The total number of students is calculated by dividing the total number of chess club sign ups by the proportion of students who signed up Therefore, 210/0.6 = 840 students in the school.
15 students out of 25 signed up for chess club.
Therefore, 15/25 = 0.6 of the students signed up for chess club.
Therefore, 0.6 x total number of students = 210 (the number of students who signed up for chess club).
Therefore, 210/0.6
= 840 students in the school.
In one class, 15 out of 25 students signed up for the chess club. This means that 0.6 (or 60%) of the students in the class decided to join. If this rate stays constant across the entire school, then it is possible to calculate the total number of students in the school by using the proportion of students who signed up for the chess club. To calculate the total number of students, we use the equation: 0.6 x total number of students = 210 (the number of students who signed up for chess club). By dividing both sides of the equation by 0.6, we get 210/0.6 = 840 students in the school. Therefore, there are 840 students in the whole school if 210 signed up for chess club.
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Draw a line representing the "rise" and a line
representing the "run" of the line. State the
slope of the line in simplest form.
Click twice to plot each segment.
Click a segment to delete it.
-10 -9 -8 -7 -6 -5 -4 -3
-2
-1
y
10
9
8
7
6
5
4
3
2
1
-1
-2
ỗ có có ý ới ơi Á có nó
4
-5
-6
-8
-9
-10
1
2
3
45
6
78
9
10
·x
Answer:
Step-by-step explanation:
rise is up and run is over.
The first number would be y and the second number would be x
and x is run
y is rise.
which expression has a negative value
A. x + y
B. x - y
C. x*y
D. x/y
Answer:
It depends on the values of x and y. If x is positive and y is negative, then option A (x + y) would have a negative value. If y is greater than x, then option B (x - y) would have a negative value. If either x or y (or both) is negative, then option C (x*y) could have a negative value. Option D (x/y) could also have a negative value if x is negative and y is positive, or if both x and y are negative.
Answer:
Step-by-step explanation:
B because it has subtraction
What is the total area, in square centimeters, of the shaded sections of the below? 6.4 cm 9.1 cm 5.2 cm 9.6 cm
The total area, in square centimeters, of the shaded sections of the below would be 33. 93 cm ²
How to find the area ?The area of the shaded sections can be found by finding the area of the two triangular sections that are shaded.
Area of first triangle :
= 1 / 2 x base x height
= 1 / 2 x 5. 3 x 5 . 8
= 15. 37 cm ²
The area of the second triangle is :
= 1 / 2 x 6 . 4 x 5 . 8
= 18. 56 cm ²
The total area of the shaded sections is:
= 15. 37 + 18. 56
= 33. 93 cm ²
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In an elementary chemical reaction, single molecules of two reactants A and B form a molecule of the product C: A+B - C. The law of mass action states that the rate of reaction is proportional to the product of the concentrations of A and B: dc dt = k[A]B] (See Example 3.7.4.) Thus, if the initial concentrations are [A] = a moles/Land (B] = b moles/L and we write r = (C), then we have do dt ka - x)( - ) a. Assuming that a b, find as a function of t. Use the fact that the initial concentration of C is o. b. Find (t) assuming that a = b. How does this expression for a(t) simplify if it is known that 1 [C] - a after 20 seconds?
For the given elementary chemical reaction, the solution to the question is: C = a^2 * (1-t^2/400(1-a))
The question asks about calculating the concentration of C in a chemical reaction. Given that the reaction equation is as follows: A + B → C The rate of reaction can be expressed as: dc/dt = k[A][B] Where, k is the rate constant[A] is the concentration of reactant A in moles/L[B] is the concentration of reactant B in moles/L, c is the concentration of product C in moles/L
The initial concentration of A and B is [A] = a moles/L, [B] = b moles/L Let r be the rate of reaction, i.e. r = dc/dt Thus, using the equation r = k[A][B], we get r = k(a)(b)Now, we can write a differential equation for the concentration of C as follows: dc/dt = r, with initial concentration of C as 0 moles/L∴ dc/dt = kab
Substituting r = k(a)(b) in the equation, we get dc/dt = kabdc/db = kab*dt Differentiating both sides, we get, ln(C) = kab*t + C where C is a constant, ln(C) = ln(a^2) = 2ln(a) = C When a = b, the concentration of C will be maximum at t = (1/k)(ln(a)).
Thus the concentration of C as a function of time (when a = b) is given by C = a^2 * (1-t^2/2)If [C] = a after 20 seconds, then using the equation, we get a = a^2 * (1 - 20^2 * k^2/2)Therefore, 1 = a * (1 - 200k^2) Solving this equation for k, we get, k = ± sqrt[(1-a)/200a^2] For the positive value of k, the concentration of C as a function of time is given by C = a^2 * (1-t^2/400(1-a)).
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What is the answer to this question?
Answer:
Step-by-step explanation:
The domain is found by setting the denominator equal to 0 and solving for y. This value of y gives you the values that cause the denominator to go to 0, which is a problem. In this rational expression, there are no real numbers that cause the denominator to go to 0, so the domain is all real numbers.
A bookstore sells 7 books for $89.25. Which table represents the relationship between number of books and the total price?
Answer: C is our answer.
The first thing that we can do is divide the known number of books into the price that they sold for.
Our equation would be 89.25 divided by 7, which is 12.75. This means that one single book is 12.75. We can look at the charts and point out where one book is 12.75, that is both A and D. While Chart B and C have 7 books for 89.25 which we know is correct.
Lets look at chart D.The next part we can solve is the price of 2 books. 12.75 x 2 is 25.50, so we can mark question B incorrect since two books are 25.50 not 13.75.Chart B is incorrect because 14 books is double 7, so it should be twice as much as 89.25, which we should know 90 dollars is not two times as much 80. Chart A is incorrect because 11 x 12.75 is 140.25, while the chart reads as 22.75.
Now lets look at chart C. Next we can solve the price of 8 books. 8 x 12.75 is 102. Then we solve for 9 books. 12.75 x 9 is 114.75, which means that C is correct.
I hope this helped & Good Luck <3!!
Calculate the following without using a calculator -5×(-3+7)+20÷(-4)
Answer:
-25
Step-by-step explanation:
simplification using BODMAS
[tex]-5 * 4 + -5[/tex]
-20 - 5
= -25
a car dealership has 5 exterior color choices, 6 interior color choices and 2 model choices. how many different ways can you choose a car
Determine whether enough information is given to prove that the triangle PQR and triangle STU are congruent. Explain your answer.
Step-by-step explanation:
I do not believe you are given enough info to prove they are congruent....you only have ONE angle and one side that are equal ....you need another side or another angle to prove congruency....
I've added an illustration to show how the two triangles would not be congruent without changing the info given in the pic
.
Data are drawn from a bell-shaped distribution with a mean of 120 and a standard deviation of 5. There are 900 observations in the data set. a. Approximately what percentage of the observations are less than 130? (Round your answer to 1 decimal place.) Percentage of observations 0 b. Approximately how many observations are less than 130? (Round your answer to the nearest whole number.) Number of observations
The percentage of observations less than 130 is 97.7%, and the number of observations less than 130 = 879
The question asks about the percentage and number of observations that are less than 130 in a data set that follows a bell-shaped distribution with a mean of 120 and a standard deviation of 5.
a. To find the percentage of observations that are less than 130, we can use the z-score formula:
z = (x - μ) / σ
where x is the value we are interested in, μ is the mean, and σ is the standard deviation.
Plugging in the given values, we get:
z = (130 - 120) / 5
z = 10 / 5
z = 2
Using a standard normal table or calculator, we can find that the probability of a z-score being less than 2 is approximately 0.9772. This means that approximately 97.7% of the observations are less than 130.
b. To find the number of observations that are less than 130, we can multiply the percentage by the total number of observations:
Number of observations = 0.9772 * 900
Number of observations = 879.48
Rounding to the nearest whole number, we get that approximately 879 observations are less than 130.
Therefore, the answers are:
a. Percentage of observations less than 130 = 97.7%
b. Number of observations less than 130 = 879
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A traditional western pack of playing cards consists of four suits. Each suit has 13cards. Find the fraction of the playing cards are:
a)red. B)diamonds
c)face cards. D)black and face cards
a) 1/2, b) 1/4, c) 3/13, d) 7/26 (fraction of black and face cards) in a traditional Western pack of playing cards.
A traditional Western pack of playing cards consists of four suits: Hearts (colored red), Diamonds (colored red), Spades (colored black), and Clubs (colored black). Each suit has 13 cards: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, and King.
a) To find the fraction of the playing cards that are red, we need to add up the number of red cards and divide by the total number of cards in the deck. There are two red suits, Hearts and Diamonds, and each has 13 cards. So there are 26 red cards in total. Since there are 52 cards in a deck, the fraction of red cards is 26/52 or 1/2.
b) To find the fraction of cards that are Diamonds, we simply divide the number of Diamonds (13) by the total number of cards (52). This gives us a fraction of 13/52 or 1/4.
c) To find the fraction of face cards, we need to add up the number of face cards and divide by the total number of cards in the deck. In each suit, there are three face cards: King, Queen, and Jack. So there are 12 face cards in each deck (4 suits x 3 face cards per suit). Therefore, there are 12/52 or 3/13 face cards in the deck.
d) To find the fraction of black and face cards, we need to count the number of black cards and the number of face cards that are also black. There are two black suits, Spades and Clubs, and each has 13 cards. So there are total 26 black cards. Of these 26 cards, there are 12 face cards (King, Queen, and Jack) which are not black, leaving 14 black cards which are face cards. Therefore, the fraction of black and face cards is 14/52 or 7/26.
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PLEASE HELP WITH THIS PROBLEM ASAP
16. The base side y = 10.565 and altitude x = 22.657
17. The hypotenuse c = 49.70 and base y = 46.70.
18. The value of AB = 30√3 and AC = 45
19. The value of AB = 36√3 and BC = 18√3.
What is a hypotenuse?In geοmetry, a hypοtenuse is the lοngest side οf a right-angled triangle, the side οppοsite the right angle. The length οf the hypοtenuse can be fοund using the Pythagοrean theοrem, which states that the square οf the length οf the hypοtenuse equals the sum οf the squares οf the lengths οf the οther twο sides.
16. Given hypotenuse = 25
θ = 25°
Sin θ = opposite/hypotenuse
Sin 25° = y/25
y = Sin 25° × 25
y = 10.565
Given hypotenuse = 25
θ = 25°
Cos θ = adjacent/hypotenuse
Cos 25° = x/25
x = Cos 25° × 25
x = 22.657
17. Given Side = 17
θ = 20°
Sin 20° = 17/c
c = 17/Sin 20°
c = 49.70
Cos θ = adjacent/hypotenuse
Cos 20° = y/49.70
y = Cos 20° × 49.70
y = 46.70
18. Given BC = 15√3
In a 30°−60°−90° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is 3√ times the length of the shorter leg.
Thus, BC = 15√3
AB = 2(15√3)
= 30√3
and
AC = √3(15√3)
= 15 × 3
= 45
Thus, when BC = 15√3, then AB = 30√3 and AC = 45
19. Given AC = 54
In a 30°−60°−90° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is 3√ times the length of the shorter leg.
Thus, BC = x and AC = x√3
54 = x√3
54 = x√3
x = 54/√3
x = 18√3
BC = 18√3
AB = 2x = 2(BC) = 2(18√3)
= 36(√3)
Thus, when AC = 54, then AB = 36√3 and BC = 18√3.
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Given the expression
Choose all the equivalent expressions as your answer.
The equivalent expressions of [tex]x^3[/tex] are[tex]\frac{(x ^ 6)}{(x ^ 3)}[/tex]and [tex]\frac{(x^{-3}) }{(x^{-6}) }[/tex], the expressions [tex]\frac{(x^{30}) }{(x^{10})}[/tex] and [tex]\frac{(x ^ 4) ^ 2)}{x ^ 2}[/tex] are not equivalent to [tex]x^3[/tex].
What are equivalent expressions?
Equivalent expressions are different algebraic expressions that have the same value when evaluated for a particular set of variables.
The equivalent expressions [tex]x^3[/tex] are:
[tex]\frac{(x ^ 4) ^ 2)}{x ^ 2}[/tex] : This expression can be simplified as follows:
=[tex]\frac{(x ^ 4) ^ 2)}{x ^ 2}[/tex]
= [tex]\frac{(x ^ 8)}{(x ^ 2) }[/tex]
=[tex]x^{8-2}[/tex]
= [tex]x^6[/tex]
[tex]\frac{(x ^ 6)}{(x ^ 3)}[/tex] : This expression can be simplified as follows:
=[tex]\frac{(x ^ 6)}{(x ^ 3)}[/tex]
= [tex]x^{6-3}[/tex]
=[tex]x^3[/tex]
[tex]\frac{(x^{30}) }{(x^{10})}[/tex] : This expression can be simplified as follows:
=[tex]\frac{(x^{30}) }{(x^{10})}[/tex]
=[tex]x^{30-10}[/tex]
=[tex]x^{20}[/tex]
[tex]\frac{(x^{-3}) }{(x^{-6}) }[/tex] : This expression can be simplified as follows:
=[tex]\frac{(x^{-3}) }{(x^{-6}) }[/tex]
=[tex]x^{-3-(-6)}[/tex]
=[tex]x^{-3+6}[/tex]
=[tex]x^{3}[/tex]
Therefore, the equivalent expressions of [tex]x^3[/tex] are[tex]\frac{(x ^ 6)}{(x ^ 3)}[/tex]and [tex]\frac{(x^{-3}) }{(x^{-6}) }[/tex] , the expressions [tex]\frac{(x^{30}) }{(x^{10})}[/tex] and [tex]\frac{(x ^ 4) ^ 2)}{x ^ 2}[/tex] are not equivalent to [tex]x^3[/tex].
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When the mortgage is completely paid off for Mark and Lynne's house, it will be 5 times as old as it is now. If they have 28 years left on the mortgage, how old
is the house right now?
The house is now
years old
Mark and Lynne have 28 years left on their mortgage. To figure out how old their house is right now, we need to divide the remaining years on the mortgage by 5.
This is because when the mortgage is paid off, their house will be 5 times as old. Therefore, 28 divided by 5 is equal to 5.6 years old. This means that the house is currently 5.6 years old. After 28 years, the house will be 33.6 years old.
Mark and Lynne have a mortgage on their house that still has 28 years remaining on it. To figure out the age of the house currently, we need to do a simple calculation. When the mortgage is paid off, their house will be 5 times as old as it is now. Therefore, if we divide the remaining years on the mortgage by 5, we will get the current age of the house. 28 divided by 5 is equal to 5.6 years old. This means that the house is currently 5.6 years old. In 28 years, when the mortgage is paid off, the house will be 33.6 years old. It is important to pay off the mortgage in a timely manner, as this will save Mark and Lynne a lot of money in the long run.
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Do the Ratios 6/5 and 4/3 fit a Proportion
Answer:
No
Step-by-step explanation:
[tex]\frac{6}{5}=1.2[/tex]
[tex]\frac{4}{3} =1.33[/tex]
[tex]\frac{6}{5} < \frac{4}{3}[/tex]
Hope this helps.
Answer:
No
Step-by-step explanation:
6/5=4/3
18=20
9≠10
whats the missing side lengths !
Answer:
x = 6
y = 3√2
Step-by-step explanation:
tan45 = y / (3√2)
y = (3√2)(tan45) = 3√2
x = (3√2) / cos45 = 6
this is a 45-45-90 isosceles triangle
Please help with this please.
With the applicatiοn οf Distributive Prοperty οf Multiplicatiοn, the fοllοwing equatiοn 3 (x + 2) + 5 can be written as
3*x + 3*2 + 5
What is Distributive Prοperty οf Multiplicatiοn?The distributive prοperty οf multiplicatiοn is a mathematical rule that states that the prοduct οf a number and a sum can be οbtained by adding the prοducts οf the number and each term in the sum. In οther wοrds, a(b+c) = ab + ac. This prοperty can be used tο simplify expressiοns by breaking them dοwn intο smaller parts.
It is an impοrtant cοncept in algebra and is οften used tο sοlve equatiοns and simplify expressiοns. The distributive prοperty can alsο be applied tο variables and expοnents, and is a fundamental principle in the study οf algebraic structures such as rings and fields.
With the applicatiοn οf Distributive Prοperty οf Multiplicatiοn, the fοllοwing equatiοn 3 (x + 2) + 5 can be written as
3*x + 3*2 + 5
further simplified will give 3x + 6 + 5 = 3x + 11
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Find the area of the shaded region. The area of the shaded region is____
Answer:
[tex]x^{2}[/tex]
Step-by-step explanation:
x*x=[tex]x^{2}[/tex]
(Helpppp)Write slope-intercept form of the line which is perpendicular bisector to
a segment with endpoints A(5,9), B(7,13).
Answer:
the slope-intercept form of the line which is perpendicular bisector to the segment with endpoints A(5,9), B(7,13) is y = (-1/2)x + 14
PLEASE I NEED HELP BADLY
Answer:
Given as steps.
Step-by-step explanation:
Step 2: Transitive Property of Equality
Step 3: SSS Congruency Therom
Step 5: If alt. Interior angles are congruent when two lines are cut by a transversal then the lines are parallel
Step 6: Quadrilateral with opposite sides parallel and congruent is a parallelogram
hope it helps.
1.Let X 1 ,X 2 ,…,X 10 y Y 1 ,Y 2 ,…,Y 11 be two independent random samples from N(μ X ,4) y N(μ Y ,4) , respectively, that is, they have a common variance σ 2 =4 . Determine the Probability P(S p 2 <6.9157)
Probability 0.919
The probability that the pooled sample variance, S2p, is less than 6.9157 is given by:
P(S2p < 6.9157) = P(S2p - S20 < 6.9157 - S20)
where S20 = ((n1-1)S21 + (n2-1)S22)/(n1+n2-2)
Here, n1 = 10 and n2 = 11. The individual sample variances S21 and S22 are both equal to 4, since both X and Y are samples from N(μ, 4).
Therefore, S20 = ((10-1)4 + (11-1)4)/(10+11-2) = 4.
Hence, P(S2p < 6.9157) = P(S2p - 4 < 6.9157 - 4) = P(S2p - 4 < 2.9157)
The probability can be computed using a chi-square cumulative distribution table. We obtain:
P(S2p - 4 < 2.9157) = 0.919.
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The Probability P(Sp² <6.9157) is 0.6672.
To solve this problem, we need to first recognize that the statistic Sp² follows a chi-squared distribution with 10+11-2 = 19 degrees of freedom, where:
Sp² = [(nX-1)*SX² + (nY-1)*SY²]/(nX+nY-2)
Here, nX = 10, nY = 11, SX² is the sample variance of X and SY² is the sample variance of Y.
Since X and Y are both normally distributed, we know that the sample variances SX² and SY² follow chi-squared distributions with 9 and 10 degrees of freedom, respectively, and scaled by the common variance sigma² = 4.
So we have:
SX² ~ chi-squared(9)*4 = chi-squared(36)
SY² ~ chi-squared(10)*4 = chi-squared(40)
Now we can use the fact that the sum of two independent chi-squared random variables with k1 and k2 degrees of freedom follows a chi-squared distribution with k1+k2 degrees of freedom.
Therefore, Sp² = [(nX-1)*SX² + (nY-1)*SY²]/(nX+nY-2) follows a chi-squared distribution with 9+10 = 19 degrees of freedom and scale parameter 4/(nX+nY-2) = 4/19.
To find P(Sp² < 6.9157), we can use a chi-squared distribution table or calculator. Using a chi-squared calculator, we find:
P(Sp² < 6.9157) = 0.6672
Therefore, the probability that Sp² is less than 6.9157 is 0.6672.
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Which two sequences of transformations could be used to prove figure 1 and figure 2 are congruent?
In some circumstances, it might also be essential to demonstrate congruence using various transformations.
what is transformations ?In mathematics, transformations are modifications done to a geometric figure in a coordinate plane, such as a shape, point, or line. Applying various operations or functions on the coordinates of the points that make up the figure will result in these changes. Four fundamental types of transformations exist: Translation: A figure is moved horizontally, vertically, or both while maintaining its size, form, and orientation.
Translation, rotation, and reflection are the three fundamental transformations that can be employed to demonstrate the congruence of two figures.
To demonstrate that Figures 1 and 2 are congruent with one another, the following two transformational sequences could be used:
Figure 1 should be translated to overlap with Figure 2, then rotated.
b. Rotate Figure 1 about a point until it aligns with Figure 2's orientation.
c. Evaluate the two figures side by side to ensure that all related sides and angles match.
Rotation after reflection:
a. Create a mirror image of Figure 1 by reflecting it across a line.
b. Rotate the reflected Figure 1 about a certain point until it aligns with Figure 2's orientation.
c. Evaluate the two figures side by side to ensure that all related sides and angles match.
To ensure that the two figures are congruent, the transformations must be used in a precise order.
In some circumstances, it might also be essential to demonstrate congruence using various transformations.
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Calculate the following using the Long Division Method. Do not use a calculator. 8328÷24
Answer:347
Step-by-step explanation:=
347 ⇔ 347 R 0
8328 divided by 24
=
347 with a remainder of 0
8. Calculate the area of the triangle below. A. 25cm² B. D. 16cm² E. - 12cm 24cm² 15cm² 8cm 30⁰ C. 20cm²
The area of the triangle is given as follows:
22.8 ft².
How to obtain the area of a triangle?The area of a triangle of base b and height h is given by half the multiplication of these two dimensions, according to the equation presented as follows:
A = 0.5bh.
From the image given at the end of the answer, the dimensions of the triangle are given as follows:
b = 8 ft.h = 5.7 ft.Hence the area of the triangle is given as follows:
A = 0.5 x 8 x 5.7 = 22.8 ft².
Missing InformationThe triangle from which we are going to calculate the area is given by the image presented at the end of the answer.
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Mr. Golv is practicing his jiu-jitsu drill where he does
5
55 guard passes and
2
22 kimura arm locks. A guard pass takes
G
GG seconds, and a kimura arm lock takes
K
KK seconds
Mr. Golv's total time to complete the jiu-jitsu drill is 7GG + 2KK seconds, where GG is the time taken for guard passes and KK is the time taken for kimura arm locks.
Mr. Golv's total time to complete the jiu-jitsu drill can be calculated as follows:
Guard passes: 5 x GG = 5GG seconds
Kimura arm locks: 2 x KK = 2KK seconds
Total time: 5GG + 2KK = (5 x GG) + (2 x KK) = 7GG + 2KK seconds
Therefore, the total time required by Mr. Golv to complete the jiu-jitsu drill is 7GG + 2KK seconds.
For example, if GG = 10 and KK = 6, then the total time required by Mr. Golv to complete the jiu-jitsu drill is (5 x 10) + (2 x 6) = 50 + 12 = 62 seconds.
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complete question
How much time will Mr. Golv take to complete his jiu-jitsu drill which includes 5 guard passes and 2 kimura arm locks, where a guard pass takes GG seconds and a kimura arm lock takes KK seconds?
In the system shown below, how might multiplying each term in the second equation by 2 help us use elimination to solve the system of equations?
4d + 200m = 450
2d + 400m = 300
The solution to the system of equations is d = 100 and m = 1/4. Multiplying each term in the second equation by 2 helped us to eliminate the variable d and solve for m.
How to Solve a System of Equations by Elimination?To solve the system of equations, we can use the elimination method, which involves adding or subtracting the two equations to eliminate one of the variables.
In this case, if we add the two equations as they are, we won't be able to eliminate one of the variables.
Multiply each term in the second equation by 2, we will get:
4d + 200m = 450
4d + 800m = 600
Now, we can subtract the first equation from the second equation to eliminate d:
(4d + 800m) - (4d + 200m) = 600 - 450
600m = 150
m = 1/4
Substituting this value of m back into either of the original equations, we can solve for d:
4d + 200(1/4) = 450
4d + 50 = 450
4d = 400
d = 100
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Question 2
1 pts
At a community event, a vendor lets attendees spin their prize wheel. The wheel consists of 5
colored sections that the vendor claims to be equally likely. One of the sections is labeled "winner!"
A diligent observer records the outcomes of 75 spins. Let X = the number of spins that resulted in a
win.
Use this normal distribution to calculate the probability that AT MOST 10 of the spins result in a
win. Use up to 4 decimal places for the final answer. Use Table A for this one. Stapplet will give a
different value.
Next ▸
Use a system of equations to find the cubic function f(x)=ax3+bx2+cx+d that satisfies the equations. Solve the system using matrices. f(−2)=−7; f(−1)=2; f(1)=−4; f(2)=−7
The solution of the system is a = -1, b = 1, c = 0, and d = -3.
To find the cubic function f(x) = ax³ + bx² + cx + d that satisfies the given equations by using a system of equations and solving the system using matrices, we proceed as follows:Equations for the given cubic function:f(-2) = a(-2)³ + b(-2)² + c(-2) + d = -7 ...(1)f(-1) = a(-1)³ + b(-1)² + c(-1) + d = 2 ...(2)f(1) = a(1)³ + b(1)² + c(1) + d = -4 ...(3)f(2) = a(2)³ + b(2)² + c(2) + d = -7 ...(4)The matrix form of the system of equations is given by AX = B, whereA = [(-2)³ (-2)² -2 1; (-1)³ (-1)² -1 1; (1)³ (1)² 1 1; (2)³ (2)² 2 1],X = [a; b; c; d], andB = [-7; 2; -4; -7].The augmented matrix form of the system of equations is given by [A|B] = [(-2)³ (-2)² -2 1 -7; (-1)³ (-1)² -1 1 2; (1)³ (1)² 1 1 -4; (2)³ (2)² 2 1 -7].Performing the row operations, we get the row echelon form of the augmented matrix as follows:[A|B] = [1 0 0 0 -1; 0 1 0 0 1; 0 0 1 0 0; 0 0 0 1 -3].Therefore, the solution of the system is a = -1, b = 1, c = 0, and d = -3.Hence, the cubic function f(x) = ax³ + bx² + cx + d that satisfies the given equations is given by f(x) = -x³ + x² - 3.
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Select the graph that would represent the best presentation of the solution set for |x| < 5.
Based on the principle of Inequality, Attached image is a graph of the inequality for |x| < 5. The red region is the solution set.
What is the graph equation?A mathematical statement known as an equation demonstrates the relationship between two or more numbers and variables by utilizing mathematical operations such as addition, subtraction, multiplication, division, exponents, and so forth.
Therefore, An expression that demonstrates a non-equal comparison of numbers and variables is called an inequality. So, the graph that best represents this solution set is a number line with open circles at x = -5 and x = 5 and a shaded region in between, indicating that all values of x within this range satisfy the inequality.
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the birthday problem - there are 23 people in this class. what is the probability that at least 2 of the people in the class share the same birthday?
The probability that at least 2 of the people in the class share the same birthday is approximately 0.507 or 50.7%.
The probability that at least two people share the same birthday in a class of 23 people can be calculated using the formula for a complement of an event, which states that the probability of an event happening is 1 minus the probability of it not happening.
Therefore, let’s first calculate the probability that no two people share the same birthday in a class of 23 people.
There are 365 days in a year, and if we assume that all the days are equally likely to be birthdays, then the first person can choose any day, and the probability of the second person not having the same birthday is (364/365), and for the third person, it is (363/365), and so on for the other people.
Therefore, the probability of none of them sharing the same birthday is
(364/365) × (363/365) × … × (343/365) which is approximately 0.493.
The probability of at least two people sharing the same birthday is the complement of the probability that none of them share the same birthday.
Therefore, the probability of at least two people sharing the same birthday in a class of 23 people is
1 − 0.493 ⇒ 0.507.
Hence, there is a 50.7% chance that at least two people share the same birthday in a class of 23 people.
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