find a8 of the sequence 10, 9.75, 9.5, 9.25

Answers

Answer 1

the 8th term would be 8.25 because it decreases by .25 each term. 10,9.75, 9.5, 9.25, 9, 8.75, 8.5, 8.25

Answer 2

Good evening.

Let:

[tex]\mathsf{a_1 = 10}\\ \mathsf{a_2=9.75}\\ \mathsf{a_3 = 9.5}\\ \mathsf{a_4 = 9.25}[/tex]

Note that:

[tex]\mathsf{a_2 -a_1 = a_3-a_2=a_4-a_3 = -0.25 = r}[/tex]

Now we can make the General term formula:

[tex]\mathsf{a_n= a_1 +(n-1)r}\\ \\ \boxed{\mathsf{a_n = 10 - (n-1)0.25}}[/tex]

Now we calculate a₈:

[tex]\mathsf{a_8 = 10-(8-1)0.25}\\ \\ \mathsf{a_8 = 10 - 7\cdot0.25}\\ \\ \mathsf{a_8 = 10 - 1.75}\\ \\ \boxed{\boxed{\mathsf{a_8=8.25}}}[/tex]

Related Questions

A car dealer recently sold five cars for the following profits: $10,126, $9,999, $12,398, $12,007, and $4,567. What was the mean for the profits of the sales?

Answers

Mean or Average is all of the sums divided by how many of the choices are there, so all of 10,126+9,99+12,398+12,007+4567=49097 and divided by all the choices you have which is 5 is 9819.4

Answer:

$9819.4

Step-by-step explanation:

We have been given that a car dealer recently sold five cars for the following profits: $10,126, $9,999, $12,398, $12,007, and $4,567. We are asked to find the mean for the profits of the sales.

Since mean is the average of numbers. So let us add all the profits and divide the sum of profits by number of cars.

[tex]\text{Mean for the profits of the sales}=\frac{10126+9999+12398+12007+4567}{5}[/tex]

[tex]\text{Mean for the profits of the sales}=\frac{49097}{5}[/tex]

[tex]\text{Mean for the profits of the sales}=9819.4[/tex]

Therefore, the mean for the profits of sales is $9819.4.

An architectural drawing lists the scale as 1/4 = 1. If a bedroom measures 3 1/2 by 5 1/4 on the drawing, how large is the bedroom

Answers

The bedroom is 14x21. I hope this helps :)

Answer:

The measure of the bedroom is 14 by 21

Step-by-step explanation:

This scale represents the every measure in the drawing is a 1/4 of the original measure, so to find the original measure you must multiply the measure you find in the drawing by 4.

So for the beadroom (3 1/2, 5 1/4), you multiply each one by 4

The real measures of the beadroom are:

(3 1/2 * 4, 5 1/4 * 4)

(14,21)

The measure of the bedroom is 14 by 21

The restaurant bill you and your friend received was not itemized. You ordered 2 drink refills and the egg breakfast, for a total of $8.40. Your friend ordered 3 refills and the egg breakfast for $9.35.
(a) Write a system of equations for the situation. Use r for the amount charged for a refill and b for the amount charged for the egg breakfast.
(b) Graph the equations in the system.
(c) Use your graph to estimate how much each item cost.

Answers

Show work: Total=$17.75 R=$0.95×5 R=$4.75 $17.75-$4.75=$13.00 $13.00÷2=$6.50

Answer:
(1) Egg Breakfast $6.50
(2) Egg Breakfast $6.50
(3) Refill #1 $0.95
(4) Refill #2 $0.95
(5) Refill #3 $0.95
(6) Refill #4 $0.95
(7) Refill #5 $0.95

Check answer: $6.50+$6.50=$13.00
$0.95+$0.95=$1.90
$0.95+$0.95=$1.90
$1.90+$1.90=$3.80
$3.80+$0.95=$4.75
$13.00+$4.75=$17.75

Total: $17.75

The net of a square pyramid is shown below: What is the surface area of the solid?What is the surface area of the solid?

32 square inches 14 square inches 20 square inches 24 square inches 32 square inches

Answers

approximately 24 square inches. See picture

Haley and Samuel can each make one gift box in two hours. Rachael takes three hours to make the gift box alone. If Haley, Samuel, and Rachael work together, how long will it take them to make one gift box?

Answers

It will take 40 minutes for them to make one gift box.

Combined rates

Given that Haley and Samuel can each make one gift box in two hours, while Rachael takes three hours to make the gift box alone, to determine, if Haley, Samuel, and Rachael work together, how long will it take them to make one gift box, the following calculation must be performed, using combined rates:

1/2 + 1/2 + 1/3 = X3/6 + 3/6 + 2/6 = X8/6 = X6/6 = 1 hour8/6 = 40 minutes

Therefore, it will take 40 minutes for them to make one gift box.

Learn more about combined rates in https://brainly.com/question/10729109

#SPJ1

Answer:It will take 40 minutes for them to make one gift box

Step-by-step explanation:

If n = 8 and 16 • 2m = 4n – 8, then m = ?

Answers

Hello there! Thank you for asking your question here at Brainly. I will be assisting you today with answering your question, and will teach you how to handle it on your own in the future.

First, let's examine the question, and proceed to evaluate once we understand what we're dealing with.

"If n = 8, and 16 • 2m = 4n - 8, then m = ?"
This question is requesting for us to input the value for n, and then solve for m.

Here is our equation:
16 • 2m = 4n - 8

Let's plug in 8 for n.
Our equation should look like this now:
16 • 2m = 4(8) -8
First, let's get 4(8) by itself; Add 8 to both sides.
16 + 8 = 24
-8 + 8 = 0

Our equation is now:
24 • 2m = 4(8)
Multiply 4 by 8 to simplify the right side of the equation.
4 • 8 = 32

Now we have:
24 • 2m = 32

To solve for m, we need to isolate 2m and then divide both sides by 2.
Subtract 24 from both sides to isolate 2m.
24 - 24 = 0
32 - 24 = 8

Our equation is now:
2m = 8
Divide both sides by 2 to solve for m.
2m / 2 = m
8 / 2 = 4

Our final equation and solution is:
m = 4.
The value for m is 4.
I hope this helps!

Final answer:

The value of m is 0.75 when n = 8 and the equation 16 • 2m = 4n – 8 is satisfied, by performing simple algebraic operations to isolate and solve for m.

Explanation:

To find the value of m when n = 8 and 16 • 2m = 4n – 8, we first replace n with 8 in the second equation:

16 • 2m = 4(8) – 8

16 • 2m = 32 – 8

16 • 2m = 24

Now we divide both sides of the equation by 16 to isolate 2m:

2m = 24 / 16

2m = 1.5

Finally, to find m, we divide both sides of the equation by 2:

m = 1.5 / 2

m = 0.75

So the value of m that satisfies the given conditions is 0.75.

Arlene is comparing the prices of two truck rental companies. Company A charges $7 per hour and an additional $30 as service charges. Company B charges $8 per hour and an additional $40 as service charges.

Part A: Write an equation to represent each company's total charges for renting a truck for a certain number of hours. For both equations (one for Company A and one for Company B), define the variable used. (4 points)

Part B: Which company would charge less for renting a truck for 8 hours? Justify your answer. (3 points)

Part C: How much money is saved by using the services of Company A instead of Company B to rent a truck for 2 hours? (3 points)

Answers

Part A:
Company A: $7 per hour +$30 service charge =money spent
Company B: $8 per hour +$40 service charge =money spent

Part B:
Company A: $7(8)+$30 = $86
Company B: $8(8)+$40 = $104

Part C:
Company A: $7(2)+$30 = $44
Company B: $8(2)+$40 = $56
You would save $12 if you use Company A instead of Company B's truck rental.

Which planet is 10 times as far as earth is from the Sun

Answers

the answer to 15 is Saturn

Saturn is the answer

how to write unit form for (2 tens 1 one) x 10

Answers

Numbers are arranged by their place values. Place values give a quantity of value to a certain digit in a number. Given a number, the rightmost number is the ones place, followed by the tens place, hundreds, thousands, ten thousands, hundred thousands, millions, ten millions, hundred millions, as so on and so forth. The place value of a certain digit is 10 times bigger than its adjacent digit to the right.

So for this problem, all you have to do is multiply the number of units of each place value, then multiple them all by 10.

(2(10) + 1(1))×10
21 × 10 = 210

Therefore, the number is equivalent and written as 210.

If the APY of a savings account is 2.4% and if the principal in the savings account is $2200 for an entire year, what will be the balance of the savings account after all the interest is paid for the year? A. $2200 B. $2252.80 C. $2300 D. $2205.28

Answers

To solve this problem, we must recall that the formula for money with compound interest is calculated as:

Total = Principal × ( 1 + Rate ) ^ n

Total = $2,200 × ( 1 + 0.024 ) ^ 1

Total = $2,252.80

Therefore the answer is letter B.

Which factor does the width of the peak of a normal curve depend on?

Answers

the answer would be standard deviation.

Answer: The width of the peak depends on the Standard Deviation. The standard deviation is a measure used to quantify the variation or dispersion in the data set. If the standard deviation is low, this means that the set of data tends to be closer to the mean, then the width of the peak in the normal curve is small, for other part if the standard deviation is big, this means that the variation is big and the data set is more spread, this causes that the width of peak to be larger.

K+3d=8c-8d

solve for d

Answers

Move k to the other side to isolate d.

So we will get 3d = 8c - 8d - k

Now divide both sides by 3 to isolate d.

So d = 8/3c - 8/3d - k/3

what is the value of D to the nearest tenth ?

Answers

If two secants intersect from a point outside of the circle, then you can use formula:

26(26 + d) = 22(22 + 40)
676 + 26d = 22 * 62
26d = 1364 - 676
26d = 688
d = 688/26
d = 26.5 ← to the nearest tenth

A triangle has squares on its three sides as shown below. What is the value of x?

FIRST ONE GETS BRAINLIEST AND 12 PTS!!

Answers

x=10

Here's how!
Use Pythagorean theorem, which is a^2+b^2=c^2, and only applies to right triangles.
Rules: 'c' is always your hypotenuse! (Longest side) Your 'a' and 'b' are your legs (the other two sides.)

Plug in your information-
a^2+b^2=c^2
8^2+6^2=x^2

Solve!
64+36=x^2
100=x^2
(square root of 100)=(square root of x^2)
10=x
☺☺☺☺☺

Help me plz so bad I don't want to get bad grade on this

Answers

Answer:

1. 16666666666667 2. .72727272727 3. .25

Step-by-step explanation:

all you do is divide the top number by the bottom number to get it in decimal form

HELPPPPPPPPPPPPPPPPPPPP

Answers

A.
the y intercept is where x=0
x represents the number of months
when the number of months is 0, that is the initial number of games won

that looks to be a little below y=2, so maybe y=1.8?
the y intercept is y≈1.8
it represents the number of games won with 0 months of practice

B.
we can use y=mx+b
m=slope
b=y intercept
we know the y intercept
find the slope
slope=rise/run
the I'm going from x=0 to x=10
the rise is about 18.95 (from 1.8 to 20.75)
the run is 10
so slope would be 18.95/10=1.895

the equation would be y=1.895x+1.8
the points were (0,1.8) and (10,20.75)

A restaurant did a survey among 100 customers to find their food preferences. The customers were asked about their preferences for beef or chicken. Out of the total 75 people who liked beef, 60 also liked chicken. There were 80 people who liked chicken.

Part A: Summarize the data by writing the values that the letters A to I in the table below represent. (5 points)

Like beef Do not like beef Total
Like chicken A D G
Do not like chicken B E H
Total C F I

Part B: What percentage of the survey respondents did not like either beef or chicken? (3 points)

Part C: Do the survey results reveal a greater dislike for beef or chicken? Justify your answer. (2 points)

Answers

like beef.......do not like beef......total
like chicken 60 20 80
do not like c 15 5 20
-------------------------------------------------------------------------
total 75 25 100

B. did not like beef or chicken.....5/100 = 0.05 = 5%
C. the survey reveals a greater dislike for beef...because 15% like just beef, but 20% like just chicken

Answer:

like beef do not like beef total

like chicken 60 20 80

do not like chicken 15 5 20

total 75 25 100

B: 5%

C: Beef. 20% of the people do not like chicken. 25% do not like beef ( 5% from each dislike both.)

Step-by-step explanation:

Which graph represents the solution to the system of inequalities?

x + y ≤ 4

y – x ≥ 1

Answers

ANSWER

The correct answer is C.

EXPLANATION

To find which set represents the solution set of the system of inequalities, the best thing is to graph the inequalities and locate the intersection of the solution region of the two graphs.

The given inequalities are,

[tex]x + y \leqslant 4 \: \: and \: \: y - x \geqslant 1[/tex]

Let us start with,

[tex]x + y \leqslant 4[/tex]

To graph this inequality, we first of all graph the corresponding linear equation,

[tex]x + y = 4[/tex]

using the intercepts,
[tex](0,4) \: and \: (4,0)[/tex]

We plot the above points and draw a solid straight line through them.

We test for the origin to determine which half plane should be shaded.

[tex]0 + 0 \leqslant 4[/tex]

[tex]0 \leqslant 4[/tex]

This statement is true, so we shade the lower half plane.

We repeat the same process to graph,

[tex]y - x \geqslant 1[/tex]

So we graph the corresponding straight line,

[tex]y - x = 1[/tex]

using the intercepts,

[tex](0,1) \: and \: (-1,0)[/tex]

We plot the intercepts and draw a solid line through them.

We test for the origin again to see which half plane to be shaded.

[tex]0 - 0 \geqslant 1[/tex]

[tex]0 \geqslant 1[/tex]

This statement is false, so we shade the
upper half plane.

The intersection of the two region is the region in option C of the graphs provided.

Which is an obtuse angle?

∠CAB

∠BAC

∠BCA

∠ABC

Answers

BCA is an obtuse angle

Obtuse angle is an angle that is greater than 90° but less than 180°

∠BCA ← answer

An angle measures 20° more than the measure of a complementary angle. What is the measure of each angle?

Answers

complementary angles, sum = 90
so
x + x + 20 = 90
2x = 70
x = 35

35 + 20 = 55

answer
the measure of each angle: 55 and 35

ANSWER BOTH QUESTIONS IF U CANT SEE THE CHOICES ITS FINE! ALL U NEED IS THE QUESTION

Answers

12.
Area of a triangle = (bh)/2
Counting the squares in the figure, the base (bottom) of the triangle looks to be about 8. The height looks like 5.
b = 8
h = 5
A = (8*5)/2
A = (40)/2
A = 20
So the closest answer would be
A. 21.5 square units

13.
Area of a trapezoid = [(b₁ + b₂)/2]h
b₁ = 3
b₂ = 9
h = 6
A = [(3 + 9)/2]6
A = [12/2]6
A = (6)6
A = 36
Since I can't see the answer choices, it would be the closest number to 36.

Answer:

12 and 13

Step-by-step explanation:

Express without negative exponents

Answers

1/5^-1 = 5

.4^-2 = 6.25

so it would be 5 x 6.25

For the equation x^2+3x+j=0 , find all the values of j such that the equation has two real number solutions. Show your work.

Answers

The solution is j<2.25, meaning all values of j less than 2.25 will provide two real solutions.

For the equation [tex]x^2+3x+j=0,[/tex] to have two real number solutions, the discriminant must be greater than 0. The discriminant, D, of a quadratic equation [tex]ax^2+bx+c=0[/tex] is given by [tex]D=b^2-4ac[/tex].

In this case, a=1, b=3, and c=j. Applying the values, we get:

[tex]D=3^2-4(1)(j)[/tex]

D=9-4j

For two real solutions, D>0. Therefore:

9-4j>0

To find the values of j, solve the inequality:

9>4j

j<9/4

Thus, all the values of j that satisfy j<2.25 will ensure that the equation x^2+3x+j=0 has two real number solutions.

Nick has two more than twice as many quarters as dimes.. one fewer than three times as many nickels as dimes, and eight more pennies than dimes.. he has $7.37. How many of each coin does he have?

Thank you so much :)

Answers

Let's say we have x dimes.
This would mean we have:
(2x + 2) quarters,
(3x - 1) nickels and
(x + 8) pennies
The total value is 737 cents ($7.37)
We can thus say that if we multiply the number of each type of coin by the value of that coin and add it all, we will get 737, so we can write an equation:
10x + 25(2x + 2) + 5(3x - 1) + x+8 = 737
And if we tidy this up by multiplying out the brackets and collecting like terms, we get:
76x + 53 = 737
Now, solve for x:
76x = 684
x = 9
So by subbing into the expressions constructed at the start, we find how many of each coin we have:
9 dimes,
(2(9) + 2) quarters,
(3(9) - 1) nickels and
((9) + 8) pennies.
so... 9 dimes, 20 quarters, 26 nickels and 17 pennies.

Which of the following best describes the expression 6(y + 3)?

1.)The product of two constant factors six and three plus a variable
2.)The sum of two constant factors six and three plus a variable
3.)The product of a constant factor of six and a factor with the sum of two terms
4.)The sum of a constant factor of three and a factor with the product of two terms

Answers

6(y + 3)

The product of a constant factor of 6 and a factor with the sum of 2 terms

Answer: Hence, option '3' is correct.

Step-by-step explanation:

Since we have given that

[tex]6(y+3)[/tex]

This expression can be written in statement.

Here, we can see that there are two terms:

1) A constant factor of 6

2) Sum of two terms

So, according to options it can be written as :

The product of constant factor of 6 and a factor with the sum of two terms i.e. y and 3.

Hence, option '3' is correct.

A net can be folded to form a cube. The numbers on the three faces meeting at any vertex can be multiplied together. What is the smallest such product for the vertices of this cube

Answers

Folding this net, we will have this following pair of squares that are facing each other

the square with number 5 will face the square with number 10 = 5×10 = 50
the square with number 7 will face the square with number 6 = 7×6 = 42
the square with number 8 will face the square with number 9 = 8×9 = 72

The smallest product is 42

If p-1 is a factor of p^4+p^2+p-k the value of k is

Answers

p=1
p^4+p^2+p-k=0

1+1+1-k=0 k=3

The value of k is 3 if p - 1 is a factor of [tex]p^4+p^2+p-k[/tex]

How to determine the value of k?

The expression is given as:

[tex]p^4+p^2+p-k[/tex]

The factor is given as:

p - 1

Set the factor to 0

p - 1 = 0

Add to both sides

p = 1

Substitute 1 for p in the expression and equate it to 0

[tex]1^4+1^2+1-k = 0[/tex]

Evaluate the exponents

1+1+1-k = 0

Evaluate the sum

3-k = 0

Add k to both sides

k = 3

Hence, the value of k is 3 if p - 1 is a factor of [tex]p^4+p^2+p-k[/tex]

Answers

By definition, a quadrilateral is a two-dimensional figure that is composed of four sides. Since you are given with the coordinates of the vertices, the first logical thing to do is to plot the points in a Cartesian plane as shown in the attached picture. Next, find the midpoints of each side of the quadrilateral as denoted by the red dots. Then, create a line connecting the opposite midpoints which represents the length of the paths.

Our first solution is to find the midpoint of each sides. This is done by taking the average of each coordinate. The equation would be:

x,midpoint = (x₁+x₂)/2
y,midpoint = (y₁+y₂)/2

So, applying the equation:

midpoint jk = (-3+1/2, 1+3/2) = (-1,2)
midpoint kl = (1+5/2, 3+⁻1/2) = (3,1)
midpoint ml = (5+⁻1/2, ⁻1+⁻3/2) = (2,-2)
midpoint jm = (⁻3+⁻1/2, 1+⁻3/2) = (-2,-1)

Next, we find the lengths of the paths by using the distance formula:

d = √(x₂ - x₁)² + (y₂ - y₁)²

Distance between jk and ml = √(⁻1-2)² + (2 - ⁻2)² = 5
Distance between jm and kl = √(3-⁻2)² + (1-⁻1)² = √29
Total distance = 5 + √29 = 10.385 units

Since the scale is 1 unit = 10 meters, the actual total length of paths is equal to:

Actual Total Distance = 10.385*10
Actual Total Distance = 103.85 meters

Write an equation ten times the sum of half a number and 6 is 8.

Answers

10(1/2x+6)=8
Is the equation. Hope this helped!

10(x/2+6)=8
the x/2 means x over two

A triangle has angles that measure 30, 60, 90. The hypotenuse of the triangle measures 10 inches. Which is the best estimate for the perimeter of the triangle?

Answers

10cos60=5
10sin60=8.66
since you have the measure of the hypotenuse, add 10+5+8.66
=23.66

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