What is the value of x?
X
30°
24
Express your answer in radical form.
Enter your answer in the box.

For given function function f(x)=-x+3-2, the domain is x > -3 and the range is y ≤ 2. So, correct option is D.

The function f(x)=-x+3-2 is a linear function in the form y=mx+b, where m is the slope and b is the y-intercept. In this case, the slope is -1 and the y-intercept is 1. Therefore, the graph of the function is a straight line that intersects the y-axis at (0,1) and has a slope of -1, meaning that it decreases by 1 for every 1 unit increase in x.

The domain of the function is the set of all possible values of x for which the function is defined. Since there are no restrictions on the value of x in the equation f(x)=-x+3-2, the domain is all real numbers, or (-∞, ∞).

The range of the function is the set of all possible values of y that the function can output. In this case, the lowest possible value of y occurs when x approaches positive infinity, and the highest possible value of y occurs when x approaches negative infinity. Therefore, the range is all real numbers less than or equal to 2, or y ≤ 2.

So, the domain is x ∈ (-∞, ∞) and the range is y ≤ 2. Alternatively, the domain can also be expressed as x > -3, since that is the minimum value of x at which the function is defined.

Correct option is D.

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Complete question is:

What are the domain and range of the function f(x)=-x+3-2?

A) domain: -3 -2

B) domain: -3 -3 range: y<-2

C) domain: x>-3 range:y>-2

D) domain : x>-3 range: y ≤ 2

Monique gave away a greater fraction of cake than Chris.

We can represent the fraction of cake Chris gave away as 3/8, and the fraction of cake Monique gave away as 4/8 (which can be simplified to 1/2)

3/8 ______ 1/2

In order to compare the fractions, we can convert them to have a common denominator. The smallest common multiple of 8 and 2 is 8, so we can write:

3/8 = 3/8

1/2 = 4/8

Now we can fill in the symbol to complete the comparison:

3/8 < 1/2

Therefore, Monique gave away a greater fraction of cake than Chris.

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The vector v can be decomposed into v₁ = -2i - 2j and v₂ = -6i + 6j.

The decomposition of the vectors is calculated as follows;

v₁ = (v · w / |w|²) w

v₂ = v - v₁

The dot product of v and w is calculated as;

v · w = (-8)(1) + (4)(1)

v · w = -4

The magnitude of w is calculated as;

|w| = √1² + 1²)

|w|= √2

|w|² = 2

The value of v₁ is calculated as;

v₁ = (-4 / 2) (i + j)

v₁  = -2i - 2j

The value of v₂ is calculated as follows;

v₂ = v - v₁

v₂  = (-8i + 4j) - (-2i - 2j)

v₂ = -6i + 6j

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Answer:

Step-by-step explanation:

The required probability is simply the (shaded area)/(area of the whole box)

The area of the whole box would be:

6r*2r = 12 r^2

The shaded area is tough to calculate, but you can get the

white area instead.

The left hole (white area) consists of a semi-circle and a rectangle.

The center hole is a circle.

The right hole (white area) consists of a semi-circle and a rectangle.

The 2 semi-circles in the left and right hole combine to be a circle.

The 2 rectangles in the left and right hole combine to be a square.

The total area of holes are:

(area of circle)*2 + (area of square)       ### 2 circles 1 square in total

=r^2*pi*2 + (2r)^2

=r^2*pi*2 +4*r^2

then we can get the shaded area by:

(area of the whole box) - (The total area of holes)

= 12 r^2 - (r^2*pi*2 +4*r^2)

=8*r^2 - r^2*pi*2

Finally:

(shaded area)/(area of the whole box)

=(8*r^2 - r^2*pi*2)/(12 r^2)

=(8-pi*2)/(12)

=0.143067891

=14.3% (corr. to 3 sig. fig.)

The rank of the matrix is 3, since there are three linearly independent rows.

The rank of a matrix is the maximum number of linearly independent rows or columns in the matrix. It is denoted by the symbol "rank(A)" for a matrix A.

To find the rank of the matrix:

[-2, -1, -3, -1] [ 1, 2, -3, -1] [ 1, 0, 1, 1] [ 0, 1, 1, -1]

We can perform row operations to reduce the matrix to row echelon form, which will help us determine the rank.

[tex]R_2 = R_2 + 2R_1 R_3 = R_3 + 2R_1 R_4 = R_4 + R_2[/tex]

This gives us the following matrix:

[-2, -1, -3, -1] [ 0, 0, -9, -3] [ 0, -1, -1, 1] [ 0, 0, -4, -4]

We can see that the third row is not a linear combination of the first two rows, and the fourth row is not a linear combination of the first three rows. Therefore, the rank of the matrix is 3, since there are three linearly independent rows.

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Answer: 2,001.57

Step-by-step explanation:

there ya go!

Answer:

G^-1(t)=t/7+4

Step-by-step explanation:

G(t) = 7(t - 4)

y = 7(x - 4)

x = 7(y - 4)

x/7 = y - 4

y = x/7 + 4

G^-1(t) = t/7 + 4

Answer: G^-1(t)=t/7+4

The experimental probability that an arrangement will contain at least one red balloon and at least one blue balloon is 0.53. Therefore, option B is the correct answer.

The given sample space is {ybrr bybb rbbb rrry rbbb rryy yybb ryry ryyr rbyr ryyr rryy rrrr yrby bbyy byyr byyr byyb rbby ybry rryy rbrr rybb bbbr rrbr ybry ryrr rryb rrrb rryr}

We know that, probability of an event = Number of favorable outcomes/Total number of outcomes.

Here, total number of outcomes = 30

Number of favorable outcomes =16

Probability of an event 16/30

= 0.53

Therefore, option B is the correct answer.

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Answer:

AB = 90° , AC = BC = 135°

Step-by-step explanation:

the arc AB is equal to the measure of the central angle it subtends, then

AB = 90°

the sum of the arcs in a circle = 360° , then since AC and BC are congruent

AB + AC + BC = 360° ( since AC = BC ), then

90° + 2AC = 360° ( subtract 90° from both sides )

subtract 90° from both sides

2AC = 270° ( divide both sides by 2 )

AC = 135°

since AC = BC , then

AC = BC = 135°

The area of a regular hexagon with side length 14 inches is 509.22 square inches.

Given that, a regular hexagon with side length 14 inches.

We know that, area of a regular hexagon can be calculated using A=3√3/2 a².

Here, area of a regular hexagon = 3√3/2 ×14²

= 3√3 ×98

= 509.22 square inches

Therefore, the area of a regular hexagon with side length 14 inches is 509.22 square inches.

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Answer:

=997

Step-by-step explanation:

46-15=31

31×32=992

992+5=997

Answer:  997

Step-by-step explanation:

Answer:

Here is a Venn diagram that illustrates the information:

```

           ___________

          |           |

          |    N      |

          |_____  ____|

          |\    ||    /|

          | \   ||   / |

          |  \  ||  /  |

          |   \ || /   |

          |  C \||/ T  |

          |_____\v/____|

              A

```

In the diagram, N represents the set of students who read the novel, C represents the set of students who read the comics, and T represents the set of students who read the textbook. The region labeled A represents the set of students who read all three.

Using the Venn diagram, we can find the number of students who read:

a. comics and novel only: This corresponds to the region of the diagram that is exclusively shaded with the circles for comics and novel, but not for textbook. This region has 9 students.

b. textbook and novel only: This corresponds to the region of the diagram that is exclusively shaded with the circles for textbook and novel, but not for comics. This region has 1 student.

c. none of the 3: This corresponds to the region of the diagram that is outside of all three circles. This region has 13 students.

Therefore, the number of students who read a. comics and novel only is 9, b. textbook and novel only is 1, and c. none of the 3 is 13. Answer: a. 9, b. 1, c. 13.

Step-by-step explanation:

5^(x+2)  <= 3^x    

5^x  *  5^2  <= 3^x

25 <=  3^x / 5^x

25<= (3/5)^x                  LOG both sides

log 25 <= x log (3/5)

log 25 / log (3/5) <= x

- 6.3 <= x

The standard error is 0.0912.

The standard error (SE) is a measure of the precision of the sample mean estimate compared to the true population mean. To calculate the SE, we use the formula SE = standard deviation / square root of sample size.

In this scenario, the population parameter is 0.7, and the sample size is 30. If we assume that the sample mean is an unbiased estimator of the population mean, then the SE can be calculated using the above formula. However, we do not know the standard deviation of the population, so we use the sample standard deviation as an estimate.

Assuming the sample is large enough to assume normality, the formula becomes SE = [tex]\sqrt{(0.7*0.3)/30}[/tex]   = 0.0912. Therefore, the standard error for a sample size of 30 is 0.0912. This means that if we were to take multiple samples of size 30 from the same population, the standard deviation of the means of those samples would be around 0.0912 away from the population parameter of 0.7 on average.

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Carleigh, Inc. should separate the organ meats from the residual and sell them abroad, as it would increase their total revenue by $17,150 per week.

To determine whether Carleigh, Inc. should separate the organ meats and sell them abroad, we need to calculate the incremental revenue and incremental costs associated with this decision.

The incremental revenue would be the revenue generated from selling the organ meats abroad, which is $52,000 per week. The incremental cost would include the cost of further processing ($27,500 per week), transportation cost ($12,100 per week), and the increase in resource spending for other activities ($3,120 per week).

Therefore, the incremental cost would be $42,720 per week. Subtracting this from the incremental revenue of $52,000, we get an incremental profit of $9,280 per week.

However, this decision would also decrease the value of the residual from $9,800 to $2,650 per week. Therefore, we need to subtract this decrease in value from the incremental profit. This gives us a net increase in profit of $17,150 per week ($9,280 - $7,130).

Thus, it would be beneficial for Carleigh, Inc. to separate the organ meats and sell them abroad.

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The required two column proof is explained below.

A midpoint is a point which divides a line segment into two equal parts. Thus it can be referred to as the middle point of the line segment.

The two column proof for the information is given as:

M is the midpoint of CD    (Given)

CD = CM + MD   (addition property of a line segment)

CM = MD  (definition of a midpoint)

So that;

5x – 2 = 3x + 2    (Definition of midpoint)#

Then,

5x - 3x = 2 + 2 (collecting like terms)

2x = 4

x = 2

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Assuming that a fair coin was tossed twice, the probability that exactly one of the tosses is a head and the other toss is a tail is 1/2.

The probability of a certain event happening is the number of ways that event can occur, divided by the total number of possible outcomes. In this case, we are interested in finding the probability that exactly one of the two coin tosses results in a head and the other results in a tail.

There are two possible outcomes that satisfy this condition: HT and TH. Since the coin is fair, each of these outcomes has a probability of 1/4. Therefore, the total probability of getting exactly one head and one tail is:

P(HT or TH) = P(HT) + P(TH) = 1/4 + 1/4 = 1/2

In other words, there is a 50-50 chance of getting exactly one head and one tail when a fair coin is tossed twice.

To see why this is the case, we can think of each toss as an independent event with two possible outcomes (head or tail). There are four possible outcomes when we toss a coin twice, and two of these outcomes satisfy the condition of exactly one head and one tail. Therefore, the probability of getting exactly one head and one tail is 2/4, which simplifies to 1/2.

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The probability that a statistics teachers do not know the true meaning of life is 46.8%

From the question, we have the following parameters that can be used in our computation:

53.2% of Americans say they believe that statistics teachers know the true meaning of life.

This means that

P(Believe) = 53.2%

For the required probability, we have

P(Not believe) = 1 - P(Believe)

So, we have

P(Not believe) = 1 - 53.2%

Evaluate

P(Not believe) = 46.8%

Hence, the probability that a statistics teachers do not know the true meaning of life is 46.8%

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Answer: The number of different ways the teacher can choose the team of three students from a class of 23, where the order of the speakers is not important, is 1771.

Step-by-step explanation:

To solve this problem, we can use the combination formula:

nCr = n! / r!(n - r)!

where n is the total number of items, r is the number of items to be selected, and ! represents factorial, which means the product of all positive integers up to the given number.

In this case, we need to choose 3 students out of 23, without regard to the order in which they will speak. Therefore, we need to use the combination formula with n = 23 and r = 3:

23C3 = 23! / (3!(23 - 3)!)

= 23! / (3!20!)

= (23 × 22 × 21) / (3 × 2 × 1)

= 1771

Therefore, there are 1771 different ways the teacher can choose the team of three students for the competition, where the order of the speakers is not important.

[tex]\frac{5}{25} = \frac{9}{x +4}[/tex] when simplified, the value of x = 41

Equation is  a mathematical statement that is made up of two expressions connected by an equal value.It says that two things are equal and it expresses equality of two mathematical expressions.

How to determine this

[tex]\frac{5}{25} = \frac{9}{x +4}[/tex]

To find the value of x,

By cross multiplying

5(x+4) = 9(25)

Open bracket

5x + 20 = 225

Collect like terms

5x = 225 - 20

5x = 205

Divides through by 5

5x/5 = 205/5

x = 205/5

x = 41

Therefore, the value of x = 41

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Answer:A,D

Step-by-step explanation:

y = [5.3, 27]

x= [-1,3]

The solution of the triangle have been shown below.

To solve a triangle means to find the values of all its angles and sides. The method for solving a triangle depends on the given information.

Given that;

a/Sin A = b/SinB

Sin B = bSin A/a

B = Sin-1(bSin A/a)

B = Sin-1 (23Sin 40/17)

B = 60.4 degrees

Then we have that

C = 180 - (40 + 60.4)

= 79.4 degrees

Then;

a/sinA = c/Sin C

c= aSin C/Sin A

c = 17 * Sin 79.4/Sin 40

c =   16.71/0.643

c = 25.9

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Answer:

Beauty algebra is not a recognized term or concept within the field of mathematics. Therefore, there is no main idea associated with it in mathematical context. It is possible that the term is used in a different context or field, but without additional information, it is not possible to provide a more accurate answer.

Answer:

a

Step-by-step explanation:

We can write the quadratic in standard form as:

y = x² -18x - 1053

For a quadratic equation whose solutions are:

x = x₁

x = x₂

We can write it as:

y = (x - x₁)*(x - x₂)

Here the solutions are:

x = 9 + 9√13

x = 9 - 9√13

Then we can write the quadratic as:

y = (x - 9 - 9√13)*(x - 9 + 9√13)

Expanding that:

y = x² -18x - 81*13

y = x² -18x - 1053

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Answer: E. 1

Explanation: The slope (m) of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

We can use this formula to find the slope of the line passing through points (4, 6) and (2, 4):

m = (y2 - y1) / (x2 - x1)

m = (4 - 6) / (2 - 4)

m = -2 / -2

m = 1

The slope of the line passing through points (4, 6) and (2, 4) is 1.

The answer is E) 1.

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The given expression ((−3⁴)⁻⁷)⁻³ using only positive exponents is equal to  (-3)⁻⁸⁴.

To write the expression ((−3⁴)⁻⁷)⁻³ using only positive exponents, we can apply the rule of exponentiation that states that a negative exponent can be converted to a positive exponent by moving the base to the denominator and changing the sign of the exponent.

In this case, we have a negative exponent raised to another negative exponent, so we need to apply this rule twice.

First, we can rewrite the expression as:

((-3⁴)⁻⁷)⁻³ = (-3⁴)⁷³

Next, we can apply the rule of negative exponent to obtain:

(-3⁴)⁷³ = (1/(-3⁴))⁻²¹

Finally, we can simplify the expression by moving the negative exponent to the numerator, changing the sign of the exponent and using the power rule of exponents to get:

(1/(-3⁴))⁻²¹ = (-3⁻⁴)²¹ = (-3)⁻⁸⁴

In conclusion, we can convert a negative exponent to a positive exponent by moving the base to the denominator and changing the sign of the exponent. We can use this rule multiple times to simplify expressions with negative exponents.

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The distance between the points (5, 8) and (-3, 4) is equal to 4√5 units.

In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represent the data points (coordinates) on a cartesian coordinate.

By substituting the given end points into the distance formula, we have the following;

Distance = √[(-3 - 5)² + (4 - 8)²]

Distance = √[(-8)² + (-4)²]

Distance = √[64 + 16]

Distance = √80

Distance = 4√5 units.

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Answer: Given b=2√14 and c=9,

a = 5

Step-by-step explanation: