what s the length of the arc for the half circle

The model is a representation of the polynomial factors using algebraic

tiles.

The equation represented by the model is the option;

Reasons:

The parameters of the model of the polynomial and the factors of the

polynomial are;

The number of factors of the polynomial = 2

1 of the four tiles is labelled x

3 of the four tiles is labelled -ve

Therefore;

A factor of the polynomial is x-tile, -tile, -tile, -tile = (x tile - 3 tiles) = (x - 3)

1 of the two tiles is labelled x

1 of the two tiles is labelled -ve

Which gives;

A factor of the polynomial is x, -tile = (x-tile - 1 tile) = (x - 1)

The 8 tiles are as follows;

1 of the 8 tiles is labelled x²

4 of the 8 tiles are labelled -x

3 of the 8 tiles are labelled +

Which gives;

The product of the polynomial is; (x²-tile - 4·x-tiles + 3-tiles) = (x² - 4·x + 3)

Multiplying the factors gives;

(x - 3) × (x - 1) = x² - 3·x - x + 4 = x² - 4·x + 3

The correct option is therefore;

The question options are;

x² - 2·x - 3 = (x - 3)·(x + 1)

x² - 4·x + 3 = (x - 3)·(x - 1)

x² + 2·x + 3 = (x + 3)·(x - 1)

x² + 4·x - 3 = (x + 3)·(x + 1)

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Answer:

n = 2

Step-by-step explanation:

14 = n

7       1

cross-multiply:  7n = 14

n = 2

Probability= Number of people who do not either read a newspaper or watch news on television/ Total number of people =50/250=0.2 Hence, the answer is A. 0.80.

Given that a survey of 250 people concerning how they obtain information about current events, 70 people read a newspaper each day, 130 watch news on television each day, and 30 read a newspaper and watch news on television each day.In order to find the probability that a person does not either read a newspaper or watch news on television each day, let us find the number of people who do not either read a newspaper or watch news on television each day.

Number of people who read a newspaper = 70

Number of people who watch news on television = 130

Number of people who read a newspaper and watch news on television = 30

Number of people who do not either read a newspaper or watch news on television=Total number of people - (Number of people who read a newspaper + Number of people who watch news on television - Number of people who read a newspaper and watch news on television)

=250-(70+130-30)=50

Therefore, the number of people who do not either read a newspaper or watch news on television each day is 50.

Hence, the (empirical) probability that the person does not either read a newspaper or watch news on television each day is:

Probability= Number of people who do not either read a newspaper or watch news on television/ Total number of people =50/250=0.2 Hence, the answer is A. 0.80.

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Answer:

neither

Step-by-step explanation:

Parallel lines need to have the same slope.

Perpendicular lines have opposite reciprocal slopes.

-5/2 and -2/5 are opposite reciprocals nor are they equal.

The coordinates of the midpoint M of line segment AB is  ( -1/2, 1/2 ).

The midpoint formula is expressed as;

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

Given the data in the question;

Point A (-3, -5)

Point B (2,6)

To determine the midpoint, plug the given points into the formula above and simplify.

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

M = ( (-3 + 2 )/2, ( -5 + 6)/2 )

M = ( (-1 )/2, ( 1 )/2 )

M = ( -1/2, 1/2 )

Therefore, the midpoint of the line is ( -1/2, 1/2 ).

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The correlation coefficient that represents the strongest relationship between two variables is -0.75.

In correlation coefficients, the absolute value indicates the strength of the relationship between variables. The strength of the association increases with the absolute value's proximity to 1.

The maximum absolute value in this instance is -0.75, which denotes a significant negative correlation. The relevance of the reverse correlation value of -0.75 is demonstrated by the noteworthy unfavorable correlation between the two variables.

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From the hypothesis test, it is found that the p-value of the test is of 0.6634

At the null hypothesis, we test if the mean is still the same, that is, of 10.2 hours per week, thus:

H₀ : μ = 10.2

At the alternative hypothesis, we test if the mean has increased, that is, if it is greater than 10.2 hours per week, thus:

H₀ :  μ > 10.2

Ten students were surveyed, so there are 9 degree of freedom. The test statistic is t = 0.45, and it is a one-tailed test, as we are testing if the mean is greater than a value.

Thus, using a t-distribution calculator, the p-value of the test is of 0.6634

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Answer:

C no es equivalente a 6/11.

Step-by-step explanation:

24/42 no es equivalente a 6/11 porque, cuando se simplifica, no es igual a este número. Si usamos el número 6 para simplificar, la respuesta a 24/42 sería 4/7, que no es igual a 6/11.

Answer:

la respuesta es  24/42

Step-by-step explanation:

24/42 no es equivalente a 6/11 porque, cuando se simplifica, no es igual a este número. Si usamos el número 6 para simplificar, la respuesta a 24/42 sería 4/7, que no es igual a 6/11.

Answer:

Step-by-step explanation:

i believe it would be A...

First, set the coordinate points on a graph, and joint them to form a graph

By looking at the graph we can see that:

width : 3

length: 6

Area of a rectangle : Length x width : 6 x 3 = 18

Answer:

Step-by-step explanation:

Given:

For en exponential function f(a):

\(f(-3)=18\)

\(f(1)=59\)

To find:

The value of f(0).

Solution:

The general form of an exponential function is:

\(f(x)=ab^x\)          ...(i)

Where, a is the initial value and b is the growth/ decay factor.

We have, \(f(-3)=18\). Substitute \(x=-3,f(x)=18\) in (i).

\(18=ab^{-3}\)            ...(ii)

We have, \(f(1)=59\). Substitute \(x=1,f(x)=59\) in (i).

\(59=ab^{1}\)            ...(iii)

On dividing (iii) by (ii), we get

\(\dfrac{59}{18}=\dfrac{ab^{1}}{ab^{-3}}\)

\(3.278=b^{1-(-3)}\)

\(3.278=b^{4}\)

\((3.278)^{\frac{1}{4}}=b\)

\(1.346=b\)

Substituting the value of b in (iii).

\(59=a(1.346)^1\)

\(\dfrac{59}{1.346}=a\)

\(43.83358=a\)

\(a\approx 43.83\)

The initial value of the function is 43.83. It means, \(f(0)=43.83\).

Therefore, the value of f(0) is 43.83.

Answer:

a

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:  yours is correct

Step-by-step explanation:

Since P = -2 and D = 5,

P - D = -2 - 5 = -7

P + D = -2 + 5 = 3

D - P = 5 - -2 = 7

this makes P - D the smallest, and D - P the largest

Answer:

Probability of a line living less than 10.1 years is 16%.

Step-by-step explanation:

It is given that, lifespan of lines in a particular zoo are normally distributed.

Mean =12.5

standard deviation= 2.4

We need to find the P(x<10.1)

So, let's use Empirical rule.

mean± standard deviation = 68%

Mean±2 standard deviation= 95%

mean ±3 standard deviation=99.7%

Now, let's use this rule to solve our problem.↑

The length of one side of the sandbox is 7y4 - 13x3 inches. To find the length of one side of a regular pentagon, we divide the perimeter by the number of sides (pentagon has 5 sides).

The given perimeter is 35y4 - 65x3 inches. So, the length of one side is (35y4 - 65x3) / 5 = 7y4 - 13x3 inches. In a regular pentagon, all sides are equal in length, and the sum of all interior angles is 540 degrees. However, this information is not needed to determine the length of one side in this specific problem.

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QUESTION:

Joan is building a sandbox in the shape of a regular pentagon. The perimeter of the pentagon is 35y4 – 65x3 inches. What is the length of one side of the sandbox?

5y – 9 inches

5\(y^{4}\) – 9\(x^{3}\) inches

7y – 13 inches

7\(y^{4}\) – 13\(x^{3}\) inches

The vectors u, v, and w are linearly independent if and only if k ≠ -8.

To understand why, let's consider the determinant of the matrix formed by these vectors:

| -4   -3    -4   |

| -3   -3    -11+k |

| 5    -11+k  7    |

If the determinant is nonzero, then the vectors are linearly independent. Simplifying the determinant, we get:

(-4)[(-3)(7) - (-11+k)(-11+k)] - (-3)[(-3)(7) - 5(-11+k)] + (-4)[(-3)(-11+k) - 5(-3)]

= (-4)(21 - (121 - 22k + k^2)) - (-3)(21 + 55 - 55k + 5k) + (-4)(33 - 15k)

= -4k^2 + 80k - 484

To find the values of k for which the determinant is nonzero, we set it equal to zero and solve the quadratic equation:

-4k^2 + 80k - 484 = 0

Simplifying further, we get:

k^2 - 20k + 121 = 0

Factoring this equation, we have:

(k - 11)^2 = 0

Therefore, k = 11 is the only value for which the determinant becomes zero, indicating linear dependence. For any other value of k, the determinant is nonzero, meaning the vectors u, v, and w are linearly independent. Hence, k ≠ 11.

In conclusion, the vectors u, v, and w are linearly independent if and only if k ≠ 11.

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Answer:

3

Step-by-step explanation:

Step-by-step explanation:

\( \frac{360 - 2(99)}{2} = \\ = \frac{360 - 198}{2} = \\ = \frac{162}{2} = \\ = 81\)

Answer: 81°

Step-by-step explanation:

Angles on a straight line always add up to 180°.

So as a and 99° are on the same straight line you would have to do 180-99=81°

Hope this helps :)

The probability that a person who reaches their 70th birthday will also reach their 80th birthday is 1/3 or approximately 0.333.

To find the probability that a person who reaches their 70th birthday will also reach their 80th birthday, we can use conditional probability.

Let's denote:

A: Event of living to be older than 70

B: Event of living to be older than 80

We are given:

P(A) = 0.6 (probability of living to be older than 70)

P(B) = 0.2 (probability of living to be older than 80)

We want to find:

P(B|A) = Probability of living to be older than 80 given that the person has already reached their 70th birthday.

According to conditional probability, we have:

P(B|A) = P(A ∩ B) / P(A)

Since the person has already reached their 70th birthday, we know they belong to event A. So, P(A ∩ B) represents the probability of living to be older than 80 and older than 70, which is the same as P(B).

P(B|A) = P(B) / P(A) = 0.2 / 0.6 = 1/3

Therefore, the probability that a person who reaches their 70th birthday will also reach their 80th birthday is 1/3 or approximately 0.333.

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Answer:

it would be the one where it says reflect on the x axis and 180 rotation

Step-by-step explanation:

it is because after reflecting on the x axis 180 degrees puts it in the same exact spot which deems that one incorrect

mark brainliest please I hope this helps

Answer:

y = -240

Step-by-step explanation:

If y varies jointly as x and z, then y/(xz) = k where k is the constant of proportion

60/10(-3) = 60/-30 = -2 = k

Now,  y/(xz) = -2

          y/8(15) = -2

          y/120 = -2

                y = -240

The probabilities for:

a. P(48 <X <66) = 0.978.

b. P(X> 69) = 0.0618.

c. P(X <= 65)  = 0.8051

d. P(X < 60) = 0.5

a. P(48 < X < 66) can be approximated using the normal distribution as follows:

mean, μ = np = 150 × 0.4 = 60

standard deviation, σ = \(\sqrt{(np(1-p)) }\)= \(\sqrt{(150 * 0.4 * 0.6)\) = 5.81

We can standardize using the formula z = (x - μ) / σ to find the area under the standard normal distribution between the z-scores corresponding to x = 48 and x = 66:

z1 = (48 - 60) / 5.81 = -2.06

z2 = (66 - 60) / 5.81 = 1.03

Using a standard normal distribution table, we find the area between these z-scores to be approximately 0.978. Therefore, P(48 < X < 66) ≈ 0.978.

b. P(X > 69) can be approximated using the normal distribution as follows:

mean, μ = np = 150 × 0.4 = 60

standard deviation, σ = \(\sqrt{(np(1-p)) }\)= \(\sqrt{(150 * 0.4 * 0.6)\) = 5.81

We can standardize using the formula z = (x - μ) / σ to find the area under the standard normal distribution to the right of the z-score corresponding to x = 69:

z = (69 - 60) / 5.81 = 1.55

Using a standard normal distribution table, we find the area to the right of this z-score to be approximately 0.0618. Therefore, P(X > 69) ≈ 0.0618.

c. P(X <= 65) can be approximated using the normal distribution as follows:

mean, μ = np = 150 × 0.4 = 60

standard deviation,  σ = \(\sqrt{(np(1-p)) }\)= \(\sqrt{(150 * 0.4 * 0.6)\)= 5.81

We can standardize using the formula z = (x - μ) / σ to find the area under the standard normal distribution to the left of the z-score corresponding to x = 65:

z = (65 - 60) / 5.81 = 0.86

Using a standard normal distribution table, we find the area to the left of this z-score to be approximately 0.8051. Therefore, P(X <= 65) ≈ 0.8051.

d. P(X < 60) can be approximated using the normal distribution as follows:

mean, μ = np = 150 × 0.4 = 60

standard deviation, σ = sqrt(np(1-p)) = sqrt(150 × 0.4 × 0.6) = 5.81

We can standardize using the formula z = (x - μ) / σ to find the area under the standard normal distribution to the left of the z-score corresponding to x = 60:

z = (60 - 60) / 5.81 = 0

Using a standard normal distribution table, we find the area to the left of this z-score to be 0.5. Therefore, P(X < 60) ≈ 0.5.

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Step-by-step explanation:

We are dealing with theoretical probability. This means that our probability of said outcome is

\( \frac{x}{y} \)

where x is the outcome we want, and y is the total number of outcomes possible.

28. There is 3 triangles out of 6 polygons so the probability is 1/2.

29.There is 1 Pentagon so the probability is 1/6.

30. This is a complement to question 28. A complement is the inverse of the problem. A complement and its original add to 1 so the probability of both getting a triangle is 1/2.

31. There is 4 non quadraletrial so the probability is 2/3.

32. There is 3 figures that has more sides than three so 1/2 is the probability.

33.There is only multi right angles figures so 1/2 is the probability.

34. There is 30 days in April so the probability it's the 29th is

\( \frac{1}{30} \)

35. There is 31 days in July and 15 days after the 16th. So the probability

is

\( \frac{15}{31} \)

Answer:

The correct answer is B. 20,000

Step-by-step explanation:

To determine the man's total monthly salary, we can set up a simple equation using the given information. Let's denote the total monthly salary as "x."

According to the information provided, 33% of the man's monthly salary is equal to Birr 6600. We can express this relationship mathematically as:

0.33x = 6600

To solve for "x," we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 0.33:

x = 6600 / 0.33

Evaluating the right side of the equation gives:

x ≈ 20,000

Therefore, the man's total monthly salary is approximately Birr 20,000.

Hence, the correct answer is B. 20,000.

The length HI in the quadrilateral is 63.7 units.

A quadrilateral is a polygon with 4 sides. The quadrilateral BCDE is similar to quadrilateral FGHI.

Two quadrilaterals are similar quadrilaterals when the three corresponding angles are the same and the corresponding sides are a ratio of each other.

Therefore,

18 / HI = 13 / 46

cross multiply

46 × 18 = 13 HI

828 = 13HI

divide both sides by 13

HI = 828 / 13

HI = 63.6923076923

Therefore,

HI = 63.7 units

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You would need to wait approximately 51.33 years from now to grow your initial investment of $39,000 to $174,000 at an interest rate of 10% per year.

To calculate the number of periods (years) required to grow an initial investment to a desired future value, we can use the formula for compound interest:

FV = PV * \((1 + r)^n\)

Where:

FV is the future value

PV is the present value (initial investment)

r is the interest rate per period

n is the number of periods

In this case:

PV = $39,000

FV = $174,000

r = 10% per year

Let's calculate the number of periods (years):

FV = PV * \((1 + r)^n\)

174,000 = 39,000 * \((1 + 0.10)^n\)

Divide both sides by 39,000:

4.4615 = \((1.10)^n\)

Take the logarithm of both sides to solve for n:

log(4.4615) = n * log(1.10)

n ≈ log(4.4615) / log(1.10)

n ≈ 2.1270 / 0.0414

n ≈ 51.33 (rounded to two decimal places)

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100th digit of the pi is 7

Pi (represented by the Greek letter π) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. It is approximately equal to 3.14159,

The decimal representation of pi (π) is an infinite non-repeating sequence of digits, so there is no simple formula or algorithm to determine the value of its digits. However, you can use a computer program or online tool to calculate the digits of pi to a certain number of decimal places.

Assuming you are looking for the 100th decimal digit of pi, it is 7. This means that if you write out the first 100 digits of pi, the 100th digit is 7.

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