The requried simplified expression for [tex]y^{5/4}[/tex] is given by [tex]y^{5/4}= 32 * 10^{10k}[/tex]
To find an expression for [tex]y^{5/4}[/tex] in terms of k, we'll substitute the given value of y into the expression and then apply the exponent (5/4).
Given: [tex]y = 16 *10^{8k}[/tex]
Now, let's calculate [tex]y^{5/4}[/tex]:
[tex]y^{5/4} = (16 *10^{8k})^{5/4}[/tex]
To apply the exponent (5/4), we raise each factor to the power of (5/4):
[tex]y^{5/4}= 16^{5/4} * (10^{8k})^{5/4}[/tex]
Since [tex](10^8)^k[/tex] is [tex]10^{(8k)}[/tex], we have:
[tex]y^{5/4}= 16^{5/4}* 10^{8k * 5/4)[/tex]
[tex]y = 16*10^{8k}[/tex]
[tex]y^{5/4}= 2^5 * 10^{10k}[/tex]
Finally, we can write the expression in terms of k:
[tex]y^{5/4}= 32 * 10^{10k}[/tex]
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Out of a sample 650 high school students, 321 take the bus to school every day. construct a 99% confidence interval for the population mean of high school students that take the bus to school every day.
a.ci=(43.23%,51.18%)
b.ci=(44.34%, 54.43%)
c.ci=(45.54%, 53.23%)
d.ci=(46.16%,52.16%)
A 99% confidence interval for the population mean of high school students that take the bus to school every day is b) ci=(44.34%, 54.43%)
We need to find the 99% confidence interval for the population mean of high school students that take the bus to school everyday
A confidence interval is a range of estimates for an unknown parameter. The confidence interval is calculated at the specified confidence level; the most common is the 95% confidence level, but sometimes other levels are used, such as 90% or 99%.
The confidence interval of proportions is given by:
π ± z √(π (1-π) /n)
π is the sample proportion.
z is the critical value.
n is the sample size.
For 99% confidence interval the value of z is 2.58
π = 321/650
The confidence interval is given by
=321/650 ± 2.58 √( (321/650) × [ 1 - (321/650) ] ÷ 650)
= (0.493846 ± 0.050594)
=(0.4434 , 0.5443)
=(44.34 % , 54.43 %)
Hence a 99% confidence interval for the population mean of high school students that take the bus to school every day is ci=(44.34%, 54.43%)
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In gym class, the students are going to design and build obstacles for an upcoming field day. Before they can start building, each student has to submit a two-dimensional scale drawing of the obstacle they want to build. Barbara's drawing of her obstacle is shown below.
Note: Figure not drawn to scale.
In Barbara's drawing, the obstacle has a total area of______ square feet.
This obstacle will have a width of 4 feet. The volume of the obstacle is____cubic feet.
The obstacle has a total area of 69 square feet and a volume of 276 cubic feet.
The total area of the obstacleTo determine the total area, we calculate and add up the area of each shape.
The shapes in the figure are:
Triangle: Base = 1, Height = 6Triangle: Base = 5, Height = 8Square: Length = 2Rectangle: Length = 7; Width = 6Using the area formula of each shape, the total area is:
Total = 0.5 * 1 * 6 + 0.5 * 5 * 8 + 2 * 2 + 7 * 6
Evaluate
Total = 69
Hence, the obstacle has a total area of 69 square feet.
The volume of the obstacleThis is calculated as:
Volume = Base area * Height
The height is 4.
So, we have:
Volume = 69 * 4
Evaluate
Volume = 276
Hence, the obstacle has a volume of 276 cubic feet.
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Fair coin say you flip a coin 10 times. It comes up tails 8 times and heads twice. Is this a fair coin?
State if the three side lengths 3 mi, 12 mi, 13 mi?
Since the sum of any two sides is greater than the third, hence the three sides for the sides of a triangle
What is a triangle?A triangle is a 2-D shape with 3sides and angles. According to the question, we are to determine whether the given measures form sides of a triangle.
For the following measure to form the sides of a triangle, the sum of any two sides must be equal to the third as shown:
3 + 12 = 15 > 13
3 + 13 = 16 > 12
13 + 12 = 25 > 3
Since the sum of any two sides is greater than the third, hence the three sides for the sides of a triangle
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Arrange the tiles on both boards to find the value of x.
Board sum: 3x + (-5) = 1
What x value solves the equation?
3x - 5 = 1
X =
Answer:
3x-5=1
3x=5+1
3x=6
x=6/3
x=2
Find a linear inequality with the following solution set. Each grid line represents one unit.
Give your answer in "standard form" ax+by+c>0 or ax+by+c\geq0 where a, b, and c are integers with no common factor greater than 1.)
The linear inequality in standard form is: x + y < -2 or x + y + 2 < 0
How to Write a Linear Inequality?To determine what sign to use, follow these rules:
Use "<" or ">" when the boundary line is dotted or dashed.Use "<" or "≤" when the shaded area is under the boundary line (dotted or dashed).Use "≤" or "≥" when the boundary line is not dotted or dashed.Use ">" or "≥" when the shaded area is above the boundary line (dotted or dashed).The graph given has the following features:
It has a boundary line that is dotted/dashed.It has a shaded area that is under the boundary line.Thus, the inequality sign we would use is, "<".Find the slope:
Slope (m)= rise/run = -(2 units) / (2 units).
Slope (m) = -1.
The y-intercept (b) = -2.
Substitute m = -1 and b = -2 into y < mx + b:
y < (-1)x + (-2)
y < -x - 2
Rewrite
x + y < -2
x + y + 2 < 0
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I AM ASKING AGAIN HELP GUYZ
Answer:
[tex]\huge\boxed{\sf C, \ D \ and \ E}[/tex]
Step-by-step explanation:
Given expression:
= 2(4f + 2g)Distribute 2 to both terms.
= 8f + 4gWe can also split 8f into 4f and 4f.
= 4f + 4f + 4gIf we take 4 common
= 4(f + f + g)
= 4(2f + g)[tex]\rule[225]{225}{2}[/tex]
Answer: Heya! ~
8f + 4g also 4(2f + g) and 4f + 4f+ 4gStep-by-step explanation:
Given: Expression 2(4f + 2g)
We have to choose an equivalent expression to the given expression 2(4f + 2g)
Consider the given expression 2(4f + 2g)
Apply Distributive property, a( b + c) =ab + ac
We have,
a = 2, b = 4f and c = 2g
2(4f + 2g) = 8f + 4g
Now, take 4 common from each term, we have,
8f + 4f = 4 (2f + g)
Now, We have,
a = 2, b = 4f and c = 2g
2(4f + 2g) = 8f + 4g
Now, take 4 common from each term, we have,
8f + 4f = 4 (2f + g)
Now, an equivalent expression to the given expression 2(4f + 2g) is 8f + 4g and 4 (2f + g)
- Keira
The radius of a circle is 58 centimeters. enter the circumference of the circle
Answer:
C = 364.24
Step-by-step explanation:
Comment
The circumference and the radius are related to one another. The constant relating them is pi which is a fixed number of 3.14 The formula for the circumference is C = 2*pi * r
Givens
pi = 3.14
r = 58 cm
Circumference = ?
Formula
C = 2*pi * r
C = 2 * 3.14 * 58
C = 364.24
Which of the following systems of equations has the solution (1, 6)?
y = –5x – 1
y = –x + 7
y = 5x + 1
y = x – 7
y = 5x + 1
y = –x – 7
y = 5x + 1
y = –x + 7
Answer:
Step-by-step explanation:
hello :
the system is : y = 5x + 1
y = –x + 7
put : x=1 you have y = 6
The nth term of a sequence is 2n2² - 4n+4 Work out the 8th term of the sequence. 8th term= Submit Answer Skip for Now
The nth term of a sequence exists 2n2² - 4n+4 is 36.
What is PEMDAS' order of operations?The order of operations exists as a rule that describes the right sequence of measures for estimating a math expression. We can recognize the order utilizing PEMDAS: Parentheses, Exponents, Multiplication, and Division (from left to right), Addition, and Subtraction (from left to right).
[tex]$2*8*2^{2} - 4*8+4[/tex]
Follow the PEMDAS order of operations
Calculating the exponents, we get 2² = 4
[tex]= 2*8*4 - 4*8+4[/tex]
= 64-32 +4
= 36
Therefore, the nth term of a sequence that exists 2n2² - 4n+4 is 36.
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Identify the function with a period of 4 and an amplitude of 2.
Answer:
it's only 2pi/B because the period of sin and cos is 2pi. If we were dealing with tan it'd be pi/B, since the period of tan is just pi.
Ruby buys 24 books and 5 pens.she pays with a 500 rupee note and get rs90 as change.shania bought 12 books and 10 pens for rs280.find the cost of 1 pen.
The cost of one pen is Rs 15.
How to find the cost of one pen?It is given that Ruby paid with a 500 rupee note and got Rs 90 back.
This means that she spent 410 rupees.
Therefore the cost of 24 books and 5 pens is Rs 410.
Let the cost of books be x and the cost of pens be y.
Therefore, we can form the following equations:
24x + 5y = 410 (1)
12x + 10y = 280 (2)
We have to find the value of y.
Multiply the second equation by 2:
24x + 20y = 560 (3)
Now subtract the first equation from the third equation:
24x + 20y - 24x - 5y = 560 - 410
15y = 150
y = 15.
The variable y represents the cost of one pen.
This means that the cost of one pen is Rs 15.
Therefore, we have found that the cost of one pen is Rs 15.
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Rationalize the denominator:
GRADE 9
CBSE
Answer:
1. a)
[tex] \begin{gathered} \frac{2}{ \sqrt{3} - 1 } = \frac{2}{ \sqrt{3} - 1} \times \ \frac{ \sqrt{3} + 1}{ \sqrt{3} + 1 } \\ = \frac{2 \sqrt{3} + 2 } {( \sqrt{3} ) {}^{2} - 1 {}^{2} } = \frac{2 \sqrt{} 3}{3 - 1} = \frac{2 \sqrt{3} }{2} \\ = \sqrt{3} \end{gathered}[/tex]
[tex]\\[/tex]
b)
[tex]\begin{gathered} = > \: \: \frac{7}{ \sqrt{12} - \sqrt{5} } \\ \\ = > \: \: \frac{7}{ \sqrt{12} - \sqrt{5} } \times \frac{ \sqrt{12} + \sqrt{5} }{ \sqrt{12} + \sqrt{5} } \\ \\ = > \: \: \frac{7( \sqrt{12} + \sqrt{5} ) }{ {( \sqrt{12}) }^{2} - {( \sqrt{5}) }^{2} } \\ \\ = > \: \: \frac{7( \sqrt{12} + \sqrt{5}) }{12 - 5} \\ \\ => \: \: \frac{ \cancel{7}( \sqrt{12} + \sqrt{5} ) }{ \cancel{7}} \\ \\ => \: \: \sqrt{12} + \sqrt{5} \end{gathered}[/tex]
1-:
[tex] \displaystyle \frac{2}{ \sqrt{3} - 1 } [/tex]
[tex] \displaystyle = \frac{2}{( \sqrt{3} - 1)( \sqrt{3} + 1 } \\ [/tex]
[tex] \displaystyle2 \frac{ \sqrt{3} + 1 }{ \sqrt{3 {}^{2} - 1 {}^{2} } } [/tex]
by( a-b×a+b=a²b²)[tex] \displaystyle2 \frac{ \sqrt{3} + 1}{3 - 1} [/tex]
[tex] \displaystyle \: \sqrt{3} + 1[/tex]
[tex] \displaystyle2 - ) \frac{7}{ \sqrt{12} - \sqrt{5} } [/tex]
[tex] \displaystyle\frac{ \sqrt{12} \sqrt{5} }{ \sqrt{12 {}^{2} } \times \sqrt{5 {}^{2} } } [/tex]
[tex] \displaystyle7\frac{ \sqrt{12} + \sqrt{5} }{7} = \sqrt{12} + \sqrt{5} [/tex]
[tex] \displaystyle3) = \frac{8 + 3 \sqrt{5} }{64 - 45} \\ = \frac{8 - 3 \sqrt{5} }{19} [/tex]
Define the domain and range of each function. GRAPH IS BELOW :)
Domain:
Range:
FIRST PERSON TO ANSWER GETS BRAINLIEST OR 5 STARS!
Answer:
Domain: ( Positive infinity, Negative Infinity)
Range: (-3, Positive Infinity )
Step-by-step explanation:
Ammonia (NH3) can be made using the reversible reaction shown. Which change would keep this reaction from shifting to form more of the produce Decreasing the pressure in the reaction ? 3H2 + N2 ⇄ 2NH3 + energy A. Decreasing the pressure in the reaction vessel
Decreasing the pressure in the reaction vessel will keep this reaction from shifting to form more of the produce(ammonia).
What is Pressure?This is defined as the force per unit area of a body and the S. I unit is in Pascal.
Ammonia production involves reaction between hydrogen and nitrogen gas in which pressure has an effect on the reaction rate unlike in solids and liquids. An increase in pressure will result in more products being formed and vice versa.
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3. Which of the following is equivalent to (10a³b³) (5a³b²)?
Answer:
50a^6b^5
Step-by-step explanation:
I don't see answer choices, but this is the simplified version. To do this, multiply 10*5, a^3 * a^3 (which adds the exponents), and then b^3*b^2.
Find the equation of the line that passes through (-1,2) and is perpendicular to y =2x+1 . Leave your answer in the form y = m x + c
write each as the sum of two terms in the form t_n,r. t_5,3 , t_11,2 , t_15,13
The sum of two terms are:
t₅, ₃ = 8t₁₁, ₂ = 13 t₁₅,₁₃ = 28.What is the sum about?The sum of two numbers is one that tells you to find the sum of two or more numbers, and as such, you have to add the numbers altogether.
t₅, ₃ = 5 + 3
= 8
t₁₁, ₂ = 11 + 2
= 13
t₁₅,₁₃ = 15 + 13
= 28.
Hence the correct sum of two terms are:
t₅, ₃ = 8t₁₁, ₂ = 13 t₁₅,₁₃ = 28.Learn more about sum from
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This question is worth 15 points.
A bedding set that regularly sells for $86
is on sale with a 20% discount. How
much will the total sale be including a 5%
sales tax?
The total sale of the bedding set including 5% sale tax is $69.66
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Discount = 20% of 86 = 0.2 * 86 = 17.2
Selling price of bed = 5% of 17.2 = 0.05 * 17.2 = 0.86
Total sale = 86 - 17.2 + 0.86 = 69.66
The total sale of the bedding set including 5% sale tax is $69.66
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The science teacher has to write report cards for all her students. It takes 1/8 of an hour to complete one report card. How many report cards can the teacher complete in 14 hours?
Answer:
112
Step-by-step explanation:
If she takes 1/8 of an hour to complete one then she can finish 8 in 1 hour.
8 x 14 = 112
Which of these shapes are congruent
Answer:
Option A is probably the answer
If you have any question please contact me
Answer: A is the answer, should be right
Find the distance between the points C(−6, 5) and D(−3, 1).
Answer:
5 units
Step-by-step explanation:
Given the following question:
To find the answer to this question we will use the formula to calculate distance.
(6, 5) = (x1, y1)
(-3, 1) = (x2, y2)
[tex]d=\sqrt{(x1-x2)^2+(y1-y2)^2}[/tex]
[tex]d=\sqrt{(-6-(-3))^2+(5-1)^2}[/tex]
[tex]-6+3=-3[/tex]
[tex]5-1=4[/tex]
[tex]d=\sqrt{(-3^2+4^2)}[/tex]
[tex]-3^2=-3\times-3=9[/tex]
[tex]4^4=4\times4=16[/tex]
[tex]d=\sqrt{9+16}[/tex]
[tex]9+16=25[/tex]
[tex]\sqrt{25}[/tex]
[tex]\sqrt{25} =5\times5=25[/tex]
[tex]=5[/tex]
Which means the distance between the two points is "5 units."
Hope this helps.
This table shows values represented by an exponential function x= 0,1,2,3,4,5,6 y=1,3,9,27,64,125,216 what is the average rate of change for this function for the interval from x=2 to x=4?
27.5 is the answer
For this case we know that the average rate of change of a function is given by this general expression:
m = f(b) - f(a)/ b-a
For this special case from the info in the table we have:
a =2 , f(2) = 9
a =4 , f(4) = 64
And replacing the data with the average rate formula we got:
m = 64 - 9/4 - 2 = 27.5
And then the best answer for this case would be:
27.5
The exponential function is a mathematical function represented by f (x) = \ exp or e ^ {x}. Unless otherwise specified, the term generally refers to a function of a positive value of a real variable, but it can also be extended to complex numbers or generalized to other mathematical objects such as matrices and Lie algebras.
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At the trial of a contract dispute, the plaintiff has offered to testify to what she heard the defendant say in a private conversation between the two of them, which the plaintiff secretly recorded on an audiotape that she did not offer in evidence. Is the plaintiff's testimony admissible
The plaintiff's testimony is admissible because plaintiff as personal knowledge of the statement of a party-opponent.
How to illustrate the information?The recording is coincidental with firsthand knowledge. The person could testify based upon firsthand knowledge and could also lay the foundation under Article 9 to authenticate the tape.
In this case, the tape is not required as a matter of the original writing rule, giving the proponent options to offer testimony from memory, and/or the opportunity to corroborate the in-court testimony by a demonstrative exhibit
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a colony of bacteria grows by 5% every hour. how long does it take for the colony to double in size
Answer:
20 hrs
Step-by-step explanation:
growth per hour=5%
no of hrs to double=100/5=20
(it may be wrong)<3
The frequency table shows a set of data collected by a doctor for adult patients who were diagnosed with a strain of influenza.
A 2-column table with 4 rows. The first column is labeled age range with entries 25 to 29, 30 to 34, 35 to 39, 40 to 45. The second column is labeled number of sick patients with entries 3, 6, 5, 4.
Which dot plot could represent the same data as the frequency table?
The dot plot that could represent the same data as the frequency table is the second plot. This is further explained below.
What is dot plot?Generally, Data points are represented as dots on a graph with an x- and y-axis in a dot plot sometimes referred to as a strip plot or dot chart, which is a straightforward kind of data visualization.
The frequency table displays the number of ill patients in each age group. The first two plots are incorrect because the sum of the dots connecting the numbers 24, 25, 26, 27, 28, and 29 in the first two plots is 3, but not in the other two plots.
In conclusion, there are only 4 ill individuals when the dots from the 30-34 age range on the first plot are added together. There are a total of 6 cases in that age group on the second graph. As a result, the second dot plot is the one that matches the frequency table.
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Answer:
id b on edge
David has kept track of his family’s grocery bills for the past 10 weeks, as shown in the table.
Week 1 2 3 4 5 6 7 8 9 10
Bill ($) 92 106 129 115 100 84 110 156 98 87
Would you choose to use a histogram, a circle graph, or a line graph to display the data? Explain your choice. Then make a display.
The data should be displayed using a line graph, as shown in the attached figure.
Definition of a Line Graph
In a line graph, also known as a line plot or a line chart, each data point is connected by its own line. A line graph displays numerical values across a chosen time span.
Why is a line graph the best choice in this situation?
A line graph would be the best option for showing the data for David's family's grocery spending over the previous 10 weeks because it would show us the trend in the data. This graph tells us of how we can recognize instances where there were significant expenses by analyzing the trend from the line graph.
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In the Michigan lottery game, LOTTO 47, the state selects six balls randomly out of 47 numbered balls. The player selects six different numbers out of the first 47 positive integers. Prizes are given for matching all six numbers in any order (the jackpot) and matching five numbers ($2500). A ticket costs $1.00 and this dollar is not returned to the player. Find the probabilities of matching
The probability of matching six numbers is [tex]\frac{1}{47C_{6}}[/tex].
How to find the probability of matching six numbers?To find the probability, we have to divide the favorable events by the total number of events.
The total number of events is given by:
[tex]47C_{6}[/tex]
We use combinations since the order doesn't matter.
The total number of favorable events is given by:
[tex]6C_{6}[/tex]
The probability is given by:
[tex]\frac{\text{Favorable events}}{\text{Total events}}=\frac{6C_{6}}{47C_{6}} \\= \frac{1}{47C_{6}}[/tex]
We have found the probability of matching all six balls to be [tex]\frac{1}{47C_{6}}[/tex].
Therefore, we have found that the probability of matching six numbers is [tex]\frac{1}{47C_{6}}[/tex].
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Disclaimer: The question was incomplete, the complete question is attached below.
Question: In the Michigan lottery game, LOTTO 47, the state selects six balls randomly out of 47 numbered balls. The player selects six different numbers out of the first 47 positive integers. Prizes are given for matching all six numbers in any order (the jackpot) and matching five numbers ($2500). A ticket costs $1.00 and this dollar is not returned to the player. Find the probability of matching six numbers.
Find 8. Round to the nearest degree.
OA. 68°
OB. 69°
OC. 22°
OD. 21°
Answer:
A
Step-by-step explanation:
[tex]\cos \theta=\frac{3}{8} \\ \\ \theta=\cos^{-1} \left(\frac{3}{8} \right) \\ \\ \theta \approx 68^{\circ}[/tex]
The shallowest section of an underground tunnel is -50 feet. The deepest section of the tunnel is -135 feet. How many feet below the shallowest section is the deepest section?
A. -95 feet
B. -185 feet
C. 85 feet
D. 195 feet
Answer:
c
Step-by-step explanation:
1) eliminate the negative answers since we need the amount of feet below a section and a negative number below a section doesn't make sense in this context and would result in a distance higher than the shallowest section.
Just find the absolute value or the difference between 135 and 50 resulting in 85