Answer:
slope = 2Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have
[tex](-3;\ -8)\to x_1=-3;\ y_1=-8\\(4;\ 6)\to x_2=4;\ y_2=6[/tex]
Substitute:
[tex]m=\dfrac{6-(-8)}{4-(-3)}=\dfrac{6+8}{4+3}=\dfrac{14}{7}=2[/tex]
The formula for the slope m of the line that passes through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is the following:
[tex]m=\dfrac{y_1-y_2}{x_1-x_2}[/tex]
We have points (4,6) and (-3,-8). Let's plug these values into the formula for slope:
[tex]m=\dfrac{6-(-8)}{4-(-3)}[/tex]
[tex]=\dfrac{14}{7}=2[/tex]
The slope of the line passing through the two points is 2. Let me know if you need any clarifications, thanks!
What is the next term in the sequence −10,−17,−24,−31,…?
Answer:
-38
Step-by-step explanation:
it's subtracting 7 everytime, and -31-7=-38
Check whether these statements are wff or not:(a) (p˅q) ∧∼r
Answer:
It is a well formed formula
Step-by-step explanation:
1 - p,q,r are well formed formulas.
2 - [tex]p \ \lor \ q[/tex] is a well formed formula as well.
3 - [tex]\neg r[/tex] is a well formula as well
4 - [tex](\ p \ \lor \ q) \ \land \ \neg r[/tex] is a well formula as well.
2
A student winds a strip of paper eight times
round a cylindrical pencil of diameter 7 mm.
Use the value 22/7 for pie to find the length of
the paper.
Answer:
176 mm
Step-by-step explanation:
The circumference of a circle is the perimeter of a circle (length of a circle). The circumference of a circle is given as:
Circumference (C) = 2πr = πd, where d is the diameter
The circumference of a circle with diameter 7 mm is:
C = πd = 22/7(7) = 22 mm
The length of the paper to round the cylindrical pencil is the same as the perimeter of the pencil which is 22 mm.
To round the pencil 8 times, the length of the paper needed = 8 × 22 mm = 176 mm
72 students choose to attend one of three after school activities: football, tennis or running.
There are 25 boys.
27 students choose football, of which 17 are girls.
18 students choose tennis.
24 girls choose running.
A student is selected at random.
What is the probability this student chose running?
Give your answer in its simplest form.
Answer:
P = 0,3749 or P = 37,49 %
Step-by-step explanation:
17 girls play football 10 boys do ⇒ 27 students
24 girls running 3 boys do ⇒ 27 students
then 6 girls play tennis and 12 boys do ⇒ 18 students
Probability of student running P is equal to P1 (probability of student (boy) running ) plus P2 (probability of student (girl) running )
P = P1 + P2
P1 (probability of girl running ) is equal to choose a girl out of 72 students, times the probability of the girl running
Probability of girl 47/72 = 0,6528
Probability of running is equal to 24/47 = 0,5106
Then the probability of girl running is equal to
P2 = 0,6528*0,5106 = 0,3333 or 33,33 %
P2 = 0,3333 or P2 = 33,33 %
Now we have 72 students 25 boys, then the probability of choosing a boy is = 25/72 = 0,3472
And the probability of running is 3/25 = 0,12
Then
P1 = 0,3472*0,12
P1 = 0,04166 and
P = P1 + P2
P = 0,04166 + 0,3333
P = 0,3749 or P = 37,49 %
What the answer now fast
sine(X) = opposite side / hypotenuse
sine(X) = (2√11) / (4√11)
sine(X) = (2/4)
sine(X) = 0.5
X = arcsine(0.5)
X = 30°
Answer: m∠x = 30°
Step-by-step explanation:
In a right triangle, if the short side of the right angle is Half the length of the hypotenuse, the triangle has angles of 30°, 60° and 90°
∠x is the smallest one, so m∠x = 30°
It is possible to figure the sine and get the angle from that, but in this case it might not be necessary. ;-)
Solve application problems using radical equations. A hang glider dropped his cell phone from a height of 450 feet. How many seconds did it take for the cell phone to reach the ground?
Answer:
[tex]\large \boxed{\text{5.29 s}}[/tex]
Step-by-step explanation:
The appropriate free fall equation is
y = v₀t + ½gt²
Data:
v₀ = 0
g = 32.17 ft·s⁻²
Calculation:
[tex]\begin{array}{rcl}450 &=& v_{0}t + \dfrac{1}{2}gt^{2}\\\\& = & 0 \times t + \dfrac{1}{2}\times 32.17t^{2}\\\\& = & 16.08t^2\\t^{2}& = & \dfrac{450}{16.08}\\\\& = & 27.97\\t & = & \textbf{5.29 s}\\\end{array}\\\text{It took $\large \boxed{\textbf{5.29 s}}$ for the phone to reach the ground.}[/tex]
A manager receives 8 applications for a specific position. She wants to narrow it down to 5. In how many ways can she rank 5 applications?
Answer:
56 number of ways
Step-by-step explanation:
This question is a combination question since it involves selection.
Generally, if r objects are to be selected from n pool of objects, this can be done in nCr number of ways.
nCr = n!/(n-r)!r!
If a manager receives 8 applications for a specific position and wants to narrow it down to 5, the number of ways he can do this is 8C5
8C5 = 8!/(8-5)!5!
= 8!/3!5!
= 8*7*6*5!/3*2*5!
= 8*7*6/3*2
= 8*7
= 56 number of ways.
This means that the manager can rank 5 applications in 56 number of ways
The number of ways that can she rank 5 applications should be 6720.
Calculation of the number of ways:Since A manager receives 8 applications for a specific position. She wants to narrow it down to 5.
So here we do apply the permutation here:
[tex]= 8!\div 5!3! \times 5!\div 0!\\\\= 8\times 7\times 6\times 5\times 4[/tex]
= 6720
Hence, The number of ways that can she rank 5 applications should be 6720.
Learn more about ways here: https://brainly.com/question/18988173
A cubical container measures 9 ft on each edge. What does it cost to fill the container at $2.58 per cubic ft?
Answer:
1,880.82
Step-by-step explanation:
If the secant value is 37^ * , the cosine value to the hundredths degree is: A 0.80 B1.25 C0.60
Answer:
The value of the cosine function at 37º is 0.80. A. 0.80
Step-by-step explanation:
The correct statement is: "If the secant of 37º is 1.25, the cosine value to the hundredths degree is:"
Secant and cosine functions are related by the following trigonometric identity:
[tex]\sec 37^{\circ} = \frac{1}{\cos 37^{\circ}}[/tex]
[tex]\cos 37^{\circ} = \frac{1}{\sec 37^{\circ}}[/tex]
[tex]\cos 37^{\circ} =\frac{1}{1.25}[/tex]
[tex]\cos 37^{\circ} = 0.80[/tex]
The value of the cosine function at 37º is 0.80. The right answer is A.
Which of these descriptions matches the graph?
Jimmy is walking to a friend's house at a constant
rate.
Jimmy is running late, so he starts to run to school
but needs to take breaks.
Jimmy is riding the bus to school at a decreasing
rate.
Jimmy's bus drives at the same speed for parts A
and C.
Answer:
Step-by-step explanation:
121212121211212 its B
Answer:
answer is B
Step-by-step explanation:
Examine today’s stock listing for SFT Legal, shown below. 52 wk High 52 wk Low Symbol Div. Close Net Change 74.80 44.61 SFT 8.94 56.11 5.74 What was the price of SFT Legal yesterday? a. $47.17 b. $56.11 c. $50.37 d. $61.85
Answer:
c. $50.37
Step-by-step explanation:
Close price was $56.11 and net change was $5.74. so subtract the net change from the close to get yesterday's price.
Answer:
c.50.37
Step-by-step explanation:
In an episode of the old school version of the game show Family Feud, 43 out of a random sample of 100 people said they pick their noses at red lights. Find a 95% confidence interval of the proportion of all people who pick their noses at red lights.
Answer:
95% of confidence interval of the proportion of all people who pick their noses at red lights
(0.3342 , 0.5258)
Step-by-step explanation:
Step(i):-
Given sample size 'n' = 100
Given data 43 out of a random sample of 100 people said they pick their noses at red lights.
sample proportion
[tex]p^{-} = \frac{x}{n} = \frac{43}{100} = 0.43[/tex]
Level of significance = 0.05
Z₀.₀₅ = 1.96
Step(ii):-
95% of confidence interval of the proportion of all people who pick their noses at red lights
[tex](p^{-} -Z_{\alpha } \sqrt{\frac{p(1-p)}{n} } ,p^{-} +Z_{\alpha } \sqrt{\frac{p(1-p)}{n} })[/tex]
[tex](0.43 -1.96 \sqrt{\frac{0.43(1-0.43)}{100} } ,0.43 +1.96 \sqrt{\frac{0.43(1-0.43)}{100} })[/tex]
( 0.43 - 0.0958 , 0.43 + 0.0958)
(0.3342 , 0.5258)
Conclusion:-
95% of confidence interval of the proportion of all people who pick their noses at red lights
(0.3342 , 0.5258)
The standard deviation of samples from supplier A is 0.4582, while the standard deviation of samples from supplier B is 0.3358. Which supplier would you be likely to choose based on these data and why
Complete Question
The standard deviation of samples from supplier A is 0.4582, while the standard deviation of samples from supplier B is 0.3358. Which supplier would you be likely to choose based on these data and why?
1 Supplier A, as their standard deviation is higher and, thus easier to fit into our production line
2 Supplier B, as their standard deviation is higher and, thus, easier to fit into our production line
3 supplier B, as their standard deviation is lower and, thus, easier to fit into our production line
4 Supplier A, as their standard deviation is lower and, thus, easier to fit into our production line
Answer:
Option 3 is correct
Step-by-step explanation:
From the question we are told that
The standard deviation of A is [tex]\sigma_a = 0.4582[/tex]
The standard deviation of B is [tex]\sigma _b = 0.3358[/tex]
Generally standard deviation defines the deviation element of a data set with respect to the mean of the set
So sample it mean that samples from A deviates more from it mean(the standard value) than the samples from B so the best supplier to chose is B
Solve for x: ( 1/2 )^(x−1)=2^(3x−4)
Answer:
[tex]\huge\boxed{x=\dfrac{5}{4}}[/tex]
Step-by-step explanation:
[tex]\left(\dfrac{1}{2}\right)^{x-1}=2^{3x-4}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\\left(2^{-1}\right)^{x-1}=2^{3x-4}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{(-1)(x-1)}=2^{3x-4}\qquad\text{use the distributive property}:\ a(b+c)=ab+ac\\\\2^{(-1)(x)+(-1)(-1)}=2^{3x-4}\\\\2^{-x+1}=2^{3x-4}\iff-x+1=3x-4\qquad\text{subtract 1 from both sides}\\\\-x+1-1=3x-4-1\\\\-x=3x-5\qquad\text{subtract}\ 3x\ \text{from both sides}\\\\-x-3x=3x-3x-5\\\\-4x=-5\qquad\text{divide both sides by (-4)}[/tex]
[tex]\dfrac{-4x}{-4}=\dfrac{-5}{-4}\\\\x=\dfrac{5}{4}[/tex]
Determine the measure of the unknown variables.
Answer:
75
Step-by-step explanation:
x = 75°
yes x = 75°(OPPOSITE ANGLES ARE EQUAL)
..
Determine a differential equation that models the growth of a population of fish as a function of time in days under each of the following hypotheses:
a) The rate of population increase is proportional to the size of the population. The population increases by 2 percent per day. (Treat time in days as a continuous variable, i.e. the rate at which the population increases is .02 times the population size.) dP/dt =
b) The rate of population increase is again proportional to the size of the population with the same constant of proportionality but 4 percent of the population is harvested each day. dP/dt =
c) The rate of population increase is again proportional to the size of the population with the same constant of proportionality but 1000 fish are harvested each day. dP/dt =
d) The equation in part c) has a threshhold. What is it?
Step-by-step explanation:
a).
It is given that rate at which the population increases is directly proportional to size of the population. Thus we have,
[tex]\frac{dP}{dt}\propto P[/tex]
It is given in the question that the population increases by 2% in one day. Now we know that the time in days is a continuous variable, so we have
2% of P = [tex]$\frac{2}{100}\times P$[/tex]
[tex]$\therefore \frac{dP}{dt}=0.02 P $[/tex]
b).
It is given that the population is harvested by 4 % in one day
[tex]$\therefore \frac{dP}{dt} =0.02P-0.04P$[/tex]
(Since 4% of the P is harvested.)
[tex]$\therefore \frac{dP}{dt}=-0.02P$[/tex]
c).
It is given that 1000 fish are being harvested or removed in one day.
[tex]$\therefore \frac{dP}{dt}= 0.02 P-1000$[/tex]
d).
The threshold is given by
[tex]$0.02 P_{eq}-1000=0$[/tex]
[tex]$\therefore P_{eq}=\frac{1000}{0.02}$[/tex]
or [tex]$P_{eq}=5\times 10^4$[/tex]
please need help with this math question
Answer:
third option
Step-by-step explanation:
We just have to calculate 2x² - 4x - (x² + 6x). 2x² - x² = x² and -4x - 6x = -10x so the answer is x² - 10x.
Answer:
x^2-10x
Step-by-step explanation:
f(x)-g(x)
(2x^2-4x)-(x^2+6x)
carry through the negative
2x^2-4x-x^2-6x
x^2-10x
Find the 12th term of the following geometric sequence.
10, 30, 90, 270, ...
Answer:
r = 90/30
r = 3
T12 = 10 × 3¹¹
T12 = 1771470
Solve the simultaneous equations 2x-y=7 3x+y=3
Answer:
( 2 , - 3 )Step-by-step explanation:
Using elimination method:
2x - y = 7
3x + y = 3
--------------
5x = 10
Divide both sides of the equation by 5
[tex] \frac{5x}{5} = \frac{10}{5} [/tex]
Calculate
[tex]x = 2[/tex]
Now, substitute the given value of X in the equation
3x + y = 3
[tex]3 \times 2 + y = 3[/tex]
Multiply the numbers
[tex]6 + y = 3[/tex]
Move constant to R.H.S and change it's sign
[tex]y = 3 - 6[/tex]
Calculate
[tex]y = - 3[/tex]
The possible solution of this system is the ordered pair ( x , y )
( x , y ) = ( 2 , -3 )---------------------------------------------------------------------
Check if the given ordered pair is the solution of the system of equation
[tex]2 \times 2 - ( - 3) = 7[/tex]
[tex]3 \times 2 - 3 = 3[/tex]
Simplify the equalities
[tex]7 = 7[/tex]
[tex]3 = 3[/tex]
Since all of the equalities are true, the ordered pair is the solution of the system
( x , y ) = ( 2 , - 3 )Hope this helps..
Best regards!!
Which phrase best describes the graph of a proportional relationship?
A) a straight line passing
B) a straight line
C) a curve
D) not a straight line
Answer:
A. a straight line passing
Step-by-step explanation:
Answer:
a straight line passing
Step-by-step explanation:
A cosine function is graphed below. Use the drop-down menus to describe the graph. The amplitude of the graph is __ . The equation of the midline is __ . The period of the function is __ . The function is shifted __ left. The function is shifted __ units up.
Amplitude:4
Equation of Midline: 2
Period of function:3
Function shifted left:0.5
Function shifted up: 2
From the graphed cosine function we are given, we have;
1) Amplitude = 4
2) Equation of midline; m = 2
3) Period of the function = 3π
4) The function shifted 0.5 units left.
5) The function shifted 2 units up.
1) The amplitude is the distance between the center line and the positive or negative peak of the graph. Now, the positive peak is 6 and the negative one is 2. Thus, Amplitude = 6 - 2 = 42) Equation of the midline is the line that divides the entire sinusoidal curve into 2 equal parts along the x-axis. Since amplitude is 4, then the equation of midline is; m = 4/2 ; m = 2.3) The period is the time it takes for the graph to repeat or complete one cycle and in this graph, it is 3π.4) Looking at the graph, ideally the coordinate (-0.5π, 6) should have been on the y-axis which is at (0π, 6). This means it was shifted by 0.5 units to the left side.5) The positive peak should be equal to the negative peak but in this case, positive is 6 and negative is 2. This means, for them to be equal, they have to each be 4. Thus, the graph was shifted by 2 units upwards .Read more; https://brainly.com/question/16280305
Please answer this correctly without making mistakes
Simplify the correct answer
Answer:
[tex]\frac{109}{122}[/tex]
Step-by-step explanation:
Well first we need to find the total amount of Winter Olympic medals won.
550 + 540 + 130
= 1220
Now we need to find the amount won from the Western and Northern Europe.
550 + 540
= 1090
Now we can make the following fraction,
1090/1220
Simplify
= 109/122
Thus,
the answer is [tex]\frac{109}{122}[/tex].
Hope this helps :)
Hi there!! (✿◕‿◕)
⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐
Northern Europe: 550 medals
Western Europe: 540 medals
550 + 540 = 1,090
Northern Europe and Western Europe: 1,090
Other: 130
1,090 + 130 = 1,220
European Regions: 1,220 medals
1,090/1,220 = 109/122
Hope this helped!! ٩(◕‿◕｡)۶
An epidemiologist wishes to know what proportion of adults living in a large metropolitan area have subtype ayr hepatitis B virus. Determine the sample size that would be required to estimate the true proportion to within 3% margin of error with 95 percent confidence.
Answer:
Sample size 'n' = 1067
Step-by-step explanation:
Explanation:-
Given margin of error of the true proportion
M.E = 0.03
The margin of error is determined by
[tex]M.E =Z_{\alpha } \frac{\sqrt{p(1-p)} }{\sqrt{n} }[/tex]
Level of significance = 0.95
The critical value Z₀.₀₅ = 1.96
The margin of error is
[tex]0.03 =1.96 \frac{\sqrt{p(1-p)} }{\sqrt{n} }[/tex]
we know that
[tex]\sqrt{p(1-p} \leq \frac{1}{2}[/tex]
[tex]0.03 =\frac{1.96 X\frac{1}{2} }{\sqrt{n} }[/tex]
on cross multiplication , we get
√n = 32.66
Squaring on both sides, we get
n = 1066.6≅1067
Rolling a 6-sided die and counting the number of each outcome that occurs is a bionomial random variable. True or False? Which option gives the most accurate response?
Answer:
False.
Step-by-step explanation:
This is NOT an example of a binomial random variable, because a binomial random variable can only have TWO possible outcomes: success or failure. In the case of rolling a die, there are SIX possible outcomes: 1, 2, 3, 4, 5, or 6.
So, rolling a 6-sided die and counting the number of each outcome that occurs is NOT a binomial random variable.
Hope this helps!
The given statement "Rolling a 6-sided die and counting the number of each outcome that occurs" is false.
What is Binomial distribution?A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,
P(x) = ⁿCₓ (pˣ) (q⁽ⁿ⁻ˣ⁾)
Where,
x is the number of successes needed,
n is the number of trials or sample size,
p is the probability of a single success, and
q is the probability of a single failure.
The given statement "Rolling a 6-sided die and counting the number of each outcome that occurs" is not an example of the binomial random variable. This is because the binomial random variable can only have two possible outcomes, which is not true in the case of a die that had six faces and six outcomes for each through.
Although if the probability is needed to be calculated for the same digit occurring or not it can be calculated using the binomial random variable.
Hence, The given statement "Rolling a 6-sided die and counting the number of each outcome that occurs" is false.
Learn more about Binomial Distribution:
https://brainly.com/question/14565246
#SPJ5
Given the radius of a circle is 7 cm, what is the circumference?
Answer:
14π or 43.96
Step-by-step explanation:
C = 2πr and we know that r = 7 so C = 14π or 43.96.
Please answer this correctly without making mistakes
Answer:
Step-by-step explanation:
2.8 kilometers farther. Subtract 12.1km for Winchester and 9.3 for Stamford to get 2.8 kilometers.
Samuel needs to replace a portion of his rain gutter. The height of the roof is 25 feet and the
length of his ladder is 30 feet. What is the maximum distance away from house that he can place
the ladder? Round your answer to the nearest foot.
Answer:
16.6 ftStep-by-step explanation:
The height of the house, the ground and the ladder forms a right angle triangle, with the following parameters stated below.
1. the hypotenuse is the length of the ladder which is 30 feet
2.the opposite is the height of the house, which is 25 feet
3. the adjacent is the distance of the ladder away from the building, this is the parameter we are solving for.
Since we have two sides of the triangle given, we can employ Pythagoras theorem to solve for the third side of the triangle
let the the opposite be x
we know that
[tex]hyp^2= opp^2+adj^2\\\\ 30^2= x^2+25^2\\\\ 900= 625+x^2\\[/tex]
Solving for x we have
[tex]x^2= 900-625\\\\X^2= 275\\\\x=\sqrt{275} \\\\x= 16.58[/tex]
Hence the maximum distance away from house that he can place
the ladder is 16.6 ft to the nearest foot
The original price of a 2018 Honda Shadow to the dealer is $17,715, but the dealer will pay only $16,985 after rebate. If the dealer pays Honda within 15 days, there is a 2% cash discount.
Answer:
The final price to be paid after the 2% discount has been made will be $ 16,645.30.
Step-by-step explanation:
Since there is a 2% discount on the price of the Honda Shadow in the event that the dealer pays Honda within 15 days, and that after a rebate the price of the vehicle is $ 16,985, to obtain the value of the discount and the final amount to be paid must be calculated as follows:
16,985 x 2/100 = X
33,970 / 100 = X
339.70 = X
Thus, the discount to be made will be $ 339.70, with which the final price to be paid after the 2% discount has been made will be $ 16,645.30.
A system of equations is created by using the line that is created by the equation 3 x minus 2 y = negative 4 and the line that is created by the data in the table below. x y –3 –9 –1 –5 3 3 5 7 What is the y-value of the solution to the system?
Answer:
17
Step-by-step explanation:
A graphing calculator is useful for writing a linear equation from a table of values. The one shown below says the table can be represented by the equation ...
y = 2x -3
The graph of the two equations shows the solution is (10, 17).
The y-value of the solution is 17.
Answer:
17 is correct
Step-by-step explanation:
A random sample of 61 Foreign Language movies made in the last 10 years has a mean length of 135.7 minutes with a standard deviation of 13.7 minutes. Construct a 95% confidence interval.
Answer:
95% confidensce interval of the mean (two-tail) = [132.2, 139.2]
Step-by-step explanation:
Given:
N = size of sample = 61
m = sample mean = 135.7
s = sample standard deviation 13.7
Need 95% confidence interval
Solution.
alpha (95% confidence interval) = 0.05
(1-alpha/2) = 0.975 [two sided]
Equation for confidence interval of the mean
= m +/- t(1-alpha/2,N-1) * s / sqrt(N)
= 135.7 +/- 2.0003 * 13.7 / sqrt(60)
= [132.16, 139.24]