Final answer:
The function in question involves simplifying the base 4^3 multiplied by the square root of 4. Through understanding exponent rules and square root operations, this simplifies to 128, demonstrating the importance of algebraic fundamentals.
Explanation:
Understanding the Simplified Base of 4^3 \sqrt{4}
The question asks which function has a simplified base of 4^3 \sqrt{4}. Simplifying this expression requires understanding of exponent rules and square roots. The cube of 4, or 4^3, equals 64. The square root of 4 is 2, hence \(\sqrt{4}\) simplifies to 2. Combining these, we see that 4^3 multiplied by \(\sqrt{4}\) equals 64 * 2 = 128.
To put this into perspective, we would express the original operation as 4 raised to the power of 3 and then multiplied by the square root of 4, which can also be depicted as 4^3 * 2 since \(\sqrt{4} = 2\). Thus, the simplified base is not a direct function but rather an arithmetic operation resulting in 128.
It's crucial to note that while operations like these involve basic principles of exponents and roots, each step must be carefully followed to ensure accuracy. The concept behind these operations is grounded in the mathematical principles of handling integers, powers, and roots, highlighting the importance of solid fundamentals in algebra.
Owen made a down payment of $1,600 on a car that was 20% of the total price what was the total price of the car
Please help this doesnt really make sense. If you want to see the paper just press that pic right up there
fill in the blanks on the pattern 98,97,95,92,88 ? ?
The last two numbers of the given sequence are respectively gotten to be; 83 and 77
How to find the sequence of numbers?
From the sequence, we see that;
From 98 to 97, there is a decrease of 1
From 97 to 95, there is a decrease of 2
From 95 to 92, there is a decrease of 3
From 92 to 88, there is a decrease of 4
The sequence pattern of decrease is seen to be: 1, 2, 3, 4
Thus, by inference we can say that the next decrease is 5. Thus,
Next number in sequence = 88 - 5 = 83
The number after that will be; 83 - 6 = 77
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Which of the following are examples of exponential decay?
The numerator of a fraction (which is in its simplest form) is 5 less than the denominator. If the numerator is multiplied by 2, and the denominator is increased by 16, then the fraction becomes smaller by 1/3 of it. Find the original fraction.
Final answer:
The original fraction, based on the provided conditions, is found to be 3/8 by setting up an equation relative to the changes described and solving for the unknown numerator and denominator.
Explanation:
The question involves solving for the numerator and denominator of a fraction based on provided conditions. Let's denote the denominator as x and the numerator as x - 5, since the numerator is 5 less than the denominator. According to the given conditions, when the numerator is multiplied by 2 and the denominator is increased by 16, the fraction becomes smaller by 1/3 of its original value.
Original fraction: [tex]\(\frac{x - 5}{x}\)[/tex]. After the modifications: [tex]\(\frac{2(x - 5)}{x + 16}\)[/tex]. The condition that the fraction becomes smaller by 1/3 of its original value leads to the equation: [tex]\(\frac{x - 5}{x} - \frac{1}{3} \cdot \frac{x - 5}{x} = \frac{2(x - 5)}{x + 16}\)[/tex].
Simplifying this equation, we first express the reduced original fraction as [tex]\(\frac{2(x - 5)}{3x}\)[/tex]. Then, setting it equal to the modified fraction, we get[tex]\(\frac{2(x - 5)}{3x} = \frac{2(x - 5)}{x + 16}\)[/tex]. Canceling out [tex]\(2(x - 5)\)[/tex] from both sides and solving for x, we find that x = 8. Therefore, the original denominator is 8, and the numerator is 3, making the original fraction 3/8.
If the edge length of a cube is 11 feet, what is the correct way to write the expression to represent the volume of the cube in exponential form? (2 points)
11 × 11 × 11
311
11
113
PLEASE HELP!!!!
Different types of parallelograms have distinguishing traits. Compare and contrast the rectangle, rhombus, and square based upon the characteristics of their angles. Which one(s) have angles whose sum is 360 degrees? Which one(s) have both pairs of opposite angles that are congruent? Which one(s) have four angles?
The square, rectangle, and rhombus are all considered parallelograms. Squares have four sides, four 90 degree angles, 2 pairs of opposite congruent angles (all the angles are congruent), the angles add up to a sum of 360 degrees. Rectangles have four sides, four 90 degree angles that add up to 360 degrees, 2 pairs of opposite congruent angles (all the angles are congruent). Rhombuses have four sides, four angles in total measuring up to 360 degrees no matter the combination of angles because the oposite angles are congruent (2 acute angles and two obtuse angles).
While the rhombus is the only shape within this trio to have a pair of congruent acute and a pair of congruent obtuse angles the square and rectangle both have 4 congruent angles. All 3 shapes have a sum of 360 degrees when the angles are added together, all 3 have pairs of opposite angles being congruent, and all 3 shapes have 4 angles in total.
A campus radio station surveyed 500 students to determine the types of music they like. the survey revealed that 207 like rock, 172 like country, and 126 like jazz. moreover, 33 like rock and country, 27 like rock and jazz, 32 like country and jazz, and 13 like all three types of music. what is the probability that a randomly selected student likes at least two of the three types of music?
The probability that a randomly chosen student like at least two of the three styles of music will be 0.21.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences. Then the probability is given as,
P = (Favorable event) / (Total event)
A school radio station polled 500 students to find out what kind of music they appreciate. According to the study, 207 people prefer rock, 172 prefer country, and 126 choose jazz. Furthermore, 33 like rock and country, 27 prefer rock and jazz, 32 prefer country and jazz, and 13 prefer all three forms of music.
The number of favorable events is given as,
Favorable events = 33 + 27 + 32 + 17
Favorable events = 105
Then the probability is given as,
P = 105 / 500
P = 0.21
P = 21%
The probability that a randomly chosen student like at least two of the three styles of music will be 0.21.
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Simplify
[tex]4(2 + 3i) -2 (6 - 8i)[/tex]
Find the value of t in the equation t + 5 + 3t = 1. A. 1.5 B. 6 C. 3 D. –1
Answer:
D. -1
Step-by-step explanation:
All the variable terms are on the left, so subtract the constant on the left (5) from the equation and collect terms.
... 4t = -4 . . . . . . . variable term on one side; constant term on the other
Divide by the coefficient of t.
... t = -1
The exchange rate of U.S. dollars to British pounds (£) .63. You have $4000 to convert to British pounds. How many british pounds will you receive?
A) £3937
B) £6349
C) 4063
D) 2520
With an explanation please bc my answer that I got isn't on here
what is the length of DE?
Which graph shows the complex number i-1
This circle is centered at the origin, and the length of its radius is 10. what is the circle's equation?
The equation of the circle that you are looking for is x^2 + y^2 = 100.
You can find this by using the base formula for a circle:
(x - x1)^2 + (y - y1)^2 = r^2
In which x1 is the x-coordinate of the origin, y1 is the y-coordinate of the origin, and r is the radius. So we put in the values we know and simplify.
(x -0)^2 + (y - 0)^2 = 10^2
x^2 + y^2 = 100
The equation of a circle centered at the origin such that the length of its radius is 10 units will be x² + y² = 100.
What is a circle?
Circle is a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center).
Given is a circle is centered at the origin, and the length of its radius is 10 units.
The equation of the circle whose center is at origin is given by -
x² + y² = r²
We have radius [r] = 10 units
Therefore, we can write the equation of the circle as -
x² + y² = 10 x 10
x² + y² = 100
Therefore, the equation of a circle centered at the origin such that the length of its radius is 10 units will be x² + y² = 100.
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Which of the following best describes the expression 4(y + 6)?
The interior angles of a triangle have measures (2x−5)° , (4x−1)° , and 30°. What is the value of x? Enter your answer in the box.
which is the equation of the line that has a slope of 4 and passes through point (1,6)?
Which expression is equivalent to 3i(4 + 7i)?
Events X and Y are independent. The probability of X occurring is 1/3 . The probability of Y occurring is 1/2 . What is P(X and Y)?
a. 1/6
b. 1/3
c.2/3
d.5/6
Answer: a. [tex]\dfrac{1}{6}[/tex]
Step-by-step explanation:
Given : Events X and Y are independent.
