Harris has $20.92 to spend on video-game rentals. The store charges $3.95 per video-game rental plus 8.125% tax.What is the maximum number of videos he can rent?

Answer:

looks proportional to me

Step-by-step explanation:

Answer:

Proportional

Step-by-step explanation:

Direct proportion:

y = kx

1*4 = 4

2*4 = 8

3*4 = 12

Given values in the table satisfy the equation of direct proportion. So, it is a direct proportion.

Answer 2: The correct answer is: "The median is the best measure of center, and it equals 19."

Answer 6: The correct answer is: "Circle graph."

Answer 9: The correct answer is: "The college will have about 1,440 students who prefer ice cream."

What is median?

Median is a measure of central tendency that represents the middle value in a dataset when the values are arranged in order of magnitude

Answer 2:

Based on the given box plot, the appropriate measure of center for the data is the median, as it is less sensitive to extreme values. The median can be estimated by finding the middle value of the data, which corresponds to the vertical line in the box. In this case, the line in the box is at 19, so the median is 19. Therefore, the correct answer is: "The median is the best measure of center, and it equals 19."

Answer 5:

Since there were 900 people in attendance and 80 of them were in the exhibit room, the fraction of the attendees in the exhibit room is 80/900. If we assume that this fraction is representative of the entire conference, we can estimate the number of principals in attendance by multiplying the total number of attendees by this fraction and then multiplying by the fraction of principals in the exhibit room.

Thus, the estimated number of principals in attendance is: 900 * (80/900) * (15/80) = 15. Therefore, the correct answer is: "There were about 15 principals in attendance."

Answer 6:

The best graphical representation for the data on the subject preferences of 100 students in a particular school would be a bar graph or a pie chart. These graphs are suitable for displaying categorical data, where each category (in this case, the different subjects) is represented by a bar or a sector of the pie, and the frequency or percentage of the category is shown on the y-axis or as labels on the pie. Stem-and-leaf plots and histograms are more suitable for displaying quantitative data. Therefore, the correct answer is: "Circle graph."

Answer 7:

The best graph to display this categorical data is a bar graph. Each category of sport can be represented by a bar, with the height of the bar corresponding to the number of students who prefer that sport. Therefore, the correct answer is: "bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44."

Answer 8:

The best graph to represent this data is a circle graph or a pie chart, as it shows the proportion of visitors who used each type of transportation. The size of each sector in the pie corresponds to the percentage of visitors who used that type of transportation. Therefore, the correct answer is: "circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent."

Answer 9:

To estimate the number of students who prefer ice cream, we can use the proportion of students in the sample who prefer ice cream and assume that it is representative of the entire population of 4,000 students. The proportion of students who prefer ice cream in the sample is 81/225, or 0.36.

Therefore, the estimated number of students who prefer ice cream is: 0.36 * 4,000 = 1,440. Thus, the correct answer is: "The college will have about 1,440 students who prefer ice cream."

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Answer: x= -5/2  y=-5

Step-by-step explanation:

This is the general solution to the given differential equation, where C is the arbitrary constant.

general solution to the given differential equation, we can follow these steps:

Step 1: Put the problem in standard form:

Rearrange the equation to have the derivative term on the left side and the other terms on the right side:

dy/dx - x + x^2y = x^2 - x.

Step 2: Find the integrating factor:

The integrating factor, p(x), can be found by multiplying the coefficient of the y term by -1:

p(x) = -x^2.

Step 3: Rewrite the equation using the integrating factor:

Multiply both sides of the equation by the integrating factor, p(x):

-x^2(dy/dx) + x^3y = x^3 - x^2.

Step 4: Simplify the equation further:

Rearrange the equation to isolate the derivative term on one side:

x^2(dy/dx) + x^3y = x^3 - x^2.

Step 5: Apply the integrating factor:

The left side of the equation can be rewritten using the product rule:

d/dx (x^3y) = x^3 - x^2.

Step 6: Integrate both sides:

Integrating both sides of the equation with respect to x:

∫ d/dx (x^3y) dx = ∫ (x^3 - x^2) dx.

Integrating, we get:

x^3y = (1/4)x^4 - (1/3)x^3 + C,

where C is the unknown constant.

Step 7: Solve for y(x):

Divide both sides of the equation by x^3 to solve for y(x):

y = (1/4)x - (1/3) + C/x^3.

This is the general solution to the given differential equation, where C is the arbitrary constant.

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Answer: The lowest possible product would be -6724 given the numbers 82 and -82.

We can find this by setting the first number as x + 164. The other number would have to be simply x since it has to have a 164 difference.

Next we'll multiply the numbers together.

x(x+164)

x^2 + 164x

Now we want to minimize this as much as possible, so we'll find the vertex of this quadratic graph. You can do this by finding the x value as -b/2a, where b is the number attached to x and a is the number attached to x^2

-b/2a = -164/2(1) = -164/2 = -82

So we know one of the values is -82. We can plug that into the equation to find the second.

x + 164

-82 + 164

82

Step-by-step explanation: Hope this helps.

Answer:

They are 12, 13, 14 and 15.

Step-by-step explanation:

If the least integer is x, then:

x + x + 1 + x + 2 + x + 3 = 54

4x + 6 = 54

4x = 48

x = 12.

We can plot in the coordinate plane if an ordered pair is known to us.

The space or plane in where location of points is represented by a pair of numerical terms with respect to some reference lines or reference direction is called coordinate plane.

let we have some pair of numerical terms such as A (4, 9) and B (6, 10)

that is needed to plot in the coordinate plane.

At first, we will plot the point A (4, 9)

we will start from the origin and move horizontally along the direction of X axis up to 4 unit. In the next, start again and move up vertically in the direction of y axis up to 9 unit. And we will draw a point at the final location.

By the same way, we can plot the point B.

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Answer:

68.2 degrees

Step-by-step explanation:

\(1.19\frac{180}{\pi }\)

\(68.2\) degrees

Answer:

There are 3 common factors of 8 and 20, that are 1, 2, and 4. Therefore, the greatest common factor of 8 and 20 is 4.

Answer:

245.22° (nearest hundredth)

Step-by-step explanation:

To calculate the direction of the jogger's resultant vector, we can draw a vector diagram (see attachment).

Since the two vectors form a right angle, we can use the tangent trigonometric ratio.

\(\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$ \tan x=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $x$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}\)

The resultant vector is in quadrant III, since the person jogs south (negative y-direction) and then west (negative x-direction).

As the direction of a resultant vector is measured in an anticlockwise direction from the positive x-axis, we need to subtract the angle found using the tan ratio from 270°.

The angle between the y-axis and the resultant vector can be found using tan x = 360 / 780. Therefore, the expression for the direction of the resultant vector θ is:

\(\theta=270^{\circ}+\arctan \left(\dfrac{360}{780}\right)\)

\(\theta=270^{\circ}-24.7751405...^{\circ}\)

\(\theta=245.22^{\circ}\; \sf (nearest\;hundredth)\)

Therefore, the direction of the plane's resultant vector is approximately 245.22° (measured anticlockwise from the positive x-axis).

Answer:

a) \(p \geq 60\,ft^{2}\), b) \(w \geq 36\,ft\), c) \(1\,qt \leq q \leq 2\,qt\), d) \(0.70\cdot p + 0.10\cdot w + 8\cdot q \leq 65\)

Step-by-step explanation:

In this question we proceed to translate each sentence into mathematical language and, more specifically, inequations:

a) At least 60 square feet of plywood for the surface

Let \(p\) the surface area of plywood, measured in square feet, and the inequation is:

\(p \geq 60\,ft^{2}\) (Eq. 1)

b) At least 36 feet of wood planks for the frame of the dog house

Let \(w\) the total length of wood planks, measured in feet, and the inequation is:

\(w \geq 36\,ft\) (Eq. 2)

c) Between 1 and 2 quarts of paint

Let \(q\) the total capacity of paint, measured in quarts, and the inequation is:

\(1\,qt \leq q \leq 2\,qt\) (Eq. 3)

d) Han's budget is $ 65. Plywood costs $ 0.70 per square foot, planks of wood cost $ 0.10 per foot and paint costs $ 8 per quart.

Dimensionally speaking, we understand that cost equals unit cost multiplied by physical variable (i.e. Area, length or capacity). Let \(p\), \(w\) and \(q\) the surface area of plywood, the total length of wood planks and the total capacity of paint, respectively. The sentence is represented by the following inequation:

\(0.70\cdot p + 0.10\cdot w + 8\cdot q \leq 65\) (Eq. 4)

Write an inequality to represent each constraint(material and cost)

Plywood:

plywood ≥ 60 square feet

Planks:

planks ≥ 36 feet

Paints

1 quarts ≤ paints ≤ 2 quarts

Inequality to represent cost constraint

Plywood = $0.70

planks of wood = $0.10

paint costs $8

Total cost = $65

0.70 × p + 0.10 × pw + 8 × Pa ≤ 65

0.70p + 0.10pw + 8pa ≤ 65

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Answer:

$2000

Step-by-step explanation:

Given the following :

Total amount invested = 14000

Total interest earned = 670

Amount invested in 4% (0.04) account = a

Amount invested in 6% (0.06) account = b

Amount invested in 5% (0.04) account = a + b

a + b + (a + b) = 14000

2a + 2b = 14000

a + b = 7000 - - - (1)

