Answer:
t=2.25
Step-by-step explanation:
9 divided by 4 is 2.25
and 4 x 2.25 is 9
Answer t = 9/4
Divide both sides of the equation by the same term
9 = 4t
9/4=9/4
Convert the fraction 6/10 to a decimal.
Answer:
0.60
Step-by-step explanation:
Answer:
.60
Step-by-step explanation:
There are 600 cars in the parking lot. The ratio of red cars to white cars is 3:5. How many red cars and how many white cars are there in the parking lot?
Answer:
225 red cars & 375 white cars
Step-by-step explanation:
According to the specified ratio, there are 225 red cars and 375 white cars in the parking lot.
What is ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
given, There are 600 cars in the parking lot. The ratio of red cars to white cars is 3:5. let ratio is in the term of variable x
Thus,
3x + 5x = 600
=> 8x = 600
=> x = 75
Total number of red cars = 3x
Total number of red cars = 3 * 75
Total number of red cars = 225
Total number of white cars = 5x
Total number of white cars = 5*75
Total number of white cars = 375
Therefore, there are 225 red cars and 375 white cars in the parking lot as per the given ratio.
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Please help me solve this fast!
Answer:
1) 7/8 8/7
2) 4.4
3) 3.7
4) 2.8
Step-by-step explanation:
Length of bottom side of Figure A: 8 cm
Length of bottom side of Figure B: 7 cm
From Figure A to Figure B, the scale factor is 7/8.
7/8
8/7
5 × 7/8 = 35/8 = 4.375
4.4
3.2 × 8/7 = 3.657...
3.7
3.2 × 7/8 = 2.8
2.8
Which of the following expressions can be used to find the area of a square with a side length of fraction 1 over 3 m?
A. fraction 1 over 3 whole squared m2
B. fraction 1 over 3 whole cubed m2
C. fraction 1 over 3 multiplied by 2 m2
D. 2 multiplied by fraction 1 over 3 m2
Answer:
The answer is A.
Step-by-step explanation:
Since it is a square we are finding the area of, we are multiplying two numbers. Which means 1/3 by the power of 2.
Graph the line with slope 1/3 and y-intercept −2.
The graph of the function y = 1/3x - 2 is added as an attachment
Sketching the graph of the functionFrom the question, we have the following parameters that can be used in our computation:
Slope = 1/3y-intercept = -2So, the equation is
y = 1/3x - 2
The above function is a linear function that has been transformed as follows
Vertically stretched by a factor of 1/3Shifted down by 2 unitsNext, we plot the graph using a graphing tool by taking note of the above transformations rules
The graph of the function is added as an attachment
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Find two numbers whose sum is 12 and whose product is 35.
I've been tryna call
I've been on my own for long enough
Maybe you can show me how to love, maybe
I'm going through withdrawals
You don't even have to do too much
You can turn me on with just a touch, baby
I look around and
Sin City's cold and empty (oh)
No one's around to judge me (oh)
I can't see clearly when you're gone
I said, ooh, I'm blinded by the lights
No, I can't sleep until I feel your touch
I said, ooh, I'm drowning in the night
Oh, when I'm like this, you're the one I trust
(Hey, hey, hey)
I'm running out of time
'Cause I can see the sun light up the sky
So I hit the road in overdrive, baby, oh
The city's cold and empty (oh)
No one's around to judge me (oh)
I can't see clearly when you're gone
I said, ooh, I'm blinded by the lights
No, I can't sleep until I feel your touch
I said, ooh, I'm drowning in the night
Oh, when I'm like this, you're the one I trust
I'm just walking by to let you know (by to let you know)
I can never say it on the phone (say it on the phone)
Will never let you go this time (ooh)
I said, ooh, I'm blinded by the lights
No, I can't sleep until I feel your touch
(Hey, hey, hey)
I said, ooh, I'm blinded by the lights
No, I can't sleep until I feel your touch
A 40-foot powerboat is for sale by the owner. How long is the boat to
the nearest yard?
Solve for the variable. 4/5 = 20/?
A. x = 5
B. x = 16
C. x = 20
D. x = 25
Answer:
Its 25
Step-by-step explanation:
It is 25 as 4x5 is 20 so u have the denominator so u do the same for 5 , 5x5 is 25 so 4/5=20/25
Complete the algebra tile grid to model the product of (x + 2)(x – 3).
Answer: x^2 -x-6
Step-by-step explanation:
Mat
The product of (x + 2)(x - 3) is x² - x - 6
What is algebraic expression?"It is a mathematical statement which consists of constants, variables and mathematical operations."
For given question,
We have been given an algebraic expression (x + 2)(x - 3)
We need to find the product of (x + 2)(x - 3).
(x + 2)(x - 3)
= x (x - 3) + 2(x - 3)
= x² - 3x + 2x - 6
= x² - x - 6
Therefore, the product of (x + 2)(x - 3) is x² - x - 6
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suppose you draw 5 cards from a standard deck of 52 playing cards. (a) what is the probability that the hand contains exactly 3 cards from the heart suit? (b) what is the probability that the hand contains 4 or fewer cards from the heart suit? (c) what is the probability that every card in the hand is from a different suit? (d) what is the probability that every card in the hand is red or every card in the hand is black? 1
a. the probability of getting exactly 3 cards from the heart suit is approximately 0.0585. b. the probability of getting 4 or fewer cards from the heart suit is approximately 0.7681. c. the probability that every card in the hand is from a different suit is approximately 0.395. d. the probability that every card in the hand is red or every card in the hand is black is approximately 0.00198.
(a) To calculate the probability of getting exactly 3 cards from the heart suit, we can use the combination formula:
number of ways to choose 3 hearts out of 13 hearts * number of ways to choose 2 non-hearts out of 39 non-hearts / number of ways to choose 5 cards out of 52 cards
= (13 choose 3) * (39 choose 2) / (52 choose 5)
= 0.0585 (rounded to 4 decimal places)
Therefore, the probability of getting exactly 3 cards from the heart suit is approximately 0.0585.
(b) To calculate the probability of getting 4 or fewer cards from the heart suit, we can use the complement rule:
1 - (number of ways to choose 5 non-hearts out of 39 non-hearts / number of ways to choose 5 cards out of 52 cards)
= 1 - (39 choose 5) / (52 choose 5)
= 0.7681 (rounded to 4 decimal places)
Therefore, the probability of getting 4 or fewer cards from the heart suit is approximately 0.7681.
(c) To calculate the probability that every card in the hand is from a different suit, we can use the multiplication principle:
number of ways to choose 1 card of each suit / number of ways to choose 5 cards out of 52 cards
= (13 choose 1) * (13 choose 1) * (13 choose 1) * (13 choose 1) / (52 choose 5)
= 0.395 (rounded to 3 decimal places)
Therefore, the probability that every card in the hand is from a different suit is approximately 0.395.
(d) To calculate the probability that every card in the hand is red or every card in the hand is black, we can use the addition rule:
probability of all red cards + probability of all black cards
= (26 choose 5) / (52 choose 5) + (26 choose 5) / (52 choose 5)
= 0.00198 (rounded to 5 decimal places)
Therefore, the probability that every card in the hand is red or every card in the hand is black is approximately 0.00198.
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What’s the integral of 1/2
What is the third quartile of the following data set?
20, 21, 24, 25, 28, 29, 35, 36, 37, 43, 44
Answer:
37
Step-by-step explanation:
Before we find quartile, we have to arrange the data set in order first from least to greatest which this problem has already arranged the data for us.
Next, proceed with the calculation. The formula for finding position of quartile is:
\(\displaystyle{Q_r = \dfrac{r(N+1)}{4}}\)
Where \(\displaystyle{Q_r}\) means the rth quartile, N means number of data set. Since we want to find the third quartile, substitute r = 3 and there are 11 data so substitute N = 11:
\(\displaystyle{Q_3 = \dfrac{3(11+1)}{4}}\\\\\displaystyle{Q_3 = \dfrac{3(12)}{4}}\\\\\displaystyle{Q_3 = 3\cdot 3}\\\\\displaystyle{Q_3 = 9}\)
So the position of third quartile is at 9th position which is 37.
Henceforth, the third quartile is 37.
Answer:
37.
Step-by-step explanation:
The data is in ascending order, which is what we need to get the answer.
As there are 11 numbers the 9th number is the upper(third) quartile.
The median ( middle) number is 29 and the upper quartile is the middle number of the 5 numbers to the right of the median.
It is 37.
Aisha just received a $40 paycheck from her new job. She spends some of it buying music online and saves the rest in a bank account. Her savings is given by f(x)=40-1.25x, where x is the number of songs she downloads at $1.25 per song. Graph the function.
The graph of saving function f(x) = 40 - 1.25x has been plotted with a slope of -1.25.
How to plot a graph?A graph is a diagram that shows the fluctuation of one variable in relation to one or more other variables.
In order to plot the graph, we need to find out y's values corresponding to x's value
Given the function,
f(x) = 40 - 1.25x
Now to plot it we need to put x = 0
f(0) = 40 so y-intercept is (0,40)
Now keep f(x) = 0
Then 0 = 40 - 1.25x
x = 40/1.25 = 32
So x-intercept is (32,0)
So plot a straight line using points (0,40) and (32,0).
Hence "The graph of saving function f(x) = 40 - 1.25x has been plotted".
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Why do you think the cart rolls farther when it starts from a higher position?
Answer:
It has higher PE which can be converted into kinetic energy. The car also has had more work done on it when its at a higher position.
Step-by-step explanation:
This is because the cart gains speed as it goes from the top of higher point to bottom.
a. Find parametric equations and symmetric equations for the line passing through the points (-2, 4, 3) and (1, 2, 7).
b. At what point does this line intersect the yz-plane?
a) The parametric equations of the line are: x(t) = −2 + 3t, y(t) = 4 − 2t, z(t) = 3 + 4t and The symmetric equation of the line are: (x + 2)/3 = (y − 4)/−2 = (z − 3)/4
b) The line intersects yz-plane at (0, 8/3, 17/3)
The given points on the line are:
(x₁, y₁, z₁) = (−2, 4, 3)
(x₂, y₂, z₂) = (1, 2, 7)
The direction ratios of this line are:
⟨a, b, c⟩ = ⟨x₂ − x₁, y₂ − y₁, z₂ − z₁⟩
= ⟨1 + 2, 2 − 4, 7 − 3⟩
= ⟨3, −2, 4⟩
a) Parametric equations of the line:
These are given by:
x(t) = x₁ + at = −2 + 3t
y(t) = y₁ + bt = 4 − 2t
z(t) = z₁ + ct = 3 + 4t
Symmetric equation of the line:
This is given by:
(x − x₁)/a = (y − y₁)/b = (z − z₁)/c
(x + 2)/3 = (y − 4)/−2 = (z − 3)/4
b) When a line intersects the yz-plane, its x-coordinate is zero.
Using the parametric equations of the part (a):
x = 0
−2 + 3t = 0
3t = 2
t = 2/3
Substitute this in the parametric equations corresponding to y and z as well:
y = 4 −2t
= 4 − 2(2/3)
= 8/3
z = 3 + 4t
= 3 + 4(2/3)
= 17/3
Hence, the required point is: (x, y, z) = (0, 8/3, 17/3)
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A car travels 2 5/8 miles 3 1/2 minutes at a constant speed. How far did the car travel in 5 minutes?
Answer:
2.3333333 miles in 3.5 minutes = 2.3333333 / 3.5 =
2/3 miles per minute or
.66666666 miles per minute
In 34 minutes, it can travel 34 * (2/3) = (68/3) =
22 (2/3) miles
The first term of a geometric sequence is 5 and the multiplier, or ratio, is –2. What is the sum of the first 5 terms of the sequence?
Step-by-step explanation:
s1 = 5
s2 = s1 × -2 = 5×-2 = -10
s3 = s2 × -2 = -10 × -2 = 20
...
now, we could do all that manually.
but there is also a formula for geometric sequence.
in fact, there are 2 - one for finite and one for infinite sequences.
and I was not completely honest, each of these 2 had some sub-forms depending on the size of the multiplier or ratio.
since we need the sum of the first 5 terms, which of the 2 do you think we need ?
of course, finite, because 5 is a normal number we can "touch". it is not infinity.
so, the formulas for finite sums of geometric sequences are :
if |r| < 1, Sn = a(1 - r^n)/(1 - r)
if |r| > 1, Sn = a(r^n - 1)/(r - 1)
if r = 1, Sn = na
if r = -1, then Sn = a or 0 depending on if n is odd or even.
the sequence is in general
s1 = a
sn = sn-1 × r
in our case a = 5, r = -2.
so, what form of the formula do we need ?
|-2| = 2, and 2 > 1, so ...
S5 = 5(-2^5 ‐ 1)/(-2 - 1) = 5(-32 - 1)/-3 = 5×-33/-3 =
= 5 × 11 = 55
quick check, as the 5 terms are
5
-10
20
-40
80
and their sum is : 55
correct !
a fair die is rolled 100 times.the results are shown below
number:. 1. 2. 3. 4. 5. 6
no of times:. 12. 16. 25. 18. 15. 14
what is the probability of getting
1?
2?
3?
4?
5?
6?
1.) Probability of getting 1: 0.12 or 12%.
2.) Probability of getting 2: 0.16 or 16%.
3.) Probability of getting 3: 0.25 or 25%.
4.) Probability of getting 4: 0.18 or 18%.
5.) Probability of getting 5: 0.15 or 15%.
6.) Probability of getting 6: 0.14 or 14%.
To calculate the probability of getting a specific number on a fair die, we divide the number of times that number appears by the total number of rolls. In this case, the die was rolled 100 times, and the results are given as follows:
Number: 1 2 3 4 5 6
Times: 12 16 25 18 15 14
To find the probability of getting each number, we divide the corresponding number of times by the total number of rolls (100):
Probability of getting 1 = 12 / 100 = 0.12.
Probability of getting 2 = 16 / 100 = 0.16.
Probability of getting 3 = 25 / 100 = 0.25.
Probability of getting 4 = 18 / 100 = 0.18.
Probability of getting 5 = 15 / 100 = 0.15.
Probability of getting 6 = 14 / 100 = 0.14.
Therefore, the probabilities of getting each number on a fair die, based on the given results of 100 rolls, are approximately:
1: 0.12 or 12%,
2: 0.16 or 16%,
3: 0.25 or 25%,
4: 0.18 or 18%,
5: 0.15 or 15%,
6: 0.14 or 14%.
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Two factory workers win the in-house raffle with a prize of £240. Monika and Robert share the prize money in a ratio of 3:5. How much does Monika get?
Answer:
Monika gets £90
Step-by-step explanation:
Let us use the ratio method to solve this question
∵ Monika and Robert are Two factory workers
∵ They win the in-house raffle with a prize of £240
∵ Monika and Robert share the prize money in a ratio of 3: 5
→ That means the total of the ratio is equivalent to the value of the prize
∵ The total of the ratio = 3 + 5 = 8
→ By using the ratio method
→ Monika : Robert : Total
→ 3 : 5 : 8
→ x : y : 240
→ By using the cross multiplication
∵ x × 8 = 3 × 240
∴ 8x = 720
→ Divide both sides by 8
∵ \(\frac{8x}{8}\) = \(\frac{720}{8}\)
∴ x = 90
∵ x represents the share of Monika
∴ Monika gets £90
The automaker of your new car recommended an oil change following the 5,000 miles and then every 3,000 miles thereafter.if you plan to drive the car 250 miles a week, how many oil changes will you need the first year?
Answer:
3 oil changes
Step-by-step explanation:
1. Find an equation that represents this word problem: 3000x + 5000 = y
Where y = the # of miles total. y = 250 miles/week * 52 weeks/year = 13000 miles.
2. Solve for x: 3000x + 5000 = 13000 3000x=8000
3. x = 8/3 integer round down x = 2 oil changes, but plus the one after 5000 miles is a total of 3 oil changes that year
6.34 in expanded form
Answer:
Expanded Notation Form:
6.34
=
6
+
0.3
+
0.04
Expanded Factors Form:
6.34
=
6 ×
1
+
3 ×
0.1
+
4 ×
0.01
Expanded Exponential Form:
6.34 =
6 × 100
+
3 × 10-1
+
4 × 10-2
Cual es el perímetro de un rectángulo si tiene 20 de largo y 11 de ancho?
The perimeter of the rectangle is 62 square units.
How to find the perimeter of a rectangle?The perimeter of a rectangle can be calculated using the formula:
P = 2(L + W)
Where:
L is the length of the rectangle
W is the width of the rectangle
We have:
L = 20 units
W = 11 units
Substituting into the formula:
P = 2(20 + 11)
P = 2(31)
P = 62 square units
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Question in English
What is the perimeter of a rectangle if it is 20 long and 11 wide?
PLEASE HELP ASAP!! (NO LINKS)
Tell whether the ordered pair
(-5, -4) is a solution of the system.
A squirrel climbs 15 feet up a tree. He then runs 8.26 feet down the tree. How much further does the squirrel need to
go before reaching the ground?
7.36 feet
7.26 feet
6.74 feet
8.11 feet
Answer:
C 6.74
Step-by-step explanation:
thats the answer
Answer:
C 6.74
Step-by-step explanation:
I caculated it.
what is the estimated sum of 4 5/12 + 3 8/14
A.7
B.7 1/2
C.8
D.9
The estimated sum of 7 83/84 is 8 to the nearest whole number.
Addition of mixed fractions:Mixed fractions are fraction that has a whole number attached to an improper fraction. A mixed fraction can be added by first adding the real whole numbers together, then adding their improper fraction counterparts with it.
Also, we can add two mixed fractions together by first converting all the mixed fractions to improper fractions before adding them together.
Using the first process:
= 4 5/12 + 3 8/14
The whole number are 4 and 3, adding those two together, we have:
= 7 (5/12 + 8/14)
The L.C.M of 12 and 14 is 84.
= 7( (7×5)+ (6*8) ) /84
= 7 (35+ 48/84)
= 7 (83/84)
To decimal, we get 7.988. Therefore, the estimated sum of 7 83/84 is 8 to the nearest whole number.
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what is the GCF of 8b and 16a?
Fifteen SmartCars were randomly selected and the highway mileage of each was noted The analysis yielded a mean of 47 miles per gallon and a sample standard deviation of 5 miles per gallon Which of the following would represent a 90% confidence interval for the average highway mileage of all SmartCars? a. 47 plusminus (1.753*(5 + 3.8730) b. 47 plusminus (1.345*(5 + 3.8730) c. 47 plusminus (1.765*(5 + 3.8730) d. 47 plusminus (1.645*(5 + 3.8730)
Answer: a. 47 plusminus (1.753*(5 ÷ 3.8730)
Step-by-step explanation:
Confidence interval is written in the form,
(Sample mean - margin of error, sample mean + margin of error)
The sample mean, x is the point estimate for the population mean.
Margin of error = z × s/√n
Where
s = sample standard deviation = 5
n = number of samples = 15
z represents the test statistic
From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the test statistic score
In order to use the t distribution, we would determine the degree of freedom, df for the sample.
df = n - 1 = 15 - 1 = 14
Since confidence level = 90% = 0.90, α = 1 - CL = 1 – 0.90 = 0.1
α/2 = 0.1/2 = 0.05
the area to the right of z0.05 is 0.05 and the area to the left of z0.05 is 1 - 0.05 = 0.95
Looking at the t distribution table,
z = 1.753
Margin of error = 1.753(5 ÷ 3.8730)
Confidence interval = 47 ± 1.753(5 ÷ 3.8730)
A survey of 400 students yielded the following information: 262 were seniors, 215 were commuters, and 150 of the seniors were commuters. How many of the 400 surveyed students were seniors or were commuters?
Out of the 400 surveyed students, 327 were either seniors or commuters.
To find the number of students who were either seniors or commuters out of the 400 surveyed students, we need to add the number of seniors and the number of commuters while avoiding double-counting those who fall into both categories.
According to the information given:
There were 262 seniors.
There were 215 commuters.
150 of the seniors were also commuters.
To avoid double-counting, we need to subtract the number of seniors who were also commuters from the total count of seniors and commuters.
Seniors or commuters = Total seniors + Total commuters - Seniors who are also commuters
= 262 + 215 - 150
= 327
Therefore, out of the 400 surveyed students, 327 were either seniors or commuters.
It's important to note that in this calculation, we accounted for the overlap between seniors and commuters (150 students who were both seniors and commuters) to avoid counting them twice.
This ensures an accurate count of the students who fall into either category.
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The data set below represents the number of books checked out at the library each day. 21, 12, 15, 17, 6, 3, 19 Choose the correct answer from each drop-down menu to complete the statements. The range is books checked out. The median is books checked out.
The median and the range for the data-set are given as follows:
Median of 15 books checked out.Range of 18 books checked out.How to obtain the median and the range of a data-set?The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than. Hence, the median also represents the 50th percentile of a data-set.
The ordered data-set is given as follows:
3, 6, 12, 15, 17, 19, 21.
The middle value is of 15, hence it represents the median of the data-set.
The range of a data-set is defined as the difference between the largest and the smallest value in the data-set, hence:
21 - 3 = 18.
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I NEED HELP ASAP plsssssss
Answer:
#1=24 #2=36 #3=77 #4=21
Step-by-step explanation:
Hope this helps
Answer:
1-8×3=24
2-9×4=36
3-11×7=77
4-7×3=21
but don't forget to put units and put square