Determine which of the following are solutions to the equation below.

If mark has a total of 39 coins  consisting of nickels and quarters and the total value of the coins is $4.35. By using the substitution method , found that he has 27 nickels and 12 quarters

The total number of coins=39 coins

Mark has a total of 39 coins consisting of nickels and quarters

Consider the number of nickels as x  and number of quarters as y

Then the equation will be,

x+y=39

x=39-y

The total value of the  coins=$4.35

The value of one nickel=$0.05

The value of one quarter=$0.25

Then the equation will be

0.05x+0.25y=4.35

0.05(39-y)+0.25y=4.35

1.95-0.05y+0.25y=4.35

0.2y=2.4

y=12

Then

x=39-y

x=39-12

x=27

Hence, if mark has a total of 39 coins  consisting of nickels and quarters and the total value of the coins is $4.35. By using the substitution method, found that he has 27 nickels and 12 quarters

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Answer: The given statement is true.

Step-by-step explanation:

Significant figures are defined as the figures that are present in a number. It expresses the magnitude of a quantity to a specific degree of accuracy.

There are some rules to detect the significant figures in a number:

Rule applied when numbers are added or subtracted:

The number having less number of significant figures after the decimal point will determine the number of significant figures in the final answer.

Hence, the given statement is true.

The measure of each exterior angles of rectangle is 90°

From the question, we have the following parameters that can be used in our computation:

A rectangle

A rectangle is a polygon with 4 sides

So, the measure of the exterior angle can be calculated using the formula for the exterior angles in a polygon

The exterior angles in a polygon are found by using:

Exterior of a rectangle in a polygon =  360°/Number of sides of the polygon

In this case,

The number of sides of the rectangle = 4

So, we have

Exterior of a rectangle =  360°/4

Evaluate

Exterior of a rectangle =  90°

Hence, the value of the measure of each exterior angles of rectangle is 90°

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Complete question

Find the measure of each exterior angles of rectangle?

Step by step​

Answer:

- 10

Step-by-step explanation:

-6+8×5÷-10

-6+40÷-10

-6-4

-10

Answer and Step-by-step explanation:

According to PEMDAS (Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction),

First we multiply, then divide, then finally add/subtract.

-8 times 5 is -40.

-40 divided by -10 is 4.

-6 - 4 = -10

The answer to the expression is -10.

#teamtrees #PAW (Plant And Water)

Answer:

117%

Step-by-step explanation:

17.433=x/100(14.9)

1743.3/14.9=x

117

When the matrices A and B commute, or when they fulfill AB=BA, this is a significant exception.

A matrix is a rectangular array or table of numbers, symbols, or formulae used to represent mathematical objects or qualities of such things. It is often arranged in rows and columns. For instance, a matrix contains two rows and three columns. a group of integers organized in a rectangular array in rows and columns. Matrix elements or entries refer to numbers. In several disciplines of engineering, physics, economics, statistics, and mathematics, matrices have a wide range of applications.

The eigenvalues and eigenvectors of the sum of two matrices are typically not the same as the sums of the eigenvalues and eigenvectors of the individual matrices. In actuality, there is no way to separate the eigenvalues of A and B from one another.

When a vector v is an eigenvector of both A and B, it is also an eigenvector of A+B, with an eigenvalue equal to the sum of its eigenvalues for A and B, respectively. There is, however, no reason to anticipate that two matrices will share an eigenvector in general. There is no method to create an eigenvector of A+B from two random eigenvectors of A and B alone.

When the matrices A and B commute, or when they fulfill AB=BA, this is a significant exception. In this situation, their invariant spaces coincide, and if both of them are diagonalizable, they are concurrently diagonalizable, which means that their eigenvectors do as well. As was already noted, in this specific instance, the eigenvectors of A+B are likewise the same.

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Answer:

I'm so confused. I don't get the question. I know the options are:

A) 3,4, 5

B) 2, 10, 4

C) 2, 10, 3

D) 2, 15, 2

but I don't understand the question. Could you maybe be a bit more specific?

Answer:

-11, -2, -1.25, 0, 1.25, 3, 12

Step-by-step explanation:

bigger negative numbers are greater

To find the equation of a line passing through two points, (-1, -5) and (5, 4), we can use the point-slope form of a linear equation.

The formula for the point-slope form is: y - y1 = m(x - x1), where (x1, y1) are the coordinates of one of the points on the line, and m is the slope of the line.

First, let's calculate the slope (m) using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) = (-1, -5) and (x2, y2) = (5, 4).

m = (4 - (-5)) / (5 - (-1))

m = 9 / 6

m = 3/2

Now, we can choose one of the points, let's use (-1, -5), and substitute the values into the point-slope form:

y - y1 = m(x - x1)

y - (-5) = (3/2)(x - (-1))

y + 5 = (3/2)(x + 1)

To convert this equation to the standard form (Ax + By = C), we can multiply through by 2 to eliminate the fraction:

2(y + 5) = 3(x + 1)

2y + 10 = 3x + 3

3x - 2y = 7

So, the equation of the line passing through the points (-1, -5) and (5, 4) is 3x - 2y = 7.

Answer:

C. 1/1,000

Step-by-step explanation:

yes or no ?

Answer:

1. Expression: y = 235x

Answer: 1,175

2. The cost of the shirts is 5 dollars. Alex has 15 dollars in his wallet. He wants to buy 3 shirts. Write an expression that represents this problem.

Step-by-step explanation:

5. 235 per second

5 x 235 = 1,175

Expression: y = 235x

In both the short run and the long run, the characteristic of a monopolistically competitive firm is that the market price will be equal to its marginal cost (p = mc).

A monopolistically competitive firm is characterized by several conditions, both in the short run and the long run. In the short run, a monopolistically competitive firm will have a market price that is greater than its marginal cost (p > mc).

In the long run, a monopolistically competitive firm will have a market price that is equal to its marginal cost (p = mc). This is because, in the long run, the firm faces increased competition and has to set its price at the level where its marginal cost equals its price.

In conclusion, in both the short run and the long run, the characteristic of a monopolistically competitive firm is that the market price will be equal to its marginal cost (p = mc). This is because in the short run, the firm has some market power and can charge a higher price, and in the long run, the firm faces increased competition and has to set its price at the level where its marginal cost equals its price.

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The angle on the unit circle is solved to be

56.01 degrees (to the nearest tenth)

To find the angle of the terminal side through the given point on the unit circle, we can use the inverse trigonometric functions.

given that P = ((√5)/4, (√11)/4)

θ = arctan ((√11)/4 / (√5)/4)

θ = arctan((√11)/(√5))

θ ≈ 56.01 degrees

hence to the nearest tenth of a degree, the angle of the terminal side through the point P = ((√5)/4, (√11)/4) on the unit circle is approximately 56.01 degrees.

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Answer:

(d) All people who voted in the poll.

Step-by-step explanation:

The poll can only be generalized to the people who voted in the poll.

Out of this poll we get a estimation of the population proportion. But about the people who listen to the show but did not vote in the poll or even the ones that visit the website but did not vote, we can not infere nothing using the results of the poll as we don't know if they are against the proposed increases or not.

If the people who voted in the poll were a representative sample of certain group, then we could generalize the results for this group.

Answer:

6.2 meters

Step-by-step explanation:

Use pythagorean theorem to find b:

b = √(2.8² - 2.7²) = √0.55 = 0.7 (nearest tenth)

Perimeter of triangle = sum of all its sides = 2.8 + 2.7 + 0.7

Perimeter = 6.2 meters

Answer:

\(n = 12h\)

Step-by-step explanation:

Given

\(r = 12/hr\) --- rate

\(h \to hours\)

\(n \to amount\)

Required

Determine which solution is correct or incorrect

The solutions are not given. So, I will provide a general explanation

The amount (n) is calculated as:

\(n = r * h\)

So, we have:

\(n = 12 * h\)

\(n = 12h\)

The above is the general equation to solve for the amount, given h hours

When h = 2.5, we have:

\(n = 12*2.5\)

\(n = 30\)

Answer:

going to add a picture

Step-by-step explanation:

:)

Answer:

exponential

Step-by-step explanation:

just took the test

Answer:

Well..

Step-by-step explanation:

Do 23,882 by 11, then do the answer of that problem divided by 11 and so on

The equation \(P = -\log(c)\) is an illustration of logarithms. The hydronium ion concentration is approximately \(0.0005012\)

Given that:

\(P = -\log(c)\)

When the pH level is 3.3; it means that:

\(P = 3.3\)

So, we have:

\(3.3 = -\log(c)\)

Divide both sides by -1

\(-3.3 = \log(c)\)

Take antilog of both sides

\(10^{-3.3} = c\)

So, we have:

\(c = 10^{-3.3}\)

\(c = 0.00050118723\)

Approximate

\(c = 0.0005012\)

Hence, the hydronium ion concentration is approximately \(0.0005012\)

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Answer:

The correct answer would be 5.01 x 10^-4

Explanation:

Not only did I take the test and get it right, BUT, P = -log(c) aka 3.3 = -log(c), c is equal to 0.00050118, and the expanded form of 5.01 x 10^-4 is 0.000501...

Using the Pythagorean theorem we know that the value of x in the given situation is 15 units respectively.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.

According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

So, the Pythagorean formula is as follows:

c = √a² + b²

Now, insert values as follows:

c = √a² + b²

c = √12² + 9²

c = √144 + 81

c = √225

c = 15 units

Therefore, using the Pythagorean theorem we know that the value of x in the given situation is 15 units respectively.

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The measure of v is 61 degree.

We have,

Interior angle = (v - 19) or v

Exterior angle = v + 42

Using exterior Angle Property

Exterior angle= Sum of opposite interior angle

v + 42 = v - 19 + v

v + 42 = 2v - 19

v - 2v = -19 - 42

-v = -61

v= 61

Thus, the value of v is 61.

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Subtracting 10 from the original equation will shift the graph down 10 units

The answer is D.

The width RQ of the river is approximately 61.98 ft.

To find the width RQ of the river, we can use the properties of perpendicular lines and collinearity.

Given that Karl starts at point R and walks perpendicular along the edge of the river 42 ft to point S, we can draw a line segment RS of length 42 ft.

From point S, Karl walks 28 ft further to point T. We can draw another line segment ST of length 28 ft.

Now, Karl turns 90° from point T and walks until his location (point U), point S, and point Q are collinear. Let's denote the length of this line segment as UQ.

From the given information, we know that TU = 68 ft.

Since U, S, and Q are collinear, we can form a right triangle by connecting UQ and US.

The length of UQ can be found using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, we have:

UQ² = TU² - US²

UQ² = 68² - 28²

UQ² = 4624 - 784

UQ² = 3840

Taking the square root of both sides, we have:

UQ = √3840

UQ ≈ 61.98 ft

Therefore, the width RQ of the river is approximately 61.98 ft.

Note: It's important to keep in mind that this solution assumes the river is a straight line and that Karl's path is perpendicular to the river's edge. In reality, the river's edge may not be perfectly straight, and the path Karl walks may not be exactly perpendicular.

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Answer:

3 boxes

Step-by-step explanation:

Take the total spent and divide by the cost per box

$6/ $2

3

She bought 3 boxes

Answer:

Check Explanation

Step-by-step explanation:

Complete Question

Employees from Company A and Company B both receive annual bonuses. What information would you need to test the claim that the difference in annual bonuses is greater than $100 at the 0.05 level of significance? Write out the hypothesis and explain the testing procedure.

Solution

The information required to run an hypothesis test to compare the annual bonuses of employees at company A and employees at company B.

- First of, we require a sample of bonuses from each of the two firms, to calculate the mean bonus at each of the companies and the standard deviation.

- We also need the data to satisfy the conditions necessary for an hypothesis test.

the major conditions for an hypothesis test is that

1) The sample must be a random sample extracted from the population, with each variable in the sample independent from one another.

2) The sample should be exrracted from a normal distribution population or approximate a normal distribution, so as to ensure almost normal behaviour from the samples

Then, to do the test,

Step 1

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.

For this test, we want to investigate if the difference in annual bonuses for employees of company A and employees of company B is greater than $100.

Hence, the null hypothesis is that there is no sufficient evidence to suggest that the difference in annual bonuses for employees from company A and employees from company B is greater than $100.

And the alternative hypothesis is that there is sufficient evidence to suggest that the difference in annual bonuses for employees from company A and employees from company B is greater than $100.

Mathematically, if the difference in mean annual bonuses for employees from company A and employees from company B is μ

The null hypothesis is represented as

H₀: μ ≤ 100

The alternative hypothesis is represented as

Hₐ: μ > 100

Step 2

The testing procedure for this is a two-sample hypothesis test, Hence, we compute the test statistic in the next step.

Note that we must have had the mean of each of the samples (μ₁ and μ₂) and their standard deviations from the sample of annual bonuses of employees from both firms (s₁ and s₂)

Such that μ = μ₁ - μ₂

Test statistic = (μ - 100)/σₓ

σₓ = √[(s₁²/n₁) + (s₂²/n₂)]

Test statistic =

[(μ₁ - μ₂) - 100] ÷ √[(s₁²/n₁) + (s₂²/n₂)]

Step 3

Using the test statistic calculated, the significance level, the degree of freedom and the p-value table, we obtain the p-value.

Degree of freedom = n₁ + n₂ - 2

Step 4

The interpretation of p-values

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

Hope this Helps!!!

Answer:

10π cm

Step-by-step explanation:

Given

Area of the circle=25π cm^2

Solution

πr^2=25π

r^2=25

r=√25

r=5

So circumference of the circle=2πr

=2π×5

=10π cm

So the answer is 10π cm

Answer:

b = 4

Step-by-step explanation:

4/6 is equivalent to 2/3, so with the slopes and y-intercepts being the same, there will be infinitely many solutions

Answer:

22 units

Step-by-step explanation:

The perimeter is all the sides of any polygon added up.

A rectangle has 4 sides, but we only need two sides to solve this because a rectangle has symmetry

There are two ways

Method 1:

x+2 + x-1 + x+2 + x-1   OR   2(x+2) + 2(x-1)

simplify: 2x + 4 + 2x - 2

              4x +2

Plug 5 into x: 4(5) + 2

Answer: 22

Method 2:

plug in x to get the sides: 7 and 4

now add: 7 + 7 + 4 + 4   OR   2(7) + 2(4)

simplify: 14 + 8

Answer: 22

The perimeter of the rectangle when x = 5 is 22 units.

Its the sum of length of the sides used to made the given figure.

The perimeter is all the sides of any polygon added up.

WE know that rectangle has 4 sides, but we only need two sides to solve because a rectangle has symmetry

Given that A rectangle has side lengths x + 2 and x - 1.

Then plug in x to get the sides: 7 and 4

Now add:

7 + 7 + 4 + 4  

OR  

2(7) + 2(4)

Then simplify:

14 + 8

22

Hence, the perimeter of the rectangle when x = 5 is 22.

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To prove that there are only these five regular polyhedra, we can consider Euler's polyhedron formula, which states that for any convex polyhedron, the number of vertices (V), edges (E), and faces (F) satisfy the equation V - E + F = 2.

The five regular polyhedra, also known as the Platonic solids, are the only convex polyhedra where all faces are congruent regular polygons, and the same number of polygons meet at each vertex.

The five regular polyhedra are:

1. Tetrahedron: It has four triangular faces, and three triangles meet at each vertex.

2. Cube: It has six square faces, and three squares meet at each vertex.

3. Octahedron: It has eight triangular faces, and four triangles meet at each vertex.

4. Dodecahedron: It has twelve pentagonal faces, and three pentagons meet at each vertex.

5. Icosahedron: It has twenty triangular faces, and five triangles meet at each vertex.

To prove that there are only these five regular polyhedra, we can consider Euler's polyhedron formula, which states that:

"for any convex polyhedron, the number of vertices (V), edges (E), and faces (F) satisfy the equation V - E + F = 2".

For regular polyhedra, each face has the same number of sides (n) and each vertex is the meeting point of the same number of edges (k). Therefore, we can rewrite Euler's formula for regular polyhedra as:

V - E + F = 2  

=>  kV/2 - kE/2 + F = 2  

=>  k(V/2 - E/2) + F = 2

Since each face has n sides, the total number of edges can be calculated as E = (nF)/2, as each edge is shared by two faces. Substituting this into the equation:

k(V/2 - (nF)/2) + F = 2  

=>  (kV - knF + 2F)/2 = 2  

=>  kV - knF + 2F = 4

Now, we need to consider the conditions for a valid polyhedron:

1. The number of faces (F), edges (E), and vertices (V) must be positive integers.

2. The number of sides on each face (n) and the number of edges meeting at each vertex (k) must be positive integers.

Given these conditions, we can analyze the possibilities for different values of n and k. By exploring various combinations, it can be proven that the only valid solutions satisfying the conditions are:

(n, k) pairs:

(3, 3) - Tetrahedron

(4, 3) - Cube

(3, 4) - Octahedron

(5, 3) - Dodecahedron

(3, 5) - Icosahedron

Therefore, there exist only five regular polyhedra.

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The quadrilateral PQRS is a parallelogram since opposite sides PQ and SR have the same lengths and slopes.

To determine the correctness of the statements and calculate the lengths and slopes of the given quadrilateral PQRS, let's perform a coordinate proof.

Length and slope of PQ:

The coordinates of points P and Q are P(0, 2) and Q(3, -4), respectively.

Length of PQ: √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(3 - 0)² + (-4 - 2)²]

= √[9 + 36]

= √45

= 3√5 (approx.)

Slope of PQ: (y₂ - y₁) / (x₂ - x₁)

= (-4 - 2) / (3 - 0)

= -6 / 3

= -2

Therefore, the length of PQ is approximately 3√5, and its slope is -2.

Length and slope of SR:

The coordinates of points S and R are S(-2, 1) and R(1, -5), respectively.

Length of SR: √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(1 - (-2))² + (-5 - 1)²]

= √[9 + 36]

= √45

= 3√5 (approx.)

Slope of SR: (y₂ - y₁) / (x₂ - x₁)

= (-5 - 1) / (1 - (-2))

= -6 / 3

= -2

Therefore, the length of SR is approximately 3√5, and its slope is -2.

Length and slope of SP:

The coordinates of points S and P are S(-2, 1) and P(0, 2), respectively.

Length of SP: √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(0 - (-2))² + (2 - 1)²]

= √[4 + 1]

= √5

Slope of SP: (y₂ - y₁) / (x₂ - x₁)

= (2 - 1) / (0 - (-2))

= 1 / 2

Therefore, the length of SP is √5, and its slope is 1/2.

Length and slope of HQ:

The coordinates of points H and Q are H(0, 2) and Q(3, -4), respectively.

Length of HQ: √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(3 - 0)² + (-4 - 2)²]

= √[9 + 36]

= √45

= 3√5 (approx.)

Slope of HQ: (y₂ - y₁) / (x₂ - x₁)

= (-4 - 2) / (3 - 0)

= -6 / 3

= -2

Therefore, the length of HQ is approximately 3√5, and its slope is -2.

Based on the calculations, we can conclude that both statements are correct:

The quadrilateral PQRS is a parallelogram since opposite sides PQ and SR have the same lengths and slopes.

The quadrilateral PQRS is not a rectangle since the lengths of the adjacent sides PQ and SP are not equal.

Summary:

Length of PQ is approximately 3√5, and its slope is -2.

Length of SR is approximately 3√5, and its slope is -2.

Length of SP is √5, and its slope is 1/2.

Length of HQ is approximately 3√5, and its slope is -2.

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