20 points for both questions

Answer:

Interest  = $261.42

Step-by-step explanation:

amount of interest earned is $

(Round to the nearest cent as needed.)

Amount = Principal + Interest

Amount - Principal = Interest

$ 5,261.42 -  $5000 = Interest  = $261.42

Answer:

its 23.5

Step-by-step explanation:

Answer:

d 26

Step-by-step explanation:

AC=24

AB=AC/2=12

AD²=AB²+BD²

AD²=5²+12²=25+144=169

AD=√169=13

AE=2*13=26

Answer:

[tex]k = 1[/tex]

[tex]P(x > 3y) = \frac{2}{3}[/tex]

Step-by-step explanation:

Given

[tex]f \left(x,y \right) = \left{ \begin{array} { l l } { k , } & { 0 \leq x} \leq 2,0 \leq y \leq 1,2 y \leq x } & { \text 0, { elsewhere. } } \end{array} \right.[/tex]

Solving (a):

Find k

To solve for k, we use the definition of joint probability function:

[tex]\int\limits^a_b \int\limits^a_b {f(x,y)} \, = 1[/tex]

Where

[tex]{ 0 \leq x} \leq 2,0 \leq y \leq 1,2 y \leq x }[/tex]

Substitute values for the interval of x and y respectively

So, we have:

[tex]\int\limits^2_{0} \int\limits^{x/2}_{0} {k\ dy\ dx} \, = 1[/tex]

Isolate k

[tex]k \int\limits^2_{0} \int\limits^{x/2}_{0} {dy\ dx} \, = 1[/tex]

Integrate y, leave x:

[tex]k \int\limits^2_{0} y {dx} \, [0,x/2]= 1[/tex]

Substitute 0 and x/2 for y

[tex]k \int\limits^2_{0} (x/2 - 0) {dx} \,= 1[/tex]

[tex]k \int\limits^2_{0} \frac{x}{2} {dx} \,= 1[/tex]

Integrate x

[tex]k * \frac{x^2}{2*2} [0,2]= 1[/tex]

[tex]k * \frac{x^2}{4} [0,2]= 1[/tex]

Substitute 0 and 2 for x

[tex]k *[ \frac{2^2}{4} - \frac{0^2}{4} ]= 1[/tex]

[tex]k *[ \frac{4}{4} - \frac{0}{4} ]= 1[/tex]

[tex]k *[ 1-0 ]= 1[/tex]

[tex]k *[ 1]= 1[/tex]

[tex]k = 1[/tex]

Solving (b): [tex]P(x > 3y)[/tex]

We have:

[tex]f(x,y) = k[/tex]

Where [tex]k = 1[/tex]

[tex]f(x,y) = 1[/tex]

To find [tex]P(x > 3y)[/tex], we use:

[tex]\int\limits^a_b \int\limits^a_b {f(x,y)}[/tex]

So, we have:

[tex]P(x > 3y) = \int\limits^2_0 \int\limits^{y/3}_0 {f(x,y)} dxdy[/tex]

[tex]P(x > 3y) = \int\limits^2_0 \int\limits^{y/3}_0 {1} dxdy[/tex]

[tex]P(x > 3y) = \int\limits^2_0 \int\limits^{y/3}_0 dxdy[/tex]

Integrate x leave y

[tex]P(x > 3y) = \int\limits^2_0 x [0,y/3]dy[/tex]

Substitute 0 and y/3 for x

[tex]P(x > 3y) = \int\limits^2_0 [y/3 - 0]dy[/tex]

[tex]P(x > 3y) = \int\limits^2_0 y/3\ dy[/tex]

Integrate

[tex]P(x > 3y) = \frac{y^2}{2*3} [0,2][/tex]

[tex]P(x > 3y) = \frac{y^2}{6} [0,2]\\[/tex]

Substitute 0 and 2 for y

[tex]P(x > 3y) = \frac{2^2}{6} -\frac{0^2}{6}[/tex]

[tex]P(x > 3y) = \frac{4}{6} -\frac{0}{6}[/tex]

[tex]P(x > 3y) = \frac{4}{6}[/tex]

[tex]P(x > 3y) = \frac{2}{3}[/tex]

Answer:

Step-by-step explanation:

There are an infinite number of solutions.

Answer:

acute

Step-by-step explanation:

Answer:

A. 66 square cm

Step-by-step explanation:

HOPE IT HELPSS! :D

Answer:

the correct answer is 197 in^2

Answer:

56,067

Step-by-step explanation:

there are 52 weeks in a year. and they work 40 hours a week.

[tex]26.96*40=1078\\1078*52=56,067[/tex]

Answer:

The answer is C.

Step-by-step explanation:

Answer:

[tex]Period = \pi[/tex]

Step-by-step explanation:

Given

[tex]y = -\frac{1}{3} * \sin(2x)[/tex]

Required

The period

A sine function is represented as:

[tex]y =A \sin(Bx + C) + D[/tex]

Where

[tex]Period = \frac{2\pi}{B}[/tex]

By comparing:

[tex]y =A \sin(Bx + C) + D[/tex] and [tex]y = -\frac{1}{3} * \sin(2x)[/tex]

[tex]B = 2[/tex]

So, we have:

[tex]Period = \frac{2\pi}{2}[/tex]

[tex]Period = \pi[/tex]

Hence, the period of the function is [tex]\pi[/tex]

Answer:

[tex]6 \frac{1}{5} [/tex]

Step-by-step explanation:

31/5

6/1/5

Answer:

The correct answer is A. The actual height of the Eiffel Tower is 301 meters.

Step-by-step explanation:

Given that a model of the Eiffel Tower uses a scale of 1 cm - 4 meters, if the model is 75 1/4 a centimeters tall, to determine what is the actual height of the Eiffel Tower the following calculation must be performed:

1 = 4

1/4 = 0.25

75.25 x 4 = X

301 = X

Therefore, the actual height of the Eiffel Tower is 301 meters.

Answer:

Hello Love! Answer: 8000

volume is just length x width x height

so 20 x 20 x 20 = 8000

Answer:

8,000 in³

Step-by-step explanation:

All you have to do is multiply all the sides so it would be

20 · 20 · 20 = 8,000 in³

Hope this helped.

If you are willing to give me a brainliest you can its your choice.

I just need one more to level up.

Well anyways

STAY SAFE!!!!!

Answer:

V= 160 ft

Step-by-step explanation:

First 10×8×6 then ÷ 3 = 160

Answer:

2000 milliliters

Step-by-step explanation:

2 liters = 2000 milliliters

Answer:

2000 milliliters

Step-by-step explanation:

1 liter=1000 milliliters

2x1000=2000

2000 milliliters

Answer:

Perimeter of rectangle EFGH = 24 unit

Step-by-step explanation:

Given:

E: (4,2)

F: (10,2)

G: (10,8)

H: (4,8)

Find:

Perimeter of rectangle EFGH

Computation:

Distance = √(x1 - x2)² + (y1 - y2)²

Distance between EF = √(4 - 10)² + (2 - 2)²

Distance between EF = √36

Distance between EF = 6units

Distance between FG = √(10 - 10)² + (2 - 8)²

Distance between FG = √36

Distance between FG = 6 units

Distance between GH = √(10 - 4)² + (8 - 8)²

Distance between GH = √36

Distance between GH = 6 units

Distance between HE = √(4 - 4)² + (8 - 2)²

Distance between HE = √36

Distance between HE = 6 units

Perimeter of rectangle EFGH = 6 + 6 + 6 + 6

Perimeter of rectangle EFGH = 24 unit

9514 1404 393

Answer:

  ∠A and ∠G

  ∠C and ∠E

Step-by-step explanation:

Vertical angles have the same vertex and are formed from opposite rays. In this figure, the pairs of vertical angles are ...

  {A, G}, {B, H}, {C, E}, {D, F}

Of these pairs, the ones listed in your answer choices are ...

  ∠A and ∠G

  ∠C and ∠E

Answer:

item total cost: 4.19

Answer:

13. rational, integer, white number, natural

14. irrational

Step-by-step explanation:

the third root of 125 is 5.

so, it is everything of the list except for irrational.

pi is a prime example of an irrational number. any calculation not eliminating the irrational number is also irrational.

Answer:

4/15

Step-by-step explanation:

Answer:

so, where the dotted line is that is called the height, so you would times it and find your answer.

Answer:

B) 20

The 10-15 x axis bar graph shows 20 cars on the y axis

Step-by-step explanation:

.........................

.......

Answer:

$728

Step-by-step explanation:

The formula for simple interest is I = PRT, where I = interest earned/paid, P = principal amount deposited or borrowed, R = rate of interest as a decimal, and T = time in years.

I = PRT

I = (4000)(0.052)(3.5)

I = 728

Simple Interest earned on $4000 in three and half year with 5.2% interest rate is $ 728.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

Here, Principal = $ 4000

          Time = [tex]3\frac{1}{2}[/tex] years = 7/2 years = 3.5 years

          Rate = 5.2 % =  0.052

Now, SI = P.R.T/100

         SI = 4000 X 3.5 X 5.2 / 100

         SI = $ 728

Thus, Simple Interest earned on $4000 in three and half year with 5.2% interest rate is $ 728.

Learn more about Simple Interest from:

https://brainly.com/question/22621039

#SPJ2

Answer:

[tex]1) 3x+45=90[/tex]

[tex]3x=90-45[/tex]

[tex]3x=45[/tex]

[tex]\frac{3x}{3} =\frac{45}{3}[/tex]

[tex]x=15[/tex]

1) The angles are complementary

[tex]--------[/tex]

[tex]2)x-20+x=90\\[/tex]

[tex]2x=90+20[/tex]

[tex]2x=110[/tex]

[tex]x=55[/tex]

2) The angles are complementary

[tex]--------[/tex]

[tex]3)2x+(3x+25)=180[/tex]

[tex]2x+3x+25=180[/tex]

[tex]2x+3x=180-25[/tex]

[tex]5x=155[/tex]

[tex]x=\frac{155}{5}[/tex]

[tex]x=31[/tex]

3) The angles are supplementary

[tex]----------[/tex]

hope it helps..

have a great day!!

Answer:

1.  LCD= 24

2. LCD= 18

Answer:

y = [tex]\frac{1}{2}x+8[/tex]

Step-by-step explanation:

From the table given in the picture,

Two points lying on the graph are (-4, 6) and (-2, 7)

Let the linear function is,

y = mx + b

Here, m = slope of the line

b = y-intercept

Since, slope of a line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,

Slope (m) = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Therefore, slope of the line passing through (-4, 6) and (-2, 7) will be,

m = [tex]\frac{7-6}{-2+4}[/tex]

m = [tex]\frac{1}{2}[/tex]

y-intercept is a point for which x = 0

From the given table,

For x = 0, y = 8

Therefore, y-intercept (b) = 8

Equation of the linear function will be,

y = [tex]\frac{1}{2}x+8[/tex]

Answer:

x= -2 y = ([tex]\frac{1}{49}[/tex])

x= 0 y = 1

x= 2 y = 49

Step-by-step explanation:

x= -2  -> (7)² = 49, negative power makes it inverse to a fraction

y = ([tex]\frac{1}{49}[/tex])

x= 0  -> anything to the power of 0 is always 1

y = 1

x= 2 -> 7² = 7 × 7 = 49

y = 49

Answer:

4/11...................

Answer: 4/11

Step-by-step explanation:

The total number of books is 35+20=55, which will be the denominator, because the question is asking what fraction of all the books are hardcover. The number of hardcover books, 20, will be the numerator, so we end up with the fraction 20/55. 20 and 55 are both divisible by 5 (this means that when divided by 5, both numbers have a whole number quotient). 20/5= 4 and 55/5=11

So, the answer is 4/11