5 divided by -3 minus 3 times the square root of 3

The functions f(x) = cos 2x + 1 and g(x) = sin x + 2 intersect at x = pi/6, pi/2, 5pi/6, and 3pi/2 in the interval [0, 2π).

To find the intersection points, we set f(x) equal to g(x) and solve for x.

cos 2x + 1 = sin x + 2

Rearranging, we get:

cos 2x = sin x + 1

Using the identity cos 2x = 1 - 2sin²x, we can rewrite this as:

1 - 2sin²x = sin x + 1

Simplifying and factoring, we get:

2sin²x + sin x = 0

sin x(2sin x + 1) = 0

Therefore, sin x = 0 or sin x = -1/2. Solving for x in the interval [0, 2π), we get x = pi/6, pi/2, 5pi/6, and 3pi/2. These are the values at which f(x) and g(x) intersect.

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The confidence interval is 0.52±0.067.(option c)

What is confidence interval?

In statistics,  confidence interval means that the probability in which a population parameter will fall between a set of values for a certain proportion of times.

A political pollster wants to know what proportion of voters are planning to

vote for the incumbent candidate in an upcoming election. A poll of 150

randomly selected voters is taken from the more than 2,000 voters in the

population, and 78 of those selected plan to vote for the incumbent

candidate.

The formula for confidence interval(CI) is given by:

                      CI=  p ± z √{p(1-p)/n} ----------------(1)

Here from the given data p= 78/150= 0.52

                                          n= 150

For 90% confidence interval the value of z= 1.645.

Putting all the values in equation (1) we get,

                         CI= 0.52± 1.645√{(0.52×0.48)/150}

                             = 0.52±1.645×0.04

                             = 0.52±0.067

Hence, the confidence interval is 0.52±0.067.

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Using the data given such as the margin of error, sample size and z-score, the maximum sample size required is 499

To solve this problem, we need to know the minimum sample size required. The formula for this is given as;

n = (z² * p(1 - p))/ E²

Substituting the values into the formula;

n = (1.645² * 0.21(1 - 0.21))/ 0.03²

n = 498.8

The sample size should be at least approximately 499

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The accrued value of Staci's investment in the account in the year 2029 is $26933.59

The statements in the question can be sumarrized as

The formula to calculate amount on investment is

Amount = P * (1 + r)ⁿ

Where

When the values are substituted in the amount equation, we have

Amount = 14500 * (1 + 3.5%)¹⁸

Evaluate

Amount = 26933.59

Hence, the amount after the investment is $26933.59

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The function is not defined for x > 5, as a result ƒ(7) does not exist.

The given piece-wise function is:

f(x) = {x - 2}²- 1

1

-x+1

x < 2

x = 2

2 < x ≤ 5

Step 2

f(x) = (x-2)² - 1

1

-x+1

x < 2

x = 2

2 < x ≤ 5

Note that the function is not defined for x > 5.

Step 3

Since the function is not defined for > 5, therefore ƒ(7) does not exist.

The function is not defined for x > 5, therefore ƒ(7) does not exist.

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Answer:

1213124

To add 213341 and 444233 in base 5, we need to line up the digits of the two numbers according to their place values, and then add them digit by digit, carrying over to the next place value if the sum of the digits is 5 or greater.

Here's how to do it:

 2   1   3   3   4   1

+ 4   4   4   2   3   3

-----------------------

 1   2   1   3   1   2   4

Therefore, the sum of 213341 and 444233 in base 5 is 1213124.

The range, median and mode of the data-set are given as follows:

Considering the stem-and-leaf plot, the data-set is given as follows:

54, 55, 60, 66, 69, 72, 73, 74, 75, 75, 81, 82, 88, 89, 95, 96.

The range of a data-set is calculated as the difference between the highest value and the lowest value in the data-set, thus:

96 - 54 = 52.

The data-set has an even cardinality of 16, hence the median is calculated as the mean of the two middle elements as follows:

Median = (74 + 75)/2

Median = 74.5.

The mode of a data-set is the observation that appears the most times in the data-set, hence it is of 75, which is the only observation that appears twice in the data-set.

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Answer:

The true statements:

6 is an element of D

12 is an element of D

She earn fοr each year frοm 2014 thrοugh 2016 is 80628.40. The average οf her last five years οf wοrking $78,302.80. His annual retirement benefit was $28,423.92.

a) Salary οf 2014 : $76000

Salary in 2014 is the salary in 2015 increased by 3% οf the salary

= $76,000+3%

Salary οf 2015 = $78,280

Salary in 2015 is the salary in 2016 increased by 3% οf the salary

=$78,280+3%

Salary οf 2016 = $80,628.40

Hence, she earn fοr each year frοm 2014 thrοugh 2016 is 80628.40

b) The average οf the last three years is the sum οf the salaries divided by the number οf salaries.

= $76,000+$78,280+$80,628.40 / 3

= $78,302.80

Hence, the average οf her last five years οf wοrking $78,302.80

c ) The annual retirement benefit is the prοduct οf the rate and the average and the number οf years οf service.

= 1.65%×$78,302.80×22

=$28,423.92

Hence,  his annual retirement benefit was $28,423.92.

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If the number 48700 is written in scientific notation, it will be in form 4.87×10ⁿ, and the value of n is 4.

Scientific notation describes the shorthand way of writing very large or very small numbers in standard forms.

Writing in scientific notation, a number between 1 and 10 is multiplied by a power of 10.

48700 = 4.87×10ⁿ = 4.87×10⁴

Thus, the n represents the exponent of power 10 to which the number is reduced.

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To find out how many visitors Jackson's Ice Cream Shop needs on Saturday to make a profit for the week, we need to first calculate the total number of visitors for the six days already given in the table. Then we can find out the number of visitors needed on Saturday to reach the required mean of 110 visitors per day for the week.

Total number of visitors for the six days = 63 + 77 + 121 + 96 + 137 + 154 = 648

To make a profit for the week, the total number of visitors for the entire week needs to be:

110 visitors/day × 7 days/week = 770 visitors/week

We already have 648 visitors for the six days, so the number of visitors needed on Saturday to make a profit can be found by subtracting the total number of visitors already counted from the total number of visitors needed for the week:

770 - 648 = 122

Therefore, the answer is (C) 122 visitors on Saturday are needed to make a profit for the week.

Six types of costs are:

For assets attained in exchange for a deferred payment contract, the asset should be documented at its fair worth, which is the prevailing market rate. If establishing the fair value of the asset proves to be impracticable, the asset should be recorded based on the current value of upcoming payments due under the deferred payment agreement, stated using an apposite interest rate.

Generally, assets acquired in exchange of other non-monetary commodities should be appraised at their fair worth. If the truthful appraisal of the exchanged assets is uncertain, the assets should be noted down according to the seized amount of the items provided, including any received or paid cash during the transaction.

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Answer: the increase in price from $25 to $25.25 would result in a small increase in annual pass revenue of $178.50 or about 0.3%.

Step-by-step explanation: we can calculate the modern yearly pass income by increasing the modern amount requested by the unused cost of $25.25:

Unused yearly pass income = Modern cost x Modern amount requested

Unused yearly pass income = $25.25 x 2482 = $62,678.50

We as of now know that the ancient yearly pass income is $62,500 (since 2500 passes were sold at $25 each), so ready to calculate the alter in yearly pass income:

Alter in yearly pass income = Unused yearly pass income - Ancient yearly pass income

Alter in yearly pass income = $62,678.50 - $62,500 = $178.50

The critical value for an 80% confidence interval is 1.28 (rounded to three decimal places).

Statistics is a branch of mathematics that involves the collection, analysis, interpretation, presentation, and organization of data.

To find the critical value for an 80% confidence interval, we need to determine the z-score corresponding to the level of confidence. We can use a standard normal distribution table or a calculator to find this value.

Using a standard normal distribution table, we can find the z-score that corresponds to an 80% confidence level by finding the area between the mean and the upper tail of 10%, which is (100% - 80%)/2 = 10%.

The area between the mean and 10% is 0.5 - 0.10 = 0.40. Using the standard normal distribution table, the z-score that corresponds to an area of 0.40 is approximately 1.28.

Hence, the critical value for an 80% confidence interval is 1.28 (rounded to three decimal places).

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The dimensions of the rectangular block indicates;

(a) The largest number of bricks that can be cut from the block is 48 bricks

(b) The volume of the wood left is 216 cm³

The volume of the rectangular block is the product of the length, L, width, W, and height, H.

1. The dimensions of the rectangular block indicates that the block volume is; V = 24 cm × 9 cm × 7 cm = 1,512 cm³

The largest number of bricks that have side lengths of 3 cm that can be cut from the block is therefore;

Number of cubes; (24)/3 × (9)/3 × (7)/3 ⇒ 8 × 3 × 2 = 48

(b) The volume of wood left = 1512 - 48 × 3 × 3 × 3 = 216

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the correct expression which can also be used to determine the total time needed to cook x batches of boiled cornbread is,

B) 10x + 10x + 20 - 5.

Given that;

The expression 20x + 15 represents the total time needed to cook x batches of boiled cornbread.

We can simplify this expression by factoring out the common factor of 5: = 20x + 15

= 5(4x + 3)

Therefore, the expression that can also be used to determine the total time needed to cook x batches of boiled cornbread must have a factor of 5 in it.

Option A:

18x + 4x + 6 + 7 does not have a factor of 5,

so it cannot be the correct answer.

Option B:

10x + 10x + 20 - 5

= 20x + 15,

which is the same as the original expression.

Therefore, Option B is equivalent to the original expression and can also be used to determine the total time needed to cook x batches of boiled cornbread.

Option C:

6(5x + 5) - 10x + 15 = 30x + 15 - 10x + 15 = 20x + 30,

which does not have a factor of 5.

Therefore, Option C is not correct.

Option D:

3(x + x + x + 3) + 2x + 15 = 9x + 6 + 2x + 15 = 11x + 21,

which does not have a factor of 5.

Therefore, Option D is not correct.

Therefore, the correct answer is,

B) 10x + 10x + 20 - 5.

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a) A function for the amount of money in the account, B, after t months with an initial deposit of $100 isB(t) = [tex]100(1 + 0.002)^t[/tex]

b) The amount in the account increases by a factor of approximately 1.002 every month, approximately 1.025 every year and approximately 1.099 every five years.

a) The function for the amount of money in the account after t months with an initial deposit of $100 and an increase of 0.2% per month can be written as:

B(t) = [tex]100(1 + 0.002)^t[/tex]

where t is the number of months.

b) To determine the factor by which the amount in the account increases every month, year, and five years, we can calculate the value of the function for t = 1, t = 12, and t = 60, respectively, and then divide each value by the previous one.

For each month:

B(1) = 100(1 + 0.002) = $100.20

B(2) = 100(1 + 0.002)² = $100.40

B(2)/B(1) = $100.40/$100.20 = 1.001993

The amount in the account increases by a factor of approximately 1.002 every month.

For each year:

B(12) = 100(1 + 0.002)¹² = $102.44

B(24) = 100(1 + 0.002)²⁴ = $105.01

B(24)/B(12) = $105.01/$102.44 = 1.0249

The amount in the account increases by a factor of approximately 1.025 every year.

For every five years:

B(60) = 100(1 + 0.002)⁶⁰ = $110.41

B(120) = 100(1 + 0.002)¹²⁰ = $121.20

B(120)/B(60) = $121.20/$110.41 = 1.0991

The amount in the account increases by a factor of approximately 1.099 every five years. Therefore, the amount in the account increases by a small factor every month, a moderate factor every year, and a larger factor every five years.

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The surface area of the cube is 384 mm².

A cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.

Since there are six square that makes up a cube, to find the surface area of the cube, we find the area of one of the square and multiply by six

Where:

From the question,

Given:

Substitute this value into equation 1

Hence the right option is D. 384 mm².

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Answer:

12 / min

720 / hr

17,280 / day

6,307,200 / yr

Now divide 1,000,000,000 by 6,307,200 (darn close to your 158!)

If a study of the consultants in a particular industry has determined that the standard deviation of the hourly fee of the consultants is $23.  the 99% confidence interval for the true mean hourly fee of all consultants in the industry is (107.1, 118.9).

The formula for a confidence interval for the population mean is:

CI = X- bar ± z* (σ/√n)

where:

X- bar  = sample mean

z* = z-score for the desired level of confidence (99% in this case)

σ = population standard deviation

n = sample size

Substituting the given values, we get:

CI = 113 ± 2.576 * (23/√100)

Calculating the standard error:

SE = σ/√n = 23/√100 = 2.3

Now we can substitute this value into the formula:

CI = 113 ± 2.576 * 2.3

CI = 113 ± 5.92

So,

Lower limit: 107.1

Upper limit: 118.9

Therefore, the 99% confidence interval for the true mean hourly fee of all consultants in the industry is (107.1, 118.9).

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Answer:

12.5 is the answer

Step-by-step explanation:

7 × 60 ( 7 being the minutes, 60 being the hour )

= 420

+ 30

= 450

450 ÷ 3600 × 100

45000 ÷ 3600

450 ÷ 30

= 12.5

12.5 being the answer

Answer: 1; 520/9 number 2: 9/2 number 3: d number 4:d number 5: 151.7

Step-by-step explanation:

read the paragraph and then you’d have all the information that you need

Answer:

First braclets coast 3$ and necklaces coast 6$ so now in the box you can put 3in the first one then 6 in the next and keep going its like multiples of 3 and 6 :) Hope this helps.

Step-by-step explanation:

Answer:

so first off if its six grandchildren and 3 children then that means 9 people but if the children get double the amount distributed then lets treat it like 12 people so 25,000 each meaning each child of the police officer gets 50 thousand and each grandchild gets 25 thousand

Step-by-step explanation:

hope this helps !

There are exactly 250 blocks with exactly one face painted red.

What is cube ?

A cube is a three-dimensional solid shape with six square faces of equal size that meet at 90-degree angles. It is a special case of a rectangular prism, where all of the edges have the same length.

When the 10 x 10 x 10 cube is painted red on all faces, it means that all of the 1000 unit cubes inside the large cube are red.

When the cube is cut into ten 10 x 10 x 1 slices, each slice will contain 100 unit cubes. When each slice is cut into twenty-five 2 x 2 x 1 blocks, each block will contain 4 unit cubes.

Therefore, each 2 x 2 x 1 block will come from 4 unit cubes, and each unit cube will contribute to 4 different blocks.

To count the number of blocks with exactly one face painted red, we can focus on the blocks that have a red face on the bottom (or top) and three unpainted faces on the other sides. Each such block will correspond to one of the 100 unit cubes in a slice, and there are 10 slices, so there are 1000 such blocks in total.

However, each of these blocks has four unit cubes, so we need to divide by 4 to get the number of blocks. Therefore, the answer is:

1000 ÷ 4 = 250

Therefore, there are exactly 250 blocks with exactly one face painted red.

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Answer:

Larger number: 36

Smaller number: 13

Answer:

y = (3/4)x + 2

Step-by-step explanation:

A line (or linear function) can be represented by the equation y = mx + b where "m" is the slope and "b" is the y-intercept.

The y-intercept is when x = 0 or when the line crosses the y-axis. In the graph, notice that the line crosses at (0, 2). Thus, the y-intercept is at y = 2 and "b" must be "2".

Next, we have to find the slope, "m". The slope is defined as a change in "y" divided by a change in "x". Lets use the two points which are marked on the graph already, (4, 5) and (0, 2). We first subtract the y-values, and then divide that by the difference between corresponding x-values:

(5 - 2)/(4 - 0) = 3/4                           The slope is 3/4, so m = 3/4

Now, plug "m" and "b" into the equation:

y = (3/4)x + 2

Answer:

y=(3/4)x+2

Step-by-step explanation:

So first you need to find the slope (3/4). To find that you can use the rise over run method. In this case they have already chosen two points on the line, but you could use any exact points. Count how many up from 2 to 5 (in green), which is 3 then how many across (in red) which is 4. Then put the rise (3) over the run (4) so 3/4.

Then b (2) is equal to y in the y intercept which is (0,2)

(11) The value of expression 3/y + 2y/4 when y = 4 is [tex]2\frac{3}{4}[/tex].

Hence the correct option is (b).

(12) The value of expression 12/y + 3y/4 when y = 8 is [tex]7\frac{1}{2}[/tex].

Hence the correct option is (c).

(13) 2x/3 + 4 = 10 equation does x = 9.

Hence the correct option is (b).

(11) The given expression is,

3/y + 2y/4 = 3/y + y/2

Substituting the value of y = 4 we get,

3/4 + 4/2 = 3/4 + 2 = [tex]2\frac{3}{4}[/tex].

Hence the correct option is (b).

(12) The given expression is,

12/y + 3y/4

Substituting y = 8 in the given equation we get,

12/8 + (3*8)/4 = 3/2 + 6 = 1 + 1/2 + 6 = [tex]7\frac{1}{2}[/tex].

Hence the correct option is (c).

(13) Given the solution is x =9.

For first option: (2/3)*9 - 6 = 6 - 6 = 0

2x/3 - 6 = 12 does not satisfied by x = 9.

For second option: (2/3)*9 + 4 = 6 + 4 = 10

So, x = 9 satisfies 2x/3 + 4 = 10.

For third option: 3*9 - 12 = 27 - 12 = 15

So x = 9 does not satisfy 3x - 12 = 21.

For fourth option: 3*9 + 12 = 27 + 12 = 39

So x = 9 does not satisfy 3x + 12 = 19.

Hence the correct option is (b).

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