Solve for x the equation 6cos^2 x+4sin^2 x=5.Forex 2 question 6 cos square x + 4 sin square x is equal to 5 ​

When Gracie distributes her carrots equally among the 5 bunnies, each bunny gets 7,878 whole carrots, and 3,939 whole carrots remain without being given to a bunny. These figures are whole numbers.According to the statement, Gracie has 5 pet bunnies that love to eat whole carrots. Gracie has 3,939 carrots to feed the bunnies, and she will use as many carrots as she can and give each bunny the same number.

To calculate the number of carrots each bunny will get:Total number of whole carrots ÷ Total number of bunnies = Number of whole carrots each bunny gets Gracie distributes the 3,939 carrots equally among the 5 bunnies, with each bunny getting 7,878 carrots. This is illustrated in the calculation below:3,939 ÷ 5 = 7,878Hence, the number of whole carrots each bunny gets is 7,878.

When it comes to the number of carrots that remain without being given to a bunny, we need to calculate it using the following formula:Total number of whole carrots − (Number of whole carrots each bunny gets × Total number of bunnies) = Number of whole carrots that remain without being given to a bunnyUsing the figures from the above calculations, the computation will be as follows:3,939 − (7,878 × 5) = 3,939 − 39,390 = -35,451. Therefore, the number of whole carrots that remain without being given to a bunny is -35,451. However, since the answer must be a whole number, we can round this up to 0 carrots. This implies that all of the carrots were given to the bunnies.

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Answer:

The three correct corresponding pairs that gives the same area are;

The areas are the same in each case because the product of each pair is the same.

Explanation:

Given the base and height pairs in the question.

Let us use the corresponding pairs that gives the same area.

Firstly, for the first pair;

Secondly, the second pair is;

Thirdly, the third pair;

Therefore, the three correct corresponding pairs that gives the same area are;

The areas are the same in each case because the product of each pair is the same.

Answer:

-3 ≤ x < 2

Step-by-step explanation:

The approximate probability that the total score is at least 375 when a fair six-sided die is rolled 100 times is (d) 0.4420.

When a fair six-sided die is rolled, the random variable X represents the outcome. The mean (μX) of X is 3.5, and the standard deviation (σX) is 1.71.

To find the probability that the total score is at least 375 when the die is rolled 100 times, we can use the Central Limit Theorem. According to the theorem, the sum of a large number of independent and identically distributed random variables approximates a normal distribution.

In this case, the sum of the outcomes of 100 rolls of the die follows a normal distribution with a mean of μX multiplied by the number of rolls (100) and a standard deviation of σX multiplied by the square root of the number of rolls (10). Therefore, the approximate probability can be calculated by finding the probability that the sum is greater than or equal to 375.

Using a normal distribution table or a calculator, we can find that the approximate probability is 0.4420, which corresponds to answer (d). This means that there is a 44.20% chance that the total score will be at least 375 when the die is rolled 100 times.

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The actual distance in miles between the campsite and the trail is 9 miles.

Map can be defined as  a symbolic depiction emphasizing relationships between elements of some space such as objects and regions.

To convert from centimeters on the map to miles, we use the scale of 1 centimeter represents 5 miles.

So, 1.8 centimeters on the map represents 1.8 * 5 = 9 miles in real life.

Therefore, The actual distance in miles between the campsite and the trail is 9 miles.

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Answer:

you are correct it is a

Step-by-step explanation:

Answer:

Its A

Step-by-step explanation:

Answer:

30 students are 6th graders

Step-by-step explanation:

3/7×70= 30

Answer:

1

Step-by-step explanation:

2x^2 + x -1 = 2

2x^2 + x-1-2 = 0

2x^2 + x -3 = 0

2x^2 -2x + 3x-3 = 0

2x(x-1) + 3(x-1) = 0

(2x + 3)(x-1) = 0

2x + 3 = 0

or x-1 = 0

x = -3/2 or 1

Answer:

20%

Step-by-step explanation:

Divide 4 (tip) by 20 (total bill) and you get 20 percent.

Answer:

20% tip

Step-by-step explanation:

4/20 = 0.2

Convert to a percentage:

0.2*100 = 20%

Answer:

y = x - 3

Step-by-step explanation:

a linear equation has the form

y = ax + b

the only equation in this form is

y = x - 3

Answer:

Here's the exponential equation to model the card's value:

y = 98.70 * 2^x

where x is the number of years after Mr. Olsen purchased the card.

To find the value of the card after 5 years:

x = 5

y = 98.70 * 2^5 = 98.70 * 32 = $3162.40

So, Mr. Olsen can expect the card's value to be $3162.40 5 years after he purchased it.

Step-by-step explanation:

Answer:

Step-by-step explanation:

m

Answer:

1. C   Add/subtract the same quantity to/from both sides

2. A  Yes

Step-by-step explanation:

Start with Equation A.

3x - 1 = 7

Add 1 to both sides.

3x = 8

First question:

How can we get Equation B from Equation A?

Answer:

C   Add/subtract the same quantity to/from both sides

Second question:

Based on the previous answer, are the equations equivalent?

Since by doing a valid step (adding 1 to both sides) Equation A became Equation B, the two equations are equivalent.

Answer:

A  Yes

Answer: 5 hours

Step-by-step explanation:

4/5 = 1/3 hour.

1 hour = 12/5 miles swam, 2 2/5 = 2.4

2.4 x 5 = 12.

1 hour x 5 = 5 hours.

It took the group of penguins 5 hours to swim 12 miles.

Hope this helps!

Answer:

6803.89

Step-by-step explanation:

Answer:

A=12,000 m^3

Step-by-step explanation:

First, here is the area of the pyramid.

A= 1/3 Bh

Now, let's define our variables.

B= 900 m^2

h= 40 m

We will plug them into the equation.

A= 1/3 (900)(40)

I will simplify by dividing 900/3 to get rid of the fraction.

A= 300(40)

A=12,000

Hope this helps!

Answer:

(8-5)/(7-2)= 3/5

Step-by-step explanation:

proper fraction

Given,Two buses are leaving Jackson, Mississippi at the same time and travel in opposite directions. The eastbound bus travels at 60 miles per hour, and the westbound at 40 miles per hour.

We have to determine in how many hours will the buses be 125 miles apart?

Let’s use d to represent the distance travelled by the slower bus, then the distance travelled by the faster bus is 125 - d To get the time, we’ll divide the distance by the speed. Therefore, we’ll have: Time taken by the slower bus (westbound bus)

= distance / speed

\(\frac{d}{40}\)

Time taken by the faster bus (eastbound bus)

= distance / speed

\(\frac{125-d}{60}\)

Since they both start at the same time, they’ll meet when the sum of their times is equal to the total time. So:

\(\frac{d}{40} + \frac{125 - d}{60} = T\)

where T is the total time taken by both buses.To solve this equation for d, we’ll first multiply both sides by 120 (which is the least common multiple of 40 and 60):

\(=3d + 2(125 - d)\)

\(= 120T3d + 250 - 2d\)

\(= 120Td\)

\(=3d + 2(125 - d)\)= 120T - 250.

Hence, it is observed that the distance covered by the slower bus is 120T - 250, and the distance covered by the faster bus is

\(125 - (120T - 250)\)

= 510 - 120T.

Now, we can substitute these values into any of the two time formulas we derived earlier. Let’s substitute them into the time formula for the faster bus, since it’s simpler: Time taken by the faster bus (eastbound bus)

= distance / speed

\(\frac{510 - 120T}{60}\)

We know that the total time is T, so we can equate these two expressions and solve for T:

=510 - 120T

= 60T510

= 180T3

= T

Therefore, the total time taken by both buses is T = 3 hours. Answer: \boxed{3}.

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Answer:

-4.2c+4.8d

Step-by-step explanation:

(−7c+8d)0.6

Distribute

-7c*.6 + 8d * .6

-4.2c+4.8d

Answer:

-4.2c + 4.8d

Step-by-step explanation:

We would like to distribute the 0.6 in the expression (-7c + 8d) * 0.6.

Remember that when distributing, we multiply the "outside number" (0.6 in this case) by each of the "inside numbers" (-7c and 8d) and then add those products.

So, the first product will be: 0.6 * (-7c) = -4.2c. The second product will be: 0.6 * 8d = 4.8d. Add these together: -4.2c + 4.8d.

The answer is thus -4.2c + 4.8d.

~ an aesthetics lover

The approximation of the number of gallons of water in the tank at time 9 min. is 52 gallons.

Using the trapezoidal sum, the approximation of the number of gallons of water in the tank at time t = 9 is given by:

Approximation =\([((t_1 - t_0) / 2) * (r(t_0) + r(t_1))] + [((t_2 - t_1) / 2) * (r(t_1) + r(t_2))] + [((t_3 - t_2) / 2) * (r(t_2) + r(t_3)))]\)

where \(t_0 = 0, t_1 = 4, t_2 = 7, t_3 = 9\).

Substituting the given values of r(t), we get:

Approximation = [((4 - 0) / 2) * (9 + 6)] + [((7 - 4) / 2) * (6 + 4)] + [((9 - 7) / 2) * (4 + 3))]

= (2 * 15) + (1.5 * 10) + (1 * 7)

= 30 + 15 + 7

= 52

Therefore, the approximation of the number of gallons of water in the tank at time t = 9 is 52 gallons. The answer is (A) 52.

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Answer:

Step-by-step explanation:

there are 6 sides on a cube

surface area = 6 times the area of one face of the cube

                     = 6 times ( a side times another side)      note all sides are equal

                     = 6(side)²         is a side equal to 2/3 ??   if it is ....

                     = 6(2/3)²

                     = 6(2/3)(2/3)     one of the 3s divide into 6 twice

                     = 2(2)(2/3)

                     = 2³ / 3

                     = 2x2x2 / 3

                     = 8 /3

                     = 2 and 2/3  units²

Answer:

Took L for my gang   keep working hard

Step-by-step explanation:

Answer:

x = 7

Step-by-step explanation:

The triangles are similar

12/8 = (x+3+5)/(x+3) cross multiply expressions

12x + 36 = 8x + 64

12x - 8x = 64 - 36

4x = 28 divide both sides by 4

x = 7

If a student answered exactly one question correctly, there is a 93.7% probability that they were well-prepared for the quiz.

Let A be the event that a student is well-prepared and B be the event that a student answered 1 question correctly. We want to find P(A|B), the probability that a student was well-prepared given that they answered 1 question correctly. Using Bayes’ Theorem, we have:

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

where P(B|A) is the probability of answering 1 question correctly given that the student is well-prepared, P(A) is the prior probability of being well-prepared (0.8), and P(B) is the total probability of answering 1 question correctly.

To compute P(B|A), we note that a well-prepared student has a 85% chance of answering each question correctly. Therefore, the probability of answering exactly 1 question correctly is:

\(P(1 correct | A) = (5 choose 1) * (0.85)^1 * (0.15)^4\) = 0.385

To compute P(B), we use the Law of Total Probability:

P(B) = P(B|A) * P(A) + P(B|A’) * P(A’)

where A’ is the complement of A (i.e., the event that a student is not well-prepared). Since 20% of students are not well-prepared, we have:

\(P(B|A’) = (5 choose 1) * (0.5)^1 * (0.5)^4\) = 0.15625

Therefore,

P(B) = P(B|A) * P(A) + P(B|A’) * P(A’) = 0.385 * 0.8 + 0.15625 * 0.2 = 0.3285

Finally, we can compute P(A|B):

P(A|B) = P(B|A) * P(A) / P(B) = 0.385 * 0.8 / 0.3285 ≈ 0.937

Therefore, if a student answered exactly one question correctly, there is a 93.7% chance that they were well-prepared for the quiz.

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The accrued amount after 7 years as interest is compounded annually is $1,766.47.

The formula accrued amount in a compounded interest is expressed as;

A = P( 1 + r/n )^( n × t )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given that;

Plug the given values into the above formula and solve for A.

A = P( 1 + r/n )^( n × t )

A = $1,320.00( 1 + 0.0425/1 )^( 1 × 7 )

A = $1,320.00( 1.0425 )⁷

A = $1,766.47

Therefore, the accrued amount is  $1,766.47.

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Cookies sold by Billy are 10 and by Betty are 5;

Total cookies sold by Billy and Betty are 15;

Let the cookies sold by Billy be 'C₁' and by Betty be 'C₂';

what is Permutation?

In mathematics, permutation relates to the act of arranging all of the contributors of a hard and fast into a few sequence or order. In other words, if the set is already ordered, then the rearranging of its elements is called the process of permuting. diversifications occur, in extra or less prominent methods, in almost every place of arithmetic. They regularly stand up whilst one of a kind orderings on positive finite sets are considered.

what's a combination?

The mixture is a manner of selecting objects from a collection, such that (not like permutations) the order of selection does now not matter. In smaller instances, it is feasible to be counted the wide variety of combinations. combination refers back to the mixture of n things taken ok at a time with out repetition. to consult combos in which repetition is authorized, the terms k-choice or k-mixture with repetition are regularly used.

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To make a decision for the hypothesis test, we need to analyze the ANOVA summary table for the test of significance of the overall regression model.

From the table, we can see that the regression sum of squares (SS) is given as 20, and the residual sum of squares (SS) is given as 400. We also know that the total sum of squares (SS) is the sum of the regression SS and the residual SS.

Since the degrees of freedom (df) for the regression model is equal to the number of predictor variables (k) minus 1 (k - 1), and the df for the residual is the total sample size (n) minus the number of predictor variables (k), we can calculate the df for the regression and the residual.

Given that the sample size (n) is 45 and the number of predictor variables (k) is 4, we can calculate:

df for regression = k - 1 = 4 - 1 = 3

df for residual = n - k = 45 - 4 = 41

Next, we need to calculate the mean square (MS) for the regression and the residual by dividing the SS by their respective degrees of freedom.

MS for regression = SS for regression / df for regression = 20 / 3

MS for residual = SS for residual / df for residual = 400 / 41

Finally, we can calculate the F-statistic by dividing the MS for regression by the MS for residual.

F = (MS for regression) / (MS for residual)

Now, we can compare the calculated F-statistic to the critical F-value at the given significance level (α = 0.05). If the calculated F-statistic is greater than the critical F-value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

Without the information of the critical F-value or the calculated F-statistic, we cannot make a definitive decision or final conclusion for the hypothesis test. Please provide the necessary values, and I will be able to help you with the decision and conclusion.

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Answer:

The value of sin 15° is equal to the y-coordinate (0.2588). ∴ sin 15° = 0.2588

The value of cos 15° = (√3+1)/2√2. Explanation: We have to find the value of cos 15 using cos (A - B) identity.

Answer:

i) 134

ii) Number of bottles sold on Tuesday:   \(\dfrac{x}{45}\)

iii) Number of bottles sold on Wednesday:  \(\dfrac{(x-75)}{48}\)

iv) \(x=3915\)

Therefore, 87 bottles were sold on Tuesday and 80 bottles were sold on Wednesday

Step-by-step explanation:

i) You need to ensure that the values are both in the same format (either both in dollars, or both in cents).

45 cents = 45/100 dollars = 0.45 dollars

60.30 ÷ 0.45 = 134

ii) both values are in cents, so no need to convert one of them.

Let n be the number of bottles sold.

So 45n = x

Therefore, n = x/45

ii)

Let n be the number of bottles sold.

So 48n = (x - 75)

Therefore, n = \(\dfrac{(x-75)}{48}\)

iv)

Number of bottles sold on Tuesday:   \(\dfrac{x}{45}\)

Number of bottles sold on Wednesday:  \(\dfrac{(x-75)}{48}\)

If the number of bottles sold on Tuesday was 7 more than those sold on Wednesday:

\(\implies \dfrac{x}{45}-7=\dfrac{(x-75)}{48}\)

multiply both sides by 48:  

\(\implies \dfrac{48x}{45}-336=x-75\)

multiply both sides by 45:

\(\implies 48x-15120=45x-3375\)

\(\implies 3x=11745\)

\(\implies x=3915\)

Therefore, 87 bottles were sold on Tuesday and 80 bottles were sold on Wednesday

The formula to calculate the geometric mean of two numbers is the square root of their product.

So in this case, the geometric mean can be calculated as follows:

Geometric Mean = √(8 * 12) = √96 = 10

The growth factors for the population of Chattanooga in the past two years have a geometric mean of 10.

The geometric mean is a measure of central tendency that is used to describe the average growth rate of a set of numbers. It is especially useful when working with data that represents exponential growth or decay, such as population growth or the rate of return on an investment. Unlike the arithmetic mean, the geometric mean takes into account both the size and the direction of growth. This makes it a better measure of central tendency for data that is not symmetrically distributed.

In the case of population growth, the geometric mean can be used to determine the average annual growth rate over a given period of time. For example, if the population of a city grows by 8% in one year and then by 12% the following year, the average annual growth rate over the two years can be estimated using the geometric mean.

It is important to note that the geometric mean is always smaller than the arithmetic mean for the same set of numbers, and it can be a better representation of the underlying growth trend in some cases.

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