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The number of kilometer, k, an airplane flew is shown in the table, where the time, t, is hours after take off. Choose the most appropriate scale for graphing this data set.

Value of cot690° is -√3 .

Given,

The circular measure of the angle is given as 690° .

Thus according to trigonometric ratios ,

Cot (690)

Further simplifying cot (690) in the known range of angles .

Then,

cot(690) = cot(720 - 30)

cot (720 - 30) = cot (-30)

cot(-30) = -√3

Hence the value of cot 690 will be -1.73 .

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Answer:

Information

General form of an exponential function:  \(y=ab^x\)

where:

Also, growth rate \(r=b-1\)

Domain:  input values - independent variable ⇒ \(x\)

Range:  output values - dependent variable ⇒ \(y\)

y-intercept:  when \(x=0\)

Asymptote:  the line(s) that the curve approaches as it tends towards infinity

Given function:  \(f(x)=200(1.08)^x\)

Solution

Domain:   \(-\infty < x < +\infty\)

Range:   \(y > 0\)

y-intercept (\(a\)):  \((0, 200)\)

Asymptote:   \(y=0\)

Growth Rate (\(b-1\)):   \(0.08\)

Growth Factor (\(b\)):   \(1.08\)

End behaviors:

\(\textsf{as } x \rightarrow -\infty, f(x) \rightarrow0\)

\(\textsf{as } x \rightarrow +\infty, f(x) \rightarrow+\infty\)

Answer:

5/12

Step-by-step explanation:

convert 1/3 to 4/12 and 1/4 to 3/12 so 3+4=7 so 7/12 dropped out so now 12-7=5 so 5/12 is the answer

Answer:

20.0

Step-by-step explanation:

We can use the distance formula, d = \(\sqrt{(x_{1}-x_{2}) ^{2} +(y_{1}-y_{2}) ^{2}}\)  to find the length of three sides separately.

AB =  \(\sqrt{(-4+2) ^{2} +(1-3}) ^{2}}\) = \(\sqrt{8}\)

BC =  \(\sqrt{(-2-3) ^{2} +(3+4) ^{2}}\) = \(\sqrt{74}\)

CA =  \(\sqrt{(3+4) ^{2} +(-4-1) ^{2}}\) = \(\sqrt{74}\)

Perimeter = \(\sqrt{74}\) + \(\sqrt{8}\) + \(\sqrt{74}\) = 20.0330776588 units

Answer:

Step-by-step explanation:

Dylan, since he grew by 4 centimeters. Also, the starting number is lower, which means the percentage would also be bigger in the first place.

Answer:

B. both a relation and a function

Step-by-step explanation:

A relation is a set of one or more ordered pairs.

A function is a relation in which each element of the domain is paired with exactly one element of the range.

The vertical line test can be used to determine that the graph of this equation has one y-coordinate for every x-coordinate.

Therefore, it is both a relation and a function.

The equation written when r is the subject is:

\(\displaystyle{r=\dfrac{5p}{m}-n}\)

To make the term r as the subject of equation means to isolate r-term. In order to do that, we will apply properties of equality.

Properties of equality are properties regarding equations/equality where states that when either sides are done by something (addition, subtraction, multiplication, division, etc.) then the other sides will also act the same as the acted side.

Example

Suppose we are given an equation of x = y. In this case, x and y are equal to each other. If x = 1 then y = 1. If we decide to add +2 to x we’d have to add it to y too so the result will be x + 2 = y + 2.

Same also applies to other equations!

Isolating r-term, first, we will apply division property where we divide both sides by m-term:

\(\displaystyle{\dfrac{m(n+r)}{m}=\dfrac{5p}{m}}\\\\\displaystyle{n+r=\dfrac{5p}{m}}\)

Next, we use subtraction property to subtract both sides by n:

\(\displaystyle{n+r-n=\dfrac{5p}{m}-n}\\\\\displaystyle{r=\dfrac{5p}{m}-n}\)

Please let me know if you have any questions!

Hey there!

Answer:

There isn't any options to choose from, however an equivalent expression to the given expression above would be \(13h\).

Hope this helps! If not, comment below and lmk what else I can do to better assist you.

\(\huge \bf༆ Answer ༄\)

let's solve ~

\({ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:7x + 5y = - 56\)

\({ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:5y = - 56 - 7x\)

\({ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:y = \dfrac{1}{5} ( - 7x - 56)\)

\({ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:y = - \dfrac{7}{5} x - \dfrac{56}{5} \)

or

\({ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:y = - \bigg( \dfrac{7}{5} x + \dfrac{56}{5}\bigg) \)

I hope it helped ~

Answer:

A

jeud7dhdhdkd9e87ehehe

Answer:

1. z = -1.91429

The z score tells us that the head circumference of the girl with the down syndrome ( 44.5 cm) is 1.91429 standard deviations below the mean or average head circumference

2. 2.7792%

Step-by-step explanation:

1. Relative to the WHO data, what is this girls z-score?

z score formula is:

z = (x-μ)/σ, where

x is the raw score = 44.5 cm

μ is the population mean = 47.18cm

σ is the population standard deviation = 1.40cm

z = 44.5 - 47.18/1.40

z = -1.91429

What does the z score tell us?

The z score tells us that the head circumference of the girl with the down syndrome ( 44.5 cm) is 1.91429 standard deviations below the mean or average head circumference

2. Using the WHO data in a normal model, what percentage of the girls has a head circumference that is smaller than the girl with Down's Syndrome?

z score = -1.91429

Probability value from Z-Table:

P(z =-1.91429) = P(x<44.5) = 0.027792

Converting to percentage = 0.027792 × 100

= 2.7792%

If there are 12 coins under the couch and every coin is either a nickel or a penny and together they are forming 32 cents then the equations which represent the problem will be x+y=12, 0.01x+0.05y=0.32. The correct option is B which is x+y=12, 0.01x+0.05y=0.32.

Given There are 12 coins and total money is 32 cents.

Let the number of pennies be x and the number of  nickels be y.

According to question there are 12 coins so the first equation becomes:

x+y=12.

Then we have been told that together they amount to 32 cents.

We know that 1 penny is 1 cent coin and 1 nickel is 5 cent coin so the equation becomes :

1*x+5*x=32

x+5y=32

converting into dollar

0.01x+0.05y=0.32.

Hence the right equations showing the problem of nickel and pennies are x+y=12, 0.01x+0.05y=0.32.

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The probability that at least one of the 5 people selected has been vaccinated is 0.998, or 99.8%.

To solve this problem, we can use the complement rule, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening. In this case, the event we're interested in is at least one person being vaccinated.
First, we need to find the probability that none of the 5 people selected have been vaccinated. Since 62% of the population has been vaccinated, that means 38% have not been vaccinated. So the probability of any one person not being vaccinated is 0.38.
Using the multiplication rule for independent events, the probability that all 5 people have not been vaccinated is:
0.38 x 0.38 x 0.38 x 0.38 x 0.38 = 0.002
Now we can use the complement rule to find the probability that at least one person has been vaccinated:
1 - 0.002 = 0.998
So the probability that at least one of the 5 people selected has been vaccinated is 0.998, or 99.8%.

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Answer:

A

Step-by-step explanation:

I think

Answer: .9369

Step-by-step explanation: Since 9,639 is over 10,000, you literally just but a decimal in front of 9,639.

Answer:

9,639/10,000 as a decimal number is

=0.9639

Answer:

y = 2x

Step-by-step explanation:

A direct proportion follows the equation:

y = kx,'where k is the slope.

We see in the graph the points (0, 0) and (1, 2).

The slope is (2 - 0)/(1 - 0) = 2/1 = 2

The formula is y = 2x.

Answer: y = 2x

Answer:

y=2x

Step-by-step explanation:

When using slope intercept find the  slope using either the graph or points on the line and that get you the 2 that in front of x.

the formula means that 2 units of dough are prepared in every hour

9514 1404 393

Answer:

  B.  4

Step-by-step explanation:

Equating exponents, we have ...

  2x +7 = 15

  2x = 8 . . . . . subtract 7

  x = 4 . . . . . . divide by 2

The equation is true when the value of x is 4.

hope this helps enjoy.

Answer:

True

Step-by-step explanation:

That is the distance formula.

Answer:

FALSE

Step-by-step explanation:

Distance Formula: \(\sqrt{(x_{2}-x_1)^2 + (y_2-y_1)^2}\)

Answer:

(5,18)  & (-5 , 38)

Step-by-step explanation:

  A linear equation represented by a line in a graph intersect the quadratic equation represented by a parabola zero, one or two times.

f(x) = x² - 2x + 3   -------------------(I)  

f(x) = -2x + 28   ---------------------(II)

x² - 2x + 3 = -2x + 28

x² - 2x + 2x + 3 - 28 = 0

x² - 25 = 0

x²         = 25

         x = √25 = √5*5

        x = ± 5

Plugin x = 5 in equation (II),

                    f(5) = -2*5 + 28

                          = -10 + 28

                          = 18

(5 , 18)

Plugin x = -5 in equation (II),

 f(-5) = -2*(-5) + 28

         = 10 + 28

         = 38

(-5, 38)

Answer:

(5, 18) and (-5, 38)

Step-by-step explanation:

Given system of equations:

1) f(x) = x² - 2x + 3 ⇒ y = x² - 2x + 3

2) f(x) = -2x + 28 ⇒ y = -2x + 28

Solve using the Substitution Method:

Step 1: Substitute the the first equation into the second equation.

⇒ x² - 2x + 3 = -2x + 28

Step 2: Solve for x.

x² - 2x + 3 = -2x + 28 [ Add 2x to both sides. ]

x² - 2x + 2x + 3 = -2x + 2x + 28

⇒ x² + 3 = 28 [ Subtract 28 from both sides. ]

x² + 3 - 28 = 28 - 28

⇒ x² - 25 = 0 [ Factor using the following rule: a² - b² = (a - b)(a + b). ]  

(x - 5)(x + 5) = 0

⇒ x - 5 = 0, x + 5 = 0 [ Solve for the values of x. ]

x - 5 + 5 = 0 + 5, x + 5 - 5 = 0 - 5

⇒ x = 5, x = -5

Step 3: Solve for y.

Substitute the found x-values into one of the given equations.

y = x² - 2x + 3 ⇒ y = (5)² - 2(5) + 3 ⇒ y = 25 - 10 + 3 ⇒ y = 18

y = x² - 2x + 3 ⇒ y = (-5)² - 2(-5) + 3 ⇒ y = 25 + 10 + 3 ⇒ y = 38

The solutions to the system of equations are:

⟹ x₁ = 5, y₁ = 18 ⇒ (5, 18)

⟹ x₂ = -5, y₂ = 38 ⇒ (-5, 38)

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The equation for finding the length between two points is:

where point 1 has coordinates (x1, y1) and point 2 has coordinates (x2, y2).

We assign A to be point 1 and B be point 2

Therefore,

Answer: Vertical asymptotes is x = 0 and the horizontal asymptotes is y = 12.

The average cost approaches to 12 when the number of shirts increases.

Step-by-step explanation:

Since we have given that

Initial cost for a steamer to apply the declas = $100

Cost of material for  each shirt = $12

Function representing the band's average cost per t-shirt  after x t-shirt are sold is given by:

We need to find the vertical asymptotes , horizontal asymptotes and the average cost to make a t-shirt approaches as the number of t-shirts increases,

For vertical asymptotes , we will make denominator equal to zero.

So, it will be

Thus, vertical asymptotes is x= 0.

Similarly,

For horizontal asymptotes, we first check the degree of both numerator and denominator.

Since we can see that both have the same degree i.e. 1.

So,

So, the horizontal asymptotes is y = 12.

When the number of shirts increases ,The average cost to make a T-shirt approaches is given by

Hence, the average cost approaches to 12 when the number of shirts increases.

Answer:

The vertical asymptote is x = 0

The horizontal asymptote is y = 12

The average cost to make a t-shirt approaches $12 as the number of t-shirts made increases.

Step-by-step explanation:

To confirm the congruence between Shape II and Shape I, a sequence of transformations can be applied. The specific sequence depends on the given information about the shapes and the desired congruence criteria.

Congruence between two shapes means that they have the same shape and size. To confirm the congruence of Shape II and Shape I, we need to perform a series of transformations that preserve both shape and size.

Common transformations that preserve congruence include translation (slide), rotation (turn), reflection (flip), and dilation (resize). The specific sequence of transformations depends on the given information about the shapes.

For example, if Shape II can be obtained from Shape I through a combination of translation, rotation, and reflection, we would need to apply those transformations in the correct order and direction to confirm congruence. The sequence might involve translating Shape I to coincide with Shape II, rotating Shape I to match the orientation of Shape II, and reflecting Shape I to align with Shape II.

It is important to analyze the given shapes, their corresponding sides, angles, and other properties to determine the appropriate sequence of transformations that confirm their congruence. By applying the correct sequence, we can demonstrate that the two shapes are congruent.

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The length in units of the line segment A'B' in the resulting figure is the same as the length of line segment AB in the previous rectangle.

Form the task content;

The translation which occurs on the rectangle only shifts the whole rectangle leftward and downward and hence, each line segment in the rectangle still retains its length.

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Answer:

length of the longest pencil that can fit must be less than 13cm

Step-by-step explanation:

To get the longest pencil that fit the case, we will use the pythagoras theorem;

diameter = 10cm

radius = 10/2

radius = 5cm

Height = 12cm

Get the length of the longest side

l² = r²+h²

l² = 5²+12²

l² = 25 + 144

l² = 169

l = √169

l = 13cm

Hence the length of the longest pencil that can fit must be less than 13cm

Answer:

64

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

Answer:

45 degrees

Step-by-step explanation:

A basis for W is B = {[1, 0, 2]}. The dimension of W is equal to the number of vectors in its basis, which in this case is 1. Therefore, the dimension of W is 1.

To find a basis for W, we need to determine a set of vectors that span W and are linearly independent.

Given that W = span{[1, 0, 2]}, we can see that any vector in W can be written as a linear combination of [1, 0, 2]. Therefore, [1, 0, 2] is a spanning vector for W.

To check if it is linearly independent, we can set up the equation:

c[1, 0, 2] = [0, 0, 0]

where c is a scalar. This equation implies:

c = 0

0 = 0

2c = 0

From the first equation, we can see that c must be 0. Plugging c = 0 into the second and third equations, they are both satisfied.

Since the only solution to the equation is c = 0, we can conclude that the vector [1, 0, 2] is linearly independent.

Therefore, a basis for W is B = {[1, 0, 2]}.

The dimension of W is equal to the number of vectors in its basis, which in this case is 1. Therefore, the dimension of W is 1.

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The probability that he grabbed exactly 3 bronze caps and exactly 1 silver caps is 0.1247.

In this problem, we need to find the probability of Olav randomly grabbing 6 caps and getting exactly 3 bronze caps and exactly 1 silver cap.

To solve this problem, we can use the concept of combinations. The number of ways to choose 3 bronze caps out of 6 is given by the combination \(^6C_{3}\), and the number of ways to choose 1 silver cap out of 5 is given by the combination \(^5C_{1}\).

The number of ways to choose the remaining 2 caps (which must be gold) out of 5 is given by the combination \(^5C_{2}\).

Therefore, the total number of ways that Olav can grab 6 caps with exactly 3 bronze and 1 silver is given by:

\(^6C_{3}\)* \(^5C_{1}\) * \(^5C_{2}\) = 20 * 5 * 10 = 1000

The total number of ways to choose 6 caps out of 16 is given by

\(^{16}C_{6}\\\), which is:

\(^{16}C_{6}\\\)= 8008

Therefore, the probability that Olav grabbed exactly 3 bronze caps and exactly 1 silver cap is:

P = 1000 / 8008 = 0.1247 (rounded to 4 decimal places)

Hence, the probability that Olav grabbed exactly 3 bronze caps and exactly 1 silver cap is 0.1247.

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