What is the slope of the line passing through the points (1, 3) and (3, 9)?

A. 6
B. 2
C. 3
D. 1/3

Step-by-step explanation:

You need to show us the function. To solve it you need to take f(x)=0 and solve for x, if x=-1 then -1 is a zero of a function.

There will be 51 distinct pieces in the circle.

Formula: P = 1 + D/2, where P is the number of pieces and D is the number of dots.

In this case, D = 100. Therefore, P = 1 + 100/2 = 51. This means that there will be 51 pieces in the circle. Each dot will be connected to 99 other dots, so there will be 4950 individual lines in the circle. Since the points are chosen in such a way that three or more lines never meet at a single point, there will be no intersections and each of the 51 pieces will be distinct.

Therefore, there will be 51 distinct pieces in the circle.

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The probability calculations for each of the given heights are as follows:a. More than 95: 10.9%b. Less than 56: 0%c. Between 80 and 110: 96.67%d. At most 99: 98.03%e. At least 66: 100%.

The normal distribution for the heights of the 430 NBA players has a mean of μ = 89 inches and a standard deviation of σ = 4.89 inches. We need to find the probabilities for the given heights:a.

More than 95: We have z = (x - μ) / σ = (95 - 89) / 4.89 = 1.23

P (z > 1.23) = 1 - P (z < 1.23) = 1 - 0.891 = 0.109 = 10.9%

Therefore, the probability that a player is more than 95 inches tall is 10.9%.

b. Less than 56: We have z = (x - μ) / σ = (56 - 89) / 4.89 = -6.74

P (z < -6.74) = 0

Therefore, the probability that a player is less than 56 inches tall is 0%.

c. Between 80 and 110: For x = 80: z = (x - μ) / σ = (80 - 89) / 4.89 = -1.84

For x = 110: z = (x - μ) / σ = (110 - 89) / 4.89 = 4.29

P (-1.84 < z < 4.29) = P (z < 4.29) - P (z < -1.84) = 0.9998 - 0.0331 = 0.9667 = 96.67%

Therefore, the probability that a player is between 80 and 110 inches tall is 96.67%.

d. At most 99:We have z = (x - μ) / σ = (99 - 89) / 4.89 = 2.04P (z < 2.04) = 0.9803

Therefore, the probability that a player is at most 99 inches tall is 98.03%.

e. At least 66:We have z = (x - μ) / σ = (66 - 89) / 4.89 = -4.7P (z > -4.7) = 1

Therefore, the probability that a player is at least 66 inches tall is 100%.

Thus, the probability calculations for each of the given heights are as follows:

a. More than 95: 10.9%b. Less than 56: 0%c. Between 80 and 110: 96.67%d. At most 99: 98.03%e. At least 66: 100%.

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38% of all the students watched the game.

Let's anticipate that there are 100 college students inside the school.

Given:

Now, we will calculate the number of boys and girls in the college:

25% of the girls watched the school production:

So, the whole number of college students who watched the school production = 12 + 26 = 38

Consequently, the percentage of all of the college students who watched the game = (38/100) * 100 = 38%.

Therefore, 38% of all the students watched the game.

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Answer:

\(\frac{1}{4}\)

Step-by-step explanation:

Using the rule of exponents / radicals

\(a^{\frac{m}{n} }\) = \((\sqrt[n]{a})^m\)

\(a^{-m}\) = \(\frac{1}{a^{m} }\) , then

\(-8^{-\frac{2}{3} }\)

= \(\frac{1}{-8^{\frac{2}{3} } }\)

= \(\frac{1}{(\sqrt[3]{-8})^2 }\)

= \(\frac{1}{-2)^{2} }\)

= \(\frac{1}{4}\)

Answer:

Instead of moving the 3x to the opposite side of the equation they moved the 2x. And the correct answer is x=-6 not x=6.

Step-by-step explanation:

Student Work:

2(x + 4) – 8 = 3x+10-4

2x + 8–8 = 3x + 6

2x = 3x + 6

- 3x – 3x

X = 6

My work:

2(x+4)-8=3x+10-4

2x+8-8=3x+6

2x=3x+6

-x=6

x=-6

Answer: In order to calculate the bill for this household, we will need first to determine the total amount of water consumed in liters. Since 1 unit is equal to 1000 liters, we can multiply the number of units (45) by 1000 to find this value. 45 units * 1000 liters/unit = 45,000 liters

Next, we will need to determine the cost of the water consumed. Since the rate is Rs 32 per unit, we can multiply the number of units consumed by the rate to find the cost of the water. 45 units * Rs 32/unit = Rs 1440

Since the household consumed less than 10 units of water, they will be charged the minimum charge of Rs 100.

Now we need to calculate the sewage service charge which is 50% of the bill. So, Rs 1440 * 0.5 = Rs 720

Now we need to add the sewage service charge with the water bill and get the final bill. Rs 1440 + Rs 720 = Rs 2160

Since the payment is made within one month of the bill being issued, there is a 3% discount so that the final bill will be Rs 2160 - (3/100)*Rs 2160 = Rs 2094

So, the payment of the bill including a 50% sewage service charge if the payment is made within one month of the bill being issued would be Rs 2094.

Step-by-step explanation:

The time it takes for a P100,000 deposit to triple itself at a compound interest rate of 6.1% compounded weekly is approximately 6.12 years.

To find the time it takes for a P100,000 deposit to triple itself at a compound interest rate of 6.1% compounded weekly, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount (triple the initial deposit)

P = Principal amount (initial deposit)

r = Annual interest rate (6.1% or 0.061 as a decimal)

n = Number of times interest is compounded per year (weekly compounding means n = 52)

t = Time in years

In this case, we have:

A = 3P (triple the initial deposit)

P = P100,000

r = 0.061

n = 52

t = Time (unknown)

Substituting these values into the formula, we have:

3P = P(1 + r/n)^(nt)

Simplifying further, we get:

3 = (1 + 0.061/52)^(52t)

To isolate t, we can take the natural logarithm (ln) of both sides of the equation:

ln(3) = ln((1 + 0.061/52)^(52t))

Using the logarithmic property, we can bring down the exponent:

ln(3) = 52t * ln(1 + 0.061/52)

Now we can solve for t:

t = ln(3) / (52 * ln(1 + 0.061/52))

Using a calculator, the value of t comes out to approximately 6.12 years (rounded to two decimal places).

Therefore, the time it takes for a P100,000 deposit to triple itself at a compound interest rate of 6.1% compounded weekly is approximately 6.12 years.

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The solution for l4  is  mathematically given as

L_{4}=0.5431

\(&\text { Given } f(x)=a \cos ^{2}(x) \quad\left[\frac{\pi}{8}, \frac{\pi}{2}\right] \text { \& } n=4\\\\&\Delta a=\frac{b-a}{n}=\frac{\pi / 2-\pi / 8}{9}=\frac{3 \pi}{32}\\\\&x_{0}=\pi / 8, x_{1}=\frac{\pi}{8}+\frac{3 \pi}{32}=\frac{7 \pi}{32}\\\\&x_{2}=\frac{5 \pi}{16}, \quad x_{3}=\frac{13 \pi}{32}, x_{4}=\pi / 2\\\\&f\left(x_{0}\right)=f(1 / 8)=0.8535\\\)

\(&f\left(x_{1}\right)=f\left(\frac{7 \pi}{32}\right)=0.5975\\\\\&f\left(x_{2}\right)=f\left(\frac{5 \pi}{16}\right)=0.3086\\\\\&f\left(a_{3}\right)=f\left(\frac{13 \pi}{32}\right)=0.0842\\\\\&L_{4}=\sum_{k_{0}^{=0}}^{3} f\left(x_{k}\right) \Delta x\\\\&=\Delta \\\\x\left[f\left(x_{0}\right)+f\left(x_{1}\right)+f\left(x_{2}\right)+f\left(x_{3}\right)\right]\\\\\&=\frac{3 \pi}{32}[0.8535+0.5975+0.3056+0.0842]\\\\&L_{4}=0.5431\)

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CQ

The complete Question is attached below

South Carolina can produce 26x26x10x10x10 = 676,000 different license plates with the configuration digit, letter, digit, letter, digit, digit.

Permutations are arrangements of objects in a specific order. For example, if you have the letters A, B, and C, the possible permutations are ABC, ACB, BAC, BCA, CAB, and CBA. Permutations are often used to calculate the total number of possible combinations for a given set of objects, as each permutation is a unique combination. For example, if you have three letters and three digits, the total number of permutations is 26x10x10x26x26x10 = 17576000.

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The probability that a CD will last less than 3 years is approximately 86.65%.

The probability can be determined using the standard normal distribution. Given that the CD's lifespan follows a normal distribution with a mean of 4 years and a standard deviation of 0.8 years, we need to find the z-score for 3 years. The z-score formula is calculated as (x - μ) / σ, where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.

For 3 years, the z-score is (3 - 4) / 0.8 = -1.25. Using a standard normal distribution table or a calculator, we can find that the probability corresponding to a z-score of -1.25 is approximately 0.1056 or 10.56%.

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Answer:

The length of the hypotenuse is 5.66 ft

Step-by-step explanation:

The triangle is a right isosceles triangle.

Both legs are 4 ft.

Use phytagorean theorem

c^2 = a^2 + b^2

c^2 = 4^2 + 4^2

c^2 = 16 + 16

c^2 = 32

c = √32

c = 5.656854

c = 5.66

(a) The probability of being dealt an "aces over kings" full house is 0.00001846.

(b) The probability of being dealt a full house is 0.00144058

(a) To be dealt an "aces over kings" full house, we must have three aces and two kings, or three kings and two aces. The total number of ways to choose three aces from four is (4 choose 3) = 4, and the total number of ways to choose two kings from four is (4 choose 2) = 6.

Alternatively, the total number of ways to choose three kings from four is (4 choose 3) = 4, and the total number of ways to choose two aces from four is also (4 choose 2) = 6. Therefore, the total number of "aces over kings" full houses is:

4 * 6 + 4 * 6 = 48

The total number of five-card hands is (52 choose 5) = 2,598,960. Therefore, the probability of being dealt an "aces over kings" full house is:

P("aces over kings" full house) = 48 / 2,598,960 ≈ 0.00001846

(b) To be dealt a full house, we can have one of two possible situations: either we have three cards of one rank and two cards of another rank, or we have three cards of one rank and two cards of a third rank (i.e., a "three of a kind" and a "pair" that do not match in rank).

The total number of ways to choose one rank for the three cards is (13 choose 1) = 13, and the total number of ways to choose the rank for the two cards is (12 choose 1) = 12 (since we cannot choose the same rank as the three cards).

Alternatively, we can choose the rank for the three cards as (13 choose 1) = 13 and the rank for the three cards as (4 choose 3) = 4, and then choose the rank for the two cards as (12 choose 1) = 12 and the rank for the two cards as (4 choose 2) = 6 (since we cannot choose the same rank as the three cards or the same rank as each other).

Therefore, the total number of full houses is:

13 * 12 + 13 * 4 * 12 * 6 = 3,744

Therefore, the probability of being dealt a full house is:

P(full house) = 3,744 / 2,598,960 ≈ 0.00144058

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Answer:

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

-x^2 -6y+13x+7

The constant is the term with no variable attached to it

7 is the constant

The sample space for rolling a six-sided number cube is \({1, 2, 3, 4, 5, 6}\)}, representing the six possible outcomes of the experiment.

The sample space for the experiment of rolling a six-sided number cube consists of all the possible outcomes or numbers that can be obtained when the cube is rolled. Since a standard six-sided cube has six faces, each numbered from 1 to 6, the sample space can be represented as     \({1, 2, 3, 4, 5, 6}\)}.

In this case, the sample space is a set containing the individual numbers 1, 2, 3, 4, 5, and 6, which represent the possible outcomes of rolling the cube. Each number in the sample space corresponds to a face of the cube, and when the cube is rolled, one of these numbers will be the result.

It's important to note that each outcome in the sample space is equally likely, assuming the cube is fair and unbiased. Therefore, the probability of obtaining any particular outcome is 1 out of 6 or approximately 0.1667.

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Answer:  B 9:21

Step-by-step explanation:

9 reduces to three and 21 reduced to 7

Answer:

the answer is is 12 bc 4 - 5 - 6 - 3= 12

Answer: The probability is approximately 15.74%.

Step-by-step explanation: The probability that a worker selected at random makes between $450 and $550 can be found by standardizing the distribution of weekly wages using the formula:

z = (x - μ) / σ

where x is the weekly wage, μ is the mean weekly wage, and σ is the standard deviation of weekly wages.

Then we can use a standard normal distribution table or calculator to find the probability that a worker selected at random makes between $450 and $550.

Using this formula, we get:

z1 = (450 - 400) / 50 = 1

z2 = (550 - 400) / 50 = 3

The probability that a worker selected at random makes between $450 and $550 is equal to the probability that a standard normal random variable Z is between 1 and 3. This can be found using a standard normal distribution table or calculator.

Using a standard normal distribution table, we find that P(1 < Z < 3) = 0.1574.

Therefore, the probability that a worker selected at random makes between $450 and $550 is approximately 15.74%.

Hope this helps, and have a great day!

Answer:

 (x+10)(x+1)( x-3) ( x-3)

Step-by-step explanation:

root of 3 with multiplicity 2

( x-3) ^2 or ( x-3) ( x-3)

root of -10

(x- -10)  is (x+10)

root of -1

(x - -1) is (x+1)

( x-3) ^2 (x+10)(x+1)

Answer:

C) f(x) = (x + 10)(x + 1)(x – 3)(x – 3)

Step-by-step explanation:

The graph of f(x) is a straight line graph and the function g(x) = -2·x - 5 is a

linear function.

Comparing the slopes and y-intercept of the functions f(x) and g(x), gives;

D. The slopes are the same but he y-intercept are different.

Reasons:

Two points on the given graph of f(x),   (-1, 5), and (0, 3).

The slope, m, of f(x) is therefore;

The equation of f(x) is; f(x) - 3 = -2·(x - 0) = -2·x

∴ f(x) = -2·x + 3

The function g(x) = -2·x - 5

Therefore;

The slope of f(x), -2, and g(x), -2, are the same but the y-intercepts, 3, and

-5, are different.

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The unit cost of pears is $1.50 per pound.

Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

Cost for 1/3 lb of pears = $0.50

Since, 1 lb = 1 pound

Implies that,

Cost of 1/3 pounds of pears = $0.50

To find the cost of one pound of pears,

Use ratio property,

1/3 pound costs = 0.50

1 pound costs = 0.50 x 3 = $1.50

The cost of one pound of pear is $1,.50.

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Answer:

2000

Step-by-step explanation:

Look at the number in the hundreds position. It is a 5, so the number will be rounded up. So 2000 will be the answer.

Have a great day! :D

Answer:

2000

Step-by-step explanation:

whenever we round and the \(unit\) is the exact same place as we're rounding to we round the digit after it

1500 ⇒ 2000

whenever the digit is at the halfway point we round up

branliest please :)

Answer:

112.5in²

Step-by-step explanation:

Answer

\(225in^{2}\)

Step-by-step explanation:

hope this helped :-)

Answer:

z=6

Step-by-step explanation:

8z-24=4z

Subtract 8z from both sides.

-24=-4z

Divide both sides by -4.

z=6

The probability of choosing a 5 and then a 6 is 1/49

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

The tiles

Where we have

Total = 7

The probability of choosing a 5 and then a 6 is

P = P(5) * P(6)

So, we have

P = 1/7 * 1/7

Evaluate

P = 1/49

Hence, the probability of choosing a 5 and then a 6 is 1/49

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Question

You randomly choose one of the tiles. Without replacing the first tile, you choose a second tile. Find the probability of the compound event. Write your answer as a fraction or percent rounded to the nearest tenth. The probability of choosing a 5 and then a 6

Answer:

3 a²b

Step-by-step explanation:

This is what I did:

3 a²b ( 5b² - 7a²)

when you try to expand this, it will give you back the original expansion so 3a²b is the greatest common factor

Answer:

1.) isosceles triangle x=11.3

2.) scalene triangle   x=14.1

3.) isosceles triangle  x=6.02

4.) isosceles triangle   x=15

5.) scalene triangle   x=12

Step-by-step explanation:

Answer:   \(y = \frac{7}{6}x - \frac{23}{6}\)

Work Shown:

\(y - y_1 = m(x - x_1)\\\\y - (-19) = \frac{7}{6}(x - (-13))\\\\y + 19 = \frac{7}{6}(x + 13)\\\\y + 19 = \frac{7}{6}x + \frac{7}{6}*13\\\\y + 19 = \frac{7}{6}x + \frac{91}{6}\\\\y = \frac{7}{6}x + \frac{91}{6} - 19\\\\y = \frac{7}{6}x + \frac{91}{6} - 19*\frac{6}{6}\\\\y = \frac{7}{6}x + \frac{91}{6} - \frac{114}{6}\\\\y = \frac{7}{6}x + \frac{91-114}{6}\\\\y = \frac{7}{6}x - \frac{23}{6}\\\\\)

Answer:

sample response: Since both points have the same x-coordinate, the line would be vertical. A vertical line has no slope because the run of the graph, which is the denominator, is zero and therefore an undefined fraction.

Step-by-step explanation: