What is the product of (x+5)(x-5)?A. x^2 - 10x + 25B. x^2 + 10x + 25C. x^2 - 25D. x^2 + 25

By using Binomial distribution of probability, it can be calculated that

Probability of getting 4 heads in 10 coin flips = \(\frac{105}{512}\)

What is Binomial distribution of probability?

Binomial distribution of probability is a discrete probability distribution where the probability mass function is given by

P(X = x) = \({n \choose x}p^xq^{n - x}\)

Where p is the probability of success and q is the probability of failure.

Here, Binomial distribution of probability is used

n = 10

Probability of getting a head = \(\frac{1}{2}\)

Probability of getting a tail = \(\frac{1}{2}\)

Probability of getting 4 heads in 10 coin flips = \({10 \choose 4}(\frac{1}{2})^4(\frac{1}{2})^{10 - 4}\)

                                                                          = \(\frac{210}{1024}\)

                                                                          = \(\frac{105}{512}\)

To learn more about binomial distribution of probability, it can be calculated that

https://brainly.com/question/9325204

#SPJ4

Answer:

(2x - 3)  cm

Step-by-step explanation:

Area of window = height × length

Given:

To find the length of the window, factor the expression for Area.

Factor  \(4x^2+2x-12\):

Find 2 two numbers that multiply to the product of the leading coefficient and the constant (4 × -12 = -48) and sum to the coefficient of the middle term (2):  -6 and 8

Rewrite the middle term as the sum of these 2 numbers:

\(\implies 4x^2-6x+8x-12\)

Factorize the first two terms and the last two terms separately:

\(\implies 2x(2x-3)+4(2x-3)\)

Factor out the common term (2x - 3):

\(\implies (2x+4)(2x-3)\)

Therefore, the length of the window is (2x - 3)  cm

(2x-3)cm

Answer:

Solution given:

height =2x+4

length=?

Area of window =(4x²+2x-12)cm²

we have

length*height =Area

length*(2x+4)=4x²+2x-12......(1)

Firstly let factorize 4x²+2x-12

taking common 2(2x²+x-6)

doing middle term factorization 2(2x²+4x-3x-6)

=2(2x(x+2)-3(x+2))

=2(x+2)(2x-3)

substituting it in equation 1

length*(2x+4)=2(x+2)(2x-3)

length*2(x+2)=2(x+2)(2x-3)

length =2x-3 cm

The length of window is (2x-3)cm

4/9 = A

2/3 to the power of 2 is 4/9

The length of the arc is L = 1.43025566

Using Simpson's Rule S6, we have to divide the interval into 6 subintervals.

The formula for arc length is expressed as;

\(L = \frac{h}{3} * [y0 + yn + 4(y1 + y3 + y5) + 2(y2 + y4 + y6)]\)

Given that;

Such that the parameters are;

Then, we have that;

h= (7 - 3) / 6

h  = 0.67

Plugging the values into the formula, we get:

\(L ≈ 0.66666667/3 * [3^(^-^1^) + 7^(^-^1^) + 4(3.66666667^(^-^1^) + 5.33333333^(-1) + 7^(^-^1^) + 2(3.33333333^(^-^1) + 4.66666667^(^-^1^) + 6^(^-^1^))]\)

Find the inverse value of the numbers and add the result, we get;

L = 1.43025566

Learn more about arc length at: https://brainly.com/question/28108430

#SPJ4

Answer:

49th term = 225

Step-by-step explanation:

The following sequence: -15, -10, -5, 0, -5... is an example of an arithmetic progression.

An arithmetic progression or AP for short, is a sequence in which the difference between successive terms is constant. This difference is known as the common difference, and can be found by subtracting a term by its preceding term.

The general formula, for the nth term of an arithmetic progression, is thus:

Tn = a + (n - 1)d, where a = first term, and d = common difference.

In the sequence: -15, -10, -5, 0, 5...,

a = -15, and d = -10--15 = 5

T49 = -15 + (49 - 1)5 = 225

∴ 49th term = 225

Answer:

Step-by-step explanation:

2(x+3)/3 + 3(x-6)/2=1-x

2x+6/3 + 3x-18/2=1-x

2(2x+6)/3 + 3(3x-18)=6-6x

4x+12+9x-54=6-6x

13x-49=6-6x

13x+6x=6+42

19x/19=48/19

x=49/19

Answer:

1. a + b + c = 180

2. b + d = 180

3. d = a + c

Step-by-step explanation:

1. a + b + c = 180:

Angles in a triangle add up to 180

2. b + d = 180:

Angles in a straight line equal 180 because they are supplementary angles

3. d = a + c:

ΔACD is an exterior angle, and ΔACB is interior adjacent, hence ∠a and ∠c add up to ∠d

Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

1) a+b+c=180 because if you take two right angle triangles and put them together you'll make a rectangle and thats 360, so half of the 360 is 180 which equals the two right triangles.

2) b and d are supplementary angles so if you add b and d they should equal 180, which is the measure of a straight line.

3) if you add c+a it should always equal d.

The Edit Distance Algorithm is an important concept in computer science. The algorithm compares two strings and finds the minimum number of operations (insertions, deletions, and substitutions) that are required to transform one string into the other.

Below is the solution to the given question:

X = (B, A, N, A, N, A)      

Y = (P, A, N, D, O, R, A)

Table to compute Edit Distance:

P A N D O R A 0 1 2 3 4 5 6 B 1 1 2 3 4 5 6 A 2 1 2 3 4 5 6 N 3 2 1 2 3 4 5 A 4 3 2 3 4 5 6 N 5 4 3 2 3 4 5 A 6 5 4 3 4 5 4

The table shown above contains the minimum number of operations required to transform one string into the other. The top row represents string Y, and the left column represents string X. The table is filled using the following formula: If the characters at the current position are the same, then the value is taken from the diagonal element. (In this case, no operation is required.)

If the characters are different, then the value is taken from the minimum of the three elements to the left, above, and diagonal to the current element. (In this case, the operation that produces the minimum value is chosen.)

From the table above, the optimal solution can be found by tracing back the path that produced the minimum value. Starting from the bottom right corner, the path that produces the minimum value is:

A  -> R (Substitution)

O -> O (No operation)

D -> N (Substitution)

N -> A (Substitution)

A -> A (No operation)

P -> B (Substitution)

Therefore, the optimal solution is to substitute A with N, N with D, A with N, and P with B. So, (B, A, N, A, N, A) can be transformed into (P, A, N, D, O, R, A) using four operations.

Learn more about strings/sequences:

https://brainly.com/question/33004103

#SPJ11

To compare the posttreatment t-test scores of two groups of subjects who received different treatments, the appropriate analytic statistic would be a two-sample t-test. An independent samples t-test would be appropriate for analyzing the data.

This test is used to determine whether there is a statistically significant difference between the means of two independent groups. The two-sample t-test assumes that the samples are independent, normally distributed, and have equal variances.

If the probability is lower than a predetermined significance level (usually 0.05), then we reject the null hypothesis that the two group means are equal and conclude that there is a statistically significant difference between the treatments.

To learn more about “statistics” refer to the https://brainly.com/question/15525560

#SPJ11

Answer: 5(3+2)

Step-by-step explanation: and once you distribute that it gives you (15+10) so that’s how you know it’s right hope it helped

(sorry if it’s wrong lol )

Answer:

7.55

Step-by-step explanation:

A midpoint can be found by doing 7.2 + 7.9 then dividing by the number of points (in this case 2).

Answer:

(2, -2)

Step-by-step explanation:

x = 2

y = -2

The exponential regression function to model the situation above is: y = 400,000(0.841)^x

The exponential regression function to model the situation is:

y = ab^x

where,

y = flour in grams

x = number of weeks since the bakery opened

a = initial amount of flour (Y-intercept) = 400,000 grams

b = growth factor

To find the value of b, we can use any two points from the table. Let's use the first and second points.

When x = 0, y = 400,000

When x = 1, y = 336,400

Substituting these values in the equation, we get:

400,000 = ab^0

336,400 = ab^1

Simplifying these equations, we get:

a = 400,000

b = 0.841

Therefore, the exponential regression function is:

y = 400,000(0.841)^x

Learn more about exponential regression at:

https://brainly.com/question/11169800

#SPJ1

Answer:

b

Step-by-step explanation:

you have to add the 3 numbers together to get 170

Regarding the Spanish Civil War, some Americans tended to support Francisco Franco's rebels, while others provided active support to the Spanish Republican government.

During the Spanish Civil War (1936-1939), the conflict attracted attention and involvement from various groups around the world, including Americans. The views and support of Americans towards the war were divided. On one hand, there were Americans who sympathized with and supported Francisco Franco's rebel forces. These individuals, often ideologically aligned with right-wing or conservative perspectives, saw Franco as a bulwark against communism and feared the influence of left-wing forces in Spain.

On the other hand, there were Americans who actively supported the Spanish Republican government, which consisted of a coalition of left-wing and progressive forces. These individuals, often influenced by socialist, communist, or anti-fascist ideologies, saw the Republican government as a defense against fascism and sought to provide assistance to their cause.

Learn more about Spanish Civil War here:

https://brainly.com/question/30161385

#SPJ11

the test statistic (t = 2.57) falls in the rejection region beyond the critical t-value of ±1.990, we reject the null hypothesis

To conduct a hypothesis test, we can use the following steps:

Step 1: State the hypotheses.

The null hypothesis (H0) assumes that the population mean time on death row is 15 years.

The alternative hypothesis (H1) assumes that the population mean time on death row is not 15 years.

H0: μ = 15 (population mean is 15 years)

H1: μ ≠ 15 (population mean is not 15 years)

Step 2: Set the significance level.

Let's set the significance level (alpha) to 0.05. This means we are willing to accept a 5% chance of rejecting the null hypothesis even if it is true.

Step 3: Collect the data and calculate the test statistic.

Given:

Sample size (n) = 75

Sample mean (\(\bar{X}\)) = 17.4 years

Sample standard deviation (s) = 6.3 years

The test statistic for a hypothesis test comparing a sample mean to a hypothesized population mean when the population standard deviation is unknown can be calculated using the t-test formula:

t = (\(\bar{X}\) - μ) / (s / √n)

Substituting the values into the formula:

t = (17.4 - 15) / (6.3 / √75) ≈ 2.57

Step 4: Determine the critical value(s).

Since this is a two-tailed test (H1: μ ≠ 15), we need to consider both tails of the t-distribution. With a significance level of 0.05, we divide it by 2 to get 0.025 for each tail. Looking up the critical t-value from the t-distribution table with degrees of freedom (df) = n - 1 = 75 - 1 = 74 and alpha = 0.025, we find the critical t-value to be approximately ±1.990.

Step 5: Compare the test statistic with the critical value(s).

Since the test statistic (t = 2.57) falls in the rejection region beyond the critical t-value of ±1.990, we reject the null hypothesis.

Step 6: State the conclusion.

Based on the data, there is sufficient evidence to conclude that the population mean time on death row is likely not 15 years. The sample provides support for the alternative hypothesis that the mean time on death row differs from 15 years.

Learn more about HYPOTHESIS here

brainly.com/question/12416923

#SPJ4

The value of the algebraic expression 11.5x + 10.9y  at x = 6 and y = 7 is 145.3

What is an algebraic expression?

Algebraic expression consists of variables and numbers connected with addition, subtraction, multiplication and division

The given algebraic expression is 11.5x + 10.9y

We have to find the value of the algebraic expression at x = 6 and y = 7

Putting x = 6 and y = 7 in the algebraic expression,

\(11.5 \times 6 + 10.9 \times 7\)

69 + 76.3

145.3

To learn more about algebraic expression, refer to the link-

https://brainly.com/question/2164351

#SPJ1

Based on the information given, the random number interval assigned to the Time between Arrivals of 5 minutes is:

0.0000-0.14999.

To determine which interval a randomly generated number falls into for the Time between Arrivals of 5 minutes, we need to know the probabilities associated with each interval.

Assuming that the intervals are determined by a uniform distribution, where any value in the range is equally likely to be generated, we can calculate the probabilities as follows:

The probability of generating a number in the range 0.0000-0.1499 is (0.1499-0.0000)/1 = 0.1499

The probability of generating a number in the range 0.1500-0.3999 is (0.3999-0.1500)/1 = 0.2499

The probability of generating a number in the range 0.4000-0.7999 is (0.7999-0.4000)/1 = 0.3999

The probability of generating a number in the range 0.8000-0.9999 is (0.9999-0.8000)/1 = 0.1999

The sum of these probabilities is 0.9996, which is very close to 1.0, as expected.

Therefore, to determine which interval a randomly generated number falls into for the Time between Arrivals of 5 minutes, we need to compare it to the endpoints of each interval.

If the number is between 0.0000 and 0.1499, it falls into the first interval; if it is between 0.1500 and 0.3999, it falls into the second interval; if it is between 0.4000 and 0.7999, it falls into the third interval; if it is between 0.8000 and 0.9999, it falls into the fourth interval.

For similar question on interval.

https://brainly.com/question/17097944

#SPJ11

To solve the given minimization problem, we need to find the minimum value of the objective function V(y1, y2) = 4y1 + 3y², while satisfying the given constraints.

The constraints are:

y1 + y2 ≥ 3

y1 - y2 ≥ 1

y1, y2 ≥ 0

We can solve this problem graphically by plotting the feasible region defined by the constraints and finding the point that minimizes the objective function within that region.

The feasible region is the intersection of the regions defined by the individual constraints. It is the area where all the constraints are satisfied.

Plotting the feasible region on a graph, we find that it is a triangular region with vertices at (1, 2), (1, 3), and (2, 1). The region is bounded by the lines y1 + y2 = 3, y1 - y2 = 1, y1 = 0, and y2 = 0.

To find the minimum value of V within this region, we evaluate the objective function at each vertex of the feasible region:

V(1, 2) = 4(1) + 3(2) = 10

V(1, 3) = 4(1) + 3(3) = 13

V(2, 1) = 4(2) + 3(1) = 11

The minimum value of V is 10, which occurs at the point (1, 2).

Therefore, the minimum value of V is 10.

Learn more about minimum value  from

https://brainly.com/question/30236354

#SPJ11

The odds in favor of the event happening are 5 to 4.

We have,

To find the odds in favor of an event happening, we use the formula:

Odds in favor = Probability of the event happening / Probability of the event not happening

In this case,

The probability of the event happening is 5/9.

The probability of the event not happening is 1 - 5/9, which simplifies to 4/9. So the odds in favor of the event happening are:

Odds in favor

= 5/9 / 4/9

= 5/4

Therefore,

The odds in favor of the event happening are 5 to 4.

Learn more about probability here:

https://brainly.com/question/14099682

#SPJ1

Answer:

C. 17 - 15

Step-by-step explanation:

Answer:

Step-by-step explanation:

-9y + 17 is equivalent to the following:

17 - 9y  Only order in which the terms appear is different here

-9(y - 17/9) (This is just a regrouping of -9 + 17)

Answer:

\(y=2x+4\)

Step-by-step explanation:

\((y-2)= 2(x-(-1))\)

\((y-2)=2(x+1)\)

\(y-2=2x+2\)

\(y=2x+4\)

A function that satisfies the condition of having its square plus the square of its derivative equal to 1 is given by f(x) = sin(x).

The function f(x) = sin(x) has the property that its square, sin^2(x), is equal to 1 when added to the square of its derivative, \($\frac{d}{dx}\sin(x))^2 = \cos^2(x)$\).

This can be seen by directly evaluating the expression: \(sin^{2}(x) + cos^{2}(x) = 1\), which is a fundamental identity in trigonometry.

The sine function is periodic with a period of 2π, and its derivative, cosine function, also has the same period. This means that for any x, the function sin(x) and its derivative cos(x) will satisfy the given condition.

Geometrically, the sine function represents the y-coordinate of a point on the unit circle as the corresponding angle is varied. Its derivative, the cosine function, represents the rate of change of this y-coordinate with respect to the angle. The squares of the sine and cosine functions add up to 1, which is the square of the radius of the unit circle. This property is fundamental in trigonometry.

Learn more about sine function here:

https://brainly.com/question/29277391

#SPJ11

Answer:

this answer would be -3

Step-by-step explanation:

I have done this question so many times lol

Step-by-step explanation:

Change the equation to the general form \(Ax + By + C = 0\).

\(y - 15 = - 6(x + 7) \\ y - 15 = - 6x - 42 \\ 6x + y - 15 + 42 = 0 \\ 6x + y + 27 = 0\)

The slope

\( = - \frac{A}{B} \)

\( = - \frac{6}{1} \)

\( = - 6\)

Answer:  Slope is -6

Step-by-step explanation:

We want to rearrange the equation to the form of y=mx+b, where m is the slope and b the y-intercept.

y−15=−6(x+7)

y−15=−6x-42

y=−6x-42+15

y = -6x - 27

The slope is -6

Answer:

Their are many other answers to this question this is one of the ones that are correct.

Answer: You're right. You've figured it out correctly!