The expression (2⁷ · 3⁻⁵ · 9)⁴ is equivalent to the power expression 2²⁸ / 3¹² = 505.109.
How to simplify an expression involving power expressions
In this problem we find an expression involving several numbers in power form and we must simplify into a single real number by using algebra properties:
(2⁷ · 3⁻⁵ · 9)⁴ Given(2⁷)⁴ · (3⁻⁵)⁴ · (3²)⁴ Power of a product of numbers / Definition of power2²⁸ · 3⁻²⁰ · 3⁸ Power of a power2²⁸ · 3⁻¹² Multiplication of powers with equal base2²⁸ / 3¹² Power of a power / Definition of division / ResultTo learn more on power properties: https://brainly.com/question/26480839
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Pleeeeeeeaaaaaaaaaase Help? I need asistance with how to solve an problem like this one.
Using the Triangle Midsegment Theorem, the value of x in the figure is: 4.
How to Apply the Triangle Midsegment Theorem?The Triangle Midsegment Theorem states that:
The length of segment DE = 1/2(the length of segment BC)
Given the following;
DE = x + 1
BC = 4x - 6
Substitute
x + 1 = 1/2(4x - 6)
2(x + 1) = 4x - 6
2x + 2 = 4x - 6
2x + 2 - 4x = 4x - 6 - 4x
-2x + 2 = - 6
-2x + 2 - 2= - 6 - 2
-2x = -8
-2x/-2 = -8/-2
x = 4
Thus, using the Triangle Midsegment Theorem, the value of x in the figure is: 4.
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Solve: 5x - 7x + 6 = -2(x - 3).
A 0
B 3/4
C 2
D no solution
E infinitely many solutions
I will give 80 points
Answer: E: Infinitely many solutions
Step-by-step explanation:
Starting with 5x - 7x + 6, let's combine like terms.
5x - 7x is -2x.
Thus, we have -2x + 6 = -2(x-3)
Using the distributive property for the right side, we multiply -2 * x, and get -2x, and -2 * -3 and get +6.
Now we have -2x + 6 = -2x + 6. We have the same equation here, and know that there is infinitely many solutions here off the bat.
For sake of computations, let's solve and show our work.
Subtracting 6 from both sides, we have -2x = -2x.
Adding 2x to both sides, we get 0 = 0.
Thus, we have infinitely many solutions.
a. no, the program is not statistically significant because the results are unlikely to occur by chance. b. no, the program is not statistically significant because the results are likely to occur by chance. your answer is correct.c. yes, the program is statistically significant because the results are likely to occur by chance. d. yes, the program is statistically significant because the results are unlikely to occur by chance. part 2
The weight loss program is not statistically significant because the results are likely to occur by chance. (Option D)
What is statistical significance?Statistical significance can be used to determine whether a result is more likely the consequence of chance or an important element. Significant results simply imply that you can be sure they are true rather than that you were fortunate (or unfortunate) in the sample you used.Now,
In the given case, 7 subjects have lost around 43 lbs and there is 22% chance of getting these results with a diet that has no effect.In accordance to the definition of statistical significance, it implies that the given program is more likely the consequence of chance.As a result, we can say that in such case, the result occur by chance, i.e., they are followed by a specific probability in terms of occurrence.Hence, the given program is not statistically significant because the results are likely to occur by chance. (Option D)
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(COMPLETE QUESTION:
Determine whether the results below appear to have statistical significance, and also determine whether the results have practical significance.
In a study of a weight loss program, 7 subjects lost an average of 43 lbs. It is found that there is about a 22% chance of getting such results with a diet that has no effect.
Does the weight loss program have statistical significance?
A.No, the program is not statistically significant because the results are unlikely to occur by chance.
B.Yes, the program is statistically significant because the results are unlikely to occur by chance.
C.Yes, the program is statistically significant because the results are likely to occur by chance.
D.No, the program is not statistically significant because the results are likely to occur by chance.)
Charlie watches as a pattern develops. In month 1, he starts with 3 guppy fish in his fish tank. The next month, he finds 6 guppy fish in his tank. The following month, he finds 11 guppy fish in his fish tank. Write an expression to model the pattern of guppy fish in Charlie’s fish tank. Use your expression to determine the number of guppy fish Charlie will observe in month 6.
In month 6, Charlie should observe
_______
The expression for modelling the pattern is n² + 2
Charlie can observe 38 guppy fish in month 6.
Given,
Number of guppy fish in Charlie's fish tank for the first time = 3
Number of guppy fish after one month = 6
Number of guppy fish in the following month = 11
The increasing pattern of guppy fish in the tank:
First month = 6 - 3 = 3
Second month = 11 - 6 = 5
So, we get that the number of guppy fish is increasing by odd numbers.
That is, 3, 6, 11, ........
Now, we have to find an expression for this pattern.
First term is 3.
That is, first term² + 2 = 1² + 2 = 3
Let n be the number of term.
n = 3
So, third term be:
3² + 2 = 9 + 2 = 11
So the expression for modelling the pattern is n² + 2
Now, we have to find the number of guppy fish in month 6.
That is,
n = 6
So,
n² + 2
6² + 2 = 36 + 2 = 38
That is, Charlie can observe 38 guppy fish in month 6.
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Which inequality is true? Use the number line to help.
A number line going from negative 5 to positive 3 in increments of 1.
1.5 greater-than 2 and one-half
One-half greater-than 0.5
Negative 2.5 greater-than negative 1.5
Negative 3 and one-half greater-than negative 4.5
Answer:
Negative 2.5 greater-than negative 1.5
C
Step-by-step explanation:
-2.5 < -2
x+20)4x²+10x+2(
PLEASE SOLVE AND ANSWER.
Answer:
4x[tex] \sf {}^{3} [/tex] +80x²+10x+2
Step-by-step explanation:
(x+20)4x²+10x+2
Let's simplify step-by-step.
(x+20)(4)x²+10x+2
Distribute:
=4x[tex] \sf {}^{3} [/tex] +80x²+10x+2
16. <1 and <2 form a linear pair. The
measure
of <2 is six more than twice the
of <1. Find m<2.
The measure of the angle 2 is 122°.
What is referred as the linear pair?When lines intersect at a single point, a linear pair of angles is formed. If the angles are adjacent to one another after the two lines intersect, they are said to be linear. The sum of the angles of the a linear pair will always be 180°. These angles are also referred to as supplementary angles.Given that angles 1 and 2 form a linear pair,
angle 1 + angle 2 = 180 degrees —— (1)
We've also been notified that angle 2 is 6 times the size of angle 1.
That is to say: angle 2 = (2×angle 1) + 6 ———- (2)
Putting the angle 2 value in (1) from (2)
180 = angle 1 + 2×angle 1 + 6
3×angle 1 = 174
1st angle = 58 degrees ———-(3)
(1) and (3) come from:
angle 2 + 58 = 180
2nd angle = 122 degrees
As a result, angle 2 has a measure of 122 degrees.
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a square garden has an area of 144 square feet. the owner wants to put ups deer fence around the garden that costs $3.50 per linear foot. how much will it coat to put up a whole fence around the garden?
A group of students visited the zoo café for lunch. Each student received a bacon cheeseburger
and milkshake, and the total bill was $104.00. How many students were in the group? Please show your work.
Sandwiches Sides Beverages
Hamburger $3.25
Bacon Cheeseburger $4.75
Chicken Fajita Taco $3.50
French Fries, Small $1.55
French Fries, Large $1.90
Onion Rings $2.40
Cole Slaw $1.45
Soft Drink, Small $1.30
Soft Drink, Large $1.65
Milkshake $3.25
Juice $1.80
Answer:
13
Step-by-step explanation:
A recipe for homemade modeling clay includes cup of salt for every cup of water. If there are 6 cups of salt, how many gallons of water are needed?
Answer:
0.375
Step-by-step explanation:
see above
answer this please and thank you :)
Answer:
The diver is at a depth of [tex]-5\frac{1}{15}[/tex].
_____________________________________
What we have given:
Initial dive: [tex]1\frac{2}{3}[/tex] = [tex]x[/tex]
Additional dive: [tex]3\frac{2}{5}\\[/tex] = [tex]z[/tex]
Given the context, we can assume that sea level is 0ft.
So we have:
[tex]d=0-1\frac{2}{3}-3\frac{2}{5}[/tex] (d = depth)|
[tex]d=0-\frac{5}{3}-\frac{17}{5}[/tex] <- Convert mixed numbers to improper fractions.
[tex]d=-\frac{5}{3}-\frac{17}{5}[/tex] <- Simplify.
[tex]d=-\frac{25}{15}-\frac{51}{15}[/tex] <- The LCM between 3 and 5 is 15, so adjust the fractions accordingly.
(NOTE: Remember everything you do to the denominator must be replicated on the numerator as well!)
[tex]d=\frac{-25-51}{15}[/tex] <- Since the denominators are equal, combine the fractions.
[tex]d=\frac{-76}{15}[/tex]
[tex]d=-\frac{76}{15}[/tex] <- Apply the following fraction rule = [tex]\frac{-a}{b}=-\frac{a}{b}[/tex]
[tex]d=-5\frac{1}{15}[/tex] <- Convert the improper fraction to a mixed number and there is your final answer.
___________________________________
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Have a WONDERFUL day!
helpppppppppp meeeeeeeeeee 50points
Answer:
1) 48
2)44
Step-by-step explanation:
Answer: 48 44 Are The Correct Answers
Step-by-step explanation:Hope This Helps
What are the arithmetic and geometric (answer in that order.) average returns for a stock with annual returns of 9.4 percent, 8.2 percent, -7.3 percent, 4.1 percent, and 9.5 percent?
The arithmetic and geometric average returns for a stock with annual returns of 9.4 percent, 8.2 percent, -7.3 percent, 4.1 percent, and 9.5 percent are 4.78% and 4.58% respectively.
What is a stock?The shares of ownership in a corporation or company that make up stock (also known as capital stock) in the financial world. A single share of stock represents a fractional ownership in the firm in relation to the entire number of shares (especially in American English, where the word "stocks" is also used to refer to shares). This typically entitles the shareholder (stockholder) to that portion of the company's earnings, proceeds from the sale of assets (after paying off all senior claims such as secured and unsecured debt), or voting rights, often allocating these in proportion to the amount of money each stockholder has invested.
Calculations:
Arithmetic returns=Total returns/Total time period
=(9.4+8.2-7.3+4.1+9.5)/5=4.78%
Geometric returns=[(1+rate1)(1+rate2)........(1+rate5)]^(1/5)
=[(1+0.094)(1+0.082)(1-0.073)(1+0.041)(1+0.095)]^(1/5)
=4.58%
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Write a expression for the following problem.
Frank was going on a trip. He filled his car with 14 gallons of gas. He then drove to his destination and used 14 gallons of gas.
The expression is 14 - 14.
What is the expression?Subtraction is a mathematical operation that is used to determine the difference between two or more numbers. The sign used to depict subtraction is -. Other mathematical operations are addition, multiplication and division.
In order to determine the expression for the amount of gas left, we need to subtract the gas bought from the gas used: 14 - 14
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7 grade go math lesson 1.1 adding integers with a common sign
Adding integers with a common sign.
When adding two integers with a common sign, we just add the absolute value of the numbers and the resulting answer is marked with the same sign given in the question.
This question has two possible answers.
Possibility 1:
Both the integers are of positive sign. As a result, the resulting integer after addition is positive.
Example:
Let c = 45 and d = 53.
The sum of c and d is then
sum = c + d = 45 + 53 = 98
Possibility 2:
Both the integers are of negative sign. As a result, the resulting integer after addition is negative.
Example:
Assume c = -23 and d = -61.
The sum of c and d is then
sum = c + d = (-23) + (-61) = -(23 + 61) = -84
Hence, we have added integers with a common sign.
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What’s the slope of the line?
Answer:
slope = - [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 1) and (x₂, y₂ ) = (2, - 1)
m = [tex]\frac{-1-1}{2-(-2)}[/tex] = [tex]\frac{-2}{2+2}[/tex] = [tex]\frac{-2}{4}[/tex] = - [tex]\frac{1}{2}[/tex]
Evaluate the expression.
Answer: 1
Step-by-step explanation:
4^(-1) / 4^(-1)=
1/4 / 1/4=
1/4 * 4/1= ==> Dividing by a number is basically multiplying its reciprocal
1*4/(4*1)=
4/4=1
what is the argument in the logarithmic function f(x)=log,4
Answer:
The expression or number to which the logarithm is operated on is called the argument. From the mathematical expression (x=logbn) ( x = l o g b n ) , n is the argument of the logarithm. The argument of a log function is always positive and should not be equal to 1. Hope this answer helps you.
find all parts show work 25 points
HELP
The solution of the system of linear equations behind the geometric system is (x, z) = (29, 13). The measures of the angles RIG and ZIM are 59° and 140°, respectively.
What are the variables behind a geometric system formed by three lines?
In this problem we find a geometric system generated by lines GZ, AM and IR, in which two variables are shown (x, z) and whose values can be found by applying the concepts of complementary and supplementary angles.
A group of angles are complementary if the sum of their measures equals 90°, and supplementary if that sum equals 180°. This system can be represented by the following system of linear equations:
(3 · x - 56) + 90 + (4 · z + 7) = 180 (1)
(4 · z + 7) + (x + 2) = 90 (2)
By (1):
(3 · x - 56) + (4 · z + 7) = 90
3 · x + 4 · z - 49 = 90
3 · x + 4 · z = 139 (1b)
By (2):
x + 4 · z = 81 (2b)
The solution of the system of linear equations behind the geometric system is (x, z) = (29, 13).
Then, the measures of the angles RIG and ZIM are, respectively:
m ∠ RIG = 4 · z + 7
m ∠ RIG = 4 · 13 + 7
m ∠ RIG = 59°
m ∠ ZIM = 360° - (3 · x - 56) - 90° - (4 · z + 7) + (x + 2)
m ∠ ZIM = 360 - 3 · 29 - 56 - 90 - 4 · 13 + 7 + 29 + 2
m ∠ ZIM = 140°
The measures of the angles RIG and ZIM are 59° and 140°, respectively.
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Complete the sentence.
180g = ___ kg
180g = 0.180 kg or there are 0.180 kilograms in 180 grams.
In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume or even currency to another.
A conversion factor is a number used to change one set of units to another, either by multiplying or dividing.
The sentence states an equality between a units of weight in grams (g) and kilograms (kg).
From there, we can say that we are asked how many kilograms are there in 180 grams.
Converting grams to kilograms, we must use the conversion
1 g = 0.001 kg
180g = 180 (0.001) kg
180g = 0.180 kg
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you are the administrator of an annual essay contest scholarship fund. this year a $52,000 college scholarship is being divided between the top two contestants so that the winner receives three times as much as the runner-up. how much will each contestant receive (in dollars)?
The amount each contestant will receive is as follows:
First position = $39,000Runner up = $13,000How to find the amount each contestant will receive?This year $52,000 college scholarship is being divided between the top two contestants .
Therefore,
Total amount to share to the top winners = 52000 dollars
The winner receives three times as much as the runner-up.
Therefore,
let
x = Amount received by the runner-up
Hence,
Amount the winner received = 3x
Therefore,
52,000 = 3x + x
52,000 = 4x
divide both sides by 4
4x / 4 = 52,000 / 4
x = 13000 dollars
Hence,
Amount the winner received =3(13000) = $39000
Amount received by the runner-up = $13,000
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A. 5x=20
B. x=4
What formula is this?
Answer:
5 x 4=20
Step-by-step explanation:
the x is a smaller number to tell you how many 5's there are which x=4 so the are 4 5's but you have to times(multiple) the two numbers.
5x4
=20
HELP!! PLEASE!! DUE!! TODAY!! Joanna's vegetable Garden covers an area of 1/6 of a square mile. if the garden is 1/4 mile wide, how long does the garden stretch?
The garden will stretch by 2/3 miles.
Given that Garden covers an area of 1/6 of a square mile and the garde is 1/4 mile wide.
As we know, the garden is a rectangle shape.
Here, we will use the formula of area of rectangle.
Area of rectangle is equal to the product of length and breadth.
Area =l×b
Here, the give area=1/6 miles² and b=1/4 mile.
Now, we will substitute the values in the formula, we get
1/6=l×(1/4)
Further, we will multiply both sides with 4, we get
4/6=4l/4
4/6=l
Now, we will simplify the left hand side, we get
2/3=l
Hence, the length of garden stretch when garden covers an area of 1/6 of a square mile and 1/4 mile wide is 2/3 mile.
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Determine the truth value of the following conditional.
14. If two adjacent angles form a right angle, the, then angles are complementary
The statement that "If two adjacent angles form a right angle, then the angles are complementary", is true
How to determine the truth value of the conditional?The conditional is given as:
If two adjacent angles form a right angle, then the angles are complementary
As a general rule, complementary angles add up to 90 degrees i.e. right angle
This means that adjacent angles that add up to 90 degrees are complementary angles
Hence, the statement that "If two adjacent angles form a right angle, then the angles are complementary", is true
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Bob is interested in examining the relationship between the number of bedrooms in a home and its selling price. After downloading a valid data set from the internet, he calculates the correlation. The correlation value he calculates is only 0. 5. What does bob conclude?.
According to the calculations made by Bob after downloading and calculating the correlation value as 0.5 from a given data set, he concludes that as the number of bedrooms in a particular home increase there is an increase in the selling price of the bed.
This increase in the selling price due to the increase in the number of bedrooms can be explained with the help of the Law of Demand which states that as the demand for a certain product increases its cost or the selling price also increases.
Thus, when Bob calculates the correlation factor, he finds that as the number of bedrooms increases there is also a hike in the selling price. As there should be a surplus to fulfill the demand for bedrooms.
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Selena Gomes owes her mom $5 she gets a part time job making $25/hour so she can pay her mom back & have her own money ?
Answer:
She will pay her mom back and have 20 dollars over if she works one hour.
Step-by-step explanation:
4(7) is ___ units from 4, in the _______ direction.
Answer:
4(7) is 7 units from 4, in the forward direction.
Step-by-step explanation:
The circle x2 + y2 – 12x + 6y – 19 = 0 is translated one unit right and two units down. Which is the radius and center of the translated circle?
Center (6, –3); r = 8
Center (7, –5); r = 8
Center (6, –3); r = 64
Center (7, –5); r = 64
According to the question, the standard equation for the circle is [tex]x^{2} +y^{2} =r^{2}[/tex] in which the points (x, y) are the circumference point and 'r' is the radius of the circle.
The given expression for the circle is shown below:
[tex]x^{2} +y^{2} -12x+6y-19=0[/tex]
Bring same variable terms to one side and again re-write the expression:
[tex]x^{2} -12x+y^{2} +6y-19=0[/tex]
Now, to do factors of the given expression add and subtract 36,9 on both the sides
[tex]x^{2} -12x+36+y^{2} +6y+9=19+36+9[/tex]
Factors can be re-written as:
[tex](x-6)^{2} +(y+3)^{2}=64[/tex]
Comparing the calculated equation for the circle with the standard equation, we circle
The center points as (6,-3) and radius as (r = 8).
Hence, the correct answer is Center(6,-3), r = 8.
What is circle?
The circle can be defined as a symmetrical shaped. It has more than one points and all are at the equidistant from the center.
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Answer:
B
Center (7, –5); r = 8
Step-by-step explanation:
you are employed at a grain processing plant that sells cornmeal for $1.28 per pound. if a sack of cornmeal weighs 4 pounds 12 ounces, how much does it cost?
Answer:
$6.08
Step-by-step explanation:
16 ounces = 1 pound
4 pounds 12 ounces = 4 12/16 pounds OR 4 ¾ pounds
4¾ ≈ 4.75
4.75 pounds x $1.28 = $6.08
Vertex (-2,-5) passes through (4,4) in vertex form
The equation of parabola is [tex]y=1/4x^{2}+x/2-4\\\\[/tex].
What is parabola?A symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity follows a curve of this shape. A plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line.
Given:
The equation of parabola in vertex form is
[tex]y=a(x-h)^{2} +k[/tex]
Being vertex here
h=-2
k=-5
According to given question we have
∴
Equation of parabola in vertex form is
[tex]y=a(x+2)^{2} -5[/tex]
. The parabola passes through point (4,4) So the point (4,4) will satisfy the equation .
[tex]4=a(4+2)^{2} -5\\\\4=a*36-5\\\\9=a*36\\\\a=9/36\\\\a=1/4[/tex]
Hence the equation of parabola is
[tex]y=1/4(x+2)^{2} -5\\\\y=1/4(x^{2} +4+2x)-5\\\\y=1/4x^{2} +1+x/2-5\\\\y=1/4x^{2}+x/2-4\\\\[/tex]
Therefore, the equation of parabola is [tex]y=1/4x^{2}+x/2-4\\\\[/tex].
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the equation of parabola is missing