Answer: Uncle Luke is at 50 years old
Step-by-step explanation: I went through trial and error first with simple t-charts. In the first one, I simply implemented the piece of info that Luke was 5 times older than the nephew. But then, I realized that Luke would always be 5 years older than his nephew. Here was the info for that t-chart:
[tex]\left \{ {{N=1} \atop {L=5}} \right. \left \{ {{N=2} \atop {L=6}} \right. \left \{ {{N=3} \atop {L=7}} \right.[/tex]
Next, I tried a chart starting with the nephew at 2 years of age, and got an age gap of 8. This helped me realize that I would have to start at 4 years of age in order to have an age gap of 16
[tex]\left \{ {{N=2} \atop {L=10}} \right.[/tex] | [tex]\left \{ {{N=4} \atop {L=20}} \right. \left \{ {{N=5} \atop {L=21}} \right.[/tex] (remember there are 1 increments)
Next, I realized that N=4, L=20 was 40 years ago, so if now the nephew was 44, we can increment 16 to get 50
44+16=50
Priya starts
with $50 in her bank account. She then
deposits $20 each week for 12 weeks.
Write an equation that represents the relationship
between the dollar amount (y) in her bank account
and the number of weeks (x) of saving.
Answer:
y = 20x + 50============================
GivenInitial deposit = $50,Weekly deposit = $20,Number of weeks = 12.SolutionThe total deposit over 12 weeks:
y = 12*20 + 50 = 240 + 50 = 290Equation in general form:
y = 20x + 50, where x- number of weeks, y- amount of savingsThe area of a rectangle is 110 square units. Its length measures 11 units. Find the length of its diagonal. Round to the nearest tenth of a un
it
The length of the diagonal of the Triangle is 14.86 units
What is Diagonal?
When two polygonal vertices are not on the same edge, a diagonal is a line segment connecting them. Any sloping line is known as a diagonal informally.
Given,
Area of Rectangle = 110square units
Length = 11units
Breadth = ?
Area of Rectangle = length x breadth
Breadth = Area of Rectangle / length
Breadth = 110 / 11
Breadth = 10units
Length of diagonal (Pythagoras Theorem)
H^2 = P^2 + B^2
H^2 = (11)^2 + (10)^2
H^2 = 121 + 100
H^2 = 221
H = [tex]\sqrt{221}[/tex]
H = 14.86 units
Hence, The length of its diagonal is 14.86 units
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Here are the ages of 14 coworkers:
Note that based on the graph given, the mean is at point B, while the median is also at point B:
What is mean?The mean is the average of a set of variables in mathematics and statistics. The mean may be calculated in a variety of methods, including the simple arithmetic mean (add the integers and divide the total by the number of occurrences), geometric mean, and harmonic mean.
The median, on the other hand, is the number in the middle of a sorted, ascending or descending list of numbers, and it might be more descriptive of the data set than the average.
For the median:
Given the above definition, and the fact that we have 14 data points, the median is going to be somewhere between the 7th and 8th data points. By graph analysis, it is easy to see the following:
For the mean:
Given that the graph is representative of a Normal Distribution, the mean is also at point B.
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Full Question:
Here are the ages of 14 coworkers: [See attached graph]
Where is the mean?, and Where is the median?Deb wants to put up a fence around her garden.
The fence costs £3 per metre.
The fencing company charges £200 to install the fence.
What is the total cost of the fence for Deb's garden?
The total cost of fencing the garden will be 3x+200 where x is the perimeter of garden that is variable according to the length and breadth of the garden.
What is length?Distance is measured in length. Length has the dimension of distance in the International System of Quantities. The majority of measurement systems choose a base unit for length from which all other units are derived. The metre serves as the foundational unit of length in the International System of Units.
What is Perimeter?A closed path that encompasses, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are numerous uses in real life for perimeter calculations.
Here,
Let x be the perimeter to be fenced.
the cost is 3 rupees per meter.
so the equation will be= 3x+200
The total cost of fencing the garden will be 3x+200, where x is the garden's perimeter and is dependent on the garden's length and width.
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Find the distance between points M(6,16) and Z(−1,14) to the nearest tenth.
Answer:
7.3units
Step-by-step explanation:
[tex] \sqrt{(x2 - x1) {}^{2} + (y2 -y1) {}^{2} } [/tex]
[tex] \sqrt{ (- 1 - 6) { \\ }^{2} + (14 - 16) {}^{2} } [/tex]
[tex] = 7.3[/tex]
I need the answer soon!
A museum charges $10 for general admission and $2 for each special exhibit you attend.
What does f(0) = 10 represent in the context of this problem?
In linear equation, If the person doesn't attend any events, n = 0, and the price stays at 10, therefore f(n) = 10 + 2n.
What in mathematics is a linear equation?
An x-y linear relationship, or two variables in which the value of one of them (often y) relies on the value of the other one, is what is known as a linear equation in two variables (usually x).The dependent variable in this scenario is y since it depends on the independent variable, x.To describe the cost of attending n events, create an equation using function notation.
A 10 dollar entrance fee is required each time, and a further 2 dollars must be paid for each unique exhibit that a visitor chooses to visit.
The function, which would depend on n events, is
If the person doesn't attend any events, n = 0, and the price stays at 10, therefore f(n) = 10 + 2n.
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Find the x- and y-intercepts of the graph of 4x-4y=324x−4y=32. State each answer as an integer or an improper fraction in simplest form.
Answer:x-intercepts (5,0)
y-intercepts (0,-5)
Step-by-step explanation: To find the x-intercept substitute in 0 for y and solve for x. to find the y-intercept subsitute 0 for x and solve for y
Alfred and Rani both picked different two-digit numbers. If you multiply Alfred's number by 5 and double Rani's number, the sum is 300. If you double
Alfred's number and multiply Rani's number by 3, the sum of the two numbers is 252. What is the sum of their two numbers?
O 96
O 112
O 128
O 144
O 150
Rationalise the denominator and simplify
6/square root 3
Answer:
2[tex]\sqrt{3}[/tex]
Step-by-step explanation:
[tex]\frac{6}{\sqrt{3} }[/tex] They do not want a radical in the denominator. So you need to multiple the numerators and the denominator by [tex]\sqrt{3}[/tex]
[tex]\frac{6}{\sqrt{3} }[/tex] x [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex] = [tex]\frac{6\sqrt{3} }{3}[/tex] = 2[tex]\sqrt{3}[/tex]
[tex] \frac{6}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } = \frac{6 \sqrt{3} }{3} = 2 \sqrt{3} [/tex]
hope it will work
systems of equations homework
a) (2, -2)
[tex]\begin{gathered} 3x+y=4 \\ 3(2)-2=4 \\ 6-2=4 \\ 4=4 \\ \text{and} \\ x-3y=-4 \\ 2-3(-2)=-4 \\ 2+6=-4 \\ 8=-4 \end{gathered}[/tex]answer: the ordered pair is not a solution of the given system
b) ( -1, 5)
[tex]\begin{gathered} -x+y=6 \\ -(-1)+5=6 \\ 1+5=6 \\ 6=6 \\ \text{and} \\ 2x+3y=13 \\ 2(-1)+3(5)=13 \\ -2+15=13 \\ 13=13 \end{gathered}[/tex]answer: the ordered pair is a solution of the given system
There were 7.2 gallons of water in Sandra's bathtub. Then 6.27 gallons drained out. How much water is left in the bathtub?
The amount of water left in the bathroom is 0.93 gallons
How to determine the amount of water left?From the question, the given parameters are:
Total amount of water in the bathroom = 7.2 gallonsAmount of eater drained out = 6.27 gallonsThe amount of water left is the difference between the total amount of water in the bathroom and the amount of eater drained out
This is represenetd as
Amount left = Total amount of water in the bathroom - Amount of eater drained out
Substitute the known values in the above equation
Amount left = 7.2 - 6.27
Evaluate
Amount left = 0.93
Hence, the amount left is 0.93 gallons
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The required measure of the volume of water left in the bathtub is 0.93 gallons.
As per the given data, There were 7.2 gallons of water in Sandra's bathtub. Then 6.27 gallons drained out. How much water is left in the bathtub is to be determined.
Here,
According to the question, the water left after the 6.27 gallons of draining out can be evaluated by the arithmetic subtraction of the initial volume to the volume that drained out, that is,
The volume of water left in the tub = 7.2 - 6.27 = 0.93.
Thus, the required measure of the volume of water left in the bathtub is 0.93 gallons.
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Hi I need this Answered right now please I have school in 60 min
At a school, 460 of the students walk to school
Thew number of students who ride the school bus is 110% of the number of students who walk. How many students ride the school bus?
Determine whether each triangle below will form a unique triangle, no triangle or more than one triangle based on the criterion given.
Answer:
A: A unique triangle
B: A unique triangle
C: More than a triangle
middle.
Submit
<
1 103 <
What is the answer to this I literally suck at math
Answer:
I think it's 4 on the left and 5 on the right side
Step-by-step explanation:
4*4*4=64
and
5*5*5=125
A boat can travel 228 miles on 19
gallons of gasoline. How much gasoline
will it need to go 48 miles?
Round the answer to two decimal digits
Answer: 4 gallons
Step-by-step explanation:
The boat can travel 228 miles on 19 gallons of gasoline. We can divide 228 by 19 to find out how many miles the boat can travel on 1 gallon of gasoline, which is 12. For the boat to go 48 miles, we can divide 48 by 12 to get the answer, which is 4. The boat can travel 48 miles with 4 gallons of gasoline.
Solve for y:
4x-8y=32
Answer: y = -4 + x/2
Step-by-step explanation:
A man realizes he lost the detailed receipt from the store and only has the credit card receipt withthe after-tax total. If the after-tax total was $1,656.99, and the tax rate in the area is 8.396, what wasthe pre-tax subtotal?
The pre-tax subtotal was $171.00.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that:
After-tax total = $1,656.99
Tax rate in the area = 8.396%
The pre-tax price would be 100% and this tax rate is an addition.
Total percent = (100+8.396)% = 108.3%
Consider x be the pre-tax amount.
The total bill= (after-tax total) = (pre-tax subtotal) + 8.3% · (pre-tax subtotal)
(after-tax total) = (pre-tax subtotal) 108.3
Divide by the coefficient on the right;
(pre-tax subtotal) = (after-tax total)/108.3
= $1,656.99/108.3
= $171.00
Therefore, The pre-tax subtotal was $171.00.
The pre-tax amount was $130.
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PLEASE HELP MATH TEST TOMORROW
if 1cm is equivlent to 50km how many km is in 50cm
Answer:
2,500
Step-by-step explanation:
1cm=50km
50cm*50km=2500km
Answer:
2500 km
Step-by-step explanation:
If 1 cm is equal to 50 km, we can multiply the 1 cm by 50 to get 50 cm. In order to do this, we also have to multiply the 50 km (which was equal to the 1 cm) by 50 as well.
50 x 50 = 2500
Whatever we do to one side, we have to do to the other to make it equivalent.
n Bill's physics class, he had to solve the equation 6 = 12kx2 for k. Each step of his work is shown below.
The unknown value from the given linear expression is 1/4
Solving linear equationsAx+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5.
When an equation is given in this format, finding both intercepts is rather simple (x and y).
Given the equation below;
6 = 12k * 2
6 = 24k
Divide both sides by 24
24k = 6
k = 6/24
k = 1/4
Hence the value of k from the given expression is 1/4
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when atc has not imposed any climb or descent restrictions and aircraft are within 1,000 feet of assigned altitude, pilots should attempt to both climb and descend at a rate of between a. 500 feet per minute and 1,500 feet per minute. b. 1,000 feet per minute and 2,000 feet per minute. c. 500 feet per minute and 1,000 feet per minute.
In the absence of ATC restriction on climb or descent, and aircraft are within 1,000 feet of assigned altitude. pilots should attempt to both climb and descend at a rate of between 500 fpm and 15000 fpm. (Option A)
An Air Traffic Controller (ATC) clearance refers to an authorization by ATC for the purpose of preventing known aircraft collision. The rate of climb or descend expected by ATV is when an aircraft is within 1000 feet of assigned altitude, descend, or climb at an optimum rate consistent with the operating characteristics of the aircraft to 1,000 feet above or below the assigned altitude, and then attempt to descend or climb at a rate of between 500 and 1,500 fpm until the assigned altitude is reached.
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46 x 2 in standard algorithm
Answer:
92
Step-by-step explanation:
1
46
x 2
92
(40 points) need answer asap the x=38
If point A, havingcoordinates (p, 3) andpoint B, with coordinates(6, p) lie on a line havinga slope of 2, what is thevalue of p?
Take into account that the slope of a line is given by the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1,y1) and (x2,y2) are two points on the line.
In this case:
(x1,y1) = (p,3)
(x2,y2) = (6,p)
By replacing the previous values into the formula for m, we get:
[tex]m=\frac{p-3}{6-p}[/tex]Now, by making m = 2 and solving for p, we obtain:
[tex]\begin{gathered} \frac{p-3}{6-p}=2 \\ p-3=2(6-p) \\ p-3=12-2p \\ p+2p=12+3 \\ 3p=15 \\ p=\frac{15}{3}=5 \end{gathered}[/tex]Hence, the value of p is p = 5
Luke receives an electric bill of \$84.21$84.21dollar sign, 84, point, 21 for the month of April. The electric company charges \$0.14$0.14dollar sign, 0, point, 14 per kilowatt-hour (\text{kWh})(kWh)left parenthesis, start text, k, W, h, end text, right parenthesis of electricity. Given that April has 303030 days, about how many kilowatt-hours did Luke use per day during the month of April?
Choose 1 answer:
Given that April has 30 days, Luke used, on average, 20.05 kilowatt-hours of electricity per day during April.
What is average?The average is the mean value obtained by dividing the total value of a data set by the number of items.
In this situation, we can divide the total electric bill for April by 30 to obtain the average daily charge.
In addition, we can divide the average charge per day by the cost per kilowatt-hour to obtain the number of kilowatt-hours used per day.
The total electric bill for April = $84.21
The charge per kilowatt-hour (kWh) = $0.14
The number of days in April = 30
The bill per day = $2.807 ($84.21/30)
The kilowatt-hours per day = 20.05 kWh ($2.807/$0.14)
Thus, Luke used an average of 20.05 kilowatt-hours per day in April.
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Find the number that makes the ratio equivalent to 3:5
Answer:
6:109:1512:20
Step-by-step explanation:
Find the number that makes the ratio equivalent to 3:5
multiply or divide 3 (numerator) and 5 (denominator) by the same number, the result of the division will be equal, therefore equivalent
6:10
9:15
12:20
the result of all ratios is 0.6, therefore equivalent
Use point-slope form to write the equation of a line that passes through the point (13,5) with slope 1.
The equation of the line is y = x - 8 which passes through the point (13,5) with slope 1.
We have to determine the equation of a line that passes through the point (13,5) with slope 1.
What is the slope of the line?The slope of a line is defined as the angle of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
Let the required line would be as
⇒ y - y₁ = m (x - x₁ )
The required line passes through the point (13, 5)
Here x₁ = 13 and y₁ = 5 and m = 1
Substituting these inputs into the above equation obtains the line equation.
⇒ y - 5 = (1)(x - 13)
⇒ y - 5 = (x - 13)
⇒ y = x - 13 + 5
⇒ y = x - 8
Thus, the equation of the line is y = x - 8 which passes through the point (13,5) with slope 1.
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Would HL, ASA, SAS, AAS, or SSS be used to justify that the pair of triangles is congruent?
The theorem that justifies that the pair of triangles are congruent is: AAS.
What is the AAS Congruence Theorem?The AAS is known as the angle-angle-side congruence theorem, which justifies why two triangles that have a pair of non-included congruent side and two pairs of corresponding congruent sides.
The diagram shows that the two triangles have two corresponding congruent angels that are marked, and they share a common side, which means they have a pair of non-included congruent sides.
This goes to show that the criterion for proving that the two triangles are congruent by the AAS are already given and known.
Therefore, the triangles are congruent to each other by the AAS congruence theorem.
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Use the function f(x) = 2-5x to fill out the table.
X | f(x)
——————
-2 |
-1 |
0 |
1 |
2 |
Answer:
Step-by-step explanation: f(x) =2-5x
2-5(-2)=12
2-5(-1)=7
2-5(0)=2
2-5(1)= -3
2-5(2)-8
I hope this helps. All you have to do is plug in the numbers in the equation for x and then solve!
hi I need help with this question anyone got answers??? please its due tmrrrr!!!!!
5 1/4 ÷ 2/4
a marketing research organization wishes to estimate the proportion of television viewers who watch a particular prime-time comedy on may 24th. the proportion is thought to be about 0.30. what is the least number(sample size) of viewers that should be randomly selected to ensure that a 95% confidence interval for the true proportion of viewers will have a width of 0.06 or less?
Least number (sample size) of viewers that should be randomly selected to ensure that a 95% confidence interval for the true proportion of viewers will have a width of 0.06 or less is 225.
E = 0.06,
P = 0.30
c= 95%
& = 1 - 0. 95
To x/2 = 0-025
21096*/ 2 = 0-025
Margin of error
P ( 1 - P )
To ac / 2 ) 2 P ( 1 - P )
E= ( 1. 96* 0 . 30 x ( 1 - 0 - 30 )0-06
=224.09 ~ 225
round to next number
225
In order to guarantee that a 95% confidence interval for the true proportion of viewers would have a width of 0.06 or less, the minimum number of viewers (sample size) that should be chosen at random is 225.
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