Answer:
t varies inversely to 30/r
Step-by-step explanation:
t varies inversely to r
(lol I can't seem to find the variation sign in the keyboard)
when you introduce the constant K the sign changes to =
t=k/r
if t=6, r=5
substitute the values
6=k/5
k= 6×5
k=30
we have found the constant so we add it to our initial equation
t inversely varies to 30/r
PLEASE QUICK!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Which number completes the system of linear inequalities represented by the graph? y > 2x – 2 and x + 4y > -12 -3 4 6
Answer:
-12
Step-by-step explanation:
Edge 2021
A soccer team sold raffle tickets to raise money for the upcoming season. They sold three different types of tickets: premium for $6, deluxe for $4, and regular for $2. The total number of tickets sold was 273, and the total amount of money from raffle tickets was $836. If 118 more regular tickets were sold than deluxe tickets, how many premium tickets were sold?
Answer:
45 premium tickets were sold
Step-by-step explanation:
p = premium
d = deluxe
r = regular
p+d+r = 273
6p+4d + 2r = 836
118+d = r
Replace r with 118+d
p+d+118+d = 273
p +2d = 273-118
p+2d = 155
6p+4d + 2(118+d) = 836
6p+4d + 236+2d = 836
6p +6d = 836-236
6p + 6d = 600
Divide by 6
p+d = 100
d = 100-p
Replace d in p +2d= 155
p +2(100-p) = 155
p+200-2p = 155
-p = 155-200
-p =-45
p =45
45 premium tickets were sold
Answer:
Step-by-step explanation
We get three linear equations from the information given, where
p= number of premium tickets
d = number of deluxe tickets
r = number of regular tickets:
[tex]\left \{ {{p+d+r=273} \atop \\{6p+4d+2r=836} \right.[/tex]
and the applying third r=118+d, we get
[tex]\left \{ {p+d+118+d=273} \atop {6p+4d+2d+236=836}} \right.[/tex]
[tex]\left \{ {{p+2d=115} \atop {6p+6d=600}} \right.[/tex]
Now we get from the upper one
p=115-2d
solving the another equation gives us
6*115-12d+6d=600,
hence d=15
and by replacing
p=115-2*15=85.
85 premium tickets were sold
what it 17.15 in 12hour clock
Answer:
Step-by-step explanation:
Hello friend
The answer is 5:15 in 12 hour clock
Answer:
5:15 PM
Step-by-step explanation:
12:00 + 5:00
17:00 in 12 hour clock is 5:00 PM.
15 minutes + 5:00 PM
⇒ 5:15 PM
What is the output of the following function for x = -4?
F(x) = 3x^5 + 4x^3 -x +11
Answer:
-3313
Step-by-step explanation:
3x^5 + 4x^3 - x +11
Put x as -4 and evaluate.
3(-4)^5 + 4(-4)^3 - (-4) + 11
-3072 + - 256 + 4 + 11
= -3313
Jennifer and Stella are cooks at a restaurant that serves breakfast. On a particular day, the two of them tracked the number of pancakes they cooked. The number of pancakes that Jennifer cooked is represented by the following function, where x is the number of hours. The number of pancakes that Stella cooked is shown by the graph below. Who cooked more pancakes in 8 hours?
Answer:
Stella
Step-by-step explanation:
I guessed and got it right
Not sure how I would find what axis
Answer:
Quad 1
Step-by-step explanation:
PLS HELP. The question is in the photo :)
Answer:
So each strawberry is 4 calories
Step-by-step explanation:
First find the slope of the line
Two points on the line are
(0,0) and (3,12)
m = (y2-y1)/(x2-x1)
= (12-0)/(3-0)
= 12/3
= 4
So each strawberry is 4 calories
What is a square root
solve for x.
x/3 < -6
Answer: x < -18
Step-by-step explanation:
Simply multiply both sides by three to get x < -18
Step-by-step explanation:
x/3 < - 6
x < - 18
This should be the answer
The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time t and has a half-life of 3.3 hours. If 1 gram of this isotope is present initially, how long will it take for 95% of the lead to decay?
