Answer:
(5) The mid-segment AB = 17
(6) The set of numbers that will form a triangle is 3,3,5 (OPTION 2)
Step-by-step explanation:
(5) The mid-segment is calculated as follows;
\(3x -1 = \frac{34}{2} \\\\3x-1 = 17\\\\3x = 18\\\\x = \frac{18}{3} \\\\x = 6\)
The mid-segment AB = 3(6) - 1
= 18 - 1
= 17
(6) The set of numbers that will form a triangle is calculated as follows;
If A, B and C are three sides of a triangle, then the sum of any two sides must be greater than the third side.
Example; A + B > C
The only option with the correct set of numbers is 2.
2. 3,3,5 ( 3 + 3 > 5)
Please help me find a
Answer:
Step-by-step explanation:
The triangle shown below has an area of 16 units2.
Find z.
4
2
units
Answer:
8 units
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh where b is the base and h is the height
16 = 1/2 (4)*x
16 = 2x
Divide each side by 2
16/2 = 2x/2
8 =x
Simplify (−3)4 and −34. Show all the work
Answer:
-12
Step-by-step explanation:
(-3)4
-3*4
-12
Elaborate ur question about - 34
For each of the following properties write down a matrix that has this property or explain why there is no such matrix (Hint: Check first whether the dimensions add up)
(a) The column space contains (1,0,0)T, (0,0,1)T while the row space contains (1,1)T and (1, 2)T.
(b) The column space is generated by (1,1,1)7T, the null space (or kernel) is generated by (1,2,3)T
(c) The column space is R4 and the row space is R3.
Answer:
a) A = \(\left[\begin{array}{ccc}1&0\\0&0\\0&1\end{array}\right]\) 3*2
b) attached below ( Matrix dose not exist )
c) attached below ( Matrix does not exist )
Step-by-step explanation:
a) Matrix
A = \(\left[\begin{array}{ccc}1&0\\0&0\\0&1\end{array}\right]\) 3*2
From the matrix ; Column 1 and Column 2 Belong to COL(A)
while : (1,1)^T = ( 1,0 )^T + ( 0,1 )^T i.e. (1,1)^T ∈ Row( A )
and (1, 2)^T. = ( 1,0 )^T + 2 ( 0,1 )^T i.e. (1, 2)^T ∈ Row( A )
Hence ; all requirements are fulfilled in Matrix A
b) The column space is generated by (1,1,1)7T, the null space (or kernel) is generated by (1,2,3)T
Matrix is Non-existent because condition is not met
attached below
c) Rank | A |
dimension of column space= 4 , dimension of Row space = 3
Given that ; column space ≠ Row space
Hence Matrix does not exist
There were 470 people at a play. The admission price was $3 for adults and $1 for children.
The admission receipts were $910. How many adults and how many children attended?
Answer:
220 adults and 250 children
Step-by-step explanation:
we require to set up 2 equations and solve simultaneously.
let a be the number of adults and c the number of children , then
a + c = 470 → (1) based on number of people
3a + c = 910 → (2) based on ticket sales
subtract (1) from (2) term by term to eliminate c
(3a - a) + (c - c) = 910 - 470
2a + 0 = 440
2a = 440 ( divide both sides by 2 )
a = 220
substitute a = 220 into (1) and solve for c
220 + c = 470 ( subtract 220 from both sides )
c = 250
that is 220 adults and 250 children attended
HELP PLEASE FAST EXTRA POINTS
Show that (16^1/4)^3 and (16^3)^1/4 are equivalent
Step-by-step explanation:
\(LHS : \)
\( { ({16}^{ \frac{1}{4} } )}^{3} \)
\( = { (\sqrt[4]{16}) }^{3} \)
\( = {2}^{3} \)
\( = 8\)
\(RHS : \)
\( { ({16}^{3} )}^{ \frac{1}{4} } \)
\( = {4096}^{ \frac{1}{4} } \)
\( = \sqrt[4]{4096} \)
\( = 8\)
LHS = RHS
HENCE VERIFIED
Originally, a Petri dish contained 200,000 bacteria. After a scientist applied an antibiotic, the number of bacteria decreased by 75% per hour.
Which function could model this situation?
well, we know the number of bacteria is decreasing, so we can use a Decay equation for that, with a 75% rate of decay.
\(\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &200000\\ r=rate\to 75\%\to \frac{75}{100}\dotfill &0.75\\ t=hours \end{cases} \\\\\\ A = 200000(1 - 0.75)^{t} \implies A = 200000(0.25)^t\)
what is the mean of 24 13 12 1 and 0
Answer:10
Step-by-step explanation:24+13+12+1+0=50/5=10
Suppose you have a 6-face unfair dice with numbers 1,2,3,4,5,6 on each of its faces. If the probability distribution of throwing a number up is as follows:
1 with probability 1/12
2 with probability 1/12
3 with probability 1/12
4 with probability 1/12
5 with probability 1/12
6 with probability 1/2
Which of the following statement is correct?
a. The mathematical expectation of the dice throwing a number up is 3.5
b. The mathematical expectation of the dice throwing a number up is 6
c. The mathematical expectation of the dice throwing a number up is 4.25
d. This is not a proper probability distribution because all the probabilities do not sum up to one
Answer:
D is correct
Step-by-step explanation:
Here, we want to select which of the options is correct.
The correct option is the option D
Since the die is unfair, we expect that the probability of each of the numbers turning up
will not be equal.
However, we should also expect that if we add the chances of all the numbers occurring together, then the total probability should be equal to 1. But this does not work in this case;
In this case, adding all the probabilities together, we have;
1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/2
= 5(1/12) + 1/2 = 5/12 + 1/2 = 11/12
11/12 is not equal to 1 and thus the probability distribution cannot be correct
A person who is paid
earns a set income and is expected to work as
many hours as necessary to complete a job.
OA. an hourly wage
B. in tips
C. in interest
OD. a salary
A person who is paid earns a set income and is expected to work as many hours as necessary to complete a job earn a salary. Option D
What is a salary?
A salary is the regular payment by an employer to an employee for employment that is expressed either monthly or annually, but is paid most commonly on a monthly basis,
A salary does not change on a weekly or monthly basis. Salaries are calculated annually, divided by twelve and paid out each month.
Workers on wages are typically paid time-and-one-half for every hour of overtime work
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A cylinder has a height of 4 meters and a diameter that is 12 meters. Using 3.14 for pi, which of the following can be used to calculate the volume of the cylinder?
Group of answer choices
Answer:
Step-by-step explanation:
h = 4 m
d = 12 m
r = 12/2 = 6 m
Volume of cylinder = πr²h
= 3.14 * 6 * 6 * 4
= 452.16 m³
Find the volume of the cone.
Either enter an exact answer in terms of it or use 3.14 for and round your final answer to the nearest
hundredth.
The volume of the cone will be 21 cubic units.
What is the volume?Volume is defined as the space occupied by any object in the three dimensions. All three parameters are required for the volume like length, width, and height of the cube.
The formula for the volume of a cone is ⅓ r²h cubic units, where r is the radius of the circular base and h is the height of the cone.
Volume = ⅓ r²h
Volume = ⅓ x x 2² x 5
Volume = 21 cubic units
Therefore, the volume for the given shape of the cone will be 21 cubic units.
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HELP PLEASE 15 POINTS
A study conducted to determine the relationship between the age, x, in years of a certain brand of motorcycle and its value, y, in dollars. The equation y = -750x + 8500 best models the data. Based on the equation, what is the estimated value of a motorcycle that is 5 years old?
Based on the equation, y = -750·x + 8500, the estimated value of a
motorcycle that is 5 years old is $4,750.
How can the given equation help to estimate the value of the motorcycle?The regression equation that models the data is; y = -750·x + 8500
Where;
y = The value of the brand of motorcycle in dollars
x = The age of the motorcycle
When the motorcycle is 5 years old, we have;
x = 5
y = -750 × 5 + 8500 = 4750
Based on the equation, the estimated value of a motorcycle that is 5 years old, y = $4,750
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Hi can someone please help me solve the following system of inequalities and state the coordinates in the solution setz
The graph of the system of the inequalities is attached.
To graph the inequalities y < -x - 4 and y ≥ (3/5)x + 4, we can start by graphing the corresponding equations and then shade the appropriate regions based on the inequality signs.
Let's begin with the equation y = -x - 4:
Choose a range of x-values to plot.
For simplicity, let's use x-values from -10 to 10.
Substitute different x-values into the equation to find corresponding y-values.
For example:
When x = -10, y = -(-10) - 4 = 10 - 4 = 6.
When x = 0, y = -(0) - 4 = -4.
When x = 10, y = -(10) - 4 = -10 - 4 = -14.
Plot these points on the coordinate plane and draw a straight line passing through them.
This line represents the equation y = -x - 4.
Next, let's graph the equation y = (3/5)x + 4:
Again, choose a range of x-values to plot. Let's use the same range of -10 to 10.
Substitute different x-values into the equation to find corresponding y-values. For example:
When x = -10, y = (3/5)(-10) + 4 = -6 + 4 = -2.
When x = 0, y = (3/5)(0) + 4 = 0 + 4 = 4.
When x = 10, y = (3/5)(10) + 4 = 6 + 4 = 10.
Plot these points on the coordinate plane and draw a straight line passing through them.
This line represents the equation y = (3/5)x + 4.
Now, let's shade the regions based on the inequalities:
For y < -x - 4, we need to shade the region below the line y = -x - 4.
For y ≥ (3/5)x + 4, we need to shade the region above or on the line y = (3/5)x + 4.
Hence, the region where the shaded regions overlap represents the solution to both inequalities.
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There are 10 roller coasters at 6 flags. If you only have time to ride 3 before the park closes. How many different ways can you create a path to 3 different roller coasters?.
There are 120 different ways to create a path to 3 different roller coasters at Six Flags.
There are a total of 10 choose 3 ways (120) to choose 3 roller coasters out of the 10 available at Six Flags. To calculate this, we can use the combination formula.
The combination formula is:
nCr = n!/(r!(n-r)!).In this case, n is 10 and r is 3, so the total number of possible combinations is
10!/3!7! = 120.To calculate the number of combinations without using a formula, we can use the following method: Start with the first roller coaster, then add a second roller coaster, then a third. There are 10 choices for the first roller coaster, then 9 for the second, and 8 for the third. This results in:
10x9x8 = 720 possible combinationswhich is 6 times more than the 120 calculated by the combination formula. This is because the combinations ABC and CBA are the same, and so are other combinations that are just permutations of each other.
Therefore, there are 120 different ways to create a path to 3 different roller coasters at Six Flags.
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НИК
LEVEL 2 TASK 10
Using each of following numbers once,
write an expression equal to 9:
NUMBERS & SYMBOLS
18 4 12 6
[(
+
х
]
speaker notes
Answer:
(12 ÷ 4) × (18 ÷ 6)
Step-by-step explanation:
(12 ÷ 4) × (18 ÷ 6)
If we solve this or simply this, we would get 9 as our result.
Let's solve and see. Mind you, we've used each of the given numbers just once in the expression.
Thus:
(12 ÷ 4) × (18 ÷ 6)
Solve the parentheses first
3 × 3 = 9.
Therefore,
(12 ÷ 4) × (18 ÷ 6) = 9
Which graph corresponds with the inequality x< 10 ?
Answer:
C
Step-by-step explanation:
Geoff earns $9.25 per hour before taxes, and he works 40 hours per week. Geoff's employer withholds (takes out) 10.65% of geoff's income for taxes. What are geoff's total weekly earnings after taxes are withheld?
A) $ 39.41
B) $59.90
C) $ 330.60
D) $ 370.00
Answer:
a
Step-by-step explanation:
Use algebraic methods to find as many intersection points of the following curves as possible. Use graphical methods to identify the remaining intersection points. R = 6 sin theta and r = 6 cos theta the intersection point(s) is/are_______
(Type an ordered pair. Type exact answer for each coordinate, using phi as needed. Type the coordinate for theta in radians between 0 and phi. Use a comma to separate answers as needed)
The intersection points are (6, 6) and (-6, -6).
What is Intersection points?
The point at which two lines or curves intersect is referred to as the point of intersection. The point at which two curves intersect is crucial because it is the point at which the two curves take on the same value.
The given curves are the polar equations of two circles with radii 6. To find their intersection points, we can set the two equations equal to each other and solve for Ф.
6 sin(Ф) = 6 cos(Ф)
Dividing both sides by 6 and rearranging terms, we get:
tan(Ф) = 1
This equation has infinitely many solutions, but we are only interested in those that lie in the interval [0, π/2].
Ф = π/4 satisfies this condition and corresponds to the point (6, 6) in Cartesian coordinates.
Since the two curves are circles, they are symmetrical about the origin. Therefore, we can deduce that the other intersection point is (-6, -6).
Therefore, the intersection points are (6, 6) and (-6, -6).
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Given f(x) = 3x + 1, solve for x when f(x) = 7.
Answer:
x = 2
Step-by-step explanation:
Step 1: Define
f(x) = 3x + 1
f(x) = 7
Step 2: Substitute
7 = 3x + 1
Step 3: Solve for x
6 = 3x
x = 2
If 2 person take 10 days to pick the apples from a tree, how many days will it take 4 people to do the same job?
Answer:
5 days
Step-by-step explanation:
Answer:
It will take 5 days for 4 people to do the job.
How to do it :
2 is half of 4.
5 is half of 10.
Find the value of x
Answer:
x = 20
Step-by-step explanation:
We know that the vertically opposite angles are equal.
Accordingly,
41 = 2x + 1
Subtract 1 from both sides.
41 - 1 = 2x
40 = 2x
Divide both sides by 2.
x = 20
a meeting started at 10:35am and ended at 3:15pm. how long was the meeting
Answer:
4H40mn
Step-by-step explanation:
because their start
Rectangle A measures 12 cm by 3 cm. ..
If Rectangle B is a dilation of Rectangle A and B's
dimensions are 4 cm by 1 cm, what is the scale factor?
Answer:
1:3
Step-by-step explanation:
Yo have to find the difference between the primary dimensions and the scaled dimensions. And because the scaled dimensions are smaller than the original ones. You can say that the scale factor is 1:3
\(12 \div 4 = 3\)
I just need to know how to work it out for future problems. (Business Calc)
Find the price elasticity of the demand function as a function of p.
1. q=D(p)=600-3p
A)E(p)= p/p-200
B)E(p)= p/600-3p
C)E(p)= p/200-p
D)E(p)= p(200-p)
The price elasticity of the demand function as a function of p is C. E(p)= p/200-p
How to illustrate the information?It should be noted that the price elasticity of demand simply means the ratio of the percentage change in quantity demanded to the percentage change in price.
In this case, the function is given as:
q = D(p) = 600-3p
Differentiate with respect to p
D'(p) = 3
The elasticity of demand will be:
= (P / 600 - 3p) × (-3)
= P / (200 - P)
In conclusion, the correct option is C.
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8 less than a number is less than or equal to 5
Answer:
x-8<_5
Step-by-step explanation:
Order the rational numbers from least to greatest.
Answer:
2.3,2 4/5, 3.01, 3.017, 3.10, 4 1/8, 4.2
What are the solutions to the equation 0=|3x+3|+3
Therefore, the solutions to the equation 0 = |3x + 3| + 3 are x = -2 and x = 0.
To solve the equation 0 = |3x + 3| + 3, we need to eliminate the absolute value. Remember that the absolute value of a number is always non-negative.
First, let's isolate the absolute value term on one side of the equation:
|3x + 3| = -3
Since the absolute value cannot be negative, there are no solutions to the equation as it stands. However, if we modify the equation to make the right side positive, we can find a solution.
To eliminate the absolute value, we can rewrite the equation as two separate equations, considering both the positive and negative cases:
3x + 3 = -3
-(3x + 3) = -3
Solving equation 1:
3x + 3 = -3
3x = -6
x = -2
Solving equation 2:
-(3x + 3) = -3
-3x - 3 = -3
-3x = 0
x = 0
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What is the degree of 24x?
Answer:
one
Step-by-step explanation: