Given:
30-hour review course average a score of 620 on that exam.
70-hour review course average a score of 749.
To find:
The linear equation which fits this data, and use this equation to predict an average score for persons taking a 57-hour review course.
Solution:
Let x be the number of hours of review course and y be the average score on that exam.
30-hour review course average a score of 620 on that exam. So, the linear function passes through the point (30,620).
70-hour review course average a score of 749. So, the linear function passes through the point (70,749).
The linear function passes through the points (30,620) and (70,749). So, the linear equation is:
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-620=\dfrac{749-620}{70-30}(x-30)[/tex]
[tex]y-620=\dfrac{129}{40}(x-30)[/tex]
[tex]y-620=\dfrac{129}{40}(x)-\dfrac{129}{40}(30)[/tex]
[tex]y-620=\dfrac{129}{40}(x)-\dfrac{387}{4}[/tex]
Adding 620 on both sides, we get
[tex]y=\dfrac{129}{40}x-\dfrac{387}{4}+620[/tex]
[tex]y=\dfrac{129}{40}x+\dfrac{2480-387}{4}[/tex]
[tex]y=\dfrac{129}{40}x+\dfrac{2093}{4}[/tex]
We need to find the y-value for [tex]x=57[/tex].
[tex]y=\dfrac{129}{40}(57)+\dfrac{2093}{4}[/tex]
[tex]y=183.825+523.25[/tex]
[tex]y=707.075[/tex]
[tex]y\approx 707.1[/tex]
Therefore, the required linear equation for the given situation is [tex]y=\dfrac{129}{40}x+\dfrac{2093}{4}[/tex] and the average score for persons taking a 57-hour review course is 707.1.
write an equation of the function in the form y=a(b)^x -c that has a y intercept of -6, asymptote of y= -2 and goes through (2,-18)
Step-by-step explanation:
Asymptote: y = 2 y-intercept: (0,8)
Step-by-step explanation:
The given function is
f(x) = 6(0.5)^{x} + 2f(x)=6(0.5)
x
+2
This function is of the form:
f(x) = a {b}^{x} + cf(x)=ab
x
+c
where y=c is the horizontal asymptote.
By comparing , we have c=2 hence the horizontal asymptote is
y = 2y=2
To find the y-intercept, we put x=0 into the function to get:
f(0) = 6(0.5)^{0} + 2 = 6 + 2 = 8f(0)=6(0.5)
0
+2=6+2=8
Therefore the y-intercept is (0,8).
find the common difference
9514 1404 393
Answer:
(a) 1/12
Step-by-step explanation:
The difference of adjacent terms is ...
1/4 -1/6 = 3/12 -2/12 = 1/12
a positive integer n is called special if n is divisible by 4, N+1 is divisible by 5 and n+2 is divisible by 6. how many special integers smaller than 1000 are there?
Answer:
17
Step-by-step explanation:
these positive integers are :
4, 64, 124, 184 ... , 964
964 = 4 + (n-1) (60)
964 = 4 + 60n -60
964 = 60n -56
60n = 1020
n = 1020/60
n = 17
so, the number of special integers smaller than 1000 are = 17
The digits n, n+1 and n+2 implies that the special numbers are consecutive i.e. they follow one another. The count of special numbers less than 1000 is 17.
Given that:
[tex]\{n,n+1,n+2\} = \{4,5,6\}[/tex]
[tex]Range = 1000[/tex]
First, calculate the LCM of 4, 5 and 6.
[tex]4 = 2 \times 2[/tex]
[tex]5 = 5[/tex]
[tex]6 = 2 \times 3[/tex]
So, the LCM is:
[tex]LCM = 2 \times 2 \times 5 \times 3[/tex]
[tex]LCM = 60[/tex]
This means that the special digit occurs after every other 60 digits (i.e. the difference between a special digit and another is 60)
To calculate the count of special digits, we make use of arithmetic progression formula
[tex]L = a + (n - 1) \times d[/tex]
Where
[tex]L = 1000[/tex] --- the last term
[tex]a = 4[/tex] --- the first special digit
[tex]d = 60[/tex] --- the common difference as explained above
So, we have:
[tex]L = a + (n - 1) \times d[/tex]
[tex]1000 = 4 + (n - 1) \times 60[/tex]
Collect like terms
[tex]1000 - 4 =(n - 1) \times 60[/tex]
[tex]996 =(n - 1) \times 60[/tex]
Divide both sides by 60
[tex]16.6 =n - 1[/tex]
Add 1 to both sides
[tex]1 + 16.6 =n[/tex]
[tex]17.6 =n[/tex]
Rewrite as:
[tex]n =17.6[/tex]
Remove the decimal part (do not approximate)
[tex]n =17[/tex]
Hence, the special numbers are 17 in total (that are less than 1000).
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A parabola is graphed below.
What is the equation in vertex form of this parabola?
A
y=2(x−2)2−3
B
y=2(x+2)2−3
C
y=12(x−2)2−3
D
y=12(x+2)2−3
thank you so much! please hurry <3
Answer:
B
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here the vertex = (- 2, - 3 ) , then
y = a(x - (- 2))² - 3 , that is
y = a(x + 2)² - 3
To find a, substitute any point on the graph into the equation
Using the coordinates of the y- intercept (0, 5 )
5 = a(0 + 2)² - 3 ( add 3 to both sides )
8 = a(2)² = 4a ( divide both sides by 4 )
2 = a
y = 2(x + 2)² - 3 → B
Find the largest prime factor of 18! + 19! + 20!
Answer: Prime Factors for 18: 2, 3, and 3
Prime Factors for 19: 19
Prime Factors for 20: 2, 2, and 5
Can you mark brainlest
Step-by-step explanation:
what is the height of the water prism
Answer:
32 because I Don't know please vote my answer please
Answer:
12 (10) cm 937 637 = hafe 2929888389292822
Mr. Barry invested some money at 5% and amount half as great as 4%. His total annual income from both investments was $210. Find the amount invested at 4%
A) $1000
B) $1500
C) $2000
D) $2500
The amount invested at 4% is 1500.
How to estimate the amount invested at 4%?Let x be the amount invested at 4%.
2x be the amount invested at 5%.
0.04x + 0.05(2x) = 210
Multiply by 100 to eliminate decimals
4x + 5(2x) = 21000
Remove parentheses: (a) = a
[tex]4 x+5 \cdot 2 x=21000[/tex]
Multiply the numbers: [tex]$5 \cdot 2=10$[/tex]
4x+10x = 21000
Add similar elements:
4x+10x = 14x
14x=21000
Divide both sides by 14
[tex]$\frac{14 x}{14}=\frac{21000}{14}[/tex]
Simplifying the above equation, we get
x = 1500
The amount invested at 4% is 1500.
Therefore, the correct answer is option B) $1500.
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Find the area of the shaded region.
Answer:
pi × 18cm^2
Or approximately,
56.52cm^2 (using 3.14 for pi)
or
56.5487cm^2 (using pi button on calculator)
Step-by-step explanation:
Area of a circle is pi times [radius squared].
All circles are 360°.
Problem can be solved by finding area of whole circle, and then using ratios.
Whole Circle: area = pi × (9cm)^2 = pi × 81cm^2
80° / 360° = Area[shaded] / (pi × 81cm^2)
pi × 18cm^2 = Area[shaded]
((If you read my answer before the edit, I am sorry. I made a calculator error.))
Can anyone help me with this?
I thing it lies on the negativity side of the number line between -2,24
The diameter of a $1 coin is 26.5 mm. Find the area of one side of the coin. Round to the nearest hundredth.
The area of one side of the coin is 41.605 mm².
Given that, the diameter of a $1 coin is 26.5 mm.
We need to find the area of one side of the coin.
What is the area of a circle formula?The area of a circle formula is A=πr².
Now, radius=26.5/2=13.25 mm.
Area of a coin=3.14×13.25=41.605 mm².
Therefore, the area of one side of the coin is 41.605 mm².
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Use a table of function values to approximate an x-value in which the exponential function exceeds the polynomial
function.
f(x) = 2^(5x-6)
h(x) = 3x^5 - 2x^3 - 4x + 7
x=4
x=7
x = 6
x=5
Answer: ¿Hablas español porque no entiendo esto? Si lo haces, ¿puedes decirme en español?
Step-by-step explanation:
factorize the expression:
mn² + mnp + 3mn + 3mp
Answer:
(mn+3m)(n+p)
Step-by-step explanation:
Answer:
(mn + 3m)(n + p)
Step-by-step explanation:
Factorize by grouping:
[tex]mn^2+mnp\\mn(n+p)\\\\3mn+3mp\\3m(n+p)\\\\(mn+3m)(n+p)[/tex]
find the next three sequence of 1,3, 9, 27,
Answer: 81, 243, 729
Step-by-step explanation:
STEP ONE: Find a pattern in the sequence
3 ÷ 1 = 3
9 ÷ 3 = 3
27 ÷ 9 = 3
As we can see from the given sequence, each number multiplies 3 to get the next term.
STEP TWO: Find the next three terms
27 × 3 = 81
81 × 3 = 243
243 × 3 = 729
Hope this helps!! :)
Please let me know if you have any questions
Evelyn wants to buy a dictionary that costs $9, a dinosaur book that costs $18, and a children's cookbook that costs $12. She has saved $30 from her allowance. How much more money does Evelyn need to buy all three books?
Answer:
First, you have to add 9, 18, and 12. When we add this we get 39. She has 30 dollars, do we can see that she needs $9 more to get all three books.
Step-by-step explanation:
What are the solutions to the quadratic equation 3(x - 4)2 = 75?
O x = -9 and x = 1
O x = -5 and x = 5
O x = -4 and x = 4
O x = -1 and x = 9
Answer:
4th option, x = -1 and x = 9
Step-by-step explanation:
3(x-4)²=75
or, (x-4)²=25
or, x²-8x+16-25=0
or, x²-8x-9=0
or, x²-9x+x-9=0
or, x(x-9)+1(x-9)=0
or, (x-9)(x+1)=0
so, x-9=0 or, x=9
and x+1=0 or, x=-1
The two solutions of the quadratic equation are:
x = -1 and x = 9
How to solve the quadratic equation?The quadratic equation is:
3*(x - 4)^2 = 75
We can expand it as:
3*x^2 - 3*2*4*x + 3*16 = 75
3x^2 - 24x -27 = 0
Now, using Bhaskara's formula we get:
[tex]x = \frac{-(-24) \pm \sqrt{(-24)^2 - 4*3*(-27)} }{2*3} \\\\x = \frac{24 \pm 30 }{6}[/tex]
So the two solutions are:
x = (24 + 30)/6 = 9
x = (24 - 30)/6 = -1
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The plot of land illustrated in the accompanying diagram has a perimeter of 34 yards. Find the length, in yards, of each side of the figure
Answer:
Length of x+3= 6.75
Length of 4x=15
Length of 3x-1=10,25
Step-by-step explanation:
First make an equation and find x x+3+3x+1+4x=34Then solve for x, answer will be 3,753,75 represents xplease find the answer
there are options given below
plz give answer asap
Answer
33.3
Step-by-step explanation:
if u multiply the 2, and then find the ratio of them in comparison to the number under, you will find the rate decreases by 10 percent every time, the first situation it is 4/8 = 5/10, second situation is it 32/80= 4/10, and htis situation is most like 3/10, right ? so the answer would be 33.3 :)
4) In the proof below, what is the missing reason?
9514 1404 393
Answer:
(c) CPCTC
Step-by-step explanation:
Even if you don't know the meaning of CPCTC, you can eliminate the other choices because they refer to the whole triangle, not two corresponding angles.
Angles B and D are corresponding angles in the congruent triangles. The reason they are congruent is ...
Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
8. Colleen times her morning commute such that there is an equal likelihood that she will arrive early or late to work on any given day. If she always arrives either early or late, what is the probability that Colleen will arrive late to work no more than twice during a five-day workweek
Solution :
Case I :
If Collen is late on [tex]0[/tex] out of [tex]5[/tex] days.
[tex]$= \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} $[/tex]
[tex]$=\frac{1}{32}[/tex]
Case II :
When Collen is late on [tex]1[/tex] out of [tex]5[/tex] days.
[tex]$= \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times ^5C_1$[/tex]
[tex]$=\frac{1}{32} \times 5$[/tex]
[tex]$=\frac{5}{32}[/tex]
Case III :
When Collen was late on [tex]2[/tex] out of [tex]5[/tex] days.
[tex]$= \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times ^5C_2$[/tex]
[tex]$=\frac{1}{32} \times 10$[/tex]
[tex]$=\frac{5}{16}[/tex]
Therefore, the [tex]\text{probability}[/tex] that Collen will arrive late to work no more than [tex]\text{twice}[/tex] during a [tex]\text{five day workweek}[/tex] is :
[tex]$=\frac{1}{32} + \frac{5}{32} + \frac{5}{16} $[/tex]
[tex]$=\frac{1}{2}$[/tex]
7.
Which kind of function best models the data in the table? Graph the data and write an equation to model the data.
A. exponential; y = 3x – 1
B. linear; y = x – 1
C. quadratic; y = x2 – 1
D. linear; y = –x – 1
Answer:
D. linear; y = –x – 1
Step-by-step explanation:
Linear; y=-x - 1
The slope is negative since it’s decreasing. So it’s not the first equation. It’s not a quadratic equation because there is no forming U shape for this data. It’s not a exponential function because the slope is not 3 and a exponential function is in the form y=a(b)^x
...............................................................................................................................................
Answer:
The correct answer is D) linear; y = –x – 1
Step-by-step explanation:
To find this, use any values in the table and it will produce a true statement. This is how we check to see if a model is correct. See the two examples below for proof.
(4, 5)
y = -x - 1
-5 = -4 - 1
- 5 = -5 (TRUE)
(0, -1)
y = -x - 1
-1 = 0 - 1
-1 = -1 (TRUE)
Someone help pleasee
Answer:
-80
Step-by-step explanation:
We can write the quadratic as
ax^2 + bx+c
4x^2 +8x+9
a=4 b = 8 c=9
The discriminant is
b^2 -4ac
8^2 - 4(4)(9)
64 - 144
-80
Answer:
-80
Step-by-step explanation:
The discriminant is the value under the radical in the quadratic formula. The part of the quadratic formula that is under the radical is [tex]\sqrt{b^2-4ac}[/tex]. So, plug in the needed values and solve for what is under the radical. The b-value is 8; this squared is 64. Then, plug in a and c, 4 and 9. Then multiply these by 4, 4*4*9=144. Finally subtract, 64-144=-80.
16789047+65390-49532578=?
Answer:
-32678141
Step-by-step explanation:
I need an explanation written out for (0.345)(2.1)
Thank you
Answer:
0.07245
Step-by-step explanation:
Just work out 345*21 and then divide by 10,000 because 0.345 is 3 digits from zero and 2.1 has 1 digit from zero, so total of 4 zeroes (10,000 since 10,000 has 4 zeroes).
Refer to picture
Need help on Q.8
Answer:
Rajan = 436.36 rupees and Kamal = 363.63 rupees
Step-by-step explanation:
Total ratio = 11/30
Amount to be shared = 800
Rajan = Individual ratio / Total ratio x the total amount to be shared
1/5 ÷11/30 × 800 = 436.36
Kamal = 1/6 ÷ 11/30 × 800 = 363.63
Gabriella has a smart phone data plan that costs $25 per month that includes 10 GB of data, but will charge an extra $15 per GB over the included amount. How much would Gabriella have to pay in a month where she used 5 GB over the limit? How much would Gabriella have to pay in a month where she used went over by x x GB?
Rachel has 37 videos and decides to purchase 2 more each week. Write an equation describing this situation.
the cross sectional area of this circular duct is 226.865 square inches.
what would be the diameter of the duct
Answer:
D. 17
Step-by-step explanation:
No-
Someone please explain this to me like you would a child
thank you
Answer:
12 degrees
Step-by-step explanation:
Answer:
15 degrees
Step-by-step explanation:
okay haha
so basically the cosine of an angle is the side adjacent to it, divided by the hypotenuse. the sine is the side opposite to that angle divided by the hypotenuse, and the tangent is the side opposite to that angle divided by the side adjacent to it.
in this case we are given the angle and the side opposite to it which is 10, and we are also given the hypotenuse of 39.
what trig function deals with opposite and hypotenuse?
the answer is sine
so we would find the sine of that angle which equals to opposite over hypotenuse:
sin(angle) = 10/39
but, they are asking for the inverse trig function. the inverse of sine is arcsin.
so :
arcsin(10/39) = angle
in a calculator, this would be equal to about 14.857 which is closest to 15.
Have fun all !!! This is my trash account. You all can have my points.
Answer:
Step-by-step explanation:
OK
Answer:
rshjgdlf
FGshjfgsfds
Step-by-step explanation:
GIMME'
Divide. Write your answer as a fraction in simplest form.
−7/10÷ 2/5= help
Answer:
- [tex]\frac{7}{4}[/tex]
Step-by-step explanation:
Given
- [tex]\frac{7}{10}[/tex] ÷ [tex]\frac{2}{5}[/tex]
Leave the first fraction
Change division to multiplication
Turn the second fraction upside down
= - [tex]\frac{7}{10}[/tex] × [tex]\frac{5}{2}[/tex] ← cancel 5 and 10 by 5
= - [tex]\frac{7}{2}[/tex] × [tex]\frac{1}{2}[/tex]
= - [tex]\frac{7(1)}{2(2)}[/tex]
= - [tex]\frac{7}{4}[/tex]
