There is one third of a pie shared equally between 5 children. How much of the pie does each child receive? one ninth pie one fifteenth pie one eighteenth pie one twentieth pie

Answer: x/7=5 or x/5=7

Step-by-step explanation: Well If each person got 7 crackers, and there were 5 people, there were a total of 35 crackers. Division is just multiplication backwards.

The variables x, y, and z correspond to the entries in the last column. Therefore, the solution to the system of linear equations is x = 1, y = 0, and z = -2 (option d).

To find the solution of the system of linear equations represented by the given augmented matrix, we can perform row operations to bring the matrix into row-echelon form or reduced row-echelon form. By analyzing the resulting matrix, we can determine the values of the variables x, y, and z. In this case, after performing the necessary row operations, we find that the solution to the system of linear equations is x = 1, y = 0, and z = -2 (option d).

Let's perform row operations to bring the given augmented matrix into row-echelon form or reduced row-echelon form. The matrix we have is:

[12 5 -9 | 2]

[-2 4 -6 | 0]

[1 -3 6 | 1]

First, we will divide the first row by 12 to make the leading coefficient of the first row 1:

[1 5/12 -3/4 | 1/6]

[-2 4 -6 | 0]

[1 -3 6 | 1]

Next, we will eliminate the leading coefficient of the second row by adding 2 times the first row to the second row:

[1 5/12 -3/4 | 1/6]

[0 19/6 -15/2 | 2/3]

[1 -3 6 | 1]

Similarly, we will eliminate the leading coefficient of the third row by subtracting the first row from the third row:

[1 5/12 -3/4 | 1/6]

[0 19/6 -15/2 | 2/3]

[0 -19/12 27/4 | 1/6]

Now, we will divide the second row by (19/6) to make the leading coefficient of the second row 1:

[1 5/12 -3/4 | 1/6]

[0 1 -5/4 | 2/19]

[0 -19/12 27/4 | 1/6]

Next, we will eliminate the leading coefficient of the third row by adding 19/12 times the second row to the third row:

[1 5/12 -3/4 | 1/6]

[0 1 -5/4 | 2/19]

[0 0 6 | 9/19]

Finally, we will divide the third row by 6 to make the leading coefficient of the third row 1:

[1 5/12 -3/4 | 1/6]

[0 1 -5/4 | 2/19]

[0 0 1 | 3/38]

Now, we can read off the solution from the row-echelon form. The variables x, y, and z correspond to the entries in the last column. Therefore, the solution to the system of linear equations is x = 1, y = 0, and z = -2 (option d).


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The value of a+b+c will be 16 if  \(\frac{5}{2-\sqrt{3}}\) rationalize as  \(\displaystyle{\frac{a + b\sqrt{3}}{c}}\).

Given,

y = \(\frac{5}{2-\sqrt{3}}\)

To solve the given expression we multiply the numerator and denominator by the conjugate of the denominator

\(= \frac{5}{2-\sqrt{3}} \frac{2+\sqrt{3} }{2+\sqrt{3}}\)

\(= \frac{10+5\sqrt{3} }{2^2 - \sqrt{3}^2 }\)

\(= \frac{10+5\sqrt{3} }{4-3 }\)

\(= \frac{10+5\sqrt{3} }{1 }\) = \(\displaystyle{\frac{a + b\sqrt{3}}{c}}\)

Now, by comparing the result we get

a = 10, b = 5, c = 1

hence, a+b+c = 10+5+1 = 16

Therefore, the value of a+b+c will be 16.

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Step-by-step explanation:

If y varies inversely as x, it means that their product is constant. We can write this relationship as y x k = constant, where k is the constant of variation.

To find the value of k, we can use the initial values given: "x=-1 when y=3". Substituting these values into the equation gives us:

3 x k = constant

We don't need to know the value of the constant, just that it is the same throughout. Now we can use this relationship to find x when y is 15:

y x k = constant

15 x k = constant

We can solve for x by isolating it:

15 x k = constant

x = constant / k

Since the constant is the same throughout, we can use the initial values to find k:

3 x k = constant

-1 x k = constant

Dividing these equations gives us:

3 / (-1) = -k / k

-3 = -k^2 / k

Simplifying:

k = -k^2 / 3

Multiplying both sides by -3:

3k = k^2

Rearranging:

k^2 - 3k = 0

Factorizing:

k(k - 3) = 0

So k = 0 or k = 3.

