Liliana puts 35% of each of her paychecks into a savings account. She earns $400 a week, and receives a paycheck at the end of each week. How much money does Liliana have left from her paycheck each week after she sets aside the 35%?
A $140
B $180
C $260
D $280​

Algebraic Operations

Divide 4 by v. The result can be written as:

This result must be tripled, that is, multiplied by 3:

Operating:

Answer:

The inverse is,

\(f^{-1}(x) = \sqrt[5]{x} - 3\)

Step-by-step explanation:

f(x) = (x+3)^5

Finding the inverse,

\(f(x) = (x+3)^5\\or,\\y = (x+3)^5\)

We replace x with y and vice versa

so,

\(x = (y+3)^5\)

Solving for y,

the the 5th root,

\(\sqrt[5]{x} = y + 3\\y = \sqrt[5]{x} - 3\)

hence the inverse function is,

\(f^{-1}(x) = \sqrt[5]{x} - 3\)

Step-by-step explanation:

f(x)=(x+3)×5

Y=5X+15

now

interxchanging x and y we get,

x=5y+15

5y=x-15

y=x-15/5

therefor f~1(x)=x-15/5

Answer:

9/4

Step-by-step explanation:

1. \(\frac{y_2-y_1}{x_2-x_1}\)

2. \(\frac{-1-(-10)}{-1-(-5)}\)

3. \(\frac{9}{4}\)

Therefore, the slope is 9/4.

Answer

x = 32

step by step explanation

Answer: it’s x^3-5x^2+15x-88+390/x+5!

Step-by-step explanation:

Answer:

\(\dfrac{155}{18} \pi \textrm{ cm}\)

Step-by-step explanation:

This problem asks us to find the length of an arc ACB on the circumference of a circle with center O and a radius of 5 cm.

We first must solve for the total circumference (perimeter) of the circle. This is represented by the formula C = 2πr. Hence, the circumference of this circle is:

C = 2π(5) cm

C = 10π cm

Next, we have to find what fraction of 360º the major arc ACB is in order to deduce how much of the circle's total circumference the arc takes up.

\(\dfrac{(360 - 50)\textdegree}{360\textdegree} = \dfrac{31}{36}\)

Finally, we can multiply the amount of circumference that arc ACB takes up by the length of the whole circumference to get the length of arc ACB.

\(\textrm{Length of arc } ABC = \dfrac{31}{36} \cdot 10\pi\)

\(= \dfrac{310}{36} \pi\)

\(= \dfrac{155}{18} \pi \textrm{ cm}\)

Answer:

\(\textsf{Length of major arc $\overset{\frown}{ACB}$}: \;\; \boxed{\dfrac{155}{18}\pi\; \sf m}\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{6.4 cm}\underline{Arc length}\\\\Arc length $= \pi r\left(\dfrac{\theta}{180^{\circ}}\right)$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in degrees.\\\end{minipage}}\)

Angles around a point sum to 360°.  Therefore:

\(\begin{aligned}\implies m \angle BOA&=360^{\circ}-m \angle AOB\\&=360^{\circ}-50^{\circ}\\&=310^{\circ}\end{aligned}\)

Therefore, the given values are:

To find the length of the major arc ACB, substitute the given values into the arc length formula:

\(\begin{aligned}\implies \overset{\frown}{ACB}&=\pi \cdot 5 \cdot \left(\dfrac{310^{\circ}}{180^{\circ}}\right)\\\\&=5\pi \cdot \dfrac{31}{18}\\\\&=\dfrac{155}{18}\pi\; \sf m\end{aligned}\)

Answer:

0.1662 = 16.62% probability that exactly 2 will stay with the same company for more than five years

Step-by-step explanation:

For each graduate, there are only two possible outcomes. Either they stay for the same company for more than five years, or they do not. Graduates are independent. This means that we use the binomial probability distribution 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.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

Eight percent of all college graduates hired by companies stay with the same company for more than five years.

This means that \(p = 0.08\)

Sample of 11 college graduates:

This means that \(n = 11\)

The probability, rounded to four decimal places, that in a random sample of 11 such college graduates hired recently by companies, exactly 2 will stay with the same company for more than five years is: the absolute tolerance is +-0.0001

The tolerance means that the answer is rounded to four decimal places.

The probability is P(X = 2). So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 2) = C_{11,2}.(0.08)^{2}.(0.92)^{11} = 0.1662\)

0.1662 = 16.62% probability that exactly 2 will stay with the same company for more than five years

Answer: D) 7 3/4

Step-by-step explanation:

With averages, we add all the values and divide by the number of values. Here, we know three out of the four days, let's label the day we don't know x. There are four days, so we can divide by four. 7 1/4 is the average, so we can set the equation equal to 7 1/4.

7 1/4 = (7 1/2 + 7 3/8 + 6 3/8 + x) / 4

Let's multiply both sides by 4 to get rid of the fraction. Let's also add what is in the parentheses

29 = 21 1/4 + x

Now we can isolate x by subtracting 29-21 1/4

so

x = 7 3/4 thus the answer is D

Answer:

D) 7 3/4

Step-by-step explanation:

Let x = amount of last feeding.

7 1/4 = (7 1/2 + 7 3/8 + 6 3/8 + x)/4

4 × 7 1/4 = 7 1/2 + 7 3/8 + 6 3/8 + x

28 + 1 = 7 4/8 + 7 3/8 + 6 3/8 + x

29 = 20 10/8 + x

(20 10/8 is the same as 20 + 10/8 = 20 + 8/8 + 2/8 = 20 + 1 + 1/4 = 21 + 1/4 = 21 1/4)

29 = 21 2/8 + x

29 = 21 1/4 + x

x = 29 - 21 1/4

x = 28 4/4 - 21 1/4

x = 7 3/4

Answer: 7 3/4

The complete table of values of the function is

x    0    1    2    3

y     0   9   18   27

The equation of the function is given as

y = 9x

The above function is a linear function

This is so because it has the following representation

y = mx + c

Where

The slope or the constant rate is m and the y-intercept is c

When this function is compared to the equation y = 9x, we have the following notations

Slope, m = 9

y-intercept, c = 0

From the incomplete table of values, we have the x values to be

x = 1, 2, 3

Substitute x = 1, 2, 3 in the equation y = 9x

So, we have

When x = 1, y = 9 * 1 = 9

When x = 2, y = 9 * 2 = 18

When x = 3, y = 9 * 3 = 27

When these values are represented on a table, we have

x    0    1    2    3

y     0   9   18   27

The above represents the complete table

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Complete question

complete the table on the right for the given equation y=9x

x    0    1    2    3

y     0

Answer: £84

Step-by-step explanation:

The number of pupils in the class is 30, and the average number of correct spellings for each pupil is 14.

The total expected correct spellings is 30 x 14 = 420 spellings.

The average sponsorship for each correct spelling is 20p which = £0.20.

Therefore, the number of pounds the class is expected to raise for charity is 420 x 0.20 = £84.

Number of pounds the class is expected to raise for charity is 8400 pounds.

Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.

Number of pupils in the class = 30

Average number of correct spellings for each pupil = 14.

The total expected correct spellings is 30 x 14 = 420 spellings.

The average sponsorship for each correct spelling is 20 pounds

The number of pounds the class is expected to raise for charity is 420 x 20 = 8400 pounds

Thus, number of pounds the class is expected to raise for charity is 8400 pounds.

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Answer:

10.74666666666667 per quart

Step-by-step explanation3 divided 36.24

Answer: B

Step-by-step explanation:

(I) \(3x + 2y = 45\)

(II) \(4x - y = 5\)

Get \(y\) alone in equation (II)

\(4x - y = 5\\y = 4x - 5\)

Insert new equation (II) in equation (I)

\(3x + 2(4x - 5) = 45\\3x + 8x - 10 = 45\\3x + 8x = 45 + 10\\11x = 55\\x = 5\)

Insert \(x = 5\) in equation (II)

\(y = 4 \cdot 5 - 5\\y = 20 - 5\\y = 15\)

Answer:

  y = -5/2x +1

Step-by-step explanation:

You want the slope-intercept form equation for the line through the point (-2, 6) that is parallel to 5x +2y = -4.

The equation of a parallel line can be the same as the given equation, except for the constant. The new constant can be found by substituting the given point coordinates:

  5(-2) +2(6) = c

  -10 +12 = c

  2 = c

Now we know the equation of the parallel line can be written as ...

  5x +2y = 2

Solving for y puts this in slope-intercept form:

  2y = -5x +2 . . . . . . . . subtract 5x

  y = -5/2x +1 . . . . . . . . divide by 2

We don't know what your boxes look like, but we can separate the numbers to make it look like this:

  \(\boxed{y=\dfrac{-5}{2}x+1}\)

#95141404393

Answer:

123

Step-by-step explanation:

The given function is :

\(f(x)=3x^2 - 11x - 21\)

We need to find the value of f(9). It can be done by putting x = 9 in the above function as follows :

\(f(9)=3(9)^2 - 11(9) - 21\\\\=243-99-21\\\\=123\)

So, the value of f(9) is 123.

Answer:

Step-by-step explanation:

y = -3

Answer:

explanation:

(a)

∠1 and ∠8 = 130°, corresponding angles are equal

(b)

∠4  = 130°, vertically opposite angle to ∠1

∠6 = interior angles add to 180°, ∠6 = 180° - 130° = 50°

(c)

∠3 = adjacent angles add to 180°, ∠3 = 180° - 130° = 50°

∠5 = interior angles add to 180°, ∠5 = 180° - 50° = 130°

(d)

∠3 and ∠6 = 50°, alternate angles are equal

Answer:

7/11 or

7

--

11

Step-by-step explanation:

Hope this helps :)

The gradient of the line K that is perpendicular to the line H that has a gradient of 7 is -1/7

Perpendicular lines are lines that form a right angle (90 degrees angle) at the point of their intersection, in which the slope of one of lines is the negative reciprocal of the slope of the other line.

The gradient of the line H = 7

The relationship between the lines K and line H is; Line K is perpendicular to the line H

The slope of a line a, which is perpendicular to another line b with slope m is; -1/m

Therefore, the slope of the line K is -1/7

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is simply changing from percentage form to a decimal form usually, but the fractional form works the same.  Check the picture below.

The key features of the given quadratic functions are listed below.

In Mathematics and Geometry, the graph of any quadratic function would always form a parabolic curve because it is a u-shaped. Based on the first quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0) i.e 3 > 0.

For the quadratic function y = 3x² - 5, the key features are as follows;

Axis of symmetry: x = 0.

Vertex: (0, -5).

Domain: [-∞, ∞]

Range: [-5, ∞]

For the quadratic function y = -2x² + 12x - 15, the key features are as follows;

Axis of symmetry: x = 3.

Vertex: (3, 3).

Domain: [-∞, ∞]

Range: [-∞, 3]

For the quadratic function y = -x² + 1, the key features are as follows;

Axis of symmetry: x = 0.

Vertex: (0, 1).

Domain: [-∞, ∞]

Range: [-∞, 1]

For the quadratic function y = 2x² - 16x + 30, the key features are as follows;

Axis of symmetry: x = 4.

Vertex: (4, -2).

Domain: [-∞, ∞]

Range: [-2, ∞]

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The method is: Find the increase and find the ratio of the increase and the old price.

The percentage increase is 20%

A percentage is defined as the ratio that can be expressed as a fraction of 100.

The method below shows how you would calculate the % increase.

First step: Find the increase:

increase = 480 - 400 = $80

Second step: Find the ratio of the increase and the old price and multiply by 100 to express in percentage:

80/400 * 100 = 20%

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They should charge for its premium in order to have an expectation of $0 for the policy is $85.

Given that, the probability that a 50-year-old male in the U.S. will die within one year is about 0.00142.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

Here, probability of alive 100-0.00142

= 0.99858

P(A)=0.99858A+0.00142(A+60000)

Put A=0, in the obtained function, we get

P(0)=0.99858(0)+0.00142(0+60000)

=0.00142×(60000)

=$85.2

= $85

Therefore, they should charge for its premium in order to have an expectation of $0 for the policy is $85.

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Answer:

Step-by-step explanation:

787

Answer:

1

Step-by-step explanation:

digit in ten-thousands place is 8

digit in tens place is 7

difference:  8 - 7 = 1

Answer:

Step-by-step explanation:

how dare youuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu

Answer:

(0.9464,1.034)

Step-by-step explanation:

First find the mean μ of all values as;

(0.95+1.02+ 1.01+ 0.98 ) /4 =0.99

μ=0.99

Find the standard deviation as;

-For each value subtract the mean and square the results

0.95-0.99 = -0.04 , -0.04² = 0.0016

1.02-0.99= 0.03, 0.03²=0.0009

1.01-0.99= 0.02, 0.02²= 0.0004

0.98-0.99 = -0.01, -0.01²=0.0001

Find mean of squared deviations as;

(0.0016+0.0009+0.0004+0.0001)/4 =0.00075 ----variance

Standard deviation = √0.00075 = 0.0274

δ = 0.0274

n=4

Thus n< 30 , confidence interval for μ = x ± t*δ/√n ---------(i)

Degree of freedom (df) = n-1 =4-1 =3

The t value for 95% confidence with df= 3 is t=3.182

Substituting the values in equation (i)

0.99 ± 3.182 * 0.0274/√4

0.99 ± 3.182 * 0.0274/2

0.99 ± 3.182 * 0.0137

0.99 ± 0.0436

(0.9464,1.034)

Hope it helps...

Have a great day :P

Answer:

A reduction of 450ml

Step-by-step explanation:

Given

\(V_1 = 200ml\) -- To glass 1

\(V_2 = 250ml\) --- To glass 2

Required

The final change to the carton

To do this, we simply add V1 and V2

So, we have:

\(Total = V_1 + V_2\)

\(Total = 200ml + 250ml\)

\(Total = 450ml\)

This implies that the changes is a reduction of 450ml

This statement in the article is wrong because $2.69 is not the mean price ($2.81)

The prices from 5 gas stations surveyed are given as:

$2.79, $2.99, $2.69, $2.89, and $2.69.

There are no outliers in the dataset

So, the dataset can be summarized by the mean

The mean is

Mean = Sum/Count

So, we have

Mean = ($2.79+ $2.99+ $2.69+ $2.89+$2.69)/5

Evaluate

Mean = 2.81

The article quoted $2.69 as the typical price

This statement in the article is wrong because $2.69 is not the mean price ($2.81)

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