You invest $2000 in an account that is compounded annually at an interest rate of 5% . You never withdraw money from the account. How much money will be in the account after 4 years?

The answer in the first quadrant is

(2,3)

Answer:

Final answer is [tex]P(B/A)=0.5[/tex]

Step-by-step explanation:

Given that P(A) =0.20

P(B) = 0.25

P(A and B) = 0.10.

Now we need to find about what is the value of P(B/A).

P(A and B) = P(A) * P(B/A)

Plug the given values into above formula:

[tex]0.10=0.20\cdot P(B/A)[/tex]

[tex]\frac{0.10}{0.20}=P(B/A)[/tex]

[tex]0.5=P(B/A)[/tex]

[tex]P(B/A)=0.5[/tex]

Hence final answer is [tex]P(B/A)=0.5[/tex]

Answer:

c is the answer

Step-by-step explanation:

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

Explanation:

"given that the first die rolled is a 2" means we know 100% that the first die shows a 2. Either we can see the die or a friend is telling us the status. Since we know the first die is a 2, this means we can effectively ignore it. Everything will hinge on the second die. If the second die shows an odd number, something like 1, then 2+1 = 3 is the result which is also odd.

The general rule is odd+even = odd and even+even = even.

Therefore, the two dice must together be even for the sum to be even.

Of the six possible ways to roll a die {1,2,3,4,5,6}, there are 3 even values {2,4,6} so the chances of rolling an even number on the second die is 3/6 = 1/2. Again we dont need to consider the first die at all since everything practically hinges on this second die.

Answer:

50%

Step-by-step explanation:

For the total to be even, when the first number is even, the second number also has to be even.

2, 4, and 6 are even, out of 6 numbers. That is 3 numbers out of 6, which gives us that the probability is 1 out of 2, or 50%.

Answer:

Both

Step-by-step explanation:

The total number of options that will be are 6. The representation made by both Elroy and Rose is correct.

The total number of options available is the product of a total number of options available in different sectors.

Given that number of colors is 3 while the number of formats is two. Therefore, the total number of options that are available will be 6 which is the product of the two.

As we can see that both have pointed out each of the six options, therefore, the representation made by both Elroy and Rose is correct.

Learn more about Number of options:

https://brainly.com/question/11185799

Answer:

[tex]\$14.18[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=10\ years\\ P=\$10\\ r=0.035\\n=12[/tex]  

substitute in the formula above  

[tex]A=P(1+\frac{0.035}{12})^{12*10}=\$14.18[/tex]  

Answer:

The measure of angle theta is [tex]\theta=2.25\ radians[/tex]

Step-by-step explanation:

step 1

Find the circumference of the circle

The circumference is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=20\ ft[/tex]

substitute

[tex]C=2\pi (20)[/tex]

[tex]C=40\pi\ ft[/tex]

step 2

Find the measure of angle theta

we know that

The circumference of a circle subtends a central angle of [tex]2\pi\ radians[/tex]

so

using proportion

Find out the measure of the central angle by a length of arc equal to 45 ft

[tex]\frac{40\pi}{2\pi}=\frac{45}{\theta}\\ \\\theta=2*45/40\\ \\ \theta=2.25\ radians[/tex]

Answer: 2.25 radians

Step-by-step explanation:

Answer:

225

Step-by-step explanation:

15(1+15/2) *2= 240-15=225

The sum of the arithmetic series given by the terms (2n - 1) for n=1 to 5 is 25, computed using the formula for the sum of an arithmetic series.

The series in question is an arithmetic series with a difference of 2 and the sum of the first n terms can be represented by the formula for the sum of an arithmetic series, Sn = n/2[2a + (n-1)d], where 'a' is the first term and 'd' is the common difference between the terms.

In the provided series, each term is of the form (2n - 1) starting with n=1 and going till n=5. So the first term, a = 2(1) - 1 = 1, and the common difference, d = 2 since each subsequent term increases by 2.

We can compute this sum directly by evaluating S5, using the formula for an arithmetic series: S5 = 5/2[2(1) + (5-1)(2)] = 5/2[2 + 8] = 5/2[10] = 25. So, the sum of the series is 25.

Add 8 to both sides of the equation.

You need to get x by itself. The only way to do that here is to do the opposite of subtracting 8, which is adding 8.

Also, when you do something to one side of the equation, you have to also do it to the other side to keep the equation equal.

Answer: Add 8 to both sides of the equation

Step-by-step explanation:

d - 8 = 9

in this equation you need to solve for d. To do that you have to get d by itself.

By adding 8 to both sides of the equation you cancel out the -8 and add 8 to 9 which solves for d.

Answer:

See below.

Step-by-step explanation:

This inequality is < 0 for all real values of x. We see this by solving  -x^2 - 6 = 0 for x:

-x^2  - 6 = 0

-x^2 = 6

x^2 = -6   for which there are no real solutions of x. So the graph does not pass through the x axis.

At x = 0. f(x) < -6 so that is the one critical value - all values of f(x) are below this value.

Answer:

0 critical points

Step-by-step explanation:

Just did it and got it right

Answer:

Option B

Part a) The focus is [tex](1/28,0)[/tex]

Part b) The directrix is [tex]x=-1/28[/tex]

Part c) The equation is  [tex]y^{2}= (1/7)x[/tex]

Step-by-step explanation:

step 1

Find the equation of the parabola

we know that

The parabola in the graph has a horizontal axis.

The standard form of the equation of the horizontal parabola is

[tex](y - k)^{2}= 4p(x - h)[/tex]

where

p≠ 0

The vertex of this parabola is at (h, k).

The focus is at (h + p, k).

The directrix is the line x= h- p.

The axis is the line y = k.

If p > 0, the parabola opens to the right, and if p < 0, the parabola opens to the left

In this problem we have that the vertex is the origin

so

(h,k)=(0,0)

substitute in the equation

[tex](y - 0)^{2}= 4p(x - 0)[/tex]

[tex]y^{2}= 4p(x)[/tex]

The points (7,1) and (7,-1) lies on the parabola-----> see the graph

substitute the value of x and the value of y in the equation and solve for p

[tex](1)^{2}= 4p(7)[/tex]

[tex]1= 28p[/tex]

[tex]p=1/28[/tex]

The equation of the horizontal parabola is

[tex]y^{2}= 4(1/28)(x)[/tex]

[tex]y^{2}= (1/7)x[/tex]

step 2

Find the focus

we know that

The focus is at (h + p, k)

Remember that

[tex](h,k)=(0,0)[/tex]

[tex]p=1/28[/tex]

substitute

[tex](0+1/28,0)[/tex]

therefore

The focus is at

[tex]F (1/28,0)[/tex]

step 3

Find the directrix

The directrix is the line x = h- p

Remember that

[tex](h,k)=(0,0)[/tex]

[tex]p=1/28[/tex]

substitute

[tex]x=0-1/28[/tex]

[tex]x=-1/28[/tex]

Answer:

B

Step-by-step explanation:

Confirmed on E D G 2021

Answer:3/4

Step-by-step explanation: Since he read 1/4 on Monday and 2/4 on Tuesday that would add up to 3/4

Answer:

g, f, h

Step-by-step explanation:

By definition, the average rate of change of a function f over an interval [a,b] is given by

[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

So, in your case, we want to compute the quantity

[tex]\dfrac{f(3)-f(0)}{3}[/tex]

for all the three function

Average rate of change of f:

We will simply use the table to check the values for f(3) and f(0):

[tex]\dfrac{f(3)-f(0)}{3}=\dfrac{10-1}{3} = 3[/tex]

Average rate of change of g:

We will use the graph to to check the values for g(3) and g(0):

[tex]\dfrac{g(3)-g(0)}{3}=\dfrac{8-1}{3} = \dfrac{7}{3}[/tex]

Average rate of change of h:

We can plug the values in the equation to get h(3) and h(0):

[tex]h(3)=3^2+3-6=9+3-6=6,\quad h(0)=0^2+0-6=-6[/tex]

And so the average rate of change is

[tex]\dfrac{h(3)-h(0)}{3}=\dfrac{6-(-6)}{3} = 4[/tex]

Answer:

g,f,h

I just took the test and was right

Step-by-step explanation:

Remember to be mindful of signs when adding and subtracting. 2c^2+5c+4

Answer:

A

Step-by-step explanation:

The formula for the Perimeter of a rectangle is P = 2W + 2L.

Let's equate this to 60 units and substitute 11 for W and 24 units for L:

2(11 units) + 2(24 units) = 22 units + 48 units = 70 units.  NO (Answer A)

Answer:

domain:   (-∞, ∞) ; range: [-5, 0]

Step-by-step explanation:

Let's begin with the basics:

The domain of cos x is (-∞, ∞); the range is [-1, 1].

The domain of cos²x is still (-∞, ∞).

Likewise, the domain of -5 cos²x is(-∞, ∞).

The range of cos²x differs: it is [0, 1] because squaring a negative number results in a positive output.

Multiplying cos²x by 5 expands the range to [0, 5].

Finally, multiplying 5 cos²x by -1 changes the range to [-5, 0].

Answer:

C

Step-by-step explanation:

Cuz edge

35%

First, we need to find the amount of money that is being spent. Add all of the amounts together.

$350 + $100 + $120 + $80

$450 + $120 + 80

$570 + $80

$650

So, Ian spends $650 of his budget each month. How much does that leave for savings? Just subtract $650 from $1,000 to find that he saves $350 each month.

Now, you just need to find the percentage. The percentage is the same as the numerator in a fraction with a denominator of 100, so x% = x/100. For example, 1% = 1/100. $350 / $1000 = x / 100

How do we turn 1,000 into 100? Divide it by 10. And if you do something to the denominator of a fraction, you have to do it to the numerator as well. So, divide $350 by 10 and divide $1000 by 10, leaving you with $35 / $100 = x / 100

Multiply both sides by 100 to get x by itself. This leaves you with 35 = x, so 35% of Ian’s budget with go towards saving.

Answer:

A

Step-by-step explanation:

y bar basically means the average of the y-values.

To get the average, we add up all the y-values in the table and divide by the total number of values (here we have 5 values). Hence,

y bar = [tex]\frac{5+7+10+15+18}{5}=11[/tex]

correct answer is A

Answer:

D) π/2 and 3π/2

Step-by-step explanation:

The equation can be factored:

(1 -sin(x))(1 +sin(x)) = 0

The factors will be zero when ...

sin(x) = 1 ⇒ x = π/2

sin(x) = -1 ⇒ x = 3π/2

Answer:

T= 2.35 seconds

Step-by-step explanation:

⇒The question is on the time of flight.

⇒Time of flight is the time taken for a projected object to reach the ground.It depends on the projectile angle and the initial velocity of the projectile

Given;

Initial velocity of ball= 110ft./sec.

The projectile angle= 20°

Acceleration due to gravity, g=32 ft./s²

⇒Formulae for time of fright T= (2×u×sin Ф)/g

Where T=time of fright, u=initial velocity of projectile, Ф=projectile angle and g=acceleration due o gravity.

Substituting values

T= (2×u×sin Ф)/g

T=( 2×110×sin 20°) / 32

T= 2.35 seconds

Answer:

Option B - Time taken for the ball to hit the ground is 2.47 seconds.

Step-by-step explanation:

Given :  A ball is thrown with a slingshot at a velocity of 110 ft./sec. at an angle 20 degrees above the ground from a height of 4.5 ft.

To find : How long does it take for the ball to hit the ground?

Solution :

According to question,

The equation that models the height of the ball in feet as a function of time is

[tex]h(t) = h_0 + v_0t -16t^2[/tex]

Where, [tex]h_0[/tex] is the initial height,

[tex]v_0[/tex] is the initial velocity and

t is the time in seconds.

We have given,

Initial height, [tex]h_0=4.5 ft.[/tex]

A ball is thrown with a slingshot at a velocity of 110 ft./sec. at an angle 20 degrees.

The initial speed, [tex]v_0=110\times \sin(206\circ)[/tex]

[tex]v_0=37.62ft/s[/tex]

We have to find the time for the ball to hit the ground i.e. h(t)=0

Substitute all the values in the formula,

[tex]0 =4.5+ 37.62t -16t^2[/tex]

Applying quadratic formula to solve the equation,

The solution of quadratic general equation [tex]ax^2+bc+c=0[/tex] is

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Where, a=-16 , b=37.62 , c=4.5

Substituting in the formula,

[tex]t=\frac{-37.62\±\sqrt{(37.62)^2 -4(-16)(4.5)}}{2(-16)}[/tex]

[tex]t=\frac{-37.62\±\sqrt{1703.2644}}{-32}[/tex]

[tex]t=\frac{-37.62\±41.270}{-32}[/tex]

[tex]t=\frac{-37.62+41.270}{-32},\frac{-37.62-41.270}{-32}[/tex]

[tex]t=-0.114,2.47[/tex]

neglecting the negative value

t=2.47 seconds

Therefore,Option B is correct.

Time taken for the ball to hit the ground is 2.47 seconds.

For this case we have to, by definition:

[tex]cos (F) = \frac {h} {26.4}[/tex]

This means that, the cosine of the angle F, will be equal to the leg adjacent to the angle on the hypotenuse of the triangle.

So, by clearing h we have:

[tex]h = 26.4 * cos (35)\\h = 26.4 * 0.81915204\\h = 21.6256[/tex]

Rounding out the value of h we have:

[tex]h = 21.6[/tex]

Answer:

Option B

Answer:

The correct answer is option b.   21.6

Step-by-step explanation:

Points to remember:-

Trigonometric ratio

Cos θ = adjacent side/Hypotenuse

From the figure we can see a right triangle triangle FGH.

To find the value of h

It is given that, g=26.4 and F= 35°

Cos F =  adjacent side/Hypotenuse

Cos 35 =  adjacent side/Hypotenuse

     = FG/FH = h/g

h = g * Cos F = 26.4 * Cos 54 = 26.4 * 0.8191 = 21.62 ≈ 21.6  

Therefore the correct answer is option b.  21.6

Answer:

46¢

Step-by-step explanation:

Note that there are 12 cola's in all. The total cost is $5.46. Divide the total cost with the amount of cola's there is:

5.46/12 = 0.455

Round: 0.455 rounded to the nearest hundredths is $0.46 (You round to the nearest hundredths, for the smallest amount for US currency is a penny, which is 1/100 of a dollar bill).

Each cola costs $0.46

~

Answer:

Length = 13

x = 80

Step-by-step explanation:

Question One

Let the width = x

Let the length = x + 5

Area = 104

Equation

Area = L * W

Area = (x+5)*x

Solution

x ( x + 5) = 104                  Remove the brackets

x^2 + 5x = 104                  Subtract 104 from both sides.

x^2 + 5x - 104 = 104 - 104

x^2 + 5x - 104 =  0            Factor the equation    

(x + 13)(x - 8) = 0

Only x - 8 = 0 works

x = 8

The width = 8

The Length = 8 + 5 = 13

Question Two

Draw AP

<BAP = 20o                     The triangle (APB) is isosceles: 2 sides are radii

<BPA = 180 - 20 - 20      The three angles of a triangle = 180

<BPA = 140                      Combine

Similarly <CAP = 140       Go through exactly the same steps.

<BPA + <CAP + X = 360  The total of the 3 angles in the center = 360

140 + 140 + X = 360         Combine

280 + X = 360                 Subtract 280 from both sides.

x = 80

[tex]\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope~of~AB}{\cfrac{4}{3}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{3}{4}}\qquad \stackrel{negative~reciprocal}{-\cfrac{3}{4}}}\impliedby \textit{slope of QA} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf A(\stackrel{x_1}{6}~,~\stackrel{y_1}{-5})\qquad Q(\stackrel{x_2}{2}~,~\stackrel{y_2}{y}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{y-(-5)}{2-6}=\stackrel{\textit{QA's slope}}{-\cfrac{3}{4}}\implies \cfrac{y+5}{-4}=\cfrac{-3}{4} \\\\\\ 4y+20=12\implies 4y=-8\implies y=\cfrac{-8}{4}\implies \boxed{y=-2}[/tex]

Answer:

The median price of a new home

Step-by-step explanation:

Answer:

72

Step-by-step explanation:

The two acute angles add up to 90 degrees. That's because the given triangle is a right triangle.

So x + 4x + 90 = 180           All triangles = 180°. Combine left side terms.

5x + 90 = 180                      Subtract 90°

5x + 90 - 90 = 180 - 90      Combine

5x = 90                                Divide by 5

5x/5 = 90/5                         Combine

x = 18

The larger angle is 4x so

The larger angle = 4*18 = 72

Answer:

Kylie could have a $5 bill and seven quarters while Ethan could have two $1 bills and forty pennies.

Step-by-step explanation:

Since Kylie has seven quarters, that is seven multiplied by the value of the quarter, a quarter is 25 cents. So 7 x 25 = 125 OR $1 and 25 cents. Leaving Kylie with a total of $7 and 25 cents with the addition of the $5 bill.

Ethan has two $1 bills and forty pennies, forty multiplied by the value of the penny, a penny is 1 cent. So 40 x 1 = 40 OR 40 cents. Leaving Ethan with $2 and 40 cents with the addition of the two $1 bills from earlier.

Ethan has more bills and coins than Kylie and yet still has less money than Kylie.

Answer:

B

Step-by-step explanation:

First

Get totals for food items:

Pizza $14.95 ×2=$29.90

Salad=$4.35

Drinks $2.49 ×4=$9.76

Total Bill

$29.90

$ 4.35

+$ 9.76

$44.21 Food Bill

Second Step

Find Tip Amount Before Tax

Total Bill $44.21 × .15=$6.63 Tip

Third Step

Find Tax on Total Food Bill

$44.21 × .07675=$3.39

Fourth Step

Find amount left from paying bill with tax.

Total Bill including tax:

$44.21 (bill) +$3.39 tax=$47.60

Cash $ 50.00

Total Bill - $47.60

$ 2.40 Change left over

Fifth Step

Find amount needed to give $6.63 tip from above.

We have $2.40 we need $6.63

Subtract $6.33 -$2.40=$4.23 more money needed for tip

The correct option is B. $ 4.23. Mr. Wright needs an additional $4.23 to leave a 15% tip.

First, we need to calculate the total cost of the meal before tax and tip. The Wright family ordered two pizzas at $14.95 each, a salad at $4.35, and four drinks at $2.49 each. So, the cost of the pizzas is [tex]2 \times $14.95[/tex], the salad is $4.35, and the drinks are 4 \times $2.49.

Cost of pizzas: [tex]2 \times $14.95 = $29.90[/tex]

Cost of salad: $4.35

Cost of drinks: [tex]4 \times $2.49 = $9.96[/tex]

Total cost before tax: [tex]\$29.90 +\$\4.35 + \$\9.96 = \$\44.[/tex]21

Next, we calculate the sales tax, which is 7.675% of the total cost before tax.

Sales tax: [tex]\$\44.21 \times 7.675% = \$\44.21 \times 0.07675 = \$\3.39[/tex]

Now, we add the sales tax to the total cost before tax to get the total cost including tax.

Total cost with tax: [tex]\$\44.21 + \$\3.39 = \$\47.60[/tex]

Mr. Wright wants to leave a 15% tip on the total bill before tax. So, we calculate 15% of the total cost before tax.

Tip: [tex]\$\44.21 \times 15% = \$\44.21 \times \$\0.15 \times \$\ 6.63[/tex]

Mr. Wright paid with a $50 bill, so we subtract the total cost with tax from $50 to find out how much change he should receive.

Change from [tex]\$50: $50 - $47.60 = $2.40\[/tex]

To find out how much more money Mr. Wright needs to leave a 15% tip, we subtract the change he receives from the tip amount.

Additional money needed: [tex]\$6.63 - $2.40 = $4.23\[/tex]

Therefore, Mr. Wright needs an additional $4.23 to leave a 15% tip.

BC also has length 12 because arcs DC and CE add up to 117 degrees in measure, so that arc DE is congruent to arc BC, and the chords DE and BC that respectively intercept these arcs must also be congruent.

I believe it’s B. hope it’s right!