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1 year ago

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A store sells 12-packs of ballpoint pens for $1.09 each and composition books for $2.79 each. Cindy buys m packs of ballpoint pe

ns and n composition books. The store offers a 5% discount for every 50th customer who makes a purchase. If Cindy gets the 5% discount, which expression will represent Cindy’s bill?
0.05 − 1.09m + 2.79n
1.05 + 1.09m + 2.79n
1.05(1.09m + 2.79n)
0.95(1.09m + 2.79n)

2 answers:

vaieri [72.5K]1 year ago

8 0

I will put 0.95(1.09m+2.79n) as my answer.

Ludmilka [50]1 year ago

5 0

<span>There are two possible ways where you can express this. First, is by presenting the equation net of 5 percent which is "x=1.0355n+2.6505m". The other way to express such is by presenting it with gross amount which is "x= (1-0.05)(1.09n+2.79m)"
</span>

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If s(x) = x – 7 and t(x) = 4x2 – x + 3, which expression is equivalent to (t circle s) (x)?

Georgia [21]

Answer:

If s(x) = x – 7 and t(x) = 4x2 – x + 3, which expression is equivalent to (t*s)(x)? 4(x – 7)2 – x – 7 + 3 4(x – 7)2 – (x – 7) + 3 (4x2 – x + 3) – 7 (4x2 – x + 3)(x – 7)

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1 year ago

Read 2 more answers

A bakery sells rolls in units of a dozen. The demand X (in 1000 units) for rolls has a gamma distribution with parameters α = 3,

bearhunter [10]

Answer:

The value is $E(X) = \$ 1.7067$

Step-by-step explanation:

From the question we are told that

The parameters are α = 3, θ = 0.5

The cost of making a unit on the first day is c = $2

The selling price of a unit on the first day is s = $5

The selling price of a leftover unit on the second day is v = $ 1

Generally the profit of a unit on the first day is

$p_1 = 5 - 2$

$p_1 = \$3$

The profit of a unit on the second day is

$p_2 = 1 - 2$

=> $p_2 = - \$1$

Generally the probability of making profit greater than $ 1 is mathematically represented as

$P(X > 1 ) = Gamma (X ,\alpha , \theta)$

=> $P(X > 1 ) = Gamma (1 ,3 , 0.5)$

Now from the gamma distribution table we have that

$P(X > 1 ) = 0.67668$

Generally the probability of making profit less than or equal to $ 1 is mathematically represented as

$P(X \le 1 ) = 1 - P(X > 1 )$

=> $P(X \le 1 ) = 1 - 0.67668$

=> $P(X \le 1 ) = 0.32332$

So the probability of making $3 is $P(X > 1 ) = 0.67668$

and the probability of making -$1 is $P(X \le 1 ) = 0.32332$

Generally the value of profit per day is mathematically represented as

$E(X) = 3 * P(X > 1 ) + (-1 * P(X \le 1 ) )$

=> $E(X) = 3 * 0.67668 + (-1 * 0.32332 )$

=> $E(X) = \$ 1.7067$

4 0

1 year ago

If θ=0rad at t=0s, what is the blade's angular position at t=20s

babunello [35]

The attached figure represents the relation between ω (rpm) and t (seconds)
To find the blade's angular position in radians ⇒ ω will be converted from (rpm) to (rad/s)
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              ω = 100 (rpm) = 100 * (2π/60) = (10/3)π    rad/s

and from the figure it is clear that the operation is at constant speed but with variable levels
            ⇒   ω = dθ/dt   ⇒   dθ = ω dt

            ∴    θ = ∫₀²⁰ ω dt

while ω is not fixed from (t = 0) to (t =20)
the integral will divided to 3 integrals as follow;
       ω = 0                                          from t = 0 to t = 5
       ω = 250 (rpm) = (25/3)π            from t = 5   to t = 15
       ω = 100 (rpm) = (10/3)π            from t = 15 to t = 20

∴ θ = ∫₀⁵ (0) dt   + ∫₅¹⁵ (25/3)π dt + ∫₁₅²⁰ (10/3)π dt

the first integral = 0
the second integral = (25/3)π t = (25/3)π (15-5) = (250/3)π
the third integral = (10/3)π t = (25/3)π (20-15) = (50/3)π

∴ θ = 0 + (250/3)π + (50/3)π = 100 π

while the complete revolution = 2π
so instantaneously at t = 20
∴ θ = 100 π - 50 * 2 π = 0 rad

Which mean:
the blade will be at zero position making no of revolution = (100π)/(2π) = 50

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2 years ago

Bob Rohrman is offering a 2016 Toyota Camry for $29,000. If you have a $5,000 down payment and are able to borrow the rest at a

vova2212 [387]

Answer:

The monthly payment will be $531.12

Step-by-step explanation:

Consider the provided information.

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$29,000-$5,000=$24,000

APR is 2.99% or APR = 0.299%

Therefore, $r=\frac{0.0299}{12}$

n = 48

We can calculate the monthly payment by using the formula:

$P=\frac{r(PV)}{1-(1+r)^{-n}}$

Where P is the monthly payment, PV is the present value, r is the rate per period and n is the number of period.

Substitute the respective values in the above formula we get,

$P=\frac{\frac{0.0299}{12}(24000)}{1-(1+\frac{0.0299}{12})^{-48}}$

$P=\frac{59.8}{0.112593}$

$P\approx531.12$

Hence, the monthly payment will be $531.12

4 0

1 year ago

Learning Task 3. Find the equation of the line. Do it in your notebook.

Wewaii [24]

Answer:

1) The equation of the line in slope-intercept form is $y = 5\cdot x +9$ . The equation of the line in standard form is $-5\cdot x + y = 9$ .

2) The equation of the line in slope-intercept form is $y = \frac{2}{5}\cdot x +\frac{14}{5}$ . The equation of the line in standard form is $-2\cdot x +5\cdot y = 14$ .

3) The equation of the line in slope-intercept form is $y = 3\cdot x +4$ . The equation of the line in standard form is $-3\cdot x +y = 4$ .

4) The equation of the line in slope-intercept form is $y = 2\cdot x + 6$ . The equation of the line in standard form is $-2\cdot x +y = 6$ .

5) The equation of the line in slope-intercept form is $y = \frac{5}{6}\cdot x -\frac{7}{6}$ . The equation of the line in standard from is $-5\cdot x + 6\cdot y = -7$ .

Step-by-step explanation:

1) We begin with the slope-intercept form and substitute all known values and calculate the y-intercept: ( $m = 5$ , $x = -1$ , $y = 4$ )

$4 = (5)\cdot (-1)+b$

$4 = -5 +b$

$b = 9$

The equation of the line in slope-intercept form is $y = 5\cdot x +9$ .

Then, we obtain the standard form by algebraic handling:

$-5\cdot x + y = 9$

The equation of the line in standard form is $-5\cdot x + y = 9$ .

2) We begin with a system of linear equations based on the slope-intercept form: ( $x_{1} = 3$ , $y_{1} = 4$ , $x_{2} = -2$ , $y_{2} = 2$ )

$3\cdot m + b = 4$ (Eq. 1)

$-2\cdot m + b = 2$ (Eq. 2)

From (Eq. 1), we find that:

$b = 4-3\cdot m$

And by substituting on (Eq. 2), we conclude that slope of the equation of the line is:

$-2\cdot m +4-3\cdot m = 2$

$-5\cdot m = -2$

$m = \frac{2}{5}$

And from (Eq. 1) we find that the y-Intercept is:

$b=4-3\cdot \left(\frac{2}{5} \right)$

$b = 4-\frac{6}{5}$

$b = \frac{14}{5}$

The equation of the line in slope-intercept form is $y = \frac{2}{5}\cdot x +\frac{14}{5}$ .

Then, we obtain the standard form by algebraic handling:

$-\frac{2}{5}\cdot x +y = \frac{14}{5}$

$-2\cdot x +5\cdot y = 14$

The equation of the line in standard form is $-2\cdot x +5\cdot y = 14$ .

3) By using the slope-intercept form, we obtain the equation of the line by direct substitution: ( $m = 3$ , $b = 4$ )

$y = 3\cdot x +4$

The equation of the line in slope-intercept form is $y = 3\cdot x +4$ .

Then, we obtain the standard form by algebraic handling:

$-3\cdot x +y = 4$

The equation of the line in standard form is $-3\cdot x +y = 4$ .

4) We begin with a system of linear equations based on the slope-intercept form: ( $x_{1} = -3$ , $y_{1} = 0$ , $x_{2} = 0$ , $y_{2} = 6$ )

$-3\cdot m + b = 0$ (Eq. 3)

$b = 6$ (Eq. 4)

By applying (Eq. 4) on (Eq. 3), we find that the slope of the equation of the line is:

$-3\cdot m+6 = 0$

$3\cdot m = 6$

$m = 2$

The equation of the line in slope-intercept form is $y = 2\cdot x + 6$ .

Then, we obtain the standard form by algebraic handling:

$-2\cdot x +y = 6$

The equation of the line in standard form is $-2\cdot x +y = 6$ .

5) We begin with a system of linear equations based on the slope-intercept form: ( $x_{1} = -1$ , $y_{1} = -2$ , $x_{2} = 5$ , $y_{2} = 3$ )

$-m+b = -2$ (Eq. 5)

$5\cdot m +b = 3$ (Eq. 6)

From (Eq. 5), we find that:

$b = -2+m$

And by substituting on (Eq. 6), we conclude that slope of the equation of the line is:

$5\cdot m -2+m = 3$

$6\cdot m = 5$

$m = \frac{5}{6}$

And from (Eq. 5) we find that the y-Intercept is:

$b = -2+\frac{5}{6}$

$b = -\frac{7}{6}$

The equation of the line in slope-intercept form is $y = \frac{5}{6}\cdot x -\frac{7}{6}$ .

Then, we obtain the standard form by algebraic handling:

$-\frac{5}{6}\cdot x +y =-\frac{7}{6}$

$-5\cdot x + 6\cdot y = -7$

The equation of the line in standard from is $-5\cdot x + 6\cdot y = -7$ .

6 0

1 year ago