The sum of 8 terms is 43690.
What of series?A series is the cumulative sum of a given sequence of terms.
Given:
2+8+32+...
a=2. r= 4
So, the sum of 8 terms
Sn = a(r^n - 1) / (r - 1),
S8 = 2( 65536 -1)/ (4-1)
S8= 65535*2/
S8 = 43690.
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Stephanie is taking out a loan in the amount of $15,000. Her choices for the loan are a 4-year loan at
3% simple interest and a 5-year loan at 5% simple interest. What is the difference in the amount of interest
Stephanie would have to pay for each of these two loans?
$1,950
$3,750
$4,550
$1,800
Answer:
$1950
Step-by-step explanation:
Simple interest amount payable is given by
A=P(1+rt) where p is principal amount, A is final amount paid, t is time and r is rate of interest. For the first case
A=15000(1+0.03*4)=$16800
For second case
A=15000(1+0.05*5)=$18750
Difference will be 18750-16800=$1950
Directions: Consider a 2-kg bowling ball sits on top of a building that is 40 meters tall. It falls to the ground. Think about the amounts of potential and kinetic energy the bowling ball has:
What is the kinetic energy of the ball as it is half way through the fall?
Answer:
392 Joules
Step-by-step explanation:
A cone ___ has a square base
never
always
sometimes
Answer:
Never
Step-by-step explanation:
Cuz cone has a round base
Answer:
never - a cone has a circular base
Step-by-step explanation:
solve for r
r/16 ≥8
a)r≥2
b)r≤128
c)r≤2
d)r≥128
The solution to the inequality [tex]\frac{r}{16}\geq 8[/tex] is r≥128.
Step-by-step explanation:
Given inequality is;
[tex]\frac{r}{16}\geq 8[/tex]
We will solve the inequality for r.
Therefore;
Multiplying both sides by 16
[tex]\frac{r}{16}*16\geq 8*16\\x\geq 128[/tex]
Therefore;
The solution to the inequality [tex]\frac{r}{16}\geq 8[/tex] is r≥128.
6 miles
10 miles
Joe is trying to determine the shortest route he can take to get back home. He is currently at point A and can only travel the
boundary lines to get to point D. He knows that segment AD bisects LA
Which route is shortest and by how much?
Answer:
C) Going from A to C to D and it is shorter by 3 miles.
Step-by-step explanation:
Angles
AB is 6 miles
BD is _12__ miles
AC is 5 miles
CD is 10 miles
First you need to find BD, so AB times CD. 6(10) = 60. then divide 60 with AC. 60/5 = 12. So BD = 12.
Now add
AB and BD,
{ 6+ 12 = 18} ABD = 18
Now add
AC and CD
{ 5 + 10 = 15 } ACD = 15
18 - 15 = 3
So ACD is 3 miles shorter then ABD.
Got right on the test
The shortest route is to take segment AD which is 8 miles long.
Explanation:To determine the shortest route, we need to find the length of segment AD and compare it to the combined length of segments AC and CD. Since segment AD bisects LA, we can use the properties of a line segment bisector to find its length.
AC = 6 milesCD = 10 milesSince segment AD bisects LA, we can say that AC = CD
Therefore, the shortest route is to take segment AD, which is 8 miles long, since it is equal to the combined length of segments AC and CD.
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Write two expressions where the solution is 30
Answer:
(15+0)2
Step-by-step explanation:
Here is a diagram and its corresponding equation. Find the solution to the equation.
Answer: The answer would be x=5/3
Step-by-step explanation:
First you would subtract 11 from both sides, cancelling out the 11 on the left while making 21-11=10. Your equation at this point would be 6x=10. Now you would divide by 6 on both sides making the answer x=5/3.
The value of x is 5/3.
What is an equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given is an equation, 6x+11 = 21
Solving for x,
6x+11 = 21
6x = 10
x = 5/3
Hence, the value of x is 5/3.
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A circle has a sector with area 17/2 pi and central angle of 17/9 pi radians. What is the area of the circle?
Answer:
A(sector) = (1 - 1/9)πr² = (17/2)π
(8/9)r² = 17/2
r = √((17/2)(9/8)) = (1/4)√153
= (3/4)√17
A(circle) = π((3/4)√17)² = 17(9/16)π
= (153/16)π
Round to the nearest hundredth.
27.8 = 1.55y
y≈0.06
y≈17.94
y=26.25
y=29.35
The correct answer is y = 17.94.
To solve the equation 27.8 = 1.55y for y, we first divide both sides of the equation by 1.55 to isolate y:
[tex]\[ y = \frac{27.8}{1.55} \][/tex]
Now, we perform the division:
[tex]\[ y \approx 17.935483871 \][/tex]
When rounding to the nearest hundredth, we look at the third decimal place. If it is 5 or more, we round up. If it is less than 5, we round down. In this case, the third decimal place is 5, so we round up:
[tex]\[ y \approx 17.94 \][/tex]
Therefore, the solution to the equation, rounded to the nearest hundredth, is y = 17.94.
Shaquira is baking cookies to put in packages for a fundraiser. Shaquira has made 86 chocolate chip cookies and 42 sugar cookies.
Shaquira wants to create identical packages of cookies to sell, and she must use all of the cookies.
What is the greatest number of identical packages that Shaquira can make?
To solve this question, first you would add 86 to 42 which gets you 128. Then, you should divide 128 by 2 which gets you to 64, which is the greatest number of packages you can sell.
Answer:
the REAL answer would be 2
Step-by-step explanation:
What are two different ways of
factoring -5x - 15? Select all
that apply.
Two possible factorizations for the given sum are:
-5x - 15 = 1*(5x + 15)
-5x - 15 = 5*(-x - 3)
How to factorize an expression?
For a given sum like the one we have:
a + b
A factorization is something like:
a + b = k*(j + l), where k is a common factor between a and b.
In this case, our sum is: -5x - 15
One possible factorization is if we take the negative sign as the common factor we get:
-5x - 15 = 1*(5x + 15)
Another possible factorization is if we take 5 as the common factor:
-5x - 15 = 5*(-x - 3)
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Simplify 20 radical 16
Answer:
80
Step-by-step explanation:
Simply radical 16 which will give you 4, then multiply 4 by 20 which equals 80
A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 5 large boxes and 6 small boxes has a total weight of 187 kilograms. A delivery of 3 large boxes and 2 small boxes has a total weight of 87 kilograms. How much does each type of box weigh? pls help!!!
Answer:
large: 18.5 kgsmall: 15.75 kgStep-by-step explanation:
Let b and s represent the weights of the big and small boxes, respectively. Then the two delivered weights can be summarized as ...
5b +6s = 187
3b +2s = 87
We can eliminate the "s" variable by subtracting the first equation from 3 times the second:
3(3b +2s) -(5b +6s) = 3(87) -(187)
4b = 74 . . . . . collect terms
b = 18.5 . . . . . divide by 4
Using this value in the second equation, we find ...
3(18.5) +2s = 87
2s = 31.5 . . . . . . . . subtract 55.5
s = 15.75 . . . . . . . . divide by 2
The large box weighs 18.5 kg; the small box weighs 15.75 kg.
Find the value of x.
Answer: 49.8 is the answer
Step-by-step explanation:
a model of a tower uses a scale of 1/3 inch = 2 feet. if the actual tower is 207 feet tall, find the height of the model
Answer
34.5 inches
Step-by-step explanation:
What is the surface area of the right cone below?
O A. 126x units
O B. 54 units
OC. 63x units
D. 998 units
O
Answer:
[tex]SA=54\pi\ units^2[/tex]
Step-by-step explanation:
we know that
The surface area of the cone is given by the formula
[tex]SA=\pi r^{2}+\pi rl[/tex]
where
r is the radius of the base
l is the slant height
we have
[tex]r=3\ units\\l=15\ units[/tex]
substitute
[tex]SA=\pi (3)^{2}+\pi (3)(15)[/tex]
[tex]SA=54\pi\ units^2[/tex]
How yo use the distributive property to multiply 5×180
Answer:
900
Step-by-step explanation:
5 * 180
(5 * 100) + (5 * 80) + (5 * 0)
500 + 400 + 0
900
Answer: 900
Which type of graph would be best used for showing the percentage of students in each grade level at a middle school
Answer:
A pie graph would be a good graph to use
A tennis resort has 1,200 guests. If
65% of the guests play doubles and
singles, how many guests will play
both games?
Answer:
780 people
Step-by-step explanation:
65% of 1,200 is 780
Answer:
780
Step-by-step explanation:
To find the % of something simply convert 65% to a decimal > .65 then 1,200*.65=780
8x-4y=16 8x+4y=16 What does x= what does y=
Answer:
x = 2 y=0
Step-by-step explanation:
We can solve using elimination method
8x - 4y = 16 __________(1)
8x + 4y =16 ___________(2)
Subtract equation (2) from equation (1)
-8y = 0
Divide both-side of the equation by -8
-8y/-8 = 0/-8
y = 0
Substitute y=0 into equation (1)
8x - 4y = 16
8x - 4(0) = 16
8x = 16
Divide both-side of the equation by 8
8x/8 = 16/8
(On the left-hand side of the equation, 8 at the numerator will cancel-out 8 at the denominator leaving us with just x while on the right-hand side of the equation 16 will be divided by 8)
x = 16/8
x = 2
Therefore x = 2 and y=0
Question 40 and it about adding and subtracting polynomials
Answer:
39x-7
Step-by-step explanation:
The perimeter is all the sides added together so
9x + 8x - 2 + 5x + 1 + 17x - 6
Since you can't solve it you just want to simplify the equation, add the like terms together
9x+8x+5x+17x = 39x
-2+1-6 = -7
Your equation is 39x-7
Carl claims that for some centers of dilation of a line, the line will remain
unchanged. He is tasked to prove his claim using the line y = 5x - 10 and a dilation
with a scale factor of 2. Which center of dilation could be used to support Carl's
claim?
A. (0,0)
B. (-5, 35)
C. (1, -5)
D. (2, 20)
Answer:
Option C.
Step-by-step explanation:
Dilation of a line:
If center of dilation lies on the line, then the line remains same.
If center of dilation does not lies on the line, then the dilated line is parallel to the original time.
The given equation of line is
[tex]y=5x-10[/tex]
The line will remain same if center of dilation lies on this line.
For x=0,
[tex]y=5(0)-10=-10\neq 10[/tex]
It means (0,0) does not lies on given line.
For x=-5,
[tex]y=5(-5)-10=-35\neq 35[/tex]
It means (-5,35) does not lies on given line.
For x=1,
[tex]y=5(1)-10=-5[/tex]
It means (1,-5) lies on given line.
For x=2,
[tex]y=5(2)-10=0\neq 20[/tex]
It means (2,20) does not lies on given line.
Center of dilation (1,-5) could be used to support Carl's claim.
Therefore, the correct option is C.
Calculate the area of a rectangular prism that is 5 cm x 9 cm and 11 cm high
Answer: 398cm²
Step-by-step explanation:
Surface area of a Rectangular Prism: 2lw+2lh+2wh
l= 5cm
w= 9cm
h= 11cm
Area= (2x5x9)+(2x5x11)+(2x9x11)
=398cm²
HELP PLEASE QUICKLY I CAN'T FAIL MY CLASS.: The distance of Mercury from the Sun is about 3.6×10^7 miles, while the distance of Pluto from the Sun is about 3.7×10^9 miles. About how many times farther from the Sun is Pluto than Mercury?
Answer: approximately 102.8 times farther
Step-by-step explanation: If you divide the distance of Mercury to the Sun (3.6E7) from the distance of Pluto to the Sun (3.7E9) you get 102.777777. That is the approximate distance. Rounded you get 102.8
What is the geometric mean of 5 and 18?
Answer:
[tex]\sqrt{90} =9.48683298051[/tex]
Step-by-step explanation:
First, mulitply the numbers
[tex]5*18=90[/tex]
Square root the last result
[tex]\sqrt{90} = 9.48683298051[/tex]
Solve the system using elimination.
3x + 16y = 3
3x - 16y = 3
The solution is a
(Type an ordered pair.)
The solution is (1,0)
Explanation:
The two equations are [tex]3x+16y=3[/tex] and [tex]3x-16y=3[/tex]
We need to solve the equation using elimination method.
Adding the two equations, we get,
[tex]3x+16y=3\\3x-16y=3\\-------\\6x=6[/tex]
[tex]x=1[/tex]
Thus, the value of x is 1
Substituting [tex]x=1[/tex] in the equation [tex]3x+16y=3[/tex] , we get,
[tex]3(1)+16y=3[/tex]
Simplifying, we get,
[tex]16y=3-3[/tex]
[tex]16y=0[/tex]
[tex]y=0[/tex]
Thus, the value of y is 0.
The solution is (1,0)
Find the amount of interest owed for a $1,895 loan for 4 years at a 7.9% interest rate.
Answer: The amount of interest owed is $598.82.
Step-by-step explanation: 7.9% of $1,895 is 149.705. So, 149.705 x 4 years would be $598.82 for 4 years.
Final answer:
The total interest owed on a $1,895 loan at a 7.9% interest rate over 4 years is calculated using the formula for simple interest, resulting in a total interest amount of $598.43.
Explanation:
To find the amount of interest owed on a $1,895 loan for 4 years at a 7.9% interest rate, you can use the formula for calculating simple interest, which is Interest = Principal × Rate × Time. The principal (P) is $1,895, the rate (r) is 7.9% or 0.079 when expressed as a decimal, and the time (t) is 4 years.
So the calculation would be:
Interest = $1,895 × 0.079 × 4
Let's perform the calculation:
Interest = $1,895 × 0.079 × 4 = $598.43
The total interest owed on the loan after 4 years would be $598.43.
I could use help with this asap
Answer:
Step-by-step explanation:
Earn $23
Spend $2.46 and $$7.96
Save $10
Share ?
Answer:
12.58
Step-by-step explanation:
Answer:
3.42
Step-by-step explanation:
OWN
23-20.42=3.42
GET RID OF
2.46+7.96=10.42
+10(save)
20.42
An employee’s new salary is $26.355 after getting a 5% raise. What was the salary before the increase pay?
Answer:
$25.03725
Step-by-step explanation:
Step 1: Multiply both sides by %5 to get the raise
26.355 * %5 is same as 26.355 * 0.05
$1.31775 is the raise
Step 2: Subtract the raise from the new salary
26.355 - 1.31775
25.03725
Answer: $25.03725