The circumference of a circular garden is 78.5 feet. What is the radius of the garden? Use 3.14 for it and do not round your answer.
?

[tex]~~~~~~ \stackrel{\textit{\LARGE University Bank}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]A=4000\left(1+\frac{0.05}{4}\right)^{4\cdot 4}\implies A=4000(1.0125)^{16}\implies \boxed{A\approx 4879.56} \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~ \stackrel{\textit{\LARGE Rosemont Savings Bank}}{\textit{Compound Interest Earned Amount}}[/tex]

[tex]A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus two} \end{array}\dotfill &2\\ t=years\dotfill &4 \end{cases} \\\\\\ A=4000\left(1+\frac{0.055}{2}\right)^{2\cdot 4}\implies A=4000(1.0275)^8\implies \boxed{A\approx 4969.52}[/tex]

well, "better" meaning more amount per same 4000, clearly the latter will be better.

Answer:

Rosemont Savings Bank; interest is $969.52

Step-by-step explanation:

because i said so <3

Let's consider the information at hand:

         ⇒ has some special property about its side length

             ⇒ look at the diagram I attached

Using the same ratios of side length as seen in the diagram:

  ⇒ we get the equation:

        [tex]\frac{1}{\frac{\sqrt{2} }{2} } =\frac{x}{3\sqrt{2} } \\\frac{\sqrt{2} }{2}*x=3\sqrt{2} \\\frac{x}{2}=3\\ x=3*2\\x=6[/tex]

Thus x = 6.

Answer: x = 6

Hope that helps!

The pair of rational numbers with their sum are matched.

The numbers in the form of p/q is called the rational number.

1. -2/a²b +2/ab² = ( -2ab² +2a²b) / a³b³

                          = 2(a-b)/a²b²

2. 1/2ab -1/4a²b² =( 4a²b² -2ab) / 8a³b³

                            = 2ab -1 /4a²b²

3. 2/a²b³ -2/ab = (2ab -2a²b³) / a³b⁴

                         = 2( 1- ab²) /a²b³

4. 1/ab³ -1/a²b = a²b - ab³ / a³b⁴

                       = (a - b²) / a²b³

Thus, all the rational numbers are matched with their sum.

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The least expensive is the Stock Transportation charges $500 to cover the cost for the drivers plus $6 per student.

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically.

For example, if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4.

If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

Let the number of students the bus carries be x.

First Student charges $350 per bus. They will need 7 buses.

Therefore, the cost of the school hiring the bus is:

C = 7*350

C = 2450

The charge of per student

= 2450 / 260

= $ 9.4

Stock Transportation charges $500 to cover the cost for the drivers plus $6 per student.

C = 500 + 6*260

C = 500 + 1560

C = 2060

Switzer-Carty costs $7 for every student that they bus.

Therefore, the cost of the school hiring the bus is:

C = 7 * x

C = 7x

To bus 260 students, then, the cost will be:

C = 7 * 260

C = $1820

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Answer:

Solution and how to convert 8 / 21 into a percentage

0.38 times 100 = 38.1. That's all there is to it!

Step-by-step explanation:

hope this helps

Inequalities help us to compare two unequal expressions. (-6, 3) is not the solution to the system of inequalities.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

The graph of y ≥ −3x + 3 will be a solid line with the equation y=−3x + 3, this solid line signifies that the value on this line is also included in the solution. Since the symbol is '≥' therefore the area above the line will have the solutions.

The graph of y<(3/2)x -6 will be a dashed line with the equation y=(3/2)x - 6, this dashed line signifies that there is no solution on the line. since the inequality symbol is '<' therefore, the area under the dashed line will have all the solutions.

The area where both shaded areas meet is the area that will have all the possible solutions.

PartB:

y ≥ −3x + 3

3 ≥ -3(-6) + 3

3 ≥ 18 + 3

Since the above inequality is not satisfied, (-6, 3) is not the solution to the system of inequalities.

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The step of Talia that's incorrect.The step that is incorrect is: C. Step 3

The slope of a line or straight object is the ratio of how much amount of rise occurs in correspondence to the increment in the run.

Thus, we get:

Slope = rise/ run

Calculating the slope using two points on the line, (2, 5) and (1, 3), we have:

Slope (m) = (5 - 3)/(2 - 1)

Slope (m) = (2)/(1)

Slope (m) = 2

This shows that the ratio of the slope calculated by Talia was wrong. The step that is incorrect is: C. Step 3

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Answer: C. y - 1 = 1/2(x-5)

Step-by-step explanation:

point-slope form: y - y1 = m(x - x1)

m = 1/2

y1 = 1

x1 = 5

y - 1 = 1/2(x-5)

Answer:

[tex]\frac{1}{16}[/tex]

Step-by-step explanation:

[tex](\frac{1}{4}) ^{2}[/tex] can also be written as [tex](\frac{1}{4} )(\frac{1}{4} )[/tex]

So the answer is just [tex]\frac{1}{16}[/tex]

The cost of a tea cup and a cup of coffee in the shop is £0.90 and £1.50 respectively.

let

x + 2y = 3.90

3x + y = 4.20

Multiply (1) by 3 to eliminate x

3x + 6y = 11.70

3x + y = 4.20

5y = 7.50

y = 7.50/5

y = 1.50

Substitute y = 1.50 into (1)

x + 2y = 3.90

x + 2(1.50) = 3.90

x + 3 = 3.90

x = 3.90 - 3

x = 0.90

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[tex]\text{Given that,}\\\\~~~~~~~2x^4 +2y^4 +2z^4 = 144\\\\\implies 2(x^4+y^4 +z^4) = 144\\\\\implies x^4 +y^4 +z^4 = \dfrac{144}{2}\\\\\implies x^4 +y^4 +z^4 = 72\\\\\text{Mean} = \dfrac{x^4+y^4+z^4}{3}\\\\~~~~~~~~=\dfrac{72}{3}\\\\~~~~~~~~=24[/tex]

The cost of one pair of shoes is $8.

The cost of one shirt is $12.

2a + b = 32 equation 1

2a + 3b = 48 equation 2

Where:

Subtract  equation 1 from  equation 2

2b = 16

b = 16/2

b = $8

Substitute for b in equation 1

2a + 8 = 32

2a = 32 - 8

2a = 24

a = 24 / 2

a = $12

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Answer:

y=-2x+10

Step-by-step explanation:

i graphed it i graphed all of them

Answer:

y-2x-2

Step-by-step explanation:

The way I would do this is by first using the information given and making an equation in point-slope form, before bringing it to y=mx+b.

We know that the slope is -2, and we have a point, (2,-6). The formula for equations in point slope form is [tex]y-y_{1} =m(x-x_{1} )[/tex]. So, we can insert the given information into this formula to get [tex]y+6=-2(x-2)[/tex].

Next, we distribute the slope to the the parenthesis to get [tex]y+6=-2x+4[/tex]

Then, we subtract 6 from both sides to get [tex]y=-2x-2[/tex]

Since this equation is now in the form [tex]y=mx+b[/tex], the answer is [tex]y-2x-2[/tex]

Hope this helps! :)

Answer:

see explanation

Step-by-step explanation:

since the triangles are congruent, then corresponding angles are congruent.

∠ B = ∠ F

∠ FCE ≅ ∠ BDA

∠ EFC ≅ ∠ ABD

∠ FEC ≅ ∠ BAD

note that the order of letters in Δ ABD follows the same order as those in Δ BDA

The true statements about the diagram given are:

3. m∠JKL = 45°

4. m∠MKQ + m∠PKQ = m∠PKM

5. PK is an angle bisector

An angle bisector is a segment that divides a given angle into two parts that are congruent to each other.

The missing part of the question is in the image attached below.

In the image given, PK bisects the straight angle JKM since angles JKP and MKP both equal 90 degrees (right angle).

Therefore, m∠JKL = m∠PKL = 45°

m∠MKQ + m∠PKQ = m∠PKM based on the angle addition theorem.

Therefore, the true statements are:

3. m∠JKL = 45°

4. m∠MKQ + m∠PKQ = m∠PKM

5. PK is an angle bisector

(see image attached below)

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Answer:

Step-by-step explanation:

2500( 7 years )

????? (15 years )

15*2500=37 500

Answer:

10

Step-by-step explanation:

give brainliest please!

hope this helps :)

so these two angles add up to 180 degrees

7x -3 + 12x -7 = 180

7x+12x=180+7+3

19x=190

x=10

to check if this is true we can input 10 for x in each side.

7(10)-3 = 67

12(10)-7 = 113

113+67 = 180

The mistake he made is that he Yuri divided by n instead of n -1.

Standard deviation is used to determine how the values in a group differs from the mean of the values in the group.

In order to determine the standard deviation, take the following steps:

• Determine the mean of the observation: 14

Determine the difference between each value and the mean and then square the result: (12 - 14)² + (14 - 14)² + (9 - 14)² + (21 - 14)² = 78

Determine the mean of the sum of the squared differences and then find the square root of the mean: √78/(n - 1) = 5.1

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Answer:

Yuri divided by n instead of n -1.

Step-by-step explanation:

The answer above is correct.

Answer:

This is put together very weird, can you put the answers more clearly?

Step-by-step explanation:

?

The final coordinates after the transformations will be:

A" is (-1, 5),

B" is (0, 1),

C" is (-3, -1).

Reflect across the y-axis: For any point (x, y), the reflection across the y-axis is (-x, y).

Translation by vector <1, 3>: For any point (x, y), the new coordinates after translation are (x + 1, y + 3).

Let's apply these transformations step by step:

A (2, 2):

Reflect across y-axis: (-2, 2).

Translate by <1, 3>: (-2 + 1, 2 + 3) = (-1, 5).

So, A" is (-1, 5).

B (1, -2):

Reflect across y-axis: (-1, -2).

Translate by <1, 3>: (-1 + 1, -2 + 3) = (0, 1).

So, B" is (0, 1).

C (4, -4):

Reflect across y-axis: (-4, -4).

Translate by <1, 3>: (-4 + 1, -4 + 3) = (-3, -1).

So, C" is (-3, -1).

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Answer:

25

Step-by-step explanation:

50/2=25

Answer:

No solution.

Step-by-step explanation:

When two lines have the same slope but different y-intercepts, they are parallel.  Parallel lines never intersect, and therefore there is no solution.

The purpose of using slang is mostly for social purposes such as:

Slangs is often used in the Sharing and keeping  of a constantly altering vocabulary aids.

It is used to show group solidarity and it is often used to include or exclude members.

The common sports slangs are:

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Some examples of additions with integers with 5 terms or more are:

In mathematics, an integer is a whole number that is used to represent a value and is not a fraction.

Furthermore, we can make the addition of integers as they would increment based on the number they are being incremented with and this has been shown above.

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[tex]\\ \rm\Rrightarrow \dfrac{1-cos^2\theta}{cos^2\theta}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{sin^2\theta}{cos^2\theta}[/tex]

[tex]\\ \rm\Rrightarrow tan^2\theta[/tex]

Option C

Answer:

Trigonometric identities

[tex]\large \begin{aligned}\cos^2 \theta + \sin^2 \theta & = 1\\\implies \quad \quad \sin^2 \theta & = 1 - \cos^2 \theta\\\\\tan \theta=\dfrac{\sin \theta}{\cos \theta} \end{aligned}[/tex]

Therefore, using the identities, the given expression can be simplified as follows:

[tex]\large\begin{aligned}\implies \dfrac{1- \cos^2 \theta}{\cos^2 \theta} & = \dfrac{\sin^2 \theta}{\cos^2 \theta}\\\\& = \tan^2 \theta\end{aligned}[/tex]

Answer:

72 mins or 1 hour 12 mins

Step-by-step explanation:

1 miles = 9 mins

8 miles = 9×8 mins

8 miles = 72 mins = 1 hour 12 mins

Hope this helped and brainliest please

If the volume of the aluminum brick will be 2218.5 cubic cm. Then the approximate density of the aluminum will be 8.9 grams per cubic cm.

Density is defined as the mass per unit volume. It is an important parameter in order to understand the fluid and its properties. Its unit is kg/m³.

The mass and density relation is given as

Density = mass/volume

A brick of aluminum weighs 19,745 grams and has the following dimensions: length 29 cm, height 15 cm, and width 51 mm.

Then the approximate density of the aluminum will be

The volume of the aluminum brick will be

V = 29 x 15 x 5.1

V = 2218.5 cubic cm

Then the density will be

D = 19,745 / 2218.5

D = 8.900 gram per cubic cm

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Answer:

hope you can understand

Answer:

x = 7 or -6

Step-by-step explanation:

Let a number be x.

Its square = x²

x - x² = 42

-x² + x - 42 = 0

-(x² - x + 42) = 0

x² - x + 42 = 0

(x - 7)(x + 6) = 0

x - 7 = 0 or x + 6 = 0

x = 7 or x = -6