Executive Limousine rentals charges an initial fee of $200 and $40 per hour that the limousine is in service. Jet Limousine rentals charges an intial fee of $120 and $50 per hour that the limosine is in service. At how many hours of service do the two limousine rental companies charge the same amount?

Answer:

Height of Cara at the end of the Third grade is 51 inches.

Step-by-step explanation:

Given:

Height of Cara at the start of second grade = 44 inches

In second grade she grew = 3 inches.

Hence height of Cara at the end of the second grade will be equal to sum of Height of Cara at the start of second grade and height she grew in second grade.

Framing the equation we get;

height of Cara at the end of the second grade = 44 + 4 = 48 inches

Also Given:

Height she grew in third grade = 3 inches

We need to find Height of Cara at end of third grade.

Hence height of Cara at the end of the Third grade will be equal to sum of Height of Cara at the end of second grade and height she grew in third grade.

Framing in equation form we get;

Height of Cara at the end of the Third grade = 48 + 3 = 51 inches

Hence Height of Cara at the end of the Third grade is 51 inches.

Answer:

51 inches

Step-by-step explanation:

44 + 4 + 3= 51

Answer:

A. The Long family paid $2.63 too little for their purchases.

Step-by-step explanation:

We have been given that the Long family spent $38.62 for school supplies and $215.78 for new school clothes. They paid 6.8% sales tax on their purchases.

First of all, we will add both amounts as:

[tex]\$38.62+$215.78=\$254.40[/tex]

Now, we will find 6.8% of 254.40.

[tex]\text{Amount of tax paid}=\$254.40\times \frac{6.8}{100}[/tex]

[tex]\text{Amount of tax paid}=\$254.40\times0.068[/tex]

[tex]\text{Amount of tax paid}=\$17.2992[/tex]

Upon adding $254.40 and $17.2992, we will get total amount paid by Long family.

[tex]\text{Total amount paid by Long family}=\$254.40+\$17.2992[/tex]

[tex]\text{Total amount paid by Long family}=\$271.6992[/tex]

Now, we will subtract $271.6992 from $269.07:

[tex]\$269.07-\$271.6992[/tex]

[tex]-\$2.6292\approx -\$2.63[/tex]

Since the long family paid $2.63 less than actual amount, therefore, the Long family paid $2.63 too little for their purchases and option A is the correct choice.

Answer:

A

Step-by-step explanation:

Good evening

Answer:

f(-3) = -4

Step-by-step explanation:

just using the calculator replace x by -3

f(-3) = 4(-4-(-3)) = 4(-4+3) = 4×(-1) = -4.

:)

Answer:

-4

Step-by-step explanation:

How you start the equation is by plugging  -3 into both of the x's in the problem to make it:

f(-3) =  4(-4 - (-3))

f(-3) = 4(-4 + 3)

f(-3) = 4(-1)

f(-3) = -4

The answer would be written as:

f(-3) = -4

I hope this helps!

Answer: x = ln 22.8; 3.13

Step-by-step explanation:

Given the exponential equation

e^x = 22.8

We apply ln to both sides since only natural logarithm can cancel out exponents.

lne^x = ln 22.8

x = ln 22.8

x = 3.13

Answer: I agree with 6/5 and with 1 1/5

Step-by-step explanation: okay, to find the value of the amount of 5/6 in 1, we simply just divide 1 by 5/6

Taking a similar problem with different numbers. Let's the the amount of 2s in 10, we do 10/2 which equals 5, so we have 5 2s in 10, you get? 2,4,6,8,10

So dividing 1 by 5/6

I / (5/6)

Change since to multiplication

1 * 6/5

= 6/5

Changing this to a mixed fraction, we get 1 whole number, 1 over 5 = 1 1/5

Answer:Answer: I agree with 6/5 and with 1 1/5

Step-by-step explanation:

Step-by-step explanation: okay, to find the value of the amount of 5/6 in 1, we simply just divide 1 by 5/6

Taking a similar problem with different numbers. Let's the the amount of 2s in 10, we do 10/2 which equals 5, so we have 5 2s in 10, you get? 2,4,6,8,10

So dividing 1 by 5/6

I / (5/6)

Change since to multiplication

1 * 6/5

= 6/5

Changing this to a mixed fraction, we get 1 whole number, 1 over 5 = 1 1/5

(copied from another user) so credit to her

Answer:

$120

Step-by-step explanation:

Suppose the  woman had x dollars in her purse at the beginning of the shopping.

First, she spent 4/5 of all the money she had, therefore she had 1-4/5=1/5 left

1/5 of x = (1/5)x or 0.2x

Then she lost 2/3 of what was remaining, which is 2/3 * (1/5)x= (2/15)x

What will be left will be (1-2/3) or 1/3 of that 1/5x left after shopping.

This will be 1/3*(1/5)x=(1/15)x

It is given from the problem statement that this is $10 left.

Therefore, (1/15)x= 10

Multiplying through by 15 and simplifying,

x= $150.

Now she spent 4/5 of this $150, which is

(4/5)*150=$120

To find out how much money the woman spent, we need to determine the amount she had in her purse and then calculate the difference after spending and losing some. We can solve this using a step-by-step approach.

To calculate how much money the woman spent, we need to follow these steps:

Let's solve this step-by-step:

Step 1: X = Amount she had in her purse

Step 2: Y = (4/5) * X * (1/3)

Step 3: Y = $10

Step 4: Calculate X - Y to find how much money she spent.

Answer:

Is below

Step-by-step explanation:

1.

b. x </= -7 OR x > 4

d. x >/= -7 AND x < 4

e. x >/= -7 OR x < 4

c. x </= -7 AND x < 4

a. x </= -7 OR x < 4

2.

( - the absolute sign

(d - 3.5) </= 1.5

d - 3.5 </= 1.5 (positive case)

d </= 5

(d - 3.5) >/= 1.5

d - 3.5 >/= -1.5 (negative case)

d >/= 2  

D. Is the number line graph of the inequality.

Tan(Angle) = Opposite leg / Adjacent leg

Tan(B) = 4/5

B = arctan(4/5)

B = 51.34 degrees.

Answer:

15 books

Step-by-step explanation:

Given that Victor read a total of 12 books over 4 months which means for 1 month he reads 12/4 = 3 books

Also given that he belongs to the book club for 5 months

We know that he reads 3 books in 1 month

So in 5 months he reads [tex]5\times3=15books[/tex]

A driver can be jailed up to one year and fined up to $5,000 if he or she refuses to bring his or her vehicle to a stop when given a visual or an audible signal by a police officer.

Answer: Option B

Step-by-step explanation:

This Vehicle codes 2800.1 state a violation or avoidance of police. The rules as follows: "Any person who, while driving a motor vehicle and intentionally avoiding it, intentionally escapes or attempts to escape from a peace officer " Any driver who "intentionally fails or refuses to stop the vehicle or otherwise, an attempt to escape or prosecute the pursuing police officer when he receives a visual and audible signal to stop the vehicle.

"Visual and audible" signals include sirens, lights, hand signals and voice commands. You must have been able to hear and / or see these signals to be accused of escaping and attempting to escape from the police. This is a level II or level 3 crime, and any penalties for those fleeing or trying to avoid a police officer will depend on the scale of the crime they are suspected of.

A driver can be jailed up to one year and fined up to $5,000 if he or she refuses to bring his or her vehicle to a stop when given a visual or an audible signal by a police officer.

The correct answer is B. refuses to bring his or her vehicle to a stop when given a visual or an audible signal by a police officer.

Under Georgia law, a driver can be jailed up to one year and fined up to $5,000 if they refuse to stop their vehicle when signaled by a police officer. This is considered a serious offense because it puts both the driver and other people's safety at risk.

Examples of situations where a driver may refuse to stop include fleeing from law enforcement, attempting to evade arrest, or engaging in dangerous driving behaviors that necessitate a traffic stop.

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Answer:

C

Step-by-step explanation:

This is a combination question.

In the first instance, we select 5 from 20 and in the second case , we select 4 from 20.

The total number of ways to solve the first instance is 20C5 = 15504 ways

The total number of ways to solve the second instance is 20C4 = 4,845

The ratio of the first to the second scenario is 15,504/4,845 = 3.2 = 16 to 5

Answer:

Step-by-step explanation:

160+112n=180k

112n=180k-160

for k=1

180-160=20(not divisible by 112)

k=2

180*2-160=360-160=200(not divisible by 112)

k=3

180*3-160=540-160=380(not divisible by 112)

180*4-160=720-160=560(divisible by 112)

so number of sides=560/112 +1=5+1=6

or (n-2)180=720

n-2=720/180=4

n=4+2=6

Answer:

6

Step-by-step explanation:

The sum of interior angle of a polygon is (n - 2)180.

But in the convex polygon given in the question, we know that the sum of the interior angles is as follows: : 160 + 112(n - 1)

Equating both will yield the following:

180n -360 = 112n - 112 + 160

180n - 360 = 112n + 48

180n - 112n = 360 + 48

68n = 408

n = 408/68 = 6

Hence , the convex polygon has 6 sides

Answer:

  v = 2

Step-by-step explanation:

Eliminate parentheses by using the distributive property.

  -18v +6 = -10v -10

  6 = 8v -10 . . . . . . . . . add 18v

  16 = 8v . . . . . . . . . . .  add 10

  2 = v . . . . . . . . . . . . . divide by the coefficient of v

The answer is v = 2.

Answer:

v = 2

Step-by-step explanation:

6 (-3v + 1) = 5 (-2v - 2)

- 18v + 6 = - 10v - 10

- 18v + 10v = - 10 - 6

- 8v = - 16

- v = - 16/8

- v = - 2

v = 2

Test hypothesis :

[tex]H_0 : \mu =5\\\\ H_a: \mu >5[/tex]

Since alternative hypothesis is right-tailed and population standard deviation is known σ = 1 , so we perform a right-tailed  z-test.

Test statistic : [tex]z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

, where [tex]\overline{x}[/tex] = sample mean

[tex]\mu[/tex] = population mean

[tex]\sigma[/tex] =population standard deviation

n= Sample size

Substitute values, we get

[tex]z=\dfrac{ 5.3-5}{\dfrac{1}{\sqrt{500}}}[/tex]

[tex]z=\dfrac{ 0.3}{0.04472135955}\approx6.7[/tex]

Critical value for 0.01 significance level in z-table is 2.326.

Decision : Test statistic (6.7)> Critical value ( 2.326), it means we reject that null hypothesis.

i.e. [tex]H_a[/tex] is accepted.

We conclude that there is sufficient evidence that the mean time to approval is actually longer than advertised.

Answer:

  It has a single solution x=-3 y=26

Step-by-step explanation:

The ratios of coefficients of x and y are different, so the pair of equations has one solution. It is easy to tell the first offered solution (15, 17) does not satisfy the first equation, so that choice is eliminated.

Fortunately, the second offered solution, (x, y) = (-3, 26), satisfies both equations.

The equations have a single solution: (x, y) = (-3, 26).

Answer: The equation has a single solution x = -3 , y = 26.

( -3, 26 )

Step-by-step explanation:

3x + y =17 ---------------------(1)

x + 2y = 49 -------------------(2)

Using substitution approach

From (2)

x = 49 - 2y --------------------(3)

Now put (3) in equation (1) and solve.

3(49 - 2y) + y = 17

Open the bracket and solve

3 x 48 - 3 x 2y + y = 17

147 - 6y + y = 17

Gather like terms

-5y = 17 - 147

-5y = -130

Multiple through by (-1)

5y = 130

Divide by 5

y = 130/5

y = 26.

Substitute for y now in equation (3) to get the value of x

3x + y = 17

3x + 26 = 17

3x = 17 - 26

3x = -9

Now , divide by 3

x = -3

The equation had a single solution of x = -3 , y = 26

Chech.

3 x -3 + 26

-9 + 26

= 17

Cos(Angle) = Adjacent leg / Hypotenuse

Cos(X) = 3.5/4.6

X = arccos(3.5/4.6)

X = 40.46 degrees.

Answer:

  1

Step-by-step explanation:

An odd number will be the difference of an even and an odd number. The only even prime is 2, so the other prime must end in 5. There is only one such.

Only 3 = 5 -2 can be written as the difference of primes.

Answer:

1

Step-by-step explanation:

Notice that when we subtract two integers, the difference can only be odd if one integer is even and one integer is odd (even - even = even and odd - odd = even). If one integer is even, then that integer is divisible by 2 and thus not prime. The only exception is 2, the only even prime number. So one of the primes must be 2. If we add 2 to each number in the set to find the other prime, we end up with $\{5, 15, 25, 35, \ldots\}$. All of the numbers in the set are divisible by 5, which means the only prime number in the set is 5. So the only number in the set $\{3,13,23,33, \ldots\}$ that can be written as the difference of two primes is $5-2=3$. The answer is $\boxed{1}$ number.

Yes I copied and pasted the proper answer from a different site. I didn't want to write it out.

Answer:

[tex]\displaystyle a_n=8+9(n-1)[/tex]

Correct option: C]

Step-by-step explanation:

Arithmetic Sequences

Each term in an arithmetic sequence is obtained as the previous term plus a constant number called the common difference. The general term is

[tex]\displaystyle a_n=a_1+(n-1).r[/tex]

We are given this information

[tex]\displaystyle a_1=8\ ,\ a_7=62[/tex]

Replacing those values in the formula

[tex]\displaystyle 62=8+(7-1).r[/tex]

Solving for r

[tex]\displaystyle r=\frac{62-8}{6}=\frac{54}{6}=9[/tex]

[tex]\displaystyle r=9[/tex]

The general term is, then

[tex]\displaystyle a_n=8+(n-1)9[/tex]

Or equivalently

[tex]\displaystyle a_n=8+9(n-1)[/tex]

Correct option: C]

Answer:

Sarah family will get 2 cards

Step-by-step explanation:

The total number of cards is 32

Sarah sent half of the Christmas cards to her friends,= 1/2 *32= 16 cards for Sarah's friends

Richard sent three eights of them to his friends.

3/8 *32=12 cards for Richards friends

Total = 12+16= 28

Card left= 32-28=4

Since Sarah and Richard want to send an even number of cards to their families. Then Sarah's family and Richard's family will receive 2 apiece.

Sarah's family would receive 2 cards after accounting for the cards Sarah and Richard sent to their friends from the total of 32 cards.

To solve how many Christmas cards Sarah's family will get, first calculate how many cards Sarah and Richard sent to their friends. Sarah sent half of 32, which is 16 cards. Richard sent three eights of 32, which can be calculated as (3/8) * 32 = 12 cards. Together, they sent 28 cards to their friends. Since there are 32 cards in total, the remaining cards for their families would be 32 - 28 = 4 cards. If these 4 cards are to be distributed evenly, both families would get 2 cards each. Thus, Sarah's family would get 2 cards.

Answer:

it would be A if you choose 100 random people then they would give you some explanation of why you should or shouldn't change the dress code.

Answer:

Option a - [tex]xy^2+5[/tex]

Step-by-step explanation:

Given : Polynomial [tex]x^3y^2+8xy^2+5x^2+40[/tex]

To find : Select one of the factors of polynomial ?

Solution :

The polynomial  [tex]x^3y^2+8xy^2+5x^2+40[/tex]

We factor of above polynomial by taking common terms,

[tex]xy^2(x^2+8)+5(x^2+8)[/tex]

[tex](xy^2+5)(x^2+8)[/tex]

From the given options,

[tex]xy^2+5[/tex] is one of the factors of polynomial.

Therefore, option a is correct.

Answer:

  (d)  sometimes a natural number and sometimes an irrational number

Step-by-step explanation:

Consider the natural numbers 3 and 4:

√4 = 2, a natural number

√3 ≈ 1.73205080756887729352744634150..., an irrational number

Answer:

The decimal value is 99.

Step-by-step explanation:

We want to convert 01100011 to decimal.

We start counting the digit from the rightmost digit using zero-index system:

0 = 7

1 = 6

1 = 5

0 = 4

0 = 3

0 = 2

1 = 1

1 = 0

We multiply each digit by 2 having the index as power:

[tex]= (0 * 2^{7} ) + (1 * 2^{6} ) + (1 * 2^{5} ) + (0 * 2^{4} ) + (0 * 2^{3} ) + (0 * 2^{2} ) + (1 * 2^{1} ) + (1 * 2^{0} )\\= (0 * 128) + (1 * 64) + (1 * 32) + (0 * 16) + (0 * 8) + (0 * 4) (1 * 2) + (1 * 1)\\= 0 + 64 + 32 + 0 + 0 + 0 + 2 + 1\\= 99[/tex]

Therefore, the decimal value of "c" is 99.

The decimal value of the given binary value 0110 0011 is 99.

Given information:

The binary value of the ASCII letter "c" is 0110 0011.

It is required to convert the given binary value into a decimal number.

So, to convert a binary code to a decimal code, it is required to multiply the binary numbers with indices of 2.

The code can be converted to decimal number as,

[tex]d=2^0\times 1+2^1\times1+2^2\times0+2^3\times0+2^4\times0+2^5\times1+2^6\times1+2^7\times0\\d=1+2+0+0+0+32+64+0\\d=99[/tex]

Therefore, the decimal value of the given binary value 0110 0011 is 99.

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Answer:the number of children that swam at the public pool is 259

the number of adult that swam at the public pool is 280

Step-by-step explanation:

Let x represent the number of children that swam at the public pool that​ day.

Let y represent the number of adult that swam at the public pool that​ day.

On a certain hot​ summer's day,539 people used the public swimming pool. This means that

x+ y = 539

The daily prices are $ 1.25 for children and $ 2.50 for adults. The receipts for admission totaled $ 1023.75. This means that

1.25x + 2.5y = 1023.75 - - - - - - - - - -1

Substituting x = 539 - y into equation 1, it becomes

1.25(539 - y) + 2.5y = 1023.75

683.75 - 1.25y + 2.5y = 1023.75

- 1.25y + 2.5y = 1023.75 - 683.75

1.25y = 350

y = 350/1.25 = 280

Substituting y = 280 into x = 539 - y , it becomes

x = 539 - 280 = 259

The required width of the mat around the photo is given as 3 inches.

Given that,
The combined area of the photo and mat needs to be 224 square inches. The equation that represents the combined area is (2w+8)(2w+10)=224, where w represents the width of the mat around the photo.

The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.

here,
(2w + 8)(2w + 10) = 224
4w² + 16w + 20w + 80 = 224
4w² + 36w - 144 = 0
w² + 9w - 36 = 0
[w -3][w + 12] = 0
w = 3 and w = -12
Since the measure of width cannot be negative so -12 can be neglected.
w = 3 preferred,

Thus, the required width of the mat around the photo is given as 3 inches.

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Answer:

The value of p would be [tex]\frac{1}{50}[/tex]

Step-by-step explanation:

Given,

[tex]p = \left ( 1 - \frac{1}{2} \right )\left ( 1 - \frac{1}{3} \right )\left ( 1 - \frac{1}{4} \right )...\left ( 1 - \frac{1}{50} \right )[/tex]

[tex]p = \left ( 1 - \frac{1}{2} \right )\left ( 1 - \frac{1}{3} \right )\left ( 1 - \frac{1}{4} \right )...\left ( 1 - \frac{1}{49} \right )\left ( 1 - \frac{1}{50} \right )[/tex]

[tex]p=\frac{2-1}{2}.\frac{3-1}{3}.\frac{4-1}{4}......\frac{49-1}{49}.\frac{50-1}{50}[/tex]

[tex]p=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}......\frac{48}{49}.\frac{49}{50}[/tex]

[tex]p=\frac{1.2.3.4.........48.49}{2.3.4........49.50}[/tex]

[tex]p=\frac{1}{50}[/tex]

Hence, the value of p is 1/50.

P is the product, indicated above, of all the numbers of the form , where k is an integer from 2 to 50, inclusive. Value of P is 2) 1/50.

To find the value of [tex]\( P \)[/tex], we can simply multiply all the terms together:

[tex]\[ P = \left(1 - \frac{1}{2}\right)\left(1 - \frac{1}{3}\right)\left(1 - \frac{1}{4}\right) \ldots \left(1 - \frac{1}{50}\right) \][/tex]

We start with [tex]\( k = 50 \)[/tex]. and go up to [tex]\( k = 50 \)[/tex]. Let's calculate it:

[tex]\[ P = \left(1 - \frac{1}{2}\right)\left(1 - \frac{1}{3}\right)\left(1 - \frac{1}{4}\right) \ldots \left(1 - \frac{1}{50}\right) \][/tex]

[tex]\[ P = \left(\frac{1}{2}\right)\left(\frac{2}{3}\right)\left(\frac{3}{4}\right) \ldots \left(\frac{49}{50}\right) \][/tex]

[tex]\[ P = \frac{1}{50} \][/tex]

So, the value of [tex]\( P \) is \( \frac{1}{50} \).[/tex]

[tex]p = \left ( 1 - \frac{1}{2} \right )\left ( 1 - \frac{1}{3} \right )\left ( 1 - \frac{1}{4} \right )...\left ( 1 - \frac{1}{50} \right[/tex]) P is the product, indicated above, of all the numbers of the form [tex]1 – \frac{1}{k}[/tex], where k is an integer from 2 to 50, inclusive. the value of P is  [tex]\( P \) is \( \frac{1}{50} \).[/tex]

Question:-

[tex]p = \left ( 1 - \frac{1}{2} \right )\left ( 1 - \frac{1}{3} \right )\left ( 1 - \frac{1}{4} \right )...\left ( 1 - \frac{1}{50} \right )[/tex]

P is the product, indicated above, of all the numbers of the form [tex]1 – \frac{1}{k}[/tex], where k is an integer from 2 to 50, inclusive. What is the value of P ?

1.) [tex]\frac{1}{100}[/tex]

2.) [tex]\frac{1}{50}[/tex]

3.) [tex]\frac{1}{49}[/tex]

4.) [tex]\frac{49}{50}[/tex]

5.)[tex]\frac{99}{100}[/tex]

Answer:

Step-by-step explanation:

we are to distinguish between

dependent variable independent variable

vs

response variable explanatory variable

An independent variable is one which is not affected by any other variable for example, the amount we spend, the time we study ,etc.  

An explanatory variable is a type of independent variable but not fully independent but depends on some factors.

Though explanatory and independent variables are practically used interchangeably the main difference is explanatory variable is not independent but explains the variations in the response varaible.

In experimental research, the independent variable is manipulated to observe its effect on the dependent variable, which is subsequently measured. Control variables are kept constant to ensure valid results. The dependent variable depends on the independent variable, such as the growth of plants depending on the amount of fertilizer applied.

In the context of experimental research, an independent variable, also known as an explanatory variable, is the one that is changed or controlled by the experimenter to examine its effect on another variable. On the other hand, a dependent variable, also referred to as a response variable, is what is measured or observed in the experiment to determine the effect of the independent variable.

For instance, if a study is conducted to see how the amount of fertilizer affects the growth of plants, the amount of fertilizer would be the independent variable because it is what the experimenter varies during the study. The growth of the plants, typically measured in height or biomass, would be the dependent variable because it is the result that is measured in response to the manipulation of the independent variable.

The control variables are equally crucial as they answer the question "What do I keep the same?" They need to be maintained consistently to ensure that the results are due only to the manipulation of the independent variable and not to other extraneous factors.

The authors of a study analyzing the effect of marital status on support for a football team would manipulate the marital status (independent variable) to measure the change in support or opposition for the team (dependent variable).

Answer:

[tex]f(x)=3*cosine(x)[/tex]

Step-by-step explanation:

We are looking for a trigonometric function which contains the point (0, 3), and has an amplitude of 3.

We know that for a sine function [tex]f(x)=sin(x)[/tex], [tex]f(0)= 0[/tex]; therefore the function we a looking for cannot be a sine function because it is zero at [tex]x=0[/tex].

However, the cosine function [tex]f(x)=cos(x)[/tex] gives non-zero value at [tex]x=0:[/tex]

[tex]f(0)=cos(0)=1[/tex]

therefore, a cosine function can be our function.

Now, cosine function with amplitude [tex]a[/tex] has the form

[tex]f(x)=a*cos(x)[/tex]

this is because the cosine function is maximum at [tex]x= 0[/tex] and therefore, has the property that

[tex]f(0)=a*cos(0)= a[/tex]

in other words it contains the point [tex](0, a)[/tex].

The function we are looking for contains the point [tex](0, 3)[/tex]; therefore, its amplitude must be 3, or

[tex]f(x)=3cos(x)[/tex]

we see that this function satisfies our conditions: [tex]f(x)[/tex] has amplitude of 3, and it passes through the point (0, 3) because [tex]f(0)=3[/tex]

Answer:

D

Step-by-step explanation:

edge

Answer:

7.23%.

Step-by-step explanation:

We are asked to find APY (Annual Percentage Yield) to the nominal rate of 7% compounded semiannually.

We will use annual percentage yield formula to solve our given problem.

[tex]APY=(1+\frac{r}{n})^n-1[/tex], where,

r = Annual interest rate in decimal form,

n = Number of times interest is compounded per year.

Let us convert 7% into decimal form.

[tex]7\%=\frac{7}{100}=0.07[/tex]

Semiannually means two times per year.

[tex]APY=(1+\frac{0.07}{2})^{2}-1[/tex]

[tex]APY=(1+0.00583333)^{12}-1[/tex]

[tex]APY=(1.00583333)^{12}-1[/tex]

[tex]APY=1.0722900804298071-1[/tex]

[tex]APY=0.0722900804298071[/tex]

[tex]APY\approx 0.0723[/tex]

Let us convert 0.0723 into percentage by multiplying with 100.

[tex]0.0723\times 100=7.23\%[/tex]

Therefore, annual percentage yield would be 7.23%.

The APY for a 7% nominal rate compounded quarterly is approximately 7.19%.

To find the APY (Annual Percentage Yield) for a nominal rate of 7% compounded quarterly, we use the following formula:

APY = (1 + r/n)ⁿ - 1

where r is the nominal interest rate and n is the number of compounding periods per year.

Convert the nominal rate from a percentage to a decimal: 7% = 0.07.

Identify the number of compounding periods per year: quarterly means n = 4.

Plug the values into the formula:

APY = (1 + 0.07/4)⁴ - 1

Calculate inside the parenthesis first: 0.07/4 = 0.0175.

Add 1: 1 + 0.0175 = 1.0175.

Raise to the fourth power: (1.0175)⁴ ≈ 1.071889

Subtract 1: 1.071889 - 1 ≈ 0.071889

Convert the decimal back to a percentage to get the APY: 0.071889 × 100 ≈ 7.19%.

Therefore, the APY corresponding to a 7% nominal interest rate compounded quarterly is approximately 7.19%.

Complete Question :

Find the APY corresponding to the following nominal rate 7% compounded quarterly The APY is %. (Type an integer or a decimal. Round to the nearest hundredth as needed. Do not round until the final answer)