Which represents the solution of the graphed system of equations, y=x^2-2x and y=-2x-1

Answer:

8 hours

Step-by-step explanation:

25%= 2 hrs

100%=8 hrs

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=====================================================

Work Shown:

A = mass, in kg, of 1 apple

B = mass, in kg, of 1 empty basket

10A = mass of 10 apples

10A+B = mass of 10 apples and basket = 0.5

35A = mass of 35 apples

35A + B = mass of 35 apples and basket = 1.05

The system of equations we have is

[tex]\begin{cases}10A+B = 0.5\\35A+B = 1.05\end{cases}[/tex]

There are a number of ways to solve. As the top left corner of your paper indicates, we can use a matrix to solve. Either using row reduction or matrix inverse math.

We could also use elimination which I find easiest in this case. I'll use that method. Subtract the equations straight down. Note how the B terms become B-B = 0B = 0 which go away. The A terms become 10A-35A = -25A, and the terms on the right hand side become 0.5-1.05 = -0.55

--------

We're left with the equation

-25A = -0.55

Divide both sides by -25 to isolate A

A = -0.55/(-25)

A = 0.022

The mass of one apple is 0.022 kg

--------

Use this value of A to find B

10A + B = 0.5

10*0.022 + B = 0.5

0.22 + B = 0.5

B = 0.5 - 0.22

B = 0.28

Or we could use the other equation to solve for B

35A + B = 1.05

35(0.022) + B = 1.05

0.77 + B = 1.05

B = 1.05 - 0.77

B = 0.28

Either way, the empty basket's mass is 0.28 kg

Answer:

5,000

Step-by-step explanation:

If it decreases by 5% a year, it'll decrease by 75% in 15 years

i.e 1 year = 5%

15 years = x

Cross multiply

x = 75%

Therefore, since it decreases by 75%

100 - 75 x 20,000 = 5,000

100

Answer:

Step-by-step explanation:

From the give information: A new vaccination is being used in a laboratory experiment to investigate whether it is effective. There are 275 subjects in the study. Is there sufficient evidence to determine if vaccination and disease status are related?

Vaccination Status         Diseased         Not Diseased      Total

Vaccinated                           53                    17                      70

Not Vaccinated                    62                    143                   205

Total                                     115                     160                  275

In this study, we have two variables   ( Vaccination and diseases status ) The null and the alternative hypothesis can be stated as follows:

Null hypothesis: The two variables   ( Vaccination and diseases status ) are independent

Alternative hypothesis : The two variables   ( Vaccination and diseases status ) are dependent

The Chi-square test statistics can be computed as:

The Expected Values for the table can be calculated by using the formula:

[tex]E_i=\dfrac{row \ total \times column \ total}{grand \ total}[/tex]

Vaccination Status         Diseased         Not Diseased      Total

Vaccinated                       29.273                 40.727              70

Not Vaccinated                85.727                 119.273             205

Total                                     115                     160                  275

[tex]Chi - Square \ X^2 = \dfrac{(O_i-E_i)^2}{E_i}[/tex]

Vaccination Status         Diseased         Not Diseased      Total

Vaccinated                       19.232                13.823              33.055

Not Vaccinated                6.564                 45.573              52.137

Total                                  25.796               59.396             85.192

Therefore;

the Chi-Square Test Statistics = 85.192

For this study; we two rows and two columns

Therefore, the degree of freedom = (rows-1) × (columns-1)

the degree of freedom = (2 - 1) × (2 - 1)

the degree of freedom =  1 × 1

the degree of freedom =  1

Using the level of significance of ∝ = 0.05 and degree of freedom = 1 for the chi-square test

The p-value for the test statistics  = 0.00001

Decision rule: Since the P-value is lesser than the level of significance , therefore we reject the null hypothesis at the level of significance of 0.05

Conclusion:

We accept the alternative hypothesis and  conclude that the two variables

(Vaccination and diseases status ) are dependent  i.e the  vaccination and disease status are related

Answer:

x=−3

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :  7*x-8-(8*x-5)=0

Pull out like factors :  -x - 3  =   -1 • (x + 3)

Solve  :    -x-3 = 0  

Add  3  to both sides of the equation :    -x = 3

Multiply both sides of the equation by (-1) :  x = -3

Answer:

56x^2−99x+40

Step-by-step explanation:

 Evaluate (8x−5)(7x−8)

Apply the distributive property by multiplying each term of 8x−5 by each term of 7x−8.

56x^2−64x−35x+40

Combine −64x and −35x to get −99x.

56x^2−99x+40

Answer:

A. [tex]x^5+C[/tex]

Step-by-step explanation:

This is a great question! The first thing we want to do here is to take the constant out of the expression, in this case 5. Doing so we would receive the following expression -

[tex]5\cdot \int \:x^4dx[/tex]

We can then apply the power rule " [tex]\int x^adx=\frac{x^{a+1}}{a+1}[/tex] ", where a = exponent ( in this case 4 ),

[tex]5\cdot \frac{x^{4+1}}{4+1}[/tex]

From now onward just simplify the expression as one would normally, and afterward add a constant ( C ) to the solution -

[tex]5\cdot \frac{x^{4+1}}{4+1}\\[/tex] - Add the exponents,

[tex]5\cdot \frac{x^{5}}{5}[/tex] - 5 & 5 cancel each other out,

[tex]x^5[/tex] - And now adding the constant we see that our solution is option a!

Answer:

Answer A

Step-by-step explanation:

Use the property of integrals. You now have [tex]5 x\int\limits\,x^{4}dx[/tex] where the first x next to the 5 stands for multiplication. Let's evaluate it. We get [tex]5 (\frac{x^{5} }{5})[/tex]. From here, we can simplify this into [tex]x^{5}[/tex]. Add the constant of integration, which will give you the answer of [tex]x^{5} + C[/tex].

Answer:

answer is B

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

25/5

=5✖️5=25

=5/1

Answer:

25÷5 = 5 and 25/5 = 125

Step-by-step explanation:

hope this helps!

Answer:

nine hundred five thousand two hundred thirty-eight

Answer:

The  number expected to pass that test is  [tex]k = 14 \ employees[/tex]

Step-by-step explanation:

From the question we are told that

      The probability of  success is  p  =  0.91

       The sample size is  n  =  15  

 The number of employee that will pass the test is mathematically represented as

          [tex]k = n * p[/tex]

substituting values

        [tex]k = 15 * 0.91[/tex]

      [tex]k = 14 \ employees[/tex]

Answer:

d = 115.4 mi

Step-by-step explanation:

Since it gives us the distance in between the locations, we simply label the distances:

From the Garbage to the Hotel is 58.3 miles.

From the Hotel to the Hardware Store is 57.1 miles.

We are trying to find the distance from the Garbage to the Hardware Store, we simply add the distances between:

58.3 mi + 57.1 mi = 115.4 mi

The answer is C.) I, III, and V

The statement 1, 2, and 5 will be correct hence option (C) will be correct.

A frequency table is a list of objects with the frequency of each item shown in the table.

In other words, a frequency table is a table in which we have some data and their frequency.

The frequency of an occurrence or a value is the number of times it happens.

In option (C)

1st statement;

Math is the most popular subject in the 10th grade.

In 10th grade, maths is 104 rest are less so it is correct.

3rd statement;

Science is more popular than math among 12th-grade students.

The number of science lovers in the 12th is 78

The number of maths lovers in 12th is 52

So it is also correct.

5th statement;

Overall favorite course is history.

A number of overall favorite courses is history = 403 which is higher than others hence it is also correct.

So option (C) is correct rest are incorrect.

To learn more about the frequency table

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Answer:

4:00 pm

Step-by-step explanation:

To find the time it takes Malik to finish his English essay, let's start by subtracting one hour.

5:30 minus 1 hour is 4:30.

Now, subtract 30 minutes.

4:30 minus 30 minutes is 4:00.

Malik started working on his English essay at 4:00 pm.

Hope that helps.

Answer:

ln(60)

Step-by-step explanation:

We have the equation [tex]5e^x=300[/tex]. We can divide both sides of the equation by 5, getting [tex]e^x=60[/tex]. Finally, we can take the natural log of both sides, getting that x is equal to [tex]\ln(60)[/tex].

Answer:

[tex]-5<x<26[/tex].

Step-by-step explanation:

We know that if two corresponding sides of two triangles are equal, then third sides of the triangles depend on angle between equal sides.

Angle opposite to larger side is larger.

Since, 14 < 15, therefore

[tex]2x+10<62[/tex]

[tex]2x<62-10[/tex]

[tex]2x<52[/tex]

[tex]x<26[/tex]          ...(1)

We know that, angle can not not negative.

[tex]2x+10>0[/tex]

[tex]2x>-10[/tex]

[tex]x>-5[/tex]        ...(2)

From (1) and (2), we get

[tex]-5<x<26[/tex]

Therefore, the range of values of x is [tex]-5<x<26[/tex].

Answer:

0.6921 (69.21%)

Step-by-step explanation:

The area of the shaded region between the two z-scores refer to the probability between the two z-scores value( The total area under a standard normal distribution curve is 1)

So the area we want to determine in this case is as follows;

P(-1.24<z<0.84) = P(z<0.84) - P(z<-1.24)

What we use to calculate this finally is the standard normal distribution table

We use this to get these values so we can calculate the probability.

Using the standard normal distribution table;

P(-1.24<z<0.84) = 0.69206 which is approximately 0.6921

Answer: the intersection point is (2.4, -4.8)

Step-by-step explanation:

A) we have the function:

y = 0.5*x - 6.

First we want to know if this function intersects the line y´ = -1.5*x

Now, first we can recall that two lines are parallel only if the slope is the same for both lines, here we can see that the slopes are different, so the lines are not parallel, which means that the lines must intersect at some point.

Now, to find the intersection point we asumme y = y´ and want to find the value of x.

0.5*x - 6 = -1.5*x

(0.5 + 1.5)*x - 6 = 0

2.5*x = 6

x = 6/2.5 = 2.4

Now, we evaluate one of the functions in this value of x.

y = 0.5*2.4 - 6 = -4.8

So the intersection point is (2.4, -4.8)

Answer:

  0

Step-by-step explanation:

The determinant of this matrix is zero (0).

Answer:

[tex]C.\ 200[/tex]

Step-by-step explanation:

Given

Let R represents rows and C represents Columns

When R = 8, C = 25

When R = 10, C = 20

Required

Given that there exist an inverse variation, determine the constant of proportionality;

We start by representing the variation;

[tex]R\ \alpha \ \frac{1}{C}[/tex]

Convert proportion to an equation

[tex]R\ = \ \frac{k}{C}[/tex]

Where k is the constant of proportion;

[tex]R * C\ = \ \frac{k}{C} * C[/tex]

Multiply both sides by C

[tex]R * C\ = k[/tex]

Reorder

[tex]k = R * C[/tex]

When R = 8, C = 25;

The equation  [tex]k = R * C[/tex] becomes

[tex]k = 8 * 25[/tex]

[tex]k = 200[/tex]

When R = 10, C = 20;

The equation  [tex]k = R * C[/tex] becomes

[tex]k = 10 * 20[/tex]

[tex]k = 200[/tex]

Hence, the concept of proportionality is 200

Answer:

x = 60°

Step-by-step explanation:

All the angles in a triangle add up to 180°. So, you have this equation.

87° + 33° + x = 180°

120° + x = 180°

x = 60°

The measure of angle x is 60°.

Hope that helps.

Answer:

-4,4,16

Step-by-step explanation:

They are all even integers.

-4^2=16

4^2=16

16^2=256

the square of the third,16 is 256 which is more than the square of the second,4=16

The three consecutive even integers such that the square of the third is 60 more than the square of the second are -18, -16 and -14.

Any positive or negative number without fractions or decimal places is known as an integer, often known as a "round number" or "whole number."

Given:

Let the three even consecutive integers are 2n-2, 2n and 2n + 2.

According to the question,

So,

(2n + 2)² = (2n)² - 60

4n² + 4 + 8n = 4n² -60

8n = -64

n = -8

That means, the integers are -18, -16 and -14.

Therefore, the required even integers are -18, -16 and -14.

To learn more about the integers;

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Answer: B) -2/3

Step-by-step explanation:

First turn this equation into slope-intercept form(y = mx + b), where m is the slope.

2x+3y=4

3y=-2x+4

y=-2/3x+4/3

Thus, the slope is -2/3

Hope it helps <3

Answer:

Step-by-step explanation:

[tex]2x + 3y = 4?\\\mathrm{Slope}\:\mathbf{m}\:\mathrm{of\:a\:line\:of\:the\:form}\:\mathbf{Ax+By=C}\:\mathrm{equals}\:\mathbf{-\frac{A}{B}}\\\mathbf{A}=2,\:\mathbf{B}=3\\m=-\frac{2}{3}[/tex]

Answer:

a) P(B'|A) = 0.042

b) P(B|A') = 0.625

Step-by-step explanation:

Given that:

80% of the light aircraft that disappear while in flight in a certain country are subsequently discovered

Of the aircraft that are discovered, 63% have an emergency locator,

whereas 89% of the aircraft not discovered do not have such a locator.

From the given information; it is suitable we define the events in order to calculate the probabilities.

So, Let :

A = Locator

B = Discovered

A' = No Locator

B' = No Discovered

So; P(B) = 0.8

P(B') = 1 - P(B)

P(B') = 1- 0.8

P(B') = 0.2

P(A|B) = 0.63

P(A'|B) = 1 - P(A|B)

P(A'|B) = 1- 0.63

P(A'|B) = 0.37

P(A'|B') = 0.89

P(A|B') = 1 - P(A'|B')

P(A|B') = 1 - 0.89

P(A|B') = 0.11

Also;

P(B ∩ A) = P(A|B) P(B)

P(B ∩ A) = 0.63 × 0.8

P(B ∩ A) = 0.504

P(B ∩ A') =  P(A'|B) P(B)

P(B ∩ A') = 0.37 × 0.8

P(B ∩ A') = 0.296

P(B' ∩ A) = P(A|B') P(B')

P(B' ∩ A) = 0.11 × 0.2

P(B' ∩ A) = 0.022

P(B' ∩ A') =  P(A'|B') P(B')

P(B' ∩ A') = 0.89 × 0.2

P(B' ∩ A') = 0.178

Similarly:

P(A) = P(B  ∩  A ) + P(B'  ∩  A)

P(A) = 0.504 + 0.022

P(A) = 0.526

P(A') = 1 - P(A)

P(A') = 1 - 0.526

P(A') =  0.474

The probability that it will not be discovered given that it has an emergency locator is,

P(B'|A) =  P(B' ∩ A)/P(A)

P(B'|A) = 0.022/0.526

P(B'|A) = 0.042

(b) If it does not have an emergency locator, what is the probability that it will be discovered?

The probability that it will be discovered given that it does not have an emergency locator is:

P(B|A') = P(B ∩ A')/P(A')

P(B|A') = 0.296/0.474

P(B|A') = 0.625

Answer:

[tex]y=\frac{4}{3}x-1.75[/tex]

Step-by-step explanation:

If the slope of a line is 4/3,

and we wanna find the equation of a line that is parallel to it and crosses through (5,5).

So we already have the slope because the slope of 2 parallel lines are the same.

y = 4/3x

Look at the image below↓

So now we just need to find the y-intercept.

After some numbers we got,

[tex]y=\frac{4}{3}x-1.75[/tex]

Look at the other image below↓

Thus,

the equation of the parallel line is [tex]y=\frac{4}{3}x-1.75[/tex].

Hope this helps :)

Answer:

True

Step-by-step explanation:

Inverse variation on a graph is depicted by the movement of the graph diagram (line) in a downward motion

Answer:true

Step-by-step explanation:

Answer:

The frequency of f(x) is two times the frequency of the parent function.

Step-by-step explanation:

We can say that the number that is beside the x is equal to [tex]2\pi *f[/tex], where f is the frequency.

Then, for the parent function, we get:

[tex]1 = 2\pi f_1[/tex]

or solving for [tex]f_1[/tex]:

[tex]f_1=\frac{1}{2\pi }[/tex]

At the same way, for f(x), we get:

[tex]2=2\pi f_2\\f_2=2(\frac{1}{2\pi })[/tex]

But [tex]\frac{1}{2\pi }[/tex] is equal to [tex]f_1[/tex], so we can write the last equation as:

[tex]f_2=2f_1[/tex]

It means that the frequency of f(x) is two times the frequency of the parent function.

Answer:

Step-by-step explanation:

Using elimination method:

2x - y = 7

3x + y = 3

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

5x = 10

Divide both sides of the equation by 5

[tex] \frac{5x}{5} = \frac{10}{5} [/tex]

Calculate

[tex]x = 2[/tex]

Now, substitute the given value of X in the equation

3x + y = 3

[tex]3 \times 2 + y = 3[/tex]

Multiply the numbers

[tex]6 + y = 3[/tex]

Move constant to R.H.S and change it's sign

[tex]y = 3 - 6[/tex]

Calculate

[tex]y = - 3[/tex]

The possible solution of this system is the ordered pair ( x , y )

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

Check if the given ordered pair is the solution of the system of equation

[tex]2 \times 2 - ( - 3) = 7[/tex]

[tex]3 \times 2 - 3 = 3[/tex]

Simplify the equalities

[tex]7 = 7[/tex]

[tex]3 = 3[/tex]

Since all of the equalities are true, the ordered pair is the solution of the system

Hope this helps..

Best regards!!

Answer:

-11/24

Step-by-step explanation:

5/12 - 7/8

We need to get a common denominator of 24

5/12 *2/2  - 7/8 *3/3

10/24 - 21/24

-11/24

Answer:

-11/24

Step-by-step explanation:

Well to solve 5/12 - 7/8 we need to find the LCM.

12 - 12, 24, 36, 48

8 - 8, 16, 24, 32, 40

So the LCM is 24.

Meaning we need to make both denominators 24.

12*2 = 24 5*2 = 10

10/24

8*3 = 24 7*3 = 21

21/24

10/24 - 21/24

= -11/24

Thus,

the answer is -11/24.

Hope this helps :)

Answer: -4/3

Step-by-step explanation: To find the negative reciprocal of a fraction, all you have to do is flip the fraction and change the sign.

So the negative reciprocal of 3/4 is -4/3.

Answer:

Categorical independent variables are ___FACTORS__

The independent variables that are categorial should be factors.

In terms of mathematics, factor represents the no of algebraic expression where it split the other number that contains the zero remainder. As the factor of 12 should be 3 and 4. So based on this, the independent variables that are categorical should be considered as the factors.

Therefore, we can conclude that The independent variables that are categorial should be factors.

Learn more about variable here: https://brainly.com/question/18953210