Mathematics College

P(A) = 1/4 P(A n B) = 1/12 P(AUB) = 13/24 Find P(B) c 21/24 5/24 O O O 3/8 11/24

Answers

Answer 1

Okay, here we have this:

Considering that P(AUB)=P(A)+P(B)-P(AintersectionB), we obtain that:

P(B)=P(AUB)-P(A)+P(AnB)

P(B)=(13/24)-(1/4)+(1/12)

P(B)=3/8

Finally we obtain that P(B) is equal to 3/8.

Related Questions

Solve the inequalities|4x + 5| + 2 > 10

Answers

We have to solve this inequality:

[tex]\begin{gathered} |4x+5|+2>10 \\ |4x+5|>10-2 \\ |4x+5|>8 \end{gathered}[/tex]

We now use the properties of the absolute value. We will have two boundaries: one corresponding to when 4x+5 is negative and the other is when 4x+5 is positive.

When 4x+5 is negative, the absolute value function will change the sign of the expression, so we will have:

[tex]\begin{gathered} -(4x+5)>8 \\ -4x-5>8 \\ -4x>8+5 \\ -4x>13 \\ x<\frac{13}{-4} \\ x<-3.25 \end{gathered}[/tex]

The other interval will be defined when 4x+5 is positive. In this case, the absolute function does not change the sign and we get:

[tex]\begin{gathered} 4x+5>8 \\ 4x>8-5 \\ 4x>3 \\ x>\frac{3}{4} \\ x>0.75 \end{gathered}[/tex]

Then, the solution set is the union of the intervals x < -3.25 and x > 0.75.

We can express the interval as (-∞, -3.25) ∪ (0.75, ∞).

Answer: (-∞, -3.25) ∪ (0.75, ∞)

Find a function of the form y = A; A * sin(kx) + C or y = A * cos(kx) + C whose graph matches this one:I don’t understand how my answer is wrong

Answers

Recall that the graph of the cosine function is:

Now, notice that the given graph is the above graph but with a midline

[tex]y=1,[/tex]

and amplitude equal to 4. The frequency is also different.

Therefore, the equation of the function given in the graph is:

[tex]y=4cos(\frac{\pi}{5}x)+1.[/tex]Answer: [tex]y=4cos(\frac{\pi x}{5})+1.[/tex]

Write an exponential expression: Let 10 be the base and an even number between 1 and 10 be the exponent.
Then write the exponential expression in expanded form and standard form.

Answers

The exponential expression as required to be chosen is; 10⁴.

The expanded form of the expression is; 10 × 10 × 10 × 10.

The standard form of the expression is; 10,000.

Exponential expressions in expanded form and Standard form.

It follows from the task content that the exponential expression is to be written in expanded and standard form.

Since the exponential expression must have 10 as the base and an even number between 1 and 10 as the exponent.

An example of such exponential expression is therefore;

10⁴.

Hence, to write the expression in expanded form; it is written as a product of factors as follows;

10 × 10 × 10 × 10

Also, the expression can be written in standard form as the result of the multiplication above;

= 10,000.

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ratio problems that I am struggling with

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7 out of every 500 Americans are aged 13-17 years generation are vegetarian

Thus the ratio of the vegetarian is 7 : 500

In a group of 350,

Let x be the number of people who are vegetarian

So, the ratio out of 350 who are vegetarian are : x : 350

SInce the ratio is same so:

[tex]\begin{gathered} 7\text{ : 500=x:250} \\ \frac{7}{500}=\frac{x}{250} \\ \text{ Simplify for x,} \\ x=\frac{7}{500}\times250 \\ x=\frac{7}{2} \\ x=3.5 \\ x\approx4 \end{gathered}[/tex]

So, the number of people who are vegetarian out of 350 people is 4 people

A person standing 306 feet from the base of a church observed the angle of elevation to the church’s steeple to be 20°. How tall is the church. Give answer to the nearest whole number

Answers

Solution

- The solution steps are given below:

[tex]\begin{gathered} \text{ Applying SOHCAHTOA, we have:} \\ \frac{h}{306}=\tan20 \\ h=306\tan20 \\ \\ h=111.374...ft\approx111ft\text{ \lparen To the nearest whole number\rparen} \end{gathered}[/tex]

Final Answer

111 ft

So ABC and DEF are the same triangle, this question is asking me to write an equation between the relationships of DEF. How do I write that?

