Answer:
n = - 3
Step-by-step explanation:
We have to solve the equation [tex]2^{n} = \frac{1}{8}[/tex] for n.
Now, as the variable is in power, we will take a log on both sides.
So, [tex]2^{n} = \frac{1}{8}[/tex]
⇒ [tex]\log 2^{n} = \log \frac{1}{8}[/tex]
⇒ n log 2 = log 1 - log 8 {Since we know the property of logarithm [tex]\log a^{b} = b \log a[/tex] and [tex]\log \frac{a}{b} = \log a - \log b[/tex]}
⇒ n log 2 = - log 2³ { Since, log 1 = 0}
⇒ n log 2 = - 3 log 2
⇒ n = - 3 (Answer)
4. Which of the following might feel limp?
(a) a sheet of wet cardboard (c) a sheet of ice
(b) a sleeping child
(d) a sheet of plywood
The correct answer is (a) a sheet of wet cardboard, which becomes limp when moistened as the material loses its rigidity and strength, unlike the other items listed which maintain their form and firmness.
Explanation:Among the options provided, a sheet of wet cardboard is most likely to feel limp. When cardboard absorbs water, the material becomes weak and loses its rigidity, making it bend or flop easily. The other materials listed, such as a sheet of ice, a sleeping child, and a sheet of plywood, retain their form and rigidity better when they are not altered by external factors like moisture.
A sheet of ice remains solid until it melts, a sleeping child is not an inanimate object and doesn't become limp simply because they are asleep, and a sheet of plywood is a construction material designed to remain sturdy even when faced with various environmental conditions. Therefore, (a) a sheet of wet cardboard is the correct answer as it is the one that could be expected to feel limp when wet.
13 + 2k = 3k + 4(k - 3)
Answer:
k=5
Step-by-step explanation:
7
k
−
12
=
13
+
2
k
Move all terms containing
k
to the left side of the equation.
Find a quadratic function that includes the set of values below.
(0,9). (2,15) (3,12)
Answer:
[tex]f(x) = -2x^2 + 7x + 9[/tex]
Step-by-step explanation:
[tex]f(x) = ax^2 + bx + c\\f(0) = 9 => c = 9;\\f(2) = 15 = 4a + 2b + 9 <=> 2a + b = 3\\f(3) = 9a + 3b + 9 = 12 <=> 3a + b = 1\\Subtract the second equation from the first:\\-a = 2 => a = -2; b = 7; c = 9\\f(x) = -2x^2 + 7x + 9[/tex]
To find a quadratic function, substitute each given coordinate into the equation and solve the resulting system of equations.
Explanation:To find a quadratic function, we need to use the form y = ax^2 + bx + c. From the given set of values, we can substitute each coordinate (x, y) into the equation to get three different equations. So:
When x = 0, y = 9, we get: 9 = a(0)^2 + b(0) + c, which simplifies to c = 9.When x = 2, y = 15, we get: 15 = a(2)^2 + b(2) + 9, which simplifies to 4a + 2b = 6.When x = 3, y = 12, we get: 12 = a(3)^2 + b(3) + 9, which simplifies to 9a + 3b = 3.Now we have a system of equations that we can solve simultaneously. Solving the second and third equations using any appropriate method, we find that a = -1 and b = 5.
Therefore, the quadratic function that includes the given set of values is y = -x^2 + 5x + 9.
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What is the 10th term of the sequence -4, -1, 2, 5
Answer:
23
Step-by-step explanation:
Note there is a constant difference between consecutive terms
- 1 - (- 4) = - 1 + 4 = 3
2 - (- 1) = 2 + 1 = 3
5 - 2 = 3
This indicates that the sequence is arithmetic with n th term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = - 4 and d = 3, thus
[tex]a_{10}[/tex] = - 4 + (9 × 3) = - 4 + 27 = 23
The graph shows how the number of key chains in your collection increased since you began collecting. 5 months ago. During which month did you collect the most key chains?
Answer:
4th month
Step-by-step explanation:
As this graph shows the evolution of your collection over time, and not the number of key chains you collected in each month, you need to look for the month with the highest increase.
According to the graph on the first month you collected 4 key chains. After the 2nd month you had 6 key chains, so, you collected:
keys on 2nd month - keys on 1st month = 6-4 = 2 keys
In month 3 you went from 6 to 10 key chains, so you collected
keys on 3rd month - keys on 2nd month = 10-6 = 4 keys
On the next, month 4, you had 16, so you collected
keys on 4th month - keys on 3rd month = 16-10 = 6 keys
Finally, on the last month you had 18, having collected:
keys on 5th month - keys on 4th month = 18-16 = 2 keys
So, the month you most collected was the 4th, with 6 key chains. All the others months collected less keys (2 on the 2nd, 4 on the 3rd and 2 on the 5th).
I hope it is understandable.
Based on the graph, the month in which you collected the most key chains is May which is 4th month.
To determine this, we can look at the slope of the line between each pair of points. The slope of a line represents the rate of change, so a steeper slope indicates that the change is happening more quickly.
The slope of the line between the points for April and May is the steepest, which means that the number of key chains increased at the fastest rate during that month. Therefore, we can conclude that you collected the most key chains in May.
Here is a table of the slopes between each pair of points on the graph:
Month Previous Month Slope
May April 2.5
April March 2
March February 1.5
February January 1
As you can see, the slope between April and May is the highest, which indicates that you collected the most key chains during that month.
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Which value satisfies the inequality 5x + 7 ≤ 8x - 3 + 2x?
A) -2
Eliminate
B) -1
C) 0
D) 2
Answer:
D) 2
Step-by-step explanation:
5x + 7 [tex]\leq[/tex] 8x -3 +2x
5x + 7 [tex]\leq[/tex] 10x - 3
7 + 3 [tex]\leq[/tex] 10x - 5x
10 [tex]\leq[/tex] 5x
2[tex]\leq[/tex] x
x[tex]\geq[/tex]2
There are 12 eggs in 1 dozen eggs.
How much is
of 2 dozen eggs?
A. 4 eggs
B. 6 eggs
c. 8 eggs
D. 10 eggs. E. 12 eggs
Answer:
2 dozen eggs are 24 eggs
Solve the system of equations: 2x + 3y = 13 x = 2 + 3y
PLEASE HELP ME I don’t know the answer
Answer:
7 and 8 would work
Step-by-step explanation:
just insert them as w and they have to be greater than 20. I hope this helps.
Answer:
7 and 8
Step-by-step explanation:
Solving the inequality
5w - 10 > 20 ( add 10 to both sides )
5w > 30 ( divide both sides by 5 )
w > 6
The only values from the solution set greater than 6 are
7 and 8
A Web music store offers two versions of a popular song, The size of the standard Version is 2.7 megabytes (MB), The size of the high quality version is 4.4 MB
Yesterday, there were 1090 downloads of the song, for a total download size of 3623 MB. How many downloads of the high quality version were there?
O
EXPLANATION
4/77 = 12/x!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
231
Step-by-step explanation:
Given
[tex]\frac{4}{77}=\frac{12}{x}[/tex]
Cross Multiply
[tex]x \times 4=12\times 77\\x=\frac{12\times 77}{4} \\x= 3\times 77\\x= 231[/tex]
Therefore x=231
1. Tommy and Robbie share 48 marbles between them in the ratio 5 How many
marbles does Tommy get?
Answer:
The number of marbles does Tommy will get is 18 .
Step-by-step explanation:
Given as :
The total number of marbles share between Tommy and Robbie = 48
The marbles were distributed between then in the ratio 3 : 5
Let the number of marbles does Tommy have = 3 x
The number of marbles does Robbie have = 5 x
Now,
According to question
The total number of marbles share between Tommy and Robbie = 48
Or, the number of marbles does Tommy have + The number of marbles does Robbie have = 48
Or, 3 x + 5 x = 48
Or, 8 x = 48
∴ x = [tex]\frac{48}{8}[/tex]
I.e x = 6
So, the number of marbles does Tommy have = 3 × 6 =18
The number of marbles does Robbie have = 5 × 6 = 30
Hence the number of marbles does Tommy will get is 18 . Answer
The highest mountains in the world are the Himalayas, at the border between the Indian and Eurasian plates. The Himalayas formed in a ________________.
A. subduction zone
B. divergent boundary
C. collision zone
D. transform boundary
Answer: collision zone
Step-by-step explanation:As a result of this collision, the sedimentary rocks which were settled in the large-scale depression in the Earth's crust called Tethys were folded and formed the Himalayas.
C collision zone
The Himalayas are the world's highest mountains, straddling the Indian and Eurasian plates. The Himalayas were formed by a collision zone.
What is meant by collision zone?A collision zone occurs when two tectonic plates with continental lithosphere collide at a convergent boundary. A collision zone occurs when two tectonic plates with continental lithosphere collide at a convergent boundary. Because continental lithosphere is rarely subducted due to its low density, the result is a complex orogeny involving folding and thrust faulting as blocks of continental crust pile up above the subduction zone. This includes the collision zone in Eastern Anatolia. Tropical Asia is a hotspot for plate collisions between the northward-drifting Australian plate and plates from the Pacific and the Asian mainland. As a result, the area is mountainous and shaped by shear zones and volcanism. as well as the Banda Arc-Australian collision zoneTo learn more about collision zone, refer to:
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The area of a square region is 1yd^2. What is the length of one side of the region?
Answer:
1 ydStep-by-step explanation:
The formula of an area of a square:
[tex]A=s^2[/tex]
s - side of a square
We have
[tex]A=1yd^2[/tex]
Therefore
[tex]s^2=1yd^2\to s=\sqrt{1yd^2}=1yd[/tex]
Kenny had 35 baseball cards in his collection last year. This year he has 20% more baseball cards. Kenny sold 8 of his baseball cards for extra money. How many baseball cards does Kenny have after he sold 8 for extra money? Show Work!
(A) 7 baseball cards left
(B) 34 baseball cards left
(C) 35 baseball cards left
(D) 42 baseball cards left
The right answer is Option B.
Step-by-step explanation:
No. of baseball cards = 35
Increase = 20%
Number of increased cards = 20% of 35
[tex]Increased\ cards = \frac{20}{100}*35\\Increased\ cards=\frac{700}{100}\\Increased\ cards=7[/tex]
Total cards = 35+7 = 42
No. of cards sold = 8
Cards left = Total cards - No. of cards sold
[tex]Cards\ left=42-8\\Cards\ left=34[/tex]
The right answer is Option B.
Keywords: Addition, subtraction
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If y varies inversely as the square of x and y=2 when x=4.Find x when y=4/5
Answer:
hnjmmm
Step-by-step explanation:
m,,\
l;'
Answer:
x = 2[tex]\sqrt{10}[/tex]
Step-by-step explanation:
Given that y varies inversely as the square of x then the equation relating them is
y = [tex]\frac{k}{x^2}[/tex] ← k is the constant of variation
To find k use the condition y = 2 when x = 4
k = yx² = 2 × 4² = 2 × 16 = 32
y = [tex]\frac{32}{x^2}[/tex] ← equation of variation
When y = [tex]\frac{4}{5}[/tex], then
[tex]\frac{4}{5}[/tex] = [tex]\frac{32}{x^2}[/tex] ( cross- multiply )
4x² = 160 ( divide both sides by 4 )
x² = 40 ( take the square root of both sides )
x = [tex]\sqrt{40}[/tex] = [tex]\sqrt{4(10)}[/tex] = 2[tex]\sqrt{10}[/tex]
help will rate you 5 stars!!!!!!!!!
Answer:
first proof should be cpctc, second proof is the triangle sum theorem
What is the sum of the multiples of 3 between 100 and 1000
Answer:
165150 is the sum of the multiples of 3 between 100 and 1000.
Step-by-step explanation:
We need to find the sum of multiples of 3 between 100 and 1000.
First we will find the Total number of multiples of 3 between 100 and 1000.
Let a be the first multiple and l be the last multiple of 3
100 is not the multiple of 3.
101 is not the multiple of 3.
102 is the multiple of 3.
Hence first term a = 102
Similarly.
1000 is not a multiple of 3
999 is a multiple of 3
hence last term l = 999
Also d is the common difference.
hence d = 3.
Now by using Arithmetic progression formula we get;
[tex]T_n(l) =a+(n-1)d\\ 999=102+(n-1)3\\999-102=(n-1)3\\897=(n-1)3\\\frac{897}{3}=n-1\\\\n-1=299\\n=299+1\\n=300[/tex]
Hence there are 300 multiples of 3 between 100 and 1000
Now n=300, a=102, l = 999
Hence to find the sum of all the multiples we use the Sum of n terms in AP formula;
Sum of n term [tex]S_n= \frac{n}{2}(a+l)[/tex]
[tex]S_{300}= \frac{300}{2}(102+999)\\\\S_{300}= 150(102+999)\\S_{300}= 150\times 1101\\S_{300}= 165150[/tex]
Hence,165150 is the sum of the multiples of 3 between 100 and 1000.
What does x equal if x-10 divided by x-4 equals 50 divided by -6
Answer:
x=65/14
Step-by-step explanation:
(x-10)/(x-4)=50/-6
-50/6=-25/3
(x-10)/(x-4)=-25/3
x-10=-25/3(x-4)
x-10=-25/3x+100/3
x-(-25/3x)=100/3+10
x+25/3x=130/3
28/3x=130/3
x=(130/3)/(28/3)
x=(130/3)(3/28)
x=130/28
x=65/14
Elsa is taking physical fitness tests in her strength training class. Each day, her results are compared to her results from previous days. The first day she completes a test is considered the baseline and is represented by 0. For instance, on the first day she did the flexibility test, her result was calculated as 0. On the second day, in comparison to her first day's result, she was able to reach 1/16inches less than the first day, which was recorded as - 1/16. Then, on the third day, Elsa recorded a result of -5/8.
A. On which day did Elsa reach farther: the second or third day?
B. By how much?
HELP ME D:
Answer:
A) The second day
B) 9/16 inches
Step-by-step explanation:
A) Elsa reached farther on the second day because -1/16 > -5/8
B) To calculate this we must first put both fractions above the same denominator. We can then subtract the smaller one from the bigger one:
-1/16 - (-10/16) = 9/16
Elsa reached 9/16 inches farther on the second day then she did on the first.
Final answer:
Elsa reached farther on the second day than the third day during her flexibility tests. She reached 9/16 inches farther on the second day compared to the third day.
Explanation:
Elsa is taking physical fitness tests in her strength training class where she tracks her progress by comparing her flexibility results to the baseline (first day). A negative value indicates she did not reach as far as the baseline.
A. On the second day, Elsa's flexibility test result was recorded as - 1/16 inches, and on the third day, it was -5/8 inches. Since -1/16 is greater than -5/8 (closer to zero), it means Elsa reached farther on the second day than the third day.
B. To find out by how much Elsa reached farther on the second day compared to the third day, we calculate the difference between the two measurements: (-1/16) - (-5/8) = 5/8 - 1/16. We must find a common denominator to subtract these fractions, which is 16. So we have (10/16) - (1/16) = 9/16 inches. Therefore, Elsa reached 9/16 inches farther on the second day compared to the third day.
3. Evaluate a + b for a = -46 and b= 34.
A:-12
B:80
C:-80
D:12
Answer:
A: -12Step-by-step explanation:
Put the values of a = -46 and b = 34 to the expression a + b:
-46 + 34 use the commutative property a + b = b + a
= 34 + (-46) = 34 - 46 = -12
The question is asking to evaluate the expression a + b, with a being -46 and b being 34. Evaluating the expression, we substitute the given values in to get -12. Therefore, the correct answer is A: -12.
Explanation:In algebra, when a question asks us to evaluate an expression, that simply means we need to substitute the given values into the equation and perform the operations to simplify it. In this problem, the expression is a + b, and the values given are a = -46 and b = 34.
To evaluate this, we substitute the given values in: (-46) + 34. When you add -46 and 34 together, you get a result of -12. Therefore, the correct answer is A: -12.
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A pipe is leaking at the rate of 8 fluid ounces per minute. How many gallons is the pipe leaking per hour
Answer: 3.75 gallons
Step-by-step explanation:
8 fl oz x 60 (minutes)=480 fl oz
480 fl oz ÷ 128=3.75 gallons
Water flow rate is defined as the volume of the fluid passing by some location. The water leaking from the pipe per hour is 3.75 gallons
Given information-A pipe is leaking at the rate of 8 fluid ounces per minute.
Water flow rateWater flow rate is defined as the volume of the fluid passing by some location.
As the flow rate is 8 fluid ounces per minute. In a hour there is total 60 minutes. Thus the flow rate of the pipe in fluid ounces per hour is,
[tex]Q=8\times60[/tex]
[tex]Q=480[/tex]
A fluid ounces is the unit of the measurement of the liquid. There is total 128 fluid ounces in a gallons. Thus the flow rate of the water in gallon can be calculated by dividing the 480 by 128. Thus the flow rate of pipe in gallons per hour is,
[tex]Q=\dfrac{480}{128}[/tex]
[tex]Q=3.75[/tex]
Hence the water leaking from the pipe per hour is 3.75 gallons.
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Jose's banquet hall charges a one time fee of $100 plus $50 per guest for weddings. Another wedding venue, Palace of Aaron, Charges a one-time fee of $200 in addition to $45 per guest. Letting "g" represent the number of wedding guests, Write an algebraic expression to represent the cost of renting each of the banquet halls.
(First part)
(Second part)
At how many wedding guests is the cost the same for both venues? Show your work.
Answer:
Part 1:
Jose's Banquet Hall: 50g+100
Palace of Aaron: 45g+200
Part 2:
20 guests
Step-by-step explanation:
Part 1:
$50 per guest plus $100 fee
50g+100
$45 per guest plus $200 fee
45+200
Part 2:
$50(20)+$100=$1100
$45(20)+$200=$1100
Answer:
II. [tex]\displaystyle 20\:wedding\:guests[/tex]
I. [tex]\displaystyle 100 + 50g = 200 + 45g[/tex]
Step-by-step explanation:
100 + 50g = 200 + 45g
- 200 - 50g - 200 - 50g
___________________
[tex]\displaystyle \frac{-100}{-5} = \frac{-5g}{-5} \\ \\ 20 = g[/tex]
So, at twenty wedding guests, the cost will balance for both venues.
I am joyous to assist you anytime.
if 3x - y = 3 and -x + y = 3 then xy=___?
First find x and y.
Solve system of equations by elimination.
3x-y=3
+(-x+y=3)
---------------
2x=6
x=3
Now plug in x into one of the equations to find y.
-3+y=3
y=6
xy=3x6=18
Final answer:
The product of xy, given the system of equations 3x - y = 3 and -x + y = 3, is 18. This is found by first solving for x and y using the elimination method and then multiplying the obtained values.
Explanation:
To find the product of xy, we need to solve the system of equations given by 3x - y = 3 and -x + y = 3. Here we'll use the elimination method. Adding both equations together, we eliminate y:
3x - y + (-x + y) = 3 + 3
Which simplifies to:
2x = 6
Dividing both sides by 2, we get:
x = 3
To find y, we substitute x back into one of the original equations, for example, the second equation -x + y = 3:
-(3) + y = 3
-3 + y = 3
Adding 3 to both sides gives us:
y = 6
Now we can find the product of xy:
xy = 3 * 6
xy = 18
Therefore, the product of xy is 18.
A student in Greece discovers a pottery bowl
that contains 21% of its original amount of C-
14.
N = Noe-kt
No = inital amount of C-14 (at time t = 0)
N = amount of C-14 at timet
t = time, in years
k = 0.0001
age of the pottery bowl to the nearest year??
Answer:
The age of the pottery bowl to the nearest year is 15606 years.
Step-by-step explanation:
Let the initial amount of C-14 in the bowl i.e. [tex]N_{0} = 100[/tex] and today (say after t years) the amount of C-14 in the bowl i.e. N = 21.
Therefore, from the given equation we can write
[tex]21 = 100 e^{- 0.0001t}[/tex] {Since, k is give to be 0.0001}
⇒ [tex]0.21 = e^{- 0.0001t}[/tex]
Now, taking ln on both sides we get
ln 0.21 = - 0.0001t (ln e) {Since, [tex]\ln a^{b} = b \ln a[/tex]}
⇒ - 1.560647 = - 0.0001t {We have ln e = 1}
⇒ t = 15606.47 years ≈ 15606 years
Therefore, the age of the pottery bowl to the nearest year is 15606 years.(Answer)
ts Graph the line whose x-intercept is 5 and whose y-intercept is 3
Answer:
The equation of line whose x-intercept is 5 and whose y-intercept is 3
is given as 5 y + 3x = 15.
Step-by-step explanation:
Here, the given x - intercept = 5.
⇒ The point on the given equation is (x,0) = (5,0)
And, the y- intercept is given as 3
⇒ The point on the given equation is (0,y) = (0,3)
So, the two points given on the equation of line is A(5,0) and B(0,3)
Now, the slope of the line equation [tex]m = \frac{y_2 - y_2}{x_2-x_1}[/tex]
So, here the slope of line AB is [tex]m = \frac{3- 0}{0-5} = -\frac{3}{5}[/tex]
Now by POINT SLOPE FORMULA:
The equation of a line with point (x0,y0) and slope m is given as:
(y- y0) = m (x-x0)
⇒The equation of line AB is given as
[tex]( y - 0) = -\frac{3}{5} (x -5)\\\implies 5 y = -3x + 15\\\implies 5 y + 3x = 15[/tex]
Hence, the equation of line AB is given as 5 y + 3x = 15.
A hospital director is told that 30% of the treated patients are uninsured. The director wants to test the claim that the percentage of uninsured patients is less than
the expected percentage. A sample of 340 patients found that 85 were uninsured. State the null and alternative hypotheses.
Answer: [tex]H_0: p=0.30[/tex]
[tex]H_a: p <0.30[/tex]
Step-by-step explanation:
Definition:
Null Hypothesis : It is a statement about the population parameter that contains = , ≤ and ≥ signs.
Alternative hypothesis : It is also a statement about the population parameter against the null hypothesis that contains ≠ , < and > signs.
For the given situation.
Let [tex]\mu[/tex] be the population proportion of treated patients are uninsured.
A hospital director is told that 30% of the treated patients are uninsured.
Then, Null Hypothesis : [tex]H_0: p=0.30[/tex]
The director wants to test the claim that the percentage of uninsured patients is less than the expected percentage.
i.e. Alternative hypothesis : [tex]H_a: p <0.30[/tex]
Hence, the set of hypothesis :
[tex]H_0: p=0.30[/tex]
[tex]H_a: p <0.30[/tex]
please help ASAP!!! Drag the tiles to the correct boxes to complete the pairs. not all tiles will be used.
match each situation to its corresponding function
F(x)=13x - 270
F(x)=17(1.23)^x
F(x)=2.7+1.3x
F(x)=23(1.17)^x
F(x)=17x + 23
F(x)=27(1.13)^x
(The last one to the inserted photo states >>>
Daniel studies the characteristics of two elements in his laboratory. the temperature of element A is 44(1.13)^x, and that of element B is 17(1.13)^x. By how much will the temperature of element A be more than the temperature of element B after X hours?
Answer:
First situation matches to F(x) = 23(1.17)^x.
Second is 17x + 23 .
Third is 13x - 270.
Last one is 27(1.13)^x.
Step-by-step explanation:
2.3 is 46% of what number
Answer:
46% × 2.3 =
(46 ÷ 100) × 2.3 =
(46 × 2.3) ÷ 100 =
105.8 ÷ 100 =
1.058 ≈
1.06;
1.) In this parallelogram segment EJ is 12, how long is segment EG?
2.) Angle HEF is 110 degress. Find measures of EHG and HGF.
Answer:
1.) 24
2.) 70°
Step-by-step explanation:
1.) 12*2=24
2.) 180°-110°=70°