Answer: At the end of May, there will be $372.
Explanation:
Since we have given that
On the first day of May, each one save =$0.25
Number of friends = 3
Total save on the first day of May is given by
[tex]0.25\times 3=\$0.75[/tex]
Similarly,
On the second day of May, each one save =$0.25
Total save on the second day of May is given by
[tex]0.50\times 3=\$1.5[/tex]
Similarly,
On the third day of May, each one save =$0.25
Total save on the third day of May is given by
[tex]0.75\times 3=\$2.25[/tex]
This series becomes arithmetic progression,
[tex]0.75,1.5,2.25......[/tex]
Here, a = 0.75
d=common difference is given by
[tex]d=a_2-a_1=1.5-0.75=0.75\\d=a_3-a_2=2.25-1.5=0.75[/tex]
Since there are 31 days in the month of May,
So, n=31
We need to calculate the sum of 31 terms to get our answer,
[tex]S_n=\frac{n}{2}(2a+(n-1)d)\\\\S_{31}=\frac{31}{2}(2\times 0.75+(31-1)\times 0.75)\\\\=\frac{31}{2}(1.5+30\times 0.75)\\\\=\frac{31}{2}(24)\\\\=31\times 12\\\\=\$372[/tex]
Hence, at the end of May, there will be $372.
The total amount in the fund at the end of May is 239.25.
Explanation:To find the total amount of money in the fund at the end of May, we need to calculate the sum of the money put into the fund on each day. The students decide to put 0.25 on the first day, 0.50 on the second day, 0.75 on the third day, and so on. This is an arithmetic sequence, where the first term (a) is 0.25 and the common difference (d) is 0.25. The formula to find the sum of an arithmetic sequence is:
S = (n/2)(2a + (n-1)d)
In this case, n = 31 (since there are 31 days in May), a = 0.25, and d = 0.25. Plugging these values into the formula, we get:
S = (31/2)(2 * 0.25 + (31-1) * 0.25) = 239.25
Therefore, at the end of May, there will be 239.25 in their fund.
you are studying for your final exam of the semester. up to this point,you recieved 3 exam scores of 83%,85%, and 84%. to recieve a grade of B in the class you must average exam score between 80% and 89% for all 4 exams including the final.
Find the widest range of scores that you can get on the final exam in order to recieve a grade of B for the class.Use interval notation ...?
Answer:
The widest range lies between [68,100]
Step-by-step explanation:
Given is - to receive a grade of B in the class you must average exam score between 80% and 89% for all 4 exams including the final.
So, the range of the addition of all 4 scores is -
[tex]80*4=320[/tex]
[tex]89*4=356[/tex]
Now given scores addition is = [tex]83+85+84=252[/tex]
Now, the widest range of scores that you can get on the final exam in order to receive a grade of B can be found as :
[tex]320-252= 68[/tex]
[tex]356-252= 104[/tex]
So, the range lies between [68,100]
Verify the identity.
tan(x+(pi/2)) = -cot x
Which mathematical property is demonstrated?
5 + 3w + 2 = 5 + 2 + 3w
associative property of addition
commutative property of multiplication
associative property of multiplication
commutative property of addition
Answer:
commutative property of addition
Step-by-step explanation:
What is the answer to 86-11/11+4
Another math help ^_^
The scientific notation 2.15 × 10-3 has what value?
Answer:
The scientific notation 2.15 × 10-3 has a value of
0.00215
Step-by-step explanation:
Step one
This problem bothers conversion from standard form otherwise known as scientific notation to decimal form
Step two
Now we are presented with the expression
2.15 × 10-³
To convert this it is equivalent to
2.15/10³= 2.15/1000
= 0.00215
On the other hand this can also be achieved without calculations by visually counting from the decimal point to the right 2 placements before inserting the first integer
This method saves alot of time expecialy when time is of essence.
Hence the scientific notation 2.15 × 10-3 has a value of
0.00215
Factors of 14 least to greatest
Sanjay’s dog weighs 46 pounds on earth. multiply the dog’s earth weight by 0.38 to find how much it would weigh on mars, and by 2.36 to find how much it would weigh on jupiter. how much less would the dog weigh on mars than on jupiter
A rectangle has a length of x inches and a width 2 inches less than the length. If the dimensions were tripled what would be the area of the new rectangle in terms o x
Juan charges $3.50 per hour for babysitting. Write a rule to describe the amount of money (M) earned is a function of the number of hours (h) spent baby-sitting. HELP PLEASE
Can anyone show me steps on how to solve this equation.. I will upvote!
5x+7=4x+10
What is the value of the sum 5 + 10 + 15 + ... + 95 + 100? ...?
(x + 2)4 = x4 + 8x3 +... Use the Binomial Theorem to complete the binomial expansion. Enter only the next three terms; use the ^ key for exponents, example: 10x^2+20x+30.
Simplify the expression using the properties of exponents. Expand any numerical portion of your answer and only include positive exponents. ( 4 x 3 y −2 ) 3 (4x3y-2)3
Use the prime factoriations of 24 and 28 to find their greatest common factor
A number n is at least 7
The inequality would be equal to n ≥ 7.
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.
We are given that the phrase as;
"A number n is at least 7"
Therefore, the inequality would be;
n ≥ 7
Or
n = 7
Thus, the inequality would be equal to n ≥ 7.
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!!!!!!!!!!!!!!!!!!!!!!HELP ASAP!!!!!!!!!!!!!!!!!!!!
Jayden used the following steps to simplify the given expression.
-3 + 2(2 + x + 3)
Step 1: = -3 + 2(x + 2 + 3)
Step 2: = -3 + 2(x + 5)
Step 3: = -3 + 2x + 10
Step 4: = 2x + (-3) + 10
Step 5: = 2x + 7
What property of real numbers was used in step 3?
A)distributive property
B)associative property of addition
C)commutative property of addition
D)associative property of multiplication
Answer:
Option A -distributive property
Step-by-step explanation:
Given : expression -3 + 2(2 + x + 3)
Step 1: = -3 + 2(x + 2 + 3)
Step 2: = -3 + 2(x + 5)
Step 3: = -3 + 2x + 10
Step 4: = 2x + (-3) + 10
Step 5: = 2x + 7
In step 3 distributive property is applied i.e. c(a+b)=ca+cb
in step 2- 2(x+5) when we apply distributive property it became
2x+10
Therefore, option A is correct
Tim is buying packages of paper plates and cups. He wants to have equal amounts of each, but plates come 24 per pack, and cups come 16 per pack. What is the least amount of plates and cups Tim will have to buy to get the same number of each?
8
16
24
48
simplify the ratio
60 cents: $2
The ratio 60 cents: $2 simplifies to 3:10 after converting dollars to cents and dividing both terms by the greatest common divisor, which is 20.
To simplify the ratio 60 cents: $2, we need to first express both quantities in the same units. Since 1 dollar is equal to 100 cents, $2 is equivalent to 200 cents. Thus, the ratio becomes 60 cents : 200 cents.
Next, we simplify the ratio by dividing both sides by the greatest common divisor. In this case, both 60 and 200 are divisible by 20, which is the greatest common divisor. So we divide both sides by 20:
[tex]\frac{60}{20}[/tex] = 3
[tex]\frac{200}{20}[/tex] = 10
Therefore, the simplified ratio is 3:10.
Bobby will buy coffe and hot chocolate for his co-workers each cup of coffe costs $2.25 and each cup of hot chocolate costs $1.50 .he pays a total of $15.75 for 8 cups
( please answer me as quickly as possible)
Final answer:
Bobby can buy 5 cups of coffee at $2.25 each and 3 cups of hot chocolate at $1.50 each to meet his budget of $15.75 for 8 cups in total. We find this by solving a system of equations.
Explanation:
Bobby wants to buy a total of 8 cups of coffee and hot chocolate for his co-workers with a budget of $15.75. Since each cup of coffee costs $2.25 and each cup of hot chocolate costs $1.50, we need to find out how many cups of each he can buy.
Let's denote the number of cups of coffee as C and the number of cups of hot chocolate as H.
The total cost for coffee will be $2.25 × C and for hot chocolate $1.50 × H.
The total amount spent is $15.75, and the total number of cups is 8, so we have two equations: 2.25C + 1.50H = 15.75 and C + H = 8.
We can solve this system of equations using substitution or elimination. For simplicity, we'll use substitution.
From C + H = 8, we can express H in terms of C: H = 8 - C.
Substitute H in the cost equation: 2.25C + 1.50(8 - C) = 15.75.
Simplify and solve for C: 2.25C + 12 - 1.50C = 15.75, which simplifies to 0.75C = 3.75, and therefore C = 5.
Now, plug C = 5 into H = 8 - C to find H: H = 3.
Bobby can buy 5 cups of coffee and 3 cups of hot chocolate.
100, 96, 104, 88, 120, 56, ? what comes next? here are the choices (184, 140, 77, 124, 128)
Write the expression 4 log x − 6 log (x + 2) as a single logarithm
To write the expression 4 log x − 6 log (x + 2) as a single logarithm, apply the properties of logarithms.
Explanation:To write the expression 4 log x − 6 log (x + 2) as a single logarithm, we can make use of the following logarithmic properties:
The logarithm of a product of two numbers is the sum of the logarithms of the two numbers: log(xy) = log(x) + log(y)The logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number: log(x^n) = n log(x)The logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers: log(x/y) = log(x) - log(y)Using these properties, we can simplify the given expression as follows:
4 log x − 6 log (x + 2) = log(x^4) - log((x + 2)^6)
Therefore, the expression can be written as the single logarithm log(x^4) - log((x + 2)^6).
solve.
3/4x=18 please show work ...?
Help Please
A group of 9 friends go bowling.How many different possibilities are there for the order in which they play if the youngest person is to bowl first.
Please explain your answer. Thanks ...?
Consider the level surface given by
x2−y2+z2=2. Draw a picture for the following:
1. Slice for y=2
2. Slice for x=1
3. Slice for y=0
4. Slice for x=2 ...?
Answer:
First of all, each slice represents an intersecting plane at that level.
For example, y = 2 is a plane that passes thorugh that level and cuts the volume given by [tex]x^{2} -y^{2}+z^{2}=2[/tex]
1. Slice for y = 2.We replace this value in the given volume.
[tex]x^{2} -y^{2}+z^{2}=2\\x^{2} -(2)^{2}+z^{2}=2\\x^{2}+z^{2}=2+4\\x^{2}+z^{2}=6[/tex]
So, results in a circumference with radius [tex]\sqrt{6}[/tex], because a circumference is defind as [tex]x^{2} +y^{2} =r^{2}[/tex]. (On plane XY).
2. Slice for x = 1.We repeat the process.
[tex](1)^{2} -y^{2}+z^{2}=2\\z^{2}-y^{2}=2-1\\z^{2}-y^{2}=1[/tex]
It forms a horizontal hyperbola on plane ZY.
3. Slice for y = 0.[tex]x^{2} -0^{2}+z^{2}=2\\x^{2}+z^{2}=2[/tex]
Another circle with radius of [tex]\sqrt{2}[/tex] on plane XZ.
4. Slice for x = 2.[tex](2)^{2} -y^{2}+z^{2}=2\\z^{2}-y^{2}=2-4\\z^{2}-y^{2}=-2\\\frac{z^{2}-y^{2}}{-2} =\frac{-2}{-2} \\\frac{y^{2} }{2} -\frac{z^{2} }{2} =1[/tex]
It forms a hyporbola on plane YZ.
what number is 82% of 230
write an equation in slope intercept form with a slope 3/2 and y-intercept -2
A dilation on a rectangle has a scale factor of 4. what is the effect on the perimeter of the rectangle ? ...?
The dilation of a rectangle with a scale factor of 4 will result in each side of the rectangle being multiplied by 4, thus the perimeter will also be quadrupled.
Explanation:When a rectangle undergoes a dilation with a scale factor of 4, the lengths of all sides of the rectangle are multiplied by 4. Since perimeter is the sum of all the side lengths of a rectangle, the perimeter will also be affected by the scale factor. Therefore, if the original perimeter of the rectangle is P, the new perimeter after dilation will be 4 × P.
Using the property of dilations, the new dimensions of the rectangle will be proportional to the original dimensions. For example, if the original length l and width w of the rectangle are scaled by a factor of 4, the new dimensions will be 4l and 4w respectively. Subsequently, the new perimeter will be 2(4l + 4w) which is the same as saying 4 × (2l + 2w), proving the perimeter is scaled by the same factor of 4.
1.For f(x)= 5x+1 : Find(-4).
a.-19 b.1 c.-21 d. 21
2. Write in Standard form an equation of the line passing through the given point with the given slope.
slope=-8 ; (-2,-2)
a.8x+y=-18 b.-8x+y=-18 c. 8x-y=-18 d.8x+y=18
1.a. -19 at x = -4 for f(x) = 5x + 1.
2.a. 8x + y = -18 the standard form of the equation.
What is a line ?A line has no definite length it can extend in both the directions indefinitely.
According to the given question a functions f(x) = 5x + 1 is given and we have to find the value of this function when x = -4.
Given f(x) = 5x + 1
f(-4) = 5(-4) + 1
f(-4) = -20 + 1
f(-4) = -19.
In the second question we have to write an equation of the line passing through the point (-2,-2) with slope -8.
We know equation of a line in slope intercept form is y = mx + b.
∴ -2 = (-8)(-2) + b
-2 = 16 + b
b = - 18.
So, y = -8x -18 OR 8x + y = -18.
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a boat travels 66 miles in 2 hours. what is its rate in feet per minute?
The rate of the boat that travels 66 miles in 2 hours is approximately 2904 feet per minute.
Given:
Distance traveled = 66 miles
Time taken = 2 hours
We know that:
1 mile = 5280 feet
66 miles = 66 [tex]\times[/tex] 5280
348,480 feet
Next, we'll convert the time from hours to minutes.
1 hour = 60 minutes,
2 hours = 120 minutes
Now, we can calculate the rate in feet per minute:
Rate (feet per minute) = [tex]\dfrac{ Distance \ in\ feet}{Time\ in\ minutes}[/tex]
Rate = [tex]\dfrac{348480}{120}[/tex]
Rate ≈ 2904 feet per minute
So, the rate of the boat is approximately 2904 feet per minute.
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