The track lap time of the runner will be 3 3/5 minutes.
How to illustrate the information?From the information, the runner has a track lap time of 1 minute while at a run, 4 minutes while at a jog, and 7 minutes while at a walk. If 2/5 of the lap is paced at a run, 1/3 at a jog, and 4/15 at a walk.
The track lap time of the runner will be:
= (2/5 × 1 minute) + (1/3 × 4 minutes) + (4/15 × 7 minutes)
Note that 1 minute = 60 seconds
(2/5 × 1 minute) + (1/3 × 4 minutes) + (4/15 × 7 minutes)
= 24 seconds + 80 seconds + 112 seconds
= 216 seconds
= 3 minutes 36 seconds.
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2. Find two ordered pairs that make the equation – 2x + y = 8 true. Show all work.
Answer:
(0, 8) and (-4, 0)
Step-by-step explanation:
Equation is -2x + y = 8
Manipulate this equation so that it becomes a slope-intercept form of equation
To do this:
Add 2x on both sides
-2x + 2x + y = 2x + 8
y = 2x + 8
Once we have this, 2 points which definitely lie on the line are its x and y intercepts
This is the equation of a line with slope = 2 and x-intercept = 8
x-intercept is y-value when x = 0
We can check by plugging in 0 for x in y = 2x + 8
=> y = 2(0) + 8 = 8
=> Point(0, 8) is one of the ordered pairs
Similarly we can find the x-intercept by setting y = 0 and solving for x
Setting y = 0 in y = 2x + 8
=> 0 = 2x + 8
Switch sides
2x + 8 = 0
Subtract 8 from both sides
2x + 8 - 8 = 0 - 8
2x = -8
Divide both sides by 2
=> 2x/2 = -8/2
x = -4
So (-4, 0) is another point on the line
Two ordered pairs are therefore
(0, 8) and (-4, 0)
The attached graph shows you that it is indeed so
Grant orders a $55 bouquet of flowers to be delivered to his sister. He pays the bill plus a 6.5% sales tax and a 15% tip on the total cost including tax. He also pays a $10 delivery fee that is charged after the tax and tip. How much change does he receive to the nearest cent, if he pays the delivery driver with a $100 bill?
The change that Grant received to the nearest cent after giving the delivery driver with a $100 bill is $ 32.6.
This is a question of percentages.
Given that:-
Price of bouquet of flowers = $ 55
Sales tax % = 6.5 %
Tip % = 15 %
Delivery fee= $10
We have to find the change that Grant received to the nearest cent after giving the delivery driver with a $100 bill.
Sales tax = (6.5/100)*55 = $3.575
$55 + $3.575 = $58.575
Tip = (15/100)*58.575 = $ 8.78625
Total money paid by Grant = 55 + 3.575 + 8.78625 = $ 67.36125 ≈ $ 67.4
Hence,
Change received by Grant = 100 - 67.4 = $ 32.6
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Select the correct answer from each drop-down menu. This graph represents gasoline price trends in New Mexico. and then it First the price of gasoline in New Mexico
We have the following:
We can see that time is located on the x axis and the price of gasoline is located on y, we can conclude that in both periods the price increases, but in the first it increases slowly and in the second it increases quickly
Therefore, the answer is:
First, the price of gasoline in New mexico increases slowly, and then it increases quickly
Write the sentence as an equation.
40 is equal to 208 subtracted from the product of 184 and j
Type a slash (/) if you want to use a division sign.
Answer:
40 = (184*j) - 208 or 40 = 184j - 208
If x2=16, find x3?
If x3=125, find x2
Answer:balls
Step-by-step explanation:your mom
Find the constant of variation and the degree. Is it a power function? (See pictures)
Answer:
The given function is a power function.
[tex]\textsf{The constant of variation is $\sqrt[3]{\dfrac{7}{5}}$}.[/tex]
[tex]\textsf{The power is $\dfrac{1}{3}$}.[/tex]
Step-by-step explanation:
Power function
Any function that can be written in the form:
[tex]\boxed{f(x)=k \cdot x^a}[/tex]
where:
a is the power.k is the constant of variation.Given function:
[tex]f(x)=\sqrt[3]{\dfrac{7x}{5}}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}:[/tex]
[tex]f(x)=\sqrt[3]{\dfrac{7}{5}\cdot x}[/tex]
[tex]\implies f(x)=\sqrt[3]{\dfrac{7}{5}} \cdot \sqrt[3]{x}[/tex]
[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]
[tex]\implies f(x)=\sqrt[3]{\dfrac{7}{5}} \cdot x^{\frac{1}{3}}[/tex]
Therefore, the given function is a power function.
[tex]\textsf{The constant of variation is $\sqrt[3]{\dfrac{7}{5}}$}.[/tex]
[tex]\textsf{The power is $\dfrac{1}{3}$}.[/tex]
an employer pays 22 for 2 hours. use the ratio table to determine how much she chargesfor 5 hours
The employer will charge $55 for 5 hours
How to calculate the amount charged for 5 hours ?The first step is to calculate the amount charged for an hour
22= 2
x= 1
cross multiply
2x= 22
x= 22/2
x= 11
The amount charged for 5 hours can be calculated as follows
11= 1
y= 5
cross multiply
y= 55
Hence $55 will be charged for 5 hours
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simplify the expression (-6)^-4 using positive exponents
there u gooooooooooooooooooooooooooooooooo
In a running competition, a bronze, silver and gold medal must be given to the top
three girls and top three boys. If 15 boys and 11 girls are competing, how many
different ways could the six medals possibly be given out?
Answer:
2702700
Step-by-step explanation:
Hi there ,
Given:
In a running competition, a bronze, silver and gold medal must be given to the top three girls and three boys. If 15 boys and 11 girls are competing.
To find:
How many different ways could the six medals possible be given out?
Explanation:
As given,
The number of boys competing in a competition = 15
The number of girls competing in a competition = 11
Three medals are given to top three girls and three medals are given to top three boys.
(I have given the rest of the answer in the images below :-)
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A fellow mate
Cheers !
Write the following comparison as a ratio reduced to lowest terms.
114 hours to 13 days
The ratio of 114 hours to 13 days is 19:52.
How to calculate the ratio?It should be noted that ratio is simply used to show the comparison between two things that are illustrated.
In this case, we want to calculate the ratio of 114 hours to 13 days. It should be noted that 24 hours make one day. Therefore, 13 days will be:
= 13 × 24 = 312 hours.
The ratio of 114 hours to 13 days will be:
= 114 / 312
= 19 / 52
The ratio is 19:52.
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Question
Solve: 9(x - 1) - 13x = -3(x + 5).
Provide your answer below:
X =
Answer:
x=6
Step-by-step explanation:
[tex]9(x - 1) - 13x = - 3(x + 5)[/tex]
[tex]9x - 9 - 13x = - 3x - 15[/tex]
[tex]9x - 13x + 3x = - 15 + 9[/tex]
[tex] - x = - 6[/tex]
[tex] \frac{ - \times }{ -1 } = \frac{ - 6}{ - 1} [/tex]
[tex]x = 6[/tex]
Please help I’ll mark you as brainliest if correct!!
Answer:
4 6 3
_ 1 3 9
________
3 2 4
Step-by-step explanation:
you think of of a number
or use logic to answer it
jjjjjjjjjjjjjjjjjjjjjjjjj
To solve this problem we will use the following property of triangles:
So if we are given the angles a and b of a triangle, the third side c, must be:1) The angles are a =
[tex]\begin{gathered} a+b+c=180^{\circ}, \\ c=180^{\circ}-a-b\text{.} \end{gathered}[/tex][tex]c=180^{\circ}-48^{\circ}-62^{\circ}=70^{\circ}\text{.}[/tex]
i. 70°
2) a = 48° and b = 62°, so we have:
[tex]c=180^{\circ}-71^{\circ}-36^{\circ}=73^{\circ}.[/tex]h. 73°
3) a = 41° and b = 86°, so we have:
[tex]c=180^{\circ}-41^{\circ}-86^{\circ}=53^{\circ}.[/tex]j. 53°
4) a = 61° and b = 88°, so we have:
[tex]c=180^{\circ}-61^{\circ}-88^{\circ}=31^{\circ}.[/tex]d. 31°
5) a = 55° and b = 92°, so we have:
[tex]c=180^{\circ}-55^{\circ}-92^{\circ}=33^{\circ}.[/tex]b. 33°
Answers
0. j. 70°
,1. h. 73°
,2. j. 53°
,3. d. 31°
,4. b. 33°
11. A 20 foot ladder is leaned against a wall. The base of the ladder is 10 feet from the wall. How much longer is the ladder than the height of the wall? Round to the nearest hundredth. You may use a calculator. Hint: draw a right triangle, label the sides appropriately, and use the pythagorean theorem.
Okay so draw a diagram with a ladder leaning against a wall and draw the ground now label the diagram take the hypotenuse is ladder and the base is distance between the ladder and the wall while the perpendicular is the wall
As we know hypo=√perpendicular^2+base^2 if we want to finder the p(perpendicular) the formula changes to p=√hypo^2-base^2 put the no in the places of the equation It should look something like this p=√20^2-10^2 use calculate to solve the answer should be 17. 32
Data
Given;
Hypo(h)= 20
Base(b)= 10
Required;
Perpendicular (p)=
Solution
As we know
hypo=√perpendicular^2+base^2
by changing the formula to find p
p=√hypo^2-b^2 -----eqi
by putting the values in eq i
p=√20^2-10^2
p=17.32
On January 1, a company purchased new furniture ata cost of $26,000. The furniture is estimated to have a useful life of 5 years and a salvage value of $3200
If on January 1, a company purchased new furniture at a cost of $26,000. The furniture is estimated to have a useful life of 5 years and a salvage value of $3200. The book value of the furniture on December 31 of the first year is: $21,440.
Book valueGiven data:
Cost = $26,000
Useful life = 5 years
Salvage value = $3,200
First step is to calculate the depreciation expenses:
Particular Amount
Cost $26,000
Less: Salvage value ($3,200)
Net cost (a) $22,800
Useful life (b) 5
Depreciation expenses (a/b) $4,560
($22,800 / 5 years)
Second step is to compute the book value of furniture on 31 Dec of first year:
To determine the book value we would have to deduct the depreciation expenses from the cost.
Particular Amount
Cost of an furniture $26,000
Less: Depreciation ($4,560)
Book value $21,440
Therefore we can conclude that the book value is the amount of $21,440.
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The complete question is:
On January 1, a company purchased new furniture ata cost of $26,000. The furniture is estimated to have a useful life of 5 years and a salvage value of $3200The company uses the straight-line method of depreciation. What is the book value of the furniture on December 31 of the first year?
Which equation represents a line parallel to the line of the one shown on the graph
Line goes through -2,0 and 0,-4
Answer:
A
Step-by-step explanation:
The Gift Basket Store had the following premade gift baskets containing the following combinations in stock.CookiesMugsCandyTotalCoffee57820Tea73313TOTAL12101133Choose 1 basket at random. Find the probability that it contains cookies given that it contains coffee (to three places after the decimal point).
We are asked to find the probability that it contains cookies given that it contains coffee.
This is called conditional probability and is given by
[tex]P(A|B)=\frac{P(A\: and\: B)}{P(B)}[/tex]This means that the probability of event A given that event B has occurred.
For the given case, it becomes
[tex]P(Cookies|Coffee)=\frac{P(Cookies\: \: and\: \: Coffee)}{P(Coffee)}[/tex]The probability P(Cookies and Coffee) is the intersection of the column "Cookies" and the row "Coffee" divided by the grand total.
[tex]P(Cookies\: \: and\: \: Coffee)=\frac{5}{33}[/tex]The probability P(Coffee) is the row total of the row "Coffee" divided by the grand total.
[tex]P(Coffee)=\frac{20}{33}[/tex]Finally, the conditional probability is
[tex]P(Cookies|Coffee)=\frac{P(Cookies\: \: and\: \: Coffee)}{P(Coffee)}=\frac{\frac{5}{33}}{\frac{20}{33}}=\frac{5}{33}\cdot\frac{33}{20}=\frac{5}{20}=\frac{1}{4}=0.25[/tex]Therefore, the probability that it contains cookies given that it contains coffee is 0.25
Hello! I need some help with this homework question posted below. Q17
To solve an inequality, we need to isolate the value of x, and to do so we will perform a series of calculations in such a way that it remains the inequality unchanged, or at least still true.
To do so, we will perform first a sum of 2x to both sides of it, as follows:
[tex]\begin{gathered} 7-2x+2x\ge3+2x \\ 7\ge3+2x \end{gathered}[/tex]Now, we subtract 3 from both sides:
[tex]\begin{gathered} 7-3\ge3+2x-3 \\ 4\ge2x \end{gathered}[/tex]To finish it, we divide both sides by 2:
[tex]\begin{gathered} \frac{4}{2}\ge\frac{2x}{2} \\ \\ 2\ge x \end{gathered}[/tex]In another way, we can express the following:
[tex]\mleft\lbrace x|x\le2\mright\rbrace or(-\infty,2\rbrack[/tex]It means that the solution is option B.
To solve the second part, we need a filled line that comes from the negative infinity and goes until 2, but it must be including the number 2, and for this reason, the correct answer in the second part is:
D.
Three sides of a quadrilateral are the same length, q. The length of the fourth side is 7 inches. The perimeter of the quadrilateral is 40 inches. Write an equation that represents the situation.
The equation that represent the situation of the quadrilateral is 40 = 3q + 7
How to write equation to represent the side of a quadrilateral?A quadrilateral is a polygon with 4 sides.
Three sides of a quadrilateral are the same length, q.
The length of the fourth side is 7 inches.
The perimeter of the quadrilateral is 40 inches.
The equation to represent the situation is as follows:
perimeter of a figure is the sum of the whole sides.
Hence,
perimeter of the quadrilateral = q + q + q + 7
perimeter of the quadrilateral = 3q + 7
Therefore,
40 = 3q + 7
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Answer:
3q + 7 = 40
Step-by-step explanation:
I got this lesson
The product of seven and a number, increased by three, is equal to twice the number, subtracted from 39. Find the number
It is given that the product of 7 and a number, increased by 3, is equal to twice the number, subtracted from 39.
It is required to find the number.
To do this, write the statement as an algebraic statement.
Let the number be x.
The product of 7 and a number is:
[tex]7x[/tex]The product of 7 and a number increased by 3 is:
[tex]7x+3[/tex]Twice the number is:
[tex]2x[/tex]Twice the number subtracted from 39 is:
[tex]39-2x[/tex]Since it is given that these expressions are equal, it follows that:
[tex]7x+3=39-2x[/tex]Solve the resulting equation for x:
[tex]\begin{gathered} \text{ Collect like terms:} \\ \Rightarrow7x+2x=39-3 \\ \Rightarrow9x=36 \\ \text{ Divide both sides by }9: \\ \Rightarrow\frac{9x}{9}=\frac{36}{9} \\ \Rightarrow x=4 \end{gathered}[/tex]The number is 4.
Sets B and G are defined as follows. B=(-2, 2, 3, 5) G=(-1,0,2,4,7) - Answer each part below. Write your answer in roster form or as (a) Find the intersection of B and G. B n G=0 (b) Find the union of Band G. BU G=0 X
Answer
B n G = {2}
B u G = {-2, -1 , 0 , 2, 3, 4, 5, 7)
Step-by-step explanation:
Given the following two sets
B = { -2, 2, 3, 5}
G = { -1, 0, 2, 4, 7}
Part A
Find the intersection of B and G
The intersection of two sets is defined as the set of all the elements in set A that is also present in set G
Hence, the set of elements that is present in set B and set G is 2
Mathematically, B n G = {2}
Part B
Find the union of set B and set G
The union of two sets is a set containing all elements that are in both sets B and G
B u G = {-2, -1 , 0 , 2, 3, 4, 5, 7)
A coach has 12 jerseys. He buys 2 sets of jerseys. Each has 10 jerseys. How many jerseys does he have now?
Total number of jerseys he have now is 32 jerseys.
A coach has 12 jerseys in beginning. Now, he buys 2 sets of jerseys.
Each set of jerseys have 10 jerseys.
2 set of jerseys have 20 jerseys.
Using unitary method this can also be written as,
1 set ----------------> 10 jerseys
2set ----------------> 20 jerseys
So, total of 20 jerseys are present in 2 sets of jerseys.
Total number of jerseys he have now = 12 jerseys + jerseys in two sets
Total number of jerseys he have now = 12 jerseys + 20 jerseys = 32 jerseys
So we can write, he have total of 32 jerseys now.
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Suppose that the relation H is defined as follows.
H={(6, q), (7, p), (0, 6), (7, n)}
Give the domain and range of H.
Write your answers using set notation.
domain =
range =
Answer:
Domain = {0, 6, 7}Range = {6, n, p, q}Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
The perimeter of the rectangle below is 104 units. Find the length of side AD.
Write your answer without variables.
D
52-2
4z
C
B
AD =
0
HELP PLEASE!
Answer: 28
Step-by-step explanation:
Using the formula for the perimeter of a rectangle,
[tex]2(5z-2+4z)=104\\\\9z-2=52\\\\9z=54\\\\z=6\\\\\therefore AD=5(6)-2-28[/tex]
The table shows the distance a small
motor scooter can travel using one gallon
of gasoline. Complete the table to find the
number of miles the scooter can travel for
other amounts of gasoline.
Answer:
0.1 gallons = 11.8 miles
10 gallons - 1,180 miles
Step-by-step explanation:
Select the postulate that specifies the minimum number of points in space.
Postulate 1: A line contains at least two points.
Postulate 1a: A plane contains at least three points not all on one line.
Postulate 1b: Space contains at least four points not all on one plane.
Postulate 2: Through any two different points, exactly one line exists.
•
Postulate 3: Through any three points that are not one line, exactly one plane exists.
Postulate 4: If two points a lie in a plane, the line containing them lies in that plane.
Postulate 5: If two planes intersect, then their intersection is a line.
The postulate specifies the minimum number of points in space is, Postulate 1b: Space contains at least four points not all on one plane.
A postulate is an assumption or a claim that is made without providing any supporting evidence. The fundamental claims that are used to support other claims known as theorems are known as postulates. Once a theorem is established, it can be applied to the establishment of other theorems.
By examining each postulate, we may effectively respond to this query.
Postulate 1a: establishes that if G and H are distinct points on plane R, then R contains a third point rather than GH.
Postulate (1b): establishes the bare minimum within a space.
Postulate 1: This describes a line segment with two points, say A and B.
Postulate 2: It asserts that two points determine a line.
Postulate 3: This one explains why, for example, if one leg is shorter than the other three, a table with four legs would wobble, but a table with three legs would not wobble.
Postulate 4: When points A and B are in Q, it is confirmed that AB is in plane Q.
Postulate 5: It concerns two planes.
According to the data presented above, the appropriate response to our query is:
Postulate 1b: Space contains at least four points not all on one plane.
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Find the indicated z score. The graph depicts the standard normal distribution with
mean 0 and standard deviation 1.
The indicated z score is
(Round to two decimal places as needed.)
Z 0
0.8289
Using the normal distribution, it is found that the indicated z-score is Z = 1.08. A normal distribution with a mean of zero and a standard deviation of one is known as the standard normal distribution.
What is meant by standard normal distribution?A normal distribution with a mean of zero and a standard deviation of one is known as the standard normal distribution. The standard normal distribution is centered at zero, and the standard deviation indicates how much a specific measurement deviates from the mean.
While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
The z-score of a measure X in a normal distribution with mean and standard deviation is given by:
z = (x-μ)/σ,
It counts the number of standard deviations the value deviates from the mean.
We look at the z-score table after determining the z-score to determine the p-value, which is the percentile of X.
We want Z in this problem to have a p-value of 0.8599, thus Z = 1.08.
The complete question is,
Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. Shaded area is 0.8599.
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need help with this one
Applying the relations given, considering equivalent angles, the trigonometric measures for the angles are given as follows:
sin(240º) = -sqrt(3)/2.cos(225º) = -sqrt(2)/2.tan(225º) = 1.How to find the sine of 240º?The sine of 240º can be written as follows:
sin(240º) = sin(180º + 60º).
Applying the first relation given on the second line, we have that:
sin(180º + 60º) = -sin(60º)
It is known that sin(60º) = sqrt(3)/2, hence the sine of 240º is given as follows:
sin(240º) = -sin(60º) = -sqrt(3)/2.
How to find the cosine of 225º?The cosine of 225º can be written as follows:
cos(225º) = cos(180º + 45º).
Applying the second relation given on the second line, we have that:
cos(180º + 45º) = -cos(45º)
It is known that cos(45º) = sqrt(2)/2, hence:
cos(225º) = -cos(45º) = -sqrt(2)/2.
How to find the tangent of 225º?The tangent of 225º can be written as follows:
tan(225º) = tan (180º + 45º).
Applying the third relation given on the second line, we have that:
tan(180º + 45º) = tan(45º)
It is known that tan(45º) = 1, hence:
tan(225º) = tan(45º) = 1.
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please help 4. What is the loan payment on a fixed-rate/fixed-term mortgage loan of $100,000 at 8% for 30 years? (LO 7-3).
the loan payment on a fixed term mortgage loan of $100,000 at 8% for 30 years will be $ 340,000.
Principal amount = $ 100,000
Interest rate = 8 %
Time period = 30 years.
Now, the interest is simple interest as it is a fixed rate/ fixed term mortgage.
So, the interest will be:
Simple interest = p r t / 100
SI = 100,000 × 8 × 30 / 100
SI = $ 240,000
Amount will be:
A = $100,000 + $ 240,000
A = $ 340,000
Therefore, we get that, the loan payment on a fixed term mortgage loan of $100,000 at 8% for 30 years will be $ 340,000.
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Please help I’ll mark you as brainliest if correct!!
Answer:
A) 384, 216
b) 14575
Step-by-step explanation:
A) to find the missing values you do 3-1 which gives you 2.
here is a trick!
then you take your answer (in this case it is 216) and add it to your second row (168) to get the first row's answer (384). so you are basically going backward.
B) here you do the same thing go backward!
5967+8608 = 14575
then if you want you can double-check by subtracting them.
I hope this helps!