There are 5 lunch choices in a hospital cafeteria: Salad, Pizza, Spaghetti, Sub Sandwiches and Soup. The percentage of people that chose Pizza is 25%. If 50 people chose pizza, what is the total number of people at ate lunch?

The probability that 115 or fewer of the 250 homes were partially financed by the seller is approximately 0.9733.

This problem can be solved using the binomial distribution, where

n = 250 is the total number of home sales in the sample.

p = 0.4 is the probability that any given home sale is partially financed by the seller.

X is the number of home sales in the sample that are partially financed by the seller, which we are interested in.

The probability of X successes in n independent Bernoulli trials, each with success probability p, is given by the probability mass function of the binomial distribution

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items out of n without regard to order.

To solve this problem, we need to calculate the cumulative probability of 115 or fewer home sales being partially financed by the seller

P(X ≤ 115) = P(X = 0) + P(X = 1) + ... + P(X = 115)

We can use a statistical software or calculator to calculate this probability directly, or we can use the normal approximation to the binomial distribution, which is valid when n is large and p is not too close to 0 or 1.

The mean of the binomial distribution is μ = np = 250 * 0.4 = 100, and the standard deviation is σ = sqrt(np(1-p)) = sqrt(60) ≈ 7.746.

To use the normal approximation, we standardize the random variable X as follows

Z = (X - μ) / σ

Then, we can use the standard normal distribution to calculate the probability

P(X ≤ 115) ≈ P(Z ≤ (115 - μ) / σ)

P(Z ≤ (115 - μ) / σ) = P(Z ≤ (115 - 100) / 7.746) ≈ P(Z ≤ 1.934)

Using a standard normal table or calculator, we find that P(Z ≤ 1.934) ≈ 0.9733.

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Answer:

6°F

58°F

Step-by-step explanation:

From the data Given :

Temperature rise in Buffalo by noon time = 14°F

The initial temperature at Buffalo = - 8°F

Rise in temperature = 14°F

Therefore, temperature at noon = (-8 + 14)°F = 6°F

B.)

Temperature at 6am in St. Louis = 32°F

Temperature at 6am in Juneau = - 26°F

Temperature difference :

(32 - (-26))°F

32 + 26

= 58°F

Temperature in St. Louis is 58°F higher

Answer:

7-3x<0

7 < 3x

3x > 7

x > 7/3

Hope it helps :)

Answer:

7-3x<0

7-3+5

-1

__&96&6$96&6 $96$6*"586*6)*5)"-*-*6*=$6=*)5$)5"

Answer:

36

Step-by-step explanation:

because if 6x6=36

Solution

The exponential function

The final answer

Option B

Answer:

Height of lamppost = 23.835 ft (Approx)

Step-by-step explanation:

Given:

Man's distance from lamppost = 15 ft

Shadow length = 5 ft

Angle of elevation = 50°

Find:

Height of lamppost

Computation:

Using trigonometry application.

Total base length = 15 ft + 5 ft

Total base length = 20 ft

Tan 50° = Height of lamppost / Total base length

1.19175359 =  Height of lamppost / 20

Height of lamppost = 23.835 ft (Approx)

Answer:

To the nearest foot it is about 24 feet

Answer:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Step-by-step explanation:

Angle 1: Same-side interior angle of Line 1

Angle 2: Same-side interior angle of Line 2

We know that the difference between the angles is 50 degrees. Since the angles are supplementary, we can write the equation:

Angle 1 + Angle 2 = 180

Now, we need to express the difference between the angles in terms of Angle 1 or Angle 2. We can choose either angle, so let's express it in terms of Angle 1:

Angle 1 - Angle 2 = 50

We can rewrite this equation as:

Angle 1 = 50 + Angle 2

Now substitute this expression for Angle 1 into the first equation:

(50 + Angle 2) + Angle 2 = 180

Combine like terms:

2Angle 2 + 50 = 180

Subtract 50 from both sides:

2Angle 2 = 130

Divide by 2:

Angle 2 = 65

Now substitute this value back into the equation for Angle 1:

Angle 1 = 50 + Angle 2

Angle 1 = 50 + 65

Angle 1 = 115

Therefore, the angles are as follows:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

The given function is not linear as it does not satisfy the property of additivity. Therefore, it cannot be expressed in the form f(x) = ax + b.

To determine if the given function is linear, we need to check if it satisfies the two properties of linearity:

1. Additivity: f(x + y) = f(x) + f(y) for all x and y.

2. Homogeneity: f(cx) = cf(x) for all x and scalar c.

Let's check if f(x) = (1/2)(5x - 3) satisfies these properties:

Additivity:

f(x + y) = (1/2)(5(x + y) - 3) = (1/2)(5x + 5y - 3)

f(x) + f(y) = (1/2)(5x - 3) + (1/2)(5y - 3) = (1/2)(5x + 5y - 6)

Since (1/2)(5x + 5y - 3) is not equal to (1/2)(5x + 5y - 6), the function does not satisfy additivity, and therefore it is not linear.

So the answer is:

NOT LINEAR.

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The statement "P(A or B) = P(A) + P(B)" is False.

The correct statement is "P(A or B) = P(A) + P(B) - P(A and B)," which is known as the general law of addition for probabilities. This law takes into account the possibility of events A and B overlapping or occurring together.

The general law of addition for probabilities states that the probability of either event A or event B occurring is equal to the sum of their individual probabilities minus the probability of both events occurring simultaneously. This adjustment is necessary to avoid double-counting the probability of the intersection.

Let's consider a simple example. Suppose we have two events: A represents the probability of flipping a coin and getting heads, and B represents the probability of rolling a die and getting a 6. The probability of getting heads on a fair coin is 0.5 (P(A) = 0.5), and the probability of rolling a 6 on a fair die is 1/6 (P(B) = 1/6). If we assume that these events are independent, meaning the outcome of one does not affect the outcome of the other, then the probability of getting heads or rolling a 6 would be P(A or B) = P(A) + P(B) - P(A and B) = 0.5 + 1/6 - 0 = 7/12.

In summary, the general law of addition for probabilities states that when calculating the probability of two events occurring together or separately, we must account for the possibility of both events happening simultaneously by subtracting the probability of their intersection from the sum of their individual probabilities.

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The point (7, -π/2) in polar coordinates corresponds to the rectangular coordinates (0, -7), representing a point on the negative y-axis.

In polar coordinates, a point is represented by its distance from the origin (r) and its angle from the positive x-axis (θ). For the given point (7, -π/2), the distance from the origin is 7 units (r = 7), and the angle is -π/2 radians.

To convert this point to rectangular coordinates, we can use the following formulas:

x = r * cos(θ)

y = r * sin(θ)

Applying these formulas to the given values, we get:

x = 7 * cos(-π/2)

y = 7 * sin(-π/2)

The cosine of -π/2 is 0, and the sine of -π/2 is -1, so we can substitute these values into the formulas:

x = 7 * 0 = 0

y = 7 * (-1) = -7

Therefore, the rectangular coordinates for the point (7, -π/2) are (0, -7). This represents a point on the negative y-axis, where the x-coordinate is 0 and the y-coordinate is -7.

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Answer:

The perimeter is 37 inches (3 ft. 1 in.)

Step-by-step explanation:

24 + 13 = 37

12 x 2 = 24

6.5 x 2 = 13

Answer:

Step-by-step explanation:

Answer:

y=-1/2x-0.5

Step-by-step explanation:

y+2=-1/2(x+5)

y+2=-1/2x-2.5

Nielsen collects data from two primary sources: set-top boxes/main units in homes and people meters. These sources help gather accurate information about TV viewership

Nielsen collects data from two primary sources: set-top boxes/main units in homes and people meters. These devices track viewership and other data for TV programming and provide valuable insights for advertisers and media companies. Additionally, Nielsen also collects data through diaries, where households manually record their TV viewing habits. All of this data helps to inform important decisions in the media industry.

Nielsen collects data from two primary sources: set-top boxes/main units in homes and people meters. These sources help gather accurate information about TV viewership, allowing for the analysis of audience data in terms of demographics and other relevant factors.

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Answer:

[see below]

Step-by-step explanation:

The bike's original price is 300 dollars. It has been discounted by 30%.

300 * 0.3 = 90

The price would be 90 dollars off.

300 - 90 = 210

$210 would be the subtotal.

There is also an 8% sales tax.

210 * 0.08 = 16.80

210 + 16.80 = 226.80

Hope this helps you!

Answer:

cost of the bike =$300

discount = 30%

Price of the bike ={ (30/100)×300}-300=210

Sales tax= 8%

Final cost =( 8/100)×210=16.80+210=226.80

Answer:

send the complete question . there are some missing signs .

Answer:

160:40 or 160 to 40, 80:320 or 80 to 320, 400:1000 or 400 to 1000

Step-by-step explanation:

Answer:

x=10

Step-by-step explanation:

We know that the values will be the same because of a geometry rule (i don't remember which one sorry) so we can rewrite the equation as

6x=5x+10      Then, subtract 5x from both sides

x=10

I'm assuming this is what the question is asking

The margin of error for the population mean is 5.601

What does the term "margin of error" mean?

Your results will deviate by how many percentage points from the actual population value, according to your margin of error. It is described as a very small percentage that is allowed for error in calculations.

Given c = 0.95

The significance level is obtained as follows:

alpha = 1 - c

alpha = 1 - 0.95

alpha = 0.05

Also, it is given that n = 150 and sigma = 35 .

The critical value of Z distribution at 0.05 level of significance can be computed in MS Excel using + NORMS INV (alpha/2) function as follows:

Thus, \(Z_{0.005/2}=1.96\)

Now, the margin of error can be computed as follows: ME = Critical Value x Standard Error

\(Z_{0.005/2}*\frac{sigma}{\sqrt{n} } \\= 1.96 * \frac{35}{\sqrt{150} } \\= 5.601\)

Thus, the margin of error for the population mean is 5.601

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Answer:

-3.5 and -0.5

Step-by-step explanation:

Answer:

En la clase hay 25 alumnos.

Step-by-step explanation:

La regla de tres es una forma de resolver problemas de proporcionalidad entre tres valores conocidos y una incógnita, estableciendo una relación de proporcionalidad entre todos ellos.

De todos los estudiantes en la clase, 5 quieren una fiesta de helado. Sabiendo que el 20% de los estudiantes de la clase quiere una fiesta de helado, se puede aplicar la regla de tres: si el 20% de los estudiantes de la clase son 5 estudiantes, el 100% (totalidad de los alumnos) cuántos alumnos son?

\(totalidad de los alumnos=\frac{100*5}{20}\)

totalidad de los alumnos= 25

En la clase hay 25 alumnos.

M = A + |B| is the function's highest possible value. When sin or cos x equals 1, this maximum value is reached. m = A |B| is the function's lowest possible value. If either cos x or sin x is equal to 1, this minimum will be reached.

Example :

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a) The ratio of the distance Colton has traveled to the amount of time he has been traveling is; 14 mph which represents the average velocity

b) The value of d when travelling for 6 hours at the same velocity is; 84 miles

c) The value of h when he bikes 200 miles is; 14.3 hours

a) We are given;

Distance traveled = 49 miles

Time taken = 3.5 hours

Ratio of distance to time = 49/3.5 = 14 mph

This represents the average velocity

b) We are told that he traveled the same rate for 6 hours. Thus;

Distance is gotten from the formula;

d = velocity * time

d = 14 * 6

d = 84 miles

c) He wants to bike 200 miles. When h is the number of hours taken, then; h = d/v

h = 200/14

h = 14.3 hours

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An inverted pyramid is being filled with water at a constant rate of 55 cubic centimeters per second. The rate at which the water level is rising when the water level is 9 cm is 5 cm/s.

To find the rate at which the water level is rising when the water level is 9 cm, we can use similar triangles and the formula for the volume of a pyramid.

Let's denote the rate at which the water level is rising as dh/dt (the change in height with respect to time). We know that the pyramid is being filled at a constant rate of 55 cubic centimeters per second, so the rate of change of volume is dV/dt = 55 cm³/s.

The volume of a pyramid is given by V = (1/3) * base area * height. In this case, the base area is a square with sides of length 6 cm and the height is 14 cm. We can differentiate the volume equation with respect to time, dV/dt, to find an expression for dh/dt.

After differentiating and substituting the given values, we can solve for dh/dt when the water level is 9 cm.

By substituting the values into the equation, we get dh/dt = 5 cm/s.

Therefore, the rate at which the water level is rising when the water level is 9 cm is 5 cm/s.

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The area of the parallelogram is (b) 2x³ - 6x - 14x + 24

from the question, we have the following parameters that can be used in our computation:

The parallelogram (see attachment)

Where, we have

Base = 2x² + 2x - 6

Height = x - 4

The area is calculated as

Area = Base * height

So, we have

Area = (2x² + 2x - 6) * (x - 4)

Evaluate

Area = 2x³ - 6x - 14x + 24

Hence, the simplified expression of the area  is (b) 2x³ - 6x - 14x + 24

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a. The median number of calls = 55

b. The first and third quartiles, Q1 = 48 and Q3 = 66

c. The first decile and the ninth decile, D1 = 45 and D9 = 71.

d. The 33rd percentile = 52.5

To answer the questions, let's first organize the data in ascending order:

38 40 41 45 48 48 50 50 51 51 52 52 53 54 55 55 55 56 56 57 59 59 59 62 62 62 63 64 65 66 66 67 67 69 69 71 77 78 79 79

(a) The median is the middle value of a dataset when arranged in ascending order.

Since we have 40 observations, the median is the value at the 20th position.

In this case, the median is the 55th visit.

(b) The quartiles divide the data into four equal parts.

To find the first quartile (Q1), we need to locate the position of the 25th percentile, which is 40 * (25/100) = 10.

The first quartile is the value at the 10th position, which is 48.

To find the third quartile (Q3), we need to locate the position of the 75th percentile, which is 40 * (75/100) = 30.

The third quartile is the value at the 30th position, which is 66.

Therefore, Q1 = 48 and Q3 = 66.

(c) The deciles divide the data into ten equal parts.

To find the first decile (D1), we need to locate the position of the 10th percentile, which is 40 * (10/100) = 4.

The first decile is the value at the 4th position, which is 45.

To find the ninth decile (D9), we need to locate the position of the 90th percentile, which is 40 * (90/100) = 36.

The ninth decile is the value at the 36th position, which is 71.

Therefore, D1 = 45 and D9 = 71.

(d) To find the 33rd percentile, we need to locate the position of the 33rd percentile, which is 40 * (33/100) = 13.2 (rounded to 13). The 33rd percentile is the value at the 13th position.

Since the value at the 13th position is between 52 and 53, we can calculate the percentile using interpolation:

Lower value: 52

Upper value: 53

Position: 13

Percentage: (13 - 12) / (13 - 12 + 1) = 1 / 2 = 0.5

33rd percentile = Lower value + (Percentage * (Upper value - Lower value))

                = 52 + (0.5 * (53 - 52))

                = 52.5

Therefore, the 33rd percentile is 52.5.

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If A and B are sets with A⊆B the a) A ∪B = B, b) A∩B = A.

a) Let A⊆B

Let x ∈ A∪B

Then x ∈ A or x ∈ B .....(i)

By definition of union we have

x ∈ A ⇒ x ∈ B .....(ii)

Using (i) and (ii), if x ∈ A, then x ∈  b. If x ∈ B, then clearly x ∈ B.

Thus given A⊆ B, then A∪B = B.

b) First assume A∩B which implies that x ∈ A and x ∈ B.

Hence we can implies the

A∩ B ⊆ A (we started with the element in A∩B and concluded that it is in A) ------(i)

Now, let x ∈ A which implies x ∈ B ( as A⊆ B)

Hence, x ∈ A∩B, which in turn imply

A ⊆ A∩B -----(ii)

From (i) and (ii) we get

A∩B = A

Therefore if A and B are sets with A⊆B, then A ∩B = B and A∩B = A.

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Answer:

2184

Step-by-step explanation:

This question involves permutations. We can solve it using the formula

\(\frac{n!}{(n-r)!}\)

where n=14 (because we are choosing from 14 people)

and r=3 (because we are choosing 3 people)

and we are using the permutation formula because the order or placement in which these 3 people are choosing matters (having a person 1 being a director is different from having person 1 being a chief executive officer)

14!/(14-3)!

= 14!/11!

= 14 x 13 x 12

= 2184

Answer:

Significant Figures

   7

   4857.169

Decimals

   3

   4857.169

Scientific Notation

   4.857169 × 103

E-Notation

   4.857169e+3

Words

   four thousand eight hundred fifty-seven point one six nine

Explanation: Mark Brainliest plz

Answer:

plz mark me as a brainliest i really need it

Step-by-step explanation:

4857.169

Sig Figs

7

4857.169

Decimals

3

4857.169

Scientific Notation

4.857169 × 103

E-Notation

4.857169e+3

Words

four thousand eight hundred fifty-seven point one six nine