Simplify the following expression as much as possible.
4^10/4^10 x 7^O=?

Answer:

  a) 30 kangaroos in 2030

  b) decreasing 8% per year

  c) large t results in fractional kangaroos: P(100) ≈ 1/55 kangaroo

Step-by-step explanation:

We assume your equation is supposed to be ...

  P(t) = 76(0.92^t)

__

a) P(10) = 76(0.92^10) = 76(0.4344) = 30.01 ≈ 30

In the year 2030, the population of kangaroos in the province is modeled to be 30.

__

b) The population is decreasing. The base 0.92 of the exponent t is the cause. The population is changing by 0.92 -1 = -0.08 = -8% each year.

The population is decreasing by 8% each year.

__

c) The model loses its value once the population drops below 1/2 kangaroo. For large values of t, it predicts only fractional kangaroos, hence is not realistic.

  P(100) = 75(0.92^100) = 76(0.0002392)

  P(100) ≈ 0.0182, about 1/55th of a kangaroo

Answer:

See below :)

Step-by-step explanation:

Given ordered pairs :

( 2 , 3 ) , ( - 2 , 4 ) , ( 4 , 8 ) , ( - 2 , 5 )

Domain is the set of all x -coordinates in the set of ordered pairs.

( 2 , 3 ) , ( -2 , 4 ) , ( 4 , 8 ) , ( -2 , 5 )

List them :

Domain = { - 2 , 2 , 4 )

Range is the set of all y - coordinates in the set of ordered pairs.

( 2 , 3 ) , ( - 2 , 4 ) , ( 4 , 8 ) , ( - 2 , 5 )

List them :

Range = { 3 , 4 , 5 , 8 }

Hope I helped !

Best regards!!

Answer:

Technically neither, but Mia is correct.

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Since our slope m is equal to 6, it is a positive number. That means that the slope/line will be positive, so the line should be going up, not down. That means the blue line would be correct. Therefore, Mia is correct.

Technicality:

Since the blue line is dotted, the equation should be a inequality and not a linear equation. No solutions on the line would technically work. If the equation was y < 6x + 4 or something with an inequality sign, then it would be correct.

Answer:

[tex]\displaystyle \int\limits^5_1 {(x^2 - x + 1)} \, dx = \frac{100}{3}[/tex]

General Formulas and Concepts:

Calculus

Integration

Integration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                     [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Addition/Subtraction]:                                                       [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \int\limits^5_1 {(x^2 - x + 1)} \, dx[/tex]

Step 2: Integrate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Answer: 5\int_0^5 3^(3)\sqrt(x^(2)) dx

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

First we need to subtract the 50 students enrolled in English class.

150 - 50 = 100

Next, let's add the mathematics students and the physics students.

80 + 60 = 140

Then we subtract the total amount of mathematics and physics students by the total number of students.

140 - 100 = 40

Therefore, there are 40 students who take both mathematics and physics.

Answer:

Step-by-step explanation:balls

Answer:

3. C

Step-by-step explanation:

16 / 4 = 4 which is a counting number.

- 30 / 5 = -6 which is a integer.

-31/8 = -3.875 which is rational number

30/9 = 10/3 = 3.333333333.... which is an irrational number

So your answer is C

Answer:

|w - v| or |v - w|

Step-by-step explanation:

The answer is the absolute value of the difference of the two numbers written in either order.

|w - v| or |v - w|

Answer:

B |w-v|

Step-by-step explanation:

khan academy

Answer:

(D) 2

Step-by-step explanation:

If two or more vectors are linearly dependent, then one of them can be expressed as a linear combination of the rest. In other words, vectors are dependent linearly on one another if the determinant of the matrix that they form is zero.

Given vectors:

i+j+2k

i+pj+5k

5i+3j+4k

Now, since they are linearly dependent, then the determinant of their matrix should be zero. i.e

Let their matrix be A and is given by;

A =   [tex]\left[\begin{array}{ccc}1&1&2\\1&p&5\\5&3&4\end{array}\right][/tex]

Where;

the first column holds the i components of the vectors

the second column holds the j components of the vectors and

the third column holds the k components of the vectors

=> |A| = det(A) = 0

 [tex]det(A) = det \left[\begin{array}{ccc}1&1&2\\1&p&5\\5&3&4\end{array}\right] = 0[/tex]

Now, let's calculate the determinant.

[tex]det \left[\begin{array}{ccc}1&1&2\\1&p&5\\5&3&4\end{array}\right] = 1(4p - 15) - 1(4 - 25) + 2(3 - 5p) = 0[/tex]

=> 4p -15 - 4 + 25 + 6 - 10p = 0

=> 4p - 10p + 12 = 0

=> 6p = 12

=> p = 2

Therefore, the value of p for which the vectors are linearly dependent is 2

Answer:

296.5 miles

Step-by-step explanation:

Round trip distance of City X to City Y is 647 miles.

Round trip includes to and fro.

i.e. City X to City Y and then City Y to City X back.

Let the distance between City X and City Y = D

Distance traveled in round trip between City X and City Y = D + D = 2D

Given than 2D = 647

OR

D = [tex]\frac{647}2[/tex] = 323.5 miles

Kindly refer to the attached diagram, for the location of City Z.

Distance between XY = Distance from X to Z + Distance from Z to Y.

Distance XY = XZ +ZY

323.5 = 27 +ZY

ZY =296.5 miles

Answer:

1/273

Step-by-step explanation:

5/15 * 4/14 * 3/13 * 2/12

= 1/3 * 2/7 * 3/13 * 1/6

= 1/273

Answer:

16Km due east of school P

Step-by-step explanation:

Given

A school P is 16km due west of a school Q

Thus, we can say that distance PQ = 16 km.

________________________________

now we have to find  the bearing of Q from P​

As distance is same

distance PQ = distance QP

Thus,

Distance will remain same of 16 km.

For direction,

If Q is west of P, then P will be east of Q[tex]P------------------>Q[/tex]

as shown in figure P is west of Q,

now from point P , Q is west P.

Thus,

Bearing of  School Q from P is 16Km due east of school P

Answer:

(B) [tex]b + 2b - 83 = 259[/tex]

Step-by-step explanation:

We can first create the equation [tex]b + g = 259[/tex], since we know that there are a total of 259 students in this freshman class.

Now, the amount of girls is 83 less than twice the number of boys, so that is [tex]2b - 83[/tex].

Now, we can substitute this in the previous equation as g.

[tex]b + 2b - 83 = 259[/tex]

Hope this helped!

Answer:

b

Step-by-step explanation:

Answer:

9.31

Step-by-step explanation:

Given the following :

- - - - - - - - - - df - - - - - SS - - - MS - - - F - - - signiF

Regression - 1 - 13555.42 - 13555.41 - 156.38 - 0

Residual - - 8.00 - 693.48 - - 86.68

Total - - - - 9.00 - 14248.90

What is the value of the standard error of estimate?

The standard error estimate :

Mean square error or Residual (MSE)

Standard Error (SE): √MSE

MSE = 86.68

Standard Error = √86.68

Standard error = 9.3102094

= 9.31

Answer:  The number has to be less than 27.

Step-by-step explanation:

81 + n > 4n  

      -n    -n

81  > 3n

n<27

Answer:

see below (I hope this helps!)

Step-by-step explanation:

When n < 1, Declan's statement is incorrect because 4 * 0 = 0 which is not greater than 4 and this continues for all n values that are less than 1.

Answer:

-1 and -8

Step-by-step explanation:

x^2+2*9/2*x+(9/2)^2-(9/2)^2+8=0

(x+9/2)^2+32/4-81/4=0

(x+9/2)^2-49/4=0

(x+9/2)^2=(7/2)^2

so

x+9/2=7/2

x=7/2-9/2

x=-2/2

x=-1

or

x+9/2=-7/2

x=-7/2-9/2=-16/2

x=-8

The correct answer is A. 12y + 11

Explanation:

In mathematics, the word "product" is mainly used to refer to multiplication. For example, the product of 5 and 2 is 10 as 5 x 2 = 10. This means, the section "the product of 12 and y" means 12 needs to be multiplied by y, which can be expressed as 12y. Additionally, the word "increased" refers to addition, which means 11 needs to be added to 12y. This means the final expression is 12y + 11, and therefore the correct answer is the first one or option A.

Answer: the answer is 12y + 11

Step-by-step explanation:

i too the test and got a 100

Answer:

  1 foot

Step-by-step explanation:

Using the formula for the area of a triangle, fill in the given information and solve for the unknown.

  A = (1/2)bh

  0.75 = (1/2)b(1.5)

  b = 0.75/0.75 = 1 . . . . divide by the coefficient of b

The base is 1 foot.

Answer:The answer is C

Step-by-step explanation:

I just had the question and i got it right :D

Step-by-step explanation:

Hello!

For this you multiply the numbers that intersect at that box

Box A 2x and 4 intersect

2x * 4 = 8x

Box B 3 and 4 intersect

3 * 4 = 12

Box C 2x and x intersect

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

Box D 3 and x intersect

3 * x = 3x

To solve this we put all these together

[tex]2x^{2} +3x+8x+12[/tex]

Combine like terms

[tex]2x^{2} +11x+12[/tex]

Hope this helps!

Answer:

[tex]\frac{3}{13} i+\frac{11}{130} j-\frac{6}{65} k\\[/tex]

Step-by-step explanation:

Given A = 5i + 11j – 2k and B = 4i + 7k​, the vector projection of B unto a is expressed as [tex]proj_ab = \dfrac{b.a}{||a||^2} * a[/tex]

b.a = (5i + 11j – 2k)*( 4i + 0j + 7k)

note that i.i = j.j = k.k  =1

b.a = 5(4)+11(0)-2(7)

b.a = 20-14

b.a = 6

||a|| = √5²+11²+(-2)²

||a|| = √25+121+4

||a|| = √130

square both sides

||a||² = (√130)

||a||²  = 130

[tex]proj_ab = \dfrac{6}{130} * (5i+11j-2k)\\\\proj_ab = \frac{30}{130} i+\frac{11}{130} j-\frac{12}{130} k\\\\proj_ab = \frac{3}{13} i+\frac{11}{130} j-\frac{6}{65} k\\\\[/tex]

Hence the projection of b unto a is expressed as [tex]\frac{3}{13} i+\frac{11}{130} j-\frac{6}{65} k\\[/tex]

Answer:

n = 3

Step-by-step explanation:

Hello!

p = 2n - 3

the question asks for when p is equal to 3 so we put 3 in for p

3 = 2n - 3

Now we can solve this

3 = 2n - 3

Add 3 to both sides

6 = 2n

Divide both sides by 2

3 = n

The answer is n = 3

Hope this Helps!

Answer:

Derek needs to add 3/4 cups of flour.

Step-by-step explanation:

If Derek has already used 1/4 cup of flour, he needs 3 more cups of flour to get to 1 full cup of flour.

Answer:

Step-by-step explanation:A batch of cookies requires 2 1/4 cup of flour and 1 egg. You have in your kitchen 8 cups of flour and a half dozen eggs. a) How many batches of cookies

Answer:

2 and 4 6/7

Step-by-step explanation:

1. First equation

2. Second equation

Answer:

2x + 5 = 61

Step-by-step explanation:

Let x be equal to the temperature in Boise.

Since the temperature in San Diego is 5 degrees warmer than twice the temperature in Boise, we must double the temperature in Boise and then add 5 degrees. To do this we put a 2 in front of the x and then add 5 to that.

2x + 5

Since we know the temperature in San Diego is 61 we can make the equation equal to 61.

2x + 5 = 61

Answer:

B-$100=$372

The is is the smartest way I could look at this

OR

$372 - $100= b

Hope this helps

MARNIE OUT!

Answer: There is no x-intercept for this quadratic equation.

Step-by-step explanation:

An x-intercept is when the y-value of the point if equal to zero. There is no x-intercept for this quadratic equation. This can be supported by the fact that this equation cannot be factored.

Answer:

B

Step-by-step explanation:

So we have a 45-45-90 triangle.

This is a special right triangle. In a 45-45-90 triangle, the side lengths are x, and the hypotenuse will be x√2

Since the hypotenuse is 3, we can set it equal to x√2 to solve for x. Therefore:

[tex]x\sqrt2=3[/tex]

Divide both sides by √2:

[tex]x=\frac{3}{\sqrt2}[/tex]

Rationalize:

[tex]x=\frac{3\sqrt2}{2}[/tex]

Our answer is B.

Hiroshi is correct; after you draw

the line from the first point to the other three, one of

the lines from the second point is already drawn.