Answer: a) Virtual School Gold Card
Step-by-step explanation: To compare the monthly interest rates of the three credit cards, we need to convert the annual and quarterly rates to monthly rates.
For Canadian Express, the monthly interest rate is 19.9% / 12 = 1.6583%.
For Virtual School Gold Card, the monthly interest rate is 1.67%.
For Bank of Brennan Super Credit Card, the monthly interest rate is (4.99% / 4) = 1.2475%.
Therefore, the Virtual School Gold Card offers the lowest monthly interest rate at 1.67%.
Owen has two options for buying a car. Option A is 1.3 % APR financing over 36 months and Option B is 5.2 % APR over 36 months with $1500 cash back, which he
would use as part of the down payment. The price of the car is $32,020 and Owen has saved $3200 for the down payment. Find the total amount Owen will spend on the
car for each option if he plans to make monthly payments. Round your answers to the nearest cent, if necessary.
Option A:
Option B:
Answer: Option A:
To calculate the total amount Owen will spend on Option A, we need to calculate the monthly payment and then multiply it by the number of months:
First, we need to calculate the total amount of the loan. Owen is making a down payment of $3200, so he will be borrowing $28,820 (the price of the car minus the down payment).
Next, we can use the formula for calculating the monthly payment for a loan:
P = (r * A) / (1 - (1 + r)^(-n))
where P is the monthly payment, r is the monthly interest rate, A is the total amount of the loan, and n is the number of months.
For Option A, the monthly interest rate is 1.3% / 12 = 0.01083, the total amount of the loan is $28,820, and the number of months is 36. Plugging these values into the formula, we get:
P = (0.01083 * 28,820) / (1 - (1 + 0.01083)^(-36)) = $860.45
Therefore, the total amount Owen will spend on Option A is:
36 * $860.45 = $30,975.98
Option B:
For Option B, we need to take into account the $1500 cash back that Owen will receive as part of the down payment. This means that the total amount of the loan will be $32,020 - $3200 - $1500 = $27,320.
To calculate the monthly payment, we can use the same formula as before:
P = (r * A) / (1 - (1 + r)^(-n))
For Option B, the monthly interest rate is 5.2% / 12 = 0.04333, the total amount of the loan is $27,320, and the number of months is 36. Plugging these values into the formula, we get:
P = (0.04333 * 27,320) / (1 - (1 + 0.04333)^(-36)) = $825.53
Therefore, the total amount Owen will spend on Option B is:
36 * $825.53 + $1500 = $30,316.08
Therefore, Option A will cost Owen a total of $30,975.98, and Option B will cost him a total of $30,316.08. Therefore, Option B is the cheaper option for Owen.
Step-by-step explanation:
Trangle ABC has an area 25 square feet and perimeter of 65.5 feet of triangle ABC is dilated by a factor of 5/2 to create now calculate the area of trangle DEF using the scale factor
So, the area of triangle DEF is 312.5 square feet, using the scale factor of 5/2.
What is dilation?the context of mathematics and geometry, dilation is a transformation that changes the size of an object. It is a type of transformation that scales an object by a certain factor, without changing its shape or orientation.
In other words, dilation involves multiplying the coordinates of a geometric figure by a fixed constant, which results in an enlarged or reduced version of the original figure. The constant is known as the dilation factor or the scale factor, and it can be any real number greater than zero.
For example, if we dilate a circle by a scale factor of 2, every point on the circle will be moved twice as far away from the center, resulting in a new circle with a diameter twice as large as the original.
Let's start by using the formula for the perimeter of a triangle:
[tex]Perimeter of triangle ABC = AB + BC + AC = 65.5 feet[/tex]
We can also use Heron's formula to find the area of triangle ABC:
[tex]Area of triangle ABC = \sqrt(s(s-AB)(s-BC)(s-AC))[/tex]
where s is the semi perimeter of the triangle:
[tex]s = (AB + BC + AC) / 2[/tex]
We can use these equations to solve for the side lengths of triangle ABC:
[tex]AB + BC + AC = 65.5[/tex]
[tex]s = (AB + BC + AC) / 2[/tex]
[tex]25 = \sqrt(s(s-AB)(s-BC)(s-AC))[/tex]
Solving for AB, BC, and AC gives us:
AB = 15
BC = 20
AC = 30.5
Now, let's dilate triangle ABC by a factor of 5/2 to create triangle DEF. This means that each side of triangle ABC will be multiplied by 5/2 to get the corresponding side length of triangle DEF.
DE = AB * (5/2) = 37.5
EF = BC * (5/2) = 50
DF = AC * (5/2) = 76.25
Now we can use Heron's formula again to find the area of triangle DEF:
s = (DE + EF + DF) / 2 = 81.875
Area of triangle DEF = sqrt(s(s-DE) (s-EF) (s-DF)) = 312.5 square feet
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What is the circumference of the circle? Use 3.14 for π
. Round your answer to the nearest hundredth. please help 100 points
Answer:
b)
Step-by-step explanation:
Use circle K for problems 11-13
After calculation we get
11) d. m/JML = 90 degrees, a. m/GMH = 45 degrees, b. mLH = 90 degrees, c. m/LKH = 45 degrees
12) a. AGKH is an isosceles triangle, b. Another triangle formed by two radii is an equilateral triangle.
13) a. m/GKH = 33.4 degrees, c. m/KHJ = 33.4 degrees, e. mJL66.8 degrees, b. m/KGH = 66.8 degrees, d. m/JKL = 113.2 degrees
What is quadrilateral?A quadrilateral is a geometric shape with four straight sides and four angles. Examples of quadrilaterals include squares, rectangles, parallelograms, trapezoids, and kites.
According to the given information:
a. Since m/LGH and m/GHJ are both 45°, GH is a bisector of ∠JGL. Therefore, m/GMH = 90° - 45° = 45°.
b. Since GH is a bisector of ∠JGL, m/LGH = m/HGL = 45°. Also, since LH is a straight line, m/LGH + mLH + m/HGL = 180°. Thus, mLH = 90° - 45° = 45°.
c. Since GH is a bisector of ∠LJK, m/GHK = m/JHK = 45°. Also, since LK is a straight line, m/LKH + m/JHK + m/LJK = 180°. Thus, m/LKH = m/LJK = (180° - 2*45°)/2 = 45°.
d. Since GH is a bisector of ∠JGL and JML is a straight line, m/JML = m/JGH + m/HGL = 45° + 45° = 90°.
a. AGKH is a quadrilateral with two sides that are radii of the circle. Since all radii of a circle are equal, AGKH is a kite. Furthermore, since the two radii AG and KH are perpendicular to each other, AGKH is also a rectangle.
b. Another triangle formed by two radii is AKJ, where AK and AJ are radii of the circle and KJ is a chord.
a. Since GH is a diameter of the circle and GKH is a right triangle with ∠GHK = 90°, m/GKH = 180° - 90° = 90°.
b. Since GH is a diameter of the circle and KJ is a chord, m/KGH = m/KJ = 1/2 * m/KHJ = 1/2 * (180° - 113.2°) = 33.4°.
c. Since GH is a diameter of the circle and KHJ is a right triangle with ∠KHJ = 90°, m/KHJ = 180° - m/GKH = 180° - 90° = 90°.
d. Since GH is a diameter of the circle and JKL is a right triangle with ∠JKL = 90°, m/JKL = 180° - m/KJ - m/JKH = 180° - 33.4° - 45° = 101.6°.
e. Since JL is a chord of the circle and ∠JGL is an inscribed angle that intercepts it, m/JGL = 1/2 * m/JL = 1/2 * (180° - m/JKL) = 1/2 * (180° - 101.6°) = 39.2°. Also, since GH is a diameter of the circle and GJL is a right triangle with ∠GJL = 90°, m/GJL = 90° - m/GHL = 90° - 45° = 45°. Therefore, m/JLH = m/JGL - m/GLH = 39.2° - 45° = -5.8°. Note that the negative value indicates that ∠JLH is a reflex angle.
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Translate in two ways each of these statements into logical expressions using predcates quantifiers and logical connective first let the domain consist of the students in your class and second let it consist of all people a) everyone in your class has a cellular phone
For all x, P(x) (using universal quantifier ∀) and It is not the case that there exists an x such that ~P(x) (using negation ¬ and existential quantifier ∃)
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
Let S be the set of students in your class and P(x) be the predicate "x has a cellular phone". Then, we can represent the statement "everyone in your class has a cellular phone" as:
1. For all x in S, P(x) (using universal quantifier ∀)
2. It is not the case that there exists an x in S such that ~P(x) (using negation ¬ and existential quantifier ∃)
If we want to represent the same statement for all people, we can use the same predicate P(x) and consider the domain of all people. Then, the statement "everyone has a cellular phone" can be represented as:
For all x, P(x) (using universal quantifier ∀)
It is not the case that there exists an x such that ~P(x) (using negation ¬ and existential quantifier ∃)Let S be the set of students in your class and P(x) be the predicate "x has a cellular phone". Then, we can represent the statement "everyone in your class has a cellular phone" as:
For all x in S, P(x) (using universal quantifier ∀)
It is not the case that there exists an x in S such that ~P(x) (using negation ¬ and existential quantifier ∃)
If we want to represent the same statement for all people, we can use the same predicate P(x) and consider the domain of all people. Then, the statement "everyone has a cellular phone" can be represented as:
1. For all x, P(x) (using universal quantifier ∀)
2. It is not the case that there exists an x such that ~P(x) (using negation ¬ and existential quantifier ∃)
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Can someone help me with this problem? I need to find x and y
Answer:
x = √17
y = 10.1
Step-by-step explanation:
x² + 8² = 9²
x² = 81 - 64 = 17
x = √17
sin∅ = √17/9
∅ = 27.27°
9/y = cos(27.27)
y = 9/cos(27.27) = 10.13
y = 10.1
The numbers of students in the 9 schools in a district are given below.
(Note that these are already ordered from least to greatest.)
164, 225, 227, 250, 261, 268, 277, 379, 523
Send data to calculator
Suppose that the number 523 from this list changes to 424. Answer the following.
(a) What happens to the mean?
(b) What happens to the median?
It decreases by
O It increases by 0.
It stays the same.
O It decreases by 0.
It increases by
It stays the same.,
X
5
if we change the value of 523 to 424 in the list of numbers, then the mean decreases by approximately 3.22 and the median stays the same.
How to calculate the mean?
To calculate the mean, we add up all the numbers in the list and divide by the total number of values. Before the change, the sum of the numbers is:
164 + 225 + 227 + 250 + 261 + 268 + 277 + 379 + 523 = 2494
And there are 9 numbers in the list. So the mean is:
2494 / 9 ≈ 277.11
If we change the value of 523 to 424, then the sum becomes:
164 + 225 + 227 + 250 + 261 + 268 + 277 + 379 + 424 = 2465
And there are still 9 numbers in the list. So the new mean is:
2465 / 9 ≈ 273.89
So the mean decreases by approximately 3.22.
To calculate the median, we find the middle value of the list. If the list has an odd number of values, then the median is the middle value. If the list has an even number of values, then the median is the average of the two middle values. In this case, the list has an odd number of values, so the median is:
261
If we change the value of 523 to 424, then the list becomes:
164, 225, 227, 250, 261, 268, 277, 379, 424
And the median is still:
261
So the median stays the same.
In summary, if we change the value of 523 to 424 in the list of numbers, then the mean decreases by approximately 3.22 and the median stays the same.
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Tom is preparing for a 100 meters race competition. During his practice last week, a sample of seven 100
meters races is reviewed, and the finishing times (in seconds) were as below:
13.4
15.6
13.1
14.5
14.2
13.3
15.3
It is reasonable to assume his finishing times are normally distributed.