Answers

Explanation

The first step is to draw a representation of the given parameters.

Since this is a right-angle triangle, the Pythagorean theorem applies. This can be seen below;

[tex]\text{Longest Leg}^2=sum\text{ of the square of the short legs}[/tex]

We can then apply it to the sides of the triangle.

DF is the longest side. Therefore,

Answer

[tex]DF^2=DE^2+EF^2[/tex]

If cos A = 3/√13 and angle A is not in quadrant I, determine the exact value of sin A.

Answers

To determine the exact value of sin A we get -2/√13

What is determinant?

the determinant is a scalar of value that is a function of to the entries of a square matrix. It is allows characterizing of some properties of to the matrix and the linear map of represented by the matrix.

It is a scalar value which is associated with the square matrix.

Sol-Cos A =3/√13

angle A is not in quadrant I

So angle A is in quadrant IV

Thus,

Sin A =-√(√13)^2-3^2/√13

=-√13-9/√13

=-√4/√13

=-2/√13

Thus the answer is -2/√13.

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12.Work backwards to write a quadratic equation that will have solutions of x = -1/2 and x = 4. (Your equation must only have integer coefficients, meaning no fractions or decimals.)

Answers

In general, a quadratic equation can be written in terms of its solutions:

[tex]y=(x-a)(x-b).[/tex]

Now, notice that:

[tex]x+\frac{1}{2}=0\text{ }[/tex]

when x= -1/2, and it is equivalent to:

[tex]2x+1=0.[/tex]

Therefore, you can write the quadratic equation as:

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

Computing the above multiplication, you get:

[tex]y=2x^2-8x+x-4.[/tex]

Simplifying the above equation you get:

[tex]y=2x^2-7x-4.[/tex]Answer: [tex]y=2x^{2}-7x-4[/tex]

Triangle Inequality TheoremDetermine if a triangle can be formed with the given lengths. If so, classify the triangle by its angle.YESorNO

Answers

Given:-

[tex]7,20,12[/tex]

To find:-

Wheather the given sides form a valid triangle.

So now let,

[tex]A=7,B=20,C=12[/tex]

To check we use the condition,

[tex]A+B>C,B+C>A,C+A>B[/tex]

Substituting the values we get,

[tex]7+20>12,20+12>7,12+7>20[/tex]

In the above condition 12+7>20 is wrong.

So the condition fails and the given sides doesnt form a triangle.

пеу Fabric Sale At a fabric store, fabrics are sold by the yard. A dressmaker spent $46 on 5 yards of silk and cotton fabrics for a dress. 1 x + y = 5 117x + 4y = 46) Silk is $17 per yard and cotton is $4 per yard. Here is a system of equations that represent the constraints in the situation. What does the solution to the system represent?

Answers

It is said that the dressmaker bought 5 yards of cotton and silk. Let's see the first equation of the system:

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

And that he spent $46 on those 5 yards. Also, it is said that silk costs $17 per yard and cotton $4 per yard. Let's see the second equation of the system:

[tex]17x+4y=46[/tex]

If 46 is how much the dressmaker spent, and 17 and 4 represent how much silk and cotton cost PER YARD then we know that x and y represent how much of each fabric did the dressmaker bought. Also, in the first equation you see that the total is 5 yards. So, if you solve this system you will find that 'x' is how many yards of silk the dressmaker bought and 'y' is how many yards of cotton he bought.

In summary, the solution of this system represents how may yards of silk (x) and cotton (y) the dressmaker bought.

Evalue each expression for the given value(s) of the variable(s)exponents

Answers

Any number raised to the power of zero equals 1, then

[tex]r^0s^{-2}=1\cdot s^{-2}=s^{-2}[/tex]

then, we need to substitute the value 10 in the variable s. It yields,

[tex]s^{-2}=\frac{1}{s^2}\Rightarrow\frac{1}{10^2}=\frac{1}{100}[/tex]

Then, the answer is

[tex]r^0s^{-2}=\frac{1}{s^2}\Rightarrow\frac{1}{100}[/tex]

that is, 1 / 100.

The formula k=5/9(f-32)+273.15 converts temperature of the object in a laboratory is cooled to 1.5 kelvin. What is the temperature of the object in degrees fahrenheit?

Answers

[tex]\begin{gathered} k=\frac{5}{9}(f-32)+273.15 \\ k=1.5 \\ 1.5=\frac{5}{9}(f-32)+273.15 \\ \text{Subtract 273.15 from both sides} \\ 1.5-273.15=\frac{5}{9}f-\frac{160}{9}\Rightarrow\frac{5}{9}f=1.5-273.15+\frac{160}{9} \\ \frac{5}{9}f=-253.872 \\ MultiplyBothSideBy,\frac{9}{5} \\ f=\frac{9}{5}\cdot(-253.872) \\ f=-456.97^{\circ} \end{gathered}[/tex]

The temperature of the object is -456.97 degrees

Attached is a photo of my written question, thank you.

Answers

Given:

The function is,

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

Explanation:

Determine the function for f(x + h).

[tex]\begin{gathered} f(x+h)=-2(x+h)^2-(x+h)+3 \\ =-2(x^2+h^2+2xh)-x-h+3 \\ =-2x^2-2h^2-4xh-x-h+3 \end{gathered}[/tex]

Determine the value of expression.

[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{-2x^2-2h^2-4xh-x-h+3-(-2x^2-x+3)}{h} \\ =\frac{-2h^2-4xh-h}{h} \\ =-2h-4x-1 \end{gathered}[/tex]

So exprression after simplification is,

-2h - 4x - 1

Brandon's car used 10 gallons to travel 310 miles. At what rate does the car use gas, in miles per gallon?On the double number line below, fill in the given values, then use multiplication or division to find the missing value.

Answers

Given:

At 10 gallons, the car is able to cover 310 miles.

Find: At 1 gallon, the car can travel ____ miles.

Solution:

First, let's fill in the number line with the given values.

To solve for the question mark at 1 gallon, simply divide 310 by 10.

[tex]310\div10=31[/tex]

Hence, the car uses gas at 31 miles per gallon.

Part A. 150% of what number is 156 Part B. 4.4 is 5.5% of what number

Answers

EXPLANATION

Since 150% represents a percentage bigger than 156, the appropiate relationship would be as follows:

[tex]Part\text{=}\frac{\text{Percentage}}{100}\cdot\text{Whole}[/tex]

Where the whole number is 156 and the percentage is 150%:

[tex]\text{Part}=\frac{150}{100}\cdot156[/tex][tex]\text{Part}=1.5\cdot156=234[/tex]

In conclusion, the solution is 234

riangle QRS has vertices Q(8, −4), R(−1, 2), and S(3, 7). What are the coordinates of vertex Q after the triangle is reflected across the y-axiriangle QRS has vertices Q(8, −4), R(−1, 2), and S(3, 7). What are the coordinates of vertex Q after the triangle is reflected across the y-axi

Answers

The coordinates of Q should be (-8, -4) because when you reflect over the y-axis the x coordinate become the opposite

What is the average rate of change from f(-1) to f(1)?Type the numerical value for your answer as a whole number, decimal or fractionMake sure answers are completely simplified

Answers

The average rate of change of the function is the average rate at which one quantity is changing with respect to another.

Average rate of change = (y2 - y1)/(x2 - x1)

y represents the output values and it is also called f(x)

x represents the input values

For the given interval,

for f(- 1), x = -1 and f(x) = 8

For f(1), x = 1, f(x) = 4

Average rate of change = (4 - 8)/1 - - 1) = - 4/(1 + 1) = - 4/2

Average rate of change = - 2

i need help, im confused

Answers

Answer:

Step-by-step explanation:

simplify 3^5×3^4.a. 3×20b. 3^9c. 6^9d. 3^20I think its b but I am unsure.

Answers

Recalling the laws of exponents:

[tex]a^m\cdot a^n=a^{m+n}[/tex]

So, for the number 3^5 times 3^4, we have:

[tex]3^5\cdot3^4=3^{5+4}=3^9[/tex]

Therefore, the answer is the option b) 3^9.

Miles east of 100 80 60 40 20 1 2 3 4 5 6 7 8 9 10 Time (hours) Where were the two cars in relation to each other when they began traveling? O A. Car B was 5 miles east of car A. O B. Car B was 20 miles east of car A. O C. Car Awas 15 miles east of car B. D. Car A was 5 miles east of car B. < PREVIOUS

Answers

Car B was 5 miles east of car A, Option A

Help pleas Which statement best completes the diagram.

Answers

The statement which best completes the cause and effect diagram is that: A. British leaders limit the ability of colonists to expand westward.

What is a cause and effect graphic organizer?

A cause and effect graphic organizer is also referred to as cause and effect diagram and it can be defined as a type of chart which highlights and shows the relationship between two things, phenomenon, or events in which an occurrence of one (cause) typically leads to the occurrence of another (effect).

During the late 18th to mid 19th centuries, the United States of America began to grow westward and this led to the emigration of Native American tribes who had in this geographical region for thousands of years before the arrival of European colonists.

Consequently, conflict developed between them which was known as "The French and Indian War" and this caused British leaders to limit the ability of many European colonists to continue expanding westward.

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Complete Question:

Which statement best completes the diagram?

A. British leaders limit the ability of colonists to expand westward.

B. British merchants refuse to buy raw materials from the colonies.

C. British military forces are ordered to leave North America.

D. British leaders end policies that strictly controlled the colonies.

Please help me don't understand

Answers

Answer:

x=13

Step-by-step explanation:

50+3x=89

89-50=3x

39=3x

13=x

You need 30 ounces of chocolate chips to bake some cooldes. You already have 8 ounces of chocolate chips at home. Write an inequality that could beused to find how many ounces of chocolate chips you need to buy.whats the inequality:

Answers

Given:

Amount of chocolate chips needed = 30 ounces

Amount of chocolate you have already = 8 ounces

Let's find the inequality that can be used to find the ounces of chocolate chips you need to buy.

To write the inequality, we have:

8 + x ≥ 30

Where x represents the ounces of chocolate chips you need to buy.

Therefore, the inequality that could be used to fid how many ounces of chocolate chips needed is:

8 + x ≥ 30

ANSWER:

8 + x ≥ 30

Find the measure of the arc or central angle indicated. Assume that lines which appear to bediameters are actual diameters.

Answers

From the given circle, the measure of the arc or the central angle indicated is as shown at the center of the circle is subtended by the arc

Hence, the measure of the arc or central angle indicated is 65° ,Option B

Find the mzEFH, given that mzEFG = 50°. F E G . I

Answers

By theorem, we will have that m

=> m

=>2m

Then, we replace values and solve:

2m m

So, we have that m

Which is the upper left quadrant on the coordinate plane?A coordinate plane.Quadrant IQuadrant IIQuadrant IIIQuadrant IV

Answers

The quadrants on the coordinate plane are the following:

then, we have that the upper left quadrant is quadrant II

URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS!!!!!!!!

Answers

Answer:

Option 2

Step-by-step explanation:

hope this helps

Classify each set of measures as AAS, ASA, SSA, SAS, or SSS. Then find the indicated length or angle measure (to the nearest tenth).

Answers

Hello there. To solve this question, we'll have to remember some properties about triangles.

Given the triangle:

Notice in this case we have two consecutive angles and a side between them. This is a case of ASA (angle-side-angle).

With respect to the side with measure x, we have two consecutive angles then the side, hence AAS.

To find x, we'll have to apply the law of sines:

[tex]\dfrac{A}{\sin(\alpha)}=\dfrac{B}{\sin(\beta)}=\dfrac{C}{\sin(\gamma)}=2R[/tex]

In this case, the angle opposite to x measures 73º and the angle opposite to 4 measures 85º, hence:

[tex]\dfrac{x}{\sin(73^{\circ})}=\dfrac{4}{\sin(85^{\circ})}[/tex]

Multiply both sides by a factor of sin(73º)

[tex]x=\dfrac{4\sin(73^{\circ})}{\sin(85^{\circ})}[/tex]

Using a calculator, we get the following approximation (rounding to the nearest tenth):

[tex]x\approx3.8[/tex]

This is the measure of x we're looking for.

10) f(x) = x5 - 10x4 + 42x3 -124 x2 + 297x - 306; zero: 3i ? A) 2, -3i, -4 - i, -4 + i C) 2, -3i, 4 - i, 4 + i B) -2, -3i, -4 -i, -4 + i D) -2, -3i, 4-i, 4 + i

Answers

Answer

Option C is correct.

The roots of the given function include

2, -3i, (4 + i), (4 - i)

Explanation

To solve this, we would put the given roots of the solution into the place of x. The ones that give 0 are the roots of the expression

The expression is