The errors in the equation is shown below.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 8 is an equation.
We have,
4a² x 3[tex]a^5[/tex]
= 4 x 3 x [tex]a^{2 + 5}[/tex]
= 12 [tex]a^7[/tex]
[tex]x^6[/tex] x (x) x x³
= [tex]x^{6 + 1 + 3}[/tex]
= [tex]x^{10}[/tex]
[tex]3^4[/tex] x 2³
= 3 x 3 x 3 x 3 x 2 x 2 x 2
= 81 x 8
= 648
Thus,
The equation is solved correctly above.
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i need help !!!!!
WEIGHT A paper clip weighs about 10−3 kilograms. A draft horse weighs about 103 kilograms. How many orders of magnitude as heavy is a draft horse than a paper clip?
The weight of the draft horse is [tex]10^6[/tex] times the weight of the paper clip.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Weight of the paper clip = [tex]10^{-3}[/tex]
Weight of the draft horse = 10³
Now,
Weight of the draft horse.
= [tex]10^6[/tex] x Weight of the paper clip
= [tex]10^6[/tex] x [tex]10^{-3}[/tex]
= [tex]10^6[/tex] x 1/10³
= 10³
Thus,
The weight of the draft horse is [tex]10^6[/tex] times the weight of the paper clip.
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Answer:
the answer is 6
can someone please help
The length of the other side of the triangle is 30 cm. Thus, option b is correct.
What is Pythagoras theorem?The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this. Base AB, height AC, and hypotenuse BC are all used in this equation. The longest side of a right-angled triangle is its hypotenuse, it should be emphasized.
Here given that hypotenuse = 32 and one side = 16
Using Pythagoras theorem
32² = 16² + x²
x = [tex]\sqrt{32^2 - 16^2}[/tex]
x = 30
Hence, the length of the other side of the triangle is 30 cm.
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5g > 45 as a true and false statement
The true statement of the inequality is that g is greater than 9 and as a false statement, g is less than 9.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, An inequality of 5g > 45.
Dividing both sides by 5 we have (5/5)g > 45/5.
g > 9.
Now, The true statement is 'g' is greater than 9 and as a false statement 'g' is less than 9.
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decrease 90 by 65%
pls do simple working out :)
Answer:31.5
Step-by-step explanation: Since we are decreasing 90 by 65%, we want to find 35% of 90. To do this, simply multiply 90 by 0.35 to get 31.5.
Given the series − 20/8 + 80/64 − 320/512 + 1280/4096 ⋯ Does this series converge or diverge?If the series converges, find the sum: ____________
The series is the converge series and the sum of the converges is 55/16
The term converge series in math is defined as a series is the sum of the terms of an infinite sequence of numbers
Here we have know that the series 20/8 + 80/64 − 320/512 + 1280/4096.
When we simplify this series the we get,
=> 20/8 + 80/64 − 320/512 + 1280/4096
=> 5/2 + 5/4 - 5/8 + 5/16
As per the following rule If ∑an is conditionally convergent and r is any real number then there is a rearrangement of ∑an whose value will be r.
Based on these we have to simplify then we get, here with unlike denominators find the Least Common Denominator (LCD)
=> LCD = 16
Multiplying numerators and denominators to get the LCD in all fraction denominators
Then we get,
=> 40/16 + 20/16 - 10/16 + 5/16
=> 55/16
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What is the solution to this system of equations?
Negative 5.9 x minus 3.7 y = negative 2.1. 5.9 x + 3.7 y = 2.1.
What is the solution to this system of equations?
Negative 5.9 x minus 3.7 y = negative 2.1. 5.9 x + 3.7 y = 2.1.
(0, 2.1)
(0, -2.1)
no solution
infinitely many solutions
The system of equations has an infinite number of solutions. The correct answer would be an option (D).
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The system of equations is given in the question, as follows:
-5.9x - 3.7y = -2.1 .....(i)
5.9x + 3.7y = 2.1 .....(ii)
As we know that when a solution set of infinite points exists, a system of linear equations has an infinite number of solutions.
Here the system of equations has an infinite number of solutions because both equations are identical.
Hence, the correct answer would be an option (D).
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given a j = 3 2 and b j = −3 4 , where j = −1 , find (use just pencil and paper, not software or calculators)
Value of the following expressions for a = 3 + 4j and b = 3 - 4j , where j = √−1 are as follow :
1. a + b = 6
2. a × b = 25
Calculation of the value for the required expression by substituting the given values are:
1. a + b
= ( 3 + 4 j ) + ( 3 - 4j )
Take like terms together we get,
= ( 3 + 3 ) + ( 4j - 4j )
= 6 + 0j
= 6
To get the value of second expression substitute the value of 'a' and 'b' we get :
2. a × b
= ( 3 + 4 j ) × ( 3 - 4j )
Apply the formula : ( x + y ) (x - y ) = x ² - y²
= ( 3 )² - ( 4j )²
= 9 - 16j²
Here j = √-1 ⇒ j² = -1
= 9 - 16 (-1 )
= 9 + 16
= 25
Therefore, the value of 1. a + b = 6 and 2. a × b = 25.
The above question is incomplete, the complete question is:
Given a = 3 + 4j and b = 3 - 4j , where j = √−1 , find (use just pencil and paper, not software or calculators) Find the value of the following :
1. a + b 2. a × b
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if a1 = 4 and an =2an-1-1 then find the value of a4
The value of [tex]a_{4} = 37[/tex]
We need to find value of [tex]a_{4}[/tex].
What is Sequence?A sequence is a collection of elements that are arranged according to a specific pattern.
Arithmetic sequence is a sequence where each consequtive term has a common constant difference.
Now,
Given that value of [tex]a_{1} = 3[/tex]
[tex]a_{n} = 4 a_{n-1} -1[/tex]
Then to find value of [tex]a_{4}[/tex], we can find [tex]a_{2} , a_{3}[/tex]as;
[tex]a_{2} = -2(a_{1} ) - 1\\a_{2} = -2(4) - 1\\a_{2} = -9[/tex]
[tex]a_{3} = -2(a_{2} ) - 1\\a_{3} = -2(9) - 1\\a_{3} = -19[/tex]
Hence, the value of [tex]a_{4}[/tex] as;
[tex]a_{4} = -2(a_{3} ) - 1\\a_{4} = -2(-19) - 1\\a_{4} = 37[/tex]
Therefore, The value of [tex]a_{4}[/tex]= 37.
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Caron want to put up a glow in the dark contellation diplay in hi bedroom he need a pack of two ided tape which cot $12 the tar ticker cot $14 per pack and he want to buy 3 pack what i a good etimation of how much change Caron will get back if he give $75?
If Caron gives $75, he will get $21 as a change, when he buys a constellation display.
To estimate the amount of change Caron will get back, we need to calculate the total cost of the two-sided tape and the star stickers. The two-sided tape costs $12 and Caron wants to buy 3 packs of star stickers which cost $14 each, so the total cost of the star stickers is 3 * $14 = $42. The total cost of both the two-sided tape and the star stickers is $12 + $42 = $54.
If Caron gives $75, he will get $75 - $54 = $21 as change. This is a rough estimate of the amount of change Caron will get back, and it's always a good idea to have a little extra money in case the actual cost is slightly higher.
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You are given two independent Poisson variables X and Y where X has a mean of 3 and Y has a mean of 4.Given that X+Y=7, what is the probability that X = 2?A -0.06B 0.18C 0.20D 0.22E 0.24
For the given Poison variables, the probability that X = 2 is 0.22.
Poisson variables are used to model count data, such as the number of customers arriving at a store in an hour, or the number of goals scored in a soccer match. The mean and variance of a Poisson variable are equal.
In this problem, you are given two independent Poisson variables, X and Y, where X has a mean of 3 and Y has a mean of 4. The sum of these two variables is 7. Your goal is to find the probability that X = 2.
Here we need to solve this problem, we can use the formula for the Poisson distribution. The probability of X = k is given by:
=>[tex]P(X = k) = \frac{(e^{-\mu}) * (\mu^k)}{k!}[/tex]
where μ is the mean of the Poisson variable, and e is the mathematical constant approximately equal to 2.718.
Now by substituting the values for X, we have:
=> [tex]P(X = 2) = \frac{(e^{-3}) * (3^2)}{2!}[/tex]
=> P(X = 2) = (0.0498) * (9) / 2
=> 0.224
Therefore the correct option is D) 0.22.
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please help in due in like 30 mins and I dont know how to work it out
The fraction by which the income decreased in August is given as follows:
1/5.
How to obtain the fraction?The total income is given by a proportional relationship of the cost per item and the number of items sold, hence:
y = kx.
In which:
y is the total income.k is the price per item.x is the number of items sold.For August, the parameters are given as follows:
k: 4k/3, as 1/3 + 1 = 4/3.x: 3x/5, as 1 - 2/5 = 3/5.Hence the August expression is given as follows:
y = 4k/3 x 3x/5
y = 12kx/15
y = 4kx/5.
Hence the decrease is given as follows:
1 - 4/5 = 5/5 - 4/5 = 1/5.
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Based on these data, estimate the number of days that the dow decreased by more than 1% in these 61 days.
Number of the 61 days in 2009 the Dow decreased by more than 1% is 0.514.
What is normal distribution?A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.
Given:
61 days in 2009 the Dow decreased by more than 1%.
In 2009
z = (1- (-0.198))/2.331
z = 0.514
In 2010
z = (1-0.078)/0.821
z = 1.123
Thus, number of the 61 days in 2009 the Dow decreased by more than 1% is 0.514.
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how many solutions does -x+y=-5,3x+5y=15 have
Answer: It could be 7 or 10 or 113
Step-by-step explanation: Just to make sure that you don't think it's only for 5. If I just get something, that something is equal to itself, which is just going to be true no matter what x you pick.
How many miles is equal to 13 kilometers?
Step-by-step explanation: 1 kilometer is equal to 0.621371 miles. To convert 13 kilometers to miles, you can multiply 13 by 0.621371.
13 kilometers * 0.621371 miles/kilometer = 8.042443 miles
So 13 kilometers is equal to 8.042443 miles.
Write sin t in terms of cos t using the Pythagorean Identity for:
The solution to sin(t) is sin(t) = -√[1 - cos²(t)]
How to determine the solution to sin(t)From the question, we have the following parameters that can be used in our computation:
The angle t is the quadrant IV
This means that
sin²(t) + cos²(t) = 1
Subtract cos²(t) from both sides of the equation
So, we have the following representation
sin²(t) = 1 - cos²(t)
Take the square root of both sides
sin(t) = ±√[1 - cos²(t)]
sin(t) is negative in quadrant IV
So, we have
sin(t) = -√[1 - cos²(t)]
Hence, the solution is sin(t) = -√[1 - cos²(t)]
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Special right triangle
Using properties of right angle, The value of a will be 32 units.
What is the special right triangle rule?Particular Right Triangle Formula
The right triangle formula, which states that the square of a right-angled triangle's right triangle is equal to the product of its other two squares, is the fundamental Pythagoras theorem formula.
How long are the other two legs if a hypotenuse of a triangle with a 45°, 45°, and 90° angle is 32 units.
We are aware that Leg: Ankle: Length x = x: x: x2 is the formula for a triangle with a 45°, 45°, and 90° angle.
We can state that x2 = 32 because it is a known that the hypotenuse equals 32. As a result, x = 3 is determined.
After replacing this number of x = 3, the lengths of the empty sides may now be determined.
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Complete question -
Find values of a and b -
Anne is painting her house light blue. To make the color she wants, she must add 3 cans of white paint to every 2 cans of blue paint.
1. How many cans of white paint will she need to mix with 6 cans of blue?
2. Rate needed (white/blue)
3. What is the unit rate?
4. Interpretation of unit rate?
1. 9 cans of white paint will she need to mix with 6 cans of blue
2. The rate of white to blue is 9 : 6.
3. The unit rate is 3/2.
What is Ratio?Given:
Anne must add 3 cans of white paint to every 2 cans of blue paint.
So, the ratio of white to blue = 3:2
and, for 6 cans of blue paint the white paint needed
= 6 x 3/2
= 3x 3
= 9 cans
2. The rate of white to blue is 9 : 6.
3. The unit rate is 3/2.
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Half of the sum of two numbers is 12, while one-fourth of their product is 35. Find the numbers.
The heptagon at the right ha been diected into five triangle with angle labeled a hown ue the five triangle to prove that the um of the interior angle of any heptagon i alway 900°
If the Heptagon has been dissected into five triangle , the the proof that sum of the interior angle of any heptagon is always 900° is shown below .
To prove that the sum of the interior angles of a heptagon is 900°, we can use the five triangles that have been dissected from the Heptagon, as follows: let the 5 triangles be A , B , C , D and E .
we know that the sum of interior angle of triangle is always 180° ;
Triangle A: The sum of the angles of triangle A is 180°.
Triangle B: The sum of the angles of triangle B is 180°.
Triangle C: The sum of the angles of triangle C is 180°.
Triangle D: The sum of the angles of triangle D is 180°.
Triangle E: The sum of the angles of triangle E is 180°.
So , the sum of all the angles in the five triangles is 180°×5 = 900°, which is also equal to the sum of the interior angles of the heptagon.
Therefore , we can conclude that the sum of the interior angles of any heptagon is always 900°.
The given question is incomplete , the complete question is
The Heptagon has been dissected into five triangle with angle labeled , use the five triangle to prove that the sum of the interior angle of any heptagon is always 900° .
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use the number 8, 15, and 23, to make two adition facts and two subtratio9n facts
Answer:
8-15
8-23
and
15+23
15+8
Step-by-step explanation:
Please solve 1 SIMPLE question!
The value of tanФ = -1/4 in the III quadrant is -14⁰:
How to find the tan?A trigonometric ratio is a ratio between two sides of a right triangle. The tangent ratio is just one of these ratios. In this tutorial, you'll see how to find the tangent of a particular angle in a right triangle.
Tangent = opposite /Adjacent
Tan ∅ = -1/4
Tan ∅= -0.25
Taking the tangent inverse to get ∅
∅=Tan⁻0.25
∅=-14
This is to say that in the III quadrant, Tan ∅=-1/4 is -14⁰
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What is the slope of the line passing through the points 12/7 and 16/7
Answer:
(12,7) and (16,7)
There is no slope as both points are on the same line. So the equation would be:
y=7
Step-by-step explanation:
Solve.
6|w-5/+3≤45
Help help help
Answer:
The solution is w ≤ 18
3/1 = d/9
d=
Help please!
[tex] \frac{3}{1} = \frac{d}{9} \\ [/tex]
cross multiply...
[tex]d = 27[/tex]
Start at 2⅓, add 2¼. I need the first 4 multiples
The multiple of 2⅓, add 2¼. is 2 7/12.
What are multiple?A multiple in mathematics is created by multiplying any number by an integer. In other words, if b = na for some integer n, known as the multiplier, it can be said that b is a multiple of a given two numbers, a and b. This is equivalent to stating that b/a is an integer if an is not zero.
In other words, the product of 4 and any natural integer is the multiple of 4. For instance, the result of multiplying 4 by 4 is 16, making 16 a multiple of 4. Examples of multiples of four are 4, 12, 20, 24, and so forth.
Start at 2⅓, add 2¼. I need the first 4 multiples?
→2 1/3+2 1/4
⇒2 3+4/12
⇒2 7/12
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Two classes of fifth graders are raising money for a field trip. The two classes bake cherry cherry pies that are all the same size to sell at the winter festival. Each cherry pie is cut in eight equal pieces. The fifth graders sell each piece of cherry pie for sixty cents. At the end of the bake each sale class reports how much cherry pie was sold. 4 2/8 5 1/2
A circular pie cut in 8 pieces and sold at a fractional form 4(2/8) and 5(1/2), yields a total sale of 78 pieces of pie.
What is a circle?
A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.
A pie is made in a circular shape.
Number of pieces in one pie = 8 pieces
Number of pieces of pie sold by first class of fifth grades = 4(2/8)
Number of pieces of pie sold by second class of fifth grades = 5(1/2)
The total number of pieces sold is = Pieces sold by first class + Pieces sold by second class
To find the pieces sold by first class multiply the fractional form by number of pieces -
4(2/8) × 8
34/8 × 8
34
The first class sold 34 pieces of pie.
To find the pieces sold by second class multiply the fractional form by number of pieces -
5(1/2) × 8
11/2 × 8
11 × 4
44
The second class sold 44 pieces of pie.
The total number of pies sold is -
The total number of pieces sold is = 34 + 44
The total number of pieces sold is = 78
Therefore, 78 pies were sold.
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in a chi-square test of goodness of fit, the p-value of the test is 3.2578x10-13 and the level of significance of the test α=0.05. what statistical decision could you make from this information?
In this particular case, the p-value is 3.2578x10⁻¹³, which is much smaller than the level of significance of 0.05.
A chi-square test of goodness of fit is a statistical test used to compare the observed data to a theoretical distribution.
In mathematical terms, the null hypothesis states that the observed data follows the theoretical distribution, and is represented by
H0= The observed data follows the theoretical distribution. The alternative hypothesis, which is the opposite of the null hypothesis, states that the observed data does not follow the theoretical distribution, and is represented by
HA= The observed data does not follow the theoretical distribution.
Based on the p-value of 3.2578x10⁻¹³ and the level of significance of 0.05, we can make the following statistical decision:
p-value < α (3.2578x10-13 < 0.05),
Therefore reject H0 and accept HA.
n other words, we can conclude that the observed data does not follow the theoretical distribution, and there is strong evidence to support this conclusion. The chi-square test of goodness of fit is a useful tool for making statistical decisions about the distribution of data.
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a particular city with a population of 44,700 people has a total of 42 cell phone towers. how many people are assigned to a single cell phone tower?
The total number of people are 1064 to whom the single cell phone towers are assigned in a particular city.
In a graphical or tabular format, a frequency distribution displays the frequency of repeated entries. It provides a visual representation of the frequency of various items or counts their occurrences.
There are total of 44,700 people in the city and total of 42 cell ,
so to find out the number of people using single cell tower is,
Number of people on single cell tower = 44700/42
=1064.285 ≈ 1064 people
The gathered information is arranged in tables using the frequency distribution method. The information might include student grades, local weather information, volleyball match point totals, etc. We must provide data in a relevant way for improved understanding after data gathering. Create a table that contains a summary of all the data's characteristics. The term "frequency distribution" refers to this.
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a population of bacteria, growing according to the malthusian model, doubles itself in 10 days. if there are 1000 bacteria present initially, how long will it take the population to reach 10,000?
It will take 70 days for the population of bacteria to reach 10,000 from 1000, if it is growing according to the Malthusian model and doubling itself in 10 days.
This can be calculated using the exponential growth formula: N(t) = N0 * (1 + r)^t, where N0 is the initial population size (1000), r is the growth rate (2/10 = 0.2), and t is the time in days (70).
The Malthusian model of population growth is an exponential growth model developed by Thomas Robert Malthus in 1798. It states that the population of a species increases exponentially, doubling every generation, and is limited only by the available resources.
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find the value of m for which the simultaneous equations 3x my = 5 (m 2)x 5y = m a have infinitely many solutions b have no solution.
In the simultaneous equations the value of m is 3 and the equation have many solution.
The term called equation in math is known as a condition on a variable (or variables) such that two expressions in the variable have equal value.
Here we have know that the general solution is calculated as,
=> x = (m-5)/(m-3)
and
=> y = 2/(m-3)
When we equate the equations then we get,
=> (m - 5) / (m -3) = 2/(m - 3)
=> m - 5 = 2
=> m = 3
So this dependent system has infinitely many solutions.
When m=3 the equations become look like 3x+3y=5 and 5x+5y=3.
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