Answer:
2[tex]\sqrt{13x^{2} }[/tex]
Step-by-step explanation:
To simplify the expression √52x^4, we can break it down as follows:
√(52x^4) = √(4 * 13 * x^4)
Since the square root of a product is equal to the product of the square roots, we can simplify further:
√(4 * 13 * x^4) = √4 * √13 * √(x^4)
The square root of 4 is 2, and the square root of x^4 is x^2:
2 * √13 * x^2
Therefore, the simplified expression is 2√13x^2.
Answer:
[tex]\large\text{$2\sqrt{13}\;x^2$}[/tex]
Step-by-step explanation:
Given expression:
[tex]\sqrt{52x^4}[/tex]
Prime factorization is the process of representing a positive integer as a product of its prime factors.
The prime factorization of 52 is 2² · 13. Therefore, rewrite 52 as 2² · 13:
[tex]\sqrt{2^2 \cdot 13 \cdot x^4}[/tex]
[tex]\textsf{Apply the radical rule:} \quad \sqrt{abc}=\sqrt{\vphantom{b}a}\sqrt{b}\sqrt{c}[/tex]
[tex]\sqrt{2^2} \sqrt{13} \sqrt{x^4}[/tex]
[tex]\textsf{Apply the radical rule:} \quad \sqrt{a^2}=a, \quad a \geq 0[/tex]
[tex]2\sqrt{13} \sqrt{x^4}[/tex]
[tex]\textsf{Apply the radical rule:} \quad \sqrt[n]{a^m}=a^{\frac{m}{n}},\quad \textsf{assuming} \;a\geq 0[/tex]
[tex]2\sqrt{13} \;x^{\frac{4}{2}}[/tex]
[tex]2\sqrt{13} \;x^2[/tex]
Therefore, the simplified expression is:
[tex]\large\boxed{2\sqrt{13}\;x^2}[/tex]
Guadalupe goes out to lunch. The bill, before tax and tip, was $11.25. A sales tax of 9% was added on. Guadalupe tipped 23% on the amount after the sales tax was added. What was the total cost of the meal, plus tax and tip? Round to the nearest cent.
Answer: $14.10
Step-by-step explanation:
11.25 * 9 = 101.25
101.25/100 = 1.0125
11.25 + 1.0125 = 12.2625
--
12.2625 * 26 = 282.0375
282.0375/100 = 2.820375
11.25 + 2.820375 = 14.070375
--
14.070375 rounded = 14.10
what possible values can x % 10 evaluate to? (x is an integer). 0..9 means that possible values are 0, 1, 2, and so on up to 9. and so on.
The possible values of x % 10, where x is an integer, are integers between 0 and 9, inclusive, i.e. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
The modulo operation (represented by the percent symbol %) returns the remainder of the division of one number by another. For example, when x is divided by 10, the result of x % 10 is the remainder of that division.
Since 10 is a positive integer, when x is divided by 10, the result is always a non-negative integer. Furthermore, since the range of x is all integers, the result of x % 10 will always be less than 10.
Therefore, the possible x % 10 are integers in the range of 0 to 9, including 0 and 9. These are the remainders that can result from dividing x by 10. For example:
7 % 10 = 7
17 % 10 = 7
27 % 10 = 7
In all of these cases, the remainder is 7 when the number is divided by 10.
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What are three ratios that are equivalent to 8:14
Answer:
4:7, 16:28, 32:56, 64:112
Step-by-step explanation:
You can go down 1, and you can also keep doubling. I hope this helped, I hope you get it right! Have a Good Day!
please help so hard due soon
Answer:
the answer I think is the 1st
Step-by-step explanation:
as the change (+4) is in y
not in x
Henry runs 8 miles in 47 minutes. How many miles does he run per minute?
Answer:
.17 miles per minute
Step-by-step explanation:
You are trying to figure out how many Miles he ran in EACH minute, so you would do 8(Miles)/47(minutes)
8/47 = .17
how to find 20.5% of 1850
Answer: make my answer brainliest
Step-by-step explanation:
379.25
participants in a study on the effects of viagra are assigned to groups. one group receives a sugar pill (a zero dose of viagra) while the other group receives viagra. the number of erections over 30 days is recorded by participants in a journal. in this example, what is the independent variable?
Participants in a study on the effects of viagra are assigned to groups, the independent variable is The viagra.
In an algebraic equation, an independent variable is a variable whose values are not impacted by changes. It is claimed that the value of y is a function of the value of the independent variable (x), also known as the x value, and the value of y is known as the dependent variable, in an algebraic equation with two variables (x and y), if any value of x is related to any other value of y.
The alphabetic letter that conveys a numerical value or a number is known as a variable in mathematics. In algebraic equations, a variable is used to represent an unknowable quantity.
For these variables, any alphabet from a to z may be used. Most frequently, the variables "a," "b," "c," "x," "y," and "z" are utilised in equations.
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data set containing 36 sequential data points is divided into 9 quantiles. what is the maximum number of data points that falls below the second quantile?
the maximum number of data points that fall below the second quantile is 4.
4 data points.
Quantiles divide a set of data into four equal parts, each with an equal number of data points. In this case, 36 data points are divided into 9 quantiles, meaning each quantile contains 4 data points. Therefore, the maximum number of data points that fall below the second quantile is 4.
Quantiles divide a set of data into equal parts, each with an equal number of data points. The number of quantiles is determined by the total number of data points. For example, if there are 36 data points, then it is divided into 9 quantiles, each with 4 data points. The lower the quantile, the lower the value of the data points it contains. Therefore, the maximum number of data points that fall below the second quantile is 4.
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The table below shows the different combinations of honey and oats that can be used in making granola.
Which honey to oats ratio does not follow the pattern in the table?
5:2
10:4
15:7
20:8
Two friend shop for fresh fruit Elena buys a watermelon for 7.55 and 4 pounds of cherries Tonya buys a pineapple for $2.25 And 3 pounds of Cherries used the variable p to represent the price in dollars per pound of cherries 
Elena spent an amount of $4.10 + p more than Taniy.
What is the expression?Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.
Let's represent the amount spent by Elena and Taniy as E and T, respectively. We know that:
E = 8.25 + 4p (since Elena bought a watermelon for $8.25 and 4 pounds of cherries for 4p)
T = 4.15 + 3p (since Taniy bought a pineapple for $4.15 and 3 pounds of cherries for 3p)
The expression to represent how much more Elena spent can be represented as:
E - T = (8.25 + 4p) - (4.15 + 3p)
Expanding the right side:
E - T = 8.25 + 4p - 4.15 - 3p
Combining like terms:
E - T = 4.10 + p
So Elena spent $4.10 + p more than Taniy.
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Find the exact solution to the equation. (5 points)
one hundred times one fifth to the power of quantity x divided by four equals four.
Answer:
x = 2
Step-by-step explanation:
We can start by rewriting the equation as follows:
100 * (1/5)^x / 4 = 4
Next, we'll multiply both sides by 4 to cancel out the division by 4:
400 * (1/5)^x = 16
Finally, we'll divide both sides by 400 * (1/5)^x to isolate (1/5)^x:
1/((1/5)^x) = 16 / 400 = 1/25
Taking the reciprocal of both sides:
(1/5)^x = 25
Taking the power of 5 to both sides:
x = log(25)/log(5) = 2
So x = 2 is the solution to the equation.
Florida has 8 less than 5 times the number of counties $a$ in Arizona.
Georgia has 25 more than twice the number of counties $f$ in Florida.
The expression which represents Arizona and Florida is 5a - 8 and 2f + 25 respectively.
How to write expressions?Number of countries in Arizona= a
Number of countries in Florida= f
Florida:
5a - 8
Georgia:
2f + 25
Therefore, 5a - 8 and 2f + 25 represents the expression of each country respectively.
Complete question:
Write an expression for the number of counties in Georgia.
Florida has 8 less than 5 times the number of counties, a, in Arizona.
Georgia has 25 more than twice the number of counties, f, in Florida.
a. Write an expression for the number of counties in Florida.
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A box shaped like a right rectangular prism measures 8 inches by 6 inches by 5 inches.
What is the length of the interior diagonal of the prism to the nearest hundredth?
A 10.77 inches
10.68 inches
B 11.18 inches
D 11.92 inches
The diagonal length of a right rectangular prism is given by the formula (l2 + w2 + h2) units. The length of the diagonal of this rectangular box is 5√2 cm.
How do you find the length of a diagonal in a rectangular prism?Therefore, the equation for the diagonal length of a right rectangular prism is (l2+w2+h2), where l is the length, b is the breadth, and h is the height.
d2 = l2 + w2 + h2
Take the square root of either side of the equation to find the value of d:
d = √(d2) = √(l2 + w2 + h2)
d = √(l2 + w2 + h2)
The diagonal length is as follows given that the rectangular box in question is 6 cm x 8 cm x 5 cm in size:
d = √(36 + 64 + 25)
d = √(125)
d = √(62.5)·√(2)
d = 5√(2)
Therefore, the length of the diagonal of this rectangular box is 5√2 cm.
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write the following expression without negative exponents and without parentheses (-9x)^-2
The value of the expression is 1/(9x)^2
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
(-9x)^-2
We can write the expression without negative exponents by using a fraction with a positive exponent:
(-9x)^-2 = 1/(-9x)^2
And without parentheses, this expression becomes:
1/(9x)^2
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Can same one teach me how to multiply 3-digit by 2-digit numbers
please and thank you
Step-by-step explanation:
put the 3-digit on top and 2-digit on bottom
multiply last # on the 2-digit by by the 3digit then add a 0 placeholder then reapeat
kari is buying aa batters and d batteries. the store sells aa batteries in packs of 6 and d batteries in packs of 10. if kari wishes to buy the same number of aa and d batteries, what is the smallest number of each battery type that she can buy
Kari can buy 30 AA batteries and 30 D batteries. We used simple LCM for this solution.
To find the smallest number of each battery type that Kari can buy, we must find the least common multiple (LCM) of 6 and 10. The LCM is the smallest multiple that both numbers can divide into evenly. To find the LCM, we can list the multiples of each number until we find a common multiple. In this case, the LCM of 6 and 10 is 30. So, Kari can buy 30 AA batteries and 30 D batteries, which gives her an equal number of both battery types.
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List the sample space of a fair, 7-sided number cube rolled while playing a board game.
S = {7}
S= {1,7}
S = {1, 2, 3 ,4, 5, 6, 7}
S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
The sample space of a fair, 7-sided number cube rolled while playing a board game is,
S = {1, 2, 3, 4, 5, 6, 7}
The correct option is C.
What is sample space?A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of potential experiment results. Depending on the experiment, a sample area could contain a variety of results.
Given:
7-sided number cube rolled while playing a board game.
The sample space is the collection of all the numbers.
So, the sample space is,
S = {1, 2, 3, 4, 5, 6, 7}
Hence, S = {1, 2, 3, 4, 5, 6, 7}.
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Tonya saved $564 in one year. If she saved the same amount each month, how much did Tonya save in two months?
On solving the provided question, we can say thatthe equations will be each moth will be 564/x = 564/12 = $47 and 2 moths will be = 47x = 47*2 = $94
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
Tonya saved $564 in one year.
the equations will be
each moth will be 564/x
= 564/12 = $47
2 moths will be = 47x = 47*2 = $94
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Translate The difference between a number squared and 14 is 50
Answer:
[tex]x^{2} - 14 = 50[/tex]
Step-by-step explanation:
Let x = Unknown number
Number squared = [tex]x^{2}[/tex]
Difference between the number squared and 14 is 50:
= [tex]x^{2} - 14 = 50[/tex]
= [tex]x^{2} = 14 + 50[/tex]
= [tex]x^{2} = 64[/tex]
(NOTE: It cannot be [tex]14 - x^{2} = 50[/tex] since:
[tex]x^{2} = 14 - 50[/tex] which would mean [tex]x^{2} = -36[/tex] and a square of a number CANNOT be a negative number)
Taking the square root of both sides to get rid of the square:
= [tex]x = \sqrt{64}[/tex]
= x = ±8
RO
ROCK
each
Shirts on sale at concert!
uppose David has $65 to spend on his ticket and some shirts. He already
Dent $32.25 on his ticket and fee. Write an inequality that could be used
o find the maximum number of shirts he can buy.
hat is the maximum number of shirts he can buy?
He can buy a maximum of 2 shirts.
Answer: Let x be the number of shirts that David buys.
The cost of the shirts can be represented by the equation: $15x.
The total amount of money that David has spent can be represented by the equation: $32.25 + $15x.
Since David has a total of $65 to spend, we can write the inequality:
$32.25 + $15x ≤ $65
Solving for x, we get:
$15x ≤ $65 - $32.25 = $32.75
$15x ≤ $32.75
$x ≤ $32.75 / $15 = 2.183333
Since David can only buy a whole number of shirts, the maximum number of shirts that he can buy is 2.
So, the maximum number of shirts David can buy is 2.
Step-by-step explanation:
7-2 Enrichment
Multiplying Polynomials
An architect is preparing to design an office building. She creates a sketch of the basic shape of the structure and
the relative dimensions of each piece shown. The angles in the sketch are all right angles. Find the volume of the structure using each approach. Draw lines on the sketches and record your expressions.
1. Divide the structure into two different rectangular
prisms. Add the volumes of the two prisms to create
an expression for the total
Volume
2. Divide the structure into three different rectangular
prisms. Add the volumes of the three prisms to create
an expression for the total volume.
3. View the structure as one prism with 2 equal sized prisms. Find the volume of the large prism and subtract the volumes of the smaller pieces to find the expression for the total volume!!
Thanks for helping!! (We are learning polynomials right now, like (2+x)^2 for clarification for the problems!!!) :)
The volume of the composite prism using the three methods is 4x^3 - 26x^2 -2x + 160
The volume using two prismsFrom the question, we have the following parameters that can be used in our computation:
The composite figure
Using two prisms, we have the following dimensions
Rectangular prism 1: (x + 4) by (x - 5) by (x - 8)Rectangular prism 2: x by (x - 5) by (3x - 2)The volume is the product of the dimensions
So, we have
Volume = (x + 4) * (x - 5) * (x - 8) + x * (x - 5) * (3x - 2)
Evaluate
Volume = 4x^3 - 26x^2 -2x + 160
The volume using three prismsHere, we have the following dimensions
Rectangular prism 1: (x + 4) by (x - 5) by (x - 8)Rectangular prism 2: x by (x - 5) by (3x - 2 -x + 3)Rectangular prism 3: x by (x - 5) by (x - 3)The volume is the product of the dimensions
So, we have
Volume = (x + 4) * (x - 5) * (x - 8) + x * (x - 5) * (3x - 2 - x + 3) + x * (x - 5) * (x - 3)
Evaluate
Volume = 4x^3 - 26x^2 -2x + 160
The volume as a single prismIn (a) and (b), we have
Volume = 4x^3 - 26x^2 -2x + 160
For the large prism, we have
Large = x * (x - 5) * (3x - 2)
Evaluate
Large = 3x^3 -17x^2 + 10x
Subtract 3x^3 -17x^2 + 10x from the total volume to get the smaller volume
Smaller = 4x^3 - 26x^2 -2x + 160 - (3x^3 -17x^2 + 10x)
Evaluate
Smaller = x^3 - 9x^2 - 12x + 160
Hence, the volume of the prism is 4x^3 - 26x^2 -2x + 160
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HELPPP PLEASE ILL MARK BRAINLIEST RNN!!!
Answer: the answer is 0=0
Step-by-step explanation:
5-12=-7
x-7=x-7 x-7+7=x-7+7
x=x x-x=x-x
0=x-x
0=0
Find total surface area of the cylinder whose radius is 3m and height is 6m...
Find the perimeter and area of triangle ABC with altitude BD, given A(-5, 2) B(-3, 5), C(5, 2), and D (-3, 2).
Answer:
The perimeter of triangle ABC with altitude BD can be found by using the Distance Formula. The coordinates of the vertices are A(-5, 2), B(-3, 5), C(5, 2), and D(-3, 2). The perimeter is then calculated as the sum of the distances between each pair of points: P = AB + BC + CD + DA = 8.24 units. The area can be found using Heron's Formula, which gives an area of 6.00 units.
Step-by-step explanation:
The perimeter of triangle ABC with altitude BD can be found by using the Distance Formula. The coordinates of the vertices are A(-5, 2), B(-3, 5), C(5, 2), and D(-3, 2). Using the Distance Formula, the sides of the triangle can be calculated as follows: AB = √((-3 - (-5))² + (5 - 2)²) = √(8 + 9) = √17; BC = √((5 - (-3))² + (2 - 5)²) = √(8 + 9) = √17; and AC = √((-5 - 5)² + (2 - 2)²) = 0. Therefore, the perimeter of triangle ABC is AB + BC + AC = 17√2 units.
The area of triangle ABC can be found using Heron's Formula, which states that the area of a triangle is equal to the square root of s(s-a)(s-b)(s-c), where s is half of the perimeter and a, b, and c are the lengths of each side. In this case, s is half of 17√2 or 8.5√2 units. Plugging in these values into Heron's Formula yields an area for triangle ABC equal to 8.5√2 * 4 * 3 * 1.5√2 or 36√2 units squared.
Answer:
12 units
Step-by-step explanation:
AB^2 = [(-5) - (-2)]^2 + [(-2) - (-2)]^2 = 9
AB = 3
So similarly, BC = 5 and AC = 4
Hence, the perimeter = AB + BC + AC = 12 units
Which shows the solution of the combined inequality?
−1≤2−j<−5
Responses
Number line ranging from negative six to zero with a line beginning with an open point at negative five and ending with a closed point at negative one
Image with alt text: Number line ranging from negative six to zero with a line beginning with an open point at negative five and ending with a closed point at negative one
Number line ranging from negative six to zero with a line beginning with a closed point at negative five and ending with an open point at negative one
Image with alt text: Number line ranging from negative six to zero with a line beginning with a closed point at negative five and ending with an open point at negative one
Number line ranging from zero to six with a line beginning with a closed point at one and ending with an open point at five
Image with alt text: Number line ranging from zero to six with a line beginning with a closed point at one and ending with an open point at five
no solution
The correct option regarding the solution of the compound inequality is given as follows:
No solution.
How to solve the inequality?The inequality for this problem is defined as follows:
−1≤2−j<−5
Hence the first condition is of:
j - 2 ≤ 1
j ≤ 3.
The second condition is of:
2−j<−5
j < -7
j > 7.
We have an and operation, meaning that the two conditions must be satisfied simultaneously.
A number cannot be simultaneously less or equal to 3 and greater than 7, hence the compound inequality has no solution.
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Question content area top
Part 1
Suppose a compact disk (CD) you just purchased has tracks. After listening to the CD, you decide that you like of the songs. The random feature on your CD player will play each of the songs once in a random order. Find the probability that among the first songs played (a) you like 2 of them; (b) you like 3 of them; (c) you like all of them.
a) The probability that among the first songs played you like 2 of them
= 0.404
b)The probability that among the first songs played you like 3 of them
= 0.2246
c) The probability that among the first songs played you like all of them
= 0.0024
What is Combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.
Given:
Total tracks= 18
a) The probability that among the first songs played you like 2 of them
= C(7 , 2) x C( 11, 3) /C(18, 5)
= 21 x 165 / 8568
= 0.404
b)The probability that among the first songs played you like 3 of them
= C(7 , 3) x C( 11, 2) /C(18, 5)
= 35 x 55 / 8568
= 0.2246
c) The probability that among the first songs played you like all of them
= C(7 , 5) x C( 11, 0) /C(18, 5)
= 0.0024
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g let a and b be two events, and assume that 0 < p( b ) < 1. what is smallest value ( p( a | b ) p( not a | b ) )/2 might have?
The smallest value that (p(a|b) p(not a|b))/2 might have is 0.
The smallest value that (p(a|b) p(not a|b))/2 might have is 0. If p(a|b) = 0, then (p(a|b) p(not a|b))/2 = 0. This means that if event a does not occur, given that event b has already occurred, then the value of (p(a|b) p(not a|b))/2 will be 0.
On the other hand, if p(not a|b) = 0, then (p(a|b) p(not a|b))/2 = 0, which means that if the event, not a, does not occur given that event b has already occurred, then the value of (p(a|b) p(not a|b))/2 will also be 0. Therefore, the smallest value that (p(a|b) p(not a|b))/2 might have is 0.
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ou are paid 1.5 times your normal hourly rate for each hour you work over 40 hours in a week. you worked 46 hours this week and earned $612.50. part a: which equation can you use to solve for $x$ , your normal hourly rate? responses $612.50\
The equation to solve for your normal hourly rate is x = (612.5 - 1.5 * 46 + 46 * x) / 40.
In this equation, x represents your normal hourly rate. The first term in the parentheses, 612.5, is your total earnings for the week. The second term, 1.5 * 46, represents the overtime pay you received for working 6 hours over 40 hours. The third term, 46 * x, represents the amount you earned for your 40 hours of regular pay. The final term, 40, represents the number of hours you worked at your regular rate. By dividing both sides of the equation by 40, we can isolate x and solve for your normal hourly rate.
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Complete Question:
You are paid 1.5 times your normal hourly rate for each hour you work over 40 hours in a week. you worked 46 hours this week and earned $612.50. part a: which equation can you use to solve for x , your normal hourly rate?
i need help comparing box plots
Answer:
Step-by-step explanation:
Box plots, also known as box-and-whisker plots, are a graphical representation of the distribution of a set of data. To compare two or more box plots, you should consider the following aspects:
Central Tendency: Compare the medians of the box plots to see if they are similar or if there are significant differences. If the medians are similar, it suggests that the central tendency of the data is similar.
Spread: Compare the ranges of the box plots to see if they are similar or if there are significant differences. If the ranges are similar, it suggests that the data has similar spread.
Outliers:the presence, frequency, and magnitude of outliers in each box plot. Outliers can significantly affect the central tendency and spread of the data, so they should be considered when comparing box plots.
Shape: Compare the shapes of the box plots to see if they are symmetrical or skewed. Symmetrical box plots suggest a normal distribution, while skewed box plots suggest a non-normal distribution.
Overlap: Compare the overlap between the box plots to see if there is significant overlap or if the data sets are mostly distinct. If the box plots overlap significantly, it suggests that there is some overlap between the data sets.
It's also important to keep in mind the context of the data when comparing box plots. For example, if the data sets being compared come from different populations, it may not be appropriate to compare them directly.
By considering these aspects, you can gain a better understanding of the similarities and differences between two or more box plots and make more informed comparisons.
If f(x)=2x+4, which graph represents f-1(x)
The graph of f-1(x) is (d)
How to determine the graph of f-1(x)From the question, we have the following parameters that can be used in our computation:
f(x) = 2x + 4
This means that
y = 2x + 4
Swap x and y
So, we have
x = 2y + 4
Make y the subject
So, we have
y = 0.5x - 2
This equation is represented by graph (d)
Hence, the graph is (d)
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