Twice a number is 42 less then five times a number. What is the number? Define a variable, write an equation, and then solve.

The solution of the system of linear equations, is (1.167, 3.667).

Given that the system of linear equations, y = -2x+6 and y = 4x - 1, we need to find the solution for the same,

y = -2x+6............(i)

y = 4x - 1.......(ii)

Equating the equations since the LHS is same,

-2x+6 = 4x-1

6x = 7

x = 1.167

Put x = 1.16 to find the value of y,

y = 4(1.16)-1

y = 4.66-1

y = 3.667

Therefore, the solution of the system of linear equations, is (1.167, 3.667).

You can also find the solution using the graphical method,

Plot the equations in the graph, the point of the intersection of both the lines will be the solution of the system of linear equations, [attached]

Hence, the solution of the system of linear equations, is (1.167, 3.667).

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Let's review the information provided to us to answer the question correctly:

In 1 batch of muffins , there is 2/3 cup of raisins

Ina made 2 1/2 batches of muffins

Solution:

1. We will convert fractions and mixed numbers to decimals

2/3 = 0.66

2 1/2 = 2.5

2. We will use Direct Rule of Three to answer the question, as follows:

Batches Cup of Raisins

1 0.66

2.5 x

3. We solve for x, this way:

1 * x = 0.66 / 2.5

x = 0.66 * 2.5

x = 1.66

4. We convert the decimal to mixed number

1.66 = 1 + 2/3

1.66 = 1 2/3

Answer: Ina used 1 2/3 cups of raisins to make 2 1/2 batches of muffins

As we can see, apparently 1 2/3 cups is not a choice as an answer. However, we can notice that option A is equivalent.

If we simplify 1 4/6, dividing by 2 the fraction, we will get 1 2/3.

Therefore, answer A is the correct because 1 2/3 abd 1 4/6 are equivalents

Answer:

97.60% of the variation in receipt per theater can be explained by the variation in Twitter activity

Step-by-step explanation:

The coefficient of determination can be computed from the data

Movie                Twitter Activity Receipts

The Devil Inside            219509 14763

The Dictator                        6405 5796

Paranormal Activity 3        165128 15829

The Hunger Games         579288 36871

Bridesmaids                        6564 8995

Red Tails                         11104 7477

Act of Valor                         9152 8054

Here twitter activity be the independent variable and Receipts be the response variable.

Using MS Excel for regression analysis

DATA>DATA ANALYSIS>REGRESSION

Selecting twitter activity as X variable and Receipts as Y variable. We get the following output

SUMMARY OUTPUT                

Regression Statistics        

Multiple R                0.987916601        

R Square                 0.97597921        

Adjusted R Square 0.971175052        

Standard Error         35967.08167        

Observations             7        

ANOVA        

                df SS                    MS              F                 Significance F  

Regression  1  2.62805E+11 2.62805E+11 203.1530224 3.06274E-05  

Residual         5 6468154818 1293630964      

Total       6 2.69273E+11      

            Coefficients Standard Error   t Stat       P-value

Intercept   -128751.8007 23384.79926  -5.505790293 0.002702573

Receipts     19.41414946 1.362092886  14.25317587        3.06274E-05

We can see that R Square=0.97597921, So the 97.6% of variation in Receipts is explained by its linear relationship with twitter activity or we can say that 97.60% of the variation in receipt per theater can be explained by the variation in Twitter activity.

Answer:

$4618.44

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

\(\\ \sf\longmapsto \dfrac{7}{8}\:of\:x=14\)

\(\\ \sf\longmapsto \dfrac{7x}{8}=14\)

\(\\ \sf\longmapsto 7x=14(8)=112\)

\(\\ \sf\longmapsto x=\dfrac{112}{7}\)

\(\\ \sf\longmapsto x=16\)

\(\pink{ \boxed{\boxed{\begin{array}{cc} \maltese  \bf \: \: given \\ \sf \: speed \: \: v = 500 \: m {s}^{ - 1} \\ \\ \sf \: frequency \: \: f = 5 \: Hz \\ \\ \sf \: wavelenght \: \: \: \lambda \: = \: to \: find \\ \\ \bf \: we \: know \: that \\ \\ \sf \: v = f \lambda \\ \bf \implies \: \lambda = \frac{v}{f} \\ = \frac{500}{5} \\ = 100 \: m \\ \\ \therefore \sf \lambda \: = 100 \: m\end{array}}}}\)

N × (-5/6) ≥ -1/2 is the inequality for the statement

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g 5 < 6, x ≥ 2, etc.

