Answer:
$7875
Step-by-step explanation:
1 Month 4000 Paid
2 Months 2000 Paid
3 Months 1000 Paid
4 Months 500 Paid
5 Months 250 Paid
6 Months 125 paid
Total = $7875 Paid
Hope this helped ;)
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Calculate simple interest
Question
Carolyn makes a deposit of $2,800 into a savings account. The bank calculates simple interest annually at a rate of 7.5%.
Interest is added every year on the anniversary of the initial deposit. How many years must Carolyn wait before her
investment exceeds $3,500? Give your answer in years. Do not include units in your answer.
Provide your answer below:
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Answer:
4
Step-by-step explanation:
A=P0(1+rt).
We know that A=$3,500,P0=$2,800 and r=7.5%=0.075, so we can rearrange the formula for A to get an explicit expression for t:
A=P0(1+rt)⟹t=A−P0P0r,
and substituting the known quantities gives
r=$3,500−$2,800$2,800×0.075=3.33,
which means, since the interest is paid annually, that she must wait four years for the total investment to exceed $3,500.
what is the solution set for the equation (x-2)(x-8)=0
Answer:
x=2 x =8
Step-by-step explanation:
(x-2)(x-8)=0
Using the zero product property
x-2 = 0 x-8 = 0
x=2 x =8
Answer:x = 2 and x = 8
Step-by-step explanation:
( 2 - 2)( 8 - 8)
(0)(0)
=0
On day two of a study on body temperatures, 106 temperatures were taken. Suppose that we only have the first 10 temperatures to work with. The mean and standard deviation of these 10 temperatures were 98.44oF and 0.30oF, respectively. Construct a 95% confidence interval for the mean of all body temperatures.
Answer:
The 95% confidence interval for the mean of all body temperatures is between 97.76 ºF and 99.12 ºF
Step-by-step explanation:
We have the standard deviation for the sample, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 10 - 1 = 9
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 9 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.2622
The margin of error is:
M = T*s = 2.2622*0.3 = 0.68
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 98.44 - 0.68 = 97.76 ºF
The upper end of the interval is the sample mean added to M. So it is 98.44 + 0.68 = 99.12 ºF
The 95% confidence interval for the mean of all body temperatures is between 97.76 ºF and 99.12 ºF
Jaleel and Lisa are simplifying the expression 2(x-2) + 2 as shown
Answer:
Jaleel is correct because 2 (x + 2) = 2x - 4
Step-by-step explanation:
To solve 2 (x - 2) + 2:
2 (x - 2) + 2
Distribute
2x - 4 + 2
Combine like terms
2x - 2
Lisa did not distribute correctly :)
Answer:
D
Step-by-step explanation:
Roxie is picking out some movies to rent, and she is primarily interested in horror films and documentaries. She has narrowed down her selections to 66 horror films and 1515 documentaries. Step 2 of 2 : How many different combinations of 33 movies can she rent if she wants at least two documentaries?
Answer:
1,085
Step-by-step explanation:
The calculation of number of different combinations of 3 films she can rent if she needs at least two documentaries is shown below:-
[tex]= N\times (2 \times documentaries\ and\ 1\ horror \ movies)+N\times (3\ documentaries)[/tex]
[tex]=(6C_1)\times (15C_2)+(6C_0)\times (15C_3)[/tex]
= 630 + 455
= 1,085
Therefore for calculating the number of different combinations of 3 films she can rent if she needs at least two documentaries we simply applied the above formula and here we consider one number in the question as it shows the double number.
Five people have just won a $100 prize, and are deciding how to divide the $100 up between them. Assume that whole dollars are used, not cents. Also, for example, giving $50 to first person and $10 to the second is different from vice versa. (a) How many ways are there to divide up the $100, such that each gets at least $10?
Answer:
give $20 to each person
Step-by-step explanation:
The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $9 each and will sell 500 tickets. There is one $2,000 grand prize, four $400 second prizes, and sixteen $10 third prizes. You just bought a ticket. Find the expected value for your profit. Round to the nearest cent.
Answer:
expected profit = $-1.48
Step-by-step explanation:
The required expected value can be solved below.
The total number of ticket they will sell = 500 tickets.
So,
expected profit = expected return - expected cost
1 grand price of 2000 = 1/500 × 2000 = 4
4 second price of $400 = 4/500 × 400 = 3.2
16 third price of $10 = 16/500 × 10 = 0.32
expected return = 4 + 3.2 + 0.32 = $7.52
expected cost = $9
expected profit = expected return - expected cost
expected profit = 7.52 - 9
expected profit = $-1.48
Find the diameter and radius of a circle with a circumference of 65.98 Please help
Answer:
21 and 10.5 respectively
Step-by-step explanation:
Remember circumference of a circle is given as;
C= 2×π×r; r is raduis
r = C / 2×π
=65.98/(2×3.142)= 10.50
D= 2× r = 2× 10.50= 21.0( D represent diameter)
Note π = 3.142 a known constant
Determine whether the description corresponds to an observational study or an experiment.
Research is conducted to determine if there is a relation between hearing loss and exposure to mumps. exposure to mumps.
Does the description correspond to an observational study or an experiment?
A. Observational study
B. Experiment
Answer:
A. Observational study
Step-by-step explanation:
In research, an observational study is a type of study in which the researcher observes a phenomenon and tries to establish some relationship between the different variables he/she is observing. In other words, the researcher only observes and doesn't give a treatment.
On the other hand, when we have a experiment, we usually have 2 different groups (one that will receive a treatment and one who won't) and the researcher compares the differences between these two groups because of the treatment. In other words, the researcher does something other than just observing.
In this example, the research is going to determine if there is a relation between hearing loss and exposure to mumps. In this example the researcher is only going to observe how people who have been exposed to mumps are regarding hearing loss (we can say this since it will be unethical for example for the researcher to create an experiment in which he/she exposes a group to mumps). Therefore, he is going to observe how the past exposure to mumps could be related with the hearing loss.
Thus, this is an observational study.
Merely needs to add enough water to 11 gallons of an 18% detergent solution to make 12% detergent solution which equation can she used to find g the number of gallon of water she should add?
1 × 18/100 = 12/100(g+11), is the equation. The answer is 12/100 gallons
What is the solution of the following linear system? y = 3x + 1 2y = 6x + 2
Answer:
y = 3x +1 (1)
2y = 6x +2 (2)
We can devide equation (2) by 2 and we got:
[tex] y =3x +1[/tex] (3)
And since equations (1) and (3) are equal we can do this:
[tex] 3x +1 = 3x+1[/tex]
And that implies:
[tex] 0=0[/tex]
And for this case we will have infinite solutions for the sytem given since we have two lines equal
Step-by-step explanation:
For this case we have the following system of equations given:
y = 3x +1 (1)
2y = 6x +2 (2)
We can devide equation (2) by 2 and we got:
[tex] y =3x +1[/tex] (3)
And since equations (1) and (3) are equal we can do this:
[tex] 3x +1 = 3x+1[/tex]
And that implies:
[tex] 0=0[/tex]
And for this case we will have infinite solutions for the sytem given since we have two lines equal
Please help. I’ll mark you as brainliest if correct!
Answer:
a = 13
b = 0
Step-by-step explanation:
Conjugate of -3 + 2i is -3 - 2i
(-3 + 2i) (-3 - 2i)
We need to expand:
9 + 6i + -6i + -4i^2
-4i^2 =(-4)(-1) = 4
9 + 4 = 13
a = 13
b = 0
The set of whales is a proper subset of the set of mammals.
Jack has a rectangular patio with a length that is one foot less than twice its width. His neighbor Ron's patio has the same width but a length that is 5 feet more than its width. If Jack's patio is 120 square feet and Ron's patio is 104 square feet, how many square feet longer is Jack's patio than Ron's?
Answer:
difference in area = 16 ft²
if you use 8 the difference in length between Jack patio and his neighbor patio will be will be 15 - 13 = 2 ft
if you use 13 the difference i length will be 25 - 18 = 7 ft
Step-by-step explanation:
Jacks rectangular patio
width = a
length = 2a - 1
area = lw
where
l = length
w = width
area = 120 ft²
a(2a - 1)
2a² - a - 120 = 0
(a - 8) (2a + 15)
a = 8 or -15/2
Ron's rectangular patio
width = a
length = a + 5
area = lw
area = 104 ft²
a (a + 5) = 104
a² + 5a -104 = 0
(a + 8) (a - 13)
a = -8 or 13
How many square feet longer is jack patio longer than Ron's patio is the difference in their area. Therefore,
120 - 104 = 16 ft²
The value 8 or 13 can be used for a since the width a have to be the same.
if you use 8 the difference in length between Jack patio and his neighbor patio will be will be 15 - 13 = 2 ft
if you use 13 the difference i length will be 25 - 18 = 7 ft
Determine 6m 9m how much greater the area of the yellow rectangle is than the area of the gree rectangle 2m 5m
Step-by-step explanation:
multiple 6 by 9 then 2 by 5 then subtract them
Answer:
44
Step-by-step explanation:
(6*9) - (2*5)
54 - 10
44
PLEASE HELP ME GUYS!!
Answer:
[tex]\frac{7}{3}[/tex]
Step-by-step explanation:
csc(Ф) is equivalent to the inverse of sin(Ф)
[tex]csc = \frac{1}{sin}[/tex]Since sin(Ф) = 3/7, the inverse of this would be 7/3
So, [tex]csc = \frac{1}{\frac{3}{7} }=\frac{7}{3}[/tex]
The president of a university claimed that the entering class this year appeared to be larger than the entering class from previous years but their mean SAT score is lower than previous years. He took a sample of 20 of this year's entering students and found that their mean SAT score is 1,501 with a standard deviation of 53. The university's record indicates that the mean SAT score for entering students from previous years is 1,520. He wants to find out if his claim is supported by the evidence at a 5% level of significance. True or False: The null hypothesis would be rejected.
Answer:
False.
The null hypothesis failed to be rejected.
At a significance level of 5%, there is not enough evidence to support the claim that the entering class has a mean SAT score that is significantly lower than 1520.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the entering class has a mean SAT score that is significantly lower than 1520.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=1520\\\\H_a:\mu< 1520[/tex]
The significance level is 0.05.
The sample has a size n=20.
The sample mean is M=1501.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=53.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{53}{\sqrt{20}}=11.851[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{1501-1520}{11.851}=\dfrac{-19}{11.851}=-1.6[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=20-1=19[/tex]
This test is a left-tailed test, with 19 degrees of freedom and t=-1.6, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-1.6)=0.063[/tex]
As the P-value (0.063) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the entering class has a mean SAT score that is significantly lower than 1520.
A rectangle has an area of 96cm2 it's length is 4cm longer than it's width. Calculate the length and width.
Answer:
I think l
Step-by-step explanation:
first add 96 and4 then 2 I think
A, B, and C are collinear points. B is between A and C. AB = 5x + 8 BC = 6x - 1 AC = 12x - 11 Find AC.
Answer:
AC = 198
Step-by-step explanation:
Since all these points are collinear, we know that the addition of AB plus BC should give the same as AC. We can then set an equation that addresses this identity:
AB + BC = AC
5x +8 +6x - 1 = 12x - 11
Now re-arranging like terms in order to combine them:
8 - 1 + 11 = 12x - 5x - 6x
19 - 1 = 12x - 11x
18 = x
Now that we know the value of 'x", we can determine the value of AC:
AC = 12x - 11
AC = 12 (18) - 11
AC = 216 - 18
AC = 198
The mean of three numbers is 4
Two of the numbers are 1, 9
What is the missing number?
Answer:2
Step-by-step explanation: 9+1+2=12
12\3=4
ANSWER : 2
select the point that is a solution to the system of inequalities
This point is below both the red diagonal line and the blue parabola. We know that the set of solution points is below both due to the "less than" parts of each inequality sign.
In contrast, a point like (2,2) is above the parabola which is why it is not a solution. It does not make the inequality [tex]y \le x^2-3x[/tex] true. So this is why we can rule choice A out.
Choice C is not a solution because (4,1) does not make [tex]y \le -x+3[/tex] true. This point is not below the red diagonal line. We can cross choice C off the list.
Choice D is similar to choice A, which is why we can rule it out as well.
#2 Jamal is an apprentice on a boat on Long Island Sound. He is helping the captain collect samples of
marine life for an environmental study, and the captain is teaching him about nautical navigation.
When the boat leaves the environmental station, it will return to its home port 9 nautical miles away.
If
the boat maintains a constant speed of 15 knots (nautical miles per hour), how many minutes will the
trip take?
Answer:
The trip will take 36 minutes.
Step-by-step explanation:
This question can be solved using a rule of three.
The boat maintains a constant speed of 15 knots (nautical miles per hour). How many minutes it will take to return to its home port 9 nautical miles away?
So in 60 minutes, 15 nautical miles. How many minutes for 9 nautical miles?
60 minutes - 15 nautical miles
x minutes - 9 nautical miles
[tex]15x = 60*9[/tex]
[tex]x = \frac{60*9}{15}[/tex]
[tex]x = 36[/tex]
The trip will take 36 minutes.
If the measure of angle 2 is (5 x + 14) degrees and angle 3 is (7 x minus 14) degrees, what is the measure of angle 1 in degrees?
2 lines intersect to form 4 angles. From top left, clockwise, the angles are 1, 2, 3, 4.
88 degrees
89 degrees
90 degrees
91 degrees
Answer:
89 degrees
Step-by-step explanation:
The angle 1 is the same as angle 3.
Angle 2 is the same as angle 4.
The sum of these four angles is 360 degrees.
We have that:
Angle 2 = Angle 4 = 7x - 14
Angle 3 = Angle 1 = 5x + 14
Finding x:
Angle 1 + Angle 2 + Angle 3 + Angle 4 = 360
2*(5x + 14) + 2*(7x - 14) = 360
10x + 28 + 14x - 28 = 360
24x = 360
x = 15
Angle 1:
5x + 14 = 5*15 + 14 = 89 degrees
Answer:
I think it is B
Step-by-step explanation:
What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?
Answer:
–2(5 – 4x) < 6x – 4
<=>
-10 + 8x < 6x - 4
<=>
2x < 6
<=>
x < 3
Hope this helps!
:)
Answer:
Step 1: –10 + 8x < 6x – 4
Step 2: –10 < –2x – 4
Step 3: –6 < –2x
Step 4: ________
What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?
A. x < –3
B. x > –3
C. x < 3
D. x > 3
Step-by-step explanation:
The correct answer here is C. x < 3
A bag contains 1p,20 and 5p coins 3/8 of the bag are 1p coins There are as many 5p coins as 1p coins in the bag. There are 640 coins in total. Work out the number of 20 coins in the bag
Answer:
160 off 20p coins
Step-by-step explanation:
1 p, 20 p, 5 p coins1 p= 3/8 of the bag5 p= 1 p= 3/8 of the bagtotal coins= 64020 p coins= 640 - 640*(3/8+3/8)= 640*(1- 6/8)= 640 * 2/8= 640* 1/4= 160
The pressure p(in lbs/in^2) that a 160 pound persons shoe exerts on the ground when walking varies inversely with the area A(in in^2) of the sole of the shoe when the shoes have a sole area of 40 in^2 The pressure is 4 lbs/in^2 find equation that relates these variables
A=
Answer:
[tex]A = \dfrac{40}{P}[/tex]
Step-by-step explanation:
Pressure [tex]p(in lbs/in^2)[/tex] varies inversely with the area [tex]A(in$ in^2)[/tex] of the sole of the shoe.
This is written as:
[tex]P \propto \frac{1}{A}\\ $Introducing the constant of variation$\\P = \dfrac{k}{A}[/tex]
When:
[tex]When: A= 40 in^2, P =4 lbs/in^2\\$Substituting into the equation\\P = \dfrac{k}{A}\\4 = \dfrac{k}{40}\\$Cross multiply\\k=4*40\\k=160\\Therefore, the equation that connect these variables is given as:\\P = \dfrac{40}{A}\\$In terms of P\\AP=40\\\\A = \dfrac{40}{P}[/tex]
Find x in this 45°-45°-90° triangle.
145972
x
X=
4.572
9
18
Sally earns $12.50 an hour cleaning houses. If she works from 8:00am to 6:00pm, how much money will she make?
Answer:
She will make 125 dollars
Step-by-step explanation:
First figure out how many hours are in between 8 AM and 6PM
Second multiply that number by the salary she makes per hour. In this case its 12.50*10
Lastly Get the answer and add a dollar sign :D
x + 10 + 9x=14x-58 can anyone answer this?
The answer to your problem is: X=17
Answer:
17
Step-by-step explanation:
x + 10 + 9x=14x-58
x + 9x + 10 =14x-58
10x + 10 =14x-58
By grouping like terms by moving 14x to the left and 10 to the right of the equation; we have:
10x - 14x =-58-10
-4x=-68
x=-68/-4=17{ dividing both sides by -4}
Can someone please help me with this question the first one