The probability of event A is 0.56. and the probability of event B is 0.34. If A and B are independent events, then P(A and B) =

0.1904
0.289
0.8096
0.90

[tex]\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{-\frac{9}{2}})~\hspace{10em} slope = m\implies -\cfrac{1}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\left( -\cfrac{9}{2} \right)=-\cfrac{1}{4}[x-(-2)] \\\\\\ y+\cfrac{9}{2}=-\cfrac{1}{4}(x+2)\implies y+\cfrac{9}{2}=-\cfrac{1}{4}x-\cfrac{1}{2}\implies y=-\cfrac{1}{4}x-\cfrac{1}{2}-\cfrac{9}{2}[/tex]

[tex]\bf y=-\cfrac{1}{4}x-\cfrac{10}{2}\implies y=-\cfrac{1}{4}x\stackrel{\stackrel{b}{\downarrow }}{\boxed{-5}}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

Answer:

radius = 30 yd , cost of cement = $7065

Step-by-step explanation:

First we will find the area of the circular sectors. From that we can find the cost of cement and their radius.

The area of the playground is ...

playground area = (109 yd)^2 = 11,881 yd^2

Then the area of the skating rinks is:

rink area = playground area - remaining field

rink area = 11,881 yd^2 - 9,055 yd^2 = 2,826 yd^2

Then the cost of cement for the rink area is ...

(2826 yd^2)($2.50 yd^2) = $7065

The four quarter-circle skating rinks add to a total area of a full circle. That area is given by ...

A = πr^2

Put the values in the formula:

2826 = 3.14r^2

Divide both sides by 3.14

900 = r^2

By taking square root at both sides we get,

30 = r

The radius of each quadrant is 30 yards....

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}x-3y-2z=-3&(1)\\3x+2y-z=12&(2)\\-x-y+4z=3&(3)\end{array}\right\\\\\text{add both sides of the equations (1) and (3):}\\\\\underline{+\left\{\begin{array}{ccc}x-3y-2z=-3\\-x-y+4z=3\end{array}\right}\\.\qquad-4y+2z=0\qquad\text{add 4y to both sides}\\.\qquad2z=4y\qquad\text{divide both sides by 2}\\.\qquad\boxed{z=2y}\\\\\text{Put it to (2)}:\\\\3x+2y-2y=12\\3x=12\qquad\text{divide both sides by 3}\\\boxed{x=4}\\\\\text{Put the value of x to (1) and (3):}[/tex]

[tex]\left\{\begin{array}{ccc}4-3y-2z=-3&\text{subtract 4 from both sides}\\-4-y+4z=3&\text{add 4 to both sides}\end{array}\right\\\left\{\begin{array}{ccc}-3y-2z=-7&\text{multiply both sides by 2}\\-y+4z=7\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-6y-4z=-14\\-y+4z=7\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-7y=-7\qquad\text{divide both sides by (-7)}\\.\qquad\boxed{y=1}\\\\\text{Put the value of y to the second equation:}[/tex]

[tex]-1+4z=7\qquad\text{add 1 to both sides}\\4z=8\qquad\text{divide both sides by 4}\\\boxed{z=2}[/tex]

To simplify the expression √(5/8), you can simplify the numerator and denominator separately. The square root of 8 can be simplified to 2√2. Rationalizing the denominator, the final simplified form is √10 / 4.

To simplify the expression √(5/8), we can first simplify the numerator and denominator of the fraction separately. The square root of 5 is not a perfect square, so we cannot simplify it further. The square root of 8, however, can be simplified. We can write 8 as 4 * 2, and since 4 is a perfect square, we can take its square root. So, we have √(5/8) = √5 / √8.

Next, we can simplify the square root of 8. √8 can be written as √4 * √2, and since √4 is 2, we have √8 = 2√2. Substituting this back into our expression, we get √(5/8) = √5 / 2√2.

Finally, we can simplify the expression further by rationalizing the denominator. We can multiply the numerator and denominator by √2 to get rid of the radical in the denominator. This gives us the final simplified form: √(5/8) = (√5 * √2) / (2√2 * √2) = (√10) / (2 * 2) = √10 / 4.

Answer:

3

Step-by-step explanation:

You add the total number of pets, and get 15. Then divide it by the number of people and get 3.

Answer: The mean is 3

Step-by-step explanation: In order to find the mean, you must add all the numbers (4+2+5+1+3) and then in this problem, you have to divide it by five since Spencer surveyed only five of his friends.

4+2+5+1+3=15

15 divided by 5 equals 3

ANSWER

One real root.

EXPLANATION

The graph of the function

[tex]f(x) = {x}^{3} + 6{x}^{2} + 12x + 8[/tex]

is shown in the attachment.

According to the Fundamental Theorem of Algebra, this function must have 3 roots including real and complex roots.

The x-intercepts gives the number of real roots.

Observe that the graph has only one intercept.

This implies that, the equation:

[tex]{x}^{3} + 6{x}^{2} + 12x + 8 = 0[/tex]

has only one real solution.

[tex]4-2x \cdot 4x = 64\\-8x^2=60\\x^2=-\dfrac{15}{2}\\x\in\emptyset[/tex]

Step-by-step explanation:

The probability of getting tails is 0.5.  The probability of getting tails 335 times is:

P = (0.5)^335

P = 1.43×10^-101

P ≈ 0

Answer:

Step 2: Olivia incorrectly determined 1/2 of 10% of 720

Step-by-step explanation:

1/2 of 720 = 360

10% of 720 = .10*720 = 72

1/2 of 72 = 36

This is not the same as 31

This is the incorrect step

Step 2

Answer:

Step 2: Olivia incorrectly determined One-half of 10% of 720.Step-by-step explanation:

Final answer:

To find out how much Julia's movie ticket cost, we subtracted the cost of the popcorn ($7) from the total amount spent ($15) to get the movie ticket price of $8.

Explanation:

The student's question asks how much Julia's movie ticket cost if she spent a total of $15 on a movie ticket and popcorn combined, given that the popcorn cost $7. To solve this, we subtract the cost of the popcorn from the total amount spent.

Here's the calculation step by step:

Start with the total amount spent: $15.

Subtract the cost of the popcorn: $15 - $7.

The result gives us the cost of the movie ticket: $8.

Therefore, Julia's movie ticket cost $8.

Answer:

-9x^3(x - 7)(x + 3)

Step-by-step explanation:

Answer:

13 x + 6

Step-by-step explanation:

Perimeter of triangle  =  All the sides added together

( 5 x + 3 ) + ( 5 x + 5 ) + ( 3 x - 2 ) = 13 x + 6

Final answer:

The perimeter of the triangle, given its side lengths as linear expressions 5x + 3, 5x + 5, and 3x – 2, is found to be 13x + 6 after combining like terms.

Explanation:

To calculate the perimeter of the triangle, we simply need to add together the lengths of its three sides. The expressions for the side lengths are given as 5x + 3, 5x + 5, and 3x – 2.

The perimeter (P) can be written as a linear expression by summing these expressions:

P = (5x + 3) + (5x + 5) + (3x – 2)

Now, let's combine like terms:

P = 5x + 5x + 3x + 3 + 5 – 2

P = 13x + 6

Hence, the linear expression for the perimeter of the triangle is 13x + 6, which is the simplified form.

Answer: [tex]x=2[/tex]

Step-by-step explanation:

Inverse proportion equation has this form:

[tex]y=\frac{k}{x}[/tex]

Where  "k" is the constant of variation.

We know that  "y" is inversely proportional to "x" and when [tex]x=3[/tex], [tex]y=6[/tex]

Then, we can substittute these values into the equation and solve for "k" to  find its value:

[tex]6=\frac{k}{3}\\\\6*3=k\\\\k=18[/tex]

Finally, we need to substitute "k" and [tex]y=9[/tex] into the equation and solve for "x":

[tex]9=\frac{18}{x}\\\\x=\frac{18}{9}\\\\x=2[/tex]

Answer:

x=2

Step-by-step explanation:

y is inversely proportional to x is written as:

x ∝ 1/y

When the proportion is removed, a constant is introduced. We have to find the constant first to find the value of x in y = 9

So,

Removing the proportionality symbol will give us:

x=k/y

As we know that x=3 for y=6 so

3 = k/6

3*6=k

So,

k=8

Hence the value of proportionality constant is 8.

Now putting the value of y which is 9

x=k/y

=>x=18/9

=>x=2

Answer: I'm pretty sure it's 200x - 120x = 1,200

Step-by-step explanation:

Answer:

200x - 120x = 1,200

Step-by-step explanation:

The break-even point is when the amount of money he spends equals the amount he earns.  

Let's see how much he earns and how much he spends per month:

He earns $200 per hour. If x represents the number of hours per month, we can write the earns as 200x.

He spends $1,200 per month and $120 per hour. We can write it as 1,200 + 120x.

So, we need 200x = 1,200 + 120x

We don't have this exact equation in our options but if we subtract 120x from both sides, we have:

200x - 120x = 1,200 + 120x - 120x

200x - 120x = 1,200

The correct answer is the first equation.

Answer:

Step-by-step explanation:

hundred thousandths

In the number 587,096, the value of the digit 5 would be 500,000 because it is in the hundred thousands position. We can express this as 5*100,000.

In the number 587,096, the digit 5 is in the hundred thousands place. This means that the value of the digit 5 is not simply 5, but rather 500,000. To express this, we can write the number as 5*100,000. We multiply the actual digit (5) by its place value (100,000).

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Answer:a -10

Step-by-step explanation:

-10 +8 = 2

ANSWER

[tex]x = - 10[/tex]

EXPLANATION

The given equation

[tex]x + 8 = - 2[/tex]

This is a linear equation in x.

To solve this equation, we add the additive inverse of 8 to both sides to get;

[tex]x + 8 + - 8 = - 2 + - 8[/tex]

We simplify to get:

[tex]x + 0 = - 10[/tex]

This implies that,

[tex]x = - 10[/tex]

The correct answer is A.

Answer:

B. y = 2/3x + 4

Step-by-step explanation:

the equation is Y = mx + b

m = slope

b = y-intercept

your answer is B. y = 2/3x + 4

Answer:

Step-by-step explanation:

It's B

The general equation of a slope intercept line is

y = mx + b

m = the slope

m = 2/3

b = the y intercept

b = (0,4)

So the equation is

y = 2/3 x + 4

Answer:

Step-by-step explanation:

Put the value of x = 0.3 to the equation 5x + 2y = 20, and solve it for y:

5(0.3) + 2y = 20

1.5 + 2y = 20           subtract 1.5 from both sides

2y = 18.5          divide both sides by 2

y = 9.25

Your question is so confused. Are you looking for the measure of angle B?

Below is my work on how to find the angle B.

Answer:

B = 46°

Step-by-step explanation:

Cos(B) = Adj./Hypo.

Cos(B) = AB/BC

Cos(B) = 20/29

Cos(B) = 0.6897

B = Cos^-1(0.6897)

B = 46°

For this case we have to define trigonometric relations of rectangular triangles that the cosine of an angle is given by the leg adjacent to the angle on the hypotenuse of the triangle. Then, according to the figure we have:

[tex]cos (B)= \frac {20} {29}\\cos (B)= 0.689655172414[/tex]

So:

[tex]B = arccos (0.689655172414)\\B = 46.39718103[/tex]

Rounding off we have that B is 46 degrees

Answer:

46 degrees

Answer:

-1 1/2

Step-by-step explanation:

9/10 ÷ -3/5

Copy dot flip

9/10 * -5/3

-45/30

Divide the top and bottom by 15

-3/2

Change this to a mixed number

-1 1/2

Answer:

The value of (g*h) (-3)  is [tex]=-\frac{112}{3}[/tex]

Step-by-step explanation:

If [tex]g(x) = x+\frac{1}{x}-2[/tex] and [tex]h(x)=4-x[/tex]

We have to find (g*h) (-3)

First multiply g(x) with f(x)

[tex] (x+\frac{1}{x}-2)\times (4-x)[/tex]

[tex]Distribute\:parentheses[/tex]

[tex]=x\cdot \:4+x\left(-x\right)+\frac{1}{x}\cdot \:4+\frac{1}{x}\left(-x\right)+\left(-2\right)\cdot \:4+\left(-2\right)\left(-x\right)[/tex]

[tex]\mathrm{Apply\:minus-plus\:rules}[/tex]

[tex]+\left(-a\right)=-a,\:\:\left(-a\right)\left(-b\right)=ab[/tex]

[tex]=4x-xx+4\cdot \frac{1}{x}-\frac{1}{x}x-2\cdot \:4+2x[/tex]

simplify

[tex]=-x^2+6x+\frac{4}{x}-9[/tex]

Now, put x= -3 in above expression

[tex]=-(-3)^2+6(-3)+\frac{4}{-3}-9[/tex]

[tex]=\left(-\frac{1}{3}-3-2\right)\left(4+3\right)[/tex]

[tex]=\left(-\frac{16}{3}\right)\left(4+3\right)[/tex]

[tex]=7\left(-\frac{16}{3}\right)[/tex]

[tex]=-\frac{16}{3}\cdot \:7[/tex]

[tex]=-\frac{112}{3}[/tex]

Therefore, the value of (g*h) (-3) is [tex]-\frac{112}{3}[/tex]

From the given histogram, the mean of the distribution is 5. Therefore, option B is the correct answer.

In statistics, the mean refers to the average of a set of values. The mean can be computed in a number of ways, including the simple arithmetic mean (add up the numbers and divide the total by the number of observations).

From the given histogram, the frequency distribution is

Number      Frequency

     1                    1

     2                   2

     3                   3

     4                   1

     5                   1

     6                   2

     7                   3

     8                   1

     9                   1

Now, the mean is (1×1+2×2+3×3+4×1+5×1+6×2+7×3+8×1+9×1)/15

= (1+4+6+4+5+12+21+8+9)/15

= 70/15

= 4.67

≈ 5

Therefore, the mean is 5.

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The mean of the data distribution is 6.3.

The mean of a data distribution can be calculated by summing all the values and dividing by the total number of values. Considering the data set 4, 5, 6, 6, 6, 7, 7, 7, 7, 8, the mean is:

(4 + 5 + 6 + 6 + 6 + 7 + 7 + 7 + 7 + 8) / 10 = 63 / 10 = 6.3

Answer:

(2, 0)

Step-by-step explanation:

Given

y = x² + 3x - 10

To find the x- intercepts let y = 0, that is

x² + 3x - 10 = 0 ← in standard form

Consider the factors of the constant term (- 10) which sum to give the coefficient of the x- term (+ 3)

The factors are + 5 and - 2, since

5 × - 2 = - 10 and 5 - 2 = + 3, hence

(x + 5)(x - 2) = 0

Equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5

x - 2 = 0 ⇒ x = 2

x- intercepts are (- 5, 0) and (2, 0)

Answer:

Step-by-step explanation:

To graph the function h(x) = 8|x+1| - 1, plot key points at (-3, 15), (-1, -1), and (1, 15). The graph exhibits vertical stretching due to the coefficient 8 and symmetry around the line x = -1.

To graph the function (h(x) = 8|x+1| - 1), follow these steps:

1. Identify Key Points:

  Determine critical points where the expression inside the absolute value becomes zero. Here, when (x = -1), (h(x) = -1). Additionally, consider points on either side of -1.

2. Plot Points:

  Plot these points on the coordinate plane: (-3, 15), (-1, -1), and (1, 15).

3. Determine Behavior:

  Understand that the absolute value function |x+1| ensures symmetry around the vertical line x = -1. The coefficient 8 stretches the graph vertically, and the constant -1 shifts it downward.

4. Connect Points:

  Draw a smooth curve connecting the points, considering the shape of the absolute value function.

5. Label Axes:

  Label the x-axis and y-axis appropriately.

The resulting graph represents the function [tex]\(h(x) = 8|x+1| - 1\)[/tex].

Answer:

[tex]648\ yd[/tex]

Step-by-step explanation:

step 1

Find the circumference of the complete circle

The circumference is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=35\ yd[/tex]

substitute

[tex]C=2\pi(35)[/tex]

[tex]C=70\pi\ yd[/tex]

step 2

Find the measure of the arc length for a central angle of 280 degrees

Remember that the circumference subtends a central angle of 360 degrees

so by proportion

[tex]\frac{70\pi}{360}=\frac{x}{280}\\ \\x=280*(70\pi )/360\\ \\x=54.44\pi\ yd[/tex]

step 3

Find the perimeter of the playground

[tex]P=54.44\pi+45=54.44*3.14+45=215.96\ yd[/tex]

Multiply by 3

[tex]215.96*(3)=647.87\ yd[/tex]

Round to the nearest integer

[tex]647.87=648\ yd[/tex]

Find the circumference of the full circle:

Circumference = 2 x PI x radius.

The radius is given as the length of chain 16 feet.

Circumference = 2 x 3.14 x 16 = 100.48 feet.

The dog can walk 130 degrees.

Multiply the circumference by the fraction of a complete circle ( 360 degrees)

Distance = 100.48 x (130/360) = 36.28 feet

Round to 36.3 feet.

The answer is (4) 36.3 feet.

Answer:

7x² - 40x - 12 = 0

Step-by-step explanation:

Solve the rational equation by combining expressions and isolating the variable. After doing that, then apply the Quadratic Formula to the listed answer choices to see if they give you the exact same x-intercepts, EXCEPT for this one, where you can easily factor this one. It is "process of elimination". Sometimes you have to try it.

Answer:

Correct.

Step-by-step explanation:

I am assuming you want to verify the above. If you enter this product into your calculator you'll get a result of 1.

Answer:

see explanation

Step-by-step explanation:

Using the double angle identity

sin2x = 2sinxcosx

Consider the left side

cos20. cos40. cos80

= [tex]\frac{1}{2sin20}[/tex] (2sin20cos20)cos40.cos80

= [tex]\frac{1}{2sin20}[/tex] (sin40cos40cos80

= [tex]\frac{1}{4sin20}[/tex] (2sin40cos40)cos80

= [tex]\frac{1}{4sin20}[/tex] (sin80cos80)

= [tex]\frac{1}{8sin20}[/tex] (2sin80cos80)

= [tex]\frac{1}{8sin20}[/tex] sin160

= [tex]\frac{1}{8sin20}[/tex] sin(180 - 20)

= [tex]\frac{1}{8sin20}[/tex] sin20

= [tex]\frac{1}{8}[/tex]

Hence

8(cos20cos40cos80) = 8 ×[tex]\frac{1}{8}[/tex] = 1 = right side

-2z +2

-3z+z+2 distribute the - to make them positive

-3z+z equals -2z

Answer:

The mean of this data set is  [tex]\mu = 24[/tex]

Step-by-step explanation:

By definition, the mean of a data set [tex]x_1, x_2, x_3, ..., x_n[/tex] is

[tex]\mu = \frac{\sum^n_i x_i}{n}[/tex]

Where n is the total number of data.

In this case we have 7 data

12, 13, 15, 28, 28, 30, 42

So the mean is:

[tex]\mu = \frac{12+ 13 +15 +28 +28 +30+ 42}{7}[/tex]

[tex]\mu = 24[/tex]