Answers
Answer:
see explanation
Step-by-step explanation:
given that W varies jointly with l and d² then the equation relating them is
W = kld² ← k is the constant of variation
(a)
to find k use the condition W = 6 when l = 6 and d = 3 , then
6 = k × 6 × 3² = 6k × 9 = 54k ( divide both sides by 54 )
[tex]\frac{6}{54}[/tex] = k , then
k = [tex]\frac{1}{9}[/tex]
W = [tex]\frac{1}{9}[/tex]ld² ← equation of variation
(b)
when W = 10 and d = 2 , then
10 = [tex]\frac{1}{9}[/tex] × l × 2² ( multiply both sides by 9 to clear the fraction )
90 = 4l ( divide both sides by 4 )
22.5 = l
(c)
when d = 6 and l = 1.4 , then
W = [tex]\frac{1}{9}[/tex] × 1.4 × 6² = [tex]\frac{1}{9}[/tex] × 1.4 × 36 = 1.4 × 4 = 5.6
Related Questions
Suppose chang places $7000 and an account that pays 2% interest compounded each year. Assume that no withdraws are made from the account.Follow the instructions below. Do not do any rounding
Answers
In general, the compound interest formula is
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ P\rightarrow\text{ initial amount} \\ r\rightarrow\text{ interest rate} \\ n\rightarrow\text{ number of times the interest is applied per period of time \lparen t\rparen} \\ t\rightarrow\text{ years} \end{gathered}[/tex]In our case, since it is not specified how often the interest is compounded, we will assume that n=1; then,
[tex]A=7000(1+\frac{0.02}{1})^{1*t}=7000(1.02)^t[/tex]a) Set t=1
[tex]\begin{gathered} t=1 \\ \Rightarrow A(1)=7000(1.02)^t=7140 \\ \end{gathered}[/tex]The answer to part a) is 7140b) Set t=2,
[tex]A(2)=7000(1.02)^2=7282.8[/tex]The answer to part b) is 7282.8Notice that we are not given the number of times the interest is applied per year; therefore, we had to assume that it compounds 1 time annually.
Pls, answer in a minute. PLS
Answers
Answer: No, It is not a right-angled triangle.
Step-by-step explanation:
Find the length of the last side first. To do this, add AB and BC together, then deduct that sum from the 22 cm circumference of Triangle ABC.
ABC - (AB + BC) ⇒ 22cm - (8cm + 5cm)
22cm - 13cm = 9cm
Since the hypotenuse of a triangle is always its longest side, we can be certain that the side we identified is the hypotenuse. The Pythagorean Theorem can now be used to determine whether the triangle is a right triangle.
Pythagorean Theorem: a² + b² = c², where a and b are legs and c is the hypotenuse. The triangle is a right triangle if a2 + b2 do equal c2.
8² + 5² = 9²
64 + 25 = 81
89 > 81
The triangle is not a right triangle, but since a and b are longer than c, we can conclude that it is obtuse.
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What is the correct answer to this question The options are A. 24B. 44C. 40D. 52
Answers
Given that
There is a square with its side as PQ = 2x + 8 and the perimeter is 96. And we have to find the side PQ of the square.
Explanation -
As it is a square and all the sides of the square are the same.
Since the perimeter is the sum of all the sides and its formula is given as
[tex]Perimeter\text{ of square = 4}\times side[/tex]On substituting the value we have
[tex]\begin{gathered} 96=4\times(2x+8) \\ \frac{96}{4}=2x+8 \\ 24=2x+8 \\ 2x=16 \\ x=8 \\ So,\text{ PQ = 2}\times8+8=16+8=24 \\ PQ=24 \end{gathered}[/tex]So the correct option is A.
Hence, the final answer is 24.carmen wants to estimate the percentage of people who lease a car. she surveys 250 individuals and finds that 105 lease a car. find the margin of error for the confidence interval for the population proportion with a 95% confidence level. z0.10 z0.05 z0.025 z0.01 z0.005 1.282 1.645 1.960 2.326 2.576. Use the table of common z-scores above, around the final answer of threee decimal place
Answers
Answer: 0.049
Step-by-step explanation:
Answer:
Step-by-step explanation:
0.061
Hello,Can you help me with the following: Evaluate the give binomial coefficientQuestion # 63
Answers
(63)
From the question, we are to evaluate the given binomial coefficient.
(90)
( 2 )
Using the formula:
(n) = n! = n! = 1
(0) 0!(n - 0)! 1 * n!
inputting into the formula
90C2 = 90!
2!(90-2)!
90C2 = 90!
2!(88)!
90C2 = 14857159644817614973095227336
2 * 18548264225739843911479684564
90C2 = 14857159644817614973095227336
3709652845179687822959369129
90C2 = 4005
2. Which equation is y=-3x²-12x - 2 rewritten in vertex form?
Oy=-3(x + 2)² +10 .
Oy=-3(x - 2)² +10
Oy=-3(x + 2)² - 14
Oy=-3(x - 2)²-2
Answers
Answer:
the first : y = -3(x + 2)² + 10
Step-by-step explanation:
let's do the operations :
-3(x + 2)² + 10 = -3(x² + 4x + 4) + 10 = -3x² - 12x - 12 + 10 =
= -3x² - 12x - 2
and that's exactly the original expression.
what is the median of 6 5 9 9 6 7 and 6
Answers
Answer:
6
Explanation:
To know the median, we first need to organize the data from least to greatest, so:
5 6 6 6 7 9 9
Then, the median will be the value that is in the middle, so:
5 6 6 6 7 9 9
Therefore, the median is 6 because there are 3 values to the left of 6 and 3 values to the right of 6.
4 g = 16 g= please solve
Answers
To solve for g in the expression 4g=16, we need to follow these steps:
[tex]\begin{gathered} 4g=16 \\ \frac{4}{4}\times g=\frac{16}{4} \\ g=\frac{16}{4}=4 \end{gathered}[/tex]Be Precise Of the number of sixth grade students at a middle school, 120 prefer online magazines over print magazines. Of the number of seventh grade students, 140 prefer online magazines. A student said that this means a greater percent of seventh grade students prefer online magazines than sixth grade students. Is the student correct? Choose the correct statement that uses precise mathematical language to explain. Multiple choice question. cross out A) no; A percent compares the part to the whole. In this case, the only known value is the part. To compare percents, the whole, the total number of sixth grade students and the total number of seventh grade students, must be known. cross out B) yes; A percent compares the part to the part. In this case, both parts are known. The number of sixth grade students who prefer online magazines, 120, can be compared to the number of seventh grade students who prefer online magazines, 140. So, a greater percent of seventh grade students prefer online magazines than sixth grade students. cross out C) no; A percent must always be less than 100. There are 120 sixth grade students who prefer online magazines and 140 seventh grade students who prefer online magazines, and both of these values are greater than 100. So, they cannot be compared as percents. cross out D) yes; A percent compares the part to the whole. In this case, the known values are 120, which is the part, and 140, which is the whole. Because 140 is greater than 120, a greater percent of seventh grade students prefer online magazines than sixth grade students. Need help with this question? Tools are not currently accessible ©2022 McGraw Hill. All Rights Reserved. Privacy CenterOpens in a new window Terms of UseOpens in a new window Minimum Requirements
Answers
No. There are 120 sixth-grade students who prefer online magazines and 140 seventh-grade students who prefer online magazines, and both of these values are greater than 100. So, they cannot be compared as percentages crossed out.
What is a percentage?It is a branch of Mathematics. It is a number or ratio expressed in the form of a fraction. A percentage can be denoted by the symbol %. It is a dimensionless number and it does not have any unit of measurement. The percentage is mainly used in shopping malls for giving discounts on clothes to customers. And the percent is used in salary increments in the company. The percentage is a very easy concept to learn by students or any other person. Percentage plays a key role in our daily life.
The number of students cannot be compared as percentages as the total number of students for both grades are not given.
So, the correct option is (c) No. There are 120 sixth-grade students who prefer online magazines and 140 seventh-grade students who prefer online magazines, and both of these values are greater than 100. So, they cannot be compared as percentages crossed out.
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if I had matrix [1 2 0 -1 -3 2 ; 0 0 1 3 -3 1; 0 0 0 1 -1/6 1/2; 0 0 0 0 1 3/11; 0 0 0 0 0 0]. i need to find the general solution of the systemI was given a system of linear equations and told to put it in reduced row echelon form and then find the general solution of the system. I'm not sure how to write each x1 = , x2=
Answers
With the given matrix, the system of equations you have is:
[tex]\begin{gathered} x_1+2x_2-x_4-3x_5=2 \\ x_3+3x_4-3x_5=1 \\ x_4-\frac{1}{6}x_5=\frac{1}{2} \\ x_5=\frac{3}{11} \end{gathered}[/tex]Then, you already know x5=3/11.
Now replace these value in the equation above and solve for x4:
[tex]\begin{gathered} x_4-\frac{1}{6}\cdot\frac{3}{11}=\frac{1}{2}^{} \\ x_4-\frac{3}{66}=\frac{1}{2} \\ x_4-\frac{1}{22}=\frac{1}{2} \\ x_4=\frac{1}{2}+\frac{1}{22} \\ x_4=\frac{22+2}{44}=\frac{24}{44} \\ x_4=\frac{6}{11} \end{gathered}[/tex]Now, replace x4 and x5 into the next above equation:
[tex]\begin{gathered} x_3+3\cdot\frac{6}{11}-3\cdot\frac{3}{11}=1 \\ x_3+\frac{18}{11}-\frac{9}{11}=1 \\ x_3+\frac{9}{11}=1 \\ x_3=1-\frac{9}{11}=\frac{11-9}{11} \\ x_3=\frac{2}{11} \end{gathered}[/tex]find slope and y-intercept of 2x+3y=12
Answers
Answer:
Slope = -2/3
y-intercept= (0,4)
Step-by-step explanation:
Hope this helps!!!
Answer:
slope= - 2/3
y-intercept = 4
Step-by-step explanation:
convert to y=mx+b where m = slope and b= y-intercept
2x+3y=12
3y= -2x+12
y = -2/3x+4
slope= - 2/3
y-intercept = 4
Pls mark as brainliest
Figure 1 and Figure 2 below are congruent. Which angle corresponds to angle L?
Answers
Answer:
angle E
Step-by-step explanation:
Have 109% in geometry
help meeeeeeeeeeeeeeeeeeee pleaseee rnnnn rn!!!!
Answers
The ball will be 213ft above the ground after 2.4 secs and after 5.6 seconds.
What is quadratic equation?A second-order polynomial equation in one variable with the notation x = ax2 + bx + c = 0 and a 0 is known as a quadratic equation. It is a second-order polynomial problem, which guarantees that it has at least one solution according to the fundamental theorem of algebra.
Calculations = 213 solve for t
213 = -16t² + 128t
in standard form
16t² - 128t + 213 = 0
using shridharacharya formula
t = 2.4 , 5.6
so the ball will be 213ft above the ground after 2.4 secs and after 5.6 seconds
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evaluate the algebraic expression -x^2y^3+2xy^2-3xy when x=2 and y=-1
Answers
Given expression is:
[tex]f(x,y)=-x^2y^3+2xy^2-3xy[/tex]To find the value at x=2and y=-1 put these valuesin given expression:
[tex]\begin{gathered} f(2,-1)=-(2)^2(-1)^3+2(2)(-1)^2-3(2)(-1) \\ f(2,-1)=4+4+6 \\ f(2,-1)=14 \end{gathered}[/tex]So the value of algebric expression at x=2and y=-1 is 14.
X'Y'Z' is the image of XYZ under a dilation through point C. XZ=30 and X'Z'=10
What scale factor was used in the dilation?
Answers
The scale factor that was used in the dilation is 3
The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller). For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, say, 2.
The image of XYZ after dilation through point C is X'Y'Z. X'Z' = 10 and XZ = 30
For Calculating the scale factor, er divide XZ and X'Z'
So, we have :
[tex]\frac{XY}{X'Y'} =\frac{30}{10} =3[/tex]
Hence, the scale factor that was used in the dilation is 3.
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4. From ThursdaySimplify the e2 (p + 4) + 6p
Answers
the given equation is ,
2(p+4) + 6p
now , we solve it
2p + 8 + 6p
8p + 8
So, the answer is 8p + 9.
What is the domain of the radical function shown on the graph?
y
-10
y=-x-2-4
A.
all real numbers
B. (XIX50)
+10
2
-6
-8
--10-
Answers
Answer:
A
Step-by-step explanation:
the function is in all the graph from left to right
Stella is a salesperson who sells computers at an electronics store. She makes a base pay amount each day and then is paid a commission as a percentage of the total dollar amount the company makes from her sales that day. Let P represent Stella's total pay on a day on which she sells x dollars worth of computers. A graph of P is shown below. Write an equation for P then state the y-intercept of the graph and determine its interpretation in the context of the problem.
Answers
step 1
Find the slope of the line
the slope is giving by the formula
m=(y2-y1)/(x2-x1)
we need two points
From the graph we take the points
(0,80) and (4000, 140)
substitute
m=(140-80)/(4000-0)
m=60/4000
m=6/400
m=3/200
m=0.015
step 2
Find the equation of the line in slope intercept form
P=mx+b
we have
m=0.015
b=80
therefore
P=0.015x+80
Remember that the y-intercept is the value of y when the value of x is zero
In this problem
the y-intercept represent a base pay amount each day
so
$80
pleeeeeese help me solve
Answers
Substitution means that the equation which solves for one variable by using the other equation and the values of the variable [tex](x,y)=(29,53)[/tex]
What is substitution?
A strategy for solving systems of equations that includes solving for one variable and using that solution to find the other variable.
Here the given linear equation is
[tex]y=3x-34 \\\\y=2x-5[/tex]
From the equation [tex](1)[/tex] , [tex](2)[/tex], we get
[tex]y-3x=-34 .....(1)\\\y-2x=-5 ......(2)[/tex]
And the graphical representation is of the form:-
In an equation [tex](2)[/tex], we get
[tex]y=2x-5[/tex]
Put the value [tex]y[/tex] in the equation [tex](1)[/tex], and we get
[tex](2x-5)-3x=-34\\2x-5-3x=-34\\-x-5+34=0\\-x+29=0\\x=29[/tex]
Now, substituting the value of [tex]x[/tex] in the equation [tex](2)[/tex], we get
[tex]y=2x-5\\y=2(29)-5\\y=58-5\\y=53[/tex]
Hence, the values are of the form:-
[tex](x,y)=(29,53)[/tex]
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EMERGENCY WILL GIVE BRAINLIEST.
GRAPH Y=1/2X FOR ME PLEASE!
ON A COORDINATE PLANE
Answers
The graph of y = 1/2x is as shown below.
In this question, we need to graph an equation y = 1/2 x on the coordinate plane.
First we find the the coordinates of points passing through y = 1/2 x
The function is undefined at x =0 .
For x = 1,
y = 1/2
For x = -1
y = -1/2
For x = 2,
y = 1/4
So, we get coordinates (1, 1/2), (-1, -1/2), (2, 1/4)
We plot these points on the coordinate plane.
Therefore, the graph of y = 1/2x is as shown below.
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in your own words state the segment addition postulate.
Answers
see the attached figure
the points A, B and C are collinear (the three points lies on the same line)
so
AC=AB+BC ------> by addition segment postulate
the total length is equal to the sum of its parts
What is the distance between A and B? Round your answer to the nearest tenth. (4 points) A coordinate plane is shown. Point A is located at negative 1, 5, and point B is located at 4, 1. A line segment connects the two points. ?
Answers
The distance between the 2 points A(-1, 5) and B(4, 1) is √41.
What is the distance?Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. The distance can refer to a physical length in physics or to an estimate based on other factors in common usage.The length of the line connecting two places represents the distance between them. Subtracting the different coordinates will reveal the distance if the two points are on the same horizontal or vertical line.So, the diatence between A(-1, 5) and B(4, 1):
Formula: d=√((x2 – x1)² + (y2 – y1)²Now, calculate as follows:
d=√((x2 – x1)² + (y2 – y1)²d=√((4 – (-1))² + (1 – 5)²d=√(5)² + (-4)²d=√25 + 16d=√41Therefore, the distance between the 2 points A(-1, 5) and B(4, 1) is √41.
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Ryan is working his way through school. He works two part-time jobs for a total of 22 hours a week. Job A pays $6.20 per hour, and Job B pays $7.40 per hour. How many hours did he work at each job the week that he made $150.80.
Answers
We could write the following equations according to the problem:
Hours equation:
[tex]a+b=22[/tex]And, the payment equation: (cents)
[tex]620a+740b=1508[/tex]We could solve this system of equations using the elimination method:
[tex]\begin{cases}a+b=22 \\ 620a+740b=1508\end{cases}[/tex]We're going to multiply the first equation by -620:
[tex]\begin{cases}-620a-620b=-13640 \\ 620a+740b=15080\end{cases}[/tex]Now, we're going to sum both equations eliminating variable a, so we get a linear equation in terms of b:
[tex]\begin{gathered} 120b=1440 \\ b=12 \end{gathered}[/tex]Now we know that he did 12 hours at job b.
As he worked 22 hours in total, then he worked 10 hours at job a.
Answer:
Step-by-step explanation:
a+b = 22 -- equation 1
6.20a + 7.40b = 150.80 replacing decimals
620a + 740b = 15080 --- equation 2
From eq. 1 a = (22 - b)
putting a's value in equation 2
620(22 - b) + 740b = 15080
13640 - 620b + 740b = 15080
120b = 15080 - 13640
b = 1440/120 = 12
From equation 1 a + 12 = 22
a = 10
Verify your answer by equation 2 putting the value of a and b
620*10 + 740*12 = 15080
4. Is 4(2x - 3) < 8(x + 1) always, sometimes, or never true?
Answers
The given inequality is always true for all real numbers.
Given, the inequality is :
4(2x - 3) < 8(x + 1)
Reduce the greatest common factor for both of the sides of the inequality:
2x - 3 < 2(x+1)
Apply Multiplicative distribution law:
2x - 3 < 2x + 3
Rearrange unknown terms to the left of the side of the equation:
2x - 2 < 2 + 3
Combine the like terms:
0 < 2+3
Calculate the sum or the difference.
0 < 5
The solution of the inequality is always true.
Hence we get the solution as the inequality being true to all real numbers.
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If G¹(x) is the inverse of G(x), what is the value of G¹(G(x))?
Ο A. x
OB. x¹
O C. 1
OD. O
SUBMIT
Answers
The value of G⁻¹(G(x)) is x , So the correct answer among the following options is A) x
What is function?
A function is described as a relationship between a set of inputs and one output for every one of them. Simply described, a function is an association of inputs where each input is coupled to a single, distinct output. Each function has a codomain or range.
What is inverse function?An inverse function, sometimes known as an antI function, is a function that can change into another function. In other words, if any function "f" takes x → y, then the inverse of that function will take y to x. The inverse of a function denoted by "f" or "F" is denoted by "f-1" or "F-1." Not to be mistaken with an exponent or a reciprocal in this case is (-1).
Given, function G(x)
inverse of the given function G⁻¹(x)
Let G(x) = x
Then G⁻¹(x) = x
So value of G⁻¹(G(x)) is,
Put G(x) = x,
Hence, G⁻¹(G(x)) = x
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what type of function is this? (quadratic or exponential)
Answers
Answer:
exponential
Step-by-step explanation:
a builder wishes to fence in 60,000 m2 of land in a rectangular shape. because of security reasons, the fence along the front part of the land will cost $2 per meter, while the fence along the other three sides will cost $1 per meter. how much of each type of fence will the builder have to buy in order to minimize the cost of the fence? what is the minimum cost?
Answers
To minimize the cost, the builder should but 200 meters of fence costs at $2 per meter and 800 meters of fence costs at $1 per meter. The minimum cost is $1,200.
Recall that if we have a function f(x), then at the extremum point, its derivative is equal to zero.
f ' (x) = 0
In the given problem, let:
p = length of the rectangle
q = width of the rectangle
Then,
p x q = 60,000 or q = 60,000/p
Assume that the front side is p, then the function that describe the cost is:
f(p,q) = 2xp + 1 x (p + q + q)
f(p,q) = 3p + 2q
f(p) = 3p + 2 x 60,000/p
f(p) = 3p + 120,000/p
Take the derivative:
f '(p) = 3 - 120,000/p² = 0
p² = 40,000
p = 200 meters
Substitute p = 200 to get q,
q = 60,000/200 = 300
Hence, the type of fences the builder have to buy to minimize the cost is:
200 meters fence with cost $2 per meter and 200+300+300= 800 meters fence with cost $1 per meter.
The minimum cost is:
f(p) = 3p + 120,000/p
f(min) = f(200) = 3x200 + 120,000/200 = $1,200
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mr. x teaches freshman english, and mrs. x teaches freshman history. they hosted a party at their home for members of their classes and their dates. twenty-three of the students were in mr. x's class, 31 were in mrs. x's class, 9 were in both mr. and mrs. x's classes, and 18 other students were in neither class. how many students were at the party?
Answers
twenty-three of the students were in mr. x's class, 31 were in mrs. x's class, 9 were in both mr. and mrs. x's classes, and 18 other students were in neither class. then there are 63 students in the party
twenty-three of the students were in mr. x's class,
31 were in mrs. x's class,
9 were in both mr. and mrs. x's classes,
and 18 other students were in neither class.
therefore 23+31 - 9 =45
and 18 were other students
hence it becomes 45+18= 63 students were in the party
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“One subtracted
from the
product of 4 and
a number is 1 1”
how would i write it??
Answers
Please help me I would appreciateeeeeeeeeeeeee
Answers
The value of the variable x in first figure will be 15.
The value of the variable x in second figure will be 20.
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
There are two figure is shown in figure.
Now,
In first figure;
The sum of all the interior angle in a triangle is 180°.
So, We can formulate;
⇒ (6x - 10)° + (2x + 20)° + (3x + 5)° = 180°
Solve for x as;
⇒ (6x - 10)° + (2x + 20)° + (3x + 5)° = 180°
⇒ 6x - 10 + 2x + 20 + 3x + 5 = 180°
⇒ 11x + 15 = 180
⇒ 11x = 180 - 15
⇒ 11x = 165
⇒ x = 15
Thus, The value of the variable x in first figure will be 15.
For second figure;
We can formulate by the corresponding angle of the parallel lines as;
⇒ x + 50 = 70
⇒ x = 70 - 50
⇒ x = 20
Thus, The value of the variable x in second figure will be 20.
Therefore,
The value of the variable x in first figure will be 15.
The value of the variable x in second figure will be 20.
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