Trigonometry question foundation

Answer:

80+ 0.3x = 60 + 0.4x

20 = 0.1x

x = 200

Therefore, at 150 miles, the best deal changes companies

Step-by-step explanation:

Answer:

elimination

Step-by-step explanation:

They only cross out answers you don't want

Answer:

slope is 3

Step-by-step explanation:

10,17

7,8

8-17=-9

7-10=-3

-9/-3=3

Extra people required is 50.

Each of the five workers should increase their efficiency to a rate of 15 sandwiches per 10 hour shift.

Proportions are defined as the concept where two or more ratios are set to be equal to each other.

Question 1 :

Number of associates = 30

Number of direct workers = 30 - 2 = 28

You work 8 hours a day and 5 days a week with two 15 minutes break or 30 minutes break per day.

Direct rate = 150 units per hour

Number of working hours in a week with break = 8 × 5 = 40 hours per week Number of working hours in a week = 7.5 hours per day × 5 days a week

                                                            = 37.5 hours per week

Units that department produce in a 40 hour week = 37.5 × 150 = 5625 units

28 people produce 5625 units in a week

Let x people produce 10,000 + 5625 = 15,625 units in a week

Using proportion,

28 : 5625 = x : 15,625

28 / 5625 = x / 15,625

x = (28 × 15,625) / 5625 = 77.78 ≈ 78

Extra people required = 78 - 28 = 50

Question 2 :

Number of sandwiches made in 10 minutes = 1

Number of sandwiches made in 10 hours = 60

5 workers are there. one worker makes 60/5 = 12 sandwiches

But Deli want number of sandwiches in 10 hours = 75

One worker should make 75/5 = 15 sandwiches instead of 12.

Number of sandwiches made in 8 minutes should be 1.

So the working efficiency on each worker should be increased and produce each one should produce 15 sandwiches in a 10 hour shift.

Hence extra people required in question 1 is 50 and efficiency of each worker in question 2 should be increased to 15 sandwiches in 10 hours shift.

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the slope of the line on the graph is 3 .

Slope is calculated by dividing the "vertical change" by the "horizontal change" between any two distinct points on a line. The ratio can alternatively be expressed as a quotient, which yields the same result for any two separate locations on the same line ("rise over run"). A negative "rise" indicates a falling line. A road surveyor may judge that the line is useful, or it may show up in a diagram of a road or a roof as a description or a design. The steepness, incline, or grade of a line can be measured using the slope's absolute value. A slope with a larger absolute value denotes a steeper line.

to find the slope of the graph we will take two points which lies on the same line i.e. they must be collinear .

the points i m choosing is (-2,0) and (-1,3)

now for finding the slope we will use the formula

m = (y2-y1)/(x2-x1)

m = (3 - 0 ) / (-1+2)

m = 3 / 1

m = 3

so the slope of the line on the graph is 3 .

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Answer:

C(m) = 41(flat rate) + .10m(rate per mile)

Step-by-step explanation:

The sample space

even number

Solution

Probability of selecting even number

Probability of selecting a 13

Answer:

it has 1 solution of 1/2 or decimal form of 0.5

Etta needs to add the source of the information to better arrange these notes.

A note is a place where information about a specific item is recorded for later reference. The main goals of taking notes are to promote active learning and create study materials for tests. You should be able to organise material into an understandable format that will aid in your learning process by developing note-taking skills.

As a result, it is clear from the question that Etta is making notes for the purpose of creating a webpage about healthy eating. Once her notes have been organised with the relevant facts and information, Etta will need to cite her sources.

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Answer:

B

Step-by-step explanation:

a fraction is equal to 0 when the numerator is 0

x - 4 = 0

x = 4

The correct answer is x=4.

Step-by-step explanation:

When the numerator is 0, a fraction is equal to 0.

x - 4 = 0

x = 4

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Answer:

5/18

Step-by-step explanation:

The total number of horses present is 9

The probability that the first selected horse is tan is 4/9

So , now for the second choice , we are left with 8 total horses of which 5 is brown

The probability is 5/8

So the joint probability is the product of this two

That will be;

5/8 * 4/9 = 5/18

An unsecured line of credit is a type of credit that does not require collateral to secure the loan.

Unlike a secured line of credit, which requires an asset such as a home or car to be used as collateral, an unsecured line of credit is not tied to any specific asset.

Instead, the lender approves the borrower based on their creditworthiness, income, and other financial factors.

This type of credit may be useful for individuals who need access to funds but do not have any assets to use as collateral. Unsecured lines of credit may have higher interest rates than secured lines of credit because the lender is taking on more risk by not requiring collateral.

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The number of balloons which will not be used by Anissa is 4 balloons.

To make all 5 hats the same, Anissa needs to use the same number of balloons for each hat.

Let us call the number of balloons she uses for each hat "x". Since she's making 5 hats, she'll use a total of 5x balloons. We know that she has 54 balloons in total, so we can set up an equation:

5x = 54

To solve for x, we can divide both sides by 5:

x = 54 / 5

x = 10.8

Since she can't use a fraction of a balloon, she'll need to use 10 balloons for each hat.

= 5 hats x 10 balloons/hat

= 50 balloons used

So Anissa will not use:

= 54 - 50

= 4 balloons.

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Answer: (Likely) y = -2x

Step-by-step explanation:

1. We know the line y = 2x + 4, it intersects 4 and it's rate of change is 2. We also know the point it is passing, (-4,-1).

2. With this info, It is best to confirm the slope is likely -2, since it is likely that lines when perpendicular are likely to be congruent.

3. So, how about the y intercept? Well, it's simple as well, we will substitute x for 0, and 2 times 0 equals 0, and y = 0, so the perpendicular line is y = -2x

The probability of selecting a defective roofing sheet from the finished products of ABC is 2.45%. If a randomly selected defective sheet is found, the probability that it was made by machine B3 is approximately 54.55%.

To determine the probability of selecting a defective roofing sheet from the finished products of ABC, we need to calculate the weighted average of the defect rates for each machine.

The weighted average defect rate is calculated by multiplying the defect rate of each machine by its corresponding proportion of production and summing the products.

Weighted Average Defect Rate = (0.02 * 0.30) + (0.03 * 0.45) + (0.02 * 0.25)

                            = 0.006 + 0.0135 + 0.005

                            = 0.0245

Therefore, the probability of selecting a defective roofing sheet from the finished products of ABC is 2.45%.

To calculate the probability that a randomly selected defective sheet was made by machine B3, we need to consider the proportion of defective sheets contributed by B3 out of the total defective sheets.

The proportion of defective sheets from B3 = (0.02 * 0.30) / 0.0245

                                            = 0.006 / 0.0245

                                            ≈ 0.245

The probability that a defective sheet was made by machine B3 can be obtained by dividing the proportion of defective sheets from B3 by the overall probability of selecting a defective sheet.

Probability of sheet made by B3 = (0.245 / 0.0245) * 100

                              ≈ 54.55%

Therefore, if a randomly selected defective roofing sheet is found, the probability that it was made by machine B3 is approximately 54.55%.

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Answer:

75+75×15/100=75+11.25=86.25$

Answer:

d. 20

Step-by-step explanation:

To answer the question given, we will follow the steps below:

we need to first find p(3)

p(x) = x+ 7/ x-1

we will replace all x by 3 in the equation above

p(3) = 3+7 / 3-1

p(3) = 10/2

p(3) = 5

Similarly to find q(2)

q (x) = x^2 + x - 2,

we will replace x by 2 in the equation above

q (2) = 2^2 + 2 - 2

q (2) = 4 + 0

q (2) = 4

The product of p(3) and q(2)   =   5 × 4   = 20

By using a trigonometric relation, we will see that the value of x is 60.57°

On the image, we can see a right triangle where x represents one of the angles.

We can see that the length of the two catheti are shown, such that the adjacent cathetus is 2.2, and the opposite cathetus is 3.9, then we can use the trigonometric relation:

tan(a) = (opposite cathetus)/(adjacent cathetus)

Then we can write:

tan(x) = 3.9/2.2

Using the inverse tangent function in both sides, we will get:

Atan( tan(x)) = Atan(3.9/2.2)

x = Atan(3.9/2.2) = 60.57°

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Answer:

\(x\geq 6\)

\(y\geq 5\)

Step-by-step explanation:

A bell-shaped probability distribution that is symmetrical about its mean is the student's t-distribution. In the following situations, it is thought to be the distribution that should be used to build confidence intervals when working with little samples that have fewer than 30 components if it is unclear what the population variance is.

When the involved distribution is either normal or nearly normal.

A t-distribution is used to test the following in addition to being used to build confidence intervals:

Individual population mean

The variations in two population means.

The average variation among paired (dependent) populations.

The correlation coefficient for the populace.

If the sample size is high enough for the central limit, a t-distribution may still be viable for usage even in the absence of explicit normality for a specific distribution theorem that must be used. In this scenario, the distribution is regarded as roughly normal.

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The graph of line a and line b is shown in the image attached below. The lines do not intersect each other.

To check if both lines intersect, we need to graph the system of equations. First, use the points given to write out the equations.

Line a:

Slope (m) = change in y / change in x = 6 - 4 / 8 - 0 = 2/8

m = 1/4

Find the y-intercept (b) by substituting m = 1/4, x = 0 and y = 4 into y = mx + b:

4 = 1/4(0) + b

b = 4

The equation of line a is: y = 1/4x + 4.

Line b:

Slope (m) = change in y / change in x = 1 - (-2) / 8 - 0

m = 3/8

Find the y-intercept (b) by substituting m = 3/8, x = 0 and y = -2 into y = mx + b:

-2 = 3/8(0) + b

b = -2

The equation of line b is: y = 3/8x - 2.

Both lines are graphed in the image attached below. Line a is the red line and line b is the red line. They do not intersect at any point.

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Answer:

AC ≈ 12

Step-by-step explanation:

the angle between the tangent AC and the radius BC is 90°

then Δ ABC is right

note that BC = 9 ( radius of circle )

using Pythagoras' identity in the right triangle

AC² + BC² = AB²

AC² + 9² = (9 + 6)² = 15²

AC² + 81 = 225 ( subtract 81 from both sides )

AC² = 144 ( take square root of both sides )

AC = \(\sqrt{144}\) = 12

The statements that are True about the Correlations is , "Correlations are a measure used to determine the degree to which two variables are related" , the correct option is (c) .

In the question,

few statements about Correlation is given ,

we need to find the statement that is True .

we know that , Correlation is the term that is used to measure the degree of relationship between two variable ,

the correlation can be negative , positive or 0 ,

and the negative correlation implies that if one variable increases then other variable decreases and vice a versa .

So , from the above information about Correlation ,

we conclude that , the True statement is "Correlations are a measure used to determine the degree to which two variables are related. "

Therefore , the statement in option (c) is True  .

The given question is incomplete , the complete question is

Select the statement below that is true about correlations.

(a) Correlations can only be negative

(b) Correlations are a measure of how much one variable changes as the other variable changes

(c) Correlations are a measure used to determine the degree to which two variables are related.

(d) Correlations are a measure of causation between two variables

(e) A negative correlation implies no relationship between variables

(f) Correlations can only be positive .

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The quadrant the angle C lies is the quadrant I

From the question, we have the following parameters that can be used in our computation:

Point P = (4, 5)

This point is in the terminal side

This means that the angle C is located in the quadrant of the terminal side

The point P has the following coordinates

x = 4 -- positive

y = 5 -- positive

This means that the quadrant the angle C lies is the quadrant I

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Answer:

5 marbles are black.

Step-by-step explanation:

7-2=5

Answer:

53.658

Step-by-step explanation:

Answer:

≈ 10.63

Step-by-step explanation:

Pythagorean Theorem... Possibly the most easy theory in math once you understood it.

Here's the formula.

\(A^2+B^2=C^2\)

AB would be the hypothenuse

BC would be the opposite

CA would be the Adjacent.

But let's not make it complicated though, the question is actually quite easy.

You are asked to find AB, the hypothenuse.

The hypothenuse would be C.

BC and CA would be A and B.

It doesn't matter where are you going to place the numbers.

So, \(7^2 + 8^2\)

\(7^2 + 8^2 = 49 + 64\\\)

= 113

Now we would have to square root 113 since \(A^2+B^2=C^2\)

\(\sqrt{113}\) is an irrational number, and the question asks you to round ro the nearest tenth.

\(\sqrt{113}\) =10.63014581

≈ 10.63

Your answer would be 10.63

It will take approximately 39.532 days for $9500 to earn $800 at an annual interest rate of 8.25%.

To find the number of days it will take for $9500 to earn $800 at an annual interest rate of 8.25%, we need to use the formula for simple interest:

Interest = Principal * Rate * Time

In this case, we are given the interest ($800), the principal ($9500), and the annual interest rate (8.25%). We need to solve for time.

Let's denote the time in years as "t". Since we're looking for the number of days, we'll convert the time to a fraction of a year by dividing by 365 (assuming a standard 365-day year).

$800 = $9500 * 0.0825 * (t / 365)

Simplifying the equation:

800 = 9500 * 0.0825 * (t / 365)

Divide both sides by (9500 * 0.0825):

800 / (9500 * 0.0825) = t / 365

Simplify the left side:

800 / (9500 * 0.0825) ≈ 0.1083

Now, solve for t by multiplying both sides by 365:

0.1083 * 365 ≈ t

t ≈ 39.532

Therefore, it will take approximately 39.532 days for $9500 to earn $800 at an annual interest rate of 8.25%.

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Since you have the option to choose any number from 1 to 100, you need to calculate the expected payout for each case and choose the number that yields the highest expected value.

Let's denote the number of marbles you put in the bag as n. The probability of your marble being picked is 1/n, as there are n marbles in total and only one is chosen. In this case, your payout would be (100 - n). Therefore, the expected payout can be calculated.

To find the optimal number of marbles, we need to maximize the expected payout. We can do this by taking the derivative of the expected payout with respect to n and setting it equal to zero. Solving this equation will give us the value of n that maximizes the expected payout.

However, since the equation is not a simple linear or quadratic equation, solving it analytically might be challenging. Therefore, numerical methods or optimization algorithms can be employed to find the optimal value.

In this scenario, it is difficult to determine the exact optimal number of marbles without further information or assumptions about your preferences or risk aversion. However, through the use of mathematical techniques, you can determine the expected payouts for different numbers of marbles and choose the one that aligns with your desired outcome or risk tolerance.

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