The value of r is found as 3/2 such that line that passes through the pair of points.
Describe the term slope of the line?The ratio of both the altitude to that same horizontal distance (rise across run) between two places is typically used to calculate the slope, a numerical value that represents how steep a line is. A line's slope provides information on the steepness and direction of the line. By calculating the difference between coordinates of the two points, (x1,y1) and (x2,y2), it is simple to calculate the slope of either a straight line between them. The letter "m" is frequently used to denote slope.The slope is given bye the equation;
m = (y2 - y1)/(x2 - x1)
For the given question, the points are given as;
(x1, y1) = (r, -5),
(x2, y2) = (3, 13)
m = 8
8 = (13 + 5)/(3 - r)
8(3 - r) = 18
8r = 6
r = 3/2
Thus, the value of r is found as 3/2 such that line that passes through the pair of points.
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The correct question is-
Find the value of r so the line that passes through each pair of points has the given slope. (r, -5), (3, 13), m = 8
a drawer contains 20 socks. 10 are black. 6 are blue. 4 are red. two socks are taken out at random. what is the probability that one is blue and one is red?
Chance is also referred to as probability and the probability that one is blue and one is red is 4/19
probability = Number of event/Total samples space
If there are 10 black socks,20 white socks,2 red socks, and 6 blue socks in a drawer, the total number of socks will be the sample space
Sample space = 10+20+2+6
Sample space = 38
Total number of blue and red socks is the event
Number of event one blue and one red = 8 blue socks
Chance that the socks is blue = n(E)/n(S)
Chance that the socks is one red and one blue = 8/38
Chance that the socks is red and blue = 4/19
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a sector of a circle has a central angle of $100^\circ$. if the area of the sector is $250 \pi$, what is the radius of the circle?
The required radius of given circle is 30 units.
What is circle and area of its sector?
A circle is a shut two-layered figure wherein the arrangement of the multitude of focuses in the plane is equidistant from a given point called "focus". Each line that goes through the circle shapes the line of reflection evenness. Likewise, it has rotational evenness around the middle for each point.
Area of sector of circle:Picture result for What is circle and region of its area?
The equation for the region of the area of a circle is(r2) /360where r is the span of the circle and is the point of the area.
According to question:Angle of sector = 100 degree, area= 250π
Let radius of circle be r
Then,
area of sector = (r^2) /360
250π = (r2) 100/360
r^2 = 250×360/100
r = √25×36 = 30 units
Thus, radius of the circle is 30units.
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A juice box is 5 cm long, 3 cm wide and
10 cm tall. The juice is poured into a
glass with a radius of 3 cm.
What is the depth of juice in the glass?
Answer in centimetres to 1 decimal place.
The depth of the juice in the glass is 5.30cm
Given in the question,
length of juice box = 5cm
width of juice box = 3cm
Height of juice box = 10cm
Volume of juice box = volume of cuboid = length× width× height
= (5)(3)(10)
=(15)(10)
= 150 cm³
This juice then poured into a glass with radius of 3 cm
Glass is of cylindric shape
So, volume of cylinder = πr²h
= π(3)²h
Volume of juice should be equal to volume of glass
=> π(3)²h = 150 cm³
=> (3.14)(9)h=150
=> h = 150 / (3.14)(9)
h = 150/28.26
h = 5.30cm
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Jan traveled 260 miles using 8 gallons of gas. What was the car’s miles per quart on this trip?
Answer:
130 mi/ per quart
Step-by-step explanation:
260 mi/8 gallons =32.5 mi/gallon
1 gallon = 4 quarts, so 32.5 gallons is 130 quarts
tom is a big green bay packers and aaron rodgers fan. he claims that aaron rodger's average number of touchdowns per game is 2.45. dave (a hardcore bears fan) believes that tom might be inflating rodgers's statistics. from his debut until november 18, 2019, aaron rodgers has played 175 games! dave does not want to look at all of them. he randomly selects 52 games that rodgers played and finds the sample average number of touchdowns to be 1.942 with a standard deviation of 1.42. do a hypothesis test and state your conclusion. use the significance level
After doing a hypothesis test the conclusion is reject [tex]H_0[/tex] .
Given:
tom is a big green bay packers and aaron rodgers fan. he claims that aaron rodger's average number of touchdowns per game is 2.45. dave (a hardcore bears fan) believes that tom might be inflating rodgers's statistics. from his debut until november 18, 2019, aaron rodgers has played 175 games! dave does not want to look at all of them. he randomly selects 52 games that rodgers played and finds the sample average number of touchdowns to be 1.942 with a standard deviation of 1.42.
here n = 52
σ = 1.42
x = 1.942
μ = 2.45
z = x - μ / σ/√n
= 1.942 - 2.45 / 1.42/√52
= -2.58
p value = 0.0049
[tex]H_0:mean = 2.45[/tex]
[tex]H_a:mean < 2.45[/tex]
Rejection rule:Reject [tex]H_0[/tex] if p value < 0.05
Conclusion Reject [tex]H_0[/tex]
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What is an outlier in 6th grade math?.
If the data collection contains the given following numbers: 1, 19, 25, 32, 36, 38, 31, 42, 57, 45, and 87 , Here 1 and 87 represents the outlier.
What is characteristics of statistics ?The important characteristics of the Statistics that are given as follows:
Statistics have always been numerically expressed.
It had an aggregate of all the facts and dataData are to be collected in proper wayIt should be always comparable to one anotherData are collected for a well planned purposeOutliers are the data's most wildly divergent values.For instance, if the data collection contains the following numbers: 1, 19, 25, 32, 36, 38, 31, 42, 57, 45, and 87
The display of all data and outliers
The numbers 1 and 87, which are at the extreme and are hence outliers in the number line above, may be seen to be at these extremes.
The group outliers are a part of it, but they are not always close to the other group members.
Outliers are a concern as they cause an imbalance in the data set, which is why they are typically eliminated. Furthermore, an error can sometimes cause an outlier to appear in a data collection.
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in a casino, you play the following game: you choose a number between 1 and 6 and then throw 3 fair six-sided dice. after tossing, for each die showing your chosen number, the casino pays you $1. In order to play this game, you have to pay the casino a stake of S1 Let X denote your net win after one round of gambling (i.e., the payment received from the casino minus your stake) (a) Determine the state space Sx of X (b) Compute the probability mass function px of X (c) Compute the expected value E[X] of X (d) In general, a game is called a fair game if the net win of the gambler is 0 "on average" Is the above game a fair game? If not, what should be the stake of the gambler in order to make this a fair game? Give a reason for your answer.
By using the concept of probability, it can be calculated that
a) State space S(x) = {-1, 0, 1, 2}
b) The required probability mass function is
P(X = -1) = [tex]\frac{125}{216}[/tex]
P(X = 0) [tex]= \frac{25}{72}[/tex]
P(X = 1) [tex]= \frac{5}{72}[/tex]
P(X = 2) [tex]= \frac{1}{216}[/tex]
c) Expected value of X = -0.5
d) the stake of the gambler in order to make this a fair game is $0.5
What is probability?
Probability gives us the information about how likely an event is going to occur
Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.
Probality of any event is greater than or equal to zero and less than or equal to 1.
Probability of sure event is 1 and probability of unsure event is 0.
a) Let a number n be chosen between 1 and 6
Three fair six sided dice are thrown
The following cases can occur
1) Number n occur on none of the three dice
2) Number n occur on one dice
3) Number n occur on two dice
4) Number n occur on three dice
Let X denote your net win after one round of gambling (i.e., the payment received from the casino minus your stake)
1) X = 0 -1 = -1
2) X = 1 - 1 = 0
3) X = 2 - 1 = 1
4) X = 3 - 1 = 2
State space S(x) = {-1, 0, 1, 2}
b) P(X = -1) = [tex]{3 \choose 0}(\frac{1}{6})^0(\frac{5}{6})^3 = (\frac{5}{6})^3 = \frac{125}{216}[/tex]
P(X = 0) = [tex]{3 \choose 1})(\frac{1}{6})(\frac{5}{6})^2 = \frac{25}{72}[/tex]
P(X = 1) = [tex]{3 \choose 2}(\frac{1}{6})^2\frac{5}{6} = \frac{5}{72}[/tex]
P(X = 2) = [tex]{3 \choose 3}(\frac{1}{6})^3(\frac{5}{6})^0 = \frac{1}{216}[/tex]
The required probability mass function is
P(X = -1) = [tex]\frac{125}{216}[/tex]
P(X = 0) [tex]= \frac{25}{72}[/tex]
P(X = 1) [tex]= \frac{5}{72}[/tex]
P(X = 2) [tex]= \frac{1}{216}[/tex]
c) Expected value of X = [tex]-1 \times \frac{125}{216} + 0 \times \frac{25}{72} + 1 \times \frac{5}{72} + 2\times \frac{1}{216}[/tex]
= [tex]\frac{-125 + 0 + 15 +2}{216}\\[/tex]
= [tex]-\frac{108}{125}[/tex]
= -0.5
d) The gambler looses $0.5 on a average
So this is not a fair game
Let the stake of the gambler in order to make this a fair game be t
By the problem,
-0.5 + t = 0
t = 0 + 0.5
t = $0.5
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Tulip bulbs are sold in packs of 25 or 40
lily buys a pack of 25 and kiki buys in a pack of 40
what is the smallest number of packs they can each buy so they have the same number of bulbs?
show working please, if solve you will be thanks and marked as the brainliest.
The line egment i rotated 270 degree clockwie about the origin to form P'Q'. Which tatement decribe P'Q'
The line segment i rotated 270 degree clockwise about the origin to form P'Q' the statement describe P'Q'. The accurate alternative is (B) P'Q' is same in period to PQ.
That line phase PQ is proven at the co-ordinate grid. The line phase PQ is turned around 270 ranges counter clockwise approximately the foundation to shape P'Q'.We are to pick out the announcement that describes P'Q'.From the graph, we observe that the co-ordinates of factor P are(- 5, 3) and the co-ordinates of Q are (- 1, 3) .So, the period of PQ as calculated the usage of distance system is given byPQ = [tex]sqrt((- 1 + 5) + (- 3 + 3) ) = sqrt(+ )[/tex] = 4 units.We understand that if a factor is turned around 270 ranges counterclockwise, then its co-ordinates modifications as follows:(x, y) -> (y, - x)So, after the rotation, the co- ordinates of P and Q becomes[tex]P(-5,3) P^ (3, 5)G(- 1, 3) Q^ (3,1[/tex].The period of the road phase P'Q' as calculated the usage of distance system isP^ top Q^ top = sqrt([tex](3 - + (1 - ) = sqrt[/tex]= 4 units.Thus, the lengths of PQ and P'Q' are same.Read more about segment :
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as a seismologist, janet understands the devastating effects that earthquakes can have. so, she keeps her basement stocked with canned food, like chili. janet buys cans of chili from an online retailer that charges a shipping fee plus the cost of each can of chili. this table shows the relationship between the number of cans of chili janet buys, x, and the total cost (in dollars), y. x (cans) y (dollars) 12 $26.40 44 $56.80 66 $77.70 100 $110 according to the values in the table, do x and y have a proportional relationship?
As a seismologist, Janet understands the devastating effects that earthquakes can have. so, she keeps her basement stocked with canned food, like chili. This table shows the relationship between the number of cans of chili Janet buys, x, and the total cost (in dollars), y.
[tex]\begin{tabular}{|c|c|c|}\underline{x(cans)}&\underline{y(dollars)} \\12 & \$\ 26.40 \\ 44 & \$\ 56.80 \\ 66 & \$\ 77.70 \\ 100 & \$\ 110 \end{align}[/tex]
According to the values in the table, x and y have not a proportional relationship.
Prove x and y have a proportional relationshipTable
[tex]\begin{tabular}{|c|c|c|}\underline{x(cans)}&\underline{y(dollars)} \\12 & \$\ 26.40 \\ 44 & \$\ 56.80 \\ 66 & \$\ 77.70 \\ 100 & \$\ 110 \end{align}[/tex]
Specifies the gradient (m) in rows 1 and 2
m₁ = [tex]\displaystyle \frac{56.80 - 26.40}{44-12}[/tex]
m₁ = [tex]\displaystyle \frac{30.40}{32}[/tex]
m₁ = [tex]\displaystyle \frac{19}{20}[/tex]
Specifies the gradient (m) in rows 2 and 3
m₂ = [tex]\displaystyle \frac{77.70 - 56.80}{66-44}[/tex]
m₂ = [tex]\displaystyle \frac{20.9}{22}[/tex]
Because the values of m₁ and m₂ are not the same [tex]\displaystyle \frac{19}{20}[/tex] ≠ [tex]\displaystyle \frac{20.9}{22}[/tex], then x and y have not a proportional relationship.
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Put these numbers in order from greatest to least.
-0.85
12.45
0.25
-12
Answer:
12.45, 0.25, -0.85, -12
Step-by-step explanation:
The larger the negative the lesser the value, opposite for positive numbers
How many triangles exist with the given side lengths?.
Exactly one unique triangle exists with the given side lengths, option B is correct.
Here, we are given that the three sides of triangle are- 12, 15 and 18.
According to the triangle inequality theorem- “The sum of the length of any two sides of a triangle should be greater than the third side”. Let us see if this holds in this case-
(12 + 15) > 18
(15 + 18) > 12
(12 + 18) > 15
Thus, we see that the triangle inequality theorem is satisfied. So there is only one triangle possible with the sides of given lengths.
Hence, exactly one unique triangle exists with the given side lengths, option B is correct.
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Your question was incomplete. Check for full content below-
How many triangles exist with the given side lengths?
12 in, 15 in, 18 in
A) No triangle exists with the given side lengths.
B) Exactly one unique triangle exists with the given side lengths.
C) More than one triangle exists with the given side lengths.
which of these statements is not true? if the average variance inflation factor is greater than 1 then the regression model might be biased. multicollinearity in the data is shown by a vif (variance inflation factor) greater than 10. tolerance values above 0.2 may indicate multicollinearity in the data. the tolerance is 1 divided by the vif (variance inflation factor).
Point C - Tolerance values above 0.2 may indicate multi collinearity in the data is correct.
Given that
It must be below 0.2, along with VIF above 10.
The remaining options are not correct.
A. If the average variance inflation factor is greater than 1 then the regression model might be biased.
B. Multi collinearity in the data is shown by a VIF (variance inflation factor) greater than 10.
D. The tolerance is 1 divided by the VIF (variance inflation factor).
Hence the answer is Point C - Tolerance values above 0.2 may indicate multi collinearity in the data is correct.
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If the first and second terms of a geometric sequence are 3 and 12, what is
the expression for the value of the 24th term of the sequence?
Answer:
[tex]3(4)^{23}[/tex]
Step-by-step explanation:
Let the first term be [tex]a[/tex] and the common ratio be [tex]r[/tex].
We know [tex]a=3[/tex] and [tex]ar=12[/tex], meaning [tex]r=4[/tex].
This means the 24th term is [tex]3(4)^{23}[/tex].
Suppoe Jerome read the following number of page each day. Will he meet hi goal of reading at leat 85 page by the end of the day Friday?
If p = 6, he will not meet his goal.
If p = 7, he will meet his goal.
If p = 8, he will meet his goal.
What is inequality?
In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.
Here, we have
Jerome has already read 50 pages of a novel and read p pages each day from Monday to Friday.
If Jerome read at least 85 pages by the end of Friday, inequality will be,
50 + 5p ≥ 85
If Jerome reads 6 pages each day,
If p = 6,
Inequality will be,
50 + 5(6) ≥ 85
80 ≥ 85
It's not true.
Hence, he will not meet his goal.
If p = 7,
Inequality will be,
50 + 5(7) ≥ 85
85 ≥ 85
It's true.
Hence, he will meet his goal.
If p = 8,
Inequality will be,
50 + 5(8) ≥ 85
90 ≥ 85
It's true.
Hence, he will meet his goal.
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which of the following is equivalent to sum from n equals 1 to infinity of 12 times quantity negative five eighths end quantity to the power of n question mark
The sum of given equation is 96/13.
Given equation is sum from n equals 1 to infinity of 12 times negative five eighths end quantity to the power of n that means
∑ n=1 to ∞ [12(-5/8)ⁿ]
This is in the form of geometric expression
that is an = ar^(n-1)
therefore we get
a = 12 and r = - 5/8
We have to find the sum.
Sum of infinity of the sequence is expressed as
Sum = a / (1-r)
where a = first term of the series
and r = common ratio between two consecutive terms
Now we will substitute values of a and r in the above equation
Sum = [tex]\frac{12}{1-(-5/8)}[/tex]
= [tex]\frac{12}{1 + 5/8}[/tex]
= [tex]\frac{12}{13/8}[/tex]
Sum = [tex]\frac{96}{13}[/tex]
Hence the sum of given equation is 96/13.
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What is the solution to the system of equations y x 10 2x y 4?.
The solution to the system of equation is [tex](\frac{14}{3},-\frac{16}{3})[/tex]
What is a system of equations ?A system of equations is a set of two or more equations with the same variables. A solution to a system of equations is a set of values for the variable that satisfy all the equations simultaneously.
Differentiate between substitution and elimination method.
The major difference between the substitution and elimination method is that the substitution method is the process of replacing the variable with a value, whereas the elimination method is the process of removing the variable from the system of linear equations.
The system of equations are :
y = x - 10 and
2x + y = 4
On solving two equations by using substitution method ,we get
By substituting the value of y in another equation ,we obtain the equation in terms of one variable :
Now, according to the question
⇒ 2x + (x - 10) = 4
⇒ (2x + x) = (4 + 10)
⇒ 3x = 14
⇒ x = 14/3
Further for y ,we substitute obtained value of x in the equation
y = x - 10
Now,
[tex]y = \frac{14}{3}-10[/tex]
[tex]=\frac{(14-30)}{3}[/tex]
[tex]= (\frac{-16}{3})[/tex]
[tex]= - (\frac{16}{3})[/tex]
Hence ,the solution is (x,y) : [tex](\frac{14}{3},-\frac{16}{3})[/tex]
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1) Four cards labeled A, B, C, and D are randomly placed in four boxes labeled A, B, C, and D. Each box receives exactly one card.
In how many ways can the cards be placed in the boxes?
_______ ways
2)four cards labeled A, B, C, and D are randomly placed in four boxes labeled A, B, C, and D. Each box receives exactly one card.
Count the number of elements in the event that no box contains a card with the same letter as the box.
________ elements
If no box has a card with the same letter as the box, then count the number of elements as 24 ways.
Given that,
Four randomly selected cards with the letters A, B, C, and D are placed in the corresponding boxes. There is exactly one card in each box.
We have to find If no box has a card with the same letter as the box, then count the number of elements.
We know that,
What is the permutation?A permutation is a mathematical calculation that establishes the number of possible arrangements for a given set, taking into account the arrangement's order.
From the given information:
The permutation approach can be used to represent the four cards that are randomly placed in the four boxes and can be used to express the following:
=⁴P₄
Since no box contains a card that begins with the same letter as the box, it follows that
Card A can be inserted into a box four different ways,
Card B three different ways,
Card C two ways, and
Card D one way.
The four cards' permutation can then be calculated as follows:
⁴P₄=4!/0!=4×3×2×1/1=24.
Therefore, If no box has a card with the same letter as the box, then count the number of elements as 24 ways.
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rapheal pays 7$ for 1/2 pound of cashews how much would he pay for one pound
Answer:
$14
Step-by-step explanation:
since there are 2 halves in a pound we just need to multiply 7 by 2
7x2
14
Hopes this helps please mark brainliest
It's $7 for 1/2 a pound so we have to double it to get our answer so...
$14 would be our answer.
[tex]1/2+1/2=1[/tex]
Government data show that 26% of the civilian labor force has at least 4 years of college and that 15% of the labor force works as laborers or operators of machines or vehicles. Can you conclude that because (0.26)(0.15) = .039 about 4% of the labor force are college-educated laborers or operators?
(a) Yes, by the multiplication rule
(b) Yes, by conditional probabilities
(c) Yes,bythelawoflargenumbers
(d) No, because the events are not independent
(e) No, because the events are not mutually exclusive
d
Option (d)- No, because the events are not independent. Hence we can not conclude that because (0.26)(0.15) = 0.039 about 4% of the labor force are college-educated labors or operators.
We have given that government data show that 26% of the civilian labor force has at least 4 years of college and that 15% of the labor force works as laborers or operators of machine or vehicle.
So here,
event A = 26% of civilian labor force hast at least 4 years of college
event B = 15% of the labor force works as laborers or operators of machines or vehicles
Therefore it is observe that both the events are not independent.
Hence we cannot conclude that because (0.26)(0.15) = 0.039 about 4% of the labor force are college-educated laborers or operators.
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Suppoe the domain of the propoitional functionP (x, y) conit of pair x and y, where x i 1, 2, or 3 and y i 1, 2, or 3. Write out thee propoition uing dijunction and conjunction. A) ∀x∀yP (x, y) b) ∃x∃yP (x, y) c) ∃x∀yP (x, y) d) ∀y∃xP (x, y)
These are the preposition for the given conditions:
(P(1,1) ∧ P(1,2) ∧ P(1,3)) ∧ (P(2,1) ∧ P(2,2) ∧ P(2,3)) ∧ (P(3,1) ∧ P(3,2) ∧ P(3,3)).
(P(1,1) ∨ P(1,2) ∨ P(1,3)) ∨ (P(2,1) ∨ P(2,2) ∨ P(2,3)) ∨ (P(3,1) ∨ P(3,2) ∨ P(3,3)).
(P(1,1) ∨ P(1,2) ∨ P(1,3)) ∧ (P(2,1) ∨ P(2,2) ∨ P(2,3)) ∧ (P(3,1) ∨ P(3,2) ∨ P(3,3)).
(P(1,1) ∧ P(1,2) ∧ P(1,3)) v (P(2,1) ∧ P(2,2) ∧ P(2,3)) v (P(3,1) ∧ P(3,2) ∧ P(3,3)).
The domain of the propositional P(x, y) consists of pairs x and y, where x is 1, 2, 3 and y is 1, 2, 3.
What are the disjunction and conjunction?
In logic functions, there are two kinds of compound statements. These are referred to as conjunction and disjunction. A conjunction implies that both statements are correct, whereas a disjunction implies that at least one of the statements is correct. A conjunction connects statements with the word "and," whereas a disjunction connects statements with the word "or."
By using disjunction and conjunction we get,
a) ∀x∀y P(x, y) is written as:
(P(1,1) ∧ P(1,2) ∧ P(1,3)) ∧ (P(2,1) ∧ P(2,2) ∧ P(2,3)) ∧ (P(3,1) ∧ P(3,2) ∧ P(3,3)).
b) ∃x ∃y P (x, y) is written as:
(P(1,1) ∨ P(1,2) ∨ P(1,3)) ∨ (P(2,1) ∨ P(2,2) ∨ P(2,3)) ∨ (P(3,1) ∨ P(3,2) ∨ P(3,3)).
c) ∃x∀y P(x, y) is written as:
(P(1,1) ∨ P(1,2) ∨ P(1,3)) ∧ (P(2,1) ∨ P(2,2) ∨ P(2,3)) ∧ (P(3,1) ∨ P(3,2) ∨ P(3,3)).
d) ∀y∃x P(x, y) is written as:
(P(1,1) ∧ P(1,2) ∧ P(1,3)) v (P(2,1) ∧ P(2,2) ∧ P(2,3)) v (P(3,1) ∧ P(3,2) ∧ P(3,3)).
Hence, these are the preposition for the given conditions:
(P(1,1) ∧ P(1,2) ∧ P(1,3)) ∧ (P(2,1) ∧ P(2,2) ∧ P(2,3)) ∧ (P(3,1) ∧ P(3,2) ∧ P(3,3)).
(P(1,1) ∨ P(1,2) ∨ P(1,3)) ∨ (P(2,1) ∨ P(2,2) ∨ P(2,3)) ∨ (P(3,1) ∨ P(3,2) ∨ P(3,3)).
(P(1,1) ∨ P(1,2) ∨ P(1,3)) ∧ (P(2,1) ∨ P(2,2) ∨ P(2,3)) ∧ (P(3,1) ∨ P(3,2) ∨ P(3,3)).
(P(1,1) ∧ P(1,2) ∧ P(1,3)) v (P(2,1) ∧ P(2,2) ∧ P(2,3)) v (P(3,1) ∧ P(3,2) ∧ P(3,3)).
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Can some one help me with this urgent?
Hotel Nights Price (in dollars)
A 3 192
B 5 300
C 7 455
Which hotel costs the least per night?
if the pile contains only 15 quarters and only 20 dimes but at least 30 of each other kind of coin, how many collections of 30 coins can be chosen?
The number of ways to choosing coins with at least 15 quarters and 20 dimes is 4354.
In the given question, if the pile contains only 15 quarters and only 20 dimes but at least 30 of each other kind of coin, then we have to find the collections of 30 coins can be chosen.
Number of coins only of quarters = 15
Number of coins only of dimes = 20
The number of ways to choosing coins with at least 15 quarters and 20 dimes= Total- [tex](^{18}C_{3}+^{13}C_{3})[/tex]
The number of ways to choosing coins with at least 15 quarters and 20 dimes= [tex]^{33}C_{3}-(^{18}C_{3}+^{13}C_{3})[/tex]
Using [tex]^{n}C_{r}=\frac{n!}{r!(n-r)!}[/tex]
The number of ways to choosing coins with at least 15 quarters and 20 dimes= [tex]\frac{33!}{3!(33-3)!}-(\frac{18!}{3!(18-3)!}+\frac{13!}{3!(13-3)!})[/tex]
The number of ways to choosing coins with at least 15 quarters and 20 dimes= [tex]\frac{33!}{3!30!}-(\frac{18!}{3!15!}+\frac{13!}{3!10!})[/tex]
Simplifying
The number of ways to choosing coins with at least 15 quarters and 20 dimes= [tex]\frac{33\times32\times31\times30!}{3\times2\times1\times30!}-(\frac{18\times17\times16\times15!}{3\times2\times1\times15!}+\frac{13\times12\times11\times10!}{3\times2\times1\times10!})[/tex]
The number of ways to choosing coins with at least 15 quarters and 20 dimes= 11×16×31-(3×17×16+13×2×11)
The number of ways to choosing coins with at least 15 quarters and 20 dimes= 5456-(816+286)
The number of ways to choosing coins with at least 15 quarters and 20 dimes= 5456-1102
The number of ways to choosing coins with at least 15 quarters and 20 dimes= 4354
If the pile contains only 15 quarters and only 20 dimes but at least 30 of each other kind of coin, the number of ways to choosing coins with at least 15 quarters and 20 dimes is 4354.
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What is the distance from the center of the circle C to chord AB?
Answer:
Step-by-step explanation:
8.5
What is an equation of the line that passes through the point ( 8 , 2 ) (8,2) and is parallel to the line x + 4 y = 28 x+4y=28?.
The equation of the line that passes through the point (8,2) and is parallel to the line x+4y = 28 is y = -x/4+4.
According to the question,
We have the following information;
Point thorough which line is passing = (8,2)
Equation of the line:
x+4y = 28
Now, we will convert this equation into the slope-intercept form:
4y = -x+28
Dividing by 4 on both sides of the equation:
y = -x/4+28/4
y = -x/4+7
Slope of the line = -1/4
We know that the following formula is used to find the equation of the line:
(y-y') = m(x-x')
(y-2) = -1/4(x-8)
y-2 = -x/4+2
Adding 2 on both sides:
y = -x/4+4
Hence, the equation of the line that passes through the point (8,2) and is parallel to the line x+4y = 28 is y = -x/4+4.
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8. in the pcr process, if we assume that each cycle takes 5 minutes, how many fold amplification would be accomplished in an hour?
The answer to the given question is 4096-fold. If it assumed that each cycle in the PCR process takes 5 minutes, then total 4096-fold amplification could be accomplished in an hour.
What are the steps in PCR Amplification?PCR is based on 3 simple steps needed for any DNA synthesis reaction. Those steps are: denaturation of the template to the single strands; annealing of the primers to every original strand for a new strand synthesis; and development of the new DNA strands from the primers.
In this case, each cycle takes 5 minutes and doubles the DNA.
Thus, in one hour, there would be 60 / 5 = 12 cycles.
So, the DNA would be amplified 212 = 4096-fold.
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a wheat farmer has a storage bin that holds 6,846 1/4 cubic feet.if a bushels of wheat fills 11/4 cubic feet, how many bushels cam the storage bin hold
The storage bin can hold 5477 bushels.
We have total capacity of the storage bin which is given to us in mixed fraction form.
If we convert this into improper fraction, it is equivalent to =27385/4
Now, in the same way ,we have also given that some amount of wheat already fills which is also given in mixed fraction form.
If we convert this into improper fraction form, it is equivalent to
=5/4
Now, to find the the number of bushels storage bin maximally hold is =(total volume of storage bin)/(Volume of wheat fills)
=>N = (27385/4)/(5/4)
=>N=27385/5
=>N=5477
Hence, total number of bushels which storage bin can hold is 5477.
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helpppppppppppppppppppppp plsssss..
Answer:
The function crosses the Y axis (the up down axis) at -1
Step-by-step explanation:
A boat traveled 27 miles in 2 hrs. At this rate, How many miles will the boat travele in 1/2 hrs
Answer:
In explanation down below.
Step-by-step explanation:
So if the boat was able to travel 27 miles in 2 hours that means that it traveled 13.5 miles an hour. I think that you want to know how many miles the boat will travel in 1/2 an hour. Which is 6.75.
1 hour: 13.5 miles
1/2 hour the boat has traveled 6.75 miles.
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F(x)= 12x-5 and G(x) = 2x²+3
Find (G-F) (-2) =
The domain of the function is 24.The collection of all potential inputs for a function is known as its domain.
How do you locate the domain?Let y = f(x) be a function with x as the independent variable and y as the dependent variable. A value for x is said to be in the domain of a function f if it can be used to successfully produce a single value, y, using another value for x.The collection of all potential inputs for a function is known as its domain. For instance, the domain of f(x)=x2 is all real numbers, and the domain of g(x)=1/x is all real numbers other than x=0.Determine the input values. Exclude any real numbers that produce a negative value in the radicand since there is an even root. Set the radicand to be bigger than or equal to Calculate x from zero. The area of the function where the solution(s) lie.Explanation:
F(x)= 12x-5 and G(x) = 2x²+3
Find (G-F) (-2) , put x = 0 , 2+3-12-5 = -12.
-12 * -2 = 24.
The domain of the function is 24.
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