BIOLOGY AND PAINTING
There are 530 students in the Sophomore class.
1. There are 200 students enrolled in both Biology and
Painting.
2. There are 420 Art students and 330 Biology students.
3. There ar

Therefore, the linear speed of the wheel on a bike is approximately 0.9π miles per hour.

The pace at which an object travels a specific distance in a predetermined amount of time is known as linear speed. By dividing the distance traveled by the time it takes to cover that distance, it may be used to determine how rapidly an item is travelling in a straight line. For instance, if a car moves 100 meters in 10 seconds, its linear speed is 10 meters per second. Linear speed is distinct from average speed, which takes into account any variations in velocity or direction throughout the duration of a voyage. Linear speed is also distinct from tangential speed, which is the pace at which an item travels along a circular route. Physics' fundamental idea of linear speed.

How to solve?

C=2πr,

C=2π(19)=38π.

linear speed of v=(38π/60)*5280=33.6π feet per second.

final speed of v=(33.6π/3600)*60=0.9π miles per hour.

Therefore, the linear speed of the bike is approximately 0.9π miles per hour.

To learn more about linear speed, visit:

https://brainly.com/question/3930773

#SPJ4

Answer:

9179.84

Step-by-step explanation:

150 grams to milligrams is 9179.84

Answer:

0.011, 0.5, 0.625, 1.0625, 1.25

Step-by-step explanation

f(n) = ϴ(g(n)) is not true in cases B(sqrt(n)log(n), C(\(3^n 5^n\)), and D(sin(n)+3 cos(n)+1).

A) \(log(n^200) log(n^2)\)

Here, f(n) = \(log(n^200)\) and g(n) = \(log(n^2)\). Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:

f(n) / g(n) = \([log(n^200) / log(n^2)]\) = 100

This means that as n approaches infinity, the ratio f(n) / g(n) is constant, and so we can say that f(n) = ϴ(g(n)). Therefore, f(n) = ϴ(g(n)) is true in this case.

B) sqrt(n) log(n) Here, f(n) = sqrt(n) and g(n) = log(n). Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:

f(n) / g(n) = [sqrt(n) / log(n)]

As log(n) grows much slower than sqrt(n) as n approaches infinity, this limit approaches infinity. Therefore, we cannot say that f(n) = ϴ(g(n)) is true in this case.

C) 3^n 5^n

Here, f(n) = \(3^n\) and g(n) = \(5^n\) . Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:

f(n) / g(n) = \([3^n / 5^n]\)

As \(3^n\) grows much slower than \(5^n\) as n approaches infinity, this limit approaches zero. Therefore, we cannot say that f(n) = ϴ(g(n)) is true in this case.

D) sin(n) + 3 cos(n) + 1

Here, f(n) = sin(n) + 3 and g(n) = cos(n) + 1. Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:

f(n) / g(n) = [sin(n) + 3] / [cos(n) + 1]

As this limit oscillates between positive and negative infinity as n approaches infinity, we cannot say that f(n) = ϴ(g(n)) is true in this case.

Therefore, f(n) = ϴ(g(n)) is not true in cases B, C, and D.

To know more about log refer here:

https://brainly.com/question/32621120

#SPJ11

Answer:

42

Step-by-step explanation:

45 divided by 5 is 9.

210 divided by 5 is 42.

Hope It Helps

Sorry If I'm Wrong

Answer:

The expression √x+5+√1-x is defined for all values of x such that the value under the square root sign is non-negative. We can find the values of x that satisfy this condition by considering each of the square roots separately.

For the first square root, the value under the square root must be non-negative, so we have the following inequality:

x + 5 ≥ 0

x ≥ -5

For the second square root, the value under the square root must be non-negative, so we have the following inequality:

1 - x ≥ 0

x ≤ 1

Therefore, the expression is defined for all values of x that satisfy both of these inequalities. This means that the expression is defined for values of x in the range -5 ≤ x ≤ 1. The correct answer is therefore option D.

Answer: y intercept = 3 ✅

Step-by-step explanation:

Hii, do you need to know the y intercept of the line that is described by the line y=-6x+3? No problem. (:

Note that this particular equation is given to us in "slope intercept" form.

The "slope intercept" formula is y=mx+c, in which "m" denotes the slope and "c" denotes the y intercept.

Looking back at our equation, let's consider this:

"What is the y intercept of the line that is described by the equation y=-6x+3?"

Note that the y intercept is a constant number; it does not come before any variables.

\(\large\boldsymbol{\therefore,\;the\;y\;intercept\;is\;3}\)

Voila! There's our solution, cheers! (:

--

Hope that this helped! Best wishes.

\(\it Reach\qquad far.}\\Aim\qquad high.}\\Dream\qquad big.\)

--

\(\bigstar\underbrace\)

Answer:

4/95

Step-by-step explanation:

convert -4.75 into the fraction 19/4 and  -0.2 into -2/10 then multiply across and simplify

Tangent Half-Angle Identity relates the tangent of an half angle to suitable cosines and sines. Pythagorean identity is a trigonometric identity that relates the sine and cosine using Pythagorean theorem which states that s\(sin^{2} + cos^{2} = 1\).

In this case, we have been given the identity as tan A/2=1-cos A/sin A, so after rationalizing the RHS with the numerator, we get:

\(\frac{1-cos A}{sin A} * \frac{1+cos A}{1+cos A}\)

\(\frac{1 - cos^{2}A }{sin A(1+cos A)}\)

\(\frac{sin^{2}A }{sinA(1+cosA)}\)

\(\frac{sin A}{1 + cos A}\)

Hence Proved

Therefore, with the help of Tangent Half-Angle Identity and a Pythagorean identity we proved that tan A/2 = sin A / 1 + cos A.

To know more about Tangent Half-Angle Identity:

https://brainly.com/question/10057984

#SPJ4

An increase in the exchange rate of the U.S. dollar relative to a trading partner can result from higher interest rates and higher inflation in the U.S. The correct answer is option (e).

This is because higher interest rates attract foreign investors to the U.S., increasing demand for the U.S. dollar and causing its value to rise relative to other currencies.

Higher inflation in the U.S. also makes the dollar less attractive to foreign investors, causing its value to decline.

The other options listed may affect trade and economic activity, but do not directly impact the exchange rate.

Therefore, the correct option is (e) higher interest rates and higher inflation in the U.S.

To know more about exchange rate refer here :

https://brainly.com/question/30540100#

#SPJ11

Approximately 24% of the shoes in the closet are black.

Percentage is a way of expressing a fraction or proportion as a fraction of 100. It is commonly used to represent a portion of a whole or to compare quantities.

Percentage = (Part / Whole) * 100

To find the percentage of black shoes, we need to divide the number of black shoes by the total number of shoes and then multiply by 100.

Number of black shoes = 12

Total number of shoes = 50

Percentage of black shoes = (Number of black shoes / Total number of shoes) * 100

Percentage of black shoes = (12 / 50) * 100

Percentage of black shoes = 24%

Learn more about percentage:

https://brainly.com/question/843074

#SPJ11

The x value is 3.99 by logarithm when the expression is 0.3=log(x-2).

Given that,

The expression is 0.3=log(x-2)

We have to find the x value

Just another approach to write exponents is with a logarithm. When exponents are not an option, we turn to logarithms to address the issue. The rules of exponents can be used to derive various logarithm formulas.

The use of a logarithm can be utilized to solve issues that cannot be resolved using the concept of exponents alone. A logarithm is simply another way to describe exponents.

Take the expression,

0.3=log(x-2)

x=3.99

Therefore, the x value is 3.99 by logarithm when the expression is 0.3=log(x-2).

To learn more about logarithm visit: https://brainly.com/question/28346542

#SPJ1

The obtained value must be compared against the critical value. Hence, the correct option is b.

In hypothesis testing, the critical value is a threshold or cutoff point that is determined based on the chosen significance level (alpha level) and the distribution of the test statistic. It helps in determining whether to reject or fail to reject the null hypothesis.

After calculating the test statistic (such as z-score or t-statistic) from the observed data, it is compared to the critical value associated with the chosen significance level.

If the test statistic exceeds the critical value, it falls into the critical region, leading to the rejection of the null hypothesis.

If the test statistic is less than or equal to the critical value, it falls into the non-critical region, resulting in a failure to reject the null hypothesis.

Therefore, the obtained value must be compared against the critical value to make a decision in hypothesis testing. Hence, the correct answer is option b.

To know more about critical value refer here:

https://brainly.com/question/32389590#

#SPJ11

Answer:

To have a right triangle, the side lengths should make Pythagorean theorem true

Since the hypotenuse is always the longest side of a triangle, the biggest number will be c

Set the rest two numbers as a and b

Use a^2 + b^2 = c^2 to plug in the numbers

If you get true equation, meaning you have the same number on the left and right sides of equation, then it is going to create a right triangle

Answer:

y<1/2+2

Step-by-step explanation:

Answer:

I think the answer is A because I learned about slope last year

Answer:

it depends.

Step-by-step explanation:

A perfect square is a number that can be expressed as the product of an interger by itself or as the second exponent of an interger. For example, 25 is a perfect square because it is the product of interger 5 by itself, 5 × 5 =25.

The value equivalent to the expression 2² × 7² is 196.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. In a equation say : ax + b, [a] is called coefficient of [x] and [b] is independent of [x] and hence is called constant.

We have the following expression -

2² × 7²

The given expression is -

2² × 7²

Solving, we get -

(2 x 2) x (7 x 7)

4 x 49

196

Therefore, the value equivalent to the expression 2² × 7² is 196.

To solve more questions on equation solving, visit the link below-

brainly.com/question/18067015

#SPJ1

The value of unknown number y for the equation  8 superscript y baseline = 16 superscript (y+2) is -8.

When the power of a number is raised by another number, then multiply both the powers and the result of this product keep as the power of the number.

Let suppose there is a number a. For this number the above rule can be given as,  

\((a^m)^n=a^{m\times n}\\(a^m)^n=a^{mn}\)

The expression which consist unknown variable y is given as,

\(8^y=16^{y+2}\)

The above equation can be written as,

\((2\times2\times2)^y=(2\times2\times2\times2)^{y+2}\\(2^3)^y=(2^4)^{y+2}\\(2)^{3y}=(2^)^{4y+8}\)

As the base of both side of the equation is same. Thus, the value of their exponent can be compared.

\(3y=4y+8\\4y-3y=-8\\y=-8\)

Thus, the value of unknown number y for the equation  8 superscript y baseline = 16 superscript (y+2) is -8.

Learn more about the  power raised by another number here;

https://brainly.com/question/960886

Answer:

ujhb ;jenwpfeuw9oytr87w4i4398743203irjfgk

Step-by-step explanation:

frylgbrbbiyebvkhweylirgkhbngiwoerulkhbvlihrfkvbruilefjkvgbwiulrejkfmngvhb jrio;e;jfeir'spgvnjth'\w/to;jnjf';thgbv;trjkvnrtjkgvbv jrkfds,

mvpbinh54utgj['p4\iwujgi5ptjnrtgojltngibklrtjngirglihnir

Answer:

What is the answer Choices? message me and ill answer.

Step-by-step explanation:

The critical value for the 0.05 level of significance is k = 21.

To find the critical value, we can use the binomial distribution. The binomial distribution models the number of successes in n independent Bernoulli trials, each with probability p of success. In this case, the number of successes is the number of dog owners who say Woof Chow is their regular brand, and the number of trials is n = 100. The null hypothesis is that the true market share of Woof Chow is 25%, and the alternative hypothesis is that it is not 25%.

We can use the binomial cumulative distribution function (CDF) to find the critical value. The CDF gives the probability of getting k or fewer successes in n trials, given a probability of success p. The critical value is the smallest value of k such that the CDF at k is greater than or equal to 1 - alpha, where alpha is the level of significance. In this case, alpha = 0.05.

So, we want to find the smallest k such that:

P(X <= k) >= 1 - 0.05

where X is a random variable representing the number of dog owners who say Woof Chow is their regular brand. We can use a binomial calculator or a software package to calculate the binomial CDF, or we can use a table of critical values for the binomial distribution.

The critical value for the 0.05 level of significance is k = 21. This means that if the true market share of Woof Chow is 25%, then the probability of getting 23 or more dog owners who say Woof Chow is their regular brand is less than 0.05. Since the observed number of dog owners who say Woof Chow is their regular brand is 23, which is greater than 21, we can reject the null hypothesis that the true market share is 25%.

This means that based on the survey results, we cannot conclude that Woof Chow has a market share of 25%. The survey results suggest that Woof Chow may have a market share that is greater than 25%.

To learn more about critical value here:

https://brainly.com/question/30168469

#SPJ4

The value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

(1). angle B = 180 - (22 + 90) {sum of interior angles of a triangle}

angle B = 68°

Given that the triangle ∆ABC is similar to the triangle ∆PQR.

(2). PQ/7.5cm = 12cm/18cm

PQ = (12cm × 7.5cm)/18cm {cross multiplication}

PQ = 5cm

(3). 13cm/BC = 12cm/18cm

BC = (13cm × 18cm)/12cm {cross multiplication}

BC = 19.5cm

(4). area of ∆PQR = 1/2 × 12cm × 5cm

area of ∆PQR = 6cm × 5cm

area of ∆PQR = 30cm²

Therefore, the value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

Read more about similar triangles here:https://brainly.com/question/14285697

#SPJ1

Answer:

Amount of butter left= 3/16 cups

Step-by-step explanation:

explanation: Given: Total amount of butter = 15/16

Each cake needs butter = 1/4

Total cake = 3

Find: amount of butter left

Computation: amount of butter left = total amount of butter - [each cake needs butter] [total cake] amount of butter left = 15/16 - [3] [1/4]

Amount of butter left = 3/16 cups

Answer:

115 lbs = 52.16 kilograms

Step-by-step explanation:

115 pounds is a little over 52kg

The required solution for the given arithmetic problems are,
A) 2/5
B) 72 / 125
C) 6, 3/4, 12/5, and 3/10
D) 4, 1/6 and 6

A) 12/25 times 15/18.
Division of two fractions performed as multiplication of numerator of one fraction with a denominator of another function over a denominator of one function with a numerator of another function.
= 12 / 25  * 15 / 18 = 2 / 5

Similarly

b) 12/25 divided by 15/18.
= [12 / 25 ] / 15 / 18
= 12 / 25 * 18 / 15
= 72 / 125

C) 6 and 3/4 times 1 and 2/5
 6 * 1 = 6
3 / 4 * 1 = 3/4
6 * 2/5 = 12/5
3/4 * 2/5 = 3 / 10

D) 4 and 1/6 divided by 1 and 2/3.
= 4 / 1 = 4
= 1/6  / 1 = 1/6
= 4 / 2/3 = 6
= 1/6 / 2/3 = 1/4

Thus, the required solution for the given arithmetic problems is mentioned above.

Learn more about arithmetic here:

brainly.com/question/14753192

#SPJ1

The distance between the two points is 14.6 units. The distance is always positive.

What is a point?

A point is a basic concept in classical Euclidean geometry that represents an exact location in space and has no length, width, or thickness. In contemporary mathematics, a point more broadly refers to a component of a set known as a space.

Given points are (–5,5) and (9.6,5).

The y-coordinate of both points is the same. The distance between two points is the absolute value of the difference of x-coordinates.

The x-coordinate of (–5,5) is -5.

The x-coordinate of (9.6,5) is 9.6.

The distance between points is

|-5 - 9.6| units

=|-14.6| units

= 14.6 units

To learn more about the coordinate system, click on the below link:

https://brainly.com/question/28986695

#SPJ1

There are 5 choices left), and 5 ways to choose the remaining element of Y. This gives us a total of 7 × 5 × 5 = 175 ordered pairs (X,Y).

Let's first consider the possible values of |X ∪ Y|.

If |X ∪ Y| = 1, it means that X and Y have no elements in common, and each set has only one element. There are 7 such sets: {1},{2},{3},{4},{5},{6},{7}.

If |X ∪ Y| = 2, it means that X and Y have one element in common. There are 7 ways to choose the common element, and 6 ways to choose the remaining element of X (it cannot be the same as the common element, so there are only 6 choices left), and 6 ways to choose the remaining element of Y (again, it cannot be the same as the common element or the element of X, so there are only 6 choices left). This gives us a total of 7 × 6 × 6 = 252 ordered pairs (X,Y).

If |X ∪ Y| = 3, it means that X and Y have two elements in common. There are 7 ways to choose the common elements, and 5 ways to choose the remaining element of X (it cannot be any of the common elements, so there are 5 choices left), and 5 ways to choose the remaining element of Y. This gives us a total of 7 × 5 × 5 = 175 ordered pairs (X,Y).

for such more question on word problems

https://brainly.com/question/13818690

#SPJ11

The dimension of the given rectangle is 7.071 and 7.071 and perimeter will be 28.28 feet.

Let the length of the rectangle be L and width be W

Area of the rectangle will be LW

As area = A = 50 sq ft

50 = LW

Therefore, L = 50/W

Now the P = perimeter = 2L + 2W

P = 2(50/W) + 2W

P = 100/W + 2W

differentiating with respect to W, we get

dP/dW = -100/\(W^{2}\) + 2

For dP/dW = 0

\(W^{2}\) = 50

W = sqrt(50)

W = 7.071

L = 50/7.071 = 7.071

Therefore, Perimeter = 2L + 2W = 28.28

Therefore, Length = 7.071

Width = 7.071

Perimeter = 28.28 feet

To know more about the minimum and maximum possible area, visit here:

https://brainly.com/question/12133485

#SPJ4