Tyler's mom purchased a savings bond for Tyler. The value of the savings bond increases by 5% each year. One year after it was purchased, the value of the savings bond was $131.25. Find the value of the bond when Tyler's mom purchased it. The value of the bond when his mom purchased it was? Enter only the numeric value, no symbols or spaces. $
.

The time it will it take him to grade 150 papers is 32 minutes, 4 seconds

It is important to note that proportion is a method of comparison in which two expressions or equations are made equal to each other.

From the information given, we have that;

Mr. B grades a total of 12.5 papers in 2.7 minutes.

Then, for 150 papers, we would have;

If 12. 5 papers = 2.7 minutes

Then 150 papers = x

Cross multiply the values

12.5x = 2.7(150)

multiply the values

12.5x = 405

Divide the values by the coefficient of x, we get;

x = 405/12.5

x = 32 minutes, 4 seconds

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Answer:

see explanation

Step-by-step explanation:

\(\frac{pq+1}{9}\)

= \(\frac{(3x+1)(3x-1)+1}{9}\)

= \(\frac{9x^2- 1+1}{9}\)

= \(\frac{9x^2}{9}\)

= x²

Answer:

Hello,

Step-by-step explanation:

\(Using\ the\ formula\ (a+b)(a-b)=a^2-b^2\\p=3x+1\\q=3x-1\\\\p*q=(3x+1)*(3x-1)=9x²-1\\\\p*q+1=9x^2\\\\x^2=\dfrac{p*q+1}{9} \\\)

Answer:

8

Step-by-step explanation:

From the problem, we have a triangle and we need to find the measurements of the angles marked in blue.

Note that angles adjacent to each other in a straight line have a sum of 180 degrees.

That will be :

The other angle is :

Now we have the two angles in a triangle, 40 and 90 degrees, and the sum of interior angles in a triangle is always 180 degrees.

That will be :

ANSWER :

p = 50 degrees

The derivative of the function 4 / x - 1 / y = 3 is equal to y' = 4 / (4 - 3 · x)².

In this problem we must use two differentiation methods in a function to obtain its first derivative. These methods are (i) explicit differentiation and (ii) implicit differentiation. Each procedure is described below:

Explicit differentation

Implicit differentiation

Explicit differentiation

Step 1

4 / x - 1 / y = 3

1 / y = 4 / x - 3

1 / y = (4 - 3 · x) / x

y = x / (4 - 3 · x)

Step 2

y' = [(4 - 3 · x) - x · (- 3)] / (4 - 3 · x)²

Step 3

y' = 4 / (4 - 3 · x)²

Implicit differentiation

Step 1

- 4 / x² + [1 / (y²)] · y' = 0

Step 2

(1 / y²) · y' = 4 / x²

Step 3

y' = 4 · y² / x²

Step 4

y' = 4 · [x / (4 - 3 · x)]² / x²

y' = 4 / (4 - 3 · x)²

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Answer:

143

Step-by-step explanation:

A = \(\frac{Base1 + Base2}{2}\) x h

A = \(\frac{8 + 18}{2}\) x 11

A = \(\frac{26}{2}\) x 11

A = 13 x 11

A = 143

Answer:

none of the multiple choice are right, it's 143

Step-by-step explanation:

use trapezoid formula

a+b

------- h

2

26

----- h

2

13×11= 143

It takes Hiroshi 30 years to reach his investment goal.

The formula for calculating the amount received on the principal amount (P) after t years at r% rate of interest is-

Amount = P(1 + r/100)^t

Let the principle amount with Hiroshi be P

then, the amount that Giulio starts with = 3P

Let time period for Giulio's investment = t

Then, the time period for Hiroshi's investment = 5t

Rate = 5%

As the investment goals of both the people are equal, they will get the same amount.

Therefore, we get the following equation-

P(1 + 20/100)^5t/4 = 3P(1 + 20/100)^t/4

(1 + 20/100)^5t/4 = 3(1 + 20/100)^t/4

[(1 + 20/100)^5t/4] /[(1 + 20/100)^t/4] = 3

(1 + 20/100)^(5t/4- t/4) = 3

(1 + 20/100)^(4t/4) = 3

(1 +0.2)^t = 3

(1.2)^t = 3

Taking log on both sides-

Log (1.2)^t = log 3

t log 1.2 = log 3

t = log 3/ log 1.2

t = 6.025

Time taken by Hiroshi to reach his investment goal = 5t

= 5(6.025)

= 30.128

Thus, it takes Hiroshi 30 years to reach his investment goal.

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Answer:

1380 children and 820 adults went to the zoo that day

Step-by-step explanation:

System of Equations

Define the following variables

x = number of children that went to the zoo

y = number of adults that went to the zoo

On a certain day,  2000 people went to the zoo, thus:

x + y = 2000

Solving for x:

x = 2000 - y        [1]

The admission ticket is $1.50 for children and $4.00 for adults and that same day, $5050 was collected, then:

1.50x + 4y = 5050       [2]

Substituting x from [1]:

1.50(2000 - y) + 4y = 5050

Operating:

3000 - 1.50y + 4y = 5050

3000 + 2.5y = 5050

Subtracting 3000

2.5y = 5050 - 3000 = 2050

Dividing by 2.5

y = 820

From [1]

x = 2200 - 820 = 1380

1380 children and 820 adults went to the zoo that day

Answer:

Step-by-step explanation:

Because a square has 4 equal sides:

P = 4x

A = \(x^{2}\)

\(P=\frac{4x^2+4}{x^2-2x+1}\)                              (original P equation)

\(4x=\frac{4x^2+4}{x^2-2x+1}\)                             (substitute P = 4x)

\(4x(x^2-2x+1)={4x^2+4}\)         (multiply denominator on both sides)

\(4x^3-8x^2+4x={4x^2+4}\)          (distribute 4x)

\(4x^3-12x^2+4x-4=0\)            (combine like terms, set = to 0)

\(4(x^3-3x^2+x-1)=0\)             (factor)

Continue using quadratic formula to find x

Hope this helps! Cannot finish answer right now, so sorry

side=Perimeter/4

side:-

\(\\ \rm\Rrightarrow \dfrac{4(x^2+1)}{4(x^2-2x+19}\)

\(\\ \rm\Rrightarrow \dfrac{x^2+1}{x^2-2x+19)}✓/tex]

Area=side ²

\(\\ \rm\Rrightarrow \left(\dfrac{x^2+1}{x^2-2x+19}\right)^2\)

Answer:

I am writing a Python program:

def most_common_letter (string):  #function that takes a string as argument and returns the most commonly occurring letter in string

   string = string.lower()  # converts the string into lower case

   inp_string="".join(string.split())  #splits the string in to a list and joins the elements of the list

   maximum = 0  #sets the value of maximum to 0

   letter = ""  #stores the most commonly occurring letter

   length = len(inp_string)  #returns the length of the input string

   counter = 0  #counts the occurrences of the letter in the string

   for i in range(0, length):  # iterates through the length of string        

       j = 0  #initializes j to 0

       char = inp_string[i]  #  holds letter of input string at index position i

       while length > 0:  # iterates until the length of string exceeds 0

           if (char == inp_string[j]):  # if letter in char is equal to letter at index j of the string

               counter += 1  #adds 1 to the count

           j += 1  #increments j by 1

           length -= 1    #decrements value of length by 1

           if (maximum <= counter):  #if maximum value is less than counter

               maximum = counter  #sets the maximum number of occurrences of a letter to maximum

               letter = char #sets the most occuring letter in string to letter

   return letter  #returns the most commonly occurring letter in the input string

#in order to check if the function works properly use following statement

print(most_common_letter("This is a test of the function I have written")) #calls most_common_letter method by passing a string to it

Step-by-step explanation:

The program works as follows:

I will explain this with the help of an example. Suppose the string is:

string = "hello worLd"

first this string is converted to lowercase using lower() method. So the string becomes:

string = "hello world"

Next the string is split into a list using split() method. The string becomes:

['hello', 'world']

Then using join() this string is joined together on the basis of "" empty space

So the string becomes

helloworld

This string is assigned to the inp_string variable. Hence

inp_string = "helloworld"

The value of maximum is initialized to 0 and variable letter is also declared

which holds the most commonly occurring letter in the inp_string

len function is used to get the length of the inp_string

counter is initializes to 0. This counts the number of times the letter occurs in a string

The for loop iterates through the inp_string

Inside the loop the statement char = inp_string[i] sets the letter at the i-th index of inp_string to char.

i is initialized to 0 so inp_string[i] is inp_string[0] which is the first element of the string i.e. "h".

The program control then moves to the while loop. As length>0 so the program moves to the body of while loop which has an if statement:            if (char == inp_string[j]):      

This checks if the letter stored in char is equal to the letter at j-th index of the string. Now as j is initialized to 0. So

if (char == inp_string[0]):   this evaluates to true and value of counter is incremented to 1. Next value of j also incremented to 1 and length of string is decremented to 1 Hence

counter = 1

j = 1

length = 9

Next if (maximum <= counter): condition checks if value of maximum is less than or equal to counter. It is true because maximum=0 and counter =1

So    maximum = counter  assigns counter value to maximum and letter = char assigns char to letter which was initially empty.

  maximum = 1

  letter = 'h'

At occurrence each iteration each letter in a string is counted and the letter that occurs the most in the string is returned by the function. For the above example hello world, letter l appears 3 times in the string and it is the most commonly occurring letter in the input string. So letter "l" is returned by this function. Hence the output of this program is l.

Answer:

AC = PF

Step-by-step explanation:

So, the area of the figure is 54.5 square miles.

In mathematics, the area is the measurement of the size of a two-dimensional surface or region, usually expressed in square units. It is a quantity that expresses the extent of a two-dimensional shape or figure in a plane. The area of a figure is calculated by multiplying the length and width of the shape, in the case of a rectangle, or by using the appropriate formula for other shapes such as triangles, circles, or irregular polygons.

Here,

The area of rectangle R1 is:

Area of R1 = 5 mi x 2 mi

= 10 square miles

The area of rectangle R2 is:

Area of R2 = 2 mi x 14 mi

= 28 square miles

The area of the triangle TRI is:

Area of TRI = (1/2) x base x height

           = (1/2) x 11 mi x 3 mi

           = 16.5 square miles

Therefore, the total area of the figure is:

Area of figure = Area of R1 + Area of R2 + Area of TRI

              = 10 + 28 + 16.5

              = 54.5 square miles

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Answer:

33.7692307692 or for it to be rounded, 34 or 33.8

Step-by-step explanation:

Answer:

439/13

Step-by-step explanation:

When carpet sells for $4 per square foot and will cost you $616 to carpet your rectangular room, if you room is 14 feet long then the width is 11 feet

Given,

The cost of Carpet per square foot = $4

Total cost of the carpet = $616

We know

Area of the rectangle = Length × Width

Length = 14 feet

Consider the width of the rectangular room as x

Then the area of the room = 14x

Total cost of carpet = Area of the rectangular room× Cost of carpet per foot

Substitute the values

14x×4=616

14x=154

x=11 feet

Hence, When carpet sells for $4 per square foot and will cost you $616 to carpet your rectangular room, if you room is 14 feet long then the width is 11 feet

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Answer: 1/2 times 6x equals 3x  and then you do 1/2 times 4 and that equals 2 then multiply the 3 and 4 in the parenthesis and that is 12 then add 12 to the 3 and 2 and your answer is 17.

Step-by-step explanation:

Answer:

$3900.71 is the amount of money subtracted from the next model

51099.29 is the cost of the second model

Step-by-step explanation:

Answer:  A

Step-by-step explanation:

Benny's Pizza

13.60 + 2.50(3)

13.60 + 7.50

21.10

Ricco's Pizza

14.60 + 2(3)

14.60 + 6

21.60

Answer:

f(x) =4x^2-5x

f(-3)=4(-3)²-5×-3=4×9--15=36+15=51

Answer:

D

Step-by-step explanation:

An obtuse angle is one over 90. They both have one of them.

Answer:

\(x=-2\)

Step-by-step explanation:

\(\sf -33=3(x-9)\)

\(\sf 3\left(x-9\right)=-33\)

\(\sf \frac{3\left(x-9\right)}{3}=\frac{-33}{3}\)

\(\sf x-9=-11\)

\(\sf x-9+9=-11+9\)

\(\sf x=-2\)

Answer:

x=-2

Step-by-step explanation:

-33/3=-11

-11+9=-2

CHECKING

-33=3(-2-9)

-33=3•-11

-33= -33

Answer:

3

Step-by-step explanation:

y + 1 = 3(x - 4)

y + 1 = 3x - 12

y = 3x - 13

Slope: 3

Work Shown:

2(3c+3) < 6c+9

6c+6 < 6c+9 .... distribute

6c+6-6c <6c+9-6c .... subtract 6c from both sides

6 < 9 ... note the c terms go away entirely

We're left with a statement that is always true since 6 is always less than 9 regardless of what value of c we pick. So there are infinitely many solutions. Any real number can replace c to get a true statement.

Answer:

B. All Real Numbers

Step-by-step explanation:

Answer:

I believe the answer is 65 square root 13, if im wrong pls give me the options to choose from

a. To estimate the fraction of all likely voters who preferred the incumbent (p), we can use the fraction of survey respondents who preferred the incumbent (p^​). In this case, 215 out of 400 respondents preferred the incumbent. So, the estimate for p would be 215/400 = 0.5375, or 53.75%.

b. The estimator of the variance is np^​(1−p^​), where n is the sample size (400) and p^​ is the fraction of survey respondents who preferred the incumbent (0.5375). Plugging these values into the formula, we get the variance estimate as 400 * 0.5375 * (1 - 0.5375) = 86.4.

To calculate the standard error of the estimator, we take the square root of the variance estimate. So, the standard error would be √86.4 ≈ 9.29.

c. The p-value for the test of H0​:p=0.5 vs. H1​:p≠0.5 can be calculated by conducting a two-tailed test. We compare the estimated p value (0.5375) to the assumed value (0.5) and use the standard error (9.29) to calculate the test statistic. Based on the test statistic, we can determine the p-value. Without the specific values for the test statistic, we cannot calculate the exact p-value.

d. The p-value for the test of H0​:p=0.5 vs. H1​:p>0.5 can be calculated by conducting a one-tailed test. We compare the estimated p value (0.5375) to the assumed value (0.5) and use the standard error (9.29) to calculate the test statistic. Based on the test statistic, we can determine the p-value. Without the specific values for the test statistic, we cannot calculate the exact p-value.

e. To determine if the survey contains statistically significant evidence that the incumbent was ahead of the challenger at the time of the survey, we need to compare the p-value obtained from the test to a significance level (such as 0.05). If the p-value is less than the significance level, we can conclude that there is statistically significant evidence that the incumbent was ahead of the challenger.

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The velocity of the car traveling from one city to another that is 163 km away and takes 2 and a half hours to reach can be calculated as 65.2 km/hour. This is determined by dividing the distance traveled by the time taken, or 163 km / 2.5 hours.

Velocity is a measure of an object's displacement over time. It specifies both the object's speed and direction of movement, and is expressed in units of distance per unit of time, such as meters per second or kilometers per hour.

Distance is the measure of how far apart two points or objects are. It is typically measured in units such as kilometers, miles, meters, or feet.

According to the given information:

To find the velocity of the car, we need to use the formula:

Velocity = Distance / Time

In this case, the distance traveled by the car is 163km and the time taken to travel that distance is 2.5 hours.

Substituting the values into the formula, we get:

Velocity = 163 km / 2.5 hours

Simplifying, we get:

Velocity = 65.2 km/h

Therefore, the velocity of the car is 65.2 km/h.

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Answer:

19-44.

Step-by-step explanation:

I simply looked up the answer with a calculator.

Answer:

Age 18 and under: 175

Age 19 - 44: 1,750

Age 45 - 64: 1,500

Age 65 and over: 1,000

Step-by-step explanation:

I asked my mom and she kept roasting me :( So I kinda figured it out

Answer: welp what is inside of the arrays

Step-by-step explanation:

Answer:

y = 2x + 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = A (1, 7 ) and (x₂, y₂ ) = B (- 3, - 1 )

m = \(\frac{-1-7}{-3-1}\) = \(\frac{-8}{-4}\) = 2 , then

y = 2x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (1, 7 )

7 = 2(1) + c = 2 + c ( subtract 2 from both sides )

5 = c

y = 2x + 5 ← equation of line