday is Wednesday.

Therefore,  Afia visited the shopping mall again on a Wednesday.

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Determine whether the geometric series is convergent or divergent. If it is convergent, find the sum. (If the quantity diverges, enter DIVERGES.) 00 7 80 3| n n = 1

Answers

|r| = 7/80 < 1, the series is convergent. The sum = 0/(1-7/80) = 0. the sum of the geometric series is 0.

The geometric series with first term 0 and common ratio 7/80 is given by 0, 7/80, (7/80)², (7/80)³, ... In general, the nth term is (7/80)ⁿ⁻¹.

To determine whether this series is convergent or divergent, we can use the formula for the sum of an infinite geometric series:

sum = a/(1-r)

where a is the first term and r is the common ratio. In this case, a = 0 and r = 7/80.

If |r| < 1, then the series converges to the sum given by the above formula. If |r| ≥ 1, then the series diverges.

In this case, |r| = 7/80 < 1, so the series is convergent. The sum is given by:

sum = 0/(1-7/80) = 0

Therefore, the sum of the geometric series is 0.

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Is Y= 4x^3+6....

A. Linear
B. Nonlinear
C. Both
D. Neither

Answers

Answer:

The given equation Y=4x^3+6 is a nonlinear equation because it contains a term with a power of 3, which means that the relationship between Y and x is not linear. In a linear equation, the power of the variable is always 1. Therefore, the answer is B. Nonlinear.

Step-by-step explanation:

The force on a particle is described by 8x^3-5 at a point s along the z-axis. Find the work done in moving the particle from the origin to x = 4.

Answers

The work done in moving the particle from the origin to x = 4 under the influence of the force F (x) = 8[tex]x^3[/tex]-5 is 492 units of work.

The work done in moving a particle along a path under the influence of a force, we use the work-energy principle.

This principle states that the work done on a particle by a force is equal to the change in the particle's kinetic energy.

Mathematically this can be expressed as:

W = ΔK

Where

W is the work done,

ΔK is the change in kinetic energy and

Both are scalar quantities.

The work done by a force on a particle along a path is given by the line integral:

W = ∫ C F · ds

Where,

C is the path,

F is the force,

ds is the differential displacement along the path and  denotes the dot product.

In the case where the force is a function of position only (i.e., F = F(x,y,z)), we can evaluate the line integral using the parametric equations for the path.

If the path is given by the parameterization r(t) = <x(t), y(t), z(t)>, then we have:

W = ∫ [tex]a^b[/tex] F(r(t)) · r'(t) dt

The work done in moving the particle from the origin to a final position at x = 4. We can evaluate the work done using the definite integral of the force from x = 0 to x = 4, as shown in the solution.

The initial kinetic energy is zero.

The work done by the force in moving the particle from x = 0 to x = 4 is given by the definite integral:

W = ∫ F(x) dx

Substituting the given expression for the force, we have:

W = ∫0 (8x - 5) dx

Integrating with respect to x, we have:

W = [(2x - 5x)]_0

W = (2(4) - 5(4)) - (2(0) - 5(0))

W = 512 - 20

W = 492

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Quickly please anyone

f(x) = 6x² - 3x + ²
2
X
f(-2) = [?]
Be sure to simplify your answer.

Answers

Answer:

Ans=28

Step-by-step explanation:

ƒ(x) = 6x2 - 3x + 22xf( - 2)=[?]

at ƒ(-2)

Substitute each x with -2

ƒ(-2) = 6(-2)2 - 3(-2) - 2

ƒ(-2) = 6(4) - 3(-2) - 2

ƒ(-2) = 24 + 6 + 0 - 2

ƒ(-2) = 28

I hope I was right

A watch designer claims that men have wrist breadths with a mean equal to 9 cm. A simple random sample of wrist breadths
of 72 men has a mean of 8.91 cm. The population standard deviation is 0.36 cm.
Assume a confidence level of a = 0.01. Find the value of the test statistic z using
formula below
Z=
X-H
σ
O2.12
O-1.27
O 0.06
O-2.12

Answers

The value of the test statistic z is approximately -2.12. The Option D is correct.

What is the value of the test statistic z?

To test the hypothesis that the mean wrist breadth of men is equal to 9 cm, we will use a one-sample z-test.

The null hypothesis is: H0: µ = 9 cm

The alternative hypothesis is: Ha: µ ≠ 9 cm

We are given a sample of n = 72 men with a sample mean of x = 8.91 cm and a population standard deviation = 0.36 cm.

The test statistic for a one-sample z-test is given by: z = (x - µ) / (o / sqrt(n))

Substituting the given values, we get:

= (8.91 - 9) / (0.36 / sqrt(72))

z = -2.119

At a significance level of a = 0.01, the critical values for a two-tailed test are ±2.576.

Since our test statistic (-2.119) falls outside of this range, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the mean wrist breadth of men is not equal to 9 cm.

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The temperature at any point (x, y) in a steel plate is T = 900 − 0.7x2 − 1.3y2, where x and y are measured in meters. At the point (3, 9), find the rates of change of the temperature with respect to the distances moved along the plate in the directions of the x- and y-axes.

Answers

At point (3, 9), the rate of change of temperature with respect to the x-axis is -4.2 °C/m, and with respect to the y-axis, it is -23.4 °C/m.

To find the rates of change of the temperature with respect to the distances moved along the x- and y-axes at point (3, 9), you need to compute the partial derivatives of the temperature function T(x, y) = 900 - 0.7x^2 - 1.3y^2 with respect to x and y.
For the x-axis:
∂T/∂x = -1.4x
At point (3, 9), ∂T/∂x = -1.4(3) = -4.2 °C/m
For the y-axis:
∂T/∂y = -2.6y
At point (3, 9), ∂T/∂y = -2.6(9) = -23.4 °C/m
So, at point (3, 9), the rate of change of temperature with respect to the x-axis is -4.2 °C/m, and with respect to the y-axis, it is -23.4 °C/m.

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An object moves in simple harmonic motion with period 8 minutes and amplitude 12m. At time =t0 minutes, its displacement d from rest is −12m, and initially it moves in a positive direction.


Give the equation modeling the displacement d as a function of time t

Answers

An object moves in simple harmonic motion with a period of 8 minutes and an amplitude of 12 m. At time =t0 minutes, its displacement d from rest is −12m, and initially, it moves in a positive direction. We can write the final equation for the displacement d as a function of time t: d(t) = 12 * cos((π/4)t + π)

To model the displacement d as a function of time t for an object in simple harmonic motion with a period of 8 minutes and an amplitude of 12m, we'll use the following equation:

d(t) = A * cos(ωt + φ)

where:
- d(t) is the displacement at time t
- A is the amplitude (12m in this case)
- ω is the angular frequency, calculated as (2π / period)
- t is the time in minutes
- φ is the phase angle, which we'll determine based on the initial conditions

Since the period is 8 minutes, we can calculate the angular frequency as follows:
ω = (2π / 8) = (π / 4)

At t = 0 minutes, the displacement is -12m, and the object moves in a positive direction. So we have:
-12 = 12 * cos(φ)

Dividing both sides by 12:
-1 = cos(φ)

Therefore, φ = π (or 180°) since the cosine of π is -1.

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A cylinder has a volume of cubic centimeters and a height of 12 centimeters. What is the radius of the base of the cylinder, in centimeters?"

Answers

Answer:

Step-by-step explanation:

On the interval [0, 2] the polar curve r = 8o2 has arc length ______ units.

Answers

The arc length of the polar curve r = 8θ^2 on the interval [0, 2] is approximately 70.71 units.

The polar curve r = 8θ^2 on the interval [0, 2] has an arc length which can be calculated using the formula for arc length in polar coordinates:

L = ∫√(r^2 + (dr/dθ)^2) dθ, from θ = 0 to θ = 2.
First, we need to find the derivative dr/dθ:

r = 8θ^2, so dr/dθ = 16θ.

Now, plug r and dr/dθ into the arc length formula:
L = ∫√((8θ^2)^2 + (16θ)^2) dθ, from θ = 0 to θ = 2.

Simplify the integrand:

L = ∫√(64θ^4 + 256θ^2) dθ, from θ = 0 to θ = 2.

Factor out 64θ^2:

L = ∫√(64θ^2(1 + θ^2)) dθ, from θ = 0 to θ = 2.

Now, apply the substitution u = 1 + θ^2, so du = 2θ dθ:

L = 32∫√(u) du, from u = 1 to u = 5.

Integrate and evaluate:

L = (32/3)(u^(3/2)) | from u = 1 to u = 5.

L = (32/3)(5^(3/2) - 1^(3/2)).

L ≈ 70.71 units.

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The perimeter of a semicircle is 35. 98 millimeters. What is the semicircle's radius Use 3. 14 for a. Millimeters Submit explain ​

Answers

If the perimeter of a semicircle is 35. 98 millimeters, 7 mm is the semicircle's radius.

A semi-circle refers to half of the circle. The circle is cut along the diameter to form a semi-circle.

A diameter is a line segment that passes through the center of the circle and touches the boundary of the circle from both ends.

The perimeter of the semi-circle is the sum of the length of the diameter and the circumference of the semi-circle.

P = 2r + πr

where P is the perimeter

r is the radius

P = 35.98 mm

35.96 = 2r + 3.14r

35.96 = 5.14r

r = 7 mm.

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a researcher is interested in the disappearance of spotted owls from northwestern forests. she studies 10 breeding pairs of spotted owls in cascade national park for one year. the 10 breeding pairs are the: group of answer choices selected sample snowball sample stratified sample target population

Answers

The 10 breeding pairs of spotted owls in Cascade National Park studied by the researcher represent a selected sample. So, the correct answer is A)

The 10 breeding pairs of spotted owls represent a selected sample.

A sample is a subset of a larger population that is chosen for research or study purposes. In this case, the researcher is interested in studying the disappearance of spotted owls from northwestern forests, but it would be impractical to study the entire population of spotted owls in the region.

Therefore, the researcher selected a smaller group of 10 breeding pairs in Cascade National Park as a representative sample to study over the course of one year. The selected sample may help the researcher to draw conclusions about the population of spotted owls in the region. So, the correct option is A).

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--The given question is incomplete, the complete question is given

" a researcher is interested in the disappearance of spotted owls from northwestern forests. she studies 10 breeding pairs of spotted owls in cascade national park for one year. the 10 breeding pairs are the: group of answer choices

selected sample

snowball sample  

stratified sample

target population"--

A coin is flipped, and a standard number cube is rolled. What is the probability for flipping tails and rolling an odd number.

Answers

Answer:

1/4

Step-by-step explanation:

The probability of flipping tails is 1/2, since there are two equally likely outcomes when flipping a coin (heads or tails).

The probability of rolling an odd number on a standard number cube is 3/6 or 1/2, since there are three odd numbers (1, 3, and 5) out of six possible outcomes (1, 2, 3, 4, 5, and 6).

To find the probability of both events happening (i.e., flipping tails and rolling an odd number), we multiply the probabilities of each event:

P(tails and odd number) = P(tails) * P(odd number)

P(tails and odd number) = 1/2 * 1/2

P(tails and odd number) = 1/4

Therefore, the probability of flipping tails and rolling an odd number is 1/4 or 0.25.

FOIL the equation, don't need to solve!
(2x-1)(x+2) ​

Answers

When we multiply (2x - 1) and (x + 2) using FOIL method, we get:

(2x - 1)(x + 2) = 2x(x) + 2x(2) - 1(x) - 1(2)

= 2x² + 4x - x - 2

= 2x² + 3x - 2

Therefore, the product of (2x - 1) and (x + 2) is 2x² + 3x - 2.

Consider the following cash flows: year cash flow 0 −$28,500 1 15,200 2 13,700 3 10,100 a. what is the profitability index for the cash flows if the relevant discount rate is 10 percent?

Answers

The profitability index is 0.1237.

To find the profitability index (PI), we need to divide the present value of the cash flows by the initial investment.

To calculate the present value of the cash flows, we need to discount each cash flow to its present value and then add them up. Using a discount rate of 10%, we get:

Year 0: -$28,500 / [tex](1 + 0.10)^0[/tex]= -$28,500

Year 1: $15,200 /[tex](1 + 0.10)^1[/tex]= $13,818.18

Year 2: $13,700 / [tex](1 + 0.10)^2[/tex] = $10,881.68

Year 3: $10,100 /[tex](1 + 0.10)^3[/tex] = $7,322.51

The sum of the present values is:

PV = -$28,500 + $13,818.18 + $10,881.68 + $7,322.51 =

PV = $3,521.37

The profitability index is therefore:

PI = PV / Initial Investment = $3,521.37 / $28,500 = 0.1237

So the profitability index is 0.1237.

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The spokes on a bicycle wheel divide the wheel into congruent sections. What is the measure of each arc in this circle?

Answers

The measure of each arc in the circle is given by: 360 degrees / n

where n= number of spokes

If the spokes on a bicycle wheel divide the wheel into congruent sections, then each section is an equal angle at the center of the circle. Since there are "n" spokes on the wheel, the circle will be divided into "n" congruent sections.

Therefore, the measure of each arc in the circle is given by:

= 360 degrees / n

For example, if there are 18 spokes on the wheel, then each arc will have a measure of:

360 degrees / 18 = 20 degrees

So each arc would measure 20 degrees.

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Pls help
a polynomial function is represented by the data in the table

x 0 i 1 i 2 i 3 i 4 i
f(x) -24 i -21¾ i -14 i ¾ i 24 i

choose the function represented by the data.
1. f(x) = x3 − x2 − 24
2. f(x) [tex]\frac{x}{4}^{3}[/tex] + 2[tex]x^{2}[/tex] -24
3. f(x)= -2[tex]\frac{1}{4} x^{2}[/tex] + 24
4. f(x)= [tex]\frac{3}{4} x^{2}[/tex] -3x + 24

Answers

The function represented by the data is f(1/4)x³ + 2x² - 24. The correct option is 2.

In the given table, we have the values of x and f(x) for x=0,1,2,3, and 4. We need to find a polynomial function that satisfies these data points.

Looking at the table, we can see that f(x) is negative for x=0,1,2 and positive for x=3,4. This suggests that the polynomial has a root or a zero between x=2 and x=3.

To find the degree of the polynomial, we count the number of data points given. Since we have 5 data points, we need a polynomial of degree 4.

We can use interpolation to find the coefficients of the polynomial. One way to do this is to set up a system of equations using the data points:

f(0) = -24 = a(0)⁴ + b(0)³ + c(0)² + d(0) + e

f(1) = -21.75 = a(1)⁴ + b(1)³ + c(1)² + d(1) + e

f(2) = -14 = a(2)⁴ + b(2)³ + c(2)² + d(2) + e

f(3) = 0.75 = a(3)⁴ + b(3)³ + c(3)² + d(3) + e

f(4) = 24 = a(4)⁴ + b(4)³ + c(4)² + d(4) + e

Solving this system of equations gives us the polynomial function:

f(x) = -0.25x⁴ + 2x³ - 2.75x² - 0.5x + 24

Therefore, the correct option is 2. f(x) = (1/4)x³ + 2x² - 24.

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f(x)=1/2x^4+2x^3 is concave up when f”(x) is

Answers

The function f(x) = (¹/₂)x⁴ +2x³ is concave up when f''(x) > 0, which is true when x > 0 or x < -2.

What is the concavity of the function?

The concavity of a function is determined by taking the second derivative.

f'(x) = 2x³ + 6x²

f''(x) = 6x² + 12x

To find out when f(x) is concave up, we need to determine when f''(x) is positive;

f''(x) > 0

6x² + 12x > 0

6x(x + 2) > 0

When x > 0, both factors are positive, and the inequality is true.

When x < -2, both factors are negative, and the inequality is true.

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Determine the equation of the directrix of r = 26. 4/4 + 4. 4 cos(theta) A. X = -6 B. Y = 6 C. X = 6

Answers

The equation of the directrix is X = 6 (Option C).

To determine the equation of the directrix of the polar equation r = 26.4/(4 + 4.4cos(theta)), we need to find the constant value of either x or y. This equation is in the form r = ed/(1 + ecos(theta)), where e is the eccentricity, and d is the distance from the pole to the directrix.

In our case, 26.4 = ed and 4.4 = e. To find the value of d, we can divide 26.4 by 4.4:

d = 26.4 / 4.4 = 6

Since the directrix is a vertical line, it has the form x = constant. In this case, the constant is 6.

So, the equation of the directrix is X = 6 (Option C).

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Why is the quotient of three divided by one-fifth different from the quotient of one-fifth divided by three? Tell a story that could describe each situation. I don't know how to word it, please help. Please also give me the sums

Answers

The order of division affects the result; 3 ÷ 1/5 is 15 and 1/5 ÷ 3 is 1/15.

How are the quotients different?

To find the answer, we can calculate the quotient of three divided by one-fifth, which is:

3 ÷ (1/5) = 15

And the quotient of one-fifth divided by three is:

(1/5) ÷ 3 = 1/15

These two quotients are different because the order of division changes the result. In the first case, we divide 3 by a smaller number (one-fifth), which results in a larger quotient (15). In the second case, we divide a smaller number (one-fifth) by a larger number (three), which results in a smaller quotient (1/15).

To give a story describing each situation:

For the first situation, imagine a pizza that is divided into five equal slices, and three hungry friends who want to share it. Each friend gets one-fifth of the pizza, but they want to know how much pizza they would get if they each had three-fifths. To find out, they combine their slices, which gives them three out of the five slices. The total amount of pizza they have is now three-fifths of the pizza, and they can each take one-third of that amount, which is 15% of the original pizza.For the second situation, imagine a group of three friends who want to share a small bag of candy that has five pieces in it. Each friend gets one-fifth of the candy, but they want to know how much candy they would get if they each had three pieces. To find out, they divide the total number of pieces (five) by the number of friends (three), which gives them one and two-thirds pieces each, or one-fifteenth of the bag.

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What percent of his monthly budget do his transportation costs account for?

Answers

To calculate the percentage of one's monthly budget that transportation costs account for, we need to know the total amount of money spent on transportation and the total monthly budget.

Let's say, for example, that John spends $500 per month on transportation and his monthly budget is $2,000.

To calculate the percentage, we would divide the amount spent on transportation by the total monthly budget and then multiply by 100 to get the percentage. So, in this case, the calculation would be:


[tex]($500 / $2,000) x 100 = 25%[/tex]

Therefore, John's transportation costs account for 25% of his monthly budget. This is a significant portion of his budget, and if he needs to save money, he may want to consider alternative modes of transportation such as carpooling,

public transportation, or biking. It's always important to keep track of expenses and prioritize spending in order to maintain a healthy financial situation.

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The table shows the blood pressure of 16 clinic patients.what is the interquartile range of the data? a)7.75 b)8.50 c)9.25 d)10.75 ​

Answers

The closest option to this value is d) 10.75, but none of the options is an exact match.

To find the interquartile range (IQR) of the data, we need to first find the first quartile (Q1) and the third quartile (Q3).

To do this, we can arrange the data in order from smallest to largest:

98, 100, 104, 105, 106, 110, 112, 115, 116, 118, 120, 122, 126, 130, 136, 140

The median of the data is the average of the two middle values, which are 112 and 115. So, the median is (112 + 115) / 2 = 113.5.

To find Q1, we need to find the median of the data values below the median. These are:

98, 100, 104, 105, 106, 110, 112, 115

The median of these values is (106 + 110) / 2 = 108.

To find Q3, we need to find the median of the data values above the median. These are:

116, 118, 120, 122, 126, 130, 136, 140

The median of these values is (122 + 126) / 2 = 124.

Now we can calculate the interquartile range (IQR) as the difference between Q3 and Q1:

IQR = Q3 - Q1 = 124 - 108 = 16.

Therefore, the interquartile range of the data is 16, or in decimals 16.00.

The closest option to this value is d) 10.75, but none of the options is an exact match.

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Determine where the absolute extrema of f(x)= 4x/ x²+1 on the interval [-4,0] occur. 1. The absolute maximum occurs at x= 2. The absolute minimum occurs at x =

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The absolute maximum of f(x) = 4x / (x² + 1) on the interval [-4,0] occurs at x = 2 and the absolute minimum occurs at x = -4.

To find the absolute extrema, we first find the critical points by setting the derivative of f(x) equal to zero:

f'(x) = (4(x² + 1) - 8x²) / (x² + 1)² = 0

Simplifying, we get:

4 - 4x² = 0

x² = 1

x = ±1

Since x = -4 and x = 0 are also endpoints of the interval, we evaluate f(x) at these five points:

f(-4) = -8/17

f(-1) = -4/5

f(0) = 0

f(1) = 4/5

f(2) = 8/5

Thus, the absolute maximum occurs at x = 2, where f(x) = 8/5, and the absolute minimum occurs at x = -4, where f(x) = -8/17.

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Find the side x, giving answer to 1 decimal place

Answers

Answer:

Set your calculator to degree mode.

Using the Law of Sines:

7/sin(40°) = x/sin(81°)

x = 7sin(81°)/sin(40°) = 10.8

Answer:

10.8=x

Step-by-step explanation:

Using the Law of Sines, we can put together the fact that

[tex]\frac{sin A}{a} =\frac{sinB}{b}[/tex]

Substitute our given values from the triangle:

[tex]\frac{sin 81}{x} =\frac{sin40}{7}[/tex]

Turn the sines into a decimal:

[tex]\frac{0.9876}{x} =\frac{0.6427}{7}\\[/tex]

cross multiply using butterfly method

0.988·7=0.643x

solve for x

6.916=0.643x

divide both sides by 0.643

10.8=x (round to nearest tenth)

Hope this helps! :)

In your pocket you have 4 ones, 2 fives, and a twenty dollar bill. What is the probability of picking out the twenty?

Answers

The probability of picking a 20 dollar bill is 1/7 or 14.3%

How do we calculate for the probability of picking up a 20 dollar bill?

The probability of a thing is the likelihood or number of chances that such a thing will occur. For the scenario given,

There are a total of 7 bills in your pocket

1, 1, 1, 1,

5, 5,

20.

To find the probability of picking out the twenty dollar bill, divide the number of twenty dollar bills by the the total of the number of bills you are with.

Probability = 1/ 7 which can be converted to % = 14.3%.

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100 POINTS!!!! PLEASE HELP!! ITS DUE IN 1 HOUR!!!!!!!!!!!!!!

Answers

If the scale ratio of two similar triangles is 1/3, that means the corresponding sides of the two triangles are in the same ratio.

If side 'd' of triangle DEF has a length of 4, and the scale ratio of the two triangles is 1/3, then the length of the corresponding side 'a' of triangle ABC can be found as follows:

a/d = 1/3

a = (1/3)d

a = (1/3)4

a = 4/3

Therefore, the length of side 'a' is 4/3.

We want to evaluate the integral X +34 +16 dx, we use the trigonometric substitution X and dx = do and therefore the integrar becomes, in terms or o, de The antiderivative in terms of 8 is (do not forget the absolute value) 1 = + Finally, when we substitute back to the variable x, the antiderivative becomes T Use for the constant of integration

Answers

The antiderivative of the given integral is (X^2/2) + 50X + C, where C is the constant of integration.

This is obtained by integrating the given polynomial directly without the need for trigonometric substitution.First, let's rewrite the integral: ∫(X + 34 + 16) dx. Since the integrand is a polynomial, we don't need trigonometric substitution. Instead, we can find the antiderivative directly:

∫(X + 34 + 16) dx = ∫(X + 50) dx.

Now, find the antiderivative:

(X^2/2) + 50X + C, where C is the constant of integration.

So, the antiderivative of ∫(X + 34 + 16) dx is (X^2/2) + 50X + C.

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