A third-degree polynomial function f has real zeros -2, 12, and 3, and its leading coefficient negative. Write an equation for f. Sketch the graph of f. How many different polynomial functions are possible for f?

Answer:

10

Step-by-step explanation:

5+10=15

15×2=30

so the answer to your question is 10

Answer:

x = 10.

Step-by-step explanation:

Given: Two times the sum of 5 and some number is 30. What is the number?

First, write the equation:

2(5 + x) = 30

Simplify the brackets with distribution property:

10 + 2x = 30

Then collect like terms:

2x = 30 - 10

Finally, calculate:

2x = 20   (Divide both sides by 2)

x = 10

Answer:

10,000 mm

Hope that helps!

Step-by-step explanation:

Answer:

10000 mm

Step-by-step explanation:

1m = 1000mm

10 x 1000 = 10000mm

Answer:

11 : 44

Step-by-step explanation:

There are 11 6th graders and a combination of 44 7th and 8th graders. Therefore, the ratio is 11 : 44. Hope this helps!

The unconfined compression strength of the clay sample is equal to the major stress at failure, which is 3,000 psf.

To determine the unconfined compression strength of the clay sample, given that the major stress at failure is 3,000 psf, you can follow these steps:

1. Identify the major stress at failure, which is 3,000 psf in this case.

2. The unconfined compression test measures the unconfined compressive strength (UCS) of the clay sample. Since there is no lateral confinement in this test, the major stress at failure is equal to the unconfined compressive strength.

3. Therefore, the unconfined compression strength of the clay sample is 3,000 psf.

In summary, the unconfined compression strength of the clay sample is equal to the major stress at failure, which is 3,000 psf.

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This recursive formula states that each term in the sequence (except for the first term) is obtained by dividing the previous term by 4.

To write a recursive formula for the sequence, we need to identify the pattern in how each term is related to the previous term.

In the given sequence, each term is obtained by dividing the previous term by 4. Starting with the first term, 12, we can express the relationship as:

a1 = 12

an = an-1 / 4

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Answer:

x = 29

Step-by-step explanation:

The sum of the 3 angles is 180 degrees since it is a straight line

x-1 + 3x+2  + 2x+5 = 180

Combine like terms

6x +6 = 180

Subtract 6 from each side

6x+6-6= 180-6

6x =174

Divide y 6

6x/6 =174/6

x = 29

Answer:

it's 29

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

61%

Step-by-step explanation:

Area of square:

=a²

=12²

=144

Area of two quarter circles:

=2(¼×π×r²)

=2(¼×π×6²)

=2×28.72

=56.55

Finding the percentage:

=(56. 55÷144)×100

=0.3937×100

=39.27

subtract 100% by 39.27% to find the percentage of how much is shaded

=100-39.27

=60.73

=61 (rounded off to the nearest whole percent)

a) The set {1, 2, 3} does not represent vectors, but rather a collection of scalars. Therefore, there are no vectors in {1, 2, 3}.

b) The number of vectors in "col a" cannot be determined without additional context or information. "Col a" could refer to a column vector or a collection of vectors associated with a variable "a," but without further details, the exact number of vectors in "col a" cannot be determined.

c) Without knowing the specific context of "p" and "col a," it is impossible to determine if "p" is in "col a." The inclusion of "p" in "col a" would depend on the definition and properties of "col a" and the specific value of "p."

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Answer:

Step-by-step explanation:

y = 2.5  sin \(\frac{2}{3}\) x  

a = 2.5

b = \(\frac{2}{3}\)

Answer: \(5x-3\)

Step-by-step explanation:

First, \(4x-6+x+3~ < --- Simplify ~the ~expression\)

\(4x+x-6+3\)

Add the numbers \(-6+3=-3\):

\(4x+x-3\)

Add similar elements \(4x+x=5x\):

\(=5x+3\)

Answer:

\(\boxed{\tt 5x−3}\)

Step-by-step explanation:

\(\tt 4x−6+x+3 \)

Combine 4x and x = 5x:-

\(\tt 5x−6+3\)

Now, Add -6 and 3 = -3:-

\(\tt 5x−3\)

- :)

Therefore, the 97.5th percentile of a normal distribution with mean 0 and standard deviation 1 is 1.96.

