Triangle is an isosceles triangle.
We have to given that;
The vertices of triangle DEF are D(1, 19), E(16, -1), and F(-8, -8).
Now, We know that;
The distance between two points (x₁ , y₁) and (x₂, y₂) is,
⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²
Hence, The distance between two points D(1, 19) and E(16, -1) is,
⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²
⇒ d = √(16 - 1)² + (- 1 - 19)²
⇒ d = √15² + 20²
⇒ d = √225 + 400
⇒ d = √625
⇒ d = 25
And, The distance between two points E(16, -1), and F(-8, -8). is,
⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²
⇒ d = √(16 + 8)² + (- 1 + 8)²
⇒ d = √24² + 7²
⇒ d = √576 + 49
⇒ d = √625
⇒ d = 25
And, The distance between two points D (1, 19), and F(-8, -8). is,
⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²
⇒ d = √(1 + 8)² + (19 + 8)²
⇒ d = √9² + 27²
⇒ d = √81 + 729
⇒ d = √810
⇒ d = 28.1
Hence, Triangle is an isosceles triangle.
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The sum of two odd numbers is 80 and their difference is 6. work out these numbers.
The two odd numbers are 43 and 37.
What are whole numbers?Whole numbers are positive numbers belonging to the set W ∈ {1, 2,3, 4, ...}
The two odd numbers can be represented as (2m-1) and (2n-1) respectively sum=80 and difference = 6
Let m and n be two whole numbers
Therefore
,[tex]2m-1) + (2n-1)= 80\\(2m-1) - (2n-1)= 6\\\\2(m+n-1)=80\\2(m-n)=6\\\\m+n = 41\\m-n=3\\[/tex]
Adding the two equations
[tex](m+n)+(m-n)=2m=44\\m=22\\n=m-3=19\\[/tex]
so m=22 ad n=19. our two odd numbers are 2m-1 = 43 and 2n-1 = 37
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Which of the following are identities? I. y=x II. 4=3x2+2 III. x=x−−√ A. II and III B. I and III C. all D. none
None of the expressions is an identity
How to determine the identities?The expressions are given as:
I. y=x
II. 4 = 3x^2 + 2
III. x=x
In algebra, there are three identities; and they are
(x+y)^2 = x^2 + y^2 + 2xy(x-y)^2 = x^2 + y^2 – 2xyx^2 – y^2 = (x+y) (x-y)None of the given expression take the above forms
Hence, none of the expressions is an identity
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the half life of an element in the periodic table measured over a period of time, t, is modeled by the function f(t)=16(1/2)^t. what is the initial amount of the element
The initial amount of the element is 16
How to determine the initial amount?The function is given as:
f(t) = 16(1/2)^t
Set t = 0, to determine the initial amount
f(0) = 16(1/2)^0
This gives
f(0) = 16 * 1
Evaluate
f(0) = 16
Hence, the initial amount of the element is 16
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Evaluate 5 - 3(a3 – b2)2 when a = 3 and b = 5.
Answer:
Step-by-step explanation:
Evaluate 5 - 3(a3 – b2)2 when a = 3 and b = 5.
5 - 3 × (a³-b²)² a=3 and b=5
5 - 3 × (3³ - 5²)² =
5 - 3 × (27 - 25)² =
5 - 3 × (2)² =
5 - 3 × 4 =
5 - 12 =
-7
Solve the quadratic equation numerically (using tables of x- and y- values). x(x + 6) = 0 a. x = -1 or x = 3 c. x = 0 or x = -3 b. x = 0 or x = 6 d. x =0 or x = -6
Answer:
d. x =0 or x = -6
Step-by-step explanation:
x(x + 6) = 0
This is telling us that either x is 0 or x is -6, because:
1) when x = 0, 0*(0+6)=0, and
2) when x = -6, -6*(-6+6) = 0; -6(0) = 0
A manufacturer produces a commodity where the length of the commodity has approximately normal distribution with a mean of 6.5 inches and standard deviation of 0.5 inches. If a sample of 46 items are chosen at random, what is the probability the sample's mean length is greater than 6.3 inches? Round answer to four decimal places.
The probablity that the sample's mean length is greate than 6.3 inches is0.8446.
Given mean of 6.5 inches,standard deviation of 0.5 inches and sample size of 46.
We have to calculate the probability that the sample's mean length is greater than 6.3 inches is 0.8446.
Probability is the likeliness of happening an event. It lies between 0 and 1.
Probability is the number of items divided by the total number of items.
We have to use z statistic in this question because the sample size is greater than 30.
μ=6.5
σ=0.5
n=46
z=X-μ/σ
where μ is mean and
σ is standard deviation.
First we have to find the p value from 6.3 to 6.5 and then we have to add 0.5 to it to find the required probability.
z=6.3-6.5/0.5
=-0.2/0.5
=-0.4
p value from z table is 0.3446
Probability that the mean length is greater than 6.3inches is 0.3446+0.5=0.8446.
Hence the probability that the mean length is greater than 6.3 inches is 0.8446.
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Use cylindrical or spherical coordinates, whichever seems more appropriate. Evaluate z dV E , where E lies above the paraboloid z
The resulted integral is [tex]I=\frac{8}{3} \times \frac{5 \pi}{16}=\frac{5 \pi}{6}[/tex].
What is integrals?In mathematics, an integral is either a number representing the region under a function's graph for a certain interval or just an added to the initial, the derivative of which is initial function (indefinite integral).
Computation of the integrals:
Step 1: We employ the equations in cylindrical coordinates.
[tex]x=r \cos \theta, y=r \sin \theta, z=z[/tex]
Thus, in cylindrical coordinate system,
E lies above the paraboloid [tex]z=r^{2}[/tex] and below the plane [tex]z=2 r \sin \theta[/tex] .
Therefore, the top part E is [tex]z=2 r \sin \theta[/tex] is the cross-section between paraboloid and the plane.
Now, at the cross-section use, [tex]r^{2}=2 r \sin \theta[/tex] and [tex]z=2 r \sin \theta[/tex] .
Thus, the limits are given as ;
[tex]r^{2} \leq z \leq 2 r \sin \theta \quad 0 \leq r \leq 2 \sin \theta[/tex]
Apply the limits as compute the integration;
[tex]\begin{aligned}I=\iiint_{E} z d V &=\int_{0}^{\pi} \int_{0}^{2 \sin \theta} \int_{\tau^{2}}^{2 r \sin \theta} z r d r d z d \theta \\&=\int_{0}^{\pi} \int_{0}^{2 \sin \theta}\left[\frac{z^{2}}{2}\right]_{r^{2}}^{2 r \sin \theta} r d r d \theta \\&=\frac{1}{2} \int_{0}^{\pi} \int_{0}^{2 \sin \theta}\left[4 r^{2} \sin ^{2} \theta-r^{4}\right] r d r d \theta\end{aligned}[/tex]
[tex]\begin{aligned}&=\frac{1}{2} \int_{0}^{\pi} \int_{0}^{2 \sin \theta}\left[4 r^{3} \sin ^{2} \theta-r^{5}\right] d r d \theta \\&=\frac{1}{2} \int_{0}^{\pi}\left[r^{4} \sin ^{2} \theta-\frac{r^{6}}{6}\right]_{0}^{2 \sin \theta} d \theta \\&=\frac{8}{3} \int_{0}^{\pi} \sin ^{6} \theta d \theta\end{aligned}[/tex]
Step 2: Now, calculate for the [tex]I_{1}=\int_{0}^{\pi} \sin ^{6} \theta d \theta[/tex].
[tex]\begin{aligned}\sin ^{6} \theta &=\left(\sin ^{2} \theta\right)^{2} \times \sin ^{2} \theta \\&=\left[\frac{1-\cos 2 \theta}{2}\right]^{2} \times\left[\frac{1-\cos 2 \theta}{2}\right] \\&=\frac{1}{8}\left(1-2 \cos 2 \theta+\cos ^{2} 2 \theta\right)(1-2 \cos 2 \theta) \\&=\frac{1}{8}\left(1-2 \cos 2 \theta+\frac{1+\cos 4 \theta}{2}\right)(1-2 \cos 2 \theta)\end{aligned}[/tex]
[tex]\begin{aligned}&=\frac{1}{16}(3-4 \cos 2 \theta+\cos 4 \theta)(1-2 \cos 2 \theta) \\&=\frac{1}{32}(10-15 \cos 2 \theta+6 \cos 4 \theta-\cos 6 \theta)\end{aligned}[/tex]
Further compute the value of
[tex]\begin{aligned}I_{1} &=\int_{0}^{\pi} \sin ^{6} \theta d \theta \\&=\frac{1}{32} \int_{0}^{\pi}(10-15 \cos 2 \theta+6 \cos 4 \theta-\cos 6 \theta) d \theta \\&=\frac{1}{32}\left[10 \theta-\frac{15 \sin 2 \theta}{2}+\frac{3 \sin 4 \theta}{2}-\frac{\sin 6 \theta}{6}\right]_{0}^{\pi} \\&=\frac{5 \pi}{16}\end{aligned}[/tex]
Therefore, the obtained integral is [tex]I=\frac{8}{3} \times \frac{5 \pi}{16}=\frac{5 \pi}{6}[/tex].
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The complete question is -
Use cylindrical or spherical coordinates, whichever seems more appropriate. Evaluate ∫∫∫E z dV, where E lies above the paraboloid
z = x² + y²
and below the plane z = 2y. Use either the Table of Integrals or a computer algebra system to evaluate the integral.
A sphere of radius 222 inches is cut by three planes passing through its center. This partitions the solid into 888 equal parts, one of which is shown above. The volume of each part is t\pitπt, pi cubic inches. What is the value of ttt?
The value of t based on the information about the sphere is 1.3π.
How to calculate the value?It should be noted that the volume of a sphere is 4/3πr³. In this case, it's divided into 8 equal parts.
Volume of each part = 1/8 × 4/3πr³
= 1/8 × 4/3 × π × 8
= 4/3π
= 1.3πin³
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2. A high-speed train travels at a speed of 200 km/h. If the train sets off from Station A at 12 24 and reaches Station B at 14 12, find the distance between the two stations, giving your answer in metres.
The distance between the two stations is 360km.
What is speed?Speed is the rate of change of distance.
Rate is a measure of one quantity against another in this case distance and time.
Analysis:
time at station A = 12:24
time at station B = 14:12
time spent = 14:12 - 12:24 = 1 hour 48 minutes = convert 48 minutes to hour
we divide 48 by 60 = 0.8
Total time = 1.8 hours
Distance = speed x time = 200 x 1.8 = 360 km
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which of the following statements would be most similar to an electiral current passing through a metal wire
The correct option is A. hot water moving through a pipe.
Electrical current passing through a metal wire is similar to hot water moving through a pipe.
What is Electrical current?Electrical charge carriers, often electrons or atoms deficient in electrons, travel as current. The capital letter I is a typical way to represent current. The ampere, denoted by the letter A, is the common unit.
The method of flowing of electrical current in metal wire is-
Faraday's Law established that when spinning magnets are close to a coil of wire, a voltage results. With the help of that voltage, you can force electrons through wires, and the moving electrons will travel to their intended locations and do useful tasks. In essence, that is how the electrical grid functions.Comparison of flow of electricity with flow of water in pipe-
Electrical charge (a current) flowing through a wire is comparable to water flowing through a conduit without any bubbles or leaks. The flow of charge is resisted by a resistor, just as the flow of water is resisted by a constriction in a pipe. A circuit's voltage can be compared to a pipe's pressure.To know more about Electric current, here
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The complete question is-
which of the following situations would be mist similar to an electrical current passing through a metal wire in a closed circuit?
A. hot water moving through a pipe
B. an automobile traveling through a tunnel
C. an airplane flying through clouds
D. a flying pan heating up on a hot plate
E. a bird building a nest
A rectangle room has a perimeter of 70m.what would be the length of the longest side of the room?
Answer:
The longest side of room is 24m
Measure the angle shown below. a protractor showing an angle going through the tenth tick mark after ten degrees 15° 17° 20° 22°
The value of the angle will be C. 20°
How to calculate the angle?From the information given, it was stated that the protractor showed an angle going through the tenth tick mark after ten degrees.
This means the value of the angle will be:
= 10° + 10°
= 20°
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Jim jogged from his house to the gym at 15 km/hr. On the trip home on the same route he walked at 10 km/hr. Together the two trips took him two hours. What is the distance from his home to to the gym
The distance from Jim's home to the gym is 12 km.
What is Speed?Speed is defined as the rate at which the position of object is changed.
Speed = Distance / Time
Here, there are two different speeds given for the same distance.
Average speed is the total distance travelled by the total time taken.
If distance is a constant,
Average speed = 2xy / (x + y), where x and y are two different speeds for the same distance.
Average speed = (2 × 15 × 10) / (15 + 10)
= 12 km/hr
So, Total distance travelled = Average speed × total time taken
= 12 × 2
= 24
Distance = 24 / 2 = 12
Hence, the distance from Jim's home to the gym is 12 km when average speed is taken.
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The ________ could be used to describe a data set by itself, while ___________ would almost never be used to describe a data set by itself.
The mean could be used to describe a data set by itself, while interquartile range would almost never be used to describe a data set by itself.
Brief Description of Mean and Interquartile Range
While interquartile range only assesses the middle half of the data, mean and range deal with the entire set of data. The mean is significant in statistics because it helps us determine where a dataset's "center" is. The mean contains information from each observation in a dataset as a result of how it is calculated.
The interquartile range in descriptive statistics reveals the spread of your distribution's middle half. Any distribution that is sorted from low to high is divided into four equal portions using quartiles. The second and third quartiles, or the center half of your data set, are contained in the interquartile range (IQR).
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please help me im stuck on this
Answer:
Step-by-step explanation:
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For which interval(s) is the function increasing and decreasing? y=3x^3 -16x+2
Considering the critical points of the function, we have that:
The function is increasing for |x| > 1.63.The function is decreasing for |x| < 1.63.What are the critical points of a function?The critical points of a function are the values of x for which:
[tex]f^{\prime}(x) = 0[/tex]
In this problem, the function is:
[tex]f(x) = 3x^3 - 16x + 2[/tex]
The derivative is:
[tex]f^{\prime}{x} = 6x^2 - 16[/tex]
The critical points are given as follows:
[tex]6x^2 - 16 = 0[/tex]
[tex]x^2 = \frac{16}{6}[/tex]
[tex]x = \pm \sqrt{\frac{16}{6}}[/tex]
[tex]x = \pm 1.63[/tex]
For x < -1.63, one example of the derivative is:
[tex]f^{\prime}{-2} = 6(-2)^2 - 16 = 8[/tex]
Positive, hence increasing.
For -1.63 < x < 1.63, one example of the derivative is:
[tex]f^{\prime}{0} = 6(0)^2 - 16 = -16[/tex]
Negative, hence decreasing.
For x > 1.63, one example of the derivative is:
[tex]f^{\prime}{2} = 6(2)^2 - 16 = 8[/tex]
Positive, hence increasing.
Hence:
The function is increasing for |x| > 1.63.The function is decreasing for |x| < 1.63.More can be learned about critical points at https://brainly.com/question/2256078
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In the figure below, O is the center of the circle. Name a diameter of the circle.
The diameter of circle O in the image given is: AB.
What is the Diameter of a Circle?The diameter of a circle can be referred to as the largest chord in a circle which is the line segment that passes through the center of a circle with both ends on the circle.
In the image given, AB is the largest chord and also passes through the center of the circle, O.
Thus, the diameter is: AB.
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kathy uses a 1/2 cup of milk with every bowl of her favorite cereal if there are only 3 3/5 cups of milk left, then how many bowls of cereal would kathy have?
Taking a quotient, we will see that she can make 7 bowls of cereal (and some leftover milk).
How many bowls of cereal would kathy have?We know that for each bowl, she needs 1/2 cups of milk.
And we also know that she has a total of (3 + 3/5) cups of milk.
To know how many bowls she can make, we need to take the quotient between the total that she has and the amount that she needs for each bowl:
(3 + 3/5)/(1/2)
We can rewrite the total as:
3 + 3/5 = 15/5 + 3/5 = 18/5
Then the quotient becomes:
(18/5)/(1/2) = (18/5)*2 = 36/5 = 35/5 + 1/5 = 7 + 1/5
So she can make 7 bowls of cereal (and some leftover milk).
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The square of y varies directly as the cube of x. when x = 4, y = 2. which equation can be used to find other combinations of x and y?
The equation can be used to find other combinations of x and y is y^2 = (1/16)x^3
How to determine the equation?The direct variation from the square of y to the cube of x is represented as:
y^2 = kx^3
Where k represents the variation constant.
When x = 4, y = 2.
So, we have:
2^2 = k * 4^3
This gives
4 = 64k
Divide both sides by 64
k = 1/16
Substitute k = 1/16 in y^2 = kx^3
y^2 = (1/16)x^3
Hence, the equation can be used to find other combinations of x and y is y^2 = (1/16)x^3
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Celia uses the steps below to solve the equation Negative StartFraction 3 over 8 EndFraction (negative 8 minus 16 d) + 2 d = 24.
Step 1 Distribute Negative StartFraction 3 over 8 EndFraction over the expression in parentheses.
3 minus 16 d + 2 d = 24
Step 2 Simplify like terms.
3 minus 14 d = 24
Step 3 Subtract 3 from both sides of the equation.
Negative 14 d = 21
Step 4 Divide both sides of the equation by –14.
d = StartFraction 21 over negative 14 EndFraction = Negative three-halves = negative 1 and one-half
Which corrects the error in the step in which Celia made the first error?
In step 1, she should have also distributed Negative StartFraction 3 over 8 EndFraction over 2d, to get 3 minus 16 d + (negative three-fourths d) = 24.
In step 1, she should have also distributed Negative StartFraction 3 over 8 EndFraction over –16d, to get 3 + 6 d + 2 d = 24.
In step 3, she should have added 3 to both sides of the equation to get Negative 14 d = 27.
In step 3, she should have first divided both sides by –14 to get 3 + d = 24
The error in the steps is that In step 1, she should have also distributed -3/8 over –16d, to get 3 + 6 d + 2 d = 24
Simplifying linear equationsGiven the following equation as shown below
-3/8(-8-16d)+2d = 24
Step 1 Distribute -3/8 over the expression in parentheses
3 + 6d + 2d = 24
Simply the like terms
3 + 8d = 24
Subtract 3 from both sides of the equation.
8d = 24 - 3
8d = 21
d = 21/8
Hence the error in the steps is that In step 1, she should have also distributed -3/8 over –16d, to get 3 + 6 d + 2 d = 24
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On a coordinate plane, a curved line with a minimum value of (negative 2.5, negative 12) and a maximum value of (0, negative 3) crosses the x-axis at (negative 4, 0) and crosses the y-axis at (0, negative 3).
Which statement is true about the graphed function?
F(x) < 0 over the interval (–∞, –4)
F(x) < 0 over the interval (–∞, –3)
F(x) > 0 over the interval (–∞, –3)
F(x) > 0 over the interval (–∞, –4)
The points on the graph of (-4, 0), (-2.5, -12), and (0, -3), gives;
F(x) > 0 over the interval (-∞, -4)Which method can be used to find the true statement?From the description of the graph, we have;
Furthest point left of the graph = (-4, 0)
The furthest point right on the graph = (0, -3) = The maximum point
The minimum point = (-2.5, -12)
F(x) < 0 at the minimum point
The minimum point is to the right of x = -4
The point the graph crosses the y-axis = (0, -3)
Therefore;
The interval of the graph where F(x) is larger than 0 is to the left of (-4, 0), is the interval (-∞, -4)
The true statement is therefore;
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PLEASE HELP I HAVE AN HOUR LEFT!!
Which statement correctly identifies an asymptote of g (x) = StartFraction 42 x cubed minus 15 Over 7 x cubed minus 4 x squared minus 3 EndFraction using limits?
Limit of g (x) as x approaches plus-or-minus infinity= 5, so g(x) has an asymptote at x = 5.
Limit of g (x) as x approaches plus-or-minus infinity= 6, so g(x) has an asymptote at x = 6.
Limit of g (x) as x approaches plus-or-minus infinity= 5, so g(x) has an asymptote at y = 5.
Limit of g (x) as x approaches plus-or-minus infinity = 6, so g(x) has an asymptote at y = 6.
The statement that correctly describes the horizontal asymptote of g(x) is:
Limit of g (x) as x approaches plus-or-minus infinity = 6, so g(x) has an asymptote at y = 6.
What are the asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.The horizontal asymptote is the limit of f(x) as x goes to infinity, as long as this value is different of infinity.In this problem, the function is:
[tex]g(x) = \frac{42x^3 - 15}{7x^3 - 4x^2 - 3}[/tex]
The horizontal asymptote is given as follows:
[tex]y = \lim_{x \rightarrow \infty} g(x) = \lim_{x \rightarrow \infty} \frac{42x^3 - 15}{7x^3 - 4x^2 - 3} = \lim_{x \rightarrow \infty} \frac{42x^3}{7x^3} = \lim_{x \rightarrow \infty} 6 = 6[/tex]
Hence the correct statement is:
Limit of g (x) as x approaches plus-or-minus infinity = 6, so g(x) has an asymptote at y = 6.
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By use of technology, we investigated Mary’s investment and created the model, M(x) = 3.03(1.28)2x, in thousands of dollars. What was Mary’s initial investment? $4.96 $3,030 $4,960 $3.03
Using an exponential function, it is found that Mary's initial investment was of $3,030.
What is an exponential function?An exponential function is modeled by:
[tex]y = ab^x[/tex].
In which:
a is the initial value.b is the rate of change.Her investment model, in thousands of dollars, is:
[tex]M(x) = 3.03(1.28)^{2x}[/tex]
Then a = 3.03, since we measure the amount in thousands of dollars, Mary's initial investment was of $3,030.
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The roots of the equation (p+2)x^2-2px=5-p are complex; find the range of values of p
Range of values of the variable p is [tex]0\leq p\leq \frac{10}{3}[/tex]
Step-by-step explanation:
From general quadratic equation [tex]ax^{2} +bx+c[/tex], for imaginary case-
[tex]D\leq 0\\b^2-4ac\leq 0[/tex]
In given question, [tex]a= p+2[/tex], [tex]b=2p[/tex], [tex]c= 5-p[/tex]
using above condition-
[tex]b^2-4ac = 4p^2-4(2p)(5-p)\leq 0\\4p^2 - 40p+8p^2\leq 0\\12p^2-40p\leq 0\\4p(3p-10)\leq 0[/tex]
Here, [tex]4p\leq 0, p\leq 0[/tex]
and
[tex]3p-10\leq 0\\p\leq \frac{10}{3}[/tex]
Therefore, range of values of the variable p is [tex]0\leq p\leq \frac{10}{3}[/tex].
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Choose the correct simplification of the expression ( expression in photo! )
A. G^7h
B. G^3h
C. G^7h^7
D. G^3/h^7
Use the rules of exponents to simplify the expression.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{g^{5}h^{4} }{g^{2}h^{3} } \end{gathered}$}[/tex]
To divide powers with the same base, subtract the exponent in the denominator from the exponent in the numerator.
[tex]\large\displaystyle\text{$\begin{gathered}\sf g^{5-2}h^{4-3} \end{gathered}$}[/tex]Subtract 2 from 5.
[tex]\large\displaystyle\text{$\begin{gathered}\sf g^{3 }h^{3-2} \end{gathered}$}[/tex]Subtract 3 from 4.
[tex]\large\displaystyle\text{$\begin{gathered}\sf g^{3 }h^{1} \end{gathered}$}[/tex]For any term t, t¹ =t.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf g^{3}h \end{gathered}$} }[/tex]Therefore, the correct option is "B".
The width of a rectangle is 4 less than twice its length. if the area of the rectangle is 75 cm 2 , what is the length of the diagonal?
Answer:
Step-by-step explanation:
A house is octagon-shaped, and each side measures 22 feet long. How many lineal feet of exterior wall does this house have
Length of each side is 176 feet ² .
What is octagon ?A polygon of eight angles and eight sides.It has eight lines of reflective symmetry and rotational symmetry of order 8. A regular octagon is represented by the Schläfli symbol {8}. The internal angle at each vertex of a regular octagon is 135° ( radians). The central angle is 45° ( radians).each side of house = 22 feet long
Perimeter of octagon = 8 × sides
Length of each side of house = 8 × 22 ⇒ 176 feet²
Therefore, length of each side is 176 feet ² .
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A rectangular gate measures 1.2 m by 2.3 m with a 2.4 m diagonal. Is the gate
square? If not, should the diagonal be longer or shorter?
Of the last 16 people at a carnival booth, 6 won a prize. what is the experimental probability that the next person at the booth will win a prize? write your answer as a fraction or whole number. p(win)
The experimental probability that the subsequent booth competitor will receive a reward is 3/8.
Probability calculationThe possibility of an event occurring is determined by probability.
The probability of the occurrence ranges from 0 to 1.
If the event doesn't happen, it = 0;
otherwise, it = 1.
For instance, the likelihood that it will storm on Sunday ranges from 0 to 1. If it storms, the event is given a value of 1. If it doesn't, the event is given a value of zero.
Depending on the outcome of a study that has been run several times, the experimental probability is calculated.
The number of winners in the games divided by the total number of competitors in those games determines the probability that the following competitor will earn a reward.
So, here the probability = 6/16 = 3/8 (by dividing both the numerator and the denominator by 2).
Therefore, the final solution is P= 3/8 .
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In a group of 55 people, 3x+5 people like banana and x+5 people like apple. If all the people who like apple also like banana and if 2x+15 people like at least one of fruit then find how many like
(i) bananas only,
(ii) none of the fruits
(iii) at most one fruit
also show subset
i. The number of people who like banana only is 20.
ii. The number of people who like none of the fruits is zero.
iii. The number of people who like at most one fruit is 30.
The question has to do with sets.
What is a set?A set a collection of well ordered items
i. How to find how many people like banana only.Since we have 55 people, 3x + 5 people like banana and x + 5 people like apple. If all the people who like apple also like banana and if 2x + 15 people like at least one of fruit then, we have that
3x + 5 + x + 5 + 2x + 15 = 55
3x + 2x + x + 5 + 5 + 15 = 55
6x + 30 = 55
6x = 55 - 25
6x = 30
x = 30/6
x = 5
Since the number of people who like banana only is 3x + 5.
So, number of people who like banana only is n = 3x + 5
= 3(5) + 5
= 15 + 5
= 20
So, the number of people who like banana only is 20.
ii. The number of people who none of the fruits.Since from the question, a person likes at least one fruit, either banana, apple or both. No one likes none of the fruits.
So, the number of people who like none of the fruits is zero.
iii. The number of people who like at most one fruit?To like at most one fruit, the person either likes apple or banana.
So, their sum is n = 3x + 5 + x + 5
= 4x + 10.
Since x = 5, we have n = 4x + 10.
= 4(5) + 10
= 20 + 10
= 30
So, the number of people who like at most one fruit is 30.
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