The required simplified value of the function at x = 2 is -23.
An expression, [tex]f(x) = x^4-8x^3+4x^2+6x-3,[/tex] solution of the expression at x = 2 is to be determined.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
In order to simplify the given expression association of the terms that have equal value in the exponent.
[tex]f(x) = x^4-8x^3+4x^2+6x-3,[/tex]
Put x = 2
[tex]f(2) = 2^4-8*2^3+42^2+6*2-3,[/tex]
f(2) = -23
Thus, the required simplified value of the function at x = 2 is -23.
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Someone Please Please Answer this (20 POINTS)
Answer:
Step-by-step explanation: Simple plug x in.
x=1
(Square root) 4 -1=1
x=6
(square root) 9 -1=2
x=13
(square root ) 16-1=3
x=1 Y=1
x=6 Y=2
x=13 Y=3
PLEASE GIVE ME BRAINLIEST THX-9x5
81 devided by (-9)
What is the effect on the gravitational force if?
a. Both masses are multipled by 3
b. The distance between centers is X4
c. One mass is X2 and the other X3
d. The distance is divided by 2
e. The distance is divided by 2 and one mass X3
The effect on the gravitational force if:
a. Both masses are multipled by 3: the gravitational force becomes 9 times.
b. The distance between centers is X4: the gravitational force gets reduced by 16 times.
c. One mass is X2 and the other X3 : the gravitational force becomes 6 times.
d. The distance is divided by 2: the gravitational force becomes 4 times.
e. The distance is divided by 2 and one mass X3: the gravitational force becomes 12 times.
We know that the gravitational force between two objects is given by,
F = Gm1m2 / r² ...........(1)
We need to find the effect on the gravitational force if
a. Both masses are multipled by 3
F1 = G(3m1)(3m2) / r²
F1 = 9 Gm1m2 / r²
F1 = 9F ...........(from equation (1))
Thus the gravitational force becomes 9 times.
b. The distance between centers is X4
F2 = Gm1m2 / (4r)²
F2 = Gm1m2 / 16r²
F2 = 1/16 ( Gm1m2 / r²)
F2 = 1/16 * F ...........(from equation (1))
Thus the gravitational force gets reduced by 16 times.
c. One mass is X2 and the other X3
F3 = G(2m1)(3m2) / r²
F3 = 6 * Gm1m2 / r²
F3 = 6F ...........(from equation (1))
Thus the gravitational force becomes 6 times.
d. The distance is divided by 2
F4 = Gm1m2 / (r/2)²
F4 = Gm1m2 / (r²/4)
F4 = 4 ( Gm1m2 / r²)
F4 = 4F ...........(from equation (1))
Thus the gravitational force becomes 4 times.
e. The distance is divided by 2 and one mass X3
F5 = G(3m1)m2 / (r/2)²
F2 = 3Gm1m2 / (r²/4)
F2 = (3*4) ( Gm1m2 / r²)
F2 = 12 F ...........(from equation (1))
Thus the gravitational force becomes 12 times.
Therefore, The effect on the gravitational force if:
a. the gravitational force becomes 9 times.
b. the gravitational force gets reduced by 16 times.
c. the gravitational force becomes 6 times.
d. the gravitational force becomes 4 times.
e. the gravitational force becomes 12 times.
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5
Σ -2n-1
n=1
How do I solve this
Answer:
-35
Step-by-step explanation:
Knowledge Needed
This notation is called sigma notation (or summation). It is used later on in Calculus too.
The number on top of the sigma sign is called the top index.
The number on bottom of the sigma sign is called the lower index.
To the right of the sigma sign is an expression.
I will give you an example to help.
3
Σ n^2
n = 1
To start, look at the bottom number. Then, plug all numbers from the lower index to the top index (including the top index) into the expression.
n^2
(1) ^ 2
(2) ^ 2
(3) ^ 2
We stop at 3 because 3 is the top index.
Simplify.
1 ^ 2 = 1
2 ^ 2 = 4
3 ^ 2 = 9
Add the numbers.
9 + 4 + 1
14
The answer is 14.
Question
Start at 1 and go to 5.
-2n-1
-2(1)-1
-2(2)-1
-2(3)-1
-2(4)-1
-2(5)-1
Stop at the 5, the top index.
Simplify.
-2 - 1 = -3
-4 - 1 = -5
-6 - 1 = -7
-8 - 1 = -9
-10 - 1 = -11
Add.
-3 + -5 + -7 + -9 + -11
-35
Christian is 1.35 meters tall. At 10 a.m., he measures the length of a tree's shadow t
be 38.65 meters. He stands 34.4 meters away from the tree, so that the tip of his
shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest
hundredth of a meter.
1.35 m
•34-4 m
•38.65 m
It’s not 1.52
Answer:
The answer is 1.52.
Step-by-step explanation:
I don't know why it's not 1.52 no matter how I calculate it's 1.52
Slope is -4, and (3, 4) is on the line.
What is a slope in math?
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
Whenever the equation of a line is written in the form y = mx + b, it is called the slope-intercept form of the equation. The m is the slope of the line. And b is the b in the point that is the y-intercept (0, b). For example, for the equation y = 3x – 7, the slope is 3, and the y-intercept is (0, −7).
To find the correct answer, we need to look at the formula for a straight line: y=mx+b where m= the slope of the line and b= the y intercept. We know from the problem that the slope must be equal to -4, leaving us with y= -4x +b. From here you can substitute the given point in the equation and solve for b.
-3= -4(4) +b
-3= -16+b
+16 +16
13= b
This tells us that b=13, now we simply substitute that into the formula.
The solution to your question is y=-4x+13
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The following table shows the breakdown of opinions for both faculty and students in a recent survey about the new restructuring of the campus to include an Honors College. Find the probability that a randomly selected person is either a student opposed to the change or a faculty member who has an opinion either for or against. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Survey Results on Restructuring Campus to Include an Honors College
Category Favor Oppose Neutral Total
Faculty 6 15 15 36
Students 41 41 58 140
Total 47 56 73 176
The probability that a randomly selected person is either a student opposed to the change or a faculty member who has an opinion either for or against is given as follows:
31/88.
How to calculate the probability?A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
The total number of outcomes in this problem is given as follows:
176 people.
The desired outcomes are given as follows:
Student opposed to the change: 41.Faculty member who is either for or against: 6 + 15 = 21.(these outcomes are both calculated from the data given by the table).
Hence the probability is calculated as follows:
p = (41 + 21)/176 = 62/176 = 31/88.
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3. Here is a quadrilateral ABCD with M as the midpoint of
segments AC and BD.
Prove: Angle ABM is congruent to angle CDM
Portfolio Question
Answer: Depends if AB and CD are equal, as they both have M in the same spot that can be eliminated, look at the quadrilateral and make a guess based off the information that AB and CD have to be equal
Step-by-step explanation:
Solve 1/2 + 1/2x = x^2 − 7x+10/4x by rewriting the equation as a proportion. Which proportion is equivalent to the original equation?
Name the true solution(s) to the equation
Name the extraneous solution(s) to the equation.
The proportion that is equivalent to the original equation [tex]\frac{x+1}{2x} =\frac{x^{2} -7x+10}{4x}[/tex]
The true solution to the equation [tex]x_{1} =1, x_{2}=8[/tex]
The extraneous solution to the equation.x=0
You are given the equation
[tex]\frac{1}{2} + \frac{1}{2x}=\frac{x^{2} -7x+10}{4x}[/tex]
we will note that
[tex]\frac{1}{2} + \frac{1}{2x}=\frac{x+1}{2x}[/tex]
this equation can now be rewritten as proportions as
[tex]\frac{x+1}{2x}=\frac{x^{2} -7x+10}{4x}[/tex]
Solving this equation using the main property of proportion:
[tex]4x. (x+1) =2x.(x^{2} -7x+10.\\[/tex]
[tex]2x(2x+2-x^{2} +7x-10) =0,[/tex]
[tex]2x(-x^{2} +9x-8) =0[/tex]
x cannot be equal to 0 (it is placed in the denominator of the initial equation and the denominator cannot be 0), so x=0 is the extraneous solution to the equation.
This will hence translate to
[tex]-x^{2} +9x-8=0[/tex]
[tex]x^{2} +9x+8=0,[/tex]
[tex]x_{1,2} = \frac{\sqrt{(-9)^2-4 . 8} }{2} =[/tex] 9±7/2
=1, 8
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The correct answers on Edge are explained and shown below.
Solve 1/2 + 1/2x = x^2 − 7x+10/4x by rewriting the equation as a proportion.
