The middle 95% of Jace's finishing times in the 400 meter race is between 82 and 92 seconds.
Approximately 68% of the data falls within 1 standard deviation of the mean (i.e., between μ - σ and μ + σ).
Approximately 95% of the data falls within 2 standard deviations of the mean (i.e., between μ - 2σ and μ + 2σ).
Approximately 99.7% of the data falls within 3 standard deviations of the mean (i.e., between μ - 3σ and μ + 3σ).
We want to find the interval of times that represents the middle 95% of Jace's finishing times, which means we want to find the interval that falls between μ - 2σ and μ + 2σ.
Substituting the given values, we get:
μ - 2σ = 87 - 2(2.5) = 82
μ + 2σ = 87 + 2(2.5) = 92
Therefore, the middle 95% of Jace's finishing times in the 400 meter race is between 82 and 92 seconds.
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Can y’all please help me with this whole thing :/
Answer:
Slope-Intercept Form: y=2x+1
Standard Form: 2x-y=6
1. [tex]y=\frac{1}{3}x-1[/tex]
2. [tex]y=-\frac{2}{5}x[/tex]
3. [tex]y=x+8[/tex]
4. [tex]y=-\frac{1}{2}x+3[/tex]
5. [tex]y=2x+1[/tex]
6. [tex]y=-4x-5[/tex]
7. [tex]y=-x+2[/tex]
8. [tex]y=\frac{2}{3}x-4[/tex]
9. [tex]y=x\\[/tex]
suppose tire pressure is normally a distribution random variable with a standard deviation equal to 3 psi. if the car's average tire pressure is on target, what is the probability that the TPMS will trigger a warning? round to 4 decimal places
The probability of the TPMS triggering a warning is 0.0198 or about 0.02, rounded to four decimal places.
What is a probability?It is used to predict and estimate the likelihood of future events and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Let's assume that the tire pressure follows a normal distribution with a mean of 32 psi and a standard deviation of 3 psi.
Let's also assume that the TPMS warning is triggered when the tire pressure falls below 25 psi or rises above 39 psi.
Using a standard normal distribution table or calculator, we can find the z-scores corresponding to 25 psi and 39 psi:
z₁ = (25 - 32) / 3 = -2.3333
z₂ = (39 - 32) / 3 = 2.3333
Then, we can find the probabilities associated with these z-scores:
P (z < -2.3333) = 0.0099
P (z > 2.3333) = 0.0099
The total probability of the TPMS triggering a warning is the sum of these two probabilities:
P(TPMS warning) = P(z < -2.3333) + P(z > 2.3333) = 0.0099 + 0.0099 = 0.0198
Therefore, the probability of the TPMS triggering a warning is 0.0198 or about 0.02, rounded to four decimal places.
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how do i work out 320.041 - 47.96
To subtract 47.96 from 320.041, you can align the decimal points and then subtract each digit from right to left.
First, write the numbers with the decimal points aligned:
320.041
- 47.960
Next, subtract the digits in the ones place, which is 1 minus 0, resulting in 1. Then, subtract the digits in the tenths place, which is 4 minus 6. Since 4 is less than 6, you need to borrow 1 from the digit to the left, making the 2 into a 1 and adding 10 to the 4, giving you 14. So, 14 minus 6 equals 8.
Continue subtracting each digit in the same way:
320.041
- 47.960
= 272.081
Therefore, 320.041 minus 47.96 is equal to 272.081.
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Johnny’s Donut Shop is running a “buy one get one 50% off” sale today. During the sale, Laine bought 4 glazed donuts for only $3.78. What is the regular price for one glazed donut at Johnny’s Donut Shop?
Answer:
Step-by-step explanation:
Set up a simple system.
Price = 4x where x = price of donut
For the sale, the price = 3.78, but the x value is 0.5x as it is half off.
$3.78 = 4(0.5x)
Solve for x =$1.89
Therefore, the original price of the donuts were $1.89.
Check by doing 4 x 50%(.5) of 1.89 which equals 3.78!
7cm 5cm 10cm what is the total surface area of the figure and what is the volume of the figure. figure.
The total surface area of the cuboid with 7cm,5cm, and 10cm as dimensions is 310 square. cm and the volume is 350 cubic. cm.
Given dimensions of the figure are 7cm,5cm, and 10cm.
Length = 7cm.
Width = 5cm.
Height = 10cm.
The surface area of the cuboid = 2(lw+wh+lh).
Now, let us substitute the given values in the above formula.
2(7*5+5*10+7*10)
2(35+50+70)
2(155) = 310.
Therefore, the surface area of the figure is 310 square. cm.
Now, we have to find the volume of the figure.
Volume = Length x Width x Height.
Volume = 7*5*10
Volume = 350.
Therefore, the volume of the figure is 350 cubic. cm.
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The stem-and-leaf plot displays the amount of time, in minutes, that 10 players spent practicing their serving skills for an upcoming tennis tournament.
1 2, 2, 9
2 0, 2, 6
3 1, 1
4 0
5
6 8
Key: 3|1
means 31
Part A: Calculate the mean, median, mode, and range for the data given. Show your work. (8 points)
Part B: Should the tennis players report the mean or median value to show they are less prepared for the tournament? Explain based on the scenario. (4 points)
Part A:
To calculate the mean, we add up all the values and divide by the total number of values:
12 + 12 + 19 + 20 + 22 + 26 + 31 + 31 + 40 + 68 = 281
Mean = 281 / 10 = 28.1
To find the median, we need to find the middle value. Since there is an even number of values, we take the average of the two middle values:
Median = (22 + 26) / 2 = 24
The mode is the value that appears most frequently. In this case, there is no mode as no value appears more than once.
The range is the difference between the highest and lowest values:
Range = 68 - 12 = 56
Part B:
The median may be a better measure of central tendency in this scenario as there is an outlier value of 68 that can skew the mean. Since outliers can have a significant impact on the mean, reporting the median may give a better representation of the typical amount of time spent practicing for the tournament. Therefore, the tennis players should report the median value.
Consider a football team with a 13
-game schedule. Each game ends with a win (W), a loss (L), or a tie (T). Once the schedule is set, how many ways can the schedule end with 9
wins, 3
losses, and 1
ties?
Answer:
Step-by-step explanation:
To find the answer, we can use the formula for combinations:
nCr = n! / r!(n-r)!
where n is the total number of games, r is the number of losses, and n-r-1 is the number of ties (since we already know there are 9 wins).
Substituting the values, we get:
13C3 * 10C1
= (13! / 3!10!) * (10! / 1!9!)
= (13*12*11 / 3*2*1) * 10
= 2860
Therefore, there are 2860 ways the schedule can end with 9 wins, 3 losses, and 1 tie.
you have $5000 toward the purchase of a small boat that will cost $6000. how long will it take the $5000 to grow to $6000 if it is invested at 5% compounded monthly? solve algebraically. round to the nearest hundredth.
Verify the following identity. To transform the left side into the right side, should be changed to and the left side simplified.
To transform the left-hand side of the given identity "1 + cos(2x)" into the right-hand side "[tex]2cos^2(x)[/tex]", the expression "1" should be changed to "[tex]2sin^2(x)[/tex]" and the left-hand side should be simplified.
What is the meaning of trignometric identities?Trigonometric identities are mathematical equations that may be used to express trigonometric functions. These identities, which are also used to solve trigonometric equations, can be utilised to simplify and manage trigonometric expressions.
Trigonometric identities, which are derived from the geometric properties of triangles and the unit circle, provide a way to describe trigonometric functions in terms of other trigonometric functions or constants. In many areas of mathematics, physics, engineering, and other fields where trigonometry is used, they are commonly used.
Replacing "1" with "[tex]2sin^2(x)[/tex]".
[tex]1 + cos(2x) -- > 2sin^2(x) + cos(2x)[/tex]
Using the double angle formula for cosine
The double angle formula for cosine is: cos(2x) = [tex]2cos^2(x) - 1[/tex]
Substitute the double angle formula into the expression for cos(2x) on the left-hand side.
[tex]2sin^2(x) + cos(2x) -- > 2sin^2(x) + (2cos^2(x) - 1)[/tex] [Substitute cos(2x) with [tex]2cos^2(x) - 1[/tex]]
Simplify the expression on the left-hand side.
[tex]2sin^2(x) + (2cos^2(x) - 1) -- > 2sin^2(x) + 2cos^2(x) - 1[/tex] [Simplify using distributive property]
[tex]2sin^2(x) + 2cos^2(x) - 1 -- > 2(sin^2(x) + cos^2(x)) - 1[/tex] [Apply trigonometric identity [tex]sin^2(x) + cos^2(x) = 1[/tex]]
[tex]2(sin^2(x) + cos^2(x)) - 1 -- > 2(1) - 1[/tex] [Substitute [tex]sin^2(x) + cos^2(x)[/tex]with 1]
[tex]2(1) - 1 -- > 2 - 1\\2 - 1 -- > 1[/tex]
So, following simplification, the left-hand side equation "1 + cos(2x)" may be changed into "1." As a result, "1" in the equation needs to be altered to "2sin(x)" and the left side should be simplified to "1".
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The figure shows an isosceles right triangle. What is the length of the hypotenuse? Show your work.
The length of the hypotenuse is 4√2.
What is the Pythagoras theorem?
A fundamental relationship in Euclidean geometry between a right triangle's three sides is known as the Pythagorean theorem or Pythagoras' theorem. According to this rule, the area of the square with the hypotenuse side is equal to the sum of the areas of the squares with the other two sides.
Here, we have
Given: base = 4
perpendicular = 4
We have to find the length of the hypotenuse.
We apply here Pythagoras theorem and we get
b² + p² = h²
(4)² + (4)² = h²
16 + 16 = h²
32 = h²
h = 4√2
Hence, the length of the hypotenuse is 4√2.
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A quadratic function has x-intercepts at -7 and 1. The vertex of the function is at (-3, 16). What is the equation of the function?
A. f(x) = x^2 + 6x -7
B. f(x) = -x^2 - 6x+ 7
C. 7(x)=x^2 - 6x + 7
D. f(x)=-x^2 + 6x -7
[tex]f(x) = x^2 + 6x - 7[/tex] is the equation of the function.
What is the function?A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
To find the equation of the quadratic function, we need to use the vertex form of the equation:
[tex]f(x) = a(x - h)^2 + k[/tex]
where (h, k) is the vertex of the parabola.
We know that the vertex is (-3, 16), so h = -3 and k = 16. We also know that the x-intercepts are at -7 and 1, which means that the factors of the quadratic function are (x + 7) and (x - 1).
To find the value of 'a', we can use either of the x-intercepts:
[tex]f(-7) = a(-7 + 3)^2 + 16 = 0\\\\16a = 16\\\\a = 1[/tex]
Therefore, the equation of the quadratic function is:
[tex]f(x) = (x + 7)(x - 1)\\\\f(x) = x^2 + 6x - 7[/tex]
So the answer is (A)[tex]f(x) = x^2 + 6x - 7[/tex].
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Triangle P is rotated 180° about (0, 0) to give triangle Q.
Triangle Q is translated by 5 -2
to give triangle R.
(a) Describe fully the single transformation that maps triangle P onto triangle R.
Answer:
The single transformation that maps triangle P onto triangle R is a reflection about the origin followed by a translation of 5 units to the right and 2 units down.
Which two lanes are parallel
1. p || q
2. r || s
3. q || r
4. p || r
Answer:
4
Step-by-step explanation:
1p:80°-140。＝40°，40°
*Time limit help*
Tell me the domain and range
Tell me if the graph is a function or not.
Pick the right answer choice
A. Yes
B. No
C. -2<=x<=6
D. x>=-2
E. All real number
F. x<=6
G. -6<=y<=2
H. y>=-6
I. y<=2
J. y<=6
Examining the graph it can be deduced that
The domain is
C. -2<=x<=6The range is
G. -6<=y<=2The graph is not a function
How to tell if a graph is a function
To qualify as a function, any input (x-value) of a graph must be linked to a single output (y-value). Therefore, each x-value ought to have one and only one y-value that matches it.
A method for identifying whether or not a given graph is representative of a function is by conducting a vertical line test. To achieve this, vertically draw lines through the graph. When every vertical line hits the graph at just one point, then the illustration aptly presents a function. Conversely, if the graph forms multiple intersection points with any vertical line, it isn't classified as a functional representation.
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PLS HELP I NEED ASAP PLS
The number of volumes of the encyclopedia on the bottom shelf is given as follows:
H) 19.
How to obtain the number of volumes of the encyclopedia?The number of volumes of the encyclopedia on the bottom shelf obtained as the subtraction between the highest number and the lowest number identifying the numbers, adding one.
We add one as the amount of numbers between n and n + 1, inclusive, is of n + 2. For example, between 12 and 13, we have two numbers.
Then the number of volumes of the encyclopedia on the bottom shelf is given as follows:7
30 - 12 + 1 = 19.
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Write the trigonometric ratio as a simplified fraction.
10. sin B
C9
A
C
6
15 C
B
11. cos A
12. tan A
10.
11.
12.
The value of the trigonometric ratios are;
sin A = 2/5
cos A = 3/5
tan A = 2/3
How to determine the ratiosIt is important to note that there are six different trigonometric identities and their ratios.
We have;
sine cosinetangentcotangentsecantcosecantFrom the diagram shown, we have;
sin θ = opposite/hypotenuse
cos θ = adjacant/hypotenuse
tan θ = opposite/adjacent
Then,
sin A = 6/15 = 2/5
cos A = 9/15 = 3/5
tan A = 6/9 = 2/3
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The value of the trigonometric ratios are;
sin A = 2/5
cos A = 3/5
tan A = 2/3
How to determine the ratiosIt is important to note that there are six different trigonometric identities and their ratios.
We have;
sine cosinetangentcotangentsecantcosecantFrom the diagram shown, we have;
sin θ = opposite/hypotenuse
cos θ = adjacant/hypotenuse
tan θ = opposite/adjacent
Then,
sin A = 6/15 = 2/5
cos A = 9/15 = 3/5
tan A = 6/9 = 2/3
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What are the values of s and t?
S-62 degrees
T-76 degrees
Step-by-step explanation:
IJ and KJ are congruent, so s would have the same measurement as I.
You would simply subtract from both s and i to get t.
which is not a function and what is a function
17. La inscripción en una clase de negocios disminuyó de 25 a 15 estudiantes. ¿Cuál fue el porcentaje de disminución en la inscripción
Answer:
40%
Step-by-step explanation:
In parallelogram NPQR if RS=19 find SP.
Answer:
SP = 19
Step-by-step explanation:
the diagonals of a parallelogram bisect each other, then
SP = RS = 19
reflect the figure over the line y= -2x - 1
The reflection of the figure over y = -2x - 1 is attached accordingly.
What is reflection in math?A reflection in mathematics is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a fixed point set; this set is known as the axis or plane of reflection.
Because the line of reflection has a slope of -1/2, each image point will be on a line with a slope of 2 that passes through the associated pre-image point.
It might be simplest to count the grid squares between the pre-image point and the line, then from the line to the image point's location. Those measurements will be the same.
The second attachment shows the mirrored image.
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Some sources report that the weights of full-term newborn babies in a certain town have a mean of pounds and a standard deviation of pounds and are Normally distributed.
a. What is the probability that one newborn baby will have a weight within pounds of the meanthat is, between and pounds, or within one standard deviation of the mean?
b. What is the probability that the average of babies' weights will be within pounds of the mean; will be between and pounds?
c. Explain the difference between (a) and (b).
the screenshot is below
Answer:
Step-by-step explanation:
A
I need help with this ?
The solution of the equation is [tex]z = \frac{[-9 \±9\sqrt{3 i}]}{2}[/tex]
Given is an equation, [tex]\frac{1}{z+9} -\frac{1}{z} = \frac{1}{9}[/tex], we need to solve it,
[tex]\frac{1}{z+9} -\frac{1}{z} = \frac{1}{9}[/tex]
[tex]\frac{z-(z+9)}{z(z+9)} = \frac{1}{9}[/tex]
[tex]\frac{-9}{z^2+9z} =\frac{1}{9}[/tex]
[tex]z^2+9z = -81\\\\z^2+9z+81 = 0[/tex]
Using the quadratic formula,
[tex]x = \frac{[-b \±\sqrt{(b^2-4ac)}]}{2a}[/tex]
here, a = 1, b = 9 and c = 81.
So,
[tex]z = \frac{[-9 \±\sqrt{(81-4(81))}]}{2}\\\\z = \frac{[-9 \±\sqrt{(-243)}]}{2}\\\\\\\\\z[/tex]
[tex]z = \frac{[-9 \±9\sqrt{3 i}]}{2}[/tex]
Hence, the solution of the equation is [tex]z = \frac{[-9 \±9\sqrt{3 i}]}{2}[/tex]
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an industrial comp machine has the ability to reduce image dimensions by a certain percentage each time it copies. A design began with a length of 16 inches, represented by the point (0,16). after going through the comp machine once, the length is 12, represented by the point (1,12). Enter the correct answer in the box by replacing the values of a and b. f(x)=a(b)^x
Answer:
f(x) = 16*0.75^x
Step-by-step explanation:
first off let's use this coordinate (the one given) :
(0,16)
let's substitute this into the equation with x being 0 and f(x) being 16
16 = a*b^0
*anything to the power of 0 is 1*
so:
a = 16
now use the second coordinate :
(1,12)
and do the same by substituting 1 for x and 12 for f(x), we also know what 'a' is:
12 = 16*b^1
12 = 16 * b
b = 3/4
so :
f(x) = 16*0.75^x
Which of the following is the solution to the system of linear equations graphed below?
The solution to the system of linear equations graphed below is (3, -1).
Given are two graphs of linear equations.
The solution of a system of linear equations can be solved either numerically or graphically.
In the graphical method, the solution of a system of linear equations is the point where all the lines intersect.
Here the lines of both the equations intersect at (3, -1).
This means that the intersecting point is (3, -1).
Solution is (3, -1).
Hence the required solution is (3, -1).
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Verify the following Pythagorean identity for all values of x and y:
(x² + y²)² = (x² - y²)² + (2xy)²
The identity (x² + y²)² = (x² - y²)² + (2xy)²
What is an identity?An identity is a mathematical equation which shows that one side of the equation is equivalent and equal to the other side of the equation.
To verify the following Pythagorean identity for all values of x and y:
(x² + y²)² = (x² - y²)² + (2xy)², we need to shows that
left-hand side L.H.S = right hand side
So, we proceed as follows
L.H.S = (x² + y²)²
Expanding the brackets, we have that
(x² + y²)² = (x² + y²)(x² + y²)
= (x²)² + 2x²y² + (y²)²
= (x²)² + (y²)² + 2x²y²
Now, we know that (a - b)² = a² + b² - 2ab. So,
a² + b² = (a - b)² + 2ab
Let a = x² and b = y²
So, we have that
(x²)² + (y²)² = (x² - y²)² + 2x²y²
So, substituting this into the equation, we have that
(x²)² + (y²)² + 2x²y² = (x² - y²)² + 2x²y² + 2x²y²
= (x² - y²)² + 4x²y²
= (x² - y²)² + 2²x²y²
= (x² - y²)² + (2xy)²
So, Since L.H.S = R.H.S
(x² + y²)² = (x² - y²)² + (2xy)²
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Pls help me by 11 pm
Answer:
Surface Area = 2×(3.5×10 + 3.5×8 + 10×8) = 286 feet
Step-by-step explanation:
First, multiply 3.5 by 10 (35)
Secondly, multiply 3.5 by 8 (28)
Then, multiply 10 by 8 (80)
Next, add all the values together (143)
And lastly, multiply 143 by 2 (286)
Please turn this into your own work, (By making it look like it's worked out) since they can catch you for Plagiarism.
Measure the lengths of the following segments in inches.
A.
Length of : __________ in.
B.
Length of : __________ in.
9. Measure the lengths of the following segments in BOTH centimeters and
millimeters. (2 points each)
A.
Length of : __________ cm
Length of : __________ mm
B.
Length of : __________ cm
Length of : __________ mm
Answer:
is the answer A????????????
to be honest I’m only here for the answers but I also need the points
The graph of y=g(x) is shown. Draw the graph of y=-g(x)+1
The graph of the absolute value function y = -g(x) + 1 is shown in the image attached below.
The graph of the absolute value function y = 2h(x + 4) is shown in the image attached below.
What is a translation?In Mathematics, the translation a geometric figure or graph upward simply means adding a digit to the value on the y-coordinate of the pre-image or function.
In Mathematics, a vertical translation to the positive y-direction (upward) is modeled by this mathematical expression g(x) = f(x) + N.
Where:
N represents an integer.g(x) and f(x) represent a function.In this scenario, we can logically deduce that the equation of the first parent absolute value function is g(x) = |2x| and it would be reflected over the y-axis, and then translated by 1 units upward;
g(x) = |2x|
y = -g(x) + 1 = |2x| + 1
h(x) = |2x + 4| - 4
y = 2h(x + 4)
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Denzel used the spinner shown below to compare theoretical probability and experimental probability. He spun the spinner 180 times and recorded the letter that it landed on each time. The results are shown in the table.
Which statement correctly compares the theoretical probability and experimental probability for one of the letters on the spinner?
A. The theoretical probability of landing on a C is greater than the experimental probability of landing on an C.
B. The theoretical probability of landing on a D is greater than the experimental probability of landing on an D.
C. The theoretical probability of landing on a B is less than the experimental probability of landing on an B.
D. The theoretical probability of landing on an A is less than the experimental probability of landing on an A.
Comparing the two probabilities option d: The theoretical probability of landing on an A is less than the experimental probability of landing on an A. is correct.
What is theoretical probability?The chance of an event based solely on mathematical precepts or hypotheses, without any actual experiments or observations, is known as theoretical probability. Probability theory frequently uses theoretical probability to create predictions about the chance of events occurring based on presumptions or models.
On the other hand, experimental probability is the likelihood of an event based on real observations or experiments. A set of trials or experiments are conducted to determine the experimental probability, and the number of times the event occurs during those trials is counted.
For the given spinner the theoretical probability of landing on any one letter is:
P(one letter) = 1/4
Now, experimental probability is given as:
Experimental probability of A = 36/180 = 0.2
Experimental probability of B = 48/180 = 0.2667
Experimental probability of C = 51/180 = 0.2833
Experimental probability of D = 45/180 = 0.25
Thus, comparing the two probabilities option d: The theoretical probability of landing on an A is less than the experimental probability of landing on an A. is correct.
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