Michael is organizing 5,272 blocks into bins at the toy store. He needs to put the same number of blocks in each bin without any leftover blocks. How many bins could Michael use for the blocks? A) 3. B) 4. C) 5. D) 9.

The rational expression [tex]\dfrac{x + 1}{4x^2} + \dfrac{x + 1}{x^2}[/tex] using the least common denominator is [tex]\dfrac{5 + 5x}{4x^2}[/tex]

How to express the rational expression using the least common denominator?

From the question, we have the following parameters that can be used in our computation:

[tex]\dfrac{x + 1}{4x^2} + \dfrac{x + 1}{x^2}[/tex]

Take the LCM of the expression

So, we have

[tex]\dfrac{x + 1}{4x^2} + \dfrac{x + 1}{x^2} = \dfrac{x + 1 + 4(x + 1)}{4x^2}[/tex]

Expand the bracket

[tex]\dfrac{x + 1}{4x^2} + \dfrac{x + 1}{x^2} = \dfrac{x + 1 + 4x + 4}{4x^2}[/tex]

So, we have

[tex]\dfrac{x + 1}{4x^2} + \dfrac{x + 1}{x^2} = \dfrac{5 + 5x}{4x^2}[/tex]

Hence, the rational expression using the least common denominator is [tex]\dfrac{x + 1}{4x^2} + \dfrac{x + 1}{x^2} = \dfrac{5 + 5x}{4x^2}[/tex]

When using the formula for the volume of a pyramid, substituting the given values of base area and volume results in a candy box height calculation of 20 inches.

The question asks about the height of a box of candy shaped like a triangular pyramid, given the volume and the area of the base. The volume of a pyramid is given by the formula V = 1/3 * Base Area * height. In this case, the box volume equals 120 in³, and the base area equals 18 in². We can use these values to solve for the height.

By rearrangement of the formula, height = V / (1/3 * Base Area). If we plug in the values, height = 120 in³ / (1/3 * 18 in²) = 20in. Therefore, the height of the candy box is 20 inches.

https://brainly.com/question/32057490

#SPJ12

The height of the candy box is 20 inches.

To find the height of the candy box, we need to use the formula for the volume of a triangular pyramid, which is V = (1/3) * A * h, where V is the volume, A is the area of the base, and h is the height.

We are given that the volume is 120 in³ and the area of the base is 18 in², so we can plug these values into the formula and solve for h.

120 = (1/3) * 18 * h

Simplifying the equation, we get:

360 = 18h

Dividing both sides by 18, we find that h = 20.

Therefore, the height of the candy box is 20 inches.

https://brainly.com/question/24086401

#SPJ12

Answer:

b

Step-by-step explanation:

Look at the pattern

it might be wrong but i am pretty sure it’s right but 537.15

Answer:

The estimated volume would be 594 feet.

Step-by-step explanation:

Well, since this is an estimate you should round all your numbers and multiply them together.

5.6 is rounded to 6

8.8 is rounded to 9

and 10.9 is rounded to 11

Multiply 6 and 9 and you get 54. Then multiply 54 by 11 and that gives you 594.

- Your freshman friend :)

Answer:

P(-2,7)

P'(-2,-7), ANSWER

reflection across the x-axis rule:

(×,y) ===> (x,-y)

Easy way to do this is draw the point on graph paper and count the same units above/below the x-axis. This example you are 7 units above the x-axis so you would count 7 units below the x-axis giving you the point.

Reflection of a point across an axis involves flipping the sign of the coordinate for that axis. So the reflection of point P(-2,7) on the x-axis is P'(-2,-7).

The concept described in your question refers to the reflection of a point across the x-axis. Given a point P(-2,7), the reflection of this point across the x-axis, denoted as Rx-axis(P), reverses the sign of the y-coordinate. This happens because a reflection is a transformation that flips a figure across an axis of reflection.

So, if we consider P(-2,7) to reflect about the x-axis, we just switch the sign of y-coordinate. Therefore reflection of point P(-2,7) about x-axis will be P'(-2,-7).

https://brainly.com/question/15487308

#SPJ3

Still don't know what the given line is, so I'm just going to attach images of the graphs of each equation.

Graph 1: y = -2x

Graph 2: x = 4

Graph 3: y = x

Graph 4: y = 3

Hope this helps!

Answer:

B:  The salaries

Step-by-step explanation:

B:  The salaries.  While not strictly continuous, the range of salaries is closest of these four choices to being continuous.  In contract, "number of employees," "number of printers," and "number of phone calls" are all discrete random variables.

The statement at D "The number of phone calls made daily from an office" is a continuous random variable.

A random variable is defined for all the values in an interval or between two values.

A. The number of employees in an office.

It is a constant value. It's not a continuous random variable.

B. The salaries of employees in an office

It is a constant value. It has only one value means represented in a closed interval. So, not a continuous random variable

C. The number of printers in an office

This is also a constant value. So, not a continuous random variable

D. The number of phone calls made daily from an office

The number of phone calls made daily, may not be the same and are continuous. If the interval of a month, there may be a different number of phone calls. So, it is a continuous random variable.

So, option D is correct.

Learn more about continuous random variables here:

https://brainly.com/question/15238425

#SPJ2

Answer:

[tex]\left[\begin{array}{cc}7&1\\3&-3\end{array}\right][/tex]

Step-by-step explanation:

We simply add entry of each column of matrix 1 with its corresponding column entry of second matrix.

[tex]= \left[\begin{array}{cc}3&1\\0&-2\end{array}\right] + \left[\begin{array}{cc}4&0\\3&-1\end{array}\right]\\= \left[\begin{array}{cc}3+4&1+0\\0+3&-2+(-1)\end{array}\right]\\=\left[\begin{array}{cc}7&1\\3&-3\end{array}\right][/tex]

For this case we must add the following matrices:

[tex]\left[\begin{array}{ccc}3&1\\0&-2\end{array}\right][/tex]

And

[tex]\left[\begin{array}{ccc}4&0\\3&-1\end{array}\right][/tex]

Adding up:

[tex]\left[\begin{array}{ccc}3+4&1+0\\0+3&-2+(-1)\end{array}\right]=\\\left[\begin{array}{ccc}3+4&1+0\\0+3&-2-1\end{array}\right]=\\\left[\begin{array}{ccc}7&1\\3&-3\end{array}\right][/tex]

Answer:

[tex]\left[\begin{array}{ccc}7&1\\3&-3\end{array}\right][/tex]

The answer is B (6x-5)(x+2)

Answer:

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

Step-by-step explanation:

Distribute each until you find the answer:

A) 6x^2+17x+10

B) 6x^2+7x-10

Answer:

Step-by-step explanation:

1)

f(x) = x + 4

f(3) = 3 + 4 = 7

g(x) = 12x - 6

g(-1) = 12(-1) - 6 = -12 - 6 = -18

f(3) + g(-1) = 7 + (-18) = -11

2)

f(x) = 2x + 3, g(x) = 4x

f(x) · g(x) = (2x + 3)(4x)             use the distributive property

f(x) · g(x) = (2x)(4x) + (3)(4x)

f(x) · g(x) = 8x² + 12x

3)

f(x) = 2x - 3

f(2) = 2(2) - 3 = 4 - 3 = 1

g(x) = 4x

g(3) = 4(3) = 12

f(2) - g(3) = 1 - 12 = -11

1) Given f(x)=x+4 and g(x)=12x-6, what is f(3)+g(-1)?

C) -11

2) what is f(x).g(x) if f(x)= 2x+3 and g(x)=4x?

C) 8x^2+12

3) f(x)=2x-3 and g(x)=4x what is f(2)-g(3)

B) -11

Hey

Since a coin has 1/2 chances on both sides and a six-sided cube has 1/3 chance of getting a less than three, multiply those chances and you will get the probability of 1 / 6

So the answer is option A, [tex]\frac{1}{6}[/tex]

The probability that the coin lands on tails in the outcome on the number cube is a number less than 3 is 1/6.

Given:

Find:

Solution:

A coin is tossed and a six-sided cube is rolled.

We have to find the probability of getting a tail on the coin and a number less than 3 in the cube.

The probability of getting a tail in the coin is 1/2.

The probability of getting a number less than 3 is 2/6 = 1/3.

Probability of getting a tail on the coin and a number less than 3 on a cube is 1/2*1/3 = 1/6.

Hence, The probability that the coin lands on tails in the outcome on the number cube is a number less than 3 is 1/6.

Therefore, Option A is the correct answer.

To learn more about probability, refer to:

https://brainly.com/question/3151088

#SPJ2

You start by distributing the 5x, so that it’s 5x(2x) and 5x(3y). That becomes 10x^2 and 15xy. Put it back, and it’s 10x^2 - 15xy.

Expand

5x × 2x + 5x × -3y

Rake out the constants

(5 × 2)x + 5x × -3y

Simplify 5 × 2 to 10

10x + 5x × -3y

Use the product rule: x^ax^b = x^a + b

10x^2 + 5x × -3y

Simplify 5x × -3y to -15xy

= 10x^2 - 15xy

Answer:

Third Option

[tex]P(x\geq 9) =0.212[/tex]

Step-by-step explanation:

Note that the variable x is a discrete random variable that can be modeled using a binomial distribution. For a discrete random variable the probability that x is greater than a number b is:

[tex]P(x\geq b) =\sum_{x=1}^{b}{P(x)} = P(1) + P(2) + P(3) + ... + P(b)[/tex]

In this case we look for the probability of selecting 9 or more girls

This is:

[tex]P(x\geq 9) =\sum_{x=9}^{14}{P(x)} = P(9) + P(10) + P(11) +P(12)+ P(13) + P(14)[/tex]

Looking in the attached table we have to

[tex]P(x\geq 9) =0.122 + 0.061 + 0.022 + 0.006+ 0.001 + 0[/tex]

[tex]P(x\geq 9) =0.212[/tex]

Answer: C. [tex]\dfrac{6}{336}[/tex]

Step-by-step explanation:

Given: The number of different prizes = 3

The number of people entered the drawing = 8

The total number of ways to award the prizes. = 336

Now, The number of ways to select for 3 prizes, such that  you win first prize and your mom wins second prize is given by :-

[tex]1\times1\times(8-2)=6[/tex]

Hence, the probability that you win first prize and your mom wins second prize=[tex]\dfrac{6}{336}[/tex]

Answer:

314.25

Step-by-step explanation:

To find the total of all three checks, we add them together, lining up the decimals

 36.98

  17.27

260.00

--------------------

314.25

The total is 314.25

Answer:

1 → D

2 → A

3 → B

4 → C

Step-by-step explanation:

You need to remember that:

[tex]cos\alpha=\frac{adjacent}{hypotenuse}\\\\sin\alpha=\frac{opposite}{hypotenuse}\\\\tan\alpha=\frac{opposite}{adjacent}[/tex]

Then:

-For angle B, you can identify in the figure that:

[tex]opposite=b\\adjacent=c\\hypotenuse=a[/tex]

Then, you can substitute values and get:

[tex]cosB=\frac{c}{a}[/tex]

[tex]sinB=\frac{b}{a}[/tex]

[tex]tanB=\frac{b}{c}[/tex]

- For angle C, you can identify in the figure that:

[tex]opposite=c\\adjacent=b[/tex]

Therefore, substituting values, you get that:

[tex]tanC=\frac{c}{b}[/tex]

Answer:

1. cosB = c/a

2. tanC = c/b

3. sinB = b/a

4. tanB = b/c

Step-by-step explanation:

Plato Answer!!

Step-by-step explanation:

kdkeksoodkdlsospslpss

ANSWER

Average Rate of Change

[tex] = \frac{f(b) - f(a)}{b - a} [/tex]

EXPLANATION

To find the average rate of change of y=f(x) from x=a to x=b means finding the slope of the secant line joining the points

(a,f(a)) and (b,f(b))

The slope of the secant line joining these points is

[tex] = \frac{f(b) - f(a)}{b - a} [/tex]

This gives the average rate of change of the function.

To find the average rate of change of a function, you need to subtract the function values at two different points and divide by the difference in the input values.

To find the average rate of change of a function, you need to calculate the change in the function's output divided by the change in its input. This can be done by subtracting the function values at two different points and dividing by the difference in the input values. For example, if you have a function f(x) and want to find the average rate of change between x = a and x = b, you would use the formula:

Average Rate of Change = (f(b) - f(a)) / (b - a)

This will give you the average rate at which the function is changing over the interval from a to b.

https://brainly.com/question/34758264

#SPJ12

Taken together, these three facts imply that triangles AOB and COB are congruent (side-side-side congruence postulate).

Now, it's not exactly clear whether A and C lie on the same line (it's possible that the figure is not drawn to scale). If they do, then both angles AOB and COB are right angles, so angle BOK has measure 45º, and so [tex]m\angle AOK=135^\circ[/tex].

By applying the theorems of an isosceles triangle and an angle bisector, m<AOK = 135 degrees.

Recall the Theorem of Isosceles Triangle:

We would apply the above stated to solve the problem given.

We know the following:

We can deduce that:

m<AOK = m<AOB + m<BOK

m<AOK = 90 + 45

m<AOK = 135 degrees.

Therefore, by applying the theorems of an isosceles triangle and an angle bisector, m<AOK = 135 degrees.

Learn more here:

https://brainly.com/question/19238666

Answer:

The surface area is [tex]404.8\ in^{2}[/tex]

Step-by-step explanation:

we know that

The surface area of the figure is equal to

[tex]SA=2B+PL[/tex]

where

B is the area of the trapezoidal face

P is the perimeter of the trapezoidal face

L is the length of the figure

Find the area of B

[tex]B=\frac{1}{2}(15+5)8\\ \\B=80\ in^{2}[/tex]

Find the perimeter P

[tex]P=(8+5+12.8+15)=40.8\ in[/tex]

we have

[tex]L=6\ in[/tex]

substitute the values

[tex]SA=2(80)+(40.8)(6)=404.8\ in^{2}[/tex]

Answer: A and B are independent events if P(A∩B)=P(A).P(B)=0.15.

Step-by-step explanation:

Let A be the event that a shopper buys bread.

Let B be the event that a shopper buys cheese.

So, P(A∪B)=100

Probability that a shopper buys bread during a visit to the grocery store =n 0.60

P(A) = 0.60

Similarly, Probability that a shopper buys bread = 0.25

P(B) = 0.25

Since A and B are independent then,

[tex]P(A\cap B)=P(A).P(B)=0.60\times 0.25=0.15[/tex]

So, A and B are independent events if P(A∩B)=P(A).P(B)=0.15.

Answer:

A. left parenthesis 3 comma 2 right parenthesis

Step-by-step explanation:

The point A is at (-2, 2)  which is 2 units to the left and 2 units up from zero

We want 5 horizontal units from A.  Horizontal means left and right

If we go 5 units to the right

(-2 +5 , 2) = (3,2)

If we go 5 units to the left

(-2 -5 , 2) = (-7,2)

Answer:

Option C. AB/BC=CD/DE

Step-by-step explanation:

we know that

In the triangle ABC the slope is equal to

m=AB/BC -----> equation A

In the triangle CDE the slope is equal to

m=CD/DE -----> equation B

Remember that the slope of a line is a constant

so

equate equation A and equation B

AB/BC=CD/DE

Answer:

C is the answer

Step-by-step explanation:

Answer:

(-8+i )

Step-by-step explanation:

We'll multiply these 2 binomials like any other pair of binomials: using the FOIL method.

(-3+2i)•(2+i) after being FOILed is:

(-3•2)+(-3•i)+(2i•2)+(2i•i)

this equation simplified equals

-6-3i+4i+2i²

Whenever we see i², we should know that is equals -1, so our equation rewritten again is

-6-3i+4i+(2•-1)

Simplifying that, we get

-6-3i+4i+-2

From here, we just continue to simplify by subtracting  2 from −

6.

−8−3i+4i

Finally, add −3i and 4i to get our answer of

−8+i

Answer:

slope   3/5

Step-by-step explanation:

3x − 5y − 6 = 0

To find the slope, we want to solve for y

(y = mx+b   slope intercept form of the equation(

Add 5y to each side

3x − 5y+5y − 6 = 0+5y

3x-6 = 5y

Divide by 5

3/5x -6/5 = 5y/5

3/5 x -6/5 = y

The slope is 3/5 and the y intercept is -6/5

In tandem with general linear equation, the slope of the equation is 3/5

Another name for slope is gradient. From the general linear equation,

Y = mx + c

To determine the slope of the line 3x − 5y − 6 = 0,

Make y the subject of formula and make the equation in line with general linear equation.

5y = 3x - 6

y = 3x/5 - 6/5

Therefore, from the equation above, the slope is 3/5

Learn more about slope here: https://brainly.com/question/21727173

The base is 11 cm and the height is 8 cm.

Answer:

Because it is

Step-by-step explanation:

You don't need to. You can explain yourself using words but it takes ages that way. You use equations to solve problems, equations, and later on with functions and methods as you develop your math career. All I can say is, don't ignore it.

Answer:

An equation is the mathematical representation of those two things which are equal, one on each side of an 'equals' sign. Equations are useful to solve math problems in which multiple numbers are in the need of being solved.. Most of the times we take pre-algebra help to resolve real life problems.

Step-by-step explanation:

PLZZ MARK BRAINLIST!!!!!

I believe you just multiply 150x3 and get 450

A basketball court that is 150 feet long is equivalent to 50 yards, calculated by dividing the total length in feet by the conversion factor of 3 feet per yard.

To determine how many yards make up a basketball court that is 150 feet in length, we use the conversion factor that 1 yard equals 3 feet. Therefore, we divide 150 feet by 3 to convert feet to yards:

150 feet / 3 = 50 yards.

Thus, a basketball court that is 150 feet long is 50 yards long. This is a calculation often used in converting units, an essential skill in mathematics and various practical contexts, such as sports, construction, and everyday measurements. Knowing how to convert between feet and yards can be useful in understanding the dimensions of a playing field, like a basketball court or football field.

ANSWER

The circumcenter is (2,1)

EXPLANATION

The midpoint of BC is (-3,2)

The equation of the perpendicular bisector of BC is x=2

The midpoint of AB is (-1,1)

The midpoint of AB is (-1,1)

The perpendicular bisector of AB is y=1.

These two lines intersect at (2,1).

The point of intersection of the perpendicular bisectors of a triangle is called the circumcenter of the triangle.

Based on the graph, the coordinates of the circumcenter of this triangle are (2, 1).

In Mathematics and Euclidean Geometry, a circumcenter is the point where perpendicular bisectors (right-angled lines to the midpoint) of the sides of a triangle meet together or intersect.

This ultimately implies that, the circumcenter of any triangle is always equidistant from all the rays (vertices) of that triangle.

By critically observing the graph of triangle ABC, we can logically deduce the following parameters;

Based on the equation of the perpendicular bisector of BC and AB, the coordinates of the circumcenter are (2, 1).

Read more on circumcenter here: https://brainly.com/question/19806453

#SPJ3

Answer:

D

Step-by-step explanation:

If x° and y° are complementary angles, then x°+y°=90° and

[tex]\sin x^{\circ}=\cos y^{\circ} \ [\text{Cofunctions rule}][/tex]

Check all options:

A. 18°+72°=90°, so

[tex]\sin 18^{\circ}=\cos 72^{\circ}\ [\text{true}][/tex]

B. 55°+55°=110°, these angles are not complementary and

[tex]\sin 55^{\circ}\neq\cos 55^{\circ}\ [\text{false}][/tex]

C. 72°+18°=90°, so

[tex]\sin 72^{\circ}=\cos 18^{\circ}\ [\text{true}][/tex]

D. Both A and C are true.