Answer:
The numbers that are at a distance of 2 from the number 8 can be expressed using absolute value notation as:
|x - 8| = 2
Step-by-step explanation:
The numbers that are at a distance of 2 from the number 8 are the numbers that are satisfied by the equation:
|x - 8| = 2
The equation is written in the notation of absolute value as required.
A number is chosen at random from 1 to 10. Find
the probability of selecting 4 or a factor of 6.
Step by step.
Answer:
1/2
Step-by-step explanation:
The possible outcomes are
1,2,3,4,5,6,7,8,9,10
Factors of 6 are 1,2,3,6
or a 4
1,2,3,4,6 are the outcomes we want
There are 5 "good" outcomes
P( 4 or a factor of 6) = "good" outcomes/ total
= 5/10
=1/2
Answer:
[tex]\boxed{\frac{1}{2} }[/tex]
Step-by-step explanation:
There are total 10 outcomes.
[tex]1,2,3,4,5,6,7,8,9,10[/tex]
The probability of selecting 4 is 1 outcome out of total 10 outcomes.
Factors of 6 are [tex]1,2,3,6[/tex].
These are 4 outcomes out of total 10 outcomes.
The probability of selecting 4 or a factor of 6 is:
[tex]\displaystyle \frac{1}{10} +\frac{4}{10} =\frac{5}{10} =\frac{1}{2}[/tex]
Write 8:18 as a fraction in simplest form.
Ratio as a Fraction:
Fraction in Simplest Form:
Answer:
[tex]\text{Ratio as a fraction - \: \boxed{\frac{8}{18}}}[/tex]
[tex]\text{Fraction in simplest form - \boxed{\frac{4}{9}}}[/tex]
Step-by-step explanation:
Part 1: Writing a ratio as a fraction
A fraction and a ratio are the same thing - just a different name. Therefore, the colon in a ratio is the same as a divisor line in a fraction. Therefore, to write a ratio as a fraction,
Replace the colon with a divisor line or the divisor line with a colon (use the first portion to transform a ratio into a fraction and the second form to transform a fraction into a ratio).Therefore, 8:18 as a fraction is 8/18.
Part 2: Fraction in simplest form
To put a fraction in simplest form, first divide the numerator by the denominator. If it contains a remainder, you cannot use this step to verify it.
8 only goes into 18 twice and leaves a 2 as a remainder, so this method does not work.
Instead, if both numbers are even, divide by 2.
8/2 = 4
18/2 = 9
Check to see if the new numerator and denominator can reduce any further.
4/9 = 4/9
The fraction in simplest form is 4/9.
A company has 8 mechanics and 6 electricians. If an employee is selected at random, what is the probability that they are an electrician
Answer:
[tex]Probability = \frac{3}{7}[/tex]
Step-by-step explanation:
Given
Electrician = 6
Mechanic = 8
Required
Determine the probability of selecting an electrician
First, we need the total number of employees;
[tex]Total = n(Electrician) + n(Mechanic)[/tex]
[tex]Total = 6 + 8[/tex]
[tex]Total = 14[/tex]
Next, is to determine the required probability using the following formula;
[tex]Probability = \frac{n(Electrician)}{Total}[/tex]
[tex]Probability = \frac{6}{14}[/tex]
Divide numerator and denominator by 2
[tex]Probability = \frac{3}{7}[/tex]
Hence, the probability of selecting an electrician is 3/7
Frank and Gregory leave Centreville traveling in opposite directions on a straight road. Gregory drives 22 miles per hour faster than Frank. After 2.25 hours, they are 216 miles apart. Find Frank's speed and Gregory's speed.
Answer:
Frank speed = 37mi/hGregory speed = 59mi/hrStep-by-step explanation:
Let the speed of Frank be x and speed of Gregory be y. If Gregory drives 22 miles per hour faster than Frank, then y = 22+x. SInce they they are 216miles apart after 2.25 hours,
Speed = Distance/Time
Total time travelled by them = 2.25hours
Total distance = 216 hours
Total speed = x+y = x+22+x
Substituting this parameters into the formula given to get x we will have;
x+22+x = 216/2.25
2x+22 = 96
2x = 96-22
2x = 74
x = 74/2
x = 37
Hence the speed of Frank is 37miles per hour while that of gregory is 37+22 = 59miles/hour
Bighorn sheep are beautiful wild animals found throughout the western United States. Data for this problem are based on information taken from The Desert Bighorn, edited by Monson and Sumner 9University of Arizona Press). Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information:
x 1 2 3 4 5
y 14 18.9 14.4 19.6 20.0
∑x=15 ; ∑y=87.3;∑x2=55; ∑y2=1569.77; ∑xy=275
(a) Draw a scatter diagram.
(b) Find the equation of the least-squares line, and plot the line on the scatter diagram of part (a).
(c) Find the correlation coefficient r. Find the coefficient of determination . What percentage of variation in y is explained by the variation in x and the least squares model?
Answer:
The answer and explanation are below
Step-by-step explanation:
i followed the data that was given in the question.
∑x=15 ; ∑y=87.3;∑x2=55; ∑y2=1569.77; ∑xy=275
a.) please refer to the attachment for the scatter diagram. Y was plotted against X.
b. The equation is given as:
Y = b₁ + b₀X
∑x=15 ; ∑y=87.3;∑x2=55; ∑y2=1569.77; ∑xy=275
b₁ = n∑xy - (∑x)(∑y)/n(∑x²) - (∑x)²
b₁ = 5 x 275 - 15 x 87.3/5 x 55 - (15²)
= 1375-1309.5/275-225
= 65.5/50
= 1.31
b₀ = 87.3/5 - 1.31(15/5)
= 87.3/5 - 1.31x3
= 13.53
the regression line is
Y = 13.53 + 1.31X
please refer to the attachment for the diagram for the regression line.
c. we are required to find r.
r = n∑XY - (∑X)(∑Y)/√n∑X²-(∑X)² × √n∑y²-(∑y)²
∑x=15 ; ∑y=87.3;∑x2=55; ∑y2=1569.77; ∑xy=275
inserting these values:
r = 5 x 275-(15)(87.3)/√275-225 x √7848.85 - 7621.29
= 65.5/106.69
= 0.6139
Coefficient of determination = r²
r = 0.6139
r² = 0.3769 = 37.69%
Therefore 37.69% variation in y is explained by variation in x and the least square model.
1.Find the value of x in the equation below
3^(2x+1)÷3^(3x-4)×3^(6-7x)=27x
2.Solve the equation 2^(x+y)=8 and 3^(x-y)=1 simultaneously
Answer:
Step-by-step explanation:
Hello, please consider the following.
Question 1.
[tex]\dfrac{3^{2x+1}}{3^{3x-4}\cdot 3^{6-7x}}=27^x\\\\<=> 3^{2x+1}\cdot 3^{-3x+4}\cdot 3^{-6+7x}=3^{2x+1-3x+4-6+7x}=(3^3)^x=3^{3x}\\\\<=> 2x+1-3x+4-6+7x=3x\\\\<=> 6x-1=3x\\\\<=> 3x=1\\\\<=> \boxed{x=\dfrac{1}{3}}[/tex]
Question2.
[tex]2^{x+y}=8=2^3 <=>x+y=3\\\\3^{x-y}=1=3^0<=>x-y=0[/tex]
So, it gives (by adding the two equations) 2x = 3
[tex]\boxed{x=\dfrac{3}{2} \ \ and \ \ y = x = \dfrac{3}{2} }[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Pulse rates of women are normally distributed with a mean of 77.5 beats per minute and a standard deviation of 11.6 beats per minute.
1. What are the values of the mean and standard deviation after converting all pulse rates of women to z scores using z = (x - mu )?
2. What are the units of the corresponding z scores?
A. The z scores are measured with units of "beats per minute".
B. The z scores are measured with units of "minutes per beat".
C. The z scores are measured with units of "beats."
D. The z scores are numbers without units of measurement.
Answer:
D. The z scores are numbers without units of measurement.
Step-by-step explanation:
Z-scores are without units, or are pure numbers.
In a recent year, a sample of grade 8 Washington State public school students taking a mathematics assessment test had a mean score of 281 with a standard deviation of 34.4. Possible test scores could range from 0 to 500. Assume that the scores are normally distributed. Question 9 (2.5 points) If 2000 students are randomly selected, how many would you expect to have a score between 250 and 305?
Answer:
The number is [tex]N =1147[/tex] students
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 281[/tex]
The standard deviation is [tex]\sigma = 34.4[/tex]
The sample size is n = 2000
percentage of the would you expect to have a score between 250 and 305 is mathematically represented as
[tex]P(250 < X < 305 ) = P(\frac{ 250 - 281}{34.4 } < \frac{X - \mu }{\sigma } < \frac{ 305 - 281}{34.4 } )[/tex]
Generally
[tex]\frac{X - \mu }{\sigma } = Z (Standardized \ value \ of \ X )[/tex]
So
[tex]P(250 < X < 305 ) = P(-0.9012< Z<0.698 )[/tex]
[tex]P(250 < X < 305 ) = P(z_2 < 0.698 ) - P(z_1 < -0.9012)[/tex]
From the z table the value of [tex]P( z_2 < 0.698) = 0.75741[/tex]
and [tex]P(z_1 < -0.9012) = 0.18374[/tex]
[tex]P(250 < X < 305 ) = 0.75741 - 0.18374[/tex]
[tex]P(250 < X < 305 ) = 0.57[/tex]
The percentage is [tex]P(250 < X < 305 ) = 57\%[/tex]
The number of students that will get this score is
[tex]N = 2000 * 0.57[/tex]
[tex]N =1147[/tex]
A video rental store keeps a list of their top 15 movie rentals each week. This week the list includes 6 action, 4 comedies, 3 dramas, and 2 mysteries. The store manager removes a copy of each of the 15 movies from the shelf, then randomly selects 3 of the 15 to show on the display monitors in the store. What is the probability that she selected 2 comedies and 1 action movie?
Answer:
32/1125Step-by-step explanation:
Probability is the likelihood or chance that an event will occur.
Probability = Expected outcome of event/Total outcome.
If a video rental store keeps a list of their top 15 movie rentals each week, the total outcome is 15.
If the list for the week includes 6 action, 4 comedies, 3 dramas, and 2 mysteries and the store manager removes a copy of each of the 15 movies from the shelf, then randomly selects 3 of the 15 to show on the display monitors in the store, the probability that she selected 2 comedies and 1 action movie will be calculated as shown;
Probability of selecting 2 comedies = 4/15*4/15 = 16/225 (Note that the expected outcome in this case is 4).
Probability of selecting 1 action movie = 6/15 = 2/5
Hence, the probability that she selected 2 comedies and 1 action movie will be equivalent to 16/225*2/5 = 32/1125
Note that the rented movies will have to be returned hence reason for the replacement.
what number should replace the question mark
Answer: The missing number is 5.
Step-by-step explanation:
In the table we can only have numbers between 1 and 9,
The pattern that i see is:
We have sets of 3 numbers.
"the bottom number is equal to the difference between the two first numers, if the difference is negative, change the sign, if the difference is zero, there goes a 9 (the next number to zero)"
Goin from right to left we have:
9 - 6 = 3
6 - 2 = 4
4 - 9 = - 5 (is negative, so we actually use -(-5) = 5)
4 - 4 = 0 (we can not use zero, so we use the next number, 9)
3 - 3 = 0 (same as above)
? - 1 = 4
? = 4 + 1 = 5
The missing number is 5.
Given the function f ( x ) = 2 x + 8 , evaluate and simplify the expressions below. See special instructions on how to enter your answers.
Answer:
[tex]f(a) = 2a + 8[/tex]
[tex]f(x + h) = 2x + 2h + 8[/tex]
[tex]\frac{f(x + h) - f(x)}{h} = 2[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 2x + 8[/tex]
Required
[tex]f(a)[/tex]
[tex]f(x + h)[/tex]
[tex]\frac{f(x + h) - f(x)}{h}[/tex]
Solving for f(a)
Substitute a for x in the given parameter
[tex]f(x) = 2x + 8[/tex] becomes
[tex]f(a) = 2a + 8[/tex]
Solving for f(x+h)
Substitute x + h for x in the given parameter
[tex]f(x + h) = 2(x + h) + 8[/tex]
Open Bracket
[tex]f(x + h) = 2x + 2h + 8[/tex]
Solving for [tex]\frac{f(x + h) - f(x)}{h}[/tex]
Substitute 2x + 2h + 8 for f(x + h), 2x + 8 fof f(x)
[tex]\frac{f(x + h) - f(x)}{h}[/tex] becomes
[tex]\frac{2x + 2h + 8 - (2x + 8)}{h}[/tex]
Open Bracket
[tex]\frac{2x + 2h + 8 - 2x - 8}{h}[/tex]
Collect Like Terms
[tex]\frac{2x - 2x+ 2h + 8 - 8}{h}[/tex]
Evaluate the numerator
[tex]\frac{2h}{h}[/tex]
[tex]2[/tex]
Hence;
[tex]\frac{f(x + h) - f(x)}{h} = 2[/tex]
What is the radius of the circle whose center is the
origin and that passes through the point (5,12)?
Answer:
13 units
Step-by-step explanation:
Use the equation of a circle, (x - h)² + ( y - k )² = r², where (h, k) is the center and r is the radius.
Plug in the values and solve for r:
(5 - 0)² + (12 - 0)² = r²
25 + 144 = r²
169 = r²
13 = r
if 2500 amounted to 3500 in 4 years at simple interest. Find the rate at which interest was charged
Answer:
35%
Step-by-step explanation:
[tex]Principal = 2500\\\\Simple\:Interest = 3500\\\\Time = 4 \:years\\\\Rate = ?\\\\Rate = \frac{100 \times Simple \: Interest }{Principal \times Time}\\\\Rate = \frac{100 \times 3500}{2500 \times 4} \\\\Rate = \frac{350000}{10000}\\\\ Rate = 35 \%[/tex]
[tex]S.I = \frac{PRT}{100}\\\\ 100S.I = PRT\\\\\frac{100S.I}{PT} = \frac{PRT}{PT} \\\\\frac{100S.I}{PT} = R[/tex]
Answer:
35%
Step-by-step explanation:
I REALLY HOPE I HELPED
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
A large population has a bell-shaped distribution with a mean of 200 and a standard deviation of 40. Which one of the following intervals would contain approximately 95% of the measurements?
a. (160, 240)
b. (140, 260)
c. (120, 280)
d. (200, 320)
The intervals would contain approximately 95% of the measurements will be (120, 280). Then the correct option is C.
What is a normal distribution?The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.
In numerical documentation, these realities can be communicated as follows, where Pr(X) is the likelihood capability, Χ is a perception from an ordinarily circulated irregular variable, μ (mu) is the mean of the dispersion, and σ (sigma) is its standard deviation:
The interval for 95% will be given as,
Pr(X) = μ ± 2σ
Pr(X) = 200 ± 2(40)
Pr(X) = 200 ± 80
Pr(X) = (200 - 80, 200 + 80)
Pr(X) = (120, 280)
The intervals would contain approximately 95% of the measurements will be (120, 280). Then the correct option is C.
More about the normal distribution link is given below.
https://brainly.com/question/12421652
#SPJ5
a function includes the points (4, -3) and (-9,4). what fraction in lowest terms represents the output value of this function for an input of zero
Answer:
-11/13
Step-by-step explanation:
The equation of the line through these points can be written using the 2-point form of the equation of a line:
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
y = (4 -(-3))/(-9-4)/(x -4) -3
y = (-7/13)x +28/13 -3
For x=0, the value of y is ...
y = 28/13 -39/13 = -11/13
The output for an input of 0 is -11/13.
which expression is equivalent to x^-5/3
Answer:
B
Step-by-step explanation:
Since the power is negative, you automatically know it has to be a or b, because the only way it would be negative is if it was brought from the denominator to the numerator.
The answer is B, because the numerator of the power, is what is inside the square root, while the denominator is what is outside the square root.
To the nearest square inch, what is the surface area of the square pyramid shown in the image? A. 175 in.^2 B. 200 in.^2 C. 400 in.^2 D. 700 in.^2 Please show ALL work! :D
Answer: C. 400 in^2
Step-by-step explanation:
First find the surface area or the area of the base which is in the shape of a square and has a side length of 10 in. So square 10 to find the area.
Area of base: 10 * 10 = 100
Next find the area of one of the triangles.
As we could see the triangle has a slant height of 15 in and a base of 10. To find the area of a triangle we multiply the base times the height and multiply it by half.
Area of one triangle. 15 * 10 = 150 * 1/2 = 75
Since one side of the triangle has a surface area of 75 inches we will multiply it by 4 since there are four triangles to find the total surface area of the four faces.
75 * 4 = 300
We now know that the the 4 triangles surface area dd up to 300 so we will add it to the area of the base which is 100 to find the whole surface area of the figure.
300 + 100 = 400
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
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.
In a study of 24 criminals convicted of antitrust offenses, the average age was 60 years, with a standard deviation of 7.4 years. Construct a 95% confidence interval on the true mean age. (Give your answers correct to one decimal place.)___ to____ years
Answer: 56.9 years to 63.1 years.
Step-by-step explanation:
Confidence interval for population mean (when population standard deviation is unknown):
[tex]\overline{x}\pm t_{\alpha/2}{\dfrac{s}{\sqrt{n}}}[/tex]
, where [tex]\overline{x}[/tex]= sample mean, n= sample size, s= sample standard deviation, [tex]t_{\alpha/2}[/tex]= Two tailed t-value for [tex]\alpha[/tex].
Given: n= 24
degree of freedom = n- 1= 23
[tex]\overline{x}[/tex]= 60 years
s= 7.4 years
[tex]\alpha=0.05[/tex]
Two tailed t-critical value for significance level of [tex]\alpha=0.05[/tex] and degree of freedom 23:
[tex]t_{\alpha/2}=2.0687[/tex]
A 95% confidence interval on the true mean age:
[tex]60\pm (2.0686){\dfrac{7.4}{\sqrt{24}}}\\\\\approx60\pm3.1\\\\=(60-3.1,\ 60+3.1)\\\\=(56.9,\ 63.1)[/tex]
Hence, a 95% confidence interval on the true mean age. : 56.9 years to 63.1 years.
A plane took off at a point that is 42 meters from the control tower. The flight path takes the plane over the control tower that is 98 meters high. After traveling 83 meters, which statement is most accurate?
A. The plane needs to be about 15 meters higher to clear the tower.
B. The plane clears the tower with about 27 meters to spare.
C. The plane clears the tower with about 15 meters to spare.
D. The plane needs to be about 27 meters higher to clear the tower.
Answer:
D. The plane needs to be about 27 meters higher to clear the tower.
Step-by-step explanation:
In this scenario a triangle is being formed. The base the plane's takeoff point to the tower base which is 42 meters (x).
The hypothenus is the distance travelled by the plane which is 83 meters (h)
The height of the tower is 98 Meters
We want to calculate the height of our triangle (y) so we can guage if the plane scaled the tower.
According to Pythagorean theorem
(x^2) + (y^2) = h^2
y = √ (h^2) - (x^2)
y = √ (83^2) - (42^2)
y= √(6889 - 1764)
y= 71.59 Meters
The height from the plane's position to the top of the tower will be
Height difference = 98 - 71.59 = 26.41 Meters
So the plane should go about 27 Meters higher to clear the tower
A researcher examines typing speed before a typing class begins, halfway through the class, and after the class is over. 4. Identify the number of levels: 5. Identify the type of design: 6. Identify the dependent variable:
Answer:
Number of levels = 2
Type of design = Repeated measure
Dependent variable = Typing Speed
Step-by-step explanation:
The number of levels in an experiment simply refers to the number of experimental conditions in which participants are subjected to. In the scenario above, the number of levels is 2. Which are ; Halfway through the class and After the class is over.
The type of designed employed is REPEATED MEASURE, this is because the participants all took part in each experimental condition.
The dependent variable is TYPING SPEED, which is the variable which is measured with respect to the independent variable. Hence the observed value depends on period that is (halfway through the class or after the class is over).
What is the perimeter of the image attached?? (PLEASE HELP I WILL MARK BRAINLIEST)
Answer:
[tex] Perimeter = 3x + 3 [/tex]
Step-by-step explanation:
Perimeter of the given triangle in the figure is the sum of all three sides.
The expressions for the 3 sides are given as, [tex] x, (x - 3), (x + 6) [/tex].
Therefore,
[tex] Perimeter = x + (x - 3) + (x + 6) [/tex]
Simplify,
[tex] Perimeter = x + x - 3 + x + 6 [/tex]
Collect like terms
[tex] Perimeter = x + x + x - 3 + 6 [/tex]
[tex] Perimeter = 3x + 3 [/tex]
find the value of each variable and the measure of each angle
Answer:
Left angle = 60°
Top angle = 120°
Right angle = 60°
Step-by-step explanation:
Use what you know about angle relationships to set up equations you can solve for each variable.
The top top angle, for example, added to one of the other angles must equal 180° because they are supplementary.
You have two variables, so you need at least two equations (I made three but only used two).
The work is in my attachment, comment of you have questions.
Brainliest! Jared uses the greatest common factor and the distributive property to rewrite this sum: 100 + 75 Drag one number into each box to show Jared's expression. Brainliest!
Answer:
25(4 + 3)
Step-by-step explanation:
100 = 2^2 + 5^2
75 = 3 * 5^2
GCF = 5^2 = 25
100 + 75 =
= 25 * 4 + 25 * 3
= 25(4 + 3)
Apply the distributive property to factor out the greatest common factor. 18d+12 =18d+12=18, d, plus, 12, equals
Answer:
[tex]\huge\boxed{6 ( 3d + 2 )}[/tex]
Step-by-step explanation:
18d + 12
The greatest common factor is 6, So we need to factor out 6
=> 6 ( 3d + 2 ) [Distributive property has been applied and this is the simplest form]
Answer:
6(3d+2)
Step-by-step explanation:
6 is the gcd of the two terms.
Find a set of parametric equations for y= 5x + 11, given the parameter t= 2 – x
Answer:
[tex]x = 2-t[/tex] and [tex]y = -5\cdot t +21[/tex]
Step-by-step explanation:
Given that [tex]y = 5\cdot x + 11[/tex] and [tex]t = 2-x[/tex], the parametric equations are obtained by algebraic means:
1) [tex]t = 2-x[/tex] Given
2) [tex]y = 5\cdot x +11[/tex] Given
3) [tex]y = 5\cdot (x\cdot 1)+11[/tex] Associative and modulative properties
4) [tex]y = 5\cdot \left[(-1)^{-1} \cdot (-1)\right]\cdot x +11[/tex] Existence of multiplicative inverse/Commutative property
5) [tex]y = [5\cdot (-1)^{-1}]\cdot [(-1)\cdot x]+11[/tex] Associative property
6) [tex]y = -5\cdot (-x)+11[/tex] [tex]\frac{a}{-b} = -\frac{a}{b}[/tex] / [tex](-1)\cdot a = -a[/tex]
7) [tex]y = -5\cdot (-x+0)+11[/tex] Modulative property
8) [tex]y = -5\cdot [-x + 2 + (-2)]+11[/tex] Existence of additive inverse
9) [tex]y = -5 \cdot [(2-x)+(-2)]+11[/tex] Associative and commutative properties
10) [tex]y = (-5)\cdot (2-x) + (-5)\cdot (-2) +11[/tex] Distributive property
11) [tex]y = (-5)\cdot (2-x) +21[/tex] [tex](-a)\cdot (-b) = a\cdot b[/tex]
12) [tex]y = (-5)\cdot t +21[/tex] By 1)
13) [tex]y = -5\cdot t +21[/tex] [tex](-a)\cdot b = -a \cdot b[/tex]/Result
14) [tex]t+x = (2-x)+x[/tex] Compatibility with addition
15) [tex]t +(-t) +x = (2-x)+x +(-t)[/tex] Compatibility with addition
16) [tex][t+(-t)]+x= 2 + [x+(-x)]+(-t)[/tex] Associative property
17) [tex]0+x = (2 + 0) +(-t)[/tex] Associative property
18) [tex]x = 2-t[/tex] Associative and commutative properties/Definition of subtraction/Result
In consequence, the right answer is [tex]x = 2-t[/tex] and [tex]y = -5\cdot t +21[/tex].
The driveway needs to be resurfaced. what is the BEST estimate of the area of the driveway?
Answer:
125π ft²
Step-by-step explanation:
1/4π(30)² - 1/4π(20)² = 125π
Answer gets BRAINLIEST If q varies inversely as r, and g = 10 when r = 2.5, find the equation that connects a
and r.
Answer:
D.
Step-by-step explanation:
In direct variations, we would have:
[tex]q=kr[/tex]
Where k is some constant.
Since this is indirect variation, instead of that, we would have:
[tex]q=\frac{k}{r}[/tex]
To determine the equation, find k by putting in the values for q and r:
[tex]10=\frac{k}{2.5}\\k=2.5(10)=25[/tex]
Now plug this back into the variation:
[tex]q=\frac{25}{r}[/tex]
The answer is D.
in a gp the sixth term is 8 times the third term, and the sum of the seventh and eighth term is 192. determine the common ratio
Answer:
common ratio = 2
Step-by-step explanation:
T6 = ar^5
T3 = ar²
T6 = 8 x T³
ar^5 = 8 x ar²
ar^5/ar² = 8
r³ = 8
r = ³√8
r = 2
* The American Diabetes Association estimates that 8.3% of people in the
United States have diabetes. Suppose that a medical lab has developed
a simple diagnostic test for diabetes that is 98% accurate for people who
have the disease and 95% accurate for people who do not have it. The
medical lab gives the test to a randomly selected person. What is the
probability that the diagnosis is correct? Explain each step.
Answer:
The probability that the diagnosis is correct is 0.95249.
Step-by-step explanation:
We are given that the American Diabetes Association estimates that 8.3% of people in the United States have diabetes.
Suppose that a medical lab has developed a simple diagnostic test for diabetes that is 98% accurate for people who have the disease and 95% accurate for people who do not have it.
Let the probability that people in the United States have diabetes = P(D) = 0.083.
So, the probability that people in the United States do not have diabetes = P(D') = 1 - P(D) = 1 - 0.083 = 0.917
Also, let A = event that the diagnostic test is accurate
So, the probability that a simple diagnostic test for diabetes is accurate for people who have the disease = P(A/D) = 0.98
And the probability that a simple diagnostic test for diabetes is accurate for people who do not have the disease = P(A/D') = 0.95
Now, the probability that the diagnosis is correct is given by;
Probability = P(D) [tex]\times[/tex] P(A/D) + P(D') [tex]\times[/tex] P(A/D')
= (0.083 [tex]\times[/tex] 0.98) + (0.917 [tex]\times[/tex]0.95)
= 0.08134 + 0.87115
= 0.95249
Hence, the probability that the diagnosis is correct is 0.95249.
