The correct answer is 317.
The sum of the first 8 terms of the series, to the nearest integer is,
⇒ S₈ = 317
What is Geometric sequence?An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.
Given that;
The series is,
⇒ 16, 20, 25,
Now, We get;
Common ratio = 20 / 16 = 5 / 4
And, 25 / 20 = 5 / 4
Thus, The series is geometric series.
Hence, The sum of the first 8 terms of the series, to the nearest integer is,
⇒ S₈ = 16 ((5/4)⁸ - 1) / (5/4 - 1)
⇒ S₈ = 16 (390625/65,536 - 1) / (1/4)
⇒ S₈ = 16 × 4 (325,089 / 65,536)
⇒ S₈ = 317.46
⇒ S₈ = 317
Thus, The sum of the first 8 terms of the series, to the nearest integer is,
⇒ S₈ = 317
Learn more about the geometric sequence visit:
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Pls help
If a varies jointly as b and c, find a when b = 4 and c = -3.
a = -96 when b = 3 and c = -8
a=
Answer:
a=4bc
a=4(4)(-3)=-48
a= - 48 when b equals to 3 is equals to - 8
The required answer by direct variation a is equal to 96. In other words, when b = 4 and c = -3, the value of a is 96.
When a variable varies jointly as two other variables, it means that the relationship between the variables can be expressed using direct variation. In this case, we have that "a varies jointly as b and c."
To find the value of a when b = 4 and c = -3, we can set up the proportion based on the direct variation relationship:
a/bc = k
where k is the constant of variation.
Substituting the given values:
a/(4)(-3) = k
Simplifying, we have:
a/-12 = k
Now, we can find the value of a when b = 4 and c = -3 by substituting these values into the equation and solving for a:
a/(-12) = k
a/(-12) = -96/-12 (since k = -96 when b = 3 and c = -8)
a = 96
Therefore, the required answer by direct variation a is equal to 96. In other words, when b = 4 and c = -3, the value of a is 96.
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A welder is making a metal sphere. The diameter will be 130 inches. What is the surface area of the metal sphere? Use 3.14 for π and round to the nearest tenth.
Answer:
53092.92 square inches
Step-by-step explanation:
Surface Area of a Sphere = 4πr2
Radius = ½D = 130÷2 = 65
4 × 3.14 × 65² = 53092.92
Michael made a scale model of the Empire State Building. The building has an actual height of 381m. Michael's models used a scale in which 1 cm = 50 m. what is the height of of the model in cm
Answer:
7.62 cm
Step-by-step explanation:
set up a proportion then cross-multiply:
1 / 50 = x / 381
50x = 381
x = 381/50
A spinner has 6 equal sections marked 1 through 6. You spin and land on a number less than 6?
The net of a triangular pyramid is shown.
Each triangle in the net has a base length that measures 6 inches and a height that measures 4 inches. What is the surface area of the pyramid that can be formed from this net?
Answer:
48 in²
Step-by-step explanation:
4x1/2x4x6=48
HELP PLEASE ALGEBRA 1
Answer: See below. I did the first one as an example
Step-by-step explanation:
to find slope between 2 points use the formula
[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
1) (19,-16) ( -7,-15)
the first value in each pair is the x, the 2nd value is the y
19= x1
-7-x2
-16=y1
-15=y2
[tex]m=\frac{-15--16}{-7-19} \\m=\frac{1}{-26} \\m=-\frac{1}{26}[/tex]
Brad has a garden with dimensions 12 feet long x 7 feet wide. He wants to enlarge the garden to an area of 119 square feet. How much farther will he need to extend the length of the garden to attain his desired area?
Answer:
he needs to increase the length to 17 feet
Step-by-step explanation:
[tex]12 \times 7 \\ = 84 \\ to \: get \: {119}^{2} feet \: he \: must \: say \: \\ 119 \div 7 \\ = 17 \\ = 17 \times 7 = 119 \\ [/tex]
Answer:
28
Step-by-step explanation:
f58t85h85y8578
If Sin C= 9/20, then which of the following is closest to the measure of angle C?
Show work
A) 31 degrees
B) 36 degrees
C) 27 degrees
D) 41 degrees
Answer:
Step-by-step explanation:
A square has an area of 64 square ft. What would be the measureme of its side? *
8ft
hope this helps, have an amazing day <3
Answer:8
Step-by-step explanation:
8x8=64
A recipe for 12 cookies calls for 1 1/3 cups milk, 2 1/2 cups flour, and 1 3/4 cups other ingredients. How many cups of milk, flour, and other ingredients are needed to make 24 cookies?
Each evening, Billy jogs around the high school track at a constant rate. The following equation describes the relationship between t, the time he jogs in hours, and d, the distance he jogs in kilometers. d = 7t Which graph represents the relationship between the amount of time Billy jogs and the distance he jogs?
The slope of the given line d = 7t is 7 kilometers per hour. Then the correct option is A.
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
Each evening, Billy jogs around the high school track at a constant rate.
The following equation describes the relationship between t, the time he jogs in hours, and d, the distance he jogs in kilometers.
d = 7t
The slope of the line will be 7,
Then graph A is correct.
More about the linear system link is given below.
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Please help \^.^/
What is the solution to the inequality below?
x² =< 49
the answer would be B. I used m a th way to find out what the answer was, you could use that app if you ever come across a similar question!
Computer software generated 500 random numbers that should look like they are from the uniform distribution on the interval 0 to 1. They are categorized into five groups:
1. less than or equal to 0.2
2. greater than 0.2 and less than or equal to 0.4
3. greater than 0.4 and less than or equal to 0.6
4. greater than 0.6 and less than or equal to 0.8
5. greater than 0.8.
The counts in the five groups are 113, 95, 108, 99, and 85, respectively. The probabilities for these five intervals are all the same. What is this probability? Compute the expected number for each interval for a sample of 500. Finally, perform the goodness of fit test and summarize your results.
Answer:
0.2 ; 100 ; 4.84
Step-by-step explanation:
Given that the probability of each of the 5 groups is the same :
Sum of probability = 1
Hence, Probability of each group = 1 / number of groups = 1 / 5 = 0.2
Expected number for each interval for a sample of 500 : ; X = 500
E(X) = X * P(x) = 500 * 0.2 = 100
Goodness of fit (X²) :
X² = Σ(X - E)² ÷ E
Groups :
113, 95, 108, 99, and 85
X : 113 ____ 95 ____ 108 ____ 99 _____ 85
(113 - 100)^2 / 100 = 1.69
(95 - 100)^2 / 100 = 0.25
(108 - 100)^2 / 100 = 0.64
(99 - 100)^2 / 100 = 0.01
(85 - 100)^2 / 100 = 2.25
(1.69 + 0.25 + 0.64 + 0.01 + 2.25) = 4.84
Rosalind made 969 donuts and put 8 donuts into each box. How many boxes of donuts were made
Answer:
121 donuts in each box
Step-by-step explanation:
969 divided by 8 = 121.125
(Ignore the remainder)
Step by step solution:
We know that there are 969 doughnuts, and there are 8 doughnuts per box. What we need to find out is how many boxes of doughnuts were made.
Step 1:
Set up an equation for Number of doughnuts (969) / Number of doughnuts per box (8) = Number of boxes made (x), which would look like this:
969/8 = x
Step 2:
Doing this, we can get 121.125, which leaves us with
121.125 = x
121.125 = 121.125
Which gives us the answer of 121.125, which we can shorten to 121, as the decimal is not necessary.
Checking our answer:
We can check our answer simply be rewording our 1st equation to solve for the number of doughnuts made. This would give us the equation Number of doughnuts per box (8) * Number of boxes made (121.125) = x. Solving this equation would look like
8 * 121.125 = x
969 = x
969 = 969
Answer: By completing the steps above we get 121, and we can check our work by rewording the problem to solve for the number of Doughnuts. Good Luck!
Use the given information to write the standard form equation of a circle:
a) x²+y²+10x+14y+70=0 translated 1 unit to the right and 2 units down.
Answer:
The formula for the equation of a circle is (x – h) 2 + (y – k) 2 = r 2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle. If a circle is tangent to the x-axis at (3,0), this means it touches the x-axis at that point.
Step-by-step explanation:
If p is inversely proportional to the square of q, and p is 25 when q is 3, determine p
when q is equal to 5.
Answer:
p = 9 when q = 5.
Step-by-step explanation:
p is inversely proportional to the square of q
This means that:
[tex]p = \frac{k}{q^2}[/tex]
In which k is a constant multiplier.
p is 25 when q is 3
We use this to find k.
[tex]p = \frac{k}{q^2}[/tex]
[tex]25 = \frac{k}{3^2}[/tex]
[tex]k = 25*9 = 225[/tex]
So
[tex]p = \frac{225}{q^2}[/tex]
Determine p when q is equal to 5.
[tex]p = \frac{225}{q^2} = \frac{225}{5^2} = 9[/tex]
p = 9 when q = 5.
What is the probability of choosing a numbered card from a deck of cards? Type your answer as a fraction.
Answer:
36/52 or 9/13
Step-by-step explanation:
Ace-9 for all suits; Diamond, Hearts, Spades and Clubs
CAN YALL HELP ME PLEASE Deanna's times, seconds, for running the 100 meter dash this week were: 10.80 0,10.99,11.02,10.80,11. and 10.96 . 10.78 1.10, 10.88, 10.72, 10.15 Which measure of center would most accurately describe Deanna's typical time, and what is the value of that measure of center? Move a word and a value to complete the sentence . The best center of measure for this data is the which is equal toseconds mean median 10.88 10.9010,8 11.1
Answer:
MEDIAN11.1Step-by-step explanation:
[tex]{hope it helps}}[/tex]
MEAN and 10.90
this is the answer i got u guys PLZ LIKE THIS so i can get my level up
Please help me out!! :)
Answer:
3/4
Step-by-step explanation:
Tangent is opposite/adjacent
Therefore, 6/8 would be the answer which simplifies to 3/4.
Tyler sold a total of $115,000 of exercise equipment last month. If his commission is 6.5% of sales, how much commission did he earn?
A.
$2,342
B.
$7,475
C.
$12,719
D.
$115,065
Answer:
B
Step-by-step explanation:
Do 115000/100x6.5 You get 7.475k
please help with these questions
Answer:
False, False, True, False
Step-by-step explanation:
1. False. D and F are not parallel as they are intersecting in the diagram.
2. False. Angles 1 and 3 are not corresponding. They are opposite. A pair of corresponding angles would be angles 1 and 5.
3. True. A transversal line is a line that passes through two other lines.
4. False. Angle 6 = 63˚ through corresponding angles. Angle 6 + Angle 7 = 180. 63 + Angle 7 = 180. Angle 7 = 117˚.
i hope this helped :)
a
Henry runs business
preparing peoples taxes.
He has monthly expenses
off $25.30 for printer ink
and $52 for advertising.
So far his revenue for the
month has been $3,456,
what is the profit that he
had made?
Answer:
3,378.70
Step-by-step explanation:
First, find the total amount Henry spends a month. 25.30 for printer ink and 52 for advertising. 25.30+52=$77.30.
Subtract what he has spent from what he has made.
3,456-77.30=3,378.70
That is his profit.
Which describes the cross section of a cube that passes through the vertices A, B, C, and D shown below?
a rectangle that is not a square
a square
a paralelogram that is not a rectangle or a square
a trapezoid
Answer:
B. A square
Step-by-step explanation:
2 to the 4th power divided by [(3.35 x 0.8) + 5.32]
Answer:
2Step-by-step explanation:
First we need to rewrite this part word problem completely into numbers
2⁴ ÷ [(3.35 × 0.8) + 5.32]
Now we must solve. Remember to do parenthesis first.
3.35 × 0.8 = 2.68
2.68 + 5.32 = 8
Now we need to find the value of 2⁴
2⁴ = 2 × 2 × 2 × 2 = 16
Finally we need to divide 16 by 8
16 ÷ 8 = 2
So our final answer is 2
Help me I having a hard time with This one
Answer:
4
Step-by-step explanation:
4 students studied 4 hours or more.
Answer:
8
Step-by-step explanation:
at least means minimum so how many students studied a minimum of 4 hours?
Plz plz plz plz help
Answer:
we can substract the power 4 by taking up with 15 because using indices rule
Find the volume of the figure below. Use 3.14 for π, and round your final answer to the nearest tenth.
Answer:
79.25 mm³
Step-by-step explanation:
The figure can be decomposed into 2 different half cylinders and a rectangular prism
Volume of the figure = volume of the smaller half cylinder + larger half cylinder + rectangular prism
✔️Volume of smaller half cylinder = ½(πr²h)
r = ½(2) = 1 mm
h = 5 mm
π = 3.14
Volume of smaller half cylinder = ½(3.14*1²*5)
= 7.85 mm³
✔️Volume of larger half cylinder = ½(πr²h)
r = ½(4) = 2 mm
h = 5 mm
π = 3.14
Volume of smaller half cylinder = ½(3.14*2²*5)
= 31.4 mm³
✔️Volume of rectangular prism = L*W*H
L = 5 mm
W = 4 mm
H = 2 mm
Volume = 5*4*2 = 40 mm³
✅Volume of the figure = 7.85 + 31.4 + 40
= 79.25 mm³
How to write 4 508 300
in words?
At a middle school, 24 of the 144 students speak Vietnamese. What is the ratio of students that do not speak Vietnamese to students who speak Vietnamese?
Answer:
1:6
Step-by-step explanation:
24 and 144 are divisible by 6. Do the math, it comes out as 1:6.
24:144 = 1:6
A small airplane used 7 1/3 gallons of fuel to fly a 3 hour trip. How many gallons were used each hour? Each day?
Answer:
approximately 2.44 per hour, and 175.92 per day
Step-by-step explanation:
We can use 7.33 as 7 and 1/3rd.
If you take 7.33 and divide by 3, representing 3 hours, it equals 2.44333333.
If you round this to the nearest hundredth, you get the answer 2.44
For each day, you take the original number, 7.33, and multiply it by 8 to assume that the trip was 24 hours.
7.33 * 24 = 175.92.
Answer:
Step-by-step explanation: