Example 2: The GPAs of 20 students are listed.
Make a stem-and-leaf plot for this data.
1.8 2.9 0.9 4.0 3.3
2.4 2.3 1.6 1.6 4.0
1.7 0.5 3.6 3.4 1.9
4.0 2.1 1.9 1.1 0.5

How do I make a stem and leaf plot for these numbers?

Answer:

AC = DF

Step-by-step explanation:

The SSS Postulate occurs when all three corresponding pairs of sides are congruent, therefore, the only missing pair is AC = DF.

Answer:

The full production costs are:

ABC = $22,900,000

PQR = $1,700,000

Step-by-step explanation:

Traditional costing method is a costing method that allocates or applies overhead based on a particular metric determined by a company. It therefore add both direct cost of production and production overheads absorbed to obtain the full cost of production.

Since production overheads in this question is absorbed on demand sales basis, the full production costs for ABC and PQR can be computed as follows:

ANZ Corporation

Computation of Full Production Costs

Particulars                                      ABC                 PQR    

Sales demand                             30,000             15,000

Cost                                                   $                        $    

Direct cost:

Direct materials cost (w.1)        1,350,000           900,000

Direct labor cost (w.2)                900,000          600,000  

Total direct cost                     22,500,000        1,500,000

Indirect cost:

Production overhead (w.3)        400,000          200,000

Full production cost            22,900,000        1,700,000

Workings:

w.1: Computation of direct material cost

Direct material cost = Direct material cost per unit * Sales demand

Therefore;

ABC Direct material cost = $45 * 30,000 = $1,350,000

PQR Direct material cost = $60 * 15,000 = $900,000

w.2: Computation of direct labor cost

Direct labor cost = Direct labor cost per unit * Sales demand

Therefore;

ABC Direct material cost = $30 * 30,000 = $900,000

PQR Direct material cost = $40 * 15,000 = $600,000

w.3: Allocation of production overhead

Production overheads allocated to a model = Production overheads * (Model's Sales Demand / Total Sales demand)

Total Sales demand = 30,000 + 15,000 = 45,000

Therefore, we have:

Production overhead allocated to ABC = $600,000 * (30,000 / 45,000) = $400,000

Production overhead allocated to PQR = $600,000 * (15,000 / 45,000) = $200,000

Answer:

[tex]\boxed{ \sf 41.81}[/tex]

Step-by-step explanation:

The triangle is a right triangle.

We can use trigonometric functions.

[tex]\sf sin(\theta)=\frac{opposite}{hypotenuse}[/tex]

[tex]\sf sin(?)=\frac{2}{3}[/tex]

[tex]\sf ?=sin^{-1}(\frac{2}{3})[/tex]

[tex]\sf ?= 41.81031489...[/tex]

Answer:

[tex]\boxed{41.81}[/tex]

Step-by-step explanation:

∠B is opposite of side AC, which has a length of 2 units. The hypotenuse of the triangle is equivalent to 3 units.

The trigonometric function that uses the opposite side and the hypotenuse is sine function. This is represented by [tex]sin = \frac{opposite}{hypotenuse}[/tex]. The side that is opposite to the angle being solved for is the opposite side (it does not border the angle and it is not the hypotenuse).

However, you are solving for an angle. So, you need to use the inverse sine function ([tex]sin^{-1}[/tex]) to solve this question properly.

Simply type into a calculator [tex]sin^{-1} (\frac{2}{3})[/tex] and it will evaluate the answer to approximately 41.81°.

Answer:

30.5

Step-by-step explanation:

This sequence is defined by f(n)=6.5 + 4.5

The term inside the parentheses (n) is the value you should input to get an output.

n varies from 0 to infinity

Now to find the fifth term put in mind that 0 is the first term.

This means that f(5) isn't the fifth term. In fact, it's the sixth term. So f(4) is the fifth term.

To find f(4) replace n by 4.

f(4) = 6.5 *4 +4.5 = 26+4.5=30.5

Answer:

Hey there!

Your answer would be 4/50. The total times she drawed a purple tile was 4, and she drawed 50 times.

Hope this helps :)

Answer:

4x² + 30x - 2 = 0

Step-by-step explanation:

Given:

Area = 58 square feet

Width = 7 feet

Length = 8 feet

Since the area is 58, writing the equation, we have:

(8 + 2x)(7 + 2x) = 58

Now expand the equation:

56 + 16x + 14x + 4x² = 58

56 + 30x + 4x² = 58

Collect like terms:

30x + 4x² + 56 - 58 = 0

30x + 4x² - 2 = 0

Rearrange the equation to a proper quadratic equation:

4x² + 30x - 2 = 0

The quadratic equation that can be used to determine the thickness of the frame, x is 4x² + 30x - 2 = 0

Answer:

Hope it helps <3

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▹ Answer

Use a graphing calculator. Attached is an image.

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

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Answer:

x=5y-3

Step-by-step explanation:

[tex]4x+12=20y\\4x=20y-12\\x=\frac{20y-12}{4} \\x=\frac{20y}{4}- \frac{12}{4} \\x=5y-3[/tex]

Answer:

[tex]\boxed{15 \ dime \ and \ 10 \ nickel \ coins}[/tex]

Step-by-step explanation:

1 dime = 10 cents

1 nickel = 5 cents

So,

If there are 15 dimes

=> 15 dimes = 15*10 cents

=> 15 dimes = 150 cents

=> 15 dimes = $1.5

Rest is $0.5

So, for $0.5 we have 10 nickels coins

=> 10 nickels = 10*5

=> 10 nickels = 50 cents

=> 10 nickel coins = $0.5

Together it makes $2.00

Answer:

d.

Step-by-step explanation:

[tex]f(g(x))=3(g(x))^2-12=3(5x+3)^2-12=3(25x^2+30x+9)-12=75x^2+90x+27-12=75x^2+90x+15[/tex]

Step-by-step explanation:

A t

eacher is calling on students to present their reports. He calls on Mario first and then chooses the next presenter from the remaining students. The girls’ basketball team is playing against the boys’ basketball team. The coach chooses a captain for the girls’ team and then chooses a captain for the boys’ team. Yasmin is picking flowers from a garden to create a bouquet. She picks a flower, keeps it for the bouquet, and then she picks another. Felipe is making a dentist appointment. First he chooses the day for his appointment, and then he chooses the time from the available openings.

Answer:

A.The school play opens tonight and it is raining.

B.Neva is hungry and she buys a snack from the concession stand.

C. Ari chooses a partner for a group project and then Ezekial chooses a partner from the remaining classmates.

D.Luka paints during school and he stains his shirt.

Answer:

1/5 are towboats

Step-by-step explanation:

In order to find the answer, we need to find the total number of flag vessels. We can find this by adding all the categories together

30k + 10k + 10k= 50k

In total there are 50,000 flag vessels

Of those 50,000, 10,000 of them are tow boats

10,000/50,000 can be simplified to 1/5

1/5 are towboats

Answer:

1/5

Step-by-step explanation:

Well to find the fraction we first need to know the total amount of Flag Vessels.

30,000 + 10,000 + 10,000 = 50,000

If there are 10,000 towboats we can make the following fraction.

10,000/50,000

Simplified

1/5

Thus,

the answer is 1/5.

Hope this helps :)

Answer:

[tex]\boxed{\sf B \ and \ C}[/tex]

Step-by-step explanation:

The triangle is a right triangle.

We can use trigonometric functions to solve.

[tex]\sf sin(\theta)=\frac{opposite}{hypotenuse}[/tex]

[tex]\sf sin(60)=\frac{5.2}{KL}[/tex]

[tex]\sf KL=\frac{5.2}{sin(60)}[/tex]

[tex]\sf sin(90-60)=\frac{3}{KL}[/tex]

[tex]\sf KL=\frac{3}{sin(90-60)}[/tex]

Answer:

0.65463

Step-by-step explanation:

From the given question:

It is stated that 2% of the parts are defective (D) out of 50 parts

Therefore the probability of the defectives;

i.e  p(defectives) = [tex]\dfrac{N(D)}{N(S)}[/tex]

p(defectives) = [tex]\dfrac{2}{50}[/tex]

p(defectives) = 0.04

The probability of the failure is the P(Non-defectives)

p(Non-defectives) =  1 - P(defectives)

p(Non-defectives) =  1 - 0.04

p(Non-defectives) =  0.96

Also , Let Y be the number of non -defective out of the 52 stock parts.

and we need Y ≥ 50

P( Y ≥ 50) , n = 52 , p = 0.96

P( Y ≥ 50) = P(50 ≤ Y ≤ 52) = P(Y = 50, 51, 52)

= P(Y = 50) + P(Y =51) + P(Y=52)    (disjoint events)

P(Y = 50) = [tex](^{52}_{50}) ( 0.96)^{50}(1-0.96)^2[/tex]

[tex]P(Y = 50) = 1326 (0.96)^{50}(0.04)^2[/tex]

P(Y = 50) = 0.27557

P(Y = 51) =[tex](^{52}_{51}) ( 0.96)^{51}(1-0.96)^1[/tex]

[tex]P(Y = 51) = 52(0.96)^{51}(0.04)^1[/tex]

P(Y = 51) = 0.25936

(Y = 52) =[tex](^{52}_{52}) ( 0.96)^{52}(1-0.96)^0[/tex]

[tex]P(Y = 52) = 1*(0.96)^{52}(0.04)^0[/tex]

P(Y = 52) = 0.1197

∴

P(Y = 50) + P(Y =51) + P(Y=52) = 0.27557 + 0.25936 + 0.1197

P(Y = 50) + P(Y =51) + P(Y=52) = 0.65463

[tex]|\Omega|=2\cdot6\cdot52=624\\|A|=1\cdot3\cdot16=48\\\\P(A)=\dfrac{48}{624}=\dfrac{1}{13}[/tex]

Answer:

1/13

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

Hello,

11011 in base 2 is

1 * 16 + 1 * 8 + 0 * 4 + 1 * 2 + 1 in base 10

which is 16 +8+2+1=27

Do not hesitate if you have any question

Answer:

(0, 0), (-1, 0), (2, 0), (3, 0) are the zeros.

First graph in top row is the answer.

Step-by-step explanation:

The given function is, f(x) = x⁴ - 4x³ + x² + 6x

For zeros of the given function, f(x) = 0

x⁴ - 4x³ + x² + 6x = 0

x(x³ - 4x² + x + 6) = 0

Therefore, x = 0 is the root.

Possible rational roots = [tex]\frac{\pm 1, \pm 2, \pm 3, \pm 6}{\pm1}[/tex]

                                      = {±1. ±2, ±3, ±6}

By substituting x = -1 in the polynomial,

x⁴ - 4x³ + x² + 6x = (-1)⁴ - 4(-1)³+ (-1)² + 6(-1)

                           = 1 + 4 + 1 - 6

                           = 0

Therefore, x = -1 is also a root of this function.

For x = 2,

x⁴ - 4x³ + x² + 6x = (2)⁴ - 4(2)³+ (2)² + 6(2)

                           = 16 - 32 + 4 + 12

                           = 0

Therefore, x = 2 is a root of the function.

For x = 3,

x⁴ - 4x³ + x² + 6x = (3)⁴ - 4(3)³+ (3)² + 6(3)

                           = 81 - 108 + 9 + 18

                           = 0

Therefore, x = 3 is a root of the function.

x = 0, -1, 2, 3 are the roots of the given function.

In other words, (0, 0), (-1, 0), (2, 0), (3, 0) are the zeros.

From these points, first graph in top row is the answer.

Answer:

9

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

Answer:

25 students

Step-by-step explanation:

Given the equation of the best line of fit, [tex] y = 0.677x + 1.77 [/tex] , the number of students predicted to be in the matching band, if we have 35 students in the concert band, can be approximated by plugging in 35 as "x" in the equation of the best line of fit, and solve for "y". y would give us the predicted number of students to expect in the marching band.

[tex] y = 0.677(35) + 1.77 [/tex]

[tex] y = 23.695 + 1.77 [/tex]

[tex] y = 25.465 [/tex]

The approximated number of to be in the marching band, with 35 students in the concert band is roughly 25 students.

Answer:25 students

Step-by-step explanation:

We are given [tex]\triangle ABC \cong \triangle EFG[/tex]

The order of the letter sequence is important. The letters pair up based on how they are arranged. We see that A and E are the first letters of the sequences. So this means that angles A and E are the same measure

angle A = angle E

3x+20 = 5x-80

3x-5x = -80-20

-2x = -100

x = -100/(-2)

x = 50

Use this x value to find the measure of angle A

angle A = 3x+20

angle A = 3(50)+20

angle A = 150+20

angle A = 170 degrees

Answer:

3+x

Step-by-step explanation:

sum= addition

a number= a number

Answer:

3+x  

eplanation                                  

Answer:

[tex]\boxed{\sf x - 5 = 10}[/tex]

Step-by-step explanation:

Taking away 5 from x ⇒ subtracting 5 from x

[tex]\large {\sf x - 5[/tex]

Gives 10 ⇒ result is 10

[tex]\large {\sf x - 5 = 10[/tex]

Answer:

Option(A) is correct

Jersey numbers are nominal data that are just replacements for names, so the resulting statistics are meaningless.

Step-by-step explanation:

The given data set in the question are ;33, 29, 97, 56, 26, 78, 83, 74, 65, 47, 58

the range can be determined by finding the highest value and subtract it to the lowest value. In this case the values are:

Highest = 97

Lowest = 71

Range = highest value - Minimum value

Range = 97 - 26 = 71

[tex] Range= 71[/tex]

mean of the data is the summation of all the numbers in the data set divided by the number of given samples.

Mean = (33 + 29 + 97 + 56+ 26 + 78 + 83 74+ 65 + 47 + 58)/11

= 647/11

[tex]Mean value =58.7[/tex]

Now to find the variance of the data set by using below formular

σ²=[ (xᵢ -mean)²]/n-1

[(33-58.7)² +(29-58.7)²+( 97-58.7)²+( 56-58.7)²+( 26 -58.7)²+(78-58.7)²+( 83 -58.7)²+(74-58.7)²+( 65-58.7)²+( 47 -58.7)²+(58 -58.7)²]/10

[tex]Variance=546[/tex]

Now, we will calculate standard deviation by taking square root over variance

σ =√(variance)

σ =√(546)

[tex]Standard deviation= 23.4[/tex]

Hence, the range is 71 ,variance is 546 and standard deviation is 23.4 therefore,

Option A is the answer that is Jersey numbers are nominal data that are just replacements for names, so the resulting statistics are meaningless.

Answer:

26^7=8 031 810 176

Step-by-step explanation:

The word has 7 letters. So the word have 7 places where any of 26 letters can be placed.

Any of 26 letters can stay at 1st place

Any of 26 letters can stay at 2-nd place (because letters can be repeated)

Any of 26 letters can stay at 3rd place  

Any of 26 letters can stay at 4th place

Any of 26 letters can stay at 5th place

Any of 26 letters can stay at 6th place

Any of 26 letters can stay at 7th place  

So N= 26*26*26*26*26*26*26=26^7=8 031 810 176

Answer:

42 gallons 45% antifreeze

28 gallons 95% antifreeze

Step-by-step explanation:

If x is volume of 45% antifreeze, and y is volume of 95% antifreeze, then the total volume is:

x + y = 70

And the total amount of antifreeze is:

0.45 x + 0.95 y = 0.65 (70)

Solving by substitution:

0.45 x + 0.95 (70 − x) = 0.65 (70)

0.45 x + 66.5 − 0.95 x = 45.5

21 = 0.5 x

x = 42

y = 28

The company must produce and sell 350 dishwashers in order to maximize profit.

To determine the number of dishwashers the company must produce and sell in order to maximize profit, we need to find the value of x that corresponds to the maximum point of the profit function.

The profit (P) is given by the equation:

P(x) = Revenue - Cost

The revenue is calculated by multiplying the price per dishwasher (p) by the number of dishwashers sold (x):

Revenue = p * x

The cost is given by the function C(x):

Cost = C(x)

Therefore, the profit function can be expressed as:

P(x) = p * x - C(x)

Substituting the given expressions for p and C(x):

P(x) = (420 - 0.3x) * x - (5000 + 0.3x²)

Expanding and simplifying the equation:

P(x) = 420x - 0.3x² - 5000 - 0.3x²

Combining like terms:

P(x) = -0.6x² + 420x - 5000

To find the value of x that maximizes profit, we need to find the vertex of the quadratic function. The x-coordinate of the vertex can be determined using the formula:

x = -b / (2a)

In our case, a = -0.6 and b = 420:

x = -420 / (2 * -0.6)

x = -420 / (-1.2)

x = 350

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350 dishwashers must the company produce and sell in order to maximize profit.

Maxima means a point at which the function attains the maximum value.

Given the following information:

Price per dishwasher, p = 420 - 0.3x

Total cost of producing x dishwashers, C(x) = 5000 + 0.3x2

Profit= Total Selling price- Total Cost Price

Total Selling price of x dishwasher, S.P= xp

S.P=x(420 - 0.3x)

S.P=420x - 0.3x²

Profit= 420x - 0.3x² - ( 5000 + 0.3x²)

Profit= 420x - 0.3x² - 5000 - 0.3x²

Profit=  -0.6x²+420x-5000

So, profit, f(x)=-0.6x²+420x-5000

To determine the value of x so that maximum profit is possible:

1. Calculate the first derivative of profit function and calculate the value of x by equating it to zero.

2. Select that value of x for which the profit function attains the maximum value, to check the maxima calculate 2nd derivative, if it gives a negative value for the value of x. Then, x is the point of maxima for the given function.

[tex]f(x)=-0.6x^2+420x-5000\\f\prime(x)=-1.2x+420\\f\prime(x)=0\\-1.2x+420=0[/tex]

Calculating the value of x by transposing,

x=420/1.2

x=350

To check maxima, calculating second derivative.

[tex]f\prime(x)=-1.2x+420=0\\f\prime\prime(x)=-1.2[/tex]

2nd derivative is negative, it means that x=350 is the point of maxima.

Thus, a company must produce and sell 350 dishwashers in order to maximize profit.

Learn more about maxima:

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Answer:

Step-by-step explanation:

Given : A right triangle

To do : Solve for x

Solution,

[tex]cos \: 55 = \frac{x}{20} [/tex] ( by definition of cos function, adjacent / hypotenuse )

[tex]0.5736 = \frac{x}{20} [/tex]

multiply both sides of the equation by 20

[tex](0.5736) \times 20 = x[/tex]

Calculate the product

[tex]11.471 = x[/tex]

Swipe both sides of the equation

[tex]x = 11.471[/tex]

Round answer to nearest hundredth

[tex]x = 11.47[/tex]

Hope this helps...

Best regards!!

Answer:

853.8cm^3

Step-by-step explanation:

[tex]h = 9.5cm\\d = 1.5cm + 9.5 = 10.7\\r =d/2=10.7/2=5.35\\\\V = \pi r^2 h\\V = 3.14 \times (5.35)^2 \times 9.5\\\\V =853.8 cm^3[/tex]

Answer:

Step-by-step explanation:

The claim: "Less than 40% of college students graduate with student loan debt."

The null hypothesis: more than 40% of college students graduate with student loan debt." p >= 40%

If the actual percentage of college graduates with student loan debt is 45%. The researcher was supposed to fail to reject the null but since he rejected it when it was actually true, it is a type I error.

A type I error occurs when the research rejects the null when it is actually true.