Solve using the substitution method. What is the y coordinate of the solution?

y = 3x - 6

15 x + 3y= 30

Question 1 options:

y = 2


y = -2


y= 3x -6


y = 0

The steps to solve the inverse variation will be:

The example will be y varies inversely with x and y = 2 when x = 5. Find y when x = 30

Step 1: Write the variation equation: y = k/x or k = xy:

k = xy

Step 2: Substitute in for the given values of x and y:

k = (2)(5) = 10

Step 3: Rewrite the variation equation: y = k/x with the known value of k (10):

y = 10/x

Step 4: Substitute the remaining values and find the unknown:

y = 10/30

y = 1/3

Therefore, y is 1/3 when x is 30.

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Each member of the club needs to pay £ 4.895 to cover the cost of hiring the buses.

A youth club's 143 members and eight leaders ride a bus to a bowling alley.

The buses for hire by the beezer bus company hold 32 passengers each.

The cost of each bus to hire is £140.

There are eight leaders and 143 members.

Therefore, there are a total of 143 + 8 = 151 passengers.

So, the number of buses required will be:

= 151 / 32 =  4.7 ≈ 5 buses

Therefore, the cost of hiring 5 buses will be:

= 5 × £140 = £ 700

As the eight leaders will not ay.

Therefore, the amount each member needs to pay is:

= £ 700 / 143

= £ 4.895

Each member of the club needs to pay £ 4.895 to cover the cost of the buses.

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In this question about matrices, we know that If m equals n and the rank of A is n, A is invertible,  If the rank of A is smaller than the rank of A's augmented matrix, there is no solution for the linear system, and if the rank of A equals the rank of A's augmented matrix, there is a unique solution for the linear system. So, options A, C, and D are the correct answers.

The Number of independent rows determines a matrix's rank.

A square matrix has "full rank" and is non-singular when its rank equals the number of rows, at which point it has an inverse.

So, statement "A" is right.

Dimension of row space and column space may not be equal even if the matrix is square.

So, Statement "B" is incorrect.

For "No solution", the condition is that the Rank of the matrix is lesser than the augmented matrix.

So, the statement "C" is correct.

For the "Unique solution", the condition is that the Rank of the matrix is equal to the augmented matrix.

So, the statement "D" is correct.

So, we can check option B as the incorrect option.

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Answer:

210-20x=y

Step-by-step explanation:

150 is after 3 weeks of withdrawing 20 so $60

150+60=210 is the beginning amount

210-20x=y

Answer:

54 mi/hr

Step-by-step explanation:

\(\frac{226.8}{4.2}=54\) mi/hr

Answer:

m<CAB = 54°

m<ABC = 21°

m<ACB = 105°

m<DCB = 75°

Step-by-step explanation:

Part 1: Solve for x

The sum of the 3 interior angles of a triangle always equals 180°.

** Take note

Lets call m<CAB, angle A.

Lets call m<ABC, angle B.

Lets call m<ACB, angle C.

Lets call m<DCB, angle D.

So A + B + C = 180

Therefore we have

\((13x-11)+(4x+1)+C=180\)

We have 1 more angle.

They gave us an exterior angle to help us find angle C.

A straight line is 180°.

They gave us one of 2 angles.

So

\(180-(18x-15)=C\)

We can substitute \(180-(18x-15)\) for \(C\) in our first equation.

All together we have.

\((13x-11)+(4x+1)+(180-(18x-15))=180\)\(13x-11+4x+1+180-(18x-15)=180\)

Now lets simplify and solve for \(x\).

Simplify each term.

Apply the distributive property.

\(13x-11+4x+1+180-(18x)--15=180\)

\(13x-11+4x+1+180-18x+15=180\)

Simplify by adding like terms.
Add \(13x\) and \(4x\).

\(17x-11+1+180-18x+15=180\)

Subtract \(18x\) from \(17x\).

\(-x-11+1+180+15=180\)

Simplify by adding numbers.

Add \(-11\) and \(1\).

\(-x-10+180+15=180\)

Add \(-10\) and \(180\).

\(-x+170+15=180\)

Add \(170\) and \(15\).

\(-x+185=180\)

Move all terms not containing \(x\) to the right side of the equation.

Subtract \(185\) from both sides of the equation.

\(-x=180-185\)

Subtract \(185\) from \(180\)

\(-x=5\)

Divide each term by − 1 and simplify.

\(\frac{-x}{-1} =\frac{-5}{-1}\)

\(x=5\)

Part 2: Find the numerical value of each angle

We can now substitute 5 for x into the equations from the picture.

\((13*5-11)+(4*5+1)+C=180\)

Angle A is \(13x-11\)

So A equals 54°

Angle B is \(4x+1\)

So B equals 21°

Remember \(A + B + C = 180\). We can solve for \(C\) and we get.

\(C=180-A-B\)

\(C=180-54-21\)

So C equals 105°

Remember a straight line is 180°.

We have 2 angles on the straight line.  C and D

Therefore, \(C+D=180\)

\(D=180-C\)

\(D=180-105\)

So D equals 75°

We can check. It gave us \(D=18x-15\)

\(D=18*5-15\)

\(D=90-15\)

\(D=75\)

The given regressions analyze the relationship between wages and gender by considering the average hourly earnings for females and males in a population. The coefficients in the equations provide insights into the average wage differences between genders.

The given question asks us to consider three regressions that hold for the same population. The three regressions are as follows:

1. Wage = A0 + A1 * Female + Ui
2. Wage = B0 + B2 * Male + Vi
3. Wage = C1 * Female + C2 * Male + Ei

In these equations, "Wage" refers to average hourly earnings, "U," "V," and "E" are the error terms of the regressions, and "Female" is a variable that takes the value of 1 if the observation refers to a female and 0 if it refers to a male. Similarly, "Male" is a variable that takes the value of 1 if the observation refers to a male.

Let's break down these equations:

1. The first regression equation states that the wage is equal to A0 plus the product of A1 and the "Female" variable, added to an error term "Ui."

2. The second regression equation states that the wage is equal to B0 plus the product of B2 and the "Male" variable, added to an error term "Vi."

3. The third regression equation states that the wage is equal to the product of C1 and the "Female" variable, plus the product of C2 and the "Male" variable, added to an error term "Ei."

These regressions are used to analyze the relationship between wages and gender. By including the variables "Female" and "Male" in the equations, we can estimate the impact of gender on wages.

The coefficients A1, B2, and C1 represent the average difference in wages between females and males, while the coefficients A0, B0, and C2 represent the average wages for males when the respective gender variable is 0.

It's important to note that these equations are specific to the population being studied and the variables included in the analysis.

The error terms (Ui, Vi, and Ei) account for factors not included in the regressions that affect wages, such as education, experience, and other socioeconomic variables.

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According to this, 3/10 of an inch on a map corresponds to 7/8 miles in actual distance.

In the case of a unit rate expressed as a fraction, the denominator is 1 unit. Divide the denominator by the denominator to represent a rate as a unit rate.

According to this, 3/10 of an inch on a map corresponds to 7/8 miles in actual distance.

Conversion Unit, This unit of conversion, also known as a rate, is utilized to help us map out greater numbers on a smaller piece of paper. Miles to Inches conversion factor is

Data provided 3/10 in equals 7/8 miles.

This suggests that we would depict the real 7/8 miles of distance on the map by 3/10 inches. Inevitably, this would result in a reduction in size or length.        

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To make a 1 litter solution of 0.45 M K₂SO₄ using K₂SO₄ powder and water, you'll need to follow these steps:

Determine the number of moles of K₂SO₄ needed:

The molarity (M) of a solution is defined as the number of moles of solute per liter of solution. In this case, the desired molarity is 0.45 M, and the volume of the solution is 1 liter.

Moles of K₂SO₄= Molarity × Volume

= 0.45 mol/L × 1 L

= 0.45 mol

Calculate the mass of K₂SO₄ needed:

To determine the mass of K₂SO₄ required, you need to know the molar mass of K₂SO₄. The molar mass of K₂SO₄ is the sum of the atomic masses of its constituent elements: 2 potassium (K) atoms, 1 sulphur (S) atom, and 4 oxygen (O) atoms.

Molar mass of K₂SO₄ = 2 × atomic mass of K + atomic mass of S + 4 × atomic mass of O

= 2 × 39.10 g/mol + 32.07 g/mol + 4 × 16.00 g/mol

= 174.27 g/mol

Mass of K₂SO₄ = Moles × Molar mass

= 0.45 mol × 174.27 g/mol

= 78.42 g

You will need approximately 78.42 grams of K₂SO₄ powder.

Dissolve K₂SO₄ in water:

Measure out the calculated mass of K₂SO₄(approximately 78.42 grams) using a balance. Add the K₂SO₄ powder to a clean, dry container. Then, gradually add water while stirring to dissolve the powder completely. Use a graduated cylinder to measure 1 litterof water, and make sure the K₂SO₄ is fully dissolved in the water.

Adjust the final volume:

After dissolving the K₂SO₄, check the final volume. If the solution is slightly below 1 litter, you can add additional water to reach the desired volume of 1 litter. Stir the solution to ensure uniformity.

By following these steps, you will have prepared 1 litterof a 0.45 M solution of K₂SO₄ using K₂SO₄ powder and water.

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The estimated area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints is approximately 0.8916.

To estimate the area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints, we can use the right Riemann sum method.

The width of each rectangle, Δx, is given by the interval width divided by the number of rectangles.

In this case, Δx = (π/2 - 0)/4 = π/8.

To calculate the right endpoint values, we evaluate f(x) at the right endpoint of each rectangle.

For the first rectangle, the right endpoint is x = π/8.

For the second rectangle, the right endpoint is x = π/4.

For the third rectangle, the right endpoint is x = 3π/8.

And for the fourth rectangle, the right endpoint is x = π/2.

Now, let's calculate the area for each rectangle by multiplying the width (Δx) by the corresponding height (f(x)):

Rectangle 1: Area = f(π/8) * Δx = 5cos(π/8) * π/8

Rectangle 2: Area = f(π/4) * Δx = 5cos(π/4) * π/8

Rectangle 3: Area = f(3π/8) * Δx = 5cos(3π/8) * π/8

Rectangle 4: Area = f(π/2) * Δx = 5cos(π/2) * π/8

Now, let's calculate the values:

Rectangle 1: Area = 5cos(π/8) * π/8 ≈ 0.2887

Rectangle 2: Area = 5cos(π/4) * π/8 ≈ 0.3142

Rectangle 3: Area = 5cos(3π/8) * π/8 ≈ 0.2887

Rectangle 4: Area = 5cos(π/2) * π/8 ≈ 0

Finally, to estimate the total area, we sum up the areas of all four rectangles:

Total Area ≈ 0.2887 + 0.3142 + 0.2887 + 0 ≈ 0.8916

Therefore, the estimated area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints is approximately 0.8916.

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Answer:

The percentage should be 6%

Step-by-step explanation:
Calculation of percentage:

Since we know about the  45c as a percentage of $3
c=3/45
which equals 0.06%

Answer:

160

Step-by-step explanation:

72=0.45x

72/0.45=x

x=160

The required difference in time taken by bob and sam is 0.8 hour.

Speed is defined as. The rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude.

Bob can drive 50 miles in 40 minutes.

So, Speed of bob = 50×60/40 = 75 miles/hour

And Sam can drive 90 miles in 105 minutes.

Speed of Sam = 90×60/105 = 51.4 miles/hour

Now/

Time taken by bob(d) = 120/75 = 1.6

Similarly,

Time taken by Sam(e) = 120/51.4 = 2.4

So,

d - e

|1.6 - 2.4|

0.8

Thus,required difference in time is 0.8.

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Answer:

d.81

Step-by-step explanation:

81 can be represented by a 9x9 square grid. The rest of the numbers would be represented on rectangular grids.

Answer:

D. 81

Step-by-step explanation:

81 can be represented by 9X9 square grid

9^2 = 81

The given identity is verified as follows:

Starting with the left side of the equation: tan(A - B)

Using the trigonometric identity for the difference of two angles, we have:

tan(A - B) = (tan A - tan B) / (1 + tan A tan B)

This matches the right side of the equation: (tan A - tan B) / (1 + tan A tan B)

To verify the given identity, we need to manipulate the left side of the equation using trigonometric identities and simplify it until it matches the right side of the equation.

Starting with the left side, we have tan(A - B). Using the trigonometric identity for the difference of two angles, we can express this as (tan A - tan B) / (1 + tan A tan B).

By applying the identity for the difference of two angles, we can rewrite tan(A - B) as (tan A - tan B) / (1 + tan A tan B). This is because tan(A - B) is equivalent to the ratio of the difference of the tangent values of the angles A and B, divided by 1 plus the product of the tangent values of angles A and B.

After simplification, we see that the left side of the equation matches the right side of the equation, (tan A - tan B) / (1 + tan A tan B).

Therefore, the given identity is verified.

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Rate of change of x with respect to \(\alpha\) when \(\alpha =\frac{\pi }{3}\) is 5ft/s.

Since the ladder is 10ft long resting against a vertical wall.

Let the angle between the top of the ladder and the wall is \(\alpha\) .

And let the distance from the bottom of the ladder to the wall is x.

Thus we need to find the rate of change of x with respect to \(\alpha\)  when \(\alpha =\frac{\pi }{3}\)

Consider L to be the length of the ladder.

Then, L = 10ft

Thus, we get the relation between the angle and distance x i.e.

x = L \(\sin \alpha\)

On differentiating the above equation,

\(\frac{dx}{dt} =L \cos \alpha\)

Now after putting the values \(\alpha =\frac{\pi }{3}\) in above equation, we get,

\(=(10)\cos(\frac{\pi }{3} )=(10)(\frac{1}{2} )=5\)

Therefore, \(\frac{dx}{dt} =5\) ft/s

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Answer:

Pictograph

Step-by-step explanation:

The total number of seeds that Josiah would plant would be = nR×S

To determine the total number of seeds that Josiah will plant will be to add the seeds in the total number of rooms he planted.

Let each row be represented as = nR

Where n represents the number of rows planted by him.

Let the seed be represented as = S

The total number of seeds he planted = nR×S

Therefore, the total number of seeds that was planted Josiah would be = nR×S.

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Answer:

y = -2x+9

negative slope starts at 9 ( y intercept)

Answer:

to simplify 3^4 you need to do 3x3x3x3 which is 3x3=9 9x9=81 so your final awnser is 81 :)

Step-by-step explanation:

Based on the given information, Mrs. Cheng's class lost fewer pencils overall based on the data displayed.

The reason behind this is:

Range: The range is the difference between the highest and lowest values in the data.

In Mrs. Cheng's class, the range is 50 - 5 = 45 pencils, while in Mr. Johnson's class, the range is 45 - 7 = 38 pencils. Since the range is smaller in Mrs. Cheng's class, it indicates a narrower spread of data.

2. Median: The median is the middle value in the data when it is arranged in ascending order.

In Mrs. Cheng's class, the median is 16 pencils, while in Mr. Johnson's class, the median is 11 pencils. Since the median is smaller in Mr. Johnson's class, it suggests a smaller value at the center of the data.

Therefore, based on the smaller range and smaller median value, Mrs. Cheng's class lost fewer pencils overall according to the displayed data.

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The volume of the  is right triangular prism is   600 cubic feet.

In a right triangular prism, the area of the triangular base is 50 square feet, and the height of the prism is 12 feet. To find the volume of the prism, we can use the formula:

Volume = Base Area × Height

Step 1: Identify the base area, which is given as 50 square feet.
Step 2: Identify the height of the prism, which is given as 12 feet.
Step 3: Multiply the base area by the height to find the volume.

Volume = 50 square feet × 12 feet = 600 cubic feet

So, the volume of the right triangular prism is 600 cubic feet.

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Answer:

C

Step-by-step explanation:

just took the quiz

A function assigns the value of each element of one set to the other specific element of another set. The output of the function is 6, 2, –3, 4.

A function assigns the value of each element of one set to the other specific element of another set.

The output of the given function in the value of the dependent variable, in the given case, x is the independent variable and upon this independent variable the value of the function will be dependent, therefore, the function will be the output of the function.

Thus, the values in the table that are under g(x) are the range or the output of the function.

Hence, the output of the function is 6, 2, –3, 4.

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Answer:

(2;-5) and (0;-4).

Step-by-step explanation:

if the given graph is the same as in the attached picture (y=-0.5x-4), then two points only belong to it.

Answer:

y = 5x - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (1, 4) and (x₂, y₂ ) = (2, 9)

m = \(\frac{9-4}{2-1}\) = \(\frac{5}{1}\) = 5 , then

y = 5x + c ← is the partial equation

To find c use any ordered pair from the table and substitute into the partial equation.

Using (3, 14 ) , then

14 = 15 + c ⇒ c = 14 - 15 = - 1

y = 5x - 1 ← equation of line

The missing angle is 90°. So, to obtain the values of the sides given the lengths we will have:

8. PT = 1

   PV = 2

9. VT = 0.76

   PV = 0.66

10. PT = 3

     PV = 6

11. PV =0.58

    PT =1.154

12. PT = 1.73

    VT = 3

13. VT = 3

     PV = 3.5

The given triangle is a scalene triangle because of the three different angles it has which sum up to 180 degrees. The sides will also be different.

For the first triangle whose known side is √3, the missing values can be obtained this way:

sin 60°/ √3 = sin 90/PV

PV = √3 Sin 90/ sin 60

PV = 1.732/0.866

= 2

PT = sin 60/ √3 = sin 30/ PT

PT = √3 sin 30/sin 60

PT = 1

Using this same pattern, the values for the other figures can be obtained.

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Answer:

Undefined

Step-by-step explanation:

The Xs are the same!

The lower limit of the 90% confidence interval is 0.429 when in a survey of 200 randomly chosen American adults, 104 responded in favor of the proposed proposal.

Given that

In a survey of 200 randomly chosen American adults, 104 responded in favor of the proposed proposal. Calculate a 90% confidence interval for the percentage of all U.S. adults who support the proposal based on the results of this poll (at the time of the poll). Complete the table below after that. Carry your calculations to a minimum of three decimal places.

We have to find the lower limit of 90%.

We know that

In a poll of 200 randomly selected U.S. Among adults, 104 expressed support for the novel idea.

p-hat = 104/200 = 0.52

ME = z×√[pq/n] = 2.5758×√[0.52*0.48/200] = 0.091

Now, the lower limit of the 90% confidence interval well be

p-hat-ME = 0.52-0.091 = 0.429

Therefore, The lower limit of the 90% confidence interval is 0.429 when in a survey of 200 randomly chosen American adults, 104 responded in favor of the proposed proposal.

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