The quotient of - 3.32 / - 2.2 is 8 ÷5.
What is the quotient?Given fraction:
-3.32 / -2.2
First step is to re-write the given fraction which is - 3.52 / - 2.2
3.52 / 2.2
Second step is to convert the decimal to fraction
352 ÷ 100 / 22 ÷10
Third step is to reduce the fraction
reducing 352/100
=(2^5 × 11)/(2^2 × 5^2)
= [(2^5 × 11) ÷ 2^2] / [(2^2 × 5^2) ÷ 2^2]
= (2^3 × 11)/5²
= 88/25
Reducing 22/10
Divide the numerator and denominator by the greatest common divisor
= 22 ÷ 2 / 10 ÷ 2
= 11 /5
Now let determine or find the quotient
88 ÷ 25 × 11 ÷ 5
= 8 ÷ 5
Therefore we can conclude that 8 ÷ 5 is the quotient.
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Which expression uses the commutative property to make it easier to evaluate
Let's begin by listing out the given information:
The commutative property states that for addition, the order in which we add numbers does not change their sum & for multiplication, the order in which we multiply does not change their product.
Mathematically expressed as:
[tex]\begin{gathered} x+y+z=y+z+x \\ x\cdot y\cdot z=y\cdot z\cdot x \end{gathered}[/tex]Therefore, the commutative property of this is:
[tex]\begin{gathered} \frac{4}{3}\cdot\frac{1}{5}\cdot18=\frac{4}{3}\cdot18\cdot\frac{1}{5} \\ \Rightarrow\frac{4}{3}\cdot18\cdot\frac{1}{5} \\ \end{gathered}[/tex]Therefore, Option D is the correct answer
To the nearest hundredth, what is the value of x? X 40°
The given triangle is a right angle triangle,
Apply the trignometry ratio of tan
[tex]\tan \emptyset=\frac{Perpendicular}{Base}[/tex]From the given figure we have,
Perpendicular=x and base=72 and angle =40 degree
[tex]\begin{gathered} \tan 40^{\circ}=\frac{x}{72} \\ 0.839=\frac{x}{72} \\ x=0.839\times72 \\ x=60.408 \\ x=60.41 \end{gathered}[/tex]So the value of x is 60.41
Find mCBD. the number might be a bit blurry but it is 192
Circle is 360 degrees.
Arc DB = 360 - 192 = 168°
The measure of angle CBD is half the measure of Arc DB.
Thus,
[tex]\begin{gathered} \angle\text{CBD}=\frac{1}{2}(168) \\ =84\degree \end{gathered}[/tex]Perform the indicated operation by removing the parentheses and combining like terms.(5x + 3) + (x2 – 8x + 4)
Given the sum of the functions expressed as:
[tex]\mleft(5x+3\mright)+x^2-8x+4[/tex]Collecting the like terms:
[tex]x^2+5x-8x+3+4[/tex]Group the terms based on their degrees
[tex]x^2+(5x-8x)+(3+4)[/tex]Simplify the result to determine the final answer:
[tex]\begin{gathered} x^2+(5x-8x)+(3+4) \\ x^2+(-3x)+7 \\ x^2-3x+7 \end{gathered}[/tex]Hence the required sum of the functions is x^2 - 3x + 7
You deposit $400 into a savings account that earns interest annually. The function g(x) = 400(1.05)x can be used to find the amount of money in the savings account, g(x), after x years. What is the range of the function in the context of the problem?
ℝ
[0, 400]
[0, ∞)
[400, ∞)
Answer:
Step-by-step explanation:
The constant percent rate of change in the case of a deposit of $400 into a savings account is compounded annually.
With an example, what is compound interest?
When you add the interest you have already earned back into your principal balance, you are earning compound interest, which increases your profits.
Consider that you have $1,000 in a savings account earning 5% interest annually. If you made $50 in the first year, your new balance would be $1,050.
Principal - $400
rate of interest is compounded annually
g(x) = 400( 1.03)ˣ equation 1.
Formula used
A = P( 1 + r )ⁿ
here n = x
Solution:
Putting the value of n, and principal in the formula
A = P( 1 + r )ⁿ ................... equation 2
now comparing both equation 1 and equation 2,
400( 1.05)ˣ = 400( 1 + r )ˣ
( 1.05)ˣ = ( 1 + r )ˣ
1.05 = 1 + r
r = 1.05 - 1
r = 0.05
r % = 0.05 × 100
r % = 5 %
thus, the constant percent rate of change = 5 %
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find the sum of all two-digit natural numbers which are not divisible by 3。Want formulas and algorithms
The sum of all two-digit numbers which are not divisible by 3 is 2240.
What is Arithmetic progression?
An arithmetic sequence or progression is defined as a sequence of numbers in which for every pair of consecutive terms, the second number is obtained by adding a fixed number to the first one.
The sum of two-digit number in AP is Sn = n/2[2a+(n-1)d]
First, sum of two digit number 10, 11.....99 is
n = 90, a = 10 an= 99
Sn = n/2[2a+(n-1)d]
Sn = 90/2[2(10)+(90-1)1]
Sn = 45[20+89]
Sn= 4905
Now, the sum of two digit number divisible by 3 =
12, 15,...99
a = 12, n = 30, d = 3
Sn = n/2[2a+(n-1)d]
Sn=30/2[2(12)+(30-1)3]
Sn= 1665
Hence, sum of two digit number not divisible by 3 are 4905-1665
=2240
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helpppppppppppppppppppp
Answer: [tex]f^{-1}[/tex] = {(17, 16), (8, 3), (3, 8), (4, 4)}
Step-by-step explanation:
To list the inverse function, we will simply switch the x- and y-values in each coordinate pair. Coordinate points are written as (x, y).
f = {(16, 17), (3, 8), (8, 3), (4, 4)}
[tex]f^{-1}[/tex]= {(17, 16), (8, 3), (3, 8), (4, 4)}
Americans who are 65 years of age or older make up 13.2% of the total population. If there at 30.3 million american in this age group, find the total u.s. population
Given:
Americans who are 65 years of age or older make up 13.2% of the total population.
Required:
The total u.s. population
Explanation:
Let the total population of u.s be x.
According to the given condition.
[tex]13.2\text{ \% of x = 30.3 billion}[/tex]Therefore,
[tex]\begin{gathered} \frac{13.2}{100}\text{ }\times\text{ x = 30.3} \\ x\text{ = }\frac{30.3\text{ }\times\text{ 100}}{13.2} \\ x\text{ = 229.55 billion} \end{gathered}[/tex]Answer:
Thus the total population of u.s is 229.55 billion.
which three statements are true about the line segment CBit's the radius of the circleit is the circumference of the circleit is a cordit is 6cm longit is diameter of the circle it is 7cm longit is 1.75cm long
Answer:
It is the diameter of the circle
it is 7 cm
it is a chord
Explanation:
First, we notice that the line segment CB passes through the centre of the circle and its endpoints touch the circumference - this tells us that CB is the diameter.
Furthermore, any line segment whose endpoints lie on the circumference of the circle is a chord (meaning that the diameter is the longest chord), and so we deduce that CB is also a chord.
Since CB is the diamter, its length is 2 times the radius. The raduis of the circle we know is DA = 3.5 cm; therefore, the dimater is CB = 2 DA = 2 * 3.5 = 7 cm.
Hence, the correct choices are:
It is the diameter of the circle
it is 7 cm
it is a chord
.Find the area of the sector with radius 4 and central angle, ∅= 45°
Remember that the formula for the area of a sector is:
[tex]A=\frac{\pi\cdot r^2\cdot\theta}{360}[/tex]Where:
• r, is the radius
,• Theta ,is the central angle (in degrees)
Using this formula and the data given,
[tex]\begin{gathered} A=\frac{\pi\cdot4^2\cdot45}{360} \\ \rightarrow A=2\pi \end{gathered}[/tex]Will give brainliest thank you..!
Answer:
4
Step-by-step explanation:
4
4
4
4
14 Tom can whitewash a fence alone in 4 hours, and Huck can whitewash the same fence in 5 hours working by himself. Tom whitewashes with Huck for 1 hour and then leaves. How long will it take Huck to finish whitewashing the fence?
Given:
Time it takes Tom = 4 hours
Time it takes Huck = 5 hours
Tom then whitewashes with Huck for 1 hour and then leaves.
Let's find how long it will take Huck to finish whitewashing the fence.
We have:
Tom's rate = 1/4
Huck's rate = 1/5
Total rate:
[tex]\frac{1}{4}+\frac{1}{5}=x[/tex]Now, let's find the time it will take them to whitewash together.
[tex]\begin{gathered} \frac{1}{T}=\frac{5+4}{20} \\ \\ \frac{1}{T}=\frac{9}{20} \\ \\ T=\frac{20}{9} \\ \\ T=2.22 \end{gathered}[/tex]It will take them 2.22 hours to whitewash together.
Now they both whitewash together for 1 hour before Huck leaves.
We have:
[tex]2.22-1=1.22[/tex]When Huck leaves after one hour, the time left for both of them to finish together is 1.22 hours.
Since only Huck will finish whitewashing the fence, the time it will take him will be:
[tex]5(1-\frac{1.22}{2.22})=2.25[/tex]Therefore, it will take Huck to finish whitewashing the fence is 2.25 hours.
ANSWER:
2.25 hours
Use the binomial expression (p+q)^n to calculate abinomial distribution with n = 5 and p = 0.3.
ANSWER :
The binomial distributions are :
0.16807
0.36015
0.3087
0.1323
0.02835
0.00243
EXPLANATION :
In a binomial distribution of (p + q)^n :
n = 5
p = 0.3 and
q = 1 - p = 1 - 0.3 = 0.7
[tex]_nC_x(p)^x(q)^{n-x}[/tex]We are going to get the values from x = 0 to 5
[tex]\begin{gathered} _5C_0(0.3)^5(0.7)^{5-0}=0.16807 \\ _5C_1(0.3)^5(0.7)^{5-1}=0.36015 \\ _5C_2(0.3)^5(0.7)^{5-2}=0.3087 \\ _5C_3(0.3)^5(0.7)^{5-3}=0.1323 \\ _5C_4(0.3)^5(0.7)^{5-4}=0.02835 \\ _5C_5(0.3)^5(0.7)^{5-5}=0.00243 \end{gathered}[/tex]Aaquib can buy 25 liters of regular gasoline for $58.98 or 25 liters of permimum gasoline for 69.73. How much greater is the cost for 1 liter of premimum gasolinz? Round your quotient to nearest hundredth. show your work :)
YOU WILL GET 70 POINTS!
The cost for 1 liter of premium gasoline is $0.43 greater than the regular gasoline.
What is Cost?This is referred to as the total amount of money and resources which are used by companies in other to produce a good or service.
In this scenario, we were given 25 liters of regular gasoline for $58.98 or 25 liters of premium gasoline for $69.73.
Cost per litre of premium gasoline is = $69.73 / 25 = $2.79.
Cost per litre of regular gasoline is = $58.98/ 25 = $2.36.
The difference is however $2.79 - $2.36 = $0.43.
Therefore the cost for 1 liter of premimum gasoline is $0.43 greater than the regular gasoline.
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37)You need at least 15 pencils or markers. You want to spend at most $14 onpencils and markers. Pencils p are $0.85 each and markers m are $1.45each. Which system of inequalities models the situation?A) p+m>150.85p+1.45m<14B) p+m>140.85p+1.45m>15C) p+m≥150.85p+1.45m≤14D) p+m≥140.85p+1.45m≤15
Given:
Minimum number of pencils or markers = 15
Maximum amount to spend on pencils and markers = $14
Cost of a pencil = $0.85
Cost of a marker = $1.45
Required: System of inequalities models the situation
Explanation:
Let p denote the number of pencil and m be the number of markers
Since the minimum number of pencils or markers is 15, it gives the inequality
[tex]p+m\geq15[/tex]Since the maximum amount to spend on pencils and markers is $14, it gives the inequality
[tex]0.85p+1.45m\leq14[/tex]Final Answer:
[tex]\begin{gathered} p+m\ge15 \\ 0.85p+1.45m\leqslant14 \end{gathered}[/tex]
f(x) = - 3x + 4; g(x) = f(x) + 1
Graph it and then describe the graph
The graph of function f(x) and g(x) is parallel lines separated by 1 unit.
In this question we have been given two functions f(x) = - 3x + 4 and g(x) = f(x) + 1
We need to graph these functions and then describe the graph.
The graph of given functions is as shown below.
The graph of function f(x) is a straight line with slope -3 and y-intercept 4.
The function g(x) is nothing but but function f(x) translated upward by 1 unit.
The graph of function g(x) is also a straight line with slope -3 and y-intercept 5.
Therefore, the graph of function f(x) and g(x) is parallel lines separated by 1 unit.
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How many ways can Rudy choose 4 pizza toppings from a menu of 16 toppings if each can only be chosen once
ANSWER:
1820 different ways
STEP-BY-STEP EXPLANATION:
We can use here combination rule for selection:
[tex]_nC_r=\frac{n!}{r!(n-r)!}[/tex]In this case n is equal to 16 and r is equal to 4, therefore, replacing and calculating the number in different ways, there:
[tex]\begin{gathered} _{16}C_4=\frac{16!}{4!(16-4)!}=\frac{16!}{4!\cdot12!} \\ \\ _{16}C_4=1820 \end{gathered}[/tex]So in total there are 1820 different ways Rudy can choose 4 pizza toppings.
Jan 10, 7:17:08 PM Which equation represents a line which is perpendicular to the line x - 2y = -14? Oy= -27 -1 Oy= 2x + 8 Submit Answer Oy=x+4 Oy = -x + 2
You need to determine which line is perpendicular to the line
[tex]x-2y=-14[/tex]For two lines to be considered perpendicular their slopes must be the inverse positive, that is, if, for example, you have the lines
[tex]y_1=mx_1+b[/tex][tex]y_2=nx_2+c[/tex]For them to be perpendicular one slope must be the inverse negative of the other such as
[tex]n=-\frac{1}{m}[/tex]The first step is to write the given line in slope-intercept form:
1) Pass the x term to the right side of the equal sign
[tex]\begin{gathered} x-2y=-14 \\ x-x-2y=-14-x \\ -2y=-x-14 \end{gathered}[/tex]2) Divide both sides of the expression by "-2"
[tex]\begin{gathered} -\frac{2y}{-2}=-\frac{x}{-2}-\frac{14}{-2} \\ y=\frac{1}{2}x+7 \end{gathered}[/tex]The slope of the line is
[tex]m=\frac{1}{2}[/tex]So the slope of a line perpendicular to it will be the inverse negative of it
[tex]\begin{gathered} n=-(\frac{1}{\frac{1}{2}}) \\ n=-2 \\ \end{gathered}[/tex]The correct option is the one that has slope -2
can u find a b and c its parallelogramthank u
To answer this question, we need to remember two theorems of parallelograms:
1. If a quadrilateral is a parallelogram, the two sets of its opposite angles are congruent:
2. The consecutive angles of parallelograms are supplementary (they sum 180 degrees):
Then, with this information, we have that:
[tex]97\cong m\angle c\Rightarrow m\angle c=97[/tex]And also, we have that the diagonal forms two congruent triangles, and the sum of internal angles of a triangle is equal to 180, then, we have:
[tex]m\angle c+26+m\angle b=180\Rightarrow97+26+m\angle b=180\Rightarrow m\angle b=180-97-26[/tex]Then, we have:
[tex]m\angle b=180-123\Rightarrow m\angle b=57[/tex]Then, using that the consecutive angles of parallelograms are supplementary (they sum 180 degrees), we have:
[tex]97+m\angle a+m\angle b=180\Rightarrow97+m\angle a+57=180\Rightarrow m\angle a=180-97-57_{}[/tex]Thus, we have that the measure for angle a is:
[tex]m\angle a=180-154\Rightarrow m\angle a=26[/tex]In summary, we have that (all the measures in degrees):
m< a = 26
m< b = 57
m< c = 97
y - 7.8= 5.5 I got 2.9 but I want to be sure I understand and took the right steps
Given the equation:
[tex]y-7.8=5.5[/tex]You need to solve for "y" in order to find its value. In this case, you need to apply the Addition Property of Equality, which states that, if:
[tex]a=b[/tex]Then:
[tex]a+c=b+c[/tex]Therefore, you need to add 7.8 to both sides of the equation in order to solve for "y":
[tex]\begin{gathered} y-7.8+(7.8)=5.5+(7.8) \\ y=13.3 \end{gathered}[/tex]Hence, the answer is:
[tex]y=13.3[/tex]Original cost $21.99 Markup 5%. What's the new price?
Explanation:
We have to find 5% of the original cost first:
[tex]21.99\times\frac{5}{100}=21.99\times0.05=1.0995[/tex]And then add it to the original price:
[tex]21.99+1.0995=23.0895[/tex]Since it's a price, we have to round this result to the nearest hundredth
Answer:
The new price is $23.09
Which equation represents the values in the table? x–1012y–13711A.y = 4x + 3B.y = −x − 1C.y = 3x − 1D.y = 1/4x − 3/4
We know it's a linear function, which is like
[tex]f(x)=mx+b[/tex]We can find the slope "m" of the linear function doing
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]There the points x₂, x₁, y₂ and y₁ we can take what's more convenient for us, just be careful, if you do x₁ = 0, you must take the correspondent y₁, the value of y on the same column, therefore y₁ = 3, for example.
I'll do x₁ = 0 which implies y₁ = 3 and x₂ = 1 which implies y₂ = 7. Therefore
[tex]\begin{gathered} m=\frac{7_{}-3}{1_{}-0_{}} \\ \\ m=\frac{7_{}-3}{1_{}}=4 \end{gathered}[/tex]Therefore the slope is m = 4, then
[tex]y=4x+b[/tex]To find out the "b" value we can use the fact that when x = 0 we have y = 3, therefore
[tex]\begin{gathered} y=4x+b \\ \\ 3=4\cdot0+b \\ \\ 3=b \\ \end{gathered}[/tex]Then b = 3, our equation is
[tex]y=4x+3[/tex]The correct equation is the letter A.
From the table below, determine whether the data shows an exponential function. Explain why or why not. x31-1-3y1234a.No; the domain values are at regular intervals and the range values have a common sum 1.b.No; the domain values are not at regular intervals.c.Yes; the domain values are at regular intervals and the range values have a common factor 2.d.Yes; the domain values are at regular intervals and the range values have a common sum 1.
Solution:
Given:
The table of values is given:
From the table,
We see the data is a linear function. This is because a linear function has domain values at regular intervals.
Also, the linear equation can be formed as shown below, indicating it is a linear function.
Considering two points, (3,1) and (1,2)
where,
[tex]\begin{gathered} x_1=3 \\ y_1=1 \\ x_2=1 \\ y_2=2 \\ \\ \text{Then,} \\ \text{slope, m is given by;} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ \\ \text{Substituting the values into the formula above,} \\ m=\frac{2-1}{1-3} \\ m=\frac{1}{-2} \\ m=-\frac{1}{2} \end{gathered}[/tex]A linear equation is of the form;
[tex]\begin{gathered} y=mx+b \\ \text{where m is the slope} \\ b\text{ is the y-intercept} \\ \\ To\text{ get the value of the y-intercept, we use any given point} \\ U\sin g\text{ point (3,1)} \\ y=mx+b \\ 1=-\frac{1}{2}(3)+b \\ 1=-\frac{3}{2}+b \\ 1+\frac{3}{2}=b \\ 1+1.5=b \\ b=2.5 \\ \\ \\ \text{Thus, the linear equation is;} \\ y=-\frac{1}{2}x+2.5 \end{gathered}[/tex]From the above, has confirmed it is a linear function and not an exponential function, we can deduce that;
a) The function is not an exponential function.
b) The domain values (x-values) are at regular intervals
c) The range values (y-values) have a common difference of 1
Therefore, the correct answer is OPTION A
helpppppppppp!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:f(x) = 1/4x
Step-by-step explanation:
Assuming this is a linear equation, we simply use the two points given to find the slope (or gradient depending on where you’re from), to find the equation. So just do rise over run:
Edited: I divided backwards, apologies!
-3 - (-2)/-8 - (-12) = -5/-20 = 1/4x.
A pound of rice crackers cost 42.88 Jacob purchased a 1/4 pound how much did he pay for the crackers?
Answer:
10.72
Step-by-step explanation:
The price per pound is 42.88
We are getting 1/4 pound.
Multiply 42.88 by 1/4
42.88 * 1/4 =10.72
Answer:
So you know that a pound of rice crackers cost $42.88. You also know that Matthew bought 1/4 or 25% or 0.25 of a pound. This means that by 42.88 divided 4 will equal the answer.
42.88 ÷ 4 = 10.72
Therefore, Matthew paid or $10.72 for 1/4 pound of rice crackers.
An ice cream truck began its daily route with 95 gallons of ice cream. The truck driver sold 58% of the ice cream. How many gallons of ice cream were sold? round to nearest gallon
Start making the percentage as a fraction
[tex]\begin{gathered} 58\text{\%}=\frac{58}{100} \\ \end{gathered}[/tex]multiply the fraction by the total of the daily routine
[tex]95\cdot\frac{58}{100}=55.1\approx55gallons[/tex]question 1 A new streaming company charges a rate of $5.99 per month. in order to generate some additional revenue upfront the company is offering a VIP rate of only $3.49 Per month to any subscriber who purchases a VIP pass for one time fee of $21 set up in solving any qualities to determine how many months it would take for subscriber to save money by purchasing the VIP pass
21 + 3.49x < 5.99x
x > 8.4
Explanations:The normal monthly rate = $5.99
The VIP monthly rate = $3.49
The one time VIP fee = $21
Let the number of months be x
At normal rate, the total charge for x months = 5.99x
For the VIP:
The total charge for x months = 21 + 3.49x
For a subscriber to save money by purchasing the VIP pass, it means the total charge for the VIP must be less than the total charge for the normal subscribers5.99x
Therefore, the inequality to determine how many months it will take for a subscriber to save money by purchasing the VIP pass is:
21 + 3.49x < 5.99x
Solve the inequality above:
21 < 5.99x - 3.49x
21 < 2.5x
2.5x > 21
x > 21/2.5
x > 8.4
Therefore, for a subscriber to save money by purchasing the VIP pass, it would take more than 8.4 months
Over a set of 5 chess games, Yolanda's rating increased 10 points, increased 4 points,
decreased 21 points, increased 23 points and decreased 8 points.
Her rating is now 1647.
What was her rating before the 5 games?
A. 1639
B. 1649
C. 1655
D. 1661
Answer:
C. 1655
Step-by-step explanation:
+10, +4, -21, +23, -8
Adding all those terms together we get 8
1647 + 8 = 1655
which of the following statements is correct?A XYZ ~ wvz by AA similarityB XYZ ~ WVZ by SAS similarityC XYZ ~ WVZ by SSS similarityD XYZ and WVZ are not similar
We have two triangles, XYZ and WVZ.
They shared the vertex Z, formed by the intersection of two lines, XW and VY.
Also, XY and VW are parallel.
Then, we have a pair of congruent angles at vertex Z, as they are vertical angles.
We also have another pair of congruent angles: V and Y, because they are alternate interior angles between parallel lines.
Then, as we have two pair of congruent angles, the third pair of angles have to be congruent too, as the measures of the interior angles of a triangle always add 180°.
Then, if we have 3 pair of congruent angles, we have similar triangles.
We can not say anything about congruent sides because we don't know any relation or proportion between them, so the other postulates, SAS or SSS, can not be used.
Answer: XYZ ~ WVZ by AA similarity (Option A)
A test was given to a group of students. The grades and gender are summarized below A B C TotalMale 5 9 2 16Female 7 11 12 30Total 12 20 14 46If one student is chosen at random from those who took the test, find the probability that the student got a 'C' GIVEN they are female.
Probability that the student got a 'C' GIVEN they are female = number of females that got a C in the test/number of females
From the information given,
number of females that got a C in the test = 12
number of females = 30
Thus,
Probability that the student got a 'C' GIVEN they are female = 12/30
We would simplify the fraction by dividing the numerator and denominator by 6. Thus,
Probability that the student got a 'C' GIVEN they are female = 2/5
