You randomly survey middle school students and high school students about whether they prefer spring or winter. The results
are shown in the two-way table. Find the percent of middle school students that prefer each season and the percent of high school students that prefer each season

Using the a pair of adjacent angles, we will see that:

Z° = 137°

When we have an intersection between two lines, we know that any pair of adjacent angles (they share a side) are congruent angles, thus, their measures add up to 180°.

Then here we can write a linear equation for z.

z + 43 = 180

Solving that for z, we will get:

z = 180 - 43

z = 137

That is the measure of the angle.

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Answer:

The correct answer is D. y = 3.35x + 73.96.

Step-by-step explanation:

D. y = 3.35x + 73.96

Answer:

  20 cubic yards

Step-by-step explanation:

You want to know the volume in cubic yards of a layer of topsoil that is 6 inches deep over an area 31 feet by 34 feet.

You know that ...

Then the dimensions of the volume being applied are ...

  6 inches = 6/36 yards

  31 feet = 31/3 yards

  34 feet = 34/3 yards

The volume is the product of the dimensions of the space:

  V = LWH

  V = (31/3 yd)(34/3 yd)(6/36 yd) ≈ 19.519 yd³

About 20 cubic yards are needed to fill the garden.

[tex]\begin{array}{ccll} words&minutes\\ \cline{1-2} 90 & 4\\ x& 10 \end{array} \implies \cfrac{90}{x}~~=~~\cfrac{4}{10} \\\\\\ \cfrac{ 90 }{ x } ~~=~~ \cfrac{ 2 }{ 5 }\implies 450=2x\implies \cfrac{450}{2}=x\implies 225=x[/tex]

Using a system of equations, the number of each type of coffee that Julia and her husband should buy is as follows:

A system of equations is two or more equations solved concurrently or at the same time.

A system of equations can also be described as simultaneous equations.

The cost per pound of City Roast Columbian coffee = $6.50

The cost per pound of French Roast Columbian coffee = $8.20

The total quantity of the blend = 34 pounds

The cost per pound of the blend = $6.90

The total cost of the 34 pounds = $234.60 ($6.90 x 34)

Let the number of pounds of City Roast coffee = x

Let the number of pounds of French Roast coffee = y

x + y = 34 ... Equation 1

6.5x + 8.2y = 234.6 ... Equation 2

Multiply Equation 1 by 6.5:

6.5x + 6.5y = 221 ... Equation 3

Subtraction Equation 3 from Equation 2:

6.5x + 8.2y = 234.6

-

6.5x + 6.5y = 221

1.7y = 13.6

y = 8

Substitute, y = 8 in Equation 1:

x + y = 34

x = 34 - 8

x = 26

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Answer:

Step-by-step explanation:

The terms "4/10, 2/30, n/60" indicate that the buyer can take a discount of 4% if they pay within 10 days from the invoice date, or pay the full amount within 30 days from the invoice date. If the payment is made after 30 days, the buyer must pay the full amount plus any late fees that may apply.

Since the invoice was dated October 15 and the payment was sent on October 28, the payment was made within 30 days from the invoice date, so the buyer cannot take the 4% discount.

The total cost of 50 pairs of shoes at $85 per pair is 50 * 85 = $4250.

Therefore, the total amount of the check would be $4250, which is the full amount of the purchase price without the 4% discount.

Now , to find the area

Total area of figure = Area of first Triangle + Area of second triangle

The area of the triangle = ( 1/2 ) x Length x Base

Total area of figure = ( 1/2 ) x ( 36 x 15 ) + ( 1/2 ) x ( 15 x 8 )

= ( 1/2 ) x 540 + ( 1/2 ) x 120

= 270 + 60

= 330 inches²

Therefore , the value is 330 inches²

Hence , The area of the figure is 330 inches²

The two lengths that Bottom 7%: L= 6.04 cm

Top 7%: L= 6.22 cm

What does "z-score" mean?

The Z-score provides information on how far a given value deviates from the standard deviation. The amount of standard deviations a given data point is above or below the mean is represented by the Z-score, also known as the standard score.

                                       The level of variability within a particular data collection is effectively reflected in the standard deviation.

Mean length of the population (μ) = 6.13 cm

Standard deviation (σ) = 0.06 cm

The z-score for any given length 'X' is

        Z = X - μ/σ

     What we want to know is the length at the 7-th percentile and at the 93-rd percentile.

According to a z-score table, the 7-th percentile has a correspondent z-score of -1.476 and the 93-rd percentile has a z-score of 1.476. Therefore, the bottom 7% and top 7% are separated by the following lengths

      Z(Xb) = Xb - μ/σ

  - 1.476 = Xb - 6.13/0.06

      Xb = 6.04

  z(Xt ) = Xt - μ/σ

   1.476 = Xt - 6.13/0.06

     Xt = 6.22

Bottom 7%: L= 6.04 cm.

Top 7%: L= 6.22 cm.

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The value of JI in the given triangle is 11.

A triangle is a polygon with three sides, vertices and angles.

Given that, in a triangle DEF, J is the intersection of the three medians.

EI = 33, we are asked to find the value of JI,

Since, all the median is intersecting at J, therefore, J is the centroid.

We know that, the centroid divides each median into two parts, which are always in the ratio 2:1.

Therefore,

Let, EI = 3x,

JI = x,

Therefore, JI = 11

Hence, the value of JI in the given triangle is 11.

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The complete question is :

In Δ DEF, J is the intersection of the three medians. If EI = 33, find JI.

Figure is attached

The values of sec a - cosec a/sec a+cosec a is 4/25.

The trigonometric ratios of any acute angle in a right-angled triangle are the ratios of its sides to that angle.

In a right-angled triangle,

Here we have

tan A = 21/29

As we know Tan θ = Opposite side/Adjacent side  

=> Opposite side = 21

=> Adjacent side = 29

In a right-angle triangle,

=> Hypotenuse² = Opposite side² + Adjacent side²  

=> Hypotenuse² = 21² +29²    

=> Hypotenuse² = 441 + 841    

=> Hypotenuse² = (35.8)²  

Cos a = Adjacent side /Hyopenuse = 29/ 35.8

Sin a = Opposite side/Hypotenuse = 21/35.8

The given expression can be solved as follows

=> [tex]\frac{seca - coseca}{seca+coseca } = \frac{ \frac{1}{cos a}-\frac{1}{sina} }{\frac{1}{cos a }+\frac{1}{sin a} }[/tex]      

=> [tex]\frac{ \frac{sin a - cosa}{cos a sn a} }{\frac{sin a + cos a}{cos a sin a} }[/tex]  

=> [tex]\frac{sin a - cosa}{cos a+ sin a}[/tex]  

=> [tex]\frac{ \frac{21}{35.8} - \frac{29}{35.6} }{\frac{29}{35.8} + \frac{21}{35.8} }[/tex]  

=> [tex]\frac{21- 29}{29+21}[/tex]  

=>  [tex]\frac{8}{50}[/tex]  

=>  [tex]\frac{4}{25}[/tex]  

Therefore,

The values of sec a - cosec a/sec a+cosec a is 4/25.

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Answer:

240 cm, 320 cm, 400 cm

Step-by-step explanation:

The drawing length multiplied by the scale factor gives the real length.

3 cm × 80 = 240 cm

4 cm × 80 = 320 cm

5 cm × 80 = 400 cm

Answer: 240 cm, 320 cm, 400 cm

Answer:

0.0075

Step-by-step explanation:

Answer: In each question you have two options, T and F. Then in 6 questions you have 2 options for the first, two for the second, two for the third... At the end you get 2·2·2·2·2·2 = 26 options and 26 = 64.

Step-by-step explanation:

The equation to represent the total cost, y, for x months is y = 12x + 30.

From the given table, we can observe that the total cost increases by $12 for each additional month of usage.

This means that the rate of change, or the slope of the equation, is $12 per month.

We can represent this relationship using the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.

In this case, the slope (rate of change) is $12, and the y-intercept can be determined by examining the table. When x = 0 months, the total cost is $30. Therefore, the y-intercept is $30.

Putting it all together, the equation to represent the total cost, y, for x months is:

y = 12x + 30

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Answer:

Below

Step-by-step explanation:

Put '9' where  'n' is and compute

(9)^2 + 6(9) ÷ 3 =

81  +    54 ÷3  =

81  + 18 =   99

The doubling time for the investment as required to be determined is; 15.58 years.

It follows from the task content that the model function is;

A(T)=650 (1.0455) ^T

For doubling time;

2 = (1.0455)^T

ln (2) = T ln (1.0455)

T = ln 2 / ln (1.0455)

T = 15.58 years.

Ultimately, the doubling time of the investment as required is; 15.58 years.

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For product=6 and sum=7, the numbers or integers  are 1 and 6.

What exactly are integers?

In mathematics, integers are the collection of positive and negative numbers. Integers, like whole numbers, do not include the fractional element. Thus, integers are numbers that can be positive, negative, or zero, but not fractions. On integers, we can do all arithmetic operations such as addition, subtraction, multiplication, and division. Integers include numbers such as 1, 2, 5, 8, -9, -12, and so on. "Z" is the symbol for integers.

now,

As given product=6 and sum=7  

make factors for 6 i.e 1,2,3,6

from these choose the numbers whose sum=7

and they are 1,6.

Hence,

           For product=6 and sum=7, the numbers are 1 and 6.

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Answer:

Step-by-step explanation:

inequality form

d≤ 1

Interval Notation:

(−∞,1]

The quotient rule is proved below.

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).

Given is the expression -

Q(x) = F(x)/G(x)

Quotient rule in calculus is a method used to find the derivative of any function given in the form of a quotient obtained from the result of the division of two differentiable functions. Mathematically, for a function f(x), we can write -

f'(x) = [u(x)/v(x)]' = [v(x) × u'(x) - u(x) × v'(x)]/[v(x)]²

Now, let f(x) = u(x) and g(x) = v(x).

Q(x) = u(x)/v(x)

Q(x) = u(x) v⁻¹(x)

Using the product rule -

Q'(x) = u'(x) v⁻¹(x) + u(x) {d/dx v⁻¹(x)}

Q'(x) = u'(x) v⁻¹(x) + u(x) (-1)(v(x)⁻²) v'(x)

Q'(x) = u'(x)/v(x) - u(x)v'(x)/v²(x)

Q'(x) = [v(x) × u'(x) - u(x) × v'(x)]/[v(x)]²

Therefore, the quotient rule is proved above.

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If the temperature dropped at a constant rate, it would have dropped 4°C per hour. This can be calculated by taking the difference in temperature (24°C) and dividing it by the number of hours that passed (4 hours).

The probability of choosing a preschooler who is a girl and prefers the color blue is 0.3 or 30%.

The total number of preschoolers who were asked about their color preference is 70. Out of these, 35 girls chose pink, 15 girls chose blue, 5 boys chose pink, and 15 boys chose blue.

To find the probability of choosing a girl who prefers blue, we need to use the formula:

Probability = (Number of favorable outcomes) / (Total number of outcomes)

Here, the favorable outcome is choosing a girl who prefers blue. We can see that 15 girls chose blue as their preferred color. Out of these, we need to choose a girl, so the total number of favorable outcomes is 15.

The total number of outcomes is the total number of preschoolers, which is 70. Out of these, the number of girls is 35+15=50. Therefore, the total number of outcomes where a girl can be chosen is 50.

Putting these values in the formula, we get:

Probability = 15/50 = 0.3

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Complete Question;

70 preschoolers were asked whether they preferred blue or pink.

35 Girls chose pink as preferred color, 15 girls chose blue as preferred color, 5 boys chose pink as preferred color, and 15 boys chose blue as preferred color.

Assuming one of the preschoolers is chosen at random determine the probability of choosing a preschooler that is a girl that prefers the color blue. Round answer to 2 decimal places.

The location of Kris' signature on the $601.73 check Elmo wrote to Kris and which Kris deposited into her checking account is on the back of the check. The correct option is option C.

C. Only on the back of the check

A checking account is an account opened at a financial institution into which deposits and withdrawals can be made by a customer. A checking account can also be referred to as a transaction account, a credit unions share draft account, demand deposit account or current account.

The amount of check Elmo wrote Kris = $601.73

The amount Kris deposited into her checking account = The check Elmo issued to her

The location to sign before depositing a check into a checking account is at the back of the check, including informing the cashier that the specified  check is to be deposited into the checking account.

The correct option is therefore option C.

C. Only on the back of the check

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No, the marked price of $73.25 is not correct.

To calculate the sale price, we start by multiplying the original price by the discount percentage:

$95.00 * 0.25 = $23.75

This means that the original price of $95.00 should be reduced by $23.75 to find the sale price:

$95.00 - $23.75 = $71.25

Since the marked price is $73.25, this means that the store made a mistake and overpriced the shoes by $2.00. The correct sale price should have been $71.25.

Answer:

21.7% to win $3, thats ~1/5

Step-by-step explanation:

100/6 = 10.(6) % to roll for each number (let it be just ~10.7)

for rolling a 3 or a 1 u will get $3

10.7 + 10.7 = 21.7% to win $3, thats 1/5

73 degrees is the equivalent meausure of m<A

From the given line geometry below, the sum of the adjacent angles is 180 degrees as shown:

m∠A + m∠B = 180

Given the following

∠A = 6x - 35

∠B = 3x + 53

Substitute the given parameters

6x - 35 + 3x + 53 = 180

9x + 18 = 180

9x = 180 - 18

9x = 162
x = 162/9

x = 18

Determine the measure of <A

<A = 6x - 35

<A = 6(18) - 35

<A = 108 - 35

<A = 73 degrees

Hence the measure of angle A from the given diagram is 73 degrees

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The set builder notation is A = { 9x | x ∈ N } which is a set of all x’s containing multiples of 9

The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B, whereas the intersection of two sets A and B is the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B

The union of two sets is a new set that contains all of the elements that are in at least one of the two sets

The intersection of two sets is a new set that contains all of the elements that are in both sets

Given data ,

Let the set be represented as A

Now , the value of A is

A = { 9 , 18 , 27 , 36 , ... }

The set A contains all the positive multiples of 9

So , let x be the set of natural numbers and the value of A is

A =  { 9x | x ∈ N } , and

A = set of all x’s containing multiples of 9

Hence , the set builder notation is { 9x | x ∈ N }

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