The solution of the linear equation 4 - (5 / 2)(x / 10) = 1 will be 12.
The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The equation is given below.
4 - (5 / 2)(x / 10) = 1
Simplify the equation, then we have
4 - (5 / 2)(x / 10) = 1
4 - x / 4 = 1
x / 4 = 4 - 1
x / 4 = 3
x = 3(4)
x = 12
The solution of the linear equation 4 - (5 / 2)(x / 10) = 1 will be 12.
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An Isosceles triangle and a square have the same perimeter. Find the side lengths of the triangle.
triangle base: 3x
triangle height: 2x+1
square length: 4
Answer: 5, 5, 6
How you get this answer?
If the perimeters are the same. Then the dimension of the triangle will be 5, 5, and 6.
What is the perimeter of the geometry?The peripheral of a form is defined in mathematics as the entire length of its boundaries. The surrounding of a form is calculated by summing the lengths of all the vertices and edges that surround it. It is measured in linear quantities like cm, meters, inches, and feet.
Let 'x' be the isosceles sides and the 'y' be the third side. Then the equation is given as,
x + x + y = 4 × 4
2x + y = 16
2x + y = 2(5) + 6
Then the dimension of the triangle will be 5, 5, and 6.
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8(2x + 3y)
In distributive property
Answer:
16x+24y
Step-by-step explanation:
8(2x+3y)
8*2x+8*3y
16x+24y
Need help please!!!!
Pls help. Thank you.
The following is a basic formula to find the scale factor of a dilated figure is: : Scale factor = Dimension of the new shape ÷ Dimension of the original shape.
What's the scale factor of the dilation?Sizing Factor (Dilation) The image's size will depend on the scale factor, which is used to dilate a mathematical entity (compared to the original object). An expansion happens when the scaling factor's absolute value exceeds one.
What is Dilation Geometry?Dilation is the process of increasing an object's size without altering its shape. Depending on the scale factor, the object's size may increase or shrink. A square of side 5 units can be widened to a square of side 15 units using dilation math, but the square's shape doesn't change.
In geometry, dilation math is used to enlarge and reduce two- or three-dimensional figures.
The Scale FactorA scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is the ratio of the original figure's and dilated figure's sizes.
You can use r or k to represent the scaling factor.
If the scale factor is more than 1 (k > 1), the image is expanded.
If the scale factor is less than 1 (0 k 1), the image is condensed.
If the scale factor is 1 (k = 1), the image doesn't change.
It should be noted that the scale factor's magnitude is taken into account and that it cannot be 0.
Scale Factor FormulaAn object's size can change depending on the scale factor, either growing or shrinking. The following is a basic formula to determine a dilated figure's scale factor:
Scale factor = Dimension of the new shape ÷ Dimension of the original shape.Another approach to express this formula that aids in determining the new shape's dimensions is as follows:
Dimensions of the original shape × Scale factor = Dimension of the new shapeTo know more about Scale factor of the dilation refer to:
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3.1 (3 points) Given the following infix expression, draw an expression tree and re-write this expression in prefix and postfix forms. Infix expression: (A − B) + C * (D / E)
The infix expression given is (A-B)+C*(D/E)
Steps to draw the expression tree
The order of operations should be considered while drawing the expression tree.
The following steps are followed:
First, draw a node for the operator with the highest precedence,
which is multiplication (symbol *).Second,
draw nodes for the other operators, in the order of their precedence, which is division (symbol /), and addition (symbol +).
Third, draw the leaf nodes for the operands in the order that they appear in the infix expression.
A B CD E- /* + Steps to re-write in prefix form
The prefix form of the infix expression is obtained by traversing the expression tree in the pre-order fashion.
That is, the operator is written before its operands.
The prefix form of the infix expression (A-B)+C*(D/E) is obtained as follows:+ - A B * C / D E
Steps to re-write in postfix form
The postfix form of the infix expression is obtained by traversing the expression tree in the post-order fashion.
That is, the operator is written after its operands.
The postfix form of the infix expression (A-B)+C*(D/E) is obtained as follows: A B - C D E / * +
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What is the annual discount rate if a cashflow of £52 million in 5 years' time is currently valued at £25 million?
a. 86.37\% b. 15.77% c. 21.60% d. 115.77% e. 108.00%
The correct answer is option b. 15.77%. The annual discount rate, also known as the discount rate or the rate of return, can be calculated using the present value formula.
Given that a cash flow of £52 million in 5 years' time is currently valued at £25 million, we can use this information to solve for the discount rate.
The present value formula is given by PV = CF / (1 + r)^n, where PV is the present value, CF is the cash flow, r is the discount rate, and n is the number of years.
In this case, we have PV = £25 million, CF = £52 million, and n = 5. Substituting these values into the formula, we can solve for r:
£25 million = £52 million / (1 + r)^5.
Dividing both sides by £52 million and taking the fifth root, we have:
(1 + r)^5 = 25/52.
Taking the fifth root of both sides, we get:
1 + r = (25/52)^(1/5).
Subtracting 1 from both sides, we obtain:
r = (25/52)^(1/5) - 1.
Calculating this value, we find that r is approximately 0.1577, or 15.77%. Therefore, the annual discount rate is approximately 15.77%, corresponding to option b.
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In the figure below lines l and m are parallel lines cut by transversal line p. What is the value of x
a student takes an examination consisting of 20 true-false questions. the student knows the answer to n of the questions, which are answered correctly, and guesses the answers to the rest. the conditional probability that the student knows the answer to a question, given that the student answered it correctly, is 0.824. calculate n
The student knows the answer to approximately 5 questions out of the 20.
Let's denote the event that the student knows the answer to a question as K and the event that the student answers the question correctly as C. We are given the following information:
P(K) = n/20 (probability that the student knows the answer)
P(C|K) = 1 (probability of answering correctly given that the student knows the answer)
P(K|C) = 0.824 (conditional probability that the student knows the answer given that the student answered correctly)
We can use Bayes' theorem to find the value of n:
P(K|C) = P(C|K) * P(K) / P(C)
P(C) = P(C|K) * P(K) + P(C|not K) * P(not K)
= 1 * (n/20) + (1/2) * ((20-n)/20)
= n/20 + (20-n)/40
= (2n + 20 - n) / 40
= (n + 20) / 40
Now, substituting the values into Bayes' theorem:
0.824 = 1 * (n/20) / ((n + 20) / 40)
0.824 = (2n / 20) * (40 / (n + 20))
0.824 = 4n / (n + 20)
Cross-multiplying:
0.824 * (n + 20) = 4n
0.824n + 16.48 = 4n
3.176n = 16.48
n = 16.48 / 3.176
n ≈ 5.18
Therefore, the student knows the answer to approximately 5 questions out of the 20.
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6. Solve for x!! please help!
x/2 = -7
=> x = -7 × 2
=> x = -14
Answer:
x=-14
Step-by-step explanation:
\(\frac{x}{2} =-7\\\\x=-14\\\)
2) Solve for A
-0.2a – 4.4 = 6.2
Write your answer as a decimal.
a = ?
Answer:
a=-53
Step-by-step explanation:
-0.2a-4.4=6.2
+4.4 on both sides
-0.2a=10.6
divide -0.2 on both sides
a=-53
Find the next number in the pattern.
4, 6, 11, 19, 30, ______
a.41
b.42
c.43
d.44
The next number in the pattern will be 44. Then the correct option is D.
What is the sequence?A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.
The pattern is given below.
4, 6, 11, 19, 30,
The pattern is given as,
4 + 2 + 3 x 0 = 6
6 + 2 + 3 x 1 = 11
11 + 2 + 3 x 2 = 19
19 + 2 + 3 x 3 = 30
30 + 2 + 3 x 4 = 44
The next number in the pattern will be 44. Then the correct option is D.
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Mary wants to invest an amount every three months so that she will have $12,000 in three years to buy a new car. The account pays 2% compounded quarterly. How much should she deposit each quarter to have $12,000 after 12 deposits
Answer: $972.7972 or $973
To find the amount of money Mary should deposit each quarter, we will use the following equation:
\(A=P\frac{((1+i)^n-1)}{i}\)Where:
P = deposit made n times
i = is the interest rate r compounded m times per year
Since Mary wants to invest every three months, that would be 4 times per year and have the interest rate of 2% = 0.02,
\(i=\frac{0.02}{4}=0.005\)The amount she wants to save is A = $12000, and she will invest 12 times, n = 12.
Substituting these to the formula and we will have:
\(12000=P\frac{(1+0.005)^{12}-1)}{0.005}\)\(12000=P\frac{((1.005)^{12}-1)}{0.005}\)\(P=\frac{12000(0.005)}{((1.005)^{12}-1)}\)\(P=\$972.7972\)This means that Mary has to pay approximately $972.7972 or $973 each quarter.
Which one of the following fraction is smaller
¼ or ¾
Answer:
1/4
Step-by-step explanation:
1/4 because whenever 2 fractions have the same denominator if the numerator is lower then the other numerator it is less but if it is more than it is more
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What is the value of n? enter your answer in the box.
The value of "n" is 6.
"n" is related to a circle with intersecting chords labeled 5, n+4, 7, and n+8 [1]. To find the value of "n", we can use the property that states that if two chords intersect inside a circle, the products of their segments are equal. Using this property, we can set up the following equation:
7(n+4) = 5(n+8)
Expanding the brackets, we get:
7n + 28 = 5n + 40
Simplifying, we get:
2n = 12
n=6
A circle is a two-dimensional geometric shape that is defined as a set of all points in a plane that are at a fixed distance (called the radius) from a given point (called the center). It is a closed shape, meaning that it has no beginning or end, and its boundary is a continuous curve.
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Henry has a bag of marbles. The bag contains 4 red marbles, 2 blue
marbles, 3 green marbles, and 1 yellow marbles. She will randomly select two marbles from
the bag one at a time without replacement What is the probability that Henry will select a
blue marble first and then a yellow marble?
an account with an apr of 4% and quarterly compounding increases in value every three months by
a.1%
b.1/4%
c.4%
The account increases in value by 1% every quarter, which is equivalent to 1/4% every month.
Savings interest is calculated on a daily basis and deposited into the account on the first day of the next quarter. The interest rate will depend on the balance in the account. Now it's between 3% and 3.5%.
To find the increase in value for an account with an APR of 4% and quarterly compounding, we'll first need to convert the APR to a quarterly interest rate.
1. Divide the APR by the number of compounding periods in a year: 4% / 4 = 1%.
2. The account increases in value by 1% every quarter.
Your answer: a. 1%
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Name the property of real numbers illustrated by the equation. -4(x + 4) = -4x – 16 O A. Associative Property of Addition B. Commutative Property of Addition OC. Associative Property of Multiplication O D. Distributive Property
we are given the following relationship:
\(-4(x+4)=-4x-16\)Let's remember that the distributive property for addition is the following:
\(a(b+c)=ab+ac\)Therefore, the property that was used was the distributive property of multiplication.
What mode of observation is 5'7 8?
The mode for a particular set of observations is 5 since it occurs the majority of the time.
What is mode?The mode formula is described in statistics as the formula for calculating the mode of a given collection of data. The value that occurs most frequently in a particular set is referred to as the mode, and the mode differs across grouped and ungrouped data sets. The mode may be calculated quite easily. Put all of the numbers in a given set in order, either lowest to highest or highest to lowest, and then count how many times each number appears in the set. The mode is the one that appears the most.
Here,
given set of observation:
5, 7, 8, 5, 7, 6, 9, 5, 10, 6
Mode is the number which occurs the highest time.
So here 5 occurs the highest times(3 times).
So,5 is the mode.
The mode for given set of observation is 5 as it occurs most time.
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Major went to the Appalachian Fair. The entrance fee was $10, and he purchased 25 tickets. Write an equation to find the price of each ticket if he spent a total of $47.50. You do NOT have to solve it.
Answer:
25x+10=47.50
Step-by-step explanation:
x represents the ticket amount and if he buys 25 tickets then that will be 25 times x. Plus the $10 entrance fee.
How much work (in Joules) must be done to stop a 1200 kg car moving at 99 km/h in a straight path? 453750 0 −453750 Not enough information is provided.
To stop a 1200 kg car moving at 99 km/h in a straight path,
the work that must be done in Joules is 453750.
Step-by-step Given,
Mass of car, m = 1200 kg
Initial velocity, u = 99 km/h = 27.5 m/s
Final velocity, v = 0 m/s (as the car is brought to rest)
Initial kinetic energy, K.E1 = 1/2 m u²
Final kinetic energy, K.E2 = 1/2 m v²
Work done to bring the car to rest,
W = K.E1 - K.E2W
= 1/2 m u² - 1/2 m v²W
= 1/2 × 1200 × (27.5)² - 1/2 × 1200 × (0)²W
= 1/2 × 1200 × (27.5)²W
= 453750 J
Therefore, the work that must be done in Joules to stop the car is 453750.
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If (-3,5) and (3,-5) are two points that lie on function f, then is f even, odd, or neither?
f(-3) ≠ f(3) and f(-3) ≠ -f(3), which means that the function f does not satisfy the properties required for it to be even or odd.
To determine whether the function f is even, odd, or neither, we need to evaluate the symmetry of the function with respect to the y-axis and the origin.
For a function to be even, it must satisfy the property f(x) = f(-x) for all values of x in the function's domain. This means that if we substitute -x for x in the function, we should obtain the same output as when we evaluate the function at x.
For a function to be odd, it must satisfy the property f(x) = -f(-x) for all values of x in the function's domain. This means that if we substitute -x for x in the function, we should obtain the negative of the output we obtain when we evaluate the function at x.
Let's evaluate the function f using the given points (-3,5) and (3,-5):
For the point (-3,5):
f(-3) = 5
For the point (3,-5):
f(3) = -5
We can see that f(-3) ≠ f(3) and f(-3) ≠ -f(3), which means that the function f does not satisfy the properties required for it to be even or odd.
We can conclude that the function f is neither even nor odd.
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a company had 80 employees whose salaries are summarized in the frequency distribution below. find the standard deviation.
The standard deviation of the salaries for the company's 80 employees is calculated to be X, where X represents the numerical value of the standard deviation.
The standard deviation measures the dispersion or variability of a set of data points. In order to calculate the standard deviation, we need to first find the mean (average) of the salaries. Then, for each salary, we calculate the difference between the salary and the mean, square that difference, and sum up all the squared differences. Next, we divide the sum by the total number of salaries (80 in this case) minus 1 to obtain the variance. Finally, the standard deviation is obtained by taking the square root of the variance. This accounts for the fact that the squared differences are in squared units, while the standard deviation should be in the original units (currency in this case).
By following this process, we can find the standard deviation of the salaries for the 80 employees in the company. This value represents the measure of variability or spread in the salary distribution, providing insights into how salaries deviate from the mean.
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Elisa withdrew $26 at a time from her bank account and withdrew a total of $208. Frances
withdrew $49 at a time from his bank account and withdrew a total of $245. Who made the
greater number of withdrawals?
And how many withdrawals did each person make?
(Please help me!)
Answer:Elisa made the greater number of withdrawals
Step-by-step explanation:
208 divided by 26 is 8
245 divided by 49 is 5
Answer:
5
Step-by-step explanation:
divid lol
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What is the biconditional statement of the following conditional statement?
"If the product of the slopes of two lines is −1, then the lines are perpendicular."
If the lines are perpendicular, then the product of the slopes of two lines is −1.
The product of the slopes of two lines is −1 if and only if the lines are perpendicular.
If the product of the slopes of two lines is not −1, then the lines are not perpendicular.
If the two lines are not perpendicular, then the product of the slopes of two lines is not −1.
The biconditional statement of the given conditional statement is “the product of the slopes of two lines is −1 if and only if the lines are perpendicular”, the correct option is A.
We are given that;
The statements
Now,
The given conditional statement is “if the product of the slopes of two lines is −1, then the lines are perpendicular”. The hypothesis is “the product of the slopes of two lines is −1” and the conclusion is “the lines are perpendicular”. The converse of this statement is “if the lines are perpendicular, then the product of the slopes of two lines is −1”. The hypothesis is “the lines are perpendicular” and the conclusion is “the product of the slopes of two lines is −1”.
To form a biconditional statement, we need to combine the conditional statement and its converse with the phrase “if and only if”. This gives us “the product of the slopes of two lines is −1 if and only if the lines are perpendicular”.
Therefore, by the statement the answer will be “the product of the slopes of two lines is −1 if and only if the lines are perpendicular”.
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The least common denominator is the least common multiple of the _______ of the factions fill in the blank
Write a proportion comparing the rise to the run for each of the similar slope triangles shown at the right. Then find the numeric value.
Answer:
AB/CΔ=BC/ΔE {similar triangles}
\(2/4=2/4\)
\(1/2=1/2\\\)
so numeric value= 1/2
---------------------------------
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CAN ANYONE HELP ME WITH THIS QUESTION
Answer:
4+4+4+12+5+5=34
Step-by-step explanation:
aygwgsAnswer:
in my opinion which maybe 34cm
Step-by-step explanation:
4 + 4 + 4 + 5 + 5 + 12 cm equals to 34 CM
fifa is expected to make how much revenue from the world cup?
Answer:
Step-by-step explanation:
$4.7 billion ..
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The roasting guide for a turkey suggests cooking for a total of 100
minutes plus an additional 8 minutes per pound.
question: How much time would it take to roast a 27
lb turkey?
Answer minutes
Answer:
i think its 316 ?
Step-by-step explanation:
27 x 8 = 216, then add that to the 100 minutes and you get 316 minutes
How many terms are in the arithmetic sequence 7, 0, –7, …,–175?
Answer:
27 terms
Step-by-step explanation:
a1 = 7
nth term is -175
common difference d= 0-7 = -7 or -7 - 0 = -7
nth term = first term + ( n-1) * common difference
-175 = 7 + ( n - 1 ) * (- 7)
-175 = 7 - 7n + 7
-175 = 14 - 7n
-175-14 = -7n
-189 = - 7n
n= -189 /-7
n=27