Answers
The derivative of the function [tex]y = 5^x + e^7[/tex] with respect to 'x'
is [tex]\frac{dy}{dx} = 5^xln5 + 0[/tex].
What is differentiation?Differentiation, in mathematics, process of finding the derivative, or rate of change, of a function also known as the slope.
We know, [tex]\frac{dy}{dx} a^x = a^xlna[/tex], where 'a' is a constant.
Given, [tex]y = 5^x + e^7[/tex].
Now, The derivative of the function with respect to 'x' is,
[tex]\frac{dy}{dx} = 5^xln5 + 0[/tex], As [tex]e^7[/tex] is a constant, and the derivative of any constant term is zero because the slope of a constant term is zero.
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Related Questions
In ΔA B G, if m ∠C is nine less than m ∠A and m ∠B is fifteen less than four times m ∠A, find the measure of ∠B
A) 125° hula hooping
B) 121° doing the Nae Nae
C) 57° finger painting
D) 34° playing clarinets
Answers
The measure of angle B is 121°
The correct option is B) 121° doing the Nae Nae
"Information available from the question"
In the question:
In ΔA B C, if m ∠C is nine less than m ∠A and m ∠B is fifteen less than four times m ∠A,
To find the measure of ∠B.
Now, According to the question:
We know that:
The sum of the measures of the angles of a triangle are 180
m<A + m<B + m<C = 180°
m<C = m<A - 9
m<B = 4*m<A - 15
m<A + 4*m<A - 15 + m<A - 9 = 180°
6m<A - 24 = 180°
6m<A = 204
m<A = 34°
Now, To find the measure of ∠B
m<B = 4*m<A - 15
m<B = 4* 34 - 15
m<B = 121°
The correct option is B) 121° doing the Nae Nae
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All fourth grade children on Long Island are given an examination on mathematical achievement. A random sample of 60 fourth graders are selected. Their examination results are summarized in the following stem-and-leaf plot. Find the sample upper quartile.4 6 6 6 88 01 7 7 7 7 7 8 33 445 6667777 8888889 00011111 2233333 4455 66777 8 8 8 8 899 9 001 9 223 45 9
Answers
The sample upper quartile of the data set is 91 and the lower quartile is 67 for the students of the given examination.
The median and quartiles of a data set:
The data set's median, or 50th percentile, separates the bottom half from the higher half.
The first quartile is the median of the data set's first half.
The third quartile is the median of the data set's second half.
Because there are an even number of items 60, the median is the mean of the31st element elements, with the first half consisting of 30 elements ranging from 1 to 29, and the second half consisting of 12 elements ranging from 31 to 60.
The first quartile is the mean of the elements, 67 and 68, respectively, therefore Q1 = 60/4 =15th element = 67
The third quartile is defined as the mean of the sixth and seventh elements of the second half, hence Q3 = 3×60 / 4 = 91.
Hence the quartiles are at 67 and 91 respectively.
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Suppose you have two Single Factor ANOVA experiments with the same degrees of freedom, if the resulting F test statistics are: Experiment 1, F = 2.68 Experiment 2, F = 20.15 Which statement is TRUE in regards to comparing Experiment 1 and Experiment 2? A.Procedure 1 has a smaller test statistic and therefore will result in stronger evidence in favor of the alternative hypothesis. B.Procedure 2 has a larger test statistic and therefore will result in stronger evidence in favor of the alternative hypothesis. C.We should reject the null for both tests. D.Impossible to know without more information.
Answers
TRUE - Procedure 2 has a larger test statistic and therefore will result in stronger evidence in favor of the alternative hypothesis.
what is degrees of freedom?Degrees of freedom are the maximum number of logically independent, or potentially different, values in the sample of data. One is subtracted from the number of elements in the data sample to determine the degree of freedom.
There are degrees of flexibility in the third column. Degrees of freedom (df1) between treatments equals k-1. df2 = N - k is the degree of freedom for the error. The total degree of freedom is N-1; additionally, (k-1) plus (N-k) equals N-1.
Fisher's Least Significant Difference (LSD) and the Bonferroni Method stand out among the techniques. These two use the t-test as their foundation. According to Fisher's LSD, run an F-test first, then if you find evidence to reject the null hypothesis, run regular t tests on all possible pairs of means. Similar but only requiring that you choose beforehand is the Bonferroni technique.
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set up, but do not evaluate, a triple integral that gives the volume of the right circular cylinder enclosed by the surfaces x^2 +y^2 =4,z=−10, and z=0
Answers
This triple integral gives the volume of the right circular cylinder which is enclosed by the given surfaces and extends from z = 0 to z = -10.
What in mathematics is an integral?
Mathematicians define an integral as either a number equal to the area under the graph of a function for a certain interval or as a new function whose derivative is the original function (indefinite integral).
In general, the word "integral value" refers to the result of integrating or summing the terms of a function that has an infinite number of terms.
The triple integral that gives the volume of the right circular cylinder enclosed by the surfaces x^2 + y^2 = 4 , z=-10 and z=0 is:
∫∫∫dV = ∫∫∫dx dy dz
where the limits of the integration are:
0 ≤ x ≤ 2*sqrt(2), -2*sqrt(2) ≤ y ≤ 2*sqrt(2), 0 ≤ z ≤ -10.
This triple integral gives the volume of the right circular cylinder which is enclosed by the given surfaces and extends from z = 0 to z = -10.
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Need Help ASAP!!! Giving away 50 pts
Given the equation 7m − 11 = 5m + 43 and the possible solution set S: {2, 27, 54, 86}:
Determine which integer(s) in the solution set makes the equation false. Show all work.
Answers
The required integers from the solution set are 2, 54 and 86.
How to solve a linear equation?A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.
The given equation is 7m − 11 = 5m + 43.
It can be solved as follows,
7m − 11 = 5m + 43
⇒ 7m - 5m = 43 + 11
⇒ 2m = 54
⇒ m = 27
Now, in the given solution set {2, 27, 54, 86}, only one integer 27 satisfies the given equation.
Hence, the integers in the solution set that make the equation false are 2, 54 and 86.
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Complete the proof of the identity by choosing the Rule that justifies each step. Sin^2x + 4cos^2x = 4 -3sin^2x To see a detailed description of a Rule in the Rule menu, select the corresponding question mark. Statement Rule sin^2 x + 4cos^2 x sin^2 x + 4 (1 -sin^2 x) Rule? sin^2 x + 4 -4sin^2 x Rule? 4 -3sin^2 x Rule? Reciprocal identities: sin u = 1/csc u cos u = 1/sec u tan u = 1/cot u csc u = 1/sin u sec u = 1/cos u cot u = 1/tan u Quotient identities: tan u = sin u/cos u cot u = cos u/sin u Pythagorean identities: sin^2u + cos^2u = 1 tan^2u + 1 = sec^2 u cot^2 u + 1 = csc^2 u Odd/Even function identities: sin(-u) = -sin(u) cos(-u) = cos(u) tan(-u) = -tan(u) csc(-u) = -csc(u) sec(-u) = sec(u) cot(-u) = -cot(u)
Previous question
Answers
Hence, the proof is completed by choosing the identities of the rules.
Trigonometry identities
Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation. There are various distinct trigonometric identities involving the side length as well as the angle of a triangle. The trigonometric identities hold true only for the right-angle triangle.Given that :
Complete the proof of the identity by choosing the Rule that justifies each step.
Sin^2x + 4cos^2x = 4 -3sin^2x
Statement Rule
[tex]sin^{2} x + 4 cos^{2}x[/tex]
= [tex]sin^{2}x + 4 (1 - sin^{2} x )[/tex] [tex]sin^{2}u + cos^{2}u = 1[/tex]
[by using Pythagorean identities]
= [tex]sin^{2}x + 4 - 4 sin^{2}x[/tex] [tex](1 - sin^{2}x )[/tex]
[ multiplied by 4 ]
= [tex]4 - 3 sin^{2}x[/tex]
Sin^2x + 4cos^2x = 4 -3sin^2x
Hence proved.
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Zachariah paid $126 for 6 concert tickets. At this rate, what is the cost of 10 concert tickets?
Answers
Marcus worked 45 hours this week. His hourly rate of pay is $9.00. What was the pay
for Overtime hours only?
Answers
Marcus' overtime pay for the week is $67.50.
How is the overtime pay determined?The overtime pay is paid at the hourly rate and a half.
This translates to the regular rate of pay x 1.5 x overtime hours worked.
The total hours worked this week = 45 hours
Normal working hours per week = 40 hours (5 days x 8 hours)
Overtime hours = 5 hours (45 - 40)
Hourly rate = $9.00
Overtime rate = $13.50 ($9 x 1.5)
Overtime pay = $67.50 ($13.50 x 5)
Thus, for this week, Marcus has earned overtime pay of $67.50 above his normal weekly pay of $360.
