A clothing store is having a sale in which customers can receive 30% off their purchase and $10 off using a coupon. The function f(x) = 0.7x represents the price after a 30% discount and the function g(x) = x − 10 represents the price after a $10 discount. Which of the following is the function f(g(x)) and what does it represent? (1 point)
f(g(x)) = 0.7x − 7 represents the purchase price after a $10 discount and then 30% off the remaining amount
f(g(x)) = 0.7x − 10 represents the purchase price after a 30% discount and then $10 off the remaining amount
f(g(x)) = 0.7x − 3 represents the purchase price after a $10 discount and then 30% off the remaining amount
f(g(x)) = 0.3x − 10 represents the purchase price after a 30% discount and then $10 off the remaining amount

Answer:

The approximate user base of the social media site 10 months from now would be approximately 52,374.

Step-by-step explanation:

To calculate the approximate user base of the social media site 10 months from now, considering a 4% increase per month, we can use the following steps:

1. Calculate the monthly growth factor: 1 + (4% / 100) = 1 + 0.04 = 1.04

2. Apply the growth factor to the current user base for each month:

  Month 1: 35,930 * 1.04 = 37,387.2 (approx.)

  Month 2: 37,387.2 * 1.04 = 38,868.49 (approx.)

  ...

  Month 10: Previous Month * 1.04

By repeating this calculation for each month, we can determine the approximate user base 10 months from now.

Month 1: 37,387.2

Month 2: 38,868.49

Month 3: 40,391.33

Month 4: 41,957.61

Month 5: 43,569.34

Month 6: 45,228.24

Month 7: 46,936.32

Month 8: 48,695.44

Month 9: 50,507.45

Month 10: 52,374.40 (approx.)

Therefore, the approximate user base of the social media site 10 months from now would be approximately 52,374.

In a case whereby a number has the same digits in its hundreds place and it’s hundredths place the number of times that the value is greater in the hundreds place than the value of the digit in the hundreds place is 10,000 times.

The question can be interpreted that the particular number has the same digit  which is seen in hundreds place  hence  hundredths place.

we can then represent the digit  as '1'.

The value of number's hundreds place can be represented as  100

we can as well represent the number's hundredths place as 0.01

the number of times the value of the hundreds place digit exceeds the value of the hundredths place digit can be expressed as 100/0.01 =(100*100)/1 = 10, 000

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missing options:

A. 100,00

B. 100

C. 1,000

D. 10,000

Answer:

20%

Step-by-step explanation:

p(outcomes)=#of favourable outcomes/#of possible outcomes

=1/5

=0.2

=20%

The equivalent expression of the given expression is (2/5)¹⁴

From the question, we are to write an equivalent expression for the given expression

The given expression is

"two fifths raised to the fourth power times two fifths raised to the third power all raised to the second power"

That is,

[(2/5)⁴ × (2/5)³]²

Simplifying

[(2/5)⁴ × (2/5)³]²

Applying the multiplication law of indices, we get

[(2/5)⁴⁺³]²

Simplify further

[(2/5)⁷]²

This becomes,

(2/5)⁷ˣ²

(2/5)¹⁴

Hence, the equivalent expression of the given expression is (2/5)¹⁴

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Answer:

32449.3

Step-by-step explanation:

use the formula A = P(1+r / 100)^t

20000 × (1+ (8.4 / 100))^6

=32449.3

From the given table, it is found that:

1. The linear regression equation is: y = 16.96x + 3.

2. The meaning of the slope is that he hiked an average of 16.96 miles a day.

3. In 52 days, Sean had hiked 885 miles.

4. In 22 days, Sean had hiked 377 miles.

To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are given on a table or in a scatter plot in the problem.

In the context of this problem, the points are given as follows:

(0,0), (19,308), (34, 578), (67, 1070), (91, 1715), (112, 1902), (134, 2200).

Using a calculator, the equation is given as follows:

y = 16.96x + 3.

The input of the function and the output of the function are given as follows:

The slope is the rate of change, that is, change in the output divided by change in the input. Hence the slope of 16.96 means that he hiked an average of 16.96 miles a day.

In 52 days, the number of miles hiked is:

y = 16.96(52) + 3 = 885 miles.

The number of days is took to hike 377 miles is found as follows:

377 = 16.96x + 3

x = 374/16.96

x = 22 days.

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Answer:

67

Step-by-step explanation:

5x+4y

5(7)+4(8)

35+32

67

Answer:

The change should Sara receive from the $10 bill is $3.56.

Step-by-step explanation:

Given:

The table shows the prices of some breakfast items at a restaurant.

Item                                      Price

One egg                               $1.69

Slice of bacon                      $1.49

Glass of orange juice          

$1.09

Sara ordered 2 eggs, a slice of bacon, and  a glass of orange juice for breakfast.

The sales tax for the order was $0.48.

She paid for her breakfast with a  $10 bill.

Now, to find the change should Sara receive from the $10 bill.

Bill for the Sara's breakfast:

2 eggs =

A slice of bacon = $1.49.

A glass of orange = $1.09.

The sales tax = $0.48.

Total bill =

Sara paid for the breakfast bill = $10.

Now, to get the change Sara should receive we subtract the amount of bill from the money Sara paid for the bill:

Therefore, the change should Sara receive from the $10 bill is $3.56.

Answer:

Her change would be 3 dollars and 56 cents

Step-by-step explanation:

1.69 times 2 because she ordered 2 eggs

1.49 for the bacon

1.09 for the orange juice

0.48 for the sales tax

add them all up

it would equal 6.44

then subtract 6.44 from 10 which would equal 3.56

To find EF, we will use the formula;

cosθ = adjacent / hypotenuse

From the diagram,

adjacent = 9√3

hypotenuse =EF

cos 30 = 9√3 / EF

EF = 9√3 / cos 30

EF= 18

To find DE, we will use the formula;

tan θ = opposite / adjacent

tan 30 = DE /9√3

DE= (9√3) tan 30

DE= 9

To find m

30° + 90° + m

120° + m

subtract 120° from both-side of the equation

m

m< E = 60°

Answer:

13/15

Step-by-step explanation:

We Know

2/3 of them are chocolate chip cookies.

1/5 of them are sugar cookies.

What fraction of the cookies are chocolate chip or sugar?

2/3 + 1/5 = 10/15 + 3/15 = 13/15

So, 13/15 of the cookies are chocolate chip or sugar.

answer: 12.5% of the pizza each

Answer:

(-4,-2)

Step-by-step explanation:

The equations of the composite functions are (h o h)(x) = (x² + 3)² + 3 and (f o f)(x) = x

From the question, we have the following equations that can be used in our computation:

h(x) = x² + 3

f(x) = 3/4x

From the above, we have

(h o h)(x) = h(h(x))

So, we have

(h o h)(x) = (x² + 3)² + 3

Also, we have

(f o f)(x) = 3/[4(3/4x)]

Evaluate

(f o f)(x) = x

Hence, the composite functions are (h o h)(x) = (x² + 3)² + 3 and (f o f)(x) = x

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The correct option for the given question is c) lim x→a¯ f(x) = f(a) when the function f(x) is said to have jump discontinuity at a point x=a.

Jump continuity is a concept in calculus that describes the behaviour of a function at a specific point where the function jumps from one value to another value without any intermediate values. In other words, a function is considered jump continuous at a point if the function approaches a finite limit from both the left and right sides of that point, but the function values on the left and right sides of the point are not equal.

According to the given information:

The correct notation for the left-hand limit as x approaches a from the left side is lim x→a¯, where the horizontal line above the "a" indicates approaching from the left side.

The statement "lim x→a¯ f(x) = f(a)" means that the limit of f(x) as x approaches a from the left side is equal to the value of f(a) at x = a. This indicates that the function f(x) has a jump discontinuity at x = a, where the function jumps from one value to another value at that specific point.

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\(x^2-8x+10=x^2-8x+16-6=(x-4)^2-6\)

Answer:

Step-by-step explanation:

Which tables give sets of values that satisfy the linear function y = 2x – 6

Answer:

Step-by-step explanation:

13.3 + 6.7 = 20

\(\frac{13.3}{20} = \frac{x}{x + 10} \\\\ 20x = 13.3(x + 10) \\\ 20x = 13.3x + 133 \\\ 20x - 13.3x = 133 \\\ 6.7x = 133 \\\ x = \frac{133}{6.7} \\\\ x ≈ 19.85 \\\ x ≈ 20\)

I hope I've helped you.

The confidence interval is 0.559 < p < 0.641 and expected value is 0.600

To construct a confidence interval for the true population proportion, we can use the formula:

p ± Z * √((p × (1 - p)) / n)

Where:

p = sample proportion (336/560)

Z = critical value for the desired confidence level

95% confidence = Z-value of approximately 1.96

n = 560

Let's calculate the confidence interval:

p = 336/560 ≈ 0.600

Z ≈ 1.96 (for a 95% confidence level)

n = 560

Plugging these values into the formula:

p ± Z × √((p × (1 - p)) / n)

0.600 ± 1.96 × √((0.600 × (1 - 0.600)) / 560)

0.600 ± 1.96 × √((0.240) / 560)

0.600 ± 1.96 × √(0.0004285714)

0.600 ± 1.96 × 0.020709611

0.600 ± 0.040564459

The confidence interval is:

0.559 < p < 0.641

Therefore, the 95% confidence interval for the true population proportion of adults with children is 0.559 < p < 0.641.

For proportions, the expected value is simply the sample proportion, which is approximately 0.600.

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Answer:

1.8

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

to get the area of a parallelogram you just do base times height

The required distance from the corner to each end of the bracket is 5.7 inches.

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

Since the distance from the corner to each end is equal.

So ABC make an isosceles right triangle, where

AB = x inches

AC = x inches

BC = 8 inches

According to the Pythagoras theorem, we have

AB² + AC² = BC²

x² + x² = 8²

2x² = 64

x² = 64/2

x² = 32

x = √32

x = 5.668

Round to the nearest tenth, and we get

x = 5.7

Thus, the distance from the corner to each end is 5.7 inches.

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With  the empirical rule, we can estimate that the number of farms in the sample whose land and building values per acre are between $1100 and $1500 is approximately 50 farms.

The empirical rule (also known as the 68-95-99.7 rule) states that for data sets with a bell-shaped distribution:

68% of the data falls within one standard deviation of the mean.

95% of the data falls within two standard deviations of the mean.

99.7% of the data falls within three standard deviations of the mean.

Using this rule, we can estimate the number of farms whose land and building values per acre are between $1100 and $1500 as follows:

The mean value of land and buildings per acre from the sample of farms is $1300, and the standard deviation is $200.

$1100 is 1.5 standard deviations below the mean:

($1100 - $1300) / $200 = -1.0.

$1500 is 1 standard deviation above the mean:

($1500 - $1300) / $200 = 1.0.

Therefore, we can estimate that approximately:

68% of the farms in the sample have land and building values per acre between $1100 and $1500 plus or minus one standard deviation of $200. This is equivalent to approximately 50 farms, which is 68% of the sample size of 74 farms.

95% of the farms in the sample have land and building values per acre between $900 and $1700 plus or minus two standard deviations of $200. This is equivalent to approximately 70 farms, which is 95% of the sample size of 74 farms.

99.7% of the farms in the sample have land and building values per acre between $700 and $1900 plus or minus three standard deviations of $200. This is equivalent to approximately 73 farms, which is almost the entire sample size of 74 farms.

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Note: The full question is:-

The mean value of land and buildings per acre from a sample of farms is $1300, with a standard deviation of $200. The data set has a bell-shaped distribution. Assume the number of farms in the sample is 74. Use the empirical rule to estimate the number of farms whose land and building values per acre are between $1100 and $1500.

Answer:

27 units

Step-by-step explanation:

12 over 4

36 over x

x = 27

linear equation

Answer:alt  account

Step-by-step explanation:

Answer:

12.

Step-by-step explanation:

if to re-write the given condition, then

\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)

it is clear, the required constant is 12 (12 per hour).

The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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Answer:

t = 2,250

Step-by-step explanation:

If the cost of a chair is Rs. 1400 and the cost of 4 tables and 5 chairs is RS. 16000, find the cost of a table.​

4t + 5c = 16,000       when c = 1,400

4t + 5(1,400) = 16,000

4t + 7,000 = 16,000

subtract 7,000 from both sides:

4t + 7,000 - 7,000 = 16,000 - 7,000

4t = 9,000

divide both sides by 4:

4t/4 = 9,000/4

t = 2,250

Answer:

Is there supposed to be a picture?

There are 120 different combinations of 3 programmers that can be chosen to transfer to the new department

From the question, we have

Total number of programmers, n = 10

Numbers to programmers to select, r = 3

The number of ways of selection could be drawn is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 10 and r = 3

Substitute the known values in the above equation

Total = ¹⁰C₃

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 10!/(7! * 3!)

Evaluate

Total = 120

Hence, the number of ways is 120

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Answer:

6 3/10 mph.

Step-by-step explanation:

Answer: 308.65

:) Good luck

\(1 \ \text{lb} = 0.45359 \ \text{kg}\)

\(140 \ \text{kg} \times (1 \ \text{lb})\div(0.45359 \ \text{kg}) = 308.65 \ \text{lb}\)

\(\bold{140 \ kg=308.65 \ lb}\)