The probability of an event can not be more than the number 1.
The probability of success is 1/4.The probability of failure is 3/4.What is probability?Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.
As the probability of an event can not be more than the number 1.
Thus the probability of failure of a event is equal to the difference of the 1 to the success of the event. As,
[tex]Probability[/tex] [tex]of[/tex] [tex]faliure=1-[/tex] [tex]Probability[/tex] [tex]of[/tex] [tex]success[/tex]
Given information-Rina spins the spinner less than the 30 times.
A success occurs when the spinner lands on a number that is greater than 6.
A spinner is divided into 8 equals sections and the sections are labeled 1 through 8.
As the probability of success occurs when the spinner lands on a number that is greater than 6, thus the number should grater than six.
This number should be less than 30 as the spinner spins less than the 30 times.
Thus the total number of outcome of this event is,
[tex]=30-6[/tex]
[tex]=24[/tex]
Thus the probability of success is,
[tex]P=\frac{6}{24}[/tex]
[tex]P=\frac{1}{4}[/tex]
Hence the probability of success is 1/4.
As the probability of failure of a event is equal to the difference of the 1 to the success of the event.
Thus the probability of failure is,
[tex]P^-=1-P[/tex]
[tex]P^-=1-\frac{1}{4}[/tex]
[tex]P^-=\frac{4-1}{4}[/tex]
[tex]P^-=\frac{3}{4}[/tex]
The probability of failure is 3/4.
Hence,
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The table below shows some inputs and outputs of function f(x). _1 0 2 4 8 f(a) 1 5 13 21 37 Which statement best describes the function? O f(x) is a linear function because z and f(z) are both increasing. O f(2) is an absolute value function because 2 and f(a) are both increasing. O f(z) is a linear function because f(z) is increasing by 4 for each increase in z by 1.
A statement which best describes the function include the following: A. f(x) is a linear function because x and f(x) are both increasing.
What is a linear function?In Mathematics, a linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate. This ultimately implies that, a linear function has the same slope and it is typically used for uniquely mapping an input variable to an output variable, which both increases simultaneously.
Next, we would determine the slope by using the points contained in the table as follows;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (5 - 1)/(0 + 1)
Slope (m) = 4.
Slope (m) = (13 - 5)/(2 - 0)
Slope (m) = 4
Slope (m) = (21 - 13)/(4-2)
Slope (m) = 8/2 = 4.
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2. A container holds 5 red pens, 4 purple pens and 3 blue pens. Find the
probability P(red pen, purple pen) without replacement. (use the simplest
fraction)
The probability P(red pen, purple pen) without replacement is 10/33.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given that a container holds 5 red pens, 4 purple pens and 3 blue pens.
We need to find the probability P(red pen, purple pen) without replacement.
P(red pen, purple pen) = (number of ways to select a red pen and a purple pen) / (total number of ways to select two pens)
Total number of ways to select two pens=¹²C₂=66 ways.
Number of ways to select a red pen and a purple pen = (number of ways to select a red pen) x (number of ways to select a purple pen from the remaining pens)
Number of ways to select a red pen = 5
Number of ways to select a purple pen from the remaining pens = 4
Therefore, the number of ways to select a red pen and a purple pen without replacement is:
Number of ways to select a red pen and a purple pen = 5 x 4 = 20
P(red pen, purple pen) =20/66
=10/33
Hence, the probability P(red pen, purple pen) without replacement is 10/33.
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Find the y-Intercept and x-intercept of the line.
5x - 2y = 10
The x-intercept and the y-intercept of the line 5x - 2y = 10 include the following ordered pairs:
x-intercept = (2, 0).
y-intercept = (0, -5).
What is the x-intercept?In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).
What is y-intercept?In Mathematics, the y-intercept is sometimes referred to as an initial value (base value) and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).
In this exercise, we would use an online graphing calculator to plot the linear function in order to determine the x-intercepts and y-intercepts as shown in the image attached below.
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If the numerator of a fraction is multiplied by 4 and the denominator is reduced by 2,the result is 4 . If the numerator of the fraction is increased by 15 and 2 subtracted from the double of the denominator, the result is 5/4. Find the fraction.
The original fraction described in the question is; 25/31
How to simplify fractions?Let the numerator be x and let the denominator be y.
We are told that the numerator of a fraction is multiplied by 4 and the denominator is reduced by 2,the result is 4. Thus;
4x/(y - 2) = 4
4x = 4y - 8
4x - 4y = -8 -----(1)
The numerator of the fraction is increased by 15 and 2 subtracted from the double of the denominator, the result is 5/4. Thus;
(x + 15)/(2y - 2) = 5/4
4x + 60 = 10y - 10
4x - 10y = - 70 ----(2)
Subtract eq 2 from eq 1 to get;
6y = 62
y = 31/3
Thus;
4x - 4(31/3) = -8
Multiply through by 3 to get;
12x - 124 = -24
12x = 100
x = 25/3
Thus, the fraction is;
(25/3)/(31/3) = 25/31
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Which shape has two pairs of parallel sides
The shape with two pairs of parallel sides is called a parallelogram.
What is a paralellogram?A parallelogram is a shape that has four sides, in which the two opposite lengths are:
Parallel to each other.Have the same measure.As there are four sides, divided two by two, the shape has two pairs of parallel sides, and is called a parallelogram.
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Can somebody help me on this? I answered all of them on the right side but I don’t know if it’s right. The answer choices are- additive property of angle measure / additive property of length / all right angles are congruent / alternate interior angles theorem / angle side angle / definition of angle bisector/ definition of equilateral triangle / definition of midpoint / given/ and reflexive property of congruence. I know this a lot but that is all the answer choices.
The completed two-column table that proves ΔQTU is congruent to ΔRSU can be presented as follows;
Statement [tex]{}[/tex] Reasons
1. [tex]\overline{RS}[/tex] ⊥ [tex]\overline{RT}[/tex] [tex]{}[/tex] Given
2. [tex]\overline{QT}[/tex] ⊥ [tex]\overline{QS}[/tex] [tex]{}[/tex] Given
3. [tex]\overline{QU}[/tex] ≅ [tex]\overline{RU}[/tex] [tex]{}[/tex] Given
4. ∠Q ≅ ∠R [tex]{}[/tex] All 90° angle are congruent
5. ∠QUT ≅ ∠RUS [tex]{}[/tex] Vertical Angle Theorem
6. ΔQTU ≅ ΔRSU [tex]{}[/tex] ASA
What are congruent triangles?Congruent triangles are triangles that have the same size and shape.
The details of the reasons that are used to prove that the triangles ΔQTU and ΔRSU are congruent, can be presented as follows;
All 90° angle are congruent
The segments [tex]\overline{RS}[/tex] and [tex]\overline{RT}[/tex] are perpendicular, which indicates that the angle ∠R is a 90° angle. Similarly, segments [tex]\overline{QT}[/tex] and [tex]\overline{QS}[/tex] are perpendicular, therefore, ∠Q is a 90° angle, which indicates that we get;
m∠Q = m∠R = 90°
The definition of congruent angles, indicates; ∠Q ≅ ∠R
Vertical Angle Theorem
The vertical angle theorem states that the vertical angles formed by two intersecting lines are congruent.
ASA
The Angle-Side-Angle, (which can be abbreviated as ASA) congruence postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
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An architect is drawing a floor plan for the basement of a house. He has drawn the
plans as shown. On the plan, 1/4 inch represents 4 feet in length in the house.
What is the area of the basement?
The area of the basement will be 576 square feet.
What is an area?The area is defined as the space covered by the object in a two-dimensional plane. The area of the rectangle is calculated by the multiplication of the length and the width.
Given that a basement floor plan for a house is being created by an architect. He drew the plans as they are seen. On the plan, one-fourth of an inch corresponds to four feet in the house.
The area of the basement will be calculated as:-
Area = 12 x 6
Area = 72 square inches
Area = 72 x 8 feet
Area = 576 square feet
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what is the answer to this?
Answer:
Step-by-step explanation:
If I see this correctly it would be about 16 minutes he played football.
What are the outliers in this data set?
26, 51, 53, 57, 57, 62, 65, 71, 93
Select EACH correct answer.
Answer:
What are the outliers in this data set?
26, 51, 53, 57, 57, 62, 65, 71, 93
Select EACH correct answer.
26, 71, 93Step-by-step explanation:
Tell me if I'm wrong, You're welcome.
What is -8/9 divided 2/3??
Answer:
-1.33333333333
Step-by-step explanation:
Answer:
-1 1/3
Step-by-step explanation:
pls help me on all questions if you can
All the answers to the questions except which are impossible are illustrated below.
What is a polygon?A polygon is a closed more than two-sided and can be made up of a finite number of straight line segments and is a type of planar figure in geometry.
Each line of the polygonal circuit's segments are referred to as its edges or sides.
9. We know, The sum of all the interior angles of a 'n' sided polygon is,
= 180(n - 2).
= 180(10 - 2).
= 180×8.
= 1440°.
11. 180(n - 2) = 1260.
180n - 360 = 1260.
180n = 1620.
n = 9.
13. Mesure of exterior angles is,
= 360/n.
= 360/5.
= 72°.
14. 360/60 = 6 sides, As EA = 360/n, n = 360/EA.
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Claire goes to the gym every 4 days and the
park every 6 days. If she does both today,
how many days will pass until the next time
she goes to the gym and park on the same
day?
GCF or LCM? (circle one)
Required, after 12 days Claire will have the day where she has gone to the gym and the park an equal number of times.
What is the least common multiple (LCM)?The least common multiple (LCM) of two numbers represents the smallest multiple that is divisible by both numbers.
Here,
In this case, the LCM of 4 and 6 is 12, which is the smallest number that is divisible by both 4 and 6. This means that after 12 days, Claire will have gone to the gym and the park an equal number of times, and will thus be back at the same point. Therefore, the answer is LCM.
Thus, the required, after 12 days Claire will have the day where she has gone to the gym and the park an equal number of times.
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You can work at most 20 hours next week. You need to earn at least $90 to cover
you weekly expenses. Your dog-walking job pays $7.50 per hour and your job as a
car wash attendant pays $6 per hour. Write and graph a system of linear
inequalities to model the situation. Use the graph to list 3 solutions
The system of inequalities is.
x + y ≤ 20
x*7.5 + y*6 ≥ 90
And some solutions can be:
(10, 5)
(11, 5)
(12, 6)
How to write the system of inequalities?Let's define the variables we will be using:
x = number of hours dog-waling
y = number of hours at the car wash.
We know that you can work at most 20 hours, then:
x + y ≥ 20
And you need toearn at least $90, then wecan write:
x*7.5 + y*6 ≥ 90
The system of inequlities is:
x + y ≤ 20
x*7.5 + y*6 ≥ 90
And the graph is the one below. The solutions are all the points in the dark blue region, some solutions we can see there are:
(10, 5)
(11, 5)
(12, 6)
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What is the cube root of 12 167?
From the given information provided, the cube root of 12,167 by prime factorization method is approximately 23.
You can find the cube root of 12,167 using a calculator or by using the prime factorization method.
Using the prime factorization method, we can express 12,167 as the product of its prime factors:
12,167 = 19 × 641
Since the cube root of a product is equal to the product of the cube roots of the factors, we can find the cube root of 12,167 as follows:
∛12,167 = ∛(19 × 641)
∛12,167 = ∛19 × ∛641
∛12,167 = 2.7144 × 8.0186
∛12,167 = 23.1649 (rounded to four decimal places)
Therefore, the cube root of 12,167 is approximately 23.
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Can a continuous random variable take all values in an interval?
A continuous random variable can take all values in an interval, assuming that the interval is unbounded.
This is because a continuous random variable has an infinite number of possible outcomes, and the probability density function (PDF) of a continuous random variable is defined over a range of values rather than specific values.
For example, consider the normal distribution, which is a common continuous probability distribution. The PDF of a normal distribution is a bell-shaped curve that extends from negative infinity to positive infinity.
This means that a continuous random variable following a normal distribution can take any value on the real number line, with some values being more likely than others.
However, if the interval is bounded, then it is possible for a continuous random variable to not take all values within the interval. In this case, the probability density function is zero outside of the interval, and the random variable is restricted to the range of values within the interval.
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A quadrilateral has two angles that measure 232° and 86°. The other two angles are in a ratio of 4:17. What are the measures of those two angles?
The two missing angles of the quadrilateral are 10.5° and 2.47°, calculated from the given angles of 232° and 86°, and a ratio of 4:17.
The angle sum of a quadrilateral is 360°. Therefore, we need to find the sum of the two missing angles.We can start by subtracting the two known angles from the total angle sum and then dividing the difference by the ratio given.
360° - 232° - 86° = 42°
To find the two missing angles, divide the sum by the ratio given.
42° ÷ 4:17
The find the measure of the first angle, divide 42° by 4:
42° ÷ 4 = 10.5°
To find the measure of the second angle, divide 42° by 17:
42° ÷ 17 = 2.47°
Therefore, the two missing angles of the quadrilateral are 10.5° and 2.47°.
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Bisectors of triangles
Find RT
The length of RT is 13 units
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
As T is the centroid of the given triangle.
TN=TP
x+10=4x-17
Now solve for x
27=3x
x=9
Now TP=4(9)-17
TP=36-17
TP=19
Now from pythagoras theorem we find the length of RT
19²=14²+RT²
361-196=RT²
165=RT²
Take square root on both sides
RT=13
Hence, the length of RT is 13 units
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2. In a bag of fruit Skittles, the ratio of strawberry to orange to lemon-lime is 4: 3:7. There are 56 Skittles in a bag.
Find the number of lemon-lime Skittles in the bag.
Answer:
28
Step-by-step explanation: 4+3+7=14
56/14=4
7*4=28
Answer:
28
Step-by-step explanation:
4x+3x+7x = 56
14x=56
x=4
7x ---> 7(4) ---> 28
So there are 28 lemon lime skittles in a bag
Ben has 300 marbles in a bag.
He gives
65 of the marbles to Sofia
80 of the marbles to Paul
35 of the marbles to Lucas
What fraction of his 300 marbles has Ben given away?
Give your fraction in its simplest form.
Answer:
Ben had given away 3/5 of his fraction.
Step-by-step explanation:
total number of marbles Ben give away,
= 65+80+35
= 180
180/300= 3/5
Which display is most likely to reveal association between X and Y ? A. Dot plot B. Scatter plot C. Histogram D. Pareto chart
Scatter plot Answ
Step-by-step explanation:
If a hexagon represents 1 whole, what fraction does each of the following shapes represent? Be prepared to show or explain your reasoning
The triangle represents 1/4 of the whole trapezoid, the rhombus represents 1/2 of the whole trapezoid, and the hexagon represents 1/1 of the whole trapezoid.
Determine the fractionEach of the shapes represent a different fraction of the whole trapezoid.
The triangle represents 1/4 of the whole trapezoid. This is because there are four triangles in the trapezoid, and each one is equal in size. Therefore, each triangle is 1/4 of the whole trapezoid. The rhombus represents 1/2 of the whole trapezoid. This is because there are two rhombuses in the trapezoid, and each one is equal in size. Therefore, each rhombus is 1/2 of the whole trapezoid.
The hexagon represents 1/1 of the whole trapezoid. This is because there is only one hexagon in the trapezoid, and it is equal in size to the whole trapezoid. Therefore, the hexagon is 1/1, or the whole trapezoid.
In conclusion, the triangle represents 1/4 of the whole trapezoid, the rhombus represents 1/2 of the whole trapezoid, and the hexagon represents 1/1 of the whole Hexagon. These fractions can be used to determine the value of each shape in relation to the whole trapezoid.
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The breadth of a rectangle is half of its length. If its perimeter is 76m,find its length and breadth.
The length and breadth of the rectangle are 25.33 meters and 12.67 meters,
What is a rectangle?A rectangle is a quadrilateral having four sides and the sum of the angles is 180 in the rectangle the opposite two sides are equal and parallel and the two sides are at 90-degree angles.
We are given that the breadth of the rectangle is half of its length, so we can write:
B = 0.5L
We are also given that the perimeter of the rectangle is 76m. The perimeter of a rectangle is the sum of the lengths of all four sides, which in this case is:
Perimeter = 2(L + B)
Substituting the value of B from the first equation, we get:
Perimeter = 2(L + 0.5L)
Perimeter = 2(1.5L)
Perimeter = 3L
Now we can solve for L:
3L = 76
L = 25.33
So the length of the rectangle is 25.33 meters.
To find the breadth, we can substitute this value of L back into the first equation:
B = 0.5L
B = 0.5(25.33)
B = 12.67
So the breadth of the rectangle is 12.67 meters.
Therefore, the length and breadth of the rectangle are 25.33 meters and 12.67 meters, respectively.
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to find the value of a numerical or algebraic expression is called?
The process of finding the value of a numerical or algebraic expression is called evaluation.
Evaluation involves substituting the given values of the variables in the expression and then simplifying the expression using the order of operations (PEMDAS).
For example, if we are asked to evaluate the expression 3x + 2y when x=4 and y=5, we would substitute these values to get 3(4) + 2(5), which simplifies to 12 + 10 = 22. Therefore, the value of the expression 3x + 2y when x=4 and y=5 is 22.
In algebra, evaluation is an important process because it allows us to find the value of an expression for specific values of the variables, which can help us to solve equations or inequalities, and to simplify expressions.
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Consider the experiment of rolling a pair of dice. Suppose that we are interested in the sum of the face values showing on the dice. (a) How many sample points are possible?
(b) What is the probability of obtaining a value of 7?
(c) What is the probability of obtaining a value of 8 or greater?
a) There are 36 sample points that are possible.
b) The probability of obtaining a value of 7 is 1/12.
c) The probability of obtaining a value of 8 or greater is 1/6.
(a) When rolling a pair of dice, each die has six possible outcomes: 1, 2, 3, 4, 5, or 6. The possible outcomes for the pair of dice can be represented by the set of all ordered pairs (a, b), where a and b represent the outcomes of the first and second die, respectively.
Since each die has six possible outcomes, there are a total of 6 x 6 = 36 possible outcomes for rolling a pair of dice.
(b) To obtain a sum of 7, we must have one die showing 1 and the other die showing 6, or one die showing 2 and the other die showing 5, or one die showing 3 and the other die showing 4, for a total of three possible outcomes.
Since each die has six possible outcomes, there are a total of 6 x 6 = 36 possible outcomes. Therefore, the probability of obtaining a sum of 7 is 3/36, or 1/12.
(c) We must have one die showing 2 and the other die showing 6, or one die showing 3 and the other die showing 5, or one die showing 4 and the other die showing 4, or one die showing 4 and the other die showing 5, or one die showing 5 and the other die showing 3, or one die showing 6 and the other die showing 2, for a total of 5 + 1 = 6 possible outcomes.
Therefore, the probability of obtaining a sum of 8 or greater is 6/36, or 1/6.
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How do you solve verifying identity with calculator?
Verifying Identity with a calculator requires an individual to enter specific numerical values into a calculator and then solve a given equation. This can be used to prove the validity of an equation, or the accuracy of a given answer.
The equation is typically written in algebraic form and includes numerical values.Verifying Identity with a calculator requires an individual to enter specific numerical values into a calculator and then solve a given equation. This can be used to prove the validity of an equation, or the accuracy of a given answer. For example, if an individual is asked to verify the identity [tex]sin^2x + cos^2x[/tex]= 1, they will be given numerical values to plug into the equation. For example, if they are given x = 60, they would enter[tex](sin60)^2 + (cos60)^2[/tex] into the calculator and solve. This should result in an answer of 1, proving the equation is accurate.
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Please answer both questions in the photo!!! (20p)
Answer:
(2.4, 2)
(4, -3.4)
Step-by-step explanation:
Brainliest Please
Help pleaseee
Solve for g
Answer:
g=4f-k+h
Step-by-step explanation:
f=g-h+k
4
4f=g-h+k
4f-k=g-h
4f-k+h=g
1001₂ = ______ (base 6)
A. 13
B. 14
C. 15
D. 21
E. 23
The binary number will be equal to 14 in base 6
1001₂ = 14 (base 6)
What is a number base?Base is defined as a set of digits used to represent numbers. There are different number systems which make use of different combinations of digits as the base.
One of the most common which is the binary number system uses only 2 digits, i.e., 0 and 1 to represent numbers, while the Octal number system uses 8 digits, i.e., 0 to 7, to represent numbers.
The most common number system that is in use is the decimal number system that uses the base 10, which includes digits from 0 to 9 for writing numbers.
1001₂ = 1 x 2^3 + 0 x 2^2 + 0 x 2^1 + 1 x 2^0
1001₂ = 1 x 8 + 1 x 1
1001₂ = 8 + 1
1001₂ = 9
Converting 9 into base 6
6 9
6 1 r 3
0 r 1
From downwards pointing up
9 = 13 (base 6)
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Solve for x
A. Solve using the change of base formula.
Logby= log y/log b
B. Solve using a different method.
C. verify your solutions by substituting your value back into the original equation.
A) By using the change of base formula, the solution of the expression is,
⇒ x = - 2/3
B) The solution of the expression is,
⇒ x = - 2/3
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 5³ˣ⁻² = 125²ˣ
Now, We have the change of base formula,
⇒ [tex]log_{b} y = \frac{log y}{log b}[/tex]
Here, The expression is,
⇒ 5³ˣ⁻² = 125²ˣ
⇒ 5³ˣ⁻² = 5⁶ˣ
Take log on both side,
⇒ log 5³ˣ⁻² = log 5⁶ˣ
⇒ (3x - 2) log 5 = 6x log 5
⇒ 3x - 2 = 6x
⇒ - 2 = 6x - 3x
⇒ 3x = - 2
⇒ x = - 2/3
B) By using another method as;
The expression is,
⇒ 5³ˣ⁻² = 125²ˣ
⇒ 5³ˣ⁻² = 5⁶ˣ
By comparing we get;
⇒ 3x - 2 = 6x
⇒ - 2 = 6x - 3x
⇒ 3x = - 2
⇒ x = - 2/3
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The population in a small town is increasing annually by 2.8%. What is the quarterly rate of population increase?
Answer:
To find the quarterly rate of population increase, we first need to find the annual rate of population increase in decimal form, which is 2.8% expressed as 0.028.
To find the quarterly rate, we need to divide the annual rate by 4, since there are 4 quarters in a year:
0.028 / 4 = 0.007
Therefore, the quarterly rate of population increase is 0.007 or 0.7%