Andrew and Kate have $30 to spend on dinner, tax, and gratuity at Mo's Restaurant. Tax is 6%, and they will give a 15%
tip on the total bill after taxes. Their dinner costs $21.00. Which statement correctly explains whether Andrew and Kate Have enough money to pay their bills

The real life example of cartesian coordinate system, is given below.

What is cartesian coordinate system?

A Cartesian coordinate system in a plane is a system of coordinates that uniquely identifies each point by a pair of numerical coordinates. These numerical coordinates are the signed distances from two fixed perpendicular oriented lines to the point, measured in the same unit of length.

The real life use of cartesian coordinate system is,

In real life, there are many straightforward situations where the Cartesian coordinate plane of x and y works well.

For instance, you can create a two-dimensional grid representing the room and use the appropriate unit of measurement to plan where to place various pieces of furniture in the room.

Define a location as your starting point and choose one direction to be x and the other (perpendicular) direction to be y. (i.e., the zero coordinate on both axes).

For example, (3, 5) would be 3 meters in the x-direction and 5 meters in the y-direction from your selected (0, 0) point. You can specify any position in the room with two numbers in the format (x, y).

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Answer:

D

Step-by-step explanation:

if x=5 then,

y=-6×1+11

=-6+11

=5

The total number of samples will be 1109 .

Given ,

Margin of error 0.02

Here,

According to the formula,

\(Z_{\alpha /2} \sqrt{pq/n}\)

Here,

p = proportions of scientist that are left handed

p = 0.09

n = number of sample to be taken

Substitute the values,

\(Z_{0.01} \sqrt{0.09 * 0.91/n} = 0.02\\ 2.33 \sqrt{0.09 * 0.91/n} = 0.02\\\\\\\)

n ≈1109

Thus the number of samples to be taken will be approximately 1109 .

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In statistical analysis, the mean absolute deviation (MAD) is a measure of the average distance between each data point and the mean of the data set. For Doctor A's data set on corrective lenses, the MAD is calculated as 0.42, while for Doctor B's data set, it is calculated as 0.38.

This shows that Doctor B's data set has a slightly smaller variation compared to Doctor A's data set.

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Answer:

-90

Step-by-step explanation:

1/5 = 0.2

18/0.2 = 90

90*-1 = -90

Answer:

-90

here u go)))

Answer:

Jamie's account has a greater balance after 6 months

Step-by-step explanation:

Jamie's savings account: b = 30(6) + 75

                                          b = 180 + 75

                                          b = 255

Carmen's savings account: b = 25(6) + 100

                                             b = 150 + 100

                                             b = 250

Hope this helps!

Carmen's savings account has a greater balance after 6 months than Jamie's savings account,

Two expressions, which may or may not include variables or integers, are said to be equal in a mathematical equation. Equations are fundamental problems and attempts to methodically address these problems have been the main inspirations for the development of mathematics.

It is given that, Jamie opens a savings account with $75. She makes a monthly contribution of $30 into her account. The equation gives the balance of Carmen's savings account.

b = 25m + 100

Since b represents account balance and m is the number of months.

Substitute the given data for, Jamie's savings account,

b = 30(6) + 75

b = 180 + 75

b = 255

Substitute the given data for, Carmen's savings account,

b = 25(6) + 100

b = 150 + 100

b = 250

Thus, Carmen's account has a greater balance for a given time.

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Answer:

20 %

Step-by-step explanation:5 divided by 1 hundred is 20

Answer:

  4) Stored chemical energy is converted to mechanical energy.

Step-by-step explanation:

The battery represents energy stored in the form of chemical compounds. The motion represents mechanical energy. The transfer occurs between these forms of energy.

  4) Stored chemical energy is converted to mechanical energy.

If the derivative is positive, the particle is moving upward, and if it is negative, the particle is moving downward.

Without knowing the specific path of the particle, we cannot find the time t when the line tangent to the path of the particle is vertical. However, we can determine the direction of motion of the particle at that moment.

If the tangent line to the path of the particle is vertical, it means that the slope of the tangent line is undefined (since the denominator of the slope formula, which is the change in x, is zero). This implies that the particle is moving in a vertical direction, either upward or downward.

To determine the direction of motion, we need to look at the sign of the derivative of the particle's position function with respect to time. If the derivative is positive, it means the particle is moving upward, and if the derivative is negative, it means the particle is moving downward.

For example, if the particle's position function is given by y = f(t), then the derivative of this function with respect to time t gives the velocity of the particle, which tells us whether the particle is moving upward or downward. If the velocity is positive, the particle is moving upward, and if it is negative, the particle is moving downward.

So, to determine the direction of motion of the particle at the moment when the tangent line is vertical, we need to evaluate the sign of the derivative at that moment. If the derivative is positive, the particle is moving upward, and if it is negative, the particle is moving downward.

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Answer:

0 is sin 90⁰ ...hmmm...kui

The solutions of the given Quadratic equations are as follows:

1)

The given quadratic equation is (k + 1)(k − 5) = 0

Setting each factor to zero and solving for k, we get:

k + 1 = 0 or k − 5 = 0

k = −1 or k = 5

So, the solutions are k = −1 and k = 5.

2)

(a + 1)(a + 2) = 0

Setting each factor to zero and solving for a, we get:

a + 1 = 0 or a + 2 = 0

a = −1 or a = −2

So, the solutions are a = −1 and a = −2.

3)

(4k + 5)(k + 1) = 0

Setting each factor to zero and solving for k, we get:

4k + 5 = 0 or k + 1 = 0

k = −5/4 or k = −1

So, the solutions are k = −5/4 and k = −1.

4)

(2m + 3)(4m + 3) = 0

Setting each factor to zero and solving for m, we get:

2m + 3 = 0 or 4m + 3 = 0

m = −3/2 or m = −3/4

So, the solutions are m = −3/2 and m = −3/4.

5)

x^2 − 11x + 19 = −5

Moving all terms to the left-hand side, we get:

x^2 − 11x + 24 = 0

Factoring the left-hand side, we get:

(x − 3)(x − 8) = 0

Setting each factor to zero and solving for x, we get:

x − 3 = 0 or x − 8 = 0

x = 3 or x = 8

So, the solutions are x = 3 and x = 8.

6)

n^2 + 7n + 15 = 5

Moving all terms to the left-hand side, we get:

n^2 + 7n + 10 = 0

Factoring the left-hand side, we get:

(n + 5)(n + 2) = 0

Setting each factor to zero and solving for n, we get:

n + 5 = 0 or n + 2 = 0

n = −5 or n = −2

So, the solutions are n = −5 and n = −2.

7)

n^2 − 10n + 22 = −2

Moving all terms to the left-hand side, we get:

n^2 − 10n + 24 = 0

Factoring the left-hand side, we get:

(n − 6)(n − 4) = 0

Setting each factor to zero and solving for n, we get:

n − 6 = 0 or n − 4 = 0

n = 6 or n = 4

So, the solutions are n = 6 and n = 4.

8)

n^2 + 3n − 12 = 6

Moving all terms to the left-hand side, we get:

n^2 + 3n − 18 = 0

Factoring the left-hand side, we get:

(n + 6)(n − 3) = 0

Setting each factor to zero and solving for n, we get:

n + 6 = 0 or n − 3 = 0

n = −6 or n = 3

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a) Build the probability distribution of X =  0.125.  b) Find the mean value of X= 1.875.  c) Find the standard deviation of X = 1.0533

a)

For a fair coin,

P(H) = P(T) = 0.5

Outcome X Probability

T 1 0.5

HT 2 0.5*0.5 = 0.25

HHT 3 0.5*0.5*0.5 = 0.125

HHHT 4 0.5*0.5*0.5*0.5 = 0.0625

HHHH 4 0.5*0.5*0.5*0.5 = 0.0625

So, the probability distribution of X is

X P(X)

1 0.5

2 0.25

3 0.125

4 0.0625+0.0625 = 0.125

b)

X P(X) X*P(X) X2*P(X)

1 0.5 0.5 0.5

2 0.25 0.5 1

3 0.125 0.375 1.125

4 0.125 0.5 2

\(\sum\) 1 E(X) = 1.875 E(\(x^{2}\)) = 4.625

Mean = \(\sum\)X* P(X) = 1.875

c)

Variance = E(\(x^{2}\)) - E\((x^{2} )\)= 4.625 – \(1.875^{2}\)  = 1.1094

Standard Deviation = \(\sqrt{variance} = \sqrt{1.1094} = 1.0533\)

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To find the dot product, we substitute the given values into the formula:

a · b = 40 * 30 * cos(34°)

Calculating the cosine of 34 degrees (cos(34°)), we find its value to be approximately 0.829.

Substituting this value into the equation, we get:

a · b ≈ 40 * 30 * 0.829 = 993.6

Therefore, the dot product of vectors a and b is approximately 993.6.

The dot product of two vectors represents the extent to which they align with each other. In this case, we have two vectors, a and b, with magnitudes of 40 and 30, respectively, and an angle of 34 degrees between them. The dot product formula involves multiplying the magnitudes of the vectors and the cosine of the angle between them. By substituting the given values into the equation, we find that the dot product of a and b is approximately 993.6. This value indicates that the vectors have a moderate alignment, as the dot product is positive and greater than zero.

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Answer:

\( \frac{m}{12} - 8 = 4 \\ \frac{m}{12} = 4 + 8 \\ m = 12×12 \\ m = 144\)

Hope it will help u...

Answer:

(-1, 7)

Explanation:

X-int: 1, if you go two units left then you go to -1.    1 -2 = -1

Y-int: 8, If you go down 1 unit then you got to 7.     8 -1 = 7

The number of children who like both pistachio and chocolate ice cream is 73.

Here we have to find at least one kind of ice cream liked by the children.

It is given that the total number of children is 395. The number of children who don't like any ice cream is 170.

So we get the number of students who like one or both the ice cream is 395 - 170 = 225.

Here it is provided that 123 children like pistachio ice cream and 175 children like chocolate ice cream.

So the total number of children who like pistachio and chocolate ice cream is 175+ 123 = 298. Which cannot be greater than 225.

So the number of children who like both ice creams is 298 - 225 = 73.

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Answer:

a=−2 and b=−2

Step-by-step explanation:

Let's solve your system by substitution.

7a−12b=10;−2a−4b=12

Step: Solve7a−12b=10for a:

7a−12b=10

7a−12b+12b=10+12b(Add 12b to both sides)

7a=12b+10

7a/7=12b+10/7

(Divide both sides by 7)

\( \sf \: a = \frac{12}{7} b + \frac{10}{7} \)

Step: Substitute: 12/7b+10/7 for a in−2a−4b=12:

−2a−4b=12

−2(12/7b+10/7)−4b=12

−52/7b + −20/7=12(Simplify both sides of the equation)

−52/7b+−20/7+20/7=12+20/7

(Add 20/7 to both sides)

−52/7b=104/7

\( \sf \: \frac{ \frac{ - 52}{7}b }{ \frac{ - 52}{7} } = \frac{ \frac{104}{7} }{ \frac{ - 52}{7} } \)

(Divide both sides by (-52)/7)

b=−2

Step: Substitute −2 for b in a =12/7b+10/7:

a=/12/7b+10/7

a=12/7(−2)+10/7

a=−2(Simplify both sides of the equation)

The formula used is \($N(t) = N_0 e^{rt}$\). If a new social network has 1000 users currently and at growth rate of 10% per month, it can be predicted that there will be approximately 2452 users in seven and a half months assuming similar exponential growth.

In the formula used in the spreadsheet model for measuring exponential growth i.e. \($N(t) = N_0 e^{rt}$\)

N(t) is the number of cases at time t

N₀ is the initial number of cases

e is the mathematical constant approximately equal to 2.71828

r is the growth rate (expressed as a decimal)

To adapt this formula to predict the number of users of a new social network, we can replace the variables with the appropriate values. For example, if the new social network has 1000 users currently and is growing at a rate of 10% per month, we can write:

N(t) = 1000 x \(e^{rt}$\)

To find the predicted number of users in seven and a half months, we can substitute t = 7.5 into the equation and solve for N(7.5):

N(7.5) = 1000 x \(e^{rt}$\)

N(7.5) ≈ 2452.22

Therefore, we would expect to have approximately 2452 users on the new social network in seven and a half months if it continues to experience similar exponential growth.

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The complete question is :

What is the formula used in the spreadsheet model discussed in this module for measuring exponential growth of an epidemic, and how can it be adapted to predict the number of users of a new social network at a future date assuming similar exponential growth? In particular, if the new social network has 1000 users currently and is growing at a rate of 10% per month, how many users would we expect to have in seven and a half months?

Pete is standing 4 feet away from a mirror on the ground, if mirror is 20 feet away from the base of the tree the height of tree is 30 feet.

let,

Pete is standing 4 feet away from a mirror on the ground.

Pete is 6 feet tall and can just see the top of the tree in the mirror from where he is standing.

We can say two triangles are formed are similar,

So if the mirror is 20 feet away from the base of the tree

After talkig the similarity theorem we get,

\(\frac{6}{4} = \frac{x}{20}\)

So x = 6*5

x = 30 feet.

The height of the mirror is 30 feet.

Height is a measurement of vertical distance, or how high something or someone is (how tall they are) (how "high" a point is).

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The function can be written in y = mx + b form. The given function represents a linear function.

Suppose the considered function whose graph is to be made is  f(x)

The values of 'x' (also called input variable, or independent variable) are usually plotted on horizontal axis, and the output values  f(x) are plotted on the vertical axis.

They are together plotted on the point  (x,y) = (x, f(x))

This is why we usually write the functions as:  y = f(x)

The given function represents a linear function

y = mx + b

here, "m" is the slope, "b" is the y-intercept (the y value when x = 0) or (0,y)

You can find the slope by using the slope formula and plugging in two points, or you use this:

slope = rise / run

Rise is the number of units you go up(+) or down(-)

Run is the number of units you go to the right.

from the graph, from each point, you go up 1 unit, and to the right 1 unit. So the slope is 1/1 or 1.

y = mx + b

m = 1  and it represents the slope of the line

b = 2 and it represents the y-intercept of the line

y = 1x + 2   or    y = x + 2

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The probability that the sample of four balls contains two white balls and two red balls is 0.39.

Let E be an event a sample of selecting four balls from an urn are two red balls and two white balls.

According to the given question.

Total number of marbles in an urn = 17 + 20 = 37

Total number of white marbles = 17

Total number of red marbles = 20

Now, the number of ways of selecting four marbles form an urn = \(^{37} C_{4}\)

And, number of ways of selecting 2 white and two red marbles = \(^{17} C_{2} \times\ ^{20} C_{2}\)

As, we know that probability of an event is calculated by taking the ratio of total number of favorable outcomes to the total number of outcomes.

Therefore, the probability that the sample of four balls contains two white balls and two red balls is given by

\(P(E) = \frac{^{20}C_{2} \times ^{17}C_{2} }{^{37}C_{4} }\)

\(\implies P(E) = \frac{\frac{20!\times 17!}{2!18!(2!!15!)} }{\frac{37!}{4!33!} }\)

\(\implies P(E) = \frac{\frac{20(19)(17)(16)}{2(2)} }{\frac{37(36)(35)(34)}{(4)(3)(2)} }\)

⇒ P(E) = 5(19)(17)(16)/(37(3)(35)(17))

⇒ P(E) = 19(16)/37(3)(7)

⇒ P(E) = 304/777

⇒ P(E) = 0.39

Hence, the probability that the sample of four balls contains two white balls and two red balls is 0.39.

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In linear equation, $869,776  will her total payment for the home be .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                               Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

You have to use the number in the intersection of the row for 5.25% interest and the column for 20 years.

The number is $6.74.

That means that, for every $1,000 borrowed for 20 years at 5.25% interest you will pay $6.74 every month.

2. Amount borrowed

You will make a 22% down payment:

Thus the amount borrowed is $426,000 - $93,720 = $332,280

3. Monthly payment

Multiply the monthly payment per 1,000 by the amount borrowed divided by 1,000:

4. Total monthly payments:

Multiply the number of payments by the monthly payment.

Number of payments = 20 years × 12 payments /year = 240 payments.

5. Total payment for the home.

The total payment for the home will be the down payment plus the amount paid to the bank:

$322,280 + $537,496 = $869,776

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There are two main methods to determine if it is a rainy day at a given location: measuring rainfall using weather instruments, and using radar and satellite imagery.

Measuring rainfall using weather instruments involves setting up a rain gauge, an instrument that measures the amount of rainfall in a specific location. These instruments measure the amount of rainfall at a given time and provide more accurate readings than radar or satellite imagery.

Using radar and satellite imagery is another way to measure if it is a rainy day at a given location. Radar and satellite imagery show precipitation patterns, cloud types, and the movement of the clouds. These images can help identify where it is raining and how much rainfall is expected in the near future.

Both methods are useful for predicting rain or other types of precipitation. Rainfall measurements from weather instruments provide more accurate data, while radar and satellite imagery offer a bigger picture of the overall weather patterns in a given area.

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The correct sentence regarding the sets is given as follows:

{1,3,5} C {x|x is an odd counting number}.

The set of counting numbers is composed by the non-negative numbers that are not decimals, hence they are given as follows:

{0, 1, 2, 3, 4, ...}

The set of odd numbers is composed by the numbers that are not divisible by 2, hence numbers that finish with digits 1, 3, 5, 7 or 9.

A set A is contained into another set B when it is a subset of the set B, that is, all of the elements of A belong to B. The symbol that represents if a set is contained into another is given by letter c.

In the context of this problem, we have that the elements 1, 3 and 5 are:

Hence the set is contained, and the correct sentence is:

{1,3,5} C {x|x is an odd counting number}.

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Answer:

53

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

You put the 3 in the place of the X

which means X^2 would be 3^2

That would be 9

You would then add 9 + 2

11 would be your answer

There is a 16% probability that the individual actually had the disease given a positive test result.

The probability that the individual had the disease can be calculated as follows:

Let A = Event of testing positive and actually having the disease

Let B = Event of testing positive but not actually having the disease

We are looking for P(A|B), which is the probability of actually having the disease given a positive test result.

Using Bayes' Theorem, we have:

P(A|B) = P(A) * P(B|A) / P(B)

Bayes' theorem is a mathematical formula used in probability theory to calculate the probability of an event based on prior knowledge of conditions that might be related to the event.

It states that the conditional probability of an event A given event B is equal to the product of the probability of event B and the conditional probability of event A given event B, divided by the probability of event B. The formula is represented as P(A|B) = P(B|A) * P(A) / P(B).

Where:

P(A) = 1/500 (probability of having the disease)

P(B|A) = 0.95 (probability of a correct positive result given that the individual has the disease)

P(B) = P(B|A) * P(A) + P(B|A') * P(A') (probability of a positive test result)

= 0.95 * 1/500 + 0.01 * 499/500 (probability of a false positive result given that the individual does not have the disease)

Plugging in the values, we have:

P(A|B) = (1/500) * 0.95 / [0.95 * 1/500 + 0.01 * 499/500] = 0.16 or 16%

Therefore, there is a 16% probability that the individual actually had the disease given a positive test result.

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Answer:

a = 9r²

Step-by-step explanation:

Given

r = \(\frac{\sqrt{a} }{3}\) ( multiply both sides by 3 to clear the fraction

3r = \(\sqrt{a}\) ( square both sides )

(3r)² = (\(\sqrt{a}\) )²

9r² = a