The mean and standard deviation of the x sampling distribution for each of the following sample sizes will be [tex]N(100,10/\sqrt{41} ), N(100,10/\sqrt{130} )[/tex].
What is the distribution of the sample mean for large samples?Suppose X has a distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma,[/tex]then,
the distribution of the mean of samples of size n, drawn from the values of X, is normally distributed with a mean equal to the mean of X, and a standard deviation equal to [tex]\sigma/\sqrt{n}[/tex]
Symbolically, we write it as:
[tex]X \sim N(\mu, \sigma) \implies \overline{X} \sim N(\mu,\sigma/\sqrt{n} )[/tex]
A random sample is selected from a population with a mean = of 100 and a standard deviation = of 10.
The mean and standard deviation of the x sampling distribution for each of the following sample sizes.
If N=41
[tex]X \sim N(100, 10) \implies \overline{X} \sim N(100,10/\sqrt{41} )[/tex]
If N=130
[tex]X \sim N(100, 10) \implies \overline{X} \sim N(100,10/\sqrt{130} )[/tex]
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5
сл
Type the correct answer in each box.
A circle is centered at the point (-7, -1) and passes through the point (8, 7).
The radius of the circle is
units. The point (-15,
) lies on this circle.
Part 1: Finding radius
The radius of a circle is defined as the distance from the center to a point on the circle's circumference.
Using the distance formula,
[tex]r=\sqrt{(-7-8)^{2}+(-1-7)^{2}}=\boxed{17}[/tex]
Part 2: Finding the point with x-coordinate -15
Let the y coordinate of the point be y. Then, we have the point (-15, y). Substituting into the distance formula,
[tex]\sqrt{(-15-(-7))^{2}+(-1-y)^{2}}=17\\\\64+(-1-y)^{2}=289\\\\(-1-y)^{2}=225\\\\-1-y =\om 15\\\\y=\boxed{-16, 14}[/tex]
Help please!! I’m stuck with these questions. :)
Answer:
20 elements.
Step-by-step explanation:
Lets say
n(U) = 114
n(A) = 57
n(B) = 79
n(A n B)= 42
Now,
n(A U B) = n(A) + n(B) - n(A n B)
= 57 + 79 - 42
= 94
Now,
n(A U B) compliment = n(U) - n(A U B)
= 114 - 94
= 20
please help me solve what is on that document
The most misleading graph is graph B because the blue rectangle and the red rectangle do not have the same width when plotted on the same scale
The ratio of the median weekly earningsFrom the graph, we have the median weekly earnings to be:
High school diploma = $750Bachelor's degree = $1250So, the ratio is:
Ratio = $750 : $1250
Simplify
Ratio = 3 : 5
Hence, the ratio of the median weekly earnings is 3 : 5
The ratio of the area of the red rectangle to the blue rectangle in graph A?
In (a), we have:
Ratio = 3 : 5
The scale on the horizontal axis is given as:
1 unit per grid mark
Both rectangles have a width of 1 unit.
So, we have:
Ratio = 3 * 1: 5 * 1
Simplify
Ratio = 3 : 5
Hence, the ratio of the area of the red rectangle to the blue rectangle in graph A is 3 : 5
The ratio of the area of the red rectangle to the blue rectangle in graph B?In (a), we have:
Ratio = 3 : 5
The scale on the horizontal axis is given as:
1 unit per grid mark
The red rectangle has a width of 3 units, while the blue has 5 units as its width
So, we have:
Ratio = 3 * 3 : 5 * 5
Simplify
Ratio = 9 : 25
Hence, the ratio of the area of the red rectangle to the blue rectangle in graph B is 9 : 25
The ratio of the volume of the red cube to the blue cube in graph C?
In (a), we have:
Ratio = 3 : 5
The scale on the horizontal axis is given as:
1 unit per grid mark
The red rectangle has a width of 3 units, while the blue has 5 units as its width.
Since the base are squares, we have:
Ratio = 3 * 3 * 3 : 5 * 5 * 5
Simplify
Ratio = 27 : 125
Hence, the ratio of the volume of the red cube to the blue cube in graph C is 27 : 125
The most misleading graph
The most misleading graph is graph B.
This is so because the blue rectangle and the red rectangle do not have the same width when plotted on the same scale
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. It costs C(x) = [tex]\sqrt{x}[/tex] dollars to produce x golf balls. What is the marginal production cost to make a golf ball? What is the marginal production cost when x = 25? when x= 100? (Include
units.)
The marginal cost when x = 25 and when x = 100 are $0.1 and $0.05 respectively.
What is a Marginal Production Cost?A marginal production cost is a derivative of a cost function. From the information given, the total cost is:
C(x) = [tex]\mathbf{\sqrt{x}}[/tex]The marginal production cost can be expressed as:
[tex]\mathbf{C'(x) = \dfrac{d}{dx}(\sqrt{x})}[/tex]
[tex]\mathbf{C'(x) = \dfrac{1}{2\sqrt{x}}}[/tex]
However, when the cost is 25, the marginal production is:
[tex]\mathbf{C'(25) = \dfrac{1}{2\sqrt{25} }}[/tex]
[tex]\mathbf{C'(25) = \dfrac{1}{2\times5}}[/tex]
[tex]\mathbf{C'(25) = \dfrac{1}{10}}[/tex]
C' (25) = $0.1
Also, when the cost is 100, the marginal production is:
[tex]\mathbf{C'(100) = \dfrac{1}{2\sqrt{100} }}[/tex]
[tex]\mathbf{C'(100) = \dfrac{1}{2\times10}}[/tex]
[tex]\mathbf{C'(100) = \dfrac{1}{20}}[/tex]
C' (100) = $0.05
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Find the greatest number which divides 6168, 2447, and 3118 leaving the same remainder in each case.
Answer:
Greatest number which divides 6168 is 3084,the greatest number which divides 2447 is1223.5 , and the greatest number which divides 3118 is 1559.
can i charge my hp laptop more than 1000 times
An empty rectangular tank was 25 cm long, 23 cm wide and 18 cm high. Ravi filled 5 identical bottles with water to the brim. Then he poured all the water from the 5 bottles into the empty tank and the tank became What was the capacity of each bottle? height of water, = = 1/2 X 18 3 23 cm Co 25 cm 3 full. 18 cm 2 An empty rectangular tank was 25 cm long , 23 cm wide and 18 cm high . Ravi filled 5 identical bottles with water to the brim . Then he poured all the water from the 5 bottles into the empty tank and the tank became What was the capacity of each bottle ? height of water , = = 1/2 X 18 3 23 cm Co 25 cm 3 full . 18 cm
If a line has a slope of 4 and goes through the point open parentheses short dash 1 comma 1 close parentheses, then the equation for the line in slope-intercept form is ______________.
a.)
y equals short dash 4 x minus 3
b.)
y equals 4 x plus 3
c.)
y equals 4 x plus 5
d.)
y equals short dash 4 x minus 5
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of the line will be y =4x+5. Thus, the correct option is C.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is the y-intercept.
Given the slope of the line is 4 and it goes through (-1,1), therefore, the equation of the line will be,
y = mx + c
y = 4x + c
Substitute the value of points,
1 = 4(-1) + c
1 = -4 + c
5 = c
Hence, the equation of the line will be y =4x+5. Thus, the correct option is C.
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If a widget factory as a fixed operating cost of $2,500 per day plus a cost of $1.50 per widget produced. If a widget sells fro $5.00, what is the least number of widgets that must be sold per day to make a profit?
At least 714 numbers of widgets must be sold per day to make a profit.
Given fixed operating cost = $2,500 per day cost of widget =$ 1.50
widget sells = $ 5.00
Cost function = C(X)=1.50x+2500
Revenue function = R(X)=5 x
At Break Even point R (X) = C (X)5
X= 1.50X+25003.5
X =2500X =714
hence to reach break even point or make profit 714 no to be sold.R(714)= 3571.
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please help me. 50 pts
Which quantity is multiplied by pi () in the formula for the area of a circle?
A. d
OB. 2
O c. d
D. r
Option: B
The area of a circle is pi times the radius squared (A = π r²).
Based only on the information given in the diagram, it is guaranteed that
ARST AUVW.
R
72°
S
TV
18⁰
A. True
B. False
Answer:
TrueExplanation -
In triangle SRT
angle R = 72°
angle T = 90°
angle S = 18° ( by angle sum property of a triangle)
in triangle VWU
angle W = 90°
angle V = 18°
angle W = angle T
side RS = side uv ( if two corresponding angles of two triangles are equal then their sides are also equal)
angle R = angle V
by angle side angle criteria both the triangles are congruent.
1-tan^2(x)/sec^2 = cos(2x)
By applying the formula of trigonometric function the right hand side will
be equal to right hand side which is 1-[tex]tan^{2} x[/tex]/[tex]sec^{2}x[/tex]=cos2x.
Given: 1-[tex]tan^{2} x[/tex]/[tex]sec^{2}x[/tex]=cos2x.
Taking right hand side first which is cos2x.
We know that cos2x=[tex]1-tan^{2}x/1+tan^{2}x[/tex]
Now we will solve the left hand side of the equation give which is
1-[tex]tan^{2} x[/tex]/[tex]sec^{2}x[/tex]
=1-[tex]tan^{2}x[/tex]/1+[tex]tan^{2}x[/tex]
[secant square x minus tangent square x is equal to 1]
By putting both values left hand side and right hand side we will find our solution which is :
1-tan^{2}x/1+tan^{2}x=1-[tex]tan^{2}x[/tex]/1+[tex]tan^{2}x[/tex].
Hence proved
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3.8% of a population are infected with a certain disease. There is a test for the disease, however the test is not completely accurate. 93.9% of those who have the disease test positive. However 4.1% of those who do not have the disease also test positive (false positives). A person is randomly selected and tested for the disease. What is the probability that the person has the disease given that the test result is positive?
The conditional probability that the person has the disease given that the test result is positive is of 0.4750 = 47.50%.
What is Conditional Probability?
Conditional probability is the probability of one event happening, considering a previous event. The formula is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which:
P(B|A) is the probability of event B happening, given that A happened.[tex]P(A \cap B)[/tex] is the probability of both A and B happening.P(A) is the probability of A happening.In this problem, the events are:
Event A: Positive test.Event B: Has the disease.The percentages associated with a positive test is:
93.9% of 3.8%(has the disease).4.1% of 100 - 3.8 = 96.2%(does not have the disease).Hence:
[tex]P(A) = 0.939(0.038) + 0.041(0.962) = 0.075124[/tex]
The probability of both a positive test and having the disease is given by:
[tex]P(A \cap B) = 0.939(0.038) = 0.035682[/tex]
Hence the conditional probability is given by:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.035682}{0.075124} = 0.4750[/tex]
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x + 4 = x2? Assume x greater-than 0
Answer:
The value comes out to be
[tex]x=\frac{1}{2}+\frac{\sqrt{17}}{2}[/tex]
Step-by-step explanation:
The quadratic equation is an equation containing a single variable of degree [tex]2[/tex]. Its general form is [tex]ax^{2} +bx + c=0[/tex].
The discriminant is the part of the quadratic formula underneath the square root symbol: b²- 4ac. The discriminant tells us whether there are two solutions, one solution, or no solutions.
The equation we are given is :[tex]x+4=x^{2} \\x^{2} -x-4=0\\[/tex]
We know the formula as :
[tex]x=[-b[/tex]±[tex]\sqrt{b^{2}-4ac}][/tex] ×[tex]\frac{1}{2a}[/tex]
[tex]x=[-(-1)[/tex]±[tex]\sqrt{(-1)^{2} -4(1)(-4)}][/tex]×[tex]\frac{1}{2(1)}[/tex]
[tex]x=\frac{1}{2}[/tex] ±[tex]\frac{\sqrt{17} }{2} }[/tex]
Since [tex]x[/tex]≥[tex]0[/tex]
Other negative option is neglected
[tex]x=\frac{1}{2}+\frac{\sqrt{17}}{2}[/tex]
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if the degree mesures of the angles in a triangle are in the ratio 2:3:4, what is the degree measure of the largest angle
The largest angle of the triangle is equal to 80 degrees.
Concept: Angle sum property of a triangle i.e., the sum of all angles of a triangle is equal to 180 degree
Given : Degree measures of the angles in a triangle are in the ratio 2:3:4
Let one part of each angle of the triangle be x, so the different angles of triangle are 2x,3x,4x (taking the ratios given in the question and multiplying by each of them by x)
2x +3x +4x = 180x
180x = 20
The angles of a triangle are 40,60,80
The largest angle of the triangle is equal to 80 degrees.
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An event manager recorded the number of people in different age groups who attended a music concert:
A histogram titled Concert Audience is shown. The horizontal axis is labeled Age Group in years with bins 18 to 24, 25 to 31, 32 to 38, and 39 to 45. The vertical axis labeled Number of People with values from 0 to 120 at intervals of 20. The first bin goes to 80, the second goes to 120, the third goes to 40, and the last goes to 20.
Which data table accurately represents the data in the histogram?
A:
Age Group Number of People
18–24 80
25–31 120
32–38 40
39–45 20
B:
Age Group Number of People
18–24 80
25–31 200
32–38 240
39–45 260
C:
Age Group Number of People
18–24 20
25–31 40
32–38 120
39–45 80
D:
Age Group Number of People
18–24 260
25–31 240
32–38 200
39–45 80
Answer: C) Age Group Number of People:
18–24 20
25–31 40
32–38 120
39–45 80
Have a good day/night! I hoped this helped. :D
Answer:
A:
18–24: 8025–31: 12032–38: 4039–45: 20Step-by-step explanation:
You want to know the table that accurately reflects the data in the described graph.
MatchingAs presented here, this is a reading comprehension problem.
The problem statement tells you the first bin is labeled 18–24, and the graph there extends to 80. This eliminates tables C and D. Tables A and B show 80 people in the 18–24 age group.
The second bin is labeled 25–31, and the graph there extends to 120. This matches the entry in Table A.
Table A matches the graph.
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Find the equation of the line that is perpendicular to y=-2x-9 and contains the points (8,-4)
The slope of the given line is -2, and since perpendicular lines have negative reciprocal slopes, the slope of the line we want to find is 1/2.
Substituting into point-slope form,
[tex]y+4=\frac{1}{2}(x-8)\\\\y+4=\frac{1}{2}x-4\\\\\boxed{y=\frac{1}{2}x-8}[/tex]
Answer:
Equation of line perpendicular to y= -2x-9 is y=x/2-8 .
Step-by-step explanation:
The slope of a line gives the measure of its steepness and direction. The slope of a curve at a point is equal to the slope of the straight line that is tangent to the curve at that point.
The general equation of a line is y = mx + c, where m is the slope of the line and c is the y-intercept. It is the most common form of the equation of a straight line that is used in geometry.
The product of slopes of two perpendicular lines gives (-1).
m1m2=(-1)
(-2)m2=(-1)
m2=1/2
y=m2x+c
Point (8,-4) satisfies the given equation :
(-4)=1/2 x 8 + c
c = (-8)
Line perpendicular to y= -2x-9 will be -
y=x/2-8
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A company finds that there is a linear relationship between the amount of money that it spends on advertising and the number of units it sells. If it spends no money on advertising, it sells 250 units. For each additional $4000 spent, an additional 25 units are sold. If x is the amount of money that the company spends on advertising, find a formula for y, the number of units sold as a function of x.
The formula for the equation of y, the number of units sold as a function of x is y = 0.00625x + 250
How to illustrate the equation?From the information given, when the company spends no money on advertising, it sells 250 units and for each additional $4000 spent, an additional 25 units are sold.
The formula for y will be:
y = (25/4000)x + 250
y = 0.00625x + 250
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A treasure map says that a treasure is buried so that it partitions the distance between a rock and a tree in a 5:9 ratio. Marina traced the map onto a coordinate plane to find the exact location of the treasure.
x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1
y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1
What are the coordinates of the treasure? If necessary, round the coordinates to the nearest tenth.
(11.4, 14.2)
(7.6, 8.8)
(5.7, 7.5)
(10.2, 12.6)
Using proportions, it is found that the coordinates of the treasure as given as follows: (7.6, 8.8).
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Researching the problem on the internet, the coordinates are as follows:
Rock (3,2).Treasure (x,y).Tree (16,21).The treasure is buried between a rock and a tree in a 5:9 ratio, hence the expression is:
[tex]Ts - R = \frac{5}{14}(Tr - R)[/tex]
Hence, for the x-coordinate:
[tex]x - 3 = \frac{5}{14}(16 - 3)[/tex]
x - 3 = 5 x 13/14
x = 7.6.
For the y-coordinate:
[tex]y - 2 = \frac{5}{14}(21 - 2)[/tex]
y - 2 = 5 x 19/14
y = 8.8.
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Answer: the answer is b
Step-by-step explanation:
The age of trees in a forest is known to be approximately normal with an average age of 40 years and a standard
deviation of 10 years. What is the standardized score for a tree that is 34 years old?
A. 1.90
B.-0.60
C. -1.90
D. 0.60
Answer:
B -o.60
Step-by-step explanation:
34 - 40 = -6. -6 divide by 10 = -3/5 or - 0.6. So answer is B
Convert the following angle from degrees to radians. Express your answer in simplest
form.
495°
Answer:
11/4 Pi
Step-by-step explanation:
because 1.= 70/180. (180.=Pi)
so 495 x 70/180
=11/4 Pi
What factors do the numbers 16 and 36 have in common?
A. 1, 2, 4, 8
B. 1, 2, 4, 6
C. 1,2,4
D. 1, 2, 8, 16
Answer: C. 1, 2, 4
Step-by-step explanation:
A factor is an integer that is a divisor of a number. In other words, the number can be divided by this integer and result in another integer.
To answer this question, we can list the factors of both numbers. I have underlined and bolded integers that appear in both lists, giving us our answer.
Factors of 16: 1, 2, 4, 8 and 16
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
C. 1, 2, 4
Select all the correct answers. Function g is a transformation of the parent exponential function. Which statements are true about function g? A Linear graph function where red line g intercepts y-axis at (0, 4) and passes through (minus 10, 3) and (3, 10) Function g is positive over the interval . The domain of function g is . Function g has a y-intercept of . Function g decreasing over the interval . Function g is 4 units above function f. The range of function g is .
The correct statements are:
Function g has a y-intercept of (0,4)
The range of the function g is (3, ∞).
The function g is positive over the interval (-∞ , ∞ ).
The parent function i.e. exponential function is defined by:
y=f(x)=aˣ
From the graph given below,
1. The graph of the function g is 3 units above the graph of the parent exponential function. as the parent exponential function aˣ cuts the y-axis at (0,1) and the child transformed function cut at (0,4) for which g is 4-1=3 units above the parent function
2. The domain of the function is set of all the inputs for which function is defined. From the graph of function g, it is clear tha the domain of the function is (-∞ , ∞ ) as the domain of the parent exponential function is also (-∞ , ∞ ).
3. The y-intercept is the point at which function cut the y-axis. Graph of function g cut the y-axis at (0, 4). Therefore, Function g has the y-intercept at (0,4).
4. From the graph it is clear that Function g increases over the interval (-∞, 0) .
5. The range of the function is the output values of the function. From the graph, it is observed that the range of function g is (3, ∞). as its minimum value is 3 then the maximum value is ∞.
6. As, the graph of function g is drawn above the x-axis. Therefore, Function g lies completely on +ve y-axis, so function g is positive over the interval (-∞ , ∞ ).
Therefore The correct statements are:
Function g has a y-intercept of (0,4)
The range of the function g is (3, ∞).
The function g is positive over the interval (-∞ , ∞ ).
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Can someone answer this
The order of the graphs from largest to lowest correlation coefficients is:
Graph D, Graph A, graph C, graph B.
Which graph has the largest correlation coefficient?The correlation coefficient between two variables is a coefficient that tells us "how much" these variables relate.
So, in the case for linear correlation, as "more linear" the data appears to be, a large correlation is between the two variables.
With that in mind, we conclude that the order of the graphs (going for larger correlation coefficient to smaller correlation coefficient) is:
Graph D, Graph A, graph C, graph B.
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Which relation is a function??????
Answer:
A
Step-by-step explanation:
there cannot be 2 different points on the same x coordinate
Please help me!!! I will give brainliest to the correct answer.
Given:
EA = 2EC = 3EB = EA + AB = 2 + 10 = 12ED = EC + CD = 3 + yFormula:
AB × AD = AC × AE
Here if applied:
EA × EB = EC × ED
2 × 12 = 3 × (3 + y)
24 = 9 + 3y
3y = 15
y = 5
Answer:
y = 5
Step-by-step explanation:
Secant: a straight line that intersects a circle at two points.
Segment: part of a line that connects two points.
The given diagram shows two secant segments EB and ED drawn to the circle from one exterior point E. Therefore, using the Intersecting Secants Theorem, the product of the measures of one secant segment and its external part is equal to the product of the measures of the other secant segment and its external part.
⇒ EB · EA = ED · EC
⇒ (2 + 10) · 2 = (3 + y) · 3
⇒ (12)2 = 3(3 + y)
⇒ 24 = 9 + 3y
⇒ 15 = 3y
⇒ y = 5
if the figure forms the base of a right solid 110 centimeters high, find the surface area
Answer:
[tex]60200cm^{2}[/tex]
Step-by-step explanation:
(I am assuming that the units for the measurements in this question are all centimeters)
Surface area = 2 * (Area of Base) + (Perimeter of base)*(Height)
First, we'd need to solve for the area of the base by finding the area of the triangle and subtracting it from the area of the rectangle. The area of the rectangle is [tex]100 * 150 = 15000[/tex]. The area of the triangle is [tex]\frac{1}{2} * 120 * 90 = 5400[/tex]. (We can do this because it is a right triangle with leg lengths in the pattern of a 3-4-5 triangle.) Now, subtracting the area of the triangle from the rectangle, we get [tex]15000 - 54000 = 9600[/tex]. This is the area of the base.
Next, the perimeter of the base is [tex]100 + 150 + 90 + 120 = 460[/tex]. Multiplying this by the height, we get [tex]460 * 110 = 50600[/tex].
Finally, we add 9600 and 50900 to get [tex]9600 + 50900 = 60200[/tex].
B is the set of odd numbers greater than 5 and less than 21
Answer:
List method: {7,9,11,13,15,17,19}
Set method: {X:N where N is odd, N>5 and N<21}
The odd numbers greater than 5 and less than 21 are {7, 9,11,13,15,17,19}.
What are odd numbers?Odd numbers are the numbers that cannot be divided by 2 evenly. It cannot be divided into two separate integers evenly.
Odd numbers are opposite to even numbers this means that even numbers are numbers that can be divided by 2.
When we say numbers greater than 5 and less than 21 this means 5< x < 21
The odd numbers greater than 5 and less than 21 are ;
{7, 9,11,13,15,17,19}. These odd numbers are greater than 5 and less than 21.
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NEED HELP ASAP WILL MARK BRAINLIEST!
Answer:
[tex]\boxed {1)log_{b}(75) = 4.317}[/tex]
[tex]\boxed {2)ln(20) = 2.9957}[/tex]
Step-by-step explanation:
[tex]\textsf {Question l :}[/tex]
[tex]\longrightarrow \mathsf {log_{b}(3) = 1.099}[/tex]
[tex]\longrightarrow \mathsf {log_{b}(5) = 1.609}[/tex]
[tex]\textsf {Identities applied :}[/tex]
[tex]\boxed {log(ab) = loga + logb}[/tex]
[tex]\boxed {log(a)^{x} = xloga}[/tex]
[tex]\textsf {We can rewrite the problem as :}[/tex]
[tex]\longrightarrow \mathsf {log_{b}(75)}[/tex]
[tex]\longrightarrow \mathsf {log_{b}(25 \times 3)}[/tex]
[tex]\longrightarrow \mathsf {log_{b}(5^{2} \times 3)}[/tex]
[tex]\longrightarrow \mathsf {log_{b}(5)^{2} + log_{b}(3)}[/tex]
[tex]\longrightarrow \mathsf {2log_{b}(5) + log_{b}(3)}[/tex]
[tex]\textsf {Now, substitute the values :}[/tex]
[tex]\longrightarrow \mathsf {2(1.609) + (1.099)}[/tex]
[tex]\longrightarrow \mathsf {3.218 + 1.099}[/tex]
[tex]\longrightarrow \mathsf {4.317}[/tex]
[tex]\boxed {log_{b}(75) = 4.317}[/tex]
[tex]\textsf {Question ll :}[/tex]
[tex]\longrightarrow \mathsf {ln(4) = 1.3863}[/tex]
[tex]\longrightarrow \mathsf {ln(5) = 1.6094}[/tex]
[tex]\textsf {Rewriting the problem :}[/tex]
[tex]\longrightarrow \mathsf {ln(20)}[/tex]
[tex]\longrightarrow \mathsf {ln(4 \times 5)}[/tex]
[tex]\longrightarrow \mathsf {ln(4) + ln(5)}[/tex]
[tex]\longrightarrow \mathsf {1.3863 + 1.6094}[/tex]
[tex]\longrightarrow \mathsf {2.9957}[/tex]
[tex]\boxed {ln(20) = 2.9957}[/tex]
Answer:
[tex]\sf \log_b(75)=4.317[/tex]
[tex]\sf \ln (20)=2.9957[/tex]
Step-by-step explanation:
Question 1
Given:
[tex]\sf \log_b(3)=1.099[/tex]
[tex]\sf \log_b(5)=1.609[/tex]
To evaluate [tex]\sf \log_b(75)[/tex], replace 75 with (5 × 5 × 3):
[tex]\implies \sf \log_b(5 \cdot 5 \cdot 3)[/tex]
[tex]\textsf{Apply the Product log law}: \quad \log_axy=\log_ax + \log_ay[/tex]
[tex]\implies \sf \log_b5+\log_b5+\log_b3[/tex]
Substitute the given values to solve:
[tex]\implies \sf 1.609 + 1.609 + 1.099=4.317[/tex]
Question 2
Given:
[tex]\sf \ln(4)=1.3863[/tex]
[tex]\sf \ln(5)=1.6094[/tex]
To evaluate ln(20) replace 20 with (4 × 5):
[tex]\implies \sf \ln (4 \cdot 5)[/tex]
[tex]\textsf{Apply the Product log law}: \quad \ln xy=\ln x + \ln y[/tex]
[tex]\implies \sf \ln (4)+\ln (5)[/tex]
Substitute the given values to solve:
[tex]\implies \sf 1.3863+1.6094=2.9957[/tex]
There are 192 pencils in 8 Super Saver packs. If there are the same number of pencils in each Super Saver pack, how many pencils are in 5 packs?
