Haley bought 1.6 pounds of almonds for $13.20. How much did she pay per pound?

There is a probability of 22% that exactly 4 defective parts will be found in a sample of 100.

Probability of a machine producing a defective part is 0.05,

p = 0.05

q  = 1 - p = 1 - 0.05 = 0.95

n = 100

P(x)  = ⁿCₓ pˣqⁿ⁻ˣ

x = 4  

P(4) = ¹⁰⁰C₄(0.05)⁴(0.95)⁹⁶

P(4) = 0.215569

=  0.2156

0.2156 is the probability of finding exactly 4 defective parts from a sample of 100.

The probability of defective parts is the likelihood that a part will be defective. This can be due to a variety of factors, such as poor quality control, incorrect manufacturing process, or use of sub-standard materials. A high probability of defective parts can lead to serious problems, such as faulty products, safety hazards, and financial losses.

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Answer:To find out how much change Lucinda received, we subtract the cost of the video game from the amount she paid:

Amount paid - Cost of the video game = Change

$100 - $63.48 = $36.52

Therefore, Lucinda received $36.52 in change.

Step-by-step explanation:

Answer:

220

Step-by-step explanation:

2b^3+c-d

2(3)^3+7-3

6^3+7-3

216+7-3

223-3

220

Answer:

75

Step-by-step explanation:

lok at the image for explanation, you just need to expand the table

Answer: 1320

Step-by-step explanation:

Given,

HCF of two numbers = 40

Product of two numbers = 52800

To find,

LCM of two numbers =?

Formula required,

HCF × LCM = product of two numbers

Calculation,

Using formula

→ HCF × LCM = product of two numbers

→ ( 40 ) × LCM = 52800

→ LCM = 52800 / 40

→ LCM = 1320

Therefore,

LCM of two numbers would be 1320.

The statement, "A statistic is a formula calculable with data," is True. A statistic is a mathematical calculation that uses data to summarize, organize, analyze, and interpret data.

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. In summary, a statistic is a numerical value that represents a piece of information about a particular data set. It is calculated using mathematical formulas, statistical models, or algorithms.

The purpose of using statistics is to provide objective and accurate descriptions of the data, measure the degree of variability, identify patterns and trends, make inferences, and test hypotheses. In conclusion, statistics are used in different fields such as social sciences, business, finance, medicine, engineering, and environmental studies, to name a few, to make informed decisions based on data analysis.

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The option that best describe the transformation is

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object.

Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

the transformation is the problem is reflection which is equivalent to 180 degree rotation hence we say it is a certain angle rotation of point about the circle's center.

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Answer: $5.49

Step-by-step explanation:

Unit price = 21.96/4 = 5.49

a. P(G1 and Gy) = The probability of drawing a green card first (G1) and a yellow card second (Gy).

The probability of drawing a green card first is 6/11 (since there are 6 green cards out of 11 total cards remaining after the first draw).

After drawing a green card, there will be 5 green cards remaining and 5 yellow cards remaining out of a total of 10 cards. So, the probability of drawing a yellow card second is 5/10.

To find the probability of both events occurring, we multiply the individual probabilities:

P(G1 and Gy) = (6/11) * (5/10) = 30/110 = 3/11

b. P(At least 1 green) = The probability of drawing at least one green card.

To calculate this probability, we can find the complement of drawing no green cards.

The probability of not drawing a green card on the first draw is 5/11 (since there are 5 yellow cards out of 11 total cards remaining).

The probability of not drawing a green card on the second draw, given that a yellow card was drawn first, is 4/10 (since there are 4 yellow cards remaining out of 10 cards).

To find the probability of drawing no green cards, we multiply the probabilities:

P(No green) = (5/11) * (4/10) = 20/110 = 2/11

The probability of drawing at least one green card is the complement of drawing no green cards:

P(At least 1 green) = 1 - P(No green) = 1 - (2/11) = 9/11

c. P(G2G1) = The probability of drawing a green card second (G2) given that a green card was drawn first (G1).

After drawing a green card first, there will be 5 green cards remaining and 5 yellow cards remaining out of a total of 10 cards.

The probability of drawing a green card second is 5/10.

P(G2G1) = 5/10 = 1/2

d. Are G1 and G2 independent?

To check if G1 and G2 are independent, we need to compare the joint probability of both events (drawing a green card first and drawing a green card second) to the product of their individual probabilities.

P(G1 and G2) = (6/11) * (5/10) = 30/110 = 3/11

P(G1) = 6/11

P(G2) = 5/10 = 1/2

If P(G1 and G2) = P(G1) * P(G2), then G1 and G2 are independent.

In this case, (3/11) does not equal (6/11) * (1/2), so G1 and G2 are not independent.

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The equilibrium of this game is {s1 = 1/2, s2 = 1/4} and Player 2 plays A if sA2 = 3/4 and plays B if sB2 = 1/2.

Consider the following two-player game. Si = [0, 1], for i = 1, 2. Player 2 is equally likely to be type A or type B, and the realization of her type is private information to her.

Payoffs are as follows:

u1(s1,s2)=1−[s1 −(1/2)s2]^4

uA2(s1,sA2)=100−[sA2 −s1−1/4]^2

uB2 (s1,sB2 )=100−[sB2 −s1]^2.

To find a Bayes-Nash equilibrium of this game, we need to solve this problem by backwards induction.

The equilibrium of this game is {s1 = 1/2, s2 = 1/4} and Player 2 plays A if sA2 = 3/4 and plays B if Subs = 1/2.

A Bayes-Nash equilibrium is a pair of strategies, one for each player, such that each player's strategy is optimal given the other player's strategy and her private information about the game.

This is a refinement of the Nash equilibrium that takes into account the players' information about the game.

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The surface area of the triangular prism is 81 square feet.

To find the surface area of the triangular prism

we need to calculate the area of each face and then sum them up.

Let's calculate the areas of each face:

Rectangular face 1: Length = 3 feet, Width = 6 feet

Area = Length × Width

= 3 feet × 6 feet = 18 square feet

Rectangular face 2

Area = Length × Width = 3 feet × 7.5 feet

= 22.5 square feet

Rectangular face 3:

Length = 3 feet, Width = 4.5 feet

Area = Length × Width = 3 feet × 4.5 feet

= 13.5 square feet

Triangular face 1: Base = 6 feet, Height = 4.5 feet

Area = (Base × Height) / 2

= (6 feet × 4.5 feet) / 2 = 13.5 square feet

Triangular face 2: Base = 6 feet, Height = 4.5 feet

Area = (Base × Height) / 2 = (6 feet × 4.5 feet) / 2 = 13.5 square feet

Total surface area = 18 square feet + 22.5 square feet + 13.5 square feet + 13.5 square feet + 13.5 square feet

= 81 square feet

Therefore, the surface area of the triangular prism is 81 square feet.

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What is the surface area of the triangular prism? a triangular prism. the rectangular sides are 3 feet by 6 feet, 3 feet by 7.5 feet, and 3 feet by 4.5 feet. the triangular sides have a base of 6 feet and height of 4.5 feet. [not drawn to scale] 54 square feet 67.5 square feet 81 square feet

An associate in a scatter plot tells us the relation between the two variables. The points that are true about the given scatter plot are C and F.

An associate in a scatter plot tells us the relation between the two variables. There are 4 types of associates:

Positive associate: If the value of one variable is increasing the value of another increase as well, but the relation is not linear.

Negative associate: If the value of one variable is decreasing with the value of another increasing as well, but the relation is not linear.

Linear Associate: If the value of one is dependent on the other such that they follow a function of line, and all the data points are on that function line.

Non-linear Associate: If the data points of the plot are scattered and random, such that there is no relationship between the points.

The points that are true about the given scatter plot are:

C.) There appears to be a positive association.

F.) A cluster appears to be at the bottom left corner.

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The odd cubic function f(x) = x³ - 4x² + 5 is approaching (x → ∞, y → ∞).

A polynomial function's final behavior is how its graph behaves as x gets closer to positive or negative infinity.

The graph's final behavior is determined by a polynomial function's degree and leading coefficient.

The function f(x) = x³ - 4x² + 5 is an odd cubic function that is symmetric about the origin.

As x approaches negative infinity the function f(x) also approaches negative infinity but at a faster rate and as approaches positive infinity the function f(x) also approaches positive infinity at a faster rate.

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The clinic should hire at least 7 doctors in order to serve 122 patients per day.

To determine how many doctors the clinic should hire in order to serve 122 patients per day, we need to calculate the number of patients each doctor can see within their working hours.

Let's start by calculating the total number of minutes each doctor works per day. Since each doctor works 8 hours per day and there are 60 minutes in an hour, the total minutes worked by a doctor per day would be 8 hours × 60 minutes = 480 minutes.

Next, we need to find out how many patients a doctor can see within their working hours. Given that each patient requires an average of 27 minutes with a doctor, the number of patients a doctor can see per day would be 480 minutes ÷ 27 minutes per patient = 17.7778 patients.

Since we can't have a fractional number of patients, we need to round this number up to the nearest whole number to ensure that each patient gets the required attention. Therefore, each doctor can see approximately 18 patients per day.

To serve 122 patients per day, we divide the total number of patients by the number of patients each doctor can see per day: 122 patients ÷ 18 patients per doctor = 6.7778 doctors.

Again, we can't have a fractional number of doctors, so we need to round this number up to the nearest whole number. Therefore, the clinic should hire at least 7 doctors to serve 122 patients per day.

In summary, the clinic should hire at least 7 doctors in order to serve 122 patients per day.

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To find the coordinates of the centroid for the region bounded by the curves y=16x, y=9/x, y=0, and x=10, we need to calculate the x-coordinate and y-coordinate of the centroid separately. First, let's find the x-coordinate of the centroid.

We can use the formula: x-bar = (1/A) ∫[a,b] xf(x) dx, where A is the area of the region. The intersection points of the curves y=16x and y=9/x can be found by setting the equations equal to each other: 16x=9/x.

Solving this equation, we get x=±√(9/16)=±3/4. Since the region is bounded by x=10, we take the positive value x=3/4. To find the area A, we integrate the difference between the curves: A=∫[3/4,10] (16x-9/x) dx. Evaluating this integral, we find A=400-9ln(10).

Now we can calculate the x-coordinate of the centroid: x-bar=(1/A) ∫[3/4,10] x(16x-9/x) dx. Simplifying the integral and evaluating it, we get x-bar=(8160-36ln(10))/(400-9ln(10)). Next, let's find the y-coordinate of the centroid.

Since the region is symmetric about the x-axis, the y-coordinate of the centroid will be y-bar=0. Therefore, the exact coordinates of the centroid for the given region are: (x-bar, y-bar)=((8160-36ln(10))/(400-9ln(10)), 0).

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Answer:

314 cm^2

Step-by-step explanation:

pi(r^2)

r= d/2

pi= 3.14

3.14(10^2)

3.14(100)

314

Answer:

  100π cm^2

Step-by-step explanation:

The area of a circle is given by the formula ...

  A = πr^2

where r represents the radius, which is half the diameter. For a circle of radius 10 cm, the area is ...

  A = π(10 cm)^2 = 100π cm^2

Answer:

129.82

Step-by-step explanation:

I got the right answer

The cost to make the spinner is $132.50.

The spinner of the compass is two congruent isosceles triangles connected by their bases as shown in the diagram. The base of each of these triangles is 2 centimeters and the legs are 5 centimeters.

The area of each triangle is (1/2) * base * height = (1/2) * 2 * 5 = 5 square centimeters.

The total area of the spinner is 2 * 5 = 10 square centimeters.

The cost to make the spinner is 10 * $13.25 = $132.50.

Rounded to the nearest cent, the cost is $132.51.

Here is the calculation:

Area of each triangle = (1/2) * base * height = (1/2) * 2 * 5 = 5 square centimeters

Total area of the spinner = 2 * 5 = 10 square centimeters

Cost to make the spinner = 10 * $13.25 = $132.50

Rounded to the nearest cent, the cost is $132.51

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Answer:

B. 1.00 x 10 to the 4th power

Step-by-step explanation:

Answer:

(-8/3, 19/27) and (3, -17/2).

Step-by-step explanation:

To find the coordinates of the points on the graph of ƒ(x) = ½x³ − ¹⁄₂x² − 8x + 7 where the gradient is 4, we need to find the points where the derivative of ƒ(x) is equal to 4.

First, we need to find the derivative of ƒ(x):

ƒ'(x) = 3/2x² - x - 8

Next, we need to set ƒ'(x) = 4 and solve for x:

3/2x² - x - 8 = 4

3/2x² - x - 12 = 0

Multiplying both sides by 2 to eliminate the fraction:

3x² - 2x - 24 = 0

Factoring the quadratic equation:

(3x + 8)(x - 3) = 0

So x = -8/3 or x = 3.

Now we can find the corresponding y-coordinates:

When x = -8/3:

ƒ(-8/3) = 1/2(-8/3)³ - 1/2(-8/3)² - 8(-8/3) + 7 = 19/27

So one point on the graph with gradient 4 is (-8/3, 19/27).

When x = 3:

ƒ(3) = 1/2(3)³ - 1/2(3)² - 8(3) + 7 = -17/2

So another point on the graph with gradient 4 is (3, -17/2).

Therefore, the coordinates of the points on the graph of ƒ(x) = ½x³ − ¹⁄₂x² − 8x + 7 where the gradient is 4 are (-8/3, 19/27) and (3, -17/2).

Answer:

C

Step-by-step explanation:

-2x + 10  Means that the line crosses the y axis at 10.  The slope is -2 that means that as the y changes by -2, the x changes by 1.  

The second equations means that we have a horizontal line with no slope that goes through -28 1/2

Answer:

Sarah bought 30 pencils

Step-by-step explanation:

1. Let define p, as the number of pencils bought, and m, as the number of markers bought.

2.

\(0.15p+0.30m=7.50\)

\(p=3m\)

3. Substitute p in the first equation to 3m since p=3m as defined.

\(0.15(3m) + 0.30m=7.50\\0.45m+0.30m=7.50\\0.75m=7.50\\m=10\)

plug m into equation p=3m to find the number of pencils bought

\(p=3m=3(10)=30\)

The categorical variables goes in gf_facet_grid().

Based on a characteristic, a categorical variable value can be classified into a countable number of different categories. You can apply categories to a categorical variable, but there is no inherent order to the categories.

The most typical graph for displaying frequency distributions is a histogram. It closely resembles a bar chart.

You use it to split up histograms. Usually, the facets are described by an unnamed formula argument. We usually use this to show categorical variables.

eg) gf_histogram(~ Thumb, data = Fingers) %>%

gf_facet_grid(. ~ Sex)

So, we can say that categorical variables goes in gf_facet_grid().

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Answer:

11.0833333

5 1/4

5.83

11.08

Answer:

11.08

Step-by-step explanation:

Because the 3’s are repeating we don’t need to put all of them

The simplified form of trigonometric expression, cosec θ / sin θ + cos θ cot θ is 1.

Given,

The trigonometric expression = cosec θ / sin θ + cos θ cot θ

We have  to simplify this expression.

For that we can use trigonometric identities.

cosec θ = 1 / sin θ

cot θ = cos θ / sin θ

We can substitute the above given identities in the expression.

Then we get,

cosec θ / sin θ + cos θ cot θ = (1 / sin θ) / (sin θ + cos θ x (cos θ/sin θ))

= (1 / sin θ) / ((sin²θ + cos²θ) / sin θ)

Cancel sin θ from both numerator and denominator.

= 1 / sin² θ + cos² θ

We know that sin² θ + cos² θ = 1

So, we get,

1 / sin² θ + cos² θ = 1 / 1 = 1

Therefore, the simplified form of  cosec θ / sin θ + cos θ cot θ is 1.

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Answer:

The vertex of the parabola is at (1,5), opens upwards, the y-intercept is at (0,6), and the axis is at y=1

Step-by-step explanation:

To be certain to get one sock of each color, we need to pull at least the maximum number of socks of any single color.

In this case, there are 10 black socks, so we need to pull at least 10 socks to be certain to get one of each color.

Therefore, the minimum number of socks that must be pulled at random to be certain to get one of each color is 10.

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19 socks must be pulled at random to guarantee obtaining one sock of each color. To be certain to get one of each color, we need to consider the worst-case scenario. Let's assume we first pull out all the red socks. In this case, we would still need to pull out the remaining blue and black socks.

Since there are 8 blue socks and 10 black socks, the maximum number of socks we would need to pull out to guarantee having one of each color is 8 + 10 + 1 = 19.

To understand why we add 1 at the end, let's break it down:
- We pull out 8 blue socks, and at this point, we have 6 red and 2 black socks left.
- Next, we pull out the remaining 6 red socks, and we have 2 black socks remaining.
- Finally, we pull out the remaining 2 black socks, and now we have one of each color.

Therefore, we can conclude that we need to pull out a total of 19 socks to be certain of getting one sock of each color.

In conclusion, 19 socks must be pulled at random to guarantee obtaining one sock of each color.

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