Simplify the expression 82 + 9 (12: 3 x 2) – 7.

Explain each of your steps.

Answer: 829.44 ft²

Step-by-step explanation:

Correction - The walkway is 31.2 feet wide.

To solve this, first find the area of the fountain:

Area of a square = Length * Width

= 12 * 12

= 144 ft²

The find the area of the walkway including the fountain:

= 31.2 * 31.2

= ‭973.44‬ ft²

To find the area of the walkway alone, subtract the area of the square from the area of the rectangle:

= 973.44 - 144

= 829.44 ft²

Each friend will receive "x/5" antique letters, where "x" represents the total number of antique letters in the box.

Sasha wants to give an equal number of letters to each of her five friends. The box of antique letters contains the letters that she wants to distribute among her friends. The question is to determine how many antique letters each friend will receive.

The total number of antique letters in the box is unknown. Let's assume that there are "x" antique letters in the box. If Sasha wants to distribute "x" letters among five friends equally, she can find out how many letters each friend will receive by dividing the total number of antique letters by the number of friends. Hence, each friend will receive x/5 letters.

To summarize, each friend will receive "x/5" antique letters.

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20 month needed to start saving money overall.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

One is  Super Cool X1400 for 800

and, another is Efficient Energy X2000 for 1200.

So, total cost for each type of conditioner is

Super Cool X1400, Cost = 800+ 60m

and, Efficient Energy X2000 Cost= 1200 + 40m

Now, to start saving money overall

800+ 60m = 1200+ 40m

20m = 400

m= 20

Hence, 20 month needed to start saving money overall.

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Answer:

5. -10/9

6. -5500/21

7. 1 39/167

8. -31/492

Completing the equalities using the given options, we have:

\(a) sin^(-1)(1) = 90°\\b) cos^(-1)(1/2) = 60°\\c) tan^(-1)(√3) = 60°\)

a) \(sin^(-1)(1) = 90°\)

The inverse sine function, \(sin^(-1)(x)\)gives the angle whose sine is equal to x. In this case, we are looking for the angle whose sine is equal to 1. The angle that satisfies this condition is 90 degrees, so\(sin^(-1)(1) = 90°\).

b) \(cos^(-1)(1/2) = 60°\)

The inverse cosine function, cos^(-1)(x), gives the angle whose cosine is equal to x. Here, we are looking for the angle whose cosine is equal to 1/2. The angle that satisfies this condition is 60 degrees, so \(cos^(-1)(1/2)\)= 60°.

c) \(tan^(-1)(√3) = 60°\)

The inverse tangent function, tan^(-1)(x), gives the angle whose tangent is equal to x. In this case, we are looking for the angle whose tangent is equal to √3. The angle that satisfies this condition is 60 degrees, so tan^(-1)(√3) = 60°.

Completing the equalities using the given options, we have:

\(a) sin^(-1)(1) = 90° b) cos^(-1)(1/2) = 60°c) tan^(-1)(√3) = 60°\)

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a) The completed equalities are:

sin-¹(x) = 30°, sin-¹(x) = 45°, sin-¹(x) = 60°

b) The completed equalities are:

cos-¹(x) = 30°, cos-¹(x) = 45°, cos-¹(x) = 60°

c) The completed equalities are:

tan-¹(x) = 30°, tan-¹(x) = 45°, tan-¹(x) = 60°. C.

a) sin-¹(x) = 30°, 45°, 60°

The inverse sine function, sin-¹(x), gives the angle whose sine is equal to x.

Let's find the angles for each option given:

sin-¹(x) = 30°:

If sin-¹(x) = 30°, it means that sin(30°) = x.

The sine of 30° is 0.5, so x = 0.5.

sin-¹(x) = 45°:

If sin-¹(x) = 45°, it means that sin(45°) = x.
The sine of 45° is √2/2, so x = √2/2.

sin-¹(x) = 60°:

If sin-¹(x) = 60°, it means that sin(60°) = x.

The sine of 60° is √3/2, so x = √3/2.

The completed equalities are:

b) cos-¹(x) = 30°, 45°, 60°

The inverse cosine function, cos-¹(x), gives the angle whose cosine is equal to x.

Let's find the angles for each option given:

cos-¹(x) = 30°:

If cos-¹(x) = 30°, it means that cos(30°) = x.

The cosine of 30° is √3/2, so x = √3/2.

cos-¹(x) = 45°:

If cos-¹(x) = 45°, it means that cos(45°) = x.
The cosine of 45° is √2/2, so x = √2/2.

cos-¹(x) = 60°:

If cos-¹(x) = 60°, it means that cos(60°) = x.

The cosine of 60° is 0.5, so x = 0.5.

Therefore, the completed equalities are:

c) tan-¹(x) = 30°, 45°, 60°

The inverse tangent function, tan-¹(x), gives the angle whose tangent is equal to x.

Let's find the angles for each option given:

tan-¹(x) = 30°:

If tan-¹(x) = 30°, it means that tan(30°) = x.

The tangent of 30° is 1/√3, so x = 1/√3.

tan-¹(x) = 45°:

If tan-¹(x) = 45°, it means that tan(45°) = x.

The tangent of 45° is 1, so x = 1.

tan-¹(x) = 60°:

If tan-¹(x) = 60°, it means that tan(60°) = x.

The tangent of 60° is √3, so x = √3.

The completed equalities are:

tan-¹(x) = 30°, tan-¹(x) = 45°, tan-¹(x) = 60°. c)

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Answer:

h = 12 m

\( v_{cylinder}= 235.5 \: {m}^{3} \)

Step-by-step explanation:

Radius of cylinder (r) = 5/2 = 2.5 m

\( {h}^{2} = {13}^{2} - {5}^{2} \\ h = \sqrt{ {13}^{2} - {5}^{2} } \\ h = \sqrt{169 - 25} \\ h = \sqrt{144} \\ h = 12 \\ \\ v_{cylinder} = \pi {r}^{2} h \\ v_{cylinder}= 3.14(2.5) ^{2} (12) \\ v_{cylinder}= 235.5 \: {m}^{3} \)

The general term for the recurrence T(n) = 3T(n/2) + O(n) is O(nlog3). To get the answer, we should plug in k = log3. For the second recurrence, we cannot use the master theorem since it does not cover this case.

To solve this recurrence, we have to use the substitution method, where we guess a solution of the form T(n) = an^k and then prove that this is indeed a solution. This can be done by substituting the guessed solution back in to the recurrence. If the substitution works, then we have solved the recurrence. If not, we can try different values for a and k until the substitution works.

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Answer:

©

\(( {5}^{4} . { {b}^{ - 10}) }^{ - 6} = ( {5}^{4. - 6} ).( {b}^{ - 10. - 6} ) \\ = {5}^{ - 24} . {b}^{ 60} \\ = \frac{ {b}^{60} }{ {5}^{24} } \)

The probability that the sample mean will be greater than 57.95 is 0.0495.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. This is the basic probability theory, which is also used in the probability distribution.

To solve this question, we need to know the concepts of the normal probability distribution and of the central limit theorem.

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The Central Limit Theorem establishes that, for a random variable X, with mean \(\mu\) and standard deviation \(\sigma\), a large sample size can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(\frac{\sigma}{\sqrt{\text{n}} }\).

In this problem, we have that:

The probability that the sample mean will be greater than 57.95

This is 1 subtracted by the p-value of Z when X = 57.95. So

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

By the Central Limit Theorem

\(Z=\dfrac{X-\mu}{\text{s}}\)

\(Z=\dfrac{57.95-53}{3}\)

\(Z=1.65\)

\(Z=1.65\) has a p-value of 0.9505.

Therefore, the probability that the sample mean will be greater than 57.95 is 1-0.9505 = 0.0495

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Answer: B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

i just got the biggest brain ever

The stratified random sampling is a sampling method that may allow for more accurate inferences to be made about a population.

It is the true statement.

Given,

In the question:

Stratified random sampling is a sampling method that may allow for more accurate inferences to be made about a population.

To check the above statement is true or false.

Now, According to the question:

Let's know about

Stratified random sampling is a method of sampling that involves the division of a population into smaller subgroups known as strata. In stratified random sampling, or stratification, the strata are formed based on members' shared attributes or characteristics, such as income or educational attainment.

In stratified random sampling, the strata are formed based on member's shared characteristics (e.g. female or male, occupation, education) or attribute (e.g. black or white).

Hence, The stratified random sampling is a sampling method that may allow for more accurate inferences to be made about a population.

It is the true statement.

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Answer:

x = 6.

Step-by-step explanation:

x - y = 4

x + y = 8

2x = 12

x = 6.

6 - y = 4

-y = -2

y = 2

6 + y = 8

y = 2

Hope this helps!

The solution to the system of equations is (6, 2).

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

The given system of equations are

x-y=4 ------(i)

x+y=8 ------(ii)

Subtract equation (ii) from equation (i), we get

x+y-(x-y)=8-4

x+y-x+y=4

2y=4

y=2

Substitute y=2 in equation (i), we get

x-2=4

x=6

So, the solution is (6, 2)

Therefore, the solution to the system of equations is (6, 2).

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Answer:

1024

Step-by-step explanation:

You could put 4^5 into your calculator. It’s 4*4*4*4*4= 1024

Answer:

  18

Step-by-step explanation:

You want the number of vertices such that the number of pairs of vertices is 153.

The number of n objects taken 2 at a time is ...

  N = (n)(n -1)/2

You want to find n for N=153.

We notice that multiplying by 2 gives a near square:

  2N = n(n -1)

The square root of this will have a value approximately equal to n-1/2:

  n -1/2 ≈ √(2·153) = √306 ≈ 17.5   ⇒   n = 18

We can check this:

  (18)(17)/2 = 9·17 = 153

The mystic rose with 153 lines has 18 vertices.

__

Additional comment

We could solve the quadratic equation 306 = n(n-1) by any of several means. The method used here is about the fastest.

If you want to get formal about solving the equation this way, you can define z = n-1/2, then the equation becomes ...

  306 = (z +1/2)(z -1/2) = z² -1/4

  306.25 = z²   ⇒   z = 17.5   ⇒   n = 18

By leaving off the 0.25 addition to 306, the root we get is slightly low, but still close enough to 17.5 to show us what the answer is.

Answer:

D No; the graph of a proportional relationship must pass through (0, 0).

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

A number consists of 2 digits whose sum is 9 => x + y = 9

If the order of the numbers is inverted, the result is equal to the given number plus 9 units => (10*y + x) + 9 = (10*x + y)

Thus:

x + y = 9  => multiply by -9 => 9*y + 9*x = 81

10*y + x + 9 = 10*x + y =>  9*y - 9*x = -9

We are left then that:

9*y + 9*x = 81  (1)

9*y - 9*x = -9  (2)

we add both equations

18y = 72

y = 72/18 = 4

replacing

x + y = 9

x + 4 = 9

x = 5

Therefore the number is (10y + x) => (10 * 4 + 5) => 45

Answer:

a) 2x + 1, 4x + 7

b) L = 19 cm, W = 7 cm, A = 133 cm^2

Step-by-step explanation:

8x^2 + 18x + 7

ax^2 + bx + c

ac = 8 * 7 = 56

56 = 4 * 14

8x^2 + 18x + 7 =

= 8x^2 + 14x + 4x + 7

= 2x(4x + 7) + 1(4x + 7)

= (2x + 1)(4x + 7)

a) 2x + 1, 4x + 7

b)

2(3) + 1 = 7

4(3) + 7 = 19

A = LW = 19(7) = 133

The equation that represents the grade for the assignments is:

Y = 6(X) + 50

The general formula for the equation of a line in slope intercept form is expressed as:

y = mx + c

where:

m is slope

c is y-intercept

We are told that they give 6 points each for each assignment done and a base grade of 50. Thus, using the format of linear equation in slope intercept form, we have the equation as:

Y = 6(X) + 50

Here 6 is the slope.

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Answer: A

Step-by-step explanation:

\(m\angle ABC=59^{\circ}\) by the inscribed angle theorem.

Answer:

9

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

The median is the middle value of the data set arranged in ascending order. If there is no exact middle value then it is the average of the values either side of the middle.

Given

8    10    12    14     ← in ascending order

          ↑ middle

The middle is between 10 and 12, thus

median = \(\frac{10+12}{2}\) = \(\frac{22}{2}\) = 11

The distribution does not represent a probability distribution. The correct option is b.

A probability distribution should satisfy two main conditions: (1) the sum of the probabilities for all possible outcomes should be equal to 1, and (2) the probabilities for each outcome should be between 0 and 1 (inclusive).

In this distribution, the probabilities for the outcomes are 0.3, 0.4, 0.3, and 0.1 for the values of X as 3, 6, 9, and 0, respectively. However, the sum of these probabilities is 1.1, which violates the first condition of a probability distribution.

Therefore, this distribution does not meet the requirements of a probability distribution and is not a valid probability distribution. The correct answer is option b.

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Answer -rational numbers and irrational numbers

Using number sets, it is found that the set of dense numbers is composed of rational and irrational numbers. Therefore, option C is the correct answer.

From options, we need to check which answer describes the type of numbers that are dense.

Numbers are an integral part of our everyday lives, right from the number of hours we sleep at night to the number of rounds we run around the racing track and much more. In math, numbers can be even and odd numbers, prime and composite numbers, decimals, fractions, rational and irrational numbers, natural numbers, integers, real numbers, rational numbers, irrational numbers, and whole numbers.

Numbers can be classified as:

Whole numbers: All positive numbers and 0, so: {0,1,2,...}

Integer numbers: Positive or negative, not decimal so: {...,-2,-1,0,1,2,....}

Rational numbers: Integer plus decimals that can be represented by fractions, that is, they either have a pattern or have a finite number of decimal digits, for example, 0, 2, 0,45(finite number of decimal digits), 0.3333(3 repeating is the pattern), 0.32344594459 (4459 repeating is the pattern).

Irrational numbers: Decimal numbers that are not represented by patterns, that is, for example, 0.1033430290339, which can be approximated to the rational 0.1.

Real numbers: Rational plus irrational.

A subset is dense of the rational numbers if all numbers can be approximated to rational numbers, and thus, rational and irrational numbers are dense.

Therefore, option C is the correct answer.

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Answer:

C i think

Step-by-step explanation:

pls mark brainyest

In order to create a diagram that represents the quantities of each ingredient adde, could be:

CM = X X X

FB = X X

CS = x

Where CM is Cups of Milk, FB is Frozen Bananas and CS is Chocolate Syrup. There, x representent the ammount of each ingredient.

Now, we determine the proportions of the ingredients:

There are 3 cups of milk per two frozen bananas (3:2)

There are 2 frozen banas per tablespoon of chocolate syrup (2:1).

There are 3 cups of milk per tablespoon of chocolate syrup (3:1).

Now, in order to write 3 sentences that contain the ratio of the ingredients we could think of it as a recipe:

*"In order to get this smoothie we will need 3 cups of milk and a tablespoon of chocolate syrup."

*"We will also add 2 frozen bananas for each tablespoon of chocolate syrup."

*"Remember that that is the ammount of ingredients per serving, so if you want more servings you will also need another extra 3 cups of milk, 2 frozen bananas and 1 tablespoon of chocolate syrup for each extra serving."

Thus, the two possible values for angle A are 67.4° and 112.6° to the nearest tenth of a degree.

In △ABC, you have given B = 51°, b = 35, and a = 36. To find the two possible values for angle A, we can use the Law of Sines.

The Law of Sines states: (sinA)/a = (sinB)/b

Plugging in the given values, we get:
(sinA)/36 = (sin51°)/35

Now, solve for sinA:
sinA = 36 * (sin51°)/35 ≈ 0.923

Since sinA = 0.923, we can find the two possible values for angle A using the inverse sine function:

1. A = arcsin(0.923) ≈ 67.4°
2. A = 180° - arcsin(0.923) ≈ 112.6°

So, the two possible values for angle A are 67.4° and 112.6° to the nearest tenth of a degree.

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Answer:

A. True

Step-by-step explanation:

If two angles of a triangle are congruent to the corresponding angles or the second triangle than the third angles must be congruent to each other.

The sum of the interior angles of a triangle is 180.  Let's say 2 angles to one triangle is 100 and the second angle is 35.  That forces the third angle to be 45 (100 + 35 + 45 = 180)

Helping in the name of Jesus.

Answer:

A. True

Step-by-step explanation:

In congruent triangles...All angles and sides have to be equal.

The function rule of a table calculator, you need to examine the given input-output pairs in the table and look for patterns or relationships between the inputs and outputs.

The step-by-step process to determine the function rule:

Identify the pattern: Look for any consistent relationship between the input and output values. Consider how the output changes as the input changes.

Determine the type of relationship: Based on the pattern, determine the type of relationship between the input and output. It could be linear, quadratic, exponential, or some other mathematical relationship.

Write the general function rule: Once you determine the type of relationship, write a general function rule that expresses the output (y) in terms of the input (x) using appropriate mathematical operations and constants.

Test the function rule: Check if the function rule you derived matches the given input-output pairs in the table. Plug in the input values into the function rule and verify if the corresponding outputs match the given outputs in the table.

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The pick-up rate in this scenario would be 80%. This is calculated by dividing the number of rooms occupied (160) by the number of rooms reserved (200), and then multiplying by 100 to get a percentage. So, (160/200) x 100 = 80%. This means that 80% of the reserved rooms were ultimately occupied.

It's important to note that a pick-up rate of 80% is generally considered to be a good result in the hospitality industry. It indicates that the hotel was able to accurately predict the number of rooms that would be needed by the groups, and that the groups themselves followed through on their reservations. A lower pick-up rate could suggest that the hotel overestimated demand, or that some of the groups cancelled their bookings at the last minute. On the other hand, a higher pick-up rate could indicate that the hotel was too conservative in its initial estimates, or that some of the groups requested additional rooms after the initial reservation was made. Ultimately, the pick-up rate is a useful metric for assessing the accuracy of a hotel's forecasting and planning processes.

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1 ream = 250 papers

1 booklet = 8 papers

Therefore, with 4 reams of paper, Jacob will be able to create 125 booklets.

Hoped this helped.

\(-BrainiacUser1357-\)