During two years in college, a student earned $9,500. The second year she earned $500 more than twice the amount she earned the first year. How much did she earn the first year?

Answer:

4x^2-22x+30

=2(2x^2 - 11x + 15)

=2(2x^2 -6x -5x +15)

= 2 { 2x(x-3) - 5(x-3) }

= 2 (x-3) (2x - 5)

Step-by-step explanation:

Hey, there!!!

The answer is option B

here, we have;

=4x^2-22x+30

=4x^2-(10+12)x+30

= 4x^2-10x-12x+30

now, taking common,

=2x(2x-5) -6(2x-5)

= 2(x-3)(2x-5).

Hope it helps

Answer:

-6x² -4x -16

Step-by-step explanation:

be watchful of signs to avoid making errors

Answer:

9

Step-by-step explanation:

13-4=9

Answer:

32

Step-by-step explanation:

If there are 16 independent variables (groups) then there would need to be 2 unique exercises x 16 groups = 32 exercises. If the independent variable is the number of students, then they would only need 8.

The Total Exercises each group will do 2x/4

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Total exercises individual need is y = 4x/2

y - 4x/2

The No. of groups = 4

Each group has to do exercises = 2

Total no. of exercises individual need is y

Total Exercises each group will do 2x/4

Total exercises individual need

y = 2x/4 (4)

y - 4x/2                    

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x=2.86

Step-by-step explanation:

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

[tex] {24}^{2} + {32}^{2} = 40[/tex]

[tex]c = 40[/tex]

[tex]6x + 6 + 9x - 9 = 40[/tex]

[tex](6x + 9x) + (6 - 9) = 40[/tex]

[tex]15x - 3 = 40[/tex]

[tex]15x = 43[/tex]

[tex]x = 2.866[/tex]

[tex]23.16 + 16.74 = 39.9[/tex]

the

[tex]6(2.86) + 6 = 23.16[/tex]

[tex]9(2.86) - 9 = 16.74[/tex]

Answer:

bgd=cgd+cgb

agf=cgd

50=cgd

cgd=50

bgd=90

so cgd=50

bgc=40

bgd=90

Answer:

C  90-degrees

Step-by-step explanation:

Using alternate interior angles, you can say m<CGD = 50 degrees.

From here, using the fact that line BE is a bisector of line CF, we know that the sum of degrees of the line BE would be 180 degrees.

So we can say m<EGD + m<CGD + m<BGC = 180.  Plug in our known values.

90 + 50 + m<BGC = 180

m<BGC = 40

And we can see that m<BGD = m<BGC + m<CGD

Thus, m<BGD = 40 + 50 = 90.

So the m<BGD = 90 degrees.

Cheers.

Answer: 72

Step-by-step explanation:

no. of family pizzas-  2

cost of one family pizza - 24 each

total cost for family pizza -48

one family pizza's cost equals to 3 small pizzas

which is cost of 3 small pizzas = 24

therefore, total cost= 24+48

=72

Answer:

Perimeter=60.18cm

Area=215.495cm^2

Step-by-step explanation:

Given:

Length of book=18.34cm

Breadth=11.75cm

Solution:

Perimeter=2(l +b)

P=2(18.34+11.75)

P=2 x 30.09

P=60.18cm

Area=l x b

A=18.34 x 11.75

A=215.495 cm^2

Thank you!

Answer: 7

Step-by-step explanation:

f(0) means that x is equal to zero and so you substitute all the x's for zeros which means -3 times 0 plus 7 is equal to 7

Answer:

[tex]x=\frac{7}{3}[/tex]

Step-by-step explanation:

Since any number multiplied by zero equals zero, our equation is really:

0 = -3x+7

First, we'd have to subtract the 7 from both sides:

-7 = -3x

Now we need to divide the negative three from both sides to isolate the x.

7/3 = x

So, our answer is x=7/3

Hope this helps!! <3 :)

See the attached picture

[tex]\bold{\text{Answer:}\quad \dfrac{(x+4)^2}{81}+\dfrac{(y-5)^2}{25}=1}[/tex]

Step-by-step explanation:

A "horizontal" ellipse means that the x-radius is bigger than the y-radius.  Thus, x is the major axis and y is the minor axis.

The equation of an ellipse is: [tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex]      where

It is given that the center is at (-4, 5) --> h = -4, k = 5

It is given that the major axis has a length of 18 --> x-radius = 9

It is given that the minor axis has a length of 10 --> y-radius = 5

Input those values into the equation of an ellipse to get:

[tex]\dfrac{(x-(-4))^2}{9^2}+\dfrac{(y-5)^2}{5^2}=1[/tex]

Simplify to get:

[tex]\dfrac{(x+4)^2}{81}+\dfrac{(y-5)^2}{25}=1[/tex]

Answer:

  60

Step-by-step explanation:

If the sides of the triangle have lengths a, b, c, the perimeter is their sum:

  P = a + b + c

Any of the side lengths can be found using the distance formula. However, since two of the sides are aligned with the axes, their lengths are easily found by subtracting coordinates.

If the points are labeled A, B, C, in order, then the two right-angle sides are ...

  c = AB = 3 -(-7) = 10

  b = AC = 9 -(-15) = 24

The Pythagorean theorem tells you that you can find the third side from the relation ...

  a² = b² +c²

  a² = 10² +24² = 676

  a = √676 = 26

Now, we can use these values in the formula for the perimeter:

  P = a + b + c = 26 + 24 + 10

  P = 60

The perimeter of the triangle is 60 units.

proving statements!

it's the very definition of it

Answer:

0.25.

Step-by-step explanation:

To find the common difference, you need to find the number that each value increases by.

1.75 - 1.5 = 0.25.

1.5 - 1.25 = 0.25.

1.25 - 1 = 0.25.

All values apparently increase by 0.25. So, that is your common difference.

Hope this helps!

Answer:

0.25

Step-by-step explanation:

The common difference is the value added to the first term to get the second term, then added to the second to get the third and so on.

To find the common difference, subtract the first term from the second. Then check by subtracting the second term from the third.

The sequence is:  1,1.25,1.5,1.75

second term - first term

1.25- 1= 0.25

third term- second term

1.5 -1.25= 0.25

The common difference in the arithmetic sequence is 0.25

Answer:

C) w+4

Step-by-step explanation:

w=the variable

+4= increased by 4

HOPE THIS HELPS!!!!!! :)

<33333333333

Answer: [tex]-44\dfrac{4}{9}[/tex]

Step-by-step explanation:

The given expression: [tex]-36\dfrac{4}{9}-(-10\dfrac{2}{9})-(18\dfrac{2}{9})[/tex]

Here, [tex]36\dfrac{4}{9}=\dfrac{36\times9+4}{9}=\dfrac{328}{9}[/tex]

[tex](10\dfrac{2}{9})=\dfrac{92}{9}\\\\(18\dfrac{2}{9})=\dfrac{9\times18+2}{9}=\dfrac{164}{9}[/tex]

That is

[tex]-36(\dfrac{4}{9})-(-10\dfrac{2}{9})-(18\dfrac{2}{9}) = -\dfrac{328}{9}-(-\dfrac{92}{9})-\dfrac{164}{9}\\\\=-\dfrac{328}{9}+\dfrac{92}{9}-\dfrac{164}{9}\\\\=\dfrac{-328+92-164}{9}\\\\=\dfrac{-400}{9}\\\\=-44\dfrac{4}{9}[/tex]

Answer:

Mean: 55.9

Median: 55

Mode: None

Step-by-step explanation:

First, find the mean by dividing the sum by the number of elements:

(72 + 58 + 62 + 38 + 44 + 66 + 42 + 49 + 76 + 52) / 10

= 55.9

Next, find the median by putting the numbers in order and finding the middle one:

38, 42, 44, 49, 52, 58, 62, 66, 72, 76

There is no middle number, so we will take the average of 52 and 58, which is 55.

Lastly, to find the mode, we have to find the number that occurs the most.

All of the numbers occur one time, so there is no mode.

Answer:

y=3x

Step-by-step explanation:

If the line cannot be in quadrants II or IV, it must pass through the origin(0,0) and be in quadrants I and III.

Substitute (0,0) for y and x to find the answer.

1) x=3, 0=3 NO

2) y=3x, 0=3(0), 0=0 YES

3) y=3x+3, 0=3(0)+3, 0=3 NO

4) y=-3x-3, 0=-3(0)-3, 0=-3 NO

So the answer must be 2) y=3x

Answer:

He can be on either the lower end of that 95%, or on the higher end. this guy is not a too short, nor is he extremely tall.

Sry if it's nor right, It was a little confusing.

Hope this helps!（づ￣3￣）づ╭❤～

He can be on either the lower end of that 95%, or on the higher end.

This guy is not too short, nor is he extremely tall.

We have given that

Height =2

Everything on the normal model is within 2 standard deviations away from the mean.

The standard deviation is a measure of the amount of variation or dispersion of a set of values.

So He can be on either the lower end of that 95%, or on the higher end.

This guy is not too short, nor is he extremely tall.

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Answer:

Step-by-step explanation:

Hello,

[tex]f(g(x))=\dfrac{8}{x^2}+4[/tex]

So if we take

[tex]f(x)=\dfrac{8}{x}+4 \ \ and \\\\g(x)=x^2\\ \\f(g(x))=\dfrac{8}{g(x)}+4=\dfrac{8}{x^2}+4[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

The standard error of the sample mean is [tex]\sigma_{\= x } = 0.40[/tex]

Step-by-step explanation:

From the question we are told that

     The population mean is  [tex]\mu = 5.30 \ hours[/tex]

     The population standard deviation is [tex]\sigma = 3.20 \ hours[/tex]

      The sample size is  [tex]n = 64[/tex]

Generally the standard error of the sample mean is mathematically represented as

               [tex]\sigma_{\= x } = \frac{\sigma}{\sqrt{n} }[/tex]

substituting values

                [tex]\sigma_{\= x } = \frac{3.20}{\sqrt{64} }[/tex]

                [tex]\sigma_{\= x } = 0.40[/tex]

Answer:

shown below..I can't see..

Answer:

93.5 for area

Step-by-step explanation:

there is no picture so that's  a simple guess

Answer:

At 3 hours, the trains will be equidistant from the station.

Step-by-step explanation:

The first train leaves at 75 miles per hour and has a 2 hour head start.  This will put the first train at mile marker 150 (75 * 2) when the second train leaves the station at 125 mph.

To solve when they will be near each other, we set up an equation to solve for t.

150 + 75t = 125t

150 = 50t

3 = t

So given this value, we know the trains will be equidistant from the train station on parallel tracks after 3 hours.

Cheers.

Answer:

a; H0: u= 140 Ha: u ≠ 140 two tailed test.

b. Therefore reject H0 as t= 3 ≠ t≤ t ( ∝/2) (n-1) =2.353 or

3 > t ( ∝/2) (n-1) =2.353    

c. If we check from the table the p- value is 0.6 which lies between 0.1 and 0.05  therefore reject H0.

d. Again reject H0 as 140 < 150.163

e. A type II error has not been committed as H0 is rejected.

Step-by-step explanation:

We formulate the null and alternative hypotheses as

a; H0: u= 140 Ha: u ≠ 140 two tailed test.

For a two tailed test the significance level ∝= 0.1 the critical region is given by

t ≤ t ( ∝/2) (n-1) and t > t ( ∝/2) (n-1)

So the critical region will be

t≤ t ( ∝/2) (n-1) =2.353

where

t= x` - u / s/ √n

Sr. No X X²

1 150 22500

2 150 22500

3 180 32400

4 170 28900

∑ 650 106,300

X`= ∑x/n = 650/4= 162.5

s²= 1/n-1 (x-x`)²= 1/n-1 [ ∑x² -(∑x)²/n ]

= 1/3[106,300 -650²/4] = 225

s= 15

Putting the values in the above equation

t= 162.5- 140/ 15/ √4

t= 3

So calculated value of t= 3

b. Therefore reject H0 as t= 3 ≠ t≤ t ( ∝/2) (n-1) =2.353 or

3 > t ( ∝/2) (n-1) =2.353    

c. If we check from the table the p- value is 0.6 which lies between 0.1 and 0.05  therefore reject H0.

d. a 90% confidence interval based on the calculated values will be

x`± 1.645 (s)/ √n

Putting the values

162.5 ±1.645 ( 15/2)

162.5 ±12.3375

174.84 , 150.163

d. Again reject H0 as 140 < 150.163

e. A type II error has not been committed as H0 is rejected.

Answer:

20 days

Step-by-step explanation:

Renting a car costs $30 per day.

y = 30x

Renting a car costs $600 per month

y = 600

Set the two equations equal to each other.

30x = 600

(30x)/30 = (600)/30

x = 20

After 20 days, the two options have an equal cost.

Answer:

  0.4 meters

Step-by-step explanation:

The volume is ...

  V = LHB

  12.8 m³ = (8(5B))(5B)(B) = 200B³ . . . fill in given values

  0.064 m³ = B³ . . . . . simplify

  ∛0.064 m = B = 0.4 m

The breadth of the wall is 0.4 meters.

Answer:

So option B is the answer.

If x + 2 is the only factor of the polynomial P(x) then we need to find the P(2) is Not Zero. Therefore, the option B is the correct answer.

Suppose the considered polynomial is of only one variable.

Then, the standard form of that polynomial is the one in which all the terms with higher exponents are written on left side to those which have lower exponents.

Given information;

If x + 2 is the only factor of the polynomial P(x) then we need to find the P(2) :

P(x) = x + 2

p(2) = 2 + 2

p(2) = 4

The P(2) is Not Zero.

Therefore, the option B is the correct answer.

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Answer:

x≥4

Step-by-step explanation:

The required solution for the inequality 5 - 2x ≤ -3 is x ≥ 4 or x ∈ [4, ∞).

Inequality shows relation between two expression which are not equal to each others.

The given inequality is,

5 - 2x ≤ -3.

Solve the inequality,

Add 3 to both the sides,

5 - 2x + 3 ≤ -3 + 3

8 - 2x ≤ 0

-2x  ≤ -8

Multiply -1 both the sides,

2x ≥ 8

x ≥ 4

The solution for the inequality is x ≥ 4 or x ∈ [4, ∞).

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With such a larger sample size, the margin of error lowers (grows or decreases), whereas, at a higher confidence level, it increases (increases or declines).

             Margin of error [tex](E) = Z_c * {\frac{\sigma}{\sqrt{n}}}[/tex]

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Answer:

2/3

Step-by-step explanation:

We can find the slope using the slope formula

m = ( y2-y1)/(x2-x1)

   = (1- -7)/(9 - -3)

   = ( 1+7)/( 9+3)

   = 8/12

Simplifying

   = 2/3

Answer:

C. 2/3

Step-by-step explanation:

You can use the equation: [tex]y_{2} - y_{1}/x_{2} - x_{1}[/tex] to find the slope.

y2 is equal to the y coordinate of the second point: 1

y1 is equal to the y coordinate of the first point: -7

x2 is equal to the x coordinate of the second point: 9

x1 is equal to the x coordinate of the first point: -3

So if you plug these values into the equation, you will get:

1 - (-7)/ 9- (-3)

= 1 + 7/ 9 + 3

= 8/12

= 2/3

Answer:

c

Step-by-step explanation:

c. a descriptive technique