Saskatchewan Widgets and Manitoba Widgets are two companies that were founded at the same time. Saskatchewan Widgets started 101010 million dollars in debt, and they make a constant yearly profit. After 555 years, they were 666 million dollars in debt. The graph of the balance (in millions of dollars) of Manitoba Widgets as a function of time (in years) is shown below. Which company started with a greater balance?

Answer:

a = 4

Step-by-step explanation:

Multiply by 2 on each side

6a = 24

a = 4

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:

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:

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:

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:

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:

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:

 -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)

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:

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:

0.136m

This is because if you draw a diagram, and label all the sides of the triangle (opp, hyp, adj), the adjacent angle is 3m. You can now use the sine rule to find the hypotenuse (length of ladder) by doing: cos 20= 3/h. You divide cos(20) by 3 and you get the answer of 0.13602m

Answer:

B. Jazz and opra

Step-by-step explanation:

40 percent of 55 is 22. Find whatever is equal to 22

B) Jazz & Opera music combo were chosen by 40% of people surveyed

Given : Total respondents = 55

So, 40% of total respondents = 40% of 55 = 22

County & Opera are chosen by 15 + 10 = total 25 respondents, ie not equal to 40%

Jazz & Opera are chosen by 12 + 10 = total 22 respondents, ie equal to 40%

Jazz, Opera, Rock & Country, Jazz, Rock are totally more respondents.

To learn more about Percentage Respondents, refer https://brainly.com/question/8191920?referrer=searchResults

Answer:

M=0

Step-by-step explanation:

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:

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:

And for this case we can begin completing the square like this:

[tex] f(x) = x^2 +10x + (10/2)^2 +21 -(10/2)^2[/tex]

And after aggrupate the terms we got:

[tex] f(x) = (x+5)^2 +21 -25 [/tex]

And finally we have:

[tex] f(X)= (x+5)^2 -4[/tex]

And for this case our vertex would be:

[tex] (h,k) = (-5,-4) [/tex]

Step-by-step explanation:

For this case we have the following equation given:

[tex] f(x) = x^2 +10x +21[/tex]

And we want to find a formula in terms in the vertex form given by:

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

And for this case we can begin completing the square like this:

[tex] f(x) = x^2 +10x + (10/2)^2 +21 -(10/2)^2[/tex]

And after aggrupate the terms we got:

[tex] f(x) = (x+5)^2 +21 -25 [/tex]

And finally we have:

[tex] f(X)= (x+5)^2 -4[/tex]

And for this case our vertex would be:

[tex] (h,k) = (-5,-4) [/tex]

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:

The 95% confidence interval for the standard deviation of the diameter is (0.0014; 0.0036).

Step-by-step explanation:

We have to calculate a confidence interval for the standard deviation.

The confidence level is 95%.

The size of the sample is n=10.

The sample standard deviation is s=0.002.

The lower limit is calculated as:

[tex]LL=s\sqrt{\dfrac{n-1}{\chi_{(1-\alpha)/2;n-1}}}\\\\\\LL=0.002\sqrt{\dfrac{10-1}{19.02}}=0.002\sqrt{0.473}=0.002*0.688=0.0014[/tex]

[tex]UL=s\sqrt{\dfrac{n-1}{\chi_{\alpha/2;n-1}}}\\\\\\UL=0.002\sqrt{\dfrac{9}{2.7}}=0.002\sqrt{3.33}=0.002*1.826=0.0036[/tex]

The 95% confidence interval for the standard deviation of the diameter is (0.0014; 0.0036).

Answer:

7719

Step-by-step explanation:

2,573*3=7719

Answer:

[tex] \boxed{C. \: 7,719} [/tex]

Step-by-step explanation:

Amount saved by Kate's family last year = 2,573 pennies

Amount saved by Zoe's family last year = 3 × Amount saved by Kate's family last year

= 3 × 2,573

= 7,719 pennies

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).

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Answer:

La ecuación química necesita ser equilibrada para que siga la ley de conservación de la masa.

Step-by-step explanation:

Answer:

26.39

Step-by-step explanation:

sin B = 4/9

B = inverse sin 4/9 = 26.387

Answer:

The test statistic Z = 1.844 < 1.96 at 0.05 level of significance

Null hypothesis is accepted

Yes he is right

The manager claims that at least 95 % probability that the plant is operating properly

Step-by-step explanation:

Explanation:-

Given data Population mean

                                           μ     = 885 tons /day

Given random sample size

                                          n = 60

mean of the sample

                                        x⁻  = 875 tons/day

The standard deviation of the Population

                                      σ = 42 tons/day

Null hypothesis:- H₀: The manager claims that at least 95 % probability that the plant is operating properly

Alternative Hypothesis :H₁: The manager do not claims that at least 95 % probability that the plant is operating properly

Level of significance =  0.05

The test statistic

 [tex]Z = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }[/tex]

[tex]Z = \frac{875 -885}{\frac{42}{\sqrt{60} } }[/tex]

[tex]Z = \frac{-10}{5.422} = -1.844[/tex]

|Z| = |-1.844| = 1.844

The tabulated value

                         [tex]Z_{\frac{0.05}{2} } = Z_{0.025} = 1.96[/tex]

The calculated value Z = 1.844 < 1.96 at 0.05 level of significance

Null hypothesis is accepted

Conclusion:-

The manager claims that at least 95 % probability that the plant is operating properly

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:

Bicycle : $117

Tricycle : $87

Unicycle : $183

Step-by-step explanation:

Write a system of equations:

x + 3y + z = 561

7x + y = 906

2x + 7y + 5z = 1758

Where:

x = price of bicycle

y = price of tricycle

z = price of unicycle

Solve for x, y, and z.