The probability for success of an event is P(A), and the probability of success of a second event is P(B). What is the
probability of both events occurring, in that order?

​A.) P(A + B)
B.) P(A) . P(B)
C.) P(A) + P(B)
D.) P(A x B)

Answer:

a = 1, b = 7

Step-by-step explanation:

Given the 2 equations

3a + 6b = 45 → (1)

2a - 2b = - 12 → (2)

Multiply (2) by 3 and add to (1) to eliminate the term in b

6a - 6b = - 36 → (3)

Add (1) and (3) term by term

(3a + 6a) + (6b - 6b) = (45 - 36)

9a = 9 ( divide both sides by 9 )

a = 1

Substitute a = 1 in either (1) or (2) and solve for b

(1) → 3 + 6b = 45 ( subtract 3 from both sides )

6b = 42 ( divide both sides by 6 )

b = 7

The answer to this question is the 3rd on (b)

Answer:

the answer is B or C

Step-by-step explanation:

i hope this some what helps

Answer:

[tex]\frac{cos^2(\frac{\pi}{2}-x)}{\sqrt{1-sin^2(x)}}=\frac{sin^2(x)}{|cos(x)|}[/tex]

Step-by-step explanation:

To simplify this expression you must use the following trigonometric identities

[tex]cos(\frac{\pi}{2}-x) = sinx[/tex]     I

[tex]1-sin (x) ^ 2 = cos ^ 2(x)[/tex]      II

Remember that

[tex]\sqrt{f(x)^2} =f(x)[/tex]

Only if [tex]f(x)> 0[/tex]  for all x

If f(x) is not greater than 0 for all x then

[tex]\sqrt{f(x)^2} =|f(x)|[/tex]

Now we have the expression:

[tex]\frac{cos^2(\frac{\pi}{2}-x)}{\sqrt{1-sin^2(x)}}[/tex]

then using the trigonometric identities I and II we have to:

[tex]\frac{cos^2(\frac{\pi}{2}-x)}{\sqrt{1-sin^2(x)}}=\frac{sin^2(x)}{\sqrt{1-sin^2(x)}}\\\\\\\frac{sin^2(x)}{\sqrt{1-sin^2(x)}}= \frac{sin^2(x)}{\sqrt{cos^2(x)}}[/tex]

[tex]cos(x)[/tex] is not greater or equal than 0 for all x. So.

[tex]\frac{sin^2(x)}{\sqrt{cos^2(x)}}=\frac{sin^2(x)}{|cos(x)|}[/tex]

Finally  

[tex]\frac{cos^2(\frac{\pi}{2}-x)}{\sqrt{1-sin^2(x)}}=\frac{sin^2(x)}{|cos(x)|}[/tex]

[tex]\frac{35}{50}=\frac{m}{10}[/tex]   Multiple 10 on both sides to get m by itself

[tex](10)\frac{35}{50}=\frac{m}{10}(10)[/tex]

[tex]\frac{350}{50}=m[/tex]  Simplify

7 = m

First, cross multiply

35 * m = 50 * 10

35m = 500

Then, Divide both sides by 35

m = 500 / 35

m = 14[tex]\frac{2}{7}[/tex] or 14.29

Answer:The answer is D. .116 fr Plato

The probability that If a person is selected at random the person is taller than 180 centimeters and has black hair is 0.116.

The probability helps us to know the chances of an event occurring.

[tex]\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

The number of people who are having black hair and are taller than 180 cm is 29. And the total number of employees in the company is 250. Therefore, the probability that the person is taller than 180 centimeters and has black hair can be written as,

[tex]\rm Probability=\dfrac{\text{Number of people with black hair and taller than 180 cm}}{\text{Total number of employees in the company}}\\\\\\Probability = \dfrac{29}{250} = 0.116[/tex]

Thus,  the probability that If a person is selected at random the person is taller than 180 centimeters and has black hair is 0.116.

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Answer:

X= 20

Step-by-step explanation:

4x + 8 = 88

4x +8 - 8 = 88 - 8

4x = 80

4x/4 = 80/4

X = 20

For this case we must find the value of "x" of the following linear equation:

[tex]4x + 8 = 88[/tex]

We subtract 8 on both sides of the equation:

[tex]4x = 88-8\\4x = 80[/tex]

We divide between 4 on both sides of the equation:

[tex]\frac {4x} {4} = \frac {80} {4}\\x = 20[/tex]

So, the value of x is 20

Answer:

[tex]x = 20[/tex]

Answer:

The solution is (3,13) and (-1,-3). So none of the mentioned options is correct.

Step-by-step explanation:

Given that

[tex]y = 4x + 1  (i)[/tex]

[tex]y = x^2 + 2x -2 (ii)[/tex]

Now, by susbstituting the value of 'y' from equation i to equation ii, we get

[tex]4x+1=x^2 + 2x -2[/tex]

[tex]0=x^2 + 2x -2-4x-1[/tex]

[tex]0=x^2 + (2x -4x) +(-2-1)[/tex]

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

[tex]0=x^2 -2x -3[/tex]

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

Now by factorization, equation iii can be written as

[tex]x^2 -3x +x -3 = 0[/tex]

[tex]x(x -3) + 1(x -3) = 0[/tex]

[tex](x -3)(x +1) = 0[/tex]

x = 3 and x = -1

By putting the values of x in equation i, we get

y = 4(3) + 1

y = 12 +1

y = 13

and

y = 4(-1) + 1

y = -4 +1

y = -3

Therefore, the solution is (3,13) and (-1,-3). So none of the mentioned options is correct.

Answer:

The pizza price after discount is $10.20

Step-by-step explanation:

turn 15% to decimal

0.15

multiply by $12 to find how much 15% of 15 is

12 x 0.15 = 1.8

know subtract the discount [$1.8]

12 - 1.8 = 10.2

$10.20

Hope this helped! Please mark as brainliest! Thanks!

Answer:

You can subtract the discount percent from 100% and then multiply that by the original price.

Steps

1. Subtract the discount percent from 100%.

2. 100% – 15% = 85%

3. Multiply the original price by this percent.

4. The discounted price is $10.20.

Answer:

• cos(α/2) = (4/17)√17

• sin(α/2) = (√17)/17

Step-by-step explanation:

The appropriate hαlf-angle identities are:

sin(α/2) = √((1 -cos(α))/2)

cos(α/2) = √((1 +cos(α))/2)

Putting in your given values for cos(α), we have ...

cos(α/2) = √((1 +15/17)/2) = √(16/17) = 4(√17)/17

sin(α/2) = √((1 -15/17)/2) = √(1/17) = (√17)/17

The answer is:

The domain of the function is all the real numbers except the number 13:

Domain: (-∞,13)∪(13,∞)

This is a composite function problem. To solve it, we need to remember how to composite a function. Composing a function consists of evaluating a function into another function.

Composite function is equal to:

[tex]f(g(x))=(f\circ} g)(x)[/tex]

So, the given functions are:

[tex]f(x)=x+7\\\\g(x)=\frac{1}{x-13}[/tex]

Then, composing the functions, we have:

[tex]f(g(x))=\frac{1}{x-13}+7\\[/tex]

Therefore, we must remember that the domain are all those possible inputs where the function can exists, most of the functions can exists along the real numbers with no rectrictions, however, for this case, there is a restriction that must be applied to the resultant composite function.

If we evaluate "x" equal to 13, the denominator will tend to 0, and create an indetermination since there is no result in the real numbers for a real number divided by 0.

So, the domain of the function is all the real numbers except the number 13:

Domain: (-∞,13)∪(13,∞)

Have a nice day!

Answer:

36

Step-by-step explanation:

Add up all the numbers and divide by 1/4

Answer:

34+2

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

Answer:

2/3 of a cup

Step-by-step explanation:

One third of a dozen = 4.

The recipe yields 24.

24 ÷ 4 = 6.

4 cups ÷ 6 = 2/3 of a cup

Answer:

The answer would be D., 15t + 4 dollars.

Step-by-step explanation:

All you have to do is add the like terms.  So, do 8t + 7t which equals 15t.  Next, do -1 + 5, which equals 4.  So, 15t + 4 dollars.  Hope this helps!

Answer:

D. 15t + 4 dollars

Step-by-step explanation:

To be able to know the sum of the two days you just have to add them.

7t-1 +(8t+5)=

7t+8t=15t

-1+5=4

The sum of the two days is 15t+4 and this is the total earnings that you are supposedly made on Monday and Tuesday.

Answer:

Identify the slope, m. This can be done by calculating the slope between two known points of the line using the slope formula.

Find the y-intercept. This can be done by substituting the slope and the coordinates of a point (x, y) on the line in the slope-intercept formula and then solve for b.

Step-by-step explanation:

The general formula is y = mx +b.

m = slope.

b = y-intercept of the line  

Answer:

(D.) 6h + 26 > 80

Step-by-step explanation:

$6 an hour + the $26 > the $80 needed to buy the skis

The inequality represents the number of hours (h) Linda could babysit to earn at least enough money to buy the ski pass is 6h+26>80. Therefore, option D is the correct answer.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Given that, Linda has $26. She wants to buy a ski pass for $80.

Let the number of hours Linda worked in babysitting be h.

Now, the inequality is

6h+26>80

The inequality represents the number of hours (h) Linda could babysit to earn at least enough money to buy the ski pass is 6h+26>80. Therefore, option D is the correct answer.

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Answer:

The rock will take about 4.5 seconds to reach the river

Step-by-step explanation:

* lets study the situation of the rock

- The rock is dropped means the initial velocity is zero

- The motion is free fall under earth gravity

- The rock dropped from a bridge 320 feet above the river

- The equation of the pathway is h = -16t² + 320

- When the rock reach to the ground the height will be zero

* Now lets substitute h by zero in the equation to find t

∵ h = -16t² + 320

∵ h = 0

∴ 0 = -16t² + 320 ⇒ add 16t² to both sides

∴ 16t² = 320 ⇒ divide both sides by 16

∴ t² = 320/16 = 20

∴ t² = 20 ⇒ take √ for both sides

∴ t = √20 = 2√5 ≅ 4.5 seconds

* The rock will take about 4.5 seconds to reach the river

The final answer is D: 4.5 seconds.

let's go through the solution in more detail.

Given the equation [tex]\( h = -16t^2 + 320 \)[/tex], where [tex]\( h \)[/tex] represents the height of the rock above the river at time [tex]\( t \),[/tex] we're trying to find out when the rock reaches the river, which means its height will be 0.

So, we set [tex]\( h \)[/tex] to 0:

[tex]\[ 0 = -16t^2 + 320 \][/tex]

To solve for [tex]\( t \),[/tex] we isolate [tex]\( t \)[/tex] by moving [tex]\( -16t^2 \)[/tex] to the other side of the equation:

[tex]\[ 16t^2 = 320 \][/tex]

Now, to solve for [tex]\( t \),[/tex] we divide both sides by 16:

[tex]\[ t^2 = \frac{320}{16} \]\[ t^2 = 20 \][/tex]

To find [tex]\( t \),[/tex] we take the square root of both sides:

[tex]\[ t = \sqrt{20} \][/tex]

Now, let's simplify [tex]\( \sqrt{20} \):[/tex]

[tex]\[ \sqrt{20} = \sqrt{4 \times 5} \]\[ \sqrt{20} = \sqrt{4} \times \sqrt{5} \]\[ \sqrt{20} = 2\sqrt{5} \][/tex]

Approximately, [tex]\( \sqrt{5} \)[/tex] is around 2.24, so [tex]\( 2\sqrt{5} \)[/tex] is approximately [tex]\( 2 \times 2.24 \),[/tex] which is approximately 4.48.

So, it will take approximately 4.5 seconds for the rock to reach the river.

Therefore, the correct answer is option D: 4.5 seconds.

Answer:

The Metric System

Step-by-step explanation:

Answer:

The metric system

Step-by-step explanation:

Because the exact definition is "the decimal measuring system based on the meter, liter, and gram as units of length, capacity, and weight or mass. The system was first proposed by the French astronomer and mathematician Gabriel Mouton (1618–94) in 1670 and was standardized in France under the Republican government in the 1790s." therefore it would be the metric system because it uses different lengths

Answer:

16682.7 cm³

Step-by-step explanation:

The total volume is the volume of the cone plus half the volume of a sphere:

V = ⅓ π r² h + ½ (4/3 π r³)

V = ⅓ π r² h + ⅔ π r³

V = ⅓ π r² (h + 2r)

Given that r = 4.15 cm and h = 10.2 cm:

V = ⅓ π (4.15)² (10.2 + 2×4.15)

V ≈ 333.65

The volume needed for 50 cones is therefore:

50V ≈ 16682.7 cm³

Final answer:

The car's average speed over the course of 5 days for a distance of 2359 miles was approximately 19.66 mph, which rounds to 20 mph.

Explanation:

To calculate the car's average speed in miles per hour, you divide the total distance traveled by the total time taken. In this case, the car traveled 2359 miles over the course of 5 days. Since there are 24 hours in a day, the total time in hours is 5 days multiplied by 24 hours per day.

Total time in hours = 5 days × 24 hours/day = 120 hours

Now we calculate the average speed using the formula:

Average speed = Total distance / Total time

Average speed = 2359 miles / 120 hours

When calculated, the average speed is approximately 19.66 miles per hour. Rounding to the nearest mile per hour gives us an average speed of 20 mph.

Answer:

0

Step-by-step explanation:

quotient means to divide

4/0=0

The answer is 0

4 divided by 0 is 0

Answer:

D.

Step-by-step explanation:

First figure: 2 dots by 1 dot

Second figure: 3 dots by 2 dots

Third figure: 4 dots by 3 dots

The numbers of dots are going up by one both horizontally and vertically, so I expect the next one to be

Fourth figure: 5 dots by 4 dots which is option D.

The next term of the given series 2,6,12, ( after converting the dots into numbers ) is 20.

A series is an arrangement of real numbers which follows some pattern. We can also say a series is a function from set of natural number to a particular set of numbers.

We can write the series mathematically as

2, 6,12,

which is equivalent to 2, 2²+2, 3²+3 etc

In this process the next term will be 4²+4, which is equal to 16+4=20

Therefore the next term will be 20.

Hence the next step of the given series will be 20.

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Answer:

Average mean salary [tex]=$26327.83[/tex]

Step-by-step explanation:

We have been given year and respective salaries in each year.

1960 $4,995

1970 $8,626

1980 $15,970

1990 $31,367

2000 $41,807

2010 $55,202

Now we nee do to determine the average mean salary for the six decades, 1960 – 2010.

So we just need to add all those six salaries and divide that sum by 6 to find the average mean salary.

Average mean salary [tex]=\frac{(4995+8626+15970+31367+41807+55202)}{6}[/tex]

Average mean salary [tex]=\frac{(157967)}{6}[/tex]

Average mean salary [tex]=26327.83333333[/tex]

Hence final answer is approx:

Average mean salary [tex]=$26327.83[/tex]

The answer would be 26327.83

Add up all the salaries and you will get $157,967

Then divide 157,967 by how many salaries there are which there’s 6

You will then get the answer 26327.83

Hello,

You're asking: (3^5−3^4)(3^3+3^2)/24.

First, start with the three. (3^5)

(243−3^4)(3^3+3^2)/24

Do the 3 to the power of 4.

(243−81)(3^3+3^2)

Subtract 243-81 to 162.

162(3^3+3^2)/24

Do 3^3 to get 27.

162(27+32)/24

Then, do 3^2 to 9.

162(27+9)/24.

Add 27+9 to get 36 then set up multiplication.

(162)(36)/24

Multiply.

5832/24

Divide.

Therefore, you get 243 as your final answer.

Answer:

30

Step-by-step explanation:

If we get 40% off, we still have to pay 100-40% = 60%

Take the original price * the percent we have to pay

50 * 60%

Change to decimal form

50 *.6

30

We have to pay $30

Answer:

Step-by-step explanation:

Zero in on the highest power of x.  It's 4.  Thus, this polynomial is of the 4th degree.

Note:  Please use " ^ " to indicate exponentiation:

-2x^4 - x^3 + 8x^2 - 12

The equation -2x^4 - x^3 + 8x^2 = 12 is a 4th degree polynomial because the highest power of the variable is 4.

The equation given is a polynomial equation, and polynomials are classified by degree, which is the highest power of the variable. In the given equation -2x4 - x3 + 8x2 = 12, we can see that the highest power is 4, which is the degree of the x variable. Thus, this equation is a 4th degree polynomial equation.

The variable with the highest degree is used to classify the polynomial. In this case, the variable x has the highest degree, making it a 4th degree polynomial. The value of the degree helps us to understand the shape of the graph of the equation. In this case, a 4th degree polynomial could have 0, 2, or 4 real roots and the graph can have 2 turning points.

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Answer:

k = 13

smallest zero = -6

Step-by-step explanation:

f(x) is basically the function of x.

x could be any integer. f(x) is the solution of the function of x.

f(x) is defined as x² + 3x - 10

f(x) = x² + 3x - 10

Now, f(x+5) = x² + kx + 30

This statement here says that if the value of x is x+5, then the answer would be x² + kx + 30.

f(x) = x² + 3x - 10

f(x+5) = (x+5)² + 3(x+5) - 10

f(x+5) = x² + 10x + 25 + 3x + 15 - 10

f(x+5) = x² + 13x + 40 - 10

f(x+5) = x² + 13x + 30

x² + 13x + 30 = x² + kx + 30

hence, k = 13

Smallest zero = The smallest x value.

f(x+5) = x² + 13x + 30

Let's take f(x+5) = 0

x² + 13x + 30 = 0

which two numbers products give us 30 and add up to 13?

== 6 and 5

(x+6)(x+5) = 0

x+6 = 0

x = -6

x+5 = 0

x = -5

The two solutions are -6 and -5

The smallest out of these two is -6.  

Answer: read below

Step-by-step explanation: 5+5=10-9=1x69= Baby

Answer:

B.

Step-by-step explanation:

Perpendicular lines always intercept at a right angle (90 degrees).

Answer:

b. lines that meet at a 90 angle

Step-by-step explanation:

Perpendicular lines are lines that intersect at a right (90 degrees) angle.

So, the correct answer is b. lines that meet at a 90 angle.

If you want to know if two equations are perpendicular, take their slopes. The slopes of perpendicular lines are opposite reciprocals of each other.

Answer:

It would be Symmetric,

Uniform is when all of the lines are almost lined up perfectly with each other.

Symmetric is when the lines are in a mountain formation with both sides looking the same

Skewed it where one side will look very steep and the other side looks like a hill

Answer:

The answer is B. symmetric

Step-by-step explanation:

A symmetric distribution is one in which the two halves of the histogram appear as mirror-images of one another. So, this histogram is symmetric.

A "skewed left" or "skewed right" distribution is one in which the tail is on the left side or on the right side.

A uniform histogram has almost same height bars. This means that the data has approximately the same number of values in each group.