A real estate agent, working entirely on commission, makes a weekly average of $850 with da
standard deviation of $260 selling property in the city, and an average of $1340 with a standard
deviation of $390 selling property in the suburbs. Assuming independence, what are the mean and
standard deviation of her total weekly sales?

Answer:

A = 24t² + 2t

Step-by-step explanation:

The shaded area (A) is calculated as

A = area of outer square - area of rectangle

   = (5t)² - t(t - 2)

   = 25t² - t² + 2t

    = 24t² + 2t

Note that the area of the paperboard that remains uncut is:  492.03 inches. This solution is arrived at using the knowledge of the area of a semi-circle and that of a rectangle.

Note that the area of a semi-circle when the diameter is known is:
πd²/8

Where d is the diameter; and

π is 3.14

Recall that the diameter which also coincides with the width is: 22 inches.

Thus the area of the semi-circle  is:

A = (3.14 * 22²)/8

A =  (3.14 * 484)/8

A = 1519.76/8

A  = 189.97in

Next, we find the area of the Full rectangle  which is:

L x B

Where L = 31 in and B = 22in

Thus,

A = 682in

Thus the area of the paperboard that remains is:
Area of the Full Paper board less the Area of the Semi-Circle

= 682 - 189.97

= 492.03in

Thus, the area of the Paperboard that remains is 492.03 inches.

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Full Question:

See attached Image

Answer:

There are 8 apples in basket

The given infinite series Σ 4+3^m/5^m converges with sum equal to 19/8.

To determine whether the given series converges or diverges, we can use the ratio test:

| (4 + 3^(m+1) / 5^(m+1)) / (4 + 3^m / 5^m) |

= | (4/5) + (3/5)(3/4)^m+1 |

As the limit of this expression as m approaches infinity is less than 1, by the ratio test, the series converges.

To find the sum of the series, we can use the formula for a convergent geometric series:

Σ ar^n = a / (1-r)

where a is the first term and r is the common ratio.

In this case, a = 4 and r = 3/5. Therefore, the sum of the series is:

4 / (1 - 3/5) = 19/8.

Hence, the given infinite series converges with sum equal to 19/8.

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Answer:

x≤61/12

Step-by-step explanation:

distribute the -3

8-12x+3≥-49

add like terms

12-12x≥-49

subtract 12 from both sides

-12x≥-61

divide by -12, when you divide by a neg the lessthan/greaterthan sign flips

x≤61/12

The simplified expression is sec(x) csc(x) /1 + tan(x) = 1 / (tan(x) + 1).

The given expression issec(x) csc(x) /1 + tan(x) By substituting the given values, we getsec(x) csc(x) /1 + tan(x)=1/cos(x) * 1/sin(x) /1 + sin(x)/cos(x) Multiply numerator and denominator of LHS by cos(x)sec(x) csc(x) /1 + tan(x)=1/sin(x) / (cos(x) + sin(x))/cos(x)By multiplying numerator and denominator of RHS by cos(x)sec(x) csc(x) /1 + tan(x)=cos(x)/sin(x) / (cos(x) + sin(x))Canceling the cos(x) in the numerator and denominator of RHS, we getsec(x) csc(x) /1 + tan(x) = 1 / (sin(x) / cos(x) + 1)Recall tan(x) = sin(x) / cos(x) sec(x) csc(x) /1 + tan(x) = 1 / (tan(x) + 1)

The given question is,sec(x) csc(x) /1 + tan(x) = 1 / (sin(x) / cos(x) + 1) By multiplying the numerator and denominator of LHS by cos(x), we getsec(x) csc(x) /1 + tan(x)=1/sin(x) / (cos(x) + sin(x))/cos(x) By multiplying the numerator and denominator of RHS by cos(x), we getsec(x) csc(x) /1 + tan(x)=cos(x)/sin(x) / (cos(x) + sin(x)) Canceling the cos(x) in the numerator and denominator of RHS, we getsec(x) csc(x) /1 + tan(x) = 1 / (sin(x) / cos(x) + 1)Recall tan(x) = sin(x) / cos(x)sec(x) csc(x) /1 + tan(x) = 1 / (tan(x) + 1)

Therefore, the simplified expression is sec(x) csc(x) /1 + tan(x) = 1 / (tan(x) + 1).

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Answer:

Pencils = 35

Notebooks = 15

Step-by-step explanation:

15 cents = 15/100 = $0.15

85 cents = 85/100 = $0.85

p + n = 50                    Eq. 1

0.15p + 0.85n = 18       Eq. 2

p = number of pencils

n = number of notebooks

From Eq. 1

p = 50 - n               Eq. 3

Replacing Eq. 3 in Eq. 2:

0.15(50-n) + 0.85n = 18

(0.15*50 + 0.15*-n) + 0.85n = 18

(7.5 - 0.15n) + 0.85n = 18

7.5 + 0.7n = 18

0.7n = 18 - 7.5

0.7n = 10.5

n = 10.5 / 0.7

n = 15

From Eq. 3:

p = 50 - n

p = 50 - 15

p = 35

Check:

From Eq. 2

0.15p + 0.85n = 18

0.15*35 + 0.85*15 = 18

5.25 + 12.75 = 18

e

Answer:

y=3x-2

Step-by-step explanation:

y=mx+b where m=slope and b=y-intercept

y=3x-2

Answer:-8 1/10

Step-by-step explanation:

-2 3/5 - 5 1/2

-13/5 -11/2

-81/10

-8 1/10

The simplified expression of the statement is -81/10

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

negative 2 and three fifths minus 5 and one half.

Express as numbers

So, we have

-2 3/5 - 5 1/2

Convert the fractions to improper fractions

So, we have

-13/5 - 11/2

Take the LCM of the above fractions

(-13 * 2 - 11 * 5)/10

Evaluate the difference

So, we have

-81/10

Hence, the value of the expression is -81/10

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The total amount of dish soap added to both amounts will be 786.89 ml.

Describe addition.

In math, addition is the process of adding two or more integers together.

Since you currently have 224.14 mL of dish soap at home, you decide to buy a 562.75 ml container of it.

We will combine the two amounts together to get the total amount of dish soap.

Dish soap is 786.89 ml total (562.75 ml plus 224.14 ml).

Consequently, there is 786.89 ml of dish soap in total.

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I decided to put them as decimals. 5/12 is equivalent to 0.416. Then there is a decimal already there, which is also 0.416. Then there is 42% which as a decimal is 0.42.

In order it is

0.416, 0.416, and 0.42

The first two are equivalent :P

Answer: 0.416, 5/12, 42%

The middle value is 5/12

Step-by-step explanation: I converted all of them into decimals, so it would be easier to compare. (5/12=0.41666667) (0.416=0.416) (42%=0.42)

If you want me to show you how to convert into decimals just let me know.

Thus, the test for homogeneity follows the same procedures as the test for independence because the assumptions for performing the chi-square test for independence and chi-square test for homogeneity are the same.

The procedures for the chi-square test of homogeneity are the same as for the chi-square test of independence. The data is different for both tests. Tests of independence are used to determine whether there is a significant relationship between two categorical variables from the same population. One population is segmented based on the value of two variables. So there will be a column variable and a row variable.

The chi-square test of homogeneity of proportions can be used to compare population proportions from two or more independent samples, determining whether the frequency counts are distributed identically among different populations.

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Answer:

\( = q < 3\)

Step-by-step explanation:

\(2(q - 8) < - 10 \\ 2q - 16 < - 10 \\ 2q < - 10 + 16 \\ 2q < 6 \\ \frac{2q}{2} < \frac{6}{2} \\ q < 3\)

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

b. is the right answer of your question

Answer:

106.5=0.01065

26.6=0.00266

60.35=0.00266

53.25=0.005325

The probability of the new engine design being approved given that it is low-energy is 0.2, or 20%.

To find the probability of the new engine design being approved, we need to use the concept of conditional probability.

We can use Bayes' Theorem to calculate this conditional probability:

P(A|H) = P(H|A) x P(A) / P(H)

where P(A|H) is the probability of the engine being approved given that it is high-energy, P(H|A) is the probability of the engine being high-energy given that it is approved, P(A) is the overall probability of the engine being approved (irrespective of energy consumption), and P(H) is the overall probability of the engine being high-energy.

Using the values given in the problem, we can substitute in these probabilities:

P(H|A) = 0.1 (given)

P(A) = P(H)P(A|H) + P(L)P(A|L) = 0.50.1 + 0.50.2 = 0.15

P(H) = 0.5 (given)

Therefore, we can calculate:

P(A|H) = 0.1 x 0.5 / 0.15 = 1/3 = 0.333

This means that the probability of the new engine design being approved given that it is high-energy is 0.333, or approximately one-third. Similarly, we can find the probability of the engine being approved given that it is low-energy:

P(A|L) = P(L|A) x P(A) / P(L)

P(L|A) = 1 - P(H|A) = 0.9 (given)

P(L) = 0.5 (given)

P(A|L) = 0.2 * 0.5 / 0.5 = 0.2

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Answer:

Step-by-step explanation:

Answer:

Sum = 180 degrees

Angle A = 85 degrees

Angle B = 95 degrees

Step-by-step explanation:

A triangle's angles will always be equivalent to 180 degrees when finding their sum.

For this triangle, 80, 15, and A will equal 180 degrees.

80 + 15 + A = 180

Combine like terms

95 + A = 180

Isolate variable A by subtracting both sides by 95

A = 85

85 degrees

Similar to a triangle, a straight line is also equivalent to 180 degrees

A + B = 180

Plug in the value for variable A

85 + B = 180

Isolate variable B by subtracting both sides by 85

B = 95

The measure of angle x of the right angled triangle is x = 22°

Given data ,

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

Now , the angle ∠ABC = 90° ( given )

So , the measure of ∠68° + x° = 90°

Subtracting 68° on both sides , we get

x = 90 - 68

x = 22°

Hence , the angle is x = 22°

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The equation based on the information is:

34 = x - 18

In mathematics, an equation is an expression that states that two expressions are equal by joining them with the equal sign =. Equations and their cousins ​​in other languages ​​may have subtly different meanings. For example, in French an equation is defined as containing one or more variables, whereas in English any well-formed expression consisting of two expressions joined by an equal sign is an equation. To solve an equation involving variables, it is necessary to determine which values ​​of the variables make the equation true. The variables for which the equation must be solved are also called unknowns, and the values ​​of the unknowns that satisfy the equation are called the solution of the equation. There are two types of equations: identities and constraints. The ID applies to all values ​​of the variable. A constraint expression applies only to specific values ​​of a variable.

Given that :

Bella is baking 34 cookie for the holiday party tonight. She baked 18 before leaving for school and will bake the ret when he return home.

Therefore, the equation is:

34 = x - 18

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Take into account:

x = speed of the airplane

y = speed of the air

consider that the product in between time and speed is equal to the distance traveled in the time.

Then, if the airplane took 3 hours complete 600 miles, agaist the wind, you have that the distance traveled by the airplane is 3x without wind. The speed of the wind decelerates the airplane. The "distance traveled by the wind is 3y"

Then, when you subtract the previous terms you obtain:

3x - 3y = 600 factorize 3 left side

3(x - y) = 600

Answer: HI = 5.3 cm

Let HI = x

GH = 2cm

m< H = 68 degrees

to find HI, we will need to apply the SOH CAH TOA RULE

HI = hypotenus

GH = adjacent

Cos 68 = adjacent / hypotenus

Cos 68 = 2 / x

Cross multiply

2 = x * cos 68

cos 68 = 0.3746

2 = x * 0.3746

Isolate x

x = 2/0.3746

x = 5.3cm

Therefore, HI is 5.3cm

Answer:

None of the answers provided are equivalent

Step-by-step explanation:

To solve it would be best to simplify each of the expressions you have listed by combining like terms all the x^2 terms have been bolded, the x terms italicized, and the constant terms are underlined

(4x + 1.2) + (2x ^ 2 - 6x + 5) = 2x ^ 2 - 6x + 6.2

(x ^ 2 - 5x + 13) + (x ^ 2 + 3x - 6) = 2x^2 -2x +7

(4x ^ 2 - 6x + 11) + (2x ^ 2 - 4x + 4) = 6x^2 -10x +15

(5x ^ 2 - 8x + 120) + (- 3x ^ 2 + 10x - 13) = 2x^2 + 2x + 107

Based on the given data, we can calculate the control limits using 3-sigma for the diameter of the auto pistons.

a) The value of x is 155.56 mm (rounded to two decimal places).

b) The value of R is 4.44 mm (rounded to two decimal places).

c) Using 3-sigma, the Upper Control Limit (UCL) for the diameter is calculated as:

UCL = x + 3R = 155.56 + 34.44 = 156.93 mm (rounded to two decimal places)

The Lower Control Limit (LCL) for the diameter is calculated as:

LCL = x - 3R = 155.56 - 34.44 = 154.19 mm (rounded to two decimal places)

d) Using 3-sigma, the Upper Control Limit for the Range (UCLR) is calculated as:

UCLR = D4 * R = 2.115 * 4.44 = 7.89 mm (rounded to two decimal places)

The Lower Control Limit for the Range (LCLR) is always 0 in this case since negative ranges are not possible.

e) If the true diameter mean should be 155 mm, the new centerline (nominal line) would be 155 mm. In this case, the UCL and LCL would be calculated using 3-sigma as follows:

UCL = Nominal + 3R = 155 + 34.44 = 156.37 mm (rounded to two decimal places)

LCL = Nominal - 3R = 155 - 34.44 = 153.63 mm (rounded to two decimal places)

Please note that the control limits calculated using 3-sigma assume a normal distribution and the data follows the same pattern in the future.

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The complete question is:

What is the value of x? = x= 155.56 mm (round your response to two decimal places). b) What is the value of R? R= 4.44 mm (round your response to two decimal places). c) What are the UCL, and LCL; using 3-sigma? Upper Control Limit (UCL) = 156.93 mm (round your response to two decimal places). Lower Control Limit (LCL) = 154.19 mm (round your response to two decimal places). d) What are the UCLR and LCLR using 3-sigma? Upper Control Limit (UCLR)= 7.89 mm (round your response to two decimal places). Lower Control Limit (LCLR)= 0.99 mm (round your response to two decimal places). e) If the true diameter mean should be 155 mm and you want this as your center (nominal) line, what are the new UCL and LCL? Upper Control Limit (UCL)= 156.37 mm (round your response to two decimal places). Lower Control Limit (LCL;)= 153.63 mm (round your response to two decimal places). Refer to Table 56.1-Factors for Computing Control Chart Limits (3 sigma) for this problem Auto pistons at Wemming Chung's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows: Day 1 2 3 4 5 Mean x (mm) 150.9 153.2 153.6 153.5 154.6 Range R (mm) 4.0 4.8 4.1 4.8 4.5

The equation of the regression line for the given data can be determined by performing linear regression analysis.

The regression line represents the best-fit straight line that describes the relationship between the independent variable (number of years studied) and the dependent variable (proficiency exam grades). The equation of the regression line can be expressed as y = a + bx, where y is the predicted value of the dependent variable, x is the independent variable, a is the y-intercept, and b is the slope of the line.

To find the equation of the regression line, we first need to calculate the slope and y-intercept using the given data. We can use statistical software or a calculator to perform the regression analysis and obtain the values of a and b. Once we have these values, we can plug them into the equation of the regression line to get the final equation.

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Answer:

See below.

Step-by-step explanation:

Let the price of drinks be x and the price of candies be y.

9x + 4y = 60 --------------------(1)

10x + 2y = 57.50 --------------(2)

2(10x + 2y) = 57.50*2

20x + 4y = 115 --------------(3)

9x + 4y - 20x - 4y = 60 - 115

9x - 20x = -55

-11x = -55

11x = 55

x = 55/11

Put x = 5 in Eq. (1)

9(5) + 4y = 60

45 + 4y = 60

4y = 60 - 45

4y = 15

y = 15/4

So, the cost of one drink is $5 and the cost of one candy is $3.75.

\(\rule[225]{225}{2}\)

Answer:

week one

Step-by-step explanation:

3*5=15 2*5=10

week 1=10

5*3=15

3*3=9

Week 2=9

Week one had more boys

Answer:

Perimeter = 2(length) + 2(width)

Perimeter = 2(17.4x - 0.8) + 2(6X)

Perimeter = 34.8x - 1.6 + 12x

Perimeter = 46.8x - 1.6

Answer:

The area of a parallelogram is given by the formula A = base x height. In this case, the base has a length of x meters, and the height is x - 1 meters. So we can write:

A = x(x - 1)

We are told that the area is 306 square meters, so we can set up an equation:

x(x - 1) = 306

Expanding the left side gives:

x^2 - x = 306

Bringing all the terms to one side gives a quadratic equation:

x^2 - x - 306 = 0

We can solve for x using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

Here, a = 1, b = -1, and c = -306, so:

x = (1 ± sqrt(1 - 4(1)(-306))) / 2(1)

x = (1 ± sqrt(1 + 1224)) / 2

x = (1 ± sqrt(1225)) / 2

x = (1 ± 35) / 2

So x is either (1 + 35) / 2 = 18 or (1 - 35) / 2 = -17/2. Since x represents a length, it cannot be negative, so the value of x is 18 meters.

Therefore, the answer is x = 18.