Side of the given square room flooring is 12 foot
What is a square and its area?
A Square is a closed, two dimensional shape which has four sides and all four sides are equal and at 90 degree angle to each other .
As all four sides are equal, Let each of the side of a square is a
Area of the square is given by = a*a
Given that a designer paid $4 per square feet for a square flooring
Total amount spent by the designer = $600
Total area of flooring = total amount spent /rate of per unit area
= $600/$4 square foot =150 sq foot
Let the side of the given square flooring be x
Then area of the floor = [tex]x^{2} =150\\[/tex]
Thus side of the room floor = [tex]x=\sqrt{150}[/tex] = 12.25 = 12 foot
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The order states to give 0.75g of a medication. The label reads 50,000mcg /1ml. How many ml would you give to the client??
Answer: what the states says to
Step-by-step explanation:
A box has 15 ping pong balls in it, numbered 1 through 15. How many distinct sets of four different numbers can be chosen from the box of ping pong balls if the order in which the numbers are chosen is not important?
Answer:
1365
Step-by-step explanation:
The number of ways in which you can choose r items as a set from n available items is given by n choose k which can be represented as
Here n = 15, r = 4
C(n, r)
C(n,r) = C(15,4)
The formula is
[tex]C(n,r) = \binom{n}{r} = \dfrac{n!}{( r! (n - r)! )}[/tex]
where ! represents factorial of a number
n! = n x (n-1) x (n-2) x.......x 3 x 2 x 1
So
[tex]C(15,4) = = \dfrac{15!}{( 4! (15 - 4)! )}\\\\ = \dfrac{15!}{4! \times 11! }\\\\\\= 1365[/tex]
Answer: 1365 combinations
Step-by-step explanation:
What you're looking for if the order doesn't matter is the number of combinations.
You can use this formula for it:
[tex]\frac{n!}{r!(n-r)!} \\[/tex]
Where n is the number of objects there are and r is the number of objects you take out.
We'll be using the variables:
n = 15
r = 4
Plug them in and solve:
[tex]\\\frac{15!}{4!(15-4)!} \\\\= \frac{15!}{4!* 11!} \\\\= \frac{1307674368000}{24 * 39916800} \\\\= \frac{1307674368000}{958003200} \\= 1365[/tex]
How do you verbally say:
m AB but the AB has a line over it?
Answer:
measure of line segment AB
what is the equation of the line that passes through the point (-4,-3) and has a slope of -3/4
Answer:
Step-by-step explanation:
Benicio locks his safe by setting
each of the three dials to 8. To unlock the safe, he turns
the left dial 90° counterclockwise, the middle dial
270° clockwise, and the right dial 180° counterclockwise.
Which three numbers, in order, unlock the safe?
The three numbers, in order that will unlock the safe are 2, 2, 4.
We know that there are 8 numbers on each dial. Suppose, The dial is in a shape of a circle. Now, we can divide it into 8 equal pieces with same angles.
For each piece, the angle formed is 360/8 = 45° ( As in a circle, total angle formed without any divisions is 360° )
Now, When we turn the left dial 90° counterclockwise ( anticlockwise)
that is 45° + 45° ( two times 45°). Therefore, the dial moves by two places and we get the first number = 6 ( from 8 to 7 and then from 7 to 6).
Now, We turn the middle dial 270° clockwise. And get 45° + 45° + 45° + 45° + 45° + 45° (six times 45°). Therefore, the dial moves by six places. Hence, we get the second number = 2.
Now, We turn the right dial 180° counterclockwise that is anticlockwise or in backward direction. 180° = 45° + 45° + 45° + 45° ( four times 45°). Therefore, the dial moves by six places and thus we get our third number = 4.
Therefore, The three numbers, in order that will unlock Benicio's safe are 2, 2, 4.
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Select all sets that √7 belong to.
Onatural numbers
Owhole numbers
O integers
O rational numbers
Oirrational numbers
Oreal numbers
All sets that √7 belong to irrational numbers
The number √7 is a number inside a square root. Also, note that the number 7 is a whole number, but not a perfect square. Therefore, by our rule, we have that √7 belongs to the set of real numbers and to the set of irrational numbers.
In mathematics, the irrational numbers (from in- prefix assimilated to ir- (negative prefix, privative) + rational) are all the important numbers that are not rational numbers.
That is, irrational numbers can't be expressed as the ratio of two integers. When the ratio of lengths of two line segments is a real number, the road segments are also described as being incommensurable, meaning that they share no "measure" in common, that is, there's no length ("the measure"), regardless of how short, that would be used to express the lengths of both of the two given segments as integer multiples of itself.
Among irrational numbers are the ratio π of a circle's circumference to its diameter, Euler's number e, the golden ratio φ, and therefore the square root of two. In fact, all square roots of natural numbers, aside from perfect squares, are irrational.
Like all real numbers, irrational numbers are often expressed in positional notation, notably as decimal numbers. within the case of irrational numbers, the decimal expansion doesn't terminate, nor end with a repeating sequence.
for instance, the decimal representation of π starts with 3.14159, but no finite number of digits can represent π exactly, nor does it repeat.
Conversely, a decimal expansion that terminates or repeats must be a real number. These are provable properties of rational numbers and positional number systems and aren't used as definitions in mathematics.
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1. Han's teacher asked him to draw a polygon similar to polygon A. Here is his work.
Which explanation shows that polygons A and C are similar to each other?
A. Use a protractor to measure all four angles in polygon A and all four angles in
polygon C. Since each angle in polygon A has a matching angle measure in
polygon C, the polygons are similar.
Since each side in polygon C is three times as long as the corresponding side in
polygon A, the figures are similar.
C. Dilate polygon C with center at the upper-left vertex and a scale factor of
Then, translate 7 units to the left. Since polygon C can be taken to polygon A
with a dilation followed by a translation, the figures are similar.
D. Dilate polygon C with center at the upper-right corner and a scale factor of 3.
Since polygon C can be taken to polygon A with a dilation, the polygons are
similar.
You invest $15,000 in two funds (stock A and stock B) paying 6.3% and 7.1%
simple interest respectively. The total annual interest is $1050. How much did
you invest in each fund?
a = amount invested at 6.3%
how much is 6.3% of "a"? (6.3/100) * "a", namely 0.063a.
b = amount invested at 7.1%
how much is 7.1% of "b"? (7.1/100) * "b", namely 0.071b.
we know the total amount invested is $15,000, so whatever "a" and "b" might be, we know that a + b = 15000.
we also know that the yielded amount in interest is $1050, so if we simply add their interest, that'd be 0.063a + 0.071b.
[tex]\begin{cases} a + b = 15000\\ b = 15000 - a\\[-0.5em] \hrulefill\\ 0.063a+0.071b=1050 \end{cases} \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{0.063a+0.071(\underset{b}{15000-a})=1050}\implies 0.063a+1065-0.071a=1050 \\\\\\ 0.063a-0.071a=-15\implies -0.008a=-15\implies a=\cfrac{-15}{-0.008} \\\\\\ \boxed{a = 1875}\hspace{15em}\boxed{\stackrel{15000~~ - ~~1875}{b = 13125}}[/tex]
Which of the following values are in the domain of the function graphed
below? Check all that apply.
Answer:
B
Step-by-step explanation:
The domain of a graph is its turning point
4. Jay measured the exterior angles in
this polygon. Explain how you know
his measurements are wrong.
80
80
60
75
70
Answer:
535 is not equal to 360
Step-by-step explanation:
the total interior angle = 360 degree
180-80=100
180-80=100
180-75=105
180-70=110
180-60=120
100+100+105+110+120= 535 which is not equal to 360. Since the total interior angle is not 360, Jay's measurements are wrong .
#12) A freight elevator can hold up to 4,500 pounds. How many tons can the freight elevator hold?
Answer:
2.25 tons
Step-by-step explanation:
1 ton = 2000 pounds
Can someone help me with this question? It's due tomorrow :(
Answer: Angle B = 32deg, Angle D = 43deg, and Angle F = 105deg
Step-by-step explanation:
Angle B = Angle C, Angle D is on a line = to 180 deg, the line is intercepted into a 137deg portion, and a 43deg portion, all angles in a triangle add up to 180, so 32+43=75, 180-75=105 (Angle F)
Please let me know if this helped!
Solve using long division (6x^3-8x+5) ÷ (2x-4)
The solution to the long division 6x³ - 8x + 5 divided by (2x-4) is 3x² - 6x + 8 and the remainder is -27
The long divisionWhen 6x³ - 8x + 5 is divided by (2x-4) the answer in this format
q(x) + r(x) / b(x) is express as 3x² - 6x + 8
The long division application is uploaded as a picture below.
The answer should be express in this format:
q(x) + r(x) / b(x)
where,
q(x) = quotientr(x) = remainderb(x) = divisorThe quotient is the result obtained by dividing one value by another. The quotient is 3x² - 6x + 8 .
The remainder is the number left over after performing the division. The remainder is -27
The divisor is the value that divides another completely or with a remainder. The divisor is 2x - 4
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Evaluate -4a² + 2a - 1 when a = - 3.
Answer:
-43
Step-by-step explanation:
-4(-3)² + 2(-3) - 1
=-4×9+2(-3)-1
=-36+2(-3)-1
=-36-6-1
=-43
Find the volume of a rectangular prism if the length is 4x, the width is 5x, and the height is x2 + x + 2. Use the formula V = l ⋅ w ⋅ h, where l is length, w is width, and h is height, to find the volume.
Group of answer choices
20x3 + 20x2 + 40x
20x4 + 20x3 + 40x2
20x4 + x + 29
20x4 + 9x3 + 18x2
Answer:
2D
Step-by-step explanation:
i times two is 5
How many baseball cards did he start with?
Answer:
108
Step-by-step explanation:
22+86=108
Answer:
108 baseball cards
Step-by-step explanation:
x = baseball cards he started with
x - 22 = 86
add 22 to both sides
x = 108
108 baseball cards
Jermey subtracted the following rational expressions. his teacher told him that his answer was incorrect. explain jeremys error in the simplification process and provide the correct results.
2x^2-10\x-5 - x^2+15\x-5 = x^2+5\x-5
This is likely what Jeremy did
[tex]\frac{2\text{x}^2-10}{\text{x}-5}-\frac{\text{x}^2+15}{\text{x}-5}\\\\\frac{2\text{x}^2-10-\text{x}^2+15}{\text{x}-5}\\\\\frac{\text{x}^2+5}{\text{x}-5}\\\\[/tex]
The error happens in line 2
This is what his steps should be
[tex]\frac{2\text{x}^2-10}{\text{x}-5}-\frac{\text{x}^2+15}{\text{x}-5}\\\\\frac{2\text{x}^2-10-(\text{x}^2+15)}{\text{x}-5}\\\\\frac{2\text{x}^2-10-\text{x}^2-15}{\text{x}-5}\\\\\frac{\text{x}^2-25}{\text{x}-5}\\\\\frac{(\text{x}-5)(\text{x}+5)}{\text{x}-5}\\\\\text{x}+5[/tex]
On the 2nd step, we subtract all of (x^2+15) and not just the x^2 part. The negative distributes to each term in step 3. Then we combine like terms, factor and cancel out the (x-5) terms.
Therefore, [tex]\frac{2\text{x}^2-10}{\text{x}-5}-\frac{\text{x}^2+15}{\text{x}-5}=\text{x}+5[/tex] is an identity as long as [tex]\text{x} \ne 5[/tex] to avoid a division by zero error.
Which word not be a step in solving 18=2(4+x)
The correct option is B) Collect variables terms on one side because there is one value for the variable.
What is defined as the variables?In the perspective of a math concept or experiment, a variable is a quantity that really can change. A variable is typically represented by a single letter. Variables are commonly represented by the alphabets x, y, and z. We will sometimes select a letter which further tells us of the quantity this represents, including such t for time, v voltage, and any b for bacteria.The given equation in this case is,
18 = 2(4+x)
By using the Distributive property on the right side,
18 = 8 + 2x
After subtracting 8 from both sides ( Isolating variable x )
18 - 8 = 8 + 2x - 8
Compile similar terms,
10 = 2x
By dividing both sides by two ( Isolating variable x )
x = 5
As a result of the preceding explanation, it is completely obvious that we utilized all options but apart from option B.
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The complete question is-
Which would not be a step in solving 18=2(4+x)?
A) Use the distributive property.
B) Collect variables terms on one side.
C) Collect like terms.
D) Isolate the variable.
Solve for x using the image below:
Answer:
x=-14
Step-by-step explanation:
7x+156=9x+184
2x=-28
x=-14
Find n(A) for the set A
Reason:
Your teacher wants you to find out how many elements are in set A.
Focus on the numerators only.
That sequence is 1,2,3,..., 37,38 which consists of 38 numbers.
If you wanted to focus on the denominators, then we go from 3 to 40 which is a gap of 40-3 = 37, but then add on 1 to account for the first item. So we get to 37+1 = 38.
please need help on this #3
Answer:
a. 5
b. 10
c. 15
d. 4
e. 6
f. 9
Step-by-step explanation:
It asks for the indicated distance, which would translate as the absolute value of the distance between the two points. Using that, it is simple subtraction to find your answer.
Marie sells outdoor grills. She knows she earns a 10% commission on the first $10,000 and 12% on the next $15,000. She does not remember the rate on the sales of more than $25,000 but her total sales for the month are $29,665, and her total commission is $4,891. What is her rate of commission for the sales over $25,000?
The commission rate is 44.8%.
What is the commission rate?The first step is to determine the commission on the first $10,000 : 0.1 x 10,000 = 1,000
The second step is to determine the commission on the next $15,000: 0.12 x $15,000 = $1,800
The third step to determine the commission on amounts more than $25,000 : x%(29,665 - 25,000)
x%(4,665)
Total commissions earned on amount more than $25,000 : $4,891 - (1,800 + 1,000) = $2091
Now, determine the commission rate : $2091 / $4,665 = 0.448 = 44.8%
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Tickets of a program at college cost $5 for general admission or $4 with a student ID. If 180 people paid to see a performance and $795 was collected, how many of each type of ticket were sold?
The number of tickets for general admission is 75 and with student id's is 105.
Given that,
Tickets of a program at college cost $5 for general admission or $4 with a student ID.
180 people paid to see a performance and $795 was collected, how many of each type of ticket were sold is to be determined.
Here,
Number of admission with general admission = x
Number of admission with college id = y
According to the given conditions,
x + y = 180
x = 180 - y - - - - - - (1)
5x + 4y = 795 - - - - - (2)
Now put the value of the equation in equation 2
5 (180 - y) + 4y = 795
900 - 5y + 4y = 795
-y = 795 - 900
-y = -105
y = 105
Now put y in equation 1
x = 180 - 105
x = 75
Thus, the number for tickets with general admission is 75 and with student id is 105.
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HELLO CAN SOMEONE PLEASE ANSWER THIS MATH QUESTION ASAP I WILL MARK YOU THE BRAINLIEST
The expression for one fifth the difference of a number and 17 is B. 1/5( n - 17).
How to illustrate the information?It should be noted that an expression is used to show the relationship between the variables.
In this case, the information is to find the expression for one fifth the difference of a number and 17.
Let the number be n. The expression will be:
1/5( n - 17).
In conclusion, the correct option is B.
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Difference between a Keynesian economists and classical economists and their views on how they would respond to an economy falling into a recession
Classical economics emphasizes that unfastened markets provide efficient results and are self-regulating.
Classical economics means that the long time mixture deliver curve is inelastic, therefore any divergence from complete employment is most effective transitory. The Classical version emphasizes the want of minimizing authorities interference and operating to preserve markets freed from any impediments to effective functioning.
Keynesians declare that because of imperfect markets, the economic system can function at less than full potential for an extended period of time.
Keynesians consider that expansionary economic policy (authorities intervention) has a larger role in overcoming recession.
The Keynesian angle on lengthy-run mixture deliver differs.
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Question Find the distance between the points A(13, 2) and B(7, 10)?
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{13}~,~\stackrel{y_1}{2})\qquad B(\stackrel{x_2}{7}~,~\stackrel{y_2}{10})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AB=\sqrt{(~~7 - 13~~)^2 + (~~10 - 2~~)^2} \implies AB=\sqrt{( -6 )^2 + ( 8 )^2} \\\\\\ AB=\sqrt{ 36 + 64 } \implies AB=\sqrt{ 100 }\implies AB=10[/tex]
write equations for the following statements
1)Three fourth of t is 15
2)If you add 3 to one third of 2,you get 30
3)One fourth of a number x minus 4 gives 4
Answer:
i'm not sure the second is right
HELP PLEASE!!!!!!!
Find the measurement of the angle indicated for each trapezoid.
The required measure of the angle of the trapezoid is 50° and 101°.
The angle can be defined as the one line inclined over another line.
Where angle measures in degree and radian.
Here,
For trapezoid one 1.
The Sum of the adjacent angle is 180°.
So, 130 + ∠C = 180
∠C = 180 - 130
∠C = 50
For trapezoid 2.
Sum of all the angle should be equal to 360°
but ∠Q = ∠S
110 + 48 + 2∠Q = 360
∠Q = 101°
Thus, the required measure of the angle of the trapezoid is 50° and 101°.
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Your friend's averages 56 miles per hour while driving to a college. On the return trip, your friend averages 48 miles per hour due to construction. The total driving time is 6 hours and and 30 minutes. How long does each trip take?
the first trip takes 3 hours
and the second one takes 3 hours and 30 minute
(2-I)(3+5i) multiple
Answer:
ii-7i
Step-by-step explanation:
These can be multiplied in a manner similar to expanding brackets:
(
2
+
i
)
(
3
−
5
i
)
=
6
+
3
i
−
10
i
−
5
i
2
Remember that
i
=
√
−
1
so
i
2
=
−
1
This will in turn allow us to gather the like terms like so:
6
+
5
+
3
i
−
10
i
=
11
−
7
i
