Use the continuous change function A(t) = Pe^rt to answer the question.

You invest $2,500 in an account that grows 5% each year. What will be your investment amount after 6 years?

A.
$2,699.72

B.
$3,374.65

C.
$15,769.07

D.
$13,272.96

AB:BC = 3:2

so AB=3/2BC

AB+BC=AC=20

substitute 3/2BC+BC=20

5/2BC=20

BC=2*20/5=8

AB=3/2*8=12

Apply a:b=c:d as a/b=c/d

AB:BC = 3:2 is AB/BC=3/2

AB=3/2*BC

AC=20=AB+BC

So 20=3/2*BC+BC

1 3/2BC=20

BC=8cm

AB=20-8=12cm

Answer:

Y = 5

Step-by-step explanation:

Since we know six is the value of X we can go ahead and multiply 4 and 6

4 X 6 = 24

Now there are different ways to find the value of Y

How I find the value is I subtracted 24 from 9

That gives you 15

Next you find what number you need to multiply by 3 to get 15

In this case your answer is 5

Then to be extra sure subtract 24 and 15 and you'll get 9

Hope this helps!

y = 5

substitute x = 6 into the equation and solve for y

(4 × 6 ) - 3y = 9

24 - 3y = 9 ( subtract 24 from both sides )

- 3y = - 15 ( divide both sides by - 3 )

y = 5

Answer:

No.

Step-by-step explanation:

You have to imagine (or create a physical model so you can see) that the left and right frame pieces are joined to the top frame piece. The angle each "vertical" piece makes with the horizontal is the sum of the angles shown at each corner: 37° + 50° = 87°.

The angles at each of the corners constitute same-side interior angles where the horizontal transversal crosses the "vertical" lines of each of the side pieces. If the side pieces were parallel, those angles would be supplementary (add to 180°). Instead, they add to 87° + 87° = 174° ≠ 180°. Hence the "verticals" are not parallel.

_____

Usually, a "square" frame has right-angle corners. Here, the corner angles add to 87°, a few degrees short of a right angle. The effect will be to make the side pieces closer together at the bottom than they are at the top. (Parallel lines are the same distance apart everywhere.)

The projectile has a maximum height of 1353.991 feet.

In this case we need to determine the maximum height reached by a projectile. Height equation of the projectile is now introduced:

y = y' + v' · t + 0.5 · g · t²

Where:

First, determine the height equation of the projectile:

y = 65 + 288 · t - 16.087 · t²

Second, graph the equation and find the maximum height by means of a graphing tool. (The maximum height is the y-coordinate of the vertex)

The maximum height of the projectile is 1353.991 feet.

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The maximum height attained by the projectile is calculated using the formula H = [tex](v^2) / (2g),[/tex] resulting in a height of 644.2 feet above the launch point. Adding the height of the structure, the projectile reaches a total maximum height of 709.2 feet above the ground.

To calculate the maximum height attained by a projectile, we need to consider the initial velocity, the height from which it is projected, and the acceleration due to gravity. The initial velocity is given as 288 feet per second, and the projectile is launched from a structure 65 feet high. The maximum height will be achieved when the projectile momentarily stops moving upwards before accelerating downwards due to gravity, which in the imperial system is approximately 32.2 feet per second squared in the negative direction.

Using the formula for vertical motion [tex]h = v^2 / (2g)[/tex] where h is the maximum height (from the point of launch), v is the initial vertical velocity, and g is the acceleration due to gravity, we can find the maximum height relative to the top of the structure. We then add the height of the structure to get the total maximum height above the ground.

The maximum height (H) from the launch point can be calculated using the formula: H = [tex](v^2) / (2g)[/tex]. Plugging in the values, we get H = (2882) / (2 * 32.2), which gives us H = 41,472 / 64.4 / 644.2 feet. To find the maximum height above the ground, we add the height of the structure: 644.2 feet + 65 feet = 709.2 feet.

Thus, the maximum height attained by the projectile is 709.2 feet above the ground.

It is 6561 because 3^12 is 531441 and 3^4 is 81 so when you divide you get 6561.

The value of csc(19°) evaluated using cofunctions of complementary angles is equal to sec(71°), since 19° and 71° are complementary angles, and the sine of one angle is equal to the cosine of its complement.

To evaluate csc(19°) using cofunctions of complementary angles, we recall that cosecant (csc) is the reciprocal of the sine function and that the secant (sec) function is the reciprocal of cosine. We also use the fact that complementary angles add up to 90 degrees. Thus, since 19° and 71° are complementary (19° + 71° = 90°), we have:

csc(19°) = 1/sin(19°)

Since sin(19°) is equal to cos(71°) (because sine of an angle is equal to the cosine of its complement), we can write this as:

csc(19°) = 1/cos(71°)

And since sec() = 1/cos(), we can conclude:

csc(19°) = sec(71°)

for every member to get a shirt you would need to order 9 packages of shirt (because 5 times 9 is 45) and for caps the minimum to order would be 15 packages of caps

explanation

caps=3 per package

shirts=5 per package

divide 45 by and get 15

15 is the total packages of hats needed to order

for shirt 45 divided by 5 is 9

9 is the total packages of shirts needed to order

Answer:

15 pack of caps n 9 pack of shirts

Step-by-step explanation:

There are 45 science club members.

If the caps come in packages of 3, least no. of package of caps is 45/3=15

If the shirts come in packages of 5, least no. of package of caps is 45/5=9

Answer: The correct option is A, itis the product of the initial population and the growth factor after h hours.

Explanation:

From the given information,

Initial population = 1000

Increasing rate or growth rate = 30% every hour.

No of population increase in every hour is,

[tex]1000\times \frac{30}{100} =1000\times 0.3[/tex]

Total population after h hours is,

[tex]1000(1+0.3)^h[/tex]

It is in the form of,

[tex]P(t)=P_0(t)(1+r)^t[/tex]

Where [tex]P_0(t)[/tex] is the initial population, r is increasing rate, t is time and [tex(1+r)^t[/tex]  is the growth factor after time t.

In the above equation 1000 is the initial population and [tex](1+0.3)^h[/tex] is the growth factor after h hours. So the equation is product of of the initial population and the growth factor after h hours.

Therefore, the correct option is A, itis the product of the initial population and the growth factor after h hours.

Answer:

the answer should be A

Step-by-step explanation:

f(x)=4x^3 - 6x^2 + 2x - 5

f(-2)

Replace X with -2:

4(-2)^3 - 6(-2)^2 + 2(-2) - 5 =

Calulate the powers:

4(-8) - 6(4) +(-4) -5=

Multiply:

-32 - 24 -4 -5=

Subtract

-65

2x * x : 2 = 400

x = 20 (side x)

20 * 2 = 80 (side 2x)

√80²+20²=

82.46 (side H)

The length of the sides of the triangle are x = 20 units , 2x = 40 units , and H = 44.72 units.

Given data:

Let the triangle be represented as ΔABC

Now, the measure of the sides of the triangle are:

The measure of AB = 2x

The measure of BC = x

And, the measure of hypotenuse H = H

The area of the triangle is 400 units²

So, 400 = ( 1/2 )(x ) (2x )

x² = 400

x = 20 units

So, the measure of AB = 40 units

And, the hypotenuse is H = √ [ ( 2x )² + ( x )² ]

H = √ ( 1600 + 400 )

H = √2000

H = 44.72 units

Hence, the length of the triangle is solved.

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To simplify the expression 12 - 3 * 12 * 10 * 120, follow the order of operations: Multiply 3 * 12, then 36 * 10, then 360 * 120, and finally subtract 12 from the result to get 43,188.

To simplify the expression 12 - 3 * 12 * 10 * 120, you need to follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Multiply 3 * 12 = 36

Multiply 36 * 10 = 360

Multiply 360 * 120 = 43,200

Finally, subtract 12 from 43,200 to get 43,188.

There are no parentheses or exponents, so the Order of Operations tells you to start by performing division and multiplication left to right.

7-3+4÷2×6

= 7-3+2×6

= 7-3+12

After you have done that, you perform addition and subtraction left to right.

= 4 +12

= 16

______

A Google or Bing search box will evaluate expressions such as this according to the order of operations.

ANSWER

The correct answer is D

EXPLANATION

To graph the inequality

[tex]x+3y\le 6[/tex]

we first graph the corresponding equation,

[tex]x+3y= 6[/tex]

We then test the origin to determine which half-plane to shade the inequality,

[tex]0+3(0)\le 6[/tex]

[tex]0\le 6[/tex]

The above statement is true so we shade the lower half plane.

Next, we graph

[tex]4x+6y\ge 9[/tex]

By first graphing the corresponding equation,

[tex]4x+6y=9[/tex]

Then we test the origin again,

[tex]4(0)+6(0)\ge 9[/tex]

[tex]0\ge 9[/tex]

This statement is false, so we shade the upper half plane

Next, we graph,

[tex]x\ge 0[/tex]

Draw the vertical line [tex]x=0[/tex] and shade to the right.

Finally, we graph,

[tex]y\ge 0[/tex]

Draw the horizontal line [tex]y=0[/tex] and shade the upper region.

the intersection of all the shaded regions is called the feasible region.

The four vertices of the feasible region are

[tex](0,\frac{3}{2}),(0,2),(6,0),( \frac{9}{4},0)[/tex]

Hence the correct answer is D

Answer:

D)

Step-by-step explanation:

Source: Trust me bro

so alex would have 2 markers plus jills 2 markers plus 8 markers is 12 markers all together, feel free to comment if you don't understand fully, and i will try to better my explanation

Answer:

81 1/3 . . . . . (none of the offered choices is appropriate)

Step-by-step explanation:

According to the order of operations, expressions inside parentheses are evaluated first.

= 12[5^2 ÷ (25 -16) +4]

= 12[5^2 ÷ 9 + 4]

Exponentials are evaluated before multiplication or division.

= 12[25 ÷ 9 + 4]

Division is performed before addition

= 12[(2 7/9) +4]

= 12[6 7/9]

And finally, the multiplication is performed

= 72 +84/9 = 72 +9 1/3

= 81 1/3

_____

A Google search box can be relied upon to apply the order of operations when evaluating an arithmetic expression.

== == == == ==

If the problem is ...

... 12[6^2 ÷ (25 -16) +4]

then the result is A. 96.

(f+g)(x) = f(x) + g(x)

Now all you have to do is plug in the equations:

(x/2-3) + (4x^2 + x -4)

Combine like terms:

3x/2-7+4x^2

This is equal to the third equation, so the answer is:

C

To find the sum of the functions f(x) and g(x), combine them like so: (f + g)(x) = (x/2 - 3) + (4x^2 + x - 4), which simplifies to (f + g)(x) = 4x^2 + 3/2x - 7.

Given the functions f(x) = x/2 - 3 and g(x) = 4x^2 + x - 4, the operation (f + g)(x) signifies the summation of the two functions. You simply add the two functions together.

To find (f + g)(x), we combine f(x) and g(x) like so: (f + g)(x) = f(x) + g(x) = (x/2 - 3) + (4x^2 + x - 4).

By combining like terms, we simplify to: (f + g)(x) = 4x^2 + 3/2x - 7.

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The amount of money remaining in Luisa's account is her original balance minus the amount of the check she wrote:

$541.82 - 27.19 = $514.63

Answer:

There are three kind of beta-thalassemia.

Total possible outcome=  3 types of beta- thalassemia + 1 [child will have no trace of disease] = 4

As we know Probability(outcome) = [tex]\frac{\text{ Total favorable outcome}}\text{Total possible outcome}[/tex]

Probability that the child will have beta-thalassemia major =\frac{_{1}^{3}\textrm{C}}{_{1}^{4}\textrm{C}}

     =[tex]\frac{3}{4}[/tex]

   ∴ favorable=[tex]_{1}^{3}\textrm{C}[/tex]

 And , Total =[tex]_{1}^{4}\textrm{C}[/tex]

Probability that the child will have no trace of the disease=[tex]\frac{1}{4}[/tex]

The probability of Mrs. R's child having beta-thalassemia major or no trace of the disease depends on the genetic status of both parents. A 25% chance exists for beta-thalassemia major if both parents are carriers, with a 25% chance for no trace of the disease. Specific probabilities require knowledge of both parents' genetic status.

Beta-thalassemia is a genetic blood disorder that results from a mutation in the beta-globin gene, leading to a deficiency in the synthesis of the beta-chain of hemoglobin. To determine the probability that Mrs. R's child will have beta-thalassemia major or no trace of the disease, we would need to know the genetic status of both parents. If both parents are carriers (heterozygous for the beta-thalassemia trait), there is a 25% chance that the child will inherit two defective genes resulting in beta-thalassemia major, a 50% chance the child will be a carrier like the parents, and a 25% chance the child will inherit two normal genes and thus have no trace of the disease.

If one parent has beta-thalassemia major and the other is a carrier, every child will have at least one defective gene; hence, they all will be at least carriers. If one parent has beta-thalassemia major and the other has normal genes, each child has a 100% chance of being a carrier. Without knowing the specific genetic status of Mrs. R and her partner, we cannot provide exact probabilities.

I believe the answer is Graph D

Answer:

Graph D

Step-by-step explanation:

Given is the function

f(x) =[tex]5x^3+x-8[/tex]

When leading term is changed to negative we get new function

g(x) = [tex]-5x^3+x-8[/tex]

To find y intercept:

Put x=0

Y intercept = 5(0)+0-8 =-8

Since only graph D has y intercept -8, we get graph D is the answer.

[tex]\frac{11}{18}[/tex]

let n represent the number to be found

simplify the ratio on the right by multiplying both parts by 3

we now have

[tex]\frac{n}{11}[/tex] = [tex]\frac{1}{18}[/tex] ( cross-multiply )

18n = 11 ( divide both sides by 18 )

n = [tex]\frac{11}{18}[/tex]

The complete ratio for __:11= 1/3 :6   is   [tex]\frac{11}{18} : 11 = \frac{1}{3} : 6[/tex]

The given equivalent ratio expression is:

__:11= 1/3 :6

This can be re-written as:

[tex]x : 11 = \frac{1}{3}:6[/tex]

Rewrite the ratio in fraction form:

[tex]\frac{x}{11} = \frac{1}{3} \div 6[/tex]

Change the division sign on the right to multiplication, and 6 to 1/6

[tex]\frac{x}{11} = \frac{1}{3} \times \frac{1}{6} \\\\\frac{x}{11} = \frac{1}{18}[/tex]

Cross multiply:

18x   =  11

Divide both sides bu 18

[tex]\frac{18x}{18} = \frac{11}{18} \\\\x = \frac{11}{18}[/tex]

Therefore, the equivalent ratio is [tex]\frac{11}{18} : 11 = \frac{1}{3} : 6[/tex]

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25. 9/20

Steps-

1) Simplify 1/5 and 1/4

2) Find the common denominator

4/20+5/20

3) (4+5)/20

4) 9/20

Answer- 9/20

Try the rest on your own! :)

The answer is C because AO and BO are equal. And with AO being three times the length of CO, BO should be the length of DO

the expression for mean in this case is

[tex]50 = \frac{1}{5}(d + 20 + 75 + 20 + 90) = \frac{1}{5}(d+205)[/tex]

with d standing for expenditure in December. Now solve for d:

[tex]250 = d + 205\\d = 45[/tex]

The student has to spend $45 to meet his goal.

By calculating the total money spent in the past 4 months and subtracting it from the mean spending goal for 5 months, the college student can spend $45 on music in December.

The student's goal is to spend a mean of $50 a month towards music for the remaining 5 months of the year. Considering for the other 4 months his spending amounted to $20 , $75 , $20 , and $90, respectively, we add these amounts together, which results in $205. The total spending for 5 months should be $50 * 5 = $250 because of the mean spending goal. Therefore, the amount he can spend in December is $250 - $205 = $45.

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First add 3+4+6= 13 times 7=91

Lol

91 is the correct answer.   I will give you a hint! *You had to used order of operations stands for pemdas: p-parenthesis, e-exponents, m-multiply, d-divide, a-add, and s-subtracting. First you had to calculate with parenthesis first, and it gave us, [tex](3+6+4)=13[/tex]. And then you had to multiply and divide from left to right, and it gave us the answer is 7*13=91. 91 is the correct answer. Hope this helps! And thank you for posting your question at here on brainly, and have a great day. -Charlie

Apparently, the calculator at the link in your lesson is fully capable of giving you the necessary numbers. My own TI-84 work-alike gives me the account balances, but the rest of the numbers need to be figured.

In 30 years, there are 12×30 = 360 months, or 4×30 = 120 quarters. See the calculator results below. Your table can be filled in using the given information to find the contribution amount. The calculator gives the final balance. The interest amount is found by subtracting the contribution amount from the final balance.

[tex]\begin{array}{cccc}\text{Opt}&\text{Contributions}&\text{Int}&\text{Final Bal}\\1&360\cdot 25=9000&6250.50&15250.50\\2&120\cdot 75=9000&8467.04&17467.04\\3&1000&5489.17&6489.17\end{array}[/tex]

9/2 would be on the right -7/2 will be on the left hope i helped

Answer:

The easiest way to plot the fraction in the number line is to change the fraction into the decimal then plot it, as decimal is easily detected in the number line as compare to the fraction.

The Fraction [tex]\frac{9}{2} = 4.5[/tex]

and value 4.5 lies exact between 4 and 5.

The Fraction [tex]\frac{-7}{2} = -3.5[/tex]

and value 4.5 lies exact between -4 and -3.

It is shown below.

Perimeter of the triangle ABC is 18.7 units.

Coordinate of the point A is (4, -1), B is (-1, 4) and C is (0, -3).

Length of the side AB = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]

AB = [tex]\sqrt{(-1-4)^{2}+(4+1)^{2}} =\sqrt{50}[/tex]

AB = 7.07 units = 7.1 units ( rounded to the nearest 10th)

Length of the side BC = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]

BC = [tex]\sqrt{(0+1)^{2}+(-3-4)^{2}}[/tex]

BC = [tex]\sqrt{50}[/tex]

BC = 7.07 units = 7.1 units ( rounded to the nearest 10th)

Length of the side CA =[tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]

CA = [tex]\sqrt{(4-0)^{2}+(-1+3)^{2}}[/tex]

CA = [tex]\sqrt{20}[/tex]

CA = 4.47 units = 4.5 ( rounded to the nearest 10th)

Perimeter of the triangle ABC = sum of all three sides = (7.1 + 7.1 + 4.5) units = 18.7 units  

a) 4  

b) 47

c) 225

d) 120/400

Answer:

a. Whole is 4

b. Whole is 225

c. part is 47

d.Part is 120 whole is 400

Step-by-step explanation:

With this problems of basci math you just have to think how much out of how much, the whole is the complete part and the part is what you are taking of or calculating, with fractions is easy because the whole is the number that is below and the part is the number on top of the fraction, and with percentages the number tha comes after teh "of" is the whole, and the number before is the part.

(b)

A polynomial has the form

[tex]a_{0}[/tex][tex]x^{n}[/tex] ± [tex]a_{1}[/tex][tex]x^{n-1}[/tex] + ....

the only expression fitting this description is : x² + 2x + 7