8³/30 is the expression in simplified form of 2/135*6 - 3√15*6.
What is simplified form?The simplest form of a fraction is one with a relatively prime numerator and denominator. It indicates that, other than 1, there is no common factor between the fraction's numerator (upper part or top) and denominator (lower part or bottom).
The reduced form of a fraction is another name for its simplest form. For instance, the simplest form of a fraction with a common factor of 1 is 3/4 However, because 2/4 can be further condensed and written as 1/2, it is not the simplest form. In this case, we can also state that 1/2 and 2/4 are equivalent fractions.
Given to find the expression in simplified form
2/135 *6 - 3√15 *6
6(2/135-3√15)
6(2/3√15-3√15)
6(2/3√15×3√15 - 3√15/ 3√15)
6(2×3√15/135- 3√15/1)
6(2×3√15/3√15- 3√15/1)
6(2- 3√15)
8³/30
Thus, 8³/30 is the expression in simplified form of 2/135*6 - 3√15*6.
Learn more about simplified form
https://brainly.com/question/13242938
#SPJ1
3) A shoe store was having a back to school sale where you could buy 5 pairs of
shoes for $47.40. If a large family decided to buy 6 pairs of shoes, how much
would it cost them?
$56.4 is the cost of the 6 pairs of shoes.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given that shoe store was having a back to school sale where you could buy 5 pairs of shoes for $47.40.
If a large family decided to buy 6 pairs of shoes then the cost of these 6 pair of shoes we have to find.
Let x be the cost of 6 pair of shoes.
5/47=6/x
Apply cross multiplication
5x=282
Divide both sides by 5
x=56.4
Hence, $56.4 is the cost of the 6 pairs of shoes.
To learn more on Ratios click:
https://brainly.com/question/13419413
#SPJ1
If the figure below has rotational symmetry, find the angle of rotation about the center that results in an image that matches the original figure.
90
120
210
no rotational symmetry
Using the concept of rotational symmetry, the angle of rotation about the center that results in an image that matches the original figure is; Option A: 90
How to identify rotational symmetry?Rotational symmetry is defined as a process that requires the rotation of a given object about a reference point to produce its image which has the same characteristics. This tells us that its dimensions, measure of internal angles and size do not change except its orientation. The orientation depicts the way in which the object is positioned.
The sum of an angle formed at a point is 360 degrees. Thus turning a given object about a point implies its rotation with respect to a measured angle.
Thus in the diagram given in the question, the pattern shown divides the angle at the centered point into four equal parts.
Thus;
Angle of rotation = 360/4 = 90 degrees
Read more about rotational symmetry at; https://brainly.com/question/29977243
#SPJ1
A bowl contains 6 balls, marked with the numerals 1 through 6. If two balls are picked out at random, what is the probability that numbers 5 and 6 will both be picked?
(1) 1/30 (2) 1/15 (3) 1/5
(4)1/6
(5)1/12
The probability that numbers 5 and 6 will both be picked is 1/15.
Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event will not occur and 1 indicating that the event will definitely occur.
If a bowl contains 6 balls, marked with the numerals 1 through 6, and two balls are picked out at random, then there are 15 possible outcomes.
6C2 = 15
Since there is only one chance where 5 & 6 will both be picked from 15 total possible outcomes, then the probability is 1/15.
p = 1 / 15
Learn more about probability here: brainly.com/question/24756209
#SPJ4
A ball bounces to a height of 5.2 feet on the first bounce. Each subsequent bounce reaches a height that is 83% of the previous bounce. What is the height, in feet, of the fifth bounce? Round your answer to thousandths place.
The ball reaches a height of approximately 1.60256 feet on the fifth bounce.
How to calculate the height?We can use the formula for the height of the nth bounce, h(n) = h(1) * (0.83)^(n-1), where h(n) is the height of the nth bounce, h(1) is the height of the first bounce, and 0.83 is the bounce coefficient (the percentage of the previous height that the ball reaches on each subsequent bounce).
Given that the first bounce reaches a height of 5.2 feet, we can plug in h(1) = 5.2 into the formula and solve for h(5), the height of the fifth bounce.
h(5) = 5.2 * (0.83)^4
h(5) = 5.2 * 0.30769
h(5) = 1.60256
The height is 1.60256 feet.
Learn more about height on
https://brainly.com/question/12446886
#SPJ1
A cell phone tower that is 80 meters tall is built on level ground and casts a shadow 170 meters long at a particular moment Find the angle of elevation of the sun relative to an observer standing at the tip of the shadow .
Answer: c
Step-by-step explanation:
Answer:
Step-by-step explanation:
An engineer erects a 75-foot cellular telephone tower. Find the angle of elevation to the top of the tower at a point on level ground 50 feet from its base.
Use function composition to determine if f(x) and g(x) are inverse functions.
f(x)=\sqrt[3]{x-1} and g(x)=x^3+1
The functions f(x) = ∛x - 1 and g(x) = x³ + 1 are inverse functions.
How to determine if the functions f(x) and g(x) are inverse functions.From the question, we have the following parameters that can be used in our computation:
Distinct Functions
The functions are represented as
f(x)=\sqrt[3]{x-1} and g(x)=x^3+1
Rewrite the functions properly
So, we have the following representations
f(x) = ∛x - 1 and g(x) = x³ + 1
Using the function compositions, the following equation must be true
f(g(x)) = x
Substitute the known values in the above equation, so, we have the following representation
f(g(x)) = ∛x³ + 1 - 1
Evaluate the like terms
f(g(x)) = ∛x³
So, we have
f(g(x)) = x
Hence, the functions are inverse functions
Read more about inverse functions at
https://brainly.com/question/3831584
#SPJ1
You want to stay at least 7 nights. At least one night should be spent at a large resort. Large resorts average $250 per night and small inns average $75 per night. Your budget permits no more than $1,600 for lodging.
Use this graph of the system to approximate its solution.
O A. (-)
O B. (, -¹)
Oc. (-)
O D. (-5, 13)
nhts reserved
-2x + 5y = 19
y =
-6 -4 -2
6-
4
2-
2
+4-
- - ㅎ
X
keeping in mind that a solution to a system of equations is where their graph intersect, Check the picture below.
find three consecutive even integers such that the sum of the smaller and three times the larger Is 84
Using the concept of the word problem and utilizing the provided conditions and values, The answer is 18, 20, and 22.
What is a word problem?A word problem in mathematics is a problem or exercise that is expressed in a natural language, rather than in mathematical notation. These types of problems often present a real-world situation that involves mathematical concepts, such as numbers, operations, or measurements. They typically require the use of mathematical reasoning and problem-solving skills to understand the problem and find a solution. Examples of word problems include: "If a train travels 60 miles per hour and you want to know how far it will travel in 4 hours", "If a rectangle is 6 meters long and 4 meters wide, what is its area?", "If a bag contains 3 red balls and 4 blue balls, what is the probability of picking a blue ball?"
What are conditions of the problem?In a mathematical problem, the conditions refer to the specific information or constraints provided in the problem statement that must be taken into account in order to find a solution. These conditions can include information about the quantities involved in the problem, the operations that need to be performed, or the specific requirements that the solution must meet.
Let x be the smallest of the three consecutive even integers. Then the next two integers are x+2 and x+4. We know that:
x + (x+4) * 3 = 84
Expanding and solving for x:
x + 3x + 12 = 84
4x = 72
x = 18
So the three consecutive even integers are 18, 20, and 22.
To learn more about word problems visit:
https://brainly.com/question/14319273
#SPJ1
Abigail is the volunteer coordinator for a company that puts on running races. Last year, the company organized 7 - 5K races and 9 – 10K races, which required a total of 935 volunteers. This year, the company organized 7 – 5K races and 7 – 10K races, which required 805 volunteers in total. How many volunteers does each type of race require? Find the variables for this situation. Responses
The number of volunteers needed for the 5k races is 50 and the number of volunteers needed for the 10k races is 65.
How many volunteers are needed for each type of race?The system of equations that represent the question is:
7a + 9b = 935 equation 1
7a + 7b = 805 equation 2
Where:
a = number of volunteers needed for the 5k racesb= number of volunteers needed for the 10k racesThe elimination method would be used to determine the values of a and b.
Subtract equation 2 from equation 1
2b = 130
b = 130 / 2
b = 65
Substitute for b in equation 1 :
7a + 9(65) = 935
7a + 585 = 935
7a = 935 - 585
7a = 350
a = 350 /7
a = 50
To learn more about system of equations, please check: https://brainly.com/question/25875552
#SPJ1
find dy/DX
y = 3ex
y = x2ex
y = ex/x3
Answer:
[tex]a) \frac{d}{dx} (3e {}^{x} ) \\ [/tex]
Recall the property
[tex]\frac{d}{dx} [c \times f(x)] = c \times f'(x) \\[/tex]
[tex] = 3 \frac{d}{dx} e {}^{x} = 3e {}^{x} \\ [/tex]
[tex]b.) \: \: \frac{d}{dx} (x {}^{2} e {}^{x} ) \\ [/tex]
[tex] = x {}^{2} \times e {}^{x} +e {}^{x} \times 2x \\[/tex]
[tex] = e {}^{x} (x {}^{2} \times 2x) \\ [/tex]
[tex]c.) \: \: \frac{d}{dx}( \frac{e {}^{x} }{x {}^{3} } ) \\ [/tex]
[tex] = \frac{x {}^{3} \times e {}^{x} - e {}^{x} \times {3x}^{2} }{ {x}^{6} } \\ [/tex]
[tex]= \frac{x {}^{2} {e}^{x} (x - 3) }{ {x}^{6} } \\ [/tex]
[tex]= \frac{ {e}^{x} (x - 3) }{ {x}^{4} } \\ [/tex]
The formula distance equals = rate times time (D=RT) describes the relationship
between distance travelled, speed and time. It can be transposed to calculate any of the three variables.
At what rate of speed must a vehicle travel to cover 132 kilometres in one and a half hours?
The rate of speed that a vehicle must travel to cover 132 kilometers in one and a half hours is 88 kilometers per hour.
What is the rate of speed?The rate of speed is the quotient of distance and time.
Similarly, the time taken to cover a distance can be determined as the quotient of distance and speed.
The formula describing the relationship between distance traveled, speed, and time is Distance = Rate of Speed x Time.
The total distance traveled = 132 kilometers
The time taken to travel the distance = 1¹/₂ hours = 1.5 hours
Rate of speed = Distance/Time
= 88 kilometers per hour (132/1.5)
Thus, the rate of speed for the vehicle to cover 132 kilometers is 88 kilometers per hour.
Learn more about distance, speed, and time at https://brainly.com/question/26046491
#SPJ1
Which graph shows a correlation coefficient closest to -1 ?
Answer:
The first graph (topmost graph)
Step-by-step explanation:
Correlation coefficient of -1: Negative correlation
As variable x (horizontal axis) increases, variable y (vertical axis) should decrease.
Hence, gradient of the graph is negative, sloping downwards as x increases.
Graph 2 is eliminated (positive correlation approximately 1)
Graph 4 is also wrong as there is simply no correlation. (Points are random with no fixed pattern or trend)
Graphs 1 and 3 show negative correlation.
However, for graph 3, several points are not accurate, leading to a straight line not being drawn accurately. (Slightly off) . Correlation of this graph is negative but not closest to -1.
Hence, the first graph is the closest to -1 in terms of correlation coefficient.
13 out of the 25 employees at the sports shop are part-time employees. What percentage of the employees at the sports shop work part-time. Write your answer using a percentage sign (%).
Answer:
52%
Step-by-step explanation:
13/25 x 100 = 52%
Answer:
52%
Step-by-step explanation:
13/25 = .52
To change a decimal to a percent, multiply the decimal by 100%
.52 x 1005 = 52%
This makes sense because half of 25 is 12.5 which would be 50% and 13 is just a little more than 12.5
Limited partnerships have two classes of partners. The
▼
limited
general
partner actually runs the business and faces unlimited liability for the firm's debt, while the
▼
limited
general
partner is only liable up to the amount the
▼
limited
general
partner invested
The general partner actually runs the business and faces unlimited liability for the firm's debt, while the limited partner is only liable up to the amount the limited partner invested.
What does limited partnership mean?A limited partnership is a legal entity that consists of at least one general partner (who has unlimited personal liability) and one limited partner (whose liability is limited to their investment in the company).
In this case, the general partners are primarily responsible for managing the business and making business decisions in order to achieve the stated business goals, whereas the limited partners, also known as silent partners, are only responsible for investing in the business and not running it.
Read more about limited partnership
brainly.com/question/13032294
#SPJ1
Mrs. Perkey bought 16 tickets to the Pink concert.
The group rate saved her $5.75 per ticket.
Mrs. Perkey paid a total of $296 for the tickets.
1) Write an equation that can be used to solve for the price of each ticket.
2) Show your steps as to how you solved the equation.
The equation that can be used to solve for the price of each ticket is $296 = 16t - 92. The cost of each ticket is $24.25.
What is the cost of each ticket?Theequqtion represents the total cost of the tickets
Total amount paid by Mrs. Perkey = total cost of the tickets - total amount saved
$296 = (16 x t) - (16 x $5.75)
$296 = 16t - 92
$296 + 92 = 16t
$388 = 16t
t = $388 / 16
t = $24.25
To learn more about mathematical equations, please check: https://brainly.com/question/26427570
#SPJ1
6.
A=f/g
f=2.75 correct to 2 decimal places
g=0.3 correct to 1 decimal place
Calculate the upper bound of the value of A
The upper bound of the value of A is 10.71
How to determine the upper bound of the value of AFrom the question, we have the following parameters that can be used in our computation:
f = 2.75 correct to 2 decimal placesg = 0.3 correct to 1 decimal placeThe equation of A is then given as
A = f/g
The number of decimal places implies that:
f = 2.75 + 1 = 3.75
g = 0.3 + 0.05 = 0.35
Substitute the known values in the above equation, so, we have the following representation
A = 3.75/0.35
Evaluate the quotient
A = 10.71
Hence, the upper bound is 10.71
Read more about approximation at
https://brainly.com/question/24491627
#SPJ1
The width is
The length of a rectangle is nine more than triple the width. If the perimeter is 106 inches, find the
dimensions.
Answer:
w = 11
l = 42
Step-by-step explanation:
in word problems :
'more than' means +
'triple' means 3 times
'is' means =
perimeter means 2 times width plus 2 times the length
'length of a rectangle is nine more than triple the
width' means :
l = 9+3w
'perimeter is 106 inches' means
2l + 2w = 106
divide by 2
l + w = 53
substitute l with 9+3w to get the width
9+3w + w = 53
9 + 4w = 53
4w = 44
w = 11
go back to the perimeter equation
l + w = 53
put 11 for w
l + 11 = 53
l = 42
Candace sold 125 stickers on Monday. This is 50% of the total amount she sold during the whole week. How many stickers did she sell in all?
25 stickers
75 stickers
250 stickers
350 stickers
Answer: I THINK 250
Step-by-step explanation: 125 is half and 125 times 2 is 250.
1. A shopper bought a 12-pound bag of oranges for $18.75. What was the unit price?
A $0.64
C $1.73
B $1.56
D $6.40
Answer: B, $1.56
Step-by-step explanation:
The unit price is simply the price of a good per unit. In this case, the price per pound.
Divide the cost by the number of pounds.
18,75/12 = ~1,56
Therefore, Option B is the correct answer.
The table gives the daily high and low temperatures for a week in Anchorage, Alaska. On which day or days is the low temperature farthest from
0°C?
From the table, we conclude that on Wednesday and Sunday the low temperature farthest from 0°C
What are the types of representation of data?The investigator must summarize the facts in tabular form after gathering them in order to study their prominent features. The presentation of data is the name given to such a configuration.
Any acquired data may be arranged in a frequency distribution table and then displayed using pictograms or bar graphs. The lengths of the equally wide bars that make up a bar graph are controlled by the frequency and scale you select.
Observing the data is represented in a table form where rows represent the number of days in a week and two columns represent the high and low temperatures of Anchorage, Alaska.
On Wednesday and Sunday, the low temperature was - 13°C and it is the farthest from 0°C.
learn more about the representation of data here :
https://brainly.com/question/13149249
#SPJ1
Simplify the expression x^-2/y^4
Therefore ,we can state after answering the given question that the exponents value is 0.
Exponents are what?Exponentiation is a mathematical expression represented by the letter bn that involves numeric values: a base amount, b, and a multiplier, or power, n. It is also referred to as "b raised here to nth power." Exponents demonstrate the number of times that a number has indeed been increased by itself. For example, 2-3 (expressed as 23) means: 2 x Two x 4 = 8. 2 + 3 does not equal 6, nor does 23. Remember that an integer whose power is one is equal to itself. Exponents can be used as a way to express large numbers as powers. Exponent, then, seems to be the quantity that conveys how many time a quantity can be expressed.
Here,
Given : x⁻² /y⁴
=> here x= 0
So,
=> 0/y⁴
=> 0
hence,
the total is 0.
Therefore ,we can state after answering the given question that the exponent value is 0.
To know more about exponents visit:
brainly.com/question/3987569
#SPJ1
The complete question is "How do you simplify and write x⁻² /y⁴ with positive exponents?"
Select the correct answer.
You work delivering food for a local farmer. You sell onions from the farm at these prices: 2 for $1.04, 4 for $2.52, 8 for $4.32, and 16 for $9.12. What is the best deal for buying onions?
A.
2 onions for $1.04
B.
4 onions for $2.52
C.
8 onions for $4.32
D.
16 onions for $9.12
The best deal for buying onions include the following: A. 2 onions for $1.04.
What is price?In Business management, price can be defined as an amount of money which is primarily set by the seller of a good (product), and it must be paid by a buyer to the seller, so as to enable the acquisition of this good (product).
How to determine the best deal for buying onions?Based on the information provided, we can calculate each of the price of the onions as follows;
2 for $1.04 = 1/2 × 1.04
2 for $1.04 = $0.52
4 for $2.52 = 1/4 × 2.52
4 for $2.52 = $0.63
8 for $4.32 = 1/8 × 4.32
8 for $4.32 = $0.54
16 for $9.12 = 1/16 × 9.12
16 for $9.12 = $0.57
Therefore, the best deal would be buying 2 onions for $1.04 because it offers the cheapest price.
Read more on onions and price here: https://brainly.com/question/28785724
#SPJ1
Solve the equation
2^2x+1 +5(2^x) -3=0
Please help
Answer:
The answer is -1
Step-by-step explanation:
2^(2x+1) = 2^2x × 2^1 = 2^2x × 2
after this we can make appointments
2^x = t
and then solve it :)
in an iso triangle the length of a leg is 17 cm in the base is 16 cm find the length of the altitude to the base
If the length of the leg of the isosceles triangle is 17 cm and the base is 16 cm then the length of altitude to the base is 15cm .
An Isosceles triangle is defined as a triangle in which any two side are of equal length .
The Length of the leg is = 17cm ,
the base of the triangle is = 16cm ;
let the length of the altitude to the base be = x cm ,
The altitude to the base of the triangle divides it into two right angle triangle.
So , in one of the right angle triangles, Base = 16/2 = 8 cm
the Hypotenuse of triangle = length of the leg = 17 cm
By Applying Pythagoras theorem,
we get ,
17² = 8² + x² ,
289 = 64 + x² ,
x² = 289 - 64
x² = 225 ,
taking Square root(√) on both the sides ,
we get , x = 15 .
Therefore , the length of the altitude to the base is = 15 cm .
Learn more about Triangle here
https://brainly.com/question/8550762
#SPJ4
To find the altitude of an isoceles triangle with a base length of 16 cm and a leg length of 17 cm, use the Pythagorean Theorem. Calculate 17² + 16² = c², then solve for c² to get c = √545 = 23.3 cm.
The altitude of the triangle can be found using the Pythagorean Theorem.
a² + b² = c²
17² + 16² = c²
289 + 256 = c²
545 = c²
c = 23.3 cm
(or)
17² + 16² = c² => 289 + 256 = c²
=> 545 = c²
=> c = √545 = 23.3 cm
The altitude of an isoceles triangle can be found by using the Pythagorean Theorem. The formula for the theorem is a² + b² = c², where a and b are the two sides and c is the hypotenuse, which is the altitude. In this situation, a is the leg length of 17 cm and b is the base length of 16 cm. Substituting these values into the equation gives 17² + 16² = c². Solving for c² gives c = √545 = 23.3 cm, which is the length of the altitude.
Learn more about triangle here
https://brainly.com/question/2773823
#SPJ4
Write the equation of the line in fully simplified slope-intercept form.
[tex]y=\frac{1}{2}x +4[/tex]
Step-by-step explanation:Slope-intercept form is a common way of representing linear functions. Slope-intercept is written as y = mx + b, where m is the slope and b is the y-intercept.
Slope
To find the slope-intercept equation we first need to find the m-value. Slope is often defined as rise over run. This means the change in y divided by the change in x. So, we can find the slope by counting how much the y-value and the x-value increases between 2 points.
For example, we can take the points (2,5) and (4,6). The y-value increases by 1 and the x-values increase by 2. This means that the slope is 1/2. We can plug this into slope-intercept form to get part of the equation: [tex]y = \frac{1}{2}x+b[/tex].
Y-Intercept
Next, we need to find the b-value. The y-intercept of a graph is the y-value where the function intersects with the y-axis (the vertical axis). By looking at the graph, we can tell that the function crosses the y-axis at y = 4; this occurs at the point (0,4). The y-intercept always occurs when x = 0.
Now, we can plug 4 in for b to get the final equation: [tex]y=\frac{1}{2}x +4[/tex].
find the value of x so that the points (x, -8) and (8,1) lie on a line with a slope of 1/2
Step-by-step explanation:
. My sister asked me, "Have you seen my dog?" ____________________________________________ 2. Vijay asked "Have you gone to market?" ____________________________________________ 3. My mother asked, "Why are you crying?" ____________________________________________ The rickshaw puller asked me, "Do you speak English?" ____________________________________________
add or subtract
4a^2-1/a^2-4-2a-1/a-2
The given can be simplified as [tex]\frac{6a^{2} -1}{a^{2} }[/tex].
What is an Algebraic expression?An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.
The variable part of an algebraic expression can never be added or subtracted from the constant part.
The given expression is [tex]\frac{4a^{2} -1}{a^{2} } - \frac{4 - 2a}{a-2}[/tex]
It can be simplified as follows,
[tex]\frac{4a^{2} -1}{a^{2} } - \frac{4 - 2a}{a-2}[/tex]
⇒ [tex]\frac{4a^{2} -1}{a^{2} } - \frac{2(2 - a)}{a-2}[/tex]
⇒ [tex]\frac{4a^{2} -1}{a^{2} } + 2[/tex]
⇒ [tex]\frac{6a^{2} -1}{a^{2} }[/tex]
Hence, the simplification of the given expression is obtained as [tex]\frac{6a^{2} -1}{a^{2} }[/tex].
To know more about algebraic expression click on,
brainly.com/question/953809
#SPJ1
Choose all the measurements that are
greater than 4 cups.
☐ 30 fluid ounces
☐ 2 pints
☐ 3 pints
☐ 1 quart
☐ 1 gallon
Answer:
☐ 3 pints
☐ 1 gallon
Step-by-step explanation:
4cups = 32 fluid ounces = 2 pints = 1 quart = 0.25 gallons
30 fl oz is less than 4 cups
2 pints is exactly 4 cups but we are looking for numbers greater than 4 cups
3 pints is more than 4 cups so this is a correct choice
1 quart is exactly 4 cups but we are looking for numbers greater than 4 cups
1 gallon is 16 cups so a valid choice
Identify the parent function.
•
A. Cube root
B. Reciprocal
C. Absolute value
D. Square root
