A plumber used 2.895 m of pipe during a job. How much pipe did he use rounded to 1 decimal place?

Explain how you could write a quadratic function in factored form that would have a vertex with an x-coordinate of 3 and two dis

dem82 [27]

Two distinct roots means two real solutions for x (the parabola needs to cross the x-axis twice)

Vertex form of a quadratic equation: (h,k) is vertex

y = a(x-h)^2 + k

The x of the vertex needs to equal 3

y = a(x-3)^2 + k

In order to have two distinct roots the parabola must be (+a) upward facing with vertex below the x-axis or (-a) downward facing with vertex above the x-axis. Parabolas are symmetrical so for an easy factorable equation make "a" 1 or -1 depending on if you want the upward/downward facing one.

y = (x-3)^2 - 1

Vertex (3,-1) upwards facing with two distinct roots 4 and 2

y = x^2 -6x + 9 - 1

y = x^2 -6x + 8

y = (x - 4)(x - 2)

7 0

2 years ago

Read 2 more answers

Use the values on the number line to find the sampling error.

pantera1 [17]

Part 1:

Given a number line with the point $\bar{x}=3.8$ and the point $\mu=4.27$

The sampling error is given by:

$\bar{x}-\mu=3.8-4.27=-0.47$

Part 2:

Given a number line with the point $\bar{x}=26.43$ and the point $\mu=24.67$

The sampling error is given by:

$\bar{x}-\mu=26.43-24.67=1.76$

4 0

2 years ago

Consider the following regression model: Humidity = β0 + β1Temperature + β2Spring + β3Summer + β4Fall + β5Rain + ε, where the du

FinnZ [79.3K]

Answer:

The regression equation for the winter rainy days is "Humidity = (β0 + β5) + β1Temperature".

Step-by-step explanation:

Given:

Humidity = β0 + β1Temperature + β2Spring + β3Summer + β4Fall + β5Rain + ε ...........(1)

Since there can be only one of spring, summer,fall, and winter at a point in time or in a season, we will have the following when there are winter rainy days:

Spring = 0

Summer = 0

Fall = 0

Rain = 1

Substituting all the relevant values into equation (1) and equating ε also to 0, a reduced form of equation (1) can be obtained as follows:

Humidity = β0 + β1Temperature + (β2 * 0) + (β3 * 0) + (β4 * 0) + (β5 * 1) + 0

Humidity = β0 + β1Temperature + 0 + 0 + 0 + β5 + 0

Humidity = (β0 + β5) + β1Temperature

Therefore, the regression equation for the winter rainy days is "Humidity = (β0 + β5) + β1Temperature".

3 0

2 years ago

A lotion is made from an oil blend costing $1.50 per ounce and glycerin costing $1.00 per ounce. Four ounces of lotion costs $5.

Svet_ta [14]

Answer:

A (4-g)1.5

Step-by-step explanation:

hope this helps if you need a explanation just ask in the comments and I will.

8 0

2 years ago

Please help!!

rusak2 [61]

ANSWER TO QUESTION 1

The set of natural numbers that are factors of 20 are natural numbers that divides 20 exactly without a remainder.

These natural numbers are;

{ $1,2,4,5,10,20$ }

Therefore the correct answer is D

ANSWER TO QUESTION 2

Given that the universal set U has elements

{ $1,2,3,4,5,6,7,8,9,10$ }

and the set P also has elements

{ $2,4,6,8,10$ }

The elements of P' are the elements that are in the universal set but are not in set P.

These elements are;

{ $1,3,5,7,9$ }

The correct answer is C

ANSWER TO QUESTION 3

The distance is given by the absolute value equation

$d=|130-25t|$

If the is 15 feet away then $d=15$

This implies that;

$15=|130-25t|$

We now split the absolute value sign to obtain,

$15=130-25t$

or

$-15=130-25t$

We now solve for t to obtain;

$15-130=-25t$

or

$-15-130=-25t$

$\frac{115}{25}=t$

or

$\frac{145}{25}=t$

This gives us

$4.6=t$

or

$5.8=t$

The correct answer is C

ANSWER TO QUESTION 4

Given

P={ $0,1,2,3,4,56,7,8,9$ }

and

V={ $2,4,6,810,1216,18,20$ }

P $\cap$ V={2,4,6,8}

P\V are elements in P only .

This means that we have to take out the elements of the intersection of the two sets from P.

P\V ={0,1,3,5,5,7,9}

The correct answer is B

ANSWER TO QUESTION 5

The correct answer is B.

In listing the elements of a set, we do not repeat the element. In order words we list only distinct elements.

Blueberry is repeating in both sets but we have to list it once.

ANSWER TO QUESTION 6.

The correct answer is 220

We were told that 250 play basket ball

If 120 play both sports, then

250-120=130

play only basketball

Now the number of people who play only baseball

$350-250=100$

But the number of people who play baseball

$120+100=220$

see diagram

7 0

2 years ago