Rewrite the expression
(10¹) ³ =

Answer:

To calculate the amount Sophia needs to invest to reach a certain value in a specific time, given an interest rate compounded monthly, we can use the formula:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the investment

P = the initial principal or investment amount

r = the annual interest rate (expressed as a decimal)

n = the number of times the interest is compounded per year

t = the number of years the investment is held

Since the interest is compounded monthly, we need to divide the annual rate by 12 to find the monthly rate. So:

r/12 = 0.034/12 = 0.002833

Now we can plug in the values into the formula:

A = P(1 + 0.002833)^(12*14)

A = P(1.002833)^(168)

We know that A = $1,450 and we want to find P (the initial principal or investment amount).

So we can rearrange the equation to find P:

P = A/(1.002833)^(168)

Solving for P, we get:

P ≈ $973.99

So Sophia would need to invest around $973.99 to reach $1,450 in 14 years with an annual interest rate of 3.4% compounded monthly.

Step-by-step explanation:

Answer:

4x>= 10

Step-by-step explanation:

i believe thats the answer

There are 48, 64, 96 and 144 quarts of milk for 3,4,6 and 9 crates shipped.

Coordinate pair means the two numerical pair bounded by a parenthesis but separated by comma. The first numerical term denotes the X coordinate and the 2nd numerical term indicate Y coordinate. The coordinate pair is used to locate a point on the cartesian plane.

A dairy farm ships crates of milk to food store. There are 48 quarts of milk for every 3 crates shipped.

for every 3 crates shipped there are 48 quarts of milk.

for 4 crates shipped there will be milk quarts = (48 × 4) / 3

                                                            = 64 quarts

for 6 crates shipped milk quarts = (6 × 48) / 3 = 96 quarts milk

for 9 crates shipped number of milk quarts = (9×48)/ 3 = 144

if ship crates are denoted by X axis and milk quarts is denoted by Y axis

then the coordinate pairs will be (3, 48), (4, 64), (6, 96) and (9, 144)

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The bricks having same cost per brick are 1500 bricks for $1,110, 35 bricks for $25.90 and 230 bricks for $170.20. The solution has been obtained using the unitary method.

What is a unitary method?

The value of a single unit is calculated in the unitary approach before the value of the necessary number of units is determined. In order to obtain value of a single unit from a given multiple, the unitary technique is used, to put it simply.

We know that Cost per brick = number of bricks / price of bricks

Therefore, using this, we get

1500/$1110 = $1.35

1300 / $845 = $1.54

230 / $170.20 = $1.35

100 / $75 = $1.33

35 / $25.90 = $1.35

Hence, the bricks having same cost per brick are 1500 bricks for $1,110, 35 bricks for $25.90 and 230 bricks for $170.20.

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Question: The prices for different types and amounts of building bricks are given. Select the options that have the same cost per brick.

1500 bricks for $1,110.00

1300 bricks for $845.00

230 bricks for $170.20

100 bricks for $75.00

35 bricks for $25.90

Answer:

Equivalent expression:

= 15

Step-by-step explanation:

Distributive proprty:

(10-7)5 = 10*5 + 10*-7

= 50 - 35

= 15

Evaluate:

(10-7)5 = 3*5

= 15

Using exponents law, the  required product is [tex]v^{83}[/tex]

What are Exponents?

A number's exponent demonstrates how many times we are multiplying a given number by itself. 3^4, for instance, indicates that we are multiplying 3 by four. 3*3*3*3 is its expanded form. The power of a number is another name for an exponent. A whole number, fraction, negative number, or decimal are all acceptable.  Exponent times power is how you raise a number with an exponent to a power.

[tex]v^6 \times v^{22} \times v^{55}[/tex]

Use the exponents law:

[tex]a^m \times a^n = a^{m+n}[/tex]

So, we get [tex]v^{6+22+55} = v^{83}[/tex]

Thus, the required product  is [tex]v^{83}[/tex]

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Answer: 2

Step-by-step explanation: The value x in f(x) is a value on the x-axis that we input into the function. F(x) is a value on the y-axis. F(2) means we are inputting the value of 2 on the x-axis and looking for the corresponding point on the y-axis. If we look at the graph at x=2, we can see that the graph is above when y=2. This means that (2,2) is a point that satisfies f(x).

The missing length x is equal to the square root of 10 units.

A triangle is a three sided polygon with 3 angles and three sides it is one of the most basic and fundamental safe in geometry and is used in many different areas of methane science triangle are also after use in architecture art in other areas of the design triangle come in many different form such as equatorial isosceles and scalene and can be classified by their angles side or both.

The formula for finding the area of a triangle is A = 1/2(base × height). In this case, the base and height are both x, so A = 1/2(x2). Plugging in the given area of 5, we have 1/2(x2) = 5 and solve for x to get x = √(10). So the missing length x is equal to the square root of 10 units.

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Answer:

The circumference of the wheel is 2 * pi * r = 2 * 3.14 * 225 mm = 1413.8 mm.

The number of arcs between each spoke is 25 - 1 = 24.

So, the arc length between each spoke is the circumference of the wheel divided by the number of arcs, which is 1413.8 mm / 24 = 58.91 mm.

Answer:

m is equal to [tex]34\sqrt{2}[/tex]

Step-by-step explanation:

We can use the cosine function to evaluate m.

Note that [tex]m[/tex] is the hypotenuse in this triangle.

[tex]cos(x)=\frac{A}{H}[/tex]

[tex]A[/tex] is the adjacent side

[tex]H[/tex] is the hypotenuse

Lets look at the 60 degree angle.

The side adjacent to it is [tex]17\sqrt{2}[/tex].

Therefore we can say that

[tex]cos(60)=\frac{17\sqrt{2} }{H}[/tex]

Lets solve for [tex]H[/tex].

[tex]cos(60)[/tex] is equal to [tex]\frac{1}{2}[/tex].

[tex]\frac{1}{2} =\frac{17\sqrt{2} }{H}[/tex]

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

[tex]1*H=17\sqrt{2}*2\\H=17\sqrt{2}*2\\H=34\sqrt{2}[/tex]

So on solving the provided question, we can say that by unitary method saving = 25 - 7.3333333336 = $17.6666666664

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

by unitary method,

12 pack of can, costs = $2

cost of 3 12 pack can - $2 *3 = $6

12 pack can = 12 days

1 can = $2/12 = $0.1666666667

8 can = $0.1666666667*8 = $1.3333333336

original cost of 1 can = $1.25

ordinal cost of 20 cans = $1.25*20 = 25

sale cost of 20 cans = $1.3333333336 +  $6 = 7.3333333336

saving = 25 - 7.3333333336 = $17.6666666664

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Answer:

Below

Step-by-step explanation:

96 heads out of 200 flips

96/200 = 48 %

Answer: 48%

Step-by-step explanation: 96 is 48% of 200, therefore the probability of landing on heads is 48%.

Answer:

A bar graph with x-axis labeled from 0 to 10, and y-axis labeled from 0 to 4, with 4x-2 marked with a solid line.

Answer:

2

Step-by-step explanation:

because 6 can't Divide 20 so,

18/6

rem:2

now,

Total money-Giving money

20-18

2$

A protractor is used to measure angles in degrees (°). With the aid of a protractor, one may measure and calculate angles in terms of degrees.

Through the use of a protractor, angles are measured in degrees (°). In order to calculate or draw angles in terms of degrees, a protractor is a measuring tool that is utilised. Using a protractor, for instance, we can observe that the black arrow in the image below crosses the 90° line at 100°. Thus, the angle has a 100° measurement.

Generally speaking, supplementary angles are those where the total of two angles is greater than 180 degrees. A supplement to another angle is stated to exist for each of the angles. By deducting an angle's complement from 180 degrees, we can calculate its value.

A 113 degree angle's complement is a 67 degree angle.

Therefore, the answer is 67 degree.

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Answer: 5-5x

Step-by-step explanation:

The exact length of the given curve is 62/3

We can calculate the above answer by following the steps given below,

We have been given the following values,

x = 1/3 √y (y - 3), 4 ≤ y ≤ 16

The curve is of the length, x = f(y) from y =a to y = b is given by:

x = 1/3 √y (y - 3)

x = 1/3 (- 3)

dx/dy = 1/3 [(3/2)- (3/2)]

= 1/3 [(3/2) - (3/2)]

= 1/2 [ - 1/]

= (y-1)/2√y = f'(y)

Now we will calculate the length of the curve

= [tex]\int\limits^a_b {\sqrt{1+f'(y)^{2} } } \, dy[/tex]

= [tex]\int\limits^a_b{\sqrt{1+ (\frac{y-1}{2\sqrt{y} } )^2} } \, dy[/tex]  (here a= 4, b=16)

= [tex]\int\limits^{16} _4 {\sqrt{1+ (\frac{y^2+2y-1}{4y} } )^} } \, dy[/tex]

= [tex]\int\limits^{16} _4 {\sqrt{\frac{4y+ y^2+ 2y-1}{4y} } } \, dy[/tex]

= [tex]\int\limits^{16}_4 {\frac{y+1}{2\sqrt{y} } } \, dy[/tex]

= [tex]\int\limits^{16}_4 {\frac{1}{2}\sqrt{y} } \, dy+ \int\limits^{16}_4 {\frac{1}{2\sqrt{y} } } \, dy[/tex]

= [1/3 (64-8)] +[4-2]

= (56/3)+2

= 62/3

Therefore the exact length of the curve that we get after solving the equation for curve is x = 1/3, 4 ≤ y ≤ 16, is 62/3.

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Answer:

Nine hundred thirty-eight one hundred twenty thousandths.

-Hope this helps!

Answer:

  A.  63°

Step-by-step explanation:

You want to know the base angle in the isosceles triangle in the given figure.

Angle ABC is the sum of its parts:

  ∠ABC = ∠ABD +∠DBC

The figure shows ∆DBC is equilateral, so ∠DBC = 60°. This lets us solve for the measure of angle ABD:

  114° = ∠ABD +60°

  54° = ∠ABD

∆ABD is isosceles, so the two base angles are congruent. The sum of angles in the triangle is 180°, so we have ...

  ∠ABD +∠BAD +∠BDA = 180°

  54° +2(∠BAD) = 180° . . . . . . . ∠BAD =∠BDA

  ∠BAD = 90° -27° . . . . . . divide by 2, subtract 27°

  ∠BAD = 63°

The statement and reasons are

The complete question is added as an attachment

With the given information and the image attached below, we can state that the two triangles are congruent by SAS,

Then go ahead to use the CPCTC to show that any of their corresponding parts are congruent as well.

Part of the proof is as follows:

Statement Reason

1. AB ≅ BC, AE ≅ FC 1. Given

2. AC ≅ AC 2. Reflexive property of congruence

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Note that Tiana's work is wrong.  Tiana made a mistake going from Step 2 to Step 3. Tiana should have subtracted 2 from 21 before adding. The order of operations says to add and subtract from left to right. The rule in operation here is known as PEMDAS. Note that when corrected and evaluated, the expression results in 27. (Option B)

The order of operations is a rule that specifies the right sequence of actions to be taken while evaluating a mathematical equation. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Using the order of operations (PEMDAS), the expression 21 - 2 + 60 ÷ 15*2  would be evaluated as follows:

Parentheses -  None

Exponents - None

Multiplication and Division (from left to right) - 60 + 15 = 4

Addition and Subtraction (from left to right) - 21 - 2 + 4*2 = 19 + 8 = 27

So the correct result is 27.

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Full Question:

See attached Image.

Depth is the result of form having the illusion of the third dimension.

Even while the human brain perceives many flat pictures, such as those in movies and photographs, as being two dimensional, nothing actually exists without all three dimensions (2D). This is due to the fact that everything physically existing is made of atoms, which are imperceptible to the human sight yet include all three spatial dimensions. Human eyes have the capacity to perceive "depth" or three dimensions. The three spatial dimensions of the world may be perceived by someone who possesses depth perception. Each human eye's visual brain first interprets the three spatial dimensions as 2D pictures. Contrarily, stereoscopic vision, which is unique to humans, alters the image seen by the two eyes.

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Answer: x = 5

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

7 − 8(x − 3) = x − 14

7 + (−8)(x) + (−8)(−3) = x + − 14 (Distribute)

7+ (−8x) + 24 = x + (−14)

(−8x) + (7+24) = x − 14 (Combine Like Terms)

−8x + 31 = x − 14

−8x + 31 = x − 14

Step 2: Subtract x from both sides.

−8x + 31 − x = x − 14 − x

−9x + 31 = −14

Step 3: Subtract 31 from both sides.

−9x + 31 − 31 = −14 − 31

−9x = −45

Step 4: Divide both sides by -9.

−9x/−9 = −45/−9

x = 5

If shelby is attending a school orchestra concert.   The two teacher are far apart by 35ft.

Using Pythagoreans theorem  formula to find the length

c² = √ a² -b²

Where:

c = Length of the hypotenuse

a = 45

b= 28

Let plug in the formula

c² = √45² - 28²

c² = √2025 -784

c² = √1241

c = 35ft

Therefore we can conclude that the two teacher are far apart by 35ft.

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The number of each type of tickets which August sold is equal to: B. 20 students and 15 adults.

In order to write a system of linear equations to describe this situation, we would assign variables to the number of adult tickets sold and number of student tickets sold, and then translate the word problem into an algebraic equation as follows:

Since Adults pay $7 a ticket while students pay $5 a ticket for a total cost of $205, an algebraic equation to model is given by;

7a + 5s = 205

For the sales of 35 tickets, we have:

a + s = 35      

Solving for a, we have the following:

7a + 5(35 - a) = 205

7a + 175 - 5a = 205

2a = 205 - 175

2a = 30

a = 30/2

a = 15 adult tickets.

For the number of student tickets, we have:

s = 35 - a

s = 35 - 15

s = 20 student tickets.

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Complete Question:

August is selling tickets for his school play.

-Adults pay $7 a ticket while students pay $5 a ticket.

-August sells 35 tickets and collects $205.

How many of each type of tickets did he sell?

A. 40 students and 32 adults

B. 20 students and 15 adults

C. 4 students and 5 adults

D. 15 students and 20 adults

Decay constant: the ratio of the number of radioactive atoms in a population to the rate at which they are vanishing due to radioactive decay. The rate of change is determined by the equation dN/dt = N, where is the decay constant, assuming N is the size of a population of radioactive atoms at a particular time t and dN is the amount by which the population declines in time dt.

When this equation is integrated, N = N0et is obtained, where N0 is the starting population size of radioactive atoms at time t = 0. This demonstrates that the rate of population decay is dependent on the decay constant and is exponential.

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The decay constant: the ratio of the number of radioactive atoms in a population to the rate at which they are vanishing due to radioactive decay.

The rate of change is determined by the equation dN/dt = N,

where is the decay constant, assuming N is the size of a population of radioactive atoms at a particular time t and dN is the amount by which the population declines in time dt.

When this equation is integrated, N = N0et is obtained, where N0 is the starting population size of radioactive atoms at time t = 0. This demonstrates that the rate of population decay is dependent on the decay constant and is exponential.

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let x = the number of 2-point baskets Anya made

y = the number of 3-point baskets Anya made

Equations:

x + y = 14

2x + 3y =

Multiply the 1st equation by 3 to get:

3x + 3y = 42

Subtract above equation by 2nd equation to get:

(3x-2x) + (3y - 3y) = 42 -30

x = 12

Anya made 12 2-point baskets.

3⁵ means, multiply 5 factors of 3.

No. of players and reporters in stadium = 275

No. of spectators and stadium workers in stadium = 42225

Seating Arrangement is a process of making a group of people sit as per a prefixed manner.

Given,

Stadium capacity = 42500

General capacity seating = 31750

Reserved Seating = 10475

Total spectator seating  = 31750 + 10475

                                        = 42225

No. of players, radio and newspaper reporters = 42500 - 42225

                                                                              = 275

There could be 275 players, news and radio reporters and 42225 spectators in addition to stadium workers, at the game.

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