Express your answer as a polynomial in standard form. f(x) = x^2 + 5x + 12 g(x) = -x+5 Find: f(g(x))

Yes, I can help them determine how they did within their respective groups. A higher Z-score indicates a faster time compared to the average for their group, while a lower Z-score indicates a slower time.

To do this, we will calculate the standard score or Z-score for each of them, which measures how many standard deviations above or below the mean their finishing time was. Calculation is as follows:

For Leo:

Z = (4948 - 4313) / 583 = 1.01

For Mary:

Z = (5513 - 5261) / 807 = 0.33

So, Leo finished 1.01 standard deviations above the mean for the Men, Ages 30 - 34 group, while Mary finished 0.33 standard deviations below the mean for the Women, Ages 25 - 29 group.

As for your second question, if the distributions of finishing times were not nearly normal, then the values of the standard score would change. This is because the standard score is calculated using the mean and standard deviation, which are important parameters of a normal distribution, these parameters may not accurately represent the data, and therefore the standard score would not be an accurate measure of relative performance.

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Answer:

4√2

Step-by-step explanation:

(−2)×√(−1+6+3)

-1+6+3 = 8

(-2)√8=(-2)(64) {I took off the root sign for now}

-128

√-128 --> 4√2

Answer:

2d-6

Step-by-step explanation:

Since the d is doubled you are multipling then subtracting 6 from the result

Answer:

Step-by-step explanation:

x2–5x+6 x2-x-2

x2+x-12 x2 +5x+4

i) x² - 5x + 6

⇒ x² - 3x - 2x + 6

⇒ x(x - 3) -2(x - 3)

⇒ (x - 2) (x - 3)    

Answer:

m = -1/4

Step-by-step explanation:

m = 2-(-1)/-4-8

m = 3/-12

m = -1/4

Answer:

100

Step-by-step explanation:

u add the two together and u should multiply them by 3 in order to get ur answer

Answer:

6 smaller portions

Step-by-step explanation:

1 pound (lb) = 16 ounces (oz)

3 lbs = 48 oz

1/2lb = 8oz

48oz (total)/8oz (amount in each portion) = 6 portions

The distance AD is 49 miles.

As per the given values of speed and time, we will calculate the distance AC. Firstly equalising the units.

As per the known fact, 60 minutes = 1 hour

30 minutes = (1/60)×30

30 minutes = 0.5 hour

Now, speed, distance and time are related as -

Speed = distance ÷ time

Distance = speed × time

Distance = 62 × 0.5

Distance = 31 miles

So, AC = 31 miles and BC = 25 miles.

Therefore, AB = AC - BC

AB = 31 - 25

AB = 6 miles

The distance AD = AC + CD

AD = 31 + 3 × AB

AD = 31 + 3 × 6

AD = 31 + 18

AD = 49 miles

Therefore, the distance between AD is 49 miles.

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The complete question is attached.

The sampling technique used for this situation is given by:

c) Cluster.

Samples may be classified as:

In this problem, the population is divided into groups, and each element of the groups are survived, hence cluster sampling was used.

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per annum, namely compound interest with an APR of 5%.

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$15000\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per annum, thus once} \end{array}\dotfill &1\\ t=years\dotfill &3 \end{cases}\)

\(A=15000\left(1+\frac{0.05}{1}\right)^{1\cdot 3}\implies A=15000(1.05)^3\implies A=17364.375 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{the interest earned is simply}}{17364.375 - 15000}\implies 2364.375\)

Answer:

b only

Step-by-step explanation:

Statement 1: Some cats like turkey, the form is I, the subject class is Cats, and the predicate class is Turkey, statement 2: There are burglars coming in the window, the form is E, the subject class is Burglars, and the predicate class is Not coming in the window and statement 3: Everyone will be robbed, the form is A, the subject class is Everyone, and the predicate class is Being robbed.

The given categorical propositions and their forms are as follows:

(1) Some cats like turkey - Form: I:

Subject class: Cats,

Predicate class: Turkey

(2) There are burglars coming in the window - Form: E:

Subject class: Burglars,

Predicate class: Not coming in the window

(3) Everyone will be robbed - Form: A:

Subject class: Everyone,

Predicate class: Being robbed

In the first statement:

Some cats like turkey, the form is I, the subject class is Cats, and the predicate class is Turkey.

In the second statement:

There are burglars coming in the window, the form is E, the subject class is Burglars, and the predicate class is Not coming in the window.

In the third statement:

Everyone will be robbed, the form is A, the subject class is Everyone, and the predicate class is Being robbed.

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There are total of 152 students in 5th grade, then the number of pencils altogether will be equal to 2,736 pencils.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the given information in the question,

Total number of students in 5th grade = 152

Amount of pencil each student have = 18

Then, the total number of pencils altogether,

= 152 × 18

= 2,736 pencils.

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Answer:

\(\displaystyle 1 = \frac{cos∠A}{cos∠B}\)

Step-by-step explanation:

\(\displaystyle \frac{OPPOSITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOSITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOSITE} = csc\:θ \\ \frac{ADJACENT}{OPPOSITE} = cot\:θ\)

Since this is a 45°-45°-90° triangle, you will have two IDENTICAL legs and the hypotenuse is the value of the leg multiplied by the square root of 2:

\(\displaystyle x\sqrt{2} = HYPOTENUSE \\ x = LEGS \\ \\ 4,242640687 ≈ 3\sqrt{2} \\ \\ \frac{3}{4,242640687} ≈ cos∠B \\ \frac{3}{4,242640687} ≈ cos∠A \\ \\ \frac{\frac{3}{4,242640687}}{\frac{3}{4,242640687}} = 1\)

I am joyous to assist you anytime.

The value of expression cos A / cos B is,

⇒ cos A / cos B = 1

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

Triangle ABC is shown in figure.

Now., We know that;

cos A = Base / Hypotenuse

cos A = 3 / 4.24

And, cos B = 3 / 4.24

Thus, The value of expression cos A / cos B is,

⇒ cos A / cos B = (3/4.24) / (3/4.24)

⇒ cos A / cos B = 1

So, The value of expression cos A / cos B is,

⇒ cos A / cos B = 1

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Answer:

c

Step-by-step explanation:

Answer:

i would say it will be the thrid one

Step-by-step explanation:

hope this helps

Answer:

G

Step-by-step explanation:

substitute the values in the function and u get the answer.

hope it helps

The value of the equation x² - x + 3 is 37/9.

We have,

We can start by multiplying both sides of the equation by x:

2x - 3/x = x + 1

2x - 3 = x^2 + x

Rearranging and simplifying, we get:

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

x^2 - x + 3 = x^2 + 2x - 3

-x + 3 = 2x - 3

5 = 3x

x = 5/3

Now we can substitute x into the equation x^2 - x + 3:

x^2 - x + 3 = (5/3)^2 - 5/3 + 3

x^2 - x + 3 = 25/9 - 15/9 + 27/9

x^2 - x + 3 = 37/9

Therefore,

The value of x² - x + 3 is 37/9.

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Using proportions, the estimate of the per capita consumption from 2011 was 29.25 gallons.

A proportion is a fraction of the total amount, the measures are related using a rule of three.

The amount in 2012 was an increase of 5.3% from 2011,

105.3% = 1.053 of x,

The consumption per capita was 30.8 gallons,

hence:

1.053x = 30.8

x = 30.8/1.053

x = 29.25 gallons.

(ii) The sales in 2011

= 9.1 billion gallons in 2011.

(iii) The per capita consumption from 2011

= 9.1 / 11.8

= 0.77 billion

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The coefficient of determination indicates the strength of the linear relationship between cube strength and axial strength in explaining the observed variation in the data.

(a) The equation of the least squares line for the regression of axial strength (y) on cube strength (x) is y = -32.2782 + 0.9921x (rounded to four decimal places). This equation represents the relationship between the two variables based on the sample data. The slope of the line is 0.9921, which means that for every one MPa increase in cube strength, the predicted axial strength is expected to increase by approximately 0.9921 MPa.

(b) The coefficient of determination, denoted as R-squared, is calculated as 0.6372 (rounded to four decimal places). The coefficient of determination represents the proportion of the observed variation in the dependent variable (axial strength) that can be explained by the independent variable (cube strength). In this case, 63.72% of the variation in axial strength of the asphalt samples can be attributed to its linear relationship with cube strength. The remaining 36.28% of the variation is due to other factors not accounted for in the regression model.  The higher the coefficient of determination, the more closely the regression line fits the data and the more accurately the cube strength predicts the axial strength.

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Answer:

=

3

2

Step-by-step explanation:

Answer:

4x^2+8x=3 or 4x^2+8x-3

Step-by-step explanation:

-(2±√7)/2

Answer:

28

Step-by-step explanation:

The ratio of the triangles is 12:15 which is equal to 4:5

Then you can use that ratio to find the ?

35 would be the 5 so 4 would be multiplyed by 7

Which is equal to 28

The object will first reach an altitude of 51,000 feet approximately 199.24 seconds after it is propelled upward.

To find the time it takes for the object to reach an altitude of 51,000 feet, we need to set the height equation equal to 51,000 and solve for time (t):

\(s = 3200t - 16t^2\\51,000 = 3200t - 16t^2\)

To solve this quadratic equation, we rearrange it to the standard form:

16t^2 - 3200t + 51,000 = 0

Next, we can either factorize or use the quadratic formula. Let's use the quadratic formula:

\(t = (-b \pm \sqrt(b^2 - 4ac)) / (2a)\)

Plugging in the values from the equation:

\(t = (-(-3200) \pm \sqrt((-3200)^2 - 4(16)(51,000))) / (2(16))\)

Simplifying:

\(t = (3200 \pm \sqrt(10,240,000 - 32,640)) / 32\\t = (3200 \pm \sqrt10,207,360) / 32\\t = (3200 \pm 3,195.80) / 32\)

Now we solve for the two possible values of t:

t₁ = (3200 + 3,195.80) / 32 ≈ 199.24

t₂ = (3200 - 3,195.80) / 32 ≈ 0.05

The negative value of t₂ is not physically meaningful in this context, so we discard it.

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There are 3,628,800 ways to seat the four women and six men in a row of ten chairs when there are no restrictions.

If there are no restrictions on the seating arrangement of the four women and six men, then the number of ways to seat them in a row of ten chairs can be calculated as follows:

First, we have 10 choices for the person who will sit in the first chair. After this, we have 9 choices for the person who will sit in the second chair, as one person has already been seated.

We continue in this way until we have only one choice left for the person who will sit in the tenth chair. Therefore, the total number of ways to seat the ten people in a row is:

10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3,628,800

So there are 3,628,800 ways to seat the four women and six men in a row of ten chairs when there are no restrictions.

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The mean value and the variance of z are 3.5 and 0.486, respectively.

Suppose that a die is rolled twice and the average of the two numbers of spots is recorded as a quantity z. What are the mean value and the variance of z?

Let X be the first number of spots and Y be the second number of spots. As X and Y are independent and have the same distribution, we have

E(X) = E(Y) = (1 + 2 + 3 + 4 + 5 + 6) / 6 = 21 / 6 = 3.5,
Var(X) = Var(Y) = (1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2) / 6 - (21 / 6)^2 = 2.9167.

Let Z = (X + Y) / 2 be the quantity of interest. Then

E(Z) = E[(X + Y) / 2] = E(X) / 2 + E(Y) / 2 = 3.5,
Var(Z) = Var[(X + Y) / 2] = Var(X) / 4 + Var(Y) / 4 = 0.486.

Therefore, the mean value and the variance of z are 3.5 and 0.486, respectively.

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To find a matrix M whose characteristic polynomial is x² – 3x + 2, we need to construct a 2x2 matrix with suitable entries. The eigenvalues of M can be determined by finding the roots of the characteristic polynomial. To find a basis of eigenvectors, we can solve the system of equations (M - λI)v = 0, where λ represents the eigenvalues and I is the identity matrix.

If the system has non-trivial solutions, a basis of eigenvectors exists; otherwise, it does not.

(a) To construct a matrix M whose characteristic polynomial is x² – 3x + 2, we can set up a general 2x2 matrix with entries a, b, c, and d:

M = | a  b |

      | c  d |

Next, we can find the characteristic polynomial of M by taking the determinant of (M - λI), where λ represents the eigenvalues and I is the identity matrix. Equating this to x² – 3x + 2, we can solve for the entries a, b, c, and d.

(b) To find the eigenvalues of M, we can solve the characteristic equation x² – 3x + 2 = 0. By factoring or using the quadratic formula, we can determine the values of x that satisfy the equation. These values will be the eigenvalues of M.

(c) To determine if a basis of eigenvectors exists, we need to solve the system of equations (M - λI)v = 0 for each eigenvalue λ. If the system has non-trivial solutions (i.e., solutions other than the zero vector), then a basis of eigenvectors exists. If the system only has the trivial solution (the zero vector), it means that there are no linearly independent eigenvectors, and thus, a basis of eigenvectors does not exist.

By following these steps, we can find the matrix M, determine its eigenvalues, and ascertain whether a basis of eigenvectors exists.

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The intervals on which function f(x) = sin x -1 increasing or decreasing is (0, π/2) (B).



The given function is f(x) = sin x -1, 0 < x < 2 π.

A sinusoidal function is a function that can be written in the form f(x) = a sin(bx + c) + d or f(x) = a cos(bx + c) + d, where a, b, c, and d are constants.

The graph of the given function is a sine curve shifted downward by 1 unit.

The function is increasing on the interval (0, π/2) because the slope of the curve is positive on this interval.

The function is decreasing on the interval (π/2, 3π/2) because the slope of the curve is negative on this interval.

The function is increasing again on the interval (3π/2, 2π) because the slope of the curve is positive on this interval.

Therefore, the correct answer is option B. (0, π/2).

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Answer:

1/5(1-x)

Step-by-step explanation:

Distributed

1/5-1/5x

Answer:1/5 (n-1)

Step-by-step explanation: Because say 1/5 and difference means subtract and number means variable and 1 means subtract it with the variable.