Factor x2 - 4x + 5.
O Prime
O (x + 5)(x - 1)
O (x - 5)(x - 1)
O (x + 5)(x + 1)

The constant angular acceleration of the centrifuge is approximately \(-331283\) rad/min² in the negative direction.

To find the constant angular acceleration of the centrifuge, we can use the following kinematic equation:

ω² = ω₀² + 2αθ

Here, ω is the final angular velocity (0 rad/min, since it comes to rest), ω₀ is the initial angular velocity (3450 rev/min), α is the constant angular acceleration we want to find, and θ is the angular displacement (45.8 revolutions).

First, we need to convert the given angular values to radians. We know that 1 revolution equals 2π radians.

Initial angular velocity, ω₀ = 3450 rev/min × 2π rad/rev = 6900π rad/min

Angular displacement, θ = 45.8 rev × 2π rad/rev = 91.6π rad

Now, substitute the values into the kinematic equation:

\(0 = (6900π)² + 2α(91.6π)\)

\(α = - (6900π)² / (2 × 91.6π)\)

\(α ≈ -331283 rad/min²\)

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If someone wants the product of two line segments to be represented as another line segment, they can make use of similar triangles

The correlation between the lengths of line segments can be established by creating a geometric shape comprising of two triangles that are identical and share one side.

If the legs of the triangles are used to represent the two line segments and their shared side represents the resulting line segment, it is possible for the lengths to be proportional through the similarity of the triangles.

To represent the product of the two original line segments, it is necessary to ensure that they and the resulting line segment are a collection of similar triangles. This is because the length of the resulting line segment can represent the product of the initial segments.

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Answer:

-3, -3

Step-by-step explanation:

eeeeeAnswer:

Step-by-step explanation:

The final simplified expression for the derivative of h(z) is h'(z) = (-4z^3)/(b^4 - z^4).

To differentiate the function h(z) = ln[(b^2 - z^2)/(b^2 + z^2)], we can use the quotient rule and the chain rule of differentiation.

Rewrite the function:

h(z) = ln[(b^2 - z^2)/(b^2 + z^2)]

= ln(b^2 - z^2) - ln(b^2 + z^2)

Apply the chain rule for the first term:

d/dz [ln(b^2 - z^2)] = 1/(b^2 - z^2) * (-2z)

= -2z/(b^2 - z^2)

Apply the chain rule for the second term:

d/dz [ln(b^2 + z^2)] = 1/(b^2 + z^2) * (2z) = 2z/(b^2 + z^2)

Combine the derivatives:

h'(z) = -2z/(b^2 - z^2) + 2z/(b^2 + z^2)

Now, we can simplify the expression if desired, but this is the final result of differentiating the function h(z) = ln[(b^2 - z^2)/(b^2 + z^2)] with respect to z.

To further simplify the expression for the derivative of

h(z) = ln[(b^2 - z^2)/(b^2 + z^2)], we can combine the terms with a common denominator.

Recall that the common denominator of -2z/(b^2 - z^2) and 2z/(b^2 + z^2) is (b^2 - z^2)(b^2 + z^2).

So, we can rewrite the expression as follows:

h'(z) = (-2z(b^2 + z^2) + 2z(b^2 - z^2))/[(b^2 - z^2)(b^2 + z^2)]

Simplifying further:

h'(z) = (-2zb^2 - 2z^3 + 2zb^2 - 2z^3)/[(b^2 - z^2)(b^2 + z^2)]

Combining like terms:h'(z) = (-4z^3)/[(b^2 - z^2)(b^2 + z^2)]

The derivative of h(z) simplifies to:

h'(z) = (-4z^3)/(b^4 - z^4)

So, the final simplified expression for the derivative of h(z) is h'(z) = (-4z^3)/(b^4 - z^4).

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If Rachana randomly selects two mugs from the set, the probability that she gets two different mugs is 0.1556 or 15.56%.

To solve this problem, we can use the concept of combinations. Since there are 10 mugs in the set, there are 10 choose 2 = 45 ways to select two mugs without considering order.

Out of these 45 ways, we need to count the number of ways Rachana can select two different mugs. Since there are 3 different types of mugs, Rachana can choose any one of the three types for the first mug. There are 10 mugs in the set, out of which 3 belong to the chosen type. Therefore, the probability of choosing a mug of the chosen type is 3/10.

For the second mug, Rachana can choose from the remaining 9 mugs. Since she needs to choose a different type of mug, she can choose any one of the 2 remaining types. There are 7 mugs left from the other 2 types. Therefore, the probability of choosing a mug of a different type is (7/9) * 2/3 = 14/27.

Therefore, the probability of selecting two different mugs is the product of the probabilities of selecting a mug of the chosen type and a mug of a different type. This is given by (3/10) * (14/27) = 7/45, which is approximately 0.1556 or 15.56%.

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Complete question is:

Rachana has a set of ten mugs the set up is made of 3 different mugs. If Rachana randomly selects two mugs from the set, what is the probability that she gets two different mugs?

Answer:

it will take 3 sticks to make pattern n

_

| |

Answer:

4

Step-by-step explanation:

no complicated calculations are needed here

if two lines are parallel, they have the same slope

so the answer is 4

Answer:

C. If a number has a negative cube root, then the number is negative.  

Step-by-step explanation:

took the quiz

The inverse of the conditional statement is " If a number does not have a negative cube root, then the number is not negative. "

A conditional statement is a type of logical statement that expresses a relationship between two propositions or statements. It typically takes the form "if p, then q" where p and q are propositions. The statement "if p, then q" is read as "if p is true, then q is true" or "p implies q".

The truth value of a conditional statement depends on the truth values of its antecedent (p) and its consequent (q). If p is true and q is true, then the conditional statement is true. If p is true and q is false, then the conditional statement is false. If p is false, then the truth value of the conditional statement is irrelevant and it is said to be vacuously true.

Given data ,

Let the statement be represented as A

Now , the inverse of the statement is A'

where A = "If a number is negative, then it has a negative cube root."

Now , the inverse of the conditional statement is

A' = " If a number does not have a negative cube root, then the number is not negative. "

Hence , the inverse is " If a number does not have a negative cube root, then the number is not negative. "

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The alternative hypothesis would be: The proportion of people who own cats is smaller than 90%.

The null hypothesis for this test would be: The proportion of people who own cats is equal to or greater than 90%.

To conduct the hypothesis test, we would need to collect a random sample of 1400 individuals and determine how many of them own cats. Based on this information, we could calculate the sample proportion of cat owners and use this to test the claim that the population proportion is smaller than 90%.

We would use a one-tailed hypothesis test with a significance level of 0.005. If the p-value for our test is less than 0.005, we would reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis that the proportion of people who own cats is smaller than 90%.
Hi! I'd be happy to help you with this question. You want to test the claim that the proportion of people who own cats is smaller than 90% at the 0.005 significance level.

To do this, we will set up our null and alternative hypotheses as follows:

Null Hypothesis (H0): The proportion of people who own cats is equal to 90% (p = 0.90)
Alternative Hypothesis (H1): The proportion of people who own cats is smaller than 90% (p < 0.90)

Here's a step-by-step explanation of how to test this claim:

1. Determine the sample size (n) and the number of cat owners in the sample (x): In this case, n = 1400, and x = 615.

2. Calculate the sample proportion (p-hat): p-hat = x/n = 615/1400 ≈ 0.439.

3. Determine the significance level (alpha): In this case, alpha = 0.005.

4. Calculate the standard error (SE) of the sample proportion: SE = sqrt[p*(1-p)/n] = sqrt[0.9*(1-0.9)/1400] ≈ 0.008.

5. Calculate the z-score: z = (p-hat - p)/SE = (0.439 - 0.9)/0.008 ≈ -57.63.

6. Find the critical z-value for a one-tailed test at the 0.005 significance level: z-critical = -2.576 (from a standard normal distribution table).

7. Compare the calculated z-score with the critical z-value: Since the calculated z-score (-57.63) is less than the critical z-value (-2.576), we reject the null hypothesis.

In conclusion, based on this analysis, we have enough evidence to support the alternative hypothesis that the proportion of people who own cats is smaller than 90% at the 0.005 significance level.

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Answer:

its the 2 one you welcome

Answer:

1 1/2

Step-by-step explanation:

it is one whole and a half

As per the given scenario, a cereal comes in three different package sizes.

The ratio of the cost of an 8-ounce box to a 16-ounce box of cereal can be calculated as follows :Ratio of 8-ounce box to 16-ounce box= 8 : 16Here, the ratio of 8 and 16 can be simplified by dividing both the terms by \(8.8 : 16 = 1 : 2\)

Therefore, the ratio of the cost of an 8-ounce box to a 16-ounce box of cereal is 1 : 2.

Note: The answer should be represented in the simplest form possible.

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The angle between vectors A and B is approximately 89.78 degrees.

To find the angle between vectors A and B, we can use the dot product formula:

A · B = |A| |B| cos(θ)

Given that Ā· B = 4 and knowing the magnitudes of vectors A and B:

|A| = √(22² + 33²)

    = √(484 + 1089)

    = √(1573)

    ≈ 39.69

|B| = √((-1)² + 23² )

    = √(1 + 529)

    = √(530)

    ≈ 23.02

Substituting the values into the dot product formula:

4 = (39.69)(23.02) cos(θ)

Now, solve for cos(θ):

cos(θ) = 4 / (39.69)(23.02)

cos(θ) ≈ 0.0183

To find the angle θ, we take the inverse cosine (arccos) of 0.0183:

θ = arccos(0.0183)

θ ≈ 89.78 degrees

Therefore, the angle between vectors A and B is approximately 89.78 degrees.

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Answer:

B.)58?

Step-by-step explanation:

Hope I helped..

Answer:

b: 58

Step-by-step explanation:

The value of y is 26.

We have,

From the figure,

∠1 and 3y - 4 are corresponding angles.

Now,

Corresponding angles are equal.

So,

m∠1 = 3y - 4

74 = 3y - 4

74 + 4 = 3y

3y = 78

y = 26

Thus,

The value of y is 26.

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Answer:

(0,5)

Step-by-step explanation:

Answer:i think its 115 degres

Step-by-step explanation:

Answer:

Subtract \(3\frac{1}{5}\) from both sides.

Step-by-step explanation:

We want to isolate the variable \(n\). To do this, we have to get rid of \(3\frac{1}{5}\), which we can do by subtracting itself, since it equals 0.

\(3\frac{1}{5} + n =9\)

\(n = 5\frac{4}{5}\)

Answer:

ITS A

Step-by-step explanation:

Answer:

The solution to the system of equations is

x = -2

y = 5

Explanation:

Given the pair of equations:

3x + y = -1 ............................................................................(1)

2x - 2y = -14 .......................................................................(2)

To solve the system by elimination, first of all

Divide equation (2) by 2, to simply have:

x - y = -7 ...............................................................................(3)

To eliminate y

Add equation (1) and (3) together

3x + x + y - y = -1 - 7

4x = -8

Divide both sides by 4

x = -8/4 = -2

To eliminate x

Multiply equation (3) by 3

3x - 3y = -21 .........................................................................(4)

Subtract equation (4) from equation (1)

3x - 3x + y - (-3y) = -1 - (-21)

y + 3y = -1 + 21

4y = 20

Divide both sides by 4

y = 20/4 = 5

Therefore, x = -2, and y = 5

Answer:

4 units

Step-by-step explanation:

A triangle has vertices on the coordinate grid at points D (3, -3), E (0, 2), and F (-1, -3). What is the length, in units, of DF ?

A triangle is a polygon with three sides and three angles.

The distance between two points \((x_1,y_1)\ and\ (x_2,y_2)\) on the coordinate plane is given by:

\(Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Given A triangle with vertices at points D (3, -3), E (0, 2), and F (-1, -3). The length of side DF is given as:

\(DF=\sqrt{(-1-3)^2+(-3-(-3))^2}=4\ units\)

Answer:

10 MILES

20 MINUTES

20 MILES

30MINUTES

Answer:

a)30 mph

b.)40 mph

c.)36mph

Step-by-step explanation:

Answer: A number which is divided by 5, with the result as 50 less than if the number had been divided by 6 would be; -1500

How to solve Algebra Word Problems?

Let the number be x. We are asked that it is divided by 5, and the result is 50 less than if the number had been divided by 6;

(x/6) - (x/5) = 50

Multiply by 30 to get;

5x - 6x = 1500

-x = 1500

x = -1500

Let the older turtle be represented x and the younger one be y.

Todays age,

Older turtle = 11y years

Younger turtle = y years

Also the equation form as;

11y + 24 = 7(y + 24)

11y + 24 = 7y + 168

11y - 7y = 168 - 24

4y = 144

y = 144/4

y = 36

Thus;

Age of older turtle today = 396 years

Age of younger turtle today = 36 years

Therefore,

3(36 + t) = 396 + t

108 + 3t = 396 + t

2t = 292

t = 292/2

t = 146 years

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Step-by-step explanation:

Answer:

x=10

Step-by-step explanation:

3(4x-12) = 84

Divide each side by 3

3/3(4x-12) = 84/3

4x-12 =28

Add 12 to each side

4x-12+12 = 28+12

4x= 40

Divide each side by 4

4x/4 = 40/4

x = 10

The slant height of given square pyramid is √45 inch.

A square pyramid is a geometric solid that has a square base and four triangular faces that meet at a common vertex. It belongs to the family of pyramids, which are three-dimensional shapes that have a palled the apex.

With the help of the Pythagoras theorem, we can find out the slant height of pyramid using the formula:

\(s^{2} =H^{2} +(\frac{a}{2} )^{2}\)

Here, height of square pyramid is H.

take an equilateral triangle, where a triangle has all sides are equal.

so, the height of the triangle (h) = \(\sqrt{a^{2} + (\frac{a}{2}) ^{2} }\) = \(\sqrt{6^{2} + (\frac{6}{2}) ^{2} }\) = √45 inch

the height of the square pyramid (H) is:

\(H^{2} + (\frac{a}{2}) ^{2} } = h^{2}\)

\(H^{2} = (\sqrt{45} )^{2} - (\frac{6}{2}) ^{2} }\)

H = 6 inch

The slant height of pyramid using the formula:

\(s^{2} =6^{2} +(\frac{6}{2} )^{2}\) = 36 + 9 = 45

s = √45 inch

Therefore, the slant height of given square pyramid is √45 inch.

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In standard deviation, 52 is the associated number of degrees of freedom for reading the t value.

What is standard deviation?

n = 53

x = 34

Determine the degrees of freedom (df)

     df = n - 1

     df = 53 - 1

      df = 52

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the area of the dartboard is approximately 254.34 square inches.

The area of a dartboard can be calculated using the formula for the area of a circle, which is given by:

Area = π * \(radius^2\)

Given that the radius of the dartboard is 9 inches, we can substitute this value into the formula:

Area = π * \(9^2\)

Area = π * 81

To calculate the area, we need to use the value of π (pi). Pi is an irrational number and is commonly approximated as 3.14. Using this approximation, we can calculate the area:

Area ≈ 3.14 * 81

Area ≈ 254.34 square inches

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The transformation rule used to transform Triangle PQR to P'Q'R' is; (x, y) → (⁵/₂x, ⁵/₂y)

We are given from the question that the triangle P'Q'R' was transformed from the triangle PQR.

We see from the image that the coordinates of the original triangle PQR are;

P(-1, 1)

Q(2, 0)

R(-1, -2)

We also see that the coordinates of the transformed triangle P'Q'R' are;

P(-5/2, 5/2)

Q(5, 0)

R(-5/2, -5)

Thus, we can conclude that the transformation rule used here is;

(x, y) → (⁵/₂x, ⁵/₂y)

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