AP CALC HELP!!! Worth 38 points. AP Calc AB differental FRQ

Answer:

  $328.95

Step-by-step explanation:

By the Pythagorean theorem, the diagonal of the garden has a length that is the root of the sum of the squares of the side lengths:

  d = √(77² +36²) = √7225 = 85

Then the cost of the fence is the product of this number of feet and the cost per foot:

  (85 ft)·($3.87/ft) = $328.95

The total cost of the length of the fence is $328.95

The garden is in the form of a rectangle. A line that divides the rectangle from one corner to the other corner is known as an hypotenuse. The hypotenuse divides the rectangle into two right-angles triangles. The length of the hypotenuse has to be first determined using Pythagoras theorem.

The Pythagoras theorem: a² + b² = c²

where a = length

b = base

c = hypotenuse

77² + 36²

5929 + 1296 =7225

√7225 = 85 feet

Cost of the total length of the fence = length of fence x cost per foot

$3.87 x 85 = $328.95

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The sequence in question is a geometric sequence, with a common ratio of 0.5. The explicit formula for the sequence is f(n) = 16 * (0.5)^(n-1).

The sequence described in the problem, where Achilles eats half of the remaining pizza slices every hour, is a geometric sequence. A geometric sequence is a sequence of numbers where each term after the first is obtained by multiplying the preceding term by a fixed, non-zero number called the common ratio.

In this case, the common ratio is 0.5 (since Achilles is eating half of the remaining pizza each time). If we let n be the hour (or term number in the sequence), the explicit formula for this sequence is: f(n) = 16 * (0.5)^(n-1)

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Answer:

FINAL ANSWER: f is a geometric sequence

EQUATION: [tex]f(n)=8*(\frac{1}{2})^{n-1}[/tex]

Step-by-step explanation:

KHAN ACADEMY

Answer:

x=54

Step-by-step explanation:

Because one side of the triangle is tangent (touching) to the circle while the other is the radius itself, we can conclude that the angle that is not named is 90°.

Knowing this, we can then add 36° and 90° to get 126°.

All of the angles in a triangle add up to 180°; therefore, we can subtract 126° from 180° to get 54°.

I really hope this helps and explains it well!

Answer:

x = 54°

Step-by-step explanation:

Since the lower segment is a tangent to the circle then

the angle between the tangent and the diameter is right.

The sum of the 3 angles in a triangle = 180°

Subtract the sum of the 2 known angles from 180 for x, that is

x = 180° - (90 + 36)° = 180° - 126° = 54°

Answer:

15/20 or 3/4

Step-by-step explanation:

9 green marbles(GM) + 5 yellow marbles(YM) + 6 red marbles(RM) = 20 marbles total(TM)

GM = 9/20

YM = 5/20

RM = 6/20

TM = 20/20

For the probability of choosing a GM or RM you just add their respective values:

9/20 + 6/20 = 15/20

Simplified this answer is 3/4

Probability of selecting a green or red marble is 3/4

Given that;

Number of green marble = 9

Number of red marble = 6

Number of yellow marble = 5

Find:

Probability of selecting a green or red marble

Computation:

Probability of selecting a green = 9 / [9 + 6 + 5]

Probability of selecting a green = 9 / 20

Probability of selecting a red = 6 / [9 + 6 + 5]

Probability of selecting a green = 6 / 20

Probability of selecting a green or red marble = [9/20] + [6/20]

Probability of selecting a green or red marble = 15 / 20

Probability of selecting a green or red marble = 3/4

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The angle between the legs labeled [tex]x[/tex] and [tex]y[/tex] is complementary to the angle with measure 31 degrees, so that angle has measure 90 - 31 = 59 degrees. Then

[tex]\sin59^\circ=\dfrac{400}x\implies x=\dfrac{400}{\sin59^\circ}\approx466.7[/tex]

Answer:

C

Step-by-step explanation:

Given

cosB = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{A B}[/tex] = [tex]\frac{255}{257}[/tex]

Then the hypotenuse AB = 257 and BC = 255

sinA = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{255}{257}[/tex]

A = [tex]sin^{-1}[/tex] ([tex]\frac{255}{257}[/tex]) = 82.8° → C

Answer:

13.8 percent

Step-by-step explanation:

75 // common factor is 3

The answer is x=8.6 units

After simplifying the fraction, we find that x = 7/17.

In
ΔABC, J is on AB, K is on BC, and JK is parallel to AC. We're given that JB = 5, AJ = 17, BK = x+4, and KC = 5x. By the properties of parallel lines and similar triangles, we can state that ΔAJK ~ ΔACB. Considering the sides of these triangles, the ratios of corresponding sides must be equal, which gives us the proportion:

AJ/JB = AC/BC

Substituting in given values and variables, we get:

17/5 = (17 + 5)/(5x + x + 4)

Solving for x, we multiply each side by the denominators to eliminate the fraction:

17(5x + x + 4) = 5(22)

85x + 17x + 68 = 110

102x + 68 = 110

102x = 42

x = 42/102

x = 7/17

After simplifying the fraction, we find that x = 7/17.

Answer:

80 min = 1 hr 20 min

1 hr 20 min after 1:57 pm is 3:17 pm.

Between 3:17 pm and 4:00 pm there are 43 minutes.

Tony has 43 minutes between the end of the project and the beginning of band practice.

Step-by-step explanation:

Tony had 46 minutes between the end of the project and the beginning of band practice.

To solve this problem, we need to calculate the time Tony finished his math project and then determine how much time there was between the end of the project and the start of his band practice.

1. First, we find the time Tony finished his math project. Since he started at 1:57 pm and worked for 80 minutes, we add 80 minutes to 1:57 pm.

2. To add 80 minutes to 1:57 pm, we convert 80 minutes into hours and minutes. There are 60 minutes in an hour, so 80 minutes is 1 hour and 20 minutes (since 60 minutes is 1 hour and 20 minutes is the remainder).

3. Adding 1 hour and 20 minutes to 1:57 pm gives us 3:17 pm (1:57 pm + 1 hour = 2:57 pm, and then adding the remaining 20 minutes gives us 3:17 pm).

4. Now, we need to find out how much time is between 3:17 pm (when Tony finished his project) and 4:00 pm (when his band practice starts).

5. From 3:17 pm to 4:00 pm is a duration of 45 minutes (from 3:17 pm to 4:00 pm is 43 minutes, plus the 2 minutes from 3:17 pm to 3:19 pm).

6. However, we must remember that Tony started at 1:57 pm, which is 1 minute before 1:58 pm. So, we need to add this 1 minute to the total time between the end of the project and the start of band practice.

7. Therefore, the total time Tony had between finishing his math project and starting band practice is 45 minutes + 1 minute = 46 minutes.

Answer:

  5

Step-by-step explanation:

Vertices are where edges meet. Count the circles on the diagram below.

Answer:

1,560

Step-by-step explanation:

156=2

2x10=20

156x10=1560

Answer:156 times 10 thats your answer

Step-by-step explanation:

Answer: [tex]JK=8[/tex]

Step-by-step explanation:

You can observe in the figure that JK is a tangent and KH is a secant and both intersect at the point K. Then, according to the Intersecting secant-tangent Theorem:

[tex]JK^2=KE*KH[/tex]

You know that:

[tex]KH=KE+HE[/tex]

Then KE is:

[tex]KE=KH-HE[/tex]

[tex]KE=16-12[/tex]

[tex]KE=4[/tex]

Now you can substitute the value of KE and the value of KH into  [tex]JK^2=KE*KH[/tex] and solve for JK. Then the result is:

[tex]JK^2=4*16\\JK^2=64\\JK=\sqrt{64}\\JK=8[/tex]

Both intersecting point K, JK is a tangent and KH is a secant. You can use the intersecting secant-tangent Theorem:

JK^2=KH*EK

First you can do

KH=EK+EH

KE=4

Then you can substitute.

JK^2=64

JK=8

Answer:

Step-by-step explanation:

It's a quadratic function. The graph is a parabola.

The coefficient of x² is equal 1 > 0. Therefore the parabola is open up.

Conclusion: The minimum is in a vertex.

[tex]f(x)=ax^2+bx+c\\\\(h,\ k)-vertex\\\\h=\dfrac{-b}{2a},\ k=f(h)[/tex]

We have

[tex]g(x)=x^2-6x-12\to a=1,\ b=-6,\ c=-12\\\\h=\dfrac{-(-6)}{2(1)}=\dfrac{6}{2}=3\\\\k=g(3)=3^2-6(3)-12=9-18-12=-21\\\\(3,\ -21)-vertex[/tex]

Answer:

b = 14[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Since the triangle is right use the cosine ratio to find b

cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{b}{28}[/tex]

Multiply both sides by 28

28 × cos45° = b

28 × [tex]\frac{\sqrt{2} }{2}[/tex] = b ( cancel the 28 and 2 )

b = 14[tex]\sqrt{2}[/tex]

Answer:

14√2.

Step-by-step explanation:

This is a 45-45-90 triangle so the ratio of the sides is 1:1:√2.  ( By the Pythagoras theorem).

so b / 28 = 1 / √2

√2 b = 1*28

b = 28 / √2

= 28√2 / 2

= 14√2  answer.

Answer:

A. It has reflectional symmetry

B. It is symmetrical

D. It has five lines of symmetry

Step-by-step explanation:

we know that

A regular pentagon has 5 sides and 5 lines of symmetry. The number of lines of symmetry in a regular polygon is equal to the number of sides

Every regular polygon has reflectional symmetry

Regular polygons are symmetrical

therefore

A. It has reflectional symmetry ------> Is true

B. It is symmetrical -----> Is true

C. It has exactly one line of symmetry ----> Is false

D. It has five lines of symmetry -----> Is true

Answer:

A. It has reflectional symmetry

B. It is symmetrical

D. It has five lines of symmetry

Step-by-step explanation:

Answer:

Final answer in simplified form is [tex]9x^2-4x+5 [/tex]

Step-by-step explanation:

Given expression is [tex](x+2)-(-9x^2+5x-3) [/tex]

Now we need to find an equivalent expression for[tex](x+2)-(-9x^2+5x-3) [/tex]

First we can distribute the negative sign and remove the parenthesis the combine like terms

[tex](x+2)-(-9x^2+5x-3) [/tex]

[tex]=x+2+9x^2-5x+3 [/tex]

[tex]=9x^2+x-5x+2+3 [/tex]

[tex]=9x^2-4x+5 [/tex]

Hence final answer in simplified form is [tex]9x^2-4x+5 [/tex]

Answer:

It's the second option x = (3y - 11) / 5.

Step-by-step explanation:

3/5 = x+1/y-2

Cross multiplying:

3(y - 2) = 5(x + 1)

3y - 6 = 5x + 5

5x =  3y - 6 - 5

5x = 3y - 11

x = (3y - 11) / 5.

At least 5 Schools have participated

Answer:

The point that is being intersected is (4,2).

Answer:

Step-by-step explanation:

Amplitude is twice the coefficent of the sine function. In this case, [tex]2*2=4[/tex]

Period is [tex]2\pi[/tex] divided by the coefficent of x, in this case, [tex] \frac {2\pi} 1 =2\pi [/tex]

Phase shift, is how much you sum or subctract from x inside the sine, in this case [tex] \pi [/tex].

Midline you get by hiding the sine and reading what's left, in this case, -4.

Use pemdas (parenthesis, exponents, multiplication/division, addition/subtraction) This is the list in which you need to simplify the expression. Do any parenthesis first, so 2.5 + - 0.6 = 1.9 and 3.75 + - 0.7 = 3.05

70(1.9) + 25(3.05) now multiply

133 + 76.25; add

The new expression is 209.25

To simplify the expression, we need to apply the order of operations. After simplifying the expressions within the parentheses, we multiply and add the results to get the final answer of 209.25.

To simplify the expression using the order of operations, we need to follow the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication, and Division (from left to right), and Addition and Subtraction (from left to right). Let's break down each step:

Therefore, the simplified expression is 209.25.

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Answer:

P(A ∩ B) = 11/15 ⇒ answer A

Step-by-step explanation:

* Lets revise the meaning of ∪ and ∩

# A ∪ B means all the elements in A or B without reputation

- Ex: If A = {2 , 3 , 5} and B = {3 , 4 , 7}

∴ A ∪ B = {2 , 3 , 4 , 5 , 7} ⇒ we don't repeat the element 3

# A ∩ B means all the elements in A and B

- Ex: If A = {2 , 3 , 5} and B = {3 , 4 , 7}

∴ A ∩ B = {3}

- From the examples above

∵ n(A) = 3 and n(B) = 3

∵ n(A ∪ B) = 5

∵ n(A ∩ B) = 1

∴ n(A) + n(B) = n(A ∪ B) + n(A ∩ B)

* Now lets solve the problem

∵ P(A ∪ B) = 11/15

∵ P(x) = n(x)/total

- That means the total elements in the problem is 15 and n(A ∪ B) is 11

∴ n(A ∪ B) = 11

∵ P(A) = 2/3 ⇒ simplest form

- To find P(A) without simplification and you now the total is 15

  then multiply up and down by 5

∴ P(A) = (2×5)/(3×5) = 10/15

∴ n(A) = 10

∵ P(B) = 4/5 ⇒ simplest form

- To find P(B) without simplification and you now the total is 15

  then multiply up and down by 3

∴ P(B) = (4×3)/(5×3) = 12/15

∴ n(B) = 12

- To find n(A ∩ B) use the rule above

∵ n(A) + n(B) = n(A ∪ B) + n(A ∩ B)

∵ 10 + 12 = 11 + n(A ∩ B) ⇒ subtract 11 from both sides

∴ 11 = n(A ∩ B)

- The number of elements in A ∩ B is 11

∵ P(A ∩ B) = n(A ∩ B)/total

∴ P(A ∩ B) = 11/15

Answer:

It would take Jenny 20 minutes to walk 1 mile

Step-by-step explanation:

To find how many minutes it would takes her to walk 1 mile, you have to find out the rate of her walking 2.5 miles.

So divide 2.5/50

She walked 0.05 miles per minute

there are 20 0.05 in one mile so

It would take Jenny 20 minutes to walk 1 mile

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Answer:

y = 8

Step-by-step explanation:

Since the 2 triangles are similar then the ratio of corresponding sides are equal, that is the sides 15 and 10 and y + 4 and y, thus

[tex]\frac{15}{10}[/tex] = [tex]\frac{y+4}{y}[/tex] ( cross- multiply )

10(y + 4) = 15y ← distribute left side

10y + 40 = 15y ( subtract 10y from both sides )

40 = 5y ( divide both sides by 5 )

8 = y

Answer:

4.62%

Step-by-step explanation:

To find the percentage of patient with AB blood type, we would need:

If you see the Row labeled "AB" and go to the last column labeled "Total", we can see that 33 patients have blood type AB.

If you look at the right most block, we see the grand total of all patients of all blood types, which is 714 patients.

To find our answer, we divide 33 by 714 and multiply by 100 to get percentage.

Percentage of patients with blood type AB = [tex]\frac{33}{714}*100=4.62[/tex]

Answer:

4.6%

Step-by-step explanation:

To find the percentage of patient with AB blood type, we would need:

total number of patients with blood type AB

total number of all patients of all blood types

(33/714)* 100 = 4.6%

Answer:

The diagonal of a square with 90 ft. per side is 127.28 which should be rounded down to 127 and the throw from 2nd to 3rd is 90 ft totaling 217 ft

The baseball moves 217.4 feet across the field in total.

Measured from the middle of the backstop to the apex of the home plate. Place second base in the centre by drawing a line from the backstop's centre point over the pitcher's mound, through the apex. The distance that needs to be measured is between the centre of the second base and the top of the home plate.

So we are given that each side of a square is 90 feet.

By finding how far the ball will travel, we are basically finding the distance from 2nd base to home

Well, let's picture a baseball field, and we find out that they are diagonal across from one another.

Well, let's draw a diagonal connecting home to 2nd base.

Since the field is a square, it has a right angle at 1st base

We now know 2 legs in a right triangle, which calls for the Pythagorean Theorem

(You could also do a 45-45-90 special right triangle, which would give you the answer very quickly)

So we have 90²+90²=c²

Which is

16200=c²

We are finding c

, so √16200=c

We can simplify this to √162⋅100 which is 10√162

Then we can simplify this to 10√81⋅2, that is 10⋅9√2

Finally, we multiply the values outside of the root to get = 90√2

the throw from 2nd to 3rd is 90 ft

total distance covered = 90 + 90√2

total distance covered = 217.4

Therefore, baseball travels in the field a total of 217.4 feet

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Answer:

42 min

Step-by-step explanation:

Joanna takes 2 mins to send a text.

2 mins = 2 x 60 sec = 120 sec

Anna takes 40 seconds to send a text

120 ÷ 40 = 3

Anna can text 3 messages in 120 sec

Together, in 120 sec ,

both of them can send out 1 + 3 = 4 texts

Number of 120 seconds needed to send 84 texts

= 84 ÷ 4

= 21

Number of seconds needed

= 21 x 120

= 2520

25020 sec = 2620 ÷ 60 min = 42 min

Secant sec(x) = 1/cos

Answer:

Step-by-step explanation:

Easiest way, pick any two even numbers in that range, they will have at least 2 as a common factor.