Answer: Therefore, the correct formula is {a}_{21} = 2000 * 0.5^{20}.
Step-by-step explanation:
A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the previous term by a constant factor called the common ratio. In this case, the common ratio is 0.5, since each term is found by dividing the previous term by 2.
To find the nth term in a geometric sequence, we can use the formula:
a_n = a_1 * r^(n-1)
where a_1 is the first term in the sequence, a_n is the nth term, and r is the common ratio. In our case, the first term is 2000, the nth term is the 21st term, and the common ratio is 0.5. Therefore, the formula we need to use is:
a_21 = 2000 * 0.5^(21-1)
= 2000 * 0.5^20
Therefore, the correct formula is {a}_{21} = 2000 * 0.5^{20}.
True or false. When y is positive, the value of y^2 is always greater than the value of y. Why?
however if you have 0.5^2 which is 0.25 is that not smaller than 0.5
Answer: False
Step-by-step explanation:
If [tex]y=0.5[/tex], then [tex]y^2=0.25[/tex], whereas [tex]y=0.5[/tex].
Therefore, this is a counterexample. Hence, the statement is false.
If a fair die is rolled 4 times, what is the probability, rounded to the nearest thousandth, of getting at least 3 twos?
7.08 is the probability, rounded to the nearest thousandth.
What does the math term "probability" mean?
The simple definition of probability is the likelihood that something will occur.
We can discuss the probabilities of various outcomes to determine how likely they are whenever we are uncertain about the result of an event. Statistics describes the examination of events subject to probability.
Probability of getting a six on rolling a dice = 1/3
Here ,
n = 4 , p = 1/3
So, For P(X <= 1) = P(X = 0) + P(x = 1)
4C0 * (1/6)^0 * (1 - 1/3)^(4-0) + 4C1 * (1/3)^1 * (1-1/3)^(4-1)
= 1 * 1 * (5/3)^4 + 4 * (1/3) *
= 5.75 + 1.33
= 7.08
= 7.08 (nearest thousandth)
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What values of b and c make AGHI AZYX?
G
b
||
CE
48
I
b
H
X
17
Y
8c
Z
The value of b = 17 and c = 6 makes ΔGHI ≅ ΔZYX.
What is congruence?
In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
If and only if two angles have equal measurements, they are said to be congruent. If and only if two segments have equal amounts of each, they are congruent. If and only if all of the corresponding angles and sides are congruent, two triangles are said to be congruent.
Here, we have
Given the sides of both the triangle and
we have to find the value of b and c that makes ΔGHI ≅ ΔZYX
b = 17 and,
48 = 8c
c = 6
Hence, the value of b = 17 and c = 6 that makes ΔGHI ≅ ΔZYX.
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Find the volume of a cube if one face of which has an area of 64 sq.metre
The volume of a cube is 512 m3.
Given,
The one-face area is nothing but the area of a square since it is a cube.
So, (a2) = 64 m2.
Then, a = 8m
Hence, the side of the cube is 8 m.
Formula to calculate the volume of the cube :
The volume of the cube = a3
Volume = (8)3
Volume = 512m3
Therefore, the volume of the cube is 512m3.
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Problem 5 Claire is planning to buy a phone plan for two cell phones that costs $350 for the phones themselves and $65 per month for service. Claire's daughter offers to chip in $125 for her phone and $12 per month for her phone. Write as many expressions as you can to represent the cost to Claire of the two phones and their service for m months.
The cost to Claire for the phones and their service for m months is $350 + $65*m.
The cost to Claire for the two phones is $350, and the cost for the service for m months is $65m, for a total cost of $350 + $65m.
What are expressions to represent the cost to Claire?Generally, Claire will pay a total of $350 + $65*m for the two phones and their service for m months.
The total cost for Claire for the two phones and their service for m months is $350 + $65*m.
The cost of the phones and service for m months to Claire is $350 + $65*m.
Claire will pay $350 for the phones and $65m for the service for a total of $350 + $65m for m months.
The cost to Claire for the two phones and their service for m months is $350 + m*$65.
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help me solve this asap emergency
Answer:
a. -4
b. 1/4
Step-by-step explanation:
a. [tex]\textrm{slope}_{||} = \dfrac{\textrm{rise}}{\textrm{run}} = \dfrac{-4}{1} = -4[/tex]
b. [tex]\textrm{slope}_\perp = \dfrac{-1}{\textrm{slope}_{||}} = \dfrac{-1}{-4} = \dfrac{1}{4}[/tex]
the confidence interval approach is the correct method by which to determine sample size. true false
The confidence interval approach is the correct method by which to determine sample size. True
Confidence Interval:
The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test.
