we have 4 women and 5 men and want to create a committee with 2 women and 2 men. in how many ways we can do this?

Answers

Answer 1

126 number of ways we can arrange the men, women in order to committee with 2 women and 2 men ,the combination is explained below as

We can use the combination formula to find  out the number of ways to choose 2 women and 2 men from a group of 4 women and 5 men.

as we know the  formula for combination as :

C(n ,k) = n! / (k!(n-k)!)

where n is the total number of people, k is the number of people we want to choose, and ! denotes factorial to find the number of combinations  (i.e. the product of all integers up to that number, e.g. 4! = 432*1 = 24).

In this case,  to choose the number of individuals as = 4 + 5 = 9 and k = 2 + 2 = 4. So, the number of ways to choose the committee is:

C(9,4) = 9! / (4!(9-4)!) = 126 ways

Hence the number of ways to choose committee is 126 ways.

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Related Questions

Aume that y varie inveraly with x. If y equal 7 when x equal 2/3, find y when x =7/3

Answers

If y equals 7 when x equal 2/3, so when x =7/3 the y is equal to 14/7

If y varies inversely with x, this means that the product of x and y is a constant. So if we know that y = 7 when x = 2/3, then we can set up the equation: x*y = k, where k is the constant.

Substituting the known values we get: (2/3)*7 = k.

So we know that k = 14/3

Now, we can use this value of k to find the value of y when x = 7/3.

x*y = k

(7/3)*y = 14/3

y = 14/7

So, when x = 7/3, y = 14/7

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according to westgard and clia, how many specimens should be run by each method on the same day for 8 to 20 days to compare a test method with a comparative method?

Answers

According to Westgard and CLIA , 40-100  specimens should be run by each method on the same day for 8 to 20 days to compare a test method with a comparative method.

CLIA stands for  Clinical Laboratory Improvement Amendments  . The regulations under CLIA includes, the federal standards which is applicable to all U.S. facilities or sites which are test human specimens for health assessment or it is used to diagnose, prevent, or treat disease.

The Federal Register is the official daily publication for federal agencies and the organization's notices, proposed regulations, and final rules, as well as executive orders and other presidential papers. The regulations published in the Code of Federal Regulations and enforced by federal agencies are known as final rules.

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1. Kevin regularly travels from Manchester to Oxford.
He travels on two different trains.
His first train is from Manchester to Birmingham and his second train is from Birmingham to
Oxford.
On the 1st train, the probability that a seat has a table is 3/5
On the 2nd train, the probability that a seat has a table is
3/10
The 1st train has a total of 400 seats.
(a) Work out an estimate for the number of these 400 seats that have a table.

Answers

Answer:

240 seats with tables

Step-by-step explanation:

Let's start by making our fraction out of 10 on the first train to make it easier on us, this fraction would be [tex]\frac{6}{10}[/tex]. Then, to get the number of seats on this train that would have a table, we need to multiply 400 by our fraction, giving us:

[tex]400 * \frac{6}{10} = 2400/10 = 240[/tex]

So, the 1st train should have approximately 240 seats with tables.

Hope this helped!

State the fifth and seventh terms of the sequence -2, -3, -4½..​

Answers

Answer:

see explanation

Step-by-step explanation:

there isa common difference between consecutive terms, that is

[tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-3}{-2}[/tex] = [tex]\frac{3}{2}[/tex]

[tex]\frac{a_{3} }{a_{2} }[/tex] = [tex]\frac{-4\frac{1}{2} }{-3}[/tex] = [tex]\frac{3}{2}[/tex]

this indicates the sequence is geometric with nth term

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

here a₁ = - 2 and r = [tex]\frac{3}{2}[/tex] , then

[tex]a_{n}[/tex] = - 2 [tex](\frac{3}{2}) ^{n-1}[/tex] , thus

a₅ = - 2 ([tex](\frac{3}{2}) ^{4}[/tex] = - 2 × [tex]\frac{81}{16}[/tex] = - [tex]\frac{81}{8}[/tex]

and

a₇ = - 2 [tex](\frac{3}{2}) ^{6}[/tex] = - 2 × [tex]\frac{72 9}{64}[/tex] = - [tex]\frac{729}{32}[/tex]

The volume of a rectangular prism is given by the expression10x3 + 46x2 – 21x – 27. The area of the base of the prism is given by the expression 2x2 + 8x – 9. Which of the following expressions represents the height of the prism? (V = Bh)

8x - 3

3x - 5

5x + 3

42x + 3

Answers

The height of the prism is 5x + 3 units.

What is volume?

A measurement of three-dimensional space is volume. It is frequently expressed numerically using SI-derived units, as well as different imperial or US-standard units. Volume and the definition of length are related.

Given:

The volume of a rectangular prism is given by the expression

10x^3 + 46x^2 – 21x – 27. The area of the base of the prism is given by the expression 2x^2 + 8x – 9.

We have to find the height of prism.

Volume of the rectangular prism = Base × Height

The expression is in the Question be

10x ³ + 46 x² - 21x -27

And the  area of the base of the prism is given by the expression

2x² + 8x - 9 .

Put in the formula

10x ³ + 46 x² - 21x -27  = 2x² + 8x - 9  × Height

The factor of 10x ³ + 46 x² - 21x -27 are (5x +3 )(2x² + 8x - 9) .

put in the formula

(5x +3 )(2x² + 8x - 9) = (2x² + 8x - 9) × Height

Cancelled 2x² + 8x - 9 on both side.

(5x+3)unit = Height

Hence, the height of the prism is 5x + 3 units.

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my sock drawer is always a mess. at the beginning of the week, i have 4 pairs of black socks, 5 pairs of blue socks, 3 pairs of brown socks, and 2 pairs of multi-colored socks. every morning, i grab a pair and hope for the best. if on the 1st three days i pick 1 black pair and 2 blue pairs, what is the probability that i'll pick a solid color on the 4th day?

Answers

The probability of picking a solid color on the 4th day is 8/10 = 4/5.

The probability of picking a solid color on the 4th day is calculated by taking the total number of solid color pairs remaining in the drawer and dividing by the total number of pairs remaining.

On the first three days, you picked 1 black pair and 2 blue pairs, so you have 3 black pairs, 3 blue pairs, 3 brown pairs and 2 multi-colored pairs left in your drawer.

The total number of solid color pairs remaining is 8, and the total number of pairs remaining is 8+2 = 10.

So, the probability of picking a solid color on the 4th day is 8/10 = 4/5.

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Add and Subtract Fractions Quiz

Select the correct solution for the expression.
2/5+3/8

A. 2/5+3/8=5/13

B. 16/40+15/40=31/40

C. 10/40+24/40=34/40

D. 2/5+3/8=6/40

Answers

Answer:

B.

Step-by-step explanation:

You need to find a common denominator.  In this case, 40.  Convert 2/5 to 16/40 and 3/8 to 15/40.  Add the numerators (16 + 15) together.  The denominator stays the same.

Evaluate: 2−1 × 23 /24

Answers

Answer:

0.9583

Step-by-step explanation:

(2-1) * (23÷24)

1*0.983

=0.9583

Answer:

[tex]\frac{23}{24} = 0.95[/tex]

Step-by-step explanation:

According to BODMAS

What is the volume of the cylinder? Round to the nearest hundredth and approximate using π = 3.14.

cylinder with a segment from one point on the circular base to another point on the base through the center labeled 2.6 feet and a height labeled 4.4 feet

23.35 cubic feet
35.92 cubic feet
71.84 cubic feet
93.4 cubic feet

Answers

Answer:

23.35 cubic feet

Step-by-step explanation:

The volume of a cylinder can be calculated using the formula: V = π * r^2 * h, where r is the radius of the circular base, h is the height of the cylinder.


To find the radius, we use the formula for the circumference of a circle: C = 2πr

The circumference of the circular base is 2.6 feet, so we can set this equal to 2πr and solve for r: 2.6 = 2πr, r = (2.6) / (2π) = 0.816

Now that we know the radius, we can substitute it into the volume formula: V = π * (0.816)^2 * 4.4 = 23.35 cubic feet

So the answer is 23.35 cubic feet, which closest to A. 23.35 cubic feet

amy was born on a tuesday. what is the probability that exactly two of her three best friends were also born on tuesday? express your answer as a common fraction.

Answers

The probability of being born on a Tuesday is= 18/343

What is probability ?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

The likelihood that an event will occur increases with its probability.

A straightforward illustration is tossing a fair (impartial) coin.

The coin is fair, thus the outcomes "heads" and "tails" are equally likely; the likelihood of "heads" is equal to the likelihood of "tails"; and because there are no other conceivable outcomes, the likelihood of either "heads" or "tails" is 1/2 (which is also an acceptable spelling).

Hence, The probability of being born on a Tuesday is= 18/343.

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pls help super simple !!

Answers

The values of the expression are given by the inequality below:

11/3 < 5/x + 2 < 9/2

How to find the possible values of the expression?

Here we want to find the possible values of the expression:

5/x + 2

Where we have the restriction:

2 < x < 3

Notice that x is on the denominator, so when x takes the largest value x = 3, we will have a lower bound for the expression:

5/3 + 2 = 5/3 + 6/3 = 11/3

When x takes the smallest value, we will get the upper bound:

5/2 + 2 = 5/2 + 4/2 = 9/2

Then the possible values of the expression are:

11/3 < 5/x + 2 < 9/2

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The inverse of f(x) would be represented by:

f(x)
ƒ¹(x)
f(x)-¹
fog(x)
None of the choices are correct.

Answers

If g(x) is the inverse function of f(x)  and[tex]$f^{\prime}(x)=\frac{1}{1+x^4}$[/tex], then [tex]$g^{\prime}(x)$[/tex]  is [tex]1+[\mathrm{g}(\mathrm{x})]^4\end{aligned}[/tex]

What is Inverse function?By applying the formula x=-b/2a to find the quadratic's vertex, the result can then be used to replace y in the original equation. Substitute the vertex into the equation y=a(x-h)2+k in the vertex form. (A will not change; h is x; and K is y.) It is referred to as being in standard form when the quadratic function f(x) = a(x - h)2 + k is not equal to zero. The graph opens either upward or downward depending on whether an is positive or negative. The vertex is the point, while the vertical line x = h is the line of symmetry (h,k).

Correct option is A)

[tex]& \mathrm{g}=\mathrm{f}^{-1} \\[/tex]

[tex]& \mathrm{f}(\mathrm{g}(\mathrm{x}))=\mathrm{x}[/tex]

Differentiate w.r.t.x

[tex]& \mathrm{f}^{\prime}(\mathrm{g}(\mathrm{x})) \cdot \mathrm{g}^{\prime}(\mathrm{x})=1 \\[/tex]

[tex]& \therefore \frac{1}{1+(\mathrm{g}(\mathrm{x}))^4} \cdot \mathrm{g}^{\prime}(\mathrm{x})=1 \\[/tex]

[tex]& \mathrm{~g}^{\prime}(\mathrm{x})=1+[\mathrm{g}(\mathrm{x})]^4\end{aligned}[/tex]

The complete question is,

If [tex]$\mathrm{g}(\mathrm{x})$[/tex]is the inverse function of [tex]$\mathrm{f}(\mathrm{x})$[/tex] and [tex]$\mathrm{f}^{\prime}(\mathrm{x})=\frac{1}{1+\mathrm{x}^4}$[/tex], then [tex]$\mathrm{g}^{\prime}(\mathrm{x})$[/tex]is

A [tex]$1+[\mathrm{g}(\mathrm{x})]^4$[/tex]

B [tex]$1-[g(x)]^4$[/tex]

C [tex]$1+[\mathrm{f}(\mathrm{x})]^4$[/tex]

D [tex]$\frac{1}{1+[\mathrm{g}(\mathrm{x})]^4}$[/tex]

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Suppose you want to have 800,000 for retirement in 35 years your account earns 9% interest how much would you need to deposit in the account each month

Answers

Therefore , the solution of the given problem of interest rate comes out to be $271.94 you will be depositing every month.

What is interest, exactly?

The original capital is multiplied by the interest rate, the loan term, and other factors to calculate simple interest. A simple return is equal to the principal plus interest hrs. This method of calculating interest is the simplest. The most typical method is to calculate it as a fraction of the principal amount. For instance, he was only liable for paying his portion of the interest if he acquired $100 from a buddy and agreed to repay the money on 5% interest. $x (0.05) = $5. When you make loans or lend money, you both have to pay interest. Interest is frequently determined as a percentage of a loan.

Here,

Given  :  interest = 9%

time  =35 years

amount = 800000

Using formula :

=> FV.( r / [tex](1+r) ^{n}[/tex] -1)

=>  800000 (0.09/12 / [tex](1 + 0.09/12 )^{12*35}[/tex] - 1 )

=> 271.94

Therefore,

the total amount you deposit will only be

=> 35*12 times $271.94, or

roughly total amount => 35*12*271.94= 114214.8 dollars, out of the estimated $800,000.

The balance will be what the account earns or accumulates over the next 35 years.

Therefore , the solution of the given problem of interest rate comes out to be $271.94 you will be depositing every month.

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Identify the surface with the given vector equation. r(s, t) = (s, t, t^2-s^2) elliptic cylinder circular paraboloid hyperbolic paraboloid plane circular cylinder

Answers

Therefore , the solution of the given problem of equation comes out to be x² + z²= y, a circular paraboloid.

What is equation?

When a math formula employs the equals symbol (=), it appears to be a rule that connects two expression and denotes equality. An equation in algebra is a factual declaration that shows that several mathematical variables are all equal. For instance, the values ptdc + 6 and 12 in the equation obd + 6 = 12 have an equal sign. The link between the words on either side of each letter is described by a mathematical formula. The sentence and the insignia are frequently same.

Here,

The vector solution is r(s, t) = s, t, t² - s².

When comparing to r(s, t) = x, y, and z, x = s, y = t, and z = 2 - s²

So, z = y² - x²

, a hyperbolic paraboloid (2)

r(s, t) = s sin³t, s², s cos³t is the vector equation that is presented.

When comparing with withr(s, t) = x, y, and z,

x = ssin³t, y = s², and z = s* cos³t²

As a result, x2 + z2 = s2 (sin23t + cos23t),

sin23t + cos23t = 1,

x² + z² = s², s² = y, and x² + z²= y,

a circular paraboloid.

Therefore , the solution of the given problem of equation comes out to be x² + z²= y, a circular paraboloid.

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after a hailstorm, a large car dealership wants to determine the proportion of cars that have damage. the service department randomly selects 50 cars on the dealership lot, examines them, and determines that 18 have damage. assuming all conditions have been met, they construct a 99% confidence interval for the true proportion of cars with damage from the storm. what are the calculations for this interval?

Answers

On solving the provided question we can say that 50 vehicles, 11 of which are damaged, leave 39 intact. Conditions for inference are satisfied because both proportion number of successes and failures is greater than 10.

what is proportionality?

Relationships that consistently have the same ratio are referred to as proportionate. For instance, the average quantity of apples per tree determines how many trees there are in an orchard and how many apples are in a harvest of apples. In mathematics, proportional denotes a linear relationship between two numbers or variables. The other amount doubles when the first quantity does. The other lowers as well when one of the variables falls to 1/100th of its prior value.

Yes, the prerequisites for inference are satisfied.

Inference requirements:

The sample must have at least 10 successes and 10 failures in order to construct a confidence interval for a population proportion.

50 vehicles, 11 of which are damaged, leave 39 intact.

Conditions for inference are satisfied because both the number of successes and failures is greater than 10.

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Match each rational expression to its simplest form.
2m²
2(m-2)
m².. 2m.t.d
1
m²-3m +2
m
926
06
M
774
m²-m-2

Answers

The simplification of rational expressions can be achieved by using the Greatest Common Factor (GCF).

How do you write a rational expression in simplest form?

Take the common terms in the numerator and denominator and remove them from the expression to make it simpler.

The simplification of rational expressions can be achieved by using the Greatest Common Factor (GCF).Similar to fractions with variables in the denominators, rational expressions appear like them (and often numerators too).

For instance, the expression x 2 x + 3 is a rational expression: x squared, divided by x, plus 3, end fraction.

1)2m^2-4m)/2(m-2)

=[2m(m-2m)]/2(m-2)

= 2m/2

=m

2)m^2-2m+1/m-1

= (m-1)^2/(m-1)

=(m-1)(m-1)/(m-1)

=(m-1)

3)m^2-3m+2/m^2-m

=m^2-m-2m+2/m(m-1)

=m(m-1)-2(m-1)/m(m-1)

= (m-1)(m-2)/m(m-1)

=(m-2)/m

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Simplify: 1. Write the prime factorization of the radicand. 2. Apply the product property of square roots. Write the radicand as a product, forming as many perfect square roots as possible.

Answers

The prime factorization of the radicand 2 is 9√15.

A number can be expressed as the product of its prime components through the process of prime factorization. A number with precisely two elements, 1 and the number itself, is said to be a prime number.

As an illustration, let's use the number 30. We know that 30 = 5 × 6, but 6 is not a prime number. The number 6 can further be factorized as 2 × 3, where 2 and 3 are prime numbers. Therefore, the prime factorization of 30 = 2 × 3 × 5, where all the factors are prime numbers.

Given that,

x= 3√135

Solving the equation further using the rule √A*B = √A*√B

x= 3√9*15

x= 3√9*√15

x=3*3*√15

x= 9√15

Therefore, the prime factorization of the radicand 2 is 9√15.

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Kevin is travelling from Manchester to Oxford tomorrow.
(b) Complete the probability tree diagram to show the outcomes of Kevin's seating on the two
trains.
Label clearly the branches of the probability tree diagram.
The probability tree diagram has been started in the space below.
315
Seat on the
first train
with a
table
without
a table
Seat on the
second train

Answers

Answer:

I don't know the answer to this question

Sorry, but may I ask what the answer to this question is?
Which is not a combination that can be made if Joe has a pair of yellow, orange, black, and blue shoes with yellow, red, and brown shoelaces?

A. orange shoes with red shoelaces
B. black shoes with yellow shoelaces
C. blue shoes with brown shoelaces
D. yellow shoes with black shoelaces

Answers

C definitely, cause that would look wild and dirty

Answer:

D

Step-by-step explanation:

There are no black shoelaces

How do you this help please

Answers

Answer:

Step-by-step explanation:

The height of her pear tree is 20 inches

First subtract 46 from 26 to get 20. So 20+26=46inches

x=20

Step-by-step explanation:

you know how to transform an equation ?

you need to apply the same operating to both sides of the equation. always. otherwise the equality relation is destroyed.

x + 26 = 46

to get to "x = ..." the "+ 26" is in the way.

clearly we need to subtract 26. but we need to do it on both sides.

x + 26 - 26 = 46 - 26

x = 20

that simply means the last tree is 20 in.

it is 26 in shorter than 46 in (fig tree).

that's all there is to it.

How do I do this help me please

Answers

Answer: x = 81

Step-by-step explanation:

Quite a straightforward question.

Given equation is 61+20=x

So you just need to add 61 and 20 to get the value of x,

x=81

Complete answer is: x=1

select the correct answer. it is estimated that approximately one-half of all aluminum cans will be recycled each year. if a soft drink company produces 350,000 cans one year, how many cans are still in use after 4 years of recycling and re-using, using this function? nt

Answers

After 4 years of recycling and re-using, approximately average one-half of the original 350,000 cans produced by the soft drink company would still be in use.

1. 350,000 cans produced in 1 year

2. 50% of cans recycled each year

3. 50% of 350,000 cans = 175,000 cans

4. After 4 years, 175,000 cans still in use.

Each year, it is predicted that about half of all aluminum cans will be recycled. This means that if a soft drink company produces 350,000 cans one year, then after four years, approximately one-half of the original cans produced would still be in use. This can be calculated by taking the initial number of cans produced (350,000), multiplying it by fifty percent (50%), and then multiplying that number by four (4). The final result is that after four years of recycling and re-using, approximately 175,000 cans would still be in use.

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the region inside the cardioid r = 1 + cos(θ) and outside the circle r = 3 cos(θ)

Answers

The region inside cardioid r = 1 + cos(θ) and outside the circle r = 3 cos(θ) is equal to [tex]\frac{\pi}{4}[/tex]

Now, According to the question:

We will first draw both of them on the same plane and then find their point of intersection. Then using the given information, we will shade the region whose area we have to find.

The point of intersection of  r = 1 + cos(θ) and  r = 3 cos(θ)

1 + cos(θ)  = 3 cos(θ)

1 = 2 cos(θ)

=> cos(θ) = 1/2

=> θ = [tex]cos^-^1[/tex][tex]\frac{1}{2}[/tex]

=> θ = ±[tex]\frac{\pi }{3}[/tex]

So, two curves intersect at θ = ± [tex]\frac{\pi }{3}[/tex]

Area of the cardioid,

[tex]A_1 = \int\limits^\pi _\frac{\pi }{3} {\frac{1}{2}(1+cos\theta)^2 } \, d\theta= \frac{1}{2} \int\limits^\pi _\frac{\pi }{3} (1+cos^2\theta+2cos\theta) } \, d\theta=\frac{1}{2}[/tex]

          [tex]\int\limits^\pi _\frac{\pi }{3} {(1 + \frac{cos2\theta+1}{2} +2cos\theta)} \, d\theta[/tex]

 => [tex]A_1 = \frac{1}{2}[\theta+\frac{1}{2}(\frac{sin2\theta}{2} +\theta)+2sin\theta ]^\pi _\frac{\pi }{3}[/tex]

=> [tex]A_1= \frac{1}{2}[\frac{3\pi }{2}+0+0-\frac{\pi }{2}-\frac{\sqrt{3} }{8} -\sqrt{3} ][/tex]

=> [tex]A_1= \frac{1}{2} [\pi +\frac{-9\sqrt{3} }{8} ]\\\\A_1 = \frac{\pi }{2} - \frac{9\sqrt{3} }{16}[/tex]

Area of the circle,

[tex]A_2 = \int\limits^\frac{\pi }{2} _\frac{\pi }{3} {\frac{1}{2}(3cos\theta)^2 } \, d\theta \\\\A_2 = \frac{9}{2} \int\limits^\frac{\pi }{2} _\frac{\pi }{3} \frac{cos2\theta+1}{2}d\theta\\ \\A_2 = \frac{9}{4}[\frac{sin2\theta}{2}+\theta ]^\frac{\pi }{2}_\frac{\pi }{3}[/tex]

[tex]A_2 = \frac{9}{4}[0+\frac{\pi }{2} -\frac{\sqrt{3} }{4} -\frac{\pi }{3} ][/tex]

[tex]A_2=\frac{9}{4}[\frac{\pi}{6}-\frac{\sqrt{3} }{4} ][/tex]

[tex]A_2= \frac{3\pi }{8}-\frac{9\sqrt{3} }{16}[/tex]

Area of the shaded region,

[tex]A = A_1-A_2[/tex]

[tex]A = \frac{\pi }{2} - \frac{9\sqrt{3} }{16} - \frac{3\pi }{8}+\frac{9\sqrt{3} }{16}[/tex]

[tex]A = \frac{\pi }{8}[/tex]

This is the area of the shaded region in the first and the second quadrant. We see that by symmetry, the area of the shaded region in the first and the second quadrant is equal to the area of the shaded region in the third and the fourth quadrant.

So, the total area is 2 ×[tex]\frac{\pi}{8}[/tex] = [tex]\frac{\pi}{4}[/tex]

Hence, the region inside cardioid r = 1 + cos(θ) and outside the circle r = 3 cos(θ) is equal to [tex]\frac{\pi}{4}[/tex]

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A rectangular field measures 63.9m by 104.6metres find the minimum number of poles to be Erected for fencing if they are to be at most 2.4meters apart.​

Answers

The minimum number of poles to be Erected for fencing are 26.

What is the perimeter of a rectangle?

The perimeter of a rectangle is -

P = 2{L + B}

Given is that a rectangular field measures 63.9 meters by 104.6 meters.

The perimeter of the rectangular field will be -

P = 2(63.9 + 104.6)

P = 2(168.5)

P = 337

Let the total number of poles that can be erected are {x}. Then, we can write that -

2.4x ≤ 63.9

x ≤ (63.9/2.4)

x ≤ 26.66

x = 26 {approx.}

Therefore, the minimum number of poles to be Erected for fencing are 26.

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In parallelogram ABCD, AB = 14cm. The altitude corresponding to AB is 6 cm and the altitude corresponding to BC is 7 cm. Find AD.

Answers

If in parallelogram ABCD, AB = 14cm. The altitude corresponding to AB is 6 cm and the altitude corresponding to BC is 7 cm. The AD is 8.57.

How to find AD?

Given data:

AB= 14cm

Altitude corresponding  AB =6cm

Altitude corresponding to BC =7cm

So,

1/2 × AB × altitude 1 = 1/2 × AD × altitude 2

AB × altitude 1 =AD × Altitude 2

10 × 6 = AD × 7

60 = AD × 7

AD = 60/7

AD = 8.57

Therefore we can conclude that AD is 8.57.

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Ted runs a coffee-distributing company with monthly fixed costs of $3600. he also spends $1.50 for each 16 ounce bag of coffee that he sells (%). during the month of september, his total costs were $12,000. which of the
following equations represent his total september costs? select all that apply.
3600 1.50x 12,000
1.50(2400x12,000
1.50(3600+) 12,000
3601.50 x 12.000
1.50 + 3600x12,000
(3600+ 1.50) x 12.000

Answers

The correct equations to represent Ted's total September costs are: (3600+ 1.50) x 12.000 1.50(3600+) 12,000.

What is cost?

Cost is the total expenditure or loss incurred in the production, acquisition, or use of a product or service. It can be calculated as the sum of fixed costs (such as rent and labor costs) plus variable costs (such as materials and energy). Cost can be expressed both in monetary terms (such as dollars or euros) or in terms of resources (such as time or effort). In business, cost is a crucial factor for determining profitability and should be taken into consideration when making decisions about production, sales, and pricing strategies.
The first equation calculates the cost of the fixed monthly costs plus the cost of the 16 ounce bags of coffee multiplied by the total number of bags sold. The second equation calculates the cost of the 16 ounce bags of coffee multiplied by the fixed monthly costs plus the total number of bags sold.

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Gertrude takes out a $5,500 subsidized stafford loan, which must be paid back in ten years. gertrude will graduate four years after taking out the loan. if the loan has an interest rate of 6.8%, compounded monthly, and gertrude makes monthly payments, how much interest will she pay by the time the loan is repaid? round all dollar values to the nearest cent. a. $4,462.40 b. $1,213.28 c. $1,713.69 d. $2,094.80 please select the best answer from the choices provided a b c d

Answers

$2094.28 interest will she pay by the time the loan is repaid.

What is compounded monthly?

Theoretically, continuously compounded interest means that an account balance continuously earns interest as well as reinvesting that interest into the balance so that it too earns interest.

As we know the formula of per month installments

[tex]E.M.I = \frac{P*r*(1+r)^n}{(1+r)^n^-^1}[/tex]

By putting the value of P (loan applied for)=$5500

r (Monthly rate of interest)  [tex]= \frac{6.8}{12*100}[/tex]

n = number of monthly installments = 10 × 12 = 120

[tex]E.M.I = \frac{5500*(\frac{6.8}{12*100} )(1+\frac{6.8}{1200} )^1^2^0}{(1+\frac{6.8}{1200} )^1^2^0-1}\\ E.M.I= \frac{5500*0.00567*1.971}{1.971-1}\\ E.M.I = \frac{61.461}{0.971} \\E.M.I = 63.29[/tex]

E.M.I.=$63.29

Total Installments of loan =120

Therefore total amount paid against loan = $63.39 × 120 = 7594.28

So interest paid = 7594.28 - 5500= $2094.28

Hence, $2094.28 interest will she pay by the time the loan is repaid.

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Help me with this question for BRAINLIEST

Last year, Christine had $20,000 to invest. She invested some of it in an account that paid 8% simple interest per year, and she invested the rest in an account that paid 10% simple interest per year. After one year, she received a total of $1920 in interest. How much did she invest in each account?
First account:
Second account:

Answers

Answer:

First account: $16,000

Second account: $4,000

Step-by-step explanation:

Let x be the amount Christine invested in the 8% account and y be the amount she invested in the 10% account. We know from the problem that:

x + y = $20,000 (the total amount she had to invest)

0.08x + 0.1y = $1920 (the total amount of interest she received)

We can use the first equation to solve for one variable in terms of the other.

x = $20,000 - y

Now we substitute this expression into the second equation:

0.08($20,000 - y) + 0.1y = $1920

Solving for y:

0.08x + 0.1y = $1920

0.08($20,000 - y) + 0.1y = $1920

1,600 - 0.08y + 0.1y = $1920

-0.08y = -320

y = $4,000

Now, we know that Christine invested $4,000 in the 10% account, we can use the first equation again to find out how much she invested in the 8% account:

x + y = $20,000

x + $4,000 = $20,000

x = $16,000

So Christine invested $16,000 in the 8% account and $4,000 in the 10% account

You are going to use an incline plane to lift a heavy object to the top of a shelving unit with a height of 5 ft. The base of the incline plane is 14 ft
from the shelving unit. What is the length of the incline plane?

Answers

an incline plane to lift a heavy object to the top of a shelving unit with a height of 5 ft. The base of the incline plane is 221 ft from the shelving unit

How does the length of the inclined plane affect its slope?A ramp or inclined plane, which is a flat support surface tilted at an angle from vertical with one end higher than the other, is used to help raise or reduce a weight.This implies that as the plane lengthens, the task will become easier in terms of force, but the distance will always need to adjust proportionally. This is due to the fact that the angle of elevation of the ramp lowers as length increases. The Pythagorean Theorem is used to compute the slope length, where rise and run are the vertical and horizontal distances, respectively: [tex]rise^{2} + run^{2} =slope length^{2}[/tex]The inclination plane is long, measuring [tex]5^{2} +14^{2} =221ft^{2}[/tex] .

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Using Pythagoras' theorem, calculate the length of the hypotenuse in this right-angled triangle. Give your answer in centimetres (cm) to 1 d.p. 4.8 cm 2 cm Not drawn accurately​

Answers

Answer: 5.2 cm

Step-by-step explanation:

4.8 squared + 2 squared is 23.04 + 4, which is 27.04. The square root of that is 5.2

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