A library buys 36 English books, 48 Science books and 72 Mathematics books. The thickness of each book is the same. Now, the librarian wants the books to be placed in stacks, such that each stack has books of the same subject, and the height of each stack is the same. Also, the librarian wants as few stacks as possible. How many stacks of books will there be?

Answer:

$947

Step-by-step explanation:

12,000(1 + .05/1)^(15*1) = $24,947.14

12,000 + (12,000*.07*15) = $24,600

difference is $947

Answer:

a

Step-by-step explanation:

you have to multply

Answer:

A

Step-by-step explanation:

Answer:

Please check explanation

Step-by-step explanation:

Here, we want to do a matching.

We shall be matching the given statements with the features we have on the graph

Hence we shall be looking closely at the graph to answer the questions.

The y-intercept is the point at which the graph touches the y-axis

And it was at -3 degrees celsius at the beginning of the day.

The temperature was above zero between 8am and 8pm. The matching statement is that it is increasing or decreasing interval

We can see that the graph rose from 8am before it finally comes to zero at 8pm

Positive or negative interval matches with it was getting warmer between 2am and 2pm.

While temperature was lowest at 2am, we can see a peak at 2pm.

Answer:

b=-a

Step-by-step explanation:

Answer:

x=3

Step-by-step explanation:

To solve for x, we will follow the steps below:

First note that exterior angle =two  opposite interior angle

From the diagram below

(25x) ° + (57 + x)°   = (45x)°

25x° + 57° + x° = 45x°

next step is to collect the like term

45x° - 25 x°  - x°  =  57°

19x° = 57°

Divide both-side of the equation by 19

19x°/ 19 = 57° /19

On the left-hand side of the equation 19 will cancel out 19 leaving us with just x°  while on the right-hand side of the equation 57 will be divided by 19

x  =   3

Answer:

1) 33.11 m

2) 58.1°

3) 35·√2

4) 491.925 m²

Step-by-step explanation:

Side length of the pyramid = 35 m

The height of the pyramid = 22 m

The slant height = √(Height² + (1/2 Side length)²)

The slant height = √(22² + (1/2×35)² = 28.11 m

1) The slant edge length = √((Slant height)² + (1/2 Side length)²

The slant edge length = √(28.11² + (1/2×35)²) = 33.11 m

2) The base angle = tan⁻¹((Slant height)/(1/2 Side length))

The base angle = tan⁻¹(28.11/(1/2×35)) = 58.1°

3) The distance between the center pf the base and the corner of the pyramid is half the length of the base diagonal

The length of the base diagonal = √((Side length)² + (Side length)²)

The length of the base diagonal = √(35² + 35²) = 35·√2

The distance between the center pf the base and the corner of the pyramid = 35·√2/2 = 24.75 cm

4) The area of the side of the pyramid = 1/2×(Side length)× (slant height)

The area of the side of the pyramid = 1/2*35*28.11 = 491.925 m²

Answer:

i am very sure that the answer is D which is domain does not change and the range changes.

Step-by-step explanation:

it is because always range value can varry more over when H(x) is equal to A and range is equal to B .

A=B

similarly

A= -B

Answer:

The correct option is;

Both spreads are best described by the standard deviation

Step-by-step explanation:

The given information are;

,                                    College                       High School

High,                              20                               20

Low,                                6                                 3

Q₁,                                   8                                 5.5

Q₃,                                  18                                16

IQR,                                 10                                10.5

Median,                           14                                11

Mean,                              13.3                             11

σ,                                      5.2                             5.4

Checking for outliers, we have

College

Q₁ - 1.5×IQR gives 8 - 1.5×10 = -7

Q₃ + 1.5×IQR gives 18 + 1.5×10 = 33

For high school

Q₁ - 1.5×IQR gives 5.5 - 1.5×10.5 = -10.25

Q₃ + 1.5×IQR gives 16 + 1.5×10.5 = 31.75

Therefore, there are no outliers and the data is representative of the population

From the data, for the college students, it is observed that the difference between the mean, 13.3 and Q₁, 8, and between Q₃, 18 and the mean,13.3 is approximately the standard deviation, σ, 5.2

The difference between the low and the high is also approximately 3 standard deviations

Therefore the college spread is best described by the standard deviation

Similarly for the high school students, the IQR is approximately two standard deviations, the  difference between the mean, 11 and Q₁, 5.5, and between Q₃, 16 and the mean,11 is approximately the standard deviation, σ, 5.4

Therefore the high school spread is also best described by the standard deviation.

Answer:

Both spreads are best described by the standard deviation

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

The answer is b because we are looking for opposites

The opposite of +x is -x

While the opposite of -3 is +3

with this, we can switch them around.

this gives us the inverse of 3-x

Answer:

Step-by-step explanation:

First we have to find out area of the base

[tex]s = \frac{a + b + c}{2} [/tex]

[tex] = \frac{5 + 12 + 13}{2} [/tex]

[tex] = \frac{30}{2} [/tex]

[tex] = 15[/tex]

Area of base = [tex] \sqrt{s(s - a)(s - b)(s - c)} [/tex]

[tex] = \sqrt{15(15 - 5)(15 - 12)(15 - 13)} [/tex]

[tex] = \sqrt{15 \times 10 \times 3 \times 2} [/tex]

[tex] = \sqrt{5 \times 3 \times 5 \times 2 \times 3 \times 2} [/tex]

[tex] = 2 \times 3 \times 5[/tex]

[tex] = 30 \: {cm}^{2} [/tex]

Now, let's find the volume of triangular pyramid

[tex] = \frac{1}{3} \times a \times h[/tex]

[tex] = \frac{1}{3} \times 30 \times 12[/tex]

[tex] = 120 \: [/tex] cm³

Hope this helps..

best regards!!

Answer: is your  first option

Step-by-step explanation:

after going over all the available equations, your first option is the only one that had results that were much more reasonable than the others. hope it helps.

Answer:

86.55 ft

Step-by-step explanation:

First find the perimeter for 3 sides of the rectangle that are solid

24+15+24 = 63

The we find the circumference for 1/2 of the circle

C = pi d

The diameter is 15 and pi = 3.14

But we only want 1/2

1/2 C = 1/2 pi d

        = 1/2 ( 3.14) * 15

       =23.55

Add the lengths together

23.55+63 =86.55 ft

Answer:

C: SSS

Step-by-step explanation:

Two triangle are said to be similar if they have the same shape and proportion. This means that their angles are the same or their sides are in proportion. They are similar if:

i) All three corresponding angles are the same (AAA)

ii) All three corresponding sides are the same proportion (SSS)

iii) Two corresponding angles are equal and a side is in the same proportion (ASA)

iv) Two sides are in the same proportion and a corresponding angles are the same (SAS)

Given that:

AB = 12, BC = 6, AC = 3, DE = 24, EF = 12 and DF = 6

[tex]\frac{DE}{AB} =\frac{DF}{AC} =\frac{EF}{BC}\\\\\frac{24}{12}=\frac{6}{3}=\frac{12}{6}=2[/tex]

Since All the sides are in the same proportion, it supports the SSS rule.

Answer: SSS

I have done this assignment before

Answer:

It is C

Step-by-step explanation:

42.60=43.00

587.70=588.00

27.99=28.00

Answer:

Option D. 6√5.

Step-by-step explanation:

Please see attached photo for details.

The value of x can be obtained by using pythagoras theory as illustrated below:

In triangle ΔABC:

x² = z² + 12².... (1)

In triangle ΔABD:

15² = x² + y²...... (2)

In triangle ΔACD:

y² = z² + 3²....(3)

Substitute the value of y² in equation 3 into equation 2. We have:

15² = x² + y²

15² = x² + z² + 3²... (4)

From equation:

x² = z² + 12²

Make z² the subject

z² = x² – 12²

Substitute the value of z² into equation 4. We have:

15² = x² + z² + 3²

15² = x² + x² – 12² + 3²

15² = 2x² – 12² + 3²

225 = 2x² – 144 + 9

Collect like terms

225 + 144 – 9 = 2x²

360 = 2x²

Divide both side by 2

360/2 = x²

180 = x²

Take the square root of both side

x = √180

Expressing in surd form, we have:

x = √(36 x 5)

x = √36 x √5

x = 6√5

Answer:

n = 2

Step-by-step explanation:

Given

5( [tex]\frac{n-1}{10}[/tex] ) = [tex]\frac{1}{2}[/tex] ← distribute parenthesis on left side

[tex]\frac{n-1}{2}[/tex] = [tex]\frac{1}{2}[/tex]

Since denominators are both 2 then equate numerators

n - 1 = 1 ( add 1 to both sides )

n = 2

Answer:

Total number of animals in the group = 170

Step-by-step explanation:

Let the number of sheep = a

Number of dragons in the group = 75

Number of dragons opposite dragons = 37

Number of sheep opposite to the dragon = 1

Number of sheep left = a - 1

Number of sheep opposite to sheep = [tex]\frac{(a-1)}{2}[/tex]

Since. number of sheep opposite to sheep is 10 more than of dragons opposite dragons,

[tex]\frac{(a-1)}{2}[/tex] = 37 + 10

[tex]\frac{(a-1)}{2}=47[/tex]

a - 1 = 94

a = 95

Then total number of animals in the group = Total number of sheep + Total number of dragons

= 95 + 75

= 170

Therefore, total number of animals in the group are 170.

Answer:

Sister is 70

Step-by-step explanation:

John is 39.

8 less than twice his age is

39*2-8 = 70

Answer:

70 years old.

Step-by-step explanation:

Since John's sister is 8 years younger than TWICE his age, we just need to multiply 39*2 which equals 78. Now we just need to subtract 8 which equals 70.

Hope this helps!! <3

Answer:

59.0

Step-by-step explanation:

Given a right angled triangle, ∆XYZ, to know which trigonometric ratio formula to apply in finding the measure of angle X, note the following:

Opposite side to angle X = 6

Hypotenuse = 7

Therefore, we would apply the following trigonometric ratio formula to solve for m<X:

[tex] sin X = \frac{6}{7} [/tex]

[tex] sin X = 0.8571 [/tex]

[tex] X = sin^{-1}(0.8571) [/tex]

[tex] X = 58.99 [/tex]

[tex] m < X = 59.0 [/tex] (rounded to nearest tenth)

Answer:

x=17

Step-by-step explanation:

7x and 2x+27 are supplementary meaning they add up to be 180 degrees.

so, 7x + 2x + 27 = 180

9x + 27 =180

9x = 153

x = 17

hope this helped

Answer:   [tex]t_9=\dfrac{1}{2^8}[/tex]

Step-by-step explanation:

[tex]t_n=t_1\times r^{n-1}\\\\Given: t_1=1,\quad r=\dfrac{1}{2}\\\\\\t_9=1\times\bigg(\dfrac{1}{2}\bigg)^{9-1}\\\\\\.\quad =\large\boxed{\dfrac{1}{2^8}}[/tex]

x=−0.23240812,−1.43425854

Answer:

m∠D = 94°

Step-by-step explanation:

Quadrilateral ABCD is also called a cyclic quadrilateral or a quadrilateral that is inscribed in a circle.

Opposite angles in a cyclic Quadrilateral are supplementary, i.e the sum of two opposite angles in a Quadrilateral = 180°

m∠A + m∠C = 180°

m∠A = 74°

74° + m∠C = 180°

m∠C = 180° - 74°

m∠C = 106°

In a cyclic quadrilateral, the total sum of the angles outside the circle = 360°

i.e =

m∠AB + m∠BC + mDC + mAD = 360°

m∠DAB= ( m∠C) × 2

= 106° × 2 = 212°

m∠DAB = m∠AD + m∠AB

m∠AD = 79°

212° = 79° + m∠AB

m∠AB = 212° - 79°

= 133°

m∠ABC = m∠AB + m∠BC

m∠AB = 133°

m∠BC= 55°

m∠ABC = 133° + 55°

= 188°

We are asked to find m∠D

m∠D = 1/2m∠ABC

m∠ABC = 188°

m∠D = 1/2 × 188°

m∠D = 94°

Therefore, m∠D = 94°

Answer:

(-1, -2) last answer

Step-by-step explanation:

x = 1 is a vertical line

Answer:

(-1, -2)

Step-by-step explanation:

This is because the x-coordinate goes 2 units left to the line x = 1 and the y-coordinate remains the same.

Answer:

9*((2-1)/9)

or

2 -1

9

2-9 =-7

9. 9

9× -7

9

=-7

2- 3

9. -3

=(1.22222222222)

or

11/9

or

1*(2/9)

Answer:

Colin is wrong

Step-by-step explanation:

The question is incomplete because the chart or the table which shows the data is not given. I have attached the full question at the bottom. Consult it for better understanding.

We can clearly see in the chart the number of lates in January is 30, while the number of lates in March is 20.

As the half of 30 is 15, not 20, we can say that the statement of Colin is wrong, because the number of lates in March should be 15 to prove his statement true

Answer:

the probability that they find enough subjects for their​ study is 0.9515

Step-by-step explanation:

From the given information:

Let X be the random variable that follows a normal distribution.

Therefore:

X [tex]\sim[/tex]Binomial(n=733,p=0.04)

[tex]\mu = np[/tex]

[tex]\mu = 733*0.04[/tex]

[tex]\mu = 29.32[/tex]

[tex]\sigma = \sqrt{np(1-p)}[/tex]

[tex]\sigma = \sqrt{29.32(1-0.04)}[/tex]

[tex]\sigma = \sqrt{29.32(0.96)}[/tex]

[tex]\sigma = \sqrt{28.1472}[/tex]

[tex]\sigma = 5.305[/tex]

The probability of P(X ≥ 21) lies in the region between 20.5 and 21.5 by considering a discrete contribution of a continuous normal distribution. Eventually, X > 20.5

∴

P(X >20.5)= P(Z > z)

Using  standard normal z formula:

[tex]z = \dfrac{x-\mu}{\sigma}[/tex]

[tex]z = \dfrac{20.5-29.32}{5.305}[/tex]

[tex]z = \dfrac{-8.82}{5.305}[/tex]

[tex]z = -1.662582[/tex]

z = -1.66

P(X >20.5)= P(Z > -1.66)

From the standard z tables ;

P(X >20.5)= 1 - 0.0485

P(X >20.5)= 0.9515

Answer:  Exponential function

Step-by-step explanation:

A linear function is the form[tex]f(x)=mx+c[/tex] , where m is the constant rate of change of y with respect to x and c is the y-intercept.

An exponential growth function is in the form [tex]f(x)=A(1+r)^x[/tex], where r is the rate of growth (generally in percent) and A is initial value.

If the population of a certain type of seahorse grew by 13% from year to year, then the rate of growth is 13% .

Hence it is an exponential equation.