The null hypothesis (H0) for this situation would be that there is no difference in the proportion of male and female students with an overall GPA of 3.5 or higher.
The alternative hypothesis (Ha) would be that there is a difference in the proportion of male and female students with an overall GPA of 3.5 or higher.
Formally, we can write the hypotheses as:
H0: p_male = p_female (where p_male represents the proportion of male students with an overall GPA of 3.5 or higher, and p_female represents the proportion of female students with an overall GPA of 3.5 or higher)
Ha: p_male ≠ p_female
The president of the university can test these hypotheses using a hypothesis test for the difference in proportions. She can calculate the test statistic using the sample proportions and sample sizes for male and female students, and then compare it to the appropriate critical value or p-value based on the desired level of significance.
If the test results provide strong evidence against the null hypothesis, she can reject it and conclude that there is a statistically significant difference in the proportion of male and female students with an overall GPA of 3.5 or higher. If the test results do not provide enough evidence to reject the null hypothesis, she can fail to reject it and conclude that there is not enough evidence to suggest a difference in grades between males and females.
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how many shortest lattice paths start at (2, 2) and
a) end at (11, 11) and pass through (8, 10)?
b) end at (11,11) and avoid (8,10)
A. The number of shortest lattice paths from (2, 2) to (11, 11) that pass through (8, 10) is 28 * 4 = 112.
B. The number of shortest lattice paths from (2, 2) to (11, 11) that avoid (8, 10) is the total number of paths minus the number of paths that pass through (8, 10), which is 48620 - 112 = 48508.
What is combinatorics?
Combinatorics is a branch of mathematics that deals with counting and arranging the possible outcomes of different arrangements and selections of objects.
For part (a), the number of shortest lattice paths from (2, 2) to (11, 11) that pass through (8, 10) is given by the product of the number of shortest lattice paths from (2, 2) to (8, 10) and from (8, 10) to (11, 11).
To find the number of shortest lattice paths from (2, 2) to (8, 10), we can count the number of ways to choose 6 steps up out of 8 total steps (the remaining 2 steps are to the right), which is 8 choose 6 = 28.
Similarly, the number of shortest lattice paths from (8, 10) to (11, 11) is the number of ways to choose 1 step up out of 4 total steps (the remaining 3 steps are to the right), which is 4 choose 1 = 4.
Therefore, the number of shortest lattice paths from (2, 2) to (11, 11) that pass through (8, 10) is 28 * 4 = 112.
b) To find the number of shortest lattice paths from (2, 2) to (11, 11) that avoid (8, 10), we can use the principle of inclusion-exclusion.
Let's first count the number of shortest lattice paths from (2, 2) to (11, 11) without any restrictions. Since we can only move up or to the right, the number of such paths is the number of ways to choose 9 steps up out of 18 total steps (the remaining 9 steps are to the right), which is 18 choose 9 = 48620.
Next, we count the number of shortest lattice paths from (2, 2) to (11, 11) that pass through (8, 10). Using the method described in part (a), we found that the number of such paths is 28 * 4 = 112.
Therefore, the number of shortest lattice paths from (2, 2) to (11, 11) that avoid (8, 10) is the total number of paths minus the number of paths that pass through (8, 10), which is 48620 - 112 = 48508.
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A farmer wants to fence an area of 750 000 m² in a rectangular field and divide it in half with a fence parallel to one of the sides of the rectangle. How can this be done so as to minimize the cost of the fence?
The farmer should construct a rectangle that is twice as long as it is wide, with dimensions of 1216.56 m x 608.28 m, and should use 7301.36 m of fence to divide it in half parallel to the shorter side in order to minimize the cost of the fence.
To minimize the cost of the fence, the farmer should construct a rectangle that is twice as long as it is wide, with the dividing fence parallel to the shorter side. This will result in two identical rectangles each with an area of 375 000 m².
The perimeter of the rectangle can be calculated as follows:
P = 2L + 2W
where L is the length and W is the width.
Since the area of the rectangle is 750 000 m² and the length is twice the width, we can write:
L x W = 750 000
L = 2W
Substituting L = 2W into the equation for area, we get:
2W x W = 750 000
2W² = 750 000
W² = 375 000
W = 608.28 m
L = 2W = 1216.56 m
So the dimensions of the rectangle are 1216.56 m x 608.28 m.
The perimeter of each rectangle is:
P = 2L + 2W
P = 2(1216.56) + 2(608.28)
P = 3650.68 m
The total length of fence needed is twice the perimeter, since we are dividing the rectangle in half:
Total fence length = 2 x 3650.68 = 7301.36 m
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The polynomial â 2x2 + 700x represents the budget surplus of the town of Alphaville.
Betaville's surplus is represented by x2 - 100x + 80,000. If x represents the tax revenue in
thousands from both towns, enter the expression that represents the total surplus of both
towns together.
The expression that represents the total surplus of both towns together is ?
The total surplus of both towns together is represented by the polynomial [tex]3x^2 + 600x + 80,000.[/tex]
The expression that represents the total surplus of both towns together is (â 2x2 + 700x) + (x2 - 100x + 80,000).?To find the total surplus of both towns together, we need to add the budget surplus of Alphaville and Betaville.
The budget surplus of Alphaville is represented by the polynomial [tex]2x^2 + 700x.[/tex]
The budget surplus of Betaville is represented by the polynomial x^2 - 100x + 80,000.
Therefore, the expression that represents the total surplus of both towns together is:
[tex](2x^2 + 700x) + (x^2 - 100x + 80,000)[/tex]
Simplifying this expression, we get:
[tex]3x^2 + 600x + 80,000[/tex]
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Can someone help me fast!?!?
Trying to get better at doing these kinds of problems.
Graph the line -3x + 5y = 15
Which one would it be? This will help a lot :D
According to the question the graph the line -3x + 5y = 15, we can start by solving for y:
-3x + 5y = 15
5y = 3x + 15
y = (3/5)x + 3
Define graph.As an algebraic framework that depicts a specific function by joining a collection of points, a graph is defined. It establishes a pairwise connection among the items. The graph is made up of nodes (vertices) linked by edges. (lines).
Briefing :
Now we have the equation in slope-intercept form (y = mx + b) where the slope is 3/5 and the y-intercept is 3.
To graph the line, we can start at the y-intercept (the point (0, 3)) and then use the slope to find additional points. Since the slope is 3/5, we can move up 3 units to the right 5 units to get to the point (5, 6), and down 3 units to the left 5 units to get to the point (-5, 0). Connect these points to get the line.
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10% of people are left handed. If 800 people are randomly selected, find the likelihood that at least 12% of the sample is left handed
The likelihood of at least 12% of the sample being left-handed is approximately 0.007 or 0.7%.
Let X be the number of left-handed people in a sample of 800 individuals. Since the probability of a person being left-handed is 0.1, the probability of a person being right-handed is 0.9. Then, X follows a binomial distribution with n = 800 and p = 0.1.
P(X ≥ 0.12*800) = P(X ≥ 96)
where 96 is the smallest integer greater than or equal to 0.12*800.
[tex]P(X > =96)-P(X < 96)=1-[K=0 to 95](800 CHOOSE )(0.1^{k} (0.9)^{2} (800-k)[/tex]
This is the complement of the probability of getting less than 96 left-handed people in the sample. Using a calculator or statistical software, we can find that:
P(X ≥ 96) ≈ 0.007
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Use the properties of logarithms to simplify as much as possible. 3) In(4x^5) – In (x^3)- In 4 4) The price of beef has inflated by 2%. If the price of beef inflates 2% compounded biannually, how lung will it take for the price of beef to triple?
3) The expression In(4x^5) - In(x^3) - In 4 can be simplified using the properties of logarithms. We know that ln(a) - ln(b) = ln(a/b) and ln(a^n) = n ln(a), so we can write:In(4x^5) - In(x^3) - In 4 = In[(4x^5)/(x^3)] - In 4= In(4x^2) - In 4= In(4x^2/4)= In(x^2)Thus, the simplified expression is In(x^2).4) To solve this problem, we need to use the formula for compound interest:A = P(1 + r/n)^(nt)where A is the final amount, P is the initial amount, r is the interest rate (as a decimal), n is the number of times interest is compounded per year, and t is the number of years.We want to find t when A = 3P and r = 0.02 (since the price of beef has inflated by 2%). We are told that interest is compounded biannually, so n = 2. Plugging in these values and solving for t, we get:3P = P(1 + 0.02/2)^(2t)3 = (1.01)^2tln(3) = ln(1.01^2t)ln(3) = 2t ln(1.01)t = ln(3) / (2 ln(1.01))Using a calculator, we find t ≈ 34.64 years. Therefore, it will take about 34.64 years for the price of beef to triple at a 2% biannual inflation rate.
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It will take approximately 110 years for the price of beef to triple when inflating 2% compounded biannually.
3) To simplify the expression In(4x^5) - In(x^3) - In(4), we will use the properties of logarithms:
- In(a) - In(b) = In(a/b)
- In(a^b) = b * In(a)
So, we can rewrite the expression as:
In(4x^5 / (x^3 * 4))
Now, we can simplify the expression inside the natural logarithm:
(4x^5) / (4x^3) = x^(5-3) = x^2
Thus, the simplified expression is:
In(x^2)
4) To find how long it will take for the price of beef to triple when inflating 2% compounded biannually, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
where A is the final amount, P is the initial amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years. In this case, we want the final amount to be triple the initial amount:
3P = P(1 + 0.02/2)^(2t)
To solve for t, we can divide both sides by P:
3 = (1 + 0.01)^(2t)
Now, take the natural logarithm of both sides and use the properties of logarithms:
ln(3) = ln((1 + 0.01)^(2t))
ln(3) = 2t * ln(1 + 0.01)
Finally, isolate t:
t = ln(3) / (2 * ln(1 + 0.01))
t ≈ 109.96
It will take approximately 110 years for the price of beef to triple when inflating 2% compounded biannually.
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Un árbol ha sido roto por el viento de tal manera que sus dos partes forman un triángulo rectángulo. la parte superior tiene una longitud de 10 m, y la distancia medida sobre el piso hasta la cúspide del árbol es de 6 m. hallar la altura que tenía el árbol.
Se puede utilizar el teorema de Pitágoras para resolver este problema. Si se considera que la altura del árbol es la hipotenusa del triángulo rectángulo,
entonces la parte superior de la parte rota del árbol es uno de los catetos, y la distancia medida sobre el piso hasta la cúspide del árbol es el otro cateto.
Por lo tanto, se tiene que:
[tex]altura^2 = cateto1^2 + cateto2^2[/tex]
Reemplazando los valores conocidos, se tiene:
[tex]altura^2 = 10^2 + 6^2[/tex]
[tex]altura^2 = 136[/tex]
Tomando la raíz altura^2 = 136, se obtiene:
[tex]altura = √136[/tex]
altura ≈ 11.66 m
Por lo tanto, la altura que tenía el árbol antes de ser roto por el viento es de aproximadamente 11.66 metros.
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AutoTrader would like to estimate the number of years owners keep the cars that they purchased as a new vehicle. The following data shows the age of seven vehicles that were sold for the first time by their owners. Using this sample, the 90% confidence interval that estimates the average age of cars sold for the first time is ________. Group of answer choices (2. 56, 10. 30) (5. 14, 7. 72) (1. 27, 11. 59) (3. 93, 8. 93)
The 90% confidence interval that estimates the average age of cars sold for the first time is (2.56, 10.30).
To calculate the confidence interval, we can use the formula:
CI =[tex]\bar{X}[/tex] ± tα/2 * (s/√n)
where [tex]\bar{X}[/tex] is the sample mean, s is the sample standard deviation, n is the sample size, tα/2 is the critical value from the t-distribution table with (n-1) degrees of freedom and a confidence level of 90%.
Using the given data, we find that the sample mean is 6.43 years and the sample standard deviation is 2.69 years. With a sample size of 7, the critical value from the t-distribution table is 1.895.
Plugging in these values, we get:
CI = 6.43 ± 1.895 * (2.69/√7)
Simplifying this expression gives us the confidence interval (2.56, 10.30). Therefore, we can say with 90% confidence that the average age of cars sold for the first time is between 2.56 and 10.30 years.
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A circle is centered at c(0,0)c(0,0)c, left parenthesis, 0, comma, 0, right parenthesis. the point m(0,\sqrt{38})m(0, 38 )m, left parenthesis, 0, comma, square root of, 38, end square root, right parenthesis is on the circle.where does the point n(-5,-3)n(−5,−3)n, left parenthesis, minus, 5, comma, minus, 3, right parenthesis lie
The point N(-5,-3) lies inside the circle centered at C(0,0) with radius √38.
How we find the point lies inside the circle?Since the point M(0, √38) lies on the circle with center C(0,0), we can find the radius of the circle by finding the distance between M and C:
r = √[tex]((0 - 0)^2[/tex] + (√[tex]38 - 0)^2)[/tex] = √38
Now that we know the radius of the circle is √38, we can determine where the point N(-5,-3) lies relative to the circle. We can find the distance between N and the center of the circle:
d = √[tex]((-5 - 0)^2[/tex] + [tex](-3 - 0)^2)[/tex] = √34
Since the distance between N and the center of the circle is less than the radius of the circle, the point N is inside the circle. Therefore, N lies inside the circle centered at C(0,0) with radius √38.
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Challenge paints ornaments for a school play. Each ornament is as shown and is made up of two identical cones. uses one bottle of paint to paint 210 . How many bottles of paint does he need in order to paint 50 ornaments? Use 3.14 for .
The number of paint bottles required is 49.716 bottles
Thus, 50 bottles are needed to paint the ornaments.
What is Surface Area?Surface area is the sum of all exterior surfaces on a three-dimensional object, representing the quantity of material that covers it. Computing an object's surface area entrails measuring each of its faces and then adding up their areas altogether.
If we take, for instance, a cube, its surface area would be calculated by multiplying the measurement of one face width by another and then multiplying this value by six (each cube has six sides). The units applied to measure surface area are usually in square feet or square centimeters.
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A van can ferry a maximum of 12 people. By setting up an inequality, find the maximum number of vans that are needed to ferry 80 people
By setting up an inequality, the maximum number of vans that are needed to ferry 80 people are 7 vans.
To find the maximum number of vans needed to ferry 80 people using the given terms, let's set up an inequality. Let's use the variable "v" to represent the number of vans.
Since a van can ferry a maximum of 12 people, we can write the inequality as:
12v ≥ 80
Now, let's solve for "v":
Divide both sides of the inequality by 12.
v ≥ 80/12
Simplify the inequality.
v ≥ 6.67
Since we cannot have a fraction of a van, we need to round up to the nearest whole number:
v ≥ 7
Therefore, the maximum number of vans needed to ferry 80 people is 7 vans.
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In a graph, x represents the number of months since a business opened, and y represents the total amount of money the business has earned. The following three points are from the graph:
(2, 1990) (5, 4225) (9, 7205)
Find the slope and y-intercept. Explain what each represents.
Use first two points and the slope equation to find the slope:
m = (4225 - 1990)/(5 - 2) = 745The slope is 745.
Use the first point and point-slope equation to find the y-intercept:
y - y₁ = m(x - x₁), where m- slope, (x₁, y₁) - the given pointy - 1990 = 745(x - 2)y - 1990 = 745x - 1490y = 745x - 1490 + 1990y = 745x + 500The y-intercept is 500.
The slope of 745 represents the profit per month and the y-intercept of 500 represents the initial profit.
what is the product of -5 and -10 sign and result
Answer:
50, positive
Step-by-step explanation:
(-5) * (-10) = 50
When a negative multiplies by another negative, the answer is positive
So, the answer is 50 and the sign is positive
Mr. Woodley invested $1200 at 5% simple interest at the beginning of each year for a period of 8 years. Find the total accumulated value of all the investments at the end of the 8-year period.
It would be helpful if u used a geometric or arithmetic sequence formula.
Answer:
$1680
Step-by-step explanation:
PV = $1200
i = 5%
n = 8
Simple interest formula:
FV = PV (1 + i × n)
FV = 1200 (1 + 5% x 8)
FV = $1680
Suppose 60 seventh-grade students were surveyed.
How many can be expected to say that bike riding is
their favorite hobby?
Please IM IN NEED OF HELP
thx
We need to make some assumptions. Let's assume that the survey allowed students to choose one favorite hobby and that bike riding was one of the options.
We also need to know the percentage of students who chose bike riding as their favorite hobby. If this information is not given, we cannot accurately estimate the number of students who would say that bike riding is their favorite hobby.
Suppose that 30% of the surveyed students chose bike riding as their favorite hobby. To find out how many students this represents, we can use the following formula:
Expected number of students = Percentage of students x Total number of students surveyed
Plugging in the values we have, we get:
Expected number of students who say bike riding is their favorite hobby = 0.30 x 60 = 18
Therefore, we can expect that approximately 18 of the 60 seventh-grade students surveyed would say that bike riding is their favorite hobby, based on the assumption that 30% of the students chose this option.
It's important to remember that this is just an estimate based on the information we have. The actual number may be different depending on the survey results.
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Solve for x WILL MAKE BRAINLIEST QUESTION IN PHOTI ALSO
The measure of x in the intersected chord is 16.
How to find the angle in an intersected chord?If two chords intersect in a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.
Using the chord intersection angle theorem,
5x - 7 = 1 / 2 (119 + 27)
5x - 7 = 1 / 2 (146)
5x - 7 = 73
add 7 to both sides of the equation
5x - 7 = 73
5x - 7 + 7 = 73 + 7
5x = 80
divide both sides of the equation by 5
x = 80 / 5
x = 16
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If the equation, in which n, m, and r are constants, is true for all positive values of a, b, and c, what is the value of n?
The value of n is 6
Given expression is [tex]\frac{48a^{12}b^8c^{15}}{(2a^2bc^4)^3}=6a^nb^mc^r[/tex]
To find the value of n, we need to simplify the expression:
(48 × a¹² × b⁸ × c¹⁵) / (2 × a² × b × c⁴)³
First, we can simplify the denominator:
(2 × a² × b × c⁴)³ = 2³ × (a²)³ × b³ × (c⁴)³
= 8 × a⁶ × b³ × c¹²
(48 × a¹² × b⁸ × c¹⁵) / (8 × a⁶ × b³ × c¹²) = (8 × 6a⁶ × a⁶ × b⁵ × b³ × c₁₂ × c³) / (8 × a⁶ × b³ × c¹²)
Simplifying further, we get:
= 6 × a⁶ × b⁵ × c³
on comparing with R H S
a⁶ = aⁿ
So, n=6
Therefore, the value of n is 12, since that is the exponent of the variable "a".
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Given question is incomplete, the complete question is given below
For the expression below
[tex]\frac{48a^{12}b^8c^{15}}{(2a^2bc^4)^3}=6a^nb^mc^r[/tex]
If the equation, in which n, m, and r are constants, is true for all positive values of a, b, and c, what is the value of n?
The function f(x) = –x2 – 4x + 5 is shown on the graph. On a coordinate plane, a parabola opens down. It goes through (negative 5, 0), has a vertex at (negative 2, 9), and goes through (1, 0). Which statement about the function is true? The domain of the function is all real numbers less than or equal to −2. The domain of the function is all real numbers less than or equal to 9. The range of the function is all real numbers less than or equal to −2. The range of the function is all real numbers less than or equal to 9.\
The statement that is true is: "The range of the function is all real numbers less than or equal to 9
What is the function about?This quadratic function is indicated by a downward-opening parabola due to the negative coefficient of the squared term.
Found at coordinates (-2, 9), the vertex will be the highest point on this curved graph
Located on the x-axis at points (-5, 0) and (1, 0), each one serves as an intersection. Because of these intersections the following statement can be confidently said: "The range of the function consists of all actual numbers that are lesser or equal to 9."
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Sam makes mini pancakes for breakfast. Each pancake is a circle with a diameter of 6 centimeters.
a) Calculate the circumference of each pancake.
b) Calculate the area of each pancake.
Answer:
a) 18.84 cm
b) 28.26 cm²
Step-by-step explanation:
We Know
Each pancake is a circle with a diameter of 6 centimeters.
a) Calculate the circumference of each pancake.
Circumference of circle = d · π
d = 6 cm
We Take
6 · 3.14 = 18.84 cm
So, the circumference of each pancake is 18.84 cm.
b) Calculate the area of each pancake.
Area of circle = r² · π
r = 1/2 · d
r = 1/2 · 6 = 3 cm
We Take
3² · 3.14 = 28.26 cm²
So, the area of each pancake is 28.26 cm².
El 91 no es un número primo porque tiene más divisores que el 1 y el 91 verdadero o falso
The statement''El 91 no es un número primo porque tiene más divisores que el 1 y el 91'' is true because 91 is not a prime number.
A prime number is a positive integer that has only two divisors, 1 and itself. To check if 91 is a prime number, we need to find its divisors. We can start by dividing 91 by 2, but we find that 2 is not a divisor of 91. Next, we can try dividing it by 3, and we get 30 with a remainder of 1. This means that 3 is not a divisor of 91 either.
We continue dividing by 4, 5, 6, and so on until we reach 13, which gives us 7 as a quotient and 0 as a remainder. Therefore, the divisors of 91 are 1, 7, 13, and 91, which means that 91 is not a prime number because it has more than two divisors. Hence, the statement is true.
91 ÷ 2 = 45 r 1
91 ÷ 3 = 30 r 1
91 ÷ 4 = 22 r 3
91 ÷ 5 = 18 r 1
91 ÷ 6 = 15 r 1
91 ÷ 7 = 13 r 0
Since 91 has more than two divisors, it is not a prime number.
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Mr. Vega is going to buy a blue tractor that weighs 3/5 of a ton or a red tractor weighs 4/6 of a ton. Which tractor is heavier
The red tractor is heavier.
To determine which tractor is heavier, Mr. Vega needs to compare the weights of the blue and red tractors. The blue tractor weighs [tex]\frac{3}{5}[/tex] of a ton, and the red tractor weighs [tex]\frac{4}{6}[/tex] of a ton.
First, we need to simplify the fractions if possible. In this case, we can simplify the red tractor's fraction by dividing both the numerator and denominator by 2:
[tex]\frac{4}{6} = \frac{\frac{4}{2} }{\frac{6}{2} } = \frac{2}{3}[/tex]
Now we can compare the simplified fractions:
[tex]Blue tractor: \frac{3}{5}[/tex]
[tex]Red tractor: \frac{2}{3}[/tex]
To compare these fractions, we can find a common denominator. The least common multiple of 5 and 3 is 15. To convert the fractions to the same denominator, we multiply the numerators and denominators by the necessary factors:
[tex]Red tractor: (\frac{2}{3}) (\frac{5}{5}) = \frac{10}{15}[/tex]
[tex]Blue tractor: (\frac{3}{5}) (\frac{3}{3}) = \frac{9}{15}[/tex]
Now we can easily compare the weights:
[tex]Blue tractor: \frac{9}{15}[/tex]
[tex]Red tractor: \frac{10}{15}[/tex]
Since [tex]\frac{10}{15}[/tex] is greater than [tex]\frac{9}{15}[/tex] , the red tractor is heavier.
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A baseballâ player's batting average is 0. 343â, which can be interpreted as the probability that he got a hit each time at bat. â Thus, the probability that he did not get a hit is 1â0. 343=0. 657. Assume that the occurrence of a hit in any givenâ at-bat has no effect on the probability of a hit in otherâ at-bats. In oneâ game, the player had 5 âat-bats. What is the probability that he had 3 âhits? What expression can be used to calculate theâ probability?
0.135 or 13.5% is the probability that he had 3 âhits
The probability that the player had 3 hits in 5 at-bats can be calculated using the binomial probability formula, which is:
P(x) = (nCx) * p^x * (1-p)^(n-x)
where:
- P(x) is the probability of getting x hits
- n is the number of at-bats (in this case, 5)
- x is the number of hits we want to find the probability for (in this case, 3)
- p is the probability of getting a hit in one at-bat (in this case, 0.343)
- (1-p) is the probability of not getting a hit in one at-bat (in this case, 0.657)
Plugging in the values, we get:
P(3) = (5C3) * 0.343^3 * 0.657^(5-3)
P(3) = (10) * 0.039304527 * 0.4305961
P(3) = 0.134912947
Therefore, the probability that the player had 3 hits in 5 at-bats is approximately 0.135 or 13.5%.
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12. A normal distribution has a mean of 34 and a standard deviation of 7. Find the range of
values that represent the middle 95% of the data.
F. 27
G. 20 X 48
H. 13
J. 6
The range of values that represent the middle 95% of the data is from 20.18 to 47.82 or (20.18, 47.82).
What is Hypothesis test?A measurable speculation test is a strategy for factual deduction used to conclude whether the information within reach adequately support a specific speculation. We can make probabilistic statements about the parameters of the population thanks to hypothesis testing.
According to question:The middle 95% of a normal distribution is located within 1.96 standard deviations from the mean in both directions.
Therefore, the lower limit is:
34 - 1.96(7) = 20.18
And the upper limit is:
34 + 1.96(7) = 47.82
So the range of values that represent the middle 95% of the data is from 20.18 to 47.82 or (20.18, 47.82).
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WILL MARK BRAINLIEST!!
The amount that Benjamin must save every month to pay off the discounted premium is $ 40. 80
The total premium for the year would be $ 637. 20
How to find the amount saved ?The amount that Benjamin's discounted premium would come to for the year is:
= 1, 080 x ( 1 - 66 %)
= $ 367. 20
The amount he would need to save every month on deployment is :
= 367. 20 / 9
= $ 40. 80
His total premium would be :
= 367. 20 + ( 1, 080 / 12 x 3 months when he comes back )
= $ 637. 20
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Using the formulas, answer the question.
A = P(1 + =)nt
A = Pert
Ted invests $500 in an account that compounds interest quarterly with a 3.5%
rate. How much money will he have after 15 years? Round to the nearest
dollar.
Answer:
First, convert R as a percent to r as a decimal
r = R/100
r = 3.5/100
r = 0.035 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 500.00(1 + 0.035/4)(4)(15)
A = 500.00(1 + 0.00875)(60)
A = $843.30
A = $843 (round-off)
In triangle abc, point d is on side ac, ab=bd=dc=12 inches, and measurement of angle bdc= 2 times the measurement of angle abd. find ac
The length of AC in triangle ABC is 24 inches.
In triangle ABC, let point D be on side AC such that AB = BD = DC = 12 inches. We are given that the measure of angle BDC is twice the measure of angle ABD.
To find the length of AC, we can use the Law of Cosines. This law relates the lengths of the sides of a triangle to the cosine of one of its angles. In this case, we can apply the Law of Cosines to triangle ABD to find the length of AD:
AD^2 = AB^2 + BD^2 - 2 * AB * BD * cos(ABD)
Since AB = BD = 12 inches, we have:
AD^2 = 12^2 + 12^2 - 2 * 12 * 12 * cos(ABD)
AD^2 = 288 - 288 * cos(ABD)
Now, let's consider triangle BDC. We are given that the measure of angle BDC is twice the measure of angle ABD. Let's denote the measure of angle ABD as x. Therefore, the measure of angle BDC is 2x.
Since the sum of angles in a triangle is 180 degrees, we can write:
x + 2x + angle BCD = 180
3x + angle BCD = 180
angle BCD = 180 - 3x
Now, let's apply the Law of Cosines to triangle BDC to find the length of BC:
BC^2 = BD^2 + CD^2 - 2 * BD * CD * cos(BDC)
BC^2 = 12^2 + 12^2 - 2 * 12 * 12 * cos(2x)
BC^2 = 288 - 288 * cos(2x)
Since AD = DC, we have AD = 12 inches. Now we can write the equation for the total length AC:
AC = AD + DC
AC = 12 + 12
AC = 24 inches
Therefore, the length of AC in triangle ABC is 24 inches.
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Gabby had 578
7
8
yards of fabric. she used 3215
2
15
yards of fabric. estimate the amount of fabric gabby has left.
The same method of subtracting the amount of fabric used from the amount she started with to estimate the amount of fabric Gabby has left.
How to estimate the amount of fabric Gabby has left?To estimate the amount of fabric Gabby has left, we can subtract the amount of fabric she used from the amount she started with:
57878 - 3215215 ≈ -3157337
However, we can see that this result is negative, which doesn't make sense in the context of the problem. It's not possible for Gabby to have negative yards of fabric left.
It's likely that there was a mistake in the problem statement or in the numbers given. If the problem were corrected, we could use the same method of subtracting the amount of fabric used from the amount she started with to estimate the amount of fabric Gabby has left.
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Asap!!!! Solve the equation for v. v over 8 minus 4 equals negative 12 (18 points)
v = -128
v = -64
v = 16
v = 92
Answer:
v = -64
Step-by-step explanation:
First, you add 4 to both sides to isolate the variable term:
v/8 = -8
Next, you multiply both sides by 8 to isolate the variable on one side:
v = -64
So, the solution to the equation v/8 - 4 = -12 is v = -64.
One gallon of paint covers 50 square feet. A wall that measures 32 feet by 16 feet is going to be painted.
Area of Wall:
How many gallons of paint will it take?
If paint costs $27 per gallon, how much money will it take to paint the wall?
Answer:
10.24 gallons
$276.48
Step-by-step explanation:
The area of the wall can be calculated by multiplying the length and height of the wall:
Area of wall = length x height = 32 x 16 = 512 square feet
To calculate the number of gallons of paint needed, we need to divide the area of the wall by the coverage of one gallon of paint:
Number of gallons of paint = Area of wall / Coverage of one gallon of paint
Number of gallons of paint = 512 / 50
Number of gallons of paint = 10.24
Therefore, it will take approximately 10.24 gallons of paint to paint the wall.
To calculate the cost of the paint, we need to multiply the number of gallons of paint by the cost per gallon:
Cost of paint = Number of gallons of paint x Cost per gallon
Cost of paint = 10.24 x $27
Cost of paint = $276.48
Therefore, it will cost $276.48 to paint the wall.
1 ml =
a
litres
ii)
b
ml = 1 litre
iii) 1 cl =
c
litres
iv)
d
cl = 1 litre
v) 1 cl =
e
ml
vi)
f
cl = 1 ml
The corresponding measure of the parameters are;
i. 1ml = 0. 001 liter a.
ii. 1000ml = 1 liter b.
iii. 1 cl = 0. 01 liter c.
iv. 10dcl = 1 liter d.
v. 1cl = 100ml e.
v. 0. 01 cl = 1ml f.
How to determine the valuesTo convert the factors, we need to know the following conversion rates.
We have;
1 milliliter = 0. 001 liter
1 centiliter = 0. 01 liter
1 deciliter = 0. 1 liter
1 cubic centimeter = 1 millimeter
Hence, the sizes are determined by the corresponding factor.
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Complete question:
Convert the following to their equivalent measurement for each letter
i. 1 ml = a liters
ii) b ml = 1 liters
iii) 1 cl = c liters
iv)d cl = 1 liters
v) 1 cl = e ml
vi) f cl = 1 ml
