10
8
12
10
14
?

a. 16
b. 10
c. 12
d. 18

Solution :

Given :

n = 221

x = 17

a). [tex]$p=\frac{17}{221}$[/tex]

       = 0.076

b). At the 95 confidence interval

   Value of z = 1.96

  Margin of error

    [tex]$=1.96 \times \sqrt{\frac{p(1-p)}{n}}$[/tex]

    [tex]$=1.96 \times \sqrt{\frac{0.076(1-0.076)}{221}}$[/tex]

   [tex]$=1.96 \times \sqrt{\frac{0.076\times 0.924 }{221}}$[/tex]

   = 1.96 x 0.017

   = 0.03332

c). confidence interval

   = ( 0.076-0.033,  0.076+0.033)

   = ( 0.043, 0.109 )

d). The confidence interval does not contain null value, so it is significant.

[tex] \displaystyle \int \bf \: \frac{2 \: tan \: x. {sec}^{2} \: x }{1 + {tan}^{2} \: x } \: \: dx \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ = 2 \displaystyle \int \bf \: \frac{tan \: x \: . \: \cancel{ {sec}^{2} \: x}}{ \cancel{ {sec}^{2} \: x}} \: \: dx \: \: \: \: \pink{ \{ \because \: {sec}^{2} \: x - {tan}^{2} \: x = 1 \}} \\ \\ = 2 \displaystyle \int \bf \: tan \: x \: \: dx \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ = 2 \displaystyle \int \bf \: \frac{sin \: x}{cos \: x} \: \: dx \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ = - 2 \displaystyle \int \bf \: \frac{ - \: sin \: x}{ \: cos \: x} \: \: dx\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ = \bf \: - 2 \ln \: |cos \: x| + c\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \green{ \{ \because \: \displaystyle \int \bf \: \frac{ {f}^{′} (x)}{f(x)} \: dx = \ln \: |f(x)| + c \}}[/tex]

Answer:

Step-by-step explanation:

I am assuming i is the imaginary number:

Factor:

(3 + i)x - (4-2i) = 0.

In order for this to equal 0, x must be equal to 1-i.

I don't want to be reported to so take my word for it.

Also I plugged it into wolfram alpha so if it is wrong, blame the most powerful math equation solver available on the internet.

Using BTS he properties, find the unit's digit of the cube of each of the following numbers

Answer:

24

6

1/12

Step-by-step explanation:

a) This is a counting problem 4*3*2*1 = 24 different ways.

b) 1 * 2 * 1 * 1   = 2 ways

This is one you should try.

Jim Kat Larry Kim

Jim Larry Kat Kim

You can't get another way.

c)

There are 2 ways that Jim can arrive first and Kim Last shown in b

2/24 = 1/12

Answer:

sauce is 177013

Step-by-step explanation:

Answer:

y=9 and x=9*sqrt(2)

Step-by-step explanation:

tan(45)=9/y, 1=9/y, y=9

sin(45)=9/x, 1/sqrt(2)=9/x, x=9*sqrt(2)

Step-by-step explanation:

we don't see the parallelogram nor any description of it.

so, it is impossible to tell you the right answer.

as I only answer questions by don't ask any, I don't know how you can add a picture.

Answer:

2

Step-by-step explanation:

the number before the x² is regarded as the identity element

Answer:

What three consecutive integers have a sum of 87? Which means that the first number is 28, the second number is 28 + 1 and the third number is 28 + 2. Therefore, three consecutive integers that add up to 87 are 28, 29, and 30. We know our answer is correct because 28 + 29 + 30 equals 87 as displayed above.

Step-by-step explanation:

Consecutive integers are as simple as 1, 2, 3!  

Integers are consecutive if one follows another.  How do we "jump" from one integer to the next?  We add 1, right?  7, 8 and 9 are three consecutive integers.  Add one to 7 to get 8 and add one more to get 9.

Now lets think about this in algebraic terms.  Lets name these consecutive integers , x, y and z.  

The problem tells us that their sum is -87.  (Recall, "sum" is just a fancy word for the answer when we add.)

x+y+z = -87  

Here is the trick!  We need to rewrite this equation so that we have only one variable.  Easy!

y is one more that x, so y= x+1

And z is one more than y, so z= y+1.  But y is also equal to (x+1)!  So z=y+1=(x+1)+1=x+2

Now we have a problem that we can solve!  x+(x+1)+(x+2)=-87.  

Combining term.:  3x+3=-87  

Subtract 3 from both sides of the equation:  3x=84

Divide each side of the equation by 3:  x=28

We have solved for x, but we are not done!  We need to find y and z.  I know you can do this.  Remember y is one more than x and z is one more than y.

Check your work!  Make sure these three consecutive numbers do in fact add up to -87.

Step-by-step explanation:

1. The given expression is, [tex]A=lw[/tex]

We need to solve it for w.

[tex]w=\dfrac{A}{l}[/tex]

2. The given expression is, [tex]C=\pi D[/tex]

We need to solve it for D.

[tex]D=\dfrac{C}{\pi}[/tex]

3. The given expression is, [tex]v=s+gt[/tex]

We need to solve it for s.

[tex]s=v-gt[/tex]

4. The given expression is, [tex]5x-2y=11[/tex]

We need to solve it for y.

[tex]D=\dfrac{5x-11}{2}[/tex]

5. The given expression is, [tex]P_1V_1=P_2V_2[/tex]

We need to solve it for P₂. So,

[tex]P_2=\dfrac{P_1V1}{V_2}[/tex]

Answer:

1: A=1

2: -3

3: C

Step-by-step explanation:

1: If 3x+4 is a factor, then -4/3 is equal to x. Substitute it in for x and solve for a.  This gives us A=1.

For the commenter not understanding how I got -4/3: 3x+4 being a factor means that it equals 0. It might help you understand this if you remember that after factoring, like I did for 38 in my photo, we take expressions like x-4 and set them equal to 0 to get x=4, a solution. So, subtract 4 from both sides to get 3x=-4, then divide both sides by 3 to get x alone. Thus, x=-4/3.

2: To find the sum, we first need to find the two solutions. We can factor to get (x+7)(x-4). This gives us x=-7 and x=+4. The solution of these two would be (-7)+4 is -3.

3: B is a close answer, but the signs are wrong on the bottom. Factoring the question would give us 2(x-2) / 2(x^2-x-2). Factoring that equation is 2(x-2) / 2(x+1)(x-2). Simplifying this gives us 1 / x+1.

Sorry for the bad penmanship, I wanted to make it a little clearer for you! I really hope I helped! :)

Answer:

The diameter is 6. The radius is 3. For the half of the orange circle.

The area of the half of the small orange circle is = pi*r*r = pi*3*3.

The diameter is 24. The radius is 12.

The area of the half of the light orange circle and the other colors is = pi*r*r = pi*12*12

The area of dark orange, light blue, purple and green figures = pi*12*12 – pi*3*3 = 135*pi

To get the area of the blue figure we need to divide 135*pi into ¼ and you will get the area of the blue figure.

The area of the blue figure =( ¼ )*135*pi *(1/2) = ¼ *1/2 = 1/8

The area of the blue figure is = 135pi / 8

B) outside perimeter of the window frame = 28 +pi*14 = 71.98

Hope this helps you :)

A line has an equation of,

[tex]y=mx+n[/tex].

m is called a slope

n is called y-intercept

We are also given two points [tex](x_1,y_1)=(4,-1),(x_2,y_2)=(6,-7)[/tex].

We begin with computing the slope,

[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{-7-(-1)}{6-4}=\frac{-7+1}{2}=\frac{-6}{2}=\boxed{-3}[/tex]

We have computed the slope m and our equation is almost done,

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

Next step is to find out what y-intercept n is. I will use point [tex](4,-1)[/tex] and insert x and y it into already known equation, then solve for n,

[tex]-1=-3(4)+n[/tex]

[tex]-1=-12+n\implies n=\boxed{11}[/tex]

The reason I can insert coordinates of a point as x and y is because this particular point is in the line described by equation,

[tex]\boxed{y=-3x+11}[/tex]

Hope this helps. :)

Answer:

litrally I don't understand what you are telling

9514 1404 393

Answer:

Step-by-step explanation:

Let a, o, v represent the prices of one each of apples, oranges, and avocados, respectively. Then the equations describing the purchases can be written ...

  6a +6o +6v = 19.50

  12a +2o +1v = 