Answer:
Below
Step-by-step explanation:
Everywhere there is a local max or minima, the slope = 0
IF you take the first derivative, set it = 0 and solve for the x values, you will get these local max/min points ....but you will not know if they are a max or a min....
so take the SECOND derivative and sub in each of the values that you got ......if you get a POSITIVE result it is a min.... a negative result is a max point...... when you find the min point(s) ...use that value of 'x' in the original equation to find the corresponding 'y' coordinate.....
OR: You can graph the function to SEE the min points .....
How do you determine whether the sequence a_n=(2^n+3^n) / (2^n−3^n) converges, if so how do you find the limit?
You determine the limit by [tex]\lim_{n \to \infty} a_n = -1[/tex].
A limit in mathematics is a point at which a function approaches the output for the specified input values. Calculus and mathematical analysis depend on limits, which are also used to determine integrals, derivatives, and continuity. The concept of limit, which is founded on the idea of closeness, is largely used to give values to some functions at points when none are defined in a way that is consistent with values close by.
Divide the denominator and numerator by 3n as shown.
[tex]\lim_{n \to \infty} a_n = \lim_{n \to \infty} \frac{2^n+3^n}{2^n-3^n\\}[/tex]
[tex]= \lim_{n \to \infty} \frac{(\frac{2}{3})^n+1 }{(\frac{2}{3})^n-1 } \\=\frac{0+1}{0-1} \\=-1[/tex]
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Given the equation 8x = 4y + 16, generate a plan to rewrite it in slope-intercept form. Which variable do you solve for?
Answer: Convert the equation to slope-intercept form by solving for the variable y. Use the properties of equality to subtract 16 from both sides, and then divide both sides by 4.
This is for future people who don't want to watch adds or have hit their daily limit, have a nice day!
The slope-intercept form of the equation 8x = 4y + 16 will be y = 2x -4.
What is equation straight line?
Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.
The equation given is 8x = 4y + 16.
We must solve for y as follows;
8x = 4y + 16
4y = 8x -16
By dividing through by 4; we have;
y = 2x -16
Hence the equation for both lines will be y = x +3 and y = x+13
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21) Submarine A is sent to explore the ocean floor in the Atlantic Ocean. It descends to 126
feet below sea level, For the next 4 ½ hours, it descends further at a rate of 15 feet per hour
and then reaches its destination.
Submarine B is sent to explore the ocean floor in the Pacific Ocean. It begins its descent at
sea level and reaches the same elevation as Submarine A over the course of 6.5 hours. At
what rate does Submarine B descend? Show and explain your thinking.
The rate at which Submarine B descends is 29.8 feet per hour.
What is the rate?The rate refers to the average speed of an object in motion from one point to another.
The rate can be determined by dividing the distance by the time.
The rate or average speed is the quotient between distance and time.
The distance descended by Submarine A = 193.5 feet (126 + 4 ½ x 15)
The time Submarine B descends = 6.5 hours
Submarine B's rate of descent = 29.77 feet (193.5/6.5) per hour
= 29.8 feet
Thus, we can conclude that Submarine B descends at the rate of 29.8 feet every hour, whereas, Submarine A descends 15 feet per hour.
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the sum of the age of father and son at present iz 45 year.if both live on until the son age become equal to the father present age the sum of their agr then become 95 years .find the present ages.
Answer:
10 yrs old and 35 yrs old
Step-by-step explanation:
I figured it out by trial and error but here's the thinking process.
10 + 35= 45
Son becomes dad's age so 35-10=25, so plus 25 year to each age.
10+25=35
35+25= 60
35+60=95
I hope that makes enough sense!
e throw a fair die three times. if we observe the first throw is a 4, what is the probability that there is at least two 4s in the three throws?
The probability that there is at least two 4s in the three throws is 0.05 or 5%
Probability
In statistics, probability deals with the possibility of happening of the events.
Given,
Here we know that the throw a fair die three times. if we observe the first throw is a 4.
And we need to find the probability that there is at least two 4s in the three throws.
According to the given question, we know that the dice is thrown 3 time.
Then the sample space of the given event is 216.
Here we know that the first throw has 4.
And we need to find the probability of getting two 4s in the 3 throws,
So, the possible number of events are.
=> {444, 441, 442, 443, 445, 446, 414, 424, 434, 454, 464}
So, the total possible number is 11.
Then the probability is,
=> 11/216
=> 0.05 or 5%
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what are the steps to -3+7x-9+8x=54
Answer: 67/15
Step-by-step explanation:
-3+7x-9+8x=54
-12 + 15x = 54
15x = 67
x = 67/15
Help me please I don’t understand
The age of Michelle is 30 years old (option A).
What is Michelle's age?The mathematical operation that would be used to determine the required value is multiplication. Multiplication is the process of determining the product of two or more numbers. The sign that represents multiplication is ×.
The first step is to determine Fiona's age.
Fiona's age = Madeline's age x 2
Fiona's age = 5 x 2 = 10
The second step is to determine Michelle's age.
Michelle's age = Fiona's age x 3
Michelle's age = 10 x 3
Michelle's age = 30
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How do you simplify 24 ⋅ 2^ − 2 ?
Answer:
Step-by-step explanation:
We can use one of the properties of exponents to change the −2 into +2 by sending the base to the denominator as:24⋅2−2=24⋅12+2=244=6
Answer:
We can use one of the properties of exponents to change the −2 into +2 by sending the base to the denominator as:
24⋅2−2= 24⋅1/2 OVER +2= 24/4= 6
Step-by-step explanation:
Principal = 6,000, rate of interest = 10% p.a., time = 3 years
please solve
Answer:
$7800
Step-by-step explanation:
1 year = 10%
3 years = 30%
30% = 0.3
6000 times 0.3 = $1800
6000 + 1800 = $7800
So, they will pay $7800
Marcus monthly salary is $1,500 plus 10% of sales. How much could Marcus earn per month with salary and 9% sales? Please explain your answer.
pls
If Marcus monthly salary is $1,500 plus 10% of sale, then he could earn 1500 + 0.09x per month with salary and 9% sales
Monthly salary of Marcus = $1500
The percentage incentives for sales = 10%
If the percentage of incentive for sales is 9 %
Consider the amount of sales is $x
Therefore the monthly salary of Marcus = Monthly salary of Marcus + (The amount of sales × 9/100)
Substitute the values in the equation
The monthly salary of Marcus = 1500 + (x×9/100)
Divide the numbers in the equation
= 1500 + (x × 0.09)
Multiply the numbers the numbers
= 1500 + 0.09x
Therefore, the monthly salary of Marcus will be 1500 + 0.09x
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Delux Coffee is a mixture of Coffee A and Coffee B. The ratio of mixture is coffee A: coffee B= 3:2. What is the quantity of Coffee B in a bag of 25kg of delux coffee?
The quantity of coffee B in a 25 kg delux bag is 10kg
What is a ratio?Ratio is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another. In a ratio, two quantities are compared using division. Here the dividend is called the 'antecedent' and the divisor is called the 'consequent'.
total division of the 25kg bag is 3 + 2 = 5
so that each division would weigh 25/5 = 5kg
coffee B has 2 division so that its total quantity is 5 x 2 = 10kg
In conclusion the total quantity of coffee B is 10kg
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There are two option for tickets & admission to the carnival. Option #1 requires you to pay a $5 admission fee plus $0.30 per ride ticket. Option #2 requires you to pay a $3 admission fee plus $0.80 per ride ticket. Garrett chose option #1 and Meagan chose option #2. If they wound up paying the same amount of money, how many tickets did they each purchase?
The number of tickets they purchased is 4.
How many tickets did they purchase?The expression that would b used to represent the total cost at the carnival is a linear expression. A linear expression is an expression that has a single variable that is raised to the power of one.
The form of the linear expressions that can be used to represent the total cost at the carnival is:
Total cost = admission fee + (price per ride x number of rides)
Total cost in option 1 = $5 + 0.30r
Total cost in option 2 = $3 + $0.80r
Where r = number of rides
When they pay the same amount of money, the linear functions would be equal:
$5 + 0.30r = $3 + $0.80r
$5 - $3 = $0.80r - 0.30r
$2 = $0.50r
r = 2 / 0.5
r = 4
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3√y^2=6√x y=n√x
Find n
Answer:
n = 4
Step-by-step explanation:
Given equation:
[tex]\sqrt[3]{y^2} =\sqrt[6]{x}[/tex]
[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]
[tex]\implies y^{\frac{2}{3}}=x^{\frac{1}{6}[/tex]
Take both sides of the equation to the power of ³/₂:
[tex]\implies \left(y^{\frac{2}{3}}\right)^\frac{3}{2} =\left(x^{\frac{1}{6}\right)^\frac{3}{2}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies y^{\frac{2}{3} \cdot \frac{3}{2}}=x^{\frac{1}{6} \cdot \frac{3}{2}}[/tex]
Simplify:
[tex]\implies y^{\frac{6}{6}}=x^{\frac{3}{12}[/tex]
[tex]\implies y^1=x^{\frac{1}{4}[/tex]
Apply exponent rule a¹ = a :
[tex]\implies y=x^{\frac{1}{4}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{\frac{1}{n}}=\sqrt[n]{a}:[/tex]
[tex]\implies y=\sqrt[4]{x}[/tex]
the function that has the least minimum value is function . the function that has the greatest minimum value is function .
Function h is the one with the lowest minimum value.
Explain about the function?An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for creating physical links in the sciences.
A function is more precisely defined as a set of ordered pairs (x,y) with the limitation that there may only be one ordered pair with the same value of x given a set of inputs (domain) X and a set of potential outputs (codomain).
A graph is considered to be a function if any vertical line formed can cross it at most one point. A vertical line cannot cross the graph at more than two points in any location.
Considering the query
f(x) = x² - 2x - 6
given the graph
at its lowest value (1,-7)
h(x) = 2(x-1)²
h(x) = 2 (x² + 1 -2x )
h(x) = 2x² - 4x + 2
Creating the graph
We may view the
Lowest value at (1,0)
The complete question is,
Consider continuous functions f, g, and k. Then complete the statements.
The function that has the least minimum value is function _____. The function that has the greatest minimum value is function _____.
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Lucy will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $55 and costs an additional $0.50 per mile driven. The second plan has no initial fee but costs $0.60 per mile driven. How many miles would Lucy need to drive for the two plans to cost the same?
The two plans will cost the same when Lucy has driven 550miles. ($55 + $0.50 x 550)= $330
(0.6*550)=$330
The difference between both the trip rate is .10$
and the difference between initial fee is 55$
so after 1 mile the difference is .10$
the 55$can be earn after
55*10=550 mile.
What are typical speeds and an illustration?Divide the overall distance traveled by the time period to find the average speed. An someone traveling at an average speed of 40 miles divided by 40 minutes, or 1 mile per minute, would be driving 20 miles north and then 20 miles south to arrive at the same location (60 mph)
Why is the average speed determined?The overall distance traveled by an object over the total amount of time is the thing's average speed. The average speed v of an object during a motion that covers a total distance of d and a total duration of t can be estimated using the formula v = d t.
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the test statistics for one-way anova follows the _______.
The test statistics for one-way Anova follows, the comparing of the T Statistic with the T critical value.
Z-test definition:On data that is dispersed normally, the Z test is a parametric process that is applied. The z-test can be applied to proportions, two samples, or one sample to test hypotheses. When the population variance is known, it is possible to determine whether the means of two significant groups differ.
The second is one-way analysis of variance (ANOVA), which checks if three or more samples originate from populations with the same mean using the F-distribution.
The test statistic should be compared to the crucial value. If the test statistic is more extreme in favor of the alternative than the crucial value, the alternative hypothesis should be considered instead of the null hypothesis. If the test statistic is not as extreme as the crucial value, the null hypothesis should not be disregarded.
Therefore,
The test statistics for one-way Anova follows, the comparing of the T Statistic with the T critical value.
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if f(x)=2x²-6, then find f(4)
Answer:
Substitute x = 4 into the equation.
f(4) = 2(4)² - 6
= 2(16) - 6
= 32 - 6
= 26
Caroline babysit for two families-Nelsons and the smiths. use the information below to compare her earnings
Answer:
6.25h
Step-by-step explanation:
Each minute, a faucet allows 4/7 gallons of water to enter a large tub, and the drain allows 5/7 gallons to leave the tub.
What is the change in the amount of liquid in the tub after 1/4 minute?
Enter your answer as a fraction in lowest terms in the box.
gal.
Answer: -1/28 gallon
Step-by-step explanation:
divide both numbers by 4 since its 1/4 a minute (-5/7 ÷ 4 and 4/7 ÷ 4) then add them, (-5/28 + 4/28= -1/28)
Answer: -1/28 gallon
Step-by-step explanation:
Question 1 (Multiple Choice Worth 2 points)
(Evaluating Algebraic Expressions LC)
If w = 24, what is the value of 2w - 18?
Answer:
30
Step-by-step explanation:
2 multiplied by 24 = 48
48 - 18 = 30
for a random sample of 50 such pairs, what is the (approximate) probability that the sample mean courtship time is between 115 min and 135 min? (round your answer to four decimal places.)
The required probability that the sample mean courtship time is between 115 min and 135 min is 0.5269.
We know that probability is defined as the proportion of number of favorable outcomes to the total number of outcomes.
Probability implies plausibility. A piece of math deals with the occasion of a sporadic event. The worth is communicated from zero to one. Likelihood has been acquainted in Maths with foresee how likely occasions are to occur.
The significance of likelihood is essentially the degree to which something is probably going to occur. This is the fundamental likelihood hypothesis, which is likewise utilized in the likelihood dispersion, where you will get familiar with the chance of results for an irregular examination. To track down the likelihood of a solitary occasion to happen, first, we ought to know the complete number of potential results.
We have μ=115min
n=50
P(x₁<X<x₂)=P(z₂< (x₂-μ) /S.D) -P(z₁<(x₂-μ)/S.D)
S.D=√(σ²/ n)
=>S.D=√(115)²/50
=>S.D = √(13225)/50
=>S.D = √264.5
=>S.D = 16.26
P(115<X<135)=P(z₂< (135-115)/16.26)-P(z₁ <(100-115) / 16.26)
=>P((115<X<135)=P(z₂<20/16.26)-P(z₁< -15/16.26)
=>P(115<X<135)=P(z₂<1.23) - P(z₁<-0.922)
From the probability distribution table
P(z₂<1.23)=0.6255
P(z₁<-0.922)=0.0986
P(115<X<135)=0.6255-0.0986
=>P(115<X<135)=0.5269
Hence, required probability is 0.5269
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a landscaper is designing a flower garden in the shape of a trapezoid he wants the shorter base to be 2 yards greater than the height of the trapezoid h and the longer base to be
The length of the bases of the trapezoid shape yard will be 18 yards and 22 yards.
What is a Trapezoid?A quadrilateral with at least one set of parallel sides is called a trapezoid in American and Canadian English.
In British and other varieties of English, it is termed a trapezium.
In Euclidean geometry, a trapezoid is a convex quadrilateral by definition.
The parallel sides are called the basis of the trapezoid.
So, we have:
The height should be 3 yards higher than the shorter base.
b₁=h+3
The height should be 3 yards higher than the shorter base.
b₂=h+7
Formula for Area of trapezoid = 1/2(b₁+b₂)h
Now, using the formula, calculate as follows:
150=1/2(h+3+h+7)h
150=(2h+10)h/2
150=2h²+10h/2
150=2h²+5h
h²+5h-150=0
h²+15h-10h-150=0
h(h+15)-10(h+15)=0
(h-10)(h+15)=0
h=10 or h-15
h should be positive:
b₁=h+3=15+3=18
b₂=h+7=15+7=22
Therefore, the length of the bases of the trapezoid shape yard will be 18 yards and 22 yards.
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Complete question:
A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3 yards greater than the height, and the longer base to be 7 yards greater than the height. the total area of the flower garden is 150 square yards. what will the length of each base be
henry wants to earn at least trimming trees. he charges per hour and pays in equipment fees. what are the possible numbers of hours henry could trim trees?
The possible number of hours Henry could trim trees is t > 10.
The given information represents a scenario which demonstrates an inequality statement as Henry wants to earn at least $ 56, which means the amount earned should be greater than 56.
Let t be the possible number of hours Henry trim trees. As his per hour charge is $6 and he pays $4 in equipment fee, the inequality statement is:
6t – 4 > 56
Solving,
6t > 56 + 4
6t > 60
t > 10.
In order to earn at least $56, Henry must trim trees for at least 10 hours or more.
Note: The question is incomplete. The complete question probably is: Henry wants to earn more than $56 trimming trees. He charges $6 per hour and pays $4 in equipment rental fees. What are the possible number of hours Henry could trim trees?
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if triangle pqrs is similar to triangle wxyz find the value of x?
Answer:
x=60
Step-by-step explanation:
these shapes seem to be flipped
side WZ seems to be similar to PS
and Side ZY seems to be similar to RS
ewe can make ratios on the side lengths
40/75=32/x
cross multiply
40x=75(32)
40x=2400
/40. /40
x= 60
hopes this helps please mark brainliest
Which of the following congruence does not occur * A SSS B SAS C SSA D RHS?
Answer:
Answer Option C: SSA
1000 liters equal 1 what
kiloliter
One thousand liters is called a kiloliter. A kiloliter is equal to 264.172 gallons. One liter is equal to 0.264172, so if you want to find how many gallons there are in 1 kiloliter, just multiply 0.264172 by 1000
Answer:
1000 liters
Step-by-step explanation:
In his free time, Gary spends 9 hours per week on the Internet and 12 hours per week playing video games. If Gary has five hours of free time per day, what percent of his free time is spent on the Internet and playing video games
Answer: 11.64%
Step-by-step explanation:
you are bored at a lunch meeting and surreptitiously place a raisin in your glass of water. the raisin swells to twice its original size. relative to the water, the raisin must have been:
If the raisin swells to twice its original size, relative to the water, the raisin must have been a)hypertonic solution. So, correct option is a.
Hypertonic alludes to an answer with higher osmotic strain than another arrangement. At the end of the day, a hypertonic arrangement is one in which there is a more noteworthy fixation or number of solute particles outside a layer than there are inside it.
A hypertonic arrangement is one which has a higher solute fixation than another arrangement.An illustration of a hypertonic arrangement is the inside of a red platelet contrasted and the solute centralization of new water.At the point when two arrangements are in touch, solute or dissolvable moves until the arrangements arrive at harmony and become isotonic concerning one another.Hence, correct option is a.
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(Complete question) is:
You are bored at a lunch meeting and surreptitiously place a raisin in your glass of iced tea. The raisin shrinks to half its original size. The raisin must have been a __?__ solution.
a)hypertonic
b)aquatonic
c)hypotonic
d)isotonic
You start at (4, 0). You move up 10 units. Where do you end?
Answer: (4, 10)
Step-by-step explanation:
The first number, 4, is the number on the x axis, the horizontal axis. The second number 0 is the number on the y axis, the vertical axis.
If you move up you would moving on the y axis, therefore the second number, 0, would change.
You moved 10 units so starting at 0 move up 10 units. 0 + 10 = 10
Now you're at (4, 10)
Find the missing side of the triangle
Round your answer to the nearest tenth
The length of missing side of triangle is 11cm.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The given triangle is a right angled triangle.
In the triangle hypotenuse is 12cm, opposite side is 4.8cm.
We need to find the adjacent side which is represented by x.
By pythagoras theorem we find the missing side
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides
12²=4.8²+x²
144=23.04+x²
subtract 23.04 on both sides
120.96=x²
Take square root on both sides
x=10.99
x=11
Hence, the length of missing side of triangle is 11cm.
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