The manager of cups R' Us handed out 125 coupons to his customers on Monday, c coupons on Tuesday, and 220 coupons on the Wednesday. Write an expression for the total number of coupons the manager handed out. Then simplify the expression.

I think the sum is supposed to be

[tex]\displaystyle\sum_{n=1}^4\frac n{n!}=\sum_{n=1}^4\frac1{(n-1)!}[/tex]

since [tex]n!=n\cdot(n-1)![/tex]. Then

[tex]\displaystyle\sum_{n=1}^4\frac1{(n-1)!}=\frac1{0!}+\frac1{1!}+\frac1{2!}+\frac1{3!}[/tex]

and [tex]0!=1[/tex] by definition so that the sum has a value of [tex]\dfrac83[/tex].

B. x=5

Two shapes are congruent if you can turn one into the other by moving, rotating or flipping. So if we rotate 180 degrees, say, trapezoid WXYZ and then moving it to the left, it will match trapezoid ABCD. If so, it will be true that:

[tex]\angle BAD=\angle XWZ \\ \\ \angle BAD=4x-7 \\ \\ \angle XWZ=2x+3 \\ \\ 4x-7=2x+3 \\ \\ Solving \ for \ x: \\ \\ 4x-2x=7+3 \\ \\ 2x=10 \\ \\ \boxed{x=5}[/tex]

Answer:

Answer is B x=5

Step-by-step explanation:

Hope this helps!!

Answer:

  D)  √3/3

Step-by-step explanation:

The coordinates of the point at the angle π/6 are shown as (√3/2, 1/2). The tangent of the angle is the ratio of the y-coordinate to the x-coordinate:

  tan(π/6) = (1/2)/((√3)/2) = 1/√3 = (√3)/3 . . . . matches choice D

I honestly need help on this to

Step-by-step explanation:

b

Answer: Option B.  Ellipse

[tex]\frac{(x-\frac{1}{4})^2}{\frac{129}{16}}+\frac{(y-0)^2}{\frac{129}{32}}=1[/tex]

Step-by-step explanation:

To know what type of conic section the function is

[tex]2x ^ 2-9x + 4y ^ 2 + 8x = 16[/tex] we must simplify it.

[tex]2x ^ 2-9x + 4y ^ 2 + 8x = 16\\\\2x^2 -x +4y^2 =16[/tex]

complete the square of the expression:

[tex]2x ^ 2 -x\\\\\\2(x^2 -\frac{1}{2}x)\\\\2(x^2-\frac{1}{2}x +\frac{1}{16})-2\frac{1}{16}\\\\2(x-\frac{1}{4})^2 -\frac{1}{8}[/tex]

So we have

[tex]2(x-\frac{1}{4})^2 -\frac{1}{8}+4y^2 =16\\\\2(x-\frac{1}{4})^2+4y^2 =\frac{129}{8}\\\\\frac{8}{129}[2(x-\frac{1}{4})^2] +\frac{8}{129}[4y^2] =1\\\\\frac{16(x-\frac{1}{4})^2}{129}+\frac{32(y-0)^2}{129}=1[/tex]

[tex]\frac{(x-\frac{1}{4})^2}{\frac{129}{16}}+\frac{(y-0)^2}{\frac{129}{32}}=1[/tex]

We know that the general equation of an ellipse has the form

[tex]\frac{(x-h)^2}{a^2} +\frac{(y-k)^2}{b^2}=1[/tex]

Then the equation

[tex]\frac{(x-\frac{1}{4})^2}{\frac{129}{16}}+\frac{(y-0)^2}{\frac{129}{32}}=1[/tex]

is an ellipse with center [tex](\frac{1}{4}, 0)[/tex]

[tex]a =\sqrt{\frac{129}{16}}[/tex]  and  [tex]b=\sqrt{\frac{129}{32}}[/tex]

Observe the attached image

Answer:

Q1. 168 words from sixth sentence.

Q2. 171 words from line 3.

Q3. 177 words from the first three sentences.

Q4. Method 3.

Step-by-step explanation:

Question 1.

The paragraph has seven sentences.

I chose the sixth sentence ("gentle vegetarian"). It contains 24 words.

7 sentences × (24 words/1 sentence) = 168 words

Question 2.

The passage contains 19 lines.

I chose line 3 ("amazing powers"). It contains nine words.

19 lines × (9 words/1 line) = 171 words.

Question 3.

I chose the first three lines. They contain 28 words.

Words per line = 28 words/3 lines = 9.33 words per line

Total words = 19 lines × (9.33 words/1 line) = 177 words

Question 4

The passage contains 176 words. Method 3 comes closest to the actual number of words.

Answer:

c

Step-by-step explanation:

Since there's no service fee, Answer c is correct.  Here, 0 represents the zero service fee and 45 represents the $45 cost of each ticket.

Answer:

see below

Step-by-step explanation:

sin x                                 1

-------------------              = -----------

sec^2 x - tan ^2 x               csc x

Sec = 1/cos   and tan = sin/cos

sin x                                         1

-------------------                     = -----------

1/ cos ^2 x -sin^2/cos ^2 x       csc x

Factor the denominator

sin x                                         1

-------------------                     = -----------

(1-sin^2 x)/ cos ^2 x                csc x

We know that 1 - sin^2 x = cos ^2

sin x                                         1

-------------------                     = -----------

(cos^2 x)/ cos ^2 x                csc x

sin x                                         1

-------------------                     = -----------

1                                               csc x

Multiply the top and bottom of the left hand side by 1/ sin x

sin x  * 1/ sin x                              1

-------------------                     = -----------

1     * 1 sin x                             csc x

1                                                1

-------------------                     = -----------

       1 sin x                             csc x

We know that 1/sin x = csc

1                              1

---------               = -----------

csc (x)                   csc x

Answer: The answer is 0.04

Step-by-step explanation:

To determine the height of a triangle-shaped density curve spanning from 0 to 50 years, we use the fact that the area under the density curve must equal 1. The equation (50 * height) / 2 = 1 allows us to solve for the height, which is 0.04 on the probability density scale.

To determine the height of the triangle representing a density curve for possible ages, we need some information about the properties of that triangle and density curves in general. A density curve shows how the proportion of a particular measurement (in this case, ages) is spread out over a range. The area under a density curve must equal 1 (or 100%) since it represents the total probability distribution.

In this scenario, we have a triangle as a density curve stretching from 0 to 50 years, which suggests that 0 and 50 are the bounds of our variable (age). The base of the triangle spans these 50 years. If we assume a right-angled triangle for simplicity's sake (which isn't specified in the question but is a common assumption), then the area of the triangle, which represents the probability, would be (base * height) / 2.

To ensure that the total area under the curve equals 1, we set up the following equation: (50 * height) / 2 = 1. Solving this equation for height gives us height = 2 / 50, which simplifies to height = 0.04. Therefore, the height of the density triangle is 0.04 on whatever scale is being used for probability density (e.g., per year).

Answer:

hexagonal prism

Step-by-step explanation:

This solid is a hexagonal figure because the shape of its base is a hexgaon.

Answer:

The answer is hexagonal prism.

Hope this helps.☻♥

Answer:

A)

62/3 = 20.67 hours

B)

60.00 hours

C)

2074.29 miles

Step-by-step explanation:

If we assume the earth is a perfect circle, then in a complete rotation the earth covers 360 degrees or 2π radians.

A)

In 24 hours the earth rotates through an angle of 360 degrees. We are required to determine the duration it takes to rotate through 310 degrees. Let x be the duration it takes the earth to rotate through 310 degrees, then the following proportions hold;

(24/360) = (x/310)

solving for x;

x = (24/360) * 310 = 62/3 = 20.67 hours

B)

In 24 hours the earth rotates through an angle of 2π radians. We are required to determine the duration it takes to rotate through 5π radians. Let x be the duration it takes the earth to rotate through 5π radians, then the following proportions hold;

(24/2π radians) = (x/5π radians)

Solving for x;

x = (24/2π radians)*5π radians = 60 hours

C)

If the diameter of the earth is 7920 miles, then in 24 hours a point on the equator will rotate through a distance equal to the circumference of the Earth. Using the formula for the circumference of a circle we have;

circumference = 2*π*R = π*D

                         = 7920π miles

Therefore, the speed of the earth is approximately;

(7920π miles)/(24 hours) = 330π miles/hr

The distance covered by a point in 2 hours will thus be;

330π * 2 = 660π miles = 2074.29 miles

Answer:

i think it should be tan2x = 24/7, i hope i am not wrong

Step-by-step explanation:

If sin x = -3/5 and x is in quadrant 3, then tan 2x = 24/7.

Given:

[tex]$Sin x = \frac{-3}{5}[/tex]

To estimate cos x by identity

[tex]$Cos^{2} x=1-Sin^{2} x[/tex]

[tex]$Cos^{2} x =1-\frac{9}{25}[/tex]

[tex]$=\frac{16}{25}[/tex]

cos x = ±(4/5)

Since x exists in Quadrant III, then cos x exists negative.

tan x = Sin x/Cos x

= (−35)/(−54) = 3/4

By using the trigonometric identity, we get

tan 2x = 2 tan x / [tex]$1-tan^{2} x[/tex]

tan 2x = (6/4) / (1−9/16)

= (6/4)(16/7)

= 24/7

Therefore, tan 2x = 24/7.

To learn more about trigonometric identity

https://brainly.com/question/25024376

#SPJ2

Answer:

17 days

Step-by-step explanation:

For each day she works, she earns +55 and each day she DOES NOT work she earns -66. Total 30 days.

Let number of days she works be x

thus, number of days she DOES NOT work is 30 - x

We can setup an equation as:

55(x) + -66(30-x) = 77

This means, she works x days for 55 each and 30 - x days getting -66 each, totalling 77.

We can solve for x to find number of days she worked. Work shown below:

[tex]55(x) + -66(30-x) = 77\\55x-66(30)+66x=77\\121x -1980 = 77\\121x = 77+1980\\121x = 2057\\x=\frac{2057}{121}\\x=17[/tex]

Thus, she worked 17 days

Answer:

b = 6√3.

Step-by-step explanation:

Use trigonometry.

cos 30 = adjacent side / hypotenuse = b / 12

√3 / 2 = b / 12

2b = 12√3

b = 6√3 answer.

Answer:

2h+2f=10.50

4h+3f=19.50

Step-by-step explanation:

2h+2f=10.50

4h+3f=19.50

• To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

{2h2f=10.5,4h3f=19.5}

• Choose one of the equations and solve it for h by isolating h on the left hand side of the equal sign.

2h+2f=10.5

• Subtract 2f from both sides of the equation.

2h=−2f+10.5

• Divide both sides by 2.

h=1/2 (−2f+10.5)

• Multiply 1/2  times −2f+10.5.

h=−f+21/4

• Substitute −f+21/4  for h in the other equation, 4h+3f=19.5.

4(−f+21/4)+3f=19.5

• Multiply 4 times −f+21/4.

−4f+21+3f=19.5

• Add −4f to 3f.

−f+21=19.5

• Subtract 21 from both sides of the equation.

−f=−1.5

• Divide both sides by −1.

f=1.5

• Substitute 1.5 for f in h=−f+21/4. Because the resulting equation contains only one variable, you can solve for h directly.

h=−1.5+21/4

• Add 21/4  to −1.5 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

h=15/4  

The sum of two number a and b is [tex]a+b[/tex]

Its square is [tex](a+b)^2[/tex]

Half of c is [tex]\frac{c}{2}[/tex]

And we have to subtract this from what we got before:

[tex](a+b)^2-\dfrac{c}{2}[/tex]

Finally, we multiply everything by 5:

[tex]5\left[(a+b)^2-\dfrac{c}{2}\right][/tex]

Queremos, a partir de una frase, escribir la correspondiente expresión algebraica.

Obtendremos:

[tex][(a + b)^2 - c/2]*5[/tex]

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

Lo que nos dan es:

"Si al cuadrado de la suma de dos números a y b le restamos la mitad de c y la diferencia resultante la multiplicamos por 5"

Veamos esto en partes, la primera dice:

"Si al cuadrado de la suma de dos números a y b..."

El cuadrado de la suma de dos números a y b se escribe como:

[tex](a + b)^2[/tex]

Ahora tenemos:

"Si al cuadrado de la suma de dos números a y b le restamos la mitad de c ..."

Ahora le restamos la mitad de c a lo que encontramos antes:

[tex](a + b)^2 - c/2[/tex]

Finalmente:

"Si al cuadrado de la suma de dos números a y b le restamos la mitad de c y la diferencia resultante la multiplicamos por 5"

Es decir, debemos multiplicar por 5 a la diferencia (la resta) de arriba:

[tex][(a + b)^2 - c/2]*5[/tex]

Está es la expresión que queriamos encontrar.

Si quieres aprender más, puedes leer:

https://brainly.com/question/24758907

But in cost

(50×4)-(42.5×4)

Rs30

Answer:a reflection across the line containing AB

Step-by-step explanation:

The correct option is A).

Step-by-step explanation:

Given :

First Transformation is a translation of vertex B to vertex R.

AB = RQ   (refer the given figure)

Solution :

The second transformation is obviously a reflection across the line containing AB because AB = RQ and there is translation of vertex B to vertex R therefore there is also a translation of vertex A to vertex Q and through observing the given diagram we can say that there is a reflection across the line containing AB.

Hence, the correct option is A).

For more information, refer the link given below

https://brainly.com/question/21454252?referrer=searchResults

Answer:

D. 10

Step-by-step explanation:

The chord is bisected as shown by the perpendicular lines and right angle, so both segments are 6.

Draw a radius from the center to the end of the chord to create a right triangle. 8 and 6 are the legs, use pythagorean theorem to find the length of the segment you drew because its the hypotenuse.

8^2+6^2=x^2

64+36

100

square root of 100 is 10

So, 10 is the length of the segment. Both the x segment and the 10 segment are radii because they are draw from the center to a point on the circle.

They are equal.

x=10

ANSWER

10

EXPLANATION

The value of x is the radius of the circle.

The radius of the circle is also the hypotenuse of the right triangle formed by the chord, the radius and the segment bisecting the chord through the center.

We apply the Pythagoras Theorem to obtain:

[tex] {x}^{2} = {8}^{2} + {6}^{2} [/tex]

[tex] {x}^{2} = 64 + 36[/tex]

[tex] {x}^{2} = 100[/tex]

Take positive square root

[tex]x = \sqrt{100} [/tex]

[tex]x = 10[/tex]

Answer:

66

Step-by-step explanation:

x is the second angle

3x is the first angle

x+70 is the third angle

x+3x+x+70=180

5x = 110

x= 22

first angle: 3x = 3*22 = 66

Answer:

Second angle: 22°

And the other angles are:

First angle: 66°

Third angle: 92°

Step-by-step explanation:

Let be:

[tex]x[/tex] the measure of the second angle.

[tex]3x[/tex] the measure of the first angle.

[tex](x+70)[/tex]: the measure of the third angle.

Then, knowing that the sum of the interior angles of a triangle is 180 degrees, you can write this expression and solve for "x",to calculate the measure of the second angle:

[tex]x+3x+(x+70)=180\\5x+70=180\\5x=180-70\\\\x=\frac{110}{5}\\\\x=22\°[/tex]

You can also know that:

First angle:

[tex]3x=2(22\°)=66\°[/tex]

Third angle:

[tex]x+70\°=22\°+70\°=92\°[/tex]

Answer:

$5,000

Step-by-step explanation:

NOT 100% SURE BUT I THINK ITS LIKE THIS

2% = 0.02 tax in a decimal form

$250,000 price of home

0.02 x 250,000= 5,000

The amount that the owner pay in property taxes is: $5,000.

Using this formula

Property taxes amount=House value×Property tax rate

Where:

House value=$250,000

Property tax rate=2%

Let plug in the formula

Property taxes amount=$250,000×2%

Property taxes amount=$5,000

Inconclusion the amount that the owner pay in property taxes is $5,000.

Learn more about property taxes here:https://brainly.com/question/25844719

Answer:

Step-by-step explanation        

∣

∣

∣

x

{x|x≥8/3}

Answer:

"Third graph" in the attached picture.

Step-by-step explanation:

The correct graph would be the "intersection" of the lines:

y = -3, and

x - y = 8

We know, y = -3 is a horizontal line at y = -3 and the next is a line. By looking at the first equation, we can eliminate 2 graphs and thus find the correct graph.

y = -3 is a horizontal line at y = -3, the first graph has the line y = 3, so we can eliminate this even without looking at the graph of 2nd equation.

The second graph has a vertical line, no horizontal, so we can eliminate this choice as well.

The third graph has y = -3 (horizontal line at y = -3) and thus this is the correct choice. Also, x - y = 8 means y = x -8, which is the other graph shown.

correct answer is the "third graph".

Answer: last option.

Step-by-step explanation:

 The equation of the line in slope-intercept form is:

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

Where m is the slope and b the intersection with the y-axis.

The line [tex]y=-3[/tex] is a line with slope 0 that cut the y-axis at (0,-3)

Solve for y from the second equation:

[tex]x-y=8\\x-8=y[/tex]

The line [tex]y=x-8[/tex] is a line with slope 1 that cut the y-axis at (0,-8)

You can identify these lines in the last graph, where the point of intersection between them is the solution of the system of equations.

Answer:

C.

Step-by-step explanation:

The topic is on: 'impossible geometric construction"

The three areas of concern are : Trisecting an angle, squaring a circle and doubling a cube.

In double a cube the , when the edge in 1 unit will give the equation will give the equation x³=2 whose solution yields cube root of 2. This problem can not be solve because cube root of 2 is not an Euclidean number.

Answer:

C. Doubling the cube.

Step-by-step explanation:

Geometric construction is majorly a two dimensional drawing, excluding some form of projections (isometric and oblique drawing) which are three dimensional. Essential instruments to use in construction are; a pair of compass and straightedge (eg ruler).

From the options stated in the given question, doubling the cube is difficult to construct using the instruments given. A cube is a three dimensional shape that has all sides to be equal. It is a prism formed from a square, and it has six faces.

Answer:

[tex]\boxed{ \frac{ 1}{ 2}x - 18}[/tex]

Step-by-step explanation:

          x = fans at Friday's game

       ½x = half the fans at Friday's game

½x – 18 = 18 fewer than half the fans at Friday's game

[tex]\boxed{ \frac{ 1}{ 2}x - 18}[/tex] = fans at Saturday's game.

Answer:

Step-by-step explanation:

(3w^4-8w^2z^2+4z^4)-(5w^4+7w^2z^2-8z^4)

=3w^4-8w^2z^2+4z^4-5w^4-7w^2z^2+8z^4

=(3-5)w^4+(-8-7)w^2z^2+(4+8)z^4

so she made mistake in step 2.

Answer:

its D

Step-by-step explanation:

Answer:it would be c because the stock increased by 5.74 over yesterday’s price

Step-by-step explanation:

Answer:

The change of area A(t) = t^4 - 3t^(5/2) + 2t ⇒ answer C

Step-by-step explanation:

* Lets study the problem

- The metal strip is in a shape of rectangle

- The change in length l(t) = t² - √t

- The change is the width w(t) = t² - 2t^1/2

* We must find function gives the change of area

∵ The area of the rectangle = length × width

∴ The change of rate of area A(t) = l(t) × w(t)

- We can write the √t in exponential form t^1/2

∴ l(t) = t² - t^1/2

∵ w(t) = t² - 2t^1/2

∵ A = l × w

∴ A(t) = l(t) × w(t)

∴ [tex]A(t)=(t^{2}-t^{\frac{1}{2}})(t^{2}-2t^{\frac{1}{2}})[/tex]⇒use the foil method

∴ [tex]A(t)=(t^{2})(t^{2})+(t^{2})(-2t^{\frac{1}{2}})+(-t^{\frac{1}{2}})(t^{2})+(-t^{\frac{1}{2}})(-2t^{\frac{1}{2}})[/tex]

- If we multiply two same numbers have exponents, then we add

 the power of them

∴ [tex]A(t)=(t^{2+2})-2t^{2+\frac{1}{2}}-t^{\frac{1}{2}+2}+2t^{\frac{1}{2}+\frac{1}{2}}[/tex]

∴ [tex]A(t)=t^{4}-2t^{\frac{5}{2}}-t^{\frac{5}{2}}+2t[/tex]

* Now lets add the like terms

∴ [tex]A(t)=t^{4}-3t^{\frac{5}{2}}+2t[/tex]

* The change of area A(t) = t^4 - 3t^(5/2) + 2t

Answer:

the answer is C

Step-by-step explanation:

D is the correct answer.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

For this case we have by definition that the volume of the pyramid shown is given by:

[tex]V = \frac {A_ {b} * h} {3}[/tex]

Where:

[tex]A_ {b}:[/tex] Is the area of the base of a square

h: It's the height

According to the data of the figure shown we have:

[tex]A_ {b} = 10 * 10 = 10 ^ 2 = 100 \ units ^ 2\\h = 81 \ units[/tex]

Substituting:

[tex]V = \frac {100 * 81} {3}\\V = \frac {8100} {3}\\V = 2700 \ units ^ 3[/tex]

Answer:

Option D

Answer:

The correct answer is option D.  2700 units²

Step-by-step explanation:

Formula:-

Volume of pyramid = (a²h)/3

Where a -  side of base

h - height of pyramid

To find the volume of pyramid

Here base side = 10 units and h = 81 units

Volume = (a²h)/3

 = (10² * 81)/3 = 8100/3 = 2700  units²

Therefore the correct answer is option D.  2700 units²