Answer: The interval in which the greatest number of scores would occur is between (20 - 2.6) and (20 + 2.6), which is approximately 17.4 and 22.6 respectively. This interval is also known as the "bell curve" or the "normal distribution curve" and it is centered at the mean (20) and covers approximately 68% of all possible scores. Most of the data points would fall within one standard deviation of the mean, hence the greatest number of scores would occur in this interval.
Step-by-step explanation:
Solve for x in the equation x squared 11 x startfraction 121 over 4 endfraction = startfraction 125 over 4 endfraction.
The solutions are { -1,-11}
Lets solve the given equation:
x^2 + 11x + 121/4 = 125/4
Subtracting 125/4 from both sides:
=>x^2 + 11x + 121/4-125/4= 125/4 -125/4
=> x^2 + 11x - (-4/4) = 0
=> x^2 +11x -(-1) = 0
=>x^2 + 11 x + 1 = 0
This is a quadratic equation so we will use the determinant (b^2-4ac)
a = 1
b = 11
c = 1
b^2-4ac = 11^2-4*1*1 = 117
So this equation has two solutions:
x = (-b -/+ √(b^2-4ac) ) / 2a
x = (-11 -/+ √(117) ) / 2
x = (-11 -/+ 3√(13))/ 2
x = -0.91 or x = -10.9
x = -1 or x = -11 ( rounding off)
hence the solutions are { -1,-11}.
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Consider this expression.
x
2
+
x
−
72
Replace the values of a and b to rewrite the given expression.
Answer:
(x+9) (x-8)
Step-by-step explanation:
Edmentum/Plato
(1)[3 Pts] The probability of producing a high-quality color print is 0.10. How many prints do you have to produce so that the probability of producing at least one quality print is larger than 0.90
The number of prints that the probability of producing at least one quality print is 22.
Given that the probability of producing a high-quality color print is 0.10.
The binomial distribution summarizes the number of trials or observations when each trial has an equal chance of reaching a certain value. The binomial distribution determines the probability of observing a particular number of positive results in a defined number of tests.
Probability of high-quality color print (P) = 0.1
Probability of producing not high-quality color print (1-P) = 0.9
Assume the no. of prints to produce 'n' and these are produced independently say 'x' be the no. of producing quality prints, which follows a binomial distribution.
The probability function of binomial distribution is
[tex]P(X=x)\left(\begin{array}{l}n\\ x\end{array}\right)P^x(1-P)^{n-x},x=0,1,2,.....,n[/tex]
Given that
P(X≥1)≥0.90
1-P(X=0)≥0.90
1-(1-P)ⁿ≥0.90
1-(0.90)ⁿ≥0.90
(0.90)ⁿ≥0.10
Now, taking log of both sides, we get
nlog(0.90)≥log(0.10)
n(0.1053)≥2.3025
n≥21.86
n≈22
Hence, the probability of producing a high-quality color print is 0.10 and the number of prints to produce so that the probability of producing at least one quality print is larger than 0.90 is 22.
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C
The graph of f(x) is shown.
O-4,0,2
For what values of x does f(x) = 0?
O-2.0.4
O-5.0.17
45
O-17.0.5
40 bcpp
Answer: -4, 0, 2
Step-by-step explanation:
The graph intersects the x-axis at [tex]x=-4, x=0, x=2[/tex].
Solve for x. − 15 = 22 x + 7
Answer:
x = - 1
Step-by-step explanation:
- 15 = 22x + 7 ( subtract 7 from both sides )
- 22 = 22x ( divide both sides by 22 )
- 1 = x
write an equation for the line through (5,7) parallel to 2x-5y=15
Answer:
I don't know.i don't know
cannonball is shot into the air. its height can be described by the equation h = -5t2 + 40t, where h is the height in feet and t is the time is seconds. when will the cannonball hit the ground?
Answer:
Step-by-step explanation:
hello :
the cannonball hit the ground when h=0
-5t² + 40t=0 means : -5t(t- 8)=0
t=8
A popular roller coaster ride lasts 10 minutes. There are 20 people on average on the roller coaster during peak time. How many people are stepping onto the roller coaster per minute at peak time
There are 2 people are stepping onto the roller coaster per minute at peak time
According to statement
Given Flow time = 10 minutes.
Given Inventory = 20.
We use the formula then
I = R × T,
Therefore R = I / T.
Substitute the values in formula then
Flow rate = 20 / 10 = 2 people per minute.
So, There are 2 people are stepping onto the roller coaster per minute at peak time
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Which graph represents the function p(x) = |x-1|?
-3
O
-2-
-3.
O
64-3
3.
2
2
3
O
5
Graph is in the attached image.
A client has just inherited a property. the deed is quite old, but she knows where the front two corners of the property are and that the distance between them is 210 feet. the shape is an irregular quadrilateral and the other three sides have distances of 515 feet, 232 feet, and 542 feet in a clockwise direction from the front left corner. more importantly, it is known that the front left corner of the property is a right angle.
This exercise involves the construction of a blueprint. To do so, we need to solve for angles using the Cos Rule. See the step by steps procedure below.
What is a blueprint?A blueprint is a masterplan that highlights how a structure will be look like when it is completed.
What is the solution to the above blueprint?Let the dimensions of the property be labelled QRST.Recall that the distance between the two corners are QR = 210 ftOther sides are: 515ft, 232ft, and 542ft going in a clockwise direction.Recall that the front left corner of the property is a right angle.From the above, see attached the first simple quadrilateral QRST (Draft I) that is indicates the above information.
Next Step
We have to derive ∠T, ∠ S, and ∠R.
In order to achieve the above, we must split the quadrilateral into two triangles.
As noted in the image, the quadrilateral is bisected from R to T.
∠R and ∠T are also divided into R1 R2 and T1, T2 respectively.
Next step - Derive ∠T1 and ∠R1 .
To do the above, we must deploy the Pythagoras Theorem. (PT)
PT requires:
TR² = QT² + QR²
TR² = (210)² + (515)²
TR² = 44,100 + 265,225
TR² = 309,325
TR = √309,325
TR = 556.17
Next step, Derive T1
We can derive T1 using the cos rule:
Cos T1 = QR/QT
= 515/556.17
Cos T1 = 0.926
Therefore
T1 = Cos⁻¹(0.926)
T1 = 22.18°
Next we derive R1
R1 = 180° - (90° + 22.18°)
R1 = 67.82°
In ΔTRS, by using Cosine Rule,
Cos T2 = [TS² + QR² - RS²]/2(TS) * (TR)
Cos T2 = [(232)² + (556.16)² - (542)²]/ 2 * (232) x (556.16)
Cost T2 = 69,373.945/258,058
Cost T2 ≈ 0.269
Therefore,
T2 = Cos⁻¹(0.269)
T2 ≈ 74.4°
Applying the same process, we can derive R2
Cos R2 = TR² + RS² - TS²
Cos R2 = [(556.16)² + (542)² - (232)²] / 2 (556.16) * (542)
Cost R2 = 0.911
R2 = Cos ⁻1 (0.911)
R2 = 24.34°
From the above, we can execute the following iterations:
∠S = 180° - (R2 + T2)
= 180 ° - (24.34 + 74.4)
∠C = 81.26°
Likewise:
∠R = R1 + R2
= 67.82 + 24.34
∠B = 92.16°
Lastly:
∠T = T1 + T2
= 22.18 + 74.40
∠T = 96.48°
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Full Question:
A client has just inherited a property. The deed is quite old, but she knows where the front two corners of the property are and that the distance between them is 210 feet. The shape is an irregular quadrilateral and the other three sides have a distance of 515 feet, 232 feet, and 542 feet in a clockwise direction from the front left corner. More importantly, it is known that the front left corner of the property is a right angle.
-Construct a blueprint of the property labeling the measures of all sides and angle of the property.
Total area=
Help me please thanks so much :)
The surface area of the square pyramid is: 220 units².
What is the Surface Area of a Square Pyramid?Surface area of a square pyramid = 1/2(base perimeter)(slant height) = 1/2(P)(l).
Given the following:
Perimeter of base (P) = 4(10) = 40 units
Slant height (l) = 11 units
The surface area of the square pyramid = 1/2(40)(11)
Surface area of the square pyramid = 220 units²
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The tree diagram represents an experiment consisting of two trials
P(D)=?
For the given tree diagram of the experiment consisting of two trials, P(D) = 0.74
A method that can be infinitely repeated and has a clearly defined range of potential outcomes, or sample space, is referred to as an experiment or trial in probability theory. If there are multiple possible outcomes from an experiment, it is considered to be random; if there is just one, it is said to be deterministic.
Calculation of P(D) for the given experiment:
From the first branch of the tree, P(D) = 0.7 × 0.6
P(D) = 0.42
From the second branch of the tree, P(D) = 0.8 × 0.4
P(D) = 0.32
Hence, the probability of getting D in the experiment is,
P(D) = P(D) from first branch of the tree + P(D) from the second branch of the tree
P(D) = 0.42 + 0.32
P(D) = 0.74
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Please answer both questions.
Answer:
1) (x-6)^2=49
2) C
Step-by-step explanation:
Subtract 12 x and you get
-x^2-12x+13=0
You will be left with, after making a perfect square
(x-6)^2=49
To get rid of the squared/2nd power, add plus or minus to the opposite side and square root both sides. You will be left with
x-6=plus or minus 7
Your answer comes out to the to problem. Setting both to 0, you get -13, and 1. -6 plus 7 is 1, and -6 plus a -7 is -13.
Hugh bought some magazines that cost $3.95 each and some books that cost $8.95 each. he spent a total of $47.65. the equation that models the problem is 3.95m+8.95b=47.65, where m is the number of magazines and b is the number of books
Hugh bough 4 books.
What is linear equation ?
A linear equation only has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction. When you find pairs of values that make a linear equation true and plot those pairs on a coordinate grid, all of the points lie on the same line.The cost of magazines =
3.95(3) + 8.95b = 47.65
11.85 + 8.95b = 47.65
Subtract 11.85 from both sides.
8.95b = 35.8
Divide 8.95 from both sides.
b = 4
Therefore, Hugh bough 4 books.
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The complete question is -
Hugh bought some magazines that cost $3.95 each and some books that cost $8.95 each. He spent a total of $47.65. If Hugh bought 3 magazines, how many books did he buy? The equation that models the problem is 3.95m + 8.95b = 47.65, where m is the number of magazines and b is the number of books.
Which expression is equivalent to (r^5/4
Answer:
2
Step-by-step explanation:
• Multiplying two numbers with same bases is the same as adding their powers:
∴ [tex](\frac{4^{\frac{5}{4} } \cdot 4^{\frac{1}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }[/tex]
⇒ [tex](\frac{4^{\frac{5}{4} } ^ + ^{\frac{1}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }[/tex]
⇒ [tex](\frac{4^{\frac{6}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }[/tex]
• Dividing two numbers with same bases is the same as subtracting their powers:
∴ [tex](\frac{4^{\frac{6}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }[/tex]
⇒ [tex](4^{{\frac{6}{4} - \frac{1}{2} }})^{\frac{1}{2} }[/tex]
⇒ [tex](4^{1})^{\frac{1}{2} }[/tex]
⇒ [tex]4^{\frac{1}{2}[/tex]
• Raising anything to the power of [tex]\frac{1}{2}[/tex] is the same as square-rooting it:
∴ [tex]4^{\frac{1}{2}[/tex]
⇒ [tex]\sqrt{4}[/tex]
⇒ 2
2
The trapezium, ABCD, has four angles as shown.
All the angles are in degrees.
A
2x + 5
B
3y-20
(i) Show that 7x + 4y = 390.
(ii) Show that 2x + 3y = 195.
PLEASE HELP THIS IS URGENT!!!
A random sample of 1001 Americans aged 18-24 years showed that 51% believe their health is extremely important. The interval that is 95% certain to contain the proportion of all 18-24 year olds who believe that their health is extremely important is
Between 48% and 54% believe that their health is extremely important.
According to the statement
Given that a random sample of 1001 Americans aged 18-24 years showed that 51% believe their health is extremely important.
Here
Sample size n =1001
sample proportion p = 0.51
By these values we calculate the Standard error of proportion.
So, Standard error of proportion = 0.0158.
Since sample size is sufficiently large we can take Z critical value for confidence interval
Z critical value for 95% = 1.96
Margin of error = ±1.96*std error
= ±0.0310
confidence interval = 0.51 ±0.0310
= (0.48, 0.54)
So, Between 48% and 54% believe that their health is extremely important.
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Triangle L N M is shown. Angle L N M is 90 degrees and angle N M L is 20 degrees. The length of L N is 21.
Use the diagram to complete the statements.
The measure of angle L is
°.
The trigonometric ratio that uses ∠M and LN to solve for NM is
.
The length of NM, to the nearest tenth, is approximately
.
The length of the triangle will be equal to 2.7.
How to calculate the length?It should be noted that that sin will be the opposite divided by the hypothenuse.
The measure of angle L is 20°.
This will be:
sin 20 = LN/8
NM = 8 sin 20
NM = 2.7
In conclusion, NM is 2.7.
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Answer: 2.7
Step-by-step explanation: TRUST ME!!! Answer is correct on Edge!!! :)
EXTRA POINTS
x/4 ÷ 2/3 = 1/5 solve for x
Answer:
x=40
Step-by-step explanation:
first you simplify both sides of the equation, then you isolate the variable
40/4= 10
10 times 3/2 = 15
I need a proper answer and its urgent pls
perimeter of triangle park is x+y+xy meter. Length of two sides are x-z+yx meter and z+x+xz meter find the third side
Answer:
Step-by-step explanation:
hello :
the perimeter of triangle is : P= (x-z+yx)+( z+x+xz)+A
given P=x+y+xy calculate the third side A
x+y+xy = (x-z+yx)+( z+x+xz) so : A=x+y+xy -x+z-yx-z-x-xz....continu
a=
If the perimeter of the triangle park is x + y + xy meter. Then the third length of the triangle will be y - x - xz meters.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The perimeter of the triangle is determined by adding together all of its sides.
The perimeter of the triangle park is x + y + xy meter. The length of the two sides are x - z + yx meter and z + x + xz meter.
Let the third side be 'A'. Then the third length of the triangle is given as,
x + y + xy = (x - z + xy) + (z + x + xz) + A
x + y + xy = x - z + xy + z + x + xz + A
y = x + xz + A
A = y - x - xz
If the perimeter of the triangle park is x + y + xy meter. Then the third length of the triangle will be y - x - xz meters.
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The theater club of a local high school is planning a production. The amount of time t needed to assemble the set is inversely proportional to the number of people n working. Twelve people can assemble the set in 5 hours.
Write an equation to represent the situation.
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If the average (arithmetic
mean) of 2, 7, and x is 12,
what is the value of x?
Answer: 27
Step-by-step explanation:
Mean = Sum of data/Number of data = (2 + 7 + x)/3 = 12
(x+9)/3 = 12
x+9 = 36
x = 27
A data set that includes the values given by customers to determine their level of satisfaction with their purchases. the scale used is very satisfied, somewhat satisfied, somewhat dissatisfied, and very dissatisfied. the data of the customer responses would be classified as what type of data
The data of the customer responses would be classified as ordinal data.
What is ordinal data?Ordinal data is a category of categorical data that has a predetermined order or scale. Ordinal data, for instance, is said to have been gathered when a respondent rates their level of financial contentment on a scale from 1 to 10. There is no established scale for measuring the variance of each score in ordinal data.
Ordinal data is a categorical statistical data type when the distances between the categories are unknown and the variables have naturally occurring, ordered categories. On an ordinal scale, these data are available. By having a ranking, the ordinal scale differs from the nominal scale.
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Find the surface area of the composite figure. Round your answer to the nearest tenth if necessary.
The surface area of the composite figure is 444m².
Given a composite figure which is shown in the question.
The area of a shape (in square units) is the number of unit squares required to cover the entire area without gaps or overlaps. If a hologram has planes, those faces are called faces.
Firstly, we will find the area of front and end triangles by using the formula
Area=(1/2)×b×h and we will multiply this area by 2 because we are finding the area of two same triangles.
Here, h=6 and b=16 and substitute these values in the formula, we get
A₁=2×(1/2)×16×6
A₁=2×8×6
A₁=96m²
Now, we will find the area of the left and right side rectangles which joined both the triangles.
We will find the area by using the formula Area=l×b and we will multiply this area by 2 because we are finding the area of two same rectangles.
here, l=10 and b=5 and substitute these values in the formula, we get
A₂=2×10×5
A₂=100m²
Further, we will find the area of the front and end side rectangles that joined both by the base of the triangles.
We will find the area by using the formula Area=l×b and we will multiply this area by 2 because we are finding the area of two same rectangles.
here, l=16 and b=4 and substitute these values in the formula, we get
A₃=2×16×4
A₃=128m²
Furthermore, we will find the area of the left and right side rectangles which joined by the front and end rectangles.
We will find the area by using the formula Area=l×b and we will multiply this area by 2 because we are finding the area of two same rectangles.
here, l=4 and b=5 and substitute these values in the formula, we get
A₄=2×4×5
A₄=40m²
Now, we will find the area of the base of the composite figure which is rectangle.
We will find the area by using the formula Area=l×b.
here, l=16 and b=5 and substitute these values in the formula, we get
A₅=16×5
A₅=80m²
So, the surface area of the given composite figure will be
Surface area=A₁+A₂+A₃+A₄+A₅
Surface area=96m²+100m²+128m²+40m²+80m²
Surface area=444m²
Hence, the surface area of the given composite figure is 444m².
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One column of numbers consists of 28,42,14. When the digits of the numbers are added together, the result is 2+8+4+2+1+4=21, and when the digits of 21 are then added together, the end result is 2+1=3. If the same process is performed on the numbers in a second column, what can be concluded?
Option D. What we can conclude is that If the end result from the second column is not 3, then the sum of the numbers in the first column is not equal to the sum of the numbers in the second column.
How to solve for the solutionAn operation is done on a first column of numbers. When this operation is repeated on the second column, we would have option D.
If the sum of the numbers that are in the third can be seen to be greater than three, then the sums are not going to be seen as equal
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Complete questionOne column of numbers consists of 28, 42, and 14. When the digits of the numbers are added together, the result is 2 + 8 + 4 + 2 + 1 + 4 = 21, and when the digits of 21 are then added together, the end result is 2 + 1 = 3. If the same process is performed on the numbers in a second column, what can be concluded?
A. If the end result from the second column is also 3, then the sum of the numbers in the first column is not equal to the sum of the numbers in the second column.
B. If the end result from the second column is not 3, then the sum of the numbers in the first column is equal to the sum of the numbers in the second column.
C. If the end result from the second column is also 3, then the sum of the numbers in the first column is equal to the sum of the numbers in the second column.
D. If the end result from the second column is not 3, then the sum of the numbers in the first column is not equal to the sum of the numbers in the second column.
Felix’s total credit card balance is described by the following function: f(p) = p(1.30). If Felix owes $2500, what is the total bill plus interest?
$3,250
$32,500
$325
None of the choices are correct.
The total bill plus interest on the credit card is $3,250
What is credit card?
Credit card gives its holder the opportunity to make purchases on credit such that amount spent and the interest that accrues thereon would be paid by the credit card holder at a future time.
In this case, the function shows the relationship between the amount owed and the interest so as to give the outstanding balance.
f(p) = p(1.30)
p=amount owed=$2,500
f(p)=$2,500*(1.30)
f(p)=$3,250
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In which diagram do angles 1 and 2 form a linear pair?
2 lines intersect and form 4 angles. Labeled clockwise from the top: blank, 2, blank, 1.
3 lines extend from a point and form 2 angles, labeled 1 and 2. Both angles add up to 90 degrees.
A horizontal line has 2 lines extending from a midpoint forming 3 angles. Labeled from left to right: 1, 2, 3.
A horizontal line has 1 line extending from it. Angles 1 and 2 are formed.
Mark this and return
The diagram where angles 1 and 2 form a linear pair is option D which is that a horizontal line has 1 line extending from it. Angles 1 and 2 are formed.
Given that angle 1 and 2 form a linear pair.
We know that a linear pair is an angle that are formed when two lines intersect each other at a single point.
In our case when a horizontal line has 1 line extending from it and when angles 1 and 2 are formed shows a linear pair.
In first part when two lines intersect they donot form 4 angles.
In second part when 3 lines extend from a point they don't form right angle between the lines.
Hence the linear pair angles are shown by the statement that a horizontal line has 1 line extending from it. Angles 1 and 2 are formed.
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Sean tried to drink as fast as he could. He drank the slushy at a constant rate. There were originally 275 milliliters of slushy in the cup. After 13 seconds, 210 milliliters of slushy remained. (Please help and explain.)
How fast did Sean drink?
How long did it take Sean to drink all the slushy?
The rate at which Sean drank the slushy is 5 milliliters per second.
The time it would take to drink all the slushy is 55 seconds.
How fast did Sean drink?In order to determine the speed at which the slushy was drank, divide the slushy drank in 13 seconds by 13 seconds.
Speed = slushy drank in 13 seconds / time
(275 - 210) / 13
65 / 13 = 5 milliliters per second
Time it would take to drink all the slushy =total milliliters of the slushy / speed
275 / 5 = 55 seconds.
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Six sophomores and 14 freshmen are competing for two alternate positions on the debate team. which expression represents the probability that both students chosen are sophomores? startfraction (20 c 6) (19 c 5) over 20 c 2 endfraction startfraction (20 p 6) (19 p 5) over 20 p 2 endfraction
The probability expression is [tex]\frac{^{6}C_2}{^{20}C_2}[/tex]
How to determine the probability expression?The given parameters are
Sophomore = 6Freshmen = 14The total number of people is
n = 20
2 of the 20 people are to be selected.
So, the number of selection is
[tex]n = ^nC_r[/tex]
This gives
[tex]n = ^{20}C_2[/tex]
The expression that represents both students being sophomore is
[tex]n = ^{6}C_2[/tex] --- i.e. 2 students selected from 6
The probability is then represented as:
[tex]\frac{^{6}C_2}{^{20}C_2}[/tex]
Hence, the probability expression is [tex]\frac{^{6}C_2}{^{20}C_2}[/tex]
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Answer:
a
Step-by-step explanation:
edge 2023
Find Q2 of the following data set 3, 9, 12, 4, 6, 40, 25, 14, 10
Answer:
Q₂ = 10
Step-by-step explanation:
Given data set: 3, 9, 12, 4, 6, 40, 25, 14, 10
Q₂ is the median (the middle value) of the given data set when the data set is ordered from smallest to largest.
Order the values in the data set:
3, 4, 6, 9, 10, 12, 14, 25, 40
As the number of values is odd, the middle value is the 5th value.
Therefore, the median (Q₂) of the given data set is 10.
If the number of data values is even, and therefore there are two middle values, the median is halfway between them.