Use the definition of continuity to determine whether f is continuous at a. f(x) = 5x4 - 9x3 + x - 7a = 7

Answer:

The two numbers are .8*160=128 and .85*240=204

Step-by-step explanation:

First sentence:                 x+y=400

Second sentence           .8x+.85y=400-68

Solve y in the first sentence:  y=400-x

Plug first into second:     .8x+.85(400-x)=332

Distribute:                        .8x+.85(400)-.85x=332

Combine like terms:        -.05x+.85(400)=332

Simplify(multiply):              -.05x+      340=332

Subtract 340 on both sides:    -.05x       =332-340

Simplify(subtract):                     -.05x        =-8

Divide both sides by -.05:              x        =-8/-.05

Simplify (division):                           x        = 160

So y=400-x=400-160=240

Answer:

128 and 204. your welcome.

Step-by-step explanation:

Let x = the first number

Let y = the second number

So we can set up two equations:

x+y = 400

.8x + .85y = 400-68

Use substitution:

y = 400 - x

.8x + (.85)*(400-x) = 332

.8x + 340 -.85x = 332

8 = .05x

x = 160

So that makes y = 240

We want the decreased values so:

160*.8 = 128

240*.85 = 204

So the answers are 128 and 204

Answer:

The answer is C.

Step-by-step explanation:

[tex]{( {x}^{4} y)}^{3} = {x}^{4 \times 3} {y}^{3} = {x}^{12} {y}^{3} [/tex]

Answer:

  $3930.56

Step-by-step explanation:

The sum of her required payments is ...

  $950 +238 +149 +78 = $1415

In order for that to be 36% of her income, she must have income that matches ...

  1415 = 0.36 × income . . . . . . . to solve, we divide this equation by 0.36

  1415/0.36 = income ≈ 3930.56

Gina's gross monthly income would need to be $3930.56 to get approved.

_____

Comment on this answer

Often the DTI calculation will include the proposed loan payment. If that is the case, we would need to know the amount of the payment on the loan Gina is applying for. That amount would be added to her existing debt before dividing by 0.36.

Answer:

B.  6Fx + 6Gy = 6H

    Qx + Ry = S

Step-by-step explanation:

Equivalent equations can be created many ways. One of the simplest is to multiply both sides of the equation by the same number. In the answer above, the first equation has been multiplied by 6. Nothing has been done to the second equation.

_____

Comments on other choices

A: some terms have been multiplied by 6. This changes the equation(s) so they are no longer equivalent to the ones you started with.

B: the correct choice

C: see A.

D: the first equation has been multiplied by 6, so that is equivalent to the original. The second equation has the sign of one of the terms changed, so it is now a different equation.

Answer: B.  6Fx + 6Gy = 6H

                     Qx + Ry = S

Answer:

The quotient is 4x- 3.

Step-by-step explanation:

The original price rounded to the nearest cent was; $106.95

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We are given that hat is marked down 45% and its new price is $69.

45% = 0.45

Therefore, we have;

1.00 - 0.45 = 0.55

$69 x 0.55 = 37.95

Then the original price rounded to the nearest cent was;

$69 + 37.95 = $106.95

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Final answer:

To calculate the original price of the hat before a 45% discount resulted in a new price of $69, divide the new price by 0.55. This calculation gives an original price of approximately $125.45, which is the price before the markdown rounded to the nearest cent.

Explanation:

To determine the original price of the hat before the markdown, we start with the new price which is after a 45% reduction. Since 100% - 45% is 55%, the new price represents 55% of the original price. We use the equation new price = (original price) x (percentage after discount) to solve for the original price.

So we have $69 = (original price) x 0.55. To find the original price, we divide the new price by 0.55:

Original price = $69 / 0.55

Calculating this gives us an original price of approximately $125.45. However, we need to round to the nearest cent resulting in $125.45 as the original price of the hat.

Answer:

(-1, -3)

Step-by-step explanation:

We suppose your notation means you want to reflect given point P across the horizontal line y=1.

The x-coordinate will remain the same.

The new y-coordinate will be such that y=1 is the midpoint between the original and its reflection:

(5 + y)/2 = 1

5 + y = 2 . . . . multiply by 2

y = 2 -5 = -3 . . . subtract 5

The reflected point is (-1, -3).

___

The same sort of math applies whenever you have a midpoint and want to find the other end point. Double the midpoint value and subtract the end point you have in order to find the other end point.

Answer:

3/1.5

x=3

y=1.5

x÷y= 2

I hope this helps. Question was worded odd.

If x equals a increased by 50% of a and y equals b decreased by 50% of b, the value of x/y is:

[tex]\frac{x}{y} =2[/tex]

Concept of Ratio

The ratio of a to b is 2 to 3

This can be written as:

[tex]a:b=2:3[/tex]

This can also be re-written as:

[tex]\frac{a}{b}=\frac{2}{3}[/tex]

x equals a increased by 50% of a

x  =  1.5a

x  =  1.5(2)

x  =  3

y equals b decreased by 50% of b

y  =  0.5b

y  =  0.5(3)

y  =  1.5

Therefore, the ratio x/y will be:

[tex]\frac{x}{y} =\frac{3}{1.5} \\\\\\\frac{x}{y} =2[/tex]

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Answer:

1/2

Step-by-step explanation:

The unit fraction for an area (or anything, for that matter) divided into n equal parts is 1/n. For 2 equal parts, it is 1/2.

Answer:

3, 7, 12, 14, 21

Step-by-step explanation:

3 is the minimum value of the data set.

The median is 12. (it is in the middle of 3 and 12 if you look at the question)

The first quartile is 7 (if you count, it is equidistant from either end)

the third quartile is 14. (it is in the middle of 12 and 21 if you look at the question)

21 is the maximum value of the data set.

Answer: 3 is minimum, 7 is first quartile, 12 is median, 14 is third quartile, and 21 is maximum.

Answer:

65.4% to 74.6%

Step-by-step explanation:

68% is approximately plus minus 1 standard deviations.

sigma=sqrt(n*p*(1-p))=sqrt(100*.7*.3)=4.58

so we're looking at  70+4.6 and 70-4.6.

Answer: [tex](65.4\%,\ 74.6\%)[/tex]

Step-by-step explanation:

Given : Out of 100 students sampled, 70 of them said that they hoped to get married someday.

i.e. Sample size : n= 100 and Sample proportion:[tex]\hat{p}=\dfrac{70}{100}=0.7[/tex]

Using standard normal table for z,

Critical z-value(two-tailed) for 68% confidence = [tex]z_{\alpha/2}=0.9945[/tex]

Now, confidence interval for population proportion:-

[tex]\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\=0.7\pm(0.9945)\sqrt{\dfrac{(0.7)(0.3)}{100}}\\\\=0.7\pm0.0455737152863\\\\\approx0.7\pm0.046\\\\=(0.7-0.046,\ 0.7+0.046)=(0.654,\ 0.746)\\\\=(65.4\%,\ 74.6\%)[/tex]

Hence, the approximate percentage of the students in the population who hope to get married someday = [tex](65.4\%,\ 74.6\%)[/tex]

Answer:

12

Step-by-step explanation:

For a cube of side length, L

The following formulas apply:

Area = 6L²

Volume = L³

Area / Volume = 6L² ÷ L³ = 6/L

Try L = 12

Area / Volume = 6/12 = 1/2

Hence 12 is the answer.

Answer:

Step-by-step explanation:

In the equation given, y = 51.20x + 32.96, x is the number of hours worked.  The number of hours worked is multiplied by the rate the plumber charges per hour.  So the choice in the left hand column is "the amount the charges increase for each additional hour off work".  In other words, if he works only 1 hour, x = 1, then the charge for his labor is 51.20(1) = 51.20.  If he works 2 hours, the charge for his labor is 51.20(2) = 102.40.

The 32.96 is fixed as the average cost of the parts.  The choice in the right-hand column is "average cost of parts for each visit".

Here is the set up:

Use a^2 + b^2 = c^2

Let c = length of ladder

Let b = distance of ladder's base from the building.

We must find a.

(a)^2 + (8.2)^2 = (15.5)^2

a^2 = (15.5)^2 - (8.2)^2

a^2 = 173.01

Take the square root on both sides.

sqrt{a^2} = sqrt{173.01}

a = 13.1533265754

We now round off to the nearest tenth of a foot.

a = 13.2 feet

Did you follow?

The distance between the point of the base of the building to the point where the ladder touches it for this case is 13.14 ft approx.

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

Consider the diagram attached below.

We've got:

Usually buildings are vertical, so perpendicular to the ground.

Therefore, we can take ABC a right angled triangle, and therefore, use Pythagoras theorem here:

[tex]|AC|^2 = |AB|^2 + |BC|^2\\\\15.5^2 = |AB|^2 + 8.2^2\\|AB|^2= 240 - 67.24\\\\|AB| = \sqrt{172.76} \approx 13.14 \: \rm ft[/tex]

(took only positive root as length cannot be negative).

Thus, the distance between the point of the base of the building to the point where the ladder touches it for this case is 13.14 ft approx.

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Answer:

240

Step-by-step explanation:

Profit = revenue - cost

p(x) = 3^x - 1.25^x

5 seasons would be x = 5

p(5) = 3^5-1.25^5

p(5) = 239.948

It would be around 240

Answer: The profit after 5 seasons is $239.94.

Step-by-step explanation:

Since we have given that

Revenue function is given by

[tex]t(x)=3^x[/tex]

Cost function is given by

[tex]r(x)=1.25^x[/tex]

So, We need to find the total profit:

As we know the formula for profit:

Profit = Revenue - Cost

[tex]P(x)=t(x)-r(x)\\\\P(x)=3^x-1.25^x[/tex]

We need to evaluate the profit after five seasons:

[tex]P(5)=3^5-1.25^5\\\\P(5)=\$239.94[/tex]

Hence, the profit after 5 seasons is $239.94.

Answer:

Step-by-step explanation:

Answer:

  b = 2√22 ≈ 9.381

Step-by-step explanation:

The Pythagorean theorem tells you ...

  a^2 + b^2 = c^2

Filling in the given numbers, we can solve for b.

  9^2 +b^2 = 13^2

  b^2 = 169 -81 = 88

  b = 2√22 . . . . . . . . take the square root and simplify

Answer:

B. 7/18

Step-by-step explanation:

(-1/6)/(-3/7)

= -1/6 * -7/3

= -1*-7/6*3

= 7/18

(pls give brainliest)

For this case we must find the quotient of the following expression:

[tex]\frac {\frac {-1} {6}} {\frac {-3} {7}} =[/tex]

Applying double C we have:

[tex]\frac {-1 * 7} {6 * -3} =[/tex]

We have by law of signs of multiplication that:

[tex]- * + = -[/tex]

So:

[tex]\frac {-7} {- 18} =\\\frac {7} {18}[/tex]

Answer:

Option B

Answer:

The coordinates of A' are (-9,4)

Step-by-step explanation:

we know that

Each point of the original figure and its image are the same distance away from the line of reflection

so

step 1

reflected the point A(3,4) over the line x=2

The distance of the point to the line of reflection is 3-2=1 units

therefore

The coordinate of the reflected point is (2-1,4) ----> (1,4)

step 2

reflected the point (1,4) over the line x=-4

The distance of the point to the line of reflection is 1-(-4)=5 units

therefore

The coordinate of the reflected point is (-4-5,4) ----> (-9,4)

Answer: is c (-9,4) the guy had it right but wrong letter

Step-by-step explanation:

Answer:

D. poor reputation

Step-by-step explanation:

Step-by-step explanation:

Let's say S is the number of small boxes and L is the number of large boxes.

There were 6 more small boxes than large boxes, so:

S = L + 6

Each small box weighs 45 pounds, and each large box weighs 70 pounds.  The total weight was 1305 pounds, so:

45S + 70L = 1305

We can now solve the system of equations.  Using substitution:

45(L + 6) + 70L = 1305

45L + 270 + 70L = 1305

115L = 1035

L = 9

S = 9 + 6

S = 15

There are 15 small boxes and 9 large boxes.

We are required to determine the number of small boxes shipped and the number of large boxes shipped.

let

x = number of small boxes shipped

y = number of large boxes shipped

Weight of small boxes = 45 pounds

Weight of large boxes = 70 pounds

Total weight of boxes = 1305 pounds

There were 6 more small boxes shipped than large boxes

x = y + 6 (1)

x = y + 6 (1)45x + 70y = 1305 (2)

substitute x = y + 6 into (2)

45x + 70y = 1305

45(y + 6) + 70y = 1305

45y + 270 + 70y = 1305

45y + 70y = 1305 - 270

115y = 1035

divide both sides by 115

y = 1035 / 115

y = 9

Recall,

x = y + 6

x = 9 + 6

x = 15

Therefore,

the number of small boxes shipped is 15 and the number of large boxes shipped is 9

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Answer:

Step-by-step explanation:

you will have to divide them then you will be able to find the missing side

Answer:

Step-by-step explanation:

The radius of the ball is ...

  r = C/(2π) = (16π cm)/(2π) = 8 cm

The formula for the area of a sphere is ...

  A = 4πr²

Filling in the value of the radius, we find the area of the ball to be ...

  A = 4π(8 cm)² = 256π cm² ≈ 804.25 cm²

Then 256π or 804.25 is the number of square centimeters needed to cover the given ball with one coat of latex.

If the ball is only considered to be covered when it has two coats of latex, then twice that amount, 512π or 1608.50 square centimeters of latex are required.

The amount of latex needed to cover a rubber ball with two coats, when the circumference of the ball is 16π cm, is 512π cm².

To calculate the amount of latex needed to paint a rubber ball, we first need to calculate the surface area of the ball. The formula for the surface area of a sphere is 4πr², where r is the radius of the sphere. Given that the circumference of the sphere (rubber ball) is 16π cm, we can substitute this into the formula 2πr to find the radius, which equals 8 cm.

Substituting the radius into the surface area formula, we get 4π(8 cm)² = 4π(64 cm²) = 256π cm². This is the surface area for one layer of latex. But as the toy factory paints their balls with two coats of latex, we need to double this surface area, which gives us 512π cm² as the total area to be covered with latex.

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Answer:

(x, y) = (10, 18)

Step-by-step explanation:

In a parallelogram, adjacent angles are supplementary, and opposite angles are congruent.

∠A = ∠D

54 = 3y

18 = y . . . . . divide by 3

___

∠B = ∠C

12x +6 = 6x +66

6x = 60 . . . . . . . . . subtract 6x+6

x = 10 . . . . . divide by 6

The values of x and y are 10 and 18, respectively.

Answer:

4 hours = 4(60)=240min

2 hours = 2(60)=120min

120<=x<=240

f(x)=1.20||x/2||

So your answer is :

F(X)=1.20||x/2||, if 120<= x<= 240

Answer:

  x ≈ 1.8 cm gives the greatest volume

Step-by-step explanation:

After cutting x cm from each corner in each direction, the cardboard can be folded up to make a box that is x cm deep and (12 -2x) by (10 -2x) in length and width. Clearly, values of x are limited to 5 or less, since cutting 5 cm from each side would leave a width of zero. Then the volume is given by ...

  V = x(12 -2x)(10 -2x)

The plot below shows the value of this cubic equation for volume, and identifies the peak as (x, V) ≈ (1.8, 96.8). That is, a cut of 1.8 cm will result in a box of approximate volume 96.8 cm³.

Answer:

A. $1,056,000 ≤ x ≤ $1,344,000

Step-by-step explanation:

The average annual salary of each of the 48 employees is given as;

$25,000

The total salary that the company pays to its employees annually is thus;

$25,000 * 48 = $1,200,000

Now, the total annual maximum variance  of the employees salaries would be;

$3,000 * 48 = $144,000

The lower limit of the total salary that the company pays to its employees annually is calculated as;

$1,200,000 - $144,000 = $1056000

The upper limit of the total salary that the company pays to its employees annually is calculated as;

$1,200,000 + $144,000 = $1344000

Therefore, the range of the total salary that the company pays to its employees annually is;

$1,056,000 ≤ x ≤ $1,344,000

The total annual salary range for a company with 48 employees, where each earns an average of $25,000 with a maximum variance of $3,000, is calculated by multiplying the number of employees by the minimum and maximum salaries. The range is from $1,056,000 to $1,344,000 (Option A).

The goal is to find the range of the total annual salary that the company pays to its employees. The average annual salary for each of the 48 employees is $25,000, with a possible variance of $3,000 either way. This means that the lowest possible salary could be $22,000 ($25,000 - $3,000) and the highest possible salary could be $28,000 ($25,000 + $3,000).

To find the range of the total salary that the company pays annually, we multiply the number of employees by the minimum and maximum possible salaries.

Therefore, the range of the total salary that the company pays to its employees annually is from $1,056,000 to $1,344,000. The correct answer to the question is A. $1,056,000 ≤ x ≤ $1,344,000.

[tex]

3 \frac{2}{3} + 2.3 \\

\implies 3 \frac{2}{3} + \frac{23}{10} \\

\implies \frac{11}{3} + \frac{23}{10} \\

\implies \frac{110+69}{30}

\implies \frac{179}{30}[/tex]

For this case we must indicate the value of the following expression:

[tex]3 \frac {2} {3} +2.3[/tex]

We have the following mixed number:

[tex]3 \frac {2} {3} = \frac {3 * 3 + 2} {3} = \frac {9 + 2} {3} = \frac {11} {3} = 3.6667[/tex]

So, we have:

[tex]\frac {11} {3} + \frac {23} {10} = \frac {10 * 11 + 3 * 23} {30} = \frac {110 + 69} {30} = \frac {179} { 30}[/tex]

In mixed number we have:

[tex]5 \frac {29} {30}[/tex]

ANswer:

[tex]5 \frac {29} {30}[/tex]

Answer:

B. 11%

Step-by-step explanation:

Using the formula

Real rate of return = nominal rate - inflation rate

Note that the nominal rate of a business is the return on investment in a particular year.

Therefore if Josephine earned a 15% return on her investments last year, her nominal rate is also 15%

Since the inflation rate is 4%

Rate of return = 15%-4%

Rate of return = 11%

1. Find how much gas can be obtained: $10 goes into $2.50 4 times, so you can get 4 gallons.

2. Find how much gas is in the car: 1/4 of the maximum 13 gallons is 3.25 gallons, so there is already 3.25 gallons in your car.

3. Find how many gallons you have total: 4 gallons + 3.25 gallons =

7.25 gallons

The total gallons you have in your car after you put $10 worth of gas is 7.25 gallons.

It is required to find out how many total gallons you have in your car after you put $10 worth of gas.

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

Best way to start this is to figure out how much gas you can get for that $10.  

Since gas is $2.50/gallon and you buy $10 worth, that says you'll get 4 gallons of gas ($2.50 * 4 = $10).  Now figure out how many gallons you have left in your car.  If you car holds 13 gallons, 1/4 of that is 3.25 gallons. Add the 3.25 gallons left to the 4 gallons you bought and you get 7.25 gallons in your car.

Therefore, the total gallons you have in your car after you put $10 worth of gas is 7.25 gallons.

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