Answer:
The midpoint is (-2,-1)
Step-by-step explanation:
To find the x coordinate of the midpoint, add the x coordinates of the endpoint and divide by 2
( -7+3)/2 = -4/2 =-2
To find the y coordinate of the midpoint, add the y coordinates of the endpoint and divide by 2
(-6+4)/2 = -2/2 =-1
The midpoint is (-2,-1)
Good amount of points
Good answer = Brainliest
Abdsurd answer = report
Javier wants to prove that triangle MNP is similar to triangle RSP.
What missing piece of information does Javier need to prove that triangle MNP is similar to triangle RSP by the Angle-Angle Similarity Postulate?
A. Javier needs to know the measure of angle P.
B. Javier needs to know the measure of angle M.
C. Javier needs to know the measure of angle S.
D. Javier needs to know that segment MN is parallel to segment SR.
Answer:
Hello!!! Princess Sakura here ^^
Step-by-step explanation:
In triangles MNP and RSP, if there are two pairs of corresponding angles that are congruent or equal, it means that triangle MNP is similar to triangle RSP. The corresponding angles in both triangles are....
P corresponding to P
M corresponding to R
N corresponding to S
Therefore, the missing piece of information that Javier needs to prove that triangle MNP is similar to triangle RSP by the Angle-Angle Similarity Postulate is....
A. Javier needs to know the measure of angle P.
Write this expression using exponents
34
Answer: 17²
Step-by-step explanation:
Suppose Capital One is advertising a 60-month, 5.54% APR motorcycle loan. If you need to borrow $7,200 to purchase your dream Harley-Davidson, what will be your monthly payment? (Note: Be careful not to round any intermediate steps less than six decimal places.)
Your monthly payment will be $ . (Round to the nearest cent.)
Your monthly payment for the 60-month, 5.54% APR motorcycle loan to purchase your dream Harley-Davidson will be $136.88.
To calculate the monthly payment for a motorcycle loan, we can use the formula for the present value of an annuity. The formula is:
PMT = PV * r / (1 - (1 + r)^(-n))
Where:
PMT = Monthly payment
PV = Present value of the loan
r = Monthly interest rate
n = Number of months
In this case, the present value of the loan (PV) is $7,200, the monthly interest rate (r) is 5.54% divided by 12 (0.0554 / 12), and the number of months (n) is 60.
Plugging in these values into the formula, we get:
PMT = 7200 * (0.0554 / 12) / (1 - (1 + (0.0554 / 12))^(-60))
Evaluating this expression, the monthly payment comes out to be approximately $136.88.
Therefore, your monthly payment for the 60-month, 5.54% APR motorcycle loan to purchase your dream Harley-Davidson will be $136.88.
Learn more about monthly payment here:-
https://brainly.com/question/26192602
#SPJ11
1
What is the range of the following numbers?
12, 20, 18, 25,6
Data Set: 3,4,3,9,3,5,8,5 What is the interquartile range? (Offering brainliest!)
The interquartile range (IQR) is a measure of statistical dispersion, specifically the range between the first quartile (Q1) and the third quartile (Q3) in a dataset. To calculate the interquartile range for the given dataset (3, 4, 3, 9, 3, 5, 8, 5), we follow these steps:
Step 1: Arrange the dataset in ascending order: 3, 3, 3, 4, 5, 5, 8, 9.
Step 2: Calculate the median (Q2), which is the middle value of the dataset. In this case, the median is (4 + 5) / 2 = 4.5.
Step 3: Calculate the lower quartile (Q1), which is the median of the lower half of the dataset. In this case, the lower half is (3, 3, 3, 4), and the median of this subset is (3 + 3) / 2 = 3.
Step 4: Calculate the upper quartile (Q3), which is the median of the upper half of the dataset. In this case, the upper half is (5, 5, 8, 9), and the median of this subset is (5 + 8) / 2 = 6.5.
Step 5: Calculate the interquartile range (IQR) by subtracting Q1 from Q3: IQR = Q3 - Q1 = 6.5 - 3 = 3.5.
Therefore, the interquartile range for the given dataset is 3.5.
[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]
♥️ [tex]\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]
The volume of the solid obtained by rotating the region enclosed by y=x^2, x=y^2
about the line x=−7 can be computed using the method of discs or washers via an integral.
V = integral from a to b of ?
with limits of integration a = 0 and b = 1
The volume of the solid obtained by rotating the region enclosed by y=x², x=y² about the line x=−7 can be computed using the method of discs or washers via an integral.
The given region enclosed by y=x², x=y² can be represented as:
As we need to rotate the region about the line x = -7, then we need to perform the following transformation:
x = t - 7So, the region enclosed by y=x², x=y² can be represented as:
y = (t - 7)², t = y²
The limits of integration of the variable 't' will be a = 0 and b = 1
As we are using the method of cylindrical shells, then the volume of the solid obtained can be represented as:
V = 2π∫₀¹ (y)(t(y)) dy
where, (y)(t(y)) = (t - 7)²
The integral can be written as:
V = 2π∫₀¹ (t - 7)² dy
By substituting t = √y, we have the following:
dt/dy = 1/2y^(-1/2)
Therefore, the integral becomes:
V = 2π∫₀¹ (t - 7)²
dy= 2π∫₀¹ (√y - 7)²
dy= 2π∫₀¹ y - 14√y + 49
dy= 2π[(1/2)y² - (28/3)y^(3/2) + 49y] from 0 to 1
By substituting the limits of integration a = 0 and b = 1, we have:
V = 2π[(1/2) - (28/3) + 49] = 2π[97/6]
Therefore, the volume of the solid obtained is V = 97π/3 square units.
learn more about integration here
https://brainly.com/question/27419605
#SPJ11
Linda is currently working at GM as a mechanical engineer. She is taking master of architecture design program in LTU and has paid $5,000 tuition in 2022. What’s amount of deductions she can take in 2022 as unreimbursed employee education expenses? If she is a single and her modified AGI is $60,000, what’s amount of deductions she can take in 2022 as qualified tuition and related expenses under section 222? Is it deduction for AGI or from AGI?
Linda would not be able to deduct the $5,000 tuition she paid in 2022 as unreimbursed employee education expenses due to the suspension of miscellaneous itemized deductions.
However, she may be eligible for a deduction for qualified tuition and related expenses under Section 222, which allows her to deduct qualified education expenses as an adjustment to income. The amount of the deduction would depend on her MAGI and the phase-out limits applicable for the tax year.
In 2022, Linda can potentially deduct the unreimbursed employee education expenses as a miscellaneous itemized deduction. However, it's important to note that miscellaneous itemized deductions, including employee education expenses, are no longer deductible for tax years 2018 to 2025, unless they are specifically allowed under the tax code. Therefore, Linda would not be able to deduct the $5,000 tuition she paid in 2022 as unreimbursed employee education expenses.
However, there is an alternative deduction available for qualified tuition and related expenses under Section 222 of the Internal Revenue Code. This deduction allows eligible taxpayers to deduct qualified education expenses as an adjustment to income, rather than as an itemized deduction. The deduction for qualified tuition and related expenses is available whether or not the taxpayer itemizes deductions on their tax return.
To determine the amount of the deduction, we need to consider Linda's modified adjusted gross income (MAGI) and her filing status. In this case, she is single with a modified AGI of $60,000. The deduction for qualified tuition and related expenses is gradually phased out for taxpayers with MAGI between certain income thresholds.
For tax year 2022, the deduction begins to phase out at a MAGI of $65,000 for single taxpayers. The deduction is completely phased out at a MAGI of $80,000 or higher. Since Linda's MAGI is below $65,000, she would be eligible for the full deduction for qualified tuition and related expenses under Section 222.
Learn more about unreimbursed employee here:
brainly.com/question/28168184
#SPJ11
What is the quotient of -8 and -4?
Answer:
2
Step-by-step explanation:
[tex]\frac{-8}{-4} = \frac{8}{4}[/tex] [tex]\frac{8}{4}[/tex] = 8 ÷ 4 = 2I hope this helps!
Answer:
you answer is 2...
hope it helps
jason has 3 friends he gives his friends 1/4 how much does each person get
HELP ASAP
Answer: 25%
Step-by-step explanation:
Is this what you wanted if sorry.
A recipe shows that the yeast needed for a bread recipe is 2 and one-thirdounces. Which of the following decimals is equivalent to this number?
2.13
2.3
2.ModifyingAbove 3 with bar
3.2
Answer:
2.3 b
Step-by-step explanation:
i got it right
Answer:
2.3 i did quiz
Step-by-step explanation:
i know im late sorry
Sandy's 8th grade class receives $13.50 for every 5 boxes of chocolates that they sell. Which graph shows this relationship with the same unit rate?
Answer:
See Explanation
Step-by-step explanation:
Incomplete Question: This question requires options
Let the amount received be represented with y
Let the number of boxes be represented with x
From the question, we have that:
x = 5 ; y = 13.50
Multiply the values of x and y by 2Similarly,
x = 10; y = 27
This gives:
[tex](x_1,y_1) = (5,13.5)[/tex]
[tex](x_2,y_2) = (10,27)[/tex]
The slope of the graph is calculated as follows:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{27 - 13.5}{10 - 5}[/tex]
[tex]m = \frac{13.5}{5}[/tex]
[tex]m = 2.7[/tex]
The equation of the graph is calculated as follows:
[tex]y - y_1 = m(x - x_1)[/tex]
Substitute values for m, x1 and x2
[tex]y - 13.5 = 2.7 * (x - 5)[/tex]
Open Brackets
[tex]y - 13.5 = 2.7x - 13.5[/tex]
Collect Like Terms
[tex]y = 2.7x - 13.5 + 13.5[/tex]
[tex]y = 2.7x[/tex]
The above equation can be used to determine the graph
See Attachment
Lee has the following utility function: U(x, y) = (y + 1), where r and y are quantities of two consumption goods whose prices are p. and p, respectively. Lee has a budget of m. Therefore the Lee's maximization problem is x(y + 1) + X(m-P₂ - Py) 1. Write down the Lee's maximization problem and the Lagrangian function. 2. Write the first order conditions. 3. Using the first order conditions, find expressions for the demand functions y = y(Pr.P₂, m) x = x(pr. P₂, m), 4. Verify that Lee is at a maximum by checking the second order conditions. 5. The indirect utility function U=U (P., Py, m) gives the consumer's maximal attainable utility given goods prices and income. By substituting a and y into the utility function, find an expressions for the indirect utility function. 6. The expenditure function m = m (pz. P. Uo) reveals the minimum expenditure/income required to attain a specific level of utility, Uo, nt given prices, p, and Py. Rearrange the indirect utility function from question 5 in terms of m to derive an expression for the expenditure function. 7. Find Om/Op, and Om/Opy. Interpret this expression.
The expenditure function is given by the inverse of the indirect utility function, i.e., Om/Opy = -V/p2².
The given utility function is U(x, y) = (y + 1), where x and y are the amounts of two consumption goods and p1 and p2 are their respective prices.
Let Lee's budget be m.
Lee's maximization problem is:
Maximize U = y+1
Subject to m = p1x + p2y
Lee's Lagrangian function is:
L(x, y, λ) = y + 1 + λ(m - p1x - p2y)
First-order conditions:
dL/dx = -λp1
= 0
dL/dy = 1 - λp2
= 0
dL/dλ = m - p1x - p2y
= 0
Solving the above three equations, we get:
y = 1/p2
x = m/p1 - p2/p1
The second order conditions are:
d²L/dx² = -λp1 < 0
d²L/dy² = -λp2 < 0d²L/dx.
d²L/dy = 0
Therefore, Lee is at a maximum.
By substituting a and y into the utility function, the indirect utility function is derived as:
V(p1, p2, m) = m/p1 + 1/p2
The expenditure function is given by the inverse of the indirect utility function, i.e.,
m(V) = Vp1/p2 - 1/p2
Om/Op = Vp1/p2²
Om/Opy = -V/p2²
Om/Op tells us how much the required budget changes with a change in the price of the first good, while Om/Opy tells us how much the required budget changes with a change in the price of the second good.
Know more about the expenditure function
https://brainly.com/question/28954246
#SPJ11
Your hospital has just reset the safety stock level for sleeping pills to be 220 pills.
If your hospital consumes an average of 1,155 per day with a standard deviation of 81 pills, what is the chance that your hospital will run out of sleeping pills on any day? (Keep four decimal places in your answer, which should be a number not a percentage)
The chance that the hospital will run out of sleeping pills on any given day is 0.5000 (or 0.5000 with four decimal places).
To calculate the chance that the hospital will run out of sleeping pills on any given day, we can use the normal distribution and Z-score.
First, let's calculate the Z-score using the formula:
Z = (X - μ) / σ
Where:
X = consumption rate per day (1,155 pills)
μ = average consumption rate per day (1,155 pills)
σ = standard deviation (81 pills)
Z = (1,155 - 1,155) / 81
Z = 0
Now, we need to find the probability associated with this Z-score. However, since the demand for sleeping pills can be considered continuous and not discrete, we need to calculate the area under the curve from negative infinity up to the Z-score. This represents the probability of not running out of sleeping pills.
We discover that the region to the left of a Z-score of 0 is 0.5000 using a basic normal distribution table or statistical software.
To find the probability of running out of sleeping pills, we subtract this probability from 1:
Probability of running out of sleeping pills = 1 - 0.5000
Probability of running out of sleeping pills = 0.5000
Therefore, on any given day, the hospital has a 0.5000 (or 0.5000 with four decimal places) chance of running out of sleeping tablets.
Learn more about probability on:
https://brainly.com/question/23417919
I NEED HELP ASAP WELL MARK YOU BRAINLIST SHOW Your WORK PLEASE
Answer:
(12, 9, 11)Step-by-step explanation:
Given
(3*5)^4* (2*3)^5*(2*5)^7 = 2^x*3^y*5^zSolving in steps
3^4*5^4*2^5*3^5*2^7*5^7 =2^(5+7)*3^(4+5)*5^(4+7) =2^12*3^9*5^11x = 12, y= 9, z = 11 (12, 9, 11)An environmental agency is analyzing water samples from 80 lakes for pollution. Five of the lakes have dangerously high levels of dioxin. Six lakes are randomly selected from the sample. Using technology, how many ways could one polluted lake and five non-polluted lakes be chosen?
There are 658,008 ways to choose 5 non-Polluted lakes from the remaining 79 lakes.
To determine the number of ways to choose one polluted lake and five non-polluted lakes from a sample of 80 lakes, we can use the concept of combinations.
The total number of ways to choose a group of lakes from a larger set is given by the formula for combinations, which is denoted as "n choose r" and calculated as:
C(n, r) = n! / (r!(n-r)!)
Where n represents the total number of lakes and r represents the number of lakes to be chosen.
In this case, there are 80 lakes in the sample and we want to choose 1 polluted lake and 5 non-polluted lakes. Therefore, we have:
n = 80 (total number of lakes)
r = 1 (number of polluted lakes to be chosen)
Using the combination formula, we can calculate:
C(80, 1) = 80! / (1!(80-1)!)
= 80! / (1! * 79!)
= 80
So there are 80 ways to choose 1 polluted lake from the sample of 80 lakes.
Next, we want to choose 5 non-polluted lakes from the remaining 79 lakes (after choosing 1 polluted lake). Using the combination formula again:
C(79, 5) = 79! / (5!(79-5)!)
= 79! / (5! * 74!)
= 79 * 78 * 77 * 76 * 75 / (5 * 4 * 3 * 2 * 1)
= 658,008
Therefore, there are 658,008 ways to choose 5 non-polluted lakes from the remaining 79 lakes.
To find the total number of ways to choose one polluted lake and five non-polluted lakes, we multiply the number of ways for each category:
Total number of ways = 80 * 658,008
= 52,640,640
Hence, there are 52,640,640 ways to choose one polluted lake and five non-polluted lakes from the given sample of 80 lakes.
For more questions on Polluted .
https://brainly.com/question/14653613
#SPJ8
PQR, SQT and TRU are straight line. Calculate the value of X and Y. HELPPPPP !!!!! will mark as brainliest !???
Answer:
∠X = 56°, ∠Y = 118°
Step-by-step explanation:
∠X=∠SPQ [QS=PS]
∠X+∠SPQ+∠PSQ = 180°
∠X+∠X+68° = 180°
2∠X = 180° - 68°
∠X = 112° ÷ 2 = 56°
∠X = ∠TQR = 56°
∠TQR+∠QTR+∠QRT = 180°
56°+62°+∠QRT = 180°
118°+∠QRT = 180°
∠QRT = 180° - 118° = 62°
∠Y = 180° - ∠QRT
∠Y = 180° - 62° = 118°
Answer:
∠X = 56°, ∠Y = 118°
Step-by-step explanation:
Because it is the "Correct Answer"
A recent study showed that women who lived near a freeway had an unusually high rate of rheumatoid arthritis. Sarah said, "They should move away from freeways." Select the correct fallacy in Sarah's reasoning? (You may select more than one answer. Click the box with a check mark for the correct answer and double click to empty the box for the wrong answer.) Pitfall 1: Conclusions from Small Samples Pitfall 3: Conclusions from Rare Events Pitfall 4: Poor Survey Methods Pitfall 5: Assuming a Causal Link Pitfall 6: Generalization to Individuals
Sarah has made an assumption that all women who live near a freeway have rheumatoid arthritis. Sarah's assumption is an example of fallacy of Generalization to Individuals.Fallacies are mistakes or errors that occur in arguments. They're frequently used to distract or deceive the audience in order to achieve an objective.
A logical fallacy is a flaw in the reasoning used to develop an argument that renders it invalid.
Sarah's reasoning is based on a fallacy of generalization to individuals. Sarah made the mistake of generalizing from a group of people that live near a freeway to an individual's circumstance. She assumes that all women who live near a freeway will have a high incidence of rheumatoid arthritis. The fact is that the sample size was too small to draw a conclusion based on it. Pitfall 1: Conclusions from Small Samples - Occurs when the sample size used to draw conclusions is too small. Sarah made the mistake of drawing a conclusion based on a small sample of women who lived near a freeway. Pitfall 6: Generalization to Individuals - Occurs when a group's characteristics are generalized to an individual. Sarah assumed that all women who lived near a freeway would have a high incidence of rheumatoid arthritis.
Therefore, Sarah's reasoning is based on the fallacy of generalization to individuals. Her conclusion is not valid since she is using a small sample size to generalize to all women living near a freeway.
To know more about rheumatoid arthritis :
brainly.com/question/31842567
#SPJ11
Answer as soon as possible, thank you
Answer:
C.
Step-by-step explanation:
Answer:
C - Definition of Right angle.
Step-by-step explanation:
It has that square. Which is only gives in right angles
Anybody know how to solve this?? Pls lend a hand here lol !!
Steve hit eight and larry hit two
Harry bought 3 files and 5 markers for $19. 1 file and 1 marker cost $5. How much did he pay for a marker?
Answer:32
Step-by-step explanation:You have to Add to get your answer.I'll show you how I got 32:
5+3=8
8+19=27
27+5=32
Your answer is: 32
Find the distance between the two points. (-4,-1) and (-39,-121)
Answer:
The answer is 125 unitsStep-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\[/tex]
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(-4,-1) and (-39,-121)
The distance between them is
[tex]d = \sqrt{ ({ - 4 + 39})^{2} + ({ - 1 + 121})^{2} } \\ = \sqrt{ {35}^{2} + {120}^{2} } \: \: \: \: \\ = \sqrt{1225 + 14400} \\ = \sqrt{15625} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ = 125 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
We have the final answer as
125 unitsHope this helps you
what is 672x787=___?
Answer:
528864
Step-by-step explanation:
10. The sum of three consecutive integers is 45. What are the three integers?
Answer:
14, 15, 16Step-by-step explanation:
The consecutive integers iincrease by 1. So the middle integer of an odd number of consecutive integers is their mean. Three is an odd number of integers.
45:3 = 15 ← middle number
15 - 1 = 14 ← the smallest number
15 + 1 = 16 ← the largest number
A rectangle has a width of 4 and a length of 6. Find its area.
Answer:
Area = 24
Step-by-step explanation:
area = length x width
= 6 x 4 = 24
Answer :
Given -
Width (w) = 4 cm.Length (l) = 6 cm.To find -
Area of the rectangle.Solution -
As we know that, A = wl
→ 4 × 6
→ 24 cm.
Therefore, the area of the rectangle is 24 cm.
Your math teacher spends 7/20 of his day at work grading papers. His working hours are from 7 a.m. to 4
p.m. How much time does your math teacher spend grading papers each day?
Answer:
9hr
Step-by-step explanation:
cause it just its easy
Answer:
3 hours and 15 mins
Step-by-step explanation:
first you have to find out how much 7/20 of an hour is which is 21 mins
then multiply it by the amount of time he works a day which is 9 hrs
21 x 9 = 189 mins
then convert 189 mins to hrs which is 3 hrs and 15mins
1. Combine Like terms: 8x^2 + 2x^2 + 7x *
Step-by-step explanation:
8x^2 and 2x^2 are like terms
8x^2 + 2x^2 + 7x
= 10x^2 + 7x
Answer:
[tex]10x^2+7x[/tex]
Step-by-step explanation:
First let's identify the two terms: [tex]x^{2}[/tex] and [tex]x[/tex].
The equation isn't combined or simplified rather. To simplify/combine like terms, you add/subtract the identical terms together. So let's do just that.
[tex]8x^2+2x^2+7x\\10x^2+7x[/tex]
Your final answer is : [tex]10x^2+7x[/tex]
Find positive numbers x and y such that x + y = 72 and 6xy² is maximized.
To maximize the expression 6xy² under the condition x + y = 72, we can use the method of substitution to rewrite the expression in terms of a single variable and find its maximum value. Since the second derivative at x = 96 is positive, x = 96 corresponds to the maximum value.
Given that x + y = 72, we can rewrite the expression 6xy² as 6x(72 - x)². Expanding this expression yields 6x(5184 - 144x + x²). Simplifying further gives us the quadratic expression 31104x - 864x² + 6x³.
To find the maximum value of this expression, we can take its derivative with respect to x and set it equal to zero. Taking the derivative yields 31104 - 1728x + 18x². Setting this equal to zero and solving for x gives us two critical points: x = 32 and x = 96.
To determine which critical point corresponds to the maximum value, we can evaluate the second derivative of the expression. The second derivative is -1728 + 36x. Plugging in x = 32 and x = 96 into the second derivative, we find that -1728 + 36(32) = -864 and -1728 + 36(96) = 1944, respectively. Since the second derivative at x = 96 is positive, x = 96 corresponds to the maximum value.
Learn more about expression here:
https://brainly.com/question/28170201
#SPJ11
What is the value of n?
1.8 x 10^12 = (2 x 10^5) (9x10^n)
Answer:
n = log ( 1.8⋅10 ^7/ 18 x )
Step-by-step explanation:
Take the logarithm of both sides of the equation to remove the variable from the exponent.
n = log ( 1.8⋅10 ^7/ 18 x )
Hope This Helps
Sorry, I'm Late.
Please Mark Brainliest When You Can!
4 in/sec in mph w/ steps
Answer:8.9477 mph
Step-by-step explanation:To convert a meter per second measurement to a mile per hour measurement, multiply the speed by the conversion ratio. One meter per second is equal to 2.236936 miles per hour, so use this simple formula to convert:
I will give brainliest
Show work please
Answer:
n = 10Step-by-step explanation:
4^8/(4^2)^-3 ÷ 4^4 = 4^n4^8/4^-6 ÷ 4^4 = 4^n4^(8 - (-6) - 4) = 4^n4^10 = 4^n10 = nn = 10To Find :
value of nSolution :[tex] \sf \dashrightarrow \: \frac{4 {}^{8} }{(4 {}^{2} {)}^{ - 3} } \div {4}^{4} = 4 {}^{n} \\ \\ \sf \dashrightarrow \: \frac{4 {}^{8} }{ {4}^{ - 6} } \div {4}^{4} = 4 {}^{n} \\ \\ \sf \dashrightarrow \: {4}^{8 - ( - 6)} \div {4}^{4} = {4}^{n} \\ \\ \sf \dashrightarrow \: {4}^{8 + 6} \div {4}^{4} = {4}^{n} \\ \\ \sf \dashrightarrow \: {4}^{14} \div {4}^{4} = {4}^{n} \\ \\ \sf \dashrightarrow \: {4}^{14 - 4} = {4}^{n} \\ \\ \sf \dashrightarrow \: {4}^{10} = 4 {}^{n} \\ \\ \red{\boxed{ \bf \: n = 10}}[/tex]
