a) The percentage of buyers that paid between $18,000 and $26,000 is; 95%
b) The middle 99.7% of car costs are between $16000 and $28000
c) The probability a car will cost less than $24,000 is; 68%
d) The probability a car will cost more than $26,000 is; 2.5%
How to use the empirical rule of statistics?The empirical rule of statistics states that 68% of data will be ± 1 standard deviations from the mean, 95% of data will be ± 2 standard deviations of the mean, and 99.7% of data will be ± 3 standard deviations from the mean.
a) We are given;
Mean; μ = $22000
Standard deviation; σ = $2000
$18,000 and $26,000 are both 2 standard deviations from the mean and so, the percentage of buyers is 95%.
b) Since the middle 99.7% of car costs, this is simply 3 standard deviations from the mean and as such it is between the values;
22000 - 3(2000) = $16000 and 22000 + 3(2000) = $28000
c) $24,000 is 1 standard deviation away from the mean and as such the probability will be 68% from empirical rule.
d) $26000 is 2 standard deviations from the mean and as such probability that a car will cost more than that is;
(100% - 95%)/2 = 5%/2 = 2.5%
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A train travels for 3.75 hours at 80 miles an hour. Use the formula d = r. t, where
d = distance, r = rate, and t = time, to find the distance the train traveled.
The distance traveled is
miles.
The solution is
Distance travelled is 300 miles
What is distance ?The total movement of an object, independent of direction, is its distance. The amount of space that an object has traveled, regardless of where it started or ended, is referred to as distance.
According to the given information
You know the equation: D = r × t.
where D represents the distance traveled, r is the train's speed, and t denotes the amount of time (in hours) required.
Train travels for 3.75 hours at 80 miles per hour
By putting the values in the above equation
D = 80 miles in 3.75 hours per hour
= 80 × 3.75
= 300 miles
Distance travelled is 300 miles
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A small box measures 6in by 11in by 13 in high. Find the volume of the box.
The volume of the box is 858 cube inches.
What is a cuboid?A cuboid is a three-dimensional solid shape that has 6 faces, 8 vertices, and 12 edges. It is one of the most commonly seen shapes around us which has three dimensions: length, width, and height
length of box = 13 inches
Width of box = 11 inches
height of box = 6 inches
Volume of cuboid = length x width x height
volume of cuboid = 13 x 11 x 6 which is 858 cube inches
In conclusion the volume of the box is 858 cube inches
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Income taxes that are withheld from employees' pay and not remitted as of the balance sheet date will constituted a ____________ to be verified by the auditors.
Income taxes that are withheld from employees' pay and not remitted as of the balance sheet date will constituted a liability to be verified by the auditors.
A tax placed on people or organizations in relation to their income or profits is known as an income tax. Tax rates multiplied by taxable income are typically used to calculate income taxes.
Tax rates might change depending on the taxpayer's attributes and source of income. As taxable income rises, the tax rate can also. Corporate tax, which is often assessed at a fixed rate, is the name given to the tax charged on businesses. Individual income is frequently subject to progressive taxation.
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HELP?!!? You’ve been hired to help a car company with analyzing sale trends to help them with figuring out what direction development of new products should go. Due to rising fuel costs the industry is seeing a rise in people purchasing compact cars, but the kind of features and thus price people are targeting is less clear.
Based on your initial analysis the average cost of a compact car over the last 10 years has ranged from $12,000 to $28,000. Your job is to assist your team with plotting this data on a graph to help your team with visualizing potential trends in the data. The years will be on the x-axis and the cost will be on the y-axis.
(a) What is a good maximum and minimum value along the y-axis that would be a good fit for your data on this graph? Explain your reasoning.
(b) What is a good distance between the marks along the y-axis on the graph to ensure that you have appropriate resolution for your data set? Explain your reasoning. Too few means you can’t reasonably read the data, too many will make your graph too cluttered.
(c) What is a good maximum and minimum value along the x-axis which would be a good fit for your data on this graph? Explain your reasoning.
(d) What is a good distance between the marks along the x-axis on the graph to ensure that you have appropriate resolution for your data set? Explain your reasoning. Too few means you can’t reasonably read the data, too many will make your graph too cluttered.
Write an equation of the line that passes through the given points.
(−7,0),(−7,5)
The given points form an equation for a line that has a value of 14.
How do you determine the equation of a line that goes through two points?Utilize the slope formula to determine the slope. To determine the y-intercept, use the slope and one of the points (b). Once you are aware of the values for m and b, you can enter these values into the slope-intercept form of a line (y = mx + b) to obtain the equation for the line.The equation that depicts the line that crosses the coordinates (-7 , 0) and (-7, 5).A line's equation is y=mx+c. Since you have two points, you may use the formula m=y2y1x2x1 to determine the slope.Explanation:
m =( -5 - -7)(0 - -7)
= 2*7
= 14.
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At noon, ship A is 10 nautical miles due west of ship B. Ship A is sailing west at 16 knots and ship B is sailing north at 21 knots. How fast (in knots) is the distance between the ships changing at 4 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)
At [tex]$5 \mathrm{pm}$[/tex] the distance between the ships is changing at the speed of [tex]$\mathbf{3 0 . 2 1}$[/tex] knots
Firstly we need to an equation to represent both ships and the distance between each. A is moving [tex]$25 \mathrm{knots}$[/tex] west and [tex]$B$[/tex] is moving [tex]$17 \mathrm{knot}$[/tex] north. [tex]$D$[/tex]will be the distance between the two. Drawing it, you'll notice that it creates a right triangle.
So we use the Pythagorean Theorem:
[tex]$$D^{\wedge} 2=A^{\wedge} 2+B^{\wedge} 2$$[/tex]
Differentiate in relation to time:
[tex]$$2 \mathrm{D}(\mathrm{dD} / \mathrm{dt})=2 \mathrm{~A}(\mathrm{dA} / \mathrm{dt})+2 \mathrm{~B}(\mathrm{~dB} / \mathrm{dt})$$[/tex]
Now we must find all of our variables.
[tex]& A=\text { time(speed })+\text { original distance }=5(25)+10=135 \\[/tex]
[tex]& B=5(17)+0=85 \\[/tex]
[tex]& D=V\left(A^{\wedge} 2+B^{\wedge} 2\right)=159.53 \\[/tex]
[tex]& d A / d t=25 \\[/tex]
[tex]& d B / d t=17[/tex]
Plug in all your variables and solve for
[tex]$(\mathrm{dD} / \mathrm{dt})$ :[/tex]
[tex]& 2 \mathrm{D}(\mathrm{dD} / \mathrm{dt})=2 \mathrm{~A}(\mathrm{dA} / \mathrm{dt})+2 \mathrm{~B}(\mathrm{~dB} / \mathrm{dt}) \\[/tex]
[tex]& 2(159.53)(\mathrm{dD} / \mathrm{dt})=2(135)(25)+2(85)(17) \\[/tex]
[tex]& 319.061(\mathrm{dD} / \mathrm{dt})=9640 \\[/tex]
[tex]& \mathrm{dD} / \mathrm{dt}=9640 / 319.061 \\[/tex]
[tex]& \mathrm{dD} / \mathrm{dt}=30.21 \text { knots }\end{aligned}[/tex]
At [tex]$5 \mathrm{pm}$[/tex] the distance between the ships is changing at the speed of [tex]$\mathbf{3 0 . 2 1}$[/tex] knots
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Solve
3 x+10=14 y
8 x-7 y=34
Answer:
x = 6, y = 2
Step-by-step explanation:
Solve for the first variable in one of the equations, then substitute the result into the other equation.
suppose a researcher finds that the p-value of a test statistics is 0.08. which of the following significance levels gives you a chance of finding a statistically significant result? -0,01 -0,001 -0,1 -0,05
the best chance of finding a statistically significant result would be 0.1. This is because the p-value of 0.08 is less than the significance level of 0.1, but greater than the significance levels of 0.01, 0.001, and 0.05
The p-value of a test statistic is a measure of the probability of obtaining a result that is at least as extreme as the one observed, given that the null hypothesis is true. In other words, it is a measure of the strength of the evidence against the null hypothesis.
If the p-value of a test statistic is 0.08, it means that there is an 8% chance of obtaining a result at least as extreme as the one observed, given that the null hypothesis is true. This does not necessarily mean that the result is statistically significant at any particular significance level.
To determine whether a result is statistically significant, you need to compare the p-value to a predetermined significance level, also known as the alpha level. The alpha level is the probability of rejecting the null hypothesis when it is actually true (also known as a type I error).
If the p-value is less than the alpha level, then the result is considered statistically significant. For example, if the alpha level is set at 0.05, and the p-value of the test statistic is 0.03, then the result would be considered statistically significant.
In the case of the options you provided, the significance level that gives you the best chance of finding a statistically significant result would be 0.1. This is because the p-value of 0.08 is less than the significance level of 0.1, but greater than the significance levels of 0.01, 0.001, and 0.05.
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. If F F G H text is a rhombus, find each missing value
J G=
F J=
m ∠ E F H=
m ∠H G E=
2. If J K Z If is a square, find each missing value
J L=
M A=
m ∠ R N L=
R∠ M E U=
The value of JG = 24,
FJ = 7,
∠EFH = 74°,
∠HGE = 16°
What are the properties of a diagonal of rhombus?
In a rhombus, diagonals bisect each other at right angles. Diagonals bisect the angles of a rhombus. The sum of two adjacent angles is equal to 180 degrees. You will get a rectangle when you join the midpoint of the sides.
Solution:
Given :
EJ = 24
∴ GJ = 24
∠FHG = 74°
∴ ∠EFH = 74° by alternate angle properties
Now, we know
FG² =FJ² + GJ² - 2FJ × GJ × cos(90) ------ diagonals of the rhombus are perpendicular to each other
Substitute FG = 25, GJ = 24, we get
25² = FJ² + 24² - 2FJ × GJ × cos(90)
FJ² = 49
∴FJ = 7
180 =∠GHJ +∠HGJ + ∠GJH ------ sum of all angles of a triangle is 180°
∴ ∠HGE = ∠HGJ = 180 - 90 - 74
∴ ∠HGE = 16°
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2. The value of JL = 14
ML = 7√2
∠KNL = 90°
∠MKJ = 45°
What are the properties of diagonals of a square?
The diagonals of the square bisect each other at 90°.The two diagonals of the square are equal to each other. The diagonal of the square divide it into two similar isosceles triangles.
Solution:
Given; NM = 7
We know that diagonals of the square are equal
∴ NM = NL = NK = NJ = 7
∵ JL = JN + NL
∴ JL = 7 + 7
∴JL = 14
∠KNL = 90° ----- as we know that diagonals bisect each other at 90°
For ∠MKJ
we know that KM = KN + NM = 14
KJ = JM = 7√2------- property of isosceles triangle
∠KJM = 90° ----- all angles of square are 90°
We know that diagonals of a square dissects the square into two equal isosceles triangle.
∴ ∠MKJ = JMK = ∠KJM/2
∴ ∠MKJ = 90/2
∴ ∠MKJ = 45°
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The value of JG = 24 , FJ = 7, ∠EFH = 74°, ∠HGE = 16°
What are the properties of a diagonal of rhombus?
In a rhombus, diagonals bisect each other at right angles. Diagonals bisect the angles of a rhombus. The sum of two adjacent angles is equal to 180 degrees. You will get a rectangle when you join the midpoint of the sides.
Given :
EJ = 24
∴ GJ = 24
∠FHG = 74°
∴ ∠EFH = 74° by alternate angle properties
Now, we know
FG² =FJ² + GJ² - 2FJ × GJ × cos(90) ------ diagonals of the rhombus are perpendicular to each other
Substitute FG = 25, GJ = 24, we get
25² = FJ² + 24² - 2FJ × GJ × cos(90)
FJ² = 49
∴FJ = 7
180 =∠GHJ +∠HGJ + ∠GJH ------ sum of all angles of a triangle is 180°
∴ ∠HGE = ∠HGJ = 180 - 90 - 74
∴ ∠HGE = 16°
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2. The value of JL = 14
ML = 7√2
∠KNL = 90°
∠MKJ = 45°
What are the properties of diagonals of a square?The diagonals of the square bisect each other at 90°.The two diagonals of the square are equal to each other. The diagonal of the square divide it into two similar isosceles triangles.
Given; NM = 7
We know that diagonals of the square are equal
∴ NM = NL = NK = NJ = 7
∵ JL = JN + NL
∴ JL = 7 + 7
∴JL = 14
∠KNL = 90° ----- as we know that diagonals bisect each other at 90°
For ∠MKJ
we know that KM = KN + NM = 14
KJ = JM = 7√2------- property of isosceles triangle
∠KJM = 90° ----- all angles of square are 90°
We know that diagonals of a square dissects the square into two equal isosceles triangle.
∴ ∠MKJ = JMK = ∠KJM/2
∴ ∠MKJ = 90/2
∴ ∠MKJ = 45°
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pls solve before friday
The result of the given mathematical expression is 8459.46
What is Mathematical expression and decimal
Mathematical expression consist of combination of numbers along with addition, subtraction, multiplication and division.
Decimal numbers are those numbers which have an integer part and a fractional part.
Decimal can be terminating as well as non terminating.
Terminating decimals are those numbers which have finite number of digits after decimal point.
Non terminating decimals are those numbers which have infinite number of digits after decimal point.
Mathematical expression to be solved
[tex]31520 \times 0.029 \times \frac{(1+0.029)^4}{(1+0.029)^4-1}[/tex]
Decimal number is present in the above expression.
The given expression is to be simplified to get a solution
Now,
[tex]31520 \times 0.029 \times \frac{(1+0.029)^4}{(1+0.029)^4-1}\\\\31520 \times 0.029 \times \frac{(1.029)^4}{(1.029)^4-1}\\\\31520 \times 0.029 \times \frac{1.1211442633}{0.1211442633}[/tex]
8459.46
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A large container holds 4.7 gallon of water. Use the following information to convert this amount of water to liters.1 gallon =4 quarts 1L =1.057 quarts
Answer:
Step-by-step explanation:
To convert the amount of water in gallons to liters, we need to first convert the number of gallons to quarts and then convert the number of quarts to liters.We know that 1 gallon is equal to 4 quarts, so 4.7 gallons is equal to 4.7 gallons * 4 quarts/gallon = 4.7*4=18.8 quarts.We also know that 1 liter is equal to 1.057 quarts, so to convert the number of quarts to liters, we can divide the number of quarts by 1.057 quarts/liter: 18.8 quarts / 1.057 quarts/liter = 18.8/1.057=17.8 liters.Therefore, 4.7 gallons is equal to 17.8 liters.
How do you write 5 as a fraction??
Ples answer quick its grading day
Answer:
5/1
Step-by-step explanation:
I think?
PLS HEEEEEEELP For 100 Points!!!!
Ana was washing dishes at the end of her shift at a restaurant. She washed 40 plates from 7:20 to 7:30.
When she finishes washing all the plates, her shift will end.
(a) If she started washing plates at 7:10 and ended at 7:35, estimate how many plates she washed in
total. Explain your reasoning.
(b) Write an equation to represent how many plates Ana has left to wash at a particular time after her
start at 7:10. Explain your reasoning.
Answer:
If Ana started at 7:20, ended at 7:38, and she washes 6 dishes per minute, than she has 108 dishes left to wash.
Step-by-step explanation:
Answer:
Step-by-step explanation:Answer: 138 plates are to be washed by her if she started at 7:15 and ends at 7:38, and the function will be f(x)=6x.
Step-by-step explanation:
Since we have given that
She washed 30 plates from 7:30 to 7:35,
That means in 5 minutes, the number of plates get washed here = 30
We need to find the number of plates from 7:15 to 7:38
First, we count the number of minutes
In 1 minute, the number of plates gets washed by her is given by
In 23 minutes, the number of plates gets washed by her is given by
The equation to represent how many plates Ana has left to wash at a particular time after her start at 7:15 is given by
Hence, 138 plates are to be washed by her if she started at 7:15 and ends at 7:38, and the function will be f(x)=6x.
Need help please:
show that the two quadrilaterals are congruent
The two quadrilaterals JKLQ and LMNP are congruent.
What is congruent quadrilaterals?
You will always have two opposite pairs of parallel sides if the two pairs of opposite sides in a quadrilateral are congruent. They must measure similarly to be considered congruent. Consider this: two congruent sides must always maintain the same separation between the opposing lines to maintain the other pair of opposite sides.
To prove that all corresponding pairs of sides and angles are congruent, you must put the interior angles and sides of one quadrilateral in correspondence with those of another.
For the given quadrilaterals JKLQ and LMNP it is given that,
JK ≅ MN, JQ ≅ NP, QL ≅ PL and KL ≅ ML
Also,
∠J ≅ ∠N, ∠Q ≅ ∠P, ∠K ≅ ∠M, and ∠L is the common for both quadrilaterals.
Here the corresponding sides and angles of the quadrilaterals are congruent.
Hence, the two quadrilaterals JKLQ and LMNP are congruent.
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Graph the compound inequality on the number line
x ≤-6 or x≥6
Answer:
I think like this but I not sure what format you learn
Martin will receive a pay raise of 6%. He currently makes $30 per hour. What will be his new hourly rate?
Answer:
New hourly rate is $31.8-------------------
GivenCurrent rate is $30,Pay raise is 6%,SolutionNew rate is:
$30 + 6% = $30 + $30*6/100 =$30 + $1.8 = $31.8Select the postulate that confirms each statement.
a. Angles GFH and are supplementary angles.
Linear Pair Postulate
Segment Addition Postulate
Vertical Angle Postulate
Angle Addition Postulate
The correct postulate is the Linear Pair postulate. It can be find out by the concept of supplementary angles.
What is supplementary angles?
Two angles are said to be supplementary if their sums total 180 degrees.
Linear Pair postulate: When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°.
Segment Addition Postulate: According to the segment addition postulate, if two points on a line segment, A and C, are given, a third point, B, will only be found on line segment AC if and only if the distances between the points satisfy the conditions of the equation AB + BC = AC. This option is not correct.
Vertical Angles: When two lines intersect each other then the angles made on the opposite sides of the intersection point is known as vertical angles and they give equal measurment. This option is not correct.
Addition Postulate states: The measure of an angle formed by two angles side by side is the sum of the measures of the two angles. This option is not correct.
Hence, the correction postulate is the Linear Pair postulate. It can be find out by the concept of supplementary angles.
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Write an equation for a line passing through points (-2,3) and (3,5)
Answer:
[tex]y=\frac{2}{5}x+\frac{31}{5}[/tex]
Step-by-step explanation:
The slope of the line is [tex]\frac{3-5}{-2-3}=-\frac{2}{5}[/tex].
So, the equation is:
[tex]y-5=-\frac{2}{5}(x-3) \\ \\ y-5=-\frac{2}{5}x+\frac{6}{5} \\ \\ y=\frac{2}{5}x+\frac{31}{5}[/tex]
Which expression is equivalent to √80
4√2·√5
√2⁴.√5
√2.√2.√5
√2².√2².√5²
As we can solve the square root 80 or [tex]\sqrt{80\\}[/tex] = [tex]\sqrt{2^4}.\sqrt{5}[/tex]
so [tex]\sqrt{2^4}.\sqrt{5}[/tex] is the correct answer for square root 80
What is Square root?
The component of a number that, when multiplied by itself, yields the original number is known as the square root of the number. Special exponents include squares and square roots. Think about the number 9. When the number 3 is multiplied by itself, the result is 9. This can be expressed as either 32 or 3 3. We refer to this as a square since there is a 2 exponent. When the exponent is now 1/2, the square root of the integer is being discussed. For instance, when n is a positive integer, n = n1/2
The value of a number's power 1/2 is the number's square root. It is the number whose product by itself yields the original number, to put it another way. It is symbolised by the character "." The number behind the square root sign is referred to as the radicand, whereas the square root symbol itself is known as a radical.
1)
[tex]\sqrt[4]{2} .\sqrt{5}[/tex] =[tex]2^{\frac{1}{4} } .\sqrt{5}[/tex]
which is not equal to [tex]\sqrt{80\\}[/tex]
2)
[tex]\sqrt{2^4}.\sqrt{5}[/tex] = [tex]2^{4.\frac{1}{2} } .\sqrt{5}[/tex]
=[tex]4\sqrt{5}[/tex] or[tex]\sqrt{16 * 5} =\sqrt{80}[/tex]
3)
[tex]\sqrt{2}. \sqrt{2}. \sqrt{5} =2\sqrt{5}[/tex]
which is not equal to [tex]\sqrt{80\\}[/tex]
4)
[tex]\sqrt{2^{2} } .\sqrt{2^{2} } .\sqrt{5^{2} } = 2.2.5 \\\\\4.5 = 20[/tex]
which is not equal to [tex]\sqrt{80\\}[/tex]
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A high - powered model rocket is traveling at 150 mph What is the rockets speed in feet per second ?
Speed of rocket travelling at 150 m/h into feet per second is 0.1367 feet per second
How to covert meter to feet ?3.28084 feet is about equal to one meter. Multiply 3.28084 feet to the given meter value to convert
According to the given information
Speed of rocket in meter per hour is 150 m/h
To know the speed of rocket in feet per second
1 meter = 3.280 feet
15o meter = 150 × 3.280
= 492 feet
1 hour = 60 × 60
= 3600 second
So,
speed of rocket in feet per second = [tex]\frac{492}{3600}[/tex]
= 0.1367 feet per second
Speed of rocket travelling at 150 m/h into feet per second is 0.1367 feet per second
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PLS HURRY A recipe calls for 6 ounces of raisins. How many milligrams of raisins is this? (1 ounce = 28.35 grams and 1 gram = 1,000 milligrams)
170.1 milligrams
1,701 milligrams
17,010 milligrams
170,100 milligrams
Answer:
170,100 milligrams
Step-by-step explanation:
1 ounce = 28.35 grams
6 ounces = ?
6*28.35 = 171.10 grams
1 gram - 1000 milligrams
171.10 grams = ?
171.10*1000 =
171,100 milligrams
Answer:
A recipe calls for 170,100 milligrams of raisins.
Step-by-step explanation:
I took the exam and got it right
A school hockey team was given a budget at the start of
the year. The team used 60% of the money for uniforms,
10% for equipment, and 30% for travel. Which circle
graph shows this information?
The circle which shows the distribution of the money has been attached.
What is a circle?A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.
In our daily life, we always see circular objects for example our bike wheel.
As per the given,
The team used 60% of the money for uniforms,10% for equipment, and 30% for travel.
60% of the area of the circle is used for uniforms.
10% of the area of the circle is used for equipment.
30% of the area of the circle is used for travel.
Hence "The attached circle depicts how the funds were distributed.".
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URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
Answer: b. The radius is the same as a cylinder with a volume of 500(3) and the same height.
Step-by-step explanation:
The volume of a cylinder is 3 times that of a cone (assuming they have the same perpendicular height and radius).
Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
h(p) =
p − 4 /
p^2 + 5
The critical points of the given function are p = 2 ± √13.
What are functions?A relation between a collection of inputs and outputs is known as a function.
A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
Each function has a range, codomain, and domain.
Critical function:
The key points are locations inside the function's domain where the function's nature changes.
The function stops increasing or decreasing at these places.
The function is: [tex]h(p)=\frac{p-2}{p^2+9}[/tex]
The derivative test will be applied here:
[tex]\begin{aligned}& \therefore h^{\prime}(p)=0 \\& \Rightarrow \frac{d}{d p}\left(\frac{p-2}{p^2+9}\right)=0 \\& \Rightarrow \frac{\frac{d}{d p}(p-2)\left(p^2+9\right)-\frac{d}{d p}\left(p^2+9\right)(p-2)}{\left(p^2+9\right)^2}=0 \\& \Rightarrow \frac{1 \cdot\left(p^2+9\right)-2 p(p-2)}{\left(p^2+9\right)^2}=0 \\& \Rightarrow \frac{-p^2+4 p+9}{\left(p^2+9\right)^2}=0 \\& \Rightarrow-p^2+4 p+9=0\end{aligned}[/tex]
Then,
[tex]\begin{aligned}& \Rightarrow p_{1,2}=\frac{-4 \pm \sqrt{4^2-4(-1) 9}}{2(-1)} \\& \Rightarrow p_{1,2}=\frac{-4 \pm \sqrt{52}}{-2} \\& \Rightarrow p_{1,2}=-\frac{-4 \pm \sqrt{52}}{2} \\& \Rightarrow p_{1,2}=-\frac{-4 \pm 2 \sqrt{13}}{2} \\& \Rightarrow p_{1,2}=2 \pm \sqrt{13}\end{aligned}[/tex]
Therefore, the critical points of the given function are p = 2 ± √13.
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Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels 18 miles per hour slower than the westbound train. If the two trains are 320 miles apart after 2 hours, what is the rate of the eastbound train?
Answer:
71 mph
Step-by-step explanation:
Lets call the speed of the eastbound train E and the speed of the westbound train W.
E = W - 18
distance travelled = speed * time
thus
Wt + Et = 320
Wt + (W - 18)t = 320
factor out t
t * (2W - 18) = 320
t = 2 hours
2 * (2W - 18) = 320
2W - 18 = 160
2W = 178
W = 89
Then, E = (89) - 18 = 71 mph
Emma needs to order liquid fertilizer for her landscaping company. She plans to keep the fertilizer in a large cylindrical storage tank, but isn’t sure how much it will hold. The tank is 10 feet tall and the circular base has a radius of 5 feet. What is the volume of her storage tank?
It is to be noted that the volume of Emma's storage tank is: 785.3cubic feet.
What is the rationale for the above calculation?
Start by calculating the area of the base of the storage tank. The area of a circle is calculated by: A = π*r², where r is the radius of the circle.
Where:
π = 22/7
r = radius of the circular base
Recall that for Emma’s cylindrical storage tank, the radius of the base is 5 feet.
So we replace this value in the formula and calculate the area of the base, which is equal to:
A = π*5²
A = 22/7 * 5²
= 78.5714285714
[tex]\approx[/tex] 78.54 square feet.
Now we need to compute the volume of the cylindrical storage tank. The volume of a cylinder is calculated by:
V = π*r²*h,
where r is the radius of the circle and h is the height of the cylinder.
Recall that for Emma’s tank, the height is 10 feet. Hence,
We substitute these values in the formula and calculate the volume, which is equal to:
V = π*5²*10 = 785.4 cubic feet.
Therefore, Emma’s cylindrical storage tank has a capacity of 785.4 cubic feet.
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if sinθ 1÷2 and θ is in quadrant , evaluate each expression. a) sin 2θ b) cos 2θ c) tan 2θ
The values of sin 2θ, cos 2θ, and tan 2θ are:
a) sin 2θ = √(3)/2
b) cos 2θ = 1/2
c) tan 2θ = √(3)
What is a quadrant?Generally, If sin θ = 1/2 and θ is in quadrant I, then θ is equal to 30 degrees.
To evaluate each expression, we can use the trigonometric identities:
a) sin 2θ = 2 * sin θ * cos θ
= 2 * (1/2) * (√(3)/2)
= √(3)/2
b) cos 2θ = cos^2 θ - sin^2 θ
= (√(3)/2)^2 - (1/2)^2
= (3-1)/4 = 1/2
c) tan 2θ = (2 * tan θ) / (1 - tan^2 θ)
= (2 * (√(3)/3)) / (1 - (√(3)/3)^2)
= 2 * √(3) / (4 - 3)
= √(3)
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The approximate length of side XY is
units
The approximate length of side YZ
units.
The approximate length of side ZX is
v units.
The approximate perimeter of triangle XYZ is
units
please mark me brainlieset and click the stars i spent so long on this :>
Answer:
ZX = 3√2, XY =√10, YZ = 4, Perimeter of ΔXYZ = 14√5 units
Step-by-step explanation:
1. We can see that if we were to draw an altitude from vertex X to side ZY of this triangle, the length of this altitude would be: 3 units
2. The length of ZX can be determined through Pythagorean Theorem. If this altitude were to be called XW, it would be one of the legs of a mini triangle ZXW, along with leg ZW. ZW clearly = 3, thus ZX^2 = 3^2 + 3^2 = 18, and ZX = √18 units = 3√2.
3. The same thing can be applied to another "mini" triangle YXW. This triangle would have legs XW (altitude of the triangle ZXY) and YW. Knowing XW to have a length of 3 units, and YW to have length of 1 unit ⇒ XY^2 = XW^2 + YW^2 = 3^2 + 1^2, and XY = √10.
4. YZ is visualized to have a length of 4 units.
5. Knowing that ZX = 3√2, XY =√10, and YZ = 4 ⇒ Perimeter of ΔXYZ = ZX + XY + YZ = 3√2 + √10 + 4 = 14√5 units. To simplify this, it would be that the Perimeter of ΔXYZ = 14√5 units
ZX = 3√2, XY =√10, YZ = 4, Perimeter of ΔXYZ = 14√5 units
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
1. We can see that if we were to draw an altitude from vertex X to side ZY of this triangle,
the length of this altitude would be: 3 units
2. The length of ZX can be determined through Pythagorean Theorem.
If this altitude were to be called XW, it would be one of the legs of a mini triangle ZXW, along with leg ZW.
ZW clearly = 3,
thus
[tex]ZX^2 = 3^2 + 3^2 = 18[/tex],
and ZX = √18 units = 3√2.
3. The same thing can be applied to another "mini" triangle YXW. This triangle would have legs XW (altitude of the triangle ZXY) and YW.
Knowing XW to have a length of 3 units, and YW to have a length of 1 unit [tex]= > XY^2 = XW^2 + YW^2 \\= > 3^2 + 1^2[/tex],
and XY = √10.
4. YZ is visualized to have a length of 4 units.
5. Knowing that
ZX = 3√2, XY =√10, and YZ = 4
⇒ Perimeter of ΔXYZ = ZX + XY + YZ
⇒ Perimeter of ΔXYZ = 3√2 + √10 + 4
⇒ Perimeter of ΔXYZ = 14√5 units.
To simplify this, it would be that the Perimeter of ΔXYZ = 14√5 units
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4. Classify the system as independent, dependent, or inconsistent.
-3x + y = 4
x-1/3y = 1
The system of equation is dependent because both equation has same slope.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
An equation is an expression that shows the relationship between two or more numbers and variables.
We are given a system of equation as;
-3x + y = 4
x-1/3y = 1
Therefore, we need to write as straight line equation.
-3x + y = 4
y = 3x + 4
Thus, the slope is 3 and the y intercept is 4
Now x-1/3y = 1
x= 1 + 1/3y
y = 3x - 3
Thus, the slope is 3 and the y intercept is -3
The system of equation is dependent.
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An arch has the shape of a semi-ellipse (the top half of an ellipse). The arch has a height of 6 feet and a span of 22 feet. Find an equation for the ellipse. (Assume a center at (0, 0)). Use the equation to find the height of the arch at a distance of 3 feet from the center. (Round your answer to two decimal places.)
The equation of ellipse is [tex]\frac{x^2}{11^2} + \frac{y^2}{6^2} = 1[/tex] and height of arch is 5.77 feet
Assume that the center of the ellipse is at the origin.
So, The general equation for an ellipse is:
[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1[/tex]
Where:
x is Horizontal distance, in feet.
y is Vertical distance, in feet.
a is Horizontal semiaxis length (half-width), in feet.
and b is Vertical semiaxis length (height), in feet.
According to the question,
x = 3 , a = 11 and b = 6
Putting all the values ,
So , the equation of ellipse will be
[tex]\frac{x^2}{11^2} + \frac{y^2}{6^2} = 1[/tex]
Putting x = 3,
[tex]\frac{3^2}{11^2} + \frac{y^2}{6^2} = 1[/tex]
Solving for y,
[tex]\frac{y^2}{36} = 1 - \frac{9}{121}[/tex]
=> [tex]y^2 = \frac{(121 - 9)36}{121}[/tex]
=> y² = 4032 / 121
=> y = √33.32
=> y = 5.77 feet
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