Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms. Second-degree, with zeros of −7 and 6, and goes to −∞ as x→−∞.

Hey there! I'm happy to help!

We see that 1 peso is equal to 0.55 U.S. dollars. So, the amount we will get in U.S dollars is the same as $5000×0.55 because 0.55 US dollars is equal to one peso!

5000×0.55=2750

Therefore, you will receive $2750.

Have a wonderful day!

Answer: 45.5

Step-by-step explanation:

Im in 6th grade and all you had to do was add 18.3 and 27.2 and you’ll get 45.5

Answer:

The garbage dump is 58.3 miles west of the hotel, and the hotel is 57.1 miles west of the hardware store. The hardware store is 44.8 miles west of the library. The hardware store is 57.9 miles north of the office supply store, and the office supply store is 55.5 miles north of the science lab.

Step-by-step explanation:

Answer:

Part A- 6

Part B- 3

Part C- 3/22100

Step-by-step explanation:

Part A-

Use the permutation formula and plug in 3 for n and 2 for k.

nPr=n!/(n-k)!

3P2=3!/(3-2)!

Simplify.

3P2=3!/1!

3P2=6

Part B-

Use the combination formula and plug in 3 for n and 2 for k.

nCk=n!/k!(n-k)!

3C2=3!/2!(3-2)!

Simplify.

3C2=3!/2!(1!)

3C2=3

Part C-

It is given that the total number of three-card hands that can be dealt from a deck of 52 cards is 22100. Use the fact that the probability of something equals the total successful outcomes over the sample space. In this case the total successful outcomes is 3 and the sample space is 22100.

I believe the answer is 3/22100

I honestly suck at probability but I tried my best.

Answer:

  16x^3 +64x^2 -40x

Step-by-step explanation:

Use the distributive property. The factor outside parentheses multiplies each term inside parentheses:

  8x(2x^2 +8x -5) = (8x)(2x^2) +(8x)(8x) +(8x)(-5)

  = 16x^3 +64x^2 -40x

Answer:

A) 1  2/3 yards

Step-by-step explanation:

Hope this helped

Answer:

The answer is A

Let me finish the quiz then upload a picture to this answer showing you the correct answer is A

Step-by-step explanation:

Answer:

Step-by-step explanation:

f(x) = 4x + 1

g(x) = x² – 5

To find (f – g)(x) subtract g(x) from f(x)

That's

(f – g)(x) = 4x + 1 - ( x² - 5)

Remove the bracket

(f – g)(x) = 4x + 1 - x² + 5

Group like terms

(f – g)(x) = - x² + 4x + 1 + 5

We have the final answer as

Hope this helps you

Answer:

Hey there!

Area for a triangle: 0.5bh, where b is the base, and h is the height.

Plugging in the values: 0.5(4)(8), or simplified to 16.

The area of the polygon is 16 units^2

Hope this helps :)

Answer:

[tex]\boxed{16 \: units^2}[/tex]

Step-by-step explanation:

Apply formula for area of a triangle.

Area of a triangle = [tex]\frac{1}{2} bh[/tex]

[tex]b:base\\h:height[/tex]

The base is 4 units. The height is 8 units.

[tex]\frac{1}{2} (4)(8)[/tex]

[tex]\frac{1}{2} (32)=16[/tex]

Answer:

[tex] A = 70.6 [/tex] ≈ 71°

[tex] x = 36.5 [/tex]

Step-by-step explanation:

Step 1: Use the Law of sine to find A

[tex] \frac{sin(A)}{38} = \frac{sin(44)}{28} [/tex]

Cross multiply:

[tex] sin(A)*28 = sin(44)*38 [/tex]

[tex] sin(A)*28 = 0.695*38 [/tex]

Divide both sides by 28:

[tex] \frac{sin(A)*28}{28} = \frac{0.695*38}{28} [/tex]

[tex] sin(A) = 0.9432 [/tex]

[tex] A = sin^{-1}(0.9432) [/tex]

[tex] A = 70.6 [/tex]

A ≈ 71°

Step 2: find the measure of the angle opposite side x

Angle opposite side x = 180 - (71+44) (sum of triangle)

= 180 - 115 = 65°

Step 3: find x using the law of sines

[tex] \frac{x}{sin(65)} = \frac{28}{sin(44)} [/tex]

[tex] \frac{x}{0.906} = \frac{28}{0.695} [/tex]

Multiply both sides by 0.906

[tex] x*0.695= 28*0.906 [/tex]

Divide both sides by 0.695

[tex] \frac{x*0.695}{0.695} = \frac{28*0.906}{0.695} [/tex]

[tex] x = \frac{28*0.906}{0.695} [/tex]

[tex] x = 36.5 [/tex]

Answer:

The answer is

Step-by-step explanation:

x² + 2x - 3 - 2x² + x + 4

Group like terms

That's

x² - 2x² + 2x + x - 3 + 4

Simplify

- x² + 3x + 1

when x = 3

We have

(-3)² + 3(3) + 1

9 + 9 + 1

18 + 1

19

Hope this helps you

Answer:

The probability of winning the bet is 1/336

Step-by-step explanation:

We should understand that there is only one possible arrangement of the winning selection

Now, the horse that comes first can be selected in 8 ways given that all the horses have equal chances

The horse that comes second can be selected in 7 ways given that all the horses have equal chances

The horse that comes third can be selected in 6 ways given that all the horses have equal chances

Now the total number of ways of selection would be;

8 * 7 * 6 = 336

Since there is only one of the selections that is correct, the probability of making the correct choice is thus 1/336

Answer:

1:3

Step-by-step explanation:

3/3=1

9/3=6

Answer:

Option A is the correct option.

Step-by-step explanation:

Given,

Number of pears = 3

Number of apples = 9

Find : Ratio of the number of pears to the number of apples on the fruit salad

Now,

[tex] \frac{pear}{apples} [/tex]

Plug the values

[tex] = \frac{3}{9} [/tex]

Divide the numerator and denominator by 3

[tex] = \frac{3 \div 3}{9 \div 3} [/tex]

Divide the numbers

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

It can be written as :

1 : 3

Hope this helps..

Best regards!!!

Answer:

182

Step-by-step explanation:

The sequence has a common difference of +3.

Answer:

It's none of those. It's supposed to be 171.

Step-by-step explanation:

That's because in an arithmetic sequence it's a list of numbers with a definite pattern, and all you're doing is adding 3 to each number.

Answer:

Factor 9 out of 18x.

9(2x)−9

Factor 9 out of −9

9(2x)+9(−1)

Factor 9 out of 9(2x)+9(−1)

9(2x−1)

Answer:

9 ( 2x - 1 )

Step-by-step explanation:

→ Look for the HCF of the whole numbers

HCF of 18 and 9 is 9

→ Put 9 outside the brackets

9 ( ? - ? )

→ Perform the calculation 18x ÷ 9 to determine the first question mark

18x ÷ 9 = 2x ⇔ 9 ( 2x - ? )

→ Perform the calculation 9 ÷ 9 to determine the second question mark

9 ÷ 9 = 1 ⇔ 9 ( 2x - 1 )

Hey there! I'm happy to help!

PART A

There are 3 $1 bills, 1 $5 bill, and 1 $10 bill. This gives us 5 total bills.

First, we want to find the probability of winning $12. Well, to win, you have to draw the $10 bill. You only have room for two dollars beforehand to equal $12 dollars after pulling out the ten. So, this is the probability of drawing two one dollar bills and the the ten. Let's calculate this below.

[tex]\frac{3}{5} *\frac{1}{2} *\frac{1}{3} =\frac{1}{10}[/tex]

Where did I get these numbers from? Well 3 of the 5 bills are $1, so the first probability is 3/5. Then, if we draw one of the $1 bills, there are only 2 of those left and 4 total bills, so the probability is then one half. Finally, there would be only 3 left and you need to pick the $10 bill, which is a probability of 1/3.

The probability of winning $12 is 1/10 or 10%.

PART B

Now, we want to find the probability of picking every single bill before the ten. This means that we pick the three one dollar bills and the five dollar bill before the ten.

To pick the first $1 bill, our probability is 3/5, and then for the second it is 1/2. For the third, there are three total cards and 1 $1 bill, so the probability is 1/3. Then we have a 1/2 chance of picking the $5 bill over the $10 bill, giving us this solution.

[tex]\frac{3}{5} * \frac{1}{2} * \frac {1}{3} * \frac{1}{2}= \frac{1}{20}[/tex]

The probability of winning all bills in the urn is 1/20 or 5%.

PART C

For this event, we want to get any bill that isn't the $10 and then we want the $10 on the second one.

Since there are 4 bills that aren't the $10, our first probability is 4/5. Then, we only have 4 left, with 1 being the $10, so our second probability is 1/4.

[tex]\frac{4}{5}*\frac{1}{4}=\frac{1}{5}[/tex]

The probability of the game stopping at the second draw is 1/5 or 20%.

Have a wonderful day! :D

The probability of winning $12 will be 0.15.

The game stops after drawing$10 bill. There can also be 2 draws of $2 and $10 to make $12.

Therefore, the probability of winning $12 will be calculated thus:

= Probability of getting $2 × probability of getting $10

= 3/5 × 1/4

= 0.15

The probability of winning all balls in the urn will be:

= 4/5 × 3/4 × 2/3 × 1/2

= 0.2

Lastly, the probability of the game stopping at the second draw will be:

= First draw × Second draw

= 4/5 × 1/4

= 0.2

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Answer:

13, 21

Step-by-step explanation:

Add 8 to the next number from the left to the right.

Answer:

The next three numbers in the sequence are: 13, 21, 29.

Step-by-step explanation:

Common Pattern: +8

-27 +8 = -19

-19 + 8 = -11

-3 + 8 = 5

5 + 8 = 13

13 + 8 = 21

21 + 8 = 29

Answer:

8.4ft

Step-by-step explanation:

Formula for calculating the length of an arc is expressed as [tex]L = \frac{\theta}{360} * 2\pi r\\[/tex]

[tex]\theta[/tex] is the central angle = π/3 rad

r is the radius of the circle = 8ft

Substituting the values into the formula above we have;

[tex]L =[/tex] [tex]\frac{(\frac{\pi}{3} )}{2 \pi} * 2\pi (8)\\\\[/tex]

[tex]L = \frac{\pi}{6 \pi} * 2\pi(8) \\\\L = 1/6 * 16\pi\\\\L = 8\pi/3\\\\L = \frac{8(22/7)}{3} \\\\L = \frac{8*22}{7*3}\\ \\L = 176/21\\\\L = 8.4 ft (to\ the\ nearest\ tenth)[/tex]

Hence, the length of the arc s is approximately 8.4 ft.

Answer:

D. [tex]H_{0}[/tex] : μ = 1.70, [tex]H_{a}[/tex] : μ > 1.70

Step-by-step explanation:

The correct order of the steps of a hypothesis test is given following  

1. Determine the null and alternative hypothesis.

2. Select a sample and compute the z - score for the sample mean.

3. Determine the probability at which you will conclude that the sample outcome is very unlikely.

4. Make a decision about the unknown population.

These steps are performed in the given sequence to test a hypothesis

The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 10% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value.

Answer:

Option C - Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in

Step-by-step explanation:

We are given;

n = 15

t-value = 1.66

Significance level;α = 0.05

So, DF = n - 1 = 15 - 1 = 14

From the one-sample t - table attached, we can see that the p - value of 0.06 at a t-value of 1.66 and a DF of 14

Now, since the P-value is 0.06,it is greater than the significance level of 0.05. Thus we do not reject the null hypothesis. We conclude that there is not sufficient evidence that the true diameter differs from 0.5 in.

Answer:

the answer i would go with is A

Good luck on your Test :)

Step-by-step explanation:

B doesnt really have a constant rate of change as it depends on how many games happen and usually the longer an arena stays open has no correlation on how many people attend the games there

C has no real constant rate of change as it always ends up stopping after a little bit, and the change is usually not a constant one

D this could count, but since its a number that would go down if its not brought back up, its not a real constant rate of change, since it cant go below or above a certain range

so by process of elimination, A is the answer. also seeing as how its saying the distance with the number of times, that means that its an objective thing, as a track is a set distance, and the distance of a run or the track cant be affected by time or anything and could technically never end. so its a constant thing, meaning the longer the distance is, the higher the laps around the track are, and it could theoretically go on forever.

i hope this helped answer your question! :)

Answer:

[tex] x = 2 [/tex]

Step-by-step explanation:

Given a right-angled triangle as shown above,

Included angle = 60°

Opposite side length = 3

Adjacent side length = x

To find x, we would use the following trigonometric ratio as shown below:

[tex] tan(60) = \frac{3}{x} [/tex]

multiply both sides by x

[tex] x*tan(60) = \frac{3}{x}*x [/tex]

[tex] x*tan(60) = 3 [/tex]

Divide both sides by tan(60)

[tex] \frac{x*tan(60)}{tan(60} = \frac{3}{tan(60} [/tex]

[tex] x = \frac{3}{tan(60} [/tex]

[tex] x = 1.73 [/tex]

[tex] x = 2 [/tex] (approximated to whole number)

Integrate the force field along the given path (call it C):

[tex]W=\displaystyle\int_C\mathbf F(x,y)\cdot\mathrm d\mathbf r=\int_0^{2\pi}\mathbf F(x(t),y(t))\cdot\frac{\mathrm d\mathbf r}{\mathrm dt}\,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^{2\pi}\bigg((t-\sin t)\,\mathbf i+(6-\cos t)\,\mathbf j\bigg)\cdot\bigg((1-\cos t)\,\mathbf i+\sin t\,\mathbf j\bigg)\,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^{2\pi}(t-t\cos t+5\sin t)\,\mathrm dt=\boxed{2\pi^2}[/tex]

By direct calculation we will find that the work done is equal to 2π²

The formula to compute the work done is given by:

[tex]W = \int\limits^a_b {F(x(t), y(t))\cdot\frac{dr(t)}{dt} } \, dt[/tex]

Here we have:

[tex]r(t) = (t - sin(t))i + (1 - cos(t))j[/tex]

This means that:

[tex]x(t) = (t - sin(t))\\y(t) = (1 - cos(t))\\\\\frac{dr(t)}{dt} = (1-cos(t))i + sin(t)j = (1-cos(t), sin(t))[/tex]

And we know that 0 ≤ t ≤ 2π, so b = 0 and a = 2π

Replacing that in the work integral we get:

[tex]W = \int\limits^{2\pi}_0 {(t - sin(t), 1 - cos(t) + 5)\cdot(1-cos(t), sin(t))} \, dt \\\\W = \int\limits^{2\pi}_0 {(t - sin(t), 6 - cos(t))\cdot(1-cos(t), sin(t))} \, dt\\\\W = \int\limits^{2\pi}_0 {(-t*cos(t) +t-sin(t)+ cos(t)*sin(t)+ 6*sin(t) - cos(t)*sin(t) )} \, dt\\\\W = \int\limits^{2\pi}_0 {(-cos(t)*t + 5*sin(t) + t)} \, dt \\\\[/tex]

the sin(t) integral can be removed because it is equal to zero, so we get:

[tex]W = \int\limits^{2\pi}_0 {(-cos(t)*t + t)} \, dtW = [(-t*sin(t) - cos(t)) + \frac{t^2}{2} ]^{2\pi}_0\\\\W = -2\pi*sin(2\pi) - cos(2\pi) + 0*sin(0) + cos(0) + \frac{(2\pi)^2}{2} - \frac{(0)^2}{2}\\\\W = 2\pi^2[/tex]

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Answer:

x = $0.50

y= $0.75

Step-by-step explanation:

1. Multiply the equations to have the same coefficients

5(6x + 6y = 7.5) → 30x + 30y = 37.5

3(10x + 5y = 8.75) → 30x + 15y = 26.25

2. Subtract the equations

 30x + 30y = 37.5

- 30x + 15y = 26.25

15y = 11.25

3. Solve for y by dividing both sides by 15

y = 0.75

4. Plug in 0.75 for y into one of the equations

6x + 6(0.75) = 7.5

5. Simplify

6x + 4.5 = 7.5

6. Solve for x

6x = 3

x = 0.5

Answer:

The cost of one apple is $0.5

The cost of one orange is $0.75

Step-by-step explanation:

Given information

The cost of an apple = [tex]x[/tex]

The cost of an orange = [tex]y[/tex]

Equation to find the values are:

[tex]6x=6y=7.50\\10x+5y=8.75[/tex]

Now, convert the equations to have same coefficient as:

[tex]5(6x=6y=7.50)\\=30x+30y=37.5\\3(10x+5y=8.75)\\=30x+15y=26.25[/tex]

Now, on solving the above equation by subtracting one from another.

We get,

[tex]15y=11.25\\y=0.75[/tex]

Now , put the value of [tex]y[/tex] in one equation to find the value of [tex]x[/tex].

As,

[tex]6x+4.5=7.5\\x=0.5[/tex]

Hence,

The cost of one apple is $0.5

The cost of one orange is $0.75

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Answer:

Loan amount due after 2 years =$7,387.28

Explanation:

The amount due on the loan would be equal to the total accrued interest plus the accumulated amount amount.

Note that, since Edgar did not pay any amount off the loan in the course of the 2 years, the interest due per quarter would be equal to the quarterly  interest rate multiplied by  the unpaid balance till date.

To determine the amount due, we would compound $5,000 at a quarterly interest rate of for 8 quarters. The formula below would suffice

Loan amount due = loan balance × (1+r)^(n)

Quarterly interest rate -20%/4 =5%, number of quarters - 2× 4 =8, loan balance - 5,000

Loan amount due = 5,000 × (1.05)^(8)

                             =  7,387.28

Loan amount due after 2 years =$7,387.28

Step-by-step explanation:

Answer:

7434.57

Step-by-step explanation:

Answer:

The volume is  [tex]dV = 19.2 \pi \ cm^3[/tex]

Step-by-step explanation:

From the question we are told that

    The height is  h =  20 cm

    The diameter is  d = 8 cm

    The thickness of both top and bottom is  dh  =  2 * 0.1  =  0.2 m

     The  thickness of one the side is dr =  0.1 cm

The  radius is mathematically represented as

            [tex]r = \frac{d}{2}[/tex]

substituting values

            [tex]r = \frac{8}{2}[/tex]

           [tex]r = 4 \ cm[/tex]

Generally the volume of a cylinder is mathematically represented as      

       [tex]V_c = \pi r^2 h[/tex]

Now the partial differentiation with respect to h is  

       [tex]\frac{\delta V_v}{\delta h} = \pi r^2[/tex]

Now the partial differentiation with respect to r is  

      [tex]\frac{\delta V_v}{\delta r} = 2 \pi r h[/tex]

Now the Total differential of [tex]V_c[/tex] is mathematically represented as

       [tex]dV = \frac{\delta V_c }{\delta h} * dh + \frac{\delta V_c }{\delta r} * dr[/tex]

       [tex]dV = \pi *r^2 * dh + 2\pi r h * dr[/tex]

substituting values

      [tex]dV = \pi (4)^2 * (0.2) + (2 * \pi (4) * 20) * 0.1[/tex]

     [tex]dV = 19.2 \pi \ cm^3[/tex]

(I deleted my answer because it was incorrect)

Answer:

y = -x + 0

Step-by-step explanation:

well the equation of a line is y = mx + b

m = the slope , b = the y-intercept

m = y2 - y1 / x2 - x1

m = -1

and b is the y-intercept of the line.

finally:

y = -1x + 0

Answer:

Cada cuota tendrá un valor de $14,850.

Step-by-step explanation:

Dado que Tomás canceló la mitad del valor de la bicicleta, la cual costaba $199.900, el valor pagado al inicio fue de $99,950 (199,900 / 2).

Luego, para el valor restante, Tomás suscribió a una financiación con un interés de $4,000, elevando el monto a pagar a $103,950, pagaderos en 7 cuotas. Por lo tanto, dichas cuotas tendrán cada una un valor de $14,850 (103,950 / 7).

Explanation:

The given equation is False, so cannot be proven to be true.

__

Perhaps you want to prove ...

  [tex]2\tan{x}=\dfrac{\cos{x}}{\csc{(x)}-1}+\dfrac{\cos{x}}{\csc{(x)}+1}[/tex]

This is one way to show it:

  [tex]2\tan{x}=\cos{(x)}\dfrac{(\csc{(x)}+1)+(\csc{(x)}-1)}{(\csc{(x)}-1)(\csc{(x)}+1)}\\\\=\cos{(x)}\dfrac{2\csc{(x)}}{\csc{(x)}^2-1}=2\cos{(x)}\dfrac{\csc{x}}{\cot{(x)}^2}=2\dfrac{\cos{(x)}\sin{(x)}^2}{\cos{(x)}^2\sin{(x)}}\\\\=2\dfrac{\sin{x}}{\cos{x}}\\\\2\tan{x}=2\tan{x}\qquad\text{QED}[/tex]

__

We have used the identities ...

  csc = 1/sin

  cot = cos/sin

  csc^2 -1 = cot^2

  tan = sin/cos

Answer:

Length = 5p + 3

Perimeter = 26p + 6

Step-by-step explanation:

Given

Area = 40p² + 24p

Width = 8p

Solving for the length of deck

Given that the deck is rectangular in shape.

The area will be calculated as thus;

Area = Length * Width

Substitute 40p² + 24p and 8p for Area and Width respectively

The formula becomes

40p² + 24p = Length * 8p

Factorize both sides

p(40p + 24) = Length * 8 * p

Divide both sides by P

40p + 24 = Length * 8

Factorize both sides, again

8(5p + 3) = Length * 8

Multiply both sides by ⅛

⅛ * 8(5p + 3) = Length * 8 * ⅛

5p + 3 = Length

Length = 5p + 3

Solving for the perimeter of the deck

The perimeter of the deck is calculated as thus

Perimeter = 2(Length + Width)

Substitute 5p + 3 and 8p for Length and Width, respectively.

Perimeter = 2(5p + 3 + 8p)

Perimeter = 2(5p + 8p + 3)

Perimeter = 2(13p + 3)

Open bracket

Perimeter = 2 * 13p + 2 * 3

Perimeter = 26p + 6

Answer:

direct variation

Step-by-step explanation:

For direct variation k = [tex]\frac{y}{x}[/tex] ← k is the constant of variation

For inverse variation k = yx

Expressing the data as ordered pairs

(6, 9), (8, 12), (12, 18), (20, 30)

k = [tex]\frac{9}{6}[/tex] = [tex]\frac{12}{8}[/tex] = [tex]\frac{18}{12}[/tex] = [tex]\frac{30}{20}[/tex] = [tex]\frac{3}{2}[/tex] = 1.5 ← indicating direct variation

Equation is

y = kx = 1.5x

Answer:

-1

Step-by-step explanation:

Thanks

The product of expression (2 + √5) (2 - √5) is,

⇒ (2 + √5) (2 - √5) = - 1

We have to given that,

An expression to simplify,

⇒ (2 + √5) (2 - √5)

Now, We can simplify it by using formula,

⇒ (a - b) (a + b) = a² - b²

Hence, We get;

⇒ (2 + √5) (2 - √5)

⇒ (2² - √5²)

⇒ 4 - 5

⇒ - 1

Therefore, The product of expression (2 + √5) (2 - √5) is,

⇒ (2 + √5) (2 - √5) = - 1

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