1. How does someone find the equation of a boundary line?2. How does someone determine if the points on the boundary line are solutions to the inequality?
Answers
Answer:
D: Find the boundary line equation by replacing the inequality sign with =
Explanation:
Part 1
Given any inequality, say:
[tex]yTo find the equation of the boundary line, replace the inequality sign with the equality(=) sign. This gives the equation of the boundary line to the inequality above as:[tex]y=x+5[/tex]The correct choice is D.
Part 2
When drawing the boundary line:
• Use a solid line for the inequalities: ≤ or ≥
,• Use a broken line for the inequalities: < or >
If the boundary line is solid, the points on the boundary line are solutions to the inequality, otherwise, they are not.
Related Questions
A club consists of 15 people including Ali, Kendra,
Ted, Alice, Marie, Dan, Linda and Frank. From the 15
members, a president, vice president and treasurer
will be selected at random. An advisory committee
of 5 other individuals will also be selected at
random.
Determine the probability that Ali is selected
president, Kendra is selected vice president, Ted is
named the treasurer and the other 5 individuals
named form the advisory committee.
Answers
The required probability of the random event is 0.273.
The probability is estimated by dividing the total number of possible outcomes by the number of possible ways the event could occur.The probability and chances of that happening are two distinct ideas. Odds are calculated by dividing the probability of an event by the likelihood that it won't.Keep in mind that a president, vice president, and treasurer will be chosen at random from the 15 members. The number of options to choose from to fill these spots is thus:
[tex]_{15}P_3=\frac{15!}{(15-3)!} =2730[/tex].
The required probability of the random event is 0.273.
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A survey that 73% of adults need correction (eyeglasses, contacts, surgery, etc,) for their eyesight. If 20 adults are randomly selected, find the probability that no more than 1 of them need core for their eyesight. Is 1 a significantly low number of adults requiring eyesight correction?
Answers
The odds of there being less than one of them who needs glasses are extremely near to zero, the number one is considered to be a very low quantity.
This is further explained below.
What is a Binomial?Generally, Let X be the number of adults among 16 that needs correction. Then X ~ Binomial(n = 20, p = 0.73)
The probability that no more than 1 of them needs correction for their eyesight = P(X \le 1)
= P(X = 0) + P(X = 1)
[tex]= ^{20}C_0 * 0.73^0 * (1 - 0.73)^{20-0} + ^{20}C_1 * 0.73 * (1 - 0.73)^{20-1}[/tex]
= 2.33465379×10−10
= 0.000
The likelihood that no more than 1 of them require eyeglasses is close to 0, therefore 1 is a very low number.
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help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer:
Step-by-step explanation: get smarter
A company purchased a new truck at a cost of $72,000 on July 1, 2019. The truck is estimated to have a useful life of 5 years and a salvage value of $2,000. The company uses the straight-line method of depreciation. The book value of the truck on December 31, 2019 is:
Answers
A company purchased a new truck, then the book value of the truck on December 31, 2019 is $51,000, because the company uses the straight-line method of depreciation.
A company purchased a new truck at a cost = $72,000 on July 1, 2019.
Estimated to have a useful life time = 5 years
A salvage value = $2,000
The formula for depreciation expense, using straight line method is;
What is a depreciation expense :Depreciation expense is the cost of an asset that has been depreciated for a single period, and shows how much of the asset's value has been used up in that year. Accumulated depreciation is the total amount of depreciation expense that has been allocated for an asset since the asset was put into use.
Based on the given conditions, formulate :
= (Cost - Salvage value) / life time (Equation-1)
We consider,
Cost = $72,000
Salvage value = $2,000
Life time = 5 years
We can substitute this values in equation-1,
So,
We can write,
= ($72,000 - $2,000) / 5
= $70,000 / 5
= $14,000.
Therefore,
The book value of the truck on December 31, 2019 would be;
= (cost - book value x (difference of year + difference of months/total months))
= $72,000 - $14,000 × (1 + 6/12)
= $72,000 - $14,000 x (1+1/2)
= $72,000 - $14,000 x (1+0.5)
= $72,000 - $14,000 x 1.5
= $72,000 - $21000
= $51,000
Note that we arrived at the value of 6 because July to December is 6 months.
Therefore,
The book value of the truck on December 31, 2019 is $51,000, because the company uses the straight-line method of depreciation.
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commercials is a average of 16 minutes and a standard deviation equals 2.1 minutes. After watching the chanel for a hour randomly you observe the amount of commercials equals to 19 minutes Find the z score for the amount of commercials, round 2 decimals
Answers
To answer this question we will use the following formula to compute the z-score:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma}, \\ \text{where x is the observed value, }\mu\text{ is the mean, and }\sigma\text{ is the standard deviation.} \end{gathered}[/tex]Substituting x=19min, μ=16min, and σ=2.1min we get:
[tex]z=\frac{19\min -16\min }{2.1\min }\text{.}[/tex]Simplifying the above result we get:
[tex]z=\frac{3}{2.1}=\frac{10}{7}\approx1.43.[/tex]Answer: 1.43.
What is the volume of the following prism?this is a prism with a triangular base. The width of the triangle is 6 meters and the height of the triangle is 3 meters. The height of the prism is 7 meters.A. 63 m³B. 189 m³C. 42 m³D. 126 m³
Answers
Answer
A. 63 m³
Explanation:
The volume of the prism is equal to
V = Bh
Where B is the area of the base and h is the height of the prism.
In this case, the base is triangular, so the area of the base is equal to
[tex]\begin{gathered} B=\frac{base\cdot height}{2} \\ \\ B=\frac{6\text{ m}\cdot3m}{2} \\ \\ B=\frac{18\text{ m}^2}{2} \\ \\ B=9\text{ m}^2 \end{gathered}[/tex]Then, the volume of the prism is equal to
V = (9 m²)(7 m)
V = 63 m³
Therefore, the answer is
A. 63 m³
how do you find slope?1?!
Answers
Answer:
Pick two points on the line and determine their coordinates.
Answer:
Step-by-step explanation:
Rise over Run
1. Find 2 points
2. Count the Y distance .then the X distance
3.Y/X
EX. (0,0) and (4,4)
0 to 4 of the y-axis is 4
0 to 4 on the x-axis is 4
4/4= 1 slope 1
find an equation of the line described. write the equation in slope intercept form when possible slope 1, through (-9,4) the equation of the line is y= _
Answers
The expression for the slope intersept form of a line is,
[tex]y-y_1=m\cdot(x-x_1)[/tex]Put the values implies,
[tex]\begin{gathered} y-4=1(x-(-9)) \\ y-4=x+9 \\ y=x+13 \end{gathered}[/tex]Therefore, the slope intersept form is y=x+13.
Suppose you have an experiment where you toss a fair coin 3 time you didn't count the number of heads observe over those 3 tosses use this experiment to address each of the falling question round solution to 3 destiny places
Answers
a) In order to complete the table for the probability distribution for the variable X:
X = the number of heads observed when you flip a coin three times,
b) we create a list of all the possible outcomes. We use the notation: H = heads, T = tails.
The possible outcomes after tossing the coin three times are:
[tex]HHH,HHT,HTH,THH,TTT,TTH,THT,HTT[/tex]From the list above we see that we have 8 equiprobable events. Now, we classify the events according to the number of Heads included.
- Events with x = #H = 0: TTT
- Events with x = #H = 1: HTT, THT, TTH
- Events with x = #H = 2: HHT, HTH, THH
- Events with x = #H = 3: HHH
Using the data above we compute the probabilities for each x, we simply compute the quotient between the number of outcomes of each case by N = 8 (the total number of possible outcomes):
[tex]\begin{gathered} P\mleft(x=0\mright)=\frac{1}{8}=0.125 \\ P(x=1)=\frac{3}{8}=0.375 \\ P(x=2)=\frac{3}{8}=0.375 \\ P(x=3)=\frac{1}{8}=0.125 \end{gathered}[/tex]c) Shape of the probability disribution. The probability distribution of x is: Symmetric.
d) Using the data above, we can compute the mean number of heads for the distribution:
[tex]\begin{gathered} E(x)=\sum ^3_{n=0}x_n\cdot P(x_n_{}) \\ E(x)=0\cdot P(x=0)+1\cdot P(x=1)+2\cdot P(x=2)+3\cdot P(x=3) \\ E(x)=0+1\cdot0.375+2\cdot0.375+3\cdot0.125 \\ E(x)=\frac{3}{2}=1.5 \end{gathered}[/tex]So the mean number of heads for this distribution is 1.5
Angel Sanchez has 6 books on a shelf; 2 mysteries, 3 science fiction books, and 1 biography. Determine the probability of each situationla) Selecting one mystery and then one science fiction, with replacementb) Selecting one mystery and then one science fiction, without replacementa) The probability of selecting one mystery and then one science fiction, with replacement is
Answers
It is given that there are 6 books in total, with 2 mysteries, 3 science fiction books, and 1 biography.
Recall that the probability of an event is the ratio of the number of favorable outcomes to the total number of possible outcomes.
(a) It is required to find the probability of selecting one mystery and then one science fiction, with replacement.
The probability of selecting one mystery is:
[tex]P(M)=\frac{1}{6}[/tex]The probability of selecting one science fiction next with replacement is:
[tex]P(S)=\frac{1}{6}[/tex]The probability of independent events is the product of their respective probabilities.
Hence, the probability of selecting one mystery and then one science fiction, with replacement is:
[tex]P(M)\cdot P(S)=\frac{1}{6}\cdot\frac{1}{6}=\frac{1}{36}[/tex]The answer is 1/36.(b) It is required to find the probability of selecting one mystery and then one science fiction, without replacement.
Since there is no replacement, the probability of selecting one science fiction next without replacement is:
[tex]P(S)=\frac{1}{6-1}=\frac{1}{5}[/tex]Hence, the probability of selecting one mystery and then one science fiction, without replacement is:
[tex]P(M)\cdot P(S)=\frac{1}{6}\cdot\frac{1}{5}=\frac{1}{30}[/tex]The answer is 1/30.Sal's pizzeria charges
$414 for 23 pizzas. What
does the pizzeria charge
for one pizza?
Answers
Answer: 18 Dollars
Step-by-step explanation:
Divide 414 by 23 to get the cost per pizza. Which in this case is 18 dollars
Calculus early transcendental functions. Solve the equation.. use logs and round to 2 decimal places
Answers
This becomes:
[tex]\begin{gathered} \text{Log}_8(7(\frac{2x}{5}+9))=2\text{Log}_88 \\ \text{Log}_8(\frac{14x}{5}+63)=\text{Log}_88^2 \\ \frac{14x}{5}+63=8^2 \end{gathered}[/tex][tex]\begin{gathered} \frac{14x}{5}=8^2-63 \\ \frac{14x}{5}=64-63 \\ \frac{14x}{5}=1 \\ \text{corss}-\text{multiply} \\ 14x=5 \\ x=\frac{5}{14} \end{gathered}[/tex]HELP PLEASEEEEEEEEEEE!! ILL MARK BRAINLIEST
Answers
Answer:no 3*little5 is not same as 5*little3
Step-by-step explanation:3*little5 is 3x3x3x3x3,5*little3 is 5x5x5
Answer:
They are DIFFERENT.
Step-by-step explanation:
3^5 (exponential form) means
3×3×3×3×3 (this is the repeated multiplication)
So the standard form is 243.
The other term is:
exponential: 5^3
rep mult.: 5×5×5
standard form: 125
243 NotEqual 125
They are not the same. 3^5 and 5^3 are different.
help 50 points need help math 7
Answers
Answer:
-5v + 6.2w - 3
Step-by-step explanation:
- (5v - 6.2w) -3
= -5v + 6.2w - 3
In ASTU, SU is extended through point U to point V, m/STU = (3x + 14)°,
m/UST = (2x + 12)°, and m/TUV = (7x+6)°. What is the value of x?
Answers
By applying the exterior angle property, the value of x is equal to 5.
What is the exterior angle property?The exterior angle property can be defined as a theorem which states that the measure of an exterior angle in a triangle is equal in magnitude to the sum of the measures of the two remote or opposite interior angles of that triangle.
How to determine the value of x?In order to determine the value of x in triangle STU (ΔSTU), we would have to apply exterior angle property.
Mathematically, the exterior angle property can be used to model triangle STU (ΔSTU) and this is given by:
m<TUV = m<STU + m<UST
Substituting the given parameters into the formula, we have;
(7x+6)° = (3x + 14)° + (2x + 12)°
7x + 6 = 5x + 16
7x - 5x = 16 - 6
2x = 10
x = 10/2
x = 5.
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The following information is from Madison Corporation's accounting records for May. Check No. 3269 was returned as a double payment and voided. Checks that have not cleared the bank include No. 3252, No. 3260, and series No. 3275–3278. Check No. Amount Check No. Amount 3247 $32.64 3263 $24.87 3248 400.00 3264 45.00 3249 309.22 3265 33.78 3250 256.00 3266 756.77 3251 3,212.17 3267 84.34 3252 56.89 3268 789.00 3253 98.02 3269 48.90 3254 47.55 3270 34.41 3255 1,124.77 3271 872.00 3256 250.00 3272 22.00 3257 68.00 3273 562.38 3258 215.56 3274 512.00 3259 38.55 3275 603.50 3260 92.65 3276 67.00 3261 44.61 3277 301.61 3262 72.96 3278 47.88 In addition to the above list of checks, Madison had Check No. 2264 for $32.98 and Check No. 2655 for $45.99 outstanding previously that have not cleared. Question Content Area 1. Create an outstanding checks list for Madison at the end of May. Round your answers to two decimal places.
Answers
The outstanding checks list for Madison at the end of May shows a total of $1,169.53, including the following checks and their amounts:
Check No. Amount
3252 56.89
3260 92.65
3275 603.50
3276 67.00
3277 301.61
3278 47.88.
What are outstanding checks?Outstanding checks are checks issued by Madison to its suppliers of services and goods that have not been cleared at the bank.
Perhaps, the payees have not submitted or presented them for payment.
Issued Checks:Check No. Amount
3247 $32.64
3263 $24.87
3248 400.00
3264 45.00
3249 309.22
3265 33.78
3250 256.00
3266 756.77
3251 3,212.17
3267 84.34
3252 56.89
3268 789.00
3253 98.02
3269 48.90
3254 47.55
3270 34.41
3255 1,124.77
3271 872.00
3256 250.00
3272 22.00
3257 68.00
3273 562.38
3258 215.56
3274 512.00
3259 38.55
3275 603.50
3260 92.65
3276 67.00
3261 44.61
3277 301.61
3262 72.96
3278 47.88
Outstanding Checks:Check No. Amount
3252 56.89
3260 92.65
3275 603.50
3276 67.00
3277 301.61
3278 47.88
Total $1,169.53
Thus, the list of outstanding checks totals $1,169.53.
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A. 1/3 x +y=72x + 6y = 12Questions What’s the slope Y intercept?Number of solutions?
Answers
To identify the slope (m) and y-intercept (b) you write each equation in slope intercept form by solving for y:
[tex]y=mx+b[/tex]First equation:
Substract 1/3 x in both sides of the equation:
[tex]\begin{gathered} \frac{1}{3}x-\frac{1}{3}x+y=-\frac{1}{3}x+7 \\ \\ \\ y=-\frac{1}{3}x+7 \end{gathered}[/tex]Slope: -1/3
Y-intercept: 7
Second equation:
Substract 2x in both sides o
[tex]undefined[/tex]in the triangles below, m
Answers
In the given triangles,
∠B = ∠A
∠T = ∠M
Since, two angles of a triangle are equal, the third angle will also be equal.
Also, ΔLBT is similar to ΔHAM ........(by Angle - Angle similarity)
Now,
⇒ LB/HA = BT/AM = LT/HM ..........(Sides of similar triangles are proportional)
⇒ LB/HA = BT/AM
⇒ 4/HA = 6/10
⇒ 10 x 4 = HA x 6
⇒ HA = 40/6
⇒ HA = 20/3
⇒ HA = 6 2/3
What are Similar Triangles?Triangles that are similar in shape but differ in size are known as similar triangles. Examples of related objects are all equilateral triangles and squares with any side length. To put it another way, if two triangles are comparable, then their corresponding angles and sides are congruent and equal in size. Triangle resemblance is shown by the symbol ~ in this case.It is possible to prove that the corresponding sides of two triangles with congruent angles (also known as equiangular triangles) are proportionate. The AAA Similarity Theorem refers to this.Numerous synthetic (coordinate-free) Euclidean geometry proofs are based on similar triangles.The angle bisector theorem, geometric mean theorem, Menelaus' theorem, and Pythagorean theorem are only a few examples of basic conclusions that can be proven in this fashion. The fundamentals of right triangle trigonometry are also provided by similar triangles.
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Tom deposits $5,600 into a savings account. The simple interest rate for the account is 9.5%. If Tom does not withdraw any money from the account, how much money will be in the account after 3 years?
Answers
The amount of money in the account of Tom after 3 years with simple interest of 9.5 % is $6135.
What is simple interest?
Calculating the amount of interest that will be charged on a loan can be done quickly and easily using the simple interest formula. To calculate the simple interest, we need to multiply the principle amount, the number of days between payments (in years), and the interest rate (in decimals).
The formula to calculate Simple Interest is:
[tex]S. I. = P \times I \times T[/tex]
Here, P = Principal amount, I = interest rate (in decimals), T = time duration (in years).
putting the values from question:
[tex]S. I. = 5600 \times 0.095 \times 3[/tex]
Simple Interest = 535
The money in the account will be the sum of principal amount and the simple interest.
Final amount = Principal amount + Simple Interest.
A = 5600 + 535
A = 6135
Therefore, the money in the account after 3 years is $6135 .
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Solve this system of equations byusing the elimination method.3x + 4y = 4-X – 3y = 7=\וז ו7ro
Answers
Given:
System of equation is given as
[tex]\begin{gathered} 3x+4y=4 \\ -x-3y=7 \end{gathered}[/tex]Required:
Solve system of equation by using the method elimination.
Explanation:
By using the elimination method
we multiply second equation with 3 and then add in first equation
because by doing this process we eliminate the x
[tex]\begin{gathered} 3x+4y+3(-x-3y)=4+3*7 \\ 3x+4y-3x-9y=4+21 \\ -5y=25 \\ y=-5 \end{gathered}[/tex]now put the value of y in first equation
[tex]\begin{gathered} 3x+4(-5)=4 \\ 3x-20=4 \\ 3x=20+4 \\ 3x=24 \\ x=8 \end{gathered}[/tex]Final answer:
Solution of given system of equation is (8,-5)
Use the given conditions to write an equation for the line in point slope form and slope intercept form. Passing through (-2,1) and parallel to the line whose equation is x-3y=5
Answers
The given point is (-2,1) and the given line is x-3y=5.
The slope of the given line can be determined as,
[tex]m=-\frac{1}{-3}=\frac{1}{3}[/tex]The equation of the line which is parallel to the given line will have the same slope.
Thus, the equation of the new line passing through (-2,1) can be determined as,
[tex]\begin{gathered} \frac{y-1}{x-(-2)}=\frac{1}{3} \\ 3(y-1)=x+2 \\ 3y-3=x+2 \\ 3y=x+5 \\ y=\frac{x}{3}+\frac{5}{3} \end{gathered}[/tex]Thus, the equation of the line in slope intercept form is y=x/3+5/3.
The equation of the line in the point slope form can be determined as,
[tex]\begin{gathered} (y-1)=\frac{1}{3}(x-(-2) \\ (y-1)=\frac{1}{3}(x+2) \end{gathered}[/tex]Thus, the equation of the line in the point slope form is (y-1)=(x+2)/3
so the answer is y-1=5/3
ငါထင္ပါတယ္။
Determine whether WX and YZ are parallel, perpendicular or neither.W(6.-6), X(7.1). Y(3,-1), Z(2,6)
Answers
ANSWER
Neither
EXPLANATION
To determine whether WX and YZ are parallel or perpendicular, wehave to find their slopes and compare them.
Slope is given as:
[tex]\text{slope = }\frac{y_2-y_1}{x_{2_{}}-x_1}[/tex]SLOPE OF WX
For WX,
(x1, y1) = (6, -6)
(x2, y2) =(7, 1)
So:
[tex]\begin{gathered} \text{slope = }\frac{1\text{ - (-6)}}{7\text{ - 6}}\text{ = }\frac{1\text{ + 6}}{1} \\ \text{slope = 7} \end{gathered}[/tex]SLOPE OF YZ
For YZ:
(x1, y1) = (3, -1)
(x2, y2) = (2, 6)
So:
[tex]\begin{gathered} \text{slope = }\frac{6\text{ - (-1)}}{2\text{ - 3}} \\ \text{slope = }\frac{6\text{ + 1}}{-1} \\ \text{slope = -7} \end{gathered}[/tex]For WX and YZ to be parallel, their slope must be the same.
For WX and YZ to be perpendicular, the slope of one must be the negative inverse of the other.
Since their slopes are neither the same or the negative inverse of one another, WX and YX are neither parallel or perpendicular to one another.
ALGEBRA 1 HW!! PLEASE HELP I WILL GIVE BRAINLYEST (also please show how you got answer)
only giving brainlyest for correct answer
Answers
The slope of the line is 125.
The slope in the context represent the change in price with respect to the sizes of the houses.
The line won't pass through the point (5, 650)
How to find the slope of a line?The slope of a line is the change in y with respect to change in x.
Therefore,
slope = m = y₂ - y₁ / x₂ - x₁
using (0, 0)(2, 250)
m = 250 - 0 / 2 - 0
m = 250 / 2
Therefore,
m = 125
The slope simply implies the change in price with respect to the change in sizes of the houses.
Using the slope intercept equation we can know if the line passes through (5, 650).
Therefore,
y = 125x + 0
625 = 125(5)
Therefore, the line won't pass through the point (5, 650).
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How many years are there in 467 days?
Answers
Answer:
there are approximately 1.28 years in 467 days
Step-by-step explanation:
1 yr = 365 days
467/365 = 1.28
Answer: 1 year and 102 days.
Step-by-step explanation:
There are 365 days in a year.
TWO tailors, Aisha and Debbie, sit down to do some embroidery. Alsha can embroider 4 shirtsper hour, and Debbie can get through 6 shirts per hour. In addition, the tailors had previouslyfinished some shirts. Aisha has already completed 20 shirts, and Debbie has completed 10shirts. Aisha and Debbie decide to take a break when they have finished the same totalnumber of shirts. How long will that take?Write a system of equations, graph them, and type the solution
Answers
For the information given in the statement you have
[tex]\begin{gathered} t=4h+20\Rightarrow\text{ shirts embroidered by Aisha} \\ t=6h+10\Rightarrow\text{ shirts embroidered by Debbie} \end{gathered}[/tex]Write the transformed equation for f(x) -5, calling it h(x)
Answers
The image of the function after the translation is h(x) = 6x - 3
How to determine the equation of h(x)?The given parameters are:
f(x) = 6x + 2
The transformation is given as
f(x) - 5
This implies that we translate the function f(x) 5 units down
Mathematically, this transformation can be represented as
(x, y) = (x, y - 5)
When represented as a function, we have
h(x) = f(x) - 5
Substitute the equation f(x) = 6x + 2 in the equation h(x) = f(x) - 5
So, we have the following equation
h(x) = 6x + 2 - 5
Evaluate the like terms
h(x) = 6x - 3
Hence, the equation of h(x) is h(x) = 6x - 3
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Possible question
Given that the equation of f(x) is f(x) = 6x + 2
Write the transformed equation for f(x) -5, calling it h(x)
Select the correct answer.The Junior and senior classes at Central High School were asked to choose a destination for a field trip. The results are shown in the giventwo-way frequency table.JuniorsSeniorsTotalCentral High School Field Trip DestinationAmusement Park5764121OA 38.55%B. 19.93%OC 47.50%OD. 42.31%ntum. All rights reserved.Museum Broadway Show214465What percentage of surveyed students chose the amusement park?4258100Total120166286
Answers
The probability that the subject is physics if an assignment is submitted on time is 89.7%.
Given that,
The table is
Subject: On-time Assignment: On-time Arrival to Class:
PHYSICS 89.7% 82.3%
MATH 88.2% 88.7%
CHEMISTRY 89.4% 83.1%
BIOLOGY 90.1% 82.4%
TOTAL 88.5% 84.7%
What is probability?
The characteristic or state of being probable; the probability that something will occur or be the case:
If an assignment is turned in on time, there is an 89.7% chance that the subject will be physics.
If an assignment is turned in on time, there is an 88.2% probability that the subject is math.
If an assignment is turned in on time, there is an 89.4% probability that the subject is chemistry.
If an assignment is turned in on time, the probability that the subject is biology is 90.1%.
Therefore, the chance that the subject is physics if an assignment is submitted on time is 89.7%.
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Felix exercises by spending 12 minutes warming up and then running for 20 minutes he has exercised a total of 240 minutes this mouth
Answers
Based on the number of minutes that Felix takes to exercise and the minutes he takes to warm up, the equation given does not describe the statement.
How to describe the statement as an equation?The number of minutes that Felix spends exercising and the number of minutes he spends running, should be added together to find the number of minutes Felix spends exercising in one session.
This means that the total minutes for exercising is:
= 12 + 20
= 32 minutes per session
The number of sessions that Felix exercised to get to a total of 240 minutes is therefore:
Number of minutes per session x Number of sessions = 240 minutes
Assuming the number of sessions is x, the equation would be:
32 × x = 240
32x = 240
The given equation of 20 + 12x=240 is therefore not described by the statement.
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given the continuous function, determine how many inflection points would be found on the graph. show the approximate location of each estimate.
Answers
inflection points are where there is a change of concavity:
A fashion photographer needs to hire a stylist to prepare her models. Emmet charges $177 for showing up, plus $75 per hour. Pam charges $187 plus $70 per hour. The photographer realizes that, given the expected duration of her photo shoot, either stylist would cost her the same amount. What would the duration be? What would the cost be?
Answers
Emmet charges $177 for showing up, plus $75 per hour
Total charge = Show up charge + Per hour charges
Pam charges $187 plus $70 per hour
either stylist would cost her the same amount
i.e the total cost of photographer and stylist
Let x be the time taken in shoot
so, the charge of Emmet is 177 + 75x
The charge of palm = 187+70x
Since the charge is equal so,
[tex]\begin{gathered} 177+75x=187+70x_{} \\ 75x-70x=187-177 \\ 5x=10 \\ x=2 \end{gathered}[/tex]we get x= 2
i.e. 2 hours
The duration at which the cost of palm and emmet is equal is 2 hours
for the cost
substitute the value of x in the cost equation :
Emmet = 177 + 75x
Emmet cost=177+75(2)
Emmet cost = 327
Since the cost is same so,
The cost of emmet and palm is $327
Answer: 2 hours & $327
