I need helping finding the area of this circle.

Graph the system of equation below on a piece of paper what is the solution y=x-1 and y=-2x+5

ANTONII [103]

We are given

First equation:

$y=x-1$

we can use formula

$y=mx+b$

slope is m=1

y-intercept is b=-1

Second equation:

$y=-2x+5$

we can use formula

$y=mx+b$

slope is m=-2

y-intercept is b=5

Graph:

We can see that

both curves intersect at (2,1)

so, solution is x=2 and y=1.................Answer

6 0

4 years ago

A supervisor records the repair cost for 14 randomly selected refrigerators. A sample mean of $79.20 and standard deviation of $

Nitella [24]

Answer:

( $74.623, $83.777)

The 90% confidence interval is = ( $74.623, $83.777)

Critical value at 90% confidence = 1.645

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = $79.20

Standard deviation r = $10.41

Number of samples n = 14

Confidence interval = 90%

Using the z table;

The critical value that should be used in constructing the confidence interval.

z(α=0.05) = 1.645

Critical value at 90% confidence z = 1.645

Substituting the values we have;

$79.20+/-1.645($10.42/√14)

$79.20+/-1.645($2.782189528308)

$79.20+/-$4.576701774067

$79.20+/-$4.577

( $74.623, $83.777)

The 90% confidence interval is = ( $74.623, $83.777)

5 0

3 years ago

The inverse variation equation shows the relationship between wavelength in meters, x, and frequency, y.

wolverine [178]

Answer:

$\lambda=10^{-10}\ m$

Step-by-step explanation:

Given that,

The frequency of x-rays, $f=3\times 10^{18}\ Hz$

We need to find the wavelength for x-rays. The relation between wavelength, frequency and speed of light is given by :

$v=f\lambda\\\\\lambda=\dfrac{c}{f}\\\\\lambda=\dfrac{3\times 10^{8}}{3\times 10^{18}}\\\\=10^{-10}\ m$

So, the wavelength for x-rays is $10^{-10}\ m$ .

7 0

3 years ago

Determine the value of k

KATRIN_1 [288]

Answer:

$\displaystyle k = 6$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Algebra I

Functions
Function Notation

Algebra II

Piecewise Functions

Calculus

Limits
Continuity

Step-by-step explanation:

Step 1: Define

Identify

Continuous at x = 2

$\displaystyle f(x) = \left \{ {{2x^2 \ if \ x < 2} \atop {x + k \ if \ x \geq 2}} \right.$

Step 2: Solve for k

Definition of Continuity: $\displaystyle \lim_{x \to 2^+} 2x^2 = \lim_{x \to 2^-} x + k$
Evaluate limits: $\displaystyle 2(2)^2 = 2 + k$
Evaluate exponents: $\displaystyle 2(4) = 2 + k$
Multiply: $\displaystyle 8 = 2 + k$
[Subtraction Property of Equality] Subtract 2 on both sides: $\displaystyle 6 = k$
Rewrite: $\displaystyle k = 6$