Third-degree, with zeros of −5, −4, and 1, and a y-intercept of −15

Step-by-step explanation:

The equation is   sinθ * cosθ - sinθ = 0

θ = 0 + 2kπ

θ = 2kπ where k is any integer

The solutions to the equation are: {0 degree, 180 degree, 360 degree, 360 degree + 180 degree n, where n is any integer}

Hence, the correct option is C.

The given equation is:

sin theta × cos theta - sin theta = 0

We can factor out the sine theta:

sin theta (cos theta - 1) = 0

This means that either sin theta = 0 or cos theta - 1 = 0.

If sin theta = 0, then theta = 0, 180 degrees, 360 degrees, etc.

If cos theta - 1 = 0, then cos theta = 1, which means that theta = 0 degrees and 360 degrees.

Therefore, the solutions to the equation are:

{0 degree, 180 degree, 360 degree, 360 degree + 180 degree n, where n is any integer}

So the answer is C.

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Answer:

c. 108

Step-by-step explanation:

Given

Shape of container: Cube

Initial dimension of the container = 6ft by 6ft by 6ft

Initial Number of boxes = 4

Required

Calculate the number of boxes when the dimension is tripled

The first step is to calculate the initial volume of the box;

[tex]Volume = Length * Length * Length[/tex]

[tex]Volume = 6ft * 6ft * 6ft[/tex]

[tex]Volume = 216ft^3[/tex]

This implies that the container can contain 4 small boxes when its volume is 216;

Represent this as a ratio;

[tex]4 : 216[/tex]

The next step is to calculate the volume when the dimension is tripled;

[tex]New\ Length = Old\ Length * 3[/tex]

[tex]New\ Length = 6ft* 3[/tex]

[tex]New\ Length = 18ft[/tex]

Hence;

[tex]Volume = 18ft * 18ft * 18ft[/tex]

[tex]Volume = 5832ft^3[/tex]

Let the number of boxes it can contain be represented with x

Similarly, represent this as a ratio

[tex]x : 5832[/tex]

Equate both ratios;

[tex]4 : 216 = x : 5832[/tex]

Convert ratios to fractions

[tex]\frac{4}{216} = \frac{x}{5832}[/tex]

Multiply both sides by 5832

[tex]5832 * \frac{4}{216} = \frac{x}{5832} * 5832[/tex]

[tex]5832 * \frac{4}{216} = x[/tex]

[tex]\frac{5832 *4}{216} = x[/tex]

[tex]\frac{23328}{216} = x[/tex]

[tex]108 = x[/tex]

[tex]x = 108[/tex]

Hence, the maximum number of boxes it can contain is 108

Answer:

(1,-2)

Step-by-step explanation

y = -3x + 1

y = 2x - 4

-3x + 1 = 2x - 4

-5x + 1 = -4

-5x = -5

x = 1

y= 2(1) - 4

y = 2 - 4

y = -2

(1,-2)

Answer:

1/2

Step-by-step explanation:

Answer:

(2,1)

Step-by-step explanation:

Well first we single out y or x in one of the equations,

we’ll use 2x + y = 5 and single out y.

2x + y = 5

-2x to both sides

y = -2x + 5

So we can plug in -2x + 5 into y in 2x - 2y = 2.

2x - 2(-2x + 5) = 2

2x + 4x - 10 = 2

combine like terms,

6x - 10 = 2

Communicarice property

+10 to both sides

6x = 12

divide 6 to both sides

x = 2

If x is 2 we can plug 2 in for x in 2x + y = 5.

2(2) + y = 5

4 + y = 5

-4 to both sides

y = 1

(2,1)

Thus,

the solution is (2,1).

Hope this helps :)

Answer:

If it is warm outside, then it is summer

Step-by-step explanation:

To find the converse, interchange the hypothesis and the conclusion

"If it is summer, then it is warm outside"

If it is warm outside, then it is summer

Answer:

A. If it is warm outside, then it is summer

Step-by-step explanation:

statement "If it is summer, then it is warm outside" : warm=summer

A. If it is warm outside, then it is summer. : warm = summer ✓

B. If it is not warm outside, then it is summer. : not warm = summer x

C. If it is warm outside, then it is not summer. : warm =not  summer x

D. If it is not warm outside, then it is not summer. : not warm = not summer x

this is your answer..................

Answer:

total rotation = 90 clockwise.

Step-by-step explanation:

Rotation from B to negative y-axis = 45 degrees because B(-3,-3)

Rotation from negative y-axis to B' = 45 degrees because B(-3,3)

Therefore total rotation = 45+45 = 90 clockwise.

Answer:

210

Step-by-step explanation:

Given:

Medals in sports = 40

Medals in dance = 25

Medals in music = 212

Total students that received medals = 55

Total students that received medals in all three categories = 6

Required:

How many students get medals in exactly two of these categories?

Take the following:

A = set of persons who got medals in sports.

B = set of persons who got medals in dance

C = set of persons who got medals in music.

Therefore,

n(A) = 40

n(B) = 25

n(C) = 212

n(A∪B∪C)= 55

n(A∩B∩C)= 6

To find how many students get medals in exactly two of these categories, we have:

n(A∩B) + n(B∩C) + n(A∩C) −3*n(A∩B∩C)

=n(A∩B) + n(B∩C) + n(A∩C) −3*6 ……............... (1)

n(A∪B∪C)=n(A)+n(B)+n(C)−n(A∩B)−n(B∩C)−n(A∩C)+n(A∩B∩C)

Thus, n(A∩B)+n(B∩C)+n(A∩C)=n(A)+n(B)+n(C)+n(A∩B∩C)−n(A∪B∪C)

Using equation 1:

=n(A)+n(B)+n(C)+n(A∩B∩C)−n(A∪B∪C)−18

Substitute values in the equation:

= 40 + 25 + 212 + 6 − 55 − 18

= 283 - 73

= 210

Number of students that get medals in exactly two of these categories are 210

Answer: 4

Step-by-step explanation:

Because there are two equal angles, this is an isoceles triangle. Line JP and HP are equal. To find the variable, write the equation which would be 3x-6=x+2. X is 4.

hope this helped:)

Answer: 4 AKA D

Step-by-step explanation:

Well to start off, we must first establish that line JP and line HP are equal because of the red ticks in the corner. So once we figured that out, then 3x-6 = x+2

»Next we add 6 to both side to make 3x = x+8

»Then we subtract x from both sides to equal 2x = 8

»Then we divide both sides by 2 which equals x=4

»So the final answer would be D. 4

Hope i helped

-lvr

Answer:

120 degrees

Step-by-step explanation:

Answer:

120

Step-by-step explanation:

Add all the number then subtract it with 360.

Answer: [tex]2.25\sqrt{3}[/tex]

Not sure what you mean by terms of pi, unless you want us to find the area of the sector, not the triangle.

Step-by-step explanation:

Assuming you mean the area of the triangle...

First draw an altitude from the 120 degree angle to the opposite base.  You will find that the altitude will also be a median.  This forms 2 30-60-90 right triangles.  Thus, the height of the altitude is 1.5 and the base of the triangle is 1.5*root3.  Thus, the base of the triangle is [tex]3\sqrt{3}[/tex] and the height is 1.5.  Thus, the area of the triangle is [tex]2.25\sqrt{3}[/tex]

Answer:

AQ = 20 units

Step-by-step explanation:

I tried figuring in the pic below..

Similar triangles are triangles whose corresponding measures are proportional. All of their corresponding angles are also congruent. There are theorems and postulates that prove triangle similarity. Usually they requrie at least three parts of each triangle. The symbol for similarity is ~.

We have two triangles in the figure. ΔAQR and ΔABC. We will prove first that they are similar.

Answer:

20

Step-by-step explanation:

RQ is 1/2 of CB, so 2(2p+3)=6p-4. This would make p=5. Then, 5*4=20.

(also it is right on edgenuity)

Answer:

maximum value at (- 1, 6 )

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

• If a > 0 then minimum value

• If a < 0 then maximum value

y = - (x + 1)² + 6

with (h, k) = (- 1, 6 ) and a = - 1

Thus vertex = (- 1, 6 ) and is a maximum

Answer:

R = 21.8° to the nearest tenth

Step-by-step explanation:

To find Angle R we use tan

tan ∅ = opposite / adjacent

From the question

The opposite is 2

The adjacent is 5

So we have

tan R = 2/5

R = tan-¹ 2/5

Hope this helps you

Answer:

Step-by-step explanation:

The median is 4, which is the middle number. If there is no middle number, get the average of the two numbers closest to the median.

The mean is 4, which is the average of all the numbers. you add all of them up and divide by how many integers there are in the list.

The mode is 6, which is the integer that is shown the most.

Answer:

mean=4

median=4

mode=6

Step-by-step explanation:

Mean: add 0+2+2+4+4+6+6+6+6=36

36/ (the amount of numbers) 9= 4

Median: cross out the numbers left to right until you get to the middle which is 4.

Mode: 6 occurred four times, which is the most out of any of the other numbers in this sequence, so the answer is 6.

Answer: 42w

Step-by-step explanation:

Subtracting a negative is like adding.

Answer:

51

Step-by-step explanation:

Well we first need to find the volume of the soup in the pot using the following formula,

πr^2h

15*15 = 225

225 * 25 = 5625

5625 * pi = 17671.46

Now we need to find the volume of the ice cube using the formula,

l*w*h

7*7*7 = 343

Now we do 17671.46 ÷ 343 = 51.5202915452

You can have half an ice cube,

thus, Sharon can make 51 whole cubes.

Hope this helps :)

Answer:

130 cubes  ( if the cylindrical height is 25 in )

51 cubes ( if the cylindrical height is 25 cm)

Step-by-step explanation:

cube edges = 7 cm long

volume of the soup = pi * r² * h

where h = 25in convert it to cm = 25 in * 2.54 cm/1 in = 63.5 cm

cylindrical pot diameter d = 30 cm

Volume of cylindrical pot = 3.14 * 15² * 63.5 = 44,885.5 cm³

Volume of ice cube = 7 * 7 * 7 = 343 cm³

to get the number of cubes = 44,885.5 / 343 = 130 cubes

therefore, Sharon can make 130 whole cubes

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

if the cylindrical height is 25cm then

Volume of cylindrical pot = 3.14 * 15² * 25 = 17,671.5 cm³

Volume of ice cube = 7 * 7 * 7 = 343 cm³

to get the number of cubes = 17,671.5 / 343 = 51 cubes

Answer:

D

Step-by-step explanation:

Hello, This is a geometric sequence where the first term is [tex]a_1=-1[/tex].

It means that the sequence is [tex](a_n)_{n\geq 1}[/tex].

In other words, as the common ratio is 7 the sequence is defined by

[tex]a_1=-1[/tex]

[tex]a_{n+1}=a_n\cdot 7 \ \ \text{ for n }\geq 1[/tex]

For instance, we can estimate the first terms:

[tex]a_1=-1\\\\a_2=7a_1=-7\\\\a_3=7a_2=-49[/tex]

And we know that we can even find a formula for the [tex]n^{th}[/tex] term of the sequence by:

[tex]a_n=a_1\cdot 7^{n-1}=-7^{n-1}[/tex]

Now, to answer the question, the domain for n is all integers where [tex]n\geq 1[/tex].

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Con el conducto A abierto, el estanque se llenará en 32.5 horas.

Step-by-step explanation:

Deje que el volumen de agua presente en el estanque sea x litros

La tasa conjunta sería x / 20 litros por hora.

Para el conducto A, no sabemos la hora, llamemos a esto y así que la tasa aquí será x / y

Para el conducto B tomará 52 horas y su tasa es x / 52

Matemáticamente, cuando sumamos ambas tasas juntas, obtendremos la tasa conjunta; Así; x / y + x / 52 = x / 20

Saca x en ambos lados 1 / y+ 1/52 = 1/20

(52 + y) / 52y = 1/20

20 (52 + y) = 52y

1040 + 20y= 52y

1040 = 52y -20y

32y = 1040 y = 1040/32

y = 32.5 horas

Con el conducto A abierto, el estanque se llenará en 32.5 horas.

Answer:

Step-by-step explanation:

given data

mean = 1.9 hours

standard deviation = 0.3 hours

solution

we get here first  random movie between 1.8 and 2.0 hours

so here

P(1.8 < z < 2 )

z = (1.8 - 1.9) ÷ 0.3

z = -0.33

and

z = (2.0 - 1.9) ÷ 0.3

z = 0.33

z = 0.6293

so

P(-0.333 < z < 0.333 )

=  0.26

so random movie is between 1.8 and 2.0 hours long is 0.26

and

A movie is longer than 2.3 hours.

P(x > 2.3)

P( [tex]\frac{x-\mu }{\sigma}[/tex]  > [tex]\frac{2.3-\mu }{\sigma}[/tex] )

P (z  > [tex]\frac{2.3-1.9 }{0.3}[/tex]  )

P (z  > 1.333  )

= 0.091

so chance a movie is longer than 2.3 hours is 0.091

and

length of movie that is shorter than 94% of the movies is

P(x > a ) = 0.94

P(x <  a ) = 0.06

so

P( [tex]\frac{x-\mu }{\sigma }[/tex] <  [tex]\frac{a-\mu }{\sigma }[/tex] )

[tex]\frac{a-1.9 }{0.3 } = -1.55[/tex]

a = 1.43

so length of the movie that is shorter than 94% of the movies about 1.4 hours.

Answer:

x = 1

Step-by-step explanation:

Using the rules of logarithms

log [tex]x^{n}[/tex] ⇔ n log x

[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

Given

3[tex]log_{2}[/tex] (2x) = 3

[tex]log_{2}[/tex] (2x)³ = 3

(2x)³ = 2³

8x³ = 8 ( divide both sides by 8 )

x³ = 1 ( take the cube root of both sides )

x = 1

Answer:

x=1 is the correct answer

Step-by-step explanation:

got it right on edge!!!!

Answer:

crystal size and rock texture     D

Step-by-step explanation:

:)

Hence, the option (D) is the correct answer i.e., crystal size and rock texture.

What is the texture?

The texture is defined as a tactile quality of an object's surface. It appeals to our sense of touch, which can evoke feelings of pleasure, discomfort, or familiarity.

The texture of an igneous rock is dependent on the rate of cooling of the melt slow cooling allows large crystals to form, fast coolng yields small crystals.

Hence, the option (D) is the correct answer i.e., crystal size and rock texture.

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Solution: C

Explanation:

Use the cosine rule

A^2=B^2+C^2-2BCcos a

5^2=8^2+8^2-2×8×8cos a

cos a=(25-64-64)÷(-2×64)

a=36.419°

approx = 36

Answer:

40 m

Step-by-step explanation:

The perimeter of the flat, orange shape is the sum of all the sides that forms a boundary around the shape.

The shape is made up of 4 triangles having 2 equal side lengths each, which surrounds the center square.

Each side length of the triangle, that forms a boundary round the shape = 5 m.

There are 8 of this equal side length.

Perimeter = 8(5m) = 40 m

Answer:

(a) The probability that a randomly selected time interval between eruptions is longer than 82 ​minutes is 0.3336.

(b) The probability that a random sample of 13-time intervals between eruptions has a mean longer than 82 ​minutes is 0.0582.

(c) The probability that a random sample of 34 time intervals between eruptions has a mean longer than 82 ​minutes is 0.0055.

(d) Due to an increase in the sample size, the probability that the sample mean of the time between eruptions is greater than 82 minutes decreases because the variability in the sample mean decreases as the sample size increases.

(e) The population mean must be more than 72​, since the probability is so low.

Step-by-step explanation:

We are given that a geyser has a mean time between eruptions of 72 minutes.

Also, the interval of time between the eruptions be normally distributed with a standard deviation of 23 minutes.

(a) Let X = the interval of time between the eruptions

So, X ~ N([tex]\mu=72, \sigma^{2} =23^{2}[/tex])

The z-score probability distribution for the normal distribution is given by;

                            Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean time = 72 minutes

           [tex]\sigma[/tex] = standard deviation = 23 minutes

Now, the probability that a randomly selected time interval between eruptions is longer than 82 ​minutes is given by = P(X > 82 min)

       P(X > 82 min) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{82-72}{23}[/tex] ) = P(Z > 0.43) = 1 - P(Z [tex]\leq[/tex] 0.43)

                                                           = 1 - 0.6664 = 0.3336

The above probability is calculated by looking at the value of x = 0.43 in the z table which has an area of 0.6664.

(b) Let [tex]\bar X[/tex] = sample mean time between the eruptions

The z-score probability distribution for the sample mean is given by;

                            Z  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean time = 72 minutes

           [tex]\sigma[/tex] = standard deviation = 23 minutes

           n = sample of time intervals = 13

Now, the probability that a random sample of 13 time intervals between eruptions has a mean longer than 82 ​minutes is given by = P([tex]\bar X[/tex] > 82 min)

       P([tex]\bar X[/tex] > 82 min) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{82-72}{\frac{23}{\sqrt{13} } }[/tex] ) = P(Z > 1.57) = 1 - P(Z [tex]\leq[/tex] 1.57)

                                                           = 1 - 0.9418 = 0.0582

The above probability is calculated by looking at the value of x = 1.57 in the z table which has an area of 0.9418.

(c) Let [tex]\bar X[/tex] = sample mean time between the eruptions

The z-score probability distribution for the sample mean is given by;

                            Z  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean time = 72 minutes

           [tex]\sigma[/tex] = standard deviation = 23 minutes

           n = sample of time intervals = 34

Now, the probability that a random sample of 34 time intervals between eruptions has a mean longer than 82 ​minutes is given by = P([tex]\bar X[/tex] > 82 min)

       P([tex]\bar X[/tex] > 82 min) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{82-72}{\frac{23}{\sqrt{34} } }[/tex] ) = P(Z > 2.54) = 1 - P(Z [tex]\leq[/tex] 2.54)

                                                           = 1 - 0.9945 = 0.0055

The above probability is calculated by looking at the value of x = 2.54 in the z table which has an area of 0.9945.

(d) Due to an increase in the sample size, the probability that the sample mean of the time between eruptions is greater than 82 minutes decreases because the variability in the sample mean decreases as the sample size increases.

(e) If a random sample of 34-time intervals between eruptions has a mean longer than 82 ​minutes, then we conclude that the population mean must be more than 72​, since the probability is so low.

Answer:

Step-by-step explanation:

From the given data

mean, u = 72

Standard deviation [tex]\rho[/tex] = 23

A) Probability that a randomly selected time interval between eruptions is longer than 82​minutes

[tex]P (x > 82) = P[\frac{x-u}{\rho} > \frac{82-72}{23}]\\\\P (x > 82) = P[z > 0.43]\\\\P (x > 82) = 0.3336[/tex]

B)

[tex]P (x > 82) = P[\frac{x-u}{\frac{\rho}{\sqrtn}} > \frac{82-72}{\frac{23}{\sqrt{13}}}]\\\\P (x > 82) = P[z > 1.5676]\\\\P (x > 82) = 0.0594[/tex]

C)

[tex]P (x > 82) = P[\frac{x-u}{\frac{\rho}{\sqrtn}} > \frac{82-72}{\frac{23}{\sqrt{34}}}]\\\\P (x > 82) = P[z > 2.5351]\\\\P (x > 82) = 0.0057\\\\[/tex]

D) If the mean is less than 82minutes, then the probability that the sample mean of the time between eruptions is greater than 83 minutes decrease because the variability in the sample mean decrease as the sample size increases

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Answer:

3 ≤ n < 15

 1-2. not n

3-4. yes n

5-6. yes n

 7-8. yes n

9-10. yes n

11-12. yes n

13-14. yes n

15-16. not n

Step-by-step explanation:

Everything on this side is less than, < but everything on this side is greater.

Everything on this side could be equal or less, ≤ but everything on this side is

not.

I'm had a hard time with the number line, but imagine a line going through the periods and there being a dot where the yes ns end, and start.

Intervals has each point represent more than one number making the line shorter.

Answer:

We can arrange 4 different colored balls in 24 ways.

Step-by-step explanation:

We have to find the number of ways in which we can arrange 4 different colored balls.

Firstly, we have to decide that either we use Permutation or we use Combination.

A Permutation is used when the order of arranging the numbers matters while on the other hand, a combination is used when the order of arranging the numbers doesn't matter.

So, in our question; the ordering matters to us as a ball which is placed in the first place can't be put again put in other places.

Number of ways of arranging 4 different colored balls = [tex]^{4}P_4[/tex]

                     =  [tex]\frac{4!}{(4-4)!}[/tex]          {[tex]\because ^{n} P_r = \frac{n!}{(n-r)!}[/tex] }

                     =  4! = [tex]4 \times 3 \times 2\times 1[/tex]

                     =  24 ways

Hence, we can arrange 4 different colored balls in 24 ways.

Answer:

(3,2)

Step-by-step explanation:

Just took the test

Answer:

Excess of income over expenditure is ₹1,185,500.

Step-by-step explanation:

Note: The data in this question are merged together. They are therefore sorted before answering this question. See the attached pdf file for the sorted question.

The question is now answered as follows:

Question: Prepare Income and Expenditure A/c. for the year ending 31-03-2014.

Answer and explanation:

Note: See the attached excel file for the Income and Expenditure A/c. for the year ending 31-03-2014.

Both receipts and payments account and income and expenditure account are prepared by not-for-profit organizations such as charity organizations, human right campaign, clubs, etc.

Receipts and payments account is an account gives a summary of all the cash transitions, cash received and paid, that the organization engaged in during a particular period. It is similar to the cash book prepared by profit making organizations. The receipts and payments account is prepared in or to determine the balance of cash in hand or at bank or bank overdraft at the end of the period.

Income and expenditure account is an account gives a summary of all incomes and expenses of an organization during a particular period. It is similar to the trading and profit and loss account prepared by profit making organizations. The income and expenditure account is prepared in order to determine whether there is a surplus or a deficit balance during the period.

Answer: x=10

Step-by-step explanation:

We can use the pythagorean theorem here: a^2 + b^2 = c^2, where c is the hypotenuse.

The values for c and one of the legs are already given, so we can plug them into the equation to find the length of the other leg x:

(square root of 200)^2 + x^2 = (square root of 300)^2

200 + x^2 = 300

x^2 = 100

x = 10

Answer:

Step-by-step explanation

square root  300 square - square root 200 square = x square

300 - 200 = x square

100 = x square

square root 100 = x

10= x