A box of crackers contains 16 1/2 ounces. A serving of crackers is 1 1/2 ounces. How many servings are in the box of crackers?

The calculated scale factor from ABC to A'B'C is 1/3

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

The triangles

From the triangles, we have the following parameters

A = (0, 3)

A' = (0, 1)

Using the above as a guide, we have the following:

Scale factor of the dilation = A'/A

So, we have

Scale factor of the dilation = (0, 1)/(0, 3)

Evaluate

Scale factor of the dilation = 1/3

Hence, the scale factor of the dilation is 1/3

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Answer:

45

scalene

acute

Step-by-step explanation:

Answer: The triangle classified by the sides is 59 degrees.  The triangle is classified by the angel is 1

Step-by-step explanation:

Answer:

99% Confidence Interval = (5.824,6.036)

Step-by-step explanation:

The coffee and soup machine at the local subway station is supposed to fill cups with 6 ounces of soup. Ten cups of soup are bought with results of a mean of 5.93 ounces and a standard deviation of .13 ounces. Construct a 99 percent confidence interval for the true machine-fill amount.

The formula for confidence interval

= Mean ± z × σ/√n

Mean of 5.93 ounces

Standard deviation of .13 ounces.

n = 10 cups

z= z score of 99% confidence interval = 2.58

Confidence Interval =

5.93 ± 2.58 × 0.13/√10

5.93 ± 2.58 × 0.0411096096

Confidence Interval = 5.93 ± 0.106

= 5.93 - 0.106

= 5.824

= 5.93 + 0.106

= 6.036

Hence, Confidence Interval = (5.824,6.036)

Answer:

-102.1

Step-by-step explanation:

When adding negative numbers, act as if you are subtracting that same number, but in its positive form.

So in reality, you could rewrite the equation as: (-7.8) - 12 - 82.3 = -102.1

Answer:

I did the math there is no answer

We want to find a polynomial

f(x) = a x³ + b x² + c x + d

such that the roots of f are x = -3, x = -1, and x = 4, and f(x) takes on a value of -24 when x = -2.

The factor theorem for polynomials tells us that we can factorize f(x) as

a x³ + b x² + c x + d = a (x + 3) (x + 1) (x - 4)

Expand the right side:

(x + 3) (x + 1) (x - 4) = x³ - 13x - 12

So we have

a x³ + b x² + c x + d = a x³ - 13a x - 12a

In order for both sides to be equal, the coefficients of both polynomials on terms of the same degree must be equal. This means

a = a (of course)

b = 0 (there is no x² term on the right)

c = -13a

d = -12a

We also have that f (-2) = -24, which means

f (-2) = a (-2 + 3) (-2 + 1) (-2 - 4)

-24 = 6a

a = -4

which in turn tells us that c = 52 and d = 48.

So we found

f(x) = -4x³ + 52x + 48

The class of the equation and the cross section equation are;

The equation is a hyperboloid of two sheets

The cross sections are;

Equation at z = 0 is; y²/8 - x²/8 = 1

Equation at y = -4 is; x²/8 + z² = 1

Equation at y = 0 is; x²/8 + z² = -1

Equation at y = 4 is; x²/8 + z² = 1

Equation at x = 0 is; y²/8 - z² = 1

An equation is a mathematical statement which indicates the equivalence two expressions by joining them with the '=' sign.

The equation can be presented as follows;

y² = x² + 8·z² + 8

y² - x² - 8·z² = 8

y²/8 - x²/8 - z² = 1

The above equation is the equation of an hyperboloid of two sheets, where;

a² = 8, b² = 1, and c² = 8

Please find attached the diagram of the surface, created with an online 3D graphing tool.

The equation for the cross section at z = 0, can be obtained by plugging in z = 0, into the equation as follows;

y²/8 - x²/8 - 0 = 1

y²/8 - x²/8 = 1

The above equation is the equation of an hyperbola in the xy plane

The equation for the cross section at y = -4, can be obtained by plugging in y = -4, into the equation as follows;

4²/8 - x²/8 - z² = 1

- x²/8 - z² = 1 - 4²/8 = -1

- x²/8 - z² = -1

x²/8 + z² = 1

The above is an equation of an ellipse in the xz plane

The equation for the cross section at y = 0, can be obtained by plugging in y = 0, into the equation as follows;

0²/8 - x²/8 - z² = 1

- x²/8 - z² = 1

Therefore; x²/8 + z² = -1

The equation for the cross section at y = 4, can be obtained by plugging in y = 4, into the equation as follows;

4²/8 - x²/8 - z² = 1

- x²/8 - z² = 1 - 2 = -1

x²/8 + z² = 1

The above equation is the equation of an ellipse in the xz plane

The equation for the cross section at x = 0, can be obtained by plugging in x = 0, into the equation as follows;

y²/8 - 0²/8 - z² = 1

y²/8 - z² = 1

The equation is the equation of an hyperbola in the yz plane

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The probability that each bill is a $1 bill is given as follows:

1/16.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

The bills are replaced, hence we consider that for each trial, there is a 1/4 probability of selecting a $1 bill, as one out of the four bills are of $1.

Hence the probability that each bill is a $1 bill is obtained as follows:

p = 1/4 x 1/4

p = 1/16.

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Answer: 7 units

Step-by-step explanation:

Using the distance formula, the square root of (X2 - X1)^2 + (Y2 - Y1)^2 is equal to the distance between two points.

5-(-2) = 7 9^2 equals 49

-3-(-3) = 0

The square root of 49 plus 0 is 7, so the answer is 7 units.

The profit from Lube for Store A would be = $8.31.

Unit profit can be obtained by subtracting the cost of the product from the selling price.

Data and calculations:

Selling price for oil change = $275

Percentage of total oil revenue = 39.1%

Cost of oil per gallon = $21.25

Selling price per gallon = $29.56 ($21.25 x $1,391)

Total income = $8.31 ($29.56 - $21.25)

Therefore, the profit from Lube for Shop A would be= $8.31.

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Complete question:

Shop A charges $275.00 for an oil change and has a gross oil profit percent of 39.1% for its total oil gross profit %. Shop B charges $275.00 for an oil change and has a gross oil profit percent of 28.4% for its total oil gross profit %. Both shops pay $21.25 per gallon of oil. What is the Profit per Lube for Shop A?

Answer:

502.5pi or 1578.1415

Step-by-step explanation:

find area of one triangle (BH divided by 2), then multiply it by two since there are two, then find area of circle(pir^2),  divide in half because it is a semi-circle, add the areas together

Answer: 325

Explanation:

Let the number of adult tickets be x

( since there are an unknown amount of tickets for adults, we already know how many student tickets there are)

Let the number of student tickets be x+60

710=x+x+60

710=2x+60

 -60        -60

650=2x

650/2

= 325

Adult tickets=325

Student tickets=385

Answer:

lol

Step-by-step explanation:

Answer:

math kinda sucks. :) Brainliest pls???

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

5% of 120 is 6.

Well, if 5% of them are real, that means 95% of the calls they get each day are false alarms.  

If we set up our inequality and multiply (Which i'm assuming you know how to do) We would get 114. Therefore, 114 calls would be false alarms.

a) The algebraic fraction \(\frac{{x + 2}}{{(x - 1)^2}}\) is proper. b) The algebraic fraction \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\) can be expressed as \(-\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

Let's solve each part step by step and determine whether the fraction is proper or improper, and then express it accordingly.

a) \(\frac{{x + 2}}{{(x - 1)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 1 (linear term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is less than the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

\(\frac{{x + 2}}{{(x - 1)^2}} = \frac{A}{{x - 1}} + \frac{B}{{(x - 1)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 1)^2)\) to eliminate the denominators:

  (x + 2) = A(x - 1) + B.

Expand the equation and collect like terms:

  x + 2 = Ax - A + B.

Equate the coefficients of like terms:

  Coefficient of x: 1 = A.

  Constant term: 2 = -A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = 1.

Substituting A = 1 into the constant term equation: 2 = -1 + B, we find B = 3.

Therefore, the partial fraction decomposition is:

  \(\frac{{x + 2}}{{(x - 1)^2}} = \frac{1}{{x - 1}} + \frac{3}{{(x - 1)^2}}\).

b) \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 2 (quadratic term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is equal to the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = \frac{A}{{x - 4}} + \frac{B}{{(x - 4)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 4)^2)\) to eliminate the denominators:

  (4x^2 - 31x + 59) = A(x - 4) + B.

Expand the equation and collect like terms:

  4x^2 - 31x + 59 = Ax - 4A + B.

Equate the coefficients of like terms:

Coefficient of \(x^2\): 4 = 0 (No \(x^2\) term on the right side).

Coefficient of x: -31 = A.

Constant term: 59 = -4A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = -31.

Substituting A = -31 into the constant term equation: 59 = 4(31) + B, we find B = -25.

Therefore, the partial fraction decomposition is:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = -\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

The above steps provide the solution for each part, including determining if the fraction is proper or improper and expressing it in partial fractions.

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The function that is decreasing on the same interval as the given function f(x) is h(x) = 2x^2 + 8x + 3.

To determine if a function is increasing or decreasing, we look at the sign of its derivative. If the derivative is positive, the function is increasing, and if the derivative is negative, the function is decreasing.

Taking the derivative of h(x) with respect to x, we get h'(x) = 4x + 8. To find the interval on which h(x) is decreasing, we need to find the values of x for which h'(x) < 0.

Setting h'(x) < 0, we have 4x + 8 < 0. Solving this inequality, we find x < -2.

Therefore, h(x) is decreasing for x < -2. Since the interval where h(x) is decreasing matches the interval for the given function f(x), we can conclude that h(x) = 2x^2 + 8x + 3 is the function that is decreasing on the same interval as f(x).

Overall, the function h(x) = 2x^2 + 8x + 3 is decreasing on the interval x < -2, which aligns with the interval of the given function f(x).

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The missing quantities are

Social Security= $217

Medicare = $‭50.75‬

Net Pay is $‭2,633.67‬

First, Taxable income is therefore;

= 3,500 - (76.90 x 4 )

= $‭3,192.4‬0

Federal Income Tax (FIT).

With taxable income of $‭3,192.4‬0, the tax is $565.15 plus 28% of anything above $‭3,073.

= 565.15 + (28% x (‭3,192.4‬0 - 3,073))

= 565.15 + 33.43

= $‭598.58

and, Social Security

= Gross pay x 6.2%

= 3,500 x 6.2%

= $‭217‬

and, Medicare

= 3,500 x 1.45%

= $‭50.75‬

Then, the Net Pay

= 3,500 - 598.58 - 217 - 50.75

= $‭2,633.67‬

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Answer:

60

Step-by-step explanation:

I thinks it's the answer

The total cost is $12.74

In this question, we have been given the cost of 1 gallon of milk, 1 gallon of ice-cream and 1 1b of strawberry.

1 gallon of milk costs $2.48,

1 gallon of ice-cream costs $1.49

and 1b of strawberry costs $0.58

You buy 3 gallons of milk, 2 gallons of ice cream, and 4 lbs of strawberries.

So by unitary method total cost would be,

(3 * 2.48) + (2 * 1.49) + (4 * 0.58) = $12.74

Therefore, the total cost is $12.74

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In this case, we'll have to carry out several steps to find the solution.

Step 01:

data:

hot dog stand

Step 02:

We must analyze the problem to find the solution.

total money = $21

1 soft drink:

$21 - $1.25 = $19.75

hot dogs:

$19.75 / $2.50 = 7.9

The answer is:

He can purchase 7 hot dogs

Answer:

(5.6x10^4)x(1.3x10^8) = 7.28 x 10^12

Answer: =7.28x100010001

Step-by-step explanation: 5.6x104x(1.3x108)

Simplifies to:

7.28x100010001

Answer:

DEF/3 = BAC

AC(7) x 3 = 21

Answer:

6.03, 4, 10.03

Step-by-step explanation:

The definition of an integer is an a whole number that's not a fraction. None of these numbers are fractions, therefore they are integers. The answer is all of them :)

Answer:

y=1/3x+2

Step-by-step explanation:

................

Answer:

y=1/3x+2

Step-by-step explanation:

slope intercept form: y=xm+b

6y=2x+12

/6       /6

y=2/6x+2

y=1/3x+2

have a great day!

Answer:

Step-by-step explanation:

alright l like this answer too

Answer:

The correct option is b) \(P(D|A)=P(A|D)P(D)\).

Step-by-step explanation:

The probability of selecting the different types of tires are:

P (A) = 0.40

P (B) = 0.15

P (C) = 0.45

The defective rate for the different types of tires are:

P (D|A) = 0.02

P (D|B) = 0.01

P (D|C) = 0.05

The formula to compute the probability that the tire is defective given that it is Brand A tire as follows:

\(P(D|A)=P(A|D)P(D)\)

Answer:

Her gross earnings for that week were $ 363.24.

Step-by-step explanation:

Since Stacy Arrington is paid $ 0.73 for sewing a jacket collar, $ 0.86 for a sleeve with cuffs, and $ 0.94 for a lapel, and one week she sewed 318 jacket collars, 112 sleeves with cuffs, and 37 lapels, to find her gross earnings you must perform the following calculations:

(318 x 0.73) + (112 x 0.86) + (37 x 0.94) = X

232.14 + 96.32 + 34.78 = X

363.24 = X

Therefore, her gross earnings for that week were $ 363.24.

Answer:

64/100 or 0.64 :)

Step-by-step explanation:

It seems that the square has 100 small squares in total. Out of those small squares, 64 are green.

64/100 = 0.64