Select the correct operator for the following exponential expression.
35 ? 46
O A. =
OB. >
C.
Answer:
The correct operator for the exponential expression 3^5 ? 4^6 is > (greater than), because we can compare the values of the two exponents:
3^5 = 243
4^6 = 4096
Since 4096 is greater than 243, we can write:
3^5 < 4^6
or
4^6 > 3^5
Therefore, the correct operator for the exponential expression 3^5 ? 4^6 is > (greater than).
He works as a landscape gardener and is paid $18.25 per hour for a standard
38-hour week. He gets time and a half on evenings and Saturdays, and double time on Sundays.
Weekday hours 38
Evening/Saturday 9.5
Sunday 5.5
aCalculate Harry’s total wage for the following week.
Jessica works in a clothing shop. On a normal day she works for 7 hours and is paid $15.85 per hour. She gets time and a half for the first 3 hours of overtime she works each day, and after that she is paid double time. She earns double time and a half on public holidays.
Day
Monday6 (public holiday)
Tuesday 7
Wednesday 7
Thursday 9
Friday 0
Saturday 4.5
bCalculate Jessica’s total wage for the following week.
Staff at a restaurant are paid $7.21 per hour for working until 7pm on Monday to Friday, and paid time and a half after 7pm. They also get time and a half on Saturdays and double time on Sundays. The staff are also given an unpaid 30-minute meal break for any shift that is longer than 5 hours.
Ava’s shifts for the week are shown in this table:
Day
Tuesday4.30pm – 7.00pm
Wednesday4.30pm – 7.30pm
Thursday 5pm – 10pm
Friday 5pm – 8pm
Saturday 10am – 6.30pm
Sunday 10am – 1.30pm
cHow much will Ava earn this week?
dThe company signs a new workplace deal that removes all overtime. Instead, all staff receive $8.15 per hour. Under this new deal, how much will Ava earn for the week? Will she be better or worse off than under the old rate?
packaging idaho produce company ships potatoes to its distributors in bags whose weights are normally distributed witb. nean weight of 50 pounds and a standard deviation of .5 pounds. if a bag of potatoes is selected at random from a shipment, what is the probability that it weighs more than 51 pounds
The probability that it weighs more than 51 pounds exactly 53 pounds.
Given that, mean weight of 50 pounds and a standard deviation of 0.5 pounds.
We need to find the probability that it weighs more than 51 pounds,
P(X = 53) = 0
z = (51 - 50) / 0.5 = 2.00
P(X > 51) = P(z > 2.00) = 0.0228
z1 = (49 - 50) / 0.5 = -2.00
z2 = (51 - 50) / 0.5 = 2.00
P(49 < X < 51) = P(-2.00 < z < 2.00) = P(z < 2.00) - P(z < -2.00) = 0.9772 - 0.0228 = 0.9544
Hence, the probability that it weighs more than 51 pounds exactly 53 pounds.
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X: 1 2 3 4 5 6
Y: 782 936 966 1159 1268 1491
Use regression to find an exponential equation that best fits the data above. The equation has form y=ab^x where
a=____
b=_____
Answer:
Plot the points on the graphing calculator. Then generate an exponential regression equation.
[tex]y = 698.379( {1.131}^{x} )[/tex]
So a = 698.379 and b = 1.131 (to three decimal places).
A community has an empty field ready for development and plans to place a playground in the center. A model of the plan for the project is shown.
A large rectangle with dimensions of 35 feet by 60 feet. Inside it is a smaller rectangle with dimensions of 25 feet by 20 feet.
How much area is left for development in the field outside the playground?
500 ft2
800 ft2
1,600 ft2
2,100 ft2
Answer: The area left for development in the field outside the playground is C)1024ft^2
Step-by-step explanation:
We know that area of rectangle formula is,
Area = square unit
The total area of the field is the area of the large rectangle, which is:
=>
The area of the playground is the area of the smaller rectangle, which is:
=>
Therefore, the area left for development outside the playground is:
=>
Ajar contains four blue marbles and two red marbles. Suppose you choose a marble at random, and do not replace it. Then you choose a second marble.
K Find the probability of the following event.
Both of the selected marbles are red.
The probability that both of the selected marbles are red is
(Round to three decimal places as needed.)
Answer:
1/15 or 0.0667
Step-by-step explanation:
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bardai
chatgpt
red marble on the first draw is 2/6, or 1/3
red marble on the second draw, given that the first marble was red, is 1/5
(1/3) * (1/5) = 1/15
find the mode of these numbers:4,2,4,2,3,0,1,2,4,1,3,4,2
Answer:
4, 2
Step-by-step explanation:
the mode is the data sets that occur most frequently
7 times a number is 30 greater than the sum of twice the number and 5. what is the number
pie x pie x pie x X x X x X x X
Answer:3.14
Step-by-step explanation:This is the only number that I know that corresponds with the Pie symbol.
Which sign makes the following statement true? 1/3 _____ 6/15 Answer = < >
Answer:
<
Step-by-step explanation:
multiply 1/3 by 10 = 10/30
multiply 6/15 by 2 = 12/30
6/15 is greater
Un objeto se desplaza en linea recta a una velocidad constante. El objeto se desplaza 1/20 del trayecto en 3/4 de segundo. A esa velocidad ¿cuantos segundos le lleva al objeto desplazarse la distancia completa del trayecto? Ayúdenme estoy en media clase
It takes the object 3(3/4) seconds to travel the full distance of the trip.
We have,
The object moves at a constant speed, so we can use the formula:
distance = speed x time
Let d be the full distance of the trip, and t be the time it takes the object to travel that distance.
We can write the proportion as:
(1/20) / (3/4) = d / t
Simplifying the left-hand side:
(1/20) x (4/3) = d / t
1/5 = d / t
Now, we can solve for t by multiplying both sides by 5:
t x (1/5) = d x (1/5)
t = d/5
Now,
The time it takes the object to travel the full distance of the trip is equal to the distance divided by 5.
So, the object takes 5 times as long to travel the full distance as it takes to travel 1/20 of the distance.
And,
The time it takes the object to travel the full distance is:
t = (5 x 3/4) seconds
t = 15/4 seconds
t = 3 3/4 seconds
Therefore,
It takes the object 3 3/4 seconds to travel the full distance of the trip.
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The complete question:
An object moves in a straight line at a constant speed. The object moves 1/20 of the way in 3/4 of a second. At that speed, how many seconds does it take the object to travel the full distance of the trip?
evaluate the following 12.45x11
Answer:
136.95
Step-by-step explanation:
hope u understand
Use a graphing utility to find one set of polar coordinates of the point given in rectangular coordinates. Round your results to two decimal places.
(−9, 4)
The polar coordinates of the point (-9, 4) are approximately (9.85, -24.04°).
To find the polar coordinates (r,θ) corresponding to the rectangular coordinates (-9, 4), we can use the following formulas:
r = sqrt(x^2 + y^2)
θ = arctan(y/x)
Substituting the values x = -9 and y = 4, we get:
r = sqrt((-9)^2 + 4^2)
= sqrt(81 + 16)
= sqrt(97) ≈ 9.85
θ = arctan(4/-9)
= -0.42 radians
≈ -24.04 degrees
Therefore, the polar coordinates of the point (-9, 4) are approximately (9.85, -24.04°).
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Explain whether the research topic is best investigated through an experiment or an observational study. Then describe the design of the experiment or observational study.
1. A researcher wants to test whether stretching after exercising decreases the number of injuries due to muscle damage. Identify a potential problem, if any, with each experimental design. Then describe how you can improve it.
a) The researcher selects 400 people who exercise on a regular basis. The people are divided into two groups based on age. Within each age group, the people are randomly assigned to stretch after exercising or to not stretch. The people's occurrence of injuries due to muscle damage is monitored. The stretching after exercise significantly decreases the number of injuries due to muscle damage.
b) The researcher randomly selects 150 people who exercise on a regular basis.
Half the people stretch after exercising, and the number of their injuries due to muscle damage is monitored. The other half do not stretch after exercising, and the number of their injuries due to muscle damage is monitored. The number of injuries due to muscle damage significantly decreases for those who stretch after exercising.
The research topic of whether stretching after exercising decreases the number of injuries due to muscle damage can be best investigated through an experimental study.
We have,
The research topic of whether stretching after exercising decreases the number of injuries due to muscle damage can be best investigated through an experimental study.
a)
Potential problem:
Age can be a confounding variable, affecting the occurrence of injuries due to muscle damage. Solution: Randomly assign people to stretch or not stretch after exercising without considering their age.
Improved design:
The researcher selects 400 people who exercise on a regular basis. The people are randomly assigned to stretch after exercising or to not stretch. The people's occurrence of injuries due to muscle damage is monitored.
b)
Potential problem:
The people in the two groups may not be comparable, leading to a biased result. Solution: Randomly assign people to stretch or not stretch after exercising.
Improved design:
The researcher randomly selects 150 people who exercise on a regular basis. Half of them are assigned to stretch after exercising, and the other half are assigned to not stretch. The number of injuries due to muscle damage is monitored for both groups.
Thus,
The research topic of whether stretching after exercising decreases the number of injuries due to muscle damage can be best investigated through an experimental study.
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Next
4
Unit Post Test
Select the correct answer.
What function does this graph represent?
f(x)
The quadratic equation in the given graph can be written as:
y = -3*(x + 2)^2 + 4
Which function represents the given graph?We can see a quadratic equation that opens downwards and we can see that the vertex is at (-2, 4), then if the leading coefficient is a, we can write this as:
y = a*(x + 2)^2 + 4
We can also see that the parabola passes through (0, -8) replacing these values we will get:
-8= a*(0 + 2)^2 + 4
-8 - 4 = a*4
-12/4 = a
-3 = a
Then the quadratic equation is
y = -3*(x + 2)^2 + 4
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For each of the 6 coverage areas of a standard homeowners insurance policy, briefly describe what they cover: Dwelling, Other Structures. Personal Property,
Loss of Use, Personal Liability, Medical Payments
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Consider the function: ƒ(x) = 2/5 x- 5/2
The value of the function f(1/2) for the f(x) = 2 / 5 x- 5 / 2 is equal to -2.3.
Function is equal to,
f(x) = 2 / 5 x- 5 / 2
To get the value of f ( 1 / 2 ) .
Substitute the value of x equals to ( 1 / 2 ) we get,
f(x) = (2 / 5 ) x- ( 5 / 2 )
This implies,
f ( 1 / 2 ) = ( 2 /5 ) × ( 1 / 2 ) - ( 5 / 2 )
⇒ f ( 1 / 2 ) = ( 1 / 5 ) - ( 5 / 2 )
Take the least common multiple of 5 and 2 we get,
least common multiple of 5 and 2 is 10.
⇒ f ( 1 / 2 ) = ( 2 - 25 ) / 10
⇒ f ( 1 / 2 ) = -23 /10
⇒ f ( 1 / 2 ) = -2.3
Therefore, the value of f(1/2) for the given function is equal to -2.3.
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The above question is incomplete, the complete question is:
Consider the function: ƒ(x) = 2/5 x- 5/2 find the value of f( 1/2)?
you own a newly born german shepherd suppose the dog weighs 1kg at birth you've known from your friend that the monthly average weight gain by the dog is 5 kg if the rate of increase of the dog's weigh every month is constant determine the equation that will describe the dog's weigh predict the dog's weigh after five months using mathematical equation and graphical representation step 5 using graphing
The equation that describes the weight of the dog as a function of time is
y = 5x + 1.
We have,
To determine the equation that will describe the dog's weight, we can use the formula for linear interpolation:
y = mx + b
where y is the weight of the dog in kg, x is the number of months since birth, m is the rate of increase of the dog's weight every month in kg/month, and b is the initial weight of the dog in kg.
From the problem, we know that the initial weight of the dog is 1 kg and the monthly average weight gain is 5 kg.
Therefore, we can substitute these values into the formula:
y = 5x + 1
This equation describes the weight of the dog as a function of time.
To predict the dog's weight after five months, we can simply substitute
x = 5 into the equation:
y = 5(5) + 1 = 26 kg
Therefore, we can predict that the dog will weigh 26 kg after five months.
To represent this graphically, we can plot the equation y = 5x + 1 on a coordinate system with time (x-axis) and weight (y-axis).
We can then plot the predicted weight of the dog after five months
(x=5, y=26) as a point on the graph.
The resulting graph will be a straight line with a positive slope of 5, passing through the point (0,1) and the predicted point (5,26).
Thus,
The equation that describes the weight of the dog as a function of time is
y = 5x + 1.
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What is the approximate value of this logarithmic expression? log8 24
Answer: 1.5283
Step-by-step explanation:
When saying something like log base 8 of 24, we know that this means 8 to the power of what is equal to 24. The answer is 1.5283. If you would like to round sine it is the approximate value, do it.
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The temperature at 5PM was 14°F. By 11PM, the temperature had decreased
18°F. What was the temperature at 11PM?
Equation:
Solution:
The equation for the temperature at 11PM as required is; T(11) = T(5) - 18°F.
The solution as required in the task content is; T(11) = -4°F.
What is the temperature at 11PM as required?It follows from the task content that the temperature at 11PM is to be determined from the given information.
On this note, we have that; the equation which represents the situation is;
T(11) = T(5) - 18°F where, the temperature at 5pm T(5) = 14°F.
T (11) = 14°F - 18°F
T (11) = -4°F.
Ultimately, the temperature at 11PM is; -4°F.
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Eulerize the graph above in the most efficient way possible. The weights on the edges represent the cost to duplicate that edge. What is the total cost of your eulerization?
The total cost of your eulerization is 111.
We can Eulerize a graph by ensuring to add edges to the graph in a way that preserves its connectivity while ensuring that all vertices have even degree.
A good method to do this is by adding edges between pairs of vertices that have odd degree until all vertices have even degree.
We have to add all the edges to get the total cost
10+15+20+4+9+3+17+14+19
111
Hence, the total cost of your eulerization is 111.
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A mountain is 16, 694 feet above sea level, and a valley is 170 feet below sea level. What is the difference in elevation between the mountain and the valley?
Answer:
16864
Step-by-step explanation:
16694 + 170 = 16864
What is the surface area of a sphere with a radius of 4.75 units?
If a graph has 20 vertices with odd degree (valence), what is the smallest number of edges that would need be duplicated to eulerize the graph?
The smallest number of edges that would need be duplicated to eulerize the graph is 10.
Given that a graph has 20 vertices.
In order for a graph to be eulerized, it has to added an edge to each vertex having odd valence.
Here total number of vertices = 20
So, the smallest number of edges that would need be duplicated to eulerize the graph is half of the total number of vertices.
Number of edges = 20/2 = 10
Hence it is needed 10 edges to eulerize the graph.
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Find the total surface area of this composite figure.
In the given diagram, the total surface area of the composite figure is 361.28 square yards
Calculating the total surface area of a composite figureFrom the question, we are to calculate the total surface area of the given composite shape
In the composite shape, we have a cone and a hemisphere
The total surface area of the composite figure = Surface area of the hemisphere + Curved surface area of the cone
Surface area of the hemisphere = 2πr²
Where r is the radius
Curved surface area of a cone = πrl
Where r is the radius
and l is the slant height
In the given diagram,
Using the Pythagorean theorem,
l² = 12² + 5²
l² = 144 + 25
l² = 169
l = √169
l = 13 yd
Radius of cone and hemisphere = 5 yd
Total surface area of the composite figure = 2πr² + πrl
Substituting the parameters
Total surface area of the composite figure = 2π(5)² + π(5)(13)
Total surface area of the composite figure = 50π + 65π
Total surface area of the composite figure = 115π
Total surface area of the composite figure = 361.28 yd²
Hence,
The total surface area is 361.28 square yards
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The graph below shows the distance a car drove over a course of 18 hours. At what time did the driver end her trip?
at 20 hours
at 2 hours
at 18 hours
at 4 hours
How long will it take for an investment to double, if interest is compounded continuously at 7%?
Answer:
We don't know the initial value of the principal but we do know that the accumulated value is double (twice) the principal. It takes 9.9 years for money to double if invested at 7% continuous investment
Write the equation of the line in fully simplified slope-intercept form.
-12-11-10-9-
12
11
10
9
R
5
4
2
654-3-2-1
-2
3
4
-5
-6
-8
6
-10
-11
-12
34567 8 9 10 11 12
The equation of the line in fully simplified slope-intercept form is y = x + 7.
We have,
From the graph,
The coordinates of the line are:
(0, 7), (-7, 0), and (-2, 5).
We can use any coordinates the line touches on the graph.
We will use,
(0, 7) and (-7, 0)
The equation can be written in the form y = mx + c
m = (0 - 7) / (-7 - 0)
m = -7/-7
m = 1 ______(1)
And,
(0, 7) = (x, y)
So,
y = mx + c ______(2)
7 = 1 x 0 + c
7 = c
c = 7 ______(3)
Now,
From (1), (2), and (3).
y = x + 7
Thus,
The equation of the line in fully simplified slope-intercept form is y = x + 7.
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Pls someone help im stuck with this one and i dont know what im supposed to do with the thing at the bottom
If in a triangle ABC, right angle is at C, BA is hypotenuse, the length of side BC is 5√7 units.
In a right triangle, the hypotenuse is the longest side and is opposite the right angle. Therefore, in triangle ABC, side BA is the longest side, and it is also the hypotenuse.
Using the Pythagorean theorem, we can find the length of the third side BC. The theorem states that the square of the hypotenuse (BA²) is equal to the sum of the squares of the other two sides (BC² + CA²).
BA² = BC² + CA²
16² = BC² + 9²
256 = BC² + 81
BC² = 256 - 81
BC² = 175
BC = √175
BC = 5√7
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a circle has a cirumference of 37 5/7 inches. What is its area? use 22/7 for pi
let's firstly convert tyhe mixed fraction to an improper fraction.
[tex]\stackrel{mixed}{37\frac{5}{7}}\implies \cfrac{37\cdot 7+5}{7}\implies \stackrel{improper}{\cfrac{264}{7}} \\\\[-0.35em] ~\dotfill\\\\ \textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=\frac{264}{7} \end{cases}\implies \cfrac{264}{7}=2\pi r\implies \cfrac{264}{7}=2\cdot \cfrac{22}{7}\cdot r \\\\\\ \cfrac{264}{7}=\cfrac{44r}{7}\implies 264=44r\implies \cfrac{264}{44}=r\implies 6=r \\\\[-0.35em] ~\dotfill[/tex]
[tex]\textit{area of a circle}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=6 \end{cases}\implies A=\pi (6)^2\implies A=\cfrac{22}{7}\cdot 6^2 \\\\\\ A=\cfrac{22}{7}\cdot 36\implies A=\cfrac{792}{7}\implies A=113\frac{1}{7}[/tex]