Just explain how to do it with the answer please.

Answer:

if the diagonal is 10 then the sides are 3*2 and 4*2 which is 6 and 8 respectively because the diagonal makes it a right angled triangle whereby the the 3,4,5 line steps in, so if the diagonal(hypotenuse) is 10 the 10/5 is 2 then you multiply both 3 and 4 by 2 and that gives you the length of two sides

The couple needs to invest $9,060.52 per year to have enough money to send their daughter to university.  The couple needs to invest an additional $1,322.18 per year if they wait one year to start saving for their daughter's university education.

a. The amount of money the couple needs to invest each year can be calculated using the present value of annuity formula. The future value of the university cost after 10 years can be calculated by compounding the current cost for 10 years at an annual inflation rate of 5.6%.

Then, the present value of this future cost can be found by discounting it back to the present using the effective annual interest rate of 6.75%. Finally, this present value can be divided by the present value of an annuity factor for 9 years (one year before the university starts) at an effective annual interest rate of 6.75%.

Using these calculations, the couple needs to invest $9,060.52 per year to have enough money to send their daughter to university.

b. If the couple waits for one year, they will have nine years to save for their daughter's university education. This means they will have one less year to invest, so they will need to invest more each year to have enough money for their daughter's university education.

The additional amount they need to invest can be found by subtracting the present value of an annuity of $9,060.52 for 9 years from the present value of an annuity of $9,060.52 for 8 years.

Using these calculations, the couple needs to invest an additional $1,322.18 per year if they wait one year to start saving for their daughter's university education.

To know more about invest, refer here:

https://brainly.com/question/10908938#

#SPJ11

Answer:

B) <FBG

Step-by-step explanation:

An adjacent angle is an angle that is right next to the given angle.

In this case, the given angle is <EBF.

We can see that the only 2 options here for an adjacent set of angles is either <FBG or <EBD.

Looking at the options, we can only see that <FBG is an option, making B the correct option.

Hope this helps :)

Answer:

SSA

Step-by-step explanation:

It would be SSA (Side-Side-Angle).  They are congruent where they intersect at B (opposite angles).  Since CF is congruent to GH, and CB is congruent to HB, you have an angle and two sides congruent, in the order SSA.

The equation in slope-intercept form for the line passing through each pair of points, (-4, 4) and (-5, -3) is expressed as: y = 7x + 32

Given the points, (-4, 4) and (-5, -3), first find the slope of the line.

Slope (m) = change in y / change in x = -3 - 4 / -5 -(-4)

m = -7/-1

m = 7

Substitute m = 7, a = -4, and b = 4 into y - b = m(x - a):

y - 4 = 7(x + 4)

Rewrite im slope-intercept form:

y - 4 = 7x + 28

y - 4 + 4 = 7x + 28 + 4

y = 7x + 32

Learn more about slope-intercept form on:

https://brainly.com/question/3493733

#SPJ1

Answer: 0= -5

Step-by-step explanation:

(a) The 92% CI for overall proportion of pudding packs containing less than 3.25oz of pudding at α = 0.08 is (0.5806, 0.6994);

(b) The 99% CI for overall proportion of pudding packs containing more than 3.25oz of pudding at α = 0.01 is (0.2726, 0.4474).

Part (a) : To construct a confidence-interval for the overall proportion of pudding packs containing less than 3.25oz of pudding, we use the following formula : CI = p' ± [tex]z_{\frac{\alpha}{2} }[/tex] × √(p'(1-p')/n);

where p' is = sample proportion, [tex]z_{\frac{\alpha}{2} }[/tex]  is = critical z-value for the desired confidence level, and n is = sample size.

In this case, p' = (200-72)/200 = 128/200 = 0.64, the sample size is n = 200, and

We know that the critical z-value for a 92% confidence interval(α = 0.08) is approximately 1.75;

Substituting the values,

We get,

CI = 0.64 ± 1.75 × √(0.64(1 - 0.64)/200)

CI = 0.64 ± 0.059421;

CI = (0.5806, 0.6994);

Therefore, the required confidence interval is (0.5806, 0.6994).

Part (b) : In this case, p' = 72/200 = 0.36, the sample-size is n = 200, and

We know that the critical z-value for a 99% confidence interval (α = 0.01) is approximately 2.57;

Substituting the values,

We get,

CI = 0.36 ± 2..57 × √(0.36(1 - 0.36)/200)

CI = 0.36 ± 0.087426;

CI = (0.2726, 0.4474);

Therefore, the required confidence interval is (0.2726, 0.4474).

Learn more about Confidence Interval here

https://brainly.com/question/24131141

#SPJ4

The average change in temperature per hour during the temperature drop from 48°F to -16°F in Sioux Falls, South Dakota on February 6, 1995, was 8°F per hour.

On February 6, 1995, the temperature in Sioux Falls, South Dakota dropped dramatically from 48°F to -16°F in just eight hours. To calculate the average change in temperature per hour, we can use the formula:

Average Change in Temperature per Hour = (Change in Temperature) ÷ (Time)

Using this formula, we can calculate the average change in temperature per hour in Sioux Falls as follows:

Average Change in Temperature per Hour = (48°F - (-16°F)) ÷ 8 hours

Average Change in Temperature per Hour = 64°F ÷ 8 hours

Average Change in Temperature per Hour = 8°F per hour

Therefore, the average change in temperature per hour during that eight-hour period in Sioux Falls, South Dakota was 8°F. This rapid and significant change in temperature was likely due to a strong cold front moving through the area.

Learn more about Sioux Falls

brainly.com/question/31094149

#SPJ11

Answer:

Answer:17

Explanation: 5-0.75=4.25 4.25÷0.25=17

Hope this helps

Part a. The magnitude of the angular acceleration of the salad spinner as it slows down is 4.00 radians/s².

Part b. It takes 1.00 seconds for the salad spinner to come to rest.

Part A:

The initial angular velocity of the spinner is given by:

ω1 = 20.0 rotations / 5.00 s = 4.00 rotations/s

The final angular velocity of the spinner is zero.

The number of rotations between the initial and final angular velocities is:

Δθ = 6.00 rotations

Using the equation of motion for rotational kinematics with constant angular acceleration:

Δθ = 1/2 α t^2 + ω1 t

where α is the angular acceleration, and t is the time it takes to stop spinning.

At the final angular velocity, ω2 = 0, so we can rearrange the equation to solve for t:

t = ω1 / α

Substituting the given values:

Δθ = 6.00 rotations

ω1 = 4.00 rotations/s

t = (4.00 rotations/s) / α

Solving for α:

Δθ = 1/2 α t^2 + ω1 t

6.00 rotations = 1/2 α (t^2) + (4.00 rotations/s) t

Substituting t = (4.00 rotations/s) / α:

6.00 rotations = 1/2 α [(4.00 rotations/s) / α]^2 + (4.00 rotations/s) [(4.00 rotations/s) / α]

6.00 rotations = 8.00 rotations + 16.00 rotations/s^2 / α

α = 16.00 rotations/s^2 / (6.00 rotations - 8.00 rotations)

α = 8.00 rotations/s^2 / 2.00 rotations

α = 4.00 radians/s^2

Therefore, the magnitude of the angular acceleration of the salad spinner as it slows down is 4.00 radians/s^2.

Part B:

Using the equation of motion for rotational kinematics with constant angular acceleration:

ω2 = ω1 + α t

At the final angular velocity, ω2 = 0, so we can rearrange the equation to solve for t:

t = -ω1 / α

Substituting the given values:

ω1 = 4.00 rotations/s

α = 4.00 radians/s^2

t = -(4.00 rotations/s) / (4.00 radians/s^2)

t = -1.00 s

Since the time cannot be negative, we take the absolute value of t:

t = 1.00 s

Therefore, it takes 1.00 seconds for the salad spinner to come to rest.

To know more about angular acceleration visit;

brainly.com/question/29428475

#SPJ11

Answer:

I think the answer might be -4 = 3x.

Step-by-step explanation:

-2 times x + 2 = -4 and 5 - 2x = 3x so i think the answer is -4 = 3x. Also, you're welcome if this helps.

The power rule for derivatives is  -26/5.

The derivative is a fundamental concept that measures how much a function changes as its input changes. It is a mathematical tool used to find the instantaneous rate of change of a function at a specific point. The derivative of a function f(x) at a point x=a, denoted by f'(a), is the slope of the tangent line to the graph of f(x) at the point (a, f(a)).

a. f(x) = 2x³

Using the power rule for derivatives, we have:

f'(x) = 6x²

So, f'(2) = 6(2)² = 24.

b. g(x) = 13x^(1/2)

Using the power rule for derivatives, we have:

g'(x) = (1/2) * 13x^(-1/2) = (13/2√x)

So, g'(3) = (13/2√3).

c. h(x) = hx

Using the power rule for derivatives, we have:

h'(x) = h

So, h'(4) = h.

d. j(x) = 130x^(-1)

Using the power rule for derivatives, we have:

j'(x) = -130x^(-2)

So, j'(5) = -130(5)^(-2) = -130/25 = -26/5.

To learn more about power rule visit: https://brainly.com/question/23418174

#SPJ11

The height of the cone that the volume of a cylinder is twice the volume of a cone is 7.5 meters.

Let's first define some variables to represent the dimensions of the cone and cylinder. Let's use r for the radius of both shapes, h for the height of the cone, and 5 for the height of the cylinder.

The volume of a cone is given by V_cone = (1/3)πr^2h, and the volume of a cylinder is given by V_cylinder = πr^2h.

We are told that the volume of the cylinder is twice the volume of the cone:

V_cylinder = 2V_cone

Substituting the formulas for the volumes of the cone and cylinder, we get:

πr^2(5) = 2[(1/3)πr^2h]

Simplifying, we can cancel the π and the r^2 terms on both sides:

5 = (2/3)h

Multiplying both sides by 3/2, we get:

h = 7.5

Therefore, the height of the cone is 7.5 meters.

Learn more about volume at https://brainly.com/question/463363

#SPJ1

The value of x is 2.8 The scale factor of left polygon to the right polygon, GKNM to RPTV is 1.4.

Since the two polygons GKNM and RPTV are similar, their corresponding sides are proportional. Thus, we can set up the following proportion

(GK + KN + NM)/GK = (RP + PT + TV + VR)/RP

Plugging in the given values and simplifying, we get

(8.4 + 3x - 2 + 4)/8.4 = (x + 5 + 3 + 3 + 6.3)/(x + 5)

15.4/(3x + 2.4) = (x + 17.3)/(x + 5)

Cross-multiplying and solving for x, we get

x = 2.8

To find the scale factor of GKNM to RPTV, we can divide the corresponding side lengths

(GK + KN + NM)/(RP + PT + TV + VR) = (8.4 + 3(2.8) - 2 + 4)/(2.8 + 5 + 3 + 3 + 6.3) = 1.4

Therefore, the scale factor of GKNM to RPTV is 1.4.

To know more about scale factor:

https://brainly.com/question/30215044

#SPJ1

The doctor would prescribe 8 milliliters of acetaminophen for Jocelyn, who weighs 40 pounds.

According to the given information, pediatricians prescribe 5 milliliters (ml) of acetaminophen for every 25 pounds of a child's weight. So, if a child weighs 50 pounds, the doctor would prescribe 10 ml of acetaminophen.

Now, let's apply this formula to Jocelyn's weight. As Jocelyn weighs 40 pounds, we need to calculate how many 25-pound increments her weight contains. To do this, we can divide her weight by 25:

40 pounds ÷ 25 pounds = 1.6 increments

This means that Jocelyn's weight is equivalent to 1.6 times the 25-pound increment used in the prescription. To determine the amount of acetaminophen she needs, we can multiply 5 ml (the prescribed dose for 25 pounds) by 1.6:

5 ml × 1.6 = 8 ml

Know more about acetaminophen here:

https://brainly.com/question/14368060

#SPJ11

68% of the stores will sell a gallon of milk for between $3.57 and $3.93 with one standard deviation of the mean.

Mean =  $3.75

Standard deviation = $0.09.

Selling variations = $3.57 to $3.93.

Chebyshev's theorem states that if k is a positive number, then, in any data at least [tex](1 - 1/k^2)[/tex] of the data will fall in K standard deviations from the mean data.

For normal distributions, 68% of the values will fall within one standard deviation of the mean.

For non-normal deviations, 75% of values will fall within 2 standard deviations of the mean.

Here we need to find the Upper limit and lower limit of the data.

$3.75 - $0.09 = $3.66

$3.75 + $0.09 = $3.84

The price range will be between $3.66 and $3.84.

To calculate the minimum percentage of stores using Chebyshev's theorem

minimum percentage = [tex]1 - 1/k^2[/tex]

minimum percentage = [tex]1 - 1/(1^2)[/tex]

minimum percentage = 0

Here, 0% of stores will fall with only one standard deviation from the Mean.

Therefore, we can conclude that 68% of the stores will sell a gallon of milk for between $3.57 and $3.93.

To learn more about Chebyshev's theorem

https://brainly.com/question/31055211

#SPJ4

The equations that will find the distance between the lions and giraffes include the following:

B. 11² + 16² = c².

D. 11(2) + 16(2) = 2.

In Mathematics and Science, distance can be defined as the amount of ground that is travelled by a physical object or body over a particular period of time and speed, irrespective of its direction, starting point or ending point.

Mathematically, the distance traveled by both the lions and giraffes when they are positioned one (1) unit apart can be calculated by using this equation:

11² + 16² = c²

Additionally, the distance traveled by both the lions and giraffes when they are positioned two (2) unit apart can be calculated by using this equation:

11(2) + 16(2) = c

Learn more about distance here: brainly.com/question/10545161

#SPJ1

The best interpretation of one of the values of the function is  The number of microorganisms increases by 16% each week.

The given function of the number of the microorganisms present in the water sample at the end of x weeks is

h(x) = 146(1.16)ˣ

To find the number of microorganisms present in the water sample after one week, we substitute x = 1 in the above equation

h(1) = 146(1.16)¹

h(1) = 169.36

Therefore, after one week, there will be approximately 169 microorganisms in the water sample.

Thus, the correct interpretation of one of the values of the function is F.

To know more about Function:

https://brainly.com/question/12431044

#SPJ1

An expression to represent the number of miles both boys ran this month is 3j + 4d + 10.

To begin solving this problem, we need to use the given information and create an expression to represent the number of miles both boys ran this month.
We know that James runs 3 miles per day, so in j days, he would have run 3j miles.

Similarly, Denis runs 4 miles per day and ran an additional 10 miles this month.

So in d days, he would have run 4d + 10 miles.
To find the total number of miles both boys ran this month, we need to add the number of miles James ran to the number of miles Denis ran.

Therefore, our expression is:
Total Miles = 3j + 4d + 10
This expression represents the total number of miles both boys ran this month.

To solve for j and d, we would need more information, such as the total number of miles the boys ran or the number of days they both ran.
In summary, we can use the given information about James and Denis's daily running habits to create an expression that represents the total number of miles both boys ran this month.

This expression is 3j + 4d + 10.

For similar question on expression.

https://brainly.com/question/25968875

#SPJ11

The surface area of the pyramid is 72 + 486√3 metres.

The pyramid above is an hexagonal pyramid. The surface area of the hexagonal pyramid can be found as follows:

surface area of a hexagonal pyramid = ph / 2 + B

where

Therefore,

Base area = 1 / 2pa

where

Base area = 1 / 2 × (18 × 6) × 9√3

Base area = 1 / 2 × 108 × 9√3

Base area = 54 × 9√3

Base area = 486√3 metres

surface area of a hexagonal pyramid = 108 × 18 / 2 + 486√3

Therefore,

surface area of a hexagonal pyramid = 972 + 486√3 metres

learn more on surface area here: https://brainly.com/question/14563874

#SPJ1

To find -F+2G+H-R using the Graphical Tail-to-Tip method, measure the magnitude and direction of this resultant vector to find the sum F+2G+H-R.

To find the vector sum F+2G+H-R using the graphical tail-to-tip method, follow these steps:

Now, place the vectors tail-to-tip in the following order: F, 2G, H, and R (in opposite directions).

The sum of these vectors can be found by connecting the starting point (tail of F) to the endpoint (tip of R in the opposite direction).

Measure the magnitude and direction of this resultant vector to find the sum F+2G+H-R.

Read more about vectors here:

https://brainly.com/question/25811261

#SPJ1

The height of the replica souvenir is approximately 7.55 inches.

To find the height of the replica souvenir of the Statue of Liberty, we'll use the given scale factor of 1 inch = 20 feet. The original height of the statue is 151 feet. Divide the original height by the scale factor:

151 ft / 20 ft/in = 7.55 inches

The height of the replica souvenir is approximately 7.55 inches.

To learn more about height, refer below:

https://brainly.com/question/10726356

#SPJ11

The number of students who drive to school can be calculated as one-sixth of the total number of students.

Let's assume the total number of students in the Mupuvr CLC MLMMS4 group is represented by the variable 'x'. According to the given information, half of the students walk to school, which is equal to (1/2) * x. One-third of the students take a taxi, which is equal to (1/3) * x. The remaining students, who claim to drive, can be calculated as x - [(1/2) * x + (1/3) * x].

Simplifying this expression, we have x - (5/6) * x, which is equal to (1/6) * x. Therefore, the number of students who claim to drive to school is one-sixth of the total number of students.

Learn more about CLC MLMMS4

brainly.com/question/29026065

#SPJ11

There were approximately 586,800 elephants in Africa, rounded up to the nearest elephant.

In 1980, there were 1.2 million elephants in Africa. With a decrease of 6.8% per year, we need to calculate the population in 1987, which is 7 years later.

To find the population in 1987, we use the formula:

Final population = Initial population * (1 - decrease rate) ^ number of years

Final population = 1,200,000 * (1 - 0.068) ^ 7

Final population ≈ 1,200,000 * 0.489

Final population ≈ 586,800

In 1987, there were approximately 586,800 elephants in Africa, rounded up to the nearest elephant.

To learn more about population, refer below:

https://brainly.com/question/27991860

#SPJ11

Thus, equation that Tracy needs to use to obtain the number of tablespoons of flour to use in making 10 pancakes.

The unitary method is a method for determining the value of one unit from the values of several units or the other way around.

The unitary approach is a strategy for problem-solving that involves first determining the value of one unit, then multiplying that value to determine the required value.

Given data:

4 pancakes --->  6 teaspoon of flour.

For 1 pancake, divide above expression with 4 on both side.

1  pancakes --->  6/4 teaspoon of flour.

Now, for 10 pancake, multiply  above expression with 10 on both side.

10  pancakes --->  10* 6/4 teaspoon of flour.

Thus, equation that Tracy needs to use to obtain the number of tablespoons of flour to use in making 10 pancakes.

Know more about the unitary method:

https://brainly.com/question/23423168

#SPJ1

Answer:

V = 1,728 mi³

SA = 864 mi²

Step-by-step explanation:

We can find the volume of the triangular prism by multiplying the area of one of the triangle faces by the prism's depth.

First, we can solve for the area of one of the triangle sides:

A(triangle) = (1/2) · b · h

A(triangle) = (1/2) · 24 · 18

A(triangle) = 12 · 18

A(triangle) = 216 mi²

Next, we can get the volume of the prism by multiplying the area of the triangle face by the prism's depth.

V = A(triangle) · depth

V = 216 · 8

V = 1,728 mi³

__

We can find the surface area by finding the area of each side, then adding all of those areas together.

We already know that the area of each of the triangle sides is 216 mi².

Now, we can solve for the area of the base.

A(base) = length · width

A(base) = 24 · 8

A(base) = 192 cm²

Then, we can find the area of the top side.

A(top) = length · width

A(top) = 30 · 8

A(top) = 240 mi²

Finally, we can solve for the surface area of the prism by adding the areas of each of its sides.

SA = (2 · A(triangle)) + A(base) + A(top)

SA = 2(216) + 192 + 240

SA = 432 + 192 + 240

SA = 624 + 240

SA = 864 mi²

The resultant component of the vector addition, 1/3a - 2b is (-9, 0).

The resultant component of the vector is calculated as follows;

a = (-9, 6)

b = (3, 1)

The result of 1/3a = ¹/₃ (-9), ¹/₃(6) = (-3, 2)

The result of 2b = 2(3, 1) = (6, 2)

The result of the vector addition is calculated as follows;

1/3a - 2b

= (-3, 2) - (6, 2)

= (-3 -6, 2 -2)

= (-9, 0)

Learn more about vector addition here: https://brainly.com/question/30426215

#SPJ1

The second partial sum for the given sequence is 2 + 2(0.4) = 2.8, under the condition that first term a1 = 2 and common ratio r = 0.4.

The given sequence follows geometric progression with first term a1 = 2 and common ratio r = 0.4. Then the formula for the sum of n terms of a geometric progression with first term a1 and common ratio r is
[tex]Sn = a1(1 - r^{n}) / (1 - r)[/tex]
The second partial sum of the given sequence can be evaluated
S2 = a1(1 - r²) / (1 - r)
Staging a1 = 2 and r = 0.4 in the above formula,
S2 = 2(1 - 0.4²) / (1 - 0.4)
= 2 + 2(0.4) = 2.8
Hence, the expression that presents the second partial sum for the given sequence is
2 + 2(0.4) = 2.8.

To learn more about geometric progression
https://brainly.com/question/30303755
#SPJ4

The ratio of a : b : c : d is 3 : 7 : 2 : 7.

The ratios are determined as follows from the data given.

The given data is:

7a = 2b

b = (7/2)a.

a and b have no common factors, thus a must be even and b must be odd.

c : d is 2 : 7

For an integer x, c = 2x and d = 7x

a : d is 3 : 1

So for an integer y, a = 3y and d = y

Substituting into 7a = 2b:

7(3y) = 2(7/2)y a

21y = 7y * b

b = 3a

Substituting these expressions for a and b into c : d = 2:7, we get:

2x : 7x = 3 : 1

2x = 3y and 7x = y

y = 14x/3

a : b : c : d = 3y : 7y : 2x : 7x

a : b : c : d = 3(3y) : 3(7y) : 3(2x) : 3(7x)

a : b : c : d = 9y : 21y : 6x : 21x

a : b : c : d = 3 : 7 : 2 : 7

Learn more about ratios at: https://brainly.com/question/12024093

#SPJ1