Answers
Answer:
45
Step-by-step explanation:
\(15 = \frac{1}{3} x \\ 15 \times 3 = x \\ x = 45\)
Answer:
45
Step-by-step explanation:
Divide both sides by 3
then it will be X=15×3
. =45
Related Questions
Which statement best explains whether the table represents a linear or nonlinear function?
Input Output
(x) (y)
−2 7
−5 4
−8 1
−11 −2
A It is a linear function because there is a constant rate of change in both the input and output values.
B It is a nonlinear function because there is a constant rate of change in both the input and output values.
C It is a linear function because the input values are decreasing.
D It is a nonlinear function because the input values are increasing.
Answers
Answer:
b
Step-by-step explanation:
what is the solution to : 3(1/2 m - 3) =45
Answers
Answer:
\(m=36\)
Step-by-step explanation:
We can solve for this equation by isolating \(m\) on one side. To do this, we can "reverse" the equation.
\(3(\frac{1}{2}m - 3) = 45\)
Let's divide both sides by 3.
\(3(\frac{1}{2}m-3)\div3 = 45\div3\\\\\frac{1}{2}m - 3 = 15\)
Add 3 to both sides:
\(\frac{1}{2}m - 3 + 3 = 15 + 3\\\\\frac{1}{2}m = 18\)
Multiply both sides by two (since \(\frac{1}{2}\cdot2=1\))
\(\frac{1}{2}m \cdot 2 = 18 \cdot 2\\\\m = 36\)
Hope this helped!
Answer:
m = 36
Step-by-step explanation:
Step 1:
3 ( 1/2m -3 ) = 45
Step 2:
3/2m - 9 = 45
Step 3:
3/2m = 54
Step 4:
54 ÷ 3/2
Step 5:
54/1 × 2/3
Answer:
m = 36
Hope This Helps :)
3)
Blair expects an increase of 3% in her current annual
salary of $42,000. What would her new annual salary
be?
Answers
Answer:
$43,260
Step-by-step explanation:
You have the 3% annual income, which you can convert to a decimal. This gives:
42000 * 1.03
42000 represents Blair's initial income, and 0.03 represents the 3% increase.
I chose 1.03 because I don't have to subtract 97% and add it to 42000.
And she earns $42000
.03*42000 is 1260
42000+1260= $43260
Find the rate of change from the table
Answers
Which classifications does he number π is best fit into?
Answers
Answer:
3.14
Hoped I helped -
Sleepy~
Please show all of the steps to solve the Algebra math problems below.Evaluate the following.|10| = |-4| =Subtract. Write your answer as a fraction in simplest form.5/8 � 3/8 =Subtract.7/8 � 5/6Write your answer as a fraction in simplest form.Multiply.6*(-7/2) =Write your answer in simplest form.Divide. Write your answer as a fraction or mixed number in simplest form.6/5 / (- 12/25) =Evaluate.3 + 4^2 * 2 =Evaluate.2/3 + 5/6 * � =Write your answer in simplest form.Evaluate-16 - 12 / (-4) =Use the distributive property to remove the parentheses.-9(3w � x � 2) =Simplify.-2(w + 2) + 5w =Simplify the following expression.16x^2 + 8 � 10x � 2x^2 � 14x =Evaluate the expression when b = -5 and y = 6b � 9y =Evaluate the expression when y = -3Y^2 + 5y � 4 =Evaluate.(-4)^3 =(-7)^2 =Evaluate. Write your answers as fractions.3/5^3 =(-1/3)^2 =Evaluate the expressions.(-7)^0 =2(1/3)^0 = Multiply.3v^2(-5v^4) =Simplify your answer as much as possible.Multiply.2y^2w^4*6y*2w^8 =Simplify your answer as much as possible.Simplify.(4p^3/3p^7)^-2 =Write your answer using only positive exponents.Simplify.X^-2/x^-3 =Write your answer with a positive exponent only.
Answers
Answer:
See Explanation
Step-by-step explanation:
Please note that I'll replace all � with +
1. |10|
This implies the absolute value of 10 and it always returns the positive value;
Hence;
\(|10| = 10\)
2. |-4|
Using the same law applied in (1)
\(|-4| = 4\)
3. 5/8 - 3/8 = ?
Take LCM
\(= \frac{5 - 3}{8}\)
Subtract the numerator
\(= \frac{2}{8}\)
Divide the numerator and denominator by 2
\(= \frac{1}{4}\)
Hence:
\(\frac{5}{8} - \frac{3}{8} = \frac{1}{4}\)
4. 7/8 - 5/6
Take LCM
\(= \frac{21 - 20}{24}\)
\(= \frac{1}{24}\)
Hence;
\(\frac{7}{8} - \frac{5}{6} = \frac{1}{24}\)
5. 6 * (-7/2)
\(= 6 * \frac{-7}{2}\)
Multiply the numerator
\(= \frac{-42}{2}\)
\(= -21\)
Hence:
\(6 * \frac{-7}{2} = -21\)
5. 6/5 /(-12/25)
\(= \frac{6}{5} / \frac{-12}{25}\)
Change the divide to multiplication
\(= \frac{6}{5} * \frac{-25}{12}\)
Divide 6 and 12 by 6
\(= \frac{1}{5} * \frac{-25}{2}\)
Divide 5 and 25 by 5
\(= \frac{1}{1} * \frac{-5}{2}\)
\(= \frac{-5}{2}\)
Hence;
\(\frac{6}{5} / \frac{-12}{25} = \frac{-5}{2}\)
6. 3 + 4^2 * 2
\(= 3 + 4^2 * 2\)
Solve the exponent
\(= 3 + 16 * 2\)
Apply B.O.D.M.A.S
\(= 3 + 32\)
\(= 35\)
\(3 + 4^2 * 2 = 35\)
7. 2/3 + 5/6
\(= \frac{2}{3} + \frac{5}{6}\)
Apply LCM
\(= \frac{4 + 5}{6}\)
\(= \frac{9}{6}\)
Divide the numerator and denominator by 3
\(= \frac{3}{2}\)
Convert to mixed fraction
\(= 1\frac{1}{2}\)
Hence;
\(\frac{2}{3} + \frac{5}{6} = 1\frac{1}{2}\)
8. 16 - 12/(-4)
\(= 16 - \frac{12}{-4}\)
Solve the fraction
\(= 16 - (-3)\)
Open the bracket
\(= 16 + 3\)
\(= 19\)
Hence;
\(16 - \frac{12}{-4} = 19\)
9. -9(3w + x + 2)
\(= -9(3w + x + 2)\)
Open brackets: Distributive property
\(= -9*3w -9* x -9 * 2\)
\(= -27w -9 x -18\)
Hence;
\(-9(3w + x + 2) = -27w -9 x -18\)
10. -2(w + 2) + 5w
\(= -2(w + 2) + 5w\)
Open bracket: using distributive property
\(= -2*w -2 * 2 + 5w\)
\(= -2w -4 + 5w\)
Collect Like Terms
\(= 5w-2w -4\)
\(= 3w -4\)
Hence;
\(-2(w + 2) + 5w = 3w- 4\)
11. 16x^2 + 8 + 10x + 2x^2 + 14x
\(= 16x^2 + 8 + 10x + 2x^2 + 14x\)
Collect Like Terms
\(= 16x^2 + 2x^2 + 10x + 14x+ 8\)
\(= 18x^2 + 24x + 8\)
Expand the expression
\(= 18x^2 + 12x + 12x + 8\)
Factorize:
\(= 6x(3x + 2) + 4(3x +2)\)
\(= (6x + 4)(3x +2)\)
Hence;
\(16x^2 + 8 + 10x + 2x^2 + 14x = (6x + 4)(3x +2)\)
12. b = -5 and y = 6
\(b + 9y =?\)
Substitute -5 for b and 6 for y
\(= -5 + 9 * 6\)
\(= -5 + 54\)
\(= 49\)
Hence;
\(b + 9y = 49\)
13. y = -3
\(y^2 + 5y + 4 =?\)
Substitute -3 for y
\(= (-3)^2 + 5(-3) + 4\)
Open all brackets
\(= 9 -15 + 4\)
\(= -2\)
Hence;
\(y^2 + 5y + 4 = -2\)
14.
\((-4)^3\)
Open bracket:
\(= -4 * -4 * -4\)
\(= -64\)
Hence;
\((-4)^3 = -64\)
\((-7)^2\)
Open bracket:
\(= -7 * -7\)
\(= 49\)
Hence;
\((-7)^2 = 49\)
15. Express as fractions:
\(\frac{3}{5^3}\)
Evaluate the denominator
\(= \frac{3}{125}\)
Hence:
\(\frac{3}{5^3} = \frac{3}{125}\)
\((\frac{-1}{3})^2\)
Evaluate the exponent
\(= (\frac{-1}{3})*(\frac{-1}{3})\)
\(=\frac{1}{9}\)
Hence:
\((\frac{-1}{3})^2=\frac{1}{9}\)
16. Evaluate
\((-7)^0 =\)
Evaluate the exponent
\((-7)^0 = 1\)
\(2 * (1/3)^0\)
Evaluate the exponent
\(= 2 * 1\)
\(= 2\)
Hence;
\(2 * (1/3)^0 = 2\)
17. Evaluate
\(3v^2(-5v^4)\)
Open bracket
\(= 3 * v^2*-5* v^4\)
Reorder
\(= 3 *-5* v^4 * v^2\)
\(= -15* v^4 * v^2\)
Apply law of indices
\(= -15* v^{4 +2}\)
\(= -15* v^6\)
\(= -15v^6\)
Hence:
\(3v^2(-5v^4) = -15v^6\)
18.
\(2y^2w^4*6y*2w^8\)
Rewrite as
\(2 *y^2 * w^4*6 * y*2 * w^8\)
Reorder the terms
\(=2*6 * w^4 * w^8*y^2 * y*2\)
\(=12 * w^4 * w^8*y^2 * y*2\)
Apply law of indices
\(=12 * w^{4+8} *y^{2+2}\)
\(=12 * w^{12} *y^4\)
\(=12 w^{12} y^4\)
Hence:
\(2y^2w^4*6y*2w^8 =12 w^{12} y^4\)
19.
\((\frac{4p^3}{3p^7})^{-2}\)
Apply law of indices
\(= (\frac{4p^{3-7}}{3})^{-2}\)
\(= (\frac{4p^{-4}}{3})^{-2}\)
Apply law of indices
\(= (\frac{4}{3p^4})^{-2}\)
Apply law of indices
\(= (\frac{3p^4}{4})^{2}\)
\(= (\frac{3p^4}{4}) * (\frac{3p^4}{4})\)
Evaluate
\(= \frac{9p^8}{16}\)
Hence;
\((\frac{4p^3}{3p^7})^{-2} = \frac{9p^8}{16}\)
20.
\(\frac{x^{-2}}{x^{-3}}\)
Apply law of indices
\(= x^{-2 - (-3)}\)
\(= x^{-2 +3}\)
\(= x^1\)
\(= x\)
Hence:
\(\frac{x^{-2}}{x^{-3}} =x\)
Answer: So 5 + x = 8 beacase x is 3
Step-by-step explanation:
Two lines are perpendicular. The slope of the first line is. What is the slope of the second line?
Answers
Answer:
Therefore, the slope of the original line is 1/2. A line perpendicular to another has a slope that is the negative reciprocal of the slope of the other line. The negative reciprocal of the original line is –2, and is thus the slope of its perpendicular line.
Janet wants to purchase a new car. At the car dealership, a salesperson tells her she can choose from 10 car models, 7 exterior
colors, and 9 interior colors.
How many ways can Janet customize a car? Enter your answer as a whole number, like this: 425
evious
Answers
Janet has 630 options to customize a car based on the given features.
How to solve the question?
To determine the number of ways Janet can customize a car, we need to multiply the number of choices she has for each feature. Therefore, the total number of ways Janet can customize a car can be calculated as:
10 car models x 7 exterior colors x 9 interior colors = 630
Thus, Janet has 630 options to customize a car based on the given features.
It's worth noting that this calculation assumes that each feature (car model, exterior color, and interior color) can be combined with any other feature, without any restrictions or dependencies. However, in reality, certain car models may not be available in certain exterior or interior colors, or there may be other restrictions on the customization options.
Additionally, there may be other features that Janet can customize, such as the type of engine, transmission, or other options. Therefore, the total number of customization options may be even greater than what we have calculated here.
In summary, based on the given information, Janet has 630 ways to customize a car, but in reality, the actual number of options may be more limited or varied depending on other factors.
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If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 27. By how much do the two digits differ?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Answers
If a two-digit positive integer has its digits reversed ,The one differ with another by 3.
What in math is an integer?
A full number (not a fraction) that can be positive, negative, or zero is called an integer (pronounced IN-tuh-jer).
Integer examples include: -5, 1, 5, 8, 97, and 3,043. The numbers -1.43, 1 3/4, and 3.14 are examples of non-integer numbers.
The two digit has one at one's place and other at ten's place ;
The no. can be written as the sum of one's place digit and 10 multiplyed to the ten's digit !
For e.g. , We have a no. 36 , in which 6 is at one's place and three is at ten's place
So, 36 = 6 + 10 ( 3 )
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A can of soda can be modeled as a right cylinder. Ajay measures its height as 8.9 cm
and its radius as 1.9 cm. Find the volume of the can in cubic centimeters. Round your
answer to the nearest tenth if necessary.
Answers
Answer:
The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.
So, using the given measurements, we can substitute in the values and solve for the volume:
V = π(1.9 cm)^2(8.9 cm) = 301.958 cm^3
Rounded to the nearest tenth, the volume of the can is 301.9 cm^3.
Step-by-step explanation:
a fair coin is tossed 3 times. What is the approximate probability of heads apppearing atleast one time
Answers
Possible outcomes of a coin toss are a head or a tail.
Since the coin is tossed three times, there'll be six possible outcomes.
H - headsT - tailsH H H T T T - Possible outcomes
The possibility of a head appearing at least once is therefore 1/3.
Hope it helps. :)
If p2-8 = 17, which of the following
is a possible value of P
Answers
Answer:
+ 5, - 5
Step-by-step explanation:
p^2 - 8 = 17
p^2 = 17 + 8
p^2 = 25
= 5 x 5
p^2 = 5^2
p = ± 5
Given: Given: 2 < a < 5, 3 < b < 7
Find: A-b
Answers
Using simple mathematical operations, we know that a-b can be -1, -2, and 0.
What are mathematical operations?A mathematical "operation" is the process of calculating a value utilizing operands and a math operator.
The supplied operands or integers must adhere to a set of predefined rules that are connected to the symbol of the math operator.
Parentheses, Exponents, Multiplication, Division, and Addition Subtraction are also known as PEMDAS (from left to right).
So, we have: 2 < a < 5, 3 < b < 7
Now, a - b will be:
the values of a can be 3 and 4
Similarly, the value of b can be 4 and 5.
So there are 4 possibilities as shown:
3 - 4 = -1
3 - 5 = -2
4 - 4 = 0
4 - 5 = -1
Therefore, using simple mathematical operations, we know that a-b can be -1, -2, and 0.
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Isabella and Scarlett hung out at the mall on Saturday. They spent 1 hour and 15 minutes shopping for clothes and 1 hour and 55 minutes at the food court. Then they spent 1 hour and 40 minutes at the video arcade before heading home. If it was 12:45 P.M. when Isabella and Scarlett started shopping for clothes, what time was it when they left the mall?
Answers
Answer:
5:35
Step-by-step explanation:
i added the 15 from first to 12:45 (when they arrived) so it was 1 pm already add the other 3 hours to 1pm its 4pm 55 minutes plus 40 minutes is 1 hour and 35 minutes so 4pm +1 hour and 35 minutes = 5:35
also just saw other guys answer if people send links like that its a virus or scam so report it and dont go to the link
The graph below shows the solutions to which inequality?
A. x^2-3x+3 ≥0
B. x² + 3x-3 <0
C. x²-3x+3<0
D. x² + 3x-3>0
Answers
The inequality expression that corresponds to the solution of the inequality graph is x² + 3x - 3 < 0.
option B.
What is the solution of the inequality?The inequality expression that corresponds to the solution of the inequality graph is determined by simplifying the equations as follows;
The solution of the graph,
x > -4 and x < 1
The first equation with "≥" is ruled out because the graph doesn't have a thick dot.
Let's simplify the second expression;
x² + 3x - 3 < 0
solve using quadratic formula;
x > -3.79 or x < 0.79
The third expression is ruled out since its solution will be complex.
For the last expression;
x² + 3x - 3 > 0
x < -3.79 or x > 0.79
Thus, the correct inequality expression is x² + 3x - 3 < 0.
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Medicare would like to test if the average monthly rate for one-bedroom assisted-living facility is different from $3,300. Suppose that you collect sample information and, based on the hypothesis test, determine that the z test statistic is equal to 1.98 while the critical value of z is 2.05. How would you state the conclusion?
Answers
Answer:
We fail to reject our null hypothesis and conclude that there is not sufficient evidence to conclude that the average monthly rate for one-bedroom assisted-living facility is different from $3,300.
Step-by-step explanation:
We are given that critical value of z=2.05
z test statistic=1.98
As we are testing that whether the the average monthly rate for one-bedroom assisted-living facility is different from $3,300, so this leads to two tailed hypothesis test as hypothesis are
Null hypothesis:μ=3300
Alternative hypothesis:μ≠3300.
The critical region in case of two tailed hypothesis test is
\(|z|>z_{\frac{\alpha }{2} }\)
1.98>2.05 (which is not true)
So, the test statistic don't lie in rejection region, thus we don't reject our null hypothesis and conclude that there is insufficient evidence to conclude that the average monthly rate for one-bedroom assisted-living facility is different from $3,300.
PLEASE HELP!! What is the surface area of the cone?
Answers
Hope this helped
notacion cientifica de 760000000
Answers
Answer:
7.6^8
Step-by-step explanation:
Show your work please help me it’s due tomorrow!!!!
Answers
Answer: Consider me the brainiest. The answer is... Decimal form =4.083
Exact form= 49/12
The mixed number form=4 1/12
How do we solve fractions step by step?
Conversion a mixed number 2 1/3 to a improper fraction: 2 1/3 = 2 1/3 = 2 3 + 1/3 = 6 + 1/3 = 7/3
To find a new numerator
A; Multiply the whole number 2 by the denominator 3. Whole number 2 equally 2 * 3/3 = 6/3
b) Add the answer from the previous step 6 to the numerator 1. The new numerator is 6 + 1 = 7
c) Write a previous answer (new numerator 7) over the denominator 3.
Two and one-third are seven-thirds.
Conversion a mixed number 1 3/4 to a improper fraction: 1 3/4 = 1 3/4 = 1 · 4 + 3/4 = 4 + 3/4 = 7/4
To find a new numerator:
a) Multiply the whole number 1 by the denominator 4. Whole number 1 equally 1 * 4/4 = 4/4
b) Add the answer from the previous step 4 to the numerator 3. The new numerator is 4 + 3 = 7
c) Write a previous answer (new numerator 7) over the denominator 4. One and three quarters are seven quarters.
Add: 7/3 + 7/4 = 7 · 4/3 · 4 + 7 · 3/4 · 3 = 28/12 + 21/12 = 28 + 21/12 = 49/12 It
is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(3, 4) = 12. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 4 = 12. In the following intermediate step, it cannot further simplify the fraction result by cancelling. In other words - seven thirds plus seven quarters is forty-nine twelfths.
Find the perimeter of the figure shown above with aside length 5 unit
Answers
The perimeter of the figure with side length of 5 units is 50 units
How to determine the perimeter of the figureFrom the question, we have the following parameters that can be used in our computation:
Shape = rectangle
Smaller shapes = squares
Side lengths = 5 units
The perimeter of the figure is calculated as
Perimeter = Number of visible sides * Side length of the square shape
In this case, we have
Number of visible sides = 10
Substitute the known values in the above equation, so, we have the following representation
Perimeter = 10 * 5
Evaluate the products
Perimeter = 50 units
Hence, the perimeter is 50 units
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two numbers are in the ratio of 10:16 if the sum of numbers is 572 find the numbers.
with steps
Answers
The given ratio is 10:16
Let two number be 10x and 16x
Also given sum is 572
=> 10x+16x=572
=> 26x=572
=> x = 572/26 = 22
Now the first number is 10x = 10(22) = 220 and
Another number is 16x = 16(22) = 352
Hope this helps you dear ;)
Answer:
yo dude dont be upset im doing what you did lol!
For the following vectors, (a) find the dot product v•w ; (b) find the angle between v and w , (c) state whether the vectors are parallel, octagonal, or neither. V=-3i-4j, w=6i+8j
A- v•w
B-the angle between v and w is theta ^•?
C- the vectors v and w are?
Answers
B) The angle between vectors v and w can be found using the formula: cos(theta) = (v • w) / (||v|| ||w||), where ||v|| and ||w|| are the magnitudes of vectors v and w respectively.
First, we need to find ||v|| and ||w||:
||v|| = sqrt((-3)^2 + (-4)^2) = 5
||w|| = sqrt((6)^2 + (8)^2) = 10
Now, we can substitute in the values to get:
cos(theta) = (-50) / (5 * 10) = -1
theta = arccos(-1) = pi radians or 180 degrees.
Therefore, the angle between vectors v and w is 180 degrees.
C) Two vectors are parallel if their directions are the same, which can be determined by comparing their unit vectors.
The unit vector of v is:
v_hat = v / ||v|| = (-3/5)i + (-4/5)j
The unit vector of w is:
w_hat = w / ||w|| = (6/10)i + (8/10)j = (3/5)i + (4/5)j
We can see that the unit vectors are in opposite directions, which means that the vectors are anti-parallel or opposite. Therefore, the vectors v and w are neither parallel nor orthogonal.
Find the equation (in terms of x ) of the line through the points (-2,-2) and (3,-1)
Answers
Answer:
Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.
First find the gradient.
Formula of gradient is given as (y2-y1)÷(x2-x1) or (y1-y2)÷(x1-x2)
Gradient = (-1-(-2))÷(3-(-2))
= (-1+2)÷(3+2)
= 1/5
Equation is y = 1/5 + c
Substitute either one of the points into the equation to find c.
-2 = 1/5(-2) + c
c = -8/5
Hence equation of the line is y = 1/5x - 8/5
46. Five people L, M, n, O and P sit in a row, not necessarily in the same order.
P sits exactly in between Mand n. if Lsits exactly in between Mand O, then
which of the following must be true?
(A) O sits to the immediate right of M.
(B) L and n always sit together.
(C) M sits exactly at the centre of the row.
(D) P sits between Mand L.
caniay Gannat Dhruy. nagrai and Jiyan are
Answers
O L M P N
Solve the linear system below using the substitution method.
y = 5x – 22
3x +2y=34
Answers
Answer:
Use photo math, it will explain all the steps
Answer:
x = 6 , y = 8 ( 6 , 8 )
Step-by-step explanation:
If we solve the linear system that you gave us,
y = 5x – 22
3x +2y=34
We get that x is 6 and y is 8.
In other words, since it's a point, it should be, ( 6 , 8 )
according to census the total number of male and female was 88,51,84,692, if number of male was 45,40,34,570what was the number of number of female population
Answers
According to census the total number of male and female was 88,51,84,692, if number of male was 45,40,34,570 the number of female population is 43,11,50,122.
To find the wide variety of girl population, we will subtract the quantity of male population from the full population.
Total population = 88,51,84,692
Number of male = 45,40,34,570
Number of female = Total population - Number of male
= 88,51,84,692 - 45,40,34,570
= 43,11,50,122
Therefore, the number of female population is 43,11,50,122.
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Liam will spin the pointer one time. What is the probability that the pointer will land on red?
Answers
Answer:
Step-by-step explanation:
What are the other colors?
if there are two colors ( red and another color ) then the probability of the pointer landing on red will be 1/2
similarly if there are 3 colors ( red and two other colors) then the probability of the pointer landing on red will be 1/3 ....
depends on how many colors are there
divide 16 into the ratio 3:5
Answers
Hope that makes sense and it helps!!
Answer:
\(6,10\)
Step-by-step explanation:
Method 1:
\(\mathrm{Let\ two\ numbers\ be\ x\ and\ y\ such\ that:}\\\mathrm{x:y=3:5\ \ \ \ and\ \ \ \ x+y=16}\\\mathrm{or,\ \frac{x}{y}=\frac{3}{5}}\\\\\mathrm{or,\ 5x=3y..........(1)}\\\mathrm{Also\ we\ have}\\\mathrm{x+y=16}\\\mathrm{or,\ 5(x+y)=5(16)}\\\mathrm{or,\ 5x+5y=80}\\\mathrm{or,\ 3y+5y=80\ [From\ equation\ 1]}\\\mathrm{or,\ 8y=80}\\\mathrm{or,\ y=10}\\\mathrm{From\ equation\ 1,}\\\mathrm{5x=3y}\\\mathrm{or,\ 5x=3(10)=30}\\\mathrm{\therefore x=6}\)
\(\mathrm{So,\ the\ two\ numbers\ are\ 6\ and\ 10.}\)
Alternative method 1:
\(\mathrm{Let\ the\ two\ numbers\ be\ x\ and\ 16-x.}\\\mathrm{Then,\ we\ have}\\\mathrm{x:(16-x)=3:5}\\\\\mathrm{or,\ \frac{x}{16-x}=\frac{3}{5}}\\\\\mathrm{or,\ 5x=3(16-x)=48-3x}\\\mathrm{or,\ 5x+3x=48}\\\mathrm{or,\ 8x=48}\\\mathrm{\therefore x=6}\\\mathrm{So,\ the\ other\ number=16-x=16-6=10}\)
\(\mathrm{So,\ the\ two\ numbers\ are\ 6\ and\ 10.}\)
Alternative method 2:
\(\mathrm{Let\ the\ two\ numbers\ be\ 3x\ and\ 5x.}\\\mathrm{Then,}\\\mathrm{3x+5x=16}\\\mathrm{or,\ 8x=16}\\\mathrm{or,\ x=2}\\\mathrm{So,\ first\ number=3x=3(2)=6}\\\mathrm{Second\ number=5x=5(2)=10}\)
\(\mathrm{So,\ the\ two\ numbers\ are\ 6\ and\ 10.}\)
Assume that a coin is tossed twice. The coin may not be fair. The sample space consists of the outcomes (HH, HT, TH, TT). Outcome HH HT TH TT Probability 0.40 0.92 0.29 0.55 Is the given a probability model?
Answers
Assuming that an unfair coin is tossed with outcomes of HH, HT, TH, and TT, and the probability is 0.40, 0.92, 0.29, and 0.55, then the given probabilities do not form a valid probability model for the sample space of two coin tosses.
The given probabilities do not form a valid probability model for the sample space of two coin tosses since a valid probability model must satisfy the following conditions:
Non-negativity: The probability of each outcome must be non-negative, i.e., each probability must be greater than or equal to 0.Normalization: The sum of the probabilities of all outcomes in the sample space must equal 1.To calculate the sum of the probabilities, we simply add up all of the given probabilities:
0.40 + 0.92 + 0.29 + 0.55 = 2.16
In this case, the sum of the probabilities is 2.16, which is greater than 1. Hence, the given probabilities do not form a valid probability model for the sample space of two coin tosses.
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Which number is composite?
53, 81, 41, 47,31
O41
81
31
47
Pls hurry its a test
Answers
Answer:
81
Step-by-step explanation:
A composite number is a number that can be divisible by more than 1.
81 can be divisible by 1 and 9.
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