Answer:
False
Step-by-step explanation:
1. The inverse function should have c(n) isolated
2. When finding the inverse of a function, the variables c(n) and n are interchanged (and then c(n) is isolated).
It would look like this --->c(n)=50+4n--->n=50+4(c(n)) ---> c(n)=(n-50)/4
Define the term "surplus"in this context
In this context, "surplus" refers to the excess or additional amount beyond the ideal diameter of 24 inches that the actual diameter of the cake possesses.
It represents the difference between the actual diameter and the desired or expected diameter, taking into consideration the specified margin of error.
When a chef aims to purchase a cake with a margin of error of 3 inches, the surplus indicates the extent to which the cake's diameter surpasses the desired size.
It is a measure of how much larger the cake is compared to the ideal diameter, considering the acceptable range within the margin of error.
The surplus can be positive or negative, depending on whether the actual diameter is larger or smaller than the ideal diameter.
If the actual diameter is greater than 24 inches, the surplus will be a positive value, indicating the excess size of the cake.
Conversely, if the actual diameter is smaller than 24 inches, the surplus will be a negative value, representing the shortfall in size.
By quantifying the surplus, the chef can assess the degree to which the actual cake deviates from the ideal size and make an informed decision based on their specific requirements and preferences.
The surplus helps ensure that the cake's dimensions align with the desired specifications and meets the chef's expectations within the specified margin of error.
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⌢
In circle D, m∠EDF=70∘, and the length of EF=[tex]\frac{14}{9} \pi[/tex]. Find the length of DE.
To find the length of DE in circle D, we can use the properties of a circle and the given information.
In a circle, if two chords intersect, the product of the segments of one chord is equal to the product of the segments of the other chord. In this case, we have chord EF intersecting chord DE at point D.
Let x represent the length of segment DE, and y represent the length of segment DF. Therefore, the length of segment EF would be (x + y).
According to the chord-chord power theorem:
DE * EF = DF * DF
Substituting the given values:
x * (x + y) = y * y
x^2 + xy = y^2
We are also given that angle EDF measures 70 degrees. According to the angle intercepting chord theorem, the intercepted arc EF is twice the measure of angle EDF. So, the measure of arc EF is 2 * 70 = 140 degrees.
Now, we can use the length of arc EF to find the ratio of the lengths of segments EF and DF.
The ratio of the lengths of the intercepted arcs is equal to the ratio of the lengths of the corresponding chords. Therefore:
EF / DF = arc EF / arc DF
(x + y) / y = 140 / 360 [Using the measure of the intercepted arcs]
Simplifying this equation:
(x + y) / y = 7 / 18
Cross-multiplying:
18(x + y) = 7y
18x + 18y = 7y
18x = 7y - 18y
18x = -11y
Dividing by -11:
x = -11y / 18
We need to find the value of x, which represents the length of segment DE. Since segment lengths cannot be negative, we can disregard the negative sign.
x = 11y / 18
Substituting this value of x in the equation x^2 + xy = y^2:
(11y / 18)^2 + (11y / 18) * y = y^2
Simplifying:
121y^2 / 324 + 11y^2 / 18 = y^2
Multiplying through by 324:
121y^2 + 594y^2 = 324y^2
715y^2 = 324y^2
715y^2 - 324y^2 = 0
391y^2 = 0
y^2 = 0
Since y^2 = 0, it implies that y = 0. This means that segment DF has zero length.
Now, substituting y = 0 into the equation x = 11y / 18:
x = 11 * 0 / 18
x = 0
Therefore, the length of DE is 0.
In conclusion, the length of DE is 0.
I cannot load the image that you have provided this is what the answer is according to the text provided.
The graph below shows the solution to which system of inequalities?
of the 150 pupils in grade 7 at mpenzeni primary school, 90 passed the final examination in 2015. what percentage of the pupils pass
Given statement solution is :- 60% of the pupils in grade 7 at Mpenzeni Primary School Pass Rate the final examination in 2015.
To find the percentage of pupils who passed the final examination, you can use the following formula:
Percentage = (Number of pupils passed / Total number of pupils) * 100
Given that 90 pupils passed the final examination out of a total of 150 pupils, we can substitute these values into the formula:
Percentage = (90 / 150) * 100
Percentage = 0.6 * 100
Percentage = 60%
Therefore, 60% of the pupils in grade 7 at Mpenzeni Primary School Pass Rate the final examination in 2015.
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Prior to June 30, a company has never had any treasury stock transactions. The company repurchased 185 shares of its $1 par common stock on June 30 for $42 per share. On July 20, it reissued 90 of these shares at $46 per share. On August 1, it reissued 70 of the shares at $40 per share. What is the journal entry necessary to record the reissuance of treasury stock on July 20?
On July 20, the journal entry to record the reissuance of treasury stock is: Debit Cash for $4,140 and credit Treasury Stock for $4,140.
To record the reissuance of treasury stock on July 20, the company needs to make the following journal entry:
Date: July 20
Account Debit Credit
Cash $4,140
Treasury Stock $4,140
Explanation:
Debit to Cash ($46 per share * 90 shares) to record the cash received from the reissuance of 90 shares of treasury stock: $46 * 90 = $4,140.
Credit to Treasury Stock to remove the cost of the 90 reissued shares from the treasury stock account.
This journal entry reflects the cash inflow from the reissuance of treasury stock and reduces the balance in the treasury stock account, indicating a reduction in the number of shares held by the company as treasury stock.
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Find the domain of each expression.
√3 − 6x
√13 − (13 − 2x )
1/√x − 2
Answer:
To summarize:
√3 - 6x: Domain is all real numbers (-∞, +∞).
√13 - (13 - 2x): Domain is all real numbers (-∞, +∞).
1/√x - 2: Domain is all real numbers except x = 0, represented as (-∞, 0) U (0, +∞).
Step-by-step explanation:
To find the domain of each expression, we need to identify any restrictions or limitations on the variables that would result in undefined values.
√3 - 6x:
Since square roots are defined for non-negative numbers, the expression is defined as long as the value inside the square root (√3) is non-negative. The square root of 3 is a positive value, so there are no restrictions on the domain of this expression. Therefore, the domain is all real numbers (-∞, +∞).
√13 - (13 - 2x):
Similar to the previous expression, the square root (√13) is defined for non-negative values. However, we also need to consider the expression (13 - 2x) inside the parentheses. This expression does not have any limitations since it is defined for all real numbers. Therefore, the domain of this expression is all real numbers (-∞, +∞).
1/√x - 2:
For this expression, we need to consider both the square root (√x) and the denominator (1/√x). The square root (√x) is defined for non-negative values of x. However, the denominator 1/√x will become undefined if the value of x is zero because division by zero is undefined. Therefore, we need to exclude x = 0 from the domain. For all other non-zero values of x, the expression is defined. Therefore, the domain of this expression is all real numbers except x = 0, represented as (-∞, 0) U (0, +∞).
A car rental company charge $50 a day and 20 cents per mile for renting a car. Let y be the total rental charge (in dollar) for a car for one day and x be the miles driven. The equation for the relationship between x and y is y = 50 + 20x How much will a person pay who rents a car for one day and drives it 100miles
Answer:$2050.
Step-by-step explanation:
To find out how much a person will pay for renting a car for one day and driving it 100 miles using the given equation, you can substitute x = 100 into the equation y = 50 + 20x and solve for y:
y = 50 + 20x
y = 50 + 20(100)
y = 50 + 2000
y = 2050
Therefore, a person who rents a car for one day and drives it 100 miles will pay $2050.
Twenty-five psychology instructors have formed a committee to pick next year's textbook, and they have narrowed their decision down to two equally good books, one with a better bibliography and references, and the other with a better format and illustrations. Since the books are considered to be equally good, we will assume the probability an instructor chooses either book is 0.5 and the instructors' decisions are made independently. Using the binomial distribution, find the probability 15 or more instructors choose the book with the better format and illustrations.
To find the probability that 15 or more instructors choose the book with the better format and illustrations, we can use the binomial distribution formula.
Let's denote the event of an instructor choosing the book with the better format and illustrations as "success" (S), and the event of an instructor choosing the other book as "failure" (F). The probability of success is p = 0.5, and the probability of failure is q = 1 - p = 0.5.
We want to find the probability of 15 or more successes in a sample of 25 instructors. We can calculate this probability by summing the probabilities of exactly 15, 16, 17, ..., 25 successes.
P(X ≥ 15) = P(X = 15) + P(X = 16) + ... + P(X = 25)
Using the binomial distribution formula, the probability of exactly k successes in a sample of n trials is:
P(X = k) = C(n, k) * p^k * q^(n-k)
where C(n, k) is the binomial coefficient "n choose k," given by:
C(n, k) = n! / (k! * (n-k)!)
Applying this to our problem, we can calculate the probability as follows:
P(X ≥ 15) = P(X = 15) + P(X = 16) + ... + P(X = 25)
= Σ[ k = 15 to 25 ] ( C(25, k) * p^k * q^(25-k) )
Let's calculate this probability using the binomial distribution formula:
P(X ≥ 15) = Σ[ k = 15 to 25 ] ( C(25, k) * (0.5)^k * (0.5)^(25-k) )
Calculating this sum gives us the probability that 15 or more instructors choose the book with the better format and illustrations.
Question 1 of 10
In the ellipse shown below, each point marked with a dot is called a(n)
A. vertex
B. axis
O c. center
OD. focus
In the ellipse shown below, each point marked with a dot is called a(n) focus
What is a focus in an ellipseIn an ellipse, the focus (plural: foci) is a pair of special points that play a significant role in defining the shape of the ellipse. The focus points are located inside the ellipse along the major axis, which is the longer axis of the ellipse.
The defining property of an ellipse is that the sum of the distances from any point on the ellipse to the two foci is constant. This property is known as the "focus-directrix property."
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NO LINKS!! URGENT HELP PLEASE!!!
4. Use the theorems for interior and exterior angles of a polygon to find:
a. The sum of the interior of a 73-gon.
b. The number of sides of a regular polygon if the sum of the interior angles is 2700°
c. The number of sides of a reguluar polygon if the exterior angle is 7.2°
Answer:
see explanation
Step-by-step explanation:
a
the sum of the interior angles of a polygon is calculated as
sum = 180° (n - 2) ← n is the number of sides
here n = 73 , then
sum = 180° × (73 - 2) = 180° × 71 = 12,780°
b
here sum of interior angles = 2700° , then
180° (n - 2) = 2700° ( divide both sides by 180° )
n - 2 = 15 ( add 2 to both sides )
n = 17
number of sides is 17
c
the sum of the exterior angles of a polygon = 360°
given the polygon is regular then each exterior angle is congruent , so
number of sides = 360° ÷ 7.2° = 50
Answer:
a) 12870°
b) 17
c) 50
Step-by-step explanation:
Part aThe Polygon Interior Angle-Sum Theorem states that the sum of the measures of the interior angles of a polygon with n sides is (n - 2) · 180°.
The number of sides of a 73-gon is n = 73. Therefore, the sum of its interior angles is:
[tex]\begin{aligned}\textsf{Sum of the interior angles of a 73-agon}&=(73-2) \cdot 180^{\circ}\\&=71 \cdot 180^{\circ}\\&=12870^{\circ}\end{aligned}[/tex]
Therefore, the sum of the interior angles of a 73-gon is 12870°.
[tex]\hrulefill[/tex]
Part bThe Polygon Interior Angle-Sum Theorem states that the sum of the measures of the interior angles of a polygon with n sides is (n - 2) · 180°.
Given the sum of the interior angles of a regular polygon is 2700°, then:
[tex]\begin{aligned} \textsf{Sum of the interior angles}&=2700^{\circ}\\\\\implies (n-2) \cdot 180^{\circ}&=2700^{\circ}\\n-2&=15\\n&=17\end{aligned}[/tex]
Therefore, the number of sides of the regular polygon is 17.
[tex]\hrulefill[/tex]
Part cAccording the the Polygon Exterior Angles Theorem, the sum of the measures of the exterior angles of a polygon is 360°.
Therefore, to find the number of sides of a regular polygon given its exterior angle is 7.2°, divide 360° by the exterior angle.
[tex]\begin{aligned}\textsf{Number of sides}&=\dfrac{360^{\circ}}{\sf Exterior\;angle}\\\\&=\dfrac{360^{\circ}}{7.2^{\circ}}\\\\&=50\end{aligned}[/tex]
Therefore, the number of sides of the regular polygon is 50.
A man had a square window with sides equal to 1 metre in his house. He decided that it lets in too much light, so he boarded up half of it and still had a square window 1 metre high and 1 metre wide. How did he do that? (6) Total: 40 marks
The man rotated the window by 45 degrees and covered one of the diagonals, resulting in a smaller square window with sides measuring 1 meter.
The man achieved the transformation of his square window by dividing it into two equal halves and boarding up one of them.
Let's analyze the steps he took to accomplish this:
Initially, the man had a square window with sides measuring 1 meter
This means that the window had an area of 1 square meter (1m x 1m = 1m²).
To reduce the amount of light coming through the window, the man decided to board up half of it.
This implies that he covered one of the equal halves of the square window, while leaving the other half open.
By boarding up half of the window, he effectively blocked off half of the area of the square window.
Since the original window had an area of 1 square meter, boarding up half of it reduces the effective area to 1/2 square meter (1m² ÷ 2 = 1/2m²).
The remaining open half of the window still retains its square shape, with sides equal to 1 meter.
Therefore, the man ends up with a square window that measures 1 meter in height and 1 meter in width, but with an area of only 1/2 square meter.
In summary, the man achieved the transformation by boarding up half of the square window, effectively reducing its area to half of the original size while maintaining the same dimensions for the remaining open half. This manipulation allows him to control the amount of light entering his house while preserving the square shape of the window.
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Jaxon is flying a kite, holding his hands a distance of 3.25 feet above the ground and letting all the kite’s string play out. He measures the angle of elevation from his hand to the kite to be 24
∘
∘
. If the string from the kite to his hand is 105 feet long, how many feet is the kite above the ground? Round your answer to the nearest tenth of a foot if necessary.
In a village of 320 adults, each of them does at least farming or trading. 5/8 of them do farming and 75% of these who do farming are involved in trading. a. Find the number of people who are involved in: i. Farming ii. Trading. b. How many of the people are involved in exactly two activities?
c. Find the number of people who do only one activity.
d. What percentage of the people are traders only?
e. What is the probability of selecting an adult from the village at random who is a farmer but not a trader?
Answer:
please see answers below
Step-by-step explanation:
i) 5/8 X 320 = 200 people
ii) 0.75 X 200 = 150 (people in farming but also trade). only trade = 320 - 200 = 120.
number of people in trade = 150 + 120 = 270.
b) 0.75 X 5/8 = 3/4 X 5/8 = 15/32 = 150 people (both farm and trade).
c) only farming = 0.25 X 5/8 = 1/4 X 5/8 = 5/32 = 50.
only trade = 320 - 50 (only farm) - 150 (both farm and trade) = 120.
so, only do one activity = 50 + 120 = 170.
d) traders only = 120/320 = 3/8 = 37.5%
e) P(farmer only) = 50/320 = 0.15625
A bank offers a CD that pays a simple interest rate of 7.0%. How much must you put in this CD now in order to have $4500 for a home-entertainment center in 5 years.
The present value that must be invested to get $4500 after 5 years at an interest rate of 7.0% is $__ (Round up to the nearest cent.)
Rounding up to the nearest cent, the present value that must be invested in the CD now is approximately $3333.34.
To calculate the present value required to have $4500 after 5 years with a simple interest rate of 7.0%, you can use the formula for simple interest:
Present Value = Future Value / (1 + (Interest Rate × Time))
In this case:
Future Value = $4500
Interest Rate = 7.0%
= 0.07
Time = 5 years
Substituting these values into the formula:
Present Value = $4500 / (1 + (0.07 × 5))
Present Value = $4500 / (1 + 0.35)
Present Value = $4500 / 1.35
Present Value ≈ $3333.33
You may use the simple interest calculation to get the present value necessary to have $4500 after five years with a simple interest rate of 7.0%:
Future Value / (1 + (Interest Rate Time)) = Present Value
In this instance
$4500 is the future value.
Rate of Interest = 7.0% = 0.07
t = 5 years
Substituting these values into the formula:
$4500 / (1 + (0.07 5)) = Present Value
$4500 / (1 + 0.35) equals the present value.
Present Value = $4500 / 1.35
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The present value that must be invested now in order to have $4500 for a home-entertainment center in 5 years at an interest rate of 7.0% is approximately $3333.33
How to find the present value that must be invested to get $4500 after 5 yearsUsing the formula for calculating the future value of a single sum:
Future Value (FV) = Present Value (PV) + (PV * Interest Rate * Time)
We rearrange the formula to solve for the present value (PV):
PV = FV / (1 + Interest Rate * Time)
Plugging in the given values:
FV = $4500
Interest Rate = 7.0% = 0.07
Time = 5 years
PV = $4500 / (1 + 0.07 * 5)
PV = $4500 / (1 + 0.35)
PV = $4500 / 1.35
PV ≈ $3333.33
Therefore, the present value that must be invested now in order to have $4500 for a home-entertainment center in 5 years at an interest rate of 7.0% is approximately $3333.33 (rounded up to the nearest cent).
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MP Precision Three students measure the height of a bookshelf. Student A measures 72 units, Student B measures units, and Student C measures 6 units. The teacher says all three students are correct. What units did each student use? 15
The units that each student used, given the measurement that they got and all of them being right was:
Student A used inchesStudent B used feetStudent C used yards.How to find the units used ?The height of a bookshelf is typically measured in inches, feet, or yards .
Student A measured 72 units, which is equal to 6 feet. Student B measured 2 units, which is equal to 24 inches .
Student C measured 6 units, which is equal to 18 yards. All three students are correct, as they all used different units to measure the same height .
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Full question is:
Three students measure the height of a bookshelf. Student A measures 72 units, Student B measures 2 units, and Student C measures 6 units. The teacher says all three students are correct. What units did each student use?
determine the value of
�
(
�
∩
�
)
P(A∩B), rounding to the nearest thousandth, if necessary.
The probability of the intersection P(A∩B) is 0
What is the probability of the intersection P(A∩B)From the question, we have the following parameters that can be used in our computation:
Event A = 18
Event B = 12
Intersection = 0
Other Events = 6
Using the above as a guide, we have the following:
Total = A + B + C
So, we have
Total = 18 + 12 + 6
Evaluate
Total = 36
So, we have
P(A) = 18/36
P(B) = 12/36
For the intersection events, we have
P(A∩B) = 0/36
Evaluate
P(A∩B) = 0
Hence, the probability of P(A∩B) is 0
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In ΔNOP, p = 70 inches, n = 97 inches and ∠O=163°. Find ∠N, to the nearest degree.
Answer:
10°----------------------
In ΔNOP, we are given:
p = 70 inches, n = 97 inches, ∠O = 163°Use the law of cosines to find side o:
o² = n² + p² - 2(np)cos(∠O) o² = 97² + 70² - 2(97)(70)cos(163°) o² = 27295.61o = 165.2Now, use the law of sines to find ∠N:
sin(∠N) / n = sin(∠O) / o sin(∠N) / 97 = sin(163°) / 165.2sin(∠N) = 97*sin(163°) / 165.2sin(∠N) = 0.17m∠N = arcsin (0.17)m∠N = 9.78° ≈ 10°So, ∠N is approximately 10°.
Express y in terms of x if Log 10 x + Log 10 ( Y )= 2 Log 10 (x+1)
why two +Eleven + nine
Answer:
22 is answer
Step-by-step explanation:
Answer:
лвоалалалоала.сллслала лвлвлвл
pls solve and explain
Answer:
[tex]\theta = 60; \theta \approx 83; \theta \approx 277; \theta = 300[/tex]
Note that the approximate value you should calculate properly with the inverse cosine function of your calculator to the number of digits you want.
Step-by-step explanation:
you already have a cosine. You might as well change that sine in a cosine too:
[tex]8(1-cos^2\theta) +6cos\theta-9=0\\8cos^2\theta -6cos\theta+1 =0[/tex]
(note that in the second line I also switched every sign by multiplying by -1 just to have a positive lead coefficient - just a pet peeve of mine. Now replace [tex]x=cos\theta[/tex] and let's solve
[tex]8x^2-6x+1=0\\\frac\Delta4 = 9-8 = 1\\x=\frac {3\pm1}8[/tex]
At this point we're back to the replacement. We have two options
[tex]cos\theta = \frac48 = \frac 12 \implies \theta = 60\°; \theta = 300\°\\cos\theta =\frac 18 \implies \theta \approx 83\°; \theta \approx 277\°[/tex]
how would I solve this
[tex]\theta =\cfrac{14}{3}\pi \implies \theta =\cfrac{14\pi }{3}\implies \theta =\cfrac{6\pi +6\pi +2\pi }{3} \\\\\\ \theta =\cfrac{6\pi }{3}+\cfrac{6\pi }{3}+\cfrac{2\pi }{3}\implies \theta =2\pi +2\pi +\cfrac{2\pi }{3}[/tex]
so if we take a look at that, we can say that the angle θ does two revolutions and then it lands on 2π/3, so the terminal point of it is the same as 2π/3's, and if you check your Unit Circle, as you should have one
[tex]\sin(\theta )=\cfrac{\sqrt{3}}{2}\hspace{5em}\cos(\theta )=-\cfrac{1}{2}[/tex]
Answer:
sin∅ = √3/2
cos∅ = -1/2
Step-by-step explanation:
Notice that 14π/3 is just under 3π, so the reference angle made with the negative x-axis is π/3. Since sin(π/3) = √3/2, then sin(14π/3) is also √3/2.
cos(14π/3) works somewhat similarly. Since cos(π/3) = 0.5, and cos(14π/3) would be located in Quadrant II where the negative axis is, then cos(14π/3) = -0.5
Question 5 of 10
What can you say about the y-values of the two functions f(x) = 32 - 3
and g(x) = 7x² - 3?
A. The minimum y-value of f(x) is -3.
B. The minimum y-value of g(x) is -3.
C. g(x) has the smallest possible y-value.
D. f(x) has the smallest possible y value.
SUBMIT
The minimum y-value of g(x) is -3 and g(x) has the smallest possible y-value.
The function f(x) = 32 - 3 is a constant function, as there is no variable term involving x. It simplifies to f(x) = 29.
Regardless of the value of x, the function f(x) will always have a y-value of 29.
Therefore, option A is incorrect because there is no minimum y-value for f(x); it is a constant.
g(x) = 7x² - 3 is a quadratic function in the form of ax² + bx + c, where a = 7, b = 0, and c = -3.
The coefficient a (7) is positive, indicating that the parabola opens upward.
Since there is no linear term (bx), the vertex of the parabola is located at the point (0, -3), which corresponds to the minimum y-value of the function.
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Solve for the exact solutions in the interval [0,2]
List your answers separated by a comma, if it has no real solutions, enter DNE.
The solutions to the trigonometric equation in this problem are given as follows:
θ = π/6.θ = 5π/6.θ = 7π/6.θ = 11π/6.What are complementary angles?Two angles are said to be complementary angles when the sum of their measures is of 90º.
For complementary angles, we have that the sine of one of the angles is the cosine of the other angle, hence in this problem we have that 2θ and θ are complementary angles.
Then the value of θ is obtained as follows:
2θ + θ = 90
3θ = 90
θ = 30º.
θ = π/6.
The equivalent angles, which are also solutions to the equation, are given as follows:
θ = 5π/6. -> second quadrant.θ = 7π/6. -> third quadrant.θ = 11π/6. -> fourth quadrant.More can be learned about complementary angles at brainly.com/question/98924
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Calculate the surface area of the triangular prism
Answer:
66 inches²
Step-by-step explanation:
Area of 1 triangle = ½ × base × height = ½ × 7 × 4 = 14 in²
Area of 2 triangles = 14 × 2 = 28 in²
Area of outer rectangles = (6 × 2) × 2 = 24 in²
Area of inner rectangle = 2 × 7 = 14 in²
Total surface area = 28+24+14 = 66 in²
The equation 5/3log4(x)=9 can be written in the form x=2^y for some number y. What is y?
The value of y is 10.8.
Here, we have,
given that,
The equation is: 5/3log_4(x)=9
or, 5 log₄x = 27
or, log₄x = 27/5
now, we have,
Using the property, x = loga, a = eˣ
we get,
x = 4²⁷/⁵
or, x = 4⁵°⁴
or, x = 2¹⁰°⁸
so, comparing with x=2^y , we get,
y = 10.8
Hence, The value of y is 10.8.
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HELP! Can someone please help with the picture question below?
The probability that either event A or B will occur is 11/17.
We have,
The Addition Rule for Probability:
P(A U B) = P(A) + P(B) - P(A ∩ B),
where P(A U B) represents the probability of the union of events A and B, P(A) represents the probability of event A, P(B) represents the probability of event B, and P(A ∩ B) represents the probability of the intersection of events A and B.
Now,
P(A) = 9/17
P(B) = 2/17
There is no intersection of Q and B so,
P(A ∩ B) = 0
Now,
P(A U B) = P(A) + P(B) - P(A ∩ B),
Substituting the values.
P(A U B) = The probability that either event A or B will occur.
So,
P(A U B)
= 9/17 + 2/17 - 0
= 11/17
Thus,
The probability that either event A or B will occur is 11/17.
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Solve This Mathematical Term
The reason of discontinuity of the given function is described below.
Since we know that,
A continuous function, as the name implies, is one whose graph is continuous with no breaks or jumps. In other words, if we can draw the curve (graph) of a function without ever raising a pencil, we may claim that the function is continuous. The study of a function's continuity is critical in calculus because a function cannot be differentiable unless it is continuous.
A function is considered continuous if its graph is an uninterrupted curve with no holes, gaps, or breaks.
Now by mathematical definition of continuity
Left hand limit of a function at any point = right hand limit of function at that point = value of function at that point
Now from the graph we can see that,
At point point 3
The left hand limit and right hand limit are not equal and also the curve is discontinuous.
Hence, the given function is discontinuous function.
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A group of ten students recorded the number of minutes they spent on one math homework problem. The
mean amount of time was 9 minutes, but the MAD was 7 minutes.
Draw a dot plot to represent a data set that matches this description. Be sure to include a title and label
your axis.
1. Create a horizontal axis labeled "Time Spent on Homework Problem (Minutes)."
2. Choose an appropriate scale for the axis, such as labeling every other unit of time from 0 to 18.
3. Plot a dot for each student's data point along the horizontal axis.
4. Arrange the dots in order from smallest to largest time spent on the problem.
5. Title the dot plot to reflect the data set being represented, such as "Math Homework Problem Time Spent: Mean 9 Minutes, MAD 7 Minutes."
6. Include a legend or key if needed to clarify the meaning of the dot plot.(The dot plot is attached below)
To draw a dot plot representing a data set where the mean amount of time spent on one math homework problem is 9 minutes and the MAD is 7 minutes for a group of ten students, we can follow these steps:
The resulting dot plot may show a spread of data between 2 and 16 minutes, with more dots around the center or mean of 9 minutes and fewer dots at the tails. The MAD of 7 minutes suggests a relatively high degree of variability in the data, with some students spending significantly less or significantly more time on the math homework problem. The dot plot can help to visualize these differences and identify any potential outliers in the data.
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James exercised for 2/5 of an hour and sandile exercised for 4/12 of an hour ? Who exercised for the longest time?
Answer:
The answer James
Step-by-step explanation:
James=2/5hours
J=2/5×60=2×12=24 minutes
Sandle=4/12×60=4×5=20 minutes
need help asp please
Answer:
see explanation
Step-by-step explanation:
using any of the tangent, sine, cosine ratios in the right triangle.
tanΘ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{7}{6}[/tex] , then
Θ = [tex]tan^{-1}[/tex] ( [tex]\frac{7}{6}[/tex] ) ≈ 49.40° ( to 2 decimal places )
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sinΘ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{2}{6.32}[/tex]
cosΘ = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{6}{6.32}[/tex]
tanΘ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{2}{6}[/tex]
