Answer the statistical measures and create a box and whiskers plot for the following set of data.
Answers
Solution
The picture below is the solution to the problem
Brief explanantion
From the data given, It is obvious that:
Minimum = 2
Maximum =
The total number of the data is 3, so the number 7th term is the median
Thus,
Median = 8
To find Q1
[tex]\begin{gathered} Q_1=\frac{1}{4}(n+1)th\text{ term} \\ Q_1=\frac{1}{4}(13+1)=\frac{14}{4}=3.5 \end{gathered}[/tex]Q1 is between the third and fourth term
Therefore, Q1 is
[tex]Q_1=0.5(4)+0.5(6)=5[/tex]Similarly, to find Q3
[tex]\begin{gathered} Q_3=\frac{3}{4}(n+1)th\text{ term} \\ Q_3=\frac{3}{4}(13+1)=3\times\frac{14}{4}=3\times3.5=10.5 \end{gathered}[/tex]Q3 is between the tenth and the eleventh term
Therefore, Q3 is
[tex]Q_3=0.5(11)+0.5(11)=11[/tex]
Related Questions
the water pressure on Mustafa as he dives is increasing at a rate of 0.992 atmospheres (atm) per meter
What is the rate of increase in water pressure in atm/km
Answers
The rate of increase in water pressure in atm/km = 992 atm/km
what is pressure?Pressure can be defined as the external or internal force that acts on an area of an object which can be measured in atmosphere per meter.
The rate at which Mustafa dives = 0.992atm/meter.
That is,
0.992 atm = 1 meter
X atm = 1 km
But 1000m = 1 km
make X atm the subject of formula;
x atm = 0.992 × 1000
X atm = 992 atm/km
Therefore, the rate in atm/ km would be = 992 atm/km
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A computer part costs $7 to produce and distribute. Express the profit p made by selling 300 of these parts as a function of the price of c dollars. (Do not include $ symbol in your answer)
Answers
Given:
Each part costs $7 to produce and distribute.
The total number of parts on selling is 300 to make the profit P.
To write the function expression in terms of sale price C and profit P:
As we know,
[tex]\text{Profit}=\text{Selling price-cost price}[/tex]So, if we produce 1 part and sell that part, then the profit is
[tex]P=C-7[/tex]For 300 parts, the profit is
[tex]\begin{gathered} P=300(C-7) \\ P=300C-2100 \end{gathered}[/tex]Hence, the function is expressed in terms of P and C is,
[tex]P=300C-2100[/tex]Someone please help me with this
Answers
Polynomial equations are those created using exponents, coefficients, and variables. It may have several exponents, with the higher one being referred to as the equation's degree.
How are polynomial equations solved?Polynomial equation illustration
Write a polynomial equation in standard form before attempting to solve it. Factor it, then set each variable factor to zero after it has reached zero. The original equations' answers are the solutions to the derived equations. Factoring cannot always be used to solve polynomial equations.
6h²(5 + 9h)(5 - 9h)
6h²(9h + 5)(5 - 9h)
6h²(9h + 5)(-9h + 5)
Distribute6h²(9h + 5)(-9h + 5)
54(-9h +5)h³ + 30(-9h + 5)h²
(-486h)4 + 270h³+30(-9h+5)h²
(-486h)4 + 270h³-270h³+150h²
(-486h)4 + 150h²
Solution(-486h)4 + 150h²
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What is the value of 0 put a comma and space between answer sin61°=cos=0; cos17°=sin0;
Answers
For
[tex]\begin{gathered} \sin 61=\cos \theta \\ \theta=\cos ^{-1}(\sin 61) \\ \end{gathered}[/tex]For
[tex]\begin{gathered} \cos 17=\sin \theta \\ \theta=\sin ^{-1}(\cos 17) \\ \end{gathered}[/tex]The length of the longest slide is what inches the other two sides will each be what inches in length?
Answers
We know that the rod from which we made the triangle is 13 in long, this means that the perimeter of the triangle. from the diagram given we notice that the perimeter is:
[tex]x+(x-1)+(x-1)[/tex]equating this to 13 and solving for x we have:
[tex]\begin{gathered} x+(x-1)+(x-1)=13 \\ 3x-2=13 \\ 3x=13+2 \\ 3x=15 \\ x=\frac{15}{3} \\ x=5 \end{gathered}[/tex]Hence, the value of x=5 which means that the longest side measure 5 inches. To determine the length of the other sides we notice that they are given by x-1, which means that their length is 5-1=4 inches,
Therefore, the length of the longest side is 5 inches. The other two sides will each be 4 inches in length.
A sector of a circle has a central angle of 60∘ . Find the area of the sector if the radius of the circle is 9 cm.
Answers
Step-by-step explanation:
area of a sector is theta ÷360 ×πr²
work out sues total pay
Answers
Sue's total pay for the year given the salary, bonus and share of profit is £38,110.
What is the total pay?Sue's total pay for the year is a function of the salary, the share of the profit that she earns and the bonus.
Salary for the year = monthly salary x number of months in a year
£1410 x 12 = £16,920
The next step is to determine the profit last year
Profit = total revenue - total cost
£549,000 - £473,500 = £75,500
Now determine the share of profit that Sue would earn.
Share of profit = 26% x £75,500
0.26 x £75,500 = £19,630
Now determine the total bonus she would earn : 4 x £390 = £1560
Total salary = £1560 + £19,630 + £16,920 = £38,110
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Find the value of m and n that prove the two triangles are congruent by the HL theorem.
Answers
If both triangles are congruent by the HL theorem, then their hypotenuses are equal and at least one of the corresponding legs is equal too.
Hypothenuses:
[tex]13=4m+1[/tex]From this expression, you can calculate the value of m
[tex]\begin{gathered} 13=4m+1 \\ 13-1=4m \\ 12=4m \\ \frac{12}{4}=\frac{4m}{4} \\ 3=m \end{gathered}[/tex]Legs:
[tex]2m+n=8m-2n[/tex]Replace the expression with the calculated value of m
[tex]\begin{gathered} 2\cdot3+n=8\cdot3-2n \\ 6+n=24-2n \end{gathered}[/tex]Now pass the n-related term to the left side of the equation and the numbers to the right side:
[tex]\begin{gathered} 6-6+n=24-6-2n \\ n=18-2n \\ n+2n=18-2n+2n \\ 3n=18 \end{gathered}[/tex]And divide both sides of the expression by 3
[tex]\begin{gathered} \frac{3n}{3}=\frac{18}{3} \\ n=6 \end{gathered}[/tex]So, for m=3 and n=6 the triangles are congruent by HL
What value of Y makes this equation true?6y/-2 = 8 (-4/2)
Answers
Step 1
Given;
[tex]\frac{6y}{-2}=8(-\frac{4}{2})[/tex]Required; To find the value of y that makes the equation true
Step 2
Find the value of y
[tex]\begin{gathered} \text{Simplify} \\ -3y=4(-4) \end{gathered}[/tex][tex]\begin{gathered} \text{expand} \\ -3y=-16 \end{gathered}[/tex][tex]\begin{gathered} \text{Divide both sides by -3} \\ \frac{-3y}{-3}=\frac{-16}{-3} \end{gathered}[/tex][tex]\begin{gathered} \text{Simplify} \\ y=\frac{16}{3} \end{gathered}[/tex]Hence, the value of y that makes the equation true is 16/3
1. 3 In right AXYZ, the length of the hypotenuse YZ is 85 inches and tan Z= 3/4 What is the length, in inches, of the leg XY?
Answers
We have a right triangle XYZ.
The length of the hypotenuse is YZ=85.
We also know that the tangent of Z is 4.
We have to find the length of XY.
We can start by drawing the triangle and writing the data:
The tangent of an angle can be related with the sides by the following trigonometric ratio:
[tex]\tan (Z)=\frac{\text{Opposite}}{\text{Adyacent}}=\frac{XY}{XZ}=\frac{3}{4}[/tex]We can not find the value of the legs from the trigonometric ratio, but we have a proportion between them. We can write the previous result as:
[tex]\begin{gathered} \frac{XY}{XZ}=\frac{3}{4} \\ XZ=\frac{4}{3}\cdot XY \end{gathered}[/tex]Now we can relate XY with the hypotenuse YZ using the Pythagorean theorem:
[tex]\begin{gathered} XY^2+XZ^2=YZ^2 \\ XY^2+(\frac{4}{3}XY)^2=YZ^2 \\ XY^2+\frac{16}{9}XY^2=YZ^2 \\ (\frac{16}{9}+1)XY^2=YZ^2 \\ \frac{16+9}{9}XY^2=YZ^2 \\ \frac{25}{9}XY^2=YZ^2 \\ XY^2=\frac{9}{25}YZ^2 \\ XY=\sqrt[]{\frac{9}{25}YZ^2} \\ XY=\frac{3}{5}YZ \\ XY=\frac{3}{5}\cdot85 \\ XY=51 \end{gathered}[/tex]Answer: the length of the leg XY is 51 inches.
The measures of the angles of a triangle are shown in the figure below. Solve for x. (2x+6)° 42°
Answers
A triangle is a shape that has a total angle of 180°.
How to solve the triangle?It's important to note that a triangle is a shape that has three sides and the total sum is equal to 180°.
In this case, we have 2x + 6 and 42°. The other angle isn't given and this can't be solved further
The sides will have been illustrated as:
= a + b + c = 180
The expression given will then be allocated for each side to solve it further.
Note that an overview was given as the information is incomplete.
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Suppose 72% of students chose to study French their freshman year, and that meant that there were 378 such students. How many students chose not to take French their freshman year?
Answers
Answer:
There were 378 students who chose to study French their freshman year. This means that 72% of the total number of students chose to study French their freshman year. Therefore, the total number of students must be 378 / 0.72 = 527.5. This means that there were 148.5 students who chose not to take French their freshman year.
Step-by-step explanation:
how long does it take the snail to crawl 86 inches enter answer in decimal number
Answers
To get the equation of the line graph, first, we have to find its slope. The slope of a line that passes through points (x1, y1) and (x2, y2) is computed as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]From the picture, the line passes through the points (0,0) and (10, 1), then its slope is:
[tex]m=\frac{1-0}{10-0}=\frac{1}{10}_{}[/tex]The slope-intercept form of a line is:
y = mx + b
where m is the slope and b is the y-intercept.
From the graph, the line intersects the y-axis at y = 0, this means that b = into
the equation. Therefore, the equation is:
y = 1/10x
where x is distance (in inches) and y is time (in minutes).
To find how long it takes the snail to crawl 86 inches, we have to replace x = 86 into te equation as follows:
[tex]\begin{gathered} y=\frac{1}{10}\cdot86 \\ y=8.6 \end{gathered}[/tex]The snail takes 8.6 minutes to crawl 86 inches
In an electrical circuit, the voltage across a resistor is directly proportional to the current running through the resistor. If a current of 14 amps produces 280 volts across a resistor, how many volts would a current of 5.5 amps produce across an identical resistor?
Answers
A current of 5.5 amps produce across an identical resistor will produce 110Volts across an identical resistor
What is a current?From above,
Current 1 (I₁) = 14 amps
P.d (V₁) = 280 V
By Ohm's law which states that that for a linear circuit the current flowing through it is proportional to the potential difference across it so the greater the potential difference across any two points the bigger will be the current flowing through it.
V₁ = I₁R
= 280 = 14R
= 20Ω = R
Current 2 (I₂) = 3.5 A
Resistance (R) = 20 Ω
Assuming the resistance stays the same,
Using Ohm's law,
V₂ = I₂R
= 5.5*20
= 110 Volts
110Volts would be produced across an identical resistor
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Look at the circle below. D = 6 3What is the area of the circle if the diameter is 6 centimeters? Use 3.14 for pi. A 18.84 square centimetersB 28.26 square centimeters C 37.68 square centimeters D 113.04 square centimeters
Answers
we are asked to determine the area of a circle with a diameter of 6 cm. To do that we will use the following formula for the area of a circle:
[tex]A=\frac{\pi D^2}{4}[/tex]Replacing the value of the radius:
[tex]A=\frac{\pi(6\operatorname{cm})^2}{4}[/tex]Replacing the value of pi:
[tex]A=\frac{3.14(6\operatorname{cm})^2}{4}[/tex]Solving the operations:
[tex]\begin{gathered} A=\frac{3.14(36cm^2)}{4} \\ \\ A=3.14(9cm^2)=28.26cm^2 \end{gathered}[/tex]Evaluate the expression when x= -1/4 and y= 31. 2xyI don't understand his question.
Answers
The expression is 2xy
we will substitute x and y by the given values
x = -1/4 and y = 3
[tex]2xy=2\times(\frac{-1}{4})\times(3)[/tex]We put the values of y in the expression
Now we will calculate the value
[tex]2xy=\frac{2\times-1\times3}{4}[/tex]We will multiply the numbers in the numerator
[tex]2xy=\frac{-6}{4}[/tex]We will simplify the fraction by divide up and down by 2
[tex]\begin{gathered} 2xy=\frac{-\frac{6}{2}}{\frac{4}{2}}=\frac{-3}{2} \\ 2xy=-\frac{3}{2} \end{gathered}[/tex]1. It is h before closing time at the grocery store. It takes about h for Jane to find 1 item on her shopping list. How many items can she find before the store closes? (a) Create a model or write an equation for the situation. (b) Find the solution. Explain what you did. (c) State the solution as a full sentence.
Answers
GIVEN
The time left before the store closes is 3/4 h while the time taken to find one item is 1/8 h.
QUESTION A
Let the number of items that can be gotten before the store closes be N.
The number of items can be calculated using the formula:
[tex]N=\text{ number of hours left}\div\text{ number of hours used to find one item}[/tex]Therefore, the equation to get the number of items will be:
[tex]N=\frac{3}{4}\div\frac{1}{8}[/tex]QUESTION B
The solution can be obtained by division.
Apply the fraction rule:
[tex]\frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}[/tex]Hence, the solution will be:
[tex]\begin{gathered} \frac{3}{4}\div\frac{1}{8}=\frac{3}{4}\times\frac{8}{1} \\ \Rightarrow\frac{3\times\:2}{1\times\:1}=6 \end{gathered}[/tex]The answer is 6.
QUESTION C
Jane can find 6 items before the store closes.
f(x) = 3x² + 9x – 16
Find f(-8)
Answers
Answer: 104
Step-by-step explanation:
[tex]f(-8)[/tex] represents [tex]f(x)[/tex] evaluated at [tex]x=-8[/tex].
[tex]f(-8)=3(-8)^2 +9(-8)-16\\\\=192-72-16\\\\=120-16\\\\=104[/tex]
Question 2 of 10The one-to-one functions g and h are defined as follows.g={(-8, 6), (-6, 7), (-1, 1), (0, -8)}h(x)=3x-8Find the following.g-¹(-8)=h-¹(x) =(hoh− ¹)(-5) =
Answers
Answer: We have to find three unknown asked quantities, before we could do that we must find the g(x) from the coordinate points:
[tex]\begin{gathered} g=\left\{\left(-8,6\right),(-6,7),(-1,1),(0,-8)\right\}\Rightarrow(x,y) \\ \\ \text{ Is a tabular function} \\ \end{gathered}[/tex]The answers are as follows:
[tex]\begin{gathered} g^{-1}(-8)=0\text{ }\Rightarrow\text{ Because: }(0,-8) \\ \\ \\ h^{-1}(x)=\frac{x}{3}+\frac{8}{3} \\ \\ \\ \text{ Because:} \\ \\ h(x)=3x-8\Rightarrow\text{ switch }x\text{ and x} \\ \\ x=3h-8 \\ \\ \\ \\ \text{ Solve for }h \\ \\ \\ h=h^{-1}(x)=\frac{x}{3}+\frac{8}{3} \end{gathered}[/tex]The last answer is:
[tex]\begin{gathered} (h\text{ }\circ\text{ }h^{-1})(-5) \\ \\ \text{ Can also be written as:} \\ \\ h[h^{-1}(x)]\text{ evaluated at -5} \\ \\ h(x)=3x-8 \\ \\ h^{-1}(x)=\frac{x}{3}+\frac{8}{3} \\ \\ \\ \therefore\Rightarrow \\ \\ \\ h[h^{-1}(x)]=3[\frac{x}{3}+\frac{8}{3}]-8=x+8-8=x \\ \\ \\ \\ h[h^{-1}(x)]=x \\ \\ \\ \\ h[h^{-1}(-5)]=-5 \end{gathered}[/tex]Labron James made 255/310 baskets. What percent of the baskets did he make?
Answers
82.26%
Explanations:The ratio of baskets made by Lebron James = 255/310
To find the percentage equivalent of the ratio, multiply it by 100%
Percentage of the baskets made by Lebron James = 255/310 x 100%
Percentage of the baskets made by Lebron James = 82.26%
IF G and R denote the grade and the radian measure of an angle, then prove that G/200 = R/pie
Answers
Solution:
Given;
IF G and R denote the grade and the radian measure of an angle, i.e.
Where
[tex][/tex]If AACB = ADCE, ZCAB = 63°,ZECD = 52°, and ZDEC = 5xDE(c сx = [?]
Answers
Since angles ACB and ECD are vertical angles, they are congruent, so we have
Calculating the sum of internal angles in triangle ABC, we have:
[tex]\begin{gathered} ABC+ACB+CAB=180 \\ ABC+52+63=180 \\ ABC=180-52-63 \\ ABC=65 \end{gathered}[/tex]Since triangles ACB and DCE are congruent, we have [tex]\begin{gathered} DEC=ABC \\ 5x=65 \\ x=13 \end{gathered}[/tex]
A certain species of deer is to be introduced into a forest, and wildlife experts estimate the population will grow to P(t) = (944)3 t/3, where t represents the number ofyears from the time of introduction.What is the tripling-time for this population of deer?
Answers
Ok, so
Here we have the function:
[tex]P(t)=944(3)^{\frac{t}{3}}[/tex]Now we want to find the tripling-time for this population of deer.
If we make t=0, we will find the initial population of deer. This is:
[tex]P(0)=944(3)^{\frac{0}{3}}=944[/tex]Now, we want to find the time "t" such that this population is the triple.
This is:
[tex]\begin{gathered} 944(3)=944(3)^{\frac{t}{3}} \\ 2832=944(3)^{\frac{t}{3}} \\ \frac{2832}{944}=3^{\frac{t}{3}} \\ 3=3^{\frac{t}{3}} \end{gathered}[/tex]We got this exponential equation:
[tex]3=3^{\frac{t}{3}}[/tex]As the base is the same, we could equal the exponents:
[tex]\begin{gathered} 1=\frac{t}{3} \\ t=3 \end{gathered}[/tex]Therefore, tripling-time for this population of deer are 3 years.
&A(n)is formed when two rays have a common endpoint.Oline segmentangle
Answers
When two rays are with a common endpoint, an angle is formed and the common endpoint is called the vertex of the angle
Kuta Sotware - Infinite Algebra 2 Solving Inequalities Solve each inequality and graphite 10 > Kuin Software - Infinite Algebra 2 Graphing Linear Inequalities Sketch the graph of each linear inequality. Name Samante 1) yz-2x-2 Y-2-2 2). ys - !
Answers
Could you please send a picture of the inequality you are asked to solve?
I'll be closing the session now if you cannot do it. Please ask your question again, and send the image in the question itself to avoid this problem of your uploaded images and messages not getting to me.
Thank you, and please re-submit your question request.
In a competition of 837 people, Jenny scored at the 77th percentile.
In what place did she finish?
Answers
Answer:
Jenny scored 644th place.
Step-by-step explanation:
To find out what place she finished, you need to write it out first like this:
77% of 837.
Now, to make the equation possible to solve, we can take the 77 and make it a decimal: 0.77.
The term "of" means multiplication.
So, in turn, we have the equation:
0.77 x 837 = 644.49
And, if you round it, your answer would be:
Jenny scored 644th place.
Answer:
See below
Step-by-step explanation:
77th percentile means she scored better than 77 per cent of the test takers...
So Jenny's place was .23 * 837 = ~ 193 rd Out of 837 people
Reba is playing on the slide. Over and over, she climbs the 9-foot ladder, goes down the slide, and walks 3 feet to get back to the ladder. How far does Reba travel each time she repeats this process? If necessary, round to the nearest tenth.
Answers
we have
then find c
[tex]\begin{gathered} c^2=3^2+9^2 \\ c^2=9+81 \\ c^2=90 \\ c=\sqrt[]{90} \\ c=3\sqrt[]{10} \end{gathered}[/tex]therefore the distance is:
[tex]9+3\sqrt[]{10}+3=21.5[/tex]answer: 21.5 ft
Growing up, Mrs. Reeder's favorite book was THE ADVENTURES of TOM SAWYER.Now that she is a teacher, she buys 25 copies to read with her class. If each book coast $7.19, how much does Mrs. Reeder spend?
Answers
According to the given data we have the following:
Total copies she buys= 25 copies
book cost=$7.19
Therefore, in order to calculate the amount of money that Mrs. Reeder spend we would have to make the following calculation:
Amount of money that Mrs. Reeder spend= quantity of copies * book cost
Amount of money that Mrs. Reeder spend=25 copies*$7.19
Amount of money that Mrs. Reeder spend=$180
The amount of money that Mrs. Reeder spend was $180
A triangular pryamid is shown in the diagram. What is the volume of the triangular pyramid?
Answers
Given the following question:
[tex]\begin{gathered} V=\frac{1}{3}BH \\ B=\text{ Base Area} \\ A=\frac{1}{2}BH \\ B=7.8 \\ H=4 \\ A=\frac{1}{2}7.8(4) \\ 7.8\times4=31.2 \\ 31.2\div2=15.6 \\ A=15.6 \\ V=\frac{1}{3}BH \\ B=15.6 \\ H=4 \\ \frac{1}{3}15.6(4) \\ 15.6(4)=62.4 \\ 62.4\div3=20.8 \\ V=20.8 \end{gathered}[/tex]Volume is equal to 20.8 cubic centimeters.
Solve the method.simultaneous equation by graphicaly + 3x = 6y - 2x = 1
Answers
The equations given are
[tex]\begin{gathered} y+3x=6............1 \\ y-2x=1............2 \end{gathered}[/tex]The graph of the equations will be shown below
Hence, the solution to the equations is the point where the two equations intersect.
Therefore, the solution is
[tex](1,3)[/tex]