Persons taking a 30-hour review course to prepare for a standardized exam average a score of 620 on that exam. Persons taking a 70-hour review course average a score of 749. Find a linear equation which fits this data, and use this equation to predict an average score for persons taking a 57-hour review course. Round your answer to the tenths place.

Answer:

(mn+3m)(n+p)

Step-by-step explanation:

Answer:

(mn + 3m)(n + p)

Step-by-step explanation:

Factorize by grouping:

[tex]mn^2+mnp\\mn(n+p)\\\\3mn+3mp\\3m(n+p)\\\\(mn+3m)(n+p)[/tex]

9514 1404 393

Answer:

  (a)  1/12

Step-by-step explanation:

The difference of adjacent terms is ...

  1/4 -1/6 = 3/12 -2/12 = 1/12

Solution :

Case I :

If Collen is late on [tex]0[/tex] out of [tex]5[/tex] days.

[tex]$= \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} $[/tex]

[tex]$=\frac{1}{32}[/tex]

Case II :

When Collen is late on [tex]1[/tex] out of [tex]5[/tex] days.

[tex]$= \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times ^5C_1$[/tex]

[tex]$=\frac{1}{32} \times 5$[/tex]

[tex]$=\frac{5}{32}[/tex]

Case III :

When Collen was late on [tex]2[/tex] out of [tex]5[/tex] days.

[tex]$= \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times ^5C_2$[/tex]

[tex]$=\frac{1}{32} \times 10$[/tex]

[tex]$=\frac{5}{16}[/tex]

Therefore, the [tex]\text{probability}[/tex] that Collen will arrive late to work no more than [tex]\text{twice}[/tex] during a [tex]\text{five day workweek}[/tex] is :

[tex]$=\frac{1}{32} + \frac{5}{32} + \frac{5}{16} $[/tex]

[tex]$=\frac{1}{2}$[/tex]

Answer:

17

Step-by-step explanation:

these positive integers are :

4, 64, 124, 184 ... , 964

964 = 4 + (n-1) (60)

964 = 4 + 60n -60

964 = 60n -56

60n = 1020

n = 1020/60

n = 17

so, the number of special integers smaller than 1000 are = 17

The digits n, n+1 and n+2 implies that the special numbers are consecutive i.e. they follow one another. The count of special numbers less than 1000 is 17.

Given that:

[tex]\{n,n+1,n+2\} = \{4,5,6\}[/tex]

[tex]Range = 1000[/tex]

First, calculate the LCM of 4, 5 and 6.

[tex]4 = 2 \times 2[/tex]

[tex]5 = 5[/tex]

[tex]6 = 2 \times 3[/tex]

So, the LCM is:

[tex]LCM = 2 \times 2 \times 5 \times 3[/tex]

[tex]LCM = 60[/tex]

This means that the special digit occurs after every other 60 digits (i.e. the difference between a special digit and another is 60)

To calculate the count of special digits, we make use of arithmetic progression formula

[tex]L = a + (n - 1) \times d[/tex]

Where

[tex]L = 1000[/tex] --- the last term

[tex]a = 4[/tex] --- the first special digit

[tex]d = 60[/tex] --- the common difference as explained above

So, we have:

[tex]L = a + (n - 1) \times d[/tex]

[tex]1000 = 4 + (n - 1) \times 60[/tex]

Collect like terms

[tex]1000 - 4 =(n - 1) \times 60[/tex]

[tex]996 =(n - 1) \times 60[/tex]

Divide both sides by 60

[tex]16.6 =n - 1[/tex]

Add 1 to both sides

[tex]1 + 16.6 =n[/tex]

[tex]17.6 =n[/tex]

Rewrite as:

[tex]n =17.6[/tex]

Remove the decimal part (do not approximate)

[tex]n =17[/tex]

Hence, the special numbers are 17 in total (that are less than 1000).

Read more about arithmetic progression at:

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Answer:

D. linear; y = –x – 1

Step-by-step explanation:

Linear; y=-x - 1

The slope is negative since it’s decreasing. So it’s not the first equation. It’s not a quadratic equation because there is no forming U shape for this data. It’s not a exponential function because the slope is not 3 and a exponential function is in the form y=a(b)^x

...............................................................................................................................................

Answer:

The correct answer is D) linear; y = –x – 1

Step-by-step explanation:

To find this, use any values in the table and it will produce a true statement. This is how we check to see if a model is correct. See the two examples below for proof.

(4, 5)

y = -x - 1

-5 = -4 - 1

- 5 = -5 (TRUE)

(0, -1)

y = -x - 1

-1 = 0 - 1

-1 = -1 (TRUE)

Answer: 81, 243, 729

Step-by-step explanation:

STEP ONE: Find a pattern in the sequence

3 ÷ 1 = 3

9 ÷ 3 = 3

27 ÷ 9 = 3

As we can see from the given sequence, each number multiplies 3 to get the next term.

STEP TWO: Find the next three terms

27 × 3 = 81

81 × 3 = 243

243 × 3 = 729

Hope this helps!! :)

Please let me know if you have any questions

Answer:

0.07245

Step-by-step explanation:

Just work out 345*21 and then divide by 10,000 because 0.345 is 3 digits from zero and 2.1 has 1 digit from zero, so total of 4 zeroes (10,000 since 10,000 has 4 zeroes).

Answer: ¿Hablas español porque no entiendo esto? Si lo haces, ¿puedes decirme en español?

Step-by-step explanation:

I thing it lies on the negativity side of the number line between -2,24

Answer:

- [tex]\frac{7}{4}[/tex]

Step-by-step explanation:

Given

- [tex]\frac{7}{10}[/tex] ÷ [tex]\frac{2}{5}[/tex]

Leave the first fraction

Change division to multiplication

Turn the second fraction upside down

= - [tex]\frac{7}{10}[/tex] × [tex]\frac{5}{2}[/tex] ← cancel 5 and 10 by 5

= - [tex]\frac{7}{2}[/tex] × [tex]\frac{1}{2}[/tex]

= - [tex]\frac{7(1)}{2(2)}[/tex]

= - [tex]\frac{7}{4}[/tex]

Step-by-step explanation:

Asymptote: y = 2 y-intercept: (0,8)

Step-by-step explanation:

The given function is

f(x) = 6(0.5)^{x} + 2f(x)=6(0.5)

x

+2

This function is of the form:

f(x) = a {b}^{x} + cf(x)=ab

x

+c

where y=c is the horizontal asymptote.

By comparing , we have c=2 hence the horizontal asymptote is

y = 2y=2

To find the y-intercept, we put x=0 into the function to get:

f(0) = 6(0.5)^{0} + 2 = 6 + 2 = 8f(0)=6(0.5)

0

+2=6+2=8

Therefore the y-intercept is (0,8).

9514 1404 393

Answer:

  (c)  CPCTC

Step-by-step explanation:

Even if you don't know the meaning of CPCTC, you can eliminate the other choices because they refer to the whole triangle, not two corresponding angles.

Angles B and D are corresponding angles in the congruent triangles. The reason they are congruent is ...

  Corresponding Parts of Congruent Triangles are Congruent (CPCTC)

Answer:

12 degrees

Step-by-step explanation:

Answer:

15 degrees

Step-by-step explanation:

okay haha

so basically the cosine of an angle is the side adjacent to it, divided by the hypotenuse. the sine is the side opposite to that angle divided by the hypotenuse, and the tangent is the side opposite to that angle divided by the side adjacent to it.

in this case we are given the angle and the side opposite to it which is 10, and we are also given the hypotenuse of 39.

what trig function deals with opposite and hypotenuse?

the answer is sine

so we would find the sine of that angle which equals to opposite over hypotenuse:

sin(angle) = 10/39

but, they are asking for the inverse trig function. the inverse of sine is arcsin.

so :

arcsin(10/39) = angle

in a calculator, this would be equal to about 14.857 which is closest to 15.

Answer:

D. 17

Step-by-step explanation:

No-

Answer:

Step-by-step explanation:

OK

Answer:

rshjgdlf

FGshjfgsfds

Step-by-step explanation:

GIMME'

Answer:

32 because I Don't know please vote my answer please

Answer:

12 (10) cm 937 637 = hafe 2929888389292822

Answer:

-32678141

Step-by-step explanation:

Answer:

4th option, x = -1 and x = 9

Step-by-step explanation:

3(x-4)²=75

or, (x-4)²=25

or, x²-8x+16-25=0

or, x²-8x-9=0

or, x²-9x+x-9=0

or, x(x-9)+1(x-9)=0

or, (x-9)(x+1)=0

so, x-9=0 or, x=9

and x+1=0 or, x=-1

The two solutions of the quadratic equation are:

x = -1 and x = 9

The quadratic equation is:

3*(x - 4)^2 = 75

We can expand it as:

3*x^2 - 3*2*4*x + 3*16 = 75

3x^2 - 24x  -27 = 0

Now, using Bhaskara's formula we get:

[tex]x = \frac{-(-24) \pm \sqrt{(-24)^2 - 4*3*(-27)} }{2*3} \\\\x = \frac{24 \pm 30 }{6}[/tex]

So the two solutions are:

x = (24 + 30)/6 = 9

x = (24 - 30)/6 = -1

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Answer:

pi × 18cm^2

Or approximately,

56.52cm^2 (using 3.14 for pi)

or

56.5487cm^2 (using pi button on calculator)

Step-by-step explanation:

Area of a circle is pi times [radius squared].

All circles are 360°.

Problem can be solved by finding area of whole circle, and then using ratios.

Whole Circle: area = pi × (9cm)^2 = pi × 81cm^2

80° / 360° = Area[shaded] / (pi × 81cm^2)

pi × 18cm^2 = Area[shaded]

((If you read my answer before the edit, I am sorry. I made a calculator error.))

Answer

33.3

Step-by-step explanation:

if u multiply the 2, and then find the ratio of them in comparison to the number under, you will find the rate decreases by 10 percent every time, the first situation it is 4/8 = 5/10, second situation is it 32/80= 4/10, and htis situation is most like 3/10, right ? so the answer would be 33.3 :)

Answer:

First, you have to add 9, 18, and 12. When we add this we get 39. She has 30 dollars, do we can see that she needs $9 more to get all three books.

Step-by-step explanation:

Answer:

Rajan = 436.36 rupees and Kamal = 363.63 rupees

Step-by-step explanation:

Total ratio = 11/30

Amount to be shared = 800

Rajan = Individual ratio / Total ratio x the total amount to be shared

1/5 ÷11/30 × 800 = 436.36

Kamal = 1/6 ÷ 11/30 × 800 = 363.63

Answer: Prime Factors for 18: 2, 3, and 3

Prime Factors for 19: 19

Prime Factors for 20: 2, 2, and 5

Can you mark brainlest

Step-by-step explanation:

The amount invested at 4% is 1500.

Let x be the amount invested at 4%.

2x be the amount invested at 5%.

0.04x + 0.05(2x) = 210

Multiply by 100 to eliminate decimals

4x + 5(2x) = 21000

Remove parentheses: (a) = a

[tex]4 x+5 \cdot 2 x=21000[/tex]

Multiply the numbers: [tex]$5 \cdot 2=10$[/tex]

4x+10x = 21000

Add similar elements:

4x+10x = 14x

14x=21000

Divide both sides by 14

[tex]$\frac{14 x}{14}=\frac{21000}{14}[/tex]

Simplifying the above equation, we get

x = 1500

The amount invested at 4% is 1500.

Therefore, the correct answer is option B) $1500.

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The area of one side of the coin is 41.605 mm².

Given that, the diameter of a $1 coin is 26.5 mm.

We need to find the area of one side of the coin.

The area of a circle formula is A=πr².

Now, radius=26.5/2=13.25 mm.

Area of a coin=3.14×13.25=41.605 mm².

Therefore, the area of one side of the coin is 41.605 mm².

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Answer:

B

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here the vertex = (- 2, - 3 ) , then

y = a(x - (- 2))² - 3 , that is

y = a(x + 2)² - 3

To find a, substitute any point on the graph into the equation

Using the coordinates of the y- intercept (0, 5 )

5 = a(0 + 2)² - 3 ( add 3 to both sides )

8 = a(2)² = 4a ( divide both sides by 4 )

2 = a

y = 2(x + 2)² - 3 → B

Answer:

-80

Step-by-step explanation:

We can write the quadratic as

ax^2 + bx+c

4x^2 +8x+9

a=4  b = 8  c=9

The discriminant is

b^2 -4ac

8^2 - 4(4)(9)

64 - 144

-80

Answer:

-80

Step-by-step explanation:

The discriminant is the value under the radical in the quadratic formula. The part of the quadratic formula that is under the radical is [tex]\sqrt{b^2-4ac}[/tex]. So, plug in the needed values and solve for what is under the radical. The b-value is 8; this squared is 64. Then, plug in a and c, 4 and 9. Then multiply these by 4, 4*4*9=144. Finally subtract, 64-144=-80.

Answer:

Length of x+3= 6.75

Length of 4x=15

Length of 3x-1=10,25

Step-by-step explanation: