Answer:
B
Step-by-step explanation:
[tex]6.79 \times 0.7[/tex]
[tex]=4.753[/tex]
Answer:
The correct answer would be $4.75
Step-by-step explanation:
6.79 × 0.7
=$4.75
Hope that was helpful.Thank you!!!
At the same time a 6 foot person casts a 2 foot shadow, a nearby flagpole casts a ten foot
shadow. How tall is the flagpole?
Answer:
30 feet
Step-by-step explanation:
I found the unit. So a 6 feet person casts a 2 foot shadow
I divided both numbers by 2
Therefore getting a 3 foot person casts a 1 foot shadow
If the flagpole casts a ten foot shadow I multiplied 10×1 and 30 ×1. Meaning that the 30 foot flagpole casts a 10 foot shadow
F(x)=(x+1)(x-3)(x-4)
Answer :
x1 = -1
x2= +3
x3 = +4
I hope it helps
If you are doing it by roots how ever it would be 3
in a church wing with 8 men and 10 women members find the probability that a 5 member committee chosen randomly will have.......
a).all men.
b).3men and 2 women
Answer:
a) Probability that a 5 member committee will have all men = 0.0065
b) probability that a 5 member committee chosen randomly will have 3 men and 2 women = 0.294
Step-by-step explanation:
Number of men = 8
Number of women = 10
Total number of members = 10 + 8 = 18
Probability = (Number of possible outcomes)/(Total number of outcomes)
Number of ways of selecting a 5 member committee from 18 people = [tex]^{18}C_5 = \frac{18!}{(18-5)!5!} = \frac{18!}{13!5!}[/tex] = 8568 ways
a) Probability that a 5 member committee will have all men
Number of ways of selecting 5 men from 8 men
= [tex]^8C_5 = \frac{8!}{(8-5)!5!} = \frac{8!}{3!5!}[/tex] = 56 ways
Probability that a 5 member committee will have all men = 56/8568
Probability that a 5 member committee will have all men = 0.0065
b)probability that a 5 member committee chosen randomly will have 3men and 2 women
Number of ways of selecting 3 men from 8 men
= [tex]^8C_3 = \frac{8!}{(8-3)!3!} = \frac{8!}{5!3!}[/tex] = 56 ways
Number of ways of selecting 2 women from 10 men
= [tex]^{10}C_2 = \frac{10!}{(10-2)!2!} = \frac{10!}{8!2!}[/tex] = 45 ways
Number of ways of selecting 3 men and 2 women = 56*45
Number of ways of selecting 3 men and 2 women = 2520
Probability of selecting 3 men and 2 women = 2520/8568 = 0.294
probability that a 5 member committee chosen randomly will have 3 men and 2 women = 0.294
The tray is 90 cm x 40 cm. Each plate has a radius of 8 cm. There needs to be a 2 cm gap around each plate. How many plates can Nicola fit on the tray?
Answer: 10 plates
Step-by-step explanation:
The radius of one plate is 8, which implies its diameter is 16.
There must be a 2 inch gap between plates so 16 + 2/2 = 17 cm is how much room each plate needs.
The tray is 40 cm wide. How many 17 cm plates can you fit in that width? 2
The tray is 90 cm long. How many 17 cm plates can you fit in that length? 5
The number of plates that fit on the tray is rows x columns (length x width)
= 2 x 5
= 10
What is the measure of the third angle in the similar triangles below?
25
65
85
115
Answer:
65
Step-by-step explanation:
We know that,
The Sum of all angles of the triangle is 180°.
As given in the question,
Triangle PQR is similar to Triangle WXY
Therefore ,
Let the third angle be 'x'.
35° + 80° + x = 180°
115 + x = 180°
x = 180° - 115°
x = 65°.
Hence, 65° is the appropriate answer to the question.
I hope my answer helped!!
Harriet has a square piece of paper. She folds it in half again to form a second rectangle (the high is not a square). The perimeter of the second rectangle is 30cm. What is the area of the original piece of paper?
