How many additional teachers will have to be hired to reduce the ratio to 1:20

Answer:

.33x = 105.60

$371

Step-by-step explanation:

Answer:

63.44

Step-by-step explanation:

its 63.44697 but you round so its 63.44

Answer:

The price per ounce is $0.16

Step-by-step explanation:

We have:

Price of a 4-pound bag = $10.24

1 pound = 16 ounces

Price per ounce =?

Hence the price per ounce is:

[tex] \frac{\$ 10.24}{4 pound}*\frac{1 pound}{16 ounces} = \frac{\$ 0.16}{ounce} [/tex]

Therefore, the price per ounce is $0.16

I hope it helps you!

Answer:

a) 68%

b) 95%.

c) 2.5%

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 100,000, standard deviation of 10,000.

a. Approximately what percentage of the salaries fall between $90,000 and $110,000?

90,000 = 100,000 - 10,000

110,000 = 100,000 + 10,000

Within 1 standard deviation of the mean, so approximately 68%.

b. Approximately what percentage of the salaries fall between $80,000 and $120,000?

80,000 = 100,000 - 2*10,000

120,000 = 100,000 + 2*10,000

Within 2 standard deviations of the mean, so approximately 95%.

c. Approximately what percentage of the salaries are greater than $120,000?

More than 2 standard deviations above the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean, so approximately 5% are more than 2 standard deviations from the mean.

The normal distribution is symmetric, which means that 2.5% are more then 2 standard deviations below the mean, and 2.5% are more than 2 standard deviations above the mean, which means that 2.5% of the salaries are greater than $120,000.

Answer:

(4%) ... $8200

Step-by-step explanation:

x + y = 15000

.04x + .032y = 545.60

y = 15000 - x

.04x + .032(15000 - x) = 545.60

.008x = 65.6

x=8200

The cost a company pays a lender for a loan is called interest.

The account received an initial investment of 8200 with 4% interest.

The cost of borrowing money is called interest, and it is typically expressed as a percentage, such as an annual percentage rate (APR). Lenders may charge interest to borrowers for using their funds, or borrowers may charge interest to lenders for using their funds.

The cost a company pays a lender (creditor) for a loan is called interest. Although many different arrangements are possible, interest payments are typically based on the remaining balance of a loan and paid on a monthly basis. At a predetermined interest rate, interest is typically calculated as a percentage of the loan balance.

From the given information, we get

x + y = 15000 ........(1)

0.04x + 0.032y = 545.60 ..........(2)

From (1),

y = 15000 - x

substitute the value of y in the above equation, we get

⇒ 0.04x + 0.032(15000 - x) = 545.60

simplifying the above equation, we get

⇒ 0.008x = 65.6

x = 8200

Therefore, 8200 was initially invested in the account with 4% interest.

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Answer:

The estimate of the population proportion is 0.3232.

Step-by-step explanation:

Estimate of the population proportion:

The estimate is the sample proportion, which is the number of desired outcomes divided by the number of total outcomes.

In this question:

32 out of 99, so:

[tex]p = \frac{32}{99} = 0.3232[/tex]

The estimate of the population proportion is 0.3232.

Answer:

0.9452 = 94.52% probability that more than 3 adults in the sample prefer saving over spending

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they prefer saving over spending, or they do not. The answers for each adult are independent, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

According to a Gallup poll, 60% of American adults prefer saving over spending.

This means that [tex]p = 0.6[/tex]

Sample of 10 American adults

This means that [tex]n = 10[/tex]

What is the probability that more than 3 adults in the sample prefer saving over spending?

This is:

[tex]P(X > 3) = 1 - P(X \leq 3)[/tex]

In which

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{10,0}.(0.6)^{0}.(0.4)^{10} = 0.0001[/tex]

[tex]P(X = 1) = C_{10,1}.(0.6)^{1}.(0.4)^{9} = 0.0016[/tex]

[tex]P(X = 2) = C_{10,2}.(0.6)^{2}.(0.4)^{8} = 0.0106[/tex]

[tex]P(X = 3) = C_{10,3}.(0.6)^{3}.(0.4)^{7} = 0.0425[/tex]

Then

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0001 + 0.0016 + 0.0106 + 0.0425 = 0.0548[/tex]

[tex]P(X > 3) = 1 - P(X \leq 3) = 1 - 0.0548 = 0.9452[/tex]

0.9452 = 94.52% probability that more than 3 adults in the sample prefer saving over spending

Answer:

The original dimensions of the park are:

(23/2) yards by 7 yards.

Step-by-step explanation:

Suppose that you have a given dimension X

if you want to reduce that dimension by a scale factor k, such that:

0 < k < 1

The reduced dimension is just:

X' = k*X

Now let's solve the problem:

We know that the dimensions on the blueprint are:

(23/147)yd by (3/14)yd

And the original dimensions are:

A yd by B yd

We know that, to get the blueprint dimensions, we reduced the original dimensions by a factor of 2/147

Then we just have that:

(2/147)*A = 23/147

(2/147)*B = 3/14

Now we just can solve these two equations for A and B

A = (23/147)*(147/2) = 23/2

B = (3/14)*(2/147) = (3/7)*(1/147) = 49/7 = 7

Then the original dimensions of the park are:

(23/2) yards by 7 yards.

Answer:

[tex]x =10[/tex]

Step-by-step explanation:

Given

[tex]AB = 12[/tex]

[tex]BC = 18[/tex]

[tex]AC = 3x[/tex]

Required

Solve for x

Since B is in between both points, then:

[tex]AC = AB + BC[/tex]

This gives

[tex]3x = 12 + 18[/tex]

[tex]3x = 30[/tex]

Divide by 3

[tex]x =10[/tex]

Answer:

I guess this is the answer hope it helps

Answer:

2424.5

904.16

Step-by-step explanation:

the mean = ∑frequency /n

∑f = 5+17+36+115+125+81+47+45+22+7 = 500

∑xf = 1212250

∑x²f = 3347037625

sample mean = 1212250/500

= 2424.5

variance = 1/500-1[3347037625 - 1212250²]

= 815710.02

standard deviation is = √variance

standard deviation = √815710.02

= 904.16

Answer:

Step-by-step explanation:

-2*x +2

it is reveresed with a y interecept of 2

Answer:true

Step-by-step explanation:

i dont know

Answer:

[tex]\implies \dfrac{2}{10}< \dfrac{3}{10} [/tex]

Step-by-step explanation:

We need to compare the given two fractions .The given fractions are ,

[tex]\implies \dfrac{3}{10} [/tex]

[tex]\implies \dfrac{1}{5} [/tex]

Firstly let's convert them into like fractions . By multiplying 1/5 by 2/2 . We have ,

[tex]\implies \dfrac{1}{5} =\dfrac{1*2}{5*2}=\dfrac{2}{10} [/tex]

Now on comparing 2/10 and 3/10 we see that ,

[tex]\implies 2< 3 [/tex]

Therefore ,

[tex]\implies \dfrac{2}{10}< \dfrac{3}{10} [/tex]

Answer:

7

Step-by-step explanation:

First, add all the cards.

[tex]2 + 5 + 7 + 8 + 9 = 31[/tex]

If we remove one card, the remaining four cards average will be 6, this means that the 4 remaning cards will average total will be at 24 because 6×4=24. So we need to find a value that will equal 24 if we remove that card.

The answer is 7 because

[tex] \frac{2 + 5 + 8 + 9}{4} = 6[/tex]

9514 1404 393

Answer:

  remove 7 to make the total be 6×4 = 24.

Step-by-step explanation:

The description "mean average" is redundant to no apparent purpose. "Mean" and "average" are the same thing: the total divided by the number of contributors.

If the mean of 4 cards is 6, then we require ...

  6 = (total of 4 cards) ÷ 4

  24 = total of 4 cards . . . . . . . multiply both sides of the equation by 4

__

We note that the total of all the cards shown is ...

  2 + 5 + 7 + 8 + 9 = 31

In order to make the total be 24, we need to remove a card that has a value of ...

  31 -24 = 7

Removing 7 will bring the total to 2 + 5 + 8 + 9 = 24, and the average to 24/4 = 6.

_____

Additional comment

It is worthwhile to remember the relationship between the total and the average and the number of contributors. This shows up a lot in problems involving adjusting an average or finding a value to give a certain average.

Answer:

just combine like terms, its that simple.

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

make a column of x ,f, fx

then write income in x and no.of workers in f

andthen multiply both just like 100*3 ,100*2, 300*p, 400*2,500*1 write its answer fx

add the all fx and use this formula

mean =fx /n

260=adding total of fx divide by 5

Repeat same formula in no 2

Complete Question:

There are 12 eggs in a dozen. If a farmer's chickens produce an average of 423 dozen eggs in a month,  how many eggs are reported per month?

Answer:

The eggs reported per month are:

= 5,076 eggs.

Step-by-step explanation:

a) Data and Calculations:

A dozen eggs = 12 pieces of eggs

Average of dozen eggs produced in a month = 423

Therefore, the eggs that are reported per month should average 5,076 (12 * 423)

b) The arrangement or measurement of eggs in dozens makes it easier to calculate the number of eggs produced in the farm each period.  The result is obtained by multiplying the average of dozen eggs produced by 12.

Answer:

[tex] \cos(x) = - \frac{5}{ \sqrt{41} } [/tex]

[tex] \csc(x) = \frac{ \sqrt{41} }{4} [/tex]

[tex] \tan(x) = - \frac{4}{5} [/tex]

Step-by-step explanation:

We know that (-5,4) is the terminal side. This means out legs will measure 5 and 4 if we graph it on a triangle.

We need to find the cos, csc, and tan measure of this point.

We can find cos by using the formula of

[tex] \cos(x) = \frac{adj}{hyp} [/tex]

The adjacent side is -5 and we can find the hypotenuse by doing pythagorean theorem.

[tex] { - 5}^{2} + {4}^{2} = \sqrt{41} [/tex]

So using the info the answer is

[tex] \cos(x) = \frac{ - 5}{ \sqrt{41} } [/tex]

We can find tan but first me must find sin x.

[tex] \sin(x) = \frac{opp}{hyp} [/tex]

[tex] \sin(x) = \frac{4}{ \sqrt{41} } [/tex]

So now we just use this identity,

[tex] \tan(x) = \sin(x) \div \cos(x) [/tex]

[tex] \tan(x) = \frac{ \frac{4}{ \sqrt{41} } }{ \frac{ - 5}{ \sqrt{41} } } = - \frac{4}{5} [/tex]

So tan x=

[tex] - \frac{ 4}{5} [/tex]

We can find csc by taking the reciprocal of sin so the answer is easy which is

[tex] \frac{ \sqrt{41} }{4} [/tex]

Answer:

yes

Step-by-step explanation:

if you change it to standard form, it would be

y=1/2x

because it's in the format of y=ax then it is direct variation

Answer:

4,a

5.d

6.c

plz mark me as brainliest

Step-by-step explanation:

Answer:

1. A

2. C

3. A

Step-by-step explanation:

all the explanations are In the image above

Answer:

4/25.

Step-by-step explanation:

We need to have the 2 values in the same unit so:

converting minutes to seconds:

5 mins = 5*60 = 300 seconds.

The require fraction =

48/300              

The GCF of 48 and 300 is 12 so we have:

48/12 / 300/12  

= 4/25

The required fraction of 48 seconds to 5 minutes is  4 / 5 minutes.

Given that,
To express the ratio as a fraction in its lowest terms.48s to 5 minutes​.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
60 second = 1 minute
1 second = 1 / 60 minute
multiply both sides by 48
48 second = 48 / 60 minute
48 second = 4 / 5 minute

Thus, the required fraction of 48 seconds to 5 minutes is  4 / 5 minutes.

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Answer:

Option A, 4rad5

Step-by-step explanation:

x² = 5*(5+11)

x² = 5*16

x² = 80

x = 4√5

Answered by GAUTHMATH

Answer:

59

Step-by-step explanation:

Just get the supplement of 121.

So angle 1 is 180-121 = 59 degrees

Answer:

M = 84 , r = 32

Step-by-step explanation:

Given M is directly proportional to r then the equation relating them is

M = kr ← k is the constant of proportion

To find k use the condition when r = 2, M = 14 , then

14 = 2k ( divide both sides by 2 )

7 = k

M = 7r ← equation of proportion

(a)

When r = 12

M = 7 × 12 = 84

(b)

When M = 224 , then

224 = 7r ( divide both sides by 7 )

32 = r

Answer:

Step-by-step explanation:

Answer:

The function that passes through (0, 0) is [tex]f(x) = \frac{1}{6}\cdot e^{2\cdot x^{3}} - \frac{1}{6}[/tex].

Step-by-step explanation:

Firstly, we integrate the function by algebraic substitution:

[tex]\int {x^{2}\cdot e^{2\cdot x^{3}}} \, dx[/tex] (1)

If [tex]u = 2\cdot x^{3}[/tex] and [tex]du = 6\cdot x^{2} dx[/tex], then:

[tex]\int {e^{2\cdot x^{3}}\cdot x^{2}} \, dx[/tex]

[tex]\frac{1}{6}\int {e^{u}} \, du[/tex]

[tex]f(u) = \frac{1}{6}\cdot e^{u} + C[/tex]

[tex]f(x) = \frac{1}{6}\cdot e^{2\cdot x^{3}} + C[/tex]

Where [tex]C[/tex] is the integration constant.

If [tex]x = 0[/tex] and [tex]f(0) = 0[/tex], then the integration constant is:

[tex]\frac{1}{6}\cdot e^{2\cdot 0^{3}} + C= 0[/tex]

[tex]C = -\frac{1}{6}[/tex]

Hence, the function that passes through (0, 0) is [tex]f(x) = \frac{1}{6}\cdot e^{2\cdot x^{3}} - \frac{1}{6}[/tex].

Answer:

100

Step-by-step explanation:

√(x2 - x1)² + (y2 - y1)²

√(-93 - 3)² + [-37 - (-9)]

√(-96)² + (-28)²

√9216 + 784

√10000

= 100

Answer: (8x8x9)/3=192

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Answer:

The area of the shed=[tex]64m^2[/tex]

Step-by-step explanation:

We are given that

Side of square =8m

We have to find the area of the shed.

To find the area of shed we will find the area of square.

We know that

Area of square=[tex]side\times side[/tex]

Using the formula

Area of square=[tex]8\times 8[/tex]

Area of square=[tex]64m^2[/tex]

Area of shed=Area of square

Area of shed=64 square m

Hence, the area of the shed=[tex]64m^2[/tex]