Answer:
39.0015
Step-by-step explanation:
36.45 x 0.07 = 2.5515
36.45 + 2.5515 = 39.0015
in a geometric series, the sum of the first three terms is 14.25 and the sum of the first four terms is 24.375. find the exact value of the first term and the common ratio. give your answer in the format ‘u1,r’, without spaces.
The first term of the Geometric Series = 3 and its common ratio = 3/2.
What is a geometric Series?An unlimited number of terms with a fixed ratio between each term make up a geometric series.
For 'n' termed GP with a = first term and r = common ratio, [tex]S_{n}=\frac{a(r^{n}-1)}{r-1}[/tex]
Given:
Sum of first three terms of a G.P. = 14.25Sum of first four terms of the G.P. = 24.375To find: First term of the GP and the common ratio.
Finding:
As, [tex]S_{n}=\frac{a(r^{n}-1)}{r-1}[/tex], for n =3,
[tex]S_{3}=\frac{a(r^{3}-1)}{r-1}=14.25[/tex] (eqn 1)
=> Similarly for n = 4,
[tex]S_{4}=\frac{a(r^{4}-1)}{r-1} = 24.375[/tex]
On dividing [tex]S_3 by S_4[/tex], we get:
[tex]\frac{14.25}{24.375}=\frac{r^{3}-1}{r^{4}-1}[/tex]
=> On solving the equations, we get:
[tex]14.25r^{4}-24.375r^{3}+10.125=0[/tex]
r = 3/2 (on factorizing the equation)
Now, substituting this in eqn 1
=> [tex]14.25=\frac{a((\frac{3}{2})^{2}-1)}{\frac{3}{2}-1}[/tex]
=> a = 3 on further solving the equation for a.
Hence, the first term of the Geometric Series = 3 and its common ratio = 3/2.
To learn more about geometric series, refer to the link: https://brainly.com/question/24643676
#SPJ4
Two interior decorating teams are competing in a kitchen remodel competition. Their remodels are graded on the following categories, each worth 18 points; time to complete, design, and total cost. Time to complete is worth 75% of their final score, design is 15%, and total cost is 10%. Whoever has the largest final score wins $150,000. Suppose Team A received 15 points for time to complete, 9 points for design, and 14 points for total cost. Suppose Team B received 17 points for time to complete, 7 points for design, and 13 points for total cost. Using technology, determine which team won the competition. Team A won by 1.9 points. Team A won by 1.1 points. Team B won by 1.9 points. Team B won by 1.1 points.
Answer:
listen there is a lack of information the information you give isn't enough
The correct answer is Team B won by 1.1 points.
To determine which team won the competition, we need to calculate the final scores for both Team A and Team B based on the given weights for each category and the points they received in each category.
For Team A:
- Time to complete (75% of 15 points) = 0.75 * 15 = 11.25 points
- Design (15% of 9 points) = 0.15 * 9 = 1.35 points
- Total cost (10% of 14 points) = 0.10 * 14 = 1.4 points
Total score for Team A = 11.25 + 1.35 + 1.4 = 14 points
For Team B:
- Time to complete (75% of 17 points) = 0.75 * 17 = 12.75 points
- Design (15% of 7 points) = 0.15 * 7 = 1.05 points
- Total cost (10% of 13 points) = 0.10 * 13 = 1.3 points
Total score for Team B = 12.75 + 1.05 + 1.3 = 15.1 points
Now, we compare the total scores of both teams. Team A has a total score of 14 points, while Team B has a total score of 15.1 points. Therefore, Team B won by 1.1 points.
To learn more about the competition link is here
brainly.com/question/31865237
#SPJ3
A. 2z-1+3z=0
B. 5z-1=0
1) How can we get Equation B from Equation A?
Choose 1 answer
Add/subtract the same quantity to/from both sides.
Add/subtract a quantity to/from only one side.
Rewrite one side for both) by combining like terms.
Rewrite one side for both) using the distributive property.
2) Based on the previous answer, are the equations equivalent? In other words, do they have the
same solution?
Choose 1 answer:
Yes
No
Answer:
1.) like terms and 2.) since all you did was combine like terms you didn't change the value, it's the same as before just "fixed" so yes
b) Harri hires a pedalo for 45 minutes.
He takes the pedalo out at 2:45 pm.
At what time must he return the pedalo?
Answer:
He returns the pedalo after 3.00 pm
Find the value of y+12 when y=7?
Answer:
19
Step-by-step explanation:
When y = 7
Replace 7 with y.
[tex]7 + 12 = 19[/tex]
If this answer helped you, give this answer a heart, rate it and if you could then please mark it brainliest. Thanks!
Solve the inequality for .x.
-1/
6
x+4> −3x −8
Simplify your answer as much as possible
Answer:
x>-3
Step-by-step explanation:
collect like terms by changing the signs ..
x+4>-3x-8:to: x+3x>-8-4
Hence find the value of x
:4x>-12
4x/4 >-12/4
x>-4
Of 6.5 hectoliters of fuel, the private spilled 350 milliliters. how many liters did the private spill?
The private spilled 0.35 litres of fuel
How to calculate the amount of litres spilled ?The first step is to convert 6.5 hectolitres to litres
= 6.5 × 100
= 650 litres
Next is to convert millilitres to litres
= 350/1000
= 0.35 litres
Hence the number of litres spilled is 0.35 litres
Read more here
https://brainly.com/question/18239674?referrer=searchResults
#SPJ1
what is the perimeter of a polygon that has the coordinates of (-3,2) (2,2) (2,-4) (-1,-4) (-1,-2) (-3,-2) (-3,2)
The perimeter of a polygon is 24 units.
In this question, we have been given the coordinates of a polygon.
we need to find the perimeter of a polygon.
Let A= (-3,2), B = (2,2), C = (2,-4), D = (-1,-4), E = (-1,-2), F = (-3,-2)
First we find the length of each side of a polygon.
|AB| = √5² + 0²
|AB| = 5
|BC| = √0² + (-6)²
|BC| = 6
|CD| = √(-3)²+0²
|CD| = 3
|DE| = √0²+2²
|DE| = 2
|EF| = √(-2)²+0²
|EF| = 2
|FA| = √0²+4²
|FA| = 4
The perimeter of a polygon would be,
P = AB + BC + CD + DE + EF + FA
P = 5 + 6 + 3 + 2 + 2 + 4
P = 24 units
Therefore, the perimeter of a polygon is 24 units.
Learn more about the perimeter of a polygon here:
https://brainly.com/question/15387363
#SPJ1
2 is subtracted from the product of 5 and a number
Answer:
2 - 5 = -3.
Step-by-step explanation:
I subtracted two from five and got negative three lol
Ari has a total of 22 coins consisting of pennies and nickels. The total value of the coins is $0.54 Which equation can be used to find the number of pennies Ari has?
HELP ASAP
Find E, the midpoint of RD if R (4,-5) and D (2,3)
Answer:
(3, - 1 )
Step-by-step explanation:
given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
here (x₁, y₁ ) = R (4, - 5 ) and (x₂, y₂ ) = D (2, 3 )
midpoint = ( [tex]\frac{4+2}{2}[/tex] , [tex]\frac{-5+3}{2}[/tex] ) = ( [tex]\frac{6}{2}[/tex] , [tex]\frac{-2}{2}[/tex] ) = (3, - 1 )
Write the equation of the line in fully simplified slope-intercept form.
The equation of the line in fully simplified slope-intercept form is y = -x - 8.
How to find the equation of the line?It is assumed that a line in the graph will pass through some points on the x and y-axes.
We must determine the line's fully simplified intercept.
we know the standard form of a line that is
y = mx + b
here, m is a slope and b is the constant
On the graph, there are the y-intercept (0,-8) and the x-intercept (-8,0).
The slope of the line passing through these points is:
[tex]slope = \frac{y2 - y1}{x2 - x1} \\ [/tex]
[tex]slope = \frac{ 8 - 0}{ 0 - 8} [/tex]
slope = 8/(-8)
slope = -1
then find the value of b
if x = 0 y = -8 then
y = mx +b
-8 = -1(0) + b
-8 = b
the value of b is -8
After inserting the values for m and c, the line's equation will be.
y = - x - 8
Hence y = -x - 8 is the equation of the line in fully simplified slope-intercept form.
Learn more about general equation of line from here:
https://brainly.com/question/4227212
#SPJ9
This scale drawing of a rectangular rug
has dimensions 8 inches by 5 inches.
The actual rug is measure with a scale
factor of 4:1.
8 in
5 in
x ft
y ft.
S Enter the value of x and y for the actual rug width.
X =
y =
x would be 20 inches and y would be 32 inches.
For each of the following functions, evaluate: f(-4), f(-2), f(0), f(2), and f(4)
17.)f(x)=3x-7
19.) ƒ(x)=−2x²+5x+1
PLEASE HELPP
Subject: Trigonometry
Answer:
51.3
Step-by-step explanation:
[tex]\tan y=10/8 \\ \\ y=\arctan(10/8) \\ \\ \approx 51.3^{\circ}[/tex]
Answer:
45
Step-by-step explanation:
In what situation would a geometric model be better than a binomial model
Answer:
a geometric model shows the lay out of places like earth it tells us where our best water sources are.
Melody works at The Accokeek Ice Cream Hut. She earns $14 per hour. This week,
her boss had to cut her schedule, so she only worked 80% of the number of hours
she normally works. However, to compensate her, she was given a bonus of $30.
At the end of the week, Melody had earned $198.
The number of hours Melody worked this week was 15.
The hourly earnings of Melody at the Accokeek Ice Cream Hut are $14.Let the number of working hours in a week be "x".The number of hours Melody actually worked this week is 80 percent of "x".The number of hours Melody actually worked this week is 0.8x.The amount of compensation Melody received is $30.The total amount Melody earned at the end of the week was $198.The amount Melody should get at the end of the week is the sum of the compensation amount and the earnings for the number of hours she worked.198 = 30 + 14*0.8x168 = 11.2xx = 15Thus, Melody worked for 15 hours.To learn more about percent, visit :
https://brainly.com/question/14699403
#SPJ1
Divide £800 in the ratio 6 : 1 : 3
Answer:
6: 480
1: 80
3: 240
I hope this is what you meant, and I hope I was able to help you!
In the rectangle shown below, the length is longer than its width w. List all the possible
whole number dimensions for the rectangle, and name the dimensions that give the smallest
perimeter.
Area is 40 m2
Answer: w can be 1,2,4,5
Step-by-step explanation:
Let's recap the formula of Area:
Area = width x length = w x l
Area = 40 = w x l
The definition of a whole number: is a number without fractions; an integer such as 0, 1, 2, 3, 4, 5, 6,...
Let's start with 0. 0 times anything is equal to 0, so we cannot make 40 out of zero. Cross this out.
Next, let's try with 1:
a. 1x40 = 40
Then, applying the same concept to the rest we have these multiplications:
b. 2x20 = 40
c. 4x10 = 40
d. 5x8 = 40
e. 8x5 = 40
f. 10x4 = 40
g. 20x2 = 40
h. 40x1 = 40
Let's recap the formula of Perimeter:
P = 2 x (w + l)
So, we have the calculated perimeters (according to the above finding):
a. P= 2x(1+40)=82
b. P= 2x(2+20)=44
c. P= 2x(4+10)=28
d. P= 2x(5+8)=26
The below answers do not fit the [width < length]
e. P= 2x(8+5)=26 [not an answer]
f. P= 2x(10+4)=28 [not an answer]
g. P= 2x(20+2)=44 [not an answer]
h. P= 2x(40+1)=82 [not an answer]
Ax-5=19
I need help solving this problem?
Find the area of the figure. Write the answer is radical form
The Area of the given figure in the radical form is [tex]96\sqrt[4]{x^{9} }[/tex] .
Area of a rectangle can be found by using the formula
Area = length*breadth
in the given question
length of the rectangle
= [tex](4x)^{\frac{3}{2} }[/tex]
On simplifying we get
[tex](4x)^{\frac{3}{2} }=(2^{2} x)^{\frac{3}{2} }\\ \\ =2^{2*\frac{3}{2} } *x^{\frac{3}{2} } }[/tex] ( as (a.b)ⁿ=aⁿ.bⁿ )
[tex]=2^{3} *x^{\frac{3}{2} } }\\ \\ =8*x^{\frac{3}{2} } }[/tex]
breadth of the rectangle = [tex]12x^{\frac{3}{4} }[/tex]
The required area = length * breadth
Substituting the values we get
Area = [tex]8*x^{\frac{3}{2} } }[/tex] * [tex]12x^{\frac{3}{4} }[/tex]
=96*[tex]x^{\frac{3}{2}+\frac{3}{4} }[/tex]
taking LCM of exponents as 4 and solving further we get ,
=[tex]96x^{\frac{9}{4} }[/tex]
Expressing in radical form we get ,
Area = [tex]96\sqrt[4]{x^{9} }[/tex]
Therefore , the Area of the figure in the radical form is [tex]96\sqrt[4]{x^{9} }[/tex] .
Learn more about Area here https://brainly.com/question/23718948
#SPJ1
MARKING BRAINLEIST IF CORRECT
Answer choices:
1. Alternate Interior Angles Theorem; 2 Definition of Congruence
1. Alternate Exterior Angles Theorem; 2. Substitution Property
1. Definition of Congruence; 2. Alternate Interior Angles Theorem
1. Substitution Property; 2. Alternate Exterior Angles Theorem
Answer:
I think it's B (or A?)
Step-by-step explanation:
For alternate interior, they are alternate interior angles
Then for 2, they are equal and congruent, but they are SUBSTITITUING the angle numbers to the equation.
pls brainliest if I'm right :D
miriam reduced a square photo by cutting 3 inches away from the length and the width so it will fit in her photo album. the area of the reduced photo is 64 square inches. in the equation (x – 3)2
Original sides of the square before reducing was 11 inches.
What is a quadratic equation ?A quadratic equation has highest degree of two and it has 2 roots.
According to the given question Miriam reduced a square photo by cutting 3 inches away from the length and the width so it will fit in her photo album.
Assuming sides of the square to be x inches.
∴ From the given data
( x - 3 )( x - 3 ) = 64 ( area of a square is product any two sides )
x² - 6x + 9 = 64
x² - 6x - 55 = 0
x² - 11x + 5x - 55 = 0
x( x - 11 ) + 5( x-11 ) = 0
(x - 11 )( x + 5) = 0
∴ x = 11 or x = -5. ( length of something can not be negative )
So, the original length of the sides of the square is 11 inches.
Original area is
= (11×11)
= 121 sq inches.
learn more about quadratic equations here :
https://brainly.com/question/17177510
#SPJ4
21. a. What four factors were used to create this Product Game board?
9 15 18
21 ? 30 35 Factors:
36 42 49
b. What product is missing from the grid?
What is the missing number from the grip I need help
The four factors were used to create this Product Game board are {2, 3, 5, 7} and the product missing from the grid is 25
To see what are factors are used in the given list, we just need to write each of the numbers, as a product of prime factors such as 2, 3, 5, 7 .
9 = 3* 3
15 = 3 *5
18 = 3 *2*3
21 = 7*3
30 = 5*3*2
35 = 7*5
36 = 3*3*2*2
42 = 2*3*7
49 = 7*7
As we can see, the 4 factors used to product the numbers in the given list are {2, 3, 5, 7}
for the second part that is to find the missing number between 21 and thirty we first need to write all the numbers between 21 and thirty and check which number is having the only factors of at least one of (2,3,5,7)
the numbers are 22 , 23 ,24, 25 ,26 ,27 ,28, 29
After checking the missing number is 25(5*5) because there has to be at least 4 products who have same factor and 5 is the factor who has appeared only three times
To know more about Products, here:
https://brainly.com/question/21254539
SPJ9#
10. Solve the equation by completing the square. Round to the nearest hundredth if necessary. x²-3x - 3=0
-3.75, 6.75
2.72,0.28
0.87, 2.29
3.79,-0.79
The roots of the equation [tex]x^{2}[/tex]-3x-3=0 by completing the square method are 3.79 and -0.79.
Given that the equation is [tex]x^{2}[/tex]-3x-3=0.
We are required to find the roots of the equation by completing the square method.
Equation is basically the relationship between two or more variables that are expressed in equal to form. It may be linear equation, quadratic equation,cubic equation and many more depending on the power of the variables that are present in the equation.
The equation is [tex]x^{2}[/tex]-3x-3=0.
[tex]x^{2}[/tex]-3x=3
[tex](x+3/2)^{2}[/tex]=-(c-[tex]b^{2}[/tex]/4)
So,
[tex](x-3/2)^{2}[/tex]=-[-3-[tex](-3)^{2}[/tex]/4]
[tex](x-3/2)^{2}[/tex]=-[-3-9/4]
[tex](x-3/2)^{2}[/tex]=21/4
x-3/2=±[tex]\sqrt{21}[/tex]/2
x=([tex]\sqrt{21}[/tex]+3)/2,(-[tex]\sqrt{21}[/tex]+3)/2
x=(4.58+3)/2, (-4.58+3)/2
x=7.58/2, -1.58/2
x=3.79,-0.79
Hence the roots of the equation [tex]x^{2}[/tex]-3x-3=0 by completing the square method are 3.79 and -0.79.
Learn more about equation at https://brainly.com/question/2972832
#SPJ9
Answer:
by completing the square method the answer is 3.79 and -0.79.
Step-by-step explanation:
above
1 Compare the coordinates of the corresponding vertices of ALMN and AL'M'N' in
the Example. Describe the effect of the 270° counterclockwise rotation on the
vertices. What other rotation of ALMN would have the same effect?
CAN SOMEONE PLS HELP ME W THIS ONE PROBLEM ASAPPPP I RLLY NEED HELP
segment XY has a midpoint at M. The coordinates of X are (3,4) and the coordinates of M are (5,0). what are the coordinates of endpoint y?
endpoint y would be
(7,-4)
because when you graph all 3 points
(7,-4) adds nicely to the line that the other 2 make
They are 9 guitars sold in a week with a total of 3,611 dollars. Electrics are 479 each and acustics are 339 each. How many of each guitars were sold"?
Rationalize the denominator
-x5
√12x - 9
Answer:
Step-by-step explanation:
-2x^6-9
please give me the brainliest
What is the simple interest paid if $900 principal 6% interest rate for 2 year
Simple Interest is the method of finding the interest amount for a particular principal amount of money at a particular rate of interest.
The simple interest for $900 at an interest rate of 6% is $108.
What is simple interest?Simple Interest is the method of finding the interest amount for a particular principal amount of money at a particular rate of interest.
We have,
Principal = $900
Rate of interest = 6%
Time = 2 years.
Remember that time should always be in years.
The formula for simple interest is given by:
SI = PRT / 100
Where,
P = principal
R = rate of interest
T = Number of years
So,
SI = 900 x 6 x 2 / 100
SI = $108
Thus the simple interest for $900 at an interest rate of 6% is $108.
Learn more about simple interests here:
https://brainly.com/question/15175700
#SPJ1