The probability of getting both an even number and heads is 1/4.
A eight-sided die is rolled.
A coin is flipped.
Since a coin has only two faces, heads and tails, the probability of getting heads in one flip is given by;
P(H) = Number of ways to get heads / Total number of possible outcomes
Therefore, P(H) = 1/2
On rolling an eight-sided die, the total number of possible outcomes is 8 since there are eight faces and each face has a unique number on it. The numbers on the faces are 1, 2, 3, 4, 5, 6, 7, and 8. Therefore, the probability of getting an even number is;
P(getting an even number) = Number of ways to get an even number / Total number of possible outcomes
The even numbers on the die are 2, 4, 6, and 8, therefore the total number of ways to get an even number is 4. Hence, the probability of getting an even number on rolling the die is given by;
P(getting an even number) = 4/8 = 1/2
We can use the multiplication rule to find the probability of getting both an even number and heads.
P(getting both an even number and heads) = P(getting an even number) x P(H)
Therefore, P(getting both an even number and heads) = (1/2) x (1/2) = 1/4
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Find the equation of the straight line passing through the point (0, -1) which is perpendicular to the line y=-3/4 x-3
Answer:
y = \(\frac{4}{3}\) x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - \(\frac{3}{4}\) x - 3 ← is in slope- intercept form
with slope m = - \(\frac{3}{4}\)
Give the slope of a line m then the slope of a line perpendicular to it is
\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{-\frac{3}{4} }\) = \(\frac{4}{3}\)
The line crosses the y- axis at (0, - 1 ) ⇒ c = - 1
y = \(\frac{4}{3}\) x - 1 ← equation of perpendicular line
PLEASE HELP ASAP. WILL GIVE BRAINLIEST!!!!!!
Using trigonometric ratio, the length of BE is 10 units, the value of sin B is 0.64 and cos B is 0.64 respectively
Trigonometric RatioThis is the ratio between the angles and sides of a right-angle triangle. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
In this problem, we have that
tan B = 3/4NE = 7.51)
Using tangent of B
tan B = opposite / adjacent
tan B = NE / BE
3/4 = 7.5 / BE
BE = 7.5 / 0.75
BE = 10
2)
To find sin B, we need to calculate the hypothenuse of the triangle which we will use Pythagoras's theorem
NB² = BE² + NE²
NB² = 10² + 7.5²
NB = 12.5
sin B = NE / NB
sin B = 7.5 / 12.5
B = sin⁻¹ (7.5 / 12.5)
B = 0.64
3)
cos B = BE / NB
cos B = 10 / 12.5
B = cos⁻¹ (10/12.5)
B = 0.64
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suppose the random variables x1, x2,..., xn are independent an identically distributed , each with variance
The random variable is 3×sigma²/4.
Since, X1, X2 & X3 are independent & identically distributed.
so we have,
var(X1) = var(X2) = var(X3) = \sigma².
And,\(cov(X1 , X2) = cov(X2 , X3) = cov(X1 , X3) = 0.\)
Now, \(var(Y1) = var(X2 + X3) = var(X2) + var(X3) + 2.cov(X2 , X3) = \sigma² + \sigma² + 0 = 2.\sigma²\)
\(var[(Y1 + Y2 + Y3)/2] = (1/4). [var(Y1) + var(Y2) + var(Y3) + 2.cov(Y1 , Y2) + 2.cov(Y1 , Y3) + 2.cov(Y2 , Y3)] = (1/4). (\sigma² + \sigma² + \sigma² + 0 + 0 + 0) = 3.\sigma²/4\)
What is random variable and example?The collection of potential outcomes for a random event is referred to as the sample space, which is the domain of a random variable. When a coin is tossed, for instance, there are only two possible outcomes: heads or tails. Read Related Links as well. Probability.
Different from an algebraic variable is a random variable. An algebraic equation's variable is an unknowable but calculable value. The formula \(10 + x = 13\) demonstrates that we can determine the precise value of x, which is \(3.\) As seen in the example of the dice above, a random variable has a set of values, and any of those values could be the outcome.
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Using y/x = k, what is the value of k for Jack's data?
Answer:
1
Step-by-step explanation:
How do you find the slope of a perpendicular line with an equation and point?
First, by solving for y, convert the equation of the given line into slope-intercept form y=mx+c .You obtain the slope of the equation as m. Since the slopes of perpendicular lines are negative reciprocal, the slope of the line we're looking is the negative reciprocal of the perpendicular equation.
By entering the supplied point into the formula y = mx + b and solving for b, we arrive at the value of b. Consequently, the line's equation is formed.
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively.
m = y/x = y/x = change in y/change in x
where "m" represents a line's slope.
Additionally, the slope of the line may be shown as
tan θ = Δy/Δx
A line's slope often indicates the steepness and direction of the line.
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m = y/x = y/x = change in y/change in x
where "m" represents a line's slope.
Additionally, the slope of the line may be shown as
tan θ = Δy/Δx
why mathematics is neccessary for students?explain
If
a coccus divides along two perpendicular planes and four cells
attached together, it is called ( ). A. tetrad B. sarcina C.
staphylococcus D. streptococcus
If a coccus (a spherical bacteria) divides along two perpendicular planes and four cells remain attached together, it is called a tetrad. Therefore, the correct answer is A. tetrad.
A. Tetrad: A tetrad refers to a group of four cells resulting from the division of a single bacterium along two perpendicular planes. This arrangement forms a square or cube-like structure where the four cells remain attached together. Tetrads are commonly observed in certain bacteria, such as the genus Micrococcus.
B. Sarcina: Sarcina is a term used to describe a specific arrangement of cocci bacteria. In this arrangement, cocci divide along three perpendicular planes, resulting in packets of eight cells. Each packet resembles a cube-like structure composed of eight cells tightly attached together. Sarcinae are commonly observed in the genus Sarcina.
C. Staphylococcus: Staphylococcus refers to a genus of bacteria that are spherical (cocci) in shape. However, staphylococci typically divide randomly in multiple planes and form irregular clusters or grape-like arrangements rather than specific patterns like tetrads or sarcinae.
D. Streptococcus: Streptococcus is another genus of bacteria that are spherical (cocci) in shape. However, streptococci typically divide along a single axis and form chains or pairs rather than specific patterns like tetrads or sarcinae.
Considering the given scenario where a coccus divides along two perpendicular planes and four cells remain attached together, the correct term to describe this arrangement is A. tetrad.
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The term for a coccus bacterium dividing along two distinct perpendicular planes, resulting in four attached cells, is a 'tetrad'. This is different than 'sarcina', which is a genus of bacteria known for this behavior, and 'staphylococcus' and 'streptococcus', which are other forms of bacterial groupings.
Explanation:When a coccus bacterium divides in two distinct perpendicular planes resulting in four cells that remain adhered together, it forms a particular structure called a tetrad. This pattern of cell division and grouping is characteristic of some gram-positive bacteria. However, it's important to differentiate here that 'tetrad' just refers to this particular grouping of four cocci bacteria, whereas Sarcina is a genus of bacteria that are known for grouping in this fashion. On the contrary, Staphylococcus and Streptococcus represent other forms of groupings - spherical bacteria arranged in irregular clusters or chains, respectively.
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What is the missing number below in the solution to 968 divided by 10
Answer: 484/5
Step-by-step explanation:
For this word problem, it seems confusing with the wording but the equation would just be:
968÷10=x
solving for x, we get 484/5.
What are the solutions to the system of equations? {y=2x2+6x−10 y=−x+5
Answer:
I think this is mistake because y=2x^2+6x-10 y=x+5 this is the right
Solve the system using the addition method. Write your answer as an ordered pair.If there is no solution, write NS for your answer.s 6x + 5y = 251 4x – 5y = 15Answer 2 PointsKeypadKeyboard Shortcuts
Given:
\(\begin{gathered} 6x+5y=25\ldots\ldots\ldots\ldots(1) \\ 4x-5y=15\ldots\ldots\ldots\ldots(2) \end{gathered}\)To find: The value of x and y
Explanation:
Adding (1) and (2) we get,
\(\begin{gathered} 6x+5y+4x-5y=25+15 \\ 10x=40 \\ x=4 \end{gathered}\)Substitute x=4 in equation (2) we get,
\(\begin{gathered} 6(4)+5y=25 \\ 24+_{}5y=25 \\ 5y=25-24 \\ 5y=1 \\ y=\frac{1}{5} \end{gathered}\)Hence, the solution is,
\((4,\frac{1}{5})\)Final answer:
\((4,\frac{1}{5})\)estimate 63% of 109?
what is the answer?
Answer:
68.67
Step-by-step explanation:
Estimate 63% of 109
Change 63% to a decimal by locating the decimal which is after the 3 in 63 and move the two places to the left. So 63% as a decimal is .63
Now multiply .63 × 109
= 68.67
at a certain high school, the prom committee is going to choose new members. there are students from the junior class and students from the senior class who are willing to be new members. in how many ways can new members be chosen if more than must be from the senior class?
Answer:
Step-by-step explanation:
7 students from the Junior class.
6 students from the Senior class.
4 new members are to be chosen.
Required: Find the number of ways 4 new members can be chosen if 2 or fewer must be from the senior class. So, Therefore, the correct answer is 560 ways.
Compare the two numbers. Use > or < .
12,-√150
Compare the two numbers 12,-√150
\(-\sqrt{150} =-12.24\)
So,12 > -√150
What is a square root?
A square root is a factor of a number in mathematics that, when multiplied by itself, equals the original value.Square roots can be taken into account more broadly in any situation where the concept of an object's square is specified.Among other mathematical structures, these include function spaces and square matrices.The term square root is sometimes used to refer to the major square root of a positive number, even though it is merely one of the two square roots of that number.To learn more about square roots, refer:
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Noah spent $2.50 on 2 bags of peanuts and 1 bottle of water at a baseball game.
Emily spent $4.25 on 3 bags of peanuts and 2 bottles of water.
Lily bought 2 bottles of water and 1 bag of peanuts.
If they all paid the same amount for peanuts and water how much did lily spend?
The amount of money Lily spent on peanuts and water is 2.75 dollars.
How to find the amount Lily spent?Noah spent $2.50 on 2 bags of peanuts and 1 bottle of water at a baseball game.
Emily spent $4.25 on 3 bags of peanuts and 2 bottles of water.
Using equation,
where
x = cost of each bag of peanuty = cost of a bottle of waterTherefore,
2x + y = 2.50
3x + 2y = 4.25
multiply equation(i) by 2
4x + 2y = 5
3x + 2y = 4.25
x = 0.75 dollars
y = 2.50 - 2(0.75)
y = 2.50 - 1.5
y = 1 dollars
Therefore,
cost of Lily expenses = 2(1) + 0.75(1)
cost of Lily expenses = 2 + 0.75
cost of Lily expenses = 2.75 dollars
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Amari gathered a random sample of oranges in her town. She calculated data on different variables. For one of the variables that she collected, she-constructed a bar
graph
Which of the following variables did she use?
o Type of orange
O Diameter of the oranges
O Number of navel oranges
O Price per pound of oranges
Therefore, it is likely that Amari used either "Type of orange" or "Number of navel oranges" as the variable for her bar graph.
What do variables in math mean?In mathematics, a variable is an alphabet or phrase that denotes an elusive property, an elusive value, or an elusive quantity. The variables are utilized frequently when working with algebraic formulas or algebra. For instance, the variables x and 9 are constants in the equation x+9=4.
Based on the information provided, Amari constructed a bar graph, which suggests that she used a categorical variable for the graph.
Among the options given, "Type of orange" and "Number of navel oranges" are categorical variables, while "Diameter of the oranges" and "Price per pound of oranges" are continuous numerical variables.
Therefore, it is likely that Amari used either "Type of orange" or "Number of navel oranges" as the variable for her bar graph.
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Question Are the linear expressions equivalent? Drag the choices to the boxes to correctly complete the table. Put responses in the correct input to answer the question. Select a response,
For her final project, stacy plans on surveying a random sample of students on whether they plan to go to florida for spring break. From past years, she guesses that about % of the class goes. Is it reasonable for her to use a normal model for the sampling distribution of the sample proportion? why or why not?.
Less than 10 attempts were successful in this situation. due to the fact that 5 is less than 10. The data does not satisfy the requirement as a result.
Because the data don't fit the success or failure criteria, it is not appropriate to adopt a normal model for the sampling distribution of the sample.
50 students make up the sample. The likelihood that she assumes 10% of the class will attend is 10%. It will be demonstrated by:
1 - p = 1 - 10%
⇒ 1 - 0.10 = 0.90
np = 50 × 0.1
np = 5
This suggests the number of victories.
In this case, fewer than 10 efforts have been successful. Since 5 is less than 10, this is the situation. The data does not meet the criteria as a result.
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Order these equations to match the steps used to solve the equation
Step 1: Distributive property. Step 2: Addition property of equality
Step 3: Division property of equality
2(5x - 3) = 8. x = 7/5
10x - 6 = 8
10x = 14
Answer:
x = 7/5
Step-by-step explanation:
2(5x - 3) = 8
Step 1: Distributive property
10x - 6 = 8
Step 2: Addition property of equality
Add 6 to both sides of the equation
10x - 6 + 6 = 8 + 6
10x = 14
Step 3: Division property of equality
Divide both sides by 10
10x/10 = 14/10
x = 7/5
Answer:
10x-6=8 10x=14 x=7/5
Step-by-step explanation:
got it right on edge
which of the following is an example of a matched-pairs design? a a teacher compares the standardized test scores of students using a computer-based method of instruction with the scores of other students using a traditional method of instruction. b a teacher compares the scores of students in her class on a standardized test with the national average score. c a teacher calculates the average of scores of students on a pair of standardized tests and wishes to see if this average is larger than 80%. d a teacher compares the pretest and posttest scores of students. e a teacher compares the mean score of one class of 30 students on a standardized test with the mean score of another class of 30 students.
A teacher compares the pretest and posttest scores of students is an example of a matched-pairs design. Therefore, option d is the correct answer.
A matched-pairs design is an experimental design where the researcher analyzes the differences between two sets of data that are related.
It is used to minimize the effects of variables that are not of interest, such as individual difference.
Based on the given options,
option d : a teacher compares the pretest and posttest scores of students is an example of a matched-pairs design.
In this design, the teacher compares the students' performance before and after a specific treatment.
The design is used to minimize the differences in the individual differences in the students' academic performance is an example of a matched-pairs design.
option d is the correct answer.
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need help ASAP , midterm
-60 points .
6rs - 8s - 3 ( rs + 1) - 8s
Answer:
3rs-16s-3
Step-by-step explanation:
6rs - 8s - 3 ( rs + 1) - 8s
Distribute
6rs - 8s - 3rs + 3 - 8s
Combine like terms
6rs -3rs -8s -8s +3
3rs-16s-3
Which of the following is equivalent to 5√12 - 2√27?
Answer:
A. 4 root 3
Step-by-step explanation:
rosie is driving from knoxvile, tennesse orlando, florida. she drives 317.88 miles before she stops for lunch and then another 203 4/5 miles before taking a break. rosie has driven 4/5 of the entire trip. how many total miles is her trip?
The total miles of the trip are 521.68 miles.
What is addition?Addition in maths, a process of combining two or more numbers.
Given that, Rosie drives 317.88 miles before lunch and then \(203\frac{4}{5}\) miles before break,
Total miles = 317.88 + \(203\frac{4}{5}\) miles = 521.68 miles
Hence, The total miles of the trip are 521.68 miles.
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Write an equation to match this graph.
to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below
\((\stackrel{x_1}{3}~,~\stackrel{y_1}{15})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{35}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{35}-\stackrel{y1}{15}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{3}}} \implies \cfrac{ 20 }{ 4 } \implies 5\)
\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{15}=\stackrel{m}{ 5}(x-\stackrel{x_1}{3}) \\\\\\ y-15=5x-15\implies {\Large \begin{array}{llll} y=5x \end{array}}\)
What is 30 percent written as a fraction in lowest terms
Jane has 1 quarter, 3 dimes, and 4 nickels. What percent of dollar does Jane have?
i know the answer is 44% but can someone please explain how i got 44%??
Answer:
ok so I'm English not a hundred percent sure on your break down of money......so if I'm right in thinking that a nickel = 5 cents, dime = 10cents and a quarter =25cents
you add the amounts together
so 25 + 30 +20 = 75 cents.
there are 100 cents in a dollar so 100/100 X 75=75%
I have no idea how you got to 44%
Why do we use root mean square speed?
We use root mean square (RMS) speed to calculate the average speed of particles in a gas because it takes into account the speed of all particles in a distribution, regardless of direction.
It is particularly useful in studying gases because gas particles move in random directions with varying speeds. The RMS speed is the square root of the average of the squared speeds of all the particles in a gas.
The RMS speed is important because it is related to other properties of gases, such as temperature and pressure. For example, as the temperature of a gas increases, the RMS speed of its particles also increases.
This relationship is described by the Maxwell-Boltzmann distribution, which relates the speeds of gas particles to the temperature of the gas.
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exterior angle theorem
A) 110°
B) 34°
C) 23°
D) 30°
Answer:
D) 30°
Step-by-step explanation:
By exterior angle theorem:
? = 70° - 40°
? = 30°
If f(-1) for the polynomial….
Answer:
Yes ,because (x+1) is the factor of all degree 4 polynomial
2 people - 0 people = ? people