Melissa and Joey enjoyed dinner at a restaurant. They paid the waiter $100.50 plus a 20% tip. How much did each person pay if they split the total bill in half?

The frame for the rectangular portrait will cost $180.00.

The rectangular portrait has a width of 1 yard and a height of 2 yards. To calculate the perimeter of the portrait, which represents the length of frame required, we can use the formula:

Perimeter = 2 * (Width + Height)

Substituting the values, we have:

Perimeter = 2 * (1 yard + 2 yards) = 2 * 3 yards = 6 yards

The cost of the frame is given as $30.00 per yard. To calculate the total cost of the frame, we multiply the length of the frame (in yards) by the cost per yard:

Frame Cost = Perimeter * Cost per yard = 6 yards * $30.00/yard = $180.00

Therefore, the frame for the rectangular portrait will cost $180.00.

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7 raised to the power of 4 equals 2,401, and the exponent we were looking for is 4.

What is meant by power?

Power is a function that represents the number of times a base number is multiplied by itself. It is the rate at which work is done or energy is transferred, measured in watts.

What is meant by exponent?

An exponent is a mathematical notation used to indicate the number of times a quantity is multiplied by itself. It is written as a superscript and represents the power to which a number or expression is raised.

According to the given information

To find the value of the exponent that satisfies the equation 7ˣ = 2,401, we can take the logarithm of both sides of the equation with respect to base 7. This gives us:

log7(7ˣ) = log7(2,401)

x = log7(2,401)

Using a calculator, we can find that log7(2,401) is approximately 3. Therefore, the value of x that satisfies the equation 7ˣ = 2,401 is 3.

Alternatively, we could also use the fact that 2,401 is equal to 7⁴ - 2, which can be written as:

7⁴ - 2 = (7²)² - 2

= 49² - 2

= 2,401

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The angles that is supplementary to <HAE is <IAE

Supplementary angles are simply described as a pair of angles whose sum is 180 degrees.

Some properties of supplementary angles are;

From the information given, we can see that;

<HAE is on a straight line with <IAE , making their sum to be 180 degrees

Then, <IAE is supplementary is <HAE

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Step-by-step explanation: Well to begin, you take 15$ and multiply it by 4, since he wants to buy 4 of those tickets, which is 60$. Then, take the 10$ and multiply it by 2 since he wants 2 of those tickets, which is 20$, you then apply 10% to 60 and 20 by taking 10 percent of 60, then adding  it to 60 once have that, which is 66, you take the 3% and find 3% of 66, then add the answer of that to 66, which is 67.98$, you then do the same thing to the 20$.

Sorry if this didnt help, im sure it didnt because im a very bad explainer, but i tried..

Answer:

0.75757575757

Step-by-step explanation:

The graph shows that Connor traveled a total of seven blocks from his house to the store and then from the store to the bank.

Graph is a data structure used to represent data in a visual way. It is composed of a set of nodes and edges, where each node represents an object and each edge represents a connection between two objects. Graphs can be used to represent a variety of data structures, such as a network of roads, a family tree, or a list of friends. Graphs are powerful tools for understanding complex relationships in data.

It also shows that he stayed at the store and the bank for five and seven minutes respectively. After leaving the bank, he drove the remaining four blocks back home.

The graph also reveals that Connor was driving at a steady pace between the store and the bank and that the total journey time was twenty-two minutes. This time could have been reduced if he had driven faster. However, it is possible that he was being cautious due to the traffic or other conditions.

Overall, the graph provides a visual representation of Connor's journey and his decisions along the way. It also provides insight into his driving habits, as well as his ability to manage his time. Based on this data, it is clear that Connor was able to complete his errands in an efficient manner.

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The completed statement with regards to the area of the square and the rectangle are;

The estimated value of the length of the shaded square is 5·√5 inches. The estimated value of the area of the unshaded rectangle is 175 square inches.

The area of a square is the product of the side lengths which are congruent, therefore;

Area of a square = Side length, s × Side length, s = s²

The possible figure in the question includes;

A shaded square that is 125 square inches

An adjacent unshaded rectangle, that share a side with the square that has a side length of 7·√5 inches

Please find attached the possible drawing of the figure in the question, (not drawn to scale) obtained from a similar question posted online, created with MS Word.

Therefore;

The side length of the square = √(125) inches =  5·√5 inches

The estimated value of the side length of the square is; 5·√5 inches

The area of a rectangle = Length × Width

The length of the rectangle = 7·√5 inches

The width of the rectangle = 5·√5 inches

Therefore;

The area of the unshaded rectangle, therefore is; 5·√5 × 7·√5 = 175

The estimated area of the unshaded rectangle is 175 square inches

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The interest Raymond will pay this month is $54.98

What does APR mean?

APR means annual percentage rate, which means that since we are computing monthly interest, the annual rate which is the whole 12 months needs to be divided by 12 to ascertain the equivalent monthly interest rate

monthly interest=21.99%/12

What is the monthly interest amount in dollars?

The monthly interest amount in dollars is determined as the monthly interest rate multiplied by the credit card balance at the end of the month

monthly interest=$3,000*21.99%/12

monthly interest=$54.98

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Answer: A) no solution

Step-by-step explanation:

1) 7x-3x+3=4x+6

2) 4x+3=4x+6

3) 3 is not equal to 6, so no solution

There is no solution of the given equation.

What is linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Given that;

The equation is;

7x - 3 (x - 1) = 2(2x + 3)

Now, Solve the equation for x as;

7x - 3(x - 1) = 2(2x + 3)

7x - 3x + 3 = 4x + 6

4x + 3 = 4x + 6

Subtract 4x both side;

3 = 6

Clearly, 3 is not equal to 6.

So, There is no solution of the equation.

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Answer:

6.78

Step-by-step explanation:

Answer:

6.78 pounds

Step-by-step explanation:

Add: 3.18+1.35+2.25=6.78

(If you wanted the cost for the whole thing then you need to include the price for each of the pounds)

Answer:

x+[1+4+0]and {1×2}

Step-by-step explanation:

can you mark me brainlist

The formula can also be written as: a(n) = 25(1.025)ⁿ where 1.025 is the factor by which the initial amount is multiplied after each year of interest.

In mathematics, a function is a rule that assigns each input (or element of the domain) a unique output (or element of the range). It is a mathematical object that takes an input and produces an output based on a specified rule or set of rules. A function can be represented in different ways, such as by an equation, a graph, or a table of values. The most common notation for a function is f(x), where x is the input and f(x) is the corresponding output. Functions are used to describe relationships between quantities in various fields of mathematics and science, such as in calculus, linear algebra, statistics, physics, and engineering. They are also used in modeling real-world situations and solving problems in many areas, including finance, economics, and computer science.

Here,

The formula for calculating the amount of money in Anna's savings account with an initial deposit of $25 and 2.5% annual interest rate, compounded annually, is:

a(n) = 25(1 + 0.025)ⁿ

where t is the number of years since the account was opened.

This is the formula for calculating the future value of a present sum using compound interest formula.

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Complete question:

anna uses $25 to open a savings account. The function a(t) models the amount of money, a in her account, where t is the number of years since the account was opened. create a function that models the situation if her account earns 2.5% interest per year.

Answer:

36 cm

Step-by-step explanation:

Because the plant is growing the same amount each week you would take 12(3) and get 36 cm at the end of the 12 weeks.

Answer:

x = 5cm

Step-by-step explanation:

We Know

The x-scale is 1:5

Find x.

We Take

25 ÷ 5 = 5 cm

So, x = 5cm

Answer:

4096 horses, or 4 to the power of 6

Step-by-step explanation:

(4²)³×4 to the power of 0

We simplify the equation,

(16)³×4 to the power of 0

4096×1 (Since 4 to the power of 0 is 1)

= 4096 horses on the farm which is 4 to the power of 6

- Hope this helps!

Solving a system of equations we can see that:

We can use the variables:

x = mass of the 60% solution.

y = mass of the 85% solution.

We can write a system of equations.

x + y = 70

x*0.6 + y*0.85 = 70*0.8

We can isolate x on the first equation to get:

x = 70 - y

Replace that in the other one:

(70 - y)*0.6 + y*0.85 = 70*0.8

Now we can solve this for y.

y*0.25 = 70*0.8 - 70*0.6

y = 14/0.25 = 56

Then he needs to use 56 ounces of the 85% solution, and 14 ounces of the 60% solution.

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The answer is the A because they are similar and congruent

Answer:

A

Step-by-step explanation:

Answer: the percent decrease is 9%

Step-by-step explanation:

Formula :12500/14000x100% and this formula can use in any of question likes this

Answer:

\(P(x) -0.1(x+1)(x-3)^2\)

Step-by-step explanation:

So you can express a polynomial in factored form, where each factor of the polynomial is being multiplied by each other to get the original polynomial as such: \(p(x) = a(x+a)(x+b)(x+c)...\) notice the a in front? Sometimes the value is 1, sometimes it's not, and I'm assuming it's not 1, since the y-intercept is given.

Anyways, when we express a polynomial in factored form: \(p(x) = a(x+a)(x+b)(x+c)...\), it's pretty easy to see that -a, -b, and -c are roots, since if we plug in -a, the factor (x+a) becomes (-a + a) = 0, and since the factors are being multiplied by each other, the value p(-a) will be 0, since 0 * some value = 0.

The next thing to know is what multiplicity means. It essentially means when you have the same root "multiple times", or in other words it's the degree of the factor. For example: \(f(x) = (x+a)^3(x+b)^2(x+c) = (x+a)(x+a)(x+a)(x+b)(x+b)(x+c)\), if you took each factor, you would see that the root -a shows up 3 times, thus the multiplicity is 3, which can also be determined by just looking at the initial degree... 3. The same thing goes for b and c, except for c, the degree isn't explicitly said, it's just 1.

Since we have a zero at x=3 one of the factors will be (x-3) since plugging in 3 to this makes it 0. But this has a multiplicity of 2, so the degree of the this factor is 2. So for we have the polynomial: \(p(x) = (x-3)^2\)

Since we have a zero at x=-1, one of the factors will be at (x+1), since plugging in 1 into this makes the value 0. This has a multiplicity of 1, and you can write the degree 1, but if you don't explicitly write it, it can just be assumed to be 1, since a^1=a

So now we have the polynomial: \(p(x) = (x+1)(x-3)^2\)

So let's just assume we have an "a" value in front as mentioned in the very beginning, we have the polynomial: \(p(x) = a(x+1)(x-3)^2\) and we can solve for this value, using any point except for the zeroes. We can use the y-intercept given to solve for a

Plug in 0 as x (by definition of y-intercept) and set p(x) = -0.9

\(-0.9 = a(0+1)(0-3)^2\)

Subtract/add values

\(-0.9 = a(1)(-3)^2\)

Simplify

\(-0.9 = 9a\)

Divide both sides by 9

-0.1 = a

So now let's plug this into our polynomial to get the final result!

\(P(x) -0.1(x+1)(x-3)^2\)

Answer:

sorry yrr im also not sure

Step-by-step explanation:

there is something severely wrong with the problem definition.

when the Hypotenuse = 9, there is no 30-60-90 triangle with a leg = 6.

and when we are just focusing that this is a right-angled triangle with the Hypotenuse = 9, then 6 cannot be the longer leg.

it is also not clear what the solution is supposed to be. the 2nd leg ? the area ? the perimeter ? the height(s) ? ...

what ?

so, all I can do here is to show you why I said what I said :

30-60-90 triangle with Hypotenuse = 9

then the longer leg is opposite of the 60° angle and therefore sin(60)×9 = 7.794228634...

the shorter leg is opposite of the 30° angle and therefore sin(30)×9 = 0.5×9 = 4.5

a right-angled triangle with Hypotenuse = 9, one leg = 6 gives us per Pythagoras for the other leg

9² = 6² + leg²

81 = 36 + leg²

45 = leg²

leg = sqrt(45) = 6.708203932...

so, you see, as stated above, there is no leg with the length 6 in such a 30-60-90 triangle.

and in a more general right-angled triangle, if one leg = 6, then the other leg is actually longer.

therefore, there is everything wrong with the problem definition.

Answer:

1

Step-by-step explanation:

a) The number of possible access codes is 1000.

b) The probability of randomly selecting the correct access code on the first try is 1/1000

c) The  probability of not selecting the correct access code on the first try is 999/1000.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

a) There are 10 digits from 0 to 9.

First digit= 10 ways

Second digit= 10 ways

Third Digit = 10 ways

Then, possible outcomes

= 10 x 10 x 10

= 1000  

b) Exactly 1 out of 1000 codes will be correct

Favorable outcomes= 1

so, probability of randomly selecting the correct access code on the first try

= 1/1000

c) The probability of not selecting the correct access code on the first try.

=1- 1/1000

= 999/1000

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Answer:

First equation: 4n^2=256

Second equation: 4n*2=64

Step-by-step explanation:

First equation:

4n^2 for n = 8.

Substitute 8 for n and solve:

4*(8)^2=4*64=256

4n^2=256

Second equation:

4n*2 for n = 8.

Substitute 8 for n and solve:

4*(8)*2=32*2=64

4n*2=64

I hope this helped you.

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Have a great day!!!!!!!!!!!!

Answer:

Shown from the explanation below..

Step-by-step explanation:

From the graph, it's a graph with a vertex hence its a quadratic equation without

When g(X)=2; x=0

F(4) =-10; from x=4 on the graph of f(x)

The required value of f(4) = -10, value of function evaluated from the graph.

A graph has been shown of f(x) and g(x).
g(x) = 2 is given and f(4) is to determine with the help of the graph.

The graph is a demonstration of curves  which gives the relationship between x and y axis.

The graph has been shown to find the value of f(x) coordinates located on the curve for every x on the number line of the x-axis.
In manner to locate f(4) draw the verticle from x = 4 the intersect at cover f(x)(yellow point). Now, draw the horizontal line from the yellow mark the line intersects at y = -10 on the y axis. i.e.
f(4) = -10

Thus, the required value of f(4) = -10, value of function evaluated from the graph.

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Answer:

Step-by-step explanation:

If \(\sum a_n\) is a series, for the series to converge/diverge according to ratio test, the following conditions must be met.

\(\lim_{n \to \infty} |\frac{a_n_+_1}{a_n}| = \rho\)

If \(\rho\) < 1, the series converges absolutely

If \(\rho > 1\), the series diverges

If \(\rho = 1\), the test fails.

Given the series \(\sum\left\ {\infty} \atop {1} \right \frac{n^2}{5^n}\)

To test for convergence or divergence using ratio test, we will use the condition above.

\(a_n = \frac{n^2}{5^n} \\a_n_+_1 = \frac{(n+1)^2}{5^{n+1}}\)

\(\frac{a_n_+_1}{a_n} = \frac{{\frac{(n+1)^2}{5^{n+1}}}}{\frac{n^2}{5^n} }\\\\ \frac{a_n_+_1}{a_n} = {{\frac{(n+1)^2}{5^{n+1}} * \frac{5^n}{n^2}\\)

\(\frac{a_n_+_1}{a_n} = {{\frac{(n^2+2n+1)}{5^n*5^1}} * \frac{5^n}{n^2}\\\)

aₙ₊₁/aₙ =

\(\lim_{n \to \infty} |\frac{ n^2+2n+1}{5n^2}| \\\\Dividing\ through\ by \ n^2\\\\\lim_{n \to \infty} |\frac{ n^2/n^2+2n/n^2+1/n^2}{5n^2/n^2}|\\\\\lim_{n \to \infty} |\frac{1+2/n+1/n^2}{5}|\\\\\)

note that any constant dividing infinity is equal to zero

\(|\frac{1+2/\infty+1/\infty^2}{5}|\\\\\)

\(\frac{1+0+0}{5}\\ = 1/5\)

\(\rho = 1/5\)

Since The limit of the sequence given is less than 1, hence the series converges.

Answer:

a) The P-value is 0.

At a significance level of 0.05, there is enough evidence to support the claim that the online platform was accessed significantly more so than before the stay at home order.

b) Effect size d = 0.77

Medium.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the online platform was accessed significantly more so than before the stay at home order.

Then, the null and alternative hypothesis are:

\(H_0: \mu=1000\\\\H_a:\mu> 1000\)

The significance level is 0.05.

The sample has a size n=108000.

The sample mean is M=1378.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=489.

The estimated standard error of the mean is computed using the formula:

s_M=\dfrac{s}{\sqrt{n}}=\dfrac{489}{\sqrt{108000}}=1.488

Then, we can calculate the t-statistic as:

t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{1378-1000}{1.488}=\dfrac{378}{1.488}=254.036

The degrees of freedom for this sample size are:

\(df=n-1=108000-1=107999\)

This test is a right-tailed test, with 107999 degrees of freedom and t=254.036, so the P-value for this test is calculated as (using a t-table):

\(\text{P-value}=P(t>254.036)=0\)

As the P-value (0) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

At a significance level of 0.05, there is enough evidence to support the claim that the online platform was accessed significantly more so than before the stay at home order.

The effect size can be estimated with the Cohen's d.

This can be calculated as:

\(d=\dfrac{M-\mu}{\sigma}=\dfrac{1378-1000}{489}=\dfrac{378}{489}=0.77\)

The values of Cohen's d between 0.2 and 0.8 are considered "Medium", so in this case, the effect size d=0.77 is medium.