A circle has a center at (1,-2) and radius of 4. Does the point (3.4,1.2) lie on the circle? Justify your answer.

Answer:

Step-by-step explanation:

Hence, the tax rate is [tex]8[/tex]%.

What is the tax rate?

A tax rate is a percentage at which an individual or corporation is taxed.

The United States, both the federal government and many of the states, uses a progressive tax rate system, in which the percentage of tax charged increases as the amount of the person's or entity's taxable income increases.

Here given that,

Lamar buys $[tex]75[/tex] worth of clothes. He pays $[tex]81[/tex],including sales tax.

So,

Sales Tax = $[tex]81[/tex] - $[tex]75[/tex]

= $[tex]6[/tex]

Then the Sales Tax Rate

= [tex]\frac{6}{75}[/tex]  × [tex]100=8[/tex] %

Hence, the tax rate is [tex]8[/tex]%.

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Subtracting a-4 from 4a+16 and then simplifying the expression will be 3a + 20.

This is a simple expression and we have to subtract a-4 from 4a+16 and then simplify the answer. This will be:

(4a + 16) - (a - 4)

= 4a - a + 16 + 4

= 3a + 20

In conclusion, based on the calculation above, the answer is 3a + 20.

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Final answer:

The sample size is calculated to be 200 based on the percentage for Candidate A. From the sample, 120 students said they will vote for Candidate C. Predicting based on this sample, 1,500 students in the school will vote for Candidate C.

Explanation:

To find the number of students in the sample who said they will vote for Candidate C, we need to use the percentages given for each candidate. If Candidate A is 25%, Candidate B is 15%, and Candidate C is 60%, and knowing that 50 students in the sample voted for Candidate A, we can determine the total sample size. Since Candidate A represents 25% of the sample, we can calculate the total sample size using the equation 50 = 0.25 × (total sample size). Solving for total sample size gives us 200.

With the sample size known, we can calculate the number of students who said they will vote for Candidate C by taking 60% of 200, which is 120 students in the sample. To predict the number of students in the school who will vote for Candidate C, we use the proportion of the sample who choose Candidate C to estimate the proportion for the entire school population. Since there are 2,500 students in the school, we predict that 60% of 2,500 will vote for Candidate C, which amounts to 1,500 students.

The volume of a cube is found with the following formula:

[tex] l \times w \times h [/tex]

The length, width, and height must all be the same value in a cube. This means that you can replace variables l, w, and h with one variable, s:

[tex] \boxed{s} \times s \times s = s^3 [/tex]

The expression s can represent the length of a side of the cube.

The expression represents s, the length of a side of the cube is [tex]\rm s^3=64[/tex].

The volume of the cube formula is:

The volume of a Cube = Length × Width × Height

The volume of a cube is 64 cubic inches.

where s is the length of a side of the cube.

The side of the cube is;

[tex]\rm The \ volume \ of\ a\ Cube = Length \times Width \times Height \\\\ The \ volume \ of\ a\ Cube =s \times s \times s\\\\The \ volume \ of\ a\ Cube =s^3\\\\s^3=64[/tex]

Hence, the expression represents s, the length of a side of the cube is [tex]\rm s^3=64[/tex].

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Answer:

1,302 square feet

Step-by-step explanation:

Be

A = 2,224 total square feet to paint

B = 922 square feet already painted

C =? square feet left to paint

According to the description given,

A = B + C

Isolating C,

C = A - B

C = 2,224 - 922

C = 1,302 square feet left to paint

Hope this helps!

Answer:

D. [tex]y=5x[/tex]

Step-by-step explanation:

We have been given a table of values. We are asked to find the equation that shows the relationship between x and y.

x          y

0         0

1           5

2         10

3         15

Upon looking at our given table, we can see that with each increase in x value, the value of x increases by 5. This means that slope of our given line is 5.

We can also see that initial value or y-intercept is 0.

Upon substituting our given values in slope intercept form of equation, we will get:

[tex]y=5x+0[/tex]

[tex]y=5x[/tex]

Therefore, our required equation is [tex]y=5x[/tex] and option D is the correct choice.

To find the number of units the company needs to sell to make maximum profit, we need to find the vertex of the parabola represented by the profit function. The vertex can be found using the formula x = -b / (2a), where a and b are the coefficients of the quadratic function. In this case, the company needs to sell 1500 units to make a maximum profit.

The profit function is given as p(x) = -2[tex]x^2[/tex] + 60x - 2, where p is the profit in thousands of dollars and x is the number of units sold in hundreds. To find the quantity that yields the maximum profit, we need to find the vertex of the parabola represented by the profit function. The x-coordinate of the vertex can be found using the formula x = -b / (2a), where a and b are the coefficients of the quadratic function. In this case, a = -2 and b = 60. Plugging these values into the formula, we get x = -60 / (2*(-2)) = 15. Since x represents the number of units sold in hundreds, the company needs to sell 1500 units to make a maximum profit.

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Answer:

The y-coordinate of the solution is, 10

Step-by-step explanation:

Given the system of equation:

[tex]y = -2x+4[/tex]            ....[1]

[tex]y=x^2+4x+13[/tex]         ....[2]

Equate the equation [1] and [2] we have;

[tex]-2x+4 = x^2+4x+13[/tex]

Add 2x to both sides of an equation:

[tex]4 = x^2+6x+13[/tex]

Subtract 4 from both sides we have;

[tex]0= x^2+6x+9[/tex]

or

[tex]x^2+6x+9=0[/tex]

Using perfect square:

[tex](x+a)^2 = x^2+2ax+a^2[/tex]

⇒We can write the equation as:

[tex]x^2+2 \cdot 3x+3^2=0[/tex]

then;

[tex](x+3)^2 = 0[/tex]

⇒[tex]x+3 = 0[/tex]

Subtract 3 from both sides we have;

x = -3

Substitute value of x in [1] we have;

[tex]y = -2(-3)+4[/tex]

⇒[tex]y =6+4=10[/tex]

Solution for the given system of equation = (-3, 10)

Therefore, the  y-coordinate of the solution is, 10

The value of the expression 24 – (7 + 5) ÷ 6 + 8 is: 30

What is BODMAS rule?

The brackets must be solved first, then powers or roots (i.e. of), Division, Multiplication, Addition, and finally Subtraction, according to the BODMAS rule. Any phrase can only be solved correctly if the BODMAS rule or the PEDMAS rule is used.

In the question, The given expression is 24 – (7 + 5) ÷ 6 + 8.

we will solve this expression using the BODMAS rule

which states the order of the operator in which we should use them in an expression.

That is:

B for brackets;

O: for of

D: for Division

M: for Multiplication

A: for Addition

S: for Subtraction

So, using the same in the given expression:

24 – (7 + 5) ÷ 6 + 8

Removing the bracket by solving it first:

⇒24 – 12 ÷ 6 + 8

After that: Divide :

⇒24-2+8

Then Addition:

⇒32-2:

At last: by subtraction, we get:

⇒30

Hence, the value of the expression 24 – (7 + 5) ÷ 6 + 8

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The area of the actual playground is [tex]\( 15000 \)[/tex] square feet. To solve this problem, we need to understand the relationship between the scale drawing and the actual playground dimensions.

Let's denote:

- [tex]\( l \)[/tex] as the length of the scale drawing,

- [tex]\( w \)[/tex] as the width of the scale drawing,

- [tex]\( L \)[/tex]  as the length of the actual playground, and

- [tex]\( W \)[/tex] as the width of the actual playground.

Given that the dimensions of the actual playground are 50 times the dimensions of the scale drawing, we have the following relationships:

[tex]\[ L = 50l \][/tex]

[tex]\[ W = 50w \][/tex]

We are given that the area of the scale drawing is 6 square feet. The area of a rectangle is given by the formula [tex]\( \text{Area} = \text{length} \times \text{width} \).[/tex] So, for the scale drawing:

[tex]\[ \text{Area of scale drawing} = l \times w = 6 \][/tex]

Now, we need to find the length and width of the actual playground and then calculate its area.

From the relationship between the actual playground and the scale drawing, we have:

[tex]\[ L = 50l \][/tex]

[tex]\[ W = 50w \][/tex]

So, we can express [tex]\( l \) and \( w \)[/tex] in terms of [tex]\( L \) and \( W \)[/tex]:

[tex]\[ l = \frac{L}{50} \][/tex]

[tex]\[ w = \frac{W}{50} \][/tex]

Now, let's substitute these expressions into the equation for the area of the scale drawing:

[tex]\[ \text{Area of scale drawing} = \left(\frac{L}{50}\right) \times \left(\frac{W}{50}\right) = 6 \][/tex]

[tex]\[ \frac{L \times W}{2500} = 6 \][/tex]

To find the area of the actual playground, we need to solve for [tex]\( L \times W \):[/tex]

[tex]\[ L \times W = 6 \times 2500 = 15000 \][/tex]

Therefore, the area of the actual playground is [tex]\( 15000 \)[/tex] square feet.

Heads - 9

Tails - 16

----

Probability of heads = 9/25 = 0.36 = 36%

Probability of tails = 16/25 = 0.64 = 64%

----

Heads = 36%

Tails = 64%

----

The experimental probability basically says the answer but the theoretical probability clears out the answer.

The area of a 2D form is the amount of space within its perimeter. The given statement is true.

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

Given that radius of the circle is 12 units, and the radius of the sphere is 6 units.

The area of the circle  = π(12)² = 144π units²

The surface area of the sphere = 4π(6)² = 144π units²

As it can be observed that the area of a circle of radius 12 units is equal to the surface area of a sphere of radius 6 units.

Hence, the given statement is true.

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2[L + W] =22

L*W = 28

W = 28/L sub this in the first equation

Solve for L:

2 (L + 28/L) = 22

Divide both sides by a constant to simplify the equation.

Divide both sides by 2:

L + 28/L = 11

Write the left hand side as a single fraction.

Bring L + 28/L together using the common denominator L:

(L^2 + 28)/L = 11

Multiply both sides by a polynomial to clear fractions.

Multiply both sides by L:

L^2 + 28 = 11 L

Move everything to the left hand side.

Subtract 11 L from both sides:

L^2 - 11 L + 28 = 0

Factor the left hand side.

The left hand side factors into a product with two terms:

(L - 7) (L - 4) = 0

Find the roots of each term in the product separately.

Split into two equations:

L - 7 = 0 or L - 4 = 0

Look at the first equation: Solve for L.

Add 7 to both sides:

L = 7 or L - 4 = 0

Look at the second equation: Solve for L.

Add 4 to both sides:

L = 7       or L = 4         and        W=4      or W = 7

The cylinder has a greater volume than the sphere when both have the same diameter and the cylinder's height is equal to its diameter, as the formulas for their volumes show that V_cylinder > V_sphere.

The question asks which shape has a greater volume: a sphere with the same diameter as a cylinder or a cylinder where the height is equal to the diameter. To solve this, we need to compare their volumes using mathematical formulas.

The volume of a sphere with radius r is given by V_sphere = (4/3) * π * r^3. Since the diameter of the cylinder is the same as the diameter of the sphere, we can use the same value for r, where r is half of the diameter.

The volume of a cylinder with radius r and height h (which, in this case, is also 2r) is calculated as V_cylinder = π * r^2 * h. For the cylinder, since h = 2r, we substitute to get V_cylinder = π * r^2 * (2r) = 2 * π * r^3.

Comparing the two volumes, it is clear that the volume of the cylinder (2 * π * r^3) is greater than that of the sphere ((4/3) * π * r^3). Therefore, the cylinder has a greater volume than the sphere when both shapes have the same diameter and the cylinder's height is equal to its diameter.

Answer:

B. ma

Step-by-step explanation:

In a circle, equal chords are equidistant from the centre.

In the given circle, OE = JR = 3.8.

Therefore, chords OE and JR are equal.

Hence, they should be equidistant from the center.

Their distances from the center are:

ML and MA

So, ML is congruent to MA.