In how many ways 4 books can be chosen from 8 different books and be arranged in 4 spaces on a bookshelf? ​

Answer:

-7

Step-by-step explanation:

8-15 = -7 but since it's an absolute value, it is 7 and then you add the negative sign in front since it is not in the absolute value.

Answer:

it = my but lol

Step-by-step explanation:

lol sorry just trying to get points

Answer:

Step-by-step explanation:

the right choice is C

you use c^2=a^2+b^2

where the largest side is the hypotenuse

Answer:

C.

a triangle with sides measuring 20, 21, and 29

Step-by-step explanation:

As, √(20)²+(21)² = √400+441 = √841 = 29

The longest side is taken as the hypotenuse. So 29 is the hypotenuse. Which by using Pythagoras' theorem gives us 29 ( h=√b²+p² )

Answer:

Domain : {\(x| x\neq \frac{\pi }{2} + 2\pi n\)}

All real numbers except x cannot equal to \(\frac{\pi }{2}\) and its following

The domain of the given function is -

Domain → (- ∞, + ∞).

Given is the function as -

f(x) = 4 cos(x)/(1 − sin(x))

The given function is -

f(x) = 4 cos(x)/(1 − sin(x))

Refer to the graph of the function attached.

Doman is the set of all possible {x} values. So, we can write -

Domain → (- ∞, + ∞)

Therefore, the domain of the given function is -

Domain → (- ∞, + ∞).

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Answer:

b

Step-by-step explanation:

The graph that represents the numbers of packages of mix A and mix B that can be produced is graph (b)

The representations are:

So, the system of inequalities is:

\(8x + 4y \le 120\)

\(6x + 6y \le 96\)

Next, we plot the graphs of the inequalities (see attachment)

Hence, the graph that represents the numbers of packages of mix A and mix B that can be produced is graph (b)

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To answer this question, we can graph the situation as follows:

We graphed a right triangle to express one of the given trigonometric ratios: sin(Θ). We need to find x using the Pythagorean Theorem to find the values of the other five trigonometric functions. Then we have:

Then, we have:

Now we can express the exact values of the five remaining trigonometric functions:

The exact value for cosine function:

The exact value for the tangent function is shown above.

Now the other exact values for the other trigonometric functions are:

Cosecant:

Answer:

1,800 lbs of sand

900 lbs of gravel

600 lbs of cement

Step-by-step explanation: 11*300=3,300. 300*6=1,800, 300*3=900, and 300*2=600. This is correct because if you add 1,800+900+600 you get 3,300.

Answer:

15 more bags.

Step-by-step explanation:

360/6= 60.

270/6=45

60-45=15.

Hope this helps. <3

the  parallelogram JKLM is a square.

What is square?

Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognized by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.

We are given that rajiv wishes to make a cube without lid with cardboard.

JM = -5² = 25

KL =  -5² = 25

JK = -4²=16

LM =-4²=16

So, the parallelogram JKLM is a square.

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Answer:

The 14-ounce bottle is the better deal

Step-by-step explanation:

I know this beause inorder to figure out which one is better you have to make them the same price and then see which bottle has more ounces. So I made each price 1$ so there is 1.58-ounces per dollar in the 5-ounce bottle and 1.17 -ounces per dollar in the 14-ounce bottle.

Answer: the bottom two graphs show continuous data

Step-by-step explanation:

The values of a, b and c from the given exponential function are 7, 9 and 4 respectively

According to the exponential law of indices

\(\sqrt[c]{a^b}\)

This can be written as;

\(\sqrt[c]{a^b}=a^{\frac{b}{c} }\)

Given the exponential expression

\(7^\frac{9}{4}\)

Compare with the original expression

a = 7, b = 9 and c = 4

Hence the values of a, b and c from the given exponential function are 7, 9 and 4 respectively

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Answer:

7100+410

Step-by-step explanation:

The simplified form of -20/2(7 2/3) is -230/3.

To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.

First, let's convert the mixed number 7 2/3 to an improper fraction.

7 2/3 = (7 * 3 + 2) / 3 = 23/3

Now, let's substitute the value back into the expression:

-20/2 * (23/3)

Next, we simplify the multiplication:

-10 * (23/3)

To multiply a fraction by a whole number, we multiply the numerator by the whole number:

-10 * 23 / 3

Now, we perform the multiplication:

-230 / 3

Therefore, the simplified form of -20/2(7 2/3) is -230/3.

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The number of T-shirts and shorts did Dots sell in the month of April with the total sales of $570 are 60 and 30 respectively.

A system of equation is the set of equation in which the finite set of equation is present for which the common solution is sought.

Dots sells T-shirts ($5) and shorts ($9).

Let suppose the number of T-shirts sold is x and shorts sold is y. Dots sells T-shirts ($5) and shorts ($9) with total sales of $570. Thus,

\(5x+9y=570\)

Solve it further,

\(5x+9y=570\\9y=570-5x\\y=\dfrac{570-5x}{9}\)                  ....1

People bought 2 times as many T-shirts as shorts. Thus,

\(x=2y\)                          ....1

Put the value of y form equation in this equation as,

\(x=2\times\dfrac{570-5x}{9}\\9x=1140-10x\\10x+9x=1140\\x=\dfrac{1140}{19}\\x=60\)

Put this value of x in equation 2 as,

\(x=2\times y\\60=2\times y\\y=\dfrac{60}{2}\\y=30\)

Thus, the number of T-shirts and shorts did Dots sell in the month of April with the total sales of $570 are 60 and 30 respectively.

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The area of the composite figure is 122.24 units².

The composite figure consist of a rectangle and two semi circles. Therefore, the area of the composite figure is the sum of the area of the individua shapes.

Hence,

area of the composite figure = area of the rectangle + 2(area of semi circle)

Therefore,

area of the composite figure = 9 × 8 + 2(1 / 2 πr²)

area of the composite figure = 72 + πr²

where

r = 8 / 2 = 4 units

Therefore,

area of the composite figure = 72 + 3.14 × 4²

area of the composite figure = 72 + 3.14 × 16

area of the composite figure = 72 + 50.24

area of the composite figure = 122.24 units²

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Answer:

9r

Step-by-step explanation:

4r+9r-11r+7r

Combine like terms

13r -11r+7r

2r+7r

9r

Answer: 9r

Step-by-step explanation:

4r + 9r - 11r + 7r

13r - 11r = 2r

2r + 7r = 9r

~I hope I helped you! :)~

The dimensions of the rectangular slab are 16 meters in length and 2 meters in width.

Let's assume the length of the rectangular slab of concrete is L meters. According to the given information, the width is 14 meters less than the length, so the width would be L - 14 meters.

The formula for the area of a rectangle is A = length × width. In this case, the area is given as 32 m², so we can set up the equation:

32 = L × (L - 14)

Expanding the equation, we get:

32 = L² - 14L

Rearranging the equation, we have:

L² - 14L - 32 = 0

To solve this quadratic equation, we can either factorize it or use the quadratic formula. In this case, it's easier to use the quadratic formula:

L = (-b ± √(b² - 4ac)) / (2a)

Here, a = 1, b = -14, and c = -32. Substituting these values into the formula, we get:

L = (14 ± √((-14)² - 4 × 1 × (-32))) / (2 × 1)

Simplifying further:

L = (14 ± √(196 + 128)) / 2

L = (14 ± √324) / 2

L = (14 ± 18) / 2

Therefore, we have two possible values for L:

L₁ = (14 + 18) / 2 = 16

L₂ = (14 - 18) / 2 = -2

Since the length of the slab cannot be negative, we discard the negative value.

Thus, the length of the rectangular slab is 16 meters. To find the width, we subtract 14 meters from the length:

Width = 16 - 14 = 2 meters

Therefore, the dimensions of the rectangle are 16 meters by 2 meters.

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Answer:

y = - 3x + 180

Step-by-step explanation:

Answer:

Step-by-step explanation:

Assuming that the given dimensions of 13, 13, 13 refer to the base of the rectangular pyramid, we can calculate the surface area of the pyramid as follows:

First, we need to calculate the area of the rectangular base, which is simply length x width:

Area of rectangular base = 13 x 13 = 169 square units

Next, we need to calculate the area of each triangular face of the pyramid. Since the rectangular base has two sets of parallel sides, there are two types of triangular faces: the isosceles triangles on the sides and the right triangles on the front and back.

To calculate the area of the isosceles triangles, we need to first find the length of the slant height, which can be found using the Pythagorean theorem:

a² + b² = c²

where a and b are the base and height of the triangle (both equal to 13 in this case), and c is the slant height.

13² + 13² = c²

338 = c²

c ≈ 18.38

Now that we have the slant height, we can calculate the area of each isosceles triangle using the formula:

Area of isosceles triangle = (1/2) x base x height

Area of isosceles triangle = (1/2) x 13 x 18.38

Area of isosceles triangle ≈ 119.14 square units

To calculate the area of each right triangle, we need to use the same slant height of 18.38, along with the height of the pyramid, which is also 13. Then we can use the formula:

Area of right triangle = (1/2) x base x height

Area of right triangle = (1/2) x 13 x 18.38

Area of right triangle ≈ 119.14 square units

Since there are two of each type of triangular face, the total surface area of the pyramid is:

Surface area = area of rectangular base + 2 x area of isosceles triangle + 2 x area of right triangle

Surface area = 169 + 2 x 119.14 + 2 x 119.14

Surface area = 546.28 square units

Therefore, the surface area of the rectangular pyramid with base dimensions of 13 x 13 and height of 13 is approximately 546.28 square units.

Answer:

Of course CD is higher then investing in T-bill

Step-by-step explanation:

To differentiate the function f(x) = 1/x^3, we can use the power rule of differentiation. Here's the step-by-step process:

Write the function: f(x) = 1/x^3.

Apply the power rule: For a function of the form f(x) = x^n, the derivative is given by f'(x) = nx^(n-1).

Differentiate the function: In our case, n = -3, so the derivative is:

f'(x) = -3 * x^(-3-1) = -3 * x^(-4) = -3/x^4.

Therefore, the derivative of the function f(x) = 1/x^3 is f'(x) = -3/x^4.

Siama and Wills used different methods to find the differences between (5x + 6x) and (2x - 1) but they both arrived at the same answer.

I prefer Wills method because it is easier and less complicated.

Wills method:

(5x + 6x) - (2x - 1)

Subtract both 2x and -1

5x + 6x - 2x - - 1

5x + 4x + 1

In conclusion, Wills method is preferred when both methods are compared.

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Answer:

The length of line segment QR is 30.8 units (nearest tenth).

Step-by-step explanation:

In similar triangles, corresponding sides are always in the same ratio.

Therefore, if triangle MNO is similar to triangle PQR then:

\(\implies \sf MN:PQ=NO:QR=MO:PR\)

From inspection of the given triangles, the measures of the side lengths are:

Substitute these values into the relevant ratio to create an equation:

\(\implies \sf MN:PQ=NO:QR\)

\(\implies \sf 13:40=10:QR\)

\(\implies \sf \dfrac{13}{40}=\dfrac{10}{QR}\)

Cross multiply:

\(\implies \sf 13 \cdot QR=10 \cdot 40\)

\(\implies \sf 13 \:QR=400\)

Divide both sides by 13:

\(\implies \sf \dfrac{13 \:QR}{13}=\dfrac{400}{13}\)

\(\implies \sf QR=30.7692307...\)

Therefore, the length of line segment QR is 30.8 units to the nearest tenth.

Answer:

less than

Step-by-step explanation:

Answer:

i think 7 but i am not 100% sure

Step-by-step explanation:

An equation which is true include the following: A. 4 × n × n × n × n = 4n⁴.

In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By applying the multiplication law of exponents for powers to each of the expressions, we have the following:

4 × n × n × n × n = 4n⁴

4 × n⁴ = 4n⁴

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Answer:

Step-by-step explanation:

You want to know a thermometer's reading 4 minutes and 9 minutes after begin brought into a room with a temperature of 36 °C if its initial reading is 10 °C, and it rises to 14 °C after 2 minutes.

Newton's law of cooling tells you the temperature difference of 36 -10 = 26 °C will decline exponentially. If it declines to 36 -14 = 22 °C after 2 minutes, then the temperature reading can be modeled by ...

  T = 36 -26·(22/26)^(t/2)

At times of t=4 and t=9, the temperature readings will be ...

__

Additional comment

The time constant of this thermometer is about 12 minutes, so it will take about 67 minutes to read within 0.1 °C of the room temperature.

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Answer:

Answer: A

Step-by-step explanation: its the only one that dosent have 1/2 and i double checked it goes straight through the graph