The distance between point [tex](8, \sqrt{17})[/tex] and the center (0,0) is of 9 units, which is less than the radius, hence the correct option is:
Yes, the distance from the origin to the point [tex](8, \sqrt{17})[/tex] is of 9 units.
What is the distance between two points?Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
In this problem, we have a circle with center at (0,0) and radius 10. Hence, every point that is less than 10 units of distance from point (0,0) will be on the circle.
The distance of [tex](8, \sqrt{17})[/tex] is:
[tex]D = \sqrt{(8 - 0)^2+(\sqrt{17} - 0)^2}[/tex]
[tex]D = \sqrt{81}[/tex]
D = 9 units.
9 < 10, hence the correct option is:
Yes, the distance from the origin to the point [tex](8, \sqrt{17})[/tex] is of 9 units.
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sixteen thousand, four hundred eighty-two. Write this number in standard
In a recent year, the population of Springfield, Illinois was one hundred
form. Show your work in the space below. Remember to check your solutic
Answer:
16482 this is the answer
Arrange the Fractions in Descending order
Step-by-step explanation:
How can these fractions be arranged in descending order?Arranging fractions in descending order means arranging the fractions starting from the highest to the lowest.
Finding the LCM of 3, 16, 12, 24,
[tex] \frac{2}{3} \: \frac{5}{16} \frac{7}{12} \frac{11}{24} \\ \\ \frac{32 + 15 + 28 + 22}{48} \\ \\ Arranging \: the \: fractions \: in \: descending \: order \\ \frac{2}{3} \frac{7}{12} \frac{11} {24} \frac{5}{16} [/tex]
Helpppppp show your work
(-3²)-2(-3-4)-(-1³)
=9-2(-7)+1
=9+14+1
=24
Hope it helps!
Answer: look at the picture
Step-by-step explanation:
The probability that a rental car will be stolen is. 4. if 3500 cars are rented, what is the approximate poisson probability that 2 or fewer will be stolen?
Using the Poisson distribution, there is a 0.8335 = 83.35% probability that 2 or fewer will be stolen.
What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
x is the number of successese = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval.The probability that a rental car will be stolen is 0.0004, hence, for 3500 cars, the mean is:
[tex]\mu = 3500 \times 0.0004 = 1.4[/tex]
The probability that 2 or fewer cars will be stolen is:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
In which:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-1.4}1.4^{0}}{(0)!} = 0.2466[/tex]
[tex]P(X = 1) = \frac{e^{-1.4}1.4^{1}}{(1)!} = 0.3452[/tex]
[tex]P(X = 2) = \frac{e^{-1.4}1.4^{2}}{(2)!} = 0.2417[/tex]
Then:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2466 + 0.3452 + 0.2417 = 0.8335[/tex]
0.8335 = 83.35% probability that 2 or fewer will be stolen.
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Please help asap!!
Find the sum for the first 500 terms given the sequence -1,-3,-5,-7.....
Answer: -250000
Step-by-step explanation:
Sum of arithmetic terms = n/2[2a + (n - 1)d],
where 'a' is the first term,
'd' is the common difference between two numbers,
and 'n' is the number of terms.
'a' = -1
'd' = -2
'n' = 500
plug and chug
(500)/2[2(-1) + ((500)-1)*(-2)] =
250[-2 + -998] =
250[-1000] =
-250000
In a certain exam of grade ten, 75% students got high score in mathematics, 65%
students got high score in English. If 6% of them did not get high score in both
mathematics and English, then calculate:
i. the percent of students who got high score in both the subjects.
ii. the total number of students who got high score either in mathematics or
in English if 300 students had attended the exam.
Mathematics, grade 10
(i) The percentage of students who got high scores in both the subjects English and Mathematics is 46%.
(ii) The total number of students who got high scores either in Mathematics or in English if 300 students had attended the exam exists 138.
What is probability?The probability exists in the analysis of the possibilities of happening of an outcome, which exists acquired by the ratio between favorable cases and possible cases.
The number of students who got high scores in Mathematics was 75%.
The number of students who got high scores in English was 65%.
(i) The percentage of students who got high scores in both the subjects
100% - 6% = 94%
(75% + 65%) - 94%
= 140% - 94%
= 46%
Therefore, the percentage of students who got high scores in both the subjects English and Mathematics is 46%.
