Answer:
Albert invested $21,000
John invested $49,000
Step-by-step explanation:
First add 3 and 7
3+7=10
Now divide 70,000 by 10
70,000/10=7000
Now multiply 7000 by 3 and 7
7000x3=21,000
7000x7=49,000
Hope this helps! Plz award Brainliest : )
For the following telescoping series, find a formula for the nth term of the sequence of partial sums {Sn}. Then evaluate limn→[infinity]Sn to obtain the value of the series or state that the series diverges.
1) ∑[infinity]k = 1(1/k + 1 - 1/k + 2).
2) ∑[infinity]k = 1(1/(k + 6)(k + 7).
Answer:
The following are the solution to the given points:
Step-by-step explanation:
Given value:
[tex]1) \sum ^{\infty}_{k = 1} \frac{1}{k+1} - \frac{1}{k+2}\\\\2) \sum ^{\infty}_{k = 1} \frac{1}{(k+6)(k+7)}[/tex]
Solve point 1 that is [tex]\sum ^{\infty}_{k = 1} \frac{1}{k+1} - \frac{1}{k+2}\\\\[/tex]:
when,
[tex]k= 1 \to s_1 = \frac{1}{1+1} - \frac{1}{1+2}\\\\[/tex]
[tex]= \frac{1}{2} - \frac{1}{3}\\\\[/tex]
[tex]k= 2 \to s_2 = \frac{1}{2+1} - \frac{1}{2+2}\\\\[/tex]
[tex]= \frac{1}{3} - \frac{1}{4}\\\\[/tex]
[tex]k= 3 \to s_3 = \frac{1}{3+1} - \frac{1}{3+2}\\\\[/tex]
[tex]= \frac{1}{4} - \frac{1}{5}\\\\[/tex]
[tex]k= n^ \to s_n = \frac{1}{n+1} - \frac{1}{n+2}\\\\[/tex]
Calculate the sum [tex](S=s_1+s_2+s_3+......+s_n)[/tex]
[tex]S=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.....\frac{1}{n+1}-\frac{1}{n+2}\\\\[/tex]
[tex]=\frac{1}{2}-\frac{1}{5}+\frac{1}{n+1}-\frac{1}{n+2}\\\\[/tex]
When [tex]s_n \ \ dt_{n \to 0}[/tex]
[tex]=\frac{1}{2}-\frac{1}{5}+\frac{1}{0+1}-\frac{1}{0+2}\\\\=\frac{1}{2}-\frac{1}{5}+\frac{1}{1}-\frac{1}{2}\\\\= 1 -\frac{1}{5}\\\\= \frac{5-1}{5}\\\\= \frac{4}{5}\\\\[/tex]
[tex]\boxed{\text{In point 1:} \sum ^{\infty}_{k = 1} \frac{1}{k+1} - \frac{1}{k+2} =\frac{4}{5}}[/tex]
In point 2: [tex]\sum ^{\infty}_{k = 1} \frac{1}{(k+6)(k+7)}[/tex]
when,
[tex]k= 1 \to s_1 = \frac{1}{(1+6)(1+7)}\\\\[/tex]
[tex]= \frac{1}{7 \times 8}\\\\= \frac{1}{56}[/tex]
[tex]k= 2 \to s_1 = \frac{1}{(2+6)(2+7)}\\\\[/tex]
[tex]= \frac{1}{8 \times 9}\\\\= \frac{1}{72}[/tex]
[tex]k= 3 \to s_1 = \frac{1}{(3+6)(3+7)}\\\\[/tex]
[tex]= \frac{1}{9 \times 10} \\\\ = \frac{1}{90}\\\\[/tex]
[tex]k= n^ \to s_n = \frac{1}{(n+6)(n+7)}\\\\[/tex]
calculate the sum:[tex]S= s_1+s_2+s_3+s_n\\[/tex]
[tex]S= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}....+\frac{1}{(n+6)(n+7)}\\\\[/tex]
when [tex]s_n \ \ dt_{n \to 0}[/tex]
[tex]S= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}....+\frac{1}{(0+6)(0+7)}\\\\= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}....+\frac{1}{6 \times 7}\\\\= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{42}\\\\=\frac{45+35+28+60}{2520}\\\\=\frac{168}{2520}\\\\=0.066[/tex]
[tex]\boxed{\text{In point 2:} \sum ^{\infty}_{k = 1} \frac{1}{(n+6)(n+7)} = 0.066}[/tex]
Q. A customer hands you three (3) five-dollar bills, five (5) quarters, and two (2) dimes to pay the
full amount for an item. How much does the item cost?
A. $15.45
B. $16.35
C. $16.20
D. $16.45
Answer:
The cost would be D. 16.45
9v=27 what the answer and solve
Answer:
V=3
Step-by-step explanation:
9v=27
You have to get v on its own so you have to do the inverse operation which in this case would be division, 9/9, what you do to one side you have to do to the other so 27/9
That’s would separate v from the other numbers and so V=3
9v=27
9v/9=27/9
V=3
Answer: v=3
Step-by-step explanation:
Simplifying
9v + -27 = 0
Reorder the terms:
-27 + 9v = 0
Solving
-27 + 9v = 0
Solving for variable 'v'.
Move all terms containing v to the left, all other terms to the right.
Add '27' to each side of the equation.
-27 + 27 + 9v = 0 + 27
Combine like terms: -27 + 27 = 0
0 + 9v = 0 + 27
9v = 0 + 27
Combine like terms: 0 + 27 = 27
9v = 27
Divide each side by '9'.
v = 3
Simplifying
v = 3
a) The newbom baby, Jake, needs some supplies. Jake's mom gave you this ist of
things he needs. You and your friend have agreed to spend $115 of the $300 on
Jake. You spend 15% of it on a new blanket 25% of it on toys, and 40% of ton
clothes. How much money do you have left to spend on diapers for Jake?
Elijah decides to lease a $20,000 vehicle for two years. It is estimated that the car will be resold in two years at a price
of $12,841, The Interest being charged is 41%. What is the financing foo?
$12.23
$43.87
$56.10
$68.33
Answer:
$43.87
Step-by-step explanation:
Elijah has decided to lease her car for years. She will be earning lease rental on the car along with interest. The interest charges on the lease rentals is amortized at the lease interest rate. The lease interest rate for the vehicle is decided to be 41%.
Year 1 : $20,000 * 41% * 0.045 * .025 = $18.20
Year 2 : ($20,000 - $18.20) * 41% * 0.045 * 0.25 = $25.67
The sum of year 1 and year 2 is $43.87.
Which of the following variables are categorical?
I. Driver ID
II. Age
III. Car
IV. Gender
Answer: IV. Gender
Step-by-step explanation:
A categorical variable is a variable that has two or more categories.
Driver ID consists of numbers and alphabet and it has no category.
Age is expressed in numbers , it cannot be categorical.
Car has many types but not category.
Gender has mainly 2 categories as male and female (some times 3 if we include transgender)
So, Gender is a categorical variable.
So correct option is IV. Gender
Some people think that the behavior of the stock market in January predicts its behavior for the rest of the year. Let the explanatory variable be the percent change in a stock market index in January. Let the response variable be the percent change in the stock market index for the entire year. You have a data set with 50 cases (where each case is a calendar year). Based on this data, you have the following statistics: mean of the x-variable: 2.75% standard devation of the x-variable: 4.48% mean of the y-variable: 8.17% standard devation of the y-variable: 22.31% correlation between the two variables: 0.655 Suppose that the mean change in January is 10.81%. What is the predicted value of the change in the stock market index for the year
Answer:
1.95
Step-by-step explanation:
Formula for slope is = γ Sy/Sx
γ = Correlation, Sy = S.D. of Y value, Sx= S.D. of X value
Sy = 8.17% = 0.0817
Sx = 2.75% = 0.0275
γ = 0.655
Slope = 0.655 *(0.0817/0.0275)
Slope = 1.94595
Slope = 1.94595
Slope = 1.95
Therefore, the slope of the regression line is 1.95
Robert is building model cars as well as model trains. The cars take 4 hours to build while the trains take 6 hours
to build. He is hoping to build as many as possible before the next model fair exhibition. If he has 100 free hours
until the fair, how many can he build? Write the inequality for this problem. Let cars be the domain and trains the
range.
10 cars and 10 trains in 100 hours
it approximately take him 10 hours to build one car and one train how 6+4=10 how many times can 10 go into 100 10 times hope this helps a little
The flow-rate of your current sink faucet is 2.7 gallons per minute. If you purchase a fancy low-flow faucet for $294, the flow rate would decrease by 39%. Assuming you use your faucet for an average of 1,558 minutes per month and water costs $0.006 per gallon, compute the payback period (in months) of such a purchase.
Answer:
23
Step-by-step explanation:
There are 450 seats in a theatre. 48% of the seats are occupied. How many seats are not occupied?
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{234}}}}}[/tex]
Step-by-step explanation:
Total seats in a theatre = 450
Finding the total occupied seats
[tex] \dashrightarrow{ \sf{48\% \: of \: 450}}[/tex]
[tex] \dashrightarrow{ \sf{ \frac{48}{100} \times 450}} [/tex]
[tex] \dashrightarrow{ \sf{216}}[/tex]
Finding the seats that are not occupied
[tex] \longrightarrow{ \sf{450 - 216 = 234}}[/tex]
Hope I helped!
Best regards! :D
You can multiply -2.2 by 6.2 to find the total variation in the water level.What decimal represents the total variation in water level Ericka observed?
Answer:
-13.64 millimeters
Step-by-step explanation:
just use a calculator ._.
What number is less than 6/9 of a dollar but greater than 0.45
Answer:
0.50
Step-by-step explanation:
to get both numbers in the same unit you have to change one, I'm changing 6/9
6 divided by 9 is ABOUT 0.6 so you can choose any numbr between 0.46 and 0.59
If it is a polynomial, name the polynomial:
2/3x^4 + 7
A) Binomial
B
Monomial
C
Trinomial
D
Not a polynomial
Answer:
should be a monomial
Step-by-step explanation:
because there is only one addition or subtraction sign.
Huntington\'s disease is an inherited autosomal dominant disorder that can affect both men and women. Imagine a couple has had seven children, and later in life, the husband develops Huntington\'s disease. He is tested and it is discovered he is heterozygous for the disease allele, Hh. The wife is also genetically tested for the Huntington\'s disease allele, and her test results show she is unaffected, hh. A.) What is the percent probability that the first child of this couple will have Huntington\'s disease? B.) What is the probability that any six of the seven children will have Huntington\'s disease?
Answer:
a) probability that the first child of this couple will have Huntington's disease is 1/2 = 50%
b) probability that any six of the seven children will have Huntington's disease is 0.05468 ( 5.468% )
Step-by-step explanation:
a)
Given that;
Hh ( diseased father) and hh (normal)
H h
h Hh hh
h Hh hh
therefore Hh ⇒ 2 and hh ⇒ 2
so here we can see that chances of getting Huntington's disease is 1 : 1
so probability that the first child of this couple will have Huntington's disease is 1/2 = 50%
b)
probability that 6 out of the 7 children will have Huntington's disease;
we use the expression
<P> = (n! / (S! × t!)) × p^S × q^t
where n! is total number of children factorial
S! is diseased number of children factorial
t! is healthy number of children factorial
p is probability of diseased children
q is probability of healthy children
so we substitute
<P> = (7! / (6! × 1!)) × 1/2^6 × 1/2^1
= (7 × 6! / (6! × 1!)) × 1/2⁶ × 1/2
= 7 × 1/64 × 1/2
= 0.05468
probability that any six of the seven children will have Huntington's disease is 0.05468 ( 5.468% )
The Huntington's disease.
As per the question, the disease is a rare inherited disease that is caused by the breakdown of the nerve cells of the brain. The disease has a broad impact on functional abilities and usually results in movement, thinking, and other disorders.
Thus the answer is the chance of the disease to a child is about 50% as it starts at age of 30 to 40. The chances of six children are 5.4%.
The disease is an inherited aspect of the body genes and the disorder s created is due to the diseases allele is heterozygous The results shows that the chances of the first child to have this disease will be 1/2 that is 50% and the chances if any six people out of seven that have this disease is about 5.46%Learn more about Huntington's disease.
brainly.com/question/8935079.
An airplane descends 1.4 miles to an elevation of 7.15 miles. fund the elevation of the plane before its descent
Answer:
The plane's starting elevation was 6.75 miles
Step-by-step explanation:
Answer:
no its 9.15
Step-by-step explanation:
x − 1.4 = 7.75
+ 1.4 + 1.4 Add 1.4 to both sides.
x = 9.15
Solve y over negative 6 + 5 = 9. (1 point)
This should be your equation - (y/-6) + 5 = 9
Answer:
y/-6 = 4 <y = -24 <
Answer:
[tex]y=-24\\[/tex]
Step-by-step explanation:
Write the equation
[tex]\frac{y}{-6} +5=9[/tex]
Subtract 5 from both sides
[tex]\frac{y}{-6} =4[/tex]
Multiply both sides by -6
[tex]y=-24\\[/tex]
Hope this helps! : )
4. When rounding to the nearest ten and the nearest hundred, what number rounds to 400? a-295, b-299, c-390, d- 399
Answer:
c. and d.
Step-by-step explanation:
c when tenth
d when hundreth
Answer: D
Step-by-step explanation: D because it is closest to 400 out of the other 3 choices.
Please help! If x = 6 and b = 4, what is x+b
Hey there!
ANSWER: [tex]10[/tex]EXPLANATION:If you want to know how to solve, you will need to find the value of x and y. x is equal to 6 and b is equal to 4.
[tex]x(6)+b(4)=?[/tex]
So we basically just add 6 and 4.
[tex]6+4=10\\x+b=10(Answer)[/tex]
Hope this helps!
[tex]-TetsedHyperr[/tex]
What is the reciprocal of 9/2 and of 4/7 !pleasssee
Answer:
2/9 and 7/4(or 1 3/4)
Step-by-step explanation:
A reciprocal is just the original number flipped.
Combine the sentences into one sentence.
The zookeeper cleans the habitat.
The habitat belongs to the monkeys.
IM SEEING IF THIS WEBSITE ACCUTALLY WORKS
Answer:
The zookeeper cleans the monkeys habitat
Answer:
The zookeeper cleans the habitat that belongs to the monkeys.
Step-by-step explanation:
Write a function that takes the base and height of a triangle and return its area.
//Method/function name is areaOfTriangle
//Return type is double
//Method receives two parameters of type double - base and height
public static double areaOfTriangle(double base, double height){
//Find the area using the formula: 1/2 * base * height
double area = 0.5 * base * height;
//return the area
return area;
} //End of areaOfTriangle method
Step-by-step explanation:The function above has been written in Java.
It contains comments explaining each line of the code. Please go through the comments.
In order to test the function, a complete program containing a main method has also been written. This is shown as follows;
//Class definition begins
public class Area{
//Method/function name is areaOfTriangle
//Return type is double
//Method receives two parameters of type double - base and height
public static double areaOfTriangle(double base, double height){
//Find the area using the formula: 1/2 * base * height
double area = 0.5 * base * height;
//return the area
return area;
} //End of areaOfTriangle method
//Write the main method to call the method
public static void main(String []args){
//Call the areaOfTriangle() method in the main method
//Set the base to 12 and the height to 6
System.out.println(areaOfTriangle(12, 6));
}
} //End of class definition
Sample Output>> 36.0
Which equation can be used to represent the statement? The sum of one-sixth of a number and negative two is equal to negative two-thirds. One-sixth + n = negative 2 + two-thirds One-sixth + n = negative 2 + (negative two-thirds) One-sixth n + 2 = negative two-thirds One-sixth n minus 2 = negative two-thirds
Answer:
One-sixth n minus 2 = negative two-thirds
Step-by-step explanation:
"one-sixth of a number" is represented by "one-sixth n". The sum of that and -2 is represented by "one-sixth n minus 2". Of course, "is equal to negative two-thirds" means "= negative two-thirds". Hence the equation you're looking for is ...
One-sixth n minus 2 = negative two-thirds
Answer:
One-sixth n minus 2 = negative two-thirds
Step-by-step explanation:
what is the relationship between integers and whole numbers
Hey there! I'm happy to help!
A whole number is a type of integer. Integers are numbers without fractions or decimals. They are can be positive or negative. Whole numbers are just the positive integers.
I hope that this helps! Have a wonderful day! :D
Answer:
Whole numbers are natural numbers, and integers are like whole numbers but with negative, and positive numbers.
Step-by-step explanation
Example:
Whole number= 0, 1, 2, 3, 4,...
Integer= -4, -3, -2, -1, 0, 1, 2, 3, 4...
Name all the segments in a triangle
Answer:
Every triangle has three medians, just like it has three altitudes, angle bisectors, and perpendicular bisectors. The medians of a triangle are the segments drawn from the vertices to the midpoints of the opposite sides. The point of intersection of all three medians is called the centroid of the triangle.
Step-by-step explanation:
if you could please mark brainliest i am trying to get to the next rank!
Ans:
30.
In the figure, ACDE is a parallelogram. ZEAB = 125°, ZCBD = 78° and
ZEFD = 76º. Find ZECD.
Answer:
81°
Step-by-step explanation:
let,
ZECD be x°
125°+78°+76°+x°= 360°{ the sum of angle of parallelogram is 360°}
or, 279°+x°= 360°
or, x°= 360°- 279°
or, x° = 81°
the line plot shows the ages at which a group of musicians started to play an instrument based on the line plot which statement is not true
Answer:
Their are 34 musicians
Step-by-step explanation:
If you count the chart you will see that the number of X's equals 34
Answer:
34
Step-by-step explanation:
I did this too, just count the x's
Hope this helps!
6(x + 3) =6x + 18
is what kind of property?
Answer: Distributive Property of Multiplication.
Step-by-step explanation:
there are 16 crayons in the box. some are green and some are red. the number of green crayons is the same as the number of red crayons
Answer:
its 8+8
Step-by-step explanation:
8 red and 8 green because 8+8=16
WhaT is the calculation of Add 3 and 8 than multiply by 9
(3+8)9
3+8=11
11x9
99
hope it helps!
A study was done by an online retail store to determine the rate at which users used its website. A graph of the data that was collected is shown: A line graph with Number of Months on the x axis and Number of Users, in thousands, on the y axis. The x axis has a scale from 0 to 36 with an increment of 4. The y axis has a scale of 0 to 60 with increments of 6. A straight line connecting 0, 0 and approximately 36, 54 is drawn. What can be interpreted from the range of this graph? v
Answer:
A graph of the data that was collected is shown: A line graph with Number of Months on the x axis and Number of Users, in thousands, on the y axis. The x axis has a scale from 0 to 36 with an increment of 4. The y axis has a scale of 0 to 60 with increments of 6. A straight line connecting 0, 0 and approximately 36, 54 is drawn. What can be interpreted from the range of this graph? v .
Answer:
c
Step-by-step explanation:
