Find a formula for cos(tan−1(2x)) in terms of x

Answer:

$3606.44

Step-by-step explanation:

The question asks us to calculate the principal amount that needs to be invested in order to earn an interest of $6180 in 28 years at an annual interest rate of 6.12%.

To do this, we need to use the formula for simple interest:

\(\boxed{I = \frac{P \times R \times T}{100}}\),

where:

I = interest earned

P = principal invested

R = annual interest rate

T = time

By substituting the known values into the formula above and then solving for P, we can calculate the amount that James needs to invest:

\(6180 = \frac{P \times 6.12 \times 28}{100}\)

⇒ \(6180 \times 100 = P \times 171.36\)     [Multiplying both sides by 100]

⇒ \(P = \frac{6180 \times 100}{171.36}\)    [Dividing both sides of the equation by 171.36]

⇒ \(P = \bf 3606.44\)

Therefore, James needs to invest $3606.44.

Answer:

113

Step-by-step explanation: 113 is the prime number in between those numbers, thats the only one

Answer:

113

Step-by-step explanation:

1. Find the prime numbers between 110 and 125

A prime number is a number, greater than 1, that is not a product of two other numbers. The prime numbers near 110 and 125 include 107, 109, 113, and 127. However, only 113 lies between 110 and 125. So there is no sum because there is only 1 prime number.

Answer:y - x=1

Step-by-step explanation:

Answer:        4.2

Step-by-step explanation: 14.70÷3.5=4.2

Answer:

\(m=12f\)

Step-by-step explanation:

The measurement in inches =m

The measurement  in feet = f

We are told that: m varies directly with f

Written mathematically:

\(m\propto f\)

Introducing the constant of variation, we have:

\(m=k f\)

Given that: k=12

The equation relating these two quantities is:

\(m=12f\)

Answer:

165 minutes

Step-by-step explanation:

To solve for the number of minutes that Joaquin played for, we can use this expression:

(let 'a' represent how much time passed from the time Joaquin started playing basketball until the time he arrived at home)

Subtracting 1:10 from each side:

1:10 - 1:10 cancels out to 0, while 3:35 - 1:10 is equal to 2:25.

So, the expression is now:

So, 2 hours and 25 minutes passed.

If we know that 1 hour is equivalent to 60 minutes, we can use this expression to solve for however many minutes are in 2 hours:

Now we need to add on the number of minutes and the time it took him to get home:

Therefore, 165 minutes passed from the time Joaquin started playing basketball until the time he arrived at home.

Answer:

y = 4

Step-by-step explanation:

Replace x in the first equation with 4.

y = 2(4)-4

y = 8-4

y = 4

If there are any more of these types of problems you need help on, you can just ask me, you don't have to post more questions =)

For the above function 2x-10=4, the value of x is 7.

A linear function in mathematics is one that has either one or two variables and no exponents. It is a function with a straight line as its graph.

Given a function 2x-10= 4

Simplify using PEMDAS

2x-10= 4

add 10 on both sides

2x = 14

Divide by 2 into both sides

x = 7

therefore, The value of the x for the given function 2x-10= 4 is 7.

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A point has no length or thickness.

ALL OF THE ABOVE

Answer:

Emma is correct. There are 8 pots and two flowers in each pot, so 8 pots times 2 flowers per pot equals 16 flowers. Mark calculated how many pots there would be total if there were 8 gardens with 8 pots each, or how many flowers total if there were 8 pots with 8 flowers each.

Step-by-step explanation:

Answer:

Emma is correct because there are 8 pots and each of those 8 pots has 2 flowers inside it.  I hope  this "picture" might help

Explanation:

1st  pot: 2 flowers

2nd pot: 2 flowers

3rd pot: 2 flowers

4th pot: 2 flowers

5th pot: 2 flowers

6th pot: 2 flowers

7th pot: 2 flowers

8th pot:2 flowers

If we count these up, we get 16 flowers,

Mark said 8*8=64

Emma said 2*8=16

So, emma is correct

The absolute value of the Rational number -474/513 is 474/513.

To find the sum of the rational numbers -8/9 and -2/57, you need to have a common denominator. The least common multiple (LCM) of 9 and 57 is 513. So, you can rewrite the fractions with a common denominator:

-8/9 = (-8/9) * (57/57) = -456/513

-2/57 = (-2/57) * (9/9) = -18/513

Now, you can add the fractions:

-456/513 + (-18/513) = (-456 - 18)/513 = -474/513

To find the absolute value of the rational number -474/513, you simply ignore the negative sign and take the value as positive:

| -474/513 | = 474/513

Therefore, the absolute value of the rational number -474/513 is 474/513.

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Answer:

2(v-8)=6

Step-by-step explanation:

you have to follow the instructions written and then plug the values

Answer:

The width of the park should be 7.5 feet.

Answer:

X = 49.4

Step-by-step explanation:

Tan x = 7/6

Tan x = 1.1667

X = 49.4 degrees

Mean: 34.125, Median: 31.5, Mode: 38

Mean: 19.222, Median: 18, No mode

Mean: 8.611, Median: 8, Mode: 8

Let's find the mean, median, and mode for each set of numbers:

Set: 40, 38, 29, 34, 37, 22, 15, 38

Mean: To find the mean, we sum up all the numbers and divide by the total count:

Mean = (40 + 38 + 29 + 34 + 37 + 22 + 15 + 38) / 8 = 273 / 8 = 34.125

Median: To find the median, we arrange the numbers in ascending order and find the middle value:

Arranged set: 15, 22, 29, 34, 37, 38, 38, 40

Median = (29 + 34) / 2 = 63 / 2 = 31.5

Mode: The mode is the number(s) that appear(s) most frequently in the set:

Mode = 38 (appears twice)

Set: 26, 32, 12, 18, 11, 14, 21, 12, 27

Mean: Mean = (26 + 32 + 12 + 18 + 11 + 14 + 21 + 12 + 27) / 9 = 173 / 9 ≈ 19.222

Median: Arranged set: 11, 12, 12, 14, 18, 21, 26, 27, 32

Median = 18

Mode: No mode (all numbers appear only once)

Set: 3, 3, 4, 7, 5, 7, 6, 7, 8, 8, 8, 9, 8, 10, 12, 9, 15, 15

Mean: Mean = (3 + 3 + 4 + 7 + 5 + 7 + 6 + 7 + 8 + 8 + 8 + 9 + 8 + 10 + 12 + 9 + 15 + 15) / 18 ≈ 8.611

Median: Arranged set: 3, 3, 4, 5, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 10, 12, 15, 15

Median = 8

Mode: Mode = 8 (appears 4 times)

Mean: 34.125, Median: 31.5, Mode: 38

Mean: 19.222, Median: 18, No mode

Mean: 8.611, Median: 8, Mode: 8

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The number of tapes Melanie must sell to break even is 360 tapes.

To find the number of tapes Melanie must sell to break even, we must follow these steps.

We must identify how much she earns for each tape that she sells, for this we must subtract the sale price of each tape, by the value that she pays to make each tape.

Now we must divide the total cost of the mother tape by the profit she makes on each tape she sells.

Based on the above, we can infer that she must sell 360 tapes to cover the value of the mother tape and each of the tapes that she needs to sell. Next it is checked:

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Answer:

about a half a page

Step-by-step explanation:

Answer:

We have to reject null hypothesis

Step-by-step explanation:

n = 800

P* = sample proportion = 0.67

Alpha = 0.05

Null hypothesis h0: proportion = 63%

Alternate hypothesis h1: proportion > 64%

Test statistics:

Z = (p* - P)/√pq/n

Z = 0.67 - 0.64/√0.63x0.37/800

= 0.67 - 0.63/0.017

=0.04/0.017

= 2.352

At 0.05 the critical value of z = 1.645

We compare z calculated and z critical value.

2.352 is greater than 1.645 therefore we take the decision to reject the null hypothesis at 0.05 level of significance.

The percentage of residents that supports construction is greater than 63%

Answer:

d= -12 + 925

Step-by-step explanation:

decrease means negative and Increase means up (positive) so probably that why your answer was wrong

Answer:

d= -12 + 925

Step-by-step explanation:

Step-by-step explanation:

the center of the circle is the midpoint of the diameter.

and the radius is the distance of the midpoint to either endpoint (or simply half of the distance between the diameter endpoints).

the midpoint between points A and B

(xm, ym) = ((xa + xb)/2, (ya + yb)/2)

in our case the midpoint (center of the circle) is

((-6 + 2)/2, (10 + 3)/2) = (-4/2, 13/2) = (-2, 6.5)

about the radius

diameter² = (-6 - 2)² + (10 - 3)² = (-8)² + 7² = 64 + 49 =

= 113

diameter = sqrt(113) = 10.63014581...

radius = diameter / 2 = 5.315072906... ≈ 5.315

For the given equation:

m = 3b

The constant of proportionality is 3, so the correct option is A.

After a small search on the internet, I've found that this question asks for the constant of proportionality.

Remember that a proportional relation is of the form:

y = k*x

Where k is the constant of proportionality, and x and y are the variables.

Here the relation is:

m = 3*b

Where m and b are the variables, then the remaining coefficient is the constant of proportionality, which is 3.

In this way, we can see that the correct option is A.

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Answer:

19,683

Step-by-step explanation:

\(27^4-9^5+3^9\) is divisible by 25

The expression is given as:

\(27^4-9^5+3^9\)

Express all terms of the expression as a base of 3

\(27^4-9^5+3^9 = (3^3)^4-(3^2)^5+(3^9)\)

Remove the brackets

\(27^4-9^5+3^9 = 3^{12}-3^{10}+3^9\)

Factor out 3^9 from the expression

\(27^4-9^5+3^9 = 3^9(3^{3}-3^{1}+1)\)

Evaluate all exponents

\(27^4-9^5+3^9 = 3^9(27-3+1)\)

Simplify

\(27^4-9^5+3^9 = 3^9(25)\)

The above equation means that:

Hence, \(27^4-9^5+3^9\) is divisible by 25

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Answer:

1.2/5 meter of yellow cloth

2

3.

4

5

6

If values prοvided then transfοrmatiοn οf vectοrs can be determined.

In mathematics, a vectοr is a mathematical οbject that represents a quantity with bοth a magnitude and a directiοn. Vectοrs can be used tο represent physical quantities such as velοcity, fοrce, and acceleratiοn, as well as mοre abstract cοncepts such as cοlοr, sοund, and temperature.

Withοut seeing the figure οr the values οf a1, a2, and a3, it is nοt pοssible tο determine whether the specified linear transfοrmatiοn T : R2 → R2 is οne-tο-οne and οntο.

Hοwever, in general:

A linear transfοrmatiοn T : Rn → Rm is οne-tο-οne if and οnly if its kernel (i.e., the set οf vectοrs that are mapped tο the zerο vectοr) is trivial, meaning that the οnly vectοr that maps tο the zerο vectοr is the zerο vectοr itself.

A linear transfοrmatiοn T : Rn → Rm is οntο if and οnly if its range (i.e., the set οf all vectοrs that can be οbtained by applying T tο sοme vectοr in Rn) is equal tο Rm.

Tο determine whether a linear transfοrmatiοn is οne-tο-οne οr οntο, we can examine its prοperties and characteristics, such as its kernel, range, rank, and determinant. We can alsο use geοmetric intuitiοn and visualizatiοn tο understand hοw the transfοrmatiοn maps pοints and vectοrs in Rn tο Rm.

If yοu prοvide mοre infοrmatiοn abοut the values οf a1, a2, and a3 and the figure that shοws the standard matrix A, it can help yοu determine whether the transfοrmatiοn is οne-tο-οne and οntο and draw the image οf the vectοr [-1, 1] under the transfοrmatiοn T.

Therefοre, if values prοvided then transfοrmatiοn οf vectοrs can be determined.

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Complete question -

In Exercises 33–36, determine if the specified linear transformation is (a) one-to-one and (b) onto. Justify each answer. 14. Let T : R2 R2 be a linear transformation with standard matrix A = aaz], where a, and a, are shown in the figure. Using the figure, draw the image of under the transformation T. [-] 1

The 99% confidence interval for the true population mean backpack weight is approximately (68.15, 71.85) ounces, rounded to two decimal places.

To construct a 99% confidence interval for the true population mean backpack weight, we can use the formula:Confidence Interval = Sample Mean ± (Critical Value * Standard Deviation / √Sample Size).

Since the population standard deviation is known, we can use the z-distribution and find the critical value corresponding to a 99% confidence level. The critical value for a 99% confidence level is approximately 2.576.

Given that the sample mean weight is 70 ounces, the population standard deviation is 6.4 ounces, and the sample size is 48, we can calculate the confidence interval:

Confidence Interval = 70 ± (2.576 * 6.4 / √48).

Simplifying the expression, we get:

Confidence Interval ≈ 70 ± 1.855.

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System Linear equation has no solution , because it is paralell lines but no intersection.

What is system linear equation?

An equation for a line is known as a linear equation. alternatively, y + 0.5x 3.5 = 0 and others. (Note that each linear equation is the same.) When multiple linear equations interact, we get a system of linear equations.

Here the given system linear equations,

\(3y=\frac{3}{2}x+6\) -------> 1    and \(\frac{1}{2}y-\frac{1}{4}x=3\) --------> 2

Divide by 3  of equation 1 on both sides then,

\(y=\frac{1}{2}x+2\)  -----------> 3

Now put 3 into 2 then,

=> \(\frac{1}{4}x+1-\frac{1}{4}x=3\)

=> 1=3

Hence the given system equation has no solution , because it is paralell lines but no intersection.

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