Find all complex numbers $z$ such that $z^4 = -4.$

Note: All solutions should be expressed in the form $a+bi$, where $a$ and $b$ are real numbers.

Answer:

  70, 140, 280, 350

Step-by-step explanation:

Obviously, it must have the factors 2, 5, 7 as a minimum, so the smallest value is 2×5×7 = 70.

Any of these primes can be added to the product. In increasing order, the smallest additional factors will be 2, 4, 5, 7, 8, 10, ...

So, the four smallest numbers with prime factors of 2, 5, and 7 are ...

  70 = 2·5·7

  140 = 2²·5·7

  280 = 2³·5·7

  350 = 2·5²·7

Answer:

7/25 of a chance or a 28% chance as said in the questiom

Step-by-step explanation:

So, the question says it's a 28% chance or a 28/100 chance.

All you have to do is simplify the fraction or just still right 28% chance.  But for the fraction:

Divide the numerator and denominator by 2 to get 14/50.

Divide both by two again to simplify fully to 7/25

Answer:

x = 3

Step-by-step explanation:

Given

5 - (4 - 3x) = 10 ← distribute the terms in the parenthesis by - 1

5 - 4 + 3x = 10, that is

1 + 3x = 10 ( subtract 1 from both sides )

3x = 9 ( divide both sides by 3 )

x = 3

Answer: Independent quantity : number of jelly beans in the jar guessed.

Dependent quantity : number of the jelly beans each person was off by.

Step-by-step explanation:

In the given scenario, there are two quantities introduced:

Since, "number of the jelly beans each person was off by." depends on "number of jelly beans in the jar guessed.".

So,

Independent quantity : number of jelly beans in the jar guessed.

Dependent quantity : number of the jelly beans each person was off by.

Answer:

The identities of the terms are;

3 - 53 = y is an equation

7.5 < 2.9 is an inequality

2 + 0 is an expression

t is a term

24" is a term

Step-by-step explanation:

An equation is an expression with the equal to sign

3 - 53 = y is an equation

An inequality is a mathematical expression that contains an inequality sign

7.5 < 2.9 is an inequality

A term is a sole number or variable or the product of variables and numbers that come before and after mathematical operators such as +, ×, -, or ÷

t and 24" are terms.

Answer:

49000

Step-by-step explanation:

since it's the same worth

Answer:

49000

Step-by-step explanation:

since there was the same worth given to all

Answer:

obtuse

Step-by-step explanation:

because obtuse triangle would provide more support that acute or right as its bigger.

Answer:

Please refer to attached image for the graph of inequality.

Step-by-step explanation:

Given the inequality:

[tex]y<-\dfrac{1}{5}x+1[/tex]

To graph this, first let us convert it to corresponding equality.

[tex]y=-\dfrac{1}{5}x+1[/tex]

As we can see that the above equation is a linear equation in two variables so it will be a straight line.

Now, let us find at least two points on the above equation so that we can plot them and then extend it to get the complete graph.

Two points that can be easily found, are:

1st put [tex]x = 0[/tex] , [tex]y=-\frac{1}{5}\times 0+1 =1[/tex]

So one point is (0, 1 )

Now, put y = 0,  

[tex]0=-\frac{1}{5}\times x+1\\\Rightarrow 1=\frac{1}{5}\times x\\\Rightarrow x = 5[/tex]

Second point is (5, 0)

Let us plot the points on the graph and extend the straight line.

Now, we know that it is an inequality, the are will be shaded.

As there is no equal to sign in the inequality, so the line will be dashed.

Let us consider one point and check whether that satisfies the inequality or not.

If the point is satisfied in the inequality, we will shade that area towards the point.

Let us consider the point (0, 0).

0 < 0 +1

Point is satisfied.

Please refer to the attached image for the graph of given inequality.

the change in x  is 1 and 2 in y respectively

the points are in order from r (x,y)         to     m (9,8)         to   s (10,10

if we take - 1 from x and 2 from y we will get r, or (8,6)

Answer:

a) 3 x 20 = 60

b) -2x20 = -40

question c and d are unclear as we do not know how many questions were wrong and how many were not answered.

Sorry but I hope that helped

Answer:

a)  60 points

b)  0 point

c)  22 points

d)  -11 points

Step-by-step explanation:

a)  20 * 3 = 60 points (all answered correct)

b)   0 point (Minimum score if you don't answer any of the questions)

c)  10 * 3 = 30 points

    (14 - 10)  * -2 = -8 points

    right minus wrong =  30 - 8 = 22 points  

d)  5 * 3 = 15 points

    (18 - 5) * -2 = -26 points

    right minus wrong = 15 - 26 = -11 points

Answer:

First, an asymptote means that the function "tends to go" to a value, bt actually never reaches it.

The functions here are:

A.f(x) = 2 + 1

B.f(x) = x^2 + 1

c.f(x) = x^2 - 1

D.f(x) == +1

The functions are really poorly written, but i will try to answer this.

first:

"a root at x = -1"

Means that f(-1) = 0,

The only function that is zero when x = -1, is the option c.

f(-1) = (-1)^2 - 1 = 1 - 1 = 0.

Now, if we want to have a vertical asymptote at x = 2, then we should have a function like:

[tex]f(x) = \frac{something}{x - 2}[/tex]

So we want to have a quotient, where the denominator is equal to zero when x = 2, this will lead to a vertical asymptote.

I can not see this in the options provided, so i guess that the functions are just not well written.

For a horizontal asymptote, we have something like:

[tex]f(x) = \frac{something}{x} + 1[/tex]

So as x starts to grow, the first term in the function will start to decrease, until it becomes really close to zero (but is never equal to zero) so in that case we have an horizontal asymptote to f(x) = 1.

Answer:

45/22

Step-by-step explanation:

(a/b)/(c/d) = (a*d)/(b*c)

then

{(5/8)/(11/9)} / {1/4)}

= {(5*9)/(8*11)} / {1/4)

= {45/88} / {1/4}

= {45*4} / {88*1}

= 180/88

= 45 / 22

Answer:

14.6

Step-by-step explanation:

It is given that,

The average weight of the top 5 fish caught at a fishing tournament was 12.3 pounds. From the attached figure, the weight of 5 fish are given. We need to find the weight of Wayne S. fish.

Average = sum of terms/no of terms

Let the weight of Wayne S. is x. So,

Here the sum of terms is x+12.8+12.6+11.8+9.7 and the number of terms is 5.

[tex]12.3=\dfrac{x+12.8+12.6+11.8+9.7}{5}\\\\61.5=x+12.8+12.6+11.8+9.7\\\\61.5=x+46.9\\\\x=14.6[/tex]

So, the weight of the heaviest fish is 14.6.

Answer:

Step-by-step explanation:

Distributive property of multiplication has to do with the multiplication of numbers by the sum of that number

say in our given example $2.05.

When we decide to multiply 3 property with $2 and $0.5 which when added together will still give  $2.05, we are using distributive property of multiplication.

Hence according to distributive property 3*$2.05 is the same as

3*$2 + 3*$0.5

Answer:  d) 14

Step-by-step explanation:

Equation of a line passing through (a,b) and (c,d):

[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]

Equation of a line passing through (2, 18) and (–3, 8):

[tex](y-18)=\dfrac{8-18}{-3-2}(x-2)\\\\\Rightarrow\ (y-18)=\dfrac{-10}{-5}(x-2)\\\\\Rightarrow\ (y-18)=2(x-2)\\\\\Rightarrow\ y-18=2x-4\\\\\Rightarrow\ y=2x-4+18\\\\\Rightarrow\ y=2x+14[/tex]

Comparing resulting equation [tex]y=2x+14[/tex] to [tex]y = m x + b[/tex], we get value of b= 14.

Hence, correct option is d) 14

Answer:

174

Step-by-step explanation:

Given

132, 145, 97, 112, 128, 82

Required

Estimate amount of students in an art class

This is calculated by obtaining the mean of the given data

[tex]Mean = \frac{\sum x}{n}[/tex]

Where n is the number of observations

So;  n = 6

[tex]Mean = \frac{132+ 145+ 97+ 112+ 128+ 82}{6}[/tex]

[tex]Mean = \frac{696}{6}[/tex]

[tex]Mean = 174.0[/tex]

Hence, the estimated number of students is 174

Answer:

x = 6 gallons (of 30% alcohol)

y = 12 gallons (of 60% alcohol)

Step-by-step explanation:

Let

x = liters of 30% alcohol

y = liters of 60% alcohol

There are two unknowns, we need two equations

x + y = 18. (1)

0.30x + 0.60y = 0.50(x+y) (2)

From (1)

x + y = 18

y = 18-x

Substitute the value of y into (2) and solve for x:

0.30x + 0.60y = 0.50(x+y)

0.30x + 0.60(18-x) = 0.50(x+18-x)

0.30x + 10.8 - 0.60x = 0.50(18)

10.8 - 0.30x = 9

-0.30x = -1.8

Divide both sides by -0.30

x = 6 gallons (of 30% alcohol)

Substitute x=6 into (1) and solve for y:

x + y = 18

6 + y = 18

y = 12 gallons (of 60% alcohol)

Answer: B and D

Step-by-step explanation: since it is $30 per student the total cost would have to be a multiple of 30

Answer:

Actual SAT Score = 815.284

Equivalent ACT Score = 15.811

The equivalent ACT Score = 29.95

Step-by-step explanation:

From the given information:

Scores on the SAT test are normally distributed with :

Mean = 982

Standard deviation = 198

If a student gets an SAT score that is the 20-percentile

Then ;

P(Z ≤ z ) = 0.20

From the standard z-score for percentile distribution.

z = -0.842

Therefore, the actual SAT Score can be computed as follows:

Actual SAT score = Mean + (z score × Standard deviation)

Actual SAT score =  982 +  (- 0.842 × 198)

Actual SAT score = 982 + ( - 166.716)

Actual SAT score =  982  - 166.716

Actual SAT Score = 815.284

Scores on the ACT test are normally distributed with a mean of 19.6 and a standard deviation of 4.5.

Mean = 19.6

Standard deviation = 4.5

Equivalent ACT Score = 19.6 +  (- 0.842 × 4.5)

Equivalent ACT Score = 19.6 +  ( - 3.789)

Equivalent ACT Score = 15.811

If a student gets an SAT score of 1437, find the equivalent ACT score.

So , if the SAT Score = 1437

Then , using the z formula , we can determine the equivalent ACT Score

[tex]z = \dfrac{X - \mu}{\sigma}[/tex]

[tex]z = \dfrac{1437 - 982}{198}[/tex]

[tex]z = \dfrac{455}{198}[/tex]

z =2.30

The equivalent ACT Score = 19.6 + (2.30 × 4.5)

The equivalent ACT Score = 19.6 +  10.35

The equivalent ACT Score = 29.95

Answer:

2987.

Step-by-step explanation:

25(23) + 67(36) = 575 + 2412 = 2987.

Hi there! Hopefully this helps!

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

Answer: 2987

First we need to rewrite the equation. Since x = 23 and y = 36 the equation should look like this for easier steps:

25(23) + 67(36) = ?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Now since there numbers by other numbers in parentheses, we need to multiply them.

25 x 23 = 575.

67 x 36 = 2412.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Now that the equation is in its final form, we write it like this for the answer:

575 + 2412 =

Answer:

Area of quadrilateral ABCD = 29.79 units² (Approx)

Step-by-step explanation:

Area of triangle ABD

s = (3.48+8.66+8.6) / 2

s = 10.37

Area of triangle ABD = √10.37(10.37-8.66)(10.37-8.6)(10.37-3.48)

Area of triangle ABD = √212.4616

Area of triangle ABD = 14.5760625 unit²

Area of triangle ACD

s = (3.54+8.84+8.6) / 2

s = 10.49

Area of triangle ACD = √10.49(10.49-8.6)(10.49-8.84)(10.49-3.54)

Area of triangle ACD = √227.3558

Area of triangle ACD = 15.0783222 unit²

Area of quadrilateral ABCD = Area of triangle ABD + Area of triangle ACD

Area of quadrilateral ABCD = 14.5760625 unit² + 15.0783222 unit²

Area of quadrilateral ABCD = 29.6542units²

Area of quadrilateral ABCD = 29.79 units² (Approx)

Answer:

See below.

Step-by-step explanation:

[tex]\cot(x-\frac{\pi}{2})=-\tan(x)[/tex]

Convert the cotangent to cosine over sine:

[tex]\frac{\cos(x-\frac{\pi}{2} )}{\sin(x-\frac{\pi}{2})} =-\tan(x)[/tex]

Use the cofunction identities. The cofunction identities are:

[tex]\sin(x)=\cos(\frac{\pi}{2}-x)\\\cos(x)=\sin(\frac{\pi}{2}-x)[/tex]

To convert this, factor out a negative one from the cosine and sine.

[tex]\frac{\cos(-(\frac{\pi}{2}-x ))}{\sin(-(\frac{\pi}{2}-x))} =-\tan(x)[/tex]

Recall that since cosine is an even function, we can remove the negative. Since sine is an odd function, we can move the negative outside:

[tex]\frac{\cos((\frac{\pi}{2}-x ))}{-\sin((\frac{\pi}{2}-x))} =-\tan(x)\\-\frac{\sin(x)}{\cos(x)} =-\tan(x)\\-\tan(x)\stackrel{\checkmark}{=}-\tan(x)[/tex]

Answer:

a. Please check the explanation for filling of the empty column on the table

b. The mean of the random variable x is 7/11

Step-by-step explanation:

a. Firstly, we are concerned with completing the table.

To do this, we simply need to multiply the values in the column of x by the values in the column of p(x)

Thus, we have the following;

2. 3 * 2/36 = 6/36

3. 4 * 3/36 = 12/36

4. 5 * 4/36 = 20/36

5. 6 * 5/36 = 30/36

6. 7 * 6/36 = 42/36

7. 8 * 5/36 = 40/36

8. 9 * 4/36 = 36/36

9. 10 * 3/36 = 30/36

10. 11 * 2/36 = 22/36

11. 12 * 1/36 = 12/36

b. We want to find the mean of the random variable x.

All what we need to do here is add all the values of x•P(x) together, then divide by 11.

Thus, we have

(2/36 + 6/36 + 12/36 + 20/36 + 30/36 + 42/36 + 40/36 + 36/36 + 30/36 + 22/36 + 12/36)/11

Since the denominator is same for all, we simply add all the numerators together;

(252/36) * 11 = 252/396 = 63/99 = 7/11

Answer:

The value representing one standard deviation  to the right of the mean is 55.

Step-by-step explanation:

The provided data set is:

S = {56, 54, 45, 52, and 48}

Compute the mean and standard deviation as follows:

[tex]\mu=\frac{1}{n}\sum X=\frac{1}{5}\times [56+54+45+52+48]=51\\\\\sigma=\sqrt{\frac{1}{n}\sum (X-\mu)^{2}}=\sqrt{\frac{1}{5}\cdot {(56-51)^{2}+...+(48-51)^{2}}}=\sqrt{\frac{1}{5}\times 80}=4[/tex]

Compute the value representing one standard deviation  to the right of the mean as follows:

[tex]X=\mu+1\cdot \sigma[/tex]

    [tex]=51+(1\times 4)\\=51+4\\=55[/tex]

Thus, the value representing one standard deviation  to the right of the mean is 55.

Answer:

The constant of proportionality is 11

Step-by-step explanation:

Since the proportionality is given by:

y = r x   (with "r" the constant of proportionality)

and according to the table:

22 = r (2)

then r = 22/2 = 11

Answer:

x^2+19

Step-by-step explanation:

Answer:

n/2>8

Step-by-step explanation:

Half of N is N/2

And if 8 is less that half of N or N/2

then

N/2 has to be greater than 8

N/2>8

Answer:

1001.66 in²

Step-by-step explanation:

The following data were obtained from the question:

Pi (π) = 3.14

Slant height (l) = 18 in

Diameter (d) = 22 in

Surface Area (SA) =.?

Next, we shall determine the radius of the cone. This can be obtained as follow:

Diameter (d) = 22 in

Radius (r) =.?

Radius = diameter /2

Radius = 22/2

Radius (r) = 11 in.

Finally, we determined the surface area of the cone as follow:

Pi (π) = 3.14

Slant height (l) = 18 in

Radius (r) = 11 in.

Surface Area (SA) =.?

SA = πr² + πrl

SA = (3.14 × 11²)+ (3.14 × 11 × 18)

SA = (3.14 × 121) + 621.72

SA = 379.94 + 621.72

SA = 1001.66 in²

Therefore, the surface area of the cone is 1001.66 in²

Answer:

Era

Step-by-step explanation:

Century, Decade and Millennium have something in common and that which they have in common is that they are all measurement of time.

The keyword measurement implies that they are units of time just like seconds, minutes, hours, etc.

Century -> 100 years

Decade -> 10 years

Millennium -> 1000 years

However, era is used to describe events in history;

Take for instance; the era of the first generation of computer;

So, from the list of given options; Era best answers the question

An era describes a time period marked by a change that begins a new period.

An era :

Examples of eras include:

All the eras mentioned above were distinct in how people behaved so in conclusion we can say that an era is a time period that begins a new period of development.

Find out more at https://brainly.com/question/20315058.