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3 years ago

Verify the identity. Show your work. 1 + sec^2xsin^2x = sec^2x

1 answer:

4 0

$\bf \textit{Pythagorean Identities}
\\\\
1+tan^2(\theta)=sec^2(\theta)\\\\
-------------------------------\\\\
1+sec^2(x)sin^2(x)=sec^2(x)
\\\\\\
1+\cfrac{1}{cos^2(x)}\cdot sin^2(x)\implies 1+\cfrac{sin^2(x)}{cos^2(x)}\\\\\\ 1+tan^2(x)\implies sec^2(x)$

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7 less than fifteen times a number

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7 - 15 x n
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3 years ago

Read 2 more answers

Dakota earned $15.00 in interest in Account A and $22.50 in interest in Account B after 18 months. If the simple interest rate

11111nata11111 [884]

Answer:

Step-by-step explanation:

Dakota kiếm được 15 đô la tiền lãi trong Tài khoản A và 22,50 đô la tiền lãi trong Tài khoản B sau 18 tháng

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2 years ago

Find the value of x. *

Ludmilka [50]

Answer:

13x + 7 + 4x + 15 = 90

17x + 22 = 90

17x = 68

x = 4

4(4) + 15= 16 + 15= 31

13(4) + 7 = 52 + 7 = 59

Step-by-step explanation:

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3 years ago

An education firm measures the high school dropout rate as the percentage of 16 to 24 year olds who are not enrolled in school a

posledela

Answer:

The value of the test statistic $z = -0.6606$

Step-by-step explanation:

From the question we are told that

The high dropout rate is $\mu = 6.1$ % $= 0.061$

The sample size is $n = 1000$

The number of dropouts $x = 56$

The probability of having a dropout in 1000 people $\= x = \frac{56}{1000} = 0.056$

Now setting up Test Hypothesis

Null $H_o : p = 0.061$

Alternative $H_a : p < 0.061$

The Test statistics is mathematically represented as

$z = \frac{\= x - p}{\sqrt{\frac{p(1 -p)}{n} } }$

substituting values

$z = \frac{0.056 - 0.061}{\sqrt{\frac{0.061(1 -0.061)}{1000} } }$

$z = -0.6606$

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2 years ago

The production planner for Fine Coffees, Inc. Produces two coffee blends: American (A) and British (B). He can only get 300 poun

VladimirAG [237]

Answer:

P=2A+B where:

A= # of pounds of American blend and

B= # of pounds of British blend

Step-by-step explanation:

This is a linear programming problem. In order to solve it we need to determine how we are going to use the provided data and we need to keep in mind what we need to maximize (or minimize depending on the problem)

So, the problem states that "The goal of Fine Coffees, Inc. Is to maximize profits." This last sentence will tell us what the objective function will be. The objective function must model the desired value we want to maximize. So the objective function should represent the profits of selling the two tipes of cofee blends.

So this is the data the problem gives us:

"He can only get 300 pounts of Colombian beans per week and 200 pounts of Dominican beans per week." This part or the problem is talking about the amount of coffee beans he can get depending on its type. This will help us find the restrictions for our linear programming problem, so they are not necessary to state the objective function. Next it states:

"Each pount of American blend cofee requires 12 oz of Colombian beans and 4 oz. of Dominican beans, while a pound of British blend coffee uses 8 oz of each type of bean." Again, this data will help us find the restrictions for our linear programming problem, since they will tell us how much coffe we can manufacture, so they are not needed to find the objective function.

The next part states: "Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound." Now, we are interested in this part since it's talking about profits, which is what we need to maximize.

We set A to be the number of pounds of American blend and B to be the number of pounds of British blend. So the profit for American blend is found by using the following equation:

$P_{American}=$2.00*A$