3.3. (08.01 LC) Find the circumference and area of a circle with a diameter of 10 inches. Leave your answers in terms of pi. (4 points) . 4. (08.01 MC) Given a cube with a volume of 27 cm3, what is the volume of a square pyramid that can fit perfectly inside the cube? (4 points)

Answer:

Here's what I get  

Step-by-step explanation:

a. Net of a cube

Fig. 1 is the net of a cube  

b. Does the formula work?

Tony's formula works if you ignore dimensions.

There are six squares in the net of a cube.

If each side has a unit length s, the total area of the cube is 6s.

c. Will the formula work for any rectangular prism?

No, because a rectangular prism has sides of three different lengths — l, w, and h — as in Fig. 2.

d. Area of a rectangular prism

A rectangular prism has six faces.

A top (T) and a bottom (b) — A = 2×l×w

A left (L) and a right (R)    —   A = 2×l×h

A front (F) and a back (B) —   A = 2×w×h

                                  Total area = 2lw + 2lh + 2wh

If l = 5 m, w = 6 m and h = 8 m,

[tex]\begin{array}{rl}A &=& \text{2$\times$ 5 m $\times$ 6 m + 2$\times$ 5 m $\times$ 8 m + 2 $\times$ 6 m $\times$ 8 m}\\&=& \text{60 m}^{2} + \text{80 m}^{2} + \text{96 m}^{2}\\&=& \textbf{236 m}^{2}\\\end{array}[/tex]

Answer:

  −13.8654599313 and 0.8654599313

Step-by-step explanation:

The two numbers of interest will be the solutions to ...

  xy = -12

  x +y = -13

Substituting for y, this becomes the quadratic ...

  x(-13 -x) = -12

  x^2 +13x = 12 . . . . . multiply by -1

  x^2 +13x +6.5^2 = 12 +6.5^2 . . . . . complete the square

  (x +6.5)^2 = 54.25

  x = -6.5 ± √54.25 . . . . . . take the square root, subtract 6.5

  x ≈ -13.865499313 or 0.8654599313

The value of y is the other of these two numbers. So, the two numbers of interest are {-13.865499313, 0.8654599313}.

Answer:

The answer is 1/3

Answer:

1/3

Step-by-step explanation:

The factors of 5 are 1,5;

* The factors of 15 are 1,3,5,15.

We can see that the GCD is 5 because it is the largest number by which 5 y 15 can be divided without leaving any residue.

To reduce this fraction, simply divide the numerator and denominator by 5 (the GCF).

So, 5 /15

= 5÷5 /15÷5

= 1 /3

Answer:

4.61 m

Step-by-step explanation:

The angle of depression of the bottom of the shorter building from the top of the taller building = 48° equals the angle of elevation of the top of the taller building from the bottom of the shorter building

Using trig ratios

tan48° = H/d where H = height of taller building and d = their distance apart = 12 m

H = dtan48° = 12tan48° = 13.33 m

Also, the angle of elevation of the top of the shorter building from the bottom of the taller building is 36°

Using trig ratios

tan36° = h/d where h = height of shorter building

h =dtan36° = 12tan36° = 8.72 m

Now, the difference in height of the buildings is thus H - h = 13.33 m - 8.72 m = 4.61 m

Answer:

The greatest common factor of the expression is 25x

Step-by-step explanation:

Here, we are interested in giving the greatest common factor of the expression.

We can do this by factorization till we have no common factors left.

the expression is;

100x^2 -250xy + 75x

we start with the common factor x;

x(100x -250y + 75)

The next thing to do here is to find the greatest common factor of 100,250 and 75.

The greatest common factor here is 25.

Thus, we have;

25x(4x -10y + 3)

There is no more factor to get from the terms in the bracket. This simply means that the terms in the bracket are no longer factorizable

So the greatest common factor we have is 25x

Answer:

78 nickels and 22 dimes

Step-by-step explanation:

Nickels = n, Dimes = d

Number of coins = 100

Total sum in the piggy bank = $6.60

Consider the first equation in the second:

Answer: nickels 78 and dimes 22

Answer:

78 nikes and dimes 22

solving these linear equations simultaneously, x = 22y = 8z= 11hence the answer is B. 11

Step-by-step explanation:

Answer:

we can set the 9 as a benchmark to be the score for the passing grade so that probability of passing a student who guesses every question is less than 0.10

Step-by-step explanation:

From the given information;

Sample  size n = 12

the probability of passing a student who guesses on every question is less than 0.10

In a alternative - response question (true/false) question, the probability of answering  a question correctly  = 1/2 = 0.5

Let X be the random variable that is represent number of correct answers out of 12.

The X [tex]\sim[/tex] BInomial (12, 0.5)

The probability mass function :

[tex]P(X = k) = \dfrac{n!}{k!(n-k)!} \times p^k\times (1-p)^{n-k}[/tex]

[tex]P(X = 12) = \dfrac{12!}{12!(12-12)!} \times 0.5^{12}\times (1-0.5)^{12-12}[/tex]

P(X = 12) = 2.44 × 10⁻⁴

[tex]P(X = 11) = \dfrac{12!}{11!(12-11)!} \times 0.5^{11}\times (1-0.5)^{12-11}[/tex]

P(X =11 ) = 0.00293

[tex]P(X = 10) = \dfrac{12!}{10!(12-10)!} \times 0.5^{10}\times (1-0.5)^{12-10}[/tex]

P(X = 10) = 0.01611

[tex]P(X = 9) = \dfrac{12!}{9!(12-9)!} \times 0.5^{19}\times (1-0.5)^{12-9}[/tex]

P(X = 9) = 0.0537

[tex]P(X = 8) = \dfrac{12!}{8!(12-8)!} \times 0.5^{8}\times (1-0.5)^{12-8}[/tex]

P(X = 8)  = 0.12085

[tex]P(X = 7) = \dfrac{12!}{7!(12-7)!} \times 0.5^{7}\times (1-0.5)^{12-7}[/tex]

P(X = 7) = 0.19335

.........

We can see that,a t P(X = 9) , the probability is 0.0537 which less than 0.10 but starting from P(X = 8) downwards the probability is more than 0.01

As such, we can set the 9 as a benchmark to be the score for the passing grade so that probability of passing a student who guesses every question is less than 0.10

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▹ Answer

q = 16

▹ Step-by-Step Explanation

3(q - 7) = 27

3q - 21 = 27

Add 21 to both sides:

21 + 21 = na

27 + 21 = 48

3q = 48

Divide both sides by 3:

3/3 = q

48/3 = 16

q = 16

Hope this helps!

CloutAnswers ❁

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Answer:

q=16

Step-by-step explanation:

3q-21=27

27+21=48

48/3=16

Answer:

The answer to the nearest hundredth is 0.07 liters per minute

Step-by-step explanation:

In this question, we are told to express the given metric in liters per minute.

The key to answering this question, is to

have the given measurements in the metric in which we want to have the answer.

Hence, we do this by converting milliliters to liters and seconds to minute.

Let’s start with milliliters;

Mathematically;

1000 milliliters = 1 liters

10 milliliters = x liters

x * 1000 = 10 * 1

x = 10/1000

x = 1/100

x = 0.01 liters

For the seconds;

We need to convert the seconds to minutes;

Mathematically;

60 seconds = 1 minute

8.5 seconds = y minutes

60 * y = 8.5 * 1

y = 8.5/60

y = 0.14167 minutes

Now, our rate of flow is liters per minute, that means we have to divide the volume by the time;

Hence, we have ;

0.01/0.14167 = 0.070588235294

Which to the nearest hundredth is 0.07

Answer:

C. x-2

Step-by-step explanation:

edge

Answer: the 3rd the answer c

x-2

Step-by-step explanation:

Answer:

$76

Step-by-step explanation:

The amount changed is the total amount of the whole entire thing.

Therefore, we use absolute value or simply find the difference.

21 - (-55) = 76

So the bank account changed $76 over the 2 days.

Answer and Step-by-step explanation: The described right triangle is in the attachment.

As it is shown, AC is the hypotenuse and BC and AB are the sides, so use Pytagorean Theorem to find the unknown measure:

AC² = AB² + BC²

[tex]AB^{2} = AC^{2}-BC^{2}[/tex]

[tex]AB =\sqrt{AC^{2}-BC^{2}}[/tex]

[tex]AB =\sqrt{7^{2}-4.5^{2}}[/tex]

[tex]AB =\sqrt{28.75}[/tex]

AB = 5.4

Then, right triangle ABC measures:

AB = 5.4cm

BC = 4.5cm

AC = 7cm

Answer:

225.78 grams

Step-by-step explanation:

To solve this question, we would be using the formula

P(t) = Po × 2^t/n

Where P(t) = Remaining amount after r hours

Po = Initial amount

t = Time

In the question,

Where P(t) = Remaining amount after r hours = unknown

Po = Initial amount = 537

t = Time = 10 days

P(t) = 537 × 2^(10/)

P(t) = 225.78 grams

Therefore, the amount of iodine-131 left after 10 days = 225.78 grams

Answer:

Step-by-step explanation:

The formula we need for this is

4(4 + x) = 5(5 + 3) and

16 + 4x = 5(8) and

16 + 4x = 40 and

4x = 24 so

x = 6, choice C.

Answer:

$11286.95 second year

$10335 first year

Step-by-step explanation:

9% of 9500 is 855, 9500 plus 855 = 10335. (first year)

9% of 10335 is 931.95, and 10335+931.95 is 11286.95. (second year)

The amount in the account at the end of 1 year  $10335 (first year)

The amount in the account at the end of 2 years $11286.95.

Compound interest is when you earn interest on both the money you've saved and the interest you earn.

Formula:

A = P(1 + {r}/{n})^{n.t}

here, we have,

$9500 is placed in an account that pays 9% interest compounded each year.

so, we get,

9% of 9500 is 855,

9500 plus 855 = 10335. (first year)

again,

9% of 10335 is 931.95,

and 10335+931.95 is 11286.95. (second year)

Hence, The amount in the account at the end of 1 year  $10335 (first year)

The amount in the account at the end of 2 years $11286.95.

To learn more on Compound interest click:

brainly.com/question/29335425

#SPJ2

Answer:  48

There are many approaches to estimating stuff like this, so there isn't one set answer. My approach is shown below.

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

1 min = 60 sec

30 min = 1800 sec (multiply both sides by 30)

1/2 hr = 1800 sec (replace "30 min" with "1/2 hr")

The value 2014 is fairly close to 1800, so roughly every half hour we have a prize being won. This is an overestimate.

There are 24 hours in a day, so 24*2 = 48 half-hour periods in a day, meaning we have an estimated 48 prizes in a full day. This is an overestimate as well.

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

Extra info:

If you're curious about finding the more accurate value, then you could follow these steps

1 prize = 2014 seconds

x prizes = 86400 seconds (number of seconds in a full day)

1/x = 2014/86400

1*86400 = x*2014

86400 = 2014x

2014x = 86400

x = 86400/2014

x = 42.8997020854021

Round down to get x = 43. We round down because there isn't enough time to get that 44th prize. The value 43 is fairly close to 48, and we can see our earlier estimate of 48 was an overestimate.

Answer:

3 1/6 cups of flour.

Step-by-step explanation

Answer:

The amount of money in Enid bank account can be written as a linear equation.

Ye = Xe + $4*m

where Ye is the money that Enid has in her account, m is the number of months that have passed since she opened it, and Xe is the initial deposit.

For Jim, the equation is similar:

Yj = Xj + $3*m

where Yj and Xj are similar as above.

Between May 15 and December 31 of the same year, we have 7 months (where i am counting December because the deposit is made in the first day of the month).

Then we have that:

Ye = $72 = Xe + $4*7 = Xe + $28

Xe = $72 - $28 = $44

So in May 15, Enid deposited $44.

For Jim we have:

Yj = $72 = Xj + $3*7 = Xj + $21

Xj = $72 - $21 = $51

So in May 15, Jim deposited $51.

Answer:

H. b/a

Step-by-step explanation:

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Step 1: Label our variables

y₂ = 2b

y₁ = b

x₂ = 2a

x₁ = a

Step 2: Plug into formula

m = (2b - b)/(2a - a)

Step 3: Evaluate

m = b/a

Answer:

b/a

Step-by-step explanation:

We have two points so we can use the slope formula

m = (y2-y1)/(x2-x1)

    = ( 2b - b)/ ( 2a -a)

   = b/a

YES! quite easily.

I hope you can see the two pairs of corresponding angles between the parallel lines. they'll be equal

and then there's a pair of vertically opposite angle at centre.

that means all pairs of corresponding angles are equal, thus, triangles are similar by AAA

Answer:

[tex]\Large \boxed{\mathrm{D}}[/tex]

Step-by-step explanation:

The triangles can be proven by AA or Angle-Angle similarity.

[tex]\angle QUR \cong \angle TUS[/tex]

The vertical angles are congruent.

[tex]\angle R \cong \angle S[/tex]

The alternate interior angles are congruent.

Answer:

3/8 is your answer.

Step-by-step explanation:

Given:

8 kids bought a 3 cakes.

Required:

How many equal parts will need to divide it so that everyone can have it.

Solution:

3/8

Hope this helps ;) ❤❤❤

Answer:

p(x), q(x), and their product are all polynomials.

p(x) · q(x) = 6x² + 10x - 63

Step-by-step explanation:

First of all P(x) and q(x) are polynomials because polynomials refer to any sum, difference, or product of a collection of algebraic terms. The word polynomials is general. P(x) and q(x) are polynomials but more specifically they are binomials since they only have two terms. Their product is a polynomial as well, but more specifically its a trinomial because it has three terms.

process of multiplying

Using the distributive property (or foil method) when multiplying p(x) and q(x) you would first get the expression 6x² - 18x + 28x - 63. From here you would combine "like terms". This would give you your final answer of

6x² + 10x - 63. Sorry, I couldn't help you with the D question but I hope this helps ;)

Answer:

Yes it will occur

Step-by-step explanation:

The lobby measures 45 feet by 45 feet

Area of the lobby = 45 * 45

=2025 ft^2

So, the lobby has 2025 tiles

subtract 1 black tile in the center

2025 tiles - 1 black tile =2024 tiles

The number of blue tiles and black tiles is 2024 tiles

He wants the outer edge to be the same color as the center tile so, divide by 2

2024/2 = 1012 tiles

The number of tiles in the outer edge is 1012 tiles and the number of tiles in the center is 1012 tiles

Answer:

$5,000 per week

Step-by-step explanation:

Ruri is a 30 year old female.

there are about 4 weeks per month

there are about 52 weeks per year

52*5000 = 260,000

She would get 260,000 per year and lets see how much she would have at 40.

260,000*10

at 40 she would have 2,600,000

2,600,000*10

at 50 she would have 26,000,000

at 50 she already has earned more money that the $20 million.

She should go with the $5000 per week if she would like more money.

Answer:

3000 words

Step-by-step explanation:

450 words in 3 minutes is 150 words in 1 minute. 20 minutes = 1 times 20.          

1 minute = 150 words so 150 words times 20 minutes = 3000 words.

Answer:

Step-by-step explanation:

In order to find the value of x we use sine

sin ∅ = opposite / hypotenuse

From the question

x is the hypotenuse

the opposite is 19

So we have

sin 20 = 19/x

x = 19/sin 20

x = 55.55

We have the final answer as

Hope this helps you

Answer:

x = 55.6

Step-by-step explanation:

Answer:

Step-by-step explanation:

C=153.86153...

100000C=15386153.86153...

subtract

99999C=15386000

C=15386000/99999

2 π r=15386000/99999

r=7693000/99999π≈24.5

To add fractions with different denominators you must find the highest common factor (the highest number they both go into).

For 1 - The highest common factor is 8, 2x4 = 8, 4x2 = 8

now, whatever you do to the bottom, you must do to the top.

So:

3 x 2 = 6 and 5 x 4 = 20

Therefore, your answer would be 6/8 + 20/8

You do that for the rest of them as well, do you get it?

Answer:

    3.  4/15 + 4/5 = 4/15 + 12/15 = (4+12)/15 = 16/15

    5.  2/3  + 7/10 = 20/30 + 21/30  = (20+21)/30 = 41/30

Answer:

[tex](-5)^{11}[/tex]

Step-by-step explanation:

We can use the exponent rules. If we have [tex]\frac{a^b}{a^c}[/tex], then it will simplify to [tex]a^{b-c}[/tex].

b is 5, c is -6, and a is -5 so:

[tex]-5^{5-(-6)}\\-5^{11}[/tex]

Hope this helped!

Answer:

Step-by-step explanation:

Since the figure above is a right angled triangle we can use trigonometric ratios to find x

To find x we use cosine

cos∅ = adjacent / hypotenuse

From the question

The hypotenuse is x

The adjacent is 10

Substitute these values into the above formula and solve for x

That's

Divide both sides by cos 37

x = 12.52135

We have the final answer as

Hope this helps you

Answer:

probably 16.5

Step-by-step explanation: