help... Reference books are for use in the library. There are 16 bookshelves for the reference books. After use, they need to be returned to a special collection box for shelving. If 128 reference books are in use and 84 reference books are in the collection box, how many reference books are on the shelf?

Answer:

x = 26.3

Step-by-step explanation:

There are three trigonometric rules that this question will apply to, they are:

[tex]Sin\theta\frac{opp}{hyp} Cos\theta\frac{adj}{hyp} Tan\theta\frac{opp}{adj}[/tex]

Where opp is the length of the side opposite to angle Φ, hyp is the hypotenuse of the triangle and adj is the length of a side adjacent to angle Φ.

In the provided picture, angle Φ has been provided alongside the hypotenuse with the opposite side length needing to be calculated. A trig function that includes all three of these must be used. The only one that does have all three is sin, ergo it is what we will use.

In the current equation form, the subject is incorrect and need to be changed so that it becomes the opposite side.

[tex]Sin\theta = \frac{opp}{hyp}\\ opp = sin\theta \cdot hyp[/tex]

Plug the known values in:

[tex]x = Sin(18\textdegree) \cdot 85\\x = 0.3090169 \cdot 85\\x = 26.266\\x = 26.3[/tex]

Hope this helps!

The series 7 + 16 + 25 +34 +43 +52 + 61 is an illusration of arithmetic series

The sigma notation of the series is: [tex]\sum\limits^7_{n=1} {9n - 2}[/tex]

The series is given as:

7 + 16 + 25 +34 +43 +52 + 61

The above series is an arithmetic series, with the following parameters

Start by calculating the nth term using:

a(n) = a + (n - 1) * d

This gives

a(n) = 7 + (n - 1) * 9

Evaluate the product

a(n) = 7  - 9 + 9n

Evaluate the difference

a(n) = 9n - 2

So, the sigma notation is:

[tex]\sum\limits^7_{n=1} {9n - 2}[/tex]

Read more about arithmetic series at:

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Answer:

the one you click is correct.

Step-by-step explanation:

Answer:

$13,082.60 more

Step-by-step explanation:

Melanie:

[tex]A=P(1+\frac{r}{n})^(20)\\ A=9800(1+\frac{.045}{4})^(20)\\A=$12,257.36[/tex]

Amelia:

[tex]A=Pe^(rt)\\A=9800e^(.0475*20)\\A=$25,339.95[/tex]

Amelia-Melanie= $13,082.60

Answer: y = 12.5x

Step-by-step explanation:

Because 250 bottles are filled every 20 minutes:

250/20=12.5

So, x=1, y=12.5

Hence, x=2 y=25

Because the number of bottles is directly proportional to the operation of the machine so:

12.5=a+b, 25.2a+b

a=12.5, b=0

Therefore, the equation is y = 12.5x

The Desmos graph of y = 12.5x is attached below

Answer:

[A] (4 ÷ 2)+(0.8 ÷ 2)

Step-by-step explanation:

Divide the 2 into each digit, which must be in the same spot it was before:

Knowing that 8 in 4.8 ⇒ 0.8

Thus, you can infer that [B] is wrong

You also infer that [D]  and [C] is wrong because 4 is a whole number.

Thus, that left us with [A] 4 ÷ 2+0.8 ÷ 2 which shows the quotient of 4.8 ÷ 2

Hence, [A] 4 ÷ 2+0.8 ÷ 2 is the answer.

~Learn with Lenvy~

Answer:

Option A

Simplification:

[tex]\rightarrow (4 + 0.8) \div 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{4.8 can also be written as 4 + 0.8}][/tex]

[tex]\rightarrow \dfrac{(4 + 0.8)}{2} = \dfrac{4 + 0.8}{2}[/tex]

[tex]\rightarrow \dfrac{4}{2} + \dfrac{0.8}{2}[/tex]

[tex]\rightarrow (4 \div 2) + (0.8 \div 2) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{\large{[Option A}}][/tex]

Answer:

a=0.7

A Area

0.49

Using the formula

A=a2

Solving fora

a=A=0.49=0.7

Answer:

Step-by-step explanation:

Formulae

Area of a triangle = 1/2 x base x height

Area of a rectangle = width x length

Question 1

Surface area of square based pyramid = area of base + 4 × area of triangle

⇒ SA = (6 × 6) + 4(1/2 × 6 × 14)

         = 36 + 168

         = 204 yd²

Question 2

Surface area of a cuboid = 2 × base area + 2 × end area + 2 × side area

⇒ SA = 2(10 × 6) + 2(6 × 3) + 2(10 × 3)

         = 120 + 36 + 60

         = 216 mm²

Extra credit question

Surface area of a triangular based prism = base area + 2 × triangle area + 2 × side areas

base area = 3 × 10 = 30 mm²

triangle area = 1/2 × 3 × 2 = 3 mm²

side area = 10 × 2.5 = 25 mm²

⇒ total SA = 30 + (2 × 3) + (2 × 25)

                 = 30 + 6 + 50

                 = 86 mm²

❍ Concept :-

We can solve these questions by using the formulas of area of triangle and rectangle, which will make our work easier. So, we know that,

⠀

[tex] \blue{ \underline{ \boxed{ \begin{array}{cc} \sf1. ~Area_{Triangle} = \dfrac{1} {2} \times b \times h \qquad \: \: \: \: \: \: \: \\ \\ \\ \sf2. \: Area_{Rectangle} = Length \times Breadth \end{array}}}} \\ \\ [/tex]

Using these formulas and figuring out the number of triangles and rectangles in each shape, we will solve this question.

⠀

✰ Solution :-

⠀

1. In this square pyramid, if we closely observe, we will get to know that there are 1 rectangle and 4 triangular faces. Thus,

⠀

[tex]\sf \hookrightarrow Area=6 \times 6 + 4( \dfrac{1}{2} \times 6 \times 14) \\ \\ \\ \sf \hookrightarrow Area=36 + 168 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area= {204 \: yd}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ [/tex]

⠀

2. Now, here, we can use the formula of total surface area for cuboid, i.e.

⠀

TSA = 2( lb + bh + hl )

⠀

[tex]\sf \hookrightarrow Area=2(10 \times 6 + 6 \times 3 + 10 \times 3) \\ \\ \\ \sf \hookrightarrow Area=2(60 + 18 + 30) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area=2 \times 108 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area= {216 \: mm}^{2} \: \: \qquad \qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ [/tex]

⠀

Extra Credit Question.

⠀

Here, we can find out the total surface area by finding,

⠀

Base area i.e. length x breadth ( B.A. )

Side area i.e. length x breadth ( S.A. )

triangular area = 1/2 x b x h ( T.A. )

⠀

Now,

⠀

TSA = BA + 2 x S.A. + 2 x T.A.

⠀

[tex]\sf \hookrightarrow Area=(10 \times 3) + 2(10 \times 2.5) + 2(\dfrac{1}{2} \times 3 \times 2) \\ \\ \\ \sf \hookrightarrow Area= 30 + 2 \times 25 + 2 \times 3 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area=30 + 50 + 6 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area= {86 \: mm}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ [/tex]

Answer: 4 cups

Step-by-step explanation:

First, convert the 6 cups of water to fluid ounces:

6 cups (8 fluid ounces / 1 cup) = 48 fluid ounces.

Then, since each bowl took 4 fluid ounces, and there are 4 bowls, the total fluid ounces used must be 16.

Thus, if there was 48, and 16 were used, 32 fluid ounces must be left. Convert this to cups by dividing by 8 and getting 4 cups.

Usando proporciones, hay que:

Una proporción es una fracción de la cantidad total.

En este problema, dos automovis, en sentidos opostos, salen al mismo tiempo. Por eso, su velocidad relativa es de 90 km/h + 80 km/h = 170 km/h.

La distancia es de 255 km, por eso, el tiempo en que se encontraran, en horas, es dado por:

t = 255/170 = 1.5h

La distancia recorrida por cada auto es dada por:

dA = 90 x 1.5 = 135 km.

dB = 80 x 1.5 = 120 km.

Puede-se aprender mas a cerca de proporciones en brainly.com/question/26425852

Answer:

Formula for volume of hemisphere;

V = 2/3 * π * [tex]r^{3}[/tex]

π - pi, which is 3.14 or 22/7

r = radius (half of the diameter/ 1/2 x diameter)

Since we are given the diameter, we find 1/2 of the diameter to find the radius.

1/2 x 8.9(diameter)

8.9/2 = 4.45 is our radi.

So now, we plug in this value into our equation.

V = 2/3 * π * [tex]r^{3}[/tex]

V = 2/3 * 22/7 * 4.45^3

V = 2/3 * 22/7 * 88.12

V = 2/3 * 276.95

V = 184.63 cubic centimetres.

Answer:

15

Step-by-step explanation:

[tex]since \: \: \frac{5}{8} \times 40 \\ = 25[/tex]

[tex]those \: that \: did \: not \: sprout \: would \: be \\ \: equals \: to \: 40 - 25 \\ = 15[/tex]

Answer:

22.50

Step-by-step explanation:

25% of 30 is 7.50

30-7.50 is 22.50

Answer: A: $22.50

Step-by-step explanation:

The original price of the game, $30, is 100%.

If the game if 25% off, then it will be, (100 - 25), 75% of its original price.

All we need to do is 75% x 30:

0.75 x 30 = 7.5 x 3 = $22.50

So your answer is A: $22.50

Answer:

.0214

Step-by-step explanation:

2.14 * .01 = .0214

to check:

.0214 * 100 = 2.14

Answer:

no they dont form a Pythagorean triple

Step-by-step explanation:

a2 + b2 = c2

Answer:

Step-by-step explanation:

This is a logical question that can be d=solved thus;

To decide which decision to make,one has to calculate the amount for both methods to detrmine which is higher.

1. Using simple interest formula of ( P X R X T)/ 100

Since p  = 1500, r  = 2.5%,  T = 3

1500 x 2.5% x 3  / 100  =  1500 x 0.025 x 3 / 100

112.5 / 100 = 1.125

to find amount  = 1.125 + 1500 = 1501.25 for the three 3years.

2. Using compound interest formula of ( P ( 1 + r/n)∧nt

1 + (2%/3) ∧3(3)

1500( 0.02/3) ∧ 9

1500  x 0.006 ∧9

1500 x 2.60 = 3900

A = 3900 + 1500 = 5400

SO FROM THE ABOVE I WILL G FOR THE HIGH YIELD SAVINGS AS IT IS HIGHER THAN THE INTEREST SAVINGS

Given the data from the question, the best account to use is:

A high interest savings account, with 2.5% simple interest annually (Option 1)

I = PRT / 100

A = I + P

Where

A = P(1 + r/n)ⁿᵗ

Where

I = PRT / 100

I = (1500 × 2.5 × 3) / 100

I = $ 112.5

Thus

A = I + P

A = 112.5 + 1500

A = $ 1612.5

A = P(1 + r/n)ⁿᵗ

Since n = 1,

A = P(1 + r)ᵗ

A = 1500(1 + 0.02)³

A = $ 1591.8

SUMMARY

The amount at the end of 3 years using:

Thus, the best account to use is a high interest savings account, with 2.5% simple interest annually (option 2)

Learn more about simple interest:

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needless to say that the conversion from miles to kilometers uses a constant value, and therefore, they're directly proportional.

now, I could write the direct proportional relation blah blah but there's no need, we can simply squeeze it out of the table by simply checking how many kilometers there are in 1 mile.

well, we know that 11.0 miles give us 17.699 km, ok hmmm if we divide 17.699 ÷ 11 = 1.609.

if we do the same on table for 26 and 41.834, so 41.834 ÷ 26 = 1.609, and the next pair 54.706 ÷ 34 = 1.609, the value of 1.609 is consistent or constant, or namely that there are 1.609 kilometers in 1 mile.

Answer: A, C, F

Step-by-step explanation:

Answer:

Mariah's investement is growing faster

Step-by-step explanation:

Here to find the rate at which the savings are growing at, we have to observe the slope of the line which describes the line representing the savings of each as a function of time.

The slope of a line is given by the relation;

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

Where m is the slope.

(x1,y1) is any point on the curve.

(x2,y2) is any other point on the curve.

Let's start of with Mariah by picking any 2 points from the table.

(0,150)

(1,159)

[tex]m(mar) = \frac{159 - 150}{1 - 0} = \frac{9}{1} = 9[/tex]

Let's move on to Mauricio's line and choose 2 points that lie on that line.

(0,190)

(1,195.7)

[tex]m(mau) = \frac{195.7 - 190}{1 - 0} = \frac{5.7}{1} = 5.7[/tex]

By looking at both slopes, we see that Mariah's growth rate (slope) 9>Mauricio's growth rate (slope) which is 5.7

Answer:

1. (a. 8 b. 3 d. 6,6,12 e. 3,3,9) 2. (a. 2,3 b. 4,5 c. 6,6,2,3 d. 5,3,5) 3. (a.2/3 b.1/3 c.2/3 f.1/2 g.7/8 h.4/5)

Step-by-step explanation:

OK this is quite simple. Just multiply the top and bottom, otherwise known as the numerators and denominators, by whatever is next to it. In this case, 1a is [tex]\frac{2*4}{5*4}[/tex].

That would result in [tex]\frac{8}{20}[/tex]

Hey there!

In order to multiply fractions, we should multiply the numerator of the 1st fraction by the numerator of the 2nd fraction.

Same with denominators.

Let's multiply these fractions.

2/5=2*4/5*4=8/20

2/3=2*6/3*6=12/18

1/4=1*3/4*3=3/12

3/4=3*3/4*3=9/12

now divide:

10/15=10:5/15:5=2/3

12/18=12:6/18:6=2/3

12/15=12:3/15:3=4/5

15/25=15:5/25:5=3/5

Now, simplify the following fractions:

4/6

divide the top & bottom by 2:

2/3

next:

5/10

divide the top & bottom by 5:

1/2

next

5/15

divide the top & bottom by 5:

1/3

next:

12/18

divide the top & bottom. by 6

2/3

next

5/10

divide the top & bottom by 5

1/2

next

14/16

divide the top & bottom by 2

7/8

and then last but not least

28/35

divide the top & bottom by 7

4/5

And we're done!

Hope everything is clear.

Let me know if you have any questions!

#LearningDoesn'tEnd

:-)

After converting yards to miles:

2640 yards =  1.5 miles

Given,

2640 yards= ________ miles

Now,

To convert to yard to miles the conversion factor is 0.000568182.

So,

1 yard ⇒ 0.000568182 miles

Multiply 2640 on both sides,

2640 yards ⇒ 1.5 miles.

Therefore 2640 yards is equivalent to 1.5 miles.

Know more about unit conversion,

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Hey there!
In order to multiply fractions, all we should do is multiply the numerator of the first fraction times the numerator and the denominator of the first fraction times the denominator of the second one:

[tex]\bold{\displaystyle\frac{2}{7} x\frac{1}{3} }[/tex]

Multiply 2 times 1 and 7 times 3:

[tex]\boxed{\boxed{\bold{\displaystyle\frac{2}{21} }}}[/tex] (Final Answer)

Hope everything is clear.

Let me know if you have any questions; if so, please comment.

#LearningDoesn'tEnd

#LearningIsFun

[tex]\rule{200}{2}[/tex]

Answer:

3x=2y
Explanation:

There is a proportional relationship between the number of apples and  teaspoons of cinnamon that is 3x = 2y.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

Given that Devon’s favorite apple sauce recipe calls for 2 teaspoons of cinnamon for every 3 apples.

Now, let x be the number of apple and y be the teaspoons of cinnamon

the proportion are;

x/2 = y/3

Therefore, the proportional relationship between the number of apples and  teaspoons of cinnamon is

3x=2y

More can be learned about proportions at;

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Answer: 0.45  and -2.74

Step-by-step explanation:

You're going to want to use the Quadratic Formula, so (-b±√(b^2-4ac))/2a.

When you plug in you should get -16 ± √16^2-4(7)(-8)/2(7)

-16± √(256+224) all divided by 2 x 7 or 14

(-16 ± 22.3607)/14

0.45  and -2.74 are your answers

Answer:

hello

g (x)= x² - 5

g (3) = 3² - 5 =  9 - 5 =  4

Step-by-step explanation:

Answer:

4 quarters

Step-by-step explanation:

4 quarters = $1

14 nickels = $0.70

Step-by-step explanation:

the total surface area is the sum of the 5 individual areas in the surface :

2 triangle sides (left and right).

1 back rectangle side

1 rectangle floor

1 inclined rectangle front side

to get the length of the baseline (Hypotenuse) of the right-angled triangles on the side. we use Pythagoras

c² = a² + b²

where c is the Hypotenuse (the side opposite of the 90° angle).

c² = 3² + 4² = 9 + 16 = 25

c = 5

so, now, we have everything we need.

the area of a triangle side (since it is right-angled) :

4×3/2 = 6

2 sides, that makes 12

the area of the back side

6×3 = 18

the area of the floor

6×4 = 24

the area of the inclined front side

6×5 = 30

so, the total surface area is

12+18+24+30 = 84

The correct statement about the data set is the mean would be the best measure of central tendency for Mr Cochran's class because the data is symetrical.

A measure of central tendency attempts to describe a data set by determining the central value of the data set. Measures of central tendency are mean, median and mode.

Mean is the average of a data set. Median is the number at the center of the data set. Mode is the number that occurs most in the data set.  A data set is negatively skewed if the mean is less than the mode. If the mean is equal to the mode, the data is symmetric.

Mean of Mrs culpepper’s class = (1 + 1 + 1 + 1 + 2 + 2 + 2 + 3 + 3 + 3) / 10 = 1.9

Mode of Mrs culpepper’s class = 1

Mean of mr Cochran's class  = (1+ 1 + 2 + 3 + 3 + 3 + 3 + 4 + 9 + 9) / 10 = 3.8

Mode of mr Cochran s class = 3

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