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2 years ago

Find two consecutive integers such that four times the larger exceeds three times the smaller by 23

1 answer:

3 0

CONSECUTIVE NUMBERS; x, x+1
(x+1)4=3(x)+23
4x+4=3x+23
4x-3x=23-4
x=19
x+1=20
THEREFORE the consecutive numbers are 19&20

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8.23 A manufacturing company produces electric insulators. You define the variable of interest as the strength of the insulators

Kitty [74]

Answer:

The 95% confidence interval estimate for the population mean force is (1691, 1755).

Step-by-step explanation:

According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally.

The sample selected here is n = 30.

Thus, the sampling distribution of the sample mean will be normal.

Compute the sample mean and standard deviation as follows:

$\bar x=\frac{1}{n}\sum x=\frac{1}{30}\times 51702=1723.4\\\\s=\sqrt{\frac{1}{n-1}\sum (x-\bar x)^{2}}=\sqrt{\frac{1}{30-1}\times 232561.2}=89.55$

Construct a 95% confidence interval estimate for the population mean force as follows:

$CI=\bar x\pm z_{\alpha /2}\times\frac{s}{\sqrt{n}}$

$=1723.4\pm 1.96\times\frac{89.55}{\sqrt{30}}\\\\=1723.4\pm 32.045\\\\=(1691.355, 1755.445)\\\\\approx (1691, 1755)$

Thus, the 95% confidence interval estimate for the population mean force is (1691, 1755).

3 0

3 years ago

Find the area of the trapezoid

Sergeeva-Olga [200]

Answer:

Step-by-step explanation:

Formula

$\frac{1}{2} \times h \times (sum \: of \: parallel \: sides(b1 + b2))$

Your scale is 2cm to 2units therefore the parameters are as follows

h=4

b1=9

b2=13

$\frac{1}{2} \times 4 \times (9 + 13)$

$\frac{1}{2} \times 4 \times 22$

$\frac{1}{2} \times 88$

$\frac{88}{2} \\ = 44$

6 0

2 years ago

stacy buys 3 cds in set for $29.98 .She saved $6.44 by buying the set instead of buying the individual cd's .If each cd costs th

MrMuchimi

3 CD → $29.98

29.98 - 6.44 = 23.54 → remained

If each CD costs the same amount ... ↓

23.54 ÷ 3 = 7.8466

$7.8466

8 0

2 years ago

Read 2 more answers

0 ft elevation, diver is underwater at depth of 138 ft. In this area, the ocean floor has a depth of 247 ft. A rock formations r

KiRa [710]

We know that the ocean floor has a depth of 247 ft, and we also know that the diver is underwater at depth of 138 ft, so its distance from the ocean floor will be:
 $247-138=109$ ft

Now, the rock formations rises to a peak 171 to above the ocean floor, so to find how many feet below the top of the rock formations is the diver, we are going to subtract the distance to the driver form the ocean floor from the rock formations height:
 $171-109=62$ ft

We can conclude that the diver is 62 feet below the top of the rock formations.