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3 years ago

22

Mathematics

2 answers:

Nonamiya [84]3 years ago

8 0

Answer:

$100

Step-by-step explanation:

This is easy

12x5=60

+40=$100

Dmitry [639]3 years ago

7 0

Answer:

$100

Step-by-step explanation:

12x5=60

+40= $100

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If $-2 < x \le 3,$ then find all possible values of $5x + 1.$ Give your answer in interval notation.

kotegsom [21]

Answer: $(-9, 16]$

This is the interval from -9 to 16. Exclude -9 but include 16.

=====================================================

Work Shown:

The idea is to multiply all sides by 5, then add 1 to all sides

$-2 < x \le 3$

$5(-2) < 5x \le 5(3)$

$-10 < 5x \le 15$

$-10+1 < 5x+1 \le 15+1$

$-9 < 5x+1 \le 16$

This converts to the interval notation $(-9, 16]$

note: a curved parenthesis means "do not include this value in the solution set"; while a square bracket has us include the value. So we exclude -9 and include 16.

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You are given 10,000 to invest in either 5% tax free bonds or 10% taxable bonds. Your total investment income for a year was $67

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4 years ago

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What kind of triangles does the Pythagorean theorem work for?

Tasya [4]

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A. Right angle traingle Is the answer

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3 years ago

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What is the distance between (1,-5) and (-3,6)

spin [16.1K]

Answer:

$\large\boxed{\sqrt{137}}$

Step-by-step explanation:

The formula of a distance between two points:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

We have the points (1, -5) and (-3, 6). Substitute:

$d=\sqrt{(6-(-5))^2+(-3-1)^2}=\sqrt{11^2+(-4)^2}=\sqrt{121+16}=\sqrt{137}$

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3 years ago

I. In a shipment of 300 connecting rods, the mean tensile strength is found to be 45 kpsi and has a standard deviation of 5 kpsi

CaHeK987 [17]

Answer:

a) Between 39 and 40 rods can be expected to have a strength less than 39.4 kpsi.

b) 260 rods are expected to have a strength between 39.4 and 60 kpsi

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 45, \sigma = 5$

(a) Assuming a normal distribution, how many rods can be expected to have a strength less than 39.4 kpsi?

The percentage of rods with a stength less than 39.4 is the pvalue of Z when X = 39.4. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{39.4 - 45}{5}$

$Z = -1.12$

$Z = -1.12$ has a pvalue of 0.1314

13.14% of rods have a strength less than 39.4 kpsi.

Out of 300

0.1314*300 = 39.42

Between 39 and 40 rods can be expected to have a strength less than 39.4 kpsi.

(b) How many are expected to have a strength between 39.4 and 60 kpsi?

The percentage of rods with a stength in this interval is the pvalue of Z when X = 60 subtracted by the pvalue of Z when X = 39.4. So

X = 60

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{60 - 45}{5}$

$Z = 3$

$Z = 3$ has a pvalue of 0.9987

X = 39.4

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{39.4 - 45}{5}$

$Z = -1.12$

$Z = -1.12$ has a pvalue of 0.1314

0.9987 - 0.1314 = 0.8673

86.73% of the rods are expected to have a strength between 39.4 and 60 kpsi

Out of 300

0.8673*300 = 260

260 rods are expected to have a strength between 39.4 and 60 kpsi

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4 years ago