Answer:
87
Step-by-step explanation:
tn= a + (n-1)d
t12 = 10 + (12-1)7
=87
What is the slope of the line passing through the points (-1, 3) and (4, - 7)?
02
O-2
O
O
ده | ر
Answer:
Step-by-step explanation:
m = slope
m = (-7 -3 ) / (4 -(-1)
m = -10 / 5
m = -2
ask, if you want to understand how I got that. :)
At a local ice-cream store, 210 people were surveyed on whether they preferred eating ice cream from a cone or a cup. Of the 210 people surveyed, 70 were adults and 140 were children. Of the responses, 150 indicated the cone as the preferred method of eating ice cream. For those surveyed, there was no association between age and preferred method of eating ice cream. Which of the following tables show the distribution responses?
answer choices
Graph i
Graph ii
Graph iii
Graph iv
Graph v
Graph ii shows that 150 people preferred eating ice cream from a cone, while 60 people preferred eating ice cream from a cup. There was no association between age and preferred method of eating ice cream.
Graph ii is a table that shows the distribution of responses to the survey about preferred method of eating ice cream. The table shows that out of the 210 people surveyed, 70 were adults and 140 were children. Of the 210 people surveyed, 150 indicated the cone as the preferred method of eating ice cream, while 60 indicated the cup as the preferred method. This table indicates that there is no association between age and preferred method of eating ice cream, as the responses were evenly distributed between adults and children. This information can be used to determine the preferences of customers at the ice-cream store and can help inform decisions about how to serve the ice cream. For example, the store may choose to provide more cones than cups based on the survey results. Additionally, this table can be used to compare the preferences of different demographic groups, although in this case the survey showed that there was no association between age and preferred method of eating ice cream.
Adults: 70 people surveyed, 35 preferred cone, 35 preferred cup
Children: 140 people surveyed, 115 preferred cone, 25 preferred cup
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Let f be a differentiable function, defined for all realnumbers x, with the following properties. Find f(x). Show yourwork.
i) f'(x)=ax2+bx
ii) f'(1)=6 and f"(1)=18
iii. =18
The differentiable function f with the given properties is [tex]f(x)=4x^3-3x^2+10[/tex].
What is a differentiable function:
A function with a differentiable value of one real variable is one whose domain contains a derivative. In other words, each interior point in the domain of a differentiable function's graph has a non-vertical tangent line.
The given properties for the differentiable function f are:
[tex](i) f'(x)=ax^2+bx\\ (ii) f'(1)=6, f''(1)=18\\ (iii) \int\limits^2_1 {f(x)} \, dx =18[/tex]
From (i) we can get [tex]f''(x)=2ax+b[/tex]
By substituting (ii) in (i) we will get:
a+b=6 and 2a+b=18. By solving these two equations we will get the following:
a=12, b=-6.
We will integrate (i) on both sides, we will get:
[tex]f(x)=\frac{ax^3}{3} +\frac{bx^2}{2} +c[/tex] where c is the integration constant.
In this equation, we will substitute a,b.
[tex]f(x)=\frac{12x^3}{3} +\frac{-6x^2}{2} +c\\ \\ f(x)= 4x^3-3x^2+c[/tex]...................(iv)
Now we will substitute (iv) in (iii), and we will get:
[tex]\int\limits^2_1 {( 4x^3-3x^2+c)} \, dx =18\\ \\ (2^4-2^3+2c)-(1^4-1^3+c)=18\\ \\c=10[/tex]
Therefore [tex]f(x)=4x^3-3x^2+10[/tex].
Complete question:
Let f be a differentiable function, defined for all real numbers x, with the following properties. Find f(x). Show your work.
[tex](i) f'(x)=ax^2+bx\\ (ii) f'(1)=6, f''(1)=18\\ (iii) \int\limits^2_1 {f(x)} \, dx =18[/tex]
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This is for my calculus class, please help.
The area bounded by y = x² + 5 and the x-axis from x = 3 to x = -2 is 110/3.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
y = x² + 5
The area bounded by y = x² + 5 from x = -2 to x = 3.
= [tex]\int\limits^{3}_{-2} {(x^2 + 5)} \, dx[/tex]
= [tex][x^3/3]^{3}_{-2}[/tex] + 5 [tex][x]^{3}_{-2}[/tex]
= 1/3 [tex][(3)^3 - (-2)^3][/tex] + 5 [3 + 2]
= 1/3 [27 + 8] + 5 x 5
= 1/3 x 35 + 25
= 35/3 + 25
= (35 + 75)/3
= 110/3
Thus,
The area bounded is 110/3.
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There are only 2.1 x 10^8 metric tonnes of usable fossil fuels existing on Earth.
Assuming an estimated rate of fossil fuel use of 1 x 10^5 metric tonnes per year, calculate an order of magnitude estimation of the time left before the fossil fuel reserves run out.
Give your answer to one significant figure.
The answer is 2000 but I cannot figure out how they got it.
The time left before the fossil fuel reserves run out is 2000years(1significant figure)
What is rate?A rate is a special ratio in which the two terms are in different units. For example, if a 14-ounce can of corn costs 69¢, the rate is 69¢ for 14 ounces. Rate can also be defined as the ratio of two unlike units.
The total metric tonnes of fossil fuel on earth is 2.1×10⁸.
The rate of usage is 1×10⁵ metric tone of fossil fuel per year
as been said rate = total metric tone of fuel/ number of years to use
1×10⁵= 2.1×10⁸/no of years
no of years = 2.1×10⁸/1×10⁵
no of years = 2.1×10³years= 2100years
to 1 significant figure = 2000years
therefore the number of years for the fossil fuel to run out is 2000years
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How to Graph y-2=2/3(x+4)
Answer:
Step-by-step explanation:
To graph the equation y-2=2/3(x+4), you can follow these steps:
Begin by isolating the y term on one side of the equation. To do this, you can add 2 to both sides of the equation:
y-2+2=2/3(x+4)+2
y=2/3(x+4)+2
Next, you can simplify the right side of the equation by multiplying 2/3 by (x+4):
y=2/3(x+4)+2
y=(2/3)x+(2/3)4+2
y=(2/3)x+8/3+2
y=(2/3)x+14/3
This is the standard form of the equation y=mx+b, where m is the slope and b is the y-intercept. In this case, the slope is m=2/3 and the y-intercept is b=14/3.
To graph the equation, you can use the slope and y-intercept to plot the first point on the graph. The y-intercept is the point where the graph crosses the y-axis, so you can plot the point (0,14/3) on the graph.
From this point, you can use the slope to find the next point on the graph. The slope is the change in y over the change in x, so you can use the slope to find the change in y and the change in x between two points on the graph. For example, you could choose a point that is 1 unit to the right of the y-intercept, or (1,0). The change in y between these two points is (14/3)-0=14/3 and the change in x is 1-0=1. Using the slope, you can find the y-coordinate of the next point on the graph:
y2=y1+m(x2-x1)
y2=14/3+2/3(1-0)
y2=14/3+2/3
y2=20/3
You can repeat this process to plot additional points on the graph. For example, you could choose a point that is 2 units to the right of the y-intercept
pls help ill mark brainliest
Answer:
Step-by-step explanation:
since you are rotating the image it shows y k j and l so it would be 5.5
According to the United States Census Bureau the population of Utah was 2.12 million people in 1997 and 2.53 million people 9 years later in 2006. Use an explicit exponential model P t = P 0 ( 1 + r ) t to calculate the rate of growth of the population over this time period.
The rate of growth in the exponential function is 1.98%
Exponential FunctionAn exponential function is defined by the formula f(x) = aˣ, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.
To solve this problem, we have to model the growth in an exponential function.
Population in 1997 = 2.12 million
Population in 2006 = 2.53 million
Time = 9
Since this is an exponential growth function, we can write this as;
2.53 = 2.12(1 + r)⁹
where r = rate of growth
2.53 = 2.12(1 + r)⁹
r = 0.0198
r = 1.98%
The rate of growth is 1.98%
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46650 round it to the nearest million
The rounding of 46,650 to the nearest million is given as follows:
0.
How to round a number?To round a number, the number at the next place relative to the rounding place must be looked:
If the number is less than 5, then the number at the previous digit remains constant.If the number is of 5 or greater, then the digit at the previous digit is increased by one.Examples of rounding to the nearest tenth are given as follows:
10.52 = 10.5, as 2 < 5.10.56 = 10.6, as 6 > 5.The numbers to the nearest million are rounded according to the example given as follows:
Less than 500,000: 0.Between 500,000 and 1,500,000: 1.And so on...For this problem, we are given a number that is less than 500,000, hence the rounding of the number to the nearest million is of 0.
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PLEASE HELP
An equation of a line is shown. A second line is perpendicular to the given line and passes through the point (0,1).
Which is the equation of the perpendicular line?
Answer:
C
Step-by-step explanation:
slope of the first line = -9/2
slope of a perpendicular line = 2/9
y-(-1)= 2/9(x-0)
y + 1 = 2/9 x
y = 2/9 x -1
Select the correct answer.
Convert 3-3i to polar form.
A. 3√2cis π/4
B. 3√2cis 3π/4
C. 3√2cis 5π/4
D. 3√2cis 7π/4
(Please mark brainliest <3)
Correct option is D.
We have been given a complex number 3-3i we have to convert it in the polar form:
Polar form of a complex number: z=r(cosθ+isinθ)
Where, r=√x^2+ y^2
the general form of complex number is:
x+iy
•Here, x=3 and y=-3
•Hence, r=√3^2+(-3)^2}= √18
•And θ=tan −1 y/x
•θ=tan −1 -3/3
•θ=tan −1 (−1)
•θ=2π− π/4
•θ= 7π/4
•Hence, substituting all the values in polar form formula we get:
z= √18cos( 7π/4) + isin (7π/4)
write the ratio as a fraction in simplest form 35 to 112
Answer:
5 :16
Step-by-step explanation:
35:112 <===== divide both by '7 ' to get 5/16
determine whether each pair of triangles is congruent. if so, write a congruence statement and explain why the triangles are congruent. (lesson 5-5) 4. b c n r p f m d 5. a l e
No, these two triangles are not congruent. Congruent triangles have the same shape and size, and Triangle ABC and Triangle DEF do not have the same shape or size.
Congruent triangles are two triangles that have the same shape and size. This means that the angles and the side lengths of the two triangles must be the same. For example, if two triangles have three angles that measure 60°, 60°, and 60°, the two triangles are congruent. Similarly, if two triangles have three side lengths of 5 cm, 6 cm, and 7 cm, the two triangles are also congruent. However, Triangle ABC and Triangle DEF do not have the same shape or size, therefore, they are not congruent. The angles and side lengths of the two triangles are not the same, so they cannot be congruent.
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the complete question is
determine whether each pair of triangles is congruent. if so, write a congruence statement and explain why the triangles are congruent.
Triangle ABC and Triangle DEF
math
r,mrkmrkrmkrmkrmkr
When you start from the given set of rules and conditions and determine must be true you are using c) Deductive reasoning.
Define deductive reasoning.In deductive reasoning, conclusions are reached based on premises that are typically taken to be true. It employs a logical premise to arrive at a logical conclusion and is also known as "deductive logic." The term "top-down reasoning" is frequently used to describe deductive reasoning. If something is presumptively true and a different object is connected to the first presumption, then the original truth must also apply to the second. Syllogism is one of the most popular forms of deductive reasoning. A major and a minor assertion coming together to make a logical conclusion is referred to as a syllogism. The fact that the two statements are true indicates that the assertion will probably be true for all further premises belonging to that category.
Given,
When you start from the given set of rules and conditions and determine must be true you are using ___ reason.
c) Deductive reasoning
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you have to choose a number between 0 and 100. the winner of the game is the person whose number is closest to 2/3 times the average of all chosen numbers.
The "winning" guess when played this game has been around 18.
What is rationality?The quality of being guided by or based on reasons is referred to as rationality. In this sense, a belief is rational if it is based on strong evidence, and an individual acts rationally if they have a good reason for doing so. This quality can be applied to a skill, like reasoning in a rational animal, a psychological process, like reasoning, mental states, like beliefs and intentions, or people who have these other kinds of rationality. If something does not meet the standards of rational evaluation, it is either irrational or rational, depending on where it falls outside the realm of rational evaluation.
Given you have to choose a number between 0 and 100. the winner of the game is the person whose number is closest to 2/3 times the average of all chosen numbers,
Theoretically, concur that the answer is 0. As stated, this is due to widespread rationality knowledge. You should guess 2/3*50=33 if everyone chose equally between 0 and 100. The average would be 50. Everyone ought to guess 33 if they are all aware of this. However, if I know that everyone correctly predicted 33, then 33 is the average, and should seek 2/3*33=22. This logic continues until everyone should correctly guess 0.
People actually don't think this way, but I disagree that you should guess between 5 and 10, which I believe is too low. depending on who you play with, as a group of game theorists might get a lower average than a group of people from the average population.) In a real-world setting, you need to consider how many iterations the others will make. You should guess 22 if you think they will only do one, which would result in everyone guessing 33. If you assume that they iterate the reasoning twice on average and guess 22, you should estimate 15 and so on.
The "winning" guess when played this game has been around 18.
Hence the guess should be 18.
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the complete question is,
Several people choose an integer between 0 and 100. The winner is the person whose integer is closest to 2/3 of the average of the numbers reported by all seven participants. What value would you choose?
The sum of three numbers is 68. The first number is 8 more than the second. The third number is 2 times the second. What are the numbers?
The numbers are 23,15,30 if the sum of three numbers is 68.
What is an equation?When two expressions are connected with the equals sign (=) in a mathematical formula, it expresses the equality of the two expressions. A well-formed formula consisting of two expressions linked by an equals sign is considered to be an equation in English, but the word's cognates in other languages may have slightly different definitions. For instance, an equation is defined as having one or more variables in French.
Determine which values of the variables result in the equality to be true in order to solve an equation with variables. The values of the variables that must fulfill the equality to constitute the answer are known as the unknowns, together with the variables for which the equation must be solved.
Let the first number be x
The second number is 8 Less than the x is x-8
The third number is 2 times the second is 2(x-8)
Sum of the three numbers is 68
x+x-8+2(x-8)=68
4x-24=68
4x=92
X=23
Therefore, the numbers are 23,15,30
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Erika drives from school to soccer practice 1.3 miles away. It takes her 7 minutes.
a.
b.
C.
d.
What fraction represents her constant speed, C?
What fraction represents her constant speed, C, if it takes her x minutes to drive exactly 1 mile?
Write a proportion using the fractions from parts (a) and (b) to determine how much time it takes her to drive
exactly 1 mile. Round your answer to the tenths place.
Write a two-variable equation to represent how many miles Erika can drive over any time interval.
a. Constant speed, C = 0. 19 miles/minutes
b. The fraction representing her constant speed is 1/x miles/minutes
c. The time it takes her to drive exactly 1 mile is 5. 38 minutes
How to determine the valueThe formula for calculating constant speed is expressed as;
Constant speed = total distance covered/ total time taken
From the information given, we have that;
Total distance = 1. 3milesTime taken = 7 minutesNow, substitute the values into the formula
Constant speed = 1. 3 / 7
Divide the values
Constant speed = 0. 19 miles/minutes
When distance 1 mile, time taken = x minutes
Constant speed = 1/x miles/minutes
If 1. 3 miles = 7 minutes
Then, 1 mile = x
cross multiply
x = 7/1. 3
x = 5. 38 minutes
Hence, the constant speed is 0. 19 miles/minutes
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Solve the system of equations graphed on
the coordinate axes below.
y=-3x - 5
y =4/3x-5
Placing a point at the graph's y-intercept offor the equation (0,-5).
How to solve the system of equations graphed?Placing a point at the graph's y-intercept of -4 for the equation y =3x - 5 (0,-5). From the point (0,-5) go one down, three to the right, and then add another point because the slope is -5The two points may be connected by drawing a line using a straightedge. Keep going after the two points. Past them, continue the line.same for y = 4/3x-5. Place a point at since the y-intercept is at 2, (0,-5). Since the slope is 4/3, go up 4and to the right 3 before drawing a second point from (0,-5). The two points may be connected by drawing a line using a straightedge. Don't, once more, end at the two points. Past them, continue the line.To learn more about graph's y-intercept refer to:
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The graph is the boundary line for the inequality y ≤ 2/3x + 1. Which of the points is a solution for this inequality?
A (-4,5)
B (-10, -2)
C (0,-3)
D (1,3)
The points is a solution for this inequality is (0, -3).
What is inequality?
In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
Switch sides
[tex]\frac{2}{3} x+1 \geq y$$[/tex]
Move 1 to the right side
[tex]\frac{2}{3} x \geq y-1$$[/tex]
Multiply both sides by 3
[tex]3 \cdot \frac{2}{3} x \geq 3 y-3 \cdot 1$$[/tex]
Simplify
[tex]2 x \geq 3 y-3$$[/tex]
Divide both sides by 2
[tex]\frac{2 x}{2} \geq \frac{3 y}{2}-\frac{3}{2}$$[/tex]
Simplify
[tex]x \geq \frac{3 y-3}{2}$$[/tex]
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The scale of map is 4m = 18mi
map : 6.8m
actual : ____ mi
Answer:
30.6
Step-by-step explanation:
18/4 = 4.5
4.5 × 6.8 = 30.6
I’ll give BRAINLIEST if correct I need asap question is in the photo attached
The domain and range of the function will be Real number and [0, ∞). The parent function f(x) is get shifted down by 2 units.
What is an absolute function?The absolute function is also known as the mode function. The value of the absolute function is always positive.
If the vertex of the absolute function is at (h, k). Then the absolute function is given as
f(x) = |x - h| + k
The function is given below.
g(x) = |x + 3|
The graph of the function g(x) is given below. From the graph, the domain and range of the function will be Real number and [0, ∞).
The parent function and translated function are given below.
f(x) |x| and h(x) = |x| - 2
The parent function f(x) is get shifted down by 2 units.
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сделайте пожалуйста 5 заданий из этих
Answer:
Step-by-step explanation:
Find length, width, perimeter, and area
Answer:
length is 4 units
width is 2 units
Perimeter is 12 units
Area is 8 sq units
Step-by-step explanation:
Since you have a graph of the points, you can see the shape is a rectangle. Count to find the measure of the length and width.
Perimeter is the distance all the way around the shape.
length + width + length + width
Or 2(length)+2(width)
= 2 + 4 + 2 + 4
= 12
Area is
length × width
= 4 × 2
= 8 sq units.
Which BEST describes the decimal form of a rational number?
Responses
A either terminates in 0's or repeats. either terminates in 0's or repeats.
B eventually repeats a non-zero digit eventually repeats a non-zero digit
C neither terminates nor repeat sn either terminates or repeats
D always terminates in 0's
Answer:
Step-by-step explanation:
A.) either terminates in 0's or repeats.
Some decimals repeat and some decimals don't.
write and equivalent expression to 24x^2 +56x choose all that apply
Here is the step by step x
The equivalent expression to 24x^2 +56x is : 8x(3x+7)
What is an equivalent expression?Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).Using the equality (=) symbol, equivalent phrases are represented. Because both expressions have the same value for any value of x, 3(x + 2) and 3x + 6 are identical expressions. 3x + 6 = 3 × 4 + 6 = 18.When two expressions can be reduced to a single third expression or when one of the expressions can be expressed in the same way as the other, they are said to be equivalent. When values are replaced for the variable and both expressions yield the same result, you may also tell if two expressions are equal.Given data :
= 24[tex]x^{2}[/tex] + 56
= 24 xx + 56
Rewrite 24 as 8 * 3
Rewrite 56 as 8 * 7
= 8 * 3xx + 8 * 7x
= 8x (3x+7)
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6. Investors buy a studio apartment for $ 240,000. Of this amount, they have a down payment of $ 60,000.
a. Their down payment is what percent of the purchase price?
b. What percent of the purchase price would a $ 12,000 down payment be?
If Investors buy a studio apartment for the amount of 240,000.
a. The percent of the purchase price is 25%.
b. The percent of the purchase price is 5%.
How to find the percent of purchase price?a. Percent of purchase price
Using this formula to find the percentage of purchase price
Percent of purchase price = Down payment / Selling price
Percent of purchase price = $60,000/$240,000
Percent of purchase price = 0.25 × 100
Percent of purchase price = 25%
b. Percent of purchase price
Percent of purchase price = Down payment /Selling price
Percent of purchase price = $12,000/$240,000
Percent of purchase price = 0.05 ×100
Percent of purchase price = 5%
Therefore the percent of the purchase price is 25%, 5%.
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Find f'(x) and simplify.
f(x)=x²+5/3x-2
Which of the following shows the correct application of the quotient rule?
A. (3x-2)(2 x)-(x²+5)(3)/(3 x-2)²
B. (3 x-2)(2 x)-(x²+5)(3)/(x²+5)²
C. (x²+5)(3)-(3 x-2)(2 x)/(x²+5)²
D. (x²+5)(3)-(3 x-2)(2 x)/(3 x-2)²
The correct application of the quotient rule is f'(x) = [(3x - 2)2x - (x²+5)(3)]/[(3x - 2)]²
What is the derivative of a function?The derivative of a function f'(x) is the rate of change of the function with respect to a variable.
How to find the correct application of the quotient rule?Since we have f(x) = (x²+5)/(3x-2), to find its derivative f'(x), we use the quotient rule.
What is the quotient rule?Given a function f(x) = u(x)/v(x) then the derivative of f(x) which is f'(x) = [v(x)du(x)/dx - u(x)dv(x)/dx]/[v(x)]²
So, with f(x) = (x²+5)/(3x-2)
u(x) = (x²+5) and v(x) = (3x-2)
So, du(x)/dx = d(x²+5)/dx
= d(x²+5)/d(x²+5) × d(x²+5)/dx
= 2x
and
dv(x)/dx = d(3x - 2)/dx
= d3x/dx - d2dx
= 3 - 0
= 3
Since f'(x) = [v(x)du(x)/dx - u(x)dv(x)/dx]/[v(x)]², substituting the values of the variables into the equation, we have that
f'(x) = [v(x)du(x)/dx - u(x)dv(x)/dx]/[v(x)]²
f'(x) = [(3x - 2)2x - (x²+5)(3)]/[(3x - 2)]²
So, the quotient rule is f'(x) = [(3x - 2)2x - (x²+5)(3)]/[(3x - 2)]²
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Find all values of x that make the equation true. 3/x+3 = x-4/x
Answer:
X = -2 - 2(square root)3 or x = -2 + 2 (square root )3
Step-by-step explanation:
What is the solution and how can I solve it? I an super confused
whats the question im getting off camera blind explain it to me
assume that there is a party consisting of people between the ages of 18 and 24 inclusive. how many people would have to be at the party to guarantee that at least three people share the same birth date, birth month, and birth year? note: assume the range of birth years include 2 leap years. (
The minimum number of people that would need to be at the party to guarantee that at least three people share the same birth date, birth month, and birth year is Three (3).
To find the number of people that would need to be at the party to guarantee that at least three people share the same birth date, birth month, and birth year, we need to consider the number of possible birthdays that exist within the given age range (18 to 24 inclusive).
There are 12 months in a year, and each month has between 28 and 31 days (depending on the month). Therefore, there are a total of 12 * 31 = 372 possible birthdays within a given year.
There are 7 possible birth years within the given age range (18 to 24 inclusive), which means there are a total of 7 * 372 = 2596 possible birthdays within the given age range.
Since we want to guarantee that at least three people share the same birthday, we need at least 3 people to be at the party.
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Complete Question:
Assume that there is a party consisting of people between the ages of 18 and 24 inclusive. How many people would have to be at the party to guarantee that at least three people share the same birth date, birth month, and birth year? Note: assume the range of birth years include 2 leap years.