Three friends buy one pack of 80 stickers. T hey divide the stickers equally and give the remainder to their teacher. How many will each friend get?

Answer:

1). Option C

2). Option A

Step-by-step explanation:

The given vertices of polygon ABCDE are A(2, 8), B(4, 12), C(10, 12), D(8, 8) and E(6, 6)

After reflection new polygon formed MNOPQ has the vertices M(-2, 8), N(-4, 12), O(-10, 12), P(-8, 8) and Q(-6, 6).

By comparing the vertices we find the x-coordinates of polygon ABCDE have been changed to MNOPQ by negative notation only.Y- coordinates are same.

Therefore, polygon ABCDE has been reflected across the y-axis.

Option C. is the answer.

If polygon MNOPQ is translated 3 units right and 5 units down then the new vertices of congruent polygon VWXYZ will be

M(-2, 8) = [(-2 - 3), (8 + 5)] = (-5, 13)

N(-4, 12) = [(-4 - 3), (12 + 5)] = (-7, 17)

O(-10, 12) = [(-10 - 3),(12 + 5)] = (-13, 17)

P(-8, 8) = [(-8 - 3), (8 + 5)] = (-11, 13)

Q(-6, 6) = [(-6 -3),(6 + 5)] = (-9, 11)

Therefore, Option A. is the correct option.

Answer:

Expand the polynomial using the FOIL method.

− 8 x^ 2- 26 x − 15

Answer:

w = 93°

Step-by-step explanation:

The angle with measure 142° forms a straight angle with the third angle in the triangle and are supplementary, thus

third angle = 180° - 142° = 38°

The sum of the 3 angles in the triangle = 180°

w = 180° - (38 + 49)° = 180° - 87° = 93°

Probability=number of favorable outcomes/ number of all possible outcomes

P(1st green and 2nd blue) = 2/6 x 3/6 = 1/6

Answer:

16^3 is 16^(3/9) = 16^(1/3) = 2 ³√2

Step-by-step explanation:

is it 9 times square root of 16 cubed, or is it really 9th root? I think it's

9th root of 16^3 is 16^(3/9) = 16^(1/3) = 2 ³√2

The values of x and y, when the smaller triangle has an area of 10 cm² are x = 4cm and y = 5cm.

In the given triangle, the area can be expressed as [tex]\( \frac{1}{2} \times x \times y \)[/tex], where x and y represent the base and height of the triangle, respectively. Since the area is given as 10 cm², the equation becomes [tex]\( \frac{1}{2} \times x \times y = 10 \)[/tex].

To find x and y, we can rearrange the equation:

[tex]\[ x \times y = \frac{10 \times 2}{1} \][/tex]

[tex]\[ x \times y = 20 \][/tex]

Now, we need to find two numbers whose product is 20. The pair x = 4 and y = 5 satisfies this condition, as 4 × 5 = 20. Therefore, the values of x and y that satisfy the given area are x = 4cm and y = 5cm.

In conclusion, the solution x = 4cm and y = 5cm satisfies the given area condition. This is determined by substituting these values into the area formula, resulting in an area of 10 cm².

Answer:

10 pounds

Step-by-step explanation:

You forgot the inequality sing, but since Antoine can't spend more than $18.20, I am positive that the sign is [tex]\leq[/tex] (Antony can spend $18.20 or less than $18.20).

Therefore, our inequality is: [tex]1.30x+5.20\leq 18.20[/tex]

where [tex]x[/tex] is the pounds of oranges

Let's solve step-by-step to find how many pounds of oranges he can buy

Step 1. Subtract 5.20 fro both sides of the inequality

[tex]1.30x+5.20-5.20\leq 18.20-5.20[/tex]

[tex]1.30x\leq 13[/tex]

Step 2. Divide both sides of the inequality by 1.30

[tex]\frac{1.30x}{1.30} \leq \frac{13}{1.30}[/tex]

[tex]x\leq 10[/tex]

We can conclude that Antony can buy 10 pounds of oranges.

Answer:

The answer is C

Step-by-step explanation:

I just took the exact same test and got a 100% on it, I had previously answered this question when echo2155 rudely claimed that I didn't show any work, most people just answer the question and don't show work because most people just want the answer not the work for it. IF YOU AGREE WITH ME GIVE A THANKS AND 5-STARS, AND COMMENT "BOO echo2155!"

Thank you all who do this!

Answer: the scatter plot you just sent me the answer would be 5

Answer:

an = 600,000 (1.15)^(n-1)

Step-by-step explanation:

So the first year, a₁ = 600,000.  The next year, a₂ = 690,000.  So:

r = a₂ / a₁

r = 690,000 / 600,000

r = 1.15

So an = 600,000 (1.15)^(n-1).

