5. A raffle prize of 14x^2 /15 dollars is to be divided among 7x people. Write an expression for the amount of money that each person will receive

Answer:

m∠ABC = 120°

Step-by-step explanation:

Consider the case where point C is on the circle and long arc AC has measure 240°. Then ∠ABC is an inscribed angle, and its measure is half the measure of the intercepted arc, so is 120°.

This is still true even when point B and point C are on top of each other and BC is a tangent to the circle. That is the case shown here, so m∠ABC = 120°.

Answer:

The position vector of point C is <-3 , -17 , 8> or -3i - 17j + 8k

Step-by-step explanation:

* Lets revise how to solve the problem

- If the endpoints of a segment are (x1 , y1 , z1) and (x2 , y2 , z2), and

 point (x , y , z) divides the segment externally at ratio m1 :m2, then

 [tex]x=\frac{m_{1}x_{2}-m_{2}x_{1}}{m_{1} -m_{2}},y=\frac{m_{1}y_{2}-m_{2}y_{1}}{m_{1}-m_{2}},z=\frac{m_{1}z_{2}-m_{2}z_{1}}{m_{1}-m_{2}}[/tex]

* Lets solve the problem

∵ AB is a segment where A = (3 , 1 , 2) and B = (1 , - 5 , 4)

∵ Point C lies on line AB such that AC : BC=3 : 2

∵ From the ratio AC = 3/2 AB

∴ C divides AB externally

- Lets use the rule above to find the coordinates of C

- Let Point A is (x1 , y1 , z1) , point B is (x2 , y2 , z2) and point C is (x , y , z)

 and AC : AB is m1 : m2

∴ x1 = 3 , x2 = 1

∴ y1 = 1 , y2 = -5

∴ z1 = 2 , z2 = 4

∴ m1 = 3 , m2 = 2

- By using the rule above

∴ [tex]x=\frac{3(1)-2(3)}{3-2}=\frac{3-6}{1}=\frac{-3}{1}=-3[/tex]

∴ [tex]y=\frac{3(-5)-2(1)}{3-2}=\frac{x=-15-2}{1}=\frac{-17}{1}=-17[/tex]

∴ [tex]z=\frac{3(4)-2(2)}{3-2}=\frac{12-4}{1}=\frac{8}{1}=8[/tex]

∴ The coordinates fo point c are (-3 , -17 , 8)

* The position vector of point C is <-3 , -17 , 8> or -3i - 17j + 8k

The new triangle produced is an exact remake of the first one. The angles or size does not change between the two. Thus, this transformation is an Isometry.

Answer:

  The solutions to the equation are 1, 0.375.

Step-by-step explanation:

The equation is already in factored form.

The solutions to the system are the values of x that make one or the other of the factors be zero.

  x -1 = 0 . . . when x = 1

  8x -3 = 0 . . . when x = 3/8 = 0.375

There is only one variable, so no "ordered pairs" are involved.

The solutions are {1, 0.375}.

Answer:

1,14

0,375,12.75

Step-by-step explanation:

Answer:

  8.  1483.33

  9.  21 months

Step-by-step explanation:

8. Morgan's income after taxes is 55000/12 = 4583.33 per month. The amount  available after expenses is 4583.33 -3100.00 = 1483.33 per month.

Morgan is able to put $1483.33 per month into savings.

__

9. If Morgan is able to save $1483.33 per month, it will take her ...

  $30,000/$1483.33 ≈ 20.2

months to save $30,000. After 20 months, she won't have quite enough, so it will take her one more month to save the desired amount.

It will take Morgan about 21 months to save $30,000.

_

If you like, you can write an equation for "m", the number of months it will take Morgan to save 30,000:

  1483.33×m = 30,000

  m = 30,000/1483.33 ≈ 20.2 . . . . . . divide by the coefficient of m

Answer:

The perimeter is [tex]P=73.12\ cm[/tex]

Step-by-step explanation:

we know that

The perimeter of the figure is equal to the circumference of a semicircle

plus the perimeter of a square minus the diameter of the circle

so

[tex]P=\pi r+4(b)-D[/tex]

we have

[tex]r=8\ cm[/tex]

[tex]b=16\ cm[/tex]

[tex]D=16\ cm[/tex]

The diameter of the circle is equal to the length side of the square

substitute

[tex]P=(3.14)(8)+4(16)-16[/tex]

[tex]P=25.12+64-16[/tex]

[tex]P=73.12\ cm[/tex]

Answer:

Explanation:

The area of the octagon may be calculated as the difference of the area of the original square and the area of the four corners cut off.

1) Area of the square.

The original square's side length is the same wide of the formed octagon: 10 cm.

So, the area of such square is: (10 cm)² = 100 cm².

2) Area of the four corners cut off.

Since, the corners were cut off two centimeters from each corner, the form of each piece is an isosceles right triangle with legs of 2 cm.

The area of each right triangle is half the product of the legs (because one leg is the base and the other leg is the height of the triangle).

Then, area of one right triangle: (1/2) × 2cm × 2cm = 2 cm².

Since, they are four pieces, the total cut off area is: 4 × 2 cm² = 8 cm².

3) Area of the octagon:

And that is the answer: 92 cm².

Answer:

Rebecca have 18 nickels coins and 27 dime coins

Step-by-step explanation:

Remember that

1 nickel =$0.05

1 dime=$0.10

so

Let

x -----> the number of nickel coins

y -----> the number of dime coins

we know that

x+y=45

x=45-y ------> equation A

0.05x+0.10y=3.60 -----> equation B

Solve the system by substitution

Substitute equation A in equation B and solve for y

0.05(45-y)+0.10y=3.60

2.25-0.05y+0.10y=3.60

0.05y=3.60-2.25

0.05y=1.35

y=27

Find the value of x

x=45-y ---->x=45-27=18

therefore

Rebecca have 18 nickels coins and 27 dime coins

Rebecca has 18 nickels and 27 dimes.

Solving the Problem

Rebecca has 45 coins, composed of nickels and dimes, with a total value of $3.60. We can set up a system of linear equations to solve this problem.

Step-by-Step Explanation

Therefore, Rebecca has 18 nickels and 27 dimes.

Answer:

see explanation

Step-by-step explanation:

Using the exact values

sin45° = cos45° = [tex]\frac{1}{\sqrt{2} }[/tex]

Since the triangle is right use the sine/cosine ratios, that is

sin45° = [tex]\frac{TU}{TV}[/tex] = [tex]\frac{TU}{9\sqrt{2} }[/tex]

Multiply both sides by 9[tex]\sqrt{2}[/tex]

9[tex]\sqrt{2}[/tex] × [tex]\frac{1}{\sqrt{2} }[/tex] = TU, hence

TU = 9

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

cos45° = [tex]\frac{UV}{TV}[/tex] = [tex]\frac{UV}{9\sqrt{2} }[/tex]

Multiply both sides by 9 [tex]\sqrt{2}[/tex]

9[tex]\sqrt{2}[/tex] × [tex]\frac{1}{\sqrt{2} }[/tex] = UV, hence

UV = 9

Since TU = UV = 9 , then triangle is isosceles

and ∠T = ∠V = 45°

Check the picture below.

so the parabola looks more or less like so, bearing in mind that the directrix is a horizontal line, thusu the parabola is a vertical one, so the squared variable is the "x".

The vertex is always half-way between the focus point and the directrix, as you see there, and the distance from the vertex to the focus is "p" distance, since the parabola is opening downwards, "p" is negative, in this case -2.

[tex]\bf \textit{parabola vertex form with focus point distance} \\\\ \begin{array}{llll} 4p(x- h)=(y- k)^2 \\\\ \stackrel{\textit{we'll use this one}}{4p(y- k)=(x- h)^2} \end{array} \qquad \begin{array}{llll} vertex\ ( h, k)\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=0\\ k=0\\ p=-2 \end{cases}\implies 4(-2)(y-0)=(x-0)^2\implies -8y=x^2\implies y=-\cfrac{1}{8}x^2[/tex]

To find the standard form of the parabola with a focus at (0, -2) and a directrix at y = 2, the process involves identifying the vertex, determining direction, and substituting into the general equation to get x² = -8y.

To find the standard form of the equation of a parabola with a focus at (0, -2) and a directrix at y = 2, we start by identifying key properties of parabolas. The vertex of the parabola is midway between the focus and the directrix. Here, the distance between the focus and the directrix is 4, so the vertex is 2 units away from each, placing it at (0, 0) as the directrix and focus are symmetrically placed above and below the x-axis.

The general equation for a parabola opening upwards or downwards is (x - h)² = 4p(y - k), where (h, k) is the vertex of the parabola, and p is the distance from the vertex to the focus (positive if the parabola opens upwards, negative if downwards). Given the focus (0, -2) and the vertex (0, 0), p = -2, indicating the parabola opens downwards. Applying these values to the general equation yields: x² = -8y, which is the standard form of the equation for the described parabola.

Answer: 3/5 probability of choosing a number LESS THAN 8

To answer the question, we first need to understand the command:

The product = multiply the unknowns together

Therefore, the expression:

4ya x 5x

when simplified: 4ya x 5x= 20ayx

Hope it helps!

Answer:

4ya x 5x = ?

Step-by-step explanation:

Answer:

The answer is D (line symmetry and rotational symmetry; 180o; order 2.

Step-by-step explanation:

You can fold the figure in half and it would be the same on both sides.  The figure also has rotational symmetry because if you rotate the figure 180 degrees about the center, then it basically maps itself, or in other words, its the same.  So the ANSWER IS D

line symmetry and rotational symmetry; 180 degree; order 2. Correct option is D.

The figure described exhibits characteristics of both reflectional and rotational symmetry. Firstly, it possesses reflectional symmetry because you can fold it in half, and both sides of the fold will be identical, essentially mirroring each other. This demonstrates that the figure can be divided into two equal parts that are reflections of each other along the fold line.

Furthermore, the figure displays rotational symmetry, specifically a 180-degree rotational symmetry. When you rotate it by 180 degrees about its center, the figure aligns with itself, showing that it remains unchanged upon this rotation. This means that you can rotate the figure halfway, and it will still appear identical.

So, the correct answer is not just "D," but rather a more comprehensive explanation of the figure's symmetrical properties, encompassing both reflectional and rotational symmetry.

to know more about rotational symmetry;

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The P(draw a blue marble)=0.25

The bag has:

3 blue marbles, 4 green marbles, and 5 red marbles.

This means that the total number of marbles in bag are:

3+4+5=12 marbles.

We are asked to find the probability that the marble that is randomly drawn from a bag is: Blue marble.

Let P denote the probability of an event.

We know that the probability of drawing a blue marble is equal to the ratio that the marble drawn is blue to the total number of marbles in the bag.

Hence,

[tex]\text{P(blue\ marble)}=\dfrac{3}{12}\\\\i.e.\\\\\text{P(blue\ marble)}=\dfrac{1}{4}\\\\\\\text{P(blue\ marble)}=0.25[/tex]

Hence, the answer is:

        P(draw a blue marble)=0.25

Certainly! Let's solve this step by step.

**Step 1: Determine the number of blue marbles.**

We have 333 blue marbles in the bag.

**Step 2: Determine the total number of marbles in the bag.**

The bag contains:
- 333 blue marbles,
- 444 green marbles, and
- 555 red marbles.

To find the total number of marbles, we add these numbers together:
Total marbles = 333 (blue) + 444 (green) + 555 (red)

**Step 3: Calculate the total number of marbles.**

Now, we add up each type of marble to get the total:
Total marbles = 333 + 444 + 555

**Step 4: Calculate the probability of drawing a blue marble.**

The probability of an event is calculated by dividing the number of favorable outcomes by the number of total possible outcomes. In this case, the favorable outcomes are drawing a blue marble, and the total outcomes are the total number of marbles.

Thus, the probability P of drawing a blue marble is:
P(draw a blue marble) = Number of blue marbles / Total number of marbles

Using the numbers provided:
P(draw a blue marble) = 333 / (333 + 444 + 555)

**Step 5: Calculate the exact probability.**

To get the exact probability, we perform the addition in the denominator and then divide:
P(draw a blue marble) = 333 / (1332)

Now, let's execute this calculation.

**Step 6: Simplify the fraction (if necessary).**

In this case, the fraction 333/1332 is already in its simplest form, so we don't need to simplify it further.

**Step 7: Calculate the approximation to 2 decimal places.**

To round the probability to 2 decimal places, we will compute the exact division and then round the result:
P(draw a blue marble) ≈ 0.2500 (rounded to 4 decimal places for illustrative purposes)

However, since we need to round our answer to 2 decimal places, the result is:
P(draw a blue marble) ≈ 0.25

Therefore, the probability of drawing a blue marble, rounded to two decimal places, is 0.25.

Answer:

576 cuboids

Step-by-step explanation:

Let

x -----> the length side of the cube

n -----> number of cuboids that are needed

we know that

The volume of the cuboid is equal to

[tex]V=(2)(3)(4)=24\ cm^{3}[/tex]

The volume of the cube is equal to

[tex]V=x^{3}[/tex]

Find the number of cuboids that are needed

[tex](n)24=x^{3}}[/tex]

n*24 must be a perfect cube

so

The minimum value that satisfied n to make n*24 a perfect cube is n=576

[tex]576*24=13,824=24^{3}[/tex]

Answer:

576 Cuboids

Step-by-step explanation:

Answer:

If she gives all the earnings to her sister she would still own her $9.30

Step-by-step explanation:

Subtract the $25.63 (sisters' money) fromv $16.33(earnngs from her dad) then you get 9.30

Answer:

$9.30

Step-by-step explanation:

Answer:

The right answer is B: The probability is equal to p%.

Step-by-step explanation:

Answer:

Option B is correct

Step-by-step explanation:

Remove the parentheses from the following expression (2y + x) ÷ z

When removing the parenthesis, z will be divided by both the numbers inside the parenthesis

i.e.

2y/z + x/z

So, Option B is correct.

Answer:

[tex]\large\boxed{12.25=\dfrac{49}{4}}[/tex]

Step-by-step explanation:

[tex]12.\underbrace{25}_{2}=\dfrac{1225}{1\underbrace{00}_2}=\dfrac{1225:25}{100:25}=\dfrac{49}{4}\\\\12.25=12+0.25=12+\dfrac{25}{100}=12+\dfrac{25:25}{100:25}=12+\dfrac{1}{4}\\\\=\dfrac{12\cdot4}{4}+\dfrac{1}{4}=\dfrac{48+1}{4}=\dfrac{49}{4}[/tex]

Answer:

Step-by-step explanation:

Find two rows in the table that have the same values in the f(x) and g(x) columns.

Answer:

29

Step-by-step explanation:

Since they have given you x = 4, simply sub it into the equation,

(4)^2 + 3(4) - 7 + 8

=  29

Answer:

29

Step-by-step explanation:

Substitute 4 for x into the expression x^2+3x−7+8 and then simplify using the order of operations.

4^2+3(4)−7+8

16+12−7+8

29

The area of deltoid is defined by formula:

[tex]A=\dfrac{e\cdot f}{2}[/tex]

Where e and f are diagonals.

If you were to double the size of either one. Let's say f. You would result with:

[tex]A=\dfrac{e\cdot2f}{2}=e\cdot f[/tex]

Which means if either of diagonals double in length the area of deltoid will be twice as big as it was before.

Hope this helps.

r3t40

the kite, which looks more like a rhombus but being called a kite, will look like the one in the picture below.

now, as you see in the picture, the kite is really 4 congruent triangles, each with a base of 2.5 and a height of 5, so their area is

[tex]\bf \stackrel{\textit{area of one triangle}}{\cfrac{1}{2}(2.5)(5)}\implies 6.25\qquad \qquad \stackrel{\textit{area of all four triangles}}{4\left[ \cfrac{1}{2}(2.5)(5) \right]}\implies 25 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{doubling the base or height}}{4\left[ \cfrac{1}{2}(2.5)(5)\underline{(2)} \right]}\implies \stackrel{\textit{the area is twice as much as the original}}{\underline{(2)}~~\left[ 4\left[ \cfrac{1}{2}(2.5)(5) \right] \right]}[/tex]

[tex]\bf \textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2)~\hfill a^3-b^3 = (a-b)(a^2+ab+b^2) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ x^3-125=0\implies x^3-5^3=0\implies (x-5)(x^2+5x+5^2)=0 \\\\[-0.35em] ~\dotfill\\\\ x-5=0\implies \boxed{x=5} \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~~~~~~~\textit{quadratic formula}[/tex]

[tex]\bf \stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+5}x\stackrel{\stackrel{c}{\downarrow }}{+25} \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x=\cfrac{-5\pm\sqrt{5^2-4(1)(25)}}{2(1)}\implies x=\cfrac{-5\pm\sqrt{25-100}}{2} \\\\\\ x=\cfrac{-5\pm\sqrt{-75}}{2}~~ \begin{cases} 75=&3\cdot 5\cdot 5\\ &3\cdot 5^2 \end{cases}\implies x=\cfrac{-5\pm\sqrt{-3\cdot 5^2}}{2}[/tex]

[tex]\bf x=\cfrac{-5\pm 5\sqrt{-3}}{2}\implies x=\cfrac{-5\pm 5\sqrt{-1\cdot 3}}{2}\implies x=\cfrac{-5\pm 5\sqrt{-1}\cdot \sqrt{3}}{2} \\\\\\ x=\cfrac{-5\pm 5i\sqrt{3}}{2}\implies \boxed{x= \begin{cases} \frac{-5+ 5i\sqrt{3}}{2}\\\\ \frac{-5-5i\sqrt{3}}{2} \end{cases}}[/tex]

To solve the complex number equation x^3-125=0, we rearrange to x^3=125 and apply the rule for cube roots in the complex system. This yields three solutions: x = 5, x = 5*omega, and x = 5*omega^2.

The given equation is x^{3}-125=0. It belongs to the category of complex number equations within the complex system. We can solve this equation step-by-step by using the cube root of unity in the complex number system.

Firstly, move '125' to the right side of the equation: x^{3}=125. We find that x is the cube root of 125. The solutions to this kind of equation are given by a rule in the complex number system that the cube roots of a number a are given by [a^(1/3), a^(1/3)*omega, a^(1/3)*omega^2], where omega is a cube root of unity and equals -1/2+sqrt(3)i/2 and omega^2=-1/2-sqrt(3)i/2 .

Therefore for x^{3}=125, we get x = 5, 5*omega, and 5*omega^2. These are the solutions in the complex number system.

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Answer:

B The probability's are equal

Step-by-step explanation:

FOR  APEX Hope i helped

Option: B is the correct answer.

The probabilities are equal.

( Since, probability of landing on 1 and on 4 are equal i.e. 1/8 )

The spinner is divided into two sizes such that the larger wedges are twice the size of the smaller ones.

The numbers that come on the smaller wedge are: 1,3,4 and 6

and those who come on the large wedge are: 2 and 5

If we divide the wedge which ere twice into equal sections then the total number of sections are:

      8

We know that the probability of an event is defined as the ratio of number of favorable outcomes to the total number of outcomes.

( Since 1 is comprised of just one section out of total 8 sections)

Similarly,

( Since 2 is comprised of two sections out of total 8 sections)

( Since 3 is comprised of just one section out of total 8 sections)

Similarly,

Step-by-step explanation:

Waves have the form:

y = A sin (2π/T x + φ) + B

where A is the amplitude (the distance from the center of the wave to the max or min),

T is the period (time it takes for one cycle),

φ is the phase shift (moves the wave left or right),

and B is the offset (moves the wave up or down).

This can also be written with cosine.

Here, we have d = 6 cos(π/2 t).

The amplitude is A = 6, so the maximum distance from the equilibrium position is 6 units.

The period is:

2π / T = π/2

T = 4

So the period is 4 seconds.

Answer:

  D.  64 and 81

Step-by-step explanation:

The best benchmarks are the ones that are the closest to the value you want the root of. Perfect squares in that neighborhood are ...

The closest are 64 and 81.

Answer: Half of 1/3 would be 1/6 :)

The decimal form of it would be 0.166666

ANSWER

[tex] \frac{1}{6} [/tex]

EXPLANATION

The given fraction is

[tex] \frac{1}{3} [/tex]

We want to find half of this fraction.

We can write this expression mathematically as:

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

The 'of' in this expression means multiplication.

This implies that

[tex] \implies \: \frac{1}{2} \: of \: \: \frac{1}{3} = \frac{1}{2} \: \times \: \: \frac{1}{3} [/tex]

[tex] \implies \: \frac{1}{2 } \: of \: \: \frac{1}{3} = \frac{1 \times 1}{2 \times 3} [/tex]

We multiply out to get

[tex] \implies \: \frac{1 }{2} \: of \: \: \frac{1}{3} = \frac{1}{6} [/tex]

Answer:

  3

Step-by-step explanation:

You know that ...

  1000 = 10³

when you take the logarithm to base 10, you get

  log₁₀(1000) = 3

Multiply the total amount by the percentage.

250 mL x 0.65 = 162.5

The answer is 162.5 mL