The probability that the value of p(x) is greater than 315 is 0.063754
How to determine the probability that the value of p(x) is greater than 315?From the question, the given parameters about the distribution are
Mean value of the set of data = 283Standard deviation value of the set of data = 21The actual data value = 315The z-score of the data value is calculated using the following formula
z = (x - mean value)/standard deviation
Substitute the given parameters in the above equation
z = (315 - 283)/21
Evaluate the difference of 315 and 283
z = 32/21
Evaluate the quotient of 32 and 21
z = 1.524
The probability that the value of p(x) is greater than 315 is then calculated as:
P(x > 315) = P(z > 1.524)
From the z table of probabilities, we have;
P(x > 315) = 0.063754
Hence, the probability that the value of p(x) is greater than 315 is 0.063754
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On parallelogram ABC∧
mΔA=42 mΔB=___ mΔC___ mΔD=___
The measures of the remaining angles of the parallelogram are m ∠ B = 138°, m ∠ C = 42° and m ∠ D = 138°
How to determine the measure of missing angles in a parallelogram by geometric theorems
In this problem we know the measure of an angle and we should find the values of the three remaining angles. According to Euclidean geometry, the sum of internal angles in a parallelogram equals 360° and there exists the following property between each pair of angles:
m ∠ A = m ∠ Cm ∠ B = m ∠ Dm ∠ A + m ∠ B = m ∠ B + m ∠ C = m ∠ C + m ∠ D = m ∠ A + m ∠ D = 180°Then, the measures of the missing angles are, respectively:
m ∠ B = 180° - m ∠ A
m ∠ B = 180° - 42°
m ∠ B = 138°
m ∠ D = 138°
m ∠ C = 42°
Remark
The statement is poorly formatted, presents typing mistakes and image is missing, correct form is shown below:
On parallelogram ABCD, m ∠ A = 42, m ∠ B = ____, m ∠ C = _____, m ∠ D = _____
A representation of the parallelogram is shown in the image attached below.
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Given u = 3i − 8j and v = −4i + 8j, what is u • v? 73 8 −76 −56
Explanation:
We're applying the dot product.
u dot v = 3*(-4) + (-8)*8
u dot v = -12 - 64
u dot v = -76
The idea is that we multiply the x coordinates together, and the y coordinates together separately. Afterward you add the products. The result of any dot product is a scalar value, aka a single number.
The dot product is useful in many applications. One of which is to determine if two vectors are orthogonal.
The angle bisectors of a triangle intersect at a point called the
Answer:
incenter
Step-by-step explanation:
I need help with the questions in this photo
Part I: The correct formula is D. ((x₁ + x₂)/2, (y₁ + y₂)/2)
Part II: The midpoint of the segment with endpoints (-2, -1) and (0, 9) is (-1, 4)
Calculating the midpoint of a line segmentFrom the question, we are to determine the formula for calculating the midpoint of a segment
The midpoint of a segment can be determined by using the formula,
Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)
The correct formula is D. ((x₁ + x₂)/2, (y₁ + y₂)/2)
II. To determine the midpoint of the segment with endpoints (-2, -1) and (0, 9)
x₁ = -2
y₁ = -1
x₂ = 0
y₂ = 9
Putting the parameters into the formula,
Midpoint of the segment = ((-2 + 0)/2, (-1 + 9)/2)
Midpoint of the segment = (-2/2, 8/2)
Midpoint of the segment = (-1, 4)
Hence, the midpoint of the segment with endpoints (-2, -1) and (0, 9) is (-1, 4)
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Simplify. ‒36 ÷ (27 ÷ 3 ∙ 2)
The simplified value of expression -36/(27/3*2) is -8.
Given an expression -36/(27/3*2).
We are required to find the simplified value of given expression. To simplify the expression we need to use addition,subtraction,multiplication, division, brackets, etc. We can say that we have to use BODMAS in order to find the simplified value of expression.
Expression is combination of numbers, symbols, coefficients, determinants, indeterminants, fraction,algebraic operations,etc. usually not found in equal to form.
The given expression :
=-36/(27/3*2) (Multiplying 3 and 2 first)
=-36/(27/6)
=(-36*2)/9 (Invert the fraction given in denominator)
=-72/9 (Multiplying -36 to 2)
=-8
Hence the simplified value of expression -36/(27/3*2) is -8.
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Which table of values represents a function?
x y
-3 10
4 4
-5 -3
4 4
x y
2 8
6 9
6 3
5 7
x y
1 2
1 4
1 6
1 8
x y
5 2
-3 2
2 2
1 7
The table in the list of tables that represent an actual function is the first table i.e.
x y
-3 10
4 4
-5 -3
4 4
How to determine the table of values represents a function?The table of values is given as:
Table 1
x y
-3 10
4 4
-5 -3
4 4
Table 2
x y
2 8
6 9
6 3
5 7
Table 3
x y
1 2
1 4
1 6
1 8
Table 4
x y
5 2
-3 2
2 2
1 7
For a table to represent a function, each of the x value on the table must correspond to exactly one y value
i.e.
x1 = y1
x2 = y2
And so on
Using the above highlights, the table that represents a function is table 1
Hence, the table in the list of tables that represent an actual function is the first table i.e.
x y
-3 10
4 4
-5 -3
4 4
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y=3x-2
y=-2x+8 solve this equation
Answer:
x = 2
Step-by-step explanation:
3x - 2 = - 2x + 8
→ Add 2x on both sides
5x - 2 = 8
→ Add 2 on both sides
5x = 10
→ Divide both sides by
x = 2
Answer:
x = 2, y = 4 (2,4)
Step-by-step explanation:
Put both the equation in ax + by = c
-3x + y = -2
2x + y = 8
Find x:
Multiply 8 times 1, -2 by 1, 2 times 1, and -3 by 1
8 - (-) 2/2 - (-) 3 = x
10/5
x = 2
Plug x back into equation:
-3(2)+y = -2
y = 4
5 + 4 ⋅ ( 8 − 6 ) ^2
[tex]\boldsymbol{\sf{5+4\cdot(8-6)^{2} \ \ \longmapsto \ \ [Subtract \ 6 \ from \ 8.] }}[/tex]
[tex]\boldsymbol{\sf{5+4\cdot2^{2} }}[/tex]
Calculates 2 to the power of 2 and gets 4.
[tex]\boldsymbol{\sf{5+4\cdot4 \ \ \longmapsto \ \ [Multiply] }}[/tex]
[tex]\boldsymbol{\sf{5+16 \ \ \longmapsto \ \ [Add]}}[/tex]
[tex]\blue{\boxed{\boldsymbol{\sf{Answer \ \ \longmapsto \ \ 21}}}}[/tex]
Answer:
5+16x
Step-by-step explanation:
5+4x(8−6)
2
Subtract 6 from 8 to get 2.
5+4x×2
2
Calculate 2 to the power of 2 and get 4.
5+4x×4
Multiply 4 and 4 to get 16.
5+16x
4) One-fourth cup of yogurt contains 27.5 calories. How many calories are there in 3 1/2 cups of yogurt?
Answer:
385
Step-by-step explanation:
Rabbits are known for being extremely prolific—having a high reproductive rate. The average gestation period for rabbits is about 28 days and they have an unusual reproductive system that permits a female rabbit to be pregnant with two litters at once. This is an adaptation that allows rabbits to survive in the wild where they have a high mortality rate—they’re a source of food for many species of predators! In situations where there are no natural predators, two adult rabbits could easily become 1000 in one year’s time. i. Using this information, construct an exponential model to predict the number of rabbits after “x” years if there are no natural predators. ii. If the rabbit population were left unchecked (no predators and an abundance of food), how many rabbits would there be at the end of 3 years?
(i) The exponential growth model to predict the number of rabbits after 'x' years is [tex]A = 2e^{6.21460809842x}[/tex].
(ii) The number of rabbits at the end of 3 years will be 250000000.
A continuous exponential growth function is of the form [tex]A = Pe^{rt}[/tex], where A is the final amount, which was initially P, growing continuously at the rate of r, after a time of t years.
In the question, we are asked to construct an exponential model to predict the number of rabbits after 'x' years.
We assume the exponential growth model to be a continuous model, of the form [tex]A = Pe^{rt}[/tex], where A is the final amount of rabbits, which was initially P, growing continuously at the rate of r, after a time of t years.
The initial quantity of rabbits, P = 2.
Time, t = x years.
Substituting the values, we get:
[tex]A = 2e^{rx}[/tex] ... (i)
We have been told that after 1 year, the number of rabbits was 1000.
Thus, substituting A = 1000, and x = 1, we get:
[tex]1000 = 2e^{r*1}\\\Rightarrow 1000 = 2e^r\\\Rightarrow e^r = 1000/2 = 500[/tex]
Taking log on both sides, we get:
[tex]log_ee^r = log_e500\\\Rightarrow rlog_ee = log_e500\\\Rightarrow r = 6.21460809842[/tex]
Thus, the rate of growth, r = 6.21460809842.
Substituting r = 6.21460809842 in (i), we get:
[tex]A = 2e^{6.21460809842x}[/tex], which is the required model.
To find the number of rabbits at the end of 3 years, we put x = 3, in the above equation to get:
[tex]A = 2e^{6.21460809842*3}\\\Rightarrow A = 2e^{18.6438242953}\\\Rightarrow A = 2*125000000\\\Rightarrow A =250000000[/tex]
Thus, there would be 250000000 rabbits at the end of 3 years.
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An older person is 9 years older than four times the age of a younger person.the sum of their ages is 24.find their ages.
The age of the younger individual is 3 years, while the age of the older individual is 21 years.
Two distinct individuals' (or things') ages from the present to the past or future are often compared when resolving age-related concerns. The objective of these puzzles is often to ascertain the current age of each subject.
Let the younger person be x years of age.
The answer to the query is:
Age of senior = (4x + 9) years
Their combined ages are 24.
x+4x+9=24
5x=24-9
5x=15
x=15/5
x=3
Younger person's age is equal to x = 3 years.
Age of senior = 4x + 9 = 4(3) + 9 = 21 years
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john likes to walk the steps of the department he works for during lunch break. There are s steps in his department. Today John would like to walk the steps of the taller building next door. The number of steps in the taller building next door is 27 less than 6 times the number of steps in John's department. Which expression represents the number of steps in the taller building next door in terms of s?
Given h of x equals negative 2 times the square root of x minus 3 end root, which of the following statements describes h(x)?
The function h(x) is increasing on the interval (–∞, 3).
The function h(x) is increasing on the interval (–3, ∞).
The function h(x) is decreasing on the interval (–∞, 3).
The function h(x) is decreasing on the interval (3, ∞).
Answer:
The function h(x) is decreasing on the interval (3, ∞).
Step-by-step explanation:
Please take a look at the attached image.
You will see a graph of the given function h(x) = -2[tex]\sqrt{x-3}[/tex]. The function is decreasing.
The function starts at 3 and starts to go towards negative infinity on the x-axis. Therefore the function is decreasing on the interval (3, ∞).
Simplify: 9x + 2(x - 3) - 2x + 10
Answer: 9x+4
Step-by-step explanation: We take out the parentheses by multiplying both values by 2 (2 times x and 2 times 3) to get 2x-6. Now our equation is 9x+2x-6-2x+10. We can see that there is a +2x and a -2x so we just take both of them out as they cancel out each other. Now our equation is 9x -6+10. we add 10 to -6 to get +4. The result is 9x+4.
Answer:
9x + 4
Step-by-step explanation:
9x + 2x - 6 - 2x + 10
Rearranging,
=> 9x + 2x - 2x + 10 - 6
=> 9x + 4
Lisa is cutting a 14-inch piece of paper into 0.4-inch strips. How many strips of paper will she have when she is finished?
5.6
35
30
28
Answer:
take 14/0.4the multiply by ten both the denominator and .numerator then simplify by two your final answer will be 35
Find the x-intercept.
x + 3
X-2
y =
([?], [_])
Answer: 1
Step-by-step explanation: It's subtraction and add ion look at the right side
The length of a rectangular poster is 5 more inches than half its width. The area of the poster is 12 square inches. Solve for the dimensions (length and width) of the poster.
The dimensions (length and width) of the poster are 6 inches and 2 inches
How to determine the dimensions (length and width) of the poster?Represent the length with x and the width with y
From the question, we have the following parameters
x = 5 + 0.5y
Area, A = 12
The area of a rectangle is represented as:
A = xy
Substitute the known values in the above equation
(5 + 0.5y) * y = 12
Expand the bracket
5y + 0.5y^2 = 12
Multiply through by 2
10y + y^2 = 24
Rewrite as:
y^2 + 10y - 24 = 0
Expand
y^2 + 12y - 2y - 24 = 0
Factorize the expression
(y - 2)(y + 12) = 0
Solve for y
y = 2 or y = -12
The dimension cannot be negative.
So, we have
y = 2
Substitute y = 2 in x = 5 + 0.5y
x = 5 + 0.5 * 2
Evaluate
x = 6
Hence, the dimensions (length and width) of the poster are 6 inches and 2 inches
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Is f(x)= [tex]\sqrt{5-x^{2} }[/tex] a one to one function?
Answer:
No, it is not a one-to-one function.
Step-by-step explanation:
A one-to-one function means a value of y will only exist one value of x. This means that a value of y will only have one value of x.
An example of one-to-one function is an odd-degree polynomial such as linear function.
An example of non one-to-one function is a parabola since a value of y exists two values of x.
From the question, this function represents a graph of half circle with radius equal to [tex]\displaystyle{\sqrt{5}}[/tex]. (The graph has been attached below for visual reference.)
There's also a way to determine whether if a function is one-to-one or not. This can be done by drawing a horizontal line.
If a horizontal line and a graph have one common point then it's a one-to-one functionOtherwise (having more than one common points), a function is not a one-to-one.From the graph and a horizontal line, both have two common points. Therefore, the function is not a one-to-one function.
* The red graph represents the given function while blue graph is a horizontal line determining a one-to-one function or not *
find the value of a x 7 when a=6
Answer:
=> 42 ..
Step-by-step explanation:
Given : a = 6
=> a × 7
=> 6 × 7
=> 42
Use a graphing tool to solve the equation for x. -4x − 1 = 5x + 4
Answer:
-5/9
Step-by-step explanation:
-4x - 1 = 5x +4 Add 4x to both sides
-1 = 9x + 4 Subtract 4 from both sides
-5 = 9x Divide both sides by 9
-5/9 = x
three varieties of coffee -coffee A coffee B and coffee C are combined and roasted yield a 54 lb batch of coffee beans. twice as many pounds of coffee C which is retails for $10.39 per pound are needed as coffee a which sells for $15.21 per pound coffee b retails for $13.21 per pound. how many pounds of each coffee should be used in a blend that sells for $12.61 per pound?
8.9 pounds of coffee A, 27.3 pounds of coffee B and 17.8 pounds of coffee C are need to make a blend that sells for $12.61 per pound.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent coffee A, y represent coffee B and z represent coffee C, hence:
x + y + z = 54 (1)
Also:
2x = z (2)
And:
15.21x + 13.21y + 10.39z = 12.61(54) (3)
x = 8.9, y = 27.3 and z = 17.8
8.9 pounds of coffee A, 27.3 pounds of coffee B and 17.8 pounds of coffee C are need to make a blend that sells for $12.61 per pound.]
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You purchase a very basic cell phone plan that charges $24.99 a month. This plan allows for data usage but that will cost you $5 for every GB you use in a month. Write an equation below in slope-intercept form that models this situation.
The equation of this given condition in the intercept form would be
y = 5x + 24.99
The slope-intercept is the most “popular” form of a straight line. Many students find this useful because of its simplicity. One can easily describe the characteristics of the straight line even without seeing its graph because the slope and y-intercept can easily be identified or read off from this form.
The linear equation written in the form
y = mx + b
is in slope-intercept form where: m is the slope, and b is the y-intercept.
In the given question the slope of the equation is 5 as $5 is charged for every GB used while $24.99 would be the intercept.
