What is the approximate volume of a can that is 5 inches tall and has a 2.5 inch diameter?

ANSWER

[tex]\tan(\pi + \theta)= \frac{5}{12} [/tex]

EXPLANATION

We first obtain

[tex] \cos( \theta) [/tex]

using the Pythagorean Identity.

[tex]\cos ^{2} ( \theta) + \sin ^{2} ( \theta) = 1[/tex]

[tex] \implies \: \cos ^{2} ( \theta) + ( - \frac{5}{13} )^{2} = 1[/tex]

[tex]\implies \: \cos ^{2} ( \theta) + \frac{25}{169}= 1[/tex]

[tex]\implies \: \cos ^{2} ( \theta) = 1 - \frac{25}{169}[/tex]

[tex]\implies \: \cos ^{2} ( \theta) = \frac{144}{169}[/tex]

[tex]\implies \: \cos ( \theta) = \pm \: \sqrt{\frac{144}{169} } [/tex]

[tex]\implies \: \cos ( \theta) = \pm \: \frac{12}{13} [/tex]

In the third quadrant, the cosine ratio is negative.

[tex]\implies \: \cos ( \theta) = - \: \frac{12}{13} [/tex]

The tangent function has a period of π and [tex]\pi + \theta[/tex] is in the third quadrant.

This implies that:

[tex] \tan(\pi + \theta)= \tan( \theta) [/tex]

[tex]\tan(\pi + \theta)= \frac{ \sin( \theta) }{ \cos( \theta) } [/tex]

[tex]\tan(\pi + \theta)= \frac{ - \frac{ 5}{13} }{ - \frac{12}{13} } [/tex]

This gives us:

[tex]\tan(\pi + \theta)= \frac{5}{12} [/tex]

For this case we must find the product of the following expression:

[tex]-2x * (- 3x^2y) * (2y) =[/tex]

We take into account that:

[tex]- * - = +[/tex]

To multiply powers of the same base, the same base is placed and the exponents are added:

[tex]6x^{1 + 2}y * 2y =\\6x ^ 3 * 2y ^ {1 + 1} =\\12x ^ 3y ^ 2[/tex]

ANswer:

[tex]12x ^ 3y ^ 2[/tex]

Option A

In total, there are 16 marbles.

So the probability of first choosing a yellow marble is:

[tex]\frac{6}{16}[/tex]     (That's because in our bag if 16 marbles, 6 of them are yellow)

However, as stated in the question, we do not replace the marble.

That means we will now only have bag of 15 marbles in total (since we have already taken out the first marble)

So the probability of then choosing a blue marble is:

[tex]\frac{4}{15}[/tex] (that's because in our bag of 15 marbles, 4 of them are blue)

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

Finally to get the answer we multiply the two probabilities that we worked out. That's because in probability, and = multiply

So P(choosing a yellow marble) and P(choosing a blue marble)

= P(choosing a yellow marble)  times   P(choosing a blue marble)

So the final probability is:

[tex]\frac{6}{16}[/tex] × [tex]\frac{4}{15}[/tex] = [tex]\frac{24}{240}[/tex]

This simplifies down to [tex]\frac{1}{10}[/tex]

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

Answer:

The probability of first choosing a yellow marble and then a blue marble is:

[tex]\frac{1}{10}[/tex]

Answer:

B

Step-by-step explanation:

1° = 60 minutes = 3600 seconds

Answer:

  120 miles

Step-by-step explanation:

We have to "interpret" the problem statement, because its literal meaning is that it takes Adam a negative amount of time to drive the distance when driving faster. 2.5 times 4 hours is 10 hours. 10 hours less than 4 hours is -6 hours, meaning that driving faster gets Adam to the park 6 hours before he started driving.

So, we assume the intent of the problem is that driving faster multiplies Adam's travel time by a factor of 1/2.5, 2/5 of what it was at the lower speed. Since travel time is inversely proportional to speed, Adam's speed is effectively multiplied by 2.5 by driving faster. We can use the relation ...

  speed = distance/time

to relate the speeds (in mph) and times (in hours) given in the problem. For some distance d, we have ...

  45 + d/4 = 2.5(d/4) . . . . . adding 45 mph to his speed multiplies it by 2.5

Multiplying by 4 gives ...

  180 + d = 2.5d

  180 = 1.5d . . . . . . . . subtract d

  180/1.5 = d = 120 . . . divide by 1.5

Adam covers a distance of 120 miles to get to the park.

Answer:

25t + 3t = 9

Step-by-step explanation:

Since they are going to each other, their speeds need to be combined, since they both contribute to reduce the distance between them.

So, 25t + 3t = 9 is the answer, because

25t is the distance Jamal will drive in an hour,

3t is the distance Mike will walk in an hour,

9 is the distance to be covered so they can meet.

Answer:

25t + 3t = 9

Step-by-step explanation:

Answer:

he negative real number is -0.70.

Step-by-step explanation:

Answer:

[tex]P(A\hspace{3}or\hspace{3}B)=\frac{4}{5}=0.8 =80\%[/tex]

Step-by-step explanation:

If Events A and B are disjointed, this means that they are mutually exclusive events. Mutually exclusive events are those that if one event happens means that the other cannot occur. For this type of event the following properties are true:

[tex]A\cap B = \emptyset,\\\\P(A\cup B)=P(A\hspace{3}or\hspace{3}B)=P(A)+P(B)[/tex]

Therefore:

[tex]P(A\hspace{3}or\hspace{3}B)=P(A)+P(B)\\\\P(A\hspace{3}or\hspace{3}B)=\frac{8}{15} +\frac{4}{15} =\frac{12}{15} =\frac{4}{5} =0.8[/tex]

You can also write the result as a percentage just multiplying by 100:

[tex]P(A\hspace{3}or\hspace{3}B)=0.8*100=80\%[/tex]

Answer:

x = 5y + 6

Step-by-step explanation:

Add 5y to both sides

x - 5y + 5y = 5y + 6 (variable always goes first)

-5y + 5y = 0

x = 5y + 6

Answer:  

The correct option is C) x = 5y + 6.

Step-by-step explanation:

Consider the provided equation.

[tex]x - 5y = 6[/tex]

We need to solve the equation for x.

Add 5y to both sides of the equation.

[tex]x - 5y+5y = 6+5y[/tex]

Simplify the equation.

x=6+5y

Hence, the value of the equation for x is x=6+5y.

Therefore, the correct option is C) x = 5y + 6.

Answer:

  A)  6.3 in³

Step-by-step explanation:

The formula for the volume of a cone is ...

  V = (1/3)πr²h . . . . . where r is the radius and h is the height

Only 1/(2+1) = 1/3 of the volume of your cone is strawberry ice cream, so the volume of ice cream (in terms of cone diameter) is ...

  V = (1/3)(1/3)π(d/2)²h

  V = π(d/3)²(h/4) . . . . rearranged slightly

For our diameter of 3 inches and height of 8 inches, this is ...

  V = π(3 in/3)²(8 in/4) = 2π in³ ≈ 6.3 in³

The volume of strawberry ice cream is about 6.3 in³.

Hey there! Thanks for asking your question here on Brainly.

Let's split this question up into two parts: large and cold drink. Now that we have our two parts, we need to figure out which would be the numerator and which would be the denominator. Looking at the question, the size large would be the numerator because that is the part out of the whole we are finding. The whole would be cold drink because that is given, meaning that we are looking for the larges out of the entire cold drink section.

Now, we'll find the total amount of customers that ordered cold drinks for the whole part of our fraction. That is 25 customers. Next, we set the numerator of our fraction to the amount of customers that ordered large, cold drinks. Therefore, our fraction would be 5/25. The fraction in decimal form is 0.2, and in percent form is 20%.

Therefore, the probability that a customer ordered a large given that he or she ordered a cold drink is 20%.

Hope this helps! If there is anything else that I can help you with, please let me know! :)

Answer:

x3 + 5y2

Step-by-step explanation:

The expression 6x³ + 3y²– 5x³ + 2y² is equivalent to x³ + 5y² so option (C) will be correct.

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

An expression is a mathematical proof of the equality of two mathematical expressions.

A statement expressing the equality of two mathematical expressions is known as an equation.

Given,

6x³ + 3y²– 5x³ + 2y²

Combine all likely terms

(6x³ -  5x³) + (3y² + 2y²)

⇒ x³ + 5y²

Hence,The expression 6x³ + 3y²– 5x³ + 2y² is equivalent to x³ + 5y².

To learn more about expression,

https://brainly.com/question/14083225

#SPJ2

Answer:

(2, 8)

Step-by-step explanation:

There are a couple of different ways to do this, but I am going to use substitution since we already have one of those equations solved for y.  If y=3x+2, then we can sub 3x+2 in for y in the other equation:

-3x + 2(3x + 2) = 10 and

-3x + 6x + 4 = 10 and

3x + 4 = 10 and

3x = 6 so

x = 2.  Now that we know x = 2, we can sub a 2 in for x in either equation to solve for y:

y = 3x + 2 gives us, with the substitution, y = 3(2) + 2 so y = 8.  The solution set is (2, 8)

After calculating the monthly costs for Emily's usage, Company A would cost $400 while Company B would cost $230. Therefore, Company B is the better choice for Emily as it offers a lower total bill.

To determine which cell phone company, A or B, offers a better monthly plan for Emily who uses 400 texts, 90 minutes of talk, and 2.1 gigs of data per month, we need to calculate the total monthly costs for both companies.

Company A:

Company B:

After calculating the costs, it is clear that Company B offers a lower total bill despite the higher monthly flat fee. Hence, Emily should choose Company B because the total bill will be lower.

Answer:

For an 8-ounce salad would cost $1.52

Step-by-step explanation:

Every ounce would cost $0.19.

So you would multiply the cost with how much you would buy.

0.19(cost per ounce)×8(how much ounce)=1.52(total pay)

Answer: B. F(x) = 0.19x ; $1.52

Step-by-step explanation:

To find the cost of 8 ounce sale , substitute 8 for x .

F(x)= 0.19x

F(8)= 0.19(8)

F(8)=1.52

[tex]|\Omega|=6\cdot2=12\\|A|=4\cdot1=4\\\\P(A)=\dfrac{4}{12}=\dfrac{1}{3}[/tex]

Answer:

D.  1/3.

Step-by-step explanation:

Probability(Rolling a number < 5) = 2/3 and

probability( Getting a head) = 1/2

The required probability , since the 2 events are independent is the product of the above  = 2/3 * 1/2 = 1/3.

Answer:

four base n minus 3 is equal to 21

Step-by-step explanation:

this is verbal

Answer:

50m

Step-by-step explanation:

By using the information we have, we can create an equation using the Pythagorean theorem to solve for r. Once we have r double it to get diameter

Answer:

The answer is 50m

Final answer:

To find the total combined premium, a 10% discount is applied to the $1,000 homeowner premium, totaling $100 in savings. The new homeowner premium is $900, which is then added to the $1,500 auto premium, resulting in a total combined premium of $2,400.

Explanation:

The student has asked a question about calculating combined insurance premiums when a discount is applied for bundling home and auto insurance. To determine the total combined premium, we'll first calculate the savings on the homeowner premium and then add the reduced home premium to the auto premium.

First, we find 10% of the homeowner premium:

10% of $1,000 = 0.10 * $1,000 = $100 savings.

Next, we subtract the savings from the original homeowner premium to determine the new premium for home insurance:

$1,000 - $100 = $900.

Now, we add the discounted home premium to the auto premium:

$900 + $1,500 = $2,400.

The total combined premium for home and auto insurance would be $2,400 after the 10% discount is applied to the home insurance.

It's always easy to do these as a fraction. We want won/total games played.

Games = 8 + 10 or 18 games played.

pct = 10/18

pct = 0.5555555556

Round to 3 decimal places.

pct = 0.556

Multiply pct by 100.

So, 0.556 • 100 = 55.6.

The pct sought is 55.6%.

Answer:

4x

Step-by-step explanation:

4 is the largest number on both lists of divisors. "x" is the only variable on both lists of variables. The GCF is their product:

4·x

Answer: C. 4x

Step-by-step explanation:

Got it right on edge

Answer:

The value could replace q is 108 - n ⇒ the last answer

Step-by-step explanation:

* Lets study the values of quarters and nickles

- One quarter = 25 cents

- One nickle = 5 cents

- The number of coins is 108

- The coins are nickles or quarters only

- The coins worth $ 21

* Lets solve the problem

∵ The number of coins is 108 coins

- Let the quarter is q and the nickel is n

∴ q + n = 108 ⇒ (1)

∵ The coins worth $21

∵ $ 1 = 100 cents

∴ $21 = 21 × 100 = 2100 cents

∵ The quarter = 25 cents

∵ The nickels = 5 cents

∴ 25q + 5n = 2100 ⇒ (2)

- To find the value which replace q use equation (1)

∵ q + n = 108 ⇒ subtract n from both sides

∴ q = 108 - n

* The value could replace q is 108 - n

Answer:

TLDR: 108-n on Edge

Answer:

90

Step-by-step explanation:

Final answer:

Two teams working together will take approximately 133.33 hours or about 5.56 days to clean the city streets. This is less than the one week (7 days) available before filming begins, so the streets will be clean in time.

Explanation:

To calculate how long it will take for two teams working together to clean the city streets, we use the concept of combined work rates.

The first team requires 200 hours to clean the streets, while the second team requires 400 hours.

When working together, we can add their rates of work, which means the first team cleans 1/200 of the city per hour, and the second team cleans 1/400 of the city per hour.

The combined rate of work will be:
1/200 (team A's rate) + 1/400 (team B's rate)
= 2/400 + 1/400
= 3/400

So, together they clean 3/400 of the city per hour. To find out how many total hours it will take to clean the entire city, we take the reciprocal of their combined rate
1 / (3/400)
= 400/3
≈ 133.33 hours

Since there are 24 hours in a day, we divide the total hours by 24 to find out how many days it will take:
133.33 hours / 24 hours/day
≈ 5.56 days
Given that the crew will arrive in one week, which is 7 days, this is within the time frame required before filming begins. The teams have enough time to clean the streets before the cameras start rolling.

Answer:

24°

Step-by-step explanation:

see attached

Answer: [tex]z=24\°[/tex]

Step-by-step explanation:

We need to find the measure of "x":

Based on the figure, we know that:

[tex]48\°+x+x=180\°[/tex]

Then, we need to solve for "x". Therefore, its measure in degrees is:

[tex]48\°+2x=180\°\\\\2x=180\°-48\°\\\\2x=132\°\\\\x=\frac{132\°}{2}\\\\x=66\°[/tex]

By definition, the sum of the interior angles of a triangle is 180 degrees. Since we know the measure of "x" and we know that one of the interior angles is a the right angle (an angle that measures 90 degrees), we can conclude that:

[tex]z+90\°+x=180\°[/tex]

Substituting the value of "x" into the equation and solving for "z", we get:

[tex]z+90\°+66\°=180\°\\\\z=24\°[/tex]

Answer:

Option D) h(x), f(x), g(x)

Step-by-step explanation:

we know that

The axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex of the parabola

Part 1) we have

[tex]f(x)=4x^{2} -1[/tex]

This is a vertical parabola open upward

The vertex is a minimum The vertex is the point (0,-1)

The x-coordinate of the vertex is 0

so

The axis of symmetry is x=0

Part 2) we have

[tex]g(x)=x^{2}-8x+5[/tex]

This is a vertical parabola open upward

The vertex is a minimum

Convert the equation into vertex form

[tex]g(x)-5=x^{2}-8x[/tex]

[tex]g(x)-5+16=x^{2}-8x+16[/tex]

[tex]g(x)+11=x^{2}-8x+16[/tex]

[tex]g(x)+11=(x-4)^{2}[/tex]

[tex]g(x)=(x-4)^{2}-11[/tex]

The vertex is the point (4,-11)

The x-coordinate of the vertex is 4

so

The axis of symmetry is x=4

Part 3) we have

[tex]h(x)=-3x^{2}-12x+1[/tex]

This is a vertical parabola open downward

The vertex is a maximum

Convert the equation into vertex form

[tex]h(x)-1=-3x^{2}-12x[/tex]

[tex]h(x)-1=-3(x^{2}+4x)[/tex]

[tex]h(x)-1-12=-3(x^{2}+4x+4)[/tex]

[tex]h(x)-13=-3(x+2)^{2}[/tex]

[tex]h(x)=-3(x+2)^{2}+13[/tex]

The vertex is the point (-2,13)

The x-coordinate of the vertex is -2

so

The axis of symmetry is x=-2

Part 4) Rank their axis of symmetry from least to greatest

1) h(x) -----> axis of symmetry -2

2) f(x) -----> axis of symmetry 0

3) g(x) -----> axis of symmetry 4

so

h(x),f(x),g(x)

Answer:

  15.5 ft

Step-by-step explanation:

The geometry of the problem can be modeled by a right triangle with hypotenuse 16 ft and one side length of 4 ft. If x represents the height of the ladder on the building, then the Pythagorean theorem tells us ...

  x^2 + (4 ft)^2 = (16 ft)^2

  x^2 = 240 ft^2 . . . . . . subtract 16 ft^2

  x ≈ 15.5 ft . . . . . . . . . . take the square root

The top of the ladder is about 15.5 ft above the ground.

Step-by-step explanation:

those little lines on each side show that each side is equal length. the line in the middle divided the rhombus in half to make two triangles, therefore making them equal.

Answer:

log 5 + log 2 = 1

To find the original number of baseball cards Alphonso had, we use algebra and set up the equation c - 16 = 80. Adding 16 to both sides gives us c = 96, indicating Alphonso started with 96 cards.

The question is asking us to determine the number of baseball cards Alphonso originally had before he gave any away. We are giving the situation whereby in the end, after giving some cards away, he is left with 80 cards. To solve this, we need to use algebra with c representing the number of cards Alphonso started with.

We can set up the equation as follows: Alphonso's starting cards minus the cards he gave away equals the number of cards he has left. Mathematically, this can be written as c - 16 = 80.

To find out the value of c, we simply add 16 to both sides of the equation to isolate c on one side:

Therefore, Alphonso originally had 96 baseball cards.