Answer:
$3,659.82
Step-by-step explanation:
Adding to the checkbook those debits and credits not already there brings its balance to ...
... $3045.58 +651.84 -37.60 = $3659.82
Adjusting the bank's balance by the deposits and checks not already there brings its balance to ...
... $4262.92 +220.05 -325.50 -497.65 = $3659.82
Thus, the reconciled accounts will agree on the balance $3659.82.
The reconciled balance for Gregory Co. was $3,659.82 after accounting for all transactions including deposits, outstanding checks, credited note, and bank charges.
The question involves reconciling the checkbook balance with the bank statement balance for Gregory Co. To reconcile the bank balance with the checkbook balance, we need to account for any transactions that have not been reflected in one or the other. We start with the bank statement balance and adjust it for outstanding checks and deposits not reflected on the statement.
Starting balance: $3,045.58Add outstanding deposit: $220.05Subtract outstanding checks: $325.50 + $497.65Add credited note: $651.84Subtract bank charges: $37.60Reconciled balance calculation: $3,045.58 + $220.05 - $325.50 - $497.65 + $651.84 - $37.60 = $3,659.82Tim ran 5 miles in 35 minutes. Dan rund 7 miles in 70 minutes. If they are running a marathon 26 miles, who will finish first?
Answer:
they will tie
Step-by-step explanation:
if you divied 7 in to 70 you get 7 and if you divied 5 into 35 it 7
It takes both of them 7 mins to complet a mile
The perimeter of the rectangular playing field is 430 yards.The length of the field is 5 yards less than triple the width. What are the dimensions of the playing field?
Answer:
Answer - 160
Step-by-step explanation:
2L+2W = 430
L = 3W-5
2(3W-5)+2W = 430
6W-10+2W = 430
8W = 440
W = 55 and L = 3(55)-5 = 160
Answer:
Length = 160 and width = 55 yards
Step-by-step explanation:
Perimeter = 2L + 2W where L = the length and W = the width.
L = 3W - 5 (given).
So substituting for L is the formula for the perimeter:-
2(3W - 5) + 2W = 430
6W - 10 + 2W = 430
8W = 440
W = 55 yards.
So the Length L = [430 - 2(55]) / 2 = 160 yards.
James took 22 seconds to run the 200yard dash. How many feet per minute is that? Show work.
Answer:
1636.4 ft/min
Step-by-step explanation:
Multiply by the conversion factors that change the units you have to the units you want.
(200 yd)/(22 s) × (3 ft/yd) × (60 s/min) = 18000/11 ft/min ≈ 1636.4 ft/min
Hari’s weekly allowance varies depending on the number of chores he does. He received $16 an alarm once a week he did 12 chores, and $14 in allowance the week he did 8 chores. Write an equation for his allowance in slope-intercept form.
Answer:
y = ($0.5/ch) x + $10
Step-by-step explanation:
Let
x = number of chores
y = allowance
The relationship between y and x can be expressed in a linear equation in the slope-intercept form.
y = mx + b
where
m is the slope
b is the y-intercept
We have the ordered pairs (8, 14) and (12, 16). We can calculate the slope using the following expression.
m = Δy/Δx = $16-$14/12ch-8ch = $0.5/ch
The equation is
y = ($0.5/ch) x + b
We will replace the first point in the previous equation.
$14 = ($0.5/ch) 8ch + b
b = $10
The final equation is
y = ($0.5/ch) x + $10
This equation can be used to predict Hari's allowance for any number of chores. For example, if Hari does 10 chores, his allowance will be $12.50. The final equation is y = ($0.5/ch) x + $10.
We are given that Hari's allowance varies depending on the number of chores he does.
We are also given two points, (8, 14) and (12, 16), that represent the relationship between the number of chores and the allowance.
We can use these two points to find the slope of the line.
The slope is equal to rise over run, which in this case is equal to
$16 - $14 / 12 - 8 = 0.5/ch.
We can now plug the slope and one of the points into the slope-intercept form of the equation to find the value of b, the y-intercept.
We will use the point (8, 14).
y = mx + b
14 = ($0.5/ch) 8ch + b
14 = $4 + b
b = $10
The final equation is y = ($0.5/ch) x + $10.
This equation can be used to predict Hari's allowance for any number of chores. For example, if Hari does 10 chores, his allowance will be $12.50.
Learn more about slope-intercept form here:
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write a quadratic function whose graph has the given characteristics x-intercepts: -4,2 point on graph (0,-9)
y = (9/8)(x +4)(x -2)
Step-by-step explanation:When the x-intercepts are "a" and "b", you know factors of the function are (x-a) and (x-b). So, we can write the function as ...
... y = k(x -(-4))(x -2) = k(x +4)(x -2) . . . . . for some scale factor k
We can find k using the given point.
... -9 = k(0 +4)(0 -2) = -8k
Dividing by -8 gives ...
... 9/8 = k
The desired function is ...
... y = (9/8)(x +4)(x -2)
... = (9/8)(x² +2x -8)
please help!
1. Find the volume for 5 different spheres by randomly choosing different radii.
Using the same radii values, find the volume of 5 cylinders where the height of the cylinder is the same as the diameter of the sphere.
Answer:
[tex]\begin{array}{ccc}\text{Radius}&\text{Volume of sphere}&\text{Volume of cylinder}\\&&\\1&\dfrac{4}{3}\pi &2\pi \\&&\\2&\dfrac{32}{3}\pi &16\pi \\&&\\3&36\pi &54\pi \\&&\\4&\dfrac{256}{3}\pi &128\pi \\&&\\5&\dfrac{500}{3}\pi &250\pi\end{array}[/tex]
Step-by-step explanation:
Use formulas for the volumes:
[tex]V_{sphere}=\dfrac{4}{3}\pi r^3,\\ \\V_{cylinder}=\pi r^2h=\pi r^2\cdot 2r=2\pi r^3.[/tex]
1. When r=1,
[tex]V_{sphere}=\dfrac{4}{3}\pi\cdot 1^3=\dfrac{4}{3}\pi,\\ \\V_{cylinder}=2\pi \cdot 1^3=2\pi.[/tex]
2. When r=2,
[tex]V_{sphere}=\dfrac{4}{3}\pi\cdot 2^3=\dfrac{32}{3}\pi,\\ \\V_{cylinder}=2\pi \cdot 2^3=16\pi.[/tex]
3. When r=3,
[tex]V_{sphere}=\dfrac{4}{3}\pi\cdot 3^3=36\pi,\\ \\V_{cylinder}=2\pi \cdot 3^3=54\pi.[/tex]
4. When r=4,
[tex]V_{sphere}=\dfrac{4}{3}\pi\cdot 4^3=\dfrac{256}{3}\pi,\\ \\V_{cylinder}=2\pi \cdot 4^3=128\pi.[/tex]
5. When r=5,
[tex]V_{sphere}=\dfrac{4}{3}\pi\cdot 5^3=\dfrac{500}{3}\pi,\\ \\V_{cylinder}=2\pi \cdot 5^3=250\pi.[/tex]
Note that for all r,
[tex]\dfrac{V_{sphere}}{V_{cylinder}}=\dfrac{\frac{4}{3}\pi r^3}{2\pi r^3}=\dfrac{2}{3}.[/tex]
Answer:
Please, see the attached file.
Thanks.
Step-by-step explanation:
Please, see the attached file.
Thanks.
Line segment ABCD is split into unequal segments by points A, B, C, and D. The length of segment AD is 28 cm, and the distance between the midpoints of segments AB and CD is 16 cm. Find the length of segment BC.
Answer:
4 cm
Step-by-step explanation:
The midpoint segment has length ...
... L = AB/2 + BC + CD/2 = 16 cm
The entire segment has length ...
... AD = AB + BC + CD = 28 cm
If we subtract AD from 2L, we have ...
... 2L - AD - 2L = 2(AB/2 +BC + CD/2) - (AB +BC +CD) = 2(16 cm) -28 cm = 4 cm
... AB +2BC + CD -AB -BC -CD = 4 cm . . . . remove parentheses
... BC = 4 cm . . . . simplify
Could someone help me to solve this pls!
Answer:
15 ft²
Step-by-step explanation:
The volume of a cone is given in terms of the base area (B) and height (h) by the formula ...
... V = (1/3)Bh
Putting in the given numbers, you have ...
... 35 ft³ = (1/3)B(7 ft)
... B = (35·3/7) ft² = 15 ft² . . . . . . solve for B
What is the volume of a sphere with a diameter of 15 cm? Round the answer to the nearest whole number.
Answer:
1767 cm³
Step-by-step explanation:
We can use volume V = 4/3 π r³
We have diameter of 15 cm. To get radius, we need to divide diameter by 2.
r = 7.5 cm
So now plug in r = 7.5 then calculate V:
V = 4/3 π ( 7.5 )³
V = 4/3 π * 421.875 ≈ 1767.145 ≈ 1767
Hope this helps.
you have a job raking leaves. You charge 10 dollars plus .50 for each bag you fill with leaves. the equation y=0.50x+10 models this situation,where x is the number of bags and y is your total amount earned. how many bags do you fill if you earn 17 dollars
Answer:
14 bags
Step-by-step explanation:
If you earn $17, to find the number of bags substitute 17 for y in the equation y=0.50x+10. Then use inverse operations to solve for x.
17 = 0.50x+10 Subtract 10 from both sides.
17-10 = 0.50x
7=0.50x Divide both sides by 0.50
7/0.50 = x
14 =x
In ΔABC (m∠C = 90°), the points D and E are the points where the angle bisectors of ∠A and ∠B intersect respectively sides BC and AC . Point G ∈ AB so that DG ⊥ AB and H ∈ AB so that EH ⊥ AB .
Prove that ΔCEH and ΔCDG are isosceles.
The problem is symmetrical, so proof for ΔCDG can serve as a model for proof for ΔCEH.
Step-by-step explanation:∠DGA ≅ ∠DCA ≅ 90° . . . . given
∠GAD ≅ ∠CAD . . . . definition of angle bisector AD
AD ≅ AD . . . . reflexive property
ΔDGA ≅ ΔDCA . . . . AAS congruence theorem
CD ≅ GD . . . . CPCTC
∴ ΔCDG is isosceles . . . . definition of isosceles triangle (2 sides congruent)
_____
To do the same for ΔCEH, replace "D" with "E", replace "G" with "H", and replace "A" with "B". The rest of the logic applies.
Marne Shia walked 3/8 of a mile in 3/5 of an hour. What equation can be used to calculate her unit rate in miles per hour?
Answer:
speed = (3/8 mi)/(3/5 h)
Step-by-step explanation:
... speed = distance/time
Fill in the given values:
... speed = (3/8 mi)/(3/5 h)
_____
Comment on units
You can use the units to provide both guidance and assurance. You know speed is generally expressed in miles per hour. If you consider "per" to mean "divided by", this expression of units tells you speed is calculated by dividing miles by hours.
If you leave the units with the numbers, as we have above, they enter into the calculation the same way any variable might. You can do the arithemetic with the numbers, and you can indicate the arithmetic with the units (just as you would with any variables). Here, the result of evaluating the equation would be ...
[tex]\displaystyle\frac{\frac{3}{8}\,\text{mi}}{\frac{3}{5}\,\text{h}}=\frac{\frac{3}{8}}{\frac{3}{5}}\,\frac{\text{mi}}{\text{h}}=\frac{5}{8}\,\text{mi/h}[/tex]
The fact that the units come out mi/h (the units of speed) provides assurance that you probably did the math correctly.
Answer:
three eighths over three fifths = five eighths mile per hour
Step-by-step explanation:
In ΔABC, AC = BC side CD is the median of side AB with d belonging to side AB,AB = 4 in and CD = sqaure root of 3 in. find AC.
Answer:
AC = √7 in
Step-by-step explanation:
ΔABC is isosceles, so ΔADC is a right triangle with AD = 2 in and CD = √3 in. The length of hypotenuse AC is found using the Pythagorean theorem.
... AC² = AD² +CD² = (2 in)² +(√3 in)² = (4 +3) in²
... AC = √7 in . . . . take the square root
The table of values below represent an exponential function. Write an exponential equation that models the data.
x y
-2 21
-1 14.7
0 10.29
1 7.203
2 5.0421
a. y = 21(0.7) b. y = 14.7(1.7) c. y = 10.29(0.7) d. y = 10.29(1.3)
Answer: c
y = 10.29·0.7^x . . . . . selection c seems the closest
Step-by-step explanation:For most any exponential function, the exponential multiplier will be 1 when x=0, so the y-intercept is the overall multiplier for the function.
The values decrease as x increases, so the base of the exponential term must be less than 1.
These considerations narrow your choice to C.
... y = 10.29·0.7^x
_____
If you actually want to determine the equation, you can do it several ways. One is to make use of the exponential regression function of your graphing calculator. (See attached). Another is to take the logarithms of the y-values and find a best-fit line through them.
_____
Comment on the answer choices
You may notice that none of the offered answers appears to be anything but the product of two numbers. There are no x-variables involved, and no exponents indicated. Cutting and pasting answers like this does not work.
Answer:
c
Step-by-step explanation:
Should I round 13.9876652 to 14 or 13.99?
Answer:
14.
Unless your assignments tells you not to round to whole numbers or to round to the nearest decimal places, then 13.99. But, in most cases, you'd round to 14.
se the drawing tool to form the correct answers on the provided grid. For the sequence (1, 2, 4, 8, . . .), the index starts at 1. Let f be the function that describes this sequence. Graph as much of function f as will fit on the grid.
Answer:
See attached
Step-by-step explanation:
For each increase of 1 in the index, the function value doubles. The size of the function value rapidly exceeds the limit of any linear grid.
We've shown a few points plotted. Perhaps it will give you the idea of what you need to do.
Answer:
The index starts at 1, so the domain of the function is D = {1, 2, 3, 4, 5, 6, . . .}. The sequence is based on the add 3 rule. So, to get more terms of the sequence, add 3 to the last term to get the next one. The range values include the terms of the sequence, so the range is R = {1, 4, 7, 10, 13, 16, . . .}.
To graph the function of this sequence on a coordinate plane, pair the domain values with the corresponding range values to get {(1, 1), (2, 4), (3, 7), (4, 10), (5, 13), (6, 16), . . .}. Then plot these points on the graph.
Step-by-step explanation:
Express 4 as a fraction. A) 1 1 B) 1 4 C) 4 1 D) 4 4
The answer is C) 41 hope this helped
60 is 80% of what round to the nearest hundreth
Answer:
75.00
Step-by-step explanation:
Let x be unknown number. Then
x is 100% and
60 is 80%.
Write a proportion:
[tex]\dfrac{x}{60}=\dfrac{100}{80},\\ \\x=\dfrac{60\cdot 100}{80}=75=75.00.[/tex]
533÷41 long division
Answer: 41
Step-by-step explanation:
533÷41 = 533/41
Se photo for step -by-step of ling division
The answer to the long division of 533 by 41 is 13. This is reached by multiplying 13 by 41 which results in 533, the original dividend. The remainder is 0.
Explanation:Let's perform a long division of 533 by 41. First, write the number 533, which is the dividend, inside the long division bracket and the number 41, the divisor, outside of it. Now we need to see how many times 41 fits into 533.
It fits 13 times because 13 times 41 equals 533. Therefore, write 13 above on your long division bracket.
When you multiply 13 (your answer) by 41 (your divisor), you get 533, which is your dividend. Subtract 533 from 533 and you get a remainder of 0. The answer of the long division of 533 by 41 is 13.
Done correctly, long division is a reliable method of dividing large numbers. The important thing is to ensure all steps are followed orderly and accurately.
Learn more about Long Division here:https://brainly.com/question/28824872
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John can create 3 apps in 6 weeks while Ben can do the same job in 2 weeks. How many weeks would it take them to create 10 apps together?
plzzz answer i rlly need help
Answer:
5 weeks
Step-by-step explanation:
John creates apps at the rate ...
... (3 apps)/(6 weeks) = 1/2 app/week
Ben creates apps at the rate ...
... (3 apps)/(2 weeks) = 3/2 app/week
Together, they create ...
... (1/2) app/week + (3/2) app/week = 2 app/week
So, the time for 10 apps is ...
... (10 app)/(2 app/week) = 5 week
_____
Comment on the problem
If the guys actually work at a uniform rate like this, the result after 5 weeks will be 9 completed apps and 2 half-completed apps. Their rate is 10 apps in 5 weeks, but their actual output in that time period may not be 10 completed apps.
One should beware of the "mythical man-month." Rates of job completion depend on many factors. Individual average rates cannot always be summed when folks "work together."
find the length of arc shown in red.
Answer:
≈10.99525 cm.
Step-by-step explanation:
1. The length of the circle is L=2πr, where π≈3.1415 and r- radius of the circle.
2. if the given arc is 45° and full circle is 360°, then the length of the arc is 45/360=0.125 of full circle, that is L(arc)=0.125L=0.25πr; ⇒ L(arc)≈0.25*3.1415*14=10.99525 (cm).
Answer:
10.99 ≈ 11cm
Step-by-step explanation:
To find the length of the arc, first we need to find the circumference of the circle, which we find with the following formula :
[tex]c=2\pi r[/tex]
where [tex]r[/tex] is the radius which is indicated in the image: [tex]r=14cm[/tex].
so the circumference is:
[tex]c=2\pi(14cm)\\c=87.96cm[/tex]
This is the measure of the entire perimeter of the circle, it is the measure of the 360 ° arc.
Because we only want 45 ° of those 360 °, we divide the value of the circumference by 360 and multiply po 45:
[tex]\frac{87.96cm(45)}{360}=\frac{3958.2}{360}=10.99cm[/tex]
which can be rounded to 11cm
The length of the arc is 11cm
Help me pretty pleaseeee
7 . . . . . inches per week
Step-by-step explanation:The average rate of change of height is ...
... (change in height)/(change in time)
The height changes from 41 inches to 83 inches when the time changes from 3 weeks to 9 weeks. Then the rate of change is ...
... (83 -41) inches/((9 -3) weeks) = (42/6) inches/week = 7 inches/week
It seems likely that the required answer will just be a number: 7.
last year 950 people attended a town's annual parade. This year $1,520 people attended. What was the percent increasse in ttendancce from last year to this year
60%
Step-by-step explanation:The percent change can be found from ...
... ((new value)/(old value) -1) × 100%
... (1520/950 -1) × 100% . . . . . . filling in your numbers
... (1.6 - 1) × 100% = 60% . . . . . . simplify
Attendance this year was 60% higher than last year.
Pleaaasssee hellpppp. The farm has cows and turkeys. Between all the animals, there are 148 legs and sixty heads. How many cows and how many turkeys does the farm have?
Answer:
Step-by-step explanation:
14 cows
46 turkeys
Step-by-step explanation:If all the animals were turkeys, there would be 120 legs. There are 28 more than that. Replacing a turkey with a cow adds 2 legs, so there must be 14 such replacements.
There are 14 cows and 46 turkeys.
_____
Check
14×4 + 46×2 = 56 + 92 = 148 . . . . legs
14 + 46 = 60 . . . . . . heads
PLZ HELP I'VE BEEN STUCK ON THIS FOR A FEW HOURS
x-intercept: -4
y-intercept: +1
Step-by-step explanation:The x-axis is the horizontal line on the graph with "x" marked at the right end. It is also identified by the "0" among the numbers on the vertical scale at the left side of the graph.
You can consider the x-axis to be a number line. The numbers on that number line are those of the horizontal sequence of numbers at the bottom of the graph. (On many graphs, they're shown adjacent to the x-axis in the middle of the page. That's not the case here.) These numbers are the x-coordinate of any point with the corresponding horizontal position.
The x-intercept is where the blue line crosses the x-axis. It is marked with a dot on the vertical line that has -4 at the bottom. That -4 is the x-coordinate of the x-intercept, the value the problem is asking for.
___
The y-axis is the vertical line on the graph with "y" marked at the top end. It is also identified by the "0" among the numbers on the horizontal scale at the bottom of the graph.
You can consider the y-axis to be a number line. The numbers on that number line are those of the vertical sequence of numbers at the left side of the graph. (On many graphs, they're shown adjacent to the y-axis in the middle of the page. That's not the case here.) These numbers are the y-coordinate of any point with the corresponding vertical position.
The y-intercept is where the blue line crosses the y-axis. It is marked with a dot on the horizontal line that has 1 at the left side. That 1 is the y-coordinate of the y-intercept, the value the problem is asking for.
___
The (x, y) coordinates of the x-intercept are (-4, 0). The y-coordinate is always zero, because that is the definition of x-intercept: the x-coordinate of the point on the graph where y=0.
The (x, y) coordinates of the y-intercept are (0, 1). The x-coordinate is always zero, because that is the definition of y-intercept: the y-coordinate of the point on the graph where x=0.
Which postulate or theorem proves ∆WXY ≅ ∆WZY ?
SSS Congruence Theorem
SAS Congruence Postulate
HL Congruence Theorem
Answer:
HL Congruence Theorem
Step-by-step explanation:
Answer:
HL congruence theorem
Step-by-step explanation:
Given that WZX is an isosceles triangle with sides WX=WZ
Also given that WY is altitude on side XZ
Consider triangles WXY and WZY
WX=WZ Given
WY=WY REflexive property
Angle wyz =angle wyx Right angle
Hence by HL congruence theorem, since one leg and hypotenuse are equal we get the two triangles to be congruent.
What is the sum of the first ten terms in the Geometric series 4-12+36-108+...? A.-59,048 B.-1,048,575 C.19,684 D.118,096
A. -59,048
Step-by-step explanation:The first pair of terms sums to -8; the second pair to -72. Each pair after that sums to a value 9 times the previous one. Then the sum of 10 terms is ...
... (-8) + (-72) + (-648) + (-5832) + (-52488)
Before you even add this up, you know the answer choice is A. The sum is ...
... -59, 048
_____
Using the formula
The formula for the sum of a geometric series is ...
... S = a1·(r^n -1)/(r -1) . . . . . where a1 = 4 is the initial term, r=-3 is the common ratio, and n=10 is the number of terms.
Filling in the values and doing the arithmetic, we have ...
... S = 4·((-3)^10 -1)/(-3-1) = 4·(59,049 -1)/(-4) = -59,048
Answer:
-59,048
Step-by-step explanation:
Simplify (2p+3)2 - (2p-3)2 (Give proper detailed answer with all steps,the 2 is the symbol of square)
Answer:
24p
Step-by-step explanation:
This is the difference of 2 squares:- a^2 - b^2 = (a + b)(a - b).
So here we have:-
(2p + 3)^2 - (2p - 3)^2
= (2p + 3 + (2p - 3))(2p + 3 - (2p - 3))
= (2p + 3 + 2p - 3)(2p + 3 - 2p + 3
= 4p * 6
= 24p (answer)
Final answer:
To simplify the expression (2p+3)² - (2p-3)², apply the difference of squares formula to get ((2p+3) + (2p-3)) * ((2p+3) - (2p-3)), which simplifies to 24p.
Explanation:
To simplify the expression (2p+3)² - (2p-3)², we need to apply the difference of squares formula, which is
a² - b² = (a+b)(a-b).
Here, a is (2p+3) and b is (2p-3). The result will be the product of the sum and difference of a and b.
Let's perform the simplification step-by-step:
Simplify both products:
(4p) * (6)
Finally, multiply the results to get the simplified expression:
24p
The simplified result of the expression (2p+3)² - (2p-3)² is 24p.
The baseball team is making a circle graph to keep track of this year's games. So far, they have entered the data you see. How many games have they played this year?
A 5 games
B 15 games
C 20 games
D 25 games
Answer:
The baseball team plays 25 games
Step-by-step explanation:
If they have lost 5 games and that is 20 %, we can make a ratio.
games/ total = 20/100
5 20
------ = -----------
total 100
Using cross products
5*100 = 20*total
500 = 20* total
Divide by 20 on each side
500/20 = 20/20 * total
25 = total
Answer:
its D which is also 25 games
Step-by-step explanation:
Write each polynomial function in standard form, then classify it by degree and number of terms and describe its end behavior.
y = 2x(x^2 – 3)(x^2 + 2)
Answer:
y = 2x^5 -2x^3 -12xdegree 5, 3 terms, end behavior: (-∞, -∞), (+∞, +∞)Step-by-step explanation:
I like to form the product of something like this by multiplying binomial pairs first. The distributive property applies for that (as does FOIL).
... (x^2 -3)(x^2 +2) = x^2·x^2 + x^2·2 + (-3)·x^2 + (-3)·2
... = x^4 -x^2 -6 . . . . . the two x^2 terms combine
Now, it is a simple matter to multiply each term by 2x:
... y = 2x^5 -2x^3 -12x
_____
The highest-degree term has degree 5. There are 3 terms. (All are odd-degree, so this is an odd function, symmetrical about the origin.)
As with any odd-degree function (with positive leading coefficient) the overall shape has a positive slope (/), tending toward -∞ for large negative values of x, and tending toward +∞ for large positive values of x.