In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
12, 20, 18, 25 , 6
range = ?
We must order the data.
Step 02:
6 , 12 , 18 , 20 , 25
Range = 25 - 6 = 19
The answer is:
The range is 19
f(x) = (x ^ 2 + 2x + 7) ^ 3 then
Answer
[tex]f^{\prime}(x)=6(x+1)(x^{2}+2x+7)^{2}[/tex][tex]f^{\prime}(1)=1200[/tex]Explanation
Given
[tex]f\mleft(x\mright)=(x^2+2x+7)^3[/tex]To find the derivative, we have to apply the chain rule:
[tex][u(x)^n]^{\prime}=n\cdot u(x)^{n-1}\cdot u^{\prime}(x)[/tex]Considering that in our case,
[tex]u(x)=x^2+2x+7[/tex][tex]u^{\prime}(x)=2x+2+0[/tex]and n = 3, then:
[tex]=3\cdot(x^2+2x+7)^{3-1}\cdot(2x+2)[/tex]Simplifying:
[tex]f^{\prime}(x)=3\cdot2(x+1)(x^2+2x+7)^2[/tex][tex]f^{\prime}(x)=6(x+1)(x^2+2x+7)^2[/tex]Finally, we have to replace 1 in each x in f'(x) to find f'(1):
[tex]f^{\prime}(1)=6((1)+1)((1)^2+2(1)+7)^2[/tex][tex]f^{\prime}(1)=6(1+1)(1+2+7)^2[/tex][tex]f^{\prime}(1)=6(2)(10)^2[/tex][tex]f^{\prime}(1)=6(2)(100)[/tex][tex]f^{\prime}(1)=12(100)[/tex][tex]f^{\prime}(1)=1200[/tex]If quadrilateral WXYZ is transformed using the rule T(-1.2), in whatdirections should WXYZ be translated?O 1 unit down, 2 units rightO 1 unit left, 2 units upO 1 unit up, 2 units leftO 1 unit right, 2 units up
With aging body fat increases in muscle mass declines the graph to the right shows the percent body fat in a group of adult women and men as they age from 25 to 75 years age is represented along the X-axis and percent body fat is represented along the Y-axis use interval notation to give the domain and range for the graph of the function for women
Step 1
The domain and range of a function is the set of all possible inputs and outputs of a function respectively. The domain is found along the x-axis, the range on the other hand is found along the y-axis.
Find the domain of the graph of the function of women using interval notation.
[tex]\text{Domain:\lbrack}25,75\rbrack[/tex]Step 2
Find the range of the graph of the function of women using interval notation.
[tex]\text{Range:}\lbrack32,40\rbrack[/tex]Therefore, the domain and range in interval notation for the women respectively are;
[tex]\begin{gathered} \text{Domain:\lbrack}25,75\rbrack \\ \text{Range:}\lbrack32,40\rbrack \end{gathered}[/tex]The product of two consecutive positive even integers is 48. Find the greatest positive integer.
From that statement we can create the following equation,
[tex]n\cdot \left(n+2\right)=48[/tex]solving for n,
[tex]\begin{gathered} n^2+2n=48 \\ n^2+2n-48=0 \\ n_{1,\:2}=\frac{-2\pm \sqrt{2^2-4\cdot \:1\cdot \left(-48\right)}}{2\cdot \:1} \\ n_{1,\:2}=\frac{-2\pm \:14}{2\cdot \:1} \\ n_1=\frac{-2+14}{2\cdot \:1},\:n_2=\frac{-2-14}{2\cdot \:1} \\ n=6,\:n=-8 \end{gathered}[/tex]We can only use the positive number for this problem, therefore n = 6
From the above, the set of numbers is 6 and 6+2=8, since 6*8=48.
Answer: the greatest integer is 8
Sergio believes he is five years younger than double the age of Chloe and Chloe believes she is five yearsolder than half of Sergio's age. Are they both right?
Let S represent Sergio's age
Let C represent Chloe's age
Sergio believes he is five years younger than double the age of Chloe. This would be expressed as
S = 2C - 5
Chloe believes she is five years older than half of Sergio's age. This means that
C = 5 + S/2
If we multiply the second equation by 2, it becomes
2C = 10 + S
This means that both equations are not the same. Therefore, they are not right
Express M in terms of B and n: B = 3Mn 2
We are given the expression B=3Mn/2 and told to express M in terms of B and n. This means that we should apply mathematical operations on both sides of the equation so we "isolate " M on one side of the equality sign. We begin with the given equation
[tex]B=\frac{3\cdot M\cdot n}{2}[/tex]First, we multiply both sides by 2, so we get
[tex]2\cdot B=3\cdot M\cdot n[/tex]Next, we divide by 3 on both sides, so we get
[tex]\frac{2\cdot B}{3}=M\cdot n[/tex]Finally, we divide both sides by n, so we get
[tex]\frac{2\cdot B}{3\cdot n}=M[/tex]In this case, we have succesfully expressed M in terms of B and n
A set of pool balls contains 15 balls numbered 1-15.
Without replacement: What is the probability that an odd number ball is picked
out of a box twice without the first one being replaced?
With replacement: What is the probability that an even number ball is picked with
the first ball drawn being inserted back into the box?
Step-by-step explanation:
a probability is always
desired cases / totally possible cases
the first case I assume means that we need the probability to pick 2 odd-numbered balls in a row, if we do not put the first drawn ball back into the box.
starting condition :
15 basks in total.
1, 3, 5, 7, 9, 11, 13, 15 = 8 odd numbered balls
2, 4, 6, 8, 10, 12, 14 = 7 even numbered balls
the probability for the first ball to be odd numbered :
8/15
now we have
14 remaining balls in total.
7 remaining odd numbered balls.
the probability of the second ball being odd numbered is
7/14 = 1/2
so, the probability of both as one combined event is
8/15 × 1/2 = 4/15 = 0.266666666...
now back to the starting condition.
the probability to pick an even numbered ball is
7/15
we put the ball back in and pull a second time.
the probability to an even numbered ball is
7/15
so, the probability of both as one combined event is
7/15 × 7/15 = 49/225 = 0.217777777...
If you are not knowledgeable in college algebra please let me know so I can move on more quickly. Thanks in advance!
Given polynomial is
[tex]3x^5-4x^4-5x^3-8x+25[/tex]We have to check whether the polynomial x-2 is a factor.
If x-2 is a factor then x = 2 is a root of the given polynomial.
Substitute x = 2 in the given polynomial,
[tex]\begin{gathered} 3.2^5-4.2^4-5.2^3-8.2+25=96^{}-64-40-16+25 \\ =121-120=1 \end{gathered}[/tex]Hence 2 is not a root of given polynomial.
And so x - 2 is not a factor.
Solve the following compound inequalities. Use both a line graph and interval notation to write each solution set.
t+1-5 ort+1> 5
The value of the inequality expression given as t + 1 < -5 or t + 1 > 5 is (-oo, -6) u (4, oo)
How to determine the solution to the inequality?The inequality expression is given as
t + 1 < -5 or t + 1 > 5
Collect the like terms in the above expressions
So, we have
t < -5 - 1 or t > 5 - 1
Evaluate the like terms in the above expressions
So, we have
t < -6 or t > 4
Hence, the solution to the inequality is t < -6 or t > 4
Rewrite as an interval notation
(-oo, -6) u (4, oo)
See attachment of the number line
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Find LM if LN = 137mm.
Answer this fraction based Question I will make you btainliest & provide you 50 points
Answer:
i) 2/3, ii) 2/9,iii) 4/27,iv) Rs. 40000.Step-by-step explanation:
i)A person gives 1/3 of his wealth to his wife, then he is left with:
1 - 1/3 = 2/3 of the total amountii)Then he gives 1/3 of the remainder to his son, the son gets:
2/3*1/3 = 2/9 of the total amountiii)The remaining portion is:
2/3 - 2/9 = 6/9 - 2/9 = 4/9 of the total amountEach daughter gets 1/3 of it as there are three daughters:
4/9 * 1/3 = 4/27 of the total amountiv)If the total amount is x, the son gets 2/9x and a daughter gets 4/27x and the difference of the two is Rs 20000:
2/9x - 4/27x = 200006/27x - 4/27x = 200002/27x = 20000x = 20000*27/2x = 270000This is the total amount.
The amount obtained by a daughter is:
4/27*270000 = 40000Put the following equation of a line into slope-intercept form, simplifying all fractions.4x + 20y = -180
The equation of a straight line is
y = mx + c
4x + 20y = -180
make 20y the subject of the formula
20y = -180 - 4x
20y = -4x - 180
divide all through by 20
20y/20 = -4x/20 - 180/20
y = -1/5x - 9
The answer is y = -1/5x - 9 where your slope is -1/5 and intercept is -9
The area of a rectangle is x2 – 8x + 16. The width of therectangle is x – 4. What is the length of the rectangle?-
To answer this question, we need to remember that the area of a rectangle is given by:
[tex]A_{\text{rectangle}}=l\cdot w[/tex]And we have - from the question - that:
[tex]A_{\text{rectangle}}=x^2-8x+16[/tex]And the width of the rectangle is:
[tex]w=x-4[/tex]If we factor the polynomial that represents the area, we need to find two numbers:
• a * b = 16
,• a + b = -8
And both numbers are:
• a = -4
,• b = -4
Since
• -4 * -4 = 16
,• -4 - 4 = -8
Therefore, we can say that:
[tex]x^2-8x+16=(x-4)(x-4)=(x-4)^2[/tex]Therefore:
[tex]l\cdot w=A_{\text{rectangle}}[/tex][tex]l=\frac{A_{rec\tan gle}}{w}[/tex]Then the length of the rectangle is:
[tex]l=\frac{x^2-8x+16}{x-4}=\frac{(x-4)(x-4)}{x-4}\Rightarrow\frac{x-4}{x-4}=1[/tex][tex]l=\frac{(x-4)}{(x-4)}\cdot(x-4)\Rightarrow l=x-4[/tex]In summary, therefore, the length of the rectangle is x - 4.
[tex]l=x-4[/tex][We can check this result if we multiply both values as follows:
[tex]A_{\text{rectangle}}=l\cdot w=(x-4)\cdot(x-4)=(x-4)^2_{}[/tex]And we already know that the area of the rectangle is:
[tex]x^2-8x+16=(x-4)^2[/tex].]
Given the function [tex]y=(m^2-1)x^2+2(m-1)x+2[/tex] , find the values of parameter m for which the function is always positive.
Answer: [tex](-\infty, -1) \cup (1, \infty)[/tex]
Step-by-step explanation:
The function is always positive when it has a positive leading coefficient (since that means the graph will open up), and when the discriminant is negative (meaning the graph will never cross the x-axis).
Condition I. Leading coefficient is positive
[tex]m^2 -1 > 0 \implies m < -1 \text{ or } m > 1[/tex]
Condition II. Discriminant is negative
[tex](2(m-1))^2 -4(m^2 -1)(2) < 0\\\\4(m^2 -2m+1)-8(m^2 -1) < 0\\\\4m^2 -8m+4-8m^2 +8 < 0\\\\-4m^2 -8m+12 < 0\\\\m^2 +2m-3 > 0\\\\(m+3)(m-1) > 0\\\\m < -3 \text{ or } m > 1[/tex]
Taking the intersection of these intervals, we get [tex]m < -1[/tex] or [tex]m > 1[/tex].
A golf course charges you $54 for a round of golf using a set of their clubs, and $42 if you have your own clubs. You decide to buy a set of clubs for $280 and your friend wants to just use the course's clubs.a. Write an equation to describe the cost for x number of rounds for you.b. write an equation to describe the cost for x number of rounds for your friend.c. How many rounds must you play to recover the cost of the clubs? (Find the break-even point).
Answer
You must play 24 rounds to recover the cost of the club
Step-by-step explanation:
The amount golf charged for using their set clubs = $54
They charged $42 for using personal course
let x be the number of rounds played
let y be the total cost of the clubs
Since you will be buying a set of clubs worth $280
Then, the first equation is
a. y = 280 + 42x
b. y = 54x
c . Calculate the number of rounds that must be played to recover the cost of the clubs
To calculate this, we need to equate equations a and b together
280 + 42x = 54x
Collect the like terms
280 = 54x - 42x
280 = 12x
Isolate x by dividing through by 12
280/12 = 12x/12
x = 23.3333
Hence, you must play 24 rounds to recover the cost of the club
John starting playing video games as soon as he got home from school. He played videogames for 45 minutes. Then, it took John 30 minutes to finish his homework. When Johnfinished his homework, it was 4:25 P.M. What time did John get home from school?
Given:
After coming from school to home,
He played video games for 45 minutes.
Then he took 30 minutes to finish his homework.
When John finished his homework, it was 4:25 PM.
To find:
The time at which John got home from school
Explanation:
According to the problem,
Total time to play video games and do homework is,
[tex]\begin{gathered} 45mins+30mins=75mins \\ =1hr15mins \end{gathered}[/tex]So, the time he got home from school will be,
[tex]4:25P.M.-1hr15mins=3:10P.M.[/tex]Final answer:
The time he got home from school is 3:10 P.M.
How many different lineups can Coach Lay create using 10 girls to fill 5 spots on the basketball court. Positions do not matter.
This is the formula for combinations
In this case, n = 10 and k = 5
C = 10!/(10-5)!(5)! = 3628800/(120)(120) = 3628800/14400 = 252
Answer:
252 different line u
Refer to your equation for the line that models the association between latitude and temperature of the cities: Yours y = -12 + 120 Computer calculated y = -1.07 + 119 What does the slope mean in the context of this situation?
The slope in the equations represent the change in temperature by the change in lattitude. This means that for each unit change in the latitude the temperature will decrease by an amount given by the slope.
Multiply the expressions.
-0.6y(4.5 - 2.8y) =
answer 1
-2.86
-2.7
1.68
3.9
--------- y² +
answer 2
-2.86
-2.7
1.68
3.9
Answer:
1.68y²+ 2.7y is the answer
hope it helps
Juliet has a choice between receiving a monthly salary of $1750 from a company or a base salary of $1600 and a 3% commission on the amount of furniture she sells during the month. For what amount of sales will the two choice be equal?The two salary choices will be equal when the amount of sales is [$ ]
For an amount of sales of $5,000, the two salary choice will be equal
Let the amount of sales be $x
The 3% she will receive will be;
[tex]\frac{3}{100}\times x\text{ = 0.03x}[/tex]We add this to the base salary and equate to the former monthy salary
We have this as;
[tex]\begin{gathered} 1750\text{ =1600 + 0.03x} \\ 1750-1600\text{ = 0.03x} \\ 150\text{ = 0.03x} \\ x\text{ = }\frac{150}{0.03} \\ x\text{ = \$5000} \end{gathered}[/tex]Find (and classify) the critical points of the following function and determine if they are local max, local min, or neither: f(x) =2x^3 + 3x^2 - 120x
As given by the question
There are given that the function:
[tex]f(x)=2x^3+3x^2-120x[/tex]Now,
To find the critical point, differentiate the given function with respect to x and put the result of function equal to zero
So,
[tex]\begin{gathered} f(x)=2x^3+3x^2-120x \\ f^{\prime}(x)=6x^2+6x-120 \end{gathered}[/tex]Then,
[tex]\begin{gathered} f^{\prime}(x)=0 \\ 6x^2+6x-120=0 \\ x^2+x-20=0 \\ x^2+5x-4x-20=0 \\ x(x+5)-4(x+5) \\ (x-4)(x+5) \\ x=4,\text{ -5} \end{gathered}[/tex]Now,
To find the y-coordinate, we need to substitute the above value, x = 4, -5, into the function f(x)
So,
First put x = 4 into the given function:
[tex]\begin{gathered} f(x)=2x^3+3x^2-120x \\ f(4)=2(4)^3+3(4)^2-120(4) \\ =128+48-480 \\ =-304 \end{gathered}[/tex]And,
Put x = -5 into the function f(x):
[tex]\begin{gathered} f(x)=2x^3+3x^2-120x \\ f(-5)=2(-5)^3+3(-5)^2-120(-5) \\ =-250+75+600 \\ =425 \end{gathered}[/tex]Hence, the critical point is, (4, -304) and (-5, 425).
Now,
To find the local maxima and local minima, we need to find the second derivative of the given function:;
So,
[tex]\begin{gathered} f^{\prime}(x)=6x^2+6x-120 \\ f^{\doubleprime}(x)=12x+6 \end{gathered}[/tex]Now,
The put the value from critical point into the above function to check whether it is maxima or minima.
So,
First put x = 4 into above function:
[tex]\begin{gathered} f^{\doubleprime}(x)=12x+6 \\ f^{\doubleprime}(4)=12(4)+6 \\ f^{\doubleprime}(4)=48+6 \\ f^{\doubleprime}(4)=54 \\ f^{\doubleprime}(4)>0 \end{gathered}[/tex]And,
Put x = -5 into the above function
[tex]\begin{gathered} f^{\doubleprime}(x)=12x+6 \\ f^{\doubleprime}(-5)=12(-5)+6 \\ f^{\doubleprime}(-5)=-60+6 \\ f^{\doubleprime}(-5)=-54 \\ f^{\doubleprime}(-5)<0 \end{gathered}[/tex]Then,
According to the concept, if f''(x)>0 then it is local minima function and if f''(x)<0, then it is local maxima function
Hence, the given function is local maxima at (-5, 425) and the value is -54 and the given function is local minima at point (4, -304) and the value is 54.
if Em=11, Am=16,CF=27, What are the lengths of the following sides
We will have the following:
First, we calculate AE as follows:
[tex]AE=\sqrt[]{AM^2-EM^2}[/tex]Now, we replace values and solve it:
[tex]AE=\sqrt[]{16^2-11^2}\Rightarrow AE=3\sqrt[]{15}[/tex]From theorem AE = EC therefore EC = esqrt(15); so, the following is true:
[tex]AC=AE+EC\Rightarrow AC=2AE\Rightarrow AC=2(3\sqrt[]{15})\Rightarrow AC=6\sqrt[]{15}[/tex]Knowing this, we then determine FA as follows:
[tex]FA=\sqrt[]{AC^2-CF^2}[/tex]We then determine BE, DM & CM as follows:
Ride 'em Rodeo is a traveling rodeo show. Last night, there were 5 people wearing
boots at the rodeo for every 2 people who were not wearing boots.
If there were 125 people wearing boots at the rodeo last night, how many people were
there altogether?
The total number of people that were there altogether at the radio show is 175 people.
How to calculate the value?From the information, there were 5 people wearing boots at the rodeo for every 2 people who were not wearing boots.
It was also illustrated that there were 125 people wearing boots at the rodeo last night, those that aren't wearing boots will be illustrated by x.
2/5 = x/125
Collect like terms
5x = 125 × 2
5x = 250
Divide
x = 250/5
x = 50
Those not wearing boots = 50
Total number of people will be:
= Those wearing boots + Those not wearing
= 125 + 50
= 175
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Answer:
175
Step-by-step explanation:
What is the volume of this triangle right prism 8 cm 15 cm 12 cm
The volume of a triangle right prism is given by the formula
The entire company went in together to buy lottery tickets. Inside the safe are two different types of lottery tickets. The Mega Million Tickets cost $5 each and the Scratch Off Tickets cost $2 each. They bought 60 tickets totaling $246. what are my x and y variables?x=y=
we have the following system
[tex]\begin{gathered} \begin{cases}x+y=60 \\ 5x+2y=246\end{cases} \\ \end{gathered}[/tex]where x is the number of mega million ticktets and y the number of scratch off tickets, so we have that y=60-x and we get that
[tex]\begin{gathered} 5x+2(60-x)=246 \\ 5x-2x+120=246 \\ 3x=126 \\ x=\frac{126}{3}=42 \end{gathered}[/tex]so they bought 42 mega million tickets and 18 scratch off
I got the last question right that was similar so I’m unsure what I’m doing wrong for this one
Solve x:
[tex][/tex]I'll send a pic of the problem
Weare given a graph that relates the number of strawberries to the number of containers in pairs (x, y)
being x the number of containers, and y the number of strawberries.
The points of the graph read:
(3. 57)
(5, 95)
(7, 133)
(9, 171)
and we are asked to find the proportionality between those values.
We then calculate the slope that joins the points, using for example the first two pairs:
slope = (y2 - y1) / (x2 - x1)
in our case:
slope = (95 - 57) / (5 - 3) = 38 / 2 = 19
we check this same type of calculation with another pair of points to see if it holds true as well:
slope = (171 - 133) / (9 - 7) = 38 / 2 = 19
So we can answer that the proportionality is 19 strawberries per container.
A container built for transatlantic shipping is constructed in the shape of a right rectangular prism. Its dimensions are 9.5 ft by 5.5 ft by 9 ft. The container is entirely full. If, on average, its contents weigh 0.99 pounds per cubic foot, and, on average, the contents are worth $4.37 per pound, find the value of the container’s contents. Round your answer to the nearest cent.
step 1
Find out the volume of the rectangular container
[tex]V=L\cdot W\cdot H[/tex]Substitute given values
[tex]\begin{gathered} V=9.5\cdot5.5\cdot9 \\ V=470.25\text{ ft3} \end{gathered}[/tex]step 2
Find out the weight of the container
Multiply the volume by the density of 0.99 pounds per cubic foot
0.99*470.25=465.5475 pounds
step 3
Multiply the weight by the factor of $4.37 per pound
so
4.37*465.5475=$2,034.44
therefore
The answer is $2,034.44the day of the lowest show the most ever in a single day by random sample of 13 students calculate the 38th and the 60th percentile of data
We have that the sample consist in n=13 students. The percentile formula is given by
[tex]P_x=\frac{x}{100}\times n\text{ position}[/tex]where x denotes the percentaje. In the first case, p=38, then, we have
[tex]\begin{gathered} P_{38}=\frac{38}{100}\times13\text{ position} \\ P_{38}=4.94\text{ position} \end{gathered}[/tex]then, we get
[tex]P_{38}=41[/tex]that is, P_38 corresponds to 41 miles driven.
In the second case, by substituting x=60 in our formula, we get
[tex]\begin{gathered} P_{60}=\frac{60}{100}\times13\text{ position} \\ P_{60}=7.8\text{ position} \end{gathered}[/tex]which gives
[tex]P_{60}=56[/tex]that is, P_60 corresponds to 56 miles driven.
Then, the answers are:
[tex]P_{38}=41[/tex]This means that approximately 38% of the data lie below 41, when the data are ranked.
[tex]P_{60}=56[/tex]This means that approximately 60% of the data lie below 56, when the data are ranked.
Priya is mixing drops of food coloring to create purple frosting for a cake. She uses 24 drops of red dye and 16 drops of blue dye. Find the ratio of drops of red dye to total drops of dye. Express as a simplified ratio.
Priya uses 24 drops of red dye,
She also uses 16 drops of blue dye,
[tex]\begin{gathered} \text{Total drops of dye=}24+16 \\ =40\text{drops of dye} \end{gathered}[/tex]We are told to find the ratio of drops of red dye to the total drops dye.
[tex]=\frac{\text{red drops of dye}}{\text{total drops of dye}}[/tex][tex]\begin{gathered} =\frac{24}{40}=\frac{3}{5} \\ =3\colon5 \end{gathered}[/tex]Hence, the ratio of drops of red die to the total drops of die to the simplest rato is
3 : 5.