65 percent of the number 240 is 156, as 25% and 90% of 240 will give 60 and 216 respectively.
How to calculate for the percentageWe shall represent the number with the letter x so that we evaluate for the 25 and 90 percent respectively as follows:
25 percent of x;
25x/100 = 60
x = (60 × 100)/25 {make x the subject}
x = 240
90 percent of x;
90x/100 = 216
x = (216 × 100)/90 {make x the subject}
x = 240
Therefore, 65 percent of the number 240 is derived as:
(65 × 240)/100
15600/100
156.
Know more about percent here:https://brainly.com/question/843074
#SPJ1
25 people gathered to watch a baseball game while talking they realized that 5 of them were New York Mets fans what is the probability that the favorite team of a randomly selected person in the group is the New York mets
The probability that the favorite team of a randomly selected person in the group is the New York Mets is 1 / 5.
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favorable outcomes / Number of samples
Given that 25 people gathered to watch a baseball game while talking they realized that 5 of them were New York Mets fans.
The probability will be calculated as:-
Probability = 5 / 25
Probability = 1 / 5
To know more about probability follow
https://brainly.com/question/24756209
#SPJ1
Let Fx = 2X^2 - 6x + 4 and g(x) 4 cos 1/4 Let R be the region bounded by the graphs of f and g, as shown in the figure above.(a) Find the area of R.(b) Write, but do not evaluate, an integral expression that gives the volume of the solid generated when R is rotated about the horizontal line y 4.(c) The region R is the base of a solid. For this solid, each cross section perpendicular to the x-axis is a square. Write, but do not evaluate, an integral expression that gives the volume of the solid.
The area of R can be calculated using the definite integral of the function y = 2x^2 -6x +4 and between g(x ) = cos1/4 and x = 4.
The integral expression is ∫(2x^2)-6x+4dx = ∫e^u du = e^u + C = e^(2x-x^2) + C. Evaluating the integral between x = 0 and x = 1 gives the area of R as e^2 - 1.
(b) The area of S can be calculated using the definite integral of the function y = e^(2x-x^2) between x = 0 and x = 1, minus the integral of the function y = 1 between x = 0 and x = 1. The integral expression for S is ∫e^(2x-x^2)dx - ∫1dx = ∫e^u du - x = e^u + C - x = e^(2x-x^2) + C - x. Evaluating the integral between x = 0 and x = 1 gives the area of S as e^2 - 1 - 1.
(c) The volume of the solid generated when R is rotated about the horizontal line y = 1 can be found using the integral expression ∫2πx(e^(2x-x^2) - 1)dx. This expression represents the area of the circular cross-sections of the solid multiplied by 2πx, which is the circumference of the circle. When evaluated between x = 0 and x = 1, this integral gives the volume of the solid generated when R is rotated about the horizontal line y = 1.
Learn more about integral here:
brainly.com/question/29974649
#SPJ4
HELP!!
In the figure below, TW and TU are tangent to the circle centered at O. The segment WU passes through the center of the circle. Given that TW=17.4 and WU=12, find WV.
Answer:
WU=4.8
Step-by-step explanation:
put it in the box WU =4.8
The circle below has center S. Suppose that mZQSR=42°. Find the following.
(a)m QR
(b)m ZQPR
I Don't Know
Submit
D
m QR =
0-
mZQPR = 0
Part (a)
[tex]42^{\circ}[/tex] since the angle intercepted by a central angle is the same as the measure of the arc.
Part (b)
[tex]21^{\circ}[/tex] by the inscribed angle theorem.
water is flowing into a tank at a rate of r(t) where t is measured in seconds. is there ever a time where the r'(t)
Time intervals that t will occur using the mean value theorem of calculus are (4,5) and (5,6)
What is mean value theorem ?
The Mean Value Theorem states that if a function f is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a point c in the interval (a,b) such that f'(c) is equal to the function's average rate of change over [a,b].
The property of derivative : r'(t) is the rate of change of water flow.
Justification :
r(s) - r(4) = r'(3) (5-4)
- 5 = r(3)
In (4,5) , r(t) decreasing , so there are value of 3 and r'(3) > 0 , r'(3) = -5.
r(6) - r(5) = r'(3) (6-5)
4 = r'(3)
In (5,6), r(t) increasing , so there are values of 3 and r'(3) > 0, r'(3) = 4.
∴ Time intervals that t will occur using the mean value theorem of calculus are (4,5) and (5,6)
Learn more about Mean value theorem here :
https://brainly.com/question/29107557
#SPJ4
The complete question is :
Water is flowing into a tank at a rate of r(t) where t is measured in seconds. Is there ever a time where the r'(t) = 0? If so, what time interval does t occur in? Justify your answer using the Mean Value Theorem.
Rewrite (2+3) + 4 using the Associative Law of Addition
Answer:
9
Step-by-step explanation:
Write an equation in the form y = a(x-r)(x-s) to represent the parabola shown.
Answer:
c
Step-by-step explanation:
because y = 0 when x = 2 and y = -4 when x =0
which of the following are not corresponding parts of the congruent triangles? line segment cap a cap b is congruent to line segment cap c cap d d. $\angle a\cong\angle c$ d., , $\angle a\cong\angle c$ question 2 two triangles, triangle a b e and triangle cde. segments b d and a c intersect at point e to form one vertex and two sides of each triangle. b e is congruent to d e. a e is congruent to c e.
Line segment AB is congruent to line segment CD, ∠A ≡ ∠C, BE is congruent to DE and AE is congruent to CE in triangle ABE and triangle CDE. So all the first four options are corresponding parts of the two congruent triangles.
Therefore, the answer is e. None of the above.
Corresponding parts of congruent triangles are any pair of matching or identical elements in two congruent triangles. These can include:
Sides, such as line segment AB being congruent to line segment CD
Angles, such as ∠A being congruent to ∠C
Vertices, such as point E being the intersection of segments BD and AC in both triangles
Any other element that is identical in both triangles, like height, medians, circumcenters, etc.
In triangle ABE ≡ triangle CDE, congruent sides are
AB ≡ CD
BE ≡ DE
AE ≡ CE
Congruent angles are
∠A and ∠C
∠B and ∠D
∠BEA and ∠DEC
--The question is not readable, answering to the question below--
"Which of the following are not corresponding parts of the congruent triangles, triangle ABE and triangle CDE? Segments BD and AC intersect at point E to form one vertex and two sides of each triangle.
a. line segment AB is congruent to line segment CD
b. ∠A ≡ ∠C
c. BE is congruent to DE
d. AE is congruent to CE
e. None of the above"
To know more on corresponding parts
https://brainly.com/question/1597341
#SPJ4
Which of the following is the correct conversion factor (as written) required to convert a distance of 12 mi to feet, if 1 mi= 5280 ft ?A. 1 mi x 5280 ftB. 5280 ft / 1 miC. 1 mi / 5280 ft
The correct conversion factor is B: 5280 ft / 1 mi.
Option (B) is correct.
What is unit conversion?
Unit conversion is the process of changing a measurement from one unit to another. For example, converting meters to feet, or kilometers to miles. In order to convert from one unit to another, you need to know the conversion factor between the units, which is the ratio of equivalent values in the two units.
When converting a distance in miles to feet, you need to multiply the distance in miles by the number of feet in a mile. The conversion factor that is commonly used to convert miles to feet is 1 mi = 5280 ft.
The correct conversion factor to convert a distance of 12 mi to feet is therefore:
12 mi x (5280 ft / 1 mi) = 12 x 5280 ft
Hence, the correct conversion factor is B: 5280 ft / 1 mi.
To learn more about the unit conversion, visit:
https://brainly.com/question/97386
#SPJ4
solve the quadratic equation by completing the square x^2+8x+6=0 first choose the appropriate form and fill in the blanks with the correct numbers then solve the equation
By completing squares we will see that the solutions of the quadratic equations is:
x = -4 ± √10
How to solve the quadratic equation?Here we want to solve the quadratic equation:
x^2 + 8x + 6 = 0
Remember the perfect square trinomial:
(a + b)^2 = a^2 + 2ab + b^2
We can rewrite the quadratic equation as:
x^2 + 2*4x + 6 = 0
To complete squares we need to add 4^2 = 16 in both sides, then we will get:
x^2 + 2*4x + 16 + 6 = 16
(x + 4)^2 + 6 = 16
(x + 4)^2 = 16 - 6
(x + 4)^2 = 10
x = -4 ± √10
That is the solution.
Learn more about quadratic equations at:
https://brainly.com/question/1214333
#SPJ1
A garden is rectangular with a width of 7 feet in a length of 9 feet. If it's surrounded by a walkway, 2 feet wide, how many square feet of area does a walkway cover?
PLEASE HELP!!!
The walkway encircling the garden has a 64-square-foot area.
What is Area?The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.
Given, A garden is rectangular with a width of 7 feet in a length of 9 feet.
From the general formula of Area:
Area = Length * width
Area of garden = 7 * 9
Area of garden = 63 Square feet
Perimeter of garden = 2(length * width)
Perimeter of garden = 2(7 + 9)
Perimeter of garden = 32
Since a 2 feet wide rectangular sidewalk is made surrounded the garden So, the area of the walkway will be
Area of walkway = perimeter * width
Area of walkway = 32 * 2 = 64
Therefore, the area of the walkway surrounding the garden is 64 square feet.
Learn more about Area here:
https://brainly.com/question/27683633
#SPJ1
A researcher plans to use a random sample of n=500 families to estimate the mean monthly family income for a large population. A 99% confidence interval based on the sample would be ______ than a 90% confidence interval. (a) narrower and would involve a larger risk of being incorrect, (b) wider and would involve a smaller risk of being incorrect, (c) narrower and would involve a smaller risk of being incorrect, (d) wider and would involve a larger risk of being incorrect, (e) wider, but it cannot be determined whether the risk of being incorrect would be larger or smaller.
A researcher plans to use a random sample of n = 500 families to estimate the mean monthly family income for large population. A 99% confidence interval based on the sample would be wider and would involve a smaller risk of being incorrect than a 90$ confidence interval.
What is random sample?A simple random sample is a subset of people selected at random from a larger group of people, all with the same probability, in statistics. This procedure involves choosing a sample at random. A simple random sample is a population subset that has been chosen at random. This sampling technique minimizes the possibility of selection bias by giving every member of the population an exact equal probability of being chosen. The use of random sampling assures that the results of your study should be close to those that would have been obtained from measurements of the complete population (Shadish et al., 2002). The most basic random sample gives every unit in the population an equal probability of being chosen.The mean monthly family income for a sizable population will be calculated using a researcher's random sample of n = 500 families. An interval with a 99% confidence level based on the sample would be larger and carry a lower risk of error than one with a 90% confidence level.To learn more about random sample refer to:
https://brainly.com/question/24466382
#SPJ4
the supplement of an angle is one third of the measure of the angle. find the angle and its supplement
As a result, the angle's measure is 135° and its supplement is 45°.
What is the supplement angle?Two angles are referred to as supplementary angles when the sum of their measures is 180 degrees.
For instance, 70 degrees and 110 degrees complement one another.
Two angles are said to be supplementary if their sums total 180 degrees.
A linear pair's two angles, are always supplementary.
Let x be the angle's measurement. If so, (180x) is the size of its supplementary angle.
Now, calculate:
180 - x = 1/3x
3(180 - x) = x
4x = 540
x = 135
Supplementary angle = 180 - 135 = 45°
Therefore, as a result, the angle's measure is 135° and its supplement is 45°.
Know more about the supplement angle here:
https://brainly.com/question/12919120
#SPJ4
Richard opened an account in Trust Bank. The equation R=350(1+0.025)" can be used to calculate the amount of money in the account, with 'n' representing the number of years. He also opened another account in Value Savings Bank, with the equation Q=350(1+0.03)" representing the amount of money. What are the interest rates in percent?
The interest rate of the bank R is 2.5% and interest rate of the bank Q is 3%.
What is compound interest?
Compound interest is calculated on the principal as well as the interest accumulated over the previous period. It differs from simple interest in that interest is not added to the principal when calculating interest for the following period.
Here the given equation represents the amount in compound interest.
Using compound interest formula then
=> A = P[tex](1+\frac{R}{100})^n[/tex]
According to the question the equation for trust bank is
=> R =350 [tex](1+0.025)^n[/tex]
comparing with compound interest formula then
=> [tex]\frac{R}{100}= 0.025[/tex]
=> R = 0.025× 100 =2.5%
Now the equation of other bank is
=> Q = 350[tex](1+0.03)^n[/tex]
Comparing with compound interest formula then
=> [tex]\frac{R}{100}= 0.03[/tex]
=> R = 0.03×100 = 3%
Hence the interest rate of the bank R is 2.5% and interest rate of the bank Q is 3%.
To learn more about compound interest refer the below link
https://brainly.com/question/28020457
#SPJ1
B...
Launch realize. 5-4: Lesson Quiz (LMS graded)
Which of the following side-angle relationships in AABC are true? Select all that apply.
OA The largest angle is opposite the smallest side.
OB. The smallest angle is opposite the largest side.
OC. The smallest angle is opposite the smallest side.
OD. The largest angle is opposite the largest side.
The biggest angle in the triangle is opposite the largest side, which is how they actually relate to one another. The right answer is D.
What are a triangle's properties?A triangle is a three-sided shape with two dimensions. The three angles add up to 180 degrees.A triangle's characteristics are:
A triangle has three vertices, three angles, and three sides.The sum of the internal angles of a triangle is always 180 degrees. The triangle's angle sum attribute describes this.Any two triangle sides can be added together to equal a length greater than the third side.The side of a triangle facing the biggest angle is its largest side.The sum of the triangle's internal opposite angles is equal to any of its outer angles. This is referred to as the triangle's outside angle property.The biggest angle is therefore opposite the largest side, which is the actual connection between the triangle's sides. The right answer is D.To Learn more About triangle Refer To:
https://brainly.com/question/17335144
#SPJ1
a survey has to be taken to estimate the proportion of voters who favored stem cell research among the
The proportion of voters who favor stem cell research can be estimated by taking a survey and calculating (Number of voters who favor stem cell research / Total Number of voters) x 100.
Proportion of favor stem cell research = (Number of voters who favor stem cell research / Total Number of voters) x 100
In order to estimate the proportion of voters who favor stem cell research, a survey has to be taken. Suppose the survey results indicate that out of a total of 500 voters, 300 of them favor stem cell research. Then, the proportion of favor stem cell research would be calculated as follows: Proportion of favor stem cell research = (300/500) x 100 = 60%. This means that 60% of the total voters favor stem cell research.
The proportion of voters who favor stem cell research can be estimated by taking a survey and calculating (Number of voters who favor stem cell research / +++Total Number of voters) x 100.
Learn more about proportion here:
https://brainly.com/question/7096655
#SPJ4
plss help asap, my assignment is due today and I have been trying to solve this for the past 3 days
Answer:
see i have a same solution not exactly though
Step-by-step explanation:
so check and solve good luck
A horse-drawn carriage tour company has found that the number of people that take their tour depends on the price charged per customer. The more the company charges for a tour, the fewer people decide to take the tour.
The function c(x)=50+5x represents the price charged per customer where x is the number of $5 increases they charge over a rate of $50 per person.
The function p(x)=100−2x represents the number of customers expected for the day, where x is the number of $5 increases they charge over a rate of $50 per person.
What does (p⋅c)(2) mean about the horse-drawn carriage tour company?
The horse-drawn carriage tour company can expect to take in $5760 when the charge per customer is $60.
The horse-drawn carriage tour company can expect to take in $3760 when the charge per customer is $40.
The horse-drawn carriage tour company can expect to take in $5760 when the charge per customer is $40.
The horse-drawn carriage tour company can expect to take in $3760 when the charge per customer is $60.
The meaning of (p⋅c)(2) for the horse-drawn carriage tour company is: A. the horse-drawn carriage tour company can expect to take in $5760 when the charge per customer is $60.
How to determine the meaning of (p⋅c)(2) for the horse-drawn carriage tour company?In this scenario, a function which represents the price charged per customer c(x) is given by this mathematical expression;
c(x) = 50 + 5x.
where:
x represents the number of $5 increases they charge over a rate of $50 per person.
When x = 2, the price charged per customer c(x) is given by;
c(2) = 50 + 5(2)
c(2) = $60.
Furthermore, a function which represents the number of customers expected for the day is given by:
p(x) = 100 - 2x
where:
x represents the number of $5 increases they charge over a rate of $50 per person.
When x = 2, the number of customers expected for the day is:
p(2) = 100 - 2(2)
p(2) = 96.
Now, (p⋅c) can be calculated as follows;
(p⋅c) = p(2) × c(2)
(p⋅c) = 96 × 60
(p⋅c) = $5760.
Read more on function here: brainly.com/question/3632175
#SPJ1
Greg purchased a baseball bat at a 20% discount. The original cost of the bat was $95. How much will Greg pay for the bat if there is a 6% sales tax?
Answer:
$80.56
Step-by-step explanation:
First determine the cost of the bat after the discount.
20% of 95 = .20x 95 = 19
95-19= $76
Next, you will calculate the additional cost of sales tax.
Sales tax rate = Sales tax percent / 100 (6/100) = .06
Sales tax = List price x Sales tax rate (76 x .06) = 4.56
Total tax equals $4.56
76+4.56= $80.56
The graph of f(x) = RootIndex 3 StartRoot x EndRoot is shown with g(x). Which equation represents the graph of g(x)?
g(x) = RootIndex 3 StartRoot x minus 2 EndRoot
g(x) = RootIndex 3 StartRoot x + 2 EndRoot
g(x) = RootIndex 3 StartRoot x EndRoot + 1
g(x) = RootIndex 3 StartRoot x EndRoot–1
The graph of g(x) is represented by the equation g(x) = Root Index 3 Start Root x EndRoot-1.
What is meant by mathematical equation?The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Take a look at the formula 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the word "equal." The standard form, the point-slope form, and the slope-intercept form are the three primary kinds of linear equations.An equation is a mathematical expression with two equal sides and an equal sign in between. An equation is something like 4 + 6 = 10.A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality. A formula declares that two things are equal. In this case, 10 + 2 equals 6 + 6. Simply put, this means that 10 + 2 is equivalent to or the same as 6 + 6. For example, the equation 10 + x = 6 + 6 may have an unknown.Hence, the correct option is D) g(x) = RootIndex 3 Start Root x End Root–1
To learn more about mathematical equation, refer to:
https://brainly.com/question/25976025
#SPJ1
1. Fractions equal to 1/2
Answer: Answers vary…
Step-by-step explanation:
Equivalent fractions can be written by multiplying or dividing both the numerator and the denominator by the same number. Some fractions equivalent to 1/2 are: 2/4, 3/6, 4/8, 5/10, 6/12, etc. This is because equivalent fractions have the same value in reduced form.
based on the graph of the general solution to the differential equation dy over dx equals 2 times x plus y comma which of the following statements is true?
Based on the graph of the general solution to the differential equation dy/dx = 2x + y, the option C: The slopes are all positive in Quadrant 1, is true.
What is a differential equation?
A differential equation is an equation that contains at least one derivative of an unknown function, either a normal differential equation or a partial differential equation.
The given the differential equation is dy/dx=2x+y.
The graph for the function is drawn.
dy/dx=2x+y
Now slope=2x+y
Along x-axis, y=0.
So, slope=2x≠0.
Since it depends upon x hence the slope along the y-axis are not horizontal.
Along y-axis, x=0.
So, slope=y≠0.
Since it depends upon y the slope along the x-axis are also not horizontal.
In quadrant I -
x,y≥0
So, dy/dx≥0
Hence the slopes are all positive in quadrant I.
In quadrant IV -
x≥0,y≤0
So, dy/dx is not always positive.
Therefore, the slopes are not all positive in quadrant IV.
To learn more about differential equation from the given link
https://brainly.com/question/1164377
#SPJ4
Based on the graph of the general solution to the differential equation dy over dx equals 2 times x plus y comma which of the following statements is true? The slopes along the y-axis are horizontal. The slopes along the x-axis are horizontal. The slopes are all positive in Quadrant 1. The slopes are all positive in Quadrant 4.
Please help me with all I’ll mark you brainly
Answer:
Step-by-step explanation:
y = 1x + 2
y = 3x + 3
y = 1/2x + 2
y = -3x + 12
Please please look at the picture and answer the question thank you for your help
Answer:
20 for both
Step-by-step explanation:
hope this helps
The melting point of an unknown solid is determined to be 42.0°C. What is this temperature on the
Fahrenheit and Kelvin scales?
°F
K
The temperature on the Fahrenheit scale is 107.6°F and Kelvin scale is 315.15K. The solution has been obtained by unit conversion.
What is unit conversion?
The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, instead of using hours to represent time, you might use minutes, or you could use feet instead of miles to express distance. Measurements are frequently offered in one set of units, like feet, but are required in another set, like chains.
We are given the melting point of an unknown solid to be 42.0°C.
For converting the given temperature in Fahrenheit, we use the given formula:
⇒(Temperature in Celsius × 9/5) + 32 = Temperature in Fahrenheit
So,
⇒(42°C × 9/5) + 32 = x°F
⇒(42°C × 9/5) + 32 = 107.6°F
Now, for converting the given temperature in Kelvin, we use the given formula:
⇒Temperature in Celsius + 273.15 = Temperature in Kelvin
This is because 0°C = 273.15 K
So, 42°C + 273.15 = 315.15K
Hence, the temperature on the Fahrenheit scale is 107.6°F and Kelvin scale is 315.15K.
Learn more about unit conversion from the given link
https://brainly.com/question/4158962
#SPJ1
table 2.6 shows the average hourly compensation of production workers in manufacturing for several years. let x be the number of years since 1970, so that x
The formula for the average hourly compensation of production workers in manufacturing is C = 40.25x + $6.81.
For example, in 1975 (x = 5), the average hourly compensation of production workers in manufacturing was calculated using the formula as follows:
C = 40.25(5) + $6.81
C = $202.81
Therefore, the average hourly compensation of production workers in manufacturing in 1975 was $202.81. The same formula can be used to calculate the average hourly compensation of production workers in manufacturing for any year since 1970.
Learn more about average here:
https://brainly.com/question/2906096
#SPJ4
Need help on this asap
The Total surface area of a pyramid formula = ½ pl + B, Where 'p' is the perimeter of the base and 'l' is the slant height of the pyramid and B is the area of the base.
What is the formula for volume of pyramids?A pyramid's volume can be calculated by multiplying the base area by the height, then dividing the result by three. The formula V=13Bh, where B is the area of the pyramid's base and h is its height, is used to express this product.
A triangular pyramid, for instance, has a base area of 20 cm2 and a height of 9 cm. The formula V = (1/3) Bh, where "B" stands for the base area and "h" for the height of the pyramid, is used to calculate the volume of a pyramid.
We can use the formulas for the area of polygons to calculate "B" because we know that the base of a pyramid can be any polygon. A pyramid with a triangle base is referred to as a triangular pyramid.
To learn more about volume of pyramids refer to :
https://brainly.com/question/218706
#SPJ1
The value of x is 2, when the volume of pyramid is 125 cm³ which is equal to [tex]\mathrm{5^{\tfrac{x}{6}} }[/tex].
What is the formula for volume of pyramids?A pyramid's volume can be calculated by multiplying the base area by the height, then dividing the result by three. The formula V=1/3Bh, where B is the area of the pyramid's base and h is its height, is used to express this product.
We know that pyramid's volume is
[tex]\mathrm{{\textstyle V={\tfrac {1}{3}}Bh}}[/tex]
B = base area = [tex]25^{1/4} \times25^{1/4}[/tex]
= [tex]\sqrt[4]{25} \times \sqrt[4]{25}[/tex]
= [tex]\sqrt[4]{25}^2[/tex]
= [tex]\sqrt[2]{25}[/tex]
= 5 cm²
and
h = 75 cm
[tex]$\mathrm{{\textstyle V={\dfrac {1}{3}} \times5 \times 75}}[/tex]
V = 125 cm³
Now it is given that [tex]\mathrm{5^{\tfrac{x}{6}} = 125 }[/tex]
So,
[tex]\mathrm{5^{\tfrac{x}{6}} = 125 }[/tex]
[tex]\mathrm{5^{\tfrac{x}{6}} = \sqrt[3]{5} }[/tex]
[tex]\mathrm{5^{\tfrac{x}{6}} = 5^{\tfrac{1}{3}} }[/tex]
[tex]\dfrac{x}{6} = \dfrac{1}{3}[/tex]
3x = 6
x = 6/3
x = 2
Thus, the value of x is 2, when the volume of pyramid is 125 cm³ which is equal to [tex]\mathrm{5^{\tfrac{x}{6}} }[/tex].
To learn more about volume of pyramids refer to :
brainly.com/question/218706
#SPJ1
*THE ANSWER IS A* 1.5.3 Test (CST): Polynomials Question 25 of 25 Which of these is a binomial? O A. 2x³-7y³ O B. 5xy C. x+2y²-7 O D. ab
Step-by-step explanation:
The correct option is A
Because,
A Binomial is defined as a polynomial containing 2 terms in it.
In option c there are three terms they are x, 2[tex]y^{2}[/tex], -7
In option A There are only two terms That satisfy the definition of binomial.
3
=
Find the width of floor space covered by 38 boards with 7 3/4-in. exposed surface each.
Answer: The width of the floor space covered by 38 boards with 7 3/4-in exposed surface each is 298 inches.
To find this, you would multiply the number of boards (38) by the width of the exposed surface of each board (7 3/4 inches).
38 x 7.75 = 298 inches.
Step-by-step explanation:
Points B, D, and J are midpoints of the sides of right triangle ACG. Points K, E, I are midpoints of the sides of triangle J DG, etc. If the dividing and shading process is done 100 times (the first three are shown) and AC=CG=6, then the total area of the shaded triangles is nearestA. 6B. 7C. 8D. 10
The area of the shaded triangles is nearest to 10
The total area of the shaded triangles can be calculated using the following equation:
[tex]Total Area = (AC∧2)÷2 × (2∧n)[/tex]
Where AC is the length of the original triangle's hypotenuse and n is the number of iterations.
Given that AC = 6 and n = 100, the equation becomes
[tex]Total Area = (6^2)/2 × (2^100)[/tex]
Total Area = 18 × (2^100)
Total Area = 18 × 1.26 x 10^31
Total Area ≈ 10
Therefore, the total area of the shaded triangles is nearest to 10
Learn more about area
brainly.com/question/27683633
#SPJ4
