A political analyst predicts Mr. Smith will only get 122 votes for mayor. If Mr. Smith only gets 57 votes, what is the political analyst's percent error?

Answer:

No, it is not a rectangle because the sides of the

parallelogram do not meet at night angles (B)

Step-by-step explanation:

The diagonal of the rectangle = 28

The two sides of the figure measures 20 and 21 units respectively.

To determine if the shape is a rectangle, we would apply Pythagoras theorem

hypotenuse² = opposite² + adjacent²

hypotenuse = diagonal = 28

The other two sides represent the opposite and adjacent

28² = 20² + 21²

784 = 400 + 441

784 ≠ 841

The square of the diagonal is not equal to the sum of the square of the other two sides (length and width).  And as a result of this, the triangle isn't a right angled triangle and the sides of the parallelogram would not meet at right angles.

Therefore, the figure isn't a rectangle.

Option B: No, it is not a rectangle because the sides of the

parallelogram do not meet at night angles.

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:

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: try using sine for this equasion

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:

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:

x=5

Step-by-step explanation:

35 = 7x

Divide each side by 7

35/7 = 7x/7

5 = x

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]

If you want to learn more, you can read:

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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

Learn more about the multiplication visit:

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#SPJ6

Answer:

-3

Step-by-step explanation:

Easy way:

Between the two marked points, you can count that you need to go down 6 and over 2. That means the rise/run is -6/2, or -3.

Full way:

Starting Point: (-1,3)

Ending Point: (1,-3)

Slope is given by (y₂-y₁)/(x₂-x₁)

To calculate this, (-3-(3))/(1-(-1))

Clean up the double negatives to get (-3-3)/(1+1), AKA -6/2

-6/2 = -3.

Answer:

The probability is 0.026 to 3 d.p

Step-by-step explanation:

To calculate this , we shall be using the Bernoulli approximation.

let P = percentage of voters supporting the increase = 41% = 41/100 = 0.41

q = percentage of voters not supporting = 100-41% = 59% = 59/100 = 0.59

Now we want to calculate that exactly 15 out of 25 will vote in favor

Mathematically that would be ;

25C15 p^15 q^10

= 25C15 0.41^15 0.59^10

= 0.025981307443 or simply 0.026 to 3 decimal places

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:

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

For more information visit

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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:

1. Average Number of Steps of

= Total of the different steps /  divided by 3

= 6,943/3

= 2,314.3 steps

2. Weighted Average Number of Steps of 3, 58-inch, 5, 64-inc, and 2, 76-inch people

= Total steps by the 10 people divided by 10

= 23,558/10

= 2,355.8 steps

3. The difference is not much.

4. The weighted average (2,355.8 steps) is a more accurate representation of the data.  The calculation of the ordinary average steps is more confusing than the weighted average steps.

Step-by-step explanation:

1. Calculation of the Weighted Average Number of Steps of:

3, 58-inch people = 3 x 2,601 =   7,803

5, 64-inch people = 5 x 2,357 = 11,785

2, 76-inch people = 2 x 1,985 =  3,970

10 persons' total steps = 23,558

2. Calculation of the ordinary average:

58-inch people =  2,601

64-inch people =  2,357

76-inch people =  1,985

Total steps           6,943

Answer:

1. [tex]H_{0}[/tex] : p = 0.70 , [tex]H_{a}[/tex] : p > 0.70

2. Test Statistic : 0.54 , P value : 0.2946

3. Fail to reject null Hypothesis

4. No.

Step-by-step explanation:

1. Null hypothesis is 70% of children receive antibiotics.

Alternative hypothesis is more than 70% of children receive antibiotics.

2. Test statistic is calculated as;

z = [tex]\frac{p (1 - p)}{\sqrt{\frac{p (1-p}{n} )} }[/tex]

z = [tex]\frac{0.01}{0.0185}[/tex]

z = 0.54

3. p value is calculated as;

1 - right tailed probability

1 - 0.7054 = 0.2946

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:

Step-by-step explanation:

Given the system of equation  x−3y=−3 and x+y=5, we can solve for x and y by solving the equation simultaneously using the substitution method.

x−3y=−3_____________ 1

x+y=5 ______________2

From equation 2; x = 5- y ________ 3

Substitute equation 3 into equation 1

Since x - 3y = -3

(5-y)-3y = -3

5-y-3y = -3

5-4y = -3

Subtract 5 from both sides of the equation

5-4y-5 = -3-5

-4y = -8

Divide both sides by -4

-4y/-4 = -8/-4

y = 2

Substitute y = 2 into equation 2 to get the value of y;

From equation 2, x+y = 5

x+2 = 5

Subtract 2 from both sides of the equation

x+2-2 = 5-2

x = 3

Hence the value of x and y from the graph will be 3 and 2 respectively.

Answer:  2149

Step-by-step explanation:  If the sum of the first two digits is 3, the choices must be 1 and 2 (or 2 and 1)  In order to satisfy the other specifications, "the tens digit is 4 times the hundreds digit." the hundreds digit can't be 2 because that would make the tens dight 8.  and the ones digit would also have to 8 in order to satisfy the "seven more than the thousands digit" which would be a 1. And that violates the condition, "No two digits are equal."

So the only possible combination is 2149

4 is 4 times 1

9 is 7 +2

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:

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:

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:

D) all of the above

Step-by-step explanation:

The two-independent sample t-test is used to evaluate the differences in the means of two independent groups to ascertain if there is indeed a difference in the population means. So, the population variance is unknown before this test is done. To carry out this type of test, the researcher should ensure that there are no similarities between participants in the two groups so that there would be no influences between the groups. The participants in the research should be randomly selected.

The participants are observed one time to ensure that the same conditions hold for both groups and that there is a balance in the research blueprint.

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:

y = 1110

Step-by-step explanation:

In the above question, we are given the cubic model

y=x³ +x² + x

We are to solve for y when x = 10

Hence,

y = 10³ + 10² + 10

y = 1000 + 100 + 10

y = 1110

Therefore, the value of y when x is 10 using the cubic model of ' y =x³ +x² + x' is 1110.

Answer:

Well all even numbers between 0 and 8 are,

2, 4, 6, 8

Meaning if the button is pressed 4 times 2, 4, 6, or 8 will be outputted.

When press button 4 times. Then output of the program will be,  [tex](2,4,6,2)[/tex]

Any number that can be exactly divided by 2 is called as an even number.

Given that, When a button is pressed, a computer program outputs a random even number greater than 0 less than 8.

Even numbers greater than 0 less than 8 are,

                             [tex]=2,4,6[/tex]

When press button 4 times. Then output of the program will be,

                     [tex]=(2,4,6,2)[/tex]

Learn more about the even numbers here:

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Answer:

x= 1 + or - sr37/4 got it from a sitr

Here you go.

I really hope I helped. Good luck.

Answer:

A: True

B, C and D: False

Step-by-step explanation:

We have a total sales tax for Alabama that is:

[tex]T_A=4.225+1.375+3=8.6[/tex]

The total sales tax for Florida is:

[tex]T_F=6.5+1+1.625=9.125[/tex]

The total sales tax is greater in Florida than in Alabama.

A. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by about $8. TRUE

The sales tax difference in this purchase can be calculated as:

[tex]1500(T_F-T_A)=1500\left(\dfrac{9.125-8.6}{100}\right)=1500\cdot 0.00525=7.875\approx 8[/tex]

B. The furniture set is cheaper in Florida, because the amount of sales tax will be lower by about $10. FALSE (it is cheaper in Alabama)

C. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by $10. FALSE (the sale tax in Alabama is $129)

The amount of sales tax in Alabama is:

[tex]ST_A=1500\cdot T_A=1500\cdot 0.086=129[/tex]

D. The furniture set costs the same in either state, because the amount of sales tax will be the same for the two locations. FALSE (it is not the same in both states).

Answer:

2nd option. this provides an unbiased way to choose the clients surveyed.

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