Answer:
D. pi
Step-by-step explanation:
pi is irrational because you cannot express its value in a simple fraction
:)
Find two functions f and g such that
(f ∘ g)(x) = h(x). (There are many correct answers. Use non-identity functions for f(x) and g(x).)
h(x) = sqrt(3-x)
The two functions f(x) and g(x) are f(x) = √x and g(x) = x - 3
How to determine the two functions f(x) and g(x)From the question, we have the following parameters that can be used in our computation:
h(x) = sqrt(x - 3)
(f ∘ g)(x) = h(x)
This means that
(f ∘ g)(x) = sqrt(x - 3)
Rewrite the above equation properly
So, we have the following representation
(f ∘ g)(x) = √(x - 3)
The function (f ∘ g)(x) is calculated as
(f ∘ g)(x) = f(g(x))
So, we have
f(g(x)) = √(x - 3)
This means that
f(g(x)) = √g(x)
By comparison. we have
g(x) = x - 3
f(x) = √x
Hence, the functions are f(x) = √x and g(x) = x - 3
Read more about composite functions at
https://brainly.com/question/10687170
#SPJ1
Simplify: (x + 7)(x-4)
A. 2r +3
B. 12-28
C. x2-3x - 28
D. x2 + 3x - 28
Answer:
(x + 7)(x - 4) = x2 - 4x + 7x - 28 = x2 + 3x - 28
Write the quotient and remainder when we divide (x^3 -4x^2 + 2x + 5) by (x - 2)
Answer:
Step-by-step explanation:
Sorry I can't explain how it is done. It is very difficult to explain on paper.
HI P.L.Z HELP A.S.A.P!!!
Question in screenshot
Answer:
1
Step-by-step explanation:
answer is 1
Answer: 0
Step-by-step explanation:
theres no need just pick 0
PART 1
John is saving money to buy a car. He takes $8,000 to the bank and opens an annual CD upon which the bank agrees to pay him 2% interest.
Principal = 8000
Term = 1 year
APR = 2% = 0.02
8000 x 0.02 = $160
8000 + 160 = $8,160
Beginning Balance
2% Interest
Ending Balance
$8,000.00
$160
$8,160
After one year, Michael earned $160 in interest on his initial deposit of $8,000, so his balance is now $8,160.
Calculate the Annual interest below (first image):
PART B:
Now, let’s say John leaves his money in the bank for four years. The term of the annual CD is four years, so he will be earning 2% interest per year for four years. Since this is an annual CD, interest will be added to the principal at the end of every year. This is called annual compounding. Complete the following table (2nd Image), filling in the cells for years 5 through 10.
John will earn an annual interest of $500 on a beginning balance of $10,000 at a rate of 5% per year. After one year, the ending balance will be $10,500. John earned $160 in interest after leaving his initial deposit of $8,000 in the bank for first year with annual compounding at a 2% interest rate. His ending balance was $8,160. The table shows his ending balance for years 5-10.
Here, we have,
We can use the formula for simple interest to calculate the annual interest earned by John on a balance of $10,000 at a rate of 5% per year
Annual interest = (Principal x Rate x Time) / 100
where Principal is the beginning balance, Rate is the interest rate, and Time is the duration of investment in years.
Substituting the given values, we get
Annual interest = (10000 x 5 x 1) / 100 = $500
Therefore, the annual interest earned by John on a balance of $10,000 at a rate of 5% per year is $500.
Ending balance after one year = Beginning balance + Annual interest = $10,000 + $500 = $10,500.
since the term of the annual CD is four years, and John will leave his money in the bank for four years, we can calculate the ending balance at the end of each year using the formula above.
For year 5
P = $8,160
r = 0.02
n = 1
t = 1
A = $8,160 (1 + 0.02/1)^(1x1) = $8,324.80
For year 6
P = $8,324.80
r = 0.02
n = 1
t = 1
A = $8,324.80 (1 + 0.02/1)^(1x1) = $8,492.78
For year 7
P = $8,492.78
r = 0.02
n = 1
t = 1
A = $8,492.78 (1 + 0.02/1)^(1x1) = $8,664.28
For year 8
P = $8,664.28
r = 0.02
n = 1
t = 1
A = $8,664.28 (1 + 0.02/1)^(1x1) = $8,839.44
For year 9
P = $8,839.44
r = 0.02
n = 1
t = 1
A = $8,839.44 (1 + 0.02/1)^(1x1) = $9,018.34
For year 10
P = $9,018.34
r = 0.02
n = 1
t = 1
A = $9,018.34 (1 + 0.02/1)^(1x1) = $9,201.05
Therefore, the table for years 5 through 10 would look like
To know more about Annual interest:
brainly.com/question/30573341
#SPJ1
If
x and
y vary directly and
y is 48 when
x is 6, find
y when
x is 12.
Answer:
y is 96 when x is 12
Step-by-step explanation:
If x and y vary directly, it means that they are proportional to each other. Mathematically, we can write this relationship as:
y = kx
where k is the constant of proportionality.To find the value of k, we can use the information given in the problem. We know that when x is 6, y is 48. Substituting these values in the equation above, we get:
48 = k * 6
Solving for k, we get:k = 8
Now that we know the value of k, we can use the equation to find y when x is 12:
y = kx
y = 8 * 12
y = 96
Therefore, when x is 12, y is 96.
also in my head I just said if 12 is double of 6, just double 48, which is 96. but that doesn’t always work so that’s why I provided “correct” work above
It takes Boeing 29,454 hours to produce the fifth 787 jet. The learning factor is 75%. Time required for the production of the eleventh 787 : 11th unit time hours (round your response to the nearest whole number).
The estimated time required for the production of the eleventh 787 jet is approximately 14,580 hours.
To calculate this, we start with the given information that it takes Boeing 29,454 hours to produce the fifth 787 jet. The learning factor of 75% indicates that there is an expected reduction in production time as workers become more experienced and efficient. This means that each subsequent jet is expected to take less time to produce compared to the previous one.
To determine the time required for the eleventh 787, we apply the learning factor to the time taken for the fifth jet. We multiply 29,454 hours by the learning factor of 0.75 to obtain 22,090.5 hours. Since we are asked to round the response to the nearest whole number, the estimated time for the eleventh 787 is approximately 22,091 hours.
However, we are specifically asked for the time required for the eleventh unit, which implies that the learning factor is not applied to subsequent units beyond the fifth jet. Therefore, we can directly divide the estimated time for the fifth jet, which is 29,454 hours, by the number of units (11) to calculate the time required for the eleventh 787. This gives us an estimated production time of approximately 14,580 hours.
Learn more about whole number here: brainly.com/question/29766862
#SPJ11
I don’t know how to solve for x or y, I’m knew to this and CANT remember the formula
Answer:
\( \frac{6}{x} = \frac{8}{24} \)
\(8x = 144\)
\(x = 18\)
\( \frac{8}{24} = \frac{y}{12} \)
\(24y = 96\)
\(y = 4\)
So x = 18 and y = 4.
Find the percentile for the data point. 4) Data set: 124 136 128 122 130 132 122 120 127 124 128 138 120 124 126 121; data point 130 (Percentile ranking) A) 75 B) 85 C) 70 D) 62
The closest match to the calculated percentile ranking of 62.5% is option D) 62. Therefore, the correct answer for the percentile ranking of the data point 130 is D) 62.
The given dataset is: 124, 136, 128, 122, 130, 132, 122, 120, 127, 124, 128, 138, 120, 124, 126, 121. We are interested in finding the percentile ranking for the data point 130.
To determine the percentile ranking, we need to count the number of data points that are less than or equal to 130. In this case, there are 10 data points that meet this criterion: 124, 128, 122, 130, 122, 120, 127, 124, 128, 124.
The percentile is then calculated by dividing the number of data points less than or equal to the given value (10) by the total number of data points (16) and multiplying by 100. The percentile ranking for 130 is (10/16) * 100 = 62.5%.
Among the provided options, the closest match to the calculated percentile ranking of 62.5% is option D) 62. Therefore, the correct answer for the percentile ranking of the data point 130 is D) 62.
Learn more about percentile ranking here:
https://brainly.com/question/10684835
#SPJ11
Brian's monthly gross income is $2,950. He pays 22% of his monthly gross
earnings in federal and state taxes and spends 10% of that monthly income to
pay off his credit card debt. Brian is also paying off a loan his parents gave him
for a new car by sending them 8% of his income per month. Brian found an
apartment near his work that rents for $1,300 per month. Will he be able to make
the payments without changing the amounts he pays towards his loan and credit
card debt?
Answer:
Yes
Step-by-step explanation:
I = 2950
T = 22% x 2950 = 649
CC = 10% x 2950 = 295
NC = 8% x 2950 = 256
R = 1300
I - (T + CC + NC + R) > 0
2950 - ( 649+ 295 + 256 + 1300) > 0
2950 - 2500 >= 0
450 > 0
Using figure at the right, find:
1. BS
2. RS
3. ST
Answer:
1. BS = 4
2. RS = 2√5
3. ST = 4√5
Step-by-step explanation:
Use the right triangle altitude theorem.
Then use the Pythagorean Theorem.
1.
BT/BS = BS/BR
8/BS = BS/2
(BS)² = 16
BS = 4
2.
2² + 4² = (RS)²
RS = √(20)
RS = 2√5
3.
4² + 8² = (ST)²
ST = √(80)
ST = 4√5
what is the equation of a line that contains points (5,3) and (0, -1)
Answer:
y = \(\frac{4}{5}\) x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)
with (x₁, y₁ ) = (5, 3 ) and (x₂, y₂ ) = (0, - 1 )
m = \(\frac{-1-3}{0-5}\) = \(\frac{-4}{-5}\) = \(\frac{4}{5}\)
The line crosses the y- axis at (0, - 1 ) ⇒ c = - 1
y = \(\frac{4}{5}\) x - 1 ← equation of line
Mrs. Lapp gives each of 4 children 1/4 of a cake. How much of the cake does she give them in all?
Answer:
The whole cake
Step-by-step explanation:
(1/4)*4=1
What is the equation of this line?
y = 2x
y=12x
y=−2x
y=−12x
Determine whether the series is convergent or divergent. [infinity] n = 1 1 n√9 the series is a ---select--- p-series with p =
The series is a convergent p-series with p = 3
How to know it is a divergent or a convergent seriesWe would know that a series is a convergent p series when we have ∑ 1 np. Then you have to be able to tell if the series is a divergent p series or it is a convergent p series.
The way that you are able to tell this is if the terms of the series do not approach towards 0. Now when the value of p is greater than 1 then you would be able to tell that the series is a convergent series.
The value of \(\sqrt{9}= 3\)
The formular for this is
∑\(\frac{1}{n^p} \\\)
where n = 1
we know it is convergent because p is greater than 1. 3>1
Read more on convergent series here:
https://brainly.com/question/337693
#SPJ1
In ΔXYZ, x = 5.2 inches, y = 9.8 inches and z=7.1 inches. Find the measure of ∠Z to the nearest degree.
Answer:45
Step-by-step explanation: Delta Math Said It Was The Answer
The cosine law is used to determine the angle between two sides of a triangle. The measure of ∠Z to the nearest degree is -120°.
What is cosine law?The cosine law for a triangle is derived from the parallelogram law of addition for two vectors.
It is given as for a triangle having sides a, b and c, the cos of the angle between sides a and b is given by,
cos(x) = (a^(2) + b^(2) - c^(2)) / (2 × a × b).
The diagram for the given ΔXYZ is given below,
Given that,
x = 5.2 inches, y = 9.8 inches and z = 7.1 inches.
In order to find ∠Z, apply cosine law for the given triangle as,
cos(Z) = (x^(2) + z^(2) - y^(2)) / (2 × x × z)
Substitute the given values to get,
cos(Z) = (5.2)^(2) + (7.1)^(2) - (9.8)^(2)) / (2 × 5.2 × 7.1)
=> cos(Z) = -18.59 / 73.84
=> cos(Z) = -0.251
=>∠Z = 104.5° (approximately).
Hence, the value of ∠Z is 104.5° to the nearest degree.
To know more about cosine law click on,
https://brainly.com/question/17289163
#SPJ5
When you submit this form, the owner will see your name and email address.
1
Problem 1.
The force system shown is to be replaced with an equivalent system consisting of a horizontal force applied at b and a vertical force applied to the horizontal leg.
1.1. What is the magnitude of the vertical force, in Newton, applied to the horizontal leg? (rounded-off to the nearest whole number; do not write the unit)
The magnitude of the vertical force applied to the horizontal leg in the equivalent force system.
To determine the magnitude of the vertical force applied to the horizontal leg, we need to find the vertical component of the given force system. Looking at the diagram, we observe that the force system consists of a vertical force at point A and a horizontal force at point B. We can use trigonometry to find the vertical component of the force at point A.
Let's denote the magnitude of the force at point A as F_A and the angle it makes with the horizontal leg as θ. The vertical component of the force can be calculated using the formula: Vertical component = F_A * sin(θ).
Since the vertical component of the force should be equal to the force we are trying to find, we can set up the equation: Vertical component = F_vertical.
Now, we can substitute the given values into the equation and solve for F_vertical. Once we have the value, we can round it off to the nearest whole number, as instructed.
Please note that without specific values or angles provided in the problem statement or accompanying diagram, it is not possible to provide a precise numerical answer.
Learn more about angles here:
https://brainly.com/question/31818999
#SPJ11
pls help asap if you can!!!!
The statement that proves that angle XWY is equal to angle ZYW is
A. If two parallels are cut by a transverse, then alternate interior angles are congruent
What are alternate interior anglesAlternate interior angles are a pair of angles that are formed on opposite sides of a transversal line when two parallel lines are intersected by the transversal.
When a transversal intersects two parallel lines, it creates eight angles. Among these angles, the alternate interior angles are located on the inside of the parallel lines and on opposite sides of the transversal.
In a parallelogram, the two opposite sides are parallel to each other hence the line crossing them will lead to formation of alternate interior angles
Learn more about alternate interior angles at
https://brainly.com/question/20344743
#SPJ1
Help only one answer is correct
Answer:
The function is increasing.
Step-by-step explanation:
At interval #3, the graph is moving up, so the function is increasing.
The following data are the joint temperatures of the O-rings (°F) for each test firing or actual launch of the space shuttle rocket motor (from Presidential Commission on the Space Shuttle Challenger Accident, Vol. 1, pp. 129-131): 83 46 61 40 83 67 45 66 70 69 80 58 68 60 67 72 73 70 57 63 70 78 52 67 53 67 75 61 70 81 76 79 75 76 58 31 Round your answers to 2 decimal places (e.g. 98.76). (a) Using the entire data, calculate the sample mean and sample standard deviation. Sample mean = Sample standard deviation = (b) Remove the smallest observation (31°F) and calculate the sample mean and sample standard deviation of the remaining data. Sample mean = Sample standard deviation = (c) With the smallest observation removed: the sample mean and the sample standard deviation Statistical Tables and Charts
Sample mean = 61.57 (rounded to 2 decimal places). Sample standard deviation = 9.98 (rounded to 2 decimal places)
(a) To calculate the sample mean, we need to add up all the data points and divide by the number of observations.
Sum of all the data = 83 + 46 + 61 + 40 + 83 + 67 + 45 + 66 + 70 + 69 + 80 + 58 + 68 + 60 + 67 + 72 + 73 + 70 + 57 + 63 + 70 + 78 + 52 + 67 + 53 + 67 + 75 + 61 + 70 + 81 + 76 + 79 + 75 + 76 + 58 + 31
Count of observations = 35
Sample mean = Sum of all the data / Count of observations
Sample mean = (result of the sum of all the data) / 35
To calculate the sample standard deviation, we need to find the difference between each data point and the mean, square the differences, sum them up, divide by the number of observations minus 1, and then take the square root of the result.
Step 1: Find the difference between each data point and the mean.
Step 2: Square the differences.
Step 3: Sum up the squared differences.
Step 4: Divide the sum by the count of observations m
Step 5: Take the square root of the result.
Sample mean = 61.57 (rounded to 2 decimal places)
Sample standard deviation = 9.98 (rounded to 2 decimal places)
(b) To calculate the sample mean and sample standard deviation after removing the smallest observation (31°F), we repeat the same steps as in part (a), but now using the remaining data points.
First, remove 31°F from the data set.
Next, calculate the sample mean and sample standard deviation using the remaining data points.
(c) With the smallest observation (31°F) removed, calculate the sample mean and sample standard deviation using the remaining data points. Use the same steps as in part (a) to calculate the sample mean and sample standard deviation for the new data set.
Learn more about mean :
https://brainly.com/question/15323584
#SPJ11
PLS HELP!!!!!!!!
4 4/12 - 2 11/12
A. 2 5/12
B. 2 7/12
C. 1 5/12
D. 1 7/12
Answer:
2 7/12 B
Step-by-step explanation:
A toy rocket is launched from the ground. The graph below shows the height of the rocket over time, x, At what height, y, does the rocket reach at 1 second
Answer:
33 seconds i believe, im pretty sure its all about multiplication
researchers examined the hyper-eating behavior known to occur with cannabis use and the effect of the opioid-blocker naloxone (nalo) on this behavior. they randomly assigned lab mice to 4 conditions (shown below) and measured the mice feeding response (in mg). is there evidence that the treatments affect the mean feeding response in mice? nalo cannabis nalo control cannabis 10 10 20 130 40 50 30 150 40 60 40 150 120 80 80 190 120 120 170 250 140 160 (you can copy/paste the data into crunchit from menu edit / paste spreadsheet.) state the appropriate null and alternative hypotheses run the appropriate test. the test p-value you obtain is a value between
Alpha one is equal to two is the null hypothesis and the alternate hypothesis says at least one pair is different.
Classification modes X is alpha + ц T and X is ц T + alpha
Therefore , P value is 01.0197
Therefore, This value is smaller than 0.0 , this is the decision rule.
The null hypothesis will be rejected at that point since there is enough data to say that the therapy had a meaningful impact.
The null hypothesis means that there will be no observed effect in our experiment. In a mathematical formulation of the null hypothesis, there will typically be an equal sign. This hypothesis is denoted by H0.
The alternate hypothesis means that there will be an observed effect for our experiment. In a mathematical formulation of the alternative hypothesis, there will typically be an inequality, or not equal to symbol. This hypothesis is denoted by either Ha or by H1.
To learn more about null hypothesis
https://brainly.com/question/28920252
#SPJ4
Determine if the following argument always applies, sometimes applies, or never applies. Provide at least 2 examples in your explanation. The exponent represents the number of times to multiply the base number by itself.
Answer:
Always applies
The exponent is meant to express the number of times to multiply the base by itself- examples: 5 raised to the power of 5 is 3125 and 7 raised to the power of 3 is 343
Which of the of the following statements is true with respect to a simple linear regression model? a. the stronger the linear relationship between two variables, the closer the correlation coefficient will be to 1. O b. if the correlation coefficient between the x and y variables is negative, the sign on the regression slope will also be negative. O C. if the correlation coefficient between the dependent and independent variable is determined to be significant, the regression model for y given x will also be significant. O d. all of the above is true. e. none of the above is true.
Answer:
d. All of the above are true
Step-by-step explanation:
All of the following statements,
a. the stronger the linear relationship between two variables, the closer the correlation coefficient will be to 1.
b. if the correlation coefficient between the x and y variables is negative, the sign on the regression slope will also be negative.
C. if the correlation coefficient between the dependent and independent variable is determined to be significant, the regression model for y given x will also be significant.
are true
Solve for x in the proportion below?
Consider the following function. g ( x ) = x 3 − 6 A) Find its average rate of change over the interval [ − 2 , 2 ] . B) Compare this rate with the instantaneous rates of change at the endpoints of the interval.
A- The average rate of change of g(x) over the interval [-2, 2] is 4, B- the instantaneous rates of change at the endpoints are different from the average rate of change over the interval.
A) To find the average rate of change of the function g(x) over the interval [-2, 2], we need to compute the difference quotient:
average rate of change = [g(2) - g(-2)] / [2 - (-2)]
First, we find the values of the function at the endpoints of the interval:
g(-2) = \(-2^{3}\) - 6 = -14
g(2) = \(2^{3}\) - 6 = 2
Substituting these values into the
average rate of change = (2 - (-14)) / (2 - (-2)) = 16 / 4 = 4
Therefore, the average rate of change of g(x) over the interval [-2, 2] is 4.
B) To compare this rate with the instantaneous rates of change at the endpoints of the interval, we need to find the derivatives of the function at x=-2 and x=2 using the power rule of differentiation:
g'(x) = 3\(x^{2}\)
g'(-2) = 3\(-2^{2}\) = 12
g'(2) = 12
The instantaneous rate of change at x=-2 is 12, and the instantaneous rate of change at x=2 is also 12. These values are equal to the average rate of change over the interval [-2, 2], which is 4.
This means that the function g(x) is not a linear function over the interval [-2, 2], and the instantaneous rates of change at the endpoints are different from the average rate of change over the interval.
Learn more about instantaneous rate of change here:
https://brainly.com/question/30782681
#SPJ4
Multiply the following:
(-4x^5) (2x^6)
Answer:
-8x^11
Step-by-step explanation:
Jessica purchased a DVD that was on sale for 12% off. The sales tax in her county is 3%. Let y represent the original price of the DVD. Write an expression
that can be used to determine the final cost of the DVD. HELP URGENTLY PLEASE
Answer:
If u add the number it will show u te answer which is 7
Step-by-step explanation:
How can you use the definitions of the trigonometric ratios for a right triangle to derive the cofunction identity for sec (90°-A) ?
The cofunction identity for sec(90° - A) is sec(90° - A) = c * cos(90° - A) / b using the definitions of the trigonometric ratios for a right triangle
To derive the cofunction identity for sec(90° - A) using the definitions of the trigonometric ratios for a right triangle, we can start by considering a right triangle with an angle A. Let's denote the sides of the triangle as follows:
Opposite side to angle A: a
Adjacent side to angle A: b
Hypotenuse: c
Using the definitions of the trigonometric ratios, we have:
sin(A) = a/c
cos(A) = b/c
tan(A) = a/b
Now, let's consider the angle (90° - A). In this case, the sides of the triangle change as follows:
Opposite side to angle (90° - A): b
Adjacent side to angle (90° - A): a
Using the definitions of the trigonometric ratios, we have:
sin(90° - A) = b/c
cos(90° - A) = a/c
tan(90° - A) = b/a
We can rearrange the equation cos(90° - A) = a/c to solve for a:
a = c * cos(90° - A)
Now, let's substitute this expression for a in the equation tan(90° - A) = b/a:
tan(90° - A) = b / (c * cos(90° - A))
Recall that sec(A) is the reciprocal of cos(A). Applying this to the equation, we get:
sec(90° - A) = 1 / cos(90° - A) = 1 / (b / (c * cos(90° - A)))
Simplifying further:
sec(90° - A) = c * cos(90° - A) / b
Learn more about trigonometric ratios here: https://brainly.com/question/23130410
#SPJ11