Answer:
The area of the original piece of paper is 60cm
Answer:
the answer is 60
hope it helps :D
Step-by-step explanation:
1. A company estimates that if x thousand cedis is spent on the marketing of a certain product, Q(x)
thousand units of the product will be sold, where Q(x) = 7x / 27 + x²
(a) Determine the domain of the function defined. [2 Marks]
(b) Determine how much of the product will be sold if the company does not spend any money on
marketing. [2 Marks]
(c) Determine the amount of money the company must spend on marketing to achieve the minimum
and maximum quantities. Leave your answers to 2 decimal places. [10 Marks]
(d) Determine the maximum and minimum quantities that can be sold. Leave your answer to the
nearest whole number. [5 Marks]
(e) Determine the marketing expendure ranges on which quantity sold is increasing and decreasing
and interpret your solution. [9 Marks]
(f) Determine what happens as the company invests an infintely large amount of money on marketing.
[6 Marks]
(g) Use the information given from (a) to (f) to sketch the curve of Q(x). [6 Marks]
2. (a) The demand and supply functions of a particular good in a competitive market are defined
respectively as p = 200q
q1 and p = 30+2q. If p and q denote the price and quantity respectively,
determine the equilibrium price and quantity. [15 Marks]
(b) Let the price and quantity functions of a product be given by p = 2x + k and q = x + 2
respectively, where x is a variable and k is a constant. Find the value(s) of k for which the total
revenue function is always positive. [15 Marks
Answer:
a) x ≥ 0
b) 0
c) x = 0 ( min ) , x = 5.192 ( max )
d) Q = 0 ( min ) , Q = 0.67357 ( 1000 ) units
e) 0 < x < 5.192 ( increasing ) , x > 5.192 ( decreasing )
Step-by-step explanation:
Solution:-
- The thousand units of product [ Q(x) ] sold is modeled by the following equation:
[tex]Q(x) = \frac{7x}{27+x^2}[/tex]
Where,
x: Is the amount of cedis ( thousands ) invested
- We are to determine the domain of the function. We need to realize that the amount of money spent can only be a positive value. Hence, x ≥ 0.
- Next we check for any "discontinuity" of the function [ Q(x) ]. The discontinuity may exist for rational fractions, natural logs, and radicals.
- The defined function is the form of " rational fraction ". For such functions we equate the denominator to zero and solve for any " real values " of the independent variable ( x ):
[tex]27 + x^2 = 0\\\\ x = i\sqrt{27} = 5.1962i \\[/tex]
- The roots are imaginary; hence, the discontinuity does not exist and the [ Q ( x ) ] is valid for all real positive values of x. the domain would be:
domain: [tex]x\geq 0[/tex]
- To determine the amount of product sold when no money is spent on the marketing of the product. We simply plug ( x = 0 ) in the given relation:
[tex]Q( 0 ) = \frac{0}{27} = 0[/tex]
Answer: No unit of product is sold without the marketing expense
- To determine the amount of money spent on marketing that would lead to maximum and minimum number of product to be sold. We are asked to find the critical values of the given function.
- To determine the critical values we have to determine the first derivative of the given function:
[tex]Q'(x) = \frac{7(27-x^2)}{(27 + x^2)^2}[/tex]
[tex]Q''(x) = \frac{-14x(-x^2 + 81 )}{(x^2 + 27)^3}[/tex]
- The critical values conditions are:
[tex]Q'(x) = 0[/tex]
[tex]\frac{7(27-x^2)}{(27 + x^2)^2} = 0\\\\7(27-x^2) = 0\\\\x = \sqrt{27} = +5.1962 \\\\[/tex]
- The other critical value is defined by the domain of the function. i.e x = 0. Where, Q ( x ) = 0.
- Input the critical values x = 5.1962 and x = 0 into the second derivative and determine the nature of the critical points as follows:
[tex]Q''(5.192) = \frac{-14*5.1962( -27 + 81 )}{( 27 + 27 )^3} < 0\\\\Q''(0) = \frac{0}{27} = 0 \geq 0[/tex]
- The critical value x = 5192 is the maximizing expenditure while x = 0 is the minimizing expenditure.
- The corresponding maximum and minimum number of unit sold can be determined by plugging the critical values in the given relation [ Q(x) ]:
[tex]Q ( 5.192 ) = \frac{7*\sqrt{27} }{27+27} \\\\Q ( 5.192 ) = 0.67357 ( thou) \\\\Q ( 0 ) = \frac{7*0 }{0+27} \\\\Q ( 0 ) =0 ( thou) \\[/tex]
Answer: The maximum units sold would be 673.57. And the minimum unit sold would 0.
- We will determine the nature of function [ increasing or decreasing ] by finding a range of value for which Q'(x) > 0 or Q'(x) < 0.
- We use the domain between the critical points. [ 0 , 5.192 ]
[tex]Q'(x) = \frac{7x(x^2 - 27 )}{(27+x^2)^2} > 0[/tex] ( increasing )
- The next domain is x > 5.192.
[tex]Q'(x) = \frac{7x(x^2 - 27 )}{(27+x^2)^2} < 0[/tex] ( decreasing )
Answer: the number of unit sold increases from 0 < x < 5.192 and decreases when expenditure is x > 5.192
please help meh on dis question ty
Answer:
C only
Step-by-step explanation:
To find the answer(s) for x, first we need to calculate the absolute value of each number. ( the brackets indicate absolute value)
A:
# -4 absolute value: 4
Greater than or less than 5: less ✘ incorrect
B:
# 3 absolute value: 3
Greater than or less than 5: less ✘ incorrect
C:
# 9 absolute value: 9
Greater than or less than 5: greater ✔ correct
Thus, the correct answer is C
A sector of angle 125° is revoked from a thin circular sheet of radius 18cm. it is then folded with straight edges coinciding to form a right circular cone. what are the steps you would use to calculate the base radius, the semi- vertical, and the volume of the cone?
Answer:
Step-by-step explanation:
A sector is a portion of the circle that is bounded by 2 radii forming an angle at the center of the circle. If it is folded into a cone, the radius of the sector becomes the slant height of the cone. The length of the arc formed by the sector becomes the circumference of the circular base of the cone. Therefore, to calculate the
1) Base radius, we would apply the formula,
Circumference = 2πr
Circumference = length of arc = 125/360 × 2 × 3.14 × 18
= 39.25
Radius, r = 39.25/2 × 3.14 = 6.25 cm
2) Semi vertical height, we would apply Pythagoras Theorem with the slant height of the cone being the hypotenuse, the radius being the adjacent side and the slant height being the opposite side.
h² = 18² - 6.25² = 284.9375
h = √284.9375 = 16.88 cm
3) Volume = 1/3πr²h where h represents the vertical height
Volume = 1/3 × 3.14 × 6.25² × 16.88 = 690.15 cm³
Black walnut trees contain chemicals that inhibit the growth of other plants. In a simple experiment to test whether this is true, you grow several tomato plants in soil with and without decomposing leaves from a black walnut tree. You collect data on plant height as a measure of growth. In this experiment, __________ is the independent variable, __________ is the dependent variable, and __________ is the control.
Answer:
Height of tomato plant is the dependent variable
Presence of walnut leaves in the soil is the independent variable
Tomato plants grown without walnut leaves is the control
Step-by-step explanation:
An independent variable is the variable in an experiment that can be altered to test for a certain result. It is independent, or does not change with change in other factors in the experiment. In this case, the presence or absence, or quantity of walnut available in the soil is the independent variable in the experiment.
A dependent variable varies, and depends on the independent variable. It is what is measured in the experiment. In this case, the height of the tomato plants is the dependent variable that depends on the presence, absence or quantity of walnut in the soil.
A control in an experiment, is a replicate experiment, that is manipulated in order to be able to test a single variable at a time. Controls are variables are held constant so as to minimize their effect on the system under study. In this case, some of the tomato plants are planted without walnut in the soil, to test the effect of the absence of the walnut in the soil.
Which statement is true about the polynomial 3j4k−2jk3+jk3−2j4k+jk3 after it has been fully simplified?
Answer:
[tex]j^4k[/tex]
Step-by-step explanation:
[tex]3j^4k-2jk^3+jk^3-2j^4k+jk^2\\2j^4k-2j^4k-2jk^3+jk^3+jk^3\\j^4k[/tex]
Answer:
4
Step-by-step explanation:
give me brainliest
The Sky Train from the terminal to the rental car and long-term parking center is supposed to arrive every 16 minutes. The waiting times for the train are known to follow a uniform distribution. Find the 40th percentile for the waiting times (in minutes).
Answer:
6.4 minutes
Step-by-step explanation:
The minimum waiting time is zero minutes (arriving exactly at the same time as the train), and the maximum waiting time is 16 minutes (arriving exactly after a train has left), therefore the time range is 16 minutes. If the waiting times are uniformly distributed, the 40th percentile is simply given by:
[tex]P = 0.40*16\\P=6.4\ minutes[/tex]
The 40th percentile for the waiting times is 6.4 minutes.
Assume the time required to complete a product is normally distributed with a mean 3.2 hours and standard deviation .4 hours. How long should it take to complete a random unit in order to be in the top 10% (right tail) of the time distribution?
Answer: 3.712 hours or more
Step-by-step explanation:
Let X be the random variable that denotes the time required to complete a product.
X is normally distributed.
[tex]X\sim N(\mu=3.2\text{ hours},\ \sigma=0.4\text{ hours} )[/tex]
Let x be the times it takes to complete a random unit in order to be in the top 10% (right tail) of the time distribution.
Then, [tex]P(\dfrac{X-\mu}{\sigma}>\dfrac{x-\mu}{\sigma})=0.10[/tex]
[tex]P(z>\dfrac{x-3.2}{\sigma})=0.10\ \ \ [z=\dfrac{x-\mu}{\sigma}][/tex]
As, [tex]P(z>1.28)=0.10[/tex] [By z-table]
Then,
[tex]\dfrac{x-3.2}{0.4}=1.28\\\\\Rightarrow\ x=0.4\times1.28+3.2\\\\\Rightarrow\ x=3.712[/tex]
So, it will take 3.712 hours or more to complete a random unit in order to be in the top 10% (right tail) of the time distribution.
A TV on ebay is described to be 35.7 inches wide and 20.1 inches
high. To the nearest whole number how many inches is it's diagonal?
(Enter your answer without units.)
Answer:
41 in.
Step-by-step explanation:
You have to use the Pythagorean Theorem. You have the values for the two sides (length and width). Now, you need to solve for the hypotenuse (diagonal).
a² + b² = c²
(35.7)² + (20.1)² = c²
1274.49 + 404.01 = c²
1678.5 = c²
√1678.5 = c
c = 40.97
c ≈ 41
The diagonal length is 41 in., to the nearest whole number.
Let f(x) represent a function. Which descriptions match the given transformations? Drag and drop the answers into the boxesNeed help please!
Answer:
f(x) - 4 is f(x) is translated 4 units down
4f(x) is f(x) is vertically stretched by a factor of 4
Step-by-step explanation:
k is denoted as vertically movement. In this case, k = -4, so we move down 4 units
a is denoted as vertical stretch or shrink, depending on whether a is less than or greater than 0. In this case, a is greater than and is 4, so it is vertically stretched by a factor of 4.
Each person in a simple random sample of 1,800 received a survey, and 267 people returned their survey. How could nonresponse cause the results of the survey to be biased?
A. Those who did not respond reduced the sample size, and small samples have more bias than large samples.
B. Those who did not respond caused a violation of the assumption of independence. Those who did not respond are indistinguishable from those who did not receive the survey.
C. Those who did not respond may differ in some important way from those who did respond.
D. Those who did not respond represent a stratum, changing the random sample into a stratified random sample.
Answer: Those who did not respond may differ in some important way from those who did respond.
Step-by-step explanation:
I took the quiz and got it right.
The answer is C. Those who did not respond may differ in some important way from those who did respond.
What is Non Response Bias?Non response bias is the bias caused by the absence of the responses. The participants in the sample are not willing to return their survey. It can cause systematic errors in the sample survey.
Here the situation is that each person in a simple random sample of 1,800 received a survey, and 267 people returned their survey.
So the remaining people are not willing to attend the survey.
Most of the people has not returned the survey. So only the responses of limited participants are taken for the survey, which will miss the large diversity of the opinion.
So those who did not respond may differ in some important way from those who did respond.
Hence the non response cause the results of the survey to be biased due to the fact that those who did not respond may differ in some important way from those who did respond.
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Find the solutions to x^2 = 8
Answer:
x=2√2 is the answer
Step-by-step explanation:
x²=8
TAKING SQUARE ROOT ON BOTH SIDES
√x²=√8
x=√2×2×2
x=√2²×√2
x=2√2
i hope this will help you
Answer:
The value of x is -2.828 or 2.828
Step-by-step explanation:
In order to eliminate of square of x, you have to square root both sides :
[tex] {x}^{2} = 8[/tex]
[tex] \sqrt{ {x}^{2} } = ± \sqrt{8} [/tex]
[tex]x = \sqrt{8} \\ x = 2 \sqrt{2} \: or \: 2.828[/tex]
[tex]x = - \sqrt{8} \\ x = - 2 \sqrt{2} \: or \: - 2.828[/tex]
You could have a part-time job (20 hours per week) that pays $15 per hour, or you could have a full-time job (40 hours per
week) that pays $12 per hour. Because of the extra free time, you will spend $150 per week more on entertainment with the
part-time job than with the full-time job. After accounting for the extra entertainment expense, how much more is your weekly cash flow with the full-time job than with the part-time job? (Neglect taxes and other expenses.) Show your work.
Answer: Your weekly cash flow for the full-time job would be $480 while the cash flow for the part-time job is $150.
Step-by-step explanation:
If you work 20 hours for $15, that's $300 by the end of the week. However, because of the extra time for entertainment, that $150 takes half of your earnings. 15 x 20 = 300 - 150 = 150. Because you don't have time for entertainment with the full-time job, you only have the $480.
What is the converse of the conditional statement?
Ifxis even, then x + 1 is odd.
If x is not even, then x +1 is not odd.
If x + 1 is odd, then x is even.
If x + 1 is not odd, then x is not even.
O lfx is even, then x + 1 is not odd.
Answer:
If x + 1 is odd, then x is even.
Step-by-step explanation:
The converse of the statement ...
if P, then Q.
is ...
if Q, then P.
Here, we have P="x is even" and Q="x+1 is odd". The converse statement is ...
if x+1 is odd, then x is even.
Answer:
the answer is b on edg
Step-by-step explanation:
if the vertex of a parabola is negative for 6 and the other point of the curve is (-3,14) what is the coefficient of the squared expression in Parabola equation?
A. 6
B. 4
C. 8
D. 2
Answer:
coefficient of the square is a.6
What number is 22 ten thousands of 1 1/2
Answer: 2
Step-by-step explanation:
The number of 22 ten thousands of [tex]1\frac{1}{2}[/tex] is 33000
What is Number system?A number system is defined as a system of writing to express numbers.
First, we need to convert [tex]1\frac{1}{2}[/tex] to an improper fraction:
[tex]1\frac{1}{2}[/tex] = 3/2
Next, we can write 22 ten thousands as a decimal:
22 ten thousands = 220000
Finally, we can multiply the decimal and the fraction to find the answer:
220000 x 3/2 =33000
Therefore, 22 ten thousands of [tex]1\frac{1}{2}[/tex] is 33000
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Solve the system of equations. \begin{aligned} &-3y+4x = 13 \\\\ &-5y-6x=-67 \end{aligned} −3y+4x=13 −5y−6x=−67
Answer:
x = 7
y = 5
Step-by-step explanation:
We can do this algebraically using substation or elimination or we could do this graphically.
Answer:
x=7
y=5
Step-by-step explanation:
Write the slope-intercept inequality for the graph below. If necessary, use <=
for s or >= for
(3,-1)
(-3,-3)
Answer:
y > 1/3x - 5
Step-by-step explanation:
First, use the points to find the slope. Use the equation for slope.
[tex]m=\frac{y_{2}-y_{1} }{x_{2}- x_{1} }\\m=\frac{-3-(-1) }{-3-3}\\m=\frac{-3+1 }{-3-3}\\m=\frac{-2}{-6}\\ m=\frac{1}{3}[/tex]
Now, you need to find the y-intercept. The y-intercept is the point on the graph that crosses the y-axis. By looking at the graph, the y-intercept seems to be -5.
This gives you 1/3x - 5 for slope-intercept form.
Now, you need to find which equality to use. Because the line is dotted, it cannot be ≤ or ≥. This leaves us with < and >. To choose between the two, you need to test points. Test a point to see if it matches the solution. The point should be on the line but in the shaded area.
I'm gonna pick (0, 0). This point is not on the line, and it is in the shaded region.
y 1/3x - 5
0 1/3(0) - 5
0 0 - 5
0 > -5
The equality > is the correct one. This gives the equality y > 1/3x - 5.
Nika baked three loaves of zucchini bread. Each cake needed StartFraction 17 over 4 EndFraction cups of flour. Which expression shows the best estimate of the number of cups of flour that Nika used? ASAP Answer choices: 4 + 4 + 4 = 12 5 + 5 + 5 = 15 4 + 4 + 4 = 16 17 + 17 + 17 = 51
Answer:
(A)4 + 4 + 4 = 12
Step-by-step explanation:
Each cake needs [tex]\dfrac{17}{4}[/tex] cups of flour.
Now,
[tex]\dfrac{17}{4} =4.25 \approx 4[/tex]
Therefore, the best estimate of the number of cups of flour that Nika used to make the three loaves is:
4 + 4 + 4 = 12
Answer:
12 (A)
Step-by-step explanation:
u hate edge, i hate it more :3
Which goes in what box?
Answer:
neg,pos,pos,pos,neg,neg
Step-by-step explanation:
if the number of (–) is odd number, it will goes negative while if it (–) is even number, it will count as positive
For any set of n measurements, the fraction included in the interval y − ks to y + ks is at least 1 − 1 k2 . This result is known as Tchebysheff's theorem. A personnel manager for a certain industry has records of the number of employees absent per day. The average number absent is 8.5, and the standard deviation is 3.5. Because there are many days with zero, one, or two absent and only a few with more than ten absent, the frequency distribution is highly skewed. The manager wants to publish an interval in which at least 75% of these values lie. Use Tchebysheff's theorem to find such an interval.
Answer:
This interval is between 1.5 and 15.5.
Step-by-step explanation:
Tchebysheff's Theorem
The Tchebysheff's Theorem can also be applied to non-normal distribution. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.
At least 89% of the measures are within 3 standard deviations of the mean.
An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].
In this question, we have that:
Mean = 8.5
Standard deviation = 3.5
The manager wants to publish an interval in which at least 75% of these values lie.
By the Tchebysheff's Theorem, at least 75% of the measures are within 2 standard deviations of the mean.
8.5 - 2*3.5 = 1.5
8.5 + 2*3.5 = 15.5
This interval is between 1.5 and 15.5.
The mean temperature for the first 7 days in January was 4 °C. The temperature on the 8th day was 3 °C. What is the mean temperature for the first 8 days in January?
Answer:
Mean temperature for the first 8 days was [tex]3.88^\circ[/tex]
Step-by-step explanation:
Mean = [tex]\frac{4\cdot 7+3\cdot 1}{8}[/tex]
[tex]=3.88^\circ[/tex]
Best Regards!
Answer:
3.875
Step-by-step explanation:
The makers of a soft drink want to identify the average age of its consumers. A sample of 25 consumers was taken. The average age in the sample was 31 years with a standard deviation of 3.8 years.The Margin of error of the 99% confidence interval for the average age of the consumers is a.1.90 years b.2.13 years c.4.10 years d.1.65 years
Answer:
a.1.90 years
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
In this question:
[tex]n = 25, \sigma = 3.8[/tex]
So
[tex]M = 2.575*\frac{3.8}{\sqrt{25}} = 1.90[/tex]
So the correct answer is:
a.1.90 years
The graph represents this system of equations: A system of equations. 2 x plus y equals 3. 2 x minus 5 y equals 15. A coordinate grid with 2 lines. One line passes through (0, 3) and (1.5, 0). The other line passes through (0, negative 3) and (2.5, negative 2). What is the solution to the system of equations represented by the graph?
Answer:
(2.5, -2)
Step-by-step explanation:
The solution to the system of equations is the point where the lines on the graph cross. You can read those coordinates as ...
(2.5, -2)
3 days after picking apples, a family had 100 apples left. After 6 days, 76 apples were left. Assuming a linear function, write an equation in the form a(t)=mt+b that shows the number of apples, a(t), left t days after picking them. Be sure to include "a(t) =" in your answer.
Answer:
a(t) = -8t + 124
Step-by-step explanation:
The number of apples left 3 days after picking them is given by the following equation:
[tex]a(t) = mt + b[/tex]
3 days after picking apples, a family had 100 apples left.
This means that [tex]a(3) = 100[/tex]
So
[tex]100 = 3m + b[/tex]
[tex]3m + b = 100[/tex]
[tex]b = 100 - 3m[/tex]
After 6 days, 76 apples were left.
So a(6) = 76. Then
[tex]76 = 6m + b[/tex]
Since b = 100 - 3m
[tex]76 = 6m + 100 - 3m[/tex]
[tex]3m = -24[/tex]
[tex]m = \frac{-24}{3}[/tex]
[tex]m = -8[/tex]
b:
[tex]b = 100 - 3m = 100 - 3*(-8) = 124[/tex]
So
a(t) = -8t + 124.
