Let sin θ = -0.4567 and π ≤ θ ≤ 3π/2.
In which quadrant lies the terminating side of the angle? Find a decimal approximation for • Cos θ =
• tan θ =

Answer:

1.5 cm³

Step-by-step explanation:

Hey There!

so the first thing that we want to do is find the formula for volume of a rectangular prism

the formula is \(V=lw\frac{h}{3}\)

just so you know

l=length

w=width

h=height

now we just plug in the dimensions and get

\(v=1\frac{1}{2}1 \frac{1}{2} \frac{2}{3}\)

if you plug this into a calculator you get that the volume of the prism is 1.5 cm

1.5 cm³,A little late sorry,but I got it right on the test

tan(41π/36) can be written in terms of the tangent of a positive acute angle as (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

To express tan(41π/36) in terms of the tangent of a positive acute angle, we need to find an angle within the range of 0 to π/2 that has the same tangent value.

First, let's simplify 41π/36 to its equivalent angle within one full revolution (2π):

41π/36 = 40π/36 + π/36 = (10/9)π + (1/36)π

Now, we can rewrite the angle as:

tan(41π/36) = tan((10/9)π + (1/36)π)

Next, we'll use the tangent addition formula, which states that:

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))

In this case, A = (10/9)π and B = (1/36)π.

tan(41π/36) = tan((10/9)π + (1/36)π) = (tan((10/9)π) + tan((1/36)π)) / (1 - tan((10/9)π)tan((1/36)π))

Now, we need to find the tangent values of (10/9)π and (1/36)π. Since tangent has a periodicity of π, we can subtract or add multiples of π to get equivalent angles within the range of 0 to π/2.

For (10/9)π, we can subtract π to get an equivalent angle within the range:

(10/9)π - π = (1/9)π

Similarly, for (1/36)π, we can add π to get an equivalent angle:

(1/36)π + π = (37/36)π

Now, we can rewrite the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Since we are looking for an angle within the range of 0 to π/2, we can further simplify the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Therefore, tan(41π/36) can be written in terms of the tangent of a positive acute angle as the expression given above.

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Answer:

x < -32

Step-by-step explanation:

Answer:

A = 3.4

Step-by-step explanation:

235 = 7(4 + 6a) - 3

you're trying to make both sides equal, that means whatever is happening on one side must happen on the other. to take minus 3 out of the equation you add 3 to both sides

235 + 3 = 7(4 + 6a) -3 + 3

238 = 7(4 + 6a)

next add within the parenthesis and multiply that by 7

238 = 7(4 + 6a)

238 = 7 × 10a

238 = 70a

next divide both sides by 70

238 ÷ 70 = 70a ÷ 70

3.4 = a

Answer: For #5, a = 5

Step-by-step explanation:

First, let's open the parenthesis.

235 = 7 (4 + 6a) - 3

235 = 28 + 42a - 3

Next, subtract 28 by 3 on the right side.

235 = 28 + 42a - 3

235 = 25 + 42a

Then, we'll subtract both sides by 25.

235 - 25 = 25 - 25 + 42a

210 = 42a

Finally, let's divide both sides by 42!

210 / 42 = 42a/42

5 = a

So, a = 5.

Answer: The probability of getting two red marbles is P = 0.141

Step-by-step explanation:

We know that in the bag there are 3 blue marbles and 5 red marbles, then there is a total of 8 marbles in the bag.

The probability of taking at random a red marble is equal to the quotient between the number of red marbles and the total number of marbles, this is:

p = 3/8

Suppose we got a red marble:

Now we replace the red marble we took, so in the bag there are again 3 red marbles and 8 total marbles, then the probability of getting another red marble is again:

q = 3/8

The joint probability (this is, the probability of both events happening) is equal to the product of the individual probabilities, with gives us:

P = p*q = (3/8)*(3/8) = 9/64 = 0.141

Answer:

John is 16 and Maya is 11

Step-by-step explanation:

x=Maya's age

x+5=John's age

x+x+5=27

2x+5=27

     -5   -5

2x=22

/2    /2

x=11

x+5=

11+5= 16

The ratio of Cost of grocerie to cost of vegetable 4:1 .

What is the cost?

Cost is the amount of money spent by a business to produce or create goods or services. It excludes the profit margin markup.

                      Cost is the sum of money spent on making a good or product, as seen from the seller's perspective.

Given that,

Spent $4.80 on groceries and $1.20 on vegetables.

Total cost = 4.80 + 1.20

Total cost = $6.00

a. Cost of groceries to cost of vegetables;

Ratio = 4.80 / 1.20 = 4 / 1

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The amount the firm needs to deposit in the account now is 9,640.11. Given that the company has purchased a life truck with a useful life of 5 years, the maintenance costs for the truck during the first year are 2,000.

Also, maintenance costs are expected to increase at a rate of 300 per year over the remaining life, which is for four years. Assume that the maintenance costs occur at the end of each year.

The future maintenance costs for the truck can be calculated as shown below:

Year 1:\($2,000Year 2: $2,300Year 3: $2,600Year 4: $2,900Year 5: $3,200\)The maintenance account that earns 10% interest per year has to be set up, and all future maintenance expenses will be paid out of this account. The future value of the maintenance costs, i.e., the amount that the firm needs to deposit now to earn 10% interest and pay the maintenance costs over the next four years is given by:

\(PV = [C/(1 + i)] + [C/(1 + i)²] + [C/(1 + i)³] + [C/(1 + i)⁴] + [(C + FV)/(1 + i)⁵]\),where PV is the present value of the future maintenance costs, C is the annual maintenance cost, i is the interest rate per year, FV is the future value of the maintenance costs at the end of year 5, which is $3,200, and 5 is the total number of years, which is

5.Substituting the given values in the above equation:

\(PV = [2,000/(1 + 0.1)] + [2,300/(1 + 0.1)²] + [2,600/(1 + 0.1)³] + [2,900/(1 + 0.1)⁴] + [(3,200 + 3,200)/(1 + 0.1)⁵] = 9,640.11\)Therefore, the firm needs to deposit 9,640.11 in the account now. Hence, option (A) is the correct answer.

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A-B-A-B-A-B-A-B is the chemical structure that represents a block copolymer due to its distinct arrangement of monomer units in consecutive blocks.

In a block copolymer, the monomer units are arranged in consecutive blocks rather than being randomly distributed. This is evident in option a), where the monomer units A and B are arranged in a repetitive pattern: A-B-A-B-A-B-A-B. This arrangement indicates the presence of distinct blocks of monomer units.

A-A-B-A-A-B-B-A does not qualify as a block copolymer because it does not exhibit a distinct block structure. The monomer units A and B are not arranged in consecutive blocks, but rather show a more random distribution.

Similarly,A-A-A-A-B-B-B-B and A-A-A-B-B-B-A-A also do not represent block copolymers. They lack the characteristic block structure, as the monomer units are not arranged in consecutive blocks but rather exhibit a more random distribution.

A-B-A-B-A-B-A-B is the chemical structure that represents a block copolymer due to its distinct arrangement of monomer units in consecutive blocks.

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The greatest 3-digit base 8 positive integer that is divisible by 5 is 777.

What is divisibility?

A divisibility rule is a convenient shorthand for checking if an integer is divisible by a given set divisor without actually doing the division, typically by looking at the digits of the number.

Here,

The smallest number that has 3 digits in base 8 is 8² = 64

= 100(base 8).

In fact, in base 8 you would write the calculation as 10² = 100.

The largest 3-digit base 8 number is 777

= 10³ - 1. In base 10 it's 8³ - 1 = 511.

The base does not affect divisibility.

= 512 / 5 = 102 remainders 2,

so there are 102 multiples of 5 less than 512.

These 102 numbers have 3 or few digits.

= 64 / 5 = 12 remainders 4.

There are 12 multiples of 5 less than 64.

These have 1 or 2 digits.

So the number of multiples of 5 between 64 and 511 is 102 - 12 = 90. These numbers have exactly 3 digits.

Hence,  the greatest 3-digit base 8 positive integer that is divisible by 5 is 777.

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The function you're referring to is likely a periodic function, as Fourier series expansions are typically used for periodic functions.

The convergence of the Fourier series expansion depends on the properties of the function, such as its continuity and differentiability.

If the function is continuous and piecewise smooth, then the Fourier series will converge to the function itself.

However, if the function is not continuous or not piecewise smooth, then the Fourier series may not converge uniformly.

In some cases, the Fourier series may converge to a different function altogether, known as a Fourier series of the function.

Therefore, to determine the value at which the Fourier series converges, you would need to analyze the properties of the function itself.

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The graph of the equation y = \(2^{x}\) - 5 is obtained by shifting the graph of

y =\(2^{x}\)  downside by 5 units.

To find a graph of equation y = \(2^{x}\) - 5, we can start with the reference of the parent function y = \(2^{x}\) and also apply the necessary transformations.  Initiating with the graph of the parent function y =\(2^{x}\) - 5.

This is an exponential function that passes through the point( 0, 1) and has a positive pitch. Apply the transformation -5 units over. This means we shift the entire graph over by 5 units. The point( 0, 1) will now come( 0,-4).thus, the graph of the equation y =  \(2^{x}\)- 5 is attained by shifting the graph of y =  \(2^{x}\) downcast by 5 units. The factual shape of the graph will act as that of the parent exponential function, but it'll be shifted over by 5 units.

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The correct question is given below-

Graph the equation shown below by transforming the given graph of the parent function. y= \(2^{x}\) obtain  y=\(2^{x}\)-5.

Answer:

$4320

Step-by-step explanation:

12 divided by 2 is 6

720 x 6 = 4320

Answer:

Thats a nice fact

Step-by-step explanation:

If you plug Ur nose, an apple,orange, and onion taste the same!!

Answer:

1) Slope: 3; y-intercept: -7

2) Slope: 2/3; y-intercept: 1

Step-by-step explanation:

y = mx + b; m is slope and b is y-intercept

1. y = 3x - 7

The equation is already in slope-intercept form, so you can find the slope and intercept.

Slope: 3

y-intercept: -7

2. y - 1 = 2/3x

For this one, you have to convert this into slope-intercept form (solving for y)

y - 1 = 2/3x

Add 1 to both sides

y - 1 + 1 = 2/3x + 1

y = 2/3x + 1

Now that the equation is in slope-intercept form, you can get the slope and y-intercept.

Slope: 2/3

y-intercept: 1

Answer:

-1

Step-by-step explanation:

solution:

(-2 , -1) = (x1 , y1)

(-1 ,-2) = (x2 , y2)

we know that,

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

=(-2 - -1)/ (-1 - -2)

=(-2 + 1) / (-1 + 2)

= -1/1

=-1

slope = -1

Answer:

53.9

Step-by-step explanation:

:)

Step-by-step explanation:

Break it up into two trapezoids as shown

area = trap1 + trap2

      = 2 *   (7+3) / 2   + 3 *  ( 7 + 3) / 2 = 10 + 15 = 25 units^2

The relationship between b (the number of years since the start of the study) and y (the mass of the sample in milligrams) using the exponential function:

y = 750(0.955)ᵇ

The rate of decay is given as 4.5% per year, which means that after one year, the sample will have decayed to 95.5% of its original mass.

After two years, it will have decayed to 95.5% of that amount, and so on. We can express this relationship between b (the number of years since the start of the study) and y (the mass of the sample in milligrams) using the exponential function:

y = 750(0.955)ᵇ

Here, the initial mass of the sample is 750 milligrams, and the factor of 0.955 represents the proportion of the original mass that remains after one year.

Taking this factor to the power of b gives us the proportion of the original mass that remains after t years, which we can multiply by the initial mass to get the current mass of the sample in milligrams.

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The average value of a function ƒ(x) on an interval [a, b], we need to calculate the definite integral of the function over that interval and divide it by the length of the interval (b - a). The average value of ƒ(x) = 3x² on the interval [-4, 0] is 8.

The average value of ƒ(x) = 3x² on the interval [-4, 0].

First, we calculate the definite integral of ƒ(x) over the interval [-4, 0]:

∫(from -4 to 0) 3x² dx

To evaluate this integral, we can use the power rule for integration. The power rule states that for any term of the form ax^n, the integral is (a/(n+1))x^(n+1). Applying this rule, we have:

∫(from -4 to 0) 3x² dx = [3/3 * x^3] (from -4 to 0)

Evaluating the integral at the upper and lower limits, we get:

[3/3 * 0^3] - [3/3 * (-4)^3]

Simplifying further:

0 - [3/3 * (-64)]

0 + 64 = 64

Now, we divide this result by the length of the interval [-4, 0], which is 4 - (-4) = 8:

Average value = 64 / 8 = 8

Therefore, the average value of ƒ(x) = 3x² on the interval [-4, 0] is 8.

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x = -1

Step-by-step explanation:

\( {4}^{5x} = {2}^{2(5x)} = {2}^{10x} \)

\( {( \frac{1}{32}) }^{(1 - x)} = {2}^{ - 5(1 - x)} = {2}^{(5x - 5)} \)

or

\( {2}^{10x} = {2}^{(5x - 5)} \)

Since both sides have the same base, we can write

10x = 5x - 5

or

5x = -5

x = -1

A distribution of scores on a driver's license test forms is normally shaped. This is an example of a symmetrical distribution is TRUE.

A symmetrical distribution is a distribution where there is an equal number of data points on both sides of the center point, in which the mean, mode, and median of a data set are all similar.

A normal distribution is a bell-shaped distribution that is symmetrical, with most of the data falling near the mean and progressively less toward the tails. When data are symmetrical, the mean and median values are similar, and the standard deviation can be used to compute the proportions of data within a range of values surrounding the mean.

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9514 1404 393

Answer:

  x = (√2)/2

Step-by-step explanation:

The diagonal is √2 times the side length (x), so ...

  1 = x√2

  √2 = 2x . . . . . multiply by √2

  (√2)/2 = x . . . . divide by 2

The side length x is (√2)/2.

Answer: yes

Step-by-step explanation:

trust me on it

Answer:

Step-by-step explanation:

The expressions of all the functions are;

1) f(x) = 0.75x

2)g(x) = 0.8x

3) (f o g)(x) = 0.6x

4) (g o f)(x) = 0.6x

We are told that f(x) is the price with the $20 coupon applied, and

g(x) is the price with the 15% discount applied. Thus;

1) An expression for f(x) is;

f(x) = (1 - 0.25)x = 0.75x

f(x) = 0.75x

2) An expression for g(x) is;

g(x) = (1 - 0.2)x = 0.8x

g(x) = 0.8x

3) An expression for (f o g)(x) is;

(f o g)(x)  = f(g(x)) = 0.75(0.8x) = 0.6x

(f o g)(x) = 0.6x

4) An expression for (g o f)(x) is;

(g o f)(x) = 0.8(0.75x) = 0.6x

(g o f)(x) = 0.6x

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Madison figures out the average and range of chloride readings from wells close to the ocean. Other than a query, she has carried out an operation. The answer id option (d).

The standard deviation is a measure of variance from the mean that takes spread, dispersion, and dispersion into account. The standard deviation displays a "typical" divergence from the mean. It is a well-liked measure of variability since it retains the primary units of measurement from the data set.  A minor variation occurs when the numbers are close to the mean, while a high variation occurs when they are far from the mean.

The standard deviation describes the degree to which the results deviate from the mean. The average deviation, which depends on all values, is the most often used metric for measuring dispersion. Consequently, the standard deviation's value can be altered even by a slight change in one value.

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Answer:

first divied by 2 both sides

-1 < 5-k

sub stract 5

-6 <-k

cancel -

6 < k

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

We can see that in figure ABC, line segment AB is 5 ft.

We can also see that in figure DEF, line segment DE is 15 ft.

How did we get from 5 to 15?

We multiplied by 3, so the scale factor is 3.

Hope this helps! :)

Answer:

x = 5

Step-by-step explanation:

\(8x+38=-3(-6-4x)\\\\8x+38=18+12x\\\\8x+38-38=18-38+12x\\\\8x=12x-20\\\\8x-12x=12x-12x-20\\\\-4x=-20\\\\\frac{-4x=-20}{-4}\\\\\boxed{x=5}\)

Hope this helps!