5 to the power of one sixth (5¹/⁶) will be equal to square root of the cube root of 5.
What is the definition of square root?
The square root of a number is a value that, when multiplied by itself, yields the original number. The square root is the opposite of squaring a number. As a result, squares and square roots are ideas that are connected.
If x is the square root of y, it is denoted as x=√y, or the same equation may be expressed as x² = y. √" is the radical symbol used to symbolise the numerical root here. When a positive number is multiplied by itself, it represents the number's square. The square root of a positive number yields the original value.
Now,
Given that square root of the cube root of 5 i.e. √∛5=?
=√5¹÷³
=5¹/²*¹/³
=5¹/⁶
hence,
5 to the power of one sixth (5¹/⁶) will be equal to square root of the cube root of 5.
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Solve
#5
The formula below can be used to find the distance, d, a person can see to the horizon.
where d is the distance measured in miles and h is the person's height above the surface
of the Earth in feet.
d = 1.75h
The distance that a person with a height of 6 feet can see is given as follows:
10.5 feet.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The function for this problem is defined as follows:
d = 1.75h.
For the person with a height of 6 feet, the distance is obtained replacing the lone instance of h by 6, hence:
d = 1.75 x 6
d = 10.5 feet.
Missing InformationThe problem asks for the distance that a person with a height of 6 feet can see.
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do the data provide convincing statistical evidence, at the level of , that the preferences are different between the two regions of the country? complete the appropriate inference procedure to support your answer.
The corresponding p-value for this test statistic is 0.005, which is smaller than our significance level of α=0.05.
To begin, we define the population proportion of people who shop for groceries online in region A as p₁ and the population proportion of people who shop for groceries online in region B as p₂.
Our null hypothesis is that there is no difference in these proportions, which we can write as H0=> p₁ = p₂. Our alternative hypothesis is that there is a difference, which we can write as H1=> p₁ ≠ p₂.
Next, we need to calculate the sample proportions and standard errors for each region. We can do this using the formulas:
p₁ = x₁/n₁, p₂ = x₂/n₂
where x₁ and x₂ are the number of people in each sample who shop for groceries online, and n₁ and n₂ are the sample sizes. The standard errors are given by:
=> SE₁ = √(p₁(1-p₁)/n₁),
=> SE₂ = √(p₂(1-p₂)/n₂)
Using the given data, we find that p₁ = 0.16, p₂ = 0.24, SE₁ = 0.037 and SE₂ = 0.042.
We can now calculate the test statistic, which measures the difference between the sample proportions under the assumption that the null hypothesis is true. We use the formula:
z = (p₁ - p₂) / √(SE₁² + SE₂²)
Substituting the values we calculated, we get:
z = (0.16 - 0.24) / √(0.037² + 0.042²) = -2.83
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Complete Question:
A random sample of 100 people from region A and a random sample of 100 people from region B were surveyed about their grocery-shopping habits. From the region A sample, 16 percent of the people indicated that they shop for groceries online. From the region B sample, 24 percent of the people indicated that they shop for groceries online. At the significance level of α=0.05, do the data provide convincing statistical evidence that there is a difference between the two regions for the population proportions of people who shop online for groceries? Complete the appropriate inference procedure to support your answer.
7. A storage shed is shown below. How many cubic feet will the storage shed hold? 13 ft 13.6 ft 5 8 ft 13.6 ft 6 ft
The amount of cubic feet that the storage shed can hold is 168 ft³
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
The volume of the storage shed is the product of the base area and the height. It is given by:
Volume = base area * height
From the diagram, the base is a triangle. Hence:
Area of base = (1/2) * base * height = (1/2) * 8 ft * 7 ft = 28 ft²
Volume = base area * height = 28 ft² * 6 ft. = 168 ft³
The volume of the storage shed is 168 ft³
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help
(5th-grade math)
Answer: equation: 3/5 * 5/8 = 38 = 0.375
Spelled result in numbers/words is three eighths/ 3/8.
Step-by-step explanation:
the basketball field takes up 3/8 of the playground
3/5 * 5/8 = 38 = 0.375 = 3/8
then (simplify) 0.375 into a fraction.
3/5 * 5/8 = 38 = 3/8
Answer:
Equation: 3/8 * 5/8
Answer:3/8
Step-by-step explanation:
Equation: 3/5 * 5/8. Since it is 5/8 of 3/5, you can do 3/5 * 5/8.
Answer: 3/8. Since 3/5 * 5/8 = 3/8, the answer will be 3/8
PLEASE HELP!
Mrs. Harris is in the 20% income tax bracket. Last year, her taxable income was $75,400. How much did she need to pay in taxes?
A. $1,508
B. $15,080
C. $60,320
D. $73,892
Answer: B: 15,080
Step-by-step explanation:
Alright, let's convert 20% into a decimal: 0.20
Then multiply 0.20 x 75,400 which gets you to 15080
So she needed to pay $15,080 in taxes
The cost of producing a chocolate bar that sells for $1.50 is 60c. Calculate the profit
made on a bar of chocolate as a percentage of the production cost of a bar of chocolate.
Percentage profit on a chocolate bar is 150%
What is percentage profit?Profit percentage is a top-level and the most common tool to measure the profitability of a business. It measures the ability of the firm to convert sales into profits. i.e., 20% means the firm has generated a net profit of $20 for every $100 sale.
%profit = (selling price - cost price)/cost price × 100
%profit =( 1.50-0.6)/0.6 × 100
%profit = 0.9/0.6 × 100
= 1.5 × 100
= 150 %
therefore the percentage profit on a chocolate bar is 150%
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The price of a Loungy Chair was $400. The price of this chair has just gone up by 20%. Make a percent table to find the new price of the Loungy Chair
The percent table is:
100 % ⇒ $400
120 % ⇒ $480
The initial price of the Loungy chair was $400.
So, the initial price(P₀) = $400
The price of the chair has gone up by 20%
So, increase in price(r) = 20%
The final price will be calculated by using the formula:
P = P₀(1 + r/100) (where P is the final price)
P = 400(1 + 20/100)
P = 400(1 + 0.2)
P = 400 × 1.2
P = $480
Hence, the final price of the Loungy chair is $480
Percent table:
100 % ⇒ $400
120 % ⇒ $480
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Mrs. Townsend is giving you a test worth 100 points and it contains 40 questions. There are two-point and four-point questions on the test. How many of each type of question are on the test?
Answer:
[tex]10[/tex] four point questions and [tex]30[/tex] two point questions
Step-by-step explanation:
Let's say [tex]f =[/tex] [tex]\text{number of four point questions}[/tex] and[tex]t = \text{number of two point questions}[/tex]. The total number of questions is [tex]40[/tex], therefore [tex]t + f = 40[/tex]. We know the test is worth [tex]100[/tex] points so we can write [tex]2t + 4f = 100[/tex]. We have a system of equations: [tex]t + f = 40 \text{ and } 2t + 4f = 100[/tex]. We can rewrite [tex]t[/tex] as [tex]t = 40 - f[/tex]. We rewrite this in the equation [tex]2t + 4f = 100[/tex]. Since [tex]t = 40 - f[/tex], we have [tex]2 \cdot (40 - f) + 4f = 100[/tex]. Distributing & simplifying gives
[tex]2 \cdot (40 - f) + 4f = 100\\(80 - 2f) + 4f = 100,\\\text{Remove parentheses} 80 - 2f + 4f = 100,\\80 + (-2f) + 4f = 100\\80 + 2f = 100,\\\text{Subtract 80 from both sides} 2f = 20,\\\text{Divide 2 by both sides} f = 10.\\[/tex]
Since we determined [tex]t = 40 - f[/tex] and [tex]f = 10[/tex], subtracting [tex]10[/tex] from [tex]40[/tex] will give [tex]t = 30[/tex].
Therefore, there are [tex]10[/tex] four point questions and [tex]30[/tex] two point questions.
Hope that helps!
how do you do it please help
Answer:
5.1
Step-by-step explanation:
11.5 + 5.6 + 8.8 = 29.5
31 - 29.5 = 5.1
the pew research center internet project conducted a survey of 1,057 internet users. this survey provided a variety of statistics on them. if required, round your answers to four decimal places. (a)the sample survey showed that 90% of respondents said the internet has been a good thing for them personally. develop a 95% confidence interval for the proportion of respondents who say the internet has been a good thing for them personally.
variety of statistics for 1057 inernet users are = (0.9180, 0.8998) solve by given question .
population proportion is the share of a population that belongs to a particular category. Confidence intervals are used to estimate population proportions.
Let p be the population proportion of respondents who say the Internet has been a good thing for them personally.
=p +- z*[tex]\sqrt{p*(1-p)/n}[/tex]
where z* = Critical value p = Sample proportion,n = sample size.
As per given , we have
n= 1057 By z-table , Critical value for 95% confidence interval : z*= 1.96
Then, the 95% confidence interval for the proportion of respondents who say the Internet has been a good thing for them personally. will be :
=p +- z*[tex]\sqrt{p*(1-p)/n}[/tex]
=0.9+-1.96[tex]\sqrt{.9*(1-.9)/1057}[/tex]
=0.9180, .8998
Hence, the required 95% confidence interval for the proportion of respondents who say the Internet has been a good thing for them personally = (=0.918, .881)
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What is the length of the hypotenuse of a 30-60-90 triangle if the short leg has a length of 10?
Answer: 20
Step-by-step explanation:
30-60-90 triangles are special: Their side lengths fall in a ratio of 1:2:[tex]\sqrt{3}[/tex], in order of Shortleg : hypotenuse : longleg
Since we know the short leg is 10, the hypotenuse must be double, or 20.
Sara can read 19 pages an hour. How many pages can Sara read in 95 min? Round to the nearest whole number.
Sara can read about 30 pages in 95 minutes.
What does per hour mean?To start, multiply the weekly hours by the number of weeks in a year to get the overall number of hours worked (52). Then subtract this amount from the annual pay. For instance, if a worker earns $50,000 annually and puts in 40 hours per week, their hourly rate would be $50,000/2,080 (40 x 52) = $24.04.
Accordion to question:First, we need to convert 95 minutes to hours by dividing by 60:
95 min ÷ 60 min/hour = 1.5833 hours (rounded to 4 decimal places)
Next, we can use the conversion factor to find the number of pages Sara can read in 1.5833 hours:
19 pages/hour x 1.5833 hours = 30.1391 pages
Rounding to the nearest whole number, Sara can read about 30 pages in 95 minutes.
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Benjamin invests $400 in a savings account that earns 5\%5% interest each year. Which expression does not give the correct balance in the account after 33 years?
If Benjamin invests $400 in a savings account that earns 5% interest each year, the expression that shows the correct balance is A = 400(1 + 0.05)(1 + 0.05)(1 + 0.05)
The principal amount = $400
interest rate = 5%
The equation of the simple interest
A = P (1+ rt)
Where A is the final amount
P is the principal amount
r is the interest rate
t is the time period
The final amount after one year
= 400( 1 + 0.05×1)
= 400(1 + 0.05)
The final amount after two year
= 400(1 + 0.05)(1 + 0.05)
The final amount after three year
= 400(1 + 0.05)(1 + 0.05)(1 + 0.05)
Therefore, the balance amount after three years is A = 400(1 + 0.05)(1 + 0.05)(1 + 0.05)
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Please help, I’ll give brainliest
Answer: Distributive property and Commutative property (of multiplication)
Step-by-step explanation:
From 1 to 2, the parentheses coefficient is multiplied out to the parentheses. This is called distribution.
From 2 to 3, the numbers in each multiplication are rearranged. This would be the commutative property of multiplication.
HOPE THIS HELPS _- MM
Pls show your work thank you will mark the Brainliest
The exponential function that best models the number of game systems sold, in million, x years since 2015 is given as follows:
y = 30.5(0.7)^x.
How to model an exponential function?The standard definition of an exponential function is given as follows:
y = ab^x.
In which:
a is the initial value, the value of y when x = 0.b is the rate of change.Considering the graph, the parameters for this problem are given as follows:
a = 30.5.b = 21.35/30.5 = 0.7.Hence the function is defined as follows:
y = 30.5(0.7)^x.
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I NEED HELP, THIS IS DUE TODAY AND IM CONFUSED.
The value of x that makes the shape a parallelogram is 2/3
What is a quadrilateral?A quadrilateral is a polygon that has four sides and four angles. Types of quadrilaterals are kite, square, rectangle, parallelogram and so on.
A parallelogram is a quadrilateral with two pairs of parallel sides. Each parallel sides are equal. Also, the diagonals of a parallelogram bisect each other.
From the diagram, the diagonals bisect each other in other to be a parallelogram, hence:
6x = 3x + 2
3x = 2
x = 2/3
The value of x is 2/3
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La fábrica tiene 300 obreros de los cuales 2/3 son hombres. 3/3 trabajadores por la mañana, 1/2 son sindicalizado y 1/6 son personal de confiancia. ¿Cuántos hombres trabajan en la fábrica?_________ ¿Y cuántas mujeres?_______ ¿Cuántos hobreros trabajan por la mañana?__________ ¿Cuántos son sindicalizados?______________ ¿Cuántos son de confianza? AYUDA ES PARA MAÑANA SINO MIS PADRES ME MATAS AYUDA
From the total of 300 workers in the factory :
a. Number of men = 200 and Women = 100
b. Number of workers works in the morning = 225
c. Number of workers unionized are 150.
d. Number of workers trustworthy are 50.
Total number of workers in the factory are 300.
a. Fraction of men in the factory are ( 2/3)
= 2/3 of 300
= 200
Women
= 300 -200
= 100
b. Number of workers in the morning shift are
= 3/4 of 300
= 225
c. Total number of workers unionized
= 1/ 2 of 300
= 150
d. Number of trustworthy workers
= 1/6 of 300
= 50
Therefore, out of 300 workers in the factory answer of the following questions are:
a. Number of men and women work in the factory are 200 and 100 respectively.
b. Number of workers works in the morning is 225.
c. Unionized workers = 150
d. Trustworthy workers = 50.
The above question is incomplete , the complete question is :
The Factory has 300 workers of which 2/3 are men, 3/4 work in the morning, 1/2 are unionized and 1/6 are trusted personnel.
a. How many men work in the factory and how many women?
b. How many workers work in the morning?
c. How many are unionized?
d. How many are trustworthy?
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In AOPQ, m/O = (6x – 14)°, m/P = (2x + 16)°, and m/Q = (2x + 8)°.
Find m/Q.
The required measure of angle m∠Q is 42 degrees, as of the given condition.
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should equal to 180°
Here,
In a triangle, the sum of the angles is always equal to 180 degrees. Therefore, for triangle OPQ,
m∠O + m∠P + m∠Q = 180°
Using the given information,
m∠O = (6x - 14)°
m∠P = (2x + 16)°
m∠Q = (2x + 8)°
(6x - 14)° + (2x + 16)° + (2x + 8)° = 180°
10x + 10 = 180°
10x = 170
x = 17
Substituting the value of x back into the expression for m∠Q,
m∠Q = (2x + 8)°
m∠Q = (2 * 17 + 8)°
m∠Q = 42°
So the value of m∠Q is 42 degrees.
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The mean height of the students in Juan's math class is equal to the mean height of the students in his English class. However, while the standard deviation of the heights of students in his math class is 3.2 inches, the standard deviation of the heights of students in his English class is 6.1 inches. Which of the following statements must be true?
A) The mean height of the students in Juan's English class is 2.9 inches greater than the mean height of the students in his math class.
B) The median height of the students in Juan's English class is 2.9 inches greater than the median height of the students in his math class.
C) The median height of the students in Juan's math class is 2.9 inches greater than the median height of the students in his English class.
D) The heights of the students in Juan's math class are less variable than the heights of the students in his English class.
Answer: The statement "The mean height of the students in Juan's math class is equal to the mean height of the students in his English class" means that the center or average of both groups is the same. However, the statement "the standard deviation of the heights of students in his math class is 3.2 inches, the standard deviation of the heights of students in his English class is 6.1 inches" implies that the heights of the students in the English class are more spread out than the heights of the students in the math class.
Therefore, the answer is:
D) The heights of the students in Juan's math class are less variable than the heights of the students in his English class.
Step-by-step explanation:
Which situation most accurately matches the graph?
A
im going to guess that the top of the graph has a flat line.
its easy to visualize since the graph looks like a hill, and the story describes the graph the most accurately
Write the scale factor of abcde to zyxwv
The scale factor of abcde to zyxwv is obtained dividing one side length of zyxwv by the equivalent side length of abcde, for example:
k = zy/ab.
What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
The figures for this problem are given as follows:
Original: abcde.Dilated: zyxwv.Hence the scale factor of abcde to zyxwv is obtained dividing one side length of zyxwv by the equivalent side length of abcde, for example:
k = zy/ab.
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question 2
help me plsssss
Answer:
∠ CAB = 144°
Step-by-step explanation:
the central angle CAB is twice the measure of ∠ BDC , that is
∠ CAB = 2 × 72° = 144°
70% of ____ is 14.
O 10
O 20
O 30
O 50
Answer:
20
Step-by-step explanation:
snajakskdmcjwiwjcjf
Answer:
20
Step-by-step explanation:
70% is 70/100 = 0.70
20 x 0.70 = 14
when running Chao has a stride length of 70cm,correct to the nearet 5cm.
Chao runs a distance of 11.2 km, correct to the nearest 0.1km
work out the minumum number of stride that Chao could take to complete this distance
The minimum number of strides that Chao could take to complete a distance of 11.2 km is approximately 16,000.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
To calculate the minimum number of strides that Chao could take to complete a distance of 11.2 km, we need to first convert the distance to meters since the stride length is given in centimeters.
11.2 km = 11,200 meters (1 km = 1000 meters)
Stride length in meters = 70 cm / 100 cm/m = 0.7 m
Now, we can calculate the minimum number of strides as follows,
Minimum number of strides = (Distance covered in meters) / (Stride length in meters)
Minimum number of strides = 11,200 m / 0.7 m ≈ 16,000
Therefore, the minimum number of strides that Chao could take to complete a distance of 11.2 km is approximately 16,000.
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2. What is the length of the unknown leg of the
right triangle rounded to the nearest tenth of
a foot?
2 ft
8.2
9 ft
Answer:
See below. The answer is 8.8 feet, but none of the options offers this value.
Step-by-step explanation:
I get 8.8 feet.
2^2 + x^2 = 9^2
4 + x^2 = 81
x^2 = 77
x = 8.77496 to be exact.
The "hang time" of a football is the amount of time the football stays in the air after being kicked. Zara kicks a football, and the height (in meters) of the football above the ground at t seconds is shown in the graph below.
The completed statements with regards to the projectile motion of the football are presented as follows;
This graph is a nonlinear function
The hang time of the football is 3 seconds
The football reaches its maximum height when t = 1.5 seconds
The maximum height is about 11 meters
For t between t = 0 and t = 1.5, the height is increasing
What is a projectile motion?The motion of a projectile is one that involves an object thrown into the air or into space, which is acted upon by only gravitational force.
The graph in the question, showing the scale on the x-axis obtained from a similar question on the internet, indicates that we get;
The x-intercept of the graph are; (0, 0), and (3, 0)
Therefore;
The time the football is in the air, which is the hang time of the football can be obtained from the difference between the x-values of the x-intercept as follows;
Hang time = 3 - 0 = 3
The hang time of the football is 3 secondsThe graph indicates that the coordinates of the maximum height is (1.5, 11). Therefore;
The football reaches the maximum height when t = 1.5 second(s)The maximum height reached, obtained from the coordinate of the maximum height is 11 metersThe height at t = 0 is 0 meters, and the height at t = 1.5 seconds is 11 meters, therefore; the height is increasing between t = 0 and t = 1.5 seconds
For t between t = 0 and t = 1.5, the height is increasing
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Answer:
Nonlinear
3
1.5
11
increasing
Step-by-step explanation:
all ratios equivalent to 5:8
answer:
if you multiply the 2 sides of the ratio by a number it will give you an equivalent ratio
5:8 = 10:16 multiplying by 2
5:8 = 15:24 multiplying by 3
5:8 = 20:32 multiplying by 4
5:8 = 25:40 multiplying by 5
5:8 = 30:48 multiplying by 6
5:8 = 35:56 multiplying by 7
and so on ...
You and your friend could go to Theater X and each buy an adult ticket, drink, and popcorn, or you and your friend
could rent a video for $3.50, buy a 2 liter of cola for $1.60, and a bag of microwave popcorn for $1.98.
Which situation costs less and by how much?
The second situation costs less by
$16.92How to know the situation that cost lessThe cost of the first situation is
Adult = 8 * 2 = 16
drink = 2 * 2 = 4
popcorn = 2 * 2 = 4
Total = $24
Second situation
rent a video = $3.50
buy a 2 liter of cola = $1.60
a bag of microwave popcorn = $1.98.
Total = $7.03
The second situation costs less by
$24 - $7.03
= $16.92
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An observer in watertown, new york, would see the star polaris at an altitude of approximately. ?
44°
45°
75°
76°
Answer:
44
Step-by-step explanation:
2. How can the term unit square help you to remember
that area is measured in square units?
When ever the area is calculated the units will have a degree of two.
What is an area?The area is defined as the space covered by any two-dimensional body. The unit if the area is calculated as square units. The square units come because the area is calculated by the two parameters of length.
The area of the rectangle is calculated by the multiplication of the two lengths like length and width.
Similarly, the area of the circle is calculated by taking the square of the radius of the circle it means that the length here is also multiplied by two times.
Therefore, the area is calculated in an square units.
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