In total, Jessica and Jonathan have created 19.64 cups of lemonade. They sell the lemonade in servings of 1.25 cup.
How many FULL servings will they be able to sell?

Answer:

-$50 lol

Step-by-step explanation:

Hi :)

To find your balance after you withdraw $50, simply take your balance, and subtract $50

balance-withdraw=balance

Hope this helps,

Jeron

The correct statement that explains why △ABC is congruent to △A′B′C′ is; B: You can map ABC to A'B'C' by translating it 6 units left and reflecting it across the x-axis, which is a series of rigid motions.

In △ABC, the coordinates are:

A(1, -3)

B(5, 3)

C(4, -1).

In △A'B'C', the coordinates are:

A'(-5, 3)

B'(-1, -3)

C'(-2, 1)

Now, each point is mapped to its image as follows:

A(1, -3) → A'(-5, 3)

B(5, 3) → B'(-1, -3)

C(4, -1) → C'(-2, 1)

Comparing the x-coordinates in the pre-image and image, we notice that the image has an x-coordinate that is 6 less than that of the pre-image:

1-6 = -5

5-6 = -1

4-6 = -2

This means that the figure must be translated 6 units left; that is the only way to have this change on the pre-image to form the image.

Comparing the y-coordinates of the pre-image with those of the image, we notice that they are negated:

-(-3) = 3

-(3) = -3

-(-1) = 1

This means the pre-image was reflected across the x-axis; this is the only way to negate the y-coordinate and not change the x-coordinate.

These are rigid transformations because the shape or size remains the same.

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Answer:

25,200

Step-by-step explanation:

Increase in population per year =8%=((100+8)*10,000)/100=10,800. So,there will be an increment of 800 people to the population every year. =>after twenty years,the total population=10,000+19*(800)=25,200.

Answer:

10800

Step-by-step explanation:

10000+8%=10800

hope this helps:)

Answer:

959.72

Step-by-step explanation:

you have to simplify

Step-by-step explanation:

=1000-864%2-336%3-648%2

=1000-17.28-10.08-12.96

=-11123.36

Answer

1) 58    2) 57   3) 65   4) 65   5) 58   6) 57   7) 58   8) 122   9) 65   10) 115 11) 122   12) 58

Step-by-step explanation:

\(\huge\text{Hey there!}\)

\(\large\boxed{\mathsf{13 - 2x^1 = 9}}\\\\\large\boxed{\mathsf{\rightarrow 13 - 2x = 9}}\\\\\large\boxed{\rightarrow \mathsf{-2x + 13 = 9}}\\\\\large\boxed{\textbf{SUBTRACT 13 to BOTH SIDES}}\\\\\large\boxed{\mathsf{-2x + 13 - 13 = 9 - 13}}\\\\\large\boxed{\textbf{CANCEL out: 13 - 13 because it gives you 0}}\\\large\boxed{\textbf{KEEP: 9 - 13 because it help solve for the x-value}}\\\\\large\boxed{\textbf{NEW EQUATION: -2x = 9 - 13}}\\\large\boxed{\textbf{SIMPLIFY IT!}}\\\\\large\boxed{\mathsf{-2x = -4}}\)

\(\large\boxed{\textbf{DIVIDE -2 to BOTH SDES}}\\\\\large\boxed{\mathsf{\dfrac{-2x}{-2} = \dfrac{-4}{-2}}}\\\\\large\boxed{\textbf{CANCEL out: } \mathbf{\dfrac{-2}{-2}} \textbf{ because it gives you 1}}\\\\\large\boxed{\textbf{KEEP: } \bf \dfrac{-4}{-2} \textbf{ because it gives you the value of x}}\\\\\large\boxed{\textbf{NEW EQUATION: } \mathbf{x= \dfrac{-4}{-2}}}\\\\\boxed{\large\textsf{SIMPLIFY IT!}}\\\\\large\boxed{\textbf{x = 2}}\)

\(\huge\text{Therefore, your answer is: \boxed{\mathsf{x = 2}}}\huge\checkmark\)

\(\large\textbf{Good luck on your assignment \& enjoy your day!}\\\\\frak{Amphitrite1040:)}\)

Answer:

Angle 6 = 70

Step-by-step explanation: Using vertical angles if you look across from angle 6 you would see the angle of 70 degrees which means they are equal because they're across from each other.

The test statistic (37.96) is greater than the critical value (11.345), we can reject the null hypothesis and conclude that there is a significant relationship between admission date and birthday.

The test statistic for this test is calculated by summing the squared differences between the observed and expected frequencies in each category, divided by the expected frequency in that category. This formula is:

X² = ∑(observed - expected)² / expected

The degrees of freedom for this test are equal to the number of categories minus one (4-1=3). Using a significance level of 0.01, the critical value for this test is 11.345.

To calculate the test statistic for this sample, we first need to calculate the expected frequencies. Each category should have an expected frequency of 196/4 = 49.

Category 1: expected frequency = 49, observed frequency = 12

Category 2: expected frequency = 49, observed frequency = 22

Category 3: expected frequency = 49, observed frequency = 65

Category 4: expected frequency = 49, observed frequency = 97

Using the formula above, we can calculate the test statistic:

X² = [(12-49)²/49] + [(22-49)²/49] + [(65-49)²/49] + [(97-49)²/49]

X² = 37.96

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Complete Question:

An article focuses on the existence of any relationship between the date of patient admission for treatment of alcoholism and the patient's birthday. Assuming a 365-day year (i.e., excluding leap year), in the absence of any relation, a patient's admission date is equally likely to be any one of the 365 possible days. The investigators established four different admission categories: (1) within 7 days of birthday, (2) between 8 and 30 days, inclusive, from the birthday, (3) between 31 and 90 days, inclusive, from the birthday, and (4) more than 90 days from the birthday. A sample of 196patients gave observed frequencies of 12, 22, 65, and 97 for categories 1, 2, 3, and 4, respectively. State and test the relevant hypotheses using a significance level of 0.01. Calculate the test statistic.

Answer:

A = 1/2bh

Step-by-step explanation:

The formula for an area of a triangle is always going to be one-half of the base times the height.

Every three candy bars cost a dollar.

Divide 25 by three.  

$8.33

Answer:

\(x = 20^{\circ}\)

\(\angle A = 150^{\circ}\)

Step-by-step explanation:

Given

\(\angle A = 8x - 10\)

\(\angle B = 3x + 90\)

See attachment

From the attachment A and B are vertically opposite.

This implies that:

\(\angle A = \angle B\)

Substitute values for A and B

\(8x - 10 = 3x + 90\)

Collect Like Terms

\(8x - 3x = 10 + 90\)

\(5x = 100\)

Solve for x

\(x = \frac{100}{5}\)

\(x = 20^{\circ}\)

Substitute 20 for x in \(\angle A = 8x - 10\)

\(\angle A = 8 * 20 - 10\)

\(\angle A = 150^{\circ}\)

At the height of the swing forth, the swing seat would be at a maximum height of 2 + (6 * (1 - cos(pi/4))) = 4 feet above the ground.

Cosine is a trigonometric function that relates the length of the adjacent side of a right triangle to the length of the opposite side to the hypotenuse. It is represented by "cos" and its formula is cos(x) = adjacent / hypotenuse. It is commonly used in mathematics, physics, and engineering to solve problems related to angles and vectors.

Cosine is a fundamental trigonometric function that is used in many areas of mathematics, physics, and engineering. The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse in a right-angled triangle. It can also be defined as the dot product of the unit vector pointing in the direction of the angle and the unit vector pointing in the direction of the adjacent side. Cosine is periodic with a period of 2π and is always between -1 and 1, inclusive. It has many important properties and relationships with other trigonometric functions such as sine, tangent, and cotangent.

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The size of a matrix is typically described using the number of rows and columns, such as a 3x4 matrix, where there are 3 rows and 4 columns.

Matrices are commonly used in mathematics, engineering, physics, and computer science to represent data, perform calculations, and solve problems. The size of a matrix is an important factor in determining its properties and the operations that can be performed on it.

For instance, if T refers to a transformation matrix used in computer graphics, it could be a 4x4 matrix that describes the translation, rotation, and scaling of a 3D object in space. If T refers to a transition matrix used in Markov chains, it could be a square matrix with dimensions equal to the number of states in the chain.

In summary, the size of a matrix T depends on the context in which it is used, and without additional information, it is not possible to determine its dimensions or properties.

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Answer:

14.5 ≥ g(1.5)

g = The number of trips to the grocery store.

You will have 11.5 gallons left.

The two pairs of integers that satisfy the given conditions are (-3, 8) and (5, 24).

To solve the system of equations, let's assign variables to the two integers. Let the first integer be represented by 'x' and the second integer by 'y'.

According to the given information:

a. Fourteen more than twice the first integer gives the second integer:

This can be expressed as: 2x + 14 = y

b. The second integer increased by one is the square of the first integer:

This can be expressed as: y + 1 = x^2

Now, we have a system of equations:

1) 2x + 14 = y

2) y + 1 = x^2

To solve this system, we can substitute the value of 'y' from equation 1) into equation 2):

2x + 14 + 1 = x^2

2x + 15 = x^2

Rearranging the equation, we have:

\(x^2 - 2x - 15 = 0\)

Factoring the quadratic equation, we get:

(x - 5)(x + 3) = 0

Setting each factor equal to zero:

x - 5 = 0   -->   x = 5

x + 3 = 0   -->   x = -3

Substituting the values of 'x' back into equation 1), we can find the corresponding values of 'y':

For x = 5:

2(5) + 14 = y

10 + 14 = y

y = 24

For x = -3:

2(-3) + 14 = y

-6 + 14 = y

y = 8

Therefore, the two pairs of integers that satisfy the given conditions are (-3, 8) and (5, 24).

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The total amount that Mikaela spent on the paddleboard is $299.87. which is the correct answer would be option (D)

The percentage is defined as a ratio expressed as a fraction of 100.

We have been given that Mikaela purchased a paddleboard originally priced at $699. If all merchandise was on sale for 40% off and the state tax rate is 7.25%.

Here,

Original cost = $699

Discount = 40% = 0.40

State tax rate = 7.25% = 0.0725

Total amount = Original cost × (1 - Discount) × (1 + State tax)

Total amount = 699×(1 - 40%)×(1 + 7.25%)

Total amount = 699×(1 - 0.40)×(1 + 0.0725)

Total amount = 299.87

Thus, the total amount that Mikaela spent on the paddleboard is $299.87.

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Answer:

Its A.

Step-by-step explanation:

If you take 40 percent off 699 and then add 7.25 sale tax to it it comes to 449.81

The length of each side of the wood is 5 centimetres.

Doug has 8 square pieces of wood. Each piece of wood have a side length of s cm. The total area of all 8 pieces of wood is 200 cm².

Hence, using quadratic equation let's find the length of each side of the wood.

Therefore,

8s² = 200

Hence,

8s² = 200

divide both sides of the equation by 8

s² = 200 / 8

s² = 25

s = √25

s = 5 centimetres

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The equation of the line perpendicular to y=1/2x-1 and passing through the point (5,6) is y = -2x + 16.

To find the equation of the line perpendicular to y=1/2x-1, we need to determine its slope. We can recall that the slope of a line in slope-intercept form, y = mx + b, is given by m, the coefficient of x. So in the given equation y=1/2x-1, the slope is 1/2.

The slope of a line perpendicular to this line will be the negative reciprocal of the slope, which means it will be -2. To see why this is true, remember that the product of the slopes of two perpendicular lines is always -1. So if the slope of the original line is m, the slope of the perpendicular line will be -1/m.

Now that we know the slope of the perpendicular line is -2, we can use the point-slope form of the equation of a line to find its equation. The point-slope form is:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line.

We are given a point on the perpendicular line, (5, 6), so we can substitute that into the equation and also substitute in the slope, -2:

y - 6 = -2(x - 5)

y - 6 = -2x + 10

y = -2x + 16

Hence, the equation of the line perpendicular to y=1/2x-1 and passing through the point (5,6) is y = -2x + 16.

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Answer:

a

\(A_w  =  1.667  \ hour \)

b

 \(b  =  0.667 \  hour  \)

Step-by-step explanation:

From the question we are told that

   The mean number of ticket per hour is  \(\mu  =  12 \  tickets\)

   The  mean number of customers arrive to purchase tickets each hour is \(\lambda  =  8 \  customers\)

    Generally the average time the ticket buyer must wait is mathematically represented as

      \(A_w  =  \frac{\lambda }{ \mu [\mu -\lambda]}\)

=>    \(A_w  =  \frac{8 }{ 12 [12-8]}\)

=>     \(A_w  =  1.667  \ hour \)

Generally the portion of time is the ticket seller busy is mathematically represented as

     \(b  =  \frac{\lambda}{ \mu}\)

=>    \(b  =  \frac{8}{ 12} \)

=>    \(b  =  0.667 \  hour  \)

Answer: c = 7.25r + 9.50

Step-by-step explanation:

The total cost depends on how much Cooper goes golfing. That variable, something that can change over the course of time, is r. 7.25 times the amount of rounds, r, is how much he'll be paying without the admission ticket.

The 9.50 is an unchanging amount, because he has to pay to get in. That amount is added to the end result. So:

c = 7.25r + 9.50

Answer:

S = 2π(3^2) + 2π(3)(8.2) = 67.2π = 211 cm^3

Answer:

Increasing at a very fast rate.

Answer:

Option D is correct

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It seems that the traffic conditions at this particular intersection can be unpredictable and potentially hazardous, which is why a traffic officer is called in when necessary.  The hourly traffic pattern between 12:00 p.m. and 10:00 p.m. is random.

Based on the information provided, it appears that at a particular traffic signal in New York, if more than 17 cars are held up at the intersection, a traffic officer will intervene and direct the traffic.

The hourly traffic pattern between 12:00 p.m. and 10:00 p.m. is random, generated between 5 and 25, with no external factors affecting it.

Specifically, between 5:00 p.m. and 6:00 p.m., the letters B, D, and F are associated with the random numbers generated, while the letters A, C, and E are not mentioned. It is unclear what these letters represent, but it is possible that they are used to categorize or track different aspects of the traffic flow, such as different lanes or directions.

It is important for drivers to exercise caution and follow any  given by the officer to ensure the safety of themselves and others on the road.

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Answer:

12-4r

Step-by-step explanation:

4r<12 because r<3 so you flip it.

Answer: 4 pieces

Step-by-step explanation: you just have to divided 5.2 to 1.3 and you will get 4 pieces :).