(a) Construct a 99% confidence interval estimate of his population mean finishing time of 100 meters race.
(b) If the confidence interval estimate of his population mean finishing time of 100 meters is constructed at
95% instead of 99%, would the new confidence interval be (I) wider, (II) narrower, or (III) the same as
the interval constructed at part (a)? (Just state your answer, no calculation is needed in part (b))
Question A) A 99% confidence interval estimate of his population mean finishing time of 100 meters race is (12.8081,15.5919)
Question B) Option II) narrower is the correct Option.
What is linear equation?
An algebraic equation with simply a constant and a first- order( direct) element, similar as y = mx b, where m is the pitch and b is the y- intercept, is known as a linear equation.
The below is sometimes appertained to as a" direct equation of two variables," where y and x are the variables. Equations whose variables have a power of one are called direct equations. One illustration with only one variable is where layoff b = 0, where a and b are real values and x is the variable.
Let X be the time required to finish 100 meters race competition with Tom ( in seconds.)
A) A 99% confidence interval estimate of his population mean finishing time of 100 meters race is (12.8081,15.5919)
x = 14.2
s^2= 0.9867
s= 0.9933
α/2, n-1 = 3.7074
Margin of error= 1.3919
lower bound= 12.8081
upper bound= 15.5919
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Tyrone has $800 in a savings account that earns 10% annually. The interest is not compounded. How much will he have in total in 1 year?
Answer: $80
Step-by-step explanation:
If Tyrone's savings account earns a simple 10% annual interest and is not compounded, then the interest for one year can be calculated using the formula:
Interest = Principal × Rate × Time
where:
Principal = $800
Rate = 10% = 0.1
Time = 1 year
Interest = $800 × 0.1 × 1 = $80
Tyrone will earn $80 in interest in 1 year. To find the total amount in his account after 1 year, we add the interest to the principal:
Total amount = Principal + Interest
Total amount = $800 + $80 = $880
In 1 year, Tyrone will have $880 in total in his savings account.
Answer:
$880
Step-by-step explanation:
10% = .1
800 x .1 = 80
80 + 800= 880
What is the perimeter of the trapezoid?
A large production facility uses two machines to produce a key part for its main product. Inspectors have expressed concern about the quality of the finished product. Quality-control investigation has revealed that the key part made by the two machines is defective at times. The inspectors randomly sampled 35 units of the key part from each machine. Of those produced by machine A, 5 were defective. Seven of the 35 sampled parts from machine B were defective. The production manager is interested in estimating the difference in proportions of the populations of parts that are defective between machine A and machine B. From the sample information, compute a 98% confidence interval for this difference.
The range of the 98% confidence interval for the percentage of faulty components that differ between machines A and B is about between -0.2448 and 0.1305. (rounded to 4 decimal places).
How can you figure up a confidence interval for the proportional difference?Define the populations of interest and the characteristic you want to compare (e.g., proportion of success or failure).Collect random samples from each population and record the number of occurrences of the characteristic of interest in each sample.Calculate the sample proportions ([tex]p_1 \;and \;p_2[/tex]) by dividing the number of occurrences by the sample size for each population.Calculate the standard error (SE) of the difference in proportions using the sample proportions, sample sizes, and appropriate formula (SE = [tex]\sqrt{ [(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)}[/tex], where[tex]p_1 \;and \;p_2[/tex] are the sample proportions and[tex]n_1 \;and \;n_2[/tex] are the sample sizes for the two populations, respectively).Determine the appropriate critical value from the probability distribution (e.g., standard normal distribution for large sample sizes or t-distribution for small sample sizes) based on the desired confidence level.Calculate the margin of error (ME) by multiplying the standard error by the critical value (ME = critical value * SE).Construct the confidence interval by adding and subtracting the margin of error from the sample statistic (e.g., the difference in sample proportions, or the ratio of sample proportions).Interpret the confidence interval, stating that we can be [confidence level]% confident that the true population parameter falls within the calculated interval.Given:
Sample proportion from machine A ([tex]p_1[/tex]) = 5/35 = 0.14285714285714285
Sample proportion from machine B ([tex]p_2[/tex]) = 7/35 = 0.2
Sample size from machine A ([tex]n_1[/tex]) = 35
Sample size from machine B ([tex]n_2[/tex]) = 35
Standard error (SE) = [tex]\sqrt{ [(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)}[/tex]
= [tex]\sqrt{[0.14285714285714285 * (1 - 0.14285714285714285) / 35] + [0.2 * (1 - 0.2) / 35] }[/tex]
= 0.07058061453775912 (rounded to 11 decimal places)
Margin of error (ME) = Critical value * Standard error
= 2.660 * 0.07058061453775912 (using z-score for a 98% confidence level)
= 0.18765117789861733 (rounded to 11 decimal places)
Confidence interval (CI) = Sample statistic ± Margin of error
= [tex](p_1 - p_2) \pm ME[/tex]
= (0.14285714285714285 - 0.2) ± 0.18765117789861733
= -0.05714285714285715 ± 0.18765117789861733
The 98% confidence interval for the difference in proportions of defective parts between machine A and machine B is approximately -0.2448 to 0.1305 (rounded to 4 decimal places).
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How to solve it and the answer
Answer: The answer is, y=18x
Step-by-step explanation: This is going up by 18 as the y axis increases by 9. Hope this helped :)
HELP ASAPPP
The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds:
A: The Water Balloon height increase from 0 to 2 seconds B: Water Balloon's height stay same from 2 to 4 seconds. C: Height decreasing fastest at 4 to 6 seconds. D: Almost near to ground as resistance.
Describe Graph?A graph is a visual representation of data or mathematical relationships between variables. Graphs are used to help people better understand the information they are working with by displaying it in a more clear and organized way.
There are many different types of graphs, including bar graphs, line graphs, scatter plots, pie charts, and histograms. Each type of graph has its own strengths and weaknesses, and is used for different purposes.
In general, graphs consist of two axes: a horizontal x-axis and a vertical y-axis. The x-axis represents the independent variable, while the y-axis represents the dependent variable. Data points are plotted on the graph at the intersection of the x and y coordinates, and lines or curves are often drawn to connect the points and show trends or patterns in the data.
Part A
Ae seen from graph increases from 0 to 2 seconds.
Part B
Water Balloon's height stay same from 2 to 4 seconds
Part C
Height decreasing fastest at 4 to 6 seconds because the slope is steepest downward from 4 to 6 second as compared to 6 to 10 sec.
Part D
Height of balloon will we almost near to ground as resistance will play its role. but it will almost touch the ground.
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!! I’ll give 100 points if you answer this hurry I need an answer !!??
(07.01 HC)
Prove that the two circles shown below are similar.
The ratio of the radii is equal to the ratio of the distances between corresponding points on the two circles, we can conclude that the two circles are similar.
Describe Circle?A circle is a two-dimensional geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center. The distance between the center and any point on the circle is called the radius. The line passing through the center of the circle and connecting two points on the circumference is called the diameter, which is twice the length of the radius.
The circle is a fundamental concept in geometry and has many important properties. One of the most well-known properties of a circle is that the circumference, which is the distance around the circle, is proportional to the diameter, and this proportionality constant is pi (π).
To prove that the two circles are similar, we need to show that their radii are proportional.
Let's first find the radius of circle A. The center of circle A is at (3, 4), and one point on the circle is (0, 8). The distance between these two points is the radius of the circle:
r_A = √((0 - 3)² + (8 - 4)²) = 5
Now let's find the radius of circle C. The center of circle C is at (0, -1), and one point on the circle is (0, 1). The distance between these two points is the radius of the circle:
r_C = √((0 - 0)² + (1 - (-1))²) = 2
So the ratio of the radii of the two circles is:
r_A / r_C = 5 / 2
Next, we need to show that the distance between corresponding points on the two circles is also proportional to the ratio of the radii. Let's take the point (0, 0) on circle A and the corresponding point (2, 0) on circle C. The distance between these two points is:
d = √((0 - 2)² + (0 - (-1))²) = √(5)
So the ratio of the distances is:
d_A / d_C = √(5) / 2
Since the ratio of the radii is equal to the ratio of the distances between corresponding points on the two circles, we can conclude that the two circles are similar.
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Becky can make a monthly payment of $530 for a car. If
the annual interest rate she qualifies for is 6% for 4 years,
what price could she afford for the car?
Becky can afford a car with a price of $20,858.33 or less, given her monthly payment of $530, and assuming an annual interest rate of 6% for 4 years.
What is statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.
To calculate the price that Becky can afford for the car, we need to use the present value formula for an annuity:
PV = PMT x [tex]((1 - (1 + r/n)^{(-nt))}[/tex] / (r/n))
where:
PV = present value of the car
PMT = monthly payment
r = annual interest rate
n = number of compounding periods per year
t = number of years
In this case, PMT = $530, r = 6% (or 0.06 as a decimal), n = 12 (since monthly payments are being made), and t = 4. Plugging in these values, we get:
PV = $530 x[tex]((1 - (1 + 0.06/12)^{(-12*4)})[/tex] / (0.06/12))
PV = $20,858.33
Therefore, Becky can afford a car with a price of $20,858.33 or less, given her monthly payment of $530, and assuming an annual interest rate of 6% for 4 years.
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The table shows the monthly rainfall at a measuring station.
Month Rainfall
(inches) Month Rainfall
(inches)
Jan 2.22 Jul 3.37
Feb 1.51 Aug 5.40
Mar 1.86 Sep 5.45
Apr 2.06 Oct 4.34
May 3.48 Nov 2.64
Jun 4.47 Dec 2.14
a. What is the mean monthly rainfall? Round your answer to the nearest thousandth.
The mean monthly rainfall from the given data is 3.245 inches, using the formula to evaluate mean that is sum of all observations divided by total number of observations.
What is mean?
By dividing the sum of the given numbers by the entire number of numbers, the mean—the average of the given numbers—is calculated. Similar to the mode and median, the mean is one of the measurements of central tendency. It denotes that values for a specific set of data are distributed equally. The three most frequently employed measures of central tendency are the mean, median, and mode. The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean.When all of the values are organised in ascending order, the Median is the median value of the given data. While the number in the list that is repeated a maximum of times is the mode.
Mean= [tex]\frac{sum of all observations }{total observations}[/tex]
Given observations in inches:
2.22, 1.51 , 1.86 , 2.06 , 3.84 , 4.47 , 3.37,5.40 ,5.45 , 4.34 ,2.64,2.14
sum of all observations = 2.22 + 1.51 + 1.86 + 2.06 + 3.84 + 4.47 + 3.37 + 5.40 + 5.45 + 4.34 + 2.64 + 2.14
sum of all observations = 38.94 inches
Total number of observations = total number of months
= 12
Mean monthly rainfall= [tex]\frac{sum of all observations }{total observations}[/tex]
=[tex]\frac{38.94}{12}[/tex]
=3.245
Mean monthly rainfall=3.245 inches.
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Refer to the attachment for the table.
A big pitcher holds 2 quarts of lemonade.
How many 6 ounce servings can you get from that?
Answer:
10 servings
Step-by-step explanation:
We Know
1 quart = 32 ounces
2 quarts = 64 ounces
How many 6-ounce servings can you get from that?
We Take
64 / 6 ≈ 10.67 servings
So you can serve 10 servings
PLEASE HELPPPPPP ME PLEASE
If the the a is greater than 1, compared to the parent function the C. Stretched vertically.
How to find the comparison ?The equation y = ax^2 + c represents a quadratic function where "a" is the coefficient of the x^2 term and "c" is a constant term. The parent function of this quadratic function is y = x^2.
If the equation of a quadratic function is given in the form y = ax^2 + c and "a" is greater than 1, then the graph of the function will be stretched vertically and the vertex will be shifted up or down depending on the value of "c".
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7+3{-1+5[2-(-9-7)4]+2
Answer:
1000
Step-by-step explanation: 7+3{-1+5[2-(-9-7)4]+2} can be simplified as follows:
First, we need to solve the innermost parentheses first: -9-7 = -16
So, 7+3{-1+5[2-(-16)4]+2} becomes 7+3{-1+5[2+64]+2}
Next, we need to solve the brackets: 2+64 = 66
So, 7+3{-1+5[66]+2} becomes 7+3{-1+330+2}
Now, we need to solve the innermost parentheses again: -1+330 = 329
So, 7+3{329+2} becomes 7+3*331
Finally, we need to multiply: 3*331 = 993
So, the final answer is 7+993 = 1000.
Therefore, the value of the given expression is 1000.
Write the equation in standard form for the circle with center (0,5) and radius 7.
Answer:
[tex]x^2+(y-5)^2=49[/tex]
Step-by-step explanation:
Recall the formula for the graph of a circle:
[tex](x-h)^2+(y-k)^2=r^2\\[/tex]
Where h is the x-coordinate of the vertex, k is the y-coordinate of the vertex, and r is the radius.
We are given the vertex and the length of the radius.
Substitute the values:
[tex](x-0)^2+(y-5)^2=7^2=\\x^2+(y-5)^2=49[/tex]
Thus, the standard form is:
[tex]x^2+(y-5)^2=49[/tex]
if it cost five dollars to buy thirty candy bars how much does it cost to buy one thousand candy bars
Answer:
166.666666.......
Step-by-step explanation:
30÷5=6
1000÷6=166.6666.......
the 6 is a repeating decimal
Which choice is NOT equal to the others? Responses A −[[2/5]]−[[2/5]] B [[2/−5]][[2/−5]] C [[−2/5]][[−2/5]] D [[2/5]]
Answer:
B is the answer
Step-by-step explanation:
The expression that is not equal to the others is B [[2/−5]] The other expressions are A −[[2/5]], C [[−2/5]], and D [[2/5]].
simplify [Xn (X'nY)]'.
Answer:
(X'U'Y) + (XUY')
Step-by-step explanation:
Starting with [Xn(X'nY)]', we can use De Morgan's laws to simplify the expression:
[Xn(X'nY)]' = (Xn)' + (X'nY)'
Recall that Xn represents the logical operator "and", while X' represents "not X". Using these definitions, we can expand the expression:
(Xn)' + (X'nY)' = (X'U'Y) + (XUY')
where U represents the logical operator "or".
Therefore, [Xn(X'nY)]' simplifies to (X'U'Y) + (XUY').
6 divided by what fraction gives us a quotient of 48?
A 1/6
B 1/9
C 48
D 1/8
Answer:
D 1/8
Step-by-step explanation:
48/6 = 8
Hence, the fraction must be 1/8
This is because when 6 is divided by 1/8,
6/(1/8)
= 6 * 8
= 48
Hence, the answer is D. 1/8
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Answer:
1/8
Step-by-step explanation:
6 ÷ x = 48
Multiply each side by x.
6 ÷ x *x = 48*x
6 = 48x
Divide each side by 48
6/48 = 48x/48
1/8 = x
y varies directly as the cube of x. when x= 4, then y= 7. find y when x=5
When X = 5, Y is approximately equal to 27.34.
What is proportion?
The size, number, or amount of one thing or group as compared to the size, number, or amount of another. The proportion of boys to girls in our class is three to one.
We are given that "Y varies directly as the cube of X", which can be written as:
Y = kX³
where k is a constant of proportionality. We need to find the value of k to solve for Y when X = 5.
Using the values given in the problem, we can write:
7 = k(4³)
Simplifying this equation, we get:
7 = 64k
Dividing both sides by 64, we get:
k = 7/64
Now that we know the value of k, we can solve for Y when X = 5:
Y = (7/64)(5³) = 27.34 (rounded to two decimal places)
Therefore, when X = 5, Y is approximately equal to 27.34.
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Kyd and North are playing a game. Kyd selects one card from a standard 52-card deck. If Kyd selects a face card (Jack, Queen, or King), North pays him $6. If Kyd selects any other type of card, he pays North $3.
Kyd's expected value is positive and North's expected value is negative, Kyd has the advantage in this game
What is expected value?
Expected value is a concept used in probability theory to describe the average value or outcome of a random variable over many trials. It is calculated by multiplying each possible outcome of a variable by its probability, and then summing all of the products. This can help to estimate the most likely outcome or value of an uncertain event or situation.
The probability of selecting a face card from a standard 52-card deck is 12/52 or 3/13. The probability of selecting any other type of card is 1 - 3/13 or 10/13.
Kyd's expected value for this game can be calculated as follows:
(3/13) x (-$3) + (10/13) x $6 = $3.38
Therefore, Kyd's expected value for this game is $3.38.
North's expected value for this game can also be calculated as follows:
(3/13) x $6 + (10/13) x (-$3) = -$0.92
Therefore, North's expected value for this game is -$0.92.
Since Kyd's expected value is positive and North's expected value is negative, Kyd has the advantage in this game.
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State any domain restrictions for the expression below from least to greatest (for example: -2,-1,0,1,2), by using one answer box for each domain restriction, then simplify the expression in the last answer box. (81-x²) (x² + 2x − 63) 2x² - 6x 3x2 30x + 63 3x 81x² ÷
The domain restrictions on the function [tex]\left f(x\right)=-\frac{3x}{81\:-\:x^2}\:\cdot \frac{81\:-\:x^2}{2x^2-6x}\:\div \frac{x^2+2x-6x}{3x^2-30x+63}[/tex] are the x values -9, 0, 3, 4 and 9
From the question, we have the following function that can be used in our computation:
[tex]\left f(x\right)=-\frac{3x}{81\:-\:x^2}\:\cdot \frac{81\:-\:x^2}{2x^2-6x}\:\div \frac{x^2+2x-6x}{3x^2-30x+63}[/tex]
Next, we set the denominator to 0 and solve for x
So, we have
81 - x²: x = ±9
2x² - 6x: x = 0 and x = 3
x² + 2x - 6x: x = 0 and x = 4
Hence, the domain restrictions are the x values -9, 0, 3, 4 and 9
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please help <3 gracias
The function evaluated in x = 2 is:
3f(2) =12
How to evaluate the function?Here we know that:
f(x) = x^2
And we want to evaluate the expression:
3f(2)
To do that replace x by 2.
3f(2) = 3*(2^2) = 3*4 = 12
That is the value of the expression.
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"The quotient of 30 and a number is decreased by 2." please help
This sentence relating to the quotient can be expressed mathematically as:
(30 / x) - 2
What is the explanation for the above response?
This sentence can be expressed mathematically as:
(30 / x) - 2
where x represents the unknown number.
The word "quotient" indicates that we are dividing 30 by the unknown number x. The phrase "is decreased by 2" means that we need to subtract 2 from the quotient.
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tanya has a dog leash that is 4 yards long. she shortens the leash by 6 feet.what is the lenght of shortened leash
Answer:
2 yards or 6 feet long
Step-by-step explanation:
Each yard is 3 feet long.
If Tanya shortens the leash by 6 feet, that is 2 yards.
4-2=2
The leash is 2 yards (or 6 feet) long.
Answer:
6 foot
Step-by-step explanation:
1 yards = 3 foot
4 yards = 12 foot
We take
12 - 6 = 6 foot
So, the length of the shortened least is 6 foot.