Equation to determine the diver’s initial depth is [tex]x + 10 \frac{3}{4} = 56\frac{1}{2}[/tex].
Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.
In algebra, an equation is a condition on a variable. It is satisfied only for a definite value of the variable.
The equation in one variable means the equation containing only one variable. Let’s have a look at the below equations.
Let the distance of diver at a certain depth be x.
After some time he ascends [tex]10\frac{3}{4}[/tex] feet.
The final position of diver is : [tex]56\frac{1}{2}[/tex] feet.
Using given information we get the required equation: [tex]x + 10 \frac{3}{4} = 56\frac{1}{2}[/tex].
where x = distance of diver at a certain depth.
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The standard deviation of a sample of 100 observations equals 64. The variance of the sample equals 10 6400 4096 Question 15 (1 point) The interquartile range is the 50th percentile the difference between the third quartile and the first quartile another name for variance the difference between the largest and smallest values
The variance of a sample is 4,096. And for interquartile, the difference between the largest and smallest values. The correct answer is option D
To calculate the variance we have a small formula:
v=s^2-----(1)
v=variance
s=Standard deviation
so, given that s=64
substitute in equation(1)
v=64*64
v=4096.
variance: The variance is a measure of variability. It is calculated by taking the average of squared deviations from the mean.
Variance is denoted by a symbol: σ2.
Interquartile range (IQR) is a measure of statistical dispersion, which is used to spread the data. The IQR is also called midspread.
To calculate the IQR, the data set is divided into quartiles. These quartiles are denoted by Q1 (another name is the lower quartile), Q2 (the median), and Q3 (also called the upper quartile). The lower quartile corresponds with the 25th percentile and the upper quartile corresponds with the 75th percentile, so IQR = Q3 − Q1
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Suppose IQ scores were obtained for 20 randomly selected sets of twins. The 20 pairs of measurements yield x=98.13, y=100.6, r=0.904, P-value=0.000, ŷ=14.68+0.88x, where x represents the IQ score of the twin born first. Find the best predicted value of ModifyingAbove y with caret given that the twin born first has an IQ of 104? Use a significance level of 0.05.
The best-predicted value of Modifying Above y with caret given that the twin born first has an IQ of 104 is 106.2.
The dependent variable's predicted value in basic linear regression is given by the equation = b0 + b1x.
In order to minimize the total sum of squared errors, the values of b0 and b1 are derived from the data using the equation line = b0 + b1X. (the error is the difference between the predicted value and the actual value of y).
Use regression equation
ŷ=14.68+0.88x
plug in IQ, which is x
y = 14.68 + 0.88(104)
= 106.2
Hence, the answer is 106.2
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Can someone please explain this question. Please give a step by step explanation
Answer:
45
Step-by-step explanation:
8 numbers summed and divided by 8 = 41
8numberssummed / 8 = 41
8numberssummed = 41 * 8 = 328
now taking out two numbers whose mean is 29 is the same as taking out two 29's from the sum ....so now there are SIX numbers
6numberssummed = 8numberssummed - 29 -29
= 328 -29 -29 = 270
so to find the mean of the remaining six numbers:
6numberssummed / 6 is 270/6 = 45
Answer:
mean = 45
Step-by-step explanation:
mean is calculated as
mean = [tex]\frac{sum}{count}[/tex]
given the mean of 8 numbers is 41 , then
[tex]\frac{sum_{8} }{8}[/tex] = 41 ( multiply both sides by 8 )
sum₈ = 328
given the mean of 2 of the numbers is 29 , then
[tex]\frac{sum_{2} }{2}[/tex] = 29 ( multiply both sides by 2 )
sum₂ = 58
Then
sum₆ = sum₈ - sum₂ = 328 - 58 = 270
then the mean of the other six numbers is
mean = [tex]\frac{sum_{6} }{6}[/tex] = [tex]\frac{270}{6}[/tex] = 45
1. If the required reserve ratio is 10% and the Fed conducts an open market purchase of $100, what is the maximum possible change in the money supply?
100, 1,000, 10,000 or 10
The maximum possible change in the money supply is $1000.
In the given question, if the required reserve ratio is 10% and the Fed conducts an open market purchase of $100, we have to find the maximum possible change in the money supply.
The required reserve ratio is 10%.
The Fed conducts an open market purchase of $100.
So the maximum possible change in the money supply is
money multiplier=1/RRR
money multiplier=100/10
money multiplier=10
Open market purchase of $100
Change in money supply is 10*100=$1000
So, the maximum possible change in the money supply is $1000.
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If 45% of a number is 36, what is the number?
Answer:
The number is 28.35
Step-by-step explanation:
45% of 36
[tex]\frac{x*y}{100}[/tex]
= [tex]\frac{45*36}{100}[/tex]
= [tex]\frac{2835}{100}[/tex]
= 28.35
A warehouse with a value of $200,000 is insured for $140,000 under an 80% coinsurance policy. A fire loss of $80,000 occurs. How much of the loss will the insurance company pay for? PLEASE SHOW WORK
The amount of loss that the insurance company will pay is $70000
How do you calculate coinsurance and deductibles?Deductible plus the amount of coinsurance equals the out-of-pocket maximum.
Determine the $1,000 deductible that the insured is required to pay.
Calculate the coinsurance payment due from the insured: 20% of $5,000 equals $1,000.
What is the formula for coinsurance?The coinsurance penalty is calculated using the straightforward formula: the loss multiplied by the amount of insurance that should have been in place, less any deductible, equals the amount that was actually paid.
The following covered losses are subject to the coinsurance provision: Property value: $200,000; policy limit: $140,000; coinsurance: 80%; loss: $100,000; deductible: $250; all other numbers: $200,000; etc.
The insured only had $140,000 when they should have had $160,000 (200,000 x.80).
The coverage will cover the deductible plus $87,500. (140,000/160,000
=.875; $100,000 x .875
= $87,500; $87,500 - $250
= $77,250)
Stop Limit/Value =%, Loss Amount x% = $ Amount Policy Would Pay (-) minus $ Deductible = $ Covered Loss Amount
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Which ones are correct ✅
Answer:
Step-by-step explanation:
1)Option A)
2)Option B)
If A inversely proportional to the cube of B, A=64 and B=2.
1). Find the law connecting A and B
2). Find the value of the Constant
Answer:
See below
Step-by-step explanation:
1). A = k / (B^3) <==== this becomes A = 512/(B^3) when you use the answer from 2). (below)
2). When A = 64 and B = 2 :
64 = k / (2^3)
64 = k / 8
k = 64*8 = 512
What is the area of a rectangle 3 meters long and 7 meters high
Answer:
21 sq. meters
Step-by-step explanation:
you just need to multiply the width and the height, so 3x7.
3x7=21
Answer: 21m^2
Step-by-step explanation:
The equation finds the area of a rectangle is
Area= Width times Height
So take 7 times 3 = 21 m^2
If y varies directly with x what is the equation when y=-64andx=16
Answer: when y = -64 and x = 16 is y = -4x. This equation states that for every value of x, the corresponding value of y is equal to -4 times the value of x.
write 2 differnt expressions that involve only oots and powers of 2 which are equivalent 4 2/3 / 8 1/4
2 different expressions that involve only outs and powers of 2 which are equivalent 4 2/3 / 8 1/4
1) (4^2 * 2^-1 * 3^1) / (8^1 * 2^-2 * 4^-1)
2) (2^5 * 3^1) / (2^6 * 4^-1)
1) (4^2 * 2^-1 * 3^1) / (8^1 * 2^-2 * 4^-1)
This expression is equivalent to 4 2/3 / 8 1/4 because it is written in terms of powers of two. 4^2 is equal to 16, which is the numerator in 4 2/3. 2^-1 is the same as 1/2, which is the second fraction in 4 2/3. 3^1 is equal to 3, which is the numerator in 8 1/4. 8^1 is equal to 8, which is the denominator in 8 1/4. 2^-2 is the same as 1/4, which is the second fraction in 8 1/4. 4^-1 is equal to 1/4, which is the first fraction in 8 1/4. When all the terms are multiplied and divided, it is the same as 4 2/3 / 8 1/4.
2) (2^5 * 3^1) / (2^6 * 4^-1)
This expression is also equivalent to 4 2/3 / 8 1/4 because it is written similar to above equation.
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g an epidemic of measles has started at what rate is the modeled by the funtion p epidemic spreading after 3 days
The modeled epidemic rate cannot be determined from the information provided.
The rate of an epidemic spreading is a complex process that is influenced by many factors such as the population density, the number of people who are vaccinated, and the infectiousness of the virus. Therefore, it is not possible to accurately model the rate of an epidemic spreading after 3 days based on the information provided. To accurately model the rate of an epidemic spreading, additional information such as the population density, the number of people who are vaccinated, and the infectiousness of the virus would be needed.
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at which minimum altitude should you cross the stakk intersection? a. 10,200 feet msl. b. 11,800 feet msl. c. 10,800 feet msl.
Answer: 6,500 feet MSL
Step-by-step explanation:
I don't think any options you provide have the correct answer! It should be 6,500 feet MSL
The length of a bacterial cell is about 5 x 10−6 m, and the length of an amoeba cell is about 3.5 x 10−4 m. How many times smaller is the bacterial cell than the amoeba cell? Write the final answer in scientific notation with the correct number of significant digits.
70 times smaller is the bacterial cell than the amoeba cell.
What is 10^n?
As a result, a power of 10 is represented in long form as the number 1 followed by n zeros, where n is the exponent and is bigger than 0; for instance, 10⁶ is represented as 1,000,000. The number 1 n places after the decimal point represents the power of 10 when n is less than 0; for instance, 10⁻² is represented as 0.01.
Given that, the length of a bacterial cell is about 5 x 10⁻⁶ m, and the length of an amoeba cell is about 3.5 x 10⁻⁴ m.
To calculate times of smaller, divide the length of amoeba cell with bacterial cell.
Therefore, (3.5 x 10⁻⁴)/(5 x 10⁻⁶) = 70.
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Answer:
so the experts answer is correct but its not in scientific notation the answer is: 7 x 10^1
Step-by-step explanation:
What absolute value function is represented by the graph?
Answer: y=|x+1.5|
Step-by-step explanation:
y=|x+1.5|
a laptop computer is purchased for . each year, its value is of its value the year before. after how many years will the laptop computer be worth or less? (use the calculator provided if necessary.)
After 7 years the laptop computer will be worth $200 or less.
Given:
A laptop computer is purchased for $1400 .
Each year, its value is 75% of its value the year before.
After how many years will the laptop computer be worth $200 or less = ?
1400(0.75)t≤ 200
0.75t ≤ 1/7
ln(0.75t) ≤ ln(1/7)
tln(0.75) ≤ ln(1/7)
t ≥ ln(1/7)/ln(0.75)
t ≥ 6.76
The natural log of a number between 0 and 1 is negative, and dividing by a negative switches the sign.
So, after 7 years, the laptop computer will be worth $200 or less.
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four standard six-sided dice are rolled. what is the probability that the product of the numbers on the top faces of all four dice is a prime number? express your answer as a common fraction.
The probability that the product of the numbers on the top faces of all four dice is a prime number is [tex]\frac{1}{108}[/tex] .
We have given that,
six-sided dice are rolled 4 times
i.e. probability of this event is [tex]6^{4}[/tex] = 1296.
The condition is product of the numbers on the top faces of all four dice is a prime number.
The only way to get a prime number by multiplication is to have three of the numbers equal to one and the fourth number equal a prime.
The prime less than 6 are 2,3,5.
Each prime number will come on the all four dices top faces.
Therefore outcomes are,
{1,1,1,2}, {1,1,2,1, {1,2,1,1}, {2,1,1,1}, {1,1,1,3}, {1,1,3,1}, {1,3,1,1}, {3,1,1,1}, {1,1,1,5}, {1,1,5,1}, {1,5,1,1}, {5,1,1,1}.
there are 12 outcomes for the given probability.
Therefore required probability [tex]\frac{12}{1296}[/tex] i.e [tex]\frac{1}{8}[/tex].
Hence the probability that the product of the numbers on the top faces of all four dice is a prime number is [tex]\frac{1}{8}[/tex].
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Carson owes Nigel $110. If Carson repays this debt at a rate of $15 per week, which graph best represents when, in weeks, Carson’s debt will be less than $50?
Responses
After doing the equitation the at rate of $15 per week.
How to do graph representation?
Graph representation is a way of visualizing data as a graph or chart. It is used to easily identify relationships between data points and to illustrate trends in the data. Graphs can be used to present data in a variety of ways, such as bar graphs, line graphs, pie charts, scatter plots and more. Graphs are especially useful when trying to compare two or more sets of data and to highlight any patterns or trends that may exist. Additionally, graphs are often used to represent numerical data in a more visually appealing way. By using graphs, it is easier to identify relationships, trends and outliers in the data. Graphs also help to make data easier to interpret and understand.
Carson owes = $110
At rate of $15 per week.
The graph representation will follows:
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! if six theta = x/4 where 0 < theta < 90 and 0 < x < 4, then cos theta =
Using Pythagoras theorem If sin tetha = x/4, then cos tetha = √(16-x²)/4
What is Pythagoras theorem?Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.
The sides of this triangle have been named Perpendicular, adjascent and Hypotenuse. If sin (tetha) = x/4, this means
x = opposite and
4 = hypotenuse
From hypotenuse² = opposite² + adjacent²
4² = x²+y²
y² = 16-x²
y = √ ( 16-x²)
cos (tetha) = adjacent/ hypotenuse
cos (tetha) = √(16-x²)/4
Therefore the value of cos (tetha) = √(16-x²)/4
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How do you solve a/15 = 4/5 ?
The value of a=12
Simply use cross multiplication :
The process of multiplying numbers in the shape of a fraction is called cross multiplication. Cross multiplying, also known as cross multiplication, is the process of multiplying the numerator of one fraction by the denominator of the other fraction on the other side of an equals to symbol. Cross multiplication is a method for comparing fractions.
Both fractions with like and unlike parts are multiplied across. When employing the cross-multiplication procedure, we multiply the denominators as well as the numerators when a fraction is dissimilar, or when the denominators of two fractions are not alike.
[tex]\frac{a}{15}=\frac{4}{5}[/tex]
or, 5a=4*15
or, a= 4*15/5
or, a= 12
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The regular admission price for an amusement park is $72. For a group of 15 or more, the admission price is reduced by $25 per person. How many people need to be in a group to save $500?
20 people need to be in a group in order for them to save $500.
If there are 15 people or more, people will save $25 on each ticket.
In order to save a total of $500, the number of people who are needed is:
= Amount to be saved / Amount to be saved per ticket
= 500 / 25
= 20 people
In conclusion, if a group of 20 people came, they would save $500.
the equation for the two lines of symmetry of a rectangle.
Answer:
180
Step-by-step explanation:
xdcjuggggggggggggggggggggg
consider the matrix : what is the minimal approximation error achievable by a rank-1 approximation to ?
The minimal approximation error A-A 2achievable by a rank-1 approximation A to A is
||A - A1||₂=0 where A is 2×2 matrix.
We have given a matrix A as seen in above figure or A = [ 5 15 ; 6 18 ; -1 -3 ; -4 -12 ; 2 6]
note here that C₂= 3C₁
where Cᵢ --> iᵗʰ column
v = [ 5 ; 6 ; -1 ; -4 ; 2]
||v||² = 82 => ||v|| = √82
and A At v = 820 v
and A At = [ 82 246 ; 246 738]
AAt [1;3] = 820[1;3]
=> v1 = 1/√10(1,3)^t
Then the best rank of 1 approx
= √820 /√80√10 [ 5 ; 6 ; -1 ; -4 ; 2] [ 1 3]
= A
Since , the rank of matrix A is one so, the minimal approx. value is ||A - A1||2 = 0
Hence, the minimal Approx. ||A - A1||2 = 0 .
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Complete question:
Consider the matrix A: A = [5 15] 6 18 -1 -3 -4 -12 [26] What is the minimal approximation error A-A 2 achievable by a rank-1 approximation A to A? Hint: Can you determine this without explicitly calculating the SVD?
The population of a city decreases by 3.3% per year. If this year's population is 72,000, what will next year's population be, to the nearest individual?
Using the given information, the city's next year population will be 69,840
Determining the population of a cityFrom the question, we are to determine what the population of the city will be the following year
From the given information,
"The population of a city decreases by 3.3% per year"
and
This year's population is 72,000
Thus,
The population of the following year will be
72000 - 3% of 72000
Next year population = 72000 - 3% of 72000
Next year population = 72000 - 3% × 72000
Next year population = 72000 - 0.03 × 72000
Next year population = 72000 - 2160
Next year population = 69,840
Hence, the population will be 69,840
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How do you simplify i^100?
The solution of i^100 = 1 is [tex]i^{100} = 1[/tex] .
Simplify
Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
Power
In mathematical relationships, power is referred to the number of times a number is multiplied by itself meaning the number you get raising a number to an exponent whereas an exponent can be defined as the number of times the number is used in a multiplication. Exponents are often known as powers or indices.
Exponents
Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner. For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as 34, where 4 is the exponent and 3 is the base. The whole expression 34 is said to be power.
Rewrite [tex]i^{100}[/tex] as [tex](i^{4} )^{25}[/tex]
One to any power is one.
1
From the fact that [tex]i^{2}[/tex] = −1,
Then
([tex]-1^{50}[/tex]) = 1 as −1 raised to any even power is 1.
[tex]i^{100} = 1[/tex]
i^100 = 1
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Which ratio is equivalent to 3/7
A) 6 to 10
B) 9:21
C) 12/35
D) 7 to 3
Answer: B 9:21
Step-by-step explanation:
9 reduces to three and 21 reduced to 7
Which is the product of 56 and 5/9
1, 1 and 4/9
2, 30
3, 31
4, 31 and 1/9
Answer:
4.
Step-by-step explanation:
strange phrasing of the answer options.
anyway, the product of 56 and 5/9 is
56 × 5/9 = 56×5 / 9 = 280/9 = 31 1/9
or as the definition says 31 and 1/9.
because 31×9 = 279.
280 - 279 = 1
so, there is a remainder of 1, which means 1/9.
280/9 = 279/9 + 1/9 = 31 1/9
A company orders 10 boxed lunches from a deli for $116.50. If each boxed lunch costs the same amount, how much do 13 boxed lunches cost?
Answer:
$151.45
Step-by-step explanation:
$116.50 divided by 10 is $11.65 which is the cost of just one box lunch. So 11.65 times 13 is 151.45. So the answer is $151.45.
Answer:
15145
Step-by step explanation:ok so I multuply 116.50x13 i got my ansanswers thene i mumultiple that by 10 and the aswer is
15,145 tyyyyyyy
which of these situations can be represented by the opposite of -25
The situations that can be represented by the opposite of -25 are:
B. Leon gets paid $25. C. An airplane descends 25 feet. E. A bird flies 25 feet above sea levelHow can the opposite of -25 be calkculated?-25 can be seen as represention of the given situations fro the problem, and exploring the given options, we can see that 25 feet below the sea level with that ones balance can be gets reduced by $25.
But when exploring the But the opposite of (-25) then we can see that 25 feet above the sea level, and in this case the amount will be raised by $25. and the height by 25 feet with the increase in the debt by $25.
Therefore, option B ,C and E are correct.
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missing options:
A. A scuba diver is 25 feet below sea level. B. Leon gets paid $25. C. An airplane descends 25 feet. D. Sara has a $25 debt. E. A bird flies 25 feet above sea level
Find the volume of the cylinder with a diameter of 6 cm and height of 4 cm, as shown on the diagram below. 4 6 cm 4 cm Give your answer correct to 1 decimal place.
