Thank you very much for the excellent explanation. I lost connection after angle b, but afterwards I could see your final calculations. Have a nice day

Answer:

5/100×$1500= 75 dollar

as it is annual income we can solve the answer relative to year and considering it as 1 so the interest would be 75 annually

In the hypothesis testing, the null and alternative for the claim that mean iq of statistics teachers is greater than 140, are

\(H_0 :\mu \leqslant 140\)

\(H_a : \mu > 140\)

and the alternative hypothesis is the hypothesis of this claim.

Hypothesis testing in statistics is a process where you to test the results of a survey or experiment based sample to look if you have meaningful results. It is based on hypothesis. The null hypothesis of a test always shows no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship. The null hypothesis is the fact that should be tested and the alternative is everything else.

We have mean iq of statistics teachers is greater than 140. We have to identify the hypothesis for which this claim is true. Now, the null and alternative hypothesis are defined as in this case, \(H_0 :\mu ≤ 140\)

\(H_a : \mu > 140\)

where μ --> mean iq of statistics

From above, the hypothesis which identify the claim that mean iq of statistics teachers is greater than 140 is alternative hypothesis. Hence, the required answer is alternative hypothesis.

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Mathematically, the claim can be expressed as follows:

µ > 140

where µ represents the population mean IQ score of statistics teachers.

The null hypothesis (H0) is that the population mean IQ score of statistics teachers is not greater than 140:

H0: µ ≤ 140

The alternative hypothesis (Ha) is that the population mean IQ score of statistics teachers is greater than 140:

Ha: µ > 140

Note that the claim corresponds to the alternative hypothesis, Ha.

Null hypothesis (H0): The mean daily attendance at the park is μ = people.

Alternative hypothesis (Ha): The mean daily attendance at the park is not equal to μ ≠ people.

The claim is represented by the alternative hypothesis (Ha), which states that the mean daily attendance at the park is different from the claimed value of people.

Note that the value of μ is not specified in the claim, but it is assumed to be equal to people. The null hypothesis (H0) reflects this assumption, and the alternative hypothesis (Ha) challenges it by stating that the true mean attendance may be different from this value.

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The probability of at least one defective rivet in a seam requiring 27 rivets, assuming they are independently defective with the same probability, is approximately 68.3%.

To solve this problem, we can use the concept of probability and the binomial distribution.

The probability of a rivet being defective is denoted by "p". Since each rivet is defective independently of the others, the probability of a rivet not being defective (i.e., being good) is 1 - p.

The seam will need to be reworked if any of the 27 rivets is defective. Therefore, we want to calculate the probability that at least one rivet is defective.

The probability of at least one defective rivet can be found using the complement rule: subtracting the probability of no defective rivets from 1.

The probability of no defective rivets is given by (1 - p) raised to the power of 27 (since each rivet is independent).

So, the probability of at least one defective rivet is:

P(at least one defective rivet) = 1 - P(no defective rivets)

P(at least one defective rivet) = 1 - (1 - p)^27

Now, we can substitute any desired value for the probability of a defective rivet, "p," to calculate the probability of at least one defective rivet.

For example, if we assume a defective rivet probability of p = 0.05 (5%), the calculation would be as follows:

P(at least one defective rivet) = 1 - (1 - 0.05)^27

P(at least one defective rivet) ≈ 0.683

Therefore, with a 5% probability of a rivet being defective, the probability of at least one defective rivet in the seam is approximately 0.683 or 68.3%.

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The potential energy of an object is given by the equation:

Potential Energy = mass × gravitational acceleration × height

In this case, the mass of the drum of oil is 9 kilograms, the height it is pushed up the inclined plane is 5 meters, and the gravitational acceleration is approximately 9.8 \(m/s^2.\)

Potential Energy = 9 kg × 9.8 \(m/s^2 *5 m\)

Potential Energy = 441 J

Therefore, the potential energy of the man pushing the drum of oil up the inclined plane is 441 joules. This represents the energy that is stored in the system due to the vertical position of the drum of oil, ready to be converted into other forms of energy, such as kinetic energy, when the object is released or moved downwards.

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Answer:

243

Step-by-step explanation:

-9^2 = -9 * -9 = 81

81 * 3 = 243

As similarity theorem, the value of x that will make the triangles similar by SSS similarity theorem is 77.

Similarity theorem:

In math, similarity theorem refers the line segment splits two sides of a triangle into proportional segments if and only if the segment is parallel to the triangle's third side.

Given,

Here we need to find the t value of will make the triangles similar by the similarity theorem.

For example, we are told that the 2 triangles are similar by SSS theorem.

Here we know that, SSS means Side - Side -Side and it is a congruence theorem which states that the 3 corresponding sides of two triangles have same ratio, then we can say that the two triangles are congruent by SSS theorem

Therefore, in the triangles ,applying the SSS postulate gives;

=> x/35 = 44/20

Then by applying the multiplication property of equality, let us multiply both sides by 35 to get;

=> x = (44 * 35)/20

When we simplify this one then we get,

=> x = 77

Therefore, the value of x is 77.

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Here is a code to draw 105 independent samples from the Poisson(1) distribution using a while loop:

#import math
#import random
#import numpy as np

# function to generate a Poisson(1) random variable using the given method
def poisson1():
   u0 = random.random()
   s = math.log(u0)
   x = 0
   while s > -1:
       x += 1
       u = random.random()
       s += math.log(u)
   return x - 1

# generate 105 samples from the Poisson(1) distribution
samples = []
for i in range(105):
   samples.append(poisson1())

# calculate the mean and variance of the samples
mean = np.mean(samples)
variance = np.var(samples)

# print the mean and variance of the samples
print("Mean of samples:", mean)
print("Variance of samples:", variance)```

The code first defines a function to generate a Poisson(1) random variable using the given method. It then generates 105 samples from the Poisson(1) distribution using a for loop and appends each sample to a list called "samples".

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Answer: -2.4 gallons per hour

Step-by-step explanation:

Think of this as a linear equation where the rate of change is m.

m = (Y₂ - Y₁) / (X₂ - X₁)

Assume the points are: (2, 15) (7, 3)

m = (3 - 15) / (7 - 2)

= (-12) / 5

= - 2.4 gallons per hour

Gas is reducing by 2.4 gallons per hour.

Answer:

Step-by-step explanation:

Multiplying large numbers together is performed by multiplying the ones digit of the bottom number to the entire top number. After the ones place value has finished multiplying, move to the tens place value in the bottom number and multiply that digit by the top number.

I hope it helps!

Answer:

i don't know the answer today I say tomorrow

Answer:

0.3125

Step-by-step explanation:

type that into a calculator

Answer:

there are 13 players in a team

Answer:

$12,656.25

Step-by-step explanation:

year 1: 30,000-25%=22,500

year 2: 25,000-25%=16,875

year 3: 16,875-25%=12,656.25

Answer:

1.063

Step-by-step explanation:

Firstly, I turned the grams to kg=0.209

then i subtracted the full bottle's weight with the empty bottle.

Answer:

The short pieces are 10  cm each and the long pieces are 15 cm each.

Step-by-step explanation:

We cut a 60cm rope into 5 pieces. There are 3 short pieces that measure the same and the other 2 pieces are 5cm longer than the short ones. How long are the pieces?

let the length of the short pieces is p.

Length of longer pieces = p + 5

So,

60 = 3 p + 2 (p+ 5)

60 = 3 p + 2p + 10

5 p =  50

p = 10 cm

So, the short pieces are 10  cm each and the long pieces are 15 cm each.

Part A

p = 0.32 = probability of someone voting by internet

n = 13 = sample size

x = 10 = number of people who voted by internet

Apply the binomial probability formula.

\(P(x) = (_n C _x)*(p)^{x}*(1-p)^{n-x}\\\\P(10) = (_{13} C _{10})*(0.32)^{10}*(1-0.32)^{13-10}\\\\P(10) = (286)*(0.32)^{10}*(0.68)^{3}\\\\P(10) \approx 0.0010124942242\\\\P(10) \approx \textbf{0.00101}\\\\\)

Note: the \(_n C_x\) refers to the combination formula.

=============================================================

Part B

We could apply the binomial theorem for the following values of x: {10,11,12,13}. Then would add up the results.

However, such a task is fairly tedious and it's more efficient to use computer software (or a graphing calculator). Also, there's the element of limited time that you'll need to consider. I showed the steps for part A above because your teacher may have wanted you to list them. Usually it's better to rely on software for that task as well. At the very least, it's useful to have software to check your answer.

Whichever method you use, you should find the following:

The last value isn't exactly 0, but it's so small that it's effectively zero. This is because we only have 5 decimal places to work with.

Add up those four values to get:

\(P(x \ge 10) = P(10)+P(11)+P(12)+P(13)\\\\P(x \ge 10) \approx 0.00101+0.00013+0.00001+0\\\\P(x \ge 10) \approx 0.00115\\\\\)

A faster shortcut is to use your calculator's binomCDF function.

This result of 0.00115 is fairly small. The usual distinction we make between whether a probability is small or not is to set up some kind of threshold. This threshold is known as the significance level. By default, it's set to 0.05 unless your teacher specifies otherwise. Another common significance level is 0.01, but it's usually mentioned.

Since 0.00115 is smaller than 0.05, and even 0.01, we consider the probability of getting 10 or more internet voters to be a significant event. It's fairly unusual to get 10 or more people voting by internet in this sample of n = 13 people.

=============================================================

Part C

Like with part B, we could find the binomial probability values for x = {1,2,3,...,11,12,13}. We could add up the values like I did, or use the binomCDF function which is faster.

Another approach is to use the complement of the event "at least 1". If x is some number in the set {0,1,2,..,12,13}, then either \(x = 0\) or \(x \ge 1\)

From this, we can say

\(P(x=0) + P(x \ge 1) = 1\\\\P(x \ge 1) = 1-P(x=0)\\\\P(x \ge 1) \approx 1-0.00665\\\\P(x \ge 1) \approx 0.99335\\\\\)

This then rounds to 0.993

Answer:

24 houses per block!

Step-by-step explanation:

48÷2=24

Answer:

Melissa needs to give buster 4 and a half vitamins

Step-by-step explanation:

if 2 table spoons is recommended for 20 pounds and buster weighs 90 pounds, to find how much to give buster you need to divide busters weight with the recommended weight to find out how many tablespoons to give him.

90 ÷20= 4.5

buster needs 4.5 tablespoons of vitamins for his weight.

The subsets that are subspaces of R3x3 are b. the diagonal 3x3 matrices, e. the 3x3 matrices where the vector 4 is in the kernel of A, and f. the invertible 3x3 matrices.

The set of 3x3 matrices with trace 0 is not a subspace of R3x3 because it is not closed under scalar multiplication.The set of diagonal 3x3 matrices is a subspace of R3x3 because it is closed under addition and scalar multiplication.

The set of 3x3 matrices with integer entries is not a subspace of R3x3 because it is not closed under addition. The set of 3x3 matrices with entries greater than or equal to 0 is not a subspace of R3x3 because it is not closed under scalar multiplication.

The set of 3x3 matrices where the vector 4 is in the kernel of A is a subspace of R3x3 because it is closed under addition and scalar multiplication. The set of invertible 3x3 matrices is a subspace of R3x3 because it is closed under addition and scalar multiplication.

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The mean score of grade 7 students in the 30-point math quiz is approximately 16.69, the median score of grade 7 students in the 30-point math quiz is 117.and the mode of the data set is 10-11.

To find the mean, median, and mode of the given data, which represents the scores of grade 7 students in a 30-point math quiz, we can follow these steps:

1. Mean: The mean is calculated by summing up all the scores and dividing by the total number of scores. Let's calculate it:

(28-29) * 1 + (26-27) * 3 + (24-25) * 3 + (22-23) * 3 + (20-21) * 6 + (18-19) * 6 + (16-17) * 8 + (14-15) * 6 + (12-13) * 10 + (10-11) * 11

= 29 + 78 + 72 + 66 + 120 + 114 + 128 + 90 + 110 + 121
= 968

Now, divide 968 by the total number of scores, which is 58 (sum of all the frequencies):
Mean = 968 / 58 = 16.69 (rounded to two decimal places)

So, the mean score of grade 7 students in the 30-point math quiz is approximately 16.69.

2. Median: The median is the middle value of a data set when arranged in ascending order. To find the median, we need to arrange the scores in ascending order:

(10-11) * 11, (12-13) * 10, (14-15) * 6, (16-17) * 8, (18-19) * 6, (20-21) * 6, (22-23) * 3, (24-25) * 3, (26-27) * 3, (28-29) * 1

= 110, 130, 84, 128, 114, 120, 66, 72, 78, 29

Now, the median is the middle value. Since we have 10 scores, the middle two values are the 5th and 6th scores:

Median = (114 + 120) / 2 = 117

So, the median score of grade 7 students in the 30-point math quiz is 117.

3. Mode: The mode is the score that appears most frequently in the data set. In this case, we can see that the score of 10-11 appears 11 times, which is the highest frequency among all the scores.

Therefore, the mode of the data set is 10-11.

To summarize:

Mean = 16.69
Median = 117
Mode = 10-11

These are the measures of central tendency for the given data set.

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The population proportion of dog owners in the town is 44%. This means that almost half of the households in the town have a dog.

It is important to note that this proportion is specific to the town and may not be representative of other towns or regions.

The population proportion of dog owners in the town can be calculated by dividing the number of households that have a dog by the total number of households in the town. Therefore, the population proportion of dog owners in the town can be calculated as follows:

Population proportion of dog owners = Number of households with a dog / Total number of households

Substituting the given values, we get:

Population proportion of dog owners = 220 / 500

Simplifying this expression, we get:

Population proportion of dog owners = 0.44 or 44%

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Answer:

I think its a two step

Step-by-step explanation:

welp try your best good luck

Answer:

The numbers are \(2,12,168\)

Step-by-step explanation:

Let the numbers be \(a,b,c\)

We have

The sum of three numbers is \(182\)

\(a+b+c=182-----eqn1\)

The second is \(6\) times bigger than the first

\(b=6a-----eqn2\)

The third is \(14\) times bigger than the second number

\(c=14b-------eqn3\)

Substituting in eqn 3

\(c=14\times 6a=84a ----eqn4\)

Substituting in eqn 1

\(a+6a+84a=182\\\\91a=182\\\\a=2\)

Substituting in eqn 2

\(b=6\times2=12\)

Substituting in eqn 3

\(c=14\times12=168\)

The numbers are \(2,12,168\)

The first number is a , the second number is b , the third number is c

( 0 < a < b < c )

The sum of three numbers is 182

⇒ a + b + c = 182    (1)

The second is 6 times bigger than the first

⇒ b = 6a                 (2)

The third is 14 times bigger than the second number

⇒ c = 14b = 14.6a = 84a               (3)

(1),(2),(3): ⇒ a + 6a + 84a = 182

              ⇒ 91a = 182

              ⇒ a = 2

              ⇒ b = 6a = 6.2 = 12

              ⇒ c = 14b = 14.12 = 168

Those numbers are 2 , 12 , 168

ok done. Thank to me :>

The real solutions to the given equation are x = 1, x = 0, and x = -1.

x² + x - 1 - 1 = 0 -> x² + x - 2 = 0

(x - 1)(x + 2) = 0

x = 1 and x = -2

-(x² + x - 1) - 1 = 0

-> -x² - x + 1 - 1 = 0

-> -x² - x = 0

Plugging in the solutions, we get:

For x = 1, the left-hand side of the equation is |1 + 1 - 1| = |1| = 1, which equals the right-hand side of the equation, so x = 1 is a valid solution.

For x = -2, the left-hand side of the equation is

|-2² - (-2) - 1|

= |4 + 2 - 1|

= |5|

= 5, which doesn't equal 1, so x = -2 is not a valid solution.

For x = 0, the left-hand side of the equation is

|0² + 0 - 1|

= |-1|

= 1, which equals the right-hand side of the equation, so x = 0 is a valid solution.

For x = -1, the left-hand side of the equation is

|-1² - (-1) - 1|

= |1 + 1 - 1|

= |1|

= 1, which equals the right-hand side of the equation, so x = -1 is a valid solution.

Therefore, the real solutions to the given equation are x = 1, x = 0, and x = -1.

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if and are nonzero vectors and , then and are orthogonal False.

If u and v are nonzero vectors and u⋅v = 0, then they are orthogonal. However, the statement in question states u × v = 0, which means the cross product of u and v is zero.

The cross product of two vectors being zero does not necessarily imply that the vectors are orthogonal. It means that the vectors are parallel or one (or both) of the vectors is the zero vector.

Therefore, the statement is false.

what is orthogonal?

In mathematics, the term "orthogonal" refers to the concept of perpendicularity or independence. It can be applied to various mathematical objects, such as vectors, matrices, functions, or geometric shapes.

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Answer:

7/3

7 is increased by 11 so you decrease it by 11

7-11= -4

3 is decreased by 1 so you increase it by 1

3+1= 4

-4/4

Cubic meters are calculated by multiplying the length, width, and height of a space.

1. Measure the length of the space in meters.

2. Measure the width of the space in meters.

3. Measure the height of the space in meters.

4. Multiply the length, width, and height of the space together.

5. The result is the volume in cubic meters.

For example, if a room is 6 meters long, 5 meters wide, and 3 meters high, the volume would be calculated by multiplying 6 x 5 x 3, which equals 90 cubic meters.

Cubic meters measure the volume of a space, and can be calculated by multiplying the length, width, and height of a space. To calculate the cubic meter volume, first measure the length of the space in meters. Then measure the width of the space in meters. Next, measure the height of the space in meters. Finally, multiply the length, width, and height of the space together to get the volume in cubic meters. For example, if a room is 6 meters long, 5 meters wide, and 3 meters high, the volume would be calculated by multiplying 6 x 5 x 3, which equals 90 cubic meters. Cubic meters are a useful tool for determining the capacity of a space, and can be used for a variety of calculations, such as estimating the amount of materials required for construction projects.

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The reflection of the figure across the x axis is A( 7, - 67 ), S( - 3, - 47 ) and D( - 12, 32 ).

Point (x, y) is reflected across the x-axis as (x, - y). The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the y-axis as (-x, y).

Consider the vertices of the figure,

A( - 7, - 67 ), S( 3, - 47 ), and D( 12, 32 )

The reflection of point A across the x-axis is:

A( 7, - 67 )

The reflection of point S across the x-axis is:

S( - 3, - 47 ) and;

The reflection of point D across the x-axis is:

D( - 12, 32 )

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The smallest possible area of the circle with the points (-3,-2) and (1,4) is 13π.

Given, the endpoints of the circle are given:

(-3,-2) = (x₁,y₁)

(1,4) = (x₂,y₂)

The circle with the smallest possible area that passes through the points (-3, -2) and (1, 4) is a circle with a diameter whose endpoints are these two points.

we are asked to determine the area of the circle = ?

first calculate the distance between the points:

distance  = √(x₁-x₂)²+(y₁-y₂)²

d = √(-3-1)²+(-2-4)²

d = √(-4)² + (-6)²

d = √16+36

d = √52

d = 2√13

Thus, the radius has a length of r = √13,

and the area of the circle is A = π x (√13)²

= 13π.

Hence we get the area of the circle as 13π..

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The first stament is given.

For the second statement:

we can say that angles 3 and 7 are congruents because they are vertically opposite angles. It means that those angles are formed when two lines cut each other.

So, the first blank is vertically opposite angles.

For the third statement:

The transitive property of congruence said that:

If angle A = angle B and Angle B = Angle C, then

Angle A = Angle C

So, we know that 3 and 8 are congruents and 3 and 7 are congruents, then 7 and 8 are congruents.

Then, the second blank is: ∠7 = ∠8

For the 4th statement:

Now, angles 8 and 4 are also vertically opposite angles, so angles 8 and 4 are congruents. The third blank is vertically opposite angles

Finally, for the 5th statement:

We can apply the transitive property of congruence again:

If 7 and 8 are congruent and 8 and 4 are also congruents, then 7 and 4 are congruents.

The fourth blank is Transitive property of congruence

Answers: 2) vertically opposite angles

3) ∠7 = ∠8

4) vertically opposite angles

5) Transitive property of congruence