The single natural logarithm expression is ln(2). Therefore, correct answer is (a)
Logarithmic Equations:The expression in the form [tex]e^a=b[/tex] can also be written as In b = a which is called as logarithmic expression.
Properties of Logarithms:
1. In (mn) = In m + In n
2. In [tex]a^m =[/tex] m In a
3. In [tex]e^a[/tex] = a.
How to express as a single natural logarithm?The natural logarithm expression is:
4 + ln 2 - ln 4
Apply the product and quotient rule of natural logarithm:
4 + ln 2 - ln 4 = In (4 × 2/4)
Evaluate the quotient:
4 + ln 2 - ln 4 = In (2)
Hence, the single natural logarithm expression is ln(2).
The correct option is (a)
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Answer:
B: ln 4.
Step-by-step explanation:
It is assumed that approximately​ 15% of adults in the u.s. are​ left-handed. consider the probability that among 100 adults selected in the​ u.s., there are at least 30 who are​ left-handed. given that the adults surveyed were selected without​ replacement, can the probability be found by using the binomial probability formula with x counting the number who are​ left-handed? why or why​ not?
a. Yes, because the 100 adults represent less than 5% of the U.S. adult population, the trials can be treated as independent.
b. No, because the 30 adults represent more than 5% of the sample size, the trials are dependent.
c. No, because the 100 adults were selected without replacement, the selections are dependent.
d. No, because the probability of being right-handed is greater, x must count the number of right-handed adults.
No, the probability be found by using the binomial probability formula with x counting the number who are left-handed. The correct option is (c) No, because the 100 adults were selected without replacement, the selections are dependent.
The binomial distribution assumes that the trials are independent, meaning that the outcome of one trial does not affect the outcome of any other trial. However, in this case, the 100 adults were selected without replacement, which means that the outcome of one selection affects the probability of the next selection. Therefore, the trials are dependent, and the binomial probability formula cannot be used.
Instead, we can use the hypergeometric distribution to calculate the probability of at least 30 left-handed adults in a sample of 100 adults selected without replacement from the U.S. population. The hypergeometric distribution takes into account the fact that the selections are dependent and is appropriate for this type of problem.
Therefore, the correct option is (c) No, because the 100 adults were selected without replacement, the selections are dependent.
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Convert slope intercept form for 4y-12x=4x+3
Answer:
y = 4x + 3/4
Step-by-step explanation:
The slope intercept form is y = mx + b
Our equation is 4y - 12x = 4x + 3
4y - 12x = 4x + 3
4y = 16x + 3
y = 4x + 3/4
So, the answer is y = 4x + 3/4
The dimensions of an above-ground, rectangular pool are 25 feet long, 18 feet wide, and 6 feet deep. How much water can fit in the pool?
Answer:
2700ft³ or 76455.49 litre
Step-by-step explanation:
Given
Length = 25 feet
Width = 18 feet
Height = 6 feet
Formula for Volume of cuboid = Length×Width×Height
So,
Volume of the pool = 25×18×6 = 2700ft³ or 76455.49 liters aprox.
What is the shortcut for multiplying mixed numbers?
To multiply mixed numbers, convert to improper fractions, cancel factors, multiply the remaining factors, and simplify if possible.
Increasing blended numbers can be tedious, yet there is an easy route that can work on the interaction. To duplicate blended numbers, convert them to ill-advised portions, then drop any elements that show up in both the numerator and denominator of the divisions. At long last, duplicate the leftover elements in the numerator and denominator and work on the subsequent division if conceivable. For instance, to duplicate 2 1/2 by 3 2/3, first proselyte them to inappropriate divisions, which are 5/2 and 11/3. Then, drop the variable of 2 in the numerator of the principal portion and the denominator of the subsequent division. The outcome is 55/3, which can be improved to 18 1/3. This alternate way can save time and assist understudies with taking care of augmentation issues all the more proficiently.
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Will give Brainly please
The value of the mean excluding the outlier is 130. 5
What is an outlier?An outlier can be defined as a data point that differs significantly or greatly from other observations.
It occurs as a result of;
variability in the measurement indication of novel dataexperimental errorFrom the information given, we have that;
121, 89, 410, 203, 55, 230, 182, 148, 135, 233, 11, 219, 108, 192
Since, the outlier is 410
The mean is given as;
= 121 + 89+ 203+ 55 + 230+182 + 148 + 135 + 233+ 11+ 219 + 108 + 192/13
Add the values
= 1696/13
= 130. 5
Hence, the value is 130. 5
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Find the surface area of this triangular prism. Be sure to Include the correct unit in your answer.
Answer:
The surface area of the triangular prism is 180 square centimeters.
Step-by-step explanation:
To find the surface area of a triangular prism, we need to find the area of each face and add them up. Let's call the base of the triangle b, the height of the triangle h, and the height of the prism (the distance between the two triangular faces) H.
The triangular faces each have an area of (1/2)bh, so the total area of the two triangular faces is bh. The rectangular faces each have an area of Hb, so the total area of the two rectangular faces is 2Hb. Finally, the top and bottom faces each have an area of b^2, so the total area of these two faces is 2b^2.
Adding all of these areas together, we get:
Surface area = bh + 2Hb + 2b^2
Substituting the given values, we get:
Surface area = (6 cm)(8 cm) + 2(5 cm)(6 cm) + 2(6 cm)^2
Surface area = 48 cm^2 + 60 cm^2 + 72 cm^2
Surface area = 180 cm^2
Therefore, the surface area of the triangular prism is 180 square centimeters.
Does this graph represent a function?Explain
Check the picture below.
what is 11 roman numeral?
The number 11 in roman numerical can be written as the term of ten plus one so XI.
The ancient number system known as Roman numerals is still prevalent worldwide. The fixed positive numbers are represented by alphabets in roman numerals. I, II, III, IV, V, VI, VII, VIII, IX, and X are roman numerals that stand for the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 respectively.
Use the next procedure to write the number 11 in Roman numerals:
Start by simplifying the number 11 to its base form.
As a result, it is found that 11 Equals 10 + 1.
Write the numbers out in Roman numerals first, then add and subtract.
Hence, 10 + 1 = 11 is denoted by X + I = XI. [Note: The letters are linked together when a larger letter comes before a smaller letter.]
Thus, 11 is XI in Roman numerals.
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Which measurement represents the height of the parallelogram
In Connexus.com
Unit 2: measurement
Lesson 1: Area and perimeter of parallelograms
The measurement that represents the height of the parallelogram is A. 3 m.
Where is the height of a parallelogram ?The height of a parallelogram is the perpendicular distance between its two parallel bases. It is the distance between the two parallel bases measured at a 90-degree angle.
To find the height of a parallelogram, draw a perpendicular line from one base to the other. The length of this line is the height of the parallelogram.
On the given image, the line that shows the perpendicular distance between its two parallel bases is 3 m so this is the height.
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Solve for x. Round to the nearest tenth of a degree, if necessary.
2.1
D
4
to
E
Answer:
[tex]31.7^\circ[/tex]
Step-by-step explanation:
We use the property that the sin of the angle of a right triangle is the ratio of the side opposite that angle divided by the hypotenus
Therefore
[tex]\begin{aligned}\sin x & = \dfrac{2.1}{4}\\& = 0.525\\\end{aligned}\\\begin{aligned}x &= sin^{-1}(0.525)\\& = 31.7^\circ \end{aligned}[/tex]
What is the conversion of 29 c to f ?
The conversion of 29 Celsius to Fahrenheit is 84.2.
Celsius and Fahrenheit are two common units of temperature measurement.
Celsius, also known as centigrade, is a temperature scale used in the metric system. It is defined by setting the freezing point of water at 0 degrees Celsius and the boiling point of water at 100 degrees Celsius at standard atmospheric pressure.
To convert 29 Celsius to Fahrenheit, you can use the following formula,
°F = (°C × 9/5) + 32
Plugging in the value of 29 Celsius, we get,
°F = (29 × 9/5) + 32
°F = (261/5) + 32
°F = 52.2 + 32
°F = 84.2
Therefore, 29 Celsius is equivalent to 84.2 Fahrenheit.
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Correct Question :
What is the conversion of 29 Celsius to Fahrenheit ?
The dimensions of a cone are shown in the diagram.
Which measurement is closest to the volume of the sugar cone in cubic inches?
the volume of the sugar cone is closest to 14.14 cubic inches.
How to determine?
The volume of a cone can be calculated using the formula V = (1/3)πr²2h, where r is the radius of the base, h is the height of the cone, and π is approximately 3.14.
In this case, the diameter of the cone is 3 inches, which means the radius, r, is half of that or 1.5 inches. The height of the cone is given as 6 inches.
Plugging these values into the formula, we get:
V = (1/3)π(1.5²2)(6)
V ≈ 14.14 cubic inches
Therefore, the volume of the sugar cone is closest to 14.14 cubic inches.
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what is n in statistics
In statistics, n is used to denote sample size. This gives the total number of participants under study.
In statistics, n is defined as the sample size. It refers to the total number of participants or the total number of observations that are included in a study. This size of the sample is drawn from the given population. This value is important because this directly influences the research study.
This sample size is affected by study design, standard deviation, sampling method, significance level, and study power. For example, you have to determine the mineral concentration in different types of soil. For this, you are taking 5 different soil samples. Here, the sample size is 5.
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What is the conversion of 83 f to c?
The conversion of 83 f to c is equal to approximately 28.3°C.
As a side note: the unit of temperature Fahrenheit is named after the German physicist Daniel Gabriel Fahrenheit.The unit for temperature Celsius is named after the Swedish astronomer Anders Celsius.
To convert a temperature from Fahrenheit (F) to Celsius (C), you can use the following formula:
C = (F - 32) x 5/9,
where
C is the temperature in Celsius, and
F is the temperature in Fahrenheit.
Using this formula, we can convert 83°F to Celsius as follows:
C = (83 - 32) x 5/9
C = 51 x 5/9
C = 28.3
Therefore, 83°F is equal to approximately 28.3°C.
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unit 7 polygons and quadrilaterals homework 3 rectangles
If you are trying to find the missing measures of a rectangle, you should know that all rectangles have four sides, and each side has a length.
In other words, if you have a rectangle, two of the angles must be 90 degrees, and the other two angles must also be 90 degrees. To find the missing measures of a rectangle, you need to use the properties of rectangles.
First, find the length of each side. The length of all sides of a rectangle should be the same. Then, calculate the area of the rectangle. You can do this by multiplying the length of one side with the length of the other side.
Finally, you can use the Pythagorean Theorem to find the missing measures.
The Pythagorean Theorem states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
Using this theorem, you can find the length of the hypotenuse of the rectangle.
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Complete Question:
if each quadrilateral is given, then define the steps to find the missing measures a rectangle.
a. Find the perimeter of a triangle whose side
lengths are 5 cm, 8√3 cm, and √27 cm. Give
the answer as a radical expression in simplest
form.
Answer:
[tex]5+11\sqrt{3}[/tex]
---------------
Perimeter is the sum of side lengths:
[tex]P=5+8\sqrt{3}+\sqrt{27} =5+8\sqrt{3}+\sqrt{3^2*3} =5+8\sqrt{3}+3\sqrt{3}=5+11\sqrt{3}[/tex]how to convert 44 kg to lbs
44 kg is approximately equal to 97.0034 pounds ( rounded to four decimal places )
The conversion factor to convert kg to lbs is 2.20462
1 kg = 2.20462 pounds
The conversion is the process of changing the unit of one quantity to another units
The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing
The mass in lbs = The mass in kg × conversion factor
Substitute the values in the equation
1 kg = 2.20462 pounds
44 kg = 44 × 2.20462
Multiply the numbers
= 97.0034 pounds ( rounded to four decimal places )
Therefore, 44 kg is 97.0034 pounds
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In a data set, the number of elements will always be the same as the number of: a. data point b. independent variable c. dependent variable d.observation
The number of elements will always be the same as the number of observations.
How to find the mean of a data set?
Mean is the ratio of the sum of the values of the data set to the total number of values available in the data set.
Thus, we get;
[tex]\rm Mean = \dfrac{\text{Sum of the observations of the data set}}{\text{Total number of observations}}[/tex]
We are given that;
the number of elements=number
Now,
From observation we can say that the number of elements is equal to the number of observations.
Therefore, by mean the answer will be observation.
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Paula works at an appliance store where they make most of their money on commission. She makes 4.25% commission on the price of any appliance she sells. The store was offering 20% off on washers and dryers. Her first customer bought a washer for $685.96 and a dryer for $475.70 before applying the discount. How much money did she lose because of the sale? Round your answer to the nearest cent.
well, let's take a looksie at what it would have been had there not been a sale, so at regular price the washer and dryer are just 685.96 + 475.70 = 1161.66, well hell how much is 4.25% of that?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{4.25\% of 1161.66}}{\left( \cfrac{4.25}{100} \right)1161.66} ~~ \approx ~~ 49.37[/tex]
now, since we know the appliances are going to be 20%, that means the appliaces sale price will be 100% - 20% = 80%, so 80% of the original price, well, we know the original price for those two is 1161.66, what's 80% of that?
[tex]\stackrel{\textit{80\% of 1161.66}}{\left( \cfrac{80}{100} \right)1161.66} ~~ \approx ~~ \stackrel{ sale~price }{929.33} \hspace{5em} \stackrel{\textit{4.25\% of 929.33}}{\left( \cfrac{4.25}{100} \right)929.33} ~~ \stackrel{ \textit{Paula's commission} }{\approx ~~39.5}[/tex]
well, Paula could have made 49.37, but she ended up with 39.5, 49.37 - 39.5 ≈ 9.87.
Which of the contexts below could not be modeled by an exponential function?
• A car depreciates at a rate of 3.7% per year.
• A sunflower was growing at a rate of 2.75 inches per week.
• A certain population of 25 aggressive zombies quadruples every week.
Money invested in a savings account grows at an annual rate of 2.2%.
Answer:
The context that could not be modeled by an exponential function is "A car depreciates at a rate of 3.7% per year." Exponential functions are typically used to model situations involving growth or decay that occur at a constant rate over time. In this case, the rate of depreciation of the car is decreasing over time, so it cannot be modeled by an exponential function. A linear function or a more complex model may be more appropriate.
What is the conversion of 77 f to c?
The conversion of 77 f to c is equal to 25°C.
To convert temperatures in degrees Fahrenheit to Celsius, deduct 32 and multiply by .5556 ( or 5/9).
Temperatures, across the world, are measured either in Fahrenheit( the US temperature scale) or Celsius( the metric scale), two of the most popular and extensively used scales.
Temperature Conversion- Degrees Fahrenheit into Degrees Celsius.
To convert a temperature from Fahrenheit (°F) to Celsius (°C), we can use the formula:
°C = (°F - 32) x 5/9
By applying this formula, we can convert 77 °F to Celsius as follows
°C = (77 - 32) x 5/9
°C = 45 x 5/9
°C = 25
Therefore, 77°F is equal to 25°C.
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A transformation is applied to a figure to create a newfigure. Which transformation does not preserve congruence?O A reflection across the x-axisO A translation 7 units downO A dilation by a scale factor of 5O A rotation of 90° clockwise
A transformation is applied to a figure to create a new figure, the transformation does not preserve congruence is option C, A dilation by a scale factor of 5.
An isometry is a transformation that retains congruence. In other words, a transformation in which the side lengths and angle measurements of the Image and Pre-Image are the same. Isometries include translations, reflections, and rotations. A translation is a "direct isometry" since it not only maintains congruence but also, unlike reflections and rotations, maintains orientation.
A dilation, on the other hand, is not an isometry since its Image is not consistent with its Pre-Image.
A transformation composition indicates that two or more transformations will be executed on the same item. On the same point, for example, we may do a reflection and then a translation.
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The length of a rectangular poster is 4 more inches than two times its width. The area of the poster is 198 square inches. Solve for the dimensions (length and width) of the poster.
Answer: L=22, W=9
Step-by-step explanation:
The length of a rectangular poster is 4 more inches than two times its width. The area of the poster is 198 square inches. Solve for the dimensions (length and width) of the poster.
L=4+2W [Length] (1)
W=W [Width] (2)
P=2L+2W [perimeter] (3)
A=L*W = 198[area](4)
Subing (1) and (2) into (3) and (4)
P=2(4+2W)+2W
A=W(4+2W)
Simplify
P=8+4W+2W=8+6W
A=4W+2W^2=198
A=2W^2+4W-198
Set equal to 0 and solve for W
W=(-b+√(b^2-4ac))/2a
W=(-b-√(b^2-4ac))/2a
W=(-4+√(4^2-4(2)(-198)))/(2(2)) = 9
W=(-4-√(4^2-4(2)(-198)))/(2(2)) =-11
Disregard W =-11 since distance can’t be negative and keep W=9. Plug W=9 into Length equation (1)
L=4+2(9)=22
Final answer L=22 and W=9
Answer:
I I
Step-by-step explanation:givb
what is the square root of 4761
The square root of 4761 is found to be 69.
If there is a number a, and there is another number b. Now, if we multiply a with a and we get the number b, then we say that the number a is the square root of the number b.
It can be written as,
a = √b
This sign "√" is called the sign on under root. So, now we ae to find the square root of the number 4761,
First we will find the factor of the number 4761 and then make the pair of two each and then multiply to find the root.
4761 = 3 x 3 x 23 x 23
Now, 3 x 23
So, the square root of 4761 is 69.
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What is bell curve percentages
The Bell Curve is a symmetrical curve that represents the probability distribution of a random variable.
The Bell Curve, also known as the normal distribution or Gaussian distribution, is a statistical concept used to describe the distribution of a set of data. The Bell Curve is a symmetrical curve that represents the probability distribution of a random variable.
The Bell Curve is often used to describe the distribution of scores on a test or exam. In this context, the Bell Curve is used to represent the distribution of scores across a population. The mean score (average score) is represented by the highest point on the curve, and the standard deviation is represented by the width of the curve.
In terms of percentages, the Bell Curve can be divided into different standard deviations, with each standard deviation representing a certain percentage of the population. The percentages of the population within each standard deviation are as follows:
68.27% of the population falls within one standard deviation of the mean.
95.45% of the population falls within two standard deviations of the mean.
99.73% of the population falls within three standard deviations of the mean.
These percentages are useful for understanding how scores or data are distributed across a population and can be used to set cutoff scores or define performance categories.
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PLEASE ANSWER ASAP
The measures of the angles ABC are given by the expressions in the table, what are the measures of
Angle
A (12x+12) degrees
B 15 degrees
C (3x+18) degrees
Answer:
To find the measure of angle A, we substitute the given expression into the formula for the measure of an angle:
A = 12x + 12 degrees
To find the measure of angle C, we substitute the given expression into the formula for the measure of an angle:
C = 3x + 18 degrees
The measure of angle B is already given as 15 degrees.
Therefore, the measures of the three angles are:
Angle A = 12x + 12 degrees
Angle B = 15 degrees
Angle C = 3x + 18 degrees
What is the conversion of 52c to f?
52 °C is equal to 125.6 °F.
The Celsius( symbol °C) is an SI( International System of Units) deduced unit of temperature.
The Fahrenheit( symbol °F) is a unit of temperature that was extensively used previous to metrication.
How to Convert Celsius to Fahrenheit
F = [tex]\frac{9}{5}[/tex]C + 32
C = [tex]\frac{5}{9}[/tex](F - 32)
To convert 52 degrees Celsius to Fahrenheit,
We can use the following formula:
°F = (°C x 1.8) + 32
where °F is the temperature in Fahrenheit,
°C is the temperature in Celsius.
Substituting 52 for °C, we get:
°F = (52 x 1.8) + 32
Simplifying the expression:
°F = 93.6 + 32
°F = 125.6
Therefore, 52 degrees Celsius is equal to 125.6 degrees Fahrenheit.
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Sasha ordered a kite online. When it arrived, the kite was missing the crossbar. What length crossbar does Sasha need to complete the kite?
2ft 2ft crossbar
The length of crossbar that Sasha need to complete the kite is equal to √8 units.
How to determine the length of the crossbar?By critically observing the image of the kite shown below, we can logically deduce that the crossbar and the two (2) given lengths formed a right-angled triangle as illustrated by the right angle symbol between the two given sides.
In order to determined, we would have to apply Pythagorean's theorem. Mathematically, Pythagorean's theorem is given by this mathematical expression:
a² + b² = c²
Where:
a, b, and c represents the side lengths of a right-angled triangle.
Substituting the given parameters into Pythagorean's theorem, we have the following;
c² = a² + b²
c² = 2² + 2²
c² = 4 + 4
c = √8 units.
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what is 1 c sugar in grams?
The 1 c sugar is 200 grams.
Gram (originally grams; [1] SI unit symbol g) is a mass unit in the International System of Units (SI), equal to one thousandth of a kilogram.
Originally defined from 1795 as "the absolute mass of a volume of pure water equal to one hundredth of a cubic meter [1 cm3] and at the melting point of ice", [2] the defining temperature (~ 0 °C) ) was later changed to
°C, which is the maximum density of water to temperature.
At the end of the 19th century, however, an attempt was made to make the basic unit the kilogram and a unit derived from the gram. In 1960, the new International System of Units defined the gram as one thousandth of a kilogram (ie, a gram is 1 × 10–3 kg). As of 2019, the International Bureau of Weights and Measures defines the kilogram as a fixed numerical value of Planck's constant (h) of 6.62607015×10−3
kg⋅m2⋅s−1.[3][
] ]
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what is the altitude of the triangle
Answer:10.392
Step-by-step explanation:
Using the pythagorean theorm:a^2+b^2=c^2
We can find that the altitude=sqrt(16.8^2-13.2^2)=10.392