Let a=3/5 and let b=2/3. Compute a^2b^-3.

To calculate the average speed of the horse in miles per hour, holding the all-time record for running a 2-kilometer race in 1 min and 59.4 sec, we do the necessary conversions over distance from kilometers to miles and over time from minutes and seconds to hours.

The average speed thus calculated is 393.2722 miles per hour.

The average speed of any object is the ratio of the total distance the object travels, and the total time taken by the object to cover that distance.

Thus, Average speed = Total Distance/Time taken.

In the question, we are informed that a horse holds the all-time record for running a 2-kilometer race in 1 min and 59.4 sec.

We are asked for the necessary conversions required to calculate the average speed of the horse for the race in miles per hour.

The necessary conversions that will be required will be:

Distance: 2 kilometers to miles.

Time: 1 minute 59.4 secs to hours.

To convert from kilometers to miles, we follow the conversion rate:

1 kilometer = 0.621371 miles.

Thus, distance = 2 kilometers = 2 * 0.621371 miles = 1.24274 miles.

For the time, we first convert seconds to time, using the conversion rate:

1 second = 1/60 minutes,

Therefore, 59.4 seconds = 59.4/60 minutes = 0.99 minutes.

Thus, the total time = 1.99 minutes.

To convert from minutes to hours, we follow the conversion rate:

1 minutes= 1/60 hours.

Thus, time = 1.99 minutes = 1.99/60 hours = 0.03316 hours.

Thus, the average speed of the horse = Distance/Time = 1.24274/0.003316 miles per hour = 393.2722 miles per hour.

Thus, to calculate the average speed of the horse in miles per hour, holding the all-time record for running a 2-kilometer race in 1 min and 59.4 sec, we do the necessary conversions over distance from kilometers to miles and over time from minutes and seconds to hours.

The average speed thus calculated is 393.2722 miles per hour.

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[tex]doctors = 55\% \\ woman = 49\% \\ both = 29\%[/tex]

[tex]p(a) =0.55 + 0.49 - 0.29 \\ p(a) = 0.75[/tex]

$14.90 spent with the amount left for an extra pencil or notebook being $0.30 or $1.50 short respectively indicates that a notebook costs $1.8 more than a pencil.

Let x represent the cost of a notebook and let y represent the cost of a pencil. The following equations can be obtained;

4•x + 3•y = 14.9...(1)

Let a represent the total money Tina has, which gives;

4•x + 4•y = a - 0.3...(2)

5•x + 3•y = a + 1.5...(3)

Subtracting equation (2) from equation (3) gives;

5•x - 4•x + 3•y - 4•y = a - a + 1.5 - (-0.3) = 1.8

Which gives;

Multiplying equation (4) by 4 and subtracting the result to equation (1) gives;

4 × (x - y) = 4 × 1.8 = 7.2

4•x - 4•y = 7.2

4•x - 4•x + 3•y - (-4•y) = 14.9 - 7.2 = 7.7

7•y = 7.7

x - y = 1.8

x = 1.8 + 1.1 = 2.9

The difference between the cost of a notebook and the cost of a pencil is therefore;

x - y = $2.9 - $1.1 = $1.8

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Answer:

55.5[tex]x^{4}[/tex]+24.21x³+73.79x²+33.81x+28.49

Step-by-step explanation:

To simplify this equation, follow these steps:

(7.5x² +5.4x +3.7) (7.4x² -2.1x +7.7)

Multiply 7.5x² by all the terms in the right parenthesis.

7.5x² (7.4x² -2.1x +7.7)=55.5[tex]x^{4}[/tex] - 15.75x³+ 57.75x²

Then multiply 5.4x by all the terms in the right parenthesis.

5.4x(7.4x²-2.1x+7.7)=39.96x³-11.34x²+41.58x

Now multiply 3.7 by all the terms in the right parenthesis.

3.7(7.4x²-2.1x+7.7)=27.38x²-7.77x+28.49

Add all of those answers together.

55.5[tex]x^{4}[/tex] - 15.75x³+ 57.75x²+39.96x³-11.34x²+41.58x+27.38x²-7.77x+28.49=

=55.5[tex]x^{4}[/tex]+24.21x³+73.79x²+33.81x+28.49

The answer is 55.5[tex]x^{4}[/tex]+24.21x³+73.79x²+33.81x+28.49

Hope this helps!

If not, I am sorry.