Answer:
[tex] N(t) =N_o (\frac{1}{2})^{\frac{t}{t_{1/2}}}[/tex]
Where [tex]t_{1/2}= 3.3 hr[/tex] represent the half life and the intial amount would be [tex] N_o = 1[/tex]
And we want to find the time in order to have a 95% of decay so we can set up the following equation:
[tex] 0.05 = 1 (0.5)^{t/3.3}[/tex]
If we apply natural log on both sides we got:
[tex] ln(0.05) = \frac{t}{3.3} ln (0.5)[/tex]
And solving for t we got:
[tex] t= 3.3 *\frac{ln(0.05)}{ln(0.5)}= 14.26[/tex]
So then would takes about 14.26 hours in order to have 95% of the lead to decay
Step-by-step explanation:
For this case we can define the variable of interest amount of Pb209 and for the half life would be given:
[tex] N(t) =N_o (\frac{1}{2})^{\frac{t}{t_{1/2}}}[/tex]
Where [tex]t_{1/2}= 3.3 hr[/tex] represent the half life and the intial amount would be [tex] N_o = 1[/tex]
And we want to find the time in order to have a 95% of decay so we can set up the following equation:
[tex] 0.05 = 1 (0.5)^{t/3.3}[/tex]
If we apply natural log on both sides we got:
[tex] ln(0.05) = \frac{t}{3.3} ln (0.5)[/tex]
And solving for t we got:
[tex] t= 3.3 *\frac{ln(0.05)}{ln(0.5)}= 14.26[/tex]
So then would takes about 14.26 hours in order to have 95% of the lead to decay
A card is drawn randomly from a standard 52-card deck. Find the probability of the given event.
(a) The card drawn is a king.
(b) The card drawn is a face card.
(c) The card drawn is not a face card.
Answer:
(a) [tex]\frac{1}{13}[/tex]
(b) [tex]\frac{3}{13}[/tex]
(c) [tex]\frac{10}{13}[/tex]
Step-by-step explanation:
The probability of an event B occurring is given by;
P(B) = [tex]\frac{n(E)}{n(S)}[/tex]
Where;
P(B) = probability of the event B
n(E) = number of favourable outcomes
n(S) = total number of events in the sampled space.
From the question, the card is drawn randomly from a standard 52-card deck. The probability of
(a) drawing a "king" card is analyzed as follows.
Let the event of drawing the "king" card be B.
In a standard 52-card deck, the number of cards that are of type king is 4. i.e 1 from the diamond pack, 1 from the spade pack, 1 from the heart pack and 1 from the club pack.
Therefore, the number of favourable outcomes is 4, while the total number of events in the sampled space is 52.
The probability of drawing a "king" card, P(B) is;
P(B) = [tex]\frac{4}{52}[/tex]
P(B) = [tex]\frac{1}{13}[/tex]
(b) drawing a "face" card is analyzed as follows.
Let the event of drawing the "face" card be B.
In a standard 52-card deck, a face card can either be a Jack, Queen or a King. There are 4 Jack cards, 4 Queen cards and 4 King cards in the deck. The number of cards that are of type face is 12.
Therefore, the number of favourable outcomes is 12, while the total number of events in the sampled space is 52.
The probability of drawing a "face" card, P(B) is;
P(B) = [tex]\frac{12}{52}[/tex]
P(B) = [tex]\frac{3}{13}[/tex]
(c) drawing a card that is not a "face" is analyzed as follows;
The sum of the probability of drawing a face card and the probability of not drawing a face card is always 1.
Let the event of drawing a "face" card be B and the event of not drawing a "face" card be C.
P(B) + P(C) = 1
P(C) = 1 - P(B)
From (b) above, the P(B) = [tex]\frac{3}{13}[/tex]
Therefore,
P(C) = 1 - [tex]\frac{3}{13}[/tex]
P(C) = [tex]\frac{10}{13}[/tex]
7x-14=3x+12
Solve for x!
Answer: x = 6.5
Step-by-step explanation:
[tex]7x-14=3x+12\\\\Add(14)\\\\7x=3x+26\\\\Subtract(3x)\\\\4x=26\\\\Divide(4)\\\\x=6.5[/tex]
Hope it helps <3
Answer:
x=26/4 (simply to 13/2)
Step-by-step explanation:
Add 14 to both sides to cancel out the negative 14
7x=3x+26
Subtract 3x from both sides to cancel the 3x
4x=26
x=26/4 or 13/2
I want to fence in a rectangular vegetable patch. The fencing for the east and west sides costs $2 per foot, and the fencing for the north and south sides costs only $1 per foot. I have a budget of $40 for the project. What is the largest area I can enclose
Answer:
largets area is 32 feet cubed
Step-by-step explanation:
8=4 foot 2 for each side w and e and 32feet n and s 16 each side
A certain group of test subjects had pulse rates with a mean of 80.9 beats per minute and a standard deviation of 10.7 beats per minute. Use the range rule of thumb to identify the limits separating values that are significantly low or significantly high. Is a pulse rate of 142.3 beats per minute significantly low or significantly high?
Answer:
We want to find the usual limits using the rule of thumb and for this case rule states that we have most of the values within 2 deviations from the mean so then we can find the usual limits like this:
[tex] \mu -2*\sigma = 80.9 -2*10.7= 59.5[/tex]
[tex] \mu +2*\sigma = 80.9 -2*10.7= 102.3[/tex]
And for this case a value of 142.3 is higher than the upper limti so then we can conclude that would be significantly high with the rule of thumb criteria
Step-by-step explanation:
For this case we have the follwing info given:
[tex] \mu = 80.9[/tex] represent the mean
[tex]\sigma = 10.7[/tex] represent the deviation
We want to find the usual limits using the rule of thumb and for this case rule states that we have most of the values within 2 deviations from the mean so then we can find the usual limits like this:
[tex] \mu -2*\sigma = 80.9 -2*10.7= 59.5[/tex]
[tex] \mu +2*\sigma = 80.9 -2*10.7= 102.3[/tex]
And for this case a value of 142.3 is higher than the upper limti so then we can conclude that would be significantly high with the rule of thumb criteria
I NEED HELP PLEASE, THANKS! :)
Answer:
Option B
Step-by-step explanation:
First identify which options are a match for the hyperbola with a foci of (- 12, 6) and ( 6, 6 ). If there is only one, we can claim that that is the solution. Otherwise we would have to take the vertices into account,
The first option can be eliminated as it is present with a decimal in the denominator, indicating that the foci should also be a decimal. However, the foci of this option should be valuable to us -
[tex]\left(h+c,\:k\right),\:\left(h-c,\:k\right),\\\left(-3+c,\:6\right),\:\left(-3-c,\:6\right),\\c = ( About ) 3.6,\\\\Foci = \left(0.55808 ,\:6\right),\:\left(-6.55808,\:6\right)[/tex]
The second option squares the denominators of the first option, so the foci should be the following -
[tex]Foci = ( - 12, 6 ), ( 6, 6 )[/tex]
Which is the given! The rest of the options are similar to this second option, but are altered, thus don't have the same foci,
Solution = Option B
Complete the following proof. Given: Points R, S, T, Q on circle O Prove: m \overarc R S + m \overarc S T + m \overarc T Q = m \overarc R Q
Answer:
Answer is below.
Step-by-step explanation:
Points R, S, T, Q on Circle O - Given
m (arc) RS + m (arc) ST = m (arc) RT , m (arc) RT + m (arc) TQ = m (arc) RQ - Arc addition
m (arc) RS + m (arc) ST + m (arc) TQ = m (arc) RQ - Substitution
Hope this helps.
The proofing is as follows:
Given that,
Points R, S, T, Q on Circle O -Now
m (arc) RS + m (arc) ST = m (arc) RT , m (arc) RT + m (arc) TQ = m (arc) RQ - Arc addition
And,
m (arc) RS + m (arc) ST + m (arc) TQ = m (arc) RQ - Substitution
learn more: https://brainly.com/question/7695753?referrer=searchResults
researchers are interested in the average size of a certain species of mouse. They collect the length and gender of each mouse. What is the parameter likely estimated and the sample statistic
Answer:
E. The parameter is μmale - μfemale and the statistic is xmale - xfemale.
Step-by-step explanation:
The sample statistic is a piece of information about the individuals or objects that were selected from a given population. The sample is just a fraction of the total population. Since it is a herculean task studying an entire population, the sample forms a manageable size that allows us to have an insight into the entire population. The sample statistics are now the piece of information about the sample being studied such as the average, mean, median, or mode. The sample statistics have to be as specific as possible of the factors being measured. In the question, we would have to obtain the mean of both the male and female genders. This gives us an insight into the population under study.
The parameter, on the other hand, is a description of the entire population being studied. For example, we might want to determine the population mean. That is the factor we seek to measure. It is represented by the sign mu (μ).
what is the next term in the pattern 2, 3/2, 4/3, 5/4
Answer:
6/5, 7/6
Step-by-step explanation:
The nth term is (n+1)/n
2/1, 3/2, 4/3, 5/4
Put n as 5 and 6.
(5+1)/5
= 6/5
(6+1)/6
= 7/6
Assume that adults have IQ scores that are normally distributed with a mean of 94 and a standard deviation of 14. Find the probability that a randomly selected adult has an IQ greater than 107.1. (Hint: Draw a graph.) To help visualize the area of interest, draw a standard normal curve. Label the given values for x and mu . x 94107.1
Answer:
0.6517
Step-by-step explanation:
z = (x - μ)/σ
Z= standard score
x= observed value
μ= mean of the sample
σ= standard deviation of the sample
z = (x - μ)/σ = (107.1 - 94 )/ 14 = 0.9357
probability that a randomly selected adult has an IQ greater than 107.1. = P(Z > 0.935) = 0.6517
NB: the value is 0.6517 is pulled from the z table which can be found at the back of most math text.
the distance around the edge of a circular pond is 88m. the radius in meters is ?
(a)88π
(b)176π
(c)88/π
(d)88/2π
Answer: (d) 88/ 2π
Step-by-step explanation:
Perimeter = 88m
Perimeter of a circle = 2πr
88 = 2π x r
r = 88 / 2π
Answer:
88/2π = r
Step-by-step explanation:
The circumference is 88 m
The circumference is given by
C = 2*pi*r
88 = 2 * pi *r
Divide each side by 2 pi
88 / 2pi = 2 * pi *r / 2 * pi
88 / 2 pi = r
Given the equation y = 7 sec(6x– 30)
The period is:
The horizontal shift is:
Answer:
The period is of [tex]\frac{\pi}{3}[/tex] units.
The horizontal shift is of 30 units to the left.
Step-by-step explanation:
The secant function has the following general format:
[tex]y = A\sec{(Bx + C)}[/tex]
A represents the vertical shift.
C represents the horizontal shift. If C is positive, the shift is to the right. If it is negative, it is to the left.
The period is [tex]P = \frac{2\pi}{B}[/tex]
In this question:
[tex]y = 7\sec{6x - 30}[/tex]
So [tex]B = 6, C = -30[/tex]
Then [tex]P = \frac{2\pi}{6} = \frac{\pi}{3}[/tex]
The period is of [tex]\frac{\pi}{3}[/tex] units.
The horizontal shift is of 30 units to the left.
A girl walks 800 m on a bearing of 129°.
Calculate how far: a east b south she is from
her starting point.
Answer: a) 503.2m
b) 621.6m
Step-by-step explanation:
The diagram representing the scenario is shown in the attached photo.
A represents her starting point.
CD = x = how far east she is from her starting point
BC = y = how far south she is from her starting point
Angle BAC = 180 - 129 = 51°
Angle ACD = angle BAC = 51° because they are alternate angles
To determine x, we would apply the cosine trigonometric ratio
Cos 51 = x /800
x = 800Cos51 = 800 × 0.629 = 503.2m
To determine y, we would apply the sine trigonometric ratio
Sin 51 = y /800
y = 800Sin51 = 800 × 0.777 = 621.6m
Solve the two-step equation.-0.45x + 0.33 = -0.66What is the solution?x = -2.2x = -1.4x = 1.4x = 2.2f
Answer:
x = 2.2
Step-by-step explanation:
-0.45x + 0.33 = -0.66
Subtract .33 from each side
-0.45x + 0.33-.33 = -0.66-.33
-.45x = -.99
Divide each side by -.45
-.45x./-.45 = -.99/-.45
x = 11/5
x = 2.2
The hourly rate for a staff nurse is £13.75.
A staff nurse works 30 hours a week and 6 hours overtime at time-and-a-half.
What is her total pay for the week?
Answer:
P = £536.25
Her total pay for the week is £536.25
Step-by-step explanation:
The total pay can be written as;
P = t1(r1) + t2(r2)
Where;
t1 = normal time
r1 = normal time pay rate
t2 = overtime
r2 = overtime pay rate
Given;
t1 = 30 hours
t2 = 6 hours
r1 = £13.75
r2 = 1.5(r1) = 1.5(£13.75)
Substituting the given values into the equation 1;
P = 30(£13.75) + 6(1.5(£13.75))
P = £536.25
Her total pay for the week is £536.25
calculating the five number summary
Answer:
2) 43
4) 65
Step-by-step explanation:
The first and third quartile of the data can be found by calculating the median of the first and second halves of the data. For example, the first quartile of the data can be calculated thus:
40,41,43,50,56
41,43,50
43
and the third quartile thus:
62,63,65,78,97
63,65,78
65
Hope it helps <3
Answer:
A) 43
B) 65
Step-by-step explanation:
A) First Quartile = [tex](N+1)\frac{1}{4}[/tex]
Where N is the number of observations
=> 1st Quartile = (11+1)(1/4)
=> 1st Quartile = (12)(1/4)
=> 1st Quartile = 3rd number
=> 1st Quartile = 43B) Third Quartile = [tex](N+1)\frac{3}{4}[/tex]
=> 3rd Quartile = (11+1)(3/4)
=> 3rd Quartile = (12)(3/4)
=> 3rd Quartile = 3*3
=> 3rd Quatile = 9th number
=> 3rd Quartile = 65Please answer this correctly
Answer:
50%
Step-by-step explanation:
a. What is a residual? b. In what sense is the regression line the straight line that "best" fits the points in a scatterplot? a. What is a residual?
Answer:
a. A residual is how far off a point is from the expected value. For example, if I were to estimate the weight of my Southeastern Lubber Grasshopper, I would say it's maybe 5 ounces. But, in reality, it might be 4 ounces. So, the residual would be the reality minus the prediction, or 4 - 5, or -1 ounce.
b. The regression line is the line of predicted values for the points in the scatterplot. It tries to predict the points and make all the points be on the line.
Hope this helps!
If f(x) = x² + x - 4, evaluate f(2i).
Can anyone show a step by step process to get the answer?
Answer:
-6+2i
Step-by-step explanation:
f(2i)=2i^2+2i-4
2i^2 is -2 because i^2 is-1, times 2 is -2.
Therefore, the equation becomes -2+2i-4, leaving the answer of -6+2i.
Find the coordinates of the point on a circle with radius 4 at an angle of 2pi/3
{Please help!!}
Answer:
The coordinates of the point on a circle with radius 4 at an angle of [tex]\frac{2\pi}{3}[/tex] radians are x = -2 and y = 3.464.
Step-by-step explanation:
This problem ask us to determine the rectangular coordinates from polar coordinates. The polar coordinates of the point in rectangular form is expressed by the following expression:
[tex](x,y) = (r\cdot \cos \theta, r\cdot \sin \theta)[/tex]
Where [tex]r[/tex] and [tex]\theta[/tex] are the radius of the circle and the angle of inclination of the point with respect to horizontal, measured in radians. If [tex]r = 4[/tex] and [tex]\theta = \frac{2\pi}{3}\,rad[/tex], the coordinates of the point are:
[tex](x,y) = \left(4\cdot \cos \frac{2\pi}{3},4\cdot \sin \frac{2\pi}{3} \right)[/tex]
[tex](x,y) = (-2, 3.464)[/tex]
The coordinates of the point on a circle with radius 4 at an angle of [tex]\frac{2\pi}{3}[/tex] radians are x = -2 and y = 3.464.
Write the inverse of g(x)=x²-7
Answer:
[tex]\± \sqrt{x + 7}[/tex]
Step-by-step explanation:
y = x² - 7
Add 7 to both sides.
y + 7 = x²
Take square root on both sides.
±√(y + 7) = x
Switch variables.
±√(x + 7) = y