Type the expressions as radicals y^5/2.
Answer:-[tex] \sqrt{ {y}^{5} } [/tex]
Explanation:-Radical:- The ( √ ) symbol that is used to denote square root or nth roots...
Radicals ( Square roots , cube roots , fourth roots and so on )It can be rewritten as rational exponents ( exponents which are fractions ) using the formula:-
[tex] \sqrt[n]{x} = {x}^{ \frac{1}{n} } [/tex]
Generally, using the power rule of exponents:
[tex] \sqrt[n]{ {x}^{m} } = {( {x}^{m)} }^{ \frac{1}{n} } = {x}^{ \frac{m}{n} } [/tex]
Let's take an example to understand better:
• convertion between radicals and rational exponents:
[tex] \sqrt[7]{ {8}^{4} } = {8}^{ \frac{4}{7} } [/tex]
Since the type of radical corresponds with the denominator of a rational exponent, we know the denominator of the exponent will be 7 ..
So ,[tex] {y}^{ \frac{5}{2} } = \sqrt{ {y}^{5} } [/tex]
As , √ denotes ½ ..
Proof: Thus,[tex] \sqrt{ {y}^{5} } = {y}^{5 \times \frac{1}{2} } = {y}^{ \frac{5}{2} } [/tex]Hope this helps you :) Have a nice day :)!The expression "y 5/2" can be written as the fifth root of y squared: √[[tex]y^{2}[/tex]]^(1/5).
The expression "y 5/2" can be written as the fifth root of y squared: √([tex]y^{2}[/tex])^(1/5).
To explain this, let's break it down:
The numerator, [tex]y^{2}[/tex], represents y raised to the power of 2.
Taking the square root of [tex]y^{2}[/tex] simplifies it to √([tex]y^{2}[/tex]).
Finally, raising the result to the power of 1/5 gives us the fifth root of y squared: √([tex]y^{2}[/tex])^(1/5).
In other words, the expression "y 5/2" represents the operation of first squaring y, then taking the fifth root of the resulting value. This is equivalent to finding the value that, when raised to the power of 5, yields [tex]y^{2}[/tex].
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An individual needs a daily supplement of at least 380 units of vitamin C and 170 of vitamin E and agrees to obtain this supplement by eating two foods, I and II. Each ounce of food I contains 76 units of vitamin C and 10 units of vitamin E, while each ounce of food II contains 38 units of vitamin C and also 20 units of vitamin E. The total supplement of these two foods must be at most 22 ounces. Unfortunately, food I contains 10 units of cholesterol per ounce and food II contains 16 units of cholesterol per ounce. Find the appropriate amounts of the two food supplements so that cholesterol is minimized. Find the minimum amount of cholesterol.
The minimum amount of cholesterol is 350 units.
To minimize cholesterol intake while meeting the daily supplement requirements, we need to find the optimal amounts of foods I and II to consume. Let's denote the amount of food I as x ounces and the amount of food II as y ounces.
We have the following constraints:
- The total supplement of the two foods must be at most 22 ounces: x + y ≤ 22
- The daily vitamin C requirement is at least 380 units: 76x + 38y ≥ 380
- The daily vitamin E requirement is at least 170 units: 10x + 20y ≥ 170
To minimize cholesterol intake, we need to minimize the amount of cholesterol from both foods. Food I contains 10 units of cholesterol per ounce, so the cholesterol from food I is 10x. Food II contains 16 units of cholesterol per ounce, so the cholesterol from food II is 16y. Therefore, the total cholesterol is 10x + 16y.
Now, let's solve this problem using linear programming:
Step 1: Rewrite the constraints in terms of x and y:
x + y ≤ 22
76x + 38y ≥ 380
10x + 20y ≥ 170
Step 2: Graph the feasible region determined by these constraints.
Step 3: Identify the corner points of the feasible region.
Step 4: Substitute the corner points into the objective function 10x + 16y and find the minimum value.
After performing these steps, we find that the minimum amount of cholesterol is 350 units.
The values for x and y that correspond to the minimum cholesterol intake may vary, so it is important to verify the optimal solution by substituting the values into the constraints to ensure they satisfy all the requirements.
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Which of the following gives the correct range for the piecewise graph?
A coordinate plane with a segment going from the point negative 3 comma 2 to 0 comma 1 and another segment going from the point 0 comma 1 to 5 comma negative 4.
The correct range for the piecewise graph is [-4, 2].
To solve this problemWe need to find the minimum and maximum values of the y-coordinates.
The first segment goes from (-3, 2) to (0, 1), so the range for this segment is from 1 to 2.
The second segment goes from (0, 1) to (5, -4), so the range for this segment is from -4 to 1.
We must take into account the minimum and maximum values from each segments in order to determine the overall range. The minimum and highest values are -4 and 2, respectively.
Therefore, the correct range for the piecewise graph is [-4, 2].
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Find the measure of
Answer:
∠ ADE = 55° , ∠ ACE = 32.5° , ∠ BAD = 22.5°
Step-by-step explanation:
the measure of the inscribed angle ADE is half the measure of its intercepted arc AE , then
∠ ADE = [tex]\frac{1}{2}[/tex] × 110° = 55°
---------------------------------
the measure of the secant- secant angle ACE is half the difference of the measures of the intercepted arcs , that is
∠ ACE = [tex]\frac{1}{2}[/tex] (AE - BD) = [tex]\frac{1}{2}[/tex] (110 - 45)° = [tex]\frac{1}{2}[/tex] × 65° = 32.5°
-----------------------------------------
the measure of the inscribed angle BAD is half the measure of its intercepted arc BD , that is
∠ BAD = [tex]\frac{1}{2}[/tex] × 45° = 22.5°
Triangle NMO has vertices at N(−5, 2), M(−2, 1), and O(−3 , 3). Determine the vertices of image N′M′O′ if the preimage is reflected over x = −1.
N′(5, −2), M′(2, 1), O′(3, 3)
N′(−5, 5), M′(−2, 3), O′(−3, 7)
N′(3, 2), M′(0, 1), O′(1, 3)
N′(−5, −2), M′(−2, −1), O′(−3, −3)
The vertices of the image triangle N'M'O' are N'(5, 2), M'(2, 1), and O'(3, 3).
To determine the vertices of the image N'M'O' after reflecting triangle NMO over the line x = -1, we need to apply the reflection transformation to each vertex.
For a reflection over the line x = -1, we can find the image of a point (x, y) by finding its reflection as (2(-1) - x, y).
Applying this transformation to each vertex of triangle NMO, we get:
N' = (2(-1) - (-5), 2) = (5, 2)
M' = (2(-1) - (-2), 1) = (2, 1)
O' = (2(-1) - (-3), 3) = (3, 3)
The vertices of the image triangle N'M'O' are N'(5, 2), M'(2, 1), and O'(3, 3).
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The Hernandez family orders 3 large pizzas. They cut the pizzas so that each pizza has the same number of slices, giving them a total of 24 slices.
The Wilson family also orders several large pizzas from the same pizza restaurant. They also cut the pizzas so that all their pizzas have the same number of slices. For the Wilson family, the equation y = 10x represents the relationship, where x represents the number of pizzas and y represents the number of total slices.
Which statements best describe the pizzas bought by the Hernandez and Wilson families? Select two options.
Find the approximate mean for the following
The approximate mean of the number of cars sold by the salesman in the past 10 weeks is 4.1.
To find the approximate mean, first, we add all the numbers in the data set, and then we divide that sum by the total number of values in the data set.
The formula for finding the approximate mean is as follows: Approximate mean = sum of the values in the data set / total number of values in the data set.
The following data set is given: Number of cars sold by a salesman in the past 10 weeks: 3, 5, 2, 4, 7, 5, 6, 3, 2, 4.
To find the approximate mean, we first need to add all the values: 3 + 5 + 2 + 4 + 7 + 5 + 6 + 3 + 2 + 4 = 41 The sum of all the values is 41.
Next, we need to divide this sum by the total number of values in the data set. In this case, the total number of values is 10. Therefore, the approximate mean for the given data set is: Approximate mean = 41 / 10 = 4.1
Therefore, the approximate mean of the number of cars sold by the salesman in the past 10 weeks is 4.1.
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If Anita and Miguel do not take any money from their accounts, whose account will grow faster? Explain why.
Savings accounts and CDs are good options for people who want to save money without taking on a lot of risk.
If Anita and Miguel do not take any money from their accounts, Anita's account will grow faster than Miguel's.
This is because the interest rate for Anita's account is 6%, while Miguel's is 5%.
The interest rate is the percentage of the principal that a bank or other financial institution pays for the use of money.
It can be thought of as a fee charged for borrowing money.
The higher the interest rate, the more money a person can earn on their investment.
Anita and Miguel's accounts are probably savings accounts or CDs, which are low-risk investments that pay a fixed interest rate.
Savings accounts and CDs are good options for people who want to save money without taking on a lot of risk.
Anita and Miguel's accounts are probably savings accounts or CDs, which are low-risk investments that pay a fixed interest rate.
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What does 13 round to the nearest thousandth
What is the volume of the triangular prism?
3 in.
15 in.
13 in.
find the midpoint of the line segment with endpoints (-9,-1) and (7,0)
Answer:
Midpoint = (-1, -1/2)
Step-by-step explanation:
We can find the midpoint using the midpoint formula which is given by:
M = (x1 + x2) / 2, (y1 + y2) / 2, where
M is the coordinates of the midpoint,(x1, y1) are one point on the line segment,and (x2, y2) are another point on the line segment.Thus, we can plug in (-9, -1) for (x1, y1) point and (7, 0) for (x2, y2) in the midpoint formula:
M = (-9 + 7) / 2, (-1 + 0) / 2
M = (-2) / 2, (-1) / 2
M = -1, -1/2
Thus, (-1, -1/2) is the midpoint of the line segment with endpoints (-9, -1) and (7, 0).
3
2
пал
2 4
6 8 10
1
-1
Determine the period.
-2
-3
14/
The period of the function in this problem is given as follows:
5 units.
How to obtain the period of the function?A periodic function is a function that has the behavior repeating over intervals in the domain of the function.
Then the period of the function has the concept defined as the difference between two points in which the function has the same behavior.
Two consecutive peaks of the graph of the function in this problem are given as follows:
Input of 1 and input of 6.
Hence the period of the function is given as follows:
6 - 1 = 5 units.
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Choose the expression that is equivalent to fraction with 3 raised to the negative tenth power in the numerator and 3 raised to the fourth power times 3 raised to the zero power in the denominator.
Answer:
[tex]3^{-14}[/tex] or [tex]\displaystyle \frac{1}{3^{14}}[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{3^{-10}}{3^4*3^0}=\frac{3^{-10}}{3^4}=3^{-10-4}=3^{-14}[/tex]
Q1. An industry analyst wants to compare the average salaries of two firms, both to each other and to the industry. Firm A's average salary is 93% of the industry average, Firm B's average salary is $58,000, and the industry average salary is 96% of Firm B's average salary. a. Determine the industry average salary. b. Determine Firm A's average salary. c. Express Firm B's average salary as a percentage of Firm A's average salary. Round the percentage to two decimals.
a.The Industry Average Salary is $55,680. b.The Firm A's Average Salary is $51,718.40 .c. Firm B's average salary is approximately 112.27% of Firm A's average salary.
a. To determine the industry average salary, we can use the information that the industry average salary is 96% of Firm B's average salary. Firm B's average salary is $58,000. Therefore, we can calculate the industry average salary as follows:
Industry Average Salary = 96% of Firm B's Average Salary
= 0.96 * $58,000
= $55,680
b. Firm A's average salary is stated as 93% of the industry average salary. To calculate Firm A's average salary, we can multiply the industry average salary by 93%:
Firm A's Average Salary = 93% of Industry Average Salary
= 0.93 * $55,680
= $51,718.40
c. To express Firm B's average salary as a percentage of Firm A's average salary, we can divide Firm B's average salary by Firm A's average salary and multiply by 100:
Percentage = (Firm B's Average Salary / Firm A's Average Salary) * 100
= ($58,000 / $51,718.40) * 100
≈ 112.27%
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Two figures are said to be SIMILAR if they are the same shape. In more mathematical language, two figures are similar if their corresponding angles are congruent , and the ratios of the lengths of their corresponding sides are equal. This common ratio is called the scale factor.
Each pair of figures is similar. Find the value of the missing side (x). Round your answer to the nearest tenth if necessary.
Answer:
4.9 in
Step-by-step explanation:
6/11 = x/9
6/11 times 9 = x
x = 4.9
simplify 1200×1260÷800 leaving your answer in standard form
The simplified form of the expression 1200 × 1260 ÷ 800 in standard form is 1890.
To simplify the given expression, we perform the multiplication and division operations according to the order of operations (PEMDAS/BODMAS).
First, we perform the multiplication: 1200 × 1260 = 1,512,000.
Next, we perform the division: 1,512,000 ÷ 800 = 1890.
The result, 1890, is in standard form.
In standard form, a number is expressed as a product of a number between 1 and 10 (inclusive) and a power of 10. In this case, 1890 is already in the appropriate format and does not require any further modification.
Therefore, the simplified form of the expression 1200 × 1260 ÷ 800 is 1890 in standard form.
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1) First, calculate how much carpet is needed if your bedroom is 14 feet long and 11.5 feet wide. Algebraic formula that will be used to find this amount:
For which 161 square feet of carpet would be required.
To solve this problemWe can use the algebraic formula for the area of a rectangle.
The formula to find the area (A) of a rectangle is:
A = length × width
We may enter the bedroom's dimensions—14 feet long by 11.5 feet wide—into the calculation to determine the room's area and, thus, the required amount of carpeting.
Let:
length = 14 feet
width = 11.5 feet
Then, the formula becomes:
A = 14 feet × 11.5 feet
Now, calculate the area:
A = 161 square feet
Therefore, for which 161 square feet of carpet would be required.
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what is the result of converting 2.3 miles into yards ? remenber that 1 mile=1760 yards.
4048 yards is the answer
Step-by-step explanation:
2.3 × 1760
The Language Arts department conducts a study to see if the number of books a student reads per month affects the score on the SAT Verbal Test. Here is the data that the Language Arts department collected for 8 students. Create the scatter plot for this data set. What is the equation of the line of best fit?
A scatter plot visually represents the relationship between two variables. It shows a positive correlation between the number of books read per month and SAT Verbal Test scores, with the equation y = 6.4828x + 520.6962.
A scatter plot is a graphical representation of a set of data that allows the observer to observe the relationship between two variables. It is used to graphically display how one variable is affected by the other. It is a chart of data points plotted on a two-dimensional graph with one variable represented on the X-axis and the other variable on the Y-axis.
Scatter Plot of the Data: From the data provided by the Language Arts department, we can create the scatter plot as shown below:
Equation of the line of best fit: The line of best fit is a straight line that is used to model the relationship between the two variables. It is determined by minimizing the sum of the squares of the differences between the observed values and the predicted values.
From the scatter plot, we can see that there is a positive correlation between the number of books read per month and the score on the SAT Verbal Test. This suggests that the more books a student reads per month, the higher their score on the SAT Verbal Test.
The equation of the line of best fit for the given data set is y = 6.4828x + 520.6962. Here, y represents the score on the SAT Verbal Test and x represents the number of books read per month.
To find the equation of the line of best fit, we can use a regression analysis tool such as Excel. The regression analysis will give us the values of the slope and intercept of the line of best fit, which we can use to write the equation of the line.
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find the value of x and the measure of angle axc
Answer:
x = 4
m<AXC = 150
Step-by-step explanation:
m<1 + m<2 = m<AXC
102 + 10x + 8 = 6(6x + 1)
10x + 110 = 36x + 6
26x = 104
x = 4
m<AXC = 6(6x + 1)
m<AXC = 6(24 + 1)
m<AXC = 150
Which linear equation shows a proportional relationship?
y equals negative one sixth times x
y equals one sixth times x minus 8
y = −6x + 1
y = 6
Answer:
y = (-1/6)x represents a proportional relationship.
Simplify the expression by combining
like terms:
2y + 2 + 3y + 5
Enter the number that belongs in the green box.
[?]y + [ ]
cual es la definición de un segmento de recta
A line segment is a fundamental concept in geometry, representing a portion of a line that has a definite beginning and end. It consists of an infinite number of points situated between two endpoints.
What are the endpoints of a line segment?The endpoints themselves are distinct points on a line, and they are included as part of the line segment. Unlike a line, which extends indefinitely in both directions, a line segment is confined to a specific length.
This length is often referred to as the 'measure' of the line segment. Additionally, line segments serve as building blocks for various geometrical shapes and figures by connecting multiple points in space.
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The Question in English
What is the definition of a line segment?
Please provide the correct answers! Be careful! Thank you! comment if you have questions. Look at photo.
The absolute maximum and minimum values obtained from the graph of the functions are;
Absolute maximum of g; [1, 4]
Absolute minimum of g; [4, -3]
Absolute maximum h; [4, 3]
Absolute minimum of h; (-4, -5)
What is the absolute maximum and minimum of a function?The absolute maximum and minimum of a function are the coordinates of the highest and lowest points on the graph of the function, within the specified domain.
The points on the graph of the functions indicates that the maximum and minimum values of the functions are;
Graph of g; Absolute maximum of g = (1, 4)
Absolute minimum of g ; [4, -3]
Graph of h
Absolute maximum of h; [4, 3]
Absolute minimum of h; (-4, -5)
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0.059 and 0.01 which is greater?
restaurant owners say it is good for each customer to have about 300in2 of space at their table. how many customers would you seat at each table?
Based on unit conversions, the number of customers that would seat at each table is 12 persons.
How the number is determined?The number of customers per table can be determined using unit conversions, which involve multiplication and division.
In this situation, the total available space per table is converted to squared inches from squared feet, and divided by the required table space per customer.
Conversely, the required table space per customer can be converted to squared feet and the result used to divide the total available space per table.
The required table space per customer = 300 in²
The total available space (area) per table = 300 ft²
1 foot = 12 inches
300 ft² = 3,600 in² (12 x 300)
The number of customers per table = 12 (3,600 ÷ 300)
OR:
300 in² = 25 ft² (300 ÷ 12)
The number of customers per table = 12 (300 ÷ 25)
Thus, using unit conversions, we expect the restaurant owner to seat 12 customers per table.
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Question Completion:The area occupied by each table is 300 ft².
Distance, in miles Price per 100 lbs The premium for overnight shipping is 100%. What is the cost to ship 1,800 lbs of goods from Atlanta to Louisville (390 miles) using overnight shipping? 0-200 201-400 401-600 601-800 801-1000 $100 $120 $200 $240 $400
The cost to ship 1,800 lbs of goods from Atlanta to Louisville using overnight shipping is $7,200.
To calculate the cost of shipping 1,800 lbs of goods from Atlanta to Louisville using overnight shipping, we need to determine the price per 100 lbs and apply the 100% premium for overnight shipping.
From the information, we can see that the price per 100 lbs for the distance range of 401-600 miles is $200.
Since the distance from Atlanta to Louisville is 390 miles, which falls within the 401-600 miles range, we can use the corresponding price per 100 lbs of $200.
To calculate the cost, we need to divide the total weight of 1,800 lbs by 100 to get the number of 100 lb units: 1,800 lbs / 100 = 18 units.
Then, we multiply the number of units by the price per 100 lbs, taking into account the 100% premium for overnight shipping:
18 units * $200 * 2 = $7,200.
Therefore, the cost is $7,200.
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Shireen had a nap for 2 h. After her nap, she played badminton for 1/2h and swam for 1/5h.
(a) How long did Shireen exercise?
(b) How much more time did Shireen spend on her nap than on
her exercise?
I need to solve this, but the process is confusing and I need someone to help me understand it, please and thank you :))
[tex]\frac {x^2+5x+6}{x - 1}\ \textgreater \ 0[/tex]
Answer:
(-3, -2) ∪ (1, ∞)
Step-by-step explanation:
Given inequality:
[tex]\dfrac{x^2+5x+6}{x-1} > 0[/tex]
Begin by factoring the denominator:
[tex]\begin{aligned}x^2+5x+6&=x^2+2x+3x+6\\&=x(x+2)+3(x+2)\\&=(x+3)(x+2)\end{aligned}[/tex]
Therefore, the factored inequality is:
[tex]\dfrac{(x+3)(x+2)}{x-1} > 0[/tex]
Determine the critical points - these are the points where the rational expression will be zero or undefined.
The rational expression will be zero when the numerator is zero:
[tex](x+3)(x+2)=0 \implies x=-3,\;x=-2[/tex]
Therefore, -3 and -2 are critical points.
The rational expression will be undefined when the denominator is zero:
[tex]x-1=0 \implies x=1[/tex]
Therefore, 1 is a critical point.
So the critical points are -3, -2 and 1.
Create a sign chart, using open dots at each critical point (the inequality is greater than, so the interval doesn't include the values).
Choose a test value for each region, including one to the left of all the critical values and one to the right of all the critical values.
Chosen test values: -4, -2.5, 0, 2
For each test value, determine if the function is positive or negative:
[tex]x=-4 \implies \dfrac{(-4+3)(-4+2)}{-4-1} = \dfrac{(-)(-)}{(-)}=\dfrac{(+)}{(-)}=-[/tex]
[tex]x=-2.5 \implies \dfrac{(-2.5+3)(-2.5+2)}{-2.5-1} = \dfrac{(+)(-)}{(-)}=\dfrac{(-)}{(-)}=+[/tex]
[tex]x=0 \implies \dfrac{(0+3)(0+2)}{0-1} = \dfrac{(+)(+)}{(-)}=\dfrac{(+)}{(-)}=-[/tex]
[tex]x=2 \implies \dfrac{(2+3)(2+2)}{2-1} = \dfrac{(+)(+)}{(+)}=\dfrac{(+)}{(+)}=+[/tex]
Record the results on the sign chart for each region (see attached).
As we need to find the values for which the rational expression is greater than zero, shade the positive regions on the sign chart (see attached). These regions are the solution set.
Remember that the intervals of the solution set should not include the critical points, as the critical points of the numerator make the expression zero, and the critical point of the denominator makes the expression undefined. The intervals of the solution set are those where the rational expression is greater than zero only.
Therefore, the solution set is:
-3 < x < -2 or x > 1
As interval notation:
(-3, -2) ∪ (1, ∞)
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Select the expression that is equivalent to (n²-25)
A. n² +10n - 25
B. n²-10-25
C. (n+5)(n-5)
D. (n-5) ²
Answer:
C. (n+5)(n-5)
Step-by-step explanation:
Select the expression that is equivalent to (n²-25)
Let's check each option. A and B are wrong, so we only check C & D.
C. (n + 5) (n - 5)
n² - 5n + 5n - 25
n² - 25
D. (n - 5)²
(n - 5) (n - 5)
n² - 5n - 5n + 25
n² - 10n + 25
So, the correct answer is C. (n+5)(n-5)
What number after being increased by 22% results in a value of 305?
Answer:
250
Step-by-step explanation:
[tex]x+0.22x=305\\1.22x=305\\x=250[/tex]
Answer:
250
Step-by-step explanation:
so when you add 22% to 250 it equals 305
