5) Polly wants her math average to be more than an 85. Her current grades are 70, 85, 90 and 88. Whatis the minimum grade Polly must receive in order to achieve an average of greater than an 85?Let x =Inequality:
Answers
The Solution:
Given Polly's grades as:
\(70,85,90,88\)Let the minimum grade she needs to average more than 85 be represented with x.
By formula,
\(\text{ Average grade =}\frac{\text{ sum of grades}}{\text{ number of grades}}\)In this case,
\(\begin{gathered} \text{average grade =85} \\ \text{ sum of grades = 70+85+90+88+x} \\ \text{ number of grades = 5} \end{gathered}\)Substituting, we get the inequality that describes the situation as below:
\(\text{ 85 }\leq\frac{70+85+90+88+x}{5}\)The above inequality is the same as
\(\frac{70+85+90+88+x}{5}\ge85\)Solving the above inequality, we multiply both sides by 5.
\(\begin{gathered} \frac{70+85+90+88+x}{5}\times5\ge(85\times5) \\ \\ 70+85+90+88+x\ge425 \end{gathered}\)\(333+x\ge425\)Collecting the like terms, we get
\(\begin{gathered} x\ge425-333 \\ \\ x\ge92 \end{gathered}\)Thus, the minimum grade Polly needs is 92.
Therefore, the correct answer is 92.
Related Questions
Write Percent as a decimal 42.15%
Answers
Answer:
42.15 as a decimal is 0.4215 and you can multiply 0.4215 by a number to get 42.15 percent of that number.
Step-by-step explanation:
So the answer is 0.4215
Hope this helps! =D
Answer:0.4215
Step-by-step explanation:
42.15%÷100=0.4215
Math question
The average low temperature in City A in December is 4 C. In March it is
12 C lower. What is the average low temperature in City A in March?
Answers
Elsa bought n packs of pencils each pack has 12 pencils write an equation to represent the total number of pencils p that Elsa bought
Answers
Answer:p=12n
Step-by-step explanation:
12 pencils a pack(n) total is p
Your total is p and 12 pencils a pack so n is the number of packs, you have to multiply the number of packs by 12 so it’ll be 12n and p is you total so p=12n
solve the absolute value equation and write your answers in set notation. -2|x+6|+7=3
Answers
= -4,-8 I think
Solve for x by simplifying both sides of the equation, then isolating the variable.
The side-lengths of a triangle are increased by a scale factor of 4. Predict
how this change will affect the area.
A. The area will be one-fourth the original area.
B. The area will be 4 times greater.
C. The area will be 16 times greater.
D. The area will be increased by 4 units.
Answers
If the side-lengths of a triangle are increased by a scale factor of 4 then the area will be 16 times greater.
As given in the question,
Let 'a' be the base of the triangle
and 'h' be the height of the triangle
Area of the triangle = (1/2)×a× h
Side length increased by scale factor 4
New base = 4a
New height=4h
New area=(1/2)×4a×4h
= 16×(1/2)×a ×h
= 16 times the original area
Therefore, if the side-lengths of a triangle are increased by a scale factor of 4 then the area will be 16 times greater.
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For large parties, a restaurant charges a reservation fee of $30, plus $20 per person. The total charge for a party of x people is f(x) = 20x + 30. How will the graph of this function change if the reservation fee is raised to $65 and the per-person charge is lowered to $12?
Answers
Which of the following expressions could not be used to determine the exact value of cos 120°?
Answers
From the trigonometrical identities, we know that
\(\cos 2x=\cos ^2x-\sin ^2x=2\cos ^2-1=1-2\sin ^2x\)These identites will give us cosine of 120 when x=60.
On the other hand,
\(\sin 2x=2\sin x\cos x\)which will give us sine of 120 when x=60.
Therefore, by comparing with the given options, the answer is:
\(2\sin 60\cos 60\)A farmer has 324 feet of fencing to make three identical adjacent rectangular pens, as shown in the picture. What dimensions of each pen will maximize the total enclosed area?
Answers
The dimensions of each pen that will maximize the total enclosed area would be as; Length 81 feet; Width 81 feet.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Let the Dimension of each pen
Length = x
Width = y
Area = xy
Perimeter equation
2(x + y) = 324
x + y = 162
Substituting the perimeter equation
Area = x(162 - x)
Area = -x^2 + 162x
If the zeros of the quadratic are 0 and 162, then the median will be at where the maximum area occurs.
162/ 2
= 81
Hence, The dimensions of each pen that will maximize the total enclosed area would be as; Length 81 feet; Width 81 feet.
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using the line of best fit
Answers
The monthly cell phone bill when shared data equals zero is given as follows:
$26.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.The intercept of the line in this problem is given as follows:
b = 26.
Hence $26 is the monthly cell phone bill when shared data equals zero.
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Do you think it is a good idea to take agap year after matric? use your own words as far as possible
Answers
Answer:
Taking a gap year after matriculation can be a great idea for some students, depending on their individual needs and goals. A gap year provides an opportunity for students to take a break from academic studies and explore other interests or gain valuable life experience. During this time, they can travel, volunteer, work, or even take courses or internships to develop new skills or explore potential career paths.
A gap year can also be an excellent option for students who are not sure what they want to study or do after high school. It provides time to reflect on their interests and goals and make more informed decisions about their future. Furthermore, some universities and employers value the experiences that gap year students bring to their studies or work, which can enhance their future career prospects.
On the other hand, taking a gap year may not be the best option for everyone. It requires careful planning and consideration of finances, as students will not have the same financial aid and scholarships available as they would during a traditional academic year. Additionally, students must have a clear plan for how they will spend their time and ensure that they are using their gap year constructively.
In conclusion, whether or not taking a gap year is a good idea depends on the individual student's needs, goals, and circumstances. If they have a clear plan and the financial means to support themselves, a gap year can provide valuable experiences and benefits. However, if they are not prepared or do not have a clear purpose for their time off, it may not be the best choice.
Solve the following inequality:
Answers
Answer:
\(r \geqslant - 16\)
Step-by-step explanation:
\( \frac{ - 10 + r}{2} \geqslant - 13\)
multiply both sides by 2:
\( - 10 + r \geqslant - 26\)
add 10 on both sides:
\(r \geqslant - 16\)
Answer:
\(r \ge -16\)
Step-by-step explanation:
To solve any equation/inequality:
1. get the variable to show up exactly once
2. isolate it
\(\frac{-10+r}{2} \ge -13\)
Multiply both sides by 2 and simplify (note that we're multiplying by a positive, not a negative, so the direction of the inequality stays the same, whereas multiplying or dividing by a negative would have changed the direction of the inequality)
\(\frac{-10+r}{2} *2 \ge -13 *2\)
\(-10+r \ge -26\)
Add 10 to both sides, and simplify
\((-10+r)+10 \ge (-26)+10\)
\(r \ge -16\)
it's simple but; pls help asap
Answers
Answer:
Hey mate.......
Step-by-step explanation:
This is ur answer......
Two added to eight multiplied by four......Hope it helps!
Brainliest pls!
Follow me! :)
Given that sin(θ)=−2√13/13, and θ is in quadrant III, what is cos(θ)? Give your answer as an exact fraction with a radical, if necessary.
Answers
Answer:
Given that sin(θ) = -2√13/13 and θ is in quadrant III, we know that sin(θ) is negative and cos(θ) is also negative. We can use the Pythagorean identity to solve for cos(θ):
cos²(θ) + sin²(θ) = 1
cos²(θ) = 1 - sin²(θ)
cos(θ) = ±√(1 - sin²(θ))
Since cos(θ) is negative in quadrant III, we take the negative square root:
cos(θ) = -√(1 - sin²(θ))
Substituting sin(θ) = -2√13/13, we get:
cos(θ) = -√(1 - (-2√13/13)²) = -√(1 - 4/13) = -√9/13 = -3√13/13
Therefore, cos(θ) = -3√13/13.
A deposit of $225 as an integer
Answers
Answer:
225
Step-by-step explanation:
A deposit is positive, so a deposit of $225 as an integer (number) would be 225I hope this helps!
What Two whole numbers have their first common multiple as 6
Answers
Answer:
2, 3
Step-by-step explanation:
The prime factorization of 6 is 2(3), so one possibility is 2 and 3.
geometry need help asap
Answers
The value of angle LAF in the intersecting chords is determined as 104⁰.
What is the value of angle LAF?The value of angle LAF is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.
Also this theory states that arc angles of intersecting secants at the center of the circle is equal to the angle formed at the center of the circle by the two intersecting chords.
m∠LAF = ¹/₂ (arc LF + arc YS)
From the diagram, we have arc LF = 160⁰ and YS = 48⁰
m∠LAF = ¹/₂ (160 + 48)
m∠LAF = 104⁰
Thus, the value of angle LAF is calculated by applying intersecting chord theorem.
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Solve the equation using the distributive property and properties of equality.
1/2(x+6) = 18
What is the value of x?
O 6
O7 1/2
O 14 1/2
0 30
Answers
Answer:
x = 30
Step-by-step explanation:
1/2(x+6) = 18
Expand brackets or use distributive law.
1/2(x) + 1/2(6) = 18
1/2x + 6/2 = 18
1/2x + 3 = 18
Subtract 3 on both sides.
1/2x + 3 - 3 = 18 - 3
1/2x = 15
Multiply both sides by 2.
(2)1/2x = (2)15
x = 30
Answer:
30
Step-by-step explanation:
I need help with my algebra
Answers
Suppose given points,
\(\begin{gathered} (x_1,y_1)=(4,1) \\ (x_2,y_2)=(-2,7) \end{gathered}\)Equation in slope form.
\((y-y_1)=(\frac{y_2-y_1}{x_2-x_1})(x-x_1)\)Substitute the given points.
\(\begin{gathered} (y-4)=\frac{7-1}{-2-4}(x-4) \\ y-4=-1(x-4) \\ y-4=-x+4 \\ y=-x+8 \end{gathered}\)Therefore, the equation of slope is
\(y=-x+8\)Silvester ran around the field,
turning at each of the three backstops.
What was the average number of degrees
he turned at each of the three corners?
Answers
it is 76 ooooooooooooof
Please awnser asap I will brainlist
Answers
Answer:
V = 180 (vans)
S = 90 (small trucks)
L = 40 (large trucks)
Step-by-step explanation:
Set up the variables: Let V represent the number of vans, S represent the number of small trucks, and L represent the number of large trucks.
Write the equations:
V + S + L = 310 (total number of vehicles)
V = 2S (twice as many vans as small trucks)
35,000V + 70,000S + 60,000L = 15,000,000 (total cost of the vehicles)
Substitute equation 2) into equation 1):
2S + S + L = 310
3S + L = 310
Simplify equation 3) by substituting V = 2S:
70,000S + 70,000S + 60,000L = 15,000,000
140,000S + 60,000L = 15,000,000
Set up a system of equations:
3S + L = 310
140,000S + 60,000L = 15,000,000
Eliminate L by multiplying equation 1) by 60,000:
60,000(3S + L) = 60,000(310)
180,000S + 60,000L = 18,600,000
Subtract equation 2) from the new equation:
(180,000S + 60,000L) - (140,000S + 60,000L) = 18,600,000 - 15,000,000
40,000S = 3,600,000
Solve for S:
S = 90
Substitute the value of S into equation 1) to solve for L:
3(90) + L = 310
270 + L = 310
L = 40
Substitute the values of S and L into equation 2) to solve for V:
V = 2S
V = 2(90)
V = 180
The final answer is:
V = 180 (vans)
S = 90 (small trucks)
L = 40 (large trucks)
Answer:
180 Vans 90 Small trucks and 40 Large trucks
Step-by-step explanation:
What percent of 70 is 30?
Answers
Answer:
42.9%
Step-by-step explanation:
To find the percentage corresponding to a fraction, multiply it by 100%.
30/70 × 100% ≈ 42.9%
30 is about 42.9% of 70.
_____
Additional comments
The fraction 3/7 has a repeating decimal equivalent:
3/7 = 0.428571...(6-digit repeat)
__
You can write your question as an equation:
what% × 70 = 30
Solve it by dividing by 70:
what% = 30/70
The answer will be the fraction written as a percentage, as shown above.
Answer:
literally just 21...
Step-by-step explanation:
Find the value of X. Geometry!!!
Answers
Answer:
D. 19
Step-by-step explanation:
x+5 has to equal half of the base(3x-9)
I tried everything else. Those answers didn't work. 3*19-9=48 and 19+5=24
48/2=24 Therefore, the answer is D, 19
Which of the following is the value of a when the function (x) - 3|xlis written in the standard form of an absolute value
function?
Answers
Answer:1
Step-by-step explanation:2
2
The value of a when the function f(x) = 3|xl is written in the standard form of an absolute value function is 3.
What is meant by an absolute function ?An absolute function is defined as a function which consists of an algebraic expression that is within absolute value symbols.
Here,
The standard form of the absolute value function is written by,
f(x) = a|x|
Given that,
f(x) = 3|x|
Comparing this with the standard form, we get,
a|x| = 3|x|
Therefore, a = 3
Hence,
The value of a when the function f(x) = 3|xl is written in the standard form of an absolute value function is 3.
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Which fraction divided by 3/6 is equal to -9/10?
A. -3/2
B. -9/20
C. 9/20
D. 9/40
Answers
Reasoning: -9/20 is equal to -9/10 when divided by 3/6
because it is equivalent
Someone please help me
Answers
Answer: Pretty sure it's A
Step-by-step explanation: If you find the square root of 282 you get 16.7
Answer:
It is A
Step-by-step explanation:
It is A because you need to take the square roots of every number the square root of 282 is 16.7985562
6(__+x)-8(-3+8x) = 30-58xfill in the blank
Answers
In this expression, we have the same value on the left side is equal to the same amount on the right side.
So, let's start operating it to simplify it
6(_+x) -8(-3+8x)=30-58x
6(_+x)+24-64x=30-58x
6( ) +6x +24 -64x =30 -58x
6( ) -58x+24=30-58x
6( )-58x +58x=30-24
6( ) =14 DIviding both sides by six
( ) =7/3
Testing:
6(7/3 +x) -8(-3+8x)=30-58x
14+6x +24 -64x =30-58x
38
Given that v = (5,-4,4) and w = (9,-2,7) evaluate v • w.
A. 81
B. 19
C. (45,8,28)
D. (-40,-16,-8)
Answers
Answer:
81
Step-by-step explanation:
Evaluating v • w
Recall: Given vectors a and B in Cartesian plane, x, y and z
vector a = [ax ay az] and b = [bx by bz]
The dot product is :
a•b = axbx + ayby + azbz
Using the relation above,
v • w = (5*9) + (-4*-2) + (4*7)
v • w = 45 + 8 + 28
v • w = 81
Hence, v • w = 81
Xander walks 4 laps around a track in 16 minutes. (Use decimal numbers if appropriate)
A. How many minutes per lap is that?
B. How many laps per minute is that?
C. If Xander walks 9 laps at the same rate, how long does it take him?
Answers
B) .25 laps per minute
C)36 minutes
Answer:
a. 4 minutes per lap
b. 0.25 laps per minute
c. 36 minutes
Step-by-step explanation:
a. divide 16 by 4 to get the answer
b. divide 4 by 16 to get the answer
c. divide 9 by 4 to get 2.25 then multiply 2.25 by 16 to get 36
Energy usage is measured in kilowatt-hours, kWh. After 7 a.m., energy usage on a university campus increases at a rate of 21% per hour. Prior to 7 a.m., 15,040 kWh have been used. The university's daily goal is to keep its energy usage less than or equal to 100,000 kWh.
Which inequality can be used to determine the number of hours, t, after 7 a.m. when the energy usage on campus will be less than or equal to 100,000?
Answers
Inequality becomes 0.21t + 15,040 <= 100,000
Why energy usage is important?Energy consumption remains a principal source of human caused greenhouse gas emissions the predominant cause of climate change.
After 7 a.m., the power usage on a college campus increases at a rate of 21% per hour.
t be the number of hours
the power usage increases at a rate of 21% per hour
21% = 0.21, constant rate = 0.21 . So slope = 0.21
Prior to 7 a.m., 15,040 kWh have been used.
At 7.am , power used = 15,040kWh. so our y intercept is 15,040
We use slope intercept form y= mx+b
slope m = 0.21 and b = 15040
power usage , y = 0.21 t + 15040
The university has a daily goal to keep their power usage less than or equal to 100,000 kWh
Power usage is less than or equal to 100,000
So inequality becomes 0.21t + 15,040 <= 100,000
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Human hair grows at the average rate of 1/3 inch per month. Sara wants her hair to grow 4 2/3 inches longer. About how many months will this take?
Answers
Answer:
14 months
Step-by-step explanation:
1/3 x 12 = 4.
1/3 x 2 = 2/3.
12 + 2 = 14.
It will take her 14 months.
Hope this helps! :)