how many decimal places should be in the answer if 2.214 is added to 6.3

The chance that both the book are of statistics is [tex]\boxed{\dfrac{1}{21}}[/tex].

Further Explanation:

Given:

The total number of statistics book is [tex]2[/tex].

The total number of biology book is [tex]5[/tex].

Concept used:

Probability is defined as the ratio of favorable outcomes to total outcomes.

[tex]\boxed{\text{Probability}=\dfrac{\text{favorable outcomes}}{\text{total outcomes}}}[/tex].

Combination is defined as the selection of all or part of object without considering the order of the object.

[tex]\boxed{^{n}C_{r}=\dfrac{n!}{r!\cdot (n-r)!}}[/tex]

Here, [tex]n[/tex] is the total number of object and [tex]r[/tex] is the number of object to be chosen.

Calculation:

The total number of book is [tex]7[/tex].

The chance of getting the statistics books is the favorable outcomes for the problem.

The selection of two statistics book from two statistics book is represented as follows:

[tex]\boxed{^{2}C_{2}}[/tex]

The total outcomes can be obtained by selection of two books from seven books which is represented as follows:

[tex]\boxed{^{7}C_{2}}[/tex]

Write the formula to obtain the chance that both the books are statistics.

[tex]\boxed{P=\dfrac{^{2}C_{2}}{^{7}C_{2}}}[/tex]

Solve the above equation to obtain the chance that both the books are of statistics.

[tex]\begin{aligned}P&=\dfrac{^{2}C_{2}}{^{7}C_{2}}\\&=\dfrac{\frac{2!}{2!\cdot (2-2)!}}{\frac{7!}{2!\cdot (7-5)!}}\\&=\dfrac{1}{\frac{7\times 6}{2}}\\&=\dfrac{1}{21}\end{aligned}[/tex]

Therefore, the probability that the two selected books are of statistics is [tex]\boxed{\dfrac{1}{21}}[/tex].

Learn more:

1. Simplification: https://brainly.com/question/1602237

2. Quadratic equation: https://brainly.com/question/1332667

Answer details:

Grade: High school.

Subject: Mathematics.

Chapter: Probability.

Keywords: Probability, statistics, favorable, outcomes, total outcomes, 0.047, \frac{1}{{21}}, chance, biology books, 2, 7,  chances, randomly chosen.

Counterexample:

[tex] p=2\\
q=3\\\\
pq-2=2\cdot3-2=4 [/tex]

4 is not a prime number. So, it's false.

To determine the radius and circumference of a circle with an area of 153.86 square inches, one must first divide the area by 3.14 to solve for r², then take the square root to find the radius, and finally use the radius to calculate the circumference. The radius is approximately 7.00 inches, and the circumference is approximately 43.96 inches.

To find the radius and circumference of a circle with an area of 153.86 square inches, we first use the formula for the area of a circle, which is A = πr². Given that A is 153.86 and π is approximately 3.14, we can rearrange the formula to solve for the radius (r) as follows:

Performing the calculations, we get:

Therefore, the radius of the circle is approximately 7.00 inches, and the circumference is approximately 43.96 inches.

To find the radius from the area of a circle, use the formula r = sqrt(A/pi), with A = 153.86 sq inches and pi as 3.14. Once the radius is determined, calculate the circumference with the formula C = 2*pi*r. Both values should respect the significant figures.

The student is asking for help finding the radius and circumference of a circle given its area using 3.14 for pi. To find the radius, we start with the area formula for a circle, which is A = πr². Given the area A as 153.86 square inches, and using 3.14 for π, the radius r can be found by rearranging the formula to r = √(A/π). Plugging the numbers in, we get r = √(153.86/3.14), which we then calculate.

Once we have the radius, we can find the circumference C of the circle using the formula C = 2πr. Now that we know the radius, we plug the value into this formula to get the circumference.

Both radius and circumference should be calculated carefully, keeping in mind significant figures. The radius should then be used to calculate the circumference, which will be limited by the same degree of precision.

The ordered  pair which can be removed so that resulting graph represent a function is:

                               (1,3)

Function--

A function is a relation in which each of the element of first set is mapped to a single element of the other set.

i.e. no element is mapped to two elements i.e. there is a single image for each pre-image.

Here in the graph we have ordered pairs as:

(-5,-3)  (-4,-4)  (-2,2)  (1,-2)  (1,3)  (2,1)  (5,-4)

Hence, we see that element " 1 " is mapped two different elements

1 is mapped to -2  ( since, we have ordered pair (1,-2) )

and 1 is mapped to 3 ( since, we have ordered pair (1,3) )

If we  remove the ordered pair (1,3) then the resulting graph will be a graph of a function.

Answer:

The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.

Step-by-step explanation:

The rule we have is (x, y)→(2x, 2y).  This means that each x-coordinate and each y-coordinate are multiplied by 2.  This is a dilation by a factor of 2.

This will stretch the image by a factor of 2; this means the sides will be twice as long.  This means they will not be congruent.

Answer: The triangles are not congruent because △D′E′F′ is a dilation of △DEF .

Step-by-step explanation:

Rigid motions form congruent figures, the common rigid motions are:  

1) translation (moves figure about some distance)

2) reflection (creates mirror image)

3) rotation (rotate figure about some degrees)

Dilation : It does not create congruent images. It creates an image that is the exactly same shape as the original, but have a different size with the help of a scale factor k .

Given : The rule (x,y)→(2x,2y) maps △DEF to △D′E′F′.

Here the coordinates of the image are increased by using a scale factor 2.

So △D′E′F′ must be an enlargement of △DEF.

⇒△D′E′F′ is a dilation of △DEF

It means : The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.

Answer:

The answer is D. Hope it helps!

Answer:

7x - 2 = 2y

7x = 2y + 2

so

7x = 2y + 2

3x = 2y - 1  

----------------subtract

4x = 3

 x = 3/4

7x - 2 = 2y

7(3/4) - 2 = 2y

21/4 - 2 = 2y

21/4 - 8/4 = 2y

13/4 = 2y

so

y = 13/4 * 1/2

y = 13/8

answer

(3/4, 13/8)

Step-by-step explanation:

The two numbers that multiply to 12 and add to negative 4 are -6 and 2.

To find the two numbers, we need to solve the system of equations:

1. xy = 12 (Equation 1)

2. x + y = -4  (Equation 2)

From Equation 2, we can express y in terms of x:

y = -4 - x (Equation 3)

Now, we substitute Equation 3 into Equation 1:

[tex]\( x(-4 - x) = 12 \)\\ \( -4x - x^2 = 12 \)\\ \( x^2 + 4x - 12 = 0 \)[/tex]

We can factor this quadratic equation:

[tex]\( (x + 6)(x - 2) = 0 \)[/tex]

Setting each factor equal to zero gives us two possible solutions for x:

[tex]\( x + 6 = 0 \) or \( x - 2 = 0 \)[/tex]

So, [tex]\( x = -6 \) or \( x = 2 \)[/tex].

Using Equation 3 to find the corresponding y values:

If ( x = -6 ), then ( y = -4 - (-6) = 2 ).

If ( x = 2 ), then ( y = -4 - 2 = -6 ).

Therefore, the two pairs of numbers that satisfy both conditions are (-6, 2) and (2, -6). Since the question asks for two numbers, and both pairs contain the same numbers, the answer is -6 and 2.

volume = l x w x h

 to increase volume by 3 you would have  3*l*w*h

so 3*l*w*h= l*2*w* x *h  ( x is the scale factor)

cancel out the l w and h on both sides

3 = 2x 

Divide both sides by 2   

 x = 3/2 = 1.5

 the height should increase by a factor of 1.5

Answer:

3/2 or 3 over 2

Step-by-step explanation:

A cereal manufacturer decides to offer a new family-sized box based on the regular-sized box.

They want the volume of the family-sized box to be three times the volume of the regular-sized box. However, they want the length of the family-sized box to be the same as the regular-sized box.

If they decide to double the width to create the family-sized box, by what factor must they increase the height?

Odyssey Question

The number 8 belongs to the sets of natural numbers, integers, rational numbers, and real numbers, while the number 0.25 only belongs to the sets of rational and real numbers.

In mathematics, numbers can belong to various sets such as the natural numbers, integers, rational numbers, real numbers, etc. In this case, the number 8 belongs to all these sets because it is a whole number without fractions or decimals. Therefore, it is a natural number, integer, rational number and real number.

On the contrary, 0.25 is a decimal which belongs to the sets of rational numbers and real numbers. It does not belong to the sets of natural numbers or integers because it is not a whole number.

https://brainly.com/question/32665385