We simplify by combining like terms
therefore
[tex]\begin{gathered} -3n-8-7n+17 \\ =-3n-7n-8+17 \\ =-10n+9 \end{gathered}[/tex]Pls help! No ive asked 5 tutors and they cant do it!
The sampling distribution can be approximated to follow the normal distribution if the sample size is large, and the values of 'np' and 'n(1-p)' are much greater than 10.
Consider option A,
[tex]\begin{gathered} np=30\times0.3=9 \\ n(1-p)=30\times(1-0.3)=21 \end{gathered}[/tex]Consider option B,
[tex]\begin{gathered} np=22\times0.4=8.8 \\ n(1-p)=22\times(1-0.4)=13.2 \end{gathered}[/tex]Consider option C,
[tex]\begin{gathered} np=30\times0.8=24 \\ n(1-p)=30\times(1-0.8)=6 \end{gathered}[/tex]Consider option D,
[tex]\begin{gathered} np=22\times0.5=11 \\ n(1-p)=22\times(1-0.5)=11 \end{gathered}[/tex]It is observed that only the values in option D, give that 'np' and 'n(1-p)' are greater than 10. Therefore, option D will be the correct choice.
If ten people shake hands with each other exactly once, how many handshakes take place?
Apply the formula:
n(n+1)/2
Where n is the number of shake hands of the first person (9)
9 (9+1) /2
9 (10)/2
90/2
45 shakes
Find (w∘s)(x) and (s∘w)(x) for w(x)=7x−2 and s(x)=x^2−7x+5
(w∘s)(x)=
The two composite functions have their values to be (w o s)(x) = 7x² - 49x + 33 and (s o w)(x) = (7x - 2)² - 7(7x - 2) + 5
How to determine the composite functions?Composite function 1
The given parameters are
w(x) = 7x - 2
s(x) = x² - 7x + 5
To calculate (w o s)(x), we make use of
(w o s)(x) = w(s(x))
So, we have
(w o s)(x) = 7s(x) - 2
Substitute s(x) = x² - 7x + 5
(w o s)(x) = 7(x² - 7x + 5) - 2
Expand
(w o s)(x) = 7x² - 49x + 35 - 2
Simplify
(w o s)(x) = 7x² - 49x + 33
Composite function 2
Here, we have
w(x) = 7x - 2
s(x) = x² - 7x + 5
To calculate (s o w)(x), we make use of
(s o w)(x) = s(w(x))
So, we have:
(s o w)(x) = w(x)² - 7w(x) + 5
Substitute w(x) = 7x - 2
(s o w)(x) = (7x - 2)² - 7(7x - 2) + 5
So, the composite functions are (w o s)(x) = 7x² - 49x + 33 and (s o w)(x) = (7x - 2)² - 7(7x - 2) + 5
Read more about composite functions at
https://brainly.com/question/10687170
#SPJ1
i need help with this equation please there are two more possible answers that were cut off they are 17,2% and 19,5%
Consider that the experimental probability of an event is based upon the previous trials and observations of the experiment.
The experimental probability of occurrence of an event is given by,
[tex]\text{Probability of an event}=\frac{\text{ Number of outcomes that favoured the event}}{\text{ Total number of trials or outcomes}}[/tex]As per the problem, there are a total of 1230 trials of rolling a dice.
And the favourable event is getting a 2.
The corresponding experimental probability is calculated as,
[tex]\begin{gathered} P(\text{ getting a 2})=\frac{\text{ No. of times 2 occurred}}{\text{ Total no. of times the dice is thrown}} \\ P(\text{ getting a 2})=\frac{172}{1230} \\ P(\text{ getting a 2})\approx0.13984 \\ P(\text{ getting a 2})\approx13.98\text{ percent} \end{gathered}[/tex]Thus, the required probability is 13.98% approximately.
Theref
find the values of x and y that maximize the objective function c = 3x + 4y for the graph
Answer: The correct answer is x=0 and y=4 or (0,4) per the graph
Step-by-step explanation:
To find the maximum value, we must test each point using the equation:
Check for (0,4):
C=3x+4y
C=3(0)+4(4)
C=16
Check for (2,2):
C=3(2)+4(2)
C=6+8
C=14
Check for (4,0):
C=3(4)+4(0)
C=12
Answer:
Step-by-step explanation:
Use the graph below to answer the following questionsnegative sine graph with local maxima at about (-3,55) and local minima at (3,55)1. Estimate the intervals where the function is increasing.2. Estimate the intervals where the function is decreasing.3. Estimate the local extrema.4. Estimate the domain and range of this graph.
Answer:
1. Increasing on ( -inf, -3] and ( 3, inf)
2. decreasing on (-3, 3]
3. Local maximum: 60, Local minimum: -60
4. Domain: (-inf , inf)
Range: [-60, 60]
Explanation:
1.
A function is increasing when its slope is positive. Now, in our case we can see that the slope of f(x) is postive from - infinity to -3 and then it is negatvie from -3 to 3; it again increasing from 3 to infinity.
Therefore, we c
I can't find the last mark can someone help please
Step-by-step explanation:
right, M = ((xa + xb)/2, (ya + yb)/2) = (3.5, 3.5)
the line through O and M (I assume we need the slope-intercept form) is in general
y = ax + b
"a" is the slope, "b" is the y-intercept (the y-value when x = 0).
the slope is the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.
so, our 2 points : (0, 0) and (3.5, 3.5).
x changes by +3.5 (from 0 to 3.5).
y changes by +3.5 (from 0 to 3.5).
so, the slope "a" is +3.5/+3.5 = 1.
the point (0, 0) gives us "b" (the y-value when x = 0) directly : 0.
so, the line equation is
y = x
consider the polynomial function p given by p(x)=7x³-2x²+3x+10. Evaluate the function at x = -3.
Answer: -206
Step-by-step explanation:
[tex]p(-3)=7(-3)^3 -2(-3)^2 +3(-3)+10=-206[/tex]
A choir concert platform consists of 6 rows. The number of performers increases by 2 witheach successive row. How many performers are there in all if the back row has 36performers?A 48B 84C 186D 372
In this problem, we have the sequence
inverse sequence
36,34,32,30,28,26
The sum is equal to
S=36+34+32+30+28+26
S=186
The answer is option CIn this problem, we have the sequence
inverse sequence
36,34,32,30,28,26
The sum is equal to
S=36+34+32+30+28+26
S=186
The answer is option C4 boxes of crayons cost $12.50 How much would 16 boxes cost? (Show work) Thank you!
Answer:
$50.08
Step-by-step explanation:
Find the unit rate.
[tex]\frac{12.50}{4}[/tex] Each box cost $3.125. We cannot have .125 cents, so round up to 3.13
3.13 x 16 = $50.08
clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. before treatment 19 subjects had a mean wake time of 100.0 min after treatment the 19 subjects had a mean wake time of 71.6 min and a standard deviation of 20.4 min assume that the 19 sample value appears to be from a normally distributed population and construct a 99% confidence interval estimate of the mean wake time for a population with drug treatment what does the result suggest about the wake time of 100.0 min before the treatment does the drug appears to be effective
We have to calculate a 99% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=71.6.
The sample size is N=19.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{20.4}{\sqrt{19}}=\dfrac{20.4}{4.359}=4.68[/tex]The degrees of freedom for this sample size are:
[tex]df=n-1=19-1=18[/tex]The t-value for a 99% confidence interval and 18 degrees of freedom is t=2.878.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=2.878\cdot4.68=13.471[/tex]Then, the lower and upper bounds of the confidence interval are:
[tex]\begin{gathered} LL=M-t\cdot s_M=71.6-13.471=58.129 \\ UL=M+t\cdot s_M=71.6+13.471=85.071 \end{gathered}[/tex]The 99% confidence interval for the mean is (58.129, 85.071). This interval does not include the value 100, so we can conclude that there is statistical evidence that the treatment reduces the mean wake time.
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]Translate |f(x)=|x| so the vertex is at (-3,2)
we have the parent function
f(x)=|x| ------> vertex is (0,0)
Translate at (-3,2)
The rule of the translation is given by
(x,y) ----> (x-3,y+2)
that means ----> 3 units at the left and 2 units up
so
Applying the translation
the new function is equal to
h(x)=|x+3|+2The total fixed costs of producing a product is $36,000 and the variable cost is $124 per item. If the company believes they can sell 1,800 items at $170 each, what is thebreak-even point?667 items695 items705 items783 itemsNone of these choices are correct.
On the last day of his summer tennis camp, Zach helps his instructor sort through a basket of tennis balls to throw out the old ones. Zach ends up throwing away 13 of the balls. He returns the remaining 42 balls to the basket. Which equation can you use to find the total number of tennis balls t Zach checks?
The equation that represents the total tennis balls is t = 13 + 42 and the value is 55
How to determine the equation that represents the total tennis balls?From the question, the given parameters are
Total number of tennis ball = tNumber of tennis ball thrown away = 13Number of tennis ball returned = 42The total number of tennis ball is the sum of the number of tennis ball thrown away and the number of tennis ball returned
Mathematically, this is represented as
Total number of tennis ball = Number of tennis ball thrown away + Number of tennis ball returned
Substitute the known values in the above equation
So, we have the following equation
t = 13 + 42
Evaluate the sum
t = 55
Hence, the equation of the tennis ball is t = 13 + 42
Read more about equations at
https://brainly.com/question/2476251
#SPJ1
what is[tex](6 {x}^{2} - 13x + 5) [/tex]divided by[tex](2x - 1)[/tex]
1. Divide the first term of the dividend into the first term of the divisor:
[tex]\frac{6x^2}{2x}=3x[/tex]2. Multiply the result above by the divisor:
[tex]3x(2x+1)=6x^2+3x[/tex]3. Subtract the result above from the divident to get a new polynomial:
4. Repeat the process with the new polynomial:
[tex]\begin{gathered} -\frac{16x}{2x}=-8 \\ \\ -8(2x+1)=-16x-8 \end{gathered}[/tex]Then, the result of the division is:[tex]\frac{6x^2-13x+5}{2x+1}=3x-8+\frac{13}{2x+1}[/tex]l show how the distributive property can make the arithmetic simpler in the following problems5(108)
Firstly Example of Distributive property can be shown below.
GIiven: 6(9 - 4)
6 x 9 - 6 x 4
54 - 24 = 30
a) 3(50.15)
3(50 + 0.15)
3x50 + 3 x0.15
150 + 0.45 = 150.45
(b) 5(108)
5(100 + 8)
5x100 + 5x8
500 + 40 = 540
You start a trip when your odometer reads 23,672 miles, and you have a full tank of gas. After
driving a few hours, you fill up your tank. If you buy 16.5 gallons and your odometer reads
23,927, how many miles to the gallon are you getting, rounded to the nearest tenth of a gallon.
I need helppp with example pliss
Answer:
15.6 MPG
Step-by-step explanation:
You start a trip when your odometer reads 23,672 miles, and you have a full tank of gas. After driving a few hours, you fill up your tank. If you buy 16.5 gallons and your odometer reads 23,927, how many miles to the gallon are you getting, rounded to the nearest tenth of a gallon.
You went 23,927 - 23,672 = 255 miles
Because you started on a full tank, you went 255 miles on 16.5 gallons
to figure MPG:
255/16.5 = 15.4545... MPG
rounded to nearest 10th of gallon:
15.6 MPG
f(t) = 2t-3g(t) = t^3 + tFind (f •g)(0)
1) Given those functions, f(t) and g(t) let's find the composite function, for (f(g(0)) or (f •g)(0)
2) Let's pick the function f(t)
f(t) = 2t-3
And plug into that g(t), like this
f(g(t))= 2(t³ +t) -3
3) Finally, let's plug the value 0 into that composite function:
f(g(t))= 2(t³ +t) -3
f(g(0))= 2(0³ +0) -3 ⇒f(g(0))= 2(0) +3
f(g(0))= 3
(f •g)(0)=3
(C3) In how many distinct ways can theletters of the word LILLYPILLY bearranged?A. 3.628.800B. 480C. 7.560D. 120.960.
We have:
L = 5 L's
I = 2 I's
P = 1 P
Y = 2 Y's
so:
[tex]\frac{10!}{5!2!2!}=7560[/tex]Suppose the cost per ton f(x) to build an oil platform of x thousand tons is approximated byf(x)= 62,500 ______ x+125What is the cost per ton for x=30?
Given that
The cost per ton f(x) to build an oil platform of x thousand tons is approximated by
[tex]f(x)=\frac{62500}{x+125}[/tex]The cost per ton for x = 30, i.e f(30) will be
[tex]\begin{gathered} f(x)=\frac{62500}{x+125} \\ f(30)=\frac{62500}{x+125}=\frac{62500}{30+125}=\frac{62500}{155} \\ f(30)=\frac{62500}{155}=403.226\text{ (3 d.p)} \\ f(30)=403.226\text{ (3 d.p)} \end{gathered}[/tex]Hence, the answer is 403.226 (3 d.p)
find the Medina number of campsites.9,11,12,15,17,18
To find the median of the composite numbers, we will first have to sort the numbers
We will arrange from least to greatest.
By doing so, we will obtain
[tex]9,11,12,15,17,\text{ and 18}[/tex]Next, we will find the middle number of the set.
The median will be the average of the two numbers
[tex]\frac{12+15}{2}=\frac{27}{2}=13.5[/tex]The median of the numbers is 13.5
what is the range of the number of goals scored?
The minimum number of goals scored is 0 and maximum number of goals scored is 7. The range is equal to difference between maximum number of goals and minimum number of goals.
Determine the range for the goals scored.
[tex]\begin{gathered} R=7-0 \\ =7 \end{gathered}[/tex]So answer is 7.
How many square feet of outdoor carpet willwe need for this hele??3 ft2 ft2 ft
total square feet:
[tex]4\times12=48\text{ ft}[/tex]square feet 1:
There are 2 liters of soda left after a class party. Laura, Gavin, Anita, Emmett, and Rebecca are on the clean-up crew, and decide to split the soda equally.
How much soda does each student get?
Write your answer as a proper fraction or mixed number.
0.4 liters or 2/5
Step-by-step explanation:
Dividing the soda equally, Each student would get 0.4 liters or 2/5
which statement is true of the system of equations shown below
3x + 7y= 14
3x+7y= 10
Subtract the second equation to the first.
3x +7y= 14
-
3x + 7y= 10
_________
0x +0y = 4
0 = 4
0 is no
in CDE, J is the centroid. If DH=72 find DJ
Answer:
DJ = 24
Explanation:
We are told from the question that J is the centroid of CDE, this means that J is the midpoint of DH, CJ and FE
If J is the centroid of DH, then 2DJ = JH
Also DJ + JH = DH
The equation becomes:
DJ + 2DJ = DH
3DJ= DH
Given
DH = 72
Hence 3DJ = 72
DJ = 72/3
DJ = 24
Hence the measure of DJ is 24
Rewrite the following equation in slope-intercept form.
y + 8 = –3(x + 7)
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer: y = -3x - 21
Step-by-step explanation:
Slope intercept form: y = mx + b
m is the slope, and b is the y-intercept.
y + 8 = -3(x + 7)
Start by distributing -3 into the parenthesis.
y + 8 = -3x - 21
subtract 8 from both sides to get the final answer.
y = -3x - 29
Answer:
Slope-intercept form,
y = -3x - 29Step-by-step explanation:
Now we have to,
→ Rewrite the given equation in the slope-intercept form.
The slope-intercept form is,
→ y = mx + b
The equation is,
→ y + 8 = -3(x + 7)
Then the value of y will be,
→ y + 8 = -3(x + 7)
→ y + 8 = -3x - 21
→ y = -3x - 21 - 8
→ [ y = -3x - 29 ]
Hence, answer is y = -3x - 29.
simply
i^3+i^20
show work
==================================================
Explanation:
Recall that
i = sqrt(-1)
Squaring both sides gets us
i^2 = -1
Now let's multiply both sides by i
i*i^2 = i*(-1)
i^3 = -i
Repeat the last step
i^3 = -i
i*i^3 = i*(-i)
i^4 = -i^2
i^4 = -(-1)
i^4 = 1
----------------------------
Here's a summary so far
i^0 = 1i^1 = ii^2 = -1i^3 = -ii^4 = 1The pattern repeats every 4 items. This means we'll divide the exponent by 4 and look at the remainder.
20/4 = 5 remainder 0
Therefore i^20 = i^0 = 1
Or we can think of it like this
i^20 = (i^4)^5 = 1^5 = 1
----------------------------
This means we can then say
i^3 + i^20 = -i + 1 = 1 - i
Mary estimates the weight of her cat to be 10 pounds.the actual weight of the cat is 13.75 pounds.find the percent error.
The percentage error is the ratio of the difference between the two readings and the actual
Error = 13.75 - 10
= 3.75
Percent error = 3.75/13.75
= 27.27%
