When does the rock hit the ground? the rock hits the ground between seconds and seconds after it is dropped.

If set A shows the statistians and B shows the person who bath regularly then the notation which shows that all statistians bath regularly is A∩B.

Given that A shows the statistians and B shows the person who bath regularly.

We are required to show the sentence that "All statistians bath regularly"in set notation.

We know that set is a collection of things, place,anything which can be measured or denoted as something else.

"∪" shows union means when we put this sign between two sets then the resulting set will contain all the elements of both the sets.

"∩" shows intersection means when we put this sign between two sets then the resulting set will contain all the common elements of both the sets.

Since A represents statistians and B represents people who bath regularly and we require statistians who bath regularly is A∩B.

Hence if A shows the statistians and B shows the person who bath regularly then the notation which shows that all statistians bath regularly is A∩B.

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By the ratio test, the series converges for

[tex]\displaystyle \lim_{k\to\infty} \left|\frac{(x+2)^{k+1}}{\sqrt{k+1}} \cdots \frac{\sqrt k}{(x+2)^k}\right| = |x+2| \lim_{k\to\infty} \sqrt{\frac k{k+1}} = |x+2| < 1[/tex]

so that the radius of convergence is 1, and the interval of convergence is

|x + 2| < 1   ⇒   -1 < x + 2 < 1   ⇒   -3 < x < -1

The radius of convergence R is 1 and the interval of convergence is (-3, -1) for the given power series. This can be obtained by using ratio test.  

Ratio test is the test that is used to find the convergence of the given power series.  

First aₙ is noted and then aₙ₊₁ is noted.

For  ∑ aₙ,  aₙ and aₙ₊₁ is noted.

[tex]\lim_{n \to \infty} |\frac{a_{n+1}}{a_{n} }|[/tex] = β

Here [tex]a_{k}[/tex] = [tex]\frac{(x+2)^{k}}{\sqrt{k} }[/tex]  and  [tex]a_{k+1}[/tex] = [tex]\frac{(x+2)^{k+1}}{\sqrt{k+1} }[/tex]

Now limit is taken,

[tex]\lim_{n \to \infty} |\frac{a_{n+1}}{a_{n} }|[/tex] = [tex]\lim_{n \to \infty} |\frac{(x+2)^{k+1} }{\sqrt{k+1} }/\frac{(x+2)^{k} }{\sqrt{k} }|[/tex]

= [tex]\lim_{n \to \infty} |\frac{(x+2)^{k+1} }{\sqrt{k+1} }\frac{\sqrt{k} }{(x+2)^{k}}|[/tex]

= [tex]\lim_{n \to \infty} |{(x+2) } }{\sqrt{\frac{k}{k+1} } }}|[/tex]

= [tex]|{x+2 }|\lim_{n \to \infty}}{\sqrt{\frac{k}{k+1} } }}[/tex]

= [tex]|{x+2 }|[/tex] < 1

- 1 < [tex]{x+2 }[/tex] < 1

- 1 - 2 < x < 1 - 2

- 3 < x < - 1

We get that,

interval of convergence = (-3, -1)

radius of convergence R = 1

Hence the radius of convergence R is 1 and the interval of convergence is (-3, -1) for the given power series.

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Answer:

1053

Step-by-step explanation:

Answer: 1960.2 cm

Step-by-step explanation:

v = πr^2h

v = π7.4^2(11.4)

= π54.76(11.4)

= 171.9464(11.4)

= 1960.2

The volume of the cylinder rounded to the nearest tenth is 1,960.2 cubic cm

Volume of the cylinder = πr²h

Where,

r = radius = 7.4 cm

h = height = 11.4 cm

π = 3.14

So,

Volume of the cylinder = πr²h

= 3.14 × 7.4² × 11.4

= 3.14 × 54.76 × 11.4

= 1,960.18896

Approximately to the nearest tenth

= 1,960.2 cubic cm

Therefore, 1,960.2 cubic cm is the volume of the cylinder with radius 7.4 cm and height 12.4 cm

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Let [tex]W[/tex] be the random variable for the winnings from playing the game once.

• There are 4 jacks in the deck, so you draw a jack with probability 4/52 = 1/13. In this case you "win" $1.25 - $1.75 = -$0.50.

• There are 4 queens, with draw probability 4/52 = 1/13 and winnings $3.25 - $1.75 = $1.50.

• There are 4 kings, with draw probability 4/52 = 1/13 and winnings $4.50 - $1.75 = $2.75.

• There are 4 aces, and 3 of these are not of the spade suit, so the probability of drawing any of these is 3/52 and you win $6.50 - $1.75 = $4.75.

• There is only 1 ace of spaces, with draw probability 1/52 and winnings $7.75 - $1.75 = $6.00.

• Adding these up, it follows that the probability of drawing any other card is 1 - (1/13 + 1/13 + 3/52 + 1/52) = 10/13, in which you have the privilege of "winning" -$1.75.

So, the probability mass function for [tex]W[/tex] is

[tex]\mathrm{Pr}(W=w) = \begin{cases} \dfrac1{13} & \text{if } w \in \{-\$0.50, \$1.50, \$2.75\} \\\\ \dfrac3{52} & \text{if } w = \$4.75 \\\\ \dfrac1{52} & \text{if } w = \$6.00 \\\\ \dfrac{10}{13} & \text{if } w = -\$1.75 \\\\ 0 & \text{otherwise} \end{cases}[/tex]

The expected winnings from playing one round of this game are

[tex]\Bbb E[W] = \displaystyle \sum_w w\,\mathrm{Pr}(W=w)[/tex]

[tex]\Bbb E[W] = \dfrac{-\$0.50 + \$1.50 + \$2.75}{13} + \dfrac{3\cdot\$4.75}{52} + \dfrac{\$6.00}{52} + \dfrac{10\cdot(-\$1.75)}{13}[/tex]

[tex]\Bbb E[W] \approx \boxed{-\$0.67}[/tex]

Answer:

-16

Step-by-step explanation:

you just add all of them together

Answer: Option 2

Step-by-step explanation:

Let f(y)=x.

[tex]x=2y+3\\\\x-3=2y\\\\y=\frac{1}{2}x-\frac{3}{2}\\\\f^{-1}(x)=\frac{1}{2}x-\frac{3}{2}[/tex]

The inverse of the function is,

⇒ f ⁻¹(x) = 1/2 (x - 3)

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The function is,

⇒ f (x) = 2x + 3

Now,

We can find the inverse of function as;

⇒ f (x) = 2x + 3

Put y = f (x);

⇒ y = 2x + 3

Solve for x;

⇒ y - 3 = 2x

⇒ x = 1/2 (y - 3)

⇒ f ⁻¹(x) = 1/2 (x - 3)

Thus, The inverse of the function is,

⇒ f ⁻¹(x) = 1/2 (x - 3)

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Hello, the solution of the geometry problem is in this photo.

AOC = 136°

BOC = 44°

The divers in order from least to greatest based on the number of liters left in their oxygen tank will be Alexis, Dante, and Sofia. The correct answer is B.

In mathematics, placing numbers in ascending order refers to doing so from least to largest from left to right. When numbers are arranged in ascending order, they are done so from least to largest.

Given that three divers went scuba diving in the ocean for a couple of hours. The table for the oxygen requirement is given below:-

Diver                         Oxygen (liters)

Alexis                    Seventy nine over eighth

Dante                                9.3

Sofia                      Nine and eight over fifteenth

The Numbers are:-

Alexis  ( Seventy nine over eighth)  = 79 / 9 = 8.78

Dante                                                 = 9.3

Sofia   ( Nine and eight over fifteenth ) = 9(9/15} = 9.6

The arrangement from least to highest will be Alexis, Dante, and Sofia.

The correct options are given below:-

Sofia, Dante, Alexis

Alexis, Dante, and Sofia.

Dante, Alexis, Sofia

Dante, Sofia, Alexis

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Answer:

Dante, Alexis and Sofia

Step-by-step explanation:

please tell me if I'm wrong but I'm positive its Dante, Alexis and Sofia

The spherical coordinate that is converted from the given rectangular coordinate is (12.62, 46.67°, 35.3°).

Here, the given rectangular coordinate is (5, 5.3, 10.3).

Therefore, the value of 'x' is 5, the value of 'y' is 5.3 and the value of 'z' is 10.3.

We can convert the rectangular coordinate (x, y, z) into spherical coordinate (ρ, θ, Φ) by the below mentioned method.

We know, ρ² = (x²+y²+z²)

Therefore, ρ

= √(x²+y²+z²)

= √[(5)²+(5.3)²+(10.3)²]

= √(25+28.09+106.09)

= √(159.18)

= 12.62

Again, tan θ = (y/x)

Therefore, θ = tan⁻¹(y/x) = tan⁻¹(5.3/5) = tan⁻¹(1.06) = 46.67°

Similarly, cos Φ = (z/ρ)

Therefore, Φ = cos⁻¹(z/ρ) = cos⁻¹(10.3/12.62) = cos⁻¹(0.816) = 35.3°

Here, the spherical coordinate is (ρ, θ, Φ).

Therefore, the required spherical coordinate for the given rectangular coordinate is (12.62, 46.67°, 35.3°).

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The diameter of the water molecule is  2 * 10^-4 m or 0.2 mm.

The term microscope refers to a device that is capable of increasing the size of an object. If the object is quite large, then it can be seen with the unaided eye.

Microscopes are very important in the sphere of scientific research as it was very instrumental in the study of cells and in the process of examination of other samples. There are several kinds of microscopes hay could be used for several purposes such as;

Each of these microscopes have a unique instance in which they could be utilized.

Given that the diameter of water is about 2 * 10^-10 m,  a magnification by   1 000 000 times gives a diameter of 2 * 10^-4 m or 0.2 mm.

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At any value of x, Bruce would have always used 3 tiles less than Felicia.

Calculate to explain:

So, there is no solution.

Any value of x, Bruce would have always used 3 tiles less than Felicia.

Therefore, at any value of x, Bruce would have always used 3 tiles less than Felicia.

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The complete question is given below:
Is it possible for Bruce and Felicia to have used the same number of tiles? Use complete sentences to explain your reasoning.

Number of tiles Bruce used: 5x + 2

Number of tiles Felicia used: 5x + 5

Answer:

I forgot the name but I can show you how to do it lol

Step-by-step explanation:

x+5(-2)-1

x-10-1 we multiplied 5 and -2

x-11

x=11

how I did the last one is there is a non-existent 0 with an equal sign like my teacher says  so we added 11 to both sides.

The system of equations that represent this situation is x + y = 52 and x + 2.25y = 72

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

Let x represent the number of pounds of bananas sold and y represent the grapes sold, hence:

x + y = 52   (1)

Also:

x + 2.25y = 72    (2)

The system of equations that represent this situation is x + y = 52 and x + 2.25y = 72

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Answer:

8

Step-by-step explanation:

AB is 3 cm and AC is 2 cm, and since triangle ABC is an isosceles triangle, BC can either be 3 cm or 2 cm. We want the longest perimeter possible, so make BC 3 cm, and add the side lengths to find the perimeter.

P = 3 + 3 + 2 = 8.

The equation of [tex]f(x) = e^{-6x}[/tex] by maclaurin series is [tex]f(x)=\sum_{i=0}^{\infty} \frac{(-6.x)^{i} }{i!}[/tex].

The maclaurin series for f(x) is defined by the following formula:

[tex]f(x) = \sum_{i=0}^{\infty} \frac{f^{(i)} (0)}{i!} .x^{i}[/tex]--------------(1)

Where [tex]f^{i}[/tex] is the i - th derivative of the function

If f(x) = [tex]e^{-6x}[/tex], then the formula of the i - th derivative of the function is:

[tex]f^{i} =(-6)^{i} .e^{-6x}[/tex]----------------------(2)

Then,

[tex]f^{i}(0) = (-6)^{i}[/tex]

Lastly, the equation of the trascendental function by Maclaurin series is: [tex]f(x)=\sum_{i=0}^{\infty} \frac{(-6)^{i}.x^{i} }{i!} \\f(x)=\sum_{i=0}^{\infty} \frac{(-6.x)^{i} }{i!}[/tex]---------------(3)

Hence,

The equation of [tex]f(x) = e^{-6x}[/tex] by maclaurin series is [tex]f(x)=\sum_{i=0}^{\infty} \frac{(-6.x)^{i} }{i!}[/tex].

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Answer:

8

Step-by-step explanation:

You are correct The distance from -6 to 2 is 8.

Answer:

[tex] \frac{29}{18} = 1 \frac{11}{18} [/tex]

Step-by-step explanation:

To solve this question, we definitely need to make w the subject.

[tex]w - \frac{5}{6} = \frac{7}{9} \\ w - \frac{5}{6} + \frac{5}{6} = \frac{7}{9} + \frac{5}{6} \\ w = \frac{29}{18} \\ = 1 \frac{11}{18} [/tex]

Answer:

-2/3

Step-by-step explanation:

A rational number is a number that can be expressed as a fraction so when you add 2 fractions it’s a rational number

Answer:

a variable.

Seven is a number and cannot be a variable.

Slope can be found from two points using the equation [tex]\frac{y_{2}- y_{1}}{x_{2}- x_{1}}[/tex].

Take any two points to substitute in. In this example, I'll use the first two points, (-4, 15), and (-2, 9). Put these into the equation and you'll get

[tex]\frac{(9-15)}{(-2-(-4))}[/tex]. Simplify further to get [tex]\frac{-6}{2}[/tex]. Divide this and you'll get the slope, -3!

hope this helps!

Answer:

-41

Step-by-step explanation:

5(14-23)+8 ÷ 2

=5(-9)+4

=-45+4

=-41

The solution of the given expression 5(14-23)+8 ÷ 2 is -41.

Usually, simplification involves proceeding with the pending operations in the expression.

Example; 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form.

Simplification usually involves making the expression simple and easy to use later.

WE have given an expression as;

5(14-23)+8 ÷ 2

Solve the bracket then division;

=5(-9) + 4

=-45+4

=-41

Therefore, the solution of the given expression is -41.

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Answer:

d

Step-by-step explanation:

up and down is outside of the x stuff so its c or d

and c is moving it up

d is moving it down

Answer:

d)  y = | x | - 2

Step-by-step explanation:

In order to translate a graph downward 2 units ,we subtract 2 from the original function.

therefore,

If the Original function is  y = |x|

Then the Function of the translated graph is  y = | x | - 2

The surface area of the baseball is 176.6 cm² b.

To find the surface area of the baseball:

  r=3.75

[tex]A=4\pi r^{2}[/tex]

[tex]A=4*\pi *3.75^{2}[/tex]

A=176.6 cm² b.

The surface area of the baseball is 176.6 cm² b.

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The area of the region cleaned by the 7-in wiper blade with the angle subtended being 92⁰ as described in the task content is; 39.32in².

According to the task content, it follows that the wiper blade is 7-in long and subtends an angle of 92°.

Consequently, the area swept by the blade in discuss can be determined by the Area of sector formula and hence, is;

Area = (92/360) × (22/7) × 7².

Area = 39.32 in².

Ultimately, it follows from the solving steps above that the area of the region cleaned by the 7-in wiper blade with the angle subtended being, 92⁰ is; Area = 39.32 in².

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Answer:

  (c)  x < -5.170

Step-by-step explanation:

The given function is an exponential function with a decay factor of 0.5 and a y-intercept of 0.5^2 = 0.25. It will be larger for more negative x-values.

We know that 2^3 = 8, so (1/2)^-3 = 8. This means the exponent of 0.5 in the given inequality will be more negative than -3:

  x +2 < -3

  x < -5 . . . . . . . . subtract 2

The only answer choice in this range is ...

  x < -5.170

Taking the logarithm of both sides of the inequality, we have ...

  (x +2)log(0.5) > log(9)

  x +2 < log(9)/log(0.5) . . . . . . log(0.5) < 0, so the inequality reverses

  x < log(9)/log(0.5) -2 . . . . . . subtract 2

  x < (0.95424251)/(-0.30103000) -2 = -3.1699250 -2

  x < -5.1699250 ≈ -5.170

Answer:

Step-by-step explanation:

Miles per hour: [tex]\frac{10miles}{4hrs} = 2.5\frac{miles}{hour}[/tex]

Feet per hour:

      [tex]2.5\frac{miles}{hours} (\frac{5280ft}{1mile} )[/tex]

     [tex]=13,200\frac{ft\\}{hr}[/tex]

Answer:

x ≤ -2

Step-by-step explanation:

3(x + 2) ≤ 5(-2 - x)

Distribute on both sides.

3x + 6 ≤ -10 - 5x

Add 5x to both sides.

8x + 6 ≤ -10

Subtract 6 from both sides.

8x ≤ -16

Divide both sides by 8.

x ≤ -2

Answer:

[tex]\textsf{D. }x\leq-2[/tex]

Step-by-step explanation:

Given inequality: [tex]3(x+2)\leq5(-2-x)[/tex]

Step 1: Distribute [tex]3[/tex] and [tex]5[/tex] through the parentheses.

[tex]\implies 3(x)+3(2)\leq5(-2)+5(-x)[/tex]

[tex]\implies 3x+6\leq-10-5x[/tex]

Step 2: Subtract [tex]6[/tex] from both sides.

[tex]\implies 3x+6-6\leq-10-6-5x[/tex]

[tex]\implies 3x\leq-16-5x[/tex]

Step 3: Add [tex]5x[/tex] to both sides.

[tex]\implies 3x+5x\leq-16-5x+5x[/tex]

[tex]\implies 8x\leq-16[/tex]

Step 4: Divide both sides by [tex]8[/tex].

[tex]\implies \dfrac{8x}{8}\leq\dfrac{-16}{8}[/tex]

[tex]\implies x\leq-2[/tex]

The area of a circle with a circumference that equals the perimeter of the square is 9.62 units².

What is circle ?

the side measurements of the square is 2.75 units.

the perimeter of this square, we must multiply 2.75 by 4 because a square has four equal side measurements.

2.75 × 4 = 11

Let's use the formula for finding radius given the circumference.

[tex]Radius = \frac{circumference}{2\pi }[/tex]

the circumference because our circumference is 11 units.

Radius = [tex]\frac{11}{2pi }[/tex]

put π = 3.14 * 2

radius =  11 / 2 * 3.14

radius = 11/  6.28 ⇒ 1.75

the area of the circle = [tex]\pi r^{2}[/tex]

area = 3.14 * (1.75)²  ⇒9.61325

Lastly, we round this number to the nearest hundredth as it is asked of us in the problem.

9.61325 = 9. 62

Therefore, the area of the circle is 9.62 units².

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