Find the Volume of the rectangular prism(in cubic feet)

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

Work Shown:

C = circumference = 40 inches

d = diameter

[tex]C = \pi*d\\\\C \approx 3.14*d\\\\40 \approx 3.14*d\\\\\frac{40}{3.14} \approx d\\\\d \approx \frac{40}{3.14}\\\\d \approx 12.73885\\\\d \approx 13\\\\[/tex]

Be careful. Technically 12 inches is the largest diameter Tanya can use since 3.14*12 = 37.68 is under 40; while 3.14*13 = 40.82 is slightly over 40

So if I was the teacher, I would have said "round down to the nearest inch".

Answer:

[tex]\sf a. \quad \dfrac{21}{10+x}+\dfrac{21}{10-x}=5[/tex]

Step-by-step explanation:

Formula for calculating speed:

[tex]\boxed{\sf Speed=\dfrac{Distance}{Time}}[/tex]

Therefore:

[tex]\boxed{\sf Time=\dfrac{Distance}{Speed}}[/tex]

Given values:

If the boat is traveling downstream, the current (x mph) will be pushing the boat faster, and so the boat's speed will increase by x mph.

Therefore, the expression for the time it takes for the boat to travel downstream is:

[tex]\sf Time\:(downstream)=\dfrac{21}{10+x}[/tex]

If the boat is traveling upstream, the current (x mph) will be pushing against the boat and so the boat's speed will decrease by x mph.

Therefore, the expression for the time it takes for the boat to travel upstream is:

[tex]\sf Time\:(upstream)=\dfrac{21}{10-x}[/tex]

Therefore, if the total time it takes to travel downstream and upstream is 5 hours:

[tex]\implies \sf \dfrac{21}{10+x}+\dfrac{21}{10-x}=5[/tex]

To solve for x:

[tex]\implies \sf \dfrac{21}{10+x}+\dfrac{21}{10-x}=5[/tex]

[tex]\implies \sf \dfrac{21(10-x)}{(10+x)(10-x)}+\dfrac{21(10+x)}{(10-x)(10+x)}=5[/tex]

[tex]\implies \sf \dfrac{21(10-x)+21(10+x)}{(10+x)(10-x)}=5[/tex]

[tex]\implies \sf21(10-x)+21(10+x)=5(10+x)(10-x)[/tex]

[tex]\implies \sf 210-21x+210+21x=5(100-10x+10x-x^2)[/tex]

[tex]\implies \sf 420=500-5x^2[/tex]

[tex]\implies \sf 5x^2=80[/tex]

[tex]\implies \sf x^2=16[/tex]

[tex]\implies \sf x=\pm4[/tex]

Therefore, the rate of the current is 4 mph.

Answer:

x=19

Step-by-step explanation:

●Alternate angles are equal

therefore, angle WYZ= angle YWX

2x= angle YWX

●Angles within a triangle sum up to 180 degrees

=3x-5+2x+90=180

▪︎group like terms

=3x+2x+90-5=180

=5x+85=180

▪︎send all x terms to one side of the equation

=5x=180-85

=5x=95

▪︎divide both side by the coefficient of x ; 5

=x=19

Answer:

12 1/2% DISCOUNT:

Step-by-step explanation:

Jacket: $60.81

Tie: $13.56

Raincoat: $65.93

Answer:

it's 1 the answer is

Step-by-step explanation:

how I got it I did 2 x2 is 4 and 1÷1 is 1 so if I do 1x1 it is 1

Answer:

Step-by-step explanation:

I would expect her to find out how long each classmate spends playing video games. Then, I'd expect her to use this information and put it into a bar chart so that she can compare the numbers and find the biggest one, or who spends the most time playing video games.

Here's a random example:

Let's say she has 4 classmates, Zoe, Robert, John, and Taylor.

Zoe: 2 hours on video games

Robert: 6 hours on video games

John: 1 hour on video games

Taylor: 4 hours on video games

Then, i'd put this information into a bar chart. The screenshot is a random reference of what a bar chart looks like.

Answer: just find how much time each one spent ,  put it on a chart and yh

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

There are 12 possible outcomes, but no outcome will result in a sum greater than 7. So the probability is 0/7 = 0.

1 1

1 2

1 3

2 1

2 2

2 3

3 1

3 2

3 3

4 1

4 2

4 3

Answer:

4.82[tex]*10^{-4}[/tex]

Step-by-step explanation:

0.000082 + 0.0004 = 0.000482 = 4.82[tex]*10^{-4}[/tex]

Answer:

Step-by-step explanation:

the original price would be $80.00

50.00*0.08 = 4 50.00-4 = 46.00

46.00 for 25 radios with 4 cash back

30.00*0.15= 4.5 30.00- 4.5 = 25.50

total is 71.50

Using exponential functions, the ending balances are given as follows:

1. $1,490.07.

2. $1,073.83.

3. $358.04.

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which:

Item a:

The parameters are:

A(0) = 939, r = 0.08, t = 6.

Hence the balance is:

[tex]A(6) = 939(1.08)^6 = 1490.07[/tex]

Item b:

The parameters are:

A(0) = 823, r = 0.03, t = 9.

Hence the balance is:

[tex]A(9) = 823(1.03)^9 = 1073.83[/tex]

Item c:

The parameters are:

A(0) = 269, r = 0.1, t = 3.

Hence the balance is:

[tex]A(9) = 269(1.1)^3 = 358.04[/tex]

More can be learned about exponential functions at https://brainly.com/question/25537936

#SPJ1

Answer:

Option C; 26cm by 14 cm

Step-by-step explanation:

Answer:

As the shape forms a rectangle and line segment AB and line segment CD are parallel, you can tell that length of both line segments/sides are equal.

Step-by-step explanation:

Since the answer itself requires an explanation, I added the explanation in the answer area.

Hope that helps! Have a great day!

Answer: Both C and D are correct

Step-by-step explanation:

To remove the exponent from the v you need to square root both sides,

the exponent on the v is then canceled out giving you:

[tex]v=\sqrt{25/81}[/tex] or [tex]v=-\sqrt{25/81}[/tex]

Answer:

Both C & D are correct

Step-by-step explanation:

[tex]v^{2} =\frac{25}{81}[/tex]

Root both sides of the equation to remove the square.

[tex]v=\±\sqrt{\frac{25}{81} }[/tex]

[tex]v = \±\sqrt{\frac{5*5}{9*9} } \\v=\±\frac{5}{9}[/tex]

Therefore,

[tex]v=\sqrt{\frac{25}{81} } =-\sqrt{\frac{25}{81} }[/tex]

Answer:

38 degrees

Step-by-step explanation:

Since angles KLO and OLM are supplementary, they add up to 180 degrees

So,  angle OLM is 180-134=46 degrees

Similarly, angles OMN and OML are supplementary, so they also add up to 180 degrees

So, angle OML is 180-84=96 degrees

You also know that the angles of a triangle sum up to 180 degrees

So, 46+96+x=180

180-142=38

x=38 degrees

Answer:

4, Third option

Step-by-step explanation:

When you get 9^8 the answer is 43046721. So when raising a power to a power, the products should equal 8. Using simple math, we can determine that 4x2=8. To check our work you can calculate (9^2)^4, which equals 43046721. Now we can now for sure that this answer is correct. Hope this helps!

Answer:

(8,1) (15,2) (22,3) (29,4) (36,5) (43,6)

Step-by-step explanation:

Answer:

Step-by-step explanation:

The equation y=7x+1 is written in slope intercept form. That would be:

y=mx+b

m is the slope

b is the y intercept, or where the line first is seen on the y axis.

Because b=1, the y intercept is 1.

Because m=7, the slope is 7.

STEP 1: GRAPH THE Y INTERCEPT.

Since b=1, the line crosses the y intercept when y=1. So graph y=1 on the coordinate plane.

STEP 2: GRAPH THE SLOPE

Do this by going up 7, then right 1. Because 7 is a positive number, you go up.

hope this helps !!! brainliest would be appreciated :D

Answer:

10/6

Step-by-step explanation:

r refer to the above attachment

Answer:

This is a multiplication problem.

2 1/2 * 2/3 = 5/2 * 2/3 = 10/6 or 5/3

She will use 10/6 or 1 2/3 cups of vegetable oil (or applesauce)

Hope this helps, let me know if it's wrong!

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

We have proven that ΔACO ≅ ΔBDO using the SAS (Side-angle-side) theorem

From the question, we are to prove that ΔACO ≅ ΔBDO

From one of the congruent triangles theorem, we have that

If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

This is the SAS (Side-angle-side) theorem.

From the given information,

AB and CD intersect at point O

Thus, AO = BO

Also,

∠ACO ≅ ∠BDO

In the diagram, we can as well observe that CO ≅ DO

Thus, we can conclude that AC ≅ BD

Since sides AC, CO and the included angle ACO are congruent to sides BD, DO and the included angle BDO, we can conclude that ΔACO ≅ ΔBDO using the SAS theorem.

Hence, we have proven that ΔACO ≅ ΔBDO

Learn more on Congruent triangles here: https://brainly.com/question/2938476

#SPJ1

Answer:  not 100% but 35-20=x or 35-20=15

Step-by-step explanation:

Answer:

d.  3x + 6 = 26

Step-by-step explanation:

Definitions

The sum of three consecutive even integers

Let x be the first even integer.

As there is a difference of 2 between consecutive even integers, the next even integer after x will be (x + 2).

Therefore, the next even integer after (x + 2) will be (x + 2) + 2 = (x + 4).

So "the sum of three consecutive even integers is twenty-six" is:

x + (x + 2) + (x + 4) = 26

To solve

⇒ x + (x + 2) + (x + 4) = 26

⇒ x + x + 2 + x + 4 = 26

⇒ 3x + 6 = 26

(Please note that there are no three consecutive even integers that sum to 26, so the problem cannot be solved).

Answer:

Step-by-step explanation:

2. y interecept --> y = 1

3. pi

4. 1, 0

Answer:

13 dollars and 44 cents, 56 cents.

Step-by-step explanation:

134 dollars are 40 cents = 134.4 dollars.

10b = 134.4

b = 13.44

13 dollars and 44 cents

There are 24 cookies to a batch

24c = 13.44

c = 0.56.

so each cookie costs 56 cents

Answer:

13.44 to make 1 batch. 0.56 to make 1 cookie.

Step-by-step explanation:

If it cost 134.40 to make 10 batches, then you would divide that by 10 for how much it cost for 1 batch.

Then, 1 batch of 24 costs 13.44, you would divide it by 24 for the cost of 1 cookie.

Answer:

a

Step-by-step explanation:

Using it's concept, there is a 0.6667 = 66.67% probability of getting a total of 13 or more.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

From the tree diagram, there are 9 outcomes, of which 6 result in a total(first node + second node) of 13 or more, hence the probability is:

p = 6/9 = 0.6667.

More can be learned about probabilities at https://brainly.com/question/14398287

#SPJ1

Answer:

2

1

0

Not:

4

9

1921131

Step-by-step explanation:

x needs to be equal or less than 3. It doesn't say that x cannot be negative so any number 3 and below is fine.

Not solutions would be any number above 3 in value

The three solutions for the inequality are 1, 2, and 3.

And, the three numbers that are not solutions are 4, 5, and 6.

Used the concept of inequality that states,

A relation by which we can compare two or more mathematical expressions is called an inequality.

Given that,

The inequality is,

x ≤ 3

Now from the given inequality x ≤ 3,

The solution of the inequality is a number that is less or equal to 3.

Hence the possible three solutions for the inequality are,

x = 1, 2, 3

And, the three numbers that are not solutions are,

4, 5, and 6.

To learn more about inequality visit:

https://brainly.com/question/25944814

#SPJ7