Answer:
Let M represent the amout at any time.
She saves $40 per week so total amount becomes 40x in any specified week.
where x is the number of weeks.
In the start she has $500 in her bank account so we 'll add this amount into the savings per week. So expression becomes
M = 40x+500
Simply put number of week in place of x and find the total amount.
Step-by-step explanation:
Answer:
for c it is no
Step-by-step explanation:
it is no because she deposits 40 a week, in 4 weeks she deposits 40x4=160, which is nowhere close to the 700 she needs. Even if you count the 500 in her account it is still no since it would total up to 660, not 700
Find the distance between (9, 0) and (6, -8)
Answer:
[tex]\sqrt{73}[/tex] units (or about 8.5 units, rounding to the nearest tenth)
Step-by-step explanation:
To find the distance between a pair of points, use the distance formula, [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]. Substitute the x and y values of (9,0) and (6,-8) into the formula and simplify:
[tex]d= \sqrt{(9-6)^2+(0+8)^2} \\d = \sqrt{(3)^2+(8)^2}\\d = \sqrt{9+64} \\d = \sqrt{73}[/tex]
So, as an exact answer, the distance is [tex]\sqrt{73}[/tex] units.
To find the decimal approximation of that, put that value into a calculator. So, rounding to the nearest tenth, [tex]\sqrt{73}[/tex] is about 8.5 units.
Suppose Huang invests $720 into an annuity every month for five years. At the end of five years, the account has a balance
of $50,000. How much of this balance is interest?
Round your answer to the nearest dollar.
Do NOT round until you have calculated the final answer.
Answer:
$6,800
Step-by-step explanation:
The interest earn after 5 years will be $6800.
It is given that Huang invests $720 into an annuity every month for five years and at end of 5 years balance was $50000.
We have to find out the interest earn.
What do you mean by interest ?
Interest is an additional amount of money that is paid by the bank to customer on the amount deposited in his account.
As per the question ;
Investment made by Huang = $720 for five years
At end of five years , account balance = $50000.
So ;
Five years = 60 months
and the investment is an annuity every month for five years.
If Huang invests $720 every month for 5 years then total investment is ;
= $720 × 60
= $43200
And account balance at end of 5 years = $ 50000
So ;
Interest earn will be ;
= $50000 - $43200
= $6800
Thus , the interest earn after 5 years will be $6800.
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what angle is this I need help
The mathematics faculty at a college consists of 7 professors, 4 associate professors, 4 assistant professors, and 6 instructors. If one faculty member is randomly selected, find the probability of choosing a professor or an instructor.
Answer:
0.619 = 61.9% probability of choosing a professor or an instructor.
Step-by-step explanation:
A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this question, we have that:
7 + 4 + 4 + 6 = 21 members
7 + 6 = 13 professors or instructors.
Find the probability of choosing a professor or an instructor.
p = 13/21 = 0.619
0.619 = 61.9% probability of choosing a professor or an instructor.
Mean (M) = 6, Standard deviation (SD) = 2.45,
calculate the z-score for the specified raw score of 4.
Answer:
z = -0.816
Step-by-step explanation:
z = (x-μ)/σ
z = (4-6)/2.45
z = -0.816
Which expression represents the distance between the two numbers on the
number line?
a. -1 + 2.5
b. -1 -2.5
c. 12.5 - (-1)
d. 12.5 -11
Answer:
B.
Step-by-step explanation:
........................
Question 2 of 37
Suppose that F(x) =3/x and G(X) 3/x-10Which statement best compares
the graphs of F(x) and G(x)?
Answer:
F(x) = x^3 and G(x) = (4x)^3 − 5
so
G(x) = F(4x) -5
the visual effect is
1) shrink horizontally by 1/4
2) shift down by 5
therefore
the answer is the option
D.The graph of G(x) is the graph of F(x) compressed horizontally and shifted 5 units down.
Step-by-step explanation:
Find the area of the following figure: 2ft 6ft 6ft 12ft
Answer:
96 ft²
Step-by-step explanation:
Area of triangle + area of square
Area of triangle = (base × height)/2
= 120/2=60
Area of square = 6 × 6=36
60 + 36= 96
Use the scale to find the actual area of Janets bedroom in square feet!
Answer: 17 feet long 14 feet wide
The model has a scale of 1 : 16 so you can use a calculator like this one to find the exact length. https://www.ginifab.com/feeds/cm_to_inch/scale_converter.html
help with this question, please
Answer:
12.57 inches
Step-by-step explanation:
the formula is l = x/360 (2 pi r) so you solve from there
the arithmetic sequence ai is defined by the formula: a1 = -53 ai = ai-1 + 6 find the sum of the first 880 terms in the sequence
Answer:
The sum of the first 880 terms in the sequence is 2,273,920.
Step-by-step explanation:
Arithmetic sequence:
The difference between consecutive terms is always the same, called common difference, and the nth term is given by:
[tex]a_{n} = a_0 + (n-1)d[/tex]
In which d is the common difference.
Sum of the first n terms:
The sum of the first n terms of an arithmetic sequence is given by:
[tex]S_{n} = \frac{n(a_1+a_n)}{2}[/tex]
ai = ai-1 + 6
This means that [tex]d = 6[/tex]
In this question:
Sum of the first 800 terms, so [tex]n = 800[/tex]
First term is -53, so [tex]a_1 = -53[/tex]
The 880th term is:
[tex]a_{880} = -53 + (880-1)*6 = 5221[/tex]
Sum
[tex]S_{n} = \frac{880(-53+5221)}{2} = 440(-53+5221) = 2273920[/tex]
The sum of the first 880 terms in the sequence is 2,273,920.
Recall that a conflict of interest scenario was presented to a sample of 200 marketing researchers and that 109 of these researchers disapproved of the actions taken. (a) Let p be the proportion of all marketing researchers who disapprove of the actions taken in the conflict of interest scenario. Set up the null and alternative hypotheses needed to attempt to provide evidence supporting the claim that a majority (more than 50 percent) of all marketing researchers disapprove of the actions taken.
Answer: Null hypothesis: [tex]p\leq0.50[/tex]
Alternative hypothesis: [tex]p>0.50[/tex]
Step-by-step explanation:
A null hypothesis is a type of hypothesis that states that there is no difference between a particular parameter of a population whereas an alternative hypothesis states that there is a difference.Given: p = Proportion of all marketing researchers who disapprove of the actions taken in the conflict of interest scenario.
n= 200
Sample proportion = [tex]\hat{p}=\dfrac{109}{200}=0.545[/tex]
Claim : p>0.50
Null hypothesis: [tex]p\leq0.50[/tex]
Alternative hypothesis: [tex]p>0.50[/tex]
Please help and I’ll mark brain list!
Answer:
y = 6
Step-by-step explanation:
Answer:
Y = 6Step-by-step explanation:
5y + 1 = 31 -1 -1 [tex]\frac{5y}{5y}[/tex] = [tex]\frac{30}{5y}[/tex] Y = 61.give the sequence 8.5.2.-1,...at what term will the number become -25? A.11th term B.10th term C.12th term D.20th term 2.which of the following is an algebraic esprression? A.3+5 B.n-1-14 C.3+5=8 D.x=53 3.what is the sum of the first 5 even numbers? A.30 B.20 C.10 D.50
Answer: 1. C(12) 2. B(n-1-14) 3. A(30)
Step-by-step explanation: For number one the nth term with common difference d and first term a is a+(n-1)d=nth term, plug in the values you have and solve for n to get 12. For number 2 an algebraic expression has a variable and a constant but doesn't have an equal sign. So it is B. For number three just add them up. Hope this helped!
Please help! What's the perimeter of Trapezoid ABCD?
Answer and explanation please! <3
Answer:
Step-by-step explanation:
The formula is P= a+b+c+d
a=base
b=base
c=side
d=side
Please search perimeter of a trapezoid. It will provide the answer.
Answer:
Perimeter = 19.77 units
Step-by-step explanation:
Perimeter = AB + BC + CD + AD
BC = 5
AD = 8
AB² = 2² + 3² = 4 + 9 = 13
AB = √13 = 3.61
CD² = 1² + 3² = 1 + 9 = 10
CD = √10 = 3.16
Perimeter = 3.61 + 5 + 3.16 + 8 = 19.77
2007 Federal Income Tax Table
Single:
Over
But not over
The tax is
$0
$7.825
10% of the amount over $0
$7.825
$31.850
$788 + 15% of the amount over $7,825
$31,850
$77.100
$4,386 + 25% of the amount over $31.850
$77.100
$160.850
$15,699 + 28% of the amount over $77.100
$160.850 $349.700
$39.149 + 33% of the amount over $160,850
$349.700 And Over
$101.469 + 35% of the amount over $349.700
John Myers had $49.000 in taxable income. He figured his tax from the tax schedule:
1. Found his earned Income level.
2. Entered the base amount = $4.386
3. Found the amount over $31.850 =
4. Multiplied line 3 by 25% =
5. Added Lines 2 and 4 =
Answer:
a
Step-by-step explanation:
edge 202011
y = –3x + 7
y = 2x – 8
Answer:
Step-by-step explanation:
Using the comparison, substitution, and elimination method, the answer is:(x,y)=(3,-2)
When rewriting the equation the answer is:
3x+y=7
2x-y=8
Which is the solution to the inequality?
1/4+x<5/6
A: x<7/12
B: x>7/12
C: x<1 1/12
D: x> 1 1/12
Answer: x<7/12
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
to isolate 'x', subtract 1/4 from 5/6
you can use a common denominator of 12
1/4 = 3/12
5/6 = 10/12
x < 10/12 - 3/12
x < 7/12
Please help quickly: Thanks!
4 1/4 x 2 x 6 = ?
4 1/4 x 2 x 6 x 3/4 = ?
Please help I’m really need the help (NO LINKS ) (NO LYING ) PART 2 again
Answer:
A. 15
B. 25.6
C. 41.6
Step-by-step explanation:
You need to divide
What is the average rate of change of the function =2sin(1/2)on the interval [0, π]?
Answer:
4/x = [tex]\frac{\pi }{6}[/tex], 5 [tex]\frac{\pi }{6}[/tex]
Step-by-step explanation:
Sorry if I am wrong
The average rate of change of the function in the given interval [0, π] is [tex]\dfrac{2}{\pi }[/tex].
What is the average rate of change?The average Rate of Change of the function f(x) can be calculated as;
[tex]f(x) = \dfrac{f(b) - f(a)}{b-a}[/tex]
The given function is f(x) = 2sin(1/2)x on the interval [0, π]
Here a = 0
b = π
f(a) = 2sin(1/2)a
f(0) = 0
f(b) = 2sin(1/2)π = 2
Step 2: Find Average
[tex]f(x) = \dfrac{f(b) - f(a)}{b-a}\\\\f(x) = \dfrac{2- 0}{\pi }\\\\f(x) = \dfrac{2}{\pi }\\[/tex]
Therefore, the average rate of change of the function in the given interval [0, π] is [tex]\dfrac{2}{\pi }[/tex].
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What is the area of ADEF?
Answer:
6 sq ft
Step-by-step explanation:
The table below shows Abigail's earnings on the job.
1 pts
Time (hours) Earnings (dollars)
21
$709.80
23
$777.40
35
$1183
What is the unit rate or Constant of Proportionality shown in this table?
How much money does Abigail earn for each hour that she works?
Answer:
Option (2)
Step-by-step explanation:
In this question we have to calculate the rate of earning or proportionality constant of Abigail.
Since, earning of Abigail (y) ∝ Time worked (t)
y = kt
Here, k = Proportionality constant
From the table attached,
If y = $709.80 and x = 21 hours
709.80 = 21k
k = [tex]\frac{709.8}{21}[/tex]
k = $33.80 per hour
Therefore, rat of earning or proportionality constant is $33.80
Option (2) will be the correct option.
Amanda had five and 6700 pounds of peanuts in her pantry how is this number written in expanded notation
Answer: 6000+700+00+0
I hope that helps you
A number machine is shown below.
INPUT
ADD 9
MULTIPLY
BY 5
OUTPUT
a) Calculate the INPUT when the OUTPUT is 40.
[2]
b) Calculate the OUTPUT when the INPUT is n.
+
[2]
The graph below shows the relationship between the number of months different students practiced boxing and the number of matches they won:
The title of the graph is Boxing Matches. On x axis, the label is Number of Months of Practice. On y axis, the label is Number of Matches Won. The scale on the y axis is from 0 to 21 at increments of 3, and the scale on the x axis is from 0 to 12 at increments of 2. The points plotted on the graph are the ordered pairs 0, 3 and 1, 6 and 2, 7 and 3, 9 and 4, 11 and 5, 13 and 6, 14 and 7, 16 and 8, 17 and 9, 18 and 10,20. A straight line is drawn joining the ordered pairs 0, 4 and 2, 7.1 and 4, 11 and 6, 13.5 and 8, 17 and 10, 20.5.
Part A: What is the approximate y-intercept of the line of best fit and what does it represent? (5 points)
Part B: Write the equation for the line of best fit in the slope-intercept form and use it to predict the number of matches that could be won after 13 months of practice. Show your work and include the points used to calculate the slope. (5 points)
Answer:
(a) y intercept is approximately 4.3
(b) [tex]y = 1.5x+4.5[/tex]
Step-by-step explanation:
Given
See attachment for graph
Solving (a) The y intercept
This is the point where [tex]x =0[/tex]
From the attached graph; By observation
[tex]y \approx 4.3[/tex] when [tex]x =0[/tex]
So, the y intercept is approximately 4.3
Solving (b): The equation of best fit.
First, calculate the slope of the line using:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where
[tex](x_1,y_1) = (9,18)[/tex]
[tex](x_2,y_2) = (8,16.5)[/tex]
So:
[tex]m = \frac{16.5- 18}{8 - 9}[/tex]
[tex]m = \frac{-1.5}{- 1}[/tex]
[tex]m = 1.5[/tex]
The equation is then calculated using:
[tex]y =m(x - x_1) + y_1[/tex]
Where: [tex]m = 1.5[/tex] and [tex](x_1,y_1) = (9,18)[/tex]
[tex]y = 1.5(x - 9) + 18[/tex]
[tex]y = 1.5x - 9*1.5 + 18[/tex]
[tex]y = 1.5x - 13.5 + 18[/tex]
[tex]y = 1.5x+4.5[/tex]
-5 a root of the Quadratic
equation n² - 8n-65 = o.
What is the other root of the
equation
Answer:
13
Step-by-step explanation:
It is a quadratic equation meaning it has 2 factors and since one of it has root -5, the first factor is (n + 5),
So, we have (n + 5)(n + a) = n^2 + an + 5n + 5a
Thus, by comparison,
n^2 + (5 + a)n + 5a = n^2 - 8n - 65 = 0
5 + a = -8
5a = -65
a = -13
Thus, the other factor is (n -13) and root is 13
what is the fraction form of .8
Kristen owns a bakery and is making a cake for a wedding. The dimensions of the cake are shown below. Answer each of the questions below.
What is the frosted area of the top cake? (Round to the nearest tenth)
What is the frosted area of the bottom cake? (Round to the nearest tenth)
What is the total surface area of cake that will be frosted?
Answer:
$22.5.
Step-by-step explanation:
The total revenue that is gained from the sales of the cakes is determined by multiplying the number of cakes by the price. If we let x be the number of $1 that should be deducted from the price and y be the total revenue,
y = (25 - x)(100 + 5x)
Simplifying,
y = 2500 + 25x - 5x²
We get the value of x that will give us the maximum revenue by differentiating the equation and equating the differential to zero.
dy/dx = 0 = 25 - 10x
Answer 3. Pls pls ASAP pls pls
Answer:
a) no
b) yes
c) yes
d) no
Step-by-step explanation: