Solution
Here the first term = -2
5th term = -1/8
Now we have to find the common ratio (r)
Fifth term A5 = -1/8
-1/8 =[tex]a_{1} r^{4}[/tex]
Here [tex]a_{1} = -2[/tex]
Plug in [tex]a_{1} = -2[/tex] in the fifth term and find the value of r.
-1/8 = -2[tex]r^{4}[/tex]
[tex]r^{4} = \frac{-1/8}{-2}[/tex]
[tex]r^{4} = \frac{1}{16}[/tex]
Taking 4th root, we get
r = [tex]\frac{1}{2}[/tex]
Now let's find the second term.
[tex]a_{2} =[/tex] first term *r = -2 *1/2 = -1
2nd term = -1
3rd term = second term * 1/2 = -1 * 1/2 = -1/2
4th term = 3rd term *r = -1/2 *1/2 = -1/4
Thank you :)
The 2nd term is -1 , the 3rd term is [tex]\( -\frac{1}{2} \)[/tex], and the 4th term is [tex]\( -\frac{1}{4} \)[/tex].
To find the 2nd, 3rd, and 4th terms of the sequence, we need to determine the common ratio of the sequence since the given terms suggest it is a geometric sequence. A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
Let's denote the first term of the sequence as [tex]\( a_1 \)[/tex] and the common ratio as r. The n-th term of a geometric sequence can be found using the formula:
[tex]\[ a_n = a_1 \cdot r^{(n-1)} \][/tex]
Given:
[tex]\[ a_1 = -2 \] \[ a_5 = -\frac{1}{8} \][/tex]
We can use the fifth term to find the common ratio r by plugging in the values into the formula for the n-th term:
[tex]\[ a_5 = a_1 \cdot r^{(5-1)} \] \[ -\frac{1}{8} = -2 \cdot r^4 \] \[ r^4 = \frac{-2}{-8} \] \[ r^4 = \frac{1}{4} \] \[ r = \pm\sqrt[4]{\frac{1}{4}} \] \[ r = \pm\frac{1}{2} \][/tex]
Since we are dealing with a sequence where the terms are decreasing in absolute value and changing sign (from negative to positive), we choose the positive value for r:
[tex]\[ r = \frac{1}{2} \][/tex]
Now we can find the 2nd, 3rd, and 4th terms:
[tex]\[ a_2 = a_1 \cdot r^{(2-1)} = -2 \cdot \left(\frac{1}{2}\right)^1 = -1 \] \[ a_3 = a_1 \cdot r^{(3-1)} = -2 \cdot \left(\frac{1}{2}\right)^2 = -\frac{1}{2} \] \[ a_4 = a_1 \cdot r^{(4-1)} = -2 \cdot \left(\frac{1}{2}\right)^3 = -\frac{1}{4} \][/tex]
The final answer is:
[tex]\[ a_2 = -1, \quad a_3 = -\frac{1}{2}, \quad a_4 = -\frac{1}{4} \][/tex]
a number d minus 2 is less than -1 ?
d - 2 < -1 is how this inequality would be displayed.
However, we can solve for the value of d by treating this like a standard algebraic equation.
d - 2 < -1
Add 2 to both sides.
d < 1
The value of d is less than 1.
Let me know if you have any other questions.
Answer:
Given phrase,
a number d minus 2 is less than -1
∵ '-' is the sign of minus,
⇒ d minus 2 = d - 2
Also, '<' is the sign of less than,
⇒ d minus 2 is less than -1 = d - 2 < - 1
Hence, the required inequality would be,
[tex]d-2 < -1[/tex]
Now, by further solving,
Add 2 on the both sides of inequality ( additive property of inequality )
[tex]d < -1 + 2\implies d < 1[/tex]
⇒ d ∈ ( -∞, 1 )
How many pints are in 3 gallons?
3 gallons = 24 pints
Hope this helps you!
Always remember you are a Work Of Art!
-Nicole :) <3
What is the prime factorization of 150?
the prime factors for 150 are:
2 x 3 x 5 x 5
In exponential form:
2^1 x 3^1 x 5^2
Hope this helps
Answer:
Step-by-step explanation:the prime factors for 150 are:
2 x 3 x 5 x 5
What is the answer
A.
B.
C.
D.
E.
option A IS correct option.
Decide which of the two given prices is the better deal and why. You can buy shampoo in a 6 ounce bottle for $2.49 or in a 14 ounce bottle for $9.79. What is the cost per ounce for each bottle?
