the equation of the tangent line at (0,π/2) for x²y + sin y + 4/π y = 3eˣ

let thee present age be x.

(x-15)^2=x+15

=>x^2–31*x+210=0

=>(x-21)(x-10)=0

x=10 or x=21

present age can not be 10 as it would result at absurd negative age( -5) 15 years ago.

so present age is 21.

Let $C$ be the event that the camera gets a 10% discount, $G$ be the event that the game gets a 25% discount, and $N$ be the event that neither item gets a discount. Then the probability of each event is:

\begin{align*}

P(C) &= 0.35\cdot 0.1 = 0.035 \\

P(G) &= 0.05\cdot 0.25 = 0.0125 \\

P(N) &= 0.6\cdot 1 = 0.6

\end{align*}

The amount saved on the camera is $0.1\cdot 200=20$, and the amount saved on the game is $0.25\cdot 80=20$. So, we want to find the probability that either event $C$ or $G$ occurs. Since the events are mutually exclusive, we can use the addition rule:

$$

P(C\text{ or }G) = P(C) + P(G) = 0.035 + 0.0125 = 0.0475

$$

The amount saved in dollars at the cash register is $X = 20 + 20 = 40$. To find the probability that the total amount saved is $20$, we need to sum the probabilities of all the ways to get $X=20$. There are two ways to do this: either the camera gets a 10% discount while the game gets no discount, or the game gets a 25% discount while the camera gets no discount. Using the multiplication rule and the probabilities above, we have:

\begin{align*}

P(\text{camera gets 10% discount, game gets no discount}) &= P(C)\cdot P(N) = 0.035\cdot 0.6 = 0.021 \\

P(\text{game gets 25% discount, camera gets no discount}) &= P(G)\cdot P(N) = 0.0125\cdot 0.6 = 0.0075

\end{align*}

Therefore, the probability that the total amount saved is $20$ is:

$$

P(X=20) = P(\text{camera gets 10% discount, game gets no discount}) + P(\text{game gets 25% discount, camera gets no discount}) = 0.021 + 0.0075 = 0.0285

$$

So the chance you save a total of $20$ is $\boxed{0.0285}$.

To learn more about probability refer below:

https://brainly.com/question/32004014

#SPJ11

1) find total frequency

\(=172+190+128+172+58\\=720\)

2) divide each frequency by the total frequency

UK:

= 172 / 720

= 0.2388888889

Europe:

= 190 / 720

= 0.2638888889

USA:

= 128 / 720

= 0.1777777778

Africa:

= 172 / 720

= 0.2388888889

Other:

= 58 / 720

= 0.0805555556

3) multiply value by 360:

UK:

= 360 x 0.2388888889

= 86 degrees

Europe:

= 360 x 0.2638888889

= 95 degrees

USA:

= 360 x 0.1777777778

= 64 degrees

Africa:

= 360 x 0.2388888889

= 86 degrees

Other:

= 360 x 0.0805555556

= 29 degrees

Plans drawn for a flower garden show a triangular-shaped area with two rock walls meeting at a right angle. The length of one of the walls is fifteen feet. If d represents the length of the other wall,  d = √175 ft. This can be solved using the concept of Pythagoras theorem.

The Pythagoras formula is used to calculate the area of a right-angled triangle. It asserts that the hypotenuse's square is equal to the sum of its other two sides' squares. (Hypotenuse)² = (Base)² + (perpendicular)² is the Pythagorean formula.

As we know from Pythagoras theorem,

(Hypotenuse)² = (Base)² + (perpendicular)²

d² + 15² = 20²

d² + 225 = 400

d² = 400 - 225

d² = 175

d = √175 ft.

To know more about Pythagoras theorem refer to:

https://brainly.com/question/343682

#SPJ1

The complete question is as follows:

Plans drawn for a flower garden show a triangular-shaped area with two rock walls meeting at a right angle. The length of one of the walls is fifteen feet.

If d represents the length of the other wall, what is d?

Answer:

a

Step-by-step explanation:

From a group of two girls and five boys, all of the various ages, two pupils are randomly selected. The likelihood that the two selected students will be boys is 10/21.

In probability theory and other branches of mathematics, the term "combination" designates a series of results in which the order of the results is irrelevant.

Here given the total number of girls is 2 and boys is 5. Then, the total number of students is 7. The number of ways of selecting 2 students from 7 students is,

\(\begin{aligned}n(S)&=\frac{7C2}{2}\\&= \frac{7\times6}{2}\\&=\text{21 ways}\end{aligned}\)

The number of ways of selecting 2 boys from 5 boys is,

\(\begin{aligned}n(E)&=\frac{5C2}{2}\\&=\frac{5\times4}{2}\\&=\text{10 ways}\end{aligned}\)

Then, the required probability is calculated as,

\(\begin{aligned}P(E)&=\frac{n(E)}{n(S)}\\&=\frac{10}{21}\end{aligned}\)

Therefore, the required answer is 10/21.

The complete question is -

Two students are chosen at random from a group of two girls and five boys, all of the different ages. Find the probability that the two students chosen will be: two boys

To know more about the combination:

https://brainly.com/question/11234257

#SPJ4

Answer:

Yes

Step-by-step explanation:

they are both equal to 3:4

21:28 can be reduced by 7

21/7=3

28/7=4

and 6:8 can be reduced by 2

6/2=3

8/2=4

Answer:

180 pesos

Step-by-step explanation:

divide 900 by 5

Answer:

5%

Step-by-step explanation:

Let x represent the percentage of people that have gone to both the park and the beach.

The percentage of people that have gone only to the amusement park = 80% - x% = 80 - x

The percentage of people that have gone only to the beach = 45% - x% = 45 - x

Therefore:

100% = (80 - x) + (45 - x) + (x) + (15)

100 = 80 + 45 + 15 -x - x + x

100 = 140 - x

x = 140 - 100

x = 40%

Therefore 40% of the students have gone to both the park and the beach.

The probability that the student has gone to the beach but not to an amusement park = 45% - 40% = 5%

Answer:

The equation of the line is y = \(\frac{4}{3}\) x + 2

Step-by-step explanation:

The form of the equation that passes through two points (x1, y1) and (x2, y2) is y = m x + b, where

Let us solve the question:

∵ The line passes through the points (-3, -2) and (3, 6)

∴ x1 = -3 and x2 = 3

∴ y1 = -2 and y2 = 6

→ Use the rule of m to find it

∵ \(m=\frac{6-(-2)}{3-(-3)}=\frac{6+2}{3+3}=\frac{8}{6}\)

→ Simplify it by dividing up and down by 2

∴ m = \(\frac{4}{3}\)

→ Substitute its value in the form of the equation above

∴ y = \(\frac{4}{3}\) x + b

→ To find b substitute x and y by x1 and y1

∴ -2 = \(\frac{4}{3}\) (-3) + b

∴ -2 = -4 + b

→ Add 4 to both sides

∴ -2 + 4 = -4 + 4 + b

∴ 2 = b

→ Substitute it in the form of the equation

∴ y = \(\frac{4}{3}\) x + 2

∴ The equation of the line is y = \(\frac{4}{3}\) x + 2

The percentage gain of the company is calculated to be 10%.

The percentage gain is calculated by multiplying the fraction of the gain and the initial amount by 100.

we shall calculate for the percentage gain of the company as follows:

gain = $33 - $30 = $3

initial amount = $30

percentage gain = ($3/$30) × 100

percentage gain = (1/10) × 100

percentage gain = 10%

Therefore, the percentage gain of the company is calculated to be 10%.

Know more about percentage here:https://brainly.com/question/843074

#SPJ1

Answer:

√(564×564)=√564²=±564

Answer:

\(±564.\)

Step-by-step explanation:

\( \sqrt{564 \times 564} \)

\( \sqrt{ {564}^{2} } \)

\(±564.\)

The given argument is invalid. It says that if one person has more gray hair in their beard than another person, then they have a higher percentage of gray hair in their beard.

The argument is invalid because it is possible for one person to have a higher percentage of gray hair in their beard but a lower number of gray hairs in total.One possible counterexample by model is:Suppose Plato has 200 hairs in his beard and 50 of them are gray. So, 1/4 of his hairs are gray. Now, let's suppose Aristotle has 400 hairs in his beard, and 300 of them are gray. So, 3/4 of his hairs are gray. Even though Plato has fewer gray hairs than Aristotle, his percentage of gray hairs is more significant (1/4) than Aristotle's (3/4).

Therefore, the given argument is invalid since Aristotle's beard contains more gray hairs in quantity, but Plato has a higher percentage of gray hair in his beard.

Learn more about argument here:

brainly.com/question/2645376

#SPJ11

Answer:

no

Step-by-step explanation:

because the number of student tickets 160 is higher than the number of adult tickets 80 and the information tells us that the adult tickets were twice the amount of student tickets sold. If the numbers were swapped to be adult=160 and student=80 then it would be correct.

sorry for the long explanation especially if you find it confusing

Answer:

The 20th term in the expansion of (a + b)^22 can be found using the binomial theorem. The general term in the expansion of (a + b)^n is given by:

T_r = (n choose r) a^(n-r) b^r

where (n choose r) is the binomial coefficient, which is equal to n! / (r! (n-r)!).

Therefore, the 20th term in the expansion of (a + b)^22 is:

T_20 = (22 choose 20) a^(22-20) b^20

= (22 choose 20) a^2 b^20

Using the formula for the binomial coefficient, we have:

(22 choose 20) = 22! / (20! 2!) = (22*21) / 2 = 231

Substituting this value into the expression for T_20, we get:

T_20 = 231 a^2 b^20

Therefore, the 20th term in the expansion of (a + b)^22 is 231 a^2 b^20.

Step-by-step explanation:

Given the expression

\(-3m - [2m + (5 - m)] + 7\)

Step one

Firstly we have to open the inner bracket we have

\(-3m - [2m + 5 - m] + 7\)

Step two

we proceed further by opening up the next bracket we have

\(-3m - 2m -5 +m+ 7\)

Step three

we then have to collect like terms of m and rearrange.

\(=-3m - 2m+m -5+ 7\\=-4m+2\\=2-4m\)

The value of an excel formula that will square this number is,

⇒ N²

We have to given that;

A number is stored in cell a1.

Hence, We can formulate;

Type = N² into the empty cell, in which N is a cell reference that contains the numeric value you want to square.

And, We also get;

To display the square of the value in cell A1 into cell B1,

We can type = A1² into cell B1.

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

The nutritionist should use a statistical hypothesis test to determine if the average total cholesterol level of the population is significantly higher than the ideal standard. The test will compare the average of the 25 women to the ideal standard

The nutritionist should use a statistical hypothesis test to compare the average cholesterol of the 25 women to the ideal standard of 200 mg/dl. To do this, the nutritionist will first determine the null hypothesis, which is that the average total cholesterol of the population of women in her area is not significantly different from the ideal standard. Then, the nutritionist will calculate the test statistic, which is the difference between the average cholesterol of the 25 women and the ideal standard, divided by the standard deviation of the sample population. This test statistic will be compared to a predetermined significance level and if it is greater than this level, it will be considered statistically significant. If the test statistic is found to be statistically significant, the nutritionist can conclude that the population has a higher average cholesterol than the ideal standard.

Learn more about average here

https://brainly.com/question/24057012

#SPJ4

The formula for the volume of a cone, V = (1/3)·π·r²·h, indicates that doubling the radius, quadruples the volume while doubling the height doubles the volume. Therefore;

A cone is a three dimensional figure formed by lines that extend between a point and the circumference of the circular base, where the point is located on the a line perpendicular to and passing through the center of the circular base.

The formula for the volume of a cone is; V = (1/3) × π × r² × h

Where;

V = The volume of the cone

r = The radius of the cone

h = The height of the cone

Therefore;

When the radius is doubled, we get;

V₁ = (1/3) × π × (2·r)² × h = (1/3) × π × 4 × r² × h = 4 × (1/3) × π × r² × h

When the radius of the cone is doubled, the volume of the cone increases 4 times the initial volume

When the height of the cone is doubled, we get;

V₂ = (1/3) × π × r² × 2·h = 2 × (1/3) × π × r² × h = 2·V

When the height of the cone is doubled, the volume of the cone is doubled.

Therefore, doubling the radius of the cone which increases the volume to four times the initial volume has the greater effect on the volume of the cone than doubling the height which doubles the volume of the cone.

Learn more on the volume of a cone here: https://brainly.com/question/22757327

#SPJ1

Using the arithmetic operation of division -

a) 3 people can be fed by 1 pizza.

b) Maria would need 11 pizzas for 33 people.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

The number of pizzas ordered = 8

The number of people are = 24.

Number of people that can be fed if 1 pizza was there =

Number of people = Number of people that came/ Number of pizza

Use the arithmetic operation of division -

Number of people = 24/8

Number of people = 3

Therefore, 3 people can be fed.

Now, the number of people = 33

Number of pizzas required for 33 people can be obtained as -

Use the arithmetic operation of division -

Number of pizzas = Number of people/ Number of people fed by 1 pizza

Number of pizzas = 33/3

Number of pizzas = 11

Therefore, Maria will require 11 pizzas.

To learn more about arithmetic operation from the given link

https://brainly.com/question/20628271

#SPJ1

From the figure, you can see that ∠3 and ∠4 are supplementary because they are linear pairs.

Answer:

Linear pair

Step-by-step explanation:

Angle 3 and angle 4 form a linear pair. The measure of angle 3 is four more than three times the measure of angle 4.

Your Best Friend

s183960

The term "distance" can refer to different types of measuring  depending on the context. In general, distance is a numerical value that indicates the amount of separation between two objects or points in space.

In mathematics, distance usually refers to the length of a line segment connecting two points in a Euclidean space. The distance can be measured using various formulas, such as the Pythagorean theorem, which computes the length of the hypotenuse of a right triangle formed by the two points and the origin.

In physics, distance can refer to the separation between two objects in three-dimensional space, often measured in meters or kilometers.

In computer science and data analysis, distance can refer to a measure of similarity or dissimilarity between two objects or data points. For example, the Euclidean distance, Manhattan distance, or cosine distance can be used to quantify the difference between two vectors or sets of features.

In general, the meaning of the distance value depends on the specific context and the type of measurement being used.

To know more about Distance visit:

https://brainly.com/question/28551043

#SPJ4

The equation in point slope form and standard form are as follows:

The line passes through (2, -1) and (8, 4). The equation of the line in point slope form and standard form can be represented as follows;

Therefore, in point slope form,

y - y₁ = m(x - x₁)

where

Therefore,

slope = m = 4 + 1 / 8 - 2

m = 5 / 6

Hence, using (2, -1)

y + 1 = 5 / 6(x - 2)

In standard form,

y + 1 = 5 / 6 x - 10 / 6

y - 5 / 6 x = - 10 / 6 - 1

y - 5 / 6 x = - 8 / 3

multiply through by 6

6y - 5x = - 16

Therefore,

- 5x + 6y = - 16

learn more on equation here: https://brainly.com/question/29041142

#SPJ1

Answer:

$10.75

Step-by-step explanation:

calculator

Answer:

10.75 for deltamath

In statistical hypothesis testing, the P-value is a significant factor. It is the probability of obtaining a test statistic at least as extreme as the one calculated from the data, assuming the null hypothesis to be true. If the null hypothesis is false, the P-value is the probability of a type I error. It is the probability of rejecting the null hypothesis when it is true.

To interpret the P-value correctly, a P-value of 0.054 means that if the null hypothesis is correct, there is a 5.4% probability that the sample will produce a test statistic as extreme as, or more extreme than the one that was observed. If the calculated P-value is higher than the significance level, which is usually 0.05 or 0.01, we cannot reject the null hypothesis.

In the given situation, the sample provides insufficient evidence to reject the owner's claim that the mean weight of Gala apples this year is heavier than usual because the calculated P-value is higher than the significance level. Hence, the correct option is that the P-value suggests that there is not sufficient evidence to reject the null hypothesis.

Know more about null hypothesis here:

https://brainly.com/question/28920252

#SPJ11

The cost of each window, rounded to the nearest dollar is $280.

Estimation of a number is a reasonable guess of the actual value to make calculations easier and realistic.

Estimation means approximating a quantity to the required accuracy.

This is obtained by rounding off the numbers involved in the calculation and getting a quick and rough answer.

The total cost = $5820

Number of windows = 28

Cost of one window = 5820/28

Cost of one window = $208 (estimated)

Learn more about estimation: https://brainly.com/question/28416295

#SPJ1

0.003 is the probability that the number of calls among the 25 that involve a fax transmission exceeds the expected number by more than 2 standard deviations

To calculate the probability that the number of calls among the 25 that involve a fax transmission exceeds the expected number by more than 2 standard deviations.The mean is the expected number of calls involving a fax transmission, while the standard deviation is the measure of variability in the distribution. We then use this information to calculate the probability of exceeding the expected number by more than 2 standard deviations, which can be done using the z-score formula. The z-score for values more than 2 standard deviations away from the mean is 2.33, which corresponds to a probability of 0.003. Thus, the probability that the number of calls among the 25 that involve a fax transmission exceeds the expected number by more than 2 standard deviations is 0.003.

Learn more about probability here

https://brainly.com/question/11234923

#SPJ4

The amount budgeted for dances is approximately $380.00.

Assume that "x" is the budgeted sum for dances. The problem states that there is a 5:7 ratio between the budget for dances and the budget for charitable activities. Hence, we can write:

x/532 = 5/7

We can cross-multiply and simplify to find the answer for "x"

7x = 532 × 5

7x = 2660

x = 2660/7

x ≈ 380.00

The estimated $380.00 planned money for dances is the result.

To know more about Budget visit:

https://brainly.com/question/14196340

#SPJ9

"It can vary - it really depends on the distribution of the variable."

The number of intervals, or bins, to choose when creating a histogram can vary depending on the distribution of the variable.

Most often, about 8-10 intervals are used, but there is no set rule. It is generally recommended to have at least 5 intervals, but if the data is highly skewed or has outliers, more intervals may be needed to accurately represent the distribution.

Ultimately, the goal is to choose a number of intervals that provides a clear visual representation of the data without oversimplifying or overcomplicating the histogram.

The number of intervals or bins to be chosen when creating a histogram can vary and it really depends on the distribution of the variable.

While most often, about 8-10 bins are used, there is no hard and fast rule for the number of bins to be used in a histogram.

In general, the number of bins should be large enough to display the shape of the distribution clearly, but not so large that it obscures important features of the distribution or leads to overfitting.

A minimum of 5 bins is recommended to display the basic shape of the distribution, but more bins may be necessary for complex or multi-modal distributions.

Depending on the distribution of the variable, a histogram's number of intervals or bins can be altered.

There is no established guideline, however 8–10 intervals are typically utilized.

A minimum of five intervals are often advised, however if the data is extremely skewed or contains outliers, more intervals could be required to correctly depict the distribution.

For similar questions on variable.

https://brainly.com/question/27894163

#SPJ11