In order to calculate the subtraction of the vectors, we can do the following steps:
[tex]\begin{gathered} u-v\\ \\ =(-10i+3j)-(-3i-7j)\\ \\ =-10i+3j+3i+7j\\ \\ =(-10i+3i)+(3j+7j)\\ \\ =-7i+10j \end{gathered}[/tex]Therefore the correct option is the first one.
If 20 assemblers can complete a certain job in 6 hours, how long will the same job take if the number of assemblers is cut back to 8?
ANSWER
[tex]15[/tex]EXPLANATION
For 1 assembler, it will take;
[tex]\begin{gathered} 20\times R\times6=1 \\ R=\frac{1}{120} \end{gathered}[/tex]For 8 assemblers;
[tex]8\times R\times T=1[/tex]Substitute R
[tex]\begin{gathered} 8\times R\times T=1 \\ 8\times\frac{1}{120}\times T=1 \\ \frac{8T}{120}=1 \\ 8T=120 \\ T=\frac{120}{8} \\ =15 \end{gathered}[/tex]Perform the indicated operation -27÷-9
-27/9 = -3
answer is -3
in DEF, K is the centroid. If KH=12 find DH
the lines that cross the centroid are divided into 2 by this the short line corresponds to 1/3 of the complete line and the long line corresponds to 2/3 of the complete line
so KH is 1/3 of DH
if KH=12, then
[tex]\begin{gathered} DH=3KH \\ DH=3\times12 \\ DH=36 \end{gathered}[/tex]the value of DH is 36
1. Find the surface area and volume of box where: L = 31.59ft, W = 24.98ft and H = 43.23ft.
ANSWER
[tex]\begin{gathered} A=6469.28ft^2 \\ V=34113.58ft^3 \end{gathered}[/tex]EXPLANATION
The surface area of the box (rectangular prism) is:
[tex]A=2(LW+WH+LH)[/tex]where L = length; W = width; H= height
Therefore, we have that the surface area of the box is:
[tex]\begin{gathered} A=2\lbrack(31.59\cdot24.98)+(24.98\cdot43.23)+(31.59\cdot43.23)\rbrack \\ A=2\lbrack(789.1182)+(1079.8854)+(1365.6357)\rbrack \\ A=2(3234.6393) \\ A\approx6469.28ft^2 \end{gathered}[/tex]The volume of the box is:
[tex]V=L\cdot W\cdot H[/tex]Therefore, the volume of the box is:
[tex]\begin{gathered} V=31.59\cdot24.98\cdot43.23 \\ V\approx34113.58ft^3 \end{gathered}[/tex]Suppose a binomial trial has a probability of success of 0.3 and 450 trials are performed. What is the standard deviation of the possible outcomes?6.3614.8511.629.72
The standard deviation of a binomial distribution with n trials and a probability of success of p is given by the formula:
[tex]\sigma=\sqrt[]{n\cdot p\cdot(1-p)}[/tex]From the problem, we identify:
[tex]\begin{gathered} n=450 \\ p=0.3 \end{gathered}[/tex]Then:
[tex]\begin{gathered} \sigma=\sqrt[]{450\cdot0.3\cdot(1-0.3)}=\sqrt[]{450\cdot0.3\cdot0.7} \\ \sigma\approx9.72 \end{gathered}[/tex]How do I get to the answer of this question?
Okay, here we have this:
Considering the provided information, and that we must identify which of the provided options allow us to determine that the two triangles are similar, we obtain the following:
As the angle-angle similarity says that if two angles of one triangle are congruent with two angles of another triangle, then the triangles are similar.
Finally, we see that the only option that satisfies this statement is option D, since it indicates that two angles of the triangles are congruent. Therefore the correct option is D.
Hi!A particle moves along a straight line, so its speed is () = ^2 − + 6, where t is the time measured in seconds and the speed is measured in meters timessecond.a) Calculate the distance traveled between the seconds t=1 and t=3
In this problem
the distance traveled between the seconds t=1 and t=3 is given by
[tex]\int_1^3(t^2-t+6)dt=\frac{50}{3}\text{ m}[/tex]The answer is
50/3 metersor 16.67 metersExplanation of integrals
In this problem we have
[tex]\int_1^3(t^2-t+6)dt=\int_1^3t^2dt-\int_1^3tdt+\int_1^36dt[/tex][tex]\begin{gathered} \int_1^3t^2dt=\frac{t^3}{3} \\ Evaluate\text{ at 3 and 1} \\ \frac{(3)^3}{3}-\frac{1^3}{3}=\frac{27}{3}-\frac{1}{3}=\frac{26}{3} \end{gathered}[/tex][tex]\begin{gathered} -\int_1^3tdt=-\frac{t^2}{2} \\ evaluate\text{ at 3 and 1} \\ -\frac{3^2}{2}+\frac{1^2}{2}=-\frac{9}{2}+\frac{1}{2}=-4 \end{gathered}[/tex][tex]\begin{gathered} \int_1^36dt=6t \\ evaluate\text{ at 3 and 1} \\ 6(3)-6(1)=12 \end{gathered}[/tex]substitute
[tex]\int_1^3t^2dt-\int_1^3tdt+\int_1^36dt=\frac{26}{3}-4+12=\frac{50}{3}[/tex]what is the surface area, in square centimeters, of the pyramid ?
I tested positive for covid yesterday so i have no motivation to do this problem. Please don’t be slow when answering, I am every tired.
The value of sector KL is 52
If JM and KN are two diamters of the circle,
then they intersect at the center
The sector JK and NM are equal
Thus,
The sector JN and KM are also equal
sector KM = sector KL + sector LM
Sector JN = Sector KM
sector JN = sector KL + sector LM
125 = 6x + 4 + 8x + 9
125 = 14x + 13
14x = 125 - 13
14x = 112
x = 8
sector KL = 6x + 4
= 6(8) + 4 = 48 + 4 = 52
Therefore, the sector KL is 52
To learn more about circle refer here
https://brainly.com/question/24375372
#SPJ9
I need help with triangles
find x=, if x-3=13 please
Answer:
[tex]x - 3 = 13 \\ \\ x = 13 + 3 \\ \\ x = 16[/tex]
-3 goes to other side and changes into +3
Hello I need help with this I’m in a rush thanks
Recall that:
[tex]\frac{f}{g}(x)=\frac{f(x)}{g(x)},[/tex]and that the domain of a rational function consists of all real numbers such that the denominator is different from zero.
If f(x)=5x+3 and g(x)=4x-5 we get that:
[tex]\frac{f}{g}(x)=\frac{5x+3}{4x-5}\text{.}[/tex]The domain of the above rational function is:
[tex]\begin{gathered} \mleft\lbrace x|g(x)\ne0\mright\rbrace=\lbrace x|4x-5\ne0\rbrace \\ =\lbrace x|4x\ne5\rbrace=\lbrace x|x\ne\frac{5}{4}\rbrace\text{.} \end{gathered}[/tex]Answer: Last option.
Which Venn diagram correctly shows the relationships between the subsets of rational numbers?
By definition, consider that natural numbers are all numbers from 1 to infinity. Whole numbers are the same natutal numbers plus zero. Integers are all numbers from minus infinity to infinity and rational are all number with finite decimals, and periodic infinite decimals.
Then, based on the previous description, the diagram which correctly shows the subsets of rational numbers is:
diagram F.
Algebraically determine whether each of the following functions is even, odd or neither. then graph it B. y = x^3 – 3 C. y = 2x^3 - x
According to the even and odd function rules, we found out that the function [tex]y=x^{3}-3[/tex] is neither even nor odd and the function [tex]y=2x^{3}-x[/tex] is an odd function.
It is given to us that the functions are -
B. [tex]y=x^{3}-3[/tex]
C. [tex]y=2x^{3}-x[/tex]
We want to determine each of the following functions is even, odd or neither.
To see if the function is even, we have to check if [tex]f(-x)=f(x)[/tex]
To see if the function is odd, we have to check if [tex]f(-x)=-f(x)[/tex]
B. Here, we have
[tex]y=x^{3}-3\\= > f(x)=x^{3}-3\\= > f(-x)=(-x)^{3}-3\\= > f(-x)=-x^{3}-3[/tex]
We see that [tex]f(-x)\neq f(x)[/tex]. This implies that the function is not even.
Also, [tex]f(-x)\neq -f(x)[/tex]. This implies that the function is not odd.
Therefore, this function is neither even nor odd.
C. Here, we have
[tex]y=2x^{3}-x\\= > f(x)=2x^{3}-x\\= > f(-x)=2(-x)^{3}-(-x)\\= > f(-x)=-2x^{3}+x[/tex]
We see that [tex]f(-x)\neq f(x)[/tex]. This implies that the function is not even.
However,
[tex]f(-x)=-2x^{3}+x\\= > f(-x)= -(2x^{3}-x)\\ = > f(-x)=-f(x)[/tex]
This implies that the function is odd.
Therefore, this function is odd.
Thus, the function [tex]y=x^{3}-3[/tex] is neither even nor odd and the function [tex]y=2x^{3}-x[/tex] is an odd function.
To learn more about function visit
https://brainly.com/question/21145944
#SPJ9
find the area, to the nearest thousandth, of the standard normal distribution between the given z-scores. z= 1 and z= 1.9
The area, to the nearest thousandth, of the standard normal distribution between the z-scores z= 1 and z= 1.9 is 0.130
Josslyn has nickels and dimes in her pocket. The number of nickels is three more than seven times the number of dimes let d represent the number of dimes. Write the expression for the number of nickels
to solve this we need to translate into math terms, so
Step 1
a) let d represents the number of dimes
let n represents the number of nickles
so
re write the expressions
[tex]\begin{gathered} number\text{ of dimes=d} \\ seven\text{ times the number of dimes = 7d} \\ \end{gathered}[/tex]The number of nickels is three more than seven times the number of dimes in other words you have to add 7 to seven times the number of dimes to obtain the number of nickles
hence
[tex]n=7d+3[/tex]therefore , the expression for the number of nickles is
[tex]7d+3[/tex]I hope this helps you
which measurement could create more than one triangle measuring 20 cm / 9 cm and 10cm be a triangle with sides measuring 10 cm and 20 cm and included angle measurement 65 C a right angle with acute angles measuring 45 and 45 d a triangle with sides measuring 15 in 20 in and 25 in
Input data
The triangles created by the measurements of options A, B and D have specific side lengths. Therefore, you cannot create more than one triangle.
However, for a triangle with acute angles measuring 45° and 45°, a countless number of similar triangles (triangles with the same shape but different sizes) can be created.
The correct choice is C.
you are selling snacks at the border trade fair. you are selling nachos and lemonade. each nachos costs $2.50 and each lemonade cost $2.25. at the end of the night you made a total of $112.50. you sold a total of 94 nachos and lemonade combined. how many nachos and lemonades were sold?
In order to determine the number of nachos and lemonade sold, you first write the given situation in an algebraic way.
If x is the number of nachos and y the number of lemonades, then, you have:
2.50x + 2.25y = 112.50 cost of the nachos and lemonade sold
x + y = 94 nachos and lemonade sold
Next, solve the previous system.
Multiply the second equation by 2.50. Next, subtract the equation to the first one:
(x + y = 94)(2.50)
2.50x + 2.50y = 235
2.50x + 2.25y = 112.50
-2.50x - 2.50y = -235
-0.25y = -122.5
solve the previous equation for y:
y = -122.5/(-0.25)
y = 490
Next, replace the previous value of y into the expression x + y = 94 and solve for x:
x + y = 94
x + 490 =
The graph of a quadratic function with vertex (-1,4) is shown in the figure below. Write the domain and range in interval notation.
Background:
• Domain,: a set of all possible values of the independent variable (,x,, in this case).
,• Range,: a set of all possible values of the dependent variable (,y,, in this case), after substituting the domain.
Based on the arrows of the function, we can conclude that those extend to infinity (negative and positive).
Also, based on the coordinates of the vertex given we can see that the first value of y is 4.
Answer:
• Domain
[tex](-\infty,\infty)[/tex]• Range
[tex](4,\infty)[/tex]The graph of f(x) = x² is translated to formg(x) = (x-2)2-3.--5-4-3-2-1-2+Which graph represents g(x)?#
Step 1
Plot the graph of f(x)
[tex]f(x)=x^2[/tex]Step 2
The function of g(x) suggests that f(x);
[tex]\begin{gathered} 1)\text{ it was moved 2 units towards the right} \\ 2)\text{ It was then moved 3 units down} \end{gathered}[/tex]Thus, the graph of g(x) will look like this;
Answer;
Find the values of x and y in the equation below.a³b4a²b= a*b²X=
To divide, subtract exponents to same base variables.
[tex](ab^3)^6[/tex]Multiply exponents of exponents
[tex]a^6b^{18}[/tex]x= 6
y= 18
What is the equation for the linear model in the scatterplot obtained by choosing the two points closest to the line
consider two points closest to the line. say ,
[tex]\begin{gathered} (x_1,y_1)=(6,0) \\ (x_2_{}_{}_{},y_2)=(8,1) \end{gathered}[/tex]let us find the slope, m by the formula
[tex]m=\frac{y_2-y_1}{x_2_{}_{}-x_1}[/tex]subsitute the points in the formula,
[tex]\begin{gathered} m=\frac{1-0}{8-6} \\ m=\frac{1}{2} \end{gathered}[/tex]let us find the y - intercept.
[tex]y=mx+b\ldots(1)[/tex]subsitute the one of the point (6,0) in the above equation.
[tex]\begin{gathered} 0=\frac{1}{2}\times6+b \\ 0=3+b \\ b=-3 \end{gathered}[/tex]thus,
subsitute m= 1/2 and b = - 3 in the equation (1),
[tex]y=\frac{1}{2}x-3[/tex]A toy factory makes 5.7 x 10³ toys each day.At this rate, how many toys will be made in 9 days?Express the answer in scientific notation.
First We will put the number of toys per day in simple form:
[tex]5.7\times10^3=5.7\times1000=5700[/tex]Then, to know how many toys will be made in 9 days, let's multiply the number of toys per day by the given number of days:
[tex]5700\times9=51300[/tex]Now We will put the number in scientific notation:
[tex]5.13\times10^4[/tex]17. In trapezoid FGJK, what is the value of x? N CO 18.6 L K 23.6 9.3 11.8 ET O 13.6
Given data:
The given figure is shown.
The expression for the trapezium is,
[tex]\begin{gathered} \frac{x}{18.6}=\frac{18.6}{23.6} \\ 23.6x=18.6^2 \\ x=14.6 \\ =15 \end{gathered}[/tex]Thus, thi
Consider the scenario: A town’s population has been decreasing at a constant rate. In 2010 the population was 5800. By 2012 the population had dropped to 4,600. Assume the trend continues predict the population in 2016.
Given:
In 2010 the population was 5800.
2012 the population had dropped to 4,600.
Let 't=0' be the year 2010.
P(t) represents the year population of the town t years after 2010.
Slope of a function P(t) is
[tex]\begin{gathered} m=\frac{4600-5800}{2012-2010} \\ m=-600 \end{gathered}[/tex]Population of town t years after 2010.
[tex]P(t)=-600(t)+5800[/tex]Population in the year 2016 that is t=6
[tex]\begin{gathered} P(6)=-600(6)+5800 \\ =2200 \end{gathered}[/tex]Population in the year 2016 is 2200
Simplify. Assume that all variables result in nonzero denominators.
2n^3 y−8n^2 y/3y^4 * 12/n-4
The simplified form of given expression 2n^3 y−8n^2 y/3y^4 * 12/n-4 is 8n^2/y^3
In this question, we have been given an expression.
2n^3 y−8n^2 y/3y^4 * 12/n-4
We need to simplify given expression.
2n^3 y − 8n^2 y/3y^4 * 12/n-4
= [2n^2y (n - 4)] / 3y^4 * 12/(n - 4)
= 4 * (2n^2y)/y^4
= 8n^2/y^3
Therefore, the simplified form of given expression 2n^3 y−8n^2 y/3y^4 * 12/n-4 is 8n^2/y^3
Learn more about an expression here:
https://brainly.com/question/1859113
#SPJ1
NO LINKS!! Use the method of substitution to solve the system. (If there's no solution, enter no solution). Part 6z
Answer:
(-1, 7, - 4)(1, -1, 4)=====================
Given systemx² + z² = 174x + y = 3y + z = 3Rearrange the last two equation4x = 3 - yz = 3 - yThis gives us:
z = 4xSubstitute the value of z into fist equationx² + (4x)² = 17x² + 16x² = 1717x² = 17x² = 1x = 1 and x = - 1Find values of z and yx = 1 ⇒ z = 4*1 = 4 ⇒ y = 3 - 4 = - 1 x = - 1 ⇒ z = 4*(-1) = - 4 ⇒ y = 3 - (-4) = 7Answer:
[tex](x,y,z)=\left(\; \boxed{-1,7,-4} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y,z)=\left(\; \boxed{1,-1,4} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}x^2+z^2=17\\\;4x+y=3\\\;\;\;y+z=3\end{cases}[/tex]
To solve by the method of substitution, first rearrange the third equation to make y the subject:
[tex]\implies y=3-z[/tex]
Substitute this into the second equation and solve for z:
[tex]\begin{aligned}\implies 4x+(3-z)&=3\\3-z&=3-4x\\-z&=-4x\\z&=4x\end{aligned}[/tex]
Substitute the found expression for z into the first equation and solve for x:
[tex]\begin{aligned}\implies x^2+(4x)^2&=17\\x^2+16x^2&=17\\17x^2&=17\\x^2&=1\\x&=\pm1\end{aligned}[/tex]
Substitute the found values of x into the second equation and solve for y:
[tex]\begin{aligned}\implies x=-1 \implies 4(-1)+y&=3\\-4+y&=3\\y&=7\end{aligned}[/tex]
[tex]\begin{aligned}\implies x=1 \implies 4(1)+y&=3\\4+y&=3\\y&=-1\end{aligned}[/tex]
Substitute the found values of x into the derived expression for z and solve for z:
[tex]\begin{aligned}\implies x=-1 \implies z&=4(-1)\\z&=-4\end{aligned}[/tex]
[tex]\begin{aligned}\implies x=1 \implies z&=4(1)\\z&=4\end{aligned}[/tex]
Therefore, the solutions are:
[tex](x,y,z)=\left(\; \boxed{-1,7,-4} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y,z)=\left(\; \boxed{1,-1,4} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
Which graph represents the function f(x) = -x + 31?
Answer:
Step-by-step explanation:
I hope this helps! :) If it does could you please mark me brainliest?
Answer:
Slope : -1
y = intercept : (0,31)
Step-by-step explanation:
Question content area topPart 1A medical researcher administers an experimental medical treatment to patients. The patients in the study are categorized by blood types A, B, AB, and O. The researcher observed that the treatment had a favorable outcome for of the patients with blood type A, of the patients with blood type B, of the patients with blood type AB, and none of the patients with blood type O. Use this information to complete parts (a) through (d).
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
total patients = 300
type A:
total patients = 90
favourable patients = 27
type B:
total patients = 124
favourable patients = 31
type AB:
total patients = 6
favourable patients = 6
type O:
total patients = 80
favourable patients = 0
Step 02:
empirical probability:
probability = favourable outcomes / total outcomes
probability (A) = 27/ 90 = 0.3
probability (B) = 31 / 124 = 0.25
probability (AB) = 6 / 6 = 1
probability (O) = 0 / 80 = 0
That is the full solution.
Determine the equation of the graphed circle below!Equation should look like the example below!
Step 1:
Write the formula for the equation of a circle.
[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ \text{Center = ( a , b )} \\ \text{Radius = r} \end{gathered}[/tex]Step 2:
Locate and write the center and radius of the circle.
Step 3:
Write the equation of the circle with center (-7, -2) and radius r = 2
[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ (x-(-7))^2+(y-(-2))^2=2^2 \\ (x+7)^2+(y+2)^2=\text{ 4} \end{gathered}[/tex]Final answer
[tex](x+7)^2+(y+2)^2=\text{ 4}[/tex]