The lower and upper estimates of a car coming to a stop six seconds after the driver applies the brakes are as follows: Lower estimates = 122 Upper estimates = 298 Question: On a sketch of velocity against time, show the lower and upper estimates.

Answer:

x = 2

Step-by-step explanation:

Here's your solution

=> we know that tangents from a point to a common circle are equal

=> so, ST = SU

=> 7x - 3 = 5x + 1

=> 7x - 5x = 1 + 3

=> 2x = 4

=> x = 4/2

=> x = 2

hope it helps

Answer:

X will be 2

Step-by-step explanation:

ST=SU

7x-3=5x+1

2x=3+1

2x=4

x=4/2

x=2

hope it helps....

have a great day!!!

Answer: Koreha Segunda Etapa, Ichigo.

Step-by-step explanation:

Subsitution only works with the equation:

ax+by=c

and x or y=anything, but cannot include another x or y

So, 5x+3y=13

and y=4x-7

Replace 3y with 3(4x-7)

12x-21

5x+12x-21=13

5x+12x=34

17x=34

x=2

Answer: X=2 and Y=1

Step-by-step explanation:

5x + 3y = 13          (i)

y = 4x - 7               (ii)

Solving equations (i) and (ii) using the substitution method:

5x + 3(4x-7) = 13

5x + 12x - 21 = 13

17x = 34

x = 2

Putting the value of x in (ii)

y = 4*2 - 7 = 1

Thus,

X=2 and Y=1

Answer:

35 1/2 Miles divied by 1 1/4=28.4 gallons

Step-by-step explanation:

Answer:

lexie is correct

Step-by-step explanation:

since -68 feet is closer to 0 that means it is greater. the number that is closer to 0 when it is a negative it will be bigger that the other Ex: -5 and -34, -5 is greater because it is closer to 0.

Answer:

4a: 1

4b: 6, -6

Step-by-step explanation:

4a. (3 - 5)= -2; (9 - 6)=3

(-2 + 3) = 1

4b. We aren't told which cards Jesse pick up, only that they didn't affect his total points. Therefore, the two cards have the same number, but opposite signs. We coluld pick any teo an an example: 6 and -6, or 4 and -4, etc. They don't affect his score since they ccancel each other with a result of zero.

Answer:

294

Step-by-step explanation:

We will take our equation, and substitute in 7 for s, wherever we see it, so we have:

\(6 * 7^{2}\)

Simplifying, we have:

\(6 * 49\)

Which finally we multiply to:

6 * 49 = 294

So, your answer is 294.

Hope this helped!

Answer:

The mean of the data set is 9.3 rounded to the nearest tenth

Step-by-step explanation:

First you add them all together: 9.9 + 10.8 + 10.8 + 6.2 + 10.8 + 7.2 = 55.7

Then you divide it by how many numbers there are which is 6 in this situation:

55.7 ÷ 6 = 9.28333333333. but if we round it to the nearest tenth we get 9.3

So the answer is 9.3

Answer:

Step-by-step explanation:

△ JKL is dilated by 3/2

This transformation will result in the coordinates:

Apply the rule:

Answer:

3

Step-by-step explanation:

-6+6=0

Plus the 3

Your answer is 3

Answer:

-3 or 3

Step-by-step explanation:

○ (ƒ − g)(x) = x² − 11x +4 is the correct Answer

Answer:

ƒ(x) = 4x² – 5

g(x) = 3x² + 6x − 4.

(ƒ – g)(x) = ƒ(x)–g(x)

= 4x² – 5 –(3x² + 6x − 4)

= 4x²–5x –3x²–6x+4

= 4x²–3x² –5x–6x +4

= x² − 11x +4

\( \)

Thank you

Answer: 0.06

Step-by-step explanation:

Since we only care about winning the inflatable crayon, it is unimportant whether nothing is won or a small stuffed animal is won, just that the outcome is determined by subtracting all of the possible outcomes given from the probability of winning nothing and the probability of winning a stuffed animal. Given that the total probability of all outcomes of the event is 1, we can conclude that the probability of winning an inflatable crayon is:

\(P(\text{not winning inflatable crayon}) = P(\text{All Outcomes}) - P(\text{winning nothing})\)

\(- P(\text{winning a small stuffed animal)}\)

\(P = 1-0.67-0.27 \\ = 0.06 \ $or 6\%\)

Answer:

\(\boxed {\boxed {\sf y= 6x+5}}\)

Step-by-step explanation:

We are asked to find the slope-intercept equation of a line. Slope-intercept form is one way to write the equation of a line. It is:

\(y=mx+b\)

Where m is the slope and b is the y-intercept.

We are given a point (-1, -1) and the line is parallel to the line y= 6x-2. Since the line is parallel to the other line, they have the same slope, which is 6. We have a point and a slope, so we should use the point-slope formula to find the equation of the line.

\(y-y_1= m (x-x_1)\)

Here, m is the slope and (x₁, y₁) is the point. We know the slope is 6 and the point is (-1, -1). Therefore:

Substitute the values into the formula.

\(y- -1 = 6(x- -1) \\y+1= 6(x+1)\)

Distribute the 6. Multiply each value inside the parentheses by 6.

\(y+1 = (6*x)+ (6*1) \\y+1= 6x+6\)

Slope-intercept form requires y to be isolated. 1 is being added to y. The inverse of addition is subtraction. Subtract 1 from both sides.

\(y+1-1=6x+6-1 \\y= 6x+5\)

The equation of the line in slope-intercept form is y=6x+5

Option (B) x + 6 < 10 and (C) 5x < 20 have same graph.

From the given set of inequalities;

(A) x < 2 represents x ∈ (-∞, 2)

(B) X + 6 < 10 ⇒ x < 4

    represents x ∈ (-∞, 4)

(C) 5x < 20 ⇒ x < 4

     represents x ∈ (-∞, 4)

(D) x - 2 > 2 ⇒ x > 4

     represents x ∈ (4, ∞)

(E) x < 4 represents x ∈ (-∞, 8)

We can see that inequalities (B) and (C) both represents x ∈ (-∞, 4)

Thus, the graph of both inequalities are same.

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An explanatory variable refers to the independent variable in an experiment.The correct answer is: the independent variable in an experiment.

Explanation: In experimental studies, explanatory variables are manipulated or controlled by the researcher to observe their impact on the dependent variable. They are often referred to as independent variables because they are not influenced by other variables in the study.

The purpose of the experiment is to determine whether changes in the explanatory variable cause changes in the dependent variable. The explanatory variable is the one being tested or varied intentionally to understand its effect on the outcome or response, which is the dependent variable.

By systematically manipulating and measuring the explanatory variable, researchers can analyze its relationship with the dependent variable and draw conclusions about cause and effect.


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The length of the vertical stripe that runs from the top of the kite to its base 25.46 inches

The length of the side of the square = 18 inches

The length of the vertical stripe that runs from the top of the kite to its base is the diagonal of the square.

So when you split the square through the diagonal. It will form two right triangles

So we have to find the hypotenuse of the right triangles

According to the Pythagorean theorem

Hypotenuse square = The side square + The side square

Consider the hypotenuse as x

x^2 = 18^2 + 18^2

x^2 = 324 + 324

x^2 = 648

x = \(\sqrt{648}\)

x = 25.46 inches

Therefore, the length of the vertical strip is 25.46 inches

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Answer:

648

Step-by-step explanation:

Assuming that the vertical stripe runs along the diagonal of the square kite, we can use the Pythagorean theorem to find its length.

The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs (the sides that form the right angle) is equal to the square of the length of the hypotenuse (the side opposite the right angle).

In this case, the two legs of the right triangle are the two sides of the square kite that meet at a right angle, each of length 18 inches. The hypotenuse is the length of the vertical stripe we want to find, which runs from the top of the kite to its base.

Using the Pythagorean theorem, we have:

hypotenuse^2 = leg1^2 + leg2^2

hypotenuse^2 = 18^2 + 18^2

hypotenuse^2 = 648

Taking the square root of both sides, we have:

hypotenuse = sqrt(648)                                                                               Therefore, the length of the vertical stripe that runs from the top of the kite to its base is 648 inches.

N 7

Part A

In a direct variation

k=y/x

take one point from the graph

(2,4)

k=4/2

Part B

In a direct variation, the equation is

y=kx

we have

k=2

therefore

The linear regression model can be extended to accommodate certain forms of non-linear relationships between the response and predictor(s).  Polynomial regression is one specific method for incorporating non-linear associations within the linear regression framework.

It involves understanding the flexibility of the linear regression model and the techniques available to address non-linear relationships. While the linear regression model assumes a linear relationship between the response variable and predictors, it can still be useful in accommodating certain types of non-linear relationships.

By applying appropriate transformations to the predictor variables, such as taking their squares, logarithms, or other non-linear functions, we can introduce non-linear associations into the linear regression model. This allows the model to capture curvature or other non-linear patterns in the data.

Polynomial regression is a specific approach to incorporating non-linear relationships within the linear regression framework. It involves adding polynomial terms of the predictor variables to the model, such as squared or cubed terms. By including these polynomial terms, the model can account for non-linear relationships and capture more complex patterns.

It's important to note that while linear regression can be extended to accommodate some non-linear relationships, there may be cases where more advanced non-linear regression techniques or alternative models are necessary to adequately capture complex non-linear associations. Nonetheless, the inclusion of transformed predictor variables and the use of polynomial regression are valuable approaches to address non-linear relationships within the linear regression framework.

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Answer:

97

Step-by-step explanation:

The perimeter is adding each side together, the equation is 3+33+15+33+3+10

Answer:

\((y+2)=\frac{2}{3} (x-5)\)

Step-by-step explanation:

Point slope form is shown below:

\((y-y_1)=m(x-x_1)\)

We are given the slope m = 2/3 and the point x1 = 5, y1 = -2

Simply plug in these numbers into the above equation.

\((y--2)=\frac{2}{3} (x-5)\)

Simplify:

\((y+2)=\frac{2}{3} (x-5)\)

Answer:

The height of the pile is increasing at a rate of 16.72 feet per minute. To solve this problem, we need to use the volume formula for a right circular cone: V=pi/3 r²h. We know that the volume is 20 cubic feet per minute, the height is 14 feet and the radius of the base is 14 feet. So we can calculate the rate of change of the height by rearranging the formula to give v/(pi/3r²). So for our example, v/(pi/3*14²)=20/(pi/3*14²)=20/(3.14*196)=20/613.44=16.72 feet per minute.

The surface area of the triangular prism is 182.4 mm². Therefore, the answer is option A.

The prism have a triangular base. The triangular prims has two triangular base and 3 rectangular surface. The surface area of the triangular prism is the sum of the area of the individual surface of the prism.

Therefore,

surface area of the triangular prism = bh + l(s₁ + s₂ + s₃)

Where

surface area of the triangular prism =  8 × 6 + 5.6(10 + 8 + 6)

surface area of the triangular prism = 48 + 5.6(24)

surface area of the triangular prism = 48 + 134.4

surface area of the triangular prism = 182.4 mm²

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the answer would be h<20 i believe

Step-by-step explanation:

because she works less than 20 hours

Answer:

55

Step-by-step explanation:

55

Answer:

Step-by-step explanation:

$13

After five years, there will be roughly 41.6 hundred thousand (a) seagulls living on the small island in the Atlantic Ocean.

To determine the population of seagulls after five years, we can use the following formula and plug in t = 5 as the variable:

P(5) = 5.3 / (11/5) = 5.3 * (5/11) ≈ 2.409

We need to multiply the result by 100,000 in order to get the real population, which is represented by the letter P, which stands for "hundred thousands."

P(5) ≈ 2.409 * 100,000 ≈ 240,900

When we round this value down to the next tenth, we get a number that is close to 240,900.

As a result, the number of seagulls on the island will be close to 41.6 million after five years, which is equivalent to around 240,900 seagulls.

Please take note that the calculated result does not match any of the options that have been provided (a, c, or d). The number that comes the closest, which would be 41.6 hundred thousand, is not one of the options.

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Answer:

40

Step-by-step explanation:

Given that:

Number of options available for transmission = 2 (Standard or Automatic)

Number of options for doors = 2 (2 doors or 4 doors)

Number of exterior colors available = 10

To find:

Total number of outcomes = ?

Solution:

First of all, let us calculate the number of outcomes for the transmission mode and number of doors options.

1. Standard - 2 doors

2. Standard - 4 doors

3. Automatic - 2 doors

4. Automatic - 4 doors

Number of outcomes possible = 4 (which is equal to number of transmission mode available multiplied by number of doors options i.e. 2\(\times 2\))

Now, these 4 will be mapped with 10 different exterior colors.

Therefore total number of outcomes possible :

Number of transmission modes \(\times\) Number of doors options  \(\times\) Number of exterior colors

2 \(\times\) 2 \(\times\) 10 = 40

The number of possible outcomes of a new car will be 40. Then the correct option is B.

A sample is a collection of well-defined elements. A sample is represented by a capital letter symbol and the number of elements in the finite sample is shown as a curly bracket {..}.

A new car is available with standard or automatic transmission, two or four doors, and it is available in 10 exterior colors.

Then the number of possible outcomes will be

\(\rm Possible \ outcomes = 2*2*10\\\\Possible \ outcomes = 40\)

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The value of cos(s+t) = -16/65 and cos(s-t) = 56/65.

The branch of mathematics that studies the relationships between triangles' sides and angles is termed as Trigonometry.

It has uses in physics, engineering, architecture, surveying, and navigation, among many other disciplines.

For solving this problem, we will use the following trigonometric identities:

cos(s+t) = cos(s)cos(t) - sin(s)sin(t)

cos(s-t) = cos(s)cos(t) + sin(s)sin(t)

Given that sin(s) = 3/5 and sin(t) = 12/13, we can find cos(s) and cos(t) using the Pythagorean identity:

cos(s) = ±√(1 - sin²(s)) = ±√(1 - (3/5)²) = ±4/5

cos(t) = ±√(1 - sin²(t)) = ±√(1 - (12/13)²) = ±5/13

Note that the ± sign indicates that the cosine could be positive or negative, depending on the quadrant in which s and t lie. However, since sin(s) and sin(t) are both positive, we know that s and t lie in either the first or second quadrant, where cosine is positive.

Therefore, we can take the positive square roots to get:

cos(s) = 4/5

cos(t) = 5/13

Now we can use the trigonometric identities for cos(s+t) and cos(s-t) to find their values:

cos(s+t) = cos(s)cos(t) - sin(s)sin(t)

= (4/5)(5/13) - (3/5)(12/13)

= 20/65 - 36/65

= -16/65

cos(s-t) = cos(s)cos(t) + sin(s)sin(t)

= (4/5)(5/13) + (3/5)(12/13)

= 20/65 + 36/65

= 56/65

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The effective annual rate for a 8.65% interest compounded monthly is 9.14%.

To calculate the effective annual rate, we need to take into account the compounding frequency. In this case, the interest is compounded monthly.

We can use the formula for compound interest to calculate the effective annual rate:

Effective Annual Rate = (1 + (interest rate / compounding frequency))^compounding frequency - 1

Plugging in the given values:

Effective Annual Rate = (1 + (8.65% / 12))^12 - 1

                     = (1 + 0.0072083)^12 - 1

                     = 1.0072083^12 - 1

                     ≈ 0.0914 or 9.14%

Therefore, the effective annual rate for a 8.65% interest compounded monthly is approximately 9.14%.

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The function f(x) has horizontal tangent lines at x = 0.63 and x = 2.51 on the interval [0, 2π].

To find where the function f(x) = 19 cos(x) + 10x has horizontal tangent lines on the interval [0, 2π], we need to find the values of x where the derivative of f(x) is equal to zero.

Let's find the derivative of f(x) with respect to x:

f'(x) = -19 sin(x) + 10

Now, we set the derivative equal to zero and solve for x:

-19 sin(x) + 10 = 0

-19 sin(x) = -10

sin(x) = 10/19

To find the values of x, we can use the inverse sine function \((sin^{(-1)})\) or arcsin.

x = \((sin^{(-1)})\) 10/19)

Using a calculator, we find that \(sin^{(-1)}\) (10/19) ≈ 0.63.

Since the interval is [0, 2π], we need to check if there are any other solutions between 0 and 2π.

We can use the symmetry of the sine function to find the other solution:

sin(π - x) = sin(x)

π - x = \(sin^{(-1)}\)(10/19)

x = π - \(sin^{(-1)}\)(10/19)

Solving this, we find that π - \(sin^{(-1)}\)(10/19) ≈ 2.51.

Therefore, the function f(x) has horizontal tangent lines at x = 0.63 and x = 2.51 on the interval [0, 2π].

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