The necessary probabilities are 3/8, 1/3, 9/64, and 37/64.
What is probability?The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.
Here,
S = { G1, G2, G3, Y1, Y2, Y3, Y4, Y5 }
G = { G1, G2, G3 }
P(G) = 3/8
E = { G2, Y2, Y4 }
P(G|E) = 1/3
P(G and E) = P(G)*P(E) = (3/8)*(3/8) = 9/64
P(G or E) = P(G) + P(E) - P(G and E) = (3/8) + (3/8) - (9/64) = (6/8) - (9/64) = (48/64) - (9/64) = 37/64
The required probability is 3/8, 1/3, 9/64 and 37/64.
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5. An acute triangle has a base of 4 cm and a height of 8 cm. What is the area of the triangle?
32 cm²
12 cm²
16 cm²
64 cm²
Answer:
c) 16 cm²
Step-by-step explanation:
Given information,
→ Base = 4 cm
→ Height = 8 cm
Area of triangle formula,
→ Area = ½ × b × h
Now the area of triangle is,
→ ½ × b × h
→ ½ × 4 × 8
→ 2 × 8
→ 16 cm²
Hence, the area is 16 cm².
“Theresa’s Transportation” rental car company charges $30 to rent a car and $0.60 per mile for each rental. “Pete’s propulsions” rental car company charges $20 to rent a car and $0.85 per mile. After how many miles will it be more expensive to rent from Pete’s Propulsions than Theresa’s Transportation
On solving the provided question, we got to know that he fraction can bake 200/57 loaves or 3 29/57 loafs.
what is fraction?Mathematically speaking, fractions are represented by integers that indicate a portion of a whole. In the same way that a whole can be any quantity, value, or object, a fraction can be a portion or subset of any quantity of a whole. As an example, let's try to comprehend this idea. The pizza in the picture below is cut into 8 equally sized pieces. The chosen slice of pizza might now be expressed as 1/8 if we wanted to. This indicates that we are talking about one of eight equally sized sections. It denotes a ratio of 1/8. Reading options include: One-eighth, or
1 by 8
13 1/3 divided by 3 4/5
Let's first convert these mixed numbers to incorrect fractions.
13 1/3 = 13(3) + 1 = 39 + 1 = 40/3
3 4/5 = 3(5) + 4= 19/5
Now that we have divided 40/3 by 19/5, we can just switch the operation to multiplication and flip the second fraction because we know how to divide fractions.
40/3 x 5/19 = 200/57
he can bake 200/57 loaves or 3 29/57 loafs.
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solve the following equations graphically
x + y=3 & x-3y= -5
Answer:
[tex](x,y)\rightarrow(1,2)[/tex]
Step-by-step explanation:
Multiply first equation by 3 to help cancel out the "y" variable:
[tex]\displaystyle \left \{ {{x+y=3} \atop {x-3y=-5}} \right.\\\\\rightarrow \left \{ {{3x+3y=9} \atop {x-3y=-5}} \right.[/tex]
Combine system of equations on both sides:
[tex](3x+3y)+(x-3y)=9+(-5)\\4x=9-5\\4x=4\\x=1[/tex]
Thus,
[tex]x+y=3\\1+y=3\\y=2[/tex]
Larry and Carol are both members of a population, and a simple random sample is being conducted. If the chance of Larry being selected is 1/800, what is the chance of Carol being selected
By simple reasoning, The chance of Carol being selected is 1/800.
What in probability is a random process?A collection of random variables, typically indexed by time, makes up a random process. Here, the process S(t) is an illustration of a continuous-time random process. In general, a random process X(t) is a continuous-time random process if t can take real values in an interval on the real line.
A straightforward random sample is being taken from a population that includes both Larry and Carol.
So both of them have an equal chance of being chosen.
Now, Larry's likelihood of being chosen is 1 in 800.
The likelihood of Carol being chosen is then 1 in 800.
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OPEN ENDED NOT MULTIPLE CHOICE
Some recent studies suggest that a teenager sends an average of 60 texts per day. For each of
the following scenarios, find the linear function that describes the relationship between the input
value and the output value. Then, determine whether the graph of the function is increasing,
decreasing, or constant.
a. The total number of texts a teen sends is considered a function of time in days. The input is
the number of days, and output is the total number of texts sent.
b. A teen has a limit of 500 texts per month in his or her data plan. The input is the number of
days, and output is the total number of texts remaining for the month.
c. A teen has an unlimited number of texts in his or her data plan for a cost of $50 per month.
The input is the number of days, and output is the total cost of texting each month
Analyze the function graph.
Select the best option to describe the function graph.
Linear Increasing
Linear Decreasing
Linear Constant
Nonlinear Increasing
Nonlinear Decreasing
The function graph is Linear Constant. Option C
What is the graph?We know that when we plot a graph, there would be the vertical and the horizontal axis. We can be able to deduce the nature of the graph when we look at how the graph is going.
In this case, we can see that the graph is flat. The flatness of the graph would show us that there is neither an increase nor a decrease in the function that we have in view. The increase or the decrease can be seen from the direction of the line that is drawn across the graph.
Hence, the fact that the line is flat on the graph shows that it is linear constant.
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at a certain high school, the distribution of backpack weight is approximately normal with mean 19.7 pounds and standard deviation 3.1 pounds. a random sample of 5 backpacks will be selected, and the weight, in pounds, of each backpack will be recorded. For samples of size 5, which of the following is the best interpretation of P\left(\overline{x}>22\right)\approx0.05P(x>22)≈0.05?
The Normal probability for all sample of 5 that the sample mean will be greater than 22 pounds is approximately 0.05. In this Question The normal probability distribution and the central limit theorem were used.
What is Normal probability distribution?The most prevalent continuous probability distribution is the Normal (or Gaussian) distribution. As the curve becomes closer to zero on either side of the mean, the function calculates the likelihood that a given event will fall between any two real number limits. The area under the normal curve is always one.
Central limit theorem
The central limit theorem implies that the distribution of the sample means will be roughly normally distributed if you have a population with mean and standard deviation and take sufficiently enough random samples from the population with replacement.
Normal probability distribution, ; Problems of normally distributed samples are solved using the z-score formula.
Mean standard deviation , the z-score of a measure X is given by:
Z = x-μ/σ
Given ,
The distribution of backpack with mean deviation = 19.7 pounds
And the standard deviation = 3.1 pounds
The number of standard deviations is measured by the Z-score. The average is used as the measure.
We glance at the z-score table after determining the Z-score to determine the p-value connected to it.
The likelihood that the measure's value is less than X, or the percentile of X, is represented by this p-value.
1 is subtracted from the p value.
We calculate the likelihood that the measure exceeds X.
P(ä > 22) is the probability of the sample means being above 22.
For all samples of size 5, the probability that the sample mean will be greater than 22 pounds is approximately 0.05.
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PLEASE HELP W THE QUESTIONS IN IMAGE ILL GIVE BRAINLIEST
Answer:
53
Step-by-step explanation:
If police and fire are already on an accident scene, how many feet away should you park your ambulance
It is recommended that when an ambulance arrives at an accident scene, it should park a safe distance away from the scene, at least 500 feet away.
This is to ensure the safety of the paramedics and other emergency responders, as well as to ensure that the ambulance does not impede the movement of other emergency vehicles. Additionally, it is also to protect the privacy of the individuals involved in the accident and ensure that the scene is not tampered with.
It is also important to follow any additional instructions given by the police or fire department at the scene, as they may have specific parking instructions based on the situation.
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Explain the process how would you estimate the solution of system of equation to the nearest tenth place
The actual solution must be approximated to the tenth place.
How do you solve an equation to the nearest tenth?
To round the decimal number to its nearest tenth, look at the hundredth number. If that number is greater than 5, add 1 to the tenth value. If it is less than 5, leave the tenth place value as it is, and remove all the numbers present after the tenth place.
To estimate the tenth place, you have to determine the actual solution and the approximate.
Assume the solution to the system of equations is:
(x, y), (1.25, 1)
1.25 is to the hundredth place.
So, the next thing is to approximate 1.25 to 1.3 (the tenth place).
So, we have:
(x, y), (1.3, 1)
Hence, the actual solution must be approximated to the tenth place.
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factor the trinomial 2xsquared + 5x -42
Basic quadratic expression:
[tex]ax^2+bx+c[/tex]
[tex]2x^2+5x-42[/tex]
Factoring a quadratic expression when a ≠ 0
1. Multiply a and c values (ac=k)
[tex]2(-42) = -84[/tex]
2. Find a factor pair whose sum adds to b and has the product of k
[tex]-7,12[/tex]
[tex]-7(12)=-84[/tex] [tex]-7+12=+5[/tex]
3. Replace the middle term (bx) with newfound values
[tex]2x^2 +12x-7x-42[/tex]
4. Factor by grouping
[tex]2x(x+6) -7(x+6)[/tex]
if done correctly the expression in the parentheses will be the same5. Perform the last factorization
[tex](2x-7)(x+6)[/tex]
you can verify your answer by expanding the factors to get the same expression in the beginning5.
4.2 cm
4.2 cm
square centimeters
The total area of triangle in square centimeters is 56.7cm squared .The three angles of the triangle add up to 180 degrees.
what is triangle ?The term "trigon" is occasionally (though not frequently) used to refer to a triangle, a 3-sided polygon. Every triangle consists of a set of three angles and three sides, some of which may be the same. The three angles of the triangle add up to 180 degrees. With three sides and three vertices, triangles are a specific type of polygon in geometry. The two-dimensional figure displayed here has three straight sides. A triangle is a type of 3-sided polygon.
here
Area of each triangles is 4.2 x 8.2 or 34.44.
There are two triangles, thus you don't need to divide by two.
In addition, 8.2 is obtained by deducting the top length from the overall length. (13.5-5.3)
rectangle: 22.26 x 5.3
56.7 square meters is the entire area.
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The correct question is
What is the area, in square centimeters, of the triangles are?
a) 5.3 cm
b) 4.2 cm
c) 13.5 cm
What are the 6 parent functions?
These are the 6 parent functions: Identity, Absolute Value, Square Root, Quadratic, Cubic, Reciprocal.
A parent function is the simplest form that a function can be. Its basic shape is not in any way altered. In mathematics, you see certain graphs over and over again. For that reason, these original, common functions are called parent graphs, and they include graphs of quadratic functions, square roots, absolute values, cubics, and cube roots.
For instance, when you see a u-shaped graph that is inverted and vertically stretched, you should still recognize that it is a parabola which has undergone different transformations.
We can take a few examples to understand this concept further.
For a quadratic equation, the parent graph is [tex]f(x) = x^{2}[/tex], which is a parabola.For a cubic equation, the parent graph is [tex]f(x) = x^{3}[/tex].Now, there are 6 parent functions:
IdentityAbsolute ValueSquare RootQuadraticCubicReciprocalHence, these are the 6 parent functions: Identity, Absolute Value, Square Root, Quadratic, Cubic, Reciprocal.
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The number of views on a viral video can be modeled by the function
G(t) = 2500(5) 2-4. Write an equivalent function of the form G(t) = ab.
The equivalent expression would be; function G(t) = 86,400•3^t
What is a function in simple definition?
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range.
The number of views on a viral video can be modeled by the function
G(t) = 2500(5) 2-4.
we have to find out an equivalent function of the form G(t) = ab.
Here, we want to make a transformation
From what we have;
G(t) = 2500(5)^(t - 4)
From indices, we know that;
x^(a + b) = x^a•x^b
Thus, we have it that;
G(t) = 2500•3^t•3^2
G(t) = (9 * 9600) * 3^t
G(t) = 86,400•3^t
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Mr.Coy receives a 80 bill for his meal. He leaves 14.30 as a tip. What percent did he leave
Answer:
around 18%
Step-by-step explanation:
14.30/80=0.17875
0.17875*100=17.875
18%
Answer:
Step-by-step explanation:
the answer is [tex]\frac{14.30}{80}[/tex]=17.875%
10. Find the degree of the monomial. 7m^6n^5
11
6
7
5
Answer:
(a) 11
Step-by-step explanation:
You want the degree of the monomial 7m^6n^5.
DegreeThe degree of a monomial is the sum of the exponents of its variables.
m has an exponent of 6
n has an exponent of 5
The degree is 6+5 = 11.
Can someone please help me? :(
Step-by-step explanation:
send the pic clearly i will help surely im sorry
For what value of k the given equation 4 K X² 2k 4 x+ 8k+ 1 0 is a perfect square?
For k=0 or k=3, the given equation will be a perfect square.
Note: we are taking the equation to be: (4−k) X^2+(2k+4) x+8k+1=0
Taking,
(4−k) X2+(2k+4) x+8k+1=0
Here, a=4+k, b=2k+4, c=8k+1
The given equation will be a perfect square, When D= 0
We know, D = b^2−4ac [A perfect square trinomial is an expression that can be generated from the square of a binomial equation. If an equation has the formula ax^2 + bx + c and meets the requirement b^2 = 4ac, it is referred to as a perfect square trinomial. The formula for the perfect square has the following variations: ax2 + 2abx + b2 = (ax + b). When b^2 = 4ac, we know that an equation is a perfect square.]
b2−4ac=0
(2k+4)2−4(4−k) (8k+1) =0
4k2+16+16k−4(32k−8k2+4−k) =0
K2+4+4k−32k+8k2−4+k=0
9k2−27k = 0
K2−3k = 0
k(k−3) =0
k=0 or k=3
Hence for k=0 or k=3, the given equation will be a perfect square.
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What is g(4) when given the function g(x) = 6x + 32?
Answer:
The value of g(4) of the given function is 56.
How would the information collected using transect or quadrat sampling differ from the information collected if you had just divided the habitat into quarters and sampled only one of the quarters
I feel that dividing based off actual zoning laws and regulations would provide the best source of data. I feel as such because if you simply devise your own areas, that may make your data incorrect depending on what area a person actually associates with. If you're creating your own area, information could get misconstrued leading to inaccurate conclusions.
Sampling
Sampling means selecting the group that you will actually collect data from in your research.
zoning
Zoning is a method of urban planning in which a municipality or other tier of government divides land into areas called zones, each of which has a set of regulations for new development that differs from other zones.
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(100 points)A catering company offers meal pairings that include an appetizer of either salad or soup and an entree of either chicken or fish. At one event, they serve a total of 78 meals. Of the 46 meals that include salads, 21 also include fish. There are 35 meals with fish as the entree. Determine which two-way frequency table represents this situation. Jk
Two-way table showing meal pairings with frequency of salad, soup, chicken and fish.
Meal Pairing Salad Soup Chicken Fish
Frequency 46. 32. ?. 35
To calculate the frequency of chicken, subtract the frequency of salad and fish from the total of 78 meals.
Frequency of chicken
= 78 - 46 - 35
= 27.
Meal Pairing Salad Soup Chicken Fish
Frequency 46. 32. 27. 35
The total number of meals served is 78. Of the 46 meals that included salads, 21 also included fish. This means that the frequency of fish is 35. The frequency of chicken can be calculated by subtracting the frequency of salad and fish from the total number of meals. The frequency of chicken is 27. The two-way frequency table representing this situation is as follows: Meal Pairing, Salad, Soup, Chicken, Fish; Frequency, 46, 32, 27, 35. This table shows that there were 46 meals with salad, 32 meals with soup, 27 meals with chicken, and 35 meals with fish.
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5. Jamal got a job working on an assembly line in a toy factory. On the 20th day of work, he
assembled 137 toys. He noticed that since he started, every day he assembled 3 more
toys than the day before. How many toys did Jamal assemble altogether during his first
20 days?
(Arithmetic sequence)——
2170 toys Jamal assemble altogether during his first 20 days.
What is the arithmetic sequence?
A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms.
Here, we have
Given: Jamal got a job working on an assembly line in a toy factory. On the 20th day of work, he assembled 137 toys. He noticed that since he started, every day he assembled 3 more toys than the day before.
We have to find how many toys did Jamal assemble altogether during his first 20 days.
We apply the arithmetic sequence formula and we get
tₙ = t₁ + (n-1)d
137 = t₁ + (20-1)(3)
t₁ = 80
To calculate the total number of toys that Jamal assemble in his first 20 days,
S₂₀ = (20/2)(2×80 + (20-1)(3))
S₂₀ = 2170
Hence, 2170 toys Jamal assemble altogether during his first 20 days.
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Find value of c
[tex]48c+ 6 = 408 \div 4[/tex]
Answer:
2
Step-by-step explanation:
408 / 4 = 102
48c + 6 = 102
48c = 102 - 6
48c = 96
c = 96/48
c = 2
Hence, the value of c is 2.
Answer:
[tex] \sf \: c = 2[/tex]
Step-by-step explanation:
Given equation,
→ 48c + 6 = 408 ÷ 4
Now the value of c will be,
→ 48c + 6 = 408 ÷ 4
→ 48c + 6 = 102
→ 48c = 102 - 6
→ c = 96 ÷ 48
→ [ c = 2 ]
Hence, the value of c is 2.
A coordinate plane. The x- and y-axes each scale by one. A graph of a line intersects the points negative one, zero and zero, one. A coordinate plane. The x- and y-axes each scale by one. A graph of a line intersects the points negative one, zero and zero, one. What is the slope of the line?
The slope of the line on the given coordinate plane is equal to 1.
How to calculate the slope of a line?In Mathematics, the slope of a straight line can be calculated by using this this mathematical expression;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
From the information provided in the graph, we have the following data points on the line:
Points on x-axis = (-1, 0).
Points on y-axis = (0, 1).
Substituting the given points into the slope formula, we have the following;
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (1 - 0)/(0 - (-1))
Slope, m = 1/(0 + 1)
Slope, m = 1/1
Slope, m = 1
In conclusion, we can logically deduce that the slope of this line is equal to 1.
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I need help on this question. I dont understand it.
a. The system of equations is given as follows:
35x = 15 + 32x.
The solution is given as follows:
x = 5.
b. The meaning of the solution is that the cost to purchase 5 jackets in each company is the same.
c. Gabriela should choose Anastasia's Monogram, as the function has a lower numeric value when x = 10.
How to model the situation?The cost per jacket for each company is constant, hence a linear function is used to model the situation.
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the cost paid per each jacket.b is the y-intercept, representing the design fee, which is a one-time payment.Hence the functions for each company are given as follows:
Anastasias's Monograms: y = 15 + 32x.Monograms Unlimited: y = 35x.The system of equations is used to find when both will have the same cost, as follows:
35x = 32x + 15
3x = 15
x = 5 jackets.
For 10 jackets, the costs are given as follows:
Anastasias's Monograms: y = 15 + 32(10) = $335 -> lower cost.Monograms Unlimited: y = 35(10) = $350.More can be learned about linear functions at https://brainly.com/question/24808124
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How do you find the endpoint and midpoint?
To find the endpoint we have to calculate the distance between the known midpoint to the known endpoint. To calculate the midpoint we add two points and divide them by 2.
The formula for midpoint = (x1 + x2)/2, (y1 + y2)/2.
Substituting in the two x-coordinates and two y-coordinates from the endpoints.
Putting it together,
The endpoint formula is:
(x a ,ya)= ((2xm−xb),(2ym−yb))
( x a , y a ) = ( ( 2 x m − x b ) , ( 2 y m − y b ) ).
The end of a line at a point that is equally distant from both ends, a time interval between an event's beginning and end.
The point on a graph or figure where the figure stops might be referred to as the endpoint. It can be the point joining the sides of a polygon (the vertex), the common endpoint of two rays making an angle, the two extreme points of a line segment, the one end of a ray.
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What is the solution to the system of linear equations 3x minus 2y equals 14 5x plus y equals 32?
The solution to the system of linear equations is x = 10 and y = 22.
To solve this system of linear equations, we can use the substitution method.
First, we want to isolate one of the variables in either equation. Let's start with equation 1:
3x - 2y = 14
Add 2y to both sides to isolate x:
3x = 14 + 2y
Divide both sides by 3 to solve for x:
x = (14 + 2y) / 3
Now, substitute this expression for x into equation 2:
5x + y = 32
5(14 + 2y) / 3 + y = 32
Simplify:
70 + 10y + y = 32
Combine like terms:
11y = -38
Divide both sides by 11 to solve for y:
y = -38 / 11
y = -3.45454545...
Now, substitute -3.45454545... for y in the expression for x:
x = (14 + 2(-3.45454545...)) / 3
x = (14 - 6.9090909...) / 3
x = 7.09090909... / 3
x = 2.36363636...
x = 2.4 (rounded to nearest tenth)
Now that we have both x and y, the solution to the system of linear equations is x = 2.4 and y = -3.5.
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How do I solve e less than 5?
Answer:
e-5
Pretty simple
The tables show the prices for ordering team jerseys from two different companies. You can use the information to write ratios showing the relationship between the cost and the corresponding number of jerseys. 1/5=5 25/5=5 50/10=5 75/15=5. 5/1=5 20/5=4 40/10=4 69/15=4. These ratios are all equivalent. These ratios are not all equivalent. This relationship is proportional. This relationship is not proportional. Explain how you can tell whether a group of ratios represents a proportional relationship.
Even though this relationship is proportional, not all of these ratios are equal.
What is the solution to the 3 to 5 ratio?Verify that the ratios provided are equal. The ratios of 3:5 and 15:25 are both equal. Because the first ratio 3: 5 can be derived by multiplying the ratio 15: 25 by 5 on both the numerator and denominator. The initial ratio of 3: 5 can be multiplied by 5 to get the ratio 15: 25, and vice versa.
What is an illustration of a 4:1 ratio?This indicates that you would require an 8 fl oz can (a quarter of a quart) of Part B if you were ordering a quart of Part A. You will have 1.25 after combining Parts A and B.
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What is math trying to do with me?
seriously
:^
Answer:
1.
Y would equal to 449 after plugging in 12 for x
2.
Y would equal to 239 after plugging 7 in for x
Step-by-step explanation:
We just have to plug in the values give too us and find what y equals.
1.
y=42(12)-55
y=504-55
y=449
2.
y=42x-55
we just have to plug in 7 for x.
y=42(7)-55
42*7=294
y=294-55
y=239