In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
sample proportion = 0.3
widest 95% confidence interval
sample = ?
Step 02:
p = 0.3
1 - α = 0.95 =>> z α/2 = 1.96
We must check each value to find the solution.
A. sample = 36
[tex]\begin{gathered} 0.3-1.96\cdot\sqrt[]{\frac{0.3\cdot0.7}{36}}=0.3-0.1499 \\ 0.3+1.96\cdot\sqrt[]{\frac{0.3\cdot0.7}{36}}=0.3+0.1499 \end{gathered}[/tex]confidence interval (0.1501 , 0.4499)
difference = 0.2998
B. sample = 56
[tex]\begin{gathered} 0.3-1.96\cdot\sqrt[]{\frac{0.3\cdot0.7}{56}}=0.3\text{ - }0.120 \\ 0.3+1.96\cdot\sqrt[]{\frac{0.3\cdot0.7}{56}}=\text{ 0.3 + }0.120 \end{gathered}[/tex]confidence interval (0.18 , 0.42)
difference = 0.24
Analyzing these two values, we can conclude that the widest confidence interval will be for the smallest sample.
The answer is:
Sample = 36
-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
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.
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°
which number is 5 more than 8009998
A number which is 5 more than 8009998 is 8010003
In this question we need to find a number which is 5 more than 8009998.
Let x be a number which is 5 more than 8009998.
We get the required number by adding 5 to 8009998.
so, we write it down as:
x = 8009998 + 5
x = 8010003
Therefore, a number which is 5 more than 8009998 is 8010003
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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}.
Solve the following expression when p = 15 p/3 + 4
So, our answer is 9!
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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80% of _ = 20?4-4-4-
Let
x -----> the missing number
we know that
80%=80/100=0.80
so
0.80x=20
solve the linear equation for x
Divide by 0.80 both sides
x=20/0.80
x=25
the answer is 25
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.
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.
Suppose a basketball player has made 359 out of 449 free throws. If the player makes the next 3 free throws, I will pay you $39. Otherwise you pay me $43.
Step 2 of 2 : If you played this game 623 times how much would you expect to win or lose?
Answer: expect to lose 679.07 dollars
==========================================================
Explanation:
Assuming each free throw is independent of any other, the probability of making the next free throw is 359/449
The probability of making 3 in a row is (359/449)^3 = 0.511145 approximately which represents the probability of earning the $39
That must mean 1-0.511145 = 0.488855 is the approximate probability of losing $43
Let's make a table of outcomes and their associated probabilities.
X = amount of money the player earns (the person shooting the free throws)
[tex]\begin{array}{|c|c|} \cline{1-2}\text{X} & \text{P(X)}\\\cline{1-2}39 & 0.511145\\\cline{1-2}-43 & 0.488855\\\cline{1-2}\end{array}[/tex]
Then from here we'll multiply each X and P(X) value for each separate row.
Example: 39*0.511145 = 19.934655
Let's form a third column of these products
[tex]\begin{array}{|c|c|c|} \cline{1-3}\text{X} & \text{P(X)} & \text{X}*\text{P(X)}\\\cline{1-3}39 & 0.511145 & 19.934655\\\cline{1-3}-43 & 0.488855 & -21.020765\\\cline{1-3}\end{array}[/tex]
Add up everything in the X*P(X) column and you should get roughly -1.08611 which rounds to -1.09
The player expects, on average, to lose about $1.09 each time they play this game. Playing 623 times means they should expect to lose 623*1.09 = 679.07 dollars
Of course, given the nature of this random process, it's not a guarantee they will lose this amount. This is just the average of many attempts.
B) Use the quadratic formula to find the roots of each quadratic function.
on a map where each unit represents one kilometer two marinas are located at p(4,2) and q(8,12). if a boat travels in a straight line from one marina to the other how far does the boat travel. Answer choices: 14 kilometers 2^296 kilometer 2^5 kilometers
Solution
Step 1:
Write the two given points:
p(4,2) and q(8,12)
Step 2
Find the distance between the two points:
[tex]\begin{gathered} Distance\text{ = }\sqrt{(8-4)^2+(12-2)^2} \\ \\ =\text{ }\sqrt{4^2+10^2} \\ \\ =\text{ }\sqrt{16+100} \\ \\ =\text{ }\sqrt{116} \\ \\ =\text{ 2}\sqrt{29} \end{gathered}[/tex]Answer
[tex][/tex]Line k contains the points (-9,4) and (9,-8) in the xy-coordinate plane. What are the two other points that lie on line k?
Answer
D. (-3, 0) and (3, -4)
Explanation
Let the coordinate of the points be A(-9, 4) and B(9, -8).
We shall look for the gradient m of line using
m = (y₂ - y₁)/(x₂ - x₁)
Substitute for x₁ = -9, y₁ = 4, x₂ = 9 and y₂ = -8
m = (-8 - 4)/(9 - -9) = -12/18 = -2/3
From option A - D given, only C and D would have the same gradient of -2/3 as line AB
To know the correct option, we shall look for the equation of the line AB, that is,
(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)
(y - 4)/(x - -9) = (-8 - 4)/(9 - -9)
(y -4)/(x + 9) = -12/18
(y - 4)/(x + 9) = -2/3 -----------*
Between option C and D, only D satisfies the equation *
That is, using (-3, 0), we have (0 - 4)/(-3 + 9) = -4/6 = -2/3
Also, using (3, -4), we have (-4 - 4)/(3 + 9) = -8/12 = -2/3
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).
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]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.
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.
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.
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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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
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
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]
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
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
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
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
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.
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.Which theorem proves that the triangles are congruent?a) CPCTC b) SAS c) AAS d) SSS
Answer:
B. SAS
:)
Step-by-step explanation: