Answer:
Step-by-step explanation:
Given that:
The investment amount in account = $ 320
The rate of interest is = 8.1% compounded quarterly
Compunded quarterly means 8.1% / 4 = 0.02025
The time period = t years
The objective is to write a function showing the value of the account after t years.
From compound interest , compounded monthly.
[tex]Amount = Principal * ( 1 + \dfrac{rate}{12*100})^{12*time}[/tex]
[tex]= $320 *(1 + \dfrac{0.02025}{12*100})^{12t}[/tex]
[tex]= 320*(1+ 1.6875*10^{-5})^{12t}[/tex]
[tex]= 320 * ( 1.000016875)^{12t}[/tex]
Thus; the function after t years [tex]= $320 * ( 1.000016875)^{12t}[/tex]
The percentage of growth per year is :
= (1 + 0.02025)^4 - 1
= 1.083493758 - 1
= 0.083493758
= 8.4 % (APY) yearly
The shortest route from London to Liverpool is 210 miles. A lorry is expected to take 3.5 hours to travel this route. The lorry actually travels by a different route which increases the distance by 20%, but it still arrives in 3.5 hours. By how many more mph than the expected speed does the lorry travel?
Answer:
72 mph
Step-by-step explanation:
Please give brainliest
You have distance =210 miles
Increase it by 20%
210+(210*0.2) = 252 miles I wrote 0.2 instead of writing 20%/100% hope you understand.
The new route is 252 miles
Time travelled = 3.5 hours
Speed=distance/time
Speed = 252/3.5 = 72 mph
What are the similarities and differences between the standard form and vertex form of a quadratic equation?
Step-by-step explanation:
Standard form is ax^2 + bx + c. Vertex form is a(x-h)^2 + k, which reveals the vertex and axis of symmetry. Factored form is a(x-r)(x-s), which reveals the roots.
can anyone help me and please explain
The answer is r=2/5b
Can someone please help!!
will mark bianleast
When figure ABCD is reflected across the dotted line into figure A′B′C′D', which describes the position of B'?
5 units below the dotted line
5 units above the dotted line
3 units below the dotted line
3 units above the dotted line
Answer:
5 units above the dotted line
Step-by-step explanation:
The reason for this is that there is a distance of 5 units between point B and the line so we know that when it is reflected there will be a distance of 5 as well.
A computer technician charges a flat rate for home visits plus $ 55 per hour. The technician bills $190 for a 2-hour home visit to install a new hard drive. The equation y − 190 = 55(x − 2) gives the total amount y the technician charges for x hours of work.
What is the equation in slope-intercept form?
y = 55x + 190
y = 55x + 80
y = 190x + 55
y = 2x + 55
Answer: y = 55x + 80
Step-by-step explanation:
Answer:
1. y = 55x + 80
2. the flat rate
3. The technician worked 4.5 hours
Step-by-step explanation:
Hope this helps!
Henry was playing with his marble collection, and decided to challenge his friend Andrew to figure out how many of each color marbles he had. Henry gave Andrew the following clues. "I have x blue marbles. I have four times as many red marbles as blue marbles. I have 5 less green marbles then I do blue marbles." Altogether I have 91 marbles. How many green marbles does Henry have?
Answer:
11
Step-by-step explanation:
First, set up an equation. Since all the blue marbles+red marbles+green marbles= total number of marbles, we have: x+4x+x-5=91.
x+4x+x-5=91
6x-5=91
6x=96
x=16
Since there are x-5 green marbles, we get the number of green marbles=16-5=11.
The table of values represents the function g(x) and the graph shows the function f(x).
Which statement about the functions is true?
1. f(x) and g(x) are both absolute value functions.
2. f(−2) is greater than g(−2) .
3. f(x) and g(x) intersect at exactly two points.
4. f(x) is greater than g(x) for all values of x.
Answer:
2 and 3 are true
Step-by-step explanation:
1. Although f(x) is in fact an absolute value function and g(x) never goes below 0, g(x) is not an absolute value function because it does not grow linearly. This is known because, between even x intervals, the y value does not change the same amount.
2. f(-2)=2, and g(-2) is 1, meaning that this statement is in fact correct.
3. For this part, it would probably be a good idea to figure out the equation of both graphs. For g(x), starting at the line of symmetry at x=-3, y is 0, which means that the parabola has not been shifted up or down at all, and that its vertex is at (-3,0). Since it grows at the same rate as the parent function of a parabola, its graph is (x+3)^2. For f(x), you can see that it is an absolute value shifted left 3 and up 1, giving it an equation of |x+3|+1. Now, I've graphed both of them below, and you can see that they intersect at exactly two points, making this statement true.
4. Once again, the graph is helpful here. You can see that although f(x) starts off greater, g(x) with its exponential growth quickly overtakes it. Therefore, this statement is false.
Hope this helps!
Answer:
B and C
Step-by-step explanation:
algebra 2! what’s the answer to this? will give you all my points.
Answer:
Step-by-step explanation:
this is a radical equation:
when x=1 y=0
reflected about x
-sqrt(x)
right 1 unit
-sqrt(x-1)
it looks like y-int is about (0,1/3)
vertically compressed by a factor of 1/3
-(1/3)sqrt(x-1)
if you think the y-int is more (0,1/4), then
the function is vertically compressed by a factor of 1/4
-0.25sqrt(x-1)
PLEASE HELP! WILL MARK BRAINLIEST ANSWER!
The histogram below represents a data distribution with uniform class widths. Which of the following is the median of the data distribution?
Answer:
5
Step-by-step explanation:
the median means the number in the middle so the number in the middle would be 5
The graph of f(x) = ax^2 opens upward and is narrower than the graph of g(x) = x^2 . Which of the following could be the value of a?
A. -0.5
B. 6
C. 0.25
D. -2
Answer:
Option C.
Step-by-step explanation:
The given functions are
[tex]f(x)=ax^2[/tex]
[tex]g(x)=x^2[/tex]
It is given that the graph of [tex]f(x)=ax^2[/tex] opens upward and is narrower than the graph of [tex]g(x)=x^2[/tex].
Graph of [tex]f(x)=ax^2[/tex] opens upward, it means coefficient of [tex]x^2[/tex] must be positive.
Graph of [tex]f(x)=ax^2[/tex] is narrower than the graph of [tex]g(x)=x^2[/tex], it means coefficient of [tex]x^2[/tex] must lies between 0 to 1, i.e., [tex]0<|a|<1[/tex].
From the given options, only 0.25 is a positive number whose absolute value lies in between 0 to 1.
Therefore, the correct option is C.
Following are the solution to the graph function:
Given:
Graph function:
[tex]\to f(x)=ax^2\\\\\to g(x)=x^2\\\\[/tex]
Solution:
It is assumed that its graph of [tex]f(x)=ax^2[/tex] is narrower more expands upwards than the graph of [tex]g(x)=x^2[/tex].The graph of [tex]f(x)= ax^2[/tex] expands upward, suggesting that the [tex]g(x)=x^2[/tex] coefficient must be positive.Since the graph of [tex]f(x)=ax^2[/tex] is thinner than that of the graph of [tex]g(x)=x^2[/tex], it implies that the coefficient of [tex]x^2[/tex] has to be between 0 to 1, i.e. [tex]0<|a| <1.[/tex] .Only 0.25 is a positive number with just an absolute value between 0 and 1 among the available alternatives.Therefore, the final answer is "Option C".
Learn more about the graph:
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Does anyone understand this
Pleaseee helppp
Which of the following uses a variable to represent a person, place, or thing
that is unknown?
A. a C-sharp on the piano
B. apartment 12A
C. a B+ grade
D. Mr. X
Answer:
D. Mr. X
Step-by-step explanation:
Answer:
D.
Step-by-step explanation:
All of them could represent something or someone, but Mr. X is the closest because X is usually used as a variable.
Simplify 8a + 4a + 2
Answer:
12a+2
Step-by-step explanation:
You can add 8a and 4a together to get 12a
1 | 4
2| 8
3| 12
4| 16
Write a function rule for the table.
A. S=40
B. c=4s
C. s=c+ 4
D. C= 4+ S
b. c=4s
you multiply x times 4 to get y
A right triangle has a base equal to 13 inches and a height equal to 18 inches. Find the area of the triangle. Type a
numerical answer in the space provided. Do not include units or spaces in your answers,
Answer:
117
Step-by-step explanation:
area of a triangle= 1/2 bxh
13x18=234
divide by 2=117
Answer:
117 is the Answer
Step-by-step explanation: hope this helps!
2. (09.01 MC) In circle A shown below, the measure of ∠BAD is 148°: Circle A with angle BAD measuring 148 degrees; points B, C, D lie on Circle A. If m Arc BC is 96°, what is m Arc CD ? (3 points) 96° 22° 52° 148°
Answer:
Measure of arc CD will be 52°.
Step-by-step explanation:
In the given circle A, measure of central angle intercepted by the arc BCD at the center = 148°
And points B, C and D lie on the given circle.
[tex]m(\widehat {BCD})[/tex] = 148°
[tex]m(\widehat {BCD})=m(\widehat{BC})+m(\widehat {CD})[/tex]
148° = 96° + [tex]m(\widehat{CD})[/tex]
148 - 96 = [tex]m(\widehat{CD})[/tex]
[tex]m(\widehat{CD})[/tex] = 52°
Therefore, measure of arc CD will be 52°.
Option (3) will be the answer.
Answer:
its C
Step-by-step explanation:
Isaak is writing an explicit formula to represent the sequence.
64, 112, 196, 343,...
What value should he use as the common ratio in the formula? Write the answer as a decimal rounded to the nearest
hundredth.
O 0.75
1.75
58
279
Answer:
r = 1.75
Step-by-step explanation:
The common ratio r is found by dividing a term in the sequence by the previous term, that is
112 ÷ 64 = 1.75
196 ÷ 112 = 1.75
343 ÷ 196 = 1.75
The common ratio r = 1.75
Answer:
B
Step-by-step explanation:
A small toy rocket is launched from a 20-foot pad. The height (h, in feet) of the rocket t seconds after
taking off is given by the formula h = – 2t^2– 6t + 20. How long will it take the rocket to hit the
ground?
Answer:
t = 2 sec
Step-by-step explanation:
h = – 2t²– 6t + 20
When the rocket hits the ground. h = 0 ft.
– 2t²– 6t + 20 = 0 /: (-2)
t² + 3t - 10 = 0
(t + 5)(t - 2)=0
t = - 5, t = 2
Time can be only positive.
what is m<2? and what ism<4
Answer:
a and c
Step-by-step explanation:
∠ 1 = 60° ( vertical angle )
The sum of the 3 angles in a triangle = 180°, thus
∠ 2 = 180° - (60 + 70)° = 180° - 130° = 50° → a
(7)
∠ 3 = 180° - (60 + 40)° = 180° - 100° = 80°
∠ 3 and ∠ 4 are adjacent angles and supplementary , thus
∠ 4 = 180° - ∠ 3 = 180° - 80° = 100° → c
f f (x) = StartFraction x minus 3 Over x EndFraction and g(x) = 5x – 4, what is the domain of (f circle g) (x)?
Answer:
f(g(x))=5-(7/x)
Step-by-step explanation:
f(x)=(x-3)/x
g(x)=5x-4
f(g(x))=((5x-4)-3)/x
f(g(x))=(5x-7)/x
f(g(x))=(5x/x)-7/x
f(g(x))=5-(7/x)
Ruth contributes 18% of the total cost of her individual health care. This is $67.50
deduction from each of her biweekly paychecks. What is the total value of her individual
coverage for the year?
Total value of annual health coverage = $ 9000
Calculation of total annual health coverage
Let the total annual health care expenditure = x
Ruth pays 18% of total health care expenditure, which is $ 67.50 for two weeks (ie 15 days)
So, total paid for one month = 67.5 x 2 = 135
And, total paid for full year = 135 x 12 = 1620
As mentioned, she pays 18% of total annual health care expenditure
Hence, 18% x = 1620
18 x / 100 = 1620
x = (1620 x 100) / 18
= 9000
To learn more about Total Coverage, refer https://brainly.com/question/17596754?referrer=searchResults
Answer:
Step-by-step explanation:
Total value of annual health coverage = $ 9000
Calculation of total annual health coverage
Let the total annual health care expenditure = x
Ruth pays 18% of total health care expenditure, which is $ 67.50 for two weeks (ie 15 days)
So, total paid for one month = 67.5 x 2 = 135
And, total paid for full year = 135 x 12 = 1620
As mentioned, she pays 18% of total annual health care expenditure
Hence, 18% x = 1620
18 x / 100 = 1620
x = (1620 x 100) / 18
= 9000
I need help with finding the sum of (x^4 + 2x^3 - 7x - 9) + (x^5 - 2x^4 + 8x + 18) in standerd form
my answer is x^5 - x^4 + 2x^3 + x^2 + 9
is this correct
Answer:
Step-by-step explanation:
(x^4 + 2x^3 - 7x - 9) +
(x^5 - 2x^4 + 8x + 18)
x^5 - x^4 + 2x^3 + x + 9
which graph shows a function and it’s inverse ?
Answer: D.
Step-by-step explanation:
Trust me I been there
Graph B shows the functions and its inverse.
Graph with function and it’s inverse is to be determine.
Functions is the relationship between sets of values.
Here,
For graph A,C, and D do not have axis of symmetry that why this option can be omitted it does not contain function with its inverse.
While graph B has axis of symmetry and equal and opposite 2 function that is graph b has function and its inverse.
Graph B shows the functions and its inverse.
Learn more about function here:
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The deepest part of the Mariana trench (the deepest trench in the world’s oceans) is at an elevation of -11.033 kilometers. The elevation of the deepest part of the Atacama trench is -8.065 kilometers. What is the net change in elevation from the Atacama trench to the Mariana trench?
Answer:
The answer is -2.968
Step-by-step explanation:
I took the test and got it right unlike the other person who got it wrong for me.
Calculate the mean given the frequency table
Class
Frequency
0-9
24
10-19
20
20-29
32
Answer:
So the mean of the given data set is approximately 15.55.
Step-by-step explanation:
The mean is calculated by taking the sum of the product of each class midpoint and its corresponding frequency and dividing by the total frequency.
The midpoint of each class can be calculated as the average of the lower and upper class boundaries:
Class 0-9: Midpoint = (0 + 9) / 2 = 4.5
Class 10-19: Midpoint = (10 + 19) / 2 = 14.5
Class 20-29: Midpoint = (20 + 29) / 2 = 24.5
Now we can find the sum of the product of each midpoint and its frequency:
(4.5 * 24) + (14.5 * 20) + (24.5 * 32) = 108 + 290 + 784 = 1182
Finally, we divide this sum by the total frequency (76) to find the mean:
1182 / 76 = 15.552632
So the mean of the given data set is approximately 15.55.
Which statements are true regarding the quadratic statement?
Answer:
E
Step-by-step explanation:
I hope am right coz it seems most appropriate
Which equations are equivalent to -1/4{X}=12 Select all that apply.
Answer:
2nd, 3rd and the last one
2 - V19-(-2-4)
[-5-(-7)]2
Answer:
7
Step-by-step explanation:
1 Simplify -2-4−2−4 to -6−6.
2-19-(-6)\times (-5-(-7))\times 22−19−(−6)×(−5−(−7))×2
2 Remove parentheses.
2-19-(-6)\times (-5+7)\times 22−19−(−6)×(−5+7)×2
3 Simplify -5+7−5+7 to 22.
2-19-(-6)\times 2\times 22−19−(−6)×2×2
4 Simplify (-6)\times 2\times 2(−6)×2×2 to -24−24.
2-19-(-24)2−19−(−24)
5 Remove parentheses.
2-19+242−19+24
6 Simplify 2-192−19 to -17−17.
-17+24−17+24
7 Simplify.
7
30 POINTS!!!!!The difference between negative five times a number and three is no less than seven.
Boundary point:
Answer:
15+[tex]15x+7[/tex]
Step-by-step explanation:
Answer:
The answer would be x=8/5 or 1 3/5
