Which is a correct first step in solving the inequality –4(2x – 1) > 5

you sold $105 worth of tickets, but you spilled soda on the record sheet and don't know how many of each tickets you sold. stude

Nina [5.8K]

5x+7y=105
There are four variants are possible
1. You sold 15 adult tickets
2. You sold 7 student tickets and 10 adult tickets
3. You sold 14 student tickets and 5 adult tickets
4. You sold 21 student tickets.

8 0

3 years ago

A quality control specialist at a pencil manufacturer pulls a random sample of 45 pencils from the assembly line. The pencils ha

amm1812

Answer:

The P-value you would use to test the claim that the population mean of pencils produced in that factory have a mean length equal to 18.0 cm is 0.00736.

Step-by-step explanation:

We are given that a quality control specialist at a pencil manufacturer pulls a random sample of 45 pencils from the assembly line.

The pencils have a mean length of 17.9 cm. Given that the population standard deviation is 0.25 cm.

Let $\mu$ = population mean length of pencils produced in that factory.

So, Null Hypothesis, $H_0$ : $\mu$ = 18.0 cm {means that the population mean of pencils produced in that factory have a mean length equal to 18.0 cm}

Alternate Hypothesis, $H_A$ : $\mu\neq$ 18.0 cm {means that the population mean of pencils produced in that factory have a mean length different from 18.0 cm}

The test statistics that will be used here is One-sample z-test statistics because we know about the population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean length of pencils = 17.9 cm

$\sigma$ = population standard deviation = 0.25 cm

n = sample of pencils = 45

So, the test statistics = $\frac{17.9-18.0}{\frac{0.25}{\sqrt{45} } }$

= -2.68

The value of z-test statistics is -2.68.

Now, the P-value of the test statistics is given by;

P-value = P(Z < -2.68) = 1 - P(Z $\leq$ 2.68)

= 1- 0.99632 = 0.00368

For the two-tailed test, the P-value is calculated as = 2 $\times$ 0.00368 = 0.00736.

7 0

3 years ago

How are dot products useful?

nata0808 [166]

Answer:

An important use of the dot product is to test whether or not two vectors are orthogonal. Two vectors are orthogonal if the angle between them is 90 degrees. ... Thus, two non-zero vectors have dot product zero if and only if they are orthogonal.

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Find the product of (x2 + 2x −3)(4x2 − 5x + 6). (2 points) a 4x4 + 13x3 − 16x2 + 27x − 18 b 4x4 + 3x3 − 28x2 + 27x − 18 c 4x4 +

skad [1K]

Answer:

D

Step-by-step explanation:

We want to find:

$(x^2+2x-3)(4x^2-5x+6)$

Distribute:

$=(x^2+2x-3)(4x^2)+(x^2+2x-3)(-5x)+(x^2+2x-3)(6)$

Distribute:

$=(4x^4+8x^3-12x^2)+(-5x^3-10x^2+15x)+(6x^2+12x-18)$

Rearrange:

$=(4x^4)+(8x^3-5x^3)+(-12x^2-10x^2+6x^2)+(15x+12x)+(-18)$

Combine like terms:

$=4x^4+3x^3-16x^2+27x-18$

The answer is D.

6 0

3 years ago

A student says that if the hypothesis is false, an argument cannot be valid. How do you respond ?

Anton [14]

If a student tells me that an argument that has a false hypothesis cannot be valid, I would reply that we need to look carefully at the meaning of validity in the context of logic. In everyday speech, we tend to use “valid” to mean the same thing as “true” or “accurate.” In logic, this is not the way the term is used.

8 0

4 years ago

Read 2 more answers

Which is a correct first step in solving the inequality –4(2x – 1) > 5 – 3x? ANSWER: A