Since k cannot be zero (otherwise y would be zero for all x), we can use k = 3. Therefore, the equation is:

y x 3 = constant

Using this equation to find x when y is 15:

15 x 3 = constant

x = constant / 45

We don't need to know the value of the constant, just that it is the same throughout. Therefore, when y is 15, x is equal to constant divided by 45.

Hopes this helps

The statements that are True about the Correlations is , "Correlations are a measure used to determine the degree to which two variables are related" , the correct option is (c) .

In the question,

few statements about Correlation is given ,

we need to find the statement that is True .

we know that , Correlation is the term that is used to measure the degree of relationship between two variable ,

the correlation can be negative , positive or 0 ,

and the negative correlation implies that if one variable increases then other variable decreases and vice a versa .

So , from the above information about Correlation ,

we conclude that , the True statement is "Correlations are a measure used to determine the degree to which two variables are related. "

Therefore , the statement in option (c) is True  .

The given question is incomplete , the complete question is

Select the statement below that is true about correlations.

(a) Correlations can only be negative

(b) Correlations are a measure of how much one variable changes as the other variable changes

(c) Correlations are a measure used to determine the degree to which two variables are related.

(d) Correlations are a measure of causation between two variables

(e) A negative correlation implies no relationship between variables

(f) Correlations can only be positive .

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Answer:

so each chair will cost 205

205 will be our cost C this is our dependent due to the entire cost being base on how many chairs that will get order

the independent variable will be how many chairs that will be ordered and there are 34 chairs being ordered

34*205= 6970

the total cost will be 6970

Answer:

child byeee kid jdhuwkjikw

Step-by-step explanation:

[21] 50

190 - 90 - 40

[22] 130

180 - 50

[23] 50

Vertical angles

[24] 130

Vertical angles

[25] 40

180 - 90 - 50

[26] 30

180 - 40 - 130

Have a nice day!

    I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

- 18369919

Step-by-step explanation:

Hope that helps!

We cannot claim that the newsletter publisher's statement is incorrect. Hence, the conclusion is uncertain.

The newsletter publisher's claim is uncertain after performing a test at the 0.02 level of significance as the testing firm fails to reject the null hypothesis.

In this case, we cannot claim that the publisher's statement is incorrect without additional tests and proof. Here is an explanation of the above statement.

A hypothesis test is conducted to find out whether or not there is sufficient evidence to contradict a hypothesis. In this case, the hypothesis test's null hypothesis claims that the newsletter publisher's statement is correct.

The alternate hypothesis claims that the newsletter publisher's claim is incorrect. As a result, the null hypothesis is represented by \(H_0\):

p = 0.71 (71%) and

the alternate hypothesis is represented by \(H_a\):

p ≠ 0.71 (71%).

Where 'p' denotes the percentage of newsletter readers who own a Rolls Royce.

The test statistic for a sample proportion can be calculated by

z = (p - P) / √(P(1 - P) / n)

Where 'p' denotes the sample proportion,

P denotes the population proportion, and

n denotes the sample size.

A two-tailed test is used because the alternate hypothesis is written as \(H_a\):

p ≠ 0.71 (71%).

At a 0.02 significance level, the test statistic's critical value is ±2.58 (round off) Because the test statistic does not fall in the rejection region, we fail to reject the null hypothesis.

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The blanks in each statement about the line segment should be completed as shown below.

Since we know U is the midpoint, we can say TU=8x + 11 substituting in our values for each we get:

8x + 11 = 12x - 1

Solve for x

We now want to solve for x.

−4x+11=−1

−4x = -12

x= 3

Solve for TU, UV, and TV

This is just the first part of our question. Now we need to find TU, UV, and TV. Lets start with TU and UV.

TU=8x+11 We know that x=3 so let’s substitute that in.

TU=8(3)+11

TU= 35

We will do the same for UV. From our knowledge of midpoint, we know that TU should equal UV, however let’s do the math just to confirm.

