a man has 23 coins in his pocket, all of which are dimes and quarters. if the total value of his change is 380 cents, how many dimes and how many quarters does he have? your answer is

The number of students is 30 while the number of adults will be 37.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Suppose the number of students ticker is x and the number of adults is y.

7x + 9y = total revenute

7x + 9y = 543

Total tickets = x + y

x + y = 67

Multiply the above equation by 9

9x + 9y = 603

Subtract equations as

7x + 9y - 9x - 9y = 543 - 603

-2x = -60

x = 30

And, y = 67 - 30 = 37

Hence "The number of students is 30 while the number of adults will be 37".

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Step-by-step explanation:

Let us take the first number x and second be y

So,

4/9 = 12/x = 40/90 = y/108

Now,

4/9 = 12/x

4x = 12(9)

4x = 108

4x/4 = 108/4

x = 27

Now,

40/90 = y/108

4/9 = y/108

4(108) = 9y

432 = 9y

9y = 432

9y/9 = 432/9

y = 48

Now,

4/9 = 12/x = 40/90 = y/108

4/9 = 12/27 = 40/90 = 48/108 = 0.44

The probability of drawing three aces in a row without replacement is  0.00018 from a deck of 52 cards.

We know that probability is defined as the ratio of number of favorable outcomes to the total number of outcomes.

We are given that cards are drawn without replacement, it means counts of cards after drawing a single card will change.

We know very well that in a deck of 52 cards, count of aces is 4.

So,probability of drawing a single ace from 52 cards is =4/52.

Now,after drawing a single ace total number of cards reduce to 51 and number of aces counts reduce to 3

So, probability of drawing a single ace from 51 cards = 3/51

Similarly probability of drawing of single ace from 50 cards is =2/50

So, total probability of drawing of three aces is =(4/52) × (3/51) × (2/50)

or P(E)=(1/13) × (1/17) × (1/25) =1 / 5525 =0.00018

Hence, required probability is 0.00018 .

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True, Mandy claims that there are no fixes for the system.

What do you mean by the system of linear equation?

A system of linear equations is usually a set of two linear equations in two variables. A linear equation in two variables has an infinite number of solutions. The goal of solving a system of equations is to transform two bivariate equations into a single univariate equation.

Given system of linear equation:

9x + 15y = 6 ....(1)

5y = -3x + 4 ....(2)

Using elimination method,

Substitute the value of x from eq (1) to eq(2)

9x + 15y = 6

9x = 6 - 15y

x = [tex]\frac{6-15y}{9}[/tex]

Now, substitute this in eq(2)

5y = - 3x + 4

5y = -3( [tex]\frac{6-15y}{9}[/tex]) + 4

5y = -1([tex]\frac{6-15y}{3}[/tex]) + 4

5y = -2 + 5y + 4

5y - 5y = 2

0 = 2

Which is not possible, hence given system of linear equation has no solution.

Hence, Mandy's statement is true.

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Answer:

SAS, ASA, and AAS

Step-by-step explanation:

SSA, AAA are NOT Theorems. SSS requires three sides and HL requires the triangles to be a right triangle (90 degrees).

Also, the two triangles forms Vertical angles.

All rectangles are square is a false statement

The given statement is false statement.

What is a rectangle and square?

A rectangle is a quadrilateral with opposite sides parallel and equal and each angle is a right angle, where as a square is quadrilateral with opposite sides parallel and each side is equal. and every angle is a right angle.

We are given a statement All rectangle are squares.

As every side of a square is of equal length And only opposite sides are of equal length in rectangle

All rectangles are not square

Hence the statement is not true

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Multicollinearity can be defined as when two independent variables are correlated, multicollinearity occurs. Reason: Only the interactions between the independent variables are considered multicollinear.

Multicollinearity is the prevalence of excessive intercorrelations amongst or extra impartial variables in a more than one regression model. Multicollinearity: Multicollinearity exists whilst or extra of the explanatory variables are extraordinarily correlated.

This is a hassle as it could be tough to disentangle which ones first-rate explains any shared variance with the outcome. It additionally indicates that the 2 variables may also in reality constitute the identical underlying factor. Multicollinearity takes place whilst or extra impartial variables are extraordinarily correlated with each other in a regression model. This method that an impartial variable may be anticipated from any other impartial variable in a regression model.

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The monthly share of annual expenses is $1820/month.