Simple interest = principal * rate * time

(a * 0.04) + (b * 0.06) + [(a+b) * 0.05] = 670

0.04a + 0.06b + 0.05a + 0.05b = 670

0.09a + 0.11b = 670 - - - - (2)

from (1)

a = 7000 - b

0.09(7000 - b) + 0.11b = 670

630 - 0.09b + 0.11b = 670

= 630 + 0.02b = 670

0.02b = 670 - 630

0.02b = 40

b = 40/ 0.02

b = $2000

Amout invested in 6% account = $2000

Answer:

48 free throws

Step-by-step explanation:

25:36 is the ratio

Now divide 25 by 36 to find the probability of the basketball player scoring:

25/36=0.694

Now multiply this probability with the total number of free throws (70) in order to get the number of free throws that would be made:

70 * 0.694 = 48.6

You can't make 48.6 free throws, so you have to round down to the nearest integer since you can't make 0.6 free throws.

Hence, 48.6 ==> 48 free throws

Answer:

Option B. 2π inches

Step-by-step explanation:

From the question given above, the following data were obtained:

Radius (r) = 6 in

Centre angle (θ) = 60 °

Length of arc (L) =?

The length of arc can be obtained as follow:

L = 2πr × (θ/360°)

L = 2 × 6 × π × (60/360)

L = 12π × 1/6

L = 2π in

Thus, the length of the arc is 2π in.

The point equidistant from the three sides of a triangle is its incentre.

The incenter is the centre of the largest circle that fits inside the triangle and is tangent to all three sides. It is called the incenter because it is equidistant from the interior angles of the triangle.

The incenter is a very important point in triangle geometry, and its position can be used to calculate various other measurements, such as the triangle's area and the lengths of its medians and angle bisectors.

In summary, the incenter is the answer to the question of the point equidistant from the three sides of a triangle.

Hence, the correct answer is C.

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"meso-" and "medi-" both relate to the middle or intermediate position, but they may be used in different contexts and have distinct origins (Greek and Latin, respectively).

The prefixes "meso-" and "medi-" have different meanings:

Meso-: The prefix "meso-" generally means "middle" or "intermediate." It is derived from the Greek word "mesos," which carries the same meaning. In scientific and medical terminology, "meso-" is often used to indicate something that is located in the middle or intermediate position.

For example:

Mesoderm: The middle germ layer in the early development of an embryo.

Mesozoic: The era between the Paleozoic and Cenozoic eras, often referred to as the "Age of Reptiles."

Medi-: The prefix "medi-" typically means "middle" or "between." It is derived from the Latin word "medius," which conveys a similar sense. In various contexts, "medi-" is used to indicate something that is in the middle or intermediary position.

For example:

Median: Referring to the middle value in a set of numbers or the middle line or point dividing something into equal halves.

Mediastinum: The central area within the thoracic cavity, located between the lungs, which contains the heart, great vessels, and other structures.

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Answer:

The monthly growth rate is 2.1%

Step-by-step explanation:

To find the monthly growth rate, we have to consider what is inside the bracket

Mathematically, what we have in the bracket should be written as;

1 + r

Thus;

1 + r = 1.021

r = 1.021-1

r = 0.021

This is same as 2.1%

Answer:

\(5 - \frac{1300}{100} = 5 - 13 = - 8\)

1. Statement: True

Inverse: True

Contrapositive: True

Converse: True

2. Statement: True

Inverse: True

Contrapositive: True

Converse: True

3. Statement: True

Inverse: True

Contrapositive: True

Converse: True

(i)

Statement: If the difference x - y is even, then x and y are also even.

Inverse: If x and y are not even, then the difference x - y is not even.

Contrapositive: If x and y are not even, then the difference x - y is not even.

Converse: If x and y are even, then the difference x - y is even.

Statement: If a divides b or a divides c, then a divides bc.

Inverse: If a does not divide b and a does not divide c, then a does not divide bc.

Contrapositive: If a does not divide b and a does not divide c, then a does not divide bc.

Converse: If a divides bc, then a divides b or a divides c.

Statement: If x^2 ≥ 100 and x ≥ 0, then x ≥ 10.

Inverse: If x^2 < 100 or x < 0, then x < 10.

Contrapositive: If x^2 < 100 or x < 0, then x < 10.

Converse: If x ≥ 10, then x^2 ≥ 100.

(ii)

For each statement, we need to evaluate the truth values of the statement, inverse, contrapositive, and converse.

Statement: True

Inverse: True

Contrapositive: True

Converse: True

Statement: True

Inverse: True

Contrapositive: True

Converse: True

Statement: True

Inverse: True

Contrapositive: True

Converse: True

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Standard error of b2 = √(0.00098) = 0.0313. Intercept (b0) = 15.187 - b2 * 69.139

(a) The sum of squared residuals is not provided in the given information. It is usually denoted as SSE (Sum of Squared Errors) and represents the sum of the squared differences between the observed dependent variable values and the values predicted by the regression model.

(b) The estimated variance of b2 is 0.00098. To calculate the standard error of b2, you can take the square root of the estimated variance:

Standard error of b2 = √(0.00098) = 0.0313

(c) The squares of residuals refer to the squared differences between the observed dependent variable values and the predicted values by the regression model. These residuals are usually denoted as e^2 or SSR (Sum of Squares Residuals).

(d) The value of Σ\((x-3)^2 is\) not provided. Σ\((x-3)^2\)represents the sum of squared deviations of the independent variable x from its mean. Without the actual data or mean values, it is not possible to calculate this value.

(e) If b2 = 0.18, it means that for a 1-unit increase in the percentage of males 18 years or older who are high school graduates, the dependent variable (mean income of males who are 18 years or older) is expected to increase by 0.18 units (thousands of dollars) on average, assuming other factors remain constant.

(f) To estimate the intercept, we can use the formula:

Intercept (b0) = y - b1 * x

Given x = 69.139 and y = 15.187, we can substitute these values into the formula:

Intercept (b0) = 15.187 - b2 * 69.139

However, the value of b2 is not provided, so we cannot calculate the intercept with the given information.

(g) The value of ΣΧί represents the sum of the product of the independent variable x and the corresponding residuals (observed y - predicted y). Without the actual data or predicted values, it is not possible to calculate this value.

(h) To compute the least squares residual for Arkansas, we would need the predicted value for Arkansas, which is not provided in the given information. The residual is calculated as the difference between the observed value and the predicted value:

Residual = Observed value - Predicted value

Without the predicted value, we cannot calculate the least squares residual for Arkansas.

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Answer:

7.2

Step-by-step explanation:

(6)^2 + (4)^2

36 + 16

52

square root of 52 = 7.2

Answer:

24/3×3600=28800bottles per day

Step-by-step explanation:

Answer:

  75

Step-by-step explanation:

You want the value of y² +4y -2 when y=7.

Put the value where the variable is and do the arithmetic.

  7² +4·7 -2

  = 49 +28 -2

  = 77 -2

  = 75

The value of the expression is 75.

__

Additional comment

It is often easier to evaluate a polynomial when it is written in Horner form:

  (y +4)·y -2

  = (7 +4)·7 -2 = 11·7 -2 = 77 -2 = 75

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The spheres with center (1, -3, 6) that just touch the xy-plane, yz-plane, and xz-plane can be described by the following equations:

(a) The sphere touching the xy-plane has a radius of 6 and its equation is \(\((x-1)^2 + (y+3)^2 + (z-6)^2 = 36\)\).

(b) The sphere touching the yz-plane has a radius of 1 and its equation is \(\((x-1)^2 + (y+3)^2 + (z-6)^2 = 1\)\).

(c) The sphere touching the xz-plane has a radius of 9 and its equation is \(\((x-1)^2 + (y+3)^2 + (z-6)^2 = 81\)\).

In summary, the spheres that just touch the xy-plane, yz-plane, and xz-plane have equations \(\((x-1)^2 + (y+3)^2 + (z-6)^2 = 36\)\), \(\((x-1)^2 + (y+3)^2 + (z-6)^2 = 1\)\), and \(\((x-1)^2 + (y+3)^2 + (z-6)^2 = 81\)\) respectively.

To find the equation of a sphere with center (h, k, l) and radius r, we use the formula \(\((x-h)^2 + (y-k)^2 + (z-l)^2 = r^2\)\).

(a) For the sphere touching the xy-plane, the center is (1, -3, 6) and the radius is 6. Thus, the equation is \(\((x-1)^2 + (y+3)^2 + (z-6)^2 = 36\)\).

(b) Similarly, for the sphere touching the yz-plane, the center is (1, -3, 6) and the radius is 1. The equation becomes \(\((x-1)^2 + (y+3)^2 + (z-6)^2 = 1\)\).

(c) For the sphere touching the xz-plane, the center is (1, -3, 6) and the radius is 9. The equation is \(\((x-1)^2 + (y+3)^2 + (z-6)^2 = 81\)\).

Thus, we have obtained the equations for the spheres touching the xy-plane, yz-plane, and xz-plane respectively.

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The value of the missing angle x in the given triangle is; x = 55°

From the image attached, we are told that the line at the top is parallel to the line at the base of the triangle.

Now, alternate angles are defined as angles that occur on opposite sides of the transversal line and have the same size.

This means that the angle formed to the right of 50 degrees will be an alternate angle to 75° and as such they are congruent.

Now, we know that sum of angles on a straight line is equal to 180°. Thus;

x + 50 + 75 = 180

x + 125 = 180

x = 180 - 125

x = 55°

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Answer:75/100

Step-by-step explanation:

75%=75/100

Answer:

75/100

Step-by-step explanation:

reduced fractions of this include but are not limited too: 3/4 6/8 12/16 24/32 48/64