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3 years ago

the difference between two numbers is 9. the first number plus twice the other number is 27. find the two numbers

2 answers:

5 0

So,

Let's translate this into mathematical form.

x - y = 9
x + 2y = 27

Elimination by Addition
Divide both sides of the second equation by 2
$\frac{1}{2}x + y = 13 \frac{1}{2}$

Add the two equations together
$\frac{3}{2} x = \frac{45}{2}$

Multiply both sides by $\frac{2}{3}$
$x = \frac{90}{6} \ or \ 15$

Substitute
15 - y = 9

Subtract 15 from both sides
-y = -6
y = 6

Substitute
15 - 6 = 9
9 = 9 This checks.

15 + 2(6) = 27

Distribute
15 + 12 = 27
27 = 27 This also checks.

S = {(15,6)}

SashulF [63]3 years ago

5 0

A-b=9 ......a=9+b
a+2b=27
(9+b)+2b=27
9+3b=27
3b=27-9
3b=18
b=6
a=9+b=6+9=15

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A random sample of 100 automobile owners in thestate of Virginia shows that an automobile is driven onaverage 23,500 kilometers

Anastaziya [24]

Answer:

a) 22497.7 < μ< 24502.3

b) With 99% confidence the possible error will not exceed 1002.3

Step-by-step explanation:

Given that:

Mean (μ) = 23500 kilometers per year

Standard deviation (σ) = 3900 kilometers

Confidence level (c) = 99% = 0.99

number of samples (n) = 100

a) α = 1 - c = 1 - 0.99 = 0.01

$\frac{\alpha }{2} =\frac{0.01}{2}=0.005\\ z_{\frac{\alpha }{2}}=z_{0.005}=2.57$

Using normal distribution table, $z_{0.005$ is the z value of 1 - 0.005 = 0.995 of the area to the right which is 2.57.

The margin of error (e) is given as:

$e= z_{0.005}\frac{\sigma}{\sqrt{n} } = 2.57*\frac{3900}{\sqrt{100} } =1002.3$

The 99% confidence interval = (μ - e, μ + e) = (23500 - 1002.3, 23500 + 1002.3) = (22497.7, 24502.3)

Confidence interval = 22497.7 < μ< 24502.3

b) With 99% confidence the possible error will not exceed 1002.3

5 0

3 years ago

In ABC, what is the measure of angle B?

NeX [460]

Answer:

Step-by-step explanation:

The sum of two remote interior angles (a remote interior angle is the interior angle that is not supplementary to the exterior angle given -- in this case A and B are remote angles) equals the exterior angle.

In This case A + B = 140

A = x + 2

B = 2x

x +2 + 2x = 140

3x + 2 = 140 Subtract 2 from both sides

3x = 138 Divide by 3

x = 138/3

x = 46

<B = 2x

<B = 2*46

<B = 92

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3 years ago

A music store sold a total of 27 used trumpets and clarinets in one month. Trumpets cost $149 and clarinets cost $99. If total s

Annette [7]

Answer:

The number of clarinets musical store sold was 16. and number of trumpets musical store sold was 11.

Step-by-step explanation:

Let the musical store sells 'x' number of trumpets and 'y' number of clarinets.

According to question,

Total number of trumpets and clarinets sold is 27 that is

$x+y=27$ ..............(1)

Also given Trumpets cost $149 and clarinets cost $99.

then the shop sold x trumpets for $149x and sold y clarinets for $99y and total sales were $3233.

thus, $149x+99y=3233$ ...........(2)

Solving for equation (1) and (2),

Multiply equation (1) by 149 , we get

(1) ⇒ $149x+149y=4023$ ........(3)

Now, subtract equation (3) from equation (2) , we get

$149x+149y-(149x+99y)=4023-3233$

$\Rightarrow 149x+149y-149x-99y=790$

$\Rightarrow 149y-99y=790$

$\Rightarrow 50y =790$

$\Rightarrow y =\frac{790}{50}=15.8$

Thus, number of clarinets musical store sold was 15.8 but since clarinets are to be in whole number rounding off to the nearest integer 16.

and put y = 16 in (1) , we get

$x+y=27 \Rightarrow x+16=27 \Rightarrow x=27-16=11$

Thus, number of trumpets musical store sold was 11.

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3 years ago

For 3 consecutive odd integers, the result of adding the smallest integer to four times the largest integer is 121. What are the

irakobra [83]

Answer: 21, 23, 25

Step-by-step explanation:

Let the integers be y, y+2 and y+4.

From the question, we are informed that the result of adding the smallest integer to four times the largest integer is 121. This can be mathematically expressed as:

y + 4(y+4) = 121

y + 4y + 16 = 121

5y + 16 = 121

5y = 121-16

5y = 105

y = 105/5

y = 21

Since y = 21,

y + 2 = 21 + 2 = 23

y + 4 = 21 + 4 = 25

The integers are 21,23 and 25

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3 years ago

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Nimfa-mama [501]

Answer:

Step-by-step explanation:

1. A - times a - equals a +, which means [-(-2)] equals (2)

2. 5- (2) equals 5 - 2

3. 5-2= 3

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3 years ago

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