the function f(x) = -3cos(3x+ x/4 ) has amplitude of what

Answer:

[tex]67\dfrac{1}{2}[/tex] sq, units.

Step-by-step explanation:

See the diagram of the parallelogram with given dimensions.

We know, the area of a parallelogram = Length of any side × Perpendicular distance of this side from the opposite parallel side.

Here, it is given that the length of a pair of parallel sides is 9 units and the perpendicular distance between those parallel lines is 7.5 units.

Therefore, the area of the parallelogram is (9 × 7.5) = 67.5 square units. (Answer)

Hence, in fraction the area can be expressed as [tex]67\dfrac{1}{2}[/tex] sq, units. (Answer)

Answer:

(a) 65 gallons per minute

(b) 280 gallons

(c) 8080 gallons

(d) 150 minutes.

Step-by-step explanation:

Water is filled up by pumps into a tank at a constant rate.

The volume of water in the tank V, in gallons, is given by the equation  

V(t) = 65t + 280 ......... (1), where t is the time, in minutes.  

(a) The rate at which water is pumped into the tank is 65 gallons per minute. (Answer)

(b) 280 gallons of water was there in the tank when the pumps were turned on because f(0) = 65 × 0 + 280 = 280. (Answer)

(c) After 2 hours i.e. (2 × 60) = 120 minutes the volume of water in the tank will be f(120) = 65 × 120 + 280 = 8080 gallons. (Answer)

(d) The tank has a capacity of 10000 gallons of water.

So, if the tank starts to overflow after t minutes, then  

10000 = 65t + 280

⇒ 65t = 9720

⇒ t = 149.53 minutes ≈ 150 minutes (Answer)

Final answer:

The rate at which water is being pumped into the tank is 65 gallons per minute, the tank initially had 280 gallons of water, after two hours the volume will be 8,080 gallons, and the pumps will turn off after approximately 150 minutes when the volume reaches 10,000 gallons.

Explanation:

The water tank problem can be analyzed step by step based on the given linear equation v(t) = 65t + 280, which describes the volume V of water in gallons as a function of time t in minutes.

(a) Rate of Water Being Pumped

The coefficient of t in the equation represents the rate at which water is being pumped into the tank. Therefore, the water is being pumped at a constant rate of 65 gallons per minute.

(b) Initial Volume of Water

The constant term in the equation, 280, represents the volume of water that was in the tank when the pumps were turned on. This means the tank initially had 280 gallons of water.

(c) Volume After Two Hours

To convert two hours to minutes, we multiply by 60 minutes per hour, giving us 120 minutes. Plugging this value into the equation gives us v(120) = 65(120) + 280 = 7,800 + 280 = 8,080 gallons. So, after two hours, the volume of water in the tank would be 8,080 gallons.

(d) Time to Reach 10,000 Gallons

To find the time when the volume reaches 10,000 gallons, we set the equation equal to 10,000 and solve for t: 10,000 = 65t + 280. Subtracting 280 from both sides gives us 9,720 = 65t, and dividing both sides by 65 gives us t ≈ 149.54 minutes. To the nearest minute, the pumps will turn off after approximately 150 minutes.

1 + 2(4x + 1)​

mutiply the bracket by 2

(2)(4x)= 8x

(2)(1)= 2

1+8x+2

1+2+8x ( rearranging)

answer:

3+8x or 8x+3

Answer:

8x+3

Step-by-step explanation:

1+8x+2

1+2=3

8x+3 or 3+8x

The possible transformations that establish congruence between shapes are dilation, translation, and reflection.

The possible rules that represent a transformation mapping one shape onto another to establish congruence are:

A dilation by a scale factor of 3 about the origin stretches or shrinks the shape uniformly in all directions. A translation moves the shape without changing its size or shape. A reflection across a line is a flip of the shape over that line. These transformations can establish congruence between shapes.

Transformations that establish congruence between shapes by preserving size, shape, and orientation ensure that the transformed shape aligns with the original shape. The correct answer is option

B) A translation to the right 2 and down 6.

C) A reflection across the line y=2.

D) A counter-closckwise rotation of 90 degrees about the origin.

The rules that represent transformations mapping one shape onto another to establish congruence are:

B) A translation to the right 2 and down 6, which preserves both size and shape, simply moving the shape to a different location without changing its orientation or proportions.

C) A reflection across the line y=2, which reflects the shape across a line, maintaining its size and shape but reversing its orientation.

D) A counter-clockwise rotation of 90 degrees about the origin, which rotates the shape by a right angle, preserving its size and shape while changing its orientation.

These transformations preserve congruence by maintaining the size, shape, and orientation of the original shape.

Options B, C, and D represent transformations that map one shape onto another to establish their congruence, preserving size, shape, and orientation.

8 Hours.

If you want his debt to be 0, as in he has nothing left to owe, we will set d (his debt) to 0

0 = 100 - 12.5h

Subtract 100 to move it to the other side

-100 = -12.5h

Divide each side by -12.5

8 = h

Answer:

27

Step-by-step explanation:

square root of 9 is 3, so you multiply 3 by 9.

Answer:

27

Step-by-step explanation:

Multiply the number of hours worked by how much is made per hour:

7 hours x $10.25 per hour = $71.75 total

so it's 71.76  all i did was multiply 7 x 10.25 which equals 71.76

Answer:

The probability of getting 12 successes out of 15 trials is [tex]P(12) = 0.2501[/tex].

Step-by-step explanation:

Given:

The probability distribution is binomial distribution.

Number of trials are, [tex]n=15[/tex]

Number of successes are, [tex]x=12[/tex]

Probability of success is, [tex]p=0.8[/tex]

Therefore, probability of failure is, [tex]q=1-p=1-0.8=0.2[/tex]

Now, probability of getting 12 successes out of 15 trials is given as:

[tex]P(X=x)=_{x}^{n}\textrm{C}p^{x}q^{n-x}\\P(12)=_{12}^{15}\textrm{C}(0.8)^{12}(0.2)^{15-12}\\P(12)=455\times 0.8^{12}\times 0.2^{3}\\P(12)=0.2501[/tex]

Therefore, the probability of getting 12 successes out of 15 trials is 0.2501.

Applying the binomial distribution, we get that P(X = 12) = 0.2501.

-------------------------

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, given by:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, defined by the formula below.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Considering that p is the probability of a success on a single trial.

For this problem, the parameters are [tex]n = 15, p = 0.8[/tex], and we want to find P(X = 12). Then:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 12) = C_{15,12}.(0.8)^{12}.(0.2)^{3} = 0.2501[/tex]

Thus P(X = 12) = 0.2501.

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Answer:

The total cost is $95.32.

Step-by-step explanation:

Given:

Total came to $76.75. There is an 8% sales tax and 15% tip.

Now, to find the total cost.

8% sales tax is there so we calculate the amount after adding sales tax:

$76.75 + 8% of $76.75

[tex]76.75+\frac{8}{100}\times 76.75[/tex]

[tex]76.75+0.08\times 76.75[/tex]

[tex]76.75+6.14[/tex]

[tex]82.89[/tex]

The cost after sales tax is $82.89.

Now, the cost after 15% tip:

$82.89 + 15% of $82.89

[tex]82.89+\frac{15}{100}\times 82.89[/tex]

[tex]82.89+0.15\times 82.89[/tex]

[tex]82.89+12.43[/tex]

[tex]95.32[/tex]

The cost after the tip is $95.32.

Therefore, the total cost is $95.32.

Answer:

Part a) [tex]x+y < 400[/tex]

Part b) The graph in the attached figure

Part c) see the explanation

Part d) The number of seat tickets sold must be less than 300 tickets

Step-by-step explanation:

Part a) write an inequality to describe the constraints. specify what each variable represents

Let

x ----> number of lawn tickets sold

y ----> number of seat tickets sold

we know that

The sum of the number of lawn tickets sold plus the  number of seat tickets sold must be less than 400 tickets

so

The linear inequality that represent this situation is

[tex]x+y < 400[/tex]

Part b) use graphing technology to graph the inequality. sketch the region on the coordinate plane

we have

[tex]x+y < 400[/tex]

using a graphing tool

The solution is the triangular shaded area of positive integers (whole numbers) of x and y

see the attached figure

Remember that the values of x and y cannot be a negative number

Part c) name one solution to the inequality and explain what it represents in that situation

we know that

If a ordered pair lie on the solution of the inequality, then the ordered pair is a solution of the inequality (the ordered pair must satisfy the inequality)

I take the point (200,100)

The point (200,100) lie on the triangular shaded area of the solution

Verify

Substitute the value of x and the value of y in the inequality and compare the result

For x=200,y=100

[tex]x+y < 400[/tex]

[tex]200+100 < 400[/tex]

[tex]300 < 400[/tex] --> is true

so

The ordered pair satisfy the inequality

therefore

The ordered pair is a solution of the inequality

That means ----> The number of lawn tickets sold was 200 and the number of seat tickets sold was 100

Part d) if you know that exactly 100 lawn tickets were sold, what can you say about the number of seat tickets?

we have that

x=100

substitute in the inequality

[tex]100+y < 400[/tex]

solve for y

subtract 100 both sides

[tex]y < 400-100[/tex]

[tex]y < 300[/tex]

therefore

The number of seat tickets sold must be less than 300 tickets

Answer:

5.8m

Step-by-step explanation:

The question lacks enough information to provide a definitive answer. If we know the width of a cart, we can divide 43 by the cart width to find out how many carts fit in a row.

Unfortunately, we can't definitively answer this question as it doesn't specify the width of each cart. The number of carts that fit in a row greatly depends on the width of each cart. To calculate this, you would need to divide the total row width (43 feet) by the width of each individual cart. For example, if each cart was assumed to be 1 foot wide, then a total of 43 carts would fit in a row. However, if each cart was assumed to be 2 feet wide, then only 21 carts (with 1 foot left over) would fit in a row.

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Answer:

The correct answer is 333  1/ 3 ml 30% solution and 166  2/ 3 ml of 45% solution.  

step-by-step explanation:

Set up 2 equations. Let x be the 30% solution and y be the 45% solution. Then you have x + y =500 and .3x +.45y = .35*500. Then solve the system.

Answer:

A is your correct answer.

Step-by-step explanation:

Final answer:

The horizontal asymptote indicates that as more pure acid is added, the concentration approaches 1, meaning the acid concentration trends towards 100% purity but never fully reaches it. (Option D)

Explanation:

The horizontal asymptote of the function f(x) = x + 60 / (x + 300) describes the behavior of the acid concentration as the volume of pure acid x becomes very large. When an increasingly larger volume of pure acid is added, the concentration of the acid in the new substance approaches a certain value. This implies that, no matter how much more acid is added past a certain point, the concentration doesn't change significantly.

The correct statement regarding the horizontal asymptote is: D. As more pure acid is added, the concentration of acid approaches 1. This means that the concentration of the acid will get closer and closer to 100%, or pure acid, but it will never actually reach that concentration because you are always adding the acid to some amount of solution.

Answer:

Line c ║ line d, applying the converse of the alternate exterior angles theorem.

Step-by-step explanation:

See the given diagram attached.

It is given that ∠ 11 = ∠ 13.

Hence, from this we can conclude that line c ║ line d, applying the converse of the alternate exterior angles theorem.

The alternate exterior angle theorem says that if one line is the transverse line of any two other parallel lines then the alternate exterior angles so generated will be equal. (Answer)

Answer:

c∥d, Converse of the Alternate Exterior Angles Theorem

Step-by-step explanation:

I took the test other answer is right

Answer:

Number of  children's tickets sold  =  150

Number of adult's tickets sold = 250

Step-by-step explanation:

The total number of tickets sold  = 400

Let us assume the number of children's tickets   = m

So, the number of adult's ticket's sold  = 400 - m

Here, the cost of 1 movie ticket for adult  = $8.00

So, the cost of (400 -m) adult tickets = (400 - m) ( Cost of 1 adult ticket)

= (400 - m) ($8) = 3200 - 8 m

The cost of each ticket for child = $5.00

The cost of m children  tickets = m ( Cost of 1 children ticket)

= m($5) = 5 m

Now, total cost of tickets = Money spend on (Adult's + children's) Ticket

⇒ 2750 =  (3200 - 8 m) +  (5 m)

or,  2750 - 3200 = -8 m + 5 m

or, -450 = -3 m

or, m = 450/3 = 150

or, m = 150

Hence, the number of  children's tickets = m = 150

The number of adult's tickets sold =  400 - m = 400 -150 = 250

In Mathematics, if a six-digit code can have each digit repeat there are 10 options (0-9) for each position. Having six positions, we multiply the possibilities together, leading us to a conclusion of 1,000,000 possible codes.

The calculation of different codes for a house's security system is a problem of permutation and combination under the field of Mathematics. The code consists of six digits and each digit can be repeated, meaning that there are 10 possibilities (0-9) for each of the 6 positions in the code.

Therefore, for each of the six positions in the code, there are 10 possibilities. To determine the total number of possible codes, we would multiply the number of possibilities for each digit together: 10*10*10*10*10*10 = 1,000,000. So, there are one million possible combinations for the 6-digit code.

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Answer:

21/8

Step-by-step explanation:

3(7/8)=21/8

To multiply a whole number by a fraction, you have to change the whole number (the 3) into a fraction. To do this, simply put the 3 over 1.

3/1 x 7/8. Multiplying fractions is so easy because all you have to do is multiply the numerators together and then the denominators together.

3x7=21

1x8=8

21/8

This fraction cannot be reduced, but it can be rewritten as a mixed number.

21 divided by 8 is 2 with a remainder of 5.

The answer is 21/8 or 2 5/8. (they mean the same thing)

Answer:

Answer is A (-3p^8/4q^3)

Step-by-step explanation:

We want to simplify a fraction. The simplification is:

[tex]\frac{15*p^{-4}q^{-6}}{-20*p^{-12}*q^{-3}} = \frac{-3*p^8}{4*q^3}[/tex]

So we start with the fraction:

[tex]\frac{15*p^{-4}q^{-6}}{-20*p^{-12}*q^{-3}}[/tex]

Where:

Now, remember the rule:

[tex]\frac{x^n}{x^m} = x^{n - m}[/tex]

Then we can rewrite:

[tex]\frac{15*p^{-4}*q^{-6}}{-20*p^{-12}*q^{-3}} = \frac{15}{-20}*\frac{p^{-4}}{p^{-12}}*\frac{q^{-6}}{q^{-3}} \\\\= -\frac{-3}{4}*p^{-4 - (-12)}*q^{-6 - (-3)}\\\\= -\frac{-3}{4}*p^{8}*q^{-3}\\\\= \frac{-3*p^8}{4*q^3}[/tex]

And we can't keep simplifying this, so this is the correct answer.

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Answer:

Step-by-step explanation:

see attached to identify which is the tenth's place

How you round the tenth's place depends on the digit in the hundredths place.

If the hundredths digit is less than 5, then you keep the tenths place the same (i.e round down)

If the hundredths digit is greater or equal than 5, then you increase the tenths place by 1 (i.e round up)

Answer:

250 239 439for lawns he mods $25

There are 2 answers: Choice 1, Choice 4

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

Why is this? Because we use the rule

P(A & B) = P(A) * P(B)

which only works if events A and B are independent

----

For the first answer choice,

P(A) * P(B) = 0.6*0.4 = 0.24 = P(A & B)

so that matches.

The same applies to the fourth answer choice as well

P(A) * P(B) = 0.3*0.2= 0.06 = P(A & B)

----

The other answer choices don't match up.

The second answer choice has

P(A) * P(B) = 0.3*0.4 = 0.12 but that doesn't match with the 0.70 given

Similarly for the third answer choice,

P(A) * P(B) = 0.5*0.1 = 0.05 which doesn't match with the 0.60

Answer:

Yes

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Given that the the difference of  cubes is

a³ - b³ = (a - b)(a² + ab + b²)

Given

64[tex]x^{6}[/tex] - 27 ← a difference of cubes

with a = 4x² and b = 3, thus

= (4x²)³ - 3³

= (4x² - 3)(16[tex]x^{4}[/tex] + 12x² + 9) ← in factored form

The required expression (4x^2-3)(16x^4+12x^2+9).

To evaluate 64x^6-27 as a^3-b^3=(a-b)(a^2+ab+b^2).

Cubic identity is given as [tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex].

Here,
=64x^6-27
=(4x^2)^3-3^3

Such that, a =4x^2 and b = 3.
Put a and b in  [tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex].

[tex](4x^2)^3-3^3=(4x^2-3)(16x^4+12x^2+9).[/tex]

Thus, the required expression (4x^2-3)(16x^4+12x^2+9).

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Answer:

Part 1) The domain is the interval (-∞,-7) ∪ (-7,0) ∪ (0,∞)

Part 2) The domain is the interval (-∞,0) ∪ (0,2) (2,∞)

Part 3) The domain is the interval (-∞,-6) ∪ (-6,6) ∪ (6,∞)

Step-by-step explanation:

Part 1) we have

[tex]\frac{32}{y}-\frac{y+1}{y+7}[/tex]

we know that

The denominator cannot be equal to zero

so

The value of y cannot be equal to 0 or cannot be equal to -7

The domain for y is all real numbers except the number -7 and the number 0

The domain in interval notation is

(-∞,-7) ∪ (-7,0) ∪ (0,∞)

Part 2) we have

[tex]\frac{y^2+1}{y^2-2y}[/tex]

we know that

The denominator cannot be equal to zero

[tex]y^2-2y=0\\y^2=2y\\y=2[/tex]

so

The value of y cannot be equal to 0 or 2

The domain for y is all real numbers except the number 0 and 2

The domain in interval notation is

(-∞,0) ∪ (0,2) (2,∞)

Part 3) we have

[tex]\frac{y}{y-6}+\frac{15}{y+6}[/tex]

we know that

The denominator cannot be equal to zero

so

The value of y cannot be equal to 6 or cannot be equal to -6

The domain for y is all real numbers except the number -6 and the number 6

The domain in interval notation is

(-∞,-6) ∪ (-6,6) ∪ (6,∞)

Answer:

(6,4) is not a solution of y > -x/2 + 7 because (6,4) is on the line

The answer is D.

Hope this helps!

Answer:

No,because (6,4) is on the line.

Step-by-step explanation:

We are given that an inequality equation

[tex]y>-\frac{1}{2}x+7[/tex]

We have to find that the ordered pair (6,4) is a solution of given inequality or not.

[tex]y>-\frac{x}{2}+7[/tex]

Substitute x=6

[tex]y>-\frac{6}{2}+7[/tex]

[tex]y>-3+7[/tex]

[tex]y>4[/tex]

The value of y is greater than 4 not equal to 4.

Therefore, (6,4) is not a solution of given inequality.

No,because (6,4) is on the line.

Answer:

3/23

Step-by-step explanation:

Numbers of horses : 6

Number of total animals in farm : 28 + 12 + 6 = 46

The ratio of horses to toral animals : 6/46 ➡ simplified 3/23

Answer:75%

Step-by-step explanation:im sorry I can't get it out in words but you have the answer

Answer 67

Step-by-step explanation:65:&:8/&/&&:

Average rate of change in height will be 0.59 inch per day.

Experiment with plants started with,

Let the variable defining change in the height per day of the plant = x

Change in the height of plant A after 2 weeks or 14 days = 14x cm

Height of the plant A initially = 2.5 cm

Height of the plant after 2 weeks = 14x + 2.5

If height of the plant A after 2 weeks = y

Linear equation defining the height of the plant after 2 weeks will be,

y = 14x + 2.5

Plant A is 23.5 cm tall after 2 weeks,

23.5 = 14x + 2.5   [Substitution of y = 23.5]

23.5 - 2.5 = 14x + 2.5 - 2.5

21 = 14x

x = 1.5 cm

Since, 1 cm = 0.393701 inches

Therefore, 1.5 cm = 1.5 × 0.393701

                             = 0.591

                             ≈ 0.59 inches per day

      Hence, average rate of change in the height of plant A will be 0.59 inches per day.

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Answer:

(c)  For p = 15,  [tex]4x^2-p(x)+7[/tex] leaves a remainder of -2 when divided by (x-3).

Step-by-step explanation:

Here,  The dividend expression is  [tex]4x^2-p(x)+7[/tex] = E(x)

The Divisor = (x-3)

Remainder  = -2

Now, by REMAINDER THEOREM:

Dividend  = (Divisor x Quotient)  + Remainder

If ( x -3 ) divides the given polynomial with a remainder -2.

⇒  x = 3  is a  solution of given polynomial E(x)  - (-2) =  

[tex]E(x)  - (-2)  = 4x^2-p(x)+7 -(-2)  = 4x^2-p(x)+9[/tex] =  S(x)

Now, S(3) = 0

⇒[tex]4x^2-p(x)+9 = 4(3)^2 - p(3) + 9 = 0\\\implies 36 - 3p + 9 = 0\\\implies 45= 3p , \\or p  =15[/tex]

or, p =1 5

Hence, for p = 15,  [tex]4x^2-p(x)+7[/tex] leaves a remainder of -2 when divided by (x-3).