Find half of the time that Devon skied without falling, and write inequalities to compare it with the times others in the family skied without falling

The  exponential function to model the situation is f(x) = 130(1.05)ˣ⁺¹⁶

First of all, note that each variable represents number of years the price increases in each year

We are given,

The initial number of population = 130

Rate of growth = 5% = 0.05

Number of years = 16.

Thus, we get that the growth in population for 16 years is given by,

f(x) = 130(1.05)¹⁶

⇒f(x) = 130(1.05)¹⁶i

This gives us that the population after 16 years will be given by,

f(x) = 130(1.05)ˣ⁺¹⁶

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If a delivery truck is transporting boxes of two sizes: large and small. The number of each type of box it carrying is: Large boxes is 50 and small boxes is 70.

Let L represent the number of Large boxes.

Let S represent the number of Small boxes.

Total number of boxes = 120

L + S = 120

The two equations are:

L + S = 120

55×L + 15×S = 3800

L + S = 120 eliminate L by multiplying this equation by -55

-55×(L + S = 120)      

The equations are:

55 ×L + ×15S = 3800

-55×L -55×S = -6600

0 - 40×S = - 2800

S = -2800/(-40)

S = 70

Plug S back into one of our equations.

L + S = 120

L + (70) = 120

L = 120 - 70

L = 50

So ,

L = 50 and S = 70

Therefore the number of each type of box it carrying is: Large boxes is 50 and small boxes is 70.

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King usually becomes the most emotional during moments of reflection or when he is expressing his views on civil rights and justice. King's message of hope, courage, and resilience encourages individuals to stand up for what is right and to never give up in the face of injustice.

Dr. King utilises passion in his lectures to accentuate his message and to connect with his audience on an emotional level. He frequently speaks about the sorrow and injustice that his people have endured, eliciting an emotional response from his audience. He also inspires his audience to believe in the prospect of a brighter future, which instills hope and motivation. Furthermore, he frequently employs metaphors and analogies to underline his ideas, which may be extremely effective.

King is generally the most emotional when he is reflecting or expressing his ideas on civil rights and justice. In these times, he sends a message of hope, strength, and endurance. King usually uses compelling metaphors and parables to highlight the necessity of equality and justice. He highlights the power of our actions to effect change and the importance of never losing hope in the face of hardship. He frequently urges for unity among all races and sexes and opposes all types of prejudice. He also discusses the power of love, understanding, and mutual respect in bridging gaps and creating a better society.

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If u(t) = (sin 3t, cos 3t, t) and v(t) = (t, cos 3t, sin 3t), the derivative of cross product d/dt [u (t) x v (t)] is (3cos(6t) + 3tsin(3t), 2t - 3sin(6t), 3cos(6t) + 3tsin(3t)).

Formula 5 of the cross product theorem states that the derivative of the cross product of two vectors u and v is equal to the cross product of the derivatives of u and v:

d/dt [u(t) x v(t)] = (du/dt) x v(t) + u(t) x (dv/dt)

Where u(t) = (sin 3t, cos 3t, t) and v(t) = (t, cos 3t, sin 3t), we can find the derivatives as follows:

du/dt = (d(sin 3t)/dt, d(cos 3t)/dt, dt/dt)

= (3 cos 3t, -3 sin 3t, 1)

dv/dt = (dt/dt, d( cos 3t) /dt, d( sin 3t)/dt)

= (1, -3 sin 3t, 3 cos 3t)

Now, we can substitute these derivatives into the formula to find d/dt [u (t) x v (t)]:

d/dt [u(t) x v(t)] = (du/dt) x v(t) + u(t) x (dv/dt) = (3 cos 3t, -3 sin 3t, 1) x (t, cos 3t, sin 3t) + (sin 3t, cos 3t, t) x (1, -3 sin 3t, 3 cos 3t)

= (-3sin²3t - cos3t, t - 3cos3tsin3t, 3cos²3t + 3tsin3t) + (3cos²3t + 3tsin3t, t - 3cos3tsin3t, -3sin²3t - cos3t)

= (3cos²3t + 3tsin3t - 3sin²3t - cos3t, 2t - 6cos3tsin3t, 3cos²3t + 3tsin3t - 3sin²3t - cos3t)

= (3cos(6t) + 3tsin(3t), 2t - 3sin(6t), 3cos(6t) + 3tsin(3t))

The cross product of two vectors is a vector, and the result of the above calculation will be a vector that describes the rate of change of the cross product u(t) x v(t).

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As per the given equation, the domain is [0, 3000] and the range is [0, 600].

In the term domain is defined as the set of values that we are allowed to plug into our function where as the range of a function is the set of values that the function assumes.

Here we know that the amount of sand left in a 600 mL vase can be modeled by the equation that is written as,

=> s = – 1/5 t + 600

here s refers the amount of sand left in the vase and t refers time in minutes since the sand started leaking out

Here we also know that the vase is full of sand and sand leaks out of the vase until the vase is empty.

Then in order to find the domain we have to put the value of s as 0, then we get the domain as,

=> 0 = -1/5t + 600

=>1/5t = 600

=> t = 3000

Then the domain is [0, 3000].

Similarly, in order to find the value of range we have to put the value of t as zero, then we get

=> s = -1/5(0) + 600

=> s = 600

Then the range is [0, 600]

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Answer:

a) The two side lengths of the tenth rectangle in the sequence are 8 + (10 - 1)4 = 32 and 8 + (10 - 2)4 = 28.

b) The area of 576in2 is not possible in the given sequence because it would require a side length of 24, which does not follow the sequence given.

Step-by-step explanation:

The given sequence is represented by the equation an=8+(n−1)4, which means that for each successive rectangle in the sequence, the length of one of the sides will increase by 4. Therefore, in order for the area of a rectangle to be 576in2, the length of one of the sides must be 24, which does not follow the sequence given.

Answer:

42+25n

Step-by-step explanation:

[tex]7+5(7+5n)\\=7+35+25n\\=42+25n[/tex]

By resolving the following equation for y, you can make the work a little simpler: x + y = 6

The link between data pieces is displayed in tables of values. In science lesson, you might utilize a values table. Data is recorded in tables of values by scientists and researchers, who then examine the data to look for patterns. As a result, they can use this pattern to anticipate future events.

y = 6 - x, which means to take 6 out of both sides.

Now you can simply fill in the x-values and determine y. For instance,

y = 6 -(-2) = 8 . . . for x = -2

y = 6 - 3 = 3 . . . . for x = 3

The table and graph that are attached both display these values.

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The percentage of games that Mamadou scores between 136 and 214 is given as follows:

99.7%.

These approximate percentages are defined by the Empirical Rule, for a normally distributed variable:

For this problem, we have that

Hence the percentage is of 99.7%, as the measures are within three standard deviations of the mean.

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Answer:

48%

Step-by-step explanation:

0.6*0.8 = 0.48 = 48%

Length of side of the rhombus is 5cm.

A rhombus can be thought of as a special parallelogram since it satisfies the requirements for one (a quadrilateral with two pairs of parallel sides). Another characteristic of a rhombus is that it has four equal sides, just like a square. It is also known as a tilted square for this reason.

step1

Diagonals of a rhombus bisect each other at right angles.

Let point of intersection of diagonals be O

So, OD = 3cm , OA = 4cm

From Right angled triangle △ AOD,

⇒ AD²  = OA²  + OD²   (Pythagoras theorem)

⇒ AD² =4² + 3²

⇒ AD² = 16+9

⇒AD² =25

step2

⇒ AD² =25

⇒ AD=5 cm

AD is side of the rhombus.

So, length of side of the rhombus is 5cm

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The probability distribution of X by name is X/6 and the the probability mass function of X is X/6 - 4

The term probability mass function is defined as a function over the sample space of a discrete random variable X which gives the probability that X is equal to a certain value.

Here we know that team of three is chosen randomly from an office with 2 men and 4 women.

And let us consider that X be the number of women on the team.

Total number of members in the term is calculated as,

=> 4 + 2 = 6

Then the  the probability distribution of X by name is,

=> X/6

And the the probability mass function of X is written as,

=> x/6 - 4

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Answer:

27 is 7.5% of the number 360

Answer: 5x(3-2y)

Step-by-step explanation:

Step 1:

Find the greatest common factor (GCF):

Both values have 5x as the GCF.

Step 2:

Take out the GCF:

15x/5x=3

-10xy/5x=-2y

Step 3:

Write it out:

5x(3-2y)

Check:

Apply Distributive Property:

5x*3=15x

5x*-2y=-10xy

15x-10xy=15x-10xy

The cups of each items needed will be 9 cups of peanuts, 1.8 cups of chocolate and 7.2 cups of raisins.

From the information, 18 0ne-cup bags of tail mix is needed for the class tripThe recipe includes chocolate, chips and raisins in the ratio of 5:1:4

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number.

5x- peanuts

1x- chocolate chips

4x- raisins

5x + 1x + 4x= 18

10x= 18

x= 18/10

x = 1.8

Chocolate = 1.8 cups

Raisins = 4x

= 4 × 1.8

= 7.2 cups.

Peanut = 5x

= 5 × 1.8

= 9 cups

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The expression that shows the number of bagels Shane has left is 12-b.

Expression in math is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given;

Shane bought a package of 12 bagels

He gave b of them to his friends

Now;

Shane bought 12 bagels

Expression= 12

Shane gave b

Expression=12-b

Therefore, the expression will be 12-b.

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Answer:

The answer in intercept form will be

-1/3=5/3x+c

The number of center of rotations to produce the image is (d) infinite

An arrow pointing to the left is symmetric around its central axis.

This means that any point along the central axis of the arrow can serve as a center of rotation to produce an image of a left-pointing arrow.

The central axis is a straight line that runs through the middle of the arrow from the tip to the base, and also extend through the arrow's depth.

Hence, the number of possible centers of rotation that will produce an image of a left-pointing arrow is infinite.

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The value of the variable , k is -385/13

A function can be described an expression, equation, law or rule explaining the relationship between two variables.

These variables are known as;

From the information given, we have the function;

f(x)=-(13)/(5)x+k

Also, for the value of f(30), the function is equivalent to -1

Now, substitute the value of x as 30 and equate the function to -1. we have;

-1 = -13/(5)30 + k

Divide both sides by the cofficient of 30 + k

30 + k = -1 × -5/13

Multiply the values

30 + k = 5/13

Now, collect like terms

k = 5/13 - 30

k = -385 /13

Thus, the value is -385/13

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Answer:

let say the 3 points that make the triangle is A-B-C, you draw a line from A to the line opposite to A, make it perpendicular. If it's not inside of the triangle, you just extend the line to make it work.  Then repeat for B and C.  Then you extend the perpendicular lines (altitude) and make them intersect.  The intersect point is the orthocenter.

Step-by-step explanation:

Then you extend the perpendicular lines (altitude) and make them intersect.  The intersect point is the orthocenter.

Answer:

  see attached

Step-by-step explanation:

You want to construct the orthocenter of the given triangle.

The orthocenter of a triangle is the point of intersection of the altitudes. The construction of it requires construction of at least two altitudes of the triangle. This is accomplished using the "perpendicular through an external point" construction.

A perpendicular to a line through a point not on the line is constructed in a few simple steps:

The attachment shows arc FG using C as a center, and arc HI using A as a center. Arcs using those points as center are drawn so they intersect at points V and W.

Lines CV and AW are altitude lines that intersect at the orthocenter: point Z.

__

Additional comment

The vertices of the original triangle have been labeled A, B, C counterclockwise from upper left.

It may appear that point Z is a reflection of point C in line AB, but it is not.

The solution for the expression given above would be = 31/40. That is option B.

A fraction is defined as the part of a whole value which is written in the form of a numerator and a denominator.

The given fractions from the question;

2/5 + 3/8

Find the lowest common multiple of the figures below ( denominator) = 40

= 16 + 15/40

= 31/40

Therefore the correct fraction for the given expression = 31/40.

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[tex]6=\textit{oz of solution at x\%}\\\\ ~~~~~~ x\%~of~6\implies \cfrac{x}{100}(6)\implies \cfrac{6x}{100} \\\\\\ 9=\textit{oz of solution at 0\%}\\\\ ~~~~~~ 0\%~of~9\implies \cfrac{0}{100}(9)\implies 0 \\\\\\ \textit{15 oz of solution at 16\%}\\\\ ~~~~~~ 16\%~of~15\implies \cfrac{16}{100}(15)\implies 2.4 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{array}{lcccl} &\stackrel{oz}{quantity}&\stackrel{\textit{\% of oz that is}}{\textit{acid only}}&\stackrel{\textit{oz of}}{\textit{acid only}}\\ \cline{2-4}&\\ \textit{1st Sol'n}&6&\frac{x}{100}&\frac{6x}{100}\\ \textit{2nd Sol'n}&9&0&0\\ \cline{2-4}&\\ mixture&15&0.16&2.4 \end{array}~\hfill \begin{cases} 6 + 9 = 15\\\\ \frac{6x}{100}+0=2.4 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 2nd equation}}{\cfrac{6x}{100}=2.4}\implies \cfrac{3x}{50}=\cfrac{24}{10}\implies 30x=1200 \\\\\\ x=\cfrac{1200}{30}\implies \boxed{x=\stackrel{\%}{40}}[/tex]

Answer:

The degree is 4 because the term shown has TWO variables, while y has an exponent of 3, x has an exponent of 1, add the exponents of the variables to find the degree

Step-by-step explanation:

The solution of equation is x=-3

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given

The equation;√x+3=-6

Now,

√x=-6-3

√x=-9

x=-3

Therefore the answer of the given equation will be -3

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The function is not linear because the rate of change in not constant.

Linear functions are those whose graph is a straight line. A linear function has the following form. y = f(x) = a + bx. A linear function has one independent variable and one dependent variable.

Given:

      x                   y

      10                -6

      11                  1

       12                6

       13                12

So, the rate of Change

= 10/ (-6)

= -5/2

and, again = 11/1 = 11

As, the rate of change is not constant.

But, in linear function the rate of change is same.

Hence, the function is not linear.

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It's a fact that the sum of the angles of a triangle add up to 180º.

So, 55º + 85º + (3x+4)º = 180º.

That's the equation you need to solve:

     55 + 85 + 3x+4 = 180    (combine like terms)

                 144 + 3x = 180   (subtract 144 from both sides)

                           3x = 36     (divide both sides by 3)

                             x = 12      (you've got x)

The width of the interval based on 100 men would be about three times the width of the interval based on 900 men.

What is the width of the interval?

The width of a confidence interval for a proportion is proportional to the standard error of the sample proportion, which is proportional to the square root of the sample size.

The standard error is defined as the standard deviation of the sampling distribution of the sample proportion, which is estimated by the standard deviation of the Bernoulli distribution (square root of the sample proportion times (1 - sample proportion) divided by the sample size).

So, if the sample size is reduced by a factor of 9 (from 900 to 100), the standard error (and hence the width of the confidence interval) would increase by a factor of 3 (square root of 9).

Therefore, The width of the interval based on 100 men would be about three times the width of the interval based on 900 men.

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Dyscalculia is a learning disorder that affects a person’s ability to do the math.

A learning problem called dyscalculia diminishes a person's capacity for math. Similar to how dyslexia impairs reading-related brain regions, dyscalculia interferes with the knowledge and skills connected to math and numbers. Although dyscalculia often first manifests in childhood, it can even affect adults who are unaware of it.

The signs of this condition typically emerge in childhood, particularly as kids start to master the fundamentals of math. However, many adults who suffer from dyscalculia are unaware of it. When forced to do the math, people with dyscalculia frequently experience mental health problems like anxiety, depression, and other distressing emotions.

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If one addend of x is c, the other addend is x-c.

An addend is a term that is added to another term to form a sum. In the equation x = c + (x-c) , c and (x-c) are the two addends that make up the sum x.

The reason why x-c is the other addend is that the sum of the two addends (c and x-c) must equal x.

In other words x = c + (x-c) can be simplified to x = c + x - c which is x = x

Therefore, If one addend of x is c, the other addend is x-c.

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