According to the record of the registrar's office at a state university, 35% of the students are freshman, 25% are sophomore, 16\% are junior and the rest are senior. Among the freshmen, sophomores, juniors and seniors, the portion of students who live in the dormitory are, respectively, 80%,60%,30% and 20%. What proportion of the students live in a dormitory? Show 3 significant digits in the answer (that is, 0.XXX). NOTE: you might want to make a table for this one. According to the record of the registrar's office at a state university, 35% of the students are freshman, 25% are sophomore, 16% are junior and the rest are senior. Among the freshmen, sophomores, juniors and seniors, the portion of students who live in the dormitory are, respectively, 80%,60%,30% and 20%. What is the probability that a randomly selected student is a junior AND does not live in a dormitory? Show 3 significant digits in the answer (for example, Θ.XXX ). NOTE: you might want to make a table for this one.

Answer:

supplementary

x = 146 degrees

Step-by-step explanation:

Answer:

supplementary

Step-by-step explanation:

Answer:

Area: 71 in²

Perimeter: 35 in

Step-by-step explanation:

Answer:

160 liters

Step-by-step explanation:

"a confectioner mixes forty liters of 60%":

Equation: 40 * .60

ow plug it in

0.60*40 + 0.10x = 0.20(40+x)

"how much of the 10% syrup should she use?":

.10x

"...to make a 20% sugar syrup.":

0.20(40+x)

Now that I have split the question into equations, let's put them together:

0.60*40 + 0.10x = 0.20(40+x)

Solve:

60*40 + 10x = 20*40 + 20x

10x = 40*40

x = 160 liters (amt of 10% solution needed)

Hope this helps :)

160 liters of 10% syrup is needed to make the mixture.

An equation is an expression used to show the relationship between two or more variables and numbers.

Let x represent the amount of 10% syrup. Hence:

(60% of 40) + (x of 10%) = (x + 40) of 20%

0.6 * 40 + x * 0.1 = (x + 40) * 0.2

24 + 0.1x = 0.2x + 8

x = 160 liters

160 liters of 10% syrup is needed to make the mixture.

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Answer:i think it is 7/3

Step-by-step explanation:

Answer:

To make it trinomial it has to be ax²+bx+c

The round off of 4.776 to the nearest hundred results in 4.800.

To round 4.776 to the nearest hundred

Focus at the digit in the hundredth's place, which is the second decimal place.

In this case, the digit in the hundredth's place is 7.

Since 7 is greater than or equal to 5, we round up the previous digit, which is 7.

Therefore, rounding 4.776 to the nearest hundred results in 4.800.

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Answer:

Step-by-step explanation:

The formula for the area of a sector is

\(A=\frac{\theta}{360}*\pi r^2\) where theta is the measure of the central angle (which is the same measure as that of the arc that is intercepted by the 2 radii formig the angle), and r is the radius.

For us, theta is 90 degrees and r is 20. Filling in the formula:

\(A=\frac{90}{360}*(3.14)(20)^2\) which simplifies down a bit to

\(A=\frac{1256}{4}\) so

A = 314 m squared

Answer:

Two angles whose sum in 90 degrees

Step-by-step explanation:

Answer:

To solve this problem, we can use the formula for the area of a triangle, which is A=1/2bh, where b is the base and h is the height. In this problem, we are given that the area of the triangle is 128 square centimeters, so we can set up the following equation:

A = 1/2bh

128 = 1/2bh

We are also given that the height of the triangle is 8 centimeters greater than three times the base, so we can set up the following equation:

h = 3b + 8

We can substitute the second equation into the first equation to get the following:

128 = 1/2bh

128 = 1/2(3b + 8)b

128 = 3/2b^2 + 4b

We can then use the quadratic formula to solve for b, the base of the triangle:

b = (-4 +/- sqrt(4^2 - 4(3/2)(128)))/(2(3/2))

b = (-4 +/- sqrt(64 - 192))/3

b = (-4 +/- sqrt(-128))/3

Since the square root of a negative number is not a real number, we know that there is no solution to this equation, which means that the given information is not sufficient to determine the base of the triangle.

Therefore, the correct answer is that the base of the triangle cannot be determined from the information given.

To solve this problem, we can use the formula for the area of a triangle, which is A=1/2bh, where b is the base and h is the height. In this problem, we are given that the area of the triangle is 128 square centimeters, so we can set up the following equation:

A = 1/2bh

128 = 1/2bh

We are also given that the height of the triangle is 8 centimeters greater than three times the base, so we can set up the following equation:

h = 3b + 8

We can substitute the second equation into the first equation to get the following:

128 = 1/2bh

128 = 1/2(3b + 8)b

128 = 3/2b^2 + 4b

We can then use the quadratic formula to solve for b, the base of the triangle:

b = (-4 +/- sqrt(4^2 - 4(3/2)(128)))/(2(3/2))

b = (-4 +/- sqrt(64 - 192))/3

b = (-4 +/- sqrt(-128))/3

Since the square root of a negative number is not a real number, we know that there is no solution to this equation, which means that the given information is not sufficient to determine the base of the triangle.

Therefore, the correct answer is that the base of the triangle cannot be determined from the information given.

The function that models the horizontal displacement as a function of time in seconds is y = 5cos(2π/3 x)

The given parameters are:

Start by calculating the amplitude, A using:

A = h/2

This gives

A = 10/2

A = 5

Next, we calculate the period using:

B = π/t

This gives

B = π/1.5

Evaluate

B = 2π/3

The pendulum is at the middle.

So, it has no vertical displacement

The function is then represented as:

y = Acos(Bx)

This gives

y = 5cos(2π/3 x)

Hence, the function that models the horizontal displacement as a function of time in seconds is y = 5cos(2π/3 x)

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Answer:

r≈3.95in

Step-by-step explanation:

Answer:

cymath.com

Step-by-step explanation:

number sweet is 35

we divided ratio  =4x:3x

total  = 4x+3x

7x= 35

= 35/7

x= 5

1 st part will be 4x = 4*5= 20 sweets.

2 nd part will be 3x = 3*5= 15sweets

There are 64 different 3-digit numbers that can be formed using the digits 1, 2, 3, and 4, allowing for digit repetition.

If the digits 1, 2, 3, and 4 can be repeated, we can calculate the number of possible combinations by multiplying the number of options for each digit. In this case, we have four choices for each of the three digits. Thus, we have 4 x 4 x 4 = 64 different combinations. Each combination represents a unique 3-digit number that can be formed using the given digits.

To understand this better, let's break it down. The first digit can be any of the four given digits: 1, 2, 3, or 4. Similarly, the second and third digits can also be any of the four options. Since each digit can be repeated, we multiply the number of options for each digit to find the total number of combinations.

Therefore, there are 64 different 3-digit numbers that can be formed using the digits 1, 2, 3, and 4, allowing for repetition.

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An equation for the line perpendicular to 4x - 8 = y and has a y-intercept of 2 is y = (-1/4)x + 2.To find the equation for the line perpendicular to 4x - 8 = y and has a y-intercept of 2, we need to use the properties of perpendicular lines. Perpendicular lines have opposite reciprocal slopes.

The given equation, 4x - 8 = y, is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. Therefore, we can rewrite the equation as y = 4x - 8 and see that the slope is 4.

Since we want a line perpendicular to this line, we need to find the opposite reciprocal slope. The opposite reciprocal of 4 is -1/4.

Now we have the slope of the perpendicular line, -1/4, and the y-intercept, 2. We can use the point-slope form of a line to find the equation:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line. In this case, (x1, y1) = (0, 2) since the y-intercept is 2.

Plugging in the values, we get:

y - 2 = (-1/4)(x - 0)

Simplifying, we get:

y = (-1/4)x + 2

Therefore, an equation for the line perpendicular to 4x - 8 = y and has a y-intercept of 2 is y = (-1/4)x + 2.

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Answer:

Step-by-step explanation:

2, there are 4, making it the most.

No, these two events cannot be disjoint. Disjoint events, also known as mutually exclusive events, are events that cannot occur simultaneously.

In other words, if events A and B are disjoint, it means that the occurrence of one event excludes the possibility of the other event occurring.

However, in this case, we are given that P(A) > 0 and P(B) > 0. This means that both events A and B have non-zero probabilities of occurring. Since both events have a positive probability, they cannot be disjoint because there is a possibility of their intersection, where both events occur simultaneously.

Disjoint events would have the property that P(A ∩ B) = 0, indicating that their intersection is an empty set. But given that P(A) > 0 and P(B) > 0, it implies that there is some non-zero probability for the events A and B to occur together, making them not disjoint.

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The geometry of the fold is asymmetric.

The term "geometry of the fold" refers to the spatial arrangement or shape of a fold in rock layers. In this case, the fold is described as asymmetric. This means that the fold does not exhibit symmetry or balance in its shape, and one limb of the fold is steeper or has a different shape compared to the other limb.

The term "asymmetric" in geology typically refers to folds that have limbs with different angles of inclination or curvature. Therefore, based on the given options, the correct answer is "C. asymmetric."

Therefore, the correct answer is: A. asymmetric

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The geometry of the fold is asymmetric.

The term "geometry of the fold" refers to the spatial arrangement or shape of a fold in rock layers. In this case, the fold is described as asymmetric. This means that the fold does not exhibit symmetry or balance in its shape, and one limb of the fold is steeper or has a different shape compared to the other limb.

The term "asymmetric" in geology typically refers to folds that have limbs with different angles of inclination or curvature. Therefore, based on the given options, the correct answer is "C. asymmetric."

Therefore, the correct answer is: A. asymmetric

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4/2 is equivalent to 16/8 because 2 x 2 = 4 and 1 x 2 = 2.

Hope this helps!

Answer:

The answer is 1/6

Step-by-step explanation:

So Think of a half and then divide it into 3 parts for a half it will be 1/3 but for a meter it will be 1/6 because there is 2 half's in 1 whole

Hope this helps!! :D

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Expression 2x²-(-1) - [7x-8] is equal to 2x² - 7x +9

Expression is combination of math operations , numbers and unknown variables.

Math operation can be subtraction , addition , multiplication or division.

There are two types of expression : numerical expression and algebraic expression . Expression consists of only numbers are numerical where expression containing numbers and variables are algebraic expression.

Subtract 7x-8 from 2x²-(-1)

2x²-(-1) - [7x-8]

product of two minus is plus

2x²+1 -[7x-8]

open the bracket and change the minus sign

2x²+1 - 7x + 8

there is no x² and x term so,

2x² - 7x +1+8

2x² - 7x +9 is our required expression

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We need to know about z-score to solve the problem. The z-score of the soda is 0.6

A z-score tells you how many standard deviations away an individual data falls from the mean. We can calculate z-score from the standard deviation and mean of the data. In this question we know that the cost of a soda is $1.15 and the mean is $1.00 and the standard deviation is $0.25.We need to calculate the z-score of the soda with the given information.

z-score=x-μ/σ=1.15-1.00/0.25=0.15/0.25=0.6

Therefore the z-score of the soda is 0.6

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The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day, 3 days a week is 0.653.

We have,
Vermont had 65.3% of respondents who said yes to exercising for at least 30 minutes a day, 3 days a week.

To find the sample proportion, you can convert the percentage to a decimal by dividing the percentage by 100.

Step 1:

Convert the percentage to a decimal.
65.3 / 100 = 0.653

Thus,
The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day, 3 days a week is 0.653.

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Answer:

PART 1

1) BC = AD = 16.4

2) CD = AB = 13.9

because JKMN is a parallelogram

=> KJ = ML

<=> y + 3 = 2y - 1

<=> y = 4

we also have: KL = JM

<=> 3x + 5 = 4x

<=> x= 5

3) with y = 4 => JK = 4 + 3 = 7

4) with x = 5 => KL = 3.5 + 5 = 20

PART 2

5) W = Y = 112⁰

6) Z = 180⁰ - 112⁰ = 68⁰

ABCD is a parallelogram

=> A + B = 180⁰

<=> 2y + 4y = 180

<=> y = 30

we also have:

C + D = 180⁰

<=> x + 5x - 180 = 180

=> x = 60

7) with y = 30 => A = 2.30 = 60⁰

8) with x = 60 => D = 5.60 - 180 = 120⁰

PART 3

9) EG = 2.HG = 2.14 = 28

10) DH = 1/2.DF = 20/ 2 = 10

QRSP is a parallelogram

=> 2y + 2 = 2x

x + 9 = 2y

=> x = 11

y = 10

11) with x = 11 => RT = 11 + 9 = 20

12) QS = 2.ST = 2.2.11 = 44

Graphs are used to represent functions.

Sara's mistakes are:

Graph A

When a graph is plotted, the intervals on both axes must be uniform.

In Sara's graph, the intervals on the y-axis do not follow a uniform pattern (i.e. 0, 1, 2, 4, 8)

Instead, she could have used 0, 2, 4, 6, 8.....

Graph B

The origin of a graph is always 0

In Sara's graph, the origin is at -1.

This means that, the wrong origin was used, and the actual origin is wrongly placed.

See attachment for the correction of graph A

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A) we would send Order A to Factory 3.

B) we would send both Order B and Order C to Factory 3.

B 7,000 Factory 3

C 30,000 Factory 3

Total number of units produced for the company today: 37,000

Average cost per unit for all production today: $9.00

To make decisions about which factory to send the orders to on Monday and Tuesday, we need to compare the costs per unit for each factory and consider the total number of units to be produced. Let's go through each day's scenario and make the production decisions.

a) Monday: Order A for 15,000 units

To decide which factory to send the order to, we compare the costs per unit for each factory. We select the factory with the lowest cost per unit to minimize the average cost per unit for the company.

Let's assume the costs per unit for each factory are as follows:

Factory 1: $10 per unit

Factory 2: $12 per unit

Factory 3: $9 per unit

To calculate the total cost for each factory, we multiply the cost per unit by the number of units:

Factory 1: $10 * 15,000 = $150,000

Factory 2: $12 * 15,000 = $180,000

Factory 3: $9 * 15,000 = $135,000

Based on the calculations, Factory 3 has the lowest total cost for producing 15,000 units, with a total cost of $135,000. Therefore, we would send Order A to Factory 3.

b) Tuesday: Order B for 7,000 units and Order C for 30,000 units

We have two options: sending each order to a separate factory or sending both orders to the same factory. We need to compare the average cost per unit for each option and select the one that results in the lowest average cost per unit.

Let's assume the costs per unit for each factory remain the same as in the previous example. We will calculate the average cost per unit for each option:

Option 1: Sending orders to separate factories

For Order B (7,000 units):

Average cost per unit = ($10 * 7,000) / 7,000 = $10

For Order C (30,000 units):

Average cost per unit = ($9 * 30,000) / 30,000 = $9

Total number of units produced for the company today = 7,000 + 30,000 = 37,000

Average cost per unit for all production today = ($10 * 7,000 + $9 * 30,000) / 37,000 = $9.43 (rounded to two decimal places)

Option 2: Sending both orders to the same factory (Factory 3)

For Orders B and C (37,000 units):

Average cost per unit = ($9 * 37,000) / 37,000 = $9

Comparing the two options, we see that both options have the same average cost per unit of $9. However, sending both orders to Factory 3 simplifies the production process by consolidating the orders in one factory. Therefore, we would send both Order B and Order C to Factory 3.

Production Report for Tuesday:

Order # of Units Factory

B   7,000      Factory 3

C  30,000    Factory 3

Total number of units produced for the company today: 37,000

Average cost per unit for all production today: $9.00

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False, if an augmented square matrix in row-echelon form has a row of zeros as its last row, then the corresponding system of equations has no solution.

What does the term "echelon form" mean?

What purpose does echelon matrix serve?

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we have the expression

Applying property of exponents

Answer:

use formula

area of semicircle + area of trapezium

The required area is \(938.4 m^2\)

The combination of solids includes shapes formed by two or solid shapes, which together form a new shape.

We can draw the given diagram as given below

So this includes the given shapes as,

ACEF=Rectangle

CDE=Triangle

Arc ABC=Half circle.