Which function models this variation:
a varies directly with b and inversely with c, and when b=10 and c=20, a=14. Using your function, what is the value of a when b=18 and c=9 ?

A. a=b2c;a=1
B. a=b2c;a=2
C. a=2bc;a=1
D. a=2bc;a=2

Answer:

The number of boys are 64.

Step-by-step explanation:

We have,

The ratio of the boy to girl is 8:9.

Total number of girls are 72.

Let total boys are 8x and total girls are 9x.

According to the question,

[tex]9x=72\\\\x=8[/tex]

Since, number of boys are 8x. So,

[tex]B=8x=8\times 8=64[/tex]

So, the number of boys are 64.

Answer:

0.7463 gm/cm^3

Step-by-step explanation:

Density of any substance is mass of that substance per unit of volume.

it can be represented by given below expression

Density = mass/ volume

Given

mass = 500gm

volume = 670 cubic centimetres

Therefore, density = 500/670 gm/cubic centimetres

density = 0.7463 gm/cm^3

Thus , density of statue is 0.7463 gm/cm^3.

Answer:x=8 or x=-2

Step-by-step explanation:

log4(x-6) + log4(x)=2

log4(x(x-6))=2

4^2=x(x-6)

4x4=x(x-6)

16=x^2-6x

Arrange the quadratic equation

x^2-6x-16=0

x^2+2x-8x-16=0

x(x+2)-8(x+2)=0

(x-8)(x+2)=0

x-8=0. x+2=0

x=8. x=-2

ANSWER: D

Isosceles Right Triangle has 3 angles: 90 degrees, 45 degrees and 45 degrees

Answer:

D

Step-by-step explanation:

It is isosceles (having two sides and angles congruent) and it is right will provide enough information to find all the angles of the triangles.

Answer:

5 minutes

Step-by-step explanation:

200+15=215

214/43=5

It moved up a total of 200 + 15 = 215 meters at 43 meters per minute

t = 215 m / (43 m/min) = 5 minutes

Answer: 5 minutes

Answer:

The perimeter of the field is 21 yards

Step-by-step explanation:

See attachment 1 for the coordinates plane.

The question is best solved using an attachment.

To calculate the perimeter of the fence, we simply add the sides of the rectangle.

Attachment 2 is a labelled diagram of attachment 1.

From 2, we have that

Perimeter = A + B + C + D + E + F

Where A to F represent the length of each sides of the fence

From coordinates geometry,

A = 5

B = 4

C = 6½

D = 1½

E = 1½

F = 2½

So,

Perimeter = 5 + 4 + 6½ + 1½ + 1½ + 2½

Perimeter = 21

Hence, the perimeter of the field is 21 yards

Answer and Step-by-step explanation:

We want to verify that (1 + cos(2θ)) / 2cos(θ) = cos(θ).

Let's focus on the left side. Look at cos(2θ). This is an identity, so remember that cos(2θ) = cos²θ - sin²θ. Also, look at the 1. Remember that sin²θ + cos²θ = 1, so plug both of these expressions into our equation:

(1 + cos(2θ)) / 2cos(θ) =? cos(θ)

((sin²θ + cos²θ) + (cos²θ - sin²θ)) / 2cos(θ) =? cos(θ)

2cos²θ / 2cosθ =? cosθ

cosθ = cosθ

Thus, we have proved this is an identity.

Answer:

(1 + cos(2theta))/2cos(theta)

cos(2theta) = 2cos²(theta) - 1

(1 + 2cos²(theta) - 1)/2cos(thetal

2cos²(theta)/2cos(theta)

cos(theta)

Answer: Equilateral, isosceles and scalene.

Step-by-step explanation:

Answer:

the value of x is in the solution set of 4x-12<16=8x

Step-by-step explanation:

multiply the 4x take away from 12= 8x

Answer:

a = 27

b = 81

Step-by-step explanation:

3^{3} = 27

3^{4} = 81

Answer:

f/g(x) 1/x x=0

Step-by-step explanation:

f/g 1/x+2

x+2=0

-2      -2

x=-2

Answer:

8 goes into 11 one time with a remainder of 3

Answer:

(0,1)

Step-by-step explanation:

i got it right

Answer:

5

Step-by-step explanation:

3+5+7+8+9+4+2+1+3+8=50

50/10=5

Answer:

The unknown angle = 126°

Step-by-step explanation:

From angles in a triangle.

The total sum of angles in a triangle = 180°

Let the unknown angle be x

27 + 27 + x = 180

X = 180-27-27

X= 180-54

X = 126°

Answer: 81°

Step-by-step explanation:

m<p is a secant exterior angle which equals arcAB-arcDC divided by 2.

plug the numbers in and arcAB-27 / 2 =54 Arc AB is 27+54=81 degrees

Answer:

D understand the problem.

Step-by-step explanation:

Answer:

gathering of resources is the main first thing .....

Answer:

0.38

Step-by-step explanation:

7 is the 3rd digit, so 8 is greater then 5, so you round up, if it is correct, can you give brainiest

Answer:

0.40

Step-by-step explanation:

this is because the number before it is up to five and even more than 5 so we round it up by adding one to the next number and the remaining digit to zero

Answer:

  y = 12

Step-by-step explanation:

Ordinarily, in math, when we say "the difference between ..." we mean the second listed item is subtracted from the first. (In English, we often mean "the positive difference between ..." so the order doesn't matter.)

We'll assume we are only interested in the case where the difference is in the order listed.

  [tex]\dfrac{y+12}{y-4}-\dfrac{y}{y+4}=\dfrac{y+12}{y-4}\cdot\dfrac{y}{y+4}\\\\\dfrac{(y+12)(y+4)-(y-4)(y)}{y^2-16}=\dfrac{(y+12)(y)}{y^2-16}\\\\0=\dfrac{y^2-8y-48}{y^2-16}=\dfrac{(y-12)(y+4)}{(y-4)(y+4)}=\dfrac{y-12}{y-4}\qquad\text{$y\ne -4$}\\\\\boxed{y=12}[/tex]

There is one solution.

_____

Comment on the solution

If you were to "clear fractions" by multiplying the equation by (y^2-16), you would also obtain the extraneous solution y=-4. That is why we did not solve it that way.

Answer:

64

Step-by-step explanation:

Answer:13.6

Step-by-step explanation:

122.4 ➗ 9=13.6

Answer:

D. 221.7 cm

Step-by-step explanation:

Surface area of a sphere is: [tex]SA=4\pi r^2[/tex]

'r' - radius

We are given the radius of 4.2 centimetres.

[tex]SA=4\pi 4.2^2\\4 * \pi * 4.2^2\\\rightarrow 4.2^2 =17.64\\\text {Using 3.14 for pi: }\\4 * 3.14 *17.64\\12.56*17.64\\\boxed {221.5584}[/tex]

221.5584 ≈ 221.6

The closest answer is Option D, therefore it should be the correct answer.

Answer:third term=14 twelfth term=59

Step-by-step explanation:

first term=a=4

Common difference=d=5

Second term=4+5=9

Third term=9+5=14

Using Tn=a+d(n-1)

T12=4+5(12-1)

T12=4+5x11

T12=4+55

T12=59

Twelveth term=59

Step-by-step explanation:

(11.99+23.98+9.95)= 45.92

she has to pay = 45.92 - 20/100 (45.92)

= 45.92 - 9.18 = 36.74

so option

about 37 is right

Answer:

Fail to reject H₀

Step-by-step explanation:

To reject the null hypothesis, the P-value must be less than 0.05.

Since the P-value is 0.15 which is greater than 0.05, we would fail to reject the null hypothesis as there is no sufficient evidence against the null hypothesis.

Thus, the conclusion would be to fail to reject H₀.

Answer:

5m x 5m, 6m x 4m and 7m x 4m

Step-by-step explanation:

in interval of 0.02 and for the same value of m.

Answer:

D

If you put the equation into a calculator, it will show a graph of it.

Answer:

764

Step-by-step explanation:

Answer:

[tex]0.60 - 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.570[/tex]

[tex]0.60 + 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.630[/tex]

The 95% confidence interval for the true proportion would be given by (0.570;0.630) .

And if we convert this into % we got (57.0%, 63.0%)

Step-by-step explanation:

The information given we have the following info given:

[tex] n = 1019[/tex] represent the sampel size

[tex] \hat p=0.6[/tex] represent the sample proportion of interest

The confidence level is 95%, our significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value would be given by:

[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]

The confidence interval for the mean is given by the following formula:  

[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]

Replacing the info given we got:

[tex]0.60 - 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.570[/tex]

[tex]0.60 + 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.630[/tex]

The 95% confidence interval for the true proportion would be given by (0.570;0.630) .

And if we convert this into % we got (57.0%, 63.0%)

Answer:

Graph B

Step-by-step explanation: