Suppose that $11,572 is invested at an interest rate of 6.2% per year, compounded continuously.
a) Find the exponential function that describes the amount in the account after time t, in years.
b) What is the balance after 1 year? 2 years? 5 years? 10 years?
c) What is the doubling time?
a) The exponential growth function is P(t)= .
(Type exponential notation with positive exponents. Do not simplify. Use integers or decimals for any numbers in the equation.)

Answer:

x=4

Step-by-step explanation:

Using cross multiplication, we can simplify the equation to

-15x=-60

Then we can divide by -15 on both sides getting x=4

Answer:

[tex]BC = 4.8[/tex] and [tex]B_{1}D_{1} = 6.25[/tex]

Step-by-step explanation:

The parallelograms ABCD and [tex]A_{1} B_{1} C_{1}D_{1}[/tex] are similar.

Now, AB = 8 (Given in the figure), so CD = 8.

Now, we can write, [tex]\frac{BC}{B_{1}C_{1}}  = \frac{CD}{C_{1}D_{1}}[/tex]

⇒ [tex]\frac{BC}{3} = \frac{8}{5}[/tex]

{Since, given that [tex]B_{1}C_{1} = 3[/tex] and [tex]C_{1}D_{1} = 5[/tex]}

⇒ [tex]BC = \frac{8 \times 3}{5} = 4.8[/tex] (Answer)

Again, we can write, [tex]\frac{BD}{B_{1}D_{1}}  = \frac{CD}{C_{1}D_{1}}[/tex]

⇒ [tex]\frac{10}{B_{1}D_{1}} = \frac{8}{5}[/tex] {Since, BD = 5 + 5 = 10}

⇒ [tex]B_{1}D_{1} = \frac{5 \times 10}{8} = 6.25[/tex] (Answer)

Answer: 4

Step-by-step explanation:

(g*h)(5) = 4

Firstly, h(5) = 5 - 7 = -2

Then, evaluate g(-2) = (-2)^2 = 4

Answer:

Equation that represents the total cost is  y =  4 +  2 x

Step-by-step explanation:

Here,  x :  slices of pizza eaten at the dance.

y :  total cost paid in the school dance

Let a : Cost of each slice of pizza.

So, according to the question:

Entrance fee + cost 1 slice of pizza = $6

or, Entrance fee = $ 6 - Cost of 1 slice  .......  (1)

Similarly, Entrance fee + cost 3 slice of pizza = $10

or, Entrance fee = $ 10 - Cost of 3 slice ............ (2)

Comparing both equation , we get:

$ 6 - Cost of 1 slice = $ 10 - Cost of 3 slice

or, 6 - a  = 10 - 3 a

or, 2 a  = 4

⇒ a= 2, So the cost of each slice of pizza = $2

Putting the value of a in 1 we get

Entrance fee =  6 - $ 2 =$4

Now, the cost of x slice of pizza = x ( $2) = 2x

So, the total cost y for x slice of pizza = Entrance fee+ Cost of x  slices

or,  y = $ 4 +  2 x

Equation that represents the total cost is  y =  4 +  2 x

Final answer:

The equation that represents the total cost y after buying x slices of pizza is y = 2x + 4, which includes the cost of each slice of pizza ($2) and the entrance fee ($4).

Explanation:

To write an equation that represents the total cost y after buying x slices of pizza at the dance, you can use the information given to create two points: (1, $6) and (3, $10). From the first point, you know there is a fixed entrance fee plus the cost of one slice of pizza. By the time you purchase two more slices (for a total of three), the cost is $10. This scenario implies that each additional slice of pizza has a constant price.

With two points, you can find the slope of the line, which represents the price of each slice of pizza. The slope m is the change in cost divided by the change in the number of slices: m = ($10 - $6) / (3 - 1) = $4 / 2 = $2 per slice. The entrance fee is the y-intercept of the line, which is the initial cost without any pizza, and can be found by extending the line back to the y-axis. The total cost without any pizza is the cost after one slice minus the cost of that slice, which gives us $6 - $2 = $4.

The final equation becomes y = 2x + 4, where y represents the total cost and x represents the number of slices of pizza purchased.

Answer:

Yeah

Step-by-step explanation:

find a formula

Answer:

Vertex B to vertex Y

Step-by-step explanation:

The diagram shows two triangles ABC and XYZ. These triangles are congruent by SAS postulate, because

Congruent triangles have congruent corresponding sides and angles, so translation and rotation must be completed such that

So, first, translate vertex B to vertex Y. Next, rotate ΔABC about B to align the sides and angles.

Answer:

1/2e^x -3

Step-by-step explanation:

The resulting function after vertically stretching y = ex by a factor of 2, reflecting it across the x-axis, and shifting it down 3 units is y = -2ex - 3.

The original function is y = ex. To find the resulting function after the described transformations (vertically stretched by a factor of 2, reflected across the x-axis, and shifted down 3 units), we perform each transformation step by step.

Therefore, the resulting function after all transformations is y = -2ex - 3.

Answer:

35 hectometers

Step-by-step explanation:

1 kilometer=10 hectometers

3 1/2=7/2

7/2*10=35

Answer:

[tex]\large\boxed{3\dfrac{1}{2}\ kilometers=35\ hectometers}[/tex]

Step-by-step explanation:

[tex]PREFIXES\\\\mega\ (M)=10^6\\\\kilo\ (k)=10^3\\\\hecto\ (h)=10^2\\\\deko\ (da)=10\\\\decy\ (d)=10^{-1}=0.01\\\\centi\ (c)=10^{-2}=0.01\\\\mili\ (m)=10^{-3}=0.001\\\\mikro\ (\mu)=10^{-6}=0.000001[/tex]

[tex]3\dfrac{1}{2}=3.5\\\\1\ kilometers=10\ hectometers\ (1\ km=10\ hm)\\\\3\dfrac{1}{2}\ km=3.5\ km=3.5\cdot10\ hm=35\ hm[/tex]

Answer:

12 ≤ x - 7

Step-by-step explanation:

let "x" represent the number

The term decreased means subtraction.

The problem indicates that 12 cannot be greater than a number decreased by 7. Use ≤ which means less than or equal to.

≤ less than or equal to 12 means that 12 is the maximum value.

Answer:

-3°

Step-by-step explanation:

13°-16°=(-3°)

Answer:

The perimeter of the rectangle is 32 - 4y

Step-by-step explanation:

To find the perimeter, we will simply follow the steps below;

First write down the formula for finding the perimeter of a rectangle

The formula for finding perimeter in a rectangle is;

perimeter = 2l +2w

where l= length  of the rectangle  and   w is equal to width of the rectangle

From the question given, length =9 - 2y      and width =7

We can now proceed to insert the values into the formula;

perimeter = 2l +2w

                 =2(9-2y) + 2(7)

Then we will now simplify

perimeter  =2(9-2y) + 2(7)

                 =18 - 4y + 14

                = 18 + 14 - 4y

                 =32 - 4y

Therefore, the perimeter of the rectangle is 32 - 4y

The perimeter of the rectangle is 32-4y.

Step-by-step explanation:

Given information:

The length of the rectangle = 9-2y

The width of the rectangle = 7

Now

The perimeter (P) of the rectangle is :

[tex]P = 2( \text{Length} + \text{width})[/tex]

[tex]P= 2(9-2y+7)\\P=18-4y+14\\P=32-4y[/tex]

Hence, the perimeter of the rectangle is 32-4y.

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Step-by-step explanation: i think it is B

Answer:

64 nickels and 24 dimes are there in the piggy bank.

Step-by-step explanation:

There are  $5.60 in the piggy bank in nickels and dimes.

Let x number of nickels and y number of dimes are there.

Now, 1 nickel ≡ 0.05 dollars and 1 dime ≡ 0.1 dollars.

So, 0.05x + 0.1y = 5.6

⇒ 5x + 10y = 560

⇒ x + 2y = 112 ....... (1)

Again, from the condition given we can write that,

So, 3y - 8 = x ........ (2)

Now, solving (1) and (2) we get 3y - 8 + 2y = 112

⇒ 5y = 120

⇒ y = 24  

And from equation (2) we get x = 3y - 8 = 64.

So, there are 64 nickels and 24 dimes in the piggy bank. (Answer)

Answer:

 64 nickels and 24 dimes in the piggy bank.

Step-by-step explanation:

Answer:

SAS

Step-by-step explanation:

Answer:

Silver keys = 4

Gold keys = 5

Total number of keys = 9

probability of getting a silver key = P(4/9)

Step-by-step explanation:

P(4/9) because 4 keys are silver among 9 keys. Probability is the number of chosen matter divided by the total number of matters.

Final answer:

The image of the point (-6,3) after a reflection over the y-axis is (6,3), because a reflection over the y-axis changes the sign of the x-coordinate while leaving the y-coordinate unchanged.

Explanation:

The question is asking for the result of a reflection of the point (-6,3) over the y-axis. A reflection over the y-axis will invert the x-coordinate of the point but leave the y-coordinate unchanged. Hence, the reflected point will have the same y-coordinate but the opposite x-coordinate. The transformation formula for a reflection over the y-axis is (x, y) to (-x, y).

Applying this formula to the point (-6,3), we change the sign of the x-coordinate from -6 to 6, while the y-coordinate remains the same. Therefore, the image of the point (-6,3) after the reflection over the y-axis is (6,3).

Answer:

Jo's thinking about the number 20.

Step-by-step explanation:

9x-4=176

9x=176+4

9x=180

x=180/9

x=20

Answer:

82.8576

Step-by-step explanation:

Answer:

C)  The area of the sector TSV  = 1.1 sq m.

Step-by-step explanation:

Here, the angle subtended by TSV at  the center of the circle  = 3 radians.

1 Radians = 57.2958°

So, 3 radians   = 3 x 57.2958 = 171.887 °

⇒The angle of the sector TSV = 171.887 °

Now, the angle of any sector of a circle with angle Ф at the center  

=  [tex]\frac{\theta}{360}  \times \pi \times (r^2)[/tex]

Here, r  = 0.87 m

So, the area of the sector TSV  =  [tex]\frac{171.887}{360}  \times \frac{22}{7} \times (0.87)^2 = 1.1358[/tex]

or, the area of the sector TSV  = 1.13 sq m.

Now, rounding off the area to the nearest tenth ,we get:

The area of the sector TSV  = 1.1 sq m.

Answer: 6x2=y

Step-by-step explanation:

If Mitchell owns 6 pairs of hockey skates, then The equation for the number of hockey stakes can be written as, X - 12 = 0

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

Mitchell owns 6 pairs of hockey skates,

The equation for number of hockey stakes  = ?

Suppose, the number of hockey stakes = X

According to given condition,

there are 6 pairs,

It is known that,

1 pair = 2 hockey stakes

So,

The equation is,

X = 2 x Number of pairs,

X = 2 x 6

X = 12

Hence, the equation is X - 12 = 0

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P(a)

Explanation I just did it :)

For independent events A and B, the probability of both occurring P(A and B) is the product of their individual probabilities: C. P(A) * P(B).

Independent events are events in probability theory where the occurrence of one event does not affect the occurrence or likelihood of the other.

Let's use the definition of independent events to derive the formula for the probability of the intersection of two independent events.

If events A and B are independent, then the definition of independence is given by:

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

This means that the probability of both events A and B occurring is the product of the individual probabilities of A and B.

So, if A and B are independent events, P(A and B) = P(A) * P(B). Therefore, the correct answer is C. P(A) * P(B).

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Answer:

[tex]\displaystyle -6 > \frac{g}{-2}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{g}{-2} < -6[/tex]

The keywords are fewer than, so the inequality receives the less than symbol, NOT greater than or equal to.

** The above answer is written in reverse, which is the exact same result.

I am joyous to assist you anytime.

The word sentence translates to the inequality 'g / -2 < -6', representing the relationship where the quotient of a number g and -2 is less than -6.

Writing the word sentence 'The quotient of a number g and -2 is fewer than -6' as an inequality involves translating the words into a mathematical expression. Inequality symbols are used to show how two measurements, or in this case, expressions, are related. The quotient of a number and another number is represented by the division of those two numbers. 'Fewer than' indicates that the expression on the left side is less than (<) the expression or value on the right side.

Therefore, the statement can be translated to the mathematical inequality as g / -2 < -6. This inequality shows the relationship between the variable g and the numbers -2 and -6, with the quotient of g and -2 being less than -6.

Answer:

3(5) + 300 = 15 + 300 = 315

300(1.04)^5 = 300 * 1.21665 = 365

In 5 years, the second account is higher.

3(12) + 300 = 336

300(1.04)^12 = 300 * 1.601 = 480

In 12 years, the second account is higher

Answer:

a. $18.36 for 3 pizzas  :  k  = 6.12

b. $4.17 for 3 pounds of bananas .   k  = 1.39

c. $16.48 for 4 pounds of potatoes .  k  = 4.12

d. 2 cups of flour to make 24 cookie .  k  = 12

Step-by-step explanation:

PROPORTIONALITY:

Two quantities x and y are said to proportional to each other

if for x ∝ y , x = y k.

Here, k is called the PROPORTIONALITY CONSTANT.

⇒[tex]x \propto y \implies k = \frac{x}{y}[/tex]  

Now, for the given quantities:

a.  $18.36 for 3 pizzas [box]    

Here, [tex]k = \frac{x}{y} = \frac{18.36}{3}  = 6.12[/tex]

So, the proportionality constant is 6.12.

b. $4.17 for 3 pounds of bananas [box]

Here, [tex]k = \frac{x}{y} = \frac{4.17}{3}  = 1.39[/tex]

So, the proportionality constant is 1.39.

c. $16.48 for 4 pounds of potatoes [box]

Here, [tex]k = \frac{x}{y} = \frac{16.48}{4}  = 4.12[/tex]

So, the proportionality constant is 4.12.

d. 2 cups of flour to make 24 cookies

Here,  [tex]k = \frac{x}{y} = \frac{24}{2}  = 12[/tex]

So, the proportionality constant is 12.

Answer:

(c) [tex]x + 2y = 8[/tex]

Step-by-step explanation:

The question is missing some important data which is necessary to solve it.

The correct question is as follows:

Which equation shows [tex]y=-\frac{1}{2}x+4[/tex] is in standard form?

(a) [tex]2x-y=8[/tex]

(b) [tex]x + 2y=-8[/tex]

(c) [tex]x + 2y = 8[/tex]

(d) [tex]2x + y = 8[/tex]

Solution:

Given equation:

[tex]y=-\frac{1}{2}x+4[/tex]

To convert the given equation to standard form.

The standard form of a linear equation is given by:

[tex]Ax+By=c[/tex]

where

A is a positive integer  and B and C are integers

We have:

[tex]y=-\frac{1}{2}x+4[/tex]

Multiply both sides by 2  to remove the fraction

[tex]2y=(-\frac{1}{2}x\times 2)+(4\times 2)[/tex]

[tex]2y=-x+8[/tex]

Adding [tex]x[/tex] both sides

[tex]x+2y=x-x+8[/tex]

[tex]x+2y=8[/tex]

∴ The standard form of the equation is ⇒ [tex]x+2y=8[/tex]

Answer: I am getting a result around the 54,800 area, so I am selecting the 55,000 HP answer.

Answer:

37769 hp

Step-by-step explanation:

from the pro tips given w ( weight of the SS Delphine + trailer + Redeye) = 3922000 + 150000 + 4451 Lbs Crr = 4076451 ibf

coefficient of rolling resistance = 0.015

Combined CDA = 1555 ft ^2

to get Ф = tan ⁻¹ ( 0.07 ) = 4.0041 degrees

To get F (w)  you will multiply it with sin Ф

= F ( w ) = 4076451 ibf * sin( 4.0041 ) = 284655.02 Ibf

to calculate F ( rr ) you will multiply it with cos Ф

F( rr) = 4076451 ibf * 0.015 * cos ( 4.0041 ) = 60997.50 ibf

the total sum of F ( force ) will be

F ( rr ) + F ( w)

= 60997.50 + 284655.02 = 352085.82 Ibf

therefore P ( power ) will be

p = 352085.82 ibf * 59 ft/s = 20773063.27 ft*ibf/s

to calculate how much horsepower the challenger will need to tow the SS Delphine will be calculated as below

HP = (20773063.27 ft*ibf/s ) * ( 1 hp / 550 ft*ibf/s ) = 37769.21 = 37769 hp  

Answer:

1.76666666666666666

Answer:

53/30=1.7666666...

Step-by-step explanation:

Answer:41

Step-by-step explanation:

Answer:

15.43 pounds of meat in a day

Step-by-step explanation:

108 pounds per week,

1 week=7 days,

108/7=15.43

Answer:

15 remainder 3

Step-by-step explanation:

108÷7

7 because 1 week= 7 days

108÷7=

15 remainder 3