Answer:
The x-values of the inflection points of the curve are x = -52 and x = 52.
Step-by-step explanation:
Suppose we have a normal curve with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex]
The x-values of the inflection points of the curve are [tex]x = \mu - \sigma[/tex] and [tex]x = \mu + \sigma[/tex]
x ~ N(0, 52)
This means that [tex]\mu = 0, \sigma = 52[/tex]
So
[tex]x = 0 - 52 = -52[/tex]
[tex]x = 0 + 52 = 52[/tex]
The x-values of the inflection points of the curve are x = -52 and x = 52.
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
The 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
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
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
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
"Currently, only 20 percent of arrested drug pushers are convicted", cried candidate AK in a campaign speech. "Elect me and you'll see a big increase in convictions" A year after his election a random sample of 144 case files of arrested drug pushers showed 36 convictions. For a right-tailed test, find the p-value. A. 0.12 B. 0.07 C. 0.06 D. 0.04
Answer:
B. 0.07
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that the proportion of convicted drug pushers is significnalty higher than 20%.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.2\\\\H_a:\pi>0.2[/tex]
The sample has a size n=144.
The sample proportion is p=0.25.
[tex]p=X/n=36/144=0.25[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.2*0.8}{144}}\\\\\\ \sigma_p=\sqrt{0.001111}=0.0333[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi}=\dfrac{0.25-0.2}{0.0333}=\dfrac{0.05}{0.0333}=1.5[/tex]
This test is a right-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z>1.5)=0.066\approx0.07[/tex]
25% of a class do not play basketball.
27 children do play. How many
children are in the class?
Answer: 36 children
Step-by-step explanation:
3/4 of the class plays basketball. Thus 3/4x=27. Multiply each side by 4/3 to get x = 36
Find the common ratio of the geometric sequence: 12.5,−62.5,312.5,−1562.5,…
Answer:
-5
Step-by-step explanation:
its what you multiply by to get the next number
Fiona solved the equation shown 1/2-1/3(6x-3)=-13/2 what is the missing step of her solution?
Answer:
Summation of the non variable Expression within the quality sign
1/2 + 1-2x= -13/2
3/2-2x= -13/2
Step-by-step explanation:
1/2-1/3(6x-3)=-13/2
First step
Using the distributive property to simply
1/2-(6x/3)+(3/3)=-13/2
1/2 -2x +1 = -13/2
Second step
Summation of the non variable Expression within the quality sign
1/2 + 1-2x= -13/2
3/2-2x= -13/2
Third step
Isolating the variable Expression by using the addition property of equality
-2x = -13/2 - 3/2
-2x = -16/2
Fourth step
Isolating the variable by using the division property of equality
-2x = -16/2
X = -16/2 * -1/2
X = -16/-4
X= 4
Answer:
Simplify by combining like terms
Step-by-step explanation:
how would i find the mean of the histogram?
Answer:
You count the amount in each section, add them all together and divide by the total amount of variables used to find the mean. for example, if you had the numbers 3, 5, 8, and 4, the mean would be (3+5+8+4)= 5
Step-by-step explanation:
A comprehensive survey released by a college reports that the true proportion of all students at the college who use drugs is 0.3. You survey 100 students in your dorm and record that the proportion of students who use drugs is 0.15. The proportion of all students at this college who use drugs is a
Complete Question
The proportion of all students at this college who use drugs is a_____and the proportion of students who use drugs in your dorm is a _____ .
Options
a. statistic; parameter b. parameter; statistic c. population; sample d. measure of central tendency, measure of variability e. none of the aboveAnswer:
b. parameter; statistic
Step-by-step explanation:
A parameter is a summary of data for an entire population.
Statistic, on the other hand, summarizes data for a sample of the population.
The proportion of all students at this college who use drugs is a parameter and the proportion of students who use drugs in your dorm is a sample.
The correct option is B
Find the sample size needed to estimate the percentage of Democrats among registered voters in Texas. Use a 0.01 margin of error, and use a confidence level of 96% and assume LaTeX: \hat{p}
p
^
=0.28.
Answer:
Step-by-step explanation:
Hello!
You have to determine the sample size to take to estimate the population proportion of Democrats among registered voters in Texas for a 96% interval with a margin of error of 0.01 and sample proportion p'= 0.28
The interval for the population proportion is
p' ± [tex]Z_{1-\alpha /2}[/tex]*[tex]\sqrt{\frac{p'(1-p')}{n} }[/tex]
The margin of error of the interval is:
d= [tex]Z_{1-\alpha /2}[/tex]*[tex]\sqrt{\frac{p'(1-p')}{n} }[/tex]
[tex]\frac{d}{Z_{1-\alpha /2}}= \sqrt{\frac{p'(1-p')}{n} }\\(\frac{d}{Z_{1-\alpha /2}} )^2= \frac{p'(1-p)}{n} \\n*(\frac{d}{Z_{1-\alpha /2}} )^2= p'(1-p)\\n= p'(1-p)*(\frac{Z_{1-\alpha /2}}{d} )^2\\[/tex]
[tex]Z_{1-\alpha /2}= Z_{0.98}= 2.054[/tex]
[tex]n= 0.28*(1-0.28)*(\frac{2.054}{0.01} )^2= 8505.33[/tex]
n= 8506 voters
I hope this helps!
3/(2x-1)+4=6x/(2x-1)
8. What is the lateral area of the cone?
Answer:
[tex]190.07 \: {yd}^{2} [/tex]Option D is the correct option.
Step-by-step explanation:
Diameter (d) = 10 yd
Radius(r) = 10/2 = 5 yd
Slant height (l)= 12.1 yd
We know,
Lateral surface area of cone:
[tex]\pi \: r \: l[/tex]
[tex] = 3.14 \times 5 \times 12.1[/tex]
[tex] = 189.97 \: {yd}^{2} [/tex]
which is nearly 190.07 square yards.
Hope this helps...
Good luck on your assignment..
Answer:
[tex]190.07 {yd}^{2} [/tex]
Step-by-step explanation:
[tex]lateral \: \: area \\ = \pi \: rl \\ = 3.14 \times 5 \times 12.1 \\ = 189.97[/tex]
189.97 square yards which is nearly 190.07 square yards
name the blue shaded parts as an improper fraction
Answer :
option C is the correct answer
Hope this may help you━━━━━━━☆☆━━━━━━━
▹ Answer
[tex]\frac{13}{4}[/tex]
▹ Step-by-Step Explanation
4 Squares = x/4
13 parts are shaded in so...
The answer would be 13/4.
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
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)
Find the first four nonzero terms in a power series expansion about xequals0 for the solution to the given initial value problem. w prime prime plus 3 xw prime minus wequals0; w(0)equals4, w prime (0 )equals0
Answer:
The first four terms are;
w(x)= 4 + 2x² - ⁵/₆x⁴+ ¹¹/₃₆x⁶ +......
Step-by-step Explanation:
This is the interpretation of the question
w″ + 3xw′ -w=0
W(0)=4
W′(0)=0
CHECK THE ATTACHMENT FOR STEP BY STEP EXPLANATION
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]
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.
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 :)
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
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.
Not sure how to solve this
Step-by-step explanation:
You just have to plug the numbers they give you into the equation. For the first one, you have 0 + 5y = 10; 5y = 10; y = 2. For the second one, x + 5(0) = 10; x + 0 = 10; x = 10. And lastly, for the third one, x + 5(6) = 10; x + 30 = 10; x = -20.
What is the sum of the measures of the interior angles of the stop sign?
Answer:
Sum of Interior Angles = (Number of Sides -2) • 180 degrees
Sum of Interior Angles = (8 -2) * 180 = 1,080
A backyard swimming pool measure 15 ft, by 24 ft and 5 ft deep. The pool has a leak and is losing water at a rate of 4 inches per day. If the owner does not refill the water, in how many days will it be empty?
Answer:
15 days
Step-by-step explanation:
The pool is 5 ft deep.
5 ft * 12 in/ft = 60 in
The pool is 60 inches deep.
60 in/4 in = 15
Answer: 15 days
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
Find the Area of this shape
Answer:
42.5
Step-by-step explanation:
see attached image.
Answer:
42.5
Step-by-step explanation:
So first we have to split this shape into many parts
The simplest way we can do that is by simply drawing a line between the small square and the big rectangle.
Now we calculate the area of each part.
1. Big rectangle
--> So we would just simply multiply the length and width for this one which is 3.5 by 9 --> 3.5 x 9 = 31.5
2. (Left) Right Triangle
Since it's a right triangle we can simply multiply it's L and W then divide by 2
--> 2 x 2 = 4 --> 4/2 = 2
3. (Right) Right Triangle
Same way as previous right triangle l x w / 2
--> 2 x 5 = 10 --> 10/2 = 5
4. Square (Bottom)
And lastly, we have the small square at the bottom
--> l x w = area.
-->given 9 = 2 + x + 5,
x = 9 - 7 --> x = 2
so, 2 x 2 = area --> . 4
Calculate the actual area. of the whole entire shape -->
So this is very simple we just add the area of the shapes (area) we calculated below.
--> 31.5 + 2 + 5 + 4
--> Add parenthasees 31.5 + (2 + 5 + 4)
[To make calculating simpler]
=> 11 + 31.5
=> 32.5 + 10
=> 42.5
Hope this helps!
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 piece of string is 120 centimeters long. How long would the piece of string measure in meters?. Enter your answer in the box.
Answer:
1.2 metres
Step-by-step explanation:
1 metre = 100cm
so 120cm has 120 cm * 1 m/ 100cm = 1.2 m
Which of the following options have the same value as 30\%30%30, percent of 818181?
Answer:
Option B is correct = [tex]0.3 \times 81[/tex]
Step-by-step explanation:
The complete question is: Which of the following options have the same value as 30% of 81?
Group of choices is:
(A) [tex]\frac{30}{100}\times 81 \times 100[/tex]
(B) [tex]0.3 \times 81[/tex]
(C) [tex]0.03 \times 81[/tex]
(D) [tex]\frac{3}{10}\times 81 \times 10[/tex]
(E) [tex]30 \times 81[/tex]
Now, the expression given to us is 30% of 81.
Simplifying the above expression we get;
30% of 81 = [tex]\frac{30}{100} \times 81[/tex]
= [tex]\frac{3}{10} \times 81[/tex] = [tex]0.3 \times 81[/tex]
Now, we will solve each of the given options and then see which option matches with our calculation.
Option (A) is given;
[tex]\frac{30}{100}\times 81 \times 100[/tex] = [tex]30 \times 81[/tex]
This doesn't match with our answer, so this option is not correct.
Option (B) is given;
[tex]0.3 \times 81[/tex]
This matches with our answer, so this option is correct.
Option (C) is given;
[tex]0.03 \times 81[/tex]
This doesn't match with our answer, so this option is not correct.
Option (D) is given;
[tex]\frac{3}{10}\times 81 \times 10[/tex] = [tex]3 \times 81[/tex]
This doesn't match with our answer, so this option is not correct.
Option (E) is given;
[tex]30 \times 81[/tex]
This doesn't match with our answer, so this option is not correct.