what is f (5)
need help asap

Answer:

24°

Step-by-step explanation:

the total angle, made up from both a and 66°, is a mini-square, as you can see. this represents a right angle of 90°

thus, a and 66° combine to make 90°

a + 66° = 90°

subtract 66 from both sides to get a

a = 24°

The surface with the given vector equation, r(s, t) = (s cos(t), s sin(t), s), is a circular cone.

The vector equation r(s, t) = (s cos(t), s sin(t), s) represents a surface in three-dimensional space. Let's analyze the equation to determine the nature of the surface.

In the equation, we have three components: s, cos(t), and sin(t). The presence of s indicates that the surface expands or contracts radially from a central point. The trigonometric functions cos(t) and sin(t) determine the angle at which the surface extends in the x and y directions.

By observing the equation closely, we can see that as s increases, the radius of the surface expands uniformly in all directions, while the height remains constant. This behavior is characteristic of a circular cone. The circular base of the cone is defined by s cos(t) and s sin(t), and the vertical component is determined by s.

Therefore, the surface described by the vector equation r(s, t) = (s cos(t), s sin(t), s) is a circular cone.

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Answer: \(24^{\circ}\)

Step-by-step explanation:

Given

River is flowing from south to North with a velocity of \(u=1\ m/s\)

Motor boat traverses the river from east to west at a speed of \(v=2.5\ m/s\)

South component of boat velocity must compensate the river velocity in order to travel in west direction.

\(\therefore v\sin \theta=u\\\\\Rightarrow 2.5\sin \theta=1\\\\\Rightarrow \sin \theta=\dfrac{2}{5}\\\\\Rightarrow \theta=23.57^{\circ}\approx 24^{\circ} \text{south of west}\)

The linear function is given by h(x) = -500x + 4000

A linear equation is in the form:

y = mx + b

Where y,x are variables, m is the rate of change and b is the initial value of y.

Let h represent the elevation after hiking x miles.

The waterfall is at an elevation of 4,000 feet, hence b = 4000

The trail descends an average of 500 feet for every 1 mile she hikes, hence m = -500

The linear function is given by:

h(x) = -500x + 4000

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Answer:

you would weigh 140 lbs

Step-by-step explanation:

x= weeks in time

165-5x=y y being your final weight in lbs

Answer:

\(z=\frac{3 (28 + 17p)}{p + D}\)

Step-by-step explanation:

Move all terms to the left side and set equal to zero. Then set each factor equal to zero.

Answer:

4 hours

Step-by-step explanation:

he was gone for 5 hours, he spent an hour driving.

5 - = 4 hours at work.

Answer:

4 hours

Step-by-step explanation:

says he was gone 4 hours, he was at work

The vector field f(x,y) = 33x^2y^2i + 22x^3yj is conservative, and its potential function is φ(x,y) = 11x^3y^2 + 11x^2y^2 + C.

To determine if a vector field is conservative, we need to check if it is the gradient of a scalar function (i.e., a potential function). We can do this by taking the partial derivatives of each component with respect to their respective variables and checking if they are equal:

∂f_x/∂y = 66xy^2
∂f_y/∂x = 66xy^2

Since these partial derivatives are equal, the vector field is conservative. We can then find a potential function by integrating each component with respect to their respective variable:

φ(x,y) = 11x^3y^2 + 11x^2y^2 + C

where C is the constant of integration.

Therefore, the vector field f(x,y) = 33x^2y^2i + 22x^3yj is conservative, and its potential function is φ(x,y) = 11x^3y^2 + 11x^2y^2 + C.

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The probability that the white ball was drawn from urn 1 given that a white ball was drawn is approximately 0.654. Here we use Bayes' theorem P(A|B) = P(B|A) * P(A) / P(B).

Let A be the event that urn 1 was chosen, and B be the event that a white ball was drawn. We want to find P(A|B), the probability that urn 1 was chosen given that a white ball was drawn. Using Bayes' theorem, we have:

P(A|B) = P(B|A) * P(A) / P(B)

where P(B|A) is the probability of drawing a white ball given that urn 1 was chosen, P(A) is the probability of choosing urn 1, and P(B) is the probability of drawing a white ball (regardless of which urn was chosen).

We can compute these probabilities as follows:

P(B|A) = 3/8 (since urn 1 has 3 white balls out of 8 total balls)

P(A) = 1/2 (since each urn is equally likely to be chosen)

P(B) = P(B|A) * P(A) + P(B|A') * P(A') = (3/8 * 1/2) + (1/4 * 1/2) = 5/16

where A' is the event that urn 2 was chosen.

Plugging these values into Bayes' theorem, we get:

P(A|B) = (3/8 * 1/2) / (5/16) = 0.654

Therefore, the probability that the white ball was drawn from urn 1 given that a white ball was drawn is approximately 0.654.

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Given:

Number of students who has a cat and a dog = 5

Number of students who has a cat but do not have a dog = 11

Number of students who has a dog but do not have a cat = 3

Number of students who neither have a cat nor a dog = 2

To find:

The probability that a student has a cat given that they do not have a dog.

Solution:

Let the following events:

A = Student has a cat

B = Do not have a dog

Total number of outcomes is:

\(5+3+11+2=21\)

The probability that a student has a cat but do not have a dog is:

\(P(A\cap B)=\dfrac{11}{21}\)

The probability that a student do not have a dog is:

\(P(B)=\dfrac{11+2}{21}\)

\(P(B)=\dfrac{13}{21}\)

The conditional probability is:

\(P\left(\dfrac{A}{B}\right)=\dfrac{P(A\cap B)}{P(B)}\)

\(P\left(\dfrac{A}{B}\right)=\dfrac{\dfrac{11}{21}}{\dfrac{13}{21}}\)

\(P\left(\dfrac{A}{B}\right)=\dfrac{11}{13}\)

Therefore, the probability that a student has a cat given that they do not have a dog is \(\dfrac{11}{13}\).

The two of the recurring decimals below that are equivalent include 0.686.

The base-10 number system, probably the most widely used number system, is referred to as decimal. One type of number that has a whole number and a fractional component separated by a decimal point is a decimal. The decimal point is a dot that appears between the parts of a whole number and a fraction.

On the other hand, a fraction appears in the numerator or the denominator of a complex fraction. It should be noted that based on the information, 0.686 is recurring.

Repeating decimal or recurring decimal is decimal representation of a number whose digits are periodic and the infinitely repeated portion is not zero

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The missing value, rounded to the nearest hundredth, is approximately 54.46 degrees.

The equation sin ___ = 7/12 suggests that we need to find an angle whose sine is equal to 7/12. To determine the missing value, we can use the inverse sine function, also known as arcsine or sin^-1.

Using the inverse sine function, we can write the equation as ___ = sin^-1(7/12). Evaluating this expression with a calculator or a trigonometric table, we find that sin^-1(7/12) is approximately 54.46 degrees.

It's important to note that trigonometric functions have periodicity, meaning that there are multiple angles that have the same sine value. Therefore, there are other angles, such as 180 degrees minus 54.46 degrees, that also satisfy sin ___ = 7/12. However, when finding a single missing value, we typically consider the principal value within a specified range, often from -90 degrees to 90 degrees.

Thus, rounding to the nearest hundredth, the missing value that satisfies sin ___ = 7/12 is approximately 54.46 degrees.

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Answer:

The number in the green box should be, 11

in scientific notation, we get the number,

\((9.32)(10)^{11}\)

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

Look at the blue number 9.32. The decimal point is in between the 9 and the three. On the problem the decimal point is at the very end after the last zero, all the way to the right. It is understood, that means it's not written. So how many hops does it take to get the decimal from the end all the way over to in between the nine and the three? It takes 11 moves. The exponent is 11

Answer:

31.5

Step-by-step explanation:

Answer:

the point of intersection would be (2,2)

The point of intersection is at (2, 2)

A linear equation is given by:

y = mx + b;

where y, x are variables, m is the slope of the line and b is the y intercept.

Given the line with equations:

y = 3 x − 4  and y = 1/ 2x + 1

Plotting the graphs using geogebra online tool, the point of intersection is at (2, 2)

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Answer:

4.5%

Step-by-step explanation:

Simple interest:

I = Prt

112.5 = 1250(r)(2)

1250r = 56.25

r = 0.045 = 4.5%

Answer: 4.5%

Answer:

_____________

The integer is 0

Answer:

−3x^2+2x /x−2

Step-by-step explanation:

4x−9x^3/ 3x^2−4x−4

=  −9x^3+4x /3x^2−4x−4

=  x(−3x+2)(3x+2) /(3x+2)(x−2)

=  −3x^2+2x /x−2

Answer:

6:5

Step-by-step explanation:

Bubble algae cells can grow up to 5 cm in diameter. Calculate the surface area : volume ratio of this cell.

The algae is spherical in nature

Volume of the algae =4/3 pi r³

Volume of the algae = 4/3×pi×2.5³

Volume of the algae = 62.5/3 pi

Surface area = 4pi r²

Surface area = 4pi ×2.5²

Surface area = 25pi

Taking their ratio

surface area : volume ratio

= 25pi:62.5/3 pi

= 25 × 3/62.5

= 1.2

Hence the required ratio is 12/10 which is 6:5

Answer:

he bought 45 shrubs. Let me know if this worked for you.

Step-by-step explanation:

Answer:

$530.50 - $193 = $337.5

$337.5 ÷ 4.5 = $75

After interpreting the given data we come to the conclusion that the conversion of the given standard form to vertex form is y = 2(x - 2)² - 4.

In order to convert the quadratic equation from standard form to vertex form, we have to complete the square.
2x² - 8x + 4 = 2(x² - 4x) + 4
Now we have to add and subtract a constant inside the parenthesis so that we can factorize it into a perfect square.
The constant we need to add is (b/2a)².
For this case,
a = 2 and b = -8.
2(x² - 4x + 4) - 8 + 4 = 2(x - 2)² - 4
Hence, the vertex form of the quadratic equation is:
y = 2(x - 2)² - 4
The vertex of this parabola is (2,-4).
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Answer:

-5.13

Step-by-step explanation:

Step-by-step explanation:

ABD+DBC=180°

x+80°=180

x=100°

The reflexive closure of a relation on a set is the smallest reflexive relation that contains the original relation. In other words, it is the addition of pairs that ensure every element in the set is related to itself. To form the reflexive closure, we need to add pairs that relate each element in the set to itself.

To form the reflexive closure of relation r on the set {0, 1, 2, 3}, we need to add ordered pairs that ensure every element in the set is related to itself. In other words, we need to add pairs of the form (x, x) for each element x in the set that is not already present in relation r.

In this case, the reflexive closure of relation r would require adding the following ordered pairs: (0, 0), (1, 1), (2, 2), and (3, 3). These pairs ensure that every element in the set {0, 1, 2, 3} is related to itself, making the relation reflexive. These pairs ensure that every element is related to itself, satisfying the reflexivity property.

By adding these additional ordered pairs, we have modified relation r to include reflexivity, as every element now has a direct relation to itself in the set.

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The fraction is the ratio number of parts taken to the total number of item. The fraction of lasagna eaten by the guests is 2¹/₅ and the decimal is 2.2.

You have made 3 pans of lasagna. Each pan have 10 pieces. So overall you have 30 pieces of lasagna.

Guest ate 22 pieces.

So fraction of pieces they eat = Number guests eat/ total pieces = 22/30

If we are considering the number of pans, it is number guest eat/ total pieces per pan.

The number of pans of lasagna guest eat will be 2 complete pans and 2/10 out of the third pan.

So the mixed fraction will be 2 + 2/10 = 2¹/₅

The decimal  is 2 + 2/10 = 2+ 0.2 = 2.2

So the mixed fraction is 2¹/₅ and decimal is 2.2

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Answer:

11

Step-by-step explanation:

Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line (i.e. the transversal).

Based on the definition of similar quadrilaterals, the measure of side MN is: 14.1 units.

If two quadrilaterals are similar to each other, then the measure of their corresponding sides will have a ratio that is equal. This means they will have proportional side measures.

Since we are told that quadrilaterals GHIJ and KLMN are similar to each other, then their corresponding sides will have measures that are proportional to each other.

Therefore:

IJ/MN = GJ/KN

IJ = 35

MN = ?

GJ = 52

KN = 21

Substitute:

35/MN = 52/21

Cross multiply:

MN(52) = (35)(21)

MN(52) = 735

MN = 735/52

MN = 14.1 units

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The Z-score for Boris is 1.627, and the Z-score value for the Callie is 1.267, Boris scored higher relatively.

The Z test is a parametric procedure that is used on data that is dispersed in a normal fashion. For testing hypotheses, the z test can be used on one sample, two samples, or proportions. When the population variance is known, it analyzes if the means of two big groups are dissimilar.

We know the formula for the Z-test:

\(\rm Z = \dfrac{X-\mu}{\sigma}\)

(a) For Boris:

\(\rm Z = \dfrac{67-60}{4.3}\)

Z = 1.627

(b) For Callie:

\(\rm Z = \dfrac{119-110}{7.1}\)

Z = 1.267

(c) Since the measures of two different data have been set to one measure and the value of the Z-score for Boris is higher relative to the Z-score value of Callie so Boris scored higher relatively.

Thus, the Z-score for Boris is 1.627, and the Z-score value for the Callie is 1.267, Boris scored higher relatively.

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