Q1: Which proportion is equivalent to the original equation?
Answer: C. [tex]\frac{x +1}{2x} = \frac{x^{2} -7x + 10}{4x}[/tex]
or
Option 3. x + 1/2x = x^2 - 7x + 10/4x
Q2: Name the true solution(s) to the equation:
Answer: x = 1, x = 8.
Q3: Name the extraneous solution(s) to the equation:
Answer: x = 0.
You are all welcome. Hope this helps. Have a nice day. :)
What is the rule for scale factor?
The rules of the scale factor has been explained
The scale factor is the ratio of the dimension of the new figure to the dimensions of the original figure.
The equation will be
Th scale factor = The dimensions of new figure ÷ Dimensions of the original figure
The values of the scale factor can be divided into three cases
When, scale factor greater than 1
The size of the new figure will be greater than original figure
When scale factor between 0 and 1
The size of the new figure will be less than original figure
When scale factor is equal to 1
The size of the new figure and original figure are same
Therefore, these are the rules of scale factor
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airline passengers get heavier in response to the increasing weight of airline passengers, the federal aviation administration (faa) in 2003 told airlines to assume that passengers average 190 pounds in the summer, including clothes and carry-on baggage. but passengers vary, and the faa did not specify a standard deviation. a reasonable standard deviation is 35 pounds. weights are not normally distributed, especially when the population includes both men and women, but they are not very non-normal. a commuter plane carries 30 passengers. pg 447 applet 456 chapter 7 sampling distributions (a) explain why you cannot calculate the probability that a randomly selected passenger weighs more than 200 pounds. (b) find the probability that the total weight of the passengers on a full flight exceeds 6000 pounds. show your work. (hint: to apply the central limit theorem, restate the problem in terms of the mean weight.)
The solutions for a and b are given below by using probability:
What is meant by central limit theorem?According to the central limit theorem, regardless of the underlying distribution, the distribution of the sum (or average) of a large number of independently distributed variables will be roughly normal. According to the central limit theorem, if you take sufficiently large random samples from a population with mean and standard deviation and replace some of the individuals in the samples, the sample means will be distributed about normally. The central limit theorem in probability theory proves that, even when independent random variables are added together, their correctly normalized sum frequently tends toward a normal distribution.
As a result, the sampling distribution of the sample mean of 22 passengers is normally distributed, with a mean weight of 190 pounds that is the same as the population's mean σ/√n.
=35/√22
=7.46
Now, for X=4500, z=(μ)/σ
=(4500-190)/7.46
=577.74
P(X>577.4)
=1-P(X<577.4)=0
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What is the average speed of a car if it travels 150 km in 2 hours?
The average speed of the car if it travels 150 km in 2 hours is 75 kilometres per hour.
The average speed of the car will be calculated by the formula -
Average speed = total distance covered ÷ time taken
Keep the values from question in the above mentioned formula to calculate the average speed of the car
Average speed of the car = 150/2
Performing division on Right Hand Side of the equation to find the average speed of the car
Average speed of the car = 75 km/hr
Thus, the average speed of the car is 75 kilometres per hour.
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A conjecture and the paragraph proof used to prove the conjecture are shown. Given: R S T U is a parallelogram. Angle 1 and angle 3 are complementary. Prove: angle 2 and angle 3 are complementary. Parallelogram J K L M. A diagonal segment U S is drawn across the parallelogram. Angle R U S is labeled 1. Angle U S T is labeled 2. A ray is extended diagonally up to the left of UT forming an interior angle labeled as 3. Drag an expression or phrase to each box to complete the proof. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. It is given that RSTU is a parallelogram, so RU¯¯¯¯¯∥ST¯¯¯¯¯ by the definition of parallelogram. Therefore, ∠1≅∠2 by the alternate interior angles theorem, and m∠1=m∠2 by the Response area. It is also given that ∠1 and ∠3 are complementary, so m∠1+m∠3=90° by the Response area. By substitution, m∠2+ Response area = 90°, and so ∠2 and Response area are complementary by the definition of complementary.
Answer:
It is given that RSTU is a parallelogram, so RU¯¯¯¯¯∥ST¯¯¯¯¯ by the definition of parallelogram. Therefore, ∠1≅∠2 by the alternate interior angles theorem, and m∠1=m∠2 by the transitive property. It is also given that ∠1 and ∠3 are complementary, so m∠1+m∠3=90° by the definition of complementary angles. By substitution, m∠2+ m∠3 = 90°, and so ∠2 and ∠3 are complementary by the definition of complementary.
Kayla is 1. 85 meters tall. At 12 noon, she measures the length of a tree's shadow to be 28. 15 meters. She stands 23. 1 meters away from the tree, so that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
The height of the tree is 2.25 m. The problem is related to quantitative comparison.
What is a quantitative comparison?A quantitative comparison is a problem with two objects having different quantities but they can be increasing by the same factor.
Kayla is 1.85 m tall and she stands 23.1 m away from the tree. At the same time, a tree's shadow near her is 28.15 high. Determine the height of the tree!
We have:
Kayla's tall = 1.85 mKayla's shadow = 23.1 mTree's shadow = 28.15 mIf the tree's shadow is longer than Kayla's shadow, the tree's height is also higher that Kayla's tall. The tree's height is
Kayla's tall/tree's tall = Kayla's shadow/tree's shadow
1.85/tree's tall = 23.1/28.15
Tree's tall = (28.15 × 1.85)/23.1
Tree's tall = 2.25 m
Hence, the height of the tree that has a shadow of 28.15 meters is 2.25 m.
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What is the value of [-4.67]?
Answer:
the answer is letter B
Step-by-step explanation:
All you do is remove to parentheses
Answer:
-4
Step-by-step explanation:
I hope this helps
The table shows a proportional relationship between x and y.
x 12 16 28
y 3 4 7
Describe the graph of the proportional relationship, in words.
A line beginning at point (0, 0) and continuing through the point (4, 12).
A line beginning at point (0, 0) and continuing through the point (28, 7).
A line beginning at point (12, 4) and continuing through the point (7, 28).
A line beginning at point (12, 4) and continuing through the point (4, 16).
A line beginning at point (0, 0) and continuing through the point (28, 7) describes the graph of the proportional relationship. 2nd option is the answer
How to describe the graph of the proportional relationship in words?
Given: the proportional relationship
x 12 16 28
y 3 4 7
In order to know the beginning of the line, we need to find the y-intercept.
The equation of a line is of the form
y = mx + c
where m is the slope and c is the y-intercept.
m = y2-y1 /x2-x1
m = 4-3 / 16-12 = 1/4
y = mx + c
3 = 1/4(12) + c
3 = 3 + c
c = 0
Thus, the beginning of the line is (0, 0).
The coordinate of a line or graph is written in the form (x, y). Therefore, the line begins at point (0, 0) and continues through point (28, 7).
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Fill in the missing number 25% of = 24
Answer:
96
Step-by-step explanation:
25% of what is 24?
25% of X is 24
To find X we do 24/25%.
Converting percent to decimal:
25%/100 = 0.25
X = 24/0.25
X = 96
Write an equation in point-slope form, slope-intercept form, and standard form for the following lines:
A. [tex]m = -6; (-9,9)[/tex]
B. [tex](-8,-6); (4,-15)[/tex]
Answer:
Point-slope form:
A. y - 9 = -6(x - 9)
B. y + 6 = -3/2(x + 8)
Slope-intercept form:
A. y = -6x + 63
B. y = -3/2x - 27/2
Standard form:
A. -6x + y - 63 = 0
B. -3/2x - y + 27/2 = 0
Find the demand function for the marginal revenue function. Recall that if no items are sold, the revenue is 0. R'(x) = 0.06x2 – 0.05x + 152 p(x) = 0
The marginal revenue function, locate the demand function is P = 0.02x² -0.025x + 152 when R'(x) = 0.06x² - 0.05x + 152.
Given that,
We have to find for the marginal revenue function, locate the demand function.
Remember that the income is zero if no things are sold:
R'(x) = 0.06x² - 0.05x + 152
p(x) is what.
We know that,
MR = dTR/dx = 0.06x² - 0.05x + 152
Integrating the marginal revenue function , we get total revenue function,
MR = TR
= (0.06x²⁺¹)/(2+1) - (0.05x¹⁺¹)/(1+1) + 152x
= (0.06x³)/3 - (0.05x²)/2 + 152 x
TR = 0.02 x³ - 0.025 x² + 152 x
TR = (P)(Q) = (P)(x) = 0.02 x³ - 0.025 x² + 152 x
P = ( 0.02 x³ - 0.025 x² + 152 x)/x
P = 0.02x² -0.025x + 152
Therefore, The marginal revenue function, locate the demand function is P = 0.02x² -0.025x + 152 when R'(x) = 0.06x² - 0.05x + 152.
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What is the splitting strategy?
Splitting strategy is one of the technique in mathematics which help to add the larger number , two-digit and three digit and so on.
Explanation:
Splitting strategy is one of the mathematical technique :
It is useful to add the larger numbers.It split the numbers into addends , place value of the digit , factors of the given numbers .To make the calculation easy .It is also useful in making budget by dividing it into three required categories : Important, personal and Saving account.Splitting strategy also helpful to deliver or place the order fast by splitting it into different categories.Useful to divide the work in error free or reduce the chances of error.Therefore, the splitting strategy is mathematical technique to make out work effortless.
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Find the length of side x in simplest radical form with a rational denominator.
The side x of the right angle triangle is 6√3 units.
How to find the sides of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees. The sides of a right triangle is named according to the position of the angle. The side of a right triangle are as follows:
hypotenuse sideopposite sideadjacent sideThe hypotenuse side is the longest side of a right triangle.
Therefore, let's find the x side of the right triangle using trigonometric ratios.
tan 60 = opposite / adjacent
opposite side = x
adjacent side = 6
tan 60 = x / 6
cross multiply
x = 6 tan 60
x = 6 × √3
x = 6√3
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please anyone help me with this question i need it ASAP!! all it’s asking is to Write the equation of a line perpendicular to y=2x-4 and
goes through the point (4,-1). please anyone help meee!!
Answer:
y = [tex]-\frac{1}{2}[/tex]x + 1
Step-by-step explanation:
y = mx + c
Find the reciprocal and change the sign of the gradient (m), which is -[tex]\frac{1}{2}[/tex]
so
y = [tex]-\frac{1}{2}[/tex]x + c
Put in your point that you want it to intersect (4,-1):
-1 = [tex]-\frac{1}{2}[/tex](4) + c
-1 = -2 + c
-1 + 2 = c
1 = c
y = [tex]-\frac{1}{2}[/tex]x + 1
What is the value of x if the distance between the points (7, 5) and (x, -3) is 10 units?
The value of the variable x when the distance between two points is 10 is equal to 13 or 1.
As given in the question,
Given two points (7, 5) and (x, -3)
Distance between two points (7, 5) and (x, -3) is equal to 10 units
Distance = √ ( y₂ - y₁ )² + ( x₂ - x₁ )²
⇒ (10) = √ ( -3 -5 )² + ( x - 7 )²
⇒ 10 = √ ( -8 )² + x² - 14x + 49
⇒ 10² = 64 + x² - 14x + 49
⇒ 100 = 113 + x² - 14x
⇒ x² -14x + 13 = 0
⇒ x² -13x -x + 13 =0
⇒ ( x - 13) ( x - 1) = 0
⇒ x = 13 or 1
Therefore, the value of the variable x for the given distance and points is equal to 13 or 1.
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the blue catfish (ictalurus furcatus) is the largest species of north amercian catfish. the current world record stands at 143 pounds, which was caught in the john h. kerr reservoir (bugg's island lake) located in virginia. according to amercian expedition, the average weight of a blue catfish is between 20 to 40 pounds. given that the largest blue catfish ever caught was at the john h. kerr reservoir, you believe that the mean weight of the fish in this reservoir is greater than 40 pounds. a) if you going to test this claim at the 0.05 significance level, what would be your null and alternative hypotheses? h 0 : ? h 1 : ? b) what type of hypothesis test should you conduct (left-, right-, or two-tailed)?
a) The hypothesis are given as follows:
Null hypothesis: [tex]H_0: \mu \leq 40[/tex]Alterantive hypothesis: [tex]H_1: \mu > 40[/tex]b) The test is classified as a right-tailed test.
What are the hypothesis tested?The claim is given as follows:
"The mean weight of the fish in this reservoir is greater than 40 pounds".
At the null hypothesis, it is tested if there is not enough evidence to conclude that the claim is true, that is, not enough evidence to conclude that the mean is greater than 40 pounds, hence:
[tex]H_0: \mu \leq 40[/tex]
At the alternative hypothesis, it is tested if there is enough evidence to conclude that the claim is true, hence:
[tex]H_1: \mu > 40[/tex]
We are testing if the mean is greater than a value, hence this is a right-tailed test.
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Customers at a restaurant were surveyed to see which type of service they had during their visit (table service, assisted service, or self-service) and their age (18 years or younger or over 18 years old). The results of the survey were displayed in a segmented bar chart.
Which of the following describes this data set?
Categorical and univariate
Numerical and univariate
Categorical and bivariate
Numerical and bivariate
Since the customers were surveyed to see which type of service they had during their visit and their age, the data type which best describes this data set is: C. categorical and bivariate.
What is a categorical data?A categorical data can be defined as a type of statistical data that is typically used to group information that are having the same attributes or characteristics.
In Science, some examples of a categorical data include the following:
RaceReligionAgeGenderClassWhat is a bivariate data?A bivariate data can be defined as a data set which comprises information that are based on two (2) variables, usually two types of related data.
In conclusion we can reasonably infer and logically deduce that the data set above would result in data that are categorical and bivariate.
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A town has a population of 10000 and grows at 5% every year. To the nearest year, how long will it be until the population will reach 22000?.
It takes about 16 years to reach the population size of 22000.
Population growth is the term used to describe changes in population size over time, which can be either positive or negative. The population growth formula is [tex]P=P_0\times e^{rt}[/tex]. Here, P is the total population size after time t, P₀ is the initial population size, r is the rate of growth, and e is Euler's number (e=2.72).
Given the total population, after time t is 22000, the initial population is 10000, and the rate is 5%.
Then, the time is calculated as,
[tex]\begin{aligned}22000&=10000\times e^{(0.05\times t)}\\\frac{22000}{10000}&=e^{(0.05\times t)}\\\ln(2.2)&=0.05\times t\\t&=\frac{0.788}{0.05}\\&=15.76\\&\approx16\end{aligned}[/tex]
The time it takes to reach a population size of 22000 is 16 years.
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ten less the the quotient of a number and 3 is 8
x/3-10=8
Add 10 to each side x/3=18 Multiply by 3
Answer:
x/3 - 10 = 8
Step-by-step explanation:
It seems like you want me to provide an equation, so here it is:
10 less equates to "minus 10", or "10 minus". [-10]
Quotient refers to division, and "a number" can be replaced with a variable: x. This is our numerator. Our denominator is "3", as it states, "and 3". Finally, the "is" statement refers to equality, and we can replace this with the equal sign.
Putting these all together, you get the equation, x/3 - 10 = 8.
What is slope and y-intercept examples?
Slope is a measure of how much a line changes in the y-direction for every unit of change in the x-direction and y-intercept of a line is the point at which the line crosses the y-axis.
Slope: Slope is a measure of how much a line changes in the y-direction for every unit of change in the x-direction. It is typically represented by the m in the equation y = mx + b.
Example: A line with a slope of 2 would mean that for every increase of 1 in the x-direction, the y-value would increase by 2.
Y-intercept: The y-intercept of a line is the point at which the line crosses the y-axis. It is typically represented by the b in the equation y = mx + b.
Example: A line with a y-intercept of 4 would cross the y-axis at y = 4.
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Algebra2 8.2 Practice a problems
Step-by-step explanation:
Given the angle 10 let's add 360 and see if the angle is in the interval.
[tex]10 + 360 = 370[/tex]
However,
[tex]10 - 360 = - 350[/tex]
So the coterminal angle is
-350
For question 2, subtract 360
[tex]180 - 360 = - 180[/tex]
2.Lucas recorded the number of Calories he burned while jogging. The number of
Calories he burned while jogging is proportional to the number of minutes jogged.
Number of
Minutes, x
5
10
15
20
Calories Burned,
y
47.5
95.0
142.5
190.0
Part A. Write an equation that represents this relationship.
Part B. Find the constant of proportionality and interpret its meaning.
Answer:
Since the number of calories burned is proportional to the number of minutes jogged, we can represent this relationship using the equation y = kx, where y is the number of calories burned, x is the number of minutes jogged, and k is the constant of proportionality.
To find the value of k, we can use one of the given data points. For example, if x = 10 and y = 95, we have 95 = k * 10. Solving for k, we find that k = 9.5.
The constant of proportionality, k, has the meaning of the number of calories burned per minute of jogging. In this case, k = 9.5 calories/minute, so for every minute of jogging, the person burns 9.5 calories.
Step-by-step explanation: