with work please and thanks

Answer:

A

Step-by-step explanation:

Recall that the sum of an arithmetic series is given by:

[tex]\displaystyle S = \frac{n}{2}\left(a + x_n\right)[/tex]

Where n is the number of terms, a is the first term, and x_n is the last term.

We know that the initial term a is 13, the common difference is 7, and the total sum is 2613. Since we want to find the number of terms, we want to find n.

First, find the last term. Recall that the direct formula for an arithmetic sequence is given by:

[tex]x_n=a+d(n-1)[/tex]

Since the initial term is 13 and the common difference is 7:

[tex]x_n=13+7(n-1)[/tex]

Substitute:

[tex]\displaystyle S = \frac{n}{2}\left(a + (13+7(n-1)\right)[/tex]

We are given that the initial term is 13 and the sum is 2613. Substitute:

[tex]\displaystyle (2613)=\frac{n}{2}((13)+(13+7(n-1)))[/tex]

Solve for n. Multiply both sides by two and combine like terms:

[tex]5226 = n(26+7(n-1))[/tex]

Distribute:

[tex]5226 = n (26+7n-7)[/tex]

Simplify:

[tex]5226 = 7n^2+19n[/tex]

Isolate the equation:

[tex]7n^2+19n-5226=0[/tex]

We can use the quadratic formula:

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

In this case, a = 7, b = 19, and c = -5226. Substitute:

[tex]\displaystyle x =\frac{-(19)\pm\sqrt{(19)^2-4(7)(-5226)}}{2(7)}[/tex]

Evaluate:

[tex]\displaystyle x = \frac{-19\pm\sqrt{146689}}{14} = \frac{-19\pm 383}{14}[/tex]

Evaluate for each case:

[tex]\displaystyle x _ 1 = \frac{-19+383}{14} = 26\text{ or } x _ 2 = \frac{-19-383}{14}=-\frac{201}{7}[/tex]

We can ignore the second solution since it is negative and non-natural.

Therefore, there are 26 terms in the arithmetic series.

Our answer is A.

Answer:

90

Step-by-step explanation:

We know that area of ∆BCD = half of the area of rectangle BEFD, since any triangle drawn from taking a side and base and a point on the opposite side as the 3rd vertex has the half area of the rectangle

so, area of ∆BCD = 15×12/2 = 90 (since two legs of the right triangle are 15 and 12)

since area ∆BCD is half the area rectangle BEFD and sum of the area of ∆BEC and ∆CFD will be the rest of the area of rectangle BEFD, which is 90

Answer:

3.398

Step-by-step explanation:

log(2500)=log(25)+log(100)=2+2*0.699=3.398

Answer:

a)

Step-by-step explanation:

Step-by-step explanation:

Lets translate this word problem into math.

"Latoya's annual salary is $26,000" = We start with the number 26,000

"A total of $7352.24 will be deducted for taxes and health insurance" = It's the number we started with "deducted" (minus) 7352.24

"She will receive her paycheck monthly in 12 equal installments" = Our number will be divided by 12

"How much will she get paid with each paycheck?" = "Find answer pls thx"

To put it all together...

[tex]\frac{26,000-7,352.24}{12}[/tex]

Now all we have to do is solve!

[tex]\frac{26,000-7,352.24}{12}[/tex]

[tex]\frac{18,647.76}{12}[/tex]

[tex]1,553.98[/tex]

Answer:

Latoya will get paid $1,553.98 with each paycheck.

Answer:

B.y = 3x - 1

Step-by-step explanation:

Pick two points on the line

(0,1) and (2,5)

The slope using the slope formula

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

   = ( 5-1)/(2-0)

  = 4/2

  = 2

We want a slope that is greater than 2

The slope intercept form of the equation is

y = mx+b where m is the slope

y = 3x - 1  has a slope of 3 which is greater than 2

Answer:

16°

Step-by-step explanation:

For this problem, it's helpful to know SOH-CAH-TOA. When you see which sides are given, you can use that acronym to figure out which trigonometric function you need to use. In this case, the side adjacent to the angle in question (53) and the hypothenuse (55) are given. So we would look at CAH, and know we need to use cosine. However, since we are finding an angle, we need to use [tex]cos^{-1}[/tex] (inverse cosine). Now we just solve:

? = [tex]cos^{-1} (adjacent / hypotenuse)[/tex]

? = [tex]cos^{-1} (53/55)[/tex]

? = 15.5° -> 16°

Answer:

13

Step-by-step explanation:

We know that a^2+b^2 = c^2  where a and b are the legs and c is the hypotenuse

5^2 + 12^2 = c^2

25+144 = c^2

169 = c^2

Taking the square root of each side

sqrt(169) = sqrt(c^2)

13 =c

Answer:

Step-by-step explanation:

Hello!

1-3

Answer:

1/8

Step-by-step explanation:

f^-1 part makes it into a fraction

Answer:

(E) [tex]y=x+3[/tex]

Step-by-step explanation:

Hi there!

Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis).

1) Determine the slope (m)

[tex]m=\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex] where two points that fall on the line are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the given points (-4,-1) and ( -1,2):

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

Therefore, the slope of the line is 1. Plug this into [tex]y=mx+b[/tex]:

[tex]y=1x+b\\y=x+b[/tex]

2) Determine the y-intercept (b)

[tex]y=x+b[/tex]

Plug in one of the given points and solve for b:

[tex]2=-1+b\\2+1=b\\3=b[/tex]

Therefore, the y-intercept of the line is 3. Plug this back into the original equation:

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

I hope this helps!

Answer:

12

Step-by-step explanation:

f(x)=16x-30

g(x)=14x-6

f(x) - g(x) = 16x-30 - (14x-6)

               = 16x - 30 - 14x +6

                = 2x -24

Set this equal to zero

2x-24 = 0

Add 24 to each side

2x-24 +24 = 0+24

2x = 24

Divide by 2

2x/2 =24/2

x = 12

x=12

Answer:

Solution given:

f(x)=16x-30 and g(x)=14x-6

(f-g)(x)=0

or

f(x)-g(x)=0

16x-30-14x+6=0

2x-24=0

2x=24

x=24/2

x=12

Answer:

There are enough oysters

Step-by-step explanation:

Given

[tex]Volume = 18\ trillion\ gallon[/tex]

[tex]Area = 2867200\ acre[/tex]

[tex]1\ acre = 750000\ oysters[/tex]

[tex]1\ oyster = 50\ gallons[/tex]

Required

Determine if there is enough water for a day

We have:

[tex]1\ oyster = 50\ gallons[/tex]

Convert to oysters: multiply both sides by 750000

[tex]750000 * 1\ oyster = 50\ gallon *750000[/tex]

[tex]750000\ oysters = 37500000\ gallons[/tex]

Given that:

[tex]1\ acre = 750000\ oysters[/tex]

So, we have:

[tex]1\ acre= 37500000\ gallons[/tex]

Convert to acre: Multiply by 2867200

[tex]2867200 * 1\ acre= 37500000\ gallons * 2867200[/tex]

[tex]2867200\ acres= 107520000000000\ gallons[/tex]

By comparison:

[tex]18000000000000\ gallons < 107520000000000\ gallons[/tex]

i.e. the volume of water in the bay is less than the capacity of the oysters. Hence, there are enough oysters.

Answer:

Step-by-step explanation:

15) should be b) 6.7, 6 as the median is the average of the 25th and 26th result, these both occur in the 6 group and is the only option with a whole number for median

To check the mean

(2(4) + 7(5) + 17(6) + 10(7) + 8(8) + 6(9)) / 50 = 6.66 ≈ 6.7

16) mode is 1 child as the single largest grouping is 11 families

there were 46 families polled so the median occurs between 23 and 24

7 + 11 + 6 is 24 therefore median falls under 2 children.

a) 1, 2

Answer:

P=2(74)+2(5)

148+10=158

Answer:

the real is -19

the imaginary is -24 (or -24i depending on what the computer is looking for as an answer)

Step-by-step explanation:

Answer:

Rectangular prism- 12 edges

Rectangular pyramid- 8 edges

Triangular pyramid- 6 edges

Triangular prism- 9 edges

I hope this helps!

At a rate of interest of 3.86% compounded annually investment will be tripled.

that is how i was taut, sorry if is wrong

Answer:

He must sell 1390 carrots

Step-by-step explanation:

30x + 300x/30 = 55500

40x = 55500

x = 1387.5

1387.5

multiply 30 by .3 to get $9 for 30 carrots

Then add $3 to this amount to get $12 dollars.

Divide 555 by 12 to get 46 R3.

Multiply 46 by 30 because its 46 bundles of 30 carrots

Then divide the 3 dollars by .3 for each carrot to get 10 carrots

1380+10 = 1390

Hasib must sell 1390 carrots in order to earn $555.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Given information; Hasib earns 30 cents for every carrot he sells. He earns an extra $3 for every 30 carrots he sells.

So, the equation form;

30x + 300x/30 = 55500

40x = 55500

x = 1387.5

Now, multiply 30 by .3 to get $9 for 30 carrots

Then add $3 + 9 = $12 dollars.

Now, Divide 555/ 12 = 46 R3.

46 x 30  = 1380  because its 46 bundles of 30 carrots

For each carrot to get 10 carrots

1380 + 10 = 1390

Therefore, Hasib must sell 1390 carrots in order to earn $555.

Learn more about equations here;

https://brainly.com/question/10413253

#SPJ2

Answer:

Yes

Step-by-step explanation:

It's a right angled triangle as 14^2+48^2=50^2.

Answer:

Step-by-step explanation:

a) 9.5 feet above the ground

b)  max height at  of 34.5 feet  5 feet horizontal distance

c) 10.87 feet away

Step-by-step explanation:

here's the answer to your question

Answer:

2(10y + 40 -11xy)

Step-by-step explanation:

First, multiply the expression

20y +80 -6xy - 16xy

Then collect like terms

20y + 80- 22xy

And then lastly factories the expression

2( 10y + 40- 11xy )

Step-by-step explanation:

Therefore, the degree of polynomial √3 is zero.

[tex]\sf\huge\underline\color{pink}{༄Answer:}[/tex]

[tex]\tt{\sqrt{3}}[/tex] is a polynomial of degree 0

[tex]\sf\huge\underline\color{pinl}{༄Note:}[/tex]

[tex]\color{pink}{==========================}[/tex]

-#CarryOnLearning

-༄⁂✰Park Hana Moon

Answer:

22 mm

Step-by-step explanation:

Answer:

A unit rate is a rate with 1 in the denominator. If you have a rate, such as price per some number of items, and the quantity in the denominator is not 1, you can calculate unit rate or price per unit by completing the division operation: numerator divided by denominator.

Answer:

Multiplication:

Step 1: Factor both the numerator and the denominator.

Step 2: Write as one fraction.  Write it as a product of the factors of the numerators over the product of the factors of the denominators. DO NOT multiply anything out at this point.

Step 3: Simplify the rational expression.

Step 4: Multiply any remaining factors in the numerator and/or denominator.

Division:

Step 1: Completely factor both the numerators and denominators of all fractions.

Step 2: Change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal.

Step 3: Cancel or reduce the fractions. Remember that to reduce fractions; you can cancel something in the numerator with something in the denominator, but in order to cancel something in the numerator and denominator the two factors must be EXACTLY the same.

Step 4: Rewrite the remaining factor. Notice that you do NOT need to actually multiply anything in the numerator or denominator.

Answer:

a) A(x)  = 90*x/2  -  x²/2

b) A(max) = 1012.5 m²

Step-by-step explanation:

L = 90 meters of fencing

Rectangular area is

A(r) = x*y .            where  x  and  y  are the sides of the rectangle

the perimeter is  ( we are going to fence only 3 sides, then)

x + 2*y = 90    or .    y  = ( 90  - x ) /2

Area as a function of x is:

A(x)  = x * ( 90 - x)/2

A(x)  = 90*x/2  -  x²/2

Tacking derivatives on both sides of the equation:

A´(x) =45  -  2*x/2         A´(x) =45  - x

A´(x) = 0 .      45  - x = 0 .      x  = 45 . meters

and . y   =  ( 90  - x ) 2

y = ( 90- 45 )/2  

y = 22.5 meters

A(max) =  45*22.5  m²

A(max) = 1012.5 m²

If we get the second derivative of A(x) .  A"(x) = - 1       A"(x) < 0

Then A(x) has a maximum for x = 45