The length of the second shelf is 114 centimetres.
Consider the four shelves as A, B, C and D. According to the question, the length of the four shelves is 2.5 cm.
A + B + C + D = 250 cm ( 1 m = 100 cm ⇒ 2.5 * 100 = 250 ) → 1
The length of the second shelf is 18 cm longer than twice the length of the first shelf.
B = 2A + 18 → i
The length of the third shelf is 12 cm shorter than the first shelf.
C = A - 12 → ii
The length of the fourth shelf is 4 cm longer than the first shelf.
D = A + 4 → iii
Substitute i,ii and iii in 1 ⇒ A + B + C + D = 250
A + 2A + 18 + A - 12 + A + 4 = 250
5A + 22 - 12 = 250
5A + 10 = 250
5A = 250 - 10
5A = 240
A = 240/5
A = 48
Substitute A = 48 in i, ii, iii and then we get,
B = 11, C = 36 and D = 52
Therefore, the length of the second shelf B is 114 cm.
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The complete question is
Robert needs to cut four shelves from a board that is 2.5 meters long. The second shelf is 18 centimetres longer than twice the length of the first shelf. The third shelf is 12 centimetres shorter than the first shelf. The remaining shelf is 4 centimetres longer than the first shelf. If Robert must use the entire 2.5 meter board for the shelves, what is the length of the second shelf, in centimetres?
Which istogram corect shows the one Number of people Number of books
Number of people in the range 0-2 books: 3
Number of people in the range 3-5 books: 6
Number of people in the range 6-8 books: 4
Number of people in the range 9-11 books: 2
Therefore, the correct histogram is option C
Which fraction is equivalent to 80%? (in simplest fraction form)
Answer:
4/5 or four fifths
Step-by-step explanation:
First you make 80% the fraction 80/100
Next you find the greatest common factor (GCF) which in each of them is 20
Finally you divide 80 and 100 by 20 and you get 4 and five now make them a fraction and you get 4/5
Which statements correctly compare two numbers? Select all that apply.
A. 0.1 < 0.125
B. 0.2 < 0.125
C. 0.125 > 0.13
D. 0.125 > 0.12
E. 0.126 < 0.125
A statement like that. An assertion is a single statement or comment. b: an information or idea report, 1 < 0.125= True, 125 > 0.12=True, and 126 < 0.125=True
What is meant by assertion?An assertion is a precise, unequivocal mathematical statement stating that something is true (e.g., that some relation between mathematical objects holds; that some object has some property; etc.). To qualify an assertion, it is not necessary for the statement to be true. An assertion is an emphatic declaration made as part of an argument or as if it is to be understood as a statement of fact. To assert is to make a strong statement. So when someone makes an assertion, they aren't just experimenting with a new idea; they truly believe it. A fundamental assertion is a simple statement that expresses a belief, feeling, opinion, or preference.To learn more about assertion, refer to
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A lawnmower designer wants to build a lawnmower that measures
8 feet in height, 3 feet width, and 7 feet in length. She needs to construct a three dimensional model of the lawnmower. First, determine
the width for the scale model given a height of 10 inches?
The width of the scale model given a height of 10 inches as in the task content is; 3.75 inches.
What is width of the scale model given a height of 10 inches?It follows from the task content that the width of the scale model is to be determined given a height of 10 inches.
According to the design, the lawnmower measures; 8 feet in height, 3 feet width, and 7 feet in length.
Hence, since 8 feet in height corresponds to 10 inches on the scale, the width on the scale can be determined by proportion as;
8/10 = 3/x
x = ( 10 × 3 ) / 8
x = 30/8
x = 3.75 inches.
Therefore, the width on the scale as required is; 3.75 inches.
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Write 2^40 as a power with the following base: 2^10
The equivalent expression as a base of 2¹⁰ is (2¹⁰)⁴
How to rewrite the expression?The mathematical statement in the question implies that
We rewrite 2^40 as a power in the base 2^10
Start by expressing the given number properly
So, we have
2⁴⁰
Express 40 as the product of 10 and 4
So, we have
2⁴⁰ = 2¹⁰ ˣ ⁴
Express as exponents
So, we have the following representation
2⁴⁰ = (2¹⁰)⁴
Hence, the new expression is (2¹⁰)⁴
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Convert the following fraction to a decimal 3/10
Answer:
Step-by-step explanation: 0.3
Answer:
Step-by-step explanation:
1. The answer is 0.3.
help meeeeeeeeee pleasee
Answer: 2.5, 5.3
Step-by-step explanation:
[tex]-16t^2 +126t=217\\ \\ 16t^2 -126t+217=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(217)}}{2(16)}\\\\t \approx 2.5, 5.3[/tex]
HELO EMEMENEJEJJEJEH
Answer:
E
Step-by-step explanation:
[tex]3 \leq x-2 \\ \\ x-2 \geq 3 \\ \\ x \geq 5[/tex]
Answer:
E
Step-by-step explanation:
if it is supposed to be more or equal to then it has to add 5 or more. It has to add 5 or more because the 2 is negative and 5-2 is 3 so it has to be at least 5
Simplify the expression ✔️72What is the coefficient aWhat is the radicand b
we have the expression
[tex]\sqrt[]{72}[/tex]Remember that
[tex]72=2^3\cdot3^2[/tex]substitute
[tex]\sqrt[]{2^3\cdot3^2}=2\cdot3\sqrt[]{2}=6\sqrt[]{2}[/tex]therefore
a=6
b=2
1 2 What is the probability of an event that is certain?
The probability of an event is a number describing the chance that the event will happen. An event that is certain to happen has a probability of 1. An event that cannot possibly happen has a probability of zero. If there is a chance that an event will happen, then its probability is between zero and 1.
An event that is certain to happen has a probability of 1.
There is a line whose y-intercept is -5 and whose slope is 10 What is its equation in
slope-intercept form?
y=10x-5 is the slope-intercept form
y-intercept= -5,
slope m= 10,
The slope-intercept formula y = mx + b, where m is the slope and b is the intercept.
y = y coordinate
m = slope
x = x coordinate
b = y intercept
The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line.
the slope of the line to be examined and the point given is also the y-intercept (0, b)
by putting the given information in the question we get,
y=10x+(-5),
therefore,y=10x-5 is the slope-intercept form
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Simplify the equation 10x - 8x +2 + 10
need helpp pls i don't know how to do it.
Answer:
The value of angle QXS is;
[tex]m\measuredangle QXS=40^0[/tex]Explanation:
From the given diagram in question 1:
We can see that angle QXT equals the sum of angle SXT and angle QXS;
[tex]m\measuredangle QXT=m\measuredangle SXT+m\measuredangle QXS[/tex]Given in the question is the value of angle SXT and angle QXS;
[tex]\begin{gathered} m\measuredangle SXT=4x+1 \\ m\measuredangle QXS=2x-2 \end{gathered}[/tex]Substituting the values into the equation above;
[tex]\begin{gathered} m\measuredangle QXT=m\measuredangle SXT+m\measuredangle QXS \\ m\measuredangle QXT=4x+1+2x-2 \\ m\measuredangle QXT=4x+2x+1-2 \\ m\measuredangle QXT=6x-1 \end{gathered}[/tex]Since angle QXT is equal to 125 degree, then;
[tex]\begin{gathered} m\measuredangle QXT=6x-1=125 \\ 6x-1=125 \\ 6x=125+1 \\ 6x=126 \\ \frac{6x}{6}=\frac{126}{6} \\ x=21 \end{gathered}[/tex]We can now substitute the value of x to get the value of angle QXS;
[tex]\begin{gathered} m\measuredangle QXS=2x-2 \\ m\measuredangle QXS=2(21)-2 \\ m\measuredangle QXS=42-2 \\ m\measuredangle QXS=40^0 \end{gathered}[/tex]Therefore, the value of angle QXS is;
[tex]m\measuredangle QXS=40^0[/tex]jaylens snow cone stand went thourgh 10 bags of ice in the first hour it was open and 8 1/6 simplify your answer and write it as a fraction or as a whole or mixed number
The fraction form of 8 1/6 is 49/8 as the definition of fraction says, "An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are divided".
What is fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator. A fraction merely informs us of the number of parts that make up the whole. The slash that is written between the two numbers identifies a fraction. The numerator is the highest number, and the denominator is the lowest number. 1/2, for instance, is a fraction.
Here,
8 1/6=(6*8+1)/8
=49/8
According to the definition of a fraction, which states that it is "a number represented mathematically as a quotient, where the numerator and denominator are divided," the fraction form of 8 1/6 is 49/8.
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One third times the difference of thirty and a variable is three fourths. one third times the quantity 30 minus y equals three fourths one third times the quantity y minus 30 equals three fourths one third times 30 minus y equals three fourths one third times y minus 30 equals three fourths
The original statement is same as third statment and value of y is 27.
Writing the equation form for each statement -
Let the variable be represented as y.
One third times the difference of thirty and a variable is three fourths1/3(30 - y) = 3/4
one third times the quantity 30 minus y equals three fourths1/3×30 - y = 3/4
one third times the quantity y minus 30 equals three fourths1/3×y - 30 = 3/4
one third times 30 minus y equals three fourths1/3(30 - y) = 3/4
one third times y minus 30 equals three fourths1/3(y - 30) = 3/4
Based on the interpretation of all the sentences in equation form, we find the statement 3 to be same as original statement. Solving the equation to get the value of y.
1/3(30 - y) = 3/4
10 - y/3 = 3/4
10 = 3/4 + y/3
10 = (3×4 + y×4)/12
10×12 = 12 + 4y
4y + 12 = 120
4y = 120 - 12
4y = 108
y = 27
Hence, the value of y is 27.
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Answer:
the answer is A.
1 over 3 (30 - y) = 3 over 4
Can anyone help me find the scale factor?
Answer:
scal factor = 1.5
Step-by-step explanation:
the scale factor is the ratio of corresponding sides, image to original, that is
scale factor = [tex]\frac{C'D'}{CD}[/tex] = [tex]\frac{6}{4}[/tex] = [tex]\frac{3}{2}[/tex] = 1.5
Which lines are parallel if x=y?
Answer:
the horizontal lines for #9 and those slanted ones for #10
Step-by-step explanation:
parallel lines are lines that never intercept. if these following lines continue infinetly they will never touch
Write an equation of the line in point-slope form that passes through the given points in the table. Then write the equation in slope-interceptform.x1520253035HHHу160200240280320An equation of the line in point-slope form is
Point slope form: y - 160 = 8(x-15)
Slope intercept form: y = 8x + 40
Explanation:
To write an equation of the line in point-slope form that passes through the given points in the table, we need to pick any two of the points in the table for x and y axis and find the changes of x and y
Points chosen: (20, 200) and (15, 160)
m = slope = (change in y)/ (change in x)
[tex]\begin{gathered} m\text{ = }\frac{200-160}{20-15}\text{ = }\frac{40}{5} \\ m\text{ = 8} \end{gathered}[/tex]Point-slope form:
[tex]\begin{gathered} y-y_1=m(x-x_1)\text{ then we would pick any of the points used earlier} \\ U\sin g\text{ (15, 160)} \\ y\text{ - 160 = 8( x - 15)} \\ y\text{ - 160 = 8x -120} \\ y\text{ =}8x\text{ + 40} \end{gathered}[/tex]The equation in the slope intercept form:
[tex]\begin{gathered} y\text{ = mx + b} \\ y\text{ = 8x + 40} \\ \text{where m = 8 b = intercept = 40} \end{gathered}[/tex]Hence, Point slope form: y - 160 = 8(x-15)
Slope intercept form: y = 8x + 40
Solve for x: 6x + 3 = 5x - 8
О -11
О 11
о
О -5
0
О 5
F
Answer:
6x+3=5x-8
6x-5x= -8-3(match the like terms)
x= -11
PLEASE I NEED HELP ASAP WITH THIS MATH STUFF!!
-download them and draw over them or write over them
The system of equations are y = 50 + 100x and y = 300 + 75x which is linear equations in two variables.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The linear equation can be written in form of:
y = mx + c
From the question:
The equation for Little Learners Pre-School:
y = 50 + 100x
The equation for Growing Place Pre-School:
y = 300 + 75x
Thus, the system of equations are y = 50 + 100x and y = 300 + 75x which is linear equations in two variables.
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BICPPStatistics: Assignment 2.05Name:We asked 10 randomly selected students in a Speech and Debate class how manycollege courses they had passed prior to taking this class. Their responses areshown below. Find the sample mean and the median.4, 8, 14, 7, 0, 8, 2, 10, 3, 12
The rule of the mean is
[tex]Mean=\frac{Sum}{No.}[/tex]We will find the sum of the given numbers, then divide it by how many numbers
The given numbers are
4, 8, 14, 7, 0, 8, 2, 10, 3, 12
Their sum = 68
There are 10 numbers, then
[tex]Mean=\frac{68}{10}=6.8[/tex]To find the median we have to arrange the numbers from smallest to greatest, then take the middle number
0, 2, 3, 4, 7, 8, 8, 10, 12, 14
Since there are 10 numbers, then there are 2 numbers in the middle
Then we will find their average by adding them and dividing their sum by 2
The 2 middle numbers are the 5th and the 6th positions
The 2 middle numbers are 7 and 8
[tex]Median=\frac{7+8}{2}=7.5[/tex]The answers are:
Sample mean = 6.8
The median = 7.5
help meeeeeeeeeeeeeee pleaseeeeeee
Answer: Width = 4.7 meters, Length = 6.7 meters
Step-by-step explanation:
Let the width be [tex]w[/tex]. It follows that the length is [tex]w+2[/tex].
[tex]w(w+2)=32\\\\w^2+ 2w-32=0\\\\w=\frac{-2 \pm \sqrt{2^2 -4(1)(-32)}}{2(1)}\\\\w \approx 4.7 \text{ } (w > 0)\\\\\implies w+2 \approx 6.7[/tex]
9. Steve claimed he had a slow start and could not keep the pace. Use the data from the rateof change to argue or defined this.10. Explain how a graph can show a rate of change more easily that a data chart.
We can see from Steves rate of change that it was steeper than Peters. That means that it took more minutes per kilometer for each kilometer. It is easier to compare when seeing it on the graph. The steeper the line, the steeper the rate of change.
the measure of one of the acute angles in a right triangle is (2y) what is the other acute angle
The measure of the other acute angle in the right triangle is 90 - 2y
How to determine the other acute angle?The given parameters in the question are:
Shape = right triangle
Acute angle = 2y
The measures of acute angles in a right triangle add up to 90
This can be represented mathematically as
Acute angle + Other angle = 90
Substitute the known values in the above equation, so, we have the following representation
2y + Other angle = 90
This gives
Other angle = 90 - 2y
Hence, the other angle is 90 - 2y
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What are the missing parts that correctly complete the proof? given: point m is on the bisector of angle j k l. prove: point m is equidistant from the sides of angle j k l. art: three rays k j, k m, and k l point in rightward direction sharing a common endpoint at k. ray k m is horizontal and bisects angle j k l equally. the perpendicular from point m to ray k j is made by a dotted line. the perpendicular cuts ray k j at x. angle k x m is labeled a right angle. the perpendicular from point m to ray k l is made by another dotted line. the perpendicular cuts ray k l at y. angle k y m is labeled a right angle. drag the answers into the boxes to correctly complete the proof.
The missing parts of proof are:
∠JKM≅∠LKMMK≅MKAAS Congruence PostulateCorresponding parts of congruent triangle are equalDefinition of equidistantExplain property of anglesIn geometry, a line that divides an angle into two equal angles is referred to as an angle bisector. By definition, a bisector is something that divides an object or a shape into two equal parts. A ray is said to be an angle bisector if it divides an angle into two equal portions of the same measure.
Angle Bisector's Qualities:
All of the angle bisector's points are equally spaced from both of the angle's arms.Any angle, including acute, obtuse, and right angles, can have an angle bisector drawn to it.The ratio by which the angle bisector splits the opposite side of a triangle is the same as the ratio by which the other two sides are divided.Given,
KM is the bisector of ∠JKL
1. As per the definition of bisector, ∠JKM≅∠LKM
Given,
∠KXM and ∠KYM are right angles
∠KXM≅∠KYM because all right angles are congruent
2. Because of Reflexive Property of congruence, MK≅MK
3. Given △KXM≅△KYM, AAS congruence postulate
4. Given MX≅MY, this is according to CPCTE property
5. Given, Point M is equidistant from the sides of ∠JKL, as per the definition of equidistant
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there is a step missing from the solution. Which equation is the missing step?
To determine the next step, we need to slove the expression.
divide both sides by -1:
[tex]\begin{gathered} \frac{8}{-1}=\frac{-\sqrt[]{0.025x+7}}{-1} \\ -8=\sqrt{0.025x +7} \end{gathered}[/tex]Square both sides of the equation:
[tex]\begin{gathered} 8^2=(\sqrt{0.025x +7})^2 \\ 64\text{ = 0.025x + 7 } \\ 64\text{ - 7 = 0.025x } \\ 57\text{ = 0.025x } \\ Hence,\text{the missing step: }64\text{ = 0.025x + 7 (option B)} \end{gathered}[/tex]Construct a Venn diagram to determine the validity of the argument (Use Euler's diagram)Some animals are dangerousA car is not an animalTherefore a car is not dangerous
We will have the following:
Here it is the Venn diagram for both; the statement is not valid, since they fall in different categories.
How do you decide how well data represent
a population?
Use examples to explain.
The data that represent a population is helpful when we have to find the information only about one field.
In the given question we have decide how well data represent a population.
The total group you want to make judgments about is referred to as a population. Data is a set of quantitive data which refers the population only in numbers. So the data is only helpful when we have to find the only in small amount and only one field.
Data collection from a large population is typically only simple when the population is small, approachable, and cooperative.
Example: Gathering information from a population
A high school administrator is looking for trends in the final exam results of all graduating seniors. They use the entire population dataset since they are only interested in applying their findings to the graduating seniors in this high school. So the data is useful.
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Expand. Your answer should be a polynomial in standard form.
(x - 2)(x - 6) =
(x-2) (x-6)
x(x-6)-2(x-6)
x²-6x-2x-12
X²-4x-12
Suppose your math teacher was running for Governor. In a pre-election poll of 750 people, the estimate (called a point estimate) was 40%, meaning that 40% of the people would vote for your math teacher. Suppose there was a 4% margin of error. How many people (out of 750) said they would vote for your math teacher? Show your work. Write the answer as a complete sentence.
Solution
- 40% of peole would vote for the mMath teacher out f the 750 people. This implies that the number of people tahat would vote for him is
[tex]\begin{gathered} 40\%\times750 \\ \frac{40}{100}\times750=300\text{ people} \end{gathered}[/tex]- We are also told that there is a margin of error of 4%. This implies that the number of people that vote for the math teacher is either 4% more or 4% less than the 300 people
- 4% margin of error can be gotten as follows:
[tex]\frac{4}{100}\times750=30[/tex]- Thus, the number of people that vote for him is 300 give or take 30 people