Labour costs, totalling $47.25, account for 63%
of a car repair bill. Calculate the total bill.

Answer:

Which polynomial is prime?

7x2 – 35x + 2x – 10

9x3 + 11x2 + 3x – 33  

10x3 – 15x2 + 8x – 12  

12x4 + 42x2 + 4x2 + 14

Step-by-step explanation:

Which polynomial is prime?

7x2 – 35x + 2x – 10

9x3 + 11x2 + 3x – 33  

10x3 – 15x2 + 8x – 12  

12x4 + 42x2 + 4x2 + 14 SO IT IS RIGHT

Answer:

18. 84 ft² or 18.85 ft² when rounded to the nearest tenth

Step-by-step explanation:

2πrh+2πr²

2× 3.14 × 1 × 2= 12.56

2 × 3.14 × 1² = 6.28

12.56 + 6.28 = 18.84

Have a great day :)

Answer:

18.85 [tex]ft^2\\[/tex]

*You should run the numbers yourself as well. Sometimes different calculators will get marginally different numbers or use a different rounding for [tex]\pi[/tex] that gives a slightly different answer*

Step-by-step explanation:

Surface area of a cylinder: [tex]2\pi rh+2\pi r^2[/tex]

Where h is the height and r is the radius. Remember that the radius is half the diameter, and the diameter is a straight line that passes through a circle.

I could be wrong, but I think you had the correct equation but used the diameter in stead of the radius to get 50.36.

Radius: 1   Height: 2

Plug numbers into equation:

[tex]A=2\pi (1)(2)+2\pi (1)^2= 18.8495. . .[/tex]

I hope that helps!

Answer:

70kg- weight of the bag of beans, 90 kg- weight of the bag of salt

Step-by-step explanation:

Suppose the mass of a bag of beans - x kg, the mass of a bag of salt - y kg

The mass 2 bags of beans 2x, The mass 3 bags of salt 3y

2x+3y= 410

The mass of 3 bags of beans 3x, for 2 bags of salt it is 2y

3x+2y=390

We have system of equations (the equations are simultaneous)

2x+3y=410

3x+2y=390

2x= 410-3y

x=205-1.5y

3* (205-1.5y)+2y=390

615-4.5y+2y=390

2.5y= 225

y=90- the mass of the bag of salt

x= 205 - 1.5*90= 205-135= 70- the mass of the bags of beans

Answer:

1,032,564 tickets

Step-by-step explanation:

Find how many tickets they sell in total by multiplying the capacity of the stadium by the number of games in the season:

86,047(12)

= 1,032,564

So, if every game sells out, 1,032,564 tickets will be sold.

Answer:

The area shaded is 95%

Step-by-step explanation:

The total area under the curve is 100 percent

1 standard deviation away from the mean is 68 percent

2 standard deviations away is 95 percent

The area shaded is 95%

The percentage of the shaded area underneath this normal curve is 95% because it lie within two (2) standard deviations of the mean.

The 68-95-99.7 rule is also referred to as the empirical rule or the three-sigma rule and it can be defined as a shorthand which is used in statistics to determine the percentage of a population parameter that lie within an interval estimate in a normal distribution curve.

Basically, the 68-95-99.7 rule states that 68%, 95%, and 99.7% of the population parameter lie within one (1), two (2), and three (3) standard deviations of the mean respectively.

This ultimately implies that, the percentage of the shaded area underneath this normal curve is 95% because it lie within two (2) standard deviations of the mean.

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Answer:

Sara studies longer by 15 minutes.

Step-by-step explanation:

Let's calculate how long Sebastian studies for. From 3:15 - 4:15, there is 1 hour and from 4:15 to 4:45, there are 30 minutes so Sebastian studies for 1 hour and 30 minutes. Now, let's calculate how long Sara studies for. From 4:30 - 5:30, there is 1 hour, from 5:30 - 6:00, there are 30 minutes and from 6:00 - 6:15, there are 15 minutes so Sara studies for 1 hour 45 minutes. This means that Sara studies longer by 45 - 30 = 15 minutes.

Answer:

Factors are 1,2,3,4,5,6,10,12,15,20,30,60

Step-by-step explanation:

Hope this helps

Factors refers to those numbers which muntiplied that no.here, numbers that muntiply 60 are 1,2,3,4,5,6,10,12,15,20,30,60.

thus these numbers are factors of 60.

Answer: The equation is correct.

Step-by-step explanation:

from the expression,

5x + 3( y + 4x² + 3x ) + 2( y - x² ) = 14x + 10x² + 5y

Open brackets with 3 and 2

5x + 3y  + 12x² + 9x  + 2y - 2x²

Now collect like terms

5x + 9x + 12x² - 2x² + 3y + 2y

14x + 10x² + 5y = 14x + 10x² + 5y  (Q.E.D)

TH equation is correct

Answer:

39/250

Step-by-step explanation:

15 3/5 = 78/5 and percent means per 100, so

(78/5)/100 = (78/5)(1/100)

=78/500 = 39/250

The true statements about the function include:

It should be noted that a function is simply used to illustrate the relationship between variables.

In this case, the given function is f(x) = x^1/3.

The intercept is (0, 5). Also, it can be deduced that as x approaches oo, h(x) approaches infinity.

Learn more about functions on:

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Answer:

8 3/4

Step-by-step explanation:

The decimal 3.5 as an improper fraction is 35/10.

Answer:

[tex]8\frac{3}{4}[/tex]

Step-by-step explanation:

To write as a mixed number means that you will have a whole number and a fraction together. To find the mixed fraction version, see how many times the denominator (bottom) fits into the numerator (top) evenly.

4, 8, 12, 16, 20, 24, 28, 32, 36

1   2  3   4    5    6    7    8     9

4 can go into 35 '8' times without being greater than the numerator. 8 is the whole number. Now subtract the original numerator by the product of 4 and 8, which is 32:

[tex]35-32=3[/tex]

3 is the new numerator. Keep the same denominator. Insert all values:

[tex]\frac{35}{4}=8\frac{3}{4}[/tex]

:Done

Answer:

The 3 years investment earns more interest

Step-by-step explanation:

Given

Principal, P = $5,000

Required

Determine which earns more interest

When Rate = 1.75% and Year = 2

Interest is as follows;

[tex]I = \frac{PRT}{100}[/tex]

Substitute 1.75 for R, 5000 for P and 2 for T

[tex]I = \frac{5000 * 1.75 * 2}{100}[/tex]

[tex]I = \frac{17500}{100}[/tex]

[tex]I = \$175[/tex]

When Rate = 1.25% and Year = 3

Interest is as follows;

[tex]I = \frac{PRT}{100}[/tex]

Substitute 1.25 for R, 5000 for P and 3 for T

[tex]I = \frac{5000 * 1.25 * 3}{100}[/tex]

[tex]I = \frac{18750}{100}[/tex]

[tex]I = \$187.5[/tex]

Comparing the interest of both investments, the 3 years investment earns more interest

Answer:

Solution : Option A

Step-by-step explanation:

What we want to do here is eliminate the parameter t. In order to do that, we can isolate t in our first equation x = t + 6 ----- ( 1 ) and then plug that value for t in the second equation y = 3t - 1. Our solution will be an equation that is not present with t.

( 1 ) x = t + 6, t = x - 6

( 2 ) y = 3( x - 6 ) - 1 ( Distribute the " 3 " in 3( x - 6 ) )

y = 3x - 18 - 1 ( Combine like terms )

y = 3x - 19

As you can see our result will be option a, y = 3x - 19.

Answer:

x = 8

Step-by-step explanation:

Hello!

What we do to one side of the equation we have to do to the other side.

3x - 6 = 18

Add 6 to both sides

3x = 24

Divide both sides by 3

x = 8

The answer is 8

Hope this helps!

Answer:

x=8

Step-by-step explanation:

(3x-6)=18

Add 6 to each side

(3x-6+6)=18+6

3x= 24

Divide by 3

3x/3 = 24/3

x = 8

Answer:

160 liters of 25%, 20 liters of 40%, 60 liters of 60%

Step-by-step explanation:

x + y + z = 240

0.25x + 0.4y + 0.6z = 0.35*240 = 84

z = 3y

x = 160

y = 20

z = 60

Answer:

y=3x

Step-by-step explanation:

-6/-2=3, -3/-1=3, 3/1=3. 6/2=3

Answer:  4.17 steps

Step-by-step explanation:

Draw a point to use as the center and then sketch 50 units north (up) and 25 units west (left) and 315° which creates a right triangle that has an angle of 360° - 315° = 45°

Use Pythagorean Theorem to find the length of the hypotenuse.

50² + 25² = hypotenuse²   --> hypotenuse = 55.9 units

Since Musah only walked 50 units along the hypotenuse, he is 5.9 units from the center.

Create another right triangle using the remaining 5.9 units as the hypotenuse.  You can use 45°-45°-90° rules OR sin 45° to find the horizontal distance from the center to be 4.17.

see attachment for sketch

Answer: A. $16.13

Step-by-step explanation:

Total students = 82+74+96+99 =351

Sum of earnings of 82 seniors  = $26.75  x 82= $2193.5

Sum of earnings of 74 juniors  = $12.25 x 74 = $906.5

Sum of earnings of 96 sophomores  = $15.50  x 96 = $1488

Sum of earnings of 99 freshmen  =  $10.85 x 99 = $1074.15

Total earnings =  $2193.5  + $906.5+  $1488 +$1074.15

= $5662.15

(Total earnings) ÷ (Total students )

= $5662.15÷ 351

= $16.13

[tex]x-1=\dfrac{6}{x}\qquad(x\not=0)\\\\x^2-x=6\\x^2-x-6=0\\x^2+2x-3x-6=0\\x(x+2)-3(x+2)=0\\(x-3)(x+2)=0\\x=3 \vee x=-2[/tex]

Answer:

169 [tex]cm^{2}[/tex]

Step-by-step explanation:

Surface area (SA) = 2B + PH

                       SA = 2 ([tex]\frac{1}{2}[/tex] x 9 x 6) + (7+7+9) 5

                             = 2 (27) + (23) 5

                             = 54 + 115

                        SA = 169 [tex]cm^{2}[/tex]

Answer:

k=8

Step-by-step explanation:

Since y and x are in direct proportions, the equation is

y= kx, where k is a constant.

when y= 33.6, x=4.2,

33.6= k(4.2)

k= 33.6 ÷4.2

k=8

Answer:

k=8

Step-by-step explanation:

Answer:

16.67 or 16 2/3

Step-by-step explanation:

so, as BC is a tangent, it means the angle OBC is 90 degrees.

therefore, the angle BOC is 180 - 90 - 30 = 60 degrees.

that means the angle AOB is 180 - 60 = 120 degrees.

the triangle ABO must be an isosceles triangle, as the sides are both the radius of the circle. so, both remaining angles are the same : half of 180 - 120 = 60 = 30 degrees.

and so, we know that ABC is an isosceles triangle, because both "side angles" are equal = 30 degrees.

so, AB = BC.

and we know the circumference of the circle (50) and can calculate the radius

50 = 2×pi×r

25 = pi×r

r = 25/pi ≈ 7.96

now we have multiple ways to calculate AB.

AB = BC = tan(60) × r

or

AB = sqrt(r² + r² - 2×r×r×cos(120))

or ...

the first one might be easiest.

AB = tan(60) × 7.96 ≈ 13.78

oh, I just recognized, we need the arc AB (not the straight line).

even easier.

50 is the full "arc" of the circle for all 360 degrees.

but we only need the part of the angle AOB = 120 degrees.

so, this is then only the 120/360 part of the full circle circumference.

ABarc = 50 × 120/360 = 50 / 3 ≈ 16.67 or 16 2/3

Answer:

The calculated value of z= 2.7225 falls in the critical region therefore we reject the null hypothesis and conclude that at the  5% significance level, true proportion of correct responses to the question without context exceeds that for the one with context.

Step-by-step explanation:

a: 15 % of 1000= 150

b. 15.96 % of $ 1000= $ 159.6

The customer would pay = $ 1000- $ 159.6= $ 840.4 and save $ 159.6

Formulate the hypotheses as

H0: p1= p2   true proportion of correct responses to the question without context is equal that for the one with context.

Ha : p1≠ p2

We choose the significance level ∝= 0.05

The critical value for two tailed test at alpha=0.05 is ± 1.96

The test statistic is

Z = p1-p2/ √pq (1/n1+ 1/n2)

p1= true proportion students who answered the question without context correctly  = 165/200=0.825

p2=  true proportion of students who answered the question with context correctly = 142/200= 0.71

p = an estimate of the common rate on the assumption that the two proportions are same.

p = n1p1+ n2p2/ n1 + n2

p =200 (0.825) + 200 (0.71) / 400

p=  165+ 142/400= 307 /400 =0.7675

now q = 1-p= 1- 0.7675= 0.2325

Thus

z= 0.825- 0.71/ √0.7675*0.2325( 1/200 + 1/200)

z= 0.115/√ 0.17844( 2/200)

z= 0.115/0.04224

z= 2.7225

The calculated value of z falls in the critical region therefore we reject the null hypothesis and conclude that at the  5% significance level, true proportion of correct responses to the question without context exceeds that for the one with context.

Answer:

(2+7) root 3 equals 9 root 3

Answer:

The choose D. 15/16

Step-by-step explanation:

[tex] 1\frac{1}{4} \times \frac{3}{4} = \frac{15}{16} [/tex]

I hope I helped you^_^

G(x)=5x+3

[tex]\\ \sf\longmapsto G(2)[/tex]

[tex]\\ \sf\longmapsto 5(2)+3[/tex]

[tex]\\ \sf\longmapsto 10+3[/tex]

[tex]\\ \sf\longmapsto 13[/tex]

Option c is correct

Answer: y=23

Step-by-step explanation:

If Points and A,B and C lines on the same line then they will have the same slopes so since we have the coordinates of  A and B we will use the to write an equation in slope intercept form.

To write it in slope intercept form we will need to find the slope and the y intercept.

To find the slope you will find the change in the y coordinates and divide it by the change in the x coordinates.

Using the coordinates (-1,7) and (2,19)  the y coordinates are 7 and 19 and the x coordinates are -1 and 2.

Slope :  [tex]\frac{7-19}{-1-2} \frac{-12}{-3} = 4[/tex]   In this case the slope is 4 so we will use that to find the y intercept by using point A coordinate.

  The slope intercept formula says that y=mx +b  where me is the slope and b is the y intercept.

 7=4(-1) + b  

7 = -4 + b

+4   +4

 b= 11       The y intercept is 11.

Now we can write the whole equation as y=4x + 11   .

To answer the question now, where we need to find y , we will plot the x coordinate which is 3 into the equation and solve for y.

 y = 4(3) + 11  

y = 12 + 11

 y = 23

Answer:

3 2/15 <b

Step-by-step explanation:

2 3/5 <b-8/15​

Add 8/ 15 to each side

2 3/5 + 8/ 15 <b-8/15​ + 8/15

2 3/5 + 8 /15 <b

Get a common denominator

2 3/5 *3/3 + 8/15

2 9/15 + 8/15 < b

2 17/15 < b

2 + 15/15 + 2 /15 < b

3 2/15 <b

Answer:

B > 3 2/15

Step-by-step explanation:

Answer:

56

Step-by-step explanation:

Angle Formed by Two Chords= 1/2(sum of Intercepted Arcs)

75 = 1/2 (94+d)

Multiply by 2

75*2 = 94+d

150 = 94+d

Subtract 94 from each side

150-94 = d

56=d