The total number of digits used to write all the integers from 1 to 12 are 15.
What is an Integer?Integers include all whole numbers and negative numbers. This means if we include negative numbers along with whole numbers, we form a set of integers.
Given that, Rena wrote all the integers from 1 to 12.
So, the integers from 1 to 12 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
Here, 1 to 9 are single digits
10, 11 and 12 has two digits
Thus total number of digits = 9×1+3×2
= 9+6
= 15
Therefore, the total number of digits are 15.
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The total number of digits Rena wrote is:
[tex]\[\boxed{15}\][/tex]
To find the total number of digits Rena wrote when she wrote all the integers from 1 to 12, we need to consider each range of numbers separately based on their digit counts.
1. Single-digit numbers (1 to 9):
- There are 9 single-digit numbers.
- Each single-digit number contributes 1 digit.
- Total digits from 1 to 9:
[tex]\[ 9 \times 1 = 9 \][/tex]
2. Two-digit numbers (10 to 12):
- There are 3 two-digit numbers: 10, 11, and 12.
- Each two-digit number contributes 2 digits.
- Total digits from 10 to 12:
[tex]\[ 3 \times 2 = 6 \][/tex]
Adding the digits from both ranges gives us the total number of digits:
[tex]\[9 + 6 = 15\][/tex]
Thus, the total number of digits Rena wrote is:
[tex]\[\boxed{15}\][/tex]
√2
4
Suppose that $2000 is invested at a rate of 5.1%, compounded semiannually. Assuming that no withdrawals are made, find the total amount after 6 years.
Do not round any intermediate computations, and round your answer to the nearest cent.
Solution:
The formula for compound interest, including principal sum, is:
[tex]A = p( 1 + \frac{r}{n})^{nt}[/tex]
Where,
A = the future value of the investment/loan
P = the principal investment amount
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per unit t
t = the time the money is invested
From given,
p = 2000
[tex]r = 5.1 \% = \frac{5.1}{100} = 0.051[/tex]
t = 6 years
n = 2 ( compounded semiannually)
Substituting the values we get,
[tex]A = 2000( 1 + \frac{0.051}{2})^{ 2 \times 6}\\\\A = 2000( 1 + 0.0255)^{12}\\\\\A = 2000(1.0255)^{12}\\\\A = 2000 \times 1.35278\\\\A = 2705.5649[/tex]
Thus the total amount after 6 years is $ 2705.5649
Final answer:
Using the compound interest with an initial investment of $2000 at a 5.1% interest rate compounded semiannually, the total amount after 6 years is calculated to be $2710.34.
Explanation:
To calculate the total amount after 6 years when $2000 is invested at a rate of 5.1% compounded semiannually, we use the formula for compound interest, which is [tex]A = P(1 + r/n)^(nt).[/tex] Here, A represents the future value of the investment, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time the money is invested for in years.
We can plug the values into the formula:
P = $2000 (the initial investment)
r = 0.051 (5.1% interest rate expressed as a decimal)
n = 2 (since the interest is compounded semiannually)
t = 6 (the investment period in years)
Therefore, we calculate A using the following expression:
[tex]A = 2000(1 + 0.051/2)^(2*6)[/tex]
[tex]A = 2000(1 + 0.0255)^(12)[/tex]
[tex]A = 2000(1.0255)^12[/tex]
After calculating the above expression without rounding intermediate computations and rounding the final answer to the nearest cent, the total amount comes out to be:
A = $2710.34
Thus, the total amount after 6 years, with a 5.1% interest rate compounded semiannually, is $2710.34.
A delivery company pays its drivers a fixed fee for each delivery made that day. The company deducts a daily fee for the use of the company's delivery truck. The drivers net pay in dollars, p, for one day is given by the equation p = 11d − 55, where d is the number of delivers made in one day. What does the number 55 most likely represent?
Answer:
55 is probably the fixed fee that the delivery company charges before anything.
Answer:
The companies daily fee
Step-by-step explanation:
P = pay
D = deliveries
55 = the daily fee the company deducts for the use of their truck
Pay = deliveries - company deduction
The major and minor axes of an ellipse are 25 inches and 4 inches in length. What is the area of the ellipse?
Answer:
Therefore, the area of the ellipse is:
Area = 78.5 inches
Step-by-step explanation:
The formula to find the area of the ellipse is
[tex]\:a\:\times \:b\:\times \:\pi[/tex]
The major axis of an ellipse = 25 inches
The minor axis of an ellipse = 4 inches
The value of a = major axis/2 = 25/2 = 12.5 inchesThe value of b = minor axis/2 = 4/2 = 2 inchesThus
The area of the ellipse:
Area = [tex]\:a\:\times \:b\:\times \:\pi[/tex]
[tex]=\:12.5\:\times\:2\:\times\:\pi[/tex]
[tex]=25\pi[/tex]
[tex]=78.5[/tex] inches ∵ [tex]\pi =3.14[/tex]
Therefore, the area of the ellipse is:
Area = 78.5 inches
Write the equation of the line that passes through the point (-5,5) and has a slope of -8/5
A) y= -8/5 x - 3
B) y= -8/5x+3
C) 3x - 5y =0
D) 5x-3y=0
Answer:
The equation of the line that passes through the point (-5,5) and has a slope of -8/5 will be:
[tex]y=-\frac{8}{5}x-3[/tex]
Step-by-step explanation:
Given
[tex]\left(x_1,\:y_1\right)=\left(-5,5\right)[/tex][tex]m=\frac{-8}{5}[/tex]Point-Slope Form equation is
[tex]\left(y-y_1\right)=m\left(x-x_1\right)[/tex]
[tex]\left(y-5\right)=\frac{-8}{5}\left(x-\left(-5\right)\right)[/tex]
[tex]\mathrm{Apply\:rule}\:-\left(-a\right)=a[/tex]
[tex]y-5=\frac{-8}{5}\left(x+5\right)[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}[/tex]
[tex]y-5=-\frac{8}{5}\left(x+5\right)[/tex]
[tex]y-5+5=-\frac{8}{5}\left(x+5\right)+5[/tex]
[tex]y=-\frac{8}{5}x-3[/tex]
Therefore, the equation of the line that passes through the point (-5,5) and has a slope of -8/5 will be:
[tex]y=-\frac{8}{5}x-3[/tex]
You start at (4, 4). You move up 1 unit and left 6 units. Where do you end?
Answer: (10,5)
Step-by-step explanation:
add 6 do the x value
then add 1 to the y value
What is the equivalent fraction of 24/126
Answer:4/21
Step-by-step explanation:divide 6 by both sides
The equivalent fraction of 24/126 is 4/21.
To find an equivalent fraction, one can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 24 and 126 is 6.
Dividing both the numerator and the denominator by 6, we get:
[tex]\[ \frac{24 \div 6}{126 \div 6} = \frac{4}{21} \][/tex]
Therefore, the fraction 4/21 is equivalent to 24/126.
let s ={1 2 3 4 5 6}
A= {2 4 6}
B={3 4 5}
C={1 6}
find A'
A' n B
B n C'
(AuB)
(C')
Answer:
PLEASE CHECK THE ATTACHMENT.
HOPE U UNDERSTOOD
THANKS
She earns $20 per hour as a carpenter and $25 per hour as a blacksmith. Last week Giselle worked both jobs for a total of 30 hours and earn a total of $690 how long did she work as a carpenter last week and how long did she work as a blacksmith
Answer:
There is a few combinations but as carpenter it is (9.5hrs x $20=$190 ) and as a blacksmith 20 x $25= 500
Step-by-step explanation:
order this
1/2 , 1/3 , -1/2 , -1/3
let's see who is right
For least to greatest, -1/2, -1/3, 1/2, 1/3
For greatest to least, 1/3, 1/2, -1/3, -1/2
The negative numbers will be less then the positive ones
13-(-6) helpppp meee
Answer:
19
Step-by-step explanation:
Step 1: Solve
13 - (-6)
13 + 6
19
Answer: 19
Wes wants to buy 3 pepper plants from the garden center. The regular price of a pepper plant
is $5. If Wes buys 3 plants, he can use a 20%-off coupon. If he buys 4 plants, he can use a
30%-off coupon Wes wants to know if buying 4 plants is less expensive than buying 3 plants.
What is the sale price of 3 pepper plants after a 20% discount?
Answer: 12
Step-by-step explanation: cuz i said so
The sale price of 3 pepper plants after a 20% discount is $12.
Explanation:To figure out the sale price of 3 pepper plants after a 20% discount, we first calculate 20% of the regular price. The regular price of one pepper plant is $5, so 20% of $5 is $1. Therefore, the sale price of one pepper plant is $5 - $1 = $4. As Wes wants to buy 3 plants, we multiply this sale price by 3, so the total price after discount for 3 plants is $4 * 3 = $12.
So, the sale price of 3 pepper plants after a 20% discount is $12.
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What is -3t + -8 =25
Step-by-step explanation:
-3t-8=25
-3t=25+8
-3t=33
t=33/-3
t=(-11)
please someone help me !! :(
Answer: 27 times bigger.
Step-by-step explanation:
You need to use the following formula to find the volume of a Square pyramid:
[tex]V=\frac{1}{3}s^2h[/tex]
Where "s" is the edge of a side of the square base and "h" is the height of the pyramid.
Knowing that:
[tex]s_A=12\ in\\\\h_A=8\ in\\\\\\s_B=36\ in\\\\h_B=24\ in[/tex]
You can find the volume of the Pyramid A and the volume of the Pyramid B:
[tex]V_A=\frac{1}{3}(12\ in)^2(8\ in)\\\\V_A=384\ in^3\\\\\\V_B=\frac{1}{3}(36\ in)^2(24\ in)\\\\V_B=10,368\ in^3[/tex]
Finally divide the volume of the Pyramid B and the volume of the Pyramid A, in order to find how many times bigger than the Pyramid A is the Pyramid B.
You get:
[tex]\frac{10,368\ in^3}{384\ in^3}=27[/tex]
Given the functions f(n) = 11 and g(n) = −2(n − 1), combine them to create an arithmetic sequence, an, and solve for the 31st term.
To create an arithmetic sequence using the given functions, we add the functions together and substitute the desired term. The 31st term of the arithmetic sequence is -49.
Explanation:To combine the functions f(n) = 11 and g(n) = -2(n - 1) into an arithmetic sequence, we need to find the common difference between the terms. The common difference between the terms in an arithmetic sequence is obtained by subtracting one term from the previous term. In this case, the common difference is g(n). So, the arithmetic sequence can be expressed as an = f(n) + g(n).
For the 31st term, we substitute n = 31 into the equation and calculate:
a31 = f(31) + g(31)
a31 = 11 + [-2(31 - 1)]
a31 = 11 + [-2(30)]
a31 = 11 + [-60]
a31 = -49
Therefore, the 31st term of the arithmetic sequence an is -49.
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nd the 52nd term and the term named in the problem
40, 140, 240, 340, ...
Find a 32
Answer:
5140 and 3140
Step-by-step explanation:
Note there is a common difference d between consecutive terms in the sequence, that is
d = 140 - 40 = 240 - 140 = 340 - 240 = 100
This indicates the sequence is arithmetic with n th term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 40 and d = 100, thus
[tex]a_{52}[/tex] = 40 + (51 × 100) = 40 + 5100 = 5140
[tex]a_{32}[/tex] = 40 + (31 × 100) = 40 + 3100 = 3140
What is the missing number in this pattern?
1, 4, 9, 16, 25, 36, 49, 64, 81,
Answer:
no numbers are missing
Step-by-step explanation:
Don't fool others
find the unit rate 50 min?
20 calls?
Answer: 2.5 minutes per call
Step-by-step explanation:
This is a fraction equal to
50 minutes ÷ 20 calls
We want a unit rate where
1 is in the denominator,
so we divide top and bottom by 20
50 minutes ÷ 20
20 calls ÷ 20 = 2.5 minutes/ 1 call
The unit rate is 2.5 minutes per call
To find the unit rate of making phone calls, we divide the total number of minutes by the total number of calls. This gives us the average number of minutes spent on each call.
We have 50 minutes and 20 calls. Dividing these gives us the unit rate:
Unit Rate = Total Minutes ∕ Total Calls
Unit Rate = 50 minutes ∕ 20 calls = 2.5 minutes per call
Therefore, the unit rate is 2.5 minutes per call, indicating on average, each call lasts for 2.5 minutes.
The product of 5 and an odd number will end in what value?
A) 0
B) 1
C)3
D)5
Answer:
D) 5
Step-by-step explanation:
If we multiply 5 and an odd number, the end value will not be 0, 1, and 3. For example,
5 × 1 = 5
5 × 9 = 45
Therefore, in both the product, the end value is 5 and not 0, 1, and 3.
Therefore, option D is correct.
If we multiply 5 by any of the odd number, we can get the end value of 5. The following examples are the valid reasons why we will get 5.
5 × 3 = 15
5 × 5 = 25
So, option A, B, and C are wrong.
Answer:
A) 0
B) 1
C)3
D.5 ←
If each cube represents 0.25 in3, what is the volume of the prism?
A) 6 in3
B) 12 in3
C) 48 in3
D) 75 in3
Answer:B
Step-by-step explanation:
Answer:
its B
Step-by-step explanation:
i did the test and got it right
The volume of a rectangular prism is 1,000^3 mm. Use the formula V = lwh to determine which of the statements are true. Choose all that apply
The prism could be a cube with a side length of 10 mm.
It is possible for the length to be 1,000 mm.
The length, width, and height must end in zero.
It is possible that the length is 2.5 mm.
(A) The prism could be a cube with a side length of 10 mm.
(B) It is possible for the length to be 1,000 mm.
(D) It is possible that the length is 2.5 mm.
Explanation:
Volume = l×w×h
where l is the length, w is the width and h is the height
It is possible that the length is 2.5 mm
Then volume = 2.5 × 10 ×40 = 1000 mm³
It is possible for length to be 1000 mm
Then volume = 1000 × 0.1 × 10 = 1000 mm³
The prism could be a cube of length 10 mm
Then volume = 10 × 10 × 10 = 1000 mm³
Round each addend to 0,1/2, or 1. What is the best estimate for the sum of 5/6 + 3/7
Answer:
Step-by-step explanation:first round the fractions then add decide if it goes to 0,1/2,or 1
The best estimate for the sum of 5/6 and 3/7 by rounding to the nearest 0, 1/2, or 1 is 1.5 or 3/2.
To estimate the sum of 5/6 and 3/7, we round each addend to the nearest of the given values: 0, 1/2 (0.5), or 1. Five-sixths is closer to 1 than it is to 1/2 or 0. So, we round 5/6 to 1.
Three-sevenths is closer to 1/2 than to 1 or 0. So, we round 3/7 to 1/2. After rounding, our new equation for estimation is 1 + 1/2.
The best estimate for the sum thus becomes 1 + 1/2 which equals 1.5 or 3/2. This is a quick way to find a rough estimate of the sum without finding a common denominator or adding the actual fractions.
The vertices of a polygon are P(0,4), Q(5,4), R(5-3) and S(0,-3). What is the perimeter of the polygon? (Show work please)
Answer:
The perimeter of the polygon are
PQ = 5
RS = 5
PR = √74 = 8.60
QS = √74 = 8.60
QR = 7
Step-by-step explanation:
To calculate the perimeter of a polygon, polygon is like a coordinate with points, to find the length, we use this formula
d = √(x _2 - x_1)^2 + (y_2 - y_1)^2
Let's start from the first two vertices P ( 0 , 4) and Q(5 , 4)
x_1 = 0
y_1 = 4
x_2 = 5
y_2 = 4
PQ = √ ( 5 - 0)^2 + ( 4 - 4)^2
= √ 5^2 + 0^2
= √ 25
= 5
Between R( 5 , -3) and S ( 0 , -3)
x_1 = 5
y_1 = -3
x_2 = 0
y_2 = -3
RS = √ ( 0 - 5)^2 + ( -3 - (-3))^2
= √( -5)^2 + ( -3 + 3)^2
= √ 25 + 0
= √ 25
= 5
Between P( 0 , 4) and R (5 , -3)
x_1 = 0
y_1 = 4
x_2 = 5
y_2 = -3
PR = √( 5 - 0)^2 + ( -3 - 4)^2
= √ 5^2 + (-7)^2
= √ 25 + 49
= √ 74
= 8.60
Between Q ( 5 , 4) and S(0 ,-3)
x_1 = 5
y_1 = 4
x_2 = 0
y_2 = -3
QS = √ ( 0 - 5)^2 + ( -3 - 4)^2
= √ -5^2 + -7^2
= √ 25 + 49
= √ 74
= 8.60
Between Q( 5,4) and R(5 , -3)
x_1 = 5
y_1 = 4
x_2 = 5
y_2 = -3
QR = √ (5 - 5)^2 + ( -3 - 4)^2
= √ 0^2 + (-7)^2
= √ 0 + 49
= √ 49
= 7
Josie and her brother, Sean both have a job after school. For every $5.50 that Josie earns, her brother earns $6.50. On Tuesday, they earned $30.00. How much money did Josie earn? How much did her brother earn?
Answer:
Josie will earn $13.75 and her brother Sean will earn $16.25
Step-by-step explanation:
Given that For every $5.50 that Josie earns, her brother earns $6.50.
Tuesday, they earned $30.00
Using the ratio and the proportional
Josie : Sean : Total
5.5 : 6.5 : 12
x : y : 30
So, x = 5.5 * 30/12 = 13.75
And y = 6.5 *30/12 = 16.25
So, Josie will earn $13.75 and her brother Sean will earn $16.25
If your company sells basketballs. You sell
123,000 basketballs at a price of $42.50 each.
You have bills for your business equal to
$575,000. What is your profit?
123,000 x 42.50 = 5227500
5227500-575,000=4652500
your profit is 4652500
Hope this helps
Place a term into each box to complete the equation that converts 3 yards to inches.
Answer:
1 yard, 12 inches, 108 inches.
Step-by-step explanation:
there are 3 feet in a yard, 12 inches in a foot and because 12 times 3 (one yard) is equal to 36, then three yards are equal to 108 inches.
Three of the shapes have the same area. Which one does not?
Answer:A
Step-by-step explanation:
Answer:
No the answer is c. because it is the only one not equal to 24.
Step-by-step explanation:
choice a is a parallelogram which would be equal to 24 because for a parallelogram to find the area you multiply base times height.
6 times 4 is 24.
if the triangles are congruent, then X=?
Answer:
Hi there!
The correct answer to this question is: x=3
Step-by-step explanation:
because these two triangles are similar, that means the hypotenuse are similar. which means you can set the sides equal to each other like this:
13 = 4x + 1 minus one on both sides and you should get 4x = 12 and then divide 4 on both sides and you should finally get x = 3
The table below shows the cost of different numbers of goldfish at a pet store.
5----$1.50
10---$3
15---$4.50
20---$6
Which statement describes the rate of change of this function?
A.
The cost increases $3.00 each time 5 goldfish are added.
B.
The cost increases $0.30 each time 1 goldfish is added.
C.
The cost increases $6.00 each time 5 goldfish are added.
D.
The cost increases $1.50 each time 1 goldfish is added.
What is 4.49 rounded to the nearest whole number ?
Answer:
4
Step-by-step explanation:
7)
A radio costs $20. Harold buys it for $16. What percent off did he receive?
Answer:20%
Step-by-step explanation:
20-16=4
4/20=0.2
Move the decimal to the right twice and you get 20