{-3,453+5,748} - {8,9703-12,749}

a) it takes 9.61 seconds for the automobile to overtake the truck. b) The automobile was initially 165.34 meters behind the truck. c) During the overtaking, the speed of the truck is 21.142 m/s, and the speed of the automobile is 33.635 m/s.

To solve this problem, we can use the equations of motion to calculate the time it takes for the automobile to overtake the truck, the initial distance between them, and their speeds during the overtaking.

Let's denote the time it takes for the automobile to overtake the truck as t.

(a) For the truck:

Using the equation of motion s = ut + (1/2)a\(t^{2}\), where s is the distance covered, u is the initial velocity (0 in this case), a is the acceleration (2.2 m/s^2), and t is the time, we can find the distance covered by the truck when the automobile overtakes it.

s_truck = (1/2) * 2.2 * \(t^{2}\)

s_truck = 1.1 *  \(t^{2}\)

For the automobile:

s_automobile = (1/2) * 3.5 * \(t^{2}\)

s_automobile = 1.75 *  \(t^{2}\)

Given that the truck has moved 60 m when the automobile overtakes it, we can set up the equation:

s_truck = s_automobile + 60

1.1 *  \(t^{2}\)  = 1.75 *  \(t^{2}\)  + 60

Simplifying the equation:

0.65 *  \(t^{2}\)  = 60

\(t^{2}\)  = 60 / 0.65

\(t^{2}\)  ≈ 92.3077

t ≈ √92.3077

t ≈ 9.61 seconds

Therefore, it takes approximately 9.61 seconds for the automobile to overtake the truck.

(b) To find the initial distance between the automobile and the truck, we can substitute the value of t into either of the equations:

s_automobile = (1/2) * 3.5 *  \(t^{2}\)

s_automobile = (1/2) * 3.5 * \((9.61)^{2}\)

s_automobile ≈ 165.34 meters

Therefore, the automobile was initially approximately 165.34 meters behind the truck.

(c) To find the speeds of the automobile and the truck during overtaking, we can use the equation of motion v = u + at, where v is the final velocity, u is the initial velocity (0 in this case), a is the acceleration, and t is the time.

For the truck:

v_truck = 0 + 2.2 * 9.61

v_truck ≈ 21.142 m/s

For the automobile:

v_automobile = 0 + 3.5 * 9.61

v_automobile ≈ 33.635 m/s

Therefore, during the overtaking, the speed of the truck is approximately 21.142 m/s, and the speed of the automobile is approximately 33.635 m/s.

Correct Question :

An automobile and a truck start from rest at the same instant, with the automobile initially at some distance behind the truck. Then truck has a constant acceleration of 2.2 m/s2 and the automobile has an acceleration of 3.5 m/s 2. The automobile overtakes the truck when it (truck) has moved 60 m.

(a) How much time does it take to automobile to overtake the truck?

(b) How far was the automobile behind the truck initially?

(c) What is the speed of each during overtaking?

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With a 95% probability, 62 students should be sampled to be within 0.25 drinks of the population mean.

\(\alpha\) is the level obtained by subtracting 1 from the confidence interval and dividing by 2.

So,

\(\alpha\) = (1 - 0.95) ÷ 2 = 0.25

Now, find z in the Z-table, as z has a p-value of 1 - \(\alpha\).

As a result, z has a p-value of (1 - 0.025) = 0.975

so, z  = 1.96

Now, infer M as follows:

M = z × (σ ÷ √n) where n is the sample size and is σ the population standard deviation.

When M = 1, this is n.

According to the question, the standard deviation is roughly 1.

σ = 1

M = z × (σ ÷ √n)

0. 25 = 1.96 × (1 ÷ √n)

√n = 1.96 × (1 ÷ √n)

Square both sides,

(√n)² = ((1.96 × 1) ÷ 0.25)²

n = (7.84)²

n = 61.4656

n ≈ 62

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A quadratic equation is a polynomial equation of the second degree, meaning it contains at least one term that is squared (raised to the power of 2). A quadratic equation has the general form:

ax² + bx + c = 0

where a, b, and c are constants, and x is the variable. The coefficient "a" cannot be zero, as this would result in a linear equation. Quadratic equations can have two real roots, one real root (if the discriminant is zero), or two complex roots (if the discriminant is negative

1) The equation X² - 10x + 2y = -22 is a quadratic equation in two variables x and y. It can be rearranged in terms of y to get:

2y = -X² + 10x - 22

Dividing both sides by 2, we get:

y = (-1/2)x² + 5x - 11

So the equation represents a downward facing parabola with its vertex at (5,-11) and an axis of symmetry at x=5.

2) To graph the equation x² + y² - 2y = 15, we can follow these steps:

Rewrite the equation in standard form by completing the square for the y terms:

x² + (y² - 2y + 1) = 16

(x²+ 1) + (y - 1)² = 16 + 1

Identify the center and radius of the circle represented by the equation:

The center is (-1, 1) and the radius is the square root of 17.

Plot the center on the coordinate plane.

Draw the circle using the center and radius information. To do this, we can plot points that are at a distance of √17 away from the center in all directions and connect them to form the circle.

The final graph will be a circle with center at (-1,1) and radius √17.

3) To graph the equation x² + 6x + y² + 8y = -16, we can follow these steps:

Rewrite the equation in standard form by completing the square for the x and y terms:

x² + 6x + 9 + y²+ 8y + 16 = 9 + 16 - 16

(x + 3)² + (y + 4)² = 9

Identify the center and radius of the circle represented by the equation:

The center is (-3,-4) and the radius is the square root of 9, which is 3.

Plot the center on the coordinate plane.

Draw the circle using the center and radius information. To do this, we can plot points that are at a distance of 3 away from the center in all directions and connect them to form the circle.

The final graph will be a circle with center at (-3,-4) and radius 3.

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Answer:

Step-by-step explanation:

\(y=15x^2+2x-8\\\mathrm{Parabola\:equation\:in\:polynomial\:form}\\\mathrm{The\:vertex\:of\:an\:up-down\:facing\:parabola\:of\:the\:form}\:y=ax^2+bx+c\:\mathrm{is}\:x_v=-\frac{b}{2a}\\\mathrm{The\:parabola\:params\:are:}\\a=15,\:b=2,\:c=-8\\x_v=-\frac{b}{2a}\\x_v=-\frac{2}{2\cdot \:15}\\\mathrm{Simplify\:}-\frac{2}{2\cdot \:15}:\quad -\frac{1}{15}\\x_v=-\frac{1}{15}\\\mathrm{Plug\:in}\:\:x_v=-\frac{1}{15}\:\mathrm{to\:find\:the}\:y_v\:\mathrm{value}\\y_v=-\frac{121}{15}\\\)

\(\mathrm{Therefore\:the\:parabola\:vertex\:is}\\\left(-\frac{1}{15},\:-\frac{121}{15}\right)\\\mathrm{If}\:a<0,\:\mathrm{then\:the\:vertex\:is\:a\:maximum\:value}\\\mathrm{If}\:a>0,\:\mathrm{then\:the\:vertex\:is\:a\:minimum\:value}\\a=15\\\mathrm{Minimum}\space\left(-\frac{1}{15},\:-\frac{121}{15}\right)\)

Answer:

Step-by-step explanation:

We know, for square

\((side)^2=(Area)\\=>X^2=8\\\)

∴\(X=2\sqrt{2}\) unit

\(Now, Side=3X\)

\(Then,Area=(3X)^2=(3*2\sqrt{2} )^2=(6\sqrt{2} )^2=72 sq. unit\)

hope you have understood this...

pls mark my answer as the brainliest

The area of square of side 3X is 72 square unit.

The square is a 4 sided figure, each side of the square is equal and make a right angle.

The area of square having sided a unit can be given by a² square unit.

Given that,

Area of square having side X is 8.

Since, formula for area of square having side X is X².

Implies that,

X² = 8

X = 2√2

The area of square having side 3X
side =3 × 2√2

side = 6√2

The area of square = (6√2)²

                                = 36 x 2

                                = 72

The area of square is 72 square unit.

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Answer:

1/2

Step-by-step explanation:

Answer:

perpendicular

Step-by-step explanation:

The largest decimal value that can be represented with 15 bits is 32,767.

In binary representation, 15 bits can have 2^15 distinct combinations, which is equal to 32,768. However, since we need to consider both positive and negative values, one bit is reserved for the sign (positive or negative), leaving us with 15 bits for the actual value. With 15 bits, we can represent values from -32,768 to 32,767. Therefore, 32,767 is the largest positive decimal value that can be represented with 15 bits.

Now, let's calculate the largest decimal values for the other scenarios:

- 4 bytes (32 bits): With 32 bits, we can represent values from -2,147,483,648 to 2,147,483,647.

- 1 byte (8 bits): With 8 bits, we can represent values from -128 to 127.

- 7 bits: With 7 bits, we can represent values from -64 to 63.

- 25 bits: With 25 bits, we can represent values from -33,554,432 to 33,554,431.

It's important to note that the calculations assume a signed representation, where one bit is used to represent the sign of the number. In an unsigned representation, all bits are used to represent positive values, effectively doubling the maximum value that can be represented.

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Answer: \(12\sqrt{5}\)

Required theorem:

Pythagorean theorem = \(a^2 + b^2=c^2\)

In other words, one side length squared + another side length squared = the middle lined squared.

Step-by-step explanation:

\(60^2+60^2 = c^2\\\\360+360=c^2\\\\720=c^2\\\\\ \sqrt{c^2} =\sqrt{720}\\\\c=+/- 12\sqrt{5}\)

We can only have a positive distance so your final answer is :

\(12\sqrt{5}\)

The test statistic for the given hypothesis test is calculated to be -4.842. The p-value is found to be less than 0.001. At the 10% significance level, we reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis that the population correlation coefficient (rhoxy) is less than 0.

To calculate the test statistic, we can use the formula:

t = (r - ρ) / (sqrt((1 - \(r^2\)) / (n - 2)))

where r is the sample correlation coefficient, ρ is the population correlation coefficient under the null hypothesis, and n is the sample size. Plugging in the values, we get:

t = (-0.68 - 0) / (sqrt((1 - \((-0.68)^2\)) / (32 - 2)))

= -0.68 / (sqrt((1 - 0.4624) / 30))

≈ -4.842

Next, we need to find the p-value associated with this test statistic. Since the alternative hypothesis is one-tailed (rhoxy < 0), we need to find the area to the left of -4.842 in the t-distribution with (n - 2) degrees of freedom. Consulting the t-table or using statistical software, we find that the p-value is less than 0.001.

At the 10% significance level (α = 0.10), if the p-value is less than α, we reject the null hypothesis. In this case, since the p-value is less than 0.10, we reject H0. Therefore, we conclude that there is sufficient evidence to support the alternative hypothesis (HA) that the population correlation coefficient (rhoxy) is less than 0.

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The fundamental theorem of calculus asserts that the definite integral of a function from one point to another is equal to F(b)-F(a) if that function has an antiderivative called F. The net change, area, or average value of a function over a region can be determined using this theorem.

In everyday terms, an average is one number chosen to represent a list of numbers; it is often the sum of the numbers divided by the number of numbers in the list (the arithmetic mean). For example, the average of the numbers 2, 3, 4, 7, and 9 is 5. An average could be another statistic like the median or mode depending on the situation. Because the mean would be greater if the personal incomes of a few billionaires were included, the median—the amount below which 50% of personal incomes fall and over which 50% of personal incomes rise—is sometimes used to represent the average personal income. It is advised to avoid using the word "average" when discussing measures of central tendency because of this.

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Answer:

if u are asking how many more pages Matthew read then it's 48 pages. If u are asking how many they read all together then it's 144 pages.

Answer:

(x-3) (x-2)

Step-by-step explanation:

\(x^{2}\) - 5x + 6

How to break down the equation and factorise it:

-3 x -2 = 6

-3 + -2 = -5

Final Answer:

(x-3) (x-2)

Answer:

84 grams and 5 ounces

Step-by-step explanation:

because one ounce equals 28 grams, that means 3 ounces = 3 * 28 = 84

because 28 grams equals 1 ounce, 140 grams = 140 / 28 = 5 ounces

Answer:

a. 3x = 2x + 10, b. x = 10, c. 30 degrees

Step-by-step explanation:

Angle 4 and angle 6 = 180 degrees, so

3x = 2x + 10

x = 10

Angle 7 is congruent to angle 6, so it is also 2x + 10, x = 10, so it is 30 degrees.

Answer:

see explanation

Step-by-step explanation:

∠ 4 and ∠ 6 are same- side interior angles and sum to 180° , that is

(a)

3x + 2x + 20 = 180 , simplifying

(b)

5x + 20 = 180 ( subtract 20 from both sides )

5x = 160 ( divide both sides by 5 )

x = 32

(c)

∠ 6 and ∠ 7 are vertically opposite angles and are congruent , then

∠ 7 = 2x + 20 = 2(32) + 20 = 64 + 20 = 84°

In space, there can be infinitely many planes that are perpendicular to a given line at a given point on that line.

The correct answer is Option D.

The key concept here is that a plane is defined by having at least three non-collinear points.

When a line is given, we can choose any two points on that line, and then construct a plane that contains both the line and those two points. By doing so, we ensure that the plane is perpendicular to the given line at the chosen point.

Since we can select an infinite number of points on the given line, we can construct an infinite number of planes that are perpendicular to the line at various points.

Thus, the correct answer is D. infinitely many planes can be perpendicular to a given line at a given point in space.

The correct answer is Option D.

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To answer your question, we need to create an expression that represents how many gifts Eric still needs to collect.

First, let's define the problem: Eric needs 150 gifts for a charity event, and he has already collected x gifts.

To find out how many gifts Eric still needs to collect, we can subtract the number of gifts he has already collected from the total number of gifts he needs.

So the expression that represents how many gifts Eric still needs to collect is:

150 - x

This expression tells us how many gifts Eric still needs to collect in order to reach his goal of 150 gifts for the charity event.


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Answer:

y  - 7 or A

Step-by-step explanation:

7 is than a number so it would be y - 7. y - 7 = 7 less than a number

The equation of a line of best-fit that reflects a negative correlation is y = mx + b, where the slope m is negative.

When analyzing a scatter plot, a negative correlation indicates that as the independent variable increases, the dependent variable decreases. In the equation y = mx + b, the negative slope m represents the rate of decrease in the dependent variable for each unit increase in the independent variable. A negative slope means that as the x-values increase, the corresponding y-values decrease. The y-intercept b represents the value of the dependent variable when the independent variable is zero. Thus, the equation y = mx + b with a negative slope indicates a negative correlation between the variables being studied.

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"What is the equation of the line of best fit that represents a negative correlation between two variables?"

Answer:

75°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 6 , then

sum = 180° × 4 = 720°

let x be the sixth angle, then sum and equate to 720°

150 + 100 + 80 + 165 + 150 + x = 720

645 + x = 720 ( subtract 645 from both sides )

x = 75

The sixth interior angle is 75°

Answer:

Angle E = 65 degrees

Step-by-step explanation:

Since triangle DEF is similar to triangle BAC, angle E = angle A = 180 degrees - angle B - angle C = 180 degrees - 90 degrees - 25 degrees = 65 degrees

Answer: 83

Step-by-step explanation: 17% of 500 is 85. If 17% is empty, that means that you'd take away that 15%. 500 - 85 = 415. If each page holds 5 cards, we need to split those cards up between the pages. 415/5 = 83, so 83 pages will be used.