The sum of two numbers is –103. Their difference is 59. Find the numbers.

Answer:3/4

Step-by-step explanation: If you weigh a brick at 2/4 lbs, it will weigh less than a brick that weighs 3/4

The exponential grows at the same rate as the quadratic in the interval

0 ≤ x ≤ 1.

The average Rate of Change function is defined as the average rate at which one quantity is changing with respect to something else changing. In simple terms, an average rate of change function is a process that calculates the amount of change in one item divided by the corresponding amount of change in another.

The average rate of change of a function A = \((f(a) - f(b))/(b-a)\)

Given an exponential function, say f(x), such that f(0) = 1 and f(1) = 2.

A quadratic function, say g(x), such that g(0) = 0 and g(1) = 1.

The rate of change of a function f(x) over an interval a ≤ x ≤ b is given by

\((f(a) - f(b))/(b-a)\).

Thus, the rate of change (growth rate) of the exponential function, f(x) over the interval 0 ≤ x ≤ 1 is given by

 = (2-1)/1 = 1

Similarly, the rate of change (growth rate) of the quadratic function, g(x) over the interval 0 ≤ x ≤ 1 is given by

=(1 - 0)/1  = 1

Therefore, the exponential grows at the same rate as the quadratic in the interval 0 ≤ x ≤ 1.

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Answer:

Your answer would be 100! :)

Answer:

Step-by-step explanation:

Hello!

You need to test at 1% if the average highway gas mileage is the same for three types of vehicles (midsize cars, SUV's and pickup trucks) to compare the average values of the three groups altogether, you have to apply an ANOVA.

                n  |  Mean |  Std. Dev.

Midsize  | 31 |  25.8   |  2.56

SUV’s     | 31 |  22.68 |  3.67

Pickups  | 14 |  21.29  |  2.76

Be the study variables :

X₁: highway gas mileage of a midsize car

X₂: highway gas mileage of an SUV

X₃: highway gas mileage of a pickup truck.

Assuming these variables have a normal distribution and are independent.

The hypotheses are:

H₀: μ₁ = μ₂ = μ₃

H₁: At least one of the population means is different.

α: 0.01

The statistic for this test is:

\(F= \frac{MS_{Treatment}}{MS_{Error}}\)~\(F_{k-1;n-k}\)

Attached you'll find an ANOVA table with all its components. As you see, to manually calculate the statistic you have to determine the Sum of Squares and the degrees of freedom for the treatments and the errors, next you calculate the means square for both and finally the test statistic.

For the treatments:

The degrees of freedom between treatments are k-1 (k represents the amount of treatments): \(Df_{Tr}= k - 1= 3 - 1 = 2\)

The sum of squares is:

SSTr: ∑ni(Ÿi - Ÿ..)²

Ÿi= sample mean of sample i ∀ i= 1,2,3

Ÿ..= grand mean, is the mean that results of all the groups together.

So the Sum of squares pf treatments SStr is the sum of the square of difference between the sample mean of each group and the grand mean.

To calculate the grand mean you can sum the means of each group and dive it by the number of groups:

Ÿ..= (Ÿ₁ + Ÿ₂ + Ÿ₃)/ 3 = (25.8+22.68+21.29)/3 = 23.256≅ 23.26

\(SS_{Tr}\)= (Ÿ₁ - Ÿ..)² + (Ÿ₂ - Ÿ..)² + (Ÿ₃ - Ÿ..)²= (25.8-23.26)² + (22.68-23.26)² + (21.29-23.26)²= 10.6689

\(MS_{Tr}= \frac{SS_{Tr}}{Df_{Tr}}= \frac{10.6689}{2}= 5.33\)

For the errors:

The degrees of freedom for the errors are: \(Df_{Errors}= N-k= (31+31+14)-3= 76-3= 73\)

The Mean square are equal to the estimation of the variance of errors, you can calculate them using the following formula:

\(MS_{Errors}= S^2_e= \frac{(n_1-1)S^2_1+(n_2-1)S^2_2+(n_3-1)S^2_3}{n_1+n_2+n_3-k}= \frac{(30*2.56^2)+(30*3.67^2)+(13*2.76^2)}{31+31+14-3} = \frac{695.3118}{73}= 9.52\)

Now you can calculate the test statistic

\(F_{H_0}= \frac{MS_{Tr}}{MS_{Error}} = \frac{5.33}{9.52}= 0.559= 0.56\)

The rejection region for this test is always one-tailed to the right, meaning that you'll reject the null hypothesis to big values of the statistic:

\(F_{k-1;N-k;1-\alpha }= F_{2; 73; 0.99}= 4.07\)

If \(F_{H_0}\) ≥ 4.07, reject the null hypothesis.

If \(F_{H_0}\) < 4.07, do not reject the null hypothesis.

Since the calculated value is less than the critical value, the decision is to not reject the null hypothesis.

Then at a 1% significance level you can conclude that the average highway mileage is the same for the three types of vehicles (mid size, SUV and pickup trucks)

I hope this helps!

Based on the information we can infer that the equation shown in the image is 1.23 - 0.35 = 0.88 (option B).

To identify the correct equation we must look at the graph and identify the information it provides. In this case we have two squares divided into 100 squares each. Additionally, the square on the left has 88 squares painted in red and 12 squares with an X inside. In the case of the square on the right, it has 23 squares colored in red with an X inside.

In total we have 123 squares painted in red, which in decimal number is equivalent to 1.23. On the other hand, the number of squares painted red and with an X inside is 35, this value would be 0.35.

On the other hand, the squares painted only in red are 88, so the equivalent in decimal numbers would be 0.88. Therefore, the correct way to express this relationship through an equation would be:

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Answer:

The probability that their average salary;

standard error

= 10,000/sqrt(16)

=10,000/4

= 2500  

(77,500 - 75000)/2500

2,500/2500

= 1  

p (z > 1) = .1587

So, the probability that their average salary is more than $77,500 is 0.1587

Step-by-step explanation:

Answer:

$55

Step-by-step explanation:

I am not good at explaining, but, 10% of 50 is 5.

Marking up means the price goes up.

So if 10% of 50 is 5.

50 + 5 = new price

50 with a mark up of 10% = 55

Answer:

if, 1 + 3 - (8 * 334 * 123) = x

then, x = -328652

The BR is the perpendicular bisector of AC by CPCTC (corresponding parts of congruent triangles are congruent).

Based on the given information that angles ABR and ACR are right angles, and AB = AC, we can conclude that triangles ABR and ACR are right triangles.

Using the shared hypotenuse AR and the reflexive property, we can determine that side AB is congruent to side AC.

With this information, the transitive property allows us to conclude that angle BAR is congruent to angle CAR. Next, using the HL congruence postulate, we can prove that triangle ABR is congruent to triangle ACR.

This means that side BR is congruent to side CR, and angle BAC is bisected by line segment BR by the definition of bisector.

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The length of the unlabeled side is 5.5 meters

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

The quadrilateral (see attachment)

Represent the unlabeled side with x

The perimeter of the quadrilateral is the sum of the side lengths

So, we have

Perimeter = 3 + 2 + 3.5 + x

Evaluate

Perimeter = 8.5 + x

This also means that

8.5 + x = 14

So, we have

x = 5.5

Hence, the length of the unlabeled side is 5.5 meters

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The inequality that models this situation is:

l + b ≥ 12

Here we know that Sophie has two jobs, and she must work no less than 12 hours a week.

Then the inequality is of the form:

total number of hours ≥ 12 hours.

Now, we can define the variables:

b =  number of hours babysitting.

l = number of hours lifeguarding.

Then the total number of hours that she works is l + b

Then the inequality is:

l + b ≥ 12

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The difference between the actual quotient and the estimated quotient of 54,114 ÷ 29 is approximately 66.3448275862068965517241379.

To find the difference between the actual quotient and the estimated quotient of 54,114 ÷ 29, we need to first calculate the actual quotient and then the estimated quotient.

