Final answer:
The quotient of 7,684 and 78 is 98 with a remainder of 60, determined through long division.
Explanation:
To determine the quotient of 7,684 and 78, follow these steps:
Set up the division problem using long division with 7,684 as the dividend and 78 as the divisor.
Divide 78 into the first two digits of the dividend (76), which does not go evenly. Move to the first three digits (768).
Divide 78 into 768 to begin finding the quotient. 78 goes into 768 approximately 9 times because 78 x 9 = 702.
Subtract 702 from 768 to get a remainder of 66 and bring down the next digit from the dividend, which is 4, forming 684.
Divide 78 into 684. It goes 8 times because 78 x 8 = 624.
Write 8 next to the 9 in the quotient to update the quotient to 98 and subtract 624 from 684 to get a new remainder of 60. Since there are no more digits to bring down from the dividend, 60 is the final remainder.
The quotient is 98 with a remainder of 60.
In a school auditorium there are 33 seats in each row of seats. How many rows are needed for 528 students to each have a seat?
To find the number of rows needed for 528 students to each have a seat in a school auditorium with 33 seats in each row, divide the total number of students by the number of seats in each row. The answer is 16 rows.
Explanation:To find the number of rows needed for 528 students to each have a seat in a school auditorium with 33 seats in each row, we need to divide the total number of students by the number of seats in each row.
So, the number of rows needed would be:
Rows needed = Total number of students ÷ Number of seats in each row
Substituting the given values:
Rows needed = 528 ÷ 33 = 16
Therefore, 16 rows are needed for 528 students to each have a seat in the auditorium.
Learn more about Finding the number of rows needed for students to have seats here:https://brainly.com/question/15049173
#SPJ3
27.3 less than k is -57.7. What is the value of k ?
Q # 13 please Graph the image. of AMOP for the translation
What is the probability that a randomly thrown dart that lands within the rectangle lands within a shaded region? All of the circles are congruent, and the diameter of each circle is 100 cm. A. 39/200 B. 49/250 C. 98/125 D. 157/200
Turtle and vicent combine their coins to find they have all dimes and quarters .They have 8 more quarters them dimes and the coins are worth a total of 5.15 .How many dimes and quarters do they have?
Esther pays $467 per month for 5 years for a car. she made a down payment of $3,700. if the loan costs 7.1% per year compounded monthly, what was the cash price of the car?
The correct cash price is d) $27,228.33.
To determine the cash price of the car, we need to calculate the present value of all payments made by Esther, including her down payment.
Calculate the total number of monthly payments:
Total number of payments: 5 * 12 = 60
Determine the monthly interest rate:
Monthly interest rate: 0.071 / 12 = 0.0059167 (approximately)
Calculate the present value of the monthly payments using the formula for the present value of an annuity:
P = PMT × [tex]\frac{[1 - (1 + r)^{-n]} }{ r}[/tex]
P = 467 × [tex]\frac{ [1 - (1 + 0.0059167)^{-60}]}{ 0.0059167}[/tex] = $23,528.33
Add the down payment to the present value of the monthly payments to get the total cash price of the car:
Total cash price = $23,528.33 + $3,700 = $27,228.33
Therefore, the correct answer is (d) $27,228.33.
The complete question is
Esther pays $467 per month for 5 years for a car. she made a down payment of $3,700. if the loan costs 7.1% per year compounded monthly, what was the cash price of the car?
a) $23,528.33
b) $19,828.33
c) $29,820.57
d) $27,228.33
e) $37,220.57
If one can of paint contains 2 2/5 gallons, how much paint is in 12 cans of paint?
Answer:12 2/4
Step-by-step explanation:
First of all that eqation is improper. So lets make that proper. To do that you just count by five till you get close to the number. 5,10,15,20 im close so lets stay there. So then it would be 4 1/5. Then you have to multiple that by 12.
And your awnser would be 50/4
then you need to make it propper.
12 2/4
How to round 4.288 to the nearest hundredth
summation to integral? calculus
Final answer:
In calculus, summation involves adding discrete values, while integration is akin to adding an infinite number of infinitesimally small products to find areas, volumes, etc. Integral calculus extends these concepts to continuous functions and is used, for example, to find position from acceleration by integrating twice.
Explanation:
The transition from summation to integral in calculus is an important concept that bridges the discrete world with the continuous. When we summate, we're adding together values to find a total amount. In a similar vein, an integral can be thought of as a continuous sum, where we're adding up infinitely small products to calculate an area, volume, or other quantities.
When performing an integral, the dimensions of what we're integrating must be consistent. For example, if we're integrating velocity (v) with respect to time (t), we obtain a dimension that is the product of the two, such as distance. This principle is rooted in the requirement of dimensional consistency, analogously understood in the phrase "You can't add apples and oranges."
Understanding the relationship between discrete sums and continuous integrals is crucial for applications in various fields, such as physics where integrals can represent cumulative effects over time or space. For example, integrating an acceleration function gives us velocity, and further integration yields position. This process allows us to work backward from acceleration to position, utilizing the power of integral calculus.
The image below is a triangle drawn inside a circle with center O:
A triangle is shown inscribed inside a circle. The leg of the triangle labeled 4 inches passes through the center of the circle, O. The other two legs are labeled as 2 inches and 3 inches.
Which of the following expressions shows the area, in square inches, of the circle?
(π = 3.14)
3.14 ⋅ 2
3.14 ⋅ 3
3.14 ⋅ 22
2 ⋅ 3.14 ⋅ 22
Answer:
3.14 2^2
Step-by-step explanation:
The expressions shows the area, in square inches, of the circle will be 3.14 × 2² square units. Then the correct option is C.
What is a circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
The image below is a triangle drawn inside a circle with center O:
A triangle is shown inscribed inside a circle.
The leg of the triangle labeled 4 inches passes through the center of the circle, O.
The other two legs are labeled as 2 inches and 3 inches.
The expressions shows the area, in square inches, of the circle will be
Area of circle = (π/4) d²
The diameter of the circle is passing through center. Then the length of the diameter is 4.
Then the area of circle will be,
Area = (π/4) 4²
A = 3.14 × 4
A = 3.14 × 2² square units
The expressions shows the area, in square inches, of the circle will be 3.14 × 2² square units.
Then the correct option is C.
More about the circle link is given below.
https://brainly.com/question/11833983
#SPJ2
A store purchases an item wholesale for 60$ and marks it up by 70 percent if there is a 7 percent tax on the item how much will the item cost
Answer:
109.14
Step-by-step explanation:
to Start off do 60 x .70, then add the answer to 60, then multiply by .07 then add that to 102, for the answer of 109.14
Two quantities are related as shown in the table below:
x. y
2. 3
4. 4
6. 5
8. 6
Which equation best represents the relationship?
A bank account earns interest at a rate of 3.5% per year ( in other words it increases in value by that percent) and starts with a balance of $350. Which of the following equations would give the account’s worth, W, as a function of the number of years, y, it has been gaining interest?
The account's worth, W, as a function of the number of years, y it has been gaining interest is given by the equation W = $350 + ($350 imes 0.035 imes y).
Explanation:The equation that gives the account's worth, W, as a function of the number of years, y, it has been gaining interest is:
W = $350 + ($350 imes 0.035 imes y)
Here's an example:
If the account has been gaining interest for 2 years, then W = $350 + ($350 imes 0.035 imes 2) = $364.70.
Learn more about Simple interest here:https://brainly.com/question/40405117
#SPJ12
which has the smallest value 11 , 0.675,1.23,0.42,1.011
Given rectangle PQRS with PQ=QR, PQ=SP, and SQ=6√2. Find SR. a)√2. b) 6. c) 5√2 d) not enough information
average of 2.99 2.59 3.50
Answer:
6.74
Step-by-step explanation:
add all numbers and divide how many numbers there are.
x·\sqrt[4]{x}
Rewrite simplest radical form
Answer:
b
Step-by-step explanation:
asdf
Q # 18,Graph the inequality on a coordinate plane, - y < 3 x - 5
find the value of x
Answer:
43 degrees
Step-by-step explanation:
You can see that the triangle is congruent, so x is equal to 43. dont forget to include degrees!
Hey can you please help me posted picture of question
A pet store has 26 rabbits and hamsters. The number of rabbits is 2 more than double the number of hamsters. How many hamsters does the pet store have?
Let the number of rabbits in the pet store is x
And the number of hamsters in the pet store is y.
Now, we have been given that pet store has 26 rabbits and hamsters. Thus, we have the linear equation
[tex]x+y=26...........(1)[/tex]
Now, number of rabbits is 2 more than double the number of hamsters. Hence, we have
[tex]x=2+2y[/tex]
Substituting this value of x in equation 1, we get
[tex]2+2y+y=26\\ 3y=24\\ y=8[/tex]
Thus, there are 8 hamsters in the pet store.
Which of the following is the graph of y=|x-1|-4y=∣x−1∣−4y, equals, vertical bar, x, minus, 1, vertical bar, minus, 4?
Answer:
The graph of given function is shown below.
Step-by-step explanation:
The given function is
[tex]y=|x-1|-4[/tex] .... (1)
The vertex form of a absolute function is
[tex]y=a|x-h|+k[/tex] .... (2)
where, a is a constant and (h,k) is vertex.
On comparing (1) and (2), we get
[tex]a=1,h=1,k=-4[/tex]
The vertex of the function is (1,-4). The table of values is
x y
3 -2
2 -3
1 -4
0 -3
-1 -2
Plot these points on a coordinate plane. Draw a V-shaped curve by connecting these points with vertex at (1,-4).
Hey can you please help me posted picture of question
Supposed a Visa card had a credit card number of 4162 0012 3456789a where a is the check number what is the check number? A) 0 B) 3 C) 9 D) 7
Answer:
Option B) 3
Step-by-step explanation:
we have the number
4162 0012 3456 789a
Find the value of a (check number)
step 1
Multiply every even-position digit (when counted from the right) in the number by two. If the result is a two digit number, then add these digits together to make a single digit
4162 0012 3456 789a
9(2)+7(2)+5(2)+3(2)+1(2)+0(2)+6(2)+4(2)
(18)+(14)+(10)+(6)+(2)+(0)+(12)+(8)
Remember that If the result is a two digit number, then add these digits together to make a single digit
so
(1+8)+(1+4)+(1+0)+(6)+(2)+(0)+(1+2)+(8)
(9)+(5)+(1)+(6)+(2)+(0)+(3)+(8)=34
step 2
add every odd-position digit
4162 00123456 789a
so
8+6+4+2+0+2+1=23
step 3
Adds the result in step 1 and the result in step 2
34+23=57
The check-digit is what number needs to be added to this total to make the next multiple of 10
In our case, we’d need to add 3 to make 60
therefore
The check number is 3
PLEASE HURRY!! I WILL GIVE BRAINLIEST
Trapezoid K' is the image of trapezoid K after a series of transformations.
Bella and Marco described the sequence of transformations in different ways.Which sequence or sequences are correct and why?
Answer:
Option A
Step-by-step explanation:
From the graph attached, we will write the transformation as followed.
a. Trapezoid k is dilated by a scale factor of [tex]\frac{3}{2}[/tex]
[ Since scale factor = [tex]\frac{\text{Largest side of k'}}{\text{Largest side of k}}[/tex]
= [tex]\frac{12units}{8units}[/tex]
= [tex]\frac{3}{2}[/tex] ]
2. scaled trapezoid then rotated by 180°.
3. Then rotated trapezoid is shifted 1 unit down.
By these transformations Bella's sequence was correct.
Therefore, Option A is the answer.
Use part 1 of the fundamental theorem of calculus to find the derivative of the function. g(x) = x e2t2 − 4t dt 4
Using the Fundamental Theorem of Calculus Part 1, the derivative of the function g(x) = ∫ (x e2t2 - 4t) dt from x=4 is ex2 - 4x where 'x' is the variable 't' from the integral.
Explanation:The subject of this question is the use of part 1 of the Fundamental Theorem of Calculus to find the derivative of a complex function. This theorem states that if f is a function that is continuous over the interval [a, b] and F is an antiderivative of f on the interval [a, b], then the definite integral of f from a to b is equal to F(b) - F(a).
In your specific question, you are asked to find the derivative of the function g(x) = ∫ (x e2t2 - 4t) dt from x=4.
The derivative of a definite integral, from a constant to a variable, of a function is simply the original function evaluated at the upper limit.
Therefore, the derivative of the given function g(x) is simply ex2 - 4x, treating 'x' as the variable 't' from the integral.
Learn more about Derivative Calculations here:https://brainly.com/question/32605732
#SPJ3
A television is 36 inches by 18 inches. What is the area?
simplify the expression 11x-(2x^2+8x).
Using known taylor series, find the first four nonzero terms of the taylor series about 0 for the function. sqrt((1 + t))sin(t)
Answer:
T series
Step-by-step explanation:
which set of number could represent the length of the sides of a right triangle? A 9 11 14 B 15 18 21 C 7 24 25 D 8 9 10