Find three consecutive even integers such that the sum of the least integer and the middle integer is 24 more than the greatest integer.

If our equation is as follows;

We are given an initial condition. We replace the unknown by [tex]-7[/tex] to get the result.

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 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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Answer:

IGF

Step-by-step explanation:

the two angles have the same vertex and lie on the same lines

The value of b after solution of the expression, b-14 = -10, is 4.

According to the question,

We have the following expression:

b-14 = -10

Now, we will first add 14 on both sides of the above equation:

b = -10+14

We know that when two integers are of different signs then the smaller number is subtracted from the larger number but the sign in the result is of the larger number.

So, in this case, 14 is larger than 10 then the result will be positive.

So, we have the following expression:

b = 4

Hence, the correct option is B.

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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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$5539.53 is each withdrawal if the interest rate is 5% per year, compounded monthly.

What is compounded interest?

Compound interest is the interest earned on savings that are calculated on both the initial principal and the interest earned in previous periods.

We have,

Initial amount - le 5,00,000

Interest = l = 5/100 = 0.05/12 = 0.004167

Time period T = 25 x 12 = 300

[tex]A = P(1 + r)^t[/tex]

where A = total balance after t years,

P = principal amount (the amount invested),

r = interest rate (decimal form), and

t = time in years.

How much money will Jack have after 25 years?

[tex]A = 5,00,000 (1+ 0.05)^{25}[/tex]

A = 1661859

A / 300 = 5643

Therefore, $5539.53 is each withdrawal if the interest rate is 5% per year, compounded monthly.

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The pair that support Angle-Side-Angle Postulate (ASA) be used to prove that △ABC≅△XYZ is option B

Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules

examples of these rules are

The problem requires the prove by Angle - Side- Angle = ASA to ensure that the the triangles are congruent

The Angle - Side - Angle = ASA have it that the two triangles being compared should have their two angles and the included side being equal

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There are 10 multiple choice questions and 5 short response.

The following can be deduced:

The teacher gives a test with 15 questions that is worth 35 points.

Multiple choice questions = m = 1 point each

Short response questions = s = 5 points

The equation will be:

a + s = 15

a + 5s = 35

Subtract

4s = 20

Divide

s = 20/4

s = 5

Number of short response questions = 5

Number of multiple choice will be:

a + s = 15

a + 5 = 15

a = 15 - 5

a = 10

Multiple choice = 10

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Step-by-step explanation:

Find the perimeter of the rectangle. length 7 inches and area 35 square inches.

P = 2W + 2L

A = LW

because you know that L = 7:

A = LW

35 = 7W

divide both sides by 7:

35/7 = 7W/7

W = 5

substitute into first equation:

P = 2W + 2L

P = 2(5) + 2(7)

P = 10 + 14

P = 24

the anwer is 5

35 divied by 7 is 5

7 times 5 is 35

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.

Magan bought 8 cans of soup and 3 cans of frozen dinners.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Let x represent the number of cans of soup purchased and y the number of frozen dinners purchased.

Magan purchased a total of 11 cans of soup and frozen dinners.

As per the given information, we can write the equations would be as

x + y = 11   ....(i)

Also:

350x + 650y = 4750

7x +13y =95 ....(ii)

Solving equations (i) and (ii) simultaneously gives the values are:

x = 8, and y = 3

Thus, Magan bought 8 cans of soup and 3 cans of frozen dinners.

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Answer:

Q

Step-by-step explanation:

Clara's pay based on commission is $290.

Given:

Minimum wage is 15 h. Clara's commission is 5 % of sales. During one week ,Clara works 25 h and sells $5800 worth of merchandise.

commission = 5%

Clara's pay = 5800*5%

= 5800*5/100

= 58*5

= $290.

Therefore Clara's pay based on commission is $290.

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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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The required probability for 1 adult female is randomly​ selected, find the probability that her pulse rate is less than 83 beats per minute is 0.5948.

In statistics, what does a probability mean?

Let, X= The female have pulse rate

μ = 7.60 bpm , σ² = 12.5²

a) We find

P[ 1 adult female is randomly selected, her pulse rate is less than 79 bpm]

= P [ X < 79]

= P [ X - μ/ σ <  79 - μ/ σ ]

= P[ X - 76/12.5  <  79 - 76/ 12.5 ]

= P[Z < 0.24]

= 0.5948 (From standard normal cumulative probability table)

Hence, the required probability of 1 adult female is randomly​ selected, find the probability that her pulse rate is less than 83 beats per minute.is 0.5948.

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Answer:

1- 50

2- 130

3- 50

4- 130

5- 40

6- 140

7- 90

8- 140

Step-by-step explanation:

Answer:

m∠1 = 50°

Step-by-step explanation:

From inspection of the given diagram we can see that angle 1, angle 40° and a right angle are the interior angles of a right triangle.

As the interior angles of a triangle sum to 180°:

⇒ m∠1 + 40° + 90° = 180°

⇒ m∠1 + 130° = 180°

⇒ m∠1 + 130° - 130° = 180° - 130°

⇒ m∠1 = 50°

Therefore, the measure of angle 1 is 50°.

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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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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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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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 possible number of green tiles in the rectangle can be found to be H. 24.

The number of green tiles and red tiles in the rectangle will need to be expressed as whole number alone.

This means that because the ratio of the green tiles to the red tiles is 3 : 4, number of green tiles should be divisible by 3.

The numbers given are:

= 10 / 3

= 3.33

16:

= 16 / 3

= 5.33

24:

= 24 / 3

= 8

Because 24 is divisible by 3, there must be 24 green tiles in the rectangle.

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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:

Step-by-step explanation:

supplementary angles = 180°

so

3x + 5 + 9x - 17 = 180

12x - 12 = 180

12x = 180 + 12

12x = 192

x = 192 : 12

x = 16 units

--------------------------------

check

3 * 16 + 5 + 9 * 16 - 17 = 180

180 = 180

the answer is good

Answer:

log(x^2  y^3/(x+2)^3)

Step-by-step explanation:

The Z-score of a value is the count of the number of standard deviations between the value and the mean of the set. Hence, the height of a man with a z-score is [tex]25.35inches[/tex]

What is z-sore ?

The z-score of a value is the count of the number of standard deviations between the value and the mean of the set. You can find it by subtracting the value from the mean and dividing the result by the standard deviation.

Here given that,

mean=[tex]69.0 inches[/tex]

standard deviation=[tex]2.8 inches[/tex]

[tex]x=-2[/tex]

The general formula of the z-score is

[tex]z=\frac{x-mean}{standard deviation}[/tex]           .......[tex](1)[/tex]

Now, putting the values in the equation [tex](1)[/tex], we get

[tex]z=\frac{-2-69.0}{2.8}\\z=\frac{71}{2.8}\\z=25.35inches[/tex]

Hence, the height of a man with a z-score is [tex]25.35inches[/tex]

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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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