The maximum number of boxes that will fit inside the trailer according to the available volume is 540.
A semi-trailer is being packed with boxes. The side length of each box is 1.5 feet. The cargo space of the trailer is 28 feet in length, 8.5 feet wide and 9.167 feet high. Let the number of boxes that can fit according to the length, width, and height of the trailer be x, y, and z. The values of x, y, and z are the greatest whole numbers less than or equal to the ratio of the length, width, and height of the trailer to the length, width, and height of the box, respectively. The first inequality is x ≤ 28/1.5 ≤ 18.67, so the value of x is 18. The second inequality is y ≤ 8.5/1.5 ≤ 5.67, so the value of y is 5. The third inequality is z ≤ 9.167/1.5 ≤ 6.11, so the value of z is 6. The total number of boxes is the product of the three variables.
P = x*y*z = 18*5*6 = 540
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Answer these two questions
For PART A: the height of the pole in the right angle triangle is 30 ft and the correct option is C
For PART B: the lenght of wire 1 in the right angle triangle is 45 ft and the right option is D
What is a right angle triangle?A right-angled triangle is a polygon of three sides having one angle as 90 degrees(right angle).
Part A
To calculate the height of the pole in the right angle triangle, we use the formula below.
Formula:
tan∅ = opposite/adjacentFrom the diagram,
Given:
∅ = 41°Opposite = Height of the pole = PAdjacent = 34 ftSubstitute these values into equation 1 and solve for P
tan41° = P/34P = 34×tan41°P = 29.55P ≈ 30 ftPart B
Similarly, fine the length of wire 1, we use the formula below.
Formula:
cos∅ = Adjacent/Hypotenus.......... Equation 2From the diagram,
Given:
Hypotenus = Wire 1 = x∅ = 41°Adjacent = 34 ftSubstitute these values into equation 2 and solve for x
cos41° = 34/xx = 34/cos41°x = 45.05x ≈ 45 ftHence, the height of the pole is 30 ft and the lenght of wire 1 is 45 ft.
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Please i need your help! What is the slope of each line segment of QRS
Answer:ez 90 degrees
Step-by-step explanation:
Graph the linear inequality & find the coordinates 2x-y<2
Answer:
(1,0) (0,-2)
Step-by-step explanation:
The table compares the time at which Layne got on the bus to school (in minutes after 8am) and the duration of the ride(in minutes after 8 am) and the duration of the ride(in minutes), for several days.Can the duration of the ride be represented as a function of the time layne got on the bus?
ANSWER
Yes, it can.
EXPLANATION
First of all, let us sort the data according to increasing value:
Time (minutes) 18 20 20 22 22 23 25 30
Duration (minutes) 38 40 42 41 42 44 47 52
As we can already see, the duration of the ride seems to increase as the amount of time after 8 am that she got on the bus.
This means that the Duration of the ride and the time Layne got on the bus have a linear relationship and so, YES, the duration of the ride can be represented as a function of the time Layne got on the bus.
solve the system of equations by the addition method3x - 7y = 45x - 5y = 4
Kevin needs to have a toilet Kevin needs to have a toilet repaired in his house. The cost of the new plumbing fixtures is $160 and the labor is $50/hr.(a) Write a model that represents the cost of the repair C (in $) in terms of the number of hours of labor x.
Given that:
Cost of the new plumbing fixtures = $160
Labor charge per hour = $50
Let x denotes the number of hours of labor. Then,
[tex]\begin{gathered} \text{Cost of repair = Cost of the new plumbing fixtures+Labor charge per } \\ \text{hour}\cdot Number\text{ of hours of labor} \\ C=160+50x \end{gathered}[/tex]It represents the required relation.
help fast!
make up a word problem that can be represented with y=3.5x
The equation can be used for "the total cost of buying x chocolate bars, such that each one costs $3.50"
How to make a word problem that can be represented by that equation?Here we have the linear equation:
y = 3.5*x
And we want to make a word problem that can be represented by this.
The simplest example would be something like "the total cost of buying x items of a cost equal to the constant of proportionality"
So let's suppose that there is a chocolate bar in a given store that costs $3.50 per unit.
So, if you buy x of these, the total cost will be modeled (in dollars) by the equation:
y = 3.50*x
Which is the same equation that we have above:
y = 3.5*x
Where the second 0 on the constant factor is trivial and can not be written.
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Use the future value formula to find the indicated value.FV = $3648, n = 22; i = 0.08; PMT = ?PMT =?(Round to the nearest cent.)
To calculate the periodic payment (PMT) we use the following formula:
[tex]\text{PMT}=\frac{FV\times i}{(1+i)^n-1}[/tex]Where "FV" is the Future Value, "i" is the interest rate, and "n" is the number of periods. Replacing the known values we get:
[tex]\text{PMT}=\frac{3648\times0.08}{(1+0.08)^{22}-1}[/tex]Solving the operations:
[tex]\text{PMT}=52.68[/tex]PLEASE I NEED HELP RIGHT AWAY
What is the equation in point-slope form of the line that passes through the points (7, 5) and (−4, −1) ?
Responses
y+4=11/6(x+1)
=
y+1=6/11(x+4)
y−1=6/11(x−4)
y+1=6/7(x+4)
y+1=6/11(x+4) is the equation in point-slope form of the line that passes through the points (7, 5) and (−4, −1).
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The given two points are (7, 5) and (−4, −1)
m=-1-5/-4-7
=-6/-11
=6/11
The point slope intercept form is y- y₁=m(x-x₁) through (-4,-1)
y-(-1)=6/11(x-(-4))
y+1=6/11(x+4)
Hence, y+1=6/11(x+4) is the equation in point-slope form of the line that passes through the points (7, 5) and (−4, −1).
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Which of the following graphs is described by the function given below?
y=x²-4x-12
A. Graph A
B. Graph B
C. Graph C
D. Graph D
B. graph B
Represents the quadratic equation y=x²-4x-12 with D > 0 . So the equation represents 2 zeros which comes to be 6 and -2.
What is Quadratic equation ??
A second-degree polynomial equation, which must contain at least one squared component, is what is known as a quadratic. Quadratic equations is another name for them. The quadratic equation's general form is as follows:
ax + by +c = 0
How to draw Graph of Quadratic equation ?
To draw the graph of quadratic equation:
First find the minima of the graph Then, calculate the zeros.Finally plot it and draw the graph.Given quadratic equation,
x²-4x-12 = y
Put y = 0
So we get zeros as 6 and -2
Hence the graph will cut the X axis at 6 and -2
We get the desired graph as graph B.
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based on historical data, your manager believes that 35% of the company's orders come from first-time customers. a random sample of 62 orders will be used to estimate the proportion of first-time-customers. what is the probability that the sample proportion is less than 0.28?
The probability of the company's order from first-time customers with the sample proportion less than 0.28 will be 0.6103.
Total percent of company’s orders from first-time customers are 35%
Probability of the company's orders from first-time customers are 35/100 = 0.35.
Total number of customers in the random sample is 62.
Minimum given probability of company’s order from first time customers is 0.28
And the minimum probability of company’s order not from first time customers will be 1 - 0.28 = 0.72
Therefore,
As per the given question, Let P(z<0.28) is the required probability, where
Z = (0.28 - 0.35)/sqrt(0.28x0.72/62)
= (0.28 - 0.35)/sqrt(0.28x0.0112)
=(0.28 - 0.35)sqrt(0.003250)
= (-0.07)/sqrt(0.003250)
= -0.07/0.057
= -1.228
From the z-score, we can get P( z<0.28 ) = 0.6103 ( From standard normal table )
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What is the value of x? 50 points
Answer:
x=25
vertical angles are congruent so
4x-25=75
+25
4x=100
÷4
x=25
Answer:
x = 25°
Step-by-step explanation:
We know that,
→ opposite angles are equal.
Forming the equation,
→ (4x - 25)° = 75°
Now the value of x will be,
→ (4x - 25)° = 75°
→ 4x = 75° + 25°
→ x = 100°/4
→ [ x = 25° ]
Hence, the value of x is 25°.
Find the area of the polygon. (hint: you need to solve for missing apothem or sides).Also round the area to the nearest whole number
Solution
The hexagon given is a regular hexagon. With apothem of 15 in
Area of a hexagon =
[tex]\begin{gathered} =\frac{1}{2}\times a\times P \\ \text{where a = apothem} \\ p=\text{perimeter of the hexagon} \end{gathered}[/tex]Let us calculate the perimeter of the hexagon
From the triangle above,
[tex]\begin{gathered} \text{tan 60=}\frac{15}{x} \\ x\text{ tan 60 = 15} \\ x=\frac{15}{\tan 60} \\ x=5\sqrt[]{3} \end{gathered}[/tex][tex]\text{The side length of the hexagon = 2x = 2(5}\sqrt[]{3})\text{ = 10}\sqrt[]{3}\text{ in}[/tex][tex]\text{The perimeter of the hexagon = 6 x 10}\sqrt[]{3}\text{ = 60}\sqrt[]{3}\text{ in}[/tex][tex]\begin{gathered} \text{Area of the hexagon = }\frac{1}{2}\times a\times P \\ =\frac{1}{2}\text{ x 15 x 60}\sqrt[]{3} \\ =779.42in^2 \\ \\ Hence,\text{ the area of the polygon is }779in^2\text{ (to nearest wholw number)} \end{gathered}[/tex]Rewrite the following rectangular equation in polar form assuming a is a real constant.x2 + y2 = 11a=
Answer:
The polar form is
r = √11a
Explanation:
The given equation is
x^2 + y^2 = 11a
Recall,
x = rcosθ
y = rsinθ
By substituting these values into the equation, we have
(rcosθ )^2 + ( rsinθ)^2 = 11a
r^2cos^2θ + r^2sin^2θ = 11a
r^2cos^2θ + r^2sin^2θ - 11a = 0
By factorizing r^2, we have
r^2(cos^2θ + sin^2θ) = 11a
Recall, cos^2θ + sin^2θ = 1
Thus, we have
r^2 = 11a
Taking the square root of both sides,
r = √11a
The polar form is
r = √11a
help meeeeeeeeeeeeeee pleaseeeeeee
Answer: 9.7 seconds
Step-by-step explanation:
[tex]16t^2 =1503\\\\t^2 =1503/16\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]
Graph the line by locating ant tow order of pairs
start by writing the equation in standard form
[tex]-x+2y=0[/tex][tex]\begin{gathered} 2y=x \\ y=\frac{x}{2} \end{gathered}[/tex]then give values to x
for x=2
[tex]\begin{gathered} y=\frac{2}{2} \\ y=1 \\ A\colon(2,1) \end{gathered}[/tex]for x=4
[tex]\begin{gathered} y=\frac{4}{2} \\ y=2 \\ B\colon(4,2) \end{gathered}[/tex]In 2005, 10.9 out of every 50 employees at a company were women. If there are 41,646 total company employees, estimate the number of women.
Number of women's are 9,078.83.
What is Proportional?
Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
In 2005, 10.9 out of every 50 employees at a company were women.
Now,
Since, In 2005, 10.9 out of every 50 employees at a company were women.
Let number of women's in 41,646 total company employees = x
So, We can formulate by the definition of proportion as;
⇒ 10.9 / 50 = x / 41,646
Solve for x as;
⇒ 10.9 × 41,646 / 50 = x
⇒ x = 9,078.83
Thus, Number of women's are 9,078.83.
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Milo can run 12 miles in 60 minutes. He needs to reduce his time by 19%. Approximately how many minutes does he have to take off his time? Round to the nearest whole number.
Milo needs to cover 12 miles in 48.6 minutes, as the percentage.
What is percentage?
A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.
Milo can run 12 miles in 60 minutes.
She needs to reduce the time by 19%
So we have to calculate the 19%of 60
= 19/100* 60
=57/5 minutes
= 11.4
So the time he needs to achieve will be 60-11.4 = 48.6 minutes.
Hence, he needs to cover 12 miles in 48.6 minutes.
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Lines AB and CD are straight lines. Find x and y. Picture attached/
By using properties of angles, it is obtained that
x = 18.5°, y = 37°
Angle
When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle.
Here,
[tex]\angle COF = 90^{\circ}\\[/tex]
By the problem,
4x + 90 + 16 = 180 [Angle on a straight line]
4x + 106 = 180
4x = 180 - 106
4x = 74
[tex]\\x = \frac{74}{4}\\x = 18.5^{\circ}[/tex]
AB and CD are straight lines
[tex]\angle DOB = 16^{\circ}[/tex] [Vertically opposite angle]
By the problem,
90 + 2y + 16 = 180 [ Angle on a straight line]
2y + 106 = 180
2y = 180 - 106
2y = 74
[tex]y = \frac{74}{2}\\y = 37^{\circ}[/tex]
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Annie wants to arrange several plates of fruit so that each plate
has the same number of apples and the same number of apricots.
What is the greatest number of plates Annie can arrange if she
plans to use 8 apples and 20 apricots? How many apples and
how many apricots will be on each plate?
The greatest number of plates Annie can arrange if she plans to use 8 apples and 20 apricots is 4 plates.
The number of apples Annie can arrange on each plate is 2The number of apricots Annie can arrange on each plates is 5What is the greatest number of plates Annie can arrange?Number of apples = 8Number of apricots = 20To find the greatest number of plates Annie can arrange, find the greatest common factor of and 20;
8 = 1, 2, 4, and 8
20 = 1, 2, 4, 5, 10, and 20
The greatest common factor of 8 and 20 is 4
Number of apples on each plate = 8/4
= 2
Number of apricots on each plate = 20/4
= 5
In conclusion, the greatest number of plates is 4 consisting of 2 apples and 5 apricots each.
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Answer:
Step-by-step explanation:
i am also confused with this one so...
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In ️FGH, f=65 inches, g=48 inches and h=70 inches. find the measure of
Let's take a look at our triangle:
Using the law of cosines, we'll get that:
[tex]G^2=F^2+H^2-2FH\cos \angle G[/tex]Solving for angle G, we'll get:
[tex]\begin{gathered} G^2=F^2+H^2-2FH\cos \angle G \\ \rightarrow2FH\cos \angle G^{}=F^2+H^2-G^2 \\ \rightarrow\cos \angle G=\frac{F^2+H^2-G^2}{2FH} \\ \\ \rightarrow\angle G=\cos ^{-1}\frac{F^2+H^2-G^2}{2FH} \end{gathered}[/tex]This way,
[tex]\begin{gathered} \angle G=\cos ^{-1}\frac{65^2+70^2-48^2}{2(65)(70)} \\ \\ \Rightarrow\angle G=41 \end{gathered}[/tex]Mr. Jones bought 2 and 1/7 lb. of salmon. He cooked 1/5 of it for lunch. How much salmon did he have left over?
Answer:
[tex]1\frac{5}{7}\text{ lb}[/tex]
Step-by-step explanation:
First, convert [tex]2\frac{1}{7}\text{ lb}[/tex] to an improper fraction (to make the math easier):
[tex]2\frac{1}{7}=\frac{15}{7}\text{ lb}[/tex]
Next, since the question asks about how much salmon is left over, find that fraction. After cooking one-fifth of the salmon, four-fifths remain:
[tex]\frac{5}{5}-\frac{1}{5}=\frac{4}{5}[/tex]
Then, multiply the two:
[tex]\frac{15}{7}\times\frac{4}{5}=\frac{60}{35}\text{ lb}[/tex]
Finally, convert back to a mixed fraction:
[tex]\frac{60}{35}\text{ lb}=1\frac{25}{35}\text{ lb}=1\frac{5}{7}\text{ lb}[/tex]
2. Identify the vertex from the quadratic function y=-5(x-6)^2+8 *
The given function is
[tex]y=-5(x-6)^2+8[/tex]This equation represents a parabola which is expressed in its vertex form
[tex]y=a(x-h)^2+k[/tex]Where (h,k) is the vertex. Using this rule, the vertex of the given parabola would be (6,8).
Therefore, the answer is (6,8).Enter your answer and show all the steps that you use to solve this problem in the space provided. Convert the map scale to a unit rate. How many inches represent one mile? Show your work. Interpret the meaning of the unit rate. 3/ 10 in . = 7 /8 mi . please fast i dont have much time
The map, every 1-inch drawing represents 2.917 miles in reality, using conversation.
What is conversation ?
A unit's use depends on the context; for example, a room's area is expressed in metres, yet a pencil's length and thickness are expressed in centimetres and millimetres, respectively.
Therefore, converting one unit to another is necessary. We must first understand the link between units in order to comprehend the concept of unit conversion.
When addressing many problems in mathematics, unit conversion is necessary. Mathematical conversions are necessary to perform the necessary calculations.
In the map, every 1 inch drawing represents 2.917 miles in reality.
the meaning of the unit rate. 3/ 10 in. = 7 /8 mi
1 in = (7/8) mi ÷ (3/10)
= 7/8 * (10/3) = 70/24
1 in = (70/24) mi
Hence the map, every 1-inch drawing represents 2.917 miles in reality.
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Order from least to greatest. -0.36, 0.65 , - 8/15, 1/5
Step-by-step explanation:
Order from least to greatest. -0.36, 0.65 , - 8/15, 1/5
-0.36 = -0.36
0.65 = 0.65
- 8/15 = - 0.533333
1/5 = 0.2
least to greatest:
- 8/15 , -0.36 , 1/5 , 0.65
Together, the areas of the rectangles sum to 30 square centimeters.
Solution
Area of the rectangle = length x breadth
A. Write an equation to showing relationship between x and y:
[tex]\begin{gathered} \text{Area = length x breadth} \\ A=l\text{ x b} \\ A_1=3x \\ A_2=2y \end{gathered}[/tex][tex]\begin{gathered} A_1+A_2=30_{} \\ 3x+2y=30 \end{gathered}[/tex]The equation for the relationship between x and y is
3x + 2y = 30
A person is riding a 14 kg bike at velocity of 18m/s. The mass of the person is 60kg. What is the momentum of the person and the bike?
The momentum of the person is zero and the momentum of the bike is 1332.
A person is riding a 14 kg bike at velocity of 18m/s
The momentum of bike = mass x velocity
p = (14 + 60) 18
= 1332
The velocity of the person with respect to the bike is 0
p = mv
p = 60 x 0
p = 0
Therefore, the momentum of the person is zero and the momentum of the bike is 1332.
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Write each equation in slope intercept form.
12x + 4y = 8
This is a way we can organize a linear equation:
[tex]y=mx+b[/tex]
m = slopeb = y-interceptSolving the QuestionWe're given:
[tex]12x + 4y = 8[/tex]
To organize this equation in slope-intercept form, we have to focus on isolating y:
[tex]12x + 4y = 8\\4y = - 12x +8\\y = - 3x +2[/tex]
Answer[tex]y = - 3x +2[/tex]
The answer is y= negative 3 plus 2
Lucy needs to memorize words on a vocabulary list for Korean class. She has memorized 20 of the words, which is four-fifths of the list. How many words are on the list?
Given:
Lucy needs to memorize words on a vocabulary list for Korean class.
Let the number of words on the list = x
She has memorized 20 of the words, which is four-fifths of the list.
So, we can write the following equation:
[tex]\frac{4}{5}x=20[/tex]Solve the equation for (x), multiply both sides by 5/4
[tex]\begin{gathered} \frac{5}{4}*\frac{4}{5}x=\frac{5}{4}*20 \\ \\ x=\frac{100}{4}=25 \end{gathered}[/tex]So, the answer will be:
The number of words on the list = 25
Justin deposited $4000 into an account with 5.5% interest, compounded semiannually. Assuming that no withdrawals are made, how much will he have inthe account after 10 years?Do not round any intermediate computations, and round your answer to the nearest cent.
First, divide the annual interest rate by 2 to find the semiannual interest rate:
[tex]\frac{5.5}{2}=2.75[/tex]Next, identify the number of periods when the 2.75% increase will be appliad. In a period of 10 years, there are 20 semiannual periods.
Each period, the initial investment gets multiplied by a factor of:
[tex]1+\frac{2.75}{100}=1+0.0275=1.0275[/tex]Over 20 semiannual periods, the initial investment will get multiplied by a factor of:
[tex]1.0275^{20}[/tex]Therefore, after 10 years, the amount of money in the account is:
[tex]\begin{gathered} 4000\times(1.0275)^{20}=4000\times1.7204\ldots \\ =6881.7137\ldots \end{gathered}[/tex]To the nearest cent, the amount of money in the account will be:
[tex]6881.71[/tex]