Based on the calculations, the value which closest to the mean of the distribution is equal to: B. 18 inches.
What is a z-value?A z-value is also referred to as a z-score or standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.
In Statistics, z-values can either be positive or negative and it can be calculated by using this formula:
Z = (x - μ)/δ
Where:
x represents the sample mean or observed data.μ represents the mean.δ represents the standard deviation.If 15 percent of the rainbow trout are longer than 15 inches, then we have:
P(x > 15) = 0.15
From the z-table, the z-value which corresponds to a mean of 0.15 is given by:
z-value = -1.036
Substituting the given parameters into the formula, we have;
Z = (x - μ)/δ
-1.036 = (15 - μ)/2.4
-1.036 × 2.4 = 15 - μ
-2.4864 = 15 - μ
μ = 15 + 2.4864
Mean, μ = 17.4864
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Complete Question:
The distribution of lengths of rainbow trout from a certain river are normally distributed with a standard deviation of 2.4 inches. it 15% of the rainbow trout are longer than 15 inches, which of the following is closest to the mean of the distribution?
A. 26 inches
B. 18 inches
C. 30 inches
D. 33 inches
E. 34 inches
The mass of flour in a bag is about 141.6 grams. You add about 10.19 grams of flour to the bag. What is the mass of flour in the bag to the nearest tenth of a gram
The tenth of a gram closest to it is 151.79 grams.
The flour's mass is 141.6 grams.
10.19 grams are added.
The amount of flour in the bag =141.6+ 10.19
= 151.79.
A physical quantity is mass. The weight of a body serves as the unit of mass measurement. It can be measured in normal mass quantities such grams, kilograms, and pounds. Although grams are used to measure smaller objects, the kilogram is the SI unit of mass.
In the metric measurement system, a gram is a unit of weight that is one thousandth of a kilogram. When something is extremely light, its weight is measured in grams.
Therefore, 151.79 grams of flour, to the nearest tenth of a gram, are in the bag.
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find the 31st term 2,10,18
Answer:
242
Step-by-step explanation:
Fill in the blanks below in order to justify whether or not the mapping down represents a function
Answer:
The mapping diagram above represents a function since there is one number in Set A (the input) where there is only one mapping to Set B (the output).
Step-by-step explanation:
For each number in set A, there is one mapping from set A (input) to set B (output), so the mapping represents a function.
NB. The relation is a function IF AND ONLY IF each input value has only 1 output value.
-4ca: use a = 2. and c = -5
Answer:
40
Step-by-step explanation:
For this equation, all we do is simply plug in the values.
-4 (c) (a)
-4 (-5) (2)
-4*-5*2
Now, multiply, and you get your answer.
-4 * -5 = 20
20 * 2 = 40
40 is your answer
Three 6" x 6" and two 8" x 8" electrical boxes are installed in a wall between two studs. There are _ square inches of wall area taken up by the boxes.
Answer: 236 square inches
Step-by-step explanation:
Three 6" x 6" and two 8" x 8" electrical boxes are installed in a wall between two studs
The answer is 236
Divide. (6x³ + 2x² + 3x −4) ÷ (x² + 3x +4)
6x³ + 2x² + 3x - 4 is not exactly divisible by x² + 3x - 4.
Given,
The expression : 6x³ + 2x² + 3x - 4
We have to divide the given expression by x² + 3x - 4.
Let's take 6x³ + 2x² + 3x - 4 as p(x) and x² + 3x - 4 as g(x).
If p(x) is divisible by the factors of g(x), then p(x) is divisible by g(x).
So, let's factorize x² + 3x - 4
x² + 3x - 4 = (x - 1) (x + 4)
Now,
p(x) = 6x³ + 2x² + 3x - 4
By using remainder theorem,
If p(1) = 0 and p(4) = 0, then p(x) is divisible by g(x).
So,
p(1) = 6 × 1³ + 2 x 1² + 3 x 1 -4
p(1) = 6 + 2 + 3 - 4
p(1) = 11 - 4
p(1) = 7
Next,
p(4) = 6 x 4³ + 2 x 4² + 3 x 4 - 4
p(4) = 6 x 64 + 2 x 16 + 12 - 4
p(4) = 384 + 32 + 12 - 4
p(4) = 424
Here, p(1) and p(4) is not 0.
So, p(x) is not divisible by g(x).
That is, 6x³ + 2x² + 3x - 4 is not exactly divisible by x² + 3x - 4.
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Angela is arranging 32 framed pictures on a wall. How
can she arrange her pictures in equal rows? Find all
possible arrangements.
Answer:
1×32
2×16
4×8
8×4
16×2
32×1
Step-by-step explanation:
This question about arranging pictures is just trying to get you to explore the factors of 32, maybe for practicing the math ideas of factoring, or area, or max/min, or matrices.
Think of what numbers go into 32:
1, 2, 4, 8, 16, 32
Pair them up!
1×32 and 32×1 will look differently if they are pictures on a wall. So we'll list them separately. Then there's also 2×16 and 16×2, and 4×8 and 8×4.
The subtraction problem 4/5 - 2/7 can be rewritten as the addition problem _[blank].
Enter your answer as the expression that correctly fills in the blank.
Enter fractions formatted like this: 3/14
It can be written as 13/35.
how do we rewrite a fraction.
Divide the numerator by the denominator
Write down the whole number result
Use the remainder as the new numerator over the denominator. This is the fraction part of the mixed number.
A number that will divide evenly into both the numerator and denominator so it can be reduced, or
The numerator must be greater than the denominator, (an improper fraction), so it can be converted to a mixed number
4/5-3/7
⇒4×7-3×5/ 35 ( 5 and 7 have no common divisor).
⇒ 28- 15/35
⇒13/35
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Use the graph of f to determine each of the following.
(a) the domain of f
(b) the range of f
(c) the zero(s) of f
(d) f(-3.5)
(e) the intervals on which f is increasing
(f) the intervals on which f is decreasing
(g) the values for which f(x) ≤0
(h) any relative maxima or minima
(i) the value(s) of x for which f(x) = 3
() Is f(0) positive or negative?
(a) the domain of f would be an interval (−3,6]
(b) the range of f would be an interval (−6,3]
(c) the zero(s) of f are x = −0.5 and x=6.
(d) the value of f(-3.5) would be 2
(e) the intervals at (−3,3) which f is increasing
(f) the intervals at (3,6] which f is decreasing
(g) the values are (−3,−0.5] for which f(x) ≤0
(h) x = 3 which is a relative maximum point
(i) the value of x is 3 for which f(x) = 3
(j) the function would be positive if f(0)
What are the domain and range of the function?The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.
The domain of the function shown in the graph is given by the set of values x that has a point on the graph.
In other words, by launching the graph onto the x-axis we will cover the interval (−3,6]
The range of the function shown in the picture is given by the set of values y that has a point on the graph.
In other words, by launching the graph onto the y-axis we will cover the interval (−6,3]
The zeros of the function are the x-intercepts of the function, so the zeros are x = −0.5 and x=6.
The value of f(-3.5) is given by the y- coordinate of the point of intersection of the graph with the vertical line x=-3.5 So, f(-3.5)≈2.
The function is increasing whenever the y- coordinate increases if we trace the graph in the direction of positive x values.
So, the graph is increasing on (−3,3), where x=3 corresponds to the x- coordinate of the turning point on the graph.
The function is decreasing whenever the y- coordinate decreases if we trace the graph in the direction of positive x values.
So, the graph is decreasing on (3,6].
The values of x where f(x) ≤0, correspond to the points where the graph is below the x-axis, so the values of x for which f(x) ≤0 are (−3,−0.5].
The relative maxima or minima are the x-coordinate points where the continuous function has a turning point, like x=3 which is a relative maximum point
.
There are no relative minimum points for the given function.
The value of x for f(x)=3 is the x- coordinate of the point of intersection of the graph with the horizontal line y=3
So, x≈3.
we will determine the y = coordinate of the point of intersection of the graph with the vertical line
x=0, which is above 2, so f(0) is positive.
Therefore, the domain of the function is interval (−3,6], and the range of the function is interval (−6,3].
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sergio was shopping for online stocks in nvidia. he purchased 2,000 shares at 4 dollars each. if sergio plans for the stockts to triple in value by the end of next year what will his shares be worth in total?
The total worth of shares that he has is 24000$
To calculate earnings per share, take a company's net income and deduct preferred dividends from it. Divide the total by the average number of outstanding common shares.
Given Sergio purchased 2000 shares at four dollars each
the cost price of shares is 4$ each
Therefore total shares worth he has = 2000 * 4
= 8000 $
He now expects the stock to triple in value by the end of next year.
total amount of shares he owns = 8000 * 3
= 24000$
Therefore, the total amount of shares he owns is 24000$
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the ratio of red cars to blue cars in a parking lot was 5:3. If there was 40 red cars how many blue cars were there?
The ratio of red cars to blue cars in a parking lot was 5:3, total blue cars are 24.
What is ratio?A ratio in mathematics shows how many times one number is included in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.
Given, the ratio is 5:3.
Total red cars = 40
⇒ 5x = 40
⇒ x = 8
Blue cars = 8 × 3
= 24
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What is “a/b -c+d” if “a=7/8, b=-7/16, c=.8, and d=1/4”
Answer:
(7-8) / (-7/16) = -2 -(.8) + (1/4) = -.55 -2+ -.55= -2.55
Step-by-step explanation:
Find the range of f(x)=4x+2 for the domain {–2, –1, 1, 4}. Your answer:
The range of the function, f(x)=4x+2 for the domain {–2, –1, 1, 4} includes (-6, -2, 6, 18).
What is the range of a function?The range of the function, f(x)=4x+2, includes all the possible output values of the function.
What is the domain of a function?The domain of a function, f(x)=4x+2, is the set of all possible input values (domain {–2, –1, 1, 4}) of the function.
Remember that a function is a mathematical expression that equates an independent variable with a dependent variable.
Data and Calculations:f(x)=4x+2
Domain = {–2, –1, 1, 4}
The range for -2:
f(x)=4x+2 = 4(–2) + 2 = -6
Range for -1:
f(x)=4x+2 = 4(–1) + 2 = -2
Range for 1:
f(x)=4x+2 = 4(1) + 2 = 6
The range for 4:
f(x)=4x+2 = 4(4) + 2 = 18
Thus, the range of the function, f(x)=4x+2 for the domain {–2, –1, 1, 4} includes (-6, -2, 6, 18).
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Select all that have a value of 0.
cos π/2
cos 0
sin 0
sin 3π/2
tan π
Answer:
cos(π/2)sin(0)tan(π)Step-by-step explanation:
You want to know which trig functions on the given list have a value of zero.
Trig functionsSine
The sine function is zero at x=0 and multiples of π.
Cosine
The cosine function is zero at x = π/2 and for odd multiples of π.
Tangent
The tangent function is zero at x=0 and multiples of π. It is zero in the same places the sine function is zero.
List valuesThese values are zero:
cos(π/2)sin(0)tan(π)These function values are something different:
cos(0) = 1sin(3π/2) = -1A newspaper advertisement offers a $9,000 car for nothing down and 36 easy monthly payments of $317.50. What is the simple interest rate?
_____%
Help please with my math
The percentage of the actual salary that actual mortgage is is 30%.
What is the percentage of actual mortgage?Percentage is the fraction of an amount that is expressed as a number out of hundred. Percentage is a measure of frequency. The sign used to show percentage is %.
In order to transform a number into a percentage, express it as a fraction of a total amount and multiply by 100. So, actual mortgage would be divided by actual budget, the fraction would then be multiplied by 100.
Percentage of actual salary that is actual mortgage = (actual mortgage / actual salary) x 100
(1080 / 3600) x 100 = 30%
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Let s(t)=[tex]\sqrt{x+16}[/tex] be the position function. Use the Definition to find the velocity at t=0.
The velocity at t = 0 will be 4 meters per second.
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable.
A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
Given function is s(t) = √ ( t + 16 ).
The value of the function is calculated as below:-
s ( t ) = √ ( t + 16 ).
s( 0 ) = √ ( 0 + 16 ).
s( 0 ) = √ ( 16 ).
s( 0 ) = 4
Therefore, the velocity at t = 0 will be 4 meters per second.
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-3x+2<8 and 1/2x-5<-3
The values of x in the inequalities are x< -2 and x < 4
How to determine the valuesGiven the inequalities;
-3x+2<81/2x-5<-3To determine the value of x for each, we have;
-3x + 2 < 8
collect like terms
-3x < 8 - 2
-3x < 6
Make 'x' the subject
x < 6/ -3
x< -2
1/2x - 5 < -3
Find the Lowest common multiple
x - 10 / 2 < -3
cross multiply
x - 10 < -3 × 2
x - 10 < -6
collect like terms
x < - 6 + 10
x < 4
Thus, the values of x in the inequalities are x< -2 and x < 4
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Evaluate. Write your answer as a fraction in simplest form. 1/2 + 7/18 + 5/6 please help me asap
Answer:
31/18 which is changed to 1³¹/¹⁸
Step-by-step explanation:
9/18+7/18+15/18 I found the lcm or the lowest common multiple of all the three and multiplied it by each fraction first then u can add all of them and put it over 18 or add each
Target had 8x10⁹ dollars in sales last year. Explain how to find the product 8x10⁹.
Using scientific notation, The value of 8x10⁹ is 8000000000
How should a scientific notation be written?In scientific notation, the correct format is an x 10 b, where an is an integer or decimal number whose absolute value is more than or equal to one and less than ten, or 1 |a| 10. In order for the scientific notation to be mathematically identical to the original number, b must be a power of 10.
The given problem is written in scientific notation,
The multiplication of the given number will be-
8x10⁹ = 8000000000
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A gardener makes a new circular flower bed. The bed is twelve feet in diameter. Calculate the circumference and the area of the
circular flower bed.
A. circumference = 12 feet, area = 12 square feet
B. circumference = 6 feet, area = 36:
square feet
C. circumference = 12
feet, area = 144 square feet
D. circumference = 12 feet, area = 36 square feet
Answer:
Step-by-step explanation: I think the answer would be B or D they seem the most logical
the value of 86 in a dataset with the mean 101 and the standard deviation 19
The z-score of the value is -0.79
How to determine the z-score of the value?The given parameters are
Value = 86
Mean = 101
Standard deviation = 19
The z-score of the value is calculated using
z= (Value - Mean)/Standard deviation
This gives
z = (86 - 101)/19
Evaluate
z = -0.79
Hence, the z-score of the value is -0.79
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(35 POINTS!!) Given f of x is equal to 1 over the quantity x minus 3 and g of x is equal to the square root of the quantity x plus 3, what is the domain of f (g(x))?
[–3, ∞)
[–3, 6) ∪ (6, ∞)
(–∞, 3) ∪ (3, ∞)
ℝ
Answer:
the second option
[–3, 6) ∪ (6, ∞)
Step-by-step explanation:
f(x) = 1/(x - 3)
the domain is every value of x that does not turn the denominator to 0. so, x <> 3.
g(x) = sqrt(x + 3)
the domain is every value of x that does not turn (x+3) into a negative value. so, x >= -3.
f(g(x)) = 1/(sqrt(x + 3) - 3)
the domain is all values of x that are valid for g(x) AND that do not generate range values of g(x) that violate the domain of f(x).
so, it is (x >= -3) AND (sqrt(x + 3) <> 3).
and sqrt(x + 3) = 3, if (x + 3) = 9.
that means x = 6.
so, 6 is forbidden, every other value of x is allowed here.
therefore, the domain of f(g(x)) is
(x >= -3) AND (x <> 6)
and that is equivalent to
[-3, 6) u (6, infinity)
everything larger or equal to -3 and different from 6.
Hay 12 estudiantes en una clase que se presentan en el concierto de la escuela. Esto representa el 40% de la clase. ¿Cuántos estudiantes hay en la clase?
Mediante el uso de porcentajes, concluimos que la clase tiene una población total de 30 estudiantes.
¿Cuál es la cantidad de estudiantes de la clase?
En este problema tenemos a 12 estudiantes procedentes de una clase que participan en un evento cultural de su escuela y también se conoce que equivalen al 40 por ciento de su clase. El total de estudiantes de la clase se obtiene al dividir el número de estudiantes por el porcentaje:
x = 12 / 40 %
x = (12 · 100) / 40
x = 30
La clase tiene una población total de 30 estudiantes.
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Find the angle of elevation of the sun from the ground to the top of a tree when a tree that is 10 yards tall casts a shadow 14 yards long. Round to the nearest degree.
The angle of elevation of the sun from the ground to the top of a tree is 36°.
We are given that:
The sun from the ground to the top of a tree when a tree that is 10 yards tall casts a shadow 14 yards long.
Now by using the trigonometric identity .
tan θ = P / B
As figure is given below .
AB = Perpendicular = 10 yards
BC = Base = 14 yards
Putting all the values in the trigonometric identity .
tan θ = 10 / 14
θ = 36°
Therefore, the angle of elevation of the sun from the ground to the top of a tree is 36°.
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Work out the perimeter of the shaded shape. 7m 4m 1m 4m 14m
The parameter of the shaded shape is 50 meters
The parameter of any shape is sum of all sides
Measurements of some of the sides are given and some needs to be find out so the calculations are -
first side = 7m
second side = 14m
third side is equal to first side so= 7m,
fourth side = 1m
fifth side is equal to seventh side =4m
sixth side is second side- fourth side- eighth side = 14- 1-4= 9m
seventh side=4m
eighth side =4m
parameter of the shape = sum of all side = 7+ 14+ 7+ 1+4+9+4+4
=50 m
So, the parameter of the shaded shape is 50 meters
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The median annual salary for an event planner is $60,900. If the event planner pays an
8% income tax, how much money in dollars and cents will the event planner pay for
income tax?
Sunt
Answer:
$4,872.00
Step-by-step explanation:
Convert 8% into a decimal and multiply
$60,900.00 x 0.08 = $4,872.00
The domain of f(x) is all real numbers & satisfies f(x+1)=2f(x).
For [tex] \sf x \in(0,1],[/tex] f(x)=x(x+1). For value [tex]\sf x \in( - \infty ,m],[/tex] f(x)[tex] \geq \dfrac{ - 8}{9}. [/tex] What is the value of m?
The domain of f(x) is all real numbers & satisfies function f(x+1)=2f(x).
For x∈(0,1], the function f(x)=x(x-1). For value x∈(-[tex]\infty[/tex],m], f(x)≥[tex]\frac{-8}{9}[/tex]. What is the value of m?
the smallest value m=[tex]\frac{7}{3}[/tex].
Given that, for x∈(0,1], f(x)=x(x-1)
Let's plot this function
We'll go from 0 to 1 and let's graph what this function is look like
f(x)=x(x-1) will be a parabola and it's going to go between the points (0,0) and (1,0).
Will graph it in figure1 we can see.
The minimum value of this parabola is right in the middle and it is
f(0.5)=-0.25
Now, let try and graph the function in the other intervals
We know f(x+1)=2f(x)
Now we can evaluate couple of points
f(0+1)=2f(x)
f(0.5+1)=2f(0.5)
f(1+1)=2f(1)
And we quickly deduce that the graph in(1,2] is twice the height of the graph in (0,1].
We will graph a parabola in figure 2 we can see.
This parabola is going to have a graph of 2 between its twice as tall and this can be multiplied by the quantity of (x-1) multiplied by the quantity of (x-2).
It is 2(x-1)(x-2).
We graph next interval twice the height of the graph in the interval from 2 to 3. We can see the graph in figure3.
This parabola will have an equation 4 times the quantity of (x-2) and (x-3).
We can also shift this graph to the left and it going to be half the height.
Looking at this graph we want f(x)≥[tex]\frac{-8}{9}[/tex].
In the 3 interval from 2 to 3 its going to intersect .
we want to look for the points where f(x)≥[tex]\frac{-8}{9}[/tex].
We are looking for m which f(x)≥[tex]\frac{-8}{9}[/tex].
parabolas equation =[tex]\frac{-8}{9}[/tex].
4(x-2)(x-3)=[tex]\frac{-8}{9}[/tex]
[tex]x^{2} -5x+6=\frac{-2}{9} \\(x-\frac{7}{3})(x-\frac{8}{3})=0\\ x= \frac{7}{3},\frac{8}{3}\\\\[/tex]
Therefore, We will take the smallest value m=[tex]\frac{7}{3}[/tex].
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6.62 inches is more than 6.4 inches ?
Today, Sarah counted all of the wheels of all of the cycles in the shop. She found that there were 30 wheels in all. There were the same number of bikes as there were trikes. How many bikes were there? How many trikes were there? Show how you figured it out.
Answer:
Step-by-step explanation:
Bicycles have two wheels whereas Trikes have 3 wheels. Let x be the number of bicycles2x=30[tex]\frac{2x}{2} =\frac{30}{2} \\x=15[/tex]There were 15 bicyclesLet y be the number of trikes3x=30 since there were same number of trikes as bicycles[tex]\frac{3y}{3} =\frac{30}{3} \\y=10[/tex]There were 10 Trikes