Answer:
-11
Step-by-step explanation:
Our function is 2x-13x+5
2x-13x+5= -11x+5 F(0)= 5 and F(6)= -11*6+5 = -61 let m be the average change : m= (-61-5)/6= -11The monthly profit for a company that makes decorative picture frames depends on the price per frame. The company determines that the profit is approximated by f(p)= -80p + 3440p -36,000, where p is the price per frame and f(p) is the monthly profit based on that price.
Requried:
a. Find the price that generates the maximum profit.
b. Find the maximum profit.
c. Find the price(s) that would enable the company to break even.
Answer:
a. $21.50
b. $980
c. $25 and $18
Step-by-step explanation:
a. The price that generates the maximum profit is
In this question we use the vertex formula i.e shown below:
[tex](-\frac{b}{2a}, f(-\frac{b}{2a} ))\\\\[/tex]
where a = -80
b = 3440
c = 36000
hence,
P-coordinate is
[tex](-\frac{b}{2a}, (-\frac{3440}{2\times -80} ))\\\\[/tex]
[tex]= \frac{3440}{160}[/tex]
= $21.5
b. Now The maximum profit could be determined by the following equation
[tex]f(p) = 80p^2 + 3440p - 36000\\\\f($21.5) = -80(21.5)^2 + 3440(21.5) - 36000\\\\[/tex]
= $980
c. The price that would enable the company to break even that is
f(p) = 0
[tex]f(p) = -80p^2 + 3440p - 36000\\\\-80p^2 + 3440p - 36000 = 0\\\\p^2 -43p + 450 = 0\\\\p^2 - 25p - 18p + 450p = 0\\\\p(p - 25) - 18(p-25) = 0\\\\(p - 25) (p - 18) = 0[/tex]
By applying the factoring by -50 and then divided it by -80 and after that we split middle value and at last factors could come
(p - 25) = 0 or (p - 18) = 0
so we can write in this form as well which is
p = 25 or p = 18
Therefore the correct answer is $25 and $18
You can model that you expect a 1.25% raise each year that you work for a certain company. If you currently make $40,000, how many years should go by until you are making $120,000? (Round to the closest year.)
Answer:
94 years
Step-by-step explanation:
We can approach the solution using the compound interest equation
[tex]A= P(1+r)^t[/tex]
Given data
P= $40,000
A= $120,000
r= 1.25%= 1.25/100= 0.0125
substituting and solving for t we have
[tex]120000= 40000(1+0.0125)^t \\\120000= 40000(1.0125)^t[/tex]
dividing both sides by 40,000 we have
[tex](1.0125)^t=\frac{120000}{40000} \\\\(1.0125)^t=3\\\ t Log(1.0125)= log(3)\\\ t*0.005= 0.47[/tex]
dividing both sides by 0.005 we have
[tex]t= 0.47/0.005\\t= 94[/tex]
The foundation of a building is in the shape of a rectangle, with a length of 20 meters (m) and a width of 18 m. To the nearest meter, what is the distance from the top left corner of the foundation to the bottom right corner?
Answer:
27m
Step-by-step explanation:
It's the Pythagorean Theorem.
20^2+18^2=c^2
400+324=c^2
724=c^2
take the square root of both sides
26.9m=c
to the nearest meter = 27
please help me, i will give you brainliest
Answer:
52°i think
Step-by-step explanation:
148°-96°=52°
Answer:
The answer is below
Step-by-step explanation:
The answer is 52 degrees
The third option in the line
Hope the answer helps
plz give me correct answers
Answer:
Step-by-step explanation:
greatest number=8643
smallest number=3468
difference=8643-3468=5175
6.1. DCCLVI
CDXCIV
(II) 74,746
asdasd I don't actually have a question I accidentally typed this
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asndansjawjk
Answer:
that's cool . . .
\is ok everyone makes mistakes
Kara categorized her spending for this month into four categories: Rent, Food, Fun, and Other. The amounts she spent in each category are pictured here. Rent $433 Food $320 Fun $260 Other $487 What percent of her total spending did she spend on Rent? % (Please enter your answer to the nearest whole percent.) What percent of her total spending did she spend on Food? % (Please enter your answer to the nearest whole percent.) What percent of her total spending did she spend on Fun? % (Please enter your answer to the nearest whole percent.)
Answer: Rent = 29%, Food = 21%, Fun = 17%
Step-by-step explanation:
Rent = $433
Food = $320
Fun = $260
Other = $487
TOTAL = $1500
[tex]\dfrac{Rent}{Total}=\dfrac{433}{1500}\quad =0.2886\quad =\large\boxed{29\%}\\\\\\\dfrac{Food}{Total}=\dfrac{320}{1500}\quad =0.2133\quad =\large\boxed{21\%}\\\\\\\dfrac{Fun}{Total}=\dfrac{260}{1500}\quad =0.1733\quad =\large\boxed{17\%}[/tex]
Which of the following functions is graphed below
Answer:
the answer is C. y=[x-4]-2
Answer:
Step-by-step explanation:
Y=(x+4)-2
Use the data below, showing a summary of highway gas mileage for several observations, to decide if the average highway gas mileage is the same for midsize cars, SUV’s, and pickup trucks. Test the appropriate hypotheses at the α = 0.01 level.
n Mean Std. Dev.
Midsize 31 25.8 2.56
SUV’s 31 22.68 3.67
Pickups 14 21.29 2.76
Answer:
Step-by-step explanation:
Hello!
You need to test at 1% if the average highway gas mileage is the same for three types of vehicles (midsize cars, SUV's and pickup trucks) to compare the average values of the three groups altogether, you have to apply an ANOVA.
n | Mean | Std. Dev.
Midsize | 31 | 25.8 | 2.56
SUV’s | 31 | 22.68 | 3.67
Pickups | 14 | 21.29 | 2.76
Be the study variables :
X₁: highway gas mileage of a midsize car
X₂: highway gas mileage of an SUV
X₃: highway gas mileage of a pickup truck.
Assuming these variables have a normal distribution and are independent.
The hypotheses are:
H₀: μ₁ = μ₂ = μ₃
H₁: At least one of the population means is different.
α: 0.01
The statistic for this test is:
[tex]F= \frac{MS_{Treatment}}{MS_{Error}}[/tex]~[tex]F_{k-1;n-k}[/tex]
Attached you'll find an ANOVA table with all its components. As you see, to manually calculate the statistic you have to determine the Sum of Squares and the degrees of freedom for the treatments and the errors, next you calculate the means square for both and finally the test statistic.
For the treatments:
The degrees of freedom between treatments are k-1 (k represents the amount of treatments): [tex]Df_{Tr}= k - 1= 3 - 1 = 2[/tex]
The sum of squares is:
SSTr: ∑ni(Ÿi - Ÿ..)²
Ÿi= sample mean of sample i ∀ i= 1,2,3
Ÿ..= grand mean, is the mean that results of all the groups together.
So the Sum of squares pf treatments SStr is the sum of the square of difference between the sample mean of each group and the grand mean.
To calculate the grand mean you can sum the means of each group and dive it by the number of groups:
Ÿ..= (Ÿ₁ + Ÿ₂ + Ÿ₃)/ 3 = (25.8+22.68+21.29)/3 = 23.256≅ 23.26
[tex]SS_{Tr}[/tex]= (Ÿ₁ - Ÿ..)² + (Ÿ₂ - Ÿ..)² + (Ÿ₃ - Ÿ..)²= (25.8-23.26)² + (22.68-23.26)² + (21.29-23.26)²= 10.6689
[tex]MS_{Tr}= \frac{SS_{Tr}}{Df_{Tr}}= \frac{10.6689}{2}= 5.33[/tex]
For the errors:
The degrees of freedom for the errors are: [tex]Df_{Errors}= N-k= (31+31+14)-3= 76-3= 73[/tex]
The Mean square are equal to the estimation of the variance of errors, you can calculate them using the following formula:
[tex]MS_{Errors}= S^2_e= \frac{(n_1-1)S^2_1+(n_2-1)S^2_2+(n_3-1)S^2_3}{n_1+n_2+n_3-k}= \frac{(30*2.56^2)+(30*3.67^2)+(13*2.76^2)}{31+31+14-3} = \frac{695.3118}{73}= 9.52[/tex]
Now you can calculate the test statistic
[tex]F_{H_0}= \frac{MS_{Tr}}{MS_{Error}} = \frac{5.33}{9.52}= 0.559= 0.56[/tex]
The rejection region for this test is always one-tailed to the right, meaning that you'll reject the null hypothesis to big values of the statistic:
[tex]F_{k-1;N-k;1-\alpha }= F_{2; 73; 0.99}= 4.07[/tex]
If [tex]F_{H_0}[/tex] ≥ 4.07, reject the null hypothesis.
If [tex]F_{H_0}[/tex] < 4.07, do not reject the null hypothesis.
Since the calculated value is less than the critical value, the decision is to not reject the null hypothesis.
Then at a 1% significance level you can conclude that the average highway mileage is the same for the three types of vehicles (mid size, SUV and pickup trucks)
I hope this helps!
Suppose we write down the smallest positive 2-digit, 3-digit, and 4-digit multiples of 9,8 and 7(separate number sum for each multiple). What is the sum of these three numbers?
Answer:
Sum of 2 digit = 48
Sum of 3 digit = 317
Sum of 4 digit = 3009
Total = 3374
Step-by-step explanation:
Given:
9, 8 and 7
Required
Sum of Multiples
The first step is to list out the multiples of each number
9:- 9,18,....,99,108,117,................,999
,1008
,1017....
8:- 8,16........,96,104,...............,992,1000,1008....
7:- 7,14,........,98,105,.............,994,1001,1008.....
Calculating the sum of smallest 2 digit multiple of 9, 8 and 7
The smallest positive 2 digit multiple of:
- 9 is 18
- 8 is 16
- 7 is 14
Sum = 18 + 16 + 14
Sum = 48
Calculating the sum of smallest 3 digit multiple of 9, 8 and 7
The smallest positive 3 digit multiple of:
- 9 is 108
- 8 is 104
- 7 is 105
Sum = 108 + 104 + 105
Sum = 317
Calculating the sum of smallest 4 digit multiple of 9, 8 and 7
The smallest positive 4 digit multiple of:
- 9 is 1008
- 8 is 1000
- 7 is 1001
Sum = 1008 + 1000 + 1001
Sum = 3009
Sum of All = Sum of 2 digit + Sum of 3 digit + Sum of 4 digit
Sum of All = 48 + 317 + 3009
Sum of All = 3374
What is the value of x in equation 1/3 (12x -24) = 16
Thank you
Answer:
The value of x is x = 6
Step-by-step explanation:
[tex]\frac{1}{3}(12x - 24) = 16\\ 12x - 24 = 48\\12x = 48+ 24\\12x = 72\\12/12 = x\\72/12 = 6\\x=6[/tex]
Hope this helped! :)
what is 9 - 4 1/12 ??? im so stupid smh
Answer:
4 11/12
Step-by-step explanation:
Well 9 - 4 1/12 is 4 11/12
When 440 junior college students were surveyed, 200 said they have a passport. Construct a 95% confidence interval for the proportion of junior college students that have a passport.
The Confidence Interval is 0.403 < p < 0.497
What is Confidence Interval?The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. In statistics, confidence is another word for probability.
Given:
Sample proportion = 190/425
= 0.45
Now, [tex]\mu[/tex] = 1.96 x √[0.45 x 0.55/425]
[tex]\mu[/tex] = 0.047
So, 95% CI:
0.45-0.047 < p < 0.45+0.047
0.403 < p < 0.497
Learn more about Confidence Interval here:
https://brainly.com/question/24131141
#SPJ5
How do I construct bisectors, angles, & segments?
Answer:
Step-by-step explanation:
These come directly from my textbook, so I'm not sure if your teacher will accept this kind of work.
1. Angle construction:
Given an angle. construct an angle congruent to the given angle.
Given: Angle ABC
Construct: An angle congruent to angle ABC
Procedure:
1. Draw a ray. Label it ray RY.
2. Using B as center and any radius, draw an arc that intersects ray BA and ray BC. Label the points of intersection D and E, respectively.
3. Using R as center and the same radius as in Step 2, draw an arc intersecting ray RY. Label the arc XS, with S being the point where the arc intersects ray RY.
4. Using S as center and a radius equal to DE, draw an arc that intersects arc XS at a point Q.
5. Draw ray RQ.
Justification (for congruence): If you draw line segment DE and line segment QS, triangle DBE is congruent to triangle QRS (SSS postulate) Then angle QRS is congruent to angle ABC.
You can probably also Google videos if it's hard to imagine this. Sorry, construction is super hard to describe.
Prove that If A1, A2, ... , An and B1, B2,...,Bn are sets such that Aj ⊆ Bj for j = 1, 2, 3, ... , n, then ∪j=1nAj ⊆ ∪j=1nBj .
Answer:
This is proved using Proof by induction method. There are two steps in this method
Let P(n) represent the given statement ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex]
1. Basis Step: This step proves the given statement for n = 1
2. Induction step: The step proves that if the given statement holds for any given case n = k then it should also be true for n = k + 1.
If the above two steps are true this means that given statement P(n) holds true for all positive n and the mathematical induction P(n): ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] is true.
Step-by-step explanation:
Basis Step:
For n = 1
∪[tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] = ∪[tex]{ {{1} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] = A₁ ⊆ B₁ = ∪[tex]{ {{1} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] = ∪[tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex]
We show that
∪[tex]{ {{1} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] = A₁ ⊆ B₁ = ∪[tex]{ {{1} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] for n = 1
Hence P(1) is true
Induction Step:
Let P(k) be true which means that we assume that:
for all k with k≥1, P(k): ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] is true
This is our induction hypothesis and we have to prove that P(k + 1) is also true
This means if ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] holds for n = k then this should also hold for n = k + 1.
In simple words if P(k): ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] is true then ∪[tex]{ {{k+1} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪[tex]{ {{k+1} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] is also true
∪[tex]{ {{k+1} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] = ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ∪ [tex]A_{k+1}[/tex]
⊆ ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] ∪ [tex]A_{k+1}[/tex] As ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex]
⊆ ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] ∪ [tex]B_{k+1}[/tex] As [tex]A_{k+1}[/tex] ⊆ [tex]B_{k+1}[/tex]
= ∪[tex]{ {{k+1} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex]
The whole step:
∪[tex]{ {{k+1} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] = ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ∪ [tex]A_{k+1}[/tex] ⊆ ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] ∪ [tex]A_{k+1}[/tex] ⊆ ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] ∪ [tex]B_{k+1}[/tex] = ∪[tex]{ {{k+1} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex]
shows that the P(k+1) also holds for ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex]
hence P(k+1) is true
So proof by induction method proves that P(n) is true. This means
P(n): ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] is true
If Aequals[Start 2 By 2 Matrix 1st Row 1st Column 1 2nd Column negative 4 2nd Row 1st Column negative 4 2nd Column 5 EndMatrix ] and ABequals[Start 2 By 3 Matrix 1st Row 1st Column negative 10 2nd Column 1 3rd Column 9 2nd Row 1st Column 7 2nd Column negative 15 3rd Column 8 EndMatrix ], determine the first and second columns of B. Let Bold b 1 be column 1 of B and Bold b 2 be colum
Answer:
[tex]b_1=\left(\begin{array}{ccc}-3\\3\end{array}\right),b_2=\left(\begin{array}{ccc}-\dfrac{65}{11}\\\\-\dfrac{19}{11}\end{array}\right)[/tex]
Step-by-step explanation:
Given matrix A and AB below:
[tex]A=\left(\begin{array}{ccc}1&-4\\-4&5\end{array}\right)\\\\\\ AB=\left(\begin{array}{ccc}-10&1&9\\7&-15&8\end{array}\right)[/tex]
For the product AB to be a 2 X 3 matrix, B must be a 2 X 3 matrix.
Let matrix B be defined as follows
[tex]B=\left[\begin{array}{ccc}a&c&e\\b&d&f\end{array}\right][/tex]
Therefore:
[tex]\left(\begin{array}{ccc}1&-4\\-4&5\end{array}\right)\left(\begin{array}{ccc}a&c&e\\b&d&f\end{array}\right)=\left(\begin{array}{ccc}-10&1&9\\7&-15&8\end{array}\right)[/tex]
This results in the equations
a-4b=-10-4a+5b=7c-4d=1-4c+5d=-15Solving the first two equations simultaneously
a-4b=-10 (a=-10+4b)
-4a+5b=7
Substitution of [tex]a=-10+4b[/tex] into the second equation
[tex]-4(-10+4b)+5b=7\\40-16b+5b=7\\-11b=-33\\b=3[/tex]
Recall that [tex]a=-10+4b[/tex]
[tex]a=-10+4(3)=-10+7\\a=-3[/tex]
Solving the other two equations
c-4d=1 (c=1+4d)
-4c+5d=-15
Substitution of c=1+4d into the second equation
[tex]-4(1+4d)+5d=-15\\-4-16d+5d=15\\-11d=19\\d=-\dfrac{19}{11}\\ Recall: c=1+4d\\c=1+4(-\frac{19}{11})\\c=-\dfrac{65}{11}[/tex]
Therefore, we have:
[tex]a=-3, b=3, c=-\dfrac{65}{11}, d=-\dfrac{19}{11}[/tex]
Thus:
[tex]b_1=\left(\begin{array}{ccc}-3\\3\end{array}\right)\\\\\\b_2=\left(\begin{array}{ccc}-\dfrac{65}{11}\\\\-\dfrac{19}{11}\end{array}\right)[/tex]
Answer:
option c
Step-by-step explanation:
it is said that a computer repairman makes 25 dollars per hour
this column shows the right amount of money he earns per hour
Susan decides to take a job as a transcriptionist so that she can work part time from home. To get started, she has to buy a computer, headphones, and some special software. The equipment and software together cost her $1000. The company pays her $0.004 per word, and Susan can type 90 words per minute. How many hours must Susan work to break even, that is, to make enough to cover her $1000 start-up cost? If Susan works 4 hours a day, 3days a week, how much will she earn in a month.
Answer:
46.3 hours of work to break even.
$1036.8 per month (4 weeks)
Step-by-step explanation:
First let's find how much Susan earns per hour.
She earns $0.004 per word, and she does 90 words per minute, so she will earn per minute:
0.004 * 90 = $0.36
Then, per hour, she will earn:
0.36 * 60 = $21.6
Now, to find how many hours she needs to work to earn $1000, we just need to divide this value by the amount she earns per hour:
1000 / 21.6 = 46.3 hours.
She works 4 hours a day and 3 days a week, so she works 4*3 = 12 hours a week.
If a month has 4 weeks, she will work 12*4 = 48 hours a month, so she will earn:
48 * 21.6 = $1036.8
Answer:
46.3 hours of work to break even.
$1036.8 per month (4 weeks)
Step-by-step explanation:
ASAP NEED HELP PRETTY PLEASEAssuming that the petals of the flower are congruent, how many lines of symmetry does the figure have? A. 0 B. 4 C. 6 D. 8
Answer:
Hey there!
This flower has 8 lines of symmetry.
Hope this helps :)
For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal distribution as an approximation. n = 24 and p = 0.6.
Answer:
Since both np > 5 and np(1-p)>5, it is suitable to use the normal distribution as an approximation.
Step-by-step explanation:
When the normal approximation is suitable?
If np > 5 and np(1-p)>5
In this question:
[tex]n = 24, p = 0.6[/tex]
So
[tex]np = 24*0.6 = 14.4[/tex]
And
[tex]np(1-p) = 24*0.6*0.4 = 5.76[/tex]
Since both np > 5 and np(1-p)>5, it is suitable to use the normal distribution as an approximation.
Find the point, Q, along the directed line segment AB that
divides AB into the ratio 2:3. The 2:3 ratio means that the line
should be broken up in to 5 equal sections (2 + 3 = 5). This
means that each of the 5 sections can be represented by the
expression AB/5. Therefore, the point that divides AB into the
ratio 2:3 is the distance (AB/5)(2) from A.
Answer:
Point Q is at a distance of 4.7 units from A.
Step-by-step explanation:
From the graph, AC = 10 units and BC = 6 units. Applying the Pythagoras theorem,
[tex]AB^{2}[/tex] = [tex]AC^{2}[/tex] + [tex]BC^{2}[/tex]
= [tex]10^{2}[/tex] + [tex]6^{2}[/tex]
= 100 + 36
= 136
AB = [tex]\sqrt{136}[/tex]
AB = 11.6619
AB = 11.66
≅ 11.7 units
But point Q divides AB into ratio 2:3. Therefore:
AQ = [tex]\frac{2}{5}[/tex] × AB
= [tex]\frac{2}{5}[/tex] × 11.66
= 4.664
AQ = 4.664
AQ ≅ 4.7 units
QB = [tex]\frac{3}{5}[/tex] × AB
= [tex]\frac{3}{5}[/tex] × 11.66
= 6.996
QB ≅ 7.0 units
So that point Q is at a distance of 4.7 units from A.
a bank teller has 340 one hundred dollar bills. how much money does the bank teller have?
Answer:
$34,000
Step-by-step explanation:
Since a one hundred dollar bill is equal to 100, we simply multiply 340 and 100 together:
340(100) = 34000
Which statement is true about the steps that Pablo used to simplify the expression?
The solutions to the inequality y < to -x+1 sre shaded on the graph. Which point is a solution
There are two ways to confirm this is the answer. The first is to note that (3,-2) is on the boundary, so it is part of the solution set. This only works if the boundary line is a solid line (as opposed to a dashed or dotted line).
The second way is to plug (x,y) = (3,-2) into the given inequality to find that
[tex]y \le -x+1\\\\-2 \le -3+1\\\\-2 \le -2[/tex]
which is a true statement. So this confirms that (3,-2) is in the solution set of the inequality.
Over the past several years, the proportion of one-person households has been increasing. The Census Bureau would like to test the hypothesis that the proportion of one-person households exceeds 0.27. A random sample of 125 households found that 43 consisted of one person. The Census Bureau would like to set α = 0.05. Use the critical value approach to test this hypothesis. Explain.
Answer:
For this case we can find the critical value with the significance level [tex]\alpha=0.05[/tex] and if we find in the right tail of the z distribution we got:
[tex] z_{\alpha}= 1.64[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing we got:
[tex]z=\frac{0.344 -0.27}{\sqrt{\frac{0.27(1-0.27)}{125}}}=1.86[/tex]
Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true proportion of households with one person is significantly higher than 0.27
Step-by-step explanation:
We have the following dataset given:
[tex] X= 43[/tex] represent the households consisted of one person
[tex]n= 125[/tex] represent the sample size
[tex] \hat p= \frac{43}{125}= 0.344[/tex] estimated proportion of households consisted of one person
We want to test the following hypothesis:
Null hypothesis: [tex]p \leq 0.27[/tex]
Alternative hypothesis: [tex]p>0.27[/tex]
And for this case we can find the critical value with the significance level [tex]\alpha=0.05[/tex] and if we find in the right tail of the z distribution we got:
[tex] z_{\alpha}= 1.64[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing we got:
[tex]z=\frac{0.344 -0.27}{\sqrt{\frac{0.27(1-0.27)}{125}}}=1.86[/tex]
Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true proportion of households with one person is significantly higher than 0.27
Unit sales for new product ABC has varied in the first seven months of this year as follows: Month Jan Feb Mar Apr May Jun Jul Unit Sales 330 274 492 371 160 283 164 What is the (population) standard deviation of the data
Answer:
Approximately standard deviation= 108
Step-by-step explanation:
Let's calculate the mean of the data first.
Mean =( 330+ 274+ 492 +371 +160+ 283+ 164)/7
Mean= 2074/7
Mean= 296.3
Calculating the variance.
Variance = ((330-296.3)²+( 274-296.3)²+ (492-296.3)²+( 371-296.3)²+ (160-296.3)² (283-296.3)²+(164-296.3)²)/7
Variance= (1135.69+497.29+38298.49+5580.09+18577.69+176.89+17503.29)/7
Variance= 81769.43/7
Variance= 11681.347
Standard deviation= √variance
Standard deviation= √11681.347
Standard deviation= 108.080
Approximately 108
The line x + y - 6= 0 is the right bisector
of the segment PQ. If P is the point (4,3),
then the point Q is
Answer:
Therefore, the coordinates of point Q is (2,3)
Step-by-step explanation:
Let the coordinates of Q be(a,b)
Let R be the midpoint of PQ
Coordinates of R [tex]=(\frac{4+a}{2}, \frac{3+b}{2})[/tex]
R lies on the line x + y - 6= 0, therefore:
[tex]\implies \dfrac{4+a}{2}+ \dfrac{3+b}{2}-6=0\\\implies 4+a+3+b-12=0\\\implies a+b-5=0\\\implies a+b=5[/tex]
Slope of AR X Slope of PQ = -1
[tex]-1 \times \dfrac{b-3}{a-4}=-1\\b-3=a-4\\a-b=-3+4\\a-b=-1[/tex]
Solving simultaneously
a+b=5
a-b=-1
2a=4
a=2
b=3
Therefore, the coordinates of point Q is (2,3)
what is the product?
(x-3)(2x²-5x+1)
C) 2x³-11x²+16x-3
Answer:
2x^3-11x^2+16x-3
Step-by-step explanation:
1) multiply each term inside the parentheses with all other terms:
(x*2x^2)=2x^3
x*-5x=-5x^2
x*1=x
-3*2x^2=-6x^2
-3*-5x=15x
and
-3*1=-3
so
2x^3-5x^2+x-6x^2+15x-3
is our equation
to simplify:
2x^3-11x^2+16x-3 is the answer
What is the simplified form of this expression?
(-3x^2+ 2x - 4) + (4x^2 + 5x+9)
OPTIONS
7x^2 + 7x + 5
x^2 + 7x + 13
x^2 + 11x + 1
x^² + 7x+5
Answer:
Option 4
Step-by-step explanation:
=> [tex]-3x^2+2x-4 + 4x^2+5x+9[/tex]
Combining like terms
=> [tex]-3x^2+4x^2+2x+5x-4+9[/tex]
=> [tex]x^2+7x+5[/tex]
what's the equivalent expression
Answer:
2^52
Step-by-step explanation:
(8^-5/2^-2)^-4 = (2^-15/2^-2)^-4= (2^-13)^-4= 2^((-13*(-4))= 2^52
consider the difference of squares identity a^2-2b^2=(a+b)(a-b)
Answer: a= 3x and b= 7
Step-by-step explanation:
^^