The mass of a clownfish is 2.5 x 10 to the negative 1 power kilograms. The mass of a pilot whale is 3 x 10 to the third power kilograms. About how many times as massive is the pilot whale than the clownfish?

Answer:

4.75

Step-by-step explanation:

Given

f(x)=  (x^2-1)/(x-4)

The average rate of change for the interval a≤x≤b is given by:

Rate of change=  (f(b)-f(a))/(b-a)

In our question,

a=2

and

b=6

So,

f(2)=  ((2)^2-1)/(2-4)

=(4-1)/(-2)

= -3/2

And

f(6)=  ((6)^2-1)/(6-4)

=(36-1)/2

=  35/2

Rate of change=  ( 35/2-(-3/2))/(6-2)

=(35/2+3/2)/(6-2)

=  ((35+3)/2)/4

=(38/2)/4

=19/4

=4.75

The average rate of change is 4.75 ..

Answer:

Average rate of change =4.75.

Step-by-step explanation:

Given function is [tex]f\left(x\right)=\frac{x^2-1}{x-4}[/tex].

Now we need to find the average rate of change of f(x) for [tex]2\le x\le6[/tex].

So plug these values into average rate of change  (ARC) formula.

[tex]ARC=\frac{f\left(b\right)-f\left(a\right)}{b-a}[/tex]

[tex]ARC=\frac{f\left(6\right)-f\left(2\right)}{6-2}[/tex]

[tex]ARC=\frac{\frac{6^2-1}{6-4}-\frac{2^2-1}{2-4}}{4}[/tex]

[tex]ARC=\frac{\frac{36-1}{6-4}-\frac{4-1}{2-4}}{4}[/tex]

[tex]ARC=\frac{17.5-\left(-1.5\right)}{4}[/tex]

[tex]ARC=\frac{19}{4}[/tex]

[tex]ARC=4.75[/tex]

So the final answer is average rate of change =4.75.

Answer:

answerbis 2.25

Step-by-step explanation:

f(x)=9/4

f(x)=2.25

it would be a because of the -4

Answer: [tex]x=76\°[/tex]

Step-by-step explanation:

By definition the angle formed by the intersection of two chords inside a circle is:

[tex]Angle\ formed\ by\ two\ Chords=\frac{sum\ of\ intercepted\ Arcs}{2}[/tex]

You can observe in the figure that  the angle formed by the intersection of the two chords measures 94°, and the intercepteed arcs are: x° and 112°.

Therefore, you need to substitute these values into the formula and solve for "x to find its value. Then:

[tex]94\°=\frac{x+112\°}{2}\\\\(94\°)(2)=x+112\°\\\\188\°-112\°=x\\\\x=76\°[/tex]

Answer:

A fixed point equidistant from all points on the surface of the sphere

Step-by-step explanation:

we know that

The sphere is the set of all points in the space equidistant from a fixed point called the center of the sphere

therefore

The center of a sphere is a fixed point equidistant from all points on the surface of the sphere

In Geometry, the center of a sphere is: B. a fixed point equidistant from all points on the surface of the sphere.

A sphere can be defined as a round, three-dimensional solid geometric figure that has all its surface points (every point on its surface) at equal distances (equidistant) from the center.

In this context, we can infer and logically conclude that the center of a sphere simply refers to a fixed point that is equidistant or at equal distances from all points on the surface of the sphere.

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Answer:

6.4

Step-by-step explanation:

8.9 - 2.5 = 6.4

8 - 2 = 6

9 - 5 = 4

there you have it your answer 6.4

Answer:

There are two inputs for which the output is 5.

The vertex of its graph is at (0,-2)

Step-by-step explanation:

ANSWER

2nd

4th

5th

EXPLANATION

The given function is

[tex]y = |x| - 2[/tex]

The value of this function cannot be negative: False.

y = |1| - 2=-1

Its graph has a V-shape. This is true because it is the graph of y=|x| shifted downwards by 2 units.

There is only one input for which this function is zero. False

both -2 and 2 will make this function zero.

There are two inputs for which this function is 5. True, x=7 and x=-7

The vertex is (0,-2). This is true because it is the graph of y=|x| shifted downwards by 2 units.

Answer:

It can't be A. since if you only look at managers, you are missing all the sales executives.

It may be C. this option is more random but doesn't guarantee that you will represent both groups of employee's. Also, each time you would conduct the survey, you will receive the exact same results since it is the same people. 

It isn't D. for the exact same reason as A. but you're missing managers now. 

Therefore the answer is B. Some managers and some sales executives selected at random. This way you get a sample from both categories, and within those groups, it is randomly selected.

 I hope this helps!

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Step-by-step explanation:

The generalization could be valid for a sample that accurately represents the entire employee population of Ashton's company.

This sample should be large enough to be statistically significant and should be selected randomly to avoid bias.

To calculate the sample size needed for a valid generalization, Ashton could use a confidence level and margin of error. Let's say he wants a 95% confidence level with a margin of error of 5%.

First, he needs to find the population size (total number of employees at the company). Let's assume there are 500 employees.

Next, he can use the formula for sample size calculation:

[tex]\[n = \frac{{Z^2 \cdot p \cdot (1-p)}}{{E^2}}\][/tex]

Where:

- (n) = sample size

-(Z) = Z-score corresponding to the desired confidence level (for 95% confidence level, Z = 1.96)

- (p) = estimated proportion of employees using cell phones primarily for business (from the survey data)

- (E) = margin of error (0.05 for 5%)

Let's say from the survey, Ashton found that 70% of employees use cell phones primarily for business.

Plugging in the values:

[tex]\[n = \frac{{1.96^2 \cdot 0.70 \cdot (1-0.70)}}{{0.05^2}}\][/tex]

[tex]\[n = \frac{{3.8416 \cdot 0.70 \cdot 0.30}}{{0.0025}}\][/tex]

[tex]\[n = \frac{{0.719856}}{{0.0025}}\][/tex]

[tex]\[n ≈ 287.94\][/tex]

So, Ashton would need a sample size of approximately 288 employees to make a valid generalization about the entire company.

To ensure the generalization is valid, Ashton needs to collect data from a sample that accurately represents the entire employee population. This sample should be large enough to be statistically significant and should be selected randomly to avoid bias.

Using statistical methods, Ashton can calculate the minimum sample size needed for a valid generalization. By setting a confidence level and margin of error, he can determine the sample size required to achieve a certain level of accuracy.

In this case, Ashton chose a 95% confidence level with a margin of error of 5%. He used a formula that takes into account the population size, estimated proportion of employees using cell phones primarily for business, and the margin of error.

After plugging in the values, he calculated that he would need a sample size of approximately 288 employees to make a valid generalization about the entire company.

So, for the conclusion that most employees at his company use cell phones primarily for business to be valid, Ashton should survey at least 288 randomly selected employees.

Complete question:

Ashton surveyed some of the employees at his company about their cell phone habits. From the data, he concluded that most employees at his company use cell phones primarily for business. For which sample could this generalization be valid?

Answer:

[tex]\large\boxed{C.\ (x^2-1)-5(x-1)}[/tex]

Step-by-step explanation:

[tex](f-g)(x)=f(x)-g(x)\\\\p(x)=x^2-1,\ q(x)=5(x-1)\\\\(p-q)(x)=(x^2-1)-5(x-1)[/tex]

Answer:

Answer:

The definition of present value is the current value of a future sum of money.

Choice A

Step-by-step explanation:

Present value (PV) is the current value of a future streams of cash flows or sum of money at a given expected rate of return by the investor. Future payment streams are discounted at the rate of return. The present value increases with the decrease in the rate of return or the discount rate and vice versa.

Option A is correct,  the definition of present value is the current value of a future sum of money.

Present value refers to the concept of determining the value of a future sum of money in terms of its current worth.

It takes into account factors such as the time value of money and discounting to calculate the value of future cash flows in today's terms.

By discounting future cash flows, the present value represents the amount of money that would need to be invested or received today to achieve the same value as the future sum of money.

Hence, the definition of present value of the current value of a future sum of money.

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Answer:

b = -12/5

Step-by-step explanation:

5(b+6) = 18

5b + 30 = 18

5b = -12

b = -12/5

Answer:

b = -2.4

Step-by-step explanation:

5 ( b + 6 ) = 18

→ Expand brackets

5 b + 30 = 18

→ - 30 from both sides to isolate 5 b

5 b = - 12

→ ÷ Divide both sides 5 to isolate b

b = -2.4

Answer:

Option D. angle S apostrophe

Step-by-step explanation:

we know that

The transformation of the figure is a translation

The rule of the translation is

(x,y)-----> (x-3,y-7)

That means ----> left 3 units and down 7 units

Remember that a translation does not modify the internal angles of the figure as neither the length of their sides

so

∠S=∠S'

Answer:

x = 2

Step-by-step explanation:

A vertical line has the equation x = a.  This line passes through points with x-coordinate of 2, so the equation is x = 2.

Answer:

The number of roses is 16

The number of lilies is 8

The number of orchids is 21

Step-by-step explanation:

Let

x-----> the number of roses

y-----> the number of lilies

z-----> the number of orchids

we know that

x=2y ----> y=x/2 ----> equation A

z=x+5 ---> equation B

x+y+z=45 ----> equation C

substitute equation A and equation B in equation C and solve for x

x+(x/2)+(x+5)=45

(5/2)x=45-5

(5/2)x=40

x=40*2/5

x=16 roses

Find the value of y

y=x/2 ----> y=16/2=8 lilies

Find the value of z

z=x+5 -----> z=16+5=21 orchids

therefore

The number of roses is 16

The number of lilies is 8

The number of orchids is 21

Answer: a=4 or a= −3, so you can use anyone of the answers.

Step-by-step explanation:

Solve Absolute Value.

|2a−1|=7

We know either 2a−1= 7or 2a−1 = −7

2a−1=7(Possibility 1)

2a−1+1=7+1(Add 1 to both sides)

2a=8

[tex]\frac{2a}{2} = \frac{8}{2}[/tex] (Divide both sides by 2)

a=4

OR,

2a−1=−7 (Possibility 2)

2a−1+1= −7+1 (Add 1 to both sides)

2a= −6

[tex]\frac{2a}{2} =\frac{-6}{2}[/tex] (Divide both sides by 2)

a= −3

Therefor the answers are a=4 or a= −3

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The distance from New York to Hartford represents 48% of the distance from New York to Boston.

To find the percentage of the distance from New York to Boston that is the distance from New York to Hartford, we need to calculate the ratio of the two distances. First, divide the distance from New York to Hartford (120 miles) by the distance from New York to Boston (250 miles):

120 / 250 = 0.48

Convert the ratio to a percentage by multiplying by 100:

0.48 * 100 = 48%

Therefore, the distance from New York to Hartford represents 48% of the distance from New York to Boston.

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Answer:

B

Step-by-step explanation:

The image is a reflection of the original in the y- axis

The equation of the y- axis is x = 0 → B

Answer:

The correct option is B.

Step-by-step explanation:

The coordinates of polygon ABCDE are A(-2,2), B(-1,2), C(1,1), D(0,-1) and E(-2,1).

The coordinates of polygon A'B'C'D'E' are A'(2,2), B'(1,2), C'(-1,1), D'(0,-1) and E'(2,1).

The relation between preimage and image is

[tex]P(x,y)\rightarrow P'(-x,y)[/tex]

From the given figure it is clear that the figure ABCDE reflected across the y-axis.

If a figure reflected across the y-axis, then

[tex](x,y)\rightarrow (-x,y)[/tex]

The equation of y-axis is x=0, so the given figure reflected across x=0.

Therefore the correct option is B.

Answer: 9(9-4xy)

Step-by-step explanation:

You can factor out the 9, as 9*9 = 81 and 9*4 = 36.

So dividing both terms, you get 9(9-4xy)

The first option is the correct choice

Answer:

648 sq units

Step-by-step explanation:

Area of the base= 12×12= 144 sq. units

Perimeter of the base=4×12= 48

Total surface area= 1/2×48×21 + 144

=648 sq units

ANSWER

648 square units.

EXPLANATION

The surface area of the regular pyramid is the area of the base plus the area of the 4 triangular faces.

We use the formula;

[tex]S.A = {l}^{2} + 4 \times \frac{1}{2} bh[/tex]

where l=12 units is the length of the square base and h=21 units is the vertical height of the triangular faces.

We substitute the values to get;

[tex]S.A = 12^{2} + 4 \times \frac{1}{2} \times 12 \times 21[/tex]

[tex]S.A = 144+ 504[/tex]

[tex]S.A =648 {units}^{2} [/tex]

Answer:

Raquel should adjust the number of rotations  to 115.81 rotations

Step-by-step explanation:

step 1

Find the circumference of the wheels that are 2.5 cm in diameter

The circumference is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=2.5/2=1.25\ cm[/tex]

assume

[tex]\pi =3.14[/tex]

substitute

[tex]C=2(3.14) (1.25)[/tex]

[tex]C=7.85\ cm[/tex]

step 2

Find the number of rotations

Divide 10 meters by the circumference

[tex]10\ m=1,000\ cm[/tex]

[tex]1,000/7.85=127.39\ rotations[/tex]

step 3

For a diameter of 2.75 cm find how should she adjust the number of rotations so that the robot travels the same distance

Find the circumference of the wheels

The circumference is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=2.75/2=1.375\ cm[/tex]

assume

[tex]\pi =3.14[/tex]

substitute

[tex]C=2(3.14) (1.375)[/tex]

[tex]C=8.635\ cm[/tex]

step 4

Find the number of rotations

Divide 10 meters by the circumference

[tex]10\ m=1,000\ cm[/tex]

[tex]1,000/8.635=115.81\ rotations[/tex]

Answer: -1 1/2 < -1/4

Explanation: Since the number is negative, -1 1/2 is further to the left on the number line, meaning it has less value.

The relationship between -1 1/2 and -1/4 can be expressed as an inequality. In this case, -1 1/2 is less than -1/4, so the inequality is -1 1/2 < -1/4.

The relationship between -1 1/2 and -1/4 may be written as an inequality. Remember, an inequality indicates that one number is larger or smaller than another. In this case, it shows which negative number, either -1 1/2 or -1/4, is larger. On the number line, a negative number situated to the right is larger than a number situated to the left. So, in terms of value, -1/4 is larger than -1 1/2 as it's less negative. This can be written as:

-1 1/2 < -1/4

.

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Answer:

The recursively-defined function to describe this situation is:

Step-by-step explanation:

To solve the number of birds that there will be after three years, you must recognize that the function f(0) means the number of birds at time zero, in which the birds are complete (that is, the 14,000 birds), by their part, following the equation provided below we have the following calculation:

So:

Therefore, the final number of birds after three years in decline is 10206.

Answer:

See picture attached below

Step-by-step explanation:

We can easily find the answer to your question, if we plot the equation with a graphing calculator or any plotting tool.

The equation is

y = 3 cos (θ + 20) - 4

See attached picture below

phase_shift = 20

max_amplitude = -1

min_amplitude = -7

Period = 2π

Answer:

The experimental probability is 3% greater than the theoretical probability.

Step-by-step explanation:

We are given the results of flipping two coins with their outcomes and number of times they were tossed.

We are to compare the experimental and theoretical probability of getting HH.

The theoretical Outcomes are: HH HT TH TT

So theoretical probability of getting HH = [tex]\frac{1}{4} \times 100[/tex] = 25%

Total number of outcomes = [tex]28+22+34+16[/tex] = 100

So experimental probability of getting HH = [tex]\frac{28}{100} \times 100[/tex] = 28%

Therefore, the experimental probability is 3% greater than the theoretical probability.

Answer:

1. y=0.35x+35

2. If 979 minutes are used, the total cost will be $377.65 dollars.

Step-by-step explanation:

1. Let $x be the flat monthly fee and $y be the amount of money paid per minute used on the phone.

If a customer uses 210 minutes, the monthly cost will be $108.5, thus

[tex]x+210y=108.5[/tex]

If the customer uses 620 minutes, the monthly cost will be $252, then

[tex]x+620y=252[/tex]

Subtract from the second equation the first one:

[tex]x+620y-(x+210y)=252-108.5\\ \\x+620y-x-210y=143.5\\ \\410y=143.5\\ \\y=0.35[/tex]

Substitute it into the first equation

[tex]x+210\cdot 0.35=108.5\\ \\x=108.5-73.5\\ \\x=35[/tex]

We get the flat fee is $35 and the amount of money per minure used is $0.35. So, the equation of the function is

[tex]y=35+0.35x,[/tex]

where x is the number of monthly minutes used and y is the total monthly of the NextFell plan.

2. When x=979, then

[tex]y=35+0.35\cdot 979=377.65[/tex]

The answer to this question is 2.

ANSWER

[tex]y = - \frac{1}{3} x -\frac{4}{3} [/tex]

EXPLANATION

The given line is

[tex]y = 3x + 3[/tex]

The given point is

[tex](-1,-1)[/tex]

The slope of the given line is

[tex]m = 3[/tex]

We found this by comparing

[tex]y = 3x + 3[/tex]

to

[tex]y = mx + b[/tex]

If two lines are perpendicular, then one is the negative reciprocal of the other.

Hence the slope of the required line is

[tex] - \frac{1}{3} [/tex]

Using the point-slope formula or otherwise, we can find the required equation.

[tex]y-y_1=m(x-x_1)[/tex]

We substitute the slope and point to get:

[tex]y + 1 = - \frac{1}{3} (x + 1)[/tex]

[tex]y = - \frac{1}{3} x -\frac{4}{3} [/tex]

Step-by-step explanation:

ΔADG - NO (it's an equilateral triangle)

ΔAFH - NO (it's an equilateral triangle)

ΔBCH - NO (it's an equilateral triangle)

ΔBEH - NO (it's an equilateral triangle)

ΔBFG - YES

ΔCDG - YES

ΔEFG - YES

ΔDFG - NO (it's an equilateral triangle)

All equilateral triangles have the sides equal a√2 (a - length of edge).

ΔBFG has sides a, a√2 and a√3.

From Inverse Pythagorean Theorem:

a² + (a√2)² = (a√3)²

a² + 2a² = 3a²

3a² = 3a²     CORRECT :)

ΔCDG and ΔEFG have sides a, a and a√2.

From Inverse Pythagorean Theorem:

a² + a² = (a√2)²

2a² = 2a²        CORRECT :)

Answer:

3.3 hours

Step-by-step explanation:

10/3≈3.3

Answer:

You just have to divide 10 by 3 since John takes 10 hours to paint the fence

it would take 3.3 hours for john and his friends to finish painting the fence

Step-by-step explanation: