complete the table to make sense of the rate. Us the table to help you answer the main question. Kim was able to make 10 snowflakes in 2/5 of an hour. How many snowflakes can she make in 1 hour? How many in 6 hours? Show work including graphing

If a priority mail package has a maximum combined length and girth of 171 inches and is rectangular in shape with a square cross section, the maximum volume allowed is 925.

Given that,

The combined length and girth of a priority mail package cannot exceed 171 inches, according to postal standards.

We have to find calculate the size of the largest volume, cylindrical container that can be sent via priority mail.

We know that,

Let

Length= Breadth =x

Height=y

Volume can be written as

V=x²y

Now,

Combined length and girth is

7x+y=171

y=171-7x

V(x)=x²(171-7x)

V(x)=171x²-7x³

Differentiating with respect to x.

V'(x)=343x-21x²

The maximum value

V'(x)=0

343x-21x²=0

7x(49-3x)=0

x=0

and

49-3x=0

3x=49

x=49/3

Once again differentiating with respect to x.

V''(x)=343-42x

V''(x)=343-42(0)=343>0(min)

V''(x)=343-42(49/3)=-343<0(max)

The maximum volume is

Vmax=V(49/3)=(49/3)(171-7(49/3))

Vmax=925

Therefore, If a priority mail package has a maximum combined length and girth of 171 inches and is rectangular in shape with a square cross section, the maximum volume allowed is 925.

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The probability of getting a queen if a card is drawn out from a pack of 52 cards is 1/13

Probability is the chance of an event to occur with respect to the given conditions.

Probability of an event P(E) = number of favorable outcomes (n)/total number of outcomes(N)

P(E) = n/N

Total cards in a pack (N) = 52

Number of queens (n) = 4

P(getting a queen from pack of cards) = Number of queens/Total cards in a pack

P(E) = n/N

P(E) = 4/52

P(E) = 1/13

Hence, the probability of the given event is 1/13.

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The key phase that we see in our response is "Divide the numerator by the denominator" (option C).

A key phrase refers to a phrase that contains words that define the most important part of a text. A key phrase serves as a summary of a paragraph or larger text.

In this case, the key phrase would serve to establish what was the mathematical procedure that we carried out to solve a mathematical problem. According to the above, it can be inferred that the key phrase must contain the most precise information to describe this procedure.

Based on the above, the correct answer is "Divide the numerator by the denominator" because it exactly describes the procedure that was performed.

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Answer:

The answer is (-7)

Step-by-step explanation:

f(x) = -2x - 3, if f(2)

f(2) = -2(2) - 3 = -4 - 3 = (-7)

Thus, The answer is (-7)

The shorter piece is 56 inches and the longer piece is 180 inches when cut into two halves is a 224-inch pipe.

Given that,

Cut into two halves is a 224-inch pipe. The length of one component is three times that of the other.

We have to determine the shorter piece's length.

We know that,

Let's use the variable L to represent the longer pipe and the variable S to represent the shorter pipe.

Since the pipe will be the sum of L and S, we can create the following equation:

L+S=224

The longer piece is three times the shorter piece, which is another thing we know.

L=3S

Substituting the second equation for the first equation

L+S=224

3S+S=224

4S=224

S=224/4

S=56

The shorter piece is 56 inches.

The lengthier component should be used to replace the following:

L=3S

L=3(56)

L=168

The longer piece is 180 inches.

Therefore, The shorter piece is 56 inches and the longer piece is 180 inches when cut into two halves is a 224-inch pipe.

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The area of the entire floor is: C. 140 square feet.

The entire floor of the building given is composed of a trapezoid, rectangle, and a triangle.

Therefore, the area of the entire floor = area of the trapezoid + area of the rectangle + area of the triangle.

The formula are:

Area of entire floor = 1/2(a + b)h + (l × w) + 1/2(b)(h)

The variables are:

Base (a) = 4 ft

Base (b) = 8 ft

Height of trapezoid (h) = 6 ft

Length of rectangle (l) = 10 ft

Width of rectangle (w) = 8 ft

Base of triangle = 6 ft

Height of triangle (h) = 8 ft

Area of entire floor = 1/2(4 + 8)6 + (10 × 8) + 1/2(6)(8)

Area of entire floor = 36 + 80 + 24 = 140 square feet.

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Answer:

Side h and side

Therefore option a) 5x+4 is the simplified form of the equation.

Equations in mathematics are logical statements with two algebraic expressions on either side of the equals (=) symbol. The equality of the expressions on the left and right in relation to one another is shown. LHS = RHS (left hand side = right hand side) is the first step in any mathematical equation. You can solve equations to determine a variable's or quantity's value. It is not an equation if the statement lacks the "equal to" sign. It will be thought of as a phrase. Later on in this essay, there will be an explanation of the distinctions between an expression and an equation.

Here,

Given:

=>(−3x − 12) + (16 + 8x)

=> -3x-12+16+8x

=> 5x+4

So 5x+4 is the simplified form of the equation

Therefore option a) 5x+4 is the simplified form of the equation

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Answer:

Step-by-step explanation:

You want the amount spent on ads in each medium given the total and relations between amounts spent for newspaper, television, and radio ads.

Let n, t, r represent the amounts spent on ads in newspapers, television, and radio, respectively. The given relations tell you ....

  n +t +r = 87.5

  -n +t +r = 2.9

  n -t = 5.4

The augmented coefficient matrix can be reduced to row-echelon form using a suitable calculator or spreadsheet. This tells you the amounts spent in each medium. The attachment shows this.

__

Additional comment

The value of n can be found by subtracting the second equation from the first. That can be used in the third equation to find t, and both of those values can be used in either of the first two equations to find r.

Select a random sample from each voting district based on the proportion of city residents in the district so that a total of 500 is obtained.

The correct option is (B).

Now, According to the question:

Stratified sampling design divides the given population into small sub-groups called strata. The members of each strata share some common features and at any particular time, a sample is randomly selected from each stratum which is then compared to the entire population. During random sampling, a number proportional to the stratum size is selected from all strata. The randomly selected samples from each strata are then combined to form a common random sample.

Considering that the editor wants to adopt stratified sampling, option B fits (Select a random sample from each voting district based on the proportion of city residents in the district so that a total of 500 is obtained.)

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The complete question is this:

A newspaper editor wants to investigate whether residents of the city support a proposal to build a new high school football stadium. The editor hires a polling firm to conduct a survey and requests that a sample of 500 residents be selected using a stratified sampling design based on voting districts within the city. Which of the following methods will achieve the desired sampling design?

(A) Send a survey to all city residents and use the first 500 returned surveys for the sample.

(B) Select a random sample from each voting district based on the proportion of city residents in the district so that a total of 500 is obtained.

(C) Select one voting district at random, and then select a random sample of 500 from the selected voting district.

(D) Alphabetize a list of all city residents, and then select the first 500 residents on the list, classifying those selected by voting district.

(E) Select the first 500 city residents who attend the next high school football game.

The ratio a : b represented in the table of values is (c) 3 : 5

From the question, we have the following table of values that can be used in our computation:

a b

1.5 2.5

51 85

99 165

Remove the last two entries in the table

So, we have the following representation

a b

1.5 2.5

Express the remaining entries as a ratio

So, we have the following representation

Ratio = a : b

Substitute the known values in the above equation, so, we have the following representation

Ratio = 1.5 : 2.5

Divide the ratio by 0.5

So, we have the following representation

Ratio = 1.5/0.5 : 2.5/0,5

Evaluate the quotients

So, we have the following representation

Ratio = 3 : 5

Hence, the ratio is (c) 3 : 5

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The team a finishes with more points than team b with a probability of 319/512

seven teams play a soccer tournament in which each team plays every other team exactly once

in the first game of the tournament, team a beats team b

We need to find  the probability that team a finishes with more points than team b

Both teams, a and b play 6 matches each

In the first match, a wins. Now they can play 5 matches each

Of the remaining 5 games

a win 0 and b win zero

P(a > b) = 5C1/2^5 x 5C1 / 2^5 = 1/1024

a win 1 and b win 1 or zero

P(a > b) = 5C1/2^5 x(5C0 + 5C1) / 2^5 = 30/1024

a win 2  and b win 2 or 1 or zero

P(a > b) = 5C2/2^5 x(5C0 + 5C1 + 5C2) / 2^5 = 160/1024

a win 3 and b win 3 or 2 or 1 or zero

P(a > b) = 5C3/2^5 x(5C0 + 5C1 + 5C2 + 5C3) / 2^5 = 260/1024

a win 4 and b win 4 or less

P(a > b) = 5C4/2^5 x(5C0 + 5C1 + 5C2 + 5C 3 + 5C4) / 2^5 = 155/1024

a win 5 and b win 5 or less

P(a > b) = 5C1/2^5 x(5C0 + 5C1+ 5C2 + 5C3 + 5C4 + 5C5) / 2^5 = 32/1024

P(a> b) = (1 + 30 + 160 + 260 + 155 + 32)/1024 = 638/1025 = 319/512

Therefore, the  the probability that team a finishes with more points than team is 319/512

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x - y = -15 -3x + 3y = 45 (x, y) = the system of two linear equations using the method of elimination ( 5, 45).

x - y = -15

-3x + 3y = 45

written as

3x - 3y = -15

+3x + 3y = 45

6x = 30

x = 5

Substitute x = 5 into either of the linear equations to find y.

x - y = -15

5 - y = -15

y = 45

Therefore, the solution is (5, 45).

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a) The line belongs to the plane.

b) The line does not belong to the plane.

The equation of a line has the format given as follows:

[tex]\frac{x - x_1}{a} = \frac{y - y_1}{b} = \frac{z - z_1}{c}[/tex]

The equation of a plane has the format given as follows:

Ax + By + Cz + D = 0.

The line will belong to the plane if these two conditions are satisfied:

In standard format, the line for item a is given as follows:

[tex]\frac{x - 1}{4} = \frac{y + 2}{9.5} = \frac{z - 3}{1}[/tex]

Then the conditions are tested as follows:

The two conditions are satisfied, hence the line belongs to the plane.

For item b, we have that:

(-2)(-6) + 1(8) - 5(-3) + 1 = 36.

First condition already not satisfied, hence the second does not need to be tested, meaning that the line does not belong to the plane.

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The solved expression we get for 20% of 92, 45% of 76, 50% of 62, 60% of 92 and 12% of 98 is the numbers 18.4, 34.2,31,55.2 and 11.76.

Given that,

Finding the expression that can be utilised to find

20% of 92, 45% of 76, 50% of 62, 60% of 92 and 12% of 98.

From the Latin word "per centum," which means "by the hundred," the word "percentage" was borrowed. The denominator of percents is 100, making them fractions. In other words, it is the relationship between a part and a whole in which the value of the whole is consistently set to 100.

Take

20% of 92

Multiply 20%×92

=18.4

45% of 76

Multiply 45% ×76

=34.2

50% of 62

Multiply 50%×62

=31

60% of 92

Multiply 60%×92

=55.2

12% of 98

Multiply 12%×98

=11.76

Therefore,

The solved expression we get for 20% of 92, 45% of 76, 50% of 62, 60% of 92 and 12% of 98 is the numbers 18.4, 34.2,31,55.2 and 11.76.

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The ASA (angle-side-angle) congruence rule states that two triangles are congruent if two angles and the side between them are equal in both triangles.

The ASA congruence rule is a fundamental rule of geometry that states that two triangles are congruent when two angles and the side between them are equal in both triangles. This rule is especially important when solving geometry problems, as it can help determine the size and shape of a triangle.

The ASA congruence rule is applicable to all triangles, regardless of their size or shape, and can be used to find the missing angles or sides of a triangle. By applying the ASA congruence rule, students can gain a better understanding of the properties of triangles and other geometric shapes.

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The confidence interval for the task of organizing the poll for the upcoming elections be,

(222.117 , 257.883)

Given, You have been given the task of organizing a poll regarding an upcoming election.

The object is to estimate the proportion of the country that will vote to keep the current government in power.

You have been told to collect a sample and find a 95% confidence interval for the proportion.

This interval is allowed to have a margin of error of 3%. A preliminary investigation suggests that the proportion of people that will vote to keep the current government is 0.74.

We have to find the confidence interval,

Subtract 1 from your sample size. 10 – 1 = 9.

Subtract the confidence level from 1, then divide by two.

(1 – .95) / 2 = .025

For 9 degrees of freedom df and α = 0.025, margin of error is 2.262.

Divide your sample standard deviation by the square root of your sample size.

25 / √(10) = 7.90569415

Now, Multiply 2.262 × 7.90569415 = 17.8826802

For the lower end of the range

240 – 17.8826802 = 222.117

For the upper end of the range

240 + 17.8826802 = 257.883

Hence, the confidence interval be (222.117 , 257.883)

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1.35 as a fraction in simplest form is written as 27/20.

A fraction, which is expressed in the form p/q, where p and q are both integers, denotes a portion of a whole.

To convert 1.35 to a fraction, do the following:

Write the decimal number split by 1 first as follows:

1.35/1

Since the numerator has two digits after the decimal point, we must multiply the numerator and denominator by 102 to get 100, removing the decimal point.

1.35 × 100/ 1 × 100 = 135/100

Because 135 and 100 have 5 in common, we may simplify the fraction to show the same amount: 135 5/100 5 = 27/20.

We can also phrase 1.35 as an improper fraction since the numerator exceeds the denominator.

Therefore, 1.35 as a fraction in simplest form is written as 27/20.

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Since , A club has 42 members and 17 pledges. The club selects a 5-member executive committee composed of a chair and vice-chair, who must be members, and an advisory committee of 3 pledges. The executive committee can be formed in 850668 ways.

a. The number is ⁴²P₅ = 42!/37!

                                    =42×41×40×39× 38 ×37!/37!

                                    =102080160 ways.

b. The number is ⁴²C₅ = 42!/ 5! × 37!

                               =42× 41× 40× 39 ×38×37!/ 5×4×3×2×1 ×37!

                               = 850668 ways.

If you have trouble applying concepts, consider pure mathematics. Select 4 objects out of 24 to replace the first problem. Since there is a replacement, it is a permutation. So the answer is ⁴²P₅= 102080160 possibilities. Obviously there can't be a substitute for the next, so it's a combo. So the answer is ⁴²C₅= 850668 ways.

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(3,1),(4,-2),(-5,4),(4,-1),(-1,-2) match with the given coordinates of the graph thus option (B) will be correct.

A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane.

As per the given coordinates,

The coordinate is the representation of horizontal and vertical distinctions.

The (3,1) is the point that is 3 grid right or horizontal and 1 unit up or vertical from the origin.

Hence "(3,1),(4,-2),(-5,4),(4,-1),(-1,-2) match with the given coordinates of the graph".

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The relative price of ingredient A is 158, ingredient B is 131.1 and ingredient C is 96.

In the given question we have to compute the price relatives for the three ingredients A, B and C.

Now finding the relative price using the formula.

Relative Price(RP) = Ending Cost(E)/Beginning Cost(B) *100

Now from the given table;

Ingredient Beginning(B)      Ending(E)            E/B                 E/B*100

A                     2.50                3.95                    1.58                   158

B                     8.75                9.90                    1.131                   131.1

C                     0.99                0.95                    0.96                   96

Hence, the relative price of ingredient A is 158, ingredient B is 131.1 and ingredient C is 96.

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The right question is

A chemical company produces a special industrial chemical that is a blend of three chemical ingredients. The beginning-year cost per pound, the ending-year cost per pound, and the blend proportions follow. (Round your answers to the nearest integer.)

                    Cost per Pound ($)

Ingredient Beginning Ending Quantity (pounds) per 100

                                                                     Pounds of Product

A                     2.50            3.95                   25

B                     8.75            9.90                   15

C                     0.99            0.95                   70

Compute the price relatives for the three ingredients.

Item Price Relative

A

B

C

6/11 is the probability that a randomly selected student speaks French, given that the student is male

It is a branch of mathematics that deals with the occurrence of a random event.

There are 11 members who speak french and 5 are females in 11 members

5/11

p(a given b) = p(a and b) / p(b).

6 of the people in the group are men that speak french, then the probability of (a and b) becomes 6/40

probability that a person speaks french is 11/40

p(a given b)=6/40/11/40

=6/40×40/11=6/11

Hence, 6/11 is the probability that a randomly selected student speaks French, given that the student is male.

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Check the picture below.

Answer:

0.9475

Hope this Helps!

The change she should receive is $50.50 and we can find it by using simple cost and price calculations.

What is selling price?

Selling price is the amount of money that a seller charges for a product or service. It is the amount of money that a buyer pays for a product or service. The selling price is determined by a variety of factors, such as the cost of production, the perceived value of the product or service, the market demand for the product or service, competitive pricing in the market, and the profit desired by the seller. The selling price may also be affected by the availability of financing options for buyers, taxes, and other applicable fees. The selling price is an important factor in marketing and promoting a product or service. It must be set at the right level to attract buyers and ensure that the seller can make a profit.

Selling price for a shirt = $31.18

Selling price for a hat = $18.32

Total amount she have = $100

Total selling price (for both) = $49.50

So, the remaining amount = $100 - $49.50

                                            = $50.50

So, the change she should receive = $50.50

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Point E does not follow the trend with respect to the other data and is probably an outlier. The value of the car is much higher than other cars with similar miles driven.

"Information available from the question",

In the question:

In a study to determine whether miles driven is a good predictor of trade-in value, 11 cars of the same age, make, model, and condition were randomly selected. The following scatterplot shows trade-in value and mileage for those cars.

Five of the points are labeled A, B, C, D, and E, respectively.

E $6,500+ А $6,000 B $5,500+ $5,000+ $4,500+ Value $4,000 + + 50 60 70 80 90 100 Miles Driven

To find the which point is the most influential with respect to a regression of trade-in value versus miles driven?

Now, According to the question:

According to the points of labeled:

The correct answer is :

To see the figure.

Hence, Point E does not follow the trend with respect to the other data and is probably an outlier. The value of the car is much higher than other cars with similar miles driven.

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The system that has linear inequalities has the point (3, -2) in its solution set is y > -3; y ≥ 2/3x - 4.

We know that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities (makes true both inequalities)

In option B, we have

y > -3 ----> inequality A

y ≥ 2/3x - 4 ----> inequality B

In both inequality, change the values of x and y at the point (3, -2) and then compare the outcomes.

Inequality A

y > -3 ----> is true

Inequality B

y ≥ 2/3x - 4 ----> is true

Therefore

The ordered pair is a solution of the system B

As a result, the point (3, -2) in the solution set of the system with linear inequalities is y > -3; y 2/3x - 4.

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The time required for the total amount in Harrison's account to reach $410 is 4.49 years.

The simple interest formula is expressed as;

A = P( 1 + rt )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given the data in the question;

Plug the given values into the above formula and solve for time t.

A = P( 1 + rt )

A/P = 1 + rt

A/P - 1 =  rt

t = ( A/P - 1 ) / r

t = ( $410/$345 - 1 ) / 0.042

t = ( 13/69 ) / 0.042

t = 4.49 years

Therefore, the time needed to reach accrued amount is 4.49 years.

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The value of g(t) is 18 when x is 2.

Proportionality is defined as, the fact or quality of being in proper balance or relation as to size or quantity, degree, severity, etc

Given that, g(t) varies inversely with t and g(t)=9 when t=4.

According to question,

g(t) ∝ 1/t

Let k be constant of proportionality, then,

g(t) = k/t

Solving for k, we get,

9 = k/4

k = 36

When, t = 2, then

g(t) = 36/2

g(t) = 18

Hence, The value of g(t) is 18 when x is 2.

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