Kate has 6 more dimes than she has nickels. She has a total of $3.60. How many coins does she have in all?
Suppose that 16-ounce bags of chocolate chip cookies are produced with weights that follow a normal distribution with mean weight 16.1 ounces and standard deviation 0.1 ounce. for the distribution, approximately what percent of the bags will likely be underweight (that is, less than 16 ounces)?
To solve this we use the z statistic. The formula for z score is:
z = (x – u) / s
where x is the sample value = less than 16, u is the sample mean = 16.1, s is standard dev = 0.1
z = (16 – 16.1) / 0.1
z = - 1
From the standard distribution tables at z = - 1,
P (z = -1) = 0.1587
So about 15.87% is underweight.
To find the percentage of bags that will likely be underweight (less than 16 ounces), we need to find the area under the normal distribution curve to the left of 16 ounces. The probability is approximately 15.87%.
Explanation:To find the percentage of bags that will likely be underweight (less than 16 ounces), we need to find the area under the normal distribution curve to the left of 16 ounces. We can use a Z-table or a calculator to find this probability. First, we need to standardize the value of 16 ounces using the formula Z = (X - μ) / σ, where X is the given value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get Z = (16 - 16.1) / 0.1 = -1. This means that 16 ounces is 1 standard deviation below the mean.
Next, we can use the Z-table or a calculator to find the probability associated with a Z-score of -1. From the table or calculator, we find that the probability is approximately 0.1587 or 15.87%. Therefore, approximately 15.87% of the bags will likely be underweight (less than 16 ounces).
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Given the slope of 6 and a y-intercept of 2, write the equation in slope intercept form.
Answer:
The equation of the line would be y = 6x + 2
Step-by-step explanation:
Since we have a slope (6) and a point (0,2) we can use them in point slope form. The slope goes in for m and the point goes in for (x1, y1).
y - y1 = m(x - x1)
y - 2 = 6(x - 0)
y - 2 = 6x
y = 6x + 2
when constructing inscribed polygons and parallel lines how are the steps different
The area of a square boxing ring is 436 square feet. What is the approximate length, in feet, of one side of the boxing ring?
4ft
21ft
54ft
109ft
The area of the square is the square of the side thus the approximate length of the square will be 21 ft so option (B) will be correct.
What is a square?A square is a geometrical figure in which we have four sides each side must be equal and the angle between two adjacent sides must be 90 degrees.
Area of square = Side²
As per the given question,
The area of a square boxing ring is 436 square feet.
It is known that,
Area = Side²
Side² = 436
Take square root on both sides,
Side = √436 = 20.88 ≈ 21 ft
Hence "The area of the square is the square of the side thus the approximate length of the square will be 21 ft so option (B) will be correct".
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Please Help!!! :)
Ned currently has an account balance of $3,634.51. He opened the account 13 years ago with a deposit of $2,564.65. If the interest compounds twice a year, what is the interest rate on the account?
A. 4.7%
B. 5.4%
C. 2.7%
D. 1.4%
Leroy opened a savings account 18 years ago with a deposit of $2,651.43. The account has an interest rate of 2.8% compounded twice a year. How much interest has Leroy earned?
A. $4,373.68
B. $2,725.67
C. $4,358.69
D. $1,722.25
Compound interest formula is :
[tex]A=p(1+\frac{r}{n} )^{nt}[/tex]
1.
A = 3634.51
p = 2564.65
r = ?
n = 2
t = 13
Putting the values in formula, we get
[tex]3634.51=2564.65(1+\frac{r}{2} )^{2*13}[/tex]
=> [tex]3634.51=2564.65(1+\frac{r}{2} )^{26}[/tex]
=> [tex]\frac{3634.51}{2564.65}=(\frac{2+r}{2} )^{26}[/tex]
=> [tex]1.417=(\frac{2+r}{2} )^{26}[/tex]
We get [tex]\sqrt[26]{1.417}=\frac{2+r}{2}[/tex]
We get r = 0.02699 and r = -4.02699 (neglecting the negative value)
We get r = 0.027 (rounded)
And in percentage, it is 2.7%.
So, option C is the answer.
2.
p = 2651.43
r = 2.8% or 0.028
n = 2
t = 18
Putting the values in formula we get;
[tex]A=2651.43(1+\frac{0.028}{2} )^{2*18}[/tex]
=> [tex]A=2651.43(1.014)^{36}[/tex]
A = $4373.67
So, interest earned = [tex]4373.67-2651.43=1722.24[/tex] dollars
Hence, option D. $1,722.25 is the answer.
Lillian wants to buy a digital camera for $143.00. She baby-sits for $2.75 an hour. So far she has worked a total of 30 hours. How many more hours does she need to work to have enough to buy the camera?
A quadratic factor that cannot be factored further as a product of linear factors containing real numbers is said to be
Jamal is driving in Europe and finds that he has to drive 56 kilometers until he arrives at his destination. If 1 km = 0.62137 mi, about how many miles does Jamal have left on his journey?
2,) What is the solution of the system?
Use the substitution method.
y+6=4x
8x−2y=14
A) The only solution is (14, 12)
B)The only solution is (12, 14)
C)There are an infinite number of solutions.
D)There is no solution.
If ABC and DEF are supplementary, then ABC and DEF form a linear pair
The statement is true. If two angles are supplementary meaning their sum is 180 degrees, they form a linear pair because in a linear pair too, the sum of the two angles is 180 degrees.
Explanation:The question is related to the concept of angles in geometry. When angles are supplementary, it means that the sum of the two angles is 180 degrees. In a linear pair, two adjacent angles form a straight line, which also sums up to 180 degrees.
So, if angles ABC and DEF are supplementary, meaning ABC + DEF = 180 degrees, they indeed form a linear pair. Because in a linear pair too, the sum of the two angles is 180 degrees. Therefore, the statement 'If ABC and DEF are supplementary, then ABC and DEF form a linear pair' is true.
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The correct question is given below:
If ABC and DEF are supplementary, then ABC and DEF form a linear pair. True or False?
How many ways are there to distribute n distinct balls into r boxes (a box can contain any number of balls, ranging from zero (none) all the way to all n balls)?
What is the area of the polygon below
Write the expression 36+4 as a product using the greatest common factor and the distributive property.
The expression 36 + 4 can be written as a product using the greatest common factor and the distributive law is 4(9 + 1).
What are basic math properties?There are three basic math properties they are commutative property which states a + b = b + a, associative property which states
a + (b + c) = (a + b) + c and distributive property which states a(b+c) = ab + ac.
We know distributive property states a(b + c) = ab + ac.
Given 36 + 4, the here greatest common factor of 36 and 4 is 4.
∴ The expression 36 + 4 can be written as,
4(9 + 1).
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Identify the properties needed to prove n + n + n + 2n = 5n.
The properties needed to prove n + n + n + 2n = 5n are: Distributive Property of Multiplication, Associative Property of Addition, and Commutative Property of Addition.
What is Commutative Property of Addition?The commutative property of addition states that when two or more numbers are added, the order in which they are added does not affect the sum. In other words, for any two numbers a and b, a + b = b + a.
The properties required to prove n + n + n + 2n = 5n are as follows:
Distributive Property of Multiplication: This property states that a(b + c) = ab + ac. In this case, we can apply the distributive property to 2n, which gives us 2n = n + n.Associative Property of Addition: This property states that (a + b) + c = a + (b + c). We can use the associative property of addition to group the n's together and the 2n's together, which gives us (n + n + n) + (2n) = 5n.Commutative Property of Addition: This property states that a + b = b + a. We can use the commutative property of addition to rearrange the terms in the equation, which gives us (n + n + n + 2n) = (n + n + 2n + n) = 5n.Thus, these properties can be used.
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Final answer:
To prove n + n + n + 2n = 5n, we use the commutative and associative properties of addition to group and combine like terms, then apply the distributive property to show that the sum equals 5n.
Explanation:
To prove the equation n + n + n + 2n = 5n, we need to use properties of equality and algebraic manipulation. First, we apply the commutative property of addition, which allows us to rearrange the terms in any order without changing the sum.
This property isn't strictly necessary here, as all terms involve 'n', but it's a useful property in general for manipulating equations.
Next, we utilize the associative property of addition, which allows us to group numbers in any combination when adding. In this specific case, we group all the 'n' terms together:
(n + n + n) + 2n
Using the associative property, we can simplify the equation further by combining like terms:
3n + 2n = 5n
Lastly, we apply the distributive property, which in this case shows that multiplying the coefficient (being 1 for n in this example) by the number of times 'n' appears (3 for the first set and 2 for the second set), gives the same result as adding 'n' that many times.
−3x^ 4−7x+17=0
2
3
4
5
How many complex roots does the polynomial equation have?
(Show work if possible)
There are two complex roots of the polynomial equation.
What is a polynomial?They are mathematical expressions involving variables raised with nonnegative integers and coefficients and constants with only operations of addition, subtraction, multiplication, and nonnegative exponentiation of variables involved.
We have been given a polynomial expression as;
[tex]-3x^ 4-7x+17=0[/tex]
Since the Degree of a polynomial is the highest power that its terms (for multi-variables, the power of the term is the addition of the power of variables in that term).
Therefore, the highest power of the given polynomial is 4.
Thus, the Maximum possible roots are 4 but; only 2 are real and 2 are complex.
Hence, There are two complex roots of the polynomial equation.
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Given the function f(x) = 2(x + 6), find x if f(x) = 22. PLEASE ANSWER DONT PLAY I REPORT NO GAME PLAYING PLEASE
Answer:
The correct answer is 5
Step-by-step explanation:
Simplify 5x + 8y + 4x
A.17x
B.9x + 8y
C.5x + 12y
D.17xy
Simplify m - {n - [p + (m + n - p)]}.
0
2m
-2m + 2p
Answer:To simplify the following expression, we first simplify the terms inside the parenthesis from inner going outer. The first one is [p - (m + n - p)] equal to p - m- n + p = 2p - m - n. Then, n +2p - m - n equal to 2p -m. Then, m - 2p + m equal to 2m -2p. Answer is B
Step-by-step explanation:
If the area of a square room is 225 ft², what is the length of each side of the room? question 4 options: 56.25 ft 112.5 ft 15 ft 80 ft
The length of each side of the square room with an area 225 ft² is 15 ft.
What are the dimensions of a square?The area of a square is a product of it's any two sides or a product of diagonals divided by two. If side has a length a then diagonal is a√2.
The perimeter of a square is the sum of the lengths of all the sides.
Given, The area of a square room is 225 ft².
Assuming the length of each side is 'a' feet.
∴ The area of the square room is,
a×a = 225 ft².
a² = 225 ft².
a = ± 15 ft.
As length can not be negative +15 ft is the admissible value.
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3x + 2 = 14 which number makes the equation true?a)1b)2c)4d)6
Answer:
X=4
Step-by-step explanation:
3 * 4 = 12 + 2 = 14.That means your answer is C) 4.
Hope this helps! :')
Multiply. 3 ⋅ 3/5 whats the answer
Suzanne has a student loan balance of $25,904 with an average interest rate of 6.8 percent. Use the student loan repayment calculator (Links to an external site.)Links to an external site. to determine how much her monthly payment be if she selects the standard repayment option.
Since the problem is requiring us to use the loan repayment calculator and here is what the calculator gave:
Loan Balance: $25,506.00
Adjusted Loan Balance: $25,506.00
Loan Interest Rate: 6.80%
Loan Fees: 0.00%
Loan Term: 10 years
Minimum Payment: $0.00
Monthly Loan Payment: $293.52
Number of Payments: 120 months
Cumulative Payments: $35,223.07
Total Interest Paid: $9,717.07
It is projected that you will need an annual salary of a minimum $35,222.40 to be capable to have enough money to repay this loan. This approximation assumes that 10% of your gross monthly income will be keen to repaying your student loans. This resembles to a debt-to-income ratio of 0.7. If you use 15% of your gross monthly income to repay the loan, you will need an annual salary of only $23,481.60, but you may experience some financial difficulty. This corresponds to a debt-to-income ratio of 1.1.
Find the critical numbers of the function f(x) = x6(x − 1)5 what does the first derivative test tell you that the second derivative test does not?
The critical numbers of [tex]\( f(x) = x^6 (x-1)^5 \)[/tex] are [tex]\( x = 0, 1, \frac{5}{6} \)[/tex]. The first derivative test determines maxima/minima by sign change, while the second derivative test confirms concavity but not explicit categorization.
1. Calculate the first derivative [tex]\( f'(x) \)[/tex]:
Use the product rule and simplify:
[tex]\[ f(x) = x^6 (x-1)^5 \] \[ f'(x) = 6x^5 (x-1)^5 + x^6 \cdot 5(x-1)^4 \] \[ f'(x) = 6x^5 (x-1)^4 [x + 5(x-1)] \] \[ f'(x) = 6x^5 (x-1)^4 (6x - 5) \][/tex]
2. Find critical points:
Critical points occur where [tex]\( f'(x) = 0 \)[/tex] or is undefined.
Set [tex]\( f'(x) = 0 \)[/tex]:
[tex]\[ 6x^5 (x-1)^4 (6x - 5) = 0 \][/tex]
This equation is zero when:
[tex]\( 6x^5 = 0 \) -- \( x = 0 \)\\ \( (x-1)^4 = 0 \) -- \( x = 1 \)\\ \( 6x - 5 = 0 \) -- \( x = \frac{5}{6} \)[/tex]
So, the critical numbers are [tex]\( x = 0, 1, \frac{5}{6} \)[/tex].
3. First Derivative Test vs. Second Derivative Test:
- First Derivative Test: This test uses the sign of the derivative ( f'(x) ) to determine the nature of critical points:
- If [tex]\( f'(x) > 0 \) to \( f'(x) < 0 \)[/tex] at x, then ( f(x) ) has a local maximum at x.
- If [tex]\( f'(x) < 0 \) to \( f'(x) > 0 \)[/tex] at x, then ( f(x) ) has a local minimum at x.
- Second Derivative Test: This test uses the sign of the second derivative [tex]\( f''(x) \)[/tex]:
- If [tex]\( f''(x) > 0 \), \( f(x) \)[/tex] has a local minimum at x.
- If [tex]\( f''(x) < 0 \), \( f(x) \)[/tex] has a local maximum at x.
4. Difference between the tests:
- The first derivative test provides information about the nature (whether maximum or minimum) of critical points based on the sign change of the derivative.
- The second derivative test provides more precise information by confirming the concavity of the function around the critical point, but it does not give explicit information about whether the critical point is a maximum or minimum (it only confirms the direction of concavity).
A color printer prints 15 pages in 8 minutes. how many pages does it print per minute
Write the equation of a line given two points kuta
factor the trinomial x^2 - 3x - 40
(x-5)(x+8)
(x+5)(x-8)
(x+5)(x+8)
(x-5)(x-8)
The answer is (x+5)(x-8)
What is the square root of sixty four
The lines described by y = (a + 12)x + 3 and y = 4ax are parallel. what is the value of a
The lines are parallel if and only if the values of their slopes are equal. In a standard form of the equation of the line, the slope is the numerical coefficient of x. Given this condition, we determine the value of a by equation a + 12 and 4a.
Slope = a + 12 = 4a
The value of a from the equation is 4.
Answer: 4
What is the mean of the set of numbers?
-11, 22, -2, -3
add all the numbers and then divide by how many there are in the set to find the mean so
-11+22+-2+-3=6
6÷4=1.5
so 1.5 would be the mean
Hope this helps!