The ramp will rise from the ground at its highest end to a height of approximately 8.56 inches. Rounded to the nearest hundredth of an inch, this is 8.56 inches.
What is fiberboard?Fiberboard is a type of engineered wood product that is made by combining wood fibers or other plant-based fibers with a binder or adhesive, and then compressing and heating the mixture to create a dense, flat panel
According to question:We can use trigonometry to solve this problem. Let's call the height of the ramp "h" and the length of the base "b". We want to find "h".
First, we need to find "b". We know that the fiberboard is 27 inches long, so the base of the ramp will be the length of the hypotenuse of a right triangle. Using trigonometry, we can find:
b = 27 * cos(19°) ≈ 25.68 inches
Next, we can use trigonometry again to find "h". We know that the angle of elevation from the ground is 19°, so the angle of depression from the ramp to the ground is also 19°. This means we have a right triangle with the height "h", the base "b", and an angle of 19°. Using trigonometry, we can find:
tan(19°) = h/b
Solving for "h", we get:
h = b * tan(19°) ≈ 8.56 inches
Therefore, the ramp will rise from the ground at its highest end to a height of approximately 8.56 inches. Rounded to the nearest hundredth of an inch, this is 8.56 inches.
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Xavier buys a dog collar that costs $6.79. He pays for the dog collar
with a $10 bill.
How much change does Xavier receive?
Answer: Xavier will receive $3.21 in change.
Step-by-step explanation:
To find the change Xavier receives, we need to subtract the cost of the dog collar from the amount he paid with his $10 bill:
Change = $10 - $6.79 = $3.21
Therefore, Xavier will receive $3.21 in change.
P(A) = 1/2 P(B) = 3/4 and P(A U B) = 3/8 Find P(A n B)
Answer:
P(A n B) = 1/4
Step-by-step explanation:
We know that:
P(A U B) = P(A) + P(B) - P(A n B)
Substituting the given values, we get:
3/8 = 1/2 + 3/4 - P(A n B)
Simplifying, we get:
P(A n B) = 1/4
Answer: P ( A n B ) = 7/8
Step-by-step explanation: P ( A U B ) = P(A) + P(B) - P( A n B )
3/8 = 1/2 + 3/4 - P( A n B )
3/8 = 5/4 - P ( A n B )
P ( A n B ) = 5/4 - 3/8
P ( A n B ) = 7/8
The circle graph describes the distribution of preferred music from a sample of 400 randomly selected middle school students.
a circle graph titled preferred music, with five sections labeled rock 13 percent, hip hop 25 percent, pop 35 percent, classical 13 percent, and jazz 14 percent
Which of the following conclusions can we draw from the circle graph?
Pop is the preferred music for 35 students.
Jazz is the preferred music for 56 students.
Together, Hip Hop, Rock, and Jazz are the preferred music for less than half the students.
Together, Hip Hop and Pop are the preferred music for 260 students.
After answering the provided question, we can conclude that As a result, circle we cannot conclude that Hip Hop and Pop are incompatible.
What is circle?A circle seems to be a two-dimensional component defined as such collection of the all points in a jet that become equidistant from the hub. A circle is commonly portrayed with the capital "O" for centre and the lower section "r" for the radius, which is the distance from the origin to any point on the circle.
Girth (the distance from around circle) is given by the formula 2r, where (pi) is a proportionality constant roughly equal to 3.14159. The formula r² calculates the circle's circumference, which refers to the amount of room inside of the circle.
We can draw the following conclusions from the information in the circle graph:
Pop music is preferred by 35% of the sample, which means that 35% of 400 students, or 140 students, prefer pop music.
Jazz is the preferred music for 14% of the sample, which means that jazz is preferred by 14% of 400 students, or 56 students.
Hip Hop, Rock, and Jazz are preferred music by 52% of the sample, which means that these three genres are preferred by 52% of 400 students, or 208 students.
Hip Hop and Pop are preferred music by 60% of the sample, which means that 60% of 400 students, or 240 students, prefer these two genres together. As a result, we cannot conclude that Hip Hop and Pop are incompatible.
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Hanna has a bag of 20 sweets and eats 7 of them what fraction of the sweets does she eat?
The fraction of sweets that does she eat is 7/20
In this case, we will be using fractions to describe the portion of sweets that Hanna eats from her bag of 20.
Hanna has a bag of 20 sweets, and she eats 7 of them. To find out what fraction of the sweets she eats, we need to determine the ratio of the number of sweets she eats to the total number of sweets in the bag.
So in this case, Hanna eats 7 sweets, and there are 20 sweets in the bag. Therefore, the fraction of sweets she eats can be written as:
=> 7/20
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Q-15) Ahmadi, Inc. has been manufacturing small automobiles that have averaged 50 miles per gallon of gasoline in highway driving. The company has developed a more efficient engine for its small cars and now advertises that its new small cars average more than 50 miles per gallon in highway driving. An independent testing service road-tested 64 of the automobiles. The sample showed an average of 51.5 miles per gallon with a standard deviation of 4 miles per gallon.
a.Formulate the hypotheses to determine whether or not the manufacturer's advertising campaign is legitimate.
b.Compute the test statistic.
c.What is the p-value associated with the sample results and what is your conclusion? Let a = .05.
It has been established that the manufacturer is legal.
The test statistic is 13
The p-value is 0.
a. Formulate the hypotheses:
The hypotheses for this test are:
H 0: μ ≤ 50
H a: μ > 50.
b. test statistic:
The test statistic will be a t-test because we do not know the population standard deviation.
Since this is a one-sided test, we will use a one-sample t-test.
The test statistic can be calculated using the formula below:
Substituting these values into the formula gives:
t = (51.5 - 50) / (4 / √64)
t = 6.5 / 0.5
t = 13
The test statistic is 13.
c. When the p-value associated with the sample results, using a t-distribution table with 63 degrees of freedom (64 - 1), we find that the p-value associated with a t-statistic of 13 is 0.
Therefore, we can reject the null hypothesis and conclude that the manufacturer's advertising is permitted.
The sample provides sufficient evidence to show that the new small cars average more than 50 miles per gallon of gasoline.
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Draw a diagram to help you set up an equation(s). Then solve the equation(s). Round all lengths to the neatest tenth and all angles to the nearest degree.
Answer:
Were sorry! Answer is not available right now check in later.
Step-by-step explanation:
How can I use the compound angle formula to write sin 165degrees as surds?
We may approximate the sin 165 angles using trigonometric formulas as: tan 165°/(1 + tan2(165°)) (1-cos2(165°))...
Trigonometric identities enable the expression of sin 165° as,
Sin (15°) = sin(180° - 165°)
(-sin 180 + -sin 165) = -sin 345
cos(-75°) = cos(-90° - 165°)
(90 + 165)/255 = -cos 255
Explanation: We know that cos(165) is negative and sin(165) is positive because 165 is in QII. We will use 330 with in half angle formulae because 165=3302.
165 degrees are somewhere between 90 and 180 degrees. Hence, it has an acute angle.
Hence, the 165° angle's addition is 15°. Q. Below are a few angles' measurements.
525 is a positive number of interactions angle, while 195 is a negative coterminal angle.
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Given the price R64,00 (excluding VAT), find the total cost to the buyer (including VAT at 15%).
Therefore, the total cost to the buyer, including VAT at 15%, is R73,60.
What is vat?The term "VAT" usually refers to "Value Added Tax," which is a type of consumption tax that is levied on the value added to goods and services at each stage of production and distribution. It is commonly used by governments around the world as a way to generate revenue and to shift the tax burden from income and sales taxes onto consumption.
by the question.
To calculate the total cost to the buyer including VAT at 15%, you need to add the VAT amount to the original price. Here's how to do it:
Calculate the VAT amount:
VAT = 15% of R64,00
VAT = 0.15 x R64,00
VAT = R9,60
Add the VAT amount to the original price to get the total cost to the buyer:
Total cost = R64,00 + R9,60
Total cost = R73,60
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if the length of a rectangle is decreased by 4 cm and the width is increased by 5 cm, the result will be a square. the area of this square will be 40cm^2 greater than the area of the rectangle. Find the area of the rectangle.
Answer: 30 cm^2.
Step-by-step explanation:
Let the original length of the rectangle be l and its width be w. Then, according to the problem:
(l - 4) = (w + 5) (equation 1)
Also, the area of the square is 40 cm^2 more than the area of the rectangle. Mathematically, we can represent this as:
(l - 4 + 5)^2 = lw + 40
Simplifying the left-hand side and substituting equation 1, we get:
l^2 - 2lw + w^2 = lw + 40
l^2 - 3lw + w^2 - 40 = 0
(l - 8)(l - 5) = 0
Therefore, l = 8 or l = 5. If we substitute l = 8 into equation 1, we get:
w = (l - 4) - 5 = -1
This is not a valid solution since the width cannot be negative. Therefore, the only valid solution is l = 5, which gives:
w = (l - 4) + 5 = 6
So the area of the rectangle is:
A = lw = 5 x 6 = 30 cm^2.
Answer:
steps explanations: x - 4 = y + 5 (sides of a square)
(x - 4)(y + 5) = 40
Which gives;
(y + 5) (y + 5) = 40
y² + 10y + 25 = 40
y² + 10y + 25 - 40 = 0
y² + 10y - 15 = 0
a=1 b=10 and c=-15
Can someone please help me out with these two problems. I’ll award brainliest!! Thank you very very much
Answer:
QUESTION 24
To estimate the intercepts, we set f(x) to zero and solve for x:
f(x) = x^3 + 2x^2 - 5x - 6 = 0
Using synthetic division, we can find that x = -2 is a zero of the function. This means that (x + 2) is a factor of f(x), and we can write:
f(x) = (x + 2)(x^2 + x - 3)
Setting each factor to zero, we find that the intercepts are:
x + 2 = 0 -> x = -2
x^2 + x - 3 = 0 -> x = (-1 ± √13)/2
To estimate the turning points, we can use the fact that the derivative of a function is zero at a turning point. The derivative of f(x) is:
f'(x) = 3x^2 + 4x - 5
Setting f'(x) to zero, we find:
3x^2 + 4x - 5 = 0 -> x = (-2 ± √19)/3
We can now use these values to sketch the graph:
The intercepts are (-2,0) and approximately (-2.3,0.0) and (0.8,-7.5).
The turning points are approximately (-1.8,-11.1) and (0.5,-6.8).
The graph starts in the third quadrant, goes through the origin in the second quadrant, has a local maximum in the first quadrant, goes through the x-axis in the fourth quadrant, has a local minimum in the third quadrant, and goes to infinity in the second and fourth quadrants.
QUESTION 26
Here is a sketch of the graph of the polynomial function y = f(x) based on the given information:
| /
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| /
| /
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| /
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-----------+---------------
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|/
The graph has two x-intercepts, one around x = -3 and one around x = 2. There is also a turning point or local maximum around x = -1 and a turning point or local minimum around x = 1. The end behavior of the graph is that it approaches negative infinity as x approaches negative infinity and approaches positive infinity as x approaches positive infinity.
Answer:
To estimate the intercepts and turning points of the function f(x) = x^3 + 2x^2 - 5x - 6, we can use a table of values.
When x = 0, f(x) = -6. So the y-intercept is (0, -6).
Factoring the polynomial, we find that the zeros are x = -3, x = -1, and x = 2. Therefore, the x-intercepts are (-3, 0), (-1, 0), and (2, 0).
To find the turning points, we can look for where the slope changes sign. We can estimate that there is a local minimum at (-2.5, -13.6) and a local maximum at (1.1, -7.3).
Using this information, we can sketch the graph of f(x).
To sketch the graph of y = f(x) with the given information, we can plot the x-intercepts (-3, 0), (-1, 0), and (2, 0). We know that the function is positive on the intervals (-∞, -3), (-2, 0), and (2, 3), so we can sketch the function above the x-axis in these regions. Similarly, we know that the function is negative on the intervals (-3,-2), (0, 2), and (3,∞), so we can sketch the function below the x-axis in these regions.
We also know that the function is increasing on the intervals (-2.67, -1) and (1, 2.5), and decreasing on the intervals (-∞, -2.67), (1, 1) and (2.5,∞). Using this information, we can sketch the function as increasing in the intervals (-2.67, -1) and (1, 2.5), and decreasing in the intervals (-∞, -2.67), (1, 1), and (2.5, ∞).
Finally, we can connect the intercepts and turning points with smooth curves to obtain a sketch of the function y = f(x).
Loving the LED's btw!
Water flows into a lake at a constant rate.
Grace recorded that 400 litres of water flowed into the lake in 1 minute.
She recorded the number of litres to the nearest 20 litres.
She recorded the time to the nearest
10 seconds.
Calculate the upper bound for the rate at which the water could have flowed into the lake.
Give your answer in litres per second to 2 d.p.
The upper bound for the rate at which the water could have flowed into lake is 8.2 liters per second.
What is an upper bound?An upper limit is a value that is larger than or equal to all the values in a set. In mathematics, it is used to specify a cap or a maximum value for a collection of data. For instance, an upper bound is frequently employed in optimization issues to place a cap on the highest value that a function or variable may take. Upper limits are used in statistics to specify a data set's maximum range which may be used to spot outliers or other abnormalities in the data. In calculus, upper bounds are used to specify a sequence's or series' limit, or the highest number that it may possibly approach.
Given that, 400 liters of water flowed into the lake in 1 minute.
The upper bound of water flow will be the maximum amount of water.
For the nearest measures taken by Grace the amount of water needs to ne more than 400, while the time must be less than 10 seconds from the recorded 1 min.
That is time must be 60 - 10 = 50 seconds.
Approximating the values we have:
410/50 = 8.2 liters per second.
Hence, the upper bound for the rate at which the water could have flowed into lake is 8.2 liters per second.
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a biased dice was rolled and the probability distribution of the outcomes are as follows. what will be the possible probability of getting 3 and of getting 5 when rolling this dice?
The possible probability of getting [tex]3[/tex] and of getting [tex]5[/tex] when rolling this dice is 0.2.
What is the probability?Probability is a branch of math that studies the chance or likelihood of an event occurring.
A biased dice was rolled and the probability distribution of the outcomes are as follows then the outcomes are [tex] 1, 2, 3, 4, 5, 6[/tex]
Probability: [tex]0.2, 0.1, 0.3, 0.1, 0.2, 0.1[/tex]
To find the probability of getting [tex]3[/tex] and of getting [tex]5[/tex] when rolling this dice.
Probability of getting [tex]3[/tex]:
Outcome = [tex]3[/tex]
Probability of getting = [tex]^3P(3) = 0.3[/tex]
So, the possible probability of getting [tex]3[/tex] is [tex]0.3[/tex].
Probability of getting [tex]5[/tex]
So, the outcome of [tex]5[/tex]
Probability of getting [tex]^5P(5) = 0.2[/tex]
So, the possible probability of getting 5 is 0.2.
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calculate the value of expression 2x squared - 3x + 1 if x equals to -2
The value of expression is 15.
Define the term quadratic expression?A quadratic equation is a mathematical expression of the second degree, in which the highest power of the variable is 2. An expression is a mathematical phrase that combines numbers, variables, and mathematical operations to represent a value or a set of values.
It takes the form of ax² + bx + c = 0, where a, b, and c are coefficients, and x is the variable.
Given equation is;
⇒ 2x² - 3x + 1
If x = -2, then the solution of equation will be,
⇒ 2×(-2)² - 3×(-2) + 1
⇒ (2×4) + 6 + 1
⇒ 8 + 6 + 1
⇒ 15
Therefore, the value of expression 2x² - 3x + 1 if x = -2 is 15.
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Write an equation for the line on a graph below.
Check the picture below.
Answer:
x=-3
Step-by-step explanation:
What x-values are a solution to the System?
Select EACH correct answer.
Question 2 options:
x = -2
x = -1
x = 0
x = 1
x = 2
The solutions to the system equations are x = -1 and x = 0.
What is a system of equations?When two or more variables are related to one another and equations are constructed to determine each variable's value, the result is a system of equations. an equation is a balance scale, and for the equation to stay true, both sides must be equal.
Given equations are:
[tex]y=2^x - 1\\y=\frac{1}{2} x[/tex]
The solutions of the system for which; [tex]y_{1} =y_{2}[/tex]
According to the given table, the solutions to the system of both equations at x = -1 and x = 0.
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The annual salaries (in $) within a certain profession are modelled by a random variable with the cumulative distribution function F(x)= {1−kx^−3 for x>44000 {0 otherwise, for some constant k. For these problems, please ensure your answers are accurate to within 3 decimals. a)Find the constant k here and provide its natural logarithm to three decimal places. b)Calculate the mean salary given by the model.
a) The constant k is 5.427 x 10^−12 and its natural logarithm is -26.68.
b) The mean salary of the given model by using the probability density function is approximately $270.86.
a) The cumulative distribution function of the given random variable is provided as follows:
F(x) = {1−kx^−3 if x>44000, and 0 otherwise
The cumulative distribution function is given as
F(x) = 1−kx^−3 if x>44000 and F(x) = 0, if x≤44000i)
We need to check the value of the cumulative distribution function at 44000
We have, F(44000) = 0
0 = 1−k(44000)^−3
⇒ 1 = k(44000)^−3
⇒ k = 1/(44000)^−3
⇒ 5.427 x 10^−12
Taking the natural logarithm of k, we have ln(k) = −28.68 (approx.)
Hence, the constant k is 5.427 x 10^−12 and its natural logarithm to three decimal places is -28.68
b) The probability density function is given as,
f(x) = F'(x) = 3kx^−4, for x>44000 and f(x) = 0, otherwise
The mean or expected value of the random variable is given as
E(X) = ∫[−∞,∞]xf(x)dx
= ∫[44000,∞]x(3kx^−4)dx
= 3k∫[44000,∞]x^−3dx
= 3k[(−1/2)x^−2] [∞,44000]
= (3k/2)(44000)^−2
= 270.86 (approx.)
Therefore, the mean salary given by the model is $270.86 (approx.)
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which statements correctly describe how the graph of the geometric sequence below should appear? 640, 160, 40, 10, ... select two options. the graph will show exponential growth. the graph will appear linear. the domain will be the set of natural numbers. the range will be the set of natural numbers. the graph will show exponential decay.
The following statements correctly describe how the graph of the geometric sequence: 640, 160, 40, 10, ... should appear:
the graph will show exponential decay. the domain will be the set of natural numbers.About geometric sequenceThe given sequence is 640, 160, 40, 10, ... which is a geometric sequence.
Here, the first term is 640 and the common ratio is ¼
The terms of a geometric sequence can be written as an = a₁(r)⁽ⁿ⁻¹⁾
Here, a₁ = 640, and r = ¼.
Hence, the nth term of the given sequence is given by the formula:
an = 640(1/4)⁽ⁿ⁻¹⁾
The graph of the given sequence will appear as shown below:
The given sequence is a decreasing sequence, which means the terms of the sequence keep decreasing as the value of n increases.
Therefore, the graph will show exponential decay.
The domain of the sequence will be the set of natural numbers, which is {1, 2, 3, ...}, since we cannot find any term before the first term.
Therefore, the first term is the initial term and we can count the other terms of the sequence in natural numbers.
Hence, the domain will be the set of natural numbers.
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Answer:
the graph will show exponential decay.
the domain will be the set of natural numbers.
Step-by-step explanation:
The answer above is correct.
4Interpreting z-scores: Complete the following statements using your knowledge about z-scores.
a. If the data is weight, the z-score for someone who is overweight would be
zero
positive
negative
b. If the data is IQ test scores, an individual with a negative z-score would have a
average IQ
high IQ
low IQ
c. If the data is time spent watching TV, an individual with a z-score of zero would
watch the average amount of TV
watch very little TV
watch a lot of TV
d. If the data is annual salary in the U.S and the population is all legally employed people in the U.S., the z-scores of people who make minimum wage would be
positive
negative
zero
a. If the data is weight, the z-score for someone who is overweight would be positive.
b. If the data is IQ test scores, an individual with a negative z-score would have a low IQ.
c. If the data is time spent watching TV, an individual with a z-score of zero would watch the average amount of TV.
d. If the data is annual salary in the U.S and the population is all legally employed people in the U.S., the z-scores of people who make minimum wage would be negative.
The z-score represents how far a data point is from the mean in terms of standard deviations. If someone is overweight, their weight would be above the mean weight, so their z-score would be positive.
Again, the z-score represents how far a data point is from the mean in terms of standard deviations. If someone has a negative z-score for IQ test scores, it means their score is below the mean score, so their IQ would be low.
A z-score of zero means the data point is exactly at the mean, so someone with a z-score of zero for time spent watching TV would watch the average amount of TV.
Again, the z-score represents how far a data point is from the mean in terms of standard deviations. If someone is making minimum wage, their salary would be below the mean salary, so their z-score would be negative.
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Can someone assist me?The cheerleading squad at Morristown High School had 20 members with the old coach. Now, with the new coach, there are 45% more members on the squad. How many members are on the squad now?
Answer:
29
Step-by-step explanation:
First, let's find out how many members are added to the squad with the new coach:
45% of 20 = 0.45 x 20 = 9
So, with the new coach, there are 9 more members added to the squad.
Now, to find the total number of members on the squad with the new coach, we just need to add the old number of members (20) to the number of new members added (9):
20 + 9 = 29
Therefore, there are now 29 members on the cheerleading squad at Morristown High School with the new coach.
Use Lagrange multipliers to find the points on the given cone that are closest to the following point.
z^2 = x^2 + y^2; (14, 8, 0)
x,y,z=(smaller z-value)
x,y,z=(larger z-value)
By using the Lagrange multipliers, the two points on the cone that is closest to (14, 8, 0) are:
(7, 4, √65) and (7, 4, -√65)
We want to minimize the distance between the point (14, 8, 0) and the points on the cone z^2 = x^2 + y^2. The distance squared between two points (x_1, y_1, z_1) and (x_2, y_2, z_2) is given by:
d^2 = (x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2
In our case, we want to minimize the distance squared between (14, 8, 0) and a point (x, y, z) on the cone z^2 = x^2 + y^2:
d^2 = (x - 14)^2 + (y - 8)^2 + z^2
Subject to the constraint z^2 = x^2 + y^2. We can use Lagrange multipliers to solve this constrained optimization problem. Let L be the Lagrangian:
L = (x - 14)^2 + (y - 8)^2 + z^2 - λ(z^2 - x^2 - y^2)
Taking the partial derivatives of L with respect to x, y, z, and λ, and setting them to zero, we get:
2(x - 14) - 2λx = 0.....(1)
2(y - 8) - 2λy = 0.....(2)
2z - 2λz = 0.....(3)
z^2 - x^2 - y^2 = 0.....(4)
Simplifying the third equation, we get z(1 - λ) = 0. Since we want to find points where z is not zero, we must have λ = 1. Then, from the first two equations, we get x = 7 and y = 4. Substituting these values into the fourth equation, we get:
z^2 = x^2 + y^2 = 65
So the two points on the cone that is closest to (14, 8, 0) by using Lagrange multipliers are:
(7, 4, √65) and (7, 4, -√65)
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If the ratio a: b is 1 : 4 and the ratio b: c= 3:2, find the ratio (a + c) : c.
The required ratio of is (a + c) : c 11:8.
How to find ratio ?Given that a:b=1:4 and b:c=3:2.
We can simplify the ratio b:c by multiplying both sides by 4 to get b:c=12:8=3:2.
To find the ratio (a+c):c, we need to express a and c in terms of b. From the first ratio, we have [tex]a=\frac14 b$[/tex]. From the second ratio, we have [tex]c=\frac{2}{3}b$[/tex]. Substituting these values into the expression (a+c):c, we get:
[tex]$$(a+c):c = \left(\frac{1}{4}b + \frac{2}{3}b\right):\frac{2}{3}b$$[/tex]
Simplifying the expression inside the parentheses, we get:
[tex]$\frac{1}{4}b + \frac{2}{3}b = \frac{3b}{12} + \frac{8b}{12} = \frac{11b}{12}$$[/tex]
Therefore, the ratio [tex]$(a+c):c$[/tex] is:
[tex]$(a+c):c = \frac{11b}{12}:\frac{2}{3}b = 11:8$$[/tex]
Hence, the required ratio is 11:8$.
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25.71 rounded to 2 Decimal Place
Answer:
25.71 (2 d.p)
Step-by-step explanation:
[tex].[/tex]
VAT is added at 15% for good and services in South Africa. What will be the selling price of a laptop that costs R4200 before VAT
The selling price of laptop after VAT (15 percent) is Rs 4830.
To determine the quantity or percentage of something in terms of 100, use the percentage formula. Percent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed.
A number that is expressed as a fraction of hundred is what it is.
it is mostly used to compare and determine ratios and is represented by the symbol %.
We are given that:-
the selling price of laptop before VAT = Rs 4200VAT= 15%so the amount after VAT = 4200+4200*15%
= 4200+4200+0.15
= 4200+630= 4830.
therefore, the selling price of laptop after VAT is Rs 4830.
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below is survey results describing the survival rate and life expectancy in a certain population. p(n) stands for the probability of a new-born to reach the age of n years. n 55 60 65 70 p(n) 0.903 0.882 0.742 0.657 according to the given survey, answer the following questions: what is the probability of a 65 years old man to reach the age of 70? you can express your answer as a fraction, decimal, or a percentage. if you asnwer in decimal, include at least 3 digits after the decimal point. if you answer is a percentage, make sure to include a % sign in your answer. symbolic expression given that the probability that a man who just turned 70 will die within the next 5 years is 0.176, what is the probability for a man to survive till his 75th birthday, i.e., what is p(75)? you can express your answer as a fraction, decimal, or a percentage. if you asnwer in decimal, include at least 3 digits after the decimal point. if you answer is a percentage, make sure to include a % sign in your answer.
The probability that a 65-year-old man will survive to reach the age of 70 is 88.4%, and also the probability man to survive till his 75th birthday is approx.59.952%.
The probability of a 65-year-old man reaching the age of 70 is the probability of surviving from age 65 to age 70, which is given as
p(70)/p(65) ⇒ 0.657/0.742 ≈ 0.88544 or 88.544%.
The probability of a man who just turned 70 dying within the next 5 years is 0.176.
Therefore, the probability of surviving for the next 5 years after turning 70 is
⇒ 1 - 0.176 ⇒ 0.824.
Thus, the probability of a man surviving till his 75th birthday is the probability of surviving from age 70 to age 75, which is given as
p(75)/p(70) ⇒ 0.657/0.903 × 0.824
≈ 0.59952 or 59.952%.
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URGENT PLEASE HELP!!
Given that f(x)=x^2+3x-7, g(x)=3x+5 and h(x)=2x^2-4, find each of the following. Solve each of the problems showing work.
f(g(x))
h(g(x))
(h-f) (x)
(f+g) (x)
Explain what method you used when had a squared term that had to be multiplied out.
For the given functions, f(x)=x²+3x-7, g(x)=3x+5 and h(x)=2x²-4, f(g(x))= 9x² + 30x + 33, h(g(x))= 18x² + 60x + 46, (h-f)(x)= x² - 3x + 3, (f+g)(x)= x² + 6x - 2.
Describe Function?In mathematics, a function is a mathematical object that takes an input (or several inputs) and produces a unique output. It is a relationship between a set of inputs, called the domain, and a set of outputs, called the range.
Formally, a function f is defined by a set of ordered pairs (x, y) where x is an element of the domain, and y is an element of the range, and each element x in the domain is paired with a unique element y in the range. We write this as f(x) = y.
Functions can be represented in various ways, such as algebraic expressions, tables, graphs, or verbal descriptions. They can be linear or nonlinear, continuous or discontinuous, and may have various properties such as symmetry, periodicity, and asymptotic behavior.
To solve these problems, we substitute the function g(x) for x in f(x) and h(x) and simplify the resulting expressions.
f(g(x)):
f(g(x)) = f(3x+5) = (3x+5)² + 3(3x+5) - 7 (using the definition of f(x))
= 9x² + 30x + 33
h(g(x)):
h(g(x)) = h(3x+5) = 2(3x+5)² - 4 (using the definition of h(x))
= 18x² + 60x + 46
(h-f)(x):
(h-f)(x) = h(x) - f(x) = (2x² - 4) - (x² + 3x - 7) (using the definitions of h(x) and f(x))
= x² - 3x + 3
(f+g)(x):
(f+g)(x) = f(x) + g(x) = x² + 3x - 7 + 3x + 5 (using the definitions of f(x) and g(x))
= x² + 6x - 2
When multiplying out a squared term, such as (3x+5)², we can use the FOIL method, which stands for First, Outer, Inner, Last. We multiply the first terms, then the outer terms, then the inner terms, and finally the last terms, and then add up the results. For example:
(3x+5)² = (3x)(3x) + (3x)(5) + (5)(3x) + (5)(5)
= 9x² + 15x + 15x + 25
= 9x² + 30x + 25
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Write 735 as the product of its prime factor.
Answer:
[tex]735 = 3 \times 5 \times {7}^{2} [/tex]
Step-by-step explanation:
[tex]735 = 7 \times 105[/tex]
[tex]735 = 7 \times 3 \times 35[/tex]
[tex]735 = 7 \times 3 \times 5 \times 7[/tex]
[tex]735 = 3 \times 5 \times {7}^{2} [/tex]
Assume that head sizes (circumference) of new recruits in the armed forces can be approximated by a normal distribution with a mean 22.8 inches and standard deviation of 1.1 inches. Suppose a recruit was found with a head size of 23 inches Find the approximate Z-score for this recruit. a. 0 -0.18 b. 0.18 c. 0.96 d. 476.73
The approximate Z-score for this recruit is b. 0.18.
The mean of the head sizes (circumference) of new recruits in the armed forces can be approximated by a normal distribution with a mean 22.8 inches and standard deviation of 1.1 inches. The head size of a recruit was found to be 23 inches.
The approximate Z-score for this recruit. The formula for Z-score is given by:
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
where X is the head size of the recruit, μ is the mean head size of recruits, and σ is the standard deviation of head sizes of recruits. Substituting the given values in the above formula, we get,
Z=(23-22.8)(1.1)
Z=0.2/1.1
Z [tex]\approx[/tex] 0.18
Thus, the approximate Z-score for this recruit is b. 0.18.
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The obtuse angle between the hands of a clock at 2.30 a.m. is
Answer: 105
Step-by-step explanation:
OBTUSE ANGLE (105°) IS FORMED AT 2:30 IN THE CLØCK.
As we know 12 division OF 360° CIRCLE GIVES 30°
AT TWO PM THE ANGLE BETWEEN HOUR AND MINUTE HAND IS 60° AFTER 30 MIN ARM ROTATES 180° AND HOUR ARM 30°/2 = 15°
SO THE ANGLE BETWEEN TWO ARMS IS (180-(60-15)
105
What is the value of 3x + 6 if x = -5
Answer:
-9
Step-by-step explanation:
x = -5
3x + 6
Since x = -5..
Do this
3(-5) + 6
Perform
-15 + 6
Answer: -9
Therefore, when x is equal to -5, the value of 3x + 6 is -9.
What is equation?An equation is a statement that expresses the equality of two mathematical expressions using mathematical symbols such as variables, numbers, and mathematical operations. The equality is represented by an equal sign "=" between the two expressions. Equations are used to represent mathematical relationships and solve problems in various fields such as physics, chemistry, engineering, and economics.
Given by the question.
3x + 6 = 3(-5) + 6
= -15 + 6
= -9
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A dairy made 98.38 ounces of yogurt. Then a local market bought 86.2 ounces of the yogurt.
How much yogurt does the dairy have left?
The amount of yoghurt left is 12. 18 ounces
How to determine the numberThe algebraic expressions are defined as those expressions that are made up of variables, terms, constants, factors and coefficients.
The expressions are also composed of some arithmetic or mathematical operations, such as;
BracketParenthesesDivisionAdditionSubtractionMultiplicationFrom the information given,
Let the total number of ounces of yoghurt be x
Let the number of ounces of yoghurt sold be y
We have that;
The number left= x - y
= 98.38 - 86.2
= 12. 18 ounces of yoghurt
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