-9x+2y =24
x = 10-4y

The exact solutions for the equation cos⁻¹x = π will be  x=√3/2.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, the equation to be solved,

cos⁻¹x = π

[tex]6\arccos \left(x\right)=\pi \quad :\quad x=\frac{\sqrt{3}}{2}[/tex]

Divide by 6 on both the side,

[tex]\frac{6\arccos \left(x\right)}{6}=\frac{\pi }{6}[/tex][tex]\frac{6\arccos \left(x\right)}{6}=\frac{\pi }{6}[/tex]

Simplify,

[tex]\arccos \left(x\right)=\frac{\pi }{6}[/tex]

From the trigonometric inverse principle,

[tex]x=\frac{\sqrt{3}}{2}[/tex]

Thus, the exact solution for the equation cos⁻¹x = π will be  x=√3/2.

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The compound interest = $5320  

and the total amount = $5832

In this question, we need to find the compound interest and the total amount after an hour if the interest is compounded every ten minutes.

Here, principal P= $512

rate of interest R = 5% per minute

                            = 5 x 10 (interest for every 10 min)

                             = 50

Now n = 60 / 10

        n = 6

So using compound interest formula the total amount would be,

A = P(1 + R / 100)^n

A = 512 (1 + 50/100)^6

A = 512 (3/2)^6

A = 5.2 (1.5)^6

A= $5832

Now the Compound Interest = A – P

                                                 = 5832 – 512

                                                 = $5320  

Therefore, the compound interest = $5320  

and the total amount = $5832

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Suppose a person gained three pounds (a negative weight loss). Then z = -1. This z-score tells you that x = -3 is 1 standard deviation to the left of the mean.

A z-score is a statistical measurement that describes a value's relationship to the mean of a group of values in terms of standard deviations. It is calculated using the formula:

[tex]\\\mathrm {z = \frac{x - \mu}{\sigma} }[/tex]

Where:

z = z-score

x = individual data point (in this case, the weight change in pounds)

μ = mean of the data set (average weight change in pounds)

σ = standard deviation of the data set (a measure of how spread out the data is)

If the person gained three pounds (a negative weight loss), it means the value of x is -3 pounds (x = -3).

To calculate the z-score, we need to know the mean and standard deviation of the weight changes in pounds for the entire group of people.

Let's assume the mean (μ) is 0 pounds (no weight change on average), and the standard deviation (σ) is 3 pounds (for example).

z = (-3 - 0) / 3

z = -1

So, the z-score (z) is -1.

A negative z-score indicates that the data point (in this case, the weight change of -3 pounds) is below the mean.

Since the z-score is -1, this tells us that the weight change of -3 pounds is 1 standard deviation to the left of the mean.

The negative sign indicates it is below the mean, and the absolute value of the z-score (1) indicates it is 1 standard deviation away from the mean.

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if M > N then the inequality M/N > N/M will be always true

What is Linear Inequality?

The mathematical expression with unequal sides is known as an inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. In this instance, any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), or not equal to symbol (), is used in place of the equal sign "=" in the expression. Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics.

The symbols "" and ">" signify tight inequalities, while "" and "" signify slack inequalities. A linear inequality looks precisely like a linear equation, but the symbol connecting two expressions is different.

As in the question M is always greater N

So, is M is divided by a number that is less than M the answer will always be greater than 1

but on the other hand, if N is divided by a number greater than N then the answer will always be less than 1

Therefore, M/N > N/M will always be True

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If a value of 80.4° is added to the data, the range does not change.

The range is 48.

If a value of 60° is added to the data, the median change.

The median was 79.5.

The change median is 77.

It is the average value of the set given.

It is calculated as:

Mean = Sum of all the values of the set given / Number of values in the set

We have,

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

The range formula = Highest value - Lowest value

Now,

Highest value = 105

Lowest value = 57

Range = 105 - 57 = 48.

Now,

If the value of 80.4 is added the range remains the same because the range is dependent only on the value of the highest and the lowest value.

