Which of the following statements are always true? A) If f(t) is increasing, then the left-hand sum gives an overestimate of the integral from a to b of f(t)dt. B) If f(t) is concave up, then the left-hand sum gives an overestimate of the integral from a to b of f(t)dt.
Answers
(A) If f(t) is increasing, it's not true that the left-hand sum gives an overestimate of the integral from a to b of f(t)dt.
(B) f(t) is concave up, its' not true that the left-hand sum gives an overestimate of the integral from a to b of f(t)dt.
Left-Hand Sums and Right-Hand Sums give us different approximations of the area under a curve. If one sum gives us an overestimate and the other an underestimate, then we can hone in on what the actual area under the curve might be. Any left-hand sum will be an under-estimate of the area of R. Since f is increasing, a left-hand sum will use the smallest value of f on each sub-interval. This means any left-hand sum will fail to cover all of R and any right-hand sum will be an over-estimate of the area of R. Since f is increasing, a right-hand sum will use the largest value of f on each sub-interval. This means any right-hand sum will cover R and then some.
A) If f(t) is increasing then the left-hand sum gives an overestimate of the integral from a to b of f(t)dt, if the graph is increasing then the left-hand sum gives an overestimated value of the actual value.
B) If f(t) is concave up, then the left-hand sum gives an overestimate of the integral from a to b of f(t)dt, if the graph is concave up then the trapezoid approximation is an overestimate, and the midpoint is underestimated.
So, If f(t) is increasing, it's not true that the left-hand sum gives an overestimate of the integral from a to b of f(t)dt. and if f(t) is concave up, its' not true that the left-hand sum gives an overestimate of the integral from a to b of f(t)dt.
To learn more about right and left-hand sums visit: brainly.com/question/29673931
#SPJ4
Related Questions
a square room is covered by a number of whole rectangular slabs of sides 60cm by 42 cm. Calculate the least possible area of the room in square meters.
Answers
Answer:
17.64 is the answer.hope it helps.
let y1,y2 be independent random variables both having the uniform(0,1) distribution. re- call that the density function and distribution function of a uniform random variable y
Answers
A uniform random variable's density function is f(y) = 1 for y 1 and 0 otherwise. F(y) = 0 for y 0, F(y) = y for 0 y 1, and F(y) = 1 for y > 1 define the distribution function.
A uniform random variable's density function is f(y) = 1 for y 1 and 0 otherwise. Accordingly, the likelihood of any specific outcome of y is the same, and the likelihood of any range of outcomes is equal to the length of the range. F(y) = 0 for y 0, F(y) = y for 0 y 1, and F(y) = 1 for y > 1 define the distribution function. Accordingly, the length of the range multiplied by the likelihood of any specific occurrence yields the cumulative probability of any range of outcomes. Since the likelihood of any specific result in that range is 1 and the range's length is 0.5, for instance, the cumulative probability of 0 y 0.5 is 0.5. Since the likelihood of any given result within that range is still 1, but the range's length is 0.5, the cumulative probability of 0.5 y 1 is 0.75. The chance of any range of outcomes for y1 and y2 if they are independent random variables both having the uniform(0,1) distribution is just the sum of their respective cumulative probabilities.
Learn more about variable here
brainly.com/question/29583350
#SPJ4
Given rhombus ABCD, find the area if mZABC = 60° and AE = 2.
Answers
The area of the rhombus, obtained from the dimensions, of the diagonals, found from the trigonometric of sines of the angle can be presented as follows;
Area = 8·√3
What is the area of a plane figure?The area of a plane figure is the two dimensional space occupied by the figure on a plane.
The measure of the angle ABC, m∠ABC = 60°
The length of the segment AE = 2 units
The diagonals of a rhombus bisect each other at right angles, and the right angles through which they pass, therefore;
BE = ED, m∠AEB = 90°
m∠ABE = 30°
sin(30°) = AE/AB
sin(30°) = 2/AB
AB = 2/(sin(30°)) = 4
AB = 4
BE = √(4² - 2²) = √(12) = 2·√3
Therefore; AC = 2 + 2 = 4
BD = 2·√3 + 2·√3 = 4·√3
The area of a rhombus = (1/2) × The product of the length of the diagonals
Therefore;
Area of the rhombus = (1/2) × (4·√3) × 4 = 8·√3
The area of the rhombus = 8·√3
Learn more on the area of a rhombus here: https://brainly.com/question/30985956
#SPJ1
Combine the likes terms to create an equivalent expression y - (-3y)
Answers
Answer:
4y
Step-by-step explanation:
y - (-3y)
y + 3y
4y
When you see two negatives they basically become an addition symbol. In this case you then add the like terms which are y and 3y to get 4y. Hope this helps!!
Find the surface area of this rectangular prism. Be sure to include the correct unit in your answer.
Answers
Answer: 258 \(yard^{2}\)
Step-by-step explanation: To find the surface area you add the area of all the sides. And the unit for a surface area is unit (yards) squared.
Front: 5 • 9 = 45
Back: 5 • 9 = 45
Left: 6 • 5 = 30
Right: 6 • 5 = 30
Top: 9 • 6 = 54
Bottom: 9 • 6 = 54
45 + 45 + 30 + 30 + 54 + 54 = 258.
8) Consider the following sets,
A = {x | x ≤ N}
B = {x-5 < x < 105, x ≤ R}
C = {x|x is a rational number, 10 < x < 80}
Find the cardinality of the set (A − C) n B.
Answers
The cardinality of the set (A − C) n B is 35 .
Cardinality of a set is defined as the number of elements in the mathematical set. It can be finite or infinite. For example, the set A = {1, 2, 3, 4, 5, 6} has cardinality 6. Because the set A has 6 elements. Set cardinality is also known as set size. A real number can be defined as a combination of rational and irrational numbers. They can be both positive and negative, denoted by the symbol "R". Natural number all count numbers starting at 1. N = {1 ,2 , 3 ,4, .....}We have given three sets A = {x | x ≤ N} where N is a natural number .
Then , set A will get values \(A= \{1,2,3,4,5......\}\)
B = {x-5 < x < 105, x ≤ R} where R is a real number whose values is in domain of (- ∞ ,∞)
Then , set B will get values \(B=(-5,105)\)
C = {x|x is a rational number, 10 < x < 80} rational number which can expressed in \(\frac{p}{q}\) where \(q\neq 0\) .
Then , set C will get values \(=(10,80]\)
According to the question
(A − C) n B \(=(\{1,2,3,4,5 ........\}-(10,80] \sqcap (-5,105)\)
\(=\{1,2,3,4,5,6,7,8,9,10,81,82,83 .......\} \sqcap (-5,105)\\\)
={1,2,3,4,5,6,7,8,9,10,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103, 104 ,105}
Learn more about set here :
https://brainly.com/question/2166579
#SPJ9
to find the average amount of money that american college students spend on food per week, a researcher surveys 300 college students across the u.s.
Answers
The result of the calculation was $93.41 per week.
To find the average amount of money spent on food by American college students per week, a researcher conducted a survey of 300 college students across the U.S. The researcher collected data on the amount of money spent by each student on food per week and then calculated the average using the formula: Average = (sum of all the scores)/(number of scores). The researcher then added up the money spent by all 300 students and divided it by 300 to get the average amount of money spent on food per week by American college students. The result of the calculation was $93.41 per week.
Learn more about average amount here:
https://brainly.com/question/12763762
#SPJ4
What is a corresponding pair for f(-7)=5
Answers
Answer:
An ordered pair for a function f(x) looks like (x, f(x)). So the ordered pair here would be (5, f(5)) or (5, 7). Either one would work, as they are the same.
8(y+2) commutative property awnser commutative property (the order of 8x and -24 is swapped)
Answers
Answer:
solution is
Step-by-step explanation:
8y+16
and ready
Find the missing side length
Answers
Answer:
i think its 21
Step-by-step explanation:
different equation dy÷dx+ytanx=secx
Answers
Answer:
First, we rearrange the equation to isolate the y-term on one side:
dy/dx + ytanx = secx
Then, we multiply both sides by the integrating factor, which is e^(∫tanx dx) = e^(ln|secx|) = |secx|: | secx| dy/dx + ysecx tanx = 1
Next, we can write this as the derivative of a product using the product rule: d/dx (y |secx|) = 1
Integrating both sides with respect to x, we get: y |secx| = x + C
where C is the constant of integration. Solving for y, we have:
y = (x + C)/|secx|
Note that there is a singularity at x = (2n + 1)π/2, where the denominator |secx| is zero. At these points, the solution is not defined
PLS HELP ME!!! i’ll give you a brainliest answer :)
Answers
Answer:
B is the correct answer
16
Select the correct answer.
Which of the following graphs shows the solution set for the inequality below?
Ix+21+7>10
OA HH
OB. H
5
1 0 1 2 3
0 1
2 3 4
10
5 6
Answers
The solution set includes all real numbers less than -5, and all real numbers greater than 1, but does not include -5 or 1 themselves.
Option D is the correct answer.
We have,
We need to isolate the absolute value |x + 2| on one side of the inequality.
We subtract 7 from both sides.
|x + 2| > 3
Next, we can split this inequality into two separate inequalities, one for when the expression inside the absolute value is positive, and one for when it is negative:
x + 2 > 3
or
- (x + 2) > 3
Solving for x in the first inequality.
x > 1
Solving for x in the second inequality.
-x - 2 > 3
Adding 2 to both sides and multiplying by -1.
x < -5
So the solution set for the inequality |x + 2| + 7 > 10 is the set of all x-values that satisfy either x > 1 or x < -5.
Using interval notation.
(-∞, -5) U (1, ∞)
Thus,
The solution set includes all real numbers less than -5, and all real numbers greater than 1, but does not include -5 or 1 themselves.
Learn more about inequalities here:
https://brainly.com/question/20383699
#SPJ1
ead the situations below and determine which relationship is not functional.
Situation 1: a cell phone bill to the amount of minutes used
Situation 2: the perimeter of a square to the length of one of the sides of a square
Situation 3: the total amount of money charged monthly on credit cards to the number of credit cards owned
Situation
does not represent a function.
This is because
.
Answers
There can be multiple outputs (monthly charges) for a given input (number of credit cards), violating the definition of a function. hence, Situation 3 does not represent a function.
Situation 3: the total amount of money charged monthly on credit cards to the number of credit cards owned does not represent a function.
In a function, each input (or x-value) should have a unique output (or y-value). However, in this situation, the total amount of money charged monthly on credit cards depends on the number of credit cards owned. It is possible to have different credit card numbers but still have the same total amount of money charged monthly.
For example, two people could own different numbers of credit cards but have the same monthly charges.
As a result, the definition of a function can be violated by having many outputs (monthly charges) for a single input (number of credit cards).
Because of this, case 3 does not represent a function.
for such more question on function
https://brainly.com/question/16332322
#SPJ8
Writing Task 1:
Which one of the following does not belong and why?
a) log(1/1000) = X
b) log1000 (10) = x
c) (10³) = x
d) log (1000) =X
Answers
log1000(10) = x does not belong. This is because it does not have a real solution, while the other options (a, c, and d) have valid solutions.
The correct answer is option B.
To determine which one of the given options does not belong, we need to evaluate each option and compare them based on their properties and mathematical relationships.
a) log(1/1000) = x
Using the logarithmic property that log(a) = -log(1/a), we can rewrite this equation as:
log(1/1000) = log(\(1000)^(^-^1^)\)
log(1/1000) = log(\(1000)^(^-^1^)\)) = -3
b) log1000(10) = x
This equation can be rewritten as:
log base 1000 (10) = x
Here, the logarithm is asking for the power to which 1000 should be raised to obtain 10. Since 10 is not a power of 1000, this equation does not have a real solution. Therefore, this option does not belong.
c) (10³) = x
This equation represents 10 raised to the power of 3, which is equal to 1000. Therefore, x = 1000.
d) log(1000) = x
Using the logarithmic property that log base 10\((10^x)\) = x, we can rewrite this equation as:
log(1000) = log\((10^3)\) = 3
For more such information on: real solution
https://brainly.com/question/30188229
#SPJ8
According to the historical data, the life expectancy in Argentina is equal to the life expectancy in Bolivia. A new study has been made to see whether this has changed. Records of 265 individuals from Argentina who died recently are selected at random. The 265 individuals lived an average of 74.8 years with a standard deviation of 4.1 years. Records of 300 individuals from Bolivia who died recently are selected at random and independently. The 300 individuals lived an average of 75.4 years with a standard deviation of 4.3 years. Assume that the population standard deviation of the life expectancy can be estimated by the sample standard deviations, since the samples that are used to compute them are quite large. At the 0.05 level of significance, is there enough evidence to support the claim that the life expectancy, μ1, in Argentina is not equal to the life expectancy, μ2, in Bolivia anymore? Perform a two-tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)
The null hypothesis: H sub 0:
The alternative hypothesis: H sub 1:
The type of test statistic:
The value of the test statistic:
The two critical values at the 0.05 level of significance:
Can we support the claim that the life expectancy in Argentina is not equal to the life expectancy in Bolivia? Yes or No
Answers
Answer:
Step-by-step explanation:
Hello!
The historical data suggests that the life expectancy in Argentina is equal to the life expectancy in Bolivia.
With the objective of testing if that it hasn't changed, the records of recently deceased people from Argentina and Bolivia were selected at random:
Group 1: Argentina
X₁: Years of life of a recently deceased Argentinian.
n₁= 265
X[bar]₁= 74.8 years
S₁= 4.1 years
Group 2: Bolivia
X₂: Years of life of a recently deceased Bolivian.
n₂= 300
X[bar]₂= 75.4 years
S₂= 4.3 years
The parameters of interest are the population means of the years of life of people in both countries:
H₀: μ₁ = μ₂
H₁: μ₁ ≠ μ₂
α: 0.05
The statistic to use is an approximate standard deviation, and since both samples are quite large, it is valid to use the sample standard deviations in place of the population standard deviations:
\(Z= \frac{(X[bar]_1-X[bar]_2)-(Mu_1-Mu_2)}{\sqrt{\frac{S^2_1}{n_1} +\frac{S_2^2}{n_2} } }\)≈N(0;1)
\(Z_{H_0}= \frac{(74.8-75.4)-(0)}{\sqrt{\frac{16.81}{265} +\frac{18.49}{300} } }= -2.54\)
The critical values for this test are:
\(Z_{\alpha /2}= Z_{0.025}= -1.96\)
\(Z_{1-\alpha /2}= Z_{0.0975}= 1.96\)
Using the critical value approach, the decision rule is:
If \(Z_{H_0}\) ≤ -1.96 or if \(Z_{H_0}\) ≥ 1.96, reject the null hypothesis.
If -1.96 < \(Z_{H_0}\) < 1.96, do not reject the null hypothesis.
\(Z_{H_0}\) ≤ -1.96 so the decision is to reject the null hypothesis.
So with a 5% significance level, there is enough evidence to reject the null hypothesis, you can conclude that the life expectancy in Argentina is different from the life expectancy in Bolivia.
I hope this helps!
Plz I need help
......................
Answers
Answer:
B. (0, -4) and (4, -4)
Step-by-step explanation:
The solutions are the points of intersection of the circle and the parabola.
(0, -4) and (4, -4)
Question #3
Determine if the following scenario is best described as an observational study, survey, or experiment.
A researcher wants to determine the effects of eating a vegan diet on overall health. The researcher finds 200 individuals, where
of them have eaten vegan for the past five years and the other 100 have not eaten vegan for the past five years. The participants
each given a health assessment and the data is analyzed in order to draw conclusions about how eating vegan can affect one's
overall health.
Experimental Study
Observational study
Saved Survey
Answers
The type of sytudy that we have here is the observational study.
What is the observational study?
In an observational study, the researcher observes and analyzes data from individuals without actively intervening or manipulating any variables.
In this case, the researcher is observing and comparing the health outcomes of two groups of individuals: those who have eaten a vegan diet for the past five years and those who have not.
The participants are not randomly assigned to the groups, and the researcher does not actively control or manipulate the diet of the individuals.
Read more on observational study here:https://brainly.com/question/4758113
#SPJ1
I’m not sure if my answer correct. If you can please help me.
Answers
Answer:
i think it correct
Step-by-step explanation:
Answer:
The answer is
\( - \frac{13}{15} \\ \)
Step-by-step explanation:
\( \frac{7z - 12}{6 {z}^{2} - 3z } \\ \)
z = - 2
Substitute the value of z that's - 2 into the above expression
We have
\( \frac{7( - 2) - 12}{6 ({ - 2})^{2} - 3( - 2) } = \frac{ - 14 - 12}{6(4) + 6} \\ = \frac{ - 26}{24 + 6} = - \frac{26}{30} \)
Reduce the fraction with 2
We have the final answer as
\( - \frac{13}{15} \\ \)
Hope this helps you
The mean length of 4 childrens' index finger is 8.7cm.
The mean length of 11 adults' index finger is 13.4cm.
What is the mean length (rounded to 2 DP) of these 15 people's index finger?
Answers
The mean length (rounded to 2 DP) of these 15 people's index finger is 12.15 cm.
What is mean?It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.
It is given that:
The mean length of 4 children's index fingers is 8.7cm.
The mean length of 11 adults' index fingers is 13.4cm.
The mean of 15 people = [8.7x4 + 13.4x11]/15
The mean of 15 people = [34.8 + 147.4]/15
= 182.2/15
= 12.1466 cm
= 12.15 cm
Thus, the mean length (rounded to 2 DP) of these 15 people's index fingers is 12.15 cm.
Learn more about the mean here:
https://brainly.com/question/22871228
#SPJ1
Suppose you recently upgraded your gaming experience with an Wireless Controller for $74.99 and an Game Pass Ultimate service for $14.99 per month.
Answers
Answer:
$89.98
Step-by-step explanation:
$74.99+$14.99=$89.98
Write an equation in slope-intercept form for the line with y-intercept 3 and slope 2.
Answers
Answer:
y=2x+3
Step-by-step explanation:
Slope intercept form: y=mx+b
mx(slope)=2
(b)y-intercept=3
y=2x+3
Hope this helps :)
What is the nth term rule of the linear sequence below?
-5, -2, 1, 4, 7, ...
Tn
-
Answers
The nth term rule of linear sequence is aₙ = aₙ₋₁ + 3
Linear sequence is a sequence of number in order with same difference .or same ratio.
when fixed number is added to any term of a sequence to get next term . That Fixed number is known as common difference.
The sequence in the given question
-5 , -2 , 1 , 4 , 7, . . . .
The first term of sequence : a₁ = -5
The second term : a₂ = -2
Common difference : d = a₂ - a₁
=> d = -2 - (-5)
=> d = -2 + 5
=> d = 3
The nth rule of linear sequence is aₙ = aₙ₋₁ + d
replacing the value of d
aₙ = aₙ₋₁ + 3 is nth rule of the linear sequence.
To know more about Linear sequence here
https://brainly.com/question/24492686
#SPJ9
i will give you brainliest whoever answers correct first!!
Answers
Answer:
IJ = 12.8
Step-by-step explanation:
Since you are missing 1 side, set up a proportion 8 is to 3.2 as 32 is to x, so
\(\frac{8}{3.2} =\frac{32}{x}\) so solve for x by cross multiplying 8x = 102.4, so x = 12.8
When our brains store information, complicated chemical changes take place. In trying to understand these changes, researchers blocked some processes in brain cells taken from rats and compared these cells with a control group of normal cells. They report that "no difference was seen" between the two groups (P 0.45).
Say clearly what the P-value, P- 0.45, says about the response that was observed.
A) None of the options are correct.
B) P-0.45 says that a response this large or larger would be seen in sample data nearly all of the time when in fact there is no effect in the entire population of rats. That is, a response this size would often happen just by chance.
C) P-045 says that a response this large or larger would be seen in sample data almost half the time when in fact there is no effect in the entire population of rats. That is, a response this size would often happen just by chance
D) P-045 says that a response this small or smaller would be seen in sample data almost half the time when in fact there is no effect in the entire population of rats. That is, a response this size would often happen just by chance.
Answers
Answer:
D) P-045 says that a response this small or smaller would be seen in sample data almost half the time when in fact there is no effect in the entire population of rats. That is, a response this size would often happen just by chance.
Step-by-step explanation:
The P-value represents the probability of getting the test sample results given that the null hypothesis is true.
A P-value that is low enough (smaller than the significance level) gives statistical evidence to support that the null hypothesis is not true.
In this case, a P-value of 0.45 does not represent a strong evidence against the null hypothesis, as there is 45% of chances of getting this sample results if the null hypothesis is true.
In this case, as we talk about differences ("no difference was seen" between the two groups), we know that the sample difference has not been large enough to be proved statistically significant.
So the right answer is Option d).
a circle passes through the points o(0,0), a(8,4) and b(6,6). show that oa is a diameter of the circle and find the equation of the circle
Answers
9514 1404 393
Answer:
(x -4)² +(y -2)² = 20
Step-by-step explanation:
The circle is the circumcircle of triangle OAB. Then OA will be a diameter if angle OBA is a right angle. We can check that by looking at the slopes of AB and BA.
B-O = (6, 6)-(0, 0) = (6, 6) ⇒ slope = Δy/Δx = 6/6 = 1
A-B = (8, 4) -(6, 6) = (2, -2) ⇒ slope = -2/2 = -1
These slopes have a product of -1, so OB ⊥ BA. The hypotenuse (OA) of ΔOBA is the diameter of the circle.
Then the midpoint of the hypotenuse is the center of the circle.
C = (O +A)/2 = ((0, 0) +(8, 4))/2 = (4, 2)
The equation is ...
(x -h)² +(y -k)² = r² . . . . . circle with center (h, k) and radius r
The radius is the distance from O to C, so is ...
r² = 4² +2² = 20
and the equation of the circle is ...
(x -4)² +(y -2)² = 20 . . . . equation of the circle
Determine whether each quadrilateral is a parallelogram. Justify your answers.
And
Explain why the quadrilateral with the given vertices is a parallelogram. Use the indicated theorem.
Answers
The given quadrilaterals, 1 and 2, are parallelograms because the pair of opposite sides are parallel and the other pairs are congruent.
3. According to Theorem 7.9, quadrilateral ABCD is a parallelogram.
4. According to Theorem 7.12, quadrilateral PQRS is a parallelogram.
What is the proof for the parallelograms?3. Quadrilateral ABCD with vertices A(0,0), B(7,1), C(5,6), D(-2,5), and Theorem 7.9:
Theorem 7.9 states that if the opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Using the distance formula, we can calculate the lengths of the sides of quadrilateral ABCD:
AB = √((7 - 0)² + (1 - 0)²) = √50
BC = √((5 - 7)² + (6 - 1)²) = √29
CD = √((-2 - 5)² + (5 - 6)²) =√50
DA = √((0 - (-2))² + (0 - 5)²) = √29
We can see that AB = CD and BC = DA, indicating that the opposite sides are congruent.
Quadrilateral PQRS with vertices P(-2,0), Q(3,1), R(4,4), S(-1,3), and Theorem 7.12:
Theorem 7.12 states that if both pairs of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram.
Using the slope formula, we can calculate the slopes of the sides of quadrilateral PQRS:
Slope of PQ = (1 - 0) / (3 - (-2)) = 1/5
Slope of RS = (4 - 3) / (4 - (-1)) = 1/5
Slope of QR = (4 - 1) / (4 - 3) = 3
Slope of SP = (3 - 0) / (-1 - (-2)) = 3
The lengths of opposite sides can be calculated using the distance formula:
PQ = √((3 - (-2))² + (1 - 0)²) = √(25 + 1) = √26
RS = √((4 - 4)² + (4 - 1)²) = √(9) = 3
QR = √((4 - 3)² + (4 - 1)²) = √(1 + 9) = √10
SP = √((-1 - (-2))² + (3 - 0)²) = √(1 + 9) = √10
We can see that PQ = RS and QR = SP, indicate that the opposite sides are parallel and congruent.
Learn more about parallelograms at: https://brainly.com/question/20526916
#SPJ1
Someone help pls :((((
Answers
9514 1404 393
Answer:
y +1 = -3(x -3)
Step-by-step explanation:
The given point is (3, -1), and the given slope is -3. The form suggests you want the point-slope form of the equation for the line:
y -k = m(x -h) . . . . . . . . line with slope m through point (h, k)
Using the given values, the equation is ...
y -(-1) = -3(x -3)
y +1 = -3(x -3)
I think I did this right?
Answers
Answer:
I'm just gonna take a guess that you did.
Step-by-step explanation:
A delivery driver makes $78 each day that he works and makes approximately $10 in tips for each delivery that he makes. If he wants to make at least $238 in one day, at least how many deliveries does he need to make?
Answers
Answer:
16 deliveries
Step-by-step explanation:
We can model the situation using a linear inequality. Since we're told that the driver makes $10 in tips for each delivery.Thus, this is the slope.Since he makes $78 each day, this number is a constant and he makes it even when no deliveries are made. Thus, this is the y-interceptSince he wants to make at least #238, we want to find a value of d (number of deliveries) which would cause his wages to equal #238. Thus, we can use the following equation to find:238 ≤ 10d + 78
160 ≤ 10d
16 ≤ d
Thus, he needs to make at least 16 deliveries to make at least $238 in one day. Any less than 16 deliveries will cause him to fall short of his goal and any more than 16 deliveries will cause him to exceed his goal.