Dean is training for a 20 kilometre race. He wants to beat his personal best time of 3 hr 14 min 45 sec. If it takes him 9 minutes and 30 seconds to run one kilometre, will he beat his personal best? Calculate by how much will Dean beat/not beat his personal best time?
Dean will take a total time of 3 hours and 10 minutes to complete the race and will beat his personal best time
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the personal best time of Dean be = A
Now , the value of A = 3 hours 14 minutes 45 seconds
And ,
The time taken by Dean to complete 1 km = 9 minutes 30 seconds
Now , the total distance of the race lap = 20 km
So , the equation will be
Total time taken by Dean to complete 20 km race B = 20 x time taken by Dean to complete 1 km
Substituting the values in the equation , we get
Total time taken by Dean to complete 20 km race = 20 x 9 minutes 30 seconds
Total time taken by Dean to complete 20 km race = 20 x 9 minutes + 20 x 30 seconds
Total time taken by Dean to complete 20 km race = 180 minutes + 600 seconds
1 hour = 60 minutes
1 minute = 60 seconds
180 minutes = 3 hours
600 seconds = 10 minutes
So , the equation is
Total time taken by Dean to complete 20 km race B = 3 hours 10 minutes
So , the value of B < value of A
Therefore , the Dean will beat his personal best time and the race is completed in 3 hours 10 minutes
Hence , Dean will take a total time of 3 hours and 10 minutes to complete the race and will beat his personal best time
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What is an algebraic expression for 16 more than the product of 43 and a number?
A: 16 − 43y
B: 43y(16)
C: 43y − 16
D: 43y + 16
The algebraic expression that can be represented by the statement is 43y + 16
How to make a algebraic expression that can be represented by the statement?From the question, we have the following statement that can be used in our computation:
16 more than the product of 43 and a number
Represent the variable with y
So, we have the following representation
16 more than the product of 43 and y
Express the product as an actual product
So, we have the following representation
16 more than 43y
more than as used here means addition
So, we have
43y + 16
Hence, the expression is (d) 43y + 16
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Answer: 43y + 16
Step-by-step explanation:
i did the test
Shelley is searching online for airline tickets. Two weeks ago, the cost to fly from Hartford to Orlando was $210. Now the cost is $320. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with the new ticket price?
The percent increase is 56%
The percent increase if the airline charges an additional $50 baggage fee with the new ticket price is 76%
How to determine the percent increaseThe formula for determining percent increase is expressed as;
Percent increase = x₂ - x₁/x₁ × 100/ 1
Where;
x₁ is the initial valuex₂ is the final valueNow, substitute the values, we have;
Percent increase = $320 - $210/$210 × 100/ 1
Find the difference
Percent increase = $110/$210 × 100/ 1
Percent increase = 0. 52 × 100/ 1
Multiply through
Percent increase = 52%
If there is an increase of $50
Percent increase = $370-210/210 × 100/ 1
= 160/210 × 100/ 1
= 76%
Hence, the values are 52% and 76% respectively,
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Ome of the children at a chool arrive by car
- 30% of the tudent at the chool are boy
- 60% of the boy at the chool arrive by car
- 80% of the girl at the chool arrive by car
what i the probability a child choen at random from the chool arrive by car
The probability that a child chosen at random from the school arrives by car is the total of the column Car 74%.
Describe probability using an example?
By dividing the number of preferable possibilities by the total number of potential outcomes, probability, which measures the likelihood that an event will occur, is obtained.
The most basic illustration is a coin toss. There are only two outcomes that can occur when you flip a coin: either heads or tails.
You can build a two-way relative frequency table to represent the data:
These are the columns and rows:
Car No car Total
Boys
Girl
Total
Fill the table
30% of the children at the school are boys
Car No car Total
Boys 30%
Girl
Total
60% of the boys at the school arrive by car
That is 60% of 30% = 0.6 × 30% = 18%
Car No car Total
Boys 18% 30%
Girls
Total
By difference you can fill the cell of Boy and No car: 30% - 18% = 12%
Car No car Total
Boy 18% 12% 30%
Girl
Total
Also, you know that the grand total is 100%
Car No car Total
Boy 18% 12% 30%
Girl
Total 100%
By difference you fill the total of Girls: 100% - 30% = 70%
Car No car Total
Boy 18% 12% 30%
Girl 70%
Total 100%
80% of the girls at the school arrive by car
That is 80% of 70% = 0.8 × 70% = 56%
Car No car Total
Boy 18% 12% 30%
Girl 56% 70%
Total 100%
Now you can finish filling in the whole table calculating the differences:
Car No car Total
Boy 18% 12% 30%
Girl 56% 14% 70%
Total 74% 26% 100%
Having the table completed you can find any relevant probability.
The probability that a child chosen at random from the school arrives by car is the total of the column Car 74%.
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if a statistic used to estimate a parameter is such that the mean of its sampling distribution is equal to the true value of the parameter being estimated, what is the statistic said to be?
The given statistic is said to be an "unbiased estimator". In this statistic, the mean is equal to the true value of the estimated parameter.
What is an unbiased estimator?In a statistic, if the mean is equal to the estimated parameter, then that statistic is said to be an unbiased estimator. It is used to estimate a population parameter.
Calculation:Consider a statistic.
"A statistic describes a portion of the target population".
"A parameter describes the whole population".
In a statistic, the mean of the sampling distribution is equal to the true value of the estimated parameter.
I.e., μ = E(x)
So, that statistic is said to be an unbiased estimator.
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what is the total amount that First Consumer Bank will receive after lending Jane $7,000 for three years at an interest rate of 5 percent, compounded annually
Answer: it is 8103.38
Step-by-step explanation:
Example An investor Saved #120,000 For 7 years in a bank which pays interest of 11½% per annum Calculate the a. Interest which accrued b balance if # 25,000 was withdrawn from the account (N 28,276) 00
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$120000\\ r=rate\to 11.5\%\to \frac{11.5}{100}\dotfill &0.115\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per annum, thus once} \end{array}\dotfill &1\\ t=years\dotfill &7 \end{cases}[/tex]
[tex]A=120000\left(1+\frac{0.115}{1}\right)^{1\cdot 7} \implies A \approx 257101.92 \\\\\\ \underset{earned~interest}{\stackrel{257101.92 - 120000}{\text{\LARGE 137101.92}}}\hspace{10em}\underset{adjusted~balance}{\stackrel{257101.92 - 25000}{\text{\LARGE 232101.92}}}[/tex]
geologists unearth a sample of zircon that appears to be a closed system. they find 0.686 microgram of 206pb for 1.000 microgram of 238u present. approximately how old is the sample? yrs
geologists unearth a sample of zircon that appears to be a closed system. they find 0.686 micro gram of 206 Pb for 1.000 micro gram of 238U present. approximately 3.7973 × 10⁹ years old is the sample.
What is decay constant?The reciprocal of the time period during which the number of atoms in the radioactive element drops to almost A. 50% of its initial number is the decay constant.
According to the radioactive decay law, a nucleus's likelihood of decaying is a constant that is independent of time.
t1/2 of U₂₃₈ is 4.5 × 10⁹ years
moles of U₂₃₈ : (1 × 10⁻⁶ / 238) moles
moles of Pb₂₀₆ : (0.686 × 10⁻⁶ / 206) moles
Now, U₂₃₈ → Pb₂₀₆
As Pb₂₀₆ comes from U₂₃₈ hence,
moles of U₂₃₈ decayed = moles of Pb₂₀₆
= (0.686 × 10⁻⁶ / 206) moles
Therefore, initial moles of U₂₃₈:
N₀ = [(1 × 10⁻⁶ / 238) + (0.686 × 10⁻⁶ / 206)] moles
and N = (1 × 10⁻⁶ / 238) moles
Now, λ (decay constant) = 0.693 / (t1/2)
= 0.693 / ( 4.5 × 10⁹ years)
So,
t = 2.303 / λ × log (N₀ / N)
t = 2.303 / [0.693 / ( 4.5 × 10⁹ years)] × log [1 + (0.686/206)/(1/238)]
t = 14.95 × 10⁹ × 0.254
t = 3.7973 × 10⁹ years.
Thus, the sample is: 3.7973 × 10⁹ years old.
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Twice last month, Judy Carter rented a car from a car rental company and traveled around the Southwest on business. The company rents its car for a daily fee, plus an
additional charge per mile driven. Judy recalls that her first trip lasted 4 days, she drove 450 miles, and the rental cost her $256.00. On her second business trip she drove
200 miles in 3 days, and paid $159.00 for the rental. Find the daily fee, and find the mileage charge.
Answer:
the daily fee is 37 and the mileage charge is .24 per mile.
Step-by-step explanation:
256 = 450x + 4b
159 = 200x + 3b
Multiple the top equations by -3 all the way through the bottom equations by 4 all the way through then add the equation together.
-768 = -1350x -12b
636 = 800x + 12b
-132 = -550x Divide both sides by -550
.24 = x This is the charge per mile.
Plug in .24 for x into either of the original 2 equations to solve for b which is the daily fee.
256 = 450(.24) = 4b
256 = 108 + 4b Subtract 108 from both sides
148 = 4b Divide both sides by 4
37 = b This is the daily fee.
Help me please before my assignment is due
Greta's current age is m + n years.
What is an expression?An algebraic expression in mathematics is an expression that is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.).
In other words, algebraic expressions are combinations of variables, numbers, and at least one arithmetic operation
Therefore, let's convert the word's expression to an algebraic expression.
Greta was m years old n years ago. Her age now is as follows:
n years ago Greta was m years old. This simply means n years ago Greta was m years old. Her current age will be the sum of her current age and the number of years ago.
Therefore,
(m + n) years
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What value of x makes the perimeters of the figures below equal? (see imagine attached) :)
The value of x that makes the perimeters of the figures equal is; x = 3.
What is the Perimeter of a Figure?To find the perimeter of a figure, add all its side together. That is, the sum of all its sides will give you the perimeter.
Perimeter of the triangle = (x + 6) + 5x + (3x + 3)
Open the bracket and simplify
x + 6 + 5x + 3x + 3
Combine like terms
= 9x + 9
Perimeter of the square = 4(x + 6)
= 4(x) + 4(6)
= 4x + 24
Make both equation equal to each other and find x:
9x + 9 = 4x + 24
9x - 4x = -9 + 24
5x = 15
x = 3
The value of x is 3.
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Given that log,m=n, express 25n+2 in terms of m.
Answer:
25n+2 can be expressed as log,m^25+2.
Step-by-step explanation:
Since log,m=n, we can write 25n+2 as 25*log,m+2.
Using the property of logarithms that log,a+log,b=log,ab, we can rewrite 25*log,m as log,m^25.
PLEASE HELP ASAP!!!!
Answer:
statements 2 and 3 are true
Step-by-step explanation:
using the rule of exponents
[tex]a^{0}[/tex] = 1
then
1 [tex]a^{0}[/tex]≠ a ← lie
2 [tex]x^{0}[/tex] = 1 ← true
3 [tex]5^{0}[/tex] = 1 ← true
Jack is running on a treadmill at a speed of 7. 2 miles per hour a slim y equals total distance and x equals number of hours
Need help pls important!!!!!!!!
Given that he is running on a treadmill at a pace of 7.2 miles per hour, the necessary expression will be y=7.2x.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases.
Here,
Speed of him=7.2 miles/hour
Let y be the total distance and x be the number of hours,
speed=distance/time
7.2=y/x
y=7.2x
The required expression will be y=7.2x as he is running on a treadmill at a speed of 7. 2 miles per hour.
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At what number of square feet of countertop would the cost from each company be the same?
The cost from company A and company B will be the same at 40 square feet of countertop
At what number of square feet of countertop would the cost from each company be the same?Given that:
Company A will sell Mikayla a countertop according to the given
graph, which includes a $1, 000 installation fee.
Company B will sell a countertop according to the values given in the
table, which includes an $800 installation fee and a constant rate of change
With this information, you can make cost function for both Company A and Company B
Company A
A linear function is of the form y = mx + c
where c is the y-intercept (starting point) and m is the slope (rate)
c = 1000 (from the graph)
m = 1150-1000 / 10-0 (By using the 2 points on the graph: m = y2-y1/x2-x1)
m = 15
y = mx + c
y = 15x+1000
Company B
c = 800 (given)
m = 1100-1000 / 15-10 (From table)
m = 100/5 = 20
y = mx + c
y = 20x+800
Equate the two cost functions and solve for x:
20x+800 = 15x+1000
20x-15x = 1000-800
5x = 200
x = 200/5
x = 40 square feet
Therefore, at 40 square feet of countertop, the cost from each company will be the same
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Write ONE equivalent ratio for the following: 6 : 4
Ben bought one share of stock for $40. He watched the
price of his stock every day for a week. On Monday, the
stock moved 2.5 points up. On Tuesday, it moved 1.75
points down. On Wednesday, it moved p points. On
Thursday and Friday, the stock moved 0.75 points up
each day. If the price of the stock was $45 at the end of
the week, what is the value of p?
Answer:2p
Step-by-step explanation:
Whats the scale factor of triangle PQR to triangle STU.
PR =8 SU=12
RQ=6 UT=9
QP=10 TS=15
The scale factor of triangle PQR to triangle STU is 3/2
How to find the scale factor of the two trianglesScale factors are used to increase or decrease image. The situation of increment is usually called magnifying.
Taking a point of reference say PR and SU
PR = 8
SU = 12
let the scale factor be r such that
8 * r = 12
r = 12 / 8
r = 3/2
checking with other sides
PR to UT
6 * 2/3 = 9 correct
QP to TS
10 * 3/2 = 15 correct
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The expression below is the factorization of what polynomial? Write
exponents with the caret (^). For example, enter x² as x^2.
(2x+3)(3x + 5)
Write 2/5 and 1/4 with the same denominator
Answer:
Make the denominators equal by L.C.M
--> 8/20 + 5/20
--> 13/20
Nate Belloir earns a weekly commission of 2. 5% on sales of $50,000 or less and 3. 0% on sales in excess of $50,000. One week Nate's commission was $2,135. What was the total of his sales for that week?
The total of his sales for that week is $49,500.
Given :
Nate Belloir earns a weekly commission of 2. 5% on sales of $50,000 or less and 3. 0% on sales in excess of $50,000. One week Nate's commission was $2,135.
Let x be the total sales.
2135 = 2.5 % * 50000 + 3 % (x - 50000 )
= 2.5 * 50000 / 100 + 3/100 ( x - 50000 )
1235 = 2.5 * 500 + 0.03x - 0.03 * 50000
1235 = 1250 + 0.03x - 1500
0.03x = 1235 - 1250 + 1500
0.03x = -15 + 1500
0.03x = 1485
multiply by 100 on both sides
0.03x * 100 = 1485 * 100
3x = 148500
x = $49500
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identify the maximum or minimum volume to the domain and range of the graph of the function y=2(x-3)^2-4
The minimum value of the function y = 2(x - 3)² - 4 is -4. Domain of the function is set of all real numbers and the range is all real numbers ≥ -4.
What is Domain and Range of a function?Domain of a function y = f(x) is the set of all the values of x where the function is defined.
The range of the function is the set of all values of the function on the defined domain.
The given function is,
y = 2(x - 3)² - 4
y = 2(x² - 6x +9) - 4
y = 2x² - 12x + 14
This is a quadratic function and the graph of the function will be a parabola.
The parabola is directed upwards if the coefficient of x² in a quadratic equation is positive and so will be having a minimum value.
The parabola is directed downwards if the coefficient of x² is negative and so will be having the maximum value for the function.
Here, coefficient of x² = 2, is positive.
So there will be a minimum value.
The value of [tex]\frac{-b}{2a}[/tex] in the quadratic equation ax² + bx + c, is the x value of the vertex of the parabola.
x = - (-12) / (2 × 2) = 3
∴ Minimum value, y = 2 (3 - 3)² - 4 = -4
Domain of the function will be the set of all real numbers because the function is defined for all real numbers.
The range will be all real numbers ≥ -4, because any values of x in the function does not make the value of the function less than -4.
Hence the minimum value of the function is -4 and the domain and the range of the function is set of all real numbers and all real numbers ≥ -4 respectively.
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Describe a set of data in which it would be most appropriate to use the mode as the measure of central tendency.
Answer:
It would be most appropriate to use the mode for categorical data, such as favorite ice cream flavor. This is because you can't use mean or median for flavors such as chocolate or vanilla, so mode would make the most sense there.
Sam goes to lunch with a friend. The total cost of lunch is $15. Sam leaves $1.50 as a tip. What percent of the total did he tip?
(a) at least how many sets must be printed to be sure of having at least 4 identical subsets on the list?
The number of sets to be printed to ascertain at least 4 identical subset is there on the list when a computer is printing out subsets of a 5 element set is 97.
The total number of subset for a n element set is 2^{n}. Therefore, for a 5 element set is 2^{5} = 32.
Thus to ensure there are at least 4 identical subset, the computer should print 3 times the total number of subsets possible plus 1 additional subset, i.e. 3×32 + 1 = 97.
-- The question is incomplete, the correct question is as follows --
"A computer is printing out subsets of a 5 element set (possibly including the empty set). a. at least how many sets must be printed to be sure of having at least 4 identical subsets on the list?"
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Ariana has 6 posters she wants to hang on the wall. How many different ways
can the posters be arranged in a row?
THANK YOU AND HELP I’m VERY CONFUSED
Answer:
The first one is the answer
A washer and dryer cost a total of $1132. The cost of the washer is three times the cost of the dryer. Find the cost of each item.
Cost of washer:
Cost of dryer:
Answer:
Washer = $849
Dryer = $283
Step-by-step explanation:
Dryer = x
Washer = 3x
3x + x = 1132
Simplify:
4x = 1132
Divide both sides by 4:
x = 283
The dryer costs $283, and since the washer is three times the cost of the dryer, the washer is:
283x3 = 849
Please help, I'm having trouble.
Compared to the graph of y = x graph y = -x/3 is a negative slope
Compared to the graph of y = x graph y = -x/3 intersects the y axis at same point
Compared to the graph of y = x graph y = x - 2 is a parallel line
Compared to the graph of y = x graph y = x - 2 intersects the y axis at 2 units down
How to make the graph comparisonThe two graphs compared are linear function graphs
A linear function consists of functions where the variables has exponents of 1.
The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
definition of variable to suit the problem
y = output variable
m = slope
x = input variable
c = y intercept
y = x
slope = 1
c = 0
y = -x/3
slope = -1/3
c = 0
y = x - 2
slope = 1
equal slopes means the lines are parallel
c = -2 (down 2 units)
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What is the equation of the parabola with focus (1, 6) and directrix y = 1?
An equation of the parabola with focus (1, 6) and directrix y = 1 is: C. y = 1/10(x²) - 1/5(x) + 18/5
How to determine the equation of a parabola?Mathematically, the standard equation of the directrix lines for any parabola is given by:
y = a(x - h)² + 2.
Where:
h and k are the vertex.a is a point.Since the directrix is horizontal, the axis of symmetry would be vertical. Therefore, the equation of this parabola would be modeled by this standard mathematical expression;
(x - h)² = 4p(y - k)
Where:
h = 1
In Mathematics, the focus for either a right or left parabola is modeled by this mathematical expression (h + p, k) while its directrix is modeled by this mathematical expression x = h - p;
k + p = 6
k - p = 1
Solving the set of linear equations simultaneously, we have:
2k = 7
k = 7/2
For the value of p, we have;
p = 6 - k
p = 6 - 7/2
p = 5/2
Substituting the given parameters into the formula, we have;
(x - 1)² = 4(5/2)(y - 7/2)
x² - 2x + 1 = 10(y - 7/2)
x² - 2x + 1 = 10y - 35
10y = x² - 2x + 1 + 35
10y = x² - 2x + 36
y = (x² - 2x + 36)/10
y = x²/10 - x/5 + 18/5
y = 1/10(x²) - 1/5(x) + 18/5
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