Jeffrey has a fish tank that holds 8 L of water he already has a tank filled with one liter of water how many more liters of water does free need to complete feel the fish tank
Answer:
7L
Step-by-step explanation:
8-1
Minus 8-1=7
I hope it is the right answer
The sum of all the terms in an infinite geometric sequence is 81 and the sum
of all terms starting from the third is 9. What is the second term in the sequence?
Step (1)
We know that the sum of all the terms in an infinite geometric sequence finding from following equation whenever |q| < 1 .
q = magnitude
[tex]s( \infty ) = \frac{t(1)}{1 - q} \\ [/tex]
So :
[tex]s( \infty ) = \frac{t(1)}{1 - q} \\ [/tex]
[tex]81 = \frac{t(1)}{1 - q} \\ [/tex]
[tex]81(1 - q) = t(1)[/tex]
Remember it I'll use it again.
_________________________________
Step (2)
We know that the sum of the n first terms of a geometric sequence finding from following equation.
[tex]s(n) = \frac{t(1) \times (1 - {q})^{n} }{1 - q} \\ [/tex]
_________________________________
Sum of all terms starting from the third is 9.
So :
[tex]s(2) + s(3 - \infty ) = 81[/tex]
[tex]s(2) + 9 = 81[/tex]
Sides minus 9
[tex]s(2) = 81 - 9[/tex]
[tex]s(2) = 72[/tex]
So :
[tex]t(1) + t(2) = 72[/tex]
[tex]t(1) + t(1) \times q = 72[/tex]
Factoring t(1)
[tex]t(1) \times (1 + q) = 72[/tex]
We have found t(1) = 81 ( 1 - q ) in step (1).
So :
[tex]81(1 - q)(1 + q) = 72[/tex]
Divided sides by 81
[tex](1 - q)(1 + q) = \frac{72}{81} \\ [/tex]
[tex](1 - q)( 1 + q) = \frac{8}{9} \\ [/tex]
[tex]1 - {q}^{2} = \frac{8}{9} \\ [/tex]
Subtract sides minus -1
[tex] - {q}^{2} = \frac{8}{9} - 1 \\ [/tex]
[tex] - {q}^{2} = \frac{8}{9} - \frac{9}{9} \\ [/tex]
[tex] - {q}^{2} = - \frac{1}{9} \\ [/tex]
Negatives simplifies
[tex] {q}^{2} = \frac{1}{9} \\ [/tex]
Radical sides
[tex]q = + \frac{1}{3} \\ q = - \frac{1}{3} [/tex]
_________________________________
Step (4)
If q = 1/3 :
[tex]81(1 - q) = t(1)[/tex]
[tex]81(1 - \frac{1}{3}) = t(1) \\ [/tex]
[tex]81( \frac{2}{3}) = t(1) \\ [/tex]
[tex]t(1) = 27 \times 2[/tex]
[tex]t(1) = 54[/tex]
So :
[tex]t(2) = t(1) \times q[/tex]
[tex]t(2) = 54 \times \frac{1}{3} \\ [/tex]
[tex]t(2) = 18[/tex]
°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°
If q = - 1/3 :
[tex]81(1 - q) = t(1)[/tex]
[tex]81(1 - ( - \frac{1}{3})) = t(1) \\ [/tex]
[tex]81(1 + \frac{1}{3}) = t(1) \\ [/tex]
[tex]81( \frac{4}{3}) = t(1) \\ [/tex]
[tex]t(1) = 27 \times 4[/tex]
[tex]t(1) = 108[/tex]
So :
[tex]t(2) = t(1) \times q[/tex]
[tex]t(2) = 108 \times - \frac{1}{3} \\ [/tex]
[tex]t(2) = - 36[/tex]
_________________________________
And we're done.
Thanks for watching buddy good luck.
♥️♥️♥️♥️♥️
How is each one determined?
Answer:
I don't know-how to answer that
Farmland A farmer has a rectangular plot of land shaped like the figure in the graph. There is another identical plot of land 100 yards east and 120 yards north of the original plot. Graph both plots of land. Then find the combined area of the two plots of land
The graph of both plots would be the one graph in option C.
Combined area = 2(area of one rectangular plot) = 720 sq. yds.
What is the Area of a Rectangular Shape?Area of a rectangular shape = length × width
From the graph given, 1 unit represents 20 yards. Therefore:
100 yards east of the original plot is going to be 5 units to the left on the x-axis.120 yards north of the original plot would be 6 units upwards on the y-axis.Therefore, the graph of both plots would be the one given in option C.
The plot is rectangular in shape having 60 yards × 60 yards. Therefore:
Area of 1 plot = length × width = 60 × 60 = 360 square yards.
Combined area = 2(area of one rectangular plot) = 2(360) = 720 sq. yds.
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14:56 as a simplified ratio
Answer:
1:4
Step-by-step explanation:
To represent 14:56 as a simplified ratio, we need to reduce it by finding the GCF (greatest common factor) and dividing it by both terms.
The GCF of 14 & 56 is 14.
14 / 14 = 1
56 / 14 = 4
Thus we are left with our new simplified ratio, 1:4.
x equals -4 Y X + 5y equals to
Step-by-step explanation:
use -4y for x in the second equation
-4 y + 5 y = 2
so
y = 2
then x = -4(2) = -8
(-8 , 2)
Hope it helps you
:DD
14 f ( x ) = √ 7 + x range
[tex]f(x) = \sqrt{7 + x} [/tex]
We know that anything underneath a square has to be positive. so accordingly[tex]7 + x \geqslant 0[/tex]
[tex]x \geqslant - 7[/tex]
[tex]domain \: - 7 \leqslant x \leqslant \infty [/tex]
The answer to any value of x that that you plug, between -7 & ∞ will be between 0 & infinity.[tex]range \: \: 0 \leqslant f(x) \leqslant \infty [/tex]
solve -36 4/9 - (-10 2/9) - (18 2/9)
Answer:
=−148
3
(Decimal: -49.333333)
Step-by-step explanation:
−364
9
−(
−102
9
)−
182
9
A US nickel has a mass of 5.00 g a US penny has a mass of 2.50 g what is the mass in kilograms of the coins in the
bag contending 186 nickels in 72 pennys
Answer:
1110 g
Step-by-step explanation:
Here is the fastest way to solve this problem: (5 x 186) + (2.5 x 72)
However, if you want a step-by-step explanation, here it is:
The total mass of the coins in the bag is the mass of the nickels plus the mass of the pennies.
Let's start by finding the mass of the nickels in the bag.
We know that one nickel has a mass of 5 g, and that there are 186 nickels. So, the total mass of all the nickels in the bag will be 186 x 5 = 930 g.
Now, let's find the mass of the pennies in the bag.
We know that one penny has a mass of 2.5 g, and that there are 72 pennies in the bag. So, the total mass of all the pennies in the bag will be 2.5 x 72 = 180.
We now add these two masses (930 + 180) to get our final answer, 1110 g.
You go to ice cream place for dessert one day. You can get vanilla, chocolate, or twist ice cream. You have a choice of rainbow sprinkles, chocolate sprinkles, or no sprinkles. You can get your ice cream in a cup or a cone and they each come in small, medium m, and large sizes. How many different combinations are there in all?
What are the x- and y-intercepts of the line?
2x – 3y = –12
x-intercept 6, y-intercept –4
x-intercept –4, y-intercept 6
x-intercept –6, y-intercept 4
x-intercept 4, y-intercept –6
Answer:
3rd option
Step-by-step explanation:
to find the x- intercept let y = 0 in the equation and solve for x
2x - 3(0) = - 12
2x - 0 = - 12
2x = - 12 ( divide both sides by 2 )
x = - 6 ← x- intercept
To find the y- intercept let x = 0 in the equation and solve for y
2(0) - 3y = - 12
0 - 3y = - 12
- 3y = - 12 ( divide both sides by - 3 )
y = 4 ← y- intercept
I’ve been stuck on this question for a while can someone help please
I’m asking a lot of questions sorry anyone???
Answer:
For number question #8 its 8/3
Step-by-step explanation:
One way i do is multiply the denominator by the whole number and then add the numerator . For example 2 2/3
2x3=6 6+2=8
Do NOT change the numerator, it stays the same.
Which statement is not true about the data shown by the box plot below?
answer:
a is not true but C and b is true
1) Find the general solution to the following differential equation x^3•y’- y = 0
Answer:
y(x) = c_1 e^(-1/(2 x^2))
Step-by-step explanation:
Solve the separable equation x^3 (dy(x))/(dx) - y(x) = 0:
Solve for (dy(x))/(dx):
(dy(x))/(dx) = y(x)/x^3
Divide both sides by y(x):
((dy(x))/(dx))/y(x) = 1/x^3
Integrate both sides with respect to x:
integral((dy(x))/(dx))/y(x) dx = integral1/x^3 dx
Evaluate the integrals:
log(y(x)) = -1/(2 x^2) + c_1, where c_1 is an arbitrary constant.
Solve for y(x):
y(x) = e^(-1/(2 x^2) + c_1)
Simplify the arbitrary constants:
Answer: y(x) = c_1 e^(-1/(2 x^2))
∠A and ∠B are supplementary. m∠A = (6x + 5), m∠B = (2x + 15). Find the measure of each angle.
Answer:
125 and 55
Step-by-step explanation:
180=8x+20
160=8x
x=20
6(20)+5 2(20)+15=
120+5=125 degrees 40+15=55 degrees
What is the slope of a line that is perpendicular to the
line y = -1/2X + 5?
Answer:
the slope is −12
Step-by-step explanation:
The equation of a perpendicular line to y=−x2+5 y = - x 2 + 5 must have a slope that is the negative reciprocal of the original slope.
Hope it helps!!!Brainliest pls!!!-1/2
That would be the answer
First, rewrite 5/7 and 8/11 so that they have a common denominator.
common denominator = 7x11 = 77
5/7 = (5x11) / (7x11) = 55/77
and
8/11 = (8x7) / (11x7) = 56/77
5/7 and 8/11 can be rewritten as 55/77 and 56/77, respectively, so that they have a common denominator of 77.
What is a fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
To rewrite 5/7 and 8/11 with a common denominator:
We can find the least common multiple (LCM) of the denominators 7 and 11, which is 77.
Then, we can multiply each fraction by the appropriate form of 1 so that the denominators are equal to 77.
Here are the steps:
5/7 = (5/7) x (11/11) = 55/77 (multiply the numerator and denominator of the first fraction by 11)
8/11 = (8/11) x (7/7) = 56/77 (multiply the numerator and denominator of the second fraction by 7)
Therefore, 55/77 and 56/77 are the required fractions.
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please help please help
Answer:
6 quarts because 2/3 of 9 is 6 :)
The container holds 9 quarts and she wants only 2/3 of the way. 2/3 of the way is the same thing as 2/3 of 9.
[tex]\frac{2}{3} *9=6[/tex]
Thus Lauren needs to fill 6 quarts of the 9 quarts to get to the 2/3 of the way.
Hope that helps!
Solve for x in the proportion below be sure to show work 5/x=25/6
Answer:
I think it is x is equals to 5/6.
Step-by-step explanation:
5/x = 25/6
x/5 * 5/x = 25/6 * x/5
x = 5/6
▪ Answer:
x = 5/6
▪ Step-by-step explanation:
Hi there !
5/x = 25/6
x = 5×6/25
x = 30/25
simplist 5
x = 6/5
Good luck !
Using the Pythagorean Theorem:
Mary drove 60 miles east and then 20 miles north. How many miles would
Mary
have driven if she could have gone directly from her starting point to her ending
point? (Use a calculator to find the square root, and round the answer to the nearest
tenth.)
She would have driven
miles.
Answer:
60
Step-by-step explanation:
east and north are two axis that are perpendicular to each other, so if we use Pythagorean rule, sqr60^2+20^2=20sqr10, approximately 63.24555
Choose all the constant terms in the expression. 12+15x-16-4x-10
The constant terms are 12, -16, -10.
Look at the attached image for an example of how to identify constants!
Hope that helped!
Answer:
[tex]\huge\boxed{\sf{12, -16, -10}}[/tex]
Step-by-step explanation:
Hello.
Please remember that a constant is a number without any variables next to it.
Let's search for constants in this expression.
The first term is 12. It has no variables, thus, it's a constant.
The second term is 15x. It does have a variable, thus, it's not a constant.
The third term is -16. It has no variables, thus, it's also a constant.
The 4th term is -4x (not a constant)
The last term is -10 (a constant)
I hope it helps & have an outstanding day.
[tex]\boxed{imperturbability}[/tex]
R=6
Find The Area Of A Circle
Answer:
36π
Step-by-step explanation:
What improper fraction equal to the mix number 4 7/9?
Answer:
43/9
Step-by-step explanation:
Step 1
Multiply the denominator by the whole number
9 × 4 = 36
Step 2
Add the answer from Step 1 to the numerator
36 + 7 = 43
Step 3
Write answer from Step 2 over the denominator
43/9
=439
A plane travels a distance of 5,000 km in a time of 5.6 hours.
What is its average speed rounded to the nearest whole number?
Super Painters charges $1.00 per square foot
plus an additional fee of $25.00 to paint a
living room. If x represents the area of the
walls of Francesca's living room, in square
feet, and y represents the cost, in dollars,
which graph best represents the cost of
painting her living room?
You circled b and i would agree. Because Francesca is doing a living room, it would natuarly start at $25. So it cant be c. And Because x represents the walls, the graph would be a possitive corrolotion so i would say it is b
The graph b shows the adequate information for painting cost of living room. Option b is correct.
Graph that shows adequate information for cost of painting for living room to be determine.
What is graph?The graph is a demonstration of curves which gives the relationship between x and y axis.
Here, equation for the painting of living room can be given as y = 1x+25.
This relation ship clearly seen in graph b.
Thus, the graph b shows the adequate information for painting cost of living room.
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Between 0 and 1
Between 2 and 3
Between 5 and 6
Between 7 and 8
Please help me xx this is what I really need to finish
Answer:
bjc hnfj yn yt NV ubf. giving! y NV,
Answer:
x= 45°
x+10=55°
2x-10=80°
Step-by-step explanation:
According to ASP,
x+x+10+2x-10=180°
4x=180°
Therefore, x=180/4
=45°
x+10=45+10
=55°
2x-10=90-10
=80°
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The angles opposite the congruent sides of an isosceles triangle are congruent. Find the value of x in the triangle. Show all your work.
The figure shows a triangle with 2 congruent sides. The angle between the congruent sides measures x degrees and a different angle measures 70 degrees.
Answer:
40
Step-by-step explanation:
Angles opposite congruent sides in a triangle are congruent, so the other base angle is also 70 degrees.
This means that the interior angles are 70, 70, and x
Since the sum of the measures of the angles of a triangle is 180 degrees,
70+70+x=180
140+x=180
x=40
A running shoe store mounts a new promotional campaign. Purchasers of new shoes may, if dissatisfied for any reason, return them within 7 days of purchase and receive a full refund. The cost to the dealer of such a refund is $105. The dealer estimates that with an 11% probability each purchaser, for whatever reason, will return their pair of shoes and obtain refunds. Suppose that 120 pairs of shoes are purchased during the campaign period. Clearly the exact number of purchasers who return their product is unknown. Answer the following questions:
a. Describe the probability distribution of the number of pairs of shoes that will be returned for refunds.
b. What is the mean and standard deviation of the number of pairs of shoes that will be returned for refunds.
c. What is the mean and standard deviation of the total refund costs that will accrue as a result of these refunds.
Answer:
a
[tex]P(K = k ) = \ ^nC_x * p^k * (1-p)^{n-k}[/tex]
Here k is the random number of number of pairs of shoes that will be returned for refund, which can be k = 0,1 ,2,3,4 ..., 120
b
The mean is [tex]E(K) = np = 13.2[/tex]
The standard deviation is [tex]\sigma = 3.43[/tex]
c
The mean is [tex]E(C) = E(105 K) = 1386[/tex]
The standard deviation is [tex]\sigma = 381.48 [/tex]
Step-by-step explanation:
From the question we are told that
The cost to dealer for each refund is [tex]C = \$105[/tex]
The probability that a shoe will refunded is [tex]P(x) = 0.11[/tex]
The number of shoes purchased is n = 120 pairs
Generally the probability distribution of the number of pairs of shoes that will be returned for refunds is
[tex]P(K = k ) = \ ^nC_x * p^k * (1-p)^{n-k}[/tex]
Here k is the random number of number of pairs of shoes that will be returned for refund, which can be k = 0,1 ,2,3,4 ..., 120
Generally the mean is mathematically represented as
[tex]E(K) = np = 120 * 0.11[/tex]
=> [tex]E(K) = np = 13.2[/tex]
Generally the standard deviation is mathematically represented as
[tex]\sigma = \sqrt{ n* p (1-p)}[/tex]
=> [tex]\sigma = \sqrt{ 120* 0.11 (1-0.11)}[/tex]
=> [tex]\sigma = 3.43[/tex]
Generally the total refund cost is mathematically represented as
[tex]C = 105 K[/tex]
Here K denotes the number of shoes returned
Generally the mean of the total refund cost is mathematically represented as
[tex]E(C) = E(105 K) = 105 E(K)[/tex]
=> [tex]E(C) = E(105 K) = 105 * 13.2[/tex]
=> [tex]E(C) = E(105 K) = 1386[/tex]
Generally the variance of the total refund cost is mathematically represented as
[tex]Var(K) = 105^2 * E(K)[/tex]
=> [tex]Var(K) = 105^2 * 13.2[/tex]
=> [tex]Var(K) = 145530[/tex]
=> [tex]\sigma = \sqrt{145530 }[/tex]
=> [tex]\sigma = 381.48 [/tex]