Mathematics High School

Roman stands across from a flag pole.

What is the distance from Roman's feet to the base of the flag pole?

Round only your final answer to the nearest tenth.

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Answers

Answer 1
The answer is 13.2 m.
Because we are only given the hypotenuse, adjacent, and theta measurements.
the opposite side is always opposite theta. In this case, theta is 39 degrees. The hypotenuse is always the slant of the triangle, so it is 17 m. And adjacent is obviously the only one left, in this case, it is x.

You have to use sin, cos, or tan for this problem. You would use cos because cos = adjacent /hypotenuse (x/17)

so you would do cos(39) times 17
x = cos(39) * 17
x = .777 * 17
x = 13.21 

And it says round to the nearest tenth, so it is 13.2 m.
Hope this helps.

Answer 2

The distance from Roman's feet to the base of the flag pole 13.2 m.

What is Trigonometry?

It is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given:

Angle of elevation= 39.

Hypotenuse = 17 m

Using Trigonometry

cos 39 = adjacent side /hypotenuse

cos 39= base/17

0.777= base/17

base= 0.777*17

base= 13.21m

base= 13.2 m.(rounding off)

Hence, the distance from Roman's feet to the base of the flag pole 13.2 m.

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Related Questions

Please help(:
Two planes intersect to ____ form a line
A. Always
B. Sometimes
C. Never.
D. Inconclusive.

Which of the following is true?
A. All quadrilaterals are polygons with two pairs of parallel sides.
B. All quadrilaterals are polygons with four sides.
C. All quadrilaterals are polygons with at least one pair of parallel sides.
D. All quadrilaterals are polygons with four sides at least one pair of parallel sides.

Answers

Answer

Question 1. ALWAYS
Question 2. B. All quadrilaterals are polygons with four sides.

Explanations

Question 1:
When two planes meet they do so forming a line. This is to mean that the point of intersection is always a line.

Question 2:
It is not necessarily for a polygon to have a pair of parallel sides. A regular pentagon is polygon with no pair of parallel sides. So a quadrilateral is a polygon with four sides. The sides don’t have to parallel for it to be a quadrilateral. The correct answer is B.  

Answer:

1. Two planes intersect to ALWAYS form a line. If two planes intersect, they intersect in a line. The two planes that do not intersect, they form parallel lines.

2. The true statement is :

All quadrilaterals are polygons with four sides. A quadrilateral is a geometrical shape that has four sides and four angles. These are also called polygons. There are many types of quadrilaterals like - the parallelogram, the rectangle, the square, rhombus etc.

What percent of 82.5 is 21.12

Answers

100%/x%=82.5/21.12
(100/x)*x=(82.5/21.21)*x
100=3.90625*x
100/3.90625=x
25.6=x
x=25.6

Thus: 21.12 is 25.6% of 82.50

The 25.6 percentage of the number 82.5 is 21.12

Given data:

To find the percentage of 21.12 in relation to 82.5, the proportion is simplified as:

21.12 is to 82.5 as x is to 100.

This can be expressed as:

21.12/82.5 = x/100

On solving for x by cross multiplying:

21.12 * 100 = 82.5 * x

2112 = 82.5x

To isolate x, divide both sides by 82.5:

2112/82.5 = x

On simplifying:

25.6 ≈ x

Hence, 21.12 is approximately 25.6 percent of 82.5.

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Which coordinate Gird shows the correct locations of P (1,2.5) Point Q which is a reflection Of point P across the Y-axis And R (2.-2.5)

Answers

The first thing we are going to do is define point Q
 "Point Q which is a reflection Of point P across the Y-axis"
 Therefore, we have:
 Q = (-1, 2.5)
 Now we graph each ordered pair.
 Note: See attached image.

Jason draws an angle and then places the compass on the vertex and draws arc that intersects both rays. He then places the compass on each intersecting mark on each ray and draws arcs that intersect inside the angle. Which construction is he creating?

A. copying an angle
B. angle bisector
C. perpendicular bisector
D. perpendicular line through vertex of angle

Answers

the answer for apex wold be .. angle bisector<<<APEX

One inch on a map equals 300 miles. it is 1/4¨ from el paso texas, to bismarck north dakota. how many miles would it be?

Answers

if 1in=300 miles, then 1/4 of an in would be 75miles. because there are four 1/4ths in an inch. 300/4=75

The value of 1/4 inch in miles from the given map is; 75 miles

How do you convert the measurement?

We are given that;

1 inch on the map = 300 miles

Now, we want to find what 1/4 inch will give us in miles from the given conversion. Thus;

1/4 inch in miles = 1/4 * 300

⇒ 75 miles

Thus, we will conclude that 1/4 inch will yield 75 miles on the map.

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Write an equation to represent, "sum of eight and a number is one hundred". What is the number?

Answers

The equation is "8 + x = 100" and the number is "92". You get 92 by subtracting 8 from each side which leaves "x = 92"

Two cones have the same radii but one has a height four times larger than the other. How many small cones would be needed in order to have the same volume as the larger cone?

4


8


16


64

Answers

since the radius is the same but the height changes, the volume would change by the multiple of the height.
 In this case the volume of the larger cone would be 4 times as large as the smaller cone so you would need 4 small cones

Choose the graph that matches the following system of equations:
Explain to me why I got this wrong!!! Please
8x + 5y = −5
7x − 3y = 3 (6 points)

Answers

In intercept form, the equations are
.. x/(-5/8) +y/(-1) = 1
.. x/(3/7) +y/(-1) = 1

The first line has intercepts (-5/8, 0) and (0, -1).
The second line has intercepts (3/7, 0) and (0, -1)

In the second graph, the (blue) line with positive slope has an x-intercept greater than 1/2. Neither line matches that. The intercepts match those of the first graph.

Compare the properties of the diagonals of a kite with those of a square.

Answers

1.Two distinct pairs of adjacent sides are congruent (i. e they have the same angle)
2. Diagonals of a kite intersect at right angles
3. One of the diagonals is the perpendicular bisector of another.

While the square..
1. Diagonals are equal and are perpendicular bisectors of each other

Diagonals of square are congruent  while diagonals of kite are not congruent to each other.

What is diagonal?

" Diagonal is a straight line segment which connects the opposite vertices of any polygon or polyhedron."

Compare the properties of diagonal of square and kite

1) Diagonals of square are congruent while diagonals of kite are not of same length.

2) Diagonals of square bisect each other  while in kite longer diagonals bisects the smaller one.

3) Diagonals of square and kite are perpendicular to each other.

Hence, diagonals of square are congruent  while diagonals of kite are not congruent to each other.

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Find the slope of the line that contains the points named.
X(2, -1), Y(0, 4)
5/2
2/5
-5/2

Answers

[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 2 &,& -1~) % (c,d) &&(~ 0 &,& 4~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{4-(-1)}{0-2}\implies \cfrac{4+1}{0-2}\implies \cfrac{5}{-2}[/tex]
I believe following the slope formula the answer should be -5/2 
if I’m wrong I’m sorry.

PLEASE HELP ME ON THIS AND SHOW UR WORK
THX

Answers

When an exponential function is given as 
f(x)=ab^x, and
knowing that b^0=1, that means that
f(0)=ab^0=a  value of function when x=0, or the initial value.
In the case of
f(x)=20.b^x, f(0)=20.b^0 = 20  (initial value)

If b=1.2, then the hourly growth rate is (1.2-1)=0.2=20%.
If b=1.85, then the hourly growth rate is (1.85-1)=0.85=85%. 

What is the value of x?


20

40

45

85

Answers

2x+10=90
2x=80
x=40
the answer is 40.

Answer:

the answer i 40 hope this helps :)

Step-by-step explanation:

Describe the relationship among the lengths of the segments formed by the secant, , and the tangent segment, .You may use words and/or an equation.

Suppose in. and in. Is it possible to find the length of ? If so, show how to find the length. If not, explain why not.

Answers

Answer: The relationship show in the picture is that TU squared is equal to ST multiplied by RT.

If we know that RT is 9 and ST is 4, we could write the following equation.

Let TU = x

x^2 = 9 x 4
x^2 = 36
x = 6

We found the length of TU to be 6 inches.

We can write the answers as -

TU² = TR x TSTU = 6

What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the equation as -

3√x + 3 = 15

{ 1 } -

When a tangent and a secant are drawn from one single external point to a circle, square of the length of tangent segment must be equal to the product of lengths of whole secant segment and the exterior portion of secant segment. We can write -

TU² = TR x TS

{ 2 } -

We can write -

TU² = TR x TS

TU² = 9 x 4

TU² = 36

TU² = ± 6

TU = 6                         {non - negative}

Therefore, we can write the answers as -

TU² = TR x TSTU = 6

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Batteries for an MP3 player usually cost $8.00, but they are on sale for 40% off. What is the discount amount? What is the sale price for these batteries?

Answers

Let's think. What is 50% of 8.00? It's 4.00. So, 40% would be about 3.20.

Answer:

its b!

Step-by-step explanation:

discount is $8 = 40/100 to find that discout

is $3.20

sale price : $8.00 - $3.20 which is $4.80!

Your welcome! :D

Consider the functions f(x) = (4/5)^x and g(x) = (4/5)^x + 6. What are the ranges of the two functions?

f(x): {y| y > _____}
g(x): {y| y > _____}

(Fill in the blank with the correct answer)

Answers

Answers:
The number 0 goes in the first blank for f(x)
The number 6 goes in the second blank for g(x)

----------------------------------------------------------------------------------

Explanation:

As x gets larger and larger, the expression (4/5)^x will get smaller and smaller. What's going on is that we are repeatedly multiplying (4/5) with itself over and over if we assume x is some whole number. For example, if x = 100, then we'll have 100 copies of (4/5) multiplied out. Each time we multiply by (4/5), the result gets smaller. 

The results will approach 0 but not actually get there. So this is why f(x) has the horizontal asymptote y = 0. The function values f(x) will essentially be the set of positive y values, in other words, y > 0. This covers the range for f(x). To get the range of g(x), we add 6 to the range of f(x). This is because everything on g(x) is a vertical shift upward of 6 units. 

Final answer:

The range of f(x) = (4/5)^x is {y| y > 0}, and the range of g(x) = (4/5)^x + 6 is {y| y > 6}.

Explanation:

The range of a function refers to the set of all possible output values of the function. To determine the range of f(x) = (4/5)^x, we need to consider that any positive real number raised to any power will yield a positive result. Therefore, the range of f(x) is {y | y > 0}.

For g(x) = (4/5)^x + 6, we can see that adding a constant term of 6 to the function will shift the entire graph upwards by 6 units. Consequently, the range of g(x) is {y | y > 6}.

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On the rectangular coordinate system, what is the shortest distance between points (−4, 3) and (−2, −1)?

Answers

Shortest Distance = [tex] \sqrt{ (-4+2)^{2} + (3+1)^{2} } [/tex]
Shortest Distance = [tex] \sqrt{ (-2)^{2} + (4)^{2} } [/tex]
Shortest Distance = [tex] \sqrt{20} [/tex]
Shortest Distance = [tex]4.47 units[/tex]

Answer:

In other words to what the dude above me said, the answer is "a''

Step-by-step explanation:

Given the function f(x) = 0.5(3)x, what is the value of f−1(7)?

This question has been asked before but the answer is unclear to me.

Answers

as you already know, to get the inverse of any expression, we start off by doing a quick switcharoo on the variables, and then solve for "y".

[tex]\bf \stackrel{f(x)}{y}=0.5(3)^x\qquad \stackrel{inverse}{\boxed{x}=0.5(3)^{\boxed{y}}} \\\\\\ log(x)=log[0.5(3)^y]\implies log(x)=log(0.5)+log[(3)^y] \\\\\\ log(x)-log(0.5)=log[(3)^y]\implies log(x)-log(0.5)=y\cdot log(3) \\\\\\ \cfrac{log(x)-log(0.5)}{log(3)}=\stackrel{f^{-1}(x)}{y}\\\\ -------------------------------\\\\ f^{-1}(7)=\cfrac{log(7)-log(0.5)}{log(3)}\implies f^{-1}(7)\approx 2.402173502732879697[/tex]

How to find out how much you pay if there was a sale tax?

Answers

Money time tax owed

what is the value of x that equals 14 y=310-25(x)

Answers

If you want y = 14,
  x = (310 -y)/25 = (310 -14)/25 = 296/25
  x = 11.84

If you want x = 14,
  y = 310 -25*14 = 310 -350
  y = -40

Help Please!!!
A cylindrical pressure vessel has a height of 9 feet and a diameter of 6 feet. How much gas can the pressure vessel hold when full?

I know the answer is 81pi cubic ft

but not sure what formula to use to get that answer. It's not Volume of a cylinder.,

Answers

This is a volume of a cylinder question, so I wonder why you dismiss that. The equation is pi x radius^2 multiplied by height, which indeed comes to 81pi, which is somewhere in the neighborhood of 250 pounds per cubic foot.

Answer:

You would need to use the formula for the volume of cylinder in order to get this. That's how I got to the answer of 81 pi. Maybe you used a different/wrong formula but you do need the formula for the volume of a cylinder.

Two angles that are supplementary have a ratio of 7 to 5. what are their measurements?

Answers

7x + 5x = 180
12x = 180
x = 15
Therefore, the 2 angles equal (7*15) and (5*15) which equals
105 degrees and 75 degrees


Fan for everyone who helps, medal for whoever helps the most! :)

1. What is the sum of the polynomials?
(m + n + 3) + (m + n + 4)

2. Which expression can be used to find the difference of the polynomials?
(10m – 6) – (7m – 4)

3. Which expression can be used to find the difference of the polynomials?
(4m – 5) – (6m – 7 + 2n),

Answers

Answer:

1- The sum is: 2m + 2n + 7 = 2(m+n) + 7

2- The difference is: 3m - 2

3- The difference is: -2m - 2n + 2 = -2(m+n-1)

Explanation:

Before we begin, remember the following:

+ve * +ve = +ve

-ve * -ve = -ve

+ve * -ve = -ve

-ve * +ve = -ve

Also, remember that, we only add/subtract like terms. There are terms which have the same variable(s) raised to the same degree

Now, let's check the problems:

Problem 1:

Adding two polynomials:

(m + n + 3) + (m + n + 4)

We first start by getting rid of the brackets:

m + n + 3 + m + n + 4

Now, we add like terms:

2m + 2n + 7

As an additional step, we can take 2 as a common factor from the first two terms:

2(m+n) + 7

Problem 2:

Subtracting two polynomials:

(10m - 6) - (7m - 4)

We first start by getting rid of the brackets. Take care of the different signs while doing so:

10m - 6 - 7m + 4

Now, we add/subtract like terms:

3m - 2

Problem 3:

Subtracting two polynomials:

(4m - 5) - (6m - 7 + 2n)

We first start by getting rid of the brackets. Take care of the different signs while doing so:

4m - 5 - 6m + 7 - 2n

Now, we add/subtract like terms:

-2m - 2n + 2

As an additional step, we can take -2 as a common factor from the above expression:

-2(m+n-1)

Hope this helps :)

The probability that it'll rain tomorrow in Ohio is 30%
The probability that it'll rain tomorrow in both Ohio and Alaska is 12%
If it rains tomorrow in Ohio what is the probability that it will rain tomorrow in Alaska?

Answers

It raining in Alaska and raining in Ohio are independent events. One does not control the other or affect the other in any way.

For two independent events (let's call them A and B), the Probability of A and B both occurring is given by P(A and B) = P(B) x P(B).

For this problem, let A = rain in Ohio and B= rain in Alaska.

P(A and B) = P(A) x P(B)
[tex] \frac{12}{100} =(P(A))( \frac{3}{10} ) [/tex]
[tex]( \frac{12}{100}) ( \frac{100}{30} )=P(A)[/tex]
[tex]P(A)= \frac{12}{30}= \frac{2}{5} [/tex]

A sphere has a radius of 4x + 1. Which polynomial in standard form best describes the total surface area of the sphere? Use the formula S = 4pir2 for the surface area of a sphere.

Answers

Answer:
area = pi * (64x² + 32x + 4)
Using pi = 3.14:
area = 200.96 x² + 100.48 x + 12.56

Explanation:
We are given that:
area of sphere = 4 * pi * r²
radius = 4x + 1

Substitute with the radius in the given formula to get the area as follows:
area = 4 * pi * (4x+1)²
area = 4 * pi * (16x² + 8x + 1)
area = pi * (64x² + 32x + 4)

Using pi = 3.14:
area = 200.96 x² + 100.48 x + 12.56

Hope this helps :)

Suzy likes to mix and match her 3 necklaces, 2 bracelets, and 6 hats. The colors are listed in the table. On Monday, she randomly picks a bracelet, a necklace, and a hat. What is the probability of Suzy choosing a red bracelet and silver hat? NECKLACE COLORS: RED ,GREEN ,GOLD BRACELET COLORS: RED AND BLACK HAT COLORS: SILVER, YELLOW, GREEN, GOLD, BLACK, AND WHITE A. one-half B. one-fourth C. start fraction 1 over 6 end fraction D. start fraction 1 over 12 end fraction

Answers

Answer: Option D. 1/12

We have:
3 Necklaces (red, green, and gold)
2 Bracelets (red and black)
6 hats (silver, yellow, green, gold, black, and white)

The number total of combinations is:
C=3x2x6→C=36 possible combinations

What is the probability of Suzy choosing a red bracelet and silver hat?
Possible combinations with a red bracelet and silver hat:
C1=1 (red bracelet) x 1 (silver hat) x 3 (necklaces: red, green, and gold)
C1=3 possible combinations with a red bracelet and silver hat

Probability of Suzy choosing a red bracelet and silver hat: P=C1/C
P=3/36

Simplifying the fraction dividing the numerator and the denominator by 3:
P=(3/3) / (36/3)
P=1/12

Answer: The probability of Suzy choosing a red bracelet and silver hat is 1/12

Answer:

The probability of Suzy choosing a red bracelet and silver hat is 1/12

Step-by-step explanation:

Each one of the red, green, and gold necklace have a probability of 1/3.

Each one of the red and black bracelet have a probability of 1/2.

Each one of the silver, yellow, green, gold, black, and white hat have a probability of 1/6.

Hence, the probability of Suzy choosing a red bracelet and silver hat becomes:

[tex]\frac{1}{2}*\frac{1}{6} =\frac{1}{12}[/tex]

So, the answer is 1/12.

is 6km ( <, >, or =) 660m?

Answers

660 Meters is equal to 0.660 KM
6 KM is greater then 660 M
Is 6 km ( <, >, or = ).  660 m

Answer would be:  6 km is LESS THAN  660 m


Explanation:

Each Kilometer is 1000 meters

6 Kilometers is 6000 meters



Hope this helps.

Jim and Gail invested a total of $3,600 in a stock, in a ratio of 5:7. The stock made $6,450 on top of the initial capital. If the payoff is done in the same ratio, how much does Gail get?

Answers

"Since the ratio is 5:7 you can think in total there was 12 equal blocks of money invested. 5 of those blocks belonged to Jim and 7 of those blocks belonged to Gail. Since they invested $3,600 and then made $6,450 in total there is $10,050. Divide that total into 12 equal blocks of $837.50 and 5 of those blocks belong to Jim. So he will get $4,187.50"

The amount that Gail will get is $5862.5.

What is Ratio?

A ratio is a comparison of two quantities produced by dividing the first by the second. If a and b are two values of the same kind and with the same units, and b is not equal to zero, then the quotient a/b is known as the ratio between a and b. The colon sign is used to denote ratios (:). This means that the ratio a/b has no unit and can be expressed as a: b.

Given:

Jim and Gail invested a total of $3,600 in a stock, in a ratio of 5:7.

The stock made $6,450 on top of the initial capital.

Total they made

= 3600+ 6450

= $10, 050

The pay off Jim get

= 10, 050 x 5/12

= 4187.5

and, the pay off Gail  get

= 10, 050 x 7/12

= $5862.5

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please help me please

Answers

Okay. By looking at the question, 2.75 is the distance ran for ½ an hour, because DeAngelo runs at 5.5 miles an hour, but he doesn't run the full 5.5 miles, because of the time. 2.75 is the base. He increases his speed for 1.5 hours for total of 13.25 miles. The equation would be set up as this:

2.75 + 1.5p = 13.25

How to solve it:

We will solve this by subtract 2.75.5 from both sides. 2.75 - 2.75 cancels out. 13.25 - 2.75 is 10.5. We will divide that number by 1.5 now. 1.5p/1.5 cancels out. 10.5/1.5 is 7. There. DeAngelo ran the last 1.5 hours at 7 miles per hour.

Please help

According to Cavalieri's principle,
A) the volume of the sphere is equal to the volume of the cones.
B) the volume of the sphere is equal to the volume of the cylinder.
C) the volume of the sphere is equal to two times the volume of the cones.
D) the volume of the sphere is equal to the volume of the solid between the cones and the cylinder.

Answers

Answer:

Step-by-step explanation:

The answer is d.

Answer:

d

Step-by-step explanation:

What is the sum of the geometric series

Answers

Which one theres many!! :)

Answer:

Hence, the sum of the geometric series is:

                                      259

Step-by-step explanation:

We are given a geometric series as:

[tex]\sum_{i=1}^4 6^{i-1}[/tex]

i.e. we are asked to fnd the sum of first four terms of the geometric series with first term as 1

Since, the series is:

[tex]6^0+6^1+6^2+6^3[/tex]

Also, the common ratio of the series is: r=6

Since, each of the term of the series is 6 times it's preceding term.

Also we know that sum of a finite geometric series with n-terms and common ratio r is calculated by the formula:

[tex]S_n=a(\dfrac{r^n-1}{r-1})[/tex]

Here we have: a=1 and r=6 and n=4

Hence,

[tex]S_4=1(\dfrac{6^4-1}{6-1})\\\\\\S_4=\dfrac{1295}{5}\\\\\\S_4=259[/tex]

                        Hence, the sum of the series is:

                                     259

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Trayvon sells candy bars at a price of $3 each. He purchases every order of 200 candy bars for $350. If the cost of shipping is $0.15 per bar, what is Trayvons profit function? What conditions in the nucleus are likely to result in an atom undergoing radioactive decay?a. When the attraction of the strong force is weaker than the repulsion of the electrostatic forceb. When the repulsion of the strong force is weaker than the repulsion of the electrostatic forcec. When the repulsion of the strong force is greater than the attraction of the electrostatic forced. When the attraction of the strong force is greater than the attraction of the electrostatic force, After the sun exhausts its nuclear fuel, its ultimate fate may be to collapse to a white dwarf state. in this state, it would have approximately the same mass as it has now, but its radius would be equal to the radius of the earth. (a) calculate the average density of the white dwarf. Lexi bought 1 2/5 of green grapes and 2 3/10 of red grapes. Grapes are 2.99 a pound.Did lexi spend more or less then $12? The Pythagorean theorem describes the relationship between the lengths of legs a and b and the hypotenuse c of any right triangle. a 2 + b 2 = c 2 Complete the equation below by writing an expression equivalent to the length of a, the leg of a right triangle. While Joey was standing outside on a sunny day, his shadow was 5 feet long. The shadow of a nearby Oak tree was 12 feet long. If Joey is 6 feet tall, how tall is the Oak tree? A. 15.6 feet B. 14.4 feet C. 10 feet D. 13.4 feet How does the "Elastic clause" make it easier for our government to function? Si no buscas trabajo pronto, ____ que trabajar para tu padre. tendrs tenas What would happen to the speed of sound travelling through water as it freezes and becomes solid? A)The speed of sound should increase as it solidifies. B)The speed of sound should decrease as it solidifies. C)The speed of sound does not change because the chemical is still H2O. D)The speed of sound only changes with temperature. Ice freezes at a constant temperature. radical functions. please help me! Anna and Bill share some money in the ratio 2:5Anna gets ABill gets BCarl and Donna share twice as much money as Anna and Bill share.They share the money in the ratio 3:1Carl gets CDonna gets DFind A:B:C:D in its simplest form A fire fighter has to get to a burning building as quickly as he can. there are three paths that he can take. he can take his fire engine over a large hill (5 miles) at 10 miles per hour. he can take his fire engine through a windy road (7 miles) at 9 miles per hour. or he can drive his fire engine along a dirt road which is 8 miles at 12 miles per hour. Suppose a ball is completely submerged inside a cylinder filled with water displacing some of the water in the cylinder. Assume the ball and the cylinder both have a diameter of 10 centimeters, and the diameter of the ball is the same as the height of the cylinder. Determine the volume of water that can remain in the cylinder after the ball is inserted so that the water rises to the top edge of the cylinder without spilling What experience do you have caring for children? What ages of child have you worked with? What have you observed about the needs, behaviors, and abilities of children at different ages? How do you nurture different kinds of children at different stages of life? Compare your experiences with the rest of the class. Read the stanza. From The Tyger by William Blake Tyger Tyger, burning bright, In the forests of the night; What immortal hand or eye, Could frame thy fearful symmetry? In The Tyger, to what does the fearful symmetry of the tiger refer? When would a researcher be most likely to observe resource partitioning? between two allopatric populations that eat the same thing between two sympatric species that eat similar-sized seeds between two sympatric species, one herbivore and one carnivore between two species, one predator and one prey? Two angles are complementary. If the measure of one angle is twice the measure of the other angle, what is the measure of the larger angle? Tumo worked full-time at a manufacturing plant for the last ten years, but recently, a number of his co-workers were laid off and his schedule was cut back from 40 hours a week to 30 hours. There are rumors that the company is planning to shut down the plant and move its operations out-of-state. Rather than wait to lose his job, Tumo decided to go back to school part-time to train for a new career. Although he enjoys working at the plant, it was never his dream job. Instead, he always wanted to be a veterinarian. He views the recent changes in his life as an opportunity, not a setback, and he feels confident that he can learn the skills necessary to succeed in his chosen field. Which statement about Tumos motivation to go back to college part-time is true? A. Tumo was motivated both intrinsically and extrinsically.B. Tumo was only motivated intrinsically.C. Tumo was not motivated in his decision to go back to school part-time.D. Tumo was only motivated extrinsically.2. Which type of mindset did Tumo exhibit? A. GrowthB. NegativeC. FixedD. Positive 3. Which of the following is NOT a way that Tumo can build resilience after learning that the company he works for might shut down? A. Tumo can maintain a positive and hopeful outlook for the future.B. Tumo can take decisive actions rather than waiting to get fired.C. Tumo can isolate himself.D. Tumo can view this setback as an opportunity to pursue his dream career. The diagram below shows the branching tree diagram for cats.Which characteristic is shared by the greatest number of organisms? To prevent collisions and violations at intersections that have traffic signals, use the _____ to ensure the intersection is clear before you enter it.