Answer:
(B) sample size is 666
Step-by-step explanation:
given data
CI = 99%
error = 0.05
to find out
sample size
solution
we know that for CI = 99% and E = 0.05 the value of z = 2.58 from table
and no estimate of proportion is given so it is rule take q = p = 0.5
so now we can calculate sample size i.e.
n = (z/E)² ×p ×q
put the value q and p = 0.5 and z and E so we get sample size
n = (z/E)² ×p ×q
n = (2.58/0.05)² ×0.5 ×0.5
n = 665.64
so sample size is 666
so option (B) is right
Which statement is true about the end behavior of the graphed function?
As the x-values go to positive infinity, the function's values go to negative infinity.
As the x-values go to zero, the function's values go to positive infinity.
As the x-values go to negative infinity, the function's values are equal to zero.
As the x-values go to negative infinity, the function's values go to positive infinity.
Answer:
Option D (As the x-values go to negative infinity, the function's values go to positive infinity).
Step-by-step explanation:
The graphed function shows a curve which has two turning points and three x-intercepts, which means it is a cubic polynomial. To check which statement is true, we will check all the statements one by one.
Option A) The graph shows that after the second turning point, the function starts to increase. Which means that as x-values increase, the function values will approach positive infinity. Therefore, option A is incorrect.
Option B) This option is incorrect because the graph explicitly shows that f(0) = 0, which means that when x = 0, the function value is also 0.
Option C) This option is incorrect because the function value is 0 at the x-value = 0, as shown in the graph. It can be also seen that As the x-values go to negative infinity, the function's values go to positive infinity since the value of the function decreases as the value of x decreases. Hence Option D is the correct answer!!!
Answer:
The correct option is D.
Step-by-step explanation:
Consider the provided graph of the function.
As the x values go to positive infinity or negative infinity the function value increase or goes to positive infinity.
The end behavior of the function is,
[tex]f(x)\rightarrow +\infty, as x\rightarrow -\infty[/tex]
[tex]f(x)\rightarrow +\infty, as x\rightarrow +\infty[/tex]
Now consider the provided options.
Option A is incorrect because As the x-values go to positive infinity, the function's values go to positive infinity.
Option B is incorrect because As the x-values go to zero, the function's values doesn't go to positive infinity.
Option C is incorrect because As the x-values go to negative infinity, the function's values are not equal to zero.
Option D is the correct option because As the x-values go to negative infinity, the function's values go to positive infinity.
Therefore, the correct option is D.
The hypotenuse of a right triangle is three times the length of one of its legs. The length of the other leg is four feet. Find the
lengths of the three sides of the triangle. For non-integer answer(s), round your answer(s) to the nearest tenth.
Answer:
Step-by-step explanation:
Let the other leg = x
x^2 + 4^2 = (3x)^2
x^2 + 4^2 = 9x^2
4^2 = 9x^2 - x^2
16= 8x^2
16/8 = x^2
x^2 = 2
x = sqrt(2)
The lengths of the sides
x = sqrt(2)
other side =4
hypotenuse = 3*sqrt(2)
x = 1.4
other side= 4
hypotenuse = 3*1.4142
hypotenuse = 4.2
Answer:
4 feet, 1.4 feet, 4.2 feet
Step-by-step explanation:
We are looking for the lengths of the three sides of a right triangle. We are given that one leg has length 4ft. Let x be the length of the other leg. Since the hypotenuse of the right triangle is three times the length of this leg, we can represent the hypotenuse as 3x. This is a right triangle, so we can use the Pythagorean Theorem to find x.
42+x216+x2=(3x)2=9x2
Subtracting x2 from both sides, then dividing by 8 to isolate the x, we have
8x2x2x=16=2=±2–√
Considering only the positive value for x, the lengths of the three sides of the triangle are approximately 4 feet, 2–√≈1.4 feet, and 32–√≈4.2 feet.
Find the value of x. Then find the measure of each labeled angle.
Answer:
20
4x will be 80
5x will be 100
Step-by-step explanation:
So those two how pink arrows means those opposite sides are parallel.
The side at the bottom is acting as a transversal through the parallel lines.
The angle that has measurement 5x and the one that has 4x are actually same-side interior angles; some people like to call it consecutive angles.
These angles add up to be 180 degrees when dealing with parallel lines.
So we have 5x+4x=180
which means 9x=180
Divide both sides by 9 giving us x=180/9
x=180/9=20.
The angle labeled 4x will then be 4(20) which is 80.
The angle labeled 5x will then by 5(20) which is 100.
To solve for x in vector problems, identify the axes, decompose each vector into its components using trigonometric functions, combine the components to find the resultant vector, and ensure that the solution is reasonable. Be sure to use radians for angles in calculations.
Explanation:To find the value of x, we need to follow specific steps when dealing with vectors and their components. The given information suggests we have vectors A and B with specific magnitudes and angles relative to the x-axis. Here's how to proceed:
Identify the x- and y-axes that will be used in the problem.Find the components of each vector to be added along the perpendicular axes using the equations: Ax = A cos θ and Ay = A sin θ, where A is the magnitude of vector A and θ is the angle it makes with the x-axis. Repeat this for vector B to obtain Bx and By.Substitute the known values into the equations and solve for the components.Combine the x-components (Ax and Bx) and y-components (Ay and By) to find the resultant vector's components.To get the resultant vector's magnitude, use the Pythagorean theorem.To get the direction of the resultant, measure the angle it makes with the reference frame or use trigonometric relationships to determine this angle.Check your answer to see if it is reasonable, ensuring the units and the magnitude of the resultant make sense.For example, given A = 53.0 m, θA = 20.0°, B = 34.0 m, and θB = 63.0°, we can find the x-components as Ax = A cos θA. It is important to use radians when calculations involve angles.
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Tina, the owner of a home and garden store, lends $8,000 to Lana to help her open an art shop. Lana plans to repay Tina at the end of eight years with interest compounded semiannually at 8%. Using the tables found in the textbook, you can determine that at the end of eight years, Tina will receive A. $14,484. B. $14,984. C. $16,587. D. $16,857.
Answer:
B. $14,984
Step-by-step explanation:
The multiplier is ...
(1 +r/n)^(nt) . . . . where r is the nominal annual rate, n is the number of times interest is compounded per year, and t is the number of years.
Here, that multiplier is ...
(1 +.08/2)^(2·8) = 1.04^16 ≈ 1.87298
Then Lana will be paying Tina ...
$8000×1.87298 ≈ $14984
at the end of 8 years.
WANT FREE 20 POINTS + BRAINLIEST?
Help me with the geometry question and I got you
Answer:
a) J, K, W
b) any of X, Y, or P
c) 1 line
Step-by-step explanation:
a) The figure shows points J, K and W on line m.
b) Any points in the diagram other than J, K, and W are not on line m. Those include points X, Y, and P. Your answer will be one or more of these.
c) Two points define 1 line. There is only one line through any given pair of points. It can be named many ways, but it is still the same (one) line.
Answer:
1) J, K, W
2) any of X, Y, or P
3) Only one line (pyx)
Step-by-step explanation:
1) The figure shows points J, K and W on line m.
2) All points in the diagram except for j, w, and k are not on line m. These include points x, y, and p. Your answer should be one or more of these.
3) Three points define 1 line. There is only one line through any given group of points. It can be named many ways, but it will remain (one) line. The line would run through the points p, y, and x.
Hope this helps
- Que
The product of (a − b)(a − b) is a2 − b2.
A. Sometimes
B. Always
C. Never
The correct option is C. Never The product of (a - b)(a - b) is always equal to a² - 2ab + b².
The product of (a - b)(a - b) can be expanded using the distributive property:
(a - b)(a - b) = a(a) - a(b) - b(a) + b(b)
Simplify by multiplying the terms:
= a² - ab - ab + b²
Combine like terms:
= a² - 2ab + b²
As you can see, the product of (a - b)(a - b) is a² - 2ab + b², not a² - b².
However, there is a well-known algebraic identity called the difference of squares, which states that a² - b² can be factored as (a + b)(a - b). So, the correct statement is:
(a - b)(a - b) is equivalent to a² - 2ab + b², not a² - b².
Therefore, the answer is C. Never the product of (a - b)(a - b) is always equal to a² - 2ab + b².
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What is tan 11pie/6 ?
Answer:
1/root 3
Step-by-step explanation:
pi =180degrees
11×180/6
11×30
330
tan 330=tan (360-30)
=-tan30
=1/root3
i have answered ur question
I am have trouble with these x-intercepts. Please help me.
Answer:
x=8, x=2 no solution no solutionStep-by-step explanation:
For the equation ...
y = a(x -h)² +k
you can find the x-intercepts by setting y=0 and solving for x.
0 = a(x -h)² +k
-k = a(x -h)² . . . . . . subtract k
-k/a = (x -h)² . . . . . divide by a
±√(-k/a) = x -h . . . . take the square root
h ± √(-k/a) = x . . . . add h . . . . this is the general solution
__
So, for each of your problems, fill in the corresponding numbers and do the arithmetic. If (-k/a) is a negative number, the square root gives imaginary values, so there is "no solution".
1. x = 5 ± √9 = {5 -3, 5 +3} = {2, 8} . . . . the x-intercepts are 2 and 8
2. x = -3 ± √(-2) . . . . . . no solution; the roots are complex
3. x = 5 ± √(-8/4) . . . . . no solution; the roots are complex
Answer:
Step-by-step explanation:
These are all done the exact same way. I'll do the first one in its entirety, and you can do the rest, following my example.
Finding x-intercepts means that you find the places in the polynomial where the graph of the function goes through the x-axis. Here, the y-coordinates will be 0. To find these x-intercepts, you have to set y equal to 0 and then factor. First, though, we need to know exactly what the polynomial looks like in standard form. The ones you have are all in vertex form. We find the standard form by first expanding the binomial, like this:
[tex]0=(x-5)(x-5)-9[/tex]
FOIL those out to get
[tex]x^2-10x+25-9=0[/tex]
Combine like terms to get
[tex]0=x^2-10x+16[/tex]
Now we have to factor that. I'll use regular old factoring, although the quadratic formula will work also.
In our quadratic, a = 1, b = -10 and c = 16
The product of a * c = 16. The factors of 16 are:
1, 16
2, 8
4, 4
Some combination of those factors will give us a -10, the b term. 2 and 8 will work, as long as they are both negative. -2 + -8 = -10. Fit them into the polynomial with the absolute value of the largest number named first:
[tex]x^2-8x-2x+16=0[/tex]
Now we group them by 2's without ever changing their order:
[tex](x^2-8)-(2x+16)=0[/tex]
and then factor out the common thing in each set of parenthesis. The common thing in the first set of parenthesis is an x; the common thing in the second set is a 2:
[tex]x(x-8)-2(x-8)=0[/tex]
Now the common thing is (x - 8), so we factor that out and group together in a separate set of parenthesis what's left over:
[tex](x-8)(x-2)=0[/tex]
By the Zero Product Property, either x - 8 = 0 or x - 2 = 0. Solving the first one for x:
x - 8 = 0 so x = 8
Solving the second one for x:
x - 2 = 0 so x = 2
The 2 solutions are x = 2 and x = 8, choices a and d.
Expected Value (50 points)
Game: Roll two dice. Win a prize based on the sum of the dice.
Cost of playing the game: $1
Prizes:
Win $10 if your sum is odd.
Win $5 if you roll a sum of 4 or 8.
Win $50 if you roll a sum of 2 or 12.
1.Explain HOW to find the expected value of playing this game. What is the expected value of playing this game? Show your work. (30 points)
2.Interpret the meaning of the expected value in the context of this game. Why should someone play or not play this game. Answer in complete sentences. (20 points)
Answer:
the expected value is if your sum is odd because half of the values you could roll are odd witch means you have 50% chance to get odd
because their are not high odds of getting something good
Need help with this
Answer:
Answer choice C is the correct answer.
Step-by-step explanation:
Answer choice A, 4/9, is equal to roughly .44.
Answer choice B, 2/5, is equal to exactly .4.
Answer choice C, 3/6, is equal to exactly .5.
Answer choice D, 5/12, is equal to roughly .42.
A proportion implies that the fractions will equal each other in value. The fraction 7/14 is equal to 1/2 or .5. Answer choice C, when simplified, is equal to 1/2 or .5, making it the correct answer.
The perimeter of a triangle with two equal sides is 50 cm. If its base were lengthened by 3 cm and each leg were shortened by 4 cm, all three sides would be equal. Find the length of the base of the original triangle.
Answer:
Base of the original triangle is 12 cm.
Step-by-step explanation:
Let base of triangle be x
two equal legs of triangles by y
therefore perimeter of triangle
x+y+y = 50 or x+2y =50
according to the question
if base is x+3 and leg is y-4
then both are equal
that is x+3 = y-4
y-x = 7 or y =x+7
x+2y =50
x+2(x+7) = 50
x+2x +14 =50
3x +14 =50
3x = 50 -14
3x = 36
x = 12
therefore base of the original triangle is 12 cm
Susan drove an average speed of 30 miles per hour for the first 30 miles of a trip & then at a average speed of 60 miles/hr for the remaining 30 miles of the trip if she made no stops during the trip what was susan's avg speed in miles/hr for the entire trip.(A) 35(B) 40(C) 45(D) 50(E) 55
Answer:
The correct option is B.
Step-by-step explanation:
It is given that Susan drove an average speed of 30 miles per hour for the first 30 miles of a trip & then at a average speed of 60 miles/hr for the remaining 30 miles of the trip.
[tex]Time=\frac{Distance}{Speed}[/tex]
Time taken by Susan in first 30 miles is
[tex]T_1=\frac{30}{30}=1[/tex]
Time taken by Susan in remaining 30 miles is
[tex]T_2=\frac{30}{60}=0.5[/tex]
Total distance covered by Susan is
[tex]D=30+30=60[/tex]
Total time taken by susan to complete 60 miles trip is
[tex]T=T_1+T_2[/tex]
[tex]T=1+0.5=1.5[/tex]
Susan's avg speed in miles/hr for the entire trip is
[tex]S=\frac{60}{1.5}=40[/tex]
The average speed of susan for entire trip is 40. Therefore the correct option is B.
Find the area of the circle.
Use 3.14 for t.
Help Resources
d = 4 m
A = [?] m2
A=Tr2
Answer:
The area of the circle is A = 12.56 m²
Step-by-step explanation:
* Lets explain how to solve the problem
- The area of any circle is A = π r² , where r is the radius of the circle
- In any circle the length of the radius is half the length of its diameter
* Lets solve the problem
- The diameter of the circle is 4 meters
∵ The radius of the circle = 1/2 diameter
∵ The diameter = 4 meters
∴ The radius = 1/2 × 4 = 2 meters
- The area of the circle is A = π r²
∵ The value of π = 3.14
∵ The length of r = 2 meters
- Substitute the value of r in the rule of the area
∵ A = π r²
∴ A = 3.14 × (2)²
∴ A = 3.14 × 4 = 12.56 meters²
* The area of the circle is A = 12.56 m²
Need some help with this
Answer:
y = 5x - 11
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here slope m = 5, hence
y = 5x + c ← is the partial equation
To find c substitute (1, - 6) into the partial equation
- 6 = 5 + c ⇒ c = - 6 - 5 = - 11
y = 5x - 11 ← equation of line
Suppose the circumference of a crop circle is 150.7968 hectometers (hm). What's the radius of the circle? (Use π = 3.1416.)
A. 24 hm
B. 96 hm
C. 48 hm
D. 16 hm
Answer:
A. 24 hm
Step-by-step explanation:
The formula for the circumference of a circle is ...
C = 2πr
Fill in the given values and solve.
150.7968 hm = 2×3.1416×r
(150.7968 hm)/6.2832 = r = 24 hm . . . . . divide by 2π
The radius of the circle is 24 hm.
Proportions in Triangles (3)
Answer:
7 6/7
Step-by-step explanation:
Parallel segment BD creates triangle BDC similar to triangle AEC. The sides and segments of similar triangles are proportional:
x/11 = 5/7
x = 55/7 = 7 6/7 . . . . . multiply by 11
For the pair of triangles below, determine whether or not the triangles are similar. If they are similar, show your reasoning in a flowchart. If they are not similar, explain how you know.
Answer:
The triangles are similar
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional
step 1
In the right triangle FED
Find the length of side FD
Applying the Pythagoras Theorem
[tex]FD^{2}=FE^{2}+DE^{2}[/tex]
substitute the given values
[tex]FD^{2}=3^{2}+4^{2}[/tex]
[tex]FD^{2}=25[/tex]
[tex]FD^{2}=5\ units[/tex]
step 2
In the right triangle BUG
Find the length of side GU
Applying the Pythagoras Theorem
[tex]BG^{2}=BU^{2}+GU^{2}[/tex]
substitute the given values
[tex]10^{2}=6^{2}+GU^{2}[/tex]
[tex]GU^{2}=100-36[/tex]
[tex]GU^{2}=8\ units[/tex]
step 3
Find the ratio of its corresponding sides
If the triangles are similar
[tex]\frac{FD}{BG}=\frac{FE}{BU}=\frac{DE}{GU}[/tex]
substitute the given values
[tex]\frac{5}{10}=\frac{3}{6}=\frac{4}{8}[/tex]
[tex0.5=0.5=0.5[/tex] -----> is true
therefore
The triangles are similar
These long term behaviors are very hard to understand.
the first one
the degree of the polynomial in the numerator is 2.
the degree of the polynomial in the denominator is 2.
when the top and bottom have the same degree, like in this case, the horizontal asymptotes that that can afford us is simply the value of their coefficients.
[tex]\bf \cfrac{x^2-16}{x^2+2x+1}\implies \cfrac{1x^2-16}{1x^2+2x+1}\implies \stackrel{\textit{horizontal asymptote}}{y=\cfrac{1}{1}\implies y=1}[/tex]
for the second one
well, the degree of the numerator is 3.
the degree of the denominator is 2.
when the numerator has a higher degree than the denominator, there are no horizontal asymptotes, however, when the degree of the numerator is exactly 1 degree higher than that of the denominator, the rational has an oblique or slant asymptote, and its equation comes from the quotient of the whole expression, check the picture below, the top part.
for the third one
this one is about the same as the one before it, the numerator has exactly one degree higher than the denominator, so we're looking at an oblique asymptote, check the picture below, the bottom part.
A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 92.6-cm and a standard deviation of 2-cm. For shipment, 12 steel rods are bundled together. Find the probability that the average length of a randomly selected bundle of steel rods is between 92-cm and 92.4-cm. Enter your answer as a number accurate to 4 decimal places.
Answer: 0.2140
Step-by-step explanation:
Given : A company produces steel rods. The lengths of the steel rods are normally distributed with
[tex]\mu=92.6 \text{ cm}[/tex]
[tex]\sigma=2\text{ cm}[/tex]
Sample size : [tex]n=12[/tex]
Let x be the length of randomly selected item.
z-score : [tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
For x=92 cm
[tex]z=\dfrac{92-92.6}{\dfrac{2}{\sqrt{12}}}\approx-1.04[/tex]
For x=92.4 cm
[tex]z=\dfrac{92.4-92.6}{\dfrac{2}{\sqrt{12}}}\approx-0.35[/tex]
The probability that the average length of a randomly selected bundle of steel rods is between 92-cm and 92.4-cm by using the standard normal distribution table
= [tex]P(92<x<92.4)=P(-1.04<z<-0.35)=P(z<-0.35)-P(z<-1.04)[/tex]
[tex]= 0.3631693-0.14917=0.2139993\approx0.2140[/tex]
Hence, the probability that the average length of a randomly selected bundle of steel rods is between 92-cm and 92.4-cm is 0.2140.
A vine maple grows fast when it is planted under the cover of cedar trees. One month after it is planted it has grown 12 inches, and after eight weeks it had grown 19 inches. Write an equation that models the growth, in inches, of the vine maple as a function of time, in weeks.
Answer:
y = (7/4)(x -4) +12
Step-by-step explanation:
The rate of growth is ...
(19 in -12 in)/(8 wk -4 wk) = 7/4 in/wk
Using this slope in a point-slope form of the equation for a line, we get ...
y = m(x -h) +k . . . . . line with slope m through point (h, k)
y = (7/4)(x -4) +12 . . . . . line with slope 7/4 through the point (4 wk, 12 in)
An article reported that for a sample of 40 kitchens with gas cooking appliances monitored during a one-week period, the sample mean CO2 level (ppm) was 654.16, and the sample standard deviation was 165.23.
Calculate and interpret a 95% (two-sided) confidence interval for true average CO2 level in the population of all homes from which the sample was selected. (Round your answers to two decimal places.)
=(_________,__________) ppm
(b) Suppose the investigators had made a rough guess of 167 for the value of s before collecting data. What sample size would be necessary to obtain an interval width of 57ppm for a confidence level of 95%? (Round your answer up to the nearest whole number.)
=__________ kitchens
Answer: (a) (602.95,705.37)
(b) 33
Step-by-step explanation:
(a) Given : Sample size : [tex]n=40[/tex]
Sample mean : [tex]\overline{x}=654.16[/tex]
Standard deviation : [tex]\sigma= 165.23[/tex]
Significance level :[tex]\alpha=1-0.95=0.05[/tex]
Critical value : [tex]z_{\alpha/2}=1.96[/tex]
The confidence interval for population mean is given by :-
[tex]\mu\ \pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}[/tex]
[tex]=654.16\pm(1.96)\dfrac{165.23}{\sqrt{40}}\\\\\approx654.16\pm51.21\\\\=(654.16-51.21,\ 654.16+51.21)=(602.95,705.37)[/tex]
Hence, the 95% (two-sided) confidence interval for true average [tex]CO_2[/tex] level in the population of all homes from which the sample was selected.
(b) Given : Standard deviation : [tex]s= 167\text{ ppm}[/tex]
Margin of error : [tex]E=\pm57\text{ ppm}[/tex]
Significance level :[tex]\alpha=1-0.95=0.05[/tex]
Critical value : [tex]z_{\alpha/2}=1.96[/tex]
The formula to calculate the sample size is given by :-
[tex]n=(\dfrac{z_{\alpha/2}s}{E})^2\\\\\Rightarrow\ n=(\dfrac{(1.96)(167)}{57})^2=32.9758025239\approx33[/tex]
Hence, the minimum required sample size would be 33.
The graph below shows a system of equations: y = -x + 5 and y = x - 1.
The x-coordinate of the solution to the system of equations is __________. Answer for Blank 1:
Answer:
3
Step-by-step explanation:
I don't see the graph.
So I'm going to do algebra and should be x-coordinate of the intersection you see in front of you.
If y=-x+5 and y=x-1, then -x+5=x-1.
-x+5=x-1
Add x on both sides:
5=2x-1
Add 1 on both sides:
6=2x
Divide 2 on both sides:
6/2=x
Simplify
3=x
You should see them cross when x is 3.
The y there should by 3-1=2.
They should cross at the ordered pair (3,2).
Answer:
3
Step-by-step explanation:
If a graph shows a system of equations: y = -x + 5 and y = x - 1, the x-coordinate of the solution to the system of equations is 3.
y=-x+5
y=x-1
-x+5=x-1
Use the distributive property to solve the equation 3x=15?
Answer:
x = 5
Step-by-step explanation:
Ordinarily, one would not need the distributive property to solve this equation. It is quickly and easily solved by making use of the multiplication property of equality: multiply both sides of the equation by 1/3.
3x(1/3) = 15(1/3)
x = 5
___
To use the distributive property, we need the sum of two terms that have a common factor. We can get that form by subtracting 15 from both sides of the equation (subtraction property of equality):
3x - 15 = 15 - 15 . . . . subtract 15
3x -15 = 0 . . . . . . . . .simplify
Now, we can apply the distributive property to remove a factor of 3:
3(x -5) = 0
And we can use the multiplication property of equality to multiply by 1/3:
3(1/3)(x -5) = 0(1/3)
x -5 = 0 . . . . . . . . . . simplify
Finally, we can add 5 to both sides of the equation (addition property of equality):
x -5 +5 = 0 +5
x + 0 = 5 . . . . . . simplify
x = 5 . . . . . . . . . .simplify more
Answer:
X=5
Step-by-step explanation:
i believe this is the correct answer!
Can someone help with this!? :)
The system of equations provided consists of a circle and a line:
1. [tex]\( x^2 + y^2 = 49 \)[/tex] (This represents a circle with a radius of 7, centered at the origin.)
2. [tex]\( y = -x - 7 \)[/tex] (This is a linear equation.)
The first equation has already been graphed, showing a circle with a radius of 7. To find the intersection points of the circle and the line, which are the solutions of the system, we can substitute the expression for y from the second equation into the first one:
[tex]\[ x^2 + (-x - 7)^2 = 49 \][/tex]
[tex]\[ x^2 + x^2 + 14x + 49 = 49 \][/tex]
[tex]\[ 2x^2 + 14x + 49 - 49 = 0 \][/tex]
[tex]\[ 2x^2 + 14x = 0 \][/tex]
[tex]\[ x(2x + 14) = 0 \][/tex]
This gives us two solutions for x:
[tex]\[ x = 0 \quad \text{or} \quad 2x + 14 = 0 \][/tex]
[tex]\[ x = 0 \quad \text{or} \quad x = -7 \][/tex]
Now we can substitute these x-values into the second equation to find the corresponding y-values:
For [tex]\( x = 0 \)[/tex]:
[tex]\[ y = -0 - 7 \][/tex]
[tex]\[ y = -7 \][/tex]
For [tex]\( x = -7 \)[/tex]:
[tex]\[ y = -(-7) - 7 \][/tex]
[tex]\[ y = 7 - 7 \][/tex]
[tex]\[ y = 0 \][/tex]
Therefore, the system of equations has two solutions where the line intersects the circle:
[tex]\[ (0, -7) \quad \text{and} \quad (-7, 0) \][/tex]
These calculations provide us with the step-by-step solution to the system of equations. The graphical solution would show the line [tex]\( y = -x - 7 \)[/tex] intersecting the circle [tex]\( x^2 + y^2 = 49 \)[/tex] at these two points.
Here is the graph showing the system of equations:
- The circle represented by [tex]\( x^2 + y^2 = 49 \)[/tex].
- The line represented by [tex]\( y = -x - 7 \).[/tex]
The red points indicate where the line intersects the circle, which are the solutions to the system of equations. These points are at (0, -7) and (-7, 0).
A plane flies with an average velocity of -98.5 m/s for 45.0s .What is the displacement?
Answer:
-4432.5 m
Step-by-step explanation:
Displacement is measured in meters, so will be the product of velocity in m/s and time in s.
(-98.5 m/s)×(45.0 s) = -4432.5 m
___
If you're concerned with significant figures, you can round this to -4430 m, which has the required 3 significant figures.
Answer:
-4432.5 m
Step-by-step explanation:
distance (or displacement) = rate times time.
Here, the displacement is
(-98.5 m/s)(45.0 s) = -4432.5 m
A probability distribution showing the probability of x successes in n trials, where the probability of success does not change from trial to trial, is termed aa. uniform probability distributionb. binomial probability distributionc. hypergeometric probability distributiond. normal probability distribution
Answer: binomial probability
Step-by-step explanation:
A binomial probability indicates to the probability of having exactly x successes on n repeated trials in an particular binomial experiment which has only two possible outcomes.
If the probability of success on an single trial is b (which does not change) , then , the probability of failure will be (1-b) .
The binomial probability for success in x trials out of n trials is given by :-
[tex]^nC_x\ b\ (1-b)^{n-x}[/tex]
Final answer:
The distribution called for a fixed number of independent trials with a constant success probability is the binomial probability distribution, defined by the equation P(X = x).
Explanation:
The probability distribution that shows the probability of x successes in n trials, where the probability of success does not change from trial to trial, is termed a binomial probability distribution. The key characteristics of a binomial distribution include a fixed number of independent trials with two possible outcomes (success or failure) and a constant probability of success in each trial.
Mathematically, the binomial distribution is defined using the equation P(X = x) = (n choose x) * px * qn-x, where p is the probability of success, q = 1 - p is the probability of failure, and (n choose x) is the combination of n taken x at a time.
What remainder does the sum 2222+2333 leave after division? Each one has an answer! Need answer quickly! 18 points!
by 4?
by 6?
by 9?
by 12?
2222 = 2220 + 2 = 555 * 4 + 2
2333 = 2332 + 1 = 583 * 4 + 1
Then
2222 + 2333 = (555 + 583) * 4 + 3
leaving a remainder of 3.
Dividing by 62222 = 2220 + 2 = 370 * 6 + 2
2333 = 2328 + 5 = 388 * 6 + 5
Then
2222 + 2333 = (370 + 388) * 6 + 7 = (370 + 388 + 1) * 6 + 1
leaving a remainder of 1.
Dividing by 92222 = 2223 - 1 = 741 * 3 - 1
2333 = 388 * 6 + 5 = (388 * 2) * 3 + 5 = (388 * 2 + 1) * 3 + 2
Then
2222 + 2333 = (741 + 388 * 2 + 1) * 3 + 1
leaving a remainder of 1.
Dividing by 122222 = 555 * 4 + 2 = 185 * 3 * 4 + 2 = 185 * 12 + 2
2333 = 2400 - 67 = 2400 - 60 - 7 = (200 - 5) * 12 - 7
Then
2222 + 2333 = (185 + 200 - 5) * 12 - 5
leaving a remainder of -5, or 7. (because 12 - 5 = 7)
Evaluate 3x3 − 2x2 for x = -2.
Step-by-step explanation:
3x3-2x2
3(-2)3-2(-2)2
-6×3+4×2
-18+8
-10
I hope it will help you!
Answer:
-10
Step-by-step explanation:
Yes. All you have to remember is that double negatives result in POSITIVES.
I am joyous to assist you anytime.
Proportions in Triangles (10)
If you were to place $2500 in a savings account that pays 3% interest compound continually how much money will you have after 5 years. Assume you make no other deposits or withdrawals.
[tex]\bf ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$2500\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ t=years\dotfill &5 \end{cases} \\\\\\ A=2500e^{0.03\cdot 5}\implies A=2500e^{0.15}\implies A\approx 2904.59[/tex]
Answer:
C. $2904.59
Step-by-step explanation:
Compounded continually means that the principal amount is constantly earning interest and the interest keeps earning on the interest earned.
The formula to apply is
[tex]A=Pe^{rt}[/tex]
where A is the amount, P is the principal, r is rate of interest, t is time in years and e is the mathematical constant
Taking
e=2.7183, P=$2500, r=3% and t=5 years
[tex]A=Pe^{rt} \\\\\\A=2500*2.7183^{0.03*5} \\\\\\A=2500*1.1618\\\\\\A=2904.59\\\\A=2904.59[/tex]