Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group.
What does division look like?The opposite of multiplication is division. Knowing a division truth enables us to find a multiplication fact
Before moving on, keep in mind that the numbers in the equation 41 divided by 48 are defined as follows:
dividend = 41,48 = dividend.
Step 1: Arrange it so that the dividend 41 is on the right side and the divisor 48 is on the left as shown:
4 8 ⟌ 4 1
Step 2: The divisor (48) is multiplied by the dividend's initial digit (4) by 0 times (s). Hence, place 0 at the top:
0 \s 4 8 ⟌ 4 1
Step 3: Write the result of multiplying the divisor by the outcome of the previous step (48 x 0 = 0), underneath the dividend.
0 \s 4 8 ⟌ 4 1 \s 0
Step 4: Write the result below after subtracting the previous step's result from the dividend's first digit (4 - 0 = 4).
0 \s 4 8 ⟌ 4 1 \s - 0 \s 4
Step 5: Decrease the dividend (1)'s second digit as follows:
0 \s 4 8 ⟌ 4 1 \s - 0 \s 4 1
Step 6: The bottom number (41), which is the divisor, is multiplied by 0 times (s). Hence, place 0 at the top: 0 0 \s 4 8 ⟌ 4 1 \s - 0 \s 4 1
Step 7: Divide the result from the previous step by the divisor (48 x 0 = 0), and then write the result at the bottom:
0 0 \s 4 8 ⟌ 4 1 \s - 0 \s 4 1 \s 0
Step 8: Subtract the outcome from Step 7 from the number displayed above. Put the solution at the bottom (41 - 0 = 41). 0 0 \s 4 8 ⟌ 4 1 \s - 0 \s 4 1 \s - 0 \s 4 1
There are no more digits to shift down from the dividend, thus you are finished.
The top number is the solution, and the remaining value is the bottom one.
As a result, when 41 is divided by 48 using long division, the result is:
0.
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Scott is 72 inches tall and Chris is 185 centimeters tall. Who is taller? Show your work. How do we convert this?
SOLUTION:
Step 1:
In this question, we are given the following:
Scott is 72 inches tall and Chris is 185 centimeters tall.
Who is taller? Show your work.
Step 2:
Scott is 72 inches tall
and
Chris is 185 centimeters tall
Converting cm to inches, we have that:
[tex]\begin{gathered} 1\operatorname{cm}\text{ = }0.393701\text{ inch} \\ 185\text{ cm = 185 x 0.393701 = }72.\text{ 834685 }\approx\text{ 72. 8 inch} \end{gathered}[/tex]CONCLUSION:
Since Chris' height = 72.8 inch tall and Scott's height = 72 inch tall
Hence, Chris is taller.
In a study of bluetits 12 birds were trapped and their masses and wing spans were measured. The data collected are shown in this table. Calculate the estimated standard deviation for the mass of the bluetits, showing your answer to 3 significant figures.
The standard deviation of the mass of the bluetits to 3 significant figures is 1.30.
What is the standard deviation?Standard deviation is used to determine the variation of a dataset. Standard deviation is the spread of a data from the mean of the dataset. The higher the value of the standard deviation, the greater the spread of the dataset.
In order to determine the standard deviation, take the following steps:
Determine the mean of the mass : (9.9 + 9.8 + 12.2 + 13.3 + 11.8 + 10.2 + 12. 3 + 12.9 + 9.2 + 10.3 + 10.7 + 12.1) / 12 = 11.225
Determine the difference between each value and the mean and then square the result and then find the square root. The answer gotten is the standard deviation. 1.30
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help! its due tomorrow
For Question 1,
(a) Teammates eye-level depths in order from lowest to highest:
-3.5 ft < -3 ft < 0 ft < 1.5 ft
(b) Comparison between Teammate B and teammate D depths:
-3.5 ft < -3 ft
so, eye level depth of Teammate B < Teammate D.
For Question 3,
The options given to the designer are:
1 3/4 and 1 5/12
On simplifying these fractions,
1 3/4 = 7/4
1 5/12 = 17/12
On taking the LCM of the denominator of 4 and 12, we get LCM as 12,
So, 7/4 = 21/12
Now, on comparing the two distances,
21/12 > 17/12
(a) So, the distance of 17/12 is closest to the slide.
(b) On comparing the two distances,
we get, 21/12 > 17/12
(c) 17/12 will lie in between 1 and 1 1/2 on the number line whereas 21/12 will lie in between 1 1/2 and 2 on the number line.
What is Number Line?A number line, used to represent the real numbers visually in early mathematics, is a drawing of a graduated straight line. It is presumptively true that each real number and each point on a number line relate to one another. A line with carefully marked equally spaced-out points on it is frequently used to represent integers. Especially when negative numbers are involved, it is frequently used as a teaching tool for basic addition and subtraction. The set R of all real numbers, considered as a geometric space, namely the Euclidean space of dimension one, is the formal definition of the number line, often known as the real line or real number line in advanced mathematics.To learn more about the Number line, refer to:
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Given the sum of the interior angles is 12,600 of a regular polygon, determine the following:
The number of sides =
Each interior angle =
Each exterior angle =
Sum of the exterior angles =
Answer:
72 sidesinterior angle: 175°exterior angle: 5°exterior angle total: 360°Step-by-step explanation:
Given a regular polygon whose interior angles total 12,600 degrees, you want to know the number of sides, the measures of each interior and exterior angle, and the sum of the exterior angles.
Angle sumThe sum of angles of a convex polygon is given by the formula ...
angle sum = 180° × (n -2)
where n is the number of sides.
ApplicationSubstituting the given angle sum, we can solve for n:
12,600 = 180(n -2)
70 = n -2 . . . . . divide by 180
72 = n . . . . . . . add 2
The regular polygon has 72 sides.
Interior angleThe interior angles of a regular polygon are congruent, so each one is ...
12,600°/72 = 175°
Each interior angle = 175°.
Exterior angleThe exterior angle at a vertex is the supplement of the interior angle there:
180° -175° = 5°
Each exterior angle = 5°.
Sum of exterior anglesThe 72 exterior 5° angles have a total of ...
72 × 5° = 360°
Sum of the exterior angles = 360°.
__
Additional comment
The invariant with convex polygons, regular or not, is that the sum of exterior angles is 360°. This fact is what gives rise to the formula for interior angles.
The business checking account for a pottery store had a balance of $7349.44 before checks for $1349.67 and $344. 12 were written the store manager then made a deposit of $955.30. Findthe current checkbook balance.
Solution
For this case we can solve the problem with the following operation:
7349.44 -1348.67 -344.12 + 955.30 = 6611.95$
Write the ratio as a ratio of whole numbers in lowest terms $2.00 to $0.80
positive exponents.2) (22). 2)
To find the result we are going to use the following rule:
[tex](a^m)^n=a^{mn}[/tex]and
[tex]a^m\cdot a^n=a^{m+n}[/tex]Then:
[tex]\begin{gathered} ((2^2)^4\cdot2^3)^4=(2^8\cdot2^3)^4 \\ =(2^{11})^4 \\ =2^{44} \end{gathered}[/tex]Therefore the result is:
[tex]2^{44}[/tex]Homework 3.4: Compound InequalitiesScore: 10.38/1811/18 answeredQuestion 6<>04Give the interval that describes the set of values shown above.
Give the interval that describes the set of values shown above
The interval marked in blue has the following features:
* Starts with a filled blue dot at x=2
* Ends with a filled blued dot at x=4
* Runs from x=2 to x=4 with a blue line
The filled dots indicate that the endpoints are included in the interval
The line indicates that all the values in between the interval are included in the interval
There are two basic forms to indicate an interval with included endpoints:
* A pair of values (the endpoints) comma-separated included in a pair of brackets:
Interval: [2,4]
* The closed interval indicated by inequalities signs:
[tex]2\leq x\leq4[/tex]I need help with my work
In order to determine the price per orange, calculate the quotient in between 3.78 and 14:
3.78/14 = 0.27
Hence, one orange costs $0.27
i dont know how to do these please help
Answer:
Step-by-step explanation:
the formula for this is PV= nRT
where, P=Pressure, V= Volume, n = Number of moles, R= Molar gas constant, T=Temperature
for this question, P AT S.T.P= 101325 Nm^-2, V= ?, n= 1.35 mol, R= 8.31,
T= 273k
fixing the values into the formula we have,
[101325][V]=[1.35][8.31][273]
make V the subject of formula
V= [1.35][8.31][273]/101325
V= 3062.65/101325
V= 0.03 cm^3
Sharon makes money by commission rates. She gets 17% of everything she sells. If Sharon sold $37,000 worth of items this month, how much didshe make?O A $629O B. $5,180O C. $6,290O D. $14,800
Answer;
[tex]C;\text{ \$6,290}[/tex]Explanation;
Here, we want to get the amount of commission made by Sharon
Mathematically, we have that she makes 17% of what she sells as commission
We have this as;
[tex]\frac{17}{100}\times37,000\text{ = \$6,290}[/tex]Hello, I need some assistance with this homework question, please? This is for my precalculus homework. Q8
Part A (Domain and Range)
Domain
The domain is the set of all the values of x for which the function represented by the graph is defined. From the graph:
(A)The domain of the function is:
[tex]\lbrace x|-\inftyRangeThe range is the set of all the values of y for which the function represented by the graph is defined. From the graph:
(A)The range of the function is:
[tex]\lbrace y|-\inftyPart B (Intercepts)(A)The x-intercepts of the function are:
[tex]x=1.4,-1.4[/tex](A)The y-intercept of the function is:
[tex]y=-1[/tex]Part C
The horizontal asymptote is at:
[tex](A)y=-2[/tex]Part D
The vertical asymptotes are at:
[tex](A)x=-2,2[/tex]Part E
The oblique asymptote is usually slant.
From the graph, there are no obliques asymptotes.
Option B is correct here.
if log2 5=x and log2 3=y, determine an expression in terms of x ,y, and integers. the first is log 2 20
Answer:
[tex]\log _220\text{ = 2 + x}[/tex]Logarithm base 2 of a number, is the number you have to use as a power of two to get that number, for example, logatithm base 2 of 4 is 2, because 2 to the power of 2 is 4, another example, logarithm base 2 of 8 is 3, because 2 to the power or 3 is 8
[tex]\log _2(4)=2because2^{2\text{ }}=4[/tex][tex]\log _2(8)=3because2^{3\text{ }}=\text{ 8}[/tex]Help mee pleasee!!
thank you <3
The linear equation that models the average price of a new home in terms of the year x is given by y = -5600x + 294000 and the average price of a new home would be $238000 in 2014.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The line must pass through points (0, 294000) and (7, 288400) which is given in the question.
We have to determine the slope of the line :
m = (y₂ - y₁)/(x₂ -x₁ )
m = (288400- 294000)/(7 -0)
m = -5600
This represents new home per year
So with your y-intercept of 294000, your equation becomes
y = -5600x + 294000
Using this equation to predict the average price of a new home in 2014.
Let y be the average price of a new home in the year x, where x = 0 represents the year 2004.
Substitute the value of x = 10 for the year 2014
y = -5600(10) + 294000
y = -56000 + 294000
y = 238000
Hence, the average price of a new home would be $238000 in 2014.
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Find the missing coordinates to complete the following ordered-pair solutions to the given linear equation.y + 4x = 6(a) (-1, )(b) (4, )....
SOLUTION
Write out the given linear equation
[tex]y+4x=6[/tex]For the first ordered pair,
[tex]\begin{gathered} (-1,\text{?)} \\ x=-1,y=\text{?} \end{gathered}[/tex]Substitute the value of x into the linear equation to find the value of y
[tex]\begin{gathered} y+4x=6 \\ y+4(-1)=6\ldots\text{.}\ldots(\text{expand the paranthesis )} \\ y-4=6\ldots\ldots(\text{add 4 to both sides )} \\ y-4+4=6+4 \\ y=10 \\ \text{The ordered pair is (-1,10)} \end{gathered}[/tex]a). Therefore For the first ordered pair, the missing coordinate y is 10
Similarly, for the second ordered-pair
[tex]\begin{gathered} (4,\text{?)} \\ x=4,y=\text{?} \end{gathered}[/tex]Substitute the value of x into the linear equation to obtain the value of y
[tex]\begin{gathered} y+4x=6 \\ y+4(4)=6 \\ \text{Expand the parenthesis} \\ y+16=6 \\ \text{subtract 16 from both sides } \\ y+16-16=6-16 \\ y=-10 \\ \text{Ordered pair=(4,-10)} \end{gathered}[/tex]b). Therefore for the second ordered pair, the missing coordinates y is -10
Find the exact value using a half angle identity: cos 7 pi/8
Answer:
[tex]\cos \frac{7\pi}{8}=-\frac{1}{2}\sqrt[]{2+\sqrt[]{2}}[/tex]Explanation:
Given
[tex]\cos \frac{7\pi}{8}[/tex]Using the identity:
[tex]\begin{gathered} \cos (\frac{7\pi}{2\times4})=\pm\sqrt[]{\frac{1+\cos\frac{7\pi}{4}}{2}} \\ \\ =-\sqrt[]{\frac{1+\frac{1}{\sqrt[]{2}}}{2}} \\ \\ =-\sqrt[]{\frac{2+\sqrt[]{2}}{4}} \\ \\ =-\frac{1}{2}\sqrt[]{2+\sqrt[]{2}} \end{gathered}[/tex]In the diagram, CD 1 AC, BE 1 AC, AE = 17, BE = 8, and CD = 32. Find DE. 32 D В E 8 17 A 45 51 O 68 O 35 Question 3 1 pts a HE
Input data
AE = 17
BE = 8
CD = 32
Procedure
[tex]\begin{gathered} \frac{AD}{AE}=\frac{CD}{BE} \\ \frac{AD}{17}=\frac{32}{8} \\ AD=17\cdot\frac{32}{8} \\ AD=68 \end{gathered}[/tex]
Now for DE
[tex]\begin{gathered} AE+DE=AD \\ DE=AD-AE \\ DE=68-17 \\ DE=51 \end{gathered}[/tex]The answer would be DE=51
Find the average rate of change of f(x) = x°-2x² +3+ 3x from x=1 to x=3.Simplify your answer as much as possible.
The average rate of change for a function f(x) from x=a to x=b is:
[tex]\frac{f(b)-f(a)}{b-a}[/tex]For the given function:
[tex]f(x)=x^3-2x^2+3x[/tex]Averate rate of change from x=1 to x=3:
[tex]\begin{gathered} \frac{f(3)-f(1)}{3-1}=\frac{(3^3-2(3)^2+3(3))-(1^3-2(1)^2+3(1))}{3-1} \\ \\ =\frac{(27-2(9)+9)-(1-2+3)}{2} \\ \\ =\frac{(27-18+9)-(2)}{2} \\ \\ =\frac{18-2}{2} \\ \\ =\frac{16}{2} \\ \\ =8 \end{gathered}[/tex]Then, the averate rate of change for the given function from x=1 to x=3 is 8
Find the least common multiple (LCM) of 12 and 18
Answer:
0.0[infinitely reprating] 1 is the smallest
Answer:
36
Step-by-step explanation:
LCM of 12 and 18 is the smallest number among all common multiples of 12 and 18. The first few multiples of 12 and 18 are (12, 24, 36, 48, 60, 72, 84, . . . ) and (18, 36, 54, 72, . . . ) respectively
What are the correct answers the drop down both say negative or positive
Given the data set:
(-8,-10) (6, -1), (-5,-7),(3, -2) (10, 0) (4,-3) (-3,-6) , (9, 1)
We will graph the points to find the slope of the line of best fit for the data
The graph will be as shown in the following figure:-
As shown, the given points are the dots of blue color
The line of best fit is the dashed red line
As shown, the line has a positive slope and a negative y-intercept
So, the answer will be:
The line of best fit for the data will have a positive slope and a negative y-intercept value.
The amount of $In each The amount of $ Total
Let Lydia invest $x
Half of her stock pays 11% dividend.
So mathematically the amount will be
[tex]\frac{x}{2}\times\frac{11}{100}=\frac{11x}{200}[/tex]With the other half, she pays stocks in 14% interest
So mathematically
[tex]\frac{x}{2}\times\frac{14}{100}=\frac{14x}{200}[/tex]Her total annual interest is $420
So
[tex]\frac{11x}{200}+\frac{14x}{200}=420\Rightarrow25x=84000\Rightarrow x=3360[/tex]She invested $3360 in total
And $1680 in each.
If (ax + 3)(bx + 4) = 6x 2+ cx + 12 for all values of x, and a + b = 5, what are the two possible values for c ?
Answers: c = 17 and c = 18
==================================================
Explanation:
Let's expand out the left hand side and rearrange terms like shown in the steps below.
(ax + 3)(bx + 4) = 6x^2 + cx + 12
ax(bx + 4)+3(bx + 4) = 6x^2 + cx + 12
abx^2 + 4ax+3bx + 12 = 6x^2 + cx + 12
abx^2 + (4a+3b)x + 12 = 6x^2 + cx + 12
Then equate the corresponding coefficients
ab = 6 .... x^2 terms4a+3b = c .... x termsWe'll use the fact that a+b = 5. Solving for 'a' gets us a = 5-b
Plug this into the equation dealing with the x^2 coefficients.
ab = 6
(5-b)b = 6
5b-b^2 = 6
0 = b^2-5b+6
b^2-5b+6 = 0
(b-3)(b-2) = 0
b-3 = 0 or b-2 = 0
b = 3 or b = 2
If b = 3, then a = 5-b = 5-3 = 2
If b = 2, then a = 5-b = 5-2 = 3
Therefore, the solutions to this system of equations
[tex]\begin{cases}a+b = 5\\ab = 6\end{cases}[/tex]
are (a,b) = (2,3) and (a,b) = (3,2)
In other words, the answer to the question "what two numbers multiply to 6 and add to 5?" is "2 and 3". The order doesn't matter which is why we can flip the 'a' and b values.
---------------------------------
Go back to 4a+3b = c which was us equating the x coefficients.
This is the same as c = 4a+3b
Plug in a = 2 and b = 3
c = 4a+3b
c = 4*2+3*3
c = 8 + 9
c = 17 is one possible value of c.
Now let's plug in a = 3 and b = 2
c = 4a+3b
c = 4*3+3*2
c = 12 + 6
c = 18 is the other possible value of c.
Select the correct answer.
What is the completely factored form of this polynomial?
x² + 12x²+32
OA.
O B. (x²+4)(x² + 8)
(x + 4)(X + 8)
O C.
O D.
(x²+4)(x + 2)(x + 4)
(x + 2)(x-2)(x² + 8)
G
Reset
Factor form of the polynomial (x+8)(x+4)
What is Polynomial?
A polynomial is an equation made up of coefficients and indeterminates that uses only the addition, subtraction, multiplication, and powers of positive-integer variables. x2 4x + 7 is an illustration of a polynomial with a single indeterminate x.
Given polynomial,
x² + 12x+32
x² + 4x + 8x +32
x(x+4) + 8(x+4)
(x+8)(x+4)
Hence, The completely factored form of this polynomial is (x+8)(x+4)
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Select the expressions that are equivalent to - 7(f - 4).
you can multiply each term of the parentheses by -7
[tex]\begin{gathered} -7(f-4) \\ (-7\times f)+(-7\times-4) \\ -7f+28 \end{gathered}[/tex]HELP PLEASEEEEEEEEE!!!!!!!! ILL MARK BRAINLIEST
Answer:
(-3)³, (-2)⁴, (-2)³, 3⁰, -3², -2⁴
help meeee pleasee!!!
thank youu
Answer:
Domain: A, [1, 7]
Range: [-4, 2]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Put the number or question when You answer
Solve. ln(–x + 1) – ln(3x + 5) = ln(–6x + 1) –0.67 or 2 option 1 –1.58 or 0.14 option 2–0.14 or 1.58 option 3–2 or 0.67 option 4
SOLUTION
We want to solve
[tex]\ln \mleft(-x+1\mright)-\ln \mleft(3x+5\mright)=\ln \mleft(-6x+1\mright)[/tex]This becomes
[tex]\begin{gathered} \ln (-x+1)-\ln (3x+5)=\ln (-6x+1) \\ \ln (-x+1)-\ln (3x+5)-\ln (-6x+1)=0 \\ \text{From laws of logarithm } \\ \ln \frac{(-x+1)}{(3x+5)}\times\frac{1}{(-6x+1)} \\ \ln \frac{(-x+1)}{(3x+5)(-6x+1)}=0 \end{gathered}[/tex]Since ln 1 = 0, we have
[tex]\begin{gathered} \ln \frac{(-x+1)}{(3x+5)(-6x+1)}=\ln 1 \\ \text{Canceling }\ln ,\text{ we have } \\ \frac{(-x+1)}{(3x+5)(-6x+1)}=1 \\ (-x+1)=(3x+5)(-6x+1) \end{gathered}[/tex]Expanding the equation in the right hand side we have
[tex]\begin{gathered} (-x+1)=(3x+5)(-6x+1) \\ (-x+1)=-18x^2+3x-30x+5 \\ -x+1=-18x^2+3x-30x+5 \\ -18x^2+3x-30x+5=-x+1 \\ -18x^2+3x-30x+x+5-1=0 \\ -18x^2-26x+4=0 \end{gathered}[/tex]Solving the quadratic equation we have
[tex]-18x^2-26x+4=0[/tex]We have
[tex]x=-1.58\text{ or }x=0.14[/tex]Hence, the answer is option 2
What's the next term in the sequence of 1, 8, 27, 81, 243?
The next term in the sequence of 1, 8, 27, 81, 243 is 729.
What is a sequence?
Sequences are ordered collections of numbers, often known as "terms," such as 2,5,8. There are some sequences that adhere to a particular pattern that allows for endless extension. For instance, 2,5,8 adheres to the "add 3" pattern, thus we may now continue the process. There are formulas for sequences that show us where to find any given term.
It might be good to separate each phrase into its component parts to solve this problem:
1, or 3^0, is a factor of 1.
8 is 2^3
27 is 3^3
81 is 3^4
243 is 3^5
The likelihood of the following phrase is 3^6, or 729.
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the wholesale cost of shoes is 22.60$ the markup is 45% what is the selling price
Answer:
$32.77
Step-by-step explanation:
Add 45% of the wholesale cost to the entire wholesale cost to get the selling cost:
$22.60 + (45%)($22.60) = $32.77
The selling cost is $32.77.
