There are 5 days to a school week: Monday, Tuesday, Wednesday, Thursday and Friday.
Divide number of school days by 5 to find the number of weeks:
171 / 5 = 34.2 weeks.
The weeks start with Monday, so there would be 35 Mondays. ( 34 full weeks and the partial week would begin with a Monday)
Divide 171 by 7 (as there are 7 days in each week), obtaining 24.4. There's one Monday in every 7 days, so in 168 days there'd be exactly 24 Mondays, and in 171 days there'd still be exactly 24 Mondays, with 3 days left over.
Please help!!! The last one. Word answer
Often, variability is most usefully expressed in the same units as the original data. That's what standard deviation (square root of variance) does. In situations where that is the case, the variance is useful only for getting to the value of standard deviation.
Jared has taken out a loan for his car. His monthly payments amount to $650. If his loan is for 36 months, and he paid a down payment of $400, what is the total cost of the car for Jared? A. $15,050 B. $23,800 C. $28,300
B! 650 x 36 +400 = 23,800!
Answer:
$23800.
Step-by-step explanation:
Monthly payment of loan of a car = $650
His loan is for 36 months
So, Total payment of 36 months = [tex]36 \times 650[/tex]
= [tex]23400[/tex]
He paid the down payment of amount $400
So, Total cost of the car = [tex]23400+400[/tex]
= [tex]23800[/tex]
Hence the total cost of the car for Jared is $23800.
So, Option B is correct.
In LaToya’s school
3
8
of the students have a blood type of O+, and
1
12
of the students have a blood type of O–. What fraction of the students in LaToya’s school has a blood type of O+ or O–?
[tex]\frac{11}{24}[/tex]
combine the fractions of each type by adding them
[tex]\frac{3}{8}[/tex] + [tex]\frac{1}{12}[/tex]
Before we can add the fractions we require them to have the same denominator
To achieve this we require the lowest common multiple (LCM ) of 8 and 12
The LCM of 8 and 12 is 24
To change the denominators , multiply the numerator/ denominator by the appropriate value
[tex]\frac{3}{8}[/tex] = [tex]\frac{3(3)}{8(3)}[/tex] = [tex]\frac{9}{24}[/tex]
[tex]\frac{1}{12}[/tex] = [tex]\frac{1(2)}{12(2)}[/tex] = [tex]\frac{2}{24}[/tex]
Add the numerators leaving the denominator as it is
= [tex]\frac{9+2}{24}[/tex] = [tex]\frac{11}{24}[/tex]
Answer:111/24
Step-by-step explanation:
Marie is cleaning her clothes out of the closet in her spare bedroom. She started with 650 of her items in the closet. She has been able to continually decrease the number of her items in the closet at a rate of one-half per month. Her brother, Dustin, has started putting 5 items of his clothing in the closet each month as Marie cleans it out. Marie wants to know how many months it will take before the number of items Dustin adds will be equal to the number of her items in the closet.
Create a system of equations to model the situation above, and use it to determine if there are any solutions. If there are any solutions, determine if they are viable or not.
Wording is everything. Here, there are some issues. "... at the rate of 1/2 per month" can be interpreted to mean that at the end of the first month, there are 649 1/2 items in Marie's closet (decreased by 1/2 from 650).
"The number of items Dustin adds" could mean 5 items, the number he adds each month. The wording should specify the time period or whether we're talking about the total number Dustin has added.
We assume your description means that the number of items in Marie's closet at the end of each month is 1/2 what it was at the beginning. (As opposed to decreasing by 1/2 item each month.) We assume we're interested in the total number of items of Dustin's that are in the closet.
Marie's quantity can be modeled by ...
... m = 650·(1/2)^t . . . . . t = time in months
Dustin's quantity can be modeled by ...
... d = 5t
There will be one solution for d=m, at about t = 4.8. At that point, Dustin will have added about 24 items, which will be the number Marie is down to.
There is a viable solution for d=m at about t = 4.8.
Answer:
D. there is only one solution, and it is viable
Step-by-step explanation:
which of the following demonstrate closure in a polynomial? Select all that apply: A.(x^2+2) (x-1) B.(x^2+2) over (X -1) C.(x+1) plus (X^2-3X -2) D.(X +5)-(3X +6) E.4/8x
Any arithmetic operation on polynomials except division* will result in a polynomial. Appropriate choices are ...
A. (x^2+2) (x-1)
C. (x+1) plus (X^2-3X -2)
D. (X +5)-(3X +6)
E. (4/8)x . . . . . but not if you mean 4/(8x)
_____
* For division, the result may be a polynomial. In the specific example given here for B, it is not.
The term closure in mathematics refers to the property of a set, in this case, polynomials, where doing certain operations (addition, subtraction, multiplication) with any numbers from the set always yields a number within the set. The options demonstrating closure in a polynomial are A, C, D, E, all but option B, which implies division.
Explanation:The term 'closure' in mathematics refers to the property of a set under an operation where the operation performed on any numbers in the set always produces a number that is also in that set. In the case of polynomials, the operations could be addition, subtraction, or multiplication.
The expressions that demonstrate closure in a polynomial for addition, subtraction, and multiplication are all but option B. Option B, '(x^2+2) over (X -1)', isn't representative of closure in a polynomial as it implies a division operation. Polynomial closure doesn't include division because it can produce numbers outside the original set.
So, the correct answers are A.(x^2+2) (x-1), C.(x+1) plus (X^2-3X -2), D.(X +5)-(3X +6) and E.4/8x as they illustrate closure by either multiplication of two polynomials, addition of two polynomials, or subtraction of two polynomials.
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How can you tell by looking at the coordinates of the two triangles that Δ A'B'C' is a 180° rotation of Δ ABC? A) The coordinates cannot prove a 180° rotation. B) The y-coordinates of the points on ΔA'B'C' have opposite signs from the corresponding points on ΔABC. C) The x-coordinates of the points on ΔA'B'C' have opposite signs from the corresponding points on ΔABC. D) Both the x and y coordinates of the points on ΔA'B'C' have opposite signs from the corresponding points on ΔABC.
under a rotation about the origin of 180°
a point (x, y ) → (- x, - y )
hence D is correct, both the x and y coordinates of the points on ΔA'B'C' have opposite signs from the corresponding points on ΔABC
Answer:
Its D
Step-by-step explanation:
Both coordinates have opposite signs.
Solve the equation. -3x + 1 + 10x = x + 4
Answer:
[tex]x=[tex]\frac{1}{2}[/tex][/tex]
Step-by-step explanation:
Solving the equation mean finding the value of x
Equation given is:
[tex]-3x+1+10x=x+4[/tex]
Now what we need to do is take the values with x in it to the left side of the equation and the other numbers to the right side of the equation.
[tex]-3x+10x-x=4-1[/tex]
Now simplify values with x and the numbers.
[tex]6x=3[/tex]
[tex]x=[tex]\frac{1}{2}[/tex][/tex]
Therefore [tex]x=[tex]\frac{1}{2}[/tex][/tex]
x = [tex]\frac{1}{2}[/tex]
simplify the left side by collecting like terms
7x + 1 = x + 4 ( subtract x from both sides )
6x + 1 = 4 ( subtract 1 from both sides )
6x = 3 ( divide both sides by 6 )
x = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]
what is the least common denominator for the fractions 1/2 and 2/3
We are required to find the least common denominator for the fractions 1/2 and 2/3
The least common denominator for the fractions 1/2 and 2/3 3/6 and 4/6
Given:
1/2 and 2/3
Find the lowest common multiples of the denominators 2 and 3
2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 30
3 = 3, 6, 9, 12, 15, 18, 21
The lowest common multiples of the denominators 2 and 3 is 6
Check:
3/6 and 4/6
= 1/2 and 2/3
Therefore, the least common denominator for the fractions 1/2 and 2/3 is 3/6 and 4/6
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The least common denominator for the fractions 1/2 and 2/3 is 6, which is the least common multiple of their denominators. Fractions are converted to have this common denominator before performing operations such as addition or comparison.
Explanation:The least common denominator (LCD) for the fractions 1/2 and 2/3 is the smallest number that both denominators can divide into without leaving a remainder. To find the LCD, we look for the least common multiple (LCM) of the two denominators. In this case, the denominators are 2 and 3. The LCM of 2 and 3 is 6, because 6 is the smallest number that both 2 and 3 can divide into evenly. Therefore, the least common denominator for 1/2 and 2/3 is 6.
To express the fractions with the common denominator, you would convert 1/2 to 3/6 and 2/3 to 4/6. This allows you to add or compare the fractions directly.
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An employment agency specializing in temporary construction help pays heavy equipment operators $ 122 per day and general laborers $ 93 per day. If thirty dash four people were hired and the payroll was $ 3771 comma how many heavy equipment operators were employed? How many laborers?
If all were general laborers, the payroll would be 93·34 = 3162 per day. The payroll is actually 3771 -3162 = 609 more than that.
Each equipment operator makes 29 more than a laborer, so there must be ...
... 609/29 = 21 heavy equipment operators
and 34 -21 = 13 general laborers
_____
If you write an equation for the number of heavy equipment operators (h), you get the same result in the same way. 34-h is the number of laborers
... 122h + 93(34 -h) = 3771 . . . equation for total daily payroll
... 29h + 3162 = 3771 . . . . . . simplify
... 29h = 609 . . . . . . . . . . . . . subtract 3162
... h = 609/29 = 21 . . . . . . . . divide by 29
please help, need answer fast!
What is the simplified expression for -3(2x - y) + 2y + 2(x + y)
a. 8x + y
b. y - 4x
c. 7y - 4x
d. -4x - y
Hey there!!!
Given equation :
... - 3 ( 2x - y ) + 2y + 2 ( x + y )
... -6x + 3y + 2y + 2x + 2y
... -6x + 5y + 2x + 2y
... -4x + 7y
( or )
... 7y - 4x
Hope helps!
Center(-2,4) radius=6
(x + 2 )² + (y - 4)² = 36 ← is the equation of the circle
the equation of a circle in standard form is (x - a)² + (y - b)² = r²
where (a, b) are the coordinates of the centre and r is the radius
here (a, b ) =(- 2, 4) and r = 6
(x + 2)² + ( y - 4 )² = 36
!HELP!
Three is a zero of the equation x^3−4x^2−3x+18=0.
Which factored form is equivalent to the equation?
A (x+2)(x−3)^2=0
B (x−2)(x−3)^2=0
C (x+2)(x−√3)(x+√3)=0
D (x−2)(x−3)(x+3)=0
x^3−4x^2−3x+18=0
(x - 3)^2 (x + 2) = 0
Choice B
A
since x = 3 is a zero then (x - 3) is a factor
dividing x³ - 4x² - 3x + 18 by (x - 3) gives
x³ - 4x² - 3x + 18 = (x - 3)(x² - x - 6 ) = 0,
(x - 3)(x - 3 )(x + 2 ) = 0
(x + 2 )(x - 3)² = 0 → A
What is the solution of sqrt1-3x=x+3
x = - 1
given [tex]\sqrt{(1-3x)}[/tex] = x + 3
square both sides
1 - 3x = (x + 3 )² ( expand right side using FOIL )
1 - 3x = x² + 6x + 9 ( subtract 1 - 3x from both sides )
0 = x² + 9x + 8
0 = ( x + 1)(x + 8)
equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = -1
x + 8 = 0 ⇒ x = - 8
As a check
substitute these values into the equation and if both sides are equal then they are the solutions
x = - 1 : [tex]\sqrt{1+3 }[/tex] = 2 and - 1 + 3 = 2 ← true
x = - 8 : [tex]\sqrt{1+24}[/tex] = 5 and - 8 + 3 = -5 ← false
thus the only solution is x = - 1
Two large topping pizzas cost $25.00. what is the constant of proportionality (k)?
A generator runs for 2 1/2 h and uses 4 3/8 gal of fuel. How many gallons of fuel did the generator use each hour? Enter your answer as a mixed number in simplest form in the box.
1 [tex]\frac{3}{4}[/tex] gallons per gour
divide number of gallons used by running time
4 [tex]\frac{3}{8}[/tex]÷ 2 [tex]\frac{1}{2}[/tex]
change mixed numbers to improper fractions
[tex]\frac{35}{8}[/tex] ÷ [tex]\frac{5}{2}[/tex]
leave the first fraction, change division to multiplication, turn the second fraction upside down
= [tex]\frac{35}{8}[/tex] × [tex]\frac{2}{5}[/tex]
= ( 35 × 2 ) / (8 × 5 ) = [tex]\frac{7}{4}[/tex] = 1 [tex]\frac{3}{4}[/tex]
A small company had a profit of -$528 in January. If it continues to have the same profit for each month for four months, what will be the companies total profit for four months?
$2112 you just have to do 528 x 4 = 2112
The company's total profit over four months, if sustaining a consistent loss of $528 per month, would be -$2,112.
If a small company had a profit of -$528 in January, and it continues to make the same profit (which is really a loss) each month for four months, we can calculate the total profit (total loss in this case) for those four months by multiplying the monthly profit by four.
So, the calculation would be:
Monthly Profit x Number of Months = Total Profit
(-$528) x 4 = -$2,112
Therefore, the company's total profit after four months would be -$2,112. This means the company would have a loss of $2,112 total over those four months.
write an equation of the line in point slope form that passes through (-16, 8) and (4,-2)
a.) y-8=-1/2(x+16)
b.) y-8=1/2(x-16)
c.) y+8=2(x+16)
d.) y+8=-(x-16)
When the reference point is used in the point-slope form of the equation, the equation should evaluate to ...
... 0 = 0
This is only true for point (-16, 8) using the equation of selection a).
Happily, we also find that point (4, -2) satisfies the equation.
... -2-8 = -1/2(4+16)
... -10 = -1/2(20) . . . . true
The appropriate choice is ...
... a.) y-8 = -1/2(x+16)
plz help asp!!!What is the relationship between 9.125×10−3 and 9.125×102 ?
The exponents differ by 5, meaning the numbers differ by a factor of 10⁵.
9.125×10² = 100,000×9.125×10⁻³
The latter is 100,000 times the former
The graph of an equation is shown below:
Based on the graph, which of the following represents a solution to the equation?
(−2,−3)
(3, 1)
(1, 3)
(3, 2)
pleaseeeee help i will give brainliest
Answer:
(1, 3)
Step-by-step explanation:
The first number of each pair is the x-coordinate, the horizontal location of the point.
The end points of the graphed line segment are (1, 3) and (-3, -2). It looks like the answer choices are intended to see if you can tell what order the coordinates are expressed in.
The appropriate choice is (1, 3), the upper right end point.
Bank robbers leave the bank with the bounty. The cops get alerted right away, but it takes them 4 minutes before they start in hot pursuit. The police station is 10 miles down the road from the bank in the direction opposite to that in which the robbers are heading. If the robbers travel at 96 mph how fast must the cops go to catch them before they reach the state line 55 miles away
In 4 minutes, 1/15 hour, the robbers have a (96 mi/h)·(1/15 h) = 6.4 mile head start.
The cops must travel 65 miles in the time the robbers travel 48.6 miles. Hence their speed must be 65/48.6 times that of the robbers, or about
... 65/48.6×96 mi/h ≈ 128.4 mi/h
_____
The chase will be over after (55 mi)/(96 mi/h) = 34 minutes 22.5 seconds from the time of the robbery. The cops will have to cover the 65 miles in less than 30:22.5 minutes, or about 0.50625 hours.
The cops' speed then is 65 miles/(0.50625 hour) ≈ 128.39506... mi/h
he is right do not look down here to be sure so go with his answer
find the sum of (2x^2 +4x-9) +(3x^2-2x+10) please show work
You can eliminate parentheses and combine like terms.
(2x^2 +4x-9) +(3x^2-2x+10)
= 2x^2 +4x-9 +3x^2-2x+10 . . . . . nothing needs to be distributed, so we can simply drop the parentheses
= x^2(2 +3) +x(4 -2) +(-9 +10) . . . group like terms
= 5x^2 +2x +1
Write the equation of line in slope-intercept form. Line parallel to y=0.5x+3 that passes through the point (−9,12)
My answer was: y=0.5x+16.5
Bill draws a regular octagon with the perimeter of 32 units.He picks a vertex of the octagon and draws two line segments through the interior of the octagon on each different opposite vertex.His line segments divide the octagon into three quadrilaterals.what does the shape look like ?
The quadrilaterals are two congruent isosceles trap ezoids and a kite.
Online jewelry sales have increased steadily over the last 10 years. In 2003, sales were approximately 2 billion dollars, and in 2010 they were approximately 14.8 billion. (i) Find the unit rate at which online jewelry sales have been increasing. (Express your answer rounded correctly to the nearest hundredth of a billion per year.) billion dollars per year (ii) Construct a model to predict online jewelery sales. According to your model, what should the online jewelery sales be in 2019? (Express your answer rounded correctly to the nearest tenth of a billion.) billion dollars
Answer: (i) The unit rate at which online jewelry sales have been increasing is 1.33 billion dollars per year.
(ii) The online jewelry sales in 2019 will be 191.7 billion dollars.
Step-by-step explanation:
In 2003, sales were approximately 2 billion dollars and in 2010, they were approximately 14.8 billion dollars.
(i) If [tex]x[/tex] is the number of years after 2003 and [tex]y[/tex] is the amount of sales....
then the equation will be: [tex]y= ab^x[/tex] , where [tex]a[/tex] is the initial amount and [tex]b[/tex] is the growth rate.
for 2003, [tex]x=0[/tex] and for 2010, [tex]x=7[/tex]
So, the two points in form of (x, y) will be: [tex](0,2)[/tex] and [tex](7,14.8)[/tex]
Now plugging these two points int the above equation....
[tex]2= ab^0\\ \\ a= 2\\ \\ and\\ \\ 14.8=ab^7\\ \\ 14.8=2*b^7\\ \\ b^7=7.4\\ \\b= \sqrt[7]{7.4}=1.3309.... \approx 1.33[/tex]
Thus, the online jewelry sales have been increasing at a rate of 1.33 billion dollars per year.
(ii) As we got [tex]a=2[/tex] and [tex]b=1.33[/tex], so the equation will be now: [tex]y= 2(1.33)^x[/tex]
For the year 2019, the value of [tex]x[/tex] will be: (2019-2003) = 16
So plugging [tex]x=16[/tex] into the above equation, we will get.....
[tex]y=2(1.33)^16\\ \\ y=191.7150... \approx 191.7[/tex]
(Rounded to the nearest tenth)
Thus, the online jewelry sales in 2019 will be 191.7 billion dollars.
a mattress store charges 7% sales tax and a $50 delivery fee. The delivery fee is not subject to sales tax. The following functions represent the situation F(a)=1.07a and g (b)= b+50
Solve for g (f (a)).
Answer: [tex]g(f(a))=1.07a+50[/tex]
Step-by-step explanation:
The given functions are: [tex]f(a)=1.07a[/tex] and [tex]g(b)= b+50[/tex]
[tex]g(f(a))[/tex] means [tex]f(a)[/tex] is the input of the function [tex]g[/tex].
Thus, [tex]g(f(a))= g(1.07a)[/tex]
Now replacing [tex]b[/tex] as [tex]1.07a[/tex] into the given function of [tex]g(b)[/tex], we will get......
[tex]g(1.07a)= 1.07a+50[/tex]
So, [tex]g(f(a))=1.07a+50[/tex]
Which of the following statements are true?
All square matrices are diagonal matrices.
All diagonal matrices are square matrices.
The size of any square matrix is m x m, where m is a positive integer.
All coefficient matrices are square matrices.
The statements that are true are:
All diagonal matrices are square matrices. The size of any square matrix is m x m, where m is a positive integer.The following information should be considered;
All square matrices should not be diagonal matrices. All coefficient matrices should not be square matrices.Therefore, the above two options should be considered true statement.Learn more: https://brainly.com/question/1301963?referrer=searchResults
Answer: B & C
Step-by-step explanation:
on edge
Rectangle A has length 12 and width 8. Rectangle B has length 15 and width 10. Rectangle C has length 30 and width 15. Is Rectangle A a scaled copy of Rectangle B? If so, what is the scale factor? Is Rectangle B a scaled copy of Rectangle A? If so, what is the scale factor? Explain how you know that Rectangle C is not a scaled copy of Rectangle B. Is Rectangle A a scaled copy of Rectangle C? If so, what is the scale fact
Rectangles are similar figures, thus if scaled copies of each other then the ratios of corresponding sides must be equal
compare ratios of lengths and widths
rectangles A and B
k = [tex]\frac{12}{15}[/tex] = [tex]\frac{4}{5}[/tex] ← ratio of lengths
k = [tex]\frac{8}{10}[/tex] = [tex]\frac{4}{5}[/tex] ← ratio of widths
scale factors are equivalent, hence rectangle A is a scaled copy of B
rectangles C and B
k = [tex]\frac{15}{30}[/tex] = [tex]\frac{1}{2}[/tex] ← ratio of lengths
k = [tex]\frac{10}{15}[/tex] = [tex]\frac{2}{3}[/tex] ← ratio of width
scale factors (k ) are not equal, hence C is not a scaled copy of B
rectangles A and C
k = [tex]\frac{30}{12}[/tex] = [tex]\frac{5}{2}[/tex] ← ratio of lengths
k = [tex]\frac{15}{8}[/tex] ← ratio of widths
the scale factors are not equal hence A is not a scaled copy of C
For two rectangles, one of length L and width W, and other of length L' and width W', the second is a rescale of the first one only if exists a real number k such that:
L' = k*L
W' = k*W
Here we know:
Rectangle A: length = 12, width = 8Rectangle B: length = 15, width = 10Rectangle C: length = 30, width = 15Let's see if rectangle A is a scaled copy of rectangle B.
To see this, we just must see if the quotients between the lengths and between the widths are equal:
15/12 = 1.25
10/8 = 1.25
Then yes, rectangle A is a rescaled copy of rectangle B, and the scale factor is k = 1.25
Is rectangle B a rescaled copy of rectangle A?
Obviously yes. The scale factor will be the inverse of the previous one, we will get:
k = 1/1.25 = 0.8
How we do know that rectangle C is not a scaled copy of rectangle B?
Because the length of C is twice the length of B, but the width of C is not twice the width of B.
Is rectangle A a scaled copy of rectangle C?
No, as we already see that rectangle C is not a rescaled copy of rectangle B, and we know that rectangle A is a rescaled copy of rectangle B.
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I could REALLY use some help on this. I just cant seem to get it.(please help me)
Write an equation for the line parallel to the given line that contains C.
C (3, 6); y= -2 x + 7
y = - 2x + 12
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
y = - 2x + 7 is in this form with slope m = - 2
Parallel lines have equal slopes, thus
y = - 2x + c is the partial equation.
To find c, substitute (3, 6 ) into the partial equation
6 = - 6 + c ⇒ c = 6 + 6 = 12
y = - 2x + 12 ← equation of parallel line
Jacob tapes down a piece of red tape on a basketball court. The piece of tape is 3/5 yard long. He wants to divide it into sections that are each 1/10 yard long. How many sections will the piece of tape be divided into? 30 points if u answer
3/5 = 6/10 = 6×(1/10)
The piece will be divided into 6 sections of 1/10 yard each.
Answer:
3/5 = 6/10 = 6×(1/10)
The piece will be divided into 6 sections of 1/10 yard each.
Step-by-step explanation:
If i have a pay rate of $21.00 and marked up 78.7% and made a 10% profit. how did i get $41.28?
Answer: Procedure are given below :
Step-by-step explanation:
Since we have given that
Pay rate = $21.00
if he marked up by 78.7% , then
[tex]78.7\%\text{ of }21\\\\=\frac{78.7}{100}\times 21\\\\=16.527[/tex]
So, our pay rate becomes
[tex]\$21+\$16.527=\$37.527[/tex]
Now, he made a 10% profit,
[tex]10\%\text{ of }37.527\\\\=\frac{10}{100}\times 37.527\\\\=\$3.7527[/tex]
So, pay rate becomes
[tex]\$37.527+\$3.7527\\\\=\$41.2797[/tex]
which approximately $41.28