Thus the equation of this given condition in the intercept form would be
y = 5x + 24.99
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(5+2g)exp5 for g=-2
help pls
The value of the expression when g = -2 is -1
How to simplify the expressionGiven the expression;
(5+2g)exp5
(5+2g)^5
For g = -2
Let's substitute the value of g in the expression
= ( 5 + 2 ( -2) ) ^5
Expand the bracket
= ( 5 - 4) ^ 5
Find the difference
= (-1) ^5
= -1
Thus, the value of the expression when g = -2 is -1
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pls help, i will give brainliest to correct answer
Answer:
5,-1
Step-by-step explanation:
edited.... I gave 1/3 AC earlier (misread the Q)
This means AC is divided into fourths
x from 6 to 2 is -4 1/4th of this added to 6 is
6 - 1/4 * 4 = 5
y from 1 to -7 is -8 1/4th of this added to 1 is
1 - 1/4 * 8 = -1
Which of the following proves these triangles are congruent
Answer:
SAA
Step-by-step explanation:
Identify the corresponding congruent parts as either sides or angles. Look at their order of appearance around the triangle.
Corresponding partsThe sides marked with a single hash mark are identified as corresponding and congruent.
The angles marked with a single arc are identified as corresponding and congruent.
The vertical angles where the lines cross are congruent.
SequenceWorking counterclockwise around the left triangle, we encounter ...
side marked congruentvertical angles (congruent)angle marked congruentThese same features appear in the same order working counterclockwise around the triangle on the right.
The "side," "angle," and "angle" are referenced in the congruence postulate as S, A, and A.
Congruence is proved by the SAA congruence postulate.
(5.01 LC) A square is shown below. which expression can be used to find the area, in square units, of the Shaded triangle in the Square?
(answer options are in picture)
The expression can be used to find the area, in square units, of the Shaded triangle in the Square is 1/2 ( 4 · 4 ) .
What is the area of a square?The area of a square can be calculated as the square of the sides of a given figure.
The area of a square = side x side
where s = side length.
If a diagonal is drawn to create 2 halves, then area of each half is 8.
So, The area of a square = 1/2 ( 4 · 4 ) = 16.
If a square has a side length of 4, then the area of the square is 16.
The expression can be used to find the area, in square units, of the Shaded triangle in the Square is 1/2 ( 4 · 4 ) .
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What is the measure of the third angle?
Answer:
108
Step-by-step explanation:
11+61=72
We use 180 and subtract it by 72 because we know that all angles in a triangle add up to 180.
180-72=108
Someone please help me with this question! How can I prove it?
Answer:
TS=QV
Step-by-step explanation:
To prove SAS congruence, you need to prove that two lines and the angle between them are all respectively equal.
In the diagrams we already have RS=WV and ∠RST=∠WVQ, so it follows that we need to prove that TS=QV.
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
For triangles to be congruent by SAS congruency criteria, one angle and the two adjacent sides to the angle should be equal to corresponding angle and it's adjacent aides of another triangle.
And we have already been given the angle and one of the side. so the third side that need to be equal in both side to pe proved congruent are :
TS = QV[tex] \qquad \large \sf {Conclusion} : [/tex]
Correct option is 1Ian is playing video games. For every 11 enemies he defeats, he gets 6 points. If he has 24 points at the end of the game, how many enemies has Ian defeated?
Hi
if he has 24 point he scored 24/ 6 = 4 times
As he score points every 11 ennemies,
He had : 4*11= 44 ennemies.
3
Select the correct answer.
What is the inverse of the function f(x)=19/x2
If [tex]$&f(x)=\frac{19}{x^{2}} \\[/tex] then the inverse function exists [tex]$&f^{-1}(x)=\sqrt{\frac{19}{x}}[/tex].
What is the meaning of inverse function?An inverse function in mathematics exists function which "reverses" the another function.
Let f(x) = y, then the inverse function, [tex]$x=f^{-1}(y)$[/tex]
[tex]$&f(x)=\frac{19}{x^{2}} \\[/tex]
[tex]$&y=\frac{19}{x^{2}} \\[/tex]
[tex]$&x^{2}=\frac{19}{y} \\[/tex]
simplifying the equation, we get
[tex]$&x=\sqrt{\frac{19}{y}} \\[/tex]
[tex]$&x^{-1}=f^{-1}(y)=\sqrt{\frac{19}{y}} \\[/tex]
[tex]$&f^{-1}(y)=\sqrt{\frac{19}{y}},[/tex] then [tex]$&f^{-1}(x)=\sqrt{\frac{19}{x}}[/tex].
If [tex]$&f(x)=\frac{19}{x^{2}} \\[/tex] then the inverse function exists [tex]$&f^{-1}(x)=\sqrt{\frac{19}{x}}[/tex].
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