An ounce of the chemical cost in 2018 is $98.54.
Given:
The function c(x) = 72 ⋅ (1.04)ˣ models the cost in dollars, c, of 1 ounce of a certain chemical used in a laboratory.
Exponential function, involves exponents. an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function). An exponential function can be in one of the following forms.
In mathematics, an exponential function is a function of form f (x) = a^x, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
x represents the number of years since 2010.
An ounce of the chemical cost in 2018 is,
= 72 × (1.04)⁸
= $98.54
Therefore, the cost is $98.54.
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PLS ANSWER QUICK FIRST TO ANSWER RIGHT WILL GET BRAINLIEST!!!!
Answer:
xy=k
-2×4=k
k=-8
y=-8/x
Rank the following methods of timekeeping from least precise to most
precise.
A clock with only an hour hand
A clock with an hour and minute hand
A calendar
A clock with an hour, minute, and second hand
The required, methods have been arranged according to the rank from least precise to most precise.
Ranking the methods of timekeeping from least precise to most precise:
A clock with only an hour hand - This clock is the least precise, as it can only measure time in hour increments.A calendar - A calendar is more precise than a clock with only an hour hand, as it can measure time in days and months, but not precise to measure hours, minutes or seconds.A clock with an hour and minute hand - This clock is more precise than a calendar, as it can measure time in hours and minutes.A clock with an hour, minute, and second hand - This clock is the most precise, as it can measure time in hours, minutes, and seconds.Therefore, methods have been arranged according to the rank from least precise to most precise.
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the following calculation is an example of which type of measure: the number of children that had allergies in 2020 divided by an estimate of total number children in the population?
Prevalence is a commonly used metric in epidemiology and public health to describe the proportion of a population affected by a specific condition or characteristic during a specific period. In this case, it helps to understand the extent of allergies among children in 2020.
The calculation given is an example of a prevalence measure, which is used to determine the proportion or percentage of individuals in a population that have a particular health condition or disease. In this case, the number of children with allergies in 2020 is divided by an estimate of the total number of children in the population to determine the prevalence of allergies in the population.
Prevalence measures are useful for understanding the burden of a particular health condition in a population, as well as for identifying trends over time or differences between different groups within the population. However, it's important to note that prevalence measures are only as accurate as the data used to calculate them, so it's essential to use reliable sources of data and to ensure that the sample of individuals being measured is representative of the entire population.
Prevalence measures are widely used in epidemiology and public health research to understand the distribution of health conditions and diseases in populations. They can be calculated for a wide range of health outcomes, including chronic diseases, infectious diseases, mental health conditions, and more.
In addition to prevalence, other types of measures used in public health research include incidence (which measures the number of new cases of a particular health condition within a population over a specific period of time), mortality (which measures the number of deaths attributable to a particular health condition or disease), and morbidity (which measures the burden of illness associated with a particular health condition or disease, often in terms of disability-adjusted life years or quality-adjusted life years).
Ultimately, the type of measure used in a given study will depend on the research question being asked, the available data sources, and the specific health outcome being studied. However, regardless of the type of measure used, it's important to ensure that the sample of individuals being measured is representative of the entire population, and to use reliable and accurate data sources to calculate the measure.
The calculation you described, which involves dividing the number of children with allergies in 2020 by an estimate of the total number of children in the population, is an example of a prevalence measure.
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You are on a game show and are playing a game to try to win a trip to Orlando. There are 7 tiles in a bag, each with a letter of the city on it. You must pull the tiles out in the correct order to spell Orlando. What is the probability you will win the trip?
The probability that you will win the trip to Orlando would be = 1
How to calculate the probability of the given event?To calculate the probability that you will win the trip to Orlando the formula for probability should be used and this is given below;
Probability = possible outcome/sample space.
The total small space = 7
For first Letter;
Possible outcome = 1
probability = 1/7. This will be done for the total number of letters used to spell Orlando = 1/7+1/7+1/7+1/7+1/7+1/7+1/7 = 7/7 = 1
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Vik is constructing a spherical model of Earth
for his science fair project. His model has a
radius of 24 inches. Since roughly 75% of
Earth's surface is covered by water, he wanted
to paint 75% of his model blue to illustrate
this fact. Approximately how many square
inches on his model will be painted blue?
Answer:
5,428.67 inches^2
Step-by-step explanation:
for finding the surface area of a sphere, the formula is:
A = 4(pi)r^2
r = 24 in
we just fill in the equation and get a total surface area of around 7238.23 inches^2
next, we find one percent of this by dividing by 100.
7238.23 / 100 = 72.3823
multiply this by 75
72.3823 x 75 = 5428.6725
so the answer is this rounded to be approximately 5,428.67 inches^2
Which expression can be used to find the value of 3/2 divided by 1/8
The value of 3/2 divided by 1/8 is 12 (or 12/1).
To find the value of 3/2 divided by 1/8, you can use the expression (3/2) ÷ (1/8). To solve this division problem, follow these steps:
Step 1: Rewrite the division as a multiplication problem by multiplying the first fraction (3/2) by the reciprocal of the second fraction (8/1). The expression becomes: (3/2) × (8/1).
Step 2: Multiply the numerators (the top numbers) of the fractions: 3 × 8 = 24.
Step 3: Multiply the denominators (the bottom numbers) of the fractions: 2 × 1 = 2.
Step 4: Write the result as a new fraction with the product of the numerators as the numerator and the product of the denominators as the denominator: 24/2.
Step 5: Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor (in this case, 2): 24 ÷ 2 = 12 and 2 ÷ 2 = 1. The simplified fraction is 12/1.
Therefore, the value of 3/2 divided by 1/8 is 12 (or 12/1).
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Can someone please help me with this trigonometry assignment?
Directions: Write a word problem as a STORY which will require Trigonometry to solve. What is the problem? Why do we need to solve it? Who needs us to solve it? How will it help? Solve the problem clearly and accurately.
The picture above is an example on how you could create the word problem.
The final calculation revealed that the height of the mountain was approximately 350.1 meters.
How to explain the trigonometryBack in their workshop, Alex applied the tangent function to find the mountain's height. They knew that tangent is the ratio of the opposite side (the height) to the adjacent side (the horizontal distance). Setting up the equation, they plugged in the known values:
tangent(35 degrees) = height / 500 meters
Using trigonometric tables or a calculator, they found that the tangent of 35 degrees is approximately 0.7002. Now they could solve the equation:
0.7002 = height / 500 meters
To isolate the height, they multiplied both sides of the equation by 500:
0.7002 * 500 meters = height
The final calculation revealed that the height of the mountain was approximately 350.1 meters.
With this crucial information, Alex and Sarah could now design the bridge
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alejandra's tapas bar offers a menu consisting of savory and sweet dishes. you can also get a mix-and-match plate consisting of two different dishes on the menu. how many different mix-and-match plates can you get consisting of one savory and one sweet dish?
So, there are 20 different mix-and-match plates that can be created by combining one savory and one sweet dish from Alejandra's Tapas Bar's menu.
To determine the number of different mix-and-match plates that can be created from Alejandra's Tapas Bar's menu, we need to calculate the number of options for both the savory and sweet dishes and then multiply them together.
Let's assume that there are 5 savory dishes and 4 sweet dishes on the menu. To create a mix-and-match plate, we need to choose one savory and one sweet dish. The number of options for the savory dish is 5, and the number of options for the sweet dish is 4. Therefore, the total number of different mix-and-match plates that can be created is:
5 x 4 = 20
Customers can choose any combination they like and can enjoy a unique dining experience each time they visit the restaurant.
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When the piggy bank was opened, it yielded $5.22 in nickels and pennies. If there were 162 nickels and pennies altogether, how many of each were in the bank? Write your answer in the order of the sample answer: 5 nickels, 6 pennies. PLEASE GIVE AN ACTUALLY ANSWER! Thank you!
