She should score more than 77 on the fifth quiz to have an average of at least 84 .
What is average?The average is the middle value of a set of numbers. This isn't to be confused with the median, which is the middle of a set of numbers. The average is the middle value of the numbers. If you need to find the average of a set of numbers, you add them all together and divide by the amount of numbers.
Formula of average:
[tex]Average = \frac{Sum of terms }{Number of terms }[/tex]
According to the question
A student has scores on four quizzes : 85,83,98,77
she score on the fifth quiz to have an average of at least 84
Let fifth quiz score = x
By using formula of average:
[tex]Average = \frac{Sum of terms }{Number of terms }[/tex]
As average should be at least 84
[tex]84 < \frac{85+83+98+77+x }{5 }[/tex]
420 < 343+x
420 - 343 < x
77< x
Therefore,
x should be greater than 77 .
Hence, she should score more than 77 on the fifth quiz to have an average of at least 84 .
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-6(1 + 2v) – 7(v + 1) = -13
110 +0.70x = 50+ 0.90x
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = 300}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{110 + 0.70x = 50 + 0.90x}[/tex]
Move 0.90x to left hand side and change it's sign
⇒[tex] \sf{0.70x - 0.90x + 110 = 50}[/tex]
Move 110 to right hand side and change it's sign
⇒[tex] \sf{0.70x - 0.90x = 50 - 110}[/tex]
Collect like terms
⇒[tex] \sf{ - 0.2x = 50 - 110}[/tex]
Calculate
⇒[tex] \sf{ - 0.2x = - 60}[/tex]
Divide both sides of the equation by -0.2
⇒[tex] \sf{ \frac{ - 0.2x}{ - 0.2} = \frac{ - 60}{ - 0.2} }[/tex]
Calculate
⇒[tex] \sf{x = 300}[/tex]
Hope I helped!
Best regards!!
2 feet to 40 inches (ratios)
[tex]\boxed{3:5}[/tex]
We need to first change the measurement of 2 feet to inches, and then find the most simplified version of the resulting ratio.
2 feet = 24 inches (1 foot = 12 inches)
Ratio: 24:40
Simplify ratio:
24/8 = 3
40/8 = 5
Ratio: 3:5
Therefore, the simplified ratio is 3:5 inches.
If they work together, Mark and Yvonne can sort 50 library books in 1.5 hours. Working alone, it would take
Yvonne 5 hours to do the same job. How long would it take Mark if he worked alone? Express your answer in
hours and minutes.
veres
e out of
Answer:
B
Step-by-step explanation:
Rewrite the function by completing the square. f(x)=x^{2}+2x+26
Answer:
x = 4 + √3 and x = 4 − √3
Step-by-step explanation:
(a−b)^2=a^2−2ab+b2
a^2−b^2=(a−b)(a+b)
−2x^2+16x−26
=−2(1x^2−8x+13)
=−2(x^2−8x+13+3−3)
=−2(x^2−8x+16−3)
=−2(x^2−2(4)x+4^2−3)
=−2((x−4)^2−3)
=−2((x−4)^2−(√3)^2)
=−2((x−4)−√3)((x−4)+√3)
=−2((x−(4+√3)((x−(4−√3))
The zeros of the given algebraic expression are:
−2x^2+16x−26=0
−2((x−(4+√3)((x−(4−√3))=0
x = 4 + √3 and x = 4 − √3
I strongly suggest using the quadratic formula as this problem is much easier to solve using it.
x = (−b ± [tex]\sqrt{b^{2}-4ac }[/tex] ) / 2
Help plz the Question is on the attached file
Answer:
9 eazy
Step-by-step explanation:
Answer:
B.9
Step-by-step explanation:
3^4=81
3^2=9
81/9=9
Someone help me!!!! To solve this :):):):) My brain is not functioning. Please Help as soon as can thank you
Answer:
The first one is a linear function with the slope of 3 with no shift. the second is a vertical line on the 2 of the x axis. the third is a horizontal line on the -3 of the y axis.
