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3 years ago

Write an equivalent expression for 5a+30

2 answers:

8 0

Write it in factorized form.
Find the GCF
Which is 5
Place that outside the parenthesis
And you get an answer of:

5(a + 6)

Elena-2011 [213]3 years ago

7 0

We can express it at 5 (a+6)

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The point (3,-2) is rotated 90º counterclockwise about the origin and then dilated by a scale factor of 4. What are the coordina

Nezavi [6.7K]

Answer:

(-2,-3)

Step-by-step explanation:

5 0

3 years ago

Select all of the following statements that are true.

nordsb [41]

Answer:

I dont understand where are the statements

7 0

3 years ago

Bullco blends silicon and nitrogen to produce two types of fertilizers. Fertilizer 1 must be at least 40% nitrogen and sells for

leva [86]

Answer:

Maximize

z = 70(Xs1 + Xn1 ) + 40(Xs2 + Xn2 ) - 10 (Xs1 + Xs2 ) - 15(Xn1 + Xn2 )

Subject to the constraints

Xs1 + Xs2 ≤ 100

Xn1 + Xn2 ≤ 80

Xn1 ≥ 0.4 ( Xs1 + Xn1 )

Xs2 ≥ 0.7 ( Xs2 + Xn2 )

All Variables ≥ 0

Step-by-step explanation:

Firstly lets consider Xs1 and Xs2 to be the number of pounds of silicon used in fertilizer1 and fertilizer2 respectively

Also let Xn1 and Xn2 be the number of pounds of nitrogen used in fertilizer1 and fertilizer2 respectively

We know that the objective is to maximize the profits of Bullco.

z = [(Selling price of fertilizer1) (Amount of silicon and nitrogen used to produce fertilizer1) + (Selling price of fertilizer2) (Amount of silicon and nitrogen used to produce fertilizer2) - (Cost of silicon) (Amount of silicon used to produce fertilizer I and 2) - (Cost of nitrogen) (Amount of nitrogen used to produce fertilizer I and 2)]

z = 70(Xs1 + Xn1 ) + 40(Xs2 + Xn2 ) - 10 (Xs1 + Xs2 ) - 15(Xn1 + Xn2 )

Now

Constraint 1; At most, 100 lb of silicon can be purchased

Amount of silicon used to produce fertilizer 1 and 2 ≤ 100

Xs1 + Xs2 ≤ 100

Constraint 2; At most, 80 lb of nitrogen can be purchased

Amount of nitrogen used to produce fertilizer 1 and 2 ≤ 80

Xn1 + Xn2 ≤ 80

Constraint 3; Fertilizer 1 must be at least 40% of nitrogen

Amount of nitrogen used to produce fertilizer 1 ≥ 40% (fertilizer 1)

Xn1 ≥ 0.4 ( Xs1 + Xn1 )

Constraint 4; Fertilizer 2 must be at least 70% of silicon

Amount of silicon used to produce fertilizer 2 ≥ 70% (fertilizer 2)

Xs2 ≥ 0.7 ( Xs2 + Xn2 )

so the formulization of the given linear program is,

Maximize

z = 70(Xs1 + Xn1 ) + 40(Xs2 + Xn2 ) - 10 (Xs1 + Xs2 ) - 15(Xn1 + Xn2 )

Subject to the constraints

Xs1 + Xs2 ≤ 100

Xn1 + Xn2 ≤ 80

Xn1 ≥ 0.4 ( Xs1 + Xn1 )

Xs2 ≥ 0.7 ( Xs2 + Xn2 )

All Variables ≥ 0

8 0

3 years ago

A project has a forecasted cash flow of $110 in year 1 and $121 in year 2. Risk free rate is 5%, the estimated risk premium on t

Crazy boy [7]

From the question we are told that:

$Cash Flow:$

Year 1= \$110

Year 2 = \$121

Risk free rate is $r=5%$

Risk premium $R=10\%$

$\beta = 0.7.$

Generally, the equation for Equity Return is mathematically given by

$e=r+\beta*R$

$e=0.05+(0.7*0.10)$

$e=0.12$

Therefore Present Value (PV) is

$PV=\frac{110}{1+0.12}+\frac{121}{1+0.12^2}$

Generally, the equation for certainty-equivalent cash flow is mathematically given by

$CE=(1+r)\frac{Year}{1+e}$

Therefore

For Certainty-equivalent cash flow Year One

$CE__=(1+0.05)\frac{110}{1+0.12}$

$CE_1=103.125$

For Certainty-equivalent cash flow Year Two

$CE_2=(1+0.05)\frac{121}{1+0.12}$

$CE_2=113.4$

The Ratio of the certainty-equivalent cash flows to the expected cash flows in years 1 and 2 could be written as

$R=103.125:113.4$

$R=\frac{103.125}{113.4}$

7 0

3 years ago

. The mean incubation time for a type of fertilized egg kept at a certain temperature is 25 days. Suppose that the incubation ti

Paul [167]

Answer:

Step-by-step explanation:

Given that the mean incubation time for a type of fertilized egg kept at a certain temperature is 25 days.

Let X be the incubation time for a type of fertilized egg kept at a certain temperature is 25 days.

X is N(25, 1)

a) Normal curve is in the attached file

b) the probability that a randomly selected fertilized egg hatches in less than 23 days

= $P(X$

we convert x into Z score and use std normal distn table to find probability

$P(X$

i.e. we can say only 2.5% proportion will hatch in less than 23 days.

8 0

3 years ago