The shape that results from connecting the points (-4, 1), (-4, -4), (0, 3), and (0, 6) is a trapezoid.
What is a trapezoid?A trapezoid is a geometric form that has four sides, two of which are parallel and two of which are nonparallel (or skew lines). A trapezoid is also known as a trapezium (UK) or a trapeze (US).
The trapezoid's parallel sides are known as the bases, and the two nonparallel sides are known as the legs or lateral sides. The trapezoid is also sometimes referred to as the irregular quadrilateral.
How to identify a trapezoid?A quadrilateral is a shape that has four sides, four vertices, and four angles. The following are the characteristics of a trapezoid:
It has four sidesIt has two parallel sides and two nonparallel sidesIt has two opposite sides that are parallel to one another and two other sides that are not parallelIt has two acute angles and two obtuse anglesIt has diagonals that intersect at a midpointThe formula for the area of a trapezoid is as follows:
Area of a trapezoid = [ (base 1 + base 2) / 2 ] x height
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Arun’s mother’s age is 6 years more than 4 times Arun’s age. If Arun’s age is m years, find
mother’s age
As per the unitary method, Arun's mother would be 36 years old if Arun is 3 years old.
Let Arun's age be m years.
Let Arun's mother's age be n years.
From the problem statement, we know that n = 4m + 6. This means that Arun's mother's age is directly proportional to Arun's age, with a constant ratio of 4 and a constant difference of 6.
To solve for n, we can use the unitary method. We can set up a proportionality between the two ages as follows:
n / m = (4m + 6) / m
To solve for n, we can cross-multiply to get:
n = m x (4m + 6)
Expanding the right-hand side of the equation, we get:
n = 4m² + 6m
Therefore, Arun's mother's age is 4m² + 6m years. We can simplify this expression by factoring out 2m:
n = 2m(2m + 3)
This gives us a simpler form of the equation for Arun's mother's age. To find her age, we simply substitute Arun's age (m) into this expression and simplify.
If Arun is 3 years old (m = 15), then his mother's age would be:
n = 2m(2m + 3) = 2(3)(2(3) + 3) = 2(3)(6) = 36
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cindy and tom, working together, can rake the yard in 8 hours. working alone, tom takes twice as long as cindy. how many hours does it take cindy to rake the yard alone?
Cindy and tom, working together, can rake the yard in 8 hours. Working alone, Tom takes twice as long as Cindy, it takes Cindy to rake the yard 2 hours
How do we calculate the time it takes Cindy?To find the time it takes Cindy to rake the yard alone, let's use the following steps:Let x be the time taken by Cindy to rake the yard alone . Then the time taken by Tom to rake the yard alone will be 2xIt is given that Cindy and Tom can rake the yard in 8 hours when they work together.
Using the formula for working together, we get:[tex]\[\frac{1}{x} + \frac{1}{2x} = \frac{1}{8}\][/tex] Multiplying the equation by the least common multiple of the denominators, we get:[tex]\[16 + 8 = 2x\][/tex] Simplifying, we get:[tex]\[2x = 24\][/tex]Dividing both sides by 2, we get:[tex]\[x = 12\][/tex]Therefore, it takes Cindy 12 hours to rake the yard alone.
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question if all other factors are held constant, which of the following results in an increase in the probability of a type ii error? responses the true parameter is farther from the value of the null hypothesis. the true parameter is farther from the value of the null hypothesis. the sample size is increased. the sample size is increased. the significance level is decreased. the significance level is decreased. the standard error is decreased. the standard error is decreased. the probability of a type ii error cannot be increased, only decreased.
If all other factors are held constant, decreasing the significance level results in an increase in the probability of a type II error. This is true. we can say that the probability of making a type II error increases when the significance level is lowered.
What is a type II error? In hypothesis testing, a type II error occurs when a false null hypothesis is not rejected. When there is a real effect and the null hypothesis is false, this happens. It's a mistake that occurs when a researcher fails to reject a false null hypothesis.
A false negative is another term for a type II error. The power of the test, the size of the sample, the confidence level, and the effect size are all factors that influence the probability of making a type II error. Only if we decrease the significance level can the probability of a type II error be increased.
What is the significance level? The significance level is also known as alpha. It is the probability of rejecting a null hypothesis when it is true. It is represented by α. It is usually set at 0.05 or 0.01 in most studies. When the significance level is lowered, the probability of making a type I error decreases, but the probability of making a type II error increases. Therefore, we can say that the probability of making a type II error increases when the significance level is lowered.
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A function is shown in the box. What is the value of this function for f(-8)?
(Write the answer as an improper fraction in lowest terms.)
Answer:
f(x) = (5/6)x - (1/4)
f(-8) = (5/6)(-8) - (1/4)
f(-8) = (5/3)(-4) - (1/4)
f(-8) = (-20/3) - (1/4)
f(-8) = (-80-3)/12
f(-8) = -83/12
Find the following percentiles for the standard normal distribution. Interpolate where appropriate. (Round your answers to two decimal places.)a. 81stb. 19thc. 76thd. 24the. 10 th
The percentiles for the standard normal distribution
a. 0.93
b. -0.88
c. 0.67
d. -0.65
e. -1.28
To determine the percentiles for the standard normal distribution, use the standard normal distribution table. Percentiles for standard normal distribution are given by the standard normal distribution table.
The standard normal distribution is a special type of normal distribution with a mean of 0 and a variance of 1.
Step 1: Write down the given percentiles as a decimal and round to two decimal places.
For example, for the 81st percentile, 0.81 will be used.
Step 2: Use the standard normal distribution table to find the corresponding z-score.
Step 3: Round off the obtained answer to two decimal places.
a) 81st percentile:
The area to the left of the z-score is 0.81.
The corresponding z-score is 0.93.
Hence, the 81st percentile for the standard normal distribution is 0.93.
b) 19th percentile:
The area to the left of the z-score is 0.19.
The corresponding z-score is -0.88.
Hence, the 19th percentile for the standard normal distribution is -0.88.
c) 76th percentile:
The area to the left of the z-score is 0.76.
The corresponding z-score is 0.67.
Hence, the 76th percentile for the standard normal distribution is 0.67.
d) 24th percentile:
The area to the left of the z-score is 0.24.
The corresponding z-score is -0.65.
Hence, the 24th percentile for the standard normal distribution is -0.65.
e) 10th percentile:
The area to the left of the z-score is 0.10.
The corresponding z-score is -1.28.
Hence, the 10th percentile for the standard normal distribution is -1.28.
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(13-12p) × (13+12p)
...
Answer:
169 - 144p²
Step-by-step explanation:
(13 - 12p) × (13 + 12p)
each term in the second factor is multiplied by each term in the first factor
13(13 + 12p) - 12p(13 + 12p) ← distribute parenthesis
= 169 + 156p - 156p - 144p² ← collect like terms
= 169 - 144p²
Can some one solve this and show their work please
Answer:
m = 2n = 7Step-by-step explanation:
we solve with two equations between the corresponding sides
9m = 7m + 4
9m - 7m = 4
2m = 4
m = 2
----------------------------------
check
9 x 2 = 7 x 2 + 4
18 = 18
this answer is good
n + 6 = 2n - 1
n + 7 = 2n
7 = n
-----------------------------------
7 + 6 = 2 x 7 - 1
13 = 13
this answer is good
Use the integration capabilities of a graphing utility to approximate to two decimal places the area of the surface formed by revolving the polar equation over the given interval about the polar axis. r = 7 cos(20), [0, Phi/4]
The approximate area of the surface formed by revolving the polar equation over the given interval about the polar axis is 67.59 square units.
To solve the question, we can use the integration capabilities of a graphing utility to approximate to two decimal places the area of the surface formed by revolving the polar equation over the given interval about the polar axis. Polar curve is a type of curve that is made up of points that represent polar coordinates (r, θ) instead of Cartesian coordinates.
A polar curve can be represented in parametric form, but it is often more convenient to use the polar equation for a curve. According to the question, r = 7 cos(20), [0, Phi/4] is the polar equation and we need to find the approximate area of the surface formed by revolving the polar equation over the given interval about the polar axis.
To solve the problem, follow these steps: Convert the polar equation to a rectangular equation. The polar equation r = 7 cos(20) is converted to a rectangular equation using the following formulas: x = r cos θ, y = r sin θx = 7 cos (20°) cos θ, y = 7 cos (20°) sin θx = 7 cos (θ - 20°) cos 20°, y = 7 cos (θ - 20°) sin 20°
Sketch the curve in the plane. We can sketch the curve of r = 7 cos(20) by plotting the points (r, θ) and then drawing the curve through these points. Use the polar equation to set up the integral for the volume of the solid of revolution.
The volume of the solid of revolution is given by the formula: V = ∫a b πf2(x) dx where f(x) = r, a = 0, and b = Φ/4.We can find the volume of the solid of revolution using the polar equation: r = 7 cos(20) => r2 = 49 cos2(20) => x2 + y2 = 49 cos2(20)Thus, f(x) = √(49 cos2(20) - x2) = 7 cos(20°) sin(θ - 20°)
So, V = ∫a b πf2(x) dx = ∫0 Φ/4 π(7 cos(20°) sin(θ - 20°))2 dθStep 4: Use a graphing utility to evaluate the integral to two decimal places. Using a graphing utility to evaluate the integral, we get V ≈ 67.59.
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If the pyramids below are similar, what is the
ratio of their surface area?
21 in
14 in
A. 3:2
B. 6:4
C. 9:4
D. 27:8
The required ratio of the surface area of the given pyramids is (A) 3:2.
What are ratios?A ratio can be used to show a relationship or to compare two numbers of the same type.
To compare things of the same type, ratios are utilized.
We might use a ratio, for example, to compare the proportion of boys to girls in your class.
If b is not equal to 0, an ordered pair of numbers a and b, denoted as a / b, is a ratio.
A proportion is an equation that equalizes two ratios.
For illustration, the ratio may be expressed as follows: 1: 3 in the case of 1 boy and 3 girls (for every one boy there are 3 girls)
So, the given surface area is:
- 21 in
- 14 in
Now, calculate the ratio as:
= 21/14
= 3/2
= 3:2
Therefore, the required ratio of the surface area of the given pyramids is (A) 3:2.
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if (20x+10) and (10x+50) are altenative interior angle then find x
Answer:
x = 4
Step-by-step explanation:
Alternative interior angles means these angles are equal in magnitude and sign
[tex]{ \tt{(20x + 10) = (10x + 50)}} \\ \\ { \tt{20x - 10x = 50 - 10}} \\ \\ { \tt{10x = 40}} \\ \\ { \tt{x = 4}}[/tex]
Your monthly take-home pay is $900. Your monthly credit card payments are about $135. What percent of your take-home pay is used for your credit card payments?
i came up with $765
Answer:15 percent
Step-by-step explanation:
Will give brainlest to first correct answer!!!
Evelyn has a bag that contains 3 red marbles and 2 blue marbles.
Evelyn randomly pulls a marble from the bag and then puts it back in the bag. She repeats this 20 times. How many times should she expect to draw a red marble from the bag?
Answer:
She will draw 120 times for a red marble
Step-by-step explanation:
write the equation in standard form for the circle with center (5,0) passing through (5, 9/2)
The equation in standard form for the circle with center (5,0) passing through (5, 9/2) is 4x² + 4y² - 40x + 19 = 0
Calculating the equation of the circleGiven that
Center = (5, 0)
Point on the circle = (5. 9/2)
The equation of a circle can be expressed as
(x - a)² + (y - b)² = r²
Where
Center = (a, b)
Radius = r
So, we have
(x - 5)² + (y - 0)² = r²
Calculating the radius, we have
(5 - 5)² + (9/2 - 0)² = r²
Evaluate
r = 9/2
So, we have
(x - 5)² + (y - 0)² = (9/2)²
Expand
x² - 10x + 25 + y² = 81/4
Multiply through by 4
4x² - 40x + 100 + 4y² = 81
So, we have
4x² + 4y² - 40x + 19 = 0
Hence, the equation is 4x² + 4y² - 40x + 19 = 0
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Write the given third order linear equation as an equivalent system of first order equations with initial values. (t - 2t^2)y' - 4y'" = -2t with y(3) = -2, y'(3) = 2, y"(3) = -3 Use x_1 = y, x_2 = y', and x_3 = y". with initial values If you don't get this in 2 tries, you can get a hint.
The given third-order linear equation is (t - 2t^2)y' - 4y'' = -2t with y(3) = -2, y'(3) = 2, y''(3) = -3.
We can write this equation as a system of first-order linear equations with initial values by introducing three new variables x_1, x_2, and x_3 such that:
x_1 = y
x_2 = y'
x_3 = y''
with initial values x_1(3) = -2, x_2(3) = 2, x_3(3) = -3.
The resulting system of equations is:
x_1' = x_2
x_2' = x_3
x_3' = (2t^2 - t)x_2 - 4x_3 + 2t
This system can be solved numerically for the unknown functions x_1, x_2, and x_3 with the initial conditions given.
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f of x is equals to 3 - 2 x and g of x is equals to X Minus x square + 1 where x is an element of I have set of numbers find the inverse of G and the value for X for which f of G is equals to g of f.
The inverse of the function g(x) is g⁻¹(x) = 0.5 + √(1.25 - x) and the value for x for which f(g(x)) = g(f(x)) is 1
Calculating the inverse of g(x)Given that
f(x) = 3 - 2x
Rewrite as
g(x) = -x² + x + 1
Express as vertex form
g(x) = -(x - 0.5)² + 1.25
Express as equation and swap x & y
x = -(y - 0.5)² + 1.25
Make y the subject
y = 0.5 + √(1.25 - x)
So, the inverse is
g⁻¹(x) = 0.5 + √(1.25 - x)
Calculating the value of xHere, we have
f(g(x)) = g(f(x))
This means that
f(g(x)) = 3 - 2(-x² + x + 1)
g(f(x)) = -(3 - 2x)² + (3 - 2x) + 1
Using a graphing tool, we have
f(g(x)) = g(f(x)) when x = 1
Hence, the value of x is 1
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Complete question
f(x) = 3 - 2x and g(x) = x - x² + 1 where x is an element of f have set of numbers
Find the inverse of G and the value for x for which f(g(x)) = g(f(x)).
Isaiah is grounded and has to stay in his room all day. He made up a game where he throws balled-up paper called a "trashball" into his trash can. The diameter of the top of the trash can 1 the diameter of the top of is 12 in. Isaiah wants the "trashball" to have a diameter that is the trash can. > What should the diameter of Isaiah's "trashball" be? d Level G ? in. 12 in.
Answer:
Isiah Thomas
Step-by-step explanation:
I amazing fact
Answer:
the correct answer is 4
Step-by-step explanation:
yea sorry i don’t know step-by-step
a pastry chef accidentally inoculated a cream pie with six s. aureus cells. if s. aureus has a generation time of 60 minutes, how many cells would be in the cream pie after 7 hours?
After the time of seven hours, the cream pie would have approximately 768 S. aureus cells after 7 hours with a generation time of 60 minutes.
How many cells would be in the cream pie after 7 hours?Six S. aureus cells have been accidentally inoculated into a cream pie. S. aureus has a generation time of 60 minutes. S. aureus is a pathogenic bacterium found in the environment, as well as on the skin, and in the upper respiratory tract.
The generation time of this bacterium is 60 minutes, meaning that a single bacterium can produce two new cells in 60 minutes.
If there are 6 S. aureus cells in a cream pie, the number of bacteria will continue to increase as time passes.
The number of generations (n) in seven hours is calculated as:
n = t/g
n = 7 hours × 60 minutes/hour/60 minutes/generation = 7 generations
The number of cells in the cream pie after 7 hours is calculated as :
N = N₀ × 2ⁿ
N = 6 cells × 2⁷
N = 768 cells
Therefore, after seven hours, the cream pie would have approximately 768 S. aureus cells.
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Given that m∠A=(16x)°, m∠C=(8x+20)°, and m∠D=128°, what is m∠B
The value of m∠B is 212 - 24x.
How did we get the value?The totality of the angles in a quadrilateral is always amount to 360°. This is a primary property of all quadrilaterals, irrespective of their shape or size.
As a result, irrespective of the shape say if you are dealing with a square, rectangle, parallelogram, trapezoid, or any other type of quadrilateral, the totality of the angles will always be sum to 360°.
To determine the value of m∠B, one can employ the notion that the sum of the angles in a quadrilateral is 360°.
Thus,
m∠A + m∠B + m∠C + m∠D = 360
Substituting the given values, we get:
(16x)° + m∠B + (8x+20)° + 128° = 360
Simplifying and solving for m∠B, we get:
m∠B = 360 - (16x)° - (8x+20)° - 128°
m∠B = 212 - 24x
Therefore, the value of m∠B is 212 - 24x.
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Seven bags of cement weighs 3kg 52g what Is the weight of the each?
Answer:
436g
Step-by-step explanation:
1kg=1000g
3kg=3000g
3000+52=3052
3052÷7=436
Arrange the steps in the correct order to find an inverse of a modulo m for each of the following pairs of relatively prime integers using the Euclidean algorithm.
a = 55, m = 89
An inverse of a modulo m for a = 55, m = 89 using the Euclidean algorithm is 34.
In order to find an inverse of a modulo for each of the following pairs of relatively prime integers using the Euclidean algorithm can be found by:
Using the Euclidean algorithm to find the greatest common divisor (gcd) of a and m. In this case, we have:
89 = 1 x 55 + 34
The gcd of 55 and 89 is 1.
Using the extended Euclidean algorithm, work backwards up the chain of remainders to express 1 as a linear combination of a and m. In this case, we have: 34 x 55 - 21 x 89
The coefficient of a in the expression from step 3 is the inverse of a modulo m. In this case, the inverse of 55 modulo 89 is 34.
To verify that the inverse is correct, multiply a and its inverse modulo m. The product should be congruent to 1 modulo m. In this case, we have:
55 x 34 = 1870
11 = 1 x 11 + 0
Since the remainder is 0, we know that 55 x 34 is a multiple of 89, so it is congruent to 0 modulo 89. Therefore, we have:
55 x 34 ≡ 0 |89|
Adding 89 to the left-hand side repeatedly until we get a number that is congruent to 1 modulo 89, we find:
55 x 34 ≡ 0 + 89 x 7 ≡ 1 |89|
Therefore, the inverse of 55 modulo 89 is indeed 34.
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50 POINTS
A bathroom heater uses 10.5 A of current when connected to a 120. V potential difference. How much power does this heater dissipate?
Remember to identify all data (givens and unknowns), list equations used, show all your work, and include units and the proper number of significant digits to receive full credit
The power dissipated by the heater is 1260 watts (W).
What is a polynomial?
A polynomial is a mathematical expression consisting of variables (also known as indeterminates) and coefficients, which are combined using only the operations of addition, subtraction, and multiplication.
Given:
Current (I) = 10.5 A
Potential Difference (V) = 120 V
Unknown:
Power (P) = ?
The formula to calculate the power is:
P = VI
Substituting the given values:
P = 120 V × 10.5 A
P = 1260 W
It's important to note that the number of significant digits should be based on the precision of the given values. In this case, both values have three significant digits, so the answer should also have three significant digits. Thus, the final answer should be:
P = 1260 W (rounded to three significant digits).
Therefore, the power dissipated by the heater is 1260 watts (W).
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the picture pls answer my picture.
Answer:
$63 more in tax
Step-by-step explanation:
Takis is 5.25 in tax
PlayStation is 68.25
well, we know the tax is 10.5% so let's get them for both.
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{10.5\% of 49.99}}{\left( \cfrac{10.5}{100} \right)49.99} ~~ \approx ~~ 5.25[/tex]
[tex]\stackrel{\textit{10.5\% of 649.99}}{\left( \cfrac{10.5}{100} \right)649.99} ~~ \approx ~~ 68.25\hspace{9em}\underset{ \textit{taxes' difference} }{\stackrel{ 68.25~~ - ~~5.25 }{\approx\text{\LARGE 63}}}[/tex]
Can someone help me with this please?
To solve the question asked, you can say: So, the other angle of the figure is 49 degree.
what are angles?In Euclidean geometry, an angle is a shape consisting of two rays, known as sides of the angle, that meet at a central point called the vertex of the angle. Two rays can be combined to form an angle in the plane in which they are placed. Angles also occur when two planes collide. These are called dihedral angles. An angle in planar geometry is a possible configuration of two rays or lines that share a common endpoint. The English word "angle" comes from the Latin word "angulus" which means "horn". A vertex is a point where two rays meet, also called a corner edge.
here the given angles are as -
107 + (180-156) + x = 180
as total angle sum of a triangle is 180
so,
x = 180 - 131
x = 49
So, the other angle of the figure is 49 degree.
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4) Ella drives 60 miles per hour. How far will she drive in 2% hours?
Answer: 1.2 miles
Step-by-step explanation:
1 hour = 60 min
60 x 0.02 = 1.2 1 minute and 20 seconds has elapsed
60 miles/ every 60 minutes or 1 mile a minute
1 x 1.2 = 1.2
she has traveled 1.2 miles
Answer: The answer is 120 mph (miles per hour)
Step-by-step explanation:
The one thing you need to do is to figure out how many mph did Ella drive for 2 hours.
So, you need to do 60 x 2, and you will get the answer 120.
And there's your answer!
Hi help me with this question
Solve for X
30=5(X+5)
X=?
The solution for X in equation 30=5(X+5)X is X= 1.
To solve the equation, we can start by distributing the 5 on the right-hand side of the equation, which gives us:
30 = 5X + 25X
Combining like terms, we get:
30 = 30X
Dividing both sides by 30, we get:
X = 1
However, we need to check whether this value satisfies the original equation. Plugging X=1 into the equation gives us:
30 = 5(1+5)(1)
30 = 5(6)
30 = 30
Therefore, the only valid solution is X=1.
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Write the line equation of (5,-12) and (0,-2)
Answer:
To find the equation of the line passing through the points (5,-12) and (0,-2), we first need to find the slope of the line:
slope = (change in y) / (change in x)
slope = (-2 - (-12)) / (0 - 5)
slope = 10 / (-5)
slope = -2
Now that we have the slope, we can use the point-slope form of the line equation to find the equation of the line:
y - y1 = m(x - x1)
where m is the slope, and (x1, y1) is one of the given points on the line.
Let's use the point (5,-12):
y - (-12) = -2(x - 5)
y + 12 = -2x + 10
y = -2x - 2
Therefore, the equation of the line passing through the points (5,-12) and (0,-2) is y = -2x - 2.
When a homeowner has a 25-year variable-rate mortgage loan, the monthly payment R is a function of the amount of the loan A and the current interest rate i (as a percent); that is, R = f(A). Interpret each of the following. (a) R140,000, 7) - 776.89 For a loan of $140,000 at 7% interest, the monthly payment is $776.89. For a loan of $140,000 at 7.7689% interest, 700 monthly payments would be required to pay off the loan. For a loan of $140,000 at 7% interest, 776.89 monthly payments would be required to pay off the loan. For a loan of $140,000 at 7.7689% interest, the monthly payment is $700.
The monthly payment required to pay off a loan of $140,000 at 7% interest would be $776.89 is the correct statement(A).
The statement given is describing a function that relates the monthly payment R of a 25-year variable-rate mortgage loan to the loan amount A and the current interest rate i.
The given values are R = $776.89 and A = $140,000, with an interest rate of 7%. This means that the monthly payment required to pay off a loan of $140,000 at 7% interest would be $776.89.
However, the other statements are incorrect interpretations. For instance, the statement "For a loan of $140,000 at 7.7689% interest, 700 monthly payments would be required to pay off the loan" is incorrect.
This is because the number of payments required to pay off a loan depends not only on the loan amount and interest rate, but also on the term of the loan.
Similarly, the statement "For a loan of $140,000 at 7% interest, 776.89 monthly payments would be required to pay off the loan" is also incorrect, as the number of payments required would be determined by the term of the loan.
Finally, the statement "For a loan of $140,000 at 7.7689% interest, the monthly payment is $700" is also incorrect. This is because, for the given loan amount and interest rate, the monthly payment required would be $776.89, as calculated above.
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a credit risk study found that an individual with good credit score has an average debt of $15,000. if the debt of an individual with good credit score is normally distributed with standard deviation $3,000, determine the shortest interval that contains 95% of the debt values.
The shortest interval that contains 95% of the debt values is $9,492.02 to $20,507.98
How do we calculate the interval values?Given that a credit risk study found that an individual with good credit score has an average debt of $15,000 and the debt of an individual with good credit score is normally distributed with standard deviation $3,000.
Then the 95% confidence interval can be calculated as follows:
Upper limit: µ + Zσ
Lower limit: µ - Zσ
Where
µ is the mean ($15,000)Z is the z-scoreσ is the standard deviation ($3,000).The z-score corresponding to a 95% confidence interval can be found using the standard normal distribution table.
The area to the left of the z-score is 0.4750 and the area to the right is also 0.4750.
The z-score corresponding to 0.4750 can be found using the standard normal distribution table as follows:z = 1.96Therefore
Upper limit: µ + Zσ= $15,000 + 1.96($3,000) = $20,880
Lower limit: µ - Zσ= $15,000 - 1.96($3,000) = $9,120.02
The shortest interval that contains 95% of the debt values is $9,492.02 to $20,507.98.
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A circular flower garden has an area of 314m². A sprinkler at the center of the garden can cover an area of 12 m. Will the sprinkler water the entire garden?
Step-by-step explanation:
No,
if the sprinkler covers a distance of 12 m meaning the 12 m is the diameter...then to find the area that it covers we use the formula for the circle since it's circular
A=πr2
A=3.142*36
A=113.112 cm3
Ten percent of customers who walk into a golf store purchase a golf club and 30% of customers purchase golf balls. Six percent of customers purchase both clubs and balls. The percentage of customers who do not purchase clubs or balls is______. A) 0.24 B) 0.34 C) 0.41 D) 0.66
The percentage of customers who do not purchase clubs or balls is 0.66 or 66%.
Ten percent of customers who walk into a golf store purchase a golf club and 30% of customers purchase golf balls. Six percent of customers purchase both clubs and balls. The percentage of customers who do not purchase clubs or balls is 0.66.
Given that, The percentage of customers who purchase golf clubs = 10%The percentage of customers who purchase golf balls = 30%The percentage of customers who purchase both clubs and balls = 6%To find out the percentage of customers who do not purchase clubs or balls, we have to subtract the percentage of customers who purchase either clubs or balls or both from 100%.
Percentage of customers who purchase either clubs or balls or both = 10% + 30% - 6% = 34% Percentage of customers who do not purchase clubs or balls = 100% - 34% = 66%.
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