A bank offers a 1% annual interest rate for a savings account. Aaron puts $3,100
into an account to save for college. How much will be in the account after a year?

[tex]\frac{3}{5-\sqrt{3} }[/tex]

= [tex]\frac{3(5 + \sqrt{3})}{5-\sqrt{3} (5 + \sqrt{3}) }[/tex]

= [tex]\frac{15 + 3\sqrt{3} }{5^{2} - \sqrt{3}^{2} }[/tex]

= [tex]\frac{15 + 3\sqrt{3} }{25-3 }[/tex]

= [tex]\frac{15 + 3\sqrt{3} }{22 }[/tex]

Answer:

4.98

Step-by-step explanation:

Answer:

4.98

Step-by-step explanation:

Answer:

[tex]\boxed{Area = 32.5 mm^2}[/tex]

Step-by-step explanation:

Area of Triangle = [tex]\frac{1}{2} (Base)(Height)[/tex]

Where base = 13 mm, Height = 5 mm

Area = 1/2 (13)(5)

=> Area = 1/2 (65)

=> Area = 32.5 mm^2

Answer:

c. 32.5 mm²

Step-by-step explanation:

The equation for the area of a triangle is a=1/2bh. In this equation you basically multiply the length of the base of the triangle times the height of the triangle and divide that by 2 to get the area. So, you would take 13, the base, and multiply it by 5, the height to get 65. Then, you would divide that by 2 to get 32.5 mm².

Answer:

The range is 8.

Step-by-step explanation:

7, 1, 9, 3, 5

The range = Largest no. - Smallest no.

9 - 1 = 8

Answer:

[tex]8[/tex]

Step-by-step explanation:

[tex]7 \: \: \: 1 \: \: \: 9 \: \: \: 3 \: \: \: 5[/tex]

Largest value in this set = 9

smallest value in this set = 1

Range = largest value - smallest value

= 9 - 1

= 8

Answer:

Option C.

Step-by-step explanation:

It is given that radius of circle X is 6 units and radius of circle Y is 2 units.

Here, circle Y is smaller and circle X is larger.

[tex]\text{Scale factor}=\dfrac{\text{Radius of circle X}}{\text{Radius of circle Y}}[/tex]

[tex]\text{Scale factor}=\dfrac{6}{2}[/tex]

[tex]\text{Scale factor}=3[/tex]

If we translate the circles so they share a common center point, and after that we dilate circle Y by a scale factor of 3, then we get circle which is equal to circle X.

We know that, after dilation the figure and its image are similar.

Hence, we can say that both circles are similar.

Therefore, the correct option is C.

Answer:

the answer is c

Step-by-step explanation:

Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 3.

edge 2020-2021

Answer:

[tex]\boxed{\mathrm{B}}[/tex]

Step-by-step explanation:

The domain is the set of all possible values for x (input).

There are no restrictions on x.

The domain is all real numbers.

The range is the set of possible values for y (output).

Let x = 0.

[tex]F(0)=5-(0)^2[/tex]

[tex]F(0)=5[/tex]

The maximum value of y is 5.

Let x = 50

[tex]F(50)=5-(50)^2[/tex]

[tex]F(50)=5-2500[/tex]

[tex]F(50)=-2495[/tex]

The minimun value of y is [tex]- \infty[/tex] from observation.

The values of x can be a negative number.

[tex]F(-5)=5-(-5)^2[/tex]

[tex]F(-5)=5-25[/tex]

[tex]F(-5)=-20[/tex]

The range of the function is less than or equal to 5 and greater than or equal to [tex]- \infty[/tex].

Answer:

The correct answer is:

L'(5,15), M'(12,-36), and N'(-21,-11)

Step-by-step explanation:

We are given the following points:

L(-5,15)

M(-12,-36) and

N(21,-11)

To find:

Reflection of the points across the y axis.

Solution:

To find the reflection of any point across y axis, we need to consider the y axis as the mirror and we need to find the location of the image in this manner.

Property of the image:

The image of point and actual point will be equidistant from the y axis.

If we find mirror image across y axis, there is change in only x coordinate value. There is no change in y axis value.

Let us take the first point:

L(-5,15)

x coordinate value -5 is on the left side of y axis.

The reflection will be 5 units on the right side of x axis

[tex]\therefore[/tex] L' (5, 15)

Let us take the second point:

M(-12,-36)

x coordinate value -12 is on the left side of y axis.

The reflection will be 12 units on the right side of x axis

[tex]\therefore[/tex] M'(12,-36)

Let us take the third point:

N(21,-11)

x coordinate value 21 is on the right side of y axis.

The reflection will be 21 units on the left side of x axis

[tex]\therefore[/tex] N'(-21,-11)

Please have a look at the attached figure for the points and their reflection.

Reflection triangles is shown as dotted line.

The correct answer is:

L'(5,15), M'(12,-36), and N'(-21,-11)

Answer:

45 degrees

Step-by-step explanation:

corresponding angles have are equal

Answer:

Step-by-step explanation:

x +2y = 8  ----- (I)

 x = 8 - 2y

x - 3y = 6 -------(II)

Substitute x = 8 - 2y in equation (II)

8 - 2y - 3y = 6    {add like terms}

8 - 5y = 6

Subtract 8 form both sides

 -5y = 6- 8

 -5y = -2

Divide both sides by -5

 -5y/-5 = -2/-5

y = 2/5

Substitute y = 2/5 in equation (I)

[tex]x+2*\frac{2}{5}=8\\\\x+\frac{4}{5}=8\\\\x=8- \frac{4}{5}\\\\x=\frac{8*5}{1*5}-\frac{4}{5}\\\\x=\frac{40}{5}-\frac{4}{5}\\\\x=\frac{36}{5}[/tex]

x = 36/5

Answer:

Total mass =  105.8 gram (Approx)

Step-by-step explanation:

Given:

Atoms of Cl = 6.3 × 10²³

Find:

grams of AuCl₃

Computation:

Molecules of AuCl₃ = 6.3 × 10²³ / 3 = 2.1 × 10²³

1 mol of AuCl₃ = 6.022 × 10²³ molecules

Number of mol = 2.1 × 10²³ /  6.022 × 10²³

Number of mol  = 0.348 mol

So,

Molar mass of AuCl₃ = 303.33 g/mol

Total mass = 0.348 mol × 303.33 g/mol

Total mass =  105.8 gram (Approx)

Answer:

9 ft

Step-by-step explanation:

Here, we have a square wall with a value of 84 square feet for the area and we are told to find the approximate height of the walls

Mathematically, the area of a square is L^2

The height of the walls is just as one of its side

Thus;

L^2 = 84

L = √(84)

L = 9.165

which to the nearest foot is 9 ft

Answer:

-1.8,3

Step-by-step explanation:

This type of problem often results in two answers for X, and to get it, I often like to rearrange the formula to look like this: 5x^2-6x-27. There are various ways to answer this question, but since this is a quadratic equation, I commend using the quadratic formula! It may look scary, but it is actually really simple. I will attach a picture of this formula for reference when you need it.

looking at our modified formula, a= 5, b=-6, and c= -27. With these values in mind, you can go ahead and plug them in the formula. So it will look like (6±√(-6)²-4(5)(-27) )÷2(5).

Let’s break this down a bit, what this formula is saying is that you’ll have 2 operations to do now, the first one will look like this:

[tex](6+\sqrt{576})/10[/tex], this will result in 3, which is one of your values for x

the second operation will be exactly the same, but instead of adding 6 to the square root of 576 (pssst, it is 24 btw), you will be subtracting. This second operation once done will result in -1.8, which is rounded to the nearest tenth!

Answer:

d: 2.6179, e: 4.1887, f: 5.2359 all in rad

Step-by-step explanation:

(d): 150°degrees

150° × π / 180°

= 0.83333333333π rad

= 2.6179 rad

(e):240°degrees

240° × π / 180°

= 1.3333333333π rad

= 4.1887 rad

(f): 300°degrees

300° × π / 180°

= 1.6666666667π rad

= 5.2359 rad

If all my stuff is correct please give me an 5/5 and a thanks. :)

Answer:

Total no. of cases = 6954

No. of cases decided = 82

Percentage decided = (82/6954)x100 = 1.17%

Answer:

1.18%

Step-by-step explanation:

A percentage can be found by dividing the part by the whole. then multiplying by 100.

(part/whole) * 100

In this problem, the part is the cases decided by the Supreme Court. The whole is the total number of cases filed.

(cases decided / cases filed) *100

There were 82 cases decided by the Supreme Court, out of a total of 6,954 cases filed.

(82/6954) *100

First, solve the parentheses and divide.

0.0117917745* 100

Multiply

1.17917745 %

Round to the nearest hundredth. The 9 in the thousandth place tells us to round the 7 up to an 8 in the hundredth place.

1.18 %

About 1.18% of the cases filed were decided by the Supreme Court.

Answer:

Part A

The p-value indicates that the largest probability of having the two remedies having a difference as observed or larger than as observed  being equal to 0.3822

Part B:

Given that the p-value of 0.3822 is larger than the significance level α of 0.05, we fail to reject the null hypothesis and we conclude that there is enough statistical evidence to suggest that the salvage rates are the same for Remedy A and B

Step-by-step explanation:

The p-value

The test statistic is given as follows;

[tex]Z=\dfrac{\hat{p}_1-\hat{p}_2}{\sqrt{\hat{p}(1-\hat{p})\left (\dfrac{1}{n_{1}}+\dfrac{1}{n_{2}} \right )}}[/tex]

[tex]\hat p_1[/tex] = 35/220 = 7/44

[tex]\hat p_2[/tex] = 39/230

[tex]\hat p[/tex] = 74/220 = 37/110

We get our test statistic z = -0.2996381

Part A

The p-value indicates that the largest probability of having the two remedies having a difference as observed or larger than as observed  being equal to 0.3822

Part B:

Given that the p-value of 0.3822 is larger than the significance level α of 0.05, we fail to reject the null hypothesis and we conclude that there is enough statistical evidence to suggest that the salvage rates are the same for Remedy A and B.

Answer:

Step-by-step explanation:

If the kilowatt-hours stay proportional to the total bill, then you are using more electricity. If the bill goes up a lot more than the kilowatt-hours, then you are on some sort of "rate plan" that punishes peak usage

Answer:

1626.02

Step-by-step explanation:

1 gram is 0.001 kilograms. The bag weighs 2 kilograms and each popcorn is 1.23 grams. 2 kilograms weigh 2000 grams.

Answer:  1) C. Reflexive Property of Congruence

               2) A. MD ≅ SG

               3) C. 5.3

               4) D. LK || MJ & JK ≡ LM

Step-by-step explanation:

1) An angle or side is congruent to itself by the Reflexive Property

2) TM ≡ LG       Sides are congruent (given)

   ∠M ≡ ∠G       Angles are congruent (given)

   MD ≡ SG       Sides are congruent                  

ΔTMD ≡ ΔLGS  Side-Angle-Side (SAS) Theorem

Note: The angle must connect the two sides

3) Use similarity proportion

[tex]\dfrac{6}{x}=\dfrac{9}{8}\\\\\\48=9x\\\\\\\dfrac{48}{9}=x\\\\\\5.3=x[/tex]

4) In order to prove a polygon is a parallelogram, you must show

Answer:

7m(3m^6 - m^4 + 7)

Step-by-step explanation:

This is a factorization question

All we want to do here is to factor out 7m from each term of the polynomial

This becomes;

21m^7 -7m^5 + 49m = 7m (3m^6 - m^4 + 7)

Answer:

30° and 60°

Step-by-step explanation:

Step 1: Write out equation

x + (x + 30) = 90

Step 2: Solve for x

2x + 30 = 90

2x = 60

x = 30

Step 3: Find other angle

90 - 30 = 60

Answer:

30 and 60

Step-by-step explanation:

Let x be one  angle

x+30 is the other angle

Complementary angles add to 90

x+ x+30 = 90

2x+30 = 90

Subtract 30 from each side

2x=90-30

2x= 60

Divide by 2

2x/2 = 60/2

x = 30

The angles are 30 and 30+30 = 60

Answer:

y ≤[tex]\frac{7}{4}x - 5[/tex]

Step-by-step explanation:

We are to put the linear inequality;

7x - 4y ≥ 20

in slope intercept form.

We can rearrange the inequality as;

-4y ≥ - 7x + 20

Dividing throughout by -4 we get;

y ≤ [tex]\frac{7}{4} x[/tex] - 5

Note that the inequality sign '≥' changes to '≤' since we divided all through with a negative number.

Answer:

A slope is a surface of which one end or side is at a higher level than another; a rising or falling surface

Step-by-step explanation:

Answer:

y=2x-3, x=23.5

Step-by-step explanation:

This is what i got.

The rectangular form of equation is y= x² /9 - 10x/9 - 34/9.

An equation made up of variables like x and y that can be plotted on a standard Cartesian plane is referred to as a rectangular equation or an equation in rectangular form.

Given:

x=3t+5.....(1)

y=t²-1.....(2)

From equation (1), we get

t= 1/3(x-5)

Now, put t in equation (2)

y= 1/9 (x- 5)² - 1

y = 1/9 x² - 25/9 -10x/ 9 - 1

y= x² /9 - 10x/9 - 34/9

Learn more about rectangular form here:

https://brainly.com/question/10345510

#SPJ2

Answer:

Total cans = 17 (4)

Step-by-step explanation:

If Max has 8 boxes and gives half of the boxes to his teacher, then the teacher has 4 boxes.

Now, the teacher has 4 boxes but each box has 17 cans inside. To represent how many cans the teacher has, we will need to multiply the number of boxes by the number of cans each box has,

Then, the Total number of cans = [tex]17(4)[/tex] = 68.

Thus, the expression that represents the total number of cans in all the boxes that the teacher has would be: Total cans = 17 (4)

Answer:

Step-by-step explanation:

V=lwh=4*5*10=200 cubic inch or in^3

Image is missing, so i have attached it

Answer:

21.07 mm²

Step-by-step explanation:

We will use the Formulas:

Area of semicircle = πr²/2

Area_rectangle = Length x width = Lw

We are given:

Length of rectangle = 14 mm

From the attached image, the diameter of the semicircle is equal to the length of the rectangle.

Thus;

diameter of semicircle = length of rectangle

Therefore,

diameter of semicircle = 14 mm

Also, from the attached image, the radius of the semicircle is equal to the width of the rectangle.

Thus;

diameter of semicircle/2 = radius of semicircle

Hence;

radius of semicircle = 14/2 = 7mm = width of rectangle

Thus;

Area of rectangle = L*w = 14 × 7 = 98 mm²

Area of semicircle = πr²/2 = π×7²/2 = 76.93 mm²

To get the area of the shaded region, we will subtract area of the semi-circle from the area of the rectangle.

Area of shaded region = Area_rectangle - Area_semicircle = 98 - 76.93 = 21.07 mm²

Answer:

16

Step-by-step explanation:

61+3=64

16*4=64

64=64

Answer:

b

Step-by-step explanation:

Answer:

its not 14 feet

Step-by-step explanation: