To solve −3.64⋅|−5.3|−1.53, calculate the absolute value of −5.3, which is 5.3, then multiply by −3.64 to get −19.292, and finally, subtract 1.53 to result in −20.822.
Explanation:You have presented a mathematical expression involving absolute value and multiplication: −3.64⋅|−5.3|−1.53. Let's solve this step by step:
First, determine the absolute value of −5.3, which is 5.3 because absolute value represents the distance of a number from zero without considering direction.Next, multiply −3.64 by the absolute value you just calculated: −3.64 * 5.3.Once you have the result of that multiplication, subtract 1.53 from it to get the final answer.
Now performing the operations:
−3.64 * 5.3 = −19.292−19.292 - 1.53 = −20.822Therefore, the result of the given expression −3.64⋅|−5.3|−1.53 is −20.822.
Find the banker's interest to the nearest cent. Principal: $2,500; Rate: 9%; Time: 180 days: Interest: ? (based on a 365 day year).
Final answer:
The banker's interest rounded to the nearest cent is approximately $110.60.
Explanation:
To calculate the banker's interest on a principal of $2,500 at a rate of 9% for 180 days, you would apply the formula for simple interest:
Interest = Principal × rate × time
Since time needs to be expressed in years and the rate as a decimal, convert 180 days into a fraction of a year by dividing by 365:
Time (in years) = 180 / 365 ≈ 0.4932
Convert the rate to a decimal:
Rate (as a decimal) = 9% = 0.09
Now calculate the interest:
Interest = $2,500 × 0.09 × 0.4932 ≈ $110.595
Thus, the banker's interest rounded to the nearest cent is approximately $110.60.
what are two functions, f(x) and g(x), that would result in a rational function?
find the difference of the least common multiple and the greatest common factor of 12 and 32 show your work please
How many sequences of length 5 can be made when each component of the sequence can take 3 different values?
John always wears a shirt, pants, socks, and shoes. He owns 12 pairs of socks, 3 pairs of shoes, 5 pairs of pants, and 5 shirts. How many different outfits can John make?
Answer:
900
Step-by-step explanation:
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Use signed numbers to solve. A helicopter descended 1200 feet, rose 800 feet, and then descended 450 feet. What was the net gain or loss in altitude? A. lost 2450 ft B. lost 850 ft C. gained 850 ft D. gained 2450 ft
Kens turtle competed in a 0.50- meter race. His turtle had traveled 49/100 meter when the winning turtle crossed the finish line. What is 49/100 written as a decimal
Well, to make it simple it's 0.49. Hope it helps!
Janet makes homemade dolls. Currently, she produces 23 dolls per month. If she increased her production by 18%, how many dolls would Janet produce each month?
Complete the factorization of 3x2 – 5x + 2.
Which two factors can be multiplied together to make this trinomial?
(x – 2)
(x – 1)
(x + 1)
(3x – 2)
(3x + 2)
the answers are (x-1) and (3x-2)
Faelyn grouped the terms and factored the GCF out of the groups of the polynomial 6x4 – 8x2 + 3x2 + 4. Her work is shown.
Step 1: (6x4 – 8x2) + (3x2 + 4)
Step 2: 2x2(3x2 – 4) + 1(3x2 + 4)
Faelyn noticed that she does not have a common factor. Which accurately describes what Faelyn should do next?
Faelyn should realize that her work shows that the polynomial is prime.
Faelyn should go back and regroup the terms in Step 1 as (6x4 + 3x2) – (8x2 + 4).
In Step 2, Faelyn should factor only 2x out of the first expression.
Falyn should factor out a negative from one of the groups so the binomials will be the same.
Answer:
Faelyn should realize that her work shows that the polynomial is prime.
Explanation:
The only difference between her factors in Step 2 is that the 4 in the first group is negative, while the 4 in the second group is positive.
Rearranging the polynomial to factor it will not change the end result.
Factoring out a negative will make not only one, but both terms, in one of the binomials the opposite sign; this will not make the factors the same.
Factoring only 2x out of the first group will result in having (3x³+4x); this is not the same either.
She should realize that when this happens, her polynomial is prime.
The precision of what Faelyn should do is that Faelyn should realize that her work shows that the polynomial is prime. Hence, the option A is the correct option.
How to find the factors of polynomial?Factors of the polynomial which are multiplied to produce the original polynomial.
The polynomial which can not be factored is known as prime polynomial.
The standard form of the polynomial with highest power of 2 can be given as,
Given information-
The given polynomial equitation in the problem is,
[tex]6x^4 -8x^2 + 3x^2 + 4[/tex]
1) First step of Faelyn is[tex](6x^4- 8x^2) + (3x^2 + 4)[/tex]
2) Second step of Faelyn is[tex]2x^2(3x^2 - 4) + 1(3x^2 + 4)[/tex]
Faelyn noticed that she does not have a common factor. The polynomial which can not be factored is known as prime polynomial.
Thus Faelyn should realize that her work shows that the polynomial is prime. Hence, the option A is the correct option.
Learn more about the polynomial equation here;
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A moving company charges $0.60 per pound for a move from New York to Florida. A family estimates that their belongings weigh about 6 tons. About how much would it cost the family to move from New York to Florida?
Brooke earns $7 an hour at her job now. She can represent the total she makes in a week using the expression 7r. Brooke has asked for a $1 an hour raise. Which expressing would represent the amount Brooke would make in a week after the raise?
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Find the equation of the plane in xyzxyz-space through the point p=(5,5,3)p=(5,5,3) and perpendicular to the vector n=(1,2,5)
The equation of the plane in xyz-space that passes through the point p=(5,5,3) and is perpendicular to the vector n=(1,2,5) is x + 2y + 5z = 30.
Explanation:In mathematics, the equation of the plane can be found using the plane equation Ax + By + Cz = D. Given that the plane goes through point p=(5,5,3) and is perpendicular to vector n=(1,2,5). The vector n actually gives us the coefficients A, B, and C. Meaning A=1, B=2, and C=5. We get D by substituting the given point into the equation (Ax + By + Cz = D) as follows D = Ax + By + Cz = (1*5) + (2*5) + (5*3) = 5 + 10 + 15 = 30. Thus, the equation of the plane is x + 2y + 5z = 30.
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Which of these is a point-slope equation of the line that is perpendicular to y-3=4(x-10) and passes through(-3,7)
A. y+7=4(x-3)
B. y-7= -1/4(x+3)
C. y+7= -1/4(x-3)
D. y-7= -4x(x+3)
The point-slope equation of the line that is perpendicular to y-3=4(x-10) and passes through(-3,7) is:
B. [tex]y-7=\frac{-1}{4} (x+3)\\[/tex]
The slope intercept form is y=mx+b where m is slope.
We have given perpendicular line as:
y-3=4(x-10)
y-3=4x-40
y=4x-37
The slope intercept form of the given line is
y=4x-37
Slope of this line is m=4
Now, as we know the two perpendicular lines have negative reciprocal slope.
Thus the other line have slope [tex]m=-\frac{1}{4}[/tex]
Now. the equation of line passing through point (-3,7) and having slope [tex]\frac{-1}{4}[/tex] is:
[tex]y-7=\frac{-1}{4} (x+3)\\[/tex]
Therefore the correct option is B.
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Brent was looking at his cell phone bill and saw that the total number of texts he has sent is tracked, as shown below:
Month
Texts
1
120
2
237
3
354
4
471
The function representing Brent's texting per month is f(m) = 117m + 3. What does the 117 represent?
It should be the additional texts per month or D
Answer:
The number of texts he sends per month
Step-by-step explanation:
The function f(m) = 117m + 3 is a linear function, which is in the form f(x) = mx+b. In this form, m (the number beside our variable) is the slope, or rate of change, and b (the number added or subtracted) is the y-intercept.
In our function, 117 is the number beside the variable, which makes it the slope. This is the rate of change of this function; it describes how the dependent variable (number of texts) changes for every change in the independent variable (months).
In other words, it tells how many texts he sends per month.
anyone free to help with this?
Mildred Lost bought two (2) radial tires at $49.95 each and two (2) seat cushions at $16.99 each. The sales tax where she lives is 6 percent. What was the total amount of the purchase?
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1. Beatrice decides she wants to babysit a few children at the same time to earn the money faster. She tells parents that if they allow her to babysit their children at her house, she will eliminate her automatic $5 tip and will give them an additional $5 discount.
(a) Write an equation showing the total cost for each client. Identify all variables.
(b) Four parents bring their children to Beatrice’s house at the same time for babysitting. Beatrice wants to find out how many hours she must babysit the 4 children to earn exactly the $100 she needs in order to buy the present for her mother. Write and solve an equation to find the number of hours. Justify each step in the solution.
(c) One parent decides not to drop off her child. The remaining 3 parents drop their children off at 9 a.m. Two of the parents say they will be back at 1 p.m. The third parent says she will pick up her child at 2 p.m. At noon, Beatrice realizes she needs help feeding the 3 children at the same time. She tells her little sister that she will pay her if she helps feed the children. How much can Beatrice pay her little sister and still make sure she has enough money to buy her mother a $100 present? Show your work and justify your answer.
Let B be the amount Beatrice charges per hour per child
Let x be the number of hours
Let n be the number of children
a)total amount Beatrice charges = T = B*x*n - 10
b)n =4 and T = 100
100 = B*x*4 -40
x = 35/B
c)Let S be the amount she has t o pay to her sister
n = 3 and x = (4+4+5) = 13
so, 13*B*3 -30 -S = 100
S = 39B - 130
Where is the vertex of the quadratic y = (x -7)2 + 9
Final answer:
The vertex of the quadratic function y = (x -7)² + 9 is at the point (7, 9).
Explanation:
Vertex of a quadratic function is the highest or lowest point on the graph of the function. In this case, the quadratic function is in the form y = (x -7)² + 9.
To find the vertex, we notice that the function is in the form y = (x - h)² + k, where (h, k) represents the vertex. Therefore, the vertex of the given quadratic function is at (7, 9).
Lines l and m are parallel and intersected by transversals t and s as shown in the figure below.
What is m
A) 180 degrees
B) 360 degrees
C) 540 degrees
D) 720 degrees
Use the expression below to complete the following tasks. (3a2 - 5ab + b2) - (-3a2 + 2b2 + 8ab) What is the additive inverse of the polynomial being subtracted?
Answer:
Option 3
Step-by-step explanation:
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An Native American tepee is a conical tent. Find the number of cubic feet of air in a teepee 10 ft. in diameter and 12 ft. high. 100 cu. ft. 300 cu. ft. 400 cu. ft.
Answer:
100 pi cubic feet
Step-by-step explanation:
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5. Marco wrote the equation below.
cos(-pi/2)=cos(3pi/2)
which statement best describes marcos equation?
a. it is true because the cosine function is odd
b. it is false because the cosine function is even
c. it is true because the cosine function has a period of 2pi
d. it is false because the cosine function has a period of pi.
The given equation is represented below:
cos(-pi/2)=cos(3pi/2)
The value of cos(-pi/2) is 0 and the value of cos(3pi/2) is also 0
Further a function is defined as an even function if f(x) = f(-x)
Cosine function is an even function.
Therefore it is true and the correct option is c
It is true because the cosine function has a period of 2pi
Hope it helps ..!!
Answer:
Option C - It is true because the cosine function has a period of [tex]2\pi[/tex].
Step-by-step explanation:
Given : Marco wrote the equation below.
[tex]\cos (-\frac{\pi}{2})=\cos (\frac{3\pi}{2})[/tex]
To find : Which statement best describes Macro equation?
Solution :
Since, the period of the given cos function is 360°
So, it holds the property of trigonometric :
[tex]\cos \theta=\cos (2\pi+\theta)[/tex] then the function is an even function.
Taking [tex]\theta =-\frac{\pi}{2}[/tex]
Then , [tex]2\pi+\theta = 2\pi-\frac{\pi}{2}[/tex]
[tex]2\pi+\theta = \frac{4\pi-\pi}{2}[/tex]
[tex]2\pi+\theta = \frac{3\pi}{2}[/tex]
So, the given function is a even function in a period of [tex]2\pi[/tex].
Therefore, Option C is correct.
It is true because the cosine function has a period of [tex]2\pi[/tex].
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Assuming boys and girls are equally likely, find the probability of a couple having a baby boyboy when their sixthsixth child is born, given that the first fivefive children were all boysall boys.
Answer:
50% probability of a couple having a baby boyboy when their sixth child is born, given that the first five were all boys.
Step-by-step explanation:
For each child, there are only two possible outcomes. Either it is a boy, or it is a girl. The probability of a child being a boy or a girl is independent of the other children. So we use the binomial probability distribution to solve this question.
The conditional probability formula is also used.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
Find the probability of a couple having a baby boyboy when their sixth child is born, given that the first five children were all boys.
Event A: First five children being boys.
Event B: Sixth children being a boy.
P(A):
First five children being boys.
P(X = 5) when n = 5.
Equally likely to be boy or girl, so p = 0.5.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(A) = P(X = 5) = C_{5,5}.(0.5)^{5}.(0.5)^{0} = 0.03125[/tex]
Intersection:
Intersection between the first five children being boys and the sixth also being a boy, so [tex]P(X = 6)[/tex] when n = 6.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(A \cap B) = P(X = 6) = C_{6,6}.(0.5)^{6}.(0.5)^{0} = 0.015625[/tex]
Probability:
[tex]P(B|A) = \frac{0.015625}{0.03125} = 0.5[/tex]
50% probability of a couple having a baby boyboy when their sixth child is born, given that the first five were all boys.
Which of the following would NOT be a deduction from a paycheck?
Select the best answer from the choices provided.
taxes
FICA
hourly wages
health insurance
Lexi's bulletin board is 40 centimeters wide. each of her ribbons is 4 centimeters wide, and her photos are 12 centimeters wide. what combination of ribbons and photos will fit side by side with no overlap on Lexi's bulletin
Workers in france average 5 fewer days of vacation a year than italians. americans average 24 fewer vacation days than the french. if the italians average 42 vacation days each year (the most in the world), how many does the average american worker have a year?
A guy-wire is attached from the ground to the top of a pole for support. If the angle of elevation to the pole is 67° and the wire is attached to the ground at a point 137 feet from the base of the pole, what is the height of the pole (round to 2 decimal places)?
Answer:
The height of the pole is 322.75 feet.
Step-by-step explanation:
Let the triangle Δ ABC with AC be the length of wire and AB be the Height of the pole
Length between the point of attachment of wire from base of the pole = BC = 137 feet
Angle of elevation to the pole = θ = 67°
We have to find the length of the pole that is AB Let the height of pole be h feet.
According to trigonometry :
[tex]\tan C=\frac{\text{perpendicular}}{\text{base}}[/tex]
Here, C = 67° , perpendicular = AB = h , base = BC = 137
Substitute the values,
[tex]\tan 67^{\circ}=\frac{AB}{BC}[/tex]
[tex]\tan 67^{\circ}=\frac{h}{137}[/tex]
[tex]h=\tan 67^{\circ} \times 137[/tex]
[tex]h=322.75[/tex]
Thus, the height of the pole is 322.75 feet.
Answer:60.1
Step-by-step explanation:
cos
if m ABC = 116 degrees what is ABC