We have,

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

The median is the mid value of the given set of data after arranging in ascending order.

Arranging the set in ascending order.

57, 58, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105

There are 12 elements in the set.

Median = (77 + 82) / 2 = 79.5

If 60 is added we get 13 elements in the set.

The arrangement becomes,

57, 58, 60, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105

Median = 77

Thus,

If a value of 80.4° is added to the data, the range does not change.

The range is 48.

If a value of 60° is added to the data, the median change.

The median was 79.5.

The change median is 77.

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Starting with the provided assertions, a flow proof arranges statements in a logical order.

A mathematically formatted proof known as a "flow proof" uses logic to back up a truth assertion.

Thus, opening with the provided assertions, a flow proof arranges statements in a logical order. Arrows are being used to show the sequence of the assertions, and each assertion has its justification stated beneath it.

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Answer:

Q

Step-by-step explanation:

The event that has a theoretical probability of exactly Three-fourths include:

A. not picking a square

D. picking a shape that has only straight edges

E. not picking a circle

The theoretical probability is defined as the proportion of favorable outcomes to possible outcomes. The theory of probability is the science of probability.

The sample space of an object determines theoretical probability. The probability of rolling a 3 on a fair die, for example, is 1/6. This is because the number 3 represents one of the six possible outcomes of rolling a fair die

Therefore, based on the information given, it should be noted that the correct options are A, D and E.

This equation is written as follows: Theoretical Probability = the number of favorable outcomes divided by the total number of possible outcomes.

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Answer:

-60

Step-by-step explanation:

-15 = 1/3x + 5  Multiply all the way through by 3

-45 = x + 15  Subtract 15 from both sides of the equation

-60 = x

Answer: -60 = x

Step-by-step explanation:

If the output value is -15, we need to do this equation.

-15 = (1/3)x + 5.

-5                -5

-20 = (1/3)x

x3     x 3

-60 = x.

Now, let's double-check our answer.

f(60) = (1/3)(-60) + 5

f(-60) = -20 + 5

f(-60) = -15.

This means that x = -60 is our correct answer.

Answer:

32+q

Step-by-step explanation:

it doesn't ask for money

If a window in the model is 1.5 in. wide, then the actual window is  7.5 feet wide.

A two-term ratio expressed with a second term of one is referred to as a unit ratio. A unit ratio can be created from any ratio. Example. An illustration of a set of marbles is shown below. The set has eight blue marbles and two red marbles.

Having a denominator of 1, a unit rate is a ratio between two separate units. Divide the numerator by the denominator to obtain the unit rate. The unit rate is the decimal number that results. The price of a good or service is the numerator of a ratio called the unit price, and the quantity is the denominator.

Given,

The scale of the Model =5 in: 25 ft.

Dividing both sides by 5 we get,

[tex]\frac{5in}{5}[/tex] :[tex]\frac{25ft}{5}[/tex]

1 inch:5 feet

If a window on the model is 1.5 inch wide, then from the unit ratio we get,

1 inch × 1.5 : 5 feet × 1.5 feet

1.5 Inch : 7.5 feet

As a result, a window that is 1.5 inches wide in the model will actually be 7.5 feet wide.

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Answer: 15,070

Step-by-step explanation: subtraction 16200-1130=15,070

The probability of event A is 5/18.

The probability of event B is 29/36.

Probability is used to determine how likely it is that a random event would happen. The probability that the random event would happen would lie between 0 and 1.

The probability that the sum is greater than 8 = sample space that have a sum greater than 8 / total number of sample space

sample space that have a sum greater than 8 = (3,6) (4,5) (4,6) (5,4) (5,5) (5,6) (6,3) (6, 4) (6,5) (6,6) = 10

Total number of sample space = 36

The probability that the sum is greater than 8 = 10 / 36 = 5/18

The probability that the number is not divisible by 5 = sample spaces that is not divisible by 5 / total number of sample spaces

= 29 / 36

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Here is the rest of the question:

Write your answers as exact fractions.

P(a)

P(b)

The test statistic when the a simple random sample has been selected from a normally distributed population is a) -2.24

The test statistic is a number derived from a statistical test that is used to determine whether your data could have occurred under the null hypothesis.

u = 30000

x = 22298

s = 14200

n = 17

Test statistic = = (x - u) / s / ✓n

x = mean

u = theoretical value

s = standard deviation

{n} = variable set size

= (x - u) / s / ✓n

= (22298 - 30000) / 14200 / ✓17

= -2.24

Test statistic = -2.24

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The final altitude of Carl is -373 feet

What is an Equation?

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.

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 data ,

Carl began his hike at an altitude = 1482 feet

And , Carl hiked down an altitude = 2173 feet

Now , Carl is at an altitude of = 1482 - 2173 feet

                                                = -691 feet

And , Carl increased his altitude by = 663 feet

Now , Carl is at an altitude of = -691 + 663 feet

                                                 = -28 feet

And , Carl decreased his altitude by = 345 feet

Now , Carl is at an altitude of = -28 - 345

                                                = -373 feet

The final altitude of Carl is -373 feet

Hence , the final altitude is -373 feet

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The probability that the mean of the sample is between 120 and 126 gallons is 0.4176

The normal distribution describes a symmetrical plot of data around its mean value, where the width of the curve is defined by the standard deviation

Given: population mean (µ) = 123, standard deviation(σ) =21 and number of sample (n) = 15

Let X represent the gallons of water: We want to find:

P(120 ≤ X ≤ 126)

Z-score(Z) = (X-µ) / (σ/√n)

Z₁ = (120-123)/ (21/√15) = -0.55

Z₂ = 126-123/ (21/√15)= 0.55

P(-0.55≤ Z ≤ 0.55) = = 0.7088 - 0.2912 = 0.4176

(Check the image of the table attached)

Therefore, the probability that the mean of a randomly selected sample of 15 people will be between 120 and 126 gallons is 0.4176

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The number of outcomes, using the Fundamental Counting Theorem, is given as follows:

A. Red exactly 3 times and Purple exactly 2: 10.

B. Red at least ounce in 4 spins: 175.

C. Red at least ounce in 5 spins: 781.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, obtained by the following formula, involving factorials.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Item a is used with the combination formula, as it is an arrangement of five elements with 3 and 2 repetitions, hence the number of outcomes is:

[tex]C_{5,3} = \frac{5!}{3!2!} = 10[/tex]

The Fundamental Counting Principle states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the number of outcomes is calculated by the multiplication of the factorials as presented as follows:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

For item b, in four spins, each with four outcomes, the parameters are given as follows:

[tex]n_1 = n_2 = n_3 = n_4 = 4[/tex]

Hence the number of outcomes is:

N = 4^4 = 256.

For no red results, the parameters are as follows:

[tex]n_1 = n_2 = n_3 = n_4 = 3[/tex]

Hence:

N = 3^4 = 81.

Hence the number of outcomes with at least one red is:

256 - 81 = 175.

For item 3, the lone difference is that there are five trials, hence:

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Answer:

396

Step-by-step explanation:

400-4=396

Answer:

396

Step-by-step explanation:

Answer:

Half as big as little drop?

Step-by-step explanation:

The probability that a red ticket is drawn first and then the second ticket drawn is blue is 0.253.

Probability determines the odds that a random event would occur. The odds that the random event occurs has a probability value that lies between 0 and 1.

The more likely it is that the event would occur, the closer the probability value would be to 1. The more unlikely it is that the event would not happen, the closer the probability value would be to 0.

The probability that a red ticket is drawn first and then the second ticket drawn is blue = (number of red tickets / total number of tickets) x (number of blue tickets / total number of tickets)

Total number of tickets = number of blue tickets + number of red tickets

25 + 20 = 45

The probability that a red ticket is drawn first and then the second ticket drawn is blue = (20 / 45) x (25 / 44) = 0.253

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The image point of (2, −6) after the transformation R270° is (4,3).

Given:

(2,-6) and  R270° and (1,2)

Let (x,y) be the point

First translation (1,2)

(x,y) → (x+1,y+2)

Translation of  R270° for translated coordinates

(x+1,y+2) → (-(y+2),x+1)

substitute (2,-6)

= (-(-6+2),2+1)

= (-(-4),3)

= (4,3)

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If you have a 2 foot piece of string and cut off and use a piece 4 3/4 inches long and a piece 2 3/8 inches long, Then 16.875 is the remaining string.

A fraction represents a part of a whole.

1 foot =12 inches

2 foot=24 inches.

Given,

if you have a 2 foot piece of string and cut off and use a piece 4 3/4 inches long and a piece 2 3/8 inches long.

Then  how much string do you still have

We have to subtract the used strings from 24 inches string.

4 3/4 inches=19/4

2 3/8 inches=19/8

Now we have to subtract 19/4 and 19/8 from 24 inches.

24-19/4-19/8

24-4.75-2.375

16.875

Hence 16.875 is the string left with us.

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The price of the pair of shoes in the department store is $7.

The wholesale price for a pair of shoes is $4.50. A certain department store marks up the wholesale price by 50%.

To find out the price of the pair of shoes in the department store:

The price of the pair of shoes in the department store: $7

Given the wholesale price of pair of shoes is $4.50

Department store of wholesale price is 50%

Than whole sale = 1.5 times the whole sale

Price in department store = 1.5*4.5

= $6.75

Rounded to the nearest cent = $7

Hence the answer is the price of the pair of shoes in the department store is $7.

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The number of insects at t=0 is 700, the growth rate is 28e^0.04, population of insects after 10 days is 1044, and the graph of the function is attached.

What is function?

A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.

a) Number of insects at time (t) = 0 days,

Putting t = 0 in given function:

P(t) = 700e^0.04(0) = 700e^0 = 700

Hence,  the number of insects at t = 0 days is 700.

b) Growth rate of insect population,

In order to find growth we need to differentiate the given function with respect to t.

So,  dP(t)/dt = 700(0.04)e^0.04(0)

= 28e^0.04

Hence, the growth rate is 28e^0.04.

c)  Graph the function is attached in the question.

d) The population of the insects after 10 days,

putting t = 10,

= 700e^0.04(10) = 1044

Hence, population of insects after 10 days is 1044.

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Answer: x > -7, see attached

Step-by-step explanation:

    Given:

x + 6 > -1

   Subtract 6 from both sides of the equation:

x > -7

    Graph, see attached. We will graph x = -7, and shade to the right.

Answer:

no solution

Step-by-step explanation:

Answer:

======================

A ∩ D means intersection of the two sets or the common elements of A and D.

We observe that:

It means the common elements of the two sets are 14 and 16:

Answer:

A ∩ D = {14, 16}

Step-by-step explanation:

Given sets are,

→ A = {x | x is an even integer}

→ D = {13, 14, 15, 16}

Now we have to,

→ find required set of A ∩ D.

Then the answer will be,

→ A ∩ D = {2, 4, 6, 8, ... n} ∩ {13, 14, 15, 16}

→ A ∩ D = {14, 16}

Hence, the required set is {14, 16}.

The required answer would be the stick insect is 117.5 millimeters long.

Subtraction is a mathematical operation that deducts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

The stick insect measures 12 cm then a fly which is 2.5 mm long.

According to the given question, the required solution would be as:

⇒ 12 cm - 2.5 mm

Convert the centimeters into millimeters

⇒ 10 × 12 mm - 2.5 mm

⇒ 120 - 2.5

Apply the subtraction operation,

⇒ 117.5 millimeters

Thus, the required answer would be the stick insect is 117.5 millimeters long.

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