An animal shelter houses only cats and dogs,
and there are 25% more cats than dogs. If
there are 40 cats, how many dogs are there,
and how many animals are there total?

Answer:

a) The sample proportion is of 0.6.

b) The 95% confidence interval for the proportion of potential customers who prefer your product is (0.4642, 0.7358).

c) A sample size of 145 is needed.

Step-by-step explanation:

(a) Find the sample proportion.

30 out of 50. So

[tex]\pi = \frac{30}{50} = 0.6[/tex]

The sample proportion is of 0.6.

(b) Find the 95% confidence interval for the proportion of potential customers who prefer your product.

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 50, \pi = 0.6[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6 - 1.96\sqrt{\frac{0.6*0.4}{50}} = 0.4642[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6 + 1.96\sqrt{\frac{0.6*0.4}{50}} = 0.7358[/tex]

The 95% confidence interval for the proportion of potential customers who prefer your product is (0.4642, 0.7358).

(c) If you want the 95% maximum likely error to be 0.08 or less, what would you choose for a sample size

The margin of error is:

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

We need a sample size of n, and n is found when M = 0.08. So

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

[tex]0.08 = 1.96\sqrt{\frac{0.6*0.4}{n}}[/tex]

[tex]0.08\sqrt{n} = 1.96*sqrt{0.6*0.4}[/tex]

[tex]\sqrt{n} = \frac{1.96*sqrt{0.6*0.4}}{0.08}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96*sqrt{0.6*0.4}}{0.08})^2[/tex]

[tex]n = 144.1[/tex]

Rounding up

A sample size of 145 is needed.

Answer:

(2,2)

Step-by-step explanation:

hope it helps u good night

Step-by-step explanation:

the area of a parallelogram is

base × height.

so,

87 × 18.6 = 1,618.2 cm²

Answer:

x = 5

Common denominator of 3/x+1 to 1/2

If the numerator is 3 times, then so is the denominator in a proportion.

3/1=x+1/2

x+1 must equal 6 for the proportion to be equal to 1/2.

6-1=5, so x is 5.

Answer:

7, 15

Step-by-step explanation:

hope it can help you

Step-by-step explanation:

14/2 =7 so

(x+7)^2 + [  ]

if you were to multiply just the (x+7)^2 term it would look like x^2 +14x+49, but we need that final term to be equal to 64, so you can add 15 on to the end to make up for the gap.

This should get you

f(x) = (x+7)^2 + 15

Answer:

B

Step-by-step explanation:

I took the test but all you need to do is find the intersecting point with your axis to get your possible answers.

Hope this helps <3

Answer:

[tex]f'(n) = n + 3[/tex]

Step-by-step explanation:

Given

[tex]f(n) = n - 3[/tex]

Required

The inverse

[tex]f(n) = n - 3[/tex]

Replace f(n) with y

[tex]y = n - 3[/tex]

Swap positions of y and n

[tex]n = y - 3[/tex]

Make y the subject

[tex]y = n + 3[/tex]

Replace y with f'(n)

[tex]f'(n) = n + 3[/tex]

Answer:

3.14

Step-by-step explanation:

A = R*R*3.14

9514 1404 393

Answer:

  69.6°

Step-by-step explanation:

The sum of angles in a triangle is 180°, so angle X is ...

  ∠X = 180° -∠Y -∠Z

  ∠X = 180° -68.4° -42°

  ∠X = 69.6°

Answer:

4 hours

Step-by-step explanation:

32/8=4

Answer:

4 Hours

Step-by-step explanation:

just divide 32 by 8

Answer:

[tex]\Huge\boxed{x=12}[/tex]

Step-by-step explanation:

Hello There!

The following angles are complementary angles

Complementary angles have a sum of 90

So to solve for the variable (x) we use this equation

90 = 35 + 4x + 7

step 1 combine like terms

35+7=42

now we have

90 = 4x + 42

step 2 subtract 42 from each side

90 - 42 = 48

42 - 42 cancels out

now we have

48 = 4x

step 3 divide each side by 4

4x/4 = x

48 / 4 = 12

we're left with x=12

9514 1404 393

Answer:

  x = 625^(1/5) ≈ 3.62390

Step-by-step explanation:

Using the change of base formula, we have ...

  [tex]\log_x(25)=2.5\\\\\dfrac{\log(25)}{\log(x)}=2.5\\\\\log(x)=\dfrac{\log(25)}{2.5}=0.4\log(25)=\log(25^{0.4})\\\\x=25^{0.4}=\sqrt[5]{25^2}=\boxed{\sqrt[5]{625}\approx 3.62390}[/tex]

Answer:

c

Step-by-step explanation:

Answer:

1/5x+2=17

1/5x=15

x=75

Answer:

x=75

Step-by-step explanation:

[tex]\frac{1}{5}[/tex]= 0.2

17-2 = 15

0.2x75 = 15

1/5 x 75 +2 = 17

x=75

Answer:

12 | 52 | 64  |

27 | 59 | 86  |

39 | 111 | 150 |

I attempted making a chart with the answers

Answer:

k

Step-by-step explanation:

k

140°+h=180°

h=180°-140°

h=40°

Answer:

The equation of the line is [tex]y = -\frac{3x}{4} - 2[/tex]

Step-by-step explanation:

Equation of a line:

The equation of a line has the following format:

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

In which m is the slope and b is the y-intercept.

Perpendicular lines:

When two lines are perpendicular, the multiplication of their slopes is -1.

Perpendicular to the line 4x-3y=18

First, we place this line into the format, to find the slope:

[tex]4x - 3y = 18[/tex]

[tex]3y = 4x - 18[/tex]

[tex]y = \frac{4x}{3} - 6[/tex]

This line has slope 4/3. So, for the perpendicular line, the slope will be of m as such:

[tex]\frac{4m}{3} = -1[/tex]

[tex]4m = -3[/tex]

[tex]m = -\frac{3}{4}[/tex]

So the desired line will have an equation in the following format:

[tex]y = -\frac{3x}{4} + b[/tex]

Passes through the point (8,-8)

We use this to find b. This point means that when [tex]x = 8, y = -8[/tex]. So

[tex]y = -\frac{3x}{4} + b[/tex]

[tex]-8 = -\frac{3*8}{4} + b[/tex]

[tex]-8 = -6 + b[/tex]

[tex]b = -2[/tex]

So

[tex]y = -\frac{3x}{4} - 2[/tex]

Hi there!

[tex]\large\boxed{\text{None.}}[/tex]

Using the discriminant formula, we can determine if this equation is ever true:

b² - 4ac

Plug in the a, b, and c values from the equation:

(4)² - 4(1)(5)

16 - 20 = -4 < 0

Since the discriminant is less than 0, there are no zeros to the equation. Thus, the equation is never true.

Answer:

Equation to find radius = Diameter divided by 2

Area is 1319.585

Step-by-step explanation:

Diameter = 41 cm

Radius = 41÷2 = 20.5cm

Area = πr^2

Area = 3.14×(20.5)^2

Area = 3.14×420.25

Area = 1319.585cm^2

Answer:

Perimeter: 60

Area: 116

Answer:

2.55

Step-by-step explanation:

Answer:

Hey! Hope this helps!

Step-by-step explanation:

Have an awesome Friday <3

Answer:

Step-by-step explanation:

"function q has zeros of -3 and 8"

q(x) = a(x+3)(x-8)

"q passes through the y-axis at the point (0,12)"

a(0+3)(0-8) = 12

a = -½

q(x) = -½(x+3)(x-8) = -½x² + 2.5x + 12

q'(x) = -x+2.5

-x+2.5 = -1.5

x = 4

rate of change is -1.5 at the point (4,14).

Answer:

master card

Step-by-step explanation:

Cause master card would charge me low interest from the rest of the cards.

So ,to save money I would choose master card

Answer:

can u tell of which shape these sides are ??

answer:

If the numbers  you gave are the angles, then no, this is not a right triangle.

explanation:

A right triangle has at least one 90 degree angle :)

Answer:

Yes

Step-by-step explanation:

a^2+b^2=c^2

48^2+55^2=73^2

5329=5329

Answer:

14

Step-by-step explanation:

When one encounters a problem like this all one must do is divide the number to the left (84) by the number on the right (6) then to double check divide the outcome by the number on the left or multiply the outcome by the one on the right.

Feel free to check the equations below:

84 divided by 6 = 14

84 divided by 14 = 6

14 times 6 = 84

84 ÷ 14 = 6