Answer:
1/2
Step-by-step explanation:
Divide both the numerator and denominator
27/54 ÷ 27/27
Reduced fraction:
1/2
Therefore, 27/54 simplified to lowest terms is 1/2.
Answer:
27/54 =1/2
Step-by-step explanation:
27 and 54 are both multiples of 9, so 9 is a common divisordivisor.
Divide numerator and denominator by 91:
(27/9) / (54/9) = 3/6
Now 3 and 6 are both multiples of 3, so 3 is a common divisor
Divide numerator and denominator by 3:
(3/3) / (6/3) = 1/2
1 and 2 has no common divisors so 1/2 is the final answer
A square prism has a height of 12 inches and a base with an area of 30 square inches. A cylinder is inscribed inside the prism. Which statement about the volume of the cylinder, V, is true?
The volume of the cylinder (282.74 in.³) is less than the volume of the square prism (360 in.³). Then the correct option is C.
What is a rectangular prism?A rectangular prism is a closed solid that has two parallel rectangular bases connected by a rectangle surface.
What is a cylinder?A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.
A square prism has a height of 12 inches and a base with an area of 30 square inches.
A cylinder is inscribed inside the prism.
The volume of the square prism will be
[tex]V_{square} =Base[/tex] [tex]area*Height[/tex]
[tex]V_{square}=30*12[/tex]
[tex]V_{square} =360[/tex] [tex]in^3[/tex]
The volume of the cylinder will be
[tex]V_{cylinder}=\pi r^2h[/tex]
The radius of the base circle of the cylinder will be
[tex]r=\frac{\sqrt[]{30}}{2}[/tex]
[tex]r=2.7386[/tex]
Then volume will be
[tex]V_{cylinder}=\pi *(2.7368)^2*12[/tex]
[tex]V_{cylinder}=282.74[/tex] [tex]in^3[/tex]
The volume of the cylinder (282.74 in.³) is less than the volume of the square prism (360 in.³). Then the correct option is C.
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Gavin has 300 pencils
15% of the pencils need to be sharpened
Work out how many pencils need to be sharpened
Answer:
45 pencils
Step-by-step explanation:
15%/100% ×300
15% ×3
=45 pencils that needed to be sharpened and it is at easy as that
15% of 300 =
10%= 30
5%= 15
30+15 = 45
45 pencils need to be sharpened
Twice during the assembly, a student is chosen at random to assist with the presentation. after the first student has finished assisting, the student returns to the group and can be chosen a second time. what is the probability that the first student chosen is a senior and the second student chosen is a sophomore? startfraction 11 over 320 endfraction startfraction 3 over 80 endfraction startfraction 11 over 40 endfraction two-fifths
The probability that the first student chosen is a senior and the second student chosen is a sophomore is 11/320.
What is probability?Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.
Twice during the assembly, a student is chosen at random to assist with the presentation.
After the first student has finished assisting, the student returns to the group and can be chosen a second time.
There are total 80 number of students in which 22 are senior students. Thus, probability of choosing first student a senior
[tex]P(A)=\dfrac{22}{80}\\P(A)=\dfrac{11}{40}[/tex]
There are total 22 sophomores. Thus, probability of choosing second student a sophomore is,
[tex]P(B)=\dfrac{10}{80}\\P(B)=\dfrac{1}{8}[/tex]
By the chain rule, the probability that the first student chosen is a senior and the second student chosen is a sophomore is
[tex]\dfrac{11}{8}\times \dfrac{1}{8}=\dfrac{11}{320}[/tex]
Thus, the probability that the first student chosen is a senior and the second student chosen is a sophomore is 11/320.
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Answer:
A
Step-by-step explanation:
Consider the following 8 numbers, where one labelled
x
is unknown.
48
,
9
,
29
,
x
,
5
,
32
,
22
,
5
Given that the range of the numbers is 63, work out 2 values of
x
Answer:
Step-by-step explanation:
48 + 9 + 29 + x + 5 + 32 + 22 + 5 = 63
by adding all numbers except x, we get
150 + x = 63
x = 63 - 150
x = - 87
30. Tina went to batting cages with $20. She rented a bat for $3. 25 and
paid $3 for each round. What was the greatest number of rounds Tina
could have played?
Answer:
5
Step-by-step explanation:
Tina started with $20, but had to spend $3.25 on the bat.
$20-$3.25 = $16.75, which is all she has left for rounds.
Each round costs $3.00
$16.75 divided by $3.00 comes out to 5.58 rounds, but since she can't play 1/2 a round, that means she could only play 5 rounds
5 rounds X $3.00 per round comes to $15.00
5. The equation y=3/2 is rotated 180° around the origin. What is the equation of the image line?
Answer:
(d) y' = 3/2x
Step-by-step explanation:
The transformation for rotating a figure 180° about the origin is ...
(x, y) ⇒ (-x, -y)
__
Given the line ...
y = 3/2x
The translation of it is ...
-y' = 3/2(-x)
Simplifying gives ...
y' = 3/2x
_____
Additional comment
Rotation 180° about the origin is equivalent to reflection across the origin. For a line that passes through the origin, that reflection is simply the original line, as we can see in the equations above.
Which rational number is equivalent to 0.86?
[tex]0.86\\\\=\dfrac{86}{100}\\\\=\dfrac{43}{50}[/tex]
Transversal Problems with Equations (Level 1)
Delta Math
Answer:
x = 15
Step-by-step explanation:
Where a transversal crosses parallel lines, alternate exterior angles are congruent. This lets you write an equation relating the measures of the marked angles.
__
(6x +8)° = (7x -7)° . . . . the angles have the same measure
15 = x . . . . . . . . . . . . divide by °, add 7-6x
The line segment reflects across the x-axis. What are the new coordinates for the endpoints? How does the transformation affect the length of the line segment?A) (−4, −8) and (4, 1); The length of the segment does not change.B) (−4, −8) and (−4, −1); The length of the segment does not change.EliminateC) (4, −8) and (−4, 1); The transformed segment is longer.D) (4, 8) and (4, 1); The transformed segment is shorter.
Answer:
The length does not change
Step-by-step explanation:
Only dilations will change the size of something, the line is just changing locations. because it is across the x axis, apply the rule
x,-y
-4, -8
4, 1
Below is a scale drawing of a ballroom that mika is designing. a rectangle with length 11 inches and width 4 inches. using the scale 1 in. : 4 m, mika calculated the length, or the longer side of the ballroom, to be 44 m. she decides to change the scale to 1 in. : 7 m. what is the length of the new ballroom? 16 m 28 m 44 m 77 m
The length of the new ballroom (in reality, the ballroom is designed according to scale drawing) is given by: Option D: 77 m
How are scale drawings formed?For a particular scale drawing, it is already specified that all the measurements' some constant scaled version will be taken. For example, let the scale be K feet to s inches.
Then it means
[tex]\rm 1\: ft : \dfrac{s}{k}\: in.[/tex]
All feet measurements will then be multiplied by s/k to get the drawing's corresponding lengths.
We're given that:
The scale that Mika uses: 1 in: 4m (1 inch in drawing is 4 metre in real world).The scale drawing has a rectangle of 11 in to 4 inchThe longer side of the ballroom is 44 mShe changes the scale to: 1 in: 7mLength of new ballroom (the longer length) is to be found.Since in the drawing, 11 inches was representing 44 m length of the ballroom when 1 inch: 4 metre scale was being used (as 11×4=44), so when the scale is 1 inch: 7 meters, then the new length of the ballroom in reality would be: 7 metre 11 times (since there is 11 inches as length of ballroom in the scale drawing)
This evaluates to [tex]7 \times 11 = 77 \: \rm metre[/tex]
Thus, the length of the new ballroom (in reality, the ballroom is designed according to scale drawing) is given by: Option D: 77 m
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The length or the longer side of the new ballroom is 77m.
Dimensions of the model = 11 inches*4 inches
1 inch = 4m
What is a scale factor?A scale factor is a factor by which the dimension of an object is enlarged.
So, the dimensions of the ballroom will be:
Length = 11*4 = 44m
Width = 4*4 =16m
But, Mika decides to change the scale to 1 inch: 7metres
So, the length of the new ballroom = 11*7 =77m
So, the length of the new ballroom =77m
Hence, the length of the new ballroom is 77m.
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3k^2+12k-7kn-28n square meters and a length of 3k-7n meters.
What expression represents the width of the rectangle?
Step-by-step explanation:
here ! I used the formula area = length × width
and just some algrbric expressions solving
Written as a rate, 162 miles in 3 hours would be ____ miles per hour.
Answer:
54:1
Step-by-step explanation:
That is the right answer and is actually the only one written as a unit rate. All the other are not even written correctly.
Answer:
54:1
Step-by-step explanation:
Because the rate would be 162:3 but simplified, you would divide by 3 and get 54:1.
Find The Mode Of The Data 2, 4, 5, 6, 7, 2, 3, 4.
Answer:
2 and 4 is repeated mode of the data
Answer:
2 and 4
Step-by-step explanation:
The mode is the value of highest frequency in the data set2 and 4 each repeat twice whereas all other numbers only appear once2 and 4 are the mode
WILL GIVE BRAINLIEST PLS HELP
Table 101 х 30 5080 y 10 18 25 9 from "Table 101" To evaluate the fit of a model, the absolute values of the deviations (differences between the actual data values and values predicted by the model) are added together. Order the models based on the these total deviations. Place the model with the smallest total absolute deviation on top. y = 0.4x - 2 = - y = 0.3x + 2 y = 0.3x + 1
Answer:
We can determine that Option A, y = 0.4x - 2 is the correct answer
Step-by-step explanation:
Step 1: Plug in 30 into the x-value to see if the y-value matches
Equation 1 --> y = 0.4(30) - 2 = 10
Equation 2 --> y = 0.3(30) + 2 = 11 <-- WRONG Y-VALUE
Equation 3 --> y = 0.3(30) + 1 = 10
Step 2: Plug in 50 into the x-value to see if the y-value matches
Equation 1 --> y = 0.4(50) - 2 = 18
Equation 3 --> y = 0.3(50) - 2 = 13 <-- WRONG Y-VALUE
Answer: We can determine that Option A, y = 0.4x - 2 is the correct answer
what is the rate of change and y intercept please help Ill give u crown
25(q-954)=775 what is q
Answer:
q = 204
Step-by-step explanation:
25 + 954 = 979
979 - 775 = 154
Answer:
[tex]\boxed{\tt q=985}[/tex]
Step-by-step explanation:
[tex]\tt 25(q-954)=775[/tex]
Let's apply the Distributive property:-
[tex]\tt 25q-23850=775[/tex]
Add 23850 to both sides:-
[tex]\tt 25q-23850+23850=775+23850[/tex]
[tex]\tt 25q=24625[/tex]
Divide both sides by 25:-
[tex]\tt \cfrac{25q}{25}=\cfrac{24625}{25}[/tex]
[tex]\boxed{\tt q=985}[/tex]
Or we can solve it by .....
Dividing both sides by 25
[tex]\tt q-950=\cfrac{775}{25}[/tex]
[tex]\tt q-954=31[/tex]
Add 954 to both sides:-
[tex]\tt q=31+954[/tex]
[tex]\boxed{\tt q=985}[/tex]
__
What’s the answer????
Answer:
5
Step-by-step explanation:
Which is more, 6 quarts or 26 cups?
Answer:
26 cups
Step-by-step explanation:
24 cups is 6 quarts, 25 cups is 6.25 quarts, and 26 cups is 6.5 quarts.
Therefore, 26 cups = 6.5
6.5>6
26 cups is larger than 6 quarts.
Which will result in a difference of squares? (negative 7 x 4)(negative 7 x 4) (negative 7 x 4)(4 minus 7 x) (negative 7 x 4)(negative 7 x minus 4) (negative 7 x 4)(7 x minus 4)
An expression is defined as a set of numbers, variables, and mathematical operations. The expression that will result in the difference in the squares is (7x+4)(7x-4).
What is an Expression?
In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The difference between the squares can be written as,
[tex]a^2-b^2=(a+b)(a-b)[/tex]
The expression that will result in the difference in the squares will be
[tex](7x+4)(7x-4)=(7x)^2-(4)^2[/tex]
Thus, the expression that will result in the difference in the squares is (7x+4)(7x-4).
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Find the value of z.
Answer:
6√2=z
Step-by-step explanation:
As we are given a right angle we simply can apply the formula a²+b²=c².
A = 3
B = z
C = 8+1 which we add to get 9
Now, we plug this into the equation
9²=z²+3²
81=z²+9
72=z²
√72=z
√2x2x2x3x3 (expanding 72)
6√2=z
Which table contains input-output values of the function y = 2x - 7?
Answer:
The input-ouput is B.
Step-by-step explanation:
By plugging in 3, -4, and 5 into the x-values of the equation [tex]f(x)=2x-7[/tex] you provided you get
[tex]f(3) = 1 , f(-4) = -15 , f(5) = 3[/tex]
In ms Perron's class,75% of the students are boys.There are 18 boys in the class.What us the total number of students in ms. Perrons class
To solve this you first have to find your missing percentage 25%
something you can do is find the pattern that there is 75% is 3/4 of 100 so you could find what 25 %is worth out of 18 so 18/3=6.Now that you have found your 25% all you have to do is add the amount of boys to girls so 18+6=24 and you have your answer.
There are 24 students in the class in which 75% of the students are boys (18 boys)
What is an equation?An equation is an expression used to show the relationship between two or more numbers and variables.
Let x represent the total amount of students in the class.
75% of the students are boys.There are 18 boys in the class, hence:
0.75x = 18
x = 24
There are 24 students in the class in which 75% of the students are boys (18 boys)
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Answer the questions below based on the two quadratic functions.
Answer:
The vertex of Function 2 is at (2,7)
The function that has the smaller minimum value is Function 1
The smaller minimum value is 3
Step-by-step explanation:
hope this helps :)
Which difference will be positive?
O -6 - (-4)
O -4 - (-5)
0 8-9
O-4-3
What is 1/3 of $ 33,859.00 please
Answer:
11286.33333
Step-by-step explanation:
1) The numerator (1) always multiplies the number (33,859.00). "Of" implies multiplication and division.
= [tex]1 * 33,859.00[/tex]
= [tex]33,859.00[/tex]
2) The denominator (3) always divides the number (33,859.00)
= 33,859.00 ÷ 3
= 11286.33333
If you borrow $100 for 3 years at an
annual interest rate of 9%, how
much will you pay altogether?
Answer:
$127
Step-by-step explanation:
[tex]i = \sf \frac{prt}{100} [/tex]
=> 100 × 3 × 9/100
=> 3×9 = 27
Total amount= 27 + 100
=> 127
Answer :-- $127
x^2-y^2=16
y^2=-x+4
I need help to solve the system of equations
A 17-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 10 feet from the base of the building. How high up the wall does the ladder reach?
Answer:
13.747... meters
Step-by-step explanation:
Refer to image attached~
Let AC represent the length of the ladder.Let BC represent the distance from the base of the ladder from the base of the building.Let AB (x) represent the height of the building.In this case, the longest side of the triangle formed is AC. Thus, our hypotenuse is AC (17 m).
To determine the height of the building, we need to use pythogoras theorem.
Pythogoras theorem: (Hypotenuse)² = (Side)² + (Side)²
⇒ (17)² = (10)² + (x)²⇒ 289 = 100 + (x)²⇒ 289 - 100 = (x)²⇒ 189 = (x)²Take square root both sides:
⇒ √189 = √(x)²⇒ x = √189 ≈ 13.747... metersAnswer:
13.75 ft (nearest hundredth)
Step-by-step explanation:
The ladder creates a right triangle with the wall and ground, where:
leg (base) = groundleg (height) = wallhypotenuse = ladderPythagoras' Theorem: a² + b² = c²
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
Given:
a = 10 ftc = 17 ftSubstitute the given values into the formula and solve for b:
⇒ 10² + b² = 17²
⇒ b² = 17² - 10²
⇒ b² = 289 - 100
⇒ b² = 189
⇒ b = ±√(189)
As distance is positive, b = √(189) ft only
Therefore, the ladder reaches 13.75 ft (nearest hundredth) up the wall.
2 1/2 * 7 7/3 *- 5 3/7
Answer:
-126.66
Step-by-step explanation:
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The double dot plot shows the numbers of junk emails that were received by marcus and anders for the past twenty days. Which inference about the two populations is true?
A) Both sets of data have the same interquartile range.
B) Both sets of data have the same median
C) Ander’s data centers around 6 and Marcus’s data centers around 7
D) The Interquartile range for Ander’s data is 0. 5 greater than the interquartile range for Marcus’s data
The true inferences from the double dot plot for this case from the available options is given by: Option D) The Interquartile range for Ander’s data is 0. 5 greater than the interquartile range for Marcus’s data
What are quartiles?When we get data which can be compared relatively with each other, for finding quartiles, we arrange them in ascending or descending order.
Quartiles are then selected as 3 points such that they create four groups in the data, each groups approximately possessing 25% of the data.
Lower quartile, also called first quartile has approx 25% in its left partition, and on its right lies approx 75% of the data.
Similarly, second quartile (also called median) is approximately in mid of the data.
Third quartile (also called upper quartile) has approx 75% in its left partition, and on its right lies approx 25% of the data.
Left to right is said in assumption that data was arranged increasingly from left to right
How to find the interquartile range?IQR(inter quartile range) is the difference between third and first quartile.
How does the dot plot work?Suppose we're measuring something whose values are numeric. For each value of that thing we observe, we plot a dot above that value in the number line. Thus, the total number of dots in the dot plot tells us the total number of observations of the values of that thing we did.
Thus, suppose if we observed the value 'x', then we will make a dot above 'x'. If there is already a dot over 'x', then we will make a new dot over that dot.
If instead of only observations, the table of unique observation and frequency is given, then we plot dots that many times as the count written in the frequency table. Thus, if its written that the value 2 has 3 has its frequency, then we plot 3 dots one over the other above the value 2 in the horizontal axis.
For this case, getting the quartiles of each dataset one by one.
For the data for Anders:The number of dots show frequencies, therefore, from the image attached below, the data we get for Anders is:
1,2,2,3,3,5,5,5,5,5,5,6,6,6,6,7,7,7,7,7
These are total 20 observations.
Mean is the ratio of sum of all observations to the number of observations.
Sum of these values is 100, and therefore, we get:
Mean = 100/20 = 5
50% of 20 is 10 (its half). And 25% is 5, and 75% is 15.
Now, any number between the 10th and 11th value will be median because before and after that will lie ten-ten observations.
We usually take mean of these two values in such case.
The 10th value is 5, and so as the 11th value.
Thus, median of this data set is 5
Similarly, the first quartile can be taken as the average of 5th and 6th value as in mid of both lie values before which lies 25% of the data and after which lies 75% of the data.
The 5th and 6th values are 3 and 5. Their average is (3+5)/2=4
Thus, the first quartile of this data set is 4
Similarly, third quartile can be taken as average of 15th and 16th value = (6+7)/2 = 6.5
Now, the interquartile range of this dataset = third - first quartile = 6.5 - 4 = 2.5
Similarly, the data set for Marcus is:2,3,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,9,10,10
These are total 20 observations.
Mean is the ratio of sum of all observations to the number of observations.
Sum of these values is 139, and therefore, we get:
Mean = 139/20 = 6.95 (approx 7)
Also, we get:
Median can be average of 10th and 11th value = (7+7)/2 = 7
First quartile can be average of 5th and 6th value = (6+6)/2 = 6
Third quartile can be average of 15th and 16th value = (8+8)/2 = 8
Thus, IQR = third - first quartile = 8-6 = 2
So we see that option A and B are wrong as IQR and median both are different for both the datasets.
Option C is wrong since for Ander's data, we see that both mean and median (which are central measures) evaluates to 5, so Ander's data centers around 5 instead of 6.
Option D is correct as IQR for Ander's data = 2.5 is 0.5 greater than 2 which is IQR for Marcus' data.
Thus, the true inferences from the double dot plot for this case from the available options is given by: Option D) The Interquartile range for Ander’s data is 0. 5 greater than the interquartile range for Marcus’s data.
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