(a) An astronomer's infrared telescope is able to detect radiation with a wavelength of 5.32 x 10-6 meters. Write this number in standard notation.
(b) The diameter of Saturn at its equator is approximately 121,000 kilometers. Write this number in scientific notation.

Answer:

358

Step-by-step explanation:

Answer:

358

Step-by-step explanation:

(See below for the picture of how to do it.)

Answer:  C

Step-by-step explanation:

In order to be a function, you canNOT have any duplicate x's.

A) x = -2, 6, 6, 10      --> 6 is used twice so it is not a function

B) x = -2, 10, 6, 10    --> 10 is used twice so it is not a function

C) x = -2, 1, 6, 10      --> all the x's are different.  This is a function!!!

D) x = -2, 1, 6, 1        --> 1 is used twice so it is not a function

Answer:

C

Step-by-step explanation:

Relationship between independent variable and dependent variable: each x corresponds to only one y, but y can each correspond to multiple x (which is why there are multiple solutions of an equation, and a solution can only launch a counter-argument )

A, 6 -> - 3,22.6 (x) corresponding to the two y. C options and only one for each of x y.

Answer:

see below

Step-by-step explanation:

f (x) = 3x - 5

g(x) = – 4x-1

f(-2)=

Let x =-2

f(-2) = 3*-2 -5 = -6-5 = -11

g(2)=

Let x=2

g(2) = -4(2) -1 = -8-1 = -9

Answer:

[tex]\huge \boxed{\mathrm{f(-2)=-11 }} \\\\\\ \huge \boxed{\mathrm{g(2)=-9 }}[/tex]

Step-by-step explanation:

[tex]\sf f (x) = 3x - 5 \\\\\\ g(x)=-4x-1[/tex]

The input value or x value for f(-2) is -2.

[tex]\sf f (-2) = 3(-2) - 5 \\\\\\ \sf f (-2) = -6 - 5 \\\\\\ f(-2)=-11[/tex]

The input value or x value for g(2) is 2.

[tex]\sf g(2)=-4(2)-1 \\\\\\ g(2)=-8-1 \\ \\ \\ g(2)=-9[/tex]

Answer:

Positive

Step-by-step explanation:

The product of two negative numbers has a positive sign, whereas the product of a positive and a negative number is negative.

Since -35 and -625 are both negative, they would have a positive sign for their product.

Hope this helps.

Answer: Positive

Step-by-step explanation:

Answer:

  16x^2 -48xy^3 +36y^6

Step-by-step explanation:

Use FOIL or the distributive property or the form of the square of a binomial to expand the square.

  (4x -6y^3)(4x -6y^3) = 4x(4x -6y^3) -6y^3(4x -6y^3)

  = (4x)^2 -(4x)(6y^3) -(6y^3)(4x) +(6y^3)^2

  = 16x^2 -48xy^3 +36y^6

_____

The form referred to above is ...

  (a +b)^2 = a^2 +2ab +b^2

Answer:  C. quadrilateral

Step-by-step explanation:

Trapezoid means one side must be parallel, which does not exist in the image so A & D are ruled out.

Parallelogram means opposite sides are parallel which does not exist in this image so B is ruled out.

Quadrilateral means that the object contains 4 sides, which the image does so the answer is C.

Answer:

[tex]\mathbf{I =2{\sqrt{x+36}} + 6 \ In \begin {vmatrix} \dfrac{{\sqrt{x+36}}-6}{{\sqrt{x+36}}+6}\end {vmatrix}+ C}[/tex]

Step-by-step explanation:

Given that :

[tex]I = \int \dfrac{\sqrt{x+36}}{x} \dx = \int \dfrac{2u^2}{u^2-36} \ du[/tex]

x = u² - 36

Let u = [tex]\sqrt{x+36}[/tex]

Then:

[tex]du =\dfrac{1}{2 \sqrt{x+36}}dx[/tex]

[tex]2 \sqrt{x+36} \ \ du =dx[/tex]

[tex]2 u^2 \ \ du =dx[/tex]

[tex]\dfrac{2u^2}{u^2-36} \\ \\ 2u^2 \\ \\ 2u^2 - 72[/tex]

∴

[tex]I = \int 2 du + \int \dfrac{72}{u^2-36}\ du[/tex]

[tex]I = \int 2 du + 72 \int \dfrac{du}{u^2-6^2}[/tex]

[tex]I =2u+ 72 \times\dfrac{1}{2\times 6} \ In \begin {vmatrix} \dfrac{u-6}{u+6}\end {vmatrix}+ C[/tex]

[tex]I =2u + 6 \ In \begin {vmatrix} \dfrac{u-6}{u+6}\end {vmatrix}+ C[/tex]

substituting the value of u, we have:

[tex]\mathbf{I =2{\sqrt{x+36}} + 6 \ In \begin {vmatrix} \dfrac{{\sqrt{x+36}}-6}{{\sqrt{x+36}}+6}\end {vmatrix}+ C}[/tex]

Answer:

105 degrees.

Step-by-step explanation:

< DAB and <CDA are supplementary.

Therefore m < DAB = 180 - 75

= 105 degrees.

Answer:

105 degrees.

Step-by-step explanation:

Answer:

a turkey at the farm which weighs more than 90% of all the turkeys is predicted to be taller than 79.37 % of them.

The  average height for turkeys at the 90th percentile for weight is 34.554

Of the turkeys at the 90th percentile for weight, roughly the percentage that  would  be taller than 28 inches 79.37%

Step-by-step explanation:

The data given for the study can be listed as follows

For a population of turkeys at a farm, the correlation found between the weights and heights of turkeys is r = 0.64

[tex]\overline x[/tex] = 17  (i . e the average weight in pounds)

[tex]S_x[/tex] = 5 ( i . e the standard deviation of the weight in pounds)

[tex]\overline y[/tex] = 28 (i . e the average height in inches)

[tex]S_y[/tex] = 8 ( i . e the standard deviation of the height in inches)

The slope of the regression line can be expressed as :

[tex]\beta_1 = r \times ( \dfrac{S_y}{S_x})[/tex]

[tex]\beta_1 = 0.64 \times ( \dfrac{8}{5})[/tex]

[tex]\beta_1 = 0.64 \times 1.6[/tex]

[tex]\beta_1 = 1.024[/tex]

Similarly the intercept of the regression line can be estimated by using the formula:

[tex]\beta_o = \overline y - \beta_1 \overline x[/tex]

replacing the values, we have:

[tex]\beta_o = 28 -(1.024)(17)[/tex]

[tex]\beta_o = 28 -17.408[/tex]

[tex]\beta_o = 10.592[/tex]

However, the regression line needed for this study can be computed as:

[tex]\hat Y = \beta_o + \beta_1 X[/tex]

[tex]\hat Y = 10.592 + 1.024 X[/tex]

Recall that;

both the weight and height roughly follow the normal curve

Thus, the weight related to 90th percentile can be determined as shown below.

Using the Excel Function at 90th percentile, which can be computed as:

(=Normsinv (0.90) ; we have the desired value of 1.28

∴

[tex]\dfrac{X - \overline x}{s_x } = (Normsinv (0.90))[/tex]

[tex]\dfrac{X - \overline x}{s_x } = 1.28[/tex]

[tex]\dfrac{X - 17}{5} = 1.28[/tex]

[tex]X - 17 = 6.4[/tex]

X = 6.4 + 17

X = 23.4

The predicted height [tex]\hat Y = 10.592 + 1.024 X[/tex]

here; X = 23.4

[tex]\hat Y = 10.592 + 1.024 (23.4)[/tex]

[tex]\hat Y = 10.592 + 23.9616[/tex]

[tex]\hat Y = 34.5536[/tex]

So the probability of predicted height less than 34.5536 can be expressed as:

[tex]P(Y < 34.5536) = P( \dfrac{Y - \overline y }{S_y} < \dfrac{34.5536-28}{8})[/tex]

[tex]P(Y < 34.5536) = P(Z< \dfrac{6.5536}{8})[/tex]

[tex]P(Y < 34.5536) = P(Z< 0.8192)[/tex]

From the Z tables;

P(Y < 34.5536) =0.7937

Thus,  a turkey at the farm which weighs more than 90% of all the turkeys is predicted to be taller than 79.37 % of them.

The  average height for turkeys at the 90th percentile for weight is :

[tex]\hat Y = 10.592 + 1.024 X[/tex]

here; X = 23.4

[tex]\hat Y = 10.592 + 1.024 (23.4)[/tex]

[tex]\hat Y = 10.592 + 23.962[/tex]

[tex]\mathbf{\hat Y = 34.554}[/tex]

Of the turkeys at the 90th percentile for weight, roughly what percent would you estimate to be taller than 28 inches?

This implies that :

P(Y >28) = 1 - P (Y< 28)

[tex]P(Y >28) = 1 - P( Z < \dfrac{28 - 34.554}{8})[/tex]

[tex]P(Y >28) = 1 - P( Z < \dfrac{-6.554}{8})[/tex]

[tex]P(Y >28) = 1 - P( Z < -0.8193)[/tex]

From the Z tables,

[tex]P(Y >28) = 1 - 0.2063[/tex]

[tex]\mathbf{P(Y >28) = 0.7937}[/tex]

= 79.37%

20 cups

4 rows of 5 containing the 3 inch cups and 5 columns of 4 containing the 3 inch cups

Hey There!! ~

The answer to this is: 60 cups. Because, First you need to find the area of the box which would be

12in x 15in =180in

The second step would be to divide the area of the box by how tall the cups are .

180/3 = 60

Hope It Helped!~

[tex]ItsNobody[/tex]~                                                                                                                  (`~*>.^UwU^.<`~*)

Answer:

[tex]\frac{8}{15}[/tex]

Step-by-step explanation:

Therefore, the answer is [tex]\frac{8}{15}[/tex].

Answer:

Step-by-step explanation:

[tex]\frac{\sqrt{32} }{\sqrt{16} - \sqrt{2} } = \frac{4\sqrt{2} }{4 - \sqrt{2} } ----------------- (1)[/tex]

It says it can be written in the form of

[tex]\frac{A\sqrt{B} + C }{D}[/tex]

where A, B, C and D are integers, D is positive and B is not divisible by square of any prime

Rationalize equation 1:

[tex]\frac{4\sqrt{2} }{4 - \sqrt{2} } X \frac{4 + \sqrt{2} }{4 + \sqrt{2}}[/tex]

in denominator, use (a + b)(a - b) = [tex]a^{2} - b^{2}[/tex]

After multiplying numerator and denominator you should get

[tex]\frac{16\sqrt{2} + 8}{14}[/tex]

this is in the form

[tex]\frac{A\sqrt{B} + C }{D}[/tex]

where A = 16, B = 2, C = 8, and D = 14

hope this helps you ^^

Answer:

Equation 1

Step-by-step explanation:

It does not have an x value with an exponent of 2 or greater.

Answer: I would think that equation 1 represents a linear function as it fllows the y= mx +b formula.

Step-by-step explanation: Linear functions sometimes use slope intercept form which is y = mx + b in this equation 2x would be your slope and 1 would be your y intercept.

Answer: 122

Step-by-step explanation:

Since it is a geometric sequence, lets see the pattern below:

From this, we can see that we multiply each number by -3 to get the next number.

Before we find the sum, we first find the next number.

-54×-3=162

So the whole sequence will be: 2, -6, 18, -54, 162

Find the sum

 2+(-6)+18+(-54)+162

=2-6+18-54+162

=-4-36+162

=-40+162

=122

Hope this helps!! :)

Please let me know if you have any question

Answer:

B

Step-by-step explanation:

a. csc x − 1 > 0

csc x > 1

sin x < 1

x = [0, π/2) U (π/2, 2]

b. cos x − 1 > 0

cos x > 1

x = no solution

c. cot x − 1 > 0

cot x > 1

tan x < 1

x = [0, π/4) U (π/2, 2]

d. tan x − 1 > 0

tan x > 1

x = (π/4, π/2) U (π/2, 3π/4)

Of the 4 options, only B has no solution.

The only inequality that does not have a solution with the range is option B;  cos x − 1 > 0.

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

A. csc x − 1 > 0

csc x > 1

sin x < 1

x = [0, π/2) U (π/2, 2]

B. cos x − 1 > 0

cos x > 1

x = no solution

C. cot x − 1 > 0

cot x > 1

tan x < 1

x = [0, π/4) U (π/2, 2]

D. tan x − 1 > 0

tan x > 1

x = (π/4, π/2) U (π/2, 3π/4)

Therefore option B is the only inequality that does not have a solution with the range.

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Answer:

1, 4, 9, 16, 25, 36, 49, 64, 81, and 100

Step-by-step explanation:

Let's pretend that the locker number is represented as a Binary (meaning it's either open or closed).

Looking at this, we can see that each locker is only acted upon if the student number is a factor of it. This is why the 3rd person changes the state of every 3 lockers, the 4th student changes the state of every 4 lockers, etc.

The factors of a number are the numbers that the original number is evenly divisible by. When we divide these, we also receive a factor. With this information, we can conclude that unless one of the factors is the square root of the number, then the "second divided by" factor is itself. For every other number, there will be a "second divided by" factor, so an even number of them. Because an even number + 1 = odd number, then only perfect squares will have an odd number of factors.

Hope this helped!

Answer:

The open lockers are:

1,4,9,16,25,36,49,64,81,100

Step-by-step explanation:

Note that locker 1 is opened by only the first student. So it stays open throughout.

Locker 2 is first opened by student 1, then closed by student 2. Other students don't touch it. So it stays closed.

Locker 3 is first opened by student 1, then closed by student 3. Other students don't touch it. So it stays closed.

Since 4 is a multiple of 1, 2, and 4, it is changed by the 1st, 2nd, and 4th students. Since there is an odd number (3) of changes, locker 4 stays open.

Observe that a locker at position n is opened by students with factors of n.

Every number can be written as the product of a pair of distinct numbers except perfect squares. For example, 6 can be written as 1 × 6 and 2 × 3. Hence, it has 4 factors, which means it is touched an even number of times, making it stay locked.

A number like 9 is written as 1 × 9 and 3 × 3. Hence, it has 3 factors, which is odd, making it stay open.

Since the perfect squares from 1 to 100 are 1,4,9,16,25,36,49,64,81,100, then the open lockers are:

1,4,9,16,25,36,49,64,81,100

Answer:

The Correct Answer Is: ∠ABD ≅ ∠CBE

Step-by-step explanation:

I just took the test

∠ABD≅∠CBE is the true statement of congruent angles as per the given condition ∠ABC ≅∠DBE.

" Congruent angles are pair of such angles which are equal in their measurements."

According to the question,

Given,

∠ABC ≅∠DBE                                    ________(1)

As shown in the diagram drawn as per the given conditions we have,

'D' is the interior point of angle ABC.

Therefore,

∠ABC = ∠ABD + ∠CBD                         ______(2)

'C' is the interior point of ∠DBE.

Therefore,

∠DBE = ∠CBD + ∠CBE                              ______(3)

Substitute  (2) and (3) in (1) to represent congruent angles we get,

∠ABD + ∠CBD  ≅ ∠CBD + ∠CBE      

⇒∠ABD   ≅  ∠CBE                            (∠CBD is common in both)

Hence, ∠ABD≅∠CBE is the true statement of congruent angles as per the given condition ∠ABC ≅∠DBE.

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Answer:

z = - 0.02

Step-by-step explanation:

0.3 = -15z

0.3 / -15 = z

-0.02 = z

Answer:

Z= - 0.02

Step-by-step explanation:

0.3=-15 *Z

Z= 0.3 / - 15

Z= - 0.02

Answer:

i think its a

Step-by-step explanation:

its A

Answer:A

Step-by-step explanation:

Answer: $64

Step-by-step explanation:

Let x be the amount of money he had before buying the video game

Given, 3/4 of x = 48

By cross-multiplying,

x = 64

Answer:

64

Step-by-step explanation: edge 2020

Answer:

I think that it's either x= -2 or x= 0.5

Step-by-step explanation:

x=5 is the value of equation x - 3x + 4 = 3 - 9.

Two or more expressions with an Equal sign is called as Equation.

The given equation is x - 3x + 4 = 3 - 9

x minus three times of x plus four equal to three minus nine

In the given equation x is the variable and we need to solve the value of x.

x - 3x + 4 = 3 - 9

Add the like terms

-2x+4=-6

Subtract 4 from both sidees

-2x=-10

Divide both sides by -2

x=5

Hence, x=5 is the value of equation x - 3x + 4 = 3 - 9.

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Answer: 3/4 is greater

Step-by-step explanation:

3/4 and 11/16

#1 change to same denominator

the LCM (least common multiple) of 4 and 16 is 16

12/16 and 11/16

#2 compare numerator

12 > 11

this means 12/16>11/16

12/16=3/4, 3/4 is greater

Answer: P = 6 miles

Step-by-step explanation: A rectangle is a quadrilateral with opposite sides with the same measure. As Central Park is one, its parallel sides has the same measurement.

Distance of points gives the measurement of the sides of the rectangle. It is calculated as:

[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]

For the first two points, (-1.25,-0.25) and (-1.25,0.25), note that x-components is the same, so, only y-component is relevant to the distance:

[tex]d=\sqrt{(-1.25+1.25)^{2}+(0.25+0.25)^{2} }[/tex]

[tex]d=\sqrt{(0.5)^{2} }[/tex]

d = 0.5

Two sides of the rectangle are 0.5 miles.

