Tom, Sally, Bob, and Jill ran a race. Toms time was 12.03 seconds, Sally's was 12.284 seconds, Bobs was 12.62 seconds, and Jills was 12.9 seconds. In what order did they finish? who won?

8 am to 10:30 am is 2.50 hours.

Old Steamy is going 6.14 mph for 2.5 hours so travels : 6.14 * 2.5 = 15.35 miles.

This means Chug a lug has to travel 290 - 15.35 = 274.65 miles in 2.5 hours.

The speed would be 274.65 / 2.5 = 109.86 miles per hour.

Answer:

The speed of Old Steamy train = 6.14 mph

Train started at 8 a.m. and arrived at 10.30 a.m, this becomes 2.5 hours.

So, distance traveled by Old Steamy train = [tex]Speed\times time[/tex]

=> [tex]6.14\times2.5=15.35[/tex] miles

Now we get that Chug-a-Lug was 290 miles behind the Old steamy.

To know the distance traveled by Chug-a-Lug, we will add distance traveled by Old Steamy to the station plus the distance between the trains.

So, distance traveled by Chug-a-Lug = [tex]15.35+290=305.35[/tex] miles

The speed of Chug-a-Lug =[tex]\frac{Distance}{Time}[/tex]

= [tex]\frac{305.35}{2.5}=122.14[/tex] mph

Answer:

Step-by-step explanation: the cost of one donut is $0.59 because when you divide 3.54 by 6, you get 0.59.

The cost for one donut will be the sixth part of $3.54 thus it will be $0.59 or 59 cents.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Division = divide any two numbers or variables called division.

For example 4/8

As per the given,

Six donuts cost a total of $3.54

Cost of one donut = $3.54/6 = $0.59 = 59 cents

Hence "The cost for one donut will be the sixth part of $3.54 thus it will be $0.59 or 59 cents".

To learn more about the arithmetic operators,

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Answer:

x=2 ,y=-6

B (2,-6)

Step-by-step explanation:

y = -3x

x+y = -4

Substitute -3x for y in the second equation

x+y = -4

x+ (-3x) = -4

Combine like terms

-2x = -4

Divide by -2 on each side

-2x/-2 = -4/-2

x = 2

Now we still need to find y

y = -3x

Substitute x=2

y = -3(2)

y = -6

Answer:

±sqrt(7) = r

Step-by-step explanation:

21 = 3r^2

Divide each side by 3

21/3 = 3r^2/3

7 = r^2

Take the square root of each side

±sqrt(7) = sqrt(r^2)

±sqrt(7) = r

The degree of the polynomial is 4.

To determine the degree of a polynomial, we look for the highest power of the variable present in any of its terms. Let's break down the given polynomial and identify the terms:

[tex]\[ -3.1ax^4 + 2.5ax + 2ax^4 + 1.1ax^4 - 0.5ax - 2ax \][/tex]

Here, we have terms with different powers of [tex]\( x \): \( x^4 \), \( x \),[/tex] and constant terms.

Combine like terms:

[tex]\[ (-3.1a + 2 + 2.1 + 1.1 - 0.5 - 2)ax^4 \][/tex]

[tex]\[ = (-3.1a + 2 + 2.1 + 1.1 - 0.5 - 2)ax^4 \][/tex]

[tex]\[ = (-0.4a)ax^4 \][/tex]

Now, let's analyze the combined term [tex]\( (-0.4a)ax^4 \)[/tex].

The highest power of ( x ) in this term is 4. So, the degree of the polynomial is 4.

Therefore, the degree of the polynomial is 4.

Answer:

16 2/3 %

Step-by-step explanation:

To put this in a percentage, they need to have the same units.

Let convert days to hours

1 day = 24 hours

Multiply by 3

3 days = 72 hours

The percentage is part over whole

12 hours / 72 hours

We can simplify by dividing top and bottom by 12

1/6

This is a fraction, change this to a decimal

.166666666

Now multiply by 100

16.666666 %

16 2/3 %

Step by step explanation: 12.5 x 4

Answer: 50.

Answer:

see explanation

Step-by-step explanation:

Check the value of the discriminant

Δ = b² - 4ac

• If b² - 4ac > 0 then roots are real

• If b² - 4ac = 0 roots are real and equal

• If b² - 4ac < 0 then roots are not real

given (x - a)(x - b) = k² ( expand factors )

x² - bx - ax - k² = 0 ( in standard form )

x² + x(- a - b) - k² = 0

with a = 1, b = (- a - b), c = -k²

b² - 4ac = (- a - b)² + 4k²

For a, b, k ∈ R then (- a - b)² ≥ 0 and 4k² ≥ 0

Hence roots of the equation are always real for a, b, k ∈ R

the answer is 0.5531 (✿◠‿◠)

To find the probability that the car will travel a maximum distance between 125 and 135 miles, we need to calculate the z-scores for these distances and find the corresponding probabilities using a standard normal distribution table or calculator.

To find the probability that the car will travel a maximum distance between 125 and 135 miles, we need to calculate the z-scores for these distances using the formula: z = (x - mean) / standard deviation.

For 125 miles: z = (125 - 134) / 4.8 = -1.875.

For 135 miles: z = (135 - 134) / 4.8 = 0.208.

Next, we need to find the corresponding probabilities for these z-scores using a standard normal distribution table or calculator. The probability of a z-score less than -1.875 is approximately 0.0301, and the probability of a z-score less than 0.208 is approximately 0.5829.

To find the probability between 125 and 135 miles, we subtract the probability of a z-score less than 125 from the probability of a z-score less than 135: 0.5829 - 0.0301 = 0.5528.

Therefore, the probability that the car will travel a maximum distance between 125 and 135 miles is approximately 0.5528 or 55.28%.

Answer:

[tex]A(x)=5\cdot 2^x[/tex]

Step-by-step explanation:

The given scenario can be represented by an exponential growth function. The general form if the exponential growth function is,

[tex]y=a(1+r)^x[/tex]

where,

y = the future amount after time x,

a = initial amount,

r = rate of growth.

As here A(x) represents the amount of money after x years with initial deposit of  $5 and in each year the amount doubles or duplicates itself i.e r=100% = 1, so the function would be,

[tex]A(x)=5(1+1)^x=5\cdot 2^x[/tex]

At the beginning the amount was $5, so the y intercept of the graph will be at 5.

Answer:

It’s Z Bc that’s the only one that starts at 5 and then doubles each year

Answer:  The volume of the cuboid  is:  " 11 ,200 cm³ " .

_________________________________________________

Step-by-step explanation:

____________________________________________________

The formula for the volume of a "cuboid" ;

      which is given in:  "cubic units" ;  or,  "units³ " ;  is:

____________________________________________________

        →    Volume, "V" = length (L)  * width (w) * (height)  ;

____________________________________________________

 →  The 3 (three given values are "4m" , "4 cm" and "7cm" .

We need the units of measurement to be equal;  so we need to convert the " 4m " to "cm" :

 Note that:  " 1 m = 100 cm " ; {exact conversion} ;

 So:   4m ( 100 cm / 1 m) = (4 * 100) cm = 400 cm.

_____________________________________________________

Now, we can plug these values and solve for the volume; in units of "cm³ " ;

_____________________________________________________

 V = 400 cm * 4 cm * 7 cm ;

    =  400 * 4 * 7 * cm * cm * cm ;

    =  400 * 4 * 7 cm³ ;

    =  1600 * 7 cm³ ;

     =  11, 200 cm³

_____________________________________________________

The answer is:  " 11 ,200 cm³ " .

_____________________________________________________

Jay has run two-thirds of 6 miles, that is, 4 miles. When converted to yards, it is approximately 7040 yards.

To find out how far Jay has run to the nearest yard, we first need to find out 2/3 of 6 miles since Jay has run this fraction of the distance. You can calculate two-thirds of a total by multiplying the total by 2/3. So, Jay has run 2/3 * 6 miles, which equals 4 miles.

Since we want to find out how far he has run in yards, we need to convert these miles to yards. We know that 1 mile is approximately 1760 yards. Hence, Jay has run approximately 4 * 1760 = 7040 yards.

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Answer: 12 texts per dollar.

The slope of the line is 1/5

Step-by-step explanation: If Ruby can send 48 text messages for $4, we divide 48 by 4 to get amount of texts per dollar: 12. Ruby can send 12 text messages for $1.

To figure out the slope of a line, use the formula y2 - y1 / x2 - x1.

-4 - (-9) / 22 - (-3) = 5 / 25 (rise over run)

Simplify to 1/5

Answer:

The number of bricks is 16 and the number of blocks is 12

Step-by-step explanation:

Let the number of bricks be x and blocks be y.

Cost of each brick = $0.38

Total cost of x bricks = 0.38*x

Cost of each block = $1.56

Total cost of y blocks = 1.56*y

Total amount spent for the brickyard = $24.80

So,

Total cost of x bricks + Total cost of y blocks = Total amount spent for the brickyard

=> 0.38x + 1.56y = 24.80 ____equation (1)

Total number of items (bricks+blocks) = 28

So,

Number of bricks + Number of blocks = Total number of items

=> x + y= 28 ____equation (2)

We will solve the two equations by the method of elimination.

Let's multiply equation 2 by -0.38

(-0.38)*x + (- 0.38)*y  = (-0.38)*(28)

=> -0.38x - 0.38y  = -10.64 ____equation (3)

Adding equation 1 to the equation 3, we get

-0.38x - 0.38y + 0.38x + 1.56y = -10.64 + 24.80

Cancelling out -0.38x and +0.38x on the left side, we get

1.56y - 0.38y = 24.80-10.64

=> 1.18y = 14.16

Dividing both sides by 1.18, we get

[tex]\frac{1.18y}{1.18}[/tex]  =[tex]\frac{14.16}{1.18}[/tex]

=> y = 12

Plugging in y=12 in the equation 2, we get

x + y= 28

=> x + 12 =28

Subtracting 12 from both sides, we get

x+ 12 -12 = 28- 12

Cancelling out the +12 and -12 from the left side, we have

x = 16

So, the number of bricks is 16 and the number of blocks is 12.

Answer:

The value of y is 6.

Step-by-step explanation:

To find the value of y, start by using the known information we have in the equation for slope. The equation is below.

m(slope) = (y2 - y1)/(x2 - x1)

In this equation, the first ordered pair would be (x1, y1) and the second would be (x2 , y2). So we put the values in for these variables and we get.

1/2 = (7 - y)/(2 - 0)

1/2 = (7 - y)/2

Now we can use cross multiplication to solve for y.

1/2 = (7 - y)/2

1*2 = 2(7 - y)

2 = 14 - 2y

-12 = -2y

6 = y

About 16/25 fraction of the animal shelter are dogs.

Hope helps!-Aparri

Answer:

[tex]\frac{16}{25}[/tex]

Step-by-step explanation:

64% of the animals at an animal shelter are dogs.

This can also be expressed as: [tex]\frac{64}{100}[/tex] of the animals are dogs

Simplifying gives a fraction: [tex]\frac{16}{25}[/tex] of the animals are dogs.

It is closer to 1/4.

Hope this helps.

-TheOneandOnly003

If we start from the origin, then the vector would be v = (52, 12) as given. But suppose we shift its initial point. Doing so would preserve its direction. For example, if we move its initial point to (1, 1), we'd have to shift its terminus by the same amount (1 unit to the right, 1 unit up) so that its terminal point would be (52 + 1, 12 + 1) = (53, 13).

Option A is not correct. If we want the vector to start at (52, 12), we have to adjust the terminus by the same distance by adding (52, 12) to the terminus. This means the resulting vector would start at (52, 12) and end at (52 + 52, 12 + 12) = (104, 24).

One important thing to observe here is that the difference between the terminal and initial points always returns v. In the first example: (53, 13) - (1, 1) = (52, 12). In checking option A: (104, 24) - (52, 12) = (52, 12). So to eliminate any other answer choices, all you need to do is subtract.

Option B is correct by this "rule". (66, 7) - (14, -5) = (52, 12).

Options C and D are not. (0, 12) - (52, 0) = (-52, 12), and (64, -4) - (-12, 16) = (76, -20).

Final answer:

The initial and terminal points that correctly represent the vector v = (52, 12) in component form are option B: initial (14, -5); terminal (66, 7), as these points give the same components when subtracted (terminal - initial).

Explanation:

The student is asking about the initial and terminal points for a vector given in component form. The vector v is (52, 12), which means it has an x-component of 52 and a y-component of 12. This can be visually represented as a directed line segment with an initial point and a terminal point. The correct initial and terminal points for vector v would result in the same component form when subtracting the coordinates of the initial point from the coordinates of the terminal point (terminal - initial).

Option B has the initial point (14, -5) and terminal point (66, 7). By calculating the difference between the terminal and initial points: (66 - 14, 7 - (-5)) = (52, 12), we can see that these points correctly represent the vector v in component form. Therefore, the answer is B.

Answer:

The above result is proved with the help of Pythagoras theorem and explained below.

Step-by-step explanation:

Given figure ABCD in which AD=BC and all angles intersect at right angle. Hence, the triangle formed inside ADC and ABC are right angled triangle.

In triangle ADC,

By applying Pythagoras theorem, we get

[tex]AC^{2}=AD^{2}+DC^{2}[/tex]    →  (1)

In triangle ABC,

[tex]AC^{2}=AB^{2}+BC^{2}[/tex]    →  (2)

Now, from eq (1) and (2)

Peach Tree Dr. is the same distance as Sycamore Ln.

[tex]AD^{2}+DC^{2} = AB^{2}+BC^{2}[/tex]

⇒ [tex]DC^{2} = AB^{2}[/tex]              (∵ AD=BC)

⇒ DC=AB                    (∵Distance can never negative)

Therefore, Peach Tree Dr. is the same distance as Sycamore Ln.

Answer: D

Step-by-step explanation:

A. False

f(x): x → -∞, y → -∞

g(x): x → -∞, y → 1  

B. False

at x = -1, f(x) = -7

at x = -1, g(x) = 1.5

C. False

refer to A

g(x) → 1 and f(x) → -∞   so g(x) > f(x)

D. TRUE

It is hard to tell from the graph so plug in a value to check.

f(10) = 5(10) - 2

       = 50 - 2

       = 48

g(10) = 2¹⁰ + 1

        = 1024 + 1

        = 1025

g(10) > f(10)

Answer:

1. h Multiplication property for inequality

2. b Addition property for inequality.

3. i Set builder

4. f Intersection

5. k Union

6. j Subtraction property for inequalities

7. d Division property for inequality.

8. e Greater than

9. g less than

10. c compound

11. a Absolute value inequality.

Step-by-step explanation:

1/2x ≤ -5    Multiplying by 2 on both sides of the inequality

x ≤ -10

2)  8 > 4         Adding 5 on both sides of the inequality.

     8 + 5 > 4+5

      13 > 9

3)  {h/h > 43}  set builder

4) x ≥ -3  or x < -10   Intersection

5)  x ≥ -4 and x < 2

6) 4x - 1 < 7     Subtract 3 on both sides

   4x - 1 - 3 < 7 - 3

  4x - 4 < 4

7)  -3x < 9   Divide by -3 on both sides

    x > -3

8)  >  This sign means greater than

9)  < This an operation sign means less than

10) 7 > x > 1 This means that x x, 7 and x > 1.

11) /x + 6/ > 12

  This means that:

   (x + 6) > 12   or - (x + 6) > 12.   Absolute value inequality.

Answer:

p = 12+5n

Step-by-step explanation:

For every added triangle, the perimeter only increases by 5.

For n=1, the perimeter is 6+6+5 = 17

For n=2, the perimeter is 6+6+5+5 = 22

So in general, the perimeter is 12 + 5n

Answer:

Q12. p = 5n + 12

Q13. See below.

Q14. y-intercept = (0, -3); x-intercept = (-3/2, 0).

Step-by-step explanations:

Question 12. Perimeter

      One triangle: p₁ = 2×6 + 1×5

    Two triangles: p₂ = 2×6 + 2×5

Three triangles : p₃ = 2×6 + 3×5

         n triangles: pₙ = 2×6 + n×5

General formula: p = 5n + 12

===============

Question 13. Modelling a function

Here's one possible table of values.

x   y

-3    3

-2    1

-1   -1

0  -3

1   -5

You can see the graph of the function in Fig. 1 below.

===============

Question 14. x- and y-intercepts

y- intercept

y = -2x – 3     Set x = 0

y = -2×0 – 3

y = 0 – 3

y = -3

The y-intercept is at (0, -3).

=====

x-intercept

y = -2x – 3      Set y = 0

0 = -2x – 3     Add 3 to each side

3 = -2x            Divide each side by -2

x = -3/2

The x-intercept is at (-3/2, 0).

Answer:

two real different roots

Step-by-step explanation:

Consider polynomial function

[tex]M(x)=-4x^2+x+1.[/tex]

The discriminant is

[tex]D=b^2-4ac=1^2-4\cdot (-4)\cdot 1=1+16=17.[/tex]

Since [tex]D>0,[/tex] the polynomial function [tex]M(x)[/tex] has two real different roots.

Answer:

y=-0.75x+16

Step-by-step explanation:

Answer:

y=-0.75x+16

Step-by-step explanation:

Answer:

4.4

Step-by-step explanation:

The answer is 4.4 because if you know that 5*4 equal 20 so 4 can go each of the 5 groups so 24-20 leaves you with 4 so your answer is 4 remainder 4

Answer: x = 7.2

=============================

Explanation:

As shown in the diagram (see attached image below), the red interior angles are

180-10x

180-15x

180-20x

180-5x

Each of those expressions is in the form 180-E, with E as the exterior angle. Add up the interior angles. Set the sum equal to 360 and solve for x. For any quadrilateral, the four interior angles always add to 360.

(angle1)+(angle2)+(angle3)+(angle4) = 360

(180-10x) + (180-15x) + (180-20x) + (180-5x) = 360

(180+180+180+180)+(-10x-15x-20x-5x) = 360

720-50x = 360

-50x = 360-720

-50x = -360

x = -360/(-50)

x = 36/5

x = 7.2

Answer: 22 cm

Step-by-step explanation:

Answer:

Area of the base = [tex]2x^2+5x-18[/tex]

Step-by-step explanation:

We know that volume of rectangular prism = (Area of base) x (Height)

or [Area of base] = [Volume]/[Height]

So basically we need to divide given area by given height to find the answer.

given height is (x+2) that means (x+2) must be factor of volume equation

or x=-2 must be root of volume equation so write down coefficients of volume equation then we divide by -2 as shown in attached picture.

Last digit on the right is always remainder.

Remaining coefficients {2, 5, -18} will give the area equation: [tex]2x^2+5x-18[/tex]

Hence final answer is:

Area of the base = [tex]2x^2+5x-18[/tex]

Answer:

The y intercept is -2

Step-by-step explanation:

To find the y intercept, set x = 0 and solve for y

2x-5y=10

0  -5y = 10

Divide each side by -5

-5y/-5 = 10/-5

y = -2