Sandy and Steve share some prize money in the ratio 4:3. The prize money totaled $1400 How much
does Sandy receive ?
Answer:
Sandy will receive $800
Steve will receive $600
Step-by-step explanation:
Sandy : Steve = 4 : 3
Sandy = 4
Steve = 3
Total ratio = 4 + 3 = 7
Total prize money = $1400
How much does Sandy receive ?
Sandy's share = Sandy's ratio / total ratio × Total prize money
= 4 / 7 × 1400
= 4 × 200
= $800
Sandy will receive $800 out of $1400
Steve's share = Steve's ratio / total ratio × Total prize money
= 3 / 7 × $1400
= 3 × $200
= $600
Steve will receive $600 out of $1400
Check:
Sandy's share + Steve's share
= $800 + $600
= $1400
If A and B are 4 * 6 matrices and C is a 7 * 4 matrix, which of the following are defined?
1. CA.2. B^T * C^T.3. AC.4. A-B.5. B-C.6. B^T.
Answer:
1. CA is defined
2. B^T * C^T defined
3. AC is NOT defined
4. A - B is defined
5. B - C is NOT defined
6. B^T is defined
Hence, 1,2,4, and 6 are defined
Step-by-step explanation:
Order of the matrices:
Matrix A is a (4 × 6) matrix
Matrix B is a (4 × 6) matrix
Matrix C is a (7 × 4) matrix
To determine which are defined
1. CA
CA means product of Matrix C and Matrix A
To determine the product of two matrices, the number of columns in the first matrix must be equal to the number of rows in the second matrix. For example, given that matrix X is a (m × n) matrix, matrix Y is a (n × k) matrix and matrix Z is (k × n) matrix. From the definition above,
XY can be determined because number of columns in X equals number of rows in Y
XZ cannot be determine because number of columns in X is not equal to the number of rows in Z.
YZ can be determined because number of columns in Y equals number of rows in Z
(NOTE: A matrix of order (m × n) means the matrix has m rows and n columns)
Hence, for CA
Matrix C is a (7 × 4) matrix
Matrix A is a (4 × 6) matrix
Number of columns in C equals number of rows in A, hence CA is defined
2. B^T * C^T
B^T means transpose of matrix B
Transpose of a matrix is defined as a new matrix whose rows are the same as the columns of the original matrix and whose columns are the rows of the original matrix. Hence, for a matrix of order (m × k), the transpose of the matrix will have an order (k × m).
Hence,
Matrix B is a (4 × 6) matrix
∴B^T gives a matrix of order (6 × 4)
Matrix C is a (7 × 4) matrix
∴ C^T gives a matrix of order (4 × 7)
Since the number of columns in B^T equals the number of rows in C^T, then B^T * C^T defined
3. AC
Matrix A is a (4 × 6) matrix
Matrix C is a (7 × 4) matrix
The number of columns in A is NOT equal to the number of rows in C, hence AC is NOT defined
4. A - B
To find the difference between two matrices, the matrices must have the same order.
Matrix A is a (4 × 6) matrix
Matrix B is a (4 × 6) matrix
Since matrices A and B have the same order [(4 × 6)], hence A - B is defined
5. B - C
Matrix B is a (4 × 6) matrix
Matrix C is a (7 × 4) matrix
Since matrices B and C are of different orders [(4 × 6) and (7 × 4) respectively], then B - C is NOT defined
6. B^T
B^T means the transpose of matrix B
Matrix B is a (4 × 6) matrix
From the above definition
B^T gives a (6 × 4) matrix
Hence, B^T is defined
What is Half a cup in a fraction? .........
Answer:
1/2
Step-by-step explanation:
One cup is 1.
Half of a cup in decimals is 0.5, and in fraction 1/2
Answer:
it would be 1/2
1/2 a cup
3. While trick or treating with his buddies, Albert noticed he received 7 Kit Kat bars after
visiting 10 houses. If they plan on visiting 65 houses, how many Kit Kat bars might he receive
by the end of the night?
Find f(-7) if f(x) = 2x+8.
-6
03
02
22
The graph of the function f is shown. The domain of f is [0, 50]. What is the range of g(x) = 4f(x)? PLEASE HELP!
Answer: the range of g(x) is [0, 7]
Step-by-step explanation:
The domain is the set of the possible values of y.
We can see that, for y = f(x) in the domain [0, 50]
The smallest possible value of y is 0, and the largest possible value of y is 1.75 (at x = 25).
Then the range of f(x) is [0, 1.75]
Now, if we have the function g(x) = f(x)*4
Let's analyze the possible values of g(x) in these extremes of the range of f(x).
when f(x) is in the minimum, f(x) = 0, we have that g(x) is:
g(x) = f(x)*4 = 0*4 = 0.
So 0 is the minimum in the range of g(x).
Now, for the maximum of f(x) (f(x) = 1.75) we have:
g(x) = f(x)*4 = 1.75*4 = 7
Then the range of g(x) is [0, 7]
what's the answer for the question find the following Figure angle x and y angle z
from the degrees and go 47 degrees
where is figure????????????????????
Square root 50 as a decimal
Answer:
I got 7.0 try that.
A diamond ring cost $3500 in 2018. However, it increased in value by 4% in 5 point
2019 and 8% in 2020. What does the ring cost in 2020 ?
Answer:
The ring in 2020 costs around $3,931.2.
Step-by-step explanation:
We know how much the ring cost in 2018 and we know the percentages of the value as years go by.
To solve this, we will need to put the percentages into decimals, and since we are adding value, add an additional 1 [whole] in both decimals.
Should look like this:
2019: 1.04
2020: 1.08
Multiply the cost with the first year:
3500 x 1.04 = 3640
The ring costs $3,640 in 2019.
Then it says the ring went up by %8 percent in 2020.
Multiply the cost from last year with the current year:
3500 x 1.08 = 3931.2
The ring costs $3,931.2 in 2020.
I hope this helps!
If m<TUV = (9x + 1), m<TUW = (7x-9), and m<WUV = (5x - 11), find the value of x.
Answer: x = 7
Step-by-step explanation:
Suppose ray UW divides ∠TUV into two angles ∠ TUW and ∠ WUV.
Then, m∠TUV = m∠ TUW + m ∠ WUV (i)
Given, m∠TUV = (9x + 1) , m∠ TUW = (7x-9) and m ∠ WUV = (5x - 11)
Substitute these values in (i), we get
[tex]9x+1=7x-9+5x-11\\\\\Rightarrow\ 9x+1= 7x+5x-9-11\\\\\Rightarrow\ 9x+1=12x-20\\\\\Rightarrow\ 12x-9x= 1+20\\\\\Rightarrow\ 3x= 21\\\\\Rightarrow\ x=\dfrac{21}{3}\\\\\Rightarrow\ x=7[/tex]
Hence, the value of x = 7.
Answer:
x=7
Step-by-step explanation:
i need help understanding this problem, any help is appreciated :)
Answer:
B = 31.467 °
Step-by-step explanation:
Sides:
a = 13 cm
b = 9 cm
c = 17 cm
Angles:
A = 48.939 °
B = 31.467 °
C = 99.5941 °
Other:
P = 39 cm
s = 19.5 cm
K = 57.6818 cm2
r = 2.95804 cm
R = 8.62057 cm
Agenda:
A = angle A
B = angle B
C = angle C
a = side a
b = side b
c = side c
P = perimeter
s = semi-perimeter
K = area
r = radius of inscribed circle
R = radius of circumscribed circle
Formula: SSS is Side, Side, Side
Given the sizes of the 3 sides, you can calculate the sizes of all 3 angles in the triangle. Use The Law of Cosines to solve for the angles. You could also use the Sum of Angles Rule to find the final angle once you know 2 of them.
9 200 711 to the nearst ten
Answer:
9,200,711 rounded would be 9,200,710
Hope this helps!! - Maddy
(if this helps please make brainliest, rate, and thank so I know how I did!)
╰(*°▽°*)╯
Drag each equation to the correct to the correct location on the table
Answer:
x=3
2(2x-3)=65x - (3x-1)=75x-2x-4=5x=2
5(x+3)=254x-(2x+1)=3x+2x+3=9
Answer:
x=3
2(2x-3)=6
5x - (3x-1)=7
5x-2x-4=5
x=2
5(x+3)=25
4x-(2x+1)=3
x+2x+3=9
write the interval in set builder notation (-2,3)
Answer:
helium,nitrogen
Step-by-step explanation:
A set-builder notation describes or defines the elements of a set instead of listing the elements. For example, the set { 1, 2, 3, 4, 5, 6, 7, 8, 9 } list the elements. The same set could be described as { x/x is a counting number less than 10 } in set-builder notation.
The function f(x) = 4x – 0.1x2 is used to model the curve of a bridge over a small river, where x is the distance from one side of the river and the x-axis represents the ground. The mathematical range for the function is the set of real numbers.
Which statement describes the limitation for the reasonable range compared to the mathematical range
Answer:
The limitation for the resonable range restricts it to postive ral numbers
Step-by-step explanation:
the low temperature in Anchorage, Alaska today was -4°F. The low
temperature in Los Angeles, California was 63°F. What is the difference in
the two low temperatures?
Answer:
67°F
Step-by-step explanation:
-4-63 = - 67°F
Therefore temperature difference=67
What is the difference in kilowatt hours of monthly energy production between an a erage local wind speed of 15 miles per hour and an average local wind speed of 10 miles per hour?
Answer:
The difference in energy production in kilowatt hours of monthly energy produced between an average local wind speed of 15 miles per hour and an average local wind speed of 10 miles per hour is approximately 9 kWh
Step-by-step explanation:
We note that the energy produced is given by the formula;
Energy = 1/2 × m × v²
From which we have the energy per unit mass = 1/2 × v²
The energy produced by the wind traveling at 15 miles per hour is given as follows;
15 mph = 6.705 m/s
The energy per unit mass produced in a month of 30 days is therefore;
1/2×6.705²×60×60×24×30 = 58264304.4 J/kg
We note that 1 Kilowatt hour = 3.6 × 10⁶ Joules
Therefore;
58264304.4 J = 58264304.4 J/(3.6 × 10⁶) kWh = 16.184529 kWh
The energy produced by the wind traveling at 10 miles per hour is given as follows;
10 mph = 4.47 m/s
The energy per unit mass produced in a month of 30 days is therefore;
1/2×4.47²×60×60×24×30 = 25,895,246.4 J/kg
We note that 1 Kilowatt hour = 3.6 × 10⁶ Joules
Therefore;
25,895,246.4 J = 25,895,246.4 J/(3.6 × 10⁶) kWh = 7.193124 kWh
The difference in energy production in kilowatt hours of monthly energy produced between an average local wind speed of 15 miles per hour and an average local wind speed of 10 miles per hour is therefore;
16.184529 kWh - 7.193124 kWh = 8.991405 kWh. ≈ 9 kWh
A point lies in the _____ of an angle if it lies between the rays that form the angle. *
Answer:
I believe it is the vertex, of an angle.
Step-by-step explanation:
It is the vertex, because that is what you would call the bottom point of an angle.
An angle is a figure created by two rays, known as the angles' sides, that share a common terminus, known as the angle's vertex. A point lies in the interior of an angle if it lies between the rays that form the angle.
What is an angle?An angle is a figure created by two rays, known as the angles' sides, that share a common terminus, known as the angle's vertex. Angles created by two rays are located in the plane containing the rays. Angles are also generated when two planes intersect. These are known as dihedral angles.
An angle has two rays and the area that lies between the two rays is known as the interior of the angle, while the area that is not between the two rays is the exterior of the angle.
Therefore, A point lies in the interior of an angle if it lies between the rays that form the angle.
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PLEASE SOMEONE HELP ME
The bar graph shows changes in price of regular gasoline from 1996–2010.
For example, at the end of 1996, the price per gallon for regular gasoline was
$0.15 more than the price per gallon at the end of 1995, the price at the end
of 1997 was $0.12 less than the price at the end of 1996, and so on.
1. Find the average change in the price of regular gasoline for the given years.
a. 1996–2002 b. 2003–2010 c. 1996–2010
2. The price per gallon for regular gasoline at the end of 1995 was $1.08. In what
year was the price per gallon for regular gasoline the lowest? What was the
price? Explain how you found your answer.
3. How many times greater is the price per gallon in 2010 than the price per
gallon in 1996? Price change (dollars per gallon)
Answer:
The answer is 5 times
Step-by-step explanation:
First, we need to read the change in price in 2000 and 2007, from the graph.
So, the change in price in 2000 was $0.14 and in 2007 it was $0.71.
Now, we do the same thing we always do when comparing two values - we divide them. So:
0.71 / 0.14 = 5.07
Of course, we could multiply these values with 100, in order to avoid decimal numbers. Then we would get:
71 / 14 = 5.07
We could also divide this in the form of fractions:
71/100 / 14/100 = 5.07
There are several ways we could divide rational numbers, but the result will always be the same.
Change in price in 2007 was around 5 times greater than the change in 2000.
I hope this helps!!;-)
8(1 + 5x) + 5= 13 + 5x
Answer:
0 will be answer as shown in image
The larger of two numbers is 7 less than twice the
smaller number. If the sum of the numbers is 47,
find both numbers.
Answer:
larger number=29;smaller number=18
Step-by-step explanation:
let assume the two numbers are X and Y
where X is the larger number and Y is the smaller number.
From the question the larger number is 7 less than twice the smaller number. in mathematical terms this can be denoted as;
X=2Y - 7→→→→→→ equation 1
Also it was stated in the question that the sum of the two numbers is 47 which can be denoted as;
X + Y = 47→→→→→→ equation 2
Now from equation 1, X is mathematically expressed as 2Y - 7. Having known this we substitute X as 2Y - 7 into equation 2 then we have 2Y - 7 + Y = 47.
collecting like terms we have
2Y + Y = 47 + 7
solving arithmetically we have;
3Y = 54
divide both sides by 3 we have;
Y = 18.
Now if you recall from equation 1;
X = 2Y - 7;
since we now know Y as 18 we substitute Y as 18 in equation one then we have;
X = 2(18) - 7;
X =36 - 7
X = 29.
WhAt is the value of y
6√3 is the value of y...
That’s a Meanie Genie. On an archeological dig near the highlands of Tibet, Alley discovered an ancient oil lamp. Just for laughs she rubbed the lamp. She quickly stopped laughing when a huge puff of magenta smoke spouted from the lamp and an ornery genie Murray appeared. Murray gave her two balance scales and nine identical stones as per her three wishes. Alley may use each of the scales exactly once. Choose a possible way for Alley to select the slightly heavier stone containing Ramanujan from among the nine identical-looking stones.
Answer:
Step-by-step explanation:
Arrange the stones into 3groups of 3and place one group on one side of the first balance scale and another group on the other side.
If both sides weigh the same, then she knows that the (heavier) jewel must be in the third group of three. However, if one side is heavier than the other, then she knows that the jewel is one of the three that weighed more. In either case, after only one weighing, Alley is able to identify a group of only three stones among which is the Rama Nujan.
Then take 2 of the 3 stones and place one on each side of the second scale. If one weighs more than the other, then she knows that this stone is the one containing the jewel. If they both weigh the same, then she knows that the third stone must contain the jewel.
A Meanie Genie.
An archeological dig was performed by a team of researchers near the highlands of the Tibet and alley found an ancient oil lamp. She rubbed the lamp and saw a huge puff of magenta smoke coming from it. Later in the genie appeared. She gave him a balance scale and nine identical stones.
Hence answer is the third stone contains jew.
After the arrangement, of the 3 types of stones one side of the first balance scale and another on the group of the other side. Both balances scale to weight the same the heavier consists of the jew than the others.Taking two and three on the scale she knows that the third is having the jewel.Thus alley choose a slightly heavier stone which continued the Ramanujan from the 9 identical ones.Learn more about the Meanie Genie.
brainly.com/question/12420511.
find the position vectors of the points which trisect the line joining the points whose position vectors are i+2j+7k and 3i+j-k
Answer:
Step-by-step explanation:
you should have to find two position vectors between the given positional vectors . to find the first position vector take the ratio 1:2 internally and for the second positon vector take the ratio 2:1 as it is trisectedusing the position vector formula we get the respective answer's3(n+1)=5.4 Solve for n
Answer:
n =0.8Step-by-step explanation:
[tex]3(n+1)=5.4[/tex]
Expand ; 3(n+1)
[tex]3(n+1) =3n +3\\\\3n+3 =5.4[/tex]
Collect like terms and simplify
[tex]3n =5.4-3\\3n=2.4[/tex]
Divide both sides of the equation by 3
[tex]\frac{3n}{3} = \frac{2.4}{3} \\\\n = 0.8[/tex]
Answer:
The value of n is 0.8 .
Step-by-step explanation:
First, you have to expand to get rid of brackets :
[tex]3(n + 1) = 5.4[/tex]
[tex]3n + 3 = 5.4[/tex]
Next, you have to subtract 3 on both sides to remove 3 at the left side :
[tex]3n + 3 - 3 = 5.4 - 3[/tex]
[tex]3n = 2.4[/tex]
Lastly, you have to divide 3 on both sides :
[tex]3n \div 3 = 2.4 \div 3[/tex]
[tex]n = 0.8[/tex]
=> Please Help Me With My Math <=
Answer:
B
Step-by-step explanation:
Find the square root of this complex number -5+12i ? Solve
Answer:
Well you can't simplify the question anymore so I believe the question is the answer
Step-by-step explanation:
There is no equal sign so it can't be simplified anymore because it says 12i you can't combined 12i with -5 because of the variable
A political scientist surveys 38 of the current 153 representatives in a state's congress.
Answer:
What is the question? Is this a true or false question ?
Step-by-step explanation:
The percentage of surveys done if, A political scientist surveys 38 of the current 153 representatives in a state's congress is 25%.
What is percentage?As it is clear from the term, percent means measuring anything per hundred. For example, you get marks per 100 marks, so you get the percentage.
Given:
The number of surveys done = 38,
The representatives in a state's congress = 153,
Calculate the percentage as shown below,
Percentage of survey = The number of surveys done / total representative × 100,
Percentage of survey = 38 / 153 ×100
Percentage of survey = 0.25 × 100
Percentage of survey = 25 %
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The complete question is: A political scientist surveys 38 of the current 153 representatives in a state's congress. Calculate the percentage of the survey.
simplify the fraction 34%
The questions asks us to simplify the fraction 34%, first convert that into a decimal which would be .34, then change that as a fraction which would be [tex]\frac{17}{50}[/tex]
Answer:
brainliest plssssss
Step-by-step explanation:
answer is in the img below
Write the following sentence using mathematical symbols. The sum of 10 and x is -13. "The sum of 10 and x is -13" in mathematical symbols is..
Answer:
10 + x = -13
Step-by-step explanation:
The sum of 10 and x is -13.
10 + x = -13