The functions s and t are defined as follows.Find the value of t(s(- 4)) .t(x) = 2x ^ 2 + 1s(x) = - 2x + 1

Let's make a diagram to visualize the problem.

First, let's find angle A.

Then, we use the law of sines to find AB.

Given the function

Finding the derivative we have

Also

Finally

The quadrilateral ABCD was dilated by a scale factor of 3/4 to form the quadrilateral A'B'C'D'

This means that each side of the quadrilateral was multiplied by 3/4 to make the dilation.

You know that the scale factor is 3/4 and the length of D'A' is equal to 30 units, then:

Multiply both sides by the reciprocal of 3/4

The length of side DA is 40 units.

Based on the information given in the exercise, you know that the shaded region has this area:

And the area of each square region in the corners is:

Since there are four square regions, you can multiply that the area of any of them by 4, in order to find the total area of them:

Then, in order to find the total area of the figure, you must add the area of the shaded region and the total area of the square regions:

Therefore, the total of the figure is:

Linear Optimization

It consists of finding the optimum solution to a problem where all the conditions are related as linear functions.

We'll use the graphic method to solve the problem.

The problem is as follows:

Ava sells burritos amd tacos. Let's call x to the number of tacos sold and y to the number of burritos sold.

The first condition we find is that she can only produce a maximum of 130 units between tacos and burritos. This gives us the first inequality:

x + y ≤ 130 (1)

She sells each taco for $3.75 and each burrito for $6. She must sell a minimum of $600 worth of both products, so:

3.75x + 6y ≥ 600

Multiply this inequality by 4:

15x + 24y ≥ 2400

And divide it by 3:

5x + 8y ≥ 800 (2)

We are given a final condition that she can sell a minimum of 80 burritos, thus:

y ≥ 80 (3)

There are two obvious conditions not explicitly said but they can be deducted by the wording of the problem. Both x and y must be greater or equal to zero:

x ≥ 0 (4)

y ≥ 0 (5)

Let's put this all together:

x + y ≤ 130 (1)

5x + 8y ≥ 800 (2)

y ≥ 80 (3)

x ≥ 0 (4)

y ≥ 0 (5)

The optimum solution must satisfy all the conditions. They form a feasible region in the x-y coordinates system. One of the corners of that region will eventually be the best solution, depending on the objective function (not given here).

We need to graph all five lines in one common grid. It's shown below.

According to the graph, one possible solution is to sell x=50 tacos and y=80 burritos

In this question, we are given two locations of a military compound.

Let's take the coordinates of point A from the graph,

A = (-3, 2)

The new coordinates of A' = (5, 13)

translation in x-axis = 5 - (-3) = 5 + 3 = 8

translation in y-axis = 13 - 2 = 11

hence, each point of the figure will be translated to 8 units on the x-axis and 11 units on the y-axis.

The cost per minute is $0.05 and it is round off to the nearest hundredths place.

Round off:

Rounding off means a number is made simpler by keeping its value intact but closer to the next number. It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.

Given,

Advantage Cellular offers a monthly plan of $25 for 500 minutes.

Here we need to find the cost per minute and we have also need to round off the result to the nearest hundredth place.

We know that,

500 minutes cost = $25

So, to calculate the price for one minute, then we have to divide the cost by the total number of minutes.

So, it can be written as,

=> 25 ÷ 500

So, the cost for one minute is.

=> 0.050

When we rounded to the nearest hundredths place.

The 5 in the hundredths place rounds down to 5, or stays the same, because the digit to the right in the thousandths place is 0.

Therefore, the cost per minute is $0.05.

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The CLOSEST correct answer regarding "x" is the first one (answer A), since x is 79. The correct answer is: X measures 79 because it is an alternate external angle between parallel lines to the one labeled 79 in the picture.

Answer:

it would be within the range of $0.77 <x< $0.78

3x + 7y= 14

3x+7y= 10

Subtract the second equation to the first.

3x +7y= 14

-

3x + 7y= 10

_________

0x +0y = 4

0 = 4

0 is no

First, rewrite all the mixed fractions as impropper fractions:

Next, multiply the rate of chocolate production over time by the the operating time of the machines to find the total amount of pounds of chocolate frogs produced in one day:

Then, the chocolate factory can produce 16 1/2 pounds of chocolate frogs per day.

Since 16 1/2 is greater than 10 1/2, then the chocolate factory will meet their goal with the total being over 10 1/2 pounds of chocolate frogs produced.

Remember that

z =(x - μ)/σ

we have

μ=85

σ=5

For x=73

Find out the value of Z1

z1=(73-85)/5

z1=-2.4

For x=76

Find out the value of Z2

z2=(76-85)/5

z2=-1.8

using a z-scores table values

we have that

We are asked to evaluate the expression:

when x = 1 and y = -7

so we replace them as shown below, making sure we include them inside parenthesis to keep clear that the expressions in x and in y are multiplying each other:

So we see that x^2 becomes 1 and the factor y stays as -7. The final expression cancels out the negative sign in numerator (from -7) and in denominator (from -9) and gives 7/9.

SOLUTION

Given the image on the answer tab;

Explanation;

The two angles are said to be adjacent angles when they share the common vertex and side.

Considering our question;

Explanation

to figure out if a pair is a solution, just replace x and y values and check if the equation is true,then

Step 1

Step 2

Step 3

In the right triangle of sides a, b, and c

Since a = 12 and c = 20

Substitute them in the given rule

Subtract 144 from both sides

Take a square root for both sides

The answer is b = 16

Ashlee could make 2520 eight digit codes using the digits in her birthday .

In the question

it is given that

the birthdate of Ashlee is 09/08/1981.

So, the number of digits are 0,0,1,1,8,8,9,9  .

number of digits = 8

So, 8 digits can be arranged in 8! ways

8! = 8*7*6*5*4*3*2*1 = 40320

Repeating digits are

0 repeated 2 times = 2! = 2

1 repeated 2 times = 2! = 2

8 repeated 2 times = 2! = 2

9 repeated 2 times = 2! =2

So, the number of 8 digits codes is = 8!/(2!*2!*2!*2!)

= 8!/(2*2*2*2)

= 40320/16

= 2520

Therefore , Ashlee could make  2520 eight digit codes using the digits in her birthday .

The given question is incomplete , the complete question is

Ashlee was born on 09/08/1981. How many eight digit codes could she make using the digits in her birthday ?

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From the situation described in this problem, it is found that:

A. The composite function is: f(s(w)) = 36w + 30.

B. The unit of measurement of the composite function is: flowers.

C. After 36 weeks, Daisy can expect to bloom 1326 flowers.

For a composite function, the output of the inner function serves as the input of the outer function.

In the context of this problem, the functions are given as follows:

Hence the composite function that represents how many flowers Daisy can expect to bloom over a certain number of weeks is:

f(s(w)) = f(12w) = 3(12w) + 30 = 36w + 30.

The unit of measurement of the composite function is the unit of the outer function, which is flowers.

After 36 weeks, the number of flowers that Daisy can expect to bloom is given as follows:

f(s(36)) = 36(36) + 30 = 1326 flowers.

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Answer: B- interviewing college students to find what percentage expect a job immediately after graduation

Surveys are meant to collect data that can be used to analyze a population as ahwole. This option analyzes the perspective of college students as a whole, whereas option A only focuses on a minority group of elderly. Additionally, options C and D are moreso experiments and not surveys that can be applied on a larger scale.

Given:

Area of a shaded region of a rectangle is given.

Area of the rectangle is twice the area of the triangle given.

To solve this problem, the first thing we must do is find the Z-Score of the given costs: $5265 , $6735 , $4530 ,and $7470

Then we proceed to find the percentages for each interval based on the graph

z-score for $5265 )

z-score for $6735 )

z-score for $4530 )

z-score $7470 )

now, let's analyze the intervals

a ) between $5265 and $6735

This interval goes from (μ-σ) to (μ+σ)

if we look at the graph we find that this corresponds to a percentage of 68%

b) above $6735

This corresponds to what is to the right of (μ+σ)

This is a percentage of 16%

c ) below $4530

This corresponds to what is to the left of (μ-2σ)

This is a percentage of 2.5%

d ) between $5265 and $7470

This interval goes from (μ-σ) to (μ+2σ)

This is a percentage of 81.5%

Answer:

The slope is 3/5 and the equation is:

Explanation:

Given the points (0,2) and (5, 5)

The slope of a line is the ratio of the difference between the y coordinates to the x coordinates. The x coordinates are 0 and 5, the y coordinates are 2 and 5.

The equation of a straight line is given as:

y = mx + b

Where m is the slope and b is the y-intercept

Using any of the given points, we can find b

Use (0, 2), with x = 0, y = 2

2 = (3/5)(0) + b

b = 2

Now the equation is:

Answer:

Step-by-step explanation:

Given a graph of a probability density function, you want the probabilities ...

The probability of a given range of values of X is the area under the density curve for those values of x.

The triangular area to the left of X=16 has a base of 16 and a height of 0.08. Its area is given by the area formula for a triangle:

  A = 1/2bh

  A = 1/2(16)(0.08) = 0.64

The probability is P(X<16) = 0.64.

The area to the right of X=12 is a trapezoid with parallel "bases" of 0.06 and 0.10. The "height" of the trapezoid is 20-12 = 8. The area is given by the formula ...

  A = 1/2(b1 +b2)h

  A = 1/2(0.06 +0.10)(8) = 0.64

The probability is P(X>12) = 0.64.

Solution

Option 1:

- The owners asking the first 100 people they see would mean that they would see only those around them. This could be anyone at all from workers in the amusement park to people outside the park; these would not be random, and would not necessarily be a family but the survey is talking about randomly choosing 100 families. Because of these reasons, this is not the best way to randomly choose 100 families.

Option 2:

- Choosing a neighborhood near the amusement park would mean that they go to a neighborhood with families that might visit the amusement park and there would be many families to randomly choose from.

- This option seems like a good choice to randomly choose these 100 families that might visit the amusement park.

Option 3:

- Asking the first 100 families that enter the amusement park on a busy weekend would definitely bias the survey since families that you find in the amusement park are families that definitely want to be there and if they are there on a busy weekend, they certainly would not mind extending the season

SOLUTION

This is a permutation problem.

a) To find the number of possible two digits codes

There are 30 possible two-digit codes pattern.

b) To find the number of three digits codes

There are 120 possible three-digit codes pattern.

Any other pattern can be calculated using

So to predict the number of possible five-digit codes will be:

There are 720 different possible five-digit codes

the answer of this question is 720 ways

Answer:

33 days

Explanation:

If you use a half tablet for 7 days, you will consume:

0.5 x 7 days = 3.5 tablets.

So, at the end of the 7th day, you will consume 3.5 tablets and you will have 26.5 tablets left because:

30 tablets - 3.5 tablet = 26.5 tablets.

Then, you will consume 1 tablet daily, so if you have 26.5 tablets, you will have a tablet daily for 26 days.

Therefore, the day supply for 30 tablets will be the sum of the initial 7 days and the 26 days, so:

7 days + 26 days = 33 days.

Therefore, the answer is 33 days

The law of sines states that:

where alpha is the opposite angle to side a, beta is the opposite angle to side b and gamma is the opposite angle to side c.

For the triangle given we notice that:

Angle x is opposite to side 2.5.

Angle 28° is opposite to side 3.

Therefore the expression to find x is:

The situations that describe a proportional relationship are:

Jackson saves $10 in the first month and $30 in the next 3 months.

Mia saves $8 in the first 2 months and $4 in the next month.

Piyoli spends $2 in the first 2 days of the week and $5 in the next 5 days.

A relation is proportional if the rate of change of the variables is constant. The variables can either increase or decrease at a constant rate. A proportional relationship can be modelled with a linear equation.

Is Jackson's saving proportional?

Average of the amount saved in the next 3 months: $30 / 3 = $10

The relationship is proportional because the amount saved in the first month and the average is equal.

Is Mia's saving proportional?

Average of the amount saved in the first 2 months: $8 / 2 = $4

The relationship is proportional because the amount saved in the thir month and the average is equal.

Is Piyoli's spending proportional?

Average of the amount spent in the first 2 days: $2 / 2 = $1

Average of the amount spent in the next 5 days = $5 / 5 = $1

The relationship is proportional because the averages are equal.

Is Robert's spending proportional?

Average of the amount spent in the first 3 days: $2 / 3 = $0.67

Average of the amount spent in the next 4 days = $5 / 4 = $1.25

The relationship is not proportional because the averages are not equal.

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The probability is 0.57

What is meant by probability?

Probability is a discipline of mathematics that deals with appropriate units of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number ranging from zero and 1, where 0 denotes the event's feasibility and 1 represents certainty. The greater the likelihood of an occurrence, the more probable it will occur. Tossing a fair (unbiased) coin is a basic example. Because the coin is fair, the two possibilities ("heads" and "tails") are equally likely; the chance of "heads" equals the probability of "tails," and because no other outcomes are possible, the probability of either "heads" or "tails" is 1/2.

Probability of using the pool = 97/225 = 0.43

Probability that they do not use the swimming pool = 1 - 0.43 = 0.57

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