The 97.5th percentile represents the value below which 97.5% of the data falls. In a normal distribution with mean 0 and standard deviation 1, the 97.5th percentile corresponds to a z-score of 1.96.

A z-score represents the number of standard deviations a data point is from the mean. In this case, a z-score of 1.96 means that the value corresponding to the 97.5th percentile is 1.96 standard deviations above the mean.

Using a standard normal distribution table or calculator, we can find that the area under the curve to the left of a z-score of 1.96 is 0.975. This means that 97.5% of the data falls below a z-score of 1.96.

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The probability that the system will fail is 1 - ((1 - 0.09) * (1 - 0.11) * (1 - 0.28)).

To find the probability that the system will fail, we need to consider that all three components fail in series.

When components are connected in series, the system fails if any one of the components fails.

Therefore, we need to calculate the probability that at least one component fails.

The probability that the first component fails (p1) is 0.09, the probability that the second component fails (p2) is 0.11, and the probability that the third component fails (p3) is 0.28.

To find the probability that at least one component fails, we can calculate the complement of the probability that all components work. In other words, we subtract the probability that all components work from 1.

The probability that all three components work is calculated by multiplying the probabilities of each component working: (1 - p1) * (1 - p2) * (1 - p3).

Therefore, the probability that the system will fail is 1 - ((1 - 0.09) * (1 - 0.11) * (1 - 0.28)).

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I tried 14,29

Step-by-step explanat IDK

Answer:

slope = 3

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 3, 2 ) and (x₂, y₂ ) = (- 2, 5 )

m = \(\frac{5-2}{-2-(-3)}\) = \(\frac{3}{-2+3}\) = \(\frac{3}{1}\) = 3

Answer: x= negative 6

if thats what its asking for

Step-by-step explanation:

To find the result of multiplying vector a by vector b, we use the dot product or scalar product. The dot product of two vectors is calculated by multiplying the corresponding components and summing them up.

Given:

a = [1, 3, 5]

b = [1, 3, 5]

To find a · b, we multiply the corresponding components and sum them:

\(a . b = (1 * 1) + (3 * 3) + (5 * 5)\\ = 1 + 9 + 25\\ = 35\)

So, a · b equals 35.

Now, let's plot the coordinate (35) on a graph paper. Since the coordinate consists of only one value, we'll plot it on a one-dimensional number line.

On the number line, we mark the point corresponding to the coordinate (35). The x-axis represents the values of the coordinates.

First, we need to determine the appropriate scale for the number line. Since the coordinate is 35, we can select a scale that allows us to represent values around that range. For example, we can set a scale of 5 units per mark.

Starting from zero, we mark the point at 35 on the number line. This represents the coordinate (35).

The graph paper would show a single point labeled 35 on the number line.

Note that since the coordinate consists of only one value, it can be represented on a one-dimensional graph, such as a number line.

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Answer:

Step-by-step explanation:

Since the picture isn't given. I have no idea what the radius or diameter is and as such, have no definite answer for you.

However, from the question, if he's to run round the circular track once, then he must have run a total of

2πr meters, with r being the radius.

Now, the question says that he ran round the track 10 times, this means that whatever value we get there, for 1 trial, we multiply it by 10, to get the value for 10 trials. Essentially,

10 * 2πr

The value gotten is the needed answer. All you have to do is substitute r for the value you have in your diagram. We already know that π is 3.142

The solutuion to the given differntial equation is: f(t) = -1/4 e^(2t) + t e^(2t) + 3/4 sin(t)

ℒ{f(t)}(s) = 1/(s^2 - 4s + 5)

We can factor the denominator of the fraction to obtain:

s^2 - 4s + 5 = (s - 2)^2 + 1

Using the partial fraction decomposition, we can write:

1/(s^2 - 4s + 5) = A/(s - 2) + B/(s - 2)^2 + C/(s^2 + 1)

Multiplying both sides by the denominator (s^2 - 4s + 5), we get:

1 = A(s - 2)(s^2 + 1) + B(s^2 + 1) + C(s - 2)^2

Setting s = 2, we get:

1 = B

Setting s = 0, we get:

1 = A(2)(1) + B(1) + C(2)^2

1 = 2A + B + 4C

Setting s = 1, we get:

1 = A(-1)(2) + B(1) + C(1 - 2)^2

1 = -2A + B + C

Solving this system of equations, we get:

A = -1/4

B = 1

C = 3/4

Therefore,

1/(s^2 - 4s + 5) = -1/4/(s - 2) + 1/(s - 2)^2 + 3/4/(s^2 + 1)

Taking the inverse Laplace transform of both sides, we get:

f(t) = -1/4 e^(2t) + t e^(2t) + 3/4 sin(t)

Therefore, the solution to the given differential equation is:

f(t) = -1/4 e^(2t) + t e^(2t) + 3/4 sin(t)

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f(n) = ϴ(g(n)) is not true in cases B(sqrt(n)log(n), C(\(3^n 5^n\)), and D(sin(n)+3 cos(n)+1).

A) \(log(n^200) log(n^2)\)

Here, f(n) = \(log(n^200)\) and g(n) = \(log(n^2)\). Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:

f(n) / g(n) = \([log(n^200) / log(n^2)]\) = 100

This means that as n approaches infinity, the ratio f(n) / g(n) is constant, and so we can say that f(n) = ϴ(g(n)). Therefore, f(n) = ϴ(g(n)) is true in this case.

B) sqrt(n) log(n) Here, f(n) = sqrt(n) and g(n) = log(n). Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:

f(n) / g(n) = [sqrt(n) / log(n)]

As log(n) grows much slower than sqrt(n) as n approaches infinity, this limit approaches infinity. Therefore, we cannot say that f(n) = ϴ(g(n)) is true in this case.

C) 3^n 5^n

Here, f(n) = \(3^n\) and g(n) = \(5^n\) . Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:

f(n) / g(n) = \([3^n / 5^n]\)

As \(3^n\) grows much slower than \(5^n\) as n approaches infinity, this limit approaches zero. Therefore, we cannot say that f(n) = ϴ(g(n)) is true in this case.

D) sin(n) + 3 cos(n) + 1

Here, f(n) = sin(n) + 3 and g(n) = cos(n) + 1. Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:

f(n) / g(n) = [sin(n) + 3] / [cos(n) + 1]

As this limit oscillates between positive and negative infinity as n approaches infinity, we cannot say that f(n) = ϴ(g(n)) is true in this case.

Therefore, f(n) = ϴ(g(n)) is not true in cases B, C, and D.

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Answer:

we can proove by ASA congruence or SAS congruence rule

Answer: 1, 1, 6, 6, 6, 8, 8

Step-by-step explanation:

Median = 6

Mode = 6

please give me a brainliest answer

Answer:

1/3

Step-by-step explanation:

The uncertainties ⟨Δx^2⟩ and ⟨Δp^2⟩ are given by the expressions ⟨Δx^2⟩ = a^2/2 and ⟨Δp^2⟩ = (ℏ^2)/(8a^2).

To calculate the uncertainties ⟨Δx^2⟩ and ⟨Δp^2⟩ for the given wave packet, we need to find the expectation values of the observables (x^ - ⟨x⟩)^2 and (p^ - ⟨p⟩)^2, respectively.

The wave packet is represented by the function ψ(x) = [2πa^2]^(1/2) exp[-4a^2(x - ⟨x⟩)^2 + iℏpx]. Here, a is a constant, ⟨x⟩ represents the expectation value of x, and p is the momentum operator.

To find ⟨Δx^2⟩, we calculate the expectation value of (x^ - ⟨x⟩)^2 with respect to ψ(x). By integrating (x - ⟨x⟩)^2 multiplied by the squared magnitude of the wave packet over all x values, we obtain the result ⟨Δx^2⟩ = a^2/2.

Similarly, to find ⟨Δp^2⟩, we calculate the expectation value of (p^ - ⟨p⟩)^2 with respect to ψ(x). Since p is the momentum operator, its expectation value is ⟨p⟩ = 0 for the given wave packet. By integrating (p^ - 0)^2 multiplied by the squared magnitude of the wave packet over all x values, we obtain the result ⟨Δp^2⟩ = (ℏ^2)/(8a^2).

Therefore, the uncertainties ⟨Δx^2⟩ and ⟨Δp^2⟩ are given by the expressions ⟨Δx^2⟩ = a^2/2 and ⟨Δp^2⟩ = (ℏ^2)/(8a^2).

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For a hypothesis testing by considering two samples related to rate of people who exercise and who do not exercise, the observed t-value < standard so, null hypothesis does not rejected and there is no evidence to support the claim.

We have a researcher who was interested in making a comparison of resting pulse rate of people who exercise regularly and who do not exercise regularly. There is two independent samples. In 1ˢᵗ sample, sample size, n₁= 16

Sample mean, \(\bar X_1\) = 72.3

Standard deviations, s₁ = 10.3

In case of second sample, sample size, n₂ = 12

Sample mean, \( \bar X_2\) = 69.0

Standard deviations, s₂ = 8.9

Level of significance = 2.5% = 0.25

Consider the null and alternative hypothesis for the test hypothesis are defined as \(H_0 : μ_1 =μ_2\)

\(H_a : μ_1 >μ_2\)

The test statistic : using t-test formula

\(t = \frac{ \bar X_1 - \bar X_2}{\sqrt{\frac{s_1^2}{n_1} +\frac{s_2^2}{n_2}}}\)

\(= \frac{72.3- 69}{ \sqrt{ \frac {10.3^2}{16} + \frac{8.9^2}{12}}}\)

= 0.91

Degree of freedom, df = n1 + n2 - 2

= 16 + 12 -2 = 26

Using the t-distribution table, the critical value for t(0.025, df = 26) is equals to the 2.06. Now, the observed t-value = 0.91 is less than 2.06 ( standard t value), so, we do not reject H₀ . Hence, no evidence to support the researcher claim.

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Answer:

i believe its 12.55

Step-by-step explanation:

if you add both number,  12.90 and 12.20, then divide by 2.

you'll will gain the same result

Answer:1,050

Step-by-step explanation:

Answer:

Step one. Equate the two right hand sides to each other.

3x - 4 = 2x + 1

Step-by-step explanation:

Well one of the things you could do is graph the two equations. The intersection point is the solution to the system. We get 5,11 as the answer. I can hear you saying that's cheating, and it likely is, but it does get the answer.

The very first step without the graph is to equate each of the right hand sides to each other. That's because the left side are both ys and they have to be equal.

3x - 4 = 2x + 1                     Add 4 to both sides

3x - 4 + 4 = 2x + 1 + 4

3x = 2x + 5                         Subtract 2x from both sides

3x-2x = 2x-2x + 5              Combine

x = 5

y = 3x - 4

y = 3*5 - 4

y = 15 - 4

y = 11.

The mean of the team’s distances is 3.75 miles. The median of the team’s distances is 3.5 miles.

To find the mean of the distances run by the Kennedy High School cross-country running team, we will first add up all the distances and then divide by the number of distances. The distances ran by the Kennedy High School cross-country running team are:

3.5 miles, 2.5 miles, 4 miles, 3.25 miles, 3 miles, 4 miles, and 6 miles adding up these distances, we get:

3.5 + 2.5 + 4 + 3.25 + 3 + 4 + 6 = 26.25

So the sum of the distances is 26.25 miles. Now, to find the mean, we will divide by the number of distances, which is 7. Therefore, the mean of the distances is: Mean = Sum of distances / Number of distances

Mean = 26.25 / 7

Mean = 3.75 miles

To find the median of the distances run by the team, we will first arrange the distances in order from smallest to largest:2.5 miles, 3 miles, 3.25 miles, 3.5 miles, 4 miles, 4 miles, 6 miles

Now, we will find the middle value. Since there are 7 distances, the middle value will be the 4th value. Counting from the left, the 4th value is 3.5 miles. Therefore, the median of the distances ran by the team is 3.5 miles.

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The set of all pairs of real numbers (x1, y) with the operations (x1, y1) + (x2, y2) = (x1 + x2, y1 + y2) and k(x, y) = (2k, 2ky) is not a vector space.

The first axiom of a vector space is that the sum of two vectors is a vector. In this case, the sum of two vectors (x1, y1) and (x2, y2) is (x1 + x2, y1 + y2).

However, this vector does not belong to the set of all pairs of real numbers, because the second component is not necessarily a real number.

For example, if (x1, y1) = (1, 2) and (x2, y2) = (3, 4), then the sum is (4, 6), which is not a pair of real numbers.

Therefore, the set of all pairs of real numbers with the operations (x1, y1) + (x2, y2) = (x1 + x2, y1 + y2) and k(x, y) = (2k, 2ky) does not satisfy the first axiom of a vector space.

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