Answer: 10/12
Step-by-step explanation:
Make 1/4 have the same denominator as 7/12. 1/4=3/12. 7/12+3/12 = 10/12
4) The school that Kayla goes to is selling tickets to the annual talent show. On the first day of
ticket sales the school sold 8 adult tickets and 6 child tickets for a total of $192. The school took
in $279 on the second day by selling 9 adult tickets and 12 child tickets. What is the price each
of one adult ticket and one child ticket?
Answer:
Senior ticket = $10
Child's ticket = $8
Step-by-step explanation:
s = senior ticket
c = child's ticket
We need to write 2 equations, and we have 2 unknowns, s and c.
3s + 5c = $7012s + 12c = $216First solve for s using the first equation.3s + 5c = 70 Subtract 5c from each side3s + 5c - 5c = 70 - 5c3s = 70 - 5c Divide each side by 33s/3 = (70 - 5c)/3s = 70-5c/312s + 12c = 216
12() + 12c = 216
(70 - 5c) + 12c = 216
4 (70 - 5c) + 12c = 216
280 - 20c + 12c = 216
280 - 8c = 216 Add 8c to each side
280 - 8c + 8c = 216 + 8c
280 = 216 + 8c Subtract 216 from each side.
280 - 216 = 216 - 216 + 8c
280 - 216 = 8c
64 = 8c Divide each side by 8
64/8 = 8c/8
64/8 = c
8 = c
Now plug c into the first equation and solve for s.
3s + 5c = 70
3s + 5(8) = 70
3s + 40 = 70 Subtract 40 from each side.
3s + 40 - 40 = 70 - 40
3s = 70 - 40
3s = 30 Divide each side by 3
3s/3 = 30/3
s = 30/3
s = 10
So a senior ticket costs $10 and a child's ticket costs $8.
Finley has 8 game pieces that differ only in colour. Each game piece is either all red or all black. When Finley lines up the 8 game pieces in a single row, there are 28 distinguishable arrangements. Based on the information above, Finley could have i red game pieces and ii black game pieces The statement above can be completed by the information in row i, ii (1 point) 4,4 5,3 6,2 7,1
This means that when all 8 parts are arranged in a single row, probability there are 28 different conceivable configurations. Finley can have 4 red and 4 black, 5 red and 3 black, 6 red and 2 black, or 7 red and 1 black, depending on the quantity of red and black pieces.
Finley features eight game pieces, each of which is entirely either all red or all black and simply differs in colour. This indicates that there are 28 distinct configurations that may be made using the 8 pieces arranged in a single row. Finley could have 4 red and 4 black, 5 red and 3 black, 6 red and 2 black, or 7 red and 1 black, depending on the quantity of red and black pieces. This is due to the fact that the 8 pieces can be arranged in a variety of ways, and each arrangement will be deemed distinct as long as it contains at least one red and one black piece. For instance, the configuration could be as follows if there are 4 red and 4 black pieces: If there are four red pieces and four black pieces, for instance, the arrangement might be either black-red-black-red-black-red-red or red-black-red-black-red-black. No matter the configuration, there are a total of 28 arrangements.
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what is the eigenvalue for the eigenfunction sin4θ of the operator −tanθd/dθ ?\
The eigenvalue λ is equal to -tan(θ)(4cos(4θ)) / sin(4θ). The exact value of the eigenvalue depends on the specific value of θ, as both tan(θ) and cos(4θ) vary with θ.
To find the eigenvalue, we need to multiply the operator by the eigenfunction and see what we get:
(-tan(θ)d/dθ)(sin(4θ)) = -tan(θ)(d/dθ)(sin(4θ)) = -tan(θ)(4cos(4θ))
Since sin(4θ) is an eigenfunction, we expect that the result of the operator multiplied by the eigenfunction should be proportional to the eigenfunction. In other words, there should be a scalar factor multiplying the eigenfunction. This scalar factor is the eigenvalue.
So, we can write:
(-tan(θ)d/dθ)(sin(4θ)) = λsin(4θ)
where λ is the eigenvalue. Equating the right-hand sides of the two equations, we find:
-tan(θ)(4cos(4θ)) = λsin(4θ)
Dividing both sides by sin(4θ), we get:
-tan(θ)(4cos(4θ)) / sin(4θ) = λ
So, the eigenvalue λ is equal to -tan(θ)(4cos(4θ)) / sin(4θ). The exact value of the eigenvalue depends on the specific value of θ, as both tan(θ) and cos(4θ) vary with θ.
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as a project for a psychology course, a student correlated weight and intelligence scores for 250 students. the computed correlation coefficient was .00. what did the scatter plot look like?
The scatter plot for the correlation of weight and intelligence scores for 250 students would likely be very close to the origin, meaning that the majority of the points would be clustered around the point (0,0), with a very small range of points scattered further away.
This would indicate that there is no correlation between the two variables, which is reflected in the computed correlation coefficient of .00.
A scatter plot is a type of plot that displays data points on a two-dimensional graph. The data points are represented as dots or circles on the graph and show the relationship between two variables. The location of each data point is determined by the value of the two variables for that point. Scatter plots can be used to identify patterns in data, such as clusters, linear relationships, or nonlinear relationships. They can also be used to identify outliers or unusual data points.
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* Please answer fast *
The required fill-in-the-blank below as:
1.) RS ⊥ ST, RS ⊥ SQ, ∠STR ≅ ∠SQR | Given
2.) RS≅RS | Reflexive Property
3.) △RST ≅ △RSQ | AAS Triangle Congruence Property
What are congruent triangles?Two triangles are said to be congruent if their corresponding sides and angles are equal.
The given in question as:
RS ⊥ ST
RS ⊥ SQ
∠STR = ∠SQR
To prove:
△RST ≅ △RSQ
1.) RS ⊥ ST, RS ⊥ SQ, ∠STR ≅ ∠SQR | Given
2.) RS≅RS | Reflexive Property
According to AAS, two triangles are congruent if the two sides and the included angle of one triangle are equal to the corresponding sides and the included angle of the other triangle.
3.) △RST ≅ △RSQ | AAS Triangle Congruence Property
Hence, △RST ≅ △RSQ
Thus, the required fill-in-the-blank above is in the solution.
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Greg works at a floral company making flower arrangements. The table below represents the relationship between the number of hours, h, Greg works and a, the number of arrangements he can create. Which equation represents the relationship in the table?
Answer:
a
Step-by-step explanation:
because as time increases by 1 hr, the number of arrangements increases simultaneously by 3. so I can conclude that a=3hrs
help me please !! i’ll give the brainliest answers
Answer:1.25/
Step-by-step explanation:
The number of songs enjoyed from Eminem by all Learn4Life students is normally distributed with a mean of 7.0 songs and a standard deviation of 1.5 songs.
What is the probability an individual student likes between 5.5 and 8.5 songs from Eminen?
The probability that an individual student likes between 5.5 and 8.5 songs from Eminem is approximately 0.6826 or 68.26%.
To calculate the desired probabilityWe need to find the z-score corresponding to 5.5 and 8.5 and then use the standard normal distribution table to find the area under the curve between these z-scores.
Z-score for 5.5 is (5.5 - 7.0) / 1.5 = -1
Z-score for 8.5 is (8.5 - 7.0) / 1.5 = 1
The probability of a z-score being between -1 and 1 is equal to the area under the standard normal curve between these two z-scores.
According to the standard normal distribution table, this area is approximately 0.6826.
Therefore, The probability that an individual student likes between 5.5 and 8.5 songs from Eminem is approximately 0.6826 or 68.26%.
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How could Liam use red, blue, and yellow cards to describe each of the following motions? Write equations to support your answer. • A green card means move forward 2 spaces. • An orange card means move 8 spaces backward. • A purple card means move forward 10 spaces.
The integer numbers for each card describing the motions are given as follows:
Green card: x = x + 2.Orange card: x = x - 8.Purple card: x = x + 10.What are integer numbers?Integer number are numbers that can have either positive or negative signal, but are whole numbers, meaning that they have no decimal part.
Regarding the movements, the integers can be classified as positive or negative, as follows:
Positive integer represents a forward movement.Negative integer represents a backward movement.Considering the movements described for each card in the problem, the equations are built in the answer given at the beginning of the answer.
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in how many ways can a teacher distribute eight chocolate donuts and seven jelly donuts among three student helpers if each helper wants at least one donut of each kind?
Since probability each student helper must receive at least one of each type of doughnut, there are 120 ways to divide the 8 chocolate donuts and 7 jelly donuts among the three students.
If each student helper desires at least one doughnut of each flavor, there are 120 ways to divide 8 chocolate donuts and 7 jelly donuts among the three students who are helping. This is so because there are exactly as many ways to distribute donuts as there are different methods to distribute each type of doughnut. For instance, there are eight ways to divide the eight chocolate donuts among the three helpers—eight options for the first assistant, seven for the second, and six for the third—and seven ways to divide the eight jelly donuts (7 choices for the first helper, 6 for the second, and 5 for the third). The sum of these two figures (8 x 7 = 56) results in the number of combinations (56). (56). The total number of options must be multiplied by 2 to accommodate for the requirement that each helper receive at least one donut of each flavor: 56 x 2 = 120. If each student helper desires at least one doughnut of each flavor, there are 120 ways to divide 8 chocolate donuts and 7 jelly donuts among the three student volunteers.
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Evaluate: a 6.24 x 10
Which scale factors result in a expansion? -3, 0.25,9/7,-3/4
The scale factors of 9/7 and 0.25 would result in an expansion.
What is scale factor?Scale factor is a numerical value used to represent the proportional change between two similar objects. This value is often used to compare the size of objects in different measurements, such as inches to millimeters or feet to meters. Furthermore, the scale factor can be used to find the area, volume, or surface area of an object, as the measurements are proportional to the scale factor. This is especially useful when objects are enlarged or reduced, as it allows for the accurate calculation of the changed measurements.
Expansion occurs when the scale factor is greater than zero. In this case, the scale factors of 9/7 and 0.25 would result in an expansion. The scale factors of -3 and -3/4 would result in a contraction.
When an object is scaled, the size of the object changes in one or more directions. If the scale factor is greater than one, the object will expand. Conversely, if the scale factor is less than one, the object will contract. The scale factor can either be multiplied by the length of the object or by the area of the object to determine the change in size. For example, if the scale factor is two, the length of the object would double and the area of the object would quadruple.
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What part of the equation "g(x) = (x − 3)^2" says it's shifting to the right?
The part of the quadratic equation that says it's shifting to the right is -3.
What is a quadratic equation?
Any equation that can be written in the standard form where x is an unknown value, a, b, and c are known quantities, and a ≠ 0 is a quadratic equation.
f(x) = ax² bx + c = 0
The given equation g(x) = (x − 3)² is the equation of a parabola.
The general equation of a parabola is given by y = a(x – h)²+ k.
The graph of y=x² is shifted to h units to the right and k units up to produce the graph of y=a(x-h)²+k.
The above equation is similar to the equation given in the question.
Comparing,
a = 1
h = 3
So the given quadratic equation states that a parabola of the form g(x) = x² is shifted to the right by 3 units to give the resulting equation
g(x) = (x − 3)²
Therefore the part of the quadratic equation that says it's shifting to the right is -3.
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please help!!
each small square represents 1 square centimeter.
The solid formed by rotating the above rectangle around the horizontal axis shown is best described as a_________.
-cylinder with radius 6cm and height 3cm.
-cone with radius 3cm and height 6cm.
-rectangular prism with 3cm x 6cm base and height of 3cm.
-cylinder with radius 3cm and height 6cm.
The volume of this solid is_______.
108 cubic centimeters
54 cubic centimeters
18 cubic centimeters
Answer:
The solid formed by rotating the above rectangle around the horizontal axis shown is best described as a cylinder with radius 3cm and height 6cm. The volume of this solid is 108 cubic centimeters, which can be calculated as follows: V = πr2h, where r is the radius and h is the height. In this case, r = 3cm and h = 6cm, so the volume is π x (3 cm)2 x 6 cm = 108 cubic centimeters.
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you will work with a matrix whose entries are all prime numbers below 30. i) create this matrix using the function `matrix()` with five rows. save the matrix as `a`. ii) extract the second and third row out of `a`. iii) extract the entry in the 3rd row and first column of `a`. iv) generate the transpose of the matrix using the function `t()`. save this into `t.a`. what is the new dimension of this matrix?
The new dimension of the matrix t. a is 5 columns and 3 rows.
i) To create a matrix whose entries are all prime numbers below 30 using the matrix() function with five rows, you can use the following code:a <- matrix(c(2, 3, 5, 7, 11, 13, 17, 19, 23, 29), nrow = 5)ii) To extract the second and third row out of a, you can use the following code:a_rows_2_3 <- a[2:3, ]iii) To extract the entry in the 3rd row and first column of a, you can use the following code:a_entry <- a[3, 1]iv)To generate the transpose of the matrix a and save it into t.a, you can use the following code:t.a <- t(a)The new dimension of the matrix t.a is 5 columns and 3 rows.
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A polygon will be dilated on the coordinate grid to create a large polygon. The polygon i dilated uing the origin a the center of dilation
The rule for dilation around the origin with a scale factor of k is (x,y) -> (kx,ky).
Dilation is a transformation in geometry that changes the size of a figure while preserving its shape. A dilation centered at the origin involves scaling the figure down by a factor, causing it to become smaller.
In this case, the origin acts as the center of dilation, with the original figure being mapped to a smaller, similar figure.
To perform a dilation, each point of the original figure is multiplied by the same scale factor, resulting in a smaller, proportional figure.
The scale factor determines how much the figure will be reduced. It is important to note that dilations centered at the origin preserve the orientation of the figure, meaning it will look the same as the original, but just smaller.
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becca repeatedly tosses a fair coin until she gets a heads, while daniel repeatedly rolls a fair six-sided die until he gets a 3 or higher. calculate the probability that the number of die rolls needed is greater than the number of coin tosses needed.
We need to roll a die at least 3 times and a coin should be tossed at least 2 times.
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
Given this, Becca repeatedly tosses a fair coin until she gets a head.
The probability of getting a head P(H) is = 1/2.
The probability of getting a number 3 or higher is,
P(3) + P(4) + P(5) + P(6).
= 1/6 + 1/6 + 1/6 + 1/6.
= 4/6.
= 2/3.
So, to get a number 3 or higher we need at least 3 rolls, and to get a head we need at least 2 tosses.
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if two times a positive number is added to one third of its square, the result is 9,find the number
Answer:
Step-by-step explanation:
[tex]2x+\frac{1}{3} x^{2} =9[/tex]
Move all terms to l.h.s.
[tex]\frac{1}{3} x^{2} +2x-9=0[/tex]
Multiply everything by 3
[tex]x^{2} +6x-27=0[/tex]
Factorize
[tex](x+ 9)(x-3 )=0[/tex]
therefore
[tex]x+9=0[/tex] or [tex]x-3 =0[/tex]
x= -9 or x =3
Since x is a positive answer the answer must be
x=3
Of the total number of books in a library, 50% are non fiction,. 30% are historical fiction, and the rest are science fiction. There are 102 science fiction books in the library. How many books in the library are historical fiction?
Total number of historical fiction books are 153.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that of the total number of books in a library, 50% are non fiction, 30% are historical fiction, and the rest are science fiction. There are 102 science fiction books in the library.
Assume that the total number of books in the library are {x}. Then, we can write -
(50 + 30)% of {x} = {x} - 102
80% of {x} = {x} - 102
(80/100){x} = {x} - 102
8x/10 = x - 102
x - 4x/5 = 102
(5x - 4x)/5 = 102
x = 102 x 5
x = 510
Number of historical fiction books will be -
30% of 510
(30/100) x 510
3/10 x 510
3 x 51
153
Therefore, total number of historical fiction books are 153.
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explain why the function defined by M(t) = 2t + 1 has no maximum value on the interval [0,4)
The function defined by M(t) = 2t + 1 has no maximum value on the interval [0,4) as the derivative of m(t) is not equal to zero.
The maxima of the function can be calculated by the derivative of the function. The derivative is equated to 0 to calculate the critical points. If the second derivative is negative at this critical point then a maximum exists at this point.
The function is M(t) = 2t + 1 . Differentiate the function with respect to t. Now equate the derivative to 0. This will give the critical point. Since 2 is not equal to 0, the critical point does not exist on the curve of the function. Therefore, the function M(t) = 2t + 1does not have a maxima. M(t) = 2t + 1
d/dt M(t) = d/dt 2t + 1
= 2
d/dt m'(t) = 0
2 not equal to 0
The function does not have a critical point. Therefore, the maxima do not exist for the function.
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PLEASE I NEED THE ANSWERS FAST MATHEMATICS HIGHSCHOOL HOMEWORK!!!!! (I will choose the best answer)
let me know if answers are correct coz it has been a year that I learnt it and now I'm not doing those exercises so...
Step-by-step explanation:
c) 24 degree
d) 80 degree
e) 93 degree
f) 26 degree
g) ist es gegeben, dass Alpha das Zentrum ist? Wenn ja, ist der Winkel 150
h) Hier gilt das gleiche
if we flip a coin, we would expect the probability of it landing heads is the same as it landing tails (e.g., 0.50). however, we are more likely to achieve this outcome the more often we flip the coin. that is, over a large number of trials we are more likely to approximate our expected probability. this is referred to as:
if we flip a coin, we would expect the probability of its landing heads to be the same as its landing tails is referred to as the law of large numbers.
The law of large numbers is a probability and statistics, which defines that as a sample size grows, its mean gets closer to the average of the whole population.
This is due to the sample being more representative of the population as the sample becomes larger.
This is the theorem that describes the result of performing the same experiment a large number of times because the average of the results obtained from a large number of trials is close enough to the expected value.
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a box contains 3 marbles: 1 red, 1 green, and 1 blue. consider an experiment that consists of taking 1 marble from the box and then replacing it in the box and drawing a second marble from the box. describe the sample space
The sample space for this experiment is the set of all possible outcomes of drawing 2 marbles from the box, where order matters. There are 3 choices for the first marble, and 3 choices for the second marble, so the sample space is {RR, RG, RB, GR, GG, GB, BR, BG, BB}. There are 9 possible outcomes in this sample space.
Marble Draw Experiment Sample SpaceTo determine the sample space for this experiment, we first list all the possible outcomes for the first marble that we could draw. There are 3 marbles in the box (red, green, and blue), so there are 3 choices for the first marble. We can represent these choices as R, G, and B.
Next, we list all the possible outcomes for the second marble that we could draw. Since the box is being replaced with the first marble before the second draw, there are still 3 marbles in the box (red, green, and blue), so there are still 3 choices for the second marble. We can represent these choices as R, G, and B.
Finally, we list all possible combinations of the first and second marble, which forms the sample space. Since order matters, we list all the possible combinations of R, G, and B as pairs. In this case, there are 3 choices for the first marble and 3 choices for the second marble, which gives us 3 * 3 = 9 possible outcomes in the sample space: {RR, RG, RB, GR, GG, GB, BR, BG, BB}.
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4. The maximum value of the expression ax² + 10x + c
OPEN is 7. Find a pair of possible values of a and c.
The maximum value of the expression ax² + 10x + c is 7, which means that the parabola represented by this equation opens upwards and its vertex is at the highest point.
The vertex of a parabola represented by the equation ax² + 10x + c is given by (-b/2a, f(-b/2a)), where b is the coefficient of x, a is the coefficient of x² and f(x) is the function.
Therefore the vertex of this parabola is (-10/2a, 7 - c)
Since the vertex is the highest point, the y-coordinate of the vertex is the maximum value of the expression.
7 - c = 7
therefore c = 0
We also know that the x-coordinate of the vertex is -10/2a, this means that the x-coordinate of the vertex is -5/a
There are many possible combinations of a and c that work for this question, some possible combinations are:
a=1, c=0
a=2, c=0
a=-2, c=0
Another way to find a and c is by expanding the equation:
ax² + 10x + c = a(x²+ 10/a x) + c = a(x²+ 10/a x + (100-100a)/(4a²)) + c = a(x+5/a)² + c -25/a + 7
So, when a=1, c=0 and a=2, c=0 will give you the maximum value of 7, where it's a parabola that opens upwards and it's vertex is at the highest point.
How many solutions does this equation have? 5y + 4 = 10 + 5y
0, no solutions
that is the answer
PLEASE HELP MEEE!!! WILL GIVE BRAINLIEST!!
Answer:
C.
Step-by-step explanation:
deltamath.com
Plot the points A(3,-2), B(-7, -6), C(-2, 1)
on the coordinate axes below. State the
coordinates of point D such that A, B, C,
and D would form a parallelogram.
(Plotting point D is optional.)
Click on the graph to let a point Click a noi to
Answer:
D (-2, -9)
Step-by-step explanation:
Parallel slopes are equal. From C to A it is down 3 and right 5. To go from B to D go down 3 and right 5.
B go down 3 -6 - 3 = -9
B go right 5 -7 + 5 = -2
suppose you have just poured a cup of freshly brewed coffee with temperature in a room where the temperature is . newton's law of cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. therefore, the temperature of the coffee, , satisfies the differential equation where is the room temperature, and is some constant. suppose it is known that the coffee cools at a rate of per minute when its temperature is . a. what is the limiting value of the temperature of the coffee? b. what is the limiting value of the rate of cooling? c. find the constant in the differential equation. . d. use euler's method with step size minutes to estimate the temperature of the coffee after minutes. .
a) The limiting value of the temperature of the coffee is 25°C.
b) The limiting value of the rate of cooling is equals to 0.
c) The value of constant k in the
differential equation is -0.05.
d) The temperature of the coffee at time t = 10 is 66.33°C.
Newton's Law of Cooling: The rate at which an object's temperature changes is proportional to the difference in temperature between the object and its surroundings. For an object that has a temperature very close to that of its surroundings, the rate of heating or cooling becomes very small. We have the temperature of the coffee, T(t), satisfies the differential equation,
dT/dt= k(T − T (room)),
where T(room) = 25 is the room temperature, and k is some constant.
A) Limiting value of the temperature
= 25°C
B)limiting value of dT/dt = k[(limit temp) - (room temp)] = k(25 - 25)= 0
C) dT/dt = k(T - 25)
=> -2 = k (65 - 25)
=> -2 = 40k
=> k = -0.05
D) T' = -0.05 x (95-25) = - 3.5
h = 2, ∆T = -3.5x 2 = -7
T = 95- 7 = 88
Then T' = -0.05 x (88-25) = - 3.15
=> T = 88 - 2 x 3.15 = 81.7
=> 81.7 after 4 minutes
Then T' = -0.05x (81.7-25) = -2.835
T = 81.7 - 2x 2.835 = 76.03 after 6 mins
Then T' = -0.05 x (76.03-25) = -2.5515
T = 76.03 - 2 x 2.5515 = 70.92700 after 8 mins
Then T' = -0.05 x (70.927-25) = -2.29635
T = 70.927 - 2 x 2.29635
= 66.3343 after 10 minutes
so temperature = 66.33 after 10 mins by Euler's method.
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Complete question:
Suppose you have just poured a cup of freshly brewed coffee with a temperature of 90∘C in a room where the temperature is 25∘C. Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Therefore, the temperature of the coffee, T(t), satisfies the differential equation
dT/dt= k(T−Troom), where T(room) = 25 is the room temperature, and k is some constant.
Suppose it is known that the coffee cools at a rate of 2∘C per minute when its temperature is 65∘C.
A. What is the limiting value of the temperature of the coffee?
B.What is the limiting value of the rate of cooling?
C. Find the constant k in the differential equation.
D. Use Euler's method with step size h = 2 minutes to estimate the temperature of the coffee after 10 minutes_ Answer (in Celsius): T(10)
I DON'T GET THIS WHAT DID I DO WRONG FOR (4,1) (8,2)???!??!?!?!?!?!? PLS HELP!!P!P!P!P!!!?!?!?!?!
Answer:
Look at the y axis
Step-by-step explanation:
Each division is 2 units, so look and mark 8,2 carefully
If it confuses you, take 16, 4 as well because I dunno how flexible are your drawing tools
Hope this helps :)
Edit: Sorry but I have just realized what had happened, I took the time variable for the y axis. (Sorry, I am used to using the time variable on the y axis
What is the positive and negative of the function k(x)=20-x^2
Answer:
a function is said to be positive if all the values of y are above the x-axis and it is said to be negative if all the values of y are below the x-axis.
