If θ is an angle in standard position and its terminal side passes through the point (-8,9), find the exact value of \tan\thetatanθ in simplest radical form.

Answer:

\(f(x)=2x^2+2x-4\)

Step-by-step explanation:

De acuerdo con la información el frutero debe vender 20 cajas de fruta para ganar 600 euros.

Para calcular cuántas cajas debe vender el frutero para ganar 600 euros debemos tener en cuenta la información. EN este caso el frutero compra cada caja de 15kg por 22 euros y las vende en porciones de 1kg a 2 euros. Esto significa que por cada caja invierte 22 euros y gana 30 euros.

Entonces, si queremos saber cuántas cajas debe vender para ganar 600 euros debemos dividir este número en la ganancia que obtiene por caja. Entonces:

600 / 30 = 20

Por lo anterior, podemos concluir que debe vender 20 cajas para obtener 600 euros.

English version

According to the information, the greengrocer must sell 20 boxes of fruit to earn 600 euros.

To calculate how many boxes the greengrocer must sell to earn 600 euros, we must take the information into account. In this case, the greengrocer buys each 15kg box for 22 euros and sells them in 1kg portions for 2 euros. This means that for each box you invest 22 euros and earn 30 euros.

So, if we want to know how many boxes he must sell to earn 600 euros, we must divide this number into the profit he gets per box. So:

600 / 30 = 20

From the above, we can conclude that you must sell 20 boxes to obtain 600 euros.

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Answer:

{5}

Step-by-step explanation:

intersection means what's common in both sets

Answer:

{5} shows the intersection of A and B

The side length is 5 units, and the area is 25 square units

The area of a shape is the amount of space it occupies

The area of a square is the product of its dimensions

From the graph, the coordinates of the square can be assumed to be:

\(A = (0,0)\)

\(B = (4,3)\)

The side length of the square is then calculated using the following distance formula

\(d = \sqrt{(x_2- x_1)^2 + (y_2 -y_1)^2}\)

So, we have:

\(AB = \sqrt{(0 - 4)^2 + (0-3)^2}\)

\(AB = \sqrt{25}\)

\(AB = 5\)

The area of the square is the calculated as:

\(Area = AB^2\)

This gives

\(Area = 5^2\)

\(Area = 25\)

Hence, the side length is 5 units, and the area is 25 square units

See attachment for the diagram of the shape

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The number of small rooms reserved is 4.

The number of large rooms reserved is 8.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Small rooms are denoted as S.

Large rooms are denoted as L.

Now,

We will make two equations.
L = 2S _____(1)

8L + 6S = 88 ______(2)

Putting (1) in (2) we get,

8L + 6S = 88

8 x (2S) + 6S = 88

16S + 6S = 88

22S = 88

S = 88/22

S = 8/2

S = 4

Now,

Putting S = 4 in (1) we get,

L = 2 x 4

L = 8

Thus,

The number of small rooms and large rooms reserved is 4 and 8.

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The probability that the chosen ball is blue is 55.3%.

If the chosen ball is blue, the probability would be 3.33% that it came from the first urn.

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.

(a) To find P(A|B1), we use the formula P(A|B) = P(A and B)/P(B).

In this case, P(A and B1) is the probability of choosing a blue ball from the first urn, which is 7/20.

The probability of choosing the first urn is 1/2, so P(B1) = 1/2.

Plugging these values into the formula gives us P(A|B1) = (7/20)/(1/2) = 14/20 = 7/10.

To find P(A|B2), we use the same formula.

In this case, P(A and B2) is the probability of choosing a blue ball from the second urn, which is 14/19.

The probability of choosing the second urn is 1/2, so P(B2) = 1/2.

Plugging these values into the formula gives us P(A|B2) = (14/19)/(1/2) = 28/19.

To find P(A and B2), we use the formula P(A and B) = P(A|B) * P(B).

In this case, we already know that P(A|B2) = 28/19 and P(B2) = 1/2, so P(A and B2) = (28/19) * (1/2) = 28/38.

To find P(A or B2), we use the formula P(A or B) = P(A) + P(B) - P(A and B).

In this case, P(A) is the probability of choosing a blue ball overall, which is 21/38.

P(B2) is the probability of choosing the second urn, which is 1/2.

P(A and B2) is the probability of choosing a blue ball from the second urn, which is 28/38.

Plugging these values into the formula gives us P(A or B2) = 21/38 + 1/2 - 28/38 = 15/38.

The probability that the chosen ball is blue is P(A) = 21/38 = 55.3%.

(b) If the chosen ball is blue, the probability that it came from the first urn is P(B1|A) = P(B1 and A)/P(A).

We already know that P(B1 and A) is the probability of choosing a blue ball from the first urn, which is 7/20.

We also know that P(A) is the probability of choosing a blue ball overall, which is 21/38.

Plugging these values into the formula gives us P(B1|A) = (7/20)/(21/38) = 7/21.

This probability is equal to 33.3%.

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If for every amount of $d , $0.20d is tipped, then for amount of $56, $11.6 will be tipped to the waiter

A rate is a special ratio in which the two terms are in different units. For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces. This is not a ratio of two like units, such as shirts. This is a ratio of two unlike units: cents and ounces.

If for every $d , $0.20d is tipped, then this means that the total amount spent is $56 and the amount Anthony's family tip the waiter is calculated as:

0.2 × 56

= $11.6

Therefore the waiter was tipped $11.6

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Answer:

A dinner bill of d dollars calls for a tip of 0.20d dollars. You want to find how much the family tipped the waiter for a bill of d=$56.

Evaluate the expression 0.20d for d=56.

0.20d

=

0.20(56)

=

11.2

The family tipped the waiter $11.20.

Answer:

Step-by-step explanation:

Perimeter:  

     \(P=(x+y+z) \ cm\)

Semi-perimeter:

     \(SP=\frac{1}{2} (x+y+z) \ cm\)

Answer:

3 × 27

=81

mark BRAINLIEST pls

Answer:

54

Step-by-step explanation:

cause a cub has 4 sides so each side is 54

Answer:

The length of a side is 6.

Step-by-step explanation:

Since, the volume of a cube is equal to l*w*h.

V=l*w*h

Volume is equal to side cubed.

V=s^3

Cube 216 to get 6.

216=s^3

3^√216=s

Answer: 6

The probability that exactly 3 out of 4 people chosen at random favor the new building project is 0.2904.

This problem can be solved using the binomial probability formula. Let X be the number of people who favor the new building project out of the 4 chosen at random. Then X follows a binomial distribution with parameters n = 4 and p = 0.45.

The probability of having exactly k people who favor the new building project out of 4 is given by:

P(X = k) = (4 choose k) * \(0.45^{k}\) * \(0.55^{4-k}\)

where (4 choose k) is the binomial coefficient.

To find the probability that exactly 3 of the 4 people favor the new building project, we substitute k = 3 in the above formula and evaluate:

P(X = 3) = (4 choose 3) * \(0.45^{3}\) * \(0.55^{1}\)

= 0.290384375

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The interest is 16% compounded semi-annually, is Rs. 121,179.10.

To determine how much money needs to be deposited now to provide a payment of Rs. 15,000 at the end of each half year for 10 years, we will use the formula for the present value of an annuity.

Present value of an annuity = (Payment amount x (1 - (1 + r)^-n))/rWhere:r = interest rate per compounding periodn = number of compounding periodsPayment amount = Rs. 15,000n = 10 x 2 = 20 (since there are 2 half years in a year and the payments are made for 10 years)

So, we have:r = 16%/2 = 8% (since the interest is compounded semi-annually)Payment amount = Rs. 15,000Using the above formula, we can calculate the present value of the annuity as follows:

Present value of annuity = (15000 x (1 - (1 + 0.08)^-20))/0.08 = Rs. 121,179.10Therefore, the amount that needs to be deposited now to provide payment of Rs. 15,000 at the end of each half year for 10 years, if the interest is 16% compounded semi-annually, is Rs. 121,179.10.

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The corresponding rectangular coordinates for point Q is (-3√3, 3)

To convert polar coordinates  (r, θ) to rectangular coordinates  (x, y). Use the following relations:

x = rcosθ

y = rsinθ

We have:

(r, θ) = (6, 5π/6)

x = 6 cos (5π/6)

x = 6 * -√3/2

x =  -3√3

y = 6 sin (5π/6)

y = 6 * 1/2

y = 3

Therefore, the corresponding rectangular coordinates for point Q is (-3√3, 3)

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The measure of angle DCE in this problem is given as follows:

m < DCE = 22.5º.

The triangles in this problem are right triangles, meaning that the trigonometric ratios are used to find the measures.

The three trigonometric ratios are given as follows:

The segment DB is adjacent to angle of 38º, while the hypotenuse is of 12.2 cm, hence the length of segment DB is calculated as follows:

cos(38º) = DB/12.2

DB = 12.2 x cosine of 38 degrees

DB = 9.6 cm.

BE:ED = 3:1, means that segment DE is one-fourth of segment DB, and thus it's length is given as follows:

DE = 1/4 x 9.6

DE = 2.4 cm.

Then for the angle DCE, we have that the opposite side is of 2.4 cm while the adjacent side is of 5.8 cm, hence the tangent is used to find it's measure, as follows:

tan(x) = 2.4/5.8

x = arctan(2.4/5.8)

x = 22.5º

m < DCE = 22.5º.

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Answer:

x = 22.5°

Step-by-step explanation:

Answer:

7.96 × 10⁸ kg

Step-by-step explanation:

Step 1: Given data

Step 2: Determine how many more kilograms is the mass of the Golden Gate Bridge than the mass of the Eiffel Tower

To determine this ratio, we need to do the following subtraction.

mG - mE = 8.05 × 10⁸ kg - 9.16 × 10⁶ kg = 7.96 × 10⁸ kg

The Golden Gate Bridge has approximately 7.96 × 10⁸ kg more than the Eiffel Tower.

The answer is explained below.

In order to be considered a language, a system of communication must have vocabulary, grammar, syntax, and people who use and understand it. Mathematics meets this definition of a language. Linguists who don't consider math a language cite its use as a written rather than spoken form of communication.

Mathematics is pure language - the language of science. It is unique among languages in its ability to provide precise expression for every thought or concept that can be formulated in its terms. In a spoken language, there exist words, like "happiness", that defy definition.

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Answer: 283.3333333% (283.3%)

Step-by-step explanation:

First, lets turn 2 5/6 into and improper fraction. It becomes 17/6.

Now, we divide 17/6

17/6 = 2.833333333

Now, to turn it into a percent, we multiply it by 100, or move the decimal point 2 places to the right. That gives us 283.3333333% (283.3%)

Hope this helps!

Between 94 and 34 miles there are 60 miles

Between 83 and 76 hours there are 7 hours

Between 24 and 96 grams there are 72 grams

Answer:

18?

Step-by-step explanation:

An Annual is not an example of an agreement.

Let's use the distributive property on the left-hand side to expand and then simplify the whole equation. The process is shown below:

As you can see, they are basically the same for both sides!

Hence, no matter what value(s) you put in for x, it will ALWAYS be true!

Thus, this equation has infinite many solutions.

Correct Answer:

Infinitely many solutions

An 86% confidence interval for the difference in age to leave mother is -3.10091

What is confidence Interval?

The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. In statistics, confidence is another word for probability.

Given, Gorilla Baby sample

x means x bar here so, \(x_{1}\) = 3.21

\(s_{1}\) = 0.81

\(n_{1}\) = 64

Human Baby sample

x means x bar here so, \(x_{2}\) = 19.1

\(s_{2}\) = 2.16

\(n_{2}\) = 200

Confidence interval needs t score

t score = 1.18

86% confidence interval = \(x_{1}\) - \(x_{2}\) ± tc \(\sqrt{s^{2} {1} / n_{2} + s^{2} {2} / n_{2}\)

= 3.21 - 19.1 ± 1.18 √0.81²/64 +2.16²/200

= 3.21 - 19.1 ± 1.18 √0.033

= -3.10091

An 86% confidence interval for the difference in age to leave mother is -3.10091

The detail question is here,

A study based on the Association primate Ebmarah looked at the average age a baby gorilla leaves it’s mother versus the average age the human baby leaves it’s mother . Naturally they are different , so we don’t want a hypothesis test. Instead, find an  86% confidence interval  for the difference in age to leave mother.

Gorilla:

Sampled 64 babies

Stayed with mother on average 3.21 years

Standard deviation:  0.81

Human:

Sampled  200 babies

Stayed with mother on average 19.1 years

Standard deviation:  2.16

Matched  pairs  standard deviation :0.23

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Th two-way relative frequency table has been attached at the end of the solution. The relative frequencies were obtained by dividing each frequency by the total number of students (325).

Frequency refers to the number of times that a particular event or value occurs within a specific dataset or sample. In statistics, frequency is often used to represent the distribution of values in a dataset, and it can be displayed using tools such as frequency tables, histograms, or frequency polygons.

90 students are in a club and play a sport.

140 total students play a sport.

Therefore, 140 - 90 = 50 students play a sport but are not in a club.

The total number of students who play a sport is 140 + 50 = 190.

200 total students are in a club.

Therefore, 200 - 90 = 110 students are in a club but do not play a sport.

The total number of students who do not play a sport is 325 - 190 = 135.

The relative frequency of students who play a sport and are in a club is 90/325 = 0.277.

This table tends to show the proportion of students in each category and how they overlap with the other category. For example, we can see that 27.7% of the students play a sport and are in a club, while 15.4% of the students do not play a sport but are in a club. We can also see that 21.5% of the students play a sport but are not in a club, while 35.4% of the students do not play a sport and are not in a club.

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The total prorations for interest and property taxes to the nearest $100 are:

Proration for interest: $517

Proration for property taxes: $1,754

To calculate the total prorations for interest and property taxes, we need to determine how much the seller owes for each of these expenses up to the closing date of June 15.

First, let's calculate the daily interest rate on the mortgage. We can do this by multiplying the principal amount of the mortgage ($168,745.60) by the annual interest rate (8%) and then dividing by 365 (the number of days in a year):

Daily interest rate = ($168,745.60 x 0.08) / 365 = $36.94

Next, we need to determine the number of days from the start of the month (June 1) to the closing date (June 15):

Number of days = 15 - 1 = 14

Using the daily interest rate and the number of days, we can calculate the proration for interest:

Proration for interest = ($36.94 x 14) = $516.76

To calculate the proration for property taxes, we need to divide the annual property taxes ($3,893.25) by 365 to get the daily property tax rate:

Daily property tax rate = $3,893.25 / 365 = $10.65

Next, we need to determine the number of days from the start of the year to the closing date (June 15):

Number of days = 165

Using the daily property tax rate and the number of days, we can calculate the proration for property taxes:

Proration for property taxes = ($10.65 x 165) = $1,754.25

Therefore, the total prorations for interest and property taxes to the nearest $100 are:

Proration for interest: $517

Proration for property taxes: $1,754

These prorations will be subtracted from the seller's equity, since they are expenses that the seller owes up to the closing date.

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Answer:

Kukulcan

Step-by-step explanation:

it should be the letter c. Or kukulcan. This is because, Ferdinand Magellan is not a god of the Mayans and thats the same for b and c.

Therefore , the solution to the given problem of expression comes out to be -8 * 10³.

A number must be substituted for each variable and arithmetic operations must be carried out in order to verify an algebraic expression. The response variable is equivalent to 6 in the illustration above because 6 + 6 equals 12. The variables can be replaced with their values if we know what they are, and the expression can then be evaluated.

Here,

Given : - 8,000

To write -8000 with a power of 10

Thus,

-8000 written into

=> -8 * 10³

So, we get -8 * 10³ as the scientific notation for the given expression

Therefore , the solution to the given problem of expression comes out to be -8 * 10³.

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Since we want the difference between the people that aattended the fair on Friday and Saturday, we can substract 85446 from 60074 to get 25372

Therefore, 25372 more people attended the fair on saturday than on friday

Michelle opened her bank account on September 1st with $25 and continues to deposit $25 each month. Calculate the time Michelle will have a total of $500 in her account.

Answer:

19 months

Step-by-step explanation:

Initial deposit =$25

Monthly deposit = $25

Total deposit, y after x months can be modeled using the relation :

y = $25 + $25x

To have a total of $500 ; y = 500

$500 = $25 + 25x

$500 - $25 = $25x

$475 = $25x

x = $475 / $25

x = 19 months

Hence, Michelle will have deposited a total of $500 in his account after 19 months

\(\text{First I would recommend replacing the question mark with x}\\\text{We have two ratios, }\\\text{and we need to solve that hard-looking equation}\\\text{in terms of x}\)

\(\rule{300}{1.7}\)

\(\text{We can multiply x times 36:: 36x}\\\text{We can multiply 4 times 27:: 108}\)

\(\rule{300}{1.7}\)

\(\text{Now it's easier to solve for x:: 36x=108; x=3}\\\text{ (we divided by 36 on both sides of the = sign)}\)

\(\rule{300}{1.7}\)

\(\text{The missing number is 3}\)