The expected value of the number of games played is 5.5 games, and the variance is 1.25.
To find the expected value of the number of games played, we need to consider all the possible ways the match can end. Since the match is a best of 7, one team needs to win at least 4 games. The possible outcomes are:
Team A wins in 4 games: AAAA
Team A wins in 5 games: AABAA or ABAAA
Team A wins in 6 games: ABAABA, ABABAA, or ABBAAA
Team A wins in 7 games: ABABABA, ABABAB, ABBABAA, or ABBABAAA
Similarly, we can list the possible outcomes for Team B winning in 4, 5, 6, or 7 games. However, since both teams are equally likely to win each game, the probability of each outcome is the same. Therefore, the expected value of the number of games played is:
E(X) = (41/8) + (52/8) + (63/8) + (72/8) = 5.5 games
To find the variance, we need to first calculate the squared deviation from the expected value for each outcome. For example, for the outcome AABAA, the deviation is (5-5.5) = -0.5, and the squared deviation is (-0.5)^2 = 0.25. We can then multiply each squared deviation by the probability of that outcome and sum them up,
Var(X) = (1/8)(4-5.5)^2 + (2/8)(5-5.5)^2 + (3/8)(6-5.5)^2 + (2/8)(7-5.5)^2
= 1.25
Therefore, the expected value of the number of games played is 5.5 games, and the variance is 1.25.
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During a basketball game, you want to pass the ball to either Player A or Player B. You estimate that Player B is about 15 feet from you, as shown.
b. How can you prove that Player A and Player B are the same distance from the basket?
Using the Pythagorean Rule we know that player A is 19.2 ft away from us.
What is the Pythagorean Rule?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.
These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.
The Pythagorean Rule can be used to determine the distance between you and Player A since the distances between you, Player A, and Player B are in the shape of a right-angled triangle.
c² = a² + b²
Where;
c = hypotenuse = Distance between you and player A
a = Length of the triangle
b = Height of triangle
Then, calculate as follows:
c² = 12² + 15²
c² = 144 + 225
c = √369
c = 19.2 ft
Therefore, using the Pythagorean Rule we know that player A is 19.2 ft away from us.
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Correct question:
During a basketball game, you want to pass the ball to either Player A or Player B. You estimate that Player B is about 15 feet from you, as shown. How far away from you is Player A?
Are the gas company charges linear?
Gas company charges are typically not linear due to the use of fixed fees, variable charges, and tiered pricing structures. While it is possible for a company to adopt a linear rate structure, it is not common in practice.
The charges levied by gas companies can vary depending on a variety of factors, including the amount of gas used, the location, the season, and other factors. However, when considering a particular rate structure, we can analyze whether the charges are linear or not.
A linear rate structure implies that the cost of gas usage is directly proportional to the amount of gas consumed. In other words, if you use twice as much gas, you would be charged exactly twice as much.
In practice, most gas companies use non-linear pricing structures that incorporate fixed charges, variable charges, and tiered pricing structures. For instance, a gas company may charge a fixed monthly fee for the gas supply, regardless of the amount of gas used. Additionally, there may be variable charges that depend on the amount of gas consumed, with different rates applying to different usage levels. Finally, some companies may apply tiered pricing structures, where the price per unit of gas increases as consumption levels increase.
For example, suppose a gas company charges a fixed fee of $10 per month for the gas supply, and then $0.10 per cubic foot of gas for the first 500 cubic feet used in a month, and then $0.15 per cubic foot for all additional usage. In this case, the pricing structure is not linear, as the rate per cubic foot of gas changes depending on the amount consumed.
It is also important to note that gas companies may adjust their pricing structures from time to time in response to market conditions, regulatory changes, or other factors. Therefore, it is important for consumers to review their bills regularly to ensure that they understand the charges and are not being overcharged.
In conclusion, gas company charges are typically not linear due to the use of fixed fees, variable charges, and tiered pricing structures. While it is possible for a company to adopt a linear rate structure, it is not common in practice.
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OMG PLEASE HELP ME SOMEONE
Practice 1: DE is congruent to BC. Find the measure of arc BC.
88 is the measure of arc BC.
What is arc ?
In general, an arc is any smooth wind joining two points. The length of an arc is known as its arc length. In a graph, a graph arc is an ordered brace of conterminous vertices. In particular, an arc is any portion( other than the entire wind) of the circumference of a circle.
An arc is the term used to describe the convex area of a circle that curves away from an angle like this, between two line segments or rays. A circle's circumference, or outside border, is known as the arc's circumference, and it is this area that is measured when an arc is drawn along it.
DE ≅ BC
3x + 22 = 4x
4x - 3x = 22
x = 22
BC = 4X = 4 * 22
= 88
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Do you think the difference of 1.4 - 0.95 is less than one or greater than one? Explain
Answer:
The difference of 1.4 - 0.95 is less than one.
To understand why, we need to calculate the difference between the two numbers:
1.4 - 0.95 = 0.45
Since 0.45 is less than 1, we can conclude that the difference of 1.4 - 0.95 is less than one.
Step-by-step explanation:
1. Tesha wrote an expression that is equivalent to (20 + 4) ÷ 12. Which
expression could be the one Tesha wrote?
A. 36 3 x 5
B. (3 x 3 x 3) = 3 x 1
C. (5 x 6 + 2 x 3) = (3 x 2 x 3)
D. (8 x 5 x 2) = (10 x 2)
Therefore, the expression that Tesha wrote is most likely option. [tex]C: (5 *6 + 2 *3)/(3*2*3).[/tex]
What is equation?An equation is a mathematical statement that shows the equality of two expressions or values. It contains an equal's sign (=) which separates the two expressions that are equal to each other. Equations can be simple or complex and can involve one or more variables, which are typically represented by letters. Equations are used extensively in mathematics, science, engineering, and many other fields to model and solve problems. Solving an equation involves finding the values of the variables that make the equation true.
To solve this problem, we need to simplify the expression.[tex](20 + 4) /12[/tex]:
[tex](20 + 4) / 12 = 24 / 12 = 2[/tex]
So, the expression that Tesha wrote must also simplify to 2. Let's check each of the options:
A. [tex]36 / 3 *5 = 12 * 5 = 60[/tex], which is not equivalent to 2. So, option A is not the correct one.
B. [tex](3 * 3 * 3) / 3 * 1 = 27 / 3 *1 = 9 * 1 = 9[/tex], which is not equivalent to 2. So option B is not the correct one.
C. [tex](5 * 6 + 2 * 3) / (3 * 2 * 3) = (30 + 6) / 18 = 36 / 18 = 2[/tex], which is equivalent to 2. So, option C is the correct one.
D. [tex](8 * 5 *2) / (10 * 2) = 80 /20 = 4[/tex], which is not equivalent to 2. So option D is not the correct one.
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as the sample size increases, the variability among the sample means . a. decreases b. increases c. depends upon the specific population being sampled
As the sample size increases, the variability among the sample means decreases, option A.
The number of observations used to calculate estimates for a certain population is known as the sample size. The sample size was determined by drawing from the population. Sampling is the practise of choosing a portion of the population from which to draw conclusions about the characteristics of the entire population. A subset of a population is chosen for study based on the number of entities in it.
Population data is a sizable collection of information that covers the whole population under investigation. All the components that are investigated for the research make up a population.
Yet, sample data is a component of the population. Generally, computing the entire population is rather cumbersome and challenging. In this instance, a representative sample of the population is chosen. Sample data refers to this sample.
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Verify the identity so that the left side looks like the right side.
[tex]\frac{1+csc(x)}{cot(x)+cos(x)}=sec(x)[/tex]
Answer:
See below for proof.
Step-by-step explanation:
Given expression:
[tex]\implies \dfrac{1+\csc(x)}{\cot(x)+\cos(x)}[/tex]
[tex]\boxed{\begin{minipage}{4.3 cm}\underline{Trigonometric Identities}\\\\$\csc(x)=\dfrac{1}{\sin(x)}$\\\\\\$\cot(x)=\dfrac{\cos(x)}{\sin(x)}$\\\\\\$\sec(x)=\dfrac{1}{\cos(x)}$\\\\\end{minipage}}[/tex]
Use the trigonometric identities to rewrite csc(x) and cot(x) in terms of sin(x) and cos(x):
[tex]\implies \dfrac{1+\dfrac{1}{\sin(x)}}{\dfrac{\cos(x)}{\sin(x)}+\cos(x)}[/tex]
Simplify the numerator and denominator:
[tex]\implies \dfrac{\dfrac{\sin(x)+1}{\sin(x)}}{\dfrac{\cos(x)+\sin(x)\cos(x)}{\sin(x)}}[/tex]
[tex]\textsf{Apply the fraction rule:} \quad \dfrac{\dfrac{a}{b}}{\dfrac{c}{b}}=\dfrac{a}{c}[/tex]
[tex]\implies \dfrac{\sin(x)+1}{\cos(x)+\sin(x)\cos(x)}[/tex]
Factor out cos(x) from the denominator:
[tex]\implies \dfrac{\sin(x)+1}{\cos(x)(1+\sin(x))}[/tex]
Cancel the common factor (1 + sin(x)):
[tex]\implies \dfrac{1}{\cos(x)}[/tex]
Rewrite 1/cos(x) using the identity:
[tex]\implies \sec(x)[/tex]
Therefore, the equation has been verified.
Let's see
LHS
[tex]\\ \sf\longmapsto \dfrac{1+csc(x)}{cot(x)+cos(x)}[/tex]
bring all into sine cosine form[tex]\\ \sf\longmapsto \dfrac{1+\dfrac{1}{sin(x)}}{\dfrac{cos(x)}{sin(x)}+cos(x)}[/tex]
[tex]\\ \sf\longmapsto \dfrac{\dfrac{1+sin(x)}{\cancel{sin(x)}}}{\dfrac{cos(x)+sin(x)cos(x)}{\cancel{sin(x)}}}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1+sinx}{cosx(1+sinx)}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{cosx}[/tex]
[tex]\\ \sf\longmapsto sec(x)[/tex]
verified
Q9. Calculate the area of this rectangle in cm² 4.3 cm 2.5cm
Answer: 10.75
Step-by-step explanation: 1: Based on the given conditions, formulate: 4.3 x 2.5
2: Calculate 4.3 x 2.5 = 10.75.
Therefore, the answer is 10.75.
calculating standard error is not important in statistics, we only need to look at the regular standard deviation of a single data set. group of answer choices true false
False. Calculating standard error is indeed important in statistics, as it serves a different purpose than the regular standard deviation of a single data set.
While standard deviation measures the variability or dispersion within a data set, standard error is used to measure the accuracy of a sample mean as an estimate of the true population mean.
1. Standard deviation measures the dispersion or spread of data points in a single data set. It helps you understand how much the individual data points deviate from the mean (average) of that data set.
2. Standard error, on the other hand, is a measure of how accurate a sample mean is in estimating the true population mean.
It is calculated by dividing the standard deviation of the sample by the square root of the sample size (n).
Standard Error (SE) = Standard Deviation (SD) / √n
3. As the sample size increases, the standard error decreases, indicating that the sample mean becomes a more accurate estimate of the population mean.
This is because larger sample sizes tend to have a smaller sampling error.
4. In hypothesis testing and confidence interval estimation, standard error plays a crucial role.
It helps to determine the margin of error and to assess the significance of differences between sample means.
5. While standard deviation is a useful measure for understanding variability within a single data set, standard error is essential for making inferences about the population based on the sample data.
In conclusion, both standard deviation and standard error are important in statistics as they serve different purposes. Ignoring standard error would lead to inaccurate conclusions about the population mean based on sample data.
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distributive property
5(y+2)+3(y-4)?
1. 5y+2+3y-12
2. 5y+10+3y+4
3. 5y+10+3y-12
4. 5y+2+3y-4
Answer:
Step-by-step explanation:
It 3. cause you want to expand the number outside to every number or variable in the inside of the brackets
Answer:
not know but know formula
Step-by-step explanation:
8y + y-2
What is an equation of the line that passes through the points (0, -6) and (6, 2)
Answer:
y = 4/3x - 6
Step-by-step explanation:
The equation is y = mx + b
m = the slope
b = y-intercept
Slope = rise/run or (y2 - y1) / (x2 - x1)
Points (0, -6) and (6, 2)
We see the y increase by 8, and the x increase by 6, so the slope is
m = 8/6 = 4/3
Y-intercept is located at (0, -6)
So, the equation is y = 4/3x - 6
Solve the system of equations by Substitution. Show ALL your work.
4x2 + y2 = 4
y = x + 2
The system of equations has two solutions: (0,2) and (-4/5, -6/5).
Define Substitution methodThe substitution method is a way to solve a system of two linear equations with two variables. The method involves solving one of the equations for one of the variables, and then substituting that expression into the other equation in place of the same variable. This process reduces the system of two equations and two variables to a single equation and a single variable, which can then be solved.
We have the system of equations:
4x² + y² = 4 ........(1)
y = x + 2 ........(2)
We can solve this system of equations by substitution.
Substitute (2) into (1) to eliminate y:
4x² + (x + 2)² = 4
Simplify and solve for x:
4x² + x² + 4x + 4 = 4
5x²+ 4x = 0
x(5x + 4) = 0
x = 0 or x = -4/5
If x = 0, then from equation (2), y = 2. So one solution is (x,y) = (0,2).
If x = -4/5, then from equation (2), y = -6/5. So the other solution is (x,y) = (-4/5, -6/5).
Therefore, the system of equations has two solutions: (0,2) and (-4/5, -6/5).
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Please help with number 5 Quickly
Answer:
V = 75[tex]\pi[/tex] or 235.619449... cm / 235.62 cm
Hope this helps!
Step-by-step explanation:
The formula for the volume of a cone is [tex]V=\frac{1}{3} *h*\pi r^{2}[/tex].
[tex]V = \frac{1}{3} *9*\pi 5^{2}[/tex] ( Simplify 1/3 and 9 )
[tex]V=3*25\pi[/tex]
[tex]V=75\pi[/tex]
V = 235.619449019 or 235.62
A parabolic archway is 25 meters high at the vertex. At a height of 23 meters, the width of the archway is 16 meters, as shown in the figure.
How wide (in m) is the archway at ground level? (Round your answer to the nearest whole number.)
PLEASE HELP URGENT DUE VERY SOON
Answer:
y=6x-4
Step-by-step explanation:
The slope-intercept form is y=mx+b
The m in the equation stands for the slope.
The b in the equation stands for the y-intercept.
So you input the y-intercept given to you in the problem, -4, and the slope, 6.
So the equation should be: y=6x-4
Y’all help a girl out pleaseeee thanks
The graph of this inequality is located at x = 4 and is represented using a solid line with shaded region to the right of the line.
What is inequality?Using a mathematical symbol like (less than), > (greater than), (less than or equal to), or (less than), an inequality statement compares the values of two expressions (greater than or equal to). When two expressions are compared, an inequality means that they are not equal and that one expression is either greater or smaller than the other.
For instance, the inequality 5 < 7 denotes that the number 5 is lower than the number 7, whereas the inequality 2x + 3 > 7 denotes that the number 2x + 3 is higher than the number 7. Algebra, calculus, and optimisation are just a few of the areas of mathematics where inequalities are frequently employed to describe connections between numbers and to solve issues.
The given inequality is x + 10 ≥ 14.
Simplifying the expression we have:
x ≥ 14 - 10
x ≥ 4
The graph of this inequality is located at x = 4 and is represented using a solid line with shaded region to the right of the line.
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What are the domain and range of the function f(x) = 2/3 ( x- 4) squared - 5?
Select TWO correct answers.
From the given function, the domain of the function is (-∞, ∞) and range of the function is (-∞, -5].
The given function is:
[tex]f(x) = (2/3)(x - 4)^2 - 5[/tex]
The domain of a function is the set of all possible input values (x) for which the function is defined. In this case, there are no restrictions on the input, so the domain is all real numbers:
Domain: (-∞, ∞)
The range of a function is the set of all possible output values (y) that the function can produce. To find the range of the given function, we can complete the square:
[tex]f(x) = (2/3)(x - 4)^2 - 5 \\ = (2/3)(x^2 - 8x + 16) - 5\\ = (2/3)x^2 - (16/3)x + 7.33\\ = (2/3)(x - 4)^2 - 4.67\\[/tex]
Since the term [tex](x - 4)^2[/tex] is always non-negative, the smallest value of the function occurs when [tex](x - 4)^2 = 0[/tex], which happens when x = 4. Substituting x = 4 into the equation gives:
[tex]f(4) = (2/3)(4 - 4)^2 - 5 \\ = -5[/tex]
Therefore, the range of the function is all real numbers less than or equal to -5:
Range: (-∞, -5]
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Please help solve this!!!
Answer:13,595,327.65
Step-by-step explanation:
Mariya was asked to solve StartFraction a over negative 13 EndFraction less-than-or-equal-to negative 16 and then graph the solution. Her work is shown below. In which step, if any, did Mariya make a mistake in her wor
Mariya's mistake in solving the inequality and plotting the number line is in step 3.
What is Inequality?In mathematics, an inequality is a statement that compares two values or expressions, indicating whether they are equal, not equal, greater than, less than, greater than or equal to, or less than or equal to each other.
Inequalities can be solved by manipulating them in much the same way as equations, but with one important difference: when an inequality is multiplied or divided by a negative number, the direction of the inequality is reversed. For example, if we have the inequality -3x > 12, we can solve for x by dividing both sides by -3, but we also need to reverse the direction of the inequality, giving us x < -4.
The inequality is given as:
[tex]$\frac{a}{-13}\leq-16$[/tex]
Multiply both sides of the inequality by -13
a ≥ 208
The above means that the solution to the inequality are numbers greater than or equal to 208.
This means that we make use of a closed circle
In step 3 of Mariya's solution, the number line uses an open circle
Hence, Mariya's mistake is in step 3
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The complete question is:
Mariya was asked to solve Start Fraction a over negative 13 End Fraction less-than-or-equal-to negative 16 and then graph the solution. Her work is shown below. Step Mariya’s work Start Fraction a over negative 13 End Fraction less-than-or-equal-to negative 16 Step 1 (Negative 13) Start Fraction a over negative 13 End Fraction less-than-or-equal-to negative 16 (negative 13) Step 2 a greater-than-or-equal-to 208 Step 3 A number line going from 205 to 211. An open circle is at 208. Everything to the right of the circle is shaded. In which step, if any, did Mariya make a mistake in her work? Step 1 Step 2 Step 3 No mistake found
What is the solution to 4x2-25 = 0?
The correct answer is ± 5÷2
I NEED SOME HELP PLEASE
Answer:
[C] $28.39
Step-by-step explanation:
As given that-
Markie's gross pay is $457.88The amount of social security deducted is 6.2 % of gross pay.Question to answer -
How much of her gross pay will be deducted for the Social Security tax?Solve-
Turn 6.2% into a decimal - 0.062Social Security tax = 0.062 × Gross pay amountThus,
= 0.062 × 457.88
= 28.38856
= $ 28.39 (Approx)
Answer-
Hence, the Social Security tax deducted from gross pay will be $28.39 .
Which means the correct answer is [C] $28.39
RevyBreeze
OABC is a sector of a circle with centre O.
Angle AOC = 50°
AC = 12 cm
Work out the area of the shaded segment of the circle.
Give your answer correct to 3 significant figures.
Answer:
ans:88.18cm
Step-by-step explanation:
What is the sum of the polynomials? (–x2 9) (–3x2 – 11x 4) a. –4x2 – 2x + 4 b. –4x2 – 11x + 13 c. 2x2 + 20x + 4 d. 2x2 + 11x 5
Answer:
B
Step-by-step explanation:
for an account balance with a book value of $1.5 million, the sample size is 125. given this information, the sampling interval will be $
The sampling interval for this account balance is $12,000.
To calculate the sampling interval, we will use the following formula:
Sampling interval = Population value (Book value) / Sample size
Student question: For an account balance with a book value of $1.5 million, the sample size is 125.
Given this information, the sampling interval will be:
Sampling interval = $1,500,000 / 125
Sampling interval = $12,000.
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ANSWER ASAP PLS....................
GIVING BRAINLIEST FIRST ONE TO ANSWER! (Its surface area) I would be super happy if somebody helped me on this! I'm so confused...
Answer:
1. 36
2. 28
Step-by-step explanation:
You are just counting how many sides are showing.
The right side, you see 6 green sides. Although you cannot see the other side, you know that it must be 6 also. You count the orange and blue. That is 12. The bottom is 6. the back is 6.
6 + 6 + 12 + 6 + 6 = 36
Helping in the name of Jesus.
After running a marathon,Alvin reduced his training by 18 miles per week on a period of 3 weeks. Which equation can be used to represent the average weekly change in his training?
A) -18 ÷ -3 = +6
B) +18 ÷ -3= -6
C) +18 ÷ +3 = +6
D) -18 ÷ 3 = -6
Answer:
C) +18 ÷ +3 = +6
Step-by-step explanation:
The average weekly change in Alvin's training can be calculated by finding the total change in his training over the 3 weeks and then dividing it by the number of weeks. Since he reduced his training by 18 miles per week, his total change over the 3 weeks would be 18 miles/week * 3 weeks = 54 miles.
To represent the average weekly change in his training using an equation, we need to divide the total change by the number of weeks, which gives us:
Average weekly change = total change ÷ number of weeks
Substituting the values we found, we get:
Average weekly change = 54 miles ÷ 3 weeks = 18 miles/week
100 points !!!!!
1+[square root] n+11=n
A, -2 and 5 are both real solutions
B. -2 is a real solution and 5 is an extraneous solution
C. -2 is an extraneous solution and 5 is a real solution
D. -2 and 5 are both extraneous solutions
Answer:
To solve the equation, we need to isolate the square root term and square both sides of the equation. We have:
1 + √n + 11 = n
√n = n - 12
Squaring both sides:
n = (n - 12)^2
n = n^2 - 24n + 144
n^2 - 25n + 144 = 0
Factorizing the quadratic equation:
(n - 16)(n - 9) = 0
Therefore, n = 16 or n = 9. We need to check these solutions in the original equation to see if they are valid.
For n = 16:
1 + √16 + 11 = 16
1 + 4 + 11 = 16
16 = 16
The solution n = 16 satisfies the equation.
For n = 9:
1 + √9 + 11 = 9
1 + 3 + 11 = 9
15 = 9
The solution n = 9 does not satisfy the equation.
Therefore, the only real solution is n = 16, which corresponds to option C: -2 is an extraneous solution and 5 is a real solution.
Hope This Helps!
¿Qué expresión se sumaría a 5x + 7 para que sea equivalente a la expresión 9(x + 1)?
The expression that we need to add to 5x + 7 to make it equivalent to 9(x + 1) is -2x + 2.
To make the expressions 5x + 7 and 9(x + 1) equivalent, we need to find the expression that, when added to 5x + 7, will give us 9(x + 1).
First, we can simplify 9(x + 1) by distributing the 9:
9(x + 1) = 9x + 9
Now we can see that we need to find an expression that, when added to 5x + 7, will give us 9x + 9:
5x + 7 + ? = 9x + 9
To find the missing expression, we need to isolate the variable on one side of the equation and the constant terms on the other side:
5x - 9x = 9 - 7
Simplifying this expression, we get:
-4x = 2
Dividing both sides by -4, we get:
x = -1/2
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Question:-
What expression would be added to 5x + 7 to make it equivalent to the expression 9(x + 1)?
The seventh-grade class needs to elect a new class president. Mary is writing an article on the election for the school paper and surveys a random selection of students about which candidate they support. The table below shows the results so far. Mary wants to survey 10 more people.
Candidate Number supporting the candidate
Julian 15
Mariana 9
Terrell 16
Denise 10
Based on the data, estimate how many of the next 10 students surveyed will support Julian.
If necessary, round your answer to the nearest whole number.
Answer:
3
Step-by-step explanation:
To estimate the number of students out of the next 10 who will support Julian, we can use the proportion of students who have supported Julian so far.
The total number of students who have been surveyed is:
15 + 9 + 16 + 10 = 50
Out of these 50 students, 15 have supported Julian. Therefore, the proportion of students who have supported Julian so far is:
15/50 = 0.3
To estimate how many of the next 10 students surveyed will support Julian, we can multiply the proportion of students who have supported Julian so far by 10:
0.3 x 10 = 3
Therefore, we can estimate that out of the next 10 students surveyed, about 3 will support Julian.