Answer:
1. Yes, there is sufficient evidence to support the claim that men have a higher rate of red/green color blindness than women.
2. The 95% confidence interval for the difference between the color blindness rates of men and women is [0.0656, 0.1004].
Step-by-step explanation:
We are given that in a study of red/green color blindness. 1000 men and 2800 women are randomly selected and tested
Among the men, 85 have red/green color blindness. Among the women, 6 have red/green color blindness.
Let [tex]p_1[/tex] = population proportion of men having red/green color blindness.
[tex]p_2[/tex] = population proportion of women having red/green color blindness.
So, Null Hypothesis, : {means that men have a lesser or equal rate of red/green color blindness than women}
Alternate Hypothesis, : {means that men have a higher rate of red/green color blindness than women}
(1) The test statistics that will be used here is Two-sample z-test statistics for proportions;
T.S. = ~
N(0,1)
where, = sample proportion of men having red/green color blindness = = 0.085
[tex]\hat p_2[/tex] = sample proportion of women having red/green color blindness = [tex]\frac{6}{2800}[/tex] = 0.002
[tex]n_1[/tex] = sample of men = 1000
[tex]n_2[/tex] = sample of women = 2800
So, the test statistics = [tex]\frac{(0.085-0.002)-(0)}{\sqrt{\frac{0.085(1-0.085)}{1000}+\frac{0.002(1-0.002)}{2800} } }[/tex]
= 9.37
The value of z-test statistics is 9.37.
Also, the P-value of the test statistics is given by;
P-value = P(Z > 9.37) = Less than 0.0001
Since the P-value of our test statistics is less than the level of significance as 0.0001 < 0.05%, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we support the claim that men have a higher rate of red/green color blindness than women.
(2) The 95% confidence interval for the difference between the color blindness rates of men and women ([tex]p_1-p_2[/tex]) is given by;
95% C.I. for ([tex]p_1-p_2[/tex]) = [tex](\hat p_1-\hat p_2) \pm Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} }[/tex]
= [tex](0.085-0.002) \pm (1.96 \times \sqrt{\frac{0.085(1-0.085)}{1000}+\frac{0.002(1- 0.002)}{2800} } )[/tex]
= [tex]0.083 \pm0.0174[/tex]
= [0.0656, 0.1004]
Here, the crtical value of z at 2.5% level of significance is 1.96.
Hence, the 95% confidence interval for the difference between the color blindness rates of men and women is [0.0656, 0.1004].
i will mark brainliest !!!! Which method of solving quadratic equations do you prefer: factoring, completing the square, or quadratic formula? Why? Your response should be 3-5 sentences long and show that you’ve thought about the topic/question at hand. Please be aware we are looking for YOUR PERSONAL OPINION and there is not a single “correct answer.”
I prefer solving quadratic equations with the quadratic formula. The formula is great for solving any equations like ones that factoring can’t. It is also easy to memorize and type in and check with a calculator.
I always prefer quadratic formula as compared to factoring or completing the square to solve a quadratic equation.
What is a quadratic equation?"A quadratic equation is an algebraic equation of the second degree in 'x'. The quadratic equation in its standard form is ax² + bx + c = 0, where 'a' and 'b' are the coefficients, 'x' is the variable, and 'c' is the constant term."
In order to solve a quadratic equation, I always prefer quadratic formula as compared to the other methods.
In many cases, a quadratic equation can not be converted into a square or into factors.
Therefore, quadratic formula is the only method to solve all type of quadratic equation.
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Jensen and Raju had the same amount of money at first. After Jensen spent
$64 and Raju spent $148, Jensen had 3 times as much money as Raju. How
much money did each boy have at first?
Step-by-step explanation:
Both of them had $x
Later
Jensen=x-64
Raju=x-148
Jensen=3*Raju
x-64=3(x-148)
x-64=3x-444
3x-x=444-64
2x=380
x=$190
Which of the following is equivalent to -21(6 - 71)?
a (0 – 21(6-71)
b (0 + 206 - 71)
c (-2 + 1)(6 – 71)
d (6-21) – (71-21)
Answer:
a
Step-by-step explanation:
-21(-65)
= - 86
A
(0-21(6-71)
(-21-65)=-86
Welcome to Gboard clipboard, any text you copy will be saved here.
someone help please
Step-by-step explanation:
Hey, there!
Here,
[tex] = 4 {x}^{2} - 4x + 1[/tex]
[tex]or ,\: ( {2x)}^{2} - 2.2x .1 + 1[/tex]
[tex]or ,\: ( {2x - 1)}^{2} [/tex]
We got this because,
[tex]( {2x - y)}^{2} = 4 {x}^{2} - 4x + 1[/tex]
By using formula,
[tex]( {x - y)}^{2} = {x}^{2} - 2xy + 1[/tex]
Hope it helps..
Answer: (x+-0.5)²=0
Step-by-step explanation:
4x²-4x+1=0
(2x-1)²=0 ⇔ completing the square
--------------------------------------------
since the question asked for the x should be 1, then we should divide 2x by 2 so to get rid of the 2 in front of the x.
this will change the original equation into: (x+(-0.5))²=0
------------------------------------------------------------------------------------------------------------
You can also directly divide 4 from 4x²-4x+1=0 to get rid off the terms in front of x.
x²-x+0.25=0
(x-0.5)²=0
(x+(-0.5))²=0
Can someone please explain this to me? I’m really confused on how to find the limit with the piecewise function.
Answer: 2
Step-by-step explanation:
You only need to evaluate at the limit point.
f(x) = 4 - x ; x ≠ 2
Consider the solution if x = 2 (because the limit is x → 2)
f(2) = 4 - (2)
= 2
We know that f(x) = 0 ; x = 2
f(2) = 0
but we are looking for the y- value it approaches - not the y-value it is.
Look at the graph. You will see that as x gets closer and closer to 2, the y-value gets closer and closer to 2. This is the limit.
what is the angle of the triangle below?
I need help on how to do this!!!?
Let's say you had a cake that is cut into 5 equal slices. Then someone eats 2 of those slices. They ate 2/5 of the cake.
Now let's say you have another cake that you cut into 10 equal slices. If someone eats 4 of those ten, then they have eaten 4/10 = 2/5 of the cake.
Check out the diagram below to see a visual of how 4/10 and 2/5 are equivalent fractions.
Going from 2/5 to 4/10 has us multiply top and bottom by 2.
-----------
Similarly, 1/2 = 5/10 after multiplying top and bottom by 10
The original expression 2/5 + 1/2 turns into 4/10 + 5/10
Then you add the numerators to get 4+5 = 9, placing that over the common denominator of 10
Answer: 9/10A die is thrown. Describe the following events: (i) A: a number less than 7 (ii) B: a number greater than 7 (iii) C: a multiple of 3 (iv) D: a number less than 4. (v) E: an even number greater than 4 (vi) F: a number not less than 3 (vii) find A× (B∩ E), A ∩B, B ∪ C, E ∩ F∩ D. Answer this if u want to be marked as the brainliest!
A: The probability of a number rolling less than 7 is 100% or 1 because a dice only has numbers 1,2,3,4,5, and 6. 1,2,3,4,5, and 6 are all less than 7 so you are guaranteed to roll a number less than 7.
B: The probability of a number rolling more than 7 is 0% or 0 because a dice only has numbers 1,2,3,4,5, and 6. 1,2,3,4,5, and 6 are all less than 7 so it's not possible to roll a number more than 7.
C: The probability of a number rolling to be a multiple of three is 33.33(repeating)% or 1/3. Out of 1,2,3,4,5, and 6, the multiples of 3 are, 3 and 6. 3 and 6 is two numbers out of six numbers. 2 out of 6 simplifies to 1 out of 3.
D: The probability of a number rolling to be less than 4 is 50% of 1/2. Out of the numbers, 1,2,3,4,5, and 6, only 1,2, and 3 are less than 4. 1,2, and 3 is three numbers out of six numbers. 3 out of 6 simplifies to 1 out of 2.
E: The probability of a number rolling to be an even number greater than 4 is 0.166(repeating) or 1/6. Out of the numbers, 1,2,3,4,5, and 6, 2,4, and 6 are even numbers. Out of 2,4, and 6, only 6 is greater than 4. 4 is one number out of 1,2,3,4,5, and 6 (six numbers).
F: The probability of a number rolling to be a number not less than 3 is 50% or 1/2. "Not less than" actually means greater than. In the numbers, 1,2,3,4,5, and 6, only 4,5, and 6 are greater than 3. 4,5, and 6 are three numbers. 3 out of 6 simplifies to 1 out of 2.
I don't really know the answer to the last question but anyways I hope this helped! ♡
❀ Have a good day! ❀
Each gallon of gas costs $3.50. Sheridan spent $42.00 on gas. Which value of x represents the number of gallons of gas that Sheridan has purchased?
Answer:
12
Step-by-step explanation:
$42.00/($3.50 per gallon) = 12 gallons
can someone please help??
Answer:
look it up on brainly then you'll get it
Step-by-step explanation:
yes you really will
Which of the following is not a 3-D shape? A. quadrilateral B. cube C. sphere D. prism
Answer:
A.
Step-by-step explanation:
A quadrilateral is simply a shape with 4 sides, therefore it does not HAVE to be 3-D.
Answer:
Quadrilateral.
Step-by-step explanation:
A quadrilateral is a 2d shape not 3d.
Question 2
A square room of side length x is made 5 m longer (its width stays the same). What is the new area
of the room?
Answer:
To find the width, multiply the length that you have been given by 2, and subtract the result from the perimeter. You now have the total length for the remaining 2 sides. This number divided by 2 is the width.
Step-by-step explanation:
The area of any quadrilateral can be determined by multiplying the length of its base by its height. Since we know the shape here is square, we know that all sides are of equal length. From this we can work backwards by taking the square root of the area to find the length of one side. hope this helps you :)
Which choice is the solution to the inequality below?
x/10>7
O A. X>7
O B. x> 1.43
O c. X>70
D. x < 70
Answer: C. x>70
Step-by-step explanation:
x/10>7
x/10 × 10>7 × 10
x>70
Hope this helps!! :)
Please help:
A holiday punch recipe calls for 1,500 mL of fruit punch, 375 mL of pineapple juice, and 1 L of ginger ale. How many liters (L) of punch will this recipe yield if doubled?
Answer:
5.75 L
Step-by-step explanation:
2(1500mL + 375mL + 1L)
=2(1875mL + 1L)
=2(1.875L + 1L)
=2(2.875)
=5.75
The recipe will yield 5.75 liters (L) of punch when doubled.
To find the total volume of punch that the recipe will yield if doubled, we need to add the amounts of each ingredient and then multiply by 2.
Original recipe:
Fruit punch: 1,500 mL
Pineapple juice: 375 mL
Ginger ale: 1,000 mL (since 1 L = 1,000 mL)
Total volume of punch in the original recipe:
= 1,500 mL + 375 mL + 1,000 mL
= 2,875 mL
Now, if we double the recipe, we need to multiply the total volume by 2:
Total volume of punch when doubled = 2×2,875 mL
= 5,750 mL
To convert this to liters (L), we divide by 1,000 since 1 liter is equal to 1,000 mL:
Total volume of punch when doubled = 5,750 mL / 1,000
= 5.75 L
Hence, the recipe will yield 5.75 liters (L) of punch when doubled.
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The price of gas started out at 100¢/gallon on the 1st of the month. Every day since then, it has gone up 2¢/gallon. My car takes 10 gallons of gas. (As you might have guessed, these numbers are all fictional.) Let d equal the date (so the 1st of the month is 1, and so on). Let g equal the price of a gallon of gas, in cents. Let c equal the total price required to ll up my car, in cents.
a. Write a function g (d) that gives the price of gas on any given day of the month. ______________
b. Write a function c (g) that tells how much money it takes to ll up my car, as a function of the price of a gallon of gas. ______________
c. Write a composite function c (g (d)) that gives the cost of filling up my car on any given day of the month.
d. How much money does it take to ll up my car on the 11th of the month? First, translate this question into function notation then solve it for a number.
e. On what day does it cost 1,040¢ (otherwise known as $10.40) to ll up my car? First, translate this question into function notation then solve it for a number.
Answer:
Explained below.
Step-by-step explanation:
At the start of every month the price of gas started out at 100¢/gallon.
Then every day since, it has gone up 2¢/gallon.
The variables are denoted as follows:
d = the date
g = price of a gallon of gas
c = total price required to fill up my car, in cents.
(a)
The function that gives the price of gas on any given day of the month is:
g (d) = 100 + 2(d - 1)
The (d - 1) represent the number of times the price has gone up by 2¢/gallon.
(b)
The function that tells how much money it takes to fill up my car, as a function of the price of a gallon of gas is:
c (g) = 10 × g
Since the car takes 10 gallons of gas.
(c)
The composite function that gives the cost of filling up my car on any given day of the month is:
c (g (d)) = 10 × g (d)
= 10 [100 + 2(d - 1)]
c (g (d)) = 1000 + 20 (d - 1)
(d)
On the 11th day the price of gas has increased by 2¢/gallon for the past 10 days.
Compute the total price it takes to fill up my car on the 11th of the month as follows:
c (g (d)) = 1000 + 20 (d - 1)
c (g (11)) = 1000 + 20 (11 - 1)
= 1000 + (20 × 20)
= 1000 + 400
= 1400¢
Thus, the it takes to fill up my car on the 11th of the month is 1400¢.
(e)
The total price to fill the car on the nth day is 1040¢.
Compute the value of n as follows:
c (g (d)) = 1000 + 20 (d - 1)
1040 = 1000 + 20 (n - 1)
1040 - 1000 = 20 (n - 1)
40 = 20 (n - 1)
(n - 1) = 2
n = 3
Thus, the day on which it cost 1,040¢ to fill up the car is the 3rd day.
Solve for j - 1/3 = j/4 - 10/3
The value of j is equal to -4
What are like and unlike terms in an expression?In Algebra, the like terms are defined as the terms that contain the same variable which is raised to the same power. In algebraic like terms, only the numerical coefficients can vary. We can combine the like terms to simplify the algebraic expressions.
Given here: j - 1/3 = j/4 - 10/3
j-j/4 = -10/3+1/3
j = -3/0.75
j=-4
Hence, The value of j is equal to -4
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Use the coordinate plane to plot the points (6, 0) and (0, 5). Which statement is true? (0, 5) is located on the x-axis. (0, 5) is located at the origin. (6, 0) is located on the x-axis. (6, 0) is located at the origin.
Answer:
(6, 0) is located on the x-axis
Explanation:
For a point to be on the x-axis, its y-value must equal 0. (6, 0) has an x-value of 6 and a y-value of 0.
"(0, 5) is located at the origin" is not true because the origin is at (0, 0).
"(0, 5) is located on the x-axis" is not true because its y-value is 5, not 0.
"(6, 0) is located at the origin" is not true because the origin is at (0, 0).
The (6, 0) is located on the x-axis option (C) is correct because the y-coordinate is zero on the x-axis.
What is an ordered double?It is defined as a representation of coordinates in a two-dimensional coordinate plane. It has a list of two elements in it, such as (x, y).
[tex]\rm Area = |\dfrac{(x_1y_2-y_1x_2)+(x_2y_3-y_2x_3)....+(x_ny_1-y_nx_1)}{2}|[/tex]
It is given that:
The points are (6, 0) and (0, 5).
After plotting on the coordinate plane,
For a point to be on the x-axis, its y-value must equal 0. (6, 0) has an x-value of 6 and a y-value of 0.
"(6, 0) is located at the origin" is not true because the origin is at (0, 0).
Thus, the (6, 0) is located on the x-axis option (C) is correct because the y-coordinate is zero on the x-axis.
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What is the sum of the measure of the inner angle of a 13 sided polygon? A. 2340° B. 1300° C. 2700° D. 1980°
Hi there! :)
Answer:
D. 1980°
Find the sum of the measure of a 13-sided polygon using the formula:
Sum = 180(n-2), where n = number of sides
Therefore:
S = 180(13 - 2)
S = 180(11)
S = 1980°
Simplify the expression 2(-2x+4-5-3)
Answer:2 (-2x + 4 - 5 - 3)
2(-2x -4)
-4x - 8
A website reports that 70% of its users are from outside a certain country, and 60% of its users logon the website every day. Suppose that for its users from inside the country, that 80% of them log onevery day. What is the probability that a person is from the country given that he logs on the websiteevery day? Has the probability that he is from the country increased or decreased with the additionalinformation?
Answer:
The value is [tex]P (I | L ) = 0.63[/tex]
The probability has increased
Step-by-step explanation:
From the question we are told that
The percentage that are from outside the country is [tex]P(O) = 0.70[/tex]
The percentage that logs on everyday is [tex]P(L) = 0.60[/tex]
The percentage that logs on everyday that are from the inside the country is [tex]P(L | I) = 0.80[/tex]
Generally using Bayes' Rule the probability that a person is from the country given that he logs on the website every day is mathematically represented as
[tex]P (I | L ) = \frac{P(I)* P(L|I)}{ P(O) *P(L|O) + P(I) *P(L|I) }[/tex]
Where [tex]P(I)[/tex] is the percentage that are from inside that country which is mathematically represented as
[tex]P(I) = 1 - P(O)[/tex]
[tex]P(I) = 1 - 0.70[/tex]
[tex]P(I) = 0.30[/tex]
And [tex]P(L| O)[/tex] is percentage that logs on everyday that are from the outside the country which is evaluated as
[tex]P(L| O) = 1- P(L| I)[/tex]
[tex]P(L| O) = 1- 0.80[/tex]
[tex]P(L| O) = 0.20[/tex]
[tex]P (I | L ) = \frac{ 0.3* 0.80 }{ 0.7 *0.20 + 0.3 * 0.8 }[/tex]
[tex]P (I | L ) = 0.63[/tex]
Given that the percentage that are from inside that country is [tex]P(I) = 0.30[/tex]
and that the probability that a person is from the country given that he logs on the website every day is [tex]P (I | L ) = 0.63[/tex]
We see that the additional information increased the probability
A particle is moving on the x-axis. Its position is given by x = 2t^2 - 12t + 4 for times t ≥ 0
Answer:
a) - 10 m/s
b) 10 m/s
c) - 10 m/s²
Step-by-step explanation:
Given, a particle moving on the x-axis. Its position is:
x = 2t^2 - 12t + 4, t ≥ 0Let's assume unit of x is m.
For t= 0,
x = 0 - 0 + 4 = 4 mFor t = 1,
x = 2*1^2 - 12*1 + 4 = 2 - 12 + 4 = - 6 ma) Velocity at time t=1
Velocity = displacement/time = (-6- 4)/1 = - 10 m/s as it moves to the left
b) Speed at time t = 1
Speed = distance/time = (4 + |6|)/1 = 10 m/s
c) Acceleration at t = 1
Acceleration is rate of change of velocity.
It took 1 sec to change velocity from 0 to - 10 m/s
So acceleration is:
-10 m/s / 1 s = -10 m/s²Complete each equation with a number that makes it true. 8⋅______=40 8+______=40 21÷______=7 21−______=7 21⋅______=7
Answer:
8.5 =40
8+32=40
21÷3=7
21-14=7
21÷7=3
Step-by-step explanation:
The missing values are 5, 32, 3, 14, and 3 after using the arithmetic operation.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
It is given that:
8⋅______=40
8+______=40
21÷______=7
21−______=7
21⋅______=7
We can use the arithmetic operation to find the unknown values:
A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56 etc. are the numbers.
8x5 = 40
8 + 32 = 40
21 ÷ 3 = 7
21 - 14 = 7
21 ÷ 3 = 7
Thus, the missing values are 5, 32, 3, 14, and 3 after using the arithmetic operation.
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in the state of Texas, about 3/100 of the population lives in the city Fort Wroth. the population of Huston, Texas, is about 3 times the population of Fort Worth, Texas. What fraction of the population of Texas lives in Huston?
Answer:
population of Fort Worth, Texas. =9/100(x)
Step-by-step explanation:
in the state of Texas, about 3/100 of the population lives in the city Fort Wroth.
Let the population of the state of texas = X
Fort wroth population= 3/100(x)
the population of Huston, Texas, is about 3 times the population of Fort Worth, Texas. = 3*(3/100(x))
the population of Huston, Texas, is about 3 times the population of Fort Worth, Texas. =9/100(x)
The fraction of the population of Texas that lives in Huston is 9/100x.
Let the population of Texas be represented by x.
Since the state of Texas is about 3/100 of the population lives in the city Fort Wroth and the population of Huston, Texas, is about 3 times the population of Fort Worth, Texas, then the fraction of the population of Texas lives in Huston will be:
= 3/100 × 3 × x
= 9/100 × x
The fraction of the population of Texas that lives in Huston is 9/100x.
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how to solve this question
Step-by-step explanation:
A + B + C = 360
[2/3]A + B + [4/3]C = 360
[2/3]A + [4/3]B + C = 360
A + B + C = 360
We could extract from all of this that Cans A, B, C must have equal amount of paint inside in order to attain those conditions slated. Thus we could tell that the amount of paint in each can is 60L.
Answer:
A)60l
B)60l
Step-by-step explanation:
Solve for the largest value of $x$ such that $5(9x^2+9x+10) = x(9x-40).$ Express your answer as a simplified common fraction.
Hello, please consider the following.
[tex]\begin{aligned}5(9x^2+9x+10) &= x(9x-40)\\&=9x^2-40x\end{aligned}\\\\<=> 45x^2+45x+50=9x^2-40x\\\\<=> (45-9)x^2+(45+40)x+50=0\\\\<=> 36x^2+85x+50=0[/tex]
We can estimate the discriminant, and then, the solutions and we take the largest one.
[tex]\Delta=b^2-4ac=85^2-4*36*50=25=5^2\\\\x_1=\dfrac{-85-5}{2*36}=\dfrac{-18*5}{18*4}=\dfrac{-5}{4}\\\\x_2=\dfrac{-85+5}{2*36}=\dfrac{-80}{72}=\dfrac{-8*10}{8*9}=\boxed{\dfrac{-10}{9}}[/tex]
Thank you
The net of a square pyramid is shown below. What is the surface area of the pyramid?
Answer:
D. [tex] 192 cm^2 [/tex]
Step-by-step explanation:
The net of the pyramid is made up of 1 square base and 4 triangles
Surface area of the pyramid = area of square + 4(area of square)
[tex] S.A = (s^2)+ 4(\frac{1}{2}bh) [/tex]
Where,
s = 8
b = 8
h = 8
[tex] S.A = (8^2)+ 4(\frac{1}{2}*8*8) [/tex]
[tex] S.A = 64+ 4(32) [/tex]
[tex] S.A = 64+ 128 [/tex]
[tex] S.A = 192 cm^2 [/tex]
192 cm^2
Step-by-step explanation:
base = 8 x 8 = 64
1 triangle = 1/2 x 8 x 8 = 32
32 x 4 = 128
128+64 = 192 cm^2
What is the range of the function f(x) = -|3x + 3|?
Answer:
The range of the function [tex]f(x) = -|3\cdot x+3|[/tex] is every positive real numbers plus zero.
Step-by-step explanation:
According to definition of the absolute value, the range of absolute value covers positive real numbers or zero. A linear function is a continuous function, which means the existence of an image for every element from domain. The negative sign transforms the original range to all negative real numbers plus zero.
Hence, the range of the function [tex]f(x) = -|3\cdot x+3|[/tex] is every positive real numbers plus zero.
Determine the equation of the tangent line to the given path at the specified value of t. (Enter your answer as a comma-separated list of equations in (x, y, z) coordinates.) (sin(3t), cos(3t), 2t7/2); t=1
Answer:
k(t) = (sin3, cos3, 2) + [(t - 1)(cos3, -3sin3, 7)]
Step-by-step explanation:
For a path r(t), the general equation k(t) of its tangent line at a specified point r(t₀) is given by;
k(t) = r(t₀) + r'(t₀) [t - t₀] -----------------(i)
Where
r'(t) is the first derivative of the path r(t) at a given value of t.
From the question:
r(t) = (sin3t, cos3t, 2[tex]t^{7/2}[/tex]) and t₀ = 1
=> r(1) = (sin3, cos3, 2) at t₀ = 1
Find the first derivative component-wise of r(t) to get r'(t)
∴ r'(t) = (cos3t, -3sin3t, 7[tex]t^{5/2}[/tex])
=>r'(1) = (cos3, -3sin3, 7)
Now, at t₀ = 1, equation (i) becomes;
k(t) = r(1) + [ r'(1) (t-1)] [substitute the necessary values]
k(t) = (sin3, cos3, 2) + [(t - 1)(cos3, -3sin3, 7)]
Which point is a solution to this system of inequalities?
y < 1/2x – 3
y + 2x > 6
Answer: C. (5, -2)
Step-by-step explanation:
Graph each equation:
Equation 1: y < (1/2)x - 3 --> m = (1/2) b = -3, dashed line, shaded below
Equation 2: y > -2x + 6 --> m = -2 b = 6, dashed line, shaded above
or plug the values into the equations. It must be TRUE for both equations:
y < (1/2)x - 3 y > -2x + 6
(7, -8) True False
(2, -3) True False
(5, -2) True True <-- This works!
(4, 1) False True
Inequalities help us to compare two unequal expressions. The correct option is C.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
For a point to be the solution of the system of inequalities, the point when substituted in the inequalities must satisfy both the given inequalities.
A. (7, -8)
y < 1/2x – 3
-8 < (1/2)7 - 3
-8 < 0.5
y + 2x > 6
-8 + 2(7) > 6
-8 + 14 > 6
6 > 6
Since the second inequality is not satisfied, therefore, the given point is not the solution.
B. (2, -3)
y < 1/2x – 3
-3 < (1/2)2 - 3
-3 < -2
y + 2x > 6
-3 + 2(2) > 6
-3 + 4 > 6
1 > 6
Since the second inequality is not satisfied, therefore, the given point is not the solution.
C. (5, -2)
y < 1/2x – 3
-2 < (1/2)5 - 3
-3 < -2
y + 2x > 6
-2 + 2(5) > 6
-2 + 10 > 6
8 > 6
Since both the inequality are satisfied, therefore, the given point is the solution.
D. (4, 1)
y < 1/2x – 3
1 < (1/2)4 - 3
1 < -1
Since the first inequality is not satisfied, therefore, the given point is not the solution.
Learn more about Inequality:
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