Eliminate the parameter for the following set of parametric equations: x= t^2 + 2 y= 4t^2
Answers
Answer:
Solution : y = 4x - 8
Step-by-step explanation:
The first thing we want to do is isolate t², rather than t. Why? As you can see when we substitute t² into the second equation, it will be easier than substituting t, as t is present in the form t². So, let's isolate t² in the first equation --- ( 1 )
x = t² + 2,
t² = x - 2
Now let's substitute this value of t² in the second equation --- ( 2 )
y = 4t²,
y = 4(x - 2),
y = 4x - 8 ~ And hence our solution is option c.
Related Questions
Which expression is equal to (1+6i)−(7+3i) ?
Answers
Answer:
- 6+3iStep-by-step explanation:
[tex](1+6i)-(7+3i) ?\\Group\:the\:real\:part\:and\:the\:imaginary\\\:part\:of\:the\:complex\:number\\\left(a+bi\right)\pm \left(c+di\right)=\left(a\:\pm \:c\right)+\left(b\:\pm \:d\right)i\\=\left(1-7\right)+\left(6-3\right)i\\1-7=-6\\6-3=3\\=-6+3i[/tex]
Caleb made 6 quarts of trail mix for his camping trip. Each week,he ate 4 pints of the trail mix. How many weeks did Caleb have trail mix?
Sry if this is too much
Answers
Answer:
3 weeks
Step-by-step explanation:
6 quarts = 12 pints
12 divided by 3 = 4
Step-by-step explanation:
1 quart = 2 pints
6 quarts = 2 x 6 = 12 pints
12 ÷ 4 = 3
He can have 3 weeks
Which equation represents a population of 210 animals that decreases at an annual rate of 14%
Answers
Answer:
The equation i.e. used to denote the population after x years is:
P(x) = 490(1 + 0.200 to the power of x
Step-by-step explanation:
This problem could be modeled with the help of a exponential function.
The exponential function is given by:
P(x) = ab to the power of x
where a is the initial value.
and b=1+r where r is the rate of increase or decrease.
Here the initial population of the animals are given by: 490
i.e. a=490
Also, the rate of increase is: 20%
i.e. r=20%
i.e. r=0.20
Hence, the population function i.e. the population of the animals after x years is:
P(x) = 490(1 + 0.200 to the power of x
So for this, we will be using exponential form, which is y = ab^x (a = initial value, b = growth/decay).
Since we start off with 210 animals, that is our a variable.
Next, since this is *decreasing* by 14%, you are to subtract 0.14 (14% in decimal form) from 1 to get 0.86. That will be your b variable.
Putting everything together, your equation is y = 210(0.86)^x
If the statement is true, type true in the space provided. If it is false, replace the underlined
word(s) with the word(s) that will make the statement true.
* The associative (associative is underlined) property is used on the following expression: 2 + 3 = 3 + 2.
Answers
] You are scheduled to receive $20,000 in two years. When you receive it, you will invest it for six more years at 8.4 percent per year. How much will you have in eight years?
Answers
Answer:
32449.3
Step-by-step explanation:
use the formula A = P(1+r / 100)^t
20000 × (1+ (8.4 / 100))^6
=32449.3
What is the area of the trapezoid shown below?
2
15
12
help fast please!!!
Answers
Answer:
78 units2
Step-by-step explanation:
The Area of the triangle is 54 units2
The rectangle on the side has an area of 24 units2.
Add them together, and you get 78.
I hope this helps!
pls ❤ and give brainliest pls
Use technology to solve the following problem: A certain car model has a mean gas mileage of 30 miles per gallon (mpg) with a standard deviation A pizza delivery company buys 42 of these cars. What is the probability that the average mileage of the fleet is greater than
Answers
Answer:
The answer is below
Step-by-step explanation:
The question is not complete, let me solve a question that is exactly like this one.
A certain car model has a mean gas mileage of 34 miles per gallon (mpg) with a standard deviation 5 mpg. A pizza delivery company buys 43 of these cars. What is the probability that the average mileage of the fleet is greater than 33.5 mpg?
Answer:
Given that the mean (μ) is 34 miles per gallon (mpg) with a standard deviation (σ) 5 mpg. The sample (n) is 43.
The z score is used in statistics to determine by how much the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma} \\for\ a \ sample\ size:\\z=\frac{x-\mu}{\sigma/\sqrt{n} }[/tex]
For the average mileage of the fleet is greater than 33.5 mpg (x > 33.5):
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }\\z=\frac{33.5-34}{5/\sqrt{43} } =-0.66[/tex]
From the normal distribution table, The probability that the average mileage of the fleet is greater than 33.5 mpg = P(x > 33.5) = P(z > -0.66) = 1 - P(z < -0.66) = 1 - 0.2546 = 0.7454 = 74.54%
Smoking by Race for Males Aged 18-24
Smoker Nonsmoker Row Total
(S) (N)
White(W) 290 560 850
Black(B) 30 120 150
Column Total 320 680 1,000
Calculate the probabilities given below (Round your answers to 4 decimal places.):
i. P(S) 0.3200
ii. P(W) 0.8500
iii. P(S | W) 0.2720
iv. P(S | B) 0.0300
v. P(S and W) 0.9062
vi. P(N and B) 0.1765
Answers
Answer:
(i) 0.32 (ii) 0.85
(iii) 0.3412 (iv) 0.20
(v) 0.29 (vi) 0.12
Step-by-step explanation:
The data provided is as follows:
Race Smoker (S) Nonsmoker (N) Row Total
White(W) 290 560 850
Black(B) 30 120 150
Column Total 320 680 1,000
(i)
Compute the value of P (S) as follows:
[tex]P(S)=\frac{n(S)}{N}=\frac{320}{1000}=0.32[/tex]
P (S) = 0.32.
(ii)
Compute the value of P (W) as follows:
[tex]P(W)=\frac{n(W)}{T}=\frac{850}{1000}=0.85[/tex]
P (W) = 0.85.
(iii)
Compute the value of P (S|W) as follows:
[tex]P(S|W)=\frac{n(S\cap W)}{n(W)}=\frac{290}{850}=0.3412[/tex]
P (S|W) = 0.3412.
(iv)
Compute the value of P (S|B) as follows:
[tex]P(S|B)=\frac{n(S\cap B)}{n(B)}=\frac{30}{150}=0.20[/tex]
P (S|W) = 0.20.
(v)
Compute the value of P (S∩W) as follows:
[tex]P(S\cap W)=\frac{n(S\cap W)}{T}=\frac{290}{1000}=0.29[/tex]
P (S∩W) = 0.29.
(vi)
Compute the value of P (N∩B) as follows:
[tex]P(N\cap B)=\frac{n(N\cap B)}{T}=\frac{120}{1000}=0.12[/tex]
P (S∩W) = 0.12.
Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. , The mean, , is nothing. (Round to the nearest tenth as needed.)
Answers
Complete Question
Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. , The mean, , is nothing. (Round to the nearest tenth as needed.)
p = 0.6 n = 18
Answer:
The mean [tex]\mu = 10.5[/tex]
The standard deviation [tex]\sigma = 2.08[/tex]
The variance [tex]var = 4.32[/tex]
Step-by-step explanation:
From the question we are told that
The probability of success is [tex]p = 0.6[/tex]
The sample size is [tex]n = 18[/tex]
Generally given that the distribution is binomial, then the probability of failure is mathematically represented as
[tex]q = 1- p[/tex]
substituting values
[tex]q = 1- 0.6[/tex]
[tex]q =0.4[/tex]
Generally the mean is mathematically evaluated as
[tex]\mu = np[/tex]
substituting values
[tex]\mu = 18 * 0.6[/tex]
[tex]\mu = 10.5[/tex]
The standard deviation is evaluated as
[tex]\sigma = \sqrt{npq}[/tex]
substituting values
[tex]\sigma = \sqrt{18 * 0.6 * 0.4}[/tex]
[tex]\sigma = 2.08[/tex]
The variance is evaluated as
[tex]var = \sigma^2[/tex]
substituting value
[tex]var = 2.08^2[/tex]
[tex]var = 4.32[/tex]
PLEASE HELP FOR 70 POINTS!!!!!! Maria and Jackson like in adjacent neighborhoods. If they superimpose a coordinate grid on the map of their neighborhoods, Maria lives at (–9, 1) and Jackson lives at (5, –4). Each unit on the grid is equal to approximately 0.132 mile. 8. How far apart do Maria and Jackson live to the nearest thousandth? 9. If April lives equidistant to both Maria and Jackson, at what coordinate on the grid would she live? 10. How far apart would Maria and April live to the nearest thousandth?
Answers
Answer:
8) 1.962 miles
9) (-2, -1.5)
10) 0.515 miles
Step-by-step explanation:
√(-9 - 5)² + (1 - -4)² = 14.866
14.866 x .132 = 1.962
(-9+5)/2, (1 + -4)/2
-4/2, -3/2
-2, -3/2
√(-2 - 1)² + (-3/2 - -4)² = 3.905
3.905 x .132 = 0.515 miles
Suppose ACT Science scores are normally distributed with a mean of 20.8 and a standard deviation of 5.2. A university plans to send letters of recognition to students whose scores are in the top 12%. What is the minimum score required for a letter of recognition? Round your answer to the nearest tenth, if necessary.
Answers
Answer:
Hello,
Answer 26.9
Step-by-step explanation:
[tex]z=\dfrac{x-m}{\sigma} \\m=20.8\\\sigma=5.2\\\\p(z>?)\geq 0.12\ \longrightarrow 1-p(z\leq ?)=(1-0.12))\\\\Using\ table\ of\ normal\ reduce\ with\ 4 \decimals : ?=1.175\\\\x=1.175*5.2+20.8=26.91\approx{26.9}[/tex]
Point A is located at (1, 5), and point M is located at (-1, 6). If point M is the midpoint of AB, find the location of point B.
Answers
The required coordinates of point B are (-3, 7) where point M is the midpoint of AB.
What is Midpoint?A midpoint is defined as in the middle of the line connecting two points a position known as a midpoint. A location in the middle of a line connecting the two points that are equally far from both points is the midpoint.
Point A is located at (1, 5), and point M is located at (-1, 6). If point M is the midpoint of AB
We can use these coordinates to find the coordinates of point B, which is the midpoint of line segment AB.
Let the coordinates of B would be (x, y)
Substituting the coordinates of points A into the midpoint formula gives us :
-1 = (x+1)/2 ; 6 = (y+5)/2
-2 = x +1 ; 12 = y + 5
x = -3; y = 7
Therefore, the required coordinates of point B are (-3, 7).
Learn more about the midpoint here :
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a
A solid metal cone of base radius a cm and height 2a cm is melted and solid
spheres of radius are made without wastage. How many such spheres can be
made?
Answers
volume of a cone
.
.
.
volume of sphere
.
.
number of spheres that can be made......
.
.
hence a hemisphere can be formed
In a triangle ABC two points D,E are taken on BC so that angle BAD=angle DAE=angleCAE. Determine AE if AB=5,BC=10 angle BAC=90. PLEASE HELP I NEED HELP WITHIN TEN MINS PLEASE
Answers
Answer:
AE = 7.5
Step-by-step explanation:
Since <BAC = [tex]90^{0}[/tex], then;
<BAD = <DAE = <CAE = [tex]30^{0}[/tex] (complementary angles)
From ΔABC, applying the Pythagoras theorem to determine the length of side AC;
[tex]/BC/^{2}[/tex] = [tex]/AC/^{2}[/tex] + [tex]/AB/^{2}[/tex]
[tex]/10/^{2}[/tex] = [tex]/AC/^{2}[/tex] + [tex]/5/^{2}[/tex]
100 = [tex]/AC/^{2}[/tex] + 25
[tex]/AC/^{2}[/tex] = 100 - 25
[tex]/AC/^{2}[/tex] = 75
AC = [tex]\sqrt{75}[/tex]
Applying trigonometric function to ΔCAE,
Cos [tex]30^{0}[/tex] = [tex]\frac{AE}{\sqrt{75} }[/tex]
AE = [tex]\sqrt{75}[/tex] × Cos [tex]30^{0}[/tex]
= 7.5
Therefore, AE = 7.5
Math 120 - 01 Summer 2021
Consuelo Butler
08/07
Homework: Practice
Exam 3
Question 1, 12.1.13
HW Score: 10%, 3 of 30 points
Score: 1 of 1
A professor had students keep track of their social interactions for a week. The
number of social interactions over the week is shown in the following grouped
frequency distribution. How many students had at least 60 social interactions for
the week?
12
Number of Social
Interactions
30-34
35-39
40-44
45-49
50-54
55-59
60-64
65-69
70-74
75-79
Frequency
9
14
11
15
16
8
7
3
1
1
Answers
Step-by-step explanation:
Consuelo Butler
08/07
Homework: Practice
Exam 3
Question 1, 12.1.13
HW Score: 10%, 3 of 30 points
Score: 1 of 1
A professor had students keep track of their social interactions for a week. The
number of social interactions over the week is shown in the following grouped
frequency distribution. How many students had at least 60 social interactions for
the week?
12
Number of Social
Interactions
30-34
35-39
40-44
45-49
50-54
55-59
60-64
65-69
70-74
75-79
Frequency
9
14
11
15
16
8
7
By calculating the greater than cumulative frequency using the given frequency table, 12 students had at least 60 social interactions for the week.
What is greater than cumulative frequency?The greater than cumulative frequency is also known as the more than type cumulative frequency. Here, the greater than cumulative frequency distribution is obtained by determining the cumulative total frequencies starting from the highest class to the lowest class.
Class interval Frequency Cumulative frequency
30-34 9 85
35-39 14 76
40-44 11 62
45-49 15 51
50-54 16 36
55-59 8 20
60-64 7 12
65-69 3 5
70-74 1 2
75-79 1 1
[We read the cumulative frequencies with respect to the corresponding lower class limits. For example, 85 students had 'more than 30' social interactions, 76 students had 'more than 35 social interactions and so on.]
By reading the greater than cumulative frequency, we find that 12 students had at least 60 social interactions for the week.
Learn more about greater than cumulative frequency here
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Can I have help with 43 and 44 I need to see how to do them thanks.
Answers
Answer:
see explanation
Step-by-step explanation:
(43)
3[tex]x^{5}[/tex] - 75x³ ← factor out 3x³ from each term
= 3x³(x² - 25) ← this is a difference of squares and factors in general as
a² - b² = (a - b)(a + b) , thus
x² - 25 = x² - 5² = (x - 5)(x + 5)
Thus
3[tex]x^{5}[/tex] - 75x³ = 3x³(x - 5)(x + 5)
(44)
81c² + 72c + 16 ← is a perfect square of the form
(ac + b)² = a²c² + 2abc + b²
Compare coefficients of like terms
a² = 81 ⇒ a = [tex]\sqrt{81}[/tex] = 9
b² = 16 ⇒ b = [tex]\sqrt{16}[/tex] = 4
and 2ab = 2 × 9 × 4 = 72
Thus
81c² + 72c + 16 = (9c + 4)²
1. 3x^5 -75x³
=3x³(x²-25)
=3x³(x²-5²)
=3x³(x-5)(x+5)
2. 81c²+72c+16
=81c²+36c+36c+16
=9c(9c+4)+4(9c+4)
=(9c+4)(9c+4)
=(9c+4)²
Find 2
x
y у
30°
4√3
OA. 4/2
OB.22
0.8
D.4
Answers
Answer:
8
Step-by-step explanation:
The given is a special right triangle with angle measures
90-60-30 and side lengths represented by
2a-a[tex]\sqrt{3}[/tex]-a
x is the side length that sees angle measure 90 degrees so it's represented by 2a
and 4[tex]\sqrt{3}[/tex] is the side length that sees angle measure that sees 60 degrees so the value of a is 4
therefore x = 2*4 = 8
A probability experiment is conducted in which the sample space of the experiment is S={1,2,3,4,5,6,7,8,9,10,11,12}. Let event E={3,4,5,6,7,8}. Assume each outcome is equally likely. List the outcomes in Ec. Find P(Ec).The outcomes of Ec are {_____}P(Ec)=
Answers
Answer:
This list of all the outcome of [tex]E^c[/tex] is [tex]E^c = \{ 1,2,9,10,11,12,\}[/tex]
[tex]P(E^c ) = 0.5[/tex]
Step-by-step explanation:
From the question we are told that
The sample sample space is [tex]S = \{ 1,2,3,4,5,6,7,8,9,10,11,12 \}[/tex]
The number of elements in the sample space is [tex]n = 12[/tex]
The event is [tex]E = \{ 3,4,5,6,7,8 \}[/tex]
The number of outcomes in the Event is [tex]n_e = 6[/tex]
The objective in to obtain [tex]P(E^c)[/tex]
Now [tex]E^c[/tex] is the compliment of E and number of elements in [tex]E^c[/tex] ican be mathematically evaluated as
[tex]nE^c = n - n_e[/tex]
substituting values
[tex]E^c = 12-6[/tex]
[tex]E^c = 6[/tex]
This list of all the outcomes of [tex]E^c[/tex] is
[tex]E^c = \{ 1,2,9,10,11,12,\}[/tex]
Generally [tex]P(E^c )[/tex] which is the probability of [tex]E^c[/tex] is mathematically evaluated as
[tex]P(E^c ) = \frac{nE^c}{n}[/tex]
substituting values
[tex]P(E^c ) = \frac{6}{12}[/tex]
[tex]P(E^c ) = 0.5[/tex]
Convert the decimal 0.984 to a fraction.
984/100
984/1000
984/99
984/999
Answers
Answer:
[tex]\boxed{\frac{984}{1000}}[/tex]
Step-by-step explanation:
Hey there!
Well .984 is 984 over 1000 so .984 as a fraction is 984/1000.
We can check this by doing 984 / 1000 which is .984.
Hope this helps :)
For this problem, use the tables and charts shown in this section. (Use picture provided)
A United States Citizen returning to the States declares the following items at the customs office:
3 shirts at $8.50 each
2 dresses at $27.50 each
1 pair of gold cuff links at $17.50 per pair
If he has not used his duty free exemption yet, how much duty should he pay?
0 $0.00
$5.00
$10.00
$300
Answers
Answer:
0
Step-by-step explanation:
0 because there is a $100 duty free exemption.
answer:
For this problem, use the tables and charts shown in this section.
A United States Citizen returning to the States declares the following items at the customs office:
3 shirts at $8.50 each
2 dresses at $27.50 each
1 pair of gold cuff links at $17.50 per pair
If he has not used his duty free exemption yet, how much duty should he pay?
$0.00 !
$5.00
$10.00
$300
What is the value of n in the equation shown?
Captionless Image
Answers
Answer:
bzbdvdbdyrhevgdhs sdd
Step-by-step explanation:
ushebdvrudvd very
zhrjdvfjvrhfbrjrbr
hhrbdbdbfbfhfhthr
rhdjdbbffbdbbdve
whats the perimeter of a squre with a side measurement of 6 in.?
Answers
Answer:
The Perimeter is 24 inches
Step-by-step explanation:
Perimeter is all the sides of something added up. All sides on a square are equal so each side is 6 inches
6+6+6+6=24
Compute the flux H F of F(x,y) = hxy, x − yi across the boundary of the square given by −1 ≤ x ≤ 1, −1 ≤ y ≤ 1.
Answers
Answer:
4i.
Step-by-step explanation:
To find the flux through the square, we use the divergence theorem for the flux. So Flux of F(x,y) = ∫∫divF(x,y).dA
F(x,y) = hxy,x - yi
div(F(x,y)) = dF(x,y)/dx + dF(x,y)dy = dhxy/dx + d(x - yi)/dy = hy - i
So, ∫∫divF(x,y).dA = ∫∫(hy - i).dA
= ∫∫(hy - i).dxdy
= ∫∫hydxdy - ∫∫idxdy
Since we are integrating along the boundary of the square given by −1 ≤ x ≤ 1, −1 ≤ y ≤ 1, then
∫∫divF(x,y).dA = ∫₋₁¹∫₋₁¹hydxdy - ∫₋₁¹∫₋₁¹idxdy
= h∫₋₁¹{y²/2}¹₋₁dx - i∫₋₁¹[y]₋₁¹dx
= h∫₋₁¹{1²/2 - (-1)/2²}dx - i∫₋₁¹[1 - (-1)]dx
= h∫₋₁¹{1/2 - 1)/2}dx - i∫₋₁¹[1 + 1)]dx
= 0 - i∫₋₁¹2dx
= - 2i[x]₋₁¹
= 2i[1 - (-1)]
= 2i[1 + 1]
= 2i(2)
= 4i
A bag contains 4 white and 2 black balls of the same size and weight and two balls are selected at random without replacement,what are the possible outcomes ?
Answers
Answer:
Step-by-step explanation:
Total balls in bag = 4+2
= 6 balls
Total white balls = 4
Total black balls = 2
The possible outcomes are
Black and Black or White and White or White and Black or Black and White.
Probability of black and black = 2/6
= 1/3
Probability of white and white = 4/6
= 2/3
Probability of Black and white or White and black
= 1/3×2/3
= 2/9
please click thanks and mark brainliest if you like :)
possible outcomes will be white and black, white and white, black and white or black and black
Juan starts a bacteria culture and records the number of bacteria in the Petri dish for the first couple of hours.
Hours Bacteria
0
160
1
320
2
640
If the pattern continues, how many bacteria can he expect to find after 17 h?
Enter your answer in the box.
Answers
9514 1404 393
Answer:
20,971,520
Step-by-step explanation:
The population is doubling every hour, so after 17 hours it will be the initial population (160) multiplied by 2^17 = 131,072.
After 17 hours, he can expect to find 160×131072 = 20,971,520 bacteria.
Reduce to Standard form : (a) -21/91 (b) 32/(-256)
Answers
Answer:
a) -3/13
b) -1/8
Step-by-step explanation:
a) - (21 / 7) / (91 / 7) = 3/13
b) (32 / 32 ) / - (256 / 32) = -1/8
The cost of a daily rental car is as follows: The initial fee is $39.99 for the car, and it costs $0.20 per mile. If Julie's final bill was $100.00 before taxes, how many miles did she drive?
Answers
Answer:
300.05 miles
Step-by-step explanation:
initial fee= $39.99
final bill = $ 100
cost =$ 0.20 per mile
remaining amount = $ 60.01
solution,
she drive = remaining amount / cost
=60.01/0.20
=300.05 miles
Answer:
500 miles
Step-by-step explanation:
Let us use cross multiplication to find the unknown amount.
Given:
1) Cost for 1 mile=$0.20
2)Cost for x miles=$100
Solution:
No of miles Cost
1) 1 $0.20
2)x $100
By cross multiplying,
100 x 1= 0.20x
x=100/0.20
x=500 miles
Thank you!
log, (x + y)=log, y, log, x .
Solve for question D only
Answers
Answer:
4.
Step-by-step explanation:
Change of base formula is
logb x = loga x / loga b
So logx 25 = log5 25 /log5 x
Now log5 25 = log5 5^2 = 2, so:
logx 25 = 2 / log5 x
So log5 x^2 * logx 25
= log5 x^2 * 2 /log5 x
= 2 log5 x * 2 / log5 x
= 4.
What is the answer to my question?
Answers
Answer:
2/3
Step-by-step explanation:
24/36
Divide the top and the bottom by 12
24/12 =2
36/12 = 3
2/3
12. 12 ounces is roughly the same as
O A. 340 grams.
B. 356 grams.
O C. 400 grams.
O D. 120 grams.
Mark for review (Will be highlighted on the movin
Answers
Answer:
A. 340 grams
Step-by-step explanation:
My brain