The amount of slushy that was originally in the cup is 225 milliliters and the time it took Mariana to drink all the slushy is 50 seconds.
How to find the original quantity?Total quantity she took
Total quantity = 4.5 × 17
Total quantity = 76.5 milliliters
Original quantity = 148.5 + 76.5
Original quantity = 225 milliliters
b. Time taken to drink all
Time =225 milliliters /2.5
Time = 50 seconds
Therefore original quantity 225 milliliters and the time is 50 seconds.
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Which set of ordered pairs shows the result of a dilation by a factor of 2 around the origin?
The set of ordered pairs that represent dilation factor of 2 is
a. A' (2, 12) B' (12, 12) C' (2, 4)
How to find the coordinates of the imageDilation is a method of transformation which uses a scale factor. The scale factor determines if the dilation is magnification or shrinking
|0 < r < 1| is shrinking
|r > 1| is magnification
The transformation rule for dilation is as follows
(x, y) for a scale factor of r → (rx, ry)
From the graph the coordinates are read and following the given transformation rule we have
preimage image
A (1, 6) → (1 * 2, 6 * 2) → A' (2, 12)
B (6, 6) → (6 * 2, 6 * 2) → B' (12, 12)
C (1, 2) → (1 * 2, 2 * 2) → C' (2, 4)
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HELP WHATS 565 divid by 000000.666 x X -k
Answer:
565/0.666=848.348
Step-by-step explanation:
if you needed variables added to the equation then show a picture and I can answer it.
An x-ray machine for animal cot 125,000. If the loan i for 10 year, and the interet paid i $65,625, what i the interet rate on the loan?
The interest rate on loan is 5.25%.
What is principal amount?
The loan amount that the lender gives to the borrower is referred to as the primary amount. Additionally, it is the factor the lender uses to calculate interest.
What is simple interest?
Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time. The formula to calculate simple interest is I=P.r.t
Given, Principal amount=$125,000, time=10years, Interest=$65,625.
Let r be the rate of interest, on applying simplest interest formula
I=P.r.t
Where P=principal amount, r=rate, t=time.
I=125,000 x r x10
65,625=125,000 x r x10
r=[tex]\frac{65,625}{125,000(10)}[/tex]
r=0.0525
r=5.25%
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PLEASE HELP ME AND TELL ME HOW YOU DID IT AND THANKS 25 POINTS HELP
Match each number with its estimated power of 10
The matching numbers are:
1) 0.0000225 = 2 x 10⁻⁵
2) 219,000 = 2 x 10⁵
3) 3,40,000 = 3 x 10⁶
4) 297,000 = 3 x 10⁵
5) 0.0000034 = 3 x 10⁻⁶
What are Exponents?
The exponent of a number indicates how many times a number has been multiplied by itself. For instance, 34 indicates that we have multiplied 3 four times. Its full form is 3 3 3 3. Exponent is another name for a number's power. A whole number, fraction, negative number, or decimal are all acceptable.
We have to match the following terms :
1) 0.0000225 = 2 x 10⁻⁵
we can write 0.0000225 as
2.25 / 100000
or, 2.25 / 10⁵
then, 2.25 x 10⁻⁵
2) 219,000 = 2 x 10⁵
as the numbers after 2 are 5
therefore we write 10⁵
3) 3,40,000 = 3 x 10⁶
as the numbers after 3 are 6
therefore we write 10⁶
4) 297,000 = 3 x 10⁵
we round off 297 as 300
as the numbers after 3 are 5
therefore we write 10⁵
5) 0.0000034 = 3 x 10⁻⁶
we can write 0.0000034 as
3.4/ 1000000
or, 3.4 / 10⁶
then, 3.4x 10⁻⁶
Hence, the matching numbers are:
1) 0.0000225 = 2 x 10⁻⁵
2) 219,000 = 2 x 10⁵
3) 3,40,000 = 3 x 10⁶
4) 297,000 = 3 x 10⁵
5) 0.0000034 = 3 x 10⁻⁶
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For a certain population of penguins, the distribution of weight is approximately normal with mean 15. 1 kilograms (kg ) and standard deviation 2. 2 kg. Approximately what percent of the penguins from the population have a weight between 13. 0 kg and 16. 5 kg ?.
56.78% of the penguins in the population have a weight between 13.0 kg and 16.5 kg, according to the usual distribution.
Given,
The mean of the population, μ = 15.1 kg
Standard deviation, σ = 2.2 kg
We have to find the percent of the penguins from the population have a weight between 13. 0 kg and 16. 5 kg;
Here,
z score = x - μ / σ
The z-score calculates how far the measure deviates from the mean by standard deviation.The p-value for this z-score, which is the percentile of X, can be obtained by looking at the z-score table.The ratio of the p-value of Z when X = 16.5 minus the p-value of Z when X = 13 indicates the percentage of penguins in the population whose weight is between 13.0 kg and 16.5 kg.
x = 16.5
z score = x - μ / σ
z = (16.5 - 15.1) / 2.2 = 0.64
Z = 0.64 has a p-value of 0.7389.
x = 13
z score = x - μ / σ
z = (13 - 15.1) / 2.2 = -0.95
Z = -0.95 has a p-value of 0.1711.
0.7389 - 0.1711 = 0.5678.
0.5678 = 56.78% of the penguins from the population have a weight between 13.0 kg and 16.5 kg.
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The scatterplot shows the relationship between the length of a pendulum and the time it takes to complete one full swing.
Which transformations would linearize these data using a power model? Check all that apply.
ln(Length), ln(Time)
ln(Length), Time
log(Length), log(Time)
Length, log(Time)
Length, Time2
Answer:
a) ln(Length), ln(Time)
c)log(Length), log(Time)
e)Length, Time²
Step-by-step explanation:
Answer:
the person above me is correct!
Step-by-step explanation:
square root of 81 divided by 3
Answer: Yes
Step-by-step explanation: Can this help , 81 ÷ 3 is 27 which is one of the factors in the 3 multiplications
an individual was making blankets for a few friends. the individual used 6.3 feet of fabric for one blanket. if the individual makes 4 blankets, how many feet of fabric will the individual have used to make 4 blankets (round to the nearest whole number)?
Answer:
25
Step-by-step explanation:
6.3= 1 blanket
to find 4 blankets you multiply 6.3 by 4
6.3x4=25.2
to the nearest whole number
25
Complete the sentence…?
is 10 times as much as 0.11
Answer: 1.1
Step-by-step explanation:
10 * .11 is 1.1
When multiplying decimals by ten you move the decimal place once to the right.
Answer:
1.1
Step-by-step explanation:
0.11 x 10 = 1.1
You are moving the decimal point over once (x 10).
Each month, kaisorn deposits $50. 00 onto her public transportation card. It costs her $2. 50 per trip to ride the subway. Thom deposits $40. 00 on his public transportation card. It costs him $2. 00 per trip to ride the subway. If x represents the number of trips and y represents the amount remaining in each account, which system of equations represents their transportation costs? 50 − 2. 5x = y 40 − 2x = y 50 + 2. 5x = y 40 + 2x = y 50 − 2. 5y = x 40 − 2y = x 50 + 2. 5y = x 40 + 2y = x.
The system of equations represents their transportation costs is:
50 − 2. 5x = y
40 − 2x = y
The correct option is (A)
Given,
In the question:
Kaisorn deposits $50. 00 onto her public transportation card.
It costs her $2. 50 per trip to ride the subway.
Thom deposits $40. 00 on his public transportation card.
It costs him $2. 00 per trip to ride the subway.
Now, According to the question:
x → represents the number of trips
y → represents the amount remaining in each account
According to the given condition:
The system of equations represents their transportation costs is :
50 − 2. 5x = y
40 − 2x = y
Hence, The system of equations represents their transportation costs is:
50 − 2. 5x = y
40 − 2x = y
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In a game the average score was 40
Jim's score was 5/2 of the average.
What was Jim's score?
In the game where average score was 40 , then Jim's score was 100 .
In the question ,
it is given that ,
the average score in the game was 40 .
and also given that the Jim's score was 5/2 of the average .
So , the Jim's score can be calculated using the equation .
Jim's score = (5/2) × (Average score of the game)
Substituting the value of average in the equation ,
we get,
Jim's Score = (5/2) × 40
= 5 × 20
= 100
Jim's score is 100 .
Therefore , The Jim's score in the game where average score was 40 is 100 .
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f(x)= -x
r(x)= f(1/4x)
describe the transformation pls help!!
The sequence of transformations applied to function f(x) to produce function r(x) is a reflection across the y-axis and dilation by a scale factor of 1/4.
What is a reflection?A reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.
In Geometry, a reflection across the y-axis (y = x) of a graph is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, function f(x) = -x would be transformed to function r as follows:
f(x) = -(-x)
r(x) = x
By applying a dilation with a scale factor of 1/4 to function r, we have:
r(x) = (1/4 × x) → r(x) = f(1/4x)
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The bookstore sold 40 biographies and
100 mysteries. Find the ratio of biographies
to mysteries sold
Answer:
2 : 5 or 2/5
Step-by-step explanation:
The ratio is 40 : 100, which can simplify into 2 : 5.
State the coordinates of the point.
Answer:
Step-by-step explanation:
B
Answer 0,4
Answer:
(-5,-1)
Step-by-step explanation:
Start at the orginal. This is (0,0), the middle of the graph. From that point you move 5 spaces left. That is the -5 in the answer. Then from that point, you move one space down. That is the -1 in the answer.
Find the z value such that 97% of the standard normal curve lies between −z and z. (Round your answer to two decimal places.)
The positive value of Z is 2.17.
What do you mean by normal distribution?
A data collection with a normal distribution is put up so that the majority of the values cluster in the middle of the range and the remaining values taper off symmetrically in either direction. Because of its flared appearance, a normal distribution's graphic representation is occasionally referred to as a bell curve. The specific shape may change depending on how the population is distributed, but the peak and curve are always symmetrical and in the centre.
The information can be represented in the standard normal curve below:
It is given that 97% of the standard normal curve lies between −z and z.
The area in between is 0.97 meaning that one side is (0.97)/2 = 0.485
In addition, the region not shaded is the level of significance represented by (1-0.97)/2 = 0.03/2 = 0.015
From the Z-Score table (0 to Z table), this probability corresponds to the Z value of Z= 2.17 and -2.17
Thus the positive value of Z is 2.17.
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Ann and Ben tranlate document from German into Englih. A et of document that would take Ann 10 day would take Ben 12 day. Ann tart to tranlate the document. After 2 day Ann and Ben both work on tranlating the document. How many more day will it take to complete the work?
You mut how your working
After Ann start to translate the document in 2 days, they need more 4.4 days to complete the work.
A unit work would take Ann 10 days to complete, means each day Ann completes 1/10 work
She works for 2 days, hence the work done = 2 x 1/20 = 2/10
The remaining work = 1 - 2/10 = 8/10
Then Ben joins.
A unit work would take Ben 12 days to complete, means each day Ben completes 1/12 work.
Each day, both Ann and Ben will complete:
1/10 + 1/12 = 11/60 unit work
The remaining work = 8/10
Hence, if each day 11/60 work can be completed, to complete 8/10 work, they need:
8/10 : 11/60 = 48/11 = 4.4 days
Therefore we can conclude, after Ann works for 2 days, they need more 4.4 days to complete the work.
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16 = -7v - 8 + 3v Solve for v.
Simplify your answer as much as possible.
To solve for v, isolate the variable by dividing each side by factors that don't contain the variable.
Solve for v.
[tex]16=-7v-8+3v[/tex][tex]v = -6[/tex] ← Our SolutionHope this helps!
PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
7, 7/1
Step-by-step explanation:
The ratio 7:49 can be simplified to 1:7.
Which description matches the graph of the inequality y <|x-2| + 1
A shaded region above a solid boundary line matches the graph of the inequality y <|x-2| + 1.
What is inequality?
Inequality is a relationship between two expressions or values that is not equal to each other.
This inequality may be written in two ways:
(a) y < x - 2 + 1
or
y < x - 1
(b) y < -x +2 + 1
or
y < -x + 3
A graph of the inequality is shown below. The shaded region satisfies the inequality.
Hence, a shaded region above a solid boundary line matches the graph of the inequality y <|x-2| + 1.
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Consider the line y = 5/7x+1.
Find the equation of the line that is parallel to this line and passes through the point (-5, 6).
Find the equation of the line that is perpendicular to this line and passes through the point (-5, 6).
Note that the ALEKS graphing calculator may be helpful in checking your answer.
Equation of parallel line:
Equation of perpendicular line:
П
X√√
0=0
$
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]y = \stackrel{\stackrel{m}{\downarrow }}{\cfrac{5}{7}}x+1\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so for the parallel line we're really lookikng for the equation of aline whose slope is 5/7 and that it passes through (-5 , 6)
[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{5}{7} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ \cfrac{5}{7}}(x-\stackrel{x_1}{(-5)}) \implies y -6= \cfrac{5}{7} (x +5) \\\\\\ y-6=\cfrac{5}{7}x+\cfrac{25}{7}\implies y=\cfrac{5}{7}x+\cfrac{25}{7}+6\implies {\Large \begin{array}{llll} y=\cfrac{5}{7}x+\cfrac{67}{7} \end{array}}[/tex]
now, keeping in mind that perpendicular lines have negative reciprocal slopes
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{5}{7}} ~\hfill \stackrel{reciprocal}{\cfrac{7}{5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{7}{5}}}[/tex]
so for the perpendicular line we're really looking for the equation of a line whose slope is -7/5 and that it passes through (-5 , 6)
[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{7}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{- \cfrac{7}{5}}(x-\stackrel{x_1}{(-5)}) \implies y -6= -\cfrac{7}{5} (x +5) \\\\\\ y-6=-\cfrac{7}{5}x-7\implies {\Large \begin{array}{llll} y=-\cfrac{7}{5}x-1 \end{array}}[/tex]
A robot can complete 4 tasks in hour. Each task takes the same amount of time.
5/6
a. It takes the robot
(Simplify your answer.)
-
a. How long does it take the robot to complete one task?
b. How many tasks can the robot complete in one hour?
hour(s) to complete one task.
1 task will complete in 12.5 minutes
The robot can complete 9.6 task in 1 hour
Given,
Number of task a robot can complete = 4
Time taken by robot = 5/6 of 1 hour
5/6 of 1 hour = 5/6 × 60 minutes
= 300/6
= 50 minutes
Then,
4 task takes 50 minutes
1 task = 50 minutes / 4 task
= 12.5 minutes
So,
1 task = 12.5 minutes
x task = 60 minutes
1 : 12.5 = x : 60
1/12.5 = x / 60
1*60 = 12.5*x
60 = 12.5x
x = 60/12.5 = 4.8
x= 4.8
Therefore,
The robot can complete 4.8 task in 1 hour
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The sum of two numbers is 2. The difference between 8 and twice the smaller number is two less than four times the large number. Find the numbers.
Answer:
larger number = 3
smaller number = -1
Step-by-step explanation:
x = larger number
y = smaller number
x+y=2
8-2y=4x-2 ---> 10 = 4x+2y
10 = 4x+2y
5=2x+y
y = 5-2x
2x=5-y
x+5-2x = 2
-x+5=2
-x=-3
x=3
3+y=2
y=-1
1.7 × 4= with a rounded answer
P(AIB) can be read as "the probability that A occurs given that B has
occurred."
OA. True
OB. False
SUBMIT
P(AIB) can be read as "the probability that A occurs given that B has occured. This is true.
What is probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1. In this case, 0 denotes the impossibility of the event and 1 represents certainty.
Conditional probability is a measure of the likelihood of an event occurring given that another event has already occurred in probability theory.
Conditional probability: p(A|B) is the likelihood of event A occurring if event B occurs. For example, if you drew a red card, what is the likelihood that it is a four (p(four|red))=2/26=1/13? So there are two fours out of the 26 red cards (given a red card), so 2/26=1/13.
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Wich rule best represents the dilation applied to circle I to create circle II?
Answer:
Step-by-step explanation:
F 3/8x 3/8y
the power of a test is measured by its capability of a) rejecting a null hypothesis that is true. b) not rejecting a null hypothesis that is true. c) rejecting a null hypothesis that is false. d) not rejecting a null hypothesis that is false.
The power of a test is measured by its capability of rejecting a null hypothesis that is false, so option C is the correct answer
what is power with respect to probability?
Power is defined as the probability of correctly rejecting the false null hypothesis. It is the measure of the capability of rejecting a null hypothesis that is false.
Power = P[ rejecting a null hypothesis that is false.]
So, option C is correct, the power of a test is measured by its capability of rejecting a null hypothesis that is false
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11) -8x + 2x-16 <-5x+7x
solve the equation by elimination method 4x-2y=8,5x+3y=6
Answer:
Point form:
(18/11 , -8/11)
Equation form:
x=18/11 , y=-18/11
I need help with this
The value of the function (f + g)(x) = [tex]x^{2}[/tex] -5x + 9
What is a Function?function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
f(x) = - 2x + 4, g(x) = [tex]x^{2}[/tex] -3x + 5
(f+g)(x) = f(x) + g(x)
So by adding the two functions
(f + g)(x) = -2x + 4 + [tex]x^{2}[/tex] -3x + 5
(f + g)(x) = [tex]x^{2}[/tex] -5x + 9
In conclusion, the value of [tex]x^{2}[/tex] -5x + 9
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