[tex]\sqrt[3]{8}^{\frac{1}{4}x }[/tex] is equivalent to [tex]\sqrt[12]{8}^{x}[/tex].
What are cube roots?
In mathematics, the cube root of a number x is a number y, so y³ = x. Every nonzero real number has exactly one real cube root and one set of complex conjugate cube roots, and every nonzero complex number has three different complex cube roots.
The given equation is [tex]\sqrt[3]{8}^{\frac{1}{4}x }[/tex]
Solving by using the indices properties,
[tex]=\sqrt[3]{8}^{\frac{1}{4}x }\\={8}^{\frac{1}{3}\frac{1}{4}x}\\=8^{\frac{1}{12}x}\\=\sqrt[12]{8}^{x }[/tex]
Hence the solution will be [tex]\sqrt[12]{8}^{x}[/tex].
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The table shows the amount of dietary fiber in bananas. Use the table to find the constant of proportionality. Express your answer in decimal form.
Dietary fiber (g) 9.3 18.6 27.9 37.2
Servings 3 6 9 12
The Constant Of Proportionality Is 3.1
A per the table,
Amount of dietary fiber in 3 servings of banana = 9.3 grams
Amount of dietary fiber in 6 servings of banana = 9.3 grams
Amount of dietary fiber in 9 servings of banana = 9.3 grams
Amount of dietary fiber in 12 servings of banana = 9.3 grams
We need to find
The constant of proportionality.
We know that the constant of proportionality is a constant number that represents the rate at which ratios of a quantity decrease or increase.
Let the constant of proportionality be, k.
So, k = x/y
Where,
x = Quantity
y = Total Number of the quantity.
Ratio 1 = 9.3/3 = 3.1
Similarly,
Ratio 2 = 18.6/6 = 3.1
Ratio 3 = 27.9/9 = 3.1
Ratio 4 = 37.2/12 = 3.1
since all the ratios are equal;
Hence, The Constant Of Proportionality Is 3.1
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Find the length of, side x in simplest radical form with a rational denominator.
The side x is √2 cm when the right angle triangle is given with hypothesis 2 cm.
Given that,
In the picture we have a right angle triangle.
We have to find the side x.
The angles are 90°, 45° and 45°.
The hypothesis is 2cm.
By the trigonometric ratio.
The study of angles and the angular relationships between two-dimensional and three-dimensional shapes is known as trigonometry.
Sin45°= opposite side/ hypothesis
1/√2= x/2
x=2/√2
x=√2
Therefore, The side x is √2 cm when the right angle triangle is given with hypothesis 2 cm.
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A chef's specialty calls for one-twentieth of an ounce of a spice per serving. The chef has a digital scale that shows the weight as a decimal. What scale reading
does the chef need to see for this spice when preparing the specialty for 19 people?
The scale of reading that the chef needs to see for this spice when preparing the specialty for 19 people would be = 4.5 ounce.
Who is a chef?A chef is a trained individual in various aspects of preparation of dishes, who has the knowledge of combination of food products to achieve an adequate meal.
The quantity of spice per serving= 1/20 ounce.( For an individual)
The quantity of people to prepare specialty for = 90 people
The quantity of spice that would be used to prepare specialty for 90 people would be;
= 1/20 × 90
= 90/20
= 4.5 ounce.
Therefore, the scale reading the chef needs to see for preparing of specialty for 90 people would be = 4.5 ounce.
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Social Security tax: 6.2%. Maximum: $106,800. Medicare tax: 1.45%
In 2009, Dr. Kirmser's gross pay was $381,318.60.
What was her monthly gross pay?
Dr. Kirmser's monthly gross pay = $ 29345.65
Social Security tax:Employers and workers are both subject to the Social Security tax, which is used to pay for the country's Social Security program. Federal Insurance Contributions Act (FICA)-mandated payroll taxes or Self-Employed Contributions Act-mandated self-employment taxes are the two ways that Social Security tax is collected (SECA).
Here we have
In 2009, Dr. Kirmser's gross pay was $381,318.60.
Social Security tax = 6.2% [ Maximum: $106,800 ]
=> 6.2% = 6.2/100 = 0.062
Medicare tax = 1.45%
=> 1.45% = 1.45/100 = 0.0145
From the above information,
Total tax on salary =0.062 + 0.0145 = 0.0765
In 2009, Dr. Kirmser's gross pay was $381,318.60.
Tax can be calculated on Gross pay = 0.0765 × $381,318.60
= 29170.827
As we know
Net pay = gross salary - deductions
=> Monthly gross pay = $381,318.60 - $29170.827 = $ 352147.773
Therefore,
Dr. Kirmser's monthly gross pay = 352147.773 ÷ 12 = $ 29345.65
Hence,
Dr. Kirmser's monthly gross pay = $ 29345.65
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The directions on a swimming pattern says to cut an extra 15 percent of fabric to account for error chloe needs 0.75 yard of fabric to make a skirt and she cuts 0.8625 yards did chloe cut the correct amount of fabric white or why not
The directions on a swimming pattern says to cut an extra 15 percent of fabric to account for error, Chloe needs 0.75 yard of fabric to make a skirt and she cuts 0.8625 yards,
Given that the directions on a sewing pattern say to cut an extra 15% of fabric to account for an error, and Chloe needs a 0.75 yard of fabric to make a skirt, so she cuts 0.1125 yard, to determine if Chloe cut the correct amount of fabric the following calculation must be made:
0.75 x 1.15 = X
0.8625 = X
0.8625 - 0.1125 = 0.75
Therefore, the amount of fabric that Chloe cut is correct.
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Noreen can walk 13 mile in 12 minutes. What is her average speed in miles per hour?.
The average speed in miles per hour is 1.67 miles/hour
What is her average speed?
Average speed is calculated by dividing distance by time (eg miles/hour).
Given that, Noreen can walk 1/3 mile in 12 minutes.
We need to find her average speed.
We know that the total distance covered divided by the total time taken is called the average speed of Noreen.
Mathematically, it is given by :
v=d/t
t = 12 minutes = 0.2 hours
v=(1/3 mile)/0.2 hours
v = 1.67 miles/hour
So, the average speed of Noreen is 1.67 miles/hour. Hence, this is the required solution.
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This item has two parts: Part A and Part B. Use the information and table to complete Part A and Part B.
Jennifer’s bank account is modeled by the following equation where x equals the number of weeks and f(x) equals the total balance.
f(x) = 12x + 45
The balance of William’s bank account is modeled in the table.
Weeks 0 1 2 3 4
Total Balance ($) 30 44 58 72 86
Part A
What function represents the balance of William’s bank account?
g(x) = 14x + 30
g(x) = 30x
g(x) = 30x + 14
g(x) = 14x
Part B
Jennifer claims that her bank account is growing at a greater rate of change than William’s bank account. Is Jennifer CORRECT?
No, because her rate of change is $ 45 per week which is less than William’s rate of change.
Yes, because her rate of change is $ 12 per week which is more than William’s rate of change.
Yes, because her rate of change is $ 45 per week which is more than William’s rate of change.
No, because her rate of change is $ 12 per week which is less than William’s rate of change.
Answer:
A) g(x) = 14x + 30
B) The last explanation
No, because her rate of change is $12 per week which is less than William's rate of change.
Step-by-step explanation:
A:
At the beginning William as 30 dollars (0,30) Week zero he has 30. Then each week, his balance goes up 14 dollars
g(x) = 14x + 30
B:
Jennifer's bank account is increasing by 12 dollars a week, but William's is increasing 14 dollars a week.
A tank ha 120 gallon of water and i being drained at a rate of 1/2 gallon each econd. Another tank ha 100 gallon of water and i being drained at a rate of 1/4 gallon each econd. Which equation could be ued to determine x, the number of econd, when the two tank have the ame amount of water?
The equation that could be used to determine x, the number of seconds, when the two tanks have the same amount of water is 120 - 1/2(x) = 100 - 1/4(x) or x = 80.
An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question. An equation is the equality of expressions.
Let x be the number of seconds at the moment that the two tanks have the same amount of water.
If a tank has 120 gallons of water and is being drained at a rate of 1/2 gallon each second, the the amount of water left after time = x is "120 - 1/2(x)".
If another tank has 100 gallons of water and is being drained at a rate of 1/4 gallon each second, the the amount of water left after time = x is "100 - 1/4(x)".
Equate the two expressions to determine the time, x , at which the two tanks have the same amount of water left.
120 - 1/2(x) = 100 - 1/4(x)
20 = 1/4 x
x = 80
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Find the equation for the line of best fit for the scatter plot shown below.
Answer Choices:
y=1.5x+0.5
y=1.5x+4.5
y=1.5x+5
The equation for the line of best fit of the scatter plot according to the attached image is; y = 1.5x + 0.5.
What is the equation of the line of best fit of the scatter plot given?It follows from the task content that the equation of the line of best fit of the scatter plot is to be determined.
By observation, it can be inferred that the y-intercept of the line of best fit is at the point; (0, 0.5).
Also, the slope of the equation can be determined by considering the points; ( 2 , 1 ) and ( 9 , 12 ).
Therefore, since the slope is given by; m = (y2 - y1) / (x2 - x1).
In this scenario, slope, m = (12 - 1) / (9 - 2)
m = 11/7.
Hence, the slope is approximately; 1.5.
Ultimately, the equation of the line of best fit is; y = 1.5x + 0.5.
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The area of a rectangle is 44 square inches . The length of one side is 11 inches.what is the length of the other side
Answer:
Step-by-step explanation:
A = 44
a = 11
______
b - ?
A = a·b
b = A / a = 44 / 11 = 4 ( inches)
if a person usually ate 2 ounces of lean meat at lunchtime and decided to substitute cooked lentils instead, how much of the lentils would the person need to eat?
If a person substitutes 2 ounces of lean meat by cooked lentils, the lentils that the person need to eat is ½ cup as both are protein.
Lean meat and lentils are among the sources of proteins in the food intake. Protein is found throughout the human body such as in muscle, skin, hair, bone, skin, hair, and every other body part or tissue. It manufactures the enzymes that power chemical reactions and the hemoglobin that carries oxygen in your blood. Protein is required by the body to help your body repair and make new cells. The foods that contain high content of proteins include lean meat, eggs, dairy products, lentils, etc. A half cup of cooked lentils provides 9 grams of protein, and 2 ounces of lean meat provides 8 grams of proteins. As the amount of protein provided by both is similar, a person can substitute one with another and maintain their protein intake.
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Jason decided to begin a workout program. He wants to start running three times a week. At the beginning of the workout program, his weekly average per run is 1 mi. He increases his weekly average per run by 17% each week, according to an exponential growth model. Jason makes a sketch of the graph for this situation. He plots the point containing the y-intercept, (0,1) . He then plots the point representing the weekly average per run for Week 7 and rounds the coordinates of the point to the nearest tenth. What are the coordinates of the point that represents the weekly average per run for Week 7?
The coordinates of the point that represents the weekly average per run for Week 7 is (7, 3.00).
What is an exponential function?It is defined as a function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = aˣ
where a is a constant and a>1
It is given that:
Jason decided to begin a workout program. He wants to start running three times a week.
As we know, the exponential function can be represented as:
f(x) = abˣ
The weekly average per run is 1 mi.
He increases his weekly average per run by 17% each week,
The exponential function:
f(x) = 1(1.17)ˣ
Plug x = 7
f(7) = 1(3.0012)
f(7) = 3.00
Thus, the coordinates of the point that represents the weekly average per run for Week 7 is (7, 3.00).
The complete question is:
Jason decided to begin a workout program. He wants to start running three times a week. At the beginning of the workout program, his weekly average per run is 1 mi. He increases his weekly average per run by 17% each week, according to an exponential growth model. Jason makes a sketch of the graph for this situation. He plots the point containing the y-intercept, (0,1) . He then plots the point representing the weekly average per run for Week 7 and rounds the coordinates of the point to the nearest tenth. What are the coordinates of the point that represents the weekly average per run for Week 7?
options:
A. (7, 3.2)
B. (7, 2.7)
C. (7, 3.0)
D. (7, 4.6)
E. (7, 4.1)
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Answer:
7,3,0
Step-by-step explanation:
Johnson had 22,000 shares in a blue chip company before a stock split of 2:1. How many shares does Johnson have after the stock split?
Answer:
44,000 shares in a blue-chip company
Step-by-step explanation:
So since Johnson had 22,000 shares in a blue-chip company and it split 2:1, we multiple the beginning number of shares by 2 because they split into 2 different shares.
22,000*2=44,000
When abram was born, his parents put $2,000 into an account that yielded 1. 2% interest, compounded semi-annually. When he turns 16, his parents will give him the money to buy a car. How much will abram receive on his 16th birthday?.
In linear equations, $ 309.914 will abram receive on his 16th birthday .
What are examples of linear equations?
An equation with only one variable is referred to as a linear equation in one variable. It has the formula Ax + B = 0, with A and B being any two real numbers and x being an ambiguous variable with just one possible value. A linear equation in one variable would be 9x + 78 = 18, for instance.Let “M” be amount of money in account.
Let “y” be number of full years passed.
1.2/2 = 0.6(%) - interest for every 6 months
y = 16
Money in the account in 16 years:
M = 2,000(1.006)2y
= 2,000(1.06)32
= 2000 * 0.154957
= $ 309.914
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Yesterday, Grace drove 41 1/2 miles. She used 1 1/4 gallons of gasoline. What is the unit rate for miles per gallon?
33.2 miles per gallon is the unit rate for miles per gallon.
Given, Grace drove 41 1/2 miles.
She used 1 1/4 gallons of gasoline.
So, Grace drove 41 1/2 miles = Grace used 1 1/4 gallons of gasoline
41(1/2) miles = 1(1/4) gallons of gasoline
83/2 miles = 5/4 gallons of gasoline
as, 5/4 gallons of gasoline = 83/2 miles
1 gallon of gasoline = (4/5)×(83/2)
1 gallon of gasoline = (2/5)×83
1 gallon of gasoline = 166/5
1 gallon of gasoline = 33.2 miles
33.2 miles/gallon is the unit rate.
Hence, 33.2 miles per gallon is the unit rate for miles per gallon.
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HELP ASAP!!!!!!
In this situation, simple interest is calculated yearly.
How much interest was earned?
Principal: $8000
Time: 4 years
Interest rate: 12%
The simple interest accumulated on the principal at 12% rate for 4 years is $3,840.
How to determine interest accumulated?Simple interest formula is expressed as;
I = P × r × t
Where I is interest, P is principal, r is interest rate and t is time.
Given the data in the question;
Principal P = $8000Elapsed time t = 4 yearsInterest rate r = 12%Interest I = ?First, convert the interest rate from percent to decimal.
Interest rate r = 12%
Interest rate r = 12/100
Interest rate r = 0.12
Plug the given values into the above formula and solve for interest I.
I = P × r × t
I = $8000 × 0.12 × 4
I = $3,840
Therefore, the interest earned is $3,840.
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The graph shows the distance traveled by an Olympic-level sprinter over time during a race.
Find the slope of the line, and complete the sentences below.
100 meter race graph of a diagonal line on a coordinate plane going up and to the right with Time in seconds on the x axis and Distance in meters on the y axis. The line begins at the origin and passes through the point 2 comma 20.
The slope of the line is 10.
Given:
The graph shows the distance traveled by an Olympic-level sprinter over time during a race.
The line begins at the line begins at the origin and passes through the point (2,20).
slope between (0,0) and (2,20).
slope m = y2 - y1 / x2 - x1
= 20 - 0 / 2 - 0
= 20/2
= 10.
Therefore the slope of the line is 10.
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(Real-World Proportional Problems MC)
The time it takes to read 5 pages of a book can be represented with the equation y equals 4.5 divided by 5 times x, where y represents the total time in minutes and x represents the number of pages read.
Determine how long it will take to read a book that has 218 pages.
242.22 minutes
218.63 minutes
196.2 minutes
54.5 minutes
Answer:
C. 196.2 minutes===========================
Equationy = (4.5 / 5) xGivenx = 218Find yy = (4.5/5)*218 y = 0.9*218y = 196.2Correct choice is C
Answer:
c) 196.2 minutes
Step-by-step explanation:
Forming the equation,
→ y = (4.5/5) × 218
Now required value of y will be,
→ y = (4.5/5) × 218
→ y = 981/5
→ [ y = 196.2 min ]
Hence, the value of y is 196.2.
What is the value of the expression?
Drag and drop the answer into the box to match the expression.
0.3(14−1)+0.35
A -0.575
B -0.125
C 0.125
D 1.925
E 1.4
Using the figure below, which table correctly lists the steps and reasons used to find the measure of angle d?
The correct option is (c).
(A) We know that sum of the interior angles of a triangle is equal to 180°.
m∠a + m∠b + m∠c = 180° (all three are interior angles)
(B) If the sum of two angles is 180°, that angle is called a supplementary angle. In other words, when two angles add to form a straight line, they are called supplementary angles.
m∠d + m∠c = 180° (both are in a straight line making an angle)
(C) Transitive properties help establish a connection by stating that if a = b and b = c, then a = c.
m∠a + m∠b + m∠c = 180°
m∠d + m∠c = 180°
Therefore, this property
We can say,
m∠a + m∠b + m∠c = m∠d + m∠c
(D) Subtraction equality properties: Subtraction equality properties indicate that subtracting or removing an equal value from two equal elements results in a new equal quantity.
The formula for this is if a = b, then a-c = b-c
In the question,
m∠a + m∠b = m∠d
Both ∠a and ∠b are two interior angles and the exterior angle is ∠d.
According to the exterior angle property of a triangle theorem, the sum of two opposite interior angles is equal to exterior angles.
Hence, this is also correct.
Therefore, the correct option is (c) which has the correct steps and reasons for the given question.
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Work out the area Give your answer in cm² and give any decimal answers to 1 d.p.
53 cm
28 cm
The triangle's surface area is 630 cm²
What is the Pythagorean theorem in plain English?
Pythagoras' Theorem states that the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. The Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides.
Given that
hypotenuse is 53 cm
base is 28 cm
and it is a right angle triangle
Area = 1/2 x Base x height
So by using Pythagorean theorem we can find its height
Height² + Base² = Hypotenuse²
Height² + 784 = 2809
Height² = 2024
Height = 45 cm
Area = 1/2 x 28 x 45
Area = 630 cm²
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The monthly property tax for a home, in dollars, in a certain city y years after 1990 is $333 + $35y
Which of the following is correct?
OA. The property tax increased by $333 each year after 1990.
OB. The property tax decreased by $333 each year after 1990.
OC. The property tax increased by $35 each year after 1990.
OD. The property tax decreased by $35 each year after 1990.
Answer:
The property tax increases by 35
Step-by-step explanation:
The number 333 in the equation is a constant. It is added to the total no matter how many years after 1990. The 35 is what is increasing every year after 1990.
The dimensions of a room are 4.2 m by 6 m. On a plan, the longer side is equal to 4cm. What is the length of the shorter side on this plan?
The length of the shorter side on this plan is 2.8cm.
How to calculate the length?Based on the information illustrated, let the length of the shorter side on this plan be represented by x.
In this case, the dimensions of a room are 4.2 m by 6 m and on a plan, the longer side is equal to 4cm.
This will be illustrated as:
x/4 = 4.2 / 6
Cross multiply
6x = 4 × 4.2
x = (4 × 4.2) / 6
x = 2.8cm
The length is 2.8 cm.
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if you are conducting an experiment where the probability of a success is .02 and you are interested in the probability of two successes in 15 trials, the correct probability function to use is the . a. normal probability density function b. binomial probability function c. poisson probability function d. standard normal probability density function
When conducting an experiment with the probability of a success of 0.02 and you are interested in the probability of 2 successes in 15 trials, the correct probability function to use is the binomial probability function. (Option B)
Binomial probability function, in probability theory and statistics, refers to the discrete probability distribution of the number of successes in a sequence of repeated independent experiments. Generally, the binomial distribution represents data generated from a yes–no question, and each with its own Boolean-valued outcome: success or failure. As the experiment where probability of success is given and you are interested in the probability of 2 successes in 15 trials, the appropriate probability function is binomial probability function.
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The price of an item yesterday was $80. Today, the price rose to $216. Find the percentage increase.
Answer:
170%
Step-by-step explanation:
increase in price = 216 - 80 = $136
x : 100 = 136 : 80
x = 100 * 136 / 80
x = 10 * 136/8
x = 1360 / 8
x = 170 %
Answer:
170%
Step-by-step explanation:
80+170%=$216
In a certain Algebra 2 class of 24 students, 6 of them play basketball and 7 of them play baseball. There are 13 students who play neither sport. What is the probability that a student chosen randomly from the class plays basketball or baseball?
Answer:
P(basketball or baseball) = 11/24
Step-by-step explanation:
You want the probability that a randomly chosen student plays either sport, given the probability that 13 of the 24 students plays neither sport.
ComplementThe probability that a student plays at least one (of the two) sports is the complement of the probability they play neither sport. If 13 of 24 students play neither sport, then (24-13)/24 = 11/24 must play at least one of the two sports.
P(basketball or baseball) = 11/24
__
Additional comment
6+7-11 = 2 students play both sports.
<95141404393>
what is
9e-7=7e-11
e=?
Answer:
-2
Step-by-step explanation:
9e-7=7e-11
9e-7e= -11+7
2e= -4
e= -4÷2
e= -2
A salami is 2 3/5 inches long. The salami is cut into 1/8 inch thick slices.
How many slices of salami were cut?
Answer:
20 slices
Step-by-step explanation:
2 3/5 = 13/5
13/5 / 1/8
(13/5)(8/1) = 20.8
about 20 slices
PLEASE HELP ASAP
Given 2 and 1 over 10 times negative seven times 5 over 12, determine the product.
negative fourteen and 5 over 120
negative six and 1 over 8
fourteen and 5 over 60
six and 1 over 8
Answer:A
Step-by-step explanation:negative fourteen and 5 over 120
Because you multiple
2 x -7 = -14
10 x 12 = 120
1 x 5 = 5
Calculate P(3, 2)
12
8
7
6
Answer: the answer is number 6
