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Answer:

According to this diagram, the tan 62 degrees, is the ratio of the opposite side and the adjacent side of the triangle which is equal to 1.875 units.

What is the right angle triangle property?

In a right-angle triangle ratio of the opposite side to the adjacent side is equal to the tangent angle between the adjacent side and the hypotenuse side.

Here, (b) is the opposite side, (a) is the adjacent side, and is the angle made between the adjacent side and the hypotenuse side.

The sides of the triangle are 8, 15, and 17 units long and the measure of the angles of the right angle triangle is 62, 90, and 28 degrees.

Re-draw, the  Here in the given triangle, the base is the side which is 15 units long. Re-draw the triangle as shown below.

In the attached triangle below, the opposite side of the triangle is 15 units and the adjacent side of the triangle is 8 units long.

The angle between the opposite side and the adjacent side is 62 degrees. Thus using the right angle triangle property as,

Thus, according to this diagram, the tan 62 degrees, is the ratio of the opposite side and the adjacent side of the triangle which is equal to 1.875 units.

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Answer:

S) 230°

T) 45°

Step-by-step explanation:

S) m∠RST = 30°.  An inscribed angle is half the central angle, so RT = 60°.

SR = 70°, so ST = SR + RT = 60° + 70° = 130°.

SPT = 360° − ST = 360° − 130° = 230°

T) m∠DCA = 60°.  An inscribed angle is half the central angle, so AD = 120°.

DB = AD − BA = 120° − 75° = 45°

The volume of the prisms are:

1. 432 yd³

2. 36in³

3. 252 m³

4. 240 ft³

5. 576 mm³

6. 144 cm³

7. 343 m³

8. 120 yd³

9. 150 in³

The formula for calculating the volume of a rectangular prism is expressed as;

V = lwh

such that;

Now, substitute the value for each of the prisms, we have;

1. Volume = 6 × 6 ×12

Multiply

Volume = 432 yd³

2. Volume = 2 ×9 × 2

Multiply

Volume = 36in³

3. Volume = 9 × 4 × 7

Multiply

Volume = 252 m³

4. Volume = 10 × 8 × 3

Multiply

Volume = 240 ft³

5. Volume = 4 × 12 × 12

Multiply the values

Volume = 576 mm³

6. Volume = 6 × 8 × 3

Volume = 144 cm³

7. Volume = 7 × 7 ×7

Volume = 343 m³

8. Volume = 8 × 3 × 5

Volume = 120 yd³

9. Volume = 5 × 6 × 5

Volume = 150 in³

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Answer:

B. 2:1

Step-by-step explanation:

The smaller rectangle is 2x1, the bigger one is 4x2.

We obtain similarity ratio by comparing any corresponding side of two similar objects, so we can either compare the long sides

4:2; this is equivalent to 2:1

or the short sides:

2:1

Either way, we arrive at similarity ratio of 2:1

\(\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{f(x) varies directly with "x"}}{f(x) = kx}\qquad \textit{we also know that} \begin{cases} f(x)=130\\ x = 5 \end{cases} \\\\\\ 130=k5\implies \cfrac{130}{5}=k\implies 26=k~\hfill \boxed{f(x)=26x} \\\\\\ \textit{when x = 11, what is f(x)?}~~f(x)=26(11)\implies f(x)=286\)

The probability of observing such an extreme result by chance alone is 0.0124.

To find the P-value for a two-tailed test of hypothesis, we need to first determine the significance level (alpha) of the test. Let's assume a significance level of 0.05, which is a common choice.

Since this is a two-tailed test, we need to find the probability of observing a test statistic as extreme or more extreme than 2.5 in either direction. We can find this probability using a standard normal distribution table or a calculator.

Using a standard normal distribution table, we can find that the probability of observing a z-score of 2.5 or greater is 0.0062. The probability of observing a z-score of -2.5 or smaller is also 0.0062. Therefore, the P-value for the two-tailed test of hypothesis is:

P-value = 2 * 0.0062

P-value = 0.0124

This means that if the true proportion of business students who have personal computers at home differs from 30%, with a significance level of 0.05, and we obtain a test statistic of 2.5, then the probability of observing such an extreme result by chance alone is 0.0124.

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2 pounds 6 ounces in ounces is equivalent to 38 ounces.

The given measurement is -

2 pounds 6 ounces

In 1 pound, there are 16 ounces.

So, we can write that -

2 pounds 6 ounces = 2 x 16 + 6

2 pounds 6 ounces = 38 ounces

So, 2 pounds 6 ounces in ounces is equivalent to 38 ounces.

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(a) The errors made by the student are:

Incorrectly expanding 49(2) as 24 instead of 98.

Mistakenly factoring the quadratic equation as (y - 8)(y - 1) instead of

\(y^{2} - 9y + 8.\)

(b) The exact solution to the equation is x = 7/11.

(a) The student made two errors in their solution:

Error 1: In the step \("22x + 49(2) = 0,"\) the student incorrectly expanded 49(2) as 24 instead of 98. The correct expansion should be 49(2) = 98.

Error 2: In the step \("y^{2} - 9y + 8 = 0,"\) the student mistakenly factored the quadratic equation as (y - 8)(y - 1) = 0. The correct factorization should be \((y - 8)(y - 1) = y^{2} - 9y + 8.\)

(b) To find the exact solution to the equation, let's correct the errors made by the student and solve the equation:

Starting with the original equation: \(22x + 4 - 9(2) = 0\)

Simplifying: 22x + 4 - 18 = 0

Combining like terms: 22x - 14 = 0

Adding 14 to both sides: 22x = 14

Dividing both sides by 22: x = 14/22

Simplifying the fraction: x = 7/11

Therefore, the exact solution to the equation is x = 7/11.

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The notion of finiteness refers to the idea that something has a definite limit or is not infinite. It is a concept that has been applied in various fields of study, such as mathematics, computer science, and philosophy.

In mathematics, finiteness is a fundamental concept used to define various mathematical objects and structures, such as sets, numbers, and sequences. It is also used to define the properties of functions and to study the properties of mathematical systems.

In computer science, the notion of finiteness is crucial for the design and analysis of algorithms and computer programs. Computer scientists use finite state machines, which are mathematical models that describe the behavior of a system that can be in one of a finite number of states.

This concept is essential to the development of computer programs that are efficient, reliable, and secure.

In philosophy, finiteness is a concept that is often used to reflect on the nature of human existence and the limits of human knowledge. It is also used to examine the concept of time and the nature of reality.

In general, the notion of finiteness is a fundamental concept that has many applications in various fields of study.

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\(0 - (-\frac{31}{43})=0+ \frac{31}{43}=\frac{31}{43}\)

ANSWER : true

ok done. Thank to me :>

Answer:

True

Step-by-step explanation:

\(0 - ( - \frac{31}{43} ) \\ 0 + \frac{31}{43} \\ = \frac{31}{43} \)

Answer:

Step-by-step explanation:

Find the value of below:

The location of L″ is (-5, 0).

To find the location of L″, we first need to apply the first translation rule to the coordinates of trapezoid JKLM:

J': (x, y) → (x + 3, y - 3) => J'(-2+3, 1-3) = J(1, -2)

K': (x, y) → (x + 3, y - 3) => K'(1+3, 1-3) = K(4, -2)

L': (x, y) → (x + 3, y - 3) => L'(3+3, -2-3) = L(6, -5)

M': (x, y) → (x + 3, y - 3) => M'(-4+3, 2-3) = M(-1, -1)

Now, we need to apply the second translation rule to the coordinates of J', K', L', and M':

J'': (x, y) → (x - 1, y + 1) => J''(1-1, -2+1) = J''(0, -1)

K'': (x, y) → (x - 1, y + 1) => K''(4-1, -2+1) = K''(3, -1)

L'': (x, y) → (x - 1, y + 1) => L''(6-1, -5+1) = L''(5, -4)

M'': (x, y) → (x - 1, y + 1) => M''(-1-1, -1+1) = M''(-2, 0)

Therefore, the location of L″ is (-5, 0).

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Answer:

(5,-4)

Step-by-step explanation:

The amount of time it will take to completely fill the pool would be = 18 hours.

To determine the amount of time it will take to fill the pool, the volume of the pool is first calculated by dividing the figure to obtain two regular shapes of a trapezoidal prism and a square prism.

The volume of a trapezoidal prism = 1/2(a+b)×h×l

where;

a = 3m

b = 1m

h = 18-6 = 12m

l = 9m

Volume of the trapezoidal prism = 1/2(3+1)×12×9

= 4×12×9 = 432m³

Volume of square prism = length×width×height

where;

length = 6m

width = 9m

height = 1 m

Volume = 6×9×1 = 54m³

Therefore the volume of the pool = 432+54 = 486m³

If 4 hours = 2 m up from the deepest part

The volume filled for 4 hours = 1/2×2×12×9 = 108m³

If 4 hours = 108

X hours = 486

make X the subject of formula;

X = 4×486/108

= 1944/108

= 18 hours.

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The solution to the given inequality expression is: x ≤ -2

The inequality expression is given as:

5(0.5)ˣ + 1 ≤ 21

Subtract 1 from both sides to get;

5(0.5)ˣ ≤ 20

Divide both sides by 5 to get:

(0.5)ˣ ≤ 4

Using logarithm we have:

x In 0.5 ≤ In 4

x ≤ In 4/In 0.5

x ≤ -2

Thus, that is the solution of the inequality expression

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Answer:

i belive its 34% becouse you are saveing 170 dollars

Answer:

Sorry what's the question?

I don't see the equation here

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

x=-1

Step-by-step explanation:

4x+35x-15=9x-45
39x-15=9x-45
39x-9x=-45+15
30=+-30
x=-1

Answer:

\( \sf \: x = - 1\)

Step-by-step explanation:

Given equation,

→ 4x + 5(7x - 3) = 9(x - 5)

Now the value of x will be,

→ 4x + 5(7x - 3) = 9(x - 5)

→ 4x + 35x - 15 = 9x - 45

→ 39x - 15 = 9x - 45

→ 39x - 9x = -45 + 15

→ 30x = -30

→ x = -30 ÷ 30

→ [ x = -1 ]

Hence, the value of x is -1.

Answer:

Total number of votes = 5,992

Step-by-step explanation:

Given:

Ratio of Yes and No = 3:5

Total number of yes votes = 2,247

Find:

Total number of votes

Computation:

Total number of votes = Total number of yes votes [(3+5)/3]

Total number of votes = 2,247[(8)/3]

Total number of votes = 5,992

Answer:

Step-by-step explanation:

To show that the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\), we can simplify both sides of the equation using the properties of logarithms. Here are the steps:

Step 1: Simplify the expression on the left side:

\(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\)

Step 2: Apply the logarithmic property \(\ln(a) - \ln(b) = \ln\left(\frac{a}{b}\right)\) to combine the logarithms:

\(\ln\left(\frac{\sqrt{2} + 1}{\frac{1}{\sqrt{2}}}\right)\)

Step 3: Simplify the expression within the logarithm:

\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)}\right)\)

Step 4: Simplify the denominator by multiplying by the reciprocal:

\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)} \cdot \sqrt{2}\right)\)

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{\left(\frac{1}{\sqrt{2}}\right) \cdot \sqrt{2}}\right)\)

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)

Step 5: Simplify the numerator:

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)

\(\ln\left(\sqrt{2}(\sqrt{2} + 1)\right)\)

\(\ln\left(2 + \sqrt{2}\right)\)

Now, let's simplify the right side of the equation:

Step 1: Simplify the expression on the right side:

\(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\)

Step 2: Simplify the expression within the logarithm:

\(-\ln\left(\frac{\sqrt{2} - 1}{\sqrt{2}}\right)\)

Step 3: Apply the logarithmic property \(\ln\left(\frac{a}{b}\right) = -\ln\left(\frac{b}{a}\right)\) to switch the numerator and denominator:

\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)

Step 4: Simplify the expression:

\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)

\(-\ln\left(\frac{\sqrt{2}(\sqrt{2} + 1)}{1}\right)\)

\(-\ln\left(2 + \sqrt{2}\right)\)

As we can see, the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) simplifies to \(\ln(2 + \sqrt{2})\), which is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\).

Answer:

51 questions she answered correctly.

Step-by-step explanation: 85/100 x 60

= 510/10

= 51

Answer:

51 questions

Step-by-step explanation:

To do this we need to realize that 85% is equal to 85/100. This can be simplified in fraction form to .85.

Looking at the question, we see that it says "Briley answered 85% of the 60 quiz..." A key word here is of. Of always means multiply. So we can see if we were going to form an equation, we would be multiplying.

Briley answered correctly = (85%) times (60 questions)

Mathematically, ?=(.85)x(60)=51

So we know she answered 51 correctly, and that 51 is 85% of 60.

I hope this helps you!

Answer:

5%=Five percent

34%=Thirty four percent

143%=One hundred forty three percent

500%=Five hundred percent

Hope it helps

Have a great day : )

Answer:

The square root is 1.90

Step-by-step explanation:

Given

\(x = \sqrt{3.6}\)

Required

Find x

Express 3.6 as 36/10

So, we have:

\(x = \frac{\sqrt{36}}{\sqrt{10}}\)

This gives

\(x = \frac{6}{\sqrt{10}}\)

Rationalize

\(x = \frac{6}{\sqrt{10}}*\frac{\sqrt{10}}{\sqrt{10}}\)

\(x = \frac{6\sqrt{10}}{10}\)

Using a calculator

\(\sqrt{10} \approx 3.16\)

So, we have:

\(x = \frac{6*3.16}{10}\)

\(x = \frac{18.96}{10}\)

\(x = 1.896\)

Approximate

\(x = 1.90\)

Answer:

1 1/2

Step-by-step explanation:

We need to convert all of these into one denominator. 1 1/4 needs to be converted into 12ths. 4 x 3 = 12 1 x 3 = 3. Our new fraction instead of 1 1/4 is     1 3/12.

Which is closer to the whole number?

1 1/12 is 1/12 away from a whole number

1 3/12 is 3/12 away from a whole number

1 5/12 is 5/12 away from a whole number

Hope this helps!

In the given diagram,

The arc length is approximately 10 cm

The area of the sector is approximately 105 cm²

From the question, we are to determine the arc length and the area of the sector shown in the diagram.

Arc length can be determined by using the formula,

Arc length = θ/360° × 2πr

Where θ is the angle subtended by the arc at the center of the circle

and r is the radius

From the diagram,

θ = a = 30°

r = 20 cm

Thus,

Arc length = 30°/360° × 2πr

Arc length = 1/12 × 2π × 20

(Take π = 3.14)

Arc length = 1/12 × 2 × 3.14 × 20

Arc length = 10.466667

Arc length ≈ 10 cm

The area of a sector can be calculated by using the formula

A = θ/360° × πr²

Where θ is the angle at the center of the circle

and r is the radius

A = 30°/360° × π × 20²

(Take π = 3.14)

A = 30°/360° × 3.14 × 20²

A = 1/12 × 3.14 × 400

A = 104.6666667

A ≈ 105 cm²

Hence, the area of the sector is 105 cm²

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\(\quad \huge \quad \quad \boxed{ \tt \:Answer }\)

\(\qquad \tt \rightarrow \:-\dfrac{1}{\sqrt{3-2x}} \)

____________________________________

\( \large \tt Solution \: : \)

We newd to find the derivative of given function :

\(\qquad \tt \rightarrow \: y = \sqrt{3 - 2x} \)

\(\qquad \tt \rightarrow \: y = (3 - 2x) {}^{ \frac{1}{2} } \)

\(\qquad \displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{d}{dx} (3 - 2x) {}^{ \frac{1}{2} } \)

\(\qquad \displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{1}{2} \sdot(3 - 2x) {}^{ - \frac{1}{2} } \sdot( - 2)\)

\(\qquad \displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{1}{ \cancel2} \sdot\frac{1}{(3 - 2x) {}^{ \frac{1}{2} } }\sdot( - \cancel2)\)

\(\qquad \displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{ - 1}{ \sqrt{ (3 - 2x) {}^{ }} }\)

Correct option : B

Answered by : ❝ AǫᴜᴀWɪᴢ ❞