Determine the domain of the following graph:

The measure of side EF in triangle DEF is 5.34 units when angle D measures 40° and its adjacent side measures 7.6 units.

To get this answer, use the Pythagorean Theorem:

a2 + b2 = c2,

where a and b are the lengths of the sides adjacent to the right angle, and c is the length of the hypotenuse.

In this case, a = 7.6 and b = 5.34, so c = 8.93. Round this to the nearest hundredth and you get 5.34.

The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two sides adjacent to the right angle is equal to the square of the hypotenuse.

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Answer:

$17.33

Step-by-step explanation:

3.5×4.95

=17.325

= $17.33

Chebyshev's theorem says that for any set of observations, the proportion of values that lie within k standard deviations of the mean is  1 - 1/k².

In statistics, Standard deviation is a measure of the variation of a set of values.

σ = standard deviation of population

N = number of observation of population

X = mean

μ = population mean

We know that Chebyshev's theorem states that for a large class of distributions, no more than 1/k² of the distribution will be k standard deviations away from the mean.

This means that 1 - 1/k² of the distribution will be within k standard deviations from the mean.

Lets k = 1.8, the amount of the distribution that is within 1.8 standard deviations from the mean is;

1 - 1/1.8² = 0.6914

= 69.14%

Hence, Chebyshev's theorem says that for any set of observations, the proportion of values that lie within k standard deviations of the mean is  1 - 1/k².

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Answer:

it should be 11.85 if it's not I do not know what is the answer to it

Answer:

actually the answer is 64

Step-by-step explanation:

Answer: The answer is 1638 ft

Step-by-step explanation:

The formula to find area is L x W x H

Length x Width x Height

So 9 ft x 7 ft x 26 ft = 1638 ft

The number of seats in the front row of the theater is a = [2y/(n(n-1)) - x/(n-1)]/2

Let's call the number of seats in the first row "a". We can use the information given in the problem to set up an equation in terms of "n", "d", "x", and "y"

y = a + (a + d) + (a + 2d) + ... + (a + (n-1)d) (1)

We can simplify this equation by using the formula for the sum of an arithmetic series

y = [n/2][2a + (n-1)d] (2)

We can solve this equation for "a" in terms of "n", "d", and "x"

2a = (2y/n) - (n-1)d - 2xd

a = [(2y/n) - (n-1)d - 2xd]/2

Since we know that the number of seats in the last row is "x", we can substitute that into the equation

x = a + (n-1)d

x = [(2y/n) - (n-1)d - 2xd]/2 + (n-1)d

Simplifying this equation gives us

2x = (2y/n) + (n-1)d

2d = (2x - (2y/n))/(n-1)

Now we can substitute this value of "d" into the equation we found for "a"

a = [(2y/n) - (n-1)d - 2xd]/2

a = [(2y/n) - x - (2x - (2y/n))/(n-1)]/2

a = [2y/(n(n-1)) - x/(n-1)]/2

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The logarithmic form of the exponential equation 8e^x-5 = 0 is given as follows:

x = ln(5/8).

The exponential function in this problem is defined as follows:

8e^x-5 = 0.

The equation can be sorted isolating the exponential as follows:

8e^x = 5.

e^x = 5/8.

The natural logarithm(symbolized by the ln) is the opposite of the exponential function, hence the logarithmic form of the equation is presented as follows:

ln(e^x) = ln(5/8).

As stated above, the natural logarithm and the exponential functions are inverse functions, meaning that:

ln(e^x) = x.

Thus the logarithmic form of the exponential equation 8e^x-5 = 0 is given as follows:

x = ln(5/8).

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Answer:

length times witdth times height

Answer:

I think the answer wold be -5/3 or -1.666666667 .

The value of the given expression is,

\(log_8 \frac{1}{32}\) = -3/5

The given logarithmic expression is,

\(log_8 \frac{1}{32}\)

Since we know that,

The power to which a number must be increased in order to obtain additional values is referred to as a logarithm. The easiest approach to expressing enormous numbers is this manner. Numerous significant characteristics of a logarithm demonstrate that addition and subtraction logarithms may also be represented as multiplication and division of logarithms.

We can write the given expression as,

\(log_8 \frac{1}{32}\) =   \(log_8 32^{-1\)

          = - \(log_8 32\)                  [ \(log_a b^x = x log_a b\)]

          = - \(log_{2^3} 2^5\)

          =  - \(\frac{3}{5} log_{2} 2\)                 [ \(log_{a^y} b^x = \frac{x}{y} log_a b\)]

          = -3/5                       [  \(log_{a} a = 1\)]

Hence,

\(log_8 \frac{1}{32}\) = -3/5

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This contradicts our assumption that DC < BA. Therefore, our assumption that m m was incorrect, and we can conclude that m is not parallel to m.

To prove that m m, we first need to understand what it means. Two lines are said to be parallel if they do not intersect and are equidistant from each other at all points. Therefore, to prove that m m, we need to show that they are equidistant from each other.

Given that BC = DA and DC < BA, we can draw a diagram as shown below:

[Insert diagram here]

Let's assume that m m. This means that the distance between m and DC is the same as the distance between m and BA. Let's call this distance x.

Now, let's consider the triangles BCM and ADM. These triangles share the same height (the distance between m and DC), and they have equal bases (BC = DA). Therefore, they must have the same area.

Similarly, let's consider the triangles ABD and BCD. These triangles share the same height (the distance between m and BA), and they have equal bases (BD is common to both). Therefore, they must have the same area.

Now, if we add the areas of triangles BCM and ADM, we get the area of quadrilateral ABCD. Similarly, if we add the areas of triangles ABD and BCD, we get the area of quadrilateral ABCD.

Since the area of ABCD is the same, we can say that the sum of the areas of BCM and ADM is equal to the sum of the areas of ABD and BCD. In other words,

1/2 x BC x CM + 1/2 x AD x DM = 1/2 x AB x BD + 1/2 x BC x CD

Simplifying this equation, we get:

BC x CM + AD x DM = AB x BD + BC x CD

Since BC = DA, we can substitute BC for DA in the equation:

BC x CM + BC x DM = AB x BD + BC x CD

Dividing both sides by BC, we get:

CM + DM = AB/BC x BD + CD

Since DC < BA, we know that CD < AB/BC x BD. Therefore,

CM + DM < AB/BC x BD + AB/BC x BD

Simplifying this, we get:

CM + DM < 2 x AB/BC x BD

But we know that AB/BC = DA/BC = 1. Therefore,

CM + DM < 2 x BD

Now, let's consider the triangles BCM and BDM. These triangles share the same base (BD), and their heights are CM and DM respectively. Therefore,

1/2 x BC x CM < 1/2 x BD x DM

Multiplying both sides by 2, we get:

BC x CM < BD x DM

Adding this inequality to the inequality we derived earlier, we get:

2 x BC x CM + 2 x BC x DM < 2 x BD x DM + 2 x BD x CM

Simplifying this, we get:

BC x (CM + DM) < BD x (CM + DM)

But we know that CM + DM < 2 x BD. Therefore,

BC x (CM + DM) < 2 x BD x (CM + DM)

Dividing both sides by CM + DM, we get:

BC < 2 x BD

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Therefore, the area between the large loop and the small loop of the curve r = 2 + 4cos(3θ) is 70π/3.

To find the area between the large loop and the small loop of the curve, we need to find the points of intersection of the curve with itself.

Setting the equation of the curve equal to itself, we have:

2 + 4cos(3θ) = 2 + 4cos(3(θ + π))

Simplifying and solving for θ, we get:

cos(3θ) = -cos(3θ + 3π)

cos(3θ) + cos(3θ + 3π) = 0

Using the sum to product formula, we get:

2cos(3θ + 3π/2)cos(3π/2) = 0

cos(3θ + 3π/2) = 0

3θ + 3π/2 = π/2, 3π/2, 5π/2, 7π/2, ...

Solving for θ, we get:

θ = -π/6, -π/18, π/6, π/2, 5π/6, 7π/6, 3π/2, 11π/6

We can see that there are two small loops between θ = -π/6 and π/6, and two large loops between θ = π/6 and π/2, and between θ = 5π/6 and 7π/6.

To find the area between the large loop and the small loop, we need to integrate the area between the curve and the x-axis from θ = -π/6 to π/6, and subtract the area between the curve and the x-axis from θ = π/6 to π/2, and from θ = 5π/6 to 7π/6.

Using the formula for the area enclosed by a polar curve, we have:

A = 1/2 ∫[a,b] (r(θ))^2 dθ

where a and b are the angles of intersection.

For the small loops, we have:

A1 = 1/2 ∫[-π/6,π/6] (2 + 4cos(3θ))^2 dθ

Using trigonometric identities, we can simplify this to:

A1 = 1/2 ∫[-π/6,π/6] 20 + 16cos(6θ) + 8cos(3θ) dθ

Evaluating the integral, we get:

A1 = 10π/3

For the large loops, we have:

A2 = 1/2 (∫[π/6,π/2] (2 + 4cos(3θ))^2 dθ + ∫[5π/6,7π/6] (2 + 4cos(3θ))^2 dθ)

Using the same trigonometric identities, we can simplify this to:

A2 = 1/2 (∫[π/6,π/2] 20 + 16cos(6θ) + 8cos(3θ) dθ + ∫[5π/6,7π/6] 20 + 16cos(6θ) + 8cos(3θ) dθ)

Evaluating the integrals, we get:

A2 = 80π/3

Therefore, the area between the large loop and the small loop of the curve r = 2 + 4cos(3θ) is:

A = A2 - A1 = (80π/3) - (10π/3) = 70π/3

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The number of squares tiles that will be required to floor the rectangular store is approximately 1284 tiles

The rectangular store measures 6.5m by 7.9m.

Therefore,

area of a rectangle = lw

where

Therefore,

area of a rectangle = 6.5 × 7.9

area of a rectangle = 51.35 m²

The square tiles used for the floor is 20cm each. Therefore,

20 cm = 0.2m

hence

area of the square tile = 0.2² = 0.04 m²

number of tiles = 51.35 / 0.04 = 1283.5

number of tiles ≈ 1284 tiles

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In the context of analyzing the relationship between studying time and test grades, the domain of the scatterplot would be the number of minutes the students studied (option D).

The domain refers to the set of possible inputs or variables in a given context. In this case, the scatterplot is being created based on the relationship between the time students spent studying and their corresponding test grades. Therefore, the domain in this context would be the number of minutes the students studied (option D).

The domain represents the independent variable, which is the variable that is controlled or manipulated in the analysis. In this scenario, the math teacher wants to analyze the relationship between studying time and test grades, so the number of minutes studied would be the independent variable. The teacher surveys the students to collect data on the time spent studying, and this variable becomes the domain of the scatterplot.

The range, on the other hand, represents the dependent variable, which is the variable that is measured or observed as an outcome or response. In this case, the dependent variable would be the students' test grades. The scatterplot will show how the test grades correspond to the amount of time students studied.

To summarize, in the context of analyzing the relationship between studying time and test grades, the domain of the scatterplot would be the number of minutes the students studied (option D).

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Answer:

m∠JKM = 63°

m∠MKL = 27°

Step-by-step explanation:

Since ∠JKL is a right angle. This means that by summing up both m∠JKM and m∠MKL will result in the same as ∠JKL figure. Thus, m∠JKM + m∠MKL = m∠JKL which is 90° by a right angle definition.

\(\displaystyle{\left(12x+3\right)+\left(6x-3\right) = 90}\)

Solve the equation for x:

\(\displaystyle{12x+3+6x-3 = 90}\\\\\displaystyle{18x=90}\\\\\displaystyle{x=5}\)

We know that x = 5. Next, we are going to substitute x = 5 in m∠JKM and m∠MKL. Thus,

m∠JKM = 12(5) + 3 = 60 - 3 = 63°

m∠MKL = 6(5) - 3 = 30 - 3 = 27°

The enrollment of the school each year after 2000 is a linear function and the equation is f(x) = 1200 + 35x

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

Initial number of students = 1200

Rate of student per year = 35

The above parameters implies that there is a constant increment of 35 students each year since 2000

This means that the scenario is a linear equation

A linear equation is represented as

y = mx + c

In this case, we have

c = Initial number of students = 1200

m = Rate of student per year = 35

Substitute the known values in the above equation, so, we have the following representation

y = 35x + 1200

Hence, the equation is y = 35x + 1200

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With the help of addition of unlike fraction we find that 1/8 gallon of  white paint is needed to mix with red and purple to make it total 1 gallon.

The unlike fractions are fractions having dissimilar denominators. Here, the values of the denominators of fractions vary. Fractions that are fractions include 1/3, 8/6, 12/47, and 3/82 are unlike like fractions. it is difficult to add or subtract such fractions since the denominators are different.

let quantity of white paint be x,

1/2 + 3/8 + x = 1

        7/8 + x = 1

                 x = 1 - 7/8

                 x = 1/8

therefore, 1/8 gallon of  white paint is needed.

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Answer:

✏If the rod is held straight then the angle alpha equals 90°,therefore the required solution is 45°

Step-by-step explanation:

The labor quantity variance of Clark Company is $1800 U (Unfavorable). Option b is correct.

Compare the actual labor hours used with the standard labor hours allowed and multiply the difference by the standard labor rate.

Standard labor hours allowed = Standard hours per unit × Number of units produced

Standard labor hours allowed = 2 hours × 1200 units = 2400 hours

Actual labor hours used = 2500 hours

Labor quantity variance = (Actual labor hours used - Standard labor hours allowed) * Standard labor rate

Labor quantity variance = (2500 hours - 2400 hours) × $18 per hour

Labor quantity variance = 100 hours × $18 per hour

Labor quantity variance = $1800

Since the actual labor hours used exceeded the standard labor hours allowed, the labor quantity variance is unfavorable. Therefore, the labor quantity variance is $1800 U (Unfavorable).

Option b is correct.

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Answer:

Graph C

Step-by-step explanation:

First, we need to find the bottom of the parabola (or the top, left, or right). In this case, it is x=3, therefore meaning y=-25. The only one that has (3,-25), so Graph C.

Answer: B

Step-by-step explanation:

Based on the graph, we know that it is increasing if it is going up from left to right.

A: incorrect

Looking at choice A, it says the interval is from -5<x<-4. This means we have to find x=-5 and x=-4. On the graph, that interval is going down from left to right, so it is decreasing.

B: correct

Looking at choice B, it says the interval is from -2<x<2. This means we have to find x=-2 and x=2. On the graph, that interval is going up from left to right, so it is increasing.

C: incorrect

Looking at choice C, it says the interval is from 3<x<4. This means we have to find x=3 and x=4. On the graph, that interval is going down from left to right, so it is decreasing.

Therefore, B is the correct answer.

Answer:

3 inches per hour

Step-by-step explanation:

divide the number on the y axis (i'm assuming it's inches of snow) by the number on the x axis (i'm assuming its hours)

by doing this you will get 3 inches per hour

The equation relating x, y, and z is:

z = 0.5 * x * y.

In the given problem, the relationship between x, y, and z can be expressed by the equation z = k * x * y, where k represents the constant of proportionality. By substituting the values of x = 4 and y = 5, when z is equal to 10, we can determine the value of the constant of proportionality, k, and further define the relationship between the variables.

To find the constant of proportionality, we substitute the known values of x = 4, y = 5, and z = 10 into the equation z = k * x * y. This gives us the equation 10 = k * 4 * 5. By simplifying the equation, we have 10 = 20k. To isolate k, we divide both sides of the equation by 20, resulting in k = 0.5. Therefore, the equation relating x, y, and z is z = 0.5 * x * y, meaning that z is directly proportional to the product of x and y with a constant of proportionality equal to 0.5.

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The total cost of the flowers, we need to multiply the cost of each flower by the total number of flowers. The given expression is D. 48x.

Let's assume that the cost of each flower is represented by the variable "x". Since all the flowers are identical, the cost of each flower is the same.

To find the total cost, we multiply the cost of each flower (x) by the total number of flowers (48):

Total cost = x * 48

So, the expression 48x represents the total cost of the flowers.

The correct answer is D).

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--The given question is incomplete, the complete question is given below " Susie purchased 48 identical flowers . Which expression represents the total cost of the flowers

A. 48+x B. 48 - x C. 48÷x D. 48x"--

The volume of the square-based pyramid is 3888 units³. Your answer is option B. 3888 units³.

The formula to calculate the volume of a pyramid is V = (1/3)Bh,

Where B is the area of the base and h is the height.

In this case, the base is a square with edge length 9 units, so the area is B = 9² = 81 units².

The height is given as 48 units.
Plugging these values into the formula, we get:
To find the volume of a square-based pyramid, you can use the following formula:

V = (1/3) * base area * height.

In this case, the base edge is 9 units and the height is 48 units.

First, find the base area:

A = side * side = 9 * 9

= 81 square units.

Next, calculate the volume:

V = (1/3) * 81 * 48 = 3888 cubic units.
V = (1/3)(81)(48)
V = 1296 units³
Therefore, the volume of the pyramid is 1296 units³, which is option b.

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Answer:

Approximately 0.0364

Idk if this is right... :(

Step-by-step explanation:

4 dice with 12 sides

7 dice without 121 sides.

There is a \(\frac{4}{11}\) chance that the first dice has 12 sides.

There is a \(\frac{3}{10}\) chance that the second dice has 12 sides.

There is a \(\frac{7}{9}\) chance that the third dice doesn't have 12 sides.

There is a \(\frac{3}{4}\) chance that the fourth dice doesn't have 12 sides.

Multiply them up:

\(\frac{4}{11}*\frac{3}{10}*\frac{7}{9}*\frac{3}{4}=\frac{252}{3960}=0.0363636363636...\)

So approximately 0.0364

Mr. Farley used 0.4 pounds (or 6.4 ounces) of hamburger per patty.

The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers in the decimal system.

To find the amount of hamburger used per patty, we need to divide the total amount of hamburger used by the number of patties:

amount per patty = total amount / number of patties

In this case, Mr. Farley used 4 pounds of hamburger to make 10 patties:

amount per patty = 4 pounds / 10 patties

We can evaluate this expression with a calculator to obtain:

amount per patty = 0.4 pounds per patty

Therefore, Mr. Farley used 0.4 pounds (or 6.4 ounces) of hamburger per patty.

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Answer:

triangle TSU is an isocelous triangle

so, angle S = angle U = 54°

angle T = 180° - angle (S + U)

= 180° - 54° + 54°

= 180° - 108°

= 72°

angle T = 72°

angle U = 54°

triangle MNL is an isocelous triangle

so, angle M = angle N = 'x'

angle L = 180°- angle M + angle N

28 = 180° - 2x

2x = 180° - 28

2x = 152°

x = 152° / 2

x = 76°

angle M = angle N = 76°

Step-by-step explanation:

brainliest plz

1) The measure of angles T and U are,

⇒ ∠T = 72°

⇒ ∠U = 54°

2) The measure of angles M and N are,

⇒ ∠M = 76°

⇒ ∠N = 76°

We have to given that,

There are two isosceles triangle are shown in image.

Since, We know that,

In a triangle, If two sides are equal then its corresponding angles are equal to each other.

Now, From first triangle,

In triangle STU,

⇒ ∠T + ∠S + ∠U = 180°

⇒ ∠T + 54° + 54° = 180°

⇒ ∠T = 180 - 108

⇒ ∠T = 72°

Thus, The measure of angles T and U are,

⇒ ∠T = 72°

⇒ ∠U = 54°

2) In triangle LMN,

LM = LN

Hence, ∠M = ∠N = x

And, We get;

⇒ ∠L + ∠M + ∠N = 180°

⇒ 28 + x + x = 180°

⇒ 2x = 180 - 28

⇒ 2x = 152

⇒ x = 152 / 2

⇒ x = 76

Hence, The measure of angles M and N are,

⇒ ∠M = 76°

⇒ ∠N = 76°

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We will use Equation (5.9) of Fourier transform analysis to calculate the Fourier transforms of the given sequences: (a) (½)^(n-1)u[n-1] and (b) (½)^|n-1|. F(ω) = Σ (½)^(n-1)e^(-jωn) for n = 1 to ∞.  F(ω) = Σ (½)^(n-1)e^(-jωn) for n = -∞ to ∞

(a) To calculate the Fourier transform of (½)^(n-1)u[n-1], we substitute the given sequence into Equation (5.9). Considering the definition of the unit step function u[n-1] (which is 1 for n ≥ 1 and 0 for n < 1), we can rewrite the sequence as (½)^(n-1) for n ≥ 1 and 0 for n < 1. Thus, we obtain the Fourier transform as:

F(ω) = Σ (½)^(n-1)e^(-jωn)

Evaluating the summation, we get:

F(ω) = Σ (½)^(n-1)e^(-jωn) for n = 1 to ∞

(b) To calculate the Fourier transform of (½)^|n-1|, we again substitute the given sequence into Equation (5.9). The absolute value function |n-1| can be expressed as (n-1) for n ≥ 1 and -(n-1) for n < 1. Thus, we have the Fourier transform as:

F(ω) = Σ (½)^(n-1)e^(-jωn) for n = -∞ to ∞

In both cases, the specific values of the Fourier transforms depend on the range of n considered and the values of ω. Further evaluation of the summations and manipulation of the resulting expressions may be required to obtain the final forms of the Fourier transforms for these sequences.

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Answer:

45 workers.

Step-by-step explanation

In 90 hours 15 workers will build one wall

So in 90 hours it w1ll take 1 worker to build 1/15 of a wall.

In 30 hours he would build 1/45 of a wall.

So to build the whole wall in 30 days it will take 45 workers.

Answer:

45 workers

Step-by-step explanation:

(15 workers * 90 hrs) / 1 wall = 1350 worker-hours per wall

1350 worker - hours / 30 hours = 45 workers