Answer:
x = -35.375
Step-by-step explanation:
hope this helps! :)
Find an equation for the line with the given properties. Express your answer using either the general form or the slope intercept form of the equation of a line
We are given the line
x - 5y = -4
We need to get this in slope intercept form
x-5y -x = -x-4
-5y = -x-4
Divide by -5
05y/-5 = -x/-5 -4/-5
y = 1/5x + 4/5
The slope oif this line is 1/5
We want to find a line that is parallel. Parallel lines have the same slope, so the new line will have a slope of 1/5
The new line contains the point(0,0)
Slope intercept form is y = mx+b where m is the slope and b is the y intercept
y = 1/5x + 0
y = 1/5x
(We know the y intercept is 0 since the point is (0,0) it crosses the y axis at 0)
35 less the product of 4 and x
Answer:
4x - 35
Step-by-step explanation:
this shows 35 less than the product of 4 and x
Answer:
35 less the product of 4 and x
\(4 \times x - 35 \\ = (4x - 35)\)
(4x-35) is the right answer.If m∠ADB=( 3a + 10)° and m∠BDC= 13a°, find a, m∠ADB, and m∠BDC.
Given that ∠ADB and ∠BDC are complimentary angles, the numerical value of a, ∠ADB and ∠BDC are 5, 25° and 65° respectively.
What is the numerical value of a, ∠ADB and ∠BDC?When two angles have measures adding to up to 90 degrees, they are called complementary .
Given that;
m∠ADB = ( 3a + 10 )m∠BDC = 13aNumerical value of a = ?For complimentary angles;
m∠ADB + m∠BDC = 90°
Plug in the given values and solve for a.
( 3a + 10 ) + 13a = 90
3a + 10 + 13a = 90
10 + 16a = 90
16a = 90 - 10
16a = 80
a = 80/16
a = 5
Now, find the measure of ∠ADB and ∠BDC.
m∠ADB = ( 3a + 10 ) = 3(5) + 10 = 15 + 10 = 25°
m∠BDC = 13a = 13( 5 ) = 65°
Given that ∠ADB and ∠BDC are complimentary angles, the numerical value of a, ∠ADB and ∠BDC are 5, 25° and 65° respectively.
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5.) A woman put $580 into a savings account for one year. The rate of interest on the account was 6.5%. How much was the interest for the vear in dollars and cents? (Round to the nearest cent) 6.) Pamela bought an electric drill at 85% of the regular price. She paid $32.89 for the drill. What was the regular price? (Round to the nearest cent)
The amount of interest for the year was 3,770 cents, and the regular price of the electric drill that Pamela bought before the discount was 21,927 cents
To find the interest we can use this following formula:Interest = P x R x T.
Where:
P = Principal amount (the beginning balance).
R = Interest rate
T = Number of time periods
In this case, we are given that;
Principal amount (P) = $580
Interest rate (R) = 6,5 %
Time = 1 year
Hence, The amount of the interest = 6,5% of $580
= 0.065 × $580
= $37.7
1 dollar = 100 cents
Hence, $37.7 = 37.7 × 100 cents equal to 3,770 cents
To find the regular price of the electric drill, we can use this following formula:P = (1 – d) x
Where,
P = Price after discount
D = discount rate
X = regular price
In this case, we are given that:
P = $32.89
D = 85% = 0,85
Hence, the regular price:
P = (1 – D) x
32.89 = (1 – 0.85) X
32.89 = 0.15X
X = 32.89/0.15
X= 219.27
1 dollar = 100 cents
Hence, $219.27 = 219.27 × 100 cents equal to 21,927 cents
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__________________ occurs when the method of observation tends to produce values that systematically differ from the true value in some way.
When the process of observing or measuring yields results that consistently deviate in some way from the true value, this is known as observer/measurement bias. Because of the systematic mistake this adds into the data, the conclusions are incorrect or unreliable.
Observer/measurement bias is a sort of systematic error that happens when the technique used for observation or measurement yields results that consistently deviate in some way from the true value. The observer's own preconceived ideas or expectations, the measurement equipment, and the environment in which the observation or measurement is being conducted can all contribute to this form of bias.An observer's bias, for instance, could cause them to see or measure something in a way that favours one particular result or outcome over another. Similar to how external influences like noise, light, or temperature can skew results, the environment in which the observation or measurement is taking place may add a bias. If feasible, results that are inaccurate or unreliable because of observer/measurement bias should be avoided because they can lead to incorrect inferences about the data.
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An article suggests the uniform distribution on the interval (6.5, 21) as a model for depth (cm) of the bioturbation layer in sediment in a certain region. (a) What are the mean and variance of depth? (Round your variance to two decimal places.) mean variance (b) What is the cdf of depth? F(x) = {0 x < 6.5 6.5 lessthanorequalto x < 21 1 21 lessthanorequalto x (c) What is the probability that observed depth is at most 10? (Round your answer to four decimal places.) What is the probability that observed depth is between 10 and 15? (Round your answer to four decimal places.) (d) What is the probability that the observed depth is within 1 standard deviation of the mean value? (Round your answer to four decimal places.) What is the probability that the observed depth is within 2 standard deviations of the mean value?
Answer : a ) Variance = (21 - 6.5)^2/12 = 13.7708, b) 1, 21 <= x, c) Probability = 0.5862, D) Probability = 0.8552
The uniform distribution on the interval (6.5, 21) can be represented as U(6.5, 21).
(a) The mean and variance of a uniform distribution can be calculated using the following formulas:
Mean = (a + b)/2
Variance = (b - a)^2/12
where a and b are the lower and upper bounds of the distribution, respectively.
For the given distribution, a = 6.5 and b = 21.
Therefore, the mean and variance of depth are:
Mean = (6.5 + 21)/2 = 13.75
Variance = (21 - 6.5)^2/12 = 13.7708
(b) The cdf of a uniform distribution can be calculated using the following formula:
F(x) = (x - a)/(b - a)
For the given distribution, F(x) = (x - 6.5)/(21 - 6.5) for 6.5 <= x < 21.
Therefore, the cdf of depth is:
F(x) = {
0, x < 6.5
(x - 6.5)/14.5, 6.5 <= x < 21
1, 21 <= x
(c) The probability that observed depth is at most 10 can be calculated using the cdf:
P(X <= 10) = F(10) = (10 - 6.5)/14.5 = 0.2414
The probability that observed depth is between 10 and 15 can be calculated using the cdf:
P(10 <= X <= 15) = F(15) - F(10) = (15 - 6.5)/14.5 - (10 - 6.5)/14.5 = 0.5862
(d) The standard deviation of a uniform distribution can be calculated using the following formula:
Standard deviation = sqrt(Variance)
For the given distribution, the standard deviation is:
Standard deviation = sqrt(13.7708) = 3.7118
The probability that the observed depth is within 1 standard deviation of the mean value can be calculated using the cdf:
P(13.75 - 3.7118 <= X <= 13.75 + 3.7118) = F(13.75 + 3.7118) - F(13.75 - 3.7118) = (13.75 + 3.7118 - 6.5)/14.5 - (13.75 - 3.7118 - 6.5)/14.5 = 0.5118
The probability that the observed depth is within 2 standard deviations of the mean value can be calculated using the cdf:
P(13.75 - 2*3.7118 <= X <= 13.75 + 2*3.7118) = F(13.75 + 2*3.7118) - F(13.75 - 2*3.7118) = (13.75 + 2*3.7118 - 6.5)/14.5 - (13.75 - 2*3.7118 - 6.5)/14.5 = 0.8552
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y=mx+b how do you find it
Why do you multiply both sides by 4/3 next?
Answer: This is because you want to find a quad root of it and the nunber would be 4/3 to do that
Step-by-step explanation: I am very busy
The perimeter of the triangular park shown on the right is 16x - 2. What is the missing length?
The perimeter of a Triangle is the sum of three sides ; ie assuming k,l,m be the three sides of a triangle means then k+l+m = perimeter of a triangle.
here given that a two sides lengths are 2x+ 2 and 5x-4 ;
and the perimeter length is 16x-6;
let the unknown side be k;
therefore k + 2x+2 + 5x-4 = 16x-6;
resolving k + 7x-2 = 16x-6;
Ans:- k= 16x-6-7x+2 = 9x-4 ie the unknown length k is 9x-4
Factor the GCF: 9x^4 - 6x^3y^2 + 3x^2y^3.
A. 3x^2y(3x^2 - 2xy + y^2)
B. 3xy(3x^2 - 2xy + y^2)
C. 3xy^2(3x^2 - 2xy + y^2)
D. 3x^2y(3x^2 + 2xy + y^2
PLEASE HELP ME
Answer:
3x2y(3x2−2xy+y2) So C
Step-by-step explanation:
Mike's Movers charges a flat rate of 550 plus $25 per hour. If one of their customers was charged a total of $225, for how many
hours were they charged?
Please asap
not 9 the answer should be 3
Q. 5: A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mode of the data:
Number of cars Frequency
0-10 7
10-20 14
20-30 13
30-40 12
40-50 20
50-60 11
60-70 15
70-80 8
Answer:
There is no mode !
Step-by-step explanation:
Hello,
what is the mode of a set of data?
It is the value in the set that occurs most often.
To note that this is also possible to have a set of data with no mode.
in this example, let's order them
7, 8, 11, 12, 13, 14, 15, 20
There is no repetition, right? each value occurs only once.
So, there is no mode!
hope this helps
The graph shows the location of point P and point R. Point R is on the y-axis and has the same y-coordinate as point P. Point Q is graphed at (n,-2). The distance from point P to point Q is equal to the distance from point P to point R. What is the from point P to point Q? What is the value of N? Explain how you determined the distance from point P to point Q, and the value of N.
Answer:
n = 5
Step-by-step explanation:
Coordinate of P = (n,3)
R is on y-axis & the y-coordinate of P & R are equal. So coordinate of R = (3,0)
Coordinate of Q = (n,-2)
Using distance formula,
Distance between P & Q =
\( \sqrt{ {( n - n}) ^{2} + {( 3- ( - 2) })^{2} } \)
\( = > \sqrt{ {(3 + 2)}^{2} } = \sqrt{ {5}^{2} } = 5\)
Distance between P & R =
\( \sqrt{ {(n - 0)}^{2} + {(3 - 3)}^{2} } \)
\( = > \sqrt{ {n}^{2} } = n\)
But in question it is given that distance between P & Q is equal to the distance between P & R. So,
\(n = 5\)
9 in. 14 in. Find the area of the triangle shown above. [?] square inches
Answer:
63
Step-by-step explanation:
9 x 14 = 126/2 = 63
1.2.RE-2
Error Analysis The solution shown for the equation is
incorrect. What is the correct solution? What is the error?
– 9(5-1) = 18
- 45 -9r = 18
- 9 = 63
r = -7
The solution is (Type the value of r.)
1
Answer:
7
Step-by-step explanation:
the mistake they made is not changing the 9r to a positive. A negative and a negative make it positive
Use the expression, X^2-7
What is the value of the expression above when n=5
Answer:
18
Step-by-step explanation:
X^2 - 7 =
Since we need to evaluate the expression when X = 5, we replace X with 5.
= 5^2 - 7
Now, according to the correct order of operations, we need to do the exponent first. 5^2 = 5 * 5 = 25
= 25 - 7
Finally, we subtract.
= 18
Answer: 18
sin−1(sin/6)
cos−1(cos5/4)
tan−1(tan5/6) compute without using a calculator
Without using a calculator, the trigonometric expressions simplify to:
1. sin^(-1)(sin(θ/6)) = θ/6
2. cos^(-1)(cos(5/4)) = 5/4
3. tan^(-1)(tan(5/6)) = 5/6.
To compute the trigonometric expressions without using a calculator, we can make use of the properties and relationships between trigonometric functions.
1. sin^(-1)(sin(θ/6)):
Since sin^(-1)(sin(x)) = x for -π/2 ≤ x ≤ π/2, we have sin^(-1)(sin(θ/6)) = θ/6.
2. cos^(-1)(cos(5/4)):
Similarly, cos^(-1)(cos(x)) = x for 0 ≤ x ≤ π. Therefore, cos^(-1)(cos(5/4)) = 5/4.
3. tan^(-1)(tan(5/6)):
tan^(-1)(tan(x)) = x for -π/2 < x < π/2. Thus, tan^(-1)(tan(5/6)) = 5/6.
Hence, without using a calculator, we find that:
sin^(-1)(sin(θ/6)) = θ/6,
cos^(-1)(cos(5/4)) = 5/4,
tan^(-1)(tan(5/6)) = 5/6.
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Identify an example of a pair of skew line from the box below
Answer:
AB, CD
Step-by-step explanation:
Skew lines do not lie in the same plane, and do not intersect. One such pair is AB and CD.
__
Additional comment
Any of the lines, and any of the lines that intersect its diagonally-opposite edge will be skew lines.
For example, the opposite edge to line BC is line EG. Lines that intersect EG are ED, EF, GA, GH. All of those four lines are skew with respect to line BC.
PLEASE HELP ME
Amira is asked to write an exponential function to represent the value of a $5,000 investment increasing at 4% annually. What multiplicative rate of change should Amira use in her funtion?
a
1.04
b
0.96
c
0.04
d
1.96
Answer:
c) 0.04 is the answer
I would be happy if you give brainliest
IQ scores are normally distributed with a
mean of 100 and a standard deviation of
15. What percentage of people have an IQ
score less than 117, to the nearest tenth?
Answer: To find the percentage of people with an IQ score less than 117, we need to calculate the z-score first. The z-score measures how many standard deviations an individual score is from the mean in a normal distribution.
The z-score formula is given by:
z = (x - μ) / σ
Where:
x = IQ score (117 in this case)μ = mean IQ score (100)σ = standard deviation (15)
Let's calculate the z-score:
z = (117 - 100) / 15z = 17 / 15z ≈ 1.1333
Now, we need to find the percentage of people with a z-score less than 1.1333. We can look up this value in the standard normal distribution table (also known as the Z-table) or use statistical software/tools.
Using the Z-table, we find that the percentage of people with a z-score less than 1.1333 is approximately 0.8708, or 87.08% (rounded to the nearest hundredth).
Therefore, approximately 87.1% of people have an IQ score less than 117.
Mavis charged $12 an hour to babysit and then spent $3 on gas, on her way home. She deposited $45 into her account on Saturday night.
a) -12h - 3 = 45
b) - 12h + 3 = 45
c) 12h + 3 = 45
d) 12h - 3 = 45
Answer: c) 12h + 3 = 45
Explanation:
Mavis charged $12 an hour to babysit, so her earnings for h hours would be 12h. She spent $3 on gas, which means her total earnings for the night would be 12h - 3. Finally, she deposited $45 into her account, so we can set up the equation as:
12h - 3 = 45
Solving for h:
12h = 48
h = 4
Therefore, Mavis babysat for 4 hours.
Step-by-step explanation:
The value of a piece of land in a town is increasing every year . Its value, in dollars, t years after 1970 and until 2001 can be modeled by the function 31, 000(1.001) ^ t . What is the domain of the function ?
A. All whole numbers greater than or equal to 1971 and less than or equal to 2001 .
B. All real numbers greater than or equal to 1971 and less than or equal to 2001 .
C . All non - negative real numbers less than or equal to 31.
D. All whole numbers less than or equal to 31
Answer:
D. All whole numbers less than or equal to 31
Step-by-step explanation:
The x value in this situation is the number of years after 1970 and until 2001.
This means that the domain will be the number of years after 1970 and until 2001.
Since the situation calculates the value of land in years after 1970, the domain will start at 0. Since it is until 2001, which is 31 years after 1970, the domain will go up to 31.
So, the domain will include all whole numbers less than or equal to 31.
The correct answer is D. All whole numbers less than or equal to 31
The domain of the function is a real number from 1971 to 2001. Then the correct option is B.
What is an exponent?Exponential notation is the form of mathematical shorthand which allows us to write complicated expressions more succinctly. An exponent is a number or letter is called the base. It indicates that the base is to raise to a certain power. X is the base and n is the power.
The value of a piece of land in a town is increasing every year.
Its value, in dollars, in t years after 1970 and until 2001 can be modeled by the function
\(\rm y = 31, 000(1.001) ^ t\)
Then the domain of the function will be
All real numbers are greater than or equal to 1971 and less than or equal to 2001.
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write an equation for the hyperbola that has vertices (±2,0) and foci (±53‾‾‾√,0).
the equation for the hyperbola is \((x^2 / 702.25) - (y^2 / 2652) = 1.\)
The standard equation for a hyperbola with center at the origin is:
\((x^2 / a^2) - (y^2 / b^2) = 1\)
where:
a is the distance from the center to the vertex along the x-axis
b is the distance from the center to the co-vertex along the y-axis
To find the values of a and b, we can use the distance formula between the vertices and the foci:
a = 53‾‾‾√ / 2 = 26.5‾‾‾√
c = distance from the center to the focus = 53‾‾‾√ - 2 = 51.5‾‾‾√
\(b = \sqrt{(c^2 - a^2)} = √(51.5^\sqrt{2}} - 26.5^\sqrt{2}} ) = \sqrt{(2652) } = \sqrt[2]{(663)}\)
Thus, the equation for the hyperbola is:
\((x^2 / (26.5√)^2) - (y^2 / (2√(663))^2) = 1\)
Simplifying, we get:
\((x^2 / 702.25) - (y^2 / 2652) = 1\)
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The midpoint of AB is M(-3,-3). If the coordinates of A are (-8,-2), what are the coordinates of B? Please explain
Step-by-step explanation:
Hey there!!!
Here,
The midpoint of AB is M(-3,-3) and coordinates of A is (-8,-2).
Now,
Using midpoint formulae,
\((x,y) =( \frac{x1 + x2}{2} ,\frac{y1 + y2}{2} )\)
Put all values.
\(( - 3,- 3) = ( \frac{ - 8 + x}{2} , \frac{ - 2 + y}{2} )\)
As they are equal, equating with their corresponding elements we get,
\( - 3 = \frac{ - 8 + x}{2} \)
Simplify them.
\( - 6 = - 8 + x\)
\(x = - 6 + 8\)
Therefore, x= 2
Now,
\( - 3 = \frac{ - 2 + y}{2} \)
Simplify them.
\( - 6 = - 2 + y\)
\(y = - 6 + 2\)
Therefore, y = -4.
Therefore, the coordinates of B are (2,-4).
Hope it helps...
Is this answer correct?
Find the slopes of the given lines and are they parallel, perpendicular, or neither?
Picture attached
How do I find the SURFACE AREA of the shape below.
Area of 2 triangles = 2*(1/2)*6*8
= 48 square ft
Area of 1 rectangle = 10*5
= 50 square ft.
Area of 2nd rectangle = 5*6
= 30 square ft.
Area of 3rd rectangle = 5*8
= 40 square ft.
Surface area of figure = 40+30+50+48
= 168 square ft.
suppose x1, x2, ... , x10 are independent random variables that are uniformly distributed on (0, 1). calculate the coefficient of variation of max{x1, x2, ... , x10}.
Therefore, the coefficient of variation of max{x1, x2, ..., x10} is 0.848.
To calculate the coefficient of variation of max{x1, x2, ... , x10}, we first need to find the mean and standard deviation of this random variable.
The probability that the maximum value is less than or equal to x is equal to the probability that each of the 10 variables is less than or equal to x. Since each variable is uniformly distributed on (0, 1), this probability is x^10.
Therefore, the cumulative distribution function (CDF) of the maximum variable is F(x) = x^10, for 0 < x < 1. Taking the derivative of the CDF, we get the probability density function (PDF) of the maximum variable:
f(x) = 10x^9
The mean of the maximum variable is given by:
E[max{x1, x2, ..., x10}] = ∫[0,1] x f(x) dx = ∫[0,1] 10x^10 dx = 1/11
To find the standard deviation, we need to calculate the second moment of the maximum variable:
E[(max{x1, x2, ..., x10})^2] = ∫[0,1] x^2 f(x) dx
Using integration by parts, we can evaluate this integral as:
E[(max{x1, x2, ..., x10})^2] = 10/132
Therefore, the variance of the maximum variable is:
Var[max{x1, x2, ..., x10}] = E[(max{x1, x2, ..., x10})^2] - (E[max{x1, x2, ..., x10}])^2 = 10/132 - (1/11)^2 = 879/14641
Finally, the coefficient of variation is the ratio of the standard deviation to the mean:
CV = sqrt(Var[max{x1, x2, ..., x10}]) / E[max{x1, x2, ..., x10}] = sqrt(879/14641) / (1/11) = 0.848
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PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
Answer:
\(x=20; y=50\) or \((20, 50)\)
Step-by-step explanation:
Substitution means plugging in one variable's value that consists of the opposite variable. Because \(y=3x-10\) is already specified, you can plug it into the second equation's \(y\) value. After doing that, it looks like this:
\(-4x+2y=20→-4x+2(3x-10)=20\)
Then you would distribute the \(3\) across the parentheses next to it, like this:
\(-4x+2(3x-10)=20→-4x+6x-20=20\)
Then, add like terms, like this:
\(-4x+6x-20=20→2x=40\)
Then divide both side by \(2\) to isolate \(x\).
\(x=20\)
Now, you can plug \(20\) (\(x\)) into either equation, but the first one seems simpler so you would pick that. It would look like this:
\(y=3x-10→y=3(20)-10\)
Solving would look like this:
\(y=3(20)-10→y=60-10→y=50\)
So the answer is \(x=20; y=50\) or \((20, 50)\).
Answer:
the answer is 20, 50
Step-by-step explanation:
please give brainliest
Please help me! giving out brianliest!
Answer:
Hmm, remember to use distributive property with the fraction and the numbers in the parenthesis.
Step-by-step explanation:
At noon, the temperature on Mt. Washington in Maine was 0°C. The temperature dropped an average of -0.5°C an hour. At what time would the temperature be -2.5°C? Explain what you did to get your result.
Answer:
5:00 pm
Step-by-step explanation:
Given that:
Temperature at noon = 0°C
Average temperature drop rate = - 0.5°C per hour
What time would temperature be - 2.5°C
Hence, target temperature = - 2.5°C
Time taken for temperature to drop = (target temperature / temperature drop rate)
Time taken = - 2.5°C / - 0.5°C / hr
Time taken = 5 hours
Hence, the time at which temperature will be - 2.5°C equals 5 hours after noon
12: 00 noon + 5 hours = 5:00 pm
Hence, temperature will be - 2.5°C by 5:00 pm