The correct option is C.
Probability of selecting all boys from 8 boys and 6 girls for a 4-person committee is 10/143.
To find the probability that the committee consists of all boys, we need to calculate the probability of selecting 4 boys out of 8 boys and no girls out of 6 girls.
The total number of ways to choose a 4-person committee from 14 students (8 boys and 6 girls) is given by the combination formula:
[tex]\[ \text{Total number of ways} = \binom{14}{4} \][/tex]
The number of ways to choose 4 boys out of 8 is given by:
[tex]\[ \binom{8}{4} \][/tex]
And since we don't choose any gi-rls, the number of ways to choose 0 girls out of 6 is simply 1.
So, the probability of selecting all boys is:
[tex]\[ \text{Probability} = \frac{\binom{8}{4} \times \binom{6}{0}}{\binom{14}{4}} \][/tex]
Let's calculate this:
[tex]\[ \text{Probability} = \frac{\binom{8}{4} \times \binom{6}{0}}{\binom{14}{4}} = \frac{\frac{8!}{4!(8-4)!} \times \frac{6!}{0!(6-0)!}}{\frac{14!}{4!(14-4)!}} \][/tex]
[tex]\[ = \frac{\frac{8!}{4!4!} \times 1}{\frac{14!}{4!10!}} \][/tex]
[tex]\[ = \frac{\frac{8 \times 7 \times 6 \times 5}{4 \times 3 \times 2 \times 1}}{\frac{14 \times 13 \times 12 \times 11}{4 \times 3 \times 2 \times 1}} \][/tex]
[tex]\[ = \frac{70}{1001} \][/tex]
[tex]\[ = \frac{10}{143} \][/tex]
So, the correct answer is option C: [tex]\( \frac{10}{143} \)[/tex].
The complete question is here:
A four-person committee is chosen from a group of eight boys and six girls.. If students are chosen at random, what is the probability that the committee consists of all boys?
A. 4/1001
B. 15/1001
C. 10/143
D. 133/143
Find the equation in standard form of the line parallel to y=-1/5x+7 and passing through the point (-10,-3)
Answer:
the desired equation is y = (-1/5)x - 5.
Step-by-step explanation:
Parallel lines have the same slope. Here that slope is -1/5.
Let's use the slope-intercept form of the equation of a straight line:
y = mx + b
We know this new line passes through (-10, -3). Substitute -3 for y in y = mx + b, as well as -10 for x and -1/5 for m:
-3 = (-1/5)(-10) + b and solve for b:
-3 = 2 + b. Then b = -5, and the desired equation is y = (-1/5)x - 5.
The students in Nora's class chose between two options for an assignment.5/8 of the students chose option 1. If there are 32 students in Nora's class how many chose option 1? .20.24.15.28.
Answer:20 students chose option 1
Step-by-step explanation:
20 students chose option 1
answer
Answer:
20
Step-by-step explanation:
In the sentence of = multiply. So you multiply 5/8 x 32
5/8 x 32/1 next you simply
5/1 x 4/1 =20/1 = 20
Approximately how many accidents occurred between 1965 and 1970 inclusive?
Answer:
About 1,800 accidents
Step-by-step explanation:
Observing the attached figure
In 1965 ----> Approximately 260 accidents
In 1966 ----> Approximately 325 accidents
In 1967 ----> Approximately 300 accidents
In 1968 ----> Approximately 350 accidents
In 1969 ----> Approximately 360 accidents
In 1970 ----> Approximately 400 accidents
Total------> Approximately 1.920 accidents
What are the inequalities for:
x is less than 8 and greater than 3
x is less than 4 and greater than -2
x is greater than 12 and less than or equal to 17
Answer:
3 < x < 8
-2 < x < 4
12 < x ≤ 17
Step-by-step explanation:
x is less than 8 and greater than 3
i.e 3 < x < 8
x is less than 4 and greater than -2
i.e -2 < x < 4
x is greater than 12 and less than or equal to 17
i.e 12 < x ≤ 17
choose two correct answers
the expressions equivalent to [tex]\(k - \frac{k}{2}\)[/tex] are:
- Option C: [tex]\(\frac{1}{2}k\)[/tex]
- Option D: [tex]\(k + 2\)[/tex]
The correct option is (C) and (D).
the calculation step by step to find expressions equivalent to [tex]\(k - \frac{k}{2}\):[/tex]
1. Given Expression:
[tex]\[ k - \frac{k}{2} \][/tex]
2. Step 1: Find a Common Denominator:
To combine the fractions, we need a common denominator. The common denominator for \(2\) and \(1\) is \(2\). So, let's rewrite the expression:
[tex]\[ k - \frac{k}{2} = \frac{2k}{2} - \frac{k}{2} \][/tex]
3. Step 2: Subtract the Fractions:
Subtract the numerators while keeping the common denominator:
[tex]\[ \frac{2k - k}{2} = \frac{k}{2} \][/tex]
4. Step 3: Simplify:
Divide the numerator by (2):
[tex]\[ \frac{k}{2} = \frac{1}{2}k \][/tex]
Therefore, the expressions equivalent to [tex]\(k - \frac{k}{2}\)[/tex] are:
- Option C: [tex]\(\frac{1}{2}k\)[/tex]
- Option D: [tex]\(k + 2\)[/tex]
which of the following is the best definition of a vertical asymptote
Answer:
Step-by-step explanation:
B
Answer: Option A: A vertical line that the line of the graph aproaches but never intecepts it.
Step-by-step explanation:
An asymptote is a graph line that aproaches infinitely to something (in this case a vertical line), but it does not touch it (so never intercepts the graph).
This means that the graph aproaches but never intercepts the line, so the correct answer is A.
The charge for a plumbing repair was $29.60 for parts, 1 1/4 hr. For labor at $56 per hr. And a $40 for the service call. What was the total cost (c) of the repair?
Answer: $139.60
Step-by-step explanation:
$40 for coming
$29.60 for parts
56 times 1.25 for labor = 70
70 + 29.6 + 40 = 139.6
The total cost (c) of the repair is given by the sum of the costs for parts, labor, and the service call that is [tex]\$139.60[/tex]
First, we calculate the labor cost. The plumber charged $56 per hour and worked for 1 1/4 hours. To find the total labor cost, we multiply the hourly rate by the time worked:
Labor cost = [tex]hourly \ rate \times \ time \ worked[/tex]
Labor cost =[tex]\$56 \times 1 1/4 hours[/tex]
Labor cost =[tex]\$56 \times (1 + 1/4) hours[/tex]
Labor cost = [tex]\$56 \times (5/4) hours[/tex]
Labor cost = [tex]\$56 \times 1.25 hours[/tex]
Labor cost = $70
Next, we add the cost for parts and the service call to the labor cost to find the total cost:
Total cost (c) = cost for parts + labor cost + service call cost
Total cost (c) = $29.60 + $70 + $40
Total cost (c) = $139.60
Cara plants 5 seeds in 2 minutes, while Wade plants 3 times as many seeds in half the time. How many seeds can they both plant together in 10 minutes?
Answer:
together they can plant 175 seeds in 10 minutes
Answer with Step-by-step explanation:
Cara plants 5 seeds in 2 minutes.
⇒ Cara plants 5×5 seeds in 2×5 minutes
⇒ In 10 minutes Cara plant 25 seeds.
Wade plants 3 times as many seeds in half the time as Cara.
⇒ Wade plants 3×5 seeds in 2/2 minutes
i.e. Wade plants 15 seeds in 1 minute.
In 1×10 minutes Wade plants 15×10 seeds
i.e. In 10 minutes Wade plants 150 seeds.
150+25=175
Hence, they can together plant 175 seeds in 10 minutes.
What is the volume of a cylinder that has a diameter of 22km and a height of 7km
The volume of a cylinder with a given diameter and height using the formula V = πr²h is equal to 8471π km³.
The volume of the cylinder can be calculated using the formula for the volume of a cylinder: V = πr²h.
Given a diameter of 22 km (which means a radius of 11 km) and a height of 7 km, substitute these values into the formula to find the volume.
Substitute the values into the formula:
V = π × (11 km)²×7 km
Calculate the volume:
V = 8471π km³
Therefore, the volume is 8471π km³.
Two different functions are represented.
Function A:
X- 0,1,2,3,4
F(X)- 5,10,20,40,80
Function B- y=4/x
Which statement best compares the two functions?
Neither function A nor function B has an x-intercept.
Neither function A nor function B has a y-intercept.
The domain and range of both functions contain only positive numbers.
The domain and range of both functions contain only positive numbers and zero.
Answer:
Neither function A nor function B has an x-intercept.
Step-by-step explanation:
Function A has a y-intercept at (0, 5).
Function B is defined for negative numbers as well as positive numbers, but not for x=0.
These observations eliminate all answer choices but the first one.
The statement that best compares the two functions is; Neither function A nor function B has an x-intercept.
How to Interpret Functions?A y-intercept is the point where x = 0. Now, for function A we can see that when x = 0, y = 5. Thus, it has a y-intercept.
However, we are not given the point where y = 0 which is x-intercept. Thus, function A does not have an x-intercept.
Formula for Function B is y = 4/x.
This function does not have an x-intercept because at x = 0, the function is undefined.
Read more about Functions at;https://brainly.com/question/3951754
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Which table shows a proportional relationship between x and y?
Answer:c
Step-by-step explanation:
Answer: D because they are all corresponding numbers.
What is the value of
x3 + 4, when x = 6?
I'm not sure if you meant to write 3x or [tex]x^{3}[/tex] instead of x3 but I will work out both versions just in case
In the equation 3x + 4 plug 6 in for x
3(6) + 4
Multiply 3 and 6 first
18 + 4
Add 18 and 4
22
OR
In the equation [tex]x^{3}[/tex] + 4 plug 6 in for x
[tex]6^{3}[/tex] + 4
Solve the exponent
(6*6*6) + 4
216 + 4
Add the numbers together
220
Hope this helped!
Answer:
220
Step-by-step explanation:
Im going to assume x3 equals x^3, so 6^3 is 216, add this to 4 and get 220
Calculate the distance between (4,9) and (-2,6) using the distance formula.
Answer:
[tex]\large\boxed{d=3\sqrt5}[/tex]
Step-by-step explanation:
[tex]\text{the formula of a distance between two points}\ A(x_1,\ y_1)\ \text{and}\ B(x_2,\ y_2):\\\\|AB|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\=========================\\\\\text{We have}\ (4,\ 9)\ \text{and}\ (-2,\ 6).\ \text{Substitute:}\\\\d=\sqrt{(-2-4)^2+(6-9)^2}=\sqrt{(-6)^2+(-3)^2}=\sqrt{36+9}=\sqrt{45}\\\\\sqrt{45}=\sqrt{9\cdot5}=\sqrt9\cdot\sqrt5=3\sqrt5[/tex]
The distance between the points (4, 9) and (-2, 6) is approximately 6.71 units.
Identify the coordinates:
Let (x₁, y₁) = (4, 9) and (x₂, y₂) = (-2, 6).
Apply the distance formula:
The distance formula is given by:
d=√[tex]\sqrt{(x_{2}-x_{1} ) ^{2} +(y_{2}-y_{1} )^{2} }[/tex]
Substitute the coordinates into the formula:
d= [tex]\sqrt{((-2)-4)^{2} +(6-9)^{2} }[/tex]²
Simplify the terms inside the square root:
d=[tex]\sqrt{(-6)^{2} +(-3)^{2} }[/tex]
d=[tex]\sqrt{36+9}[/tex]
d=[tex]\sqrt{45}[/tex]
Simplifying further, we get:
d≈6.71
50 points An unknown number x is at most 20. Which graph best represents all the values of x? (1 point) Number line graph with closed circle on 20 and shading to the right. Number line graph with open circle on 20 and shading to the right Number line graph with closed circle on 20 and shading to the left. Number line graph with open circle on 20 and shading to the left
At most means it can either equal 20 or be less than 20.
On a number line, there would be a closed circle on the number 20 and the area to the left of 20 would be shaded.
Number line graph with closed circle on 20 and shading to the left.
One number is 4 more than another. The difference between their squares is 128. What are the numbers?
Smaller number=___
Larger number=___
Answer:
14 and 18
Step-by-step explanation:
Small number : a
Larger number : a + 4
( a + 4 )^2 - a^2 = 128
a^2 + 8 a + 16 = 128
8 a = 128 - 16
a = 112 / 8
a = 14
And a + 4 = 18
When the point (-3,7) is dilated with the center of dilation at the origin, then the image of
the point is (-12.75, 29.75).
What is the scale factor of this dilation?
1) 4
2) 4.25
3) 9.75
4) 10
Answer:
4.25
Step-by-step explanation:
To find the scale factor divide the image coordinates by the original coordinates, that is
scale factor = [tex]\frac{-12.75}{-3}[/tex] = [tex]\frac{29.75}{7}[/tex] = 4.25
The answer would be 4.25
Please help. I don't understand it. HELP ASAP....
Answer:
[tex]\large\boxed{x\leq-27}[/tex]
Step-by-step explanation:
[tex]\dfrac{x}{-9}\geq3\qquad\text{change the signs}\\\\\dfrac{x}{9}\leq-3\qquad\text{multiply both sides by 9}\\\\9\!\!\!\!\diagup^1\cdot\dfrac{x}{9\!\!\!\!\diagup_1}\leq(-3)(9)\\\\x\leq-27[/tex]
what are the solutions to the equation x^2 + 4x+5=0
Help ASAP
Answer:
Let's solve your equation step-by-step.
x2+4x+5=0
Step 1: Use quadratic formula with a=1, b=4, c=5.
x=
−b±√b2−4ac
2a
x=
−(4)±√(4)2−4(1)(5)
2(1)
x=
−4±√−4
2
Answer:
No real solutions.
Answer:
x=-2+-i
Step-by-step explanation:
Solve the equation for x by finding a, b, c of the quadratic then applying the quadratic formula.
What is the circumference of a circle with a diameter of 7 inches? (use for pi) PLEASE HELP ASAP
Answer:
C = 7pi = 21.98 inches
Step-by-step explanation:
The circumference of a circle is given by
C = pi * d
where d is the diameter
C = pi * 7
If we use 3.14 as an approximation for pi
C = 3.14 * 7
C =21.98 in
a food truck sells tacos, burrito, and drinks.
Let event A = A customer buys a taco
Let event B = A customer buys a drink
What does P(A or B) = 0.60 mean in terms of this problem?
A) The probability that a customer buys both a taco and a drink is 60%.
B) Buying a taco and buying s drink are mutually exclusive events.
C) The probability that a customer buys either a taco or a drink is 60%.
D) The probability that a customer buys neither a taco nor a drink is 60%.
Answer:
Option C is correct.
Step-by-step explanation:
P(A or B) represents that event A has occurred or event B has occurred or both events A and B are happening.
We are given P(A or B) = 0.60 or 0.60/100 = 60%
So, Option C The probability that a customer buys either a taco or a drink is 60% is correct.
Answer: Option C
Step-by-step explanation:
For two events A and B, P(A or B) represents the probability that event A occurs, or event B occurs.
In this case, event A represents a customer buys a taco and event B represents a customer buys a drink. We know that
[tex]P (A\ or\ B) = 0.60[/tex]
So this means that the probability that a customer buys either a taco or a drink is 60%
The answer is the option C
Plz answer both for me plz
Answer:
[tex]\large\boxed{\text{Table 1:}\ y=4x+1}\\\boxed{\text{Table 2:}\ y=\dfrac{1}{2}x-1}[/tex]
Step-by-step explanation:
Tables show linear functions.
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept → (0, b)
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
===================================================
Table 1:
(0, 1) → b = 1, (1, 5)
[tex]m=\dfrac{5-1}{1-0}=\dfrac{4}{1}=4\\\\y=4x+1[/tex]
Table 2:
(4, 1), (6, 2)
[tex]m=\dfrac{2-1}{6-4}=\dfrac{1}{2}\\\\y=\dfrac{1}{2}x+b[/tex]
Put the coordinateso f the point (4, 1) to the equation of a line:
[tex]1=\dfrac{1}{2}(4)+b[/tex]
[tex]1=2+b[/tex] subtract 2 from both sides
[tex]-1=b\to b=-1[/tex]
[tex]y=\dfrac{1}{2}x-1[/tex]
The formula for the perimeter of an equilateral triangle is p=3s. What is the perimeter?
In order to answer this, you have to have the unit of measurement and an illustration.
What is the volume of a right circular cylinder with a radius of 3 in, and a height of 10 in?
Answer: 90[tex]\pi \\[/tex]
Step-by-step explanation:
Final answer:
The volume of a right circular cylinder with a radius of 3 inches and a height of 10 inches is calculated using the formula V = πr²h, which gives 282.74 cubic inches.
Explanation:
To calculate the volume of a right circular cylinder, you can use the formula V = πr²h, where 'V' is the volume, 'r' is the radius, and 'h' is the height of the cylinder. In this instance, the radius (r) is 3 inches, and the height (h) is 10 inches.
Using these values, you can plug them into the formula:
V = π × (3 in)² × 10 in
V = 3.14159 × 9 in² × 10 in
V = 3.14159 × 90 in³
V = 282.74 in³
Therefore, the volume of the cylinder is 282.74 cubic inches.
What’s the smallest zero for the function h(x)=4x^2-8x-60
Answer:
-3
Step-by-step explanation:
In order to find the smallest zero, we will have to find out all the zeros of the function.
In case you are wondering what a zero is, it is the x-value or the domain intersections. The points where the parabola intersects the x-axis.
4x² - 8x - 60 = 0
Why zero?
We know that the parabola intersects the x-axis and when it does, the y-value is 0. h(x) is nothing but 'y'.
4(x²-2x-15) = 0 → I took the gcd as 4 and did it accordingly.
x² - 2x - 15 = 0 → Divide on both sides with 4
Now, what multiples to -15 but adds up to -2?
-5 and 3
x² + 3x - 5x - 15 → Grouping the terms
x ( x + 3 ) - 5 ( x + 3 ) → Taking the GCD in both groups
( x - 5 ) ( x + 3 ) = 0
x = 5 , -3
The smallest one out of these zeros is -3.
Hope it helps! :)
x divided by 12 = 12 divided by 72
Answer:
The equation to calculate what divided by 72 equals 12 is as follows:
X/72 = 12
Where X is the answer. When we solve the equation by multiplying each side by 72, you get get:
X = 864
Therefore, the answer to what divided by 72 equals 12 is 864.
I hope it helps!!
To find the value of x in the equation x/12 = 12/72, simplify 12/72 to get 1/6. Then, multiply both sides by 12 to solve for x, resulting in x = 2.
To solve the equation x divided by 12 = 12 divided by 72, we need to perform some algebraic manipulation to isolate x. First, rewrite the equation as a fraction:
x/12 = 12/72Next, simplify the fraction on the right-hand side:
12/72 = 1/6 (since 12 is 1/6th of 72)Now the equation looks like this:
x/12 = 1/6To solve for x, multiply both sides of the equation by 12:
x = 12 × 1/6x = 2So, the value of x is 2.
Please Help! Asap! I’m on a deadline!!
Answer:
the diagonals intersect at right angle i.e. slope of AC = - 1/ slope of BD and
Midpoint of AC = Z₁ is equal to Mid point of BD = Z₂
so, the parallelogram is rhombus.
Step-by-step explanation:
A parallelogram is a rhombus if diagonals intersect each other at right angle and the diagonals intersect at mid point.
We are given vertices:
A(-3,2)
B(-2,6)
C(2,7)
D(1,3)
The diagonals of the parallelogram will be:
AC and BD.
Slope of AC = y₂ - y₁ / x₂- x₁ where A = (-3,2) and C = (2,7)
Putting values:
Slope of AC = 7-2/2-(-3) = 5/5
Slope of AC = 1
Slope of BD = y₂ - y₁ / x₂- x₁ where B = (-2,6) and D = (1,3)
Putting values:
Slope of BD = 3-(6) / 1-(-2) = -3/3
Slope of BD = -1
AS, Slope of AC = - 1/ Slope of BD
So, the diagonals intersect and right angle.
Now finding the mid point Z₁ of AC and Z₂ of BD:
Midpoint of AC = Z₁ = A+C/2
Putting values:
=(-3,2) + (2,7) / 2
= (-1,9)/2
= (-1/2, 9/2)
Mid point of BD = Z₂ = B+D / 2
Putting values:
=(-2,6) + (1,3) / 2
= (-1,9)/2
= (-1/2, 9/2)
Midpoint of AC = Z₁ is equal to Mid point of BD = Z₂ i.e.
Z₁ = Z₂, the diagonals intersect at the same midpoint.
As,
the diagonals intersect at right angle i.e. slope of AC = - 1/ slope of BD and
Midpoint of AC = Z₁ is equal to Mid point of BD = Z₂
so, the parallelogram is rhombus.
Write these numbers in standard notation
3.05 x 10–3
- I think if it was standard notation then it would be 3.05 * 10 = 30.5 - 3 = 27.5.
The triangle has side lengths of 25 in, 26in, and 3.5 in. Classify acute, obtuse, or right
Answer:
Obtuse triangle
Step-by-step explanation:
The longest side of the triangle is 26 in, so that will be the hypotenuse.
By an extension of the Pythagorean theorem:
Right triangle: a² + b² = c²Acute triangle: a² + b² > c²Obtuse triangle: a² + b² < c²Where a and b are the legs, and c is the hypotenuse.
Plug in: 3.5² + 25² ₙ 26²
Powers: 12.25 + 625 ₙ 676
Add: 637.25 < 676.
That means that this triangle is obtuse.
Answer:
Obtuse
Step-by-step explanation:
Using law of cosine, we can find the angle between the shorter sides:
c² = a² + b² − 2ab cos C
26² = 25² + 3.5² − 2(25)(3.5) cos C
cos C ≈ -0.221
C ≈ 102.8°
102.8° is greater than 90°, so the triangle is obtuse.
which is most likely the solution to the system of equations shown?
Answer:
The answer is G. (-2,3)
Step-by-step explanation:
The point where they meet is (-2,3), therefore that is the solution. Hope that helps! :)
There were 442 students at Deerlake Middle School who voted on a theme for the spring carnival. Those who voted represent 76% of the entire student population. About how many students attend Deerlake Middle School?
A. 106
B.336
C.582
D.1842
Don't just guess. :p
Answer:
Option C is correct.
Step-by-step explanation:
Number of students of Deerlake middle school that voted = 442
Percentage of student that voted = 76%
Let x be the total number of student.
According to the Question,
[tex]\frac{76}{100}\times x=442[/tex]
[tex]x=442\times\frac{100}{76}[/tex]
[tex]x=582[/tex]
Therefore, Option C is correct.