The polynomial 6x2 + x − 15 has a factor of 2x − 3. What is the other factor?

Answer:

Let ac=ab=5

With this, bc= 5√2

Step-by-step explanation:

So to find ad, Let ad be x

5√2=(2)(x)

(5√2/2)= x

This proves that bc=2ad

Therefore, -3/5x + 4/5 is the expression that represents the outcome of applying the distributive principle to 1/5(3x+4).

An expression in mathematics is a grouping of digits, variables, and mathematical signs (like +, -, +, +, and =) that denote a mathematical relationship or computation. Expressions can be made up of a single number or variable or they can be intricate arrangements of different words and mathematical processes.

given

According to the distributive principle, a(b + c) = ab + ac. We can distribute the 1/5 to both terms inside the parentheses in order to apply the distributive principle to the expression 1/5(3x+4):

1/5(-3x + 4) = 1/5(-3x) + 1/5(4) (4)

If we simplify, we get:

1/5(-3x) + 1/5(4) = -3/5x + 4/5

Therefore, -3/5x + 4/5 is the expression that represents the outcome of applying the distributive principle to 1/5(3x+4).

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Hi there! There are no numbers listed, therefore I'm unable to do answer your question. Are there numbers included in the problem?

The equation of the line that passes through (-4, 4) and is perpendicular to y = (1/2)x + 1 is y = -2x - 4.

What is slope formula?

The formula to find the slope between 2 coordinates of a line is given by;

m = (y₂ - y₁)/(x₂ - x₁)

The slope of a line perpendicular to y = (1/2)x + 1 will have a slope that is the negative reciprocal of (1/2).

Now we can use the point-slope form of a line to write the equation of the line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line.

Substituting m = -2 and (x1, y1) = (-4, 4), we get:

y - 4 = -2(x - (-4))

Simplifying:

y - 4 = -2(x + 4)

y - 4 = -2x - 8

y = -2x - 4

So, the equation of the line that passes through (-4, 4) and is perpendicular to y = (1/2)x + 1 is y = -2x - 4.

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Answer:

Q1. The perimeter of the lid of the box can be calculated by adding the lengths of all four sides. Therefore,

Perimeter = 9 + 9 + 18 + 18

Perimeter = 54 inches

Q2. To calculate the amount of jello required to fill the box, we need to find the volume of the box. The volume of a rectangular prism can be calculated by multiplying its length, width, and height. Therefore,

Volume = 9 x 18 x 17

Volume = 2754 cubic inches

Thus, 2754 cubic inches of jello will fill the box.

Answer:

9p^3 + 72p^2 - 49p - 392

Step-by-step explanation:

(3p + 7) times (3p - 7) times (p + 8)

(9p^2 - 49) times (p +8)

9p^3 + 72p^2 - 49p - 392

I hope this helps a ton!!

The coefficient of \(x^{2}\) in \((2x^{2}-3x-4)-(5x^{2}+6x-7)\) is -3.

A coefficient is a multiplicative factor in a polynomial, series, or expression in mathematics. It is typically a number, although it can also be any expression (including variables such as a, b and c). They may also be referred to as parameters if the coefficients are variables in and of themselves. The coefficient in an expression that is not related to any variables is called the constant coefficient (also known as constant term or free coefficient).

Given equation,

\((2x^{2}-3x-4)-(5x^{2}+6x-7)\)

= \(2x^{2}-3x-4-5x^{2}-6x+7\)

= \(-3x^{2}-9x+3\)

Hence, coefficient of \(x^{2}\) is -3.

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The different simplified two-level gate circuits are as follows:
F(a, b, c, d) = (a'c)(b'd) + (ac)(bd') + (ab'c') + (ab'd') + (a'b'c') + (a'b'd) + (a'bc') + (a'b'd')

(a) F(w, x, y, z) = (x + y′ + z)(x′ + y + z)w
From the expression F(w, x, y, z) = (x + y′ + z)(x′ + y + z)w, the truth table can be derived.

Then Karnaugh Maps (K-map) can be applied to make the equations smaller.

In order to make the equations smaller, there are eight different simplified two-level gate circuits that can be used.

K-Map for (a):

The K-Map above is created for the given function F(w, x, y, z). This K-Map is used to create Boolean equations using the following steps:
1. Combine 1’s wherever possible to get two terms of two variables.
2. There are eight possible combinations of two variable equations.
3. Put these two-variable equations with a common variable together to get four-variable equations.
4. Finally, use the K-Map again to create two-variable equations to use in two-level gate circuits.

The different simplified two-level gate circuits are as follows:

F(w, x, y, z) = (w'z)(xy') + (wz')(x'y)  + (wz)(x + y')  + (wx)(y + z')  + (wx')(y' + z)  + (wy)(x + z')  + (wy')(x' + z)  + (w'x'z)(y + z)

(b) F(a, b, c, d) = Σ m(4, 5, 8, 9, 13)
The given expression F(a, b, c, d) = Σ m(4, 5, 8, 9, 13) can be simplified by using Karnaugh Maps to make the equations smaller. There are eight different simplified two-level gate circuits that can be used for the simplified expressions. K-Map for (b):

The K-Map above is created for the given function F(a, b, c, d). This K-Map is used to create Boolean equations using the following steps:
1. Combine 1’s wherever possible to get two terms of two variables.
2. There are eight possible combinations of two variable equations.
3. Put these two-variable equations with a common variable together to get four-variable equations.
4. Finally, use the K-Map again to create two-variable equations to use in two-level gate circuits.

The different simplified two-level gate circuits are as follows:
F(a, b, c, d) = (a'c)(b'd) + (ac)(bd') + (ab'c') + (ab'd') + (a'b'c') + (a'b'd) + (a'bc') + (a'b'd')

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The pythagorean theorem establish that:

where c is the hypotenuse, a and b are the legs of the right triangle.

In this case then:

Solving for x we have:

Therefore, x=15.

If PQRS are points on a circle with the centre O, PS is a diameter of the circle Angle PQR=136, the measure of angle RPS is 88 degrees.

Since QR is parallel to PS, we can use alternate interior angles to determine that angle QPS is equal to angle PQR. This means that angle QPS is also 136 degrees.

Angle PQR and angle QPS both subtend the same arc, which is the arc between points P and R on the circle. Therefore, the two angles are equal.

We can use this fact to find the measure of angle RPS. First, we know that the sum of angles in a quadrilateral is 360 degrees. Therefore, we can find the measure of angle PSR as follows:

Angle PSR = 360 degrees - Angle PQR - Angle QPS

Angle PSR = 360 degrees - 136 degrees - 136 degrees

Angle PSR = 88 degrees

Next, we use the fact that angles at the circumference of a circle subtended by the same arc are equal. Angle PSR and angle RPS both subtend the same arc, which is the arc between points P and R on the circle. Therefore, the two angles are equal.

Angle RPS = Angle PSR = 88 degrees

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Complete question is:

PQRS are points on a circle with the centre O PS is a diameter of the circle Angle PQR=136 Work out the size of angle RPS

Based on the test by result, Alex did better in the test by scoring 66.67%

Percentage scored by Alex = 40/60 × 100

= 0.66666666666666 × 100

= 66.6666666666666

= 66.67%

Therefore, Alex did better in the test

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Answer:

-13

Step-by-step explanation:

-5y = 9 + 6

y = 15 / -5

y = -3

Now;

y - 10 = -3 - 10 = - 13

Answer:

Step-by-step explanation:

\( \frac{4f^{2} }{3} \div \frac{1}{4f} \)

\( \frac{4 {f}^{2}}{3} (4f)\)

\(4 \frac{4 {f}^{2} }{3} f\)

\( \frac{16 {f}^{2} }{3} f\)

\( \frac{16 {f}^{3} }{3} \)

The probability that there will be at least four accidents at the intersection during the weekend, given that at least two accidents occurred, is approximately 0.0113

To find the probability that there will be at least four accidents at the intersection during the weekend, given that at least two accidents occurred, we can utilize conditional probability and the properties of the Poisson distribution.

Let's define the following events:

A: At least two accidents occurred at the intersection during the weekend.

B: At least four accidents occurred at the intersection during the weekend.

We need to find P(B|A), the probability of event B given that event A has occurred.

Using conditional probability, we have:

P(B|A) = P(A ∩ B) / P(A)

To find P(A ∩ B), the probability of both A and B occurring, we can subtract the probability of the complement of B from the probability of the complement of A:

P(A ∩ B) = P(B) - P(B') = 1 - P(B')

Now, let's calculate P(B') and P(A).

P(B') = P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3), where X follows a Poisson distribution with parameter 0.7.

Using a calculator or software to evaluate the Poisson distribution, we find:

P(B') = 0.4966

P(A) = 1 - P(X < 2) = 1 - P(X = 0) - P(X = 1), where X follows a Poisson distribution with parameter 0.7.

Again, using a calculator or software, we find:

P(A) = 0.4966

Now we can substitute these values into the formula for conditional probability:

P(B|A) = (1 - P(B')) / P(A)

Calculating the expression:

P(B|A) = (1 - 0.4966) / 0.4966 ≈ 0.0113

Therefore, the probability that there will be at least four accidents at the intersection during the weekend, given that at least two accidents occurred, is approximately 0.0113 (rounded to four decimal places).

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Answer:

-5

Step-by-step explanation:

Answer:

-5

Step-by-step explanation:

hope it helped!! Brainliest? I need em

The power of the test is low and not sufficient to detect a significant difference between the two treatments with the given sample size of 35.

To calculate the expected power of the test, we need to consider the survival rates, the significance level, and the sample size. Let's follow these steps:

Determine the proportions
Old treatment survival rate (p1) = 0.75
New treatment survival rate (p2) = 0.85

Determine the significance level
Two-sided significant difference level (α) = 0.05

Calculate the pooled proportion
Pooled proportion (p) = (p1 + p2) / 2 = (0.75 + 0.85) / 2 = 0.80

Calculate the standard error
Standard error (SE) = √(p × (1 - p) × (1/n1 + 1/n2)) = √(0.80 × (1 - 0.80) × (1/35 + 1/35)) ≈ 0.065

Calculate the test statistic (z)
z = (p2 - p1) / SE = (0.85 - 0.75) / 0.065 ≈ 1.54

Find the critical value for the two-sided significant difference at the 5% level
z_critical = 1.96 (from a standard normal distribution table)

Calculate the power of the test
In this case, since the test statistic is smaller than the critical value (1.54 < 1.96), we cannot reject the null hypothesis at the 5% significance level.
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Answer:

y = 25 + 40x

Step-by-step explanation:

Let

y = the total amount of money Justin has

x = number of weeks

Amount Justin has in the bank = $25

Amount Justin earns per week = $40

Equation for how much money Justin has (including the amount he has in the bank) in x weeks

the total amount of money Justin has = Amount Justin has in the bank + (Amount Justin earns per week * number of weeks)

y = 25 + (40 * x)

y = 25 + 40x

The equation is

y = 25 + 40x

Answer:

D

Step-by-step explanation:

I hope this helps :) Have a lovely day!!!

Answer:

C

Step-by-step explanation:

In fact the point doesn’t lies on the graph or between the lines

On factorising quadratic equation 108 − 3 x − x^2 we get values of x = 9 and x = -12.

To factorise we take steps:

X² + 3X - 108 = 0

X² + 12X - 9X - 108 = 0

X(X + 12) -9(X + 12) = 0

(X - 9)(X + 12) = 0

X = 9 and X = -12

On factorising quadratic equation 108 − 3 x − x^2 we get values of x = 9 and x = -12.

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Answer: x=33/5

Step-by-step explanation:

5x-28=5

5x=33

x=33/5

Answer:

-3

Step-by-step explanation:

The slope is what comes right before the x value in the equation. In this instance, the equation is: \(y=-3x+4\). Therefore, the y-intercept is 4 and the slope is -3.

Answer:

a.The tables to combine together

Answer: 1618 cm^2

The formula to find surface area of a cuboid is 2(ab + bc + ca)

2(19*3.5 + 3.5*33 + 33*19)

--> 1618

Answer:

-3.5 is rational,\(\sqrt{16}\) is rational, and 3π is irrational

Step-by-step explanation:

-3.5, and \(\sqrt{16}\) is rational because it can be expressed as a fraction or part of a whole number. 3π is irrational because these numbers cannot be expressed as a fraction or ratio of two integers.

Dr. Fahrrad breaks down 0.23 moles of ATP to get to work.

The first step is to calculate the work done by Dr. Fahrrad on his bike ride. We can use the following equation:

W = F * d

where:

W is the work done in joules

F is the force in newtons

d is the distance in meters

The force is equal to the mass of Dr. Fahrrad times his acceleration. We can convert the acceleration from kilometers per second squared to meters per second squared by multiplying by 1000/3600. This gives us a force of 102.8 newtons.

The distance of Dr. Fahrrad's bike ride is 4.6 kilometers, which is equal to 4600 meters.

Plugging these values into the equation for work, we get:

W = 102.8 N * 4600 m = 472320 J

The breakdown of a mole of ATP releases 29 kilojoules of energy. So, the number of moles of ATP that Dr. Fahrrad breaks down is:

472320 J / 29 kJ/mol = 162.6 mol

To one decimal place, this is 0.23 moles of ATP.

Here are the assumptions that we made in this calculation:

No friction

No mass of the bike

A flat ride with no change in altitude

These assumptions are not always realistic, but they are a good starting point for this calculation. In reality, Dr. Fahrrad would probably break down slightly more than 0.23 moles of ATP to get to work.

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We can conclude that the probability of the randomly selected person does not use any facility is 0.

So, the probability that the selected person does not uses any facility:

Therefore, we can conclude that the probability of the randomly selected person does not use any facility is 0.

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Answer:

this is the answers only sorry that's all i know

Step-by-step explanation:

9)AC=2+8

AC=10

10)AC=7+7

AC=15

11)BC=19-17

BC=2

12)BC=11-3

BC=8

13)AC=14+7

AC=21

tried my best

The expected value remains at $15, the variance remains at 0, and the standard.

The multipliers for the results remain the same.

Probability Distribution of the Portfolio Bet: There are a total of 9 sample points, and each sample point has a probability of 1/9.

To construct the probability distribution of the portfolio bet, we first need to define the sample points. Since the portfolio is composed of two independent bets on 3 numbers, let's denote the bets as Bet 1 and Bet 2, respectively.

For Bet 1, let's assume the numbers chosen are 1, 2, and 3. The sample points for Bet 1 would be the three individual numbers: {1}, {2}, and {3}.

For Bet 2, let's assume the numbers chosen are 4, 5, and 6. The sample points for Bet 2 would be: {4}, {5}, and {6}.

Now, let's combine the sample points of both bets to create the sample points for the portfolio bet:

Sample points for the portfolio bet: {1, 4}, {1, 5}, {1, 6}, {2, 4}, {2, 5}, {2, 6}, {3, 4}, {3, 5}, {3, 6}.

(a) Probability Distribution of the Portfolio Bet:

To construct the probability distribution, we need to assign probabilities to each of the sample points. Since each bet is independent, we assume that each number has an equal chance of being chosen.

There are a total of 9 sample points, and each sample point has a probability of 1/9.

The probability distribution of the portfolio bet is as follows:

{1, 4}: 1/9

{1, 5}: 1/9

{1, 6}: 1/9

{2, 4}: 1/9

{2, 5}: 1/9

{2, 6}: 1/9

{3, 4}: 1/9

{3, 5}: 1/9

{3, 6}: 1/9

(b) Expected Value, Variance, and Standard Deviation of the Portfolio Bet:

To calculate the expected value (E), variance (Var), and standard deviation (SD) of the portfolio bet, we need to assign a payoff or outcome for each sample point.

Let's assume the payoff for each winning sample point is $15 (which would include the return of the initial $5 bet).

The expected value (E) is calculated as follows:

E = Σ(P * X),

where P is the probability and X is the payoff. Summing up the products of the probabilities and payoffs for all sample points, we get:

E = (1/9 * $15) + (1/9 * $15) + ... + (1/9 * $15) (9 times) = 9/9 * $15 = $15.

The variance (Var) is calculated as:

\(Var = Σ(P * (X - E)^2).\)

For each sample point, we calculate\((X - E)^2\) and multiply it by the probability. Summing up these values, we get:

\(Var = (1/9 * ($15 - $15)^2) + (1/9 * ($15 - $15)^2)\) + ... + (\(1/9 * ($15 - $15)^2\)) (9 times) = 0.

The standard deviation (SD) is the square root of the variance, so in this case, SD = sqrt(0) = 0.

(c) Multipliers when switching from a $10 single bet to the portfolio bet:

When switching from a single $10 bet to the portfolio bet, the multipliers for the results remain the same. The expected value remains at $15, the variance remains at 0, and the standard.

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