Answers
9514 1404 393
Answer:
(b) k = 3/4
(c) a = 1/13; b = 4/13
Step-by-step explanation:
(b) Parallel to (1, 1) means the two components of the vector are equal. (They have the same ratio as 1 : 1.) Solve by setting the components of the composite vector equal:
p +kq = (1, 4) +k(3, -1) = (1 +3k, 4 -k)
We want ...
1 +3k = 4 -k
4k = 3 . . . . . . . add k-1 to both sides
k = 3/4 . . . . . . divide by 4
__
(c) Same as above: set the components of the composite vector to those of the desired sum.
ap +bq = (1, 0)
a(1, 4) +b(3, -1) = (1, 0)
(a +3b, 4a -b) = (1, 0)
The second component tells us b=4a, so we can use that to find 'a' in the first component:
a + 3(4a) = 1
13a = 1
a = 1/13
b = 4a = 4/13
Check
(1/13)(1, 4) + (4/13)(3, -1) = (1/13 +12/13, 4/13 -4/13) = (1, 0) . . . as required
Related Questions
Which expression has a greater value: log3 1/3 or logb 1/b? Explain how you know.
Answers
Answer:
They are equalStep-by-step explanation:
Given\(log_3 1/3 \ and\ log_b 1/b\)Compare the expressions\(log_31/3=log_33^{-1}=-1\)\(log_b1/b=log_bb^{-1}=-1\)As we see the two expressions are equal in value
Answer:
log3 1/3 = logb 1/b
(Both expressions are equal)
Step-by-step explanation:
Now we have to,
→ find the expression with greater value.
Then the greatest value is,
→ log3 1/3 = logb 1/b
→ log3 3^(-1) = logb b^(-1)
→ -1 = -1
→ [ LHS = RHS ]
Hence, both have same value.
b) y and z are whole numbers.
y < 70
Z <= 60
Work out the largest possible value of y + z
Answers
The largest possible value of y+z will be "129".
The given whole numbers are:
\(y<70\)\(z \leq 60\)According to the question, the exact whole numbers will be:
The maximum possible value,
→ \(y = 69\)
The maximum possible value,
→ \(z = 60\)
hence,
The largest possible value will be:
= \(y+z\)
By substituting the values, we get
= \(69+60\)
= \(129\)
Thus the above solution is correct.
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Consider the system of equations shown below. 2x - 4y + 5z = -7x + 14y + 4z = -35 Зх — 10 бу + z = 15 (a) Determine whether the nonhomogeneous system Ax = b is consistent. O consistent O inconsistent (b) If the system is consistent, then write the solution in the form x = X, + Xh, where x, is a particular solution of Ax = b and x, is a solution of Ax = 0. (If the system is inconsistent, enter INCONSISTENT in both matrices.) X = + t
Answers
Hence, the system does not have a consistent solution.
To determine whether the nonhomogeneous system Ax = b is consistent, we can perform row reduction on the augmented matrix [A | b] and check for any inconsistencies.
The given system of equations is:
2x - 4y + 5z = -7
-7x + 14y + 4z = -35
3x - 10y + z = 15
Rewriting the system as an augmented matrix [A | b]:
[ 2 -4 5 | -7 ]
[ -7 14 4 | -35 ]
[ 3 -10 1 | 15 ]
Now, let's perform row reduction to determine the consistency of the system:
R2 = R2 + 7R1
R3 = R3 - (3/2)R1
[ 2 -4 5 | -7 ]
[ 0 0 39 | -14 ]
[ 0 1 -17/2| 31/2]
The third row indicates a contradiction, as it implies 0 = -14, which is not possible. Therefore, the system is inconsistent.
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calcule (-6 ) + (+4 )
Answers
Answer:
-2
Step-by-step explanation:
Just do it
Which is the most accurate statement about the product of a number and an improper fraction?
1) It is less than 1
2)It is less than or equal to 1
3)It is greater than 1 but less than the number
4)It is greater than the number
Answers
Answer:
0 number and negative.number
A number is selected from the set {1, 2, 3, 5, 15, 21, 29, 38, 500}. If equal elemental probabilities are assigned, what is the probability that the number chosen is either less than 29 or odd? 6/9 7/9 8/9
Answers
Answer:
The required probability is \(\frac{7}{9}\).
Step-by-step explanation:
Set given is:
S = {1, 2, 3, 5, 15, 21, 29, 38, 500}
Total number of elements in set, \(n(S)\) = 9
Let A be the event that the number is less than 29 ({1, 2, 3, 5, 15, 21}).
Number of items in the event A, \(n(A)\) = 6
Probability of event A,
\(P(A) = \dfrac{n(A)}{n(S)}}=\dfrac{6}{9} \Rightarrow \dfrac{2}{3}\)
Formula for probability of any event E:
\(P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}\)
Let B be the event that the number is odd (either of {1,3,5,15,21,29}).
Number of items in the event B, \(n(B)\) = 6
Probability of event B,
\(P(B) = \dfrac{n(B)}{n(S)}}=\dfrac{6}{9} \Rightarrow \dfrac{2}{3}\)
The event A and B have a few elements in common, i.e. numbers less than 29 which are odd as well.
The common elements are represented as:
\(A \cap B = \{1, 3, 5, 15, 21\}\)
\(n(A\cap B) = 5\)
\(P(A \cap B ) = \dfrac{n(A \cap B)}{n(s)}\\\Rightarrow P(A \cap B) = \dfrac{5}{9}\)
To find probability of selecting a number which is either less than 29 (event A) or odd (event B),
We have to find \(P(A\ or \ B)\) which is represented as \(P(A \cup B)\) and the formula is:
\(P(A \cup B) = P(A) + P(B) - P(A \cap B)\\\Rightarrow \dfrac{2}{3} + \dfrac{2}{3} - \dfrac{5}{9}\\\Rightarrow \dfrac{12-5}{9}\\\Rightarrow \dfrac{7}{9}\)
The required probability is \(\frac{7}{9}\).
using the ten digits to , in how many different ways can a 8 digit number be created such that no digit in the number is repeated
Answers
There are 45, 45, 600 different ways to create an 8-digit number using the ten digits without repeating any digit.
The number of different ways to create an 8-digit number using the ten digits without repeating any digit, we can use the permutation formula. The permutation formula is: n P r = n! / (n - r)!
where n is the total number of items and r is the number of items selected.
In this case, we have 10 digits to choose from and we want to choose 8 digits without repetition. So, n = 10 and r = 8.
10 P 8 = 10! / (10 - 8)!
= 10! / 2!
= (10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / (2 × 1)
= 45, 45, 600
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how large a sample should be taken in order to estimate the proportion to within 4% with a 95.44% level of confidence?
Answers
Answer: The product of two consecutive negative integers is 600. What is the value of the lesser integer?
Step-by-step explanation:
EDGE2021
pla shop mathematics
Answers
The number of trees more than 10m tall but not more than 20m tall is 18 trees.
How many of the trees are more than 10m tall but not more than 20m tall?0 < h ≤ 5 = 5
height greater than 0m less than or equal to 5m
5 < h ≤ 10 = 9
height greater than 5m less than or equal to 10m
10 < h ≤ 15 = 13
height greater than 10m less than or equal to 15m
15 < h ≤ 20 = 5
height greater than 15m less than or equal to 20m
20 < h ≤ 25 = 1
height greater than 20m less than or equal to 25m
The number of trees that are more than 10m tall but not more than 20m tall are;
10 < h ≤ 15 = 13
15 < h ≤ 20 = 5
So,
13 + 5 = 18 trees
Therefore, the total number of trees which are 10m tall but not more than 20m tall is 18 trees.
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Solve for w:
2w > -12
(There is a line under the >)
Answers
Answer:
w≥-6
Step-by-step explanation:
You mean 2w≥-12
If so then
2w≥-12
w≥-12/2
w≥-6
5. Rizza bought 24 face masks for Php172.80 and sold them for Php10.00 each. How much profit did she get? A. Php 62.50 B. Php67.20 C. Php40.00 D. Php67.50
Answers
Answer: Rizza got a profit of Php 67.20---B
Step-by-step explanation:
Profit = Selling Price - Cost Price
But
Selling price =Php10.00 x 24=240Php
Cost Price =Php172.80
Therefore,
Profit=Php240 -Php172.80
=Php 67.20
What is the slope of -5,6 and -9,-6
Answers
Answer:
0
Step-by-step explanation:
picture
Consider the spreadsheet below that lists the hours spent studying five subjects each week by five students. Each student studies for a total of 25 hours per week. Course Study Time Per Week total hours 25 studying Name Poly Sci Math Chemistry Comp Sci Psychology 6 Jonah 7 Barry 1 Samantha 9 Evan 10 Tricia 6.5 5.5 Suppose the above spreadsheet (A6:F10) is sorted according to this criteria: Poly Sci is the primary key sorted in descending order, and Psychology is the secondary key sorted in ascending order. What student name would be in cell A8?
-Evan
-Samantha
-Jonah
-Barry
-Tricia
Answers
Based on the given criteria for sorting the spreadsheet, the student name that would be in cell A8 is Jonah.
Based on the sorting criteria mentioned, the primary key for sorting is "Poly Sci" in descending order, and the secondary key is "Psychology" in ascending order.
Looking at the data in the "Poly Sci" column, we can see that the values are sorted in descending order as follows: 10, 9, 7, 6.5, 6.
Within the "Poly Sci" values of 6, the secondary key "Psychology" comes into play to determine the order. Among the students with a "Poly Sci" value of 6, we have Jonah and Tricia.
Comparing their "Psychology" values, we can see that Jonah has a "Psychology" value of 6, while Tricia has a "Psychology" value of 5.5.
Since the secondary key "Psychology" is sorted in ascending order, Jonah should appear before Tricia.
Therefore, the student name that would be in cell A8 is Jonah.
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The sum of a number and 98 is 167. What is the number?
Answers
Answer:
The answer is 69
Step-by-step explanation:
The sum of a number and 98 means it equals 167. So all you have to do to find the missing number is plug it in to the equation.
?+ 98= 167
167-98=?
The amount of money in a bank account doubles every 3 months, what would be the growth factor for 1 month? Explain how you got your answer.
Answers
Answer:
Explanation:
Select the correct answer.Consider the piecewise function shown on the graph.A10-8642-10-8-6-44-2 02-26810-4-6-8-10Over which interval of the domain does the graph represent an exponential function?A.-3
Answers
Solution
The exponential function
\(x\ge1\)
The final answer
Option B
PLEASE HELP ME WITH FUNCTIONS I REALLY NEED IT
Answers
Answer:
D
Step-by-step explanation:
Range is on the y-axis & Domain sits on the x-axis
Let F(x) be an antiderivative of (ln x)^3/x. If F(1) = 0, then F(9) =
a. .048
b. .144
c. 5.827
d. 23. 308
e. 1,640.250
Answers
the value of F(9) is approximately 23.308.
To find the value of F(9) given that F(x) is an antiderivative of (ln x)^3/x and F(1) = 0, we can use the fundamental theorem of calculus.
According to the fundamental theorem of calculus, if F(x) is an antiderivative of a function f(x), then:
∫[a,b] f(x) dx = F(b) - F(a)
Since F(1) = 0, we can write:
∫[1,9] (ln x)^3/x dx = F(9) - F(1)
To evaluate the integral, we can make a substitution:
Let u = ln x, then du = (1/x) dx
The integral becomes:
∫[ln 1, ln 9] u^3 du
Integrating u^3 with respect to u:
[(1/4)u^4] | [ln 1, ln 9] = (1/4)(ln 9)^4 - (1/4)(ln 1)^4
Since ln 1 = 0, we have:
(1/4)(ln 9)^4 - (1/4)(ln 1)^4 = (1/4)(ln 9)^4
Therefore, F(9) - F(1) = (1/4)(ln 9)^4
Since F(1) = 0, we can conclude that F(9) = (1/4)(ln 9)^4.
Calculating this value:
F(9) = (1/4)(ln 9)^4 ≈ 23.308
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Factor each completely.
10a² - 9a + 2
Answers
Answer:
a= \(\frac{2}{5}\) or \(\frac{1}{2}\)
Step-by-step explanation:
Equate the equation to zero
\(10a^{2}\)-9a+2=0
\(10a^{2}\)-5a-4a+2=0
5a(2a-1)-2(2a-1)=0
Write out the factors
(5a-2)(2a-1)=0
Then equate each factor to zero
5a-2=0 OR 2a-1=0
5a=2 OR 2a=1
a= \(\frac{2}{5}\) OR a= \(\frac{1}{2}\)
a=\(\frac{2}{5}\) or \(\frac{1}{2}\)
BRAINLIEST ANSWER GIVEN IF YOU ARE CORRECT
A local chess tournament gives medals for first, second, and third place. There are five students from Midland High, three students from Leasburg High, and six students from Cassville High competing in the tournament.
Answers
Answer:
a b c e
Step-by-step explanation:
Answer:
A, B, C, E answer on edg
Step-by-step explanation:
which of the following fraction pairs are equivalent? 6/15 and 18/40 8/12 and 12/18 5/11 and 10/16 4/9 and 9/4
Answers
Answer:
18/40
Step-by-step explanation:
To make concrete, a person mixes 1 bag of cement to 4 bags of sand. How many bags of cement should be used with 100 bags of sand?
Group of answer choices
Answers
The answer would be 25 bags of cement to 100 bags of sand by dividing 100 by 4.
help me I got stuckk
Answers
Answer:
Step-by-step explanation:
Area of the triangle
A = b*h/2
b = 18
h = 15
Area = 18*15/2
Area = 135
Area of Parallelogram
A = b * h
b = 18
h = 15
Area = 18 * 15
Area = 270
Note: The parallelogram = 2 * Area of Triangle.
Answer:
Area of Triangle
= 135 sq cm
Area of Shaded
= 135 sq cm
Step-by-step explanation:
There is a parallelogram here and a triangle both have the same base and height.
Area (triangle)=1/2bh
Area (parallelogram)
=bh
Subtract to find the shaded region.
Area (parallelogram)
= 18 × 15
= 270
Area(triangle)
= 1/2 × 18 × 15
= 135
Area(shaded)
= 270 - 135
= 135
The shaded area is 135 square cm
HELP drag each set of coordinates to the correct location on the table not all sets of coordinates will be used
Answers
Answer:
im sorry but i tried to do it but too dumb
Step-by-step explanation:
33.)if 10,000 pounds' of cotton candy are consumed each year, how many pounds are consumed by 12 years old.
a.)16 lb
b.)160lb
c.)625lb
d.)1600lb
e.)120000lb
Answers
The number of pounds of cotton candy are consumed by a 12 year old is 120,000Ib
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious.
In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
Multiplication Formula
The multiplication formula is given by:
Multiplier × Multiplicand = Product
From the given information, 10,000 pounds of cotton candy are consumed each year.
Then, the number of pounds of cotton candy are consumed by a 12 year old is 10,000*12=120,000.
Thus, the correct option is e 120000 Ib
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determine the surface area of a right circular cone that has a slant height of 5.8 ft and a diameter of 6.4 ft? round your answer to the nearest whole.
Answers
Answer:
it is 6.4*5.8 brainliest?
Step-by-step explanation:
what is the relationship between and A and B
Answers
Answer:
Step-by-step explanation:
the varlance around the regression line varles with values of the predictor varlable.
Answers
In linear regression, the variance around the regression line represents the variability of the dependent variable (response variable) that is not explained by the regression model.
It measures the dispersion of the actual data points around the predicted values from the regression line.
The variance around the regression line can vary with different values of the predictor variable. This is because the relationship between the predictor variable and the response variable may not be constant across the entire range of the predictor variable. In other words, the spread or dispersion of the data points around the regression line may change as the predictor variable changes.
By examining the residuals (the differences between the observed values and the predicted values from the regression line) and calculating their variances, you can assess the variability of the data points around the regression line. This variability is an important aspect of understanding the goodness of fit of the regression model and the accuracy of the predictions.
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Please help! will give brainlist
Answers
Answer:
1. The formula for finding the surface area of a cylinder is:
Surface Area = 2πr(r + h)
Where:
* `r` is the radius of the cylinder
* `h` is the height of the cylinder
The surface area of a cylinder is the total area of all the surfaces that make up the cylinder. This includes the two circular bases and the lateral surface. The lateral surface is the curved surface that wraps around the cylinder.
To find the surface area of a cylinder, we first need to find the area of each of the circular bases. The area of a circle is πr², where `r` is the radius of the circle. So, the area of each of the circular bases of a cylinder is πr².
We then need to find the area of the lateral surface. The lateral surface is a rectangle with height `h` and width equal to the circumference of the base. The circumference of a circle is 2πr. So, the width of the lateral surface is 2πr.
The area of a rectangle is length x width. So, the area of the lateral surface of a cylinder is 2πrh.
Adding the areas of the two circular bases and the lateral surface, we get the total surface area of the cylinder:
Surface Area = 2πr(r + h)
2. The formula for finding the surface area of a sphere is:
Surface Area = 4πr²
Where:
* `r` is the radius of the sphere
The surface area of a sphere is the total area of all the surfaces that make up the sphere. This includes the entire curved surface of the sphere.
To find the surface area of a sphere, we simply need to square the radius of the sphere and multiply it by π.
For example, if the radius of a sphere is 5 cm, the surface area of the sphere would be:
Surface Area = 4π(5 cm)² = 523.6 cm²
Find an equation of the form ????=????(theta,phi) in spherical coordinates for the surface:
z=19
(Use symbolic notation and fractions where needed.)
Answers
The equation for the surface in spherical coordinates is given by z = 19 = r(θ,φ).
This equation can be interpreted as the radius of the surface being equal to 19 at all angles (θ,φ). The coordinates (θ,φ) represent angles in the spherical coordinate system with respect to the z-axis and x-axis, respectively.
Thus, the equation describes a spherical surface with radius 19, centered at the origin.
This equation can be rewritten in terms of the radial coordinate, r, as r = 19. As r is the distance from the origin to the surface, the equation implies that for all points on the surface, the distance from the origin is equal to 19.
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