SOLUTION
Given the question in the question tab, the following are the solution steps to answer the question.
STEP 1: Write the formula for total surface area of cuboid
[tex]\begin{gathered} 2(lb+bh+lh) \\ \text{where l is the length} \\ b\text{ is the breadth} \\ \text{h is the height} \end{gathered}[/tex]STEP 2: Get the dimension of the sides
[tex]\begin{gathered} \text{ Since the dimensions of the cuboid are in the ratio 1:2:3} \\ the\text{ dimensions are given as:} \\ x,2x\text{ and }3x \\ \text{lenght}=x \\ \text{breadth}=2x \\ \text{height}=3x \end{gathered}[/tex]STEP 3: Substitute the dimensions into the formula to get the value of x
[tex]\begin{gathered} 2(lb+bh+lh)=88 \\ By\text{ substitution,} \\ 2((x\cdot2x)+(2x\cdot3x)+(x\cdot3x))=88 \\ \Rightarrow2(2x^2+6x^2+3x^2)=88 \\ \text{Divide both sides by 2} \\ \Rightarrow\frac{2(2x^2+6x^2+3x^2)}{2}=\frac{88}{2} \\ \Rightarrow2x^2+6x^2+3x^2=44 \\ 11x^2=44 \\ \text{Divide both sides by 11} \\ \frac{11x^2}{11}=\frac{44}{11} \\ x^2=4 \\ x=\sqrt[]{4}=2 \\ x=2m \end{gathered}[/tex]STEP 4: Get the other dimensions
[tex]\begin{gathered} \text{breadth}=2x \\ \text{substitute 2 for x} \\ \text{breadth}=2(2)m=4m \\ \\ To\text{ get height} \\ \text{height}=3x \\ \text{substitute 2 for x} \\ \text{height}=3(2)m=6m \end{gathered}[/tex]Hence, the dimensions are:
[tex]2m,4m,6m[/tex]IIIALGEBRA AND GEOMETRY REVIEWUsing distribution and combining like teSimplify.-3(x + 1)- 5
-3(x + 1) - 5
(-3)(x) + (-3)(1) -5
-3x - 3 -5
-3x - 8
-2(u + 3) + 4u
-2u - 6 + 4u
2u - 6
If the calculator gives us the following values number 7
we know that
The equation is of the form
y=ax+b
The given values are
a=0.872
b=25.263
substitute
therefore
The equation is
y=0.872x+25.263Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x) = –3 2(x2 + 6x) = 3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x + 9) = –3 + 9
Inga should use the first option that is [tex]2(x^2+6x+9)=3+18[/tex] to solve the quadratic equation.
Given equation:-
[tex]2x^2+12x-3=0[/tex]
We have to find which one of the given options are needed to solve the quadratic equation.
The given quadratic equation can be rewritten as:-
[tex]2x^2+12x[/tex]-3+3=0+3
[tex]\\2x^2+12x[/tex]-3 + 3 + 18=0 +3 +18
[tex]2x^2[/tex] + 12x + 18 = 0 + 3 + 18
Hence, the answer is the first option.
Quadratic equation
Quadratic equations are the polynomial equations of degree 2 in one variable of type [tex]f(x) = ax^2 + bx + c = 0[/tex]where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where ‘a’ is called the leading coefficient and ‘c’ is called the absolute term of f (x). The values of x satisfying the quadratic equation are the roots of the quadratic equation (α, β).
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Yon buys tickets to a concert for himself and a friend. There is a tax of 6% on the price of the tickets andan additional booking fee of $20 for the transaction. Enter an algebraic expression to represent the priceper person. Simplify the expression if possible. Use variablet for the price of the 2 tickets in dollars.The algebraic expression is
Let the price of each ticket be represented by
[tex]=x[/tex]The price of two tickets will be
[tex]t=2x[/tex]The tax on the price of the tickets is 6% which be represented as
[tex]\begin{gathered} =\frac{6}{100}\times t \\ =\frac{6t}{100}=0.06t \end{gathered}[/tex]The price of the two tickets after tax will be
[tex]\begin{gathered} the\text{price of the two tickets+the tax on the two tickets} \\ =t+0.06t \\ =1.06t \end{gathered}[/tex]Therefore,
The price of the tickets after adding an additional booking fee of $20 will be given below as
[tex]=1.06t+20[/tex]Since,
We were asked to get the algebraic expression person, we would therefore divide the above expression by 2
[tex]\begin{gathered} =\frac{1.06t+20}{2}=\frac{1.06t}{2}+\frac{20}{2} \\ =0.53t+10 \end{gathered}[/tex]Hence,
The algebraic expression to represent the price per person using variable t is
=0.53t + 10
Suppose you are looking to purchase some cans to use for food storage. The can you are looking at has a diameter of 5in. and a height of 7in. What is the volume of the can? Round to the nearest hundredth
The volume of a cylinder is given by
V = pi r^2 h where r is the radius and h is the height
We are given the diameter is 5
r = d/2 = 5/2 = 2.5 in
V = pi ( 2.5)^2 (7)
V =pi ( 6.25)*7
V = 43.75 pi
Assuming a value for pi of 3.14
V =137.375 in ^3
Rounding to the nearest hundredth
V = 137.38 in ^3
Assuming a value for pi by using the pi button
V = 137.44468
Rounding to the nearest hundredth
V = 137.44 in ^3
What does the point (2, 24 ) represent in the situation ?K =
Given point:
(2, 24)
To find the constant proportionality:
In general, the constant proportionality is
[tex]\begin{gathered} k=\frac{y}{x} \\ k=\frac{24}{2} \\ k=12 \end{gathered}[/tex]Hence, the constant proportionality is 12.
Find the surface area of a right cone that has a radius of 9 inches and a height of 12 inches. Round your answer to the nearest hundredth. The surface area is about ⬜ square inches.
The surface area of the right cone is:
[tex]678.58in^2[/tex]Explanation:The surface area of a right cone is:
[tex]A=\pi r(r+\sqrt[]{r^2+h^2})[/tex]Here, r = 9 in, and h = 12 in
so
[tex]\begin{gathered} A=9\pi(9+\sqrt[]{9^2+12^2}) \\ \\ =9\pi(9+15) \\ =216\pi \\ =678.58in^2 \end{gathered}[/tex]Finding the area of a triangle is straightforward if you know the length of the base and the height of the triangle. But is it possible to find the area of a triangle if you know only the coordinates of its vertices? In this task, you'll find out. Consider AABC, whose vertices are A (2,1), B (3, 3), and C (1,6) ; let AC represent the base of the triangle. Part A Find the equation of the line passing through B and perpendicular to AC.
Answer: y = x/5 + 12/5
Explanation:
The first step is to find the equation of line AC
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m represents slope
c represents y intercept.
The formula for calculating slope of a line is expressed as
m = (y2 - y1)/(x2 - x1)
Considering line AC with points, A(2, 1) and C(1, 6),
x1 = 2, y1 = 1
x2 = 1, y2 = 6
m = (6 - 1)/(1 - 2) = 5/- 1 = - 5
Recall, if two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line. Negative reciprocal of - 5 is 1/5
Thus, slope of the perpendicular line passing through B(3, 3) is m = 1/5
We would find the y intercept, c of the line by substituting m = 1/5, x = 3 and y = 3 into the slope intercept equation. We have
3 = 1/5 * 3 + c
3 = 3/5 + c
c = 3 - 3/5
c = 12/5
By substituting m = 1/5 and c = 12/5 into the slope intercept equation, the equation of the line is
y = x/5 + 12/5
4 groups of a number
Answer:
[tex]4x[/tex]Step-by-step explanation:
In math, a group is a set equipped with an operation that combines any two elements of the set to produce a third element of the set.
Therefore, for 4 groups of a number.
Let x be the missing number
So, 4 multiply x:
[tex]4x[/tex]What is the row echelon form of this matrix?
The row echelon form of the matrix is presented as follows;
[tex]\begin{bmatrix}1 &-2 &-5 \\ 0& 1 & -7\\ 0&0 &1 \\\end{bmatrix}[/tex]
What is the row echelon form of a matrix?The row echelon form of a matrix has the rows consisting entirely of zeros at the bottom, and the first entry of a row that is not entirely zero is a one.
The given matrix is presented as follows;
[tex]\begin{bmatrix}-3 &6 &15 \\ 2& -6 & 4\\ 1&0 &-1 \\\end{bmatrix}[/tex]
The conditions of a matrix in the row echelon form are as follows;
There are row having nonzero entries above the zero rows.The first nonzero entry in a nonzero row is a one.The location of the leading one in a nonzero row is to the left of the leading one in the next lower rows.Dividing Row 1 by -3 gives:
[tex]\begin{bmatrix}1 &-2 &-5 \\ 2& -6 & 4\\ 1&0 &-1 \\\end{bmatrix}[/tex]
Multiplying Row 1 by 2 and subtracting the result from Row 2 gives;
[tex]\begin{bmatrix}1 &-2 &-5 \\ 0& -2 & 14\\ 1&0 &-1 \\\end{bmatrix}[/tex]
Subtracting Row 1 from Row 3 gives;
[tex]\begin{bmatrix}1 &-2 &-5 \\ 0& -2 & 14\\ 0&2 &4 \\\end{bmatrix}[/tex]
Adding Row 2 to Row 3 gives;
[tex]\begin{bmatrix}1 &-2 &-5 \\ 0& -2 & 14\\ 0&0 &18 \\\end{bmatrix}[/tex]
Dividing Row 2 by -2, and Row 3 by 18 gives;
[tex]\begin{bmatrix}1 &-2 &-5 \\ 0& 1 & -7\\ 0&0 &1 \\\end{bmatrix}[/tex]
The above matrix is in the row echelon form
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Given f <-2, 3> and g <1, -5> find f + 2g
Here are the steps in adding vector f and vector 2g.
1. First, multiply vector G by 2. To do this, simply multiply each component of g by 2.
[tex]<2(1),2(-5)>\Rightarrow<2,-10>[/tex]2. Add the result in step 1 to vector f.
To add, simply add each component of vector f to its corresponding component of vector g.
[tex]\begin{gathered} <-2,3>+<2,-10> \\ <-2+2,3+(-10)> \\ <0,-7> \end{gathered}[/tex]The result is <0, -7>.
Hence, f + 2g = <0, -7>. (Option 3)
Hence, f + 2g = <0, -7>. (Option 3)
Using the Smith's BBQ Report, all of your hourly personnel are getting a promotion this week. As a result, your hourly wages for next week will be 8% more than the current week. What will be the approximate Total Payroll Variance from the current week to next week if all other factors remain the same?A 156B 9265C 842D 686
Given:
The current week hour wage is 8579
Total payroll =14081.
The hourly wage will be increased 8 %.
The 8% of 8579 is
[tex]=\frac{8}{100}\times8579=686.32[/tex]The hourly wage will be increased by 686 next week.
The total payroll also will be increased by 686.
So the total Payroll Variance from the current week to next week is 686.
Hence option D is correct.
Solve. 0.25(60) + 0.10x = 0.15(60+x)
[tex]15 + 0.10x = 0.15(60) + 0.15(x) \\ 15 + 0.10x = 9 + 0.15x \\ \\ 0.10x - 0.15x = 9 - 15 \\ - 0.05x = - 6 \\ \frac{ - 0.05x}{ - 0.05} = \frac{ - 6}{ - 0.05} \\ x = 120[/tex]
ATTACHED IS THE SOLUTION
An electrician needs 6 rolls of electrical wire to wire each room in a house. How many rooms can he wire with 3/62 of a roll of wire?
Use a rule of three to find the amount of rooms wire with 3/62 rolls:
[tex]x=\frac{\frac{3}{62}rolls*1room}{6rolls}=\frac{\frac{3}{62}}{6}rooms=\frac{3}{6*62}rooms=\frac{3}{372}rooms=\frac{1}{124}rooms[/tex]Then, with 3/62 of a roll can be wire 1/124 parts of a roomMrs. Laurence just bought a new car for 26,304. She plans to pay her car off in 24 months. Mr. Gannon just bought a new car for 20,480 and plans to pay his car off in 20 months. How much more money a month does Mrs. Laurence pay in her car payment?
The amount of extra money a month that Mrs. Laurence pays in her car payment is $72.
How much more money does Mrs. Laurence pay each month?We can get the amount of extra amount that Mrs. Laurence pays each month when compared to Mr. Gannon by dividing the amount that they pay by the number of months they need to make these payments.
This can be done as follows:
26304 ÷ 24 = 1096
20480 ÷ 20 = 1024
1096 - 1024 - 72
So, the amount of extra money that Mrs. Laurence has to pay each month when compared to that of Mr. Gannon is $72.
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3. Ketin's card collection is made up of baseball cards and footbal cards. The ratio of baseball cards to football cards is 6 to 7. He has 120 baseball cards. How many cards are in Kerin's card collection? Show your work.
SOLUTION
Let the total number of cards in Ketin's card collection be k
Let the number of baseball cards be b, and
the number of football cards be f
Now, the ratio of baseball cards to football cards is 6 to 7, that is
[tex]\begin{gathered} b\colon f=6\colon7 \\ \frac{b}{f}=\frac{6}{7} \\ \text{cross multiplying, we have } \\ 7\times b=6\times f \\ 7b=6f \\ \text{dividing both sides by 7 to get b, we have } \\ \frac{7b}{7}=\frac{6f}{7} \\ b=\frac{6f}{7} \end{gathered}[/tex]Also, he has 120 baseball cards.
This means
[tex]\begin{gathered} b=120 \\ \text{but } \\ b=\frac{6f}{7} \\ \text{That means that } \\ b=\frac{6f}{7}=120 \\ So,\text{ } \\ \frac{6f}{7}=120 \\ \frac{6f}{7}=\frac{120}{1} \\ \text{cross multiplying, we have } \\ 6f=120\times7 \\ \text{dividing by 6, we have } \\ f=\frac{120\times7}{6} \\ 120\text{ divided by 6 = 20, we have } \\ f=20\times7 \\ f=140 \end{gathered}[/tex]So, the total number of cards in Ketin's card collection is
[tex]120+140=260[/tex]Hence the answer is 260
Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the graph of the equation. (3, 7); y=3x+7
The linear equation parallel to y= 3x + 7 is:
y = 3x - 2
How to find the linear equation?A general linear equation is of the form:
y = m*x + b
Where m is the slope and b is the y-intercept.
Two lines are parallel only if the lines have the same slope and different y-intercepts.
So a line parallel to y = 3x + 7 will be of the form:
y = 3x + c
To find the value of c we use the point (3, 7) which must belong to the line, replacing the values in the linear equation:
7 = 3*3 + c
7 = 9 + c
7 - 9 = c
-2 = c
The linear equation is y = 3x - 2
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a scale drawing of a school bus is 1 inch to 5 feet. if the length of the school bus is 5 inches on the scale drawing. what is the actual length of the bus?
Answer:
25 feet
Step-by-step explanation:
we can set up the proportional relationship of the drawing vs the actual size
so 1 inch to 5 feet would be 1:5
so then if we scale up 1 inch to 5 inch
then we have 1:5=5:Actual length of the bus
so then we have 5*5=25 feet
5x + 4 = x + 8. What is the solution for 'x'?
Given the equation
[tex]5x+4=x+8[/tex]To solve this first pass all x-related terms to the left side of the equation and all other terms to the right side:
[tex]5x-x=8-4[/tex]And solve
[tex]\begin{gathered} 4x=4 \\ x=\frac{4}{4} \\ x=1 \end{gathered}[/tex]452 pointsTo factor x2 + bx + c, the numbers you choose to fill in the empty spots of (x + )(x + ).1mustchoose your answer...to equal c.2Previous34Сл
The Quadratic format is
[tex]\begin{gathered} x^2\text{ + bx + c } \\ \text{The b is gotten by adding the factors } \\ \text{But the c is gotten by multiplying the factors } \end{gathered}[/tex]The answer to the question is that the factors must multiply to form c
In the figure below, m∠1 = 8x and m∠2 = (x-9). Find the angle measures.
Answer:
• m∠1 =168 degrees
,• m∠2 =12 degrees
Explanation:
From the diagram, Angles 1 and 2 are on a straight line.
We know that the sum of angles on a straight line is 180 degrees.
Therefore:
[tex]m\angle1+m\angle2=180^0[/tex]Substituting the given values, we have:
[tex]\begin{gathered} 8x+x-9=180^0 \\ 9x=180+9 \\ 9x=189 \\ x=\frac{189}{9} \\ x=21 \end{gathered}[/tex]The measures of angles 1 and 2 are:
[tex]\begin{gathered} m\angle1=8x=8\times21=168^0 \\ m\angle2=x-9=21-9=12^0 \end{gathered}[/tex]The measures of angles 1 and 2 are 168 degrees and 12 degrees respectively.
1 + c + 1.4 = c + 2.4I need help
1 + c + 1.4 = c + 2.4
c + 2.4 = c + 2.4
c = c + 2.4 - 24
c = c
Find the number that belongsin the green box.[?]109°13°6Round your answer to the nearest tenth.
step 1
Find the measure of the third interior angle of triangle
Remember that the sum of the interior angles in any triangle must be equal to 180 degrees
so
x+109+13=180
solve for x
x=180-122
x=58 degrees
step 2
Applying the law of sines
?/sin(13)=6/sin(58)
solve for ?
?=(6/sin(58))*sin(13)
?=1.6 unitsCan you help me answer part A and part B?
Part A.
Given:
P = (5, 4), Q = (7, 3), R = (8, 6), S = (4, 1)
Let's find the component of the vector PQ + 5RS.
To find the component of the vector, we have:
[tex]=\lparen Q_1-P_1,Q_2-P_2)=<7-5,3-4>[/tex]For vector RS, we have:
[tex]=\lparen S_1-R_1,S_2-R_2)=<4-8,1-6>[/tex]Hence, to find the vector PQ+5RS, we have:
[tex]\begin{gathered} =<7-5,3-4>+5<4-8,1-6> \\ \\ =\left(2,-1\right)+5\left(-4,-5\right) \\ \\ =\left(2,-1\right)+\left(5\ast-4,5\ast-5\right) \\ \\ =\left(2,-1\right)+\left(-20,-25\right) \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} =<2-20,-1-25> \\ \\ =<-18,-26> \end{gathered}[/tex]Therefoee, the component of the vector PQ+5RS is:
<-18, -26>
• Part B.
Let's find the magnitude of the vector PQ+5RS.
To find the magnitude, apply the formula:
[tex]m=\sqrt{\left(x^2+y^2\right?}[/tex]Thus, we have:
[tex]\begin{gathered} m=\sqrt{\left(-18^2+-26^2\right?} \\ \\ m=\sqrt{324+676} \\ \\ m=\sqrt{1000} \\ \\ m=\sqrt{10\ast10^2} \\ \\ m=10\sqrt{10} \end{gathered}[/tex]Therefore, the magnitude of the vector is:
[tex]10\sqrt{10}[/tex]ANSWER:
Part A. <-18, -26>
Part B. 10√10
A train leaves a station and travels north at a speed of 175 km/h. Two hours later, a second train leaves on a parallel track and travels north at 225 km/h. How far from the station will theymeet?The trains will meet (?) away from the station(Type an integer or a decimal.)
Given,
The speed of first train is 175km/h.
The speed of second train is 225 km/h.
Consider, the time taken by first train to meet is x h.
The time taken by the second train to meet is (x-2) h.
The distance is calculated as,
[tex]\text{Distance}=\text{speed}\times time[/tex]At the meeting point the distance covered by both train is same,
So, taking the distance equation of both trains in equal,
[tex]\begin{gathered} 175\times x=225\times(x-2) \\ 175x=225x-450 \\ -50x=-450 \\ x=9 \end{gathered}[/tex]The first train meet to second train after distance,
[tex]d=175\times9=1575\text{km}[/tex]The second train meet to first train after distance,
[tex]d=225\times(9-2)=1575\text{ km}[/tex]Hence, both train meet after 1575 km from the station.
You have a pizza with a diameter of 6 1/3 in., and a square box that is 6.38 in. Is the box big enough to fit the pizza inside?
Pizza diameter D is given in mixed form:
[tex]\begin{gathered} D=6\frac{1}{3}\text{ in} \\ in\text{ fraction form:} \\ D=\frac{19}{3}\text{ in} \\ In\text{ decimals, } \\ D=6.33\text{ in} \end{gathered}[/tex]Now, me must compare D with the lenght of the square box.
Since the lenght of the box is L=6.38 in. Hence, the box is big enough to
fit the pizza.
[tex]\begin{gathered} \\ \\ \\ \end{gathered}[/tex]The longest at an airport has the shape of a rectangle and an area of 2,181,600 this runaway is 180 feet wide how long is the runaway
The longest at an airport has the shape of a rectangle and an area of 2,181,600 this runaway is 180 feet wide how long is the runaway
Remember that
The area ofa rectangle is equal to
A=L*W
in this problem we have
A=2,181,600 ft2
W=180 ft
substitute given values
2,181,600=L*180
Solve for L
L=2,181,600/180
L=12,120 ftA true-false test contains 10 questions. In how many different ways can this test be completed?(Assume we don't care about our scores.)This test can be completed indifferent ways.
Explanation:
The test contains 10 questions, each one can be answered either with 'true' or with 'false' which means that for each question there are only 2 options.
We need to find the number of ways in which the test can be completed.
To answer the question we use the fundamental counting principle:
In this case, there are 2 ways to complete each question, therefore, we multiply that by the 10 questions that we have:
[tex]2\times2\times2\times2\times2\times2\times2\times2\times2\times2[/tex]This can be simplified to
[tex]2^{10}[/tex]which is equal to:
[tex]2^{10}=\boxed{1024}[/tex]Answer:
1024
Which graph represents the solution set of the
inequality 4x>-8?
Answer:
The answer is C.
Step-by-step explanation:
In order to solve this, you must use an inequality from one side of the equation.
Inequality is the growing inequality between rich and poor.
4x>-8First thing you do is divide by 4 from both sides.
[tex]\sf{\dfrac{4x}{4} > \dfrac{-8}{4}}[/tex]
Solve.
Divide these numbers goes from left to right.
-8/4=-2
[tex]\boxed{\sf{x > -2}}[/tex]
Therefore, the graph represents the solution set of the inequality of 4x>-8 is C, which is our answer.
I hope this helps, let me know if you have any questions.
The data below show the number of hits on a website per week over a random sample of five weeks. Compute the followingstatistics.
We have a sample that is:
[tex]115,39,160,240,176[/tex]a) We can find the median by first sorting the sample:
[tex]39,115,160,176,240[/tex]The median is the value that has 50% of the values below its values.
In this case, this value is in the third place of the sorted sample and has a value of 160.
b) We have to find the mean.
We can calculate it as:
[tex]\begin{gathered} \bar{x}=\frac{1}{n}\sum_{n\mathop{=}1}^5x_i \\ \\ \bar{x}=\frac{1}{5}(115+39+160+240+176) \\ \\ \bar{x}=\frac{1}{5}(730) \\ \\ \bar{x}=146 \end{gathered}[/tex]c) We have to calculate the variance. To find its value we will use the mean value we have just calculated:
[tex]\begin{gathered} s^2=\frac{1}{n}\sum_{n\mathop{=}1}^5(x_i-\bar{x})^2 \\ \\ s^2=\frac{1}{5}[(115-146)^2+(39-146)^2+(160-146)^2+(240-146)^2+(176-146)^2] \\ \\ s^2=\frac{1}{5}[(-31)^2+(-107)^2+(14)^2+(94)^2+(30)^2] \\ \\ s^2=\frac{1}{5}(961+11449+196+8836+900) \\ \\ s^2=\frac{1}{5}(22342) \\ \\ s^2=4468.4 \end{gathered}[/tex]d) We have to calculate the standard deviation. As we have already calculated the variance, we can calculate it as:
[tex]\begin{gathered} s=\sqrt{s^2} \\ s=\sqrt{4468.4} \\ s\approx66.85 \end{gathered}[/tex]e) We now have to find the coefficient of variation:
[tex]CV=\frac{s}{\bar{x}}=\frac{66.85}{146}\approx0.457876\cdot100\%\approx46\%[/tex]Answer:
a) 160
b) 146
c) 4468.4
d) 66.85
e) 46%