Answer:
the answer of the question is
104+8x
We need to simplify it. How would I do this
The simplified expression is 4(x - 3y).
What is logarithmic means ?logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = logb n. For example, 23 = 8; therefore, 3 is the logarithm of 8 to base 2, or 3 = log2 8.
Using the following logarithmic identities:
log a (bc) = log a (b) + log a (c)
log a (b/c) = log a (b) - log a (c)
We can simplify the expression as follows:
2㏒4 x - 6 log4 y = 2(㏒4) x - 6(㏒4) y
= 2(㏒4) x - 2(㏒4)3 y
= 2(㏒4)(x - 3y)
Now, we can simplify further by using the fact that ㏒4 = 2:
2(㏒4)(x - 3y) = 2(2)(x - 3y) = 4(x - 3y)
Therefore, the simplified expression is 4(x - 3y).
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The scale factor of the larger of two similar triangular prisms is 6. The surface area of the smaller prism is 36 ft2. Identify the surface area, rounded to the nearest tenth, of the larger prism
The surface area, rounded to the nearest tenth, of the larger prism is 1296 square feet.
If the scale factor of the larger prism to the smaller prism is 6, then the corresponding ratio of their surface areas is 6² or 36:1.
Scale factor is the ratio of the lengths of corresponding sides of two similar figures. It is used to determine how much larger or smaller one figure is compared to another, and it is often expressed as a fraction or a decimal.
We know that the surface area of the smaller prism is 36 ft², so we can set up the equation
x = 36 × 36
where x is the surface area of the larger prism.
Simplifying the equation
x = 1296 square feet
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Solve Triangle
Because I Need Answer My Assignment:-)
Good Perfect Complete=Brainlist
Copy Wrong Incomplete=Report
Good Luck Answer Brainly Users:-)
Answer:
x = 4√5 ≈ 8.94 (2 d.p.)
y = 8√5 ≈ 17.89 (2 d.p.)
Step-by-step explanation:
To find the values of x and y, use the Geometric Mean Theorem (Leg Rule).
Geometric Mean Theorem (Leg Rule)The altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments. The ratio of the hypotenuse to one leg is equal to the ratio of the same leg and the segment directly opposite the leg.
[tex]\boxed{\sf \dfrac{Hypotenuse}{Leg\:1}=\dfrac{Leg\:1}{Segment\;1}}\quad \sf and \quad \boxed{\sf \dfrac{Hypotenuse}{Leg\:2}=\dfrac{Leg\:2}{Segment\;2}}[/tex]
From inspection of the given right triangle RST:
Altitude = SVHypotenuse = RT = 20Leg 1 = RS = ySegment 1 = RV = 16Leg 2 = ST = xSegment 2 = VT = 4Substitute the values into the formulas:
[tex]\boxed{\dfrac{20}{y}=\dfrac{y}{16}}\quad \sf and \quad \boxed{\dfrac{20}{x}=\dfrac{x}{4}}[/tex]
Solve the equation for x:
[tex]\implies \dfrac{20}{x}=\dfrac{x}{4}[/tex]
[tex]\implies 4x \cdot \dfrac{20}{x}=4x \cdot \dfrac{x}{4}[/tex]
[tex]\implies 80=x^2[/tex]
[tex]\implies \sqrt{x^2}=\sqrt{80}[/tex]
[tex]\implies x=\sqrt{80}[/tex]
[tex]\implies x=\sqrt{4^2\cdot 5}[/tex]
[tex]\implies x=\sqrt{4^2}\sqrt{5}[/tex]
[tex]\implies x=4\sqrt{5}[/tex]
Solve the equation for y:
[tex]\implies \dfrac{20}{y}=\dfrac{y}{16}[/tex]
[tex]\implies 16y \cdot \dfrac{20}{y}=16y \cdot \dfrac{y}{16}[/tex]
[tex]\implies 320=y^2[/tex]
[tex]\implies \sqrt{y^2}=\sqrt{320}[/tex]
[tex]\implies y=\sqrt{320}[/tex]
[tex]\implies y=\sqrt{8^2\cdot 5}[/tex]
[tex]\implies y=\sqrt{8^2}\sqrt{5}[/tex]
[tex]\implies y=8\sqrt{5}[/tex]
2. Tyler leaves his house at 7:00 a.m. to go to school. He walks for 20 minutes until he reaches his school, 1 mile from his house. The function d gives the distance d(t), in miles, of Tyler from his house t minutes after 7:00 a.m. a. Explain what d(5) = 0.25 means in this context. b. On snowy days, Tyler's school has a 2 hour delayed start time (120 minutes). The function is gives Tyler's distance s(t), in miles, from home t minutes after 7:00 a.m. with a 120 minute delayed start time. If d(5) = 0.25, then what is the corresponding point on the function s? c. Write an expression for s in terms of d. A new function, n, is defined as n(t) = d(t +60) explain what this means in terms of Tyler's distance from school.
Answer: a. In this context, d(5) = 0.25 means that 5 minutes after 7:00 a.m., Tyler is 0.25 miles away from his house. This is because the function d(t) gives the distance of Tyler from his house t minutes after 7:00 a.m.
b. If d(5) = 0.25, then we know that 5 minutes after 7:00 a.m., Tyler is 0.25 miles away from his house. If there is a 120-minute delayed start time, then Tyler will walk for 20 + 120 = 140 minutes to reach his school. We want to find the corresponding point on the function s, which gives Tyler's distance from home t minutes after 7:00 a.m. with a 120-minute delayed start time. Since Tyler walks the same distance regardless of the delayed start time, we can use the same function for s as we did for d. Therefore, s(145) = 1.25, since Tyler is 1 mile away from his house after walking for 140 minutes and then an additional 5 minutes to account for the delayed start time.
c. Since Tyler walks the same distance regardless of the delayed start time, we can express s(t) in terms of d(t) by adding 120 minutes to the time t. Therefore, s(t) = d(t + 120).
d. The function n(t) = d(t + 60) gives Tyler's distance from his house t minutes after 8:00 a.m. This is because adding 60 minutes to t corresponds to adding one hour to the time, which means that Tyler leaves his house at 8:00 a.m. instead of 7:00 a.m. Therefore, n(t) gives Tyler's distance from school one hour after he leaves his house.
Step-by-step explanation:
If f(x) = 5x - 6, which of these is the inverse of f(x)?
A. f^-¹(x) = x/5 +6
B. f^-¹(x) = x/5 -6
C. f^-¹(x) = x+6/5
D. F^-¹(x) = x-6/5
To find the inverse of a function, we need to swap the positions of x and y and then solve for y. In other words, we replace f(x) with y and then solve for x.
So, let's start by swapping x and y in the function f(x) = 5x - 6:x = 5y - 6
Next, we'll solve this equation for y:
x + 6 = 5y
y = (x + 6)/5
Therefore, the inverse of f(x) is f^-1(x) = (x + 6)/5, which is option C.Any help? Please. Whoever answer it first gets brainliest!
Answer:
[tex]c + 15 > 24[/tex]
[tex]c > 9[/tex]
The additional amount will be more than $9.
Here is a bank statement.
=
$
Responsible Bank
210 2nd Street
Anytown, MH 06930
Andre Person
1729 Euclid Ave
Anytown, MH 06930
Date
2017-10-03 Previous Balance
2017-10-05 Check Number 256
2017-10-06 ATM Deposit - Cash
2017-10-10 Wire Transfer
2017-10-17 Point of Sale - Grocery Store
2017-10-25 Funds Transfer from Savings
2017-10-28 Check Number 257
2017-10-29 Online Payment - Phone Services
Description
Checking Account Statement
Page: 1 of 1
Statement Period
2017-10-01 to 2017-11-01
Withdrawals Deposits
28.50
37.91
16.43
42.00
72.50
45.00
50.00
1. If we put withdrawals and deposits in the same column, how can they be represented?
2. Andre withdraws $40 to buy a music player. What is his new balance?
3. If Andre deposits $100 in this account, will he still be in debt? How do you know?
Account No.
1120635978
Balance
39.87
11.37
56.37
18.46
2.03
52.03
10.03
-62.47
The analysis of the bank statement thus, given below. Since the result is negative, this means that Andre would still have a negative balance after depositing $100, and therefore would still be in debt.
What is bank statement analysis?1. If we put withdrawals and deposits in the same column, they can be represented as positive and negative values in a single column. Deposits would be represented with positive values, and withdrawals would be represented with negative values.
2. Andre's new balance would be $16.37. We can calculate this by subtracting $40 (the withdrawal) from his previous balance of $56.37:
$56.37 - $40 = $16.37
3. If Andre deposits $100 in this account, he will no longer be in debt. We can calculate his new balance by adding his previous balance and the deposit, and then subtracting any withdrawals:
$56.37 + $100 = $156.37 (balance after the deposit)
$156.37 - $28.50 - $37.91 - $16.43 - $42.00 - $72.50 - $45.00 - $50.00 - $10.03 - $62.47 = -$49.47
Since the result is negative, this means that Andre would still have a negative balance after depositing $100, and therefore would still be in debt.
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Walking tours at a park begin every 25 minutes and bus tours begin every 45 minutes. Both tours start at 8:00 a.m. when the park opens. When is the next time the tours will start at the same time?
The next time the walking and bus tours will start at the same time is 11:45 a.m.
What is the lcm?
The LCM is multiple which is useful if fractions need to be expressed in the same name, when the other number is multiple, LCM will have the larger number:
To find out when the walking and bus tours will start at the same time, we need to find the least common multiple (LCM) of 25 and 45, which is the smallest time interval that is a multiple of both 25 minutes and 45 minutes.
The prime factorization of 25 is 5 * 5, and the prime factorization of 45 is 3 * 3 * 5. To find the LCM, we take the highest power of each prime factor that appears in either factorization, so:
LCM = 3 * 3 * 5 * 5 = 225
Therefore, the walking and bus tours will start at the same time every 225 minutes, or 3 hours and 45 minutes. To find the next time they will start at the same time, we need to add 225 minutes to the starting time of 8:00 a.m.
8:00 a.m. + 3 hours and 45 minutes = 11:45 a.m.
Hence, the next time the walking and bus tours will start at the same time is 11:45 a.m.
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If anyone is reading this, rn i would be so flipping happy if u got this for me ive been waiting for so long and got nothing please answer correctly please
Answer: The answer is A.
Step-by-step explanation: Because I am smart don't underestimate me.
Answer:
C
Step-by-step explanation: (look at attachment)
3x + 4 = -2x -2
By looking at the y-intercepts, you automatically know the answer is C.
The y-intercept of the pink line is 4 because of 3x + 4.
The y-intercept of the blue line is -2, because of -2x - 2.
Saanvi brought a boat 13 years ago. It depreciated in value at a rate of 2.5% per year and is now worth £3115.
How much did Saanvi pay for the boat?
Saanvi paid £5329.39 for the boat 13 years ago. This is based on the assumption that the boat depreciated at a constant rate of 2.5% per year. It is important to note that there could be other factors that affect the value of the boat, such as maintenance, repairs, and upgrades, which are not accounted for in this calculation.
How to solve the question?
To find out how much Saanvi paid for the boat, we can use the concept of depreciation. Depreciation is the reduction in value of an asset over time. In this case, the boat has depreciated at a rate of 2.5% per year.
Let the initial value of the boat be 'P'. After one year, the value of the boat would be 97.5% of P. After two years, it would be 95% of P, and so on. We can write this mathematically as:
Value of the boat after n years = P x (0.975)^n
We are given that the value of the boat after 13 years is £3115. Therefore, we can write:
3115 = P x (0.975)^13
Solving this equation for P, we get:
P = 3115 / (0.975)^13
P = 5329.39
Therefore, Saanvi paid £5329.39 for the boat.
In conclusion, Saanvi paid £5329.39 for the boat 13 years ago. This is based on the assumption that the boat depreciated at a constant rate of 2.5% per year. It is important to note that there could be other factors that affect the value of the boat, such as maintenance, repairs, and upgrades, which are not accounted for in this calculation.
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5 × (10 + 7) = (5 × 10) + (5 ×7)
Answer:
Same equation just using the assocaitive property
Step-by-step explanation:
For example, 8 + (2 + 3) = (8 + 2) + 3 = 13
Hope this helps! =D
a professor at the university of florida wanted to determine if offering video tutorials for the course software would increase student engagement. the engagement ratings are below for a random sample of 5 students before and after implementing the course change. ratings were on a scale between 0 and 50. the higher scores translated to higher student engagement score. student before after 1 30 40 2 20 40 3 32 37 4 43 46 5 48 44 what is the test statistic for the wilcoxon signed rank test? group of answer choices 1
According to the information, he test statistic for this sample is 5.
How to calculate the test statistic for the Wilcoxon signed-rank test?To calculate the test statistic for the Wilcoxon signed-rank test, we need to calculate the differences between the "before" and "after" engagement ratings and rank them in order of their absolute values.
Student Before After Difference Absolute Difference Rank
1 30 40 10 10 1
2 20 40 20 20 2
3 32 37 5 5 3
4 43 46 3 3 4
5 48 44 -4 4 5
The sum of the ranks for the positive differences is 1 + 2 + 3 + 4 = 10, and the sum of the ranks for the negative differences is 5.
The smaller of the two sums (in this case, the sum of the ranks for the negative differences) is the test statistic for the Wilcoxon signed-rank test.
Therefore, the test statistic for this sample is 5.
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Find the measure of Angle A and round the answer to the nearest tenth.
(Show work if you can, thank you).
68.5 is the measure of Angle A and round the answer to the nearest tenth.
What is Trigonometry?Trigonometry is the area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangential (tan), cotangent (cot), secant (sec), & cosecant (csc) are their names, respectively.
Here we have to use the tan ratio to find the answer.
tanθ = base/perpendicular
Given: perpendicular = 19, base = 22
tan θ = 19/22
θ = tan^-1 (19/22)
tan θ = 1.2
so the angle θ is
68.5 degree
Answer: B) 68.5 degrees
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Answer:
The measure of angle A is 40.8° to the nearest tenth.
Step-by-step explanation:
The given triangle ABC is a right triangle.
We want to find the measure of angle A, and have been given the length of the sides opposite and adjacent to angle A.
The tangent ratio of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side of that angle.
Therefore, we can use the tangent trigonometric ratio to find the measure of angle A.
[tex]\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}[/tex]
Given values:
θ = angle A = xO = side BC = 19A = side AC = 22Substitute the given values into the ratio and solve for x:
[tex]\implies \tan(x)=\dfrac{19}{22}[/tex]
[tex]\implies x=\tan^{-1}\left(\dfrac{19}{22}\right)[/tex]
[tex]\implies x=40.8150838...^{\circ}[/tex]
[tex]\implies x=40.8^{\circ}\; \sf (nearest\;tenth)[/tex]
Therefore, the measure of angle A is 40.8° to the nearest tenth.
The lengths of two sides of a triangle are 5.2 inches and 3.1 inches. Which lengths, in inches, could be the length of the third side?
The length of the third side between 2.1 inches and 8.3 inches (exclusive) could be a valid length for the third side of the triangle.
Triangle Inequality Theorem:In a triangle, the length of any side must be less than the sum of the lengths of the other two sides and greater than the difference between the lengths of the other two sides.
We can apply this rule to find the possible lengths of the third side of the triangle, given that the lengths of the two sides are 5.2 inches and 3.1 inches.
Here we have
The lengths of two sides of a triangle are 5.2 inches and 3.1 inches
Let's denote the length of the third side as x. Then, we have:
3.1 + 5.2 > x > 5.2 - 3.1
8.3 > x > 2.1
Therefore, the length of the third side x must be greater than 2.1 inches and less than 8.3 inches.
We can write this as an inequality:
2.1 < x < 8.3
Therefore,
The length of the third side between 2.1 inches and 8.3 inches (exclusive) could be a valid length for the third side of the triangle.
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102, 107, 99, 102, 111, 95, 91
Mean
Mode
Median
Range
Answer:
mean: 101 (add all the numbers then divide by 7)
mode: 102 (the most frequent number in the set)
median: 102 (the number in the middle of the set)
range: 20 (the difference between the largest and smallest number)
Mean = 101
Mode = 102
Median = 102
Range = 20
MEAN: Add up all the numbers, then divide by how many numbers there are.
102 + 107 + 99 + 102 + 111 + 95 + 91 = 707
707 ÷ 7 = 101
MODE: Arrange all numbers in order from lowest to highest or highest to lowest and then count how many times each number appears in the set. The one that appears the most is the mode.
91,95,99,102,102,107,111
MEDIAN: Arrange the numbers from smallest to largest. If the amount of numbers is odd, the median is the middle number. If it is even, the median is the average of the two middle numbers in the list.
91,95,99,102,102,107,111
RANGE: Subtract the lowest number from the highest number
111 - 91 = 20
21st term: 3,8,13,18 What is the indicated term
The 21st term of the sequence 3, 8, 13, 18, .. is 103
To find the indicated term in the sequence, we first need to identify the pattern followed by the sequence. It appears that each term is obtained by adding 5 to the previous term. So, we can write the general formula for the nth term of the arithmetic sequence as
a(n) = a(1) + (n-1)d
where a(1) is the first term of the sequence, d is the common difference, and n is the term number.
In this case, we have:
a(1) = 3 (the first term)
d = 5 (the common difference)
To find the 21st term, we substitute n = 21 in the formula:
a(21) = a(1) + (21-1)d
a(21) = 3 + 20(5)
a(21) = 103
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the quality control manager at a computer manufacturing company believes that the mean life of a computer is 80 months, with a variance of 64 . if he is correct, what is the probability that the mean of a sample of 77 computers would be greater than 82.59 months? round your answer to four decimal places.
The probability that the mean of a sample of 77 computers would be greater than 82.59 months, assuming the population mean is 80 months and the variance is 64, is approximately 0.0606
The situation described can be modeled using a normal distribution, with a mean of 80 months and a standard deviation of the square root of the variance, which is 8 months (since variance = standard deviation squared).
To find the probability that the mean of a sample of 77 computers would be greater than 82.59 months, we need to standardize the sample mean using the formula
z = (x - μ) / (σ / √n)
where
x is the sample mean
μ is the population mean (believed to be 80 months)
σ is the population standard deviation (8 months)
n is the sample size (77)
Plugging in the values, we get
z = (82.59 - 80) / (8 / √77) ≈ 1.55
To find the probability of a z-score being greater than 1.55, we can use a standard normal distribution table or calculator. From the table, we find that the probability of z being greater than 1.55 is approximately 0.0606.
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Find the measures of angle a and B. Round to the
nearest degree.
The measure of angle A and B is 29° and 61° respectively
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
sin(tetha) = opp/hyp
tan(tetha) = opp/adj
cos(tetha) = adj/hyp
The opposite is 6 and the adjascent = 11
Therefore tan (tetha) = 11/6 = 1.833
tetha = tan^-1( 1.833)
= 61°( nearest degree)
The sum of angle in a triangle is 180°
therefore,
angle A = 180-( 61+90)
= 180-151
= 29°
therefore the measure of angle A and B is 29° and 61° respectively.
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A rock of radioactive material has 500 atoms in it. The number of atoms decreases at a rate of 11% a day. Write an exponential function that models this situation. f(x) type your answer... (1 choose your answer... choose your answer... ✓)^x
Answer:
[tex]f(x) = 500( {.89}^{x} )[/tex]
how many 6 card hands are there (from a standard deck) with at least 3 kings? (enter an integer without commas)
There are 73,701 different 6-card hands (from a standard deck) with at least 3 kings.
To calculate the number of 6-card hands with at least 3 K's, the problem can be divided into:
Case 1:
Exactly 3 Kings
There are 4 ways to choose 3 kings to put in the hand, then there are 48 cards left to choose the remaining 3 cards (because we used 3 cards in a 52-card deck). Therefore, the number of 6-card hands with exactly 3 kings is:
4 * (48 choose 3) = 4 * 17,296 = 69,184
Case 2:
Exactly 4 Kings
There are 4 ways to choose 4 kings to put in the hand, then there are 48 cards left to choose the remaining 2 cards. Therefore, the number of 6-card hands with exactly 4 kings is:
4 * (48 choose 2) = 4 * 1.128 = 4.512
Case 3:
Exactly 5 kings
There are 4 ways to choose the 5 kings in the hand, then there is only one card left to choose from (because we used 5 of the 52 cards in the deck of cards). Therefore, the number of 6-card hands with exactly 5 kings is:
4*1=4
Case 4:
6 cards are king
There is only one way to choose all 6 cards as king.
Therefore, the total number of 6-card hands with at least 3 kings is:
69,184 + 4,512 + 4 + 1 = 73.701
So there are 73,701 different 6-card hands with at least 3 kings.
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Maggie spent $18. 00 Of $30. 00 In her wallet which decimal represents the fraction of the $30. 00 Maggie spent
The decimal that represents the fraction of the $30.00 Maggie spent is 0.6.
Now, let's talk about decimals. Decimals are a way of expressing parts of a whole number in a fraction of 10. For example, 0.5 is the same as 1/2. In your situation, Maggie spent $18.00 out of $30.00. To figure out what decimal represents the fraction of the $30.00 Maggie spent, we need to divide the amount she spent by the total amount she had.
So, we can write this as a fraction:
$18.00 / $30.00
To turn this fraction into a decimal, we divide the numerator (top number) by the denominator (bottom number) using long division or a calculator.
$18.00 / $30.00 = 0.6
Another way to say this is that Maggie spent 60% of the money she had in her wallet.
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it is believed that 5% of all people requesting travel brochures for transatlantic cruises actually take the cruise within 1 year of the request. an experienced travel agent believes this is wrong. of 100 people requesting one of these brochures, only 3 have taken the cruise within 1 year. we want to test the travel agent's theory with a hypothesis test. if you used a significance level of 0.05, what is your decision?
Based on the given information, we can set up the following hypotheses for the hypothesis test:
Null Hypothesis (H0): The actual proportion of people taking the cruise within 1 year is equal to the believed proportion of 5%.
Alternative Hypothesis (H1): The actual proportion of people taking the cruise within 1 year is not equal to the believed proportion of 5%.
Let p be the proportion of people taking the cruise within 1 year. We can use the sample proportion, denoted as p-hat, which is calculated as the ratio of the number of people who took the cruise within 1 year (3 in this case) to the total number of people who requested the brochures (100 in this case).
Given that the significance level is 0.05, we can use a z-test to compare the sample proportion with the believed proportion of 5%. The z-test statistic is calculated as:
z = (p-hat - p) / sqrt(p * (1 - p) / n)
where n is the sample size, which is 100 in this case.
Now we can calculate the z-test statistic and compare it with the critical value for a two-tailed test at a significance level of 0.05. If the calculated z-test statistic falls outside the critical value, we would reject the null hypothesis; otherwise, we would fail to reject the null hypothesis.
Since the sample proportion p-hat is 3/100 = 0.03, and the believed proportion p is 0.05, we can substitute these values into the z-test formula:
z = (0.03 - 0.05) / sqrt(0.05 * (1 - 0.05) / 100)
Calculating the above expression, we get the value of z. We can then compare this value with the critical value for a two-tailed test at a significance level of 0.05 from a standard normal distribution table or using a statistical calculator.
If the calculated z-test statistic falls outside the critical value, we would reject the null hypothesis and conclude that the actual proportion of people taking the cruise within 1 year is different from the believed proportion of 5%. If the calculated z-test statistic falls within the critical value, we would fail to reject the null hypothesis and not conclude that the actual proportion is different from the believed proportion.
Without the actual values of the calculated z-test statistic and the critical value, we cannot provide a specific decision for this hypothesis test. Please note that hypothesis testing requires careful consideration of the sample size, significance level, and other relevant factors, and should be conducted with caution and in consultation with a qualified statistician or expert in statistical analysis.
Number 7. I don’t understand, what’s the fraction? How do you get fraction and the + a number.
Answer:
A
Step-by-step explanation:
Equation of a line is: y = mx + b where m = slope b = y axis intercept
To find the slope between any two of the given points :
say 18, 100 and 27, 85
m = slope = (y1-y2) / (x1-x2) = (85-100) / ( 27-18) = -15/12 = -5/3
so now you have
y = - 5/3 x + b we still need to find the value of b
use any point to calculate b
say 15, 106
106 = - 5/3 (15) + b
b = ~ 131
the equation is then y = - 5/3 x + 131 closest to answer 'A'
Quadrilateral ABCD has vertices A = (2, 5), B = (2, 2), C = (4, 3) and D = (4, 6). Quadrilateral A'B'C'D' is formed when Quadrilateral ABCD is dilated by a scale factor of 2. Which statement is true? Select all that apply
Choose all that apply:
A) None of the answers apply
B) The angles of Quadrilateral ABCD and Quadrilateral A'B'C'D' are the same.
C) The side lengths of Quadrilateral ABCD and Quadrilateral A'B'C'D' are the same.
The statement which is true for the quadrilateral is B.
How to determine which statements are true for the quadrilateral?To dilate a figure by a scale factor of 2, each point of the original figure is multiplied by 2.
So the coordinates of each vertex of A'B'C'D' are twice the coordinates of the corresponding vertex of ABCD.
The coordinates of A' are (4,10), B' are (4,4), C' are (8,6), and D' are (8,12).
To determine which statements are true, we can compare the angles and side lengths of the two quadrilaterals:
A) None of the answers apply. This may be a valid answer, but we should check the other options before concluding that none of them apply.
B) The angles of Quadrilateral ABCD and Quadrilateral A'B'C'D' are the same. This is true because dilation does not change angles. The corresponding angles of the two quadrilaterals are congruent.
C) The side lengths of Quadrilateral ABCD and Quadrilateral A'B'C'D' are not the same. We can see this by calculating the length of each side of both quadrilaterals.
Therefore, the correct answer is B.
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what are the first four terms if a1=2 and an= an-1 +3?
The first four terms of the sequence are a₁ = 2, a₂ = 5, a₃ = 8, a₄ = 11.
What is arithmetic progression?The difference between every two successive terms in a sequence is the same; this is known as an arithmetic progression (AP). A good example of an arithmetic progression (AP) is the series 2, 6, 10, 14,..., which follows a pattern in which each number is created by adding 4 to the previous term.
The given sequence is defined as a₁=2 and aₙ= aₙ₋₁ + 3 for n > 1.
To find the first four terms of the sequence, we can use the recursive formula repeatedly:
a₁ = 2 (given)
a₂ = a₁ + 3 = 2 + 3 = 5
a₃ = a₂ + 3 = 5 + 3 = 8
a₄ = a₃ + 3 = 8 + 3 = 11
Therefore, the first four terms of the sequence are a₁ = 2, a₂ = 5, a₃ = 8, a₄ = 11.
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Two 5-year old girls, Alyse and Jocelyn, have been training to run a 1 mile race. Alyse’s 1 mile time A is approximately Normally distributed with a mean of 13. 5 minutes and a standard deviation of 2. 5 minutes.
Jocelyn’s 1 mile time J is approximately Normally distributed with a mean of 12 minutes and a standard deviation of 1. 5 minutes.
Assuming A and J are independent random variables, what is the probability that
Alyse has a smaller time than Jocelyn in a 1 mile race on a randomly selected day?
I'm more so looking for an explanation on how to find the answer, thanks :)
The probability that Alyse has a smaller time than Jocelyn in a 1 mile race on a randomly selected day is approximately 0.2676
To find the probability that Alyse has a smaller time than Jocelyn in a 1 mile race on a randomly selected day, we need to compare the distribution of their running times.
Let X be the running time of Alyse and Y be the running time of Jocelyn. Then, we have
X ~ N(13.5, 2.5^2)
Y ~ N(12, 1.5^2)
We want to find P(X < Y). We can start by standardizing the variables:
Zx = (X - 13.5) / 2.5
Zy = (Y - 12) / 1.5
Then, we have
P(X < Y) = P(X - Y < 0)
Substituting the standardized variables, we get
P(X - Y < 0) = P((Zx - Zy) < (0 - (13.5-12)/sqrt(2.5^2 + 1.5^2)))
Using the standard Normal distribution table or calculator, we find that the probability of Zx - Zy being less than -0.624 is approximately 0.2676.
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which combination of factors would definitely cause the confidence interval to become wider? group of answer choices none of these will definitely reduce the width of a confidence interval. use a smaller sample and decrease the level of confidence use a larger sample and increase the level of confidence use a larger sample and decrease the level of confidence use a smaller sample and increase the level of confidence
To reduce the width of a confidence interval, you can use a smaller sample size and decrease the level of confidence, or use a larger sample size and decrease the level of confidence.
What are the factors?
what are factorsIn mathematics, a factor is a number that divides another number without leaving a remainder.
The combination of factors that would definitely cause the confidence interval to become wider is to use a larger sample and increase the level of confidence or to use a smaller sample and increase the level of confidence.
When using a larger sample size, the standard error of the mean decreases, and the interval will become narrower. Conversely, when using a smaller sample size, the standard error of the mean increases, and the interval will become wider. However, increasing the level of confidence will also increase the width of the interval as a wider interval is required to capture the true population parameter with a higher level of confidence.
Therefore, to reduce the width of a confidence interval, you can use a smaller sample size and decrease the level of confidence, or use a larger sample size and decrease the level of confidence.
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what is the sales tax rate on an $8.50 purchase if the sales-tax rate is 6[tex]\frac{x}{y} 1/2[/tex]%
The sales tax rate is 6%
what is the sales tax rate on an $8.50 purchase if the sales-tax rate is 6x/y1/2%?If the sales-tax rate is 6%, the tax paid on an $8.50 purchase would be:
Tax = 0.06 x $8.50
Tax = $0.51
Therefore, the total cost of the purchase including sales tax would be:
Total cost = $8.50 + $0.51
Total cost = $9.01
The sales tax rate is 6%.
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find the smallest which 108 must be multiplied to get a perfect square
Answer:
The answer is 3
Step-by-step explanation:
x×108=y
x×2²×3³=y
3×108=324
mike pain 12$ for 1 pizza. if he bought 4 pizzas, what would be an equivalent ratio of dollars to pizza
The equivalent ratio of dollars to pizza for 4 pizzas is 12 : 1.
What is ratio?A ratio is a comparison of two or more quantities that are related to each other in some way. It is expressed as a fraction or using the "colon" notation.
According to given information:If Mike pays 12 dollars for one pizza, the ratio of dollars to pizza is:
12 : 1
To find the equivalent ratio for 4 pizzas, we need to keep the ratio of dollars to pizza constant. We can do this by multiplying both the numerator and denominator of the ratio by 4, since we are now dealing with 4 pizzas instead of 1. This gives us:
12 x 4 : 1 x 4
Simplifying this ratio gives us:
48 : 4
We can further simplify this ratio by dividing both the numerator and denominator by 4, which gives us:
12 : 1
Therefore, the equivalent ratio of dollars to pizza for 4 pizzas is 12 : 1.
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