Answer:
(x - 3)² = 25---------------------------
Use the identity for the square of a sum:
(a + b)² = a² + 2ab + b²Comparing with the given we see that:
a = x, 2ab = - 6xThen find b:
2bx = - 6xb = - 3To complete the square we need to add b² = (-3)² = 9 to both sides:
x² - 6x + 9 - 16 = 9(x - 3)² - 16 = 9(x - 3)² = 25In a class of students, the following data table summarizes how many students passed a test and complete the homework due the day of the test. What is the probability that a student who did not complete the homework passed the test?
The probability that a student who did not complete the homework passed the test is 0.25.
tim wants his mean quiz score to be 90. his first 3 quiz scores were 86, 92, and 94. what score should he make on the 4th quiz in order to have a mean quiz score of exactly 90?
The score to be made on the 4th quiz in order to have a mean quiz score of exactly 90 is equal to 88.
Let us consider the score that Tim needs to get on his fourth quiz be x.
Score he needs to get in order to have a mean quiz score of 90,
Set up an equation using the formula for the mean ,
(mean score) = (sum of scores) / (number of scores)
If Tim wants his mean quiz score to be 90, then we have,
⇒ 90 = (86 + 92 + 94 + x) / 4
Multiplying both sides by 4, we get,
⇒360 = 86 + 92 + 94 + x
Simplifying this equation, we get,
⇒ x = 360 - 272
⇒ x = 88
Therefore, Tim needs to get a score of 88 on his fourth quiz in order to have a mean quiz score of exactly 90.
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Jordan is looking for a new place to live. She saw an ad in the paper and went to
the apartment building to look at the available unit. There, she met Steve, the
person who manages the property. Steve's jobs include collecting rent, making
small repairs, and screening the people who answers the ads. The rent checks
are to be made to Dave, the owner of the building. Jordan loves the apartment
and is approved to sign the lease and move in.
In this scenario, Steve is the:
O Real estate agent
O Tenant
O Landlord
O Property manager
Based on the given scenario, Steve who manages the property is a real estate agent.
The correct answer choice is option A
Who is a real estate agent?A real estate agent is a person who serves as n intermediary between tenant and landlord, buyers and sellers of properties. They collect rent, make little repairs and screen interested people. The real estate agent receives their reward based on commission, that is, a particular percentage of the property.
Therefore, Jordan is the tenant, Dave is the landlord and Steve is the real estate agent.
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In ΔHIJ, the measure of ∠J=90°, HI = 6. 7 feet, and JH = 4. 8 feet. Find the measure of ∠I to the nearest degree
The measure of angle I in the triangle HIJ using given measurements is equal to 46.05 degrees.
In the triangle HIJ,
The measure of angle J is equal to 90 degrees.
This implies ,
HI is the hypotenuse.
JH is the opposite side to angle I.
In triangle HIJ,
Using trigonometric ratio we get,
sin ∠I = Opposite side / Hypotenuse
Substitute the values we have,
⇒ sin ∠I = 4.8 / 6.7
⇒ sin ∠I = 0.72
Now , take sin⁻¹ both the side of the equation we get,
⇒sin⁻¹(sin ∠I) = sin⁻¹( 0.72 )
Here sin⁻¹(sin ∠I) = ∠I
⇒∠I = sin⁻¹( 0.72 )
⇒∠I = 46.05 degrees
Therefore, the measure of angle I is equal to 46.05 degrees.
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Jerald is having drain issues at his home and decides to call a plumber. The plumber charges $35 to come to his house and $50 for every hour they work. If the plumber charges Jerald a total of $190, how many hours did the plumber work?
Write and solve an equation to determine the number of hours worked by the plumber.
After solving equation , the plumber put in 3.1 hours of work (or 3 hours, 6 minutes).
what is equation?A mathematical assertion that demonstrates the equality of two expressions is called an equation The equals symbol (=) is used to denote the separation of two phrases. Numerous mathematical ideas and relationships, including linear functions, quadratic functions, and trigonometric functions, can be represented by equations.
Let's use the letter 'h' to indicate how many hours the plumber put in.
The plumber costs $35 to come to Jerald's residence and $50 for every hour they work. If Jerald is charged a total of $190 by the plumber, the following equation can be written:
$50h + $35 = $190
To solve for 'h,' we obtain:
$50h = $190 - $35
$50h = $155
h = 155 / 50
h = 3.1
Consequently, the plumber put in 3.1 hours of work (or 3 hours, 6 minutes).
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Phil is baking a pie with cranberries and apples. Apples cost $0.60/cup and cranberries cost $0.40/cup. Phil wants to spend no more than $4.20 on the fruit for his pie.
Question
What is an inequality that represents the combinations he can use?
cara computes the mean and variance for the set 87, 46, 90, 78, and 89. she finds the mean to be 78. her steps for finding the variance are shown below. what is the first error cara made in computing the variance?
If Cara's calculation of the sum of the squared differences i.e. 1370 from the mean is incorrect, that would be the first error she made in computing the variance.
As the steps for finding the variance are not provided, it is difficult to determine the first error Cara made.
However, the formula for calculating the variance is:
Variance = (sum of the squared differences from the mean) / (number of observations)
The first error Cara may have made is in calculating the sum of the squared differences from the mean.
The correct steps to find the variance are:
Find the mean:
Mean = (87 + 46 + 90 + 78 + 89) / 5 = 78
Calculate the differences from the mean for each observation:
87 - 78 = 9
46 - 78 = -32
90 - 78 = 12
78 - 78 = 0
89 - 78 = 11
Square each difference:
[tex]9^2 = 81[/tex]
[tex](-32)^2 = 1024[/tex]
[tex]12^2 = 144[/tex]
[tex]0^2 = 0[/tex]
[tex]11^2 = 121[/tex]
Find the sum of the squared differences:
81 + 1024 + 144 + 0 + 121 = 1370
Divide the sum of squared differences by the number of observations:
Variance = 1370 / 5 = 274.
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2. Which sequence of transformations takes the graph of y = k(x) to the graph of
y=-k(x + 1)?
A. Translate 1 to the right, reflect over the x-axis, then scale vertically by a factor of 1/2
B. Translate 1 to the left, scale vertically by 1/2 , then reflect over the y-axis.
C. Translate left by 1/2, then translate up 1.
D. Scale vertically by 1/2, reflect over the x-axis, then translate up 1.
The correct answer is option B. Translate 1 to the left, scale vertically by 1/2, then reflect over the y-axis.
What does term "transformation of a graph" means?The process of modifying the shape, location, or features of a graph is often referred to as graph transformation. Graphs are visual representations of mathematical functions or data point connections, often represented on a coordinate plane.
Translations, reflections, rotations, dilations, and other changes to the look of a graph are examples of graph transformations.
For the given problem, Transformation to get the desired result can be carried out as:
Translate '1' to the left: The transformation "x + 1" in "-k(x + 1)" shifts the graph horizontally to the left by 1 unit.Scale vertically by '1/2' : The 1/2 factor in "-k(x + 1)" vertically scales the graph, compressing it vertically.Reflect over the y-axis: The minus sign before "k" in "-k(x + 1)" reflects the graph over the y-axis, flipping it horizontally.Hence, to convert the graph of "y = k(x)" to the graph of "y = -k(x + 1)," the correct sequence of transformations is to translate 1 unit to the left, scale vertically by 1/2, and then reflect across the y-axis, which is option B.
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a region is bounded by two concentric circles, as shown by the shaded region in the figure above. the radius of the outer circle, r , is increasing at a constant rate of 2 inches per second. the radius of the inner circle, r , is decreasing at a constant rate of 1 inch per second. what is the rate of change, in square inches per second, of the area of the region at the instant when r is 4 inches and r is 3 inches? responses
The rate of change of the area is 20π square inches per second.
How to calculate area of the shaded region?The area of the shaded region can be calculated as the difference between the areas of the outer circle and the inner circle:
A = πr^2 - πr'^2
where r is the radius of the outer circle, r' is the radius of the inner circle, and π is the constant pi.
To find the rate of change of the area, we can take the derivative of both sides of the equation with respect to time t:
dA/dt = d/dt (πr^2) - d/dt (πr'^2)
Using the chain rule, we can express the derivatives in terms of the rates of change of the radii:
dA/dt = 2πr (dr/dt) - 2πr' (dr'/dt)
Substituting the given values at the instant when r=4 inches and r'=3 inches, we have:
dA/dt = 2π(4)(2) - 2π(3)(-1) = 20π
Therefore, the rate of change of the area is 20π square inches per second.
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Here is a recipe for $$ cupcakes. • Terrance has $$ cup of flour and $$ eggs. • Duri has $$ cups of flour and $$ grams of butter. • Habib has $$ cups of milk and $$ cups of sugar. • Anika has $$ cup of sugar and $$ cups of milk. If each person has enough of all the other ingredients, how many cupcakes could they make on their own?
Duri can make 72 cupcakes on his own and Habib can make 36 cupcakes on her own, assuming they have enough of all the other ingredients.
To determine how many cupcakes each person can make on their own, we need to check if they have enough of all the other ingredients required to make 12 cupcakes.
Terrance has 1 cup of flour and 6 eggs, which is not enough to make 12 cupcakes.
Duri has 12 cups of flour and 1000 grams of butter, which is more than enough to make 12 cupcakes. However, the recipe requires 3/4 cup of sugar, 2 eggs, and 3/4 cup of milk, which we do not know if Duri has enough of.
Habib has 3 cups of milk and 6 cups of sugar, which is enough to make 12 cupcakes.
Anika has 1 cup of sugar and 4 cups of milk, which is not enough to make 12 cupcakes.
Therefore, only Duri and Habib have enough ingredients to make 12 cupcakes on their own.
To determine how many cupcakes they can make, we need to calculate how much of each ingredient is required for one cupcake and then divide the available ingredients by that amount.
For one cupcake, we need:
1/6 cups of flour
1/16 cup of sugar
1/6 eggs
1/16 cups of milk
125/12 grams of butter
Duri has 12 cups of flour and 1000 grams of butter, which is enough to make 72 cupcakes. Habib has 6 cups of sugar and 3 cups of milk, which is enough to make 36 cupcakes.
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what equation represent
Answer: I'll have to say it's C or D but I think it's D
Hope it helped :D
if a contingency table has nine rows and columns, how many degrees of freedom are there for the test for independence?
There are 64 degrees of freedom for the test for independence in this contingency table.
To find the degrees of freedom for a test for independence in a contingency table, you can use the following formula:
Degrees of freedom (df) = (number of rows - 1) * (number of columns - 1).
In your case, the contingency table has nine rows and nine columns. Using the formula:
df = (9 - 1) * (9 - 1)
df = 8 * 8
df = 64.
In a contingency table, the degrees of freedom (df) for the test of independence are calculated as:
df = (number of rows - 1) x (number of columns - 1)
In this case, the contingency table has nine rows and nine columns, so the degrees of freedom are:
df = (9-1) x (9-1) = 64
This means that there are 64 degrees of freedom for the test of independence.
Degrees of freedom are important because they determine the critical values for the test statistic, which in turn affects the decision to reject or fail to reject the null hypothesis.
In general, as the degrees of freedom increase, the critical values decrease, making it easier to reject the null hypothesis.
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There are 64 degrees of freedom for the test for independence in a contingency table with nine rows and columns.
To determine the degrees of freedom for the test for independence in a contingency table with nine rows and columns, we use the formula df = (r-1)(c-1), where r is the number of rows and c is the number of columns.
Substituting in the values, we get:df = (9-1)(9-1)df = 8 x 8df = 64A contingency table is a table that shows the frequency distribution of two or more categorical variables.
A test for independence is a statistical test that checks whether the variables are related or not.
Therefore, there are 64 degrees of freedom for the test for independence in a contingency table with nine rows and columns.
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In art class students are mixing blue and red paint to make purple paint. Hawa mixes 1 cup of blue paint and 5 cups of red paint. Jacob mixes 4 cups of blue paint and 13 cups of red paint. Use Hawa and Jacob’s percent of red paint to determine whose purple paint will be redder.
Hawa percent of red paint (to nearest whole number) =
%
Jacob percent of red paint (to nearest whole number) =
%
Hawa ’s purple paint will be redder.
Jacob’s purple paint will be redder.
The two purple paints will be equally red.
attempt 1 out of 2
Miracle Jackson
Which is more? (Percent Comparison)
Apr 10, 6:51:14 PM
Watch help video
In art class students are mixing blue and red paint to make purple paint. Hawa mixes 1 cup of blue paint and 5 cups of red paint. Jacob mixes 4 cups of blue paint and 13 cups of red paint. Use Hawa and Jacob’s percent of red paint to determine whose purple paint will be redder.
Answer:
Step-by-step explanation:
A new club sent out 200 coupons to boost sales for next year's memberships. They provided 3 times as many to potential members than to existing members. How many coupons did they send to existing members?
the new club sent out 50 coupons to existing members and 150 coupons to potential members to boost sales for next year's memberships.
How to solve the question?
Let x be the number of coupons sent to existing members. Then the number of coupons sent to potential members is 3x, as they provided 3 times as many coupons to potential members than to existing members.
According to the problem, the total number of coupons sent is 200. Therefore, we can write the following equation:
x + 3x = 200
Simplifying this equation, we get:
4x = 200
Dividing both sides by 4, we get:
x = 50
Therefore, the number of coupons sent to existing members is 50, and the number of coupons sent to potential members is 3 times as many, or 150.
In conclusion, the new club sent out 50 coupons to existing members and 150 coupons to potential members to boost sales for next year's memberships.
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WILL MARK BRAINLIST PLS HELP!!
(-4,-5); slope = 1/2
Answer: y=1/2x-3
Step-by-step explanation:
I'm assuming you're trying to find it in slope intercept form!
y=mx+b
y=1/2x-3
easy
Eight identical lights are connected in series across a 110-V line. What is the voltage across each bulb? If the current is 0.56A , what is the resistance of each bulb? If the current is 0.56A , what is the power dissipated in each?
The resistance of each bulb that is connected in series with a 110 V line is 24.55 Ω with a 13.75 V Voltage difference across each bulb. The power dissipated in each bulb is 7.7 W, if 0.56 A current flows through them.
The voltage across 8 identical bulbs is 110 V
Since they are connected in a series and identical, the Voltage difference across each bulb is [tex]\frac{110}{8}[/tex] V which is 13.75 V
According to the question,
The current flowing through the bulb = 0.56 A
So according to Ohm's Law,
V = IR
13.75 = 0.56 * R
R = 24.55 Ω
The power dissipated in each bulb can be calculated as
P = VI
P = 13.75 * 0.56 = 7.7 W
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In summary, the voltage across each bulb is 13.75V, the resistance of each bulb is 24.55Ω, and the power dissipated in each bulb is 7.7W.
When eight identical lights are connected in series across a 110-V line, the voltage across each bulb will be 110/8 = 13.75 V.
To find the resistance of each bulb, we can use Ohm's law, which states that resistance is equal to voltage divided by current (R = V/I). Therefore, the resistance of each bulb is 13.75/0.56 = 24.55 ohms.
To find the power dissipated in each bulb, we can use the formula P = VI, where P is power, V is voltage, and I is current. Therefore, the power dissipated in each bulb is 13.75 x 0.56 = 7.7 watts.
To find the voltage across each bulb, divide the total voltage by the number of bulbs:
Voltage across each bulb = Total Voltage / Number of Bulbs = 110V / 8 = 13.75V per bulb
Next, use Ohm's Law to find the resistance of each bulb:
Resistance (R) = Voltage (V) / Current (I) = 13.75V / 0.56A = 24.55Ω per bulb
Finally, find the power dissipated in each bulb using the formula:
Power (P) = Voltage (V) x Current (I) = 13.75V x 0.56A = 7.7W per bulb
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First person to help me on this will be rewarded plsss
The compound interest investment earns more interest than the simple interest investment, and the difference becomes more significant over time.
After 10 years, the difference is relatively small, but after 20 years, the compound interest investment has earned over $3,700 more than the simple interest investment.
What are the amounts after 10 and 20 years of the investment?To calculate the amount after 10 and 20 years, we can use the following formulas:
Simple Interest: A = P * (1 + r * t)
Compound Interest: A = P * (1 + r/n)^(n*t)
Where:
A is the amount after t yearsP is the principal amount (the initial investment)r is the annual interest rate (as a decimal)n is the number of times the interest is compounded per yeart is the time in yearsUsing these formulas and the information given in the table, we can calculate the amount after 10 years and 20 years for each type of investment.
For simple interest, the interest is not compounded, so we just add the interest to the principal:
Amount after 10 years: A = $50,000 * (1 + 0.0275 * 10) = $68,750
Amount after 20 years: A = $50,000 * (1 + 0.0275 * 20) = $87,500
For compound interest, we need to use the formula above with n=12 (since the interest is compounded monthly):
Amount after 10 years: A = $50,000 * (1 + 0.0275/12)^(12*10) = $68,704.23
Amount after 20 years: A = $50,000 * (1 + 0.0275/12)^(12*20) = $91,262.47
To compare the two investments, we can look at the difference between the amounts after 10 and 20 years:
Difference after 10 years: $68,750 - $68,704.23 = $45.77
Difference after 20 years: $87,500 - $91,262.47 = $3,762.47
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What is the volume of a sphere with a diameter of 6. 3 cm, rounded to the nearest tenth of a cubic centimeter?
Step-by-step explanation:
Volume of a sphere is given by the formula
4/3 pi r^3 diameter = 6.3 cm so radius, r = 3.15 cm
4/3 * pi * (3.15)^3 = 130.9 cm^3
one more than the reciprocal of a particular number is $\frac{7}{3}$. what is the original number expressed as a common fraction?
Original number = $\frac{3}{4}$. The original number expressed as a common fraction is $\frac{3}{4}$.
1. Reciprocal: This is the result of switching the numerator and denominator of a fraction (or dividing 1 by a whole number).
2. Original number: This is the number we're trying to find.
3. Common fraction: This is a fraction where the numerator and denominator are both integers (whole numbers).
Step 1: Set up the equation using the given information.
One more than the reciprocal of the original number is $\frac{7}{3}$. We can express this as an equation:
Reciprocal of the original number + 1 = $\frac{7}{3}$
Step 2: Solve for the reciprocal of the original number.
Reciprocal of the original number = $\frac{7}{3}$ - 1
Step 3: Simplify the equation.
Reciprocal of the original number = $\frac{7}{3}$ - $\frac{3}{3}$
Reciprocal of the original number = $\frac{4}{3}$
Step 4: Find the original number.
Since we have the reciprocal of the original number, we can find the original number by taking the reciprocal of this value:
Original number = $\frac{1}{(\frac{4}{3})}$
Step 5: Simplify the expression.
Original number = $\frac{1}{1} \times \frac{3}{4}$
Original number = $\frac{3}{4}$
The original number expressed as a common fraction is $\frac{3}{4}$.
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A grab-bag contains 30 packages worth $. 65 each, 10 packages $. 60 cents each, and 15 packages worth $. 30 each. How much should the game owner charge to make it a fair game?
$0. 55
$0. 40
$0. 60
$0. 30
The game owner should charge option (a) $0.55 to make it a fair game
To determine how much the game owner should charge to make it a fair game, we need to calculate the average value of each package. We can do this by finding the total value of all the packages and dividing it by the total number of packages.
The total value of the 30 packages worth $.65 each is:
30 x $.65 = $19.50
The total value of the 10 packages worth $.60 each is:
10 x $.60 = $6.00
The total value of the 15 packages worth $.30 each is:
15 x $.30 = $4.50
The total value of all the packages is
$19.50 + $6.00 + $4.50 = $30.00
The total number of packages is
30 + 10 + 15 = 55
The average value of each package is
$30.00 / 55 = $0.55
Therefore, the correct option is (a) $0.55
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Quadrilateral H'I'J'K' is a translation of quadrilateral HIJK. Write the translation rule. picture above
Since quadrilateral H'I'J'K' is a translation of quadrilateral HIJK, the translation rule include the following: (x, y) → (x - 8, y + 10).
What is a translation?In Mathematics, the translation of a graph to the left is a type of transformation that simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation of a graph to the right is a type of transformation that simply means adding a digit to the value on the x-coordinate of the pre-image.
By translating the pre-image of quadrilateral HIJK horizontally left by 8 units and vertically up by 10 units, the coordinate J of quadrilateral H'I'J'K' include the following:
(x, y) → (x - 8, y + 10)
J (8, -2) → (8 - 8, -2 + 10) = J' (0, 8).
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a bank wishing to increase its customer base advertises that it has the fastest service and that virtually all of its customers are served in less than 11 minutes. a management scientist has studied the service times and concluded that service times are exponentially distributed with a mean of 4.5 minutes. determine what the bank means when it claims 'virtually all' its customers are served in under 11 minutes.
The bank's claim is exaggerated and not entirely accurate.
The bank's claim that virtually all of its customers are served in less than 11 minutes is misleading, as it implies that almost all customers are served in 11 minutes or less. However, based on the given information that service times follow an exponential distribution with a mean of 4.5 minutes, we can calculate the probability that a customer will be served in less than 11 minutes using the cumulative distribution function of the exponential distribution:
P(X < 11) = 1 - [tex]e^{(-11/4.5)[/tex] = 0.956
This means that approximately 95.6% of customers will be served in less than 11 minutes, not "virtually all." Therefore, the bank's claim is exaggerated and not entirely accurate.
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what is the volume, in cubic centimeters, of a right rectangular prism that has a length of 4 44 centimeters, a width of 9 99 centimeters, and a height of 10 1010 centimeters?
Step-by-step explanation:
Volume of rect prism = L X W X H = 4 X 9 X 10 = 360 cm^3
Select each expression that is equivalent to 3(n + 6).
Answer:
3(n + 6) = 2(n + 6) + (n + 6)
3(n + 6) = 3n + 18
PLEASE HELP ILL MARK U AS BRAINLIEST!!
Answer: 64 sqaure centimetres.
Step-by-step explanation:
- Surface area means the area of all exterior sides of a 3D dimensional shape. This means we'll have to find the area of every face and then add them all together.
Top and Bottom
4 x 4 = 16
16 x 2 = 32
Both faces are the same so once we find the area of one, we can just double it.
North, South, East and West Side
4 x 2 = 8
8 x 4 = 32
All four remaining faces had the same dimensions, meaning that once you found one, you just had to multiply that answer by 4.
To find the overall surface area add all the areas you have.
32 + 32 = 64
or
16 +_16 + 8 + 8 + 8 + 8 = 64
The recipe for one batch of
chocolate chip cookies calls
for 11/3 cups of chocolate
chips. Luca made 3½ batches
of cookies. How many cups of
chocolate chips did he use?
Answer:
Step-by-step explanation:
1 + 1 divided by 3 x 3.5 = 4.66 or 4 2/3
The Olympic record for the men's 50-meter freestyle is 21.91 seconds. Express this speed in meters per second
Answer:
50 meters/21.91 seconds = 2.282 m/sec
6. Electronics Warehouse had a Super Bowl Sale on Televisions. They offered no interest no payments for 24 months on televisions larger than 50 inches. You have been dving to have a new 85" TV, so you pick out an amazing OLED on sale for $2299.99. You take advantage of the store offering no interest, no paymenus for 24 months, and go home smiling. The fine print on the credit card agreement states a 24.99% interest rate that accrues monthly. Additionallv. if the balance is not paid in full by the end of the 24 month promotion. the interest will be apolied to the remaining balance. If vou choose to not make a payment during the 24-month period, what will your balance be when you get your first bill?
If you choose not to make a payment during the 24-month period, your balance at the end of the promotion will be $3,637.16.
Explain month
A month is a unit of time equal to one-twelfth of a year, or approximately 30.44 days. It is often used to represent periodic phenomena, such as interest rates or seasonal trends, and to calculate the duration between two dates. The number of months between two dates is calculated by dividing the difference in days by 30.44.
According to the given information
If you do not make any payments during the 24-month period, your balance will increase each month due to the interest that accrues. After 24 months, your balance will be:
$2299.99 * (1 + 0.020825)²⁴ = $3,637.16
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If you are trying to determine if an input variable may affect your key characteristic (output variable) by examining the correlation between variables, which tool should you use?
A. X-bar and R chart
B. p-chart
C. Pareto chart
D. Scatter plot diagram
E. Affinity diagram
If you are trying to determine if an input variable may affect your key characteristic (output variable) by examining the
correlation between variables, you should use the tool: D. Scatter plot diagram. therefore, option D.Scatter plot
diagram is correct.
A scatter plot diagram is a graphical representation of the relationship between two variables. It can help you visualize
the correlation between the input and output variables, making it easier to determine if there is a potential cause-and-
effect relationship.
The tool that you should use to examine the correlation between variables is D. Scatter plot diagram.
A scatter plot diagram is a graphical representation that displays the relationship between two variables.
The x-axis represents the input variable, while the y-axis represents the output variable.
By plotting the data points on the scatter plot diagram, you can visually analyze the correlation between the variables.
If there is a strong positive or negative correlation between the variables, it suggests that the input variable may affect
the key characteristic (output variable).
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D. Scatter plot diagram is the tool that should be used to examine the correlation between variables to determine if an input variable may affect your key characteristic (output variable).
The scatter plot diagram is a graphical representation that displays the relationship between two variables, and it is commonly used to identify patterns, trends, and correlations between variables. By examining the scatter plot diagram, you can determine whether there is a positive, negative, or no correlation between the variables, which can help you to identify potential cause-and-effect relationships.
To determine if an input variable may affect your key characteristic (output variable) by examining the correlation between variables, you should use:
A scatter plot diagram is a graphical tool that helps visualize the relationship between two variables, allowing you to identify any correlation between the input and output variables.
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Use the functions f(x)=√x+1, g(x)=2x-5, and h(x) = 3x² - 3 to complete the table.
x
4
10
20
34
52
f(g(x))
Answer:
To find the values of f(g(x)) for the given values of x, we need to first evaluate g(x) for each value of x, and then plug the result into f(x).
Using the given functions:
g(x) = 2x - 5
f(x) = √(x+1)
Therefore, we have:
f(g(x)) = √(g(x) + 1) = √(2x - 5 + 1) = √(2x - 4) = 2√(x - 2)
So, we can complete the table as follows:
x f(g(x))
4 2
10 4
20 6
34 8
52 10
Therefore, the completed table is:
x f(g(x))
4 2
10 4
20 6
34 8
52 10