Annie bought a package of 100 pens for $167.00. How much did each
pen cost?

Answer: There are infinite solutions.

Step-by-step explanation:

3(2x-4) = 2(3x-6)

6x - 12 = 6x - 12

-12 = -12

0 = 0

Answer:

a) [tex]w^{13} x^{5} y^{6}[/tex]

b) [tex]\frac{x}{3y^{6} }[/tex]

Step-by-step explanation:

a) [tex](w^{2} xy^{3} )^{2}(w^{3}x )^{3}[/tex]

1. Distribute the second power (2) outside the first pair of parenthesis:

[tex](w^{2(2)} x^{2} y^{3(2)} )[/tex]

= [tex]w^{4} x^{2} y^{6} (w^{3}x )^{3}[/tex]

2. Distribute the third power (3) outside the second pair of parenthesis:

[tex](w^{3(3)} x^{3} )[/tex]

= [tex]w^{4} x^{2} y^{6} w^{9} x^{3}[/tex]

3. Combine like terms:

[tex]w^{13} x^{5} y^{6}[/tex]

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

b) [tex]\frac{2x^{2} y^{5} }{6xy^{11} }[/tex]

1. Factor the number 6 (= 2 · 3):

[tex]\frac{2x^{2} y^{5} }{2(3)xy^{11} }[/tex]

2. Cancel the common factor (2):

[tex]\frac{x^{2} y^{5} }{3xy^{11} }[/tex]

3. Cancel out [tex]xy^{5}[/tex] in the numerator an denominator:

[tex]\frac{x}{3y^{6} }[/tex]

hope this helps!

Answer:

181.5 miles

Step-by-step explanation:

  80 2/3   m/hr  *   2  1/4 hr = 181. 5 miles

Answer:

25

Step-by-step explanation:

When answer questions about unique combinations, there are usually two ways people go about finding the solutions.

First, sometimes it can take a while, but it often helps people visualize the question if they jot down or sketch each different combination. Then, they can just count them up at the end to find there answer.

The easeier way is to use a quick math trick. If you have 5 runners, with 5 potential lanes each runner could start in, you can just multiply these two variables together to get your answer of the number of possible options.

So,

5 runners * 5 lanes = 25 possible combinations for each lane and runner

The number of unique ways that the runner can be arranged in 5 lanes for a race is 120.

Combinations are defined as the arrangement of objects or numbers in a way such that the order of the arrangement does not matter.

Total number of runners = 5

Total number of lanes = 5

Number of ways that 5 runners can be arranged = 5! = 120

Hence the number of ways is 120.

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A reduction means that the original figure is made smaller.

An englargement means that the original figure is made larger.

The new figure (shown by the ' next to each letter) is smaller than the original. Therefore, the dilation was a reduction.

Hope this helps!

Answer:

Step-by-step explanation:

Remark

The longer the line, the larger the arc is. So

How to put in order.

It can be shown that the angle opposite the chord is related to the arc length by α = arc length / r  Since r never changes, you are left with

α = k * chord length.

So what you conclude is that the larger the angle, the larger the arc length.

The largest angle is Q so the length of the arc opposite Q is the largest. The other two lines are handled the same way.

Answer:

Answer:

(it won't let me paste a graph here)

(but it a / line on the graph.)

Step-by-step explanation:

Use Desmos Graphic Calculator, plot this equation in and it should show up a graph of that. : )

Answer: c

Step-by-step explanation:

C is the only that gave us a single outcome so it’s a simple event

????????

Step-by-step explanation:

1,1,1

Answer:

130 square yards

Step-by-step explanation:

5 x 4 = 20

5 x 5 = 25

20 x 4 = 80

25 x 2 = 50

80 + 50 = 130

The surface area for this cube and rectangular prisms is 75 cubic square inches.

Surface area of a prism is the sum of the area of the 2 polygonal bases and the area of the lateral faces. The surface area of a prism is measured in terms of square units. The Surface Area of a Prism Formula is given as, Surface Area Of A Rectangular Prism is A = 2 (wl + lh + hw)

So  [tex]5[/tex] · [tex]4[/tex] · [tex]5=75[/tex] [tex]cubic[/tex] [tex]inches[/tex]

Therefore, The surface area for this cube and rectangular prisms is 75 cubic square inches.

A probability of 1 means that the event will happen. If the probability of a road traffic accident was 1 there would be nothing you could do to stop it.

that's my answer

Step-by-step explanation:

the probability to win is 0.2.

the probability to lose is 1-02 = 0.8.

there is no sure win after at least n trials.

on day 1 the probability to win is 0.2.

on day 2 the probability to win at least once is

the probability to have won on day 1 but not on day 2, plus the probability to have won on day 2 but not on day 1 plus the probability to have won on both days :

0.2×0.8 + 0.8×0.2 + 0.2×0.2 = 0.32 + 0.04 = 0.36

...

on day 7 we have

the probability to have won on one day but not on 6 days times the combination of picking 1 day out of 7,

plus the probability to have won on 2 days but not on 5 days times the combinations to pick 2 out of 7,

plus the probability to have won on 3 days but not on 4 days times the combinations to pick 3 out of 7,

...

plus the probability to have won on all 7 days.

that is

0.2.×0.8⁶ × 7 +

+ 0.2²×0.8⁵ × C(7, 2) +

+ 0.2³×0.8⁴ × C(7, 3) +

+ 0.2⁴×0.8³ × C(7, 4) +

+ 0.2⁵×0.8² × C(7, 5) +

+ 0.2⁶×0.8 × 7 +

+ 0.2⁷

but before we lose ourselves in tons of little operations, this is the same as the opposite of having lost on all 7 days.

that is

1 - 0.8⁷ = 1 - 0.2097152 = 0.7902848 ≈ 0.7903

so, the probability that Jorge has won at least one prize is

0.7903

#Circle 1

#Circle 2

#Circle 3

#Triangle 1

#Triangle 2

#Triangle 3

The area of each cross section of the cone and pyramid is the same which is 2[tex]\pi[/tex].

This is because the cone and pyramid are similar solids, and the cross sections are taken at equal heights.

The similarity of the cone and pyramid can be seen by comparing the triangles formed by the apex, a point on the base, and the intersection of the plane with the solid. These triangles are similar because they have the same angles.

The fact that the cross sections are taken at equal heights means that the triangles are similar in size as well. This means that the areas of the triangles are also the same.

Therefore, the area of each cross section of the cone and pyramid is the same.

[tex]\pi[/tex][tex]h^2[/tex] / (1/2) h*h = 2[tex]\pi[/tex][tex]h^2[/tex] / [tex]h^2[/tex] = 2[tex]\pi[/tex]

The cross sections of the cone and pyramid are both triangles. The triangles are similar because they have the same angles. The fact that the cross sections are taken at equal heights means that the triangles are similar in size as well. This means that the areas of the triangles are also the same. Hence, the answer is 2[tex]\pi[/tex].

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Answer:

no

Step-by-step explanation:

The cube has only 6 sides,

so it has only 6 numbers : 1, 2, 3, 4, 5 & 6.

Answer:

4 times

Step-by-step explanation:

because there's only enough space for that many in each row.

Answer:

2/5

Step-by-step explanation:

Find two integer coordinate sets  ( use the two points labelled)

slope = m = (y1-y2)/(x1-x2) =

                = ( 1 - -1 ) / (3- - 2) = 2/5

  (NOTE: it does not matter which point you choose to be  x1,y1  or x2,y2 )

Since both x + 1 and x - 1 are factors of f(x), we have the factorization

x³ + 2ax + b = (x + 1) (x - 1) (x - b)

where the last root must be x = b in order that b is the constant term in the cubic.

Expanding the right side and equating coefficients gives

x³ + 2ax + b = x³ - bx² - x + b

which tells us

-b = 0   ⇒   b = 0

2a = -1   ⇒   a = -1/2

Then we have

f(x) = x³ + 2 (-1/2) x + b = x³ - x

or

f(x) = x (x + 1) (x - 1)

Answer:

54

Step-by-step explanation:

7*a-b , a = 7 , b = - 6

7*7 - (-6)

49 + 6 = 54

If its 7 * (a - b)

7*(7 - (-6))

7 * 13

91

Answer:

See below

Step-by-step explanation:

We can find the Highest Common Factor (HCF) by the prime factorization of the terms.

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

a) 4 and 5

⇒ 4 = 4 x 1

⇒ 5 = 5 x 1

⇒ HCF (4, 5) = 1

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

b) 8 and 13

⇒ 8 = 2 x 2 x 2 x 1

⇒ 13 = 13 x 1

⇒ HCF (8, 13) = 1

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

i) 80 and 120

⇒ 80 = 40 x 2

⇒ 120 = 40 x 3

⇒ HCF (80, 120) = 40

Answer: The Sun

Step-by-step explanation:

Energy has existed from the beginning of time. The sun was the initial source of energy, providing heat and light during the day. People used light to wake up and sleep, depended on wood and dung for heat, and water power to run primitive mills.

Answer:

40 : 27

Step-by-step explanation:

[tex]3\frac{1}{3} : 2\frac{1}{4}[/tex]

Turn into improper fractions:
[tex]\frac{10}{3} : \frac{9}{4}[/tex]

Make them integers by multiplying them by 12:
40 : 27

The ratio of 3 ¹/₃ and 2 ¹/₄ is 40 : 27.

Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.

If a and b are two values, their ratio will be a:b.

The given numbers are,

3 ¹/₃ and 2 ¹/₄

To find the ratio of the given numbers,

First simplify the numbers,

3 ¹/₃ = 10 / 3

2 ¹/₄ = 9 / 4

Divide 10 / 3 and 9 / 4

= (10 / 3) / (9 / 4)

= (10 x 4) / (9 x 3)

= 40 / 27

= 40 : 27.

The required ratio is 40 : 27.

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Answer:

BD

Step-by-step explanation:

To solve this equation we must find the value of x using the other values provided in the operation.

An equation is a type of mathematical operation that is characterized by expressing an equality between two expressions, each of these expressions involved in an equation are called members and are separated by the equal sign.

On the other hand, equations are characterized by having elements or known and unknown values related by mathematical operations.

According to the above, it can be inferred that we must use an equation to calculate the value of x using the other values provided by the situation.

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Answer:

I believe it would be C

Step-by-step explanation:

71+36=107

180-107=73

it don't make sense for it to be right because none of the angles are 90°

Answer:

0.07

Step-by-step explanation:

To convert from fractions into decimals, you have to divide the numerator by the denominator. The numerator is the number on top of the fraction, and the denominator is the number on the bottom of the fraction.

7/100 = 0.07

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Turn over into vertex form

Solving

Open brackets

Accurating

Compare to Vertex form y=a(x-h)²+k

Vertex

Max profit is $897.5

Answer:

$7.50

Step-by-step explanation:

Completing the square formula

[tex]\begin{aligned}y & =ax^2+bx+c\\& =a\left(x^2+\dfrac{b}{a}x\right)+c\\\\& =a\left(x^2+\dfrac{b}{a}x+\left(\dfrac{b}{2a}\right)^2\right)+c-a\left(\dfrac{b}{2a}\right)^2\\\\& =a\left(x-\left(-\dfrac{b}{2a}\right)\right)^2+c-\dfrac{b^2}{4a}\end{aligned}[/tex]

[tex]\begin{aligned}P & =-30t^2+450t-790\\& =-30\left(t^2+\dfrac{450}{-30}t\right)-790\\\\& =-30\left(t^2+\dfrac{450}{-30}t+\left(\dfrac{450}{2(-30)}\right)^2\right)-790-(-30)\left(\dfrac{450}{2(-30)}\right)^2\\\\& =-30\left(t-\left(-\dfrac{450}{2(-30)}\right)\right)^2-790-\dfrac{450^2}{4(-30)}\\\\& =-30(t-7.5)^2+897.5\end{aligned}[/tex]

Therefore, the vertex is (7.5, 897.5)

So the ticket price that maximizes daily profit is the x-value of the vertex:  $7.50                    

Based on the inscribed angle theorem, the measurements that are correct are: B. m(arc YZ) = 120°; E. m∠YWZ = 120°.

The inscribed angle theorem states that the measure of an inscribed angle in a circle equals the twice the measure of the intercepted arc or twice the measure of the central angle.

In the circle given, since the triangle is an equilateral triangle, therefore, all its angles each equals 60°. Therefore:

m(XY) = m(YZ) = m(ZX) = 2(60°) = 120°.

The central angles, m∠XWZ = m∠XWY = m∠YWZ = 120°.

Therefore, the correct measurements are: B. m(arc YZ) = 120°; E. m∠YWZ = 120°.

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Answer:

B&E

Step-by-step explanation:

Trust me bruv

Answer:

y=-2x-4

Step-by-step explanation:

by using this website

its a graphing calculator

desmos. com/calculator

Step-by-step explanation:

Since TRIANGLE BAD is an isosceles traingle you know line BA is equal to line AD

and since C is the given midpoint of line BD you know BC is equal to CD

both triangles share line AC so the third side is also the same

so now you know traingles BAC, and CAD have three sides which all measure the same making ABC equal to ADC