Which statement is true?


A. 5x and 5 are like terms.

B. 5 and x are like terms.

C. 5x and x are like terms.

D. 5x and 5y are like terms.

Answer:

A: The expression is a trinomial with a degree of 4.

Step-by-step explanation:

The expression has three parts, so it's a tronomial.

The largest exponent is 4, so it has a degree of 4.  

Answer:

Yea he is right it is a

Step-by-step explanation:

Step-by-step explanation:

4x - 12 < 16 + 8x

Bringing like terms on one side

-12 - 16 < 8x - 4x

-28 < 4x

-28/4 < x

-7 < x

Answer:

(a) The mean and standard deviation of X is 2.6 and 1.2 respectively.

(b) The mean and standard deviation of T are 390 and 180 respectively.

(c) The distribution of T is N (390, 180²). The probability that all students’ requests can be accommodated is 0.7291.

Step-by-step explanation:

(a)

The random variable X is defined as the number of tickets requested by a randomly selected graduating student.

The probability distribution of the number of tickets wanted by the students for the graduation ceremony is as follows:

X      P (X)

0      0.05

1       0.15

2      0.25

3      0.25

4      0.30

The formula to compute the mean is:

[tex]\mu=\sum x\cdot P(X)[/tex]

Compute the mean number of tickets requested by a student as follows:

[tex]\mu=\sum x\cdot P(X)\\=(0\times 0.05)+(1\times 0.15)+(2\times 0.25)+(3\times 0.25)+(4\times 0.30)\\=2.6[/tex]

The formula of standard deviation of the number of tickets requested by a student as follows:

[tex]\sigma=\sqrt{E(X^{2})-\mu^{2}}[/tex]

Compute the standard deviation as follows:

[tex]\sigma=\sqrt{E(X^{2})-\mu^{2}}\\=\sqrt{[(0^{2}\times 0.05)+(1^{2}\times 0.15)+(2^{2}\times 0.25)+(3^{2}\times 0.25)+(4^{2}\times 0.30)]-(2.6)^{2}}\\=\sqrt{1.44}\\=1.2[/tex]

Thus, the mean and standard deviation of X is 2.6 and 1.2 respectively.

(b)

The random variable T is defined as the total number of tickets requested by the 150 students graduating this year.

That is, T = 150 X

Compute the mean of T as follows:

[tex]\mu=E(T)\\=E(150\cdot X)\\=150\times E(X)\\=150\times 2.6\\=390[/tex]

Compute the standard deviation of T as follows:

[tex]\sigma=SD(T)\\=SD(150\cdot X)\\=\sqrt{V(150\cdot X)}\\=\sqrt{150^{2}}\times SD(X)\\=150\times 1.2\\=180[/tex]

Thus, the mean and standard deviation of T are 390 and 180 respectively.

(c)

The maximum number of seats at the gym is, 500.

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sum of values of X, i.e ∑X, will be approximately normally distributed.  

Here T = total number of seats requested.

Then, the mean of the distribution of the sum of values of X is given by,  

[tex]\mu_{T}=n\times \mu_{X}=390[/tex]  

And the standard deviation of the distribution of the sum of values of X is given by,  

[tex]\sigma_{T}=n\times \sigma_{X}=180[/tex]

So, the distribution of T is N (390, 180²).

Compute the probability that all students’ requests can be accommodated, i.e. less than 500 seats were requested as follows:

[tex]P(T<500)=P(\frac{T-\mu_{T}}{\sigma_{T}}<\frac{500-390}{180})\\=P(Z<0.61)\\=0.72907\\\approx 0.7291[/tex]

Thus, the probability that all students’ requests can be accommodated is 0.7291.

Answer:

a = 4

Step-by-step explanation:

Multiply by 2 on each side

6a = 24

a = 4

Answer:

Step-by-step explanation:

Hi Sorry this took so long!

1. True

A=hbb /2 or Half of Base times Height.

2.False it would be 63

A= b * h

3.True

A=a+b/2 * h

Hope this helps!

Answer:

Option C is correct.

Step-by-step explanation:

The area of 1 side of the divider is approximately 8 x 3 = 24 < 25  

Hope this helps!

:)

Answer:

n is 41.67 degrees

Step-by-step explanation:

At the intersection point of two lines, there are two angles, a and b. The sum of these two angles is 180.

In this question:

One of the angles is (3n - 28)

The other is 83.

Then

[tex]3n - 28 + 83 = 180[/tex]

[tex]3n + 55 = 180[/tex]

[tex]3n = 180 - 55[/tex]

[tex]3n = 125[/tex]

[tex]n = \frac{125}{3}[/tex]

[tex]n = 41.67[/tex]

Answer:

  (x, y) = (4, 0)

Step-by-step explanation:

It looks like you want to solve ...

Adding the two equations gives ...

  2x = 8

  x = 4 . . . . divide by 2

Then ...

  y = 4 - x = 0

The solution is (x, y) = (4, 0).

_____

If you think about what you're seeing when you read the equations, you realize that adding or subtracting y gives the same result. Hence y=0 and x=4.

Answer:

[tex] y= 7(x+5)^2 -4[/tex]

The vertex form for a parabola is given by this expression:

[tex] y = a(x-h)^2 +k[/tex]

By direct comparison we see that for this case:

[tex] a = 7, h = -5 and k=-4[/tex]

And we know from the general expression that the vertex is:

[tex] V= (h,k)[/tex]

So then the vertex for this case is:

[tex] V= (-5,-4)[/tex]

Step-by-step explanation:

For this case we have the following function:

[tex] y= 7(x+5)^2 -4[/tex]

And we need to take in count that the vertex form for a parabola is given by this expression:

[tex] y = a(x-h)^2 +k[/tex]

By direct comparison we see that for this case:

[tex] a = 7, h = -5 and k=-4[/tex]

And we know from the general expression that the vertex is:

[tex] V= (h,k)[/tex]

So then the vertex for this case is:

[tex] V= (-5,-4)[/tex]

Answer:

 -41r - 16

Step-by-step explanation:

Step  1  :

Step  2  :

Pulling out like terms :

2.1     Pull out like factors :

  -5r - 2  =   -1 • (5r + 2)

Equation at the end of step  2  :

 -r +  -8 • (5r + 2)

Step  3  :

Step  4  :

Pulling out like terms :

4.1     Pull out like factors :

  -41r - 16  =   -1 • (41r + 16)

Answer:

one solution

Step-by-step explanation:

3x - 4y = -35

3x + 4y = 5

6x = -30

x = -5

3(-5) + 4y = 5

-15 + 4y = 5

4y = 20

y = 5

(-5, 5)

The system of equations has one solution (-5.5) which is correct option (A).

The equation is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is equal.

A linear equation is defined as an equation in which the highest power of the independent variable is always one.

Given the system of equations as :

3x - 4y = -35

3x + 4y = 5

Addition the both equations

3x - 4y + 3x + 4y = -35 + 5

6x = -30

Divided by 6 both the sides,

x = -30/6

x = -5

Substitute the value of x =2 in the equation 3x + 4y = 5

So, 3(-5) + 4y = 5

-15 + 4y = 5

4y = 20

Divided by 4 both the sides,

y = 20/4

y = 5

So, It has one solution x = -5 and y = 5

Hence, the system of equations has one solution (-5.5).

Learn more about equation here:

brainly.com/question/10413253

#SPJ5

Answer:

g(x) = 4x - 1

Step-by-step explanation:

We have that:

[tex]g(x) = ax + b[/tex]

So

[tex]g(2t) = a*(2t) + b[/tex]

Equaling both sides:

[tex]g(2t) = 8t - 1[/tex]

[tex]a*(2t) + b = 8t - 1[/tex]

b = -1.

And

[tex]2a = 8[/tex]

[tex]a = \frac{8}{2}[/tex]

[tex]a = 4[/tex]

Then

g(x) = 4x - 1

Answer:

X = 9

Step-by-step explanation:

1. Subtract 72 from both sides.

24x = 216

2. Divide 24 on both sides

x = 9

Answer:

X = 9

Step-by-step explanation:

We have to separate the like terms

72 + 24x = 288

24x = 288 - 72

24x = 216

We then divide both sides by 24

X = 9

Answer:

26.39

Step-by-step explanation:

sin B = 4/9

B = inverse sin 4/9 = 26.387

Answer:

Answer shown from explanation

Step-by-step explanation:

Area of trapezium =1/2 * sum of parallel side * height = 1/2. *(6+12) *4= 36sqft

Answer:

M=0

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Supplementary angles are angles that add up to 180° so they need to add up to 180 degrees.

Step-by-step explanation:

Answer:

Mean of original test scores is 88.5

Mean of test scores , with three marks added to each score is 91.5

The mean of the test score with three marks added to each score is higher than the original mean of score is increased by three .

Explanation : hope it works out !!

Answer:

83 posters

Step-by-step explanation:

$1,494/$18 = 83

Answer:

An online movie store made $1,494 on  poster sales last week.

It charged $18 for  each poster.

=> The number of sold posters:

N = 1494/18 = 83

Hope this helps!

:)

Answer:

The minimum number of widgets for the company to earn more than 50 dollars = 104 widgets.

Step-by-step explanation:

Complete Question

Inequality

Imagine the polynomial function shown represents the profits, in y dollars, earned by the production of x widgets.

y = -0.04x² + 40x - 3600

What is the minimum number of widgets for the company to earn more than 50 dollars?

Solution

For the profit to be more than 50

y > 50

-0.04x² + 40x - 3600 > 50

-0.04x² + 40x - 3650 > 0

0.04x² - 40x + 3650 < 0

(x - 898.4) (x - 101.6) < 0

Using the inequality table to obtain the required solution to this inequality

Eqn | x < 101.6 | 101.6 < x < 898.4 | x > 898.4

(x - 898.4) | -ve | - ve | + ve

(x - 101.6) | -ve | + ve | + ve

(x-898.4)(x-101.6) | +ve | - ve | +ve

Hence, the inequality that satisfies the equation of (x - 898.4) (x - 101.6) < 0, that is, negative, is 101.6 < x < 898.4.

And from this range, the minimum number of widgets for the company to earn more than 50 dollars = 102 widgets.

But 102 widgets give a profit of 13 dollars, 103 widgets give a profit of 47 dollars and it is until 104 widgets that the profits exceed 50 dollars truly.

Hope this Helps!!!

Answer:4

Step-by-step explanation:

Step-by-step explanation:

Random: stated

a) Conditions met Random: stated

Normal: [tex]n_{1} p_{1}=333>10[/tex]

[tex]n_{1}\left(1-p_{1}\right)=2122[/tex]

[tex]n_{2} p_{2}=499>10[/tex]

[tex]n_{2}\left(1-p_{2}\right)=1953[/tex]

Independent: Sample is less than of population.

b) (0.047,0.089) Use 2 -prop interval function of graphing utility

[tex]x_{1}: 333[/tex]

[tex]n_{1}: 2455[/tex]

[tex]x_{2}: 499[/tex]

[tex]n_{2}: 2452[/tex]

[tex]C-[/tex]Level : 0.95

c) The vaccine appears to be effective because we are 95% confident that the proportion of infants without the vaccine who got ear infections was 4.7% to 8.9% more than infants who are vaccinated.

Answer:

r = sqrt of 5 or 2.2

Step-by-step explanation:

(1)²+(2)²=r²

5 = r²

r = sqrt of 5 or 2.2

Answer:

d.

Step-by-step explanation:

x^2 because their is no other x^2

2x because their is no more x.

-7+1 equals -6

Answer:

D

Step-by-step explanation:

(f + g)(x) means that you add the two functions together, which results in (f + g)(x) = 2x + 1 + x² - 7 = D) x² + 2x - 6. Hope this helps!

Answer:

Step-by-step explanation:

Given:-

- The following system of equations is given:

                       [tex]6x_1 - 6x_2 -4x_3 = 0\\\\x_1 - 7x_2 -6x_3 = 0\\\\x_1 - 5x_2 -nx_3 = 0\\[/tex]

Solution:-

- The matrix equation consists of coefficient matrix "A" and a variable matrix " x ". These two matrices undergo multiplication to yield a solution column vector "b".

- The matrix A, is a symmetrical square matrix with its elements representing the coefficients of each variable as follows:

            [tex]A = \left[\begin{array}{ccc}a_1_1&a_1_2&a_1_3\\a_2_1&a_2_2&a_2_3\\a_3_1&a_3_2&a_3_3\end{array}\right][/tex]

- Where the elements first subscript denotes the equation number and second subscript denotes the variable number.

             [tex]A = \left[\begin{array}{ccc}6&-6&-4\\1&-7&-6\\1&5&n\end{array}\right][/tex]

- Similarly, the variable matrix " X " is a column vector that lists all the variables in the the system of equations in a ascending order.

             [tex]X = \left[\begin{array}{c}x_1&x_2&x_3\end{array}\right][/tex]

- The solution vector " b " is the corresponding solution or any number written on the right hand side of the equals to sign " = " :

              [tex]b = \left[\begin{array}{c}0&2&-2\end{array}\right][/tex]

- Now, we can express the given system in the asked format:

            [tex]A*X = b\\\\\left[\begin{array}{ccc}6&-6&-4\\1&-7&-6\\1&5&n\end{array}\right]*\left[\begin{array}{c}x_1&x_2&x_3\end{array}\right] = \left[\begin{array}{c}0&2&-2\end{array}\right][/tex]

- The augmented matrix is a matrix that combines the coefficient matrix " A " and the solution vector " b ". A solution vector "b" as an extra column to the coefficient matrix:

            [tex][ A | b ]\\\\ \left[\begin{array}{ccccc}6&-6&-4&|&0\\1&-7&-6&|&2\\1&5&n&|&-2\end{array}\right][/tex]

- Now we will perform row reduction operation such that the system is consistent and has infinite number of solution.

- Row operation: R3 - R2 & R1/6

            [tex]\left[\begin{array}{ccccc}1&-1&-\frac{2}{3} &|&0\\1&-7&-6&|&2\\0&12&n+6&|&-4\end{array}\right][/tex]  

- Row operation: R2 - R1 & R3 / 12

            [tex]\left[\begin{array}{ccccc}1&-1&-\frac{2}{3} &|&0\\0&-6&-\frac{16}{3} &|&2\\0&1&\frac{n+6}{12} &|&-\frac{1}{3}\end{array}\right][/tex]

- Row operation: R2 / 6

           [tex]\left[\begin{array}{ccccc}1&-1&-\frac{2}{3} &|&0\\0&-1&-\frac{8}{9} &|&\frac{1}{3} \\0&1&\frac{n+6}{12} &|&-\frac{1}{3}\end{array}\right][/tex]

For the above system to be consistent and have infinite many solution then the coefficient of " x3 " for the 2nd and 3rd row must be equal:

           [tex]-x_2 - ( \frac{n+6}{12})*x_3 = \frac{1}{3}[/tex]

           [tex]-x_2 - ( \frac{8}{9})*x_3 = \frac{1}{3}[/tex]

The coefficient of " x_3 " must be equal:

           [tex]( \frac{n+6}{12}) = \frac{8}{9} \\\\\\\n = \frac{14}{3}[/tex]

- The augmented matrix in reduced form becomes:

           [tex]\left[\begin{array}{ccccc}1&-1&-\frac{2}{3} &|&0\\0&1&\frac{8}{9} &|&-\frac{1}{3} \\0&0&0 &|&0\end{array}\right][/tex]

Answer: Rank = Number of non-zero rows = 2

- The number of linearly independent rows are equal to the rank of the augmented matrix.

Hence,

Answer: Number of linearly independent rows = 2

Row operation: R1 + R2

             [tex]\left[\begin{array}{ccccc}1&0&\frac{2}{9} &|&-\frac{1}{3} \\0&1&\frac{8}{9} &|&-\frac{1}{3} \\0&0&0 &|&0\end{array}\right][/tex]

- The variable "x_3" will take any arbitrary value for which the solution holds infinitely many solutions.

           [tex]x_2 + \frac{8}{9}*x_3 = -\frac{1}{3} \\\\x_2 = - ( \frac{8}{9}*x_3 + \frac{1}{3} )\\\\x_1 + \frac{2}{9}*x_3 = -\frac{1}{3} \\\\x_1 = - ( \frac{2}{9}*x_3 + \frac{1}{3} )\\[/tex]

- Taking x_3 = α:

Answers:

           [tex]x_1 = -\frac{1}{3} + \frac{2}{9} \alpha \\\\x_2 = -\frac{1}{3} + \frac{8}{9} \alpha[/tex]

Answer:

4

Step-by-step explanation:

[tex]256^{0.16}\cdot 256^{0.09}=\\256^{0.16+0.09}=\\256^{0.25}=\sqrt[4]{256}=4[/tex]

Hope this helps!

Answer:

A. a one-tailed paired t-test.

Step-by-step explanation: