someone in a car going past you at the speed of 41 m/s drops a small rock from a height of 1.6 m . How far from the point of the drop will the rock hit the ground? the acceleration due to gravity is 9.8 m/s^2​

The shadow of the person is 6.24 feet long.

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Using the midpoint theorem, the length of AM is 43

From the question, we are to determine the length of AM

From the given information,

Point M is the midpoint of AB

Thus,

From the midpoint theorem

We can write that

AM + MB = AB

AM = MB

AM + AM = AB

2AM = AB

Also, from the given information,

AM = 2x + 9

and

AB = 8x - 50

Therefore,

From 2AM = AB  

2(2x + 9) = 8x - 50

Solve for x

2(2x + 9) = 8x - 50

4x + 18 = 8x - 50

18 + 50 = 8x - 4x

68 = 4x

x = 68/4

x = 17

But,

AM = 2x + 9

Substituting the value of x

Thus,

AM = 2(17) + 9

AM = 34 + 9

AM = 43

This means the length of AM is 43

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The equation of line passing through (-4, -16) and (5, 2) are y = 2x – 8, y - 2 = 2(x - 5) and y + 16 = 2(x + 4)

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

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

The standard form for linear equation is:

y = mx + b

Where m is the slope and b is the y intercept

The equation of line passing through (-4, -16) and (5, 2) is:

y - (-16) = [(2-(-16))/(5-(-4))](x - (-4))

y + 16 = 2(x + 4)

y = 2x - 8

y - 2 = 2(x - 5)

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Exact Form:

11920928955078128/390625

Decimal Form:

30517578125

Answer

The radius of Peter's tire = 13 inches

Explanation

The radius of a circular figure is related to its diameter through

Radius = ½ (Diameter)

Diameter = 26 inches

Radius = ½ (Diameter) = ½ (26) = 13 inches

Hope this Helps!!!

Answer: [tex]\frac{1}{1024}[/tex]

Step-by-step explanation:

[tex]4^{-3} = (2^{2} )^{-3} = 2^{-6}[/tex]

[tex]\frac{2^{-6} }{2^{4} } = 2^{-6-4} = 2^{-10} = \frac{1}{2^{10} } = \frac{1}{1024}[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{4^{-3}}{2^4}}[/tex]

[tex]\mathsf{= \dfrac{\dfrac{1}{64}}{2\times2\times2\times2}}[/tex]

[tex]\mathsf{= \dfrac{\dfrac{1}{64}}{4\times4}}[/tex]

[tex]\mathsf{= \dfrac{\dfrac{1}{64}}{16}}[/tex]

[tex]\mathsf{= \dfrac{1}{1,024}}[/tex]

[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{\dfrac{1}{1,024}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

24

Step-by-step explanation:

Opposite sides on a rectangle are equal

So 2(3x+3)+2(4x)=104

Now expand, so 6x+6+8x=104

Simplify like terms, 14x+6=104

14x+6-6=104-6

14x=98

14x/14=98/14

x=7

Now just substitute the 7 in for the 3x+3 as thats what we are looking for.

3×7+3=24

Answer:

D) 24

Step-by-step explanation:

c + r = 30            Eq. 1

4r + 8c = 144       Eq. 2

r = rectangular tables

c = circular tables

From Eq. 1:

c = 30 - r             Eq. 3

Replacing Eq. 3 in Eq. 2:

4r + 8(30-r) = 144

4r + (8*30 + 8*-r) = 144

4r + 240 - 8r = 144

-4r = 144 - 240

-4r = -96

r = -96/-4

r = 24

from Eq. 3

c = 30 - r

c = 30 - 24

c = 6

Check:

from Eq. 2

4r + 8c = 144

4*24 + 8*6 = 144

96 + 48 = 144

Solution

The bullfdng dataset has its median close to the center of the boxplot.

- This implies that the dataset is symmetric.

- The wolverine dataset has its median moved to the right at 80, implying that it is NOT symmetric.

- However, because there is a skew to the left of datapoints, we say that the dataset is negatively skewed

Final Answer

OPTION A

The domain of the function y = x² - 1 in interval notation is (-∞, + ∞).

The given is y = x² - 1.

The domain of the function is;

Thus, the domain of the function in interval notation is  (-∞, + ∞).

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Using subtraction we get the value as -3 4 8 .

Subtraction is a mathematical operation that mimics the removal of elements from a collection.

The given expression is −2 1 4 + (−1 3 4 )

Simplifying we get : -2 1 4 - 3 1 4

now using subtraction we get : - 3 4 8

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If we take two ordered pairs from the table, we can find the slope with the following equation:

in this case, we can take the points (1,1/2) and (2,1) to get the following using the formula above:

we have that the slope is m = 1/2, and this means that for each 2 gallons of distilled water, Rodnika will add 1 gallon of sea salt

As given by the question

There are given that the function:

Now,

According to the answer to question #1 and the graph of the function:

It is the area under the curve from x = 0 and x = 3;

So,

Some of it is below the x-axis means negative area and some of it is above the x-axis which means positive area.

Then,

Yes, they will cancel out and the integral gives the exact net result.

Explained!

Step-by-step explanation: I hope this helps.

Answer:

When one is testing the null hypothesis that the population proportion equals 45, the. z score is -3.02.

The null and alternative hypothesis is illustrated as the population proportion equals 45,

P0 = 0.45

1 - P0 = 1 - 0.45 = 0.55

Test statistic = z

This will be illustrated as:

= 0.30 - 0.45/ [✓(0.45 * 0.55) / 100]

Test statistic = z = -3.02

Therefore, the z score is -3.02.

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The number of percussionists on the sidelines is 40.

Given:

Total number of members in high school band = 180

Let's assume "x" is the number of percussionists that are on the sidelines.

According to the question, there are two percussionists to every seven marching instruments. Then,

Number of members = 7 + 2 = 9

You can write the following proportion knowing that there are 180 total members of the high school band:

[tex]\frac{x}{180} = \frac{2}{9}[/tex]

Solving the proportion to get the value of x,

[tex]x = \frac{2}{9} * 180[/tex]

x = 40

Therefore, there are 40 percussionists on the sidelines.

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Answer:

Step by step explanation:

The total cost of a purchase is represented by:

Then, since Mr. Mishra bought:

x number of soccer balls and each soccer ball is $30.

5 baseballs and each baseball is $7

Then, the algebraic expression of the purchase is given by:

Answer:

Yes.

Step-by-step explanation:

distance = rate x time

Let r = rate

567 = r6  Divide both sides by 6

94.5 = r  If he was driving at a constant rate the whole time then he was driving at 94.5 miles per hour which is faster than 90

Answer:

(1,5) I think that's what it is

When the expression given as 6 + √27/4 - √3 is simplified, the value is 6 - 1/4√3

The expression is given as

6 + root 27over 4 - root 3

Mathematically, the expression can be represented as

6 + √27/4 - √3

Expand 27 as the product of 9 and 3

So, we have the following equation

6 + √27/4 - √3 = 6 + √(9 * 3)/4 - √3

Expand the products in the above equation

So, we have the following equation

6 + √27/4 - √3 = 6 + √9 * √3/4 - √3

Evaluate the square root of 9 in the above equation

So, we have

6 + √27/4 - √3 = 6 + 3/4√3 - √3

Evaluate the like terms in the above equation

So, we have the following equation

6 + √27/4 - √3 = 6 - 1/4√3

Hence, the value of the expression given as 6 + √27/4 - √3 is 6 - 1/4√3

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Answer:

Derivative of y=(x⁴-2x³+5x²-4)³

Step-by-step explanation:

Answer:

I think 31.72 because it 39156+214186 is 253342 it would be to low

A percentage is a number or ratio that represents a fraction of 100. 

The percentage who want to attend a festival, given that they want to travel out of state is 6.94%.

A percentage is a number or ratio that represents a fraction of 100. 

We have,

                           Attend a concert         Attend a festival

Stay in state                214                            186

Travel out of state       391                             59

The number of groups who wants to attend a concert while staying in a state:

= 214

The number of groups who wants to attend a concert while traveling out of the state:

= 391

The number of groups who wants to attend a festival while staying in a state:

= 186

The number of groups who wants to attend a festival while traveling out of the state:

= 59

The percentage who want to attend a festival, given that they want to travel out of state:

= The number of groups who wants to attend a festival while staying out of the state/ Total number of groups from all four conditions

= 59 / ( 214 + 391 + 186 + 59 ) x 100

= 59 / 850 x 100

= 6.94%

Thus,

The percentage who want to attend a festival, given that they want to travel out of state is 6.94%.

Option A is the correct answer.

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The expression 26+8 as the product of the GCF and a sum is:

2(13+4).

Given we have the expression as 26+8

We need to find the greatest common factor of the numbers 26 and 8.

26 = 2 × 13

8 = 2 × 2 × 2

Multiply all the prime factors that both numbers share in order to determine the GCF:

Therefore, GCF = 2

Now we can write the expression as:

26 + 8

=2(13 + 4)

=2×17

=34

Hence we get the required expression as 2(13 + 4).

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Answer:

Let the required number be ab.

Sum of digits = a + b ........ ( 1 )

10 a + b = 4 ( a + b )

10 a + b + 18 = 10 b + a

=> 9 a + 18 = 9 b

=> a + 2 = b

10 a + a + 2 = 4 ( a + a + 2 )

=> 11 a + 2 = 8 a + 8

=> 3 a = 6

=> a = 3

=> a + 2 = 5

=>ab = 35......... [ A ]

So the number becomes 35.

ANSWER :

The original number is 35.

hope it helps you

• (two-digit number) = 3 + 4(sum of its digits)

• (two-digit number) + 18 = Digit gets reverse

• The number.

-We will first assume the number on one's place be [tex]x[/tex] and ten's place be [tex]y[/tex] [why? because the given conditions are about the digits of number]

-Two-digit number then formed will be 10y + x and its reverse will be 10x + y[why? well let's take an example like a number 42. This number can be written in expanded form as 10×4+2×1 here 4 is number at ten's place (y) and 2 at one's place(x) It's reverse will be 24 it can be written in expanded form as 10×2+4×1 here 2 is number at ten's place (y) and 4 at one's place(x)]

-Then we will use given conditions to form the equation and will solve the equations to get the answer.

So now let's get started with our solution! :D

Let the one's and ten's digit of the number be [tex]x[/tex] and [tex]y[/tex] respectively.

According to first condition,

=> (10y + x) = 3 + 4(x + y)

=> 10y + x = 3 + 4x + 4y

=> 10y - 4y = 3 + 4x - x

=> 6y = 3 + 3x

[tex] \implies \sf \frac{6y}{3} = \frac{3}{3} + \frac{3x}{3} [/tex]

=> 2y - 1 = x ___(equation 1)

According to second condition,

=> (10y + x) + 18 = 10x + y

=> 10y - y + 18 = 10x - x

=> 9y + 18 = 9x

[tex] \implies \sf \frac{9y}{9} + \frac{18}{9} = \frac{9x}{9} [/tex]

=> y + 2 = x ___(equation 2)

Solving equation 1 and 2

y + 2 = x (equation 2)

y + 2 = 2y - 1 [From equation 1]

3 = 2y - y

3 = y (ten's place)

Now put value of y = 3 in equation 2

y + 2 = x (equation 2)

3 + 2 = x

5 = x (one's place)

So, the number formed is 35.

Step-by-step explanation:

a probability is always

desired cases / totally possible cases

a 50% probability means 1/2 or 0.5.

that means

desired cases = 1/2 × totally possible cases

at start we have

3 red

3 white

5 blue

that makes 5 + 3 + 3 = 11 totally possible cases and 3 desired cases.

so, the starting probability to pull a white marble is

3/11.

now, we need to say

(3 + x) = 1/2 × (11 + x) (= (3+x)/(11+x) = 1/2)

to make is simpler we multiply both sides by 2 (so we get rid of the 1/2 fraction).

6 + 2x = 11 + x

6 + x = 11

x = 5

we need to add 5 white marble to give us a 50% probability to pull a white marble.

we have then

3 red

3 + 5 = 8 white

5 blue

that makes 5+8+3 = 16 totally possible cases and 8 desired cases.

so, the probability is

8/16 = 1/2

=> our calculation was correct

The number of white marbles should be added to the bag to make the probability of pulling a white marble 50% will be 5.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

A bag contains 3 red marbles, 3 white marbles, and 5 blue marbles. only white marbles will be added to the bag.

Let 'x' be the number of white marble added. Then the equation is given as,

0.50 = (x + 3) / (x + 3 + 3 + 5)

Simplify the equation, then we have

0.50 = (x + 3) / (x + 3 + 3 + 5)

0.50 = (x + 3) / (x + 11)

0.50x + 5.5 = x + 3

0.50x = 2.5

x = 5

The number of white marbles should be added to the bag to make the probability of pulling a white marble 50% will be 5.

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The mean of the sampling distribution of sample means when 35 random components are tested will be 4.05 years.

From the information, it should be noted that the journalist believes that, in reality, these components have a shorter lifespan than what the company is reporting.

He the tests a random group of 35 of these components and finds a mean lifespan of 4.05 years.

Therefore from the information, we acne see that the. mean lifespan has already been given.

Therefore, the mean lifespan is 4.05 years.

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Simplify the expression.

___________________

...^Here are all three solutions depending on what you are looking for. Hope this helps! If so, please lmk! Thanks and good luck!

We know that Emma has skydived 16 times, and also Emma has skydived twice as many times as Nico, so Nico has skydived:

So, Nico has skydived 8 times.

Finally, we know that Gus has skydived 4 more times than Nico, so:

Gus has skydived 32 times.

Answer: -1/2

Step-by-step explanation:

[tex]\lim_{x \to \pi} \frac{\sin x}{2\sin x \cos x}\\\\=\lim_{x \to \pi} \frac{1}{2\cos x}\\\\=\frac{1}{2\cos \pi}\\\\=-\frac{1}{2}[/tex]

Answer:

[tex]-\frac{1}{2}[/tex]

Step-by-step explanation:

If we try direct substitution we get: [tex]lim_{x\to\pi}h(x)=\frac{sin(\pi)}{sin(2\pi)}[/tex]

The radian [tex]2\pi[/tex] is a full rotation from 0 radians, in other words it's equivalent to 0 radians.

Using the unit circle as a reference you'll remember when the angle is 0 radians, the y-value is zero, so: [tex]sin(2\pi)=0[/tex]

When the angle is: [tex]\pi[/tex] it's at a half rotation where the y-value is still zero on the unit circle.

So you get the indeterminate form of: [tex]\frac{0}{0}[/tex]

We can use L'Hôpital's rule which states: [tex]lim_{x\to c}\frac{f(x)}{g(x)}=lim_{x\to c}\frac{f'(x)}{g'(x)}[/tex] if the original limit is in indeterminate form such as the one above.

Taking the derivative of sin(x) we simply use the property that: [tex]\frac{d}{dx}[sin(x)]=cos(x)[/tex]

For the sin(2x) we can use the chain rule which essentially states: [tex]h(x)=f(g(x))\\h(x)=f'(g(x))*g'(x)[/tex]

It deals with composite equations, and in this case we can represent the composite function as:

[tex]f(x)=sin(g(x))\\g(x)=2x[/tex]

Using the chain rule we get: [tex]cos(2x)*2[/tex]

So now we have the limit: [tex]lim_{x\to \pi}\frac{cos(x)}{2cos(2x)}[/tex]

at pi radians the unit circle is at a half rotation where the x/y coordinates are: [tex](-1, 0)[/tex]

so cos(pi) = -1

at 2 * pi radians were basically back at 0 radians where the x/y coordinates are: [tex](1, 0)[/tex]

so cos(2 * pi) = 1

Now plugging in these values we get the fraction: [tex]\frac{-1}{2*1}[/tex] which just simplifies to: [tex]-\frac{1}{2}[/tex] which turns out to be the limit!