The monthly Share is calculated by dividing the annualized net amount of non-monthly billed services by 12.

Nonrecurring billing:

A one-time transaction is a non-recurring payment.

There is usually only one invoice or bill involved, and it only happens once.

Frequently, the amount is greater than the sum for recurring payments.

Subscriptions that are on monthly billing are billed on the same day each month for as long as the subscription is current.

So, we have:

Annual: $4200

Living: $670

Fixed: $800

Now, calculate as follows:

4200/12 = 350

Then,

350 + 370 + 800 = $1820/month

Therefore, the monthly share of annual expenses is $1820/month.

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Answer:

The bisector of BAC

Step-by-step explanation:

Point D and point E are equidistant from point A. Therefore, when two arcs are constructed equidistant from these points, intersecting eachother, a line drawn though this intersection and point A bisects angle BAC

Answer:

60.68

Step-by-step explanation:

9*6+.78*6=60.68

Students who test positive face serious consequences, including letters to their parents,

The slope would be the same on the graph.

What is a slope?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

                The slope-intercept form of an equation is used to represent each time the equation of a line is stated as y = mx + b.

                      M represents the line's slope. Additionally, b is the b in the y-intercepting point (0, b). For instance, the y-intercept is at (0, 7) and the slope is 3 in the equation y = 3x - 7.

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If R is (7,5), i. find the coordinates of Q and S​ are (-2, 3) if the are adjacent

You should understand that two adjacent sides can intersect if they continue to be drawn

The two given equations are

5x-y=-7 and

3x-8y=18

Using elimination method to solve for x and y we have

3(5x-y=-7) = 15x -3y = -21

Also, 5(3x-8y=18) = 15x-40y=90

Solving the two equations simultaneously we have

(15x-40y=90)-(15x-3y=-21)

Subtracting to have

-37y = 101

Making y the subject we have y≅3

Putting y≅3 in equation 1

5x-y=-7

5x+3=-7

5x=-10

x=-2

Therefore the coordinates of Q and S are (-2, 3)

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The inequality that represents the greatest number of boxes he can move in one trip is 255 + 50b ≤ 4000.

The solution of the inequality is 74.

The number of trips he would make to deliver 310 boxes is 5.

Here are inequality signs and what they mean:

> means greater than

< means less than

≥ means greater than or equal to

≤ less than or equal to

The inequality sign that would be used is ≤

The form of the inequality is:

Weight of the worker + weight of the cart + (weight of the boxes x number of boxes) ≤ 4000

160 + 95 + (50 x b) ≤  4000

255 + 50b ≤ 4000

In order to determine the value of b, take the following steps:

Combine similar terms:

50b ≤ 4000 - 255

50b ≤ 3745

b ≤ 3745 / 50

b ≤ 74.9

The number of boxes he can carry is 74

Number of trips = total number of boxes / number of boxes he can carry in one trip

= 310 / 74

= 4.1

= 5 trips

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Answer: 7x-2=10x+x+6x

Step-by-step explanation:

sub in and solve

or solve the equation

7x-2=17x

10x=-2

x=-2/10

x=-1/5

7x-2=10x+x+6x is true

the vector fields F with the plots labeled I-IV, Then give a one sentence description of the vector field would look like if you plotted it. F(x, y) = (x, xy): rot(F) = 0; The vector field would look like a series of straight lines that move away from the origin

I: F(x, y) = (y, x) - This vector field corresponds with plot I, as it forms a series of counter-clockwise circular paths.

II: F(x, y) = (1, sin y) - This vector field corresponds with plot II, as it forms a series of parallel lines.

III: F(x, y) = (x - 2, x + 1) - This vector field corresponds with plot III, as it forms a series of diagonal lines that move outward from the origin.

IV: F(x, y) = (y, 1/x) - This vector field corresponds with plot IV, as it forms a series of concentric circles with the origin as their center.

F(x, y) = (x, y): rot(F) = 0; The vector field would look like a grid of straight lines.

F(x, y) = y i = x j: rot(F) = 1; The vector field would look like a series of counter-clockwise circular paths.

F(x, y) = (y, -x): rot(F) = -1; The vector field would look like a series of clockwise circular paths.

F(x, y) = (1 + xy)i + x^2 sin y j: rot(F) = x^2; The vector field would look like a series of curves that rotate counter-clockwise around the origin.

F(x, y) = (x, xy): rot(F) = 0; The vector field would look like a series of straight lines that move away from the origin

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Answer:there is no diagram

Step-by-step explanation:

The required quadratic equation which has the roots -2, and -3 is (C) x²+5x+6=0.

Any equation in algebra that can be written in the standard form where x stands for an unspecified amount, where a, b, and c stand for known values, and where a 0 is true is known as a quadratic equation.

Factoring, using square roots, completing the square, and the quadratic formula is the four ways to solve a quadratic problem.

So, the product of a quadratic equation's elements can be used to represent any quadratic equation.

The necessary equation is created as follows:

(x - (-2))(x - (-3)) = 0

(x + 2)(x + 3) = 0

x² + 5x + 6 = 0

Therefore, the required quadratic equation which has the roots -2, and -3 is (C) x² + 5x + 6 = 0.

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Correct question:
Form a quadratic equation whose roots are -2,-3.

(A) x² - 6x + 5 = 0

(B) x² - 5x - 6 = 0

(C) x² + 5x + 6 = 0

(D) x² - 5x + 6 = 0

The probability that at least 5 will do their homework on time in a class of 50 students is 0.1

Probability

Probability is calculated by dividing the number of ways the event can occur by the total number of outcomes. Probability and odds are different concepts. Odds are the probability that something happens divided by the probability that it doesn't happen.

the probability that a randomly chosen student in a statistics class submits his/her homework on time is 0.06.

Each student does homework independently.

In a statistics class of 50 students, what is the probability that at least 5 will do their homework on time.

Probability = event occur/ total number of outcomes

                  = 5/50= 1/10=0.1

Thus the probability becomes 0.1

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If right triangle ABC with right angle ACB and altitude CD then

ΔABC ~ ΔACD

ΔABC ~ ΔCBD

ΔACD ~ ΔCBD

What is Angle-Angle Similarity (AA~) Theorem?

If two angles of one triangle and two corresponding angles of another triangle are congruent, then the triangles are similar.

According to the given question:

A right triangle is given with its altitude drawn from the right angle to its hypotenuse.

Consider the triangled ABC and ACD

By the reflexive property of angle congruence, it follows that:

∠A ≅ ∠A

Since the angles B and D are right angles, from the right angles congruence theorem, it also follows that:

∠C ≅ ∠D

Hence, by the Angle-Angle Similarity (AA~) Theorem, it follows that triangles ABC and ACD are similar. Similarly triangle ABC is similar to triangle CBD

Consider triangles ACD and CBD:

Triangles ABC and ACD are similar. Also triangle ABC is similar to triangle CBD

Therefore, Triangle CBD is similar to triangle ACD as both of them are similar to triangle ABC.

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Autumn's songs were played in 2 movies and 8 commercials combined.

What is an Equations?

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

Assume that y is the total number of movies that featured Autumn's songs, and x is the total number of commercials.

There will be the following equations that describe the given issue:

Here

30x+120y=480

x + 4y = 16 equation 1.

and

x + y = 10

y = 10-x equation 2.

putting eq 2 in 1 we have

x+4(10x) = 16

⇒-3x+40= 16

⇒x=8

⇒ y = 2

Hence, Autumn's songs were played in 2 movies and 8 commercials combined.

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Answer:

To find the cost of a ruler and the cost of a pencil, we can set up a system of equations using the given information. Let R be the cost of a ruler and P be the cost of a pencil.We know that 3R + 2P = 3.10 and 2R + 5P = 3.90Subtracting the first equation from the second, we get:5P - 3P = 3.90 - 3.10

2P = 0.80Dividing both sides by 2, we get:P = 0.40Substituting this value back into one of the original equations, we get:3R + 2(0.40) = 3.10

3R = 2.70

R = 0.90Therefore, the cost of a ruler is £0.90 and the cost of a pencil is £0.40.

Step-by-step explanation:

Answer: y=(13/3)*x-6

Step-by-step explanation: -3y=18-13x    -y=6-13/3 x

y= (13/3)x-6

As per the sampling, an appropriate test value for a z test is 0.808

Sampling:

In math, sampling means selecting the group that you will actually collect data from in your research.

Given,

In October, the campus bookstore asked a random set of freshmen and seniors how much they had spent on textbooks that semester. the bookstore believes that the two groups spent the same amount.

Here we need to find the appropriate test value for a z test.

As per the given question, first we must know the definition of z test,

The term z-test means statistical test that can be used to determine whether two population means are different.

And it is used when the variances are known or the sample size is large.

And the formula of the z value, the test statistic for two population with large sample size is given by,

z = [x₂ - x₁] / √[(s₁²/n₁) + (s₂²/n₂)]

From the question we have, x1=$320, x2=$310, s1=$62, s2=$73, n1=60 and n2 = 60.

When we apply the value then we get the z value as

=> z = [310 - 320] / √[(62²/60) + (73²/60)]

=> 0.808

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a) N = 2^8 = 256

b)N = 2^8 + 2^7 +2^6 +2^5 +2^4 +2^3 +2^2 +2^1

Given;

String of length 8, with two options (0 or 1) each.

a) for the number of bits of strings of length 8.

Each digit of the 8 digit string has 2 options.

For 8 digit, we have

N = 2×2×2.... = 2^8 =256

b) for bit of strings of length 8 or less.

For n string = 2^n

For n < 8

The number of bit strings for length 8 or less are;

N = N8 +N7 + N6 + ... +N1

N = 2^8 + 2^7 +2^6 +2^5 +2^4 +2^3 +2^2 +2^1

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The null hypothesis asserts that the data are well described by both your model and the model without independent variables.

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The equivalent expression of each expression given, using the distributive property, are:

a. 6x + 10

b. 49a + 42

c. 20a² + 40ab

d. 8xy - 6y²

e. 27z - 30z²

f. 18x + 24 + 12y

g. 22c² + 77ac

h. 40b + 16bs + 24b³

i. 7a³ - 21a² + 42a

j. 36p² + 27p - 45

If we have an expression given as a(b + c), according to the distributive property, we can write an equivalent expression by using the term "a" to multiply each of the terms within the bracket, which will give us: a(b + c) = ab + ac.

a. 2(3x + 5), applying the distributive property, multiply each of the terms within the parentheses by 2:

2(3x) + 2(5)

6x + 10

Therefore, the equivalent expression of 2(3x + 5) is 6x + 10.

b. 7(7a+6)

7(7a) + 7(6)

= 49a + 42

c. 5a(4a+8b)

= 5a(4a) + 5a(8b)

= 20a² + 40ab

d. 2y(4x-3y)

= 8xy - 6y²

e. 3z(9 - 10z)

= 27z - 30z²

f. 6(3x + 4 + 2y)

18x + 24 + 12y

g. 11c(2c + 7a)

22c² + 77ac

h. 8b(5 + 2s + 3b²)

40b + 16bs + 24b³

i. 7a(a² - 3a + 6)

7a³ - 21a² + 42a

j. 9(4p² + 3p - 5)

36p² + 27p - 45

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Answer:

see explanation

Step-by-step explanation:

since both AB and CD are at right angles to AE then

AB and CD are parallel lines.

since AB and AE are at right angles to each other then

AB and AE are perpendicular lines

no LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL

Answer:

7000

Step-by-step explanation:

70×100=7000

there is 100g in 1kg

Answer:

70,000 grams

Step-by-step explanation:

1. convert kilograms to grams

1000 grams = 1 kilogram

2. use dimensional analysis

[tex]\frac{70 kilograms }{1 gram}[/tex] * [tex]\frac{1000 grams}{1 kilogram}[/tex]

3. multiple straight across

70 * 1000 = 70,000 grams

Answer:

(5p - 7q) + (3q - 4p + 12) + (6q - 13pq - 15)

Open brackets

5p - 7q + 3q - 4p + 12 + 6q - 13pq - 15

Combine like terms,

5p - 4p - 7q + 3q + 6q - 13pq + 12 - 15

p + 2q - 13pq - 3

Thus, The answer is (p + 2q - 13pq - 3)

Answer:

p + 2q - 13pq - 3

Step-by-step explanation:

Now we have to,

→ Add the following expressions.

The expressions are,

→ 5p - 7q, 3q - 4p + 12, 6q - 13pq - 15

Let's solve the problem,

→ (5p - 7q) + (3q - 4p + 12) + (6q - 13pq - 15)

→ 5p - 7q + 3q - 4p + 12 + 6q - 13pq - 15

→ (5p - 4p) + (-7q + 3q + 6q) + (-13pq) + (12 - 15)

→ (p) + (2q) + (-13pq) + (-3)

→ p + 2q - 13pq - 3

Hence, answer is p + 2q - 13pq - 3.