The value of the given expression is 136

From the question, we are to evaluate the give expression

The given expression is

−8×(−10+(−7))

The expression can be simplified as follows

−8×(−10+(−7))

−8×(−10−7)

−8×(−17)

= 136

Hence, the value of the given expression is 136

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Answer:

49/100

Step-by-step explanation:

So you can find the area of shaded area by finding the area of the circle inside the entire circle that has a diameter of 3 cm and 4 cm and then find the area of the most inner circle which only has a diameter of 4 cm and then subtract these 2. After that you want to find the area of the entire circle and then divide the area of the shaded area by the entire circle. The formula for the area of a circle is given as: [tex]\pi r^2[/tex]

Area of the two "inner" circles of a diameter of 4 and 3 cm. This gives you an entire diameter of 7 cm with a radius of 3.5. The area of this circle is [tex]\pi(3.5)^2[/tex] which is [tex]12.25\pi[/tex].

The area of the most inner circle only has a diameter only 4 cm. The radius is 2, thus the area of this circle is [tex]\pi (2)^2[/tex] which is [tex]4\pi[/tex]. Now subtract this from the 12.25 pi to find the area of the shaded area. This gives you the equation: [tex]12.25\pi-4\pi[/tex] which equals [tex]8.25\pi[/tex].

Now to find the area of the entire circle you add up all the "diameters" which gives you 4 cm + 3 cm + 3 cm = 10 cm. So the radius is 5. This gives you the equation: [tex]\pi(5)^2[/tex] which is equal to [tex]25\pi[/tex].

Now to find the fraction of circle that is shaded we divide the area of the shaded area and the area of the entire circle. This gives you the equation: [tex]\frac{12.25\pi}{25\pi}[/tex] but since it wants it as a fraction, I'm assuming it wants integers in the decimal and numerator place. So we can represent 12.25 as 12 + 1/4. And then convert the 12 into 1/4ths by multiplying by 4 and then adding that to the numerator. This makes the fraction [tex]\frac{49}{4}=12.25[/tex]. So now all we have to is divide the two values: [tex]\frac{\frac{49}{4}}{\frac{25}{1}}[/tex]. If you're wondering where the pi's when you can just cancel them out since they're both in the numerator and denominator. Now all we have to do is keep the 49/4, change the operator to multiplication, and flip the 25/1 to 1/25. This gives you the equation: [tex]\frac{49}{4} * \frac{1}{25}[/tex] which becomes [tex]\frac{49}{100}[/tex] which is the answer

Answer:

12.56637ft

Step-by-step explanation:

Formula: c=2π*r

c=2π*2 = 12.56637ft

Answer:

C

Step-by-step explanation:

12 /13   is definitely less than 36/30   because 36/30 =  1  1/5

Answer:

a=70°

b=120°

we know,

a+b

=70+120

=190

The ratio of sin X and cos X are as follows;

sin X = √119 / 12

cos X = 5 / 12

Right angle triangle has one of its angle as 90 degrees. The side and angles can be found using trigonometric ratios.

Therefore,

sin X = opposite / hypotenuse

sin X = √119 / 12

Therefore,

cos X = adjacent / hypotenuse

cos X = 5 / 12

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20+12+15= 32+15 = 47 minutes in total

300 meters per minute

300 * 47 = 14100 meters in total

with this we can see the first race was 4/9 that distance meaning the first race was 6266.6 meters long

14100 - 6266.6 = 7833.3

2/5 of 7833.3 is 3133.32

therefore 7833.3 - 3133.32 will give the distance of the third part of the race

meaning of course the answer is 4699.98 or rounding up 4700 meters for the third race

Answer:

x = 10

Step-by-step explanation:

Proof: If a line is parallel to one side of the triangle, then it divides the other two sides proportionally.

6/9 = x/15

9x = 90

x = 10

Step-by-step explanation:

45+45

90

I guess is the answer

Answer

He needs to buy 27 Cows

Step-by-step explanation:

if the ratio from horses to cows is 5-3 then you multiply 5 by the number to get 45 and also multiply it by 3

5 x 9 = 45

3 x 9 = 27

T

Step 1 and 2: Draw an isosceles right triangle

See attachment (figure 1) for this triangle

The legs of this triangle have a length of 1 inch

Step 3: The hypotenuse

This is calculated using the following Pythagoras theorem

[tex]h^2 = 1^2 + 1^2[/tex]

This gives

[tex]h = \sqrt 2[/tex]

Step 4: Draw another isosceles right triangle

Add 1 inch to one of the legs

See attachment (figure 2) for this triangle

The legs of this triangle have lengths of 1 inch and 2 inches, respectively

This hypotenuse is calculated using the following Pythagoras theorem

[tex]h^2 = 2^2 + 1^2[/tex]

This gives

[tex]h = \sqrt 5[/tex]

Step 5: Draw another isosceles right triangle

Add 1 inch to one of the legs

See attachment (figure 3) for this triangle

The legs of this triangle have lengths of 1 inch and 3 inches, respectively

This hypotenuse is calculated using the following Pythagoras theorem

[tex]h^2 = 3^2 + 1^2[/tex]

This gives

[tex]h = \sqrt {10[/tex]

Step 6: Draw another isosceles right triangle

Add 1 inch to one of the legs

See attachment (figure 4) for this triangle

The legs of this triangle have lengths of 1 inch and 4 inches, respectively

This hypotenuse is calculated using the following Pythagoras theorem

[tex]h^2 = 4^2 + 1^2[/tex]

This gives

[tex]h = \sqrt{[17[/tex]

See that the hypotenuse is the square root of 17

Hence, the right triangle whose legs are 1 inch and 4 inches has an hypotenuse of √17

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Answer:

Put the equations in the form y=mx+c and after that, take any two values for x, fill in the equation of y=mx+c to get the corresponding y coordinate and take any value for y, to get the corresponding x coordinate. For this example i took x=0 and y=0, feel free to try it again with any other value. If you get a fraction and don't what to work with fractions, just do a trial and error till you get a whole number (as i did for Question 21 for the x and y coordinates)

The answer is [tex]11c^3[/tex].

The function that represents a geometric sequence is given by:

C. [tex]A(n) = P(1 + i)^{n-1}[/tex], where n is a positive integer.

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

Following this pattern, a function that is also a geometric sequence is:

C. [tex]A(n) = P(1 + i)^{n-1}[/tex], where n is a positive integer.

For the function, we have that:

[tex]a_1 = P, q = 1 + i[/tex].

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The solution to the inequality is x ≤ 15

The inequality is given as:

12 + x ≥ 3(x-6)

Open the bracket

12 + x ≥ 3x - 18

Evaluate the like terms

-2x ≥ -30

Divide by -2

x ≤ 15

Hence, the solution to the inequality is x ≤ 15

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The solution for x ≥ 0 and x ≥ -5 is [-5, ∞), in the interval notation.

The interval notations are used to represent numbers between two numbers excluding or including the numbers as per the use. We use the following four interval notations:

[a, b] ⇒ All numbers between a and b including both a and b.

(a, b) ⇒ All numbers between a and b excluding both a and b.

(a, b] ⇒ All numbers between a and b excluding a but including b.

[a, b) ⇒ All numbers between a and b including a but excluding b.

We are asked to write the solution for x ≥ 0 and x ≥ -5 in the interval notation.

We first write each inequality in interval notation:

x ≥ 0 ⇒ x are all numbers greater than 0 including 0. This can be written in the interval notation as [0, ∞). We don't include ∞ as it is indeterminant.

x ≥ -5 ⇒ x are all numbers greater than -5 including -5. This can be written in the interval notation as [-5, ∞). We don't include ∞ as it is indeterminant.

Now, we are asked to solve for x ≥ 0 or x ≥ -5. Since it is 'or', we take unions of the two sets, that is the solution is:

[0, ∞) ∪ [-5, ∞) = [5, ∞).

Therefore, the solution for x ≥ 0 and x ≥ -5 is [-5, ∞), in the interval notation.

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Answer:

16 ounce can sells for 85 cents

Step-by-step explanation:

29cents / 6 ounce = 4.833cents/ounce

65cents / 16 ounce = 4.0625cents/ounce

4.0625 < 4.833

then:

the better deal is:

16 ounces per 65 cents

Answer:graph a  

Step-by-step explanation:

bc if you subtract 3

from 2 you find the one you line your numbers up with

The first difference between Tn and Tn-1 where Tn= 688 is 88 if the quadratic sequence is defined as:2;12;28;50

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

The quadratic sequence:

2, 12, 28, 50

a + b + c = 2

10, 16, 22 (first difference)

3a + b = 10

6, 6 (second difference)

2a = 6

a = 3

b = 1

c = -2

Tterm:

T(n) = 3n² + n - 2  = 688 (given)

After solving the quadratic equation:

n = 15, n = -46/3(n cannot be nagatve)

n = 15

n - 1 = 14

T(14) = 600

T(n) - T(n-1) = 688 - 600 = 88

Thus, the first difference between Tn and Tn-1 where Tn= 688 is 88 if the quadratic sequence is defined as:2;12;28;50

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: \{ 0,4 \}[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: - {a}^{2} + 4a = 0[/tex]

[tex]\qquad \tt \rightarrow \: - ( {a}^{2} - 4a) = 0[/tex]

[tex]\qquad \tt \rightarrow \: {a}^{2} - 4a = 0[/tex]

[tex]\qquad \tt \rightarrow \:a(a - 4) = 0[/tex]

The two cases are :

or

We can conclude :

[tex]\qquad \tt \rightarrow \:solution \: (a) = \{ 0,4\}[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

[tex] \quad \quad \quad \quad\huge \tt \pink ❆ AnSweR \pink ❆[/tex]

[tex]\quad\quad \tt-a^2+4a= 0[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex] \quad\quad\tt⇢-1(a^2 - 4a) = 0[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\quad\quad\tt⇢-1(a-4)a = 0[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\quad\quad\tt⇢a-4=0[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\quad\quad\tt⇢a = 0[/tex]

-----------------------------------------------------------

[tex] \boxed{ \tt \blue{a = 0}}[/tex]

[tex]\boxed{ \tt\blue{a = 4}}[/tex]

Answer:

Step-by-step explanation:

Answer:

The required linear equation satisfying the given conditions f(-1)=4 and f(5)=1 is [tex]$y=\frac{-1}{2} x+\frac{7}{2}$[/tex]

Step-by-step explanation:

It is given that f(-1)=4 and f(5)=1.

It is required to find out a linear equation satisfying the conditions f(-1)=4

and f(5)=1. linear equation of the line in the form

[tex]$$\left(y-y_{2}\right)=m\left(x-x_{2}\right)$$[/tex]

Step 1 of 4

Observe, f(-1)=4 gives the point (-1,4)

And f(5)=1 gives the point (5,1).

This means that the function f(x) satisfies the points (-1,4) and (5,1).

Step 2 of 4

Now find out the slope of a line passing through the points (-1,4) and (5,1),

[tex]$$\begin{aligned}&m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\&m=\frac{1-4}{5-(-1)} \\&m=\frac{-3}{5+1} \\&m=\frac{-3}{6} \\&m=\frac{-1}{2}\end{aligned}$$[/tex]

Step 3 of 4

Now use the slope [tex]$m=\frac{-1}{2}$[/tex] and use one of the two given points and write the equation in point-slope form:

[tex]$(y-1)=\frac{-1}{2}(x-5)$[/tex]

Distribute [tex]$\frac{-1}{2}$[/tex],

[tex]$y-1=\frac{-1}{2} x+\frac{5}{2}$[/tex]

Step 4 of 4

This linear function can be written in the slope-intercept form by adding 1 on both sides,

[tex]$$\begin{aligned}&y-1+1=\frac{-1}{2} x+\frac{5}{2}+1 \\&y=\frac{-1}{2} x+\frac{5}{2}+\frac{2}{2} \\&y=\frac{-1}{2} x+\frac{7}{2}\end{aligned}$$[/tex]

So, this is the required linear equation.

Answer:

F=9/5c+32

Step-by-step explanation:

The graph that best describes the new function is shown in the image attached below.

The equation for a linear function with a slope of m and y-intercept of b is represented as y = mx + b.

Given a linear function graph passes the points (-0.5, 0) and (0, 1):

Y-intercept (b) = 1 (value of y when x = 0)

Slope (m) = change in y/change in x = (1 - 0)/(0 - (-0.5)) = 2

If the slope (1) is multiplied by 2, the new slope would be: 2

If the y-intercept (2) is increased by 3 units, the new y-intercept would be: 5

The equation of the new function would be: y = 2x + 5

The graph that best represents the function is shown in the image attached below.

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Answer: 7) Step 1 8) Step

Step-by-step explanation:

The answer to 7 is 11. The error starts in step 1, as you can see youre supposed to do 8 divided by 2 plus 3 times 3 minus 2, instead it seems like 3+3 were added instead of becoming 9 thus the answer becomes 7.

The answer to 8 is also 11. 18-14/2 is 11.

[tex]y=78^{\circ}[/tex] (alternate interior angles theorem)

[tex]x=78^{\circ}[/tex] (alternate segment theorem)

[tex]z=24^{\circ}[/tex] (angles in a triangle add to 180 degrees)