Multiply (2x^2-3x+5)(x^2+4x+1)

5. The superintendent of the local school district claims that the children in her district are brighter, on average, than the g

anygoal [31]

Answer:

We conclude that children in district are brighter, on average, than the general population.

Step-by-step explanation:

We are given the following data set:

105, 109, 115, 112, 124, 115, 103, 110, 125, 99

Formula:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{1117}{10} = 111.7$

Sum of squares of differences = 642.1

$S.D = \sqrt{\frac{642.1}{49}} = 8.44$

We are given the following in the question:

Population mean, μ = 106

Sample mean, $\bar{x}$ = 111.7

Sample size, n = 10

Alpha, α = 0.05

Sample standard deviation, s = 8.44

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 106\\H_A: \mu > 106$

We use one-tailed(right) t test to perform this hypothesis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{111.7 - 106}{\frac{8.44}{\sqrt{10}} } = 2.135$

Now,

$t_{critical} \text{ at 0.05 level of significance, 9 degree of freedom } = 1.833$

Since,

$t_{stat} > t_{critical}$

We fail to accept the null hypothesis and reject it. We accept the alternate hypothesis.

We conclude that children in district are brighter, on average, than the general population.

4 0

3 years ago

The linear function f(x) = 0.9x + 79 represents the average test score in your math class, where x is the number of the test tak

Levart [38]

Given:

The linear function for average test score in your math class is

$f(x)=0.9x+79$

where x is the number of the test taken.

The linear function g(x) in the given table represents the average test score in your science class, where x is the number of the test taken.

To find:

Part A: The test average for your math class after completing test 2.

Part B: The test average for your science class after completing test 2.

Part C: Which class had a higher average after completing test 4?

Solution:

Part A:

We have,

$f(x)=0.9x+79$

Put x=2 in the above function, to find the test average for your math class after completing test 2.

$f(2)=0.9(2)+79$

$f(2)=1.8+79$

$f(2)=80.8$

Therefore, the test average for your math class after completing test 2 is 80.8.

Part B:

From the given table it is clear that g(x) =79 at x=2.

Therefore, the test average for your science class after completing test 2 is 79.

Part C:

Put x=4 in f(x), to find the test average for your math class after completing test 4.

$f(4)=0.9(4)+79$

$f(4)=3.6+79$

$f(4)=82.6$

From the table it is clear that the value of g(x) is increased by 1 as x is increased by 1. So, the value of function g(x) at x=4 must be 1 more than 80.

$g(4)=81$

It is clear that,

$82.6>81$

Therefore, math class had a higher average after completing test 4.

3 0

3 years ago

Una página de plástico diseñada para guardar cromos puede contener hasta 9 cartas. ¿Cuántas páginas se necesitarán para almacena

adelina 88 [10]

Esto significa que debemos tener 58 páginas de plástico para contener las 517 tarjetas.´

<h3>¿Cuántas páginas se necesitarán para almacenar 517 tarjetas? </h3>

Sabemos que cada página puede almacenar hasta 9 cartas.

Entonces queremos ver cuantos grupos de 9 cartas hay en el conjunto de 517, para ver esto tomamos el cociente entre 517 y 9.

N = 517/9 = 57.44

Y no podemos tener un numero racional, así que debemos redondear al proximo número entero, que es 58.

Esto significa que debemos tener 58 páginas de plástico para contener las 517 tarjetas.

Sí quieres aprender más sobre cocientes:

brainly.com/question/3493733

#SPJ1

8 0

1 year ago

If angle 1 is 140°, then find the measure of the other angles.

Vlad [161]

<h2>Angles</h2>

<h3>If angle 1 is 140°, then find the measure of the other angles.</h3>

∠2 = 40°
∠3 = 40°
∠4 = 140°
∠5 = 140°
∠6 = 40°
∠7 = 40°
∠8 = 140°

Explanation:

The relationship between ∠1 and ∠2 are supplementary angles, so when you add up their measurements, it will become 180°. Simply subtract 180 and 140 to get the measure of ∠2. As well as ∠3, they're linear pairs. And they are also supplementary. To determine the measure of ∠6 and ∠7, notice the relationship between ∠2 and ∠6. As you noticed, it is corresponding angles. So they have the same measurement. If ∠2 = 40°, then ∠6 = 40°. As well as ∠7, because the relationship between ∠6 and ∠7 are vertical pairs. So the angle measurement of ∠7 is also 40°.

Meanwhile, the relationship between ∠1 and ∠4 are vertical pairs. It means they also have the same measurement. So ∠4 = 140°. The relationship between ∠1 and ∠5 are corresponding angles, so they also have the same measurement. If ∠1 = 140°, then ∠5 = 140°. The relationship between ∠1 and ∠8 are alternate exterior angles, and they also have the same measurement. If ∠1 = 140°, then ∠8 = 140°.

Wxndy~~

8 0

2 years ago

2. Given points A(3, -5) and B(19,-1), find the coordinates of point C such that he =

natka813 [3]

Post a picture to see the example of point C

7 0

3 years ago