UV=12x−1 We know that x=3 so let’s substitute that in.

UV=12(3)−1

UV= 35

Based on the segment addition postulate, we have:

TU+UV=TV

35+35=TV

TV= 70

Find the detailed calculations below;

TU = UV

8x + 11 = 12x - 1

8x + 11 - 11 = 12x - 1 - 11

8x = 12x - 12

8x - 12x = 12x - 12 - 12x

-4x = -12

x = 3

By using the substitution method to substitute the value of x into the expression for TU, we have:

TU = 8x + 11

TU = 8(3) + 11

TU = 24 + 11

TU = 35

By applying the transitive property of equality, we have:

UV = TU and TU = 15, then UV = 35

By applying the segment addition postulate, we have:

TV = TU + UV

TV = 35 + 35

TV = 70

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If the  dividend of  $1.50 is expected in two months. The European put price is $3.03.

Given:

K=50, r=0.1, σ=0.3, and T=0.25

First step is to find the stock price

S0 = 50−1.50e^ -0.1667×0.1

SO=48.52

Second step is to find di and d2

d1=In(48.52/50)+(0.1+0.09/2)0.25/0.3√0.25

d1 = 0.0414

d2=d1-0.3√0.25

d2 = -0.1086

Third step is to calculate European put price

European put price=-50N(0.1086)e^ -0.1×0.25−48.52N(−0.0414)

European put price=50×0.5432e -^0.1×0.25−48.52×0.4835

European put price=$3.03

Therefore If the  dividend of  $1.50 is expected in two months. The European put price is $3.03.

The complete question is:

A company stock price is $50  a dividend of $1.50 is expected in two months, risk-free rate is 10% per annum, stock price volatility is 30%  with continuous compounding for all maturities. What difference does it make to your calculations.

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Given the ratios, the value of the side is 2.1 units

From the given triangles we should note that

(x+6)/(2x+1) = 12/7.5

cross and multiply to have

7.5(x+6) = 12(2x+1)

Opening the brackets to get

7.5x+45 = 24x +12

Collecting like terms to have

7.5x-24x = 12-45

-16x = -33

making x the subject of the relation

x = -33/-16

x = 2.1

The side is = 2.1 units

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The probability of a Type II error is represented by beta. Thus, the correct answer is option B.

Beta represents the probability of failing to reject the null hypothesis when it is false.

On the other hand, Type I error (alpha) represents the probability of rejecting the null hypothesis when it is true. A Type II error occurs when a false null hypothesis is not rejected. Hence, beta is the probability of making a Type II error.

The null hypothesis is rejected when the p-value is less than or equal to the level of significance, not exceeds it.

The p-value is the probability of obtaining a result as extreme as or more extreme than the observed result when the null hypothesis is true. If the p-value is less than the level of significance, the null hypothesis is rejected, and vice versa.

Hence, the statement "The null hypothesis is rejected when the p-value exceeds the level of significance" is false.

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 y = 3/8x + 1/4 is equation of linear equation .

What in mathematics is a linear equation?

An algebraic equation of the form y=mx+b is referred to as a linear equation. with m the slope and b the y-intercept as the single constant and a first-order (linear) term.

                   The aforementioned is occasionally referred to as a "linear equation of two variables," where y and x are the variables.

                 There are three main types of linear equations: point-slope form, standard form, and slope-intercept form.

3/2x -4y+1=0

  -4y = -3/2x - 1

    y = 3/8x + 1/4

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The complete question is -

Which equation is equivalent to 3/2x -4y+1=0

Answer:

275

Step-by-step explanation:

x-35=240

x=240+35

x=275

The rule of inference being used here is Modus Tollens. Modus Tollens is a valid deductive argument form that states if a conditional statement "If P, then Q" is true and the consequent Q is false, then the antecedent P must also be false.

In the given scenario, the conditional statement is "If the guard dog doesn't know a person, then it barks."

The observation that the dog didn't bark (Q is false) leads to the conclusion that the dog must have known the person (the antecedent P is false).

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a)

Answer:

5, 8, 13, 12, 7, 10, 8, 9, 17, 17, 16, 15, 13, 10, 5, 6, 11, 8, 10, 9, 10, 10, 2, 3, 5, 8

Explanation:

Diginacci Sequence

5+8=13, 8+1=9, 1+3+1+2=7, 1+2+7=10, 7+1+0=8, 1+0+8=9, 8+9=17, 9+1+7=17

Assuming the track is straight, the distance at which they are apart one hour before they meet is; 30 km

We are told that a Nonstop trains leave Toronto and Montreal at the same time each day going to the other city along the main line.

Speed of Train 1 = 120 km/h

Speed of Train 2 = 90 km/h

Time spent by train 1 = 1 hour

Time spent train 2 = 1 hour

Formula for distance is;

Distance = Speed * time

If they leave the same time each day, it means that;

Distance of train 1 = 120 * 1 = 120 km

Distance of train 2 = 90 * 1 = 90 km

Thus, distance at which they will be apart before meeting each other is;

Distance apart = 120 - 90

Distance apart = 30 km

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Answer:

The distance between (4,9) and (10,9) is 6

Step-by-step explanation:
You need to follow this formula!
√x2 - x1^2 + y2 - y1^2

Your first point (4,9) is point 1
The other (10,9) is labeled as point 2

Take the 10 and subtract it from 4 to find the x coordinate.
10-4 = 6
Then you square it
36

Take the 9 and subtract it from the other 9.
0

So far we have √36
Simplify!
=6
Therefore, the distance between (4,9) and (10,9) is 6

The formula for the distance between point (x_1,y_1) and (x_2,y_2) is,

\(\text{d}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Determine the distance between points (4,9) and (10,9) by using distance formula.

\(\text{d}=\sqrt{(10-4)^2+(9-9)^2}\)

            \(=\sqrt{36+0}\)

               \(=\sqrt{36}\)

                  \(=6\)

So distance between the two points is 6.

Answer:

200,000 times

Step-by-step explanation:

The population of China is about 1.4 × 10⁹ . And the hometown of Julie has a population of 7,000 people . We need to find out how many times greater is the population of China than Julie's hometown .

By Question :-

\(\rm\implies Population_{China}= 1.4\times 10^9 \)

\(\rm\implies Population_{Hometown}= 7,000 \)

Times by which population of China is more:-

\(\rm\implies \dfrac{ 1.4 \times 10^9 }{7000} \\\\\rm\implies \dfrac{ 14 \times 10^8}{7\times 10^3}\\\\\rm\implies 2\times 10^{8-3} \\\\\rm\implies 2\times 10^5 \\\\\rm\implies \boxed{\quad \bf 200,000 \quad }\)

Therefore the population of China is greater than 200,000 times .

The equation to plot in the complex Cartesian plane is 2Re(z) - |z²| ≥ -3Im(iz).

To plot the equation 2Re(z) - |z²| ≥ -3Im(iz) graphically, you can follow these steps:

1. Represent the complex number z in terms of its real and imaginary parts, z = x + yi, where x is the real part and y is the imaginary part.

2. Substitute the values of x and y into the equation and simplify it.

3. Separate the equation into real and imaginary parts.

4. For each part, plot the corresponding inequality on the Cartesian plane.

- For the real part, plot the inequality 2x - |(x + yi)²| ≥ -3y.

- For the imaginary part, plot the inequality 0 ≥ 0 (as -3Im(iz) = 0 for all values of x and y).

5. Determine the common region that satisfies both inequalities. This region represents the solution to the original equation.

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The total value Luke now have is $686.29

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

Inital deposit, P = 592

Rate r = 3% annual interest compounded continuously.

Using the above as a guide, we have the following:

The amount after x years is

Amount = P * (1 + r)ˣ

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

Amount = 592 * (1 + 3%)⁵

Evaluate

Amount = 686.29

Hence, the amount is $686.29

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Answer:

djchdjcycuchrivivurtiytvivytivi8fr cgdyhcd8w

The expression where the greatest common factor (GCF) is factored completely is \(2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)\)

The expression completely factored in is

\(2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)\)

Please refer below for the remaining answers.

We have,

Part A:

To rewrite the expression 2x³y + 18xy - 10x²y - 90y so that the greatest common factor (GCF) is factored completely, we can factor out the common terms.

GCF: 2y

\(2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)\)

Part B:

To completely factor the expression, we can further factor the quadratic term.

\(2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)\)

Now,

Part A:

To determine the length of each side of the square given the area expression (9x² + 24x + 16), we need to factor it completely.

The area expression (9x² + 24x + 16) can be factored as (3x + 4)(3x + 4) or (3x + 4)².

Therefore, the length of each side of the square is 3x + 4.

Part B:

To determine the dimensions of the rectangle given the area expression (16x² - 25y²), we need to factor it completely.

The area expression (16x² - 25y²) is a difference of squares and can be factored as (4x - 5y)(4x + 5y).

Therefore, the dimensions of the rectangle are (4x - 5y) and (4x + 5y).

Now,

f(x) = 2x² - 5x + 3

Part A:

To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x.

2x² - 5x + 3 = 0

The quadratic equation can be factored as (2x - 1)(x - 3) = 0.

Setting each factor equal to zero:

2x - 1 = 0 --> x = 1/2

x - 3 = 0 --> x = 3

Therefore, the x-intercepts of the graph of f(x) are x = 1/2 and x = 3.

Part B:

To determine if the vertex of the graph of f(x) is maximum or minimum, we can examine the coefficient of the x^2 term.

The coefficient of the x² term in f(x) is positive (2x²), indicating that the parabola opens upward and the vertex is a minimum.

To find the coordinates of the vertex, we can use the formula x = -b / (2a), where a and b are the coefficients of the quadratic equation.

For f(x),

a = 2 and b = -5.

x = -(-5) / (2 x 2) = 5/4

To find the corresponding y-coordinate, we substitute this x-value back into the equation f(x):

f(5/4) = 25/8 - 25/4 + 3 = 25/8 - 50/8 + 24/8 = -1/8

Therefore, the vertex of the graph of f(x) is at the coordinates (5/4, -1/8), and it is a minimum point.

Part C:

To graph f(x), we can start by plotting the x-intercepts, which we found to be x = 1/2 and x = 3.

These points represent where the graph intersects the x-axis.

Next,

We can plot the vertex at (5/4, -1/8), which represents the minimum point of the graph.

Since the coefficient of the x² term is positive, the parabola opens upward.

We can use the vertex and the symmetry of the parabola to draw the rest of the graph.

The parabola will be symmetric with respect to the line x = 5/4.

We can also plot additional points by substituting other x-values into the equation f(x) = 2x² - 5x + 3.

By connecting the plotted points, we can draw the graph of f(x).

The steps to graph f(x) involve plotting the x-intercepts, the vertex, and additional points, and then connecting them to form the parabolic curve.

The answer in part A (x-intercepts) and part B (vertex) are crucial in determining these key points on the graph.

Thus,

The expression where the greatest common factor (GCF) is factored completely is \(2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)\)

The expression completely factored in is

\(2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)\)

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The range of x are;

1. x < -30

2. x > 8

3. x > 15

4. x < -2

A relationship between two expressions or values that are not equal to each other is called 'inequality.

1. -130 > 50x +20

-130-20> 50x

-150 > 50x

-150/50 > x

-30 > x

x < -30

2. -8(x-3) < -40

-8x +24< -40

collect like terms

-8x < -64

x > -64/-8

x > 8

3. 2x - 22 > 8

collect like terms

2x > 30

divide both sides by 2

x > 30/2

x > 15

4. -35 < -5(x+9)

-35 < -5x -45

collect like terms

10 < -5x

-2 > x

x < -2

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Answer:

a = 84°

Step-by-step explanation:

∠ QPR and ∠ TPR are adjacent and supplementary, thus

∠TPR = 180° - 123° = 57°

Given there are parallel lines , then

∠ PTR = 27° ( alternate angle )

The external angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ TRS is an external angle , thus

∠ TRS = a = 57° + 27° = 84°

Answer:

84 degrees.

Step-by-step explanation:

m < R + m < T = 123  (External angle of a triangle theorem)

m < T =  27 degrees (alternate angle to 27 degrees).

So m < R = 123 - 27 = 96 degrees.

Finally m < a = 180 - 96 = 84 degrees  ( as it is adjacent to < R)