Every 5 years, the Conference Board of the Mathematical Sciences surveys college math departments. In 2005, the board reported that 51% of all undergraduates taking Calculus I were in classes that used graphing calculators and 21% were in classes that used computer assignments. Suppose that 10% used both calculators and computers. a) What percent used neither kind of technology? b) What percent used calculators but not computers? c) What percent of the calculator users had computer assignments? d) Based on this survey, do calculator and computer use appear to be independent events? Explain

Answer:

Step-by-step explanation:

3y+6-4x=0

3y-4x=0-6

3y-4x=-6

y-4x=6/3

y-4x=2

y-x=2/4

y-x=0.5

total length = 6 ft

length of the piece = 1/3

There will be 18 pieces

Based on the given circle with center Y, each of the measure include the following:

In Mathematics and Geometry, a circle simply refers to a closed, two-dimensional (2D) curved geometric shape with no edges or corners.

Based on the given circle with center Y and line AD is perpendicular to line DB, we can reasonably infer and logically deduce that arc AC is equal to arc BC;

mAC = mBC = 71 degrees.

mAB = mAC + mBC

mAB = 71 + 71

mAB = 142 degrees.

Since line DC is the perpendicular bisector of line AB, the measure of line AB and line BD can calculated as follows;

AD = BD = AB/2

AD = BD = 60/2

AD = BD = 30 units.

Note: YB is the radius of this circle and the hypotenuse of right-angle triangle YDB, which is equal to 34 units.

In order to determine the length of YD, we would have to apply Pythagorean's theorem as follows;

x² + y² = z²

BD² + YD² = YB²

30² + YD² = 34²

YD² = 1156 - 900

YD = √256

YD = 16 units.

DC = YB - YD

DC = 34 - 16

DC = 18 units.

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Answer:

Step-by-step explanation:

For similar figures, side lengths (and any other linear measure) are proportional. Areas are proportional to the square of the scale factor for side lengths.

  Perimeter 1/Perimeter 2 = CD/EF

  21/18 = CD/6

  CD = 6(21/18)

  CD = 7 . . . cm

__

  Area 2/Area 1 = (Perimeter 2/Perimeter 1)²

  Area 2/98 = (18/21)²

  Area 2 = 98(6/7)²

  Area 2 = 72 . . . cm²

Average rate = total distance / total time

A. 28/7 = 4 km per hour

B. 28/8 = 3.5 km per hour

The circumference of the ring is determined as 10.85 ft.

The circumference of the ring is calculated by applying the following formula for circumference of a circle

Circumference = π × diameter

The given parameter include;

The circumference of the ring is calculated as follows;

Circumference = 3.14 × 3.5 feet

Circumference = 10.85 ft

Thus, the circumference of the ring is equal to the circle of a circle with equal diameter of 3.5 feet, and the magnitude is determined as 10.85 ft.

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Based on the tangent theorem, and also applying the Pythagorean theorem, the length of WX is calculated as: 42.1 units.

The tangent theorem states that a right angle is formed at the point of tangency between the tangent and the radius of the circle.

Thus, WXY is a right triangle. Use Pythagorean theorem to find WX.

WX = √(XY² - WY²)

XY = 25 + 23 = 48

WY = 23

Substitute

WX = √(48² - 23²)

WX = 42.1 units.

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Answer:

.............

Step-by-step explanation:

1720 gallons of rainwater are needed to fill the container to the top.

What does have capacity mean?

The ability to use and comprehend data to make decisions and convey those decisions is referred to as capacity.

If the container is 30% filled with rainwater, then it is 70% empty. Let's first calculate the capacity of the container when it is 100% full:

Capacity of container = (100 / 30) * 1290 = 4300 gallons

So, the container has a capacity of 4300 gallons when it is 100% full.

Since the container already has 30% of its capacity filled with rainwater, we need to add enough rainwater to fill the remaining 70% of the capacity. The amount of rainwater needed to fill the container to the top is:

Amount of rainwater needed = 70% of 4300 - 30% of 4300

= 0.7 * 4300 - 0.3 * 4300

= 3010 - 1290

= 1720 gallons

Therefore, 1720 gallons of rainwater are needed to fill the container to the top.

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Answer:

33 degrees

Step-by-step explanation:

Angles BFG + GFC = 90

5r +68 + 8r +113 =90

1

Collect like terms

13r + 181 = 90

Subract 181 from both sides

13r = 90-181

13r = - 91

r = - 7

Now insert the value of r into BFG (5r +68)

5r + 68 = 5(-7) +68

= -35 + 68

=33

Check your answer by inserting the value of r into 8r +113

8r + 113 =8(-7) +113

-56+113= 57

The two angles 33 and 57 must add up to 90, a rt angle

Answer:

Top box = 3

Second box = 5

Last box = 4

Answer:

first blank: 3

second blank: 5

third blank: 4

Step-by-step explanation:

379 × 46 = 2,274 + 15,160 = 17,434

Answer:

Step-by-step explanation:

exponent on 1 is 9

Answer:

y = 1/5 x + 2

Step-by-step explanation:

y = mx + b

m = slope = 1/5

b = y-intercept = 2

y = 1/5 x + 2

The required answer is the value of tan(2) is approximately -2352/3669.

To evaluate the expression under the given conditions, we will first determine the value of sin() using the Pythagorean identity and then use the double-angle formula for tan(2).
A Quadrant is circular sector of equal one quarter of a circle ,or  a half semicircle. A sector of two-dimensional cartesian  coordinate system.  The Pythagorean identity, are useful expression involving the function need to simplified.

Given: cos() = 7/25, and is in Quadrant I.
Step 1: Find sin()
Since we are in Quadrant I, sin() is positive. Using the Pythagorean identity, sin^2() + cos^2() = 1, we can find sin().
sin^2() + (7/25)^2 = 1
sin^2() = 1 - (49/625)
sin^2() = (576/625)
sin() = √(576/625) = 24/25

we  are called the Pythagorean identity is  Pythagorean trigonometric identity, is expression A to B .

The same value for all variables within certain range. Angle is double or multiply by 2 so we called double- angle.

Step 2: Find tan(2) using the double-angle formula
The double-angle formula for tangent is: tan(2) = (2 * tan()) / (1 - tan^2())
First, we find tan():
tan() = sin() / cos() = (24/25) / (7/25) = 24/7
Now, use the formula for tan(2):
tan(2) = (2 * (24/7)) / (1 - (24/7)^2)
tan(2) = (48/7) / (1 - 576/49)
tan(2) = (48/7) / ((49 - 576) / 49)
tan(2) = (48/7) * (49 / (-527))
tan(2) = (-2352 / 3669)
So, under the given conditions, the value of tan(2) is approximately -2352/3669.

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Population size now is = 342 + 37 - 44 + 17 - 6= 346 Therefore, the population size of turtles now is 346.

A population of turtles contained 342 individuals at the end of the year 2010. Since then, 44 have died, 37 were born, 17 immigrated, and 6 emigrated. We need to find the population size now. Step 1:Calculate the number of deaths, births, immigrated and emigrated individuals:

Number of deaths = 44Number of births = 37Number of immigrated individuals = 17Number of emigrated individuals = 6Step 2:Calculate the population size now: The population size now = Initial population size + Number of births - Number of deaths + Number of immigrated individuals - Number of emigrated individuals

Putting the values in the above formula: Population size now = 342 + 37 - 44 + 17 - 6= 346Therefore, the population size of turtles now is 346.

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The graph of the sequence may pass toward the vertical line test.

Functions are defined as a fundamental part of the calculus in mathematics. These are the special types of relations. A function is visualized as a rule, which gives a unique output for every input x.

Given the information that, he gives two away on day 1, four away on day 2, and eight away on day 3. He continues this pattern for 10 days.

Let x be the number of days and f(x) be the number of cards.

So, the pattern is

f(x)=2, when x=1

f(x)=4, when x=2

f(x)=8, when x=3

Then, the function will be f(x)=2ˣ

The equation of the graph is passing through a vertical line.

The vertical line test is a graphical method that determines whether a curve in the plane represents the graph of a function by visually examining the number of intersections of the curve with vertical lines.

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Answer: B

Step-by-step explanation: the number of times they’re charging 35 depended on the number of people attending (represented by n) so you get 35n. then 100 is their set fee, meaning it won’t fluctuate. so add your 35n + 100 and you need that total to be less than or equal to 2000.. meaning your answer is B.

i hope that made sense, good luck!

Answer:

b

Step-by-step explanation:

because I just had a question like that I dont feel like explaining it

The median is the value in the middle of a data set, meaning that 50% of data points. The y intercept of the median line for the dataset 2 3 4 5 7 8 10 12 is 1.65.

To find the y-intercept of the median-median line for the given dataset, we first need to find the median of the x-values and the median of the y-values.

The median of the x-values can be found by first arranging the dataset in ascending order:

2, 3, 4, 5, 7, 8, 10, 12

The median of this dataset is the middle value, which is 5.

The median of the y-values can be found in a similar way:

2, 3, 4, 5, 7, 8, 10, 12

The median of this dataset is also 5.

Now that we have the medians of the x- and y-values, we can use them to find the slope of the median-median line. The slope is given by:

slope = (median of y-values for points above median of x-values - median of y-values for points below median of x-values) / (median of x-values for points above median of y-values - median of x-values for points below median of y-values)

To apply this formula, we need to split the dataset into two parts: the points above the median of x-values (5) and the points below the median of x-values.

Points above median of x-values:

7, 8, 10, 12

Points below median of x-values:

2, 3, 4, 5

The median of the y-values for the points above the median of x-values is 9, and the median of the y-values for the points below the median of x-values is 3.

Plugging these values into the slope formula, we get:

slope = (9 - 3) / (10 - 2) = 0.67

Now we can use the point-slope form of a line to find the equation of the median-median line:

y - median of y-values = slope × (x - median of x-values)

y - 5 = 0.67 × (x - 5)

Simplifying this equation, we get:

y = 0.67x + 1.65

Therefore, the y-intercept of the median-median line for the given dataset is 1.65.

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Answer:

  a) see below for a listing of possible orders

  b) 0.6

Step-by-step explanation:

You are asked to list the possible permutations of 5 runners, taken 3 at a time. Then, you are asked for the fraction of those that have Andrew among them.

The formula for the number of permutations of n objects taken k at a time is ...

  P(n, k) = n!/(n -k)!

Then the number of ways three can place from five contestants is ...

  P(5, 3) = 5!/(5 -3)! = 5·4·3 = 60

For listing purposes, we can represent the runners with the letters ...

The order we choose for listing the permutations is to list a combination of three finishers, followed by the other 5 orders in which they can finish. In order of first, second, third, we can have ...

  ABC ACB BAC BCA CAB CBA  ABD ADB BAD BDA DAB DBA

  ABE AEB BAE BEA EAB EBA  ACD ADC CAD CDA DAC DCA

  ACE AEC CAE CEA EAC ECA  ADE AED DAE DEA EAD EDA

  BCD BDC CBD CDB DBC DCB  BCE BEC CBE CEB EBC ECB

  BDE BED DBE DEB EBD EDB  CDE CED DCE DEC ECD EDC

In the above list, the first three of the five lines all have Andrew as one of those who "show" in the race.

  P(Andrew shows) = 3/5 = 0.6

Answer:

x is 226.154…

Step-by-step explanation:

1) x-14=y+196

x=y+196+14

x=y+210

2)x=14y

3) 14y=y+210 collect like terms together

14y-y=210

13y=210 divide both sides by 13

y=16.154

4)x=y+210 meaning:

x=16.154+210

=226.154

The z-score corresponding to an observation of 470 is -0.97.

Given that the observation x is 470.

mean, is 570

standard deviation, σ is 103

For the occurrence score,

z = (x - μ)/σ

z = (470 - 570)/103

z = -0.97

The standard score in statistics is the amount of standard deviations that a raw score (i.e., an observed value or data point) deviates from or exceeds the mean of the thing being observed or measured. Standard scores are positive for raw scores above the mean and negative for raw scores below the mean.

It is determined by deducting the population mean from a given raw score, then dividing the result by the population standard deviation. Standardizing or normalizing is the process of transforming a raw score into a standard score (however, "normalizing" can refer to many types of ratios; see normalization for more).

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Answer:

D) 1

Step-by-step explanation:

When you start raising i to certain powers, you begin to notice a pattern.

\(i^1=i \\\\i^2=-1 \\\\i^3=-i \\\\i^4=1 \\\\i^5=i \\\\ i^6=-1 \\\\ i^7=-i \\\\i^8= 1\)

This cycle repeats forever. Since 84 is a multiple of 4, i^84 must be 1. Hope this helps!

Answer: 1

Step-by-step explanation:

Answer:

7.04

Step-by-step explanation:

To get the value of residual of the data point, we simply substitute 11 for t

The substitution equation is h = 0.6t + 0.44

Substituting 11, we have

h = 0.6(11) + 0.44

h = 6.6 + 0.44

h = 7.04

Answer:

The residual of the data point h = 0.6t + 0.44, is h = 7.04.

Step-by-step explanation:

Given the line of fit, h = 0.6t + 0.44, which Brenda collected from an experiment, at the point t = 11, the residual of the data point is obtained by replacing t with 11 in the given equation h = 0.6t + 0.44.

Doing this, we have

h = 0.6(11) + 0.44

h = 6.6 + 0.44

= 7.04

This is what we want to obtain.

Answer:

8,039

Step-by-step explanation:

4097

3188

 754

---------

8039

Answer:

4097 + 754 + 3188 = 8039

Step-by-step explanation:

4097 + 754 + 3188

4851 + 3188

8039

The quadrilaterals with exactly one pair of parallel sides are: Trapezoid and Isosceles Trapezoid.

1. Trapezoid: A trapezoid has exactly one pair of parallel sides. The other two sides are non-parallel. The parallel sides are called the bases, and the non-parallel sides are called the legs.

2. Isosceles Trapezoid: An isosceles trapezoid is a special type of trapezoid where the legs are congruent (equal in length). It has exactly one pair of parallel sides, which are the bases.

Note: In some sources, the term "parallelogram" is also included in this list because a parallelogram technically has one pair of parallel sides. However, a parallelogram is commonly defined separately as a quadrilateral with both pairs of opposite sides parallel. So, depending on the definition being used, a parallelogram may or may not be included in this list.

The quadrilaterals with exactly one pair of parallel sides are: Trapezoid and Isosceles Trapezoid.

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Answer:

\(area = \frac{\pi}{4} \times {r}^{2} \\ = \frac{\pi}{4} \times {7}^{2} \\ = \frac{\pi}{4} \times 49 \\ = 38.48451000647 \: cm \: ans......\)

Answer:

Step-by-step explanation:

area of circle=πr^2

=3.14*(7)^2

=3.14*49

=153.86 cm^2

perimeter of a circle(circumference)=2πr

=2*3.14*7

=14*3.14

=43.96 cm

Answer:

r = ∛(V/π)

Step-by-step explanation:

In algebra, when dealing with equations, we are usually given a variable with some constants and are asked to solve for said variable. Here are some examples of typical equations you'd see in algrebra:

x + 1 = 2

2(x - 2) = 6

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

But what happens if most, if not all, of the terms in an equation are variables? These equations are known as literal equations. They can be random variable equations or formulas you'd see on a formula sheet (like the Pythagorean Theorem, for example). Here are some examples of literal equations:

vw + xy = z

A = 1/2(bh)

a^2 + b^2 = c^2

In the question here, we are given an equation V = πr^3 and are asked to solve for r. Just like any equation, you'd solve for the variable by doing the order of operations (grouping, exponents, multiplication or addition, and addition or subtration) backwards.

V = πr^3

First, we divide π on both sides to isolate r^3.

V/π = r^3

Then, we take the square root of both sides to isolate r.

∛(V/π) = r

r = ∛(V/π)

(And in case you needed to solve for r for v=(4/3)πr^3, r = ∛(3V/4π).)

The critical points for this system are: (0, y), (1, y), (x, 0), and (x, -1/2).

What is the system of equations?

A system of equations is a collection of one or more equations that are considered together. The system can consist of linear or nonlinear equations and may have one or more variables. The solution to a system of equations is the set of values that satisfy all of the equations in the system simultaneously.

To find the critical points (equilibrium solutions) of the given systems of differential equations, we need to set both derivatives equal to zero and solve for x and y.

dx/dt = x - xy, dy/dt = y + 2xy

Setting dx/dt = 0, we have:

x - xy = 0

x(1 - y) = 0

This gives us two critical points: (0, y) and (1, y), where y can take any value.

Setting dy/dt = 0, we have:

y + 2xy = 0

y(1 + 2x) = 0

This gives us two critical points: (x, 0) and (x, -1/2), where x can take any value.

Therefore, the critical points for this system are: (0, y), (1, y), (x, 0), and (x, -1/2).

Regarding the stability and classification of each critical point, we need to analyze the eigenvalues of the Jacobian matrix at each point. The stability of a critical point is determined by the sign of the real parts of the eigenvalues.

To describe the basin of attraction for each asymptotically stable critical point, we would need to perform further analysis of the system's behavior near each critical point.

Hence, the critical points for this system are: (0, y), (1, y), (x, 0), and (x, -1/2).

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Answer:

15

Step-by-step explanation:

the range is the largest number take away the smallest number

56-41=15

The Natural area will be 100 feet wide.

Algebra is a branch of mathematics that deals with equations and variables.

To start, there are some specific requirements for the dimensions of the nature area. The length should be twice the width, which means that if we use "w" to represent the width, the length would be "2w". Additionally, a retaining wall that is "h" feet high will be installed around the perimeter of the space.

The total length of the retaining wall needed is given, which means we can use this information to solve for "w". To do this, we need to use a bit of algebra.

First, let's write out the equation for the total length of the retaining wall:

2(2w) + 2w = 600

6w = 600

Dividing both sides by 6, we get:

w = 100

Therefore, the width of the nature area will be 100 feet.

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