Evaluate 8x-y2-3 when x = -1/4 and y=3<br>plz help

The length of the diameter, d, of the circle is 16cm. Find the length of the radius, r, of the circle.

Anna71 [15]

The radius would be 8cm.

8 0

3 years ago

Use the null hypothesis H0 : μ = 98.6, alternative hypothesis Ha: μ < 98.6, and level of significance α = 0.05. 98 99.6 97.8

andrezito [222]

Answer:

The t-score is -1.8432

Step-by-step explanation:

We are given the following in the question:

98, 99.6, 97.8, 97.6, 98.7, 98.4, 98.9, 97.1, 99.2, 97.4, 99.1, 96.9, 98.8, 99.9, 96.8, 97, 98.7, 97.6, 98.7, 98.2

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.

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

$Mean =\displaystyle\frac{1964.4}{20} = 98.22$

Sum of squares of differences = 16.152

$s = \sqrt{\dfrac{16.152}{49}} = 0.922$

Population mean, μ = 98.6

Sample mean, $\bar{x}$ = 98.22

Sample size, n = 20

Sample standard deviation, s = 0.922

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 98.6\\H_A: \mu < 98.6$

Formula:

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

Putting all the values, we have

$t_{stat} = \displaystyle\frac{98.22 - 98.6}{\frac{0.922}{\sqrt{20}} } = -1.8432$

The t-score is -1.8432

7 0

2 years ago

Which of the following statements is not true concerning the equation x2−c=0 for c>0? A. The left-hand side of this equation

Firdavs [7]

Answer:

The correct option is;

B. This equation is not considered to be a quadratic equation because it is not in the form a·x² + b·x + c = 0

Step-by-step explanation:

A. The given equation, x² - c = 0, can be presented in the form of the difference of two squares as follows;

(x + √c)·(x - √c) = 0

B. The equation x² - c = 0, is a quadratic equation because it is a polynomial equation of degree 2

C. The equation x² - c = 0 can always be factored as (x + √c)·(x - √c) = 0

D. Where c > 0, the equation x² - c = 0 can by the square root property as follows;

x² - c = 0

x² = c

x = √c

5 0

2 years ago

A baseball diamond is a square with sides of 90 ft What is the straight Distance between 1st and 3rd bases to the nearest thenth

yuradex [85]

Answer:c=127.3ft

Step-by-step explanation:Divide the square into two on the line between 1st and 3rd base, you now have two right triangles, pick one. The triangle has two legs and a hypotenuse, the length of the hypotenuse is the distance you need. The legs are 90ft long and you need to use the Pythagorean theorem. 90 squared plus 90 squared equals c squared, so 8100+8100=c^2, 16200=c^2, c=127.27922061

5 0

2 years ago

Quiana took out a loan to pay for a new car initially she owed the lender 15,234.68. she has repaid 247.43 of the loan each mont

kykrilka [37]

Given Information:

Initial amount of loan = $15,234.68

Monthly payment = $247.43

Number of months = 5

Required Information:

Net change in loan = ?

Answer:

Net change in loan = $1,237.15 = $1,237(3/20)

Step-by-step explanation:

Quiana owed her lender an amount of 15,234.68 initially, she repaid the lender each month with an amount of $247.43 for 5 months, so the total amount that she repaid is

Total amount repaid = Monthly payment*Number of months

Total amount repaid = $247.43 × 5

Total amount repaid = $1,237.15

The remaining owed amount is given by

Balance = Initial amount of loan - Total amount repaid

Balance = $15,234.68 - $1237.15

Balance = $13,997.53

So the net change to the loan from Quiana's perspective over the past 5 months is,

Net change in loan = Initial amount of loan - Balance

Net change in loan = $15,234.68 - $13,997.53

Net change in loan = $1,237.15

or

Net change in loan = $1,237(3/20)

Therefore, the net change to the loan from Quiana's perspective over the past 5 months is $1,237.15

5 0

2 years ago

Evaluate 8x-y2-3 when x = -1/4 and y=3plz help