The evaluated values,
(1) 0.38 × 10³ = 380
(2) 0.38 × 100,000 = 38000
(3) 0.38 × 10 = 3.8
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given:
Three expressions are,
0.38 × 10³
0.38 × 100,000
0.38 × 10
Solving,
(1) 0.38 × 10³ = 0.38 x 1000 = 380
(2) 0.38 × 100,000 = 38000
(3) 0.38 × 10 = 3.8
Therefore, the evaluations are given above.
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24. Area of a Triangle = ½ Base x Height.
SAIL BOATS Tamara requests a
custom-made sail for her sailboat. The
base of her triangular sail is 2x + 1 and
the height is 4x + 6.
4x+6
2x+1
Find the area of the sail.
The area of sail is equivalent to (4x + 8x + 3) square units.
What is the area of a triangle?The area of a triangle is given as -
[tex]$A_{T} =\frac{1}{2} \times b \times h[/tex]
Given is a sail whose base is (2x + 1) units and height is (4x + 6) units.
We can write the area of sail as -
A = 1/2 x b x h
A = 1/2 x (2x + 1) x (4x + 6)
A = (2x + 1)(2x + 3)
A = 2x(2x + 3) + 1(2x + 3)
A = 3 + 2x + 6x + 4x²
A = 4x² + 8x + 3
Therefore, the area of sail is equivalent to (4x² + 8x + 3) square units.
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suppose that f(x), g(x), and h(x) are functions such that f(x) is o(g(x)) and g(x) is o(h(x)). show that f(x) is o(h(x)).
If f(x), g(x), and h(x) are functions such that f(x) is θ(g(x)) and g(x) is θ(h(x)), it is shown that f(x) is θ(h(x)).
Since f(x) is θ(g(x)), there exist constants A, B > 0 such that
A × g(x) < f(x) < B × g(x) for sufficiently large x.
Similarly, since g(x) is θ(h(x)), there exist constants C, D > 0 such that
C × h(x) < g(x) < D × h(x) for sufficiently large x.
Hence, for a sufficiently large x, we have
f(x) < B g(x) < B × (D × h(x)) = (BD) h(x), and
f(x) > A g(x) > A × (C × h(x)) = (AC) h(x).
Hence, we have constants E, F > 0 (where E = AC and F = BD) such that
E × h(x) < f(x) < F × h(x) for sufficiently large x.
Therefore, f(x) is θ(h(x)).
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Question 15 of 15 Select the equation and solution for this situation. 14 less than a number is 22. O A. x+ 14 = 22 x = 8 OB. X-14 = 22 X = 36 O C. X-14 = 22 X = 8 O D. x + 14 = 22 x = 36 QUICK DUE TODAY
The solution to the equation x - 14 = 22 is x = 36
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators like addition, subtraction, multiplication and division. Equations can be linear, quadratic.
Let x represent the number. 14 less than a number is 22, hence:
x - 14 = 22
Add 14 to both sides of the equation:
x - 14 + 14 = 22 + 14
x = 36
The solution to the equation is x = 36
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the following data has been recorded regarding the rental history of a high pressure cleaner. find the expected demand for the high pressure cleaner. demand frequency 0 20 1 23 2 27 3 14 4 16
The expected demand for the high-pressure cleaner is 1.86.
Frequency distribution is a statistical tool that organizes data into different categories and shows how often each category occurs. In this case, the demand for a high-pressure cleaner is the category, and the number of times it occurs is the frequency.
To calculate the expected demand, we need to first find the relative frequency of each demand level. The relative frequency is the percentage of the total number of demands accounted for by each demand level. We can calculate the relative frequency by dividing the frequency of each demand level by the total number of demands.
Total number of demands = 20 + 23 + 27 + 14 + 16 = 100
Relative frequency of demand level 0 = 20/100 = 0.20
Relative frequency of demand level 1 = 23/100 = 0.23
Relative frequency of demand level 2 = 27/100 = 0.27
Relative frequency of demand level 3 = 14/100 = 0.14
Relative frequency of demand level 4 = 16/100 = 0.16
Next, we multiply each demand level by its relative frequency and add the products to get the expected demand.
Expected demand = (0 × 0.20) + (1 × 0.23) + (2 × 0.27) + (3 × 0.14) + (4 × 0.16)
=> 1.86
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Complete Question:
The following data has been recorded regarding the rental history of a high pressure cleaner. Find the expected demand for the high pressure cleaner.
Demand Frequency
0 20
1 23
2 27
3 14
4 16
There are 12 inches in 1 foot. Which of the following conversion factors express this relationship correctly? Select all that apply Check all that apply. a.12 in /1 ft b. 1 in x 12 ft c. 1 ft /12 in d.1/ 1 in x 12 ft
The relationship exhibiting conversion factor correctly is the option c. 1 ft /12 in, where ft is foot and in is inches.
As per the mentioned information, the relationship will be expressed as -
12 inches = 1 foot
So, now we will use unitary method to find 1 inches, which will be the conversion factor.
Now, the formula for conversion factor (that is one unit of inches) will be = number of unit in foot/number of unit in inches
Conversion factor = 1/12
Based on this, the correct option indicating conversion factor is c. 1 ft /12 in.
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Find the value of the constant that makes the following function continuous on (−∞,∞).
The piecewise function is continuous only if a = 2.
Which must be the value of the constant a?The function will be continuous if both parts of the function have the same value on the "jump" between the two parts.
The first part evaluated in x = 1 is:
f(x) = (4x^3 - 4x)/(x - 1)
We can rewrite the numerator as:
(4x^3 - 4x) = 4x*(x^2 - 1) = 4x*(x + 1)*(x - 1)
Then we can rewrite the function as:
f(x) = 4x*(x + 1)
Evaluating in x = 1 we will get:
f(1) = 4*1*(1 + 1) = 8
Then the other piece evaluated in x = 1 also must be equal to 8, we will get:
f(x) = 4x^2 + 2x + a
f(1) = 4*1^2 + 2*1 + a = 8
= 4 + 2 + a = 8
a = 8 - 4 - 2 = 2
The value of a must be 2.
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Tricia deposits $1500 into a savings account that pays 1.2% annual interest compounded quarterly. Write a function to represent the balance A in the account after t years. B. What will be the balance after 3 years C. What will be the balance after 6 years
A. The function to represent the balance in the account after t years is:
[tex]A = 1500(1 + (0.012 / 4))^{(4t)}[/tex]
B. The balance in the account after 3 years will be $1566.66.
C. The balance in the account after 6 years will be $1639.98.
What is Compound interest?Compound interest is defined as interest paid on the original principal and the interest earned on the interest of the principal.
A = P(1+r/100)ⁿ
A. The function to represent the balance in the account after t years can be represented as:
[tex]A = 1500(1 + (0.012 / 4))^{(4t)}[/tex]
where A is the balance in the account after t years, 1500 is the initial deposit, 0.012 is the annual interest rate as a decimal, 4 is the number of compounding periods per year, and (0.012 / 4) is the interest rate per compounding period.
B. To find the balance after 3 years:
A = 1500(1 + (0.012 / 4))⁴ˣ³ = 1500 (1 + (0.012 / 4))¹²
A = 1500 × 1.0444
A = 1566.66
So, the balance in the account after 3 years will be $1566.66.
C. To find the balance after 6 years:
A = 1500 (1 + (0.012 / 4))⁴ˣ⁶ = 1500 * (1 + (0.012 / 4))²⁴
A = 1500 × 1.0932
A = 1639.98
So, the balance in the account after 6 years will be $1639.98.
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Each unit on the map represents 1 mile. To the nearest tenth of a mile, what is the distance from the library to the park?
Answer:
Step-by-step explanation:
If you are using both y & x they are easy to find
distance from 9 and 2 is seven units and the distance from each other
3 & 2 are one unit hoped it helped you so you can find the miles
Is y + 2x = 9 consistent or inconsistent
Yes, the given equation y + 2x = 9 is consistent.
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The equation y + 2x = 9 is a linear equation in two variables, x and y.
Now let us solve for y
y=-2x+9
We plot this equation graphically.
This equation represents a line with slope -2 and y-intercept 9.
So the graph of this equation is a straight line that passes through the point (0, 9) and has a slope of -2.
To determine if the equation y + 2x = 9 is consistent or inconsistent, we need to know if there exists at least one pair of values (x, y) that satisfy the equation.
We can see from the graph that there are infinitely many points on the line y + 2x = 9.
Hence, the given equation y + 2x = 9 is consistent.
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A committee must be formed with 5 teachers and 4 students. If there are 11 teachers to choose from, and 14 students, how many different ways could the committee be made?
Answer:
there are 462,462 different ways the committee can be formed.
Step-by-step explanation:
To form the committee, we need to choose 5 teachers out of 11 and 4 students out of 14. We can use the combination formula to find the number of ways:
Number of ways to choose 5 teachers out of 11:
C(11, 5) = 11! / (5! * 6!) = 462
Number of ways to choose 4 students out of 14:
C(14, 4) = 14! / (4! * 10!) = 1001
The total number of ways to form the committee is the product of these two combinations:
462 * 1001 = 462462
Therefore, there are 462,462 different ways the committee can be formed.
A plane is 107 mi north and 172 mi east of an airport. Find x, the angle the pilot should turn in order to fly directly to the airport. Round your answer to the
nearest tenth of a degree.
The pilot should turn approximately 50.7° to fly directly to the airport.
How to find the angle the pilot should turnThe problem can be solved using trigonometry.
Let x be the angle the pilot should turn in order to fly directly to the airport.
Then, we have:
tan(x) = 107 / 172
x = arc tan^-1(107 / 172)
x = 50.7 degrees
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A binomial experiment consists of 12 trials. The probability of success on trial 5 is 0.85. What is the probability of failure on trial 9?
0.17
0.72
0.64
0.9
0.15
0.44
The probability of failure on the trial 9 for the given binomial experiment is 0.15.
What is binomial experiment?An experiment with a set number of independent trials and just two results is referred to as a binomial experiment. The results of these experiments can be classified as either successes or failures. Due to the nature of the experiment's subject, results may only be categorised as successes or failures.
Due to the set number of outcomes that might occur in each experiment's trial, binomial experiments are unique from other types of studies. Binomial experiments, in particular, can only ever produce one of two outcomes.
The probability of success and failure of a trial is same for every number of trials.
Given that,
n = 12 trials
Success = 0.85
The failure is given as:
failure = 1 - success of trial
failure = 1 - 0.85
failure = 0.15
Hence, the probability of failure on the trial 9 for the given binomial experiment is 0.15.
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Kristen gets home from work at 5:34p.m. Kristen's dinner is ready at 5:15 p.m
How many seconds after Kristen gets home is her dinner ready?
After 1020 sec Kristen get her Dinner ready.
What is Unit Conversion?The same attribute is expressed using a unit conversion, but in a different unit of measurement.
For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.
Subtract Kristen's arrival time from the time her food is ready to get the number of seconds she needs to wait before eating.
So,
5 :51 pm - 5: 34 pm = 17 min
As, 1 minute = 60 minute
So, 17 minutes
= 17(60)
= 1020 sec
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Describe the functions on the sections of the graph labeled on the coordinate plane below. Explanation too
Sections A, B, C, and D represent parabolic, linear with a positive slope, linear with a negative slope, and parabolic function, respectively.
What is a function?A function is a statement, conception, or regulation that establishes an association between two parameters. Functions may be found throughout mathematics and are essential for the development of significant links.
The straight line represents the linear function.
As 'x' increases, the value of 'y' also increases, then the slope of the line function is positive.As 'x' increases, the value of 'y' also decreases, then the slope of the line function is negative.The curve represents the parabolic function.
Sections A, B, C, and D represent parabolic, linear with a positive slope, linear with a negative slope, and parabolic function, respectively.
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The length of a rectangular poster is 4 more inches than three times its width. The area of the poster is 340 square inches. Solve for the dimensions (length and width) of the poster.
31 in by 31/4 in is the required dimension of the poster
Determining the area of a rectangleThe formula for calculating the area of a rectangle is expressed as:
A = lw
If the length of a rectangular poster is 4 more inches than three times its width, then;
l = 3w - 4
Substitute
340 = w(3w - 4)
340 = 3w^2 - 4w
3w^2 - 4w - 340 =0
On factorizing, the measure of the width of the poster is 34/3 in
l = 3w - 4
l = 3(34/3) - 4
l = 31in
Hence the dimension of the given poster is 31 in by 31/4 in
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||
Initial Knowledge Check
Simplify.
(4w)²
Write your answer without parentheses.
01
6
X
Ś
The expression is 16w².
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
(4w)²
This can be expressed as,
= 4² x w²
[ 4 x 4 = 16 ]
= 16 x w²
= 16w²
Thus,
The expression is 16w².
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Please explain your answer. Will mark Brainliest (question 9)
The initial investment of the function is 20 dollars.
The rate growth in percentage is 4%.
The investment after 10 years is 29.6 dollars.
How to solve function?The function [tex]y=20(1.04)^{t}[/tex] represents the value y of a saving account after t years.
Therefore, the initial investment of the function is 20 dollars.
The rate growth in percentage can be calculated as follows;
rate growth in percent = 0.04 × 100
rate growth in percent = 4 %
Let's find the value of the investment after 10 years.
Therefore,
[tex]y=20(1.04)^{t}[/tex]
t = 10
[tex]y=20(1.04)^{10}[/tex]
[tex]y=20(1.48024428492)[/tex]
y = 29.6048856984
Therefore, the investment after 10 years is as follows:
y = 29.6 dollars
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can someone help please
The degree of the polynomial is 5 and the maximum number of real zeroes in the polynomial is 5.
What are polynomials?
A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminate in mathematics.
f(x) = 6x⁵ - 3x⁴ + 5x² + 4
According to the fundamental theorem of algebra, the polynomial with n number of degrees will have n number of zeroes and no more, so the zeroes will be the same here 5.
Therefore, The polynomial has a degree of 5, and it can have a maximum of five real zeroes.
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Adam tried to write 4 + 5x² +4 as a product of linear factors. This is his work:
2*+5 +4
= (x² + 4)(x² + 1)
= (x² + 4)(x + i)(x − i)
= (x+i√2)(x − i√2)(x+i)(x-i) Step 3
In what step did Adam make his first mistake?
Adam makes his first mistake in the first step. And the product of linear factors will be (√5x - 2i √2) and (√5x + 2i√2).
What is factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The expression is given below.
⇒ 4 + 5x² + 4
Simplify the expression, then we have
⇒ 5x² + 8
Factorize the expression, then we have
⇒ 5x² + 8
⇒ (x√5)² - (2i √2)²
⇒ (√5x - 2i √2) (√5x + 2i√2)
Adam makes his first mistake in the first step. And the product of linear factors will be (√5x - 2i √2) and (√5x + 2i√2).
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Referring to the Fig. in Question #23, find the cosine of angle S. Reduce the answer to the lowest terms.
The cosine of angle S is 4/5.
Describe Cosine?In mathematics, cosine is a trigonometric function that relates the angles of a right-angled triangle to the ratio of the length of its adjacent side to its hypotenuse.
More formally, cosine of an angle is defined as the ratio of the length of the adjacent side to the hypotenuse of a right-angled triangle containing that angle.
The cosine of an angle theta, denoted as cos(theta), is given by the formula:
cos(theta) = adjacent side / hypotenuse
The cosine function has a range of values between -1 and 1, and is periodic with a period of 2π radians or 360 degrees.
The ratio of the neighboring side to the hypotenuse is known as the cosine of an acute angle in a right triangle.
In triangle RST, the hypotenuse is RS = 10 and the adjacent side to angle S is ST = 8.
Therefore, the cosine of angle S is:
cos(S) = adjacent/hypotenuse = ST/RS = 8/10
To simplify this fraction to lowest terms, we can divide both the numerator and denominator by their greatest common factor, which is 2.
8/10 = (8/2)/(10/2) = 4/5
So, the cosine of angle S is 4/5.
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Assessment Practice
14. Write the unit fraction that represents 1 square.
Then write the fraction that represents the
whole. Select numbers from the box to write
the fractions. Numbers may be used once, more than
once, or not at all. 3.FR.1.1
12 3 4 5 6 7 8
1 square:
Whole:
The unit fraction is given by A = 2/2 and the whole number is represented by B = 4/2 = 2
What is a Fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Given data ,
Let the first fraction be represented as A
Now , the unit fraction is a fraction which has the value of 1
And , the numbers are represented by set S = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 }
The unit fraction A = 1/1 = 2/2 = 3/3
Let the whole fraction be represented as B
Now , the value of B is
B = 4/2 = 2
B = 6/3 = 2
Therefore , the value of A and B are 1/1 and 4/2 respectively
Hence , the fractions are solved
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1 a tobacco company produces blends of tobacco, with each blend containing various proportions of turkish, domestic, and other tobaccos. the proportions of turkish and domestic in a blend are random variables with joint density function (x
(a) 0.5, (b) f_Y(y) = 12y(1-y), (c) 9/128, (d) 7/36 - Probability calculations using joint density function.
(a) To find the Probability that the Turkish tobacco represents over a portion of the mix, we want to incorporate the joint thickness capability over the district where x > 0.5 and y < 1 - x. This gives:
P(X > 0.5) = ∫[0.5,1]∫[0,1-x] 24xy dy dx = 0.5
Consequently, the Probability that the Turkish tobacco represents over around 50% of the mix is 0.5.
(b) To find the negligible thickness capability for the extent of homegrown tobacco, we really want to incorporate the joint thickness capability over all potential upsides of Turkish tobacco:
f_Y(y) = ∫[0,1-y] 24xy dx = 12y(1-y) ; 0 < y < 1
Thusly, the peripheral thickness capability for the extent of homegrown tobacco is f_Y(y) = 12y(1-y).
(c) To find the Probability that the extent of Turkish tobacco is under 1/8 given that the mix contains 3/4 homegrown tobacco, we really want to utilize Bayes' standard:
P(X < 1/8 | Y = 3/4) = P(X < 1/8 ∩ Y = 3/4)/P(Y = 3/4)
We can find the numerator by coordinating the joint thickness capability over the district where x < 1/8 and y = 3/4:
∫[0,1/8] 24xy dx = 27/128
To find the denominator, we coordinate the joint thickness capability over all potential upsides of Turkish tobacco when y = 3/4:
∫[0,1/4] 24xy dx = 3
Thusly, the contingent Probability is:
P(X < 1/8 | Y = 3/4) = (27/128)/3 = 9/128
(d) To find the likelihood that the extent of homegrown tobacco is over two times the extent of the Turkish tobacco, we want to incorporate the joint thickness capability over the area where y > 2x and x + y < 1. This gives:
P(Y > 2X) = ∫[0,1/3]∫[2x,1-x] 24xy dy dx + ∫[1/3,1/2]∫[2x,1-x] 24xy dy dx
= 7/36
Accordingly, the likelihood that the extent of homegrown tobacco is over two times the extent of the Turkish tobacco is 7/36
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The complete question is:
A tobacco company produces blends of tobacco, with each blend containing various proportions of Turkish, domestic, and other tobaccos. The proportions of Turkish and domestic in a blend are random variables with joint density function (X = Turkish and Y = domestic) 24xy ;0< x, y < 1, x +y<1 fx.y(1,7) (2) ; otherwise (a) (1 point) Find the probability that in a given box the Turkish tobacco accounts for over half the blend. Page 2 (b) (1 point) Find the marginal density function for the proportion of the domestic tobacco. (c) (1 point) Find the probability that the proportion of Turkish tobacco is less than 1/8 if it is known that the blend contains 3/4 domestic tobacco. (d) (2 points) Find the probability that the proportion of domestic tobacco is more than twice the proportion of the Turkish tobacco.
A programmer erroneously wrote an expression as: 0 < x < 10. Rewrite the expression using logical AND. Use parentheses. (x > 0)
A programmer erroneously wrote an expression as 0 < x < 10. This expression 0 < x < 10 can be rewritten using logical AND as (0 < x) AND (x < 10).
The expression 0 < x < 10 is commonly used to indicate that x is a value between 0 and 10, but it is not correct in programming. In programming, logical operations like "less than" and "greater than" are usually represented by < and > symbols, respectively.
To properly express the condition that x is between 0 and 10, we need to use the logical operator AND, which allows us to combine multiple conditions.
The logical AND operator in programming is typically represented by the symbol && or the word "AND". It evaluates to true if and only if both of the conditions on either side of the operator are true. If either condition is false, the whole expression is false.
To rewrite the expression 0 < x < 10 using logical AND, we first separate the conditions into two separate expressions:
x > 0 AND x < 10
which can be written as,
(0 < x) AND (x < 10).
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16 Answer:
For what values of the variable x is the rational
expression undefined: 3/(x - 5)
17 Answer:
For what values of the variable x is the rational
expression undefined: 8/(x + 2)
Answer:
16. The rational expression 3/(x-5) is undefined when x equals 5.
17. The rational expression 8/(x+2) is undefined when x equals -2.
Step-by-step explanation:
16.
The rational expression 3/(x-5) is undefined when the denominator (x-5) is equal to zero, because division by zero is undefined. Therefore, we need to find the values of x that make the denominator zero.
To find those values, we can set the denominator equal to zero and solve for x:
x - 5 = 0
x = 5
Therefore, the rational expression 3/(x-5) is undefined when x equals 5.
17.
The rational expression 8/(x+2) is undefined when the denominator (x+2) is equal to zero, because division by zero is undefined. Therefore, we need to find the values of x that make the denominator zero.
To find those values, we can set the denominator equal to zero and solve for x:
x + 2 = 0
x = -2
Therefore, the rational expression 8/(x+2) is undefined when x equals -2.
Which figure repeats in the tessellation shown below?
• A. Figure B
• B. Figure C
• C. Figure A
• D. Figure D
The figure repeats in the tessellation is Figure B, the correct option is A
What is a regular tessellation?
A regular tessellation is a pattern made by repeating a regular polygon. In simpler words regular tessellations are made up entirely of congruent regular polygons all meeting vertex to vertex.
How many regular tessellation are possible?
There are only 3 regular tessellation.
1. Triangle
2. Square
3. Hexagon
Given;
The figure
Not more than 3 regular tessellations are possible because the sums of the interior angles are either greater than or less than 360 degrees;
Therefore, repeated tessellation will be B.
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Help
An art class is making a mural for their school which has a triangle drawn in the middle. The length of the bottom
of the triangle is x. Another side is 11 more than four times the length of the bottom of the triangle. The last side is 6 more
than the bottom of the triangle. Write and simplify an expression for the perimeter of the triangle.
What is the expression for the perimeter of the triangle?
The expression for the perimeter of the triangle 6x+17.
What is perimeter?Perimeter the sum of length of the sides used to made the given figure. A regular figure with n-sides has n equal sides in it, and they are the only parts of it(that means, nothing more than those equal lengthened n sides).
We have Given the length of the bottom of the triangle = x.
Since other side is 11 more than four times the length of the bottom of the triangle.
Also we have last side is 6 more than the bottom of the triangle.
Now, the sides of triangle;
x, 4x+11, x+6
Perimeter is the sum of lengths of all sides of figure.
x+ 4x+11+ x+6
=6x+17
Therefore, the perimeter expression will be 6x+17.
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A credit card has a balance of $3,400. The APR is 27% and the minimum payment is 3% of the balance. You will pay the minimum balance this month. If you do not use the card again then how much should the balance be next month?
The minimum payment for this month would be:
minimum payment = 3% of $3,400 = 0.03 x $3,400 = $102
The interest charged on the remaining balance after the minimum payment is made can be calculated as:
interest = APR/12 x remaining balance
where APR is the annual percentage rate and the division by 12 is to convert it to a monthly rate.
So for this month, the interest charged would be:
interest = 0.27/12 x $3,298 = $74.32
where $3,298 is the remaining balance after the minimum payment is made.
Therefore, the balance next month would be:
balance = previous balance - payment + interest
balance = $3,400 - $102 + $74.32 = $3,372.32
So the balance next month should be $3,372.32 if you only make the minimum payment and do not use the card again.
the national average for mathematics on a standardized test in 2011 was 516. suppose that the distribution of scores was approximately bell-shaped and that the standard deviation was approximately 43. round your answers to at least one decimal place as needed.
The rounded answer is that approximately 68% of scores were between 473 and 559.
To calculate this, we can use the formula for a normal distribution: P(μ−σ < X < μ+σ) = 68%, where μ is the mean and σ is the standard deviation.
For our problem, our mean is 516 and our standard deviation is 43. Therefore, our equation becomes P(473 < X < 559) = 68%. This means that 68% of scores were between 473 and 559, which is our answer.
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What is the range of the relation in the table below?
-2
-1
0
1
2
A right, isosceles triangle has hypotenuse length 50cm. How long are the two legs?
The length of the two legs is 25√2 cm
How to determine the length of the two legs?From the question, we have the following parameters that can be used in our computation:
A right, isosceles triangle has hypotenuse length 50cm
Represen the length of each leg with x
Using the above definition as a guide, we have the following:
x = Hypotenuse/√2
So, we have
x = 50/√2
This gives
x = 25√2
HEnce, the legs are 25√2 cm each
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