Condense the logarithm
log c + z log q
The condensed logarithm is given as follows:
log(cq^z).
How to obtain the condensed logarithm?The logarithmic expression for this problem is defined as follows:
log c + z log q
For the multiplication/power rule, we have that:
z log q = log q^z.
Hence the expression would be simplified as follows:
log c + q^z.
The addition of logarithms can also be represented as the logarithm of the product, hence the condensed logarithm is given as follows:
log c + q^z = log(cq^z).
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What is the answer to 2x x 3y x 3x
Answer:
2x x 3y x 3x is 18x4y hope it helps
Step-by-step explanation:
a package of aluminum foil contains 50. ft2 of foil, which weighs approximately 9.0 oz . what is the approximate thickness of the foil in millimeters?
The approximate thickness of the package of aluminum foil with given density and weight is equal to 0.002 millimeters.
1 ft = 30.48 cm
Area of aluminum foil = 50 ft²
= 50 × ( 30.48 )² cm²
= 46451.52 cm²
1 oz = 28.3495 grams
Weight of the aluminum = 9.0 oz
= 255.1455 grams
Density = 2.70 g/cm³
Density = weight / ( area × thickness )
⇒ Thickness = weight / ( area × density )
⇒Thickness = 255.1455 grams / ( 46451.52 cm² × 2.70 g/cm³ )
⇒Thickness = 0.00203
⇒Thickness = 0.002 millimeters
Therefore, approximate thickness of the aluminum foil is equal to 0.002 millimeters.
The above question is incomplete, the complete question is:
A package of aluminum foil contains 50. ft2 of foil, which weighs approximately 9.0 oz . Aluminum has a density of 2.70 g/cm3.What is the approximate thickness of the foil in millimeters?
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chad is responsible for painting the front of a barn red and the doors white. each door measures 18 feet by 6 feet. if a gallon of paint covers 250 square feet, how many gallons of red and white paint will chad need to purchase
Chad will purchase 0.432 gallons of red and white paint.
What is division?The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups.
Given
Dimension of the door = 18 feet by 6 feet
Area of the door = 108 square feet
1 gallon of paint covers 250 square feet
Let x gallon paint covers 108 square feet
Proportion of paint to area covered
1/250 = x/108
x = 108/250
x = 0.432
Hence, 0.432 gallons of red and white paint, Chad will purchase.
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help me plsssssssssssssssssss
Answer:
The answer is D.
Step-by-step explanation:
In the diagram below,
F
G
‾
FG
is parallel to
C
D
‾
CD
. If
C
D
‾
CD
is twice the length of
F
E
‾
FE
,
C
E
=
12
CE=12, and
F
G
=
6
FG=6, find the length of
F
E
‾
FE
. Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.
The value of the segment FE for the similar triangles is equal to 6.
How to calculate for FE for the similar trianglesThe triangles EFG and ECD are similar, this implies that the length FE of the smaller triangle is similar to the length CE of the larger triangle
and the length FG of the smaller triangle is similar to the length CD of the larger triangle
so;
FE/12= 6/2FE
2(FE)² = 12 × 6 {cross multiplication}
2(FE)² = 72
(FE)² = 72/2
(FE)² = 36
FE = √36 {take square root of both sides}
FE = 6.
Therefore, the value of the segment FE for the similar triangles is equal to 6.
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The hanger diagram represents 4(x+5)=32 ( answer the following please)
A. What does each circle represent?
B. Already answered.
C. What part of the equation can be divided by 4 to find the value of x+5?
D. What is the value of x?
Each circle represents a number. The left side of the equation (4(x+5)) can be divided by 4 to find the value of x+5. The value of x is 4.70
Which is a radius and which is a diameter?The distance between a circle's center and periphery is referred as the radius. Always, the diameter is twice the radius. As a conclusion, the diameter is multiplied by two to obtain the formula.
Diameter and circumference are what?The ratio of a circle's circumference to diameter serves as the basis for the traditional definition of Pi (). The diameter or length of such a circle is its circumference. A straight line connecting a point on one end of both the ring to a place on the opposite end, through the center, is the diameter.
Diameter = 2r -----------(1)
where r is the radius
The value of the diameter = 32 m and radius is given to be 4(x+5)
substitute the above into equation (1) and then solve for x
32 = 2 [ 4(x + 5)]
first open the inner bracket
32 = 5[4x + 20}
then open the outer bracket
32 = 20x + 100
subtract 16 from both-side of the equation
20x=100-32
20x=68
x=3.4
Divide both-side of the equation by 3.4
16/3.4 = 8x/3.4
4.70 = x
x = 4.70
Therefore, the value of x is 4.70
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a certain town of population size 100,000 has three newspapers: i, ii, and iii. the proportions of townspeople that read these papers are: i: 10%, i and ii: 8%, i and ii and iii: 1%, ii: 30%, i and iii: 2%, iii: 5%, ii and iii: 4%. (note that, for example, the 10% of people who read newspaper i might read only i or might read i and some other paper(s) ). a) find the number of people who read only one newspaper. b) how many people read at least two newspapers?
A. The number of people who read only one newspaper is 45,000
B. The number of people who read at least two newspapers is 15,000.
How did we get the values?a) 10% of 100,000 people read only newspaper i, 30% of 100,000 people read only newspaper ii, and 5% of 100,000 people read only newspaper iii.
10% of 100,000 = 10,000
30% of 100,000 = 30,000
5% of 100,000 = 5,000
Therefore, the number of people who read only one newspaper is 45,000.
b) 8% of 100,000 people read both newspaper i and ii, 1% of 100,000 people read all three newspapers, 2% of 100,000 people read both newspaper i and iii, and 4% of 100,000 people read both newspaper ii and iii.
8% of 100,000 = 8,000
1% of 100,000 = 1,000
2% of 100,000 = 2,000
4% of 100,000 = 4,000
Therefore, the number of people who read at least two newspapers is 15,000.
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Lin’s teacher uses the box to store her set of cubes with an edge length 1/2inch.if the box is completely full, how many cubes are in the set
The number of cubes fitted in the storage box is 448.
What is Volume?The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
Given:
Edge length of cube = 1/2 inch
So, volume of a cube = (Side)³
= (1/2)³
= (1/8)
Now, Volume of the storage box = 56 cubic inches.
So, number of cubes fitted in the storage box
= Volume of the storage box / volume of a cube
= 56/ (1/8)
= 56 x8
= 448 cubes
Hence, number of cubes fitted is 448.
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8/5w = 40
Simplify your answer as much as possible.
Answer:
w = 25
Step-by-step explanation:
8/5w = 40
Divided both sides by 8/5
w = 25
Let's check
8/5(25) = 40
40 = 40
So, w = 25 is the correct answer.
Answer: w = 25
Step-by-step explanation:
To solve for w, we will isolate the variable by using inverse operations.
Given:
[tex]\displaystyle \frac{8}{5} w=40[/tex]
Divide both sides of the equation by [tex]\frac{8}{5}[/tex]:
* Note: w is being multiplied by [tex]\frac{8}{5}[/tex], so the inverse operation is division
[tex]\displaystyle w=\frac{40}{\frac{8}{5 } } \mapsto w=40*\frac{5}{8} \mapsto w=*\frac{40*5}{8} \mapsto\frac{200}{8} \mapsto \boxed{w=25}[/tex]
the probability of tails of a weighted coin is 0.65. the number of tails is noted each of the 15 times the coin is tossed. if this procedure is repeated 100 times, what type of distribution is simulated?
Sampling distribution type distribution is simulated with the sample proportion with n = 15 and p = 0.65.
It is defined as a probability distribution of a statistic that is from a larger number of samples from a specific population.
We are given that
The probability of tails of a weighted coin, p=0.65 and n=15
We have to find the type of distribution that is simulated if this procedure is repeated 100 times.
The random variable is a proportion of a number of tails therefore, the type of distribution is the sampling distribution of the sample proportion.
Probability is something that is to happen.
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Michael is 3 times as old as Brandon. 18 years ago, Michael was 9 times as old as Brandon.
How old is Michael now?
Currently, Michael is 72 years old
How old is Michael now?Let's represent Michael's current age as "x".
Then Brandon's current age is x/3.
18 years ago, Michael's age was x-18
Brandon's age was x/3-18.
18 years ago, we can write the equation:
x - 18 = 9 * (x/3 - 18)
So, we have
x - 18 = 3x - 162
Evaluate the like terms
2x = 144
Divide by 2
x = 72
So, Michael is 72 years old now.
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luis strength trains two times per week. he uses 12-pound weights and performs three sets of eight repetitions. he wants to improve his frequency. what should he do?
If Luis trains two times per week with 12-pound weights , then to improve his strength, he should (d) Increase to three times per week.
By Increasing the frequency of his strength training sessions from two times per week to three times per week can help Luis improve his strength by exposing his muscles to more stimulation and allowing for more adaptations to occur.
It is important to remember to progress gradually and listen to his body to avoid injury.
The option (d) ; involves increasing the frequency of his strength training sessions from two times per week to three times per week. By exposing his muscles to more stimulation, he will be allowing for more adaptations to occur and potentially leading to greater strength gains.
The given question is incomplete , the complete question is
Luis strength trains two times per week. He uses 12-pound weights and performs three sets of eight repetitions. He wants to improve his frequency. What should he do?
(a) Increase to 10 repetitions.
(b) Increase to 15-pound weights.
(c) Increase to four sets.
(d) Increase to three times per week.
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how many minutes are in 2/5 of the day you must show your working
Answer:
576 minutes
Step-by-step explanation:
You first must convert the time of a day into minutes.
24 hours x 60 minutes = 1440 minutes in a day.
Now you need to multiply the sum by 2/5
1440/1 x 2/5 = 2880/5
Simplify the number into a whole number.
2880 divided by 5 = 576
Is the trapezoidal rule an overestimate or underestimate?
The trapezoidal rule is a numerical integration method that frequently overestimates the real value of a function's definite integral.
What is trapezoidal rule?The trapezoidal rule is a strategy for approximating the definite integral in calculus. The trapezoidal rule works by computing the area of the region under the graph of the function f(x) that is approximated as a trapezoid. The trapezoidal rule is commonly used to calculate the area under curves. This is achievable if the overall area is divided into smaller trapezoids rather than rectangles. The Trapezoidal Rule integration determines the area by approximating the area under a function's graph as a trapezoid. The midway rule uses rectangular areas to approximate the definite integral, whereas the trapezoidal rule uses trapezoidal approximations to approximate the definite integral. Simpson's approach works by first approximating the original function with piecewise quadratic functions.
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Find the amount in a continuously compounded account for the following condition.
Principal, $3000; Annual interest rate, 5.5%; time, 3 years
The balance after 3 years is $___
(Round the final answer to the nearest cent as needed. Round all intermediate values to five decimal places as needed.)
Answer:
9300$
Step-by-step explanation:
Graph the image of △FGH after a dilation with a scale factor of 2, centered at the origin.
Answer:
Step-by-step explanation:
1. Each point moves 3 times as far from the origin as it was.
2. Each point moves to 1/3 its previous distance from the origin.
3. Each point moves twice as far from (2, 2) as it was.
1. Each point moves 3 times as far from the - 1
Find all the missing sides and angles of this triangle. Round to the nearest tenth if necessary.
Right triangle ABC. Hypotenuse = 7 units. Angle B = 70 degrees.
Triangle ABC with a hypotenuse of 7 units and angle B equal to 70 degrees,
side AC is 5.3 units side BC is 4.7 units. Angle C is 20 degrees.How to find the sides of the triangleSince triangle ABC is a right triangle and angle B is 70 degrees, it can be deduced that angle C must be 90 - 70 = 20 degrees.
assuming
length of side AC = a
length of side BC = b.
Using the Pythagorean theorem, we can find the values of a and b.
a^2 + b^2 = 7^2
a^2 = 7^2 - b^2
a = √(7^2 - b^2)
Using the tangent function
tan C = b/a
tan 20 = b/√(7^2 - b^2)
Solving for b, we get:
b = tan(20) * √(7^2 - b^2)
We can use numerical methods to find the approximate value of b. Using a calculator, we can find that b is approximately 4.7. Rounding to the nearest tenth, b is 4.7 units.
Finally, using the Pythagorean theorem again, we can find the value of a:
a^2 + b^2 = 7^2
a^2 = 7^2 - b^2 = 7^2 - 4.7^2
a = √(7^2 - 4.7^2)
a = √(7^2 - 22.09)
Using a calculator, we can find that a is approximately 5.3. Rounding to the nearest tenth, a is 5.3 units.
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A sample of size n from a population of size N is obtained through simple random sampling if every possible sample of size n has an equally likely chance of occurring is called?
It is referred to as "simple random sampling" when a sample of size n is taken from such a population of size N and any conceivable sample of that size has an equal likelihood of occuring.
Explain about the simple random sampling?A selection of participants from such a population are chosen at random by the researcher using simple random sampling, a sort of probability sampling.
Every person in the population has the same chance of being chosen. Then, data are gathered from as much of this randomly selected subgroup as possible. Simple random sampling is a technique for selecting a smaller sample size from the a larger population so that it can be used to study and draw conclusions about the larger group.Thus, it is referred to as "simple random sampling" when a sample of size n is taken from such a population of size N and any conceivable sample of that size has an equal likelihood of occuring.
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If f(x) = 9x ^ 3 + 45x ^ 2 + 26x - 40 and x + 4 is a factor of f(x) then find all of the zeros of f() algebraically.
All the zeroes of f(x) are, - 4, 3/2, - 5/3
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The function is,
⇒ f(x) = 9x³ + 45x² + 26x - 40
And, (x + 4) is a factor of f(x).
Now, Divide the function as;
⇒ x + 4 ) 9x³ + 45x² + 26x - 40 ( 9x² + 9x - 10
9x³ + 36x²
- -
------------------------
9x² + 26x
9x² + 36x
- -
-----------------------
- 10x - 40
- 10x - 40
------------------
0
Thus, All the factors of function f (x) is,
⇒ (x + 4) (9x² + 9x - 10)
⇒ (x + 4) (9x² + 15x - 6x - 10)
⇒ (x + 4) (3x(3x + 5) - 2(3x + 5))
⇒ (x + 4) (3x - 2) (3x + 5)
Thus, All the zeroes are,
⇒ x + 4 = 0 ⇒ x = - 4
⇒ 3x - 2 = 0 ⇒ x = 2/3
⇒ 3x + 5 = 0 ⇒ x = - 5/3
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Can you please help me fast
Answer: The slope of the line is 3; option A is correct.
Step-by-step explanation:
The numerical value of the standard deviation can never be:
Zero
Negative
Larger than the variance
Which of the following statements is true:
a. (i) & (ii)
b. (ii) & (iii)
c. (i), (ii) & (iii)
d. None of the above
The numerical value of the standard deviation is never (B) less than the variance and is never negative.
What is the standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers.
While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean (also known as the anticipated value) of the collection.
The standard deviation's numerical value is always greater than the variance and can never be negative.
The lowercase Greek letter (sigma), for the population standard deviation, or the Latin symbol s, for the sample standard deviation, are most frequently used in mathematical texts and equations to indicate standard deviation.
Standard deviation may be written as SD.
Therefore, the numerical value of the standard deviation is never (B) less than the variance and is never negative.
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an airplane is at an elevation of 30000 ft when it begins to approach to an airport. its angle of depression is 8 degrees. what is the distance between the airport and the point on the ground directtly below the plane
The distance between the airport and the point on the ground directtly below the plane is x=-4411.95221
A plane in geometry is a two-dimensional, flat surface. It has no thickness and never ends. An example of a geometric plane might be a sheet of paper or the surface of a wall. The term "plane figures" refers to the flat geometric shapes. In geometry, a plane is a surface made up of all the lines that are parallel to one another and connect any two locations on it. It is a level or flat surface, to put it another way. A plane is uniquely defined in any of the following ways in a Euclidean space of any number of dimensions: with the aid of three non-collinear points. A plane is a fictitious flat surface that passes through the body.
Based on the given,
Formulate:
[tex]tan8=\frac{30000}{x}[/tex]
Evaluate the equation/expression:
[tex]x=-4411.95221[/tex]
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HELP pls will mark you the brainliest
Answer:
first one; Y=4x+8
second one; Y=2x+20
3rd: kites are fun and then windy kites
Step-by-step explanation:
Use your knowledge of special tight triangles to find the missing side lengths and angle measures exactly. No calculators are needed. You can leave everything in radical form.
9.42 m and 3 m are the missing lengths. 30 degrees is the missing angle.
What is triangle?A triangle is a three-sided polygon that is sometimes (but not always) referred to as the trigon. Every triangle has three sides and three angles, which may or may not be the same. A triangle is a three-sided polygon with three edges and three vertices in geometry. The total of a triangle's interior angles equals 180 degrees, which is its most essential feature. This is known as the angle sum property of a triangle. This figure is two-dimensional and has three straight sides. A triangle is a three-sided polygon. A triangle's three angles added together equals 180°. A single plane contains the triangle.
Here,
sin 60=p/h
√3/2=p/6
p=3√3 m
cos 60=b/h
1/2=b/6
b=3 m
90+60+x=180
x=30 degrees
The missing lengths are 9.42 m and 3 m. The missing angle is 30 degrees.
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For which system of inequalities is (-3, 1) a solution?
x+y<-2 and 2x-3y <-9
x+y<-2 and 2x-3y <-9
x+y≤-2 and 2x-3y <-9
x+y≤-2 and 2x-3y ≤-9
In light of the query we've got D)x + y ≤ -2 and 2x - 3y ≤ -9 is a pair of inequalities for (-3, 1) is the correct answer.
How may an inequality be resolved?When resolving an inequality, you can do one of the following: · Add a same number to each side; • Subtract the same amount from each side; • Multiply or divide either aspect by the exact positive amount. You must flip the inequality sign if you combine or split each end by a negative number.
According to the values x = -3, y = 1
-3 + 1 = -2, which is less than or equal to -2, so the first inequality is true.
2 * -3 - 3 * 1 = -9, which is less than or equal to -9, so the second inequality is also true.
Since both inequalities are true, (-3, 1) is a solution for the system of inequalities x + y ≤ -2 and 2x - 3y ≤ -9.
we get ,
x + y ≤ -2
2x - 3y ≤ -9
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The Complete Question :
For which system of inequalities is (-3, 1) a solution?
A. x+y<-2 and 2x-3y <-9
B. x+y<-2 and 2x-3y <-9
C. x+y≤-2 and 2x-3y <-9
D. x+y≤-2 and 2x-3y ≤-9
40
50
70
100
In the diagram of AABC below, AB AC. The
measure of ZB is 40°.
B
What is the measure of ZA?
X
The value of angle A is 100⁰.
option D is the correct answer.
What is the measure of angle A?
The measure of angle A is calculated by applying the following formula as shown below;
If line AB is similar to line AC, then angle B must be equal to angle C.
∠ B = ∠ C = 40 ⁰
The value of angle A is calculated as follows;
∠ A = 180⁰ - ( ∠ B + ∠ C ) ( sum of angles in a triangle )
∠ A = 180⁰ - ( 40⁰ + 40⁰ )
∠ A = 180⁰ - ( 80 ⁰ )
∠ A = 100⁰
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Find the mean absolute deviation for the set below 108, 53, 47, 22, 56, 62
Answer: The mean absolute deviation for the given data set is 19.
Step-by-step explanation:
The mean absolute deviation (MAD) is a measure of the variability of a set of data and is defined as the average of the absolute deviations of each data point from the mean. To find the MAD, we first need to find the mean of the data set, and then subtract each data point from the mean and take the absolute value of the result.
Here is the step-by-step process for finding the MAD for the given data set:
Find the mean of the data set: (108 + 53 + 47 + 22 + 56 + 62) / 6 = 56
Subtract the mean from each data point:
108 - 56 = 52
53 - 56 = -3
47 - 56 = -9
22 - 56 = -34
56 - 56 = 0
62 - 56 = 6
Take the absolute value of each result:
|52| = 52
|-3| = 3
|-9| = 9
|-34| = 34
|0| = 0
|6| = 6
Find the average of the absolute deviations: (52 + 3 + 9 + 34 + 0 + 6) / 6 = 19
So the mean absolute deviation for the given data set is 19.
Tony wants to use his savings at the end of march to buy video games. The game cost $35.75 each. How many games can Tony buy?
Alice wants to use her savings at the end of two months to buy concert tickets. If the concert tickets cost $17.50 each, How many can she buy?
1. The number of games that Tony can buy will be 3 games.
2. The number of tickets that Alice can buy will be 6 games.
How to calculate the valuesA word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.
The number of games that Tony can buy will be:
= (35.4 + 18.2) × 2.50 / 33.75
= 3.9
= 3 rounding down
The number of tickets that Alice can buy will be:
= (21.8 + 26.6) × 2.50 / 17.50
= 6 games.
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graph the opposite of 6 on the number line
The opposite of 6 would be -6