The number of rolls divided in the two groups so that the ratio is 3 to 5 is 27 and 45 respectively.
According to the question,
We have the following information:
Rolls are being prepared to go to grocery stores.
Now, we have to divide 72 rolls into 2 groups so the ratio is 3 to 5.
Now, let's take the number of rolls given to the first group to be 3x and the number of rolls given to the second group to be 5x.
So, we have the following expression:
3x+5x = 72
8x = 72
x = 72/8
x = 9
So, the number of rolls for the first group:
3x
3*9
27
Now, the number of rolls for the second group:
5x
5*9
45
Hence, the number of rolls divided in the given two group is 27 and 45.
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Two airplanes are flying in the air at the same height. Airplane A is flying east at 451 mi/h and airplane B is flying north at 494 mi/h. If they are both heading to the same airport, located 3 miles east of airplane A and 3 miles north of airplane B, at what rate is the distance between the airplanes changing?
The rate at which the distance between the airplanes is changing is 668.2 mi/h.
In the given question,
Speed of Airplane A:
dA/dt = 451 mi/h
and the Speed of Airplane B:
dB/dt = 494 mi/h
Aircraft A and B will form a right triangle because Aircraft A is flying east and Aircraft B is flying north, and we can use Pythagoras' theorem to calculate their distance from one another.
Let P be the distance.
P² = A² + B²
Differentiating the above equation with respect to t,
2P(dP/dt) = 2A(dA/dt) + 2B(dB/dt)
Dividing each side of the equation by 2,
P( dP/dt ) = A( dA/dt ) + B( dB/dt ) ..........(1)
Where dP/dt is the rate of change in distance between the two aircraft.
Now,
P² = A² + B²
P = √(A² + B²)
Substituting, A = 3 miles and B = 3miles;
P = √(3² + 3²)
P = √( 9+ 9)
P = √18
P = 3√2 miles
Substituting the value in the equation (i)
3√2 (dP/dt) = (3× 451) + (3× 494)
3√2 (dP/dt) = 2835
4.2426 × dP/dt = 2835
dP/dt = 2835/4.2426
dP/dt = 668.2 mi/h
Therefore, the rate at which the distance between the airplanes is changing is 668.2 mi/h
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sean earns $300 in a regular work week. A regular work week for sean consists of 5 work days with 8 hours a day. How much money does sean earn each hour
Solution:
According to the problem, a regular work week consists of 5 work days with 8 hours a day. This is equivalent to say:
5 x 8 hours every regular work week.
That is:
40 hours every regular work week
then, the money earned per hour is:
[tex]\frac{300\text{ }dollars}{40\text{ hours}}\text{ = 7.5 dollars per hour}[/tex]then we can conclude that the correct answer is:
$7.5
For triangle ABC, AB = 3 cm and BC = 5 cm.Which could be the measure of AC?A 2 cmB 4 cmC 8 cmD 15 cm
ANSWER
2, 4 and 8
EXPLANATION
We have that in a triangle ABC, AB = 3 cm and BC = 5 cm.
To find the possible length of AC, we can apply the triangle inequality theorem.
It states that in any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.
This means that:
[tex]\begin{gathered} AB\text{ + AC }\ge\text{ BC} \\ \text{and } \\ AB\text{ + BC }\ge\text{ AC} \\ \text{and} \\ AC\text{ + BC }\ge\text{ AB} \end{gathered}[/tex]So, we have that:
[tex]\begin{gathered} 3\text{ + AC }\ge\text{ 5 }\Rightarrow\text{ AC }\ge\text{ 2} \\ 3\text{ + 5 }\ge\text{ AC }\Rightarrow\text{ AC }\leq\text{ 8} \\ AC\text{ + 5 }\ge3\Rightarrow\text{ AC }\ge\text{ -2} \end{gathered}[/tex]We have to disregard the third line, since the length of a triangle side can only be positive.
So, using the first 2 lines, we see that:
[tex]2\text{ }\leq\text{ AC }\leq\text{ 8}[/tex]This means that from the options, the measure of AC can either be 2, 4 or 8.
Which theorem proves that the triangles are congruent?a) CPCTC b) SAS c) AAS d) SSS
Answer:
B. SAS
:)
Step-by-step explanation:
propriate symbols and/or words in your submissionSolve for the indicated measure.5. R = 19°, ZB = 56°, find mZT.6. R = 19, ZB'S 56°, find mZS.7. R = 19°, ZB = 56°, find mZC.8. True or false?AABC = AZXY9. Are the two triangles congruent?Yes or no?10. Use the image below to complete the proof.Identify the parts that are congruent by the given reason in the proof.STATEMENTS REASONSAB = DC GivenAB || DC Given2.Alternate Interior Angles TheoremReflexive Property of CongruenceSAS Congruence Theorem3.4.
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The sum of the internal angles in a triangle equals 180°
R + B = T = 180
Substitution
19 + 56 + T = 180
T = 180 - 19 - 56
T = 105°
Result:
T = 105°
Look at this set of ordered pairs: (-8, 19) (11, 1) (0, 15. Is this relation a function?
Answer:
Yes, the set of ordered pairs is a function.
Explanation:
To test whether a given set of ordered pairs represents a function, we have to make sure that it satisfies the definition.
By definition, a function cannot have two outputs for one input. For example, the set of ordered pairs (3, 10 ) and (4, 5) represents a function whereas (3, 10) and (3, 13) does not.
With this in mind, looking at the given set we see that every input gives a unique output; therefore, the set represents a function.
-21 < f (x) < 0 , where f (x) = - 2x- 5
We can solve this using the next property:
If a
Replace f (x) = - 2x- 5 , then:
-21 < f (x) < 0
-21 < -2x-5 < 0
Solve -21 < -2x-5 and -2x-5 < 0
Therefore:
-21 < -2x-5
Add both sides 5
-21+5 < -2x-5 +5
-16 < -2x
(-1)-16 < (-1)(-2x)
16>2x
x<16/2
x<8
and
-2x-5 < 0
Add both sides 5
-2x-5 +5 < 0+5
-2x<5
(-1)-2x < (-1)5
2x > -5
x > -5/2
Hence, the resulting interval is:
-5/2 < x < 8
OB. 1OC.If X = 24 inches, Y = 45 inches, and Z= 51 inches, what is the tangent of ZA?OA. 19715NOD. 1B
Given that
We have a right-angled triangle and have to find angle A's tangent.
Explanation -
The triangle is shown as
Here we have,
X = 24 inches
Y = 45 inches
Z = 51 inches
Then, the tangent of angle A will be
[tex]\begin{gathered} The\text{ formula for the tangent is } \\ tan=\frac{Perpendicular}{Base} \\ \\ tan=\frac{P}{B} \\ For\text{ angle A thevalues are, P = 45 and B = 24} \\ Then, \\ tanA=\frac{45}{24} \\ \\ tanA=\frac{15}{8} \end{gathered}[/tex]So the correct option is B.
Final answer -
Therefore the final answer is 15/8Writing the equation of a quadratic function given its graph
Answer:
[tex]y=-(x-1)^2+2[/tex]Step-by-step explanation:
A quadratic function in vertex form is represented as:
[tex]\begin{gathered} y=a(x-h)^2+k \\ \text{where,} \\ (h,k)\text{ is the vertex} \end{gathered}[/tex]Given the vertex (1,2) substitute it into the function:
[tex]y=a(x-1)^2+2[/tex]As you can see, we still do not know the value for ''a'', use the point given (4,-7) substitute it (x,y) and solve for ''a'':
[tex]\begin{gathered} -7=a(4-1)^2+2 \\ -7=a(3)^2+2 \\ -7=9a+2 \\ 9a=-7-2 \\ a=-\frac{9}{9} \\ a=-1 \end{gathered}[/tex]Hence, the equation of the function would be:
[tex]y=-(x-1)^2+2[/tex]Factor the common factor out of each expression (GCF).-32m^5n - 36m^6n - 24m^5n^2________________________
In order to find the greatest common factor (GCF) of the terms, first let's factor the numeric values in their prime factors:
[tex]\begin{gathered} 32=2\cdot2\cdot2\cdot2\cdot2\\ \\ 36=2\cdot2\cdot3\cdot3\\ \\ 24=2\cdot2\cdot2\cdot3 \end{gathered}[/tex]The common factor between these three numbers is the product of the common prime factors, that is, 2 * 2 = 4.
Now, to find the common factor of the variables, we choose for each variable the one with the smaller exponent:
[tex]\begin{gathered} m^5,m^6,m^5\rightarrow m^5\\ \\ n,n,n^2\rightarrow n\\ \\ \\ GCF=m^5n \end{gathered}[/tex]Therefore the common factor is -4(m^5)n.
(we can put the negative signal as well, since all terms are negative).
Convert 7 liters into gallons using measurement conversion 1 liter= 1.0567 quarts. Round to two decimals
Convert 7 liters into gallons
We have the measurement conversion 1 liter= 1.0567 quarts
and the gallons = 4 quarts
So, 7 liters = 7 * 1.0567 quarts = 7.3969 quarts
We will convert from the quarts to gallons as follows:
1 gallons = 4 quarts
x gallons = 7.3969 quarts
so, the value of x will be:
[tex]x=\frac{7.3969}{4}=1.849225[/tex]Round to two decimals
so, the answer will be 1.85 gallons
In a right triangle, one of the acute angles measures of degrees. What is the measure of the other acute angle?
A. 90-d
B. 90 d
C. 180-d
D. 180+d
The correct answer is A. 90 - d
Since the sum of all the angles in a triangle is 180° and one of the angle is 90° because the triangle is a right triangle. So the sum of the remaining angles is 90°.
And to find the other acute angle we use 90° - d.
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To the right is the graph of f(x) = x^2. The second graph, to the left of f(x) = x^2 is a new function made by stretching f(x) vertically by a factor of 2 and then translating it three units to the left and one unit down. Write the equation of the new function.
This problem invloves the topic of curved lines in a graph, curved lines or more speccifically curve line which looks like letter C (parabola) all follows a certain standard form of equation, which is;
[tex]y=ax^2+b[/tex]For example you can see that the equation for the black curve line in our picture is y=x² and notice that this equation can also be written as y = (1)x² + 0. Which simillar to the standard form given above where a is just 1 (a=1) and b is just 0 (b=0).
Since our black curve line follows the same standard form of equation as stated above, we can conclude that the RED curve line follows the same form of equation.
To summarize the steps that we must do in order to find the equation of the RED line we will list them as,
1. Sample two(2) points in the graph to be used as reference points.
2. Use the sampled points in our standar eqation in order to find the variables "a" and "b".
3. When we have the variables "a" and "b", we can just directly substitute it into our standard equation to find the equation of our RED line.
Let's start.
1. Sample 2 points to be used as refernce points. (Note that we will find the easiest points
to determine)
Let us use the points (-3, -1) and (-2, 1) as shown in the picture.
2. Use the points (-3, -1) and (-2, 1) in our standard equation.
[tex]\begin{gathered} y=ax^2+b \\ \text{where (x,y)=(-3, -1)} \\ -1=a(-3)^2+b_{} \\ 9a+b=-1 \end{gathered}[/tex]
for our 1st point we have the equation 9a+b = -1, let us now proceed to our next point.
[tex]\begin{gathered} y=ax^2+b \\ \text{where (x,y)=(-2, 1)} \\ 1=a(-2)^2+b_{}_{} \\ 1=4a+b \\ 4a+b=1 \end{gathered}[/tex]and for our 2nd point we have the equation 4a+b = 1, and by the process of subtitution and elimination we can now find "a" and "b", because we have two equations with two unknowns.
[tex]\begin{gathered} 9a+b=-1\text{ and} \\ 4a+b=1 \end{gathered}[/tex]transforming eqatuin number 1 to
[tex]9a+b=-1\text{ is just the same as b = -1 -9a}[/tex]
then substitue b = -1 -9a to the 2nd equation we have.
[tex]\begin{gathered} 4a+b=1\text{ , where b = -1-9a} \\ 4a+(-1-9a)=1 \\ 4a-1-9a=1 \\ -5a=2 \\ a=-\frac{2}{5} \end{gathered}[/tex]
since a = -2/5, we can find b using,
[tex]\begin{gathered} 4a+b=1\text{ , where a=-}\frac{2}{5} \\ 4(-\frac{2}{5})+b=1 \\ b=1+\frac{8}{5} \\ b=\frac{5}{5}+\frac{8}{5} \\ b=\frac{13}{5} \end{gathered}[/tex]therefore our a and b are;
[tex]a=-\frac{2}{5}\text{ and b = }\frac{13}{5}[/tex]3. We can now proceed in substituting it in our standard equation;
[tex]\begin{gathered} y=ax^2+b\text{ , where a = -}\frac{2}{5}\text{ and b = }\frac{13}{5} \\ y=(-\frac{2}{5})x^2+(\frac{13}{5}) \\ y=-\frac{2}{5}x^2+\frac{13}{5} \end{gathered}[/tex]you can also simplify the final equation by multiplying all sides by 5,
[tex]\begin{gathered} 5y=(5)\lbrack-\frac{2}{5}x^2+\frac{13}{5}\rbrack \\ 5y=-2x^2+13 \end{gathered}[/tex]therefore our final answer can be,
[tex]\begin{gathered} f(x)=-\frac{2}{5}x^2+\frac{13}{5} \\ or \\ 5y=-2x^2+13 \end{gathered}[/tex]
Evaluate each expression for the given value of the variable. #9 and #10
Part 9
we have
(c+2)(c-2)^2
If c=8
substitute the value of c in the expression
so
(8+2)(8-2)^2
(10)(6)^2
(10(36)
360
Part 10
we have
7(3x-2)^2
If x=4
substitute the value of x in the expression
7(3(4)-2)^2
7(10)^2
7(100)
700
Given that DE is the midsegment of the scalene AABC, answer theprompts to the right.
Answers:
Part A.
C. AD = AE
Part B.
BC = 26
Explanation:
Part A.
If DE is a midsegment of triangle ABC, D is a point that divides AB into two equal segments, so option A. 1/2 AB = AD is true.
Additionally, if DE is a midsegment of triangle ABC, its length is equal to half the length of the side that the segment doesn't cross. So:
[tex]\begin{gathered} DE=\frac{1}{2}BC \\ 2DE=2\times\frac{1}{2}BC \\ 2DE=BC \end{gathered}[/tex]Therefore, option B is also true.
Triangle ABC is scalene, it means that all their sides have different length, it means that AD is not equal to AE and option C is not true.
Finally, segments AE and EC form AB, so:
AC = AE + EC
AC - AE = AE + EC - AE
AC - AE = EC
So, option D is also true.
Therefore, the answer for part A is C. AD = AE
Part B.
We know that 2DE = BC, so replacing the expression for each segment, we get:
[tex]\begin{gathered} 2DE=BC \\ 2(2x+1)=5x-4 \end{gathered}[/tex]Solving for x:
[tex]\begin{gathered} 2(2x)+2(1)=5x-4 \\ 4x+2=5x-4 \\ 4x+2-4x=5x-4-4x \\ 2=x-4 \\ 2+4=x-4+4 \\ x=6 \end{gathered}[/tex]Now, with the value of x, we get that BC is equal to:
BC = 5x - 4
BC = 5(6) - 4
BC = 30 - 4
BC = 26
So, the answer for part B is 26.
Solve the following expression when p = 15 p/3 + 4
So, our answer is 9!
A person investigating to employment opportunities. They both have a beginning salary of $42,000 per year. Company A offers an increase of $1000 per year. Company B offers 7% more than during the preceding year. Which company will pay more in the sixth year? what will company A pay? and what will company B pay?
qANSWER
Company B will pay more
Company A =
EXPLANATION
Both companies start by paying $42,000 per year.
Company A offers an increase of $1000 per year.
This means that after n years, he would have earned:
Earnings = 42000 + 1000n
where n = number of years after the first year
So, after 6 years, he would have worked 5 years after the first, so his earnings would be:
Earnings = 42000 + 1000(5) = 42000 + 5000
Earnings = $47000
Company B offers 7% more than the previous year. That means that his earnings are compounded.
His earnings can then be represented as:
[tex]\text{ Earnings = P(1 + }\frac{r}{100})^t[/tex]where P = initial salary = $42000
r = interest rate = 7%
t = number of years spent = 6 years
Therefore, his earnings after the 6th year will be:
[tex]\begin{gathered} \text{ Earnings = 42000(1 + }\frac{7}{100})^6 \\ \text{ Earnings = 42000(1 + 0.07)}^6=42000(1.07)^6 \\ \text{ Earnings = }42000\cdot\text{ 1.501} \\ \text{Earnings = \$63042} \end{gathered}[/tex]He would have earned $63042.
Therefore, Company B will pay more.
qANSWER
Company B will pay more
Company A =
EXPLANATION
Both companies start by paying $42,000 per year.
Company A offers an increase of $1000 per year.
This means that after n years, he would have earned:
Earnings = 42000 + 1000n
where n = number of years after the first year
So, after 6 years, he would have worked 5 years after the first, so his earnings would be:
Earnings = 42000 + 1000(5) = 42000 + 5000
Earnings = $47000
Company B offers 7% more than the previous year. That means that his earnings are compounded.
His earnings can then be represented as:
[tex]\text{ Earnings = P(1 + }\frac{r}{100})^t[/tex]where P = initial salary = $42000
r = interest rate = 7%
t = number of years spent = 6 years
Therefore, his earnings after the 6th year will be:
[tex]\begin{gathered} \text{ Earnings = 42000(1 + }\frac{7}{100})^6 \\ \text{ Earnings = 42000(1 + 0.07)}^6=42000(1.07)^6 \\ \text{ Earnings = }42000\cdot\text{ 1.501} \\ \text{Earnings = \$63042} \end{gathered}[/tex]He would have earned $63042.
Therefore, Company B will pay more.
Based on the graph of f(x) shown here what is f^-1(8).
Answer
2
Explanation:
f⁻¹(8) is equal to the value of x that makes f(x) = 8. So, taking into account the graph, we get:
Therefore, f⁻¹(8) = 2. So the answer is 2
A new shopping mall is gaining in popularity. Every day since it opened, the number of shoppers is 20%, percent more than the number of shoppers the day before. The total number of shoppers over the first 4 days is 671.How many shoppers were at the mall on the first day?Round your final answer to the nearest integer.
if the number of shoppers increases by 20% daily and 671 shoppers had visited over 4 days then let the num ber of shoppers on the first day be x
The numebr of shopperes the next day will be
= x(100 + 20)%
= 1.2x
teh number of shoppers the day after
= 1.2x(100 + 20)%
= 1.44x
the next day, the number
= 1.44x (100 + 20)%
= 1.728x
Given that the total number of people that have shopped after 4 days is 671 then
x + 1.2x + 1.44x + 1.728x = 671
5.368x = 671
x = 671/5.368
= 125
if the number of shoppers increases by 20% daily and 671 shoppers had visited over 4 days then let the num ber of shoppers on the first day be x
The numebr of shopperes the next day will be
= x(100 + 20)%
= 1.2x
teh number of shoppers the day after
= 1.2x(100 + 20)%
= 1.44x
the next day, the number
= 1.44x (100 + 20)%
= 1.728x
Given that the total number of people that have shopped after 4 days is 671 then
x + 1.2x + 1.44x + 1.728x = 671
5.368x = 671
x = 671/5.368
= 125
We have a box with a circular base (diameter 20 cm) and height 4 cm.Calculate the volume.
We can calculate the volume as the product of the area of the base and the height.
The area of the base is function of the square of the diameter, so we can write:
[tex]\begin{gathered} V=A_b\cdot h \\ V=\frac{\pi D^2}{4}\cdot h \\ V\approx\frac{3.14\cdot(20\operatorname{cm})^2}{4}\cdot4\operatorname{cm} \\ V\approx\frac{3.14\cdot400\operatorname{cm}\cdot4\operatorname{cm}}{4} \\ V\approx1256\operatorname{cm}^3 \end{gathered}[/tex]Answer: the volume of the box is 1256 cm^2.
AMNP ~ AQRP N x + 8 28 M 24 P 3x - 9 R Create a proportion and find the length of side PR*
Using thales theorem:
[tex]\begin{gathered} \frac{24}{28}=\frac{x+8}{3x-9} \\ 24(3x-9)=28(x+8) \\ 72x-216=28x+224 \\ 44x=440 \\ x=\frac{440}{44} \\ x=10 \\ PR=3(10)-9=21 \end{gathered}[/tex]Each face of a pyramid is an isosceles triangle with a 70 degree vertex angle. What are the measures of the base angles?
We are given that each face of a pyramid is an isosceles triangle and that its vertex angle is 70 degrees. This problem can be exemplified in the following diagram:
Since the triangle is isosceles, its base angles are the same, and the sum of the interior angles must be equal to 180 degrees. Therefore, we have the following relationship:
[tex]70+x+x=180[/tex]Adding like terms, we get:
[tex]70+2x=180[/tex]Now we solve for "x", first by subtracting 70 on both sides:
[tex]\begin{gathered} 70-70+2x=180-70 \\ 2x=110 \end{gathered}[/tex]Now we divide both sides by 2
[tex]x=\frac{110}{2}=55[/tex]Therefore, the base angles of the pyramid are 55 degrees.
B) Use the quadratic formula to find the roots of each quadratic function.
Which of these is a simplified form of the equation 8y + 4 = 6 + 2y + 1y? 5y = 25y = 1011y = 211y = 10
Explanation:
The equation is given below as
[tex]8y+4=6+2y+1y[/tex]Step 1:
Collect similar terms, we will have
[tex]\begin{gathered} 8y+4=6+2y+1y \\ 8y+4=6+3y \\ 8y-3y=6-4 \\ 5y=2 \end{gathered}[/tex]Hence,
The simplified form of the equation will be
[tex]\Rightarrow5y=2[/tex]In the matrix equation below, what are the values of x and y? 1/2 [4 8 x+3 -4] -3 [1 y+1 -1 -2]= [-1 -5 7 4]
Using the matrix equation, the value of x and y are 5 and 2 respectively.
Consider the 2 by 2 matrix equations,
1/2 [ 4 8 ( x + 3 ) - 4 ] - 3[ 1 y+1 -1 - 2 ] = [ - 1 -5 7 4 ]
[ 2 4 (x+3)/2 -2] + [ - 3 -3y -3 +3 + 6] = [ - 1 - 5 7 4]
[ -1 -3y + 1 (x + 9)/2 + 4] = [ - 1 - 5 7 4]
Therefore,
- 3y + 1 = - 5
Subtracting 1 from each side of the equation,
- 3y + 1 - 1 = - 5 - 1
- 3y = - 6
Dividing each side of the equation by - 3,
y = 2
And;
( x + 9 )/2 = 7
Multiplying each side by 2,
x + 9 = 14
Subtracting 9 from each side of the equation,
x + 9 - 9 = 14 - 9
x = 5
Therefore, the value of x and y is 5 and 2 respectively.
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There are 152 students at a small school and 45 of them are freshmen. What fraction of the students are freshmen? Use "/" for the
fraction bar. Do not use spaces in your answer.
45/152 is fraction of the students are freshmen.
What are fraction?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction is a portion of a whole and is used to represent how many pieces of a particular size there are while speaking in ordinary English, for example, one-half, eight-fifths, and three-quarters. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. There is a proportion there in numerator or denominator of a complicated fraction. There are three main categories of fractions in mathematics. Proper fractions, incorrect fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions.
Total students = 152
Freshman = 45
Fraction = 45/152
This is the simplest form .
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Four plumbers estimated the length of the length of the radius of a cylindrial pipe. The estimates made by the plumbers are listed • 3/5 • 3/11 • 9/100 • 3.14/24 ? : . .
Different estimates:
The length of the radius of a cylindrical pipe:
Plumber W:
Radius had a length: 3/5 inches.
Plumber X:
Radius had a length: sqrt(3/11) inches.
Plumber Y:
Radius had a length of 9/100 inches.
Plumber Z:
Radius had a length of 3/14/24 inches.
Turn them into decimals:
We can turn each length into decimal:
Plumber W: 3/5 = 0.6.
Plumber X: sqrt(3/11) = 0.522222..
Plumber Y: 9/100 = 0.09
Plumber Z: 3.14/24 = 0.13083
The list from the greatest to least:
We can order this list taking into account the following reasoning: when the number is near to zero, this number is less than the other in the list. Examples: 0.001, 0.0002, 0.00004 are very near to zero.
Additionally, when a number is near 1 (the unit), this number is greater than the other less near to 1.
Examples: 0.69, 0.73, 0.888, 0.99 are near to zero.
The numbers we got in the list are decimals numbers coming from fractions and the square root was taken to the estimation of plumber X. Therefore:
From list 0.6, 0.52222..., 0.09, 0.13083
The number nearest to zero is 0.09. Then, 0.13083 is greater than 0.09 but less than the others. The following number is 0.5222..., and the greatest is 0.6.
The list that shows these lengths in order from the greatest to least is:
{0.6, 0.5222..., 0.13083, 0.09}.
Which is equivalent to:
{3/5, sqrt(3/11), 3.14/24, 9/100}.
10 of 25Jackie and Ruth both studied very hard for their history test. Ruth studied 2 hours less than twice as many hours as Jackie.Together,"heir study time was 10 hours. How many hours did Ruth study for her history test?
Answer: 6 hours
Explanation:
We have that "Ruth studied 2 hours less than twice as many hours as Jackie". I will call the hours that Ruth studied "R" and the hours that Jackie studied "J". The first equation is as follows:
[tex]R=2J-2[/tex]The hours that Ruth studied as 2 less than twice as many as Jackie. This will be referred to as equation 1.
Now, we are told that "Together, their study time was 10 hours" so we have the following equation:
[tex]R+J=10[/tex]This will be our equation 2.
The next step is to substitute equation 1 into equation 2:
[tex]2J-2+J=10[/tex]And we solve for J.
Combining like terms:
[tex]3J-2=10[/tex]We add +2 on both sides of the equation to cancel the -2 on the left side:
[tex]\begin{gathered} 3J-2+2=10+2 \\ 3J=12 \end{gathered}[/tex]And we divide both sides by 3:
[tex]\begin{gathered} \frac{3J}{3}=\frac{12}{3} \\ \\ J=4 \end{gathered}[/tex]Jackie studied for 4 hours.
Since we are asked for Ruth, we substitute J=4 into the equation 1:
[tex]\begin{gathered} R=2J-2 \\ R=2(4)-2 \\ R=8-2 \\ R=6 \end{gathered}[/tex]Ruth studied for 6 hours.
If log a=4 log b= -16 and log c=19 find value of log a^2c (——-) /—— / B
We have the following
[tex]\begin{gathered} \log a=4 \\ \log b=-16 \\ \log c=19 \\ \log (\frac{a^2\cdot c}{\sqrt[]{b}}) \end{gathered}[/tex]Let's find a, b and c in order to solve the problem
a.
[tex]\begin{gathered} \log a=4 \\ a=10^4=10000 \end{gathered}[/tex]a = 10,000
b.
[tex]\begin{gathered} \log b=-16 \\ b=10^{-16}=\frac{1}{10^{16}} \end{gathered}[/tex]b=1.0E-16
c.
[tex]\begin{gathered} \log c=19 \\ c=10^{19} \end{gathered}[/tex]c=1.0E19
Thus, the value of log [ a^2c/sqrt(c) ] is :
replace:
[tex]\log (\frac{a^2\cdot c}{\sqrt[]{b}})=\log _{10}\mleft(\frac{\left(10^4\right)^2\cdot\:10^{19}}{\sqrt{10^{-16}}}\mright)[/tex]simplify:
[tex]\begin{gathered} \frac{\left(10^4\right)^2\cdot\:10^{19}}{\sqrt{10^{-16}}}=\frac{10^8\cdot10^{19}}{10^{-8}}=10^8\cdot10^8\cdot10^{19}=10^{8+8+19}=10^{35} \\ \Rightarrow\log 10^{35}=35 \end{gathered}[/tex]Therefore, the answer is 35
Choose the correctdomain for thequadratic function.А-00 > X < 0B-00 < x < 0
The function given in the graph stretches from negative to positive infinity.
Hence the domain of the function is given by:
[tex]-\inftyOption B is correct.