tomas has $1,000 to spend on a vacation. his plane ticket costs $348.25. if he stays 5.5 days at his destination, how much can he spend each day? write an inequality and then solve.

Leo has 48 toy soldiers, since 48 is the only number between 27 and 54 that is congruent to 69 modulo 140.

We are looking for a number $x$ that satisfies the following conditions:

[tex]$\begin{align*}x &\equiv 0 \pmod{4} \x &\equiv 6 \pmod{7} \x &\equiv 3 \pmod{5}\end{align*}[/tex]

Since 4, 7, and 5 are pairwise co-prime, we can use the Chinese Remainder Theorem to solve this system of congruences.

Let [tex]$M = 4 \cdot 7 \cdot 5 = 140$[/tex], and

let [tex]$M_1 = 7 \cdot 5 = 35$[/tex], [tex]$M_2 = 4 \cdot 5 = 20$[/tex], and [tex]$M_3 = 4 \cdot 7 = 28$[/tex]. Then we need to find integers [tex]$a_1$[/tex], [tex]$a_2$[/tex], and [tex]$a_3$[/tex] such that

[tex]$a_1 M_1 \equiv 1 \pmod{4}$[/tex], [tex]$a_2 M_2 \equiv 1 \pmod{7}$[/tex], and [tex]$a_3 M_3 \equiv 1 \pmod{5}$[/tex].

We can easily verify that [tex]$a_1 = 3$[/tex], [tex]$a_2 = 5$[/tex], and [tex]$a_3 = 3$[/tex] satisfy these conditions.

Then the solution to the system of congruence is given by

[tex]$\begin{align*}x &\equiv 0 \cdot 7 \cdot 5 \cdot 3 + 6 \cdot 4 \cdot 5 \cdot 3 + 3 \cdot 4 \cdot 7 \cdot 3 \cdot 3 \pmod{140} \&\equiv 69 \pmod{140}\end{align*}[/tex]

Therefore, Leo has 48 toy soldiers, since 48 is the only number between 27 and 54 that is congruent to 69 modulo 140.

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Therefore , the solution of the given problem of equation comes out to be B has a value of -6.

Variable words are commonly used in complex algorithms to show consistency between two contradictory claims. Academic expressions called equations are used to show the equality of various academic numbers. Instead of a distinct algorithm that divides 12 into two parts and can be used to assess data received from y + 7, normalization in this case yields b + 7.

Here,

The initial line can first be expressed in slope-intercept form as follows:

=> 3x + 6y = 18

=> 6y = -3x + 18

=> y = (-1/2)x + 3

Therefore, the initial line has a slope of -1/2. The negative reciprocal, or 2, is the inclination of the line that is perpendicular to it.

Now that we know the equation of the line parallel to the initial line and passing through the point (3, 0), we can use the point-slope form of a line to determine it:

=> y - 0 = 2(x - 3)

=> y = 2x - 6

So, through position (3, 0), y = 2x – 6 is true.

Y = mx + b, where m = 2 is the slope and b = -6 is the y-intercept, is the slope-intercept version of this equation.

B therefore has a value of -6.

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The correct answer is d. Britney's subjective measure of her well-being would increase by less than 5 units.

We have, The vertical distance between points (0, a) and (0, b) is 5.

Her wealth increased from $1,050 to $1,350.Britney's subjective measure of her well-being would increase by less than 5 units. Option (d) is correct. Because the vertical distance between the points (0, a) and (0, b) is 5.

If the horizontal distance is the same as the vertical distance, then the slope is 1.

The slope of the straight line joining two points is given by;

[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Where the points are [tex](x_1,y_1), (x_2,y_2)[/tex]

Let's assume the two points are [tex](0, a) \ and \ (0, b)[/tex].

The slope of the line connecting these two points is;

[tex]\displaystyle m=\frac{b-a}{0-0}=\frac{b-a}{0}[/tex]

This is undefined as we cannot divide by 0.Hence, there is no horizontal distance, and there is no slope.

Therefore, if the vertical distance between two points is 5, and there is no horizontal distance, then she will experience less than 5 units of well-being.

Therefore, Britney's subjective measure of her well-being would increase by less than 5 units.

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Answer: The answer is A) Players on the basketball team are generally taller than players on the baseball team. This is the most likely conclusion we can draw based on the information given.

Step-by-step explanation:

We know that the interquartile range (IQR) is the range of the middle 50% of the data. So for the basketball team, the heights of 50% of the players lie within the range of 73 ± 2.5 (since the IQR is 5). Similarly, for the baseball team, the heights of 50% of the players lie within the range of 72 ± 3 (since the IQR is 6).

Comparing the medians, we see that the basketball team has a median height of 73, while the baseball team has a median height of 72.

Based on this information, we can conclude that:

A) Players on the basketball team are generally taller than players on the baseball team - this is the most likely answer, as the median height of the basketball team is higher.

B) Players on the baseball team are generally taller than players on the basketball team - this is not supported by the given information.

D) There is less variation in heights on the baseball team than on the basketball team - we cannot determine this based on the given information.

C) Players on the baseball team are generally the same height as players on the basketball team - this is not supported by the given information.

Answer:

a) 1:3:5

b) 9:10

Step-by-step explanation:

a) 7:21:35

Simplify by 7, we get the ratio

1:3:5

b) 9 min: 600 seconds

9 min = 540 seconds

540 seconds: 600 seconds

Simplify by 60, we get the ratio

9:10

Answer:

a) 1:3:5

b) 3 min: 200 s

Step-by-step explanation:

a) find a common factor you can divide them all by, in this case it would be 7.

7÷7=1

21÷7=3

35÷7=5

=1:3:5

b) find the common factor (3)

Divide all the numbers by the factor

9÷3=3

600÷3=200

=3 mins: 200 s

The sum of the angles of an N-sided convex figure is (n-2)*180 - a simple proof of which is just to decompose the figure into triangles, each of which has all of its vertices the same as three of the vertices of the original figure. (Cut a quadrilateral into two triangles along a diagonal, for instance).

So, a 7-sided figure has angles totaling 5*180 = 900. Now set up a simple equation:

3x + 4(x+15) = 900

7x + 60 = 900

7x = 840

x = 120

The figure has three angles of 120 degrees, and four angles of 135 degrees.

Means and Variances of Linear Combinations:


(a) X1 - 2X2

Mean: μa = μ1 - 2μ2

Variance: σa2 = σ12 + 4σ22 + 4σ122



(b) X1 + 2X2 - 3

Mean: μb = μ1 + 2μ2 - 3

Variance: σb2 = σ12 + 4σ22 + 4σ122



(c) 3X1 - 4X2

Mean: μc = 3μ1 - 4μ2

Variance: σc2 = 9σ12 + 16σ22



In the case that X1 and X2 are independent, then σ122 = 0, so:

(a) X1 - 2X2

Mean: μa = μ1 - 2μ2

Variance: σa2 = σ12 + 4σ22



(b) X1 + 2X2 - 3

Mean: μb = μ1 + 2μ2 - 3

Variance: σb2 = σ12 + 4σ22



(c) 3X1 - 4X2

Mean: μc = 3μ1 - 4μ2

Variance: σc2 = 9σ12 + 16σ22

Answer:

r = -2

Step-by-step explanation:

We can use the slope formula to find r.

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

3 = ( 19-4)/(r- -7)

3 = 15/(r+7)

Multiply each side by (r+7).

3 ( r+7) = 15

Divide each side by 3.

r+7 = 15/3

r+7 = 5

Subtract 7 from each side.

r+7-7 = 5-7

r = -2

Answer:

the secound one

Step-by-step explanation:

actually im not sure

2  is greater than or equal to 8 is false

2 [tex]\geq[/tex] 8 is false because 2 isn't greater or equal to 8. The sign, >, means greater than or equal to.

Number of modes in the data set 1.50, 1.70, 2.00, 2.00, 2.00, 2.00, 2.30, 2.30, 2.40, 2.40, 2.00 is option (D) 3

The mode is the most frequently occurring value in a dataset. To find the modes in a dataset, we need to determine the values that occur most frequently. In the given dataset, we can see that some values occur more than once.

To start, we can sort the values in ascending order,

1.50, 1.70, 2.00, 2.00, 2.00, 2.00, 2.30, 2.30, 2.40, 2.40, 2.00

Now, we can count the number of occurrences of each value.

1.50 occurs once

1.70 occurs once

2.00 occurs four times

2.30 occurs twice

2.40 occurs twice

From this, we can see that the values 2.00 occur most frequently, and therefore, it is a mode. However, there are two more values that occur twice, namely, 2.30 and 2.40. Hence, these two values are also modes of the dataset.

There are three modes in the dataset: 2.00, 2.30, and 2.40.

Therefore, the correct option is (D) 3

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For the given functions, f(x)=x²+3x-7, g(x)=3x+5 and h(x)=2x²-4, f(g(x))= 9x² + 30x + 33, h(g(x))= 18x² + 60x + 46, (h-f)(x)= x² - 3x + 3, (f+g)(x)= x² + 6x - 2.

In mathematics, a function is a mathematical object that takes an input (or several inputs) and produces a unique output. It is a relationship between a set of inputs, called the domain, and a set of outputs, called the range.

Formally, a function f is defined by a set of ordered pairs (x, y) where x is an element of the domain, and y is an element of the range, and each element x in the domain is paired with a unique element y in the range. We write this as f(x) = y.

Functions can be represented in various ways, such as algebraic expressions, tables, graphs, or verbal descriptions. They can be linear or nonlinear, continuous or discontinuous, and may have various properties such as symmetry, periodicity, and asymptotic behavior.

To solve these problems, we substitute the function g(x) for x in f(x) and h(x) and simplify the resulting expressions.

f(g(x)):

f(g(x)) = f(3x+5) = (3x+5)² + 3(3x+5) - 7 (using the definition of f(x))

= 9x² + 30x + 33

h(g(x)):

h(g(x)) = h(3x+5) = 2(3x+5)² - 4 (using the definition of h(x))

= 18x² + 60x + 46

(h-f)(x):

(h-f)(x) = h(x) - f(x) = (2x² - 4) - (x² + 3x - 7) (using the definitions of h(x) and f(x))

= x² - 3x + 3

(f+g)(x):

(f+g)(x) = f(x) + g(x) = x² + 3x - 7 + 3x + 5 (using the definitions of f(x) and g(x))

= x² + 6x - 2

When multiplying out a squared term, such as (3x+5)², we can use the FOIL method, which stands for First, Outer, Inner, Last. We multiply the first terms, then the outer terms, then the inner terms, and finally the last terms, and then add up the results. For example:

(3x+5)² = (3x)(3x) + (3x)(5) + (5)(3x) + (5)(5)

= 9x² + 15x + 15x + 25

= 9x² + 30x + 25

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The two positive numbers that satisfy the given requirements, the product of which is 768 and the sum of the first plus three times the second is a minimum are 16, 48.

A product is a result of multiplying two or more numbers or values together. It's a fundamental mathematical operation that is used in a variety of applications.

For example, if you have two integers, say 3 and 4, you can multiply them to get 12. The product of these two numbers is 12.

When two or more numbers are added together, the resulting value is referred to as the sum. It is one of the most basic mathematical concepts, and it is frequently used in a variety of applications.

For example, if you add 1 and 2 together, the sum is 3.

How to find two positive numbers that satisfy the given requirements?

Let's assume that the two positive numbers are x and y.

Therefore, we know the following: x * y = 768

The sum of the first plus three times the second is a minimum: x + 3y = minimum

We need to find two positive numbers that satisfy both of the above equations.

Solve for y by substituting y= 256/x into x+3y = minimum: x + 3(256/x) = minimum

Differentiate the above equation with respect to x and equate it to 0 to find the minimum value:

1-768/x² = 0x² = 768x = ±sqrt(768)

Since we need positive solutions: x = sqrt(768) = 16

Substitute x = 16 into y = 256/x to obtain:y = 256/16 = 16

Therefore, the two positive numbers that satisfy the given requirements, the product of which is 768 and the sum of the first plus three times the second is a minimum are 16, 48.

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Answer:

30cm

Step-by-step explanation:

Perimeter of an equilateral triangle = 3L

Mathematically we have;

P = 3L

Where P = perimeter of the triangle

L = Length

Therefore;

90 = 3L

Divide both side by 3

L = 30cm

Therefore, the length of each side of the triangle is 30cm.

Step-by-step explanation:

5x - 30 = 3x

2x = 30

x = 15

that's the answer

Answer:

25%

Step-by-step explanation:

The experimental probability of drawing a white marble can be found by dividing the number of times a white marble was chosen by the total number of trials:

Experimental probability of drawing a white marble = number of times a white marble was chosen / total number of trials

In this case, the number of times a white marble was chosen is 18, and the total number of trials is 80, so:

Experimental probability of drawing a white marble = 18/80 = 0.225 or 22.5%

To compare the experimental probability with the theoretical probability, we need to know the total number of marbles in the bag and the number of white marbles in the bag. Let's assume that there are 4 colors of marbles in the bag (red, white, black, and green), and that each color has an equal number of marbles. This means that there are a total of 4 x 18 = 72 marbles in the bag, and 18 of them are white.

The theoretical probability of drawing a white marble can be found by dividing the number of white marbles by the total number of marbles:

Theoretical probability of drawing a white marble = number of white marbles / total number of marbles

In this case, the number of white marbles is 18, and the total number of marbles is 72, so:

Theoretical probability of drawing a white marble = 18/72 = 0.25 or 25%

Comparing the two probabilities, we can see that the experimental probability (22.5%) is slightly lower than the theoretical probability (25%). This could be due to chance or sampling error in the experiment, or it could indicate that the actual probability of drawing a white marble is slightly lower than the theoretical probability.

The greatest common factor of 12 and 30 is 6, which is >5 and GCF of 20 and 30 is 10, which is >5. The given pair of numbers are 12 and 30, 6 and 33, 15 and 20, 3 and 20, 25 and 30 and 20 and 30.

The GCF of two natural numbers x and y is the largest possible number that divides both x and y without leaving any remainder.

Here,

GCF of 12 and 30 is 6, which is >5

GCF of 6 and 33 is 3, which is =3

GCF of 15 and 20 is 5, which is =5

GCF of 3 and 20 is 1, which is <3

GCF of 25 and 30 is 5, which is =5

GCF of 20 and 30 is 10, which is >5

The greatest common factor (GCF), also known as the greatest common divisor (GCD), is a mathematical concept used to find the largest number that divides two or more numbers without leaving a remainder. In other words, the GCF is the largest factor that two or more numbers have in common.

To find the GCF of two or more numbers, you can start by finding the factors of each number and identifying the largest factor that all the numbers share. For example, if you want to find the GCF of 12 and 18, you can list the factors of each number:

12: 1, 2, 3, 4, 6, 12

18: 1, 2, 3, 6, 9, 18

The largest factor that 12 and 18 share is 6, so the GCF of 12 and 18 is 6.

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Complete Question; -

The probability that all 4 members are teachers from a committee of 4 being formed randomly from the employees at a school which includes 6 administrators, 37 teachers, and 5 staff is 0.0147.

The probability that all 4 members are teachers from a committee of 4 being formed randomly from the employees at a school which includes 6 administrators, 37 teachers, and 5 staff is:

Probability of selecting 1 teacher out of 37 teachers, P(teacher) = 37/482)

Probability of selecting 2 teachers out of 37 teachers, P(teacher and teacher) = 37/48 * 36/473)

Probability of selecting 3 teachers out of 37 teachers, P(teacher and teacher and teacher) = 37/48 * 36/47 * 35/464)

Probability of selecting 4 teachers out of 37 teachers, P(teacher and teacher and teacher and teacher) = 37/48 * 36/47 * 35/46 * 34/45

Now, the probability that all 4 members are teachers,P(all teachers) = P(teacher and teacher and teacher and teacher)= 37/48 * 36/47 * 35/46 * 34/45= 0.0147

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Answer:

If the snowfall began with 8 inches on Ellie's lawn and then continued to fall at a constant rate of 1 inch per hour, then after 5 hours, the amount of snow on her lawn would be:

8 inches (initial amount) + 1 inch per hour × 5 hours = 8 + 5 = 13 inches

Therefore, after 5 hours of snowfall, Ellie would have 13 inches of snow on her lawn.

If t represents the number of hours of snowfall, then the amount of snow on Ellie's lawn after t hours would be:

8 inches (initial amount) + 1 inch per hour × t hours = 8 + t inches

Therefore, after t hours of snowfall, Ellie would have 8 + t inches of snow on her lawn.

The number of papers xavier have remaining after working for 12 hours is 18

Xavier can grade 6 papers per hour, so in 12 hours he can grade:

6 papers/hour x 12 hours = 72 papers

Therefore, after working for 12 hours, Xavier would have

90 - 72 = 18 papers remaining to grade.

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Answer:

25.71 (2 d.p)

Step-by-step explanation:

[tex].[/tex]

The derivative of the implicit function x · cos y = 1 at point (2, π / 3) is equal to y' = √3 / 6.

In this problem we find the case of a implicit function of the form f(x, y), whose derivative must be found. This can be done by implicite differentiation, whose procedure is shown:

Step 1 - Derive the expression by derivative rules:

cos y - x · sin y · y' = 0

Step 2 - Clear y' within the expression:

y' = cos y / (x · sin y)

Step 3 - Clear x and y in the resulting expression:

y' = cos (π / 3) / [2 · sin (π / 3)]

y' = 1 / [2 · tan (π / 3)]

y' = √3 / 6

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By answering the presented question, we may conclude that I used the following procedures to produce this graph.

Mathematicians use graphs to visually display or chart facts or values in order to express them coherently. A graph point usually represents a connection between two or more items. A graph, a non-linear data structure, is made up of nodes (or vertices) and edges. Glue the nodes, also known as vertices, together. This graph contains vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical graphs (bar graphs, pie graphs, line graphs, and so on) are graphical representations of exponential development. a logarithmic graph shaped like a triangle.

I used the following procedures to produce this graph:

I classified the personnel as full-time, part-time, and temporary.

I estimated the proportion of employees who assessed the company's work-life balance as "very good" or "excellent" for each employee category, as well as the percentage who rated it as "good" or "fair/poor."

I used the following procedures to produce this graph:

I classified the personnel as full-time, part-time, and temporary.

I estimated the proportion of employees who assessed the company's work-life balance as "very good" or "excellent" for each employee category, as well as the percentage who rated it as "good" or "fair/poor."

I made the segmented bar graph using these percentages.

The graph was made using Excel technology. You may make a similar graph with Excel or any other software that supports segmented bar graphs.

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Answer:

1x + 2y = z

Step-by-step explanation:

Here x is the price of jeans and y is the price of T-shirts

z is total money spend

The company should sell their phones for $250 each to get the maximum revenue.

What do you mean by maximum revenue?

Maximum revenue refers to the highest possible amount of income that can be generated from a particular product or service. In the context of the given problem, it means finding the price at which the company can sell its cell phones to earn the highest amount of revenue.

Finding the price at which the company should sell their phones to get the maximum revenue:

We need to find the vertex of the parabolic function [tex]r(x)=x(1,000-2x)[/tex], which represents the revenue as a function of the selling price.

To find the vertex of the function r(x), we need to first rewrite it in standard form by expanding the product:

[tex]r(x) = 1000x - 2x^2[/tex]

Now we can see that the function is a quadratic polynomial in standard form, with [tex]a=-2, b=1000[/tex], and [tex]c=0[/tex]. To find the x-coordinate of the vertex, we can use the formula:

[tex]x = -b / (2a)[/tex]

Substituting the values of a and b, we get:

[tex]x = -1000 / (2\times(-2)) = 250[/tex]

Therefore, the company should sell their phones for $250 each to get the maximum revenue. To find the maximum revenue, we can substitute this value of x into the function r(x):

[tex]r(250) = 250\times(1000-2\times250) = $125,000[/tex]

So the maximum revenue the company can expect to earn is $125,000 if they sell their phones for $250 each.

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120 is 30 percent of 400

The Shalane should keep her shop open all year round to maximize her sales and revenue.

The scatter plot with a line of best fit that was generated with technology reveals that when the temperature outside is higher, more snow cones are sold in Panama City, Florida. Since the line has a positive slope, it means that as the temperature outside increases, the number of snow cones sold also increases. As a result, if Shalane were to keep her shop open all year round, she might generate more revenue by providing snow cones during the warmer months, when more people are inclined to purchase them.Therefore, based on the scatter plot with a line of best fit that was generated with technology, Shalane should keep her shop open all year round to maximize her sales and revenue.

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Answer:

Step-by-step explanation:

divide

The intensity of the beam 10 feet below the surface can be calculated using Beer-Lambert's law, which states that the rate of decrease in intensity of light through a transparent medium is proportional to the thickness of the medium. This means that the intensity i of the beam at a depth t below the surface is given by the equation i = i0 * e^(-kt), where i0 is the initial intensity of the incident beam, k is a constant, and e is Euler's number.
For the given scenario, we know that the intensity at a depth of 3 feet is 25% of the initial intensity i0. Substituting the known values into the equation, we can calculate the value of k:
i = i0 * e^(-3k)
0.25i0 = i0 * e^(-3k)
0.25 = e^(-3k)
ln(0.25) = -3k
k = ln(0.25) / -3
k = 0.0451
Therefore, the intensity of the beam 10 feet below the surface can be calculated as follows:
i = i0 * e^(-0.0451 * 10)
i = i0 * e^(-0.451)
i = 0.6139i0

Rounding any constants or coefficients to five decimal places, the intensity of the beam 10 feet below the surface is 0.6139i0.

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