Answer:
2097150
Step-by-step explanation:
GIVEN :-
First term of G.P. = 6Forth term of G.P. = 384TO FIND :-
Sum of first 10 terms of the G.P.CONCEPT TO BE USED IN THIS QUESTION :-
Geometric Progression :-
It's a sequence in which the successive terms have same ratio.General form of a G.P. ⇒ a , ar , ar² , ar³ , ....... [where a = first term ; r = common ratio between successive terms]Sum of 'n' terms of a G.P. ⇒ [tex]\frac{a(r^n - 1)}{r-1}[/tex].[NOTE :- [tex]\frac{a(1-r^n)}{1-r}[/tex] can also be the formula for "Sum of n terms of G.P." because if you put 'r' there (assuming r > 0) you'll get negative value in both the numerator & denominator from which the negative sign will get cancelled from the numerator & denominator. YOU'LL BE GETTING THE SAME VALUE FROM BOTH THE FORMULAES.]
SOLUTION :-
Let the first term of the G.P. given in the question be 'a' and the common ratio between successive terms be 'r'.
⇒ a = 6
It's given that forth term is 384. So from "General form of G.P." , it can be stated that :-
[tex]=> ar^3 = 384[/tex]
[tex]=> 6r^3 = 384[/tex]
Divide both the sides by 6.
[tex]=> \frac{6r^3}{6} = \frac{384}{6}[/tex]
[tex]=> r^3 = 64[/tex]
[tex]=> r = \sqrt[3]{64} = 4[/tex]
Sum of first 10 terms [tex]= \frac{6(4^{10}-1)}{4 - 1}[/tex]
[tex]= \frac{6(1048576 - 1)}{3}[/tex]
[tex]= 2 \times 1048575[/tex]
[tex]= 2097150[/tex]
f(x) = x ^ 2 + 1
f(3)
Which are perfect squares? Check all that apply.
72
36
8
16
81
64
48
72,36,8,16,64,48
Step-by-step explanation:
these are right answers am'l right??
Answer:
36, 16, 81, and 64 are all of your perfect squares.
Step-by-step explanation:
Had the question got it right :)
help if cool | will give brainliest
Step-by-step explanation:
distance walked by him = 1/ 3 miles
time taken in doing so = 3/ 4 hrs.
[tex]speed \: acquired \: by \: him \: = \frac{distance}{time} [/tex]
[tex] = \frac{ \frac{1}{3} }{ \frac{3}{4} } \\ = \frac{ 1}{3} \times \frac{4}{3} \\ = \frac{4}{9} \: miles \: hr^{ - 1} [/tex]
Answer:
4/9 miles an hour
Step-by-step explanation:
You have to do 1/3 ÷ 3/4 = 4/9
HELP FAST! well give Brainliest
Mark is buying wings and hot dogs for a party. One package of wings (2) costs $5 and hot dogs (y) costs $3 per pound. He must spend less than $40. Write an inequality to represent the cost of Mark's food for the party.
Answer:
2(5)+3y<40
yes that what I know
If U = {1, 3, 5, 7, 9, 11, 13}, then which of the following are subsets of U.
A = {0}
B = {2, 4}
C = {1, 9, 5, 13}
D = {2, 3, 4, 5}
Answer:
C
Step-by-step explanation:
It is C because members in the set C can be found in the universal set (U)
What is the length of the missing side of the larger triangle?
Answer:
B
Step-by-step explanation:
Since the triangles are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{?}{6}[/tex] = [tex]\frac{18}{12}[/tex] ( cross- multiply )
12 ? = 108 ( divide both sides by 12 )
? = 9 → B
solve for q tysm:)))
Solve for q
-----------------
[tex](8q-5)^o+81=180^o[/tex]
[tex]8q-5+81=180[/tex]
[tex]8q+76=180[/tex]
[tex]8q=180-76[/tex]
[tex]8y=104[/tex]
[tex]q=13[/tex]
---------------
Answer[tex]q=13[/tex]-----------------------hope it helps...have a great day!!calcula la longitud de la variable "x"
Answer:
La longitud de [tex]x[/tex] es [tex]5\sqrt{2}[/tex] unidades.
Step-by-step explanation:
La figura es un cuadrado atravesado por una diagonal, significando que existen dos triángulos rectángulos, cuyos ángulos interiores son 45°, 45° y 90°, respectivamente. Por Geometría Euclideana, tenemos que la longitud de la hipotenusa es igual a [tex]\sqrt{2}[/tex] veces la longitud de cualquiera de sus catetos:
[tex]x = \frac{10}{\sqrt{2}}[/tex]
[tex]x = 5\sqrt{2}[/tex]
La longitud de [tex]x[/tex] es [tex]5\sqrt{2}[/tex] unidades.
Harold, the handyman, builds two similar sheds for a farm. The smaller shed is 6 feet tall and weighs 500 pounds. If it takes three times as much paint to cover the larger shed, approximately how tall is the larger shed and approximately how much does it weigh?
Answer:
18 ft
1500 pounds
Step-by-step explanation:
6 x 3 = 1 8
500 x 3 = 1500
Evaluate the expression when c=8 and d=7.
4d-c
whats the answer?
Answer:
The answer is 20.
Step-by-step explanation:
4(d) - c
4(7) - c
28 - c
28 - 8
20 is the answer.
I hope this helps, have a nice day.
PLEASE I REALLY NEED HELP I ONLY HAVE AN HOUR LEFT TO FIINISH THIS What is the relationship or pattern you see between the month and the daylight hours?
Answer:
The relationship or pattern between the month and the daylight hours is that the winter months tend to have fewer daylight hours while the summer months tend to have more daylight hours.
I reallllyy neeeeedd helpppp dont be capping put the right answer
I believe it's A, C and D.
Classify the following triangle. Check all that apply
Step-by-step explanation:
it's a right angled triangle
it's also a scalene triangle because not all sides are equal
does 32, 57, 65 form a right triangle?
Answer:
No
Step-by-step explanation:
In order to form a right triangle, you would need one of the angles to be 90 degrees. Plus all the angles don't equal 180 degrees (the angles of a triangle should add up to 180)
[Q] Mike and Jeanie played 38 games of checkers. Mike won 6 more games than Jeanie. To find out how many games Jeanie won a student used this equation.
M + J = 38
In this equation: M = number of games Mike won and J = number of games Jeanie won Which other equation would help the student to solve this problem?
(A) 38 - 6 = J
(B) M - J = 6
(C) 38 + 6 = J
(D) J - M = 6
(E) M + J = 6
Answer:
(B) M - J = 6
Step-by-step explanation:
Here we have the variables:
M = number of games that Mike won.
J = number of games that Jeanie won.
And we know that there is a total of 38 games played, then if a game can not end in a draw, we have the equation:
M + J = 38
Now we want to find the other equation needed to solve this problem:
We also know that Mike won 6 more games than Jeanie, this is written as:
M = J + 6
We can subtract J in both sides to get:
M - J = 6
This is the equation from option B, so we can conclude that the correct option is B.
3) Ming and Amanda are selling pies for a school fundraiser. Customers can buy blueberry pics and lemon meringue pies. Ming sold i blueberry pie and 3 lemon meringue pies for a total of $66. Amanda sold 4 blueberry pies and 6 lemon meringue pies for a total of $150. Find the cost each of one blueberry pie and one lemon meringue pie.
the difference of the place values of the digit 7 in 73,789
Answer:
tens of thousand vs hundred
Step-by-step explanation:
Can someone help me please
Answer:
48
Step-by-step explanation:
1 feet = 12 inches
4 feet = 48 inches
Why?
4 x 12 = 48
How are differences between the sample mean and the population mean explained when the result isn't statistically significant?
Answer and explanation:
The standard error is used to measure the difference between the sample mean and the population mean. It uses standard deviation to measure the level of deviation of the sample mean from the population mean. In other words, the accuracy of the sample mean by way of representing the mean of the population is measured using the standard error. If there is significant difference then standard error is bigger usually non-zero while it is less significant with smaller standard error.
A daycare purchases two type of snacks, granola bars and fruit rolls. One week, they purchase 10 packs of granola bars and 6 packs of fruit rolls
for a total of 152 snacks. The next week, they purchase 7 packs of granola bars and 12 packs of fruit rolls for a total of 200 snacks.
How many snacks are in one pack of granola bars and one pack of fruit rolls?
Answer:
There are 8 granola bars in a pack and 12 fruit rolls in a pack.
Step-by-step explanation:
10x+6y=152
5x+3y=76
7x+12y=200
-20x-12y=-304
-13x=-104
x=8
40+3y=76
3y=36
y=12
An angle measures 52° less than the measure of its supplementary angle. What is the measure of each angle?
Answer:
64º and 116º
Step-by-step explanation:
x + (x - 52) = 1080
2x - 52 = 180
2x = 232
x = 116º
x - 52 = 64º
Pls help with this one question
Answer:
19
Step-by-step explanation:
Cause it’s angle on a straight line which is equals to 180
Which of the following theorems verifies that XYZ - UWV
A. HL
B. AA
C. LL
D. HA
Given:
The figure of two triangle XYZ and UWV.
To find:
The theorem that is used to verify [tex]\Delta XYZ\sim \Delta UWV[/tex].
Solution:
In triangle XYZ,
[tex]m\angle X+m\angle Y+m\angle Z=180^\circ[/tex] (Angle sum property)
[tex]70^\circ+90^\circ+m\angle Z=180^\circ[/tex]
[tex]160^\circ+m\angle Z=180^\circ[/tex]
[tex]m\angle Z=180^\circ-160^\circ[/tex]
[tex]m\angle Z=20^\circ[/tex]
In triangle XYZ and triangle UWV,
[tex]m\angle Y\cong m\angle W[/tex] (Right angles)
[tex]m\angle Z\cong m\angle V[/tex] (Equal measures)
Two angles of one triangle are congruent to corresponding angles of another triangle. So, the triangles are similar by AA property of similarity.
[tex]\Delta XYZ\sim \Delta UWV[/tex] (AA similarity theorem)
Therefore, the correct option is B.
Solve 9x + 3 < 21 please help
Answer:
x<2
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form:
x < 2 x < 2
Interval Notation:
( − ∞, 2)
HELP ME AGAIN PLEASE I BEG
Answer:
Both of your answers are correct
Step-by-step explanation:
Answer:
d
e
Step-by-step explanation:
2x ≤ 5x - 15
step 1 subtract 5x from each side
2x - 5x = -3x
5x - 5x cancels out
we now have -3x ≤ -15
step 2 divide each side by -3
-3x / -3 = x
-15 / -3 = 5
IMPORTANT NOTE ( when you divide by a negative number you must flip the sign )
We would be left with x ≥ 5
now let's Plug in 10
2(10) ≤ 5(10) - 15
2(10) = 20
20 ≤ 5(10) - 15
5(10) = 50
20 ≤ 50 - 15
50 - 15 = 35
20 ≤ 35 ✓
PLEASE HELP ASAP !! DUE TONIGHT
EXPLANATION = BRAINLIEST
Question 6 options:
A sphere with a volume of 1200 cm³ is dilated by a factor of 3/5.
The volume of the dilated image is ___ cubic centimeters.
Express your answer to the nearest whole unit.
Given:
Volume of sphere = 1200 cm³
The sphere is dilated by a factor of [tex]\dfrac{3}{5}[/tex].
To find:
The volume of the dilated image.
Solution:
If two figures are similar then their volumes are proportional to cube of their corresponding sides.
We know that all sphere are similar to each other.
The sphere is dilated by a factor of [tex]\dfrac{3}{5}[/tex]. It means the ratio of new figure to original figure is
Let [tex]V_1[/tex] be the volume of original figure and [tex]V_2[/tex] be the volume of dilated figure.
[tex]\dfrac{V_2}{V_1}=\left(k\right)^3[/tex]
Where, k is the scale factor.
[tex]\dfrac{V_2}{1200}=\left(\dfrac{3}{5}\right)^3[/tex]
[tex]\dfrac{V_2}{1200}=\dfrac{27}{125}[/tex]
Multiply both sides by 1200.
[tex]V_2=\dfrac{27}{125}\times 1200[/tex]
[tex]V_2=259.2[/tex]
[tex]V_2\approx 259[/tex]
Therefore, the volume of the dilated image is 259 cubic centimetres.
Dennis walks his dog 2 times a day. Each walk is 1 mile in length. How
far will he have walked his dog in a week?
PLEASE HELP WILL GIVE brAINLIEST
Santino is renting a canoe from a local shop that charges a $10 fee, plus an hourly rate of $7.50. For how long can Santino rent a canoe if he pays a total of $70?
8. An car can hold 8 1/4 gallons of fuel. It contains 4 5/6 gallons of fuel. How
much more fuel is needed to fill the car?
Answer:
3 5/12
Step-by-step explanation:
Answer:
41/12 gallons
= 3 5/12 gallons
Step-by-step explanation:
Since it can hold 8 1/4 gallons and currently has 4 5/6 gallons, you subtract.
You need to get the common denominator to subtract cleanly so we can turn the fractions into improper fractions.
8 1/4 = 33/4 because 8 is equal to 8 full 4/4ths so multiply 8 by 4 and add 1 for the remaining 1/4.
Then 4 5/6 becomes 29/6 with the same concept earlier.
So we can change the denominator to 12 on both fractions (33/4 and 29/6) so we can subtract.
33/4 becomes 99/12 because they are still equivalent, it's just that you multiplied the top and bottom by the same number.
29/6 becomes 58/12 because we multiplied the fraction by 2/2.
Those two new fractions stated previously are the same as the original because we multiplied them by 1/1, because 3/3 and 2/2 is still equal to 1/1, and the new fractions can be simplified down to the original.
Since we have 99/12 and 58/12, we can subtract cleanly into
99 - 58 = 41
So the answer is 41/12
The ratio of dogs to cats at the animal shelter is 2:5. If there are 35 cats, how many dogs are there?
Answer:
Step-by-step explanation:
there are 18 dogs
Answer:
14
Step-by-step explanation:
So the ratio of dogs (2) to cats (5) is 2:5
How did we go from 5 to 35?
Multiply by 7
So multiply 2 with 7 which is 14
So there are 14 dogs
Hope this helps!