The diagram represents three statements: p, q, and r. For what value is both p ∧ r true and q false?

2
4
5
9

Your answer is C) The ant is crawling at 2 feet per minute.

This is because in the function y = 2t + 5, the 2 represents the slope of the line, which means that for every 1 unit that you go across, you need to go 2 units up. Therefore, for every 1 minute, the ant gains 2 feet so it is crawling at 2 feet per minute.

I hope this helps! Let me know if you have any questions :)

Answer:

[tex]x_{1} =-4+\sqrt{2} \\x_{2} =-4-\sqrt{2} \\[/tex]

Step-by-step explanation:

Using quadratic formula:

[tex]\frac{-b+-\sqrt{b^{2} -4*a*c} }{2*a}[/tex]

We will have 2 solutions.

x^2+8x+16=2

x^2+8x+14=0

a= 1    b=8   c= 14

[tex]x_{1}= \frac{-8+\sqrt{8^{2}-4*1*14} }{2*1} \\\\x_{2}= \frac{-8-\sqrt{8^{2}-4*1*14} }{2*1} \\[/tex]

We can write:

[tex]x_{1}= \frac{-8+\sqrt{{64}-56} }{2} \\\\x_{2}= \frac{-8-\sqrt{{64}-56} }{2} \\[/tex]

[tex]x_{1}= -4+\frac{\sqrt{{64}-56} }{2} \\\\x_{2}= -4-\frac{\sqrt{{64}-56} }{2} \\[/tex]

so, we have:

[tex]x_{1}= -4+\frac{\sqrt{{}8} }{2} \\\\x_{2}=-4-\frac{\sqrt{{}8} }{2} \\[/tex]

simplifying we have:

[tex]x_{1}= -4+\frac{\sqrt{{}2*4} }{2} \\\\x_{2}= -4-\frac{\sqrt{{}2*4} }{2} \\[/tex]

Finally:

[tex]x_{1}= -4+\sqrt{2} \\\\x_{2}= -4-\sqrt{2} \\[/tex]

Final answer:

To solve the inequality x^2 + 36 > 12x, rearrange the terms to have all variables on one side and the constant on the other side. Subtracting 12x from both sides, we get x^2 - 12x + 36 > 0. This is now a quadratic inequality. The solution is x > 6 or x < 6.

Explanation:

To solve the inequality x^2 + 36 > 12x, we need to rearrange the terms to have all variables on one side and the constant on the other side. Subtracting 12x from both sides, we get x^2 - 12x + 36 > 0. This is now a quadratic inequality. To solve it, we can factor the expression into (x-6)(x-6) > 0. From this, we see that the inequality is satisfied when x > 6 or x < 6, since the parabola opens upwards and the expression is equal to zero at x = 6.

Answer:

[tex]y = -\frac{1}{3} x[/tex]

Step-by-step explanation:

We are given the following two points and we are to find the equation of the line which passes through them:

(-3, 1) and (0,0)

Slope = [tex]\frac{0-1}{0-(-3)} =-\frac{1}{3}[/tex]

Substituting the given values and the slope in the standard form of the equation of a line to find the y intercept:

[tex]y=mx+c[/tex]

[tex]0=-\frac{1}{3} (0)+c[/tex]

[tex]c=0[/tex]

So the equation of the line is [tex]y = -\frac{1}{3} x[/tex]

Answer:

[tex]y = -\frac{1}{3}x[/tex]

Step-by-step explanation:

The equation of a line in the pending intersection is:

[tex]y = mx + b[/tex]

Where m is the slope of the line and b is the intercept with the y axis.

If we know two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] then we can find the equation of the line that passes through those points.

[tex]m =\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]b=y_1-mx_1[/tex]

In this case the points are  (-3, 1) and (0,0)

Therefore

[tex]m =\frac{0-1}{0-(-3)}[/tex]

[tex]m =\frac{-1}{3}[/tex]

[tex]b=1-(\frac{-1}{3})(-3)[/tex]

[tex]b=0[/tex]

Finally the equation is:

[tex]y = -\frac{1}{3}x[/tex]

[tex]\bf (\stackrel{x_1}{10}~,~\stackrel{y_1}{-9})~\hspace{10em} slope = m\implies -2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-9)=-2(x-10)\implies y+9=-2(x-10)[/tex]

Answer:

Slope intercept form is: -5=5/4(-4)

Step-by-step explanation:

The general form of slope intercept form is

y = mx+b

where m is the slope and b is y intercept

We are given the equation:

-2-3=5/4(-2*(2))

-5=5/4(-4)

so, y =-5, m= 5/4, x =-4, and b=0

so, Slope intercept form is: -5=5/4(-4)

Answer:

D

Step-by-step explanation:

The line segments drawn from each vertex of the triangle and intersecting at H are the Altitudes of the triangle.

The point H is called the Orthocenter

Answer:

D. Ortho-center.

Step-by-step explanation:

We have been given an image of a triangle. We are asked to find the term that describes point H.

We can see that point H is the point, where, all the altitudes of our given triangle EFF are intersecting.

We know that ortho-center of a triangle is the point, where all altitudes of triangle intersect. Therefore, point H is the ortho-center of our given triangle and option D is the correct choice.

Answer:

A. The data set has a median that is not in the data set

Step-by-step explanation:

The given data is:

2,4,6,8,10,12,14,16

The median for the data set is:

(8+10)/2 = 9

The data set has no mode as no number is repeated in the data set.

The IQR is:

= [(12+14)/2-(4+6)/2)]

=[26/2 - 10/2]

=13-5

=8

By looking at the options, we can see that the correct answer is:

A. The data set has a median that is not in the data set

as 9 is not a member of the data set ..

Answer:

True

Step-by-step explanation:

Bisector means to cut into two equal halves.  The midpoint is the middle point so it halves the line too.

If a segment is perpendicular to while cutting it in half, then it is called a perpendicular bisector.

Answer:

C. 7$

Step-by-step explanation:

Answer:

Samantha should plan to spend $7.

Step-by-step explanation:

Let the price of 1 pizza be = p

Let the price of 1 coke = c

Let the price of 1 pack of chips = b

As per table, we get following equations:

[tex]p+c+b=9[/tex] or [tex]p=9-c-b[/tex]   ......(1)

[tex]p+2c=10[/tex]     .......(2)

[tex]2p+2b=12[/tex]    ......(3)

Substituting the value of p from (1) in (2)

[tex]9-c-b+2c=10[/tex]

=> [tex]c-b=1[/tex]    ......(4)

Substituting the value of p from (1) in (3)

[tex]2(9-c-b)+2b=12[/tex]

=> [tex]18-2c-2b+2b=12[/tex]

=> [tex]18-2c=12[/tex]

=> [tex]2c=18-12[/tex]

=> [tex]2c=6[/tex]

c = 3

We have [tex]c-b=1[/tex]

=> [tex]b=c-1[/tex]

=> [tex]b=3-1[/tex]

b = 2

And [tex]p=9-c-b[/tex]

[tex]p=9-3-2[/tex]

p = 4

We get the following cost now.

Cost of 1 pizza = $4

Cost of 1 coke = $3

Cost of 1 chips bag = $2

We have been given that Samantha wants two bags of chips and a coke.

So, she should spend [tex](2\times2)+3[/tex]= [tex]4+3=7[/tex]

Hence, Samantha should plan to spend $7.

Answer:

[tex]2(x-2)^2-7[/tex]

Step-by-step explanation:

[tex]y=2x^2-8x+1[/tex]

When comparing to standard form of a parabola: [tex]ax^2+bx+c[/tex]

Vertex form of a parabola is: [tex]a(x-h)^2+k[/tex], which is what we are trying to convert this quadratic equation into.

To do so, we can start by finding "h" in the original vertex form of a parabola. This can be found by using: [tex]\frac{-b}{2a}[/tex].

Substitute in -8 for b and 2 for a.

[tex]\frac{-(-8)}{2(2)}[/tex]

Simplify this fraction.

[tex]\frac{8}{4} \rightarrow2[/tex]

[tex]\boxed{h=2}[/tex]

The "h" value is 2. Now we can find the "k" value by substituting in 2 for x into the given quadratic equation.

[tex]y=2(2)^2-8(2)+1[/tex]

Simplify.

[tex]y=-7[/tex]

[tex]\boxed{k=-7}[/tex]

We have the values of h and k for the original vertex form, so now we can plug these into the original vertex form. We already know a from the beginning (it is 2).

[tex]a(x-h)^2+k\\ \\ 2(x-2)^2-7[/tex]

To find the vertex form of a quadratic equation \( y = ax^2 + bx + c \), we can complete the square to transform it into the vertex form, which is written as \( y = a(x - h)^2 + k \), where \( (h, k) \) is the vertex of the parabola.
The quadratic equation given is \( y = 2x^2 - 8x + 1 \).
Here, \( a = 2 \), \( b = -8 \), and \( c = 1 \).
First, find \( h \) using the formula \( h = -\frac{b}{2a} \):
\[
h = -\frac{-8}{2 \cdot 2} = \frac{8}{4} = 2
\]
Next, we will use the value of \( h \) to find \( k \). The value of \( k \) is the y-value of the vertex, which we find by plugging \( h \) into the original equation:
\[
k = 2h^2 - 8h + 1
\]
Now substituting \( h = 2 \) into this formula, we get:
\[
k = 2(2)^2 - 8(2) + 1 = 2 \cdot 4 - 16 + 1 = 8 - 16 + 1 = -7
\]
Therefore, the vertex \( (h, k) \) is \( (2, -7) \).
Now, we rewrite the original quadratic equation in vertex form using the values of \( h \) and \( k \):
\[
y = a(x - h)^2 + k
\]
Substitute \( a = 2 \), \( h = 2 \), and \( k = -7 \) into this equation:
\[
y = 2(x - 2)^2 - 7
\]
So, the vertex form of the equation \( y = 2x^2 - 8x + 1 \) is \( y = 2(x - 2)^2 - 7 \).

Answer:

m = -5/2

Step-by-step explanation:

Solve for slope with the following equation:

m (slope) = (y₂ - y₁)/(x₂ - x₁)

Let:

(4 , -12) = (x₁ , y₁)

(-2 , 3) = (x₂ , y₂)

Plug in the corresponding numbers to the corresponding variables:

m = (3 - (-12))/(-2 - 4)

m = (3 + 12)/(-2 - 4)

m = (15)/(-6)

Simplify the slope:

m = -(15/6) = -5/2

-5/2 is your slope.

~

[tex]\text{Hey there!}[/tex]

[tex]\bf\dfrac{y_2-y_1}{x_2-x_1}}\leftarrow\text{is the slope formula}[/tex]

[tex]\bf{y_2=-12}\\\bf{y_1=3}\\\bf{x_2=4}\\\bf{x_1=-2}[/tex]

[tex]\dfrac{-12-3}{4-(-2)}\\\\\\\text{-12 - 3 = -15}\\\\\\\text{4 - (-2) = 6}[/tex]

[tex]= \dfrac{-15}{6}[/tex]

[tex]\boxed{\boxed{\bf{Answer: \dfrac{-15}{6}}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

I think your answer should be 5x and -5x

The solution of the inequality on the graph is the very dark region.

Inequality is an expression that shows the non equal comparison of two or more numbers and variables.

Given the inequalities  y ≤ –(1/3)x + 2 and y > 2x – 3, plotting the two inequalities using the geogebra online graphing tool.

The solution of the inequality on the graph is the very dark region.

Find out more on Inequality at: https://brainly.com/question/24372553

Answer:

P=0.954 or 95.4%

Step-by-step explanation:

Using the formula for the standardized normal distribution to find Z:

[tex]Z=\frac{X-\mu}{\sigma}[/tex]

Where μ is the mean (μ=20) and σ is the standard deviation (σ=2.6).  

[tex]Z_{1} =\frac{14.8-20}{2.6}=-2.0[/tex]

[tex]Z_{1} =\frac{25.2-20}{2.6}=2.0[/tex]

In the table of the normal distribution, we can look for positive values z, and these values are going to represent the area under the curve between z=0 and the values searched. the negatives values are found by symmetry (with the corresponding positive value but remember this area is under the left side of the curve).  To find a value in the table, find the units in the first column and the follow over the same row till you find the decimals required.

[tex]P_1=0.4772[/tex]

[tex]P_2=0.4772[/tex]

[tex]P_1[/tex] represents the probability of length being between 14.8 and 20 (the mean) and [tex]P_2[/tex] represents the probability of length being between 20 and 25.2, The requested probability is the sum of these two.

[tex]P=P_1+P_2=0.954[/tex]

Answer:

95%

Step-by-step explanation:

Answer:

A hole at x=-4.

Step-by-step explanation:

This is a fraction so we have to worry about division by zero.

The only time we will be dividing by 0 is when x+4 is 0.

Solving the equation

x+4=0 for x:

Subtract 4 on both sides:

x=-4

So there is either a vertical asymptote or a hole at x=-4.

These are the kinds of discontinuities we can have for a rational function.

If there is a hole at x=-4, then x=-4 will make the top zero and can be cancelled out after simplification.

If is is a vertical asymptote, x=-4 will make the top NOT zero.

Let's see what -4 for x in x^2+6x+8 gives us:

(-4)^2+6(-4)+8

16+-24+8

-8+8

0

Top and bottom are 0 when x=-4.

Let's see what happens after simplication.

We are going to factor a^2+bx+c if factorable by finding two numbers that multiply to be c and add up to be b.

So what 2 numbers together multiply to be 8 and add up to be 6.

I hoped you said 4 and 2 because (4)(2)=8 where 4+2=6.

[tex]\frac{x^2+6x+8}{x+4}=\frac{(x+4)(x+2)}{x+4}=x+2[/tex]

We we able to cancel out that factor that was giving us x=-4 is a zero.  

Therefore there is a hole at x=-4.

Answer:

3rd one. The general form of a circle is set equal to the radius squared. So right side is 4 then plug in values until true.

Answer:

The answer is the second option

[tex](x-1)^{2}+(y-4)^{2}= 4[/tex]

Step-by-step explanation:

The general equation of a circle is:

[tex](x-h)^{2}+(y-k)^{2}= r^{2}[/tex]

in this equation (h,k) is the center of the circle and r is the radius, so if the center is in (1,4) and the radius is 2, the values of the constants are:

h = 1

k = 4

r = 2

And the formula for this circle is:

[tex](x-1)^{2}+(y-4)^{2}= 2^{2}[/tex]

[tex](x-1)^{2}+(y-4)^{2}= 4[/tex]

Answer:

$5000

Step-by-step explanation:

25% of 4,000 is 1,000.

4,000 + 1,000 = 5,000

Answer:

5000 is correct

Step-by-step explanation:

This is a right triangle and to solve this you must use Pythagorean theorem:

[tex]a^{2} +b^{2} =c^{2}[/tex]

a and b are the legs (the sides that form a perpendicular/right angle)

c is the hypotenuse (the side opposite the right angle)

In this case...

a = 60

b = x

c = 65

^^^Plug these numbers into the theorem

[tex]60^{2} +x^{2} =65^{2}[/tex]

simplify

3600 + [tex]x^{2}[/tex] = 4225

Now bring 3600 to the right side by subtracting 3600 to both sides (what you do on one side you must do to the other). Since 3600 is being added on the left side, subtraction (the opposite of addition) will cancel it out (make it zero) from the left side and bring it over to the right side.

3600 - 3600 + [tex]x^{2}[/tex] = 4225 - 3600

0 + [tex]x^{2}[/tex] = 625

[tex]x^{2}[/tex] = 625

To remove the square from x take the square root of both sides to get you...

x = √625

x = 25

(option C)

Hope this helped!

Just a girl in love with Shawn Mendes

Answer:

Option D is correct.

Step-by-step explanation:

We are given c = 12

m∠B = 27°

a = 9

We need to find b

We would use Law of Cosines

[tex]b = a^2 + c^2 -2ac\,cosB[/tex]

Putting values and solving

[tex]b^2 = (9)^2 + (12)^2 -2(9)(12)\,cos(27°)\\b^2 = 81 + 144 - 216(0.891)\\b^2 = 81 + 144 - 192.456\\b^2 = 32.54\\taking\,\,square\,\,roots\,\,on\,\,both\,\,sides\\\\\sqrt{b^2} = \sqrt{32.54}\\ b = 5.7[/tex]

So, Option D is correct.

Answer:

D. 5.7

Step-by-step explanation:

We have been given that in △ABC,c=12, m∠B=27°, and a=9. We are asked to find the value of b.

We will use law of cosines to solve for b.

[tex]b^2=a^2+c^2-2ac\cdot \tect{cos}(B)[/tex]

Upon substituting our given values in law of cosines, we will get:

[tex]b^2=9^2+12^2-2\cdot 9\cdot 12\cdot {cos}(27^{\circ})[/tex]

[tex]b^2=81+144-216\cdot 0.891006524188[/tex]

[tex]b^2=225-192.457409224608[/tex]

[tex]b^2=32.542590775392[/tex]

Now, we will take square root of both sides of our equation.

[tex]b=\sqrt{32.542590775392}[/tex]

[tex]b=5.70461136059[/tex]

[tex]b\approx 5.7[/tex]

Therefore, the value of b is 5.7 and option D is the correct choice.

let's take a peek in the graph on the area from -3 to 0, namely -3 ⩽ x < 0, tis a line, so hmmm let's use two points off of it to get the equation hmmm (-3, -6) and (0,0)

[tex]\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{0}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{0-(-6)}{0-(-3)}\implies \cfrac{0+6}{0+3}\implies \cfrac{6}{3}\implies 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-6)=2[x-(-3)] \\\\\\ y+6=2(x+3)\implies y+6=2x+6\implies y=2x[/tex]

now the smaller line from 1/2 to 3/2 well, heck is just a flat-line, namely y = 3

[tex]\bf f(x)= \begin{cases} 2x&,-3\leqslant x < 0\\ 3&,\frac{1}{2}<x<\frac{3}{2} \end{cases}[/tex]

Answer:

D

Step-by-step explanation:

To convert from polar to rectangular form

• x = rcosΘ , y = rsinΘ

• r = [tex]\sqrt{x^2+y^2}[/tex] ⇒ r² = x² + y²

Given

r = 8cosΘ

r = 8 × [tex]\frac{x}{r}[/tex] ( multiply both sides by r )

r² = 8x, hence

x² + y² = 8x ⇒ D

Answer:

The correct answer is D

Step-by-step explanation:

Plato

Answer:

You will need

280 mL of the 60% solution

and  40 mL of pure alcohol.

Step-by-step explanation:

Let 'x' be the amount of 60% alcohol solution and y the amount of pure alcohol.

Therefore:

(0.6x + y)/320 = 0.65 ⇒ 0.6x + y = 208

x + y = 320

Solving the sistem of equations:

x = 280 and y = 40

Therefore, You will need

280 mL of the 60% solution

and  40 mL of pure alcohol.

Answer:

5

Step-by-step explanation:

20*5=100

Answer:

10 meters

Step-by-step explanation:

Let at 100 degrees Celsius, the aluminum bar is x m long.

We have been given that aluminum bar is 2 m long at a temperature of 20 degrees Celsius.

Thus, we have the equation

[tex]\frac{2}{20}=\frac{x}{100}[/tex]

Solve the equation for x

[tex]x=\frac{2\times100}{20}\\\\x=10[/tex]

Thus, at 100 degree Celsius, the aluminium bar is 10 meters long.

Answer:

17

Step-by-step explanation:

14 - 7 = 7

7 + 4 +9 =20

20 - 3 = 17

Answer:

A. 500 transistors

B. 50,000 capacitors

C. 100 capacitors

Step-by-step explanation:

The width of one transistor =0.004 mm

The total length filled by the 0.004 mm transistors is 2 mm.

A. In 2 mm there are: 2 mm/ 0.004 mm/transistor =500 transistors.

B. In 2 mm there are 2 mm/ 0.00004 mm/capacitor= 50,000 Capacitors.

C. The number of capacitors to fit in one transistor is given by the quotient between the width of a transistor and the width of  a capacitor.

=0.004 mm ÷0.00004 mm

=100 capacitors/transistor

Thus only 100 capacitors can fit into 1 transistor

Answer:

Step-by-step explanation:

As we go from (–2, 2) to  (3, 4), x increases by 5 and y increases by 4.  Thus, the slope of the line through (–2, 2) and (3, 4) is

m = rise / run = 4/5.

Use the slope-intercept form of the equation of a straight line:

y = mx + b becomes 4 = (4/5)(3) + b.  Multiplying all three terms by 5, we eliminate the fraction:  20 = 12 + b.  Thus, b = 8, and the equation of the line through (–2, 2) and (3, 4) is y = (4/5)x + 8.

A line parallel to this one would have the form  y = (4/5)x + b; note that the slopes of these two lines are the same, but the y-intercept, b, would be different if the two lines do not coincide.

Unfortunately, you have not shared the ordered pairs given in this problem statement.  

You could arbitrarily let b = 0.  Then the parallel line has equation

y = (4/5)x; if x = 3, then y = (4/5)(3) = 12/5, and so (3, 12/5) lies on the parallel line.

he possible ordered pairs are b) (–1, 1) and (–6, –1)  , d) (1, 0) and (6, 2)  and e) (3, 0) and (8, 2).

To find points on a line parallel to the line containing the points (3, 4) and (-2, 2), we need to find a line with the same slope. The slope of the line containing the points (3, 4) and (-2, 2) can be calculated using the formula:

[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]\[ m = \frac{2 - 4}{-2 - 3} \]\[ m = \frac{-2}{-5} \]\[ m = \frac{2}{5} \][/tex]

So, the slope of the given line is 2/5.

Now, let's check the slopes of the other lines to see if they match 2/5:

a) Slope of the line passing through (−2, −5) and (−7, −3):

[tex]\[ m = \frac{-3 - (-5)}{-7 - (-2)} = \frac{2}{-5} \][/tex]

The slope matches, so point a) is a possible point on a line parallel to the given line.

b) Slope of the line passing through (−1, 1) and (−6, −1):

[tex]\[ m = \frac{-1 - 1}{-6 - (-1)} = \frac{-2}{-5} = \frac{2}{5} \][/tex]

The slope matches, so point b) is a possible point on a line parallel to the given line.

c) Slope of the line passing through (0, 0) and (2, 5):

[tex]\[ m = \frac{5 - 0}{2 - 0} = \frac{5}{2} \][/tex]

The slope does not match, so point c) is not a possible point on a line parallel to the given line.

d) Slope of the line passing through (1, 0) and (6, 2):

[tex]\[ m = \frac{2 - 0}{6 - 1} = \frac{2}{5} \][/tex]

The slope matches, so point d) is a possible point on a line parallel to the given line.

e) Slope of the line passing through (3, 0) and (8, 2):

[tex]\[ m = \frac{2 - 0}{8 - 3} = \frac{2}{5} \][/tex]

The slope matches, so point e) is a possible point on a line parallel to the given line.

Complete question: Which ordered pairs could be points on a line parallel to the line that contains (3, 4) and (–2, 2)? Check all that apply.

a-(–2, –5) and (–7, –3)

b-(–1, 1) and (–6, –1)

c-(0, 0) and (2, 5)

d-(1, 0) and (6, 2)

e-(3, 0) and (8, 2)

[tex]x\in(-3,\infty)[/tex]

3.7 divided by 2 is 1.85, rounded to the nearest tenth is 1.9.

To divide 3.7 by 2 to the nearest tenth, you first perform the division:

[tex]\[ \frac{3.7}{2} = 1.85 \][/tex]

Now, to express this result to the nearest tenth, you look at the first decimal place after the decimal point. Here, it's 8, which is closer to 9 than to 0. So, you round up the digit in the tenths place.

Thus, 3.7 divided by 2, rounded to the nearest tenth, is [tex]\(1.9\).[/tex]

Answer: $1578

Step-by-step explanation:

1) Take your discount rate of 3.5% and convert it to decimal form (0.035)

2) Then, 0.035 * 13.5 = 1.59109

3) 1.59109 * 992 = $1578