4. Find the probability that a randomly chosen point lies inside the shaded region. 4.
Express your answer as a decimal rounded to the nearest hundredth.
Answers
0.167 or 0.17 rounded to the nearest hundredth.
How do you round off decimal to the nearest hundredth?
When rounding to the nearest hundredth, you want to look at the third decimal place, the one to the right of the hundredth place. If the value in the third decimal place is less than 5, you truncate everything to the right of the hundredth place, leaving the number unchanged.
If the value in the third decimal place is greater than or equal to 5, you add one to the number in the hundredth place.
The total area of the rectangle is 15*5 = 75 square feet.
The area of the triangle inside the rectangle is (1/2)25 = 12.5 square feet.
The shaded region is the area of the triangle, so the probability that a randomly chosen point lies inside the shaded region is
12.5/75 = 0.167 or 0.17 rounded to the nearest hundredth.
Hence, 0.167 or 0.17 is rounded to the nearest hundredth.
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Related Questions
Find the value a1
for an arithmetic sequence if the sum of 9 terms is 45 and the last term is 6
A. 4
B. 2
C. 1/4
D. 1/2
Answers
What is the angle between the lines 2x 3y =- Z and 6x =- Y =- 4z?
Answers
90° is the angle between the lines 2x = 3y = -z and 6x = -y = -2z and explained with directions of ratios as below
Direction ratios of line 2x = 3y = -z which can be mentioned as [tex]\frac{x}{1/2} = \frac{y}{1/3} = \frac{z}{-1}[/tex] hence [tex](\frac{1}{2} , \frac{1}{3} ,-1 )[/tex]
Direction ratios of line 6x = -y = -2z which can be mentioned as
[tex]\frac{x}{1/6} = \frac{y}{-1} =\frac{z}{-1/4}[/tex] hence [tex](\frac{1}{6} , -1 , \frac{-1}{4} )[/tex]
hence the dot product of the direction ratio of two line is
[tex]\frac{1}{2} .\frac{1}{6} + \frac{1}{3} . (-1) + (-1) . \frac{-1}{4}[/tex]
= [tex]\frac{1}{12} -\frac{1}{3} + \frac{1}{4}[/tex]
= 0
hence this shows that angle between the given equations is 90°
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3. 2 Roulette wheel: The game of roulette involves spinning a wheel with 38 slots: 18 red, 18 black, and 2
green. A ball is spun onto the wheel and will eventually land in a slot, where each slot has an equal chance
of capturing the ball.
a) You watch a roulette wheel spin 9 consecutive times and the ball lands on a red slot each time. What is
the probability that the ball will land on a red slot on the next spin?
(please round to four decimal places)
b) You watch a roulette wheel spin 320 consecutive times and the ball lands on a red slot each time. What
is the probability that the ball will land on a red slot on the next spin?
x (please
round to four decimal places)
Answers
The probabilities for the game of roulette that involves spinning a wheel with 38 slots, for a and b, are 0.4737, or 18/38, or 47.37%.
The following are the rationales:
(a) The probability of the ball landing on a red slot on any given spin is 18/38, or 0.4737, or 47.37%. This probability does not change based on the outcome of previous spins, as each spin is independent of the others and the probability of landing on a red slot is always the same. So, the probability of the ball landing on a red slot on the next spin is also 18/38, or 0.4737, or 47.37%.(b) The probability of the ball landing on a red slot on any given spin is 18/38, or 0.4737, or 47.37%. This probability does not change based on the outcome of previous spins, as each spin is independent of the others and the probability of landing on a red slot is always the same. So, even though the ball has landed on a red slot 300 consecutive times, the probability of the ball landing on a red slot on the next spin is still 18/38, or 0.4737, or 47.37%Learn more about probability here: brainly.com/question/25839839
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Need answer quick 65 points and brainlyest
Graph using this picture
y+4=25(x−3)
Answers
The linear function y = 25x - 79 is plotted on a graph with x - intercept at 3.16
What is Graph of Linear FunctionA graph of a linear function is a line that goes through the origin (0, 0). The line can be described by the equation y = mx + b, where m is the slope of the line and b is the y-intercept. The slope of the line can be positive, negative, zero, or undefined.
In this problem, the linear function given y + 4 = 25(x - 3) can be written in slope - intercept form and then plotted in a graph using a graphical calculator.
y + 4 = 25(x - 3), the linear function can written;
y + 4 = 25(x - 3) = y + 4 = 25x - 75 ;
This becomes y = 25x - 75 - 4;
Collecting like terms
y = 25x - 79
Plotting this on a graph;
The line passes through the x - axis at 3.16 which is the x - intercept
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Maria believes that she will get a 1 hit in 10% of her softball games, 2 hits in 30% of her games, 3 hits in 55% of her games, and 4 hits in 5% of her games. About how many hits can Maria expect to have each game
Answers
According to the probability or likelihood , Maria can expect 2 hits in the game.
What person founded probability?Blaise Pascal and Pierre de Fermat are recognized as the fathers of probability because they laid the foundation for the field by thinking through a gambling issue posed by Chevalier de Mere in 1654.
[tex]E(X)=x.P(X=x)[/tex]
Given,
[tex]P(X=1)=0.20\\P(X=2)=0.25\\P(X=3)=0.50\\P(X=4)=0.05\\[/tex]
putting in formula,
[tex]E(X) = (1*0.20)+(2*0.25)+(3*0.50)+(4*0.05)=2.4[/tex]
As the number can not be fraction, hence number of hit will be 2.
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How many liters are in a gallon and why
Answers
Answer:
There are 4 liters- in a gallon. Why? Well because for a gallon to be completely filled you need 4 liters, nothing less, and nothing more.
Answer: 3
beacuse 1 gallon is=3 liters easy i dont know why but i learn it in 4 grade
Please help me asap!!
Answers
Answer:
I can’t seem to see it properly
Step-by-step explanation:
At an archeological site, the remains of two ancient step pyramids are congruent . If ABCD cong EFGH find each of the following . (Diagrams are to scale. )
Answers
The measurements are found using congruency.
What does congruency mean?
Congruent refers to things that are exactly the same size and shape. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.
It is given that ABCD ≅ EFGH :
According to congruency,
22. AD = EH, so AD = 335 ft.
23. GH= CD, so GH = 45ft.
24. m∠GHE = m∠CDA, so m∠GHE= 52°
25. m∠BAD= m∠FEH, so m∠BAD= 52°
26. EF= AB, so EF= 45ft
27. BC= FG, so BC= 280ft
28. m∠DCB= m∠HGF, so m∠DCB= 128°
29. m∠EFG= m∠ABC, so m∠EFG= 128°
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hello please help i’ll give brainliest
Answers
Answer:
Papyrus
Step-by-step explanation:
the one that's not right is the 3rd one
Find the surface area, volume, and radius and select all the correct measurements,
Answers
Answer:
surface area ---> i
volume ---> b
radius ---> d
Step-by-step explanation:
surface area= 4πr² =4x3.14x14²=2461.76cm²
volume= (4÷3)πr³= (4÷3)x3.14x14³=11488.21cm³
radius = half the diameter = 14cm
Index form of 2m⁴-3m²+7
Answers
Answer:
2m⁴ +0m³ -3m² +0m +7
Step-by-step explanation:
You want the index form of 2m⁴-3m²+7.
Index formThe index form of a polynomial has terms with all indices present in decreasing order, using 0 coefficients where necessary.
The given polynomial is missing indices 3 and 1, so we add those with coefficients of 0:
2m⁴ +0m³ -3m² +0m +7
Answer the picture pls
Answers
Answer:
The second one!! :)
Step-by-step explanation:
Answer:
2nd one
Step-by-step explanation:
pls mark me a brainliest
The length of the base of an isosceles triangle is x. The length of a leg is 5x -2. The perimeter of the triangle is 106. Find x. X =
Answers
Answer:
x = 10
Step-by-step explanation:
the legs of an isosceles triangle are congruent.
the perimeter is the sum of the 3 sides of the triangle
sum the 3 sides and equate to 106
x + 5x - 2 + 5x - 2 = 106
11x - 4 = 106 ( add 4 to both sides )
11x = 110 ( divide both sides by 11 )
x = 10
Which one of these is correct? Could you explain
Answers
Quadratic Standard Form:
ax²+bx+c=0
Replace = sign with <:
ax²+bx+c<0
So, we want to get 0 on the right side of the inequality to be in standard form.
To do this, we’ll add 18 to both sides:
x²-9x+18<0
This cancels out the -18 on the right, making it 0 because -18+18=0, and of course to keep the equation equal, we must add 18 to the left side as well.
Now, let’s understand the inequality. In standard form, a quadratic is equal to 0 to find the zeros. This is so that we can find what x-values will produce an output (y-value) of 0, as a y-value of 0 means no vertical change. It shows what x-values intercept the x-axis, which are the zeros (or roots) of the quadratic. Therefore, this inequality means: what x-values are less than 0, or go below the x-axis. To find this, we will factor the quadratic to see what x-values produce y-values less than 0.
Factor:
We know that -3-6=-9 and -3•-6=18
(x-3)(x-6)<0
So, the zeros of the function are x=3, 6. However, for x-values 3 and 6, the output is 0 since these values are x-intercepts. The inequality states less than 0, so we need look at x-values that produce a negative output.
So, if x=3, 6, then x>3 and x<6. Let’s look at the graph:
Does 4 8 10 make a right triangle?
Answers
No, 4, 8 and 10 cannot be the sides of a right triangle. So 4, 8 and 10 does not make a right triangle.
In a right triangle, the side opposite the right angle (the hypotenuse) is the longest side. The side opposite the 90-degree angle is the hypotenuse and it follows the Pythagorean theorem which states that the square of the hypotenuse is equal to the sum of the squares of the legs, so:
c² = a² + b²
In this case, c = 10, a = 8 and b = 4,
so 8² + 4² = 64 + 16 = 80 ≠ 10²
That is it does not follows the theorem. Therefore, 4, 8 and 10 cannot be the sides of a right triangle.
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- What is the domain of the function
f(x) = x2 - 6x +1?
Answers
Answer:
(-infinity, +infinity)
Step-by-step explanation:
someone pls help me what is the equation for this graph pls help me and get it right pls :)
Answers
Answer:
y= -1/5x
Step-by-step explanation:
hope this helps :)
HELP PLEASE PLEASE!!!!!!!!
Answers
Answer:
The measure of the third angle is equal to 34°
Step-by-step explanation:
Given that,
The measure of angle 1 is 50°.
The measure of angle 2 is 96°
We need to find the measure of the third angle. We know that the sum of angles of a triangle is equal to 180°. So,
x+50+96=180
x+146=180
x = 180-146
x = 34°
So, the measure of the third angle is equal to 34°.
Select the correct answer. how many particles are in one mole?
a. 6.022 × 1023
b. 2.066 × 1023
c. 6.023 × 1022
d. 3.026 × 1022
Answers
6.022× [tex]10^2^3.[/tex]particles are in one mole.
The correct option is 6.022× [tex]10^2^3.[/tex]
Now, According to the question:
Avogadro's number
Avogadro's number, number of units in one mole of any substance (defined as its molecular weight in grams), equal to 6.02214076 × [tex]10^2^3.[/tex] The units may be electrons, atoms, ions, or molecules, depending on the nature of the substance and the character of the reaction.
Now, According to Avogadro's law, one mole of any substance contains a fixed number of particles i.e.,6.022× [tex]10^2^3.[/tex]particles (atoms, molecules or ions) which is also known by the name Avogadro's number.
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Find the sum of the first 10 terms in this geometric series.
1+3+9+27+...
Answers
Answer:
29524
Step-by-step explanation:
The sum of the first n terms is [tex]S_n=a_1\frac{1-r^n}{1-r}[/tex] where [tex]a_1[/tex] is the first term and r is the common ratio.
For the sequence in this question, [tex]a_1=1,\,r=3[/tex].
[tex]S_10=(1)\frac{1-3^10}{1-3}=\frac{-59048}{-2}=29524[/tex]
50 points!!! and BRAINLIEST IF CORRECT
An investment banker is responsible for investing a customer’s money into the greatest interest earning account. The banker has the following options for his customer’s investment:
Account A:
interest rate = 8%
term of investment = 8 years
interest compounded annually Account B:
interest rate = 7%
term of investment = 10 years
interest compounding continuously
Which account, A or B, will earn the customer the greatest amount of interest on his $50,000 investment? In your final answer, include all of your calculations.
Answers
Answer: account b
Step-by-step explanation:
account A will give 92 thousand dollars
account B will give 100 thousand dollars
I put it in a table
Answer:
SEE ANSWER BELOW
Step-by-step explanation:
A. (formula A=P(1+r/n)^nt
P=50,000(1+.08/1)^nt
P=50,000(1+.08)^nt
P=50,000(1.08)^nt
P=50,000 • 1.85
P=92,546.5
B. (formula A=Pe^rt
P=50,000e7 • 10
P=50,000 • 7
P=50,00 •2 .013
P=100689.64
B saves more
Find the x-intercept and y-intercept
from the following linear equation:
12x + 30y = 180
x - intercept = ()
y - intercept ()_
Answers
Answer:
x - intercept = (15, 0)
y - intercept = (0, 6)
Step-by-step explanation:
x-int. is when y = 0
y-int. is when x=0
Plug in y = 0 and x = 0 to get intercepts.
FOR X-INT.:
12x + 30(0) = 180
12x = 180
x = 15
x-int. is (15, 0)
FOR Y-INT. :
12(0) + 30y = 180
30y = 180
y = 6
y-int. is (0, 6)
write an equation that represents the relationship between x and y shown in the table
Answers
An equation that represents the relationship between x and y shown in the table is y = 1.5x.
How to write an equation?In order to write an equation that represents the relationship between x and y shown in the table, we would have to find the slope from the table and then write the required equation based on the data points by using the point-slope form.
Mathematically, the point-slope form of a line is given by this mathematical equation:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.By substituting the given parameters into the point-slope formula, an equation for the data points contained in this table is given by;
y - y₁ = m(x - x₁)
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 21 = (96 - 21)/(64 - 14)(x - 14)
y - 21 = 75/50(x - 14)
y - 21 = 1.5(x - 14)
y = 1.5x - 21 + 21
y = 1.5x
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How do you draw an acute angled isosceles triangle?
Answers
Answer:
To draw an isosceles acute triangle, the first step is to draw a line segment horizontally which will be the base of the triangle.
Step-by-step explanation:
Now, draw two angles of equal measurements (each should be less than 90 degrees) on both the ends of the line segment. Join the arms of the angles. In this way, we will get an acute isosceles triangle.
Find the new number given the Original number and the percent of change
Answers
Explanation: multiply 120 by the percentage of change which is 0.60 and then you can get the answer
Answer:
72
Step-by-step explanation:
Multiply the original number by 60 and divide it by 100 to find the percent change
120 * 60 / 100 = 72
please help me I only have 2 minutes left winner gets brainliest when did Qin Shi Huang become ruler
Answers
Answer: 221 B.C
Step-by-step explanation:
Answer:
221 B.C.
Step-by-step explanation:
The state of Qin, based in the Sichuan plains, eventually won out in 221 B.C. under the leadership of the ruthless King Zheng. The victorious monarch gave himself the title Qin Shi Huangdi (259–210 B.C.), First Qin Emperor.Jun 3, 2019
What is a dual of a formula?
Answers
The dual formula is a formula which we get when we replace the symbol ∨ by ∧ , ∧ by ∨ , T by F or F by T.
Basically , we can say that it is obtained by replacing tautology by contradiction.
There are certain rules which are to be followed while applying dual formula which are,
Some symbols, example ¬ remains the same while finding dual.If we will find the dual of a dual we will get the original statement.T (tautology) and F (contradiction) are duals of each other.T is changed to F and vice-versa.S1 is a tautology if and only if S2 is a contradiction.
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another oneeee T-T please help
Answers
Answer:
d=90* e=54* f=126*
Step-by-step explanation:
plz crown
Answer:
d = 90
e = 54
f = 126
Step-by-step explanation:
Have a nice day!
A chef at a restaurant uses 13 pounds of butter each day.About how many grams of butter does the chef use each day us 16ounces/1pound 28.4grams/1ounce
Answers
Answer:
5907.2 grams
Step-by-step explanation:
16 x 28.4 x 13 = 5907.2grams
In ΔSTU, = 670 inche, u = 630 inche and ∠U=67°. Find all poible value of ∠S, to the nearet degree
Answers
The measure of ∠S is 59.4° for trignometric identities
What are trigonometric identities?
There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
We have,
ΔSTU:
s = 50 inches
t = 58 inches
u = 630 inches
Applying the cosines rule on ΔSTU.
s² = t² + u² - 2 x t x u x cos S
cos S = (t² + u² - s²) / 2tu
cos S = (58² + 27² - 50²) / (2 x 58 x 27)
cos S = (3364 + 729 - 2500) / 3132
cos S = 0.5086.
∠S = (0.5086)
∠S = 59.4°
Thus,
∠s angle value is 59.4°.
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