Someone is having a wedding, and they need champagne bottles. The bottles are 25.4 oz, the glasses are 6 oz a person, and there are going to be 80 guests. How many champagne bottles are going to be needed to serve all the guests?

Using Trigonometric ratios, the value of missing angle is 60.45°.

There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

If we draw an imaginary line dividing the given triangle in 2 equal parts,

we will get 2 right angled triangles.

So, using trigonometric ratios,

Sin θ = Perpendicular / hypotenuse

⇒ Sin 70 ° = perpendicular / 14

⇒ 0.94 = perpendicular / 14

⇒ perpendicular = 0.94 × 14

⇒ perpendicular = 13.16

Now the other right angled triangle is

Sin θ = Perpendicular / hypotenuse

⇒ Sin θ = perpendicular / 15

⇒  Sin θ = 13.16 / 15

⇒ θ = sin⁻¹(13.16 / 15)

⇒ θ = sin⁻¹(0.87)

⇒ θ = 60.45

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Answer:

10%

Step-by-step explanation:

if the volume of the water increase by 10 when turns to

ice so it must be decrease by 10 if it changes to water again

the final equations are.:

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

We have the following function:

(x)  = 3x - 7

The function f translated 6 units up and 2 units rights:

6 units up:

y  = 3x - 7 + 6

2 units rigth:

y  = 3(x-2) - 7 + 6

y  = 3x - 6 - 7 + 6

Finally:

g(x)  = 3x - 7

The function f reflected about the y-axis and translated 7 units left:

reflected about the y-axis:

y = 3(-x) - 7

y = -3x - 7

translated 7 units left:

y = -3(x+7) - 7

y = -3x - 21 - 7

y = -3x -28

Finally:

g(x) = -3x - 28

The function f stretched vertically by a factor of 2 and translated up by 5 units:

stretched vertically by a factor:

y = 6x - 14

translated up by 5 units:

y = 6x - 14 + 5

y = 6x - 9

Finally:

g(x) = 6x - 9

The function f stretched vertically by a factor of 4 and translated up by 9 units:

stretched vertically by a factor of 4:

y = 12x - 28

translated up by 9 units:

y = 12x - 28 + 9

y = 12x - 19

Finally:

g(x) = 12x - 19

Thus, the final equations are.:

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An appropriate method of controlling for any confounding variables is;

The group assigned to the old drug should also drink an entire glass of water with the drug

In an experiment, there are three primary types of variables, namely;

Dependent variable

Independent variable or explanatory variable.

Confounding variable.

We know that explanatory variable seems to have some effects on the dependent variable but then confounding variable also affects the dependent variable in some way. Thus, confounding variables are having the hidden effect on the main variable.

A confounding variable is defined as an explanatory variable that was considered in a study whose effect cannot be distinguished from a second explanatory variable in the study.

Now, in this question we can say that the confounding variables could be;

-price of a daily ski pass

-temperature

-whether it has snowed recently

The method for controlling any of these is that The group assigned to the old drug should also drink an entire glass of water with the drug

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The area of the given figure is  51.63 m².

What is an Area ?

Area in geometry refers to the volume occupied by a flat shape on a plane, such as a polygon, circle, or ellipse. A shape's area is always expressed in square units.

The area of the given figure = area of given triangle + area of given rectangle + area of given semi circle.

(I) area of given triangle

  = 1/2 × base × height

  = 1/2 × 3 × 5

  = 7.5m².

(II) area of given rectangle

 = length × breadth

  = 6 × 5 = 30m².

(III) area of given semi circle

  = πr²/2

  here, r = 3 m ( 6m/2)

So, πr²/2 = (3.14 × 3² )/2

                = 28.26/2

                = 14.13 m².

Hence, The area of the given figure = 7.5 + 30 + 14.13

                                                            = 51.63 m².

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The predicted growth of job of registered nurse, food service employee, and customer service representative are 518 thousand, 282 thousand, and 422 thousand respectively.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For instance, 2x - 5 = 13.

Let us suppose the number of registered nurses = x

Let us suppose the number of food service jobs = y

Let us suppose the number of customer service jobs = z

The number of registered nurses is predicted to grow 748 thousand less than three times the number of food service jobs. This is represented as:

x = 3y - 748,000 (equation 1)

The number of customer service jobs is predicted to grow 71 thousand more than half the number of food service jobs. This is represented as:

z = (1/2) y + 71,000 (equation 2)

The total growth of these three jobs is predicted to be 1222 thousand. This is represented as:

x + y + z = 1222000 (equation 3)

Isolate the value of y in the first equation:

x = 3y - 748,000

y = (x + 748000) / 3

Substitute the value of y in the second equation:

z = (1/2) ((x + 748000) / 3) + 71,000

z = (x + 748000) / 6 + 71000

z = x/6 + 124666.66 + 71000

z = x/6 + 195666.66

Substitute the value of y and z in third equation:

x + (x + 748000) / 3 + x/6 + 195666.66 = 1222000

x + x/3 + 249333.33 + x/6 + 195666.66 = 1222000

x + x/3 +x/6 = 1222000 - 249333.33 - 195666.66

6x + 2x + x = 6 (777000.01)

9x= 4662000.06

x = 518000

Substitute the value of x in the equation of z:

z = x/6 + 195666.66

z = 518000/6 + 195666.66

z= 282000

Substitute the value of x in the equation of y:

y = (x + 748000) / 3

y = (518000 + 748000)/3

y = 422000

Hence, the predicted growth of job of registered nurse, food service employee, and customer service representative are 518 thousand, 282 thousand, and 422 thousand respectively.

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An expression which is equivalent to 5 - 2(3x + 4) is,

⇒ - 3 - 6x

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ 5 - 2 (3x + 4)

Now, We can solve the expression as;

⇒ 5 - 2 (3x + 4)

⇒ 5 - 2 × 3x - 2 × 4

⇒ 5 - 6x - 8

⇒ - 3 - 6x

Thus, The equivalent expression is,

⇒ - 3 - 6x

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y = c * 5e^t / ln(t) is the general solution to 1/ln(t)(5e^t c) .We can simplify this expression by applying the chain rule of differentiation. The chain rule states that if y = f(u) and u = g(x), then

dy/dx = dy/du * du/dx.  

The given expression is 1/ln(t)(5e^t c) .

In this case, we can let y = 5e^t c and u = ln(t).

Taking the derivative with respect to t, we get:

dy/dt = 5e^t c * (du/dt) / u

Since u = ln(t), we can use the chain rule again to find du/dt:

du/dt = 1/t

Plugging this back into the original expression, we get:

dy/dt = 5e^t c * (1/t) / ln(t)

Now we can factor out the constant c, which is an arbitrary constant of integration, giving us the final answer:

y = c * 5e^t / ln(t)

So the final answer is: y = c * 5e^t / ln(t)

It's important to note that this is only the general solution of the function, if we have an initial condition then we can find the specific solution for the function

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The average rate of change of a t over the interval 0 30 t is 0.03 pounds per day.

To find the average rate of change, we need to calculate the slope of the line representing the function a t( ) over the interval 0 to 30.

The slope is calculated by taking the change in a t over the change in t.

We can calculate the change in a t by subtracting the a t value at the start of the interval (0) from the a t value at the end of the interval (30):

a t (30) - a t (0) = 6.687 - 0 = 6.687

We can calculate the change in t by subtracting the t value at the start of the interval (0) from the t value at the end of the interval (30):

t (30) - t (0) = 30 - 0 = 30

We can now calculate the slope by dividing the change in a t by the change in t:

Slope = 6.687 / 30 = 0.03

The average rate of change of a t over the interval 0 30 t is 0.03 pounds per day.

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Y-intercept is the point on the graph where the line crosses y-axis.

Slope of a line is the proportion of difference of y-coordinates to difference of x- coordinates.

What is a line?

A line is an object which has only one dimension i.e. it has only length and not width. A line is made up of several points that are endlessly stretched in the opposing directions.

Y-Intercept

It is a point on the graph where the line crosses y-axis. We know that any point on y-axis has its x-coordinate as 0. Therefore, for y-intercept, its x-coordinate is 0.

Slope

It is the proportion of difference of y-coordinates to difference of x- coordinates. The symbol 'm' denotes the slope.

[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

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Question: Y-Intercept=

Slope=

Answer:

41 mg magnesium

42 mg calcium

Step-by-step explanation:

87% of magnesium; 48 mg of magnesium

44% of calcium; 96 mg of calcium

87% × 48 mg magnesium = 0.87 × 48 mg magnesium = 41 mg magnesium

44% × 96 mg calcium = 0.44 × 96 mg calcium = 42 mg calcium

The probability that the customer paid with a credit card is 25% and the customer bought premium gas given that she or he paid with a credit card is 16.8%.

What is the probability?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

To find the probability that the customer paid with a credit card, we can use the law of total probability.

P(credit card) = P(credit card | regular gas) * P(regular gas) + P(credit card | midgrade gas) * P(midgrade gas) + P(credit card | premium gas) * P(premium gas)

P(credit card) = 0.28 * 0.88 + 0.34 * 0.02 + 0.42 * 0.1 = 0.25

So, the probability that the customer paid with a credit card is 25%.

Given that the customer paid with a credit card, we can find the probability that she or he bought premium gas using Bayes' theorem:

P(premium gas | credit card) = P(credit card | premium gas) * P(premium gas) / P(credit card)

P(premium gas | credit card) = 0.42 * 0.1 / 0.25 = 0.168 or 16.8%

So, the probability that the customer bought premium gas given that she or he paid with a credit card is 16.8%.

Hence, the probability that the customer paid with a credit card is 25% and the customer bought premium gas given that she or he paid with a credit card is 16.8%.

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Answer:

110 cm^2 & 39 cm^3

Step-by-step explanation:

Volume = Length x Width x Height. With that in mind, volume is 39 cm^3

Surface Area = Area of all the shapes

2(13 x 1) + 2(13 x 3) + 2(3 x 1) =110 cm^

The statements that are listed above that are not propositions include the following:

A proposition statement is defined as the statement that is either a true statement or false statement but can not be both.

From the given statements,the statement that is a true proposition include the following:

The statement that is a false proposition include the following:

The statement will you be my valentine? is not a proposition but a declarative question that needs to be answered.

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The new function that takes that longer doubling time into account with starting quantity will be Aₙ = A₁ (1)ⁿ.

Consider the function:

y = a (1 ± r)ˣ

Where x is the number of times this growth occurs, a = initial amount, and r = fraction by which this growth occurs.

As per Moore's Regulation, the multiplying time for the number of semiconductors that can be placed on a microprocessor is roughly two years. That's what ongoing information proposes, starting around 2013, the pace of development anticipated by Moore's Regulation does not hold anymore.

The rate is 0%, then the equation is given as,

Aₙ = A₁ (1 + 0)ⁿ

Aₙ = A₁ (1)ⁿ

The new function that takes that longer doubling time into account with starting quantity will be Aₙ = A₁ (1)ⁿ.

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According to the information provided, it should be noted that the 750 seniors in her school make up the population of interest, and the parameter of interest is the percentage of seniors who intend to attend the prom.

Given,

Additionally, a strictly random sample is required in order to create a confidence interval. Additionally, the sample size should be examined to see if it adequately represents the population.

Using the z critical of 1.645, a 90% confidence interval will be built. The sample proportion in this case will be:

= 36/50 = 0.72

Q = 1 - 0.72 = 0.28

n = 50

As a result, the standard error will be equal to 50 squared times the multiplication of 0.72 and 0.28. This amounts to 0.0635.

For a big sample randomly selected among 750 seniors, the interval on the context suggests that we are 90% confident that the fraction of those who desire to attend the prom falls within the interval.

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Using circumcenter the value of x is 11.

What is circumcenter of triangle?

The center of a triangle's circumcircle is known as the circumcenter. It is located at the point where the perpendicular bisectors intersect. Let the circumcenter of ABC be O (x, y). Then, because there are no differences in the distances from the vertices to O, we have AO = BO = CO = Circumradius.

Here the given is PC=3x+7 , RC = 5x-15 and QC = 51-x

Now according to the circumcenter the distance of the vertices are same . Then,

=> PC = RC

=> 3x+7 = 5x-15

=> 5x-3x =15+7

=> 2x = 22

=> x = 11.

Hence the value of x is 11.

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Answer:2x3x4

Step-by-step explanation:

The volume of the segment formed when a sphere of radius r is cut by a plane is equal to (πh2(3r-h))/3. This can be found by using the formula for the volume of a spherical segment, where h is the height of the segment and r is the radius of the sphere.

Step 1: Calculate the volume of a sphere using the formula V = (4/3)πr3

Step 2: Calculate the volume of a cone using the formula V = (1/3)πr2h

Step 3: Calculate the difference between the two volumes to find the volume of the segment.

Step 4: The volume of the segment is (πh2(3r-h))/3.

To calculate the volume of the segment formed when a sphere of radius r is cut by a plane, we use the formula for the volume of a spherical segment. First, we calculate the volume of the sphere using the formula V = (4/3)πr3, then the volume of the cone using the formula V = (1/3)πr2h. By subtracting the two volumes, we find the volume of the segment, which is (πh2(3r-h))/3. This formula is useful in finding the volume of any segment formed when a sphere is cut by a plane.

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The ratio of the stated that became law would be represented as = 75%

Percentage is defined as the representation of a part of a data as per 100.

The part of states that needs to be ratified = 3/4

To represent this portion in percentage, × by 100

That is,

= 3/4× 100

= 300/4

= 75%

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The total number of seats in the auditorium is 3500.

What is the arithmetic series?

An arithmetic series is a sequence of numbers in which the difference between any two consecutive terms is always the same. It can also be defined as a sum of a finite number of terms of an arithmetic progression.

The seating capacity of the auditorium can be found by using the formula for the sum of an arithmetic series.

The formula for the sum of an arithmetic series is:

S = n/2 (2a + (n-1)d)

Where:

S is the sum of the series (total number of seats)

n is the number of terms in the series (number of rows of seats)

a is the first term in the series (number of seats in the first row)

d is the common difference between terms in the series (increase in number of seats per row)

In this case,

a = 20 (number of seats in the first row)

d = 25 - 20 = 5 (increase in number of seats per row)

n = 35 (number of rows of seats)

So,

S = 35/2 (2(20) + (35-1)(5))

S = 35/2 (40 + 160)

S = 35/2 (200)

S = 35*100

S = 3500

Hence, the total number of seats in the auditorium is 3500.

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The length of the air strip is 451feet

Perimeter is the sum of length of the sides used to made the given figure. A regular figure with n-sides has n equal sides in it, and they are the only parts of it(that means, nothing more than those equal lengthed n sides).

Given;

Perimeter= 8876feet

Let the length be x

and the width be y

Then, length will be x= 10+35y

Perimeter of rectangle= 2l+2b

8876=2(10+35y)+y

8876=20+700y+y

y=12.6

x=10+35y

x=451

Therefore, the length by the given perimeter will be 451feet

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Efficiency.Compared to solar panels' efficiency range of 18% to 22%, wind turbines typically capture 60% of the energy that flows through them.

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180° anticlockwise rotation will turn the rectangle into one that is NOT consistent with the original rectangle.

The correct option is B.

Two figures are referred to as congruent if their size and shape are the same. For instance, because they are the same size and shape, the rectangles ABCD and PQRS are congruent rectangles.

Identical shapes are referred to as congruent shapes. The angles and sides that correspond to each other are the same. To accomplish this, we must examine each shape's sides and angles. Two congruent shapes will perfectly fit on top of each other.

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I understand that the question you are looking for is:

A rectangle is graphed on a coordinate grid. Which transformation will result in a rectangle that is NOT congruent to the original rectangle?

A.  A dilation by a scale factor of

B.  rotation of 180° counterclockwise

C. translation 90°  units to the right

D. reflection across the x-axis

answer : A rotation of 180 digress counterclockwise

The volume of the given cylinder is 11304 cm³.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Given that, radius of a cylinder is 20 cm and depth of a cylinder is 9 cm.

We know that, the volume of a cylinder is πr²h.

Now, volume = 3.14×20²×9

= 3.14×400×9

= 11304 cm³

Therefore, the volume of the given cylinder is 11304 cm³.

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Answer:

5089.4cm

Step-by-step explanation:

9² x pi x 20 =5089.3800

The regression equation is y = 15.98x + 43.76. The predicted value for the final grade when a student spends an equation of 8 hours each week on math is 87.8.

The regression equation is found by using a linear regression analysis. First, the data points are plotted on a graph. Then, the best-fit line is determined. The equation of the line is then calculated by finding the slope (m) and y-intercept (b).

The slope (m) is calculated by taking the difference between the two y-values divided by the difference between the two x-values.

m = (y2 - y1) / (x2 - x1)

The y-intercept (b) is calculated by substituting the values of m and one of the data points into the equation of a line, and solving for b.

b = y - mx

Once the values of m and b are determined, the regression equation can be determined:

y = mx + b

For this data set, the regression equation is y = 15.98x + 43.76.

To find the predicted value for the final grade when a student spends an average of 8 hours each week on math, the value of x is substituted into the equation, and the result is rounded to one decimal place.

y = 15.98(8) + 43.76

y = 87.8

Therefore, the predicted value for the final grade when a student spends an average of 8 hours each week on math is 87.8.

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To calculate the dollar amount billed to the insurance plan:

What's the math rate?

A rate is a unique ratio where the two words are expressed in several units. For instance, the price is 69 for 12 ounces if a 12-ounce can of maize costs 69. This is not a proportion of two comparable units, like shirts. Cents and ounces are the two dissimilar units in this ratio.

$340.00 (total charge for office visit) x 75% (insurance reimbursement rate) = $255.00

To calculate the amount the patient must pay:

$340.00 (total charge for office visit) x 25% (patient responsibility rate) = $85.00

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Indicate probability the students with pets (01–22) and those without (23–47).Go along the random number table, selecting digits two at a time and ignoring any repeated values, until 10 students’ numbers have been selected.

1.Indicate the students with pets (01–22) and those without (23–47).

2. Go along the random number table and select two digits at a time.

3. Check if the two digits are repeated.

4. If they are repeated, select the next two digits.

5. If they are not repeated, add them to the list of 10 students.

6. Repeat steps 2-5 until 10 students’ numbers have been selected.

The students in the science club can use a table of random digits to simulate if the sample of 10 students with only one of them having a pet is unusual. First, they need to label the students with pets 01–22 and the students without pets 23–47. Then, they can go along the random number table, selecting digits two at a time and ignoring any repeated values until 10 students’ numbers have been selected. This will help to see if the sample of 10 students is unusual or not. By doing this simulation, they can check if the sample they have is significantly different from what the expected results would be if they had a random sample of 10 students. This will help them to determine if the sample they have is unusual or not.

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The value of the expression → p(q(-1)) will be → 5.

        [tex]${\displaystyle \forall x\in X,\forall y\in Y,\forall z\in Y,\quad ((x,y)\in R\land (x,z)\in R)\implies y=z.}[/tex]

        [tex]${\displaystyle \forall x\in X,\exists y\in Y,\quad (x,y)\in R.}[/tex]

Given are the graphs of two function as shown in the image.

We have to find -

p(q(-1))

Now, we can see from the graph that -

q(-1) = -2

Then, p(q(-1)) will be -

p(-2) = 5

Therefore, the value of the expression → p(q(-1)) will be → 5.

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The correct answer is This study demonstrates clearly that seat belts save children from injury.

Given that,

According to an analysis of the 27,000 child passenger vehicle incidents in Michigan with records currently available, around 10% of children who were wearing seatbelts (group SB) and 15% of children who were not (group NSB) sustained injuries. Which of the following statements is NOT appropriate for a report summarizing this study?

Options are :

(A)Driver conduct could be a complicating variable.

(B) The location of the youngster in the vehicle could be a complicating variable.

(C) Since this study was not an experiment, drawing conclusions about causes and effects is not appropriate.

(D) This study amply demonstrates how seat belts protect kids from harm.

(E) It is dangerous to draw the conclusion that seatbelts protect kids from harm, at least until the study is independently reproduced.

So,The correct answer is This study demonstrates clearly that seat belts save children from injury.

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