Final answer:
Option c, 15/16, is the correct answer because it cannot be simplified to 7/8, making it not equivalent to 7/8, while the other options are equivalent after simplification.
Explanation:
The question asks us to identify which fraction is not equivalent to 7/8. To determine this, we need to compare each option with 7/8:
Option a: 21/24 can be simplified by dividing the numerator and the denominator by 3, which gives us 7/8, so this option is equivalent.Option b: 35/40 can be simplified by dividing the numerator and the denominator by 5, which gives us 7/8, so this option is equivalent as well.Option c: 15/16 cannot be simplified to 7/8 because when we divide both by their greatest common divisor, we do not get 7/8. Therefore, this fraction is not equivalent to 7/8.Option d: 28/32 can be simplified by dividing the numerator and the denominator by 4, which gives us 7/8, so this option is equivalent.Hence, the correct answer is option c, which is not equivalent to 7/8.
is the simplified form of 2√3 - 2√3 rational?
The simplified form of 2√3 - 2√3 is 0, which is a rational number.
Explanation:In order to determine if the simplified form of 2√3 - 2√3 is rational, we first need to simplify the expression. Since we have the same terms being subtracted from each other, the expression will simplify to 0. Therefore, the simplified form is 0, and 0 is considered to be a rational number since it can be written as 0/1.
Which of the following is the solution to the equation 5/6 x = -1/6 ?
Multiply (2 – 7i)(9 + 5i)
To multiply the complex numbers (2 - 7i) and (9 + 5i), we use the distributive property to get the result of 53 - 53i.
To multiply the complex numbers (2 - 7i) and (9 + 5i), we use the distributive property, also known as the FOIL method in this context (First, Outer, Inner, Last). Applying this method, we get:
First: 2 × 9 = 18
Outer: 2 × 5i = 10i
Inner: (-7i) × 9 = -63i
Last: (-7i) ×5i = -35i²
Recall that i² = -1, so -35i² = -35(-1) = 35. Combine like terms (the real numbers with real numbers, and the imaginary numbers with imaginary numbers):
18 + 35 (real parts) + 10i - 63i (imaginary parts) equals to 53 - 53i.
Thus, the product of (2 - 7i) and (9 + 5i) is 53 - 53i.
If the polar coordinates of the point ( x , y ) are ( r , θ ), determine the polar coordinates for the following points. (Use any variable or symbol stated above as necessary.)
a) -x,y
b)-2x,-2y
c)3x,-3y
I don't understand what they are asking for because i tried the r=sqrt(x^2+y^2) and that theta = tan^-1(y/x) and it was wrong. ...?
⇒Polar Coordinate of point (x,y)=(r,Ф)
The Point (x,y) lies in First Quadrant.
r=Distance from Origin to point (x,y)
[tex]r=\sqrt{x^2+y^2}\\\\ \theta=\tan^{-1}\frac{y}{x}\\\\ \theta=A[/tex]
⇒The Point (-x,y) lies in Second Quadrant.
[tex]r=\sqrt{x^2+y^2}\\\\ \theta=\tan^{-1}\frac{y}{-x}\\\\ \theta=\pi-A[/tex]
Polar Coordinate of point (-x,y)=(r,π-Ф)
⇒The Point (-2x,-2y) lies in Third Quadrant.
[tex]r=\sqrt{(-2x)^2+(-2y)^2}\\\\r=\sqrt{4x^2+4y^2}\\\\r=2\times \sqrt{x^2+y^2}\\\\ \theta=\tan^{-1}\frac{-2y}{-2x}\\\\=\tan^{-1}\frac{y}{x}\\\\ \theta=\pi+A[/tex]
Polar Coordinate of point (-2x,-2y)=(2r,π+Ф)
⇒The Point (3x,-3y) lies in Fourth Quadrant.
[tex]r=\sqrt{(3x)^2+(-3y)^2}\\\\r=\sqrt{9x^2+9y^2}\\\\r=3\times \sqrt{x^2+y^2}\\\\ \theta=\tan^{-1}\frac{-3y}{3x}\\\\=\tan^{-1}\frac{-y}{x}\\\\ \theta=-A[/tex]
Polar Coordinate of point (3x,-3y)=(3r,-Ф)
Celine has 2 coupons. One is for $5 off a purchase and the other is for 20% off a purchase. At what purchase price will the coupons have the same value?
To find the purchase price at which the $5 off coupon and the 20% off coupon have the same value, solve the equation x - $5 = 0.8x by isolating x.
Explanation:To find the purchase price at which the $5 off coupon and the 20% off coupon have the same value, we need to set up an equation and solve for the purchase price.
Let's assume the purchase price is x dollars. The $5 off coupon would give us a discount of $5, so the price after the discount would be x - $5. The 20% off coupon would give us a discount of 20% of x, so the price after the discount would be 0.8x.
We can set up the equation:
x - $5 = 0.8x
Now we can solve for x:
x - 0.8x = $5
0.2x = $5
x = $25
Therefore, the coupons will have the same value at a purchase price of $25.
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a ball player gets 11 hits in 40 times at bat. how many hits would you predict in 1000 times at bat
What's 2015473 in expanded form
The expanded form of the number 2015473 is 2,000,000 + 10,000 + 5,000 + 400 + 70 + 3.
What is an expanded form of the number?The division of numbers into groups according to place value, such as ones, tens, hundreds, thousands, ten thousand, and so forth, results in the expanded form of the number.
The expanded form of the number is the one that is represented by the sum of each digit times its place value.
The given number is 2015473. The given number in the expanded form will be written as,
2015473 = 2,000,000 + 10,000 + 5,000 + 400 + 70 + 3.
Therefore, the expanded form of the number 2015473 is 2,000,000 + 10,000 + 5,000 + 400 + 70 + 3.
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Mustafa contributes 11% of his $67,200 annual salary to his 401(k) plan. What is his pretax income?
You have to subtract the 11% that you are putting into your 401k to find out how much you are earning and that you're not putting into retirement.
67,200*0.11 = 7,392
67,200 - 7,392 = 59,808
Mustafa's pretax income after contributing 11% to his 401(k) plan is 59808 dollars.
What is the percentage?A percentage is a value per hundredth.
Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given Mustafa contributes 11% of his $67,200 annual salary to his 401(k) plan.
∴ 11% of $67200 is = (11/100)×67200 dollars.
= 7392 dollars.
So, his pretax income is (67200 - 7392) dollars.
= 59808 dollars.
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1. ABCD is a rectangle. BD is a straight line that cuts the rectangle into equal halves. The ratio of the area of P to the area of Q is 2 : 5, and the ratio of the area R to the area of S is 4 : 3. The area of S is 9 square centimeters.
a) Find the ratio of the area of R to the area of the rectangle.
Find the area of the rectangle
What is 15/20 simplified?
if f(x)=x^2+3x+5, what is f(3+h)
A.(x^2+3x+5)(3+h)
B.h^2+9h+23
C.(3+h)^2+8+h
D.h^2+h+23
Answer:
The value of the f (3 +h) is h² + 9h + 23 .
Option (B) is correct.
Step-by-step explanation:
As the function given in the question be
f(x)= x² + 3x + 5
Now
f(3 +h )= (3 +h )²+3(3 + h)+5
Now by using the formula
(a + b)² = a² + b² + 2ab
f(3 +h )= 3² + h² + 2 × 3 × h +3 × 3 + 3 ×h +5
f(3 +h )= 9 + h² + 6h + 9 + 3h +5
f(3 +h )= h² + 9 + 9 + 5 + 3h + 6h
f(3 +h )= h² + 9h + 23
Therefore the value of the f (3 +h) is h² + 9h + 23 .
Option (B) is correct.
Write an equation that models the sequence 400, 200, 100, 50, ...
A) y = 400(2x)
B) y = 50 (2x)
C) y = 1/2x + 400
D)y = 400(1/2)X-1
Answer:
he answer is D.)y = 400(1/2)X-1
Step-by-step explanation:
Option D is correct, y=400(1/2)ˣ⁻¹ is the equation that models the sequence 400, 200, 100, 50, ..
What is Sequence?Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
The sequence 400, 200, 100, 50, ... is a geometric sequence with a common ratio of 1/2, since each term is half the previous term.
To write an equation that models this sequence, we can use the general formula for a geometric sequence:
aₙ = a.rⁿ⁻¹
where aₙ is the nth term of the sequence, a is the first term of the sequence, r is the common ratio of the sequence and n is the number of the term we want to find
Since the first term is 400 and the common ratio is 1/2, we have:
a= 400
r = 1/2
aₙ=400(1/2)ˣ⁻¹
y=400(1/2)ˣ⁻¹
Hence, option D is correct, y=400(1/2)ˣ⁻¹ is the equation that models the sequence 400, 200, 100, 50, ..
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F is the midpoint of EG. Find the length of EG , given that the length of FG is 10.9
A. 20.9
B. 21.8
C. 22.8
D. 23
Solve for x.
5x - 1 = 26
A)x=27/5
B)x=5
C)-5
There will be a circular patio with a diameter of 7 metres. greg is going to put a tiled edge around the patio. what is the circumference of the patio? m circumference of a circle = 2πr use π = 3.14
Answer: The circumference of the patio is 21.98 meters.
Step-by-step explanation: Given that there is a circular patio with a diameter of 7 meters. Greg is going to put a titled edge around the patio.
We are to find the circumference of the patio.
If 'r' units is the radius of a circle, then the circumference of the circle is given by
[tex]C=2\pi r.[/tex]
Since the diameter of the circular patio is 7 meters, so the radius 'r' will be given by
[tex]\textup{radius}=\dfrac{1}{2}\textup{ of the diameter}\\\\\Rightarrow r=\dfrac{1}{2}\times 7\\\\\Rightarrow r=3.5~\textup{meters.}[/tex]
Therefore, the circumference of the patio is given by
[tex]C=2\pi r=2\times 3.14\times 3.5=21.98~\textup{meters}.[/tex]
Thus, the circumference of the patio is 21.98 meters.
Let U = {q, r, s, t, u, v, w, x, y, z}
A = {q, s, u, w, y} B = {q, s, y, z}
C = {v, w, x, y, z}. List the elements in the set.
12) Cʹ ∩ Aʹ
[tex]\( C' \cap A' \)[/tex] contains only the element [tex]\( r \).[/tex]
To find [tex]\( C' \cap A' \)[/tex], we first need to determine the complement of sets ( A ) and ( C ) with respect to the universal set ( U ).
The complement of set ( A ), denoted as ( A' ), consists of all elements in ( U ) that are not in (A). So, [tex]\( A' = \{r, t, v, x, z\} \).[/tex]
Similarly, the complement of set [tex]\( C \),[/tex] denoted as [tex]\( C' \)[/tex], contains all elements in (U) that are not in (C). Hence, [tex]\( C' = \{q, r, s, t, u\} \).[/tex]
Now, to find the intersection of [tex]\( C' \) and \( A' \)[/tex], we list the elements that are common to both sets:
[tex]\[ C' \cap A' = \{r\} \][/tex]
Therefore,[tex]\( C' \cap A' \)[/tex] contains only the element [tex]\( r \).[/tex]
If M is the midpoint of LN and LN=27.8 , find the length of MN.
A. 13.8
B. 13.9
C. 14.2
D. 14.5
If the point (8,4) is on the graph of an even function ,what other point must also be on the graph ?
If the point (8,4) is on the graph of an even function, the point (-8,4) must also be on the graph.
Explanation:An even function is a function that satisfies the property f(x) = f(-x) for all values of x in the domain of the function. If the point (8,4) is on the graph of an even function, then the point (-8,4) must also be on the graph. This is because substituting x = -8 into the function would give the same y-value as when x = 8.
Select the following numbers that cannot represent the area of a polygon.
a. 68
b. 40
c. -5
d. square root 30
e. 0
f. -200
Answer: The answer is (c) - 5, (e) 0 and (f) - 200.
Step-by-step explanation: We are to select the correct numbers from the given options that cannot represent the area of a polygon.
We know that the area of any figure cannot be a negative number or zero.
So, the numbers which cannot represent the area of a polygon are - 5, 0 and - 200.
Thus, (c), (e) and (f) are the correct options.
Enter the degree of the polynomial below.
7x7 + 10x4 + 4x3 - 5x11 - 10x6 - 6x7
A. 6
B. 7
C. 11
D. 10 ...?
Answer:
degree of the polynomial is 11.
C is the correct option.
Step-by-step explanation:
We have been given the polynomial
[tex]7x^7+10x^4+4x^3-5x^{11}-10x^6-6x^7[/tex]
Rewrite this polynomial in standard form i.e from descending exponents
[tex]-5x^{11}-6x^7+7x^7-10x^6+10x^4+4x^3[/tex]
On simplifying, we get
[tex]-5x^{11}+x^7-10x^6+10x^4+4x^3[/tex]
Now, we know that the degree of the polynomial is the highest exponent.
Here, the highest exponent is 11.
Therefore, the degree of the polynomial is 11.
C is the correct option.
A $15,000, 11 percent, 120-day note, dated Sept. 3, is discounted on Nov. 11. Assuming a bank discount rate of 9 percent, the proceeds would be____________.
1. $15,550.00
2. $15,351.74
3. $15,531.74
4. $15,135.47
To calculate the proceeds from discounting a note, subtract the bank discount from the face value.
Explanation:To calculate the proceeds from discounting a note, we need to use the formula:
Proceeds = Face Value - Bank Discount
First, let's calculate the bank discount using the formula:
Bank Discount = Face Value * Discount Rate * Time
For the given note:
Face Value = $15,000
Discount Rate = 9%
Time = 120 days / 365 days/year (assuming a 365-day year)
Plugging in the values, we get:
Bank Discount = $15,000 * 0.09 * (120/365)
Next, we can calculate the proceeds by subtracting the bank discount from the face value:
Proceeds = $15,000 - Bank Discount
an airplane takes off with a full tank of 40,000 gallons of fuel and flies at an average speed of 550 miles per hour. after 8 hours in flight, there are 14,000 gallons of fuel left. it will take another 3.5 hours for the plane to reach its destination. how much fuel will be left in the tank when the plane lands? what is the total distance of the flight?
Fuel in aeroplane when tank was full = 40,000 gallons.
Fuel left after flying for 8 hours = 14,000 gallons
Fuel consumed in 8 hours flight =40,000-14,000= 26000 gallons.
Fuel consumed in 1 hour time = 26000÷8= 3250 gallons.
Fuel consumed in remaining 3.5 hours = 3250x3.5=11375 gallons.
Total fuel consumed = 26000+11375 =37375 gallons.
Fuel left after landing =40,000 -37375=2625 gallons.
The second part is asking us to find total distance of the flight.
Total time of flight= 8+3.5=11.5 hrs
Speed of aeroplane = 550 miles per hour.
Distance covered = speed x time
Distance (Total ) covered = 550x11.5=6325 miles.
Fran has been struggling with the tasks she has to accomplish over the next few weeks: homework due the next day (Tuesday), a French test that Thursday, an essay due in two weeks, an algebra test next Friday, and a science project the following Monday. To make things worse, she has to plan a surprise party for her best friend's birthday the weekend after next. How should she list her priorities, starting with the most urgent task? Rearrange the list below to build the right sequence.
Step-by-step explanation:
Arrangement according to her priorities are as follow:
1) Finish homework which is due the next day (Tuesday).
2) Prepare for a French test that is due on Thursday.
3) Prepare a science project that is due on the following Monday.
4) Prepare for the algebra test that is on the next friday.
5) Complete her essay that is due in two weeks.
6) Plan a surprise party for her best friend's birthday that is on weekend after next.
So I have some math questions I'd like for some one to check :)
1. Rename 4/7 as a percent. Round to the nearest tenth of a percent if necessary.
A. 47% B. 1.8% C. 57.1% D. 28% 2. Rename .709 as a percent. A. 709% B. 70.9% C. 79% D. 7.09% 3. Alice plays basketball. In one she shoot 21 free throws and makes 81.25% of them. Estimate how many free throws she makes?
A. About 16 B. about 2 C. About 20 D. About 14 4.Estimate 48% of 23.95 A. About $12.00 B. About $11.00 C. About $15.00 D. About $10.00 5. The bill at a restaurant is $58.50 and mrs. Johnson wants to leave a 15% tip. Approximately how much money should she leave?
A. About $15.00 B. About $9.00 C. About $6.00 D. About $11.00 6. What percent of 50 is 12.5? A. 4% B. 25% C. 40% D. 15% 7. 50 is 6.25% of what number? A. 8 B. 80 C. 750 D. 800 8. Which proportion can be used to solve the following percent problem? What is 50% of 70%?
A. x/70 = 50/100 B. x/50 = 70/100 C. 50/70 = x/100 D. 70/x = 50/100 My answers: 4/7 as a percent. Round to the nearest tenth of a percent
= 0.57142 = 57.142% = 57.1% C .709 as a percent 70.9% B 81.25% of 21 = about 16 A 48% of 23.95 = about 12.00 A 15% of $58.50 = about 5.8 + 2.9 = 8.7 = about 9 B 50 is 12.5? 12.5/50 = 25/100 = 25% B 50 is 6.25% of what number 50 = 0.625 times X So x = 50/0.625 = 80 B 50% of 70% = 35 So the proportion would x/70 = 50/100 A
The waitress and the hostess at a restaurant share the tips at the end of the shift. The average amount earned in tips between the two of them is $75. The waitress gets $45 and the hostess gets $30. If they continue to earn money at this rate, how many dollars will the waitress receive if they earn $350 at the end of the shift?
The answer is B.) $210
What makes the statement true? 8^-2=?
Answer:
[tex]\frac{1}{64}[/tex] makes the statement true.
Step-by-step explanation:
Given expression,
[tex]8^{-2}[/tex]
By using the property of exponent, i.e. [tex]a^m=\frac{1}{a^{-m}}[/tex]
[tex]\implies 8^{-2}=\frac{1}{8^{2}}[/tex]
[tex]=\frac{1}{64}[/tex]
Hence, the true statement would be,
[tex]8^{-2}=\frac{1}{64}[/tex]
If I have a grade of 74.98% and if I get an 80% on my test what will my grade go up to?
3x-2y=14
5x+6y=42 and what is the answer
To solve the system of equations, rewrite them in standard form, eliminate x, solve for y, and substitute the value of y into the equations to solve for x. The solution to the system of equations is x = 4 and y = 2.
Explanation:To solve the system of equations:
Rewrite the equations in the form Ax + By = CMultiply Equation 1 by 3 and Equation 2 by 2 to make the coefficients of x in both equations the same.Subtract the resulting equations to eliminate x.Solve for y.Substitute the value of y into either of the original equations to solve for x.The solution to the system of equations is x = 4 and y = 2.
To solve the provided system of linear equations, the elimination method can be used. The solution to the equations 3x - 2y = 14 and 5x + 6y = 42 is x = 6 and y = 2.
Explanation:The student has provided two linear equations which form a system of equations:
3x - 2y = 145x + 6y = 42To solve this system, we can use either the substitution method, the elimination method, or graphical method. In this case, the elimination method may be more straightforward. Here's a step-by-step explanation:
Multiply the first equation by 3 to make the coefficients of y opposites: 9x - 6y = 42.Now, add the new equation from step 1 to the second equation, 5x + 6y = 42.This results in: 14x = 84.Divide both sides by 14 to find x: x = 6.Substitute x back into the first original equation to find y:3(6) - 2y = 14 results in 18 - 2y = 14.Subtract 18 from both sides: -2y = -4.Divide both sides by -2 to get y: y = 2.Therefore, the solution to the system of equations is x = 6, y = 2.
What is 3 5/8 as a decimal?
The required 3 5/8 as a decimal is 3.625, as of the given mixed fraction.
What is decimal value?Decimal value is defined as showing the place value of the digits in a decimal number. If any proportion of the digit is lower than 1 it would be represented after the dot right to the absolute value,
Here,
To convert 3 5/8 to a decimal, we can first convert the mixed number to an improper fraction and then divide the numerator by the denominator using a long division or a calculator. Here are the steps,
3 5/8 = (3 x 8 + 5)/8 = 29/8
Dividing 29 by 8 using long division, we get:
3 5/8 = 3.625
Therefore, 3 5/8 as a decimal is 3.625.
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Jamaal spent x minutes today practicing his guitar and y minutes today on homework. If the total time he spent on both is 45 minutes or more, which inequality best represents his practice time?
a. x + y < 45
b. x + y > 45
c. x + y ≤ 45
d. x + y ≥ 45
Answer:
D on edge 2020 :)
Step-by-step explanation: