A car travels 0.75 miles every minute explain how you could use proportional reasoning to find how far the car travels in one hour

Step-by-step explanation:

5f

5 + n times of a number

Answer:

(a)See below

(b)I) 0.125  (ii)0.828125   (iii)0.234375   (iv) 0.625   (v)0.65625

Step-by-step explanation:

When an  8-sided die is rolled twice, the sample space is the set of all possible pairs (a,b) where a is the 1st outcome and b is the 2nd outcome.

The sample space is:

[tex][(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),(1, 7),(1, 8)\\(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),(2, 7),(2, 8)\\(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),(3, 7),(3, 8)\\(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),(4, 7),(4, 8)\\(5, 1), (5, 2), (5, 3), (5, 4), (5, 5),(5, 6),(5, 7),(5, 8)\\(6, 1), (6, 2), (6, 3), (6, 4)(6, 5),(6, 6),(6, 7),(6, 8)\\(7, 1), (7, 2), (7, 3), (7, 4)(7, 5),(7, 6),(7, 7),(7, 8)\\(8, 1), (8, 2), (8, 3), (8, 4)(8, 5),(8, 6),(8, 7),(8, 8)][/tex]

PART A

The sample space of the product a*b of each pair forms the required possibility diagram.

This is given as:  

[tex]1, 2, 3, 4, 5, 6,7,8\\2, 4, 6, 8, 10, 12,14,16\\3,6,9,12,15,18,21,24\\4,8,12,16,20,24,28,32\\5,10,15,20,25,30,35,40\\6,12,18,24,30,36,42,48\\7,14,21,28,35,42,49,56\\8,16,24,32,40,48,56,64[/tex]

PART B

I) A prime number

The number of products that gives prime numbers = 8  

The probability that the product is a prime number

[tex]=\dfrac{8}{64}= \dfrac{1}{8}\\=0.125[/tex]

ii) Not a perfect square  

Number of products that results in perfect squares =11

The probability that the product is not a perfect square

[tex]=\dfrac{64-11}{64}= \dfrac{53}{64}\\=0.828125[/tex]

iii) A multiple of 5  

Number of products that are multiples of 5=15

 The probability that the product is a multiple of 5

[tex]=\dfrac{15}{64}\\=0.234375[/tex]

iv) Less than or equal to 21

Number of products which are less than or equal to 21=40

 The probability that the product less than or equal to 21

[tex]=\dfrac{40}{64}=\dfrac{5}{8}\\=0.625[/tex]

v) Divisible by 4 or 6

Number of products divisible by 4 or 6= 42

 The probability that the product is divisible by 4 or 6

[tex]=\dfrac{42}{64}=\dfrac{21}{32}\\=0.65625[/tex]

Answer:

2/6 or 1/3

Step-by-step explanation:

There are two numbers who are equal or less than 2 its 1 and 2

And the total is 6 so its 2/6 which is 1/3

Sorry if this is late

Answer:

0.33

Step-by-step explanation:

Answer:

t ≤ 4.24

Step-by-step explanation:

P(t) ≥ 40000 implies

500t/(2t²+9) ≥ 40000

Multiplying through by t², we have

500t ≥ 40000(2t²+9)

500t/40000 ≥ 2t²+9

Collecting like terms

0.0125t  ≥ 2t²+9

0  ≥ 2t²+ 9 - 0.0125t

2t²+ 9 - 0.0125t  ≤ 0

2t²- 0.0125t + 9 ≤ 0

Using the quadratic formula,

[tex]t = \frac{-(-0.0125) +/-\sqrt{(-.0125)^{2} - 4 X 2 X 9} }{2 X 2} \\= \frac{0.0125 +/-\sqrt{(0.00015625 - 288} }{4}\\= \frac{0.0125 +/-\sqrt{-287.9998} }{4}\\= \frac{0.0125 +/-16.97i }{4}\\=0.00313 + 4.24i or 0.00313 - 4.24i[/tex]

The factors of the equation are (t - 0.00313 -4.24i) and (t - 0.00313 + 4.24i)

So, (t - 0.00313 -4.24i)(t - 0.00313 + 4.24i) ≤ 0

(t - 0.00313)² - 4.24² ≤ 0

(t - 0.00313)² ≤ 4.24²

taking square-root of both sides,

√(t - 0.00313)² ≤ √4.24²  

t - 0.00313 ≤ 4.24

t ≤ 4.24 + 0.00313

t ≤ 4.24313 ≅ 4.24

t ≤ 4.24

Answer:

The correct option are;

1) Could not

2) Is

Step-by-step explanation:

The parameters given are;

The survival rate of drivers using seat-belt = 67%

The survival rate of drivers not using seat-belt = 41.5%

The chance of getting the survival rate results without a correlation with the use of seat-belt < 0.0001

Given that the chance of obtaining the given survival rates without the seat-belt having an effect on survival rate is less than 0.01 percent we have;

The probability shows that the sample results could not have occurred by chance. It appears that there is sufficient evidence to conclude that seat-belts do have an effect on survival rate.

Answer:

4

Step-by-step explanation:

The n th term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given

[tex]a_{n}[/tex] = 11 +(n - 1)4 , then

d = 4

The recursive formula allows a term in the sequence to be found by adding d to the previous term, thus

[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 4

Answer:

The answer is 4

Step-by-step explanation:

Answer:

A = 3[tex]r^{2}[/tex]

Step-by-step explanation:

r = [tex]\sqrt{\frac{A}{3} }[/tex]

r = [tex](\frac{A}{3})^{1/2}[/tex]

square both sides:

[tex]r^{2}[/tex] = [tex]\frac{A}{3}[/tex]

multiply 3 to both sides:

3[tex]r^{2}[/tex]  = A

Answer:

[tex] a= 3r {}^{2} [/tex]

[tex] \sqrt{ \frac{a}{3} } = r \\ \frac{1}{3a} = r {}^{2} \\ \frac{1}{3a} \frac{1}{3} = r {}^{2} \frac{1}{3} \\ a = 3r {}^{2} [/tex]

Answer:

63 cm

Step-by-step explanation:

piece 1: x

piece 2: x - 18

First you would subtract 2x - 18 = 108

Second you would add 108 + 18 = 2x

Third you would divide 126 divided by 2x = 63

So that would mean x = 63

Answer:

63cm

Step-by-step explanation:

2 pieces of rope, and one is shorter by 18cm.

piece 1: x

piece 2: x-18

Add the equations together, combine both pieces

2x-18

2x-18 = 108

108+18 = 2x

126 = 2x

x = 63

Answer:

m = 8 and c = 0

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 8x ← is in slope- intercept form, that is y = 8x + 0

with m = 8 and c = 0

Answer:

6

Step-by-step explanation:

Since the two triangles are similar, their ratios of sides must be constant. Therefore:

[tex]\dfrac{9}{3}=\dfrac{x}{2} \\\\x=2\cdot 3=6[/tex]

Hope this helps!

Answer:

-1.67

Step-by-step explanation:

Answer:

1.0712

Step-by-step explanation:

if you increase by 4%, it means you will have a new total of 104%. In decimals it is 1.04 (divide your percentage by 100) after that you do the same with the 3% increase. you'll have a new total of 103%. In decimals 1.03. If you want to know what single multiplier you can use, you need to multiply the both decimals. So you get 1.04 x 1.03 = 1.0712

hope this will help you, have a nice day!

Answer:

y = -1/2x + 2

Step-by-step explanation:

If two lines are perpendicular then the product of their slopes are -1

m1*m2 = -1

where m1 amd m2 is slope of two lines.

_______________________________________

Given line

y = 2x-3\

it is in form of y = mx+c (slope intercept form)

where m is slope and c is y intercept

Thus, slope of line  y = 2x-3 is 2

Now we know that product of two lines are -1

let m be slope of other line

then m*2 = -1

m = -1/2

thus, slope of required line is -1/2

let the line be y = mx+c but m = -1/2

thus

y = -1/2 x + c

given that point(-6,5) lies on it

we use -6 in plca of x and 5 in place of y

5 = -1/2 *-6 + c

=>5 = 3 +c

=> c = 5-3 = 2

Thus, equation that is perpendicular to the line y=2x-3 and passes through the point (-6,5) is y = -1/2x + 2

Answer:

A=1.5 units²

Step-by-step explanation:

a²+b²=c²

2.5²+1.5²=c²

a²+2.25=6.25

a²=4.00

a=2

A=1/2 x b x h

A=1/2 x 1.5 x 2

A=1.5 units²

Answer:

1.5

Step-by-step explanation:

Use the pythagorean theorem.  a^2+b^2=c^2.  a and b are the legs, or the shorter sides of the triangle.  If you don't know which ones are shorter, just know that c is opposite of the right angle which is 2.5 in this case.  So c is 2.5 and a is 1.5.  Now you plug the values into the equation

1.5^2+b^2=2.5^2

2.25+b^2= 6.25 .Simplify the equation

b^2= 4 .Subtract 2.25 from both sides.

b= 2.  Square root both sides.  

Based on the picture, a is the base and b is the height.  The area of a triangle is 1/2(bh) .You already know the base and height you you plug it in again

1/2(1.5*2)= 1/2(3)= 1.5  

Answer:

12.1 =x

Step-by-step explanation:

Since this is a right triangle, we can use  trig functions

cos theta = adj/ hyp

cos 30 = x/14

14 cos 30 = x

12.12435565 =x

12.1 =x

Answer: [tex]y \leq \frac{1}{2} x+3[/tex]

Step-by-step explanation:

If a function has a positive slope, that means the y value is increasing with respect to x. As you go down the x-axis, the y value will continuously increase.

First you want to plot the two sets of coords that they gave you, or else you wont know what the line looks like. Or, you could visually do it in your head. We're going down -4 on the x-axis and down 1 on the y-axis. Then for our second coords, we are going to 0 on the x-axis, then up 3 on the y-axis.

You could plot this for yourself, but im going to do it in my head for simplicity. We also need to find the slope of this function in order for us to find the y-intercept. The slope is change in y divided by the change in x. Subtract the initial position from the final position.

3 - 1 = 2

0 - (-4) = 4

2/4 = 1/2

The new equation is:

[tex]y=\frac{1}{2} x+b\\plugin(0,3)\\3=\frac{1}{2} (0)+b\\b=3[/tex]

Everything is shaded below and to the right of the line. They said the line was solid, so that means less than or equal to, [tex]\leq[/tex]

Answer:

B

Step-by-step explanation:

Step-by-step explanation:

We have,

A ball is thrown into the air with an upward velocity of 36 ft/s. Its height h in feet after t seconds is given by the function :

[tex]h=-16t^2 + 36t + 10[/tex] ......(1)

Part (a) :

The maximum height reached by the ball is given by :

[tex]\dfrac{dh}{dt}=0\\\\\dfrac{d(-16t^2 + 36t + 10)}{dt}=0\\\\-32t+36=0\\\\t=\dfrac{36}{32}\\\\t=1.125\ s[/tex]

Part (b) :

The maximum height of the ball is calculated by putting t = 1.125 in equation (1) such that :

[tex]h=-16(1.125)^2 + 36(1.125)+ 10\\\\h=30.25\ m[/tex]

Answer:

From the sum of angles on a straight line, given that the rotation of each triangle attached to the sides of the octagon is 45° as they move round the perimeter of the octagon, the angle a which is supplementary to the angle turned by the triangles must be 135 degrees

Step-by-step explanation:

Given that the triangles are eight in number we have;

1)  (To simplify), we consider the five triangles on the left portion of the figure, starting from the bottom-most triangle which is inverted upside down

2) We note that to get to the topmost triangle which is upright , we count four triangles, which is four turns

3) Since the bottom-most triangle is upside down and the topmost triangle, we have made a turn of 180° to go from bottom to top

4) Therefore, the angle of each of the four turns we turned = 180°/4 = 45°

5) When we extend the side of the octagon that bounds the bottom-most triangle to the left to form a straight line, we see the 45° which is the angle formed between the base of the next triangle on the left and the straight line we drew

6) Knowing that the angles on a straight line sum to 180° we get interior angle in between the base of the next triangle on the left referred to above and the base of the bottom-most triangle as 180° - 45° = 135°.

Answer:

480 in.^3

Step-by-step explanation:

volume of pyramid = (1/3) * (area of base) * height

Since this pyramid has a square for the base, the area of the base is

A = s^2, where s = length of the side of the square

volume = (1/3) * s^2 * h

volume = (1/3)(12 in.)^2 * (10 in.)

volume = (1/3)(144)(10) in.^3

volume = 480 in.^3

The volume of the square-based pyramid is 480 cubic inches as per the concept of the pyramid.

To find the volume of a square-based pyramid, we can use the formula:

Volume = (1/3) x base area x height.

In this case, the base of the pyramid is a square with a side length of 12 inches, and the height of the pyramid is 10 inches.

First, we calculate the base area of the pyramid, which is the area of the square base:

Base area = side length x side length

                = 12 in x 12 in

                = 144 square inches.

Now, we can substitute the values into the volume formula:

[tex]Volume = \frac{1}{3} \times 144 \times 10[/tex].

Multiplying these values, we get:

[tex]Volume = \frac{1}{3} \times1440 {in}^3[/tex]

Simplifying the expression, we have:

[tex]Volume = 480\ in^3[/tex].

To learn more about the pyramid;

https://brainly.com/question/17615619

#SPJ2

Answer:

Step-by-step explanation:

The slope is 3 and the y-intercept is 2 or (0, 2)

Answer:

The y-intercept of the equation is -2.

Step-by-step explanation:

This equation is in slope-intercept form (y = mx + b). b represents the y-intercept, and m represents the slope.

Step-by-step explanation:

8x(7y+2)-4(7y+2)

=56xy+16x-28y-8

Answer:

56xy+16x-28y-8

Step-by-step explanation:

you have to use the FOIL method to solve this is problem which is

F-First

O-Outer

I-Inner

F-Last

Answer:

unanswerable,don't censore the question

Step-by-step explanation:

sorry pal

Answer:

n is the seventh term=5832

Step-by-step explanation:

a1=8

r=3

a(n)=a1*r^(n-1)=

an=8*3(n-1)

8+24+72+216+648+1944+5832=8744

Answer:

Y=15 when x=5

Step-by-step explanation:

if y= -6 when x= -2

So y=? When x=5

Y=15

Hope this helps

Good Luck

Answer:

so 2a+3b=±13

Step-by-step explanation:

4a²+9b²=97

ab=6

2a+3b=?

by using formula

(a+b)²=a²+b²+2ab

(2a+3b)²=(2a)²+(3b)²+2(2a)(3b)

(2a+3b)²=4a²+9b²+12ab

putting values

(2a+3b)²=97+12(6)

(2a+3b)²=97+72

(2a+3b)²=169

taking square root on both sides

√(2a+3b)²=√169

2a+3b=±13

i hope it will help you

Answer:

2a+3b = 13

Step-by-step explanation:

Using this formula

[tex](x+y)^2 = x^2+y^2+2xy[/tex]

Where,

x = 2a and y = 3b

Putting in the above formula

=> [tex](2a+3b)^2=4a^2+9b^2+12ab[/tex]

Putting  4a²+9b² = 97 and ab = 6

=> (2a+3b)² = 97+12(6)

=> (2a+3b)² = 97+72

=> (2a+3b)² = 169

Taking sqrt on both sides

=> 2a+3b = 13

Answer:

3fx

Step-by-step explanation:

f(x)+f(x)+f(x)

remove parenthesis: (a)=a

add similar elements: fx+fx+fx

=3fx

Answer: for edge

3f(x)

3x2

12

1 pound = 1.62 dollars.

Multiply total pounds by 1.62 for total dollars.

650 x 1.62 = $1,053

Answer:

C. y < -1/5x + 1

Step-by-step explanation:

We can eliminate A and B because the inequality sign is incorrect. If we were to graph those, the shaded area would be above the line, not below. We are left with C and D. Notice in our given graph that the line is dotted, so solution on the line are not included. So our answer would be C. because the inequality sign is y is less than and not y is less than or equal to.

Answer: y = 1/2x - 6

Step-by-step explanation:

#4 We are going to use slope intercept form, (y = mx+b)

1. The line crossing the y-intercept at (0,-6)

2. The slope is 1/2 (increasing by 1 then over 2 --> RISE OVER RUN)

3. Make the equation: y= 1/2x - 6

Answer: 3 . y = -1/3 + 4/3   4. y= 1/2x -6

Step-by-step explanation:

3.   In the first graph  they have the coordinates,  (-2,2)  and (4,0). We have to solve for the slope and the y-intercept in other to write and equation.

To find the slope we have to find the change in the y values  and divide it by the difference in the x values.

2-0 = 2

-2 -4 = -6

2/-6 =  -1/3  Now we know that the slope is -1/3  so we need to  find the y-intercept.

2= -1/3(-2) +b   where be is the y intercept.

2= 2/3 + b

-2/3  -2/3

b= 4/3  

Now we could write the equation as  y= -1/3 + 4/3  

4. The same with number 4.  

We will find the slope and the y intercept by using some points on the number line.

(0,-6)  This already have the y-intercept graphed so we will need to just find the slope.

(0,-6)

(4,-4)  

-6 - (-4) = -2

0 - 4 =  -4

-2/-4 = 1/2

Equation: y = 1/2x  -6