Answer:
Below
Step-by-step explanation:
3/4 (1/6 x +16) = 3/7 (4 3/8 - 21) expand L side and compute R side
3/24 x + 12 = - 7.125 Subtract 12 from both sides of the equation
3/24 x = -19.125 Multiply both sides by 24/2
x = -153
THIS EQUATION DOES SHOW x = -153
PERHAPS you MEANT this :
3/4 (1/(6x) +16) = 3/7 (4 3/8 - 21) Expand L side and compute R side
3/(24x) + 12 = - 7.125 subtract 12 from both sides
3/(24x) = -19.125 re-arrange
3 / (-19.125) = 24 x divide both sides by 24
3/ (-19.125 * 24) = x = - 1/153
Don't know how to find a different answer......check the equation you posted......
three points x1, x2, x3 are selected at random on a line l. what is the probability that x2 lies between x1 and x3?
By applying permutation formula, it can be concluded that the probability that x₂ lies between x₁ and x₃ is 1/3
Permutation is rearranging a collection of objects in a different order from the original order.
P(n,r) = n! / (n-r)! where
n = number of objects
r = number of object selected
We have three points x₁, x₂, and x₃ are selected at random on line L.
Number of points = 3.
Now we can calculate the number of ways of arranging 3 points:
P(3,3) = 3! / (3 - 3)!
= 3!
= 6
There are two arrangements that x₂ lies between x₁ and x₃.
Thus, the probability that X₂ lies between X₁ and X₃ = 2 / 6 = 1/3
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need help asap cause its my next class in 10 minutes
Answer: 6) 33° , 7) x=3°
Step-by-step explanation:
The sum of the three angles of any triangle is equal to 180 degrees.
6) ∡SUT= 180-102 = 78 Linear Pair
∴ ∡UTS=180-(69+78)
=180-147
= 33°
7) ∡DBC=180-123=57 Linear Pair
57+25x+2+15x+1=180
60+40x=180
40x=180-60
=120
x=120/40=3°
∴ ∡D=77
∡C=46
(4x + 2)(x -1)(3x)(2x + 3) = 194 meters squared
what is the value of X
Answer:
x ∈ {−2.18723509003, 1.68723509003}
Step-by-step explanation:
You want the value of x that satisfies the equation (4x +2)(x -1)(3x)(2x +3) = 194.
QuarticThe fact that 194 is not divisible by 3 means the real solutions will not be integer values, likely irrational. A graphical solution and some iterations tell us the solutions are ...
x = −2.18723509003
or
x = 1.68723509003
__
Additional comment
The product has units of square meters, so we presume these dimensions come in pairs of factors. It appears that both the positive and negative values of x will give factors pairs that have a positive product.
Any rational solutions would be multiples of 1/24. These solutions are not rational.
5. Are the triangles similar?
If yes, which angles are congruent?
The triangles ΔABC and ΔDEF are congruent with each other by the SAS postulate. And ∠ABC = ∠DEF, ∠BCA = ∠EFD, ∠CAB = ∠FDE, and AB / DE = BC / EF = CA / FD.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
In triangles ΔABC and ΔDEF, then we have
AB = DE
BC = EF
∠ABC = ∠DEF = 92°
Then the triangles ΔABC and ΔDEF are congruent with each other. Then we have
∠ABC = ∠DEF
∠BCA = ∠EFD
∠CAB = ∠FDE
And the corresponding ratios are given as,
AB / DE = BC / EF = CA / FD
The triangles ΔABC and ΔDEF are congruent with each other by the SAS postulate.
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I need to find x and y, help pls
At what point does the line given by the following equation cross the y-axis?
y = -2x + 3
The given line y = -2x + 3 will cross the y-axis at (0, 3).
Coordinate plane:A coordinate plane is a two-dimensional plane that consists x-axis and a y-axis. These are perpendicular to each other and will be intersected at the point called the origin.
The coordinates of the point that lies on the y-axis are (0, y), Similarly, the coordinates of the point that lies on the x-axis are (0, x).
Here we have
The equation of the line is y = -2x + 3
To find the required point take x = 0
=> y = -2(0) + 3
=> y = 0 + 3
=> y = 3
Therefore,
The given line y = -2x + 3 will cross the y-axis at (0, 3).
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Find the length of YZ
The length of YZ in the triangle is 12.5 units
How to determine the length of YZFrom the question, we have the following parameters that can be used in our computation:
The triangle
On the triangle, we have the following equivalent ratio
YZ : 5 = 10 : 4
Express as fraction
So, we have
YZ/5 = 10/4
This gives
YZ = 5 * 10/4
Evaluate
YZ = 12.5
Hence, the length is 12.5 units
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5-6. For the next school year, the soccer team will need to come up with $600.
b. Jeff is a member of a new sports team. His dad owns a bakery. to help raise money for the team, jeff's dad agrees to provide the team with cookies to sell at the concession stand usually sells about 60 to 8- baked goods per games. Using your answer from part (a), determine a percent markup for the cookies the team plans to sell at next year's opening game. Justify your answer.
The markup is of amount $97.5
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
P = $500
i = 0.5%
n= 1
Using the formula
F = P + P x i x n
F= 500 + 500 x 0.005 x 1
F= 500+ 2.5
F= $502.5
So, the team need to raise
= 600- 502.5
= $97.4
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Unit 8 Right triangles and trigonometry Homework 3
The value of x for each triangle are:
x = 6√7x = 11.6x = 21.3x = 3√29; y = 6.46; z = 2.4Please note that I only answer the circled number and please refer to the attached picture for any additional annotations.
Note that each triangles are a right angled triangle. We use phytagoras theorem to find any unknown side of a triangle.
Triangle 1x² = 14² + y²
a² = y² + 4²
x² + a² = 18²
x² + a² = 18²
(14² + y²) + (y² + 4²) = 18²
14² + 2y² + 4² = 18²
196 + 2y² + 16 = 324
2y² = 112
y² = 56
x² = 14² + y²
x² = 196 + 26
x² = 252
x = 6√7
Triangle 2(x + 28)² = a² + b²
a² = 28² + 18²
b² = x² + 18²
(x + 28)² = a² + b²
(x + 28)² = (28² + 18²) + (x² + 18²)
x² + 56x + 784 = 1432 + x²
56x = 648
x = 11.6
Triangle 3a² = b² + (x - 12)²
b² = 16² - 12²
x² = 16² + a²
x² = 16² + a²
x² = 16² + (b² + (x - 12)²)
x² = 16² + [(16² - 12²) + (x - 12)²]
x² = 256 + 112 + (x - 12)²
x² = 368 + x² - 24x + 144
24x = 512
x = 21.3
Triangle 4x² = 15² + 6²
x² = 261
x = 3√29
(15 + z)² = x² + y²
y² = z² + 6²
(15 + z)² = x² + y²
(15 + z)² = 261 + (z² + 6²)
225 + 30z + z² = 261 + z² + 36
225 + 30z + z² = 297 + z²
30z = 72
z = 2.4
y² = z² + 6²
y² = 36 + 5.76
y² = 41.76
y = 6.46
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a. what's the probability that she chooses to teach both classes? b. what are the odds in favor of her choosing to teach both classes?
The odds of an event are calculated by taking the number of positive outcomes and dividing it by the number of negative outcomes.the odds in favor of her teaching both classes are 15:85 or 1:5.5.
a. The probability that she chooses to teach both classes is 15%.
b. The odds in favor of her choosing to teach both classes are 1:5.5.
a. The probability of an event is calculated by taking the number of positive outcomes and dividing it by the total number of outcomes. In this case, the professor has a 50% chance of teaching the first class and a 30% chance of teaching the second class. Therefore, the probability of her teaching both classes is 0.5 x 0.3 = 0.15 or 15%.
b. The odds of an event are calculated by taking the number of positive outcomes and dividing it by the number of negative outcomes. In this case, there is a 15% chance of her teaching both classes and an 85% chance of her not teaching both classes. Therefore, the odds in favor of her teaching both classes are 15:85 or 1:5.5.
The complete question is :
A professor is deciding whether to teach two classes. There is a 50% chance that she will teach the first class and a 30% chance that she will teach the second class.
a. What's the probability that she chooses to teach both classes?
b. What are the odds in favor of her choosing to teach both classes?
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Given the equation −15a = 75, solve for a. −60 −5 5 90
Answer:
-5
Step-by-step explanation:
−15a = 75
a = 75/-15
a = -5
A rectangle has a length of 12 inches and a width of 5 inches whose sides are
changing. The length is increasing by 9 in/sec and the width is growing at 2 in/sec.
What is the rate of change of the area?
The rate of change of the area of the rectangle as required in the task content is; 87 in²/sec.
By what rate if the area of the Rectangle changing?It follows from the task content; The length is increasing by 9 in/sec which represents 75% of the initial length and the width is growing at 2 in/sec which represents 40% of the initial width.
Since the area of a rectangle is; A = l × w
A (initial) = 60in².
Therefore, the new area of the rectangle after every second is;
Area (new) = 1.75l × 1.4w
Area (new) = 2.45 lw
This therefore translates to the fact that the area of the rectangle is increasing by a factor of 1.45 which is equivalent to 145% of initial Area.
Therefore, the area is increasing by 1.45 × 60 = 87in²/sec.
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suppose sean makes 10 tables a month, each of which he can sell for $200. given that the average cost of making each table is $150, should sean make more or fewer tables each month?
It's impossible to say Sean should base his decision on the marginal cost and marginal benefit of creating another table. The marginal cost of making a table is not the same as the average cost of making a table. As a result, there is insufficient information to determine what Sean should do.
The opportunity cost of an activity is the value of what must be sacrificed in order to engage in the activity (plus the cost). A cost that cannot be recovered at the time a decision must be made.
The science of decision-making is often used as a crude definition of economics. This stems from the fact that economics is frequently concerned with making the best decision in the most efficient manner. One way to quantify this is to consider total costs and total benefits.
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How to do Surface Area and Volume.?
Answer:
Surface Area : find the area of each face and add them together.
Volume : multiplying height, width, and depth.
Write an equation of the parabola in vertex form. Round any decimal to the nearest thousandth.
The required form of a parabola in vertex form is y = a(x - h)² + k.
What is a parabola?A parabola is a cross-section cut out of the cone and represented by an equation.
Here,
The standard form of a parabola in vertex form is:
y = a(x - h)² + k
where (h, k) is the vertex of the parabola and a determines the direction of opening (a > 0 for an upward-facing parabola and a < 0 for a downward-facing parabola). The coefficient also determines the shape and steepness of the parabola.
Thus, the required form of a parabola in vertex form is y = a(x - h)² + k.
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The area of a rhombus is 360 sq cm if one of its diagonal is 40 cm , find the other diagonal
According to the area of rhombus and length of one diagonal, the length of other diagonal is 10.5 cm.
The formula for the length of the diagonal is as follows -
Area = product of diagonal 1 and diagonal 2/2
Keep the values in formula to find the length of diagonal
360 = 40 × diagonal 2/2
Rewriting the equation with diagonal 2 on Left Hand Side of the equation
Diagonal 2 = (360 × 2)/40
Performing multiplication on Right Hand Side of the equation
Diagonal 2 = 420/40
Performing division on Right Hand Side of the equation
Diagonal 2 = 10.5 cm
Thus, the diagonal 2 is 10.5 cm.
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Given that 6048 = 2^5 • 3^3 • 7,
find the smallest possible integer value of n for 6048y to be a perfect cube number, giving your answer as the product of its prime factors.
Answer:
6048 should be multiplied by 98.
Step-by-step explanation:
6048 = 2⁵ * 3³ * 7
To make 6048 a perfect cube, 6048 should be multiplied by 2 * 7 * 7.
2* 7 *7 = 98
Check: 6048 * 98 = 592704
592704 = 2⁶ * 3³ * 7³
[tex]\sqrt[3]{592704}= 2 * 2 * 3 * 7[/tex]
= 84
A wire that is 40 cm long is bent into the shape of a rectangle whose width is x cm.
(i) Find an expression, in terms of x, for the area, A cm², of the rectangle. Find the x-intercepts on the graph of A against x.
(ii) Find the x-intercepts on the graph of A against x.
(iii) Find the maximum area that can be formed.
(iv) Show that this maximum area is only possible if the shape formed is a square.
How do I solve (iii) and (iv)? Thank you!
Answer:(iii) To find the maximum area of the rectangle, we can use the formula for the area of a rectangle, A = lw, where l is the length and w is the width. Since the wire is 40 cm long, we have l = 40 cm - x cm = 40 - x cm. The maximum area occurs when the length and width are equal, so we set l = w and solve for x:
40 - x = x
2x = 40
x = 20
So, the maximum area of the rectangle is A = lw = (40 - x)x = (40 - 20) * 20 = 20 * 20 = 400 cm².
(iv) To show that the maximum area is only possible if the shape formed is a square, we use the result from part (iii) that the maximum area occurs when the width x = 20 cm. If the width is less than 20 cm, the length will be greater than 40 - x, and the area will be smaller. If the width is greater than 20 cm, the length will be less than 40 - x, and the area will be smaller. So, the maximum area is only possible if x = 20 cm, which means the rectangle is a square.
Step-by-step explanation:
Determine the nature of the roots of ax² + bx + c = 0 if a > 0, b < 0 and c < 0
Answer: Roots are real and distinct
Step-by-step explanation:
a = +ve b = -ve c = -ve
determinant = +ve
if determinant is positive then roots are real and distinct
how would you compute the minimum number of semesters it would take a student to take all of the courses?
The math equation for this example would be 12 courses divided by 4 courses = 3 semesters.
The formula for computing the minimum number of semesters it would take a student to take all of the courses is calculated by dividing the total number of courses by the number of courses that can be taken in a semester. For example, if a student needs to take 12 courses, and the maximum number of courses that can be taken in a semester is 4, then the minimum number of semesters it would take the student to take all of the courses is 3 semesters. The math equation for this example would be 12 courses divided by 4 courses = 3 semesters. In order to determine the exact number of semesters it would take a student to take all of the courses, the total number of courses must be divided by the number of courses that can be taken in a semester.
The formula for calculating the minimum number of semesters it would take a student to take all of the courses is Total Number of Courses divided by Number of Courses that can be taken in a semester. For example, if a student needs to take 12 courses, and the maximum number of courses that can be taken in a semester is 4, then the minimum number of semesters it would take the student to take all of the courses is 3 semesters. The math equation for this example would be 12 courses divided by 4 courses = 3 semesters.
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What is −203 − (−136)?
I need help! :((
Answer:
-67
Step-by-step explanation:
- 203 - (-136)
The 2 minuses cancel out each other, turning it into a plus sign.
-203 + 136 = -67
Basic addition
Step-by-step explanation:
Because there is a double negative in between 203 and 136 that would turn into a positive
So
-203+136
Now because 203 is negative you would take 203 and subtract 136 to get 67
Because 136 is less then 203 it would still be negative
So
The answer is -67
what 2848x4848x495948+3858 / 384
if your still awake doing school stuff, take a break if you want you can talk with me in ch.at
The result of the expression 2848 × 4848 × 495948 + 3858 / 384 is equal to 684,114,389,002.05 approximately to 2 decimal place using PEDMAS
What is PEDMASP – Parentheses First: B – Brackets First
E – Exponents
D – Division
M – Multiplication
A – Addition
S – Subtraction
The expression 2848 × 4848 × 495948 + 3858 / 384 can be simplified as follows:
2848 × 4848 × 495948 + 3858 / 384
(2848 × 4848) × 495948 + (3858 / 384)
13807104 × 495948 + 10.0469
6811753718272 + 10.0469
684,114,388,992 + 10.0469
684,114,389,002.05
Therefore, the result from applying the right order of mathematics operations for the expression 2848 × 4848 × 495948 + 3858 / 384 is equal to 684,114,389,002.05 approximately to 2 decimal place using PEDMAS.
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The bar graph shows the number of games a soccer team played each month. Use the data to find each listed value.
Median =
Lower quartile =
Upper quartile =
Interquartile range =
By using the data from the bar graph, each of the statistical value are as follows;
Median = 6.
Lower quartile = 4.
Upper quartile = 7.5.
Interquartile range = 3.5
How to calculate the median number of game?From the information provided in the bar graph above, we can logically deduce the following data set:
Data set = {3, 5, 6, 7, 8}
Median = 6.
For Q₁ of the lower half of the data set, we have:
Lower quartile, Q₁ = {3, 5}
Lower quartile, Q₁ = (3 + 5)/2
Lower quartile, Q₁ = 8/4 = 4.
For Q₃ of the upper half of the data set, we have:
Upper quartile, Q₃ = {7, 8}
Upper quartile, Q₃ = (7 + 8)/2
Upper quartile, Q₃ = 15/2 = 7.5.
Mathematically, interquartile range (IQR) is the difference between lower quartile (Q₁) and upper quartile (Q₃):
IQR = Q₃ - Q₁
IQR = 7.5 - 4
IQR = 3.5
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from 6 positive and 8 negative numbers, 4 numbers are chosen at random (without replacement) and multiplied together. what is the probability that the product is a positive number?
Let's say event A is the selection of four positive numbers, event B the selection of four negative numbers, and event C the selection of two positive and two negative numbers.
Since four numbers are chosen without replacement, n(A) = 6 × 5 × 4 × 3 = 360 n(B) = 8 × 7 × 6 × 5 = 1680. In event C, four numbers are to be chosen without replacement such that two numbers are positive and two numbers are negative.
This can be done in following ways: + + – – OR + – + – OR + – – + OR – + – + OR – – + + OR – + + – ∴ n(C) = 6 × 5 × 8 × 7 + 6 × 8 × 5 × 7 + 6 × 8 × 7 × 5 + 8 × 6 × 7 × 5 + 6 × 5 × 8 × 7 + 8 × 6 × 5 × 7 = 6 × (8 × 7 × 6 × 5) =10080 Here, total number of numbers = 14 ∴ n(S) = 14 × 13 × 12 × 11 = 24024
Since A, B, C are mutually exclusive events,
Required probability = P(A) + P(B) + P(C)
= n(A)/n(S) + n(B)/n(S)+ n(C)/n(S)
= 360+1680+10080/24024
= 505/1001
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Cost and revenue functions. The operating cost of
a company can be approximately modelled as
C(x) = 17- 8x - 2x², where x is the time in years.
Given that its revenue function is R(x) = 5 - 3x,
find the number of months during which the
company is not making a profit.
The number of months for which the company made no profit is 18 months.
What is profit?Generally speaking, a product's profit is defined as the sum received from sales, which should exceed the product's cost price. It is the gain from any type of commercial activity. In other words, if a product's selling price (SP) is higher than its cost price (CP), there has been a gain or profit. It explains the monetary gain realised if the revenue from the company activity is greater than the costs, such as taxes and expenses, involved in maintaining the business activity.
The cost function is given as: C(x) = 17- 8x - 2x²
The revenue function is given as: R(x) = 5 - 3x
Profit = Revenue - Cost
For no profit the equation becomes:
5 - 3x - 17 + 8x + 2x² = 0
2x² + 5x - 12 = 0
2x² + 8x - 3x - 12 = 0
2x(x + 4) - 3(x + 4) = 0
2x - 3 = 0 and x + 4 = 0
x = 3/2 and x = -4
Since, month cannot be a negative quantity we have x = 3/2.
That is 3/2 (12) = 18 months.
The number of months for which the company made no profit is 18 months.
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2x+y=18 and y=4x+6 using substitioiuntion
so your problem is 2x+y=18 and y=4x+6
solution
solve for the first variable in one of the equations then substitute the result into the other equation
point form:
(2,14)
equation form
x=2, y=14
b. Measure the length of the side DF.
c. Measure the height of the triangle, XF.
d. Describe in words the locus of the point that is 2cm from E and draw this onto your diagram.
e. Use compasses to bisect the angle D. You must leave your construction arcs in.
Answer:
C and D
Step-by-step explanation:
Consider the function g(x)=^3√x-1
What is the range of this function's inverse?
The range of the inverse of g(x) = √(x³ - 1) is [0, ∞).
How to find the range of the function's inverse?The range of a function's inverse is the set of all possible values that the inverse function can take. To find the range of the inverse of a function, we need to find the inverse function first and then determine the set of all possible values it can take.
For the function g(x) = √(x³ - 1), we first need to find its inverse. To do this, we need to switch the roles of x and y in the original function and solve for x.
g(x) = y
y = √(x³ - 1)
x³ - 1 = y²
x³ = y² + 1
x = ∛(y² + 1)
since x = g⁻¹(y) = ∛(y² + 1)
Thus, g⁻¹(x) = ∛(x² + 1) (Replace y with x)
This is the inverse of g(x). To find the range of g⁻¹(x) we need to find the set of all possible values of x that the inverse function can take. Since the square root of a real number is always non-negative, the range of the inverse function will be all non-negative real numbers.
So, the range of the inverse of g(x) = √(x³ - 1) is [0, ∞).
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Heather's school is selling tickets to the annual talent show. One the first day of ticket sales the school sold 3 senior citizen tickets and 4 child tickets for
a total of $46. The school took in $48 on the second day by selling 4 senior citizen tickets and 2 child tickets. What is the price of each ticket type?
The price of a child ticket is $4 and the price of a senior citizen ticket is $10
Let's call the price of a senior citizen ticket "x" and the price of a child ticket "y".
On the first day, the school sold 3 senior citizen tickets and 4 child tickets for a total of $46, so we can write the equation:
3x + 4y =46
On the second day, the school took in $48 by selling 4 senior citizen tickets and 2 child tickets, so we can write another equation:
4x + 2y = 48
Now that we have two equations, we can use substitution or elimination to find the value of x and y.
For substitution, we can solve one equation for one variable and then substitute that expression into the other equation. For example, let's solve the first equation for x:
x = (46 - 4y)/3
Then, we can substitute this expression for x into the second equation:
4((46 - 4y)/3) + 2y = 48
Expanding the left side of the equation:
(184 - 16y)/3 + 2y = 48
Multiplying both sides by 3:
184 - 16y + 6y = 144
Combining like terms on the left side:
184 - 10y = 144
Subtracting 184 from both sides:
-10y = -40
Dividing both sides by -10:
y = 4
So the price of a child ticket is $4. To find the price of a senior citizen ticket, we can substitute this value back into the equation we solved for x:
x = (46 - 4y)/3 = (46 - 4 * 4)/3 = (46 - 16)/3 = 30/3 = $10
So the price of a senior citizen ticket is $10.
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how many grades do u have to fail to get held back in 7th grade?
Answer:about 3
Step-by-step explanation: