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Alika [10]
2 years ago
13

Find a1 and d for an arithmetic sequence with these terms. a3=-8 and a7=32

Mathematics
1 answer:
Arte-miy333 [17]2 years ago
4 0
We know that
the formula for the <span>arithmetic sequence is
</span><span>an = a1 + (n - 1)*d
where
a1  is the first term
n is the numbers of terms

for n=3   a3=-8
-8=a1+(3-1)*d-----> -8=a1+2*d-----> equation 1

for n=7   a7=32
-32=a1+(7-1)*d----> -32=a1+6*d----> equation 2

multiply equation 2 by -1-----> 32=-a1-6*d------> equation 3

add equation 1 and equation 3
</span>-8=a1+2*d
32=-a1-6*d
----------------
24=-4*d------> d=-6
-8=a1+2*(-6)    (substitute the value of d in equation 1)
-8=a1-12-----> a1=-8+12-----> a1=4

the answer is
a1=4
d=-6

<span>

</span>
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fill inbthe bubble next to all the double facts you could use to find the sum of 3+2? A 2+2 B 5+5 C 3+3 D 1+1
GarryVolchara [31]

Answer:

Option A , C and D are correct.

Step-by-step explanation:

Double Facts states that the additions in which a number is added to itself.

then; by definition of double facts

Use Double facts to find the sum of 3 + 2

3 + 2

=3 + (3 - 1)

= 3+ 3 - 1

= 6 - 1

= 5

similarly,

3+2 = (1+2) + 2 = 1 + 2+2 = 1 + 4 = 5

Also;

3 + 2 = 3 + (1+1) = 3 +1+1 = 5

therefore, the double facts that used to find the sum of 3+2 are; 2+2 , 3+3 and 1+ 1.

4 0
2 years ago
It takes 32 hours for a motorboat moving downriver to get from pier A to pier B. The return journey takes 48 hours. How long doe
lina2011 [118]

Answer:

Time taken by the un powered raft to cover this distance is T = 192.12 hr

Step-by-step explanation:

Let speed of boat = u \frac{km}{hr}

Speed of current = v \frac{km}{hr}

Let distance between A & B = 100 km

Time taken in downstream = 32 hours

32 = \frac{100}{u +v}

u + v = \frac{100}{32}

u + v = 3.125 ------ (1)

Time taken in upstream = 48 hours

48 = \frac{100}{u -v}

u -v = \frac{100}{48}

u - v = 2.084 ------- (2)

By solving equation (1) & (2)

u = 2.6045 \frac{km}{hr}

v = 0.5205 \frac{km}{hr}

Now the time taken by the un powered raft to cover this distance

T = \frac{100}{v}

Because un powered raft travel with the speed of the current.

T = \frac{100}{0.5205}

T = 192.12 hr

Therefore the  time taken by the un powered raft to cover this distance is

T = 192.12 hr

3 0
2 years ago
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An insurance company reported that, on average, claims for a certain medical procedure are $942. An independent organization con
kirza4 [7]

Answer:

Step-by-step explanation:

The question is incomplete. The complete question is:

An insurance company reported that, on average claims for a certain medical procedure are $942. an independent organization constructed a 95% confidence interval of ($930, $950) for the average amount claimed for the particular medical procedure. what conclusion best evaluates the truthfulness of the number reported by the insurance company?

a) with 95% certainty, the average claim for this medical procedure is $942.

b) with 95% certainty, the average claim for this medical procedure is not $942.

c) the confidence interval is consistent with an average claim of $942 for this medical procedure

Solution:

Confidence interval is used to express how confident we are that the population parameter that we are looking for is contained in a range of given values. Looking at the given confident interval, the lower limit is $930 and the upper limit is $950. We can see that the population mean, $942 lies within these values. The correct option would be

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2 years ago
The function shown is reflected across the y-axis to create a new function. Which is true about the domain and range of each fun
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Answer:

D. The range stays the same but the domain changes

Step-by-step explanation:

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8 0
1 year ago
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A rectangle on a coordinate plane has vertices at (7,5), (-7,5), (-7,-2), and (7,-2). What is the perimeter of the rectangle?
mixer [17]
Perimeter of a rectangle;


P=2l+2w

lets say the length is horizontal and the width is vertical. the distance between the x coordinates will determine the length and the distance between the y coordinates will determine the width. once you have those numbers you can use the perimeter formula.

|7 -(-7)| = 14
l = 14
|5-(-2)| = 7
w=7

P=2(14)+2(7)
P= 28+14
P= 42
7 0
1 year ago
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