The linear equation is solved and slope is m = (24 - b) / 3 = 8
Given data ,
a)
To write a linear function that models the relationship between the cost, c, of octopus and the weight, w, in pounds, we need to determine the equation of a line in slope-intercept form, y = mx + b, where y represents the cost of octopus (c) and x represents the weight in pounds (w).
We are given that three pounds of octopus costs $24. This gives us a point on the line, which is (3, 24). Using this point, we can find the slope (m) of the line.
Let's use the slope formula:
m = (y2 - y1) / (x2 - x1)
Taking (3, 24) as our first point, and choosing another arbitrary point on the line, let's say (0, b), we can substitute the coordinates into the slope formula:
m = (24 - b) / (3 - 0)
Since the slope is constant for the linear function, we can set this expression equal to m:
m = (24 - b) / 3
Now, we have the slope (m) in terms of b. To find the value of b, we can substitute the coordinates of the known point (3, 24) into the slope-intercept form:
24 = m * 3 + b
Substituting the expression for m:
24 = [(24 - b) / 3] * 3 + b
Simplifying:
24 = 24 - b + b
24 = 24
Since the equation is true for any value of b, we can choose any value for b. Let's choose b = 0 for simplicity.
Plugging in the values of m = (24 - b) / 3 and b = 0, we have:
m = (24 - 0) / 3
m = 24 / 3
m = 8
Therefore, the slope of the linear function is 8
b)
The meaning of the slope in this context is that for each additional pound of octopus purchased, the cost increases by $8. This means that the cost of octopus is increasing at a constant rate of $8 per pound. The positive slope indicates that as the weight of the octopus increases, the cost also increases.
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The body temperatures in degrees Fahrenheit of a sample of adults in one small town are: 97.1 98.1 98 97.7 97.4 99.3 96.8 Assume body temperatures of adults are normally distributed. Based on this data, find the 90% confidence interval of the mean body temperature of adults in the town. Enter your answer as an open-interval (i.e., parentheses) accurate to 3 decimal places. Assume the data is from a normally distributed population. 90% C.I. =
The 90% confidence interval for the mean body temperature of adults in the town is approximately (97.299, 98.529).
How to solve for the confidence intervalThe given data points are:
97.1, 98.1, 98, 97.7, 97.4, 99.3, 96.8
Step 1: Calculate the sample mean (µ):
µ = (97.1 + 98.1 + 98 + 97.7 + 97.4 + 99.3 + 96.8) / 7 ≈ 97.914
sample standard deviation (s):
≈ 0.839
Step 3: Calculate the standard error (SE):
SE = s / sqrt(n)
≈ 0.839 / sqrt(7) ≈ 0.317
Step 4: Find the t-value for a 90% confidence interval with 6 degrees of freedom (n - 1 = 7 - 1 = 6).
Using a t-distribution table we find that the t-value is approximately 1.943.
Step 5: Calculate the margin of error (ME):
ME = t-value * SE
≈ 1.943 * 0.317 ≈ 0.615
Step 6: Calculate the confidence interval:
Lower limit = µ - ME ≈ 97.914 - 0.615 ≈ 97.299
Upper limit = µ + ME ≈ 97.914 + 0.615 ≈ 98.529
So, the 90% confidence interval for the mean body temperature of adults in the town is approximately (97.299, 98.529).
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Find the derivative of the function
using logarithmic differentiation.
pls help guys thank you sm
The derivative of the function [tex]f(x)=(x+2)^{x}[/tex] is [tex](x + 2)^x \left( \frac{x}{x + 2} + ln(x + 2) \right)[/tex] A, using logarithmic differentiation.
How to determine derivative of the function?To find the derivative of the function [tex]f(x)=(x+2)^{x}[/tex] using logarithmic differentiation, take the natural logarithm of both sides of the equation. This gives us the following equation:
[tex]ln(f(x)) = x ln(x + 2)[/tex]
Then differentiate both sides of this equation with respect to x. This gives us the following equation:
[tex]\frac{f'(x)}{f(x)} = \frac{x}{x + 2} + ln(x + 2)[/tex]
Multiply both sides of this equation by f(x) and solve for f′(x). This gives us the following equation:
[tex]f'(x) = f(x) \left( \frac{x}{x + 2} + ln(x + 2) \right)[/tex]
Then substitute the function [tex]f(x)=(x+2)^{x}[/tex] into this equation. This gives us the following equation:
[tex]f'(x) = (x + 2)^x \left( \frac{x}{x + 2} + ln(x + 2) \right)[/tex]
Therefore, the derivative of the function [tex]f(x)=(x+2)^{x}[/tex] is [tex](x + 2)^x \left( \frac{x}{x + 2} + ln(x + 2) \right)[/tex]
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Evaluate the integral
guys pls help thank you sm
Answer:
[tex]\textsf{A.}\quad\dfrac{1}{3} \ln \left|\sec(3x+1)+\tan(3x+1)\right|+\text{C}[/tex]
Step-by-step explanation:
Fundamental Theorem of Calculus[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]
If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.
Given integral:
[tex]\displaystyle \int \sec(3x+1)\; \text{d}x[/tex]
To evaluate the given integral, use the method of integration by substitution.
Let u = 3x + 1.
Find du/dx and rewrite it so that dx is on its own:
[tex]\dfrac{\text{d}u}{\text{d}x}=3 \implies \text{d}x=\dfrac{1}{3}\;\text{d}u[/tex]
Rewrite the original integral in terms of u and du and integrate:
[tex]\begin{aligned}\displaystyle \int \sec(3x+1)\; \text{d}x&=\int \dfrac{1}{3} \sec(u)\; \text{d}u\\\\&= \dfrac{1}{3}\int \sec(u)\; \text{d}u\\\\&= \dfrac{1}{3} \ln \left|\sec(u)+\tan(u)\right|+\text{C}\end{aligned}[/tex]
Finally, replace u with the original substitution.
[tex]\dfrac{1}{3} \ln \left|\sec(3x+1)+\tan(3x+1)\right|+\text{C}[/tex]
I don’t understand this one here I need help
The inverse function of f(x) is given as follows:
[tex]f^{-1}(x) = \sqrt{x}[/tex]
How to obtain the inverse function?The function f(x) graphed in this problem is given as follows:
f(x) = x².
Using the notation y = f(x), we have that:
y = x².
To obtain the inverse, first we exchange y and x, hence:
x = y².
Finally, we must isolate the variable y, hence:
[tex]y = \pm \sqrt{x}[/tex]
[tex]y = \sqrt{x}[/tex] -> we take only the positive and the domain is the non-negative numbers.
Hence the inverse function is:
[tex]f^{-1}(x) = \sqrt{x}[/tex]
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Tamara's tuition for her first year of college costs $8,240. Tamara received a scholarship that will
cover .25 of the cost. If Tamara has two years to save up the remaining amount, how much should she save each month in order to meet her
goal?
Answer:
Check Explanation
Step-by-step explanation:
The question is incomplete. But I can explain in a way that the full question can be easily solvable.
Note that the missing part of the question is percentage or fraction of the total college tuition cost that the scholarship covers.
For the sake of clarity, let us assume that the scholarship covers 60% of the total college tuition costs.
This means that Tamara still has to raise 40% of the total college tuition cost herself over the space of 2 years (24 months)
The total college tuition cost = $8240
Amount that Tamara still needs to raise = 40% × 8240 = $3296
She has to raise this amount over 2 years (24 months) on a monthly basis.
So, the amount she has to save monthly over 24 months = (3296/24) = $137.333
So, whatever the fraction or percentage of the total college tuition cost that the scholarship covers, just divide the rest of the college tuition cost after the scholarship has done its part (1 - fraction or 100% - percentage) by 24 months.
The answer is the amount that Tamara needs to save monthly.
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Consider the figure. Find the area of the composite figure. Enter the correct answer in the box.
Check the picture below.
[tex]\stackrel{ \textit{\LARGE Areas} }{\stackrel{ \textit{blue triangle} }{\cfrac{1}{2}(1)(2)}~~ + ~~\stackrel{ \textit{orange triangle} }{\cfrac{1}{2}(2)(1)}~~ + ~~\stackrel{ \textit{yellow rectangle} }{(2)(3)}~~ + ~~\stackrel{ \textit{purple triangle} }{\cfrac{1}{2}(3)(2)}} \\\\\\ 1+1+6+3\implies \text{\LARGE 11}[/tex]
A bead is selected at random from a bowl. The probability of selecting a bead with two holes is 0.5. The probability of selecting a bead that is both red and has two holes is 0.2. What is the probability of selecting a red bead given the bead has two holes? Enter your answer as a decimal in the box.
Answer:
0.4
Step-by-step explanation:
Let A be the event of selecting a bead with two holes and B be the event of selecting a red bead. We are given P(A) = 0.5 and P(A and B) = 0.2. We need to find P(B|A), the probability of selecting a red bead given the bead has two holes.
By definition of conditional probability, we have:
P(B|A) = P(A and B) / P(A)
Substituting the given values, we get:
P(B|A) = 0.2 / 0.5
Simplifying, we get:
P(B|A) = 0.4
Therefore, the probability of selecting a red bead given the bead has two holes is 0.4.
Answer: 0.2.
Step-by-step explanation:
The circumference of a circle is 13 pi what is the area in square inches
Answer:
42.25π or 132.73 square inches---------------------
Use the area formula:
A = πr², where A is the area and r is the radius.We are given the circumference of the circle, which is C = 2πr.
So, we can set up an equation:
2πr = 13π ⇒ r = 6.5 inchesNow, we can plug this value of r into the area formula:
A = π(6.5)² = 42.25πA = 132.73 square inches (rounded to two decimal places)Therefore, the area of the circle is 42.25π or 132.73 square inches.
3. A species of orchids have a gene encoding either a dominant pink (P) or recessive white (p) flower color trait. If a heterozygous pink and white flower were crossed, what is the probability that the offspring have white flowers?
The correct probability is indeed 0.25 or 25%.
When heterozygous pink (Pp) and white (pp) flowers are crossed, the Punnett square can be used to determine the probability of offspring having white flowers:
| P p
---------------
P | PP Pp
---------------
p | Pp pp
From the Punnett square, we can see that there are four possible combinations of alleles for the offspring: PP, Pp, Pp, and pp.
Out of these four possibilities, only one combination (pp) corresponds to the white flower trait.
Therefore, the probability of an offspring having white flowers is 1 out of 4.
In terms of probability, this can be expressed as:
Probability of white flowers = Number of favorable outcomes / Total number of possible outcomes.
= 1 / 4
= 0.25
So, the correct probability is indeed 0.25 or 25%.
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Describe the translation of figure ABCD. Complete the sentence to explain your answer. A coordinate plane showing figure A B C D and A prime B prime C prime D prime. The coordinates of the first figure are A 2 comma 3, B 1 comma 2, C 2 comma 1, and D 3 comma 2. The coordinates of the second figure are A prime 5 comma 4, B prime 4 comma 3, C prime 5 comma 2, and D prime 6 comma 3. Figure ABCD is translated unit(s) right and unit(s) up.
Figure ABCD is translated 3 units right and 1 unit up.
What is a translation?In Mathematics, the translation a geometric figure or graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image while the translation a geometric figure or graph upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.
Based on the information provided, we have the follwoing:
(x, y) → (x + h, y + k)
A (2, 3) → A' (5, 4).
5 = 2 + h
h = 5 - 2
h = 3 (3 units right).
4 = 3 + k
k = 4 - 3
k = -3 (1 unit up).
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Complete Question:
Describe the translation of figure ABCD. Complete the sentence to explain your answer.
Figure ABCD is translated unit(s) right and unit(s) up.
Solve for the remaining angles and side of the two triangles that can be created. Round to the nearest hundredth:
B=50°
, b=5
, a=6
Triangle 1: (where angle A is acute)
A=
C=
c=
Triangle 2 (where A is obtuse)
A=
C=
c=
To solve for the remaining angles and side of the triangles, we can use the Law of Sines and the Law of Cosines.
Triangle 1: (where angle A is acute)
Given:
B = 50°
b = 5
a = 6
Using the Law of Sines:
[tex]sin A / a = sin B / b[/tex]
sin A / 6 = sin 50° / 5
sin A = (6 x sin 50°) / 5
A = arcsin[(6 x sin 50°) / 5]
A ≈ 44.14°
Using the Law of Sines again:
sin C / c = sin B / b
sin C / c = sin 50° / 5
sin C = (c x sin 50°) / 5
Using the Law of Cosines:
c² = a² + b² - 2ab x cos C
c² = 6² + 5² - 2(6)(5) x cos C
c² = 36 + 25 - 60 x cos C
c² = 61 - 60 x cos C
c ≈ √(61 - 60 x cos C)
Triangle 2 (where A is obtuse):
Given:
B = 50°
b = 5
a = 6
Using the Law of Sines:
sin A / a = sin B / b
sin A / 6 = sin 50° / 5
sin A = (6 x sin 50°) / 5
A = arcsin[(6 x sin 50°) / 5]
A ≈ 44.14° (rounded to the nearest hundredth)
Using the Law of Sines again:
sin C / c = sin B / b
sin C / c = sin 50° / 5
sin C = (c x sin 50°) / 5
Since A is obtuse, C = 180° - A - B
C ≈ 85.86° (rounded to the nearest hundredth)
Using the Law of Cosines:
c² = a² + b² - 2ab x cos C
c² = 6² + 5² - 2(6)(5) x cos C
c² = 36 + 25 - 60 x cos C
c² = 61 - 60 x cos C
c ≈ √(61 - 60 x cos C)
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As seen in the diagram below, Santiago is building a walkway with a width of � x feet to go around a swimming pool that measures 20 feet by 9 feet. If the total area of the pool and the walkway will be 672 square feet, how wide should the walkway be?
Answer: 6ft
Step-by-step explanation:
180+40x+18x+4x^2=672
4x^2+58x+180x=672
4x^2+58x-492=0
2x^2+29x-246=0
(x=6)(2x+41)=0
x=6 or x=-20.5
Should be 6ft
Ian gets $9.00 for each hour he works. He also gets $10.00 for each day he works. He made the equation y=9x+10x where x is the number of hours he works.
Explain why his equation will not tell him how much he makes in a day.
A rectangle has vertices A(6, 4), B(2, 4), C(6, -2), D(2, -2).
What are the coordinates of the vertices of the image after a dilation with the origin as its center and a scale factor of 2?
A'(9, 6), B'(3, 6), C'(9, -3), D'(3, -3)
A'(3, 2). B'(1, 2), C'(3, -1), D'(1, -1)
A' (12, 8), B'(4, 8), C'(12, -4), D'(4, -4)
Answer:
A' (12, 8), B'(4, 8), C'(12, -4), D'(4, -4)
Step-by-step explanation:
Since the dilation is in the center, we just need to multiply everything by our scale factor, 2.
A (6,4) → (12, 8)
B (2,4) → (4, 8)
C (6, -2) → (12, -4)
D (2, -2) → (4, -4)
Hope this helps!
Fill out the last question on the chart for 50 points!
The expression, in the end, is 10 x 3 = 30
i.e
Length = 10
Width = 3
The number of tiles = 10 x 3 = 30
We have,
We see that,
The number of tiles:
18, 24, 30,
This is an arithmetic sequence.
So,
The next term:
= 30 + 6
= 36
Now,
The length is a sequence in ascending order of the factor of the arithmetic sequence.
So,
30 is a factor of 2, 3, 5, 6, and 10.
This means,
The expression, in the end, is 10 x 3 = 30
So,
Length = 10
Width = 3
The number of tiles = 10 x 3 = 30
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Answer the blue squares
Line segment PT ≅ line segment PT by the reflexive property.
ΔPRT ≅ ΔTVP by the SSS triangle congruence theorem
What is the SSS Congruence Theorem?The SSS congruence theorem (side-side-side congruence theorem) states that if all three sides of one triangle are congruent to the corresponding three sides of another triangle, then both are considered congruent triangles.
According to the reflexive property, a line or angle is equal to itself, therefore, Line segment PT ≅ line segment PT by the reflexive property.
This also implies that both triangles have three pairs of corresponding sides that congruent, therefore, ΔPRT ≅ ΔTVP.
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Choose the correct range of the function.
x: -2, -1, 0, 1, 2, 3
y: -11, -4, 1, 4, 5, 4
a. all real numbers
b. all numbers greater than or equal to -11
c. all numbers less than or equal to 5
d. all numbers less than or equal to 0
The range of the function is the set of all real numbers
Calculating the correct range of the function.From the question, we have the following parameters that can be used in our computation:
x: -2, -1, 0, 1, 2, 3
y: -11, -4, 1, 4, 5, 4
The range of a function is the set of y values of the function
using the above as a guide, we have the following:
Range = -11, -4, 1, 4, 5, 4
This can be expressed as
Range = -11 to 4
So, we can say that the range is the set of all real numbers
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A pharmaceutical company receives large shipments of ibuprofen tablets and uses an acceptance sampling plan. This plan randomly selects and tests 26 tablets, then accepts the whole batch if there is at most one that doesn't meet the required specifications. What is the probability that this whole shipment will be accepted if a particular shipment of thousands of ibuprofen tablets actually has a 15% rate of defects?
(Report answer as a decimal value accurate to four decimal places.)
P(accept shipment) =
Answer:
0.8475
Step-by-step explanation:
We can model the number of defective tablets in the shipment as a binomial distribution with parameters $n=26$ (the sample size) and $p=0.15$ (the probability of a defective tablet).
To calculate the probability that the whole shipment will be accepted, we need to find the probability that the number of defective tablets in the sample is at most 1, which means that the shipment meets the required specifications.
What is the tax owed by a married couple filing jointly who report a taxable income of $97,0257
To calculate the tax owed by a married couple filing jointly who report a taxable income of $97,025, we can use the 2021 tax brackets and rates provided by the IRS.
The first $19,900 of their income is taxed at a rate of 10%, which equals $1,990.
The next $60,050 of their income is taxed at a rate of 12%, which equals $7,206.
The remaining $17,075 of their income is taxed at a rate of 22%, which equals $3,756.50.
Adding these amounts together gives a total tax liability of $12,952.50.
Therefore, the tax owed by a married couple filing jointly who report a taxable income of $97,025 is $12,952.50.
Answer: 15,734
Step-by-step explanation:
If you look at the table itself it has the answer however it says at least 97,000 but less than 97,050 and it says and you are-- right under married filing jointly is 15,734
the driving distance between San fransico and Chicagois 2132 miles.The driving distance between Chicago and Key West is 1535 miles.What is the total distance in miles driven
Answer:
3667 miles driven
Step-by-step explanation:
2132 + 1535 = 3667
If the nth term of a sequence is n squared - 3. Find the first 3 terms and the tenth term
The first three terms of the Sequence are -2, 1, 6 and the tenth term is 97.
Given that the nth term of a sequence is n squared - 3.
We can find the first three terms by substituting n = 1, 2, and 3 into the formula.
When n = 1, the first term is:
a1 = 1² - 3 = -1
When n = 2, the second term is:
a2 = 2² - 3 = 1
When n = 3, the third term is:
a3 = 3² - 3 = 6
Therefore, the first three terms of the sequence are: -2, 1, 6.
To find the tenth term, we substitute n = 10 into the formula.
a10 = 10² - 3 = 97
Therefore, the tenth term of the sequence is 97.
In summary, the first three terms of the sequence are -2, 1, 6 and the tenth term is 97.
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a boat heading out to sea starts out at Point A, at a horizontal distance of 1083 feet from the lighthouse/the shore. From that point, the boat's crew measures the angle of elevation to the lighthouse's beacon-light from theat point to be 8 degrees. At some later time, the crew measures the angle of elevation from point B to be 4 degrees. Find the distance from point A to point B. Round your answer to the nearest foot if necessary.
The distance from point A to point B is approximately 920 feet.
How to find the distance from point A to point B
Let's call the distance from point A to point B as x.
From point A, the angle of elevation to the lighthouse's beacon-light is 8 degrees.
Using the tangent function to find the height of the lighthouse (h):
tan(8) = h/1083
h = 1083 tan(8) ≈ 157.6 feet
From point B, the angle of elevation to the lighthouse's beacon-light is 4 degrees.
Using the tangent function again to find the height of the lighthouse from point B (h'):
tan(4) = h'/(1083-x)
h' = (1083-x) tan(4) ≈ 78.6 - 0.07x
Since the height of the lighthouse should be the same from both points A and B, we can set h = h' and solve for x:
1083 tan(8) = (1083-x) tan(4)
x = 1083 - (157.6/tan(4)) ≈ 920 feet
Therefore, the distance from point A to point B is approximately 920 feet.
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I don’t understand this question
If f(x)=3x²-2x+5 and g(x) = x³+4x²-1 then the function obtained by multiplying two functions is 3x⁵+10x⁴-3x³+17x²+2x-5
The two functions are f(x)=3x²-2x+5 and g(x) = x³+4x²-1
We have to find (f×g)(x)
(f×g)(x)= f(x)g(x)
=(3x²-2x+5)( x³+4x²-1)
=3x⁵+12x⁴-3x²-2x⁴-8x³+2x+5x³+20x²-5
Combine the like terms
=3x⁵+10x⁴-3x³+17x²+2x-5
Hence, the function obtained by (f×g)(x) is 3x⁵+10x⁴-3x³+17x²+2x-5
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math homework 8th (pls help)
The surface area of the cone is 553 cm².
What is surface area?The surface area of a three-dimensional object is the total area of all its faces.
To calculate the surface area of the cone, we use the formula below
Formula:
A = πrl+πr².................... Equation 1Where:
A = Surface area of the coner = Radius of the of the conel = Slanght height of the coneπ = PieFrom the question,
Given:
r = 8 cml = 20 cmπ = 3.14Substitute these values into equation 1
A = (3.14×8×20)+(3.14×8²)A = 502.4+50.24A = 552.64 cm²A = 553 cm²Learn more about surface area here: https://brainly.com/question/25092270
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A sample of size =n78 is drawn from a normal population whose standard deviation is =σ5.1. The sample mean is =x47.95.
The 95% confidence interval for the population mean is (47.00, 48.90).
A sample of size n=78 is drawn from a normal population with a standard deviation of σ=5.1. The sample mean is x=47.95.
Using this information, we can estimate the population mean using the formula:
μ = x ± z*(σ/√n)
where μ is the population mean, x is the sample mean, z is the z-score for the desired level of confidence (e.g., 1.96 for a 95% confidence interval), σ is the population standard deviation, and n is the sample size.
Assuming a 95% confidence level, the z-score is 1.96. Plugging in the given values, we get:
μ = 47.95 ± 1.96*(5.1/√78)
Solving for the upper and lower bounds of the confidence interval, we get:
μ = 47.95 ± 0.95
So the 95% confidence interval for the population mean is (47.00, 48.90). This means that if we were to repeat this sampling process many times, we would expect the true population mean to fall within this interval 95% of the time.
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Can you Please calculate this:
Answer:
x=335/336
Step-by-step explanation:
First of all, we open the parentheses. 17x+14 1/2-2 3/7+7x=36. Then, we subtract the mixed fractions. 14 1/2-2 3/7=12 1/14. Then, we add the x's. 17x+7x=24x. What we get is 12 1/14+24x=36. We have to subtract 12 1/14 on both sides. 24x=23 13/14. To find x, we do 23 13/14 divided by 24=335/336. x=335/336
Find the 92nd term of the arithmetic sequence -29, -22, -15, ...
[tex]-29~~,~~\stackrel{-29+7}{-22}~~,~~\stackrel{-22+7}{-15}~~,~~...\hspace{5em}\stackrel{\textit{common difference}}{d=+7} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ a_1=-29\\ n=92\\ d=7 \end{cases} \\\\\\ a_{92}=-29+(92-1)7\implies a_{92}=-29+637\implies \boxed{a_{92}=608}[/tex]
What is the domain of the function?
The domain of a function is all of the possible x-values.
In the case of this function, we can see that the x-values begin at negative infinity, continue/change between -1 and 1, and pick up again to continue through positive infinity.
Therefore, the domain of the function is negative infinity to infinity, option D/#4.
Hope this helps!
Write one hundred twenty-seven in standard form.
Answer:
1.27 X 10²
Step-by-step explanation:
standard form is in format A X 10^n, where A is a number between 1 and 10
127 = 1.27 X 10²
Suppose that 40% of the students who drive, carry jumper cables. Your car has a dead battery and you don't have jumper cables, so you decide to stop students who are headed to the parking lot and ask them whether they have a pair of jumper cables. Clearly you would be interested in the number of students you would have to stop before finding one who has jumper cables.
a. Describe the variable of interest in a and give its range of possible values.
b. What is the probability that the third person asked, would the one who has a jumper cable?
c. What is the probability that the first person will be the one who has a jumper cables(wouldn't
that be nice, eh!)?
d. How many people would you expect to have to ask before you find the first one with a jumper
cable? Also give the distribution and appropriate parameters.
On average, you would expect to have to ask 2.5 students before finding one who has jumper cables.
The distribution is the geometric distribution with the parameter p = 0.4.
We have,
a.
The variable of interest is the number of students who need to be stopped before finding one who has jumper cables.
The range of possible values is 1, 2, 3, 4, ...
b.
The probability that the third person asked would be the one who has a jumper cable can be found using the geometric distribution with parameter p = 0.4, where p is the probability of success (i.e., finding someone with jumper cables).
The probability can be calculated as:
P(X = 3)
= (1 - p)^(3-1) x p
= (0.6)^2 * 0.4
= 0.144
c.
The probability that the first person asked will be the one who has jumper cables.
P(X = 1)
= p
= 0.4
d.
The expected value (or mean) of the number of people who need to be asked before finding the first one with jumper cables can be calculated using the geometric distribution with parameter p = 0.4.
So,
E(X)
= 1/p
= 1/0.4
= 2.5
Thus,
On average, you would expect to have to ask 2.5 students before finding one who has jumper cables.
The distribution is the geometric distribution with the parameter p = 0.4.
Learn more about probability here:
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