Match the pairs of equivalent expressions.












y – 0.32y






y + 0.32y






















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0.68y




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1.32y

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].

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:

Step-by-step explanation:

Notice that the greatest number of dots is over the '70,' indicating that 70% of the students in the town enjoy playing video games.

This problem has to do as much with your ability to interpret graphs as to apply statistics concepts correctly.

Known: 12 bags in 3 hours

Question: X bags in 8 hours

1) Find the amount of bags made in 1 hour

12/3 = 4 bags per hour

2) If each hour makes 4 bags, and the factory is running for 8 hours then multiply the rate of bag production by the time running

8*4=32

Final Answer = 32 bags

I tried to personal message you but it didn't work. I have a question about your question it says "making both at the same rate". My question is both what?

Answer:

B

Step-by-step explanation:

I would say that the owner wants people to believe that dance classes are a good form of exercise.

Answer:

sinθ = 12/15 -> 4/5

cosθ = 9/15 -> 3/5

tanθ = 12/9 -> 4/3

cscθ = 15/12 -> 5/4

secθ = 15/9 -> 5/3

cotθ = 9/12 -> 3/4

Step-by-step explanation:

The theta is where you would use to identify the numbers for the trig functions. The adjacent side is the one closest to the theta (but not the diagonal line, that is the hypotenuse), and the opposite line is the line next to the adjacent line.

For the first three trig functions, would use the method Soh Cah Toa.

Sin = opp/hypotenus, Cosine = adjacent/hypotenuse, and Tangent = opposite/adjacent. Then, there is cosecant(csc) = hyp/opp, secant = hyp/adj, and cotangent = adj/opp.

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:

This is just a guess so I'm sorry if its wrong but I'd guess that it's A

Answer:

It is A

Step-by-step explanation:

You can use the Pythagorean Theorem a^2+b^2=c^2

3^2+5^2=c^2

9+25=c^2

34=c^2

square root of 34=c

Answer:

15 is the answer

Step-by-step explanation:

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: Last option.

Step-by-step explanation:

The total amount of concrete in the ramp ([tex]V_t[/tex]) will be the sum of the volume of the  rectangular prism ([tex]V_{rp}[/tex]) and the volume of the triangular prism ([tex]V_{tp}[/tex])

[tex]V_t=V_{rp}+V_{tp}[/tex]

The formulas are:

[tex]V_{rp}=lwh[/tex]

Where "l" is the lenght, "w" is the width and "h" is the height.

 [tex]V_{tp}=\frac{bhl}{2}[/tex]

Where "l" is the lenght, "b" is the base and "h" is the height.

Substituting, we get:

[tex]V_t=V_{rp}+V_{tp}\\\\V_t=lwh+\frac{bhl}{2}\\\\V_t=(18in)(6in)(6in)+\frac{(8in)(6in)(18in)}{2}\\\\V_t=1,080in^3[/tex]

Answer:

The guy above me is correct lol

Step-by-step explanation:

For this case we have that by definition, to move from Celsius to Fahrenheit we must apply the following formula:

[tex]F = \frac {9} {5} C + 32[/tex]

Example, we want to convert 45 degrees Celsius to Fahrenheit:

[tex]F = \frac {9} {5} (45) +32\\F = 9 * 9 + 32\\F = 81 + 32\\F = 113[/tex]

Thus, 45 degrees Celsius equals 113 degrees Fahrenheit.

ANswer:[tex]F = \frac {9} {5} C + 32[/tex]

For anyone who still needs this:

1. Multiply your Celsius measurement by 9/5 (or 1.8)

2. Add 32 to the result

Formula: F = (9/5)°C + 32

Answer:

Total = Principal * (1 + rate) ^ years

We have to solve this for years:

Years = {log(total) -log(Principal)} ÷ log(1 + rate)

Jocelyn: Years = {log(total) -log(1,600)} ÷ log(1.025)

Marcus: Years =  {log(total) -log(400)} ÷ log(1.054)

We know the years must be equal but we won't know the total so we'll call that "x".

[log(x) -log(1,600)] ÷ log(1.025) = [log(x) -log(400)] ÷ log(1.054)

EDITED TO ADD

Time is about 49 Years 8 Months and total is about 5,454.00

We know the years must be equal

Step-by-step explanation:

Answer:

1, 3, 9, 27

Step-by-step explanation:

[tex] a_n = 3^{n - 1} [/tex]

You need the first 4 terms, so let n = 1, and evaluate the expression. Then do the same for n = 2, n = 3, and finally n = 4.

n = 1

[tex] a_1 = 3^{1 - 1} = 3^0 = 1 [/tex]

n = 2

[tex] a_2 = 3^{2 - 1} = 3^1 = 3 [/tex]

n = 3

[tex] a_3 = 3^{3 - 1} = 3^2 = 9 [/tex]

n = 4

[tex] a_4 = 3^{4 - 1} = 3^3 = 27 [/tex]

Answer:

Finding the mean is very simple, add them all together and divide that sum by the number of data points you have; in this case there are 45

Step-by-step explanation:

[tex]\frac{74+67+74.25+64+72+...}{45}[/tex] = mean

Answer:

Step-by-step explanation:

One

Since you are asked to solve this using a graphing tool, here is the results as graphed by Desmos.

The point you want is (3,2)

The answer is 2.

Two

Multiply the second equation by 2

2[0.5x - y = 10]

x - 2y = 20              Add the first equation

x + 2y = 16      

2x = 36                   Divide by 2

x = 36/2

x = 18

Since this is all you are asked for, x = 18 is the answer.

Three

y is an exterior angle.

It is the sum of the two (given) remote interior angles.

y = 35 + 105

y = 140

x and y are supplementary (they add up to 180o

x + y = 180

x + 140 = 180

x = 180 - 140

x = 40

y - x = 140 - 40

y - x = 100        

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:

Option B.

Step-by-step explanation:

If a quadratic equation is defined as

[tex]ax^2+bx+c=0[/tex]         .... (1)

then the quadratic formula is

[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

The given equation is

[tex]10x^2=6+9x[/tex]

It can rewritten as

[tex]10x^2-9x-6=0[/tex]            .... (2)

On comparing (1) and (2) we get

[tex]a=10,b=-9,c=-6[/tex]

Using quadratic formula we get

[tex]x=\dfrac{-(-9)\pm \sqrt{(-9)^2-4(10)(-6)}}{2(10)}[/tex]

[tex]x=\dfrac{9\pm \sqrt{81+240}}{20}[/tex]

[tex]x=\dfrac{9\pm \sqrt{321}}{20}[/tex]

Therefore, the correct option is B.

Answer:

B

Step-by-step explanation:

I got it right

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:

2 fluid ounces

Step-by-step explanation:

8 is a lot of mouthwash to use and anything aove that is a just alot...

Answer:

The cost of  chair is [tex]\$260[/tex]

The cost of  a lamp is [tex]\$65[/tex]

The cost of  a table is [tex]\$237[/tex]

Step-by-step explanation:

Let

x----> the cost of  chair

y----> the cost of  lamp

z----> the cost of table

we know that

[tex]x+y+z=562[/tex] ----> equation A

[tex]x=4y[/tex] -----> [tex]y=x/4[/tex] -----> equation B

[tex]z=x-23[/tex] ------> equation C

substitute equation C and equation B in equation A and solve for x

[tex]x+(x/4)+(x-23)=562[/tex]

[tex](9/4)x=562+23[/tex]

[tex](9/4)x=585[/tex]

[tex]x=585*4/9=\$260[/tex]

Find the value of y

[tex]y=260/4=\$65[/tex]

Find the value of z

[tex]z=260-23=\$237[/tex]

therefore

The cost of  chair is [tex]\$260[/tex]

The cost of  a lamp is [tex]\$65[/tex]

The cost of  a table is [tex]\$237[/tex]

Answer:

[tex]\large\boxed{(x,\ y)\to (x+3,\ y-2)}[/tex]

Step-by-step explanation:

[tex](4,\ -8)\to(7,\ -10)\\\\4\to7\Rightarrow4+3=7\\\\-8\to-10\Rightarrow-8-2=-10\\\\\text{Conclusion}\\\\(x,\ y)\to (x+3,\ y-2)[/tex]

Answer:

first choice: (x, y) ------> (x + 3, y - 2)

Step-by-step explanation:

The x-coordinate started as 4. Then it became 7. To change from 4 to 7, you add 3. The rule for x is to add 3.

The y-coordinate started as -8. Then it became -10. To go from -8 to -10, you subtract 2. The rule for y is to subtract 2.

Look at the choices, and pick the one that adds 3 to x and subtract 2 from y.

The answer is the first choice: (x, y) ------> (x + 3, y - 2)

Answer:

68.2 feet

Step-by-step explanation:

The angle of elevation, the one from the ground up, is given as 33 degrees.  If Kari is 105 feet from the tree, that serves as the measure of the base of the right triangle.  We are looking for the height of the tree, which is the side opposite the angle.  What we have, then, is the angle (33 degrees), the side adjacent to the angle (105 ft), and we are looking for the side opposite the angle (x).  What we need to use is the tangent ratio, which relates the side opposite the angle to the side adjacent to the angle, as follows:

[tex]tan33=\frac{x}{105}[/tex]

To solve for x we multiply both sides of the equation by 105 to get 105tan33°=x.  Plug that into your calculator in degree mode to get 68.18779729.  Round from there to get 68.2 feet.

Answer:

-240°, -600°

Step-by-step explanation:

Coterminal angles are angles that land in the same spot around a circle.

So, that means they do full turns of the circle to reach each other.

To find coterminal angles of a given angle (here 120 degrees), you add or subtract 360 (the number of degrees in a full circle).  That can go in both positive or negative directions.

So, from 120 degrees, let's find the coterminal angle that is 1 rotation above and one rotation below:

120 + 360 = 480

120 - 360 = -240

You see that 480 isn't among the possible answers, so one part of the answer is -240.  If you subtract another 360 degrees, you end up with -600 degrees... so the answer is -240°, -600°

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]

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

If a random student has a 33% probability of belonging to a minority, then there is a 67% chance that they do not. In a sample of 10 students, the probability that exactly 4 do not belong to a minority is

[tex]\dbinom{10}40.67^4(1-0.67)^{10-4}\approx0.0547[/tex]

Answer:

[tex]\lim_{x \to \pi } e^x=e^\pi[/tex]

Step-by-step explanation:

Answer:

[tex]7\frac{1}{2}\ plates[/tex]

Step-by-step explanation:

we know that

The recipe calls for 2/3 cups of cheese for each plate of nachos

so

using proportion

Find out how many plates can she make with five cups of cheese

let

x ----> the number of plates

[tex]\frac{1}{(2/3)}\frac{plate}{cups} =\frac{x}{5} \frac{plates}{cups}\\ \\x=5/(2/3)\\ \\x=7.5\ plates[/tex]

Convert to mixed number

[tex]7.5=\frac{14}{2}+\frac{1}{2}=7\frac{1}{2}\ plates[/tex]

She can make 7.5plates with 5 cups of cheese

According to the question, we are told that the recipe calls for 2/3 cups of cheese for each plate of nachos. This is expressed as:

2/3 cups of cheese = 1 plate of nachos

In order to calculate the number of plates she can make with  five cups of cheese

5 cups  = x

Cross multiply

2/3x = 5

2x = 15

x = 7.5 plates

Hence she can make 7.5plates with 5 cups of cheese

learn more on ratios and proportions here: https://brainly.com/question/2328454

Answer:

A

Step-by-step explanation:

The line passes through the points (-3,-7) and (9,1).

The slope of the line can be calculted using formula

[tex]\dfrac{y_2-y_1}{x_2-x_1}.[/tex]

Thus, the slope of the given line is

[tex]\dfrac{1-(-7)}{9-(-3)}=\dfrac{8}{12}=\dfrac{2}{3}.[/tex]

Answer:

A

Step-by-step explanation:

slope is given by the formula:

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

We need 2 points to find a line's slope.

Plugging these into the slope formula, we will get the slope:

[tex]\frac{1--7}{9--3}\\=\frac{1+7}{9+3}\\=\frac{8}{12}\\=\frac{2}{3}[/tex]

correct answer is A