Answer:
(a) The probability of waiting less than 12 minutes between successive speeders using the cumulative distribution function is 0.7981.
(b) The probability of waiting less than 12 minutes between successive speeders using the probability density function is 0.7981.
Step-by-step explanation:
The cumulative distribution function of the random variable X, the waiting time, in hours, between successive speeders spotted by a radar unit is:
[tex]F(x)=\left \{ {{0;\ x<0} \atop {1-e^{-9x};\ x\geq 0}} \right.[/tex]
(a)
Compute the probability of waiting less than 12 minutes between successive speeders using the cumulative distribution function as follows:
[tex]12\ \text{minutes}=\frac{12}{60}=0.20\ \text{hours}[/tex]
The probability is:
[tex]P(X<0.20)=|F (x)|_{x=0.20}[/tex]
[tex]=(1-e^{-8x})|_{x=0.20}\\\\=1-e^{-8\times 0.20}\\\\=0.7981[/tex]
Thus, the probability of waiting less than 12 minutes between successive speeders using the cumulative distribution function is 0.7981.
(b)
The probability density function of X is:
[tex]f_{X}(x)=\frac{d F (x)}{dx}=\left \{ {{0;\ x<0} \atop {8e^{-8x};\ x\geq 0}} \right.[/tex]
Compute the probability of waiting less than 12 minutes between successive speeders using the probability density function as follows:
[tex]P(X<0.20)=\int\limits^{0.20}_{0} {8e^{-8x}} \, dx[/tex]
[tex]=8\times [\frac{-e^{-8x}}{8}]^{0.20}_{0}\\\\=[-e^{-8x}]^{0.20}_{0}\\\\=(-e^{-8\times 0.20})-(-e^{-8\times 0})\\\\=-0.2019+1\\\\=0.7981[/tex]
Thus, the probability of waiting less than 12 minutes between successive speeders using the probability density function is 0.7981.
HELP PLEASE!!!!!!!!!!!!!!
Answer:
Savannah
Step-by-step explanation:
Emery has solved it incorrectly;
x = 100
A professor gives her 100 students an exam; scores are normally distributed. The section has an average exam score of 80 with a standard deviation of 6.5. What percentage of the class has an exam score of A- or higher (defined as at least 90)? Type your calculations along with your answer for full credit; round your final percentage to two decimal places.
Answer:
6.18% of the class has an exam score of A- or higher.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 80, \sigma = 6.5[/tex]
What percentage of the class has an exam score of A- or higher (defined as at least 90)?
This is 1 subtracted by the pvalue of Z when X = 90. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{90 - 80}{6.5}[/tex]
[tex]Z = 1.54[/tex]
[tex]Z = 1.54[/tex] has a pvalue of 0.9382
1 - 0.9382 = 0.0618
6.18% of the class has an exam score of A- or higher.
What is the vertex of f(x) = |x+ 8|– 3?
(-8, -3)
(-8,3)
(8, -3)
(8,3)
Answer:
The vertex is at (-8,-3)
Step-by-step explanation:
The function is of the form
y = a|x-h| + k where (h,k) is the vertex
f(x) = |x+ 8|– 3
f(x) = |x - - 8|– 3
The vertex is (-8,-3)
Ann pays $300 for membership to a local gym. She is allowed to bring one guest on any visit. John pays Ann $5 to go to the gym with her occasionally. Describe what the expression 300 - 5t could represent. Then evaluate the expression for T equals five 10 15 and 20
Answer:
f
Step-by-step explanation:
NEED HELP ASP Find the common difference of the arithmetic sequence -8, -15, -22, ...
Answer:
-7
Step-by-step explanation:
To find the differences in a sequence, subtract the term before:
-15 -(-8) = -7
-22 -(-15) = -7
These differences are the same, so constitute the "common" difference.
The common difference of the sequence is -7.
Let x = 8.99999 . (a) Is x < 9 or is x = 9? x < 9 It is neither; x > 9 x = 9 x < 9 and x = 9 It cannot be determined. (b) Sum a geometric series to find the value of x. x = (c) How many decimal representations does the number 9 have? decimal representations (d) Which numbers have more than one decimal representation? the integers the rational numbers except for 0 all rational numbers that have a terminating decimal representation except for 0 all integers except for 0 all real numbers
Answer: idk
Step-by-step explanation:
idk
Trey is out shopping and sees that striped shirts are on sale for $25.00 each, and plaid pants are on sale for $22.50 each. He buys 2 shirts and 4 pairs of pants. What is the total of his
purchase?
The total was $______
Answer:
$140
Step-by-step explanation:
You can add up the prices to find the total. Most of us find it easier to multiply the price by the number of items.
cost of 2 shirts = (2)($25.00) = $50
cost of 4 pants = (4)(22.50) = $90
The total was $50 +90 = $140.
What is the slope of a line that is perpendicular to the line y = x + 5?
Answer:
-1.
Step-by-step explanation:
The standard form of a line can be written y = mx + b where m is the slope.
y = x + 5 can be written as y = 1x + 5 which shows that the slope is 1.
If the slope of a line is m then the slope of a line perpendicular to it is -1/m.
So the required slope is -1/1 = -1.
Answer:
-1
Step-by-step explanation:
the line is exactly opposite like a mirror image when it is perpendicular,
so the gradient of the first line is 1 (because there is no number beside x, the gradient would be 1), that means the opposite of 1 would be -1.
The answer is -1
Math Is TU parallel to VW explain
Answer: C ( yes, both lines have a slope of 2/3. )
Step-by-step explanation:
Answer: C
Step-by-step explanation:
M is the midpoint of st. Sm= 3x+16 and MT = 6x+4. Find the length of SM.
No figure required. If M is the midpoint of ST then SM=MT or
3x + 16 = 6x + 4
12 = 3x
x = 4
SM = 3(4)+16=28
Answer: 28
The relationship between ttt and rrr is expressed by the equation 2t+3r+6=02t+3r+6=02, t, plus, 3, r, plus, 6, equals, 0. If rrr increases by 444, which of the following statements about ttt must be true?
Question:
The relationship between t and r is expressed by the equation 2t+3r+6 = 0. If r increases by 4, which of the following statements about t must be true?
Answer:
The value of t is reduced by 6 when the value of r is increased by 4
Step-by-step explanation:
Given
[tex]2t + 3r + 6 = 0[/tex]
Required
What happens when r is increased by 4
[tex]2t + 3r + 6 = 0[/tex] -------- Equation 1
Subtract 2t from both sides
[tex]2t + 3r + 6 - 2t = 0 - 2t[/tex]
[tex]3r + 6 = - 2t[/tex] --- Equation 2
When r is increased by 4, equation 1 becomes
[tex]2T + 3(r+4) + 6 = 0[/tex]
Note that the increment of r also affects the value of t; hence, the new value of t is represented by T
Open bracket
[tex]2T + 3r+12 + 6 = 0[/tex]
Rearrange
[tex]2T + 3r+6 +12 = 0[/tex]
Substitutr -2t for 3r + 6 [From equation 2]
[tex]2T -2t +12 = 0[/tex]
Make T the subject of formula
[tex]2T = 2t - 12[/tex]
Divide both sides by 2
[tex]\frac{2T}{2} = \frac{2t - 12}{2}[/tex]
[tex]T = t - 6[/tex]
This means that the value of t is reduced by 6 when the value of r is increased by 4
A gumball machine has 100 red gumballs. If the red gumballs are 25% of the total number of gumballs, how many gumballs are in the gumball machine?
Answer: 400
Step-by-step explanation:
25% is equal to one quarter (1/4). If theres 100 red gumballs then there must be 300 more gumballs in the machine because a quarter of a number is always even.
Determine whether the given value of the variable is a solution of the inequality.
Answer:
Yes, [tex]\frac{3}{4}[/tex] is a solution of the inequality.
Step-by-step explanation:
Solution of an inequality is given by the values of the variable t ≥ [tex]\frac{2}{3}[/tex]
Or t ≥ 0.67
If a solution of this inequality is t = [tex]\frac{3}{4}[/tex]
Or t = 0.75
Since, on a number line 0.75 > 0.67
Therefore, [tex]\frac{3}{4}[/tex] will be a solution of the inequality.
Please help! I don’t get what I’m supposed to put in those boxes
The volume of any cylinder is
V = pi*r^2*h
where r is the radius and h is the height. We are keeping r = 2 the same the entire time, as the first part of the instructions indicate. In contrast, h is allowed to vary or change based on the values shown in the table.
If h = 1, then,
V = pi*r^2*h
V = pi*2^2*1
V = pi*4
V = 4pi
So you'll write "4pi", without quotes of course, in the V column next to h = 1. This first row shows a height of 1 leads to a volume of 4pi.
-------------
Then if h = 2, we have,
V = pi*r^2*h
V = pi*2^2*2
V = pi*8
V = 8pi ... this is written in the second box
and finally if h = 3, we would say,
V = pi*r^2*h
V = pi*2^2*3
V = pi*12
V = 12pi .... and this is placed in the third box
---------------
The values of V we got were: 4pi, 8pi, 12pi
This is for h = 1,2 and 3 respectively in that order.
The sequence 4,8,12 is linear because we are adding 4 each time. More specifically, it fits the equation y = 4x where x = 1,2,3. Think of y = 4x as y = 4x+0 and that fits the slope intercept form y = mx+b.
Solve the equation. 4c = 3
Answer:
Brainelist~~~!!!
Step-by-step explanation:
4c=3
c=3/4
c=0.75
The solution of the linear equation 4·c = 3, obtained by solving for the variable c is; c = 3/4
What is a linear equation?A linear equation is an equation that can be expressed in the form; y = m·x + c
The equation 4·c = 3 is a linear equation
In order to solve the equation 4·c = 3 for the variable c, the variable c needs to be isolated to one side of the equation, by dividing both sides of the equation by 4 as follows;
4·c = 3
(4·c)/4 = 3/4
c = 3/4
Therefore, the solution of the equation, 4·c = 3 is; c = 3/4
Learn more on linear equations here: https://brainly.com/question/30338252
#SPJ6
Two barrels are mathematically similar
The smaller barrel has a height of [tex]h[/tex]cm and a capacity of 100 Liters
The larger barrel has a height of 90cm and a capacity of 160 Liters
-Work out the value of [tex]h[/tex]
Answer:
h ≈ 77 cm
Step-by-step explanation:
Let us convert the liters to cm³.
Smaller barrel
0.001 litres = 1 cm³
100 litres = 100000 cm³
Larger barrel
0.001 litres = 1 cm³
160 litres = 160000 cm³
For a similar solid figure the cube of their corresponding sides is equal to the volume ratio.
This means
h³/90³ = 100000/160000
cube root both sides
h/90 = ∛100000 / ∛160000
h/90 = 46.4158883/54.2883523
cross multiply
54.2883523h = 46.4158883 × 90
54.2883523h = 4177.429947
divide both side by 54.2883523
h = 4177.429947/54.2883523
h = 76.9489175858
h ≈ 77 cm
One third of the sum of 15
and thrice a certain number is
equal to twice the number. Find
the number
Answer:
x=-1/39
Step-by-step explanation:
Really easy math question!
the answer is A: 146 ≤ 9c + 10
An employee wants to invest $50,000 in a pension plan. One investment offers 6% compounded quarterly. Another offers 5.75% compounded continuously.
(a) Which investment will ear more interest in 5 yr?
(b) How much more will the better plan earn?
Answer:
a. 6% one is better
b. $12,285.95
Step-by-step explanation:
a. For determining which investment earn more first we have to calculate both the investment which are as follows
a. Based on compound quarterly, the amount is find out by using the following formula
[tex]Amount = {Present\ value\times (1 + interest\ rate)} ^{number\ of\ years}[/tex]
where,
Present value is $50,000
Interest rate is = [tex]\frac{0.06}{4}[/tex] = 0.015
And, the number of years is
= [tex]4\times4[/tex]
= 16
So, the amount is
[tex]= \$50,000 \times (1 + 0.015)^{16}[/tex]
= $63,449.28
And, based on compounded continuously, the amount is determined by using the following formula
[tex]Amount = Present\ value\times e^{rt}[/tex]
[tex]= \$50,000 \times e.^{0575(4)}[/tex]
= $51,163.33
Therefore, The the investment at 6% is better
b. Now the difference in earning is
= $63,449.28 - $51,163.33
= $12,285.95
John leaves school to go home.his bus drives 6 kilometers north and then goes 7 kilometers west.how far is John's house from the school?
Answer:
John is 9.21 km form the school.
Step-by-step explanation:
John leaves school to go home. His bus drives 6 kilometres north and then goes 7 kilometres west. It is required to find John's distance from the school. It is equal to the shortest path covered or its displacement. So,
[tex]d=\sqrt{6^2+7^2} \\\\d=9.21\ km[/tex]
So, John is 9.21 km form the school.
Please help! Correct answer only, please! The following information matrices shows how many of each vehicle type sold and the bonus amount each salesperson receives for selling that type of vehicle for the car dealership for the week. What does the element LaTeX: A_{2,3}A 2 , 3represent? A. Mark sold 2 vans B. Scott sold 1 Van C. Mark sold 4 trucks D. Kelly sold 2 trucks
Answer: B) Scott sold 1 van
Step-by-step explanation:
A₂,₃ represents: matrix A - 2nd row - 3rd column
The second row is Scott and and the 3rd row is Vans
If you look at Scott - Vans, you will see that Scott sold 1 van.
A loan of $8 000 was repaid in 2 years in
monthly payments of $400.00. The interest
on the loan, as e percentage, was?
Answer:
P = 8000
t = 2
I = p × r × t
400 = 8000 × r/100 × 2
r = 400/160 per year
r = 40/16 = 2.5 %
Graph y < x2 + 4x. Click on the graph until the correct graph appears.
Answer: The correct answer is:
_________________________
The given "graph" in the bottom right, lowest corner
Step-by-step explanation:
_________________________
Note: When there is only one (1) equation give for a graph;
and/or: only one (1) "inequality given";
we look for the symbol.
If the symbol is "not" an "equals" symbol (i.e. not an: = symbol) ;
we check for the type of "inequality" symbol.
If there is a: "less than" (<) ; or a "greater than" (>) symbol; the graph of the "inequality" will have "dashed lines" (since there will be a "boundary").
If there is an "inequality" that is a: "less than or equal to" (≤) ;
or a: "greater than or equal to" (≥) ;
→ then there will be not be a dashed line when graphed;
but rather—a "solid line" ; since "less than or equal to" ;
or "greater than or equal to" —is similar to:
"up to AND including"; or: "lesser/fewer than AND including".).
_________________________
Note: We are given the "inequality" :
→ " y < x² + 4x " .
_________________________________
Note that we have a "less than" symbol (< ) ; so the graph will have a:
"solid line" [and not a "dotted line".].
_________________________________
Note that all of the graphs among our 4 answer choices have "dotted lines".
Not that all values (all x and y coordinated) within the "shaded portion" of the corresponding graph are considered part of the graph.
As such, given any point within the shaded part, the x and y coordinates must match the inequality (i.e. the given inequality must be true when one puts in the "x-coordinate" and "y-coordinate" into the "given inequality" :
→ " y < x² + 4x " .
_________________________
Likewise, we can take any point within the "white, unshaded" portion of any of the graph, and take the "x-coordinate" and "y-coordinate" of that point, and the inequality: → " y < x² + 4x " ; will not hold true when the "x-coordinate" and "y-coordinate" values of that point— are substituted into the "inequality".
_________________________
{Note: Answer is continued on images attached.}.
Wishing you the best!
a large which has topics of Capsicum and onion in there in total there are 25 pieces of both on the pizza if there are four times as many onions pieces as capsicum pieces how many pieces of eat vegetable are there on the pizza
Step-by-step explanation:
I think there should be 5 capsicums because
4 times onions = 5 x 4 = 20
Then 5 capsicums = 20 + 5 = 25
Answer:
A large pizza has toppings of capsicum and onion. In total there are 36 pieces of both on the pizza .If there are 5 times as many onions pieces as capsicum pieces,how many of each vegetable are there on the pizza?
Step-by-step explanation:
Can you please help with this one
Every product manufactured by a company goes through 6 different tests before being shipped out. It is known that the probability that a product passes any single test is 0.9 and the tests are independent. Only those products that pass the first three tests and also pass at least one of the three remaining tests are shipped out. Find the probability that a manufactured product is shipped out.
Answer:
The Probability that the product is shipped out is 0.7283
Step-by-step explanation:
Here, we are given that, a product passes through 6 tests before it is shipped out and a product is shipped out only if it passes all the first 3 tests and at least 1 of the remaining 3 tests.
We have P(pass)= 0.9, is the Probability of passing any test.
Which implies, P(fail)= 1- 0.9= 0.1
We have to find the Probability that the product is shipped out.
P(product is shipped out) = P(it passes first 3 tests )*P(passes at least 1 of the remaining 3 tests) •••••••••••(i)
We can take the product as the tests are Independent.
Now, let us obtain
P(it passes first 3 tests ) = P(pass)*P(pass)*P(pass)
=P(pass)]^3 = (0.9)^3 = 0.729
Hence, P( it passes first 3 tests)= 0.729 •••••••(ii)
Now,
P(passes at least 1 of the remaining 3 tests)
= 1-P(fails all the 3 remaining tests)
= 1-(0.1)^3 = 1 - 0.001 = 0.999
Hence,
P(passes atleast 1 of the remaining 3 tests)=0.999 ••••••••(iii)
Now, substituting the 2nd and 3rd equations in the first equation, we have;
P(product is shipped out) = P(it passes first 3 tests )*P(passes at least 1 of the remaining 3 tests)
= (0.729)*(0.999)
= 0.728271
= 0.7283
Henry, Brian and Colin share some sweets in the ratio 6:4:1. Henry gets 25 more sweets than Colin. How many sweets are there altogether?
Answer:
There are 55 sweets in total.
Step-by-step explanation:
The total number of sweets is t.
Henry, Brian and Colin share some sweets in the ratio 6:4:1.
This means that Henry earns [tex]\frac{6}{6+4+1} = \frac{6}{11}[/tex] of the total(t).
Brian earns [tex]\frac{4}{11}[/tex] of the total.
Colin earns [tex]\frac{1}{11}[/tex] of the total
Henry gets 25 more sweets than Colin.
Henry earns [tex]\frac{6t}{11}[/tex]
Colin earns [tex]\frac{t}{11}[/tex]
So
[tex]\frac{6t}{11} = \frac{t}{11} + 25[/tex]
Multiplying everything by 1
[tex]6t = t + 275[/tex]
[tex]5t = 275[/tex]
[tex]t = \frac{275}{5}[/tex]
[tex]t = 55[/tex]
There are 55 sweets in total.
Do the measures of center make sense? A. Only the mode makes sense since the data is nominal. B. All the measures of center make sense since the data is numerical. C. Only the mean, median, and midrange make sense since the data is nominal. D. Only the mean, median, and mode make sense since the data is numerical.
Answer:
A. Only the mode makes sense since the data is nominal.
Step-by-step explanation:
Hello!
The objective of the study was to determine if deficiency of carbon dioxide in the soil affects the phenotype of peas.
The variable of study is X: Phenotype of a pea grown in soil with carbon dioxide deficiency.
Possible values of Phenotype codes:
1= smooth-yellow
2= smooth-green
3= wrinkled-yellow
4= wrinkled-green
The absolute frequencies for each phenotype are:
f(1)= 3
f(2)= 4
f(3)= 6
f(4)= 1
n= 14
a) Mean:
X[bar]= (∑xifi)/n= [(1*3)+(2*4)+(3*6)+(4*1)]/14= 33/14= 2.357= 2.36
The average value is always within range of definition of the variable but it does not necessarily correspond to an observation.
b) Median:
To determine the value that corresponds to the median you have to calculate its position:
For even samples the position is:
PosMe= n/2= 14/2= 7
Then you have to arrange the data from least to greatest, in this case, starting from the first category, you have to determine where the seventh observation is within the observed absolute frequencies. The phenotype that corresponds to the 7th observation is 2= smooth-green.
Me= 2= smooth-green.
c) Mode:
The mode corresponds to the most observed category/ value of the variable, i.e. the category with the most observations is 3= wrinkled-yellow
Md= 3= wrinkled-yellow
d) Midrange: (1 + 4)/2= 2.5
e)
As you can see the variable is qualitative and categorical. Even if all central tendency measurements can be calculated, truth is that the only one that shows any valuable information regarding the data set is the mode.
I hope this helps!
Suppose I claim that the average monthly income of all students at college is at least $2000. Express H0 and H1 using mathematical notation, and clearly identify the claim and type of testing.
Answer:
For this case we want to test if the the average monthly income of all students at college is at least $2000. Since the alternative hypothesis can't have an equal sign thne the correct system of hypothesis for this case are:
Null hypothesis (H0): [tex]\mu \geq 2000[/tex]
Alternative hypothesis (H1): [tex]\mu <2000[/tex]
And in order to test this hypothesis we can use a one sample t or z test in order to verify if the true mean is at least 200 or no
Step-by-step explanation:
For this case we want to test if the the average monthly income of all students at college is at least $2000. Since the alternative hypothesis can't have an equal sign thne the correct system of hypothesis for this case are:
Null hypothesis (H0): [tex]\mu \geq 2000[/tex]
Alternative hypothesis (H1): [tex]\mu <2000[/tex]
And in order to test this hypothesis we can use a one sample t or z test in order to verify if the true mean is at least 2000 or no
The function f determines the volume of the box (in cubic inches) given a cutout length (in inches). Use function notation to represent the volume of the box (in cubic inches) when the cutout length is 0.2 inches. Use function notation to represent the volume of the box (in cubic inches) when the cutout length is 1.3 inches. Use function notation to represent how much the volume of the box (in cubic inches) changes by if the cutout length increases from 0.2 inches to 1.3 inches. Use function notation to represent how much the volume of the box (in cubic inches) changes by if the cutout length increases from 5.5 inches to 5.6 inches.
Complete Question
A box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides. However, the size of the paper is unknown!
Answer:
(a)[tex]f(0.2)=0.2(l-0.4)(w-0.4)[/tex]
(b)[tex]f(1.3)=1.3(l-2.6)(w-2.6)[/tex]
(c)f(1.3)-f(0.2)
(d) f(5.6)-f(5.5)
Step-by-step explanation:
Let the Length of the paper =l (in inches)
Let the Width of the paper =w (in inches)
Let the length of the cutout square = x (in inches)
Base Length of the Box = l-2xBase Width of the box =w-2xHeight of the box =xVolume of the box: [tex]f(x)=x(l-2x)(w-2x)[/tex]
(a)When the cutout length is 0.2 inches.
x=0.2
Volume of the box (in cubic inches) ,
[tex]f(0.2)=0.2(l-0.4)(w-0.4)[/tex]
(b)When the cutout length is 01.3 inches.
x=1.3
Volume of the box (in cubic inches) ,
[tex]f(1.3)=1.3(l-2.6)(w-2.6)[/tex]
(c)If the cutout length increases from 0.2 inches to 1.3 inches.
Change In volume (in cubic inches):
[tex]f(1.3)-f(0.2)\\=1.3(l-2.6)(w-2.6)-0.2(l-0.4)(w-0.4)[/tex]
(d)If the cutout length increases from 5.5 inches to 5.6 inches.
Change In volume (in cubic inches):
[tex]f(5.6)-f(5.5)\\=5.6(l-11.2)(w-11.2)-5.5(l-11)(w-11)[/tex]
This chart shows Dan’s budget:
A 3-column table has 5 rows. The first column is labeled Item with entries Internet, food, rent, discretionary spending, income. The second column is labeled Amount budgeted with entries 35, 100, 500, 100, 750. The third column is labeled Amount spent with entries 35, 95, 500, 140, blank.
Did Dan stay on budget? Why or why not?
Yes, Dan spent as much as he earned.
No, Dan should move to a new apartment.
Yes, Dan uses his savings to cover extra expenses.
No, Dan should reduce his discretionary spending
The correct answer is D No, Dan should reduce his discretionary spending
Explanation:
For Dan to stay on the budget he needs to spend the amount budgeted for each expense or less than the amount budgeted. This occurred in the case of the Internet, food, and rent; for example, the amount budgeted for the internet was $35 and Dan spent this money, also, the amount budgeted for food was $100 and Dan spent $95, which means he stood in the budget. However, this did not occur with discretionary spending, which refers to other non-necessary expenses, because in this case, Dan spent $140 even when the budget limit was $100. Also, this exceeds the total income considering 35 + 95 + 500+ 140 = $770, which is above the income ($750). Thus, Dan did not stay in the budget because he spent more money than expected in discretionary spending and should reduce this.
The correct answer is D. No, Dan should reduce his discretionary spending.
Hope this helps
:)