The cost per ounce of the first bottle is $0.415 and the second bottle is $0.699.
The first bottle has the better deal because if you were to have 14 ounces of the first type of shampoo, it would only cost $5.81
Cost per ounce is:
$0.42 per ounce for the 6 ounce bottle $0.70 per ounce for the 14 ounce bottleTo find the cost per ounce for each bottle, use the formula:
= Total cost / number of ounces
6 ounce bottle:
= 2.49 / 6
= $0.42 per ounce
14 ounce bottle:
= 9.79 / 14
= $0.70 per ounce
The 6 ounce bottle is therefore the better deal.
Find out more at https://brainly.com/question/8158263.
How do you turn a percent into a fraction
Step 1: You want to remove the percent sign and then put the number over 100.
Step 2: If the percent is not a whole number then you want to multiply the top and bottom number by 10 but only for every number that comes after the decimal point.
Step 3: Always simplify if possible.
Examples:
43% = [tex]\frac{43}{100}[/tex]
78% = [tex]\frac{78}{100}[/tex] = [tex]\frac{39}{50}[/tex]
0.4% = [tex]\frac{0.4}{100}[/tex] = [tex]\frac{4}{1000}[/tex] = [tex]\frac{1}{250}[/tex]
estimate the product by rounding 5 times 5,503
27,515 is the actual answer.
Estimated, it is about 27,500
Hope I helped!
A gardener transplanted a plant from an indoor pot to an outdoor garden. After 30 days, the plant's height was 18 centimeters. After 90 days, it was 29 centimeters. Write an equation to represent the plants growth where the x is the days and the y is the height of the plant.
Let x is the days and the y is the height of the plant.
Let the change between x and y is linear.
So, the relation between x and y will take the form ⇒ y = ax + b
where a and b are constants.
At x = 30 ⇒ y = 18 ⇒⇒⇒ ∴ 18 = 30 a + b → (1)
At x = 90 ⇒ y = 29 ⇒⇒⇒ ∴ 29 = 90 a + b → (2)
solve (1) and (2) to find a and b
subtract (1) from (2)
∴ 11 = 60 a ⇒⇒⇒ ∴ a = 11/60
substitute at (1) ⇒⇒⇒ ∴ b = 25/2 = 12.5
So, the equation which represents the plants growth is
∴ y = (11/60) x + 12.5
Answer:
Let x is the days and the y is the height of the plant.
Let the change between x and y is linear.
So, the relation between x and y will take the form ⇒ y = ax + b
where a and b are constants.
At x = 30 ⇒ y = 18 ⇒⇒⇒ ∴ 18 = 30 a + b → (1)
At x = 90 ⇒ y = 29 ⇒⇒⇒ ∴ 29 = 90 a + b → (2)
solve (1) and (2) to find a and b
subtract (1) from (2)
∴ 11 = 60 a ⇒⇒⇒ ∴ a = 11/60
substitute at (1) ⇒⇒⇒ ∴ b = 25/2 = 12.5
So, the equation which represents the plants growth is
∴ y = (11/60) x + 12.5
Step-by-step explanation:
4 1/5 divided by 2/3 express your answer as a mixed number in Simplest form
4 (1/5 ) = 21/5
21 / 5 divided by 2 / 3 equals
21 / 5 * 3 / 2 equals 63 / 10 equals
6 (3 / 10)
step by step what is 4 (x - 1) -3 (x + 2)
Answer:
For this expression, you will have to use the distribution property to get your answer.
First, distribute the 4 to the x and -1
[tex]4(x)=4x[/tex]
[tex]4(-1)=-4[/tex]
[tex]4x-4-3(x+2)[/tex]
Now do the same with the -3, x and 2
[tex]-3(x)=-3x[/tex]
[tex]-3(2)=-6[/tex]
[tex]4x-4-3x-6[/tex]
Now combine like terms to get your final answer
[tex]4x-3x=x[/tex]
[tex]-4-6=-10[/tex]
Thus, your solution is: x - 10
Step one: 4(x-1)-3(x+2)=0 (set equal to zero)
Step two: 4x-4-3x-6=0 (multiply numbers on the outside to inside of "( )")
Step three: x-10=0 (combine like terms)
Step four: 0+10=10, x=10 (inverse operation)
Answer: x=10
A bag contains 3 green marbles and 8 white marbles. Suppose a marble is randomly selected what are the odds in favor of picking a white marbles
Total number of marbles : 3 + 8 = 11
8 are white.
Probability of picking a white one is 8/11
Alicia bought 4 T-shirts for $23.00. Using the unit rate, how much would 6 T-shirts cost?
i think that you would just take 23/4=$5.75
so take 6 times 5.75 and you should get $34.5
To answer this question, we first need to determine the unit cost (cost per t-shirt).
Step 1: Find the unit cost
Alicia bought 4 T-shirts for a total of $23.00. To calculate the cost per T-shirt (the unit rate), we need to divide the total cost by the number of T-shirts.
So, $23.00 (total cost) divided by 4 (number of T-shirts) equals $5.75. Thus, the unit cost of one T-shirt is $5.75.
Step 2: Calculate the cost for 6 T-shirts
Now that we know the unit cost, we can find out how much 6 T-shirts will cost. To do this, we multiply the unit cost by the number of T-shirts.
So, $5.75 (cost per T-shirt) times 6 (number of T-shirts) equals $34.50.
Therefore, it would cost $34.50 for 6 T-shirts, given the unit rate.
*WILL GET BRAINLIEST ANSWER* !
-4 = x/9 - 8
-x/9 = 4 - 8
-x/9 = -4
x = 4 * 9
x = 36
a student found the product of 8 x 10 to the 6 power + 5 x 10 to the 9th power to be 4 x 10 to 15 power what is the error
8*10^6+5*10^9 should be
5,008,000,000
Answer:
The error student make is he multiply the terms instead of addition.
Step-by-step explanation:
Given : A student found the product of 8 × 10 to the 6 power + 5 × 10 to the 9th power to be 4 × 10 to 15 power.
To find : What is the error ?
Solution :
8 × 10 to the 6 power - [tex]8\times 10^6[/tex]
5 × 10 to the 9th power - [tex]5\times 10^9[/tex]
4 × 10 to 15 power - [tex]4\times 10^{15}[/tex]
According to student, [tex]8\times 10^6+5\times 10^9=4\times 10^{15}[/tex]
We solve the expression,
[tex]=8\times 10^6+5\times 10^9[/tex]
[tex]=8\times 10^6+5000\times 10^6[/tex]
[tex]=10^6(8+5000)[/tex]
[tex]=5008\times 10^6[/tex]
The error student make is he multiply the terms instead of addition.
Pan Tomaszewski zarabiał 2000 zł, dostał podwyzke i obecnie zarabia 2500 zł. O ile % podwyższono mu pensję?
we are given
Mr. Tomaszewski earned 2,000 zlotys
so, past salary =2000
he got a raise and currently earns 2,500 zlotys
so, present salary =2500
now, we have to find raised amount
we can use formula
raised amount = (present salary) - (past salary)
now, we can plug values
and we get
raised amount = 2500 - 2000
so, we get
raised amount = 500 zlotys........Answer
I'm confused like in #1 the positive is five but what do I put for the negative
You found $5, so it's positive. You don't put anything in the negative, because you aren't losing anything.
What expression is equivalent to 18 1/5 - (-22 2/5) - (-40 1/5)
Complete the proof showing that DE is parallel to AC
Answer: The statement is [tex]\frac{AD}{DB} +1=\frac{CE}{EB}+1[/tex] and the reason is add 1 both sides.
Explanation:
The given equation is [tex]\frac{AD}{DB} =\frac{CE}{EB}[/tex].
We know that according to the addition property the equation x=y and x+c=y+c are equivalent equations, where c is a constant.
So we can add 1 both sides in the given equation.
[tex]\frac{AD}{DB} +1=\frac{CE}{EB}+1[/tex]
Now we can take LCM and we get,
[tex]\frac{AD+DB}{DB} =\frac{CE+EB}{EB}[/tex]
The above step is the third step of the given proof. By follow the given steps we can prove that DE is parallel to AC.
Therefore, the missing step is addition of 1 on both the sides of the given equation.
To prove that DE is parallel to AC, we need to show that the lines DE and AC have the same slope. By rearranging the given equations to isolate the currents I₁, I₂, and I₃, and then setting these expressions equal to each other, we can determine the relationship between the currents and thereby the slopes of DE and AC.
Explanation:To prove that DE is parallel to AC, we need to show that the lines DE and AC have the same slope. The given equations 1₁ - 12 - 13 = 0, I₁ R₁ + I₂ R₂ = V₁, and I₂ R₂ − I₃ (R₃ + R₄) = V₂ can be rearranged to isolate the currents I₁, I₂, and I₃ in terms of voltage and resistance. By setting these expressions equal to each other, we can determine the relationship between the currents and thereby the slopes of DE and AC.
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The figure below shows rectangle ABCD:
The following two-column proof with missing statement proves that the diagonals of the rectangle bisect each other:
Which statement can be used to fill in the blank space?
(A) ∠ABD ≅ ∠DBC
(B) ∠CAD ≅ ∠ACB
(C) ∠BDA ≅ ∠BDC
(D) ∠CAB ≅ ∠ACB
B would be the answer because if you were to search up a picture of alternate interior angles, it would be the same as <CAD and <ACB
Answer:
(B) ∠CAD≅∠ACB
Step-by-step explanation:
Given in the question quadrilateral ABCD is a rectangle and a table of two-column proof with missing statement for proves that the diagonals of the rectangle bisect each other.
If we want to prove that the diagonals bisects to each other, then for this first we will prove that ΔADE≅ΔCBE. But given in the two-column proof
∠ADB≅∠CBE , side BC= side AD . ∠CAD ≅ACD must be necessary for to prove that ΔADE≅ΔCBE (ASA postulate). Hence statement ∠CAD ≅ACD can be used to fill in the blank space.
Find the value of x + y for x = 75.9 and y = 2.65.
Answer:
x + y = 75.9 + 2.65 = 78.55
Step-by-step explanation:
To solve x + y given that x = 75.9 and y = 2.65. We will simply substitute the value of x in the equation with it value which is 75.9 and substitute the value of y in the equation with it value which is 2.65.
Therefore we have x + y to be
x+y
= 75.9 + 2.65
= 78.55
Therefore x + y = 78.55
A plane traveled 1176 miles to Phoenix and back. The trip there was with the wind. It took 14 hours. The trip back was into the wind. The trip back took 28 hours. What is the speed of the plane in still air? What is the speed of the wind?
The plane travels at 60 mph and the wind is blowing at 20 mph.
By setting up and solving a system of equations, we find that the speed of the plane in still air is 63 mph and the speed of the wind is 21 mph.
Explanation:To answer this question, you first need to set up equations to represent the speed of the plane and the speed of the wind. You can denote the speed of the plane in still air as 'p' and the speed of the wind as 'w'. The plane's speed with the wind (going to Phoenix) is represented by p+w and against the wind (coming back) is p-w.
For the trip to Phoenix, you know that distance = speed * time. That gives us the equation 1176 = 14(p+w). After simplification, we obtain the equation, p+w = 84.
For the return flight, our equation is 1176 = 28(p-w). On simplification, we find the equation p-w = 42.
Now you have a system of equations that you can solve: p+w = 84p-w = 42. Solving these equations together, you find that the speed of the plane (p) in still air is 63 mph, and the speed of the wind (w) is 21 mph.
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I need help!
Simplifying radical expressions
1)
[tex] \sqrt[3]{135} [/tex]
2)
[tex] - 5 {}^{3} \sqrt{40} [/tex]
3)
[tex] {2}^{3} \sqrt{5} \times {4}^{3} \sqrt{8} [/tex]
Here is the solution...
1) [tex]\sqrt[3]{135} \\[/tex]
Solution
We can rewrite [tex]\sqrt[3]{135} = \sqrt[3]{27} *\sqrt[3]{5}[/tex]
Here, [tex]\sqrt[3]{27} = 3[/tex]
Now substitute the value, we get
[tex]\sqrt[3]{135} = 3 \sqrt[3]{5}[/tex]
The answer is [tex]3\sqrt[3]{5}[/tex]
2) [tex]-5\sqrt[3]{40}
Solution
[tex]-5\sqrt[3]{40} = -5\sqrt[3]{8} *\sqrt[3]{5}[/tex]
Here [tex]\sqrt[3]{8} = \sqrt[3]{2^{3} } = 2\\[/tex]
Therefore, we get [tex]-5*2\sqrt[3]{5} = -10 \sqrt[3]{5}[/tex]
The answer is-10 \sqrt[3]{5}[/tex]
2) [tex]2\sqrt[3]{5} * 4\sqrt[3]{8}[/tex]
Solution
[tex]\sqrt[3]{8} = 2[/tex]
Now plug in the above in the given expression, we get
[tex]2\sqrt[3]{5} * 4*2 = 16\sqrt[3]{5}[/tex] {2*4*2 = 16]
The answer is [tex]16\sqrt[3]{5}[/tex]
Forty-eight pounds of sand are used to fill 12 bags. Miranda uses the five-step problem-solving plan. After completing the Solve step, how many pounds of sand should she find each bag will hold? Enter you answer in the box.
48 lbs / 12 bags
About 4 pounds of sand per bag
Each bag would hold 4 pounds of sand because 48 / 12 = 4
Twelve less than the quotient of a number and 7 is -2
(x/7)-12=-2
Add 12 to both sides.
x/7=10
Multiply both sides by 7.
x=70
Final answer: 70
hope this helps :)
A coffee bean processor can dry 4,815 pounds of coffee beans in 3 hours. Which unit rate correctly reflects the speed of the processor?
A. 1,926 pounds/hour
B. 2,408 pounds/hour
C. 10.13 pounds/minute
D. 26.75 pounds/minute
Answer:
D. 26.75 pounds/minute
Step-by-step explanation:
For calculate unit rate that reflects the speed of the processor we can use the following equation:
[tex]Speed = \frac{Total Pounds}{RequiredTime}[/tex]
Taking into account that the answers are in pounds per hour and pounds per minute, we re going to calculate the speeds in booth units.
1. Speed in Pounds per hours: Replacing Total Pounds by 4,815 and Required time by 3 hours, we get:
[tex]Speed = \frac{4,815Pounds}{3 Hours}=1,605 Pounds/hour[/tex]
2. Speed in Pounds per minute: Every hour have 60 minutes, the 3 hours have 180 minutes, so replacing Total Pounds by 4,815 and Required time by 180 minutes, we get:
[tex]Speed = \frac{4,815Pounds}{180 Hours}=26.75 Pounds/hour[/tex]
So, chosen the rate that appear in the answers, we can say that the correct answer is D. 26.75 pounds/hours.
what is the approximate distance between the points (-3 -4) and (-8 1) on a coordinate grid
What does -8 1 mean do you mean -8, 1
HELP!!!! An electrician cuts a 26 ft piece of wire into two pieces. One piece is two feet longer than the other. How long are the pieces?
Let 1 piece = X
The 2nd piece would be X + 2 feet
Add:
x +x+2 = 26 feet
2x +2 = 26 feet
Subtract 2 from each side:
2x = 24
Divide both sides by 2:
x = 24 / 2
X = 12
One piece is 12 feet the other piece is 14 feet.
m∠1=45° and m∠3=65°
What is m∠4?
2. In right △ABC with right angle B, m∠A=(3x−8)° and m∠C=(x−2)°.
What is m∠A?
47°
67°
25°
92
The measure of angle ∣4 is 250 degrees. The measure of angle ∣A is 67 degrees.
Explanation:To find the measure of angle ∣4, we can use the fact that angles around a point add up to 360 degrees.
We know that ∣1 is 45 degrees and ∣3 is 65 degrees.
To find ∣4, we can subtract the sum of angles ∣1 and ∣3 from 360 degrees.
Therefore, ∣4 = 360 - (∣1 + ∣3) = 360 - (45 + 65) = 360 - 110 = 250 degrees.
To find the measure of angle ∣A, we can use the fact that the sum of the angles in a triangle is 180 degrees.
We know that ∣B is 90 degrees because it is a right angle.
Therefore, ∣A + ∣B + ∣C = 180 degrees.
Substituting the given values, we get (3x - 8) + 90 + (x - 2) = 180. Simplifying the equation, we get 4x + 80 = 180.
Solving for x, we get x = 25.
Substituting x back into the equation for ∣A, we get ∣A = (3(25) - 8) = 67 degrees.
In 2000 South Dakota had a population of 754,844. The number of people in South Dakota increased by 7.9% in 2010. What is South Dakota's approximate population in 2010?
814,180. Hope I helped. If i didn't I am sos sorry. I would take 7.9 or .079 to 754,844 to get your number.
The approximate population of South Dakota in 2010 after a 7.9% increase from the 2000 population is 814,477 people.
To find the population of South Dakota in 2010, we need to calculate the increased population based on the given percentage increase. We are provided with a population of 754,844 in 2000 and an increase of 7.9% for 2010.
Here is the step-by-step calculation:
Multiply the population of 2000 by the increase percentage (converted to a decimal):
754,844 x 0.079 = 59,632.68.
Add this increase to the 2000 population to get the 2010 population:
754,844 + 59,632.68 = 814,476.68.
Therefore, the approximate population of South Dakota in 2010 is 814,477 people (rounded to the nearest whole number).
i have 500 pennies. If I spend 6 pennies a day until i can no longer do so, at the end of one of these days i will have exactly how many pennies left?
A) 6
B)8
C)10
D)12
A) is 164 because 6 times 6 is 36. 500 - 36 is 164