Instructions: Find the missing side. Round your answer to the
nearest tenth.
x=
30
38⁰
X

The principal amount that must be deposited as a lump sum amount is = $16,666.7

The simple interest amount = $20,000

The interest rate = 12%

The time that is given= 10 years

Therefore the principle amount =?

Using the simple interest formula;

SI= P×T×R/100

Make P the subject of formula,

P = SI ×100/T×R

P= 20,000×100/10×12

P= 2,000,000/120

P= $16,666.7

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The statement that describes the quotient of 3 over 10 division sign2 over 5 is A. The maximum amount of oil the bowl can hold is Fraction 3 over 4 cup.

From the information given, we are told that a bowl holds fraction 3 over 10 cups of oil when it is Fraction 2 over 5 full.

Therefore, the statement that best describes the quotient of 3 over 10 division sign2 over 5 will be that the maximum amount of oil the bowl can hold is fraction 3 over 4 cup.

In conclusion, the correct option is A.

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By using algebra properties and trigonometric formulas we find that the trigonometric expression [tex]\frac{1}{1 - \sin x} - \frac{1}{1 + \sin x}[/tex] is equivalent to the trigonometric expression [tex]\frac{2\cdot \tan x}{\cos x}[/tex].

In this question we have trigonometric expression whose equivalence to another expression has to be proved by using algebra properties and trigonometric formulas, including the fundamental trigonometric formula, that is, cos² x + sin² x = 1. Now we present in detail all steps to prove the equivalence:

[tex]\frac{1}{1 - \sin x} - \frac{1}{1 + \sin x}[/tex]       Given.

[tex]\frac{1 + \sin x - 1 + \sin x}{1 - \sin^{2}x}[/tex]      Subtraction between fractions with different denominator / (- 1) · a = - a.

[tex]\frac{2\cdot \sin x}{\cos^{2}x}[/tex]      Definitions of addition and subtraction / Fundamental trigonometric formula (cos² x + sin² x = 1)

[tex]\frac{2\cdot \tan x}{\cos x}[/tex]      Definition of tangent / Result

By using algebra properties and trigonometric formulas we conclude that the trigonometric expression [tex]\frac{1}{1 - \sin x} - \frac{1}{1 + \sin x}[/tex] is equal to the trigonometric expression [tex]\frac{2\cdot \tan x}{\cos x}[/tex]. Hence, the former expression is equivalent to the latter one.

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The region enclosed by the given curves are integrated with respect to x and the area is 4.2724 square units.

In this question,

The curves are y = 2/x, y = 2/x^2, x = 4

The diagram below shows the region enclosed by the given curves.

From the diagram, the limit of x is from 1 to 4.

The given curves are integrated with respect to x and the area is calculated as

[tex]A=\int\limits^4_1 {\frac{2}{x} } \, dx -\int\limits^4_1 {\frac{2}{x^{2} } } \, dx[/tex]

⇒ [tex]A=2[\int\limits^4_1 {\frac{1}{x} } \, dx -\int\limits^4_1 {\frac{1}{x^{2} } } \, dx][/tex]

⇒ [tex]A=2[\int\limits^4_1( {\frac{1}{x} } - {\frac{1}{x^{2} } } )\, dx][/tex]

⇒ [tex]A=2[lnx-\frac{1}{x} ] \limits^4_1[/tex]

⇒ [tex]A=2[(ln4-\frac{1}{4} )-(ln1-\frac{1}{1} )][/tex]

⇒ A = 2[(1.3862-0.25) - (0-1)]

⇒ A = 2[1.1362 + 1]

⇒ A = 2[2.1362]

⇒ A = 4.2724 square units.

Hence we can conclude that the region enclosed by the given curves are integrated with respect to x and the area is 4.2724 square units.

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Based on the information given about the temperature, Daniela made her error on step 3 because it says: "Find the ratio of the differences of the means compared to the mean absolute deviation.

From the information given, it van be seen that Daniela recorded the low temperatures during the school day last week and this week and her results are shown in the table.

Here, she didn't find the difference between the today and last week means. She just put the mean as a whole.

Therefore, Daniela made her error on step 3 because it says: "Find the ratio of the differences of the means compared to the mean absolute deviation. This was the error.

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Answer:

12

Step-by-step explanation:

[tex]24=2^{3} \times 3 \\ \\ 36=2^{2} \times 3^{2} \\ \\ 96=2^{5} \times 3[/tex]

Hey there!

What is GCF (Greatest Common Factor)?

Basically, the GCF is the biggest number in a data set that all of your numbers share.

What are the factors of the numbers?

24:1, 2, 3, 4, 6, 8, 12, and 24

36: 1, 2, 3, 4, 6, 9, 12, 18, and 36

96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96

What are the like terms that the numbers share?

1, 2, 3, 4, 6, 8, and 12

What is the biggest number out of the like terms?

12

What is your number?

12

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer: 5 games

Step-by-step explanation: A .500 record means that the soccer team won half of their games ( that's how I interpret it). Since they are going to play 30 games, they need to win half of 30 or 15 games to have that record. 15-10 = 5. So, they need to win 5 more games to have a .500 record.

Answer:

30 degrees

Step-by-step explanation:

They are corresponding angles.

Answer: 30 degrees

Step-by-step explanation:

mangle8 and mangle 4 are corresponding angles meaning the angles are both the same.

Answer: x^{3}(2x+9)

Step-by-step explanation:

Eliminate redundant parentheses:

(3x^{4}+3x^{3}+5x^{2})-1(x^{4}-6x^{3}+5x^{2})

3x^{4}+3x^{3}+5x^{2}-1(x^{4}-6x^{3}+5x^{2})

Distribute:

^{4}+3x^{3}+5x^{2}{-1(x^{4}-6x^{3}+5x^{2})}

3x^{4}+3x^{3}+5x^{2}

Combine like terms UNTIL YOU FIND ONE FACTOR

Answer:

Step-by-step explanation: P(x 3), Q(7, -1) and PQ= 5 .

To Find :

The possible value of x.​

Solution :

We know, distance between two points in coordinate plane is given by :

Therefore, the possible value of x are 10 and 4.

Answer:

============================

Conditions we need to meet:

To get the smallest number we'd use all 10 digits in the ascending order:

Here we can't have zero in the beginning as the number becomes 9-digit.

So swapping zero with the closest digit, 1.

Our number should be even, so we should swap 9 with one even digit.

Again it should be the closest one to 9, so it is 8.

We get the following number as a result:

To test you may swap digits, any number you get will be greater than this number.

B. number of dogs owned versus number of plane tickets bought

Answer:

A

Step-by-step explanation:

the side opposite of the angle is related to the size of this angle. Smaller angles have less space for the line to "spread out," so it will be shorter. Vice versa, bigger angles will have opposite sides longer because of more space.

The number of terms in the geometric series is 9

The geometric series given as:

96 - 48 + 24 -....,-3/8 .

Calculate the common ratio (r) as follows

r = T2/T1

Substitute the known values in the above equation

r = -48/96

Evaluate

r = -0.5

The number of terms is then calculated as:

Tn = a * r^n-1

Let n = 9

So, we have:

T9 = a * r^9

Substitute the known values in the above equation

T9 = 96 * (-0.5)^8

Evaluate the product

T9 = -3/8

Hence, the number of terms in the geometric series is 9

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Answer:

12 m

Step-by-step explanation:

Well, imagine you got this nice room. How can it reach the other corner? It has to go along the 3 dimensions. So the shortest path would be: 5 + 4 + 3  12m

Answer:

3 + √(41) = 9.4 m (nearest tenth)

Step-by-step explanation:

The room can be modeled as a rectangular prism with:

If the ant is at the top of a corner of a room and crawls to the opposite bottom corner of the room, the shortest distance will be to travel down one vertical edge of the room then to travel the diagonal of the floor of the room (or to travel the diagonal of the ceiling and then one vertical edge).

Vertical edge = height of room = 3m

The diagonal of the floor (or ceiling) is the hypotenuse of a right triangle with legs of the width and length.  Therefore, to find the diagonal, use Pythagoras Theorem.

Pythagoras Theorem

[tex]a^2+b^2=c^2[/tex]

where:

Given:

Substitute the given values into the formula and solve for c:

[tex]\implies 4^2+5^2=c^2[/tex]

[tex]\implies c^2=41[/tex]

[tex]\implies c=\sqrt{41}[/tex]

Therefore, the shortest distance the ant can travel is:

⇒ 3 + √(41) = 9.4 m (nearest tenth)

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102 degrees

Step-by-step explanation:

Angles in a quadrilateral add to 360 degrees.

y = 360 - (120 + 85 + 53)

y = 360 - 258

y = 102 degrees

Answer:

627

267

276

762

726

and the no. itself, 672

By the alternating series test, this series converges: for [tex]k\in\Bbb N[/tex],

[tex]\dfrac{k^5+1}{k^6+11}[/tex]

is a positive, decreasing sequence that converges to 0.

However,

[tex]\displaystyle \sum_{k=2}^\infty \left| (-1)^{k+1} \frac{k^5+1}{k^6+11} \right| = \sum_{k=2}^\infty \frac{k^5+1}{k^6+11} \approx \sum_{k=2}^\infty \frac1k[/tex]

is a divergent series by comparison to the harmonic series.

So the given series is conditionally convergent.

The given series is conditionally convergent. This can be obtained by using alternating series test first and then comparing the series to the harmonic series.

Initially we need to know what Absolute convergence and Conditional convergence,

If [tex]\sum|a_{n} |[/tex] → converges, and [tex]\sum a_{n}[/tex] → converges, then the series is Absolute convergence

If [tex]\sum|a_{n} |[/tex] → diverges, and [tex]\sum a_{n}[/tex] → converges, then the series is Conditional convergence

First use alternating series test,

[tex]\lim_{k \to \infty} \frac{k^{5} +1}{k^{6}+11 }[/tex] = [tex]\lim_{n \to \infty} \frac{5}{6k}[/tex] = 0,

The series is a positive, decreasing sequence that converges to 0.

Next by comparing the series to harmonic series,

[tex]\sum^{\infty} _{k=2}|(-1)^{k+1} \frac{k^{5} +1}{k^{6}+11 }|=\sum^{\infty} _{k=2}\frac{k^{5} +1}{k^{6}+11 }[/tex] ≈  [tex]\sum^{\infty} _{k=2}\frac{1}{k}[/tex] = 0

This implies that the series is divergent by comparison to the harmonic series.

First we got that the series is converging and then we got the series is divergent. Therefore the series is conditionally convergent.

[tex]\sum|a_{n} |[/tex] → diverges, and [tex]\sum a_{n}[/tex] → converges, then the series is Conditional convergence.

Hence the given series is conditionally convergent.

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Answer:

a. 1056 ft

b. 52.8 ft

Step-by-step explanation:

1 mile = 5280 feet

a.

[tex]\frac{1}{5} *5280 = 1056[/tex]

Therefore 1/5 of a mile is 1056 feet.

b.

[tex]\frac{1}{100} *5280=52.8[/tex]

Therefore 1/100 of a mile is 52.8 feet

[tex]4r {}^{3} s - rs + 7r {}^{3} s + 8rs - 3 + 8rs + 6 \\ add \: \: terms \: \: of \: \: same \: \: variables \\ 11r {}^{3} s + 15rs + 3[/tex]

Answer:

p(t) = 2950^3t

Step-by-step explanation:

I’m not sure if this is exactly what you wanted or not. Please let me know more info and I’ll write any more answers for this question in the comments. Have a great day!!

The solution for the inequality given exists x > -11/10. The inequality contains an infinite number of solutions as long as it is greater than -11/10.

Given: 4(2 – x) > –2x – 3(4x + 1)

The inequality can be simplified to

8 - 4x > -14x - 3

subtract 8 from both sides of the equation, and we get

8 - 4x - 8 > -14x - 3 - 8

- 4x > -14x - 11

Add 14x from both sides

- 4x + 14x > -14x - 11 + 14x

10x > - 11

x > - 11/10

The solution for the inequality given exists x > -11/10. This means that any number greater than -11/10 exists as a solution to the inequality given. The inequality contains an infinite number of solutions as long as it is greater than -11/10.

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Answer:    C,E

Step-by-step explanation:

you did the work

Answer:

35x71+71x65+51x23+23+49=8,345

Step-by-step explanation:

Answer:

8345

Is the correct answer

Step-by-step explanation:

hope it will help you

Answer:

Step-by-step explanation:

For missing hypotenuse: [tex]\sqrt({a^{2} + b^{2})[/tex]

Plug in the side lengths that are known to find the hypotenuse.

1. No, the angle is less than 18 degrees (closer to 15), so it is not safe

2. The length rounded to the nearest tenth is approximately 15.5 feet.

The perimeter of inside of the track is 536.44m

The perimeter of a circle is also known as the circumference of the circle. The formula for calculating the circumference is expressed as:

C = 2πr

where

r is the radius

From the given diagram

r = 46/2 = 23m

C = 2(3.14)(23)
C = 144.44m

Find the perimeter of the rectangle

P = 2(l+w)

p = 2(46+150)
P = 2(196)
P =392m

The perimeter of the inside track = 144.44 + 392

The perimeter of the inside track = 536.44m

Hence the perimeter of inside of the track is 536.44m

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The volume of the cylinder is [tex]384\pi \sqrt{3cm }^{2}[/tex].

Body of the diagonal=24cm.

Assume the length of the side= a.

[tex]a^{2} +(a^{2} +a^{2} )=24^{2}[/tex]

                   [tex]a=\sqrt[8]{3} cm[/tex]

The area of the cylinder base=[tex]\pi R^{2}[/tex]

                                                =[tex]\pi (\frac{1}{2} \sqrt[8]{3} )^{2}[/tex]

                                                =[tex]48cm^{2}[/tex]

The high of the cylinder is[tex]\sqrt[8]{3}cm[/tex]

The volume of the cylinder:

=s*h

=[tex]48\pi *\sqrt[8]{3}[/tex]

=[tex]384\pi \sqrt{3} cm^{3}[/tex]

The volume of the cylinder is [tex]384\pi \sqrt{3cm }^{2}[/tex].

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The biggest possible volume of the cylinder will be [tex]2089.497\hspace{1mm}\text{cm}^3[/tex].

Now, given that the diagonal of the cube is [tex]24[/tex] cm. So, if the side length of the cube is [tex]x[/tex] cm, then we must have

[tex]x\sqrt{3}=24\\\Longrightarrow x=\frac{24}{\sqrt{3}}\\\Longrightarrow x=8\sqrt{3}[/tex]

Thus, the side length of the cube is [tex]8\sqrt{3}[/tex] cm.

So, the height of the cylinder with maximum volume will be [tex]h=8\sqrt{3}[/tex] cm and the diameter will be [tex]d=8\sqrt{3}[/tex]cm i.e. the radius will be [tex]r=\frac{d}{2}=\frac{8\sqrt{3}}{2}=4\sqrt{3}[/tex] cm.

So, using the above formula for the volume of a cylinder, we get

[tex]V=\pi r^{2}h=\pi\times (4\sqrt{3})^2\times 8\sqrt{3}=2089.497\hspace{1mm}\text{cm}^3[/tex].

Therefore, the biggest possible volume of the cylinder will be [tex]2089.497\hspace{1mm}\text{cm}^3[/tex].

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Step-by-step explanation:

the mean value is the sum of all data points divided by the number of data points.

first we have 7 tests and their mean value :

(t1 + t2 + t3 + t4 + t5 + t6 + t7) / 7 = 54

that means

(t1 + t2 + t3 + t4 + t5 + t6 + t7) = 54 × 7 = 378

in order for the mean value to be at least 60% after 8 tests, we need to add a t8, so that

(t1 + t2 + t3 + t4 + t5 + t6 + t7 + t8) = 60 × 8 = 480

because only then we have

(t1 + t2 + t3 + t4 + t5 + t6 + t7 + t8) / 8 = 60

and the student passes.

so,

(t1 + t2 + t3 + t4 + t5 + t6 + t7) + t8 = 480

378 + t8 = 480

t8 = 480 - 378 = 102%

the student would have to achieve 102% on the 8th test.

which would be normally impossible, but maybe the tests involve some bonus points.

Answer:

d

Step-by-step explanation:

up and down is outside of the x stuff so its c or d

and c is moving it up

d is moving it down

Answer:

d)  y = | x | - 2

Step-by-step explanation:

In order to translate a graph downward 2 units ,we subtract 2 from the original function.

therefore,

If the Original function is  y = |x|

Then the Function of the translated graph is  y = | x | - 2

The expressions which demonstrates the identity property of multiplication is; 25(1) = 25 option B

Identity Property of Multiplication states that any number multiplied by 1 does not change, that is, it is constant or remains the same

Check all options

25(0) = 25

0 = 25

Not true

25(1) = 25

25 = 25

True (identity property of multiplication holds)

25 + 0 = 25

25 = 25

True (Not identity property of multiplication)

25 + 1 = 25

26 = 25

Not true

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