9. If the diagonal of a square is 12 centimeters, the area of the square is

A. 102 cm2.
B. 36 cm2.
C. 144 cm2.
D. 72 cm2.

Answer:

A. mean

Step-by-step explanation:

The mean of data is given by the ratio of the sum of all the values to the total number of values. It gives the average value of the set of values.

[tex]\bar{x}=\frac{1}{n}}\left(\sum _{i=1}^{n}{x_{i}}\right)[/tex]

Here, the manager wants to get an estimate of how much time it takes by each employee to complete a task. The mean will be the sum of time taken by each person to complete a task divided by the number of employees.

Answer:

1, 3, 6, 7, 9...

1, 4, 8, 7, 11...

Step-by-step explanation:

(1, 3, 6, 7, 9...)

This one is the sequence because it follows a specific pattern, which is 2n-1, or (2 x figure number) - 1. 1x2-1=1. 2x2-1=3. 3x2-1=7. And so on.

(1, 4, 8, 7, 11...)

This one, no matter how you look at it, has no pattern. Its not a proper sequence of numbers.

I say the third circle from the top down. The central angle is the measure of minor arc AB.

The central angle here is 60 degrees, shown by the third circle down from the top. This is the right answer.

The circle that shows chord AB to measure 60 degrees is Option(C).

A chord of a circle divides the circle into two regions, which are called the segments of the circle. The minor chord is the shorter arc connecting two endpoints on a circle . The measure of a minor chord is always less than 180° .

In the four Options given alongside diagram, Option(C) represents a minor chord with its central angle subtended by the minor segment as 60°.

Thus AB is the minor sector of the circle and the angle measures 60° with that chord itself. The other three options do not define the minor chord or segment AB therefore not measuring its central angle.

Therefore, the circle that shows chord AB to measure 60 degrees is Option(C).

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Answer:

14h=c

Step-by-step explanation:

14 times total hours boat of used (h) is the total cost of the boat > 14h=c

Answer:

  A

Step-by-step explanation:

A function is not allowed to have two Y values for the same X value. Any table with the same X value appearing more than once is not a function. Only table A qualifies as a function.

Answer:

The new area is 4 times the original area

Step-by-step explanation:

we know that

The area of a rectangle is equal to

[tex]A=bh[/tex]

where

b is the base

h is the height

If the height is multiplied by 4

then

the new area is equal to

[tex]A=(b)(4h)[/tex]

[tex]A=4bh[/tex]

therefore

The new area is 4 times the original area

Answer:

  hyperbola

Step-by-step explanation:

If the sum is constant, the figure is an ellipse.

If the difference is constant, you get a hyperbola.

If one length is constant, you get a circle.

If the length to a point is the same as the length to a line, you get a parabola.

Answer:

There are four type of conic generated when a double napped cone is cut by a plane

1.Circle

2.Parabola

3.Ellipse

4.Hyperbola

Among these four, Hyperbola is the conic , ,all points in a plane where the difference between the lengths of segments x and y remains constant.

A point on Semi major Axis=(a,0),lying on the Hyperbola.

A point on Semi Minor axis =(0,b),not lying on the Hyperbola.

Take a point D lying on the hyperbola,and two points M and N not lying on the hyperbola.

DM-DN=2a(Length of major axis)

Answer:

[tex]g^2-4g-21=(g-7)(g+3)[/tex]

Step-by-step explanation:

To complete the left side of the equation, we need to bring it to the form

[tex](g-a)(g+b)[/tex]

expanding this expression we get:

[tex]g^2+bg-ag-ab[/tex]

[tex]g^2+(b-a)g-ab[/tex]

Thus we have

[tex]g^2-4g-21=g^2+(b-a)g-ab[/tex]

from here we see that for both sides of the equation to be equal, it must be that

[tex]b-a=-4[/tex]

[tex]-ab=-21[/tex].

Getting rid of the negative signs we get:

[tex]a-b=4[/tex]

[tex]ab=21[/tex]

At this point we can either guess the solution to this system (that's how you usually solve these types of problems) or solve for [tex]a[/tex] and [tex]b[/tex] systematically.

The solutions to this set are [tex]a=7[/tex] and [tex]b=3[/tex]. (you have to guess on this—it's easier)

Therefore, we have

[tex](g-a)(g+b)=(g-7)(g+3)[/tex]

which completes our equation

[tex]\boxed{ g^2-4g-21=(g-7)(g+3)}[/tex]

Answer: -7 and +3

did the assignment

Answer:

B.3

Step-by-step explanation:

If you divide 36 by 12 or 27 by 9 or 21 by 7, you get 3, which means that triangle ABC is 3 times as large as triangle XYZ.

For this case it is observed that the measures of the small triangle are smaller than those of the large triangle, so we have to use a division scale factor. We have to:

[tex]xy = \frac {AB} {3} = \frac {27} {3} = 9\\yz = \frac {BC} {3} = \frac {36} {3} = 12\\xz = \frac {AC} {3} = \frac {21} {3} = 7[/tex]

It is observed that the factor used was [tex]\frac {1} {3}.[/tex]

ANswer:

Option D

Step-by-step explanation:

log₅ 9 = x

5^(log₅ 9) = 5^x

9 = 5^x

Answer:

The probability that the students chosen are not both girls is 62/95 ⇒ (c)

Step-by-step explanation:

* Lets explain how to find the probability of an event  

- The probability of an Event = Number of favorable outcomes ÷ Total

  number of possible outcomes

- P(A) = n(E) ÷ n(S) , where

# P(A) means finding the probability of an event A  

# n(E) means the number of favorable outcomes of an event

# n(S) means set of all possible outcomes of an event

- Probability of event not happened = 1 - P(A)

- P(A and B) = P(A) . P(B)

* Lets solve the problem

- There is a group of students

- There are 8 boys and 12 girls in the group

∴ There are 8 + 12 = 20 students in the group

- The students are sent to represent the school in a parade

- Two students are chosen at random

∴ P(S) = 20

- The students that chosen are not both girls

∴ The probability of not girls = 1 - P(girls)

∵ The were 20 students in the group

∵ The number of girls in the group was 12

∴ The probability of chosen a first girl = 12/20

∵ One girl was chosen, then the number of girls for the second

   choice is less by 1 and the total also less by 1

∴ The were 19 students in the group

∵ The number of girls in the group was 11

∴ The probability of chosen a second girl = 11/19

- The probability of both girls is P(1st girle) . P(2nd girl)

∴ The probability of both girls = (12/20) × (11/19) = 33/95

- To find the probability of both not girls is 1 - P(both girls)

∴ P(not both girls) = 1 - (33/95) = 62/95

* The probability that the students chosen are not both girls is 62/95

Answer:

I got B as my answer, hope it helps

The statements that are true about the measures of center are: Option B. The median for Group A is less than the median for Group B and Option C. The mode for Group A is less than the mode for Group B.

The median of a data set is the middle value when the values are arranged in numerical order, or the average of the two middle values if the data set has an even number of elements.

For group A, the median falls between 1 and 2, thus, we can say the median = 1 + 2/2 = 1.5.

For group B, the median falls between 2 and 3, thus, we can say the median = 2 + 3/2 = 2.5.

The mode for group A is 1, while that of group B is 3, therefore, we can conclude that:

B. The median for Group A is less than the median for Group B, and

C. The mode for Group A is less than the mode for Group B.

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[tex]arc=\frac{\pi\theta}{360}(d)[/tex]

There is no any option, but the question is answerable. The length of an arc of a circumference is a fraction of that circumference. Recall that a circumference measures 360 degrees. Suppose you have an arc whose central angle [tex]\theta[/tex] degrees, then the arc of a circumference can be found as:

[tex]\boxed{arc=\frac{\pi\theta}{360}(d)} \\ \\ Where: \\ \\ \theta: \ central \ angle \\ \\ d: \ diameter \ of \ the \ circle[/tex]

So in this case, the expression:

[tex]\frac{\pi\theta}{360}[/tex]

represents the fraction we are talking about.

The equation that gives the length of an arc is s = θ * r, where s is the distance traveled along the circular path, θ is the angle of rotation, and r is the radius of curvature.

The equation that gives the length of an arc is given by:

Length of Arc (s) = θ * r

Where:

For example, if the angle of rotation is 45 degrees and the radius is 5 units, the length of the arc would be:

s = (45 degrees) * (5 units) = 225 degrees * units

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Answer:

A(n)=130+13(n-1) ; 86

Step-by-step explanation:

Here is the sequence

130,143,156,169.......

the first term denoted by a is 130 and the common difference denoted by d is second term minus first term

143 - 130 = 13

Hence a=130 and d = 13

Now we have to evaluate to 13th term.

The formula for nth term of any Arithmetic Sequence is

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

Hence substituting the values of a ,and d  get

A(n)=130+13(n-1)

To find the 13th term , put n = 13

A(13)=130+13*(13-1)

      = 130+13*12

      = 130+156

A(13) = 286

Answer:

4. 158

Step-by-step explanation:

First let's make things a little simpler and put these arcs in terms of x.  We know that the degree measure around the outside of a circle, regardless of its size, is 360.  So let's say that arc BC is x.  That means that arc BDC is 360 - x.  This is because arc BC + arc BDC = 360.  Substituting in our x's we have:

x + 360 - x = 360 and

360 = 360.  (That's just the proof that putting in our x's as we did does in fact work!)

Following the formula then, we have

[tex]22=\frac{1}{2}(360-x-x)[/tex] and

[tex]22=\frac{1}{2}(360-2x)[/tex]

Multiply both sides by 2 to get rid of the fraction and get

44 = 360 - 2x

Subtract 360 rom both sides to get

-316 = -2x

Divide both sides by -2 to get that x = 158

Since we are looking for arc BC and we designated arc BC as our x, that means that arc BC = 158.

Answer: A. The molten mixture of rock-forming substances, gases, and water from the mantle

Magma is a mass of molten rock that is found in the deepest layers of the Earth at high temperature and pressure, and that can flow out through a volcano.

The composition of this mass is a mixture of liquids, volatile and solids that when they reach the surface in an eruption becomes lava, which when cooled crystallizes and gives rise to the formation of igneous rocks.

Answer:

Rational numbers are decimals that can't be turned into fractions and irational numbers are decimal numbers that can be turned into Fraction.

Step-by-step explanation:

Example Pi 3.14 can be 22/7

Answer:

11

Step-by-step explanation:

49-5=44

44/4=11

Answer:

  (b)  line symmetry only

Step-by-step explanation:

This question asks you to identify any applicable form of symmetry the given figure may have.

For plane figures, three kinds of symmetry are defined:

A figure is symmetrical about a point if that point is a midpoint between every point on the figure and a corresponding point on the figure.

A figure is symmetrical about a line if that line is the perpendicular bisector of the segment between any point on the figure and a corresponding point on the figure.

A figure has rotational symmetry if it can be rotated about a center and be congruent to itself. The number of different rotational angles for which this is true is the degree of the rotational symmetry.

There is no point within the bounds of the figure that matches the definition of the center of symmetry about a point.

A vertical line through the center of the figure will serve as a line of symmetry. Each point on the left side of the line corresponds to a point on the right side of the line at the same distance. So, the figure has symmetry about a line.

There is no angle other than 360° through which the figure can be rotated to map to itself. It has no rotational symmetry.

Answer:

3+2x<30

Step-by-step explanation:

3 represents that Emily is 3 years older than 2x

2x represents twice Mary's age

<30 represents that it's always less than 30

Answer:

The compound inequality is [tex]0<x<9[/tex]

Step-by-step explanation:

Consider the provided information.

It is given that Emily is three years older than twice her sister Mary's age.

Let x represent Mary's age.

Then the age of Emily is: 2x+3

The sum of their ages is less than 30.

This can be written as:

[tex]2x+3+x<30[/tex]

[tex]3x+3<30[/tex]

[tex]3x<27[/tex]

[tex]x<9[/tex]

As we know the age can't be a negative number.

Therefore, the age of Mary must be a positive number greater than 0.

Thus, the compound inequality is [tex]0<x<9[/tex]

Step-by-step answer:

There are two squares, the inner one of which is a garden, surrounded by a path 1 foot wide.

The outer square represents the periphery of the path, as shown in the attached image.

One bag of gravel covers 8 square-feet.  Need the number of bags required to cover the path.

Solution:

We first need to find the total area of the path by subtracting the area of garden from the overall area, namely the outer square.

Area of path = 12^2 - 10^2 = 144-100 = 44 sq. ft.

Number of bags required

= area (sq.ft) / area each bag covers

= 44 sq.ft / 8 (sq.ft / bag)

= 5.5 bags

Answer: 6 bags need to be purchased.

1. First, let us find the probability that the first card is a diamond.

Now, since we are given that there are four suits and there are, assumably, an equal number of cards in each suit, we can say that the probability of choosing a diamond card is 1/4. We can also write this out as such, where D = Diamond:

Pr(D) = no. of diamond cards / total number of cards

There are 52 cards in a deck, and 13 cards of each suit, thus:

Pr(D) = 13/52 = 1/4

2. Now we need to calculate the probability of not choosing a diamond as the second card.

In many cases, when given a problem that requires you to find the probability of something not happening, it may be easier to set it out as such:

Pr(A') = 1 - Pr(A)

ie. Pr(A not happening, or not A) = 1 - Pr(A happening, or A)

This works because the total probability is always 1 (100%), and it makes sense that to find the probability of A not happening, we take the total probability and subtract the probability of A actually happening.

Thus, given that we have already calculated that the probability of choosing a Diamond is 1/4, we can now set this out as such:

Pr(D') = 1 - Pr(D)

Pr(D') = 1 - 1/4

Pr(D') = 3/4

3. Now we come to the final step. To find the probability of something and then something else happening, we must multiply the two probabilities together. Thus, given that Pr(D) = 1/4 and Pr(D') = 3/4, we get:

Pr(D)*Pr(D') = (1/4)*(3/4)

= 3/16

Thus, the probability of choosing a diamond as the first card and then not choosing a diamond as the second card is 3/16.

The first card is a diamond and the second card is not a diamond when drawing cards with replacement from a standard deck is 3/16.

The subject of this question is probability, a topic in Mathematics, specifically dealing with the calculation of the likelihood of certain outcomes when drawing cards from a deck. To find the probability that the first card is a diamond and the second card is not a diamond when each card is replaced after being drawn, we must consider two independent events. The probability of drawing a diamond card from a standard deck of 52 cards is 1/4, since there are 13 diamonds out of 52 cards. Because the card is replaced, the probability that the second card is not a diamond remains the same as for any single draw where the desired outcome is not a diamond, which is 39/52 or 3/4. Thus, the combined probability of both events happening in sequence (first drawing a diamond, then drawing a non-diamond) is determined by multiplying the probabilities of individual events: (1/4) × (3/4) = 3/16.

Answer:

x=15

Step-by-step explanation:

We know that a right angle is 90 degrees. When we subtract the 30 from 90, we get 60 degrees as the other, smaller angle. Then, we divide 60 by 4 to get 15. This mean x equals 15.

Answer:

  C.  -7x

Step-by-step explanation:

Only one of the offered choices passes the horizontal line test: at most one point of intersection with any horizontal line.

__

A: a parabola opening upward, so will have two points of intersection with a general horizontal line (only one at the vertex).

B: a horizontal line, so will have an infinite number of points of intersection with a horizontal line.

D. A "V-shaped" graph that will generally have two points of intersection with a horizontal line (only one at the vertex).

Answer:

m(x)=-7x C

Step-by-step explanation:

Edge

Answer:

D (-5 , 4) → D' (1 , -4) → D" (-1 , -4) ⇒ 2nd answer

Step-by-step explanation:

* Lets revise some transformation

- If the point (x , y) translated horizontally to the right by h units

 ∴ Its image is (x + h , y)

- If the point (x , y) translated horizontally to the left by h units

 ∴ Its image is (x - h , y)

- If the point (x , y) translated vertically up by k units

 ∴ Its image is (x , y + k)

- If the point (x , y) translated vertically down by k units

 ∴ Its image is(x , y - k)

- If point (x , y) reflected across the x-axis

 ∴ Its image is (x , -y)

- If point (x , y) reflected across the y-axis

 ∴ Its image is (-x , y)

* Now lets solve the problem

- The point D is (-5 , 4)

- The vector of the translation is <6 , -8>

∵ 6 is positive number

∴ Point D will translate horizontally 6 units to the right

∵ x-coordinate of D = -5

- Add the x-coordinate of D by 6 to find the x-coordinate of D'

∴ The x-coordinate of D' = -5 + 6 = 1

∴ The x-coordinate of D' = 1

∵ -8 is negative number

∴ Point D will translate vertically 8 units down

∵ y-coordinate of D = 4

- Add the y-coordinate of D by -8 to find the y-coordinate of D'

∴ The y-coordinate of D' = 4 + -8 = -4

∴ The y-coordinate of D' = -4

∴ The coordinates of D' are (1 , -4)

- If point (x , y) reflected across the y-axis  then its image is (-x , y)

∵ D' is reflected across the y-axis

∵ D' = (1 , -4)

- Change the sign of its x-coordinate

∴ D" = (-1 , -4)

∴ The coordinates of D" are (-1 , -4)

* D (-5 , 4) → D' (1 , -4) → D" (-1 , -4)

Answer:

D (−5, 4) → D ′(1, −4) → D ″(−1, −4)

Step-by-step explanation:

Use the translation vector <6,−8>  to determine the rule for translation of the coordinates: (x,y)→(x+6,y+(−8)).

Apply the rule to translate point D(−5,4).

D(−5,4)→(−5+6,4+(−8))→D'(1,−4).

To apply the reflection across y-axis use the rule for reflection: (x,y)→(−x,y).

Apply the reflection rule to point D'(1,−4).

D'(1,−4)→D''(−1,−4).

Therefore, D(−5,4)→D'(1,−4)→D''(−1,−4) represents the translation of D(−5,4) along vector <6,−8> and its reflection across the y-axis.

Answer:

1.4%

Step-by-step explanation:

You can only include 7 and 8 in the answer because it didn't include 6 in the question. add the frequency for both of those sizes (14) and divide by the total  (1000) to get the probability. multiply by 100 to get answer as a percent. 1.4%

Answer:

1%

Step-by-step explanation:

We are given the results of survey of one thousand families to determine the distribution of families by their size.

We are to find the probability (in percent) that a given family has more than 6 people.

Frequency of people with more than 6 people = 10 + 4 = 14

Total frequency = 1000

P (families with more than 6 people) = (14 / 1000) × 100 = 1.4% ≈ 1%

Answer:

(3x² - 2)(x² + 5)

Step-by-step explanation:

Given

3[tex]x^{4}[/tex] - 2x² + 15x² - 10

Factor the first/second and third/fourth terms

= x²(3x² - 2) + 5(3x² - 2) ← factor out (3x² - 2) from each term

= (3x² - 2)(x² + 5)

Answer:

[tex](x^2+5)(3x^2-2)[/tex]

Step-by-step explanation:

The polynomial is

[tex]3x^4-2x^2+15x^2-10[/tex]

You can group the first and third term and the second and last term

[tex]3x^4+15x^2-2x^2-10[/tex]

Factorize each pair

[tex]3x^4+15x^2-2x^2-10[/tex]

[tex]3x^2(x^2+5)-2(x^2+5)[/tex]

Finally, you can factor the [tex](x^2+5)[/tex] and obtain

[tex](x^2+5)(3x^2-2)[/tex]

Then, the answer is (x2 + 5)(3x2 – 2)

Answer:

  13/20 = 0.65 mile

Step-by-step explanation:

Finding the difference of two fractions is usually done by first expressing each of them using a common denominator. Here, both 4 and 10 are factors of 20, so 20 is a suitable common denominator.

  9/10 - 1/4 = 18/20 - 5/20 = (18 -5)/20 = 13/20

This can be expressed as a decimal:

  13/20 = (13·5)/(20·5) = 65/100 = 0.65

9/10 of a mile is 13/20 of a mile larger than 1/4 of a mile. In decimal, that is 0.65 miles larger.

Answer:

Option D x=4

Step-by-step explanation:

we have

[tex]f(x)=\frac{1}{x-3}+1[/tex]

[tex]g(x)=2\sqrt{x-3}[/tex]

Solve the system by graphing

Remember that the solution of the system of equations (f(x)=g(x)) is the x-coordinate of the intersection point both graphs

The intersection point is (4,2)

therefore

x=4

see the attached figure

Answer:

C there is no mode

Step-by-step explanation:

The mode is the number that appears most often.  Since there is no number that appears more than once, there is no mode