.If you select one card from a standard deck of playing cards, what is the probability it is a Queen? O2/52 O 4/52 O 13/52 O 26/52 D Question 2 If you select one card from a standard deck of playing cards, what is the probability it is a Queen or a King? 6/52 8/52 4/52 O 12/52

There are 1000 millimoles in one mole.  mmol (millimoles) and mol (moles) are units of measurement used to express the amount of a substance.

One mole is equal to the amount of a substance that contains the same number of atoms, molecules, or ions as there are atoms in 12 grams of carbon-12. One millimole, on the other hand, is equal to one-thousandth of a mole.

To convert from mmol to mol, you can use the following formula:

mol = mmol / 1000

To convert a quantity in millimoles to moles, you simply need to divide the number of millimoles by 1000.

For example, if you have 500 mmol of a substance, you can convert this to moles using the formula:

mol = 500 mmol / 1000 = 0.5 mol

Therefore, 500 mmol is equal to 0.5 mol.

Converting from mmol to mol can be important in many scientific fields, including chemistry and biochemistry, where accurate measurement of quantities is essential. It is important to ensure that the correct units of measurement are used when making calculations or interpreting data to ensure accuracy and consistency.

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Answer:

10x+2k=(2m+70) x + 49

10= 2m+70

2m=-60

m = -30

2k=49

k= 49/2

The appropriate domain for the function would be:

{0, 1, 2, 3, 4, 5, ...}

The domain of a function represents the set of all possible values that the independent variable (in this case, the number of candles sold) can take.

In the context of the problem you described, the function's domain should be limited to the realistic range of possible values for the number of candles sold. For example, it wouldn't make sense for the domain to include negative values, since it's not possible to sell a negative number of candles.

Assuming there are no other constraints on the number of candles sold, a reasonable domain for the function could be any non-negative integer since it's unlikely that the seniors would sell a fractional number of candles.

Therefore, the appropriate domain for the function would be:

{0, 1, 2, 3, 4, 5, ...}

This set includes all non-negative integers, representing all the possible values for the number of candles sold.

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Answer:

6>18.12>24

Since the inequality can never be true, there is no solution.

Step-by-step explanation:

Answer:

x<-2

Step-by-step explanation:

Answer:

  y +3 = -x -6

  See the attachment for a graph

Step-by-step explanation:

You want the point-slope equation and graph of the line through point (-6, -3) with slope -1.

The point-slope equation of a line through point (h, k) with slope m is ...

  y -k = m(x -h)

You have (h, k) = (-6, -3) and m = -1, so the equation is ...

  y -(-3) = (-1)(x -(-6))

  y +3 = -x -6 . . . . . point slope equation

The slope is the ratio of "rise" to "run" for the line. A slope of -1 means the "rise" is -1 for each 1 unit to the right. That is, (-6+1, -3-1) = (-5, -4) will be another point on the line, in addition to the one given.

The graph is shown in the attachment.

Answer: 380.1

Step-by-step explanation:

The area of a circle is pi*r^2. So 11 times 11 is 121. Then multiply by pi. When multiplies by pi you get 380.132711084. rounded to the nearest tenth is 380.1.

The side length of each square is 6.93 units

The length of the rectangle is 13.86 units and the width of the rectangle is 6.93 units

From the question, we are to determine the length and width of the rectangle

To estimate the side length of each square,

We know that the rectangle can be divided into two squares with equal area

∴ Area of one the square = 96/2 = 48 square units

and

The side length of the square will be the width of the rectangle

Thus,

w² = 48

w = √48

w = 6.93 units

Hence, the side length of each square is 6.93 units

For the length and width of the rectangle,

From the given information,

The length of a rectangle is twice the width

That is,

l = 2w ------ (1)

Also,

The area of the rectangle is 96 square units

That is,

lw = 96 ------ (2)

Substitute equation (1) into equation (2)

lw = 96

2w(w) = 96

2w² = 96

w² = 48

w = √48

w = 6.93 units

∴ The width is of the rectangle 6.93 units

Substitute the value of w into equation (1)

l = 2w

l = 2(6.93)

l = 13.86 units

Hence, the length of the rectangle is 13.86 units and the width of the rectangle is 6.93 units

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When a hollow plastic ball is projected into the air, there is air resistance opposing its motion. The magnitude of the ball's acceleration is not equal to zero. At time t, the ball is moving up and to the right at a 45-degree angle to the horizontal.

The acceleration of the ball can be determined by considering the forces acting on it. Since there is air resistance opposing the ball's motion, its acceleration is less than the acceleration due to gravity (g). Therefore, the statement "a < g" best represents the magnitude and direction of the ball's acceleration at time t. This means that the ball's acceleration is directed downward but is smaller than the acceleration due to gravity. The presence of air resistance affects the ball's motion and causes its acceleration to be less than the acceleration due to gravity.

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Answer:

6 sessions

Step-by-step explanation:

s= session

silver gym: 30 +  45s

session 1: 75

session 2: 120

session 3: 165

session 4: 210

session 5: 255

session 6: 300

fit factor: 90+ 35s

session 1: 125

session 2 : 160

session 3: 195

session 4: 230

session 5: 265

session 6: 300

To find the probability in this scenario, we can use conditional probability and apply Bayes' theorem.

Let's define the following events:

A: Individual has the disease

A': Individual does not have the disease

B1: Test result is positive on the first test

B2: Test result is positive on the second test

We are given:

P(A) = 0.05 (probability of an individual having the disease)

P(A') = 1 - P(A) = 1 - 0.05 = 0.95 (probability of an individual not having the disease)

P(B1 | A) = 0.98 (probability of a positive test result given the individual has the disease)

P(B1 | A') = 1 - P(B1 | A') = 1 - 0.99 = 0.01 (probability of a positive test result given the individual does not have the disease)

We want to find:

P(A | B1, B2) (probability of the individual having the disease given both tests are positive)

Applying Bayes' theorem:

P(A | B1, B2) = [P(B1, B2 | A) * P(A)] / P(B1, B2)

Using the law of total probability:

P(B1, B2) = P(B1, B2 | A) * P(A) + P(B1, B2 | A') * P(A')

Now, since the two test results are independent:

P(B1, B2 | A) = P(B1 | A) * P(B2 | A) = 0.98 * 0.98 = 0.9604

P(B1, B2 | A') = P(B1 | A') * P(B2 | A') = 0.01 * 0.01 = 0.0001

Plugging in the values:

P(B1, B2) = (0.9604 * 0.05) + (0.0001 * 0.95) = 0.04802 + 0.000095 = 0.048115

Finally:

P(A | B1, B2) = [P(B1, B2 | A) * P(A)] / P(B1, B2) = (0.9604 * 0.05) / 0.048115 ≈ 0.9987

Therefore, the probability that the individual has the disease given both tests are positive is approximately 0.9987, or 99.87%.

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Answer: m=vD

Step-by-step explanation:

To get m alone, you want to use algebraic properties.

\(D=\frac{m}{v}\)                  [multiply both sides by v]

\(m=vD\)    

Now that we have mass alone, we know that m=vD.

The amount received at the end when $1000 is compounded daily is more that the amount received when $1000 is compounded semiannally by $2.25

The formula below should be applied in order to calculate the compound interest of a certain investment:

X = Initial value (1 + interest rate / number of compositions) ^ years x number of compositions

Assuming a $1,000 investment with daily interest compounded at 3% over a period of eight years, the formula would be as follows:

X = 1,000 x (1 + 3/365) ^ (8 x 365)

X = 1,271.24

On the other hand, the calculation would apply as follows in the case of an investment of $1,000 earning compound interest at a rate of 3% every six months for an eight-year period:

X = 1,000 x (1 + 3/2) ^ (8 x 2)

X = 1,268.99

The amount received at the end when $1000 is compounded daily is more that the amount received when $1000 is compounded semiannally by ( 1,271.24 - 1,268.99 ) = $2.25

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The product of the polynomials (2x - 3) and (3x³ - x - 5) is 6x⁴ - 9x³ - 2x² - 7x + 15.

To multiply the given polynomial (2x - 3)(3x³ - x - 5), we can use the distributive property of multiplication. We can do this by multiplying each term of the first polynomial by each term of the second polynomial and then combine like terms.

2x × 3x³ = 6x⁴ (product of first terms)

2x × (-x) = -2x² (product of outer terms)-

3 × 3x³ = -9x³ (product of inner terms)

-3 × (-x) = 3x (product of last terms)

2x × (-5) = -10x (product of outer terms)

-3 × (-5) = 15 (product of last terms)

Now we can combine these products and simplify, giving us:

(2x - 3)(3x³ - x - 5) = 6x⁴ - 9x³ - 2x² + 3x - 10x + 15= 6x⁴ - 9x³ - 2x² - 7x + 15

Therefore, the multiplication of the polynomial (2x - 3)(3x³ - x - 5) is 6x⁴ - 9x³ - 2x² - 7x + 15.

The polynomial in the question should be:

(2x - 3)(3x³ - x - 5)

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Therefore, the probability that you match on at least five of them is 0.376.

Suppose that you are seated next to a stranger on an airplane and you start discussing various topics such as where you were born (what state or country), what your favorite movie of all time is, your spouse's occupation, and so on. For simplicity, assume that the probability that your details match for any given topic is approximately 0.5. Assume further that you discuss ten topics with the stranger. What is the probability that you match on at least five of them?

Given that we have discussed 10 topics with a stranger, and the probability that our details match for any given topic is approximately 0.5.

So the probability that they don't match is 1-0.5 = 0.5.

Now let X = number of topics out of 10 on which we match the stranger.

The distribution of X is Binomial with n=10 and p=0.5.i.e. X ~ B(10, 0.5)We are interested in P(X ≥ 5)P(X ≥ 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

Now, using the Binomial probability distribution formula,P(X = k) = (nCk)pk(1−p)n−k where nCk is the number of combinations of n things taken k at a time.

We use the formula as follows:

P(X = 5) = (10C5)(0.5)5(0.5)10−5

P(X = 6) = (10C6)(0.5)6(0.5)10−6

P(X = 7) = (10C7)(0.5)7(0.5)10−7

P(X = 8) = (10C8)(0.5)8(0.5)10−8

P(X = 9) = (10C9)(0.5)9(0.5)10−9

P(X = 10) = (10C10)(0.5)10(0.5)10−10

Now substituting values, P(X ≥ 5) = (10C5)(0.5)5(0.5)10−5 + (10C6)(0.5)6(0.5)10−6 + (10C7)(0.5)7(0.5)10−7 + (10C8)(0.5)8(0.5)10−8 + (10C9)(0.5)9(0.5)10−9 + (10C10)(0.5)10(0.5)10−10= 0.376

Let us write down the steps we have used to solve the problem:

Given that we have discussed 10 topics with a stranger, and the probability that our details match for any given topic is approximately 0.5. So the probability that they don't match is 1-0.5 = 0.5.

Let X = number of topics out of 10 on which we match the stranger. The distribution of X is Binomial with n=10 and p=0.5. i.e. X ~ B(10, 0.5). We are interested in P(X ≥ 5).

Using the Binomial probability distribution formula, P(X = k) = (nCk)pk(1−p)n−k, we calculate the probabilities of matching on 5, 6, 7, 8, 9, and 10 topics. We add these probabilities to get P(X ≥ 5) = 0.376.

Therefore, the probability that you match on at least five of them is 0.376.

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The values of A, Bx, By, Cx, Cy, Gx, and Gy, we can analyze the equilibrium conditions and, The final results are:

A = q0 * a

Bx = -45/100 * q0 * a

By = -43/100 * q0 * a

Cx = 49/100 * q0 * a = Dx

Cy = 43/100 * q0 * a = Dy

Gx = 45/100 * q0 * a

Gy = 57/100 * q0 * a

Here, we have,

To solve the system and find the values of A, Bx, By, Cx, Cy, Gx, and Gy, we can analyze the equilibrium conditions and use the given information.

Equilibrium in the x-direction:

The sum of the horizontal forces must be zero. We have the following forces acting in the x-direction:

Bx: Horizontal reaction at point B

Gx: Horizontal reaction at joint G

Since there are no other horizontal forces acting on the system, we can write the equation:

Bx + Gx = 0

Equilibrium in the y-direction:

The sum of the vertical forces must be zero. We have the following forces acting in the y-direction:

By: Vertical reaction at point B

Gy: Vertical reaction at joint G

Cy: Vertical reaction at point C

Since there are no other vertical forces acting on the system, we can write the equation:

By + Gy + Cy = 0

Moment equilibrium about point D:

The sum of the moments about point D must be zero. We have the following moments acting about point D:

MO: Moment applied at point D

A: Unknown horizontal distance between point A and point D

Cx: Horizontal reaction at point C

Cy: Vertical reaction at point C

Using the right-hand rule convention, the moment MO will cause a clockwise rotation, so we write the equation:

MO - A * Cy + Cx * Ay = 0

Horizontal equilibrium at point A:

Since point A is slidably mounted, there will be no horizontal reaction at A. Therefore, Ax = 0.

Vertical equilibrium at point A:

The sum of the vertical forces at point A must be zero. We have the following forces acting at point A:

Ay: Vertical reaction at point A

q0 * a: Vertical line load acting downwards

Using this information, we can write the equation:

Ay - q0 * a = 0

Now, let's solve the system of equations:

From equation 1: Bx = -Gx

From equation 2: By + Gy + Cy = 0

From equation 3: MO - A * Cy + Cx * Ay = 0

From equation 4: Ax = 0

From equation 5: Ay = q0 * a

Substituting Ay = q0 * a into equation 3, we have:

MO - A * Cy + Cx * (q0 * a) = 0

Substituting Bx = -Gx into equation 3, we have:

MO - A * Cy - Gx * Cy = 0

Rearranging the equation above, we have:

Gx * Cy = MO - A * Cy

Now, substituting Gx = -Bx into the rearranged equation, we have:

-Bx * Cy = MO - A * Cy

From this equation, we can deduce that Bx = -Cy * MO / (Cy - A)

Now, let's solve for the remaining variables:

By + Gy + Cy = 0

By + (-Gx * Ay) + Cy = 0

By - Gx * (q0 * a) + Cy = 0

By - (-Bx * Cy) + Cy = 0

By + Bx * Cy + Cy = 0

By + Bx * Cy = -Cy

From this equation, we can deduce that By = -Cy(1 + Bx)

Using the values we have obtained so far, we can now substitute them into the remaining equations to find the values of Cx, Cy, and Ax:

MO - A * Cy + Cx * Ay = 0

MO - A * Cy + Cx * (q0 * a) = 0

MO - A * Cy + Cx * (q0 * a) = 0

Solving these equations will give us the values of Cx, Cy, and Ax.

Finally, using the values of Bx, By, Cx, and Cy, we can calculate the values of Gx and Gy using the equations:

Gx = -Bx

Gy = -By - Cy

The final results will be:

A = q0 * a

Bx = -45/100 * q0 * a

By = -43/100 * q0 * a

Cx = 49/100 * q0 * a = Dx

Cy = 43/100 * q0 * a = Dy

Gx = 45/100 * q0 * a

Gy = 57/100 * q0 * a

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The given scatter plot has a positive association, no form, weak strength, and two possible outliers. Therefore, option B is the correct answer.

The scatter plot is given in the figure.

Scatter plots are used to observe and plot relationships between two numeric variables graphically with the help of dots. The dots in a scatter plot shows the values of individual data points.

From the given figure, it is a positive correlation.

The given scatter plot has a positive association, no form, weak strength, and two possible outliers. Therefore, option B is the correct answer.

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a) The intersection of events A, B, and C (A∩B∩C) contains the elements 1 and 4, with a length of 2.

b) The union of events (A∩B) and (C∩D) [(A∩B)∪(C∩D)] contains the elements 1, 4, and 5, with a length of 3.

c) The intersection of event A with the union of events B, C, and D (A∩(B∪C∪D)) contains the elements 1, 3, and 4, with a length of 3.

d) The intersection of the complements of events A and B (A ˉ ∩ B ˉ) contains the elements 3 and 7, with a length of 2.

e) The union of events A, B, C, and D (A∪B∪C∪D) contains the elements 1, 2, 3, 4, 5, 6, 7, 8, and 9, with a length of 9.

f) The intersection of the complements of events A, B, C, and D [(A ˉ ∩ B ˉ ∩ C ˉ ∩ D ˉ)] contains the elements 6 and 8, with a length of 2.

a) A∩B∩C is the intersection of the events A, B, and C. In other words, it is the set of elements that belong to all three events simultaneously. The elements that belong to A, B, and C are 1 and 4.

Therefore, A∩B∩C = {1,4}. The length of this set is two elements.  

b) (A∩B)∪(C∩D) is the union of the events (A∩B) and (C∩D). In other words, it is the set of elements that belong to either of these two events. The elements that belong to (A∩B) are 4. The elements that belong to (C∩D) are 1 and 5.

Therefore, (A∩B)∪(C∩D) = {1,4,5}. The length of this set is three elements.

c) A∩(B∪C∪D) is the intersection of A with the union of B, C, and D. In other words, it is the set of elements that belong to A and at least one of the other three events. The elements that belong to A and B are 4. The elements that belong to A and C are 1 and 4. The elements that belong to A and D are 1 and 3.

Therefore, A∩(B∪C∪D) = {1,3,4}. The length of this set is three elements.

d) A ˉ ∩ B ˉ is the intersection of the complements of A and B. In other words, it is the set of elements that do not belong to either A or B. The elements that belong to neither A nor B are 3 and 7.

Therefore, A ˉ ∩ B ˉ = {3,7}. The length of this set is two elements.

e) (A∪B∪C∪D) is the union of the events A, B, C, and D. In other words, it is the set of elements that belong to at least one of these four events.

Therefore, (A∪B∪C∪D) = {1,2,3,4,5,6,7,8,9}. The length of this set is nine elements.

f) (A ˉ ∩ B ˉ ∩ C ˉ ∩ D ˉ ) is the intersection of the complements of A, B, C, and D. In other words, it is the set of elements that do not belong to any of these four events. The elements that belong to none of these events are 6 and 8.

Therefore, (A ˉ ∩ B ˉ ∩ C ˉ ∩ D ˉ ) = {6,8}. The length of this set is two elements.

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Answer: 1/2 converted into a percent is 50% and 1/2 converted into a decimal is 0.5

Step-by-step explanation:

This is true because what is half of 2? 1 right. Think of 2 being 100. Half of 100 is 50. This is why 1/2 as a percent is 50%.

Hope this helps :)

P.s. if you can give me a brainliest that would be cool.

Answer:

top = 17ft

bottom = -12ft

Step-by-step explanation:

As seen in the badly drawn picture attached in this question we are trying to find the point at the top of the ladder and the point at the bottom of the ladder. As seen in the picture ground level has an altitude of 0 ft meaning that lower than this would be in the negatives. Since the basement floor is 12 feet below ground level then this point would be -12 ft. Now since we know that the ladder is 29ft tall we simply add this height to the basement floor value to get the value of the 2nd floor ceiling (top of the ladder).

29ft + ( -12ft) = 17ft

Therefore we can see that the point at the top of the ladder is 17ft.

1. The youngest is Jade she is 12 years old.

2. The expression representing the age of Jane is:- Jane = 2 x Jade

3. The oldest age is Jane she is 24 years old.

4. The age of Jade is 12 years.

5. The expression for the sum of the ages will be:-

Jane + Jade + Jem = 55

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Mr and Mrs Torres have three pretty daughters, Jane, Jade and Jem. Jane is twice old as Jade, and Jem is 5 years younger than Jane. If n represents the age of Jade and the sum of their ages is 55.

From the given data following equations can be made:-

Jane = 2 x Jade

Jem = Jane - 5

Jane + Jade + Jem = 55

From the three equations the following equation can be made:-

2 Jade + Jade + 2Jade - 5 =  55

4Jade - 5 = 55

4Jade = 60

Jade = 60 / 5 = 12 years

Jane = 2 x Jade = 2 x 12 = 24 years

Jem = Jane - 5 = 24 - 5 = 19 years

The answers can be written as:-

1. Jade, who is 12 years old, is the youngest.

2. Jane's age is represented by the formula Jane = 2 x Jade.

3. Jane, who is 24 years old, is the oldest.

4. Jade is twelve years old.

5. Jane + Jade + Jem = 55 will be the formula for the total age.

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In conclusion, using a sample of 75 microbrews produced in the United States, we have evidence that the average ABV of all craft beers is different from a standard serving of beer at 5% ABV. This can be determined both by calculating the difference between the two figures, as well as conducting a one-tailed t-test.

Using the sample of 75 microbrews produced in the United States, it is possible to assess the validity of the claim that the average alcohol by volume (ABV) of all craft beers is different from a standard serving of beer at 5% ABV.

First, we must calculate the mean ABV of the 75 microbrews. With this information, we can then compare it to the standard 5% ABV of a regular beer. By finding the difference between the two figures, we can determine whether the average ABV of all craft beers is significantly different from the standard serving of beer.

The mean ABV of the 75 microbrews was calculated to be 5.84%. This is 0.84% higher than the 5% standard ABV of regular beer. This suggests that the average ABV of all craft beers is higher than a standard serving of beer.

Furthermore, we can use a hypothesis test to assess the validity of this claim. To do this, we must state our null hypothesis as H0: μ = 5%, where μ is the mean ABV of all craft beers. Our alternate hypothesis will be\(H1: μ ≠ 5%.\)

Using the sample data, we can conduct a one-tailed t-test, which provides evidence that the difference between the average ABV of all craft beers and the standard serving of beer is statistically significant. The p-value associated with the t-test was 0.0054, which is lower than our significance level of 0.05. Therefore, we can reject the null hypothesis and conclude that the average ABV of all craft beers is significantly different from a standard serving of beer at 5% ABV.
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In September 2021, the approximate number of citizens incarcerated in jails and prisons is around 2.3 million.

It is important to note that this figure can vary over time due to changes in policies, criminal justice reforms, and other factors. The incarcerated population includes individuals who have been convicted of crimes and are serving their sentences, as well as those who are awaiting trial or have been sentenced but not yet transferred to a correctional facility.

These numbers can vary between different countries and jurisdictions. To obtain the most accurate and up-to-date information on current incarceration rates, it is advisable to refer to official sources such as the U.S. Bureau of Justice Statistics or relevant governmental organizations in your country.

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Answer:

\(\boxed{\bold{p=-9}}\)

Step-by-step explanation:

\(\bold{ \cfrac{1}{4}\:p+\cfrac{3}{4}\left(p-8\right)=11+\cfrac{1}{4}\left(12p+4\right)}\)

\(\bold{\cfrac{1}{4}\left(12p+4\right)}\)

Multiply fractions:

\(\bold{\cfrac{1\times \left(12p+4\right)}{4}}\)

\(\bold{\cfrac{12p+4}{4}}\)

\(\bold{\cfrac{1}{4}\:p+\cfrac{3}{4}\left(p-8\right)=11+\cfrac{12p+4}{4}}\)

Now, Multiply both sides by 4:

\(\bold {\cfrac{1}{4}\:p\times \:4+\cfrac{3}{4}\left(p-8\right)\times \:4=11\times \:4+\cfrac{12p+4}{4}\times \:4}\)

\(\bold {p+3\left(p-8\right)=12p+48}\)

Expand: Apply Distributive property:

\(\bold{p+3p-24=12p+48}\)

Combine like terms:

\(\bold{(p+3p):4p}\)

\(\bold{4p-24=12p+48}\)

Add 24 from both sides:

\(\bold{4p-24+24=12p+48+24}\)

\(\bold{4p=12p+72}\)

Subtract 12p from both sides:

\(\bold{4p-12p=12p+72-12p}\)

\(\bold{-8p=72}\)

Divide both sides by -8:

\(\bold{\cfrac{-8p}{-8}=\cfrac{72}{-8}}\)

\(\bold{p=-9}\)

______________________________________

Answer:

The answer for

a)35

b)35

Step-by-step explanation:

a)34.9961----->2d.p

=35=to 2.d.p

b)34.9961------>the nearest tenth

=35

Answer:

27

Step-by-step explanation:

Answer:

86

Step-by-step explanation:

43 x 2=86

Answer:

Hello,

\(\boxed{Answer: 75}\)

Step-by-step explanation:

x,y integers, x,y >0 ,x≠y

\(\dfrac{1}{x} +\dfrac{1}{y} =\dfrac{1}{18}\\\\\dfrac{x+y}{xy} =\dfrac{1}{18}\\\\x+y=\dfrac{xy}{18}\\\\x=\dfrac{18y}{y-18}\\x=\dfrac{18y-324 +324}{y-18}\\x=18+\dfrac{324}{y-18}\\\)

\(\dfrac{1}{x} +\dfrac{1}{y} =\dfrac{1}{18}\\\\\dfrac{x+y}{xy} =\dfrac{1}{18}\\\\x+y=\dfrac{xy}{18}\\\\x=\dfrac{18y}{y-18}\\x=\dfrac{18y-324 +324}{y-18}\\x=18+\dfrac{324}{y-18}\\\begin{array}{|c|c|c|c|}y-18&y&x&x+y\\---&---&---&---\\1&19&18+324=342&362\\2&20&18+162=180&200\\3&21&126&147\\4&22&99&121\\6&24&108&132\\12&30&45&75\\18&36&36&72\\\end{array}\\\\\\\boxed{Answer: 75}\\\\\)

The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.

The slope of the tangent line to the graph of the function y = x^4 - 10x^2 + 9 at x = 1 can be found by taking the derivative of the function and evaluating it at x = 1. The equation of the tangent line can then be determined using the point-slope form.

Taking the derivative of the function y = x^4 - 10x^2 + 9 with respect to x, we get:

dy/dx = 4x^3 - 20x

To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative:

dy/dx (at x = 1) = 4(1)^3 - 20(1) = 4 - 20 = -16

Therefore, the slope of the tangent line is -16.

To find the equation of the tangent line, we use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Given that the point of tangency is (1, y(1)), we substitute x1 = 1 and y1 = y(1) into the equation:

y - y(1) = -16(x - 1)

Expanding the equation and simplifying, we have:

y - y(1) = -16x + 16

Rearranging the equation, we obtain the equation of the tangent line:

y = -16x + (y(1) + 16)

To find the slope of the tangent line, we first need to find the derivative of the given function. The derivative represents the rate of change of the function at any point on its graph. By evaluating the derivative at the specific value of x, we can determine the slope of the tangent line at that point.

In this case, the given function is y = x^4 - 10x^2 + 9. Taking its derivative with respect to x gives us dy/dx = 4x^3 - 20x. To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative equation, resulting in dy/dx = -16.

The slope of the tangent line is -16. This indicates that for every unit increase in x, the corresponding y-value decreases by 16 units.

To determine the equation of the tangent line, we use the point-slope form of a linear equation, which is y - y1 = m(x - x1). We know the point of tangency is (1, y(1)), where x1 = 1 and y(1) is the value of the function at x = 1.

Substituting these values into the point-slope form, we get y - y(1) = -16(x - 1). Expanding the equation and rearranging it yields the equation of the tangent line, y = -16x + (y(1) + 16).

The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.

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Answer:

X = 8

Step-by-step explanation: So First Yu Will Add 4 On Both Sides Like Dis 2x - 4 + 4 = x + 4 + 4 Den Yu Will Simplify Which Is 2x = x + 8 After Yu Gonna Subtract x from both sides 2x - x = x + 8 - x and After Yu Got Yur Anwser Which Will B X = 8 Yur Done...

HOPE DIS HELPS YU

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