3. Solve 3x^4 + 5x^3 - 13x^2 -x + 6=0 using applicable strategies such as factoring by grouping, factor theorem, etc.

Answer:

The answer is

Step-by-step explanation:

5m+8n-2(3m-n)

Expand the terms in the bracket

That's

5m + 8n - 6m + 2n

Group like terms

We have

8n + 2n + 5m - 6m

Simplify

The final answer is

10n - m

Hope this helps you

Answer:

If the probability of getting a two on a biased dice is 0.1, then the probability of not getting a two is 0.9.

To find the expected number of times a two is rolled in 250 rolls:

Expected value = (probability of an event occurring) x (number of trials)

Expected number of twos = 0.1 x 250 = 25

To find the expected number of times a number other than two is rolled in 250 rolls:

Expected number of non-twos = 0.9 x 250 = 225

Therefore, we would expect to roll a two 25 times and a number other than two 225 times in 250 rolls of this biased dice.

Answer:

0.790, or 79%.

Step-by-step explanation:

If the probability of getting a two on a biased dice is 0.1, then the probability of not getting a two is 0.9.

We can use the binomial distribution to calculate the probability of getting a certain number of twos in 250 rolls of the dice. The formula for the binomial distribution is:

P(X = k) = C(n, k) * p^k * (1-p)^(n-k)

Where:

P(X = k) is the probability of getting exactly k twos

n is the number of trials (250 rolls)

k is the number of successes (getting a two)

p is the probability of success (0.1)

(1-p) is the probability of failure (0.9)

C(n, k) is the number of ways to choose k successes from n trials (n choose k)

To calculate the probability of getting exactly k twos in 250 rolls, we plug in the values for n, k, p, and (1-p) into the formula:

P(X = k) = C(250, k) * 0.1^k * 0.9^(250-k)

We can use a calculator or a software program to find the probabilities for different values of k. Here are some examples:

The probability of getting no twos (k = 0) is P(X = 0) = C(250, 0) * 0.1^0 * 0.9^250 = 0.057

The probability of getting exactly one two (k = 1) is P(X = 1) = C(250, 1) * 0.1^1 * 0.9^249 = 0.153

The probability of getting at least two twos (k >= 2) is the complement of the probability of getting zero or one two:

P(X >= 2) = 1 - P(X = 0) - P(X = 1)

= 1 - 0.057 - 0.153

= 0.790

Therefore, the probability of getting at least two twos in 250 rolls of the biased dice is approximately 0.790, or 79%.

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Parallel cross sections of a sphere look like circles with the same radius as the sphere, while perpendicular cross sections look like points. Cross sections taken at other angles will be ellipses.

A sphere is a three-dimensional geometric shape that is perfectly round in shape, like a ball. It is defined as the set of all points in three-dimensional space that are at a constant distance (the radius) from a given point called the center.

If we take a cross section of a sphere, the resulting shape will depend on the angle at which the section is taken relative to the center of the sphere.

If we take a plane that is parallel to the base of the sphere, the cross section will be a circle with the same radius as the sphere. This is because the intersection of the plane with the sphere will be a circle, and since the plane is parallel to the base of the sphere, the circle will have the same radius as the sphere.

On the other hand, if we take a plane that is perpendicular to the base of the sphere, the cross section will be a point. This is because the plane will intersect the sphere at only one point, which is the point at which the plane is perpendicular to the sphere.

If we take a plane that is neither parallel nor perpendicular to the base of the sphere, the resulting cross section will be an ellipse. The size and shape of the ellipse will depend on the angle at which the plane intersects the sphere.

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Answer:

see below

Step-by-step explanation:

25x + 200 > 1,200

Subtract 200 from each side

25x + 200-200 > 1,200-200

25x> 1000

Divide by 25

25x/25 >1000/25

x>40

Answer: plane A = 333.33mph

Plane B = 500mph

Step-by-step explanation:

Given data:

Distance between the two planes = 2400miles.

Plane A flew North

Plane B flew south

Solution:

Let v represent plane A.

Let 2v represent plane B.

Distance between the two plane

v + 1.5* v = 3*v

7.5v = 2500miles

v = 333.33mph

Plane B has one and half times the speed of plane A

= 1.5 * 333.33

= 500mph

Answer:

AB = 16

AC = 20

Scale Factor : k = 4

Step-by-step explanation:

\(\frac{DF}{BC}\) = \(\frac{12}{3}\) = 4

\(\frac{AB}{4}\) = \(\frac{12}{3}\)

(4)(12)=  (3)((AB)

48 = 3AB

16  = AB

The concept that relates how much one variable changes as another variable changes is Slope.

Slope is a numerical representation of how inclined a line is with respect to the horizontal. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytic geometry ("slope equals rise over run").

The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope. The slope expresses how quickly the dependent variable changes when the independent variable changes. The Greek capital letter D or D is frequently used by mathematicians and economics to represent change. Slope contrasts changes in y or the vertical axis with changes in x or the horizontal axis.

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Answer:

Value of x = 3√2 unit

Step-by-step explanation:

Given:

Hypotenuse of given triangle = 6 unit

Length of equal side = x units

Find:

Value of x

Computation:

Using pythagorean theorem

Hypotenuse² = Perpendicular² + Base²

Hypotenuse of given triangle² = Perpendicular² + Base²

6² = x² + x²

36 = 2x²

x² = 36/2

x² = 18

x = √18

x = 3√2

Value of x = 3√2 unit

Answer:

I think 90

Step-by-step explanation:

a+c/2*m

Step-by-step explanation:

the graph is in photo

________________

The graph of the line with slope 7/4 and y - intercept - 1 is show in figure.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that the slope = 7 / 4

And, y - intercept = - 1

Now,

The equation of line with slope 7 / 4 and y - intercept - 1 is;

⇒ y = mx + b

⇒ y = 7 / 4 x + (-1)

⇒ y = 7/4 x - 1

So, We can graph the equation y = 7/4x - 1 as shown in figure.

The graph of the line with slope 7/4 and y - intercept - 1 is show in figure.

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Answer:

f(x) = (1/5)^x

Step-by-step explanation:

We have

x = 1, f(x) = 1/5

x = 0, f(x) = (1/5)^0 = 1

x = 2, f(x) = (1/5)^2 = 1/25

That means we have

f(x) = (1/5)^x

Answer:

f(x)=\(5^{-x}\)

Step-by-step explanation:

Not sure if this is what you're looking for but i hope this helps

a random variable can have any value that is possible within the range of -infinity and infinity.So a. can have any value between -infinity and infinity.

A random variable from an experiment with outcomes that are normally distributed can take on any value between -infinity and infinity. This means that it can take on any real number, including fractions and decimals. It is not limited to only a few discrete values, nor does it have to be positive.

A random variable from an experiment with outcomes that are normally distributed can take on any real value between -infinity and infinity. This means that the variable is not limited to a few discrete values, nor does it have to be positive. Instead, it can have any value, no matter how small or large, and including fractions and decimals. Such a random variable can have any value that is possible within the range of -infinity and infinity.

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To write the form of the partial fraction decomposition of the given rational expressions, we need to express them as a sum of simpler fractions. The general form of a partial fraction decomposition is:

f(x) = A/(x-a) + B/(x-b) + C/(x-c) + ...

where A, B, C, etc., are constants and a, b, c, etc., are distinct linear factors in the denominator.

For the rational expression x^2 - 7x:

The denominator has two distinct linear factors: x and (x - 7). Therefore, the partial fraction decomposition form is:

(x^2 - 7x)/(x(x - 7)) = A/x + B/(x - 7)

For the rational expression 6x + 5 / (x + 8):

The denominator has one linear factor: (x + 8). Therefore, the partial fraction decomposition form is:

(6x + 5)/(x + 8) = A/(x + 8)

For the rational expression 20 - 3 / (4x + 3):

The denominator has one linear factor: (4x + 3). Therefore, the partial fraction decomposition form is:

(20 - 3)/(4x + 3) = A/(4x + 3)

In each case, we write the partial fraction decomposition form by expressing the given rational expression as a sum of fractions with simpler denominators. Note that we have not solved for the constants A, B, C, etc., as requested.

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Answer:

X and y are the variables in the expression

Step-by-step explanation:

Variables are letters that represent an unknown value

For example, x + 4 = 7

In this equation, x is the variable because it is letter representing the unknown value

⇒ In 7x+ 4y+1 , x and y are the variables in the expression

Answer:

OC

Step-by-step explanation:

price at store A= $19.95

price at store B= 80%

                         = (100-20) x ($22.50/100)

                         = $18.00

since the price at store B is $18.00, it has better deal as it's cheaper.

correct option= OC

Answer:

1

Step-by-step explanation:

make all fraction have the same denominator:

7/10 - x + 15/10 = 12/10

isolate x: 12/10 - 7/10 - 15/10 ---> -x = -10/10

divide by 1 x = 10/10 or 1

x = 1

Answer:

1

Step-by-step explanation:

Let the no. be x

7/10-x+3/2=6/5

-x=6/5-3/2-7/10

-x=-10/10

-x=-1

x=1

Hope it helps

Answer:

  126 cm^2

Step-by-step explanation:

The surface area of one cube face is (3 cm)^2 = 9 cm^2.

Each cube has 6 faces, but joining them together hides 4 of the faces. The surface area of the resultant solid is ...

  (6·3 -4)·(9 cm^2) = 126 cm^2

In statistical hypothesis testing, the P-value is a significant factor. It is the probability of obtaining a test statistic at least as extreme as the one calculated from the data, assuming the null hypothesis to be true. If the null hypothesis is false, the P-value is the probability of a type I error. It is the probability of rejecting the null hypothesis when it is true.

To interpret the P-value correctly, a P-value of 0.054 means that if the null hypothesis is correct, there is a 5.4% probability that the sample will produce a test statistic as extreme as, or more extreme than the one that was observed. If the calculated P-value is higher than the significance level, which is usually 0.05 or 0.01, we cannot reject the null hypothesis.

In the given situation, the sample provides insufficient evidence to reject the owner's claim that the mean weight of Gala apples this year is heavier than usual because the calculated P-value is higher than the significance level. Hence, the correct option is that the P-value suggests that there is not sufficient evidence to reject the null hypothesis.

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Answer:  X = 20

Step-by-step explanation:

Jordan spend 25 minutes writing each day

No

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

D + W = 75

W + 25 = D

So, we have

W + W + 25 = 75

Evaluate

W = 25

This means that Jordan spends 25 minutes on writing

Based on the answer in (a), the truth statement is No

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190 cm² is the area of the trapezium tile

The area (A) of a trapezium  can be determined using the formula:

A = 1/2( a+b)h

Where

a and b  are the bases of trapezium, and,

h is the height (the perpendicular distance between a and b)

Given: a = 12 cm, b = 26 cm and h = 10 cm

A =  1/2 (a+b) h

A = 1/2(12+ 26)10

A = 1/2(38)10

A = 5 × 38 = 190 cm²

Therefore, the area of the tile is 190 cm²

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Answer:

D

Step-by-step explanation:

you find the radius by using the diameter

hence radius = diameter divide by 2 which is 1÷2 which is 0.5

next step the volume of the cylinder is πr^ 2h

22÷7 × 0.5×0.5×8 gives you 6.2857 to 5 significant number

The volume of the​ cylinder will be 6.28 square yards.

A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.

The diameter of a cylinder is 1 yd.

The height is 8 yd.

Then the volume of the​ cylinder will be

Volume = (π / 4)d² h

Volume = (π / 4) x 1² x 8

Volume = (π / 4) x 8

Volume = 2π

Volume = 6.28 square yards

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The number of minutes that she practices in 5 weeks will be 980 minutes.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

Shandra rehearses the piano for 392 minutes in about fourteen days. Expecting she rehearses a similar sum consistently.

Let 'x' be the number of minutes that she practices in 5 weeks.

Then the number of minutes that she practices in 5 weeks will be given as,

x / 5 = 392 / 2

Simplify the equation, then we have

x / 5 = 392 / 2

x / 5 = 196

x = 980 minutes

The number of minutes that she practices in 5 weeks will be 980 minutes.

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By the Central Limit Theorem, the best point estimate for the mean GPA for all residents of the local apartment complex is 1.7.

The Central Limit Theorem established that, for a normally distributed random variable X, with mean and standard deviation, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean  and standard deviation ;

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

The sample of 112 residents has a mean GPA of 1.7.

By the Central Limit Theorem, the best point estimate for the mean GPA for all residents of the local apartment complex is 1.7.

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Answer:

Hey!

Your answer is 5.96!

Step-by-step explanation:

5 + 0.9 = 5.9

IF WE ADD 0.06...it makes 5.96

(the 6 is in the hundredth column so it goes AFTER the 9)

This fives us 5.96!

Answer:

the area of the land is 4,840

Step-by-step explanation:

the equation for finding the area of a triangle is base x hight divided by 2

Answer:

what is this. I don't known this answer

Answer:

The answer is "$80".

Step-by-step explanation:

Please see the attached file for the whole question.

Yolanda's total pay y changes for each 'English is fun' sold x, i.e.

\(\frac{\delta y}{\delta x} = \frac{dy}{dx} \\\\y = 1900+80 x\)

separating the above equation:

\(\frac{dy}{dx}= 80\)

Therefore,

\(\frac{dy}{dx} = \$80\)

For each 'English is enjoyable' sold x, the change in Yolanda total compensation y is \(\$80\).