Answer:
90 nickels, 72 pennies
Step-by-step explanation:
0.05n+0.01p= 5.22
n+p=162
0.05(162-p)= 5.22
p= 72
n+72= 162
n=90
Write a recursive formula for an,the nth term of the sequence 3,-12,48,-192
The recursive formula for the sequence is a(n) = -4*a(n-1) . where a(1) = 3.
To find the recursive formula for the sequence 3,-12,48,-192, we need to look at how each term relates to the previous term.
Starting with the first term, we have a(1) = 3.
To get to the second term, we multiply the first term by -4. So we have a(2) = -4*a(1) = -4*3 = -12.
To get to the third term, we multiply the second term by -4. So we have a(3) = -4*a(2) = -4*(-12) = 48.
To get to the fourth term, we multiply the third term by -4. So we have a(4) = -4*a(3) = -4*48 = -192.
So we can see that each term is obtained by multiplying the previous term by -4.
Therefore, the recursive formula for the sequence is:
a(n) = -4*a(n-1)
where a(1) = 3.
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Jo has 5 sweaters. He needs to take 3 sweaters on a vacation. In how many different ways can he choose 3 sweaters out of 5?
40
30
20
10
Answer:
10 is the answer. Hope this helps!
A nervous kicker usually makes 78% of his first field goal attempts. If he makes his first attempt, his success rate rises to 94%. What is the probability that he makes his first two kicks?
Answer: 0.733
The probability of success of the first two kicks is 0.733
What is probability?Probability is the likelihood of an event
Since nervous kicker usually makes 78% of his first field goal attempts. If he makes his first attempt, his success rate rises to 94%. To find the probability that he makes his first two kicks, we notice that the events are independent events. So, the probability of independent events A and B is
P(A U B) = P(A)P(B)
Now let
P(F) = probability of success of first kick = 78% and P(S) = probability of success of second kickSo, the probability of success of the first two kicks is P(F U S) = P(F)P(S)
So, substituting the values of the variables into the equation, we have that
P(F U S) = P(F)P(S)
= 0.78 × 0.94
= 0.7332
≅ 0.733
So, the probability is 0.733
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jenny reads a book with 92 pages. jenny's book has 13 more pages than the book macy reads. which equation could you solve to find how many pages, m, macy's book has?
2.1 You are given that m is an even integer and n is an odd integer. Which of these is an
odd integer?
A: 3m + 4n
B: 5mn
C: (m + 3n)²
D: m³n²
E: 5m + 6n
The only odd integer among the choices is 5mn.
To determine which expression is an odd integer,
we need to know that the sum of an even integer and an odd integer is always odd, and the product of an even integer and an odd integer is always even.
A: 3m + 4n = 2m + m + 4n is even
since it's the sum of two even integers.
B: 5mn is odd since it's the product of an odd and an even integer.
C: (m + 3n)² = m² + 6mn + 9n² is odd since it's the sum of two odd integers and an even integer.
D: m³n² = m * m² * n² is even since it's the product of an even integer and two odd integers.
E: 5m + 6n = 2(2m + 3n) + m is odd since it's the sum of two even integers and an odd integer.
Therefore, the only odd integer among the choices is 5mn.
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This is hard so don't ask why i need help -v- (90 POINTS!)
Zach has 72 cards. he gives 23 away. how many cards does Zach have left?
Answer: 49
Step-by-step explanation:
When you have 72 and subtract it by 23 you get 49
write the equation of a line that is perpendicular to x =3 and that passes theough the point (0,-4).
If f(x) = x² + 5x - 4, then what is the remainder when f(x) is divided by
x-8?
Answer:
100-------------------------
The Remainder Theorem states that:
if you divide a polynomial f(x) by x - c, the remainder is equal to f(c).Identify the value of c in the divisor x - 8. In this case, c = 8.
Plug the value of c into the function f(x).
f(8) = (8)² + 5(8) - 4Calculate the remainder.
f(8) = 64 + 40 - 4 f(8) = 100So, the remainder is 100.
Xsquare_2x_ysquare +4y_3 hcf
The HCF of the given expression is (x + 2y).
To find the highest common factor (HCF) of the given expression, [tex]X^2 + 2xy^2 + 4y^3[/tex], we need to factorize it. However, the given expression seems to contain some typographical errors or inconsistencies, as it is not a valid mathematical expression.
If you meant to write the expression as , [tex]X^2 + 2xy^2 + 4y^3[/tex]we can proceed with finding the HCF.
The expression can be factored as follows:
[tex]X^2 + 2xy^2 + 4y^3 = (x + 2y)(x^2 - 2xy + 2y^2)[/tex]
To find the HCF, we look for the common factors among the terms. In this case, the common factor is (x + 2y). Therefore, the HCF of the given expression is (x + 2y).
Please note that if there was an error in the original expression you provided, and it differs from what was assumed here, please correct it so that a more accurate response can be given
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Note the full question is ;
Xsquare_2x_ysquare +4y_3
hcf of the given term is ?
8. (Equations)
The difference between 3 times a number x and 2 is 19. What is the
value of x?
A 7
B. 6
C. 5
D. 1
Answer: A. 7
Step-by-step explanation:
3y-2=19
3y-2+2=19+2 (add 2 to both sides)
3y=21
3y/3=21/3 (divide by 3 on each side)
y=7
Find the volume of the pyramid. Round your answer to two decimal places. 4in, 5in, and 3in.
10 c and 10 d plsssssssssssssssss
Answer:
10c a - 3; b = 4
10d See below
Step-by-step explanation:
10c
The problem asks about
3² × 4² = 12²
The given rule is
a² × b² = (a × b)²
Match each number in the problem to each variable or expression in the given rule.
a = 3; b = 4; a × b = 3 × 4 = 12
Answer: a = 3; b = 4
10d
Let's use two sets of number for the formula.
a = 2; b = 5
a² × b² = (a × b)²
2² × 5² = 4 × 25 = 100
(2 × 5)² = 10² = 100
100 = 100
a = 6; b = 8
a² × b² = (a × b)²
6² × 8² = 36 × 64 = 2304
(6 × 8)² = 48² = 2304
2304 = 2304
The formula works every time.
The formula shows you that if you have to multiply the squares of two numbers, you can also multiply the numbers first, then square the product. The result is the same.
un triangulo rectangulo tiene un angulo de 25 grados y su lado mas largo mide 12 ¿cuanto miden los lados faltantes?
los lados faltantes del triángulo rectángulo son de 5.1 y 11.83.
Para resolver este problema, necesitamos recordar las propiedades de un triángulo rectángulo. Primero, sabemos que uno de los ángulos es de 90 grados. Además, el lado opuesto al ángulo recto se llama hipotenusa y los otros dos lados se llaman catetos.
En este caso, sabemos que uno de los ángulos es de 25 grados, por lo que el otro ángulo es de 90 - 25 = 65 grados. Ahora podemos usar la ley de senos para encontrar la longitud del otro cateto.
La ley de senos establece que la longitud de un lado dividida por el seno del ángulo opuesto es igual a la longitud de otro lado dividido por el seno del ángulo opuesto. Entonces, podemos escribir:
12 / sen(90) = x / sen(25)
x = 12 * sen(25) / sen(90) = 5.1
Por lo tanto, el lado faltante tiene una longitud de 5.1. Para encontrar la longitud del otro cateto, podemos usar el teorema de Pitágoras, que establece que la suma de los cuadrados de los catetos es igual al cuadrado de la hipotenusa. Entonces, podemos escribir:
a^2 + b^2 = 12^2 - 5.1^2 = 130.19
a^2 + b^2 = 130.19
b = sqrt(130.19 - a^2)
Donde "a" es la longitud del cateto que conocemos y "b" es la longitud del cateto que queremos encontrar. Podemos usar la ecuación anterior para encontrar la longitud de "b" para diferentes valores de "a". Por ejemplo, si "a" fuera de 4, tendríamos:
b = sqrt(130.19 - 4^2) = 11.83
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Acceptance sampling. A company produces large cases of incandescent light bulbs. If there is a 1% chance that any one light bulb is defective, what is the probability that among 83 randomly sampled lightbulbs. A. . 1 or less are defective?
b. . 2 or more are defective?
Light bulbs can be calculated using the binomial distribution with n=83 and p=0.01. P(X≤1)=0.1808. light bulbs can be calculated as 1 minus the probability that 0 or 1 light bulbs are defective. P(X≥2)=1-P(X≤1)= 1-0.1808=0.8192.
a. The probability that 1 or less light bulbs are defective among 83 sampled light bulbs can be calculated using the binomial distribution with n=83 and p=0.01. P(X≤1)=0.1808.
b. The probability that 2 or more light bulbs are defective among 83 sampled light bulbs can be calculated as 1 minus the probability that 0 or 1 light bulbs are defective. P(X≥2)=1-P(X≤1)=1-0.1808=0.8192.
In acceptance sampling, a sample is taken from a large batch of items to determine if the entire batch should be accepted or rejected based on the number of defective items in the sample. In this problem, the probability of a light bulb being defective is given as 1%, and we are asked to find the probabilities of having 1 or less defective light bulbs or 2 or more defective light bulbs among a sample of 83 light bulbs. We can use the binomial distribution to calculate these probabilities, where X is the number of defective light bulbs in the sample. The probability of having 1 or less defective light bulbs can be calculated as the sum of the probabilities of having 0 or 1 defective light bulbs, and the probability of having 2 or more defective light bulbs can be calculated as 1 minus the probability of having 1 or less defective light bulbs.
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4. Put the steps for deriving the formula for the arc length of a circle in the correct order. Please help me with this.
The formula for the arc length of the circle is L = ( θ/360° ) 2πr
Given data ,
Let the circle be represented as A
Now , The central angle of a circle formula is as follows.
Central Angle = ( s x 360° ) / 2πr
where s is the length of the arc
r is the radius of the circle
Central Angle = 2 x Angle in other segment
Write the circumference of the circle
C = 2πr
Find the angle ratio that represents a percentage of the circle using the central angle θ
θ/360°
Multiply the angle ratio times the circumference to get the arc length
Arc Length = ( θ/360° ) 2πr
Hence , the arc length of the circle is L = ( θ/360° ) 2πr
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Use the segment addition postulate find the value of x EF= 7x+9 FG=3x+4 EG=143
Using the segment addition postulate, we can find that the value of x is 18.
Explanation: The segment addition postulate states that for three points A, B, and C on a line, if B is between A and C, then AB + BC = AC. In this case, we have three points on a line: E, F, and G, and we are given the lengths of two line segments, EF and FG. Using the segment addition postulate, we can set up the following equation:
EF + FG = EG
Substituting the given values, we get:
(7x+9) + (3x+4) = 143
Simplifying the equation, we get:
10x + 13 = 143
Subtracting 13 from both sides, we get:
10x = 130
Dividing both sides by 10, we get:
x = 13
Therefore, the value of x is 13.
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in the xy-plane, exactly how many x-intercepts does the graph of f of x equals, x times, open parenthesis, x minus 4, close parenthesis, squared, times, open parenthesis, x minus 5, close parenthesis, cubed have?
The function has three x-intercepts: x=0, x=4, and x=5. The graph of f(x) has three x-intercepts in the xy-plane.
To find the x-intercepts of a function, we need to set the value of y to zero and solve for x. In this case, the function is f(x) = x(x-4)^2(x-5)^3. To find the x-intercepts, we set f(x) = 0 and solve for x.
First, we notice that each factor is squared or cubed, which means that they cannot be negative. Therefore, we only need to consider the positive values of x.
Next, we see that the factor x will make the whole expression zero when x=0.
The factors (x-4)^2 and (x-5)^3 will make the expression zero when x=4 and x=5, respectively.
Therefore, the function has three x-intercepts: x=0, x=4, and x=5.
In conclusion, the graph of f(x) has three x-intercepts in the xy-plane. Includes the terms "parenthesis" and "squared."
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Brad and Allison have three girls. Brad tells Allison that he would like one more child because they are due to have a boy. What do you think of​ Brad's logic?
Brad's logic is flawed and does not hold any scientific basis. The gender of a child is determined by the combination of genetic factors from both parents
. Each pregnancy is an independent event, and the probability of having a boy or a girl is not influenced by the gender of the previous children. The belief that having a certain number of children of one gender increases the likelihood of having a child of the opposite gender is known as the "gamblers fallacy" or "Monte Carlo fallacy." In reality, the probability of having a boy or a girl remains approximately 50% for each pregnancy, regardless of the gender composition of the existing children.
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You are given the following information obtained from a random sample of 4 observations 25, 47, 32, 56. You want to determine whether or not the mean of the population from which this sample was taken is significantly different from 48. (Assume the population is normally distributed.) a. State the null and the alternative hypotheses b. Determine the test statistic. c. Determine the p-value; and at the 5% level of significance, test to determine whether or not the mean of the population is significantly different from 48. Give your conclusion.
Based on the given sample data, we do not have sufficient evidence to conclude that the population mean is significantly different from 48.
The null hypothesis (H0): The population mean is equal to 48.
The alternative hypothesis (Ha): The population mean is not equal to 48.
b. To determine the test statistic, we can use the t-test since the population standard deviation is unknown. The formula for the t-test statistic is:
t = (sample mean - hypothesized mean) / (sample standard deviation / √n)
Given:
Sample mean () = (25 + 47 + 32 + 56) / 4 = 40
Hypothesized mean (μ0) = 48
Sample standard deviation (s) = √[( (25 - 40)^2 + (47 - 40)^2 + (32 - 40)^2 + (56 - 40)^2) / (4 - 1)] = √[242] ≈ 15.56
Sample size (n) = 4
Substituting these values into the formula, we get:
t = (40 - 48) / (15.56 / √4) = -8 / 7.78 ≈ -1.028
c. To determine the p-value, we need to find the probability of observing a t-value as extreme or more extreme than the calculated test statistic under the null hypothesis. This can be done using a t-distribution table or statistical software.
For a two-tailed test at the 5% level of significance, we divide the significance level by 2, resulting in an alpha of 0.025. Degrees of freedom (df) = n - 1 = 4 - 1 = 3.
From the t-distribution table or software, we find that the p-value for a t-value of -1.028 with 3 degrees of freedom is approximately 0.381.
Since the p-value (0.381) is greater than the significance level (0.05), we fail to reject the null hypothesis. There is not enough evidence to suggest that the population mean is significantly different from 48 at the 5% level of significance.
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the axis of symmetry is the imaginary line that goes through the vertex of a parabola and splits it into mirrored halves. question 1 options: true false
A parabola is a symmetrical U-shaped curve that can be defined as a set of points in a plane that are equidistant from a fixed point (called the focus) and a fixed straight line (called the directrix). The axis of symmetry is always perpendicular to the directrix and passes through the focus and vertex of the parabola. In a quadratic equation, the coefficient of the x^2 term determines the direction of the opening of the parabola, and the vertex lies on the axis of symmetry.
True. The axis of symmetry is a line that passes through the vertex of a parabola and divides it into two identical halves.
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Can someone please help me answer this question, thank you in advance.
Answer:
Step-by-step explanation:
[tex]\frac{a^{3}.b^4.5^4}{b^2.5}\\ = a^3.b^2.5^3\\= 125a^3b^2[/tex]
[tex] { {a}^{3} } \times {b}^{2} \times 125[/tex]
When dividing variables with exponents, subtract the bottom exponent from the top. since there is no "a" in the denominator, we would leave it as is. The "b" at the top (numerator) has an exponent of 4, and the one in the bottom (denominator) has an exponent of 2, so we would do 4 - 2, which equals 2, so the exponent on b would be 2. Then, the exponent for 5 in the numerator is 4, and in the denominator, it's 1 (any number that with no visible exponent has an exponent of 1). 4 - 1 is 3, and 5^3 is 125.