Solve for x: −6 < x − 1 < 9
a. 5 < x < 10
b. −5 < x < 10
c. −5 > x > 10
d. 5 > x > −10
Answer:
-5 < x < 10
Step-by-step explanation:
−6 < x − 1 < 9 just get rid of -1 by adding 1 to all three terms
-6 + 1 < x -1 + 1 < 9 + 1
-5 < x < 10
Answer:
| − 2 | − 7 2 x− 9 ⋅ 5 x − 4 − 6 ( y − 3 )
Step-by-step explanation:
For number 1 the second part I really don’t understand
Answer:
hundred thousands
Step-by-step explanation:
You would move it to the left one place, so it would be the hundred thousands place.
Answer: The answer is hundred thousands place.
Step-by-step explanation: The question is wanting you to name the space the 8 is in. So 10's, 100's, 1000's and so on. But in this case an 8 in the hundred thousand's place has 10 times more value then an 8 in the ten thousand's place.
All of the following fractions are proper fractions, except A.11/12 B.7/5 C.1/6 D.8/15
answer:
A.7/5 is the correct answer because numerator is more than denominator.
thank me plz
Answer:
the answer is A
Step-by-step explanation:
solve the simultaneous equation 3x-2y=7 7x+2y=13
Answer: x= 2, y= -1/2
Step-by-step explanation:
The value of x is 2 and y is -1/2
equations are 3x-2y=7 --1
7x+2y=13 --2
lets consider 3x-2y=7 as equation 1,
consider 7x+2y=13 as equation 2
by putting both the equations :-
3x-2y=7
7x+2y=13
we get 10x=20
x=20/10
x=2
Now by putting the value of x in equation 1;
3(2)-2y=7
6-2y=7
-2y=1
y=-1/2
What is a simultaneous equation?Simultaneous equations are two or more algebraic equations that share variables e.g. x and y. They are called simultaneous equations because the equations are solved at the same time. Each of these equations on its own could have infinite possible solutions.
What is meant by algebraic equation?algebraic equation, a statement of the equality of two expressions formulated by applying to a set of variables the algebraic operations, namely, addition, subtraction, multiplication, division, raising to a power, and extraction of a root.
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The front of a box is a square with an area of 175 square units. What would be the best represents S, the length of the edge of the front of the box in units? Round your answer to the nearest tenth.
Answer:
13.2
Step-by-step explanation:
√175 ≈ 13.2 . . . units
The area of a square is the square of the edge length. Hence, the edge length is the square root of the area.
a. where does the parentheses go in 8+9÷3×6-5 to make a value of 11
b. where does the parentheses go in 5+3-8÷4-2 to make a total of 4
Answer:
8+9÷3×(6-5) 5+3-8÷4-2Step-by-step explanation:
[tex]8+9\div3\times6-5\\= 8+9\div \:3\times \left(6-5\right)\\\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Calculate\:within\:parentheses}\:\left(6-5\right)\::\quad 1\\=8+9\div \:3\times \:1\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:9\div \:3\times \:1\::\quad 3\\=8+3\\\\= 11[/tex]
[tex]5+3-8\div \:4-2\\\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:8\div \:4\::\quad 2\\=5+3-2-2\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:5+3-2-2\::\quad 4\\=4[/tex]
[tex]\left(5+3\right)-8\div \:4-2\\\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Calculate\:within\:parentheses}\:\left(5+3\right)\::\quad 8\\=8-8\div \:4-2\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:8\div \:4\::\quad 2\\=8-2-2\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:8-2-2\::\quad 4\\=4[/tex]
Write an equation in point-slope form for the line with the given information 1.slope=1/5;(2,6) 2.slope=0;(3,-7) 3.(-2,2)&(2,-2) are on the line. 4.(1,1)&(-5,3) are on the line
Answer:31
Step-by-step explanation:
Properties of Exponents Drag and Drop
Answer:
Step-by-step explanation:
1). [tex]a^{3}\times a^5=a^8[/tex]
2). [tex](a^3)^3[/tex] = [tex]a^{9}[/tex]
3). [tex]\frac{a^{10}}{a^3}=a^{10-3}=a^7[/tex]
4). [tex]\frac{a^2}{a^7}=\frac{1}{a^{7-2}}=\frac{1}{a^5}[/tex]
5). [tex]\frac{a^5\times a^2}{a^7}=\frac{a^{5+2}}{a^7}=1[/tex]
6). [tex]\frac{16a^5b^3}{8a^2b}=(\frac{16\times 5}{8})(\frac{a^5}{a^2})(\frac{b^3}{b})[/tex]
[tex]=\frac{80}{8}(a^{5-2})(b^{3-1})[/tex]
= 10a³b²
7). [tex]\frac{2a^3b^3}{2b^2}=(\frac{2}{2})(a^3)(\frac{b^3}{b^2})[/tex]
= a³b
8). [tex](\frac{a^{-8}}{b^{11}})^{-2}=(\frac{b^{11}}{a^{-8}})^2[/tex]
[tex]=(b^{11}a^8)^2[/tex]
= [tex]a^{16}b^{22}[/tex]
9). [tex]\frac{(2a^3)(a^4)^2}{8a^{11}}=(\frac{2}{8})(\frac{1}{a^{11-3}})(a^4)^2[/tex]
[tex]=\frac{1}{4}(\frac{a^8}{a^8})[/tex]
[tex]=\frac{1}{4}[/tex]
10). [tex]\frac{5a^7b^2}{15a^{10}b^{-3}}=(\frac{5}{15})(\frac{a^7}{a^{10}})(b^{2+3})[/tex]
[tex]=\frac{1}{3}(\frac{b^5}{a^3} )[/tex]
[tex]=\frac{b^5}{3a^2}[/tex]
11). 3a⁰ = 3(1) = 3
12). (a²b)⁴ = (a²)⁴(b)⁴
= a⁸b⁴
A 2000 kilogram sports car accelerates at a rate of 30 meters per second squared. The velocity of the car is v= at, where a us acceleration in meters per second squared, and t is time in seconds. The Kinetic energy of the car is me=1/2mv^2
Answer: KE= 900,000t^2
Step-by-step explanation:
A(0,a) is equidistant from P(3,-3) and Q(-2,2). Find a.
Answer:
a = - 1
Step-by-step explanation:
Given the points are equidistant from A then AP = AQ
Calculate the distance using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = A(0, a) and (x₂, y₂ ) = P(3, - 3)
AP = [tex]\sqrt{3-0)^2+(-3-a)^2}[/tex] = [tex]\sqrt{3^2+(-3-a)^2}[/tex] = [tex]\sqrt{9+(-3-a)^2}[/tex]
Repeat with (x₁, y₁ ) = A(0, a) and (x₂, y₂ ) = Q(- 2, 2)
AQ = [tex]\sqrt{(-2-0)^2+(2-a)^2}[/tex] = [tex]\sqrt{(-2)^2+(2-a)^2}[/tex] = [tex]\sqrt{4+(2-a)^2}[/tex]
Equating AP and AQ
[tex]\sqrt{9+(-3-a)^2}[/tex] = [tex]\sqrt{4+(2-a)^2}[/tex] ( square both sides )
9 + (- 3 - a)² = 4 + (2 - a )² ← expand parenthesis on both sides
9 + 9 + 6a + a² = 4 + 4 - 4a + a² ( subtract a² - 4a from both sides )
18 + 10a = 8 ( subtract 18 from both sides )
10a = - 10 ( divide both sides by 10 )
a = - 1
The value of a is -1 if A(0,a) is equidistant from P(3,-3) and Q(-2,2) the answer is a = -1.
What is an ordered double?It is defined as a representation of coordinates in a two-dimensional coordinate plane. It has a list of two elements in it, such as (x, y).
[tex]\rm Area = |\dfrac{(x_1y_2-y_1x_2)+(x_2y_3-y_2x_3)....+(x_ny_1-y_nx_1)}{2}|[/tex]
It is given that:
A(0,a) is equidistant from P(3,-3) and Q(-2,2).
It is required to find the value of a:
Using the distance formula:
The distance formula can be given as:
[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
AP = AQ
[tex]\rm \sqrt{(3-0)^2+(-3-a)^2} = \sqrt{(-2-0)^2+(2-a)^2}[/tex]
After simplification:
9 + (3 + a)² = 4 + (2 - a)²
9 + 9 + 6a + a² = 4 + 4 - 4a + a²
18 + 10a = 8
10a = - 10
a = - 1
The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division.
Thus, the value of a is -1 if A(0,a) is equidistant from P(3,-3) and Q(-2,2) the answer is a = -1
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is 0.35 a rational or irrational number
Answer:
I think its rational
Step-by-step explanation:
Answer: 0.35 is rational! :D Hopefully this will help others as well!
Step-by-step explanation:
Write 10 × 10 × 10 with an exponent. Explain how you decided which exponent to write.
10 x 10x 10 = Sinceit is used as a multiplied factor times, the exponent is
Need help (no beginners)
Answer:
None of the above
Step-by-step explanation:
-5/2 is not equal to 5/2
5/2 - 39/8 = -19/8
if you calculate the two options you will see that none of them is equal to -19/8
¿Un camión de carga lleva 32 costales de maíz de 20.5 Kg. Cada uno y 19 con un peso de 48.75 Kg. Cada uno. ¿Cuántos kilogramos de maíz lleva el camión?
Answer:
1,582.25 kilogramos
Step-by-step explanation:
Para determinar los kilogramos de maíz que lleva el camión, se debe multiplicar el peso de los dos tipos de bultos que lleva por la cantidad de cada uno y sumar estos valores para obtener la respuesta:
(20.5*32)+(48.75*19)=656+926.25=1,582.25
De acuerdo a esto, el camión lleva 1,582.25 kilogramos de maíz.
Brandon bought 21 chicken wings for $39.90. How much would it cost for 15 wings?
Answer:
$28.50
Step-by-step explanation:
21 chicken wings= $39.90
1 chicken wing= 39.90÷21= $1.90
15 chicken wings= 15×1.90= $28.50
What is the image of the point (8, -3) after a rotation of 90° counterclockwise about
the origin?
Answer:
[tex]\huge\boxed{(3, 8)}[/tex]
Step-by-step explanation:
When we rotate a point 90° counterclockwise around the origin, it's the same as rotating it 270° clockwise around the origin.
When we rotate something 270° clockwise around the origin, the original coordinates (x, y) becomes (-y, x).
y is -3, and -(-3) is just 3, since two negatives make a positive.
x just remains x, but it's in a different position.
This makes the new coordinate [tex](3, 8)[/tex].
Hope this helped!
Water boils at different temperatures at different elevations. The boiling temperature of water is 212 degrees * F sea level (0 feet ) but drops about 1.72 degrees * F for every 1,000 feet of elevation. Write a formula for the boiling point at a given elevation. Then solve the formula for the elevation when the boiling point for water is 190 degrees F.
Answer:
The elevation when the boiling point of water is [tex]190[/tex] °[tex]F[/tex] is 12790.70 feet
Step-by-step explanation:
Let every 1,000 feet of elevation be [tex]x[/tex]. Hence, we can write
[tex]T = 212[/tex] [tex]- 1.72x[/tex]
Where [tex]T[/tex] is the boiling temperature of water at different elevations
Now, to the determine the elevation when the boiling point of water is [tex]190[/tex] °[tex]F[/tex].
We will determine [tex]x[/tex] by putting [tex]T = 190[/tex] °[tex]F[/tex].
Hence,
[tex]T = 212[/tex] [tex]- 1.72x[/tex]
[tex]190[/tex] [tex]= 212[/tex] [tex]- 1.72x[/tex]
[tex]190 - 212[/tex] [tex]= - 1.72x[/tex]
[tex]- 22[/tex] [tex]= - 1.72x[/tex]
[tex]22 = 1.72x\\x = \frac{22}{1.72} \\x = 12.79070[/tex]
Since [tex]x[/tex] represents every 1,000 feet of elevation, then the elevation when the boiling point of water is [tex]190[/tex] °[tex]F[/tex]
[tex]12.79070[/tex] × [tex]1000\\[/tex] [tex]= 12790.70[/tex] feet
Hence, the elevation when the boiling point of water is [tex]190[/tex] °[tex]F[/tex] is 12790.70 feet
85+(-96)=? 86+(-38)=? 22+(-41)=?
Answer:
1) 85+(-96)=-11
2) 86+(-38)=48
3) 22+(-41)=-19
Step-by-step explanation:
1)
Here you are adding a negative to a positive. The if you were to take the absolute value of the negative number it would be greater than that of the positive.
Think about it like 96-85=11, but it was flipped so negative 11.
-11
2)
86+(-38) is the same as 86-38
48
3)
Here you are also adding a negative to a positive. The if you were to take the absolute value of the negative number it would be greater than that of the positive.
Think about it like 41-22=19, but it was flipped so negative 19.
-19
Hope this is helpful :-)
Find the highest common factor (HCF) of 84 and 120
Answer:
GCF-12
Step-by-step explanation:
Find the prime factorization of 84
84 = 2 × 2 × 3 × 7
Find the prime factorization of 120
120 = 2 × 2 × 2 × 3 × 5
To find the GCF, multiply all the prime factors common to both numbers:
Therefore, GCF = 2 × 2 × 3
GCF = 12
Answer: The GCF is 12
Step-by-step explanation:
84=2*2*3*7
120=2*2*2*3*5
So, the GCF is 2*2*3=12
It is a customer appreciation week at the vans shoe outlet, Which means all customers are given a 20% discount on all items. A customer comes in with an birthday coupon for an additional 10% off any shoe item, once the first discount has been applied. The customer buys 3 pairs of shoes for $120.00 each. After the two discounts how much does the customer pay?
Answer:
$278.40
Step-by-step explanation:
Note: "...an additional 10% off any shoe item, once the first discount has been applied." (emphasis added).
Note that the customer is buying 3 pairs of shoes for $120 each: 120 x 3 = $360
The first discount is the 20% discount (on every single item), the second discount is the 10% discount coupon of of any item (which signifies one item only).
Solve for the first discount:
$360 x 0.20 = $72
$360 - 72 = $288.
Next, divide $288 by 3 (to get the individual prices of the shoes:
$288/3 = $96.
The customer then uses a birthday coupon for one of the shoes, which gives an additional 10% off.
$96 x 0.10 = 9.6
$96 - 9.6 = $86.4
Remember, the other two shoes still cost $96 each. Add the price together:
$96 + $96 + $86.4 = $278.40
$278.40 will be the total.
~
Answer:
278.40
Step-by-step explanation:
Find two consecutive integers(with the least sum) whose sum is at least 107
Answer:
53 and 54
Step-by-step explanation:
x + (x+1) = 107
2x+1 = 107
2x = 107
x = 53
x+1 = 54
*DIFFICULT QUESTION PLEASE PLEASE ANSWER* An ice cream machine offers three flavors: vanilla, chocolate, and strawberry. Each flavor can be served as a milkshake, in a cone, or in a cup. What is the probability of a customer choosing either a strawberry milkshake or cone? a.) 60% b.) 40% c.) 12% d.) 20%
Answer:
c.) 20%
Step-by-step explanation:
•1/3 chnace of picking Strawberry flavor
•2/3 chance of picking a milkshake or cone serving
(1/3)*(2/3)=2/9=0.222...(approx.)=0.20=20%
Edit for more clarification:
If you have a situation where multiple outcomes are favorable ("or" statements) then you add the odds together. The customer here wouldn't have minded a milkshake or a cone, so we add their odds together to get 2/3.
If you have a situation where a specific combination of outcomes is favorable ("and" statements) then we multiply the odds. The customer would be getting a flavor and a type of serving, so we multiply the odds of each combination together.
(Note that this is technically a simplified version of the general formulas/equations for probabilities so if you go look them up on the internet they might include some other ideas.)
Answer:C
Step-by-step explanation:
quiz says it was right
PLEASE HELP, WILL GIVE MAX POINTS IF CORRECT. Look at the diagram of the tennis court below. The diagram contains examples of line segments, angles, planes, and vertices. Write the geometric term that best describes each part of the tennis court.
a. Playing Surface
b. Corner of Serving Box
c. Baseline
d. Net
e. Intersection of Baseline and Side Line
The geometric terms that best describes each part of the tennis court are Playing Surface ⇒ Plane and Corner of Serving Box ⇒ Vertex
How to determine the geometric terms?There are several geometric terms; some of them are:
Vertex: This represents a cornerLine (or line segment): used to illustrate distance between endpointsPlane:- This represents a surfacePoint: Used to represent intersections at a pointUsing the above definitions, the geometric terms that best describes each part of the tennis court are
Playing Surface ⇒ PlaneCorner of Serving Box ⇒ VertexBaseline ⇒ LineNet ⇒ PlaneIntersection of Baseline and Side Line ⇒ LineRead more about geometry terms at:
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Answer:
c
Step-by-step explanation: