To find the amount of time it takes for your neighbor to be 30 ft from you, you set up and solve an equation using the given information.
Explanation:To find the amount of time it takes for your neighbor to be 30 ft from you, we need to set up an equation and solve for t. The distance d is given by d = |120 - 4t|. The absolute value represents the distance in one direction, so it does not matter if your neighbor is walking towards you or past you. We want to find when the distance is 30 ft, so we set up the equation 30 = |120 - 4t|.
Solving this equation gives us two possibilities: 30 = 120 - 4t and 30 = -(120 - 4t). We can solve each equation separately.
For the first equation, 30 = 120 - 4t, we subtract 120 from both sides to get -90 = -4t. Dividing both sides by -4 gives us t = 22.5.
For the second equation, 30 = -(120 - 4t), we multiply both sides by -1 to get -30 = 120 - 4t. Subtracting 120 from both sides gives us -150 = -4t. Dividing both sides by -4 gives us t = 37.5.
So your neighbor is 30 ft from you after 22.5 seconds and 37.5 seconds.
Use the vertical line test to determine if the relation {(–6, –2), (–2, 6), (0, 3), (3, 5)} is a function. Explain your response.
24. a) The average height od sunflowers in a field is 64 in. with a standard deviation of 3.5 in. On a piece of paper, draw a normal curve for the distribution, including the values of the horizontal axis at one, two, and three standard deviations from the mean. Describe your drawing in as much detail as possible, and explain how you came up with each of your labels. b) If there are 3,000 plants in the field, approximately how many will be taller than 71 in.? Explain how you got your answer.
The graph is attached and 68 sunflowers will be taller than 71 inches in the field.
Given that:
- Mean (average height) = 64 inches
- Standard deviation = 3.5 inches
Standardizing the height 71 inches using the z-score formula, we have
[tex]\[ z = \frac{{x - \mu}}{{\sigma}} \][/tex]
Substitute the known values into the equation
[tex]\[ z = \frac{{71 - 64}}{{3.5}} \][/tex]
[tex]\[ z = \frac{{7}}{{3.5}} \][/tex]
[tex]\[ z = 2 \][/tex]
Using the standard distribution table, we have
P(z > 2) = 0.02275
To find the number of sunflowers taller than 71 inches:
[tex]\[ 3000 \times 0.02275[/tex]
Evaluate
68
Hence, 68 sunflowers will be taller than 71 inches in the field.
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
You have already invested $400 in a stock with an annual return of 11%. How much of an additional $1,200 should be invested at 12% and how much at 6% so that the total return on the entire $1,600 is 9%? (Round each answer to the nearest cent.)
The total return you want is 0.09 * 1600 = $144
Let a be the amount invested at 12% and b be the amount invested at 6%
0.12a + 0.06b = 144 - 44
12a + 6b = 10000
a + b = 1200
Put those 2 equations together and solve for a and b:
12a + 6b = 10000
a + b = 1200
Using elimination, a = $466.67 and b = $733.33
So, out of an additional $1200, invest $466.67 at a rate of 12% and $733.33 at a rate of 6%
To determine how much to invest at 12% and 6% to achieve a total return of 9% on $1,600, set up and solve the equation based on the given information.
Explanation:To calculate how much of the additional $1,200 should be invested at 12% and how much at 6%:
Let x be the amount invested at 12% and 1200-x be the amount invested at 6%.Set up the equation: 0.12x + 0.06(1200-x) = 0.09(1600-400).Solve the equation to find x, which represents the amount to invest at 12%.when 1600 is increased by 20% and the resulting number is decreased by y% . the answer is 1536
Using the given figure, the square ABCD is transformed to a new location.
The transformation shown is
RO,90°
DO,3
T(x, y) → (x + 5, y + 2)
Answer:
C
Step-by-step explanation:
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.
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. Which fractions are equivalent to 25/45. Please give two examples.
2. Which describes independent events?
Spinning two fours on a spinner divided into four numbered sections.
Selecting two kings from a standard deck of cards by choosing a card at random, placing it in your pocket, then choosing the second card.
Selecting two green marbles by choosing one from a bag at random, giving the first to a friend, then choosing another.
Selecting the names of two siblings by choosing slips of paper from a hat at random, pinning the selected slip on a bulletin board, and then selecting another.
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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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]
What's the volume of a cube-shaped box with edges 6 centimeters in length? A. 216 cm³ B. 18 cm³ C. 36 cm³ D. 1,296 cm³
Answer:
A. 216
Step-by-step explanation:
This is because the volume of a cube is worked out by doing . being the edge. Therefore, you just have to do (6 × 6 × 6), which is 216.
Write the equation in slope-intercept form of the line that has a slope of 6 and contains the point (1, 1). ...?
Help please....
35
14
11
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)
a ball player gets 11 hits in 40 times at bat. how many hits would you predict in 1000 times at bat
Please someone can help me with #13, 15 and 16 Thanks.
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 is 15/20 simplified?
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.
round off 15.8% to the nearest whole percent
To round 15.8% to the nearest whole percent, we round up due to the digit after the decimal point is 8, resulting in 16%.
To round off 15.8% to the nearest whole percent, we look at the first digit after the decimal point, which is 8. Since this digit is 5 or greater, we round up. Therefore, 15.8% rounded to the nearest whole percent is 16%. This rounding method ensures accuracy in representing percentages, particularly in contexts like statistical analysis, grading, and financial reporting. By rounding to the nearest whole percent, the value becomes more concise and easier to interpret, aiding in clear communication and decision-making processes where precise percentage values are essential for understanding and comparison.
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
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
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.
The surfaces intersect in a space curve C. Determine the projection of C onto the xy-plane.
The paraboloids x^2+y^2+ z=4 and x^2 +3y^2=z
The projection of the space curve C, resulting from the intersection of the two given paraboloids, onto the xy-plane is the line y=0.
Explanation:The surfaces provided are of the paraboloids x^2 + y^2 + z = 4 and x^2 + 3y^2 = z. We can find the space curve, which is the curve of intersection of these two surfaces, by setting the two equations equal to each other. We would get x^2 + y^2 + z = x^2 + 3y^2 which simplifies to 2y^2 - z = 0. The projection of this space curve C onto the xy-plane would just be the shadow this curve casts on the xy-plane. Thus, we eliminate the z variable and the result would be 2y^2 = 0 -> y = 0 , so, the projection of the curve on the xy-plane is y=0.
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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
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.
In how many ways can the letters in the word spoon be arranged?
Which fraction is greater than -5/16
A.)-1/2
B.)-1/4
C.)-3/8
D.)-11/32
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: