THIS WILL HELP A LOT OF PPL PLZ HLP!!!!!!
Determine the interval where the graph of the function is negative.

ANSWER CHOICES AND GRAPH IN IMAGES

The probability to consume more than 13 pizzas per month is 0.3707 and more than 110 pizzas in a random sample of size 10 is 0.9646.

The number of pizzas consumed per month by university students is normally distributed with a mean of 12 and a standard deviation of 3.

A. Probability that more than 13 pizzas consumed by students:

For finding the probability, we need to find the Z-score first.

z = (x - μ) / σz = (13 - 12) / 3z = 0.3333

Now, we have to use the z-table to find the probability associated with the z-score 0.3333.

The area under the normal distribution curve to the right of 0.3333 is 0.3707 (rounded off to 4 decimal places).

Thus, the probability that a student consumes more than 13 pizzas per month is 0.3707.

B. Probability that more than 110 pizzas consumed in a random sample of size 10:

Let x be the number of pizzas consumed in the random sample of size 10.

Then, the distribution of x is a normal distribution with the mean = 10 × 12 = 120 and standard deviation = √(10 × 3²) = 5.4772

We have to find the probability that the total number of pizzas consumed is greater than 110. i.e. P(x > 110).

For finding the probability, we need to find the Z-score first.z = (110 - 120) / 5.4772z = -1.8257

The area under the normal distribution curve to the right of -1.8257 is 0.9646 (rounded off to 4 decimal places).

Thus, the probability that more than 110 pizzas are consumed in a random sample of size 10 is 0.9646.

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Answer:

For real???

Step-by-step explanation:

Tysm!! <3 you deserve so much!

Answer:thanks

Step-by-step explanation:

Answer:

Step-by-step explanation:

5 boys

Answer:

me

Step-by-step explanation:

beceaus im the best Guy

The required probability is 0.2023.

Given random variable X with binomial distribution with n=150 and p=0.6.

The binomial distribution with parameters n and p has probability mass function:

$$f(x)= \begin{cases} {n\choose x} p^x (1-p)^{n-x} & \text{for } x=0,1,2,\ldots,n, \\ 0 & \text{otherwise}. \end{cases}$$

Now the mean, μ = np = 150 × 0.6 = 90 and standard deviation, σ = √(npq) = √(150 × 0.6 × 0.4) = 6

Using the normal approximation,

we have:

$$\begin{aligned}P(X ≥ 95) &\approx P\left(Z \geq \frac{95 - \mu}{\sigma}\right)\\ &\approx P(Z \geq \frac{95 - 90}{6})\\ &\approx P(Z \geq 0.8333) \end{aligned}$$

Using the standard normal table, the area to the right of 0.83 is 0.2023.

Therefore, P(X ≥ 95) = 0.2023.

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According to the given information, the required probability is 0.2019.

The random variable has a binomial distribution with n = 150 and p = 0.6.

We can use the normal approximation to the binomial distribution to find the probability P(X ≥ 95).

Normal Approximation:

The conditions for the normal approximation to the binomial distribution are:

np ≥ 10 and n(1 - p) ≥ 10

The expected value of the binomial distribution is given by the formula E(X) = np

and the variance is given by the formula [tex]Var(X) = np(1 - p)[/tex].

Let X be the number of successes among n = 150 trials each with probability p = 0.6 of success.

The random variable X has a binomial distribution with parameters n and p, i.e., X ~ Bin(150, 0.6).

The expected value and variance of X are:

[tex]E(X) = np = 150(0.6) = 90[/tex],

[tex]Var(X) = np(1 - p) = 150(0.6)(0.4) = 36[/tex].

The probability that X takes a value greater than or equal to 95 is:

[tex]P(X ≥ 95) = P(Z > (95 - 90) / (6))[/tex]

where Z ~ N(0,1) is the standard normal distribution with mean 0 and variance 1.

[tex]P(X ≥ 95) = P(Z > 0.8333)[/tex]

We can use a standard normal distribution table or a calculator to find this probability.

Using a standard normal distribution table, we find:

[tex]P(Z > 0.8333) = 0.2019[/tex]

Thus, [tex]P(X ≥ 95) = 0.2019[/tex] (rounded to four decimal places).

Therefore, the required probability is 0.2019.

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Answer:

The answer is 1/11

Step-by-step explanation:

Explanation is in the picture above

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The correct answer is option D. Since A and B are mutually exclusive events, the probability that both A and B occur is 0. In other words, P(A&B) = 0.

When two events, A and B, are mutually exclusive, it means that they cannot occur simultaneously. If one event happens, the other event cannot happen at the same time. In this scenario, the correct answer is option D, which states that the probability of both events A and B occurring together is 0, i.e., P(A&B) = 0.

To understand this concept, consider a simple example. Let's say event A represents flipping a coin and getting heads, while event B represents flipping a coin and getting tails. Since getting heads and getting tails are mutually exclusive outcomes, it is impossible for both events A and B to occur simultaneously. Therefore, the probability of both A and B occurring together is 0. In summary, when events A and B are mutually exclusive, the correct answer is option D, which states that the probability of both A and B occurring together is 0, i.e., P(A&B) = 0.

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the three numbers whose sum is 21 and whose sum of squares is a minimum are 7, 7, and 7.

To find three numbers whose sum is 21 and whose sum of squares is a minimum, we can use a mathematical technique called optimization. Let's denote the three numbers as x, y, and z.

We need to minimize the sum of squares, which can be expressed as the function f(x, y, z) = x² + y² + z²

Given the constraint that the sum of the three numbers is 21, we have the equation x + y + z = 21.

To find the minimum value of f(x, y, z), we can use the method of Lagrange multipliers, which involves solving a system of equations.

First, let's define a Lagrange multiplier, λ, and set up the following equations:

1. ∂f/∂x = 2x + λ = 0

2. ∂f/∂y = 2y + λ = 0

3. ∂f/∂z = 2z + λ = 0

4. Constraint equation: x + y + z = 21

Solving equations 1, 2, and 3 for x, y, and z, respectively, we get:

x = -λ/2

y = -λ/2

z = -λ/2

Substituting these values into the constraint equation, we have:

-λ/2 - λ/2 - λ/2 = 21

-3λ/2 = 21

λ = -14

Substituting λ = -14 back into the expressions for x, y, and z, we get:

x = 7

y = 7

z = 7

Therefore, the three numbers whose sum is 21 and whose sum of squares is a minimum are 7, 7, and 7.

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Answer:

A x<1125

Step-by-step explanation:

Answer:

it is A

Step-by-step explanation:

i remember doing this in middle school.

Answer:

8 laps in 70 seconds is faster.

Step-by-step explanation:

If we divide 70/8 and 98/12 we get the following:

70/8= 8.75

98/12=8.16

8.75>8.16

The unit rate is 1 lap in 8.75 seconds and 1 lap in 8.16 seconds

Answer:

( 21 x X ) + 1

Step-by-step explanation:

Answer:

The distance the hiker must travel is approximately 5.5 miles

Step-by-step explanation:

The distance between the two cell phone towers = 22.5 miles

The distance between the hiker's phone and Tower A = 14.2 miles

The distance between the hiker's phone and Tower B = 10.9 miles

The direction of the highway along which the towers are located = East to west

The direction in which the hiker is travelling to reach the highway quickly = South

By cosine rule, we have;

a² = b² + c² - 2·b·c·cos(A)

Let 'a', 'b', and 'c', represent the sides of the triangle formed by the imaginary line between the two towers, the hiker's phone and Tower A, and the hiker's hone and tower B respectively, we have;

a = 22.5 miles

b = 14.2 miles

c = 10.9 miles

Therefore, we have;

22.5² = 14.2² + 10.9² - 2 × 14.2 × 10.9 × cos(A)

cos(A) = (22.5² - (14.2² + 10.9²))/( - 2 × 14.2 × 10.9) ≈ -0.6

∠A = arccos(-0.6) ≈ 126.9°

By sine rule, we have;

a/(sin(A)) = b/(sin(B)) = c/(sin(C))

∴ sin(B) = b × sin(A)/a

∴ sin(B) = 14.2×(sin(126.9°))/22.5

∠B = arcsine(14.2×(sin(126.9°))/22.5) ≈ 30.31°

∠C = 180° - (126.9° - 30.31°) = 22.79° See No Evil

The distance the hiker must travel, d = c × sin(B)

∴ d = 10.9 × sin(30.31°) ≈ 5.5

Therefore, the distance the hiker must travel, d ≈ 5.5 miles.

Answer:

option c.

by Pythagoras theorem.

hypotenuse²=height ²+base²

20²=x²+12²

400=x²+144

400-144=x²

256=x²

256½=x

16=x

Answer:

x = 3, 2

Step-by-step explanation:

Answer: x = 3, 2

Step-by-step explanation:

Type I Error: A Type I error is the first kind of error that can occur when testing a hypothesis. A Type I error occurs when a null hypothesis is rejected even when it is accurate.

If we make a Type I Error on this test, it would mean that we reject a null hypothesis that is true. This mistake would be made if we made a decision to reject the null hypothesis when there is no significant evidence to support that decision. The null hypothesis is the hypothesis that claims no change or no difference between the groups being compared. Null hypothesis is the opposite of the alternative hypothesis which is the hypothesis that claims that there is a difference between groups being compared.

In this context, making a Type I Error would mean that we reject the null hypothesis which is that all groups of voters would agree that workers who have illegally entered the US should be allowed to keep their jobs and apply for US citizenship. Making this error would mean we have come to the conclusion that they do not agree, which would be incorrect.

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Answer:

100in

Step-by-step explanation:

1/2 *10*5=25

4(25)=100

Answer:

The correct statement is B (are very sensitive to change in price)

Step-by-step explanation:

Option B is correct because of the following reason -:

The degree to which a rise in price affects the quantity demanded or supplied is known as elasticity. In the case of elastic demand and supply, as the price rises, the quantity demanded falls and the quantity supplied rises more than proportionally. Inelastic price elasticity of demand and supply, on the other hand, induces a less than proportional change in quantity as prices change.

Hence , the correct option is B .

The Surface area of the cylinder with a height of 8 ft and a radius of 4 ft is approximately 301.44 square feet.

The surface area of a cylinder, we need to consider the lateral surface area and the area of the two circular bases.

The lateral surface area of a cylinder can be determined by multiplying the height of the cylinder by the circumference of its base. The formula for the lateral surface area (A) of a cylinder is given by A = 2πrh, where r is the radius and h is the height of the cylinder.

In this case, the height of the cylinder is 8 ft and the radius is 4 ft. Therefore, the lateral surface area can be calculated as follows:

A = 2π(4 ft)(8 ft)

A = 64π ft²

The area of each circular base can be calculated using the formula for the area of a circle, which is A = πr². In this case, the radius is 4 ft. Therefore, the area of each circular base is:

A_base = π(4 ft)²

A_base = 16π ft²

Since a cylinder has two circular bases, the total area of the two bases is:

A_bases = 2(16π ft²)

A_bases = 32π ft²

the total surface area, we sum the lateral surface area and the area of the two bases:

Total surface area = Lateral surface area + Area of bases

Total surface area = 64π ft² + 32π ft²

Total surface area = 96π ft²

Now, let's calculate the numerical value of the surface area:

Total surface area ≈ 96(3.14) ft²

Total surface area ≈ 301.44 ft²

Therefore, the surface area of the given cylinder, with a height of 8 ft and a radius of 4 ft, is approximately 301.44 square feet.

In conclusion, the surface area of the cylinder with a height of 8 ft and a radius of 4 ft is approximately 301.44 square feet.

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Answer:

x-intercept: (-1,0)

y-intercept: (0,3)

Vertex: (-2,-1)

Step-by-step explanation:

Answer:

x = 95

Step-by-step explanation:

Given that,

The cost of a banquet at Nick's Catering is $215 plus $27.50 per person

The total cost of a banquet was $2827.50

We need to find the number of people invited. Let there are x people. So,

215+27.5x = 2827.50

27.5x = 2827.50 -215

27.5x = 2612.5

x = 95

So, there are 95 people that were invited.

Answer: D) a rotation of 180 degrees Clockwise about the center of the parallelogram

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The perimeter of the square has to be only positive values, and so there has to be restrictions on the values. We can rule out answers A and B. Because the perimeter the values of x have to be less than 4. If they were greater than 4, then 4x>16. So we can rule out answer d. The correct answer is C.

Given that f, g ∈ L’[a, b], we need to prove the Cauchy-Schwarz inequality, |(f, g)| = ||$|| . ||$||.

The Cauchy-Schwarz inequality for inner product in L’[a, b] states that for all f, g ∈ L’[a, b],|(f, g)| ≤ ||$|| . ||$||Proof: Consider a function Q(t) = (f + tg, f + tg) for any real number t. Then, by using the rules of inner product, we can expand this expression and obtain a quadratic polynomial in t.$$Q(t) = (f + tg, f + tg) = (f, f) + t(f, g) + t(g, f) + t^2(g, g)$$$$ = (f, f) + 2t(f, g) + t^2(g, g)$$. Now, Q(t) > 0 because Q(t) is a sum of squares. So, Q(t) is a quadratic polynomial that can have at most one real root since Q(t) > 0 for all t ∈ R.

To find the discriminant of Q(t), we need to solve the equation Q(t) = 0.$$(f, f) + 2t(f, g) + t^2(g, g) = 0$$.

The discriminant of Q(t) is:$$D = (f, g)^2 - (f, f)(g, g)$$

Since Q(t) > 0 for all t ∈ R, the discriminant D ≤ 0.$$D = (f, g)^2 - (f, f)(g, g) ≤ 0$$$$\Right arrow (f, g)^2 ≤ (f, f)(g, g)$$$$\Right arrow |(f, g)| ≤ ||$|| . ||$||$$

Thus, |(f, g)| = ||$|| . ||$||, which proves the Cauchy-Schwarz inequality. Therefore, the given statement is true.

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Answer:

19. B

20. C

Step-by-step explanation:

ANSWER : D

EXPLANATION : 81 > 13 is true

(a) To argue that P(T < ∞) = 1, where T is the first time the walk visits 0 or N, we can consider each time the walk visits 1 before time T.

Suppose the walk visits 1 for the first time at time k < T. At this point, the random walk is in a state where it can either hit 0 before N or hit N before 0.

Let's define a new random variable Y, which represents the number of steps needed for the walk to hit either 0 or N starting from state 1. Y follows a geometric distribution with parameter p since the steps are +1 with probability p and -1 with probability q = 1 - p.

Now, we can compare the random variable T and Y. If T < ∞, it means that the walk has hit either 0 or N before reaching time T. Since T is finite, it implies that the walk has hit 1 before time T. Therefore, we can say that T ≥ Y.

By the properties of the geometric distribution, we know that P(Y = ∞) = 0. This means that there is a non-zero probability of hitting either 0 or N starting from state 1. Therefore, P(T < ∞) = 1, as the walk is guaranteed to eventually hit either 0 or N.

(b) To find P(J|So = n), where So = n, we need to determine the probability of hitting N before hitting 0 starting from state n.

Recall that the probability of hitting N before 0 starting from state 1 is given by (g/p)^(N-1), as shown in the Optional Stopping Theorem formula. In our case, since the walk starts at state n, we need to adjust the formula accordingly.

The probability of hitting N before 0 starting from state n can be calculated as P(J|So = n) = (g/p)^(N-n).

This probability takes into account the number of steps required to reach N starting from state n. It represents the likelihood of hitting the jackpot (N) before going bust (0) when the walk starts at state n.

It's worth noting that this probability depends on the values of p, q, and N.

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-8x-2(5+4x)

Step-by-step explanation:

-8x-10-8x -8x-8x-10 -16x-10

Answer:

20 boys

Step-by-step explanation:

If there are 4 boys for every 3 girls, multiply both numbers by 5 (3*5 = 15) to find the number of boys.

Answer:

20

Step-by-step explanation:

4/3 = ?/15

multiply both sides by 15

15*4/3 = ?

? = 20

(a) Math2 is not an unbiased estimator of μ. (b)Math1 has a variance of

σ[tex]^{2}[/tex] and Math2 has a variance of  5σ[tex]^2[/tex]/8

(a) Neither of the estimators, Math1 or Math2, is an unbiased estimator of μ. An unbiased estimator should have an expected value equal to the parameter being estimated, in this case, μ.

For Math1,

the expected value is

E[Math1] = E[([tex]X_{1}[/tex] + [tex]X_{2}[/tex]) / 2]

= (E[[tex]X_{1}[/tex]] + E[[tex]X_{2}[/tex]]) / 2

= μ/2 + μ/2 = μ,

which means Math1 is an unbiased estimator of μ.

For Math2,

the expected value is

E[Math2] = E[([tex]X_{1}[/tex] + [tex]3X_{2}[/tex]) / 4]

= (E[[tex]X_{1}[/tex]] + 3E[[tex]X_{2}[/tex]]) / 4

= μ/4 + 3μ/4

= (μ + 3μ) / 4

= 4μ/4

= μ/2.

(b) To calculate the variances of the estimators, we'll use the property that the variance of a sum of independent random variables is the sum of their variances.

For Math1,

the variance is Var[Math1]

= Var[([tex]X_{1}[/tex] + [tex]X_{2}[/tex]) / 2]

= (Var[[tex]X_{1}[/tex]] + Var[[tex]X_{2}[/tex]]) / 4

= σ[tex]^2[/tex]/2 + σ[tex]^2[/tex]/2

= σ[tex]^2[/tex]

For Math2,

the variance is Var[Math2]

= Var[([tex]X_{1}[/tex] + [tex]3X_{2}[/tex]) / 4]

= (Var[[tex]X_{1}[/tex]] + 9Var[[tex]X_{1}[/tex]]) / 16

= σ[tex]^2[/tex]/4 + 9σ[tex]^2[/tex]/16

= 5σ[tex]^2[/tex]/8

Math1 has a variance of σ[tex]^2[/tex]

and Math2 has a variance of 5σ[tex]^2[/tex]/8

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