In statistics, confidence is another word for probability. If you create a confidence interval, for instance, with a 95% level of confidence, you can be sure that 95 out of 100 times, the estimate will fall between the upper and lower values indicated by the confidence interval.
Your desired confidence level is usually one minus the alpha (α) value you used in your statistical test:
Confidence level = 1 − α
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A kangaroo hopped directly toward a lake at a constant velocity for 30seconds. In one-third of that time, the kangaroo hopped 60meters. What was the kangaroo's velocity?
Answer: The animal hopped 60 meters in 10 seconds
6 m/s (lol)
Step-by-step explanation:
First off ok and second off bye <3
I need help the question > The function f(x)=2-3x Find the value of the number K if kf(3)=7f(2) can anyone help?
The value of k for the function k f( 3 ) = 7 f( 2 ) is 2
What is a Function ?
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
According to the given information
We are given with the function
f( x ) = 2 -3x
f ( 3 ) = 2 - 3(3)
= 2 - 9
f ( 3 ) = -7
f ( 2 ) = 2 - 2(2)
= 2 - 4
f ( 2 ) = -2
We are given
k f( 3 ) = 7 f( 2 )
k ( -7 ) = 7 ( -2 )
k = 2
The value of k for the function k f( 3 ) = 7 f( 2 ) is 2
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write 987.6 in scientific notation
987.6 million written in scientific notation is 9.876 × [tex]10^{8}[/tex]
What is scientific notation?
Scientific notation is basically a shortcut for writing numbers. It is a method of expressing real numbers in terms of a significand, multiplied by a power of 10.
When using scientific notation, you're allowed to simplify all the zeros that you have in the number by writing the number as a product of a number and a power of 10. 987.6 million in exponential form is [tex]a^{b}[/tex], a is the base, and b is called the exponent . The term [tex]a^{b}[/tex] is called the exponential expression. 987.6 million = 9.876 x 100,000,000 = 9.876 ×[tex]10^{8}[/tex].
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which statement must be true?
Answer:
DF=FE
Step-by-step explanation:
first to make it easier we can find the angles to each side
the sum of all angles of a triangle equal 180 degrees so to find x we set all the angles equal to 180
(3x+5)+(4x-15)+(2x+10)=180
9x+0=180
/9. /9
x=20
now we can find each angle
3(20)+5
60+5
D=65 degrees
4(20)-15
80-15
E= 65 degrees
2(20)+10
40+10
F=50 degrees
Angle D and E are the only angles equal to each other so answer C and d ARE INCORRECT
Since there are 2 of the same angles this is an isosceles triangle
the 2 of the same angles are the base so the side going up are connecting to the top angle F so the sides will be DF and FE and these are equal
hopes this helps
5/7 of.... is 1/7. What is the missing number?
The missing number is [tex]\frac{1}{5}[/tex]
Let the missing number be x.
now, [tex]\frac{5x}{7}[/tex] = [tex]\frac{1}{7}[/tex]
on cross multiplying we get,
x= [tex]\frac{7}{35}[/tex]
on simplifying,
x= [tex]\frac{1}{5}[/tex]
Hence, the missing number is [tex]\frac{1}{5}[/tex]
What is cross multiplying?
An equation involving a variable as a component of two fractions set equal to one another can be solved by cross multiplying. Cross-multiplying lowers the proportion to one straightforward equation, enabling you to solve for the variable in issue. The variable serves as a placeholder for an unknowable number or quantity.
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12. A typical large recycling tote can hold 10 kilograms of plastic yogurt containers. What volume is
needed to hold this amount of plastic?
A typical large recycling tote can hold 10 kilograms of plastic yogurt containers. the volume is 0.01 m^3
What volume is needed to hold this amount of plastic?Generally, To determine the volume needed to hold 10 kilograms of plastic yogurt containers, you would need to know the density of the plastic and the size and shape of the containers.
The density of a material is a measure of its mass per unit volume. It is usually expressed in kilograms per cubic meter (kg/m^3). The density of plastic can vary depending on the specific type of plastic and any additives that are present.
Once you know the density of the plastic, you can use the following formula to calculate the volume needed to hold a certain mass of the material:
Volume = Mass / Density
For example, if the density of the plastic is 1000 kg/m^3 and you want to hold 10 kilograms of it, the volume needed would be:
Volume = 10 kg / 1000 kg/m^3
Volume = 0.01 m^3
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THE COMPLETE QUESTION WAS NOT FOUND
if traingle PAG is comgruent to riangle DEN, use words numbers and or symbols to state two conclsuions that can be made based upon cpctc
I have this question can anyone solve
The double bar graph collected from the survey is given by the image presented at the end of the answer.
How to build the double bar graph?A bar graph shows the number of times that each observation appears in the data-set.
The double bar graph means that for each input on the bar graph, there are going to be two bars.
The meaning of each bar is given as follows:
Number of people who like watching the sport.Number of people who like participating in the sport.The colors for each bar are given as follows:
blue bar: people who like watching the sport.red bar: people who like participating in the sport.Then the data of the table is used to give the height of each bin in the double bar graph.
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x − 3y = −12 2x − y = 1 (1 point) a line includes points 0 comma 1 and negative 3 comma negative 4. A line includes points 0 comma negative 4 and negative 6 comma negative 2 a line includes points 0 comma 4 and 1 comma 3. A line includes points negative 2 comma 2 and negative 4 comma 0 a line includes points 0 comma negative 1 and 1 comma negative 3. A line includes points 6 comma negative 10 and 3 comma negative 11 a line includes points 0 comma 4 and 3 comma 5. A line includes points 1 comma 1 and 2 comma 3
By graphing the system of equations, we can see that the solution is (3, 5).
How to solve the system of equations?
I assume we want to solve the following system of equations graphically:
x - 3y = -12
2x - y = 1
To do so we only need to graph both the lines on the same coordinate axis and find the point where the lines do intersect. The graph can be seen below.
There we can see that the intersection is at (3, 5), so that is the solution of the system of equations.
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What is 213 divided? Also how do you break 23 into tens and ones?
Answer:
What is 213 divided? 2 I think
Also how do you break 23 into tens and ones? It would be 2 tens and then it would be 3 ones
What is the area of triangle lmn? round to the nearest square meter. 3 square meters 9 square meters 28 square meters 34 square meters
9 square meters is the area of triangle LMN. Using the concept of Heron's formula.
What is Heron's formula?Heron of Alexandria is credited with creating Heron's formula, which determines a triangle's area by dividing the lengths of its sides. if the side lengths are represented in symbols by a, b, and c.
According to Heron's formula the area = √s (s - a)(s - b)(s - c)
A triangle's semi-perimeter, whose area has to be calculated, is represented by the letter s in Heron's formula. s = (a+b+c)/2 is the formula for the triangle's semi-perimeter, which is the sum of its three sides.
a triangle with three sides, a, b, and c.
given data was LM = 7,MN = 6 and perimeter was given by 16m
As we know perimeter is the sum of all the sides
so, Perimeter=LM + MN + NL
NL=Perimeter-(LM+MN)
NL=16 - 7 - 6
NL= 3
By Heron's formula,
Area = √[(s(s-a)(s-b)(s-c)].
where s = perimeter/2
so, s = 16/2 = 8
area = √[(8(8-7)(8-6)(8-3)]
area = 8.94427191 ≈ 9 square meters.
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Answer: 9m
Step-by-step explanation:
Go step by step to reduce the radical
Answer:
[tex]3 \sqrt{8} [/tex]
Step-by-step explanation:
1. we are find which factors which when multiplied will give us 192
2. so i took 3 and 64
3. now square root both factors
like this
[tex] \sqrt{3} \times \sqrt{64} [/tex]
4. then you will be left with 3 and a 8
so then we will write that as the answer given above
Insert terms to make a identity replace *
(15x+*)^2=225x^2+90xy+*
Answer:
3y, 9y²
Step-by-step explanation:
We use laws of binomial
(a+b)²=a²+2ab+b²
From this, we get
15x × * × 2 = 90xy
2×*=6y
*=3y
Now, we square this term to get the last term
3y×3y=9y²
5. Which of the following is an arithmetic
sequence?
A
B
C
D
-2, -5, -8, -11, -14, -17, ...
0,5, 0, 10, 0, 15, ...
2, 4, 8, 16, 32, ...
5, 11, 17, 23, 29, 36, ...
Answer:
A. -2, -5, -8, -11, -14, -17, ...
Step-by-step explanation:
The difference between consecutive terms is constant.
Solve for j
1 - j/4 = 3
Answer:
j = - 8
Step-by-step explanation:
1 - j/4 - 3
1 is also 4/4
so
4/4 - j/4 = 3
4 - j/ 4= 3
multiply by 4 on both sides
which gets you
-j + 4 = 12
minus 4 from both sides
-j = 8
j = -8
Answer:j=-8 I hope this helps
Step-by-step explanation:
1-j/4=3
Multiply both sides of the equation by 4
which gives you
4-j=12
Move the constant to the right-hand side and change its sign
-j=12-4
Subtract the numbers
-j=8
Change the signs on both sides of the equation
j=-8 - This is your answer
A circle has a diameter of 14 inches. A central angle of 85° intercepts an arc of the circle.
What is the intercepted arc length to the nearest tenth of an inch?
The intercepted arc measures 11.78 to the closest tenth of an inch.
What is intercepted arc?Remember that an arc is a portion of a circle's circumference.
Therefore, an intercepted arc is an arc that is created when one or more chords or line segments intersect a circle and come together at a vertex.
It's vital to keep in mind that the lines or chords can come together inside, outside, or in the center of a circle.
An interrupted arc and the inscribed and central angles of a circle have some intriguing correlations.
An inscribed angle is created in geometry between chords or lines that cut through a circle.
The center angle is a joint created by the intersection of two radii.
According to our question-
angel/360=arc/circumference
85/360=
d= 14 inches
Hence, The intercepted arc measures 11.78 to the closest tenth of an inch.
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Number 49. Please help Graphing inequalities? Why is the answer A? Please do a step by step explanation for each answer choice.
I don't see the picture. Can you send it in the message.
Alonso went to the market with \$55$55dollar sign, 55 to buy eggs and sugar. He knows he needs a package of 121212 eggs that costs \$2.75$2.75dollar sign, 2, point, 75. After getting the eggs, he wants to buy as much sugar as he can with his remaining money. The sugar he likes comes in boxes that each cost \$11.50$11.50dollar sign, 11, point, 50
The number of boxes of sugar that Alonso can buy are 4.5 boxes.
What is a mathematical function, equation and expression? function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that Alonso went to the market with $55 to buy eggs and sugar. He knows he needs a package of 12 eggs that costs $2.75. After getting the eggs, he wants to buy as much sugar as he can with his remaining money.
The money remaining after buying 12 eggs : {r} = $(55 -2.75).
Cost of one box of sugar = $11.5
The number of boxes that he can buy are -
n = (55 - 2.75)/11.5
n = 4.5 boxes {approx.}
Therefore, the number of boxes of sugar that Alonso can buy are 4.5 boxes.
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s: One skis fast.
Express the statement One does not ski fast symbolically.
The given statement can be expressed as ~S.
What is a negation of a statement?
A negation of a statement is a statement that is the opposite of the original statement. In other words, a negation of a statement is a statement that is true if and only if the original statement is false, and vice versa.
To express the statement "One does not ski fast" symbolically, we can use the negation symbol
Using the symbol "S to represent the statement "One skis fast", we can express the statement "One does not ski fast" symbolically as:
~S
This can be read as "Not S" or "It is not the case that S."
Hence, the given statement can be expressed as ~S.
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what is the slope if the line that passes through the points (10,8) and (7,14)? write your answer in simplest form
Answer:
-2
Step-by-step explanation:
we use the y2-y1/x2-x1 fomrula to find slope
14-8/7-10
6/-3
-2 is the slope
hopes this helps
In the equation y=x2+2x+5 what is the value for y when x equals 3?
The value of y in the equation y=x2+2x+5 when x=3 is y= 20
SimplifySimplifying algebraic expressions is the same idea, except you have variables (or letters) in your expression.
simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving
y=x^2+2x+5
mathematically, x=3
substitute the valve of x=3 into the equation
y= 3^2 + 2(3) + 5
y= (3x3) + 2(3) +5
Evaluate the value of y by adding the numbers together
y= 9 + 6+ 5
y= 20
Therefore, the value of y in the equation y=x^2+2x+5 is 20
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What is the m∠ c? Enter your answer as a number.
The measure of angle c is m ∠c = 103°.
What is triangle?
Three edges and three vertices define a triangle as a polygon. One of geometry's fundamental shapes is this one. The designation "triangle ABC" refers to a triangle with the vertices A, B, and C. When three points are non-collinear in Euclidean geometry, they each produce a distinct triangle and plane.
180 degrees is the sum of the triangle's three angles.
Let Δabc is given with m ∠a = 30° and m ∠b = 37°
We have to find the measure of angle c.
Since the sum of three angles of triangle is 180 degree.
⇒ m ∠a + m b + m ∠c = 180°
30° + 37° + m ∠c = 180°
77° + m ∠c = 180°
m ∠c = 180°- 77°
m ∠c = 103°
Hence, the measure of angle c is m ∠c = 103°.
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A beetle is moving along a straight line at a constant rate. It moves 23 of a foot in 15 of a minute.
What is the average speed of the beetle?
The average speed of the beetle is 1.53 feet per minute.
What is the average speed?Average speed is calculated by dividing a quantity by the time required to obtain that quantity. Meters per second is the SI unit of speed. The formula S = d/t, where S is the average speed, d is the total distance, and t is the total time, is used to determine average speed.
Given that, it moves 23 of a foot in 15 of a minute.
Here, the average speed
= 23/15
= 1.53 feet per minute
Therefore, the average speed of the beetle is 1.53 feet per minute.
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