2x+3y=0 and x+2y=-1 <br> Solve by substitution

Tutor O-Rama claims that their services will raise student SAT math scores at least 50 points. The average score on the math por

Novosadov [1.4K]

Answer:

See below

Step-by-step explanation:

The score increase was 35 points. They claimed an increase of at least 50 points. For a significance level of 5%, the z-score for the situation needs to be at smaller than -1.645. For a significance level of 1%, the z-score needs to be smaller than -2.325

The z score for our situation: z = (385 - 350)/50 = 0.7

The average score of 385 of Tutor O-Rama scores is not significantly different from the average of the other students SAT scores. The evidence doesn't support their claim of being effective tutoring.

4 0

3 years ago

Find the value of x from this adjoining figure

Fiesta28 [93]

Answer:

$x=15^\circ$

Step-by-step explanation:

Please refer to the attached figure for labeling of given diagram:

We are given the following angles:

$\angle AOC = 3x^\circ\\\angle BOD = 2x^\circ\\\angle EOF = 7x^\circ$

Angles opposite to each other when they are formed by crossing of two lines are known as vertically opposite angles. And vertically opposite angles are always equal to each other.

Using property of vertically opposite angles:

$\angle EOF = \angle AOB = 7x^\circ$

Line CD is a straight line, so $\angle COD = 180^\circ$

Also,

$\angle COD = \angle COA+\angle AOB+\angle BOD = 180^\circ\\\Rightarrow 3x + 7x + 2x=180^\circ\\\Rightarrow 12x =180^\circ\\\Rightarrow x = \dfrac{180}{12}\\\Rightarrow x = 15^\circ$

Hence, <em>answer</em> is $x = 15^\circ$ .

5 0

3 years ago

The volume of a spherical sculpture is 256 ft³. Rhianna wants to estimate the surface area of the sculpture. To do the estimate,

Brrunno [24]

Answer:

192 $ft^2$

Step-by-step explanation:

Given that

Volume of spherical sculpture = 256 ft³

$\pi$ is used as 3.

To find:

Surface area of sculpture = ?

Solution:

First of all, let us learn about the formula for Volume and Surface Area of Sphere:

1. $Volume =\frac{4}{3}\pi r^3$

2. $Surface\ Area = 4\pi r^2$

Given volume is 256 ft³.

$256 = \dfrac{4}{3}\pi r^3\\\Rightarrow 256 = \dfrac{4}{3}\times 3 r^3\\\Rightarrow 256 = 4 r^3\\\Rightarrow r^3=64\\\Rightarrow \bold{r = 4\ ft}$

Now, let us put r = 4 in the formula of Surface Area to find the value of Surface Area:

$Surface\ Area = 4\pi 4^2 = 4 \times 3 \times 16 = \bold{192\ ft^2}$

So, approximate surface area of sculpture is 192 $ft^2$ .

3 0

3 years ago

he weight of male babies less than months old in the United States is normally distributed with mean pounds and standard deviati

Degger [83]

Answer:

Step-by-step explanation:

Hello!

The variable of interest is

X: Weight of a male baby (pounds)

X~N(μ;σ²)

μ= 11.5 pounds

σ= 2.7 pounds

a) Find the 81st percentile of the baby weights.

This percentile is the value that separates the bottom 81% of the distribution from the top 19%

P(X≤x₁)= 0.81

For this you have to use the standard normal distribution. First you have to look the 81st percentile under the Z distribution and then "translate" it to a value of the variable X using the formula Z= (X- μ)/σ

P(Z≤z₁)= 0.81

z₁= 0.878

z₁= (x₁- μ)/σ

z₁*σ= x₁- μ

(z₁*σ) + μ= x₁

x₁= (z₁*σ) + μ

x₁= (2.7*0.878)+11.5

x₁= 13.8706 pounds

b) Find the 10th percentile of the baby weights.

P(X≤x₂)= 0.10

P(Z≤z₂)= 0.10

z₂= -1.282

z₂= (x₂- μ)/σ

z₂*σ= x₂- μ

(z₂*σ) + μ= x₂

x₂= (z₂*σ) + μ

x₂= (2.7*-1.282)+11.5

x₂= 8.0386 pounds

c) Find the first quartile of the baby weights.

P(X≤x₃)= 0.25

P(Z≤z₃)= 0.25

z₃= -0.674

z₃= (x₃- μ)/σ

z₃*σ= x₃- μ

(z₃*σ) + μ= x₃

x₃= (z₃*σ) + μ

x₃= (2.7*-0.674)+11.5

x₃= 9.6802 pounds

I hope this helps!

8 0

3 years ago

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 18 cm

neonofarm [45]

Answer: b

Step-by-step explanation: ik

7 0

3 years ago

2x+3y=0 and x+2y=-1 Solve by substitution