Answer:
x = 3
area = 6
Step-by-step explanation:
using phytagoras's. theorem
a² + b² = c² (with c is the longest one)
x² + (x+1)² = 5²
x² + x² + 2x + 1 = 25
2x² + 2x - 24 = 0 (divide all by 2)
x² + x -12 = 0 then factorize
(x-3)(x+4) = 0
we get x = 3 and x = -4. Take the positive one.
so now we have x = 3 then x + 1 must be 4.
the area is
A = ½ . 3 . 4 = 6
Arguably, the top 5 race horses in U.S. history are Secretariat (S), Man O'War (M), Citation (C), War Admiral (W), and Seabiscuit (B).
Required:
a. Use this information to determine the number of possible samples (without replacement) of size 22 that can be obtained from the population of size 55.
b. If a simple random sampling procedure is to be employed, the chances that any particular sample will be the one selected are:________
Answer:
a) 10
b) 0.1 = 10%
Step-by-step explanation:
The combinations formula is used to solve this question, since the horses are chosen without replacement.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
a. Use this information to determine the number of possible samples (without replacement) of size 2 that can be obtained from the population of size 5.
Combinations of 2 objects from a set of 5. So
[tex]C_{5,2} = \frac{5!}{2!(5-2)!} = 10[/tex]
b. If a simple random sampling procedure is to be employed, the chances that any particular sample will be the one selected are:________
In this procedure, the samples are all equally as likely to be chosen.
So
1/10 = 0.1 = 10%
Sugar canes have lengths X that are normally distributed with mean 365.45 cm and standard deviation 4.9 cm what is the probability of the length of a randomly selected Cane being between 360 and 370 cm
Answer:
The probability of the length of a randomly selected Cane being between 360 and 370 cm P(360 ≤X≤370) = 0.6851
Step-by-step explanation:
step(i):-
Let 'X' be the random Normal variable
mean of the Population = 365.45
Standard deviation of the population = 4.9 cm
Let X₁ = 360
[tex]Z= \frac{x-mean}{S.D}= \frac{360-365.45}{4.9}[/tex]
Z₁ = -1.112
Let X₂ = 370
[tex]Z= \frac{x-mean}{S.D}= \frac{370-365.45}{4.9}[/tex]
Z₂ = 0.911
Step(ii):-
The probability of the length of a randomly selected Cane being between 360 and 370 cm
P(x₁≤x≤x₂) = P(z₁≤Z≤z₂)
P(360 ≤X≤370) = P(-1.11≤Z≤0.911)
= P(Z≤0.911)-P(Z≤-1.11)
= 0.5 +A(0.911) - (0.5-A(1.11)
= 0.5 +A(0.911) - 0.5+A(1.11)
= A(0.911) + A(1.11)
= 0.3186 + 0.3665
= 0.6851
The probability of the length of a randomly selected Cane being between 360 and 370 cm P(360 ≤X≤370) = 0.6851
Mary crocheted a rectangular blanket whose diagonal measures approximately 7.21 feet. What are the most likely length and width measurements of the blanket ? Select the two correct answers.
Answer:
If both sides are integers, one side will be 4 feet and the other will be 6 feet. The other solution is the symmetrical solution (4 feet instead of 6 feet, and 6 feet instead of 4 feet).
Step-by-step explanation:
We have a rectangular blanket, that has a diagonal that measures h=7.21 feet.
The two sides of the rectangle a and b can be related to the diagonal h by the Pithagorean theorem:
[tex]a^2+b^2=h^2[/tex]
Then, we can express one side in function of the other as:
[tex]a^2+b^2=h^2\\\\a^2=h^2-b^2\\\\a=\sqrt{h^2-b^2}=\sqrt{7.21-b^2}=\sqrt{52-b^2}[/tex]
Then, if we define b, we get the value of a that satisfies the equation.
A graph of values of a and b is attached.
If both side a and b are integers, we can see in the graph that are only two solutions: (b=4, a=6) and (a=4, b=6).
Can someone please help? :)
Solution,
Diameter (d)=24 cm
Radius (r)=24/2 =12 cm
Circumference of circle= 2 pi r
=2*3.14*12
= 75.36 cm
Hope it helps
Good luck on your assignment
Answer:
[tex]c = 75.36cm[/tex]
Step-by-step explanation:
[tex]d = 2r \\ 24 = 2r \\ \frac{24}{2} = \frac{2r}{2} \\ r = 12cm[/tex]
[tex]circumference \\ = 2\pi \: r \\ = 2 \times 3.14 \times 12 \\ = 75.36cm[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Use properties of multiplication to show why 4 x 50 = 8 x 25.
Enter your answers in the boxes.
4 x 50 = 4 x
x 25) = (4 x
1) x 25 =
D) x 25
Answer: use the app: photomath
Step-by-step explanation:
A random sample of 1285 residents from rural and urban areas were surveyed about their opinion about using daylight savings time. Below is the gathered data. Assuming there’s no relationship between residential area and opinion on daylight savings time, how many people who live in a rural area would you expect to be in favor of continuing to use daylight savings time? Please round up to a whole number.
Stop using Daylight Savings Time Continue using Daylight Savings Time Total
Rural 341 281 622
Urban 353 310 663
Total 694 591 1285
Pearson's Chi-square test
X-squared 0.32 df= 1 p-value ?
Answer:
The expected number of people that lives in rural areas and is in favor of continuing using daylight savings time is 287.
Step-by-step explanation:
Hello!
There were 1285 residents from rural and urban areas surveyed about their opinion about using savings time. There are two variables of interest:
X₁: Area where the resident lives, categorized: "Rural area", "Urban area".
X₂: Opinion about using daylight savings time, categorized: "Stop", "Continue".
To know how many people who live in a rural area would you expect to be in favor of continuing to use daylight savings time, you have to calculate the expected frequency for that cell (See table in attachment)
The formula to calculate the expected frequencies is:
[tex]E_{ij}= \frac{O_{i.}*O_{.j}}{n}[/tex]
i: categories in rows i=1, 2
j: categories in columns j= 1, 2
Oi.: total observations for the i-row
O.j: total observations for the j-row
The category "rural" is in the first row, so its marginal is symbolized O₁.
The category "Continue" is in the second column, so its marginal is symbolized O.₂
The expected frequency for the people that live n rural areas and is in favor of continuing using daylight savings time is:
[tex]E_{12}= \frac{O_{1.}*O.2}{n}= \frac{622*591}{1285} = 286.07= 287[/tex]
I hope this helps!
A math class is having a discussion on how to determine if the expressions 4 x minus x + 5 and 8 minus 3 x minus 3 are equivalent using substitution. The class has suggested four different methods. Which describes the correct method?
Answer:
Both expressions should be evaluated with one value. If the final values of the expressions are the same, then the two expressions must be equivalent.
Step-by-step explanation:
Answer:
The answer is:
B. Both expression should be evaluated with one value if the final values of the expressions are the same then the two expressions must be equivalent
Round 954 to the nearest hundred.
Answer:
1000
Step-by-step explanation:
5 or more add one more
4 or less let it rest
so it becomes 1000
How many school buses will be needed to take the children of Anderson school on a field trip ? Each bus can carry 60 people. 390 children and 30 adults are going on the trip
Answer:
7 school buses will be needed to take the children of Anderson school on a field trip
Step-by-step explanation:
number of children = 390
We are told that each bus carries 60 people
Therefore
60 people = 1 bus
1 person = (1 ÷ 60)
∴ 390 people = [tex]\frac{1}{60}[/tex] × [tex]\frac{390}{1}[/tex] = [tex]\frac{390}{60}[/tex] = 6.5 (approx. 7 buses)
Therefore, 7 school buses will be needed to take the children of Anderson school on a field trip, but the seventh bus will be half-filled with children.
The earth moves at about 98,000 feet per second as it resolves around the Sun. How fast is that in miles per hour?> (recall that 1 mile is 5,280.00 feet.)
Answer:
[tex]\frac{98000 ft}{1 second}\times \frac{? second}{1 hour}\times \frac{1 mile}{5280 ft}[/tex]
Step-by-step explanation:
If you cancel out the same unit, one from numerator and one from denominator, you will get mile/ hour as asked. The leftover is doing your math.
You finish your work!!
I don't care about the evaluation. I do care if you can work by yourself and understand the work
If 75 g of active ingredient powder is mixed with 400 mL NS solution, what is the final concentration? Round to the nearest hundredths (w/v).
75g/400ml: Simplify per unit
÷ by bottom.
0.1875g/ml nearest hundredth
0.19g/ml
What’s the correct answer for this?
Answer:
D
Step-by-step explanation:
JK = LM because they are equidistant from the centre and hence are equal in length
Use each number only once. Add, subtract multiply, or divide to get an awnser of 3. Use all numbers, show your work
8,6,5,9,1
Answer:
these are my answers:
8-5=3
2÷6=3
5-2=3
2+1=3
3÷9=3
Answer:
9 +6 +1 -8 -5 = 3
Step-by-step explanation:
There are numerous possibilities. Among them are ...
9 +6 +1 -8 -5 = 3
(9-5)·1·6/8 = 3
(9·8)/(6·(5-1)) = 3
A travel magazine conducts an annual survey where readers rate their favorite cruise ship. Ships are rated on a 10 point scale, with higher values indicating better service. A sample of 20 ships that carry fewer than 500 passengers resulted in a average rating of 6.93 with standard deviation 0.31. A sample of 55 ships that carry more than 500 passengers resulted in an average rating of 7.07 with standard deviation 0.6. statcrunch. Assume that the population standard deviation is 4.58 for ships that carry fewer than 500 passengers and 3.95 for ships that carry 500 or more passengers.
Round your all answers to two decimal places.
a. What is the point estimate of the difference between the population mean rating for ships that carry fewer than 500 passengers and the population mean rating for ships that carry 500 or more passengers?
b. At 95% confidence, what is the margin of error?
c. What is a 95% confidence interval estimate of the difference between the population mean ratings for the two sizes of ships?
Answer:
a) The point estimate of the difference between the populations is Md=-0.14.
b) The margin of error at 95% confidence is 0.212.
c) The 95% confidence interval for the difference between means is (-0.352, 0.072).
Step-by-step explanation:
We have to calculate a 95% confidence interval for the difference between means.
The sample 1 (ships under 500 passengers), of size n1=20 has a mean of 6.93 and a standard deviation of 0.31.
The sample 2 (ships over 500 passengers), of size n2=55 has a mean of 7.07 and a standard deviation of 0.6.
The difference between sample means is Md=-0.14.
[tex]M_d=M_1-M_2=6.93-7.07=-0.14[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{0.31^2}{20}+\dfrac{0.6^2}{55}}\\\\\\s_{M_d}=\sqrt{0.005+0.007}=\sqrt{0.011}=0.11[/tex]
The critical t-value for a 95% confidence interval is t=1.993.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_{M_d}=1.993 \cdot 0.11=0.212[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M_d-t \cdot s_{M_d} = -0.14-0.212=-0.352\\\\UL=M_d+t \cdot s_{M_d} = -0.14+0.212=0.072[/tex]
The 95% confidence interval for the difference between means is (-0.352, 0.072).
In a recent survey, 70% of HR directors thought that it was very important for business students to take a course in business ethics. For a sample of 12 HR directors, what is the probability that at least one of them does not think it very important for business students to take a business ethics course
Answer:
0.9862
Step-by-step explanation:
Given: According to 70% of HR directors, business students should take a course in business ethics.
To find: the probability that at least one of a sample of 12 HR directors does not think it very important for business students to take a business ethics course
Solution:
Probability refers to chances of occurrence of an event.
According to 70% of HR directors, business students should take a course in business ethics.
Therefore,
Probability that at least one of a sample of 12 HR directors does not think it very important for business students to take a business ethics
= 1 - Probability that everyone of a sample of 12 HR directors think that it very important for business students to take a business ethics
= [tex]1-\left ( \frac{70}{100} \right )^{12}[/tex]
[tex]=1-\left ( \frac{7}{10} \right )^{12}[/tex]
[tex]=1-(0.7)^{12}\\=1-0.0138\\=0.9862[/tex]
which equation represents a circle with a radius of 8 centered at (-3,4)
Answer:
(x+3)^2 + (y-4)^2 = 64
Step-by-step explanation:
We can write the equation of a circle as
(x-h)^2 + (y-k)^2 = r^2 where ( h-k) is the center and r is the radius
(x--3)^2 + (y-4)^2 = 8^2
(x+3)^2 + (y-4)^2 = 64
in a poll 267 students voted. nominee c received 2/3 of the votes. how many votes did nominee c receive?
Answer:
89
Step-by-step explanation:
2/3 times 267 is 178 after that you have to sub 178 from 267
A truck was purchased for $120,000 and it was estimated to have a $24,000 salvage
value at the end of its useful life. Monthly depreciation expense of $2,000 was recorded
using the straight-line method. The annual depreciation rate is
Answer:
25
Step-by-step explanation:
What’s the correct answer for this? Select all the apply
Answer:
B and C
Step-by-step explanation:
AP = BP
OC = OD
The expression (2x + 1)4 is expanded and simplified. Which monomial listed below is a term in the result? 8x3 12x3 32x3 48x3
Answer:
32x^3
Step-by-step explanation:
[tex](2x+1)^4=(2x)^4+4(2x)^3(1)+6(2x)^2(1)^2+4(2x)(1)^3+(1)^4\\\\=16x^4 +\boxed{32x^3} +24x^2+8x+1[/tex]
_____
Comment on the question
It is helpful if you designate exponents with a caret (^). We expect the expanded form of (2x+1)4 to be 8x+4. (2x+1)^4 is entirely different. Similarly, 8x3 = 24x, whereas 8x^3 is something else.
32x^3
It is helpful if you designate exponents with a caret (^). We expect the expanded form of (2x+1)4 to be 8x+4. (2x+1)^4 is entirely different. Similarly, 8x3 = 24x, is the answer to the question
6114 chocolate bars are to shared equally between 24 large cake mixes how many bars does each cake mix get
Answer:
146,736
Step-by-step explanation:
6114 divided by 24 is 146,736
The linear equation graphed above gives the height in feet above the ground of Shelly t seconds after she opened her parachute when jumping from an airplane. According to the graph, how many seconds after opening her parachute will Shelly be 2,000 feet above the ground?
Answer:
[tex]\large \boxed{\text{60 s}}[/tex]
Step-by-step explanation:
Assume your graph looks like the one below.
1. Calculate the equation of the straight line
The slope-intercept equation for a straight line is
y = mx + b
where m is the slope of the line and b is the y-intercept.
The line passes through the points (0,2600) and (30, 2300)
(a) Calculate the slope of the line
[tex]\begin{array}{rcl}m & = & \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\ & = & \dfrac{2300 - 2600}{30 - 0}\\\\& = & \dfrac{-300}{30}\\\\& = & \text{-10 ft/s}\\\\\end{array}[/tex]
(b) Locate the y-intercept
The y-intercept is at 2600 ft
(c) Write the equation for the line
h = -10t + 2600
(d) Calculate the time to 2000 ft
[tex]\begin{array}{rcl}h & = & -10t + 2600\\2000 & = & -10t + 2600\\-600 & = & -10t\\t & = & \dfrac{-600}{-10}\\\\& = & \text{60 s}\\\end{array}\\[/tex]
Shelley will be at 2000 ft 60 s after opening the parachute.
Let the given line pass through the point that is [tex]\bold{(0,2600)\ \ and\ \ (20, 2400)}[/tex]
[tex]\therefore[/tex]
[tex]\to \bold{\frac{H-2400}{t-20}} \bold{= \frac{2600-2400}{0-20}}\\\\[/tex]
[tex]\bold{=\frac{200}{-20} }\\\\ \bold{= -\frac{200}{20}}\\\\ \bold{= - 10}\\\\[/tex]
[tex]\to \bold{H-2400=-10t+200}\\\\\to \bold{H+10t=2400+200}\\\\\to \bold{H+10t=2600}\\\\\to \bold{H=2600-10t}\\\\[/tex]
Let
time (t) in second
Height (h) in feet
for [tex]\bold{\ H=2000\ feet\\}[/tex]
[tex]\to \bold{2000=2600-10t}\\\\\to \bold{10t = 2600- 2000}\\\\\to \bold{10t = 600}\\\\\to \bold{t=\frac{600}{10}}\\\\\to \bold{t= 60\ second}\\\\[/tex]
Learn more:
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need!!!!!!!!!!!help!!!!!!Asap!!!!!!
Answer:
225 feet below sea level (or -225 feet)
Step-by-step explanation:
My apologies in advance if this does not format the way its supposed to. The way I did it includes arrows and may work best on a computer.
Problem: A submarine that is 245 feet below sea level descends 83 feet and then ascends 103 feet. Which represents the location of the submarine compared to sea level.
Math: Ok, so we know that whenever something descends, that means it is going down, so let's use a negative sign. These means when something ascends, it goes up. Let's use a positive sign here. Also, note the fact that we start 245 feet below sea level. This means we should start at -245.
Now, using the data we have, let's create a math problem.
A submarine that is 245 feet below sea level descends 83 feet and then ascends 103 feet. Which represents the location of the submarine compared to sea level.
-245 <---- beginning level
-83 <---- the submarine descends
+103 <---- the submarine ascends
_______
?
So grab a calculator to do this part, or do it on your own. Once you finish, plug in the answer.
-245 -245
-83 -83
+103 ---------------> +103
______ ________
? -225 feet
So as you can see, the final answer would be -225 feet or 225 feet below sea level.
Hope this helped! Have a great day!
A diameter of a particular circle has endpoints at A(-1, -2) and B(3,10). Which of the following is the
slope of the tangent drawn to this circle at point B?
A) -1/2
B) 4/5
C) -1/3
D) -4
Answer:
Option C) is correct
Step-by-step explanation:
Given: Endpoints of the diameter of the circle are A(-1, -2) and B(3,10)
To find: slope of the tangent drawn to the circle at point B
Solution:
Let [tex](x_1,y_1)=(-1,-2)\,,\,(x_2,y_2)=(3,10)[/tex]
Centre of the circle = [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})=(\frac{-1+3}{2},\frac{-2+10}{2})=(1,4)[/tex]
Let [tex](h,k)=(1,4)[/tex]
Distance formula states that distance between points (a,b) and (c,d) is given by [tex]\sqrt{(c-a)^2+(d-b)^2}[/tex]
Radius of the circle = Distance between points [tex](-1,-2)[/tex] and [tex](1,4)[/tex] = [tex]\sqrt{(1+1)^2+(4+2)^2}=\sqrt{4+36}=\sqrt{40}[/tex] units
Let r = [tex]\sqrt{40}[/tex] units
Equation of a circle is given by [tex](x-h)^2+(y-k)^2=r^2[/tex]
[tex](x-1)^2+(y-4)^2=\left ( \sqrt{40} \right )^2\\(x-1)^2+(y-4)^2=40[/tex]
Differentiate with respect to x
[tex]2(x-1)+2(y-4)\frac{\mathrm{d} y}{\mathrm{d} x}=0\\\frac{\mathrm{d} y}{\mathrm{d} x}=\frac{1-x}{y-4}[/tex]
Put [tex](x,y)=(3,10)[/tex]
[tex]\frac{\mathrm{d} y}{\mathrm{d} x}=\frac{1-3}{10-4}=\frac{-2}{6}=\frac{-1}{3}[/tex]
So,
slope of the tangent drawn to this circle at point B = [tex]\frac{-1}{3}[/tex]
Find the inequality represented by the graph
Answer:
There is no graph to find an inequality on...
Step-by-step explanation:
tg105°-cotg105° = ?
Please help fast!!! Please
Using only the trig ratios of 45 and 60 degrees, we use angle-sum to compute [tex]\tan 105^\circ=\tan(60^\circ+45^\circ)=\frac{\tan 60^\circ+\tan 45^\circ}{1-\tan 60^\circ\tan 45^\circ}=\frac{\sqrt{3}+1}{1-\sqrt{3}}=-2-\sqrt{3},[/tex] so [tex]\cot 105^\circ=\frac{1}{\tan 105^\circ}=-2+\sqrt{3}[/tex] and [tex]\tan 105^\circ-\cot105^\circ=\boxed{-2\sqrt{3}}.[/tex]
PLEASE HELP ITS URGENT! 20 POINTS WORTH (basic inverse function question)
Answer:I believe the answer is -1,-4 lies on the graph
Step-by-step explanation:
Some accounting firms give the client an option to pay a fee when the tax return is completed that guarantees tax advices and support from the accountant if the client were audited. A large accounting firm is trying to determine what fee to charge for nextyear's returns. In previous years, the actual mean cost to the firm for attending a client audit session was $690. To determine if this cost has changed, the firm randomly samples 35 client audit fees. The sample mean audit cost was $700 with a standard deviation of $65.
Required:
a. Develop a 90% confidence interval estimate for the mean audit cost.
b. Based on your confidence interval, what do you think of the claim that the mean cost has changed?
1. The interval does not contain the historical data mean $690, which supports claim the mean cost has changed.
2. The interval contains historical data mean $690, which supports the claim the mean cost has changed.
3. The interval does not contains historical data mean $690, which does not support the claim it has changed.
4. The interval contains historical data mean $690, which does not support the claim the mean cost has changed.
Answer:
a) $700+/-$18.07
Therefore,the 90% confidence interval (a,b)
= ($681.93, $718.07)
b) 4. The interval contains historical data mean $690, which does not support the claim the mean cost has changed.
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = $700
Standard deviation r = $65
Number of samples n = 35
Confidence interval = 90%
z(at 90% confidence) = 1.645
a. Develop a 90% confidence interval estimate for the mean audit cost.
Substituting the values we have;
$700+/-1.645($65/√35)
$700+/-1.645($10.98700531147)
$700+/-$18.07362373736
$700+/-$18.07
Therefore,the 90% confidence interval (a,b) = ($681.93, $718.07)
b) Since, $690 is contained between the 90% confidence interval of ($681.93, $718.07). It implies that the mean cost has not changed.
4. The interval contains historical data mean $690, which does not support the claim the mean cost has changed.
which multiplication equation can be used to explain the solution to 15 divided by 1/3
1) 5 x 3 =15
2) 45 x 1/3
3) 1/3 x 15 =5
4) 1/5 x 15 =3
Answer:
Step-by-step explanation:
"15 divided by 1/3" comes out to:
15 15 3
------- = -----* ----- = 45
1/3 1 1
Recall that to divide 15 by 1/3 we invert 1/3, obtaining 3, and then multiply 15 by 3. The correct result is 45.
Multiplication equation B can be used to explain the solution to 15 divided by 1/3. Option 2 is correct.
What is the definition of arithmetic operation?Arithmetic is a branch of mathematics that studies numbers and the various operations that can be applied to them. The four basic math operations are addition, subtraction, multiplication, and division.
The solution of the expression is;
[tex]x= \frac{15}{\frac{1}{3} } \\\\\ x= 15 \times 3\\\\ x=45[/tex]
The answer of the given equation resembles the option B. Multiplication equation B can be used to explain the solution to 15 divided by 1/3
Hence, option 2 is correct.
To learn more about the arithmetic operation, refer;
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Reduce the fraction to lowest terms. Do not use spaces in your answer.
Answer:
(r-s)/(r+s)
Step-by-step explanation:
Factor out the 5
