Answer:
The second one, third one and the fifth one should be correct. (7 to the 18th power divided 7 to the 9th power, 7 to the 3rd power to the 3rd power, and 7 to the 4th power times 7 to the 5th power)
Step-by-step explanation:
7 to the 8th power times 7 equal 40353607 so if you do all the equations shown you can rule out which ones equal 40353607 and which ones don't. Have a nice sleep!
Answer:
\(\frac{7^{18}}{7^{9}}\), (7³)³ and \(7^{4}*7^{5}\)
Step-by-step explanation:
\(7^{8}*7\) = \(7^{9}\) is equivalent to the following exponential expressions:
\(\frac{7^{18}}{7^{9}}\), as it applies to the Quotient Rule of Exponents: \(\frac{a^{m}}{a^{n}} = a^{m-n}\). Therefore, you're essentially subtracting the exponents, resulting into \(7^{9}\).
(7³)³: The Power-to-Power Rule of Exponents apply in this situation:\((a^{m})^{n} = a^{mn}\). Multiplying the exponent inside the parenthesis by the exponent outside the parenthesis results in an exponent of 9.
\(7^{4}*7^{5}\): the Product Rule of Exponents apply in this situation: \(a^{m}*a^{n} = a^{m+n}\). Adding the exponents of 4 to 5 results in an exponent of 9.
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Can 10 people be divided into two groups with a ratio of 1 : 2? Explain.
Answer:
noStep-by-step explanation:
Can 10 people be divided into two groups with a ratio of 1 : 2?
Explain.
10 : 3 = 3.33
or 10 : 3 = 9 remaining 1
since it is not possible to divide a person into three parts, your answer is no
The alpha level for each hypothesis test made on the same set of data is called ______.
a. testwise alpha
b. experimentwise alpha
c. pairwise comparison
d. the Bonferroni procedure
The alpha level for each hypothesis test made on the same set of data is called B. experimentwise alpha
What is experimentwise alpha?When numerous suppositions are examined concurrently, the likelihood of committing at least one type I mistake grows.
In order to manage the probability of erroneously rejecting the null hypothesis in all tests, scientists usually modify the alpha level for each test, with the purpose of maintaining an experimentwise alpha that reflects the probability of making a type I error in the entire set of tests.
The Bonferroni procedure is a technique utilized to regulate the experimentwise error rate by adjusting the alpha level for each hypothesis test.
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a population is modeled by the differential equation dp dt = 1.2p 1 − p 4300 .
(a) For what values of P is the population increasing and for what values of P is
the population decreasing?
(b) If the initial population is 5500, what is the limiting pupulation?
(c) What are the equilibrium solutions?
a) the population cannot be negative, the limiting population is 4300.
b)the population is increasing when 0 < p < 4300 and decreases when p > 4300.
c)the equilibrium solutions are p = 0 and p = 4300.
(a) To determine when the population is increasing or decreasing, we need to look at the sign of dp/dt.
\(\frac{dp}{dt} = 1.2p(1 - \frac{p}{4300})\)
For dp/dt to be positive (i.e. population is increasing),
we need\(1 - \frac{p}{4300} > 0, or \ p < 4300.\)
For dp/dt to be negative (i.e. population is decreasing),
we need\(1 - \frac{p}{4300} < 0, or p > 4300.\)
Therefore, the population is increasing when 0 < p < 4300 and decreases when p > 4300.
(b) To find the limiting population, we need to find the value of p as t approaches infinity.
As t approaches infinity,\(\frac{dp}{dt}\)approaches 0. Therefore, we can set \(\frac{dp}{dt}\) = 0 and solve for p.
0 = 1.2p(1 - p/4300)
Simplifying, we get:
0 = p(1 - p/4300)
So, either p = 0 or 1 - p/4300 = 0.
Solving for p, we get:
p = 0 or p = 4300.
Since the population cannot be negative, the limiting population is 4300.
(c) Equilibrium solutions occur when\(dp/dt = 0.\)We already found the equilibrium solutions in part (b): p = 0 and p = 4300.
Therefore, the equilibrium solutions are p = 0 and p = 4300.
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a) The population is increasing when 0 < p < 4300, and decreasing when p > 4300.
b) The population cannot be negative, the limiting population is 4300.
c) these are the equilibrium solutions. At p = 0, the population is not
increasing or decreasing, and at p = 4300, the population is decreasing
but not changing in size.
(a) To determine when the population is increasing or decreasing, we
need to find the sign of dp/dt. We have:
dp/dt = 1.2p(1 - p/4300)
This expression is positive when 1 - p/4300 > 0, i.e., when p < 4300, and
negative when 1 - p/4300 < 0, i.e., when p > 4300.
Therefore, the population is increasing when 0 < p < 4300, and
decreasing when p > 4300.
(b) To find the limiting population, we need to solve for p as t approaches infinity. To do this, we set dp/dt = 0 and solve for p:
1.2p(1 - p/4300) = 0
This equation has two solutions: p = 0 and p = 4300. Since the population cannot be negative, the limiting population is 4300.
(c) To find the equilibrium solutions, we need to solve for p when dp/dt = 0. We already found that the only solutions to dp/dt = 0 are p = 0 and
p = 4300.
Therefore, these are the equilibrium solutions.
At p = 0, the population is not increasing or decreasing, and at p = 4300,
the population is decreasing but not changing in size.
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Given are five observations collected in a regression study on two variables.
xi 2 6 9 13 20
yi 7 18 9 26 23
(a) Compute b0 and b1 (to 1 decimal).
b1
b0
(b) Complete the estimated regression equation (to 1 decimal).
Y^ =_ + _ x
(c) Use the estimated regression equation to predict the value of y when x = 6 (to 1 decimal).
Y^ = _?
a) The coefficients of the regression equation are given as follows:
b1 = 0.9. b0 = 7.6.b) The regression equation is defined as follows: y = 0.9x + 7.6.
c) The estimate of y when x = 6 is given as follows: y = 13.
How to obtain the regression equation?The slope-intercept definition of the regression equation is given as follows:
y = b1x + b0.
In which the parameters are given as follows:
b1 is the slope.b0 is the intercept.The points from the table in this problem are given as follows:
(2,7), (6, 18), (9,9), (13, 26), (20,23).
Inserting these points into a linear regression calculator, the equation is given as follows:
y = 0.9x + 7.6.
Then the estimate of the value of y when x = 6 is obtained as follows:
y = 0.9(6) + 7.6 = 13.
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1) Find the Mean (Ungrouped)
Earthquake Strengths Twelve major earthquakes had Richter magnitudes
shown here.
7.0, 6.2,7.7, 8.0, 6.4,6.2,7.2,5.4,6.4,6.5,7.2,5.4
Answer:
6.6333333
The mean is an average, so you add all the numbers together and divide by the number a values added together.
Answer:
6.633...
Step-by-step explanation:
(7.0 + 6.2 + 7.7 + 8.0 + 6.4 + 6.2 + 7.2 + 5.4 + 6.4 + 6.5 + 7.2 + 5.4) / 12
Esteban has a big jar f change in his room, he has 600 coins total, and 240 of them are pennies.
What percent of the coins are pennies?
Answer:
40%
Step-by-step explanation:
240/600 = 0.40 * 100% = 40%
Don’t know how to do it.
Answer:
C
Step-by-step explanation:
How do you write 0.0045 in scientific notation?
Answer:
\(4.5 x 10^{-3} \\\)Step-by-step explanation:
A quadratic equation is shown:
x2 − 8x + 13 = 0
Which of the following is the first correct step to write the above equation in the form (x − p)2 = q, where p and q are integers?
A) x2 − 8x + 13 − 5 = 0 − 5
B) x2 − 8x + 13 − 3 = 0 − 3
C) x2 − 8x + 13 + 5 = 0 + 5
D) x2 − 8x + 13 + 3 = 0 + 3
Option B subtracts the constant term of 3, which is the correct constant to add later in the process of completing the square. Therefore, option B is the best choice. So, the answer is B) x² - 8x + 13 - 3 = 0 - 3.
To write the quadratic equation in the form (x - p)² = q, we need to complete the square. Here are the steps to follow:
x² - 8x + 13 = 0 (given)
x² - 8x = -13 (subtract 13 from both sides)
x² - 8x + 16 = -13 + 16 (add 16 to both sides)
(x - 4)² = 3
Therefore, the value of p is 4 and the value of q is 3. To get this result, we added 16 to both sides of the equation to make the left-hand side a perfect square, and then we simplified the right-hand side.
Out of the given options, none of them represent the first correct step to write the equation in the desired form. However, if we look at the options closely, we can see that options A and B subtract a constant term from the left-hand side of the equation, while options C and D add a constant term to the left-hand side of the equation. While these operations do not directly lead to the desired form, they are steps that can be taken in the process of completing the square.
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PLEASE HELP!!! Find the length of AB. Leave
your answer in terms of T.
А
20° AB = [?]
27
B
Enter
Answer:
3π
Step-by-step explanation:
Arc length is given in terms of central angle θ in radians as ...
s = rθ
For r = 27 and θ = (20/180)π, the arc length is ...
s = (27)(20/180)π = 3π
The arc length is 3π units.
You have learned about quadratic and linear function in earlier grades. Explain in a variety of ways how you can distinguish the exponential function
f(x)=2^x
from the quadratic function
f(x) = x^2
and linear function
f(x) = 2x
. (Hint: compare the rate of change using finite differences in tables of values, and identify a constant ratio in the table of values).
We can distinguish between the linear, exponential function and quadratic functions graphically. The graph of the functions is as follows:
linear function f(x) = 2x will be straight line,
for exponential function f(x) = 2^x will rise or fall quickly in one direction
and for quadratic function f(x) = x^2 will be a parabola.
What is an exponential function?An exponential function is a type of mathematical function expressed in the form f(x) = a^x. where "x" is a variable and "a" is a constant called the base of the function, which must be greater than 0. The most commonly used exponential base is the transcendental number e, which is approximately equal to 2.71828. The exponential function is defined by the formula f(x) = ax. where the input variable x is displayed as an exponent. Exponential curves grow or fall exponentially. A quantity that increases or decreases at a regular rate should exhibit either an exponential increase or an exponential decay.To learn more about exponential function from the given link :
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The four Western provinces cover about 2/7 of Canada's area. Alberta covers about 1/14 of Canada's area. What fraction describes how much of Canada's area is covered by British Columbia, Manitoba, and Saskatchewan? Explain
Answer:5/14
Step-by-step explanation:if you're just combining them all 2/7 is equal to 4/14 and add that to the existing 1/14 so 4/14+1/14=5/14 total area covered
Find the length of the arc. Round to the nearest tenth decimal place.
19 ft
150°
the length of the arc is approximately 19.8 ft when rounded to the nearest tenth decimal place.
To find the length of an arc given the radius and the degree measure of the central angle, we can use the formula:
arc length = (central angle in degrees / 360°) x 2πr
where r is the radius of the circle.
In this problem, we are given the radius as 19 ft and the central angle as 150°. Thus, we can plug these values into the formula and get:
arc length = (150° / 360°) x 2π(19 ft) ≈ 19.8 ft
what is angle?
An angle is a geometric figure formed by two rays, called the sides of the angle, that share a common endpoint, called the vertex of the angle. Angles are commonly measured in degrees or radians and are used in geometry, trigonometry, and many other areas of mathematics and science.
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yo did i do this right, no links pls
Answer:
yea you did it right
Step-by-step explanation:
Which equation can be used to find V, the volume of the cylinder in cubic centimeters?
А
V = 7(3)h
B
V = *(3h)
CV = +(1.5)h
DV = +(1.5h)
This is a new version of the question. Make sure you start new workings.
A farmer wants to build a fence around the edge of a field shaped like a right-
angled triangle, as shown below. The fence costs £1.28 per metre.
Calculate the total cost of the fence.
Give your answer to the nearest pound.
The total length of the fence is 24 meters. Then the total cost of the fence will be £30.72.
Given that:
Rate, r = £1.28 per metre
The length of the fence is calculated as,
P = 10 + 6 + 8
P = 24 meters
Then the total cost of the fence will be calculated as,
Total cost = P x r
Total cost = 24 x £1.28
Total cost = £30.72
The total length of the fence is 24 meters. Then the total cost of the fence will be £30.72.
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The missing diagram is given below.
To determine the annual yield (rate of return) on an investment, divide the income from the investment for the year by the original amount invested. Look at the example. Then, calculate the annual yield for the other investment
Savings account: $4 / $200 = 0.02 x 100 = 2%
Bond: $85 / $1000 = 0.085 x 100 = 8.5%
Real Estate: $6,400 / $40,000 = 0.16 x 100 = 16%
Sketch the region enclosed by the curves and find its
area.
y=x,y=3x,y=−x+4
The region enclosed by the curves y = x, y = 3x, and y = -x + 4 needs to be sketched, and its area should be found.
To sketch the region enclosed by the curves, we need to plot the three given curves on a coordinate plane. The first curve is y = x, which represents a straight line passing through the origin (0,0) with a slope of 1. The second curve is y = 3x, which is also a straight line passing through the origin but with a steeper slope of 3. The third curve is y = -x + 4, which represents a line with a y-intercept of 4 and a negative slope of -1. By plotting these three lines on the same coordinate plane, we can see that they intersect at three points: (0,0), (1,3), and (3,1). The region enclosed by these curves is a triangular region with vertices at these three points. To find the area of this triangular region, we can use the formula for the area of a triangle: A = (1/2) * base * height. Let's draw the graph:
|
4 | . (2, 2)
| .
| .
| .
0 |_____________________
0 1 2 3 4 5 6
In this graph, the first equation (y = x) is depicted by a diagonal line passing through the origin (0,0). The second equation (y = 3x) is a steeper line, while the third equation (y = -x + 4) is a downward-sloping line with a y-intercept of 4. In this case, the base of the triangle is the distance between the points (0,0) and (3,1), which is 3 units. The height of the triangle is the distance between the point (1,3) and the line y = -x + 4, which is also 3 units. Substituting these values into the area formula, we get A = (1/2) * 3 * 3 = 4.5 square units.
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Mount Rainier, in the state of Washington, is
one of the snowiest places on Earth. During
one winter snowstorm, a meteorologist
predicted 15 feet of snow at Mount Rainier.
Another meteorologist predicted 156 inches
of snow. Which snow prediction is greater?
By how much?
Answer:
156 and is greater by 141
Step-by-step explanation:
156>15
156-15=141
Step-by-step explanation:
To compare the two predictions, we need to convert the units of measurement to the same unit. We can do this by converting 15 feet to inches.
1 foot = 12 inches
Therefore, 15 feet = 15 x 12 = 180 inches.
So, the first meteorologist predicted 180 inches of snow.
Now, we can compare the two predictions:
- First meteorologist: 180 inches
- Second meteorologist: 156 inches
The first meteorologist's prediction is greater by:
180 - 156 = 24 inches
Therefore, the first meteorologist's prediction of 15 feet of snow at Mount Rainier is greater than the second meteorologist's prediction of 156 inches of snow by 24 inches.
Systems requests do not deal with factors involved in improving service.
a. true
b. false
Create your own unit rate example in which you have to determine the unit rate of two fractions with different units. Explain what the two fractions are, write the scenario, and calculate the unit rate.
what is 617.5 as a rational number
Answer:
1235/2
Step-by-step explanation:
617.5=6175/10=1235/2
Conard High School has 5050 students who play on the baseball, football, and tennis teams. Some students play more than one sport. If 1515 play tennis, 2525 play baseball, 3030 play football, 88 play tennis and baseball, 55 play tennis and football, and 1010 play baseball and football, determine how many students play all three sports.
3 students play all three sports.The number of students who play both baseball and tennis is 8, the number of students who play both tennis and football is 5, and the number of students who play both baseball and football is 10. Find the number of students who play all three sports.
Given:Conard High School has 5050 students who play on the baseball, football, and tennis teams. Some students play more than one sport. If 1515 play tennis, 2525 play baseball, 3030 play football, 88 play tennis and baseball, 55 play tennis and football, and 1010 play baseball and football.Find:How many students play all three sports?Solution:We can use the formula for three sets to solve the given problem.N(A U B U C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(B ∩ C) - n(C ∩ A) + n(A ∩ B ∩ C)Where, A, B, and C are the sets of the students who play tennis, baseball, and football respectively.n(A) = 15, n(B) = 25, and n(C) = 30n(A ∩ B) = 8, n(A ∩ C) = 5, and n(B ∩ C) = 10We have to find n(A ∩ B ∩ C)Using the formula we get:n(A U B U C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(B ∩ C) - n(C ∩ A) + n(A ∩ B ∩ C)50 = 15 + 25 + 30 - 8 - 10 - 5 + n(A ∩ B ∩ C)50 = 47 + n(A ∩ B ∩ C)n(A ∩ B ∩ C) = 50 - 47n(A ∩ B ∩ C) = 3 studentsSo, 3 students play all three sports.
Conard High School has 50 students who play more than one sport, and the number of students who play tennis, baseball, and football is 15, 25, and 30, respectively. We are given that 8 students play both tennis and baseball, 5 students play both tennis and football, and 10 students play both baseball and football. We are to find how many students play all three sports.We can use the formula for three sets to solve the given problem.N(A U B U C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(B ∩ C) - n(C ∩ A) + n(A ∩ B ∩ C)Where A, B, and C are the sets of the students who play tennis, baseball, and football, respectively. The formula is based on the fact that the number of students who play any two sports is counted twice and hence needs to be subtracted once.To use this formula, we need to determine the number of students who play tennis only, baseball only, and football only. We can do this by subtracting the number of students who play two sports from the total number of students who play each sport. Then, we can substitute these values in the formula.n(A) = 15 - (8 + 5) = 2n(B) = 25 - (8 + 10) = 7n(C) = 30 - (5 + 10) = 15n(A U B U C) = 2 + 7 + 15 - 8 - 10 - 5 + n(A ∩ B ∩ C)50 = 47 + n(A ∩ B ∩ C)n(A ∩ B ∩ C) = 50 - 47n(A ∩ B ∩ C) = 3Therefore, 3 students play all three sports.
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Work out x^2- 2x
when x =4
Answer:
8
Step-by-step explanation:
\(x^2-2x \\x=4\\(4)^2-2(4)\\16-8\\8\)
A bottle of water is 2/3
full. You drink 1/4
of the water. Use a model to find the portion of the bottle of water that you drink.
Answer:
1/6
Step-by-step explanation:
Total quantity of water = 2/3
Total quantity drank = 1/4
The portion of the water that you drank = 1/4 of 2/3
= 1/4 × 2/3
= 1*2 / 4*3
= 2 / 12
= 1 / 6
The portion of the water that you drank = 1/6
This means you drank one - sixth of the water in the bottle
PLEASE HELP ME WITH THESE PROBLEMS!
Answer:
1. Congruent, SAS
2. Congruent, SSS
3. Not congruent
4. Congruent, SAS
5. Congruent, SSS
6. Not congruent
7. Congruent, SAS
8. Not congruent
which expression represents the total cost for ava to rent a snowboard for s days and lucia to rent boots for b days?
Answer:
52s+30b
Step-by-step explanation:
What is a tree diagram?
a
A drawing with branches of all possible outcomes
b
A written list of all possible outcomes
c
A description of all possible outcomes
Answer:
Ok so a tree diaphragm is used in math. The answer is b a written list because it’s a little small diaphragm used for math also I’m in sixth grade
Step-by-step explanation:
I uploaded the photo of the math problem, if you are unable to see it, here it is written
The Centers for Disease Control and Prevention provide guidelines for the
target heart rate, in beats per minute, that an adult should try to achieve during
moderate-intensity physical activities. An adult’s target heart rate varies based on
their age. The following table shows several ages and the corresponding target
heart rates for moderate-intensity activity:
Age (years) 20 30 40 50 60 70
Target Heart Rate 150 133 126 119 112 105
(beats per minute)
(a) Determine the equation of the regression line.
(b) What is the slope of the regression line and what does it mean in the context of the problem?
(c) What is the dependent variable axis intercept and what does it mean in the context of the problem?
(d) Use the equation of the regression line to estimate the target pulse rate during moderate-intensity activity for a person who is 21 years old. Show the work that leads to your answer.
The target pulse rate during moderate-intensity activity for a person who is 21 years old is 144.46
Determine the equation of the regression lineThe table of values is given as:
Age (years) 20 30 40 50 60 70
Target Heart Rate 150 133 126 119 112 105
(beats per minute)
To determine the equation of the regression line, we enter the above values in a graphing calculator.
From the graphing calculator, we have the following summary:
Sum of X = 270Sum of Y = 745Mean X = 45Mean Y = 124.1667Sum of squares (SSX) = 1750Sum of products (SP) = -1475The regression equation is
y = bx + a
Where b represents the slope and a represents the y-intercept
So, we have:
b = SP/SSX = -1475/1750 = -0.84
a = MY - bMX = 124.17 - (-0.84*45) = 162.10
So, we have:
y = -0.84x + 162.10
Hence, the equation of the regression line is y = -0.84x + 162.10
The slope of the regression line and the interpretationIn (a), we have:
Slope, b = -0.84
This means that the slope of the regression line is -0.84 and the interpretation is the target heart beat decreases by 0.84 per year
The dependent variable axis intercept and the interpretationThe dependent variable is y.
In (a), we have:
Y-intercept, a = 162.10
This means that the dependent variable axis intercept of the regression line is 162.10 and the interpretation is the initial target heart beat is 162.10
The target pulse rate during moderate-intensity activity for a person who is 21 years oldThis means that
x = 21
So, we have:
y = -0.84 * 21 + 162.10
Evaluate
y = 144.46
Hence, the target pulse rate during moderate-intensity activity for a person who is 21 years old is 144.46
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HELP ASAP marking brainliest if you can also explain
⚠️⚠️^^^⚠️⚠️
Question is in the image
Finding slope:
Take two pairs of cordinate points from the table and use the formula y2-y1 divided by x2-x1
I choose (4,3) and (2,2)
2-3 divided by 2-4
= -1/2
Then to get the y intercept you use the formula: y=mx+b
For the x and y pick a cordinate to plug in. For m plug in your slope.
I pick (6,4)
4=-1/2×6+b
Multiply -1/2 and 6 to get -3 and plug that in
4=-3+b
Now add 3 to the -3 canceling that out to 0 and add three to the 4 making that 7
7=b
Y-intercept =7
Now plug in the slope and y-intercept into the slope intercept format and get:
Y=-1/2x+7