Step 1: Figure out when Savannah will double her account value:
We need to solve [tex]140000 = 70000\left(1+\frac{0.01375}{4}\right)^{4t}[/tex].
Divide by 70000:
[tex]2 = \left(1+\frac{0.01375}{4}\right)^{4t}[/tex]
Take the natural log of both sides and bring the exponent down:
[tex]\ln(2) = 4t\cdot\ln\left(1+\frac{0.01375}{4}\right)[/tex]
Divide by that mess multiplied by t:
[tex]\dfrac{\ln(2)}{4\ln\left(1+\frac{0.01375}{4}\right)} = t[/tex]
Throw that into a calculator and you get about 50.497297884.
Depending on how picky your teacher is, we'd need to round this to the next time the interest is compounded, since it's only compounded each quarter, so t = 50.5. (The fact is that Savannah's account will never exactly double in value.)
Step 2:
Now, we need to evaluate Carter's continuously compounded investment for 50.5 years:
[tex]B = 70000e^{0.01125\cdot(50.5)}\approx123546.825994[/tex]
B ≈ 123547 to the nearest dollar.
As a comparison, here's the other calculation with the more precise t value.
[tex]B = 70000e^{0.01125\cdot(50.497297884)}\approx123543.070375[/tex]
B ≈ 123543 to the nearest dollar.
Again, I would say the 50.5 calculation is actually more correct, since Savannah's account only compounds the interest each quarter, but you'll have to decide what your teacher would say.
Answer:
$123,543 (nearest dollar)
Step-by-step explanation:
Find the length of time Savannah has to invest her money for it to double.
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
Given:
A = $140,000P = $70,000r = 1.375% = 0.01375n = 4 (quarterly)Substitute the given values into the formula and solve for t:
[tex]\implies 140000=70000\left(1+\dfrac{0.01375}{4}\right)^{4t}[/tex]
[tex]\implies 140000=70000\left(1.0034375\right)^{4t}[/tex]
[tex]\implies2=\left(1.0034375\right)^{4t}[/tex]
[tex]\implies \ln2=\ln\left(1.0034375\right)^{4t}[/tex]
[tex]\implies \ln2=4t\ln\left(1.0034375\right)[/tex]
[tex]\implies t=\dfrac{\ln 2}{4 \ln\left(1.0034375\right)}[/tex]
[tex]\implies t=50.49729788[/tex]
Therefore, it would take approximately 50.5 years for Savannah's principal investment to double.
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\ \phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
Given:
P = $70,000r = 1.125% = 0.01125t = 50.49729788...Substitute the given values into the formula along with the found value of t and solve for A:
[tex]\implies A=70000e^{0.01125 \times 50.4972...}[/tex]
[tex]\implies A=123543.0704...[/tex]
Therefore, the amount of money that Carter would have in his account when Savannah's money has doubled in value is $123,543 (nearest dollar).
Solving
The product of 5 and the difference
between a number and 7 is 75. What is
the number?
The number whose product of 5 and the difference between a number and 7 is 75 is, 22.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
The given statement is The product of 5 and the difference
between a number and 7 is 75.
Let, The unknown number be 'n'.
∴ 5(n - 7) = 75.
Now, 5 will move from the numerator to the denominator.
n - 7 = 75/5.
n - 7 = 15.
Now, we'll move the constant to the other side such that the variable and the constants are on different sides for our further calculation.
n = 15 + 7.
n = 22.
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Chloe is older than her brother, Michael, and she never lets him forget it! When Michael is y
years old, Chloe is y + 2.5 years old. Right now Michael is 9.5 years old.
How old is Chloe?
Write your answer as a whole number or decimal.
Answer: Chloe is 12 years old
y + 2.5
y = 9.5
9.5 + 2.5 = 12
The temperature in Austin is 33.5 ◦F and rising at a rate of 2.5 ◦F per hour. The temperature in San Antonio is 37.5 ◦F and rising at a rate of 1.5 ◦F per hour. Write an inequality that shows how long the temperature in Austin will remain colder than that in San Antonio.
The inequality that shows how long the temperature in Austin will remain colder than that in San Antonio is 33.5 + 2.5t < 37.5 + 1.5t and the time is less than 4 hours
How to determine the inequality and the intervals ?From the question, we have the following parameters that can be used in our computation:
Austin
Initial temperature = 33.5 degrees Fahrenheit
Rate of increment = 2.5 degrees Fahrenheit
San Antonio
Initial temperature = 37.5 degrees Fahrenheit
Rate of increment = 1.5 degrees Fahrenheit
The above parameters mean that
Current temperature = Initial temperature + Rate of increment x Number of hours
Austin: A(t) = 33.5 + 2.5t
an Antonio: B(t) = 37.5 + 1.5t
When Austin is colder than San Antonio, we have
Substitute the known values in the above equation, so, we have the following representation
33.5 + 2.5t < 37.5 + 1.5t
Divide both sides by 1
t < 4
Hence, the interval is less than 4 hours
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4. Draw a coordinate grid from -10 to 10 on both axes. Using table of the same grid.
(i) y=x-4
(ii) y=2 x-4
(iii) y=3 x-4
The linear functions for this problem are graphed on the image given at the end of the answer.
How to graph the linear functions?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which the parameters are given as follows:
m is the slope, representing by how much y changes when x is increased by one.y is the intercept, representing the value of y of the function when it's graph crosses the y-axis.Hence the functions in this problem are graphed as follows:
y = x - 4: when x = 0, y = -4, when x increases by one, y increases by one.y = 2x - 4: when x = 0, y = -4, when x increases by one, y increases by two.y = 3x - 4: when x = 0, y = -4, when x increases by one, y increases by three.More can be learned about linear functions at https://brainly.com/question/24808124
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help meeeeeeeeeee pleaseee
The pressure of 28 inches of mercury occurs about 6 miles from the eye of the hurricane. We get this from the given algebraic expression.
What is an expression?An expression is formed by variables, constants, and algebraic operations. Since the operation among them is an algebraic or arithmetic operation, it is said to be an algebraic expression.
Calculation:It is given that the algebraic expression that relates the barometric pressure and the eye of the hurricane as
f(x) = 0.48 ln(x+2) + 27
Here x is the distance in miles from the eye of the hurricane.
f(x) is the pressure of the mercury in a barometer in inches
So, the required distance from the eye of the hurricane when the pressure of 28 inches of mercury in the meter is
(Here f(x) = 28)
f(x) = 0.48 ln(x+2) + 27
⇒ 28 = 0.48 ln(x+2) + 27
⇒ 0.48 ln(x+2) = 28 - 27
⇒ ln (x+2) = 1/0.48
⇒ ln(x+2) = 2.0833
Applying exponential base "e" on both sides, we get
(x+2) = [tex]e^{2.0833}[/tex]
⇒ x + 2 = 8.0309
⇒ x = 8.0309 - 2 = 6.0309
When the result is rounded to the nearest whole number, we get x = 6 miles.
Thus, for the pressure of 28 inches of mercury, the eye of the hurricane is 6 miles far from the barometer.
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Match the statement with the property it illustrates.
1. ∠ B=∠aD
2. If FO=N N, then RS=1 E E
3. If m ∠A=m∠B and m∠A=m∠C, then m∠A=m ∠ C F
4. If MN=DP and OP=OP, then MN=OK C
5. m<1-m<1 B
6. If m ∠3=m<4, then m∠4=m∠ 3. A
A. Meflexive Proprivy of Tquality
B. Bymenetre Pruperty of Hlquality
Q. Transitive Properiy of Elqualiry
ix. Reflexives Property of Congruence
F. Symmetric Property of Congruence.
f. Transitive Property of Congruence
Name the property that the statement illustrates.
7. If m ∠ 1=m ∠2, then m∠ 1-m ∠ 3=m∠2-m ∠ 3.
8. If K L=P Q, then 2, K L=2 . PQ.
9. If m ∠ A=m ∠ C, then m∠ A+m ∠D=m ∠ C+m ∠D.
10. If x y=5, then xy/3=5/3.
11. If m∠ 2=90° and m∠3=m∠2+44°, then m∠ 3=90°+44°.
12. In the diagram at the right, M is the midpoint of EF. Complete the argument to show that E M=1/2 EF.
E M =M F Definition of ?
E M+M F =E F ? ? Postulate
E M+E M =E F ? Property of Equality
2 . E M =E F Distributive property
E M =1/2 E F ? Property of Equality
13. In the diagram, m∠1+m ∠ 2=98°, and m ∠ 1=42°. Complete the argument to show that m∠2=56°.
m ∠1+m ∠ 2 =98° Given
m ∠1 =42° Given
42°+m∠2 =98° -?
m∠2 =56° ?
Value of AB = 9 units by using property of equality according to given equation.
What is a line?
In pure mathematics, a line is associate infinitely long object with no dimension, depth, or curvature. Thus, lines ar one-dimensional objects, although they'll exist in 2, three, or higher dimension areas. The word line might also see a line section in existence, that has 2 points to denote its ends.
Main body:
Question 12
According to question,
AB +BC = 12
BC= 3
therefore,
AB + 3 = 12
AB = 9 -------( by using property of equality)
Hence value of AB = 9 units.
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A certain lottery requires players to select 6 different numbers, in any order, from 1 to 53 inclusive. How many different sets of 6 numbers can be chosen?
221643611 ways of 6 numbers can be chosen
What is Combination?An arrangement of objects where the order in which the objects are selected does not matter.
Given,
A certain lottery requires players to select 6 different numbers in any order, from 1 to 53 inclusive.
We need to find different sets of 6 numbers can be chosen
Total=53
Numbers=6
The first number can be any of the 53 numbers
The second number can be any of the 53 numbers
The third number can be any of the 53 numbers
The fourth number can be any of the 53 numbers
And so on
Hence, number of selections is:
53×53×53×53×53×53
53⁶
221643611 ways
Hence, 221643611 ways of 6 numbers can be chosen
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For the following data set, calculate the percentage of data points that fall within one standard deviation of the mean and compare the result to the expected percentage of a normal distribution.
{8, 12, 27, 32, 45, 57, 61, 73, 82, 94}
A minimum of 68% is the expected percentage in a normal distribution and 60% is lower than what is expected.
What is the standard deviation?
In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.
The given data is:
{8, 12, 27, 32, 45, 57, 61, 73, 82, 94}
Now find the mean of the given data would be
Mean = sum of all points/n
= 491/10
= 49.1
Standard deviation(s) = [tex]\sqrt{\frac{\sum(x - \bar x)^2}{n-1}}[/tex]
Standard deviation(s) = 29.31988
Considering one standard deviation from the mean, the lower and upper limits are given by the following
[49.1-29.31988, 49.1+29.31988}
=[19.78012, 78.41988]
We can see that only 6 {27,32,45,57,61,73} out of the 10 points, which is 60%, confine to the interval of one standard deviation from the mean.
Hence, a minimum of 68% is the expected percentage in a normal distribution and 60% is lower than what is expected.
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In 1931, President Herbert Hoover was paid a salary of $75,000. Government statistics show a consumer price index of 15.2 for 1931 and 195 for 2005. President Hoover's 1931 salary is equivalent to what amount in 2005?
According to the given consumer price index, President Hoover's 1931 salary is equivalent to what amount in 2005 is $962,250
Consumer price index:
In math, the concept of consumer price index (CPI) is significant in the analysis of inflation.
The general form of CPI of current years is computed as
=> (GDP of current period / GDP of base period) x 100.
Given,
In 1931, President Herbert Hoover was paid a salary of $75,000. Government statistics show a consumer price index of 15.2 for 1931 and 195 for 2005.
Here we need to find the President Hoover's 1931 salary is equivalent to what amount in 2005.
Here we have the values of
=> CPI = 15.2 in 1931,
=> salary 75000;
=> CPI = 195 in 2005,
Then the salary is calculated as,
=> 75000 x (195/15.2)
=> 75000 x 12.83
=> 962250
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I need help , Polygon ABCDE is reflected across the line x = -2. Graph and label the image A’B’C’D’E’. Is m/_ A = m/_ A’ Explain.
point A' is the contracted point of A. The coordinate of point A is (-4,4) and coordinate of point A' is (-2,4) as per the given question and available figure.
what is dilation?The extension or contraction of image or figure based on a scale factor is called dilation. In this way, an image is transformed from one position to another.
what is scale factor?Scale factor is defined as the ratio of original image and transformed image.
As stated in the question, the polygon ABCDE is contracted and moved to a shape A'B'C'D'E'. The coordinate of point A is (-4,4) and point A' is (-2,4) as shown in figure. Angle A is equal to angle A' that means the shape of polygon was not changed.
hence, A'B'C'D'E' is the reflected image of ABCDE
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Simplify and state the restrictions on the domain:
Answer:
Step-by-step explanation:
First factor the left expression to get
Then cancel out .[tex]\frac{(x+3)(x+2)}{(x+4)(x+2)}*\frac{x+4}{2x}\\ \\\frac{(x+3)}{2x}[/tex]
The x+2 cancel's as well as the x+4's.
for a standard normal distribution, find: p(z < 0.74) express the probability as a decimal rounded to 4 decimal places.
Expressing the probability as a decimal rounded to 4 decimal places the value of p ( z < 0.74 ) is 0.7704.
Given :
for a standard normal distribution, find: p(z < 0.74) express the probability as a decimal rounded to 4 decimal places.
Standard normal distribution :
The standard normal distribution, also called the z-distribution, is a special normal distribution where the mean is 0 and the standard deviation is 1.
Probability :
Probability is a branch of mathematics that deals with the occurrence of a random event.
From z - score table :
the test statistic follows the standard normal distribution N(0,1).
the probability p = 0.7704
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on 3 of 10
Which of the numbers below are whole numbers? Check all that apply.
A. 99.6
B. 4538
C. 0.716
1
☐D. 6
E. 207.69
F. 773
A surveyor is 980 feet from the base of the world's tallest fountain at Fountain Hills, Arizona. The angle of elevation to the top of the column of water is 29.7 degrees. His angle measuring device is at the same level as the base of the fountain. Find the height of the column of water to the nearest 10 feet.
To find the height of the column of water in the Fountain Hills fountain, we can use the tangent function and the information given in the problem. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side in a right triangle. In this case, we can use the angle of elevation to the top of the fountain, the distance from the surveyor to the base of the fountain, and the height of the column of water to form a right triangle.
We can then use the tangent function to find the height of the column of water as follows:
tan(29.7°) = opposite/adjacent
opposite = tan(29.7°) * adjacent
opposite = tan(29.7°) * 980 feet
opposite = 0.56 * 980 feet
opposite = 548.8 feet
Therefore, the height of the column of water in the Fountain Hills fountain is approximately 549 feet. To the nearest 10 feet, this is 550 feet.
find the x- and y- intercepts
Answer:
(8, 0) and (0, 4)
Step-by-step explanation:
x-intercepts occur when y = 0, so just find the row in the table when y is 0, and then put the coordinates from that row into a ordered pair:
(8, 0)
y-intercepts occur when x = 0, so just find the row in the table when x is 0, and then put the coordinates from that row into a ordered pair:
(0, 4)
A sequence of positive numbers is defined by
given that a1=2
find a2 and a3 leaving your answer in a surd form
The values of a2 and a3 that satisfy the sequence [tex]a_{n+1}[/tex] = [tex]\sqrt{a_{n} ^{2} + 3 }[/tex] are [tex]\sqrt{7}[/tex] and [tex]\sqrt{10}[/tex]
What is a sequence?
A sequence is an arrangement of any objects or a set of numbers in a particular order followed by some rule. If a1, a2, a3, a4 etc. denote the terms of a sequence, then 1,2,3,4 denotes the position of the term.
the rule of the sequence is [tex]a_{n+1}[/tex] = [tex]\sqrt{a_{n} ^{2} + 3 }[/tex] when n = 1
[tex]a_{2}[/tex] = [tex]\sqrt{a_{1} ^{2} + 3 }[/tex] but [tex]a_{1}[/tex] = 2
[tex]a_{2}[/tex] = [tex]\sqrt{(2) ^{2} + 3 }[/tex]
[tex]a_{2}[/tex] = [tex]\sqrt{7}[/tex]
when n = 2
[tex]a_{3}[/tex] = [tex]\sqrt{a_{2} ^{2} + 3 }[/tex]
[tex]a_{3}[/tex] = [tex]\sqrt{a_{2} ^{2} + 3 }[/tex] but [tex]a_{2}[/tex] = [tex]\sqrt{7}[/tex]
[tex]a_{3}[/tex] = [tex]\sqrt{(\sqrt{7}) ^{2} + 3 }[/tex]
[tex]a_{3}[/tex] = [tex]\sqrt{7 + 3}[/tex]
[tex]a_{3}[/tex] = [tex]\sqrt{10}[/tex]
In conclusion [tex]a_{2}[/tex] and [tex]a_{3}[/tex] are [tex]\sqrt{7}[/tex] and [tex]\sqrt{10}[/tex] respectively.
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Corey has $89 go to shopping T shirt cost $12.50 each corey wants to buy some T shirt and have at least $14 for lunch
Answer:
6 shirts you can buy and still have $14 dollars for lunch.
Step-by-step explanation:
So let's do 89-14=75. So since we just took out the cost of the lunch it should be a lot easier to solve now.
s=shirts
So 75=12.50s
75/12.50=6
So Corey can buy 6 shirts.
I hope this helps!!!
What is the sum of the matrices shown below?
3
6 0
9
5 -2
+
6
0
-8 4
=
Answer:
Option 2
Step-by-step explanation:
[tex]\begin{bmatrix} 3+6 & 9+0 \\ 5-8 & -2+4 \end{bmatrix}=\begin{bmatrix} 9 & 9 \\ -3 & 2 \end{bmatrix}[/tex]
Answer:
(b)
Step-by-step explanation:
You want the sum of the given matrices.
Matrix sumThe sum of two matrices is the matrix of the sums of corresponding terms.
Here, we observe that we can choose the correct answer by finding the bottom right term. The sum of bottom right terms is -2+4 = 2. The only answer choice with that value at bottom right is the second answer choice.
__
Additional comment
You need to know how to work the problem, but you don't actually need to work the whole problem in order to make the correct answer choice. (This is often the case with multiple choice questions, so it pays to look before you leap.)
Twenty five out of 40 student athletes received over 3.0 gpa or better this semester. What percent of student athletes received under a 3.0 gpa?
A. 37.5
B. 35.7
C. 50
D. 39.5
Answer: A. 37.5%
Step-by-step explanation:
Technically, you can't even solve this, because you don't know how many athletes got exactly a 3.0 GPA.
Ignoring this major oversight, let's just say that no one received a 3.0 GPA. In that case, there would be 40 - 25 = 15 athletes who received a sub-3.0 GPA.
Therefore, the percentage of student athletes who received a sub-3.0 GPA is 15/40 = 3/8 = 37.5%.
Class records at a particular college indicate that a student selected at random has probability 0.67 of passing French 101. For the student who passes French 101, the probability is 0.88 that he or she will pass French 102. What is the probability that a student selected at random will pass both French 101 and French 102?
The probability that a student passes both the tests is 0.5896.
What is conditional probability?The conditional probability deals with dependent events. In order to evaluate it, Bayes' theorem is applied which can be written as P(B|A) = P(A ∩ B)/P(A), where B|A denotes the event of occurring B when A has already happened and A ∩ B denotes the occurring of both events simultaneously.
The given problem can be solved as follows,
Suppose A be the event a student passes French 101 and B be the event that he passes French 102.
Then, as per the question the probabilities are given as,
P(A) = 0.67,
And, P(B|A) = 0.88.
Suppose, A ∩ B be the event a student passes both tests.
Apply Bayes' theorem to obtain,
P(B|A) = P(A ∩ B)/P(A)
Substitute the corresponding values in the above expression.
0.88 = P(A ∩ B)/0.67
=> P(A ∩ B) = 0.88 × 0.67
=> P(A ∩ B) = 0.5896
Hence, the probability that a student selected at random will pass both French 101 and French 102 is 0.5896.
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4. Using the statistics in the following report generated for Community Hospital, calculate (round to two decimal places) the percentage of occupancy for the month of December. Remember to calculate the Total for Patient Care Units (IPSD, Bed Count and Percent of Occupancy).
The percentage of occupancy for the month of December is 86.5%.
What is percentage?
Percentage is a fundamental concept in mathematics that describes a portion or proportion of a whole number. It is expressed as a fraction or ratio of two numbers and is typically represented with a percent symbol (%). This concept is frequently used in business, finance, and other fields to compare and analyze data. For example, a company might use a percentage to track the success of a marketing campaign or to compare the amount of sales between two different stores. Percentage can also be used to calculate discounts, taxes, and other types of fees.
Given: Community Hospital December, 20XX
PCU Inpatient Service Days Bed Count Percentage of Occupancy
⇒ Med/Surg 1876, 70 = (1,876 x 100)/ (70 x 31)
= 187,600/ 2,170 = 86.45 = 86.5%
⇒ ICU 300, 10 (300 x 100)/ (10 x 31)
= 30,000/ 310 = 96.77 = 96.8%
⇒ CCU 240, 8 (240 x 100)/ (8 x 31)
= 24,000/ 248 = 96.77 = 96.8%
⇒ Rehabilitation 300, 12 (300 x 100)/ (12 x 31)
= 30,000/372 = 80.6%
⇒ Burn 75, 5 (75 x 100)/ (5 x 31)
= 7,500/ 155 = 48.38 = 48.4%
⇒ Psychiatry 200, 15 (200 x 100)/(15 x 31)
= 20,000/465 = 43.0%
⇒ Pediatric 870, 30 (870 x 100)/ (30 x 31)
= 87,000/ 930 = 93.5%
⇒ Total for patient care 3861, 150 (3,861 x 100)/ (150 x 31)
= 386,100/ 4,650 = 83.0%
⇒ Nursery 280, 10 (280 x 100)/ (910 x 31)
= 28,000/ 310 = 90.3%
For example, Med/Surg has 1,876 inpatient service days and 70 beds in the month of December (31 days). The percentage of occupancy is therefore the inpatient service days multiplied by 100 and divided by the product of the number of beds (70) and the number of days (31) to get 86.5%
⇒ (1,876 x 100)/ (70 x 31)
= 187,600/ 2,170 = 86.45 = 86.5%
Hence, the percentage is 86.5%.
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in the multiplication example shown different letters represent different digits find the value of a and of b
You forgot the question
let f(x)=8x and g(x)=8^x+5 +1 which transformations are needed to transform the graph of f(x) to the graph of g(x)
Select each correct answer.
vertical translation 1 unit up
horizontal translation 1 unit left
vertical translation 5 units up
horizontal translation 5 units night.
horizontal translation 5 units left
vertical translation 1 unit down
Transformation involves changing the form of a function. The transformations are:
vertical translation 1 unit up .
horizontal translation 5 units left.
The functions are given as:
f(x) = 8x
g(x) = [tex]8^{x+5}[/tex] + 1
Start by translating the function 5 units left.
The rule of this translation is:
f'(x) = f(x+5)
So, we have:
f'(x) = 8(x+5)
Next, translate the function 1 unit up
The rule of this translation is:
f"(x) = f'(x) + 1
∴ f"(x) = 8(x+5) + 1
Rewrite as:
g(x) = 8(x+5) + 1
Hence, the transformations are: vertical translation 1 unit up and horizontal translation 5 units left
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Transformation involves changing the form of a function. The transformations are:
Vertical translation 1 unit up Horizontal translation 5 units leftWhat are transformation?A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.
The functions are given as:
f(x) = 8x
g(x) = + 1
Start by translating the function 5 units left.
The rule of this translation is:
f'(x) = f(x+5)
So, we have:
f'(x) = 8(x+5)
Next, translate the function 1 unit up
The rule of this translation is:
f"(x) = f'(x) + 1
∴ f"(x) = 8(x+5) + 1
Rewrite as:
g(x) = 8(x+5) + 1
Hence, the transformations are: vertical translation 1 unit up and horizontal translation 5 units left
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A rectangular box of sand measures 4 inches by 12 inches by 16 inches. When resting on its smallest face, the level of the sand is 4 inches from the top of the box. How many inches from the bottom of the box will the sand level reach when the box is placed on its largest face?
The level of the sand in the box when the box is placed at the largest face will be 3 inches.
What is volume?Volume is the scalar quantity of any object that specified occupied space in 3D.
Volume has units of cube example meter³,cm³, etc.
The volume of the cube = side³.
The volume of sand when placed on a small face (4 x 12) will be as follows,
Volume = 4 x 12 x (16 - 4) = 4 x 12 x 12
When the box was kept at the largest face (16 x 12) the volume was still the same.
Let's say it goes up to h.
h x 16 x 12 = 4 x 12 x 12
h = 12/4 = 3 inches
Hence "The level of the sand in the box when the box is placed at the largest face will be 3 inches".
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Suppose an investigator has data on the amount of shelf space x devoted to display of a particular product and sales revenue y for that product. The investigator may wish to fit a model for which the true regression line passes through (0, 0). The appropriate model is Y ¼ b1x + e. Assume that (x1, y1), . . ., (xn, yn) are observed pairs generated from this model, and derive the least squares estimator of b1. [Hint: Write the sum of squared deviations as a function of b1, a trial value, and use calculus to find the minimizing value of b1.]
Hence, the least square estimator is obtained when you substitute [tex]y_i[/tex] with [tex]Y_i[/tex] is
[tex]\beta _1=\frac{\sum_{i=1}^{n}x_iY_i}{\sum_{i=1}^{n}x_i^2}[/tex]
What is the line of regression?
A regression line indicates a linear relationship between the dependent variables on the y-axis and the independent variables on the x-axis.
Here given that,
Suppose an investigator has data on the amount of shelf space [tex]x[/tex] devoted to display of a particular product and sales revenue [tex]y[/tex] for that product.
The investigator may wish to fit a model for which the true regression line passes through [tex](0, 0)[/tex]. The appropriate model is [tex]Y=\beta x+E[/tex]
Assume that[tex](x_1, y_1), . . ., (x_n, y_n)[/tex] are observed pairs generated from this model, and derive the least squares estimator of [tex]b_1[/tex].
Here, our motive is to minimize the function
[tex]f(b_1)=[/tex][tex]\sum_{i=1}^{n}(y_i-b_1x_i)^2[/tex]
Now,
[tex]f`(b_1)=0\\\\f`(b_1)=2\sum{i=1}^{n}(y_i-b_1x_i).(-x_i)\\\\[/tex]
So, the least square estimate [tex]b_1[/tex] is
[tex]\sum_{i=1}^{n}x_iy_i=b_1\sum_{i=1}^{n}x_i^2[/tex]
Hence, the least square estimator is obtained when you substitute [tex]y_i[/tex] with [tex]Y_i[/tex] is
[tex]\beta _1=\frac{\sum_{i=1}^{n}x_iY_i}{\sum_{i=1}^{n}x_i^2}[/tex].
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An unbiased die is tossed. Find the probability that the number
obtained is
(c) Greater than 6
(a) An event number (b) Less than 4
Step-by-step explanation:
greater than 6=0 cause no number on a dice is greater than six
an even number=1/2
less than 4=1/2
Use long division to rewrite the following rational expression.
Answer:
—4—
_x+1_/4x+3
-(4x+4)
———–––
-1
#4x+3/x+1=4-1/x+1
A hand soap container proudly boasts 30% more for the same price as their regular
container. The larger bottle has 9.75 ounces of soap. What is the original amount of
soap before the 30% increase?
Answer:
6.825 ounces
Step-by-step explanation:
9.75 x 0.3 = 2.925
9.75 - 2.925 = 6.825
Write an equation of the line that passes through the given points.
(−7,0),(−7,5)
Answer:
x= -7
Step-by-step explanation:
the 2 x values are the same so it is an undefined slope so we set this equation x=-7
hopes this helps please mark brainliest
If f(x)=x+7 and g(x)=1/x-13}, what is the domain of (f g)(x) ?
{x l x ≠6}
{x l x ≠-6}
{x l x ≠ 13}
{x l x ≠ 13}
domain of (f.g)(x) is {x l x ≠ 13} i.e option (c) where f(x) = x+7 and g(x) = 1/(x-13)
What is domain of function?Domain of a function is defined as all those values of x that can be substituted in function for which function is defined.
Given: f(x) = x+7
g(x) = 1/(x-13)
First we need to find (f.g)(x) i.e multiplication of f(x) and g(x)
(f.g)(x) = (x+7) ×1/(x-13) = [tex]\frac{x+7}{x-13}[/tex]
Domain of function is values of x over which function is defined
For (f.g)(x) it is defined at all values of x except when x-13=0 as at this point denominator will be zero and function will become infinite that is not defined.
So, x - 13 ≠ 0
Adding 13 on both sides, we get
x ≠ 13
So domain of (f.g)(x) is x∈R - {13} i.e {x | x≠ 13}
Hence, option (c) is correct answer.
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