Answer:
We cannot determine the exact number of votes for Tim or Selena without additional information. However, we can determine the fraction of the whole class that voted for each candidate based on the given information.
If only one third of the students cast votes, that means that two thirds did not vote. Therefore, the fraction of the whole class that voted for Tim and Selena is each equal to one third of the total number of students.
To calculate these fractions, we can use the following formula:
Fraction of class = Number of students who voted / Total number of students
Let's assume that there are N students in the class. Then, the number of students who voted for Tim is (1/3)N, and the number of students who voted for Selena is also (1/3)N.
So, the fraction of the whole class that voted for Tim is:
(1/3)N / N = 1/3
Similarly, the fraction of the whole class that voted for Selena is also 1/3.
Since we don't know the exact number of votes for each candidate, we cannot determine who received more votes.
Reasoning with similarity geometry please help. 40 points
Answer:
ABC and CEF are right triangles | definition of right triangle
ABC and CEF are 30-60-90 triangles | definition of 30-60-90 triangle
ABC is similar to CEF | Angle-Angle-Angle similarity theorem
a vat with 500 gallons of beer contains 4% alcohol (by volume). beer with 6% alcohol is pumped into the vat at a rate of 5 galymin and the mixture is pumped out at the same rate. what is the percentage of alcohol after an hour?
The percentage of alcohol after an hour will be approximately 4.9%.
What is percentage?
A percentage is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Let p(t) be the percentage of alcohol at time t.
Where t is in minutes.
Amount of alcohol in vat = Volume of vat x p/100
Rate of change of alcohol in vat = Volume of vat x dp/dt time 1/100
Rate of change of alcohol in vat = 500 x dp/dt x 1/100
Rate of change of alcohol in vat = 5 x dp/dt
Net rate of change of alcohol = (Rate of inflow of alcohol) - (Rate of Outflow of alcohol)
Rate of Inflow of alcohol = 0.06 - 5 = -4.94 gal/min
Rate of outflow of alcohol = p(t)/100 x 5 = 0.05p(t) gal/min
Therefore, the rate of change of alcohol is 0.03 - 0.05 p(t) gal/min
Finally we can write
5 x dp/dt = 0.3 - 0.05 p
Divide both sides by 5
dp/dt = 0.06 - 0.01p
Integrate both sides
[tex]\int {dp} / 0.06 -0.01p = \int dt[/tex]
-100ln (0.06 - 0.01p) = t + C
At t=0, p=4, therefore
-100ln (0.06 - 0.04) = 0 + C
391.2 = C
Substitute the value of C, to get
-100ln (0.06 - 0.01p) = t + 391.2
Substitute t = 60 and solve for p
-100ln (0.06 - 0.01p) = 60 + 391.2
-100ln (0.06 - 0.01p) = 451.2
ln (0.06 - 0.01p) = -4.512
[tex]p = \frac{0.06 - e^{-4.512} }{0.01}[/tex] ≈ 4.9%
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The surface area of a cone is given by the formula
S = πl + πr2. Solve the formula for l.
l = S – r2
l = S + r2
l = l equals StartFraction S Over pi minus r squared. – r2
l = l equals StartFraction S Over pi plus r squared. + r2
Answer:
The answer is:
[tex]l=\dfrac{S-\pi r^2}{\pi }[/tex]
Step-by-step explanation:
In order to determine the solution for I, we have to know about the equations.
In any equation there are variables. If we want to determine the value of one of them, we have to free that variable in any side of the equation.
Regarding the surface of a cone, i have attached an image that shows the real formula of the surface of a cone, We can see that in this case:
[tex]l=rI[/tex]
So, we have the next formula and we want to l:
[tex]S=\pi l+\pi r^2[/tex]
[tex]S-\pi r^2=\pi l[/tex]
[tex]\dfrac{S-\pi r^2}{\pi }=l[/tex]
Finally the solution for I is:
[tex]l=\dfrac{S-\pi r^2}{\pi }[/tex]
what ratio is commonly used as an alternative to 3.14?
The ratio commonly used as an alternative to 3.14 is 22/7 whichj commonly represents the mathematical expression of pi.
This ratio is often used as an approximation for pi (π) which is the mathematical constant representing the ratio of the circumference of a circle to its diameter. While pi is an irrational number and has an infinite number of decimal places, 22/7 is a rational number and can be easily computed.
The value of 22/7 is approximately equal to 3.1428571, which is a fairly accurate approximation for most practical applications. It is often used in situations where a quick estimate is required or where a more accurate value of pi is not necessary.
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A parabola is defined as the set of points the same distance from (6,2) and line y=4. Select all points that are on this parabola
In conclusion there are no points among the given options that are on the parabola.
why it is?
The vertex of the parabola is the midpoint between the point (6, 2) and the line y = 4, which is at (6, 3). Since the focus is below the vertex and the directrix is a horizontal line, the equation of the parabola is of the form:
(x - h)²2 = 4p(y - k)
where (h, k) is the vertex and p is the distance from the vertex to the focus (and from the vertex to the directrix).
Using the vertex and the given point (6, 2), we can find that p = 1. Therefore, the equation of the parabola is:
(x - 6)²2 = 4(y - 3)
Now we can check which of the given points satisfy this equation:
A. (4, 6)
(4 - 6)²2 = 4(6 - 3)
4 = 12 - 12
This point is not on the parabola.
B. (5, 7)
(5 - 6)²2 = 4(7 - 3)
1 = 16
This point is not on the parabola.
C. (6, 5)
(6 - 6)²2 = 4(5 - 3)
0 = 8
This point is not on the parabola.
D. (7, 6)
(7 - 6)²2 = 4(6 - 3)
1 = 12
This point is not on the parabola.
E. (8, 5)
(8 - 6)²2 = 4(5 - 3)
4 = 8
This point is not on the parabola.
Therefore, there are no points among the given options that are on the parabola.
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Complete question:
Which points are on the parabola defined as the set of points the same distance from (6,2) and the line y=4?
you want to estimate the average time college students spend studying per week. you know that the population standard deviation for studying time per week for college students is 3.5 hours. you want a 99% confidence interval with a margin of error of 30 minutes (0.50 hours). how many students do you need in your study?
You need a sample size of approximately 82 students to estimate the average time college students spend studying per week with a 99% confidence interval and a margin of error of 30 minutes (0.50 hours).
To determine the sample size, we will use the formula given below;
Where, n = sample size
Zα/2 = the z-score associated with the level of confidence
α = level of significance
σ = population standard deviation
d = margin of error of the estimation.
Substituting the given values, we have; n = [(Zα/2 * σ)/d]^2
We are given the population standard deviation, σ = 3.5 hours.
We are also given the margin of error, d = 0.5 hours.
We need to find the value of Zα/2 at 99% confidence level.
Since the sample size is large enough, we can use the z-distribution to find the z-value.
The area under the standard normal distribution curve for a 99% confidence level is as shown below;
Using the z-tables, the value of Zα/2 for a 99% confidence level is 2.576.
Substituting the values into the formula; n = [(Zα/2 * σ)/d]^2n = [(2.576 * 3.5)/0.5]^2= (9.006)^2= 81.12
Since we need a whole number for the sample size, we round up the value to get 82.
However, since the standard deviation of the population is known, we can use the z-distribution to construct a confidence interval for the population mean. This will give us an accurate interval estimate of the population mean.
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A rectangle and triangle are shown below.
The area of the rectangle is equal to the perimeter of the triangle.
Solve for x.
If your answer is a decimal, convert it to 1 d.p.
Answer:
5
Step-by-step explanation:
We know that the area of the rectangle is equal to the perimeter of the triangle
S (rectangle) = (x + 8) × (2x - 1)
P (triangle) = (5x - 1) + (6x + 8) + (8x + 15)
Now we can form an equation:
(x + 8) × (2x - 1) = (5x - 1) + (6x + 8) + (8x + 15)
[tex] {2x}^{2} - x + 16x - 8 = 5x - 1 + 6x + 8 + 8x + 15[/tex]
[tex]2 {x}^{2} - 4x - 30 = 0[/tex]
[tex]d = {b}^{2} - 4 \times a \times c = ({ - 4})^{2} - 4 \times 2 \times ( - 30) = 16 + 240 = 256 > 0[/tex]
[tex]x1 = \frac{ - b - \sqrt{d} }{2 \times a} = \frac{4 - 16}{4} = \frac{ - 12}{4} = - 3[/tex]
-3 is a negative number and we cannot use it, since x must be a natural number
[tex]x2 = \frac{ - b + \sqrt{d} }{2 \times a} = \frac{4 + 16}{4} = \frac{20}{4} = 5[/tex]
<
3
What is the measure of arc JR?
J
?
mJR
R
37°
K
L
degrees
The measure of angle subtended by the arc JR is determined as 74 ⁰.
What is the measure of arc JR?
The measure of arc JR is calculated by applying the following principle of circle geometry for a cyclic quadrilateral as shown below.
The measure of the angle tangent to the circle opposite the arc JR is given as 37 ⁰.
The measure of angle subtended by the arc JR is calculated as
m∠ JR = 2 x 37 ⁰ ( angle at the tangent is half of the angle subtended by the arc.
m∠ JR =74 ⁰
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Simplify the expression-4(-3x - 8) - 34
Answer:
12x-2
Step-by-step explanation:
-4(-3x-8)-34
12x+32-34
12x-2
Select the action you would use to solve x - 3 = 12. Then select the property that justifies this action select all that apply A. Action: add 3 to both sides B. Action: Multiple both sides by 3
Answer: A. Action: add 3 to both sides
Step-by-step explanation:
The property that justifies this action is the addition property of equality, which states that if you add the same number to both sides of an equation, the equation remains true.
PLEASE HELP ME!!!!!!!!!!!!!!
This figure is a rectangle with a semicircle on the shorter side.
What is the perimeter of this figure?
Use 3.14 for pi.
A. 20.28 ft
B. 30.28 ft
C. 46.28 ft
D. 74.24 ft
Answer: it should be b
Step-by-step explanation:
The Boeing 747-8 Intercontinental Jet can carry approximately 63,500 gallons of jet fuel, making it possible for the jet to travel 14,430 kilometers before needing to refuel.
Create a linear model that represents the amount of fuel on the plane, in gallons, as a function of the flight time, in hours. Show all of your work.
Answer: To create a linear model that represents the amount of fuel on the plane as a function of flight time, we need to use the given information to calculate the fuel burn rate of the airplane in gallons per hour.
Fuel burn rate = Fuel capacity ÷ Range
Fuel burn rate = 63,500 gallons ÷ 14,430 km = 4.4 gallons per km
We need to convert km to miles, as flight time is usually measured in hours and miles. We can use the conversion factor 1 km = 0.621371 miles to convert kilometers to miles.
Range in miles = Range in km ÷ 0.621371
Range in miles = 14,430 km ÷ 0.621371 = 23,594 miles
Fuel burn rate = Fuel capacity ÷ Range in miles
Fuel burn rate = 63,500 gallons ÷ 23,594 miles = 2.69 gallons per mile
Therefore, the linear model that represents the amount of fuel on the plane as a function of flight time, in hours, is:
Fuel on plane (in gallons) = Fuel capacity - Fuel burn rate x Flight time (in hours)
F(t) = 63,500 - 2.69t
where F(t) is the amount of fuel on the plane (in gallons) after flying for t hours.
Step-by-step explanation:
Draw triangle LMN with vertices L(2,-2), M(6,-4) and(5,4). Find the coordinates of the vertices after 90degrees rotation about the origin and about each of the point of L,M,and N
The coordinates of the vertices after rotation depend on the point around which rotation is done.
Rotation of a shape around the origin (0,0) means that each point in the shape has to be moved around the origin by a certain angle. This is done by using the equation x'=xcosθ-ysinθ and y'=xsinθ+ycosθ, where x and y are the coordinates of the point before rotation and x' and y' are the coordinates of the point after rotation. In this case, the angle of rotation is 90 degrees. When we rotate triangle LMN by 90 degrees around the origin, the coordinates of the vertices become L'(2,2), M'(-4,6) and N'(4,-5).When we rotate the triangle around any of the points of L, M, or N, the coordinates of the vertices will change accordingly. For example, if we rotate the triangle around point L, the coordinates of the vertices become L'(2,-2), M'(-2,4) and N'(-6,0). Similarly, if we rotate the triangle around point M, the coordinates of the vertices become L'(2,-2), M'(6,-4) and N'(0,6). Lastly, if we rotate the triangle around point N, the coordinates of the vertices become L'(2,-2), M'(4,5) and N'(5,4).
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What is the measure of ∠r in △pqr? round to the nearest degree. 26° 42° 45° 64°
The measure of ∠R in ΔPQR is option (a) 26⁰
Since angle P is a right angle (90 degrees), triangle PQR is a right triangle.
Using the Pythagorean theorem, we can find the length of the remaining side PQ
PQ^2 = PR^2 - QR^2
PQ^2 = 12.7^2 - 14.1^2
PQ^2 = 161.29 - 198.81
PQ^2 = 37.52
PQ ≈ 6.12
Now we can use the sine function to find the measure of angle R
sin(R) = opposite/hypotenuse = PQ/PR
sin(R) = 6.12/12.7
sin(R) ≈ 0.482
Taking the inverse sine (sin^-1) of both sides, we get:
R ≈ sin^-1(0.482)
R ≈ 26 degrees
Therefore, the correct option is (a) 26⁰
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The given question is incomplete, the complete question is
What is the measure of angle R in triangle PQR?
a) 26°
b) 42°
c) 45°
d) 64°
Penny has at least $4.50 plus 2/5 of the amount of money that Susie has. Write an expression for the amount Penny has (p) in terms of how much Susie has (s). If Susie has $11.50, use your expression to calculate how much Penny has.
We can begin by defining Penny's total wealth as a mix of a set sum and a portion of Susie's wealth to develop an expression of how much money she has. We are informed that Penny has at least $4.50 and an additional 2/5 of Susie's wealth. Hence, we can write:
p = $4.50 + (2/5)s
where p is Penny's wealth, s is Susie's wealth, and s is represented by the letters.
If Susie has $11.50, we may enter s = $11.50 into the formula for p to see how much Penny has:
p = $4.50 + (2/5)($11.50)
p = $4.50 + $4.60
p = $9.10
As a result, Penny has $9.10 and Susie has $11.50.
In conclusion, the equation for Penny's wealth in terms of Susie's wealth is p = $4.50 + (2/5)s. When we enter s = $11.50 into the formula, we obtain p = $9.10, which is how much money Penny has while Susie has $11.50.
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WHAT EVEN IS THIS! PLEASE HELP
Step-by-step explanation:
It is a trapezoid with bases 9 and 12 ft and height ( dashed line) found using Pythagorean theorem = 4 ft
area = height * average of bases = 4 * (9+12)/2 = 24 ft^2
use partial fractions to find the indefinite integral. (remember to use absolute values where appropriate. use c for the constant of integration.) 10x2 7x − 2 x3 x2 dx
The indefinite integral is:
-10 ln|x| + 3 ln|x - 2| + 7 ln|x + 1| + C
First, we factor the denominator of the integrand using partial fractions:
x^3 - x^2 - 2x = (x - 2)(x + 1)x
We then express the integrand as:
10x^2 - 7x + 2 = A/(x - 2) + B/x + C/(x + 1)
Multiplying both sides by the denominator and solving for A, B, and C, we get:
A = -4, B = 10, C = 1
Thus, we can rewrite the integrand as:
-4/(x - 2) + 10/x + 1/(x + 1)
Integrating each term separately and combining the results, we obtain the final expression for the indefinite integral.
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would most people take the following gamble? flip a coin, if heads you win $75, if tails you lose $50. explain your answer.
Answer:
50/50 Chance
Step-by-step explanation:
I'm not sure if you wrote the entire question correctly, but the highest chance you would have of winning would be 100% because the 2 sides * the 50/50 chance they have. So that would make the odds of winning 50%.
i need this answer asap with explanation
Answer:
1 , 1.01 , 1.02 , 1.03 , 1.04
Step-by-step explanation:
a sequence with steps of constant size is an arithmetic sequence.
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 1 and d has to be found
given a₅ = 1.04 , then
1 + 4d = 1.04 ( subtract 1 from both sides )
4d = 0.04 ( divide both sides by 4 )
d = 0.01
then sequence is
1 , 1.01 , 1.02 , 1.03 , 1.04
HELP SOLVE PLEASEEE ENOUGH POINTSSS
Step-by-step explanation:
$ 540 / 12 mos = $ 45 per month for all of the services
SO H + D + N = 45 and N = 2D
So H + D + 2D = 45
and H+ D = 300/12 = $25 / month
so (H+D) + 2D = 45
25 + 2D = 45
D = 10 dollars per month
then H = 15 dollars per month ( because H+D = 25)
and N = 20 dollars per month ( because N = 2D)
Graph a right triangle with the two points forming the hypotenuse. Using the sides, find the distance between the two points in simplest radical form.
(−3,−7) and (−7,−1)
The length of the hypotenuse is the line connecting the two points (-3,-7) and (-7,-1), which has length 2√13, as calculated above.
What precisely is a triangle?A triangle is a clοsed, dοuble-symmetrical shape cοmpοsed οf three line segments knοwn as sides that intersect at three places knοwn as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all factiοns equal), isοsceles, οr scalene based οn their sides.
Next, we can find the length of the hypotenuse by using the distance formula, which is:
d = √((x2 - x1)² + (y2 - y1)²)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
So, in this case, we have:
d = √((-7 - (-3))² + (-1 - (-7))²)
= √((-4)² + (-6)²)
= √(16 + 36)
= √52
= 2√13
Therefore, the distance between the two points in simplest radical form is 2√13.
The length of the hypotenuse is the line connecting the two points (-3,-7) and (-7,-1), which has length 2√13, as calculated above.
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three-fourths of the chocolates in a box are dark chocolate. three-eighths of the dark chocolates are filled with caramel. what fraction of the chocolates in the box are dark chocolate and filled with caramel?
Fraction of the chocolates in the box that are dark chocolate and filled with caramel is 3/32.
To solve this problem, we need to determine what fraction of chocolates in the box are both dark chocolate and filled with caramel. We are given that:
Three-fourths of the chocolates in a box are dark chocolate. Three-eighths of the dark chocolates are filled with caramel. We need to find out the fraction of chocolates that are dark chocolate and filled with caramel. To find out the fraction of chocolates in the box that are dark chocolate, we divide the number of dark chocolates by the total number of chocolates.
This is given by:
3/4 (dark chocolates)
To find the fraction of dark chocolates that are filled with caramel, we multiply the fraction of dark chocolates by the fraction of dark chocolates filled with caramel. This is given by:
3/4 × 3/8 = 9/32
Therefore, the fraction of chocolates in the box that are dark chocolate and filled with caramel is 9/32.
To simplify the fraction 9/32, we can divide the numerator and denominator by their greatest common factor, which is 1:9/32 = 9 ÷ 1 / 32 ÷ 1 = 9/32.
Hence, the answer is 3/32.
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The volume of a triangle
[tex]\textit{volume of a pyramid}\\\\ V=\cfrac{Bh}{3} ~~ \begin{cases} B=\stackrel{base's}{area}\\ h=height\\[-0.5em] \hrulefill\\ B=\stackrel{9\times 7}{63}\\ h=6 \end{cases}\implies V=\cfrac{(63)(6)}{3}\implies V=126~cm^3[/tex]
now, for the slanted cone, we can use Cavalieri's Principle for an slanted cylinder, thus we can say that the slanted cone will have the same volume of a non-slanted cone, now, since this one has a diameter of 6, that means is has a radius of 3.
[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3} \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=7 \end{cases}\implies V=\cfrac{\pi (3)^2(7)}{3}\implies V=21\pi \implies V\approx 66~cm^3[/tex]
Answer:
64
Step-by-step explanation:
[9,7] is the difference between 2 vectors with components [3,4] and [-6, b] what is b
The value of b is -6
We know that the difference between two vectors with components (a1, a2) and (b1, b2) is given by (b1-a1, b2-a2).
So in this case, we have
[b1 - 3, b2 - 4] = [(-6) - 3, b - 4]
Simplifying the right-hand side gives us
[-9, b - 4]
So we can set the components of the left-hand side equal to the corresponding components of the right-hand side
b1 - 3 = -9
b2 - 4 = b - 4
Solving for b in the first equation gives us
b1 = -9 + 3 = -6
Substituting this into the second equation and simplifying gives us
-6 - 4 = b - 4
-10 = b - 4
b = -10 + 4 = -6
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Please help me! This is due at 2:15 PM!!!! WHICH ALREADY PASSED!!! ITS GOING TO BE LATE> A game has 15 balls for each of the letters B, I, N, G, O. The table shows the results of drawing balls 1,250 times.
Letter Frequency
B 247
I 272
N 238
G 241
O 252
For which letter is the experimental probability closest to the theoretical probability? Explain please.
Answer: O: 252
Step-by-step explanation:
Theoretically, all of the letters would've been drawn 250 times as that is the theoretical possibility. The closest number to the theoretical number in this experiment would be 252 which belongs to O
At a local coffee shop, the manager has determined that 56% of drink orders are for specialty espresso drinks and 44% are for plain coffee. The manager also noted that 40% of customers order food. For customers who purchase the specialty espresso drinks, 35% also purchase a food item, and for customers who purchase plain coffee, 30% also purchase a food item. What is the probability that a randomly chosen customer will purchase a specialty espresso drink and a food item?
0.13
0.14
0.20
0.22
Let's use conditional probability to solve this problem. We want to find the probability of a customer purchasing a specialty espresso drink and a food item, so we can use the following formula:
P(specialty espresso drink and food) = P(food|specialty espresso drink) * P(specialty espresso drink)
We know that P(specialty espresso drink) = 0.56 and P(food|specialty espresso drink) = 0.35, so we can substitute these values into the formula:
P(specialty espresso drink and food) = 0.35 * 0.56
P(specialty espresso drink and food) = 0.196
Therefore, the probability that a randomly chosen customer will purchase a specialty espresso drink and a food item is 0.196 or approximately 0.20 (rounded to two decimal places).
So, the answer is option C: 0.20.
I NEED HELP ON THIS ASAPPP!
Answer:
i thinks its scalene
Step-by-step explanation:
scalene is under 90 degrees
equal is 90 exact
and obtuse is over 90 but under 180
Is the following equation true or false?
(14.6 ÷ 2) x 3 – 1.9 = 3 x (8 – 4)
True or false
Answer:
False
Step-by-step explanation:
14.6/2 = 7.3
7.3 x 3 = 21.9
21.9 - 1.9 = 20
Other side:
8 - 4 = 4
4 x 3 = 12
20 does not equal 12
therefore false :)
!!PLEASE HELP ASAP!!
The function g(x) is the height of a football x seconds after it is thrown in the air. The
football reaches its maximum height of 28 feet in 6 seconds, and hits the ground at
12 seconds.
What is the practical domain for the function f(x)?
Type your answer in interval notation.
Answer:
[0,12]
Step-by-step explanation:
The unit of the domain is seconds
x is greater than or equal to zero because time can't be negative
Time stops at 12 seconds since the ball hits the ground.
Brackets are used to include both 0 and 12 as values
Let x and y both represent rational numbers. Select whether each expression is always, sometimes, or never a
rational number.
x-y
x + y
Always Sometimes Never
The expressions x - y and x = y are sometimes a rational number.
From the question, we have the following parameters that can be used in our computation:
x and y = rational numbers
The difference of two rational numbers is always a rational number, so x - y is sometimes a rational number.
The sum of two rational numbers is always a rational number, so x + y is sometimes a rational number.
Therefore, both expressions are sometimes a rational number.
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