Suki makes and sells denim jackets in a small store at the mall. She has found that
the following system of equations represents the expenses and the revenue for
running her store.
C = 520 + 31n
C = 96n
Determine the minimum number of jackets she must sell to make a profit.

Answer:

Our two intersection points are:

[tex]\displaystyle (3, -2) \text{ and } \left(-\frac{53}{25}, \frac{46}{25}\right)[/tex]

Step-by-step explanation:

We want to find where the two graphs given by the equations:

[tex]\displaystyle (x+1)^2+(y+2)^2 = 16\text{ and } 3x+4y=1[/tex]

Intersect.

When they intersect, their x- and y-values are equivalent. So, we can solve one equation for y and substitute it into the other and solve for x.

Since the linear equation is easier to solve, solve it for y:

[tex]\displaystyle y = -\frac{3}{4} x + \frac{1}{4}[/tex]

Substitute this into the first equation:

[tex]\displaystyle (x+1)^2 + \left(\left(-\frac{3}{4}x + \frac{1}{4}\right) +2\right)^2 = 16[/tex]

Simplify:

[tex]\displaystyle (x+1)^2 + \left(-\frac{3}{4} x + \frac{9}{4}\right)^2 = 16[/tex]

Square. We can use the perfect square trinomial pattern:

[tex]\displaystyle \underbrace{(x^2 + 2x+1)}_{(a+b)^2=a^2+2ab+b^2} + \underbrace{\left(\frac{9}{16}x^2-\frac{27}{8}x+\frac{81}{16}\right)}_{(a+b)^2=a^2+2ab+b^2} = 16[/tex]

Multiply both sides by 16:

[tex](16x^2+32x+16)+(9x^2-54x+81) = 256[/tex]

Combine like terms:

[tex]25x^2+-22x+97=256[/tex]

Isolate the equation:

[tex]\displaystyle 25x^2 - 22x -159=0[/tex]

We can use the quadratic formula:

[tex]\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

In this case, a = 25, b = -22, and c = -159. Substitute:

[tex]\displaystyle x = \frac{-(-22)\pm\sqrt{(-22)^2-4(25)(-159)}}{2(25)}[/tex]

Evaluate:

[tex]\displaystyle \begin{aligned} x &= \frac{22\pm\sqrt{16384}}{50} \\ \\ &= \frac{22\pm 128}{50}\\ \\ &=\frac{11\pm 64}{25}\end{aligned}[/tex]

Hence, our two solutions are:

[tex]\displaystyle x_1 = \frac{11+64}{25} = 3\text{ and } x_2 = \frac{11-64}{25} =-\frac{53}{25}[/tex]

We have our two x-coordinates.

To find the y-coordinates, we can simply substitute it into the linear equation and evaluate. Thus:

[tex]\displaystyle y_1 = -\frac{3}{4}(3)+\frac{1}{4} = -2[/tex]

And:

[tex]\displaystyle y _2 = -\frac{3}{4}\left(-\frac{53}{25}\right) +\frac{1}{4} = \frac{46}{25}[/tex]

Thus, our two intersection points are:

[tex]\displaystyle (3, -2) \text{ and } \left(-\frac{53}{25}, \frac{46}{25}\right)[/tex]

We're told that "the claim that the population of student course evaluations has a mean equal to 3.50". So this means μ=3.50 makes up the null H0

The alternative would be H1: μ ≠ 3.50 since it's the opposite of the claim made in the null.

We go with answer choice D to form the null and alternative hypotheses.

The sign ≠ in the alternative hypothesis tell us that we have a two tail test.

---------------------------------------

Let's compute the test statistic

z = (xbar - mu)/(s/sqrt(n))

z = (3.44 - 3.50)/(0.67/sqrt(89))

z = -0.84483413122896

z = -0.84

The test statistic is roughly -0.84

---------------------------------------

Despite not knowing what sigma is (aka the population standard deviation), we can see that n > 30 is the case. So we can use the Z distribution. This is the standard normal distribution. When n > 30, the T distribution is fairly approximately the same as the Z distribution.

Use a calculator or a Z table to determine that

P(Z < -0.84) = 0.2005

which is approximate

Because we're doing a two-tail test, this means we double that result to get 2*0.2005 = 0.401

The p-value is roughly 0.401

-----------------------------------------

Since the p-value is larger than alpha = 0.05, we don't have enough evidence to reject the null. So you can say that we fail to reject the null, or we accept the null.

The conclusion based on that means that μ=3.50  must be true (unless other evidence comes along to disprove this). In other words, the mean evaluation score from students appears to be 3.50

Answer:

The answer is "-3.04"

Step-by-step explanation:

[tex]\to \bar{x_1}-\bar{x_2}=9-11=-2[/tex]

Sample distribution:

[tex]z=\frac{\bar{x_1}-\bar{x_2}- \bar{\mu_1}-\bar{\mu_2}}{\sqrt{\frac{\sigma_{1}^2}{n_1}+\frac{\sigma_{2}^2}{n_2}}}\\\\[/tex]

   [tex]=\frac{(-2)-0}{\sqrt{\frac{3^2}{49}+\frac{4^2}{64}}}\\\\=\frac{-2}{\sqrt{\frac{9}{49}+\frac{16}{64}}}\\\\=\frac{-2}{\sqrt{\frac{576+784}{3136}}}\\\\=\frac{-2}{\sqrt{\frac{1360}{3136}}}\\\\=\frac{-2}{\sqrt{0.433}}\\\\=\frac{-2}{0.658}\\\\=-3.039\\\\=-3.04[/tex]

Answer:

50/60 = .8333=  83.33%

Step-by-step explanation:

The probability that the call arrived when the switchboard was not fully busy is 0.75.

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.

Given:

Here X follows uniform distribution with parameter a and b.

Where,

a = 0 and b = 1.

Then,

The density function of Y is given by:

P( 15 < Y ≤ 60)

or, P( 0.25 < Y ≤ 1)

So,  P( 0.25 < Y ≤ 1) = [tex]\int\limits^{1}_{0.25}{f(y) \, dy[/tex]

                                = [tex][y]^1 _ {0.25}[/tex]

                                = (1- 0.25)

                                = 0.75

Hence, The probability that the call arrived when the switchboard was not fully busy is 0.75.

Learn more about Normal Distribution here:

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Answer:

B. suggest that you and your boss schedule regular check-ins at lunchtime and at the end of the day

Step-by-step explanation:

It allows you to be ontask at your role (which you are hired for) while at the same time helps your boss know that you are on top of everything. It is the most polite option since you are setting professional boundaries but not complaining and showing frustrations.

(also so that your boss isn't micro-checking on you)

Answer:

[tex]2\times \left(-21\right)\times \:7[/tex]

PEMDAS order of operations:

[tex]2\times \left(-21\right)=-2\times \:21=-42[/tex]

[tex]=-42\times \:7[/tex]

[tex]=-294[/tex]

D) -294 is your answer

OAmalOHopeO

Answer:

11.93

Step-by-step explanation:

First find the amount of increase

11.20 *6.5%

11.20 *.065

0.728

Rounding to the nearest cent

.73

Add this to the original wage

11.20+.73

11.93

Answer:

A = (5,7)

B = (0, -1)

C = (-8, -3)

D = (5, -8)

Step-by-step explanation:

Answer:

A = (5, 7)

B = (0, -1)

C = (-8, -3)

D = (5, -8)

To do these problems, trace along in a straight line from the coordinate to the x- axis line and then to the y-axis line. Whatever number you reach will be part of the coordinate.

Hope this helped.

for x ,

8x + 10x = 180°

[sum of linear pair is equal to 180°]

or, 18x = 180°

or, x = 180/18

therefore, x = 10°……

for z,

10z =8x

[ being corresponding angles are equal ]

or, 10z = 8 × 10°

( replacing x by 10°)

or, 10z = 80°

or, z = 80/10

thus z = 8°…………

Answer:

the x éléments représente the domain

x represents the value on the x-axis and the coordinate is also known as abscissa.

Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.

For an ordered pair left parenthesis x comma y right parenthesis in a relation that is (x, y).

Here x represents the value on the x-axis and the coordinate is also known as abscissa.

More about the coordinate geometry link is given below.

https://brainly.com/question/1601567

Answer:

Step-by-step explanation:

Answer:

True.

Step-by-step explanation:

A trinomial is an algebraic expression consisting of 3 terms. The terms in this instance are: 3xy, 4z, and -8.

Answer:

D) d ≥ 2.18

Step-by-step explanation:

d – 0.31 ≥ 1.87

d >_ 1.87 + 0.31

d >_ 2.18

Step-by-step explanation:

(=) 5 (-1-3x) >-39-2x

(=) -5-15x > -39-2x

(=) -13x > -34

=> x < 34/13

Answer:

25 weeks

Step-by-step explanation:

Since we already know that he has $35 buck-a-roons saved, we can just subtract that from the cost of the bicycle to find the actual price—which would be 375. Then, we know that for every week, he gains $15 bucks. Therefore we know that 15 would be our variable so we can create the following equation:

15x + 35 = 410

15x = 375

15x/15 = 375/15

x = 25

After 25 weeks, Ken will have enough money to buy the bicycle.

Answer:

The milk cost $2.10 each the snacks cost $1.535 each the water cost $3.07 each

Step-by-step explanation:

I think Im right

12/24

Step One: We need to convert 1/3 and 1/8 so both have the same denominator, so we need to find the a number that is able to be multiply by 3 and 8 for the process.

Step Two: 1/3 x 8= 8/24 and 1/8x3= 3/24

Step Three: Add our new fractions: 3/24+8/24= 12/24

Step Four: Subtract 12 by 24: 24-12= 12; our answer is 12/24 or half the pizza was eaten

I hope I've help!

Step-by-step explanation:

Let,

[tex] \sf \vec{a} = 5 \hat{i} - \hat{j} + \hat{k} \\ \therefore \: \sf \: | \vec{a}| = \sqrt{ {5}^{2} + {( - 1)}^{2} + {1}^{2} } \\ = \sqrt{25 + 1 + 1} \\ = \sqrt{27} \\ \\ \sf \vec{b} = 2\hat{i} - \hat{j} + \hat{k} \\ \therefore \: \sf \: | \vec{b}| = \sqrt{ {2}^{2} + {( - 1)}^{2} + {1}^{2} } \\ = \sqrt{4 + 1 + 1} \\ = \sqrt{6} \\ \\\sf \: \vec{a}. \vec{b} = (5 \hat{i} - \hat{j} + \hat{k}).(2\hat{i} - \hat{j} + \hat{k}) \\ = 5 \times 2 + ( - 1) \times ( - 1) + 1 \times 1 \\ = 10 + 1 + 1 \\ = 12 \\ \\ \sf \: angle \: between \: \vec{a} \: and \: \vec{b} \: = \theta \\ \\ \: so \\ \sf \vec{a}. \vec{b} = | \vec{a}| . | \vec{b}| cos\theta \\ = > \sf \: cos \theta \: = \frac{ \vec{a}. \vec{b}}{ | \vec{a}| . | \vec{b}| } \\ = > cos \theta = \frac{12}{ \sqrt{27} \times \sqrt{6} } = 0.94 \\ = > \theta = {cos}^{ - 1} (0.94) \\ = > \green{\theta = 19.47 ^{ \circ} }[/tex]

Answer:

a) 0.55 = 55% probability that the person is traveling on business

b) 0.14 = 14% probability that the person is traveling for business on a privately owned plane.

c) 0.2545 = 25.45% probability that the person arrived on a privately owned plane, given that the person is traveling for business reasons.

d) 0.2 = 20% probability that the person is traveling on business, given that the person is flying on a commercially owned plane.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

Question a:

50% of 60%(major airlines)

70% of 20%(privately owned airplanes)

80% of 100 - (60+20) = 20%(comercially owned airplanes). So

[tex]p = 0.5*0.5 + 0.7*0.2 + 0.8*0.2 = 0.55[/tex]

0.55 = 55% probability that the person is traveling on business.

Question b:

70% of 20%, so:

[tex]p = 0.7*0.2 = 0.14[/tex]

0.14 = 14% probability that the person is traveling for business on a privately owned plane.

Question c:

Event A: Traveling for business reasons.

Event B: Privately owned plane.

0.55 = 55% probability that the person is traveling on business.

This means that [tex]P(A) = 0.55[/tex]

0.14 = 14% probability that the person is traveling for business on a privately owned plane.

This means that [tex]P(A \cap B) = 0.14[/tex]

Desired probability:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.14}{0.55} = 0.2545[/tex]

0.2545 = 25.45% probability that the person arrived on a privately owned plane, given that the person is traveling for business reasons.

Question d:

Event A: Commercially owned plane.

Event B: Business

80% of those arriving on other commercially owned planes are traveling for business reasons.

This means that:

[tex]P(B|A) = 0.2[/tex]

0.2 = 20% probability that the person is traveling on business, given that the person is flying on a commercially owned plane.

Answer:

The function is:

According to data in the table we have:

Since we found the values of a and n, the function becomes:

The number of infected to the tenth day:

Answer:

About 6,785 people will be infected about nine months.

Step-by-step explanation:

We can write an exponential function to represent the situation. The standard exponential function is given by:

[tex]\displaystyle f(x) = a(r)^x[/tex]

Where a is the initial value, r is the rate, and x, in this case, is the time that has passed in months.

3,124 people have already been infected. Thus, our initial value a = 3124.

And an additional 9% will be infected per month. Therefore, our rate r will be 1 + 9% or 1.09.

Hence, our function is:

[tex]\displaystyle f(x) = 3124(1.09)^x[/tex]

Then after nine months, the total amount of infected people will be f(9):

[tex]\displaystyle f(9) = 3124(1.09)^{(9)}[/tex]

Use a calculator:

[tex]\displaystyle f(9) \approx 6785[/tex]

About 6,785 people will be infected about nine months.

Answer:

7,022

Step-by-step explanation:

Answer:

6¹⁰×2³⁵

Step-by-step explanation:

he has 6 choices for the first multiple choice question.

and for each of those he had again 6 more choices to answer the second question. 6×6 = 36

so, for all 10 multiple choice questions he answer in

6¹⁰ different ways = 60466176 ways

then there are 35 true/false questions, which are Bausch again multiple choice questions but with only 2 options instead of 6.

so we get 2³⁵ different possibilities. a huge number.

and they're possible for each of the 60466176 ways of the multiple choice part.

so, in total we have

6¹⁰×2³⁵ different answer possibilities.

Answer:

[tex]\frac{(6x^{5}z) ^{3} }{4x^{4} {z}^{2} } = \frac{216 {x}^{15}z^{3} }{4 {x}^{4} {z}^{2} } = \frac{4x ^{4} {z}^{2} (54x ^{11}z) }{4 {x}^{4} {z}^{2} } = 54 {x}^{11} z[/tex]

I hope I helped you^_^

Answer:

Hello,

answer is B

Step-by-step explanation:

[tex]0.\overline{46}=\dfrac{46}{99}[/tex]

The answer is a fraction with numerator is the period (46) and the denominator is a number made with 9 as longer that there are digits in the  periode (here 2 digits ==> 99)

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The remainder when f(x) is divided by x + 3 would be 76.

If there is a polynomial p(x), and a constant number 'a', then

[tex]\dfrac{p(x)}{(x-a)} = g(x) + p(a)[/tex]

where g(x) is a factor of p(x).

We have been given a function;

[tex]f(x) = -2x^3 + x^2 - 4x + 1[/tex]

We need to find the remainder when f(x) is divided by x + 3.

So, Let p(x) = x + 3

p(x) = 0

x + 3 = 0

x = -3

Substitute in the given function f(x);

[tex]f(x) = -2x^3 + x^2 - 4x + 1\\\\f(-3) = -2(-3)^3 + (-3)^2 - 4(-3) + 1\\\\f(-3) = 54 + 9 + 12 + 1\\\\f(-3) = 76[/tex]

Thus, the remainder when f(x) is divided by x + 3 would be 76.

Learn more about remainder;

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Answer:

8+i

Step-by-step explanation:

7+4i+1-3i

Combine like terms.

8+i

I hope this helps!

pls ❤ and give brainliest pls

Answer:

The first one, the second, and fourth one are correct.

Select A,B, and D.

ED2021

Answer:

A, B, and C

Step-by-step explanation:

I got it right ;)

Answer:

1 : 3

Step-by-step explanation:

We know that 1 days is 24 hours

2 days = 2*24 = 48 hours

16 hours : 48 hours

Divide each by 16

16/16 : 48/16

1 : 3

Answer:

[tex]3 : 8[/tex]

Step-by-step explanation:

[tex]18h : 2d \\ 18h : 2 \times 24h \\ 18 :48 \\ 3 : 8[/tex]