Actual quotient:

Dividing 54,114 by 29, we get:

54,114 ÷ 29 = 1,866.3448275862068965517241379 (approximated to 28 decimal places)

Estimated quotient:

Rounding the dividend, 54,114, to the nearest thousand gives us 54,000. Rounding the divisor, 29, to the nearest ten gives us 30. Now, we can perform the division with the rounded values:

54,000 ÷ 30 = 1,800

Difference between actual and estimated quotient:

Actual quotient - Estimated quotient = 1,866.3448275862068965517241379 - 1,800 = 66.3448275862068965517241379

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Answer:

n = 7/2

Step-by-step explanation:

4n^2-22=27

4n^2 = 27 + 22

4n^2/4 = 49/4

sqrtn^2 = sqrt(49/4)

n = 7/2

Answer:

4005

Step-by-step explanation:

3,998 - (-7) = ?

Two negative signs will make a positive sign.

3,998 - (-7) = 3998 + 7 = 4005

So, the answer is 4005

Ahem, here goes, my attempt at a minute-long rap in praise of the parallelogram:

Yo, listen up, the parallelogram is where it's at,

A shape so brilliant, the angles are sat.

Parallel sides that never converge,

Internal angles that never diverge.

Each side an equal length,

A geometry prodigy's dream length.

The diagonals intersect, another line through the middle they meet,

Creating symmetry so neat.

A rectangle it could be,

But it's oblong, not square, can't you see?

With depth and width in perfect balance we see,

A two-dimensional form of complexity.

While the square is simple, the parallelogram is hip,

A mathematical masterpiece, skip, skip, skip!

four right angles keep the shape so tight,

Parallel lines dominate left and right.

Rotated or reflected without a care,

Its structural integrity beyond compare.

triangles form at each corner you'll note,

Acute or obtuse, depends on the protractor's groove.

A versatile shape with reason and purpose galore,

The parallelogram, simply, carries the floor.

From geometry to art, its angles they intrigue,

As a basis for patterns, its potential we can truly plug.

A forgotten form that deserves more acclaim,

Put the parallelogram on geometry's game!

This shape so underrated, rarely appreciated it seems,

But with logic and virtue, strong foundations it gleams.

The parallelogram, the parallelogram, Hooray!

This is why the parallelogram is the best shape, I say!

The value of sin A is, 7/25.

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

The terminal side of angle A goes through the point (−24/25,7/25) on the unit circle.

Now, By definition we get;

⇒ cos A = - 24/25

⇒ Sin A = 7/25

Thus, The value of sin A is, 7/25.

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Answer:

1296

Step-by-step explanation:

\(( \frac{72}{ - 2} {)}^{2} \)

simplify it with factor 2

\(36 \times 2 = 72\)

\(( - 3 6{)}^{2} \)

\(36 \times 36\)

\(\boxed{\Answer:{\boxed{\green{ = 1296}}}}\)

Answer:

x = 5

y = 1

Step-by-step explanation:

2x - y = 9

3x + 4y = 19

We multiply the first equation by 4

8x - 4y = 36

3x + 4y = 19

11x = 55

x = 5

Now we put 5 in for x and solve for y

2(5) - y = 9

10 - y = 9

-y = -1

y = 1

Let's Check the answer

2(5) - 1 = 9

10 - 1 = 9

9 = 9

So, x = 5 and y = 1 is the correct answer.

Answer:

(-10,0)

Step-by-step explanation:

2a =[2(-2) , 2(-3)] = (-4 -6) <--- add them

-3b = [-3(1) . -3(-1)] = (-3 +3) <--- add them

2a - 3b =  

[(-4  -6), (-3  +3)] =

(-10,0)

Answer: Barry's Swimwear sold a greater fraction of the bathing suits in stock as long as the store had fewer than 72 bathing suits in stock.

Step-by-step explanation:

Barry's Swimwear sold 15 out of an unknown number of bathing suits in stock, so we can express this fraction as 15/x, where x is the total number of bathing suits in stock at Barry's Swimwear. Similarly, Philip's Sun Wear sold 5 out of 72 bathing suits in stock, so we can express this fraction as 5/72.

To compare these two fractions, we need to express them with a common denominator. One way to do this is to find the least common multiple of the two denominators, which in this case is 72. To express 15/x with a denominator of 72, we can multiply both the numerator and the denominator by a factor of 72/x. This results in the fraction 15*(72/x)/72 = 15/x. Similarly, we can express 5/72 with a denominator of 72 by multiplying both the numerator and the denominator by a factor of 72/72, which results in the fraction 5*(72/72)/72 = 5/72.

Now that we have both fractions expressed with a common denominator of 72, we can compare them directly. 15/x is greater than 5/72 as long as x is less than 72. This means that Barry's Swimwear sold a greater fraction of the bathing suits in stock as long as the store had fewer than 72 bathing suits in stock.

Answer:

  about -4.7622

Step-by-step explanation:

You want the cube root of -108.

Your calculator will tell you the cube root of -108 is about -4.7622.

__

Additional comment

Some calculators compute roots using logarithms. Since the logs of negative number are not real, they will give you an error if you try to do this directly. You have to know that the odd index root of a negative number is the opposite of the same root of its absolute value.

The prime factoring of 108 is 2²·3³. Factoring out the perfect cube gives the simplified form ...

  ∛-108 = -3∛4

<95141404393>

The Kaumajet Factory will allocate $7.20 of factory overhead to each unit of table lamp using the multiple production department factory overhead rate method with an allocation base of direct labor hours.

Two or more expressions with an Equal sign is called as Equation.

Predetermined overhead rate for Finishing Department = $550,000 / 500,000 direct labor hours = $1.10 per direct labor hour

Predetermined overhead rate for Production Department = $400,000 / 80,000 direct labor hours = $5.00 per direct labor hour

For one unit of table lamp, 2 hours of finishing and 1 hour of production are required, so the total direct labor hours for one unit of table lamp is 2 + 1 = 3 hours.

Finishing Department overhead cost per unit of table lamp = 2 hours * $1.10 per direct labor hour = $2.20

Production Department overhead cost per unit of table lamp = 1 hour * $5.00 per direct labor hour = $5.00

Total factory overhead cost per unit of table lamp

$2.20 + $5.00 = $7.20

Therefore, the Kaumajet Factory will allocate $7.20 of factory overhead to each unit of table lamp using the multiple production department factory overhead rate method with an allocation base of direct labor hours.

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The Kaumajet Factory produces two products-table lamps and desk lamps. It has two separate departments - Finishing and Production. The overhead budget for the Finishing Department is $550,000, using 500,000 direct labor hours. The overhead budget for the Production Department is $400,000 using 80,000 direct labor hours.

If the budget estimates that a table lamp will require 2 hours of finishing and 1 hour of production, how much factory overhead will the Kaumajet Factory allocate to each unit of table lamp using the multiple production department factory overhead rate methods with an allocation base of direct labor hours?

a. $4.91

b. $6.33

c. $7.20

d. $5.00

Answer:

4/6=t/(t+1)

Step-by-step explanation:

4/6=t/(t+1)

Answer:

20x = y

Step-by-step explanation:

the sales of laptops makes 5% of his sales, so you can estimate his total sales of a month if you know his sales of laptops of the same month. This is done by multiplying the amount of sales of laptops that month, x, by 20. You do this because 5% x 20 = 100%.

The profit function is P(x) = -500.523x^2 + 600x - 200.

To find the profit function, P(x), we need to subtract the cost function, C(a), from the revenue function, R(x).

Given:

Cost function: C(a) = 500x^2 + 300

Revenue function: R(x) = -0.523x^2 + 600x - 200 + 300

Profit function, P(x), is obtained by subtracting the cost function from the revenue function:

P(x) = R(x) - C(a)

P(x) = (-0.523x^2 + 600x - 200 + 300) - (500x^2 + 300)

Simplifying the expression:

P(x) = -0.523x^2 + 600x - 200 + 300 - 500x^2 - 300

P(x) = -500x^2 - 0.523x^2 + 600x + 300 - 200 - 300

P(x) = -500x^2 - 0.523x^2 + 600x - 200

Combining like terms:

P(x) = (-500 - 0.523)x^2 + 600x - 200

Simplifying further:

P(x) = -500.523x^2 + 600x - 200

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The range of values of x for which the given approximation is accurate to within the stated error (0.164375 (0.164375)3/3!=9.993513*10(-7))0.000001.

The series ∑∞n=1bnsin(nπLt) is known as the sine series of f(t) and the series a02+∑∞n=1ancos(nπLt) is known as the cosine series of f(t).

The development series of sin(x) near 0 is, according to

Sin(x) = x/1, x/3, and x/5!...............(1) (1)

Using the above estimate, S(x)=x-x3/3! ................(2)

Consequently, the incorrect phrase for the guess is

error=(2)- (1)

= -(x^5/5! - x^7/7! + x^9/9!)

According to the elective series hypothesis, we only want to make sure that the aggregate will be below as much as feasible and that the outright value of the initial term dropped (x5/5!) is not exactly as far as possible.

This declares what

|x^5/5!| < 0.000001

Speaking for x:

x^5=5!*0.000001=0.000120

x=(0.000120)^(1/5)=0.164375

In light of this, the estimation of sin(x) is x-x3/3! has a blatant error for the range [-0.164375,+0.164375] below 0.000001.

Thus,

sin(0.164375)- (0.164375)^3/3!=9.993513*10^(- 7) < 0.000001

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(a) The errors made by the student are:

Incorrectly expanding 49(2) as 24 instead of 98.

Mistakenly factoring the quadratic equation as (y - 8)(y - 1) instead of

\(y^{2} - 9y + 8.\)

(b) The exact solution to the equation is x = 7/11.

(a) The student made two errors in their solution:

Error 1: In the step \("22x + 49(2) = 0,"\) the student incorrectly expanded 49(2) as 24 instead of 98. The correct expansion should be 49(2) = 98.

Error 2: In the step \("y^{2} - 9y + 8 = 0,"\) the student mistakenly factored the quadratic equation as (y - 8)(y - 1) = 0. The correct factorization should be \((y - 8)(y - 1) = y^{2} - 9y + 8.\)

(b) To find the exact solution to the equation, let's correct the errors made by the student and solve the equation:

Starting with the original equation: \(22x + 4 - 9(2) = 0\)

Simplifying: 22x + 4 - 18 = 0

Combining like terms: 22x - 14 = 0

Adding 14 to both sides: 22x = 14

Dividing both sides by 22: x = 14/22

Simplifying the fraction: x = 7/11

Therefore, the exact solution to the equation is x = 7/11.

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Answer:

The correct answer is:

D. Action: Divide both sides by 4.

E. Property: Division property of equality.

Answer:

yes

Step-by-step explanation:

This is correct because 0.1 or 0.10 is greater than 0.03

To find the value of x, we can set the two angle measures equal to each other and solve for x.

Given:

mZA = (4x - 2)°

mZB = (6x - 20)°

Setting them equal to each other:

4x - 2 = 6x - 20

Now, we can solve for x:

4x - 6x = -20 + 2

-2x = -18

Dividing both sides by -2:

x = -18 / -2

x = 9

Therefore, the value of x is 9.

Answer:

The answer is 9.

Step-by-step explanation:

We need to use the fact that the sum of the angles in a triangle is 180 degrees. Let A, B, and C be the three angles in the triangle. Then we have:

mZA + mZB + mZC = 180°

Substituting the given values, we get:

(4x - 2)° + (6x - 20)° + mZC = 180°

Simplifying the left side, we get:

10x - 22 + mZC = 180°

Next, we use the fact that angles opposite congruent sides of a triangle are congruent. Since we know that segment AC and segment BC are congruent, we have:

mZA = mZB

Substituting the given values and simplifying, we get

4x - 2 = 6x - 20

Solving for x, we get:

x = 9

Therefore, the value of x is 9.