A whale is hunting at an elevation of −438 meters relative to sea level. How many meters below sea level is the whale?

Answer:

182.8125

Step-by-step explanation:

Given:

y = x^3

from [2,5] using 6 subdivisions

deltax = (5 - 2)/6 = 3/6 = 0.5

hence the subdivisions are:

[2, 2.5]; [2.5, 3]; [3, 3.5]; [3.5, 4]; [4, 3.5]; [4.5, 5]

hence the right endpoints are:

x1 = 2.5; x2 = 3; x3 = 3.5; x4 =4; x5 = 4.5; x6 = 5

now the area is given by:

A = deltax*[2.5^3 + 3^3 + 3.5^3 + 4^3+ 4.5^3 + 5^3]

A = 0.5*365.625

A = 182.8125

Area using Right Endpoint approximation is 182.8125

The area of the region is an illustration of definite integrals.

The approximation of the area of the region R is 182.8125

The given parameters are:

[tex]\mathbf{f(x) = x^3}[/tex]

[tex]\mathbf{Interval = [2,5]}[/tex]

[tex]\mathbf{n = 6}[/tex] ------ sub intervals

Using 6 sub intervals, we have the partitions to be:

[tex]\mathbf{Partitions = [2,2.5]\ u\ [2.5, 3]\ u\ [3,3.5]\ u\ [3.5,4]\ u\ [4,4.5]\ u\ [4.5,5]}[/tex]

List out the right endpoints

[tex]\mathbf{x= 2.5,\ 3,\ 3.5,\ 4,\ 4.5,\ 5}[/tex]

Calculate f(x) at these partitions

[tex]\mathbf{f(2.5) = 2.5^3 = 15.625}[/tex]

[tex]\mathbf{f(3) = 3^3 = 27}[/tex]

[tex]\mathbf{f(3.5) = 3.5^3 = 42.875}[/tex]

[tex]\mathbf{f(4) = 4^3 = 64}[/tex]

[tex]\mathbf{f(4.5) = 4.5^3 = 91.125}[/tex]

[tex]\mathbf{f(5) = 5^3 = 125}[/tex]

So, the approximated value of the definite integral is:

[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx \frac{1}{2}(\sum f(x))}[/tex]

This becomes

[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx \frac{1}{2}(15.625 + 27 + 42.875 + 64+91.125 + 125)}[/tex]

[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx \frac{1}{2} \times 365.625}[/tex]

[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx 182.8125}[/tex]

Hence, the approximation of the area of the region R is 182.8125

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Answer:

x = 6

Step-by-step explanation:

2x + 3(3x - 5) = 51

Expand the brackets.

2x + 9x - 15 = 51

Add like terms.

11x - 15 = 51

Add 15 on both sides.

11x = 51 + 15

11x = 66

Divide both sides by 11.

x = 66/11

x = 6

The solution to the equation 2x+3(3x-5)=51 is x = 6

The equation is given as:

2x+3(3x-5)=51

Expand

2x + 9x - 15 = 51

Evaluate the like terms

11x = 66

Divide both sides by 11

x = 6

Hence, the solution to the equation 2x+3(3x-5)=51 is x = 6

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Answer:

Step-by-step explanation:

Hello,

Factor x^2 + 64.

[tex]\boxed{x^2+64=x^2+8^2=x^2-8^2i^2=(x-8i)(x+8i)}[/tex]

Factor 16x^2 + 49.

[tex]\boxed{16x^2+49=(4x)^2-(7i)^2=(4x-7i)(4x+7i)}[/tex]

Find the product of (x + 9i)^2.

[tex]\boxed{(x+9i)^2=x^2+18xi+(9i)^2=x^2+18xi-81=x^2-81+18xi}[/tex]

Find the product of (x − 2i)^2.

[tex]\boxed{(x-2i)^2=x^2-4xi-4=x^2-4-4xi}[/tex]

Find the product of (x + (3+5i))^2.

[tex]\boxed{(x + (3+5i))^2=x^2+(3+5i)^2+2x(3+5i)=x^2+9-25+30i+6x+10xi}\\\boxed{=x^2+6x-16+(30+10x)i}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

For a relation to be a function every x value will have a single y value.

The first one has two x values of -2 but their y values are different so can’t be a function.

The second one has two 10’s with different y values so isn’t a function.

The 3rd one has 1 and -1 with the same y value, so isn’t a function.

The correct answer is the 4th choice

Answer:

[tex]\boxed{\sf \ \ \ 15a^5b^{15} \ \ \ }[/tex]

Step-by-step explanation:

hello,

[tex](3a^2b^7) (5a^3b^8)=15a^{2+3}b^{7+8}=15a^5b^{15}[/tex]

hope this helps

Answer:

if x is positive the answer is the 4th statement and if it is negative the answer is the 3rd statement

Step-by-step explanation:

We have the statement that tells us: "the graphs of the two lines y = –6 and x =?" x, we do not know it, but from the y coordinate we can do it by discard.

In the case of y-coordinate we have that y = -6 is a horizontal line with a slope of 0, therefore of the 4 statements it is reduced to 2, the third and the fourth.

Depending on the sign that has the value of x, if it is positive or negative it would be the 3rd and 4th answer.

if x is positive it is a vertical line with a slope that is undefined, but if it is negative it is a horizontal line with a slope that is undefined.

Answer:

30, 150, 120, and 60 degrees

Step-by-step explanation:

Since the sum of the interior angles in a quadrilateral is 360 degrees:

y+5y+4y+2y=360

12y=360

y=30

2y=60, 4y=120, 5y=150

Hope this helps!

Step-by-step explanation:

y+5y+ 4y + 2y=360°(sum of a Quadrilateral)

12y=360°

divide both sides by 12

y=30°

5y=(5×30)=150°

4y=(4×30)=120°

2y=(2×30)=60°

Answer:

1/64

Step-by-step explanation:

1/4 × 1/4 × 1/4

Multiply the fractions.

1/4³

= 1/64

Answer:

The answer is 1/64.

Step-by-step explanation:

1/4 x 1/4 x 1/4 = 1/64

In other ways, you can write this as: 1/4³

Hope this helped!

Answer:

Gina has 29 nickels and 72 dimes.

Step-by-step explanation:

Each nickel is $0.05, and each dime is $0.10.

If she has 101 total coins, we have:

[tex]nickel + dime = 101[/tex]

All coins worth $8.65, so we have:

[tex]0.05nickel + 0.1 dime = 8.65[/tex]

Multiplying the second equation by 20, and subtracting the result by the first equation, we have:

[tex]20(0.05nickel + 0.1 dime) - nickel - dime = 20*8.65 - 101[/tex]

[tex]1nickel +2 dime - nickel - dime = 173 - 101[/tex]

[tex]dime = 72[/tex]

Then, finding the number of nickels, we have:

[tex]nickel + 72 = 101[/tex]

[tex]nickel = 29[/tex]

So Gina has 29 nickels and 72 dimes.

Answer:

c

Step-by-step explanation:

outputs are on the right, which are the y-values.

Answer:

w = 15

Step-by-step explanation:

-9(w + 585) = -360w

-9w -5265 = -360w

351w = 5265

w=15

Answer:

a) SE = 25

b) MOE = 41

c) CI = 1951 ; 2049

Step-by-step explanation:

Normal distribution

Population mean  unknown

Population standard deviation    σ  = 350     Kwh

a) The standard error of the mean SE is

SE  =  σ/√

SE = 350 /√196

SE = 350/14

SE = 25

b) If confidence nterval is 95%    or 0,95  then

α = 0,05

And from z table we get     z(c) = 1,64

MOE = z(c) * SE

MOE = 1,64 * 350/√196

SE = 1,64 * (350)/14

SE = 41

MOE = And from z tabl we get     z(c) = 1,64

MOE = 1,64 * 350/√196

MOE = 1,64 * (350)/14

MOE = 1,64 * 25

MOE = 41

c) The confidence interval is:

Z = 2000

α = 1- 0,95

α = 0,05       ⇒   α/2   =  0,025

CI  =   Z - z(α/2) * σ/√n   ;    Z + z(α/2) * σ/√n

z(α/2)   from z-table is:     z(0,025)  = 1,96

CI = 2000 -  1,96* 350/√196   ;   2000 + 1,96* 350/√196

CI = 2000 - 1,96*25  ;  2000 +  1,96*25

CI = 2000 -  49 ;  2000 + 49

CI = 1951 ; 2049

Answer:

1. Use a straightedge

2. Draw dots on the line to mark the starting point  

3. Place the point of the compass on the point you made or was given

4. Extend the compass so that the pencil is on the 2nd point & make a an arc thru point B

5. Place the compass point on the starting point dot on the line and draw w/ the pencil to create an arc crossing the line.

Answer:

Step 1: Mark the point that will be the vertex of the new angle, and label it P.

Step 2: Draw a ray from P in any direction, with any length. This ray will be one of the sides of the new angle.

Step 3: Place the compass point on the vertex of the original angle, and adjust the compass width to a convenient size.

Step 4: Use the compass to draw an arc intersecting both rays of the original angle at two points, J and K.

Step 5: Move the compass (without changing the width) to point P, and make an arc intersecting the existing ray of the angle. Mark the intersection point, and label it M.

Step 6: Set the compass point on the original angle at point J, and set its width to the length of line segment JK.

Step 7: Move the compass point to M on the new angle, and draw an arc cutting the previous arc. Mark the intersection point and label it L.

Step 8: Draw a ray from point P through point L. The new angle is a copy of the original angle.

Step-by-step explanation:

edmentum

Answer: 0.1435

Step-by-step explanation:

Given : Mean = 479 pounds

Standard deviation = 40 pounds.

Let  X denote the weights of cows.

[tex]X\sim N(\mu=479,\sigma=40)[/tex]

The cow transport truck holds 15 cows and can hold a maximum weight of 7350.

i.e. mean weight of cow in this case =[tex]\overline{x}=\dfrac{7350}{15}=490\text{ pounds}[/tex]

If 15 cows are randomly selected from the very large herd to go on the truck, what is the probability their total weight will be over the maximum allowed of 7350 will be:-

[tex]P(\overline{x}>490)=P(\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}>\dfrac{490-479}{\dfrac{40}{\sqrt{15}}})\\\\=P(z>1.065)\ \ [\because\ z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=1-P(z\leq1.065)\\\\=1- 0.8565=0.1435\ \ [\text{By z-table}][/tex]

Hence, If 15 cows are randomly selected from the very large herd to go on the truck,  the probability their total weight will be over the maximum allowed of 7350 = 0.1435

So, the probability their mean weight will be over 479 is [tex]0.53836.[/tex]

A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values. Z-score is measured in terms of standard deviations from the mean.

It is given that,

[tex]\mu=479\\\sigma=40\\n=15\\X=maximum\ weight=7350[/tex]

Then,

[tex]\bar{x}=\frac{\sum x}{n}\\ =\frac{7350}{15}\\ =490[/tex]

Now, calculating Z-score:

[tex]Z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n} } } \\Z=\frac{490-479}{\frac{40}{\sqrt{15} } }\\ Z=1.07[/tex]

Using z table =1.07

[tex]P(Z < 1.07)=0.46164\\P(Z > 1.07)=1-P(Z < 1.07)\\=1-0.46164\\=0.53836[/tex]

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Answer:

algebraic expression is Y = 2x + 20

where x is the earning for last year

Y  is the earning for this year

Step-by-step explanation:

Let the earning of club in last year be x

given

The club earned$20 more than twice what it earned last year

twice the earning of last year = 2x

$20 more than twice the earning of last year = 2x +20

Earning this year =  2x +20

where x is the earning for last year

let the earning for this year be y

Y = 2x +20

Thus, algebraic expression is Y = 2x + 20

Answer:

x=35

Step-by-step explanation:

Answer:

The length of the rectangle is 3 feet.

Step-by-step explanation:

Area = l × w

So, for this problem, you would divide 3.6 by 1.2 in order to get the length of the rectangle.

3.6 / 1.2 = 3

So, the length of the rectangle is 3 feet.

Answer: The length is 3 feet.

Step-by-step explanation:

The area of a rectangle is the length times the width and since the area is given and the width is give  just divide the area by the width to find the length.

3.6/ 1.2 = 3

Answer:

  10. 60 in^2

  11. 27 cm^2

  12. 24 cm^2

  13. 4 in^2

  14. 24 cm^2

Step-by-step explanation:

The applicable formulas are ...

  trapezoid area: (1/2)(b1 +b2)h

  triangle area: (1/2)bh

  rectangle area: bh

  square area: s^2

where b, b1, b2 are base lengths, h is height, s is side length.

__

Fill in the numbers and do the arithmetic.

10) A = (1/2)(10 +14)(5) = 60 . . . in^2

11) A = (1/2)(6 cm)(9 cm) = 27 cm^2

12) A = (8 cm)(3 cm) = 24 cm^2

13) A = (2 in)^2 = 4 in^2

14) A = (1/2)(9 +7)(3) = 24 . . . cm^2

Answer:

x = 1, x = .333

Step-by-step explanation:

Answer:

x = 1 and x = 1/3

Step-by-step explanation:

Here the coefficients of this quadratic are a = 3, b = -4 and c = 1.

The discriminant is b^2 - 4ac, or (-4)^2 - 4(3)(1) = 16 - 12 = 4.

Thus, the roots are:

      -(-4) ± √4        4 ± 2

x = ---------------- = -------------   =>  x = 1 and x = 1/3

          2(3)                  6

Answer:

arccos (0.5) is [tex]\frac{\pi}{3}[/tex]

Step-by-step explanation:

With the arccos(0.5)  in this problem, you are asked which angle renders its cosine equal to 0.5 (or 1/2).

Recall that there are special angles in the unitary circle that render well know values like 1/2. There are two angle values between 0 and the full circle ([tex]2\pi[/tex] radians), that render cosine function equal 1/2, and they are: [tex]\frac{\pi}{3}[/tex], and [tex]-\frac{\pi}{3}[/tex].

The arccos uses just the first one as answer over the restricted domain between 0 and [tex]\pi[/tex], since otherwise it will not be considered a function.

So the answer is that the arccos (0.5) is [tex]\frac{\pi}{3}[/tex]

Answer:

(- 5, - 7 )

Step-by-step explanation:

Equate f(x) and g(x), that is

2x + 3 = - 4x - 27 ( add 4x to both sides )

6x + 3 = - 27 ( subtract 3 from both sides )

6x = - 30 ( divide both sides by 6 )

x = - 5

Substitute x = - 5 into either of the 2 functions for y- coordinate

Substituting into f(x)

f(- 5) = 2(- 5) + 3 = - 10 + 3 = - 7

Thus point of intersection = (- 5, - 7 )

Answer:

D. 0.002

Step-by-step explanation:

Given;

total number of sample, N = 500 elements

50 elements are to be drawn from this sample.

The probability of the first selection, out of the 50 elements to be drawn will be = 1 / total number of sample

The probability of the first selection = 1 / 500

The probability of the first selection = 0.002

Therefore, on the first selection, the probability of an element being selected is 0.002

The correct option is "D. 0.002"

On the first selection, the probability of an element being selected is 0.002. Option D is correct.

Given information:

A population consists of 500 elements. so, the total number of samples will be [tex]N = 500[/tex] .

We want to draw a simple random sample of 50 elements.

The probability is defined as the preferred outcomes divided by the total number of samples.

So, the probability of first selection will be calculated as,

[tex]P=\dfrac{1}{500}\\P=0.002[/tex]

Therefore, on the first selection, the probability of an element being selected is 0.002.

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Answer:

x = 19.9

Step-by-step explanation:

Given the above right angled triangle, we can find the missing side, x, using the trigonometric ratio formula.

The given angle (θ) = 19°

The adjacent length = x

Hypotenuse length = 21

Thus,

Cos (θ) = adjacent/hypotenuse

[tex] cos 19 = \frac{x}{21} [/tex]

[tex] 0.9455 = \frac{x}{21} [/tex]

Multiply both sides by 21 to solve for x

[tex] 0.9455*21 = x [/tex]

[tex] 0.9455*21 = x [/tex]

Answer:

x =

Step-by-step explanation:

Given the above right angled triangle, we can find the missing side, x, using the trigonometric ratio formula.

The given angle (θ) = 19°

The adjacent length = x

Hypotenuse length = 21

Thus,

Cos (θ) = adjacent/hypotenuse

[tex] cos 19 = \frac{x}{21} [/tex]

[tex] 0.9455 = \frac{x}{21} [/tex]

Multiply both sides by 21 to solve for x

[tex] 0.9455*21 = x [/tex]

[tex] 19.86 = x [/tex]

[tex] x = 19.86 [/tex]

The missing side = x ≈ 19.9 (to the nearest tenth)

Answer: -32

Step-by-step explanation:

I'm just going to plug in and break down the equation to make it more understandable and easier to comprehend

-(3^2) - (4*3) -11

-(9)- (12) -11

-9 - 12 - 11

-21 -11

-32

Answer:

100 times

Step-by-step explanation: vibration per second: 50 times

                               vibration for 2 seconds; 50*2=100 times

Answer:

100 times

Step-by-step explanation:

2 seconds=100 times

100÷50=2

So now you can do

Answer:

the correct answer is a reflection over the y axis

Step-by-step explanation:

The best description of the transformation shown will be;

''Reflection over the y - axis.''

What is Translation?

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Given that;

The transformation is shown in figure.

Now,

Clearly, A'B'C'D' is the mirror image of the ABCD across the y - axis.

So, The best description of the transformation shown will be;

''Reflection over the y - axis.''

Thus, The best description of the transformation shown will be;

''Reflection over the y - axis.''

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Answer:

a. The population is represented by the registered voters of the Raleigh city

b. The population size is 9,500

c. The sample size is 350

d. The proportion of people that voted for Brown was 32% >> (112 x 100) / 350 = 32%

e. The expected number of Brown's voters is 3,040 >>  (32 x 9,500) / 100 = 3,040

Step by step explanation:

In statistics, a population includes all the dataset from the study, while a sample is represented by one or more observations obtained from this dataset. The proportion can be represented by two fractions (ratios) which are equivalent to each other. Finally, the estimated size of the total population can be estimated by multiplication of the observed ratio in the sample and the size of the population (32 % x 9,500), and then dividing this number by the total ratio value.

Answer:

Step-by-step explanation:

y = -3x - 2

5x + 2y = 15

5x + 2(-3x -2) = 15

5x -6x - 4 = 15

-x - 4 = 15

-x = 19

x = -19

y = -3(-19) - 2

y = 57 - 2

y = 55

(-19, 55)

solution is b

Answer:

The roots are where the graph intercepts the x-axis

Step-by-step explanation:

Alternatively, you could factor and then solve algebraically.

Answer:

A

90 degrees

anticlockwise.

Step-by-step explanation:

It looks much more complicated than it really is. I don't know how to explain this in any other form but to give the answers.

1 A

The center of rotation is where the 90 degree angle has its vertex. So that would be A.

1 B

Follow x. It rotates 90 degrees. So every point must rotate 90 degrees.

1 C

The direction is against the way the clock tells time, so the direction of rotation is anticlockwise.