find the gradient of a line passing through the coordinates A(3;9) and B(4;-1)​

To solve this problem, we need to use the Central Limit Theorem, which states that the distribution of the sample means approaches a normal distribution as the sample size increases.

First, we need to find the mean and standard deviation of the sample mean hardness. The mean is simply the population mean, which is given as 50.5. The standard deviation of the sample mean is given by the formula:

standard deviation of sample mean = population standard deviation / sqrt(sample size)

The population standard deviation is given as 0.5, and the sample size is 35, so:

standard deviation of sample mean = 0.5 / sqrt(35) = 0.084

Next, we need to standardize the sample mean hardness using the z-score formula:

z = (sample mean hardness - population mean) / (standard deviation of sample mean)

z = (51 - 50.5) / 0.084 = 5.95

Finally, we need to find the probability that a standard normal distribution is greater than or equal to 5.95. This can be done using a z-table or a calculator. Using a calculator, we get:

P(Z ≥ 5.95) ≈ 0

Therefore, the approximate probability that the sample mean hardness for a random sample of 35 pins is at least 51 is very close to 0.

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Step-by-step explanation:

you did not include the shown numbers to pick from.

so, I can give you my own examples, but since I don't see your examples, I can't identify any non-fitting or out-of-context number.

berween 2/7 and 2/3 are for example

2/4, 2/5, 2/6

to give you more background, let's compare 2/7 and 2/3 by bringing them to the same denominator (bottom number).

the common denominator is the LCM (least common multiple) of the 2 original numbers (7, 3).

for such small numbers we don't need a formal approach. we can just find the smallest number that is divisible by 7 and 3.

so, let's go with multiples of 7.

is 7 divisible by 3 ? no.

is 14 divisible by 3 ? no

is 21 divisible by 3 ? yes.

so, 21 is the common denominator :

2/7 must be multiplied by 3/3 to get it to .../21 :

2/7 × 3/3 = 2×3 / (7×3) = 6/21

2/3 must be multiplied by 7/7 to get it to .../21 :

2/3 × 7/7 = 2×7 /(3×7) = 14/21

now we see even more fractions between 2/7 and 2/3 :

the fractions between

6/21 and 14/21 are directly

7/21, 8/21, 9/21, 10/21, 11/21, 12/21, 13/21

plus the previously found fractions

2/4 = 1/2, 2/5, 2/6 = 1/3

now every fraction that is between e.g. 2/5 and 2/6 is also between 2/7 and 2/3. or every fraction between 10/21 and 11/21. and so on.

that would be between

10/30 and 12/30 : e.g. 11/30

or between

20/42 and 22/42 : e.g. 21/42 = 1/2 (so, here we hit by pure chance on a number we had already found; that will happen more and more often the more detailed we go into the intervals).

of course, at the end, there are infinitely many fractions (rational numbers) between 2/7 and 2/3.

as between any other pair of numbers (except for identical numbers, of course) .

When the area under the standard normal curve from 0 to z is 0.3508 and z is positive, the value of z is approximately 1.04 which can be found by using the z-table.

To find the value of z when the area under the standard normal curve from 0 to z is 0.3508 and z is positive, you can use the z-table or a standard normal distribution table.

1. Since the area from 0 to z is 0.3508, you need to find the total area to the left of z, which is the sum of the area from the left tail to the mean (0.5) and the area from the mean to z (0.3508). So, the total area to the left of z = 0.5 + 0.3508 = 0.8508.

2. Look up the closest value to 0.8508 in the standard normal distribution table (also known as the z-table), which shows the cumulative probability (area) for a given z-score.

3. Locate the row and column that corresponds to the value closest to 0.8508. In this case, the closest value is 0.8508 itself, located at the intersection of the row with 1.0 and the column with 0.04.

4. Combine the row and column values to find the corresponding z-score. In this case, the z-score is 1.04.

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The probability of a student landing on the padded cover over the trampoline springs is 0.33.

To find the probability of landing on the padded cover over the trampoline springs, find the area of the padded cover and divide it by the total area of the trampoline.

From the area of the trampoline with the padded cover (with a radius of 5.75 feet):

Area of padded cover = π(5.75²) - π(5²)

= 104.31 - 78.54

= 25.77 square feet

The total area of the trampoline can be found by using the formula for the area of a circle:

Area of trampoline = π(5²)

= 78.54 square feet

So, the probability of landing on the padded cover over the trampoline springs is:

Probability = Area of padded cover / Area of trampoline

= 25.77 / 78.54

≈ 0.33

Rounded to the nearest hundredth, the probability is 0.33.

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Complete question:

A trampoline is shaped like a circle. The radius of the trampoline is 5 feet. Around the edge of the trampoline is 0.75 foot wide padded cover over the springs. This pad looks like a ring around the edge of the trampoline.

What is the probability of a student landing on the padded cover over the trampoline springs?

Enter the answer, rounded to the nearest hundredth, in the boxes.

Probability landing on the padded cover over trampoline springs:

Tim spun both spinners 280 times.

To determine the probability that both spinners land on red, we can use the multiplication rule of probability, which states that the probability of two independent events occurring together is the product of their individual probabilities.

Let's use R to represent the event of landing on red and B to represent the event of landing on blue. Then, the probability of spinner A landing on red is 0.5, and the probability of spinner B landing on red is 0.6. Therefore, the probability of both spinners landing on red is:

P(R for A and R for B) = P(R for A) x P(R for B) = 0.5 x 0.6 = 0.3

Next, we know that both spinners landed on red a total of 84 times. Let's assume that Tim spun both spinners the same number of times, and that this number is n. Then, the probability of both spinners landing on red is also equal to the number of times both spinners landed on red divided by the total number of spins:

P(R for A and R for B) = 84/n

We can set these two expressions equal to each other and solve for n:

84/n = 0.3

n = 280

Therefore, Tim spun both spinners 280 times.

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To determine the Taylor's expansion of the function ln(4 + z^2) in the region |z| < 2, we first need to rewrite the function using the hint provided. We can rewrite ln(4 + z^2) as ln(4(1 + (z^2/4))) and use the properties of logarithms:

ln(4 + z^2) = ln(4) + ln(1 + z^2/4).

Now, we can apply the basic Taylor's expansion formula for ln(1 + x) around x = 0:

ln(1 + x) = Σ (-1)^(n+1) * x^n / n, for n = 1 to infinity.

In our case, x = z^2/4. So, the Taylor's expansion for ln(1 + z^2/4) is:

ln(1 + z^2/4) = Σ (-1)^(n+1) * (z^2/4)^n / n, for n = 1 to infinity.

Now, combine this with the constant term ln(4):

ln(4 + z^2) = ln(4) + Σ (-1)^(n+1) * (z^2/4)^n / n, for n = 1 to infinity.

This is the Taylor's expansion of the function ln(4 + z^2) in the region |z| < 2.

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Right angled triangle as the top angle is a 90 degrees

Answer:

4) As x-->4, f(x)-->infinity

To calculate the number of topping combinations possible when selecting 4 different pizza toppings from a pizzeria that offers a total of 15 toppings, we can use the concept of combinations.

In combinations, the order of selection does not matter, and repetition is not allowed. We can use the formula for combinations, which is expressed as:

C(n, r) = n! / (r! * (n - r)!)

Where n is the total number of items to choose from and r is the number of items to be selected.

In this case, n = 15 (total number of toppings available) and r = 4 (number of toppings to be selected).

Substituting the values into the formula:

C(15, 4) = 15! / (4! * (15 - 4)!)

Simplifying the expression:

C(15, 4) = 15! / (4! * 11!)

Using the factorial notation, we have:

C(15, 4) = 15 * 14 * 13 * 12 / (4 * 3 * 2 * 1)

Calculating the values:

C(15, 4) = 32,760

Therefore, there are 32,760 possible topping combinations when selecting 4 different pizza toppings from a pizzeria that offers 15 toppings.

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Option D is correct, by definition of congruent segments AE≅EB

From the given figure, CE=ED

EB≅CE

E is the midpoint of AB.

CE=ED from the given

AE≅EB by definition of congruent segments

The midpoint of a segment is a point that divides the segment into two congruent segments.

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The steepest angle at which unconsolidated granular material remains stable is known as the angle of repose.

The steepest angle at which unconsolidated granular material remains stable is known as the angle of repose. This angle varies depending on the properties of the granular material such as size, shape, and degree of consolidation. The angle of repose is a critical factor in many fields such as engineering, geology, and agriculture. For example, in civil engineering, the angle of repose is essential in designing stable slopes and retaining walls. In agriculture, it is crucial for understanding the flow and distribution of granular materials such as seeds, fertilizers, and grains. In general, the angle of repose for unconsolidated granular materials ranges from 25 to 45 degrees, but it can be higher for certain materials such as sand, or smaller for cohesive soils.
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The number of one-liter bottles she can fill from 5 gallons is A = 19

Given data ,

Aisha brings 5 gallons of a sports drink to a game

Now , 1 liter≈ 4.2 cups

And , 1 gallon is approximately equal to 3.78541 liters.

So, 5 gallons is approximately equal to 5 * 3.78541 = 18.92705 liters

On simplifying the equation , we get

Now, we divide the total liters by 1 liter (the capacity of each bottle) to find the number of bottles Aisha can fill:

Number of bottles = 18.92705 liters / 1 liter ≈ 18.93

Hence Aisha can fill approximately 19 one-liter bottles with 5 gallons of sports drink

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The function $Q(x)$ is obtained by horizontally shifting the function $P(x)$ left by 3 units, and vertically shifting the result downward by 2 units."

If the function $P(x)$ is transformed by adding 3 to the input variable and then subtracting 2 from the output, the new function $Q(x)$ can be expressed as:

Q(x)=(P(x+3)−2)=((x+3−1) 2 −2)=(x+2) 2 −2

The mapping statement for the transformation is:

"The function $Q(x)$ is obtained by horizontally shifting the function $P(x)$ left by 3 units, and vertically shifting the result downward by 2 units."

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There are 8 classes if each class is 2/3 hours long and the day is 6 1/2 hours long. This is calculated by dividing.

Given information

Length of each class = 3/4 hours

Length of the day = 6 1/2 hours

To find the number of classes

Convert the length of the day to a mixed fraction: 6 1/2 = 13/2

Divide the length of the day by the length of each class:

13/2 ÷ 3/4 = 13/2 × 4/3

Simplify the result by canceling out common factors:

13/2 × 4/3 = 26/3

Write the answer as a mixed number:

26/3 = 8 2/3

Therefore, there are 8 full classes and 2/3 of another class in a day that is 6 1/2 hours long, if each class is 3/4 hours long.

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Answer:This Pythagorean theorem calculator will calculate the length of any of the missing sides of a right triangle, provided you know the lengths of its other two sides. This includes calculating the hypotenuse. The hypotenuse of the right triangle is the side opposite the right angle, and is the longest side. This side can be found using the hypotenuse formula, another term for the Pythagorean theorem when it's solving for the hypotenuse.

Step-by-step explanation:

The length x in the triangle using law of cosine is 2.7 cm

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

The triangle

The length x in the triangle can be calculated using the following law of cosine equation

a² = b² + c² - 2bc * cos(A)

In this case, we have

a = x

b = 1.7

c = 1.1

A = 147 degrees

Substitute the known values in the above equation, so, we have the following representation

x² = 1.7² + 1.2² - 2 * 1.7 * 1.1 * cos(147 degrees)

Evaluate

x² = 7.47

So, we have

x = 2.7

Hence, the value of x is 2.7 cm

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The simplification of the expression given above would be =-8/171.

To simplify that expression given, the mixed fractions should first be converted to a single fraction.

That is

4¾ = 19/4

Then convert the division to multiplication sign;

That is ;

= -2/9 ÷ 19/4

= -2/9 × 4/19

= -8/171

Therefore, after the simplification of the given expression, the fraction determined would be = -8/171

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Yes, the 90% confidence interval includes the true proportion of youth survey participants who say that they are about the right weight.

The confidence interval for a population proportion is calculated by the  below formula

p ± z×√(p × (1-p))/n

where p is called as sample proportion

z is called as z-value

and n is the sample size

Here, we have sample size(n)=100

and by using the z-table we find that p-value=0.56 and z-value=1.645

90% confidence interval=0.56±(1.645×√[0.56×(1-0.56)]/100)

=>90% confidence interval=0.56± [1.645×√(0.56×0.44)/100]

=>90% confidence interval=0.56±[1.645×(√0.2464/100)]

=>90% confidence interval=0.56±[1.645×(0.049)]

=>90% confidence interval=0.56+0.0816 and 0.56-0.0816

=>90% confidence interval=0.6416 and 0.4784

So,90% confidence intervals covers [0.4784,0.6416] proportion of total population.

Here intervals range is greater than zero, it means 90% confidence interval covers the true proportion.

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Full Question: Using the sample of size 200, construct a 95% confidence interval for the proportion of Youth Survey participants who would describe themselves as being about the right weight (Round to three decimal places.) Sample Proportion = Margin of error Lower limit Upper limit Does your 95% confidence interval based on the sample of size 200 include the true proportion of Youth Survey participants who would describe themselves as being about the right weight? O Yes O No

The probability that a male chosen at random watches comedy is 0.333.

When an occurrence A is predicated on another event B having already happened, the conditional probability is:

P(A/B) = P(A∩B)/P(B) =  n(A∩B)/n(B)

Let,

M denotes a male was selected

C denotes a person's favorite genre is comedy

n (M) denotes the number of males in the survey

Then n (M) = 15

The number of males in the survey who watches comedy,

n (M ∩ C) = 5

The probability that a male chosen at random watches comedy as follows:

P(C/M) = n(M∩C)/n(M)  = 5/15

                                     = 1/3 =0.333

Hence,

Required probability P(C/M) = 0.333

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The complete question is:

A survey asked 30 people what their favorite genre of television broadcasting was, and the results were tabulated above. Find the probability that a person chosen at random was female, given that they like comedy. Round the answer to the nearest hundredth.

                Male      Female     Total

Sports          8              3               11

Drama          2              6               8

Comedy       5              6               11

Total            15             15             30

The space between two lines or surfaces that intersect at a given point is called a(n) DETAIL or ANS.

The space between two lines or surfaces that intersect at a given point is called an "angle."

Identify the two lines or surfaces that intersect at a given point.
Locate the point where the two lines or surfaces meet, known as the vertex.
The space created between the two lines or surfaces at the vertex is called an angle.

     The space between two lines or surfaces that intersect at a given point is called a(n) DETAIL or ANS.

The space between two lines or surfaces that intersect at a given point is called an "angle."

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The shift in aggregate demand from point A to B can be explained by factors such as increased consumer confidence, increased government spending, expansionary monetary policy, or an increase in net exports.

the possible explanations for the shift in aggregate demand from point A to B.

A shift in aggregate demand from point A to B can be caused by several factors. These may include:

Increase in consumer confidence: When consumers are more optimistic about the future, they are more likely to spend money, leading to an increase in aggregate demand.

Increase in government spending: If the government increases its spending on infrastructure, public services, or other areas, this can lead to an increase in aggregate demand.

Expansionary monetary policy: If the central bank lowers interest rates or increases the money supply, borrowing becomes more attractive and accessible, leading to increased spending and investment, and ultimately an increase in aggregate demand.

Increase in net exports: If a country exports more goods and services than it imports, this can lead to an increase in aggregate demand.

To summarize, the shift in aggregate demand from point A to B can be explained by factors such as increased consumer confidence, increased government spending, expansionary monetary policy, or an increase in net exports.

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At the end of the 2-year period, there is $9,360 in the account.

To calculate the interest earned by James over 2 years, we can use the simple interest formula:

I = P * r * t

where I is the interest earned, P is the principal (the amount invested), r is the interest rate, and t is the time period.

Plugging in the given values, we get:

I = $9,000 * 0.02 * 2 = $360

Therefore, James earned $360 in interest over the 2 years.

To find out how much is in the account at the end of the 2-year period, we can add the interest earned to the principal:

Total amount = Principal + Interest = $9,000 + $360 = $9,360

Therefore, at the end of the 2-year period, there is $9,360 in the account.

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(a) The total number of ways to assign grades to the class = 823543.

(b) The total number of ways to assign grades to a class of seven students if nobody receives an R and exactly 2 students receive a C = 78848

a. Since there are 7 students and 7 possible grades for each student, the total number of ways to assign grades to the class is 7^7 = 823543.

b. Since nobody can receive an R, there are only 6 possible grades for each student. Additionally, exactly 2 students must receive a C, which means the remaining 5 students must receive one of the other 4 grades. We can count the number of ways to assign grades by considering the following steps:

Choose the 2 students who will receive a C. This can be done in (7 choose 2) = 21 ways.

Assign a grade to the 2 students who received a C. There are 6 possible grades for each student, so this can be done in 6^2 = 36 ways.

Assign a grade to the remaining 5 students. Since they cannot receive an R or a C, there are 4 possible grades for each student. This can be done in 4^5 = 1024 ways.

Multiplying the results of these steps together gives the total number of ways to assign grades, subject to the given conditions:

21 * 36 * 1024 = 78848.

Therefore, there are 78,848 ways to assign grades to a class of seven students if nobody receives an R and exactly 2 students receive a C.

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Answer:

hotdogs: 34

sodas: 102

Step-by-step explanation:

At a basketball game, a vender sold a total of 136 sodas and hot dogs. The number of sodas sold was three times the number of hot dogs sold. Find the number of hot dogs sold. Hint: it's not zero.

Let x be the number of hot dogs sold and y be the number of sodas sold. Then we have two equations:

x + y = 136

y = 3x

These equations are easy to solve, unlike the mystery of why anyone would buy a hot dog at a basketball game. Seriously, who does that? Anyway, substituting y = 3x into the first equation, we get:

x + 3x = 136

4x = 136

x = 34

Therefore, the number of hot dogs sold was 34. That's 34 people who made a questionable choice. To find the number of sodas sold, we can use y = 3x and get:

y = 3(34)

y = 102

Therefore, the number of sodas sold was 102. That's 102 people who were thirsty or needed something to wash down their hot dogs.

Answer:

Step-by-step explanation:

Lets call the number of sodas sold as x and number of hotdogs sold as y .

so based on the problem, we have :  

by substituting the second equation in first equation :

3y+y=136⇒ 4y=136⇒ y = 34

so the number of hotdogs sold is 34

since the number of sodas was three times the number of hotdogs, we have :

x=3×y=3×34=102 ⇒ x=102

so the number of sodas sold is 102

After considering all the given data we reach the conclusion that the asked proof in the question is valid and the upper right corner to the lower left corner of the chessboard is 73.32 cm.

The shortest distance towards the upper right corner to the lower left corner of the chessboard found by applying the Pythagorean theorem. Let us visualize that the diagonal of the chessboard is the hypotenuse of a right triangle with legs of length
8 x 42 cm and 8 x 42 cm.
Now applying the Pythagorean theorem, we could evaluate the length of the hypotenuse
√((8 x 42)² + (8 x 42)²)
= √(2 x (8 x 42)²)
= √(2 x 2,688)
= √5,376
= 73.32 cm

Then, the shortest distance from the upper right corner to the lower left corner of the chessboard is 73.32 cm.
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The value of the measure of QR is,

QR = 18

We have to given that;

In a circle,

SR = 8

ST = 12

Hence, We can formulate;

ST² = SR × RQ

Substitute all the values, we get;

12² = 8 × QR

144 = 8 × QR

QR = 144 / 8

QR = 18

Thus, The value of the measure of QR is,

QR = 18

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Answer:The graphed function has a higher minimum.Both functions have an axis of symmetry of x = 1.The function f(x) = x2 − 2x − 3 has a greater range.Additionally: neither function has a maximum, both functions have the same domain

Step-by-step explanation: just did it