Answers
Answer:
"Multiply the previous value by 2"
Step-by-step explanation:
Let's check the first 2 terms for all the answer choices.
1. Add [tex]\frac{1}{16}[/tex] to the previous value:
[tex]\frac{1}{32}+\frac{1}{16}=\frac{3}{32}[/tex]
Doesn't match.
2. Subtract [tex]\frac{1}{16}[/tex] from the previous value:
[tex]\frac{1}{32}-\frac{1}{16}=-\frac{1}{32}[/tex]
Doesn't match.
3. Divide the previous value by 2:
[tex]\frac{\frac{1}{32}}{2}\\=\frac{1}{32}*\frac{1}{2}=\frac{1}{64}[/tex]
Doesn't match.
4. Multiply the previous value by 2:
[tex]\frac{1}{32}*2=\frac{2}{32}=\frac{1}{16}[/tex]
DOES WORK!
Also, doing the same thing with all the other values would give us matching answer. So this choice is right.
Related Questions
Determine the intercepts of the line Y+1=3(x-4)
Answers
ANSWER
y-intercept:
(0,-13)
x-intercept:
[tex](4 \frac{1}{3} ,0)[/tex]
EXPLANATION
The given line has equation
[tex]y + 1 = 3(x - 4)[/tex]
At y-intercept , x=0.
This implies that;
[tex]y + 1 = 3(0 - 4)[/tex]
[tex]y = - 12 - 1[/tex]
[tex]y = - 13[/tex]
The y-intercept is
(0,-13).
At x-intercept y=0,
This implies that;
[tex]0+ 1 = 3(x - 4)[/tex]
[tex] \frac{1}{3} = x - 4[/tex]
[tex] \frac{1}{3} + 4 = x[/tex]
[tex]4 \frac{1}{3} = x[/tex]
The x-intercept is
[tex](4 \frac{1}{3} ,0)[/tex]
Answer:
x-intercept = [tex]\frac{13}{3}[/tex]
y-intercept = [tex]-13[/tex]
Step-by-step explanation:
We are given the following equation of a line and we are to find the x and y intercepts for it:
[tex] y + 1 = 3 ( x - 4 ) [/tex]
In order to find the x-intercept, we will substitute 0 in place of y to get:
[tex] 0 + 1 = 3 ( x - 4 ) \\\\ 1 = 3 x - 12 \\\\ 3 x = 1 + 12 \\\\ x = \frac { 13 } { 3 } [/tex]
And to find the y-intercept, we need to substitute 0 in place of x:
[tex] y + 1 = 3 ( 0 - 4 ) \\\\ y + 1 = -124 \\\\ y = - 12 - 1 \\\\ y = - 13 [/tex]
So the x-intercept is [tex]\frac{13}{3}[/tex] while the y-intercept is [tex]-13[/tex].
One 8-oz serving each of coffee, energy drink, and soda contains 199 mg of caffeine. One serving of coffee has 11 mg more caffeine than two serving of soda. One serving of energy drink contains 33 less caffeine than one serving each of soda and coffee. Find the amount of caffeine in one serving of each beverage
Answers
Answer:
soda = 35mg
coffee = 81mg
energy = 83mg
Step-by-step explanation:
coffee + energy + soda = 199
coffee = 11 + (2 * soda)
energy = (soda + coffee) - 33
(11 + (2 * soda)) + ((soda + (11 + (2 * soda))) - 33) + soda = 199
11 + 2s + s + 11 + 2s - 33 + s = 199
22 + 6s - 33 = 199
-11 + 6s = 199
6s = 210
s = 35
soda = 35mg
c = 11 + 2s
c = 11 + 2(35)
c = 11 + 70
c = 81
coffee = 81mg
e = s + c - 33
e = (35) + (81) - 33
e = 116 - 33
e = 83
energy = 83mg
Final answer:
One serving of soda contains 35 mg of caffeine, one serving of coffee contains 81 mg of caffeine, and one serving of energy drink contains 83 mg of caffeine.
Explanation:
Let's solve this problem step by step:
Let's assume the amount of caffeine in one serving of soda is x mg. Therefore, the amount of caffeine in two servings of soda is 2x mg.According to the information given, one serving of coffee has 11 mg more caffeine than two servings of soda. So, the amount of caffeine in one serving of coffee is 2x + 11 mg.The information also states that one serving of energy drink contains 33 mg less caffeine than one serving each of soda and coffee. Therefore, the amount of caffeine in one serving of energy drink is (x+2x + 11) - 33 mg.To find the value of x, we can set up an equation:
(x) + (2x + 11) + [(x+2x + 11) - 33] = 199Simplifying the equation:
6x + 22 - 33 = 199Combine like terms:
6x - 11 = 199Add 11 to both sides:
6x = 210Divide both sides by 6:
x = 35Therefore, one serving of soda contains 35 mg of caffeine. Substituting this value into the previous equations:
One serving of coffee contains 2(35) + 11 = 81 mg of caffeine.One serving of energy drink contains 35+(2(35) + 11) - 33 = 83 mg of caffeine.The number of coins Jada will have on the eighth day, if Jada starts with one coin and the number of coins doubles every day. (She has two coins on the first day of the doubling.
Answers
Answer:
256 Coins
Step-by-step explanation:
On the first day, Jada starts with one coin, so all you have to do here is multiply it by 2.
Day 1: 2 coins
Day 2: 2 x 2 = 4 coins
Day 3: 4 x 2 = 8 coins
Day 4: 8 x 2 = 16 coins
Day 5: 16 x 2 = 32 coins
Day 6: 32 x 2 = 64 coins
Day 7: 64 x 2 = 128 coins
Day 8: 128 x 2 = 256 coins
Hope this helps! Just message me if you have more questions or need more help! :)
The number of coins that Jada will have after 8 days is; 256 coins
How to solve geometric sequence?
We are told that on the first day, Jada starts with one coin and that the number of coins doubles each day. Thus;
Day 1: She has 2 coins
Day 2: She has 2 * 2 = 4 coins
This follows a geometric pattern 2ⁿ
where n is number of days
Thus, for 8 days, she will have; 2⁸ coins = 256 coins
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When two pipes fill a pool together, they can finish in 5 hours. If one of the pipes fills half the pool then the other takes over and finishes filling the pool, it will take them 18 hours. How long will it take each pipe to fill the pool if it were working alone?
Answers
The pipes can fill the pool individually in 16 and 20 hours respectively, by solving the simultaneous equations: 1/x + 1/y = 1/5 and 1/2x + 1/2y = 18.
Explanation:Let's assume one pipe can fill the pool in x hours, while the other pipe can fill it in y hours. When the two pipes work together, they complete one job in 5 hours, which can be expressed as 1/x + 1/y = 1/5.
When each pipe fills half the pool, it takes 18 hours. Since each of them is doing half the work, this can be represented as 1/2x + 1/2y = 18.
To solve these simultaneous equations, it is best to use the substitutive method. We can set the two equations equal to each other to get x = 36 - y. Plugging this into the first equation and solving for y, we find y = 20. Substituting y back into the equation x = 36 - y, we find x = 16.
So, one pipe could fill the pool alone in 16 hours, while the other could do it in 20 hours.
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The first pipe would take approximately 6.92 hours to fill the pool if it were working alone, and the second pipe would take 18 hours to fill the pool if it were working alone.
Let's assume that the first pipe can fill the pool in x hours, and the second pipe can fill the pool in y hours.
When the two pipes fill the pool together, they can complete the job in 5 hours. So, their combined rate of work is 1/5 of the pool per hour.
When the first pipe fills half the pool, it takes over for the second pipe, which then finishes filling the pool. This entire process takes 18 hours. So, the first pipe fills half the pool in 18 hours, which means that its rate of work is 1/18 of the pool per hour.
Using the concept of work done, we can set up the following equation:
1/x + 1/y = 1/5 (equation 1)
1/y = 1/18 (equation 2)
Solving the equations simultaneously, we can find the values of x and y:
From equation 2, y = 18 hours.
Substituting the value of y in equation 1, we get:
1/x = 1/5 - 1/18 = (18 - 5)/90 = 13/90.
Therefore, x = 90/13 hours.
So, the first pipe would take approximately 6.92 hours to fill the pool if it were working alone, and the second pipe would take 18 hours to fill the pool if it were working alone.
Please Help
Which of the following demonstrates the Distributive Property?
2(3a + 4) = 6a + 4
2(3a + 4) = 3a + 8
2(3a + 4) = 6a + 8
2(3a + 4) = 5a + 6
Answers
Answer:
[tex]\boxed{\bold{2(3a + 4) = 6a + 8}}[/tex]
Step-by-step explanation:
Distributive Property: [tex]\bold{a(b+c) \ = \ (a*b)+(a*c)}[/tex]
2(3a + 4)
----------------------------------------
(2 * 3a) + (2 * 4)
(2 * 3a) = 6a
(2 * 4) = 8
-------------------------------
6a + 8
Write the equation of the line in slope-intercept form that has the following points: (2, -1)(5, -3)
Answers
Answer:
[tex]\large\boxed{y=-\dfrac{2}{3}x+\dfrac{1}{3}}[/tex]
Step-by-step explanation:
The skope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (2, -1) and (5, -3). Substitute:
[tex]m=\dfrac{-3-(-1)}{5-2}=\dfrac{-3+1}{3}=\dfrac{-2}{3}=-\dfrac{2}{3}[/tex]
We have the equation:
[tex]y=-\dfrac{2}{3}x+b[/tex]
Put the coordinates of the point (2 , -1) to the equation:
[tex]-1=-\dfrac{2}{3}(2)+b[/tex]
[tex]-1=-\dfrac{4}{3}+b[/tex] add 4/3 to both sides
[tex]\dfrac{1}{3}=b\to b=\dfrac{1}{3}[/tex]
Finally we have:
[tex]y=-\dfrac{2}{3}x+\dfrac{1}{3}[/tex]
PLEASE HELP!!! PICTURE WITH ANSWER CHOICES INCLUDED!
choose the equation that represents the graph below.
Answers
y = -2x - 4 would be the answer
for the given expression, use the Commutative Property of Multiplication to enter an equivalent expression. a b =
Answers
Answer:
Step-by-step explanation:
I can't do much more than just give you the answer.
The commutative property of multiplication is turning a and b around.
commutative(a*b) = b*a
answer: b * a
Answer:
b a
Step-by-step explanation:
so the communative property is just switching the numbers ( or letters in this case) around!
If A < B, where on the number line will A appear?
A. In exactly the same location as B
B. To the left of B
C. To the right of B
Answers
Answer:
A will appear to the left of B. The answer is B) hope this helps
Step-by-step explanation:
If A < B, A will appear to the left of B on the number line.
What is the number line?A number line is a linear line on which points are marked equidistant from each other and used to represent the position of a certain linear number on it.
Where is point A in relation to B?Let us take an example where A = 2 and B = 3. Here 2 < 3.
We know that 2 is to the left of 3 on the number line.
Now let us take an example of negative numbers. A = -3 and B = -2.
Here, -3 < -2. - 3 is also to the left of - 2.
Therefore we can say that A is always to the left of B.
Therefore, if A < B, A will appear to the left of B on the number line.
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given right triangle XYX which correctly describes the location of the sides in relation to y
Answers
The answer is the 4th option.
Apply the distributive property to factor out the greatest common factor. 30+42= 30, plus, 42, equals
Answers
To factor out the greatest common factor from 30 and 42, first, find the GCF. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. The greatest common factor is 6. Using the distributive property, 30 + 42 becomes 6(5 + 7). So, the final answer is 6 times the sum of 5 and 7, which is 72.
To factor out the greatest common factor (GCF) from the expression 30 + 42, we first need to find the GCF of the two numbers, which is 6. Then we can rewrite the expression using the distributive property.
Step 1: Find the GCF of 30 and 42:
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.
The common factors are 1, 2, 3, and 6. The greatest common factor is 6.
Step 2: Rewrite the expression using the GCF:
[tex]\[30 + 42 = 6 \times 5 + 6 \times 7\][/tex]
Step 3: Apply the distributive property:
[tex]\[30 + 42 = 6 \times (5 + 7)\][/tex]
Step 4: Perform the addition inside the parentheses:
[tex]\[30 + 42 = 6 \times 12\][/tex]
Step 5: Multiply:
30 + 42 = 72
So,30 + 42 equals 72 after factoring out the greatest common factor using the distributive property.
Sets L, M, and N are shown. Which of the sets represents L ∪ (M ∩ N) (the union of L with the intersection of sets M and N)?
L = {0, 20, 40, 80, 100}
M = {5, 10, 15, 20, 25}
N = {10, 20, 30, 40, 50}
Answers
Answer:
L ∪ (M ∩ N) = {0, 10, 20, 40, 80, 100}
Step-by-step explanation:
L ∪ (M ∩ N) means "take what's common of set M and set N" and then "add it to all the elements of set L".
So, what are the common elements of set M and set N?
They are 10 & 20. So,
M ∩ N = {10,20}
Now, we add it to all the elements of set L. Note that we don't need to count 20 twice.
Thus L ∪ (M ∩ N) = {0, 10, 20, 40, 80, 100}
What is the answer to this question 4^6×4^3?
Answers
4^6= 4096
4^3= 64
4096 • 64= 262144
Answer:
262144
Step-by-step explanation:
4^6 = 4 x 4 x 4 x 4 x 4 x 4
4^3 = 4 x 4 x 4
that ends up being 4^9 if you add them up.
4^9 is 262,144
Which property can be used to solve the equation d/10=12
A. Addition property of equality
B. Subtraction property of equality
C. Multiplication property of equality
D. Division property of you equality
Answers
Multiplication property of equality. C is your answer
Multiplication property can be used for this equation because to get d by itself you have to MULTIPLY both sides by 10 to get d=122
Hope this helps
If like line A is changed to line B how will the equation change
Answers
Answer:
Line B will become line A and Line A will become line B.
Step-by-step explanation:
Which inequality is equivalent to
Answers
Equivalent inequalities are inequalities with the same solutions. They're also the most likely paired together.
Answer:
it is equivalent to the number that you want to find it out
Step-by-step explanation:
Inequalety
Solve these equations. Show solutions on a number line. |x−12| =4
Answers
Answer:
x=16, x=8
Step-by-step explanation:
since x in |x-12| can be both negative and positive, we have to find two numbers for each senario. if x-12 is negative, we flip them so it becomes 12-x. so 12-x=4 is easily solved and the answer would be 8. if it is positive, we would keep it and x-12 would be 4. we also solve this to get 16. we can check our work by putting them in to get 16-12 is 4 and |8-12| is 4
Pam has 15 candies in her bag. Her mother puts another handful of candies into the bag. Pam counts all the candies and she now has a total of 27 candies. Write an algebraic equation and determine how many candies Pam’s mom put into her bag.
Answers
Answer:
Step-by-step explanation: 15 + X = 27 Candies
Any Variable Will Work.
Answer:
c + 15 = 27
Step-by-step explanation:
c + 15 = 27
15 is the starting amount.
c is the number of candies her mom put in.
27 is the new total.
the two branches of the study of statistics are generally reffered to as
Answers
Answer:
The correct answer is: descriptive and inferential statistics.
Step-by-step explanation:
The two branches of the study of statistics are generally referred to as descriptive and inferential statistics.
Descriptive statistics are the brief summary statistic which summarizes a given data set, which can be a representation of the entire population or just a sample of it.
While Inferential statistics is the way data analysis is used to deduce the properties of an underlying probability distribution.
The study of statistics generally branches into descriptive statistics, which involves summarizing and displaying data, and inferential statistics, which makes predictions about a population based on sampled data.
Explanation:The two branches of the study of statistics are generally referred to as descriptive statistics and inferential statistics. Descriptive statistics involves the organization, summarization, and display of data. It seeks to describe a situation or sample population without offering any conclusions or inferences about the data. Examples include calculating averages, measures of central tendency like mean, median, mode, and variability measures such as range, variance, and above all standard deviation.
On the other hand, inferential statistics is a method to make predictions or inferences about a population based on a sample of data. It is used when it is not practical or impossible to examine the entire population. Examples of inferential statistics methods include hypothesis testing, chi-square tests, t-tests, ANOVA, regression analysis etc.
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Length of a rectangle is 5 cm longer than the width. Four squares are constructed outside the rectangle such that each of the squares share one side with the rectangle. The total area of the constructed figure is 120 cm2. What is the perimeter of the rectangle?
Answers
Answer:
The perimeter of rectangle is [tex]18\ cm[/tex]
Step-by-step explanation:
Let
x-----> the length of the rectangle
y----> the width of the rectangle
we know that
[tex]x=y+5[/tex] ----> equation A
[tex]120=xy+2x^{2}+2y^{2}[/tex] ---> equation B (area of the constructed figure)
substitute the equation A in equation B
[tex]120=(y+5)y+2(y+5)^{2}+2y^{2}[/tex]
[tex]120=(y+5)y+2(y+5)^{2}+2y^{2}\\ 120=y^{2}+5y+2(y^{2}+10y+25)+2y^{2}\\ 120=y^{2}+5y+2y^{2}+20y+50+2y^{2}\\120=5y^{2}+25y+50\\5y^{2}+25y-70=0[/tex]
using a graphing calculator -----> solve the quadratic equation
The solution is
[tex]y=2\ cm[/tex]
Find the value of x
[tex]x=y+5 ----> x=2+5=7\ cm[/tex]
Find the perimeter of rectangle
[tex]P=2(x+y)=2(7+2)=18\ cm[/tex]
1 by 3 + 2 by 4 + 5 by 6
Answers
Answer: 41
Step-by-step explanation:
(1 × 3) + (2 × 4) + (5 × 6)
= 3 + 8 + 30
= 11 + 30
= 41
Answer:
answer is 41
Step-by-step explanation:
In ∆ABC, which ratio equals cos C? A. B. C. D.
Answers
SOH CAH TOA
CAH
Cosine = Adjacent / Hypotenuse
∆ABC, where lets say B is the right angle.
cos C = adjacent/hypotenuse = BC/AC
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PLEASE HELPPLEASE HELP WILL GIVE POINTS!!!
Answers
Answer:
[tex] \frac{.7}{1 - .1} = \frac{.7}{.9} = \frac{7}{9} [/tex]
if a/b=2 what is the value of 4b/a
Answers
Anwer:
4b/a=2
Step-by-step explanation:
Lets assume:
a = 4 & b = 2
So a/b would equal 2.
4b/a indicates that you are going to multiply b times 4, meaning that in this scenario you would multiply 2 times 4.
4(2) = 8
and 8 divided by (4) is 2.
Why 4? Because remember a = 4 (in this scenario).
Other examples:
10/5 = 2, --> 4(5) = 20, --> 20/10 = 2.
20/10 = 2. --> 4(10) = 40, --> 40/20 = 2.
Answer:
2
Step-by-step explanation:
a/b = 2
Invert each side of the equation
b/a = ½
Multiply each side by 4
4b/a = 4 × ½ = 2
A group of students made trees out of paper for a scene in a school play. The trees are shaped like square pyramids. 2 ft How much paper will it take to make each tree, including the bottom?
Answers
Answer:
Step-by-step explanation:
The area of a triangle is base*height/2
So one triangle is 2*4/2=4
Multiplied by 4 sides, 4*4=16
Finally the base is a square, so 2*2=4
Therefore the entire shape is 16+4=20 square feet
The amount of paper it will take to make each tree, including the bottom is 20 ft²
How to find the surface area of some object?Find the area that its outer surfaces possess. Sum of all those surfaces' area is the surface area of the considered object.
Surface area of paper tree = sum of areas of those 4 slant standing triangles + area of base
Area of each of those 4 triangles are same (assuming they're symmetric).
Each triangle has height of 4 ft and base of 2 ft. (the base is a square of side length 2 ft).
Thus, we get:
Area of 4 triangles = 4(area of each tree ) = [tex]4\left (\dfrac{1}{2} \times \text{base} \times \text{height}\right) = 4\left (\dfrac{1}{2} \times 2 \times 4\right) = 16 \: \rm ft^2[/tex]
Area of square base = [tex]\text{side}^2 = 2^2 = 4 \: \rm ft^2[/tex]
Thus, we get:
Surface area of paper tree = 16 + 4 = 20 ft²
Thus, the amount of paper it will take to make each tree, including the bottom is 20 ft²
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If a train travels at 80mph for 15 min, what is the distance traveled ?
Answers
Answer:
20 miles
Step-by-step explanation:
The formula for distance is
d =rt where r is the rate and t is the time
We need to convert the time to hours since the rate is in mph
15 minutes * 1 hour/ 60 minutes = 1/4 hour = .25 hours
d = (80 mph) * .25 hours
d = 20 miles
The train goes 80 miles in an hour which is 60 minutes. 60 minutes divided by 15 minutes equals 4. 80 miles divided by 4 equals 20 miles. The train went 20 miles in 15 minutes.
Which expression is equivalent to –8?
–2–3
(-1/2)^-3
(1/2)^-3
2–3
Answers
Answer: second option. (NOTE: If the first option is [tex](-2)^3[/tex], then it would be an equivalent expression too, because: [tex](-2)(-2)(-2)=-8[/tex])
Step-by-step explanation:
To solve this problem you must keep on mind the following exponents rule:
[tex](\frac{1}{a})^-b=a^b[/tex]
Therfore, you have that:
[tex](-\frac{1}{2})^-3=(-2)^3[/tex]
This means that the number -2 must be multiply by itself three times. Therefore, you obtain the folllowing result:
[tex](-2)(-2)(-2)=-8[/tex]
If the first option is [tex](-2)^3[/tex], then it would be an equivalent expression too, because:
[tex](-2)(-2)(-2)=-8[/tex]
Answer:
[tex](\frac{-1}{2})^{-3} = -8[/tex].
Step-by-step explanation:
Given : –8.
To find : Which expression is equivalent.
Solution : We have given –8.
By the radical rule : [tex](\frac{-1}{x})^{-a} = -x^{a}[/tex].
Then
[tex](\frac{-1}{2})^{-3} = -2^{3}[/tex].
[tex](\frac{-1}{2})^{-3} = -8[/tex].
Therefore, [tex](\frac{-1}{2})^{-3} = -8[/tex].
If f(x)= 0.6(3-x) what is the value of f(-3)
Answers
Answer:
[tex]\large\boxed{f(-3)=3.6}[/tex]
Step-by-step explanation:
[tex]f(x)=0.6(3-x)\\\\f(-3)\to\text{Put x = -3 to the equation of a function:}\\\\f(-3)=0.6(3-(-3))=0.6(3+3)=0.6(6)=3.6[/tex]
Subtract.
(2p^2+q)-(p^2+q)
Is the answer
P^2
P^2+2q
P^2-2q
3p^2
Answers
Answer:
-p5q2 - p3q5 + 2p3 + 2pq2 + 2q3
____________________________
p3q2
Step-by-step explanation:
2
Simplify ——
q2
Equation at the end of step 1 :
(p+q) 2
(((2•—————)-(q3))+——)-p2
(p3) q2
Step 2 :
p + q
Simplify —————
p3 (p + q) 2
(((2 • ———————) - q3) + ——) - p2
p3 q2
Step 3 : 2 • (p + q) 2
((——————————— - q3) + ——) - p2
p3 q2 q3 q3 • p3
q3 = —— = ———————
1 p3
What is the answer to this
Answers
Answer:
You add all the scores up, then divide the sum by 24 and you get your answer.
Step-by-step explanation: