Answers
Answer:
1st box = 200
2nd box = 7
3rd box = 237
4th box = 270
5th box = 333
Step-by-step explanation:
1st box:
Related Questions
A few playing cards are missing from a standard 52-card deck. Three cards
remain when you deal the entire deck to four people. And two cards remain
when you deal the entire deck to three people OR if you deal the entire
deck to five people. How many cards are missing from the deck???
Answers
Answer:
49 cards would be left from the deck of card.good luck with future questions I hope I am right
problem 3: compute the general solution for: d 2 y dt2 − 2 dy dt − 15y = e 4t
Answers
The general solution for given equation is y = c₁e^5t + c₂e^-3t - (1/7)e^4t.
A differential equation is an equation that contains at least one derivative of an unknown function, either an ordinary derivative or a partial derivative. Suppose the rate of change of a function y with respect to x is inversely proportional to y, we express it as dy/dx = k/y.
In calculus, a differential equation is an equation that involves the derivative (derivatives) of the dependent variable with respect to the independent variable (variables). The derivative represents nothing but a rate of change, and the differential equation helps us present a relationship between the changing quantity with respect to the change in another quantity. y=f(x) be a function where y is a dependent variable, f is an unknown function, x is an independent variable.
We have to find the general solution for d²y/dt² - 2 dy/dt - 15y = e^4t
Solving the above ordinary differential equation, we get:
y = c₁e^5t + c₂e^-3t - (1/7)e^4t
Thus, the general solution for given equation is y = c₁e^5t + c₂e^-3t - (1/7)e^4t
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Mai played 10 basketball games. She recorded the number of points she scored and made a dot plot. Mai said that she scored between 8 and 14 points in most of the 10 games, but one game was exceptional. During that game she scored more than double her typical score of 9 points. Use the number line to make a dot plot that fits the description Mai gave. A blank dot plot for "points" with the numbers 8 through 22, in increments of 2, indicated
Answers
{9, 10, 11, 12, 14} U {x | x > 18} represents the values of x in Mai's dot plot.
Let's say x represents Mai's score in each basketball game. Based on Mai's description, the following can be inferred about the values of x:
8<=x<=14 for most of the 10 games.
x > 18 for one game
(because it was more than double Mai's typical score of 9 points).
Here is a representation of the dot plot
8___9___10___11___12___
14___16___18___20___22
The dots placed at 9, 10, 11, 12, and 14 represent the values of x where Mai scored between 8 and 14 points in most of the 10 games. The dot placed at a value greater than 18 represents the exceptional game where Mai scored more than double her typical score of 9 points.
Therefore, the set of values for x can be represented as:
{9, 10, 11, 12, 14} U {x | x > 18}
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evaluate the line integral where c is the straight line segment from point to point
Answers
The line integral [tex]\int_{c}xds[/tex]where c is the straight line segment from point (1, 2) to point (5, 10) is 12√5.
Using the two-point form of the line, we can compute the equation of the line connecting the points and obtain:
y = 2x
Consider x = t. Now the result is:
y = 2t
We can write C as:
[tex]\vec{r}(t)=t\hat{i}+2t\hat{j}[/tex]
Now, t ranges from t = 1 to t = 5 since x = t and x range from x = 1 to x = 5. When we differentiate the C equation, we obtain:
[tex]\vec{r}'(t)=\hat{i}+2\hat{j}[/tex]
Now finding the magnitude
[tex]|\vec{r}'(t)|=\sqrt{(1)^2+(2)^2}[/tex]
[tex]|\vec{r}'(t)|=\sqrt{1+4}[/tex]
[tex]|\vec{r}'(t)|=\sqrt{5}[/tex]
Now, the integral will be:
I = [tex]\int_{t=1}^5t\:(\sqrt 5)dt[/tex]
I = [tex]\sqrt {5}\int_{t=1}^5tdt[/tex]
Now integrating
I = [tex]\sqrt {5}\left(\frac{t^2}{2}\right)_{t=1}^{5}[/tex]
I = [tex]\sqrt {5}\left(\frac{5^2}{2}-\frac{1^2}{2}\right)[/tex]
I = √5(25/2 - 1/2)
I = √5(12.5 - 0.5)
I = 12√5
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The complete question is:
Evaluate the line integral [tex]\int_{c}xds[/tex]where c is the straight line segment from point (1, 2) to point (5, 10).
A____ is an algebraic expression that contains a variable to the power of one. _____ is an example. A _____ is a rational number that is multiplied by a variable. A _______ is a number that can be written as the ratio, or fraction, of two integers. ______ in the expression _____ is an example of a coefficient. ______ are terms whose variables and their exponents are the same. One example is _____ and -7y.
• 2y
• 6x + 5
• Like - terms
• linear expression
• rationan numbers
• 4z
• 4
• rational coefficient
Answers
A linear expression is an algebraic expression that contains a variable to the power of one. 2y is an example. A coefficient is a rational number that is multiplied by a variable. A rational number is a number that can be written as the ratio, or fraction, of two integers. 4 in the expression 4z is an example of a coefficient. Like terms are terms whose variables and their exponents are the same. One example is 4z and -7z.
In the linear expression 2y, the coefficient is the numerical factor 2. The coefficient is the rational number that is multiplied by the variable, which in this expression is y.
The coefficient of a linear expression is usually the first factor, and it is used to determine the rate of change for a variable.
For example, if the coefficient of 2y is 2, then for every increase in y by one, the result of the linear expression will increase by 2.
The coefficient of a linear expression is the numerical (or rational) factor that is multiplied by the variable. In the linear expression 2y, the coefficient is 2, since the expression is equivalent to 2*y. The coefficient is usually the first factor in a linear expression, followed by the variable and, if present, its exponent.
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The CEO of the Wild Widget Company has decided to invest $360, 000 in his Michigan facgory. His economic analysts have noted that the output of this factory is modeled by the function Q : (0,[infinity])^2 → R given by Q(KL)-60K^-1/3L^2/3 where K denotes the amount (in thousands of dollars) spent on capital equipment and L represents the amount (also in thousands of dollars) spent on labor. (a) How should the CEO allocate the $360, 000 between labor and equipment? (b) Show that
aQ/aK=aQ/aL
at the point (K, L) found in part (a)
Answers
xplanation:
a b c your way out the picture
The CEO should allocate $144,000 to labor and $216,000 to capital equipment.
How should the CEO allocate the $360, 000 between labor and equipment?Step-by-step explanation given below
The CEO should allocate $144,000 to labor and $216,000 to capital equipment. This allocation maximizes the output of the factory, which can be found by taking the partial derivatives of the function Q with respect to K and L and setting them equal to 0.
Partial derivative of Q with respect to K = -20K^-4/3L^2/3 = 0
20K^-4/3L^2/3 = 0
K^4/3L^2/3 = 20
K = (20L^2/3)^1/4
Partial derivative of Q with respect to L = -40K^-1/3L^-1/3 = 0
40K^-1/3L^-1/3 = 0
K/L = 40
K = 40L
Solving for K and L, we get:
K = (20*L^2/3)^1/4
L = 40K
Substituting K into the equation for L, we get:
L = (40*(20L^2/3)^1/4)
L = 80(20L^2/3)^1/4
L^3/4 = 160L^2/3
L^3 = 1280L^2
L^2 = 1280L
L = 1280
Substituting L into the equation for K, we get:
K = (20*1280^2/3)^1/4
K = (307200/3)^1/4
K = 144
Therefore, the CEO should allocate $144,000 to labor and $216,000 to capital equipment.
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Peterson Products calculates its pension benefits as follows: Years of service × 1.98% multiplier × Average of last two annual salaries What is Mary’s monthly pension benefit if she worked for Peterson for 28 years and her last two annual salaries were $78,000 and $80,000?
Answers
Mary's monthly pension benefit is $3,649.80.
First, we have to find the average salary.
The average is the sum of the salaries divided by the number of salaries.
($78,000 + $80,000)/2 = $79,000
Next, we can find the annual retirement rate.
The annual retirement pension is the product of the average, the rate and the number of years employed.
$79,000 x 1.98% x 28 = $43,797.60
Finally, we can find the monthly retirement pension.
The monthly retirement pension is then the annual retirement pension divided by the number of months in a year.
There are 12 months in a year.
$43,797.60 / 12 = $3,649.80
Therefore, Mary's monthly pension benefit is $3,649.80.
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The middle school band is going to take a field trip either to a water park or to an amusement park. The band director surveyed all of the middle school band members to determine the preferred field trip. The results are displayed in the table below.
Field Trip Survey
Students Amusement Park Water Park Total
Seventh-Grade 14 26 40
Eighth-Grade 16 64 80
Total 30 90 120
Which statement is true about the results of the survey?
Responses
A 33% of the students prefer the amusement park.33% of the students prefer the amusement park.
B 25% of the eighth-grade students prefer the amusement park.25% of the eighth-grade students prefer the amusement park.
C 67% of the students prefer the water park.67% of the students prefer the water park.
D 65% of the seventh-grade students prefer the water park.
Answers
The statement which is true is D. 65% of the seventh-grade students prefer the water park.
What is Percentage?Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.
A : Total number of students = 120
Number of students who prefer amusement park = 14 + 16 = 30
Percentage of students who prefer amusement park = 30 / 120 = 0.25 = 25%
B : Total number of eighth grade students = 80
Number of eighth grade students who prefer amusement park = 16
Percentage = 16 / 80 = 0.2 = 20%
C : Total number of students = 120
Number of students who prefer water park = 26 + 64 = 90
Percentage = 90 / 120 = 0.75 = 75%
D : Total number of seventh grade students = 40
Number of seventh grade students who prefer water park = 26
Percentage = 26 / 40 = 0.65 = 65%
Hence the option D is the correct percentage.
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I dont understand may you please help me
Answers
Answer:66
Step-by-step explanation:
336666
8-2. Skills Practice. Multiplying a Polynomial by a Monomial.
Answers
To multiply a polynomial by a monomial, you must first identify the terms in the polynomial, as well as the factors in the monomial. Once you have identified the components, use the distributive property to multiply each term of the polynomial by the monomial. Then, combine like terms and simplify the resulting polynomial.
For example:
To multiply 3x2 + 2x - 5 by 2x, you would use the distributive property to multiply each term of the polynomial by the monomial: 3x2 * 2x = 6x3, 2x * 2x = 4x2, and -5 * 2x = -10x. The resulting polynomial is 6x3 + 4x2 - 10x.Learn more about Polynomial: https://brainly.com/question/24662212
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A company model it net income, in thouand of dollar, with the function f(x) = 9x2 – 54x – 144, where x i the number of unit of it product old. How many unit of it product doe the company need to ell in order for the net income to equal $0?
Answers
The company needs to produce 8 units in order for the net income to equal $0
What is factoring?Is a technique that consist of decomposition of a factor into a product of another factor, which when multiplied together give the original number.
the equation given can be simplified as:
f(x) = 9x² - 54x - 144.
f(x) = 9(x² - 6x - 16)
Then factoring we have:
f(x) = 9[(x + 2)(x - 8)]
It has a net income equals to 0 when:
f(x) = 0, so the variables are:
x + 2 = 0 -> x = -2
x - 8 = 0 -> x = 8
As the amount of products sold have to be positive the amount of product is 8
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PLEASE HELP ASAP
An element with a mass of 660 grams decays by 5.1% per minute. To the nearest tenth of a minute, how long will it be until there are 280 grams of the element remaining?
Answers
The time in minutes until there are 280 grams of the element remaining is given as follows:
16 minutes.
How to model the situation?A decaying exponential function is modeled as follows:
y = a(1 - r)^t.
In which the parameters are given as follows:
a is the initial amount.r is the decay rate, as a decimal.The parameter values for this problem are given as follows:
a = 660, r = 0.051.
Hence the function is modeled as follows:
y = 660(0.949)^t.
The time until there are 280 grams remaining is given as follows:
280 = 660(0.949)^t.
(0.949)^t = 280/660
tlog(0.949) = log(280/660)
t = log(280/660)/log(0.949)
t = 16 minutes.
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HELP ASAP PLS!!!!…..,,,
Answers
The first value of the given exponential expression would be 3.
What is an exponential function?
An exponential function is a mathematical function of the form f(x) = aˣ, where "a" is a positive constant and x is a real number. The function represents an exponential growth or decay, depending on the value of "a". If "a" is greater than 1, the function increases rapidly as x increases. If "a" is between 0 and 1, the function decreases as x increases.
In the exponential expression y = 3 * q⁵, the first value is 3.
Hence, the first value of the given exponential expression would be 3.
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-5x+15
5x-25
4a+13
5x-25
Answers
The value of the equations if they are zero each are: 3, 5, -13/4 and 5
What is an equation?By definition, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =
The given equations are
-5x+15=0
-5x = -15
Making x the subject of the relation we have
x=3
2) 5x-25 = 0
Collecting like terms
5x=25
Making x the subject
x=5
3) 4a+13=0
4a = -13
Making a the subject of the relation
a=-13/4
4) 5x-25=0
Collecting like terms
5x=25
Making x the subject of the relation
x=5
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The base of the parallelogram-like figure is half the circumference of the circle, or b= 1/2 (2pir)= pir. Therefore, the area of the figure will be A=
Answers
The formula for the area of the parallelogram-like figure is A = πr
What is parallelogram?parallelogram can be defined as a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
bh, where h is the height of the parallelogram-like figure.
Therefore, The formula for the area of the parallelogram-like figure is A = πr.
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I need help ASAP. I can’t figure out the answer can someone give it or explain the answer?
Answers
1.5 cm is the data range. The number sequence "4, 6, 9, 3, 7" is an example where the lowest value is 3 and the highest is 9. The range is therefore 9 3 = 6. Just like that!
What is meant by data range?In statistics, the range of your data is the range between the lowest and greatest values of the distribution. It acts as a typical sign of unpredictable behavior.Measurements of variability provide descriptive statistics for your data set's summary, together with measures of central tendency. In a list or collection of numbers, the range is the difference between the lowest and highest integers. Place all the numbers in order before attempting to determine the range. The lowest number is then subtracted (subtracted) from the greatest number. The range is the range of values, i.e., the range between the lowest and highest values. The lowest value is 3 and the highest is 9 in the example number sequence "4, 6, 9, 3, 7." As a result, the range is 9 3 = 6. Simple as that!Q3 - Q1 is the interquartile range (IQR).
The third quartile (Q3) of the box plot is the data value that exactly matches the end of the box's edge (7 cm).
The data value exactly at the box's outside edge (5.5 cm) is the first quartile (Q1).
Range between quartiles (IQR): 7 - 5.5 = 1.5 cm
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Write 5.2288888… repeating as a fraction
Answers
Answer: 529/8
Step-by-step explanation:
How to rotate a triangle 270 degrees counterclockwise?
Answers
Rotating a triangle 270 degrees counterclockwise is the same as rotating a figure 90 degrees clockwise. The solution has been obtained using the concept of rotation.
What is rotation?
A rotation in mathematics is a transformation that revolves a shape around a fixed point.
We have a specific rule that we can use to do this that is based on the fact that a 270° anticlockwise rotation is the same as a 90° clockwise rotation. One such rotation is to rotate a triangle 270° anticlockwise.
On a graph, we can rotate a triangle 270° anticlockwise by passing each of its vertices through the transformation shown below:
Change the x and y coordinates after multiplying the x coordinate by a negative number.
Consequently, (x,y) becomes (y,-x).
Hence, this way we can rotate a triangle 270 degrees counterclockwise.
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PLS HELP WILL GIVE ALOT OF POINTS DOMAIN AND RANGE
Answers
The range of the function lies between -∞<y<∞ and the domain of the function is given by -1<x<3
What are functions?Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given here: The graph of a function
We know The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
It is clear from the graph that y ∈ (-∞,∞) and x∈ (-1,3)
we know a function is given by y=f(x)
where y is the range values and x is the domain.
Hence, The range of the function lies between -∞<y<∞ and the domain of the function is given by -1<x<3
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8. (6 pts) At a local garden shop, the price of plants includes sales tax. The cost of 4 large plants and 8
medium plants is $40. The cost of 5 large plants and 2 medium plants is $28.
b) Could the cost of one large plant be $5.50 and the cost of one medium plant be $2.25? Justify your
answer.
c)
Determine algebraically both the cost of a large plant and the cost of a medium plant
Answers
By solving a system of equations we will see that a large plant costs $4.50 and a medium one $2.75
How to find the costs of the plants?Let's define the variables:
x = cost of a large plant.
y = cost of a medium plant.
We know that " The cost of 4 large plants and 8 medium plants is $40"
4*x + 8*y = 40
And "The cost of 5 large plants and 2 medium plants is $28."
5*x + 2*y = 28
So we have a system of equations:
4*x + 8*y = 40
5*x + 2*y = 28
We can isolate x on the first equation to get:
4x + 8y = 40
4x = 40 - 8y
x = (40 - 8y)/4
x = 10 - 2y
Replacing that in the other equation we will get:
5*(10 - 2y) + 2*y = 28
50 - 10y + 2y = 28
50 - 28 = 8y
22 = 8y
22/8 = y
2.75 = y
And the value of x is:
x = 10 - 2*2.75 = 4.5
Then the cost of a lare plant is $4.5 and the cost of a medium plant is $2.75.
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Two athletes practice for a marathon by running back and forth on an 11-mile course. They start running simultaneously, one at a speed 2 mph faster than the other's speed. How fast does each run if they meet 1 hour 6 minutes after starting? (The faster runner is already returning at this point. ) How far from the starting point do the runners meet? The speed of the faster runner is mph. The speed of the slower runner is mph. The distance from the starting point is miles
Answers
The speed distance of the faster runner is 8 mph, and the speed of the slower runner is (8 - 2) = 6 mph.
The speed of the faster runner is 8 mph.
The speed of the slower runner is 6 mph.
The distance from the starting point is 5.5 miles.We can use the formula d = rt, where d is the total distance, r is the rate (speed) and t is the time taken to cover the distance.
Let us assume that the speed of the faster runner is x mph. Then, the speed of the slower runner is (x-2) mph.
Since the two runners meet 1 hour 6 minutes after starting, the total time taken is 1 hour 6 minutes = 66 minutes.
Thus, the total distance covered = (x * 66) + (x - 2) * 66 = 132x - 132
But, the total distance covered is 11 miles, so
132x - 132 = 11
Solving for x, we get
x = 8 mph
Therefore, the speed of the faster runner is 8 mph, and the speed of the slower runner is (8 - 2) = 6 mph.
Since they meet 1 hour 6 minutes after starting, they have travelled a total distance of (8 * 66) + (6 * 66) = 5.5 miles. Therefore, the distance from the starting point at which they meet is 5.5 miles.
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A pair of gloves are on sale for 20% off
the original price of $4.99. About how
much will a person save buying the
gloves on sale?
Answers
Answer: 3.99
Step-by-step explanation:
Colin the Conservationist has been investigating the IUCN Red Data list of species.
Between 66 and 67 thousand species have been assessed and placed on the list.
Your task is to work out the number of species in each of 7 categories.
There are 78 species which are "extinct in the wild".
11 times that many have gone "extinct" since 1500AD.
Respectively 6 and 9 times as many species as have gone
"extinct" are on the "critically endangered" and "endangered" lists.
24,570 species are listed as threatened, which means they are
"vulnerable", "endangered" or "critically endangered".
The number of "near threatened"
species is 468 more than a third of
the number which are "vulnerable".
The good news is that there are
7,098 more species on the "least
concern" list than in all the other
categories combined
Answers
Based on the IUCN Red Data list of species, by solving the data we get the number of species in each category as
Extinct in the Wild = 78 Extinct = 858Critically Endangered = 5,148Endangered = 7,722Threatened = 24,570Vulnerable = 12,700Near Threatened = 4,838Least Concern = 7,098Total = 67,000
The answer which has been provided above gives the number of species that are present in each of the 7 categories of the IUCN Red Data List.
The IUCN Red Data List is a list of species that are globally threatened.
The categories that are present in the IUCN Red Data List are
Extinct in the Wild, Extinct, Critically Endangered, Endangered, Threatened, Vulnerable, Near Threatened, and Least Concern.
The number of species in each category is calculated based on the given information:
There are 78 species that are extinct in the wild.
Hence,
Extinct in the Wild: 7811 times that many have gone extinct since 1500 AD.
Hence,
Extinct: 78 × 11 = 858 species.6 and 9 times as many species have gone extinct are on the critically endangered and endangered lists respectively.
Hence,
Critically Endangered: 858 × 6 = 5,148 species.Endangered: 858 × 9 = 7,722 species.24,570 species are listed as threatened In the IUCN Red Data list.
Hence,
Threatened: 24,570.According to the list, the number of near-threatened species is 468 more than a third of the number which is vulnerable.
Hence,
Vulnerable = 12,700 Near Threatened: (12,700 ÷ 3) + 468 = 4,838 species.According to the data, there are 7,098 more species on the least
Least Concern = 7,098The total number of species on the IUCN Red Data List is calculated by adding up the number of species in each category:
Total: 78 + 858 + 5,148 + 7,722 + 24,570 + 4,838 + 7,098 = 67,000 species.Learn more about IUCN:
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you decide to roll 2 6 sided dice once. what is the probability that the sum of the spots on the dice will add up to a 5
Answers
The probability of rolling a 5 with two 6-sided dice is 1/9 or approximately 0.11.
This can be found by calculating the number of combinations that add up to 5. There are 2 combinations that add up to 5: (1, 4) and (2, 3). Out of 36 possible combinations of rolling 2 dice (6 x 6), there are only 2 combinations that give us a sum of 5, so the probability is 2/36 or 1/18 or approximately 0.11.
Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event is impossible, and 1 means the event is certain to happen. A probability of 0.5 means that the event has an equal chance of happening or not happening.
The probability of an event is calculated by dividing the number of favorable outcomes by the number of possible outcomes. For example, if you flip a fair coin, the probability of getting heads is 1/2 because there are two possible outcomes (heads or tails) and only one of them is favorable (heads).
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The probability of rolling a 5 with two 6-sided dice is 1/9 or approximately 0.11.
This can be found by calculating the number of combinations that add up to 5. There are 2 combinations that add up to 5: (1, 4) and (2, 3). Out of 36 possible combinations of rolling 2 dice (6 x 6), there are only 2 combinations that give us a sum of 5, so the probability is 2/36 or 1/18 or approximately 0.11.
Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event is impossible, and 1 means the event is certain to happen. A probability of 0.5 means that the event has an equal chance of happening or not happening.
The probability of an event is calculated by dividing the number of favorable outcomes by the number of possible outcomes. For example, if you flip a fair coin, the probability of getting heads is 1/2 because there are two possible outcomes (heads or tails) and only one of them is favorable (heads).
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Rusty Reft, who lives in Territory 5, carries 10/20/5 compulsory liability insurance along with optional collision that has a $300 deductible. Rusty was at fault in an accident that caused $1,400 damage to the other auto and $3,100 damage to his own vehicle. Also, the courts awarded $12,800 and $9,200, respectively, to the two passengers in the other car for personal injuries.
a. How much will the insurance company pay?
b. What is Rusty’s share of the responsibility?
Answers
Answer:
A = $2,800 B = $12,600
Step-by-step explanation:
a. How much will the insurance company pay?
The liability insurance will cover the damages to the other car ($1,400) and the personal injury claims ($12,800 + $9,200) up to the limit of $10,000. So the insurance company will pay $10,000.
The collision insurance covers the damage to Rusty's own car, minus the $300 deductible, so the insurance company will pay $3,100 - $300 = $2,800.
Therefore, the insurance company will pay a total of $10,000 + $2,800 = $12,800.
b. What is Rusty’s share of the responsibility?
Rusty is responsible for paying the remaining amount not covered by insurance, which is $1,400 + $3,100 + $12,800 + $9,200 - $12,800 = $12,600.
Therefore, Rusty's share of the responsibility is $12,600.
Use the gcf and the distributive property to find the sum of 15+36
Answers
Answer: br uh is this even a high school question? anyway, look at the image that i sent you can see the answer there.
better give me brainliest
Step-by-step explanation:
The first steps in writing f(x) = 4x2 + 48x + 10 in vertex form are shown.
f(x) = 4(x2 + 12x) + 10
(twelve-halves) squared = 36
What is the function written in vertex form?
f(x) = 4(x + 6)2 + 10
f(x) = 4(x + 6)2 – 26
f(x) = 4(x + 6)2 – 134
f(x) = 4(x + 6)2 + 154
Answers
The function written in vertex form is:
f(x) = 4(x + 6)² - 26
Option B is the correct answer.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = 4(x² + 12x) + 10
Now,
f(x) = 4(x² + 12x) + 10
f(x) = 4 (x² + 2 x (x) x 6 + 36) - 36 + 10
f(x) = 4(x + 6)² - 26
Thus,
f(x) = 4(x + 6)² - 26 is the function in vertex form.
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Answer:
B is correct
Step-by-step explanation:
Find the radius of convergence, R, of the series. [infinity] n = 1 n 7n (x + 5)n R = Find the interval, I, of convergence of the series. (Enter your answer using interval notation.) I =
Answers
The convergence interval, I, is the set of all x values for which the series converges. Because the series converges for all |x + 5| > 1, the convergence interval is I = (-∞, -6) ∪ (-4, ∞).
What is function?A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is usual to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. Example. A function is an equation that depicts the connection between an input x and an output y, with precisely one output for each input. Another name for input is domain, while another one for output is range.
Here,
The radius of convergence, R, of a power series is the maximum value of x for which the series converges for all values of x within that range.
To find the radius of convergence for the given series, we can use the ratio test:
[infinity] n = 1 n 7n (x + 5)n
lim |(a_{n+1})/(a_n)| = lim |(7(n+1) (x + 5)^(n+1)) / (n 7n (x + 5)^n)|
= lim |(7(x + 5)) / n|
The series converges when the limit is less than 1 and diverges when the limit is greater than 1. If the limit is equal to 1, the test is inconclusive.
For |x + 5| < 1, the limit is equal to |7 * (x + 5)|, which is greater than 1, so the series diverges in this region.
For |x + 5| > 1, the limit is equal to |7| / n, which goes to zero as n approaches infinity, so the series converges in this region.
So, the radius of convergence, R, is R = 1.
The interval of convergence, I, is the set of all values of x for which the series converges. Since the series converges for all |x + 5| > 1, the interval of convergence is I = (-∞, -6) ∪ (-4, ∞).
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The first five terms of a pattern are given below.
37, 42, 47, 52, 57
Which expression can be used to determine the nth term of the pattern?
Answers
The expression aₙ = 37 + (n - 1)5 can be used to determine the nth term of the arithmetic sequence pattern?
What is an Arithmetic sequenceAn arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
The nth term of an arithmetic sequence is derived using; aₙ = a + (n - 1)d where a is the first term and d the common difference
Given the first term as 37, we have that;
a₁ = a + (1 - 1) d = 37
a₁ = a = 37
for the second term 42, substituting 37 for a;
a₂ = 37 +(2 - 1)d = 42
37 + d = 42
d = 42 - 37 {subtract 37 from both sides}
d = 5
Therefore, the arithmetic sequence increase by a common difference 5 and the expression aₙ = 37 + (n - 1)5 can be used to determine the nth term of the arithmetic sequence pattern?
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A random sample of 9th-grade students was asked if they prefer taking notes on a computer or using a pencil. Of the 180 students who were surveyed, 75 said they preferred using the computer. The resulting 99% confidence interval of the proportion of students who prefer taking notes on the computer was (0. 322, 0. 511). The school newspaper ran a story saying that less than half of the body prefers taking notes on a computer. Based on the interval, is the newspaper justified in this statement?
Answers
The newspaper's assertion is unjustified. It can be shown that the interval does not contain 0.5 based on the 99% confidence interval of (0.322, 0.511). (which is half).
This indicates that the population parameter (mean, percentage, and standard deviation) is between a and b with x% confidence.
This indicates that at least half of students prefer using a computer to take their notes. Since the interval's lower limit (0.322) is higher than 0.5, there is a 99% likelihood that the actual percentage of students who prefer taking notes on computers is higher than 0.5.
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