Write a math express for each verbal expression.

1.) The sum of 12 and x

2.) The product of 25 and p

3.) 24 increased by twice a number z

4.) The quotient of a number x and 4

5.) 6 less than a number x

6.) One-half of n squared

Answer:

5/8

Step-by-step explanation:

The value of the expression is 8/15

An expression in maths is a sentence with a minimum of two numbers or variables and at least one maths operation.

Given an expression, (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/225)

The expression is in the form of (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/n²)

We know, (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/n²) = (n+1)/2n

Here, n = 15.

So, (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/225) = (15+1)/(2.15) = 16/30

= 8/15

Hence, The value of the expression is 8/15

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Answer:

I'm confused what's the question ?

Hey there! :)

Answer:

C. (0, 5)

Step-by-step explanation:

Where the equation crosses the y axis is known as the y-intercept.

In the equation y = mx + b, the b  value represents the y-intercept where x = 0. Therefore:

Rearrange the equation pictured:

y = 5 - 3x --> y = -3x + 5

The b value in this equation is 5, so

The y-intercept of this equation is (0, 5).

Answer:

Option C is the correct option.

Here,

When X=0

y= 5-3*0

= 5-0

=5

x=0

y=5

Hope this helps...

Good luck on your assignment..

Answer:

Table 2

Step-by-step explanation:

The question is to identify the table where the relative frequency of orders for blue pants is half the relative frequency of their orders for black shorts.

We are interested in the number of blue pants and black shorts.

If we name them as p and b respectively, then we are looking for a table where s/p=2

Let's verify relevant data in all tables:

Table 1:

Table 2:

Table 3:

Table 4:

So only one of tables- the second one from top represents the required data.

Answer:

The second table

Step-by-step explanation:

I did the test.

Problem 9, part a)

Compass bearings always have north as the starting point. This is where 0 degrees is situated, and 360 degrees as well. As the bearing angle increases, you'll turn to the right toward the eastward direction. Effectively you're sweeping out a clockwise rotation. The bearing 322 degrees is in a northwest position as the diagram shows (place the ship at the bottom right corner of the triangle). The bottom right acute angle of the triangle is 322 - 270 = 52 degrees. This is the reference angle we'll use for finding the distance d.

With respect to the reference angle of 52 degrees, the side 18.5 is the opposite side and d is the adjacent side. Use the tangent ratio to get...

tan(angle) = opposite/adjacent

tan(52) = 18.5/d

d*tan(52) = 18.5

d = 18.5/tan(52)

d = 14.4537840903742

The approximate value of d is 14.4537840903742 km

This rounds to 14.5 when rounding to one decimal place.

=======================================================

Problem 9, part b)

Recall that

distance = rate*time

where "rate" is another term for "speed" or "velocity"

We can solve this for the time to get

time = distance/rate

------

We found the distance back in part a) above. We are given the rate of 48 km/h

So,

time = distance/rate

time = 14.4537840903742/48

time = 0.3011205018828

This is the time it takes in hours. Multiply by 60 to convert to minutes

0.3011205018828 hours = 60*0.3011205018828 = 18.067230112968 minutes

This rounds to the whole number 18

Answer:

Solution,

Finding the value of X,

[tex]11x + 2 = 68[/tex]

( being vertically opposite angles)

[tex]11x = 68 - 2 \\ 11x = 66 \\ x = \frac{66}{11} \\ x = 6[/tex]

Value of X is 6

Now, finding the value of z

[tex]z + 68 = 180[/tex]

(sum of angle in linear pair)

[tex]z = 180 - 68 \\ z = 112[/tex]

Value of z is 112.

Hope this helps....

Good luck on your assignment...

Answer: 2(y + 6)(-y + 6)

Step-by-step explanation: Factor 72 - 2y^2

                                             -2y^2 + 72

                                             = 2(y + 6)(-y + 6)

Answer:

[tex]-2\left(y+6\right)\left(y-6\right)[/tex]

Step-by-step explanation:

[tex]72-2y^2[/tex]

[tex]-2y^2+72[/tex]

Factor out GCF.

[tex]2(-y^2+36)[/tex]

Apply difference of two squares formula.

[tex]-2\left(y+6\right)\left(y-6\right)[/tex]

Answer:

y-intercept: (0, 2.5)

x-intercept: (1.67, 0)

Step-by-step explanation:

Right now, you have 3x + 2y = 5. You want to change it into slope-intercept form to make the problem easier to solve.

2y = -3x + 5

y = -3/2x + 5/2

From here, you can see that the y-intercept is (0, 5/2). You can also say that the y-intercept is (0, 2.5).

To get the x-intercept, substitute 0 for y.

0 = -3/2x + 5/2

3/2x = 5/2

3x = 5

x = 5/3

So, the x-intercept is (5/3, 0). You can also say that the x-intercept is (1.67, 0).

Hope this helps!

Answer:

Step-by-step explanation:

To find the x-intercept, let y = 0.  Then 3x = 5 and x = 5/3, or x = 1.667, and the x-intercept is (1.667, 0).

To find the y-intercept, let x = 0.  Then 2y = 5 and y = 5/2 or 2.5.  Then the y-intercept is (0, 2.5).

Answer:

$3.55

Step-by-step explanation:

You need to add 29% of $2.75 to $2.75.

That means the price will be 129% of $2.75.

129% of $2.75 =

= 1.29 * $2.75

= $3.55

Answer:

y intercept is -19/6

Step-by-step explanation:

The slope intercept form of a line is given by

y = mx+b where m is the slope and b is the y intercept

y = 16/13x - 19/6

The slope is 16/13 and the y intercept is -19/6

Answer:

[tex]\boxed{-\frac{19}{6} }[/tex]

Step-by-step explanation:

Use slope-intercept formula.

[tex]y=mx+b[/tex]

[tex]m[/tex] is the slope of the line.

[tex]b[/tex] is the y-intercept of the line.

The equation of the line is already in slope-intercept form.

[tex]y=\frac{16}{3} x+-\frac{19}{6}[/tex]

[tex]b= -\frac{19}{6}[/tex]

Answer:

Step-by-step explanation:

Let width = w units

Length = 4w - 3

Cost for lining corners of wall = $ 18.50

Perimeter of the wall = 18.50/0.25 =  74 ft

2*(length  +width ) = 74

2*(4w - 3 + w) =74

2*(5w - 3) =74

10w - 6 = 74   {Add 6 to both sides}

10w - 6 + 6 = 74 + 6

10w = 80

Divide both sides by 10

10w/10 = 80/10

w =  8 ft

Length = 4w - 3 = 4*8 - 3 = 32 - 3

Length = 29 ft

Area of the wall = length * width

                           = 29 * 8

                           =  232 square ft

Cost of painting the wall per square feet = 20 cents = 0.20

Cost of painting 232 square feet = 232 * 0.20

                                                             = $ 46.40

Answer: B C D

Step-by-step explanation:

just answered it for AP3X

Reasons used in the proof that the angle-bisector construction can be used to bisect any angle are as follows:

B. All of the radii of a circle are congruent

C .CPCTC

D. SSS triangle congruence postulate

" Angle bisector is defined as the ray which divides the angle into two equal parts."

According to the question,

A. Any Line segment can be extended indefinitely is not required to bisect any angle .

Therefore , it is not a correct option.

B. All of the radii of a circle are congruent : To bisect an angle draw an arc with same radii is used in constructing an angle bisector .

Therefore , Option B is a correct option.

C. CPCTC : Corresponding parts of a congruent triangle are congruent is required to proof angle bisector. As it proofs two triangles are congruent.

Therefore, Option C is the correct option.

D. SSS triangle congruence postulate : It is required an important step to prove that two triangles are congruent which imply proof of angle - bisector construction.

Therefore, Option D is the correct option.

Hence, Option B, Option C , Option D are the correct answer.

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Answer:

Step-by-step explanation:

1+2 cos α

[tex]=1+2(2 cos^{2} \frac{\alpha }{2} -1)\\=1+4 ~cos^2\frac{\alpha }{2} -2\\=4 ~cos^2\frac{\alpha }{2} -1\\=(2cos \frac{\alpha }{2} +1)(2 cos \frac{\alpha }{2} -1)[/tex]

Answer:

-17.5℃

Step-by-step explanation:

Current temperature = 0 ℃

Rate of falling per hour = -3.5 ℃

Temperature in 5 hours = -3.5 * 5 = -17.5 ℃  

Answer: 2 1/10, 3.122, 3.19, 61/10

Step-by-step explanation:

Let's first turn each number into decimal form: (1/10=.1, 2/10=.2,etc.)

2.1, 6.1, 3.122, 3.19.  Obviously, the smallest number is 2.1, because it has a 2 in the ones place.  Next, we see a tie in the ones place between 3.122 and 3.19.  Then we look at the tenths place and see another tie.  Then, at the hundredths place, we see that 3.19 is greater that 3.122.  Thus, the order of the numbers is 2.1,3.122,3.19,6.1.

Hope it helps <3

Answer: 3.5 pi.

Step-by-step explanation: Since we know the circumference formula of a circle is 2*pi*radius, we just have to substitute 7 in there, and divide by 4. So here ya go, 3.5 pi.

Answer:

25

Step-by-step explanation:

The Side Splitter Theorem says that if a line intersects two sides of a triangle and is parallel to the third side of the triangle, it divides those two sides proportionally. Therefore:

6/15 = 10/?

6*? = 10*15

? = 10*15/6

? = 25

Answer:

answer is (0,1)

Step-by-step explanation:

check

by substituting x=0 and y=1 in the equation above

- 2(0)+1> -4

1> -4

Thereby (0,1) is the required solution to the inequality

Answer:

A, C and D

Step-by-step explanation:

The missing inequality is:

y > 2x -4

To verify if a point is a solution, replace x into the equation, compute y, and see their relationship.

Option A: (-2,-5)

2(-2) -4 = -8

y = -5 > -8

then, the point is solution

Option B: (0,-4)

2(0) -4 = -4

y = -4 = -4

then, the point is not solution

Option C: (1,1)

2(1) -4 = -2

y = 1 > -2

then, the point is solution

Option D: (3,5)

2(3) -4 = 2

y = 5 > 2

then, the point is solution

Option E: (5,5)​

2(5) -4 = 6

y = 5 < 6

then, the point is not solution

Answer:

19 : 25

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

1.the equations have different slopes?  They will intersect at one point so one solution

2.the equations have the same slope and different y-intercepts.  They are parallel lines with a different y intercept so they will never intersect - no solutions

3.the equations have the same slope and same y-intercepts. they are the same line so they have infinite solutions

Answer:

1. One solution

2. no solution

3. infinite number of solutions.

Step-by-step explanation:

How many solutions a system of linear equations have if: Questions.

(assuming a system of two equations)

1.the equations have different slopes?

One unique solution, which is at the intersection point.

2.the equations have the same slope and different y-intercepts.

The equations/lines are then parallel but NOT coincident.  They will never meet, therefore NO solution.

3.the equations have the same slope and same y-intercepts.

The two lines/equations are in effect coincident.  Therefore there is an infinite number of solutions.

Answers. A.no solutions. B.infinetly as many solutions C.two solutions. D.one solution

Answer:

  78π m²

Step-by-step explanation:

The lateral area of the cylinder is ...

  LA = 2πrh

  LA = 2π(3 m)(8 m) = 48π m²

The lateral area of one cone is ...

  LA = πrh . . . . where h is the slant height

  LA = π(3 m)(5 m) = 15π m²

Then the total surface area of the figure is the area of the two cones plus that of the cylinder:

  S = 2(cone area) + cylinder area

  S = 2(15π m²) +(48π m²)

  S = 78π m²

Answer:

(a) The probability that a male is selected, then two females is 0.4352.

(b) The probability that a female is selected, then two males is 0.3348.

(c) The probability that two females are selected, then one male is 0.4352.

(d) The probability that three males are selected is 0.0717.

(e) The probability that three females are selected is 0.1583.

Step-by-step explanation:

We are given that a math class consists of 25 students, 14 female and 11 male. Three students are selected at random to participate in a probability experiment.

(a) The probability that a male is selected, then two females is given by;

Number of ways of selecting a male from a total of 11 male = [tex]^{11}C_1[/tex]

Number of ways of selecting two female from a total of 14 female = [tex]^{14}C_2[/tex]

Total number of ways of selecting 3 students from a total of 25 = [tex]^{25}C_3[/tex]

So, the required probability =  [tex]\frac{^{11}C_1 \times ^{14}C_2}{^{25}C_3}[/tex]

                                           =  [tex]\frac{\frac{11!}{1! \times 10!} \times \frac{14!}{2! \times 12!} }{\frac{25!}{3! \times 22!} }[/tex]     {[tex]\because ^{n}C_r = \frac{n!}{r! \times (n-r)!}[/tex] }

                                           =  [tex]\frac{1001}{2300}[/tex]  =  0.4352

(b) The probability that a female is selected, then two males is given by;

Number of ways of selecting a female from a total of 14 female = [tex]^{14}C_1[/tex]

Number of ways of selecting two males from a total of 11 male = [tex]^{11}C_2[/tex]

Total number of ways of selecting 3 students from a total of 25 = [tex]^{25}C_3[/tex]

So, the required probability =  [tex]\frac{^{14}C_1 \times ^{11}C_2}{^{25}C_3}[/tex]

                                           =  [tex]\frac{\frac{14!}{1! \times 13!} \times \frac{11!}{2! \times 9!} }{\frac{25!}{3! \times 22!} }[/tex]     {[tex]\because ^{n}C_r = \frac{n!}{r! \times (n-r)!}[/tex] }

                                           =  [tex]\frac{770}{2300}[/tex]  =  0.3348

(c) The probability that two females is selected, then one male is given by;

Number of ways of selecting two females from a total of 14 female = [tex]^{14}C_2[/tex]

Number of ways of selecting one male from a total of 11 male = [tex]^{11}C_1[/tex]

Total number of ways of selecting 3 students from a total of 25 = [tex]^{25}C_3[/tex]

So, the required probability =  [tex]\frac{^{14}C_2 \times ^{11}C_1}{^{25}C_3}[/tex]

                                           =  [tex]\frac{\frac{14!}{2! \times 12!} \times \frac{11!}{1! \times 10!} }{\frac{25!}{3! \times 22!} }[/tex]     {[tex]\because ^{n}C_r = \frac{n!}{r! \times (n-r)!}[/tex] }

                                           =  [tex]\frac{1001}{2300}[/tex]  =  0.4352

(d) The probability that three males are selected is given by;

Number of ways of selecting three males from a total of 11 male = [tex]^{11}C_3[/tex]

Total number of ways of selecting 3 students from a total of 25 = [tex]^{25}C_3[/tex]

So, the required probability =  [tex]\frac{^{11}C_3}{^{25}C_3}[/tex]

                                           =  [tex]\frac{ \frac{11!}{3! \times 8!} }{\frac{25!}{3! \times 22!} }[/tex]     {[tex]\because ^{n}C_r = \frac{n!}{r! \times (n-r)!}[/tex] }

                                           =  [tex]\frac{165}{2300}[/tex]  =  0.0717

(e) The probability that three females are selected is given by;

Number of ways of selecting three females from a total of 14 female = [tex]^{14}C_3[/tex]

Total number of ways of selecting 3 students from a total of 25 = [tex]^{25}C_3[/tex]

So, the required probability =  [tex]\frac{^{14}C_3}{^{25}C_3}[/tex]

                                           =  [tex]\frac{ \frac{14!}{3! \times 11!} }{\frac{25!}{3! \times 22!} }[/tex]     {[tex]\because ^{n}C_r = \frac{n!}{r! \times (n-r)!}[/tex] }

                                           =  [tex]\frac{364}{2300}[/tex]  =  0.1583

(a) The probability that a male is selected, then two females is 0.4352.

(b) The probability that a female is selected, then two males is 0.3348.

(c) The probability that two females are selected, then one male is 0.4352.

(d) The probability that three males are selected is 0.0717.

(e) The probability that three females are selected is 0.1583.

Answer:

36/100

Step-by-step explanation:

this is because you find the overlapping ranges of each bag which is 5 - 10 on the first bag and 5 - 10 on the second bag. both bags have 10 total numbers, so 6/10 * 6/10 because there are six numbers on each bag and 10 overall choices, so we multiply these two because its an and statement which gives us 36/100.

The probability that we get the same number is 9/25.

It is simply likeliness of happening an event. The probability of an event lies between 0 to 1.

Numbers in first bag=10

Numbers in second bag=10

Common numbers=5,6,7,8,9,10

Total common numbers=6

So the probability that we get the same numbers will be

= 6/10* 6/10

=36/100

=18/50

=9/25

Hence the probability that we will get the same numbers is 9/25.

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Answer:

Step-by-step explanation:

Well since AB/DE = 3/4 and AB/DE = BC/EF, then BC/EF must also be 3/4.

We now only need to find a fraction that simplifies to 3/4.

8/12 = 2/3 [tex]\neq[/tex] 3/4

12/16 = 3/4 ✅

4/6 = 2/3 [tex]\neq[/tex] 3/4

6/9 = 2/3 [tex]\neq[/tex] 3/4

This means that the correct answer is B. 12 and 16.

Answer:

B. 12 and 16

Step-by-step explanation:

Hey there! :)

Answer:

x = 5, x = -i√7, x = i√7

Step-by-step explanation:

We can factor the equation x³ - 5x² + 7x - 35 = 0 by grouping:

x²(x - 5) + 7(x -5) = 0

We get:

(x² + 7)(x - 5) = 0

or

(x + i√7)(x - i√7)(x - 5) = 0

Use the Zero Product Property to solve for the solutions:

x - 5 = 0

x = 5.

-----------

x² + 7 = 0

x² = -7 (We will have imaginary solutions in this instance)

x = ±i√7

Therefore, the zeros of this equation are:

x = 5, x = -i√7, x = i√7

The correct expression with the correct statement has matched below.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

The percentage is equivalent to the quantity of that value between 1 and 100, and it is highly helpful for forecasting. For instance, if you say 678, we must also know the whole number, but if you say 80%, it is obvious.

The price of a game that’s been discounted by 18% of its list price

It will be (x - 0.18x)  =  0.82x

The price of a toy that sells for 18% more than the amount needed to build the toy

It will be (x + 0.18x) = 1.18x

The volume of water remaining in a tank after 3/10 of its original volume is drained out.

It will be [ x - (3/10)x ] = 7/10x

The total amount of flour in a bakery after receiving new stock equal to 3/10 of the current stock.

It will be [ x + (3/10)x ] =  13/10x

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The number of buttons in C is 17 buttons

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the three tins be A , B and C respectively

The number of buttons in tin A = x

The number of buttons in tin B = 4 times the number of buttons in tin A

                                                   = 4x

The number of buttons in tin C = 7 fewer buttons than tin A

                                                    = x - 7

The total number of buttons in tin A , tin B and tin C together = 137 buttons

So , the total number of buttons =
number of buttons in tin A + number of buttons in tin B + number of buttons in tin C

So , the equation will be

Total number of buttons = x + 4x + ( x - 7 )

x + 4x + ( x - 7 ) = 137

6x - 7 = 137

Adding 7 on both sides , we get

6x = 144

Divide by 6 on both sides , we get

x = 24 buttons

So , the number of buttons in tin A is 24 buttons

So , number of buttons in tin B = 4 x 24

                                                   = 96 buttons

Therefore , the number of buttons in tin C = 17 buttons

Hence , the number of buttons in tin C is 17 buttons

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