Students in a zoology class took a final exam. They took equivalent forms of the exam at monthly intervals thereafter. After t​ months, the average score​ S(t), as a​ percentage, was found to be given by the following​ equation, whereStudents in a zoology class took a final exam. They took equivalent forms of the exam at monthly intervals thereafter. After t​ months, the average score​ S(t), as a​ percentage, was found to be given by the following​ equation, where t>=0.

Required:
a. What was the average score when they initially took the test, t=0?
b. What was the average score after 4 months?
c. What was the average score after 24 months?
d. What percentage of their original answers did the students retain after 2 years?
e. The maximum of the function is_____%.

Answer:

14.5 pounds of apples.

Step-by-step explanation:

$3.77 ÷ $.26 = 14.5

Apples = 14.5 pounds

Hope this helps! :)

Answer:

Step-by-step explanation:

18 : 2/3

can also be written as 18 / 2/3 = 18 × 3/2

= 27

Hope it helps

plz mark as brainliest!!!!!

Answer:

D

Step-by-step explanation:

The Triangle Inequality states that the sum of the two largest side lengths of a triangle must be greater than the length of the largest side. Let's check these answers.

A: Since 18 + 26 > 46 is a false statement, A is not the answer.

B: Since 18 + 26 > 49 is false, B is not the answer.

C: Since 18 + 6 > 26 is false, C is not the answer.

D: Since 18 + 26 > 32 is false, D is the answer.

Answer:

since ab=18 and bc= 26 and if u draw out the shape and write them down u would mostly get d but I not too sure is d that the best I can do

Step-by-step explanation:

Answer:

C. 2y = -12

Step-by-step explanation:

Well a function is when all x values have only one corresponding y value and on a graph we can use the vertical line test and in doing so we know that the answer is C. 2y = -12

Answer:

Step-by-step explanation:hi

Answer:

the first term is 4

Step-by-step explanation:

Given

G(3) = 36

G(6) = 972

Solution:

General formula for geometric series

G(x) = AB^x

From given data: G(6)/G(3) = 972/36 = 27

From formula: G(6)/G(3) = AB^6/(AB^3) = B^3

Therefore

B^3 = 27

B=3

Hence

G(1) = AB^1 = AB^3/B^2=36/3^2=36/9=4

Ans: the first term is 4

Answer:

a₁ = 4

Step-by-step explanation:

The n th term of a geometric series is

[tex]a_{n}[/tex] = a₁ [tex]r^{n-1}[/tex]

where a₁ is the first term and r the common ratio

Given a₃ = 36 and a₆ = 972 , then

ar² = 36 → (1)

a[tex]r^{5}[/tex] = 972 → (2)

Divide (2) by (1)

[tex]\frac{ar^{5} }{ar^{2} }[/tex] = [tex]\frac{972}{36}[/tex] , that is

r³ = 27 ( take the cube root of both sides )

r = [tex]\sqrt[3]{27}[/tex] = 3

Substitute r = 3 into (1)

9a = 36 ( divide both sides by 9 )

a = 4

The first term is 4

-- This is a right triangle. So you KNOW that

(one leg)² + (other leg)²  =  (hypotenuse)²

-- Also, since the acute angles are equal, the legs must be equal ... both x .

-- Plugging into the formula:

x² + x² = (4)²

2x²  =  (4)²

2x²  =  16

x²  =  8

√x²  =  √8

x  =  √8

x = √(4 · 2)

x = √4  ·  √2

x  =  2 · √2

(That's choice D)

Answer:

[tex]\boxed{\sf \ \ f^{-1}(x)=\dfrac{x-6}{3} \ \ }[/tex]

Step-by-step explanation:

hello,

we can write

[tex]fof^{-1}(x)=x \ and \ fof^{-1}(x)=f(f^{-1}(x))=3f^{-1}(x)+6 \ so\\3f^{-1}(x)+6=x \ \ subtract \ 6\\<=>3f^{-1}(x)=x-6 \ \ divide \ \ by \ \ 3\\<=> f^{-1}(x)=\dfrac{x-6}{3}[/tex]

hope this helps

Answer:

50

Step-by-step explanation:

The requried, race car will travel approximately 1100 feet in 5 seconds at a constant speed of 150 miles per hour.

To find out how many feet a race car traveling at a constant speed of 150 miles per hour travels in 5 seconds, we need to convert the given speed from miles per hour to feet per second.

There are 5280 feet in a mile, and there are 3600 seconds in an hour.

First, let's convert 150 miles per hour to feet per second:

= 150 miles/hour * 5280 feet/mile / 3600 seconds/hour
= 220 feet/second (approximately)

Now, we can calculate the distance traveled by the race car in 5 seconds:

Distance = Speed * Time

Distance = 220 feet/second * 5 seconds

Distance = 1100 feet

Therefore, the race car will travel approximately 1100 feet in 5 seconds at a constant speed of 150 miles per hour.

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━━━━━━━☆☆━━━━━━━

▹ Answer

0.4 = 2.5, circle with 4 pieces shaded, and the rectangle with 40 squares shaded.

0.75 = Rectangle with 3 squares shaded and 75/100

0.9 = 90/100

▹ Step-by-Step Explanation

You can change the fractions into decimals, and count the shaded parts to determine the answer.

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

.4= 2/5, the one with 10 equal parts that has 4 shaded, the one with 4/10 shaded

.75= 75/100,

.9= 90/100, the one with 2/3 shaded

Step-by-step explanation:

u have to reduce it to find ur answer

hope this helps

sorry if it was late

Answer:

Graph A

Step-by-step explanation:

Say that the car rental rate stands for c dollars ( $ ). We know that Jamal's trip lasts for 4 days, paying $ 24 in expenses for gas, and $ 128 for taxi services. Based on these requirements for his trip the question asks for a graph that models this situation, but lets start with the inequality.

______

The big key here is the part " which graph shows the range of car rental rates that would be cheaper than the taxi service. " Our inequality must thus have the variable " c " on the same side as the payment for gas ($ 24 ), and must be less than the taxi service ( $ 128 ), or in other words a less than sign. Another point is the car rental rate. We know it stands for c, but it is dependent on the number of days. Hence we can conclude the following inequality,

24 + 4c < 128 - Subtract 24 from either side,

4c < 104 - Divide by 4 on either side, isolating c,

c < 26

The range of car rental rates that would be cheaper than the taxi service should be { c | 0 ≤ c < 26 }, knowing variable c stands for the car rental rates.

______

The graph that models this range should be the first one, option A. This graph is not accurate however, as it extends infinitely in the negative direction, and you can't have negative money, or rather be in debt - in this situation.

Answer:

A is the answer

Step-by-step explanation:

Answer:

c − 135

Explanation:

Let's say that the amount of money in Bailey's checking account is  

c  dollars.

We also know that she took away  $ 135

From this variable and number, we can state the algebraic expression

 c − 135

Answer:

{ 1,3,5,7,10,15}

Step-by-step explanation:

The union means join together, or all the elements of both sets

{1, 5, 10, 15} U {1, 3, 5, 7}

= { 1,3,5,7,10,15}

Answer:

Step-by-step explanation:

Union of two sets contains the elements that belongs to A set or B set or both

A= {1,5,10, 15}

B ={1,3,5,7}

A U B = {1,3,5,7,10,15}

Answer:

2 real solutions

Step-by-step explanation:

hello,

[tex]\Delta = b^2-4ac=3^2-4*1*1=9-4=5>0[/tex]

as this is > 0 there are 2 different real solutions

hope this helps

The quadratic equation, y = x² + 3x + 1 has two real roots.

In a quadratic equation of the form, ax² + bx + c = 0, the nature of the roots depends upon the value of the discriminant (D), which is calculated by the formula, D = b² - 4ac.

If the value of D > 0, the equation has real and distinct roots.

If the value of D = 0, the equation has real and equal roots.

If the value of D < 0, the equation has imaginary roots.

In the question, we are given an equation y = x² + 3x + 1 and are asked to say how many real roots it has.

To find the roots, we first equate y to 0.

∴ y = x² + 3x + 1 = 0.

Now comparing the equation x² + 3x + 1 to the standard equation ax² + bx + c, we get a = 1, b = 3, and c = 1.

Now, the nature of the roots depends upon the discriminant (D),

D = b² - 4ac = 3² - 4.1.1 = 9 - 4 = 5.

∵ Discriminant (D) > 0, the quadratic equation, y = x² + 3x + 1 has both its root real and distinct.

∴ The quadratic equation, y = x² + 3x + 1 has two real roots.

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Answer:

C)

Step-by-step explanation:

The whole number goes on the inside of the radical and is raised to the 5 power. The 4 is on the outside.

:)

Answer:

7.10299

Step-by-step explanation:

[tex]4^{\sqrt{2} }[/tex] is best evaluated in a calc.

Answer:

Hello There. ♡ The correct answer is: f(x) = -|x-1|

The parent function is f(x) = |x|

Then the function is reflected over the x-axis, so the f(x) will become -f(x)'. The function will become: 

f(x) = -|x| 

-f(x)' = |x|

 f(x)' = -|x|

After that, the function is translated 1 unit to the right. That mean x will become x'-1. The function will become: 

 f(x) = -|x|

 f(x) = -|(x'-1)|

 f(x) = -|x'-1|

Hope It Helps! :)

ItsNobody~ ♡

Answer:

its b on edge  2020

Step-by-step explanation:

Answer:

  2444

Step-by-step explanation:

The total cost is the integral of the marginal cost.

  [tex]\displaystyle C=\int_{144}^{625}{\dfrac{94}{\sqrt{x}}}\,dx=\left. 2\cdot 94\sqrt{x}\right|_{144}^{625}=188(25 -12)=\boxed{2444}[/tex]

The total cost of producing units 144 through 625 is 2444.

_____

If all you need is a number, a graphing calculator can give you that.

Answer:

  A. Show that the diagonals form two congruent triangles using the definition of a rhombus and geometric properties. Then, use CPCTC (corresponding parts of congruent triangles are congruent) to show that the opposite interior angles are bisected.

Step-by-step explanation:

Answer choice A is the only one that applies specifically to a rhombus.

The other answer choices are true of triangles and vertical angles in general. They do not relate specifically to the problem at hand.

Answer:

[tex]\frac{x^2-16}{2} + 16ln\frac{4}{x} +16C[/tex]

Step-by-step explanation:

Given the indefinite integral [tex]\int\limits{\frac{x^2-16}{x} } \, dx[/tex], using the substitute

x = 4 sec(θ)...1

The integral can be calculated as thus;

First let us diffrentiate the substitute function with respect to θ

dx/dθ = 4secθtanθ

dx =  4secθtanθdθ... 2

Substituting equation 1 and 2 into the integral function we will have;

[tex]\int\limits{\frac{(4sec \theta)^2-16}{4sec \theta} } \, 4sec \theta tan \theta d \theta\\\int\limits{\frac{16sec^2 \theta-16}{4sec \theta} } \, 4sec \theta tan \theta d \theta\\\int\limits{\frac{(16(sec^2 \theta-1)}{4sec \theta} } \, 4sec \theta tan \theta d \theta\\\\from \ trig \ identity,\ sec^2 \theta - 1 = tan^\theta\\\\\int\limits{\frac{16 tan^2 \theta}{4sec \theta} } \, 4sec \theta tan \theta d \theta\\\\\int\limits 16 tan^3 \theta d \theta\\\\[/tex]

Find the remaining solution in the attachment.

Answer:

44

Step-by-step explanation:

We can solve the equation by simplifying it.

[tex]$\sqrt{5+n}=7$[/tex], let's square both sides.

[tex]5+n = 49[/tex]. Now lets subtract 5 from both sides.

[tex]n = 44[/tex].

Hope this helped!

Answer:

  44

Step-by-step explanation:

  [tex]\sqrt{5+n}=7\\\\5+n=7^2=49\\\\n=49-5\\\\\boxed{n=44}[/tex]

Answer: 7 years

Step-by-step explanation:

From the formula A = P(1+(r/100))^t we have

5089.12 = 4000 (1+(3.5/100))^t

=> 1.27228 = (1.035)^t

Using calculator we find that 1.035^7 gives 1.272279

Hence in 7 years $4000 will grow to $5089.12 if it’s invested at 3.5%

Answer:

140 units3

Step-by-step explanation:

The  volume of the prism below is 420 cubic units.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

The prism is a three-dimensional shape that has base area, and height. The volume of a prism is equal to the product of base area and height of a prism.

The volume of the prism= B×H

Where, B is base area of prism, and H is height of prism.

Given that,

Length of  prism (L) = 12 centimeters

Width of prism(W) = 14 centimeters

B=1/2×12×5

=30

Now volume of prism = 30×14

=420 cubic units

Hence, the  volume of the prism below is 420 cubic units.

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Answer:

To break even the local arena must sell approximately 70,589 tickets. They would have a loss of $47625.

Step-by-step explanation:

The cost per night of the Icey blades contract can be expressed as a function of the gate receipts, with the flat cost added by 40% of all the gate receipts sold. This expression is shown below:

[tex]cost(x) = 60000 +0.4*x[/tex]

Since each ticket costs $1.25, then the revenue of the arena can be shown as:

[tex]revenue(x) = 1.25*x[/tex]

In order to break even the revenue must be equal to the cost, so:

[tex]revenue(x) = cost(x)\\1.25*x = 60000 + 0.4*x\\1.25*x - 0.4*x = 60000\\0.85*x = 60000\\x = \frac{60000}{0.85} = 70,588.24[/tex]

To break even the local arena must sell approximately 70,589 tickets.

If the average attendance was 7500 per night, the profit would be:

[tex]profit = revenue(7500) - cost(7500)\\profit = 1.25*7500 - 60000 + 0.4*7500\\profit = 9375 - 60000 + 3000\\profit = -47625[/tex]

They would have a loss of $47625

Answer:

see explanation

Step-by-step explanation:

Given

16[tex]y^{4}[/tex] - 256[tex]x^{12}[/tex] ← factor out 16 from each term

= 16([tex]y^{4}[/tex] - 16[tex]x^{12}[/tex] ) ← difference of squares which factors in general as

a² - b² = (a - b)(a + b), thus

[tex]y^{4}[/tex] - 16[tex]x^{12}[/tex]

= (y² )² - (4[tex]x^{6}[/tex] )²

= (y² - 4[tex]x^{6}[/tex] )(y² + 4[tex]x^{6}[/tex] )

Now y² - 4[tex]x^{6}[/tex] ← is also a difference of squares

= y² - (2x³)²

= (y - 2x³)(y + 2x³)

Thus

16[tex]y^{4}[/tex] - 256[tex]x^{12}[/tex]

= 16(y - 2x³)(y + 2x³)(y² + 4[tex]x^{6}[/tex] )

Answer:

Step-by-step explanation:

4y^2+16x^6, 2y, 4x^3, 2y, 4x^3

The commutative property of addition tells that there is no effect of orders of addends on the result. The associative property of multiplication tells that there can be any grouping of factors, without changing the result.

The expression which uses the commutative property of addition and the associative property of multiplication to  rewrite the given expression is:

(3*3)*8 + 5

The order in which addends(quantities that are added) are written doesn't matter and the result will be same.

[tex]a + b = b + a[/tex]

The associative property of multiplication tells that there can be any grouping of factors(any association), without changing the result.

[tex]a\times (b \times c ) = (a \times b) \times c[/tex]

For given expression 5 + 3*(3*8), using the commutative property of addition, we have:

[tex]5 + 3 \times (3 \times 8) = 3 \times (3 \times 8) + 5[/tex]

For the resultant expression [tex]3 \times (3 \times 8) + 5[/tex], using the associative property of multiplication:

[tex]3 \times (3 \times 8) + 5 = (3 \times 3) \times 8 + 5[/tex]

Thus, the expression which uses the commutative property of addition and the associative property of multiplication to  rewrite the given expression is:

(3*3)*8 + 5

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Answer:

Step-by-step explanation:

side a = 10

Area of isosceles triangle = [tex]\frac{\sqrt{3}a^{2}}{4}\\\\[/tex]

           = [tex]\frac{\sqrt{3}*10*10}{4}\\\\=\sqrt{3}*5*5\\\\=25\sqrt{3}\\\\=25*1.732[/tex]

             = 43.3 square units

Complete question is;

A labourer is paid rs. 8 per hour for an 8 hour day and ½ times that rate for each hour in excess of 8 hours in a single day. if the labourer received rs. 80 for a single day's work, how long did he work on that day?

Answer:

Total working time for the day = 12 hours

Step-by-step explanation:

Money paid to the labourer for initial 8 hrs of work = 8 × 8 = rs. 64.

Now, we are told that he receives rs. 80 in total for that day. And that he receives ½ times the initial rate for each extra hour after the initial 8 hour period.

Thus;

½ × 8 × y = (80 - 64)

Where y is the duration of extra hours.

So;

4y = 16

y = 16/4 hours

y = 4 hours

Now, since extra hours = 4 hours and normal working hours = 8 hours.

Then, total working time for that day = 8 + 4 = 12 hours

Answer:  The value of m = 10.

Step-by-step explanation:

Given points, (1,5), (9,85), (2,10), (6,38), (4,3), (12,107), (7,64), (12,86), (7,47), (9,64), (4,27)

Each point is represented in the form (x,y).

The line is in the form[tex]y=mx+b[/tex], where m is the rate of change of y with respect to x.

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Take [tex]x_1=1\ \ , y_1=5;\ \ x_2=9,\ \ y_2=85[/tex]

Then,

[tex]m=\dfrac{85-5}{9-1}\\\\=\dfrac{80}{8}=10[/tex]

Hence, the value of m = 10.

Answer:

9.15

Step-by-step explanation:

I just took the test Hope this helped :D

Answer:

Step-by-step explanation:

Rewrite the function f(x) = 8√x as y = 8√x.

To find the inverse function, do the following:

1) Interchange x and y.  We get x = 8√y

                                                                             x                        x^2

2) Solve this result for y:  (x/8) = √y  =>  y = ( -------- )^2, or y = ---------

                                                                             8                        64