Answer:
Solution:
Here,
[tex]\begin{array}{ | c| c c | } \hline\ \ \text{length \: of \: iron \: rod}& \text{weight} \\ \hline 13 \rm{m}& \rm{23.4kg} \\ \hline \rm{6m}&?\\ \hline\end{array}[/tex]
Weight of 13 m of rod=23.4 kg
Weight of 1 m of rod=23.4/13 kg
[less length,less weight]
Weight of 6 m of rod=23.4/13 ×6 kg=10.8 kg
[more length,more weight]
Thus,the weight of 6 m of rod is 10.8 kg.
Alternative method:
Let,the required weight be x kg.
Then,
[tex]\begin{array}{ | c| c c | } \hline\ \ \text{length \: of \: iron \: rod}& \text{weight} \\ \hline \rm{13m}& \rm{23.4 \: kg }\\ \hline \rm{6m}& \rm{x =? } \\ \hline\end{array}[/tex]
We know that,
More length of iron rod([tex]\red{\uparrow}[/tex]) will have the more weight([tex]\red{\uparrow}[/tex]).
So,using the rule of direct proportion;
i.e. Ratio of length=Ratio of weight
[tex] \displaystyle{ \frac{13}{6} = \rm\frac{23.4}{x} }[/tex]
[tex] \rm{13x = 6 \times 23.4}[/tex]
[tex] \rm{x = \displaystyle{ \frac{6 \times 23.4}{13} }}[/tex]
[tex] \therefore{x = 10.8}[/tex]
Thus,the weight of 6 m long iron rod is 10.8 kg.
X: 4x^2+16 -20=0
What is x
Answer:
[tex]\boxed{\sf x = 1, \ x = -5}[/tex]
Explanation:
[tex]\rightarrow \sf 4x^2 + 16x - 20 = 0[/tex]
[tex]\rightarrow \sf 4(x^2 + 4x - 5) = 0[/tex]
[tex]\rightarrow \sf x^2 + 4x - 5 = 0[/tex]
[tex]\rightarrow \sf x^2 + 5x -x- 5 = 0[/tex]
[tex]\rightarrow \sf x(x + 5) -1(x+ 5) = 0[/tex]
[tex]\rightarrow \sf (x-1)(x+ 5) = 0[/tex]
[tex]\rightarrow \sf x = 1, \ x = -5[/tex]
The number of wrecks at a certain intersection varies directly as the number of cars that travel through the intersection. If there are 31 wrecks when 1,085 cars have traveled through the intersection, how many cars have passed through the intersection after 7 wrecks?
The number of cars that have passed through the intersection is 245.
How many cars passed through the intersection?Direct variation is when two variables move in the same direction. If one variable increases, the other variable increases.
The equation that represents direct variation is; c = wk
Where:
c = number of carsw = number of wrecks k = constant of proportionality1085 = k31
k = 1085 / 31
k = 35
c = 7 x 35
c = 245
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Given that y is an integer, find all values of y such that y< 6
Answer:
Values: 3,4,5
Step-by-step explanation:
I hope this helps:)
Need help with this geometry question
Answer: 10 inches
Step-by-step explanation:
Diagonals of a parallelogram bisect each other, so the top of the jack is 5(2)=10 inches off the ground.
Describe the graph of a function g by observing the graph of the base function ƒ.
A. g(x) = 2ƒ(–x) g(x)
B. g(x)= -1/2f(x)
C. g(x)= 1/2f(-x)
D. g(x)= f(-1/2x)
The correct answer is option B which is g(x)= 1/2f(-x).
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
As we can see in the graph that the value of the function g(x) will be calculated by the distance formula:-
[tex]g(x) = \dfrac{ 0 + 2}{2 - 0 }=\frac{2}{2}=1[/tex]
The value of the function f(x) will be:-
[tex]f(x) =\dfrac{2-0}{-4+0}=\dfrac{-1}{2}[/tex]
So g(x) = ( -1/2) f(x)
Therefore the correct answer is option B which is g(x)= 1/2f(-x).
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Suppose there is a big drop in interest rates in Mexico and a small drop in U.S. interest rates. Everything else equal, what is likely to happen to value of the MXN?
The value of MXN will increase.
The official currency of Mexico is The Mexican peso (MXN).
MXN is simply an abbreviation of the currency the Mexican peso, which is the official currency of the country of Mexico.
Similarly, the drop value in currency is defined as the expression that the currency is worth less as compared to all other countries.
When a currency's country interest rate drop, then the value of the currency increase. Here given in the question as there is a big drop in interest rates in Mexico and a small drop in U.S. interest rates, the value of MXN will increase as the drop is more in Mexico which affects its currency MXN.
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Read the following two statements. Then, if possible, use the Law of Detachment to draw a conclusion. The doctor recommends rest if the patient has the flu. The doctor recommends rest. not possible The patient does not have the flu. If the doctor recommends rest, the patient has the flu. The patient has the flu.
The doctor recommends rest if the patient has the flu. Then the correct option is A.
What is decision-making?Determining the proper option, acquiring evidence, and exploring various options are all steps in the decision-making process.
Read the following two statements.
Then, if possible, use the Law of Detachment to draw a conclusion.
Then the correct option is A.
The doctor recommends rest if the patient has the flu.
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How do you round 56.053 to the nearest whole number
Answer:
56
Step-by-step explanation:
all your doing is removing the .053 to get your whole number
? Question
Write an expression to represent the perimeter of Melissa's garden in terms of x.
Type the correct answer in each box. Use numerals instead of words.
Perimeter:
Question 3
? Question
x +
The expression for length and breadth of the rectangle garden in terms of the side of the square tomato patch.
l=3x+2
b=x+5
The linear equation is the equation where the highest degree of the variables is 1.
Here given that the garden is rectangular in shape and the tomato patch is square in shape.
the length of the side of the square tomato patch is x.
Asuume the length of the rectangle garden is l
and the breadth of the rectangle garden is b.
Given that
the length of the garden is greater than the 3 times of the length of the rectangular garden by 2 feet.
3 times of the length of the rectangular garden is 3x
2 feet greater than 3 times of the length of the rectangular garden= 3x+2
so from above, it is clear that l=3x+2
similarly, the breadth of the garden is greater than the length of the rectangular garden by 5 feet.
then the breadth of the garden = b= x+5
Therefore the expression for length and breadth of the rectangle garden in terms of the side of the square tomato patch.
l=3x+2
b=x+5
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What is the vertex of the parabola defined by the equation
(x-2)² =-12(y-2)?
A (-12, 2)
B.
(2, 2)
C. (6,2)
D. (2,-2)
Answer: B. (2,2)
Step-by-step explanation:
The vertex of the parabola in the form [tex](x-h)^2 = 4p(y-k)[/tex] is (h, k).
Mr. Garret has a total of 20 students in his class. The number of female students is 4 less than twice the number of male students. How many female and how many male students does he have?
Answer:
8 male, 12 female
Step-by-step explanation:
male = x
female = 2x - 4
2x - 4 + x = 20
3x - 4 = 20
3x = 24
x = 8
2(8) - 4 = 12
there are 8 male, 12 female
boat traveled downstream a distance of 60 mi and then came right back. If the speed of the current was 6 mph and the total trip took 4 hours find the average speed of the boat relative to the water.
Answer:
7.5mph
Step-by-step explanation:
Let the average speed of the boat to be x mph.
Total Distance = Avg. Speed x Total Time
60 = ((x+6) + (x-6))(4)
60 = (x+6+x-6)(4)
(2x)(4)=60
2x=60/4
2x = 15
x = 15 /2
x = 7.5mph
Answer:
15 +√261 ≈ 31.155 mph
Step-by-step explanation:
The time for the trip can be found by dividing the distance by the speed.
__
setupThe relation between time, speed, and distance is ...
time = distance/speed
The speed for the downstream leg was the sum of the boat speed (b) and 6 mph. The speed for the upstream leg was the difference. So the total trip time was ...
4 = 60/(b +6) +60/(b -6) . . . total time is the sum of the times for the legs
__
solutionMultiplying by the product of the denominators, we have ...
4(b +6)(b -6) = 60(b -6) +60(b +6)
b² -36 = 30b . . . . divide by 4 and simplify
b² -30b = 36 . . . . put in a form useful for completing the square
(b -15)² = 36 +15² . . . . . complete the square
b -15 = √261 . . . . . . . . take the square root (negative root is extraneous)
b = 15 +√261 ≈ 31.155 . . . . add 15
The average speed of the boat was about 31.155 mph.
what is the domain of the ordered pair shown in the graph?
Answer:
D.
Step-by-step explanation:
It is the only one that contains all the x-values of the points. (Domain is the set of x-values).
As sample of 105 sanitation workers for the city of Euonymus, Texas, earns an average of $24,375 per year. The average salary for all Euonymus city workers is $24,230, with a standard deviation of $523. Are the sanitation workers overpaid? Conduct both one- and two-tailed tests.
The average salary of sanitation workers in the city of Euonymus is overpaid from the one-tail test and the average salary of sanitation workers in the city of Euonymus is not 24230 from the two-tail test.
What are the null hypothesis and alternative hypothesis?The null and alternative hypotheses are two generalizations about a population that are strictly contradictory. The null hypothesis can be denoted by H₀ and the alternative hypothesis can be denoted by H₁.
We have:
Average x = 24375
u = 24230
SD = 523
n = 105
Null hypothesis and alternative hypothesis for one-tail test:
H0: the average salary of sanitation workers in the city of Euonymus is not overpaid.
u = 24230
H1: the average salary of sanitation workers in the city of Euonymus is overpaid.
u > 24230
Assume significance level = 0.05
From the Z-table:
Z(critical) = 1.645
Now,
Z = (x-u)/(SD/√n)
Z = (24375-24230)/(523/√105)
Z = 2.84
Z > Z(critical)
So, reject the null hypothesis.
The average salary of sanitation workers in the city of Euonymus is overpaid.
Now, from the two-tail test:
Null hypothesis and alternative hypothesis for one-tail test:
H0: the average salary of sanitation workers in the city of Euonymus is 24230
u = 24230
H1: the average salary of sanitation workers in the city of Euonymus is not 24230
u ≠ 24230
Assume significance level = 0.05
From the Z-table for the two-tail test:
Z(critical) = ±1.96
Now,
Z = 2.84
Z > z(critical)
∴ The average salary of sanitation workers in the city of Euonymus is not 24230.
Thus, the average salary of sanitation workers in the city of Euonymus is overpaid from the one-tail test and the average salary of sanitation workers in the city of Euonymus is not 24230 from the two-tail test.
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Students were asked to prove the identity (sec x)(csc x) = cot x + tan x.
Let's prove that (sec x)(csc x) is equal to cot x + tan x
[tex]\Longrightarrow \sf (sec(x) )(csc(x))[/tex]
[tex]\Longrightarrow \sf \dfrac{1}{\cos \left(x\right)\sin \left(x\right)}[/tex]
[tex]\Longrightarrow \sf \dfrac{\cos ^2\left(x\right)+\sin ^2\left(x\right)}{\cos \left(x\right)\sin \left(x\right)}[/tex]
[tex]\Longrightarrow \sf \dfrac{\cos ^2\left(x\right)}{\cos \left(x\right)\sin \left(x\right)} + \dfrac{\sin ^2\left(x\right)}{\cos \left(x\right)\sin \left(x\right)}[/tex]
[tex]\Longrightarrow \sf \dfrac{\cos\left(x\right)}{\sin \left(x\right)} + \dfrac{\sin \left(x\right)}{\cos \left(x\right)}[/tex]
[tex]\Longrightarrow \sf cot(x) + tan(x)[/tex]
Hence student A did correctly prove the identity properly.
Also Looking at student B's work, he verified the identity properly.
So, Both are correct in their own way.
Part BIdentities used:
[tex]\rightarrow \sf sin^2 (x) + cos^2 (x) = 1[/tex] (appeared in step 3)
[tex]\sf \rightarrow \dfrac{cos(x) }{sin(x) } = cot(x)[/tex] (appeared in step 6)
[tex]\rightarrow \sf \dfrac{sin(x )}{cos(x) } = tan(x)[/tex] (appeared in step 6)
The graph displays the relationship between the length of time an employee works at a company and the number of the employee's monthly customers.
y intercept is 2, which shows while changing the jobs employees bring two customers.
What is linear equation?A linear equation is in the form, y = mx + b where m is the rate of change (slope) and b is the y intercept (initial value of y).
The complete question is:
The graph displays the relationship between the length of time an employee works at a company and the number of the employee's monthly customers.
Time Employed (Month)
If the equation for the line of best fit is y = 4.5x + 2, which of the following can be used to interpret the y-intercept in context?
Employee training takes 2 months.
Employee training takes 4.5 months.
Employees are likely to bring 2 customers with them when changing jobs.
Employees are likely to bring 4.5 customers with them when changing jobs.
As, linear equation is
y = mx + b
Let y be the number of customers and x be the length of time.
Then, y = 4.5x + 2
As, y intercept is 2, which shows while changing the jobs employees bring two customers.
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The table shows the heights of three different plants.
Answer:
7/4 meters
Step-by-step explanation:
the tallest plant is 19/8
since they have all the same denominaters we can just compare the top numbers
so
the smallestp lant is 5/8
19/8 - 5/8 = 14/8
7/4 is your final answer after simplifying
A shopkeeper buys 72 articles for $82.80. How much will he have to pay if he buys 150 such articles.
Answer: He have to pay $172.5 if he buys 150 such articles.
72 articles for --> $82.80
1 article for - - - > 82.80/72
150 articles for --> (82.80/72)*150
= $172.5
Answer:
$172.5
Step-by-step explanation:
Given:
Shopkeeper buys = 72 articles
Price = $ 82.8
To Find:
The amount he'll need to pay If he buys 150 articles.
Solution:
Amount if he buys 150 articles
[tex] \boxed{\rm \: No. \: of \: articles \: he \:will \: buy × \cfrac{Cost \: of \: that \: article \: he \: has}{Number \: of \: articles \: he \: has}} [/tex]
[tex] = \$ \bigg(\rm150 * \cfrac{82.80}{72}\bigg) [/tex]
[tex]= \$ (150* 1.15)[/tex]
[tex] = \$172.5[/tex]
So we can conclude that:
$172.5 he will have to pay if he buys 150 such articles.
4/3 - 1/2 What is the answer
Answer:
5/6
Step-by-step explanation:
4/3-1/2
1) make the denominators the same on both fractions
8/6-3/6=?
2) subtract numerators
5/6
3) simplify
cannot simplify
Answer:
5/6
Step-by-step explanation:
4/3 -1/2
The first step is to get a common denominator of 6
4/3 *2/2 = 8/6
1/2 * 3/3 = 3/6
8/6 -3/6
5/6
Write 31/8 as a mixed number.
Reward: Mark as brainlist.
Answer:
[tex]3 \frac{7}{8}[/tex]
Step-by-step explanation:
identify the percentage in 15 is 25% of 60
Answer:
25%
Step-by-step explanation:
In the sentence "15 is 25% of 60.", 25% is the percentage.
15 is the partial amount and 60 is the total amount.
15/60 = .25
convert a decimal to a percentage by multiplying by 100
.25 × 100 = 25
Some people use a shortcut of moving the decimal two places to the right. This is the same as multiplying by 100.
15/60 is 25%
I need help with this question
Help me with this question please!! :)
Answer: 9516793/9765625
Step-by-step explanation:
We can subtract the probability none of them have been vaccinated from 1.
If 52% of people are vaccinated, then 48% of people are not vaccinated.
Thus, the probability is [tex]1-(0.48)^{5} =\frac{9516793}{9765625}[/tex]
Please help I’m confused
Answer:
Step-by-step explanation:
Circle G is shown. Line segment F G is a radius with length 3.
In circle G, r = 3 units. Maria draws a circle with double the area of circle G.
What is the area of Maria’s circle?
6Pi units squared
9Pi units squared
12Pi units squared
18Pi units squared
The area of Maria’s circle is 18π square units option fourth is correct.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
The figure is missing.
Please refer to the attached picture for the figure.
We have given the radius of the circle as 3 units
r = 3 units
Area of circle = πr² = π(3)² = 9π square units
The area of Maria’s circle = 2(9π) = 18π square units
Thus, the area of Maria’s circle is 18π square units option fourth is correct.
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helppp im stuck :(
Hope you guys help me
Answer:
[tex]y=-\dfrac{1}{2}x+2[/tex]
Step-by-step explanation:
Define two points on the line:
[tex]\textsf{let}\:(x_1,y_1)=(0,2)[/tex]
[tex]\textsf{let}\:(x_2,y_2)=(4,0)[/tex]
Use the slope formula and the defined points to find the slope:
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-2}{4-0}=-\dfrac{1}{2}[/tex]
Substitute the found slope and one of the points into the point-slope form of a linear equation:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-2=-\dfrac{1}{2}(x-0)[/tex]
Simplify:
[tex]\implies y-2=-\dfrac{1}{2}x[/tex]
[tex]\implies y=-\dfrac{1}{2}x+2[/tex]
Help pls ???????????
The second derivative of the first function is s"(x) = = -[8e^(x/5) - 2]e^(x/5)/25(e^(x/5) + 2)³.
The second derivative of the second function is; k''(t) = (36t² - 6)e^(-3t²)
How to find the second derivative?1) We are given the function;
s(x) = 4/(1 + 2e^(-0.2x)
First derivative is;
ds/dx = [8e^(x/5)]/5(e^(x/5) + 2)²
Second Derivative is;
d²s/dx² = -[8e^(x/5) - 2]e^(x/5)/25(e^(x/5) + 2)³
At x = 0;
d²s/dx² = -[8e^(0/5) - 2]e^(0/5)/25(e^(0/5) + 2)³
d²s/dx² = 8/675
B) We are given the function;
k(t) = e^(-3t²)
The first derivative is;
dk/dt = -6te^(-3t²)
The second derivative is;
k''(t) = (36t² - 6)e^(-3t²)
At t = 1, we have;
k''(t) = (36(1)² - 6)e^(-3(1²))
k"(t) = 1.494
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from a survey involving 1000 University students market research company found that 780 students on laptops 460 on cars and 380 owned cars and laptops if a university student is selected at random what is each empirical probability. (A) the student owns either a car or laptop. (B) the student owns neither a car nor a laptop is.
Considering the definition of probability:
the probability that the student owns either a car or laptop is 86%.the probability that the student owns neither a car nor a laptop is 14%.Definition of ProbabitityProbability is the greater or lesser possibility that a certain event will occur.
In other words, the probability is the possibility that a phenomenon or an event will happen, given certain circumstances. It is expressed as a percentage.
The probability of any event A is defined as the quotient between the number of favorable cases (that is, the number of times that event A may or may not occur) and the total number of possible cases:
[tex]Probability=\frac{number of favorable cases}{total number of possible cases}[/tex]
Union of eventsThe union of events, AUB, is the event formed by all the elements of A and B. That is, the event AUB is verified when one of the two, A or B, or both occurs. AUB is read as "A or B".
The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:
P(A∪B)= P(A) + P(B) -P(A∩B)
Complementary eventA complementary event, also called an opposite event, is made up of the inverse of the results of another event. That is, That is, given an event A, a complementary event is verified as long as the event A is not verified.
The probability of occurrence of the complementary event A' will be 1 minus the probability of occurrence of A:
P(A´)= 1- P(A)
Events and probability in this caseIn first place, let's define the following events:
A: The event that a student owned a laptop.
B: The event that a student owned a car.
Then you know:
P(A)= [tex]\frac{780}{1000}[/tex]= 0.78P(B)= [tex]\frac{460}{1000}[/tex]= 0.46P(F and R)= P(F∩R)= [tex]\frac{380}{1000}[/tex]= 0.38 [The intersection of events, A∩B, is the event formed by all the elements that are, at the same time, from A and B. That is, the event A∩B is verified when A and B occur simultaneously.]In this case, considering the definition of union of events, the probability that the student owns either a car or laptop is calculated as:
P(A∪B)= P(A) + P(B) -P(A∩B)
P(A∪B)= 0.78 + 0.46 -0.38
P(A∪B)= 0.86= 86%
Then, the probability that the student owns either a car or laptop is 86%.
On the other hand, considering the definition of the complementary event and its probability, the probability that the student owns neither a car nor a laptop is calculated as:
P [(A∪B)']= 1- P(A∪B)
P [(A∪B)']= 1 - 0.86
P [(A∪B)']= 0.14= 14%
Finally, the probability that the student owns neither a car nor a laptop is 14%.
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Suppose the derivative of a function is ′()=(−7)^7(−2)^2(+13)^10. Then the function is increasing on the interval _____.
Complete the coordinate proof of the theorem.
The coordinate of C( a+c , b) , AC are ((a+c)/2 , b/2) , BD are ((a+c)/2 , b/2)
What are Coordinates ?Coordinates is the value assigned to a point in a x-y graph to determine its location.
The coordinates of parallelogram is
A ( 0,0) B (a,0) , C ( __ , ___) , D ( c , b)
The y coordinate is same as D as b
and the x coordinate will be a+c
C( a+c , b)
The coordinate of the mid point of AC are ((a+c)/2 , b/2)
The coordinate of the mid point of BD are ((a+c)/2 , b/2)
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