The heights, in inches, of 12 students are listed below.61, 67, 72, 62, 65, 59, 60, 79, 60, 61, 64, 63
Answers
Correct option is Option Number 2,
Explanation:
It is not a casual relationship as the number of pages of a research paper does not depend upupothe n the typing speed.
All other options are in casual relationship.
So, correction option is 2.
Related Questions
How much will Barry pay Kim at the end of 4 years?
Answers
From the question
Kim loaned Barry $15,860 at an interest rate of 16% for 4 years
This implies
Principal (P) = $15,860
Interest Rate (R) = 16%
Time (T) = 4years
We are to find the amount Barry will pay Kim at the end of 4years
First, we need to find the interest I, using
[tex]I=\frac{\text{PRT}}{100}[/tex]By substituting values we get
[tex]I=\frac{\text{ \$15860}\times16\times4}{100}[/tex]Simplifying the expression we have
[tex]\begin{gathered} I=\frac{\text{ \$1,015,040}}{100} \\ I=\text{ \$10150.40} \end{gathered}[/tex]Hence, the interest to be paid is $10,150.40
Next, we will find the Amount Barry will pay Kim at the end of 4years
Amount (A) is given as
[tex]A=P+I[/tex]Substituting values
[tex]\begin{gathered} A=\text{ \$15,860}+\text{ \$10,150.40} \\ A=\text{ \$}26,010.40 \end{gathered}[/tex]Therefore the Amount to be paid back is $26,010.40
A game spinner has regions that are numbered 1 through 8. If the spinner is used twice, what is the probability that the first number is a 3 and the second is a 5?A. 18B. 532C. 116D. 164
Answers
The Solution:
Given:
A spinner is numbered 1 to 8.
Required:
Find the probability that the first number is 3 and the second number is 5 when the spinner is used twice.
The possible outcomes = 8
[tex]P(3)=\frac{1}{8}[/tex][tex]P(5)=\frac{1}{8}[/tex][tex]P(a\text{ 3 and a }5)=\frac{1}{8}\times\frac{1}{8}=\frac{1}{64}[/tex]Answer:
[option D]
Suppose the U.S bureau projects the population of Texas to be 23.2 million in 2014 and 26.8 million in 2018. Assuming the population growth is linear , use (t) years since 2005 and (p) the population of Texas in millions. What is the population of Nevada in 2024?
Answers
Population in 2014=23.2 million
Population in 2018=26.8 million
Population in 2024= ?
The population increase is linear, therefore:
[tex]p(t)=m*t+b[/tex]Where t, time since 2005 and p is the population.
We know two points:
P1= (t, p) = (2014, 23.2)
P2=(t , p)=(2018, 26.8)
But the time is since 2005, then:
2014-2005=9
2018-2005= 13
The points are:
P1= (t1, p1) = (9, 23.2)
P2=(t2 , p2)=(13, 26.8)
The slope is going to be:
[tex]m=\frac{p_2-p_1}{t_2-t_1}=\frac{26.8-23.2}{13-9}=\frac{9}{10}=0.9[/tex]Replacing any point in the equation to find b:
[tex]\begin{gathered} p(t)=0.9*t+b \\ 23.2=0.9*9+b \\ b=23.2-8.1=15.1 \end{gathered}[/tex]The equation is:
[tex]p(t)=0.9*t+15.1[/tex]Where 15.1 millions is the population in 2005.
Finally, the population in 2024 will be:
[tex]\begin{gathered} 2024-2005=19 \\ p=0.9*19+15.1=32.2 \end{gathered}[/tex]Answer: The population of Nevada in 2024 is: 32.2 millions.
Prove the following equality Cosx⁴ - Sinx⁴ = Cos2x
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Answer:
To prove:
Cos⁴x - Sin⁴x = Cos2x
we get,
Consider, (Left hand side (LHS))
[tex]\cos^4x-\sin^4x[/tex]we know that,
[tex](a+b)(a-b)=a^2-b^2[/tex]Usind this formula we get,
[tex]\cos^4x-\sin^4x=(\cos^2x)^2-(\sin^2x)^2[/tex][tex]=(\cos^2x+\sin^2x)(\cos^2x-\sin^2x)[/tex]we know that,
[tex]\begin{gathered} \cos2x=\cos^2x-\sin^2x \\ \cos^2x+\sin^2x=1 \end{gathered}[/tex]Substitute the values we get,
[tex]=(1)(\cos2x)[/tex][tex]\cos^4x-\sin^4x=\cos2x[/tex]Hence proved.
You want to buy a used truck and are interested in the fuel consumption rate for each of the three trucks you are considering. Using the information given, decide which of the used trucks gets the best gas mileage.:2007 Ford F-150: 250 miles on 15.6 gallons2008 Chevy Silverado: 500 miles on 29.4 gallons2006 Toyota Tundra: 428 miles on 26.4 gallons
Answers
Chevy Silverado
1) In this question, we are going to find the unit rate so that we can get the best relation: mileage/gas
2) Let's start with the 2007 Ford F-150:
[tex]\begin{gathered} m------------g \\ 250----------150 \\ x------------1 \\ 150x=250 \\ x=\frac{250}{150} \\ x=\frac{1.6m}{g} \end{gathered}[/tex]So that Ford F-150 makes 1.6 miles per gallon
b) Chevy Silverado:
[tex]\begin{gathered} m-----g \\ 500----29.4 \\ y------1 \\ 29.4y=500 \\ y=\frac{500}{29.4} \\ y=\frac{17.00m}{\text{gallons}} \end{gathered}[/tex]Thus, the Chevy Silverado makes 17 miles per gallon.
c) Toyota Tundra:
[tex]\begin{gathered} m-----g \\ 428----26.4 \\ z-----1 \\ 26.4z=428 \\ z=\frac{428}{29.4}=\frac{14.55m}{g} \\ z= \end{gathered}[/tex]3) Thus the best gas mileage is: Chevy Silverado
An object moves from point A to point B, then back to point A along the line shown in the figure belowOkmTim2km3km4lom5km6km7km8km9km10km11 kmWhat is the objects distance?What is the objects displacemt
Answers
The object's distance = 10km
Displacement of the object = 0
From the line:
The distance from A to B = 5km
The distance from B to A = 5km
The object's distance = distance A to B + distance B to A
The object's distance = 5km + 5km
The object's distance = 10km
The displacement is the change in position of an object.
Displacement = final distance - initial distance
final distance = 5km
initial distance = 5km
Displacement = 5km - 5km
Displacement of the object = 0
What is the length of the red line segment on the number line? -8 -5
Answers
Please don't close the session , the image its downloading
its downloading yet
Julia uses the shadow of the flagpole to estimate its height. She stands so that the tip of her shadow coin cides with the tip of the flagpole Shadow as shown. Julia is 5 ft tall. The distance from the flagpole to Julia is 28ft and the distance between the tip of the Shadow and Julia is 7 ft. Calculate the height of the flagpole.(ill send the image)
Answers
Since the triangles are similar we can formulate the following equation:
[tex]\begin{gathered} \frac{7}{28+7}=\frac{5}{x} \\ \frac{7}{35}=\frac{5}{x}\text{ (Adding)} \\ \frac{1}{5}=\frac{5}{x}\text{ (Simplifying on the right side)} \\ x=\frac{5}{\frac{1}{5}}\text{ (Isolating x)} \\ x=\text{ }25\text{ }(\text{Dividing fractions)} \\ \text{The answer is 25 ft} \end{gathered}[/tex]in the diagram below, angle DEF is the image of angle ABC after a reflection over the line not showing. Using only a compass and straightedge draw the line of reflection.
Answers
the next image will show the line of reflection in order to obtain the triangle
a barrel shaped like cylinder is laid on its side and rolled up a ramp that is 196 m long. the barrel has a circular base that turns 49 times in being rolled up the ramp. what us the diameter of the circular base?use the value 3.14 for pie. round your answer to the nearest tenth.
Answers
We know that
• The ramp is 196 meters long.
,• The barrel has a circular base, it turns 49 times over the ramp.
Observe the ramp longitude is 49 times greater than the lateral surface of the barrel. Let's divide.
[tex]\frac{196}{49}=4[/tex]This means the circumference of the base of the barrel is 4 meters long.
The circumference length formula is
[tex]C=\pi d[/tex]Where d is the diameter. Let's replace the circumference and solve for d.
[tex]\begin{gathered} 4=3.14\cdot d \\ d=\frac{4}{3.14}\approx1.27 \end{gathered}[/tex]Therefore, the diameter is 1.27 meters long, approximately.Graph a triangle (LMN) and rotate it 180° around the origin to create triangle L′M′N′. (10 points)
Describe the transformation using words. Make sure you refer to the characteristics and the coordinates.
Draw a line through points L and L′ and through M and M′. What do you notice about the lines you drew? Do you think you would notice the same characteristics if you drew another line through points N and N′? How do you know?
Answers
Considering the rotation of 180º degrees around the origin of triangle LMN, it is found that the lines connecting the vertices at the original triangle and at the reflected triangle intersect at the origin.
180º rotation about the originThe rule for the vertices of the triangle when it is rotated 180º degrees about the origin is given as follows:
(x,y) -> (-x,-y).
Hence the signal of the x and the y-coordinates is exchanged.
We draw a triangle LMN with vertices given as follows:
L(1,2), M(7,2), N(1,10).
Hence, applying the rotation, the vertices of triangle L'M'N' are given as follows:
L'(-1,-2), M'(-7,-2), N(-1,-10).
Given two points, there is a single line connecting these two points. These lines can be found using a calculator, and are given as follows for each vertex:
L and L': y = 2x.M and M': y = 2/7x.N and N': y = 10x.These three lines have in common an intercept of 0, meaning that they are proportional relationships, that is, they intersect at the origin, as shown by the image shown at the end of the answer.
Learn more about rotations at brainly.com/question/26249005
#SPJ1
Find the value of y.
Answers
First let find the sum of all the interior angles of the polygon
[tex]\begin{gathered} 121+130+145+180-2y+119+180-y=180\cdot4 \\ 875-3y=720 \\ 3y=875-720=155 \\ y=\frac{155}{3}=51.7 \end{gathered}[/tex]1616416413 22 32 301620What is the meanhere?
Answers
To find the mean, we have to divide the sum of all numbers by the total number of items.
[tex]\begin{gathered} \bar{x}=\frac{16+16+41+64+13+22+32+30+16+20}{10}=\frac{270}{10} \\ \bar{x}=27 \end{gathered}[/tex]Therefore, the mean of the given data set is 27.There were 80golfers in the first round of a tournament. Of the 80, 62.5% qualified for the next round. How many did not qualify?
Answers
Number of golfers that didn't qualify = 30
Explanation:Total number of golfers = 80
The percentage that qualified for the next round = 62.5% = 0.625
Number that qualified = 80 * 62.5%
= 80 * 0.625
Number of golfers that qualified = 50
Number of golfers that didn't qualify = Total number of golfers - Number of golfers that qualified
= 80 - 50
Number of golfers that didn't qualify = 30
What is the midpoint of the segment shown below? (3,5) (2, 2) - 10 10 O A. (5,7) O B. (2) O C. (5,3) OD. (5,7)
Answers
If we have a segment, we can find the coordinates of the midpoint by averaging the coordinates of the endpoints.
If the endpoints of the segment are (3,5) and (2,2), the coordinates of the midpoint will be:
[tex]\begin{gathered} x_m=\frac{x_1+x_2}{2}=\frac{3+2}{2}=\frac{5}{2} \\ y_m=\frac{y_1+y_2}{2}=\frac{5+2}{2}=\frac{7}{2} \end{gathered}[/tex]Then, the midpoint has coordinates (5/2, 7/2).
Answer: (5/2, 7/2) [Option B]
Calculate the area and perimeter of the largest figure All four-sided figures are rectangles
Answers
The Solution:
The given figure is
The perimeter of the largest figure is calculated below:
[tex]\text{ Perimeter =7+y+5+x+y+7+x+5}[/tex]Collecting the like terms, we get
[tex]\text{ Perimeter =7+7+5+5}+2x+2y=24+2x+2y=2(x+y+12)\text{ units}[/tex]The area of the largest figure is calculated below:
[tex]\begin{gathered} \text{ Area =L}\times W \\ \text{ Where} \\ L=5+x \\ W=7+y \\ \text{Substituting the values, we get} \\ \text{Area =(5+x)(7+y)=5(7+y)+x(7+y)} \\ =(35+5y+7x+xy)units^2 \end{gathered}[/tex]Which of the following segments is a radius of OA?GA. TRB. RPRC. TAD. GP
Answers
Radius of a circle is any line drawn from the center of the cirlcle to any part of the circumference of the circle
So from the figure given, the radius of the circle is line TA
A hole must be excavated for a swimming pool in the shape shown in the figure. Whatvolume of depth must be removed in order to create this hole?10 m30 m1 m4 m
Answers
The Solution:
Given:
We are asked to find the volume.
Observe that the base surface that can give a uniform cross-section is a trapezoid.
So, the formula for the volume is:
[tex]Volume=\frac{1}{2}(a+b)h\times H[/tex]In this case:
[tex]\begin{gathered} a=1m \\ \\ b=4m \\ \\ h=height\text{ of the trapezoid}=? \\ \\ H=10m \end{gathered}[/tex]Find h:
[tex]\begin{gathered} h^2+3^2=30^2 \\ \\ h^2=900-9 \\ \\ h^2=891 \\ \\ h=\sqrt{891}=29.8496m \end{gathered}[/tex]Substitute:
[tex]Volume=\frac{1}{2}(1+4)29.85\times10=5\times29.85\times5=746.241m^3[/tex]Therefore, the correct answer is 746.241 cubic meters.
Please help I will give brainliest
Answers
Answer:
y = -3x + 4
Step-by-step explanation:
Desmos works great for graphing equations like this! Here's how you can do it...
1) Enter the equation for the given line, followed by the point at which your other line must pass.
2) Then you can more easily and accurately see where to make your new line
Here is the demos graph for this equation...
Answer: y=-3x+4
Step-by-step explanation:
3x+y=3
-3x+3x+y=-3x+3
y=-3x+3 ==> slope is -3
y=-3x+b ==> x=1 and y=-7
-7=-3(1)+b
-7=-3+b
-7+3=-3+3+b
b=-4
y=-3x+4
I need to find the exact perimeter of the square.
Answers
ANSWER
P = 79.2
EXPLANATION
We want to find the perimeter of the square given only its diagonal.
To do that, we use the formula:
[tex]P\text{ = 2 }\sqrt[]{2}\cdot\text{ D}[/tex]where D = length of diagonal
The diagonal of the square is 28.
Therefore, we have that:
[tex]\begin{gathered} P\text{ = 2 }\sqrt[]{2}\cdot\text{ 28} \\ P\text{ = }2.828\cdot\text{ 28} \\ P\text{ = }\cong79.2 \end{gathered}[/tex]That is the answer.
Spiral Back : Proportions Set up the proportion The ratio of girls to boys at Rayburn Middle school is 5 to 8. If there are 64 boys, how many total students are Number of girls click to add text Total number of students Click to add text
Answers
40 girls
104 students
1) Given the ratio of girls to boys is 5:8 and there are a total of 64 boys we can write, and then cross multiply it (for this is a proportion):
[tex]\begin{gathered} \frac{5}{8}=\frac{x}{64} \\ 8x=320 \\ x=40 \end{gathered}[/tex]So there are 40 girls.
2) Hence, the number of students altogether is found by adding them up: 40+64 = 104
When you grow a culture of bacteria in a Petri dish, the area of the culture is a measure of the number of bacteria present. Suppose that the area of the culture, A(t), in square millimeters, given by this function of time t, in hours: A(t)=9(1.1^t). Find the A(0), A(5) and A(10), the area at times t=0h, 5h, and 10h, respectively.
Answers
The equation for area of the bacteria culture at time t is given as:
[tex]A(t)=9(1.1)^t[/tex]So the values of A(0), A(5) and A(10) respectively, are:
[tex]\begin{gathered} A(0)=9(1.1)^0=9 \\ A(5)=9(1.1)^5=14.49459\approx14.50 \\ A(10)=9(1.1)^{10}=23.34368\approx23.34 \end{gathered}[/tex]Hence A(0)=9 sqmm, A(5)=14.4946sqmm, A(10)=23.3437 sqmm.
Question 5 of 5Which two ratios represent quantities that are proportional?A. and 1.1B. 2 and 1eC.andola36and48
Answers
From the quantities given in the option , check the ratios that are proportional.
[tex]\frac{21}{28}=\frac{12}{16}[/tex]Simplify the proportional ,
[tex]\frac{3}{4}=\frac{3}{4}[/tex]As you can see the ratio are proportional .
Hence the correct option is B.
I need help understanding what I did wrong in this problem
Answers
EXPLANATION
By the Parallel lines cuted by a transversal line Theorem, we can see that 5x and 2x+ 5 perform a linear pair because both lines are parallel so they are supplementary angles as shown as follows:
2x + 5 + 5x = 180
Adding like terms:
7x + 5 = 180
Subtracting -5 to both sides:
7x = 180 - 5
Subtracting numbers:
7x = 175
Dividing both sides by 7:
x = 175/7
Simplifying:
x=25
Answers:
Equation --->
(2x+5) + 5x = 180
x = 25
Which of the following best describes control, a principal of experimental design?
Answers
Ok, to calculate this we need to divide the succesful outcomes by the size of the sample:
[tex]\text{Proportion}=\frac{26}{50}=0.52[/tex]The sample proportion is 0.52, option D.
Determine the y intercept of the graph of this equation: y=3x-15
Answers
EXPLANATION
Since we have the equation y= 3x - 15, the y-intercept is the point -15, or representing as an ordinated pair (0,-15)
you invest $200 in an account that earns 3% annual interest. Written a function that represents the balance after t years
Answers
the fuction will be
[tex]y(t)=200(1.03)^t[/tex]Domain: {-4 < x < 4} Range: {-4 < y < 4} Function: NO graph
Answers
Domain: {-4 < x < 4} You have to draw this interval over the x-axis
Range: {-4 < y < 4} This interval goes over the y- axis
Since we don't know the form of the function I marked the domain and range in the x and y axis. The blank circles mean that the endpoints are not included.
Find the commission: Sales: 700Comission rate: 8%What is the commission?
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As the sales are $700 and the comission rate is 8% you need to find the 8% of 700, as follow:
[tex]700\cdot\frac{8}{100}=56[/tex]Then, the comission is $56The area of the triangle below is 4.06 square meters. What is the length of the base?2.8 mET
Answers
ANSWER
b = 2.9 m
EXPLANATION
The area of a triangle is,
[tex]A=\frac{b\cdot h}{2}[/tex]Where b is the length of the base and h is the height of the triangle.
In this problem, we know that the area is A = 4.06 m² and the height is h = 2.8 m,
[tex]4.06m^2=\frac{b\cdot2.8m}{2}[/tex]We have to solve this equation for b. Multiply both sides by 2,
[tex]\begin{gathered} 2\cdot4.06m^2=\frac{b\cdot2.8m}{2}\cdot2 \\ \\ 8.12m^2=b\cdot2.8m \end{gathered}[/tex]And divide both sides by 2.8 m,
[tex]\begin{gathered} \frac{8.12m^2}{2.8m}=\frac{b\cdot2.8m}{2.8m} \\ \\ 2.9m=b \end{gathered}[/tex]Hence, the length of the base is 2.9 m.