Larry Mitchell invested $ [tex]7000[/tex] at [tex]3[/tex]% annual simple interest and $[tex]13000[/tex] at [tex]6[/tex]% annual simple interest.
What is the annual simple interest?Let's denote the amount Larry Mitchell invested at 3% annual simple interest as "x" (in dollars) and the amount he invested at 6% annual simple interest as [tex]"20,000 - x"[/tex] (since he invested the rest of the advance amount).
The formula for simple interest is:
Simple Interest (SI) = Principal (P) * Rate (R) * Time (T)
Given that the total yearly interest from both accounts was $990, we can set up the following equation:
3% of x + 6% of [tex](20,000 - x) = 990[/tex]
Converting the percentages to decimals, we get:
[tex]0.03x + 0.06(20,000 - x) = 990[/tex]
Now, we can solve for x by simplifying the equation and isolating x on one side:
[tex]0.03x + 1200 - 0.06x = 990[/tex]
[tex]-0.03x = 990 - 1200[/tex]
[tex]-0.03x = -210[/tex]
Dividing both sides by -0.03, we get:
x = (-210)/(-0.03)
[tex]x = 7000[/tex]
So, Larry Mitchell invested $7000 at 3% annual simple interest.
Substituting the value of x back into the equation, we can find the amount he invested at 6% annual simple interest:
[tex]20,000 - x = 20,000 - 7000 = 13000[/tex]
Therefore, Larry Mitchell invested $ [tex]7000[/tex] at [tex]3[/tex]% annual simple interest and $[tex]13000[/tex] at [tex]6[/tex]% annual simple interest.
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You may need to use the appropriate technology to answer this question.
The success of an airline depends heavily on its ability to provide a pleasant customer experience. One dimension of customer service on which airlines compete is on-time arrival. The tables below contains a sample of data from delayed flights showing the number of minutes each delayed flight was late for two different airlines, Company A and Company B.
Company A
34 59 43 30 3
32 42 85 30 48
110 50 10 26 70
52 83 78 27 70
27 90 38 52 76
Company B
45 63 42 32 67
104 45 27 38 84
75 46 32 50 64
41 36 33 65 64
(a)
Formulate the hypotheses that can be used to test for a difference between the population mean minutes late for delayed flights by these two airlines. (Let 1 = population mean minutes late for delayed Company A flights and 2 = population mean minutes late for delayed Company B flights.)
H0: 1 − 2 < 0
Ha: 1 − 2 = 0
H0: 1 − 2 ≤ 0
Ha: 1 − 2 > 0
H0: 1 − 2 ≥ 0
Ha: 1 − 2 < 0
H0: 1 − 2 ≠ 0
Ha: 1 − 2 = 0
H0: 1 − 2 = 0
Ha: 1 − 2 ≠ 0
(b)
What is the sample mean number of minutes late for delayed flights for each of these two airlines?
Company A
min
Company B
min
(c)
Calculate the test statistic. (Round your answer to three decimal places.)
What is the p-value? (Round your answer to four decimal places.)
p-value =
Using a 0.05 level of significance, what is your conclusion?
Do not Reject H0. There is statistical evidence that one airline does better than the other in terms of their population mean delay time.
Reject H0. There is statistical evidence that one airline does better than the other in terms of their population mean delay time.
Do not reject H0. There is no statistical evidence that one airline does better than the other in terms of their population mean delay time.
Reject H0. There is no statistical evidence that one airline does better than the other in terms of their population mean delay time.
The answers are: A)H0: μ1 − μ2 = 0; Ha: μ1 − μ2 ≠ 0
(b) Means: Company A___50.6___ min.; Company B___52.75___ min.
c)The t-value is -0.30107., The p-value is 0 .764815.
What is a Hypothesis?A hypothesis is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon
A)H0: μ1 − μ2 = 0
i.e there is no difference between the means of delayed flight for two different airlines
Ha: μ1 − μ2 ≠ 0
i.e there is a difference between the means of delayed flight for two different airlines
(b)
Company A___50.6___ min.
Company B___52.75___ min.
Mean of Company A = x`1= ∑x/n =34+ 59+ 43+ 30+ 3+ 32+ 42+ 85+ 30+ 48+ 110+ 50+ 10+ 26+ 70+ 52+ 83+ 78+ 27+ 70+ 27+ 90+ 38+ 52+ 76/25
= 1265/25= 50.6
Mean of Company B = x`2= ∑x/n =
=46+ 63+ 43+ 33+ 65+ 104+ 45+ 27+ 39+ 84+ 75+ 44+ 34+ 51+ 63+ 42+ 34+ 34+ 65+ 64/20
= 1055/20= 52.75
Difference Scores Calculations
Company A
Sample size for Company A= n1= 25
Degrees of freedom for company A= df1 = n1 - 1 = 25 - 1 = 24
Mean for Company A= x`1= 50.6
Total Squared Difference (x-x`1) for Company A= SS1: 16938
s21 = SS1/(n1 - 1) = 16938/(25-1) = 705.75
Company B
Sample size for Company B= n1= 20
Degrees of freedom for company B= df2 = n2 - 1 = 20 - 1 = 19
Mean for Company B= x`2= 52.75
Total Squared Difference (x-x`2) for Company B= SS2=7427.75
s22 = SS2/(n2 - 1) = 7427.75/(20-1) = 390.93
T-value Calculation
Pooled Variance= Sp²
Sp² = ((df1/(df1 + df2)) * s21) + ((df2/(df2 + df2)) * s22)
Sp²= ((24/43) * 705.75) + ((19/43) * 390.93) = 566.65
s2x`1 = s2p/n1 = 566.65/25 = 22.67
s2x`2 = s2p/n2 = 566.65/20 = 28.33
t = (x`1 - x`2)/√(s2x`1 + s2x`2) = -2.15/√51 = -0.3
The t-value is -0.30107.
The total degrees of freedom is = n1+n2- 2= 25+20-2=43
The critical region for two tailed test at significance level ∝ =0.05 is
t(0.025) (43) = t > ±2.017
Since the calculated value of t= -0.30107. does not fall in the critical region t > ±2.017, null hypothesis is not rejected that is there is no difference between the means of delayed flight for two different airlines.
The p-value is 0 .764815. The result is not significant at p < 0.05.
C) Do not reject H0. There is no statistical evidence that one airline does better than the other in terms of their population mean delay time.
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Find the area, to the nearest thousandth, of the indicated region of the standard normal distribution. The region where z >1.42
The area to the right of [tex]1.42[/tex] in the standard normal distribution is approximately [tex]0.0793[/tex] .
What is the standard normal distribution?The region where [tex]z > 1.42[/tex] in the standard normal distribution corresponds to the area under the curve to the right of [tex]1.42[/tex] on the z-axis.
To find this area, we can use a standard normal distribution table or a calculator with a cumulative distribution function (CDF) for the standard normal distribution.
Using a calculator with a CDF for the standard normal distribution, we can input 1.42 and calculate the area to the left of 1.42. Then, we subtract this area from 1 to get the area to the right of 1.42. Here's the calculation:
[tex]P(Z > 1.42) = 1 - P(Z < 1.42)[/tex]
Using a standard normal distribution table or a calculator, we find that [tex]P(Z < 1.42)[/tex] is approximately 0.9207. Subtracting this value from 1, we get:
[tex]P(Z > 1.42) \approx 1 - 0.9207 \approx 0.0793[/tex]
Therefore, the area to the right of [tex]1.42[/tex] in the standard normal distribution is approximately [tex]0.0793[/tex].
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In Math town,60% of the population are males and 30% of them have brown eyes. Of the total math town population 28 % have brown eyes. What percentage of the females in math town have brown eyes?
A) 20%
B) 24%
C) 25%
D) 28%
thought i would leave this but ⇒ty to whoever answers this, have an amazing day <3
The percentage of females with brown eyes as follows is 25%.
What is percentage?Percentage is a way of expressing a number as a fraction of 100. It is represented by the symbol "%". The word "percent" means "per hundred".
According to question:Let's assume that the total population of Math town is 100 people for the sake of simplicity. Then, we can use the following information to create a table:
Population Males Females
Total 60 40
Brown eyes 18 ?
From the table, we can see that 60% of the population are males, so there are 60 x 0.3 = 18 males with brown eyes.
We also know that the total population with brown eyes is 28%, so there are 100 x 0.28 = 28 people with brown eyes. Therefore, there must be 28 - 18 = 10 females with brown eyes.
Finally, we can calculate the percentage of females with brown eyes as follows:
% of females with brown eyes = (10 / 40) x 100% = 25%
Therefore, the answer is (C) 25%.
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A regular octogon is inscribed in a circle with a radius of 14 inches. Find the perimeter of the octogon. Round to 2 decimal places.
The perimeter of the octagon is:
Perimeter = 8s ≈ 100.16 inches
What is the perimeter?
The perimeter is a mathematical term that refers to the total distance around the outside of a two-dimensional shape. It is the length of the boundary or the sum of the lengths of all the sides of a closed figure.
To find the perimeter of the regular octagon inscribed in a circle with radius 14 inches, we need to use the formula:
Perimeter of octagon = 8 x length of one side
Since the octagon is regular, all sides are congruent. Let s be the length of one side of the octagon.
The radius of the circle is 14 inches, which is also the distance from the center of the circle to any vertex of the octagon. We can divide the octagon into eight congruent isosceles triangles, each with base s and legs of length 14 inches. We can then use the Pythagorean theorem to find the length of the base s:
s² = 14² - (s/2)²
s² = 196 - s²/4
5s²/4 = 196
s² = 156.8
s ≈ 12.52
Therefore, the perimeter of the octagon is:
Perimeter = 8s ≈ 100.16 inches (rounded to 2 decimal places).
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solve the equation x^2+4x-11=0 by completing the square
To solve the equation x^2 + 4x - 11 = 0 by completing the square, we can follow these steps:
Move the constant term to the right side of the equation:
x^2 + 4x = 11
Complete the square by adding the square of half the coefficient of x to both sides of the equation:
x^2 + 4x + (4/2)^2 = 11 + (4/2)^2
Simplifying the left side:
x^2 + 4x + 4 = 11 + 4
Factor the perfect square on the left side of the equation:
(x + 2)^2 = 15
Take the square root of both sides of the equation:
x + 2 = ±√15
Solve for x by subtracting 2 from both sides:
x = -2 ± √15
Therefore, the solutions to the equation x^2 + 4x - 11 = 0 by completing the square are x = -2 + √15 and x = -2 - √15.
Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.
The shaded area covers around 0.8664 square feet of space.
What is the typical normal distribution where the standard deviation is 0 and the mean 1?The mean and standard deviation of the standard normal distribution are 0 and 1, respectively. The standard deviation shows how much a particular measurement deviates from the mean, and the standard normal distribution is centred at zero.
Using a conventional normal distribution table, we must first determine the areas to the left of z= -1.5 and z=1.5, and then subtract those two areas to determine the area of the shaded zone.
Using a standard normal distribution table, we find that the area to the left of z= -1.5 is 0.0668, and the area to the left of z=1.5 is 0.9332. As a result, the darkened region's area is:
0.9332 - 0.0668 = 0.8664
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can someone please help me+explain how to do this step by step, im so confused
Your gross income is $4,520.00/month. Your deductions are FICA (7.65%), federal tax withholding (11.75%), and state tax withholding (8.5%). Your fixed expenses are 30% of your realized income. You saved 5 months' worth in an emergency fund, placing 75% in a 60-day CD at a 5.25% APR and the rest in a regular savings account at a 3.8% APR. What is the total amount of your emergency fund? How much is in the CD and savings account? How much is the total interest earned between both accounts in 60 days?
1. The total amount of your emergency fund will be $11,403.75.
2. $8,552.81 is in the CD, and $2,850.94 is in the regular savings account.
What is the total amount of your emergency fund?Your FICA deduction is 7.65% of your gross income:
7.65% of $4,520.00 = $345.98
Your federal tax withholding is 11.75% of your gross income:
11.75% of $4,520.00 = $531.40
Your state tax withholding is 8.5% of your gross income:
8.5% of $4,520.00 = $384.40
Your total deductions are:
= $345.98 + $531.40 + $384.40
= $1,261.78
Your monthly income after deductions is:
= $4,520.00 - $1,261.78
= $3,258.22
Your fixed expenses are 30% of your realized income:
= 30% of $3,258.22
= $977.47
Your monthly savings amount is:
= $3,258.22 - $977.47
= $2,280.75
You saved 5 months' worth in an emergency fund, so the total amount in your emergency fund is:
= 5 x $2,280.75
= $11,403.75
Regenerate response
How much is in the CD and savings account?You placed 75% of your emergency fund in a 60-day CD at a 5.25% APR:
= 75% of $11,403.75 = $8,552.81
You placed the remaining 25% of your emergency fund in a regular savings account at a 3.8% APR:
= 25% of $11,403.75
= $2,850.94.
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1245+557-45677/88765×345.865
Answer:
if question is a fraction then -0.001429, if not then 624.0235948
Suppose 16 cars start at a car race. In how many ways can the top 3 cars finish the race
there are 3,360 ways in which the top 3 cars can finish the race.
How to Determine the number of ways?
To determine the number of ways in which the top 3 cars can finish the race, we can use the concept of permutations. A permutation is an arrangement of objects in a specific order. In this case, the order of the cars finishing the race matters.
The number of ways to determine the first place finisher is 16, as any of the 16 cars can finish in first place. Once the first place finisher has been determined, there are only 15 cars remaining, and any one of them can finish in second place. Therefore, there are 15 possible ways to determine the second place finisher.
Similarly, once the first and second place finishers have been determined, there are 14 cars remaining, and any one of them can finish in third place. Therefore, there are 14 possible ways to determine the third place finisher.
To find the total number of ways in which the top 3 cars can finish the race, we can multiply the number of possibilities for each place together:
16 x 15 x 14 = 3,360
Therefore, there are 3,360 ways in which the top 3 cars can finish the race.
It is important to note that this calculation assumes that each car is unique and that there are no ties for any of the top 3 positions. If there were ties, the calculation would become more complicated and would involve combinations as well as permutations.
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An African mousebird is 2 feet tall. A camel is 4 times as tall as the mousebird. How tall is the camel in inches?
The length of a rectangular poster is 2 more inches than two times its width. The area of the poster is 84 square inches. Solve for the dimensions (length and width) of the poster.
Step-by-step explanation:
w = width
2w + 2 = Length
Area = W x L = 84 = w (2w+2)
84 = 2w^2 + 2w
0 = 2w^2 + 2w - 84 Use Quadratic Formula
a = 2 b=2 c = -84
to find
W = 6 then L = 14 inches
Find the logarithm
The value of the logarithm expression is Logₐ(13.3) is 2.598.
What is Logarithm?Logarithm is the exponent or power to which a base must be raised to yield a given number.
To find logₐ(13.5), we use the following techniques below
Given:
Logₐ² = 0.693Logₐ³ = 1.097But,
Logₐ(13.3) = Logₐ(27/2) = Logₐ(3³/2)Applying the law of logarithm,
Logₐ(3³/2) = Logₐ3³-Logₐ2Logₐ(3³/2) = 3Logₐ3-logₐ2........................ Equation 1Substitute the values above into equation 1
Logₐ(13.3) = 3(1.097)-0.693Logₐ(13.3) = 3.291-0.693Logₐ(13.3) = 2.598Learn more about logarithm here: https://brainly.com/question/25993029
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I need help with this
Answer:
1500
Step-by-step explanation:
Number of boxes = 12
Number of pencils in each box = 125
Total number of pencils
= 12 × 125
= 1500 pencils
The length of a side of an equilateral triangle is 14 centimeters.
What is the length of the altitude of the triangle?
2√ 7cm
3√ 7 cm
7√ 2 cm
7√ 3 cm
Answer: The altitude of the triangle is [tex]h = 7 \sqrt{3}.[/tex]
Step-by-step explanation:
Suppose that we separate the equilateral triangle with the altitude of the triangle, as shown in the diagram I attached.
Then the length of the altitude [tex]h[/tex] can be found through the Pythagorean theorem:
[tex]h = \sqrt{14^2-\left( \frac{14}{2} \right)^2} = \sqrt{147} = \boxed{7 \sqrt{3}}.[/tex]
Therefore, the altitude of the equilateral triangle is [tex]h = 7 \sqrt{3}.[/tex]
a camel can drink 15 gallons of water in 10 minutes. at this rate, how much water can the camel drink in 5 minutes?
In 5 minutes, the camel can drink = 1.5 x 5 = 7.5 gallons of water.
So, the camel can drink 7.5 gallons of water in 5 minutes.
What is unitary method?The unitary method is a mathematical technique used to solve problems related to proportionality.
It involves finding the value of a single unit and using it to determine the value of a given quantity or multiple quantities.
The unitary method is useful in solving problems that involve direct proportion or inverse proportion.
To find out how much water the camel can drink in 5 minutes, we can use the unitary method.
We know that the camel can drink 15 gallons of water in 10 minutes.
So, in 1 minute, the camel can drink = 15/10 = 1.5 gallons of water.
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Solve. Complete the table for the consecuIf the sum of a number and eight is tripled, the result is four less than twice the number. Find the number.
tive integers.
We can condense and find n's solution: 3n + 24 = 2n - 4
Since n = -14, the unknowable number is also -14.
What is an algebraic expression?A mathematical expression called an algebraic expression includes variables, integers, and mathematical operations including addition, subtraction, multiplication, and division. Algebraic expressions can be straightforward, like "2x," or they can be more complicated, like
[tex]3x^2+4y-5[/tex].
Variables are used to represent unknown quantities and have a range of possible values. In problems requiring unknown values or to represent connections between quantities, algebraic expressions are widely used.
A mathematical expression that includes variables, constants, and operations involving algebra (addition, subtraction, etc.) is known as an algebraic expression. Terms comprise expressions.
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In the year 2000, the population of Mexico was about 100 million, and it was growing by 1.53% per year. At this growth rate, the function f(x) = 100(1.0153)x gives the population, in millions, x years after 2000. Using this model, in what year would the population reach 106 million? Round your answer to the nearest year.
Answer:
2004
Step-by-step explanation:
Find the area of the triangle. Round to 2 decimal places.
Answer:
20 ..............................
A 9th grade teacher at a local high school wants to know which subject the 9th grade students in the high school like best which group of people should make up a sample that will best answer her question a, other 9th grade teachers in her school
B, parents of 9th graders in her school
C, 9th graders in her school
D,9th graders in her homeroom
The group of people who should make up a sample that will best answer her question is the 9th graders in her school. The correct option is C.
What are subjects?Subjects are the different sets of information which is studied.
9th graders in her school will be perfect because the question is specifically asking about the opinions of 9th-grade students in the high school, so it makes sense to sample this group directly.
The other options may provide some insights, but they may not be as accurate or representative of the opinions of the 9th-grade students in the school.
Thus, the correct option is C, 9th graders in her school.
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i need some help to finish this question please
Which function represents the inverse of function f?
= 3x + 5
O A. T (2)
O B.
O c.
O D.
=-3x - 5
x+ //
– ž
g(x) =
p(x) =
8(x) = 3z +5
x
The inverse function of f(x) = 3x + 5 is given as follows:
C. p(x) = 1/3x - 5/3.
How to obtain the inverse function?The function in the context of this problem is defined as follows:
f(x) = 3x + 5.
To obtain the inverse function, first we must exchange the variables x and y, hence:
y = 3x + 5
x = 3y + 5.
Now we must isolate the variable y, hence:
3y = x - 5
y = (x - 5)/3.
p(x) = 1/3x - 5/3.
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If P(x,y) is the point on the unit circle defined by real number 8, then cscg =
OA.
OB.
y
B. 1
O C.
-|X
y
OD. V
X
The value of Cscθ is 1/y.
What is a trigonometric function?
The right-angled triangle's angle and the ratio of its two side lengths are related by the trigonometric functions, which are actual functions. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.
Here, we have
Given: if p(x,y) is the point on the unit circle defined by the real number theta.
We have to find the value of the csc theta.
P(x,y) is the point on the unit circle (the unit circle has a radius of 1 and center (0,0))
Now in a diagram, we can see that
OA= x
AP= y
radius OP =1
∠POA =θ
Now in ΔAOP
Cscθ = hypotenuse/opposite side
Cscθ = OP/AP
Cscθ = 1/y
Hence, the value of Cscθ is 1/y.
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2. Triangle QRS with vertices Q(6,-2), R(4, -7) and
S(2,-5) is drawn inside a rectangle as shown
below.
What is the area, in square units, of Triangle QRS?
As a result, the triangle QRS has a surface area of **10√(58) square units**.
Define triangle area.
The total area that is bounded by a triangle's three sides is referred to as the triangle's area. In essence, it is equal to half the height times the base, or A = 1/2× b × h Triangle area is measured in square units, such as m² cm², in², and so forth
Triangle QRS's area can be calculated using the triangle's area formula. The equation is:
Area equals 1/2*base*height
where base and height refer to the triangle's base and height, respectively.
By utilizing the distance formula to calculate the sides' lengths, we can determine the triangle QRS's base and height. The formula for distance is:
(d) = √((x2 - x1)² +√ (y2 - y1))²
where d is the separation between (x1, y1)'s points and (x2, y2).
This formula allows us to determine that:
- The QR is long √(29)
√(10) is the length of RS.
is the length of QS √(20)
The base can be the length of QS, and the height can be the length of QR. Therefore, there are:
Area = 1/2 × base× height
= 1/2 × √(20) * √(29)
= 1/2 × √(580)
= 10√(58)
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How can I solve this math problem within 5 minutes
The equation a² + b² = c² represents the Pythagorean theorem.
What is the Pythagorean theorem?This is a theorem that states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).
The Pythagorean theorem is used to find the length of one of the sides of a right-angled triangle when the lengths of the other two sides are known.
To solve the problem, you need to have at least two side lengths given. Then, you can use the equation to find the length of the third side. For example:
If you know the lengths of sides a and b and need to find the length of the hypotenuse (c):
Plug in the known values for a and b into the equation and solve for c.
Example: If a = 3 and b = 4, then 3² + 4² = c², which gives 9 + 16 = c², so c² = 25, and c = sqrt(25) = 5.
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Evelyn sells 4 bags of popcorn. Her teammate Sidney sells 5 bags of popcorn. How much money do they raise in all?
x f(x) f ′(x) g(x) g′(x)
2 5 1 2 1
4 −2 −6 5 4
5 1 2 4 5
6 5 1 2 −2
The functions f and g have continuous derivatives. The table gives values of f, f ′, g, and g′ at selected values of x.
Part A: Find h′(2) if h(x) = g(f(x)). (5 points)
Part B: Find m′(2) if m(x) = f(x2). (5 points)
Part C: Let k(x) = f(g(x)). Write an equation for the line tangent to the graph of k at x = 4. (10 points)
Part D: Let j of x is equal to g of x divided by f of x. Find j′(2). (10 points)
Answer:
A. h'(2) = 5
B. m'(2) = -24
C. y = 8x - 31
D. j'(2) = 3/25 = 0.12
Step-by-step explanation:
When differentiating composite functions, use the chain rule.
[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Chain Rule for Differentiation}\\\\$\left[f\left(g(x)\right)\right]'=f'\left(g(x)\right) \cdot g'(x)$\\\end{minipage}}[/tex]
Chain Rule: The derivative of a composite function is the product of the derivative of the outer function evaluated at the inner function and the derivative of the inner function.
Part AUsing the chain rule, if h(x) = g(f(x)) then h'(x) = g'(f(x)) ⋅ f'(x).
To find h'(2), substitute x = 2 into the differentiated equation:
[tex]\begin{aligned}h'(x)& = g'(f(x)) \cdot f'(x)\\\\\implies h'(2)& = g'(f(2)) \cdot f'(2)\\& = g'(5) \cdot 1\\& = 5 \cdot 1\\&=5\end{aligned}[/tex]
Therefore, h'(2) = 5.
Part BUsing the chain rule, if m(x) = f(x²) then m'(x) = f'(x²) ⋅ 2x.
To find m'(2), substitute x = 2 into the differentiated equation:
[tex]\begin{aligned}m'(x) &= f'(x^2) \cdot 2x\\\\\implies m'(2) &= f'(2^2) \cdot 2(2)\\&=f'(4) \cdot 4\\&=-6 \cdot 4\\&=-24\end{aligned}[/tex]
Therefore, m'(2) = -24.
Part CTo find the slope of the tangent line to the graph of k at x = 4, substitute x = 4 into the derivative of k(x).
If k(x) = f(g(x)) then k'(x) = f'(g(x)) ⋅ g'(x).
Therefore, the slope of the tangent line is:
[tex]\begin{aligned}k'(x) &= f'(g(x)) \cdot g'(x)\\\\\implies k'(4) &= f'(g(4)) \cdot g'(4)\\&= f'(5) \cdot 4\\&= 2 \cdot 4\\&= 8\end{aligned}[/tex]
Now calculate k(x) when x = 4:
[tex]\begin{aligned}k(x)&=f(g(x))\\\\\implies k(4) &= f(g(4))\\&=f(5)\\&=1\end{aligned}[/tex]
To write the equation of the tangent line, substitute the found slope m = 8 and point (4, 1) into the point-slope equation:
[tex]\begin{aligned}y-y_1&=m(x-x_1)\\y-1&=8(x-4)\\y-1&=8x-32\\y&=8x-31\end{aligned}[/tex]
Therefore, an equation for the line tangent to the graph of k at x = 4 is:
y = 8x - 31Part DTo find the derivative of j(x) use the quotient rule.
[tex]\textsf{If\;\;$j(x)=\dfrac{g(x)}{f(x)}$\;\;then:}\\\\\\j'(x)=\dfrac{f(x)g'(x)-g(x)f'(x)}{(f(x))^2}[/tex]
To calculate j'(2), substitute x = 2 into the equation:
[tex]\begin{aligned} \implies j'(2)&=\dfrac{f(2)g'(2)-g(2)f'(2)}{(f(2))^2}\\\\&=\dfrac{5 \cdot 1-2 \cdot 1}{(5)^2}\\\\&=\dfrac{5-2}{25}\\\\&=\dfrac{3}{25}\\\\&=0.12\end{aligned}[/tex]
Therefore, j'(2) = 3/25 = 0.12.
I need help with this problem it's is
8x+5+3x+8=90
Answer:
x = 7
Step-by-step explanation:
8x + 5 + 3x + 8 = 90
11x + 5 + 8 = 90
11x + 13 = 90
11x = 77
x = 7
Let's Check
8(7) + 5 + 3(7) + 8 = 90
56 + 5 + 21 + 8 = 90
61 + 21 + 8 = 90
82 + 8 = 90
90 = 90
So, x = 7 is the correct answer!
Answer:
7
Step-by-step explanation:
First, collect common factors. This means put the x's together and the regular numbers together.
8x+3x=11x
5+8=13
11x+13=90
Subtract 13 from both sides
11x+13=90
-13 -13
11x=77
Divide 77 by 11
x=7
Hope this helps! :)
Question 6(Multiple Choice Worth 5 points) (Statistical Measurements LC) Which of the following is a statistical question that can result in numerical data? What is the name of your favorite pizza store? How many hours this week did you spend on homework? O How many times did you go swimming this year? How many pink erasers do the students in your class have?
The statistical question that can result in numerical data is "How many hours this week did you spend on homework?"
Identifying the statistical question that can result in numerical data?The statistical question that can result in numerical data is "How many hours this week did you spend on homework?"
This is because the question is asking for a numerical response that can be measured and counted. The other options are not statistical questions that can result in numerical data.
"What is the name of your favorite pizza store?" is a question that asks for a categorical response, "How many times did you go swimming this year?" is a question that asks for a countable response, And "How many pink erasers do the students in your class have?" is a question that asks for a discrete numerical response.Read more about statistical question at
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50 Points! Multiple choice algebra question. Transform both sides of each equation to determine which is a polynomial identity. Photo attached. Thank you!
The only equation that is a polynomial identity is (A), (c+d)³ = c³ - d³ + 3cd(c + d).
How to express the valueIt should be noted that to determine which equation is a polynomial identity, we need to simplify both sides of each equation and see if they are equal for all values of c and d.
(A) (c+d)³ = c³ + 3c²d + 3cd² + d³
= c³ - d³ + 3cd(c + d)
The left-hand side can be expanded using the binomial formula. The right-hand side is a polynomial of degree 3, so we can see that equation (A) is a polynomial identity.
(B) (c+d) = c + d³ + 3cd(c + d)
= d³ + c³ + 3cd(c + d) + c + d - c³
= d³ + c³ + 3cd(c + d) + c + d
The right-hand side can be simplified, but it is not equal to the left-hand side for all values of c and d. Therefore, equation (B) is not a polynomial identity.
(C) (c+d)³ = c³ + 3c²d + 3cd² + d³
= c³ + d³ + 3cd(c + d) + cd(c - d)
The right-hand side is not equal to the left-hand side for all values of c and d, so equation (C) is not a polynomial identity.
(D) (c+d)³ = c³ + 3c²d + 3cd² + d³
= c³ - d³ + 3cd(c - d) + c³ + d³
= 2c³ + 3cd(c - d)
The right-hand side is not equal to the left-hand side for all values of c and d, so equation (D) is not a polynomial identity.
Therefore, the only equation that is a polynomial identity is (A), (c+d)³ = c³ - d³ + 3cd(c + d).
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{[2+(11+9)]-2)+12 if you get this you get a five star rated
Answer: 32
Step-by-step explanation:
We will use the Order of Operations. First, we will do parentheses (), then brackets [], then lastly the braces {}, then lastly add 12.
Given:
{[2+(11+9)]-2)+12
Add 11 to 9:
{[2+20]-2)+12
Add 2 to 20:
{22-2)+12
Subtract 2 from 20:
20 + 12
Add 20 and 12:
32