Answer: The sum of the integers is equal to $\frac{14}{3}$ times the largest of the seven integers. What is the smallest integer that pearl wrote down?.
Step-by-step explanation:
Pls help I’ve been stuck on this for an hour
Answer: b
Step-by-step explanation:
Answer: 1/4
Step-by-step explanation: The probability that the company will hire two women for positions is : 1/4 because..
The total number of possible outcomes = 4.
The event in which two women are chosen = 1.
or (1/2)*(1/2) = 1/4
Announcements for 81 upcoming engineering conferences were randomly picked from a stack of IEEE Spectrum magazines. The mean length of the conferences was 2.91 days. The population standard deviation is 1.26 days. Assume the underlying population is normal.
Construct a 95% confidence interval for the population mean length of engineering conferences.
(i) State the confidence interval. (Round your answers to two decimal places.)
(ii) Sketch the graph. (Round your answers to two decimal places. Enter your /2 to three decimal places.)
(iii) Calculate the error bound. (Round your answer to two decimal places.)
A 95% confidence interval for the population mean length of engineering conferences is 3.70, 4.26.
The error bound based on the information will be 0.28.
How to calculate the value95% confidence interval for the population mean length of engineering conferences is:
= 3.98 +- (1.969 (0.142)
= 3.98 +- 0.218
= 3.70, 4.26
The error bound based on the information will be:
= (1.96( (0.142)
= 0.28.
Learn more about confidence interval on
https://brainly.com/question/15712887
#SPJ1
You have 9 gallons of lemonade to sell. You use cone-shaped cups that are 10 centimeters in diameter and 12 centimeters tall. Each customer uses one paper cup. How many paper cups will you need if you sell all of the lemonade? (1 gal ≈ 3785 cm3)
Answer:27 paper cups.
Step-by-step explanation:
The volume of each cone-shaped cup can be calculated using the formula:
V = (1/3)πr^2h
where r is the radius of the cone (half the diameter), and h is the height of the cone.
Substituting the given values, we get:
V = (1/3)π(10/2)^2(12) ≈ 1256.64 cubic centimeters
We can convert the 9 gallons of lemonade to cubic centimeters using the conversion factor given:
1 gallon ≈ 3785 cubic centimeters
Therefore:
9 gallons * 3785 cubic centimeters/gallon ≈ 34,065 cubic centimeters of lemonade
To find out how many paper cups are needed, we can divide the volume of the lemonade by the volume of one cone-shaped cup:
34,065 cubic centimeters / 1256.64 cubic centimeters ≈ 27 cups
Therefore, approximately 27 paper cups are needed to sell all of the lemonade.
identify the number pattern and fill in the missing numbers
1) 5, 3, 9, 2, 13
2) 24, 23, 25, 26,
3) 14, 17, 13, 15, 12
1) the number pattern is obscure2) The number pattern seems to be alternating 3) The number pattern seems to be increasing
How to find the aforementioned questions1) The pattern of the numbers is obscure. The connections between the numbers are not immediately apparent.
2) The number pattern seems to be alternating between subtracting 1 and adding 2 to the previous number. The missing numbers are 27 and 28.
3) The number pattern seems to be increasing by 3, then decreasing by 4, then increasing by 2, and so on. The missing numbers are 19 and 16.
Learn more about number pattern at https://brainly.com/question/28580633
#SPJ1
Write the equation in standard form for the ellipse with center (0,3), vertex (0,15), and co-vertex (–
10,3).
Answer:
Step-by-step explanation:
i sorry dont know
A regular hexagonal pyramid has a slant height of 15
centimeters and a base edge length of 8 centimeters.
Answer:
okay?
Step-by-step explanation:
is this a true or false
Two cities are 1580 miles apart. A plane leaves one of them traveling towards
the other at an average speed of 400 miles per hour. At that time a plane leaves
the other traveling towards the first at an average speed of 390 miles per hr.
How long will it take them to meet?
Answer:
Step-by-step explanation:
2 hour
Step-by-step explanation:
City A to City B : 1580 miles
Plane speed (C) to City B from A : 400 miles per hour
Plane speed (D) to City A from B : 390 miles per hour
Time taken for plane (C) :
=1580 ÷ 400
=3⁹/²⁰ hours
Time taken for plane (D) :
=1580 ÷ 390
=4²/³⁹ hours
Finding time difference
= 4²/³⁹ - 3⁹/²⁰
=469/780
Finding midpoint
= 469/780 ÷ 2
=469/1560
Total
= 3⁹/²⁰ + 469/1560
= Aprroximately 3¾ hours
find the composition and simplify your answer as much as possible. Write the domain using interval notation.
The composition f∘g is given by (13) / (x - 13).
The domain of the composition is all real numbers except for x = 13, which can be represented in interval notation as (-∞, 13) U (13, ∞).
To find the composition f∘g, we need to substitute g(x) into f(x) in the following way:
f(g(x)) = f(13/x) = (13/x) / ((13/x) - 1)
To simplify this expression, we can multiply both the numerator and denominator by x, which gives us:
f(g(x)) = (13) / (x - 13)
The domain of f(g(x)) is restricted by the domain of g(x), which is all real numbers except for x = 0. Therefore, the domain of f(g(x)) is the set of all real numbers except for x = 13.
Using interval notation, we can write the domain of f(g(x)) as:
(-∞, 13) U (13, ∞)
To learn more about composition click on,
https://brainly.com/question/29059805
#SPJ1
The rounding off 87654 to the nearest hundred is_the rounding off 87654 to the nearest hundred is the rounding off 87654 to the nearest hundred is what
Round off 87654 to the nearest hundred?
Marching into my territory,eh?
we need to look at the tens and ones digit of the number. The digit in the hundreds place is 6, which tells us that the number is already in the thousands place.
The tens digit is 5, which is greater than or equal to 5. This means we need to round up the hundreds place to the next digit. Therefore, the rounded number to the nearest hundred is 87700.
PLEASE HELP FAST!!!!!!
What is the volume of the right pyramid?
Answer options with 5 options
A.
186 and 2-thirds centimeters cubed
B.
84 centimeters cubed
C.
25 centimeters cubed
D.
23 and 1-third centimeters cubed
E.
18 and 2-thirds centimeters cubed
The volume of the right pyramid is 23 1/3 cm³. The correct option is E,
Given that the length of the side of the right pyramid is 3.75 cm, While the height of the pyramid is 5 cm. Therefore, the volume of the given right pyramid is:
Volume = (1/3) × (side length)² × Height
= (1/3) × (3.75 cm)² × 5 cm
= 23.33 cm³
= 23 1/3 cm³
Hence, the volume is 23 1/3 cm³.
Learn more about Right-Pyramid here:
https://brainly.com/question/30849358
#SPJ1
The complete question must be:
What is the volume of the right pyramid with the base lenght of 3.75 cm and height of 5cm?
A. 186 and 2-thirds centimeters cubed
B. 84 centimeters cubed
C. 25 centimeters cubed
D. 23 and 1-third centimeters cubed
E. 18 and 2-thirds centimeters cubed
Number graph ranging from negative four to four on the x and y axes. A line with a positive slope is drawn on the graph, passing through the labeled point A at (zero, two) and the labeled point B at three, three). What is the slope of the line passing through points A and B? Responses −3 − 3 , −15 − 1 5 14 1 4 13
The slope of the line passing through points A and B is 1/3.
The formula for the slope of a line to find the slope passing through points A and B. The formula is:
slope = (change in y) / (change in x)
Let's label the coordinates of point A as (x₁, y₁) and the coordinates of point B as (x₂, y₂).
Then, substitute the values and calculate the slope:
slope = (y₂ - y₁) / (x₂ - x₁)
slope = (3 - 2) / (3 - 0)
slope = 1 / 3
Therefore, the slope of the line passing through points A and B is 1/3.
Learn more about the Slope of the Line here:
brainly.com/question/14511992
#SPJ1
What is the answer to these questions?
1) There are 3.4 * 10^1 in Mexico than in Canada.
2) The number of ounces that were consumed is 20.8 * 10^7 ounces
3) The number of ounces of the students at the community college is 1.25 * 10^1 that of the students in the University.
What is scientific notation?Scientific notation is a way of writing very large or very small numbers using powers of 10. In scientific notation, a number is written as a coefficient multiplied by 10 raised to a power.
1) Ratio of people in Mexico to those in Canada;
1.3 * 10^8/3.8 * 10^7
= 3.4 * 10^1 : 1
2) Number of Ounces consumed by students = 5.2 * 10^4 * 4 * 10^3
= 20.8 * 10^7 ounces
3) Ratio of the number drank by community college to University
= 4 * 10^3/3.2 * 10^2
1.25 * 10^1
Learn more about scientific notation:https://brainly.com/question/18073768
#SPJ1
To celebrate Diwali, Raina lights a diya, a small clay lamp filled with oil and a cotton wick. The diya holds 35 milliliters of oil. The oil burns at a rate of 14.8 milliliters per hour. If y represents the number of milliliters of oil and x represents the time in hours, which equation models this relationship? A y 35+ 14.8x B y = -35x + 14.8 C y = -14.8 + 35x D y = -14.8x + 35
The equation that represents the relationship is y = -14.8x - 35. (option D)
What equation represents the relationship?
A linear equation is an equation that consists of a single variable that is raised to the power of one. The general form of a linear equation is y = mx + c
Where:
y = dependent variable m = slopec = interceptThe form of the equation that represents the relationship is:
Millimeters of oil = amount of oil the diya holds - (burn rate x number of hours)
y = 35 - (14.8 x x)
y = 35 - 14.8x
y = -14.8x - 35
To learn more about linear equations, please check: https://brainly.com/question/26434260
#SPJ1
que es el sistema binario
The binary system is a numerical system that uses only two digits, 0 and 1, to represent numbers.
We have,
It is also known as the base-2 system.
In contrast, the decimal system, which is the most commonly used numerical system, uses ten digits (0 to 9) to represent numbers.
In the binary system, each digit represents a power of 2, starting with 2^0, which equals 1, and then doubling for each successive position (2^1, 2^2, 2^3, and so on).
Therefore, the decimal number 10, for example, is represented in binary as 1010, where the first 1 represents 2^3, the next 0 represents 2^2, the next 1 represents 2^1, and the last 0 represents 2^0.
The binary system is used in digital electronics and computing, where the two states of a switch or transistor can represent 0 or 1.
Thus,
The binary system is a numerical system that uses only two digits, 0 and 1, to represent numbers.
Learn more about the binary system here:
https://brainly.com/question/2824068
#SPJ1
The complete question:
What is the binary system?
Find the measure of each angle in the triangles shown.
The measure of each angle in the triangle is 60 degrees each
How to determine the measure of the angleTo determine the measure of the angles, we need to note that the sum of the angles in a triangle is equal to 180 degrees.
This is represented as;
<A + <B + <C = 180
From the information given in the diagram, we have;
Then, we have that;
2x - 120 + x - 30 + 1/2x + 15 = 180
add the like terms
2x + x + x/2 = 180 + 120 + 30 - 15
Add or subtract the like terms
3x + x/2 = 315
6x + x/2 = 315
cross multiply the values
7x = 630
Divide both sides by the coefficient
x = 90
Then, the angles are;
2x - 120 = 60 degrees
x/2 + 15 = 60 degrees
x - 30 = 60 degrees
Learn about triangles at: https://brainly.com/question/17264112
#SPJ1
What is the value of A when we rewrite 6^x as A^x/4
The value of A when we rewrite 6^x as A^x/4 is 3/2
What is an algebraic expression?An algebraic expression can simply be defined as a mathematical expression that consists of terms, factors, constants, coefficients and variables.
They are also known as expressions made up of arithmetic operations, such as;
AdditionBracketParenthesesDivisionMultiplicationSubtractionFrom the information given, we have that;
The function is given as;
6^x
Here, the coefficient or rather the base is 6
To determine the value of A when ^^x is given as A^x/4
The value of A would be;
6/4 = 3/2
Learn about algebraic expressions at: https://brainly.com/question/4344214
#SPJ1
if sales tax certain county is 7.2% of the price how much is sales tax on an item the price is $27.30 Round to 2 decimal places
27.30 round to the 2nd decimal place is 27.30.
Now we have to find 7.2% of $27.30.
7.2% of $27.30 is 1.9656.
If you mean that we have to round the answer bt 2 decimal place then the answer is 1.97.
A baseball team played 154 regular season games. The ratio of the number of games they won to the number of
2/5
games they lost was g How many games did they win? How many games did they lose?
Answer: the team won 154g / (g + 1) games and lost 154 / (g + 1) games.
Step-by-step explanation: The mathematical equation "W/L = g" is expressed in a concise manner, wherein "W" refers to weight, "L" refers to the length, and "g" represents the gravitational acceleration. This equation can be utilized in various scientific and academic disciplines, particularly in the field of physics, engineering, and mechanics. The relationship between weight, length, and gravitational acceleration can be further explored and examined through research studies and experiments.
The equation in consideration may be rendered less intricate through the process of multiplication of both sides by L.
"The equation W = gL" can be expressed in an academic manner as follows: The equation denoted by W = gL can be deduced as the product of the gravitational acceleration (g) and the length (L) of an object in a given direction. This equation is commonly used in physics to determine the work (W) performed on an object as a result of a force acting on it, in correlation with the displacement it undergoes in the same direction.
It is understood that the summation of the games won and lost by the team is equivalent to the overall number of games that were played.
The equation denoting the sum of W and L yields a value of 154.
The first equation may now be replaced in the second equation, resulting in:
The mathematical equation GL + L = 154 represents an algebraic expression, where 'G' and 'L' are variables that denote unknown numerical values. The equation dictates that the sum of the values assigned to 'GL' and 'L' must equal to 154. Such equations are commonly used to solve numerical problems in mathematics and related disciplines.
One should perform the mathematical operation of factoring out the variable L on the left-hand side.
The equation L(g + 1) = 154 can be expressed with greater academic rigor.
The sides can be divided by (g + 1) to simplify the equation.
The equation L = 154 / (g + 1) represents a mathematical relationship wherein L is determined by dividing 154 by the sum of g and one.
The aforementioned equation can be utilized to derive a solution for W, ascertaining the relationship that W is equivalent to gL.
The presented expression, W = g(154 / (g + 1)), exhibits a mathematical relationship between the variables W and g, whereby W is a function of g. The numerator of the parenthetical expression, 154, is divided by the sum of g and one, then this ratio is multiplied by g to produce the value of W. The formula can be utilized in various disciplines, such as physics, engineering, and mathematics.
The expression can be simplified to yield:
The expression W can be denoted as 154g / (g + 1) in accordance with the commonly recognized conventions of formal academic writing.
A chord is 8 inches away from the center of its circle. This chord is 30 inches long. What, in inches, is the length of the radius?
Answer: The Length of the radius of the circle is 17 inches.
Factor the Trinomial
[tex]2a^2+5ab+7b^2[/tex]
The given trinomial is [tex]2a^2+5ab+7b^2[/tex]. The trinomial can be factored as (2a+7b)(a+b).
What is trinomial?A trinomial is an algebraic expression consisting of three terms. It can be written in the form ax² + bx + c, where a, b, and c are constants and x is a variable. Trinomials are also used to solve equations, such as quadratic equations.
To factor this trinomial, we will first split the trinomial into two groups. The two groups are (2a, 7b) and (a, b).
Now we will multiply the first terms of both the groups.
We will get 2a × a = 2a².
This is the first term of the trinomial. Now we will multiply the second terms of both the groups.
We will get 7b × b = 7b².
This is the last term of the trinomial. Now we will multiply the first term of the first group and the second term of the second group.
We will get 2a × b = 2ab.
This is the middle term of the trinomial.
Hence, the trinomial can be factored as (2a+7b)(a+b).
For more questions related to trinomial
https://brainly.com/question/27020215
#SPJ1
the expression negative 1 plus tangent x over 1 plus tangent x can be rewritten as which of the following
[tex]\tan(\alpha + \beta) = \cfrac{\tan(\alpha)+ \tan(\beta)}{1- \tan(\alpha)\tan(\beta)} \qquad \tan(\alpha - \beta) = \cfrac{\tan(\alpha)- \tan(\beta)}{1+ \tan(\alpha)\tan(\beta)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{-1+\tan(x)}{1+\tan(x)}\implies \cfrac{-1+\tan(x)}{1-(-1)\tan(x)} \\\\\\ \cfrac{\tan\left( \frac{3\pi }{4} \right)+\tan(x)}{1-\tan\left( \frac{3\pi }{4} \right)\tan(x)}\implies \tan\left( \cfrac{3\pi }{4} + x\right)[/tex]
Lemon-lime
soda
30%
Lemonade
15%
Cola
20%
Root beer
35%
Students at Remington High School were polled regarding their favorite drinks. The results are shown on the circle graph.
If 630 students were polled, how many preferred cola?need asap
Using the given percentages, we can see that 126 students preferred cola.
How many students preferred cola?To find this number, we just need to multiply the correspondent percent by the total number of students.
First, write the percent in decimal form, to do so, divide it by 100%.
20% of the students preferr cola, so we need to write:
20%/100% = 0.2
And the total number of students is 630, so the number that preffered cola is:
0.2*630 = 126
Learn moer about percentages at:
https://brainly.com/question/843074
#SPJ1
PLEASE HURRY AND ANSWER
The figure shows a 1175-yard-long sand beach and an oil platform in the ocean. The angle made with the platform from one end of the beach is 85 deg and from the other end is 75 deg Find the distance of the oil platform, to the nearest tenth of a yard, from each end of the beach.
kyle has a fish tank that is 16 inches long and 15 inches wide he fills the tank so the water is 12 inches high . then he placed a sand castle decoration in the tank and the water level rose to 13 inches . what is the volume of the sand castle decoration explain how you found your answer
Answer:
240 cubic inches.
Step-by-step explanation:
To calculate the volume of the sandcastle decoration in the fish tank, we can use the formula:
Volume of the decoration = Total volume of water after adding the decoration - Volume of water before adding the decoration
The volume of water before adding the decoration is the volume of the rectangular prism formed by the fish tank, which is:
Volume of water before = Length x Width x Height
= 16 x 15 x 12
= 2,880 cubic inches
After Kyle added the sandcastle decoration, the water level rose to 13 inches. This means the volume of water in the tank increased by the volume of the decoration. The new volume of water in the tank is:
Volume of water after = Length x Width x Height
= 16 x 15 x 13
= 3,120 cubic inches
Therefore, the volume of the sandcastle decoration is:Volume of decoration = Volume of water after - Volume of water before
= 3,120 - 2,880
= 240 cubic inches
Therefore, the volume of the sandcastle decoration in the fish tank is 240 cubic inches.
You owe $2,154.35 on your PBnJ credit card that has an interest rate of 9.85% APR. Rather than placing $435.00 into a savings account earning a 2.5% APR, you pay down the principal at the beginning of the month on the credit card. How much interest did you save? (Hint: Calculate the difference between the interest you would earn from the savings account and the interest you would pay on your credit card for the
Using the monthly interest rate and the principal given the interest saved is -$16.8 which shows that nothing was saved.
How much interest was saved?To find the interest saved, let's calculate the interest paid on the credit card.
Monthly interest = 9.85 / 12 = 0.82%
The monthly interest rate on the card is 0.82%
For that particular month, the interest charged will be;
Interest = 2154.35 * 0.0082 = $17.7
However, the interest earned on the savings account will be;
Interest = 2.5 / 12 = 0.21%
We can calculate the interest earned as;
Interest = 0.0021 * 435 = $0.91
The interest saved can be calculated as 0.91 - 17.7 = -16.8
This shows that nothing was saved as the interest earned is lower than the interest charged.
Learn more on APR interest here;
https://brainly.com/question/11686424
#SPJ1
1. a) Write the prime factorization of 17 850
b) Determine the greatest common factor of 735 and 1715.
c) Determine the least common multiple of 450 and 180.
PLS HELP!
The prime factorisation of 17850 is 2 × 3 × 5² × 7 × 17. The Greatest common factor of 735 and 1715 is 245 and the Lowest common multiple of 180 and 450 is 900.
What is prime factorizationPrime factorization is a way of expressing a number as a product of its prime factors. A prime number is a number that has exactly two factors, which includes 1 and the number.
Using prime factorisation:
a). 17850 = 2 × 3 × 5² × 7 × 17
b). Greatest common factor of 735 and 1715 is;
735 = 3 × 5 × 7²
1715 = 5 × 7³
GCF = 5 × 7²
GCF = 244
c). Lowest common multiple of 180 and 450 is;
180 = 2² × 3² × 5
450 = 2 × 3² × 5²
LCM = 2 × 3² × 5³
LCM = 900
Therefore, the prime factorisation of 17850 is 2 × 3 × 5² × 7 × 17. The Greatest common factor of 735 and 1715 is 245 and the Lowest common multiple of 180 and 450 is 900.
Read more about factors here:https://brainly.com/question/1081523
#SPJ1
the set of odd integer Integer
The set of odd integers between three and five can be found to be D. A null set.
What are odd integers ?An odd number is defined as an integer that cannot be split exactly by two. For example: 1, 3, 5, 7, and so on.
We are asked about the set of odd integers ranging from 3 to 5. Because the question asks for odd numbers between 3 and 5, 3 and 5 will not be considered in the set.
This indicates that 3 and 5 are out. We are left with only one even number, four.
As a result, the set of odd integers between 3 and 5 is a Null Set (it contains no numbers).
Find out more on odd integers at https://brainly.com/question/278327
#SPJ1
The full question is:
What is the set of odd integers between three and five?
4
3,4,5
all reall numbers
null set
A genetic experiment with peas resulted in one sample of offspring that consisted of 431 green peas and 152 yellow peas.
a. Construct a 95 % confidence interval to estimate of the percentage of yellow peas.
b. Based on the confidence interval, do the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow?
The answer is , (a) the 95% confidence interval for the percentage of yellow peas is (22.48%, 29.78%). , (b) we cannot definitively conclude that the results contradict the expectation.
What is Confidence interval?A confidence interval is a range of values that is used to estimate the true value of an unknown parameter, like a population mean or proportion, based on a sample of data. It is a statistical measure of the precision and reliability of an estimate, and it provides a measure of the uncertainty or margin of error associated with the estimate.
a. To construct 95% confidence interval for percentage of yellow peas, we can use following formula as :
CI = p ± z*(√((p*(1-p))/n))
Where:
p = proportion of yellow peas = 152/(431+152) = 0.2613
z = z-value for a 95% confidence interval = 1.96 (from standard normal distribution table)
n = sample size = 431+152 = 583
Plugging in the values, we get:
CI = 0.2613 ± 1.96*(√((0.2613*(1-0.2613))/583))
CI = 0.2613 ± 0.0365
CI = (0.2248, 0.2978)
Therefore, the 95% confidence interval for the percentage of yellow peas is (22.48%, 29.78%).
b. The expected percentage of the yellow peas is 25%. Since the lower limit of the confidence interval is 22.48%, which is less than 25%, it suggests that the actual percentage of yellow peas may be lower than expected. However, since the confidence interval does include 25%, we cannot definitively conclude that the results contradict the expectation.
To know more about Parameter visit:
https://brainly.com/question/30639662
#SPJ1
14) Cliff selects a letter tile at random from a bag with 5 tiles labeled A, E, I, O, and U. Then he
replaces the tile and mixes them in the bag. He repeats this 100 times and records the results
in a frequency table. Devon spins the spinner shown below 100 times and records his results
in a frequency table. Describe what you would expect to see in a frequency bar graph for
each experiment. Explain your reasoning.
For the experiment by Cliff, the bar graph will most likely have the same height for the number of times each letter appears.
For the experiment by Devon, the bar graph will most likely have the same height for the number of times the letter A, E, and U appears and the same height for the number of times O and I appear. However, the height of the bar graphs for O and I will most likely be half that of A, E, and U.
What is the probability of the letters appearing?For the experiment by Cliff, the probability of the letters appearing is given below:
Probability = number of times each letter is picked/total number of times letters are pickedThe letters have equal chances of being picked, hence, their probabilities are equal.
Probability = 1/5
For the experiment by Cliff, the probability of the letters appearing is given below:
Probability = number of times each letter is picked/total number of times letters are pickedThe letters A, E, and U have equal chances of being picked, hence, their probabilities are equal.
P(A) = 1/4
P(E) = 1/4
P(U) = 1/4
The letters O and I have equal chances of being picked, hence, their probabilities are equal.
P(O) = 1/8
P(I) = 1/8
Learn more about probability at: https://brainly.com/question/24756209
#SPJ1
Write as a logarithm with a base of 4
2 (please answer in logarithmic form)
[tex]\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b\qquad\qquad \\\\[-0.35em] ~\dotfill\\\\ \log_4(y)=2\implies 4^2=y\implies 16=y\hspace{5em} {\Large \begin{array}{llll} \log_4(16)=2 \end{array}}[/tex]