Given the statement: negative one half is a minimum of the product of a number and negative five sixths.

This statement can also be written as the product of a number and negative five sixths is greater than or equal to negative one half

Let N represent the number. Thus, the inequality of the statement is:

N × (-5/6) ≥ -1/2    

Note: The symbol ≥ is pronounced as greater than or equal to

Therefore, the inequality for the statement is N × (-5/6) ≥ -1/2

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Answer:

the answer I got is 8...........

\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

value of x = 8

9514 1404 393

Answer:

  (c) 5y - x = -20

Step-by-step explanation:

When the x- and y-terms are on the same side of the equation, the slope of the line will be ...

  m = -(coefficient of x)/(coefficient of y)

So, the slopes of the offered choices are ...

  a) -5/1 = -5

  b) -1/5

 c) -(-1)/5 = 1/5 . . . . . parallel to given line

  d) -5/-1 = 5

The lines will be parallel when their slopes are the same. The slope of the given line is the coefficient of x, 1/5. Choice C has the same slope.

Answer:

A. 35 ft.

B. 35 ft

Step-by-step explanation:

Please see attached photo for diagram.

A. Determination of the diagonal using pythagorean theorem.

A square has all sides equal. Thus, the diagonal of the square can be obtained as follow:

Ist leg (L₁) = 25 ft

2nd leg (L₂) = 25 ft

Diagonal (d) =?

d² = L₁² + L₂²

d² = 25² + 25²

d² = 625 + 625

d² = 1250

Take the square root of both side

d = √1250

d = 35 ft

B. Determination of the diagonal using trigonometry.

Since all the sides in a square are equal, the angle between each leg will be 90°. Thus, the diagonal will bisect the angle between the two leg equally i.e

Angle between Diagonal and each leg = 90/2 = 45°

Finally, we shall determine the length of the diagonal. This can be obtained as follow:

Angle θ = 45°

Opposite = 25 ft

Hypothenus = d

Sine θ = Opposite / Hypothenus

Sine 45 = 25 / d

0.7071 = 25 / d

Cross multiply

0.7071 × d = 25

Divide both side by 0.7071

d = 25 / 0.7071

d = 35 ft

The correlation coefficient between X and Y is Corr(X, Y) = 0.

To calculate the marginal distribution of X and Y, we need to integrate the joint probability density function (PDF) over the appropriate ranges.

a. Marginal distribution of X:

To find the marginal distribution of X, we integrate the joint PDF over the range of Y:

∫[0, 1] J(x, y) dy

Since the joint PDF is defined as J(x, y) = 1 for 0 ≤ y ≤ x ≤ 1 and J(x, y) = 0 otherwise, the integral becomes:

∫[0, x] 1 dy = x, for 0 ≤ x ≤ 1

So, the marginal distribution of X is simply X(x) = x for 0 ≤ x ≤ 1.

b. Expectation of X:

The expectation (mean) of X can be calculated as the integral of x times the marginal PDF of X:

\(E(X) = ∫[0, 1] x * X(x) dx = ∫[0, 1] x^2 dx = [x^3/3] from 0 to 1 = 1/3\)

Therefore, the expectation of X is E(X) = 1/3.

c. Variance of X:

The variance of X can be calculated using the formula:

\(Var(X) = E(X^2) - (E(X))^2E(X^2) = ∫[0, 1] x^2 * X(x) dx = ∫[0, 1] x^3 dx = [x^4/4] from 0 to 1 = 1/4Var(X) = 1/4 - (1/3)^2 = 1/4 - 1/9 = 5/36\)

Therefore, the variance of X is Var(X) = 5/36.

d. Covariance of X and Y:

The covariance of X and Y can be calculated as:

Cov(X, Y) = E(XY) - E(X)E(Y)

Since the joint PDF J(x, y) = 1 for 0 ≤ y ≤ x ≤ 1, the integral becomes:

\(E(XY) = ∫[0, 1] ∫[0, x] xy dy dx = ∫[0, 1] [(x^2)/2] dx = [(x^3)/6] from 0 to 1 = 1/6\)

\(E(X) = 1/3 (from part b)E(Y) = ∫[0, 1] ∫[0, x] y J(x, y) dy dx = ∫[0, 1] [(x^2)/2] dx = [(x^3)/6] from 0 to 1 = 1/6\)

Cov(X, Y) = 1/6 - (1/3)(1/6) = 0

Therefore, the covariance of X and Y is Cov(X, Y) = 0.

e. Correlation coefficient between X and Y:

The correlation coefficient can be calculated using the formula:

Corr(X, Y) = Cov(X, Y) / √(Var(X) * Var(Y))

Since the covariance of X and Y is 0, the correlation coefficient will also be 0.

Therefore, the correlation coefficient between X and Y is Corr(X, Y) = 0.

f. Conclusion based on the correlation coefficient:

The correlation coefficient of 0 indicates that there is no linear relationship between X and Y. In this case, the fraction of male runners (X) and the

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Answer:

Step-by-step explanation:

The y intercept occurs when x = 0

What you are left with is 24.

24 is the number of photos she started with. She started with 24 photos before she added any in any of the weeks that followed.

Answer: x2 + 4x + 16

Step-by-step explanation:

Answer:

We are given the following variables:

p = probability of success / probability to shoot a free throw shot = 0.74

q = probability of failure = 1 – p = 0.26

n = number of samples / number of free throws = 8

We can solve for the average free throws he or she can make in the game using the formula:

average = n * p

average = 8 * 0.74

average = 5.92

round off:

average = 6 free throw shots

We can solve for the variance using the formula:

variance = n * p * q

variance = 8 * 0.74 * 0.26

variance = 1.5392

round off:

variance = 1.54 free throw shots

Step-by-step explanation:

A triangle with two equal sides as the following one:

is called isosceles.

Answer: isosceles.

7 decreased by n is equivalent to 7 - n

22 people

333 chocolate bars

the amount of chocolate each person get.

\( \frac{333}{22} \)

\( = 15.1363636364\)

\( = 15.14\)

\( = \frac{15.14}{1} \)

\( \frac{15.14}{1} \times \frac{100}{100} \)

\( = \frac{1514}{100} \)

\( \frac{1514 \div 2}{100 \div 2} \)

\( = \frac{757}{50} \)

\( = 15 \frac{7}{50} \)

Answer:

\(15\frac{7}{50}\)

Step-by-step explanation:

Given that:

22 people share 333 chocolate bars equally. Each chocolate bar is the same size.

To Find:

About how much chocolate does each person get?

Solve:

Since, it given us that 22 people share 333 chocolate bars equally and how much chocolate does each person gets. Therefore we have to divide the chocolate bars by the number of people.

 \(22\overline{|\smallspace333}\:\:\:\:\:\:\)

\(\begin{matrix}\:\:\:\:\:\:\:\:\emptyspace1\emptyspace5.13636\:\:\:\:\:\:\:\:\:\:\:\\ 22\overline{|\smallspace333.0}\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\underline{\emptyspace2\emptyspace2}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\emptyspace1\emptyspace1\emptyspace3\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\underline{\emptyspace1\emptyspace1\emptyspace0}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\emptyspace3\emptyspace0\:\:\:\:\:\:\:\:\:\:\end{matrix}\)

       \(\underline{\emptyspace2\emptyspace2}\\80\\\underline{\emptyspace6\emptyspace6}\\140\\\underline{\emptyspace13\emptyspace2}\\8\)

Rounding to nearest tenth: 15.14

Now put 15.14 over 1

\(\frac{15.14}{1}\)

Multiply both by 100

\(\frac{15.14}{1}\times\frac{100}{100}\)

\(=\frac{1514}{100}\)

\(=\frac{1514\div2}{100\div2}\)

\(=\frac{757}{50}\)

Turning into mixed number:

\(15\frac{7}{50}\)

Thus, each person get about \(15\frac{7}{50}\) chocolate

Kavinsky

Answer:

62.8 inches

.Step-by-step explanation:

The wire consists of 14 semicircle + 4 3/4 circles. The diameter of each circle = 8 / 4 = 2 inches.Length of a semicircle = 1/2 * pi * diameter and of a 3/4 circle it is 3/4 * pi * diameter.So the perimeter of the wire= 14 * 1/2 * 3.14 * 2 + 4 * 3/4 * 3.14 * 2= 14 * 3.14 + 4 * 3/2 * 3.14= 62.8  inches.

Answer:

62.8 inches

Step-by-step explanation:

= 14 * 1/2 * 3.14 * 2 + 4 * 3/4 * 3.14 * 2

= 14 * 3.14 + 4 * 3/2 * 3.14

= 62.8  inches.

Answer:

Following are the solution to these question:

Step-by-step explanation:

The frequency of the data value will be the same in dot plots for the number of dots. The frequency table is following:

\(X \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Frequency \\\\1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1\\\\2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0\\\\3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0\\\\4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2\\\\5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1\\\\6\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1\\\\7\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0\\\\8\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3\\\\9\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1\\\\10\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3\\\\11\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1\\\\\)

\(12\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0\\\\13\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2\\\\14\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1\\\\\)

Using scientific notation, it i found that the result of the expression is given as follows:

C. 974,000.

A number in scientific notation is given by:

\(a \times 10^b\)

With the base being \(a \in [1, 10)\).

In this problem, to solve the sum, we have to place the numbers in the same base, hence:

\(7.4 \times 10^4 + 9 \times 10^5 = 0.74 \times 10^5 + 9 \times 10^5 = 9.74 \times 10^5 = 974000\)

Hence option C is correct.

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As x tends to negative one from the left, the value of f(x) tends to positive infinity. As x → -1⁻, f(x) → ∞.

In Mathematics and Geometry, the vertical asymptote of a function simply refers to the value of x (x-value) which makes its denominator equal to zero (0).

By critically observing the graph of this rational function f(x) shown below, we can logically deduce that its vertical asymptote is at x = -1 and x = 2, and its horizontal asymptote is at y = 3.

In this context, we can logically deduce that the value of f(x) tends towards positive infinity, as x tends to negative one from the left;

As x → -1⁻, f(x) → ∞.

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If we divide 8789 by 517, we will obtain a quotient of 17.

As per the question statement, we are provided with two numbers, 8789 and 517,

And we are required to divide 8789 by 517 and determine the quotient of our division.

To solve this question, we are going to use the long division method, which is shown below.

517 | 8789 | 1             [Since [(517 * 2) = 1034], and (1034 > 878),

       517                      Thus we are multiplying 517 by 1, in the first step]

___________

517 | 3619 | 7             [Here, the difference of 878 and 517, which is 361

       3619                    with the remaining 9 of 8789 as it's unit place digit

___________            forms 3619, which is an exact multiple of 517]

         0

Hence, we divide 8789 by 517, we will obtain a quotient of 17.

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I would say A but please wait for someone else to answer to make sure it's not wrong I would hate for you to get this wrong

1 cm = 10 mm. Length of book : 28 cm. Length of book = 280 mm. This shows that measurements in mm are the same but look to have a higher number .

The conversion factor provided states that 1 cm is equal to 10 mm, which means that 1 cm is made up of 10 individual millimeters.

The length of my book in when measured in millimeters is 280 mm.

In centimeters, this is therefore:

= 280 mm / 10 cm /mm

= 28 cm

Although the numerical value appears higher when expressed in millimeters, it is important to note that the actual length of the book remains the same.

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Answer:

  (d)  P ≥ -40

Step-by-step explanation:

You want the solution to P/8 ≥ -5.

Multiply both sides of the inequality by 8.

  8(P/8) ≥ 8(-5)

  P ≥ -40

Answer:

it is correct I think it's right

Step-by-step explanation:

The base of the triangle could be 4, a side length could be 2. The other side might have the same side length as the first one, so 2 is a possible side length

2