Answer:
The correct option will be: D. (6, 2)
Step-by-step explanation:
Point [tex]S[/tex] divides the line segment [tex]YB[/tex] in a ratio of [tex]4:1[/tex]
Given that, [tex]Y(-10, 6)[/tex] and [tex]B(10, 1)[/tex]
If a point [tex](x,y)[/tex] divides a line segment with endpoints as [tex](x_{1}, y_{1})[/tex] and [tex](x_{2}, y_{2})[/tex] in a ratio of [tex]m:n[/tex] , then...........
[tex](x, y)= (\frac{mx_{2}+nx_{1}}{m+n},\frac{my_{2}+ny_{1}}{m+n})[/tex]
Here, [tex](x_{1}, y_{1})=(-10,6)[/tex] and [tex](x_{2}, y_{2})=(10,1)[/tex]
Also, [tex]m:n=4:1[/tex]
Now plugging the values, we will get........
[tex]x=\frac{4(10)+1(-10)}{4+1}= \frac{40-10}{5}= \frac{30}{5}=6 \\ \\ \\ y=\frac{4(1)+1(6)}{4+1}= \frac{4+6}{5}= \frac{10}{5}=2[/tex]
So, the coordinates for point S will be: (6, 2)
A recent poll of employees working for a national fast-food chain claims that 58% of its employees eat at the fast-food chain. A sample of 200 people shows that only 42% of the employees eat at the fast-food chain.
To determine whether this sample supports the population proportion of 0.58, a simulation of 200 trials is run, each with a sample size of 50 and a point estimate of 0.42. The minimum sample proportion from the simulation is 0.31, and the maximum sample proportion from the simulation is 0.53.
What is the margin of error of the population proportion using half the range?
±0.07
±0.11
±0.13
±0.21
Answer:
Option B 0.11
Step-by-step explanation:
Given that the population proportion of 0.58, a simulation of 200 trials is run, each with a sample size of 50 and a point estimate of 0.42. The minimum sample proportion from the simulation is 0.31, and the maximum sample proportion from the simulation is 0.53.
This gives an idea that confidence interval is
(0.31, 0.53) with mean being in the middle of this interval
Margin of error = 1/2 (length of this interval)
Length of confidence interval =[tex]0.53-0.31 =0.22[/tex]
Margin of error =± 1/2(0.22) = ±0.11
Hence option B is correct
Which are solutions to the equation x3 – 5x2 + 2x + 6 = 0? Round each solution to the nearest tenth. Check all that apply. X = –0.9 x = 0.8 x = 1.7 x = 4.2 x = 6.0
Given equation is [tex]x^3-5x^2+2x+6=0[/tex]
Usually we solve this type of problem by factoring but this equation is not factorable. If we solve by grouping then also we are not getting any common factor. So factoring method is not going to help. I this type of situation we may use graphing calculator. From graph we just need to pick those points where graph crosses the x-axis. Those values will be the final answer.
Using graphing calculator we see that there are three solutions at x=-0.856, x=1.678, x=4.177 which are approx x=-0.8, x=1.7 and x=4.2
Hence final answers are x=-0.8, x=1.7 and x=4.2.
Answer:
-0.9, 1.7, and 4.2
Step-by-step explanation:
Xavier woud like to become the section leader in the band. He knows that this will require a lot of his time. He usually work 22 hours a week and makes $11 per hour. He has to cut his hours down to 12 a week. What is his opportunity cost
Algebra help - asymptotes
Find where the equation is undefined ( when the denominator is equal to 0.
Since they say x = 5, replace x in the equation see which ones equal o:
5-5 = 0
So we know the denominator has to be (x-5), this now narrows it down to the first two answers.
To find the horizontal asymptote, we need to look at an equation for a rational function: R(x) = ax^n / bx^m, where n is the degree of the numerator and m is the degree of the denominator.
In the equations given neither the numerator or denominators have an exponent ( neither are raised to a power)
so the degrees would be equal.
Since they are equal the horizontal asymptote is the y-intercept, which is given as -2.
This makes the first choice the correct answer.
Solve for given replacement set for 21- 5x -4 = x +4 ( 0, 2, 4 )
If ray NP bisects <MNQ, m<MNQ=(8x+12)°, m<PNQ=78°, and m<RNM=(3y-9)°, find the value of x and y
Step 1
Find the measure of angle x
we know that
If ray NP bisects <MNQ
then
m<MNQ=m<PNM+m<PNQ ------> equation A
and
m<PNM=m<PNQ -------> equation B
we have that
m<MNQ=(8x+12)°
m<PNQ=78°
so
substitute in equation A
(8x+12)=78+78-------> 8x+12=156------> 8x=156-12
8x=144------> x=18°
Step 2
Find the measure of angle y
we have
m<PNM=(3y-9)°
m<PNM=78°
so
3y-9=78------> 3y=87------> y=29°
therefore
the answer is
the measure of x is 18° and the measure of y is 29°
Answer: If NP bisects MNQ, MNQ=8x+12,PNQ=78, and RNM=3y-9, find the values of x and y
x= 18 y=11
Step-by-step explanation:
We know that MNQ= 8x+12
PNQ=78 and MNP is equal to PNQ
Therefore, PNQ=MNP
So since these two angles make up MNQ,
Add 78+78 which is 156
So now we need to find x
The equation to find x is 8x+12=156
8x+12=156
8x=144
x=18
Now that we know x it is time to find y.
So we know that RNM=3y-9
And we know that MNQ is equal to 156
RNM an MNQ form a straight line which means that it is equal to 180 degrees
So the equation to find y is 3y-9+156=180
3y-9+156=180
3y+147=180
3y=33
y=11
So in conclusion, x=18 and y=11
Hope this helped! :3
What are the roots of the equation?
4x^3−20x^2+24x=0
4x³ - 20x² + 24x = 0
4x(x² - 5x + 6) = 0
4x(x - 2)(x - 3) = 0
4x = 0 x - 2 = 0 x - 3 = 0
x = 0 x = 2 x = 3
Answer: 0, 2, 3
Factoring and solving a quadratic equation, it is found that the roots of the equation are:
[tex]x = 0[/tex]
[tex]x = 2[/tex]
[tex]x = 3[/tex]
The equation given is:
[tex]4x^3 - 20x + 24x = 0[/tex]
Factoring the common term:
[tex]4x(x^2 - 5x + 6) = 0[/tex]
For the roots:
[tex]4x = 0 \rightarrow x = 0[/tex]
Or
[tex]x^2 - 5x + 6 = 0[/tex]
Which is a quadratic equation with coefficients [tex]a = 1, b = -5, c = 6[/tex], and then:
[tex]\Delta = (-5)^{2} - 4(1)(6) = 1[/tex]
[tex]x_{1} = \frac{-(-5) + \sqrt{1}}{2} = 3[/tex]
[tex]x_{2} = \frac{-(-5) - \sqrt{1}}{2} = 2[/tex]
Thus, the other two roots are [tex]x = 2[/tex] and [tex]x = 3[/tex].
A similar problem is given at https://brainly.com/question/11513376
Solve for e
7(2e-1)-11=6+6e
7×2=14e
7×1=7
14e-7-11=6+6e
-6e -6e
8e-7-11=6
+7 +7
8e-11=13
+11 +11
8e=24
8e÷8=e
24÷8=3
e=3
To solve the equation 7(2e-1)-11=6+6e for e, distribute, combine like terms, subtract, add, and divide until you have isolated e. The solution is e=3.
Explanation:To solve for e in the equation 7(2e-1)-11=6+6e, first distribute the 7 on the left side of the equation:
14e - 7 - 11 = 6 + 6e
Now, combine like terms on both sides:
14e - 18 = 6 + 6e
Next, subtract 6e from both sides:
8e - 18 = 6
Add 18 to both sides:
8e = 24
Finally, divide by 8:
e = 3.
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the vehical's fuel efficiency is more than 40 miles per gallon
use f to represent the vehicle's fuel efficiency (in miles per gallon)
In this mathematical context, 'f' represents a vehicle's fuel efficiency in miles per gallon, and the given inequality f > 40 mpg indicates that the vehicle's fuel efficiency is higher than 40 miles per gallon.
Explanation:The problem refers to a situation where a vehicle achieves fuel efficiency of more than 40 miles per gallon. This efficiency is quantified using the variable 'f'.
Considering f as the vehicle's fuel efficiency in miles per gallon, you are expressing a relationship where f > 40 mpg.
Using an example: if we consider a vehicle that achieves 43 miles per gallon, this can be represented as: f = 43 mpg. This efficiency is indeed more than 40 miles per gallon, thus confirming that f > 40 mpg in this case. It's important to understand that in this context, the fuel efficiency varies from one vehicle to another. For instance, vehicles become more fuel efficient over the years due to advancements in technology and heightened fuel economy standards.
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There aré 23 students and a student admission ticket is 8$ how much will the student tickets cost
On Monday, Florencia's hair was h centimeters long. She got a haircut on Tuesday, so her hair was only 75%, percent of the length it was on Monday.
It seems that you are trying to find the length of hair of Florencia on Tuesday.
Given that length of the hair of Florencia on Monday = h centimeters
On Tuesday, she got hair cut.
So new length of the hair of Florencia on Tuesday = 75% of Monday value
= 75% of (h)
= 0.75* (h)
= 0.75h
Hence final answer is the length of the hair of Florencia on Tuesday is ( 0.75h ) centimeters.
Answer:
3/4h and 0.75h
Using the slope formula, find the slope of the line through the given points
8,5 and 6,1
8,5 and 6,1
The slope is 2
Marshall uses the polynomial identity (x−y)^2=x^2−2xy+y^2 to show that 8² = 64.
What values can Marshall use for x and y?
Marshall can use x = 8 and y = 0 to show that 8² = 64 using the polynomial identity (x−y)^2=x^2−2xy+y^2.
Explanation:Marshall can use any values for x and y to show that (x−y)^2=x^2−2xy+y^2. However, he specifically wants to show that 8² = 64. In this case, Marshall can choose x = 8 and y = 0.
Using the polynomial identity (x−y)^2=x^2−2xy+y^2, we substitute x = 8 and y = 0 to get (8 − 0)^2 = 8^2 − 2(8)(0) + 0^2. Simplifying, we have 8^2 = 64 − 0 + 0, which simplifies further to 8^2 = 64.
So, Marshall can use the values x = 8 and y = 0 to show that 8² = 64 using the given polynomial identity.
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Which system of linear equations can be solved using the information below?
Answer:
2x-3y=20
12x+8y=-192
Solution
In the determinant of the matrix to find the variable "x" [Ax], we replace the coefficients of "x" (2 and 12) by the independent terms (20 and -192 respectively).
In the determinant of the matrix to find the variable "y" [Ay], we replace the coefficients of "y" (-3 and 8) by the independent terms (20 and -192 respectively).
differentiate f(x)=x^2sin(x)
Answer:
[tex]\displaystyle \large{f\prime(x) = 2x \sin (x) + x^2 \cos (x)}[/tex]
Step-by-step explanation:
We are given a function:
[tex]\displaystyle \large{f(x) = x^2 \sin (x)}[/tex]
Notice that there are two functions multiplying each other. Recall the product rules.
[tex]\displaystyle \large{y=h(x)g(x) \to y\prime = h\prime (x) g(x) + h(x)g\prime (x)}[/tex]
You can let x^2 = h(x), sin(x) = g(x) or sin(x) = h(x), x^2 = g(x) as your desire but I’ll let h(x) = x^2 and g(x) = sin(x).
Therefore, from a function:
[tex]\displaystyle \large{f(x) = x^2 \sin (x) \to f\prime (x) = (x^2)\prime \sin(x) + x^2 (\sin (x))\prime}[/tex]
Recall the power rules and differentiation of sine.
[tex]\displaystyle \large{y = ax^n \to y\prime = nax^{n-1} \ \ \ \tt{for \ \ polynomial \ \ function}}\\ \displaystyle \large{y = \sin (x) \to y\prime = \cos (x) }[/tex]
Therefore, from differentiating function,
[tex]\displaystyle \large{f\prime(x) = 2x \sin (x) + x^2 \cos (x)}[/tex]
And we are done!
which situation demonstrates the law of large numbers ?
a. if you roll a six-sides number cube 36 times, you will roll a 4 six times.
b. if 800 people are randomly surveyed about the TV shows they watch, about 400 of them will be women.
c. if you flip a coin 44 times, you will get heads about 22 times.
d.if it showed four days last month, it will snow four days this month.
The price of three t-shirt styles are $24, $30 and $36. The probability of choosing a $24 t-shirt is 1/6. The probability of choosing a $30 t-shirt is 1/2. The probability of choosing a $36 t-shirt is 1/3. What is the expected value of a t-shirt?
$29
$30
$31
$32
The law of large numbers in probability, is a theorem that describes the result of performing the same experiment a large number of times because the average of the results obtained from a large number of trials is close enough to the expected value.
So, according to this definition and the situation given , the correct answer is option B - if 800 people are randomly surveyed about the TV shows they watch, about 400 of them will be women; because there are larger number of experiment.
Part B:
To get the expected value of a t-shirt we will multiply each of the 3 prices by the associated probability, and then add up these three products-
[tex](24\times\frac{1}{6})+(30\times\frac{1}{2})+(36\times\frac{1}{3})[/tex]
=4 + 15 + 12 = $31
Hence, option C is correct.
Answer:
1. If 800 people are randomly surveyed about the TV shows they watch, about 400 of them will be women.
2. $31
Step-by-step explanation:
Got it right on the test.
If you if 3 1/2 pounds of bananas cost $1.96, how much would one pound cost?.
There are 1000 toothpicks in a regular-sized box. If a jumbo box is made by doubling all the dimensions of the regular-sized box, how many toothpicks will the jumbo box hold?
Hi, here is the solution.
The doubling each dimensions increases the volume by 8. That is (2 * 2* 2)
There 1000 toothpicks in a regular box.
The jumbo box hold 8 *1000 = 8000 toothpicks.
Thank you.
The equation p=2.5m+35 is the cost of making bracelets where ''p'' is the price and ''m'' is the cost of materials.If a bracelet sells for $115,how much was the material?
what is the solution of the inequality shown below? 8+y>-3
Most of a volcano lies below sea level. If this volcano begins at 5993 meters below sea level and then rises 10,207 meters, find the height of the volcano above sea level.
You can subtract that height of volcano which lies below sea level from the total height to obtain height of volcano above sea level.
Thus, height of specified volcano is 4214 meters.
Given that:Volcano lies 5993 meters below sea level.Volcano rises 10,207 meters from its base.To find:The height of volcano above sea level
Finding height of volcano above sea level:You can subtract that height of volcano which lies below sea level from the total height to obtain height of volcano above sea level.
Thus:
Height of volcano above sea level = total height of volcano - depth of volcano below sea level
[tex]\text{Height of volcano above sea level} = 10207 - 5993 = 4,214 \: \rm meters[/tex]
Thus, height of specified volcano is 4214 meters.
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4,12,16,48,52,156,160,_,_,_ find the next 3 numbers
4, 12, 16, 48, 52, 156, 160, ______, _______, _______
x3 +4 x3 +4 x3 +4
That pattern is: multiply by 3, add 4, multiply by 3, add 4, ...
160 x 3 = 480
480 + 4 = 484
484 x 3 = 1452
Answer: 480, 484, 1452
The next 3 numbers are 480, 484, 1452
The given sequence is:
4,12,16,48,52,156,160,_,_,_
The rule of the sequence is:
The first two terms have a ratio of 3The next two terms have a common difference of 4The rule above continues till the end of the sequenceThe last three terms are the 7th, 8th, and 9th terms
The 7th term is:
[tex]T_7=3T_6\\\\T_7=3(160)\\\\T_7=480[/tex]
The 8th term is:
[tex]T_8=T_7+4\\\\T_8=480+4\\\\T_8=484[/tex]
The 9th term is:
[tex]T_9=3T_8\\\\T_9=3(484)\\\\T_9=1452[/tex]
Therefore, the next 3 numbers are 480, 484, 1452
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step by step explanation please :-D
Solve the equation. Check for extraneous solutions.
9|9 – 8x| = 2x + 3
To solve an absolute value equation of the form |X| = k, where X is an expression with a variable and k is a non-negative number or an expression, you must solve the compound equation X = k or X = -k.
The first step is to divide both sides by 9 to get the absolute value of an expression equal to a non-negative number.
9|9 – 8x| = 2x + 3
Divide both sides by 9.
[tex] |9 - 8x| = \dfrac{2x + 3}{9} [/tex]
Now we eliminate the absolute value by rewriting this as a compound equation.
[tex] 9 - 8x = \dfrac{2x + 3}{9} ~~~or~~~ 9 - 8x = -\dfrac{2x + 3}{9} [/tex]
We must solve both equations.
Multiply both sides by 9.
[tex] 9(9 - 8x) = 2x + 3 ~~~or~~~ 9(9 - 8x) = -(2x + 3) [/tex]
[tex] 81 - 72x = 2x + 3 ~~~or~~~ 81 - 72x = -2x - 3 [/tex]
[tex] -74x = -78 ~~~or~~~ -70x = -84 [/tex]
[tex] x = \dfrac{-78}{-74} ~~~or~~~ x = \dfrac{-84}{-70} [/tex]
[tex] x = \dfrac{39}{37} ~~~or~~~ x = \dfrac{6}{5} [/tex]
Answer: x = 39/37 or x = 6/5
To check for extraneous solutions, we plug in each solution into the original equation and check if it works.
Check 39/37:
9|9 – 8(39/37)| = 2(39/37) + 3
|81 - 72(39/37)| = 78/37 + 3
|2997/37 - 2808/37| = 78/37 + 111/37
|189/37| = 189/37
189/37 = 189/37
The solution 39/37 is valid.
Check x = 6/5.
9|9 – 8x| = 2x + 3
9|9 – 8(6/5)| = 2(6/5) + 3
|81 - 72(6/5)| = 12/5 + 15/5
|405/5 - 432/5| = 27/5
|-27/5| = 27/5
27/5 = 27/5
The solution x = 6/5 is also valid.
There are no extraneous solutions.
Can i please get help with this question?
Can someone help me for question 27 ? Pls!!!!
y = | 3x - 7 |
x-intercept is when y = 0
0 = | 3x - 7 |
0 = 3x - 7
+7 +7
7 = 3x
[tex]\frac{7}{3} = \frac{3x}{3}[/tex]
[tex]\frac{7}{3} = x[/tex]
[tex](\frac{7}{3}, 0 )[/tex]
y-intercept is when x = 0
y = | 3(0) - 7 |
y = | 0 - 7 |
y = | -7 |
y = 7
(0, 7)
Answer: [tex](\frac{7}{3}, 0 )[/tex] and (0, 7)
Simplify fully. (refer to photo)
A.
B.
C.
D.
the answer to your question :[tex]4\sqrt{5}[/tex]
hope this helps! ❤ from peachimin
Exact Form:√5
Decimal Form:2.23606797…
Linley bought a set of 20 markets at the price of $6. What does 1 marker cost?
One marker would cost approx. $0.03
Fernando paid 2.80 for potatoes. Potatoes cost 25 cents per pound. How many pounds of potatoes dead fernando by?
125.5 m/s to km/hr...Answer and Explanation
Chan rows at a rate of 8 mph in still water. It takes him three hours to row upstream from his house to the park. He rows back home, and it takes him 2 hours. What is the speed of the current?
d = r * t
time rate distance
Downstream: 2 8 + c d = 2(8 + c)
Upstream: 3 8 - c d = 3(8 - c)
Since the distance is the same, we can set the distance equations equal to each other and solve for c.
2(8 + c) = 3(8 - c)
16 + 2c = 24 - 3c
16 + 5c = 24
5c = 8
c = [tex]\frac{8}{5}[/tex]
c = 1.6
Answer: 1.6 mph