Answer:
Total Price = 1.07(0.65x)= 0.6955x.
Step-by-step explanation:
The discount percentage is, d% = 35%.
The sales tax percentage is, s% = 7%.
The variable x represent the original cost of the item(s).
The discount is subtracted from the original amount.
So, the discounted amount will be, 0.65x.
And the sales tax is added to the original amount.
So, the value of tax plus price will be, 1.07x.
Then the final price of the item(s) will be:
Total Price = 1.07(0.65x)= 0.6955x.
Answer:
It's C for those on edgenuity
Step-by-step explanation:
A car is going 8 meters per second on an access road into a highway
and then accelerates at 1.8 meters per second squared for 7.2
seconds. How fast is it then going?
Answer:
20.96 m/s is the final speed.
Step-by-step explanation:
Given that:
Initial speed of the car = 8 m/s
Acceleration of the car = 1.8 m/[tex]s ^{2}[/tex]
Time for which the car accelerates = 7.2 seconds
To find:
The speed of car after accelerating for 7.2 seconds at an acceleration of 1.8 m/[tex]s ^{2}[/tex] = ?
Solution:
First of all, let us have a look the formula given for the final velocity of an object with given initial speed, acceleration and time:
[tex]v=u+at[/tex]
Where [tex]v[/tex] is the final speed of object
[tex]u[/tex] is the initial speed of an object
[tex]a[/tex] is the acceleration of object and
[tex]t[/tex] is the time
Here, [tex]u = 8\ m/s[/tex]
[tex]a = 1.8\ m/s^{2}[/tex] and
[tex]t = 7.2\ seconds[/tex]
To find:
[tex]v = ?[/tex]
Let us put all the given values in the formula:
[tex]v =8+1.8 \times 7.2\\\Rightarrow v =8+12.96\\\Rightarrow \bold{v =20.96\ m/s}[/tex]
So, the answer is:
20.96 m/s is the final speed.
List the next three numbers for the sequence:
27, 41, 55, 69, ...
Answer:
83, 97, 111 i think that is what you are asking
Answer:
83, 97,111
Step-by-step explanation:
Please help me with this
Answer:8^20
Step-by-step explanation:
I just say 10x2=20 lol
Answer:
[tex]8^{20}[/tex]
Step-by-step explanation:
8^10*2
8^20
which number rounds to 341 when rounded to the nearest whole number
Answer:
341.5 because it makes the most sense
Answer:
340.511
Step-by-step explanation:
The five in the tenths place would make you round up.
Hope this helps! Can I get Brainliest? I’ve never had it before.
5(x – 2y)
2x+y
when x = 4 and y= -3
Answer:
50
Step-by-step explanation:
first you plug in 4 for x and -3 for y. then you solve
Answer: 50 and 5, respectively
Step-by-step explanation:
For this problem, we are given x and y. With the x and y value given, all we have to do is to plug them into the expressions and solve.
5(x-2y) [plug in x=4 and y=-3]
5((4)-2(-3)) [combine like terms by using order of operations]
5(4+6)
5(10)=50
-----------------------------------------------------------------------------------------------------------
2x+y [plug in x=4 and y=-3]
2(4)+(-3) [combine like terms by using order of operations]
8-3=5
Now that we have plugged in x=4 and y=-3 into the two expressions, we get 50 for the first expression and 5 for the second equation.
You find yourself stuck in a traffic jam. It is not rush hour. You feel frustrated and wonder what is holding up traffic Which of the following are plausible hypotheses for explaining the problem?
Check all that apply.
a) It is Friday the 13th, and you think that because this is considered a day for bad luck, that must be why there is a traffic jam. ?
b) You were in a hurry this morning, and you forgot to bring your lucky rabbit's foot with you. That's why you are now stuck in traffic.
c) There is an accident ahead, which often causes traffic to slow.
d) There is a sale at the mall near an exit up ahead, and everyone on the road is going to the sale
e) Road repairs are being made today, and you didn't know about it.
Answer:
There is an accident ahead, which often causes traffic to slow.
Step-by-step explanation:
Looking at the question closely, we understand that the traffic jam occurred at a time that is not generally regarded as a rush hour.
A traffic jam due to road repair is not really an option because roads are closed during repairs. Shop malls announce their special sales days ahead of time so that many people will hear about it.
However, it is likely that an accident occurred. An road accident may suddenly occur on an otherwise less busy road. This often leads to an unusual delay in traffic irrespective of the hour of the day when it occurs.
g 3.24 Socks in a drawer. In your sock drawer you have 4 blue, 5 gray, and 3 black socks. Half asleep one morning you grab 2 socks at random and put them on. Find the probability you end up wearing (a) 2 blue socks (b) no gray socks (c) at least 1 black sock (d) a green sock (e) matching socks
Answer:
a) 1/11 (b) 7/22 (c) 5/11 (d) 0 (e) 19/66
Step-by-step explanation:
Given the following :
Number of Blue socks = n(B) = 4
Number of Gray socks = n(G) =5
Number of black socks = n(Bl) = 3
Total number of socks = (4 + 5 + 3) = 12
Probability = ( number of required outcomes / number of total possible outcomes)
Picking 2 socks at random:
A) probability of two blue socks :
Ist pick = p(B) = (4/12) = 1/3
Number of Blue socks left = (4 - 1) =3
Total socks left = 12 - 1 = 11
2nd pick = p(B) = (3/11)
P(2 blue socks) = (1/3 * 3/11) = 3 /33 = 1/11
B) No gray socks :
Number of non - gray socks = (4 + 3) = 7
1st pick = 7/12
After 1st pick non-gray socks left = 6
Total socks left = 11
2nd pick = 6 / 11
P(non-gray) = (7/12 × 6/11) = 42/132 = 7/22
C.) Atleast one black socks = (1 - P(no black))
Number of non-black socks = (4 +5) = 9
1st pick = 9/12 = 3/4
After 1st pick, non-black left = 8, total = 11
2nd pick = 8/11
P(non - black) = (3/4 × 8/11) = 24/44 = 6/11
P(atleast 1 black) = (1 - 6/11) = 5 /11
D.) A green socks
Number of green socks = 0
P(green) = 0
E.) A matching socks :
1) matching black socks :
Ist pick = p(Bl) = (3/12) = 1/4
Number of Black socks left = (3 - 1) =2
Total socks left = 12 - 1 = 11
2nd pick = p(Bl) = (2/11)
P(matching black socks) = (1/4 * 2/11) = 2 /44 = 1/22
11) matching blue socks:
Ist pick = p(B) = (4/12) = 1/3
Number of Blue socks left = (4 - 1) =3
Total socks left = 12 - 1 = 11
2nd pick = p(B) = (3/11)
P(matching blue socks) = (1/3 * 3/11) = 3 /33 = 1/11
111) matching gray socks :
Ist pick = p(B) = (5/12) = 5/12
Number of Blue socks left = (5 - 1) =4
Total socks left = 12 - 1 = 11
2nd pick = p(B) = (4/11)
P(matching gray socks) = (5/12 * 4/11) = 20/132 = 5 /33
Summing the probabilities :
(1/22 + 1/11 + 5/33) = (3 + 6 + 10) / 66 = 19/66
Using the hypergeometric distribution, it is found that there is a:
a) 0.0909 = 9.09% probability that you end up with 2 blue socks.
b) 0.3182 = 31.82% probability that you end up with no gray socks.
c) 0.4545 = 45.45% probability that you end up with at least 1 black sock.
d) 0% probability that you end up with a green sock.
e) 0.2879 = 28.79% probability that you end up with matching socks.
Hypergeometric distribution:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. N is the size of the population. n is the size of the sample. k is the total number of desired outcomes.In this problem:
There is a total of 4 + 5 + 3 = 12 socks, hence [tex]N = 12[/tex].2 are grabbed, hence [tex]n = 2[/tex].Item a:
4 are blue, hence [tex]k = 4[/tex]The probability is P(X = 2), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,12,2,4) = \frac{C_{4,2}C_{8,0}}{C_{12,2}} = 0.0909[/tex]
0.0909 = 9.09% probability that you end up with 2 blue socks.
Item b:
5 are gray, hence [tex]k = 5[/tex]The probability is P(X = 0), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,12,2,5) = \frac{C_{5,0}C_{7,2}}{C_{12,2}} = 0.3182[/tex]
0.3182 = 31.82% probability that you end up with no gray socks.
Item c:
3 are black, hence [tex]k = 3[/tex].The probability is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,12,2,3) = \frac{C_{3,0}C_{9,2}}{C_{12,2}} = 0.5455[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.5455 = 0.4545[/tex]
0.4545 = 45.45% probability that you end up with at least 1 black sock.
Item d:
There are no green socks, hence 0% probability that you end up with a green sock.
Item e:
0.0909 probability of two blue.The probability of two gray is P(X = 2) when k = 5.The probability of two black is P(X = 2) when k = 3.Hence, for two gray:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,12,2,5) = \frac{C_{5,2}C_{7,0}}{C_{12,2}} = 0.1515[/tex]
Then, for two black:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,12,2,3) = \frac{C_{3,2}C_{9,0}}{C_{12,2}} = 0.0455[/tex]
Then, the probability of matching socks is:
[tex]p = 0.0909 + 0.1515 + 0.0455 = 0.2879[/tex]
0.2879 = 28.79% probability that you end up with matching socks.
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A cabinet costs $149. If the sales tax is 7.5%, what is the total cost of the cabinet? Round to the nearest cent
Answer: $160.18
Step-by-step explanation:
Answer:
$160.18
Step-by-step explanation:
The cabinet's sale price (or in this case, sub-total) is $149. The sales tax is 7.5%, which means you must multiply 149 x 7.5% to get 11.175. After you do this, you must add the 11.175 (which we will round to $11.18 for your tax) to your subtotal ($149). Since $149 + $11.18 = $160.18, you will have to pay a total of $160.18 for the cabinet.
Fast Food and Gas Stations Forty percent of all Americans who travel by car look for gas stations and food outlets that are close to or visible from the highway. Suppose a random sample of n = 25 Americans who travel by car are asked how they determine where to stop for food and gas. Let x be the number in the sample who respond that they look for gas stations and food outlets that are close to or visible from the highway.
a. What are the mean and variance of x?
b. Calculate the interval p-±2a. What values of the binomial random variable x fall into this interval?
c. Find P(6 ≤ x ≤ 14). How does this compare with the fraction in the interval WO for any distribution? For mound-shaped distributions?
Answer:
a
mean [tex]\mu = 10[/tex] variance [tex]\sigma^2 = 6[/tex]
b
The binomial random variable x fall into this interval ranges from
- 5 to 5
c
[tex]P(6 \le x \le 14) = 0.8969[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 25[/tex]
The percentage that look for gas stations and food outlets that are close to or visible from the highway is [tex]p = 0.40[/tex]
Generally the mean is mathematically represented as
[tex]\mu = n * p[/tex]
=> [tex]\mu = 0.40 * 25[/tex]
=> [tex]\mu = 10[/tex]
The variance is mathematically represented as
[tex]\sigma^2 = np(1- p )[/tex]
=> [tex]\sigma^2 = 25 * 0.40(1- 0.40 )[/tex]
=> [tex]\sigma^2 = 6[/tex]
The standard deviation is mathematically evaluated as
[tex]\sigma = \sqrt{\sigma^2}[/tex]
[tex]\sigma = \sqrt{6}[/tex]
[tex]\sigma = 2.45[/tex]
The interval is evaluated as
[tex]p\pm 2 \sigma[/tex]
=> [tex]p - 2 \sigma\ \ \ , \ \ \ p + 2\sigma[/tex]
=> [tex]0.40 - 2 *2.45\ \ \ , \ \ \ 0.40 + 2* 2.45[/tex]
=> [tex]-4.5\ \ \ , \ \ \ 5.3[/tex]
The binomial random variable x fall into this interval ranges from
- 5 to 5
Generally
[tex]P(6 \le x \le 14) = P(\frac{ x - \mu }{\sigma } \le \frac{14 - 10}{{2.45}} ]-P[ \frac{ x - \mu }{\sigma } \le \frac{6 - 10}{2.45 } ][/tex]
[tex]P(6 \le x \le 14) = P(Z \le 1.63 ]-P[ Z \le -1.63 ][/tex]
[tex]P(6 \le x \le 14) = [1- P(Z > 1.63 ]] -[1- P[ Z > -1.63 ]][/tex]
From the z-table
[tex]P(Z > 1.63 ) = 0.051551[/tex]
And
[tex]P(Z >- 1.63 ) =0.94845[/tex]
=> [tex]P(6 \le x \le 14) = [1-0.051551] -[1-0.94845][/tex]
=> [tex]P(6 \le x \le 14) = 0.8969[/tex]
What is the equation of the line that passes through the point (-6, -8) and has an
undefined slope?
Answer: x=-6
Step-by-step explanation:
Undefined slopes are vertical lines, so there's no y variable in the equation. so you look at the point (-6, -8) and take out the y, which is negative eight. So your answer is negative six.
The equation of the line that passes through the point (-6, -8) and has an undefined slope will be y + 8 = m (x + 6).
What is a linear equation?A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Then the equation of the line that passes through the point (-6, -8) and has an undefined slope will be
y + 8 = m (x + 6)
The equation of the line that passes through the point (-6, -8) and has an undefined slope will be y + 8 = m (x + 6).
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What is 12 5/13 as an improper fraction
Answer: 161/13
Step-by-step explanation: 1. Multiply the denominator by The number
2. add the answer from step one to the numerator
3. Write the answer from step 2 over the denominator
Consider the solid obtained by rotating the region bounded by the given curves about the y-axis. y = ln x, y = 3, y = 5. x = 0 Find the volume V of this solid. V = ____ Sketch the region, the solid, and a typical disk or washer. (Do this on paper. Your instructor may ask you to turn in this work.)
Answer:
volume = 33965.39
Step-by-step explanation:
Attached below is a detailed solution of the problem and the required sketch
volume of this solid is calculated integrating about the axis of : 5,3
Y = In x = x = e^y
the shaded region in the sketch represent the region where the rotating takes place.
Please help me please thank
Answer:
x=20
Step-by-step explanation:
<2 = <3 when the lines are parallel
3x-10 = x+30
Subtract x from each side
3x-10 -x = x+30-x
2x-10 = 30
Add 10 to each side
2x-10 +10 = 30+10
2x = 40
Divide by 2
2x/2= 40/2
x =20
What is the value of X in the given triangle?
==================================================
Work Shown:
cos(angle) = adjacent/hypotenuse
cos(x) = 5/12
x = arccos(5/12)
x = 65.375681647836 which is approximate
x = 65.4 after rounding to one decimal place
Make sure your calculator is in degree mode. The arccosine function is the same as the inverse cosine function (shortened to [tex]\cos^{-1}[/tex] ).
4.) To find the distance between (17, 3) and (17, −5), Marcia used the following equation. Is Marcia correct? Explain. WILL MARK BRAINLIEST FOR RIGHT ANSWER '
D = | 3 − (−5) | = 8
a.) Marcia is not correct. Since the points are in two-dimensions, the distance formula must be used to find the distance.
b.)Marcia is correct. For any pair of points, the distance between the points can be treated as if they are in one-dimension.
c.)Marcia is correct. Since the x-coordinates are the same, the distance between the points can be treated as if they are in one-dimension.
d.)Marcia is not correct. According to the distance formula, the distance should be D=√(17-17)^2+(3-(-5))^2=√8
Answer:
C
Step-by-step explanation:
3-(-5=8
3+5=8
They are on the same x axis so all you have to do is add 3 and 5 together.
Answer:
c) Marcia is correct. Since the x-coordinates are the same, the distance between the points can be treated as if they are in one-dimension.
Step-by-step explanation:
a) Marcia is not correct. Since the points are in two-dimensions, the distance formula must be used to find the distance.
No, in this case x-coordinates are same and this can be treated same as number lineb) Marcia is correct. For any pair of points, the distance between the points can be treated as if they are in one-dimension.
No, it is not the case for any pair of pointsc) Marcia is correct. Since the x-coordinates are the same, the distance between the points can be treated as if they are in one-dimension.
Yes, in this case x-coordinates are same (17)d) Marcia is not correct. According to the distance formula, the distance should be D=√(17-17)^2+(3-(-5))^2=√8
No, formula is correct but the answer is incorrectYou roll two fair dice, one green and one red. (a) Are the outcomes on the dice independent? Yes No (b) Find P(1 on green die and 5 on red die). (Enter your answer as a fraction.) (c) Find P(5 on green die and 1 on red die). (Enter your answer as a fraction.) (d) Find P((1 on green die and 5 on red die) or (5 on green die and 1 on red die)). (Enter your answer as a fraction.)
Answer:
1) yes ; 2) 1/36 ; 3) 1/36 ; 4) 1/18
Step-by-step explanation:
Given the following :
Two fair dice : 1 green ; 1 red
A) Are the outcomes on the dice independent:
Yes, becomes the outcome of the green dice does not have any effect on the outcome of the red dice.
B) Find P(1 on green die and 5 on red die).
Probability = (number of required outcome) / (total possible outcomes)
Total outcomes of a dice = 6
P(1 on green) = 1 / 6
P(5 on red) = 1/6
P(1 on green die and 5 on red die) :
(1/ 6) × (1/6) = 1/36
C) Find P(5 on green die and 1 on red die)
P(5 on green) = 1/6
P(1 on red) = 1/6
Find P(5 on green die and 1 on red die):
1/6 × 1/6 = 1/36
D) Find P((1 on green die and 5 on red die) or (5 on green die and 1 on red die))
P(5 on green die and 1 on red die) = 1/36
P(1 on green die and 5 on red die) = 1/36
P((1 on green die and 5 on red die) or (5 on green die and 1 on red die)) =
P(5 on green die and 1 on red die) + P(1 on green die and 5 on red die)
= (1/36 + 1/36) = 2 /36 = 1/18
3.28 in expanded form
Answer:
3 ones
2 tenths
8 hundredths
I'm sorry if I misunderstood.
Good luck though! :)
Please add Brainliest if you'd like, not that it matters.
The slant height of a cone is 8.45cm
and the diameter of the base is 14cm.
Calculate, three significant figures, the
curved surface area of the cone (Take
= 22÷7
[tex]\bf \underline{ \underline{Given : }}[/tex]
Slant height,l = 8.45 cmDiameter of base = 14 cm[tex]\bf \underline{ \underline{To \: be \: calculated : }}[/tex]
Calculate the curved surface area of the cone .
[tex]\bf \underline{ \underline{Formula \: applied : }}[/tex]
Curved surface area of cone = πrl
[tex]\bf \underline{ \underline{Solution : }}[/tex]
First of all,
Radius = Diameter/2
=> Radius,r = 14/2
=> Radius,r = 7 cm
Now,
[tex] \sf{Curved \: surface \: area \: of \: cone =\pi rl}[/tex]
[tex] \sf \: \implies \: \dfrac{22}{ \cancel7} \times \cancel7 \times 8.45[/tex]
[tex] \sf\implies22 \times 8.45[/tex]
[tex] \sf \implies 185.9 \: {cm}^{2} [/tex]
Hence,the Curved surface area of cone is 185.9 cm².
Given the following group of numbers (8, 12, 4, 8, 6, 0, 9, 11, 3, 10) which of the following is (are) true? The mean is 7.1 The median is 1.6 The mode is 0
Answer:
The mean is 7.1
The median IS NOT 1.6 (its 8)
The mode IS NOT 0 (its 8)
Step-by-step explanation:
The true statement is , The mean is 7.1.
What is mean, median, mode?The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.
The median is the middle value when a data set is ordered from least to greatest.
The mode is the number that occurs most often in a data set.
here, we have,
given data, group of numbers (8, 12, 4, 8, 6, 0, 9, 11, 3, 10)
now, we get,
The mean is 7.1.
The median IS NOT 1.6 (its 8)
The mode IS NOT 0 (its 8).
hence, The true statement is , The mean is 7.1.
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If point Q is translated 5 units to the right an 5 units down , what are the coordinates of Q?
Answer:
Q has coordinates (qx+5, qy-5)
Step-by-step explanation:
Q has coordinates (qx, qy)
we move 5 units to the right so add 5 to the value of x
Q has coordinates (qx+5, qy)
we move 5 units down so subtract 5 from the value of y
Q has coordinates (qx+5, qy-5)
Simplify. Explanation if you can.
Answer:
10
Step-by-step explanation:
This expression uses the idea of exponential edition. The basis is, when you have the same base number being multiplied, you can add the exponentials.
Consider the case of 2 * 2. We know this to be 4. When writing 2 * 2, you can write this as 2^1 * 2^1 == 2^(1+1) == 2^2 == 4. See how we added the powers to get the new exponential?
We will apply this same idea here.
10^(1/2) * 10^(1/2) == 10^(1/2 + 1/2) == 10^(1) == 10.
So, the simplified expression is 10.
Cheers.
Question 8 options: Solve for the value of X. 23X = 6
Answer:
divide both sides by 23
making it to be 0.26
The value of x from the equation 23x =6 is x= 6/23.
To solve for the value of x in the equation 23x = 6, we need to isolate x on one side of the equation.
Divide both sides of the equation by 23:
(23x) / 23 = 6 / 23
Simplifying:
x = 6 / 23
Therefore, the value of x is 6 divided by 23, which can be left as a fraction or decimal depending on the desired form.
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Find the equation of the line with slope – 3 and that contains the point (-2,-6). Write the equation in the form y = mx +b and
identify m and b.
Answer:
m = -3
b = 0
equation of line
y = -3x
Step-by-step explanation:
in the the equation in the form y = mx +b
m is the slope
b is the y intercept.
__________________________________________________
given slope = -3
thus,
m = -3
the required equation of line is
y = mx +b
put m = -3
y = -3x + b
to find b , we put x = -2, y = -6 as this equation contains point (-2,-6).
-6 = -3*-2 + b
=> -6 = -6 + b
=> b = -6 + 6 = 0
thus. m = -3
b = 0
equation of line
y = -3x
PLS HELP The diagram was constructed with straightedge and compass tools. Points A, B, C,
D. and E are all on line segment CD. Name a line segment that is half the length of
CD. Explain how you know.
Answer:
lines CD, AE, and BD are half the length of CD
Step-by-step explanation:
All circles will have the same radius "r"
then CD = 4r
½CD = 2r
CB = AE = BD = 2r
The line CD has two circles which are equidistant from the points C and D and both meet at point B.
Point B is the midpoint of Line CD dividing line CD into two equal halves.
The line segments AE , CB and BD are line segments that are half of the length of line CD.
CB and BD form the diameters of the circles.
A diameter is a line that divides the circle into 2 equal halves. It passes through the center of the circle and joins one end point to another.
A radius is the distance from the circumference to the center of the circle.
A diameter is made up of two radius.
In the figure two equal diameters divide the line segment into two equal parts.
The third circle has the diameter AE which has radius AB and AE which are also the radius of the other two circles.
Hence the three circle are equal .
Hence the line segments AE , CB and BD are line segments that are half of the length of line CD.
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At the end of a snow storm, Tristan saw there was a lot of snow on his front lawn. The
temperature increased and the snow began to melt at a steady rate. After the storm,
the snow started melting at a rate of 0.75 inches per hour and it is known that 4 hours
after the storm ended, the depth of snow was down to 9 inches. Write an equation for
S, in terms of t, representing the depth of snow on Tristan's lawn, in inches, t hours
after the snow stopped falling.
Answer:[tex]S(t)=12-0.75t[/tex]
Step-by-step explanation:
Given: The snow started melting at a rate of 0.75 inches per hour and it is known that 4 hours after the storm ended, after the storm ended, the depth of snow was down to 9 inches.
Snow melted in 4 hours = [tex]0.75\times4 =3\text{ inches}[/tex]
Initial depth of snow = 9 + 3 inches = 12 inches.
Now, depth of snow on Tristan's lawn = Initial depth -0.75(Number of hours)
Let S(t) be the depth of snow on Tristan's lawn, in inches, t hours after the snow stopped falling.
Then, [tex]S(t)=12-0.75t[/tex]
The linear equation that represents the depth of snow on Tristan's lawn, in inches, t hours after the snow stopped falling is:
[tex]S(t) = 12 - 0.75t[/tex]
A linear function in the model will have the following format:
[tex]S(t) = S(0) - mt[/tex]
In which:
S(0) is the initial amount of snow.m is the melting rate, which is the slope.The snow melts at a rate of 0.75 inches per hour, thus [tex]m = 0.75[/tex] and:
[tex]S(t) = S(0) - 0.75t[/tex]
After 4 hours, there were 9 inches, that is, when [tex]t = 4, S(t) = 9[/tex], and this is used to find S(0).
[tex]S(t) = S(0) - 0.75t[/tex]
[tex]9 = S(0) - 0.75(4)[/tex]
[tex]S(0) = 9 + 0.75(4)[/tex]
[tex]S(0) = 12[/tex]
Hence, the equation is:
[tex]S(t) = 12 - 0.75t[/tex]
A similar problem is given at https://brainly.com/question/16302622
3ab - 2bc = 12 solve for b
is -17 rational or irrational?
-17 is a rational number
What is a rational number?A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero. Rational numbers have finite or recurring decimal expansions. Irrational numbers are numbers that can not be expressed as the ratio or fraction of two integers. Irrational numbers have non-terminating and non-repeating decimal expansions.
Whereby -17 can be expressed as the value -17/1, based on the definition of a rational number, -17 is a rational number
Learn more on rational numbers here: https://brainly.com/question/16933806
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9 - 8x - 7 - 2x equals 4 solve for x
Answer:
x = -1/2
Step-by-step explanation:
Step 1: Write out equation
9 - 8x - 8 - 2x = 4
Step 2: Combine like terms (x)
9 - 10x - 8 = 4
Step 3: Combine like terms (constants)
-10x - 1 = 4
Step 4: Add 1 to both sides
-10x = 5
Step 5: Divide both sides by -10
x = -5/10
Step 6: Simplify
x = -1/2
What values of x make the equation x2 + 9x – 22 = 0 true?
To solve this polynomial equation, we will need to factor the left side.
On the left, we have a a trinomial in a special form that
can be factored as the product of two binomials.
The trinomial on the left can be factored which makes life easier.
This factors as (x + 11)(x - 2) = 0.
This means that either x + 11 = 0 or x - 2 = 0.
Solving each equation from here, we get x = -11 or x = 2.
So the solution is {-11, 2}.
Answer:
2 and -11
Step-by-step explanation:
Step 1: Use the quadratic formula to solve for x
[tex]x=\frac{-b+-\sqrt{b^{2-4ac} } }{2a} \\x=\frac{-9+-\sqrt{9^{2}-4(1) (-22)} }{2(1)} \\x=\frac{-9+-\sqrt{169} }{2(1)}\\x=\frac{-9+-13 }{2}\\x1=\frac{-9+13 }{2}\\x1=\frac{4}{2} \\x1 = 2\\x2 = \frac{-9-13 }{2}\\x2 = \frac{-22 }{2}\\x2 = -11\\[/tex]
Therefore the values of 'x' that make the equation true is 2 and -11
(6,-1) and y = – 1/3x+ 1
y = 3x + [?]
Answer:
- 19
Step-by-step explanation:
Let's consider the equation as ;
y = 3x + c
( 6, -1 ) satisfies the equation ;
-1 = 3( 6) + c
c = - 18 - 1
c = -19
So the slope - intercept is (- 19)