Answer:
The proof of area is [tex]\frac{3\sqrt{3} }{2} (p^{2}-1)x^{2}[/tex] is done
Step-by-step explanation:
Area of regular hexagon[tex]=6\times[/tex] Area of equilateral triangle
Area of regular hexagon ABCDEF with side [tex]x[/tex]
[tex]=6\times \frac{\sqrt{3} }{4} x^{2} \\\\= \frac{3\sqrt{3} }{2} x^{2}[/tex]
Area of regular hexagon FGHIJK with side [tex]px[/tex]
[tex]= \frac{3\sqrt{3} }{2} (px)^{2}\\\\=\frac{3\sqrt{3} }{2} p^{2}x^{2}[/tex]
Area of shaded region
[tex]=\frac{3\sqrt{3} }{2} p^{2}x^{2}-\frac{3\sqrt{3} }{2} x^{2}\\\\=\frac{3\sqrt{3} }{2} (p^{2}-1)x^{2}[/tex]
A drug company is considering marketing a new local anesthetic. The effective time of the anesthetic the drug company is currently producing has a normal distribution with a mean of 7.4 minutes with a standard deviation of 1.2 minutes. The chemistry of the new anesthetic is such that the effective time should be normally distributed with the same standard deviation, but the mean effective time may be lower. If it is lower, the drug company will market the new anesthetic; otherwise, they will continue to produce the older one. A sample size of 36 results in a sample mean of 7.1. A hypothesis test will be done to help make the decision
Required:
a. For a test with a level of significance of 0.10, compute the critical value; set up the appropriate hypotheses and the calculate the p-value of the test
b. Will the null hypothesis will be rejected with a level of significance of 0.10? Explain why or why not?
Using the z-distribution, we have that:
a)
The hypothesis test is:
[tex]H_0: \mu = 7.4[/tex][tex]H_1: \mu < 7.4[/tex]The p-value is of 0.0668.
The critical value is [tex]z^{\ast} = -1.28[/tex]
b) Since the test statistic is less than the critical value for the left-tailed test, there is enough evidence to conclude that the null hypothesis will be rejected.
Item a:
At the null hypothesis, it is tested if the mean is of 7.4 minutes, that is:
[tex]H_0: \mu = 7.4[/tex]
At the alternative hypothesis, it is tested if the mean is lower than 7.4 minutes, that is:
[tex]H_1: \mu < 7.4[/tex]
We have the standard deviation for the population, hence, the z-distribution is used.
The test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean. [tex]\mu[/tex] is the value tested at the null hypothesis. [tex]\sigma[/tex] is the standard deviation of the sample. n is the sample size.For this problem, the values of the parameters are: [tex]\overline{x} = 7.1, \mu = 7.4, \sigma = 1.2, n = 36[/tex].
Hence, the value of the test statistic is:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{7.1 - 7.4}{\frac{1.2}{\sqrt{36}}}[/tex]
[tex]z = -1.5[/tex]
Using a z-distribution calculator, the p-value is of 0.0668.
Also using a calculator, considering a left-tailed test, as we are testing if the mean is less than a value, the critical value with a significance level of 0.1 is of [tex]z^{\ast} = -1.28[/tex].
Item b:
Since the test statistic is less than the critical value for the left-tailed test, there is enough evidence to conclude that the null hypothesis will be rejected.
You can learn more about the use of the z-distribution to test an hypothesis at https://brainly.com/question/16313918
15+25 distributive property
Answer:
(5 x 3) + (5 x 5)
Step-by-step explanation:
hope thats what your looking for
Felipe jogs for 3 miles and then walks another 3 miles. He jogs 1 and 1/2 miles per hour faster than he walks, and the entire distance of 6 miles takes 3 hours. Find the rate at which he walks and the rate at which he jogs.
Answer:
walking: 1.5 mphjogging: 3 mphStep-by-step explanation:
Let w represent Felipe's walking speed in miles per hour. Then his total travel time is ...
time = distance/speed
3 = 3/w +3/(w+1.5) . . . . . total time is the sum of walking and jogging times
1 = 1/w +1/(w +1.5) . . . . . divide by 3
w(w +1.5) = (w+1.5) +w . . . . multiply by w(w+1.5)
w^2 -0.5w -1.5 = 0 . . . . . . subtract 2w+1.5
(w -1.5)(w +1) = 0 . . . . . . . factor
The values of w that make this equation true are w = 1.5 and w = -1. Only the value 1.5 makes any sense in this scenario. Felipe's jogging speed is then 1.5+1.5 = 3 mph.
Felipe walks at 1.5 mph and jogs at 3 mph.
Elisa and Teresa are comparing weights. If Elisa weights 52 1⁄4 kilograms
and Teresa weighs 49 4/9 kilograms, what is the difference in their
weights?
Answer:
[tex]52\frac{1}{4\\}[/tex] - [tex]49\frac{4}{9}[/tex] = [tex]\frac{101}{36}[/tex]
Step-by-step explanation:
First, we have to convert the mixed fractions to improper fractions
[tex]52\frac{1}{4\\}[/tex] = [tex]\frac{4 x 52 +1}{4}[/tex] = [tex]\frac{209}{4}[/tex]
[tex]49\frac{4}{9}[/tex] = [tex]\frac{9 x 49 + 4}{9}[/tex] = [tex]\frac{445}{9}[/tex]
[tex]\frac{209}{4}[/tex] - [tex]\frac{445}{9}[/tex] = [tex]\frac{1881}{36}[/tex] - [tex]\frac{1780}{36}[/tex] = [tex]\frac{101}{36}[/tex]
We cannot simplify [tex]\frac{101}{36}[/tex] so it is the final answer
PLZ HELLLP 50 POINTS, WILL GIVE BRAINLY PLZZZZZZZZZZ
Modified organisms may contaminate the natural, wild populations.
Which genetic technique is the statement describing an ethical issue of?
stem cell research
gene therapy
transgenic organisms
cloning
Answer:
Transgenic Organism
My reasoning:
A transgenic organism is an organism which has been modified with genetic material from another species. The biggest use of transgenic organisms is for agriculture growth, the development of genetically modified crops.
They also research with transgenic mice. Mice can be modified with human DNA for the purpose of testing medical treatments and seeing how they might behave in a human.
Researchers are concerned though that interbreeding between transgenic and wild organisms could have unforeseen consequences and could reign havoc on our ecosystem.
~That's All Folks~
-Siascon
transgenic organisms is the answer
Please help me ASAP!!
Thx
Answer:
8
Step-by-step explanation:
The fraction simplifies to 9 ^5
9^5 x 9^3 = 9^8
Simplify this question
[tex] \frac{8 - \sqrt{ - 36} }{2} \\ = \frac{8 - \sqrt{ 2 \times \: 2 \times 3 \times - 3} }{2} \\ = \frac{8 -2 \sqrt{ - 9} }{2} \\ = \frac{2(4 - \sqrt{ - 9} )}{2} \\ = 4 - \sqrt{ - 9} [/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
Answer:
Unfortunately, the problem could not be solved because there is a minus in √36. This basically means that this problem has no answer. Remember, if there is a minus in a root system, that basically means that the answer is Un-defined.
Hoped this helped.
[tex]-BrainiacUser1357-[/tex]
Solve the inequality.
-7x - 4 > 17
Answer:x<-3
Step-by-step explanation:
Answer:
x < -3
Step-by-step explanation:
[tex]-7x-4>17\\\\-7x-4+4>17+4\\\\-7x>21\\\\\frac{-7x}{-7}>\frac{21}{-7}\\\\x<-3[/tex]
Write an algebraic expression that corresponds to "the opposite of a number "
Answer:
-n
Step-by-step explanation:
If n represents "a number", then the opposite of the number is ...
-n
__
Examples:
The opposite of -3 is -(-3) = 3. The opposite of 10 is -10.
1. Which of the following is equivalent to x5/2?
1
(1)
5x
2
(3) Vr
2x
(2)
(4) Vx?
Given that the expression in the question is [tex]\displaystyle x^{\frac{5}{2} }[/tex], the equivalent expression
can be found using the rules of indices.
[tex]\displaystyle \underline{x^{\frac{5}{2} } \ is \ equivalent \ to \ x^2 \cdot\sqrt{x}}[/tex]Reasons:
The given expression is [tex]\displaystyle x^{\frac{5}{2} }[/tex]
Required:
To find the equivalent expression
Solution:
According to the rules of indices, we have;
[tex]a^{n + m} = a^n \times a^m[/tex]
[tex]a^{\frac{n}{m} } = \sqrt[m]{a^n}[/tex]
Therefore, the above expression can be expanded as follows;
[tex]\displaystyle x^{\frac{5}{2} } = x ^{2.5} = \mathbf{x^{2 + 0.5}}[/tex]
[tex]\displaystyle x^{2 + 0.5} =\mathbf{ x^2 \times x^{0.5}}[/tex]
Which gives;
[tex]\displaystyle x^2 \times x^{0.5} = \mathbf{x^2 \times \sqrt{x}}[/tex]
Therefore;
[tex]\displaystyle x^{\frac{5}{2} } \equiv x^2 \cdot\sqrt{x}[/tex], which is the form [tex]a^{\frac{n}{m} } = \sqrt[m]{a^n}[/tex]
[tex]\underline{An \ expression \ \mathbf{equivalent} \ to \ x^\frac{5}{2} \ is \ x^2 \cdot \sqrt{x}}[/tex]
Learn more about the rules of indices here:
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PLEASE HELP QUESTION IN PICTURE
D and F are correct
Answer:
B
Step-by-step explanation:
First of all we know b is a parrellogram, so it is b.
But also other reasons:
It can't be A because they are next to each other, in fact supplementary angles. It can't be C because it doesn't make any sense and same thing for E.
The Gonzales family has three children. On summer break they went to an amusement park they bought 3 child tickets for 18.50 and 2 adult tickets If they spent a total of 104.50 how much was the price of the adult ticket?
I need a complete equation and step by step explanation showing the numbers, not how you did it.
Answer:
= 24.5
Step-by-step explanation:
1 child ticket = 18.50 and they bought 3 so 18.50 x 3 = 55.5
55.5 + 2 adult tickets = 104.50
104.50 - 55.5 = 2 adult tickets
= 49 for 2 adult tickets
49/2 = 1 adult tickets
= 24.5
If A = 2x – y + 3xy, B = x + 2xy and C = 3y + xy, find the value of A + B + C
[tex]A+B+C\\\\=(2x-y+3xy)+(x+2xy) +(3y+xy)\\\\=3x+2y+6xy[/tex]
The value of the expression A + B + C is equal to 3x - 2y + 4xy.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, Are three expressions A = 2x - y + 3xy, B = x + 2xy and C = 3y + xy.
Now, A + B + C is equal to the sum of their values which is,
= (2x - y + 3xy) + (x + 2xy) + (3y + xy).
Now, we'll combine the like terms,
= 2x + x - y + 3y + 3xy + xy.
= 3x - 2y + 4xy.
So, The value of the expression A + B + C is equal to 3x - 2y + 4xy.
learn more about numerical expressions here :
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50 POINTS!!! MUST BE CORRECT OR I WILL DELETE IT AND REPORT IT!
What is the solution to the equation –3 + 5x = 42?
Answer:
x=9
Step-by-step explanation:
-3 + 5x = 42
add 3 to both sides
5x=45
divide both sides by 5
x=9
Answer:
x=9
Step-by-step explanation:
Help please please please
Answer:
Step-by-step explanation:
All angles in a triangle add up to equal 180
22x+4=180
22x=176
x=8
20x=?
20(8)=160 degrees
Line l is a perpendicular bisector of line segment R Q. It intersects line segment R Q at point T. Line l contains point S. The length of segment R S is 2 x + 8. The length of segment S Q is 8 x minus 4.
What is the length of segment SR?
Answer:
12
Step-by-step explanation:
Since RS = QS, we know 2x + 8 = 8x - 4
Subtract 2x from each side
8 = 6x - 4
Add 4 to each side
12 = 6x
Divide each side by 6
2 = x
SR is 2x + 8, so it is 2(2) + 8, so RS = 12
The length of the segment SR is 12.
What is a triangle?Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees.
Since RS = QS, we know 2x + 8 = 8x - 4
Subtract 2x from each side
8 = 6x - 4
Add 4 to each side
12 = 6x
Divide each side by 6
2 = x
SR is 2x + 8, so it is 2(2) + 8, SR = 12
Hence, the segment SR is 12.
To know more about triangles follow
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PLS HELP ASAP. QUESTION IN PICTURE
Answer:
80
Step-by-step explanation:
180 - 100 = 80
(Meeting character limit)
The temperature at 7:00 a.m, was 12 C, and by 7:00 p.m, it had dropped
to -10°C. Which expression represents the change in temperature:
(A 12 + (-10)
(B 12 - 10
(C -10 + 12
(D -10 - 12
Answer: D -10 - 12
Step-by-step explanation:
Temperature change is (Final T) - (Initial T)
(Final T) = -10C
(Initial T) = 12
(Final T) - (Initial T) = -10C - 12C
Temp Change - 22C
Find the perimeter of ABC with vertices A(0,-4), B(4,-4), and C(0,-1).
A. 7 units
B. 14 units
C. 12 units
D. 32 units
Answer:
C .12 units I think so if wrong I am sorry
Find cos 2α; the angle α is in the fourth quadrant, and sin α = -0.45. Which double-angle identity should you use?
cos2α = 1 – 2〖sin〗^2α
sin(α)cos(α) - cos(α)sin(α)
sin(α)cos(α)
2sin(α)cos(α)
Answer:
it is the last one
Step-by-step explanation:
me big brain
PLEASE HELP!! the polynomial expression x(2x^2+15)(4x^2+5x+3 where x is in inches can be used to model the number of cubic inches of cement that will be needed for a new porch. The cement contractor used 2 for the value of x. Determine the dimensions in inches of the cement needed for the porch. Height(shortest length side) width(medium length side) and length(longest length side)
Answer:
height 2 incheswidth 23 incheslength 29 inchesStep-by-step explanation:
For x=2, the dimensions are ...
height = x = 2 inches
width = 2x² +15 = 2(2²) +15 = 8 +15 = 23 inches
length = 4x² +5x +3 = (4x +5)x +3 = (4·2 +5)2 +3 = 29 inches
NEED HELP NOW!!!
Properties of Perpendicular Bisectors Properties of Both Perpendicular Bisectors and Angle Bisectors Properties of Angle Bisectors
The bisector passes through the midpoint of a segment
The bisector is equidistant from the endpoints of the segment
The bisector can only exist if the original figure is a line segment.
The bisector cuts the original figure into two congruent parts.
The bisector is equidistant from portions of the figure.
Only one of each type of bisector exists in a plane.
The bisector passes through the interior of an angle.
The bisector creates a right angle with the figure.
The bisector is equidistant from the sides of the angle.
Which piece of information is incorrectly placed in the table?
A. The bisector cuts the figure into two congruent parts.
B. The bisector is equidistant from portions of the figure.
C. The bisector passes through the midpoint of a segment.
D. The bisector creates a right angle with the figure.
D.
Explanation:
a landscape of farmland bisected by long straight roads"
divide into two parts.
hope I help you ☺️❤️
:) :>
What two numbers multiplied together equal 42 but when added they equal -13
Answer: -7 and -6
Step-by-step explanation:
= 3 and 1/2 × 3 and 1/2
Step-by-step explanation:
please mark me as brainlest
Alejandro uses the steps below to convert StartFraction 5 over 8 EndFraction to a percent. Five-eighths right arrow 8. 0 divided by 5 = 1. 6. 1. 6 = 160 percent. Which best explains Alejandro’s error? The division was computed incorrectly. The division was completed in the incorrect order. The decimal was moved to the right too many times. The decimal was moved to the right instead of the left.
Alejandro makes an error in the first steps he divides 8 by 5 which is incorrect he has to divide 5 by 8, and in the second step, he does not multiply the term by 100 and it can be determined by using fraction or percentage.
Given that,Alejandro uses the steps below to convert 5/8 to a percent.
8 divided by 5 = 1.6.,
1.6 = 160 percent
We have to determine,Which best explains Alejandro's error?
According to the question,Alejandro uses the steps below to convert 5/8 to a percent.
8 divided by 5 = 1.6.,
1.6 = 160 percent
The division was computed incorrectly.
The division was completed in the incorrect order. The decimal was moved to the right too many times.
The decimal was moved to the right instead of the left.
Alejandro uses the steps below to convert 5/8 to a percent.
To convert 5/8 into percentages following all the steps given below.
Step1; Firstly 5 is divided by 8,[tex]= \dfrac{5}{8} \\\\ = 0.625[/tex]
Step2; To convert 0.625 into percentage multiplied by 100,[tex]\rm = 0.625 \times 100\\\\= 62.5 \ percent[/tex]
Hence, Alejandro makes an error in the first steps he divides 8 by 5 which is incorrect he has to divide 5 by 8, and in the second step, he does not multiply the term by 100.
For more details about the Equation refer to the link given below.
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Answer:
Just tell me the letter.
Step-by-step explanation:
please help due any minute
Answer:
A the system has no solution
Step-by-step explanation:
Simplifying 2x + -5y = -8
Solving 2x + -5y = -8
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '5y' to each side of the equation. 2x + -5y + 5y = -8 + 5y
Combine like terms: -5y + 5y = 0 2x + 0 = -8 + 5y 2x = -8 + 5y
Divide each side by '2'. x = -4 + 2.5y Simplifying x = -4 + 2.5y
Solution for 2x-5=12 equation:
2x - 5 = 12
2x = 12 + 5
2x = 17 (divide both sides by 2 to get x)
2x/2 = 17/2
x = 8.5
Suppose two bicyclists start at the same location.
The first bicyclist rides due north and the other rides
due west. Find the speed that each bicyclist rode in
miles per hour if they are 8V2 miles apart after riding
for 2 hours at the same speed
Answer:
4 mi/h
Step-by-step explanation:
The distance between the cyclists is the hypotenuse of an isosceles right triangle. The hypotenuse is √2 times the length of the legs in such a triangle, so each cyclist must have ridden 8 miles in 2 hours.
Their speed is (8 mi)/(2 h) = 4 mi/h.
_____
Additional comment
Consider an isosceles right triangle with leg lengths 1. Then the Pythagorean theorem tells us the length of the hypotenuse is ...
c² = a² +b² . . . square of hypotenuse is sum of squares of legs
c² = 1² +1² . . . . both legs are 1 in our example triangle
c² = 2
c = √2
That is, the hypotenuse is √2 times the leg length.
A straight line passes through points (-1, 5) and (2, -4). What is the law of the function represented by this line?
Answer:
y = -3x+2
Step-by-step explanation:
See attachment.
Find the slope:
Rise = (-4 - 5) = -9
Run = (2 - (-1)) = 3
Slope(Rise/Run) = -3
Find the y-intercept:
y = mx + b
y = -3x + b
5 = -3*(-1)+b [Use point (-1,5)
b = 2
====
y = -3x + 2
How many points are on this plane?
Answer:
5
Step-by-step explanation:
A,B and C would be the inside of the plane not outside.
The Zenith occurs in fall equinox. At the same day, find the altitude of the sun at noon at Phnom Penh city (11.50N).
Note: subject Earth Science.
Answer:
78.50°
Step-by-step explanation:
On either equinox, the sun is overhead at the equator. At 11.50 N, the sun will be at elevation ...
90° -11.50° = 78.50°