For points (-1.25,0.25) and (1.25,0.25), y-component will add 0 to the formula. Then,

[tex]d=\sqrt{(1.25+1.25)^{2}+(0.25-0.25)^{2} }[/tex]

[tex]d=\sqrt{(2.5)^{2}}[/tex]

d = 2.5

Two sides of the park are 2.5 miles.

Perimeter is the sum of all the sides of a geometric figure.

Perimeter of central Park is

P = 0.5+0.5+2.5+2.5

P = 6

Central Park has perimeter of 6 miles.

Answer:

The number of hours it takes the culture to reach 12,000 bacteria is 41 hours.

Step-by-step explanation:

To predict the number of hours it takes to culture a certain number of bacteria form a regression equation of number of hours (y) based on the number of bacteria (x) using the provided data.

The general form of the regression equation is:

[tex]y=a+bx[/tex]

Compute the values of a and b as follows:

[tex]a=\frac{\sum Y\cdot\sum X^{2}-\sum X\cdot\sum XY}{n\cdot \sum X^{2}-(\sum X)^{2}}=\frac{15\cdot 32109075 - 12565\cdot 39860}{5\cdot 32109075-(12565)^{2}}=-7.203\\\\b=\frac{n\cdot \sum XY-\sum X\cdot\sum Y}{n\cdot \sum X^{2}-(\sum X)^{2}}=\frac{5\cdot 39860- 12565\cdot 15}{5\cdot 32109075-(12565)^{2}}=0.004[/tex]

*Use the Excel data sheet attached.

The regression equation of number of hours based on the number of bacteria is:

[tex]y=-7.203+0.004x[/tex]

Compute the number of hours it takes the culture to reach 12,000 bacteria as follows:

[tex]y=-7.203+0.004x[/tex]

   [tex]=-7.203+(0.004\times 12000)\\=-7.203+48\\=40.797\\\approx 41[/tex]

Thus, the number of hours it takes the culture to reach 12,000 bacteria is 41 hours.

Answer:

Step-by-step explanation:

This is an algebraic question type where we express the identity of each number using exactly four 4s method order of operation.

So, Expression using four 4s.

1   =  (4 ÷ 4) ÷ (4 ÷ 4)

2 = ( 4 ÷ 4 ) + ( 4 ÷ 4)

3  = ( 4 + 4 + 4 ) ÷ 4

4  = 4 + 4 ( 4 - 4 )

5  = ((4 × 4) +4) ÷ 4

6  = 4 +( (4+4) ÷ 4)

7 = (4+4) - ( 4 ÷ 4 )

8  = (4 × 4) - 4 - 4

9  = 4 + 4 + ( 4 ÷ 4)

10 = ( 44 - 4 ) ÷ 4

Answer:

1 = (4÷4) + (4-4)

2= (4-4)+(4-

√4)

3= (4+4+4)÷4

4= (√4+√4)+(4 - 4)

5= (4+√4)-(4÷4)

6= (4-4)+(4+√4)

7= (4+4)+(4÷4)

8= (4*√4)-(4 - 4)

9= (4+4)+(4÷4)

10=(4 -√4)+(4*√4)

Step-by-step explanation:

The

√4 = 2 and that helps to most of the equations

Answer:

7/5

Step-by-step explanation:

Answer:

  7 < third side < 13

Step-by-step explanation:

The triangle inequality requires the sum of the shortest two side lengths to be more than the longest side length. The effect of that is to limit the third side to values between the sum and difference of the other two sides:

  7 < third side < 13

Answer:

[tex] {x}^{2} + 3x[/tex]

Step-by-step explanation:

1.

Area of shaded region = Area of external rectangle - Area of internal rectangle

[tex] = 4x(x + 2) - x(3x + 5) \\ = 4 {x}^{2} + 8x - 3 {x}^{2} - 5x \\ = 4 {x}^{2} - 3 {x}^{2} + 8x - 5x \\ = {x}^{2} + 3x \\ [/tex]

2.

Let the width of the rectangle be x inches.

Therefore, length of the rectangle = (x + 3) inches

A.

Area of rectangle

[tex] =(x + 3)\times x\\

=x^2 + 3x\\[/tex]

B.

Width of rectangle = 4 inches

Length of rectangle = 4 + 3 = 7 inches

Area of rectangle = 7*4 = 28 square inches.

Answer:

It will take ≈5 hours (5.278)

Step-by-step explanation:

First we need to find how many number she counts in one hour. We know she counts 60 every one minute and there are 60 minutes in an hour. 60x60=3600

Now we divide 19,000 by 3600 to find how many hours it will take

19000/3600=5.278

It will take ≈5 hours (5.278)