Answer:
Step-by-step explanation:
If a + 3b = 7, subtract 3b from both sides of the equation
-3b = -3b then you get
a = 7-3b now plug this into the other equation: 3a-2b=8
3(7-3b) - 2b = 8
21 - 9b - 2b = 8
21 - 11b = 8 add 11 b to both sides
+ 11b +11b
21 = 8 + 11b subtract 8 from both sides
-8 -8
13 = 11b
What is 4a+b?
4(7-3b) + b =
(28 - 12b) + b =
28-11b (from above 13=11b)
28 - 13 = 15
A car's fuel efficiency is measured by the distance it can drive per a single unit of fuel. A common unit for efficiency is km/1, kilometers per liter of fuel. C(S) models the fuel efficiency of a certain car as a function of the car's speed S (in kilometers per hour). Match each statement with the feature of the graph that most closely corresponds to it.
The feature of the graph that most closely corresponds to the number of gallons of gasoline necessary to fill an automobile gas tank is the y-axis. The feature of the graph that most closely corresponds to the mass of a textbook is the line or curve representing the fuel efficiency as a function of the car's speed. The feature of the graph that most closely corresponds to the time required to drive from San Francisco to Kansas City at an average speed of 53 mi/h is the distance traveled.
Explanation:The feature of the graph that most closely corresponds to the number of gallons of gasoline necessary to fill an automobile gas tank would be the y-axis. The y-axis represents the fuel consumption or efficiency of the car, which is measured in kilometers per liter (km/1).
The feature of the graph that most closely corresponds to the number of cm in 2 m would be the x-axis. The x-axis represents the speed of the car in kilometers per hour (km/h). It shows the relationship between the car's speed and its fuel efficiency.
The feature of the graph that most closely corresponds to the mass of a textbook would be the line or curve representing the fuel efficiency as a function of the car's speed. This line or curve shows how the car's efficiency changes as its speed varies.
The feature of the graph that most closely corresponds to the time required to drive from San Francisco to Kansas City at an average speed of 53 mi/h would be the distance traveled. The distance traveled is an important factor in determining the car's fuel efficiency.
Calculate how many infected people there will be on April 25 if on March 22 there were 69 cases, use equation 15.4x+72, plug x value and simplify to get y value
Answer:
There will be 1134.6 infected people on April 25 if on March 22 there were 69 case.
Step-by-step explanation:
Given : Equation [tex]15.4x+72[/tex]
To find : Calculate how many infected people there will be on April 25 if on March 22 there were 69 case ?
Solution :
Equation [tex]y=15.4x+72[/tex]
Plug the x value in the equation,
[tex]y=15.4(69)+72[/tex]
[tex]y=1062.6+72[/tex]
[tex]y=1134.6[/tex]
Therefore, there will be 1134.6 infected people on April 25 if on March 22 there were 69 case.
Two plumbers charge different rates for service. The first plumber charges $100 for every service call plus $25 per hour of service. The second plumber charges $50 for every service call plus $50 per hour of service. After how many hours do the plumbers charge the same amount
After two hours the two plumbers will charge the same amount
Step-by-step explanation:Set up your equations
Plumber 1:
y = 25x + 100
Plumber 2:
y = 50x + 50
Set the two equal to each other and solve
25x + 100 = 50x + 50
-50 -50
25x + 50 = 50x
-25x -25x
50 = 25x
50/25 = 25x/25 <- Divide both sides by 25
x = 2
After two hours the two plumbers will charge the same amount
A ball is thrown directly upward from a height of 66 ft with an initial velocity of 2828 ft/sec. The function s(t)equals=minus−16tsquared2plus+2828tplus+66 gives the height of the ball, in feet, t seconds after it has been thrown. Determine the time at which the ball reaches its maximum height and find the maximum height.