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Mona's school tennis team is running a car wash this weekend. They will charge $13 per car, and they are hoping to
aise $200. How much money will the team have left to raise once they have washed 10 cars?
Write and solve an equation to find the answer.
Answers
Answer:
$70
Step-by-step explanation:
x = 200 - 10 · 13
x = 200 - 130
x = 70
One week gas was $1.75 per gallon. The next week gas was $2.10 per gallon. By what percentage did the price increase or decrease? % (increase or decrease)
Answers
Rate can be found by subtracting old price from new price and then dividing that by the old price
Old price = $1.75
New price = $2.10
2.10 - 1.75 = .35
.35 / 1.75 = .2 = 20% increase
Check your work
1.75 x 20% = .35
1.75 + .35 = 2.10
Problem solved!
I'm not sure how to solve the probability for the question.
Thank You for your help
Answers
The statement that corresponds to P(X = 48), using continuity correction, is given as follows:
c. P(47.5 < x < 48.5).
What is continuity correction?Continuity correction is used as a "correction" when a continuous distribution is used to approximate a discrete distribution. One example of this is the approximation of the binomial distribution to the normal distribution.
Hence, using continuity correction, the range of values that corresponds to a number of exactly x is given as follows:
x - 0.5 < x < x + 0.5.
Thus the range for exactly 48 successes is of:
47.5 < x < 48.5.
Meaning that option c is correct.
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draw in all lines of symmetry of the blue square
Answers
Answer:
Step-by-step explanation:
What are the vertex and range of y = |2x + 6| + 2?
(0, 2); 2 < y < ∞
(0, 2); −∞ ≤ y < ∞
(−3, 2); 2 < y < ∞
(−3, 2); −∞ ≤ y < ∞
Answers
The vertex and the range of y = |2x + 6| + 2 are (c) (-3, 2); 2 ≤ y < ∞
How to determine the vertex and the range?The equation is given as
y = |2x + 6| + 2
The above equation is an absolute value function
An absolute value function represented as
y = a|x - h| + k
Where
Vertex = (h, k)
So, we have
y = |2x + 6| + 2
This gives
y = 2|x + 3| + 2
This means that the vertex is
Vertex = (-3, 2)
Remove the x value
y = 2
Because the leading coefficient is positive, then the vertex is a minimum
i.e.
y ≥ 2
So, the range is 2 ≤ y < ∞
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Rachel has \frac{7}{15}
15
7
of her project done. If she can finish \frac{7}{45}
45
7
of her project each day, how many more days will it take her to complete it?
Answers
Answer:
4 days
Step-by-step explanation:
If Rachel has 7/15 of her project done, then she has 8/15 of her project left to complete.
Convert 8/15 and let it have a denominator of 45, and you get 24/45. If she can finish the rest of her project 7/45 each day, and she has 24/45 left to go, then divide 24 by 7, and you get 3 R3.
Afterwards round that to 4, because Rachel can't leave 3/45 of her project unfinished, she just doesn't have as much work the last day.
So then Rachel can finish her project in 4 days.
Hope this helps!
Answer:
4 days
Step-by-step explanation:
7/15 done ...then 8/15 to go
8/15 = 24 / 45 if she can do 7/45 per day, she will need 4 more days
(24/7) = 3.4 =~ 4 days
Suppose f(x)is a continuous differentiable function and you are given that f"(x) is always positive. Which of the following statements must be true? f(x) is always increasing. f'(x) is always increasing. f"(x) is always increasing. None of the above must be true.
Answers
According to the facts provided in the question and we know that the derivative of the function f(x) is f'(x) which refers to the slope at the point. The answer is f(x) is always increasing.
What do you mean by derivative?The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. Calculus's core tool is the derivative. The rate at which a function changes in relation to a variable Calculus and differential equations issues must be solved using derivatives.
What do you mean by slope of the line?A line's steepness can be determined by looking at its slope. The ratio of the change in the y-value to the change in the x-value can also be used to determine slope.
f(x) is the function.
f'(x) is the derivative of the function.
f'(x) is always positive which explains that the line has positive slope that is moving upwards in graph.
So, f(x) is always increasing.
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34 In the appeal of the People v. Collins case (see Exercise 4.1.28), the counsel for the defense argued as follows: Suppose, for example, there are 5,000,000 couples in the Los Angeles area and the probability that a randomly chosen couple fits the witnesses’ description is 1/12,000,000. Then the probability that there are two such couples given that there is at least one is not at all small. Find this probability. (The California Supreme Court overturned the initial guilty verdict.)
Answers
The probability that there are two such couples given that there is at least one is 1 - (4999999/12000000) = 4/12 = 1/3.
What is probability?Probability is the measure of the likelihood that a given event will occur. It is expressed as a number between 0 and 1 (or 0% to 100%). A probability of 1 indicates that the event is certain to occur, while a probability of 0 indicates that it is impossible for the event to occur. Probability is used in a wide range of disciplines including mathematics, science, engineering, finance, and philosophy. Probability can be used to make predictions and help inform decision-making. By understanding probability, we can better understand the chances of certain outcomes and make more informed decisions.
This is because the probability that the first couple matches the description is 1/12000000, and the probability that the second couple matches the description, given that the first couple does, is 1/(12000000-1). Since there are 4999999 other couples, the probability that the second couple matches the description is (4999999/12000000). Thus, the probability that there are two such couples is 1 minus the probability that the second couple does not match the description, which is 1 - (4999999/12000000) = 4/12 = 1/3.
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In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse.
If b = 16 units and c = 20 units, what is the perimeter? If necessary, round your answer to the nearest tenth.
Answers
Answer: 48
Step-by-step explanation: Use this to help you!
The equation for line g can be written as y–1= – 1/10 (x+8). Parallel to line g is line h, which passes through the point ( – 5,5). What is the equation of line h?
Answers
Answer:
point-slope form: [tex]y+5=-\frac{1}{10}(x-5)[/tex]
slope-intercept form: [tex]y = -\frac{1}{10}x - \frac{9}{2}[/tex]
Step-by-step explanation:
Point-Slope Form:We can express any one-variable linear equation as: [tex]y-y_1=m(x-x_1)[/tex], where "m" is the slope, and [tex](x_1, y_1)[/tex] is some point on the graph.
We're given the equation in point-slope form: [tex]y-1=-\frac{1}{10}(x+8)[/tex], and if we want to make a line parallel to this line, we just need the slopes to be the same. So let's just look at the value in front of the parenthesis. This is given to be: [tex]-\frac{1}{10}[/tex]
We can use this same form, to develop an equation parallel to the given line, and passing through: [tex](-5, 5)[/tex]
Plugging the values into the point-slope formula, we get:
[tex]y-(-5)=-\frac{1}{10}(x-5)\\\\y+5=-\frac{1}{10}(x-5)[/tex]
From here we can also convert this into slope-intercept form, where "y" is isolated.
[tex]\\y+5=-\frac{1}{10}(x-5)\\\\y+5=-\frac{1}{10}x + \frac{5}{10}\\\\y + \frac{10}{2} = -\frac{1}{10}x + \frac{1}{2}\\\\y + \frac{10}{2} - \frac{10}{2} = -\frac{1}{10}x + \frac{1}{2} - \frac{10}{2}\\\\y = -\frac{1}{10}x - \frac{9}{2}[/tex]
Write an equation for a parabola with x-intercepts (-1,0) and (3,0) ehich pass the point (1,-16)
Answers
The equation for a parabola with x-intercept is y = 4/3x² + 8/3x - 20.
What is equation?
In arithmetic, an equation could be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.
Main body:
The equation has the form y = Ax² + Bx + C
Since (3,0), (-1,0), (1,-16) are points on the graph, we get the following system of equations:
9A + 3B + C = 0
A - B + C = 0
A + B + C = -16
Subtracting the first 2 equations and subtracting the 3rd equation from the first, we obtain:
8A - 4B = 0
8A + 2B = 16
Since 8A - 4B = 0, 8A = 4B. So, A = 1/2B.
Therefore, 8A + 2B = 16
6B = 16 So , B = 8/3 and A = 8/6
Since A + B + C = -16 and A = 8/6 , B = 8/3, we have 4 + C = -16. So, C = -20.
An equation of the parabola is y = 4/3x² + 8/3x - 20
Hence , the equation for a parabola with x-intercept is y = 4/3x² + 8/3x - 20.
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NEED HEEEEELP PLEEEEASE HEEEEELP Solve. 4/5x+9/10=5 1/5 Enter your answer as a mixed number in simplest form in the box. x =
Answers
The value of x in the fraction 4/5x+9/10=5 1/5 is 5 3/8.
How to calculate the fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, the fraction is given as:
4/5x + 9/10 = 5 1/5
0.8x + 0.9 = 5.2
Collect like terms
0.8x = 5.2 - 0.9
0.8x = 4.3
Divide
x = 4.3 / 0.8
x = 5.375
x = 5 3/8
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A heavy rope, 40 ft long, weighs 0.5 lb/ft and hangs over the edge of a building 90 ft high. (Let x be the distance in feet below the top of the building. Enter xi* as xi.) (a) How much work W is done in pulling the rope to the top of the building? Show how to approximate the required work by a Riemann sum. lim( lim n-00 ) i = 1 Express the work as an integral. 160_v (10.5x , ) Jo Evaluate the integral. 900 X ft-lb (b) How much work W is done in pulling half the rope to the top of the building? Show how to approximate the required work by a Riemann sum. lim n7009 i = lim E(L Dax 1 Express the work as an integral. dx Evaluate the integral. ft-lb
Answers
According to Riemann sum and expressing the work as an integral,400 ft/lb work is done in pulling the rope to the top of the building.
Given,
heavy rope length = 40ft
weighs = 0.5 lb/ft
building height = 90 ft
If we divide rope into small parts with length Δx, rope weighs 0.5 lb/ft force work on each section is x*i is a point in i the such intervals.
The work done on ith part is
x*i0.5Δx
So the total done is
[tex]\lim_{n \to \infty}[/tex]= ∑0.5x*iΔx expressing work as an integral
[tex]\int\limits^40_0 {(0.5x)} \, dx[/tex] = [0.5 × x²/2]
= [0.5 × 40²/2 - 0.5 × 0²/2]
= [0.5 × 1600/2 - 0]
= 0.5 × 800 - 0
= 400 - 0
= 400 ft/lb
The work done in lifting the pieces in upper half of rope is
x*i0.5Δx
The work done in lifting lower half of the rope is
0.5Δx × 20
10Δx
Total workdone,
[tex]\lim_{n \to \infty}[/tex]∑0.5x*iΔx + [tex]\lim_{n \to \infty}[/tex]∑10Δx
= [tex]\lim_{n \to \infty}[/tex]∑(0.5x*i + 10)Δx work as an integral
[tex]\int\limits^25_0 {0.5} \, dx[/tex] + [tex]\int\limits^50_25 {10} \, dx[/tex]
= [ 0.5 * x²/2] + [10x]
= [0.5 * 20²/2] +[10(40-20)]
= [0.5 * 400/2] + [10*20]
= 100 + 200
= 300 ft/lb
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Helppp! I need an answer asap pls!
Answers
Answer: (2*sqrt3)/3
Step-by-step explanation:
csc(x)=1/sin(x)
sin(q)= 15/(10*sqrt3)= 3/(2*sqrt3)
1/(3/(2*sqrt3))= (2*sqrt3)/3
X
y
13
45° I need this
Answers
Answer:
Step-by-step explanation:
you times 13 times 45 degrees and that equals to 585
Write 2 equations and solve for the numbers
Answers
Answer:
y + x = 87
y = x + 35
x = 26
y = 61
Step-by-step explanation:
y + x = 87
y = x + 35
substitute y with x + 35 in the first equation:
(x + 35) + x = 87
2x + 35 = 87
2x = 87 - 35
2x = 52
x = 52/2
x = 26
Find y by substituting x with 26:
y = (26) + 35
y = 61
a sequential circuit has two jk flip-flop a and b and one input x. the circuit is described by the following flip-flop input equations:
Answers
D flip flop stands for a delay flip flop that produces output that is identical to input after a brief delay. The flip flop's input and next state are equal.
Z is an output, and x and x inputs.
x'y + xA = DA= A*
B* = x'B + xA
z=A (output is independent of input) (output is independent of input)
The next states are A(t+1) and B(t+1). We must provide the next state value to D of the D flip flop in order to obtain the next states A(t+1), and B(t+1) for A, B(present state). So the sequential circuit will be:
To get the next state as A(t+1)= x’A + xA, B(t+1)= x’B + xA, we have to give them to DA, DB of D flip flop because for D flip flop whatever is given to DA, DB will appear at output A, B.
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Henry correctly factored 42? + 52 - 6 as (4% - 3)(₴ + 2)
• He then claimed that the zeros of that quadratic function are located at
*=-=
and r = 2 . Did Henry correctly find the zeros of the function?
O Yes, Henry correctly found the zeros of the function.
O No, the zeros of the function are at x = 4 and =-2
• No, the zeros of the function are at z = - 5 andx = 2.
• No, the zeros of the function are at & = 4 and ≥ = -2
I attached the question and answer choices
Please help
Answers
Answer:
No, the zeros of the function are at x = 3/4 and x = –2
Step-by-step explanation:
the equation
4x² + 5x – 6 = 0
(note: since there is a coefficient of x² we need to multiply it to the last term(6))
4x² + 5x – 24 = 0
the factors are :- 8x and – 3x
4x² + 8x – 3x – 6 = 0
4x( x + 2) –3( x + 2) = 0
( 4x – 3)( x + 2) = 0
the zeros will be
4x – 3 = 0
4x = 3
[tex]x = \frac{3}{4} [/tex]
x + 2 = 0
x = – 2
the zeros are x= 3/4 or –2
i hope this helps
A speech class has eight freshmen and five sophomores. Three people are selected at random to give speeches in sequence. Find the probability that
(a) the first is a sophomore, the second is a freshman, and the third is a sophomore.
(b) all three are freshmen.
(c) the first is a sophomore and the other two are freshmen.
Answers
1716 is the probability that a sophomore, the second is a freshman, and the third is a sophomore.
What is probability explained with an example?
A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty. The likelihood that an event will occur increases with its probability.
The flip of a fair (impartial) coin serves as a straightforward illustration. The probability of an event occurring, or P(E), is defined as the ratio of the number of favorable outcomes to the total number of outcomes in the probability formula.
The total number of ways in which 3 students can be arranged for speech out of total 13 students is,
P(13,3) = 13 * 12 * 11
= 1716
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1. Assume that there is a party consisting of people between the ages of 18 and 24 inclusive. How many people would have to be at the party to guarantee that at least three people share the same birth date, birth month, and birth year? Note: assume the range of birth years include 2 leap years. (10 points)
Answers
at least 24 people must be in the party to guarantee that at least 3 people have the same date of birth, date of birth, date of birth.
To warrant that at least three people have the same date, month, and year of birth, we need to find the minimum number of people such that there is a probability that at least three people have the same date, month, and year. there is. Birth year she is 1 or more. Non-leap years have 365 days, and leap years have her 366 days. The birth year range includes two leap years, so there are 3652 + 3662 = 2,922 possible births. This means that the probability that a particular person's birthday is unique is (2922-1)÷2922 = 1÷2922.
Now we can use the birthday puzzle to calculate the probability that at least three people have the same birthday. The probability that no one has the same birthday is (1 - 1÷2922)^n, where n is the number of people in your party. At least he has 1-(1-1÷2922)^n probability that 3 of them have the same birthday. You can set this probability to 1 or more and solve for n.
1 - (1 - 1÷2922)^n >= 1
(1 - 1÷2922)^n <= 0
n >= log(0) ÷ log(1 - 1÷2922)
The logarithm of 0 is not defined, so you can use a small value on the right hand side instead. B. 10^-6. This will tell you:
n >= log(10^-6) ÷ log(1 - 1/2922)
n >= log(10^-6) ÷ log(2921/2922)
n >= log(10^-6) ÷ log(2921) - log(10^-6) / log(2922)
n >= log(10^-6) × log(2922) ÷ log(2921) - log(10^-6)
n >= log(10^-6) × log(2922) ÷ log(2921) - log(10^-6)
n >= 23.
Hence, at least 24 people must be in the party to guarantee that at least 3 people have the same date of birth, date of birth, date of birth.
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Twelve percent of the manufactured parts were defective and had to be pulled from the assembly line. Forty-eight defective parts
were pulled from the line. How many total parts were manufactured during this run?
O d) 126
O a) 400
O c) 383
Ob) 48
Answers
Answer:
a) 400---------------------------
Let the number of total parts be x.
12% of x were defective and it is 48 in number.
Find x:
0.12x = 48x = 48/0.12x = 400Correct choice is A.
Graph g(x) = −2x − 8 and identify its x-intercept.
(−8, 0)
(−4, 0)
(0, −4)
(0, −8)
Answers
Based on the graph of the function g(x) = −2x − 8, the x-intercept is equal to -4.
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively.
What is the x-intercept?In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" is equal to zero (0).
By critically observing the graph of g(x) = −2x − 8, the x-intercept is -4. This ultimately implies that, the function g(x) = −2x − 8 would cross the x-coordinate (x-axis) at point (-4, 0.
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