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What's the probability of getting a number less than 5 and a head when rolling a die and then tossing a coin?

Answer:

B the second graph

Step-by-step explanation:

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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.

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.

Answer: middle

Step-by-step explanation:

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.

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 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.

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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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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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

Answer:

Step-by-step explanation:

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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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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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!

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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