The confidence interval for confidence level of [tex]1-\alpha[/tex] is
[tex]\left(\overline x-Z_{\alpha/2}\dfrac\sigma{\sqrt n},\overline x+Z_{\alpha/2}\dfrac\sigma{\sqrt n}\right)[/tex]
where [tex]\overline x[/tex] is the sample mean, [tex]Z_{\alpha/2}[/tex] is the critical value for the given confidence level, [tex]\sigma[/tex] is the standard deviation of the population, and [tex]n[/tex] is the sample size. The margin of error is the [tex]Z_{\alpha/2}\dfrac\sigma{\sqrt n}[/tex] term.
a) For a confidence level of [tex]1-\alpha=0.90[/tex], we have [tex]Z_{\alpha/2}=Z_{0.05}\approx1.64[/tex]. So in order to have a margin of error of at most 25 points, we have
[tex]1.64\dfrac{250}{\sqrt n}=25\implies n\approx268.96[/tex]
so Raina should collect a sample of at least 269 students.
b) A confidence interval with a higher confidence level would more closely approximate and reflect the population, so it stands to reason that Luke should collect a larger sample than Raina to meet his 99% confidence spec.
c) For a confidence level of [tex]1-\alpha=0.99[/tex], we have [tex]Z_{\alpha/2}=Z_{0.005}\approx2.58[/tex]. Then the margin of error would at most satisfy
[tex]2.58\dfrac{250}{\sqrt n}=25\implies n\approx665.64[/tex]
so that Luke should collect a sample of at least 666 students.
To calculate the sample size required for a given margin of error in a confidence interval, you can use the formula: n = (z * σ) / E. For Raina's 90% confidence interval with a margin of error of 25, she should collect a sample size of 17. Luke's sample size for a 99% confidence interval should be larger than Raina's, and he should collect a minimum sample size of 26.
Explanation:To calculate the sample size required for a given margin of error in a confidence interval, you can use the formula:
n = (z * σ) / E
Where:
n = sample size
z = z-score corresponding to the desired confidence level
σ = standard deviation of the population
E = margin of error
(a) To find the sample size for Raina's 90% confidence interval with a margin of error of 25, we plug the values into the formula:
n = (1.645 * 250) / 25 = 16.45
Since sample sizes must be whole numbers, Raina should collect a sample size of 17.
(b) Luke's 99% confidence interval will require a larger sample size because the z-score for 99% confidence is larger than for 90% confidence. Therefore, without calculating the actual sample size, we can determine that Luke's sample size should be larger than Raina's.
(c) To calculate the minimum required sample size for Luke's 99% confidence interval, we use the same formula and plug in the values:
n = (2.576 * 250) / 25 = 25.76
Rounding up, Luke should collect a minimum sample size of 26.
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There are 325 children at a zoo. If 64% of the children are boys and the rest are girls, how many children at the zoo are girls?
*Please Show Work*
Answer:
117 girls
Step-by-step explanation:
If 64% are boys, the percentage of girls can be found by subtracting this amount from 100:
100 - 64 = 36
So 36% of 325 are girls.
To find the amount from a percentage use the following formula:
Original amount * [tex]\frac{percentage}{100}[/tex]
Now plug these values in:
[tex]325 * \frac{36}{100}[/tex] = 117
So there are 117 girls in the 325 children.
Answer:
117
Step-by-step explanation:
If 64% are boys, then 36% are girls. 36% of 325 equals 117, so there are 117 girls at the zoo.
The table shows the total distance (d), in kilometers, a bicycle traveled after t hours.
Time in hours (t) Distance in kilometers (d)
(t) (d)
0 0
1 8
2 16
Which equation shows the relationship between d and t?
d=8t
d=16t
d=t+8
d=t+16
Answer:
d = 8t
Step-by-step explanation:
To find a correlation, you need to find what numbers correlate and how.
Lets try multiplying the t value by 8 to get the value ( as one value is 1 and the other is 8 so it would seem suitable)
1 * 8 = 8
2 * 8 = 16
Both values match up which means that to get d, you multiply t by 8.
This means that your answer is d = 8t.
Which situation can be modeled by the inequality 48−10x≥8?
A. You have $48 to spend on socks, but you need to save at least $8 to pay for the bus trip home. You plan to spend the rest on socks at $10 each (including tax).
B. You loaned $48 to your older brother. He pays you $8 a week and needs to pay you back within 10 weeks.
C. You can buy socks in packages of 10 pairs. You have $48 to spend but want to have at least $8 left.
D. You owe your parents $48 and plan to pay them $10 a week until you owe them less than $8.
Answer:
A. You have $48 to spend on socks, but you need to save at least $8 to pay for the bus trip home. You plan to spend the rest on socks at $10 each (including tax).
Step-by-step explanation:
cause it's A
Answer:
A. You have $48.00 to spend on socks, but you need to save at least $8.00 to pay for the bus trip home. You plan to spend the rest on socks at $10.00 each (including tax).
Step-by-step explanation:
Tanya's science class had a quiz on 13 of the first 40 days of class. Which is this ratio as a decimal?
Answer:
.325
Step-by-step explanation:
If she had a quiz on 13 of the 40 days , the fraction is 13/40
13/40 = .325
Answer: The fraction of the days on which the quiz has been held expressed as a decimal is 0.325
Step-by-step explanation:
Decimal numbers are not considered as integers. They are rounded off to write an integer.
Fraction is present in the form of [tex]\frac{p}{q}[/tex] where [tex]q\neq 0[/tex]
We are given:
Number of days, the class had quiz = 13
Total number of days = 40
The fraction becomes: [tex]\frac{13}{40}[/tex]
Expression this as a decimal = 0.325
Hence, the fraction of the days on which the quiz has been held expressed as a decimal is 0.325
Elissa wants to set up a rectangular dog run in her backyard. She has 32 feet of fencing to work with and wants
to use it all. If the dog run is to be x feet long, express the area of the dog run as a function of x.
Perhaps jumping up the points will get answers.
A(x) = x(16 -x)
Step-by-step explanation:Area is the product of length and width. If the length is x, then the width will be half of the total perimeter less the two sides of length x, (32-2x)/2 = 16-x.
So, the area is ...
... A = length · width
... A(x) = x(16 -x)
_____
If you like, you can expand this to ...
... A(x) = -x² +16x
The area of a rectangular figure is calculated by multiplying the length and the width of the figure. So, the area as a function of x is: [tex]A(x) = x(16 - x)[/tex]
Given that:
[tex]P = 32[/tex] --- the perimeter of the fence
Represent
[tex]x \to[/tex] length
[tex]y \to[/tex] width
The perimeter of a rectangular fence is calculated as:
[tex]Perimeter = 2 \times (Length + Width)[/tex]
So, we have:
[tex]P= 2 \times (x+ y)[/tex]
[tex]32= 2 \times (x+ y)[/tex]
Divide both sides by 2
[tex]16= x+ y[/tex]
Make y the subject
[tex]y = 16 - x[/tex]
The area (A) of the fence is:
[tex]Area = Length \times Width[/tex]
So, we have:
[tex]A = x \times y[/tex]
Substitute [tex]y = 16 - x[/tex]
[tex]A = x \times (16 - x)[/tex]
[tex]A = x(16 - x)[/tex]
So, the area as a function of x is:
[tex]A(x) = x(16 - x)[/tex]
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If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 ft per second, then its height h after t seconds is given by the equation h(t) = -16t ^2 + 128t. What is the height after 60 seconds?
Answer:
undefined
Step-by-step explanation:
t=60 is outside the domain of the function, which is t ∈ [0, 8].
_____
If you take the function and the time at face value, ...
... h(60) = -49920 . . . feet, more than 9.4 miles below ground level*
___
*The deepest hole ever drilled into the Earth is 40,230 feet deep, so this is almost 2 miles deeper.
Answer:
C) 8 seconds
Step-by-step explanation:
find the value of the following expression. Write your answers without any exponents.
a)7^-2=1/7^2=1/49
b) (8^4)^2/8^11=8^8/8^11=1/8^3=1/512.
To find the value of an expression without exponents, divide numbers and subtract the exponents for division, and when squaring, multiply the number by itself. Any number raised to the power of 2 is squared, and to the power of 3 is cubed.
Explanation:To find the value of an expression without any exponents, you might need to use the rule: to divide two exponential numbers, divide the numbers out front and subtract the exponents. Here's an example:
If we have to find the value of 106 ÷ 103, you'll divide 10 by 10 (which is 1) and subtract the exponents (6 - 3), resulting in 103, which equals to 1000 when you remove the exponent.
In the context of squaring exponents, when you square a number like 52, it means 5 x 5, which equals 25. Squaring is also known as raising to the power of 2. Similar to this, any number raised to the power of 3 is said to be cubed.
These concepts are fundamental when calculating extreme values like $rac{4.81x10^4}{2.05x10^2}$, solving quadratics, and handling scientific notations.
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What is the
GCF of 4 and 3?
Answer:
12
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
The factors of 3 are: 1, 3
The factors of 4 are: 1, 2, 4
Then the greatest common factor is 1.
Teachers' salaries in north dakota the average teacher's salary in north dakota is $35,441. assume a normal distribution with s $5100.
a. what is the probability that a randomly selected teacher's salary is greater than $45,000?
b. for a sample of 75 teachers, what is the probability that the sample mean is greater than $38,000?
Answer:
a) about 3.0%b) about 7×10^-6Step-by-step explanation:
These sorts of calculations are best done with a calculator that knows statistics.
a) The z-value of the limit ofv interest is (45,000 -35,551)/(5100) ≈ 1.8743. The empirical rule tells you between 16 and 2.5% of the distribution will lie above a limit that is between 1 and 2 standard deviations. So, our calculator value of 3% is approximately correct.
b) The standard deviation of the sample mean is reduced by a factor of √75 from that of the parent distribution for a sample size of 75. Then the z-value is ...
... (38,000 - 35,441)/(5100/√75) ≈ 2559/588.90 ≈ 4.345
The probability of exceeding this valus is pretty small, about 6.95×10^-6.
This is a plane with two axes as a frame of reference. The x-axis is a horizontal line and the y-axis is perpendicular to it (i.e., the y-axis is vertical). The intersection of the two axes is called the origin.
Answer:
Coordinate Plane
Step-by-step explanation:
This is a plane with two axes as a frame of reference. The x-axis is a horizontal line and the y-axis is perpendicular to it (i.e., the y-axis is vertical). The intersection of the two axes is called the origin.
Answer with explanation:
≡This plane is Called→ Two Dimensional Coordinate plane or x y plane.And the given statement is true Statement.
The Plane has two axes as a frame of reference. The x-axis is a horizontal line and the y-axis is perpendicular to it (i.e., the y-axis is vertical). The intersection of the two axes is called the origin.
⇒The value of x lies from (-∞,∞) .x∈[-∞,∞]
And ⇒,the value of y lies from (-∞,∞).y∈[-∞,∞]
And the points in this plane is represented in terms of Ordered pairs that is in the form of , (x,y).
→There are four Quadrants , in this plane and description of points is as follows:
In First Quadrant , both ,x and y positive.
In Second Quadrant ,x negative, and y positive.
In Third Quadrant ,x negative and y Negative.
In Fourth Quadrant ,x positive and y Negative.
A bridge over a gorge is supported by an arch in the shape of a semi-ellipse. The length of the bridge is 400 ft. and the maximum height is 100 ft. Draw a picture of the problem and label it with numeric values. Find the height of the arch 50 ft. from the center. Round to the nearest foot.
Final answer:
To find the height of the arch 50 ft. from the center, we can use the equation of a semi-ellipse. The height of the arch is approximately 31 ft. when rounded to the nearest foot.
Explanation:
To find the height of the arch 50 ft. from the center, we can use the equation of a semi-ellipse. The equation of a semi-ellipse with a length of a and a maximum height of b is given by: ((x^2)/(a^2))+((y^2)/(b^2)) = 1. In this case, the length of the bridge is 400 ft. and the maximum height is 100 ft., so we have: ((x^2)/(200^2))+((y^2)/(100^2)) = 1. To find the height when x = 50 ft., we substitute x = 50 into the equation and solve for y. Plugging in the values, we get: ((50^2)/(200^2))+((y^2)/(100^2)) = 1. Simplifying, we have: (2500/40000)+((y^2)/(100^2)) = 1.
Multiplying both sides by 40000 to get rid of the denominators, we have: 2500 + 400((y^2)/10000) = 40000. Simplifying further, we get: 2500 + 40(y^2) = 40000. Subtracting 2500 from both sides, we have: 40(y^2) = 37500. Dividing both sides by 40, we have: (y^2) = 937.5. Taking the square root of both sides, we have: y = 30.62. So, the height of the arch 50 ft. from the center is approximately 31 ft. when rounded to the nearest foot.
Jaden made a pot of chili with 48 ounces of ground beef and 2 tablespoons of chili powder. He made another pot of chili with the same amount of ground beef, but he used 3 times as much chili powder. How many pounds of ground beef per tablespoon of chili powder did he use in the second pot of chili
Answer:
So, it is given to us that Jaden has 3 pound of beef in the first pot and 2 table spoons of chili powder.
(16 ounces = 1 pound)
(48 ounces = 3 pounds)
In he second bowl he uses the SAME amount of beef and 3 times as much chili powder.
Which means that he used 3 pounds of beef and 2*3 = 6 table spoons of chili powder in the second cup.
The question is asking you for the ratio between the two quantities in a cryptic manner.
so, it would end up being 3 pounds of beef every 6 table spoons of chili powder, which is nothing but Half (0.5 pounds of beef every tablespoon of chili powder).
1/2 pounds of beef every tablespoon of chili powder.
HOPE THIS HELPS!
Jaden used 0.5 pounds of beef for every tablespoon of chili powder in the second pot of chili when he tripled the amount of chili powder while keeping the amount of beef unchanged.
Explanation:In the first pot of chili, Jaden effectively used 48 ounces of beef per 2 tablespoons of chili powder. This equates to 24 ounces of beef per tablespoon of chili powder. However, when Jaden tripled the amount of chili powder in the second pot, the ratio of beef to chili powder decreased since more chili powder is being used for the same amount of beef. Therefore, since he used three times as much chili powder in the second pot, this resulted in a ratio of 48 ounces of beef per 6 tablespoons of chili powder. That equates to 8 ounces of beef for every tablespoon of chili powder which are used in the second pot. Furthermore, since 1 pound equals 16 ounces, the number of pounds of beef used per tablespoon of chili powder in the second pot is 8/16, or 0.5 pounds.
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Algebra help anyone?
Answer:
The answer is 20
Step-by-step explanation:
Given that f(2)=1/5
And f(n+1)=f(n)*10
Let's start from n=2
f(2+1)=f(2)*10
f(3)=(1/5)*10
f(3)=2
Now let's take n=3
f(3+1)=f(3)*10
f(4)=2*10
f(4)=20
I paid $8.50 each for movie tickets and i spend a total of $144.50. If n, represents how many tickets i bought, write and equation that would allow me to find the number of tickets
Answer:
the Answer would be 17. Hope it helped ; )
Step-by-step explanation:
Carrie has 2 meters of ribbon. She cuts off pieces of ribbon that are 5/10 meter, 1/10 meter, and 7/10 meter. How long is the remaining piece of ribbon?
Answer:
[tex]\frac{7}{10}[/tex]
Step-by-step explanation:
Carrie has 2 meters of ribbon. She cuts off pieces of ribbon that are 5/10 meter, 1/10 meter, and 7/10 meter
Lets add all the cut of pieces and subtract it from 2 meters
[tex]\frac{5}{10} +\frac{1}{10}+\frac{7}{10}=\frac{13}{10}[/tex]
Now we subtract 13/10 from 2 meters
[tex]2 - \frac{13}{10}[/tex]
To subtract , make the denominator same
[tex]\frac{2*10}{1*10} - \frac{13}{10}=\frac{20}{10} - \frac{13}{10}=\frac{7}{10}[/tex]
7/10 meter is the remaining piece of ribbon
After adding the lengths of the ribbon pieces Carrie cut (1.3 meters), the remaining ribbon length is calculated by subtracting this from the original length, leaving Carrie with 0.7 meters of ribbon.
Explanation:Carrie starts with 2 meters of ribbon and cuts off pieces measuring 5/10 meter, 1/10 meter, and 7/10 meter. To find the length of the remaining ribbon, we need to add the lengths of the pieces she has cut and then subtract this total from the original length of the ribbon.
First, we add the lengths of the cut pieces: 5/10 meter + 1/10 meter + 7/10 meter = 13/10 meters or 1.3 meters.Next, we subtract this total from the original 2 meters: 2 meters - 1.3 meters = 0.7 meters.Therefore, the remaining piece of ribbon is 0.7 meters long.
the system of equations n=m and n=4m is the point (0,0). which of the following statements is true.
A. (0,0) is a solution to n=m and to n=4m.
B.No point no the line n=m is also on the line n=4m.
C.every solution to n=m is also a solution to n=4m.
D.the graph of the solution is parallel lines.
A. (0,0) is a solution to n=m and to n=4m.
Step-by-step explanation:The equations can be solved by any of the usual means. Using substitution, we have ...
... m = n = 4m
... m(4 -1) = 0 . . . . subtract the left side
... m = 0 . . . . . . . . divide by 3
... n = m = 0
The solution is (m, n) = (0, 0).
Answer:
the answer is A, my answer got deleted
Solve. 4x+5y=40
3x=15
POSSIBLE ANSWERS:
1. x=5, y=−12
2. x=5, y=−4
3. x=5, y=4
4. x=5, y=12
Answer:4(5) + 5(4)=40 ...3(5)=15
So 20+20=40 ...15=15
I Say Answer Is 3. X=5, Y=4
Step-by-step explanation:
What is 35.6 × 10−4 in standard form?
[tex]35.6\times10^{-4}=35.6\times0.0001=0.00356[/tex]
[tex]a^{-n}=\dfrac{1}{a^n}\\\\10^{-4}=\dfrac{1}{10^4}=\dfrac{1}{10000}=0.0001[/tex]
Final answer:
0.00356.
Explanation:
The question requires us to express the product of a decimal number and a power of ten in standard form. To find 35.6 times 10^-4 in standard form, we can use the rule of multiplying a decimal number by a power of ten. Multiplying by 10^-4 means we move the decimal point four places to the left.
So, 35.6 × 10^-4 becomes 0.00356. This is the number 35.6 shifted four decimal places to the left, as the exponent on the ten is negative, indicating division by ten for each unit of the exponent.
Joe walked 2/6 of a mile on Monday. On Tuesday he walked another 2/9 of a mile. How far did joe walk on Monday and Tuesday?
Answer: 5/9 of a mile
Step-by-step explanation:
2/6 + 2/9
3/9 + 2/9
5/9
a b c or d please hurry thanks!
Answer:
C) a = 10√3, b = 5√3, c = 15 , d = 5
Step-by-step explanation:
Here we use the ratio of 30, 60, 90 degree triangle.
The ratio of sides, 1:√3:2
2x = 10
x = 5
d = 5
b = 5√3
c = 5√3√3
c = 5*3 = 15
c = 15
a = 2(5√3)
a = 10√3
Therefore, a = 10√3, b = 5√3, c = 15 and d = 5
Thank you.
Answer:
The correct answer is C.
Step-by-step explanation:
From the [tex]60\degree[/tex] right angle triangle
[tex]\sin(60\degree)=\frac{b}{10}[/tex]
[tex]10\times \sin(60\degree)=b[/tex]
[tex]10\times \frac{\sqrt{3}}{2}=b[/tex]
[tex]5\sqrt{3}=b[/tex]
From the same [tex]60\degree[/tex] right angle triangle,
[tex]\cos(60\degree)=\frac{d}{10}[/tex]
[tex]10\times \cos(60\degree)=d[/tex]
[tex]10\times \frac{1}{2}=d[/tex]
[tex]5=d[/tex]
From the [tex]30\degree[/tex] right angle triangle
[tex]\sin(30\degree)=\frac{b}{a}[/tex]
[tex]\frac{1}{2}=\frac{5\sqrt{3}}{a}[/tex]
[tex]a=2\times 5\sqrt{3}[/tex]
[tex]a=10\sqrt{3}[/tex]
From the same [tex]30\degree[/tex] right angle triangle,
[tex]\cos(30\degree)=\frac{c}{a}[/tex]
[tex]\frac{\sqrt{3}}{2}=\frac{c}{10\sqrt{3}}[/tex]
[tex]10\sqrt{3} \times \frac{\sqrt{3}}{2}=c[/tex]
[tex]5 \times 3=c[/tex]
[tex]c=15[/tex]
The correct answer is C.
Which description best defines MN¯¯¯¯¯¯¯ ?
the set of point M, point N, and all the points between point M and point N
the set of all points that are collinear with point M and point N
the set containing point M and point N
the set of all points that are the same distance from point M as point N
the set of point M, point N, and all the points between point M and point N
Step-by-step explanation:We assume you're interested in a description of line segment MN, the portion of the line containing M and N that has endpoints M and N. That description is found in "Answer:" above.
Other choices:
... all collinear points: describes line MN, not segment MN
... point M and point N: describes two points, not a line segment
... points the same distance from each: describes the line that is the perpendicular bisector of segment MN
Answer:
the set of point M, point N, and all the points between point M and point N
Step-by-step explanation:
Can someone please help me with this?
P=2l+2w and you're looking for what l is. The answer should be an equation.
Thanks so much!!!
Answer:
l = (P -2w)/2
Step-by-step explanation:
When you're working any "solve for ..." problem, first you look to see where the variable of interest is and what is done to it.
If it is only found on one side of the equation, as here, then you're in luck. If it is only found in one term, as here, you have even better luck.
Identify all the terms on the side of the equation where the variable is located that do not contain the variable. Add their opposite to both sides of the equation. The result will be a term containing the variable, equated to a bunch of other stuff.
... P -2w = 2l . . . . . we added -2w to both sides of the equation
Now, we divide the equation by the coefficient of the variable.
... (P -2w)/2 = (2l)/2
... (P -2w)/2 = l . . . . . . simplify. This is the solution you're looking for
If you like, you can distribute the multiplication by (1/2) to get
... l = P/2 - w
Month Money
1 $500
2 $525
3 $551.25
4 $578.81
The table shows the relationship between the amount of money in a bank account at the end of each month. Determine whether it's a growth or decay and whether it grows or decays by a constant percent. A) decays by percent that varies B) decays by a constant percent C) grows by percent that varies D) grows by a constant percent
Answer:
"Grows by a constant percent."
Step-by-step explanation:
5% of 500 is 25 = 525
5% of 525 is 26.25 = 551.25
5% of 551.25 is 27.56 = 578.81
Please leave a thanks. And can I have Brainliest?
3 1/4 yards is how many inches
Answer: it is 117 inches.
Step-by-step explanation:
1 yard= 36 inches
36 times 3= 108
1/4 of 36= 9
36 divided by 4 is 9 so 1/4 of 36 is 9.
108 + 9= 117
1. 2 + √c = 27
625
5
841
12.5
5.4
2.
Solve
√x = 3
81
3
1.7
27
9
3. √(x-2) = 4
14
0
18
4
16
4. Solve
1.8
2
21.6
216
18
5. √(2x) = 1
0.5
1.4
0.25
4
2
Get the surd by itself, then square and solve the resulting linear equation.
1. Subtract 2, then square
... √c = 25
... c = 25² = 625
2. √x = 3
... x = 3² = 9
3. √(x-2) = 4
... x -2 = 4²
... x = 16 +2 = 18 . . . . add 2
5. √(2x) = 1
... 2x = 1²
... x = 1/2 . . . . . . . divide by the coefficient of x
Can you please help me solve 18 and 21 please?
18. x = y = -3
21. y was substituted into the wrong equation. The solution is (x, y) = (2, 1).
Step-by-step explanation:18. Adding y to the first equation transforms it to ...
... x = y
Then you can substitute for either variable in the second equation.
... 2y -5y = 9 . . . . . substitute for x
... -3y = 9 . . . . . . . . simplify
... y = -3 . . . . . . . . . divide by the coefficient of y
.. x = -3 . . . . . . . . . x and y have the same value
___
21. The first equation is being used to find an expression for y in terms of x. If you substitute that expression back into the same equation, it will tell you nothing you didn't already know. (Here, it is telling you 5 = 5.) The expression is only useful if you substitute it into a different equation. Here, it needs to be substituted into the second equation:
... Step 2: 3x -2(-2x+5) = 4 ⇒ 7x -10 = 4 . . . . . substitute for y in the second eqn
... Step 3: 7x = 14 . . . . . add 10
... Step 4: x = 2 . . . . . . . divide by 7
... Step 5: y = -2·2 +5 = 1 . . . . . find the value of y from x using the expression from step 1. Now, you know the solution is (x, y) = (2, 1).
_____
The attached graph shows the solution to the problem of 21.
find the value of x. please help
36.6
Step-by-step explanation:The rule for secants is pretty simple. The product of the distance from the external point to the near intersection with the circle and the distance to the far intersection with the circle is a constant.
This means ...
... BC × AC = DC × (DC+x)
... 8 × 26 = 5 × (x +5) . . . . . AC=AB+BC = 18+8 = 26
... 208 = 5x +25 . . . . . . . . . simplify
... 183 = 5x . . . . . . . . . . . . . subtract 25
... 36.6 = x . . . . . . . . . . . . . divide by 5
help! with explanations if possible
Answer:
5
Step-by-step explanation:
1. according to the condition
[tex]\frac{price \ radio1}{price \ radio2} =\frac{x}{y}[/tex]
2. when the both prices are increased the ratio is
[tex]\frac{x+20}{y+20}=\frac{5}{2}[/tex]
3. when the both prices are reduced the ratio is
[tex]\frac{x-25}{y-25} =\frac{5}{1}[/tex]
4. using the equations written in steps 2&3 it is possible to make up the system of the two equations:
[tex]\left \{ {{\frac{x+20}{y+20}=\frac{5}{2} } \atop {\frac{x-25}{y-25}= \frac{5}{1} }} \right.[/tex]
where x=160; y=52.
5. ration x:y=5.
which if the following quartic functions has x = 1 and x =
y = x⁴ +4x³ +4x² +4x +3
Step-by-step explanation:The coefficients of the offered quartics (in order) have 1, 1, 1, and 0 sign changes, respectively. Descartes' rule of signs tells you this means the first three choices all have one (1) positive real root, so the negative real roots -1 and -3 are not the only ones.
The only possible polynomial is the last one. Synthetic division of that polynomial by roots -1 and -3 leave the remaining factor as x²+1, which has only complex zeros.
The appropriate choice is ...
... y = x⁴ +4x³ +4x² +4x +3
What would be the answers
Answer:
1/500000000000 is the answer
Just simplify and combine like terms to find your answer. You can add the tens to the -5 power, and the 4 and 2 on the top, then divide by the expression on the bottom.
Therefore, the only expression equivalent to this one is B.