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astruction Expressions in One Variable
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9
Writing and Evaluating Expressions
Susan is four years older than half Nathan's age. If Nathan's age is represented
by the variable n, what expression represents Susan's age?
Nathan's age =
Susan's age = (n) +

Answer:

x = 12.2

Step-by-step explanation:

to solve for 'x', we can use the sine ratio of opposite/hypotenuse

we need to find the angle opposite side 'x', which can be found by:

180-(44+90) = 46

sin46° = x/17

x = 17·sin46°

x = 12.2

9514 1404 393

Answer:

Step-by-step explanation:

Using the least common denominator, we have ...

  \(2-\dfrac{x+1}{x-2}-\dfrac{x-4}{x+2}\\\\=\dfrac{2(x-2)(x+2)-(x+1)(x+2)-(x-4)(x-2)}{(x-2)(x+2)}\\\\=\dfrac{2(x^2-4)-(x^2+3x+2)-(x^2-6x+8)}{x^2-4}\\\\=\dfrac{(2-1-1)x^2+(-3+6)x+(-8-2-8)}{x^2-4}=\boxed{\dfrac{3x-18}{x^2-4}}\)

The values of a and b are ...

  a = 3

  b = -18

The information about the distance as a function of time of given by the piecewise function include :

At 0 ≤ t < 2.5 ; D(t) = 300t + 125 ;

The starting distance at 0 hours is ;

D(0) = 300(0) + 125 = 125 miles  

At t = 2 hours

D(2) = 300(2) + 125 = 600 + 125 = 725 miles

At t = 2.5 hours ; At 2.5 ≤ t ≤ 3.5

D = 880 miles (Fixed)

At t = 3 hours ; 2.5 ≤ t ≤ 2.5

D = 880 miles

At t = 6 hours ; 3.5 < t ≤ 6

D = 75(6) + 612.5 = 450 + 612.5 = 1062.5 miles

Therefore, only statements, B, D, and E are correct.

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Complete question

The function D(t) defines a traveler’s distance from home, in miles, as a function of time, in hours.

D(t) = StartLayout enlarged left-brace 1st Row 1st column 300 t + 125 , 2nd column 0 less-than-or-equal-to t less-than 2.5 2nd Row 1st column 880, 2nd column 2.5 less-than-or-equal-to t less-than-or-equal-to 3.5 3rd Row 1st column 75 t + 612.5, 2nd column 3.5 less-than t less-than-or-equal-to 6 EndLayout

Which times and distances are represented by the function? Select three options.

The starting distance, at 0 hours, is 300 miles.

At 2 hours, the traveler is 725 miles from home.

At 2.5 hours, the traveler is 875 miles from home.

At 3 hours, the distance is constant, at 880 miles.

The total distance from home after 6 hours is 1,062.5 miles

\(\huge\mathsf\green{Answer}\)

\(5 + ( - 7) \\ 5 - 7 = - 2\)

Based on the rating factor of 75%, the normal time for the job element would be 11.19 seconds.

When given the rating factor, the normal time can be found as:

= Average time for the job element x Rating factor

Average time for the job factor is:

= [(10 x 18) + (15 x 25) + (20 x 17)] / (18 + 25 + 17)

= 14.92 seconds

The normal time for the job element is therefore:

= 14.92 x 0.75

= 11.19 seconds

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Explanation:

Turn the irrational numbers into decimals, so it is easy to understand and point on the number line graph.

Numbers provided:

√13 = 3.605551275 ≈ 3.61

√17 = 4.123105625 ≈ 4.12

Step by Step Solving:

Plot the points (circled area's):

The volume of the rectangular prism having a dimensions 12 by 8 by 2 is 192.

A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles.

The volume of a rectangular prism is expressed as;

V = w × h × l

Where w is the width, h is height and l is length

From the diagram:

Length l = 12 units

Width w = 8 units

Height h = 2 units

Plug these values into the above formul and solve for the volume:

Volume V = w × h × l

Volume V = 8 × 2 × 12

Volume V = 192 cubic units.

Therefore, the volume is 192.

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Answer:

-4.4

Step-by-step explanation:

2.8 + 7.2 = -4.4

Based on the computed 95% confidence interval, we can conclude that we are 95% confident that the true population mean falls within the range of 12.65 to 25.65.

A confidence interval is a range of values that provides an estimate of the true population parameter. In this case, we are interested in estimating the population mean (μ). The 95% confidence interval, as mentioned, is given as 12.65 ≤ μ ≤ 25.65.

Interpreting this confidence interval, we can say that if we were to repeat the sampling process many times and construct 95% confidence intervals from each sample, approximately 95% of those intervals would contain the true population mean.

The confidence level chosen, 95%, represents the probability that the interval captures the true population mean. It is a measure of the confidence or certainty we have in the estimation. However, it does not guarantee that a specific interval from a particular sample contains the true population mean.

Therefore, based on the computed 95% confidence interval, we can conclude that we are 95% confident that the true population mean falls within the range of 12.65 to 25.65.

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In order to help the museum digitize the remaining books, they will need to use the technique of data compression. What is data compression? Data compression is the process of compressing digital data to reduce its size. The goal is to save storage space and improve transmission speed. The term “compression” refers to the technique of compacting information into fewer bits, whereas “decompression” refers to the process of restoring the original data from the compressed data.

Digitize: To digitize is to transform a physical object, text, image, or sound into a digital format that can be used by computers or other electronic devices to be stored or processed. Digitizing is becoming more popular because digital files are easier to manage, edit, and store than physical documents.

Digital files: A digital file is a file that contains digital data, such as images, video, audio, or text, that can be stored, edited, and manipulated by electronic devices. Digital files are stored on a computer, server, or another electronic device, and can be accessed and shared over the internet.

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Had a stroke reading this.

Answer:

what is this pls isit a question

A set is simply the group of related item.

Let:

\(C \to\) Those who eat corn

\(M \to\)Those who eat millet

\(x \to\) Those who eat both

So, we have:

\(C = 400\)

\(M= 290\)

\(None = 60\)

\(Total = 730\)

(a) The number of those who eat both

To do this, we make use of the following equation

\(Total =C + M - x + None\)

The above equation represents the sum of all possible subsets

So, we have:

\(730 =400 + 290 - x+ 60\)

Collect like terms

\(x =400 + 290 + 60 -730\)

\(x =20\)

Hence, 20 villagers eat both

(b) Number of those that eat only one

We have:

\(C = 400\)

\(M= 290\)

The number (n) of those that eat only one is:

\(n =C -x+ M - x\)

\(n = 400 - 20 + 290 - 20\)

\(n =650\)

Hence, 650 villagers eat only one

See attachment for the Venn diagram that illustrates the set

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Answer:  The answer to the question is $59.05

Step-by-step explanation:

Good Luck

Answer:

9/5

Step-by-step explanation:

3/5 ÷ 1/3

9/5

Answer:

\(p = \frac{11}{12}\)

Step-by-step explanation:

If we roll two number cubes we can summarize the results in the following table (Check table in the attachment)

According to table of sum we roll two numbers with a sum less than or equal to 10 in 33 cases out of a total of 36 result

Then

The probability of rolling two numbers with a sum less than or equal to 10 is: 33/36 = 11/12

Step-by-step explanation:

(F+g) (-5)

={2x+x-30 +(x-5)}(-5)

={4x-35}(-5)

= -20x +175

X=175/20

X=35/4

X=8.75

...........

(f - g)(3)

={x2 + x - 30 - (x- 5)} (3)

= {2x - 25} (3)

=6x-75

X=75/6

X=12.5

..................

(f.g)(-3)

= {(x2 + x - 30). (x- 5)} (-3)

={(3x-30)(x-5)}(-3)

Answer:

Step-by-step explanation:

Therefore, in about 15 years and 2 months, the senior class will have about 100 students.

An equation is a statement that expresses the equality of two mathematical expressions using mathematical symbols such as variables, numbers, and mathematical operations. The equality is represented by an equal sign "=" between the two expressions. Equations are used to represent mathematical relationships and solve problems in various fields such as physics, chemistry, engineering, and economics.

Given by the question.

Let P be the initial population of the senior class in the high school, and r be the rate of decrease in population per year (in decimal form).

Then, we can write the following equation to represent the situation:

P\((1-r)^{n}\) = 100

We know that the current population of the senior class is 320, so we can substitute these values into the equation:

320\((1-0.07)^{n}\) = 100

Simplifying the equation, we get:

\(0.93^{n}\) = 0.3125

Taking the natural logarithm of both sides, we get:

n ln (0.93) = ln (0.3125)

Dividing both sides by ln (0.93), we get:

n = ln (0.3125) / ln (0.93)

Using a calculator, we find that n is approximately equal to 15.21 years.

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The last column evaluates to "T" in all rows. Therefore, the argument is valid since the conclusion always follows from the premises.

Let's assign symbols to represent the statements in the argument:

P: The boss snaps at you.

Q: You make a mistake.

R: The boss is irritable.

The argument can be symbolically represented as follows:

[(P ∧ Q) → R] ∧ ¬P → ¬R

To determine the validity of the argument, we can construct a truth table:

P | Q | R | (P ∧ Q) → R | ¬P | ¬R | [(P ∧ Q) → R] ∧ ¬P → ¬R

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

T | T | T |      T      |  F |  F |          T          |

T | T | F |      F      |  F |  T |          T          |

T | F | T |      T      |  F |  F |          T          |

T | F | F |      F      |  F |  T |          T          |

F | T | T |      T      |  T |  F |          F          |

F | T | F |      T      |  T |  T |          T          |

F | F | T |      T      |  T |  F |          F          |

F | F | F |      T      |  T |  T |          T          |

The last column represents the evaluation of the entire argument. If it is always true (T), the argument is valid; otherwise, it is invalid.

Looking at the truth table, we can see that the last column evaluates to "T" in all rows. Therefore, the argument is valid since the conclusion always follows from the premises.

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The coordinates of the point on the directed line segment from K (-5,-4) to L (5,1) that portions the segment into ratio of 3 to 2 are (-2.6923076923076925, -2.8461538461538463). The correct option is A.

The coordinates of the point that divides a line segment in a ratio of m to n can be calculated using the following formula:

x = mx1 + nx2 / m + n

y = my1 + ny2 / m + n

In this case, m = 3 and n = 2, so the coordinates of the point are:

x = 3 * (-5) + 2 * 5 / 3 + 2 = -2.6923076923076925

y = 3 * (-4) + 2 * 1 / 3 + 2 = -2.8461538461538463

Therefore, the coordinates of the point are (-2.6923076923076925, -2.8461538461538463).

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The probability of at least one card being a heart is 0.546 or approximately 54.6%.

To solve this problem, we can use the concept of complementary probability, which states that the probability of an event happening is equal to one minus the probability of the event not happening.

The probability of not getting a heart on the first draw is 39/52, since there are 39 non-heart cards out of a total of 52 cards. The same probability applies to the second draw, as the card is replaced. Therefore, the probability of not getting a heart on both draws is (39/52) x (39/52) = 0.454.

Using the complementary probability concept, the probability of at least one card being a heart is 1 - 0.454 = 0.546 or approximately 54.6%.

This means that if we were to repeat this experiment many times, we would expect to get at least one heart card in more than half of the trials.

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Answer:

See below

Step-by-step explanation:

You can always plug in x's and solve for y.

Answer:

32

Step-by-step explanation:

Answer:

11.6°

Step-by-step explanation:

In ΔGHI, g = 3.4 cm, i = 8.2 cm and ∠I=29°. Find all possible values of ∠G, to the nearest 10th of a degree.

We solve the above question using Law of Sines

= g/sin G = I / sin I

Substituting

= 3.4/ sin G= 8.2/ sin 29

Cross Multiply

3.4 × sin 29 = sin G × 8.2

sin G = 3.4 × sin 29/ 8.2

G = arc sin[3.4 × sin 29/ 8.2]

G = arcsin [0.2]

G = 11.59653°

Approximately = 11.6°

∠G = 11.6°

Answer:

40 and 7/10

Step-by-step explanation:

40 and 28/40 -> 40 and 7/10 (simplification). Your answer would be 40 and 7/10 in mixed number form

Answer:

I need to know the equation not only the answer

Step-by-step explanation:

here is an ex.

32/5=6R2

mixed number=6 2/5

whole number plus remainder over divisor Is the mixed number

if u put the full equation in comments, I can help u solve it :)

Answer:

sure but can u help me ban 50070356 he or she is using my pfp as hers

Step-by-step explanation:

A function f is blank 1 of 1 linear on an interval ii if, for any choice of x1 and x2 in ii, with x1 < x2.

A function f is **question blank 1 of 1** linear on an interval **ii** if, for any choice of **x1** and **x2** in **ii**, with **x1** < **x2**, the function satisfies the properties of a linear function.t

In a linear function, the rate of change (slope) between any two points on the function is constant. This means that the function's value increases or decreases at a constant rate as we move along the interval.

The blank in the question refers to the specific term that should be filled. However, based on the given context, it seems that the most suitable term to fill the blank would be **"is"**. Therefore, the sentence would read as:

"A function f is linear on an interval ii if, for any choice of **x1** and **x2** in **ii**, with **x1** < **x2**, the function satisfies the properties of a linear function."

This statement highlights the key characteristic of a linear function, where the function's behavior between any two points on the interval is consistent and can be represented by a straight line.

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Yes, line is used to define an angle.

When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

When two straight lines or rays intersect at a single endpoint, an angle is created.

The vertex of an angle is the location where two points come together.

The common point is referred to as the vertex.

The length of the angle formed when two rays or arms intersect at a common vertex is known as an angle measure in geometry.

A straight line is a straight angle.

Therefore, two lines are used to define an angle.

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Answer:

The first thing that we have to do is add 33 to both sides to try to reduce the amount of variables on the left hand side.

\(\frac{x}{6} - 33 = -27\)

\(\frac{x}{6} - 33 + 33 = -27 + 33\)

\(\frac{x}{6} = 6\)

Now that we have simplified the left hand side even more we only have one part left to get x by itself which is to multiply both sides by 6.

\(\frac{x}{6} = 6\)

\(\frac{x}{6} * 6 = 6 * 6\)

\(x = 36\)

Therefore, our final answer for what the value of x equals is 36.

Hope this helps!  Let me know if you have any questions

Take into account the following property:

Then, for the given expression you have:

Hence, the answer is approximately 3.322