Your answer is correct!

The area of a right triangle with side lengths 7 and 7 is [tex]\frac{bh}{2} = \frac{7*7}{2} = \frac{49}{2} = 24.5[/tex]

Answer: ≈ 13.98 in2

Step-by-step explanation:

A segment of a circle is a region bounded by an arc and its chord.

To determine the area of the segment, begin by finding the area of the sector defined by the central angle.

A sector of a circle is a region bounded by two radii of the circle and their intercepted arc.

The formula for the sector area is A = πr2 (m∘/360∘).

It is given in the figure that central angle MNO is a right angle. So, m∠MNO = 90∘. It is also given that r = 7 in.

Substitute the given values into the formula and simplify.

A = π(7)2 (90∘/360∘) = 49/4π in2

Find the area of △MNO.

Since the radii in a circle are congruent, NO = NM = 7.                                  To find the area of △MNO, use the formula for the area of a triangle, A = 1/2bh.

Substitute 7 for b and 7 for h, then simplify.

A = 1/2 (7) (7) = 24.5 in2

The area of the segment is the difference between the two areas, the area of the sector and the area of the triangle.

A = 49/4π − 24.5 ≈ 13.98 in2

Therefore, the area of segment MNO is ≈ 13.98 in2.

[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\[-0.5em] \hrulefill\\ r=6.5\\ s=5.7 \end{cases}\implies 5.7=\cfrac{\theta \pi (6.5)}{180}\implies 1026=6.5\pi \theta \\\\\\ \cfrac{1026}{6.5\pi }=\theta \implies \stackrel{\textit{rounded up, using }\pi =3.14}{50.27=\theta }[/tex]

The measure of the angle at the centre of the circle made by the arc of length 5.7 cm that has a radius of 6.5 cm is 50.27°.

Any smooth curve connecting two points is called an arc. The arc length is the measurement of how long an arc is. The length of an arc is given by the formula,

[tex]\rm{ Length\ of\ an\ Arc = 2\times \pi \times(radius)\times\dfrac{\theta}{360} = 2\pi r \times \dfrac{\theta}{2\pi}[/tex]

where

θ is the angle, that arc creates at the centre of the circle in degree.

As we know that the length of an arc is given by the formula,

[tex]\rm{ Length\ of\ an\ Arc = 2\pi r \times \dfrac{\theta}{360^o}[/tex]

Given the length of the arc is 5.7 cm, while the radius of the circle is 6.5cm, therefore, the angle made by the arc at the centre of the circle is,

[tex]5.7 = 2\pi (6.5) \times \dfrac{\theta}{360^o}\\\\[/tex]

θ = 50.27°

Hence, the measure of the angle at the centre of the circle made by the arc of length 5.7 cm that has a radius of 6.5 cm is 50.27°.

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Answer:

BF = 30

Step-by-step explanation:

Since B and F are midpoints then BF is parallel to CE and half it's size

BF = 0.5 × CE = 0.5 × 60 = 30

Answer:

(x, y) = (-1, 4), (2, -1), (5, -6)

Step-by-step explanation:

You can choose any value you like for either x or y, then solve for the other value. I like to plot points with integer coefficients, so I would look for sets of those.

The nature of this equation is that it will have integer solutions with x-values spaced 3 apart and y-values spaced 5 apart. (The spacing of each corresponds to the coefficient of the other.) So, the trick is to find an x-value that gives an integer solution for y. (You will need to try at most 3 consecutive integers.)

Solving the equation for y, we get ...

y = -5/3x +7/3

Right away, we know that x=0 will not give an integer solution for y. Nor does x=1. The third consecutive integer that is easy to try is x = -1, so ...

y = (-5/3)(-1) +7/3 = (5+7)/3 = 4 . . . . an integer value for y

Our first point is then (x, y) = (-1, 4).

Since the slope is negative, we know that increasing x will decrease y. Thus we can simply add (3, -5) to any point to get another point on the line.

Two more points on the line are ...

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

(2, -1) +(3, -5) = (5, -6)

Three integer-valued points on this line are (-1, 4), (2, -1), (5, -6).

the answer for this question is twelve

Answer:

Step-by-step explanation:

For 2 triangles to be similar, they have to have congruent angle measures with corresponding sides that exist in proportion to one another.  #14 shows a triangle with 2 angle measures given.  We can find the third angle in that triangle to be 65.  The one on the right in #14 shows a triangle with 66 degrees in the position corresponding to 65 on the left.  Those are not similar (we know nothing about the side lengths so we have no choice but to work with the angles).

#15 shows 2 triangles that are "attached" by angle M in the center.  Those 2 angles meet to create vertical angles, and vertical angles are congruent, so angle HMG and angle KMJ are congruent.  If both triangles have 2 angles that are corresponding and congruent, then the third angles in both will also be guaranteed to be congruent.  So those 2 triangles are similar by AA

the awnser should be -x^2 +2

Answer:

y = -x^2+2

Step-by-step explanation:

shift down y=x^2 for 2 units then it becomes y = x^2-2

reflect across x-axis then it becomes y = -(x^2-2) which is y = -x^2+2

The store will have 29 pizzas.

This is because:

D is the correct answer

Answer:

the min is 53 the max is 90 median is 65 first  quartile  is 60 and the third quartile is 82

Step-by-step explanation:

The correct answers are: Minimum: 53, First quartile: 60, Median: 65, Third quartile: 82, Maximum: 90.

To read a box plot, we look at the five-number summary: the minimum, first quartile, median, third quartile, and maximum.

The box plot shows the middle 50% of the data, which is the interquartile range (IQR). The IQR is represented by the box, with the median represented by the line inside the box.

The whiskers extend from the box to the minimum and maximum values, respectively.

In this box plot, the minimum value is 53 and the maximum value is 90. The IQR is 65 - 60 = 5, which means that the middle 50% of the data is within 5 points of the median. The median is 65, so the first quartile is 60 and the third quartile is 82.

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Answer:

The simplest form is 2(3x - 7)/x(x³ + 4)

Step-by-step explanation:

* Lets revise how can divide fraction by fraction

- To simplify (a/b)/(c/d), change it to (a/b) ÷ (c/d)

∵ a/b ÷ c/d

- To solve it change the division sign to multiplication sign and

 reciprocal the fraction after the sign

∴ a/b × d/c = ad/bc

* Now lets solve the problem

∵ [tex]\frac{\frac{3x-7}{x^{2}}}{\frac{x^{2}}{2}+\frac{2}{x}}[/tex]

- Lets take the denominator and simplify by make it a single

 fraction, let the denominator of it 2x and change

 the numerator

∴ [tex]\frac{x^{2}}{2}+\frac{2}{x}=\frac{x(x^{2})+2(2)}{(2)(x)}=\frac{x^{3}+4}{2x}[/tex]

∴ The fraction = [tex]\frac{\frac{3x-7}{x^{2}}}{\frac{x^{3}+4}{2x}}[/tex]

* Now lets change it by (up ÷ down)

∴ [tex]\frac{3x-7}{x^{2}}[/tex] ÷ [tex]\frac{x^{3}+4}{2x}[/tex]

- Change the division sign to multiplication sign and reciprocal

 the fraction after the sign

∴ [tex]\frac{3x-7}{x^{2}}[/tex] × [tex]\frac{2x}{x^{3}+4}[/tex]

∴ [tex]\frac{(2x)(3x-7)}{(x^{2})(x^{3}+4)}[/tex]

- We can simplify x up with x down

∴ [tex]\frac{2(3x-7)}{x(x^{3}+4)}[/tex]

* The simplest form is 2(3x - 7)/x(x³ + 4)

Answer:

Step-by-step explanation:

(look at the picture)

We have opposite and adjacent. Therefore we must use the tangent:

[tex]\tangent=\dfrac{opposite}{adjacent}[/tex]

[tex]adjacent=500\\opposite=x\\\tan10^o\approx0.1763[/tex]

Substitute:

[tex]\dfrac{x}{500}\approx0.1763[/tex]       multiply both sides by 500

[tex]x\approx88.15\to x\approx88.2[/tex]

Answer: if the iguana is five feet it would be 60 inches

Answer:

1/9

Step-by-step explanation:

(1/3)^2 = 1/3 x 1/3 =1/9

plus I checked the answer after I got it wrong so...

Answer:

[tex]\frac{1}{9}[/tex]

Step-by-step explanation:

This is a case of enlargement of a figure of scale factor [tex]\frac{1}{3}[/tex].

In any enlargement, [tex]Area(F')=k^2 Area(F)[/tex], where the transformation maps F onto F'.

In this case, let F be polygon XXX and let F' be polygon YYY. Hence,

[tex]Area(YYY) = k^2 Area (XXX)[/tex]

[tex]Area(YYY) = (\frac{1}{3})^2 Area(XXX)[/tex]

[tex]Area(YYY) = \frac{1}{9} Area(XXX)[/tex]

Therefore, the area of polygon YYY is [tex]\frac{1}{9}[/tex] of the area of polygon XXX.

Answer:

52 ft

Step-by-step explanation:

For each chord, the product of segment lengths is a constant. We can find that constant as the product of the segment lengths of the bisected chord:

(24 ft)·(24 ft) = 576 ft^2

Then the missing segment length (DX) of the diameter chord is ...

DX·(36 ft) = 576 ft^2

DX = (576 ft^2)/(36 ft) = 16 ft

So, the total length of the diameter chord is ...

DX +XL = 16 ft + 36 ft

DL = 52 ft

_____

We know DL is a diameter because the perpendicular bisector of any chord intersects the center of the circle.

Answer:

Option A. Ahmed wins the chess game

Step-by-step explanation:

we know that

The probability of Ahmed winning the chess games is 45%

45%=045/100=0.45

The probability of Ahmen winning the checkers games is 0.36

Compare the probability

0.45> 0.36

so

Is more likely that  Ahmed wins the chess game

Answer:

A

Step-by-step explanation:

Answer:

Option A

Step-by-step explanation:

In a train yard there are 6 flat cars, 7 box-cars and 3 livestock cars.

So total number of cars = 6 + 7 + 3

                                       = 16

Now a train is to be made by 9 cars, out of 16 cars.

So number of ways the train can be made up will be =[tex]^{n}P_{r}[/tex]

where n = 16 and r = 9

so number of ways =[tex]^{16}P_{9}[/tex]

Option A is the answer.

Considering the definition of permutation, you use 16P9 to find the number of ways the train could be made up. (Option A).

Permutation is placing elements in different positions. So, permutations of m elements in n positions are called the different ways in which the m elements can be arranged occupying only the n positions.

That is, permutations refer to the action of arranging all the members of a set in some sort of order or sequence.

In other words, permutations (or Permutations without repetition) are ways of grouping elements of a set in which:

To obtain the total of ways in which m elements can be placed in n positions, the following expression is used:

[tex]mPn=\frac{m!}{(m-n)!}[/tex]

where "!" indicates the factorial of a positive integer, which is defined as the product of all natural numbers before or equal to it.

In a train yard there are 6 flat cars, 7 box-cars and 3 livestock cars. So total number of cars is 6 + 7 + 3= 16.

A train is made up of 9 cars, out of 16 cars.

To obtain the total of ways in which 16 elements can be placed in 9 positions, you use the permutation 16P9.

Finally, you use 16P9 to find the number of ways the train could be made up. (Option A).

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Answer:

The answer is 4.

Step-by-step explanation:

I believe that, if I'm correct, 2 students are equal to 1%. 2 x 35 = 70. 2 x 33 = 66. 70 - 66 = 4 more students. I hope this is correct.

The total number of students who preferred apples than cherries are 70 if the two hundred students were surveyed about their favorite fruit option, fourth is correct.

It is defined as the ratio of two numbers expressed in the fraction of 100 parts. It is the measure to compare two data, the % sign is used to express the percentage.

From the diagram, we can see the total 35% students preferred apples.

Total number of students = 200

The number of students who preferred apples than cherries = 200×35%

= 200(35/100)

= 2(35)

= 70

Thus, the total number of students who preferred apples than cherries are 70 if the two hundred students were surveyed about their favorite fruit option fourth is correct.

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Answer:

b

Step-by-step explanation:

Answer:

73

292

173

Step-by-step explanation:

x = first number

4x = second number

100 + x = third number

x + 4x + 100 + x = 538

6x + 100 = 538

6x + 100 - 100 = 538 - 100

6x = 438

6x/6 = 438/6

x = 73

Check:

73 + 4(73) + 100 + 73 = 538

73 + 292 + 173 = 538

538 = 538

Answer:

The numbers are 73, 173 and 292.

Step-by-step explanation:

If the numbers are x, y and z we have:

y = 4x

z = x + 100

x + y + z = 538

Substituting for y in the last equation:

x + 4x + z = 538

5x + z = 538.............(1)

From the second equation:

z - x = 100................(2)

Equation (1) - (2) gives:

6x = 438

x = 73

Therefore y = 4x) = 4(73) = 292

and z = x + 100 = 73 + 100 = 173.

Answer:

1) The probability of getting an even number when rolling a six-sided number cube is 0.5. Choice A

2) 80%. Choice C

Step-by-step explanation:

1)

We are required to determine the probability of getting an even number when rolling a six-sided number cube. The six-sided number cube has the following numbers written on its faces;

1, 2, 3, 4, 5, 6

The numbers; 2, 4, and 6 are even

The probability of getting an even number;

= ( number of faces with even numbers)/ (total number of faces)

= 3/6

0.5

2)

We are required to determine the probability of choosing a letter that is not a vowel after placing the letters for the word smart in a bag.

The non-vowels in the word smart are; s, m, r, and t. There are 4 non-vowels out of a total of 5 letters. The required probability is thus;

(4/5)*100 = 80%