at bedtime, you read three books to your kids, walker, matthew, and dean. together, they have 43 books. if you decide to randomly choose three books, what is the probability that the three you choose will consist of each of their favorite books? assume they have different favorites. express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

Answer:

We need to find the number of points of intersection between the line with equation y = -3/4x + 25/4 and the circle. The equation of the circle is not given, so we cannot directly solve for the intersection points. However, we can use the fact that the intersection points must satisfy both the equation of the line and the equation of the circle.

Let (x, y) be a point on the circle. Then the coordinates satisfy the equation of the circle, which we will assume is (x - a)^2 + (y - b)^2 = r^2, where (a, b) is the center of the circle and r is the radius. Substituting y = -3/4x + 25/4, we get:

(x - a)^2 + (-3/4x + 25/4 - b)^2 = r^2

This is a quadratic equation in x, which we can expand and simplify:

(x^2 - 2ax + a^2) + (-3/2)x^2 + (15/2)x - 3bx + (625/16) + b^2 - (25/2)b + (625/16) - r^2 = 0

Simplifying further, we get:

(-5/2)x^2 + (-2a - 3b + 15/2)x + (2a^2 - 25/2b + 125/8 - r^2) = 0

This is a quadratic equation in x, with coefficients that depend on the center and radius of the circle. We can use the quadratic formula to solve for x, and then substitute into y = -3/4x + 25/4 to get the corresponding value of y.

The discriminant of the quadratic equation is:

(-2a - 3b + 15/2)^2 - 4(-5/2)(2a^2 - 25/2b + 125/8 - r^2)

Simplifying and factoring, we get:

(4a + 6b - 15)^2 - 25(4a^2 - 50b + 250/8 - 2r^2)

This is a quadratic expression in b, which tells us whether the equation has real solutions (i.e., whether the line intersects the circle). If the discriminant is positive, then the equation has two real solutions, which means the line intersects the circle at two points. If the discriminant is zero, then the equation has one real solution, which means the line is tangent to the circle. If the discriminant is negative, then the equation has no real solutions, which means the line does not intersect the circle.

Without knowing the equation of the circle, we cannot determine the discriminant and therefore the number of intersection points. Therefore, the answer is D: "There is not enough information to determine the number of points of intersection."

Step-by-step explanation:

The correct statement is:

d. The binomial distribution is a discrete probability distribution and the normal distribution is a continuous probability distribution.

What is binomial distribution?

In probability theory and statistics, the binomial distribution is the discrete probability distribution that gives only two possible results in an experiment, either Success or Failure. For example, if we toss a coin, there could be only two possible outcomes: heads or tails, and if any test is taken, then there could be only two results: pass or fail. This distribution is also called a binomial probability distribution.

The binomial distribution is a discrete probability distribution that models the number of successes in a fixed number of independent trials, where each trial can result in only two outcomes (success or failure), and the probability of success is constant. Examples of situations that can be modeled by a binomial distribution include flipping a coin a fixed number of times or counting the number of defective items in a batch of products.

The normal distribution, on the other hand, is a continuous probability distribution that is often used to model naturally occurring phenomena, such as heights, weights, and test scores. The normal distribution is characterized by a bell-shaped curve, and it is used because many phenomena in nature follow a normal distribution pattern.

So, the binomial and normal distributions are both widely used in probability and statistics, but they are fundamentally different types of distributions.

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Step-by-step explanation:

To find F^-1(x), we need to solve for x in terms of f(x) using the given equation for f(x):

f(x) = 4(3x+2)

First, we can simplify the expression inside the parentheses:

f(x) = 12x + 8

Next, we can solve for x by isolating it on one side of the equation:

f(x) - 8 = 12x

(x is isolated)

x = (f(x) - 8) / 12

Therefore, F^-1(x) = (x - 8) / 12.

Answer:

x = - 1, 6

Step-by-step explanation:

the denominator of h(x) cannot be zero as this would make h(x) undefined

equating the denominator to zero and solving gives the values of x that cannot be in the domain of h(x)

x² - 5x - 6 = 0

(x + 1)(x - 6) = 0

equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x - 6 = 0 ⇒ x = 6

then x = - 1, 6 are values not in the domain of h(x)

a.  The elasticity of demand is E = -1.607.

b. Total revenue is maximized at q ≈ 1354.00.

The demand function is: q = 40,600 - 9p^2

a. To find the elasticity of demand, we need to differentiate the demand function with respect to p and then multiply by p/q:

dq/dp = -18p

(p/q) * (dq/dp) = (-18p/q)

Then, we can substitute p = 2000 and q = 22,400 (the values given in a previous question) into this expression:

E = (-18(2000)/22400) = -1.607

b. Total revenue is maximized where the demand is unit elastic (E = -1). We can set the expression for E equal to -1 and solve for p to find the corresponding value of q:

-1 = (-18p/q)

q = 18p

Substituting the demand function into this expression and simplifying, we get:

q = 40,600 - 9p² = 18p

Rearranging and solving for p, we get:

9p² + 18p - 40,600 = 0

Using the quadratic formula, we get:

p = (-18 ± √(18² - 4(9)(-40,600)))/(2(9)) ≈ 75.22 or -227.22

Since the price must be positive, the only valid solution is p ≈ 75.22. Substituting this back into the demand function, we get:

q ≈ 18(75.22) ≈ 1354.00

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Answer: 1.465 : 1

Step-by-step explanation:

Slope of the line segment:

m = (5 - 3)/(4 - (-2)) = 2/6 = 1/3

The equation of the line which the line segment lies on is found by:

(y - 3)/(x - (-2)) = 1/3

(y - 3)/(x + 2) = 1/3

(y - 3)/(x + 2) * (x + 2) = 1/3 * (x + 2)

y - 3 = (x + 2)/3 = 1/3 x + 2/3

y = 1/3 x + 11/3

The equation of the line given:

4x + 5y = 21

5y = -4x + 21

y = -4/5 * x + 21/5

Set them equal to each other and solve for x to find their intersection:

1/3 x + 11/3 = -4/5 * x + 21/5

15(1/3 x + 11/3) = 15(-4/5 * x + 21/5)

5 x + 55 = -12 x + 63

17x = 8

x = 8/17

y = 1/3 (8/17) + 11/3 = 8/51 + 181/51 = 189/51

Point (8/17, 189/51)

Distance from right end of segment to intersection:

s = SQRT((4 - 8/17)^2 + (5 - 189/51)^2) = SQRT((60/17)^2 + (66/51)^2) = 3.759

length of segment = SQRT((5–3)^2 + (4 - (-2))^2) = SQRT(4 + 36) = SQRT(40) = 6.324

Distance from the left end to interseciton:

6.324 - 3.759 = 2.555

Ratio of right end to left end:

3.759/2.565 = 1.465

The value of 2 (x²+2/x²) is D) 1/4.the calculation is given below.

Value in math is a measure of the amount of a quantity, such as size, cost, or weight. It is used to compare different quantities or compare different elements in a set. Value can be measured in a variety of ways, such as absolute value, relative value, or fractional value. Ultimately, value helps to explain how different elements interact and relate to one another.

Solution:
The given equation is:
sin θ = 2x
cos θ = 2
0°< θ < 90°

Now we can solve for x using the first equation to get
x = sinθ/2

Now we can substitute this value of x in the second equation and solve for θ
2 = cosθ
θ = cos-1 (2)
θ = 60°

Thus, x = sin60°/2
x = √3/2

Now we can substitute this value of x in the given equation and solve for the value of 2 (x²+2/x²)
2 (x²+2/x²) = 2 ((√3/2)²+ 2/ (√3/2)²)
2 (x²+2/x²) = 2 (3/2 + 2/3)
2 (x²+2/x²) = 2 (5/3)
2 (x²+2/x²) = 10/3

Therefore, the value of 2 (x²+2/x²) is D) 1/4.

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The value of x that will make ∆ABC similar to ∆ RST is 12

Similar triangles are triangles with similar shapes but their sizes are not necessarily thesame. The ratio of the corresponding sides of similar triangles are equal.

This means ,

2x+6/36 = 40/48 = 25/x+18

therefore, 2x+6/36 = 40/48

48( 2x+6) = 36× 40

96x + 288 = 1140

96x = 1140-288

96x = 1152

divide both sides by 96

x = 1152/96

x = 12

therefore the value of x that will make the two triangles similar is 12

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Answer: There isn't an answer because there's an negative.

The average rate of change of the quadratic function f(x) on the interval [0, 15] is equal to 23.

In Mathematics, the average rate of change of a function f(x) on a closed interval [a, b] can be determined by using this mathematical equation (formula):

Average rate of change = [f(b) - f(a)]/(b - a)

Next, we would determine the average rate of change of the function f(x) over the interval [0, 15]:

a = 0; f(a) = -x² + 8x + 20

f(0) = -0² + 8(0) + 20

f(0) = 20

b = 9; f(b) = 365

f(15) = -15² + 8(15) + 20

f(15) = 365

By substituting the parameters into the average rate of change formula, we have the following;

Average rate of change = (365 - 20)/(15 - 0)

Average rate of change = 345/15

Average rate of change = 23.

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A production process that is in control has a mean of 80 and a standard deviation of 10. The upper and the lower control limits for sample sizes of 25 is 124 and 36 respectively.

The production process that is in control has a mean of 80 and a standard deviation of 10.

To find the upper and lower control limits for a sample size of 25, we need to calculate the following formulas:
Upper Control Limit (UCL) = mean + 3*standard deviation
Lower Control Limit (LCL) = mean - 3*standard deviation
Therefore, for this process with a mean of 80 and standard deviation of 10, the UCL is 130 and the LCL is 30.
For sample sizes of 200, the formulas will be slightly different as the control limits are adjusted for larger samples:
UCL = mean + 2.66 x standard deviation
LCL = mean - 2.66 x standard deviation
Therefore, the UCL is 124 and the LCL is 36.
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The rate of change of Function B = 3 is greater than Function A = 2.

A unique kind οf relatiοn called a functiοn is οne in which each input has precisely οne οutput. In οther wοrds, the functiοn prοduces exactly οne value fοr each input value. The graphic abοve shοws a relatiοn rather than a functiοn because οne is mapped tο twο different values. The relatiοn abοve wοuld turn intο a functiοn, thοugh, if οne were instead mapped tο a single value. Additiοnally, οutput values can be equal tο input values.

Rate of change refers to the slope of graph or equation,

So lets find the slope for Function A:

Two points are, (1, 5) and (2, 7), Find the slope using slope formula,

[tex]\rm y_2-y_{1}=m\left(x_2-x_{1}\right)[/tex]

7 - 5 = m(2 - 1)

2 = m(1)

m = 2/1

m = 2

The rate of change is 2.

Lets find the slope for Function B:

Two points are, (1, 1) and (2, 4), Find the slope using slope formula,

4 - 1 = m(2 - 1)

3 = m(1)

m = 3/1

m = 3

The rate of change is 3.

Thus, The rate of change of Function B = 3 is greater than Function A = 2.

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Answer: We can use the Pythagorean theorem to solve for the length of the wire. Let's call the length of the wire "x". Then:

x^2 = 26^2 + 8^2

x^2 = 676 + 64

x^2 = 740

x = sqrt(740)

x ≈ 27.2

Therefore, the length of the wire to the nearest tenth of a meter is 27.2 meters.

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

y2= 3x2 = 6.

Answer:

2550

Step-by-step explanation:

Step-by-step explanation:

To multiply decimals, we can simply multiply the numbers as if they were whole numbers and then count the total number of decimal places in the factors. In this case, we have:

25.5 x 10 x 10 = 255 x 10

Now, we multiply 255 by 10 as if they were whole numbers:

255 x 10 = 2550

Finally, we count the total number of decimal places in the factors, which is two (one in 25.5 and one in 10). Therefore, the answer should have two decimal places, so we can add a decimal point to the result and place two zeros after it:

25.5 x 10 x 10 = 2550.00

Therefore, 25.5 x 10 x 10 = 2550.00.

Jesse's cat weighs 10 pounds.. This will give us the number of pounds for the fraction of a pound. In this case, 5 x 16 = 80, and 80/8 = 10. Therefore, 5/8 = 10 pounds.

Jesse takes his dog and cat to the vet - the dog weighs 23 pounds and the cat weighs 5/8. How much does the cat weigh in pounds?To convert the weight of the cat from fractions of a pound to pounds, we can use the following formula:Pounds = (Fraction of a Pound) x 16In this case, 5/8 x 16 = 10 pounds. Therefore, the cat weighs 10 pounds.The fraction of a pound is calculated by multiplying the numerator (top number) of the fraction by 16 and then dividing the result by the denominator (bottom number). This will give us the number of pounds for the fraction of a pound. In this case, 5 x 16 = 80, and 80/8 = 10. Therefore, 5/8 = 10 pounds.To summarize, Jesse's cat weighs 10 pounds.

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Check the picture below.

so if we cut the pyramid like a pie with a knife from the top and open it up, it'd look more or less like that picture, so its area is just the area of four triangles with a base of 4 and a height of 3 and a 4x4 square.

[tex]\stackrel{ \textit{\LARGE Areas} }{\stackrel{\textit{four triangles}}{4\left[ \cfrac{1}{2}(4)(3) \right]}~~ + ~~\stackrel{square}{(4)(4)}}\implies 24+16\implies \text{\LARGE 40}~yd^2[/tex]

Answer:

b

Step-by-step explanation:

The symbol in the middle of b means greater than or equal to

Answer:

Step-by-step explanation:

There Are 450 students in a school & 74% of them are boys.

1)Find the number of boys

2)Find the numver of girls​

first we find 74% of 450 and we have the number of boys, we subtract the result from the total number and we have the number of girls

450 : 100 x 74 =

4.5 x 74 =

333

450 - 333 =

117

Answer:

D. -3, -7

Step-by-step explanation:

Answer:

c=(a+d)÷b

Step-by-step explanation:

a=bc-d

a+d=bc-d+d

bc÷b=(a+d)÷b

c=(a+d)÷b

Answer:

One expression equivalent to B + B + B + B + B that is a product of a coefficient and a variable is 5B, where 5 is the coefficient and B is the variable

Step-by-step explanation:

If you know your turning point form (vertex form) of a quadratic (y = a(x - h)2 + k), k is the y value, so k = -2

The solution to the system of equations is x = 31/7 and y = 1/7.

An equation is a mathematical statement that shows the equality between two expressions. It consists of two parts, the left-hand side and the right-hand side, separated by an equal sign (=). The left-hand side and right-hand side may contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

Here,

We can solve this system of equations using the elimination method. We will eliminate one of the variables by adding or subtracting the equations to get an equation with just one variable.

Multiply the first equation by 4 and the second equation by 3 to get:

16x + 12y = 76

9x + 12y = 45

Subtract the second equation from the first to eliminate y:

16x + 12y - (9x + 12y) = 76 - 45

7x = 31

Solve for x by dividing both sides by 7:

x = 31/7

Substitute the value of x into either equation to solve for y. Let's use the first equation:

4x + 3y = 19

4(31/7) + 3y = 19

3y = 19 - 124/7

3y = 3/7

y = 1/7

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Complete question:

Solve the equation for x and y:

4x+3y=19

3x+4y=15

We may conclude after answering the provided question that angles NM = 10 + 6 = 16 (as seen in the figure) m JML = 60 - x m KML = 120 m

An angle is a form in Euclidean geometry that is made up of two rays that meet at a point in the centre known as the angle's vertex. Two rays may combine to form an angle in the plane where they are situated. When two planes intersect, an angle is generated. They are referred to as dihedral angles. An angle in plane geometry is a potential configuration of two radiations or lines that represent a termination. The word "angle" comes from the Latin word "angulus," which meaning "horn." The vertex is the place where the two rays, also known as the angle's sides, meet.

Let x be the angle JML measurement. Next, using the angle connections we discovered earlier:

m LKN = x m KML = m LMN = 180 minus x (since they form a linear pair with angle JML)

180 - x - (180 - m LKN) m JML

JML m = LKN m - x

JML = 60 - x KML = m LMN = 180 - 60 = 120 F

JMN = JML (alternative interior angles) KMN = KML (alternate interior angles) m JMN + KMN + m N = 180 (angles in a triangle)

m JMN = 60 x m KMN = 120 60 x + 120 + m N = 180 m N = x

As a result, we have:

LK + KL = NM (segment addition postulate)

NM = 10 + 6 = 16 (as seen in the figure) m JML = 60 - x m KML = 120 m

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The solution to the offered question depends on the hypothesis the response is the determined t-worth of - 2.58 is not exactly the basic t-worth of - 2.009, we can't dismiss the invalid hypothesis.

To evaluate the hypothesis, we will play out a one-example t-test. The test measurement is determined as:

t = (test mean - populace mean)/(test standard deviation/sqrt(sample size))

Expecting an importance level of 0.05, we will dismiss the invalid hypothesis if the determined t-esteem is more noteworthy than the basic t-esteem.

Populace mean = $3,261 (given)

Test mean = $3,015

Test standard deviation = $1,745

Test size = 50

t = (3015 - 3261)/(1745/sqrt(50)) = - 2.58

Utilizing a t-table with 49 levels of opportunity (test size - 1) and an importance level of 0.05, the basic t-esteem is ±2.009.

Since the determined t-worth of - 2.58 is not exactly the basic t-worth of - 2.009, we can't dismiss the invalid hypothesis. This really intends that there isn't sufficient proof to recommend that there is a massive distinction in medical services costs per worker between last year and this year with the agreement with Grimms Wellbeing Upkeep Association having no effect.

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Using the net below, find thesurface area of the triangular prism.Start by finding thearea of each piece.6 cm9 cm[?]576 cmcm6 cm9 cmTo find the surface area of the triangular prism, we need to find the area of each face and add them up. First, let's find the area of the triangular base: Area of triangle = (1/2) x base x height The base of the triangle is 6 cm and the height is 9 cm, so: Area of triangle = (1/2) x 6 cm x 9 cm = 27 cm^2 Next, let's find the area of each rectangular face: Area of rectangle = length x width One rectangular face has a length of 9 cm and a width of 6 cm: Area of rectangular face = 9 cm x 6 cm = 54 cm^2 The other rectangular face also has a length of 9 cm and a width of 6 cm: Area of rectangular face