The probability of X occurring is [tex]\dfrac{1}{3}[/tex].
The probability of Y occurring is [tex]\dfrac{1}{2}[/tex].
Since both events are independent, then we have
[tex]\text{P(X and Y)}=\text{P(X)}\times \text{P(Y)}\\\\\Rightarrow\ \text{P(X and Y)}=\dfrac{1}{2}\times\dfrac{1}{3}=\dfrac{1}{6}[/tex]
Hence, [tex]\text{P(X and Y)}=\dfrac{1}{6}[/tex]
Thus , (a.) is the correct option.
Spencer is 51 years younger than Holly seven years ago Holly's age was four times Spencer's age how old is Spencer now
Answer:
24
Step-by-step explanation:
The given age relationships can be used to reason about their ages.
__
When Holly was 4 times Spencer's age, the difference in their ages was 4-1=3 times Spencer's age. That is, Spencer was 51/3 = 17 years old, and Holly was 68.
That was 7 years ago, so Spencer is now 17+7 = 24 years old.
A high school gym class was jumping rope. They wanted to know how many jumps each student could make before they missed. The results are listed below. 2 5 6 7 9 11 12 14 14 15 17 19 21 22 23 24 27 32 35 39 39 44 47 53 60 61 82 85 88 90 93 96 101 103 114 125 What is the median number of jumps that the students made before missing? a. 32.5 c. 33.5 b. 33 d. 34
The median number of jumps that the student made before missing is calculated as: C. 33.5.
What is the Median of a Data Set?Median is the middle value or the average of the two center values of a data set.
Given the data set:
2, 5, 6, 7, 9, 11, 12, 14, 14, 15, 17, 19, 21, 22, 23, 24, 27, 32, 35, 39, 39, 44, 47, 53, 60, 61, 82, 85, 88, 90, 93, 96, 101, 103, 114, 125
The average of the two center values is: (32+35)/2 = 33.5
Therefore, the median number of jumps is: C. 33.5.
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The sum of the perimeters of two congruent triangles is three times the perimeter of the first triangle. Always Sometimes Never
Which is the graph of f(x) = 0.5(4)x?
Answer:
The first graph, so A is the answer
Step-by-step explanation:
A rectangle is 2/5 inches long and 1/3 inches wide what is the area of the rectangle
What is the area of the shaded region?
Area = ____ ft2
Consider the numbers 4/15 and 3/10 (a) Compare the numbers. (B) find a fraction between the two given numbers
HELP PLEASE! −3.64⋅|−5.3|−1.53 what is the anwser?
The expression simplifies to approximately -20.822. It involves multiplying -3.64 by the absolute value of -5.3 and then subtracting 1.53 from the result.
To calculate this expression, follow the order of operations (PEMDAS),
which stands for Parentheses, Exponents, Multiplication and Division (left-to-right), and Addition and Subtraction (left-to-right).
In expression, there are no parentheses or exponents, so we proceed with multiplication and then subtraction:
-3.64 × |-5.3| - 1.53
Calculate the absolute value of -5.3, which is 5.3.
Multiply -3.64 by 5.3.
Finally, subtract 1.53 from the result.
-3.64 × 5.3 - 1.53
Now, do the multiplication:
-19.292 - 1.53
Now, subtract:
-19.292 - 1.53 = -20.822
Therefore, the answer for the given expression -3.64 × |-5.3| - 1.53 is approximately -20.822.
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Tina was involved in an accident in which she rear-ended another driver stopped at a stoplight. Tina is fully insured through her insurance company. Which of the following components of her insurance policy will cover the damages caused to Tina’s car in the accident?
a.
bodily injury
b.
property damage
c.
collision
d.
comprehensive damage
(Correct Answer Is C. Collision)
Answer:the answer is C. collision
Step-by-step explanation:
What is the function whose graph is the same as that of f(x) = -3x + 1 but shifted to the right 2 units and up 3 units?
write one way you can read the time 10:20