Which expression is equivalent to

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &175\\ r=rate\to 12\%\to \frac{12}{100}\dotfill &0.12\\ t=years\dotfill &10\\ \end{cases} \\\\\\ A=175(1 + 0.12)^{10}\implies A=175(1.12)^{10}\implies A\approx 543.52[/tex]

The value of x for which the lines m and l are parallel is 31 degrees

The given diagram includes two parallel lines m and l, since the line are parallel hence the sum of the angles 105 and 3x - 18 are supplementary that is;

105 + 3x - 18 = 180

Simplify for the value of x

87 + 3x = 180

3x = 180 - 87

3x = 93

x = 93/3

x = 31

Hence the value of x for which the lines m and l are parallel is 31 degrees

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[tex]\huge\sf\underline{Answer} [/tex]

[tex]\sf\longrightarrow selling \: prize \: = \frac{100 + profit\%}{100} \times cp[/tex]

[tex]\sf\longrightarrow \frac{108}{100} \times 15000 = 16200[/tex]

Let the marked prize of the TV be x .

[tex]\sf\longrightarrow discount = 20\% \: of \: x \: = \frac{20}{100}x = \frac{x}{5} [/tex]

We have SP = MP - Discount

[tex]\sf\longrightarrow 16200 \: = \: x - \frac{x}{5} [/tex]

[tex]\sf\longrightarrow 16200 \: = \frac{4x}{5} [/tex]

[tex]\sf\longrightarrow x \: = \: 20250[/tex]

Hence , The marked prize of the TV is ₹20,250 .

Hope it helps ~

The value of x is 6.

Complementary angles are angles that sum up to 90°.

Analysis:

For angles A and B, to be complementary, the sine of angle A  must be equal to the cosine of angle B.

sin A = cos B

5X+9 = 3x+21

5x - 3x = 21 - 9

2x = 12

x = 6

In conclusion, the value of x to make angles A and B complementary is 6.

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The volume of the sphere is 3,052.08 cubic millimeters. The correct answer is A.

If the given sphere is of radius r units, then its volume is given as:

[tex]V= \dfrac{4}{3} \pi r^3 \: \rm unit^3[/tex]

A glass marble has a diameter of 18 millimeters.

The radius is 9

[tex]V= \dfrac{4}{3} (3.14) (9)^3 \: \rm unit^3\\\\V = 3,052.08 cubic millimeters[/tex]

The volume of the sphere is 3,052.08 cubic millimeters. The correct answer is A.

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Answer:

see below

Step-by-step explanation:

1 9/12 = > 1 3/4

........

Answer:

Please don't hesitate to give a "thumbs up" for the answer in case the answer has helped you 1. 2 M, 2R, 2 P are placed in shelf randomly P(similar a…

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Transcribed image text: Your Turn Find the probability using permutation with repetition 1. There are 2 mystery books, 2 romance books, 2 poetry books to be randomly placed on a shelf. What is the probability that the mystery books are next to each other, the romance books are next to each other, and the poetry books are next to each other? (For example, MMRRPP). 2. The school jazz band has 4 boys and 4 girls, and are randomly lined up for a yearbook photo. Find the probability of getting all of the boys grouped together.

Step-by-step explanation:

CORRECT ME IF IM WRONG

The characteristics I notice in top 3 mobile banking vs. online banking. is that:

They are:

The top 3 banking activities done via online banking are:

Therefore, the characteristics I notice in top 3 mobile banking vs. online banking. is that:

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The number of walkways that must be shoveled to result in equal billing from both companies is 10

From the question, we are to determine how many walkways must be shoveled to result in equal billing from both companies

Let the number of walkways be x

From the given information,

Bobs snowplow business charges 300$ per season plus 10$ for each walkway shoveled

∴ If x walkways are shoveled

the billing will be $300 + $10x

For Mikes snow removal

Mikes snow removal charges 250$ per season plus 15$ per walkway

∴ If x walkways are shoveled

the billing will be $250 + $15x

Now, we are to determine the value of x for which the billings from both companies will be equal,
That is,

$300 + $10x = $250 + $15x

$15x - $10x = $300 - $250

$5x = $50

x = $50 / $5

x = 10

Hence, the number of walkways that must be shoveled to result in equal billing from both companies is 10.

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Answer:

Here is the ans ...hope it helps:)

The probability that the book is nonfiction given that it is hard-covered is 4/11

From the complete question, we have:

Total = 20

n(H ∩ N) = 4

n(H) = 11

This means that:

P(H ∩ N) = n(H ∩ N)/Total

So, we have:

P(H ∩ N) = 4/20

The conditional probability is then calculated using:

P(N | H) =4/20 ÷ 11/20

Evaluate

P(N | H) = 4/11

Hence, the probability that the book is nonfiction given that it is hard-covered is 4/11

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Answer:

Step-by-step explanation:

4/20

11/20

4/11

yw :)

Answer:

after 25 months both options cost $2000

Step-by-step explanation:

the options are the same at the point of intersection of the 2 lines

the lines intersect at (25, 2000)

That is after 25 months both options will cost $2000

Answer: 2,444

Step-by-step explanation: We can find the answer to this problem by simplifying the scientific notation, and then adding. You would end up with 2,000 + 400 + 40 + 4 if done correctly. Hope this helps!

Exact Form:

5

27

Decimal Form:

0.

¯¯¯¯¯¯

185

i hope this helps please have a nice day/night

Answer:

Exact Form:

5

27

Decimal Form:

0.

¯¯¯¯¯¯

185

i hope this helps please have a nice day/night

Step-by-step explanation:

The measure of the missing angle x is 23.22 degrees

The expression for representing cosine rule is expressed as:

c² = a² + b² - 2ab cos C

Given the following parameters

a = 26

b = 50

c = 29

Substitute

c² = a² + b² - 2ab cos C

29² = 26² + 50² - 2(26)(50) cos C

841 = 676 + 2500 - 2600cosC

2335 =2600cos C
cos C = 2335/2660

C = 23.22 degrees

Hence the measure of the missing angle x is 23.22 degrees

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Answer:

23.2 is the correct answer given you need to round to the nearest tenth.

[tex]|\Omega|=1+2+3+3=9\\|A|=3\\\\P(A)=\dfrac{3}{9}=\dfrac{1}{3}\approx33,3\%[/tex]

Answer:

300:288

Step-by-step explanation:

5+2=7

280 /7 = 4

20:8

300:288

Step-by-step explanation:

a rhombus is a parallelogram with 4 identical sides.

it has therefore two pairs of equal angles.

as any quadrilateral the sum of all interior angles is 360°.

(and yes, as add-on, the diagonals bisect each other at right angles).

so, one interior angle is 79°.

that means it has a twin that is also 79°.

together they have 79×2 = 158°.

that leaves

360 - 158 = 202°

for the other 2 angles (they must be equal too).

so, each of them has

202/2 = 101°

so, the other 3 angles are

79°, 101°, 101°

i can, first add then take away and u done!

Step-by-step explanation:

Check the picture below.

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+52}t\stackrel{\stackrel{c}{\downarrow }}{+0} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 52}{2(-16)}~~~~ ,~~~~ 0-\cfrac{ (52)^2}{4(-16)}\right) \implies \left( - \cfrac{ 52 }{ -32 }~~,~~0 - \cfrac{ 2704 }{ -64 } \right)[/tex]

[tex]\left( \cfrac{13}{8}~~,~~\cfrac{169}{4} \right)\implies \underset{\stackrel{\uparrow \hspace{3em}}{seconds\qquad }}{\stackrel{\stackrel{\qquad feet}{\hspace{3em}\downarrow }}{\left( 1\frac{5}{8}~~,~~42\frac{1}{4} \right)}}[/tex]

The circumference of the circle is 75.36 cm.

Diameter of the circle is 24 cm,

[tex]\pi = 3.14[/tex]

Circumference of the circle is [tex]2\pi r[/tex].

So, Radius, r = 24/2 = 12 cm.

Now, Putting the value in the above formula, we get

2 × 3.14 ×12 = 3.14 × 24 = 75.36 cm.

Hence, the circumference of the circle is 75.36 cm.

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Answer:

  a. $0.47 per ounce

  b. $0.36 per ounce

  c. the gallon size costs less per ounce

Step-by-step explanation:

A unit rate is a rate that is expressed with one unit in the denominator. That is, it is <some amount> per unit. The <some amount> value will generally depend on what unit is chosen. This problem suggests the desired unit is 1 oz of paint.

__

Unit cost for a quart:

  ratio = cost/ounces = $14.99/(32 oz) ≈ $0.468/oz ≈ $0.47/oz

__

Unit cost for a gallon:

  ratio = cost/ounces = $45.99/(120 oz) ≈ $0.359/oz ≈ $0.36/oz

__

The cost per ounce is less for the gallon size. If at least 3 quarts of paint is needed, then buying it in the gallon size will cost less.

If less than 3 quarts are needed, then a gallon container will cost more than is necessary for the paint required. The "better deal" depends on the amount of paint required.

Answer:

45 becasue it has to be over 43

Step-by-step explanation:

The test score of the student who joined the class will be;

⇒ 55

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The mean test score of 12 students = 42

And, A student joins the class and the mean becomes 43.

Now,

Total score for 12 students is,

⇒ x / 12 = 42

⇒ x = 42 × 12

⇒ x = 504

Here, A student joins the class and the mean becomes 43.

Let the student who join = y

So, We get;

⇒ (504 + y) / 13 = 43

⇒ 504 + y = 43×  13

⇒ 504 + y = 559

⇒ y = 559 - 504

⇒ y = 55

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Answer:

[tex]\large\boxed{\sf x^3 - 7x^2 + 7x - 10}[/tex]

Explanation:

Given:

(a) f(x) = x³ - 3x² + 2x - 3

(b) g(x) = 4x²- 5x + 7

Solve for (f - g)(x) = f(x) - g(x) :

⇒ x³ - 3x² + 2x - 3 - (4x²- 5x + 7)

distribute inside parenthesis

⇒ x³ - 3x² + 2x - 3 - 4x² + 5x - 7

group the variables

⇒ x³ - 3x² - 4x² + 2x + 5x - 3 - 7

add or subtract variables

⇒ x³ - 7x² + 7x - 10

Answer:

x³ - 7x² + 7x - 10

Step-by-step explanation:

Subtracting functions: (f - g)(x) is equivalent to f(x) - g(x)

Given:

Simplify:

(x³ - 3x² + 2x - 3) - (4x² - 5x + 7)

(x³ - 3x² + 2x - 3) - (4x²) + - (- 5x) - (7)

x³ - 3x² + 2x - 3 - 4x² + 5x - 7

x³ - 3x² - 4x² +2x + 5x - 3 - 7

x³ - 7x² + 7x - 10

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Answer:

y = 4 - 2x

Step-by-step explanation:

That is the formula, in y = a + mx but it you want it in y = mx+c, it is y = -2x + 4

Answer:

9

Step-by-step explanation:

Vertical lines are parallel so the given interior angles are supplementary and their sum is equal to 180:

4x + 9 + 16x - 9 = 180 add like terms

20x = 180 divide both sides by 20

x = 9

Step-by-step explanation:

here, given points are

(-2,-1),(-5,-3),(-5,-4)

now

(X,y)________ (-y,X)

(-2,-1)________ (1,-2)

(-5,-3)________ (3,-5)

(-5,-4)________ (4,-5)

now plot the points in the graphs

Answer:

[tex]41^{\circ}[/tex]

Step-by-step explanation:

[tex]~~~~~~\cos \theta = \dfrac{\text{Base}}{\text{Hypotenuse}}\\\\\\\implies \cos \theta = \dfrac{9}{12}\\\\\\\implies \theta = \cos^{-1} \left( \dfrac 9{12} \right)\\\\\\\implies \theta \approx 41^{\circ}[/tex]

Answer:

41°

Step-by-step explanation:

Since the adjacent side and the hypotenuse are given, let's take the cosine ratio of the missing angle.

cos θ = adjacent side / hypotenuse

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

Given :

⇒ Adjacent side = 9

⇒ Hypotenuse = 12

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

Solving :

⇒ cos θ = 9/12

⇒ cos θ = 0.75

⇒ θ = cos⁻¹ (0.75)

⇒ θ = 41.4096221....

⇒ θ = 41° (to the nearest degree)

The value of x is 8 from the diagram given.

The corresponding sides of a similar triangle are said to be in proportion if and only if the corresponding angle are also equal.

To calculate the side of line x (|x|), we have to determine the ratios of the corresponding sides as:

[tex]\mathbf{\dfrac{BC}{DC} = \dfrac{AC}{EC}}[/tex]

[tex]\mathbf{\dfrac{x}{10} = \dfrac{12}{15}}[/tex]

x = 120/15

x = 8

Therefore, we can conclude that the value of x is 8.

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