Debbie's checkbook balance is $-3,297.23, which shows an overdraft.
When does an overdraft occur?An overdraft occurs when the money (deposits) in Debbie's account does not exceed her payments or withdrawals.
While Debbie had a positive beginning balance, the ending balance shows an overdraft of $-3,297.23.
By this overdraft, Debbie's bank is extending her some short-term credit, which she should pay back with interest.
Beginning balance on checkbook = $2,715.50
Checks for the month = $-5,298.13
Deposits for the month = $250.16
Payroll check = $-2,980.66
IRS check = $2,550
Auto insurance and utilities = $-534.10
Ending balance on checkbook = $-3,297.23
Thus, Debbie's ending checkbook balance will show an overdraft of $-3,297.23.
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Evaluate the expression (c^2) + (d^3) for c = 3 and d = 3
ANSWER
36
EXPLANATION
We want to evaluate the expression for when c = 3 and d = 3.
The expression given is:
[tex]c^2+d^3[/tex]To do this, we will simply replace the values of c and d with the values given:
[tex]\begin{gathered} 3^2+3^3 \\ =\text{ 9 + 27} \\ =\text{ 36} \end{gathered}[/tex]That is the answer.
-5x + 3 > (-7x) - 12
Solve the inequality
-5x + 3 > (-7x) - 12
We want to move the variables to the left side and the numbers to the right side. The (-7x) can be eliminated from the right side by adding 7x on both sides.
Add 7x to both sides:
-5x + 3 + 7x > -12
We need to move the 3 from the left to the right side. So we subtract 3
Subtract 3 to both sides:
-5x + 7x > -12 - 3
Joining like terms:
2x > -15
Solving:
x > -15/2
The solution is every real number greater than -15/2
In interval notation, it can be written as:
[tex]\mleft(-15/2,+\infty\mright)[/tex]The left parentheses are used because the endpoint is not included in the solution
If the endpoint was included, we'd use a bracket [
Jane spends $15 each time she travels the toll roads. She started the month with $240 in her toll road account. The amount, A (in dollars), that she has left in the account after r trips on the toll roads is given by the following function.
How much money does Jane have left in the account after 8 trips on the toll roads?
(b) How many trips on the toll roads can she take until her account is empty?
$120 money does Jane have left in the account after 8 trips on the toll roads and She has to make 16 trips to make her account empty.
What is Equation?
Two or more expressions with an equal sign is called equation.
Given that Jane spends $15 each time she travels the toll roads..
Jane started the month with $240 in her toll road account.
The amount, A (in dollars), that she has left in the account after r trips on the toll roads is given by the following function
A(r)=240-15r.
Now for 8 trips the amount she left is
A(8)=240-15(8)
=240-120
=120
So $120 money does Jane have left in the account after 8 trips on the toll roads.
$240/15
=16.
She has to make 16 trips to make her account empty.
Hence $120 money does Jane have left in the account after 8 trips on the toll roads and She has to make 16 trips to make her account empty.
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The area of a square is 256cm2What is the length of its side?
The area of a square is 256cm2
What is the length of its side?
Remember that
the area of a square is equal to
A=b^2
wheer
b is the length side
in this problem we have
A=256 cm2
substitute
256=b^2
square root both sides
b=16 cm
answer is
length side is 16 cmGiven points J(2,5), A(5,4), and R(4,2), graph AJAR and its reflection image across the given line.Ry-axis
after a reflection across the x-axis:
[tex]\begin{gathered} J\to(x,-y)\to J^{\prime}=(2,-5) \\ A\to(x,-y)\to A^{\prime}=(5,-4) \\ R\to(x,-y)\to R^{\prime}=(4,-2) \end{gathered}[/tex]Suppose Rachel and Nadia buy a house and have to take out a loan for $183500. If they qualify for an APR of 3.75% and choose a 30 year mortgage, we can find their monthly payment by using the PMT formula. If Rachel and Nadia decide to pay $1500 per month, we can use goal seek to see how many years it will take to pay off the loan. Use the PMT function and goal seek (as needed) to answer the following questions about Rachel and Nadia's mortgage. a. What is their monthly payment on the 30 year loan? $ 15 year loan, what will the new monthly payment be?
We have that the PMT formula is given by:
[tex]\text{PMT}=p(\frac{\frac{r}{n}}{1-(1+\frac{r}{n})^{-ny}})[/tex]Where p is the initial principal (Loan ammount), r is the interest rate period, n is the total number of payments or periods, y is the number of years, PMT is the monthly payment.
Now, replacing the data in the formula, we will get:
*The payment will be due for 30 years, that is 12 months each year [That is our n] and y will be 30, r is 0.0375.
p will be $183500, that is:
[tex]\text{PMT}=(183500)(\frac{\frac{0.0375}{12}}{1-(1\pm\frac{0.0375}{12})^{-(12)(30)}})[/tex]Then, we will have that the monthly payment for the 30 years, should be:
[tex]\text{PMT}=849.8171105[/tex]If she wishes to pay $1500 each mothn, we then replace in the formula:
[tex]1500=(183500)(\frac{(\frac{0.0375}{12})}{1-(1+\frac{0.0375}{12})^{-12y}}[/tex]Now, solving for Y, we will have:
[tex]-12y=\frac{\ln(\frac{593}{960})}{\ln(\frac{321}{320})}\Rightarrow y\approx12.86643229[/tex]From this, we have that if they pay a monthly morgage of 1500, they would take 13 years to pay the total cost.
If they wanted to pay the morgage in 15 years, then we replace in the formula as follows:
[tex]\text{PMT}=(183500)(\frac{(\frac{0.0375}{12})}{1-(1\pm\frac{0.03755}{12})^{-12(15)}})[/tex]That is:
[tex]\text{PMT=1334.453182}\Rightarrow PMT\approx1334.45[/tex]They would have to pay $1334.45 each month in order to pay the morgage in 15 years.
Can you help me solve this problem I know how to do the others but I can’t really figure this one out
We have an inequality, this inequality is as follows
[tex]4x\ge112[/tex]To solve the inequality we must clear "x" and see what it tells us
[tex]\begin{gathered} x\ge\frac{112}{4} \\ x\ge28 \end{gathered}[/tex]The inequality indicates that "x" belongs to the set of numbers equal to or greater than 28
Of the set of numbers we have, the only ones that meet this condition are numbers 28 and 33
In conclusion, Only options D and F are correct
Joan invests $200. She earns interest at 3% per annum, compounded monthly.What is the future value of Joan’s investment after 1.5 years?
For this exercise you need to use the following formula:
[tex]FV=PV\mleft(1+r\mright)^n[/tex]Where "FV" is the future value, "PV" is the present value, "r" is the interest rate (in decimal form), and "n" number of periods.
In this case, analyzing the information given in the exercise, you can identify that:
[tex]PV=200[/tex]Remember that a percent can be written in Decimal form by dividing it by 100. Then:
[tex]\frac{3}{100}=0.03[/tex]Since she earns interest at 3% per annum and it is compounded monthly, you can determine that the interest rate per month is:
[tex]r=\frac{0.03}{12}=0.0025[/tex]Knowing that 1 year has 12 months, you know that:
[tex](12)(1.5\text{ }years)=18\text{ }months[/tex]Then:
[tex]n=18[/tex]Therefore, you can substitute all those values into the formula and then evaluate, in order to find the future value of Joan’s investment after 1.5 years:
[tex]\begin{gathered} FV=PV(1+r)^n \\ FV=(200)(1+0.0025)^{18} \\ FV=(200)(1.0025)^{18} \end{gathered}[/tex][tex]FV\approx209.19[/tex]Hence, the answer is: $209.19 (approximately).
WXYZ is a rectangle if M angle w x y equals 6X squared - 6 find a
Given the rectangle WXYZ, the angle m∠WXY=6a²-6
The given angle is a corner angle, and as you might remember all corner angles of a rectangle are right angles, so we can say that the given expression equals 90 degrees:
[tex]6a^2-6=90[/tex]From this expression you can calculate the value of a.
First step is to add 6 to both sides of the equation so that the a-related term stays alone in the left side of the equation and all costants are in the other side:
[tex]\begin{gathered} 6a^2-6+6=90+6 \\ 6a^2=96 \end{gathered}[/tex]Next divide both sides by 6:
[tex]\begin{gathered} \frac{6a^2}{6}=\frac{96}{6} \\ a^2=16 \end{gathered}[/tex]And calculate the square to both sides of the variable to reach the possible value of a:
[tex]\begin{gathered} \sqrt[]{a^2}=\sqrt[]{16} \\ a=4 \end{gathered}[/tex]Now, just because the result is positiv, that does not mean that is the only possible value for a, if you square -4 you can also get 16 as a result, so a can be negative 4 or positive 4:
a=±4
The correct option is B.
Which of the following is the correct mathematical expression
for:
The sum of x and 5
Answer:
Yes
Step-by-step explanation:
Yes
Which of the following describes the graph of the
equation 3y = 6x +12?
a line with slope 2 and y-intercept (0,4)
a line with slope 2 and y-intercept (0, 12)
a line with slope 6 and y-intercept (0,4)
a line with slope 6 and y-intercept (0, 12)
First write the equation in the form y=mx+c
[tex] \frac{3y}{3} = \frac{6x}{3} + \frac{12}{3} \\ y = 2x + 4[/tex]
YOU CAN SEE THAT NOW THE SLOPE OF THE LINE IS 2 TO GET THW Y INTERCEPT WE KNOW THAT AT THE Y-AXIS x=0
PLUG IN 0 IN THE PLACE OF X TO GET Y IN THE EQUATION OF THE LINE.
[tex]y = 2(0) + 4 \\ y = 4[/tex]
THE Y-INTERCEPT IS (0,4)
THEREFORE THE LINE HAS A SLOPE 2 AND A Y INTERCEPT (0,4)
FIRST OPTION IS THE ANSWER.
Differentiate the equation to find the functions for
Velocity v= ds/dt
Differentiation from First Principles is a formal method for determining a tangent's gradient.
What is meant by differentiation?Finding a function's derivative is the process of differentiation. It is also the process of determining how quickly a function changes in relation to its variables.
According to the Sum rule, a sum of functions' derivatives equals the sum of those functions' derivatives. The derivative of two different functions is the difference of their derivatives, according to the Difference rule.
Differentiation from First Principles is a formal method for determining a tangent's gradient. The straight line connecting any two locations on the curve that are fairly near to one another will have a gradient that is similar to that of the tangent at those places.
s(t) = ∫vdt = ∫sin(πt)dt = (-cos(πt))/π + c
substituting the values t = 3, we get
s(-3) = (-cos(-3π))/π + c = 0
simplifying the above equation, we get
(-cos(3π))/π + c = 0
1/π + c = c
c = -1/π
Therefore, the correct answer is s(t) = (-cos(πt))/π - 1/π = (-cos(πt) - 1)/π.
The complete question is:
Given the velocity v=ds/dt and the initial position of a body moving along a coordinate line, find the body's position at time t. v=sin(pi*t), s(-3)=0
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What’s the correct answer answer asap for brainlist
Answer: A
Step-by-step explanation:
37 cm50°The measure of angle A is type your answer...29 cm
The Solution:
Given:
Required:
To find the measure of angle A.
By sine rule:
[tex]\frac{\sin A}{a}=\frac{\sin C}{c}[/tex][tex]\frac{\sin A}{37}=\frac{\sin50}{29}[/tex][tex]undefined[/tex]At the ice cream factory you manage you have a rush order for 1200 gallons of wainut fudge ice cream. One machine can produce 100 gallons of ice cream every 80 minutes. If you start production on that machine at 6:00 am, about what time will be production run end end?
Given that the machine takes 80 minutes to produce 100 gallons of ice cream, so the rate of production (r) is given by,
[tex]\begin{gathered} r=\frac{100}{80} \\ r=1.25\text{ gallons/min} \end{gathered}[/tex]So the time required to produce 1200 gallons of the ice cream is calculated as,
[tex]\begin{gathered} t=\frac{1200}{r} \\ t=\frac{1200}{1.25} \\ t=960\text{ min} \end{gathered}[/tex]Thus, 960 minutes are required for producing 1200 gallons of ice cream.
Converting into hours,
[tex]\begin{gathered} 960\text{ minutes=}\frac{960}{60}\text{ hours} \\ 960\text{ minutes=}16\text{ hours} \end{gathered}[/tex]The time 16 hours after 6:00 am will be 22:00 which corresponds to 10:00 pm.
Therefore, the product run will end at 10:00 pm.
a submarine is situated at 45 feet below sea level and sing 75 ft what is the new position of the submarine?
Given
a submarine is situated at 45 feet below sea level
the submarine sink 75 ft
so, the new position will be = 45 + 75 = 120 feet below
solve for x5x - 7 = 2x + 11
Answer:
Explanation:
Given the below equation;
[tex]5x-7=2x+11[/tex]To solve for x, the 1st step is to subtract 2x from both sides of the equation;
[tex]\begin{gathered} 5x-2x-7=2x-2x+11 \\ 5x-2x-7=11 \\ 3x-7=11 \end{gathered}[/tex]The 2nd step is to add 7 to both sides of the equation;
[tex]\begin{gathered} 3x-7+7=11+7 \\ 3x=18 \end{gathered}[/tex]The final step is to divide both sides of the equation by 3;
[tex]\begin{gathered} \frac{3x}{3}=\frac{18}{3} \\ x=6 \end{gathered}[/tex]The sum of six, and a number divided by two is 0
Answer:
let the unknown be x
=x+6/2=0
=0=x+6
=-x=6
divide both sides by -1
=-x/-1=6/-1
=x=-6
Mr. Shepard,The band teacher wanted to know if a certain type of Instruments are more appealing Who won grade level or another he conduct a survey and compiled the chart
So complete If I were to multiply 23 by 15, I would get 38
if one gender finds a certain sort of instrument more attractive than the other. In order to find out his pupils' choices, he organized a poll. The findings are shown in the table below. What percentage of girls preferred woodwind instruments? So girls who prefer woodwind instruments over boys would receive instruments? So, 30 2 19 would be the result. The same thing is said at the beginning of this one as well, but it asks for the number of ladies who prefer string instruments, which is 23 out of all the pupils that performed and preferred string instruments. So complete If I were to multiply 23 by 15, I would get 38.
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complete question:
'Mr Keen, a band teacher wanted to know if certain types of instruments are more appealing to one gender or the other. So he conducted a survey of his students preferences. The results are complied in the chart below: What is the ratio of the number of girls preferring woodwind instruments to the number of boys preferring woodwind instruments? * Instruments Boys Girls 15 23 Strings Woodwind 19 30 Brass 27 13 Percussion 32 25 Your answer P Mr Kccn; band tcacher wantea t0 know certain types 0i instumenlsare morc appealing [O onc gender or the other So he conducted & survey of his students preferences; Thc results are complied In Ihe chart below: What is the ratio of the number of girls preferring woodwind instruments t0 the number of boys preferring woodwind instruments? Inatuuments Roys he Strings Woodwlnd Brass Percusslon Your answer Mr Keen; band teacher wanted t0 know if certain types of instruments are more appcaling to ore gender or the other: So he conducted survey of his students preferences, The results are complied in the chart below: What is the rallo of the number of girls preferring string instrurents to the total number of students preferring strings Instruments?
A sea lion was swimming at 2 feet below sea level. The number line showsthe location of the sea lion. It then swam down 8 feet. Describe how to usethe number line to find the new location of the sea lion.109 8-7 654 3 -2-1 0 1 2 345 6789 10OA. On the number line, move 8 units to the right. End at 10. The sealion was 10 feet above sea level.OB. On the number line, move 8 units to the left. End at -6. The sealion was 6 feet below sea level.O C. On the number line, move 8 units to the left. End at -10. The sealion was 10 feet below sea level.OD. On the number line, move 8 units to the right. End at 6. The sealion was6 feet above sea level.EPREVIOUS
Answer:
C is the correct statement. Since the sea lion started at 2 feet below sea level and went down another 8 feet, the sea lion is now at 10 feet below sea level.
The weights of the chocolate in Hershey Kisses are normally distributed with a mean of 4.5338 g and a standard deviation of 0.1039 g.
a. For the bell-shaped graph of the normal distribution of weights of Hershey Kisses, what is the area under the curve?
b. What is the value of the median?
c. What is the value of the mode?
d. What is the value of the variance?
a. The area under the curve is 1.
b. The value of the median is 4.5338.
c. The value of the mode is 4.5338.
d. The value of the variance is 0.0108.
How to illustrate the information?It should be noted that the weights of the chocolate in Hershey Kisses are normally distributed with a mean of 4.5338 g and a standard deviation of 0.1039 g.
In this case, for a normal distribution, mean = median = mode. The median is 4.5338
The mode is also 4.5338.
The variance will be the square of the standard deviation. This will be:
= (0.1039)²
= 0.0108.
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I NEED HELP ASAP!! i’m not sure how to do this.
Answer:
slope = -2/3
Step-by-step explanation:
Locations of points: (-3 , 2) and (3 , -2)
slope = rise / run
between two plotted points this means that:
slope = change in y / change in x
slope = (-2 - 2) / (3 - (-3))
slope = -4/6
reduce:
slope = -2/3
Find slope and y-intercept12x = 2y+1
12x = 2y+1
First, express in slope-intercept form
y= mx +b
Where:
m = slope
b= y -intercept
So, we have to solve for y:
12x=2y+1
-2y= -12x+1
y= (-12x+1)/-2
y = 6x-1/2
So:
Slope = 6
Y-intercept = -1/2 or -0.5 (decimal form)
determine the discriminat and use it to determine the number of x-intercepts for the graph of f(x) = 2x^2 - 8x + 9
Answer:
[tex]\begin{gathered} x=2+i14 \\ x=2-i14 \\ \text{ Complex answer, no x-intercepts} \end{gathered}[/tex]Explanation: The discriminant is the part of the quadratic formula underneath the square root symbol As we know that square root of any number is both plus and minus of a certain value:
[tex]\sqrt[]{a}=\pm c\Rightarrow(-c)^2=(+c)^2=a[/tex]Using this information about the discriminant we can determine the x-intercepts of the graph as follows:
[tex]f(x)=2x^2-8x+9=0\Rightarrow\text{ Solving this quadratic equation will give x-intercepts}[/tex]Quadratic equation solution:
[tex]\begin{gathered} f(x)=2x^2-8x+9=0\Rightarrow x=\frac{-B\pm\sqrt[]{B^2-4AC}}{2A} \\ \because\Rightarrow \\ A=2 \\ B=-8 \\ C=9 \\ \therefore\Rightarrow \\ x=\frac{-(-8)\pm\sqrt[]{(-8)^2-(4\times2\times9)}}{2\times(2)}=\frac{8\pm\sqrt[]{16^{}-72}}{4}=\frac{8\pm\sqrt[]{-56}}{4}=2\pm\frac{\sqrt[]{-56}}{4} \\ \therefore\Rightarrow \\ x=2\pm i14 \\ \rightarrow\text{ Complex answer} \\ x=2+i14 \\ x=2-i14 \end{gathered}[/tex]Graph
Note! The plot of f(x) above confirms that there are no x-intercepts of this function, so the reason for complex values of x. also discriminant is the square root of -56
The second angle of a triangle measures three times as large as the first. If the third angle measures 55 degrees more than the first, find the measure of all three angles. ( recall that the sum of the angles of a triangle add to 180 degrees )
Taking x as the measure of the first triangle, we know that the second one measures three times as x:
[tex]3x[/tex]And the third one measures 55 degrees more than the first:
[tex]x+55[/tex]We know that the sum of the angles of a triangle is 180, use this information to find x:
[tex]\begin{gathered} x+3x+(x+55)=180 \\ 5x+55=180 \\ 5x=180-55 \\ x=\frac{125}{5} \\ x=25 \end{gathered}[/tex]It means that the first angle measures 25°. Use this value to find the second and third angles:
[tex]\begin{gathered} 3x=3\cdot25=75 \\ x+55=25+55=80 \end{gathered}[/tex]It means that the second angle measures 75° and the third one measures 80°.
prove that 4^3 / 4^6 = 4^-3, without using the exponent law x^a / x^b = x^a-b.
Looking at the graph, which point shows the constant of proportionality?
(2,1)
(2,4)
(,2)
(1,2)
Answer:
I forgot maybe someone else knows
Step-by-step explanation:
:) ;) <*)))))<
Need help please and also explain it
15 points if help
Answer:
60
Explanation:
1/2 of 80 is 40. 1/4 of 80 is 20. Add them and you get 60.
Gavin rides motocross in competition. A competition-level bicycle costs $1,800. He can borrow themoney from the bank at 3.596 interest for two years. By the end of the loan, how much money willGavin end up paying the bank?
The simple interest formula is:
[tex]I=Prt\text{ }[/tex]where P is the principal, r is the interest rate and t is the time.
In this case the principal is $1800, the interest rate is 0.035 (in decimal form) and t is 2. then the interest he pays is:
[tex]I=(1800)(0.035)(2)=126[/tex]Therefore in total he will pay $1926
solve this please ???
Answer:
I am a little confused because it says the point-slope formula, but then tells you to solve for y and to distribute. Attached , I put the answer in the point slope form, but if they want the equations solves for y, then the answer would be in the slope intercept form. Below the answers are in point slope form, but I will put the answer in slope intercept form here.
1 y = 2x -1
2. y = 1/2x +3
3. y = 2/3x + 4
4. y = -3/4x -7
5.y = -2x + 1
6. y = 1/3x -5
7. y = -5/3x + 7/3
8 y = 3x + 1
Step-by-step explanation: