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3 years ago

Which values for x make this inequality true? −15x+4≤39

Mathematics

1 answer:

nadezda [96]3 years ago

8 0

Answer:

x ≥ -7/3

Step-by-step explanation:

<h3>General Formulas and Concepts:</h3>

Pre-Algebra

<h3>Order of Operations: BPEMDAS</h3>

Brackets

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

Left to Right

Equality Properties

Step-by-step explanation:

Step 1: Define Inequality

-15x + 4 ≤ 39

Step 2: Solve for x

Subtract 4 on both sides: -15x ≤ 35

Divide -15 on both sides: x ≥ -7/3

Here we see that any value x greater than or equal to -7/3 would work as a solution to the inequality.

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The decay factor would be 1 minus the percent of decrease:

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3 years ago

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2) The results of a 2012 Pew Foundation survey of high school and middle school teachers is given in the pie chart. A student as

Serggg [28]

Answer:

The calculated value z = 9.4451 > 1.96 at 5% level of significance.

Null hypothesis is rejected at 5% level of significance

yes there is difference in the distribution of types of cell phones for the teachers in 2018 at a 5% level of significance

Step-by-step explanation:

<u>Explanation</u>:-

The results of a 2012 Pew Foundation survey of high school and middle school teachers is given in the pie chart.

A student asked a random sample of teachers in 2018 and found 165 had smart-phones, 80 had a cell phone

The first sample proportion

$p_{1} = \frac{80}{165} = 0.4848$

A student asked a random sample of teachers in 2018 and found 165 had smart-phones,5 had no cell phone

The second sample proportion

$p_{2} = \frac{5}{165} = 0.03030$

<u>Null hypothesis :H₀</u>: Assume that there is no difference in the distribution of types of cell phones for the teachers in 2018

H₀ : p₁ = p₂

<u>Alternative hypothesis :H₁</u>

H₁ : p₁ ≠ p₂

<u>Level of significance : ∝=0.05</u>

The tabulated value z=1.96

The test statistic

$Z = \frac{p_{1} -p_{2} }{\sqrt{pq(\frac{1}{n_{1} } } +\frac{1}{n_{2} } )} }$

where $p = \frac{n_{1}p_{1} +n_{2} p_{2} }{n_{1} + n_{2} }$

q = 1-p

In given data n₁ = n₂ = n

$p = \frac{165 (0.4848)+165 (0.03030 }{165 + 165}$

on calculation , we get p = 0.2655

q =1-p = 1-0.2655

q = 0.7345

$Z = \frac{0.4848 -0.030}{\sqrt{0.2655X0.7345(\frac{1}{165 } } +\frac{1}{165} )} }$

Z = 9.4451

The calculated value z = 9.4451 > 1.96 at 5% level of significance.

<u>Conclusion:</u>-

Null hypothesis is rejected at 5% level of significance

yes there is difference in the distribution of types of cell phones for the teachers in 2018 at a 5% level of significance

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4 years ago

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A. The area is $78.54m^2$

B. She needs to cover 1661.9 square feet of tiles for the base of the swimming pool

Step-by-step explanation:

Question A:

Let us assume that the leash is pegged to the ground using a stake. as a result, the dog can move around the stake. The path that the motion of the dog would trace is a circle, and the radius of the circle will be the length of the leash.

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We already know that the swimming pool is circular, hence, the surface area of the base of the swimming pool will be the same as the area of a circle, with the same radius.

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