There is a two-digit number whose units digit is six less than the tens digit. Four times the tens digit plus five times the units digit equal 51. Find the digits.

Answer:

y = $1,000/car x + $40,000

20 cars

Step-by-step explanation:

Let

x = number of cars sold

y = total earnings

The relationship between y and x can be expressed through a linear equation.

y = mx + b

where,

m is the slope

b is the y-intercept

The slope is how much she earns per car sold, that is, the commission of $1,000/car (I think you meant this number instead of $1,00).

The y-intercept is what she earns even if she does not sell any car, i.e. a salary of $40,000.

The resulting equation is

y = $1,000/car x + $40,000

If she is to make $60,000 in one year (y = $60,000), the number of cars sold is:

$60,000 = $1,000/car x + $40,000

$20,000 = $1,000/car x

x = 20 car

The no. of equally likely event is 10.

Probability is chance of occurrence of a certain event out of all the possible events that can occur in a given situation.

According to the given question Tossing of four coins simultaneously as an experiment let us find he sample space and assuming that all these 4 coins are unbiased.

S = { HHHH, HHHT, HHTT, HTTT, TTTT, TTTH, TTHH, THHH, HTTH, THHT }.

∴ N(s) = 10.

As these 4 coins are unbiased there for all the events in the sample space are equally likely to happen.

So, The no. of equally likely outcome is 10.

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Answer:

The height of the ball after t =1.5 second is 7.5 feet.

Description:

The basket ball shoots from a height of 6 feet, it increase the height 1.5 feet after 1.5 seconds.

Therefore, the basketball thrown at the rate of 1 feet/per second.

Step-by-step explanation:

Given: A player shoots a basketball from a height of 6 feet. The equation,

h(t) = [tex]-16t^2 + 25t + 6[/tex]

We need to find the height of the ball when t = 1.5 and describe the height.

plug in t = 1.5 in h(t) = [tex]-16t^2 + 25t + 6[/tex]

h(1.5) = [tex]-16(1.5)^2 + 25(1.5) + 6[/tex]

Simplifying the above expression, we get

h(1.5) = -36 + 37.5 + 6

h(1.5) = -36+43.5

h(1.5) = 7.5 feet

The height of the ball after t =1.5 second is 7.5 feet

Description:

The basket ball shoots from a height of 6 feet, it increase the height 1.5 feet after 1.5 seconds.

Therefore, the basketball thrown at the rate of 1 feet/per second.

Answer:

1.463 ft.

Step-by-step explanation:

As you can see in the image, we can use the sin(6) to calculate the high.

sin(6°) = x/14

x = sin(6°)*14

x  = 1.463 ft.

To set the infusion rate for a 60 kg dog, calculate the total fluid needed (3000 mL), the total number of drops (30,000 gtts), and then determine the drops per minute (20.83 gtt/min), rounding to approximately 21 drops per minute.

To calculate the infusion rate for a 60 kg dog that needs 50 mL/kg of fluids over 24 hours using a 10 gtt/mL set, follow these steps:

Therefore, you will set the infusion to approximately 21 drops per minute (rounding to the nearest whole number).

Answer:

Solution of the system of the equations is (0.882, 0.647)

Step-by-step explanation:

As shown in the figure equations are [tex]y=-\frac{2}{5}x+1[/tex] and y = 3x - 2

Solution of the system of equations will be the common point or point of intersection of these lines.

To get the point of intersection we will solve these equations.

We will equate these equations to get the value of x.

[tex]-\frac{2}{5}x+1=3x-2[/tex]

[tex]-2x+5=15x-10[/tex]

15x + 2x = 10 + 5

17x = 15

[tex]x=\frac{15}{17}[/tex]

x = 0.882

By putting x = 0.882 in y = 3x - 2

y = 3(0.882) - 2

y = 0.647

So the solution of systems of equations is (0.882, 0.647)

Answer:

B and C

Step-by-step explanation:

Answer:

  See the attachment

Step-by-step explanation:

You want a graph of the parabola defined by f(x) = x² +10x +24.

We can add and subtract the square of half the x-coefficient to put the equation into vertex form:

  f(x) = x² +10x +24 . . . . . . . . . . given

  f(x) = x² +10x +25 +24 -25 . . . . add and subtract (10/2)² = 25

  f(x) = (x +5)² -1 . . . . . . . . . write in vertex form

Comparing to the vertex form equation f(x) = (x -h)² +k, we see that ...

  (h, k) = (-5, -1).

These are the coordinates of the vertex.

The coefficient of x² is 1, so another point can be found by adding (1, 1) to the vertex. That means a second point on the parabola is ...

  (-5, -1) +(1, 1) = (-4, 0)

The attached graph shows the parabola with vertex (-5, -1) through point (-4, 0).

__

Additional comment

When the coefficient of x² is not 1, the process is a little different. If you start with f(x) = ax² +bx +c, you can factor 'a' from the first two terms to help you get vertex form.

  f(x) = a(x² +(b/a)x) +c
  f(x) = a(x² +(b/a)x +(b/(2a))²) + c - a(b/(2a))²
  f(x) = a(x +b/(2a)x)² +(c -b²/(4a))

The vertex is (-b/(2a), c -b²/(4a)).

The second point can be found by adding (1, a) to the vertex coordinates.

Answer:

d. [tex]-15x^3y^7[/tex]

Step-by-step explanation:

By the binomial theorem,

[tex](p+q)^n=\sum_{r=0}^{n} ^nC_r (p)^{n-r} q^r[/tex]

Where,

[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

Thus,

[tex](\frac{1}{2}x-y)^{10}=(\frac{x}{2}+(-y))^{10})=\sum_{r=0}^{n} ^10C_r (\frac{x}{2})^{10-r} (-y)^{r}[/tex]

For the 8th term, r = 7,

Thus, the 8th term would be,

[tex]^{10}C_7 (\frac{x}{2})^{10-7} (-y)^{7}[/tex]

[tex]=\frac{10!}{7!(10-7)!} (\frac{x}{2})^3 (-y)^7[/tex]

[tex]=-\frac{10\times 9\times 8}{3\times 2\times 1}\times \frac{x^3}{8}\times y^7[/tex]

[tex]=-\frac{720x^3y^7}{48}[/tex]

[tex]=-15x^3y^7[/tex]

Hence, option 'D' is correct.

This problem can be solved using equivalent fractions. The first step in resolving this problem is to realize that fractions are best compared when they both have the same denominator.  In this case, I will choose to make that common denominator 100. There is no need to rewrite the fraction [tex]\frac{21}{100}[/tex] as the denominator for this fraction is already 100. The fraction [tex]\frac{1}{5} =\frac{20}{100}[/tex] . This is achieved by multiplying both the numerator and denominator by 20. Now that the two fractions have the same denominator, we can easily see that [tex]\frac{21}{100}[/tex] is greater than [tex]\frac{1}{5}[/tex] because it is greater than its equivalent fraction.

Answer:

An equivalent expression is [tex]6 - 16y[/tex]

Step-by-step explanation:

The distributive property consists in removing the parenthesis. For this problem, it is done by multiplying the number outside the parenthesis by each term inside the parenthesis and then performing a subtraction between the results because of the minus sign inside.

For the expression [tex]2(3-8y)[/tex], when applying the distributive property, you would get:

[tex]2\times 3 - 2\times 8y[/tex]

[tex]6 - 16y[/tex]

Thus, an equivalent expression is [tex]6 - 16y[/tex].

The distributive property to remove the parentheses in the expression 2(3 - 8y) is 6 - 16y

From the question, we have the following parameters that can be used in our computation:

2(3 - 8y)

When the expression is expanded, we have the following

2(3 - 8y) = 2 * 3 - 2 * 8y

Evaluate the products

This gives

2(3 - 8y) = 6 - 16y

Lastly, we have

2(3 - 8y) = 6 - 16y

Hence the expression when simplified is 6 - 16y

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Answer:

A. [tex]a_n=200+(n-1)5[/tex]

Step-by-step explanation:

Given,

The initial sprinting of Freya = 200 yards,

Also,  She gradually increases her distance by 5 yards per day,

So, in second day her sprinting = 200 + 5 = 205 yards,

In third day = 205 + 5 = 210 yards,

In fourth day = 210 + 5 = 215 yards,

....................,  so on,.....

Hence, the sequence that shows the given situation,

200, 205, 210, 215, .........

Which is an A.P.

That having first term, a = 200,

Common difference, d = 5,

Thus, the explicit formula for the given situation is,

[tex]a_n=a+(n-1)d[/tex]

[tex]\implies a_n=200+(n-1)5[/tex]

Option A is correct.

Answer:

Option A.

Step-by-step explanation:

The explicit formula of an AP is

[tex]a_n=a+(n-1)d[/tex]              .... (1)

where,

a is the first of the AP,

d is common difference.

It is given that Freya starts by sprinting 200 yards and she gradually increases her distance, adding 5 yards a day.

200, 205, 210,..., 305

Here,

First terms = 200

Common difference = 5

Substitute a=200 and d=5 in equation (1), to find the required explicit model

[tex]a_n=200+(n-1)5[/tex]

Therefore, the correct option is A.