Answer:
a) P [ X < 24 mm ] = 0,3015 or P [ X < 24 mm ] = 30,15 %
b) P [ X > 32 mm ] = 0,1251 or P [ X > 32 mm ] = 12,51 %
c) P [ 25 < X < 30 ] = 0,4964 or P [ 25 < X < 30 ] = 49,64 %
d) z(s) = 0,84
Step-by-step explanation:
Normal Distribution N ( μ₀ ; σ ) is N ( 26,5 ; 4,8 )
a) P [ X < 24 mm ] = ( X - μ₀ ) / σ
P [ X < 24 mm ] = (24 - 26,5)/ 4,8 = - 0,5208 ≈ - 0,52
P [ X < 24 mm ] = - 0,52
And from z-table we find area for z score
P [ X < 24 mm ] = 0,3015 or P [ X < 24 mm ] = 30,15 %
b)P [ X > 32 mm ] = 1 - P [ X < 32 mm ]
P [ X < 32 mm ] = ( 32 - 26,5 ) / 4,8
P [ X < 32 mm ] = 5,5/4,8 = 1,1458 ≈ 1,15
P [ X < 32 mm ] = 1,15
And from z-table we get
P [ X < 32 mm ] = 0,8749
Then:
P [ X > 32 mm ] = 1 - 0,8749
P [ X > 32 mm ] = 0,1251 or P [ X > 32 mm ] = 12,51 %
c) P [ 25 < X < 30 ] = P [ X < 30 ] - P [ X < 25 ]
P [ X < 30 ] = 30 - 26,5 / 4,8 = 0,73
From z-table P [ X < 30 ] = 0,7673
P [ X < 25 ] = 25 - 26,5 / 4,8 = - 0,3125 ≈ - 0,31
From z-table P [ X < 25 ] = 0,2709
Then
P [ 25 < X < 30 ] = 0,7673 - 0,2709
P [ 25 < X < 30 ] = 0,4964 or P [ 25 < X < 30 ] = 49,64 %
d) If 20 %
z- score for 20% is from z-table
z(s) = 0,84
Solve the equation for y. Identify the slope and y-intercept. Then graph the equation.
-3y=3x-9
Y=
M=
B=
2,17,82,257,626,1297 next one please ?
The easy thing to do is notice that 1^4 = 1, 2^4 = 16, 3^4 = 81, and so on, so the sequence follows the rule [tex]n^4+1[/tex]. The next number would then be fourth power of 7 plus 1, or 2402.
And the harder way: Denote the n-th term in this sequence by [tex]a_n[/tex], and denote the given sequence by [tex]\{a_n\}_{n\ge1}[/tex].
Let [tex]b_n[/tex] denote the n-th term in the sequence of forward differences of [tex]\{a_n\}[/tex], defined by
[tex]b_n=a_{n+1}-a_n[/tex]
for n ≥ 1. That is, [tex]\{b_n\}[/tex] is the sequence with
[tex]b_1=a_2-a_1=17-2=15[/tex]
[tex]b_2=a_3-a_2=82-17=65[/tex]
[tex]b_3=a_4-a_3=175[/tex]
[tex]b_4=a_5-a_4=369[/tex]
[tex]b_5=a_6-a_5=671[/tex]
and so on.
Next, let [tex]c_n[/tex] denote the n-th term of the differences of [tex]\{b_n\}[/tex], i.e. for n ≥ 1,
[tex]c_n=b_{n+1}-b_n[/tex]
so that
[tex]c_1=b_2-b_1=65-15=50[/tex]
[tex]c_2=110[/tex]
[tex]c_3=194[/tex]
[tex]c_4=302[/tex]
etc.
Again: let [tex]d_n[/tex] denote the n-th difference of [tex]\{c_n\}[/tex]:
[tex]d_n=c_{n+1}-c_n[/tex]
[tex]d_1=c_2-c_1=60[/tex]
[tex]d_2=84[/tex]
[tex]d_3=108[/tex]
etc.
One more time: let [tex]e_n[/tex] denote the n-th difference of [tex]\{d_n\}[/tex]:
[tex]e_n=d_{n+1}-d_n[/tex]
[tex]e_1=d_2-d_1=24[/tex]
[tex]e_2=24[/tex]
etc.
The fact that these last differences are constant is a good sign that [tex]e_n=24[/tex] for all n ≥ 1. Assuming this, we would see that [tex]\{d_n\}[/tex] is an arithmetic sequence given recursively by
[tex]\begin{cases}d_1=60\\d_{n+1}=d_n+24&\text{for }n>1\end{cases}[/tex]
and we can easily find the explicit rule:
[tex]d_2=d_1+24[/tex]
[tex]d_3=d_2+24=d_1+24\cdot2[/tex]
[tex]d_4=d_3+24=d_1+24\cdot3[/tex]
and so on, up to
[tex]d_n=d_1+24(n-1)[/tex]
[tex]d_n=24n+36[/tex]
Use the same strategy to find a closed form for [tex]\{c_n\}[/tex], then for [tex]\{b_n\}[/tex], and finally [tex]\{a_n\}[/tex].
[tex]\begin{cases}c_1=50\\c_{n+1}=c_n+24n+36&\text{for }n>1\end{cases}[/tex]
[tex]c_2=c_1+24\cdot1+36[/tex]
[tex]c_3=c_2+24\cdot2+36=c_1+24(1+2)+36\cdot2[/tex]
[tex]c_4=c_3+24\cdot3+36=c_1+24(1+2+3)+36\cdot3[/tex]
and so on, up to
[tex]c_n=c_1+24(1+2+3+\cdots+(n-1))+36(n-1)[/tex]
Recall the formula for the sum of consecutive integers:
[tex]1+2+3+\cdots+n=\displaystyle\sum_{k=1}^nk=\frac{n(n+1)}2[/tex]
[tex]\implies c_n=c_1+\dfrac{24(n-1)n}2+36(n-1)[/tex]
[tex]\implies c_n=12n^2+24n+14[/tex]
[tex]\begin{cases}b_1=15\\b_{n+1}=b_n+12n^2+24n+14&\text{for }n>1\end{cases}[/tex]
[tex]b_2=b_1+12\cdot1^2+24\cdot1+14[/tex]
[tex]b_3=b_2+12\cdot2^2+24\cdot2+14=b_1+12(1^2+2^2)+24(1+2)+14\cdot2[/tex]
[tex]b_4=b_3+12\cdot3^2+24\cdot3+14=b_1+12(1^2+2^2+3^2)+24(1+2+3)+14\cdot3[/tex]
and so on, up to
[tex]b_n=b_1+12(1^2+2^2+3^2+\cdots+(n-1)^2)+24(1+2+3+\cdots+(n-1))+14(n-1)[/tex]
Recall the formula for the sum of squares of consecutive integers:
[tex]1^2+2^2+3^2+\cdots+n^2=\displaystyle\sum_{k=1}^nk^2=\frac{n(n+1)(2n+1)}6[/tex]
[tex]\implies b_n=15+\dfrac{12(n-1)n(2(n-1)+1)}6+\dfrac{24(n-1)n}2+14(n-1)[/tex]
[tex]\implies b_n=4n^3+6n^2+4n+1[/tex]
[tex]\begin{cases}a_1=2\\a_{n+1}=a_n+4n^3+6n^2+4n+1&\text{for }n>1\end{cases}[/tex]
[tex]a_2=a_1+4\cdot1^3+6\cdot1^2+4\cdot1+1[/tex]
[tex]a_3=a_2+4(1^3+2^3)+6(1^2+2^2)+4(1+2)+1\cdot2[/tex]
[tex]a_4=a_3+4(1^3+2^3+3^3)+6(1^2+2^2+3^2)+4(1+2+3)+1\cdot3[/tex]
[tex]\implies a_n=a_1+4\displaystyle\sum_{k=1}^3k^3+6\sum_{k=1}^3k^2+4\sum_{k=1}^3k+\sum_{k=1}^{n-1}1[/tex]
[tex]\displaystyle\sum_{k=1}^nk^3=\frac{n^2(n+1)^2}4[/tex]
[tex]\implies a_n=2+\dfrac{4(n-1)^2n^2}4+\dfrac{6(n-1)n(2n)}6+\dfrac{4(n-1)n}2+(n-1)[/tex]
[tex]\implies a_n=n^4+1[/tex]
Pls help me I promise I’ll mark u brainleiest if I type in the fastest answer
Answer:
1. $-50
2. $25
Step-by-step explanation:
1. If she had $150 in her bank account and bought a bike for $200, then that means she spent all of her money PLUS $50 extra then what she had. That means $200-$150=$50. Her $150 is spent and that $50 becomes negative because she paid $200 when she only had $150.
2. If she deposits $75 in her account then it will be $75+(-50). That translates to $75-$50 which is $25.
+ and - = -
+ and + = +
- and - = +
Answer:
1. $-50
2. $25
Step-by-step explanation:
1.
We know that Clare originally had $150 in her account. She then buys a bike, which means she must have taken money out of her account for this purchase.
Since she spent $200, we need to subtract 200 from 150:
150 - 200 = -50
So, her account balance is $-50.
2.
Clare earns $75 later, which means she's receiving the money and can add it back into her account. Her current balance is -50, so we add 75 to -50:
-50 + 75 = $25
Thus, her account balance is now $25.
~ an aesthetics lover
Of every 300 magic cakes Farah makes, 90 are chocolate, what percentage of chocolate cakes Farah makes?
De cada 300 pasteles mágicos que hace Farah, 90 son de chocolate, ¿qué porcentaje de pasteles de chocolate hace Farah?
Answer:
Total magic cakes =300
chocolate cakes =90
so if you want the percentage of chocolate you will divide the number of chocolate cakes over the total number of chocolates
% of chocolate cakes = 90/300×100%
=30%
Please help! Need the answers to be able to move on.
1.) 26 times 26^8
2.) (-5)^5/(-5)^-6
3.) 8^15 divided by 8^-3
4.) Which expressions are equivalent to 1? Select all that apply.
~-(5/8)^0
~-(-3141)^0
~1291^0
~0^1
~(1/3)^0
~(-0.0008)^0
Answer:
see below
Step-by-step explanation:
1.) 26 times 26^8 = 26^1 * 26^8 = 26^(1+8) = 26^9
2.) (-5)^5/(-5)^-6 = (-5)^(5 - -6) = (-5)^(5+6) = (-5)^11
3.) 8^15 divided by 8^-3 = 8^(15 - -3) = 8^(15+3) = 8^18
4.) Which expressions are equivalent to 1? Select all that apply.
~-(5/8)^0 - (1) no
~-(-3141)^0 - (1) no
~1291^0 1 yes
~0^1 yes
~(1/3)^0 yes
~(-0.0008)^0 yes
Evaluate m^2 − 2m + 5 for m = − 2
Answer:
[tex]\huge\boxed{13}[/tex]
Step-by-step explanation:
m²-2m + 5
Given that m = -2
[tex]\sf (-2)^2-2(-2)+5\\4 +4 + 5\\13[/tex]
Answer:
13
Step-by-step explanation:
m^2 − 2m + 5
Let m = -2
(-2)^2 -2(-2) +5
4 +4 +5
13
Name the number that is
represented by the letter Y.
Y
Z
WVX
+
-10 -5
+
5
0
10
Answer:
y is 8 if you count towards the right side of the screen you will figure out that y is 8 followed by 9 leading you to 10, therefore x is 11.
I hope this helps
An Internet service provider is implementing a new program based on the number of connected devices in each household currently,customers are charged a flat rate of $175 per month.the new plan would charge a flat rate of $94 plus an additional $4.50 per device connected to the network.find the number of devices,x,for which the cost of the new plan is less than the cost of the current plan.
Answer:
(x=6) is less than 18 which would give you the cost of the current plan
Step-by-step explanation:
If you take six, first you must multiply 4.50 by 6, ($27) then add it, to $94, giving you $121. Now we have to find which phone will give us the same cost, for this I choose 18. if you do 18 x 4.50, you get $81, and if you add this to 94, it gives you 175.
Simplify your answer as much as possible
You said - 1/3 - 3/5 x = 1/2
Multiply each side by 3 :
- 1 - 9/5 x = 3/2
Multiply each side by 5 :
- 5 - 9x = 15/2
Multiply each side by 2 :
- 10 - 18x = 15
Add 10 to each side :
- 18x = 25
Divide each side by -18 :
x = - 25/18
or x = - 1 and 7/18 (same thing)
A patio 20 feet wide has a slanted roof, as shown in the figure. Find the length of the roof if there is an 8-inch overhang. Show all work and round the answer to the nearest foot. Be sure to label your answer appropriately. Then write a sentence explaining your answer in the context of the problem.
Answer:
[tex]Slanted\ Roof = 20.77\ ft[/tex]
Step-by-step explanation:
The question has missing attachment (See attachment 1 for complete figure)
Given
Width, W = 20ft
Let the taller height be represented with H and the shorter height with h
H = 10ft
h = 8ft
Overhang = 8 inch
Required
Determine the length of the slanted roof
FIrst, we have to determine the distance between the tip of the roof and the shorter height;
Represent this with
This is calculated by
[tex]D = H - h[/tex]
Substitute 10 for H and 8 for h
[tex]D = 10 - 8[/tex]
[tex]D = 2ft[/tex]
Next, is to calculate the length of the slant height before the overhang;
See Attachment 2
Distance L can be calculated using Pythagoras theorem
[tex]L^2 = 2^2 + 20^2[/tex]
[tex]L^2 = 4 + 400[/tex]
[tex]L^2 = 404[/tex]
Take Square root of both sides
[tex]\sqrt{L^2} = \sqrt{404}[/tex]
[tex]L = \sqrt{404}[/tex]
[tex]L = 20.0997512422[/tex]
[tex]L = 20.10\ ft[/tex] -------Approximated
The full length of the slanted roof is the sum of L (calculated above) and the overhang
[tex]Slanted\ Roof = L + 8\ inch[/tex]
Substitute 20.10 ft for L
[tex]Slanted\ Roof = 20.10\ ft + 8\ inch[/tex]
Convert inch to feet to get the slanted roof in feet
[tex]Slanted\ Roof = 20.1\ ft + 8/12\ ft[/tex]
[tex]Slanted\ Roof = 20.10\ ft + 0.67\ ft[/tex]
[tex]Slanted\ Roof = 20.77\ ft[/tex]
Hence, the total length of the slanted roof in feet is approximately 20.77 feet
Two basketball players average the same number of points per game. What information would be most helpful in
determining which player's game performances show the least variability?
the most and least points each player has scored in a game
the number of games each player has played
the average number of points each player's team scores per game
O the total number of points each player has scored
Answer:
number of games each player has played
the average number of points each player's team scores per
Step-by-step explanation:
number of games each player has played
the average number of points each player's team scores per
Please Solve
F/Z=T for Z
Answer:
F /T = Z
Step-by-step explanation:
F/Z=T
Multiply each side by Z
F/Z *Z=T*Z
F = ZT
Divide each side by T
F /T = ZT/T
F /T = Z
Answer:
[tex]\boxed{\red{ z = \frac{f}{t} }}[/tex]
Step-by-step explanation:
[tex] \frac{f}{z} = t \\ \frac{f}{z} = \frac{t}{1} \\ zt = f \\ \frac{zt}{t} = \frac{f}{t} \\ z = \frac{f}{t} [/tex]
c. What is f (-5)?
When the function is f(x) =-3x+7
Answer:
f(-5) = 22
Step-by-step explanation:
f(x) =-3x+7
Let x = -5
f(-5) =-3*-5+7
= 15 +7
=22
Using the graph as your guide, complete the following statement.
The discriminant of the function is ___
A. positive
B. zero
C. negative
please solution this question now .thank you very much
Answer:
5/2
Step-by-step explanation:
Let u = sin(t). Then this is the integral ...
[tex]\displaystyle\int_0^{\frac{\pi}{2}}{5u}\,du=\left.\dfrac{5u^2}{2}\right|_0^{\frac{\pi}{2}}=\dfrac{5}{2}(\sin(\frac{\pi}{2})^2-\sin(0)^2)=\dfrac{5}{2}(1-0)=\boxed{\dfrac{5}{2}}[/tex]
How long will it take for a sum of 500$ attracting simple interest
One angle of a triangle measures 108°. The other two angles are congruent.
Enter and solve an equation to find the measure x of the congruent angles.
Which of the following is not a characteristic of the F distribution? Multiple Choice It is always right-skewed. It describes the ratio of two variances. It is a family based on two sets of degrees of freedom. It is negative when s12 is smaller than s22.
Answer:
It is negative when s12 is smaller than s22.
Step-by-step explanation:
The F distribution has the following properties.
1) It is always right-skewed. but as the degrees of freedom v1 and v2 become large F distribution approaches normal distribution.
2) It describes the ratio of two variances.
3) It is a family based on two sets of degrees of freedom.
4) It is negative when s12 is smaller than s22. This is not true sometimes as the F distribution does not depend on the population variance but on the two parameters v1 and v2.
Find the inequality represented by the graph.
9514 1404 393
Answer:
y < 3x -4
Step-by-step explanation:
The boundary line has a slope (rise/run) of 3/1 = 3. It has a y-intercept of -4. The shaded area is below the line and the solution does not include the line. The relevant inequality can be written ...
y < 3x -4
Hi! quick question, whats the equation for this?
The sum of the angle measures of the polygon is 540°. Write and solve an equation to find the value of x.
[tex]\\ \sf\longmapsto 4x+4x+5x-7+5x+2+96=540[/tex]
[tex]\\ \sf\longmapsto 4x+4x+5x+5x-7+2+96=540[/tex]
[tex]\\ \sf\longmapsto 8x+10x-5+96=540[/tex]
[tex]\\ \sf\longmapsto 18x+91=540[/tex]
[tex]\\ \sf\longmapsto 18x=540-91=449[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{449}{18}[/tex]
[tex]\\ \sf\longmapsto x\approx2.4[/tex]
Answer:
x=25
Step-by-step explanation:
4x+5x-8+96+5x+2+4x=540
18x+90=540
18x=540-90=450
x=450/18=25
Find the area of the shape shown below.
3.5
2
2
Answer:
26.75 units²
Step-by-step explanation:
Cube Area: A = l²
Triangle Area: A = 1/2bh
Step 1: Find area of biggest triangle
A = 1/2(3.5)(2 + 2 + 5)
A = 1.75(9)
A = 15.75
Step 2: Find area of 2nd biggest triangle
A = 1/2(5)(2)
A = 1/2(10)
A = 5
Step 3: Find area of smallest triangle
A = 1/2(2)(2)
A = 1/2(4)
A = 2
Step 4: Find area of cube
A = 2²
A = 4
Step 5: Add all the values together
A = 15.75 + 5 + 2 + 4
A = 20.75 + 2 + 4
A = 22.75 + 4
A = 26.75
Kent Co. manufactures a product that sells for $60.00. Fixed costs are $285,000 and variable costs are $35.00 per unit. Kent can buy a new production machine that will increase fixed costs by $15,900 per year, but will decrease variable costs by $4.50 per unit. What effect would the purchase of the new machine have on Kent's break-even point in units?
0riginal break even point:
285000/ 60/35 = $166,250
New break even point = new fixed costs / ( selling price - variable cost/ selling price)
New break even point = 285,000 + 15,900. / ( 60-( 35-4.50)/60
300,900 / 60-30.50/60 = $612,000
The new break even point increases.
Which expression is not a polynomial
Answer:
the last option [tex]x^{3}[/tex] + 1 / x
Step-by-step explanation:
first option's x has the power 3
second option's x has the power 1
third option's x has the power 1
but in the last option it has the power -1
polynomials doesn't support negative power
*remember
HELP ASAP PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Option (B)
Step-by-step explanation:
The given expression is,
[tex]\sqrt{22x^6}\div\sqrt{11x^4}[/tex]
We can rewrite this expression as,
[tex]\frac{\sqrt{22x^6}}{\sqrt{11x^4} }[/tex]
Solving it further,
[tex]\frac{\sqrt{22x^6}}{\sqrt{11x^4} }=\frac{\sqrt{22(x^3)^2} }{\sqrt{11(x^2)^2} }[/tex] [Since [tex]x^3\times x^3=x^6[/tex] and [tex]x^{2}\times x^{2}=x^4[/tex]]
[tex]=\sqrt{\frac{22(x^3)^2}{11(x^2)^2} }[/tex] [Since [tex]\frac{\sqrt{a} }{\sqrt{b} }=\sqrt{\frac{a}{b} }[/tex]]
[tex]=\frac{x^3}{x^2}\sqrt{\frac{22}{11} }[/tex]
[tex]=x\sqrt{2}[/tex]
Therefore, quotient will be x√2.
Option (B) will be the correct option.
In a certain state 22% of secondary school students study a foreign language. A group of 100 students were selected in random sample and 24 of them study a foreign language. In this example: a: What is population? b: What is the value of the proportion p1? c: What is the value of the sample proportion p2？
Answer: a. population = "All Students"
b. 0.22
c. 0.24
Step-by-step explanation:
a. Population is the largest group of individuals having same characteristics by the researcher's point of view.
Here , the interest is "Students study foreign language"
So, population = "All Students"
b. Let p be the pro[portion of secondary school students study a foreign language.
In a certain state 22% of secondary school students study a foreign language.
The value of proportion [tex]p_1[/tex] =- 0.22
c. A group of 100 students were selected in random sample and 24 of them study a foreign language.
The value of proportion [tex]p_2=\dfrac{24}{100}=0.24[/tex]
Should I read Fruit's Basket? I need something to keep me busy.
Answer: Yes
Explanation: Yes because, sometimes you need to do stuff to get things of your head
find the missing side round to the nearest tenth
Answer:
x=7.23
Step-by-step explanation:
Brainliest please
Carmen Abdul and David sent a total of 78 text messages over their cell phones during the weekend . Abdul sent 10 fewer messages then Carmen . David sent two times as many messages as Abdul how many messages did they each send?
Answer:
Carmen:27
Abdul:17
David=34
Step-by-step explanation:
Carmen+Abdul+David = 78
Carmen-Abdul=10
David=2Abdul
Carmen=Abdul+10
Carmen+Abdul+David = Abdul+10+Abdul+2Abdul=78
4Abdul=68
Abdul = 68/4=17
Carmen = 17+10=27
David = 2 * 17 = 34
27+17+34=78
28. A boy decided to cut 10 pieces of wood from a length of wood so tha the first piece was 5cm the second 10cm, the third 15cm, the fourth 20cm and so on until he had cut TO pieces, each one 5cm longer than the one he had cut before. What length of the wood did he use? (a) 50cm (b) 55cm (c) 70cm (d) 200cm (e) 275cm
Step-by-step explanation:
he use 50cm length of the wood
translate into a variable expression and then simplify. five times the sum of a number and four
Answer:
5(n+4)
5n+20
Step-by-step explanation:
Let n be the number
5* (n+4)
Distribute
5n+20