(ii) The total number of students who got high scores either in Mathematics or in English if 300 students had attended the exam
= 300 [tex]*[/tex] 46%
= 300 [tex]*[/tex] (46 / 100)
= 300 [tex]*[/tex] 0.46
= 138.
Therefore, the total number of students who got high scores either in Mathematics or in English if 300 students had attended the exam exists 138.
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i don’t understand graphs
Answer:
y ≤ 2.5x + 5
Step-by-step explanation:
first step is to obtain the equation of the line in slope- intercept form
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (0, 5) ← 2 points on the line
m = [tex]\frac{5-0}{0-(-2)}[/tex] = [tex]\frac{5}{0+2}[/tex] = [tex]\frac{5}{2}[/tex] = 2.5
the line crosses the y- axis at (0, 5 ) ⇒ c = 5
y = 2.5x + 5 ← equation of line
since the line is solid then inequality will be ≤
the solution to the inequality is the blue region below the line , then
y ≤ 2.5x + 5 ← inequality represented by graph
If NR is parallel to OQ AND OQ = 130m, what is the length of NR?
Answer: 260 m
Step-by-step explanation:
Let's say the length of NR is x m, using the similarity rule, we get the equation
175/130 = (175+175)/x
x = 260
So NR is 260 m
I thought I just had to half the diameter and then put it into the volume formula for cylinders but ig I was wrong? Help please?
Answer:
10830.87 mm³
Step-by-step explanation:
Hello!
Volume of a cylinder: [tex]V = \pi r^2(h)[/tex]
[tex]\pi[/tex] = pir = radius (half diameter)h = heightThe radius for this cylinder is 9.525, after dividing 19.05 by 2.
Plug it into the volume formula to solve for the volume.
Find the Volume[tex]V = \pi r^2(h)[/tex][tex]V = \pi (9.525)^2(38)[/tex][tex]V = \pi (90.725625)(38)[/tex][tex]V = 3447.57375\pi[/tex][tex]V = 1083087236570...\approx10830.87[/tex]The volume is approximately 10830.87 cubic millimeters.
How many ways are ther eto line up the 12 people if the bride must be next to the maid of honor?
the number of ways to line up the 12 people if the bride must be next to the maid of honor is 132 ways.
How to determine the permutationThe formula for finding the number of arrangement is given as;
Permutation = [tex]\frac{n!}{n - r!}[/tex]
Where;
n is the total number of objectr is the number of selected objectsFrom the question given, we can deduce that
n = 12 people
r = 2, because they must come next to each other and is taken as 2
We then have,
Permutation = [tex]\frac{12!}{12 - 2!}[/tex]
Permutation = [tex]\frac{12!}{10!}[/tex]
Permutation = 132 ways
This is to tell us that the number of ways to arrange the people is 132 ways
Thus, the number of ways to line up the 12 people if the bride must be next to the maid of honor is 132 ways.
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Use the quadratic formula to find the solutions to the equation.
3x^2- 10x+ 5 = 0
Answer:
[tex]x =\frac{5}{3} \pm \frac{\sqrt{10}}{3} \\\\x=2.72076\\x=0.612574\\[/tex]
Step-by-step explanation:
The quadratic equation is:
[tex]3x^2 - 10x + 5 = 0[/tex]
The roots (solutions) of a quadratic equation of the form
[tex]a^2 + bx + c = 0\\[/tex]
are
[tex]x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }[/tex]
in this case we have a = 3, b = -10, and c = 5
So, substituting for a, b and c we get
[tex]x = \frac{ -(-10) \pm \sqrt{(-10)^2 - 4(3)(5)}}{ 2(3) }[/tex]
[tex]x = \frac{ 10 \pm \sqrt{100 - 60}}{ 6 }\\[/tex]
[tex]x = \frac{ 10 \pm \sqrt{40}}{ 6 }[/tex]
Simplifying we get
[tex]x = \frac{ 10 \pm 2\sqrt{10}\, }{ 6 }\\\\x = \frac{ 10 }{ 6 } \pm \frac{2\sqrt{10}\, }{ 6 }\\\\x = \frac{ 5}{ 3 } \pm \frac{ \sqrt{10}\, }{ 3 }\\\\\frac{ 5}{ 3 } + \frac{ \sqrt{10}\, }{ 3 } = 2.72076\\\\\\[/tex] (First root/solution)
[tex]\frac{ 5}{ 3 } - \frac{ \sqrt{10}\, }{ 3 } = 0.612574[/tex] (Second root/solution)
Jeremy deposited xxx dollars in his investment account on January 111, 200120012001. The amount of money in the account doubled each year until Jeremy had 480480480 dollars in his investment account on January 111, 200520052005. What is the value of xxx
The value of x is $30.
What is the value of x?From the question, it can be deduced that Jeremy's investment account earns a compound interest. Compound interest is when the amount invested and the interest that has already accrued increases in value anytime interest is paid.
The formula that can be used to determine the value of x is:
x = FV / (1+r)^t
FV = Future value = 480R = interest rate = 100%N = number of years : 2005 - 2001 = 4X = 480 / (2^4) = $30
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A radioactive material has a half life of 10 years. What is the fraction of the initial isotope is left after 60 years
Answer:
1/2^6 = 1/64
Step-by-step explanation:
Half life = 10 years
Time = 60 years
No of half life = T/t
= 60 / 10 = 6
Remaining fraction = 1/2^(no of half life)
= 1/2^6
= 1/64
Find the area of the parallelogram?
A. 13.5
B. 18
C. 16
D. 12
Answer:
12 ft²
D
Step-by-step explanation:
Area of parallelogram = Base × Height
Here, base = 3ft
height = 4ft
So, Area = 3×4 ft² = 12 ft²
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\text{Area of parallelogram is:}[/tex]
[tex]\rm{\bold{b}ase\times\bold{h}eight = \bold{a}rea}[/tex]
[tex]\huge\text{Your equation should look like: }[/tex]
[tex]\rm{3\times4 = \boxed{\bf area}}[/tex]
[tex]\huge\text{Simplify the equation above \& you will have}\\\\\huge\text{the answer to the area of the parallelogram.}[/tex]
[tex]\mathsf{3[base] \times 4[height] = ?[area]}[/tex]
[tex]\huge\text{Simplify it:}[/tex]
[tex]\rm{12\ ft^2}[/tex]
[tex]\huge\text{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{\frak{12\ ft^2}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A cylinder has a radius of 1 inch and height of 1 inch.what is the approximate volume of the cylinder? round to the nearest hundredth. use 3.14 for π.1.05 cubic inches1.57 cubic inches3.14 cubic inches6.28 cubic inches
The volume of the cylinder is [tex]3.14 inch^3[/tex]
Given that
radius = 1 inch
height = inch
we know that volume =[tex]V = \pi \times r^2 \times h[/tex]
now put the value in the above equation we get
[tex]V = 3.14 \times 1 ^2\times 1\\V = 3014inch ^3[/tex]
What is Volume?Volume is a measurement of three-dimensional space that is occupied.Numerous imperial units or SI-derived units, such as the cubic meter and liter, are frequently used to quantify it numerically (such as the gallon, quart, cubic inch).The volume of a container is typically thought of as its capacity, not as the amount of space it takes up. In other words, the volume is the amount of fluid (liquid or gas) that the container may hold.Arithmetic formulas can be used to quickly calculate the volume of several straightforward three-dimensional shapes.If a formula for the shape's boundary is known, it is possible to use integral calculus to determine the volumes of more complex shapes. objects with dimensions of zero, one, and two have no volume;To know more about volume with the given link
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Determine the slope of the line.
Answer:
2
Step-by-step explanation:
→ Find 2 points from the line
( 0 , 6 ) and ( - 3 , 0 )
→ Find the change in y coordinates
0 - 6 = -6
→ Find the change in x coordinates
-3 - 0 = -3
→ Divide the 2 results
-6 ÷ -3 = 2
What is the correct sequence of organs for the formation and elimination of urine?.
The analysis of the kidney exists named urology. The kidney exists as a bean-shaped organ. The Kidney exists metanephric in nature and is located retroperitoneal in position.
What is a kidney?The organ current in the body which regulates the fluid concentration of the body exists named the kidney.
The nephron exists as the structural and operational unit of the kidney.
The sequence of the appearance of the kidney exists as pursues:-
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x^2-15x+54=0 solve for x
Answer: x = 9 and x = 6
Step-by-step explanation:
[tex]x^2-15x+54=0\\(x-9)(x-6)\\x-9=0\\x=9\\x-6=0\\x=6[/tex]
Therefore, x = 9 and x = 6
Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
Answer:
numbers
Step-by-step explanation:
numbers
Find the hourly wage for a person with an income of $44762, who works 54
hours a week for 47 weeks.
Round your answer to 2 decimal places.
Answer:17.64
Step-by-step explanation:44762/54/47= 17.6367 or 17.64
√(2x+1)
Evaluate the integral
2
(2x + 1) In (2x + 1)
dx.
Substitute [tex]y=\ln(2x+1)[/tex] and [tex]dy=\frac2{2x+1}\,dx[/tex], so that
[tex]\displaystyle \int \frac2{(2x+1) \ln(2x+1)} \, dx = \int \frac{dy}y = \ln|y| + C = \boxed{\ln|\ln(2x+1)| + C}[/tex]
solve math problem plsss LOTS OF POINTS
The solution to 0.5^(x + 2) > 9 is x > -5.170
How to solve the inequality expression?The inequality expression is given as:
0.5^(x + 2) > 9
Take the logarithm of both sides of the inequality expression
log(0.5^(x + 2)) > log(9)
Rewrite the inequality expression as
(x + 2)log(0.5) > log(9)
Divide both sides by log(0.5)
x + 2 > -3.170
Subtract 2 from both sides
x > -5.170
Hence, the solution to 0.5^(x + 2) > 9 is x > -5.170
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A small manufacturer constructs refrigerators. the fixed monthly cost is $200,000, and it costs $450 to produce one refrigerator. the average cost function to produce x refrigerators is represented by: what is the horizontal asymptote of c(x)? y =
Horizontal asymptote of c(x) is 450.
What is Horizontal asymptote?A horizontal asymptote is a line that guides the graph of a function for x-values but is not itself a part of the graph. "far," either "far" to the right or "far" to the left. Eventually, whether the graph is large enough or little, it may intersect.
According to the information:Since we have given that
Cost to produce one refrigerator = $450
Fixed monthly cost = $200,000
Thus, the following formula represents the average cost to produce x refrigerators:
C(x) = (200000 + 450x)/x
Horizontal asymptote of c(x) would be
= 450x/x
= 450
Hence, Horizontal asymptote of c(x) is 450
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Graph the equation:
Y = 1/3x + 2
Please help!!
please explain in a way a middle schooler would understand!!
ty!
Justine wants to go to the school dance next week, but only if her friend kelly goes. she asks her mom to go, saying she will complete all her homework on time. her mom says she can go to the dance as long as she completes all her chores for the week. using this situation, describe the concepts of conditional probability and independent and dependent events and how they relate to justine’s situation.
Justine only goes when her friend goes [Conditional probability].
Mom going to PROM and Justine going to PROM are separate events. [Independent events].
Mom can't go until she finishes the housework is dependent on events
independent events. [Dependent events]
What is probability?The probability exists in the analysis of the possibilities of happening of a result, which exists acquired by the ratio between favorable cases and possible cases.
Conditional probability directs to the possibility that some outcome happens given that another possibility contains also occurred.
Justine only goes when her friend goes [Conditional probability]
Independent events exist as those possibilities whose occurrence exists not dependent on any other event.
Mom going to PROM and Justine going to PROM are separate events. [Independent events]
Dependent events exist that depend upon what occurred before.
Mom can't go until she finishes the housework is dependent on events
independent events. [Dependent events]
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A soccer ball is kicked across a field at an angle of 45° with an initial speed of 16m/s.
Determine how long the soccer ball was in the air.
1.94 s
3.89 s
2.16 s
O2.30 s
Answer:
it's C. 2.26s
but you wrote 2.16s nearly
The soccer ball was in the air for approximately 2.31 seconds. Rounding to two decimal places, the answer is approximately 2.30 seconds, option D.
How to determine how long the soccer ball was in the airTo determine how long the soccer ball was in the air, we can use the vertical motion of the ball. When a projectile is launched at an angle, its vertical motion can be analyzed separately from its horizontal motion.
In this case, the initial velocity of the soccer ball can be divided into vertical and horizontal components. The initial velocity in the vertical direction can be calculated using the sine of the launch angle:
Vertical component (Vy) = initial speed (v) * sin(angle)
Vy = 16 m/s * sin(45°)
Vy = 11.31 m/s
Now, we can use the vertical motion equation to find the time the ball spends in the air:
Vertical displacement (y) = Vy * time - (1/2) * gravity * time^2
Since the ball reaches the same vertical position when it lands as when it was launched, the vertical displacement is 0. Therefore, we can set the equation equal to zero:
0 = (11.31 m/s) * time - (1/2) * 9.8 m/s^2 * time^2
Simplifying the equation:
4.9 * time^2 = 11.31 * time
Dividing both sides by time:
4.9 * time = 11.31
time = 11.31 / 4.9
time ≈ 2.31 seconds
Therefore, the soccer ball was in the air for approximately 2.31 seconds. Rounding to two decimal places, the answer is approximately 2.30 seconds, which corresponds to option D.
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The linear density in a rod 5 m long is 10 x + 4 kg/m, where x is measured in meters from one end of the rod. Find the average density ave (in kg/m) of the rod.
The average density of the rod is 0.704 kg/m.
For given question,
We have been given the linear density in a rod 5 m long is 10 / x + 4 kg/m, where x is measured in meters from one end of the rod.
We need to find the
The length of rod is, L = 5 m.
The linear density of rod is, ρ = 10/( x + 4) kg/m
To find the average density we need to integrate the linear density from x₁ = 0 to x₂ = 5,
The expression for the average density is given as,
⇒ ρ'
[tex]=\int\limits^5_0 {\rho} \, dx\\\\=\int\limits^5_0 {\frac{m}{L} } \, dx\\\\=\int\limits^5_0 {\frac{10}{5(x+4)} }\, dx\\\\=\int\limits^5_0 {\frac{2}{x+4} }\, dx[/tex] ......................(1)
Using u = x + 4
du = dx
u₁ = x₁ + 4
u₁ = 0 + 4
u₁ = 4
and
u₂ = x₂ + 4
u₂ = 5 + 4
u₂ = 9
By entering the values above into (1), we have:
⇒ ρ'
[tex]=2\int\limits^9_4 {\frac{1}{u} } \, du\\\\ = 2[(log~u)]_4^{9}\\\\=2[(log~9-log~4)]\\\\=2\times[0.352][/tex]
= 0.704
Thus, we can conclude that the average density of the rod is 0.704 kg/m.
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17. A bag contains 2x yellow counters, 4x + 6 red counters and 6x - 10 blue counters. a. Write an expression, in terms of x, for the total number of counters in the bag.
The total number of counters in the bag is 44.
b. Work out the number of blue counters in the bag.
c. How many more red counters are there than blue counters in the bag?
Answer: 12x-4, 14 counters, 8 more counters
Step-by-step explanation: There are 2x yellow, 4x+6 red, and 6x-10 blue counters. We need to add all of this up to get the total number of counters. We first add the x's : 2x+4x+6x = 12x. Then we add the numbers. 6+ (-10) is -4. So, our expression is 12x-4. Next, we need to find out how many blue counters are in the bag. We know that there are 44 total counters and we need to find x because all the counters have x in them. 12x-4 = 44. We first add 4 to both sides to get 12x= 48 and x = 4. blue has 6x-10 counters so, blue has 24-10 = 14 counters. Red has 16+6 = 22 counters. 22-14 = 8 more counters
Geometry: complete this proof, ASAP!!!!!!!!
Answer:
1. Given
2. Definition of Congruent Angles
3. Triangle Interior Angle Sum Theorem
4. Transitive Property of Equality
5. Substitution Property of Equality
6. Definition of Congruent Angles
help me pls like srsly
The time it will take the thermometer to hit the ground is 22 seconds
Calculating TimeFrom the question, we are to determine the how long it would take the thermometer to hit the ground
From the given information,
The equation for the height as a function of time is
h(t) = -16t² + initial height
From the given information,
The thermometer falls from a weather balloon at a height of 7744 ft
∴ Initial height = 7744 ft
When the thermometer hits the ground, h(t) = 0
Thus, we get
0 = -16t² + 7744
16t² = 7744
t² = 7744/16
t² = 484
t = √484
t = 22 seconds
Hence, the time it will take the thermometer to hit the ground is 22 seconds
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