Answer:
C 12/48
Step-by-step explanation:
Original fraction:
x/y
The ratio of the numerator to the denominator is 1:4, so
x/y = 1/4
Cross multiply:
y = 4x
If three is added to the numerator and subtracted from the denominator, the new fraction reduces to one-third.
(x + 3)/(y - 3) = 1/3
Cross multiply:
3(x + 3) = 1(y - 3)
3x + 9 = y - 3
Above, we have y = 4x, so substitute 4x for y in the equation just above and solve for x.
3x + 9 = 4x - 3
12 = x
x = 12
y = 4(12) = 48
The original fraction is x/y = 12/48
Question 5 3 pts A corral for cattle is in the shape of a circle with a radius of 17.8 m; find the total area of the corral. Round your answer to the nearest whole number. Do not type the units in the space below.
Step-by-step explanation:
the area of s circle is
pi×r²
r being the radius.
so, in our case
pi×17.8² = pi×316.84 = 995.3822164... ≈ 995 m²
Peter analyzed a set of data with explanatory and response variables x and y. He concluded the mean and standard deviation for x as 7.8 and 3.70, respectively. He also concluded the mean and standard deviation for y as 12.2 and 4.15, respectively. The correlation was found to be 0.964. Select the correct slope and y-intercept for the least-squares line. Answer choices are rounded to the hundredths place.
The y-intercept is 3.78.
We have given that,
[tex]\overline{x}=7.8 ,S_x=3.70,\\\overline{y}= 12.2,S_y=4.15\\r=0.964[/tex]
What is the formula of the slope?[tex]Slope=r \times\frac{S_y}{S_x} \\\\Slope=0.964\times \frac{4.15}{3.70}\\ Slope=1.08=\overline{y}-slope\:\times \overline{x}\ intercept\\=\overline{y}-slope\:\times \overline{x}\\=12.2-1.08(7.8)\\=3.78[/tex]
Therefore the y-intercept is 3.78.
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A student's grade on the Fundamentals of Engineering exam has a z-score of 0.5. Make an observation about the student's grade.
The observation about the student's grade with the z score illustrated is that it's a half standard deviation above the mean of the total test score.
What is z score?It should be noted that the z score is a numerical measurement which describes the relationship of a value to the mean value of the group.
In this case, the observation about the student's grade with the z score illustrated is that it's a half standard deviation above the mean of the total test score.
This is illustrated as the z score is 0.5.
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Please help me with this on the picture.
Answer:
year 7 mean: ≈7.714
year 8 mean: 14
Step-by-step explanation:
mean = sum / number of observations
number of observations = 5, as there are 5 bars for each year
year 7 is the bar on the left for each day
observations for year 7:
5, 8, 9, 13, 19 (left to right)
sum = 5 + 8 + 9 + 13 + 19 = 54 for year 7
mean for year 7 = 54 / 7 ≈ 7.714
observations for year 8 (left to right):
10, 11, 18, 12, 19
sum = 10 + 11 + 18 + 12 + 19 = 70
mean = 70 / 5 = 14
From a group of 13 women and 12 men, a researcher wants to randomly select 8 women and 8 men for a study. In how many ways can the study group be selected?
The total number of ways the study can be selected is: 637065
Given,
Total number of women in a group= 13
Total number of men in a group = 12
Number of women chosen = 8
Number of men chosen = 8
∴ the total number of ways the study group can be selected = 13C₈ and 12C₈.
This in the form of combination factor = nCr
∴ nCr = n!/(n₋r)! r!
13C₈ = 13!/(13 ₋ 8)! 8!
= 13!/5!.8!
= 1287
12C₈ = 12!/(12₋8)! 8!
= 12!/5! 8!
= 495
Now multiply both the combinations of men and women
= 1287 × 495
= 637065
Hence the total number of ways the study group is selected is 637065
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The equation of the line of best fit of a scatter plot is y = 6x − 9. What is the slope of the equation?
Answer:
6
Step-by-step explanation:
The equation of the line is written in the slope-intercept form:
y = mx +b
where m is the slope and b is the y-intercept.
Matching patternsThe given equation is ...
y = 6x -9
Comparing this to the slope-intercept form, we see that ...
m = 6
b = -9
The slope of the line is m = 6.
Desperately need help. pls
By applying the concept of composition between two functions and utilizing the information given in the two tables, we find the following results: f ° g (0) = - 2, f ° g (x) = 1.
How to find the value of composition between two functions
Compositions are binary operators between two functions: f - Former function, g - Latter function.
f ° g (x)
Where the input of the former function is the output of the latter function. By a brief observation, we find the following relationships in accordance with the two tables:
Case I
f(x):
0 → 1
g(x):
1 → - 2
Case II
f(x):
1 → 0
g(x):
0 → 1
By applying the concept of composition between two functions and utilizing the information given in the two tables, we find the following results: f ° g (0) = - 2, f ° g (x) = 1.
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Which diagram represents rx ◦ RO,180°?
Answer:
if this is for edge unity the answer is B
2. For the following data, calculate the z-score. (5 points)
a. Sierra wishes to enroll her son in an exclusive academy. Her son must
score an 107 on their aptitude test in order to be accept. Calculate the z-
score for a score of 107 based on the data provided.
Score (Y) = 107
Mean = 95
Standard Deviation = 7.5
hint: Use the z-score formula to convert 107 into a z-score
The z-score for a score of 107 is 1.6
How to determine the z-score?The given parameters are:
Score (Y) = 107Mean = 95Standard Deviation = 7.5The z-score is calculated using:
[tex]z = \frac{x -\bar x}{\sigma}[/tex]
So, we have:
[tex]z = \frac{107 -95}{7.5}[/tex]
Evaluate the difference
[tex]z = \frac{12}{7.5}[/tex]
Divide
z = 1.6
Hence, the z-score is 1.6
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Linear function model
Answer:
f(x) = 800 - 75x
Step-by-step explanation:
Rachel took a loan of 800 dollars | Money Owed: f(x) = 800
She pays back 75 dollars a week <-> (x) | Money Owed: f(x) = 800 - 75x
While researching different companies, she discovers the following standard deviations of one year of daily stock closing prices.
Masterful Pocket Watches: Standard deviation of stock prices =$9.83
Eye Remember Enterprises: Standard deviation of stock prices =$1.15
Based on the data and assuming these trends continue, which company would give Donna a stable long-term investment?
a} eye remember enterprises; the smaller deviation indicates that eye enterprises have less variability in its closing prices than masterful pocket watches.
b}masterful pocket watches; the larger standard deviation indicates that masterful pocket watches have less variability in its closing prices than eye remember enterprises.
c} eye remember the enterprises; the smaller standard deviation indicates that eye remember enterprises has a greater mean closing price than masterful pocket watches.
d}masterful pocket watches; the larger standard deviation indicates that masterful pocket watches have a greater mean closing price than eye remember enterprises.
The data and assuming shows that the company that would give Donna a stable long-term investment is A. eye remember enterprises; the smaller deviation indicates that eye enterprises have less variability in its closing prices than masterful pocket watches.
How to illustrate the information?It should be noted that the information given implies that Donna needs a stable long term investment.
In this case, it's appropriate that the company that has the less standard deviation should be chosen.
This illustrates that Perfect Plungers has less variability.
In conclusion, the correct option is A.
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The cost of 25 apples is $18.50. What is the cost of one apple
Answer:
0. 74$Step-by-step explanation:
$18. 50÷25=0. 74$
Select the expression that is modeled on the number line. A number line from zero to one partitioned into sixths. There are four hops beginning at one sixth and ending at five sixths.
The answer to the question that is modeled here is one sixth plus four sixths.
How to solve for the expression
We have the following fractions
1/6 and 5/6
We are to find the fraction which when added to 1/6 would give us 5/6. Hence we have
1/6 + 4/6 = 5/6
Hence the correct answer to the question here is option a.
complete questionPLS HELP 1HOUR LEFT Select the expression that is modeled on the number line. A number line from zero to one partitioned into sixths. There are four hops beginning at one sixth and ending at five sixths one sixth plus five sixths
one sixth plus four sixths
five sixths minus one sixth
five sixths minus four sixths
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Solve the inequality and enter your solution as an inequality comparing the
variable to a number.
x+4>11
Answer:
⅝8⅝
Step-by-step explanation:
I made this with love and everything in the world of 9⁴⅝
If f(x) = 8- 10x and g(x) = 5x + 4, what is the value of (fg) (-2)?
O -196
O -168
O 22
O 78
how do i find x?? whats the answer?
Through proportionality theorem.
Therfore [tex] \frac{ 11}{121} = \frac{10}{5x + 10} \\ \\ 11(5x + 10) = 121(10) \\ (5x + 10) = \frac{121(10)}{11} \\ 5x + 10 = 110 \\ 5x = 110 - 10 \\ 5x = 100 \\ \frac{5x}{5} = \frac{100}{5 } \\ x = 20cm[/tex]HOPE THIS HELPS!find the quotient: -10/9 divided by -5/7
Answer:
70/45
Step-by-step explanation:
(-10/9) divided by (-5/7) = (-10/9) / (-5/7)
dividing two fractions is the same as multiplying the top fraction by the reciprocal of the bottom one
top fraction = -10/9
bottom fraction = -5/7
reciprocal just means switching the numerator and denominator
reciprocal of bottom fraction = 7 / -5 = -7/5
thus,
(-10/9) / (-5/7) = (-10/9) * reciprocal of (-5/7) = (-10/9) * (-7/5) = 70/45
note that to multiply two fractions, you just multiply the numerators to get your new numerator and do the same thing with the denominators
Find the value of x and y using the diagram below.
[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]
x = 2 , y = 3Step-by-step explanation:
As the given figure is a rectangle, therefore the opposite sides should be equal. So -
3x + y = 12 – y...(eqn (i) )
and
y – x = x – 1...(eqn (ii) )
Solving eqn (ii) we get -
→ y – x = x – 1
→ y = x + x – 1
→ y = 2x – 1...eqn(iii)
Solving eqn (i) we get -
→ 3x + y = 12 – y
→ 3x = 12 – y – y
→ 3x = 12 – 2y
Substituting the value of eqn (iii)
→ 3x = 12 – 2(2x– 1)
→ 3x = 12 – 4x + 2
→ 3x + 4x = 14
→ 7x = 14
→ x = 14/7
→ x = 2
Hope it helps you!!Answer:
x = 2; y = 3
Step-by-step explanation:
Since the quadrilateral has 4 right angles, it is a rectangle.
In a rectangle, opposite sides are congruent.
3x + y = 12 - y
x - 1 = y - x
We have a system of two equation is 2 variables.
Let's simplify both equations.
3x + 2y = 12
2x - y = 1
Rewrite the first equation. Multiply both sides of the second equation by 2. Add the equations.
3x + 2y = 12
(+) 4x - 2y = 2
-------------------------
7x = 14
Divide both sides by 2.
x = 2
Substitute 2 for x in the second original equation and solve for y.
x - 1 = y - x
2 - 1 = y - 2
1 = y - 2
y = 3
Answer: x = 2; y = 3
Will give brainliest
A radioactive element has a half-life of 55 days. what percentage of the original sample is left after 115 days? round to 4 decimals when necessary.
The percentage of the radioactive isotope left is 25.0000%.
What is the half life?The half life of a radioactive isotope is the time that will elapse before only half of the number of original isotopes will remain.
Now;
We are told that;
Half life (t1/2) = 55 days
Time taken (t) = 115 days
Ratio of isotope remaining = N/No
Thus;
N/No = (1/2)^t/t1/2
N/No = (1/2)^115/55
N/No = (1/2)^2
N/No =1/4
Hence, the percentage = 1/4 * 100/1 = 25.0000%
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Find the coefficient of determination, given that the value of the linear correlation coefficient, r, is –0.721.
The coefficient of determination is calculated as: 0.520.
How to Find the Coefficient of Determination?The coefficient of determination = the square of the correlation coefficient.
Given the following:
Value of the linear correlation coefficient (r) = -0.721
Therefore, we would have:
The coefficient of determination = (-0.721)²
The coefficient of determination = 0.520
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6) Simplify the following:
axaxbxb
The simplified expression of axaxbxb is a^2b^2
How to simplify the expression?The expression is given as;
axaxbxb
Rewrite properly as:
a * a * b * b
Evaluate the product
a^2b^2
Hence, the simplified expression of axaxbxb is a^2b^2
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Please solve this question
Answer:
a) 0.2098
b) 0.036
c) 0.1866
d) 0.9849
Step-by-step explanation:
Image is color coordinated for each part below,
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3. What is the measure of angle HEK in this figure?
95
55
85
150
Answer:
95 is the correct answer
Step-by-step explanation:
The initial or beginning side is H. Look on the protractor and you will see the top number is 55 degrees. That is where we start. Now, go to line E, that is where we end. The top number is 150. To find <HEK, we need to subtract 55 from 150 to get 95.
The surface area of an open-top box with length
L
, width
W
, and height
H
can be found using the formula:
A
=
2
L
H
+
2
W
H
+
L
W
Find the surface area of an open-top box with length 4 cm, width 8 cm, and height 5 cm.
Answer:
Surface Area is equal to 160 cm²
here is your answer
can someone please help with part III?? don’t use my work it’s prob wrong lol :)
Answer: formula
AB= (-1- -3)+((3-1)
(-1+3 )^2+(3-1)^2
2^2+2^2
Sq rt of 8 is 2.83
length of AB is 2
BC= (-3- -1)^2 + (5-3)^2
-3+1 =-2^2+2^2=4+4=8
Sq rt of 8 is 2.828= 2.83
Step-by-step explanation:
Ten copper pennies having a total mass of 25 grams warm up from 23oC to 38oC as you hold in your hand. If the specific heat capacity of copper is 0.39 J/(g *oC), how much energy is absorbed by the pennies?
The amount of energy absorbed by the pennies made up of copper is 146.25J
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Amount of energy absorbed = mass * temperature change * specific heat capacity
Amount of energy absorbed = 25 * (38 - 23) * 0.39 = 146.25J
The amount of energy absorbed by the pennies made up of copper is 146.25J
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Identify the segments that are parallel, if any angle ABC equals angle HCB
Answer: A. DC||AB
Step-by-step explanation:
Line DC is parallel to AB so the correct answer is option B.
What is the similarity?
If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.
In the given image we can see that the two angles ABC and HCB are congruent to each other. So the line DC is parallel to AB.
Therefore Line DC is parallel to AB so the correct answer is option B.
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Equation P: a + b = 6
Equation Q: 4a + 2b = 19
Which of the following steps can be used to eliminate the a term?
−1(4a + 2b = 19)
−4(4a + 2b = 19)
−4(a + b = 6)
4(a + b = 6)
Answer:
-4(a + b = 6)
Step-by-step explanation:
When you multiply equation P by -4, you obtain -4a - 4b = -24. You can then add this equation to equation Q to eliminate the a term.
Which of the following is correct based on this picture? A. none of these are correct B. sinZ=61/73 C. cosZ=61/73 D. tanZ=61/73
Answer:
C.) cosZ=61/73
Step-by-step explanation:
I hope you got the answer
Please help me with this on the picture
Answer:
5, 7
Step-by-step explanation:
The mode of the numbers is 5, which means that 5 should be the most common card (highest frequency). Therefore the cards should have at least one more 5 among them.
Considering that 5 is one of the hidden cards and x is the other,
• Using the equation for the mean:
[tex]mean = \frac{sum \space\ \space\ of \space\ \space\ numbers}{number \space\ \space\ of \space\ \space\ numbers}[/tex]
[tex]6 = \frac{4+5+ 9 + 5 + x}{5}[/tex]
⇒ [tex]30=23 + x[/tex]
⇒ [tex]x = 7[/tex]
This means 5 and 7 are the hidden cards.