A company is creating a new fertilizer additive for lawn seed, which will be a mixture of nitrogen, phosphate, and potash. Based on their research, the total amount fertilizer added must be at least 14 oz. per 5 lb. bag of lawn seed, but should not exceed 20 oz. per 5 lb. bag. At least ¼ oz. of nitrogen must be used for every ounce of phosphate, and at least 1 oz. of potash must be used for every ounce of nitrogen. The costs per ounce of nitrogen, phosphate, and potash are $0.30, $0.18, and $0.54, respectively. Determine the mixture of the three ingredients in a 5 lb. bag that minimizes costs, as well as that cost.

Find the four initial terms of the Maclaurin series for f(x) = tan x

A pilot flew a jet from City A to City B, a distance of 1600 mi. On the return trip, the average speed was 20% faster than the outbound speed. The round-trip took 5 h 20 min. What was the speed from City A to City B?

A wire 370 in. long is cut into two pieces. One piece is formed into a square and the other into a circle. If the two figures have the same area, what are the lengths of the two pieces of wire (to the nearest tenth of an inch)?

How much will you have accumulated, if you annually invest $1,500 into an IRA at 8% interest compounded monthly for:

a. 5 year

b. 20 years

c. 40 years

d. How long will it take to earn your first million dollars? Your answer should be exact rounded within 2 decimal places. Please use logarithms to solve. (Total of 15 points)

Quest

When proving theorems, mathematicians consider most frequently four statements:

1. the conditional statement

2. the converse to the conditional statement

3. the inverse

4. the contrapositive

Among those four statements, which ones require negation of parts, or all, of the conditional statement? When negating a statement, for which keywords must you search? How are they negated?

A wire 370 in. long is cut into two pieces. One piece is formed into a square and the other into a circle. If the two figures have the same area, what are the lengths of the two pieces of wire (to the nearest tenth of an inch)?

A box contains 2 ?red, 3 white and 3 green balls. Two balls are drawn out of the box in succession without replacement. What is the probability that both balls are the same? color?

Prove the Converse of Proposition 3.3 by using Betweenness Axiom 1. The converse is Given B ? C ? D and A ? B ? D, then A ? B ? C and A ? C ? D. Please do not use "by mapping of letters"

A wire 370 in. long is cut into two pieces. One piece is formed into a square and the other into a circle. If the two figures have the same area, what are the lengths of the two pieces of wire (to the nearest tenth of an inch)?

The table to the right gives the per capita gross national product and the per capita expenditure on defense for eight developed countries. Gross domestic product​ (GDP) is a measure of the total economic output of a country in monetary terms. Per capita GDP is the GDP averaged over every person in the country. Complete parts a though c.

H            45,758                          1700

A. Make a scatter diagram for the data.

A.

200005500002000GDPDefense Spending

A scatterplot with a horizontal axis labeled G D P from 20000 to 55000 in increments of 5000 and a vertical axis labeled Defense Spending from 0 to 2000 in increments of 200 contains 8 points. (37500, 900); (32500, 800); (35000, 500); (35000, 1300); (35000, 300); (47500, 1200); (35000, 1000); (45000, 1700). All coordinates are approximate.

B.

200005500002000GDPDefense Spending

A scatterplot with a horizontal axis labeled G D P from 20000 to 55000 in increments of 5000 and a vertical axis labeled Defense Spending from 0 to 2000 in increments of 200 contains 8 points. (32500, 800); (32500, 650); (35000, 600); (35000, 1450); (35000, 100); (35000, 1400); (35000, 1000); (35000, 1700). All coordinates are approximate.

C.

200005500002000GDPDefense Spending

A scatterplot with a horizontal axis labeled G D P from 20000 to 55000 in increments of 5000 and a vertical axis labeled Defense Spending from 0 to 2000 in increments of 200 contains 8 points. (37500, 1700); (32500, 500); (35000, 1000); (35000, 800); (35000, 900); (47500, 300); (35000, 1300); (45000, 1300). All coordinates are approximate.

D.

200005500002000GDPDefense Spending

State whether the two variables appear to be​ correlated, and if​ so, state whether the correlation is​ positive, negative,​ strong, or weak.

A.

The two variables appear to be correlated and the correlation is strong and positive.

B.

The two variables appear to be correlated and the correlation is weak and negative.

C.

The two variables appear to be correlated and the correlation is weak and positive.

D.

The two variables appear to be correlated and the correlation is strong and negative.

E.

The two variables do not appear to be correlated.

C. Suggest a reason for the correlation or lack of correlation.

A.

The higher a​ country's per capita​ GDP, the less it can spend on per capita national defense.

B.

The higher a​ country's per capita​ GDP, the more it can spend on per capita national defense.

C.

There is no correlation between a​ country's per capita GDP and spending on per capita national defense.

If

f left parenthesis x right parenthesis equals 5 x squared minus 7 x plus 9f(x)=5x2−7x+9​,

find f(0)=

A coffee distributor needs to mix a Terraza coffee blend that normally sells for $10.50 per pound with a Gazebo coffee blend that normally sells for $13.40 per pound to create 100 pounds of a coffee that can sell for $10.60 per pound. How many pounds of each kind of coffee should they mix? pounds of the Terraza Blend. pounds of the Gazebo Blend

Rosita wants to install a circular sink in her new triangular countertop.She wants to choose the largest sink that will fit.which point of concurrency must she locate? explain how to find the answer and make a sketch

A projector screen is 3.5 ft tall and 6 ft wide. You want to project a photo that is 4 in tall by 6 in wide. What are the dimensions of the image of the largest photo that will fit on the screen?