Simplify :
4a(6) + 3a

1. 24 a2 + 3 a
2. 13 a
3. 27 a
4. 27 a2

Answer:

The total weight of the purchased cherries is [tex]11\frac{1}{4}[/tex] pounds.

Step-by-step explanation:

Multiply [tex]2\frac{1}{4}[/tex] by 5.

[tex]2\frac{1}{4} * 5 = 11 \frac{1}{4}[/tex]

Answer:

11.25 or 45/4

Step-by-step explanation:

2 1/4 times 5

Answer:

45.5

Step-by-step explanation: NUN

Answer: 0.4207

Step-by-step explanation:

Let [tex]\overline{x}[/tex] be the sample mean area.

Given: Population mean : [tex]\mu=250[/tex] sq. feet

Standard deviation: [tex]\sigma=2[/tex] sq. feet

Sample size : n= 10

The probability that the sample mean area is [tex]249.6 \text{ ft}^2[/tex] or less if the manufacturer’s claim is true.

[tex]P(\overline{x}<249.6)=P(\dfrac{\overline{x}-\mu}{\sigma}<\dfrac{249.6-250}{2})\\\\= P(z<-0.2)\ \ \ \ [z=\dfrac{\overline{x}-\mu}{\sigma}]\\\\=1-P(z<0.2)\\=1- 0.5793\\\\=0.4207[/tex]

Required probability = 0.4207

Using the normal distribution and the central limit theorem, it is found that the probability that the sample mean area is 249.6 ft^2 or less if the manufacturer’s claim is true is of 0.2636.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem:

The probability that the sample mean area is 249.6 ft^2 or less if the manufacturer’s claim is true is the p-value of Z when X = 249.6, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{249.6 - 250}{\frac{2}{\sqrt{10}}}[/tex]

[tex]Z = -0.6325[/tex]

[tex]Z = -0.6325[/tex] has a p-value of 0.2636, which is the probability.

To learn more about the normal distribution and the central limit theorem, you can take a look at https://brainly.com/question/24663213

Answer:

f(-4)   =20

Step-by-step explanation:

f(-4) =  [tex](4)^{2}[/tex] +4 ( Insert -4 in)

f(-4) = 16+4

f(-4)   =20

Answer:

The minimum sample size needed is 68.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

Assuming that the standard deviation of the population of systolic blood pressures of executives of major corporations is 25 mm Hg.

This means that [tex]\sigma = 25[/tex]

What is the minimum sample size needed for the researcher to be 90% confident that his estimate is within 5 mm Hg of u?

This minimum sample size is n.

n is found when M = 5. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]5 = 1.645\frac{25}{\sqrt{n}}[/tex]

[tex]5\sqrt{n} = 1.645*25[/tex]

Dividing both sides by 5

[tex]\sqrt{n} = 1.645*5[/tex]

[tex](\sqrt{n})^2 = (1.645*5)^2[/tex]

[tex]n = 67.65[/tex]

Rounding up:

The minimum sample size needed is 68.

Answer:

89 degrees

Step-by-step explanation:

Answer:

91 degrees

Step-by-step explanation:

180-89=91 degrees

180 is the line that 89 degrees is on.

Answer:

2y+12

Step-by-step explanation:

First you subtract 5 and 3 so that you can combine them. THen, you put the solution together.

Answer:

6

Step-by-step explanation:

Nonagon=9sides

Triangle=3sides

Difference=9-3=6

Answer:

15+25x

i guess it is done this way

sry if it is wrong

Answer:

i cant read it it pretty but i still cant read it sorry

Step-by-step explanation:

sorry

Answer:

what are the questions

Step-by-step explanation:

Answer:

360

Step-by-step explanation:

Volume of a rectangle is length times width times height

Answer:

B. The product of 5 and a number.

Product means multiplication is taking place. In this case, 5 is being multiplied with n.

Hope this helps!

Answer:

D is the answer

Step-by-step explanation:

2j²/3k⁴ simplified form

The answer is The last answer choice 2j to the power of 2 over 3k to the power of 4

The area is given exactly by the definite integral,

[tex]\displaystyle\int_{-3}^2(x^2+4)\,\mathrm dx=\left(\frac{x^3}3+5x\right)\bigg|_{-3}^2=\frac{95}3\approx31.67[/tex]

We can write this as a Riemann sum, i.e. the infinite sum of rectangular areas:

• Split up the integration interval into n equally-spaced subintervals, each with length (2 - (-3))/n = 5/n - - this will be the width of each rectangle. The intervals would then be

[-3, -3 + 5/n], [-3 + 5/n, -3 + 10/n], …, [-3 + 5(n - 1)/n, 2]

• Over each subinterval, take the function value at some point x * to be the height.

Then the area is given by

[tex]\displaystyle\lim_{n\to\infty}\sum_{k=1}^nf(x^*)\Delta x_k=\lim_{n\to\infty}\sum_{k=1}^nf(x^*)\frac5n[/tex]

Now, if we take x * to be the left endpoint of each subinterval, we have

x * = -3 + 5(k - 1)/n   →   f (x *) = (-3 + 5(k - 1)/n)² + 4

If we instead take x * to be the right endpoint, then

x * = -3 + 5k/n   →   f (x *) = (-3 + 5k/n)² + 4

So as a Riemann sum, the area is represented by

[tex]\displaystyle\lim_{n\to\infty}\sum_{k=1}^n\left(\left(-3+\frac{5k}n\right)^2+4\right)\frac5n[/tex]

and if you expand the summand, this is the same as

[tex]\displaystyle\lim_{n\to\infty}\sum_{k=1}^n\left(13-\frac{30k}n+\frac{25k^2}{n^2}\right)\frac5n=\lim_{n\to\infty}\sum_{k=1}^n\left(\frac{65}n-\frac{150k}{n^2}+\frac{125k^2}{n^3}\right)[/tex]

So from the given choices, the correct ones are

• row 1, column 1

• row 2, column 2

• row 4, column 2

Answer:

Step-by-step explanation:

Answer:

4,331.25 in interest

Step-by-step explanation:

22,500.00x3.5%=787.50x5.5=4,331.25

22,500.00+4,331.25=26,831.25 total loan

Jim buys a car for $22,500. He decides to finance through the dealership at 3.5% simple interest for 5.5 years.The loan amount Jim will pay over the course of 5.5 years is $26,823.75.

To calculate the interest Jim will pay and the total loan amount over 5.5 years, we can use the formula for simple interest:

Interest = Principal * Rate * Time

Total Loan = Principal + Interest

Given:

Principal (P) = $22,500

Rate (R) = 3.5% (expressed as a decimal, 0.035)

Time (T) = 5.5 years

Calculating the interest:

Interest = $22,500 * 0.035 * 5.5

Interest = $4,323.75

Jim will pay $4,323.75 in interest over the course of 5.5 years.

Calculating the total loan:

Total Loan = Principal + Interest

Total Loan = $22,500 + $4,323.75

Total Loan = $26,823.75

Therefore, the loan amount Jim will pay over the course of 5.5 years is $26,823.75.

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Full question

Jim buys a car for $22,500. He decides to finance through the dealership at 3.5% simple interest for 5.5 years. How much interest will he pay? What is the loan Jim will pay over the course of the 5.5 years?

( No graph Needed)

Answer:

<1 = 43

<2= 17

<3= 120

<4=60

<5= 60

<6= 60

<7 =17

<8= 120

<9= 43

Step-by-step explanation:

< 4, <5, <6 are all 60

<3 and <4 are a linear pair, so they add to 180. Since <4 is 60, <3 is 180-60= 120

<6 and <8 are a linear pair, so they add to 180. Since <6 is 60, <8 is 180-60= 120

Angles 1 and 9 are congruent

4x+3=9x-47

50=5x

10=x

<1= 4(10)+4= 43

<9-9(10)-47=43

Now you have 2 angles for the triangle A B D- subtract the 2 known from 180

<2= 180-43-120=17

<7= 180-43-120=17

Answer:

c the answer is c just trust me

Answer:

The original price was $312.50

Step-by-step explanation:

If the vacuum was marked down by 20%, that means it was sold for 80% of the full price. It was sold for $250, so 80% of the original price is $250.

Let's set up an equation.

80/100 of x = 250

0.8 • x = 250

Divide both sides by 0.8.

x = 312.50

The original price was $312.50

Hope this helps!

Answer:

I think the answer is 250.00

Step-by-step explanation:

Let the original price = x

  Original Price     -     Markdown       =     Sales Price

       x                 -     (20%)x           =         $250

  Note: 20% may be 0.20 or 20/100 as needed by the problem.

       x                -    0.20x                =         $250

      0.80x = $250

           x =   $312.50

Check:

     Is      312.50  -  (0.20)312.50  = 250.00   ?

               (0.80)(312.50) = 250.00   ?

                    250.00 = 250.00   ?yes

Hope this help you! :)

Answer:

Step-by-step explanation:

7 is 1

8 is 2

Answer:

f(x) = (x + 1)*(4*x² - 3*x + 4) - 12

Step-by-step explanation:

We have:

f(x) = 4*x³ + x² + x - 8

We want to write this in:

f(x) = (x - k)*q(x) + r.

with k = -1

Then we want to write:

4*x³ + x² + x - 8 = (x - (-1))*q(x) + r

4*x³ + x² + x - 8 = (x + 1)*q(x) + r

Because f(x) is polynomial of degree 3, we know that q(x) must be a polynomial of degree 2.

then:

q(x) = a*x² + b*x + c

Then:

4*x³ + x² + x - 8 = (x + 1)*(a*x² + b*x + c) + r

4*x³ + x² + x - 8 = a*x³ + b*x² + c*x   + a*x² + b*x + c + r

if we take common factors in the right side we get:

4*x³ + x² + x - 8 = a*x³ + (b + a)*x² + (c + b)*x + (c + r)

Now, we must have:

4*x³ = a*x³

then:

4 = a

We also must have:

x² = (b + a)*x²

1 = (b + 4)

1 - 4 = b

-3 = b

We also must have:

x = (c + b)*x

1 = (c + (-3))

1 + 3 = c

4 = c

And finally:

- 8 =  (c + r)

-8 = 4 + r

-8 - 4 = r

-12 = r

Then:

f(x) = (x + 1)*(4*x² - 3*x + 4) - 12

Answer:

^5 √ 10

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:E

Step-by-step explanation:

( row total * column total ) / ( Table total)

9514 1404 393

Answer:

  12.  x = 5

  13.  -8, 0

  14.  6

Step-by-step explanation:

12. The area of a square with side length s is ...

  A = s²

The problem statement tells us the relationship between the areas is ...

  (x cm)² = (1/9)(15 cm)²

Taking the square root, we have ...

  x cm = (1/3)(15 cm)

  x cm = 5 cm . . . . . . . simplify

  x = 5

__

13. The rule is ...

  a[n] = (a[n-1] +8)/2 = (1/2)a[n-1] +4

For a[1] = -24, a[2] = (1/2)(-24) +4 = -8

For a[2] = -8, a[3] = (1/2)(-8) +4 = 0

The next two terms are -8 and 0.

__

14. The rule is ...

  a[n] = (a[n-1] -1)×5

Solving for the previous term, we find ...

  a[n] = 5·a[n-1] -5 . . . . . eliminate parentheses

  a[n] +5 = 5·a[n -1] . . . . add 5

  a[n-1] = (a[n] +5)/5 . . . . divide by 5

For a[3] = 120, a[2] = (120 +5)/5 = 25

For a[2] = 25, a[1] = (25 +5)/5 = 6

The first term of the sequence is 6.

Answer:

a straight line i think is always 180 so i think the answer is A. 81

Step-by-step explanation:

The solution is (4, 125). This means that the cost of being in soccer and band for four months is the same, $125. It's where the costs of those two clubs intersect.

Step-by-step explanation:

The solution to a system of linear equations is the point where the two functions intersect. You can see from the graph that the two lines intersect at the point (4, 125)

Answer:

Step-by-step explanation:

Suppose that f(2) = −4, g(2) = 3, f '(2) = −5, and g'(2) = 1.

Find h'(2).

(a)    h(x) = 4f(x) − 5g(x)

Use the constant multiple and difference rules:

h'(x) = 4f '(x) − 5g'(x)

h'(2) = 4*f'(2) − 5*g'(2), now substitute values and solve

h'(2) = 4*(−5) − 5*1 = −20 − 5 = −25

Answer:

A

Step-by-step explanation:

950 is 95% of 1000

so he lost 5 percent, which can be represented as -5.0%

Answer:

Step-by-step explanation:

because the value went down.. we know the the rate of return , is negative.  then we just have to think about , how much is 50 of 1000 ??  well 10 is 10% of 100 right?  so 100 is 10% or 1000,  right?  sooo  half of 100, or 50, is 5% of 1000,  

so -5% is the return on investment (roi)

Answer:

x = 6

Step-by-step explanation:

From the diagram AB = BC

4x-9 = 15

Add to both sides

4x-9+9 = 15 + 9

4x = 24

Divide both sides by 4

4x/4 = 24/4

x = 6

Hence the value of x is 6

Answer:

1) A

2) A

3) D

4) B

5) D

Step-by-step explanation:

__________________________________________________________

FACTS TO KNOW BEFORE SOLVING :-

If any 2 parallel lines are cut by a transversal line , then :-

__________________________________________________________

Q1)

According to the figure on the right side of the question paper ,

So,

∠7 + ∠8 = 180°

⇒ ∠2 + ∠8 = 180°    (∵ ∠2 = ∠7)

Hence , we can conclude that interior angles of same side are supplementary angles. So the correct option is A.

Q2)

According to the figure on the question paper ,

So ,

∠1 + ∠3 = 180°

⇒ ∠5 + ∠3 = 180°  (∵ ∠1 = ∠5)

Hence , we can conclude that exterior angles on the same side are supplementary angles. So , the correct option is A.

Q3)

According to the figure , (∠2 , ∠7) & (∠1 , ∠8) are alternate interior angles. But as (∠1 , ∠8) is there as an option , so the correct option is D.

Q4)

According to the figure , m∠1 = 129°.

Also , ∠1 & ∠7 are interior angles on the same side.

⇒ They are supplementary angles.

⇒ ∠1 + ∠7 = 180°

⇒ ∠7 = 180° - 129° = 51°

So , the correct option is B.

Q5)

According to the figure , m∠2 = 3x - 10 and m∠6 = 2x + 20

Also , ∠2 = ∠6 (∵ Corresponding angles are equal)

⇒ 3x - 10 = 2x + 20

⇒ 3x - 2x = 20 + 10

⇒ x = 30

So , ∠2 = 3×30 - 10 = 80° = ∠6 (∵ Corresponding angles are equal)

Hence , the correct option is D.