Answer: c
Step-by-step explanation:
What is the equation of the line that passes through the point (−3,2) and has a slope of -3?
Answer:
y = -3x - 7
Step-by-step explanation:
slope-intercept form: y = mx + b
given m = -3, x = -3, y = 2
2 = -3(-3) + b
2 = 9 + b
b = 2 - 9 = -7
y = -3x - 7
how many ways are there to select 8 countries in the united nations to serve on a council if 3 is selected from a block of 52, 2 are selected from a block of 64 and 3 are selected from the remaining 73 countries?
Number of ways to select 8 countries from the United Nations is 48,054,722,400
To solve this problem, we need to use the combination method, which states that if there are m ways to perform one task and n ways to perform another task after the first task is completed, then there are m x n ways to perform both tasks in sequence.
Using this principle, we can break down the selection of 8 countries into three separate tasks
Selecting 3 countries from a block of 52: There are 52C3 ways to do this, where 52C3 is the binomial coefficient "52 choose 3," which can be calculated as follows
52C3 = (52 x 51 x 50) / (3 x 2 x 1) = 22,100
Selecting 2 countries from a block of 64: There are 64C2 ways to do this, where 64C2 is the binomial coefficient "64 choose 2," which can be calculated as follows
64C2 = (64 x 63) / (2 x 1) = 2,016
Selecting 3 countries from a block of 73: There are 73C3 ways to do this, where 73C3 is the binomial coefficient "73 choose 3," which can be calculated as follows
73C3 = (73 x 72 x 71) / (3 x 2 x 1) = 1,082,790
To find the total number of ways to select 8 countries, we simply multiply these three quantities together
22,100 x 2,016 x 1,082,790 = 48,054,722,400
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Graph the line.
y - 4x = -8
2/5÷3/4 what’s the answer ?
Answer:
8/15
Step-by-step explanation:
dividing fractions you must take the reciprocal of the second fraction and then multiply it by the first fraction leaving us with
2/5 x 4/3=
8/15
Someone help please and please make sure the answer is right
Answer:
the answer is 7
Step-by-step explanation:
a standard six-sided die is rolled twice. what is the probability that the product of the rolls is even?
Answer:
3/4 or 0.75 or 75%----------------------------
The probability of rolling an even number on a single die is 3/6 or 1/2.
Consider the possible outcomes of rolling the two dice:
If both dice are odd, the product will be odd;If both dice are even, the product will be even; If one die is even and one die is odd, the product will be even.So, the only way to not have an even product is if both dice are odd.
The probability of rolling an odd number on a single die is also 1/2, so the probability of rolling two odd numbers is (1/2) x (1/2) = 1/4.
Therefore, the probability of rolling an even product is:
1 - 1/4 = 3/4 = 0.75 or 75%Find the value of x. (3x + 5) (7x – 15)
Answer:
21 x 2 − 10x − 75
Step-by-step explanation:
Cant solve for x can only simplify^
Answer:
-15x+21x(squared)-75
Step-by-step explanation:
(3x+5) (7x-15)
3x(7x-15) 5(7x-15)
21x (squared) -45x+35x-75
-15x+21x(squared)-75
If a 24-kg mass stretches a spring 15 cm, what mass will stretch the spring 10 cm
Answer:
16kgStep-by-step explanation:
This problem is borers on elasticity of materials.
according to Hooke's law, "provided the elastic limit of an elastic material is not exceeded the the extension e is directly proportional to the applied force."
\(F= ke\)
where F is the applied force in N
k is the spring constant N/m
e is the extension in meters
Given data
mass m= 24kg
extensnion=15cm in meters= \(\frac{15}{100}\)= \(0.15m\)
we can solve for the spring constant k
we also know that the force F = mg
assuming \(g=9.81m/s^{2}\)
therefore
\(24*9.81=k*0.15\\235.44=k*0.15\\k=\frac{235.44}{0.15} \\k=1569.6N/m\\\)
We can use this value of k to solve for the mass that will cause an extension of \(10cm= 0.1m\)
\(x*9.81=1569.6*0.1\\\\x= \frac{156.96}{9.81} \\\x= 16kg\)
For a recent paint job, Josh mixed red and white paint to make two different shades of pink. When the job was done, Josh ended up with leftover paint: 5 gallons of dark pink paint (80% red) and 4 gallons of light pink paint (30% red). Josh wants to make a medium pink color (50% red) to paint his daughter's bedroom. He will need 3 gallons to completely cover the walls. How much of each of the leftover paints should Josh mix to achieve his desired color?
? gallons of dark pink paint
? gallons of light pink paint
Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.
To find out how much of each leftover paint Josh should mix to achieve a medium pink color (50% red), we can set up a system of equations based on the percentages of red in the paints.
Let's assume that Josh needs x gallons of dark pink paint and y gallons of light pink paint to achieve the desired color.
The total amount of paint needed is 3 gallons, so we have the equation:
x + y = 3
The percentage of red in the dark pink paint is 80%, which means 80% of x gallons is red. Similarly, the percentage of red in the light pink paint is 30%, which means 30% of y gallons is red. Since Josh wants a 50% red mixture, we have the equation:
(80/100)x + (30/100)y = (50/100)(x + y)
Simplifying this equation, we get:
0.8x + 0.3y = 0.5(x + y)
Now, we can solve this system of equations to find the values of x and y.
Let's multiply both sides of the first equation by 0.3 to eliminate decimals:
0.3x + 0.3y = 0.3(3)
0.3x + 0.3y = 0.9
Now we can subtract the second equation from this equation:
(0.3x + 0.3y) - (0.8x + 0.3y) = 0.9 - 0.5(x + y)
-0.5x = 0.9 - 0.5x - 0.5y
Simplifying further, we have:
-0.5x = 0.9 - 0.5x - 0.5y
Now, rearrange the equation to isolate y:
0.5x - 0.5y = 0.9 - 0.5x
Next, divide through by -0.5:
x - y = -1.8 + x
Canceling out the x terms, we get:
-y = -1.8
Finally, solve for y:
y = 1.8
Substitute this value of y back into the first equation to solve for x:
x + 1.8 = 3
x = 3 - 1.8
x = 1.2
Therefore, Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.
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A medicine dropper releases about 1 liter of medicine in a day. How many milliliters of medicine would be released in an hour?
Answer:
41.7 ml milliliters of medicine would be released in an hour.
Step-by-step explanation:
1 day = 1 Liter
24 hours = 1000 ml
Now,
1000/24 = 41.7 ml
Thus, 41.7 ml milliliters of medicine would be released in an hour.
-TheUnknownScientist 72
Answer:
41.7 ml milliliters of medicine would be released in an hour.
Step-by-step explanation:
If you borrow $5.93 for nine years at an interest rate of 6%, how much interest will you pay? In terms of simple interest.
Answer: $3.20
Step-by-step explanation:
SI = p *r * t
= 5.93 * 0.06 * 9
= 3.20
Answer:
$3.20
Step-by-step explanation:
Using Simple Interest = (principal) * (rate) * (time), we get:
= 5.93 * 0.06 * 9
= $3.20
Hope this helps!
Determine whether the relation is
a function.
{(-6,3),(2,2),(6,2),(3,7)}
Answer:
Since there is one value of y{(-6,3),(2,2),(6,2),(3,7)}for every value of x in , this relation is a function.The relation is a function.
Step-by-step explanation:
Hope that help like and please give me brainiest.Aslo add me.
A, B, C, D got stuck with this problem
What type of number is 0.2681?
A. Natural
B. Whole
C. Integer
D. Rational
Answer:
D. (Rational)
Step-by-step explanation:
Natural : Counting numbers (1,2,3...)
Whole : Natural numbers including 0 (NO DECIMALS/FRACTIONS)
Integer : Whole numbers and their opposites (positive, negative.)
Rational : Any number that can be written as a fraction/decimal, a number that can terminate or repeat.
In this case, 0.2681 is rational because it is a terminating decimal.
I need some help ! The options are 25,50,65,130
Answer:
XZ=65
Step-by-step explanation:
so half of the circle would be 180
we need XZ and we know that YW+WX+XZ= 180
we also know that WX and YZ are parallel
WX=50
YW=XZ
YW+XZ=2XZ
WX+2XZ=180
50+2XZ=180
2XZ=130
XZ=65
Answer:
25
Step-by-step explanation:
diameter YZ = 50
OZ = OX = 25
thus, mXZ= 25
write -5/12 as a decimal, use bar notation if necessary
Answer:
-0.416666...
Just put the bar over the 6s :)
In ΔDEF, \overline{DF} DF is extended through point F to point G, \text{m}\angle FDE = (2x+4)^{\circ}m∠FDE=(2x+4) ∘ , \text{m}\angle DEF = (3x+3)^{\circ}m∠DEF=(3x+3) ∘ , and \text{m}\angle EFG = (7x-5)^{\circ}m∠EFG=(7x−5) ∘ . Find \text{m}\angle FDE.M∠FDE.
Answer:
18°Step-by-step explanation:
See the diagram attached:
In a triangle, the sum of interior angles is equal to the exterior angle.
According the diagram, the sum of interior angles is given as:
Sum of interior = <FDE+<DEF
Given
<FDE = 2x+4
<DEF = 3x+5
Sum of interior = 2x+4+3x+5
Sum of interior = 5x+9
Exterior angle = <EFG = 7x-5
Equate the interior to the exterior and calculate the value of x:
5x+9 = 7x-5
Collect like terms
5x-7x = -5-9
-2x = -14
x = -14/-2
x = 7
Next is to get <FDE:
<FDE = 2x+4
<FDE = 2(7)+4
<FDE = 14+4
<FDE = 18°
Hence the measure of <FDE is 18°
Answer:
its 16
Step-by-step explanation:
just did it
The half-life of a radioactive element in exponential decay depends on the initial amount of the element
A half life is the amount of time it takes for half of a radioactive substance to decay.
Yes, that is correct. The half-life of a radioactive element is the amount of time it takes for half of the initial amount of the element to decay. Therefore, the larger the initial amount of the element, the longer the half-life will be. This is because there are more atoms that need to decay in order for the half-life to occur. Conversely, if the initial amount of the element is small, the half-life will be shorter because there are fewer atoms that need to decay.
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Multiply and simplify: 3i(4 - 3i) - i (2 + i)
10 + 10i
Apply Multiplicative Distribution Law: 12i - 9 x i^2 - 2i - i^2
Rewrite by definition: i^2 = -1:12i - 9 x (-1) -2i - (-1)
Remove the parentheses: 12i + 9 - 2i + 1
Combine like terms: 10 + 10i
Answer 10 + 10i
Answer:
10 + 10i
Step-by-step explanation:
Given expression:
\(3i(4 - 3i) - i (2 + i)\)
Expand:
\(\implies 12i-9i^2-2i-i^2\)
\(\implies 12i-2i-9i^2-i^2\)
\(\implies 10i-10i^2\)
Apply the imaginary number rule i² = -1 :
\(\implies 10i-10(-1)\)
Simplify:
\(\implies 10i+10\)
Rewrite in standard complex form a + bi:
\(\implies 10+10i\)
PLEASE HELP QUICK PLEASEEE
Answer:
x=-1 4/5
first one
Euler method in Matlab
30. Solve: Nxy - 0.5ye-0.1x for osx54 with y(0) = 6.5 dx Plot the solution. =
The differential equation to be solved is Nxy - 0.5ye-0.1x for osx54 with y(0) = 6.5 dx. This can be solved using Euler's method in MATLAB.
Follow the steps below.
Step 1: Create a function file - The differential equation needs to be defined in a function file first. Let's create a function file named "odefun.m".function dydx = odefun(x,y)
dydx = N*x*y - 0.5*y*exp(-0.1*x);
where N is a constant value that needs to be defined.
Step 2: Define the given values - Define the given values such as N, initial value y(0), and step size dx.
N = ...; %
Define N herey 0 = 6.5; %
Define initial value of y here. dx = ...; %
Define step size here
Step 3: Use Euler's method to solve the differential equation - Now, use Euler's method to solve the differential equation using a for loop. The MATLAB code is as follows: x = 0:dx:54; %
Define range of x values here y = zeros(size(x)); %
Initialize y as a vector of zeros y(1) = y0; %
Assign initial value of y to y(1) for i = 1: length(x)-1 dydx = odefun(x(i),y(i)); y(i+1) = y(i) + dydx*dx; end
Step 4: Plot the solution - Finally, plot the solution using the MATLAB command plot(x,y).
The complete MATLAB code is given below:
N = ...; %
Define N here y0 = 6.5; %
Define initial value of y here dx = ...; %
Define step size here x = 0:dx:54; %
Define range of x values here y = zeros(size(x)); % Initialize y as a vector of zeros y(1) = y0; %
Assign initial value of y to y(1) for i = 1: length(x)-1 dydx = odefun(x(i),y(i)); y(i+1) = y(i) + dydx*dx; end plot(x,y)
The plot of the solution will be displayed.
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HELP PLEASE ASAP PLS PLS PLS
Answer:
Step-by-step explanation:
Mr. Tran has $24,000 to invest, some in bonds and the rest in stocks. He has decided that the money invested in bonds must be at least twice as much as that in stocks. But the money invested in bonds must not be greater than $18,000. If the bonds earn 6%, and the stocks earn 8%, how much money should he invest in each to maximize profit?
Answer:
For bond it is $16,000
And, for stocks it is $8,000
Step-by-step explanation:
Let us assume the Tran invested x amount in bonds and y amount in stocks
So, the profit could be
P = 0.06x + 0.08y
The total amount is $24,000
so, the equation would be
x + y = $24,000
Now in the case of atleast twice, the equation would be
x ≥ 2y
And, in the case of not be greather than $18,000, the equation would be
x ≤ $18,000
The linear programming problem would be shown below:
maximum P = 0.06x + 0.08y
subjected to
x + y = $24,000
x ≥ 2y
x ≤ $18,000
x ≥0, y ≥0
Now use the graphical method, the critical point is ($18,000,$6,000) or ($6,000, $18,000)
In the case when we have to maximise the profits
For bond it is $16,000
And, for stocks it is $8,000
The maximize profit for is bond is $18000.
The maximize profit for stocks is $6000
Suppose that ; Mr. Tran invested x amount in bonds and y amount in stocks.
According to given question;
The bonds earn 6% and stocks earn 8% profit ,
Then profit could be ,
P = 0.06 + 0.08
Total amount = $24,000
So, the equation can be return as
x + y = $24000
The money invested in bonds at least twice the equation can be return as\(x\geq 2y\)
the money invested in the bonds not greater than will be
\(x\leq $18000\)
The linear programming would be shown below
P =0.06x + 0.08yx + y =$24000\(x\geq 2y\)\(x\leq\)$18000By the graphical method maximize the profit .
The critical points shown in the attached image is ($6000,$18000) & ($16000,$18000)
Thus the maximize profit for bond is $18000
The maximize profit for stocks is $6000.
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PLS HELPPPPPPPPPPP Determine the approximate value of X round to the nearest hundredth
Answer:
Step-by-step explanation:
We can immediately elimate two answers since x cannot be larger than the hypotenuse, which is 9. You can cosine = adjaent/hypotenuse, which gives the equation cos(54) = x/9, which simplifies to x = 9*cos(54). When you plug this into a calculator, you should get 5.29. Keep in mind that 54 is measured in degrees and not radians because.
Answer:
D.) x = 5.29
Step-by-step explanation:
first find the last angle measure 180-90-54=36
use law of sines to find x
sin90/9=sin36/x
(sin90)(x) = (sin36)(9)
(sin90)(x) = 5.29
x = 5.29
Mr kuldeep bought 7½ kg of and Mr Rajesh bought 5¾ kg of rice .who bought more rice and by how much.
Mr. Kuldeep bought more rice than Mr. Rajesh by 1¾ kg, or 1.75 kg more than Mr. Rajesh.
Mr. Kuldeep bought 7½ kg of rice and Mr. Rajesh bought 5¾ kg of rice. To find out who bought more rice and by how much, we need to compare the two quantities.
First, let's convert the mixed numbers into improper fractions:
7½ kg = (7 x 2 + 1)/2 = 15/2 kg
5¾ kg = (5 x 4 + 3)/4 = 23/4 kg
Now, let's compare the two fractions:
15/2 kg > 23/4 kg
Therefore, Mr. Kuldeep bought more rice than Mr. Rajesh.
To find out by how much, we need to subtract the smaller quantity from the larger one:
15/2 kg - 23/4 kg = (30 - 23)/4 kg = 7/4 kg
So, Mr. Kuldeep bought 7/4 kg or 1¾ kg more rice than Mr. Rajesh. In conclusion, Mr. Kuldeep bought more rice than Mr. Rajesh by 1¾ kg.
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A spinner is divided into four equal areas and colored red, green, yellow, and blue.
Which statement is most likely to be true?
a.) The probability of the spinner landing on the green region is close to 0.25 when the number of trials is less than 250.
b.) The probability of the spinner landing on the green region is close to 0.25 when the number of trials is more than 250.
c.) The probability of the spinner landing on the green region is close to 0.25 when the number of trials is less than 25.
d.) The probability of the spinner landing on the green region is equal to 0.25 when the number of trials is less than 25.
The probability of the spinner landing on the green region is close to 0.25 when the number of trials is less than 250.
Hence, statement (a) is correct.
Use the concept of probability defined as:
Probability is the ratio of the number of favourable outcomes to the total number of outcomes for the occurrence of an event. it deals with finding out the likelihood of the occurrence of an event.
Le 'f' represents the number of favourable outcomes and 't' denotes the total number of outcomes then, the probability of an event is defined as f/t.
a.) "The probability of the spinner landing on the green region is close to 0.25 when the number of trials is less than 250."
Since the spinner is divided into four equal areas,
And each area has the same chance of being landed on,
The probability of landing on the green region would be close to 0.25.
Hence,
Statement (a) is correct.
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Tell which number is greater.
76%, 0.67
Answer:
76%
Step-by-step explanation:
first use the calculator you might find the answer on it even the calculator on your own phone
sorry i know you wont understand me
ou and i each have a fair coin. i flip n times, and you flip n 1 times. you win if i get fewer heads than you. what is the probability that you win the game?
Answer: 3
Step-by-ste3p explanation:
What term refers to the fact that correlation coefficient is
zero (or close to zero), and the relationship between two variables
isn't a straight line ?
The term that refers to the fact that the correlation coefficient is zero (or close to zero) and the relationship between two variables isn't a straight line is "curvilinear association."
A curvilinear association describes a relationship between two variables that cannot be adequately represented by a straight line. In a curvilinear association, the correlation coefficient between the variables is zero or close to zero, indicating no linear relationship.
To identify a curvilinear association, one can examine the scatterplot of the data points. If the pattern formed by the data points follows a curve or any non-linear shape, it suggests a curvilinear association.
For example, consider a situation where the relationship between studying time and test scores is examined. Initially, as studying time increases, test scores may also increase. However, after a certain point, further increases in studying time may not lead to a proportional increase in test scores.
This pattern might result in a curvilinear association, where the correlation coefficient would be close to zero due to the nonlinear relationship.
When the correlation coefficient is zero (or close to zero) and the relationship between two variables isn't a straight line, we refer to it as a curvilinear association. It signifies that the variables have a non-linear relationship.
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Hunter is making $46,500 per year and gets a 5.5%
increase in pay. Determine how much money
Munter makes after his increase and show your
work
Answer:
$49,057.50
Step-by-step explanation:
To find how much a percent is of a number you multiply that number and that percent then add the two
SO.... 46,500x5.5% is 2557.50 and then you add the 2 so 46,500 + 2557.50= 49,057.50 hope this helps