The population of Lcavetown is 123,000 people, and is decreasing at a rate of 9,4% per year What will the population of Leavetown be 100 years from now? (round to the nearest person)
Answers
Answer:
6
Step-by-step explanation:
You want the population of Leavetown in 100 years if it is 123,000 now and decreasing at the rate of 9.4% per year.
Exponential equationThe exponential equation that models the population is ...
p = 1230000·(1 -0.094)^t
where t is the number of years later.
ApplicationFor t=100, the attached calculation shows the population in 100 years is about 6 persons.
Related Questions
Hint(s) Check My Work A 2018 Pew Research Center survey found that more Americans believe they could give up their televisions than could give up their cell phones (Pew Research website). Assume that the following table represents the joint probabilities of Americans who could give up their television of cell phone. Excel File: data04-37.xlsx Could Give Up Television Yes No Could Give Up Yes 0.31 0.17 0.48 Cellphone No 0.38 0.14 0.52 0.69 0.31 a. What is the probability that a person could give up her cell phone (to 2 decimals)? that b. What is the probability that a person who could give up her cell phone could also give up television (to 2 decimals)? c. What is the probability that a person who could not give up her ell phone could give up television (to 2 decimals)? d. Is the probability a person could give up television higher if the person could not give up a cell phone or if the person could give up a cell phone? The probably a person could give up television if they could not give up a celone is Select your answer than the probability a person could give up television if they could give up a cellphone
Answers
a. The probability that a person could give up her cell phone would be 0.69.
b. Probability that a person who could give up her cell phone could also give up television would be 0.45
c. The probability that a person who could not give up her ell phone could give up television would be 0.55.
d. Probability of giving up television is higher for people who could not give up their cell phone than for those who could give up their cell phone.
What is probability?
Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.
a. The probability that a person could give up their cell phone is the sum of the probabilities in the "Could Give Up" column: 0.31 + 0.38 = 0.69.
Therefore, The probability that a person could give up her cell phone would be 0.69.
b. The probability that a person who could give up their cell phone could also give up television is the conditional probability of "Could Give Up Television" given "Could Give Up Cellphone." This is calculated by dividing the joint probability of "Could Give Up Television" and "Could Give Up Cellphone" (0.31) by the probability of "Could Give Up Cellphone" (0.69): 0.31 / 0.69 = 0.4493 or approximately 0.45.
c. The probability that a person who could not give up their cell phone could give up television is the conditional probability of "Could Give Up Television" given "Could Not Give Up Cellphone." This is calculated by dividing the joint probability of "Could Give Up Television" and "Could Not Give Up Cellphone" (0.17) by the probability of "Could Not Give Up Cellphone" (0.31): 0.17 / 0.31 = 0.5484 or approximately 0.55.
d. To compare the probabilities of giving up television for people who could or could not give up their cell phone, we need to calculate the conditional probabilities of "Could Give Up Television" given "Could Give Up Cellphone" and "Could Give Up Television" given "Could Not Give Up Cellphone" respectively.
Probability of giving up television if one could give up a cell phone: 0.31 / 0.69 = 0.4493 or approximately 0.45.
Probability of giving up television if one could not give up a cell phone: 0.17 / 0.31 = 0.5484 or approximately 0.55.
The probability of giving up television is higher for people who could not give up their cell phone than for those who could give up their cell phone.
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A machine must produce a bearing that is within 0.02 inches of the correct diameter 4.1 inches. using x as the diameter of the bearing, write this statement using absolute value notation.____ ___ Preview
Answers
A machine must produce a bearing that is within 0.02 inches of the correct diameter 4.1 inches. By writing this statement using absolute value notation is:
| x - 4.1 | ≤ 0.02
This notation expresses the requirement that the diameter of the bearing, represented by x, must be within 0.02 inches of the correct diameter of 4.1 inches. The absolute value of the difference between x and 4.1 must be less than or equal to 0.02 for the bearing to meet the specification.
The absolute value function is used to ensure that the difference between x and 4.1 is always positive, regardless of whether x is greater than or less than 4.1. This is important because the requirement is concerned with the magnitude of the difference, rather than its sign. If the absolute value of the difference is less than or equal to 0.02, then the diameter of the bearing is considered to be within the required tolerance.
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A scientist is studying wildlife. She estimates the population of bats in her state to be 345,000. She predicts the population to grow at an average annual rate of 1.2%. Using the scientist’s prediction, create an equation that models the population of bats, y, after x years.
y=345,000(0.012)^x
y=345,000(0.988)^x
y=345,000(1.012)^x
y=345,000(1.2)^x
Answers
Answer:
Step-by-step explanation:
The equation that models the population of bats, y, after x years can be found using the formula:
y = P(1 + r)^x
where P is the initial population, r is the annual growth rate as a decimal, and x is the number of years.
In this case, the initial population P is 345,000, the annual growth rate r is 1.2% or 0.012 as a decimal, and x is the number of years. Substituting these values into the formula, we get:
y = 345,000(1 + 0.012)^x
Simplifying the expression in the parentheses, we get:
y = 345,000(1.012)^x
Therefore, the equation that models the population of bats, y, after x years is:
y = 345,000(1.012)^x
Step-by-step explanation:
the other answer is correct.
I just want to point out some mechanism used here :
the increase by 1.2%
an increase by x% means adding x% to the original 100%.
so, we end up with (100 + x)%.
"%" just stands for 1/100.
so, if y = 100%, an increase by x% is
y×(100 + x)/100 = y×(1 + x/100)
in our case here that is
345,000 × (1 + 0.012) = 345,000 × 1.012
and since the increase rate of 1.2% applies per year, we multiply the end population of every year by 1.012 for the following year.
so, each year a new factor of 1.012 is being integrated into the calculation.
it goes then
345,000×1.012×1.012×1.012×...×1.012 x times after x years.
and we get
y = 345,000 × (1.012)^x
-3 (3b + 6) = 36 - 3b
Answers
Answer:
b = -9
Step-by-step explanation:
-3 (3b + 6) = 36 - 3b
-9b - 18 = 36 - 3b
-6b - 18 = 36
-6b = 54
b = -9
Let's check
-3(3(-9) + 6) = 36 - 3(-9)
-3( -27 + 6) = 36 + 27
-3( -21) = 63
63 = 63
So, b = -9 is the correct answer.
Step-by-step explanation:
-3(3b+6)=36-3b
-9b-18=36-3b
-9b+3b=36+18
-6b=54
divide both sides by -6
b= -9
Country Day's scholarship fund receives a gift of $ 165000. The money is invested in stocks, bonds, and CDs. CDs pay 3.75 % interest, bonds pay 5.2 % interest, and stocks pay 7 % interest. Country day invests $ 75000 more in bonds than in CDs. If the annual income from the investments is $ 9442.5 , how much was invested in each vehicle?
Answers
Invested in each vehicle is $40,000 if the annual investment income is $944.25.
What is meant by interest?The sum that must be repaid for a loan or the sum that is collected in exchange for a loan is known as interest. Principal is the term used to describe borrowed or lent funds. The total of the principal plus interest is referred to as the Amount. Rate of Interest refers to the amount at which interest is calculated on the principal. A percentage of the principle is how interest is most commonly computed. For instance, if you agreed to borrow $100 from a friend with 5% interest and repay it over time, the interest you would have to pay would simply be 5% of $100, or $5.Let
CD's = x
Bonds = x + 60000
Stocks = y
x + x + 60000 + y = 140000 ----> 2x + y = 80000 .......(1)
Using I = Prt; t = 1; I = Pr
2x + 3.7(x + 60000) + 11.1y = 7800(100× ) × Since I used an exact proportion, the opposite side needs to be multiplied by 100.
5.7x + 11.1y = 558000 .......(2)
Either elimination or substitution;
x = 20000 y = 40000
So CD's = 20000, Bonds = 80000, Stocks = 40000
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find the number of ordered triples (a,b,c) where a , b , and c are positive integers, a is a factor of b , a is a factor of c , and a b c
Answers
The number of ordered triples (a, b, c) where a, b, and c are positive integers and a is a factor of b, a is a factor of c, and abc=N, is 64.
To find the ordered triplets, Firstly Factorize N into its prime factors.For each prime factor. we can choose its exponent as the value of a, b, and c. The total number of ordered triples (a, b, c) is (number of exponents + 1)^3.
let N = 24. The prime factorization of 24 is 2^3 * 3^1.
The number of possible values of a is 4 (from 0 to 3), so the number of possible values of b and c is also 4.
The number of ordered triples is 4^3 = 64.
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Suppose Kala places $9500 in an account that pays 15% interest compounded each year. Assume that no withdrawals are made from the account. find the ampunt for one year
Answers
A = P * (1 + r/n)^(nt)
where:
A = the amount in the account after t years
P = the principal amount (9500)
r = the interest rate as a decimal (0.15)
n = the number of times the interest is compounded per year (1 in this case, since it's compounded once a year)
t = the number of years (1)
Plugging in the values:
A = 9500 * (1 + 0.15/1)^(1 * 1)
A = 9500 * 1.15
A = 10,925
So after one year, the amount in the account would be $10,925.
Students in a statistics class took their first test. The following are the scores they earned. Create a frequency distribution using Class Boundaries. Use 5 classes and the minimum data value for the lowest class limit. Then create a histogram and describe the shape of the distribution. 92 92 93 90 92 99 97 90 93 91 82 85 87 83 89 82 89 87 75 70 73 76 60 61 55 X quantitatve variable(s), the correct graph to make a) Since data were collected for 2 v is a histogram b) The class width is: class width = 9 Complete the frequency/relative frequency table using the given class width. Round relative frequencies to 3 decimal places. Class Boundaries Frequency Relative Frequency 54.5 - 63.5 72.5 olan 81.5 90.5
Answers
The shape of this histogram is skewed to the right since the highest frequency is found in the first class, and the frequencies decrease as the numbers increase.
The class width, also known as the class interval, is the difference between the upper and lower boundaries of a class. In this frequency distribution, the class width is 9 since the lower boundary of the first class is 54.5 and the upper boundary of the last class is 90.5. We can calculate the frequency of each class by counting how many numbers fall within the class boundaries. For example, the first class has 72 observations since there are 72 numbers that fall between 54.5 and 63.5. To calculate the relative frequency of each class, we divide the frequency of each class by the total frequency. For example, the relative frequency of the first class is 0.312 since 72/231 = 0.312. Once the frequencies and relative frequencies have been calculated, a histogram can be made to represent the data. The shape of this histogram is skewed to the right since the highest frequency is found in the first class, and the frequencies decrease as the numbers increase.
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Let V be the space of all infinite sequences of real num- bers. See Example 5. Which of the subsets of V given in Exercises 12 through 15 are subspaces of V? 12. The arithmetic sequences [i.e. sequences of the form (a,a + k;a + 2k,u 3k for some constants CL and k]
Answers
Yes , the arithmetic sequence ( written as sequences of the form (a , a+k , a+2k , a+3k for some constants a and k ) is a subspace of V .
To determine whether subsets of V in the arithmetic sequences are subspaces of V, we check if they satisfy the three conditions for a subset to be a subspace:
(i) The subset must contain the zero vector.
(ii) The subset must be closed under vector addition.
(iii) The subset must be closed under scalar multiplication.
Let S be a subset of V consisting of arithmetic sequences.
Now we check the three conditions :
(i) We find an arithmetic sequence in S that has all its terms equal to zero. The only arithmetic sequence that satisfies this is the sequence (0, 0, 0, 0, ...), which is in S.
So , the subset "S" contains zero vector.
(ii) Next we need to show that if u and v are two arithmetic sequences in S, then their sum "u + v" is also an arithmetic sequence in S.
Let U = (a, a+k, a+2k, a+3k, ...) and V = (b, b+l, b+2l, b+3l, ...) be two arithmetic sequences in S.
Then, their sum is ⇒ u+v = (a+b, a+k+b+l, a+2k+b+2l, a+3k+b+3l, ...).
This is also an arithmetic sequence,
So , subset "S" is closed under vector addition.
(iii) Next , we show that if U is an arithmetic sequence in S and C is a scalar, then CU is also an arithmetic sequence in S.
Let U = (a, a+k, a+2k, a+3k, ...) be an arithmetic sequence in S, and let c be a scalar.
we get , CU = (ca, ca+ck, ca+2ck, ca+3ck, ...) is also an arithmetic sequence,
So , subset "S" is closed under scalar multiplication.
we see that , S satisfies all three conditions, it is a subspace of V.
Therefore, any subset of V consisting of arithmetic sequences is a subspace of V.
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The given question is incomplete , the complete question is
Let V be the space of all infinite sequences of real numbers , Which of the subsets of V in The arithmetic sequences [i.e. sequences of the form (a , a+k , a+2k , a+3k for some constants a and k] are subspaces of V ?
Apply the square root principle to solve (x – 3)2 + 9 = 0.
a. x = 3 + 3i, 3 – 3i
b. x = 0, –6
c. x = 0, 6
d. x = –3 + 3i, –3 – 3i
Answers
Answer:
Step-by-step explanation:
First, let's simplify the equation:
(x – 3)² + 9 = 0
(x – 3)² = -9
Now we can apply the square root principle:
x – 3 = ±√(-9)
x – 3 = ±3i
Solving for x:
x = 3 ± 3i
Therefore, the answer is (a) x = 3 + 3i, 3 – 3i.
Respond to the following discussion prompt.
Jason uses his credit card for all his monthly expenses. He pays only the minimum payment required every month. The credit card company charges him interest that is compounded monthly and a penalty for a missed payment. Based on how principal and interest compound over time, is he doing the right thing by making the minimum payment? Justify your answer.
Answers
it is not advisable to make only the minimum payment on a credit card if Jason wants to minimize the amount of interest he has to pay and pay off his debt faster.
What is Credit card?A credit card is a payment card issued to users to enable the cardholder to pay a merchant for goods and services based on the cardholder's accrued debt.
Jason may not be doing the right thing by making only the minimum payment on his credit card, depending on the interest rate and penalty charges.
When a credit card holder makes only the minimum payment, the remaining balance accrues interest, which is added to the principal amount.
This means that the total amount owed on the credit card increases every month, even if no additional purchases are made.
The interest rate charged by the credit card company can significantly impact how much Jason ends up paying over time.
Hence, it is not advisable to make only the minimum payment on a credit card if Jason wants to minimize the amount of interest he has to pay and pay off his debt faster.
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MATH QUESTION <3 PLEASE HELP
Answers
The angle that the flagpole makes with the ground is 20°.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
We have,
Flagpole height = 16 feet
From figure B,
The angle of elevation has increased this means,
The flagpole is leaning.
Now,
The angle that the flagpole makes with the ground.
Cos m = 15/16
Cos m = 0.9375
m = [tex]cos^{-1}[/tex] 0.9375
m = 20.36
m = 20°
Thus,
The angle that the flagpole makes with the ground is 20°.
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6. Tyler went to the gym on 22 of the last 31 days. Which of the following is closest to the
percent of days that Tyler went to the gym?
(1) 66%
(3) 70%
(2) 67%
(4) 71%
Answers
Answer:
71%
Step-by-step explanation:
We know
Tyler went to the gym on 22 of the last 31 days.
Which of the following is closest to the percentage of days that Tyler went to the gym?
We take
22 divided by 31, times 100 = 71%
So, the answer is 71%
Tamika leans a 30-foot ladder against a wall so that it forms an angle of 65∘ with the ground. How high up the wall does the ladder reach? Round your answer to the nearest hundredth of a foot if necessary.
Answers
Answer:
64.34 feet.
Step-by-step explanation:
To solve this problem, we can use trigonometric ratios, specifically the tangent ratio.
Let's denote the height up the wall that the ladder reaches as "h". We can then set up the following equation:
tan(65°) = h/30
To solve for h, we can multiply both sides by 30:
30 tan(65°) = h
Using a calculator, we can find that tan(65°) is approximately 2.1445. Multiplying this by 30 gives us:
h ≈ 64.34 feet
Therefore, the ladder reaches approximately 64.34 feet up the wall. Rounded to the nearest hundredth of a foot, the answer is 64.34 feet.
A bacteria population starts at 2,032 and decreases at about 15% per day. Write a function representing the number of bacteria present each day. Graph the function. After how many days will there be fewer than 321 bacteria?
Answers
The function representing the number of bacteria present each day is f(t) = 2032[tex](0.85)^{t}[/tex].
What is meant by function?Numbers, formulae, and related structures, shapes, and the spaces they occupy are all issues in the field of mathematics, as are quantities and their variations. f(x) = x2 is a prime example of a straightforward function. The function in this equation is called f(x), and it squares the value of "x". Assume that f(3) = 9 if, for example, x = 3. Several other functions include f(x) = sin x, f(x) = x2 + 3, f(x) = 1/x, f(x) = 2x + 3, etc.Each element of X receives the exact same number of elements from Y when a function from one set to the other is used.Both the set X and the set Y are referred to as the function's domain and codomain, respectively.
Beginning in 2032, there will be a 15% daily decline in the number of microorganisms.
a function that displays the daily average amount of microorganisms.
f(x) = 2032[tex](1 - .15)^{t}[/tex]
f(x) = 2032[tex](0.85)^{t}[/tex]
Therefore f(t) = 2032[tex]0.85^{t}[/tex] is the correct answer.
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Let X1, X2, X3,.......Xn denote a random sample from the uniform distribution on the interval a:X-1/2 and b:Xn-n/n+1 find the efficiency of a and b
Answers
The efficiency of the a and b from the uniform distribution on the interval a:X-1/2 and b:Xn-n/n+1 is x.
The probability distribution known as the uniform distribution comes in two varieties: the discrete case and the continuous case. Both types of uniform distributions, as their names imply, have constant or uniform probabilities for all possible values of the random variable.
The random sample X1,X2,....,Xn is taken from the uniform distribution on the interval (0,θ).
δlog(L(x,θ))/δθ = -n/θ + ∑(xt)/θ² = 0
n/θ = ∑(xt) /θ²
θ = x
Now derivate it again with respect to θ,
∂²log(L(x;θ)) / ∂θ²
=nθ²−2∑t(xt) / θ³<0
Since, the second derivative is less than 0, ^θ is maximum likelihood estimate of θ.
Therefore, the maximum likelihood estimate of θ is ¯x.
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the box-and-whisker plot shows the number of times students bought lunch in a given month at the school cafeteria. a box and whisker plot with minimum 4, first quartile 11, median 14, third quartile 16, and maximum 20 what is the interquartile range of the data? provide your answer below:
Answers
The interquartile range of the data is
The interquartile range (IQR) is a measure of variability in a dataset that is calculated as the difference between the third quartile (Q3) and the first quartile (Q1).
The IQR is the range of the middle 50% of the data, and it provides a measure of the spread of the central part of the distribution.
From the given information, we have:
Minimum value = 4
Q1 = 11
Median = 14
Q3 = 16
Maximum value = 20
To find the IQR, we subtract Q1 from Q3:
IQR = Q3 - Q1 = 16 - 11 = 5
Therefore, the interquartile range of the data is 5.
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please help me !!!!!
Answers
Answer:28
Step-by-step explanation: because add z and x
MTH 115 Lesson 8 Practice Problems
Answer Key
1. A credit card charges 23% APR and a minimum of 2.5%. If you pay the minimum on a balance of $450 what would the decrease in your balance be? Round to the nearest cent $2.63.
2. A month has 30 days in it. You post a payment of $600 on the 15th of the month. The Balance was $2000 before the payment. What is the interest on the average daily balance if the APR is 23%? $32.58
3. The monthly payment on a house loan is $876. The purchase price of the house was $125,000. If you pay this for 30 years how much interest did you pay? $190,360
4. A house costs $275,000. The rate is 7.3% with monthly payments for 30 years. What is the payment? Round to the nearest dollar. $1885
Answers
A is the answer
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On Monday, he made 7 cakes. On Lionel makes cakes for the bake sale.
On Monday, he made 7 cakes. On Tuesday, he works an additional 2 hours and has a total of 13 cakes.
Determine how many cakes he makes in one hour. Tuesday, he works an additional 2 hours and has a total of 13 cakes.
Determine how many cakes he makes in one hour.
Answers
To determine how many cakes Lionel makes in one hour, we can use the following formula:
cakes per hour = total cakes / total hours worked
On Monday, Lionel made 7 cakes in some number of hours, so we don't know how many cakes he made per hour that day. However, on Tuesday, he made an additional 6 cakes (13 total cakes - 7 cakes made on Monday), and he worked for 2 hours longer than he did on Monday. Therefore:
cakes per hour on Tuesday = 6 cakes / 2 hours = 3 cakes per hour
So Lionel made 3 cakes per hour on Tuesday. We don't have enough information to determine how many cakes he made per hour on Monday.
Identify the Property Below:
ab² • 0 = 0 ______
(7 + 5) + 1 = 7 + (5 + 1) _____
6 = 6 ____
7(x-3) = 7x - 21 ______
x + (-x) = 0 ___
if y = 3, then 3 = y ___
if x = -1, and -1 = z, then x = z ____
4x • 1 = 4x ____
(a+b) + 0 = (a+b) ____
3 • 1/3 = 1 ___
Answers
The properties are listed below.
What is properties of multiplication and addition?Properties of addition and multiplication are defined for the various conditions and rules of addition and multiplication. The properties are:
Commutative propertyAssociative Property Distributive Property Identity Propertyab² • 0 = 0The product between any number and this one is zero. This comes from the existence of zero, which states that there must exist a value that represents nothingness, the zero.
(7 + 5) + 1 = 7 + (5 + 1)This is the associative property of addition,
6 = 6This is the reflexive property of equality, which says that every number is equal to itself.
7(x-3) = 7x - 21This is the distributive property of addition which says ,
C*(A + B) = C*A + C*B
x + (-x) = 0This is the inverse property of addition, this property says that for any real number x there exists a real number -x such that x+(-x)=0.
if y = 3, then 3 = yThis is the symmetric property.
if x = -1, and -1 = z, then x = zThis is the transitive property, we can apply it in the next way
then x = z
4x • 1 = 4xThis is the identity property of multiplication.
(a+b) + 0 = (a+b)This is identity property of addition is that when a number n is added to zero, the result is the number itself i.e. n + 0 = n.
3 • 1/3 = 1This is inverse property of multiplication. It states that if you multiply a number by its reciprocal, also called the multiplicative inverse, the product will be 1
Hence, the properties are identified.
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Please solve quickly! Within 30 minutes would be great!
Please solve for the variable indicated.
A=1/2h(b+B), solve for b
If you could break it down step by step that would be super helpful! I’m very confused. Thank you!
Answers
Answer:
Solve for B:
[tex]B = -b+\frac{5A}{6h}[/tex]
Step-by-step explanation:
[tex]A=1.2h(b+B)[/tex]
Use the distributive property to multiply [tex]1.2h by b+B[/tex]
[tex]A=1.2hb+1.2hB[/tex]
Swap sides so that all variable terms are on the left hand side.
[tex]1.2hb+1.2hB=A[/tex]
Subtract [tex]1.2hb[/tex] from both sides.
[tex]1.2hB= A - 1.2hb[/tex]
The equation is in standard form.
[tex]\frac{6h}{5} B=-\frac{6bh}{5} +A[/tex]
Divide both sides by [tex]1.2h[/tex].
[tex]\frac{5*(\frac{6h}{5})B }{6h} =\frac{5(-\frac{6bh}{5}+A) }{6h}[/tex]
Dividing by [tex]1.2h[/tex] undoes the multiplication by [tex]1.2h[/tex].
[tex]B = \frac{5(-\frac{6bh}{5}+A) }{6h}[/tex]
Divide [tex]A - \frac{6hb}{5}[/tex] by [tex]1.2h[/tex].
[tex]B = -b+\frac{5A}{6h}[/tex]
Solve For B:
[tex]B = -b+\frac{5A}{6h}[/tex]
If the area of square 2 is 64 units^2 and the area of square 3 is 36 units^2,find the area and the side length of square 1.
Answers
area of square 1 is 28 square units and its side length is[tex]$2\sqrt{7}$[/tex] units.
How to find the area and length of square?Let the side length of square 1 be x units. Then the areas of squares 1, 2, and 3 are [tex]$x^2$[/tex], 64, and 36 square units, respectively.
Since square 2 has an area of $64$ square units, its side length is [tex]$\sqrt{64}=8$[/tex] units. Similarly, square 3 has a side length of[tex]$\sqrt{36}=6$[/tex]units.
We can now set up an equation based on the fact that the sum of the areas of squares 1 and 3 is equal to the area of square 2:
[tex]$$x^2+36=64$$[/tex]
Solving for x, we get:
[tex]$$x^2=28$$[/tex]
Therefore, the area of square 1 is [tex]$x^2=28$[/tex] square units, and its side length is [tex]$\sqrt{28}=2\sqrt{7}$[/tex] units.
In summary, the area of square 1 is 28 square units and its side length is[tex]$2\sqrt{7}$[/tex] units.
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find the area a of the sector of a circle of radius 100 meters formed by the central angle 1/8 radian
Answers
The area of a sector of a circle with radius 100 meters and central angle 1/8 radian is approximately 625 * π square meters.
The area of a sector of a circle with radius 100 meters and central angle 1/8 radian can be found using the formula:
A = [tex](\theta/2\pi )*\pi r^{2}[/tex]
where A is the area of the sector, Θ is the central angle in radians, π is Pi (approximately 3.14), and r is the radius of the circle.
Plugging in the given values, we have:
A = [tex](\frac{\frac{1}{8}}{{2\pi }} )*\pi *100^{2}[/tex]
A =[tex](1/16)*\pi *100^{2}[/tex]
A = [tex](\pi /16)*100^{2}[/tex]
A = (π/16) * 10000
A = 625 * π square meters
So, the area of the sector of the circle with radius 100 meters and central angle 1/8 radian is approximately 625 * π square meters.
The area of a sector of a circle is a portion of the circle's area enclosed by two radii and an arc. The central angle of the sector determines the fraction of the circle's circumference that the arc represents, and therefore the fraction of the circle's area that is enclosed by the sector.
To find the area of a sector, we first need to find the central angle in radians. The central angle is the angle formed by two radii at the center of the circle that intercept the circumference of the circle at the endpoints of the arc.
The formula for the area of a sector is given by:
A = [tex](\theta/2\pi )*\pi r^{2}[/tex]
where A is the area of the sector, Θ is the central angle in radians, π is Pi (approximately 3.14), and r is the radius of the circle.
In the given problem, the radius of the circle is 100 meters and the central angle is 1/8 radian. We plug these values into the formula and simplify to get the final answer.
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Zeke and Erin were playing a game with a number cube and a spinner divided into equal ports red.
yellow, and blue. Zeke wins if the number cube is a factor of and the spinner lands on red Erin
wins if she rolls a 5 or 6 and the spinner lands on yellow or blue.
1 Create a probability table or free to show all outcomes of rolling a number cube and spinning the
spinner,
R₁
≤18
y₁
B3
2. What is the probability of Zeke winning? What is the probability of Erin winning?
Answers
The solution is, the required probability is p= 1/10.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
from the given information we get,
We have 5 possible parts colored red, green, blue, purple and yellow
The cube for this case have 6 possible numbers 1,2,3,4,5,6
We have the following even numbers: 2,4,6
Then the probability of obtain an even number is:
p1= 3/6= 1/2
Then the probability of obtain a blue color on the spinner is:
p2= 1/5
Then we want this probability:
Obtain an even number AND sppining a blue on the spinner
Then since the events are independent we can do this:
p = 1/2 * 1/5= 1/10
Hence, The solution is, the required probability is p= 1/10.
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Jana is wondering about the probabilities of genetic crosses. She knows that
when her gerbil had babies, there was a 50% chance of babies being male
and a 50% chance of being female. Her gerbil gave birth to 6 babies, and 4
were girls and 2 were boys. Why weren't they 50% male and 50% female?
Answers
Experimental Probability
Just because the odds are 50% for both genders doesn't mean there is any reason for it to be even. It's like flipping a coin six times. there's no reason for it to land on tails 3 times and heads 3 times. Its just more likely
Help me with this worksheet please
Answers
The trigonometry ratio values are tan(50) = 1.19 and cos(70) = 0.34
The trigonometry ratio valuesThis can be calculated using a calculator
So, we have
tan(50) = 1.19 and cos(70) = 0.34
The measures of the anglesThis can be calculated using a calculator
So, we have
sin(84) = 0.9945 and tan(75) = 3.7321
The trigonometry ratio valuesHere, we make use of the laws of cosines and sines
So, we have
cos(X) = 15/17 = 0.8824
sin(C) = 36/45 = 0.8
The measures of the indicated anglesHere, we make use of the laws of tangents and sines
So, we have
tan(?) = 6/13 = 0.4615
? = 24.77
sin(?) = 41/59 = 0.6949
? = 44.01
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Triangle EFG is an isosceles triangle.
The figure is not drawn to scale.
What is the measure, in degrees, of angle G ?
Answers
Measure of angle G is 62.5°.
What is the sum of all the exterior angles of a regular polygon?For a regular polygon of any number of sides, the sum of its exterior angle is 360° (full angle).
In triangle EFG,
Measure of angle E = 55°
Measure of angle F should be less than 180 = x/2°
By the triangle sum theorem, the Sum of measures of all interior angles of triangle = 180°
m(∠E) + m(∠F) + m(∠G) = 180°
55° + x/2° + x/2= 180°
x= 180° - 55°
x = 125
Measure of angle G = 125/2 = 62.5
Therefore, measure of angle G is 62.5°.
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The red rectangle is the pre-image and the green rectangle is the image. What would be the coordinate of A" if the scale factor of 3 is used?
Pls show all your work!
Keep in mind I will immediately mark brainliest for the right answer!
Answers
The scale factor that has been used is 1/2
How to determine what scale factor has been used?From the question, we have the following parameters that can be used in our computation:
Side length on red = 6 units
Corresponding side length on green = 3 units
Given that the red rectangle is the pre-image and the green rectangle is the image
We have
Scale factor = Green/Red
So, we have
Scale factor = 3/6
Evaluate
Scale factor = 1/2
Hence, the scale factor is 1/2
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Complete the sentences to explain how to find the dimensions of the square.
Answers
The absolute value of the x-values of the coordinates of A and B = |2 - 5| = 3 units.
The absolute value of the y-values of the coordinates of B and C = |6 - 3| = 3 units.
How to Find the Dimension of a Square on a Coordinate Plane?If two points lie on a coordinate plane, the distance between them represents the length of the segment both points form, which is determined by finding the absolute difference between the values of their coordinates that lie on the same axis.
Given that a square has the points, A (2, 6), B (5, 6), C (5, 3), D (2, 3), its dimensions can be found as explained below:
Length of AB is found by calculating the absolute value of the x-values of the coordinates of A and B, while to find the length of BC, is the absolute value of the y-values of the coordinates of B and C.
Therefore:
AB = |2 - 5| = 3 units
BC = |6 - 3| = 3 units
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