The sample distribution is approximately normal with a mean of 10 and a standard deviation of 1.
The distribution is slightly skewed to the left, with a slightly higher probability of lower readings than higher readings.
(b) If the sample minimum is lower than 9, this would indicate that the thermostat manufacturer's claim is false. This is because the manufacturer claims that the temperature will not go below 10 degrees, but the sample minimum of 9 suggests that it does. The probability of observing a sample minimum of 9 or lower is 0.25, which indicates that the probability of the temperature dropping below 10 degrees is relatively high.
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you download a digital soccer game for . you can add new players for each to upgrade your team. the total cost is a function of the number of new players that you add. which of the following statements about the domain and the graph of the function is correct?
The domain is discrete and the range is continuous, which can be an accurate statement regarding the two terms.
What are domain and range?The range of values that we are permitted to enter into our function is known as the domain of a function.
The x values for a function like f make up this set (x).
A function's range is the collection of values it can take as input.
After we enter an x value, the function outputs this sequence of values.
So, the parameters are as follows, taken from the query:
Downloaded Amount = $2.50
Added amount to each player = $1.50
Use x to indicate how many players there are.
The following representations are what we have.
Total amount = Amount to download + Amount to add each player * Number of players
Now, we obtain:
y = 2.50 + 1.50 * x
y = 2.50 + 1.5x
The number of players serves as the input to the aforementioned linear function.
The domain is discrete as a result.
The amount, though, can have decimal points
The range is continuous as a result.
Therefore, the domain is discrete and the range is continuous, which can be an accurate statement regarding the two terms.
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Add.
18 9/10 + 8 3/10
In simplest form
Answer:
136/5
Step-by-step explanation:
18 9/10 + 8 3/10
change to improper fraction
=189/10 + 83/10
Adding, you have:
=272/10
2 can further divide both numbers
= 136/5
Market for Hamburgers Supply and Demand — End of Chapter Problem In the accompanying supply and demand diagram, depicting the market for hamburgers in your hometown, first shift the demand curve, given the event described. Then move the equilibrium point to its new position. What is the effect on equilibrium price and quantity? Event: The price of tacos increases. Price per hamburger E Equilibrium price decreases. stays the same. increases. Incorrect Quantity of hambugers Incorrect Equilibrium quantity decreases. O O O increases. stays the same. IncorrectPrevious questionNext
The increase in the price of tacos shifts the demand curve to the left, causing a decrease in the equilibrium price and quantity of hamburgers.
The accompanying supply and demand diagram is depicting the market for hamburgers in your hometown. The event that is given is that the price of tacos increases. This will cause the demand curve to shift to the left, as consumers shift from hamburgers to tacos. As the demand curve shifts to the left, the equilibrium price will decrease and the equilibrium quantity will decrease. This is because the decrease in demand will cause the quantity demanded to fall and the decrease in demand will cause the price to fall. This shift in the supply and demand curves will cause the equilibrium point to move to the left and downward. The new equilibrium price will be lower than the original equilibrium price and the quantity will also be lower.
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Consider the line .3x-6y=-8
Find the equation of the line that is parallel to this line and passes through the point .4,2
Find the equation of the line that is perpendicular to this line and passes through the point . (4,2)
An equation of the line that is parallel to this line and passes through the point (4, 2) is y = 0.5x.
An equation of the line that is perpendicular to this line and passes through the point (4, 2) is y = -2x + 10.
How to determine the equation of the line?In Geometry, two (2) lines are parallel under the following conditions:
m₁ = m₂ ⇒ -1 = -1
Note: m represents the slope.
From the linear equation 3x - 6y = -8, we have:
y = 3x/6 + 8
y = 0.5x + 8
At point (4, 2), an equation of the line that is parallel to this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the data points.c represents the intercept.y - 2 = 0.5(x - 4)
y = 0.5x - 2 + 2
y = 0.5x
In Mathematics, a condition that must be met for two lines to be perpendicular is given by:
m₁ × m₂ = -1
0.5 × m₂ = -1
m₂ = -2
At point (4, 2), an equation of the line that is perpendicular to this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 2 = -2(x - 4)
y = -2x + 8 + 2
y = -2x + 10
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f(x) = 11x - 2. Find x when f(x) = 64
please show steps
Answer: the correct value of x in this will be 6.
Step-by-step explanation: According to the equation given ,
f(x) = 64
so , f(x) = 11x - 2 now putting the value of f(x) in this equation
therefore , 64 = 11x - 2
now solving the equation , 11x= 64+2
11x = 66
x = 66/11
x = 6
thus, the value of x obtained from the equation is 6
In a particular game, a fair die is tossed. If the number of spots showing is either 4 or 5, you win $1, if the number of spots showing is 6, you win $4, and if the number of spots showing is 1, 2, or 3, you win nothing. Let X be the amount that you win. The expected value of X is
(a) $0.00
(b) $1.00
(c) $2.50
(d) $4.00
(e) $6.00
The amount that you when a fair dice is tossed (showing is either 4 or 5, you win $1, if the number of spots showing is 6, you win $4, and if the number of spots showing is 1, 2, or 3, you win nothing) is $1.00
Given,
when you get either 4 or 5, the reward = $1
when you get either 6, the reward = $4
when you get 1, 2, or 3, the reward = $0
We know that,
Probability of getting 6 = 1/6
Probability of getting 4 = 1/6
Probability of getting 5 = 1/6
Probability of getting 1 = 1/6
Probability of getting 2 = 1/6
Probability of getting 3 = 1/6
Therefore,
[tex]X = \frac{1}{6}* 4 + \frac{1}{6}* 1 +\frac{1}{6}* 1+ \frac{1}{6}* 0+ \frac{1}{6}* 0 + \frac{1}{6}*0[/tex]
[tex]= \frac{4}{6} + \frac{1}{6}+ \frac{1}{6}[/tex]
[tex]= \frac{6}{6}[/tex]
[tex]= 1[/tex]
Hence, the Value of X = $1.
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seven values on the number line above are marked with letters. match the opposites. question 11 options: a) f and h; y and y b) c and l; a and k c) a and k; f and h d) c and l; f and h
The answer to the question is d) c and l; f and h.
The concept of opposite numbers on the number line can be expressed mathematically by the equation -x = y, where x is the original number and y is the opposite number. This equation can be used to calculate the opposite of any number. For example, if the number 5 is located at point a on the number line, the opposite of 5 is located at point k and can be calculated by substituting 5 for x in the equation and solving for y. -5 = y, therefore y = -5. The opposite of 5 is therefore -5. To calculate the opposite of any of the other numbers marked on the number line, the same equation can be used. The answer to the question is d) c and l; f and h.
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An accessory shop estimated that to produce one unit of a product the cost for raw materials is RM15. The fixed cost is RM5 000. The product is sold for RM25 per unit.
a. Find the profit function, P(x), where x is the number of units of the product.
b. Find the break-even point.
c. How much was the profit/loss if 350 units were sold.
d. Sketch the graph of the cost function, C(x) and the revenue function, R(x). Indicate the break-even point and shade the profit and loss areas.
please help me to answer a,b,c and d.
a. The profit function P(x) is 10x - 5000.
b. The break even point is at 500 units.
c. If 350 units were sold, the loss was Rs. 1500.
d. The graph of the functions are attached below.
The solutions are obtained using the profit function.
What is profit function?
A profit function is a mathematical relationship that represents the difference produced when the cost function is subtracted from the revenue function. The graph of a profit function shows the optimal combination of revenues and expenses to produce the maximum profit.
a. We are given cost of raw material as Rs. 15 and the fixed cost is Rs. 5000. The product is sold for Rs.25 per unit.
This means that R(x) = 25x
We know that TC= FC + VC(x)
So, TC = 5000 + 15x
Therefore, the profit function will be
⇒Profit = R(x) - TC
⇒Profit = 25x - 5000 - 15x
⇒Profit = 10x - 5000
b. For break even, the profit should be 0.
Therefore,
⇒10x - 5000 = 0
⇒10x = 5000
⇒x = 500
So, the break even will be at 500 units.
c. We are given x=350
Putting this value in profit function, we get
⇒Profit = 10(350) - 5000
⇒Profit = 3500 - 5000
⇒Profit = -1500
So, there is loss of Rs. 1500.
d. The red line represents the cost function and the blue line represents the revenue function.
The break even point is the point where the two lines are meeting.
The area below the break even is the loss area and above it is the profit area.
Hence, the solutions are obtained.
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A company sells concrete in batches of 5 cubic yards. The probability distribution of X, the number of cubic yards sold in a single order for concrete from this company, is shown in the table. The expected value of the probability distribution of X is 19.25 and the standard deviation is 5.76. There is a fixed cost to deliver the concrete. The profit Y, in dollars, for a particular order can be described by Y = 75X - 100. What is the standard deviation of Y?
answer choices
O $332.00
O $432.00
O $532.00
O $1,343.75
O $1,400.00
The standard deviation of Y is $432.00 and this can be determined by using the formula of standard deviation and the given data.
Given :
A company sells concrete in batches of 5 cubic yards.
The probability distribution of X, the number of cubic yards sold in a single order for concrete from this company, is shown in the table below.
The expected value of the probability distribution of X is 19.25 and the standard deviation is 5.76.
There is a fixed cost to deliver the concrete. The profit Y, in dollars, for a particular order can be described by (Y = 75X - 100).
The formula to obtain the standard deviation is given below:
SD(Y) = SD(75X - 100)
Simplify the above expression by substituting the value of SD(X) and SD(100) in the above expression.
SD(Y) = 75SD(X) - SD(100)
SD(Y) = 75 SD(X) - 0
SD(Y) = 75×5.76
SD(Y) = $432
Therefore, the correct option is B.
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The average yearly cumulative rainfall in Tucson by month is shown in the graph below. Does this
graph represent cumulative rainfall as a function of the day? Why or why not? What is the average
annual cumulative rainfall in Tucson? What is the approximate average rainfall in December? During
which month is average rainfall the greatest? How do you know?
The average annual cumulative rainfall is 1 inch per month. During month of August average rain fall is greatest because slope in this month is maximum.
What is the average?In maths, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.
The graph does not represent cumulative rainfall as a function of day.
Because they have average all values for month Total cumulative rainfall is 12 inches.
Total period is 12 month
So, average annual cumulative rainfall is
12/12 =1 inch per month
Average rainfall in the month of December= (average cumulative rainfall in December - average cumulative rainfall in November)
= 12-11
= 1 inch
Therefore, during month of August average rain fall is greatest because slope in this month is maximum.
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3
10 points
(5x - 4)(x + 5)
O 5x²+21x-20
O4x²-17x+4
O 10x²+20x+10
O 10x²-10
Answer:
First choice: 5x²+21x-20
Step-by-step explanation:
This is easy to answer if you realize that there is only one way an x² term can appear in the result and that is by the multiplication of 5x and x which results in 5x².
The only choice which has 5x² as a term is the first: 5x²+21x-20
However, it is important to know the FOIL method to multiply two terms together
FOIL stands for First Outer Inner Last and is a technique for multiplying two terms of the form (a+b) and (c+d)
In (a + b) (c + d),
First terms are a and c so their product is ac
Outer terms are a and d so their product is ad
Inner terms are b and c with product bc
Last terms are b and d with product bd
The result is the sum of all these terms
Let's take (5x - 4)(x + 5)
F: 5x·x = 5x²
O: 5x · 5 = 25x
I: -4 ·x = -4x
L: -4·5 = -20
Adding up these individual terms we get
5x² +25x - 4x - 20 = 5x²+21x-20
So first choice is the correct answer
DUE SOON
PLEASE EXPLAIN HOW YOU GOT THE ANSWER.
questions down below
The scale factor of the two triangles is 1/4 or 4
What is scale factor?You should understand that scale factor is the ratio of any two corresponding lengths.
Looking at the triangles, the larger triangle has sides
AB with 12 gridsAC with 11 gridsBC with 11 gridsThe smaller triangle has sides
AB with 3 gridsAC with 3 grids and BC with 3 gridsScale factor = (Larger length)/ (Smaller length) or (Smaller length/(Larger length)
This is an indication that the triangles have scale factors of:
Scale factor = 12/3 = 4 or
Scale factor = 3/12 = 1/4
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use traces to sketch the surface. (if an answer does not exist, enter dne. select update graph to see your response plotted on the screen. select the submit button to grade your response.) 9x2 y2 9z2
In order to accurately represent the surface, we would need to be able to plot the equation in 3-dimensions using 3-dimensional coordinates. Since this is not possible, the answer is dne.
In order to accurately represent the surface, we would need to be able to plot the equation in 3-dimensions using 3-dimensional coordinates. Since this is not possible, the answer is dne.
dne
Since 9x2 y2 9z2 is a 3-dimensional equation, it cannot be sketched on a 2-dimensional plane. Therefore, the answer is dne.
The equation 9x2 y2 9z2 is a 3-dimensional equation and cannot be represented on a 2-dimensional plane. Therefore, it is not possible to sketch the surface using this equation. As a result, the answer is dne. The equation contains three variables, x, y and z, and cannot be represented on a graph without the use of three axes. In order to accurately represent the surface, we would need to be able to plot the equation in 3-dimensions using 3-dimensional coordinates. Since this is not possible, the answer is dne.
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A fair dice is rolled 3 times in a row. The outcomes are shown below.
Calculate the probability of all three events occurring.
Roll Outcome
1st even
2nd prime
3rd multiple of 5
Answer: 1/24
Step-by-step explanation:
1st even = 3/6 (2,4,6)
2nd Prime = 3/6 (2,3,5)
3rd multiple of 5 = 1/6 (5)
3/6 x 3/6 x 1/6 = 9/216
9/216 = 1/24
Two cars are 298 mi apart and traveling toward each other along the same road. They meet in 2 hr. One car is traveling 7 mph slower than the other. What is
the speed of each car?
Part 1/2
The faster car travels at (blank) mph.
The faster car is traveling at 149 mph, and the slower car is traveling at 142 mph.
How to calculate the speed?Speed can be calculated using the following formula: Speed = Distance/Time.Speed is measured in units such as meters per second (m/s), kilometers per hour (km/h), miles per hour (mph), etc.To calculate the speed of an object, you must first measure the distance it has traveled and the time it took to travel that distance. If the object is moving in a straight line, the distance is the length of the line. If it's moving in a circle, the distance is the circumference of the circle.Once you have the distance and time, divide the distance by the time to get the speed of the object. For example, if an object travels 10 meters in 5 seconds, its speed is 10/5 m/s, or 2 m/s.The faster car is traveling at (298 mi / 2 hrs) = 149 mph.The slower car is traveling at (149 mph - 7 mph) = 142 mph.
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you have 30 coins worth 2.05 dollars in dimes and nickels. whats in your wallet.
The number of dimes and nickels are equal to 11 and 19 respectively.
How to determine the number of dimes and nickels?In order to determine the number of dimes and nickels, we would assign a variables to the unknown numbers and then translate the word problem into algebraic equation as follows:
Let d represent the number of dimes.Let n represent number of nickels.Since you have a total number of 30 coins, an equation which models this situation is given by;
d + n = 30 ....equation 1.
Note: 1 nickel is equal to 0.05 dollar and 1 dime is equal to 0.1 dollar.
Additionally, the coins are worth 2.05 dollars;
0.1d + 0.05n = 2.05 ....equation 2.
Solving both equations simultaneously, we have:
0.1(30 - n) + 0.05n = 2.05
3 - 0.1n + 0.05n = 2.05
3 - 0.05n = 2.05
0.05n = 0.95
n = 0.95/0.05
n = 19 nickels.
For the number of dimes;
d = 30 - n
d = 30 - 19
d = 11 dimes.
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Complete Question:
You have 30 coins worth $2.05 in nickels and dimes. What's in your wallet? Create and solve system of equations to find how many dimes and how many nickels you have.
Can someone tell me if this is right? If not please tell me the actual answer.
Answer:
That is correct.
Step-by-step explanation:
The greater the absolute value of a negative number, the lesser (farther left from zero) it is. The greater the absolute value of a positive number, the greater (farther right from zero) it is.
Thus,
-6 < -2 < 0 < 4 < 8
and
-5.5 < -5.2 < -5 < -2.5 < 5.5
Notice also how it is easier to compare numbers when they are converted to the same form—in this case decimal form.
a. Write the function if Cecily releases the ball 40 feet above the ground at a velocity of 64 feet per second
The function that describes the height of the ball as a function of time t (in seconds) can be represented as:
h(t) = -16t^2 + 64t + 40
Where h(t) is the height of the ball in feet above the ground, t is the time in seconds, and the -16t^2 represents the acceleration due to gravity. The 64t represents the initial velocity of the ball, and 40 is the initial height of the ball above the ground.
Check the picture below.
1. You are the manager of a small store that specializes in hats, sunglasses, and other accessories. You are considering a sales promotion of a new line of hats and sunglasses. You will offer the sunglasses only to those who purchase two or more hats, so you will sell at least twice as many hats as pairs of sunglasses. Moreover, your supplier tells you that, due to seasonal demand, your order of sunglasses cannot exceed 100 pairs. To ensure that the sale items fill out the large display you have set aside, you estimate that you should order at least 210 items in all. Assume that you will lose $3 on every hat and $2 on every pair of sunglasses sold. Given the constraints above, how many hats and pairs of sunglasses should you order to lose the least amount of money in the sales promotion? [Using Graphic method]
Least cost in the sales promotion is when (140, 70) i.e. Hats = 140 and pair of glasses = 70.
What is meant by Graphic method?To determine if the data support the mixing of two potential sources or the fractionation of a single source, graphical approaches are frequently used.
To better interpret their data, researchers now employ a variety of graphical tools, including scatterplots, box plots, and histograms. Graphs are excellent for illustrating trends, patterns, and correlations between variables as well as for displaying and summarizing vast volumes of numerical data.
Value of cost at (140, 70) is 3 × 140+ 3 × 70
= $630
Consider any point on the feasible line, say (150, 60)
Cost = 3 × 150 + 3 × 60 = $570
Cost is increasing towards the point (210, 0)
Thus, Least cost is when (140, 70) i.e. Hats = 140 and pair of glasses = 70.
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one positive point charge q1 is located at (x, y) coordinate (-2.22, -6.56) and a second positive point charge q2
Electric potential energy is the energy that is needed to move a charge against an electric field.
What is electrical potential energy?The power required to move a charge in opposition to an electric field is known as electric potential energy. A charge must be moved through a stronger electric field with more energy, but it also must be moved through a weaker electric field with more energy.The energy that is held in a charge as a result of its placement in an electric field is known as electric potential energy (Ep). Moving two like charges in close proximity, for instance, stores potential energy because the charges repel one another. Since the charges are attracted to one another, separating opposite charges also stores potential energy.The configuration of a particular set of point charges within a given system is connected with the potential energy known as electric potential energy, which is a product of conservative Coulomb forces.Completed question :
A point charge q1 , is held stationary at the origin. A second charge q2 is placed at a point a, and the electric potential energy of the pair of charges is -6.4 x [tex]10^{-8}[/tex] J. When the second charge is moved to point b, the electric force on the charge does 4.2 x [tex]10^{-8}[/tex] J of work. What is the electric potential energy of the pair of charges when the second charge is at point b?
Given data :
PE1 = -6.4 x [tex]10^{-8}[/tex] J
Work done = 4.2 x [tex]10^{-8}[/tex] J
PE1 = PE2 + Work done
PE2 = PE1 - Work done =
= -6.4 x [tex]10^{-8}[/tex] J - 4.2 x [tex]10^{-8}[/tex] J = -10.6 x [tex]10^{-8}[/tex] J
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9(7h−4k)+10k−5(6k−7h)
Answer:
98h - 56k----------------------------
Given expression:
9(7h - 4k) + 10k - 5(6k - 7h)Simplify it in steps below:
9(7h - 4k) + 10k - 5(6k - 7h) = Given 9(7h) - 9(4k) + 10k - 5(6k) + 5(7h) = Distribute63h - 36k + 10k - 30k + 35h = Simplifyh(63 + 35) - k(36 - 10 + 30) = Collect like terms98h - 56k AnswerAnswer:
[tex] \sf \: 98h - 56k [/tex]
Step-by-step explanation:
Given expression,
→ 9(7h - 4k) + 10k - 5(6k - 7h)
Let's simplify the expression,
→ 9(7h - 4k) + 10k - 5(6k - 7h)
→ 63h - 36k + 10k - 30k + 35h
→ (63h + 35h) + (-36k + 10k - 30k)
→ (98h) + (-56k)
→ 98h - 56k
Hence, answer is 98h - 56k.
please someone help me with this escape room question! i’ve been stuck on this problem for so long now
Answer:
all of them are 17
Step-by-step explanation:
7+9=16
16+1+0=17
9+7=16
16+1+0=17
1+0+9=10
10+7=17
7+1=8
8+9+0=17
hope this helped!
Use areas to evaluate 4xdx where 0 < a
Integration is basically used to find the areas of the two-dimensional region and computing volumes of three-dimensional objects.
What is integration?
In mathematics, an integral lends numerical values to functions to represent concepts like volume, area, and displacement that result from combining infinitesimally small amounts of data. Integration is the action of locating integrals.
Differentiation is the opposite of integration.
In other words, reversing the differentiation process merely results in integration. The example below demonstrates it:
dy/dx = 2x since y = x2 Consequently,
(dy/dx) dx = 2x dx = x2.
Together, and dx represent the integration of the function with respect to x.
The anti-differentiation is another name for integration. In this procedure, we are given a function's derivative and asked to determine the function (i.e., primitive). We are aware that cos x is the differentiation of sin x.
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b) Prabin types 765 words in 9 minutes. How many words would he type in half an hour? How long does he take to type 12,750 words at the same speed?
Answer:
Prabin types 765/9 i.e, 85 words in one minute. Therefore in 30 minutes prabin will type 30 x 85 i.e., 2550 words. Again, he types 1 word in 9/765 minutes. Therefore , he will type 12750 words in 12750 x (9/765) minutes, i.e, 150 minutes.
Prabin would type 2,550 words in half an hour at the same speed. It would take him 150 minutes to type 12,750 words at the same speed.
Explanation:To find out how many words Prabin would type in half an hour, we need to determine how many minutes are in half an hour. Since there are 60 minutes in an hour, half an hour would be 30 minutes. Now, we can set up a proportion to find the number of words Prabin would type in half an hour:
765 words / 9 minutes = x words / 30 minutes
Cross-multiplying, we get:
9 * x = 765 * 30
Simplifying, we find:
x = (765 * 30) / 9
x = 2,550 words
To find out how long it would take Prabin to type 12,750 words at the same speed, we can set up another proportion using the given information:
765 words / 9 minutes = 12,750 words / t minutes
Cross-multiplying, we get:
9 * (12,750) = 765 * t
Simplifying, we find:
t = (9 * 12,750) / 765
t = 150 minutes
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The position of an object moving along a line is given by the function s(t) = -7t^2 +70t. Find the average velocity of the object over the following intervals.
(a)​ [1,5]
​(b) ​[1,4​]
​(c)​ [1,3​]
​(d) ​[1, 1​+h] where h > 0 is any real number.
(a) Average velocity = -7(5^2-1^2) + 70(5-1) = -90 m/s.
(b) Average velocity = -7(4^2-1^2) + 70(4-1) = -62 m/s.
(c) Average velocity = -7(3^2-1^2) + 70(3-1) = -34 m/s.
(d) Average velocity = -7(1+h)^2 + 70(1+h-1) = -7h^2 + 70h m/s.
(a) Average velocity = -7(5^2-1^2) + 70(5-1) = -7(25-1) + 70(4) = -7*24 + 280 = -168 + 280 = -88 m/s.
(b) Average velocity = -7(4^2-1^2) + 70(4-1) = -7(16-1) + 70(3) = -7*15 + 210 = -105 + 210 = -95 m/s.
(c) Average velocity = -7(3^2-1^2) + 70(3-1) = -7(9-1) + 70(2) = -7*8 + 140 = -56 + 140 = -16 m/s.
(d) Average velocity = -7(1+h)^2 + 70(1+h-1) = -7(1+h)^2 + 70h = -7(1+h)^2 + 70h m/s. The average velocity of an object over a given period of time is calculated by taking the difference between the final and initial positions, and dividing it by the amount of time elapsed. In this exercise, we are given the position of an object along a line as a function of time, s(t) = -7t^2 + 70t. To solve each part, we can plug in the given time intervals into the function, and calculate the difference between the initial and final positions. We then divide this difference by the amount of time elapsed to find the average velocity. For example, in part (a), the average velocity is calculated as -7(5^2-1^2) + 70(5-1) = -90 m/s. In part (b), the average velocity is calculated as -7(4^2-1^2) + 70(4-1) = -62 m/s. In part (c), the average velocity is calculated as -7(3^2-1^2) + 70(3-1) = -34 m/s. Finally, in part (d), the average velocity is calculated as -7(1+h)^2 + 70h m/s
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20 POINTS! WRITE A LINEAR EQUATION PERPENDICUALR TO -2Y = 5X + 8 PASSING THROUGH POINT (10,-1)
The equation of the line perpendicular to -2y = 5x + 8 and passes through (10, -1) is y = 2 / 5 x - 5.
How to represent linear equation?Linear equation can be represented in slope intercept form as follows:
y = mx + b
where
m = slope of the lineb = y-interceptTherefore, the equation is perpendicular to -2y = 5x + 8 and passes through (10, -1).
Perpendicular lines have slopes that are negative reciprocals of one another.
Therefore,
-2y = 5x + 8
y = - 5 / 2 x - 4
Therefore,
slope = 2 / 5
Let's find the y-intercept using (10, -1)
-1 = 2 / 5(10) + b
-1 = 20 / 5 + b
b = -1 - 4
b = -5
Therefore, the equation of the line is y = 2 / 5 x - 5
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Evaluate the following expression.
3
8
2
(3) ².
8
11
2
(Type an integer or a simplified fraction.)
By calculating, The value of given expression 8 · (2 + 3 )²- 4² is 184
What is Algebraic expression ?
Algebraic expressions are the concept of expressing numbers the use of letters or alphabets with out specifying their actual values. The fundamentals of algebra taught us a way to explicit an unknown price using letters along with x, y, z, etc. those letters are known as right here as variables.
An algebraic expression can be a combination of both variables and constants. Any cost this is positioned before and extended by using a variable is a coefficient.
Given expression ,
= 8 · (2 + 3 )²- 4²
= 8. (5)^2 - 4^2
=8.25 - 16
= 200 - 16
= 184
so, the value of expression is 184.
Therefore, The value go given expression 8 · (2 + 3 )²- 4² is 184
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Find the circumference of a circle with a diameter of 36 units.
Answer:
Circumference = 113.097 units
Step-by-step explanation:
C = 2[tex]\pi r[/tex]
C = 2(3.14)(36/2)
C = 113.097 units
Finding a cubic function in exercises 61 and 62, find a,b,c, and d such that the cubic f(x) - ax^3 + bz^2 + cz + dsatisfies the given conditions. 61. relative maximum: (2,4) Relative minimum: (4,2) Inflection point: (3,3)
-12a is a cubic function in exercises when Relative minimum (4,2).
What in mathematics is a relative maximum?
A point (x,y) on the graph of the function whose y-coordinate is larger than all other y-coordinates on the graph at locations "near to" is known as a relative maximum point (x,y). ( x , y ) .
f'(x) = 3ax² + 2bx + c
(3,3) and (5,1 ) are print of relative maximum
so, f'(3) = f'(5) = 0
3a(3)² + 2b(3) + c = 0
or 27a + 6b + c = 0
and 3a(5)² + 2b(5) + c = 0
75a + 10b + c = 0 ...................... 2
the Inflection point occurs at point where f''(x) = 0
d/dx ( 3ax² + 2bx + c ) ∫x = 4 = 0
because (4,2) is point of Inflection .
6a(4) + 2b = 0
24a + 2b = 0
b = -12a
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A group of 12 people on a trek have enough water to last 8 days.
a) If 4 more people join the trek, how long will the water supply last the
whole group?
When the number of people is 16, the water lasts for 6 days, which is found using unitary method.
What is the unitary method?
The unitary method is a strategy for problem-solving that involves first determining the value of a single unit and then multiplying that value to determine the required value.
a) Let the amount of water present = L
Initially, this amount was considered for 12 people for 8 days.
For 12 people,
8 days = L
1 day = L/8
So the water required for one person for one day = (L/8) / 12 = L/96
But now 4 more people joined the trek,
So for 16 people, water used in one day = (L/96)*16 = L/6
Now the water will last for 6 days since,
(L/6 * 6) = L
b) The assumption that is made while solving the question is that the water required by each person is considered the same(L/96) even if the number of persons increases.
Therefore the water lasts for 6 days when the whole group consists of 16 people.
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