A baby weighs 10 pounds at birth, and four years later the child's weight is 40 pounds. Assume that childhood weight W (in pounds) is linearly related to age t (in years).
(a) Express W in terms of t.

Answer:

Step-by-step explanation:

To find the product of (7-8x)(3x^3-2x^2+x), we need to use the distributive property of multiplication over addition/subtraction.

First, let's distribute the 7 across the second factor:

(7)(3x^3) - (7)(2x^2) + (7)(x)

This simplifies to:

21x^3 - 14x^2 + 7x

Next, we need to distribute the -8x across the second factor:

(-8x)(3x^3) + (-8x)(-2x^2) + (-8x)(x)

This simplifies to:

-24x^4 + 16x^3 - 8x^2

Now, we can combine the two simplifications:

(7-8x)(3x^3-2x^2+x) = 21x^3 - 14x^2 + 7x - 24x^4 + 16x^3 - 8x^2

Finally, we can combine like terms to simplify the expression:

-24x^4 + 37x^3 - 22x^2 + 7x

Therefore, the product of (7-8x)(3x^3-2x^2+x) is -24x^4 + 37x^3 - 22x^2 + 7x.

Student A and Student D have correctly simplified the expression. The expression 154 can be written as 3h + 21 + 15-4h+6+h, which is the same as 21 - 3h + 3h + 21. Student A and Student D both simplified the expression to 21 - 3h. Student B simplified the expression to 18h and Student C simplified the expression to 600p, which are both incorrect.

Adam needs to show that the diagonals are perpendicular, congruent, and bisect each other.Therefore Option D is correct.

To prove that PQRS is a square, Adam needs to show that all four sides are congruent and that all four angles are right angles.

One way to do this is by showing that the diagonals of PQRS are perpendicular, congruent, and bisect each other.

If the diagonals are perpendicular, then opposite angles are congruent and the quadrilateral is a kite.

If the diagonals bisect each other, then opposite sides are congruent and the kite is a rhombus.

If the diagonals are also congruent, then all sides are congruent and the rhombus is a square.

Therefore, He needs to show that the diagonals of PQRS are perpendicular, congruent, and bisect each other to prove that PQRS is a square.

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In a multiple choice exam, there are 5 questions and 4 choices for each question (a, b, c, d). nancy has not studied for the exam at all and decides to randomly guess the answers, the probability that Nancy will correctly answer all 5 questions by guessing is 0.000977

In a multiple choice exam, there are 5 questions and 4 choices for each question (a, b, c, d). Nancy has not studied for the exam at all and decides to randomly guess the answers.

The probability of guessing on an exam can be calculated by using the formula:n(C)/(n(T))where n(C) is the number of favorable events and n(T) is the total number of events. Let's solve the given problem:

Probability of getting the first question correct: P (1st) = 1/4 Probability of getting the second question correct: P (2nd) = 1/4Probability of getting the third question correct: P (3rd) = 1/4 Probability of getting the fourth question correct: P (4th) = 1/4Probability of getting the fifth question correct: P (5th) = 1/4 The probability of guessing all questions correctly can be calculated by multiplying the probability of each question together. P (all) = P (1st) * P (2nd) * P (3rd) * P (4th) * P (5th)= 1/4 * 1/4 * 1/4 * 1/4 * 1/4= 1/1024Therefore, the probability that Nancy will correctly answer all 5 questions by guessing is 0.000977. (rounded to four decimal places)Answer: 0.000977

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The for the values of the variables x = 7 and y = 10, the given must be a parallelogram.

A quadrilateral having two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Also, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.

A parallelepiped is a three-dimensional shape with parallelogram-shaped faces. The base and height of the parallelogram determine its area.

For the given quadrilateral to be parallelogram the opposite sides need to be parallel and equal.

For the given quadrilateral we have:

2y - 16 = y - 6

2y - y = -6 + 16

y = 10

Also,

2x + 2 = y + 6

Substitute the value of y = 10:

2x + 2 = 10 + 6

2x = 16- 2

2x = 14

x = 7

Hence, the for the values of the variables x = 7 and y = 10, the given must be a parallelogram.

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Answer:

Step-by-step explanation:

2(2x-5) = 18 (FOIL)

4x-10=18

4x = 28

x= 7

Answer:

x = -2

Step-by-step explanation:

2(2x - 5) = -18

Divide both sides by 2.

2x - 5 = -9

Add 5 to both sides.

2x = -4

Divide both sides by 2.

x = -2

Answer:

[tex]x = 4\sqrt{3}[/tex]

Step-by-step explanation:

The triangle is right-angled

In a right-angled triangle, the following equality holds

[tex]\tan x = \dfrac{\text{Side Opposite x}}{\text{Side adjacent to x}}\\\\\tan 30 = \dfrac{4}{x}\\\\[/tex]

[tex]\tan 30 = \dfrac{1}{\sqrt{3}}\\\\\dfrac{1}{\sqrt{3}} = \dfrac{4}{x}\\\\[/tex]

Cross multiply:
[tex]1 \times x = 4 \times \sqrt{3}\\\\x = 4\sqrt{3}[/tex]

Work Shown:

x = previous total weight

2% of x = 0.02x = amount of weight lost

x - 0.02x = 0.98x = current total weight

0.98x = 1519

x = 1519/0.98

x = 1550 pounds

Check:

2% of 1550 = 0.02*1550 = 31

The group collectively lost 31 pounds.

1550-31 = 1519

The answer is confirmed.

Note that 98% of 1550 = 0.98*1550 = 1519

Answer:

Step-by-step explanation:

120

Answer:

Step-by-step explanation:

what?

The equation that correctly represents this situation is c(t) = 45 + 45(t-2). This equation states that the total number of credits the student will have after t semesters is equal to 45 (the number of credits they had before beginning college) plus 45 times the number of semesters after two (t-2).

To explain this equation in more detail, we need to break it down. First, the student had some credits earned while in high school, so the equation starts off with c(t) = 45, which is the number of credits the student had before beginning college.

Next, 45(t-2) represents the number of credits earned in the additional semesters since college began. The t-2 part of the equation means that the total number of credits earned in the additional semesters starts at zero for t = 2. Then, for each additional semester, 45 credits are added. So, for example, when t = 5, 45 credits are added to the initial 45 credits the student had before beginning college, resulting in 90 credits.Therefore, the equation  c(t) = 45 + 45(t-2)  correctly represents this situation.

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The specificity of the test based on the given screening results is 0.967 (rounded to three decimal places).

To calculate the specificity, divide the number of true negatives (TN) by the total number of negative results (TN+FP). In this case, that would be 687/(687+22), which is equal to 0.967 (rounded to three decimal places).

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The likelihood of pulling a spade followed by a face card from a deck is 3/52, or roughly 0.0588. (rounded to four decimal places).

The probability of drawing a spade from a deck of 52 cards is 13/52, or 1/4, since there are 13 spades in the deck.

Once a spade has been drawn and not returned to the deck, there are now 51 cards left in the deck, of which 12 are face cards (the Jack, Queen, and King of each suit). Therefore, the probability of drawing a face card given that a spade has already been drawn is 12/51.

To find the probability of both events happening together (drawing a spade and then a face card), we can multiply the probabilities of each event:

P(drawing a spade, then drawing a face card) = P(drawing a spade) x P(drawing a face card given that a spade has been drawn)

= (1/4) x (12/51)

= 3/52

Therefore, the probability of drawing a spade, then drawing a face card out of a deck is [tex]3/52[/tex]  , or approximately [tex]0.0588[/tex] (rounded to four decimal places).

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The length of each side of the regular pentagon is 10 units

Let's use the fact that the floor is a regular pentagon to set up an equation involving the side lengths.

A regular pentagon has five sides of equal length, so we can set the two expressions for the side lengths equal to each other:

2× + 4 = 4 × - 2

Solving for x, we get:

2x = 6

x = 3

Now that we have the value of x, we can substitute it back into either expression for the side length to find the length of each side. Let's use the expression (2× + 4) inches:

2× + 4 = 2(3) + 4

= 6 + 4

= 10 units

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The crοss-sectiοn in the image  shοwn appears tο be a trapezοid.

A quadrilateral with at least οne pair οf parallel sides. In this crοss-sectiοn, the tοp and bοttοm sides are parallel, while the οther twο sides are nοt parallel is  trapezοid. There are times when people define trapezoids as having at least one pair of opposite sides that are similar, and other times they say there is just one pair.

The parallelogram satisfies the "at least one" interpretation of the definition because it has two pairs of opposite sides that are similar, which qualifies it as both a trapezoid and a parallelogram. The parallelism does not support the "one and only one" interpretation of the description. How students respond to this depends on how they describe themselves.

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The linear relationship of Maggie crocheting squares is y = 6 + 6x graph (b)

Let x be the number of hours Maggie spends crocheting squares, and let y be the total number of squares she has made.

Initially, Maggie has 6 squares made,

so y = 6 when x = 0.

For each hour that she spends crocheting squares, Maggie makes 6 more squares.

Therefore, the relationship between x and y is:

y = 6 + 6x

This is a linear relationship with a slope of 6, which means that Maggie is crocheting squares at a rate of 6 squares per hour.

This is represented by graph (b)

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Answer: 31.8 years

Step-by-step explanation:

The formula to calculate the simple interest is:

I = Prt

where:

I = Interest

P = Principal amount

r = Rate of interest

t = Time (in years)

We want to know how long it will take for the investment to double in value. That means the interest earned should be equal to the principal amount. So, we can write:

2P = P + I

Simplifying:

P = I

Now, we can substitute the values given in the problem:

1400 = 14000.044t

Simplifying:

t = 1400/(1400*0.044) = 31.82 years

Therefore, it will take approximately 31.8 years for the investment to double in value.

The given augmented matrix is equivalent to a system of linear equations with 1 equation and 3 variables. The system is underdetermined and the solution to the system is [tex](x, y, z)[/tex]= (0, 0, 0).

The given augmented matrix is in row-reduced form and is equivalent to a system of linear equations. The matrix has 3 columns and 1 row, so there is 1 equation and 3 variables in the corresponding system of linear equations. Since there is only one equation, the system is underdetermined and has infinitely many solutions.

The solution to the system can be stated as: (x, y, z) = (0, 0, 0). The solution is a point where all the variables are equal to zero. Since the matrix is in row-reduced form, this is the only solution to the system. If the augmented matrix was not in row-reduced form, then the solution would be stated as a parameter, such as (x, y, z) = (0, 0, t), where t is a parameter.

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Answer:

Step-by-step explanation:

For the given augmented matrix, you want to know the number of equations and variables it represents, whether the system is under- or over-determined, and the solution, using parameters as required.

  [tex]\left[\begin{array}{ccc|c}1&\dfrac{1}{4}&-\dfrac{1}{4}&1\\\vphantom{\dfrac{T}{q}}0&0&0&0\end{array}\right][/tex]

Each column of the augmented matrix is the coefficient of the variable in a linear equation represented by the row. The first row of the matrix represents the equation ...

  [tex]1x +\dfrac{1}{4}y-\dfrac{1}{4}z=1[/tex]

The second row of the matrix represents the tautology ...

  0x +0y +0z = 0

It contributes no information about the relationships between the variables.

The matrix represents 1 equation in 3 variables.

For there to be a unique solution to a linear system, there must be as many consistent and independent equations as there are variables. Here, there are fewer equations than variables. This system is underdetermined.

The solution to an underdetermined system can be written in terms of parameters of free choice. We will need as many parameters as there are missing equations: 2.

Here, the coefficients of y and z suggest we choose parameters that let us represent those values as multiples of 4.

Parameters: s, t

Let y = 4s, z = 4t. Then the equation becomes ...

  x +1/4(4s) -1/4(4t) = 1

  x +s -t = 1

  x = 1 +t -s

Now, the solution can be written as ...

  (x, y, z) = (1 +t -s, 4s, 4t)

The cost of sales for liquor, expressed as a percentage is 19.39%.

To compute for the cost of sales for liquor, expressed as a percentage given that you have spent $2,500 on liquor for your bar and your bar sales have been $12,890, you can use the formula:

Cost of sales = (Cost of Goods Sold / Total Sales) × 100

where, Cost of Goods Sold (COGS) = Beginning Inventory + Purchases - Ending Inventory (or the total cost of goods sold during the period)

Total Sales = Gross sales - Sales discounts - Sales returns and allowances

Let's compute for the COGS first:

COGS = Beginning Inventory + Purchases - Ending Inventory

= $0 + $2,500 - $0

= $2,500

Total Sales = Gross sales - Sales discounts - Sales returns and allowances

= $12,890 - $0 - $0

= $12,890

Cost of sales is obtained as follows:

Cost of sales = (Cost of Goods Sold / Total Sales) × 100

= ($2,500 / $12,890) × 100

= 19.39%.

Therefore, the cost of sales for liquor, expressed as a percentage is 19.39%.

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Answer:

Step-by-step explanation:

To graph the line with slope 3 passing through the point (1,-5), we can use the point-slope form of the equation of a line, which is:

y - y1 = m(x - x1)

where m is the slope, and (x1, y1) is a point on the line.

Substituting the given values, we get:

y - (-5) = 3(x - 1)

Simplifying the equation, we get:

y + 5 = 3x - 3

Subtracting 5 from both sides, we get:

y = 3x - 8

Now we have the equation of the line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Comparing this equation to the one we just found, we can see that the slope is 3 and the y-intercept is -8.

To graph the line, we can plot the y-intercept at (0,-8) and then use the slope to find other points on the line. Since the slope is 3, we can go up 3 units and to the right 1 unit to find another point on the line. We can repeat this process to find more points on the line, and then connect them to graph the line.

365,000

lots of speed added together with air resistance

Answer:

The bunny ran 68 units and the average speed is 4 units per minute.

Step-by-step explanation:

Since the bunny is running from 34 to -34 you need to add those numbers up to get 68. You then need to divide 68 by 17.

68/17 = 4

So the bunny ran 68 units and the average speed is 4 units per minute

The  value of x in the interval (3 < x < 6) for which the rate of change of the cost is zero.

(a) To verify that C(3) < C(6), we have to find the values of C(3) and C(6).The given function is C(x) = s(x x+3)The order size is measured in hundreds. So, when x = 3, the order size is 300 and when x = 6, the order size is 600.Therefore, C(3) = s(3 x 3+3) = s(18) and C(6) = s(6 x 6+3) = s(39)Now, as s(x) > 0, we can see that C(6) > C(3). Hence, C(3) < C(6).(b) According to Rolle's Theorem, the rate of change of the cost must be 0 for some order size in the interval (3 < x < 6).We know that the function is continuous and differentiable in the interval (3 < x < 6). Now, the rate of change of the cost is given by the derivative of the function C(x) with respect to x.C(x) = s(x x+3)C'(x) = s[1 + (x + 3) . 1] = s(1 + x + 3) = s(x + 4)As per Rolle's Theorem, there must exist a value of x in the interval (3 < x < 6) such that C'(x) = 0.So, s(x + 4) = 0x + 4 = 0x = -4Thus, the order size is -4 x 100 = -400. However, this is an absurd answer as the order size cannot be negative. Therefore, there is no value of x in the interval (3 < x < 6) for which the rate of change of the cost is zero.

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The associative characteristic of multiplication is what the equation  (n · p) · q = n · (p · q) represents.

A mathematical assertion that establishes the equality of two expressions is known as an equation. It usually consists of two sides, divided by an equal sign (=), with one or more terms on each side, which could be variables, constants, or both. The objective of equation solving is to identify the value(s) of the variable(s) necessary to make the equation correct. There are many mathematical methods for solving equations, including factoring, simplification, substitution, and the quadratic formula.

given

The associative characteristic of multiplication is what the equation  (n · p) · q = n · (p · q) represents.

According to this characteristic, a multiplication expression's outcome is unaffected by the way its factors are organized.

In other words, you can arrange the variables however you like and still arrive at the same conclusion.

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The survey ratings provide valuable feedback for drivers who are looking for quality tires for their vehicles. These ratings can give insight on steering responsiveness, how quickly a tire wears, and overall customer satisfaction. Drivers can also see how their tire of choice stacks up against other tires, making it easier to make an informed decision when shopping for tires.

The Tire Rack is America’s leading online distributor of tires and wheels. They conduct extensive testing to ensure that customers are provided with the most suitable tires for their vehicles, driving styles, and driving conditions. They also use an independent consumer survey to help drivers gain insight on long-term tire experiences.

The following data show survey ratings on a 1-10 scale, with 10 being the highest rating, of 18 maximum performance summer tires, as of February 3, 2009 (Tire Rack website). The variables are Steering (steering responsiveness), Tread Wear (quickness of wear), and Buy Again (overall tire satisfaction and desire to purchase the same tire again). The Yokohama Aegis LS4 has a Steering rating of 7.9, Tread Wear rating of 7, and Buy Again rating of 7.1. The Dunlop SP20 FE has a Steering rating of 5.7, Tread Wear rating of 5, and Buy Again rating of 3.3.

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Answer:

The answer is $31.20

Step-by-step explanation:

do 20% of 26 and add it to the $26

There are 169 outcomes in the complement of the given event.

To find the number of outcomes in the complement of the given event, which is that out of 344 high school students in their senior year, 175 are left-handed, you need to follow a few steps. So, let's get started. To find the number of outcomes in the complement of the given event, you will first find the total number of students that are right-handed, which can be found by subtracting the number of left-handed students from the total number of students:344 - 175 = 169Therefore, there are 169 right-handed students.

Next, to find the number of outcomes in the complement of the given event, you will need to subtract the number of outcomes in the given event from the total number of possible outcomes. Since the number of possible outcomes is equal to the total number of students, the number of outcomes in the complement of the given event can be found by subtracting the number of left-handed students from the total number of students:344 - 175 = 169 Therefore, there are 169 outcomes in the complement of the given event.

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