Answer:
Length = 60 inches
Width = 17 inches
Step-by-step explanation:
Let width = w
Length = 3w + 9
Perimeter = 154
Perimeter = 2(length + width)
2(3w + 9 + w) = 154
8w + 18 = 154
8w = 154 - 18
8w = 136
w = 136/8
w = 17 inches
Length = 3w + 9 = 3(17) + 9 = 60 inches
Mackenzie has
22
ft of decorative fencing to line her rectangular flower garden. If her garden must have a width of
4
ft, what will the length of her garden have to be to use all
22
ft of fencing?
Answer:
the length of her garden will have to be 5.5ft
22÷4=5.5
A company is reviewing a batch of 20 products to determine if any are defective. On average, 3.7% of products are defective. Does this situation describe a binomial experiment, and why? Pick What is the probability that the company will find 2 or fewer defective products in this batch? Ex: 1.23 % What is the probability that 4 or more defective products are found in this batch? Ex: 1.28 % If the company finds 5 defective products in this batch, should the company stop production? Pick v
There is a 96.37% probability that the company will find 2 or more defective products.
There is a 2.08% probability that the company will find 4 or more defective products.
There is a 0.02% probability that the company will find 5 or more defective products. So company will give profit.
There are only two possible outcomes for each product: either it is defective or it is not. The binomial distribution is used to answer this question because each product's defect probability is independent of all other products.
Binomial probability distribution
The probability of precisely x successes on n repeated trials is known as the binomial probability.
[tex]P_x = \;^nC_r.p^x.q^{n-x}[/tex]
Where,
Px = binomial probability,
[tex]\;^nC_r =[/tex] number of combination
p = probability of success on a single trial
q = probability of failure on a single trial = (1 - p)
n = number of trials
x = number of times for a specific outcome within n trials
So, from question,
20 products mean n = 203.7% of products are defective mean p = 3.7% = 0.0371) The probability that, 2 or fewer defective products is;
P(X≤2) = P(X=0) + P(X=1)+ P(X=2) -----------------(1)
So,
[tex]P_x = \;^nC_r.p^x.q^{n-x}[/tex]
P(X=0) = [tex]\;^{20}C_0.p^0.q^{20-0}[/tex] = [tex]\; 1.(1-p)^{20-0}[/tex] = (1-0.037)²⁰ = (0.963)²⁰ = 0.4704
P(X=1) = [tex]\;^{20}C_1.p^1.q^{20-1}[/tex] = [tex]\; 20.(0.037).(0.963)^{19}[/tex] = 0.3614
P(X=2) = [tex]\;^{20}C_2.p^2.q^{20-2}[/tex] = [tex]\;190\times(0.037)^2\times(0.963)^{18}[/tex] = 0.1319
Now, putting the all values in equation (1)
P(X≤2) = P(X=0) + P(X=1)+ P(X=2) -----------------(1)
= 0.4704 + 0.3614 + 0.1319
P(X≤2) = 0.9637 = 96.37%
There is a 96.37% probability that the company will find 2 or more defective products.
2)
1.23% are defective means p = 0.0123
The probability that find 4 or more defective products are;
P(X≤4) = 1 - P(X< 4) -----------(2)
P(X< 4) = P(X=0) + P(X=1)+ P(X=2) + P(X=3)-----------------(3)
So,
P(X=0) = = [tex]\;^{20}C_0.p^0.q^{20-0}[/tex] = [tex]\; (0.9877)^{20}[/tex] = 0.7807
P(X=1) = [tex]\;^{20}C_1.p^1.(1-p)^{20-1}[/tex] = [tex]20\times (0.0123)\times (0.9877)^{19}[/tex] = 0.1944
P(X=2) = [tex]\;^{20}C_2.p^2.(1-p)^{20-2}[/tex] = [tex]190\times (0.0123)^2\times (0.9877)^{18}[/tex] = 0.0024
P(X=3) = [tex]\;^{20}C_3.p^3.(1-p)^{20-3}[/tex] = [tex]1140\times (0.0123)^3\times (0.9877)^{18}[/tex] = 0.0017
So,
P(X< 4) = 0.7807+0.1944+0.0024+0.0017 =0.9792
P(X≤4) = 1 - P(X< 4) = 1 - 0.9792 = 0.0208 = 2.08%
There is a 2.08% probability that the company will find 4 or more defective products.
3)
1.28% are defective means p = 0.0128
The probability that find 5 or more defective products are;
P(X≤5) = 1 - P(X< 5) -----------(4)
P(X< 5) = P(X=0) + P(X=1)+ P(X=2) + P(X=3)+ P(X=4)-----------------(5)
So,
P(X=0) = = [tex]\;^{20}C_0.p^0.q^{20-0}[/tex] = [tex]\; (0.9872)^{20}[/tex] = 0.7728
P(X=1) = [tex]\;^{20}C_1.p^1.(1-p)^{20-1}[/tex] = [tex]20\times (0.0128)\times (0.9872)^{19}[/tex] = 0.2004
P(X=2) = [tex]\;^{20}C_2.p^2.(1-p)^{20-2}[/tex] = [tex]190\times (0.0128)^2\times (0.9872)^{18}[/tex] = 0.0246
P(X=3) = [tex]\;^{20}C_3.p^3.(1-p)^{20-3}[/tex] = [tex]1140\times (0.0128)^3\times (0.9872)^{18}[/tex] = 0.0019
P(X=4) = [tex]\;^{20}C_4.p^4.(1-p)^{20-4}[/tex] = [tex]4845 \times (0.0128)^3\times (0.9872)^{18}[/tex] = 0.0001
So,
P(X< 5) = 0.7728+0.2004+0.0246+0.0019+0.0001 = 0.9998
P(X≤5) = 1 - P(X< 5) = 1 - 0.9998 = 0.0002 = 0.02%
There is a 0.02% probability that the company will find 5 or more defective products. So company will give profit.
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6 What types of decimal numbers are rational? What types are irrational?
7 Write down two more examples (decimal, fraction, etc.) of each type of number: rational and irrational. Explain your choices.
What is the slope of a line perpendicular to the line whose equation is x+y=-6x. Fully reduce your answer.
The slope of the equation is -7. Then the slope of the perpendicular line will be 1/7.
What is the equation of a perpendicular line?Let the equation of the line be y = mx + c. Then the equation of the perpendicular line that is perpendicular to the line y = mx + c is given as y = -(1/m) + d. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.
The equation of the line is given as,
y = - 7x
The slope of the equation is -7. Then the slope of the perpendicular line will be
⇒ -(1/(-7))
⇒ 1/7
The slope of the equation is -7. Then the slope of the perpendicular line will be 1/7.
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2.
If a train travels between two cities in 3 hours at an average speed of 65 miles per hour, how long
would it take at an average speed of 80 miles per hour?
Answer:
At 65mph the car traveled 195 miles in 3hrs.
So divide 195 miles by 80mph to get 2.4375 hrs
Find the midpoint of a line segment with endpoints A(-5, 5) and B(2, -5).
Please help show your own work
Answer: (-1.5, 0)
Step-by-step explanation:
Use the midpoint formula, [tex](\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})[/tex]. Plug in the points into the equation to get [tex](\frac{-5+2}{2},\frac{5-5}{2})[/tex] = (-1.5, 0)
Admission to a baseball game is $4.00 for general admission and $6.50 for reserved seats. The receipts were $4589.50 for 988 paid admissions. How many of each ticket were sold?
There were 733 general tickets sold and 255 reserved tickets.
How to calculate the values?Let the general admission = g
Let the reserved seats = r
Therefore, the appropriate equation will be:
g + r = 988
4g + 6.5r = 4589.50
From equation i r = 988 - g
4g + 6.5r = 4589.50
4g + 6.5(988 - g) = 4589.50
4g + 6422 - 6.5g = 4589.50
6.5g - 4g = 6422 - 4589.50
2.5g = 1832.50
g = 1832.50/2.5
g = 733
Since g + r = 988
r = 988 - 733
r = 255
Therefore, there were 733 general tickets sold and 255 reserved tickets.
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Someone please help me I’m lost i don’t understand
1. 'x' = -18/4
2. 'x' = -4/3
The equations are Not Equivalent.
1. Linear Equation :An equation between two variables that gives a straight line when plotted on a graph. Or we can say,
A linear equation is defined as an equation that is written in the form of Ax+By=C. It is the combination of two variables and a constant value present in them.
We have given
(x/3) - 2 = (5x/3) + 3
(5x/3) - (x/3) = -2 - 3
4x/3 = -6
4x = -6 × 3
x = -18/4
In first equation we got the value of x is -18/4.
2. Equivalent to Linear Equation :Two systems of linear equations are equivalent if and only if they have the same set of solutions.
To determine the equivalent of linear equation,
First, we need to find the value of "x" for each equation. If "x" is the same for both equations, then they are equivalent. If "x" is different then the equations are not equivalent.
We have equation
x(x + 1) = (x + 2)²
x² + x = x² + 4 + 4x
(We have solved (x + 2)² by using algebraic identity (a + b)² = a² + b² + 2ab.)
4x - x = x²- x² - 4
3x = -4
x = -4/3
In the second equation we got the value of x is -4/3.
Hence, as we can see it clearly that the value of x is not same in both equations so this is Not Equivalent.
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Find the area of the shaded region. Help please!
[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=10\\ \theta =85 \end{cases}\implies \begin{array}{llll} A=\cfrac{(85)\pi (10)^2}{360} \\\\\\ A=\cfrac{425\pi }{18}\implies A\approx 74.18~cm^2 \end{array}[/tex]
Jill has 4 one-dollar bills, 3 quarters, 4 dimes, and 3 pennies. Mark has 3 one-dollar bills, 4 dimes, and 2 pennies. What is the difference between the amount of money Jill has and the amount of money Mark has? A B C $1.01 $1.76 $7.85 D $8.60.
Answer: Answer choice 'B'
Step-by-step explanation:
4.00 + 0.75 + 0.40 + 0.03 = $5.18. This is Jill's amount.
3.00 + 0.40 + 0.02 = $3.42. This is Mark's amount.
To find out how much more money Jill has in comparison to how much mark has, we need to subtract Jill's money by Mark's money ($5.18 - $3.42)
if done correctly, your answer should be $1.76 (answer 'B')
There is a real number whose product with every real numbers equal zero
a. Some ___ has the property that is __.
b. There is a real number a such that the product of á __.
c. There is a real number á with the property that for every real number b __.
There is a real number whose product with every real number equals zero
a. Some real number has the property that its product with every real number equals 0.
b. There is a real number a such that the product of á and any real equals zero.
c. There is a real number á with the property that for every real number b, the product of a and b equals zero.
o qualify for security officers’ training recruits are tested for stress tolerance. The scores are normally distributed, with a mean of 62 and a standard deviation of 8.
If only the top 15% of recruits are selected, find the cutoff score.
The cutoff score is mathematically given as
x_n=70.32 (cutoff)
This is further explained below.
What is the cutoff score.?Generally, the equation for is mathematically given as
[tex]&P\left(X > x_0\right)=0.15 \Rightarrow P\left(X < x_0\right)=0.85 \\[/tex]
[tex]&\Rightarrow P\left(\frac{X-\mu}{\sigma} < \frac{x_0-\mu}{\sigma}\right)=0.85 \\[/tex]
[tex]&\Rightarrow P\left(Z < \frac{x_0-\mu}{\sigma}\right)=0.85 \\\\&\Rightarrow \frac{x_0-\mu}{\sigma}=\text { invNorm }(0.85) \\\\&\Rightarrow x_0=\mu+\sigma \times \text { invNorm }(0.85)[/tex]
Use z-table to get inv Norm() = 1.04
x_0=62+8 *(1.04)=70.32
In conclusion, Top 15% are above x_n=70.32 (cutoff)
Clearly this is 85th percentile
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- 12(x+12) + 1177 = 10 + 15
Answer:
x = 84
Step-by-step explanation:
-12(x+12) + 1177 = 10 + 15
-12x - 144 + 1177 = 25
1033 = 25 + 12x
1008 = 12x
x = 84
In August 2006, a report was issued about an Internet poll conducted on behalf of the Oxygen Television Network. The survey included 1400 women and 700 men, aged 15 to 49. The following is part of a press release about the findings.
"Apparently if it's a gadget, women gotta have it, according to a survey done by Oxygen Media, an American cable network owned and operated by women. The Women's Watch: Girls Gone Wired survey released in August indicates that 77 per cent of women fancy a new plasma TV over a diamond solitaire necklace, 78 per cent would rather have a sleek new cell phone than shoes, and 86 per cent would prefer a new digital video camera over designer footwear."
What can be said about these poll results?
Answer:
Results of the Assembly elections in five States are indeed a shot in the arm for the Bharatiya Janata Party (BJP), which won in all four States where it was in power. The Hindu editorial captures the broad trends that emerge out of these results. Prime Minister Narendra Modi has said these results have sealed the outcome of the 2024 Lok Sabha elections too in the BJP’s favour. He said people have rejected caste and dynastic politics.
Which of the following statements are true?
a) 25:35 = 45:55
b) 105: 30 = 49: 14
c) 45:48 = 60:64
HELP 50 POINTS (see image attached)
5
1
2
8
-2
The value of the function f(3) is 1
How to determine the value of f(3)?The graph represents the given parameter
The value of f(3) implies that we calculate the value of the function when x = 3
From the graph, we have
f(x) = 1, when x = 3
This means that
f(3) = 1
The above is calculated by substituting 3 for x in the equation f(x) = 1
Hence, the value of f(3) is 1
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Find the slope P=(-4,-1) Q=(-3,-3)
The slope of P=(-4,-1) Q=(-3,-3) is -2.
Given,
P=(-4,-1)
Q=(-3,-3)
The slope between two points P=(x₁, y₁)
Q=(x₂ ,y₂)
slope = (y₂-y₁)/(x₂-x₁)
So slope between P=(-4,-1) Q=(-3,-3) is
[(-3)-(-1) ]/ [(-3)-(-4)]
=-2/1
=-2
A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
Any two different points on a line may be used to compute the slope of any line. The ratio of "vertical change" to "horizontal change" between two separate locations on a line is calculated using the slope of a line formula.
The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Finding the slope between two separate locations and calculating the slope of a line are related tasks. In general, we require the values of any two separate coordinates of a line in order to determine its slope.
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Given q = √(5p²-1)²-2 find p in terms of q.
Answer:
[tex]\sf p =\sqrt{\dfrac{q+3}{5}}[/tex]
Step-by-step explanation:
To find p in terms of q, we have to isolate p.
[tex]\sf \sqrt{(5p^2 - 1)^2}-2 = q\\\\[/tex]
5p² - 1 - 2 = q
5p² - 3 = q
Add 3 to both sides,
5p² = q + 3
Divide both sides by 5,
[tex]\sf p^2 = \dfrac{q+3}{5}\\\\\text{Take square root,}\\\\p =\sqrt{\dfrac{q+3}{5}}[/tex]
Lesson 1.17
Quadrilateral ABCD is congruent to quadrilateral
A'B'C'D'. Describe a sequence of rigid motions that
takes A to A', B to B', C to C', and D.
please im begging you please help!!!
Answer:
You will translate A up until it is equal with A', then you will reflect the figure over the line of symmetry that will be half way between line segments CD and C'D'
Step-by-step explanation:
I am not sure if the polygon is drawn on a coordinate plane. I cannot see any horizontal or vertical lines to tell you exactly how many units to move up.
7.Ms. Levine went to the store to
buy candy for Star Time. She
purchases Skittles for $9.75 box
per
and she bought 8 boxes. How much
did she spend in all?
Answer:
78 dollars
Step-by-step explanation:
9.75 multiplied by 8 is 78.
14. Jennifer and Francine are running a race where Francine runs the race far faster than Jennifer.
It takes Jennifer just five seconds less than twice Francine's time to finish. If their combined
total time is 86 seconds and frepresents the amount of time it takes Francine to finish, then
which of the following equations models this situation?
(1) ƒ+2(ƒ-5)=86
(3) ƒ+2ƒ-5=86
(2) 2ƒ-5=86
(4) 2f-5=43
The answer is (2) 2f-5=86; I hope- :\
Solve for rate in the following application problem. A company reports that office income last month was $315,400, while advertising expenses were $21,447.20. What percent of last month's income was spent on advertising?
Answer:
6.8%
Step-by-step explanation:
[tex]\frac{21447.20}{315400}[/tex] When you divide this, you get 0.068. This is in decimal form. To change to a percent move the decimal to places to the right 6.8%
PLEASE HELP !! 20 POINTS
A piecewise function f (x) is defined by f of x is equal to the piecewise function of 3 to the power of the quantity x plus 1 end quantity minus 2 for x is less than or equal to 1 and the quantity negative x squared plus x plus 2 end quantity over the quantity x squared minus 3 times x plus 2 end quantity for x is greater than 1
Part A: Graph the piecewise function f (x) and determine the range. (5 points)
Part B: Determine the asymptotes of f (x). Show all necessary calculations. (5 points)
Part C: Describe the end behavior of f (x). (5 points)
From the graph of the piecewise function, we have that:
a) The range of the function is (-∞,7).
b) The vertical asymptote is of x = 2, and the horizontal asymptotes are y = -1 and y = -2.
c) The end behavior of the function is described as follows: As x -> -∞, y -> -2 and as x -> ∞, y -> -1.
What is a piecewise function?A piecewise function is a function that has different definitions, depending on the input.
For this problem, the definitions of the function are given as follows:
[tex]f(x) = 3^{x+1} - 2, x \leq 1[/tex].[tex]f(x) = \frac{-x^2 + x + 2}{x^2 - 3x + 2}, x > 1[/tex]The graph of the function is given at the end of the answer.
What is the range of the function?The range of the function is the set that contains all the output values of the function, and in a graph, this is the values of y.
Hence:
The range of the function is (-∞,7).
What are the asymptotes of the function?The asymptotes of the functions are the values of x for which the function is not defined. In this problem, the function is not defined for x = 2, hence the vertical asymptote is of x = 2.
The horizontal asymptotes are the values of the function when it goes to infinity, hence they are y = -2 and y = -1.
What is the end behavior of the function?The end behavior is given by the limits of the function as it goes to infinity, being closely related to the horizontal asympotes.
Hence:
As x -> -∞, y -> -2 and as x -> ∞, y -> -1.
Please ignore the (60,1) point plotted on the graph, it should be (60,-1).
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Mathematics in the modern world
Answer:
Mathematics shaping the modern world.
Reflexive Property of Angle Measure: mZB = ?- - -
Answer:
example of compound interest with solution
f(x)=x 3 −9xf, Over which interval does f have a positive average rate of change?
The interval in which the function has positive average rate of change is x > √3
How to determine the interval which the function has positive average rate of change?The function is given as
f(x) = x^3 - 9x
Differentiate the above function to determine the average rate of change
So, we have
f'(x) = 3x^2 - 9
Set the function to greater than 0
So, we have
3x^2 - 9 > 0
Add 9 to both sides
3x^2 > 9
Divide by 3
x^2 > 3
Take the square root of both sides
x > √3
Hence, the interval in which the function has positive average rate of change is x > √3
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100 POINTS PLEASE ANSWER QUICK
Use the box plot below to answer the questions.
Part A: Estimate the IQR for the male data.
Part B: Estimate the difference between the median values of each data set.
Part C: Describe the distribution of the data and if the mean or median would be a better measure of center for each.
The median is a better measure of center for the male's data, while the mean is a better for the female's data.
What are quartiles?When we get data which can be compared relatively with each other, for finding quartiles, we arrange them in ascending or descending order.
Quartiles are then selected as 3 points such that they create four groups in the data, each groups approximately possessing 25% of the data.
(a) The IQR of the male's data
From the given male's boxplot, we have the following data elements;
Upper quartile (Q3) = 14
Lower quartile (Q1) = 2
Then the IQR is calculated as:
IQR = Q3 - Q1
So, we have:
IQR = 14 - 2
IQR = 12
Hence, the IQR for the given males' data is 12
(b) The difference between the median values can be calculated as;
Median of male's data = 14
Median of female's data = 9
The difference (d) between the median values is;
d = 14 - 9
d = 5
Hence, the difference between the median values of each data set is 5
(c) The distribution of data
It is found that the median is a better measure of center for the male's data, while the mean is a better measure of center for the female's data.
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The median is a better measure of center for the male's data, while the mean is a better for the female's data.
What are quartiles?
When we get data which can be compared relatively with each other, for finding quartiles, we arrange them in ascending or descending order.
Quartiles are then selected as 3 points such that they create four groups in the data, each groups approximately possessing 25% of the data.
(a) The IQR of the male's data
From the given male's boxplot, we have the following data elements;
Upper quartile (Q3) = 14
Lower quartile (Q1) = 2
Then the IQR is calculated as:
IQR = Q3 - Q1
So, we have:
IQR = 14 - 2
IQR = 12
Hence, the IQR for the given males' data is 12
(b) The difference between the median values can be calculated as;
Median of male's data = 14
Median of female's data = 9
The difference (d) between the median values is;
d = 14 - 9
d = 5
Hence, the difference between the median values of each data set is 5
(c) The distribution of data
It is found that the median is a better measure of center for the male's data, while the mean is a better measure of center for the female's data.
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using associative property
(y+12)+28
A diver is located at -157 feet relative to the surface of the water. If there is a shark swimming 38 feet above him,what is the position of the shark relative to the surface of the water
Answer: -119 feet relative to the surface of the water.
Step-by-step explanation:
Shark Depth ( x ) + Distance from Shark and Diver ( 38 ) = Divers position (-157)
x = -119
The diver is at -157 feet relative to the surface. The shark is swimming 38 feet above the diver, making its position -119 feet relative to the surface.
Given that,
Diver's depth: -157 feet (relative to the surface of the water)
Shark's position: 38 feet above the diver
The question asks for the position of the shark relative to the surface of the water.
The position of the shark can be determined by adding the distance above the diver to the depth of the diver.
So, the position of the shark would be:
-157 feet (diver's depth) + 38 feet (distance above the diver) = -119 feet relative to the surface of the water.
Hence,
The shark is located at -119 feet relative to the surface of the water.
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Quantitative Reasoning :')
Answer:
Step-by-step explanation:
more taking a shower you use almost 3 gallons per a shower