Answer: Cynthia will receive $5,400, Moses will receive $8,100, John will receive $13,500
Step-by-step explanation:
First, we will see how many "portions" the money is broken up into.
2:3:5 can become 2 + 3 + 5 = 10
Next, we will see how much money each "portion" is worth using division.
$27,000 / 10 = 2,700
Finally, we will multiply to see how much each person will receive.
2:3:5
2 * $2,700 = $5,400 [Cynthia]
3 * $2,700 = $8,100 [Moses]
5 * $2,700 = $13,500 [John]
Answer:
Cynthia's money = $5,400
Moses' money = $8,100
John's money = $13,500
Step-by-step explanation:
The full ratii of the money will be 2+3+5 = 10
Cynthia's ratio = 2 × $27,000
10
= 2 × 2,700
= $5400
Moses' ratio = 3 × $27,000
10
= 3 × 2,700
= $8100
John's ratio = 5 × $27,000
10
= 5 × 2,700
= $13,500
|-a2|, given a = 5, b = -3, and c = -2.
10
25
-10
-25
Shelia starts with $50 in her checking account. She spends $45, deposits $32, spends $14, and finally desposits $30. What is her ending balance?
whats 94 1/4 divided by 7 1/4 need steps pls
The temperature is 10 degrees below zero. The sun come out and the temperature went
up 15 degrees. What is the temperature now since the sun came out?
Answer:
5 degres
Step-by-step explanation:
0-10 is -10
-10+15 is 5
Find the center and the radius of each circle. x²+y²-4 y-16=0
The center and radius of the circle given by the equation x^2 + y^2 - 4y - 16 = 0 is (0 , 2) and 2√5, respectively.
The standard form of the equation of circle is given by
(x - h)^2 + (y - k)^2 = r^2
where (h , k) is the location of the center and r is the radius of the circle.
On the other hand, the general form of the equation of circle is given by
x^2 + y^2 + Dx + Ey + F = 0
where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.
If the equation of the circle in general form is x^2 + y^2 - 4y - 16 = 0, then the coefficients are:
D = 0
E = -4
F = -16
If D = -2h and D = 0, then
0 = -2h
h = 0
If E = -2k and E = -4, then
-4 = -2k
k = 2
If F = h^2 + k^2 -r^2 and F = -16, then
-16 = 0^2 + 2^2 - r^2
r^2 = 0 + 4 + 16
r^2 = 20
r = 2√5
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What is the 2 nd term of the geometric sequence 3, II, 12, . . . . . . . ?
The second term of the given geometric sequence is: 6.
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.Given:
First term of GP = 3 (a₁).Third term of the GP = 12 (a₃).To find: Second term of the GP (a₂).
Finding:
Since the given sequence is a GP, the nth term will be given by: [tex]a_n=a_1(r^{n-1})[/tex], where r = common ratio of the GP.
Now, for n = 3, [tex]a_3=3(r^{3-1})[/tex]
=> 12 = 3 (r²)
=> 4 = r²
=> r = ±2
Since the given sequence is increasing and positive, r = 2.
Thus, a₂ = a₁ (r¹)
=> a₂ = 3 (2) = 6
Hence, The second term of the given geometric sequence is: 6.
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help me with this question
For the geometric sequence 3,12,48,192, . . . . . , find the indicated term.17 th term
The 17th term of the given geometric sequence, 3, 12, 48, 192, . . . , is 1.288490189 x 10^10.
A geometric sequence refers to a sequence of numbers, which the next term is obtained by multiplying the previous term with a constant, called a ratio.
a(n) = a r^(n-1)
Where:
a(n) = nth term
r = ratio
Given the geometric sequence 3, 12, 48, 192, . . .
Find the ratio,
r = a(n)/a(n-1)
r = a(2)/a(1)
r = 12/3
r = 4
Notice that the ratio between two succeeding terms is always 4.
Use the formula to find the 17th term of the geometric sequence.
a(n) = a r^(n-1)
a(17) = 3[4^(17-1)]
a(17) = 3(4^16)
a(17) = 1.288490189 x 10^10
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A die is rolled. Find the probability of the outcome. P( less than 2 )
When a die is rolled, the probability of outcome less than 2 is 1/6.
As given in the question,
Let the possible outcomes of the given event is represented by S.
Formula used :
Probability of an event
= (Favorable outcomes) /(Total Number of possible outcomes)
When a dice is rolled, all possible outcomes are 1, 2, 3, 4, 5, 6.
Sample space, S =(1, 2, 3, 4, 5, 6)
Favorable outcomes = Only 1 is smaller than 2, remaining number is greater than 2
So, total number of favorable outcomes = 1
Probability of outcome less than 2
= (Favorable outcomes) /(Total Number of possible outcomes)
⇒ Probability = 1/6
Therefore, when a die is rolled, the probability of outcome less than 2 is 1/6.
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Find the values of x and y given that 182x + 247 y = gcd(182, 247)
Answer:
Hello,
x=-4, y=3
Step-by-step explanation:
14*x+19*y=1 since gcd(182,247)=13
Here is a automatic calculus (using Bezout 's method)
All you have to do is to put in B1 and B2 the right numbers
The values of x and y given that 182x + 247 y = gcd(182, 247) would be x=-4 and y=3.
What does it mean to solve an equation?An equation represents equality of two or more mathematical expression.
To solve an equation, then the values of the unknowns for which that equation would be true (the equality between expressions should hold true for those values).
And Solutions to an equation are values of the variables involved in that equation for which the equation is true.
We have given the equation as;
182x + 247 y = gcd(182, 247)
Then we get
14*x+19*y=1
Thus, x=-4 and y=3.
since we have given gcd(182,247)
=13
Hence, The values of x and y given that 182x + 247 y = gcd(182, 247) would be x=-4 and y=3.
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The scatter plot shows the number of stamps Katie collected in different months:
plot ordered pairs 1, 30 and 2, 70 and 3, 110 and 4, 150 and 5, 190
What is the approximate predicted number of stamps she collected in the 25th month? (1 point)
980
990
1,000
1,010
Hello!
The approximate predicted number of stamps she collected in the 25th month is 990.
Step-by-step explanation:
The ordered pairs are as follows:
( 1, 30), ( 2, 70), ( 3, 110), ( 4, 150), and ( 5, 190).
The pattern visible is that each month the value increases by 40 from each previous month.
The equation you would have to do in order to see how many stamps she collected is:
[tex]30[/tex] + [tex]40[/tex] × [tex]24=30[/tex] + [tex]960=990[/tex]
Hope this helps!
What is the slope of a line perpendicular to the line whose equation is x+4y=16x+4y=16. Fully simplify your answer.
The slope of a line perpendicular to the line of x + 4y = 16 is 4.
What is the slope of a line perpendicular to the line of the given equation?Given the equation of line;
x + 4y = 16
First, rearrange in slope intercept form ( y = mx + b ) by solving for y
x + 4y = 16
Subtract x from both sides
x - x + 4y = 16 - x
4y = -x + 16
Divide each term by 4 and simplify
4y/4 = -x/4 + 16/4
y = -(1/4)x + 4
Using the slope intercept form ( y = mx + b ) to compare.
y = -(1/4)x + 4
Slope m = -(1/4)
Now, the equation of a perpendicular line to y = -(1/4)x + 4 must have a slope that is the negative reciprocal of the original slope.
Hence, m_perpendicular will be;
m_perpendicular = -( 1 / original slope )
m_perpendicular = -( 1 / -(1/4) )
m_perpendicular = -( -4 )
m_perpendicular = 4
Therefore, the slope of a line perpendicular to the line of x + 4y = 16 is 4.
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Write a two-column proof. (Lesson 4-4)
Given: Δ L M N is isos. with LM ≅ NM , and MO bisects ∠L M N .
Prove: Δ M L O ≅ ΔM N O
It is proved that ΔLMN is an isosceles triangle.
What exactly do we mean by a triangle's congruency?Two triangles are said to be congruent if all three corresponding sides are equal and all three corresponding angles are equal in measure.These triangles can be moved, rotated, flipped, and turned to appear identical.If they are repositioned, they will coincide.If two triangles satisfy the five congruence conditions, they are congruent.They are side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), and right angle-hypotenuse-side (RHS).So,
Given:
LM ≅ NMMO bisects ∠L M NTo prove congruency:
MO = MO (Common line)LM = NM = Given∠LM0 = ∠NMO = equal angles (As MO bisects ∠LMN)Therefore, ΔM LO ≅ ΔMNO under SSA congruency.
Since the 2 sides are similar so the angles in front of them will also be similar.So we can say that ΔLMN is an isosceles triangle.Therefore, it is proved that ΔLMN is an isosceles triangle.
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Help Please
Solve for y : | y | = 16 .
y= ____ , ____
help asap!! check screenshot
The sequence of the angles from lower to bigger will be ∠WXY < ∠YXZ < ∠WYX < ∠XZY < ∠XYZ.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
In a triangle, if the angle is small then the opposite side will be short, and if the angle increases then the side also increases.
The sides of the triangle are in ascending order, then we have
WY < YZ < WX < XY < XZ
Then the sequence of the angles is given as,
∠WXY < ∠YXZ < ∠WYX < ∠XZY < ∠XYZ
The sequence of the angles from least to biggest is ∠WXY < ∠YXZ < ∠WYX < ∠XZY < ∠XYZ.
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Find the expression for h(x)
Hello,
[tex]f(x) = - {x}^{2} + 8[/tex]
[tex]h(x) = - {x}^{2} + 8 - 3 = - { {x}^{2} } + 5[/tex]
Ms. Lopez is creating posters to decorate
her classroom. She uses 0.25 ounce of paint
per poster. If she has 4.05768 ounces of
paint, how many posters can she make?
draw base ten blocks to show the number 200 in the place value chart below
Answer:
Step-by-step explanation:
The base ten blocks to show the number 200 in the place value chart is shown below.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The number 200 in the place value.
Now,
Since, the number 200 in the place value.
Hence, The figure for the base ten blocks to show the number 200 in the place value chart is shown in figure.
Thus, The base ten blocks to show the number 200 in the place value chart is shown below.
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What does f(5) =23 mean
Answer:
Step-by-step explanation:
when f is evaluated at 5 the output is 23
Thomas took a 140-mile bus trip to visit his grandparents.
His trip is outlined on the graph
Explain what might have happened in the interval
between D and E.
a. Show work (50 points). Mark the graph
Answer:
they stopped at 110 for a restroom break?
I don't think I fully understand lol srry
Thomas and his grandparents are on a trip of 140-mile. From Points D and E, there is no movement of the bus, which means they halt at the point.
What is a graph?An orderly schematic illustration or diagram of facts or quantities is known as a graph in mathematics.
Usually, the graph's examples indicate how two or more items are related to one another.
As per the graph provided in the question,
As we can see in the graph there are covering 140 miles in a bus and the graph shows distance (in miles) and time (in hours).
From the graph we can see that between point D and E only time is increasing but the distance is constant which means they stopped at some place to halt.
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The monthly cost of using a cell phone is $29.95 plus $0.035 per minute of talk time. An equation to
represent this monthly cost would be:
C = 29.95 + 0.035x, where C represents the monthly cost and x represents the number of minutes used.
How many minutes were used during a month if the cost amounted to $43.53 ?
O 506 minutes
O 426 minutes
O 388 minutes
438 minutes
Answer:
c) 388 minutes
Step-by-step explanation:
Given equation,
→ C = 29.95 + 0.035x
Then the call duration will be,
→ C = 29.95 + 0.035x
→ 43.53 = 29.95 + 0.035x
→ 0.035x = 43.53 - 29.95
→ x = 13.58/0.035
→ [ x = 388 ]
Hence, option (c) is correct.
CCSS ARGUMENTS Write a coordinate proof for each statement.The three segments joining the midpoints of the sides of an isosceles triangle form another isosceles triangle.
The triangle formed by joining the midpoint of an isosceles triangle is also an isosceles triangle.
What is an isosceles triangle?An isosceles triangle is one with two equal-length sides. It is sometimes stated as having exactly two equal-length sides, and sometimes as having at least two equal-length sides, with the latter form containing the equilateral triangle as a particular case.
An isosceles triangle XYZ is been made as shown below. Now, for the ΔXYZ, the midpoints of the line segment XY, YZ, and ZX are A, B, and C, respectively.
Further, the length of the sides of the ΔABC can be written as,
AB = √[(x₂-x₁)² + (y₂-y₁)² ]
= √[(3 - 1)² + (1 - 1)²]
= √4
= 2
BC = √[(x₂-x₁)² + (y₂-y₁)² ]
= √[(3 - 2)² + (1 - 0)²]
= √2
AC = √[(x₂-x₁)² + (y₂-y₁)² ]
= √[(1 - 2)² + (1 - 0)²]
= √2
Since, the length of the two sides is the same, while the length of the third side is different, thus, the triangle formed by joining the midpoint of an isosceles triangle is also an isosceles triangle.
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The battery power available to operate a deep space probe is given by the formula P=42 e°.°°5t , where P is power in watts and t is time in years. For how many years can the probe run if it requires 35 watts? Round the answer to the nearest tenth year.
The life of the battery is about 36.5 years, if it requires 35 watts.
What is termed as logarithmic functions?A logarithmic term is a number expressed in logarithmic form. Some other name for it is a log term.
A number could also be the sum of two or more numbers. As a result, a term can be the product of two or even more quantities, at least one of which should be in logarithmic form. These same terms are recognised as log terms in such cases.A quantity can also be described as the variation between two quantities. However, if a term contains a quotient of quantities, or if at least one of the amounts can also be conveyed in log form, the term is referred to as a log term.Consider some formulas used in log.
Quotient Rule: ㏒(A/B) = ㏒A - ㏒BProduct Rule : ㏒A + ㏒B = ㏒(AB)Power Rule: n㏒A = ㏒AⁿBase Rule = ㏒ₐb = ㏒ₓb/㏒ₓaExponent Rule = e∧lnx = xNow, as per the given question,
The function is written as;
P = 42e∧(-0.005t).
The value of the power P is mentioned in the question; (P = 35 watt).
Thus, substitute the value of the P in teh equation;
35 = 42e∧(-0.005t).
Now, divide both sides by 42.
0.8333 = e∧(-0.005t)
Taking natural log on both side;
㏒0.8333 = ㏒e∧(-0.005t)
㏒0.8333 = -0.005t
Solve the value of the log by using calculator,
-0.182 = -0.005t
t = 36.5
Therefore, the the life for which the battery will run is 36.5 years.
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Give an example of a 2x2 matrix whose
determinant is 13.
Answer:
The method for appearing with numbers for the 2x2 matrix whose determinant is 13 is clarified.
Step-by-step explanation:
Determinant of 2×2 matrix
If we have a 2×2 matrix A of the form;
A =
\binom{a \: \: \: b}{c \: \: \: d}(
cd
ab
)
The determinant of the matrix is;
|A| = (a.d) - (b.c)
Therefore, to appear with numbers for a, b, c, and d, we must ensure; (a.d) - (b.cdeterminantse, if a = 3, d = 15, b = 2, and v = 1.
Ultimately, |A| = (3×5) - (2×1) = 13
FITNESS A fitness instructor is starting a new aerobics class using fitness hoops. She, wants to confirm that all of the hoops are the same size. What measure(s) can she use to prove that all of the hoops are congruent? Explain your reasoning.
The instructor can use Mathematical coincidence to prove that all of the hoops are congruent.
What do we mean by Mathematical coincidence?The term "coincide" refers to something happening at the same time. In mathematics, coincident lines are lines that lie on top of each other so that when we look at them, they appear to be a single line rather than double or multiple lines. Two lines as well as shapes that are exactly on top of one another.For instance, these two lines are coincidental, but they appear to be one line because they are on top of each other.So, the fitness instructor should use Mathematical coincidence and should keep the hoops on one another to check the congruency.
Therefore, the instructor can use Mathematical coincidence to prove that all of the hoops are congruent.
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What's 3/6 + 2/6? (Note: you will get 99 points if you solve this!)
================================================
the fractions have like denominators so we add numerators :
[tex]\sf{\frac{3}{6} +\frac{2}{6} =\frac{3+2}{6} =\frac{5}{6}[/tex]
5/6================================================
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[tex]\textcopyright ELIZA[/tex]
Find the values of x and y. State which theorem(s) you used.
The required simplified value of x and y is 32 and 84 respectively.
Given that,
To find the values of x and y. State which theorem(s) you used.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Vertical opposite angles
3x = 5x - 64
2x = 64
x = 32
Now,
5x - 64 = 5*32 - 64
= 160 - 64
= 96°
Now complementary angle y
y = 180 - 96°
y = 84°
Thus, the required simplified value of x and y is 32 and 84 respectively.
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#3 i
The endpoints of AB are A (-8, 5) and B (0,7). Find the coordinates of the midpoint M.
The coordinates of the midpoint M
The coordinates of the midpoint M of the segment AB is (-4,6).
What is the coordinates of the midpoint M of the segment AB?The midpoint formula is expressed as;
M = ( (x₁+x₂)/2, (y₁+y₂)/2 )
Given the data in the question;
Point A (-8, 5)
x₁ = -8y₁ = 5Point B (0,7)
x₂ = 0y₂ = 7To determine the midpoint, plug the given points into the formula above and simplify.
M = ( (x₁+x₂)/2, (y₁+y₂)/2 )
M = ( ((-8)+0)/2, (5+7)/2 )
M = ( ( -8+0 )/2, (5+7)/2 )
M = ( ( -8 )/2, (12)/2 )
M = (-4,6)
Therefore, the coordinates of the midpoint M of the segment AB is (-4,6).
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State the domain and range and determine if it’s a function
Answer:
Domain: 3, 6, 12, 18
Range: 5, 7, 9, 10
This is not a function.
Step-by-step explanation:
In a function there is a single y value for each x value. In this case, when x = 6, y can be both 5 and 10. If you were to plot all these points and graph them, you would see that the result would fail the "vertical line test" for a function.
-8(-10/7)=4(-10/7+5)+2(-10/7)
help pls
just like show solution
Answer:
Step-by-step explanation:
[tex]\displaystyle\\-8(-\frac{10}{7})= 4(-\frac{10}{7} +5)+2(-\frac{10}{7} )\\[/tex]
[tex]\displaystyle\\Let \ -\frac{10}{7} =t\\Hence,\\(-8)(t)=(4)(t+5)+(2)(t)\\-8t=(4)(t)+(4)(5)+2t\\-8t=4t+20+2t\\-8t=6t+20\\-8t+8t=6t+20+8t\\0=14t+20\\0-20=14t+20-20\\-20=14t\\-20=(14)(-\frac{10}{7} )\\-20=-\frac{(14)(10)}{7} \\\\-20=-\frac{(7)(2)(10)}{7} \\-20=-(2)(10)\\-20\equiv-20[/tex]