Answer:
Time taken to reach maximum height=0.875 seconds
Maximum height = 78.25 ft
Step-by-step explanation:
The function which models the height of the ball is given as:[tex]s(t)=-16t^2+28t+66[/tex]
The function s(t) reaches its maximum height at the axis of symmetry. For a quadratic equation of the form [tex]ax^2+bx+c=0[/tex], the axis of symmetry occurs at [tex]x=-\frac{b}{2a}[/tex].
In s(t), a=-16, b=28
[tex]t=-\frac{28}{2(-16)}=0.875 seconds[/tex]
The ball reaches its maximum height after 0.875 seconds
(b)Maximum Height
Given [tex]s(t)=-16t^2+28t+66[/tex]
At t=0.875
[tex]s(0.875)=-16(0.875)^2+28(0.875)+66=78.25 ft[/tex]
Maximum height = 78.25 ft
Answer:
time: 0.875 seconds
maximum height: 18.25 feet
Step-by-step explanation:
The function that gives the height of the ball in feet after t seconds is:
s(t) = −16t^2 + 28t + 6
The inicial velocity is 28 ft/sec, and the inicial position is 6 feet.
So, to find the time when the ball reaches the maximum heigth, we need to find the vertix of the equation −16t^2 + 28t + 6.
We can use the following formula to find it:
t_vertix = -b/2a
where a and b are coefficients of the quadratic equation (in our case, a = -16 and b = 28).
So, we have that:
t_vertix = -28/(-32) = 0.875 seconds
To calculate the maximum height we just need to use this time in the equation of position:
s(0.875) = −16*(0.875)^2 + 28*0.875 + 6 = 18.25 feet
Evaluate: log216
Select the appropriate response
A) 0
B) -1
C) 7
Answer:
4
Step-by-step explanation:
log2(16)
log2(2^4)
4 log2(2)
4 × 1
4
It should be 4
The shape of the distribution of the time required to get an oil change at a 10-minute oil-change facility is unknown. However, records indicate that the mean time for an oil change is 11.4 minutes, and the standard deviation for oil- change time is 3.2 minutes.
(a) To compute probabilities regarding the sample mean using the normal model, what size sample would be required?
(b) What is the probability that a random sample of n=45 oil changes results in a sample mean time of less than 10 minutes?
Answer:
a) sample size ≥ 30
b) 0.0017
Step-by-step explanation:
a) The central limit theorem states that for population with mean μ and standard deviation σ and take sufficiently large random samples from the population. This will hold provided the sample size is sufficiently large (usually n > 30) for a normal population.
Therefore the sample size should be greater or equal to 30 i.e n ≥ 30.
b) Given that n = 45, μ = 11.4 minutes and σ = 3.2 minutes, the z score (z) is given by the equation:
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]
Substituting values to get:
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n} } }= \frac{10-11.4}{\frac{3.2}{\sqrt{45} } }=-2.93[/tex]
Using the z table:
P(x < 10) = P(z < -2.93) = 0.0017
the probability that a random sample of n=45 oil changes results in a sample mean time of less than 10 minutes is 0.0017
For part (a), a sample size larger than 30 would be sufficient for using the normal model. For part (b), we'd use the standard error and z-score to find the corresponding probability for the sample mean time being under 10 minutes with a sample size of 45.
Explanation:The questions revolve around the normal distribution model, which is a concept in Statistics, and the sample size needed to use the normal model to make inferences about a population (in this case, the duration of oil changes). For part (a), we must note that the Central Limit Theorem allows us to assume the distribution of sample means will approximate a normal distribution if the sample size is large enough (mostly, n > 30 is sufficient).
Thus, for this particular scenario, a sample size greater than 30 would be adequate. For part (b), using the standard error (standard deviation / sqrt(n)) with n = 45, we can find the z score = (X - μ) / standard error, where X is 10. We consult a normal distribution table or use software to find the probability associated with this z-score, which would be the answer.
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How do I solve this
Answer:
c = 30 inch
Step-by-step explanation:
perpendicular (p) = 18 inch
base(b) = 24 inch
hypotenuse (h) = ?
we know by using Pythagoras theorem
h² = p² + b²
h² = 18² + 24²
h² = 324 + 576
h² = 900
h= √900
therefore h = 30 inch
Hope it will help you. :)
Kelly's recipe calls for 13 ounces of chicken. Her scale only measures in grams. Which of the following shows the number of grams of chicken, with the correct significant digits, that Kelly needs to include in her recipe in order to have 13 ounces? (1 ounce = 28.3495 grams)
A) 368.5435
B) 367.9
C) 369
D) 370
Answer:
A
Step-by-step explanation:
13 x 28.3495
Answer:
A
Step-by-step explanation:
1 ounce is 28.3495 grams and Kelly's recipe call for 13 ounces of chicken, so
13 x 28.3495 = 368.5435
I NEED HELP OBN THIS BADLY WILL GIVE YOU CROWN
A jug contained 3 1/4 pints of milk at the start of a baking class. At the end of the class, only 3 fluid ounces were left.
How many fluid ounces of milk were used during the class?
10 fl oz
23 fl oz
49 fl oz
101 fl oz
A monkey collects 60 coconuts and wants to store them in stacks that each contain the same number of coconuts. Describe all the different stacks the monkey can make, including the number of coconuts in each stack. Then find the prime factorization of 60. The monkey can make 1 stack of , 2 stacks of , 3 stacks of , 4 stacks of , 5 stacks of , 6 stacks of , 60 stacks of , 30 stacks of , 20 stacks of , 15 stacks of , 12 stacks of and 10 stacks of . The prime factorization of 60 is
Answer:
1 stack of 60
2 stacks of 30
3 stacks of 20
4 stacks of 15
5 stacks of 12
6 stacks of 10
60 stacks of 1
30 stacks of 2
20 stacks of 3
15 stacks of 4
12 stacks of 5
Prime Factorisation
[tex]60=2^{2}*3*5[/tex]
Step-by-step explanation:
To find the number of stacks you can make just divide the total by the size of the stacks. This also works in reverse.
To find the prime factorisation you just find the factors of the number by dividing it by the largest prime possible.
The monkey can arrange the 60 coconuts into different numbers of stacks, from 1 stack of 60 coconuts to 60 stacks of 1 coconut. The prime factorization of 60 is 2^2 x 3 x 5.
Explanation:The monkey, who has collected 60 coconuts, can distribute them in various different ways. The distribution depends on the number of coconuts in each stack as well as the total number of stacks. Here are the various possibilities:
1 stack with 60 coconuts 2 stacks with 30 coconuts each 3 stacks with 20 coconuts each 4 stacks with 15 coconuts each 5 stacks with 12 coconuts each 6 stacks with 10 coconuts each 10 stacks with 6 coconuts each 12 stacks with 5 coconuts each 15 stacks with 4 coconuts each 20 stacks with 3 coconuts each 30 stacks with 2 coconuts each 60 stacks with 1 coconut each
Now, for the prime factorization of 60. This involves breaking down 60 into its smallest prime factors, which are 2, 3, and 5. Thus, the prime factorization of 60 is: 22 x 3 x 5
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Darian drove 274.5 miles in 4.5 hours. What was his average speed?
Answer:
61 miles per hour
Step-by-step explanation:
because you need to divide 274.5 by 4.5 to get the average speed per hour.
Answer:
61 miles per hour
Step-by-step explanation:
To find the average speed, divide the miles by the hours
miles/hours
274.5/4.5
61
So, the average speed is 61 miles per hour
A used car costs $2,200 cash, or $600 down and $100 a month for 20 months. How much money do you save by paying cash?
Answer:
$400
Step-by-step explanation:
Cash = $2200
$600 + ($100*20) = 2600
$2600 - $2200 = 400
help with #22 please
Answer:
side c = 10.2
A = 52.6°
B = 37.4°
Step-by-step explanation:
c² = 8.1² + 6.2²
c² = 104.05
c = 10.20049018
Using cosine law:
8.1² = 10.2² + 6.2² - 2(10.2)(6.2)cos
cosA = 7687/11648
A = 52.57199409
A = 52.6°
B = 180 - 90 - 52.6 = 37.4°
Of the 60 students in a school, 24 are currently studying chemistry. Exactly 16 of the girls in the school are not currently studying chemistry. The number of girls in the school is 33. How many boys are currently studying chemistry
Answer:
7 boys.
Step-by-step explanation:
Given:
Total number of students in the school = 60
Total number of girls in the school = 33
Total number of students currently studying chemistry = 24
Total number of girls not currently studying chemistry = 16
Question asked:
How many boys are currently studying chemistry ?
Solution:
Total number of girls in the school = 33
Total number of girls not currently studying chemistry = 16
Total number of girls currently studying chemistry = Total number of girls in the school - Total number of girls not currently studying chemistry
Total number of girls currently studying chemistry = 33 - 16 = 17
Now:-
Total number of boys and girls currently studying chemistry = 24
Total number girls currently studying chemistry = 17
Total number of boys currently studying chemistry = Total number of boys and girls currently studying chemistry - Total number girls currently studying chemistry
Total number of boys currently studying chemistry = 24 - 17 = 7
Therefore, 7 boys are currently studying chemistry.
Penelope invested $32,000 in an account paying an interest rate of 7% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 14 years?
Answer:
85263
Step-by-step explanation:
In Penelope's account $ 85262.6 would be there after 14 years.
What is Compound Interest ?The compound Interest is the interest you earn on Interest .
The formula for calculating the amount when the interest is compounded continuously
P = P₀[tex]\rm e^{rt}[/tex]
Penelope invested $32,000 in an account
interest rate of 7% compounded continuously.
After 14 years the amount will be
P = 32000 * [tex]\rm e^{0.07*14}[/tex]
P = $ 85262.6
Therefore $ 85262.6 would be in the account after 14 years.
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Assume you have sea water that weighs 64 lb/ft³ and contains 35 parts per thousand (0.0035) dissolved salt by weight. How many cubic feet of the sea water would you need to place in an exaporation basin to collect 125 lb of sea salt?
Answer:
558.036 lb
Step-by-step explanation:
Let x is the amount of the sea water to collect 125 lb of sea salt
As given: 64 lb/ft³ has 0.0035 dissolved salt by weight
So the formula to find out the amount of the sea water is:
64 lb/ft³ * 0.0035 *x ft³ = 125 lb
<=> x = [tex]\frac{125}{64*0.035}[/tex] = 558.036 lb
Hope it will find you well.
Kalvins mother tells him that the chance of a coin showing heads when he tosses it is 1/2. Does this mean that every time he tosses a coin twice,he will get one head and one tail? Explain
Answer:
No
Step-by-step explanation:
The probability simply refers to the chance of an event occurring. What this means is that when a coin is tossed once, the chance that we can get a head is 50%. This is simply just referring to the likelihood of the event happening.
Now for the first toss, there is a likelihood of 50%, for the second toss too there will be a likelihood of 50%.
This is different from the fact that for every 2 throws there must be a head showing up
Anyone can help me with all of these answers 1-10 ( 18 Points ) ?
Answer:
1) 14
2) 8
3) 5
4) 11
5) 10
6) 6
7) 10
8) 17
9) 26
10) 18
Step-by-step explanation:
Merry Early Christmas :)
The wholesale price for a chair is $108. A certain furniture store marks of the wholesale price by 27%. Find the price of the chair in the furniture store. Round your answer to the nearest cent as necessary.
Answer:
The price of chair in furniture house is $137.16
Step-by-step explanation:
We are given the following in the question:
Wholesale price of chair = $108
Marked percentage = 27%
We have to find the price of the chair in the furniture store.
Increased price =
[tex]=27\%\times 108\\\\=\dfrac{27}{100}\times 108\\\\=29.16\$[/tex]
Price of chair in furniture house =
= Wholesale price + Increased price
[tex]=108 + 29.16\\=137.16\$[/tex]
Thus, the price of chair in furniture house is $137.16
The lifetime of a battery has the exponential distribution with mean 6.9 months. If it fails, I immediately replace it with another – if I have one. I need a year’s supply of the battery. In addition to the one in the flashlight, how many extra should I bring with me? 1, 2, or 3?
Answer:
You should carry 2 other batteries.
Step-by-step explanation:
If the average life of each battery tends to last 6.9 months, and what you need is a year of battery supply, you probably need to carry two batteries.
The battery inside the flashlight has probably already spent much of its half-life.
We are told that the flashlight already has a battery inside, the batteries are discharged inside the flashlight even if the flashlight is not being used.
Which means that the average life of that battery is wearing out.
It would take 2 more batteries in addition to the one already inside the flashlight to supply the need for these for a year.
GEOMETRY! PLEASE SHOW YOUR WORK.
Given:
The base of the given triangle has two part:
Left( left side of the hypotenuse) = 25
Right ( right side of the hypotenuse) = x
The altitude (h) = 60
To find the value of x.
Formula:
By Altitude rule we know that, the altitude of a triangle is mean proportional between the right and left part of the hypotenuse,
[tex]\frac{left}{altitude} =\frac{altitude}{right}[/tex]
Now,
Putting,
left = 25, altitude = 60 and right = x we get,
[tex]\frac{25}{60} = \frac{60}{x}[/tex]
or, [tex](25)(x)=(60)(60)[/tex] [ by cross multiplication]
or, [tex]x= \frac{3600}{25}[/tex]
or, [tex]x=144[/tex]
Hence,
The value of x is 144.
Answer:
x = 144
Step-by-step explanation:
Height Theorem
60² = 25·x
3600 = 25x
x = 3600 : 25
x = 144
How do i solve this problem while creating a quadratic equation ?
Answer:
f(x) = -15x² + 50x
Step-by-step explanation:
You're given the rocket start at ground level, so we can assume,
f(0) = 0
after 1 second the rocket is 35 feet up.
f(1) = 35
and after 2 second the rocket is 40 ft up.
f(2) = 40
Now you have 2 values to plug in your formula to solve.
Plug in f(x) = ax² + bx + c and solve:
f(0) = a(0)² + b(0) + c = 0
f(1) = a(1)² + b(1) + c = 35
f(2) = a(2)² + b(2) + c = 40
a(0)² + b(0) + c = 0
a(1)² + b(1) + c = 35
a(2)² + b(2) + c = 40
0 + 0 + c = 0 , we got c=0, so substitute it
a + b + c = 35
4a + 2b + c = 40
Solve for a and b
c = 0
a + b + 0 = 35
4a + 2b + 0 = 40 , solve it using elimination
-2a - 2b + 0 = -70
4a + 2b + 0 = 40
2a + 0 = -30
a = -15 , we got a, solve for b now
a + b + 0 = 35
(-15) + b + 0 = 35
b = 50
Now we got c=0, a=-15, and b=50, plug it back in your equation
f(x) = -15x² + 50x + 0
in what quradrant does the terminal side of 0 lie when tan 0 < 0 and sin 0 < 0
Answer:
Step-by-step expla0000000000000000000000000nation:
PLZ HELP ASAP 20 POINTS
Step-by-step explanation:
A (the first one)
.............
The upside down U means intersection, which would be the area the two circles overlap.
X’ and y’ would be opposite, so the area not in x or y.
The area would be outside the circles
The answer would be picture b
Find the median, first quartile, third quartile, and the interquartile of the data set.
32,47,49,53,54,66,67,71,72
Answer:
54 = median
48 = 1st quartile
69 = 3rd quartile
21 = interquartile
Hope this helped!! :)
Answer:
54 = median
48 = 1st quartile
69 = 3rd quartile
Step-by-step explanation:
Test the claim about the population mean μ at the level of significance α. Claim: μ ≠ 0; α = 0.05; σ = 2.62 Sample statistics: = -0.69, n = 60 Fail to reject H0. There is enough evidence at the 5% level of significance to support the claim. Reject H0. There is enough evidence at the 5% level of significance to reject the claim. Reject H0. There is enough evidence at the 5% level of significance to support the claim.
Answer:
Correct option:
Fail to reject H₀. There is enough evidence at the 5% level of significance to support the claim.
Step-by-step explanation:
The claim to be tested is:
Claim: μ ≠ 0.
The information provided is:
α = 0.05
σ = 2.62
Sample statistics: = -0.69
n = 60
As the population standard deviation is provided, it can be determined that a z-test for single is used to performed the test.
Decision rule:
If the p-value of the test is less than the significance level, α then the null hypothesis will be rejected and vice-versa.
Compute the p-value as follows:
[tex]p-value=2P(Z<-0.69)\\=2\times [1-P(Z<0.69)]\\=2\times [1-0.7549]\\=0.4902[/tex]
*Use a z-table for the probability.
The p-value = 0.4902 > α = 0.05.
The null hypothesis was failed to rejected at 5% level of significance.Thus, it can be concluded that there is enough evidence at the 5% level of significance to support the claim.
You have $30 dollars saved up. Every week you spend $6 at the arcade. Write an equation in slope intercept form that shows how much money you have (y) after x weeks.
Answer:
y = -6x + 30
Step-by-step explanation:
The inicial value you have is $30, so this will be the value of y after 0 weeks, that is, x = 0
After one week, you spend $6, so you will have y = 30 - 6 = 24 when x = 1.
With these pair of values, we can find the linear equation:
y = ax + b
for x = 0, y = 30:
30 = a*0 + b
b = 30
for x = 1, y = 24:
24 = a*1 + 30
a = 24 - 30 = -6
So, our equation is:
y = -6x + 30
I JUST NRRD HELP ASAP WILL GIVE CROWN
Dom and Amad are playing catch on a grassy field. The field is rectangular in shape. Dom says he knows that it has a perimeter of 48 yards. Jack says he knows that it has a width of 24 feet.
What is the length of the field in feet?
ft
Answer:
48 feet
Step-by-step explanation:
Since 1 yard = 3 feet
Therefore, 48 yards = 3* 48 = 144 feet
[tex]P = 2(l + w) \\ 144 = 2(l + 24) \\ \frac{144}{2} = l + 24 \\ 72 = l + 24 \\ 72 - 24 = l \\ l = 48 \: feet[/tex]
Hence, length of the field is 48 feet.
Answer:
48 ft im pretty sure
Step-by-step explanation:
Find the midpoint of the line segment with end coordinates of:
(
0
,
2
)
and
(
2
,
8
)
The midpoint is just the average of the coordinates,
M = (1/2) ( (0,2) + (2,8) ) = ((0+2)/2, (2+8)/2) = (1, 5)
Answer: (1,5)
Answer:
(1,5)
Step-by-step explanation:
(0,2) and (2,8)
Midpoint: (0+2)/2, (2+8)/2
2/2, 10/2
(1,5)
Sven observes a bird on top of a light pole. His eye level is 6 feet off of the ground. Sven is 48 feet from the pole. If the distance to the bird from Svens eyes is 50 feet, how tall is the pole?
The height of the pole is 20ft.
Step-by-step explanation:
Let the height of the pole be '(h+6)'
Distance between the pole and Sven = 48ft.
Height of Sven = 6 ft.
Distance between the bird and his eyes = 50 ft.
We can find the value of 'h' using pythogoras theorem,
h = √(2500-2304)
h = √(196)
h = 14 ft.
The height of the pole = h + 6
= 14 + 6
= 20ft.
The height of the pole is 20ft.