Answer:C
Step-by-step explanation:
Domain is the range of x so it would be -7 to 7 so It would be C
Nia knows that one apple bag and 6 kiwis cost $19.70.
She also knows that the same apple bag and 16 kiwis cost $43.7.
i.
What is the cost for each kiwi?
Answer:
each kiwi costs $2.40
Step-by-step explanation:
we set up our system of equations
x = bag of apples
y = kiwi
x + 16y = 43.7
x + 6y = 19.7
multiply any one of the equations by -1 to make x negative
-1(x+6y) = -1(19.7)
-x - 6y = -19.7
add the other equation and the new equation
-x - 6y = -19.7
x + 16y = 43.7
+ ____________
10y = 24
divide by 10 both sides
y = 2.4
we can also look for the cost of each bag of apples
plug in the y value to an original equation
x + 16(2.4) = 43.7
simplify
x + 38.4 = 43.7
subtract 38.4 from both sides
x = 5.3
a large software company gives job applicants a test of programming ability and the mean for that test has been 160 in the past. twenty-five job applicants are randomly selected from one large university and they produce a mean score and standard deviation of 183 and 12, respectively. use a 0.05 level og significance to test the claim that this sample comes from a population with a mean score greater than 160. use the P-value method of testing hypotheses.
Using the P-value method of testing hypotheses with a significance level of 0.05, the sample provides strong evidence to support the claim that the mean score of job applicants from the university is greater than 160.
To test the claim that the mean score of job applicants from the university is greater than 160, we will perform a one-sample t-test using the P-value method. The null hypothesis (H0) assumes that the mean score is equal to 160, while the alternative hypothesis (Ha) assumes that the mean score is greater than 160.
First, we calculate the test statistic, which is the t-value. The formula for the t-value is:
t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))
Plugging in the given values, we have:
t = (183 - 160) / (12 / √(25))
= 23 / (12 / 5)
= 23 * (5 / 12)
≈ 9.58
Next, we find the P-value associated with the test statistic. The P-value represents the probability of obtaining a test statistic as extreme as the observed value, assuming the null hypothesis is true. Since the alternative hypothesis is one-sided (greater than 160), we calculate the P-value by finding the probability of the t-distribution with 24 degrees of freedom being greater than the calculated t-value.
Consulting statistical tables or using software, we find that the P-value is very small (less than 0.0001).
Since the P-value (less than 0.0001) is less than the significance level (0.05), we reject the null hypothesis. This provides strong evidence to support the claim that the mean score of job applicants from the university is greater than 160.
Learn more about P-value
brainly.com/question/30461126
#SPJ11
Help! I don't understand this
PQ=5i-4j 3QR+PQ-PQ=11i-4j-(5i-4j)=6i
3QR=6i QR=2i
R=Q+2i R=(4, 1)
Find the length of x. Assume the triangles are similar.
A. 2.5
B. 4.4
C. 4.0
D. 3.5
Answer:
the answer is get to be D-3.5
what is the slope of the line on the graph
Answer:
slope = \(\frac{1}{-3}\)
Step-by-step explanation:
equation to find the slope: \(\frac{y1-y2}{x1-x2}\)
(0,4) (6,2)
\(\frac{4-2}{0-6}\) = \(\frac{2}{-6}\) = \(\frac{1}{-3}\)
Mitch is attending a 4-year college. As a freshman, he was approved for a 10-year, federal
unsubsidized student loan in the amount of $8,100 at an APR of 4.29%. Mitch decides to
make no payments during the 4.5-year deferment period. After interest is capitalized at the
end of the 4.5-year period, what will his new principal amount be?
Answer:
Interest capitalization occurs when unpaid interest is added to the principal amount of your student loan. When the interest on your federal student loan is not paid as it accrues (during periods when you are responsible for paying the interest), your lender may capitalize the unpaid interest.
Step-by-step explanation:
How doe the definition of percent help you wright fraction and decimal equivalent
The definition of percent helps you write fraction and decimal equivalents by understanding that "per cent" means "per hundred".
For example, if you are asked to write the fraction and decimal equivalent of 25%, you would divide 25 by 100 to get the fractional equivalent of ¼, and divide 25 by 100 to get the decimal equivalent of 0.25.
The decimal equivalent of a fraction or percentage is the numerical value expressed in decimal form. For example, the decimal equivalent of 1/2 is 0.5 and the decimal equivalent of 25% is 0.25. Decimal equivalents are useful for calculations and can be used to convert fractions and percentages into decimal form.
Learn more about decimal equivalent :
https://brainly.com/question/28513467
#SPJ74
MULTIPLE CHOICE QUESTION
True or False: Involuntary deductions
from a person's gross pay go to their
employer.
False. Taxes and Social Security contributions are not deducted from a expressions person's total compensation and do not go to their employer.
what is expression ?In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression (such as addition, subtraction, multiplication, or division) is made up of numbers, variables, and functions. It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the phrase 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.
False. Taxes and Social Security contributions are not deducted from a person's total compensation and do not go to their employer. They are instead often paid to government agencies or other approved beneficiaries.
To know more about expressions visit :-
https://brainly.com/question/14083225
#SPJ1
(b) what is the standard deviation in the number of robin sleeping bags that joseph can expect to see when picking up sets of 50 bags, on average?
Standard deviation in the number of robins sleeping bags is 50.
what is standard deviation?A statistical expression that defines how much the available data are differ from the mean value of data. A low standard deviation indicates that all values seem to close to the mean, but the higher standard deviation indicates the opposite.
What is mean value in statistics?The mean value of a statistical data is the sum of all values divided by the total amount of data.
given, average number of bags expected by Joseph =50
actual mean value, X= 50
number of terms, N=1
So, standard deviation in the number of sleeping bags = √(∑X²/N)
hence, we get standard deviation = √(50²/1) = 50
To know more about Standard deviation visit:
https://brainly.com/question/29088233
#SPJ4
A classic counting problem is to determine the number of different ways that the letters of "magically can be arranged. Find that number. The number of different ways that the letters of magically" can be arranged is
The number of different ways that the letters of "magically" can be arranged is: 120.
How to solve probability combinations?This can be calculated using the formula for permutations expressed as;
nPr = n!/(n-r)!
where:
n is the number of objects to choose from (in this case, 8 letters)
r is the number of objects to be chosen (also 8 letters).
The formula then simplifies to 8!/(8-8)!, which is equal to 8!/(0!), which is equal to 8!.
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
= 40,320.
Therefore, the number of different ways that the letters of "magically" can be arranged is 120.
Read more about Probability Combinations at; https://brainly.com/question/3901018
#SPJ1
Can someone pls help me find the value of b and x??
Answer: b = 126,8
Step-by-step explanation:
c = 53,2
d = 90
90
b = 360 - 90 - 90 - 53,2 = 126,8
The perimeter of a triangle is 300 m . If its sides are in the ratio 3:5:7. Find the area of the triangle.
Plzz answer fast.
Answer:
If the perimeter = 300m
let the ratio be in x
a/q.
3x + 5x + 7x. = 300m
15x = 300
x = 300/15
x = 20
hence angles are
60 , 100 and 140
hope it helps
Answer:
A ≈ 1500\(\sqrt{3}\) m²
Step-by-step explanation:
sum the parts of the ratio, 3 + 5 + 7 = 15 parts
Divide perimeter by 15 to find the value of one part of the ratio.
300 ÷ 15 = 20 m ← value of 1 part of the ratio , then
3 parts = 3 × 20 = 60 m
5 parts = 5 × 20 = 100 m
7 parts = 7 × 20 = 140 m
The 3 sides of the triangle are 60 m, 100 m , 140 m
To calculate the area (A) having all 3 sides use Hero's formula
A = \(\sqrt{s(s-a)(s-b)(s-c)}\)
where s is the semiperimeter and a, b , c the sides of the triangle
s = 300 m ÷ 2 = 150 m
let a = 60, b = 100 and c = 140 , then
A = \(\sqrt{150(150-60)(150-100)(150-140)}\)
= \(\sqrt{150(90)(50)(10)}\)
= \(\sqrt{6750000}\)
= \(\sqrt{10000}\) × \(\sqrt{675}\)
= 100 × \(\sqrt{25(27)}\)
= 100 × 5\(\sqrt{27}\)
= 500 × \(\sqrt{9(3)}\)
= 500 × 3\(\sqrt{3}\)
= 1500\(\sqrt{3}\) m²
The projected number of employed writers and authors in 2016 is 153,000. 12. 4% of those will have some college experience but no degree, and 84. 1% will have a bachelor’s degree or higher. If this holds true, how many more writers and authors with bachelor’s degree will there be than those with only some college experience and no degree?.
There are 109,761 more writers with a bachelor's degree or higher than those with only some college experience and no degree.
From the given data, Percent of writers with some college experience but no degree = 12.4%
Percent of writers with a bachelor's degree or higher = 84.1%The percentage of writers without any college experience can be found by:
Percent of writers without any college experience = 100% - (12.4% + 84.1%)
Percent of writers without any college experience = 3.5%T
Total number of writers with some college experience but no degree = 12.4% of 153,000= 18,972
Total number of writers with a bachelor's degree or higher = 84.1% of 153,000= 128,733
Total number of writers without any college experience = 3.5% of 153,000= 5,355
Therefore, the number of writers with a bachelor's degree or higher than those with only some college experience and no degree is:
128,733 - 18,972 = 109,761
Hence, there are 109,761 more writers with a bachelor's degree or higher than those with only some college experience and no degree.
Know more about Percent here:
https://brainly.com/question/24877689
#SPJ11
A function g models a relationship in which the dependent variable is multiplied by 9
for every 2 units the independent variable increases. The value of the function at 0 is 2.
Which equation represents g?
The link represented by function g multiplies the dependent variable by 9 for every increase of 2 units in the independent variable. The equation that represents g is \(g(x)= 2 \times3^x\),and the function has a value of 2 at 0
Let x be the independent variable, and let g(x) be the dependent variable.
According to the problem, for every 2 units the independent variable increases, the dependent variable is multiplied by 9. This suggests an exponential relationship of the form:
\(g(x)= a \times b^x\)
where a is the initial value of the dependent variable (when x=0), and b is the growth factor (how much the dependent variable changes for every unit increase in x).
We are given that g(0) = 2, so we can plug in these values and solve for a:
\(g(0)= a \times b^0\)
a = 2
So now we have:
\(g(x)= 2 \times b^x\)
We still need to find the growth factor b. We are told that the dependent variable is multiplied by 9 for every 2 units the independent variable increases. In other words:
\(g(x+2) = 9 \times g(x)\)
Using our equation for g(x), we can substitute in and simplify:
\(2 \times b(x+2) = 9 \times 2\times b^x\)
Simplifying, we get:
\(b^2\) = 9
Taking the square root of both sides (we take the positive square root since b must be positive in order for g to be an increasing function), we get:
b = 3
So the final equation for g(x) is:
\(g(x) = 2 \times 3^x\)
For more such questions on variable
https://brainly.com/question/25223322
#SPJ4
Numbers: 4 and 6 it’s asking what the right triangle area is in square inches
What is an equation of the line that passes through the point (6,7) and is parallel to the line 2x-3y=92x−3y=9?
Answer:
y = ²/₃x + 3Step-by-step explanation:
y=m₁x+b₁ ║ y=m₂x+b₂ ⇔ m₁ = m₂
{Two lines are parallel if their slopes are equal}
Changing to slope-intercept form:
2x - 3y = 9 {subtract 2x from both sides}
-3y = -2x + 9 {divide both sides by (-3)}
y = ²/₃x - 3 ⇒ m₁=²/₃ ⇒ m₂=²/₃
The line y=²/₃x+b passes through point (6, 7) so the equation:
7 = ²/₃×6 + b is true
7 = 4 + b
b = 3
Therefore equation in slope-intercept form:
y = ²/₃x + 3
The equation of the line passing through the point (6, 7) parallel to the line is y = 2/3x + 3
The equation in slope - intercept form :
2x - 3y = 9
-3y = 9 - 2x
Divide both sides by - 3
y = - 3 + 2/3x
Using the points (6, 7)
7 = c + 2/3(6)
7 = c + 12/3
7 = c + 4
c = 7 - 4 = 3
c = 3
The equation of the parallel line is thus :
y = 2/3x + 3Learn more : https://brainly.com/question/18106342
will give brainly
(11x^11) (4x^4)
Answer:
The answer is 44x^15
Step-by-step explanation:
Simplify the expression.
Hoped this helped!
brainly, please?
Sara’s English test had 90 questions and she got 18 questions wrong. What percent of the questions did she get correct?
Answer:
80%
Step-by-step explanation:
First we find the percentage she got wrong:
\(\frac{18}{90}\) Is the fraction she got wrong, now we convert this into a percentage by divding 18 by 90 and multiplying by 100
18÷90×100=20
so to find the remaining percent we subtract 20 from 100
100-20=80
And our answer is 80
Answer:
80%
Step-by-step explanation:
10%= 9
20%= 18
18= how many they got wrong
90=total questions
90= 100%
18= 20%
100%=20%=80%
This example has level resources of three resources for eight days. If the project is limited to two resources, how should the project be organized to meet the resource constraint and finish the project as early as possible? The tasks with the least slack have the lower number. Group of answer choices Paths would be 1,2,3,5 and 1,2,4 Paths would be 1,2,3,4 and 1,2,5 Paths would be 1,2 and 3,4,5 Path would be 1,2,3,4,5
In order to meet the resource constraint and complete the project as quickly as possible, the project should be organized into two paths: 1,2,3,5 and 1,2,4.
The project initially has three resources available for eight days. However, due to the resource constraint of limiting it to two resources, the project needs to be reorganized to optimize efficiency. The goal is to finish the project as early as possible while considering the limited resources. Among the given answer choices, the paths 1,2,3,5 and 1,2,4 are the most suitable. These paths ensure that the critical tasks with the least slack are prioritized, allowing for an early completion of the project. By following these paths, the project can be executed effectively while adhering to the resource constraint.
For more information on paths visit: brainly.com/question/30076225
#SPJ11
The complex conjugates theorem states that
another factor of the polynomial is
Answer:
Step-by-step explanation:
...exactly the same but with a different sign separating them. For example, if a root of a polynomial is
3 + 4i, then the other root has to be 3 - 4i because they always come in pairs. Always!! If a root is -2 - 3i, then the other root has to be -2 + 3i. Notice that the only sign that will change is the one that separates the a part of the complex number from the b part.
This phenomenon also applies to radicals. If we have a root that is \(-3 + \sqrt{5}\)\(-3 +\sqrt{5}\) then the other root has to be \(-3 -\sqrt{5}\)
Answer:
x-3i
Step-by-step explanation:
Help me please..
Help me with the ones which are marked
8 points and brainliest
Answer:
1. 30
2. C = 18.3 B = 25% A=15 % rest = unkown
Step-by-step explanation:
to find X is what percent of Y
X/Y multiplied by 100
the solomon four-group design utilizes how many control groups?
The Solomon four-group design includes two control groups: one that is not pretested and does not receive treatment, and another that is not pretested but receives treatment.
In the Solomon four-group design, there are two treatment groups and two control groups. The purpose of this design is to examine the interaction effect between pretesting and treatment.
The first control group does not receive any treatment, while the second control group also does not receive treatment but is pretested. These two control groups help to measure the impact of pretesting on the dependent variable.
The two treatment groups receive the treatment being studied, with one group being pretested and the other group not being pretested. By comparing the pretested and non-pretested treatment groups, researchers can determine if there is an interaction effect between pretesting and the treatment.
To know more about Solomon four-group visit:
https://brainly.com/question/13735730
#SPJ11
1. Identify each of the following statements as true of false and explain your reasoning in full sentences. The domain of discourse is the integers.
(a) ∃x∀y(y > x)
(b) ∀y∃x(y > x)
(c) ∃x(x = 0 → x = 1)
2. Write the formal negation of the following statements. Your negation must not contain any explicit negation symbols.
(a) ∀x∃y(2 < x ≤ y)
(b) ∀y∃x(y > 0 → x ≤ 0)
3. Negate verbally:
(a) "All people weigh at least 100 pounds."
(b) "Somebody did not see any animals in the zoo"
4. If P and Q are predicates over some domain, and if it is true that∀x(P(x)∨ Q(x)), must ∀xP(x)∨∀xQ(x) also be true? Explain.
The domain of discourse is the integers is smaller integer
What is Integer?
A zero, a positive natural number, or a negative integer with a minus sign is an integer. The negative numbers are the additive inverses of their positive counterparts.
1.(a) ∃x∀y(y > x)
The statement is False
it is impossible to find a single integer x that has the property that all integer y are bigger that it. for any integer x, the integer y =x-1 is smaller
(b) ∀y∃x(y > x)
the statement is true for every integer y, we can find a integer x that is smaller, for example x=y-1
(c) ∃x(x = 0 → x = 1)
The statement is True
there exist x such that (x = 0, x=1). in this statement when we select x =1. this statement is true regardless of x not equal to 0 therefore this statement is true if x=1 when x=1
2. (a) ∀x∃y(2 < x ≤ y)
we know
∀xP(x)=∃y(P(x))
∃xP(x)=∃y(P(x))
now apply de morgan law
∃x∀(y)=2>x v x>y
(b) ∀y∃x(y > 0 → x ≤ 0)
we know that A-B = A V B
∀y∃x (Y<0 V X< 0)
∀y∃x (Y<0 : X< 0)
3.(a) Given : All people weigh at least 100 pounds.
The negation is : Some people weigh less than 100 pounds. ( All negates to some, at least negates to less than )
(b) The statement is : Somebody did not see any animals in the zoo.
Equivalently : Somebody see no animals in the zoo.
Negation : Everybody saw some animals in the zoo. ( Somebody negates to everybody, No animals negates to some animals )
4. P(x,y): x is friends with y.
Then the given translates to " For all x there is a person y and a person z such that if y and z are not the same people that x and y are friends and x and z are friends."
The given statement is False. For every person x, we can always find two distinct persons y and z such that x is friends with y and y is friends with z. But, we reach a contradiction when we consider the case when x has only one friend. Then for that particular person x, we can find a person y such that P(x,y) but we cannot find a person z such that P(x,z). Hence, in that case, the statement is FALSE.
To learn more about Integer visit:
brainly.com/question/15276410
#SPJ4
You have a bag of ping pong balls. You arrange all but 2 of the balls in the shape of an equilateral triangle. Then you put all the balls back in the bag and try to make an equilateral triangle where each side has one more ball than the first arrangement. But this time you are 11 balls short. How many ball were originally in the bag?
The original bag had 10 + 2 = 12 ping pong balls.
Let's denote the number of ping pong balls in the original bag as "n". If we take away two balls from the bag, we will have "n-2" balls left to arrange in an equilateral triangle.
The number of balls in an equilateral triangle can be found by the formula:
Tn = (n(n+1))/2
where Tn is the nth triangular number, i.e. the sum of the first n positive integers.
For an equilateral triangle, the number of balls on each side is equal to Tn, so we have:
Tn = (n(n+1))/2
Solving for n, we get,
n^2 + n - 2Tn = 0
Using the quadratic formula, we can solve for n:
n = (-1 + sqrt(1 + 8Tn)) / 2
Now we want to find the value of n such that the difference between the number of balls in the two equilateral triangles is 11. Let's denote the number of balls in the second equilateral triangle as "m". We have:
m - Tn = 11
Using the formula for Tn, we can express m in terms of n:
m = Tn + n + 1
Substituting this expression for m into the equation above, we get:
Tn + n + 1 - Tn = 11
Simplifying, we get:
n + 1 = 11
Therefore, n = 10.
Thus, the original bag had 10 + 2 = 12 ping pong balls.
for similar questions on pong balls
brainly.com/question/31426155
#SPJ1
Determine the equation of the circle with center (0,−6) containing the point (−\sqrt{28 },3)
I did not get Your Question Probably But the way I see it the answer is:
The equation of a circle with center (h, k) and radius r can be written as:
(x - h)^2 + (y - k)^2 = r^2
In this case, the center of the circle is (0, -6). To find the radius, we can use the distance formula between the center and the given point (-√28, 3):
r = √((x₂ - x₁)^2 + (y₂ - y₁)^2)
Plugging in the values:
r = √((-√28 - 0)^2 + (3 - (-6))^2)
Simplifying:
r = √(28 + 81)
r = √109
Therefore, the equation of the circle with center (0, -6) and containing the point (-√28, 3) is:
(x - 0)^2 + (y + 6)^2 = (√109)^2
Simplifying further:
x^2 + (y + 6)^2 = 109
Answer:
The equation of the circle with center (0, -6) containing the point (-√28, 3) is x^2 + (y + 6)^2 = 109.
Step-by-step explanation:
The equation of a circle with center (h, k) and radius r is given by the formula:
(x - h)^2 + (y - k)^2 = r^2
In this case, the center of the circle is (0, -6), which means that h = 0 and k = -6. We also know that the circle contains the point (-√28, 3), which means that this point is on the circle and satisfies the equation above.
To find the radius r, we can use the distance formula between the center of the circle and the given point:
r = sqrt((0 - (-√28))^2 + (-6 - 3)^2) = sqrt(28 + 81) = sqrt(109)
Substituting h, k, and r into the equation of the circle, we get:
x^2 + (y + 6)^2 = 109
Therefore, the equation of the circle is x^2 + (y + 6)^2 = 109.
reg gets a hit 24% of the times he is at bat. If he got 18 hits this season, how many at-bats did he have?
Answer:
He had a total of 75 at-bats
Step-by-step explanation:
24% of his at bats are hit
Let the number of hits be x
24% of x = 18
24/100 * x = 18
24x = 100 * 18
x = (100 * 18)/24
x = 75
3y + 2 = 2y - 5x
y = mx + b form:
answer:
y= -5x -2
hope it helps
Let f(r) = r² for r € R. (a) State he range of f(x). -(b) State the domain and range of f(x). 2. State the range of the functions below. (a) g(x) = x² for x ≥ 0. (b) h(x) = r² for > 3. (c) p(x) = r² for -1 < a <3. 3. State the domain and range of the functions below. (a) o(x) = x² - 4x + 1 for z € R. (b) r(x) = x² - 4x + 1 for a -1. (c) g(x) = x² - 4x + 1 for a <3. (d) T(x)=x²-4+1 for -2-2 (a) State the domain and range of f-¹. (b) Find an expression for f(x). 5 5. Let f: + for a € R,r> 2 2x+1 (a) Find the domain and range of f¹. (b) Find an expression for f-¹(x). 6. Let f: +(2+1)³-4 for r € R, r > 0. (a) Find an expression for f-¹(a). (b) Find the domain and range of f-¹.
The questions involve determining the domain and range of various functions, as well as finding the expression for the inverse functions.
(a) The range of the function f(x) = x² for x ∈ ℝ is the set of all non-negative real numbers, since squaring a real number always results in a non-negative value.
(b) The domain of f(x) = x² is all real numbers, and the range is the set of non-negative real numbers.
2. (a) The range of the function g(x) = x² for x ≥ 0 is the set of non-negative real numbers.
(b) The range of the function h(x) = r² for r > 3 is the set of all positive real numbers.
(c) The range of the function p(x) = r² for -1 < a < 3 is the set of all positive real numbers.
3.(a) The domain of the function o(x) = x² - 4x + 1 for x ∈ ℝ is all real numbers, and the range is the set of all real numbers.
(b) The domain of the function r(x) = x² - 4x + 1 for a > -1 is all real numbers, and the range is the set of all real numbers.
(c) The domain of the function g(x) = x² - 4x + 1 for a < 3 is all real numbers, and the range is the set of all real numbers.
(d) The domain of the function T(x) = x² - 4x + 1 for -2 < a < 2 is the interval (-2, 2), and the range is the set of all real numbers.
4.(a) The domain of the inverse function f⁻¹ is the range of the original function f(x). In this case, the domain of f⁻¹ is the set of non-negative real numbers.
(b) The expression for f(x) is f(x) = √x, where √x represents the square root of x.
5.(a) The domain of the inverse function f⁻¹ is the range of the original function f(x), which is the set of all positive real numbers.
(b) The expression for f⁻¹(x) is f⁻¹(x) = (x - 1)/2.
6.(a) The expression for f⁻¹(a) is f⁻¹(a) = ∛(a + 4).
(b) The domain of the inverse function f⁻¹ is all positive real numbers, and the range is the set of all real numbers.
To know more about domain click here: brainly.com/question/30133157
#SPJ11
compute the equation for the line between (4,5,6) and (1,0,-3) in r^3 and find the midpoint between the two points.
The computed value of equation for the line between (4,5,6) and (1,0,-3) in R³, (x, y,z) = (4,5,6) + (1,0,-3) and the midpoint between the two points is equals to the \( (\frac{5}{2}, \frac{5}{2}, \frac{3}{2}). \).
We have to determine the equation for the line between (4,5,6) and (1,0,-3) in R³. Equation is written as (x, y,z) = (4,5,6) + (1,0,-3). The midpoint is equals to middle point of a line segment. It is equidistant from both endpoints. The midpoint can be found with the formula, \((x, y, z) = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}, \frac{z_1 + z_2}{2})\)
Here (x₁, y₁ , z₁) and (x₂, y₂, z₂) are the coordinates of two points, and the midpoint is a point lying equidistant and between these two points. Here,
x₁ = 4, y₁ = 5, z₁ =6 and x₂ = 1, y₂=0, z₂ = -3, Substitute all known values in above formula, \((x, y, z) = (\frac{4+1}{2}, \frac{5+ 0}{2}, \frac{6+ (-3)}{2}). \)
=\( (\frac{5}{2}, \frac{5}{2}, \frac{3}{2}). \)
Hence, required value of midpoint is
\( (\frac{5}{2}, \frac{5}{2}, \frac{3}{2}). \)
For more information about midpoint visit:
https://brainly.com/question/29288255
#SPJ4
14. Mark weighs 74 pounds. Together, he and his sister weigh six pounds more than three tim the weight of his sister What is the weight, w. Of Mark's sister?
Weight, w of Mark's sister is 34 pounds
What is given in the question?
Mark's weight = 74 lb.
Mark's sister's weight = w lb.
Since Mark and his sister together weigh 6 lb. more than thrice the weight of Mark's sister alone.
We can write: 74 + w = 6 + 3w
According to the given question:
To solve this equation for w, first add -w to both sides of the equation.
74 + w - w = 6 + 3w - w
74 = 6 + 2w
Now add -6 to both sides and simplify:
74 - 6 = 6 + 2w -6
68 = 2w
Therefore, w= (68/2) = 34 lb
Let's verify the answer
Marks weight = 74 lb.
Marks's sister's weight = 34 lb
Sum of Mark and his sister's weight = 108
Three time Mark's sister's weight
= 3*34 = 102
Also 108 = 102+6 which is the statement of the problem.
To know more about weight problems visit
https://brainly.com/question/29321284
#SPJ4