The percentage of students age 15 and above travel to school by bus is 47%
How to complete the table?The table of values is given as:
Method of Travel to School
Walk/Bike Bus Car Row totals
Under age 15 18 165
Age 15 and above 65 195
Column totals 152 110 98 360
Using the column total of column 1, we have:
Under age 15 + 65 = 152
This gives
Under age 15 = 87
Using the column total of column 2, we have:
Age 15 and above + 18 = 110
This gives
Age 15 and above = 92
Using the row total of row 1, we have:
Car + 87 + 18 = 165
This gives
Car = 60
Using the row total of row 2, we have:
Car + 65 + 92 = 195
This gives
Car = 38
So, the complete frequency table is
Method of Travel to School
Walk/Bike Bus Car Row totals
Under age 15 87 18 60 165
Age 15 and above 65 92 38 195
Column totals 152 110 98 360
The percentage of students age 15 and above travel to school by bus is:
Percentage = 92/195 * 100%
This gives
Percentage = 47%
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The figure below is composed of square ABCD and equilateral triangle
Answer: 225°
Step-by-step explanation:
The correct option is D)
Refer Figure
Given:
ABCD is a square
ABP is an equilateral triangle
AB=BP=BC (△ABP is equilateral and AB and BC belong to a square, hence all are equal)
∠ABC=∠ABP+∠PBC=60°+∠PBC
90°−60°=∠PBC
∠PBC=30°
In △BPC
BP=BC
∠BPC=∠BCP= 2
180−∠PBC
( angles opposite to equal sides of a triangle are equal)
∠APC=∠APB+∠BPC=(60+75)°=135°
Hence, Reflex ∠APC=(360−135)°=225°
Use the drawing tool(s) to form the correct answer on the provided graph.
Using the information provided on the graph, draw the line the line that is perpendicular to line segment AB and passes through point P
The required equation of the line is given as y = 5x -6.
Given that,
To determine the equation of a line passing through the point P(9, -8) and perpendicular to the line AB y = 3x + 6.
The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
Here,
The slope of the given line
y = 3x + 6.
m = 3
The equation of the perpendicular line is given as,
y - y₁ = -1/m (x - x₁)
Substitute the value in the above equation,
y + 8 = -1 / 3 (x - 9)
y = -x/3 + 3 - 8
y = -x/3 - 5
Thus, the required equation of the line is given as y = -x/3 - 5.
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Unit 11 volume and surface area homework 2 area of sectors
Answer:
2. KI = 20 ft 119 M K 4. YZ = 14.2 m 2 6. PO = 2.8 in R 311 8. WZ = 5.3 km w z 108
Step-by-step explanation:
solve the inequality 27>b+57
Answer:
b < -30
Step-by-step explanation:
27 > B + 57 Subtract 57 from both sides
27 - 57 > b +57 - 57
-30 > b
or
b < -30
Please hep pls easy easy proportional relationship
Answer:
Below
Step-by-step explanation:
A) Juan reads at 57 pages /hr
B) Juan reads 9 pages more per hour (57-48) than Lexi
in 7 hours this will be 7 hr * 9 p/hr = 63 pages
can someone help me with this please?
could the answer be;
a.) px=-3x^3-2x²-6x-16,r(x)=-45, and q(x)=x-3
b.) px=-3x^3-2x²-6x-16,r(x)=-117, and q(x)=x-3
c.) px=-x^3+4x²+12x+16,r(x)=-117, and q(x)=x-3
d.) px=-x^3+4x²+14x+45,r(x)=-0, and q(x)=x-3
The simplest form of the given expression is px=-3x^3-2x²-6x-16,r(x)=-45, and q(x)=x-3.
What is polynomials?
Using variables and coefficients, polynomials are algebraic expressions. The term "indeterminates" is sometimes used to describe variables. The terms Poly and Nominal, which together signify "many" and "terms," make up the word polynomial. When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable). The expression is categorized as a monomial, binomial, or trinomial based on the number of terms it contains.
(-x^4+7x^3+2x+3)/ (x-3)
=-x² + 4x² + 12x + 38 + 117/(x - 3)
Hence the simplest form of the given expression is px=-3x^3-2x²-6x-16,r(x)=-45, and q(x)=x-3.
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Graph the linear inequality y < 1/2x + 2 using slope-intercept form.
Given inequality:
y < 1/2x + 2To graph it first, consider line:
y = 1/2x + 2Find two points on the line.
Let them be x- and y-intercepts:
x = 0 ⇒ y = 1/2*0 + 2 = 2, so the point is (0, 2)y = 0 ⇒ 0 = 1/2x + 2 ⇒ 1/2x = - 2 ⇒ x = - 4, the point is (- 4, 0)Now, plot the two points.
Next, draw a dashed line trough the two points. Dashed line because the line is not included into solution set, due to '<' sign.
The last step, shade the area below the line. Below the line because 'y <' means 'y-values less than' which appears below the line.
Answer:
See attachment.
Step-by-step explanation:
Given linear inequality:
[tex]y < \dfrac{1}{2}x+2[/tex]
When graphing inequalities, temporarily replace the inequality sign for the equals sign:
[tex]\implies y=\dfrac{1}{2}x+2[/tex]
Find two points on the line by substituting two values of x into the equation:
[tex]x=0 \implies y=\dfrac{1}{2}(0)+2 =2\implies (0, 2)[/tex]
[tex]x=4 \implies \dfrac{1}{2}(4)+2=4 \implies (4,4)[/tex]
When graphing inequalities:
< or > : dashed line.≤ or ≥ : solid line.< or ≤ : shade under the line.> or ≥ : shade above the line.Therefore, to graph the given linear inequality:
Plot points (0, 2) and (4, 4).Draw a dashed straight line through the points.Shade under the dashed line.suppose we want to choose 7 objects without replacement from 11 distinct objects  how many ways can this be done if the order of the choices is relevant
In 1663200 ways objects can be chosen if the order of the choices is relevant. The solution has been obtained using permutation.
What is permutation?
An arrangement of items in a specific manner or sequence is referred to as a permutation. It is important to think about both the selection and the arrangement when dealing with permutation. Briefly put, permutations depend much on ordering. In other words, a permutation is a combination that is ordered.
We want to choose 7 objects without replacement from 11 distinct objects
So, since the order of the choices is relevant, we will use permutation.
Therefore,
⇒nPr = n! ÷ (n - r)!
⇒11P7 = 11! ÷ (11 - 7)!
⇒11P7 = 11! / 4!
⇒11P7 = (11 * 10* 9 * 8 * 7* 6 * 5)
⇒11P7 = 1663200 ways
Hence, in 1663200 ways objects can be chosen if the order of the choices is relevant.
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Can somebody please tell me how to Solve Systems by Elimination? I don't understand it at all and I'm staying up all night trying to figure it out. I especially don't understand the co-efficient part.
An example is:
2c+3d=12
5c-d=13
What would the answer be to that? Please provide an explanation!
Solving the example, hope it will help you with better understanding.
Given system:
2c + 3d = 125c - d = 13We need to eliminate one of the variables c or d. Let us eliminate d.
We see the first equation has 3d and the second equation has - d. The coefficients of d are 3 and - 1. If we multiply the second one by 3 it will become - 3, then if we add them up they will cancel, 3d - 3d = 0. By doing this we'll eliminate the variable d and left with variable c in the resulting equation.
Demonstrating how it works:
2c + 3d = 12, we leave it as is
5c - d = 13, we multiply all terms of this by 3, it becomes, 15c - 3d = 39
Now add up the two equations:
2c + 15c + 3d - 3d = 12 + 39, eliminated d17c = 51 solving for cc = 51/17c = 3Now we can find the value of d:
2c + 3d = 122*3 + 3d = 126 + 3d = 123d = 6d = 2Our solution is:
c = 3, d = 2Find the slope of the line that passes through points 2, -8 and the origin using m=rise/run
Answer:
-4
Step-by-step explanation:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}=\frac{0-(-8)}{0-2}=\frac{8}{-2}=-4[/tex]
The slope of the line that passes through the points (2, -8) and the origin is calculated using the formula m = rise/run, which gives -4.
Explanation:In this Mathematics problem, we are asked to find the slope of the line that passes through two points using the formula m = rise/run, where 'm' is the slope. The points provided are (2, -8) and the origin, which is (0, 0).
To find the slope (rise/run), we can subtract the y-values (rise) and the x-values (run) of the two points, respectively. So, the formula becomes: m = (-8 - 0) / (2 - 0) => m = -8/2 = -4.
Therefore, the slope of the line that passes through the points (2, -8) and the origin is -4.
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So far this semester, Franco is averaging a score of 70.7 points on math tests, which is 1% higher than his average last semester. What was the average of his scores last semester?
help me pleasee
Hurry - please help!!!!!!!!
Answer:
false
Step-by-step explanation:
I think it's false but I don't really remember, but I would go with someones else answer cause I'm not sure
The function () =
40+700
represents the average cost (in dollars) of making items. How
many items must be made for the average cost to fall to $5
The number of items must be made for the average cost to fall to $5 wil be; 900.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable).
We are given that function = 40x +700 represents the average cost (in dollars) of making items.
Then the item made for function average cost to fall to $5.
= 40x + 700
= 40(5) + 700
= 200 + 700
= 900
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The tallest tree in the United States is the coast redwood and your deer Smith State Park in California. It is 321 feet tall suppose you are 5‘,8“ tall and cast a shadow that is 2 feet at a certain time of day about how long is the trees shadow at the same time of day convert five point 5‘8“ to feet
The shadow of the tree at the same time of day was 113.29 foot long.
What is foot?Foot, plural feet, any of numerous ancient, mediaeval, and modern linear measures based on the length of the human foot and used only in English-speaking countries, where it typically consists of 12 inches or one-third yard (typically 25 to 34 cm).
In most countries and all areas of science, the foot and its multiples and subdivisions have been largely replaced by the metre, the basic linear unit of the metric system. Since 1959, a foot in the US has been defined as exactly 30.48 centimetres.
We know that
1 feet = 12 inches
So, 5 feet 8 inches = 5[tex]\frac{2}{3}[/tex] feet
Now, lets find the shadow of tree
5[tex]\frac{2}{3}[/tex]/2 = 321/x
x = 113[tex]\frac{5}{11}[/tex]
x = 113.29
Thus, the tree's shadow at the same time of day was 113.29 foot long
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3(4x-10)= 2(3x-30) help
The solution to the equation 3(4x-10) = 2(3x-30) is x = -5.
What is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.
Let's solve for x:
3(4x - 10) = 2(3x - 30)
First, we can simplify both sides by distributing the coefficients:
12x - 30 = 6x - 60
Next, we'll move all the x terms to one side of the equation and the constants to the other side:
12x - 6x = -60 + 30
Simplifying further:
6x = -30
Finally, we can solve for x by dividing both sides by 6:
x = -5
Therefore, the solution to the equation 3(4x-10) = 2(3x-30) is x = -5.
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Resolve F2 into components along the u and v axes determine the magnitudes of these components.
Resolving F2 into components along the u and v axes, the magnitudes of the components are determined as 150 N and 77.6 N.
According to the sine law, the side length of a triangle should be divided by the sine of the opposite angle. That is, when we divide side a by the sine of angle A, we get the same result as side b divided by angle B and side c divided by angle C.
For the given diagram, first, draw the vector components. Then, by sine law, we get,
[tex]\begin{aligned}\frac{F_u}{\sin 75^{\circ}}=\frac{F_2}{\sin 75^{\circ}}=\frac{F_v}{\sin 30^{\circ}}\end{aligned}[/tex]
Now, substitute the value of F₂, and we get,
[tex]F_u=F_2=\mathrm{150\;N}[/tex]
Now, solve for [tex]F_v[/tex], we get,
[tex]\begin{aligned}F_v&=\frac{F_2\sin 30^{\circ}}{\sin75^{\circ}}\\&=\mathrm{\frac{150\;N\times 0.5}{0.966}}\\&=\mathrm{77.64\;N}\end{aligned}[/tex]
The required answers are 150 N and 77.64 N.
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Angles 3 and 4 are supplementary. The measure of angle 3 is
thirty-five more than one-fourth the measure of angle 4.
1. What is the measure of Angle 3?
2. What is the measure of Angle 4?
The values of ∠4 and ∠3 are 116 degrees and 64 degrees respectively.
Given ,
What are supplementary angles ?
The angles are said to be in supplementary if and only if the sum of two angles is 180 degrees .
Angles 3 and 4 are supplementary.
The measure of angle 3 is
thirty-five more than one-fourth the measure of angle 4.
So,
∠3 + ∠4 = 180 degrees.
∠3 = 180-∠4 - equation 1
∠3 = 35 + (1/4 ) ∠4 - equation2
As equation 1 and 2 are equal
hence,
180-∠4 = 35 + (1/4) ∠4
180-35 = ∠4 + (1/4) ∠4
145 = ((1/4)+1) ∠4
145 = (5/4) ∠4
∠4 = 145 * 4 / 5
∠4 = 29*4
∠4 = 116
∠3 = 180-116
∠3 = 64
Hence the values of ∠4 and ∠3 are 116 degrees and 64 degrees respectively.
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Solve the following equation. 2(y +4) = 3(2y -4) SHOW YOUR WORK
Answer:
y = 5
Step-by-step explanation:
2(y + 4) = 3(2y - 4)
2y + 8 = 6y - 12
-4y = -20
y = 5
Kelly rolled scores of 254, 202, 284, 269, 151, 258 and 202 in a recent tournament. What was the mean, median and mode of her scores?
Answer:
See below!
Step-by-step explanation:
Data:254, 202, 284, 269, 151, 258, 202
Mean:The sum of data divided by the number of data is called mean.Mean of the data:
[tex]\displaystyle Mean= \frac{Sum \ of \ data}{number \ of \ data} \\\\Mean = \frac{254+202+284+269+151+258+202}{7} \\\\Mean=\frac{1620}{7} \\\\\boxed{Mean = 231.4}[/tex]
Median:The middle value of the data is median.Median of data:
Arrange the data in increasing order.
151, 202, 202, 254, 258, 269, 284
The middle value = 254
So,
Median = 254Mode:The frequently occurring value in the data is known as mode.Mode in data:
The mode, here, is 202. (occurring 2 times.)
So,
Mode = 2[tex]\rule[225]{225}{2}[/tex]
What’s the tangents ratio for F?
5/4
5/3
4/3
3/4
The tangent ratio of F by using the rule from trigonometry is 4/3
What is the trigonometry ratio?Trigonometric ratios are ratios that represent the length of a triangle's sides. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the fundamental trigonometric ratios.
The sine of the trigonometry ratio is sin θ = opposite/hypotenuse. The cosine of the trigonometry ratio is cos θ = adjacent/hypotenuse. The tangent of the trigonometry ratio is tan θ = opposite/adjacent. From the image given. The opposite side is the line facing the angle F;
Thus, the opposite side = 8, and the adjacent is the smallest side, which is 6.
Therefore, the tangent ratio for F is:
tan θ = 8/6
This can be reduced to 4/3
Therefore, we can conclude that the tangent ratio of F is 4/3.
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Which expression is the least absolute value |-28| |-1| |6| |15|
Answer: |-1|
Step-by-step explanation:
So lets just solve all of this stuff so you can just look at it and get the answer. | - 28 | = 28, |-1| = 1, |6| = 6, |15| = 15. So we have 28, 1, 6, and 15. Put this in order we have: 28, 15, 6, 1 which means 1 is the least or your could say |-1| is the least. Have a good day ;)
Find the length of ST
Answer:
ST = 10
Step-by-step explanation:
Δ RSQ and Δ RTP are similar by the AA postulate , then
the ratios of corresponding sides are in proportion , that is
[tex]\frac{RS}{RT}[/tex] = [tex]\frac{RQ}{RP}[/tex] ( substitute values )
[tex]\frac{5}{RT}[/tex] = [tex]\frac{9}{9+18}[/tex] = [tex]\frac{9}{27}[/tex] = [tex]\frac{1}{3}[/tex] ( multiply both sides by 3 to clear the fraction )
RT = 3 × 5 = 15
Then
ST = RT - RS = 15 - 5 = 10
During a series of plays in a football game, a running back carried the ball for the yardages given by 6, -3, 2, -1, 7,
-4, and -2. Find his total yards and his average yards per carry.
The total yards for the running back was
(Simplify your answer.)
Therefore ,As a result, the region's problem with the suggested solution is the playing field area measures 118 yards by 56 yards.
Define area.Add length and breadth together to calculate area. The calculation for area is L times B. Radius or area equals r2(=3.14) With the use of these techniques, it is also possible to determine the area of various quadrilaterals, a specific type of polygon with 4 sides and an angle smaller than 90 degrees. Application. Geometry has been based on the concept of area from its inception.
Here,
We find w = 56, which indicates that the parallelogram has a length of 56 yards.
Since the width is identical to 2w + 6, we can make the computation simpler by changing w to 56 to find the rectangle's length.
The rectangle's length is shown to be 118 yards.
The size of the playing area is accordingly 118 yard by 56 yards.
As a result, the proportions of the playing field—118 yards by 56 yards—are the answer to the dilemma at hand.
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ILL GIVE BRAINLIEST IF CORRECT NEED HELP ASAP PLS
Answer: y=2x-15
Step-by-step explanation:
Answer:
y=1/2x + 15
Since,her original flight plan time is X and hence the flight will reach 2 times faster the X becomes X/2 and the additional time 15 minutes which has already been delayed.So,she will arrive her destination in(1/2X+15)min from 4:00 p.m.
*mark me brainliest
The sum of the two digits number is nine
If the sum of two digits t and u is t + u = 9, then the second equation is option 2: t = 1/2 u.
What is a digit?
In math, single integers called digits are used to represent values. To represent all mathematical values, the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are employed in various combinations and repetitions.
The first equation is as given t + u = 9
Second equation t = u/2 since the number in the tens position is one half of the one in the units. So if you divide u by two, you should have one t, as the equation states.
The second equation is t = (1/2)u => u = 2t
When we replace this in first equation we get -
t + 2t = 9
3t = 9
t = 9/3
t = 3
When we replace it again in the equation -
u = 2 t
= 2 · 3
= 6
The requested number is 36.
Therefore, the number is 36 and the second equation is t=u/2.
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Let me know if I got this right
What is the solution to the equation?
lnx−ln(4x−1)=ln5
Enter your answer in the box. Enter any fractions as simplified fractions.
Answer:
x = 5/19
Step-by-step explanation:
For left side, apply logarithm division property:
[tex] \displaystyle{ \ln a - \ln b= \ln \left( \dfrac{a}{b} \right)}[/tex]
Hence:
[tex] \displaystyle{ \ln \left( \dfrac{x}{4x - 1} \right) = \ln 5}[/tex]
Since both sides have same ln, we can cancel ln both sides:
[tex] \displaystyle{ \dfrac{x}{4x - 1} = 5}[/tex]
Solve the equation for x:
[tex] \displaystyle{x = 5(4x - 1)} \\ \\ \displaystyle{x = 20x - 5} \\ \\ \displaystyle{5 = 20x - x} \\ \\ \displaystyle{5 = 19x} \\ \\ \displaystyle{x = \dfrac{5}{19}}[/tex]
Therefore, x = 5/19
Madeline spends all of her spare money on widgets, which cost $2 each, and gizmos, which cost $2 each. What is her opportunity cost if Madeline buys 12 widgets? opportunity cost:
The opportunity cost of Madeline based on the information would be 8 units of gizmos .
What is the opportunity cost of Madeline?The benefit or gain that a person might have obtained or earned if he or she had not chosen the current alternative is known as opportunity cost.
Madeline has spent $24 ($2 x 12) on the widgets in this question since she purchased 12 of them at a cost of $2 each. In this case, her opportunity cost would be the gadgets she could have purchased, which works out to $24 / $3 = 8 units.
Therefore, the opportunity cost is 8 units.
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The linear function f is defined as f(x)= -2x+3 consider the graph y =f(x)
On solving the provided question, we can say that the linear function is f(x) = -2x +3 and by the graph y = f(x) = -1
What is linear function ?Two distinct but related concepts are referred to as linear functions in mathematics. A polynomial function of degree 0 or 1 is a linear function in calculus and related subjects if its graph is a straight line. Any function that depicts a straight line on a coordinate plane is said to be linear. For instance, y = 3x - 2 is a linear function since it depicts a straight line on the coordinate plane. f(x) = 3x - 2 can be used to represent the function since f(x) can be linked to y.
here,
the linear function is f(x) = -2x +3
and by the graph y = f(x) = -2x +3 = -2(2) + 3 = -4+3 = -1
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how do write 3n - 6 as a phrase in words
Which is the mode for the data set? -1,0,3,4,-3,-1
Mode of data set -1, 0, 3 ,4, -3, -1 is - 1 with most often in data set.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The data set is,
⇒ -1, 0, 3 ,4, -3, -1
Now, We know that;
The mode is the value that appears the most often in the data set.
Here, In the data set - 1 is most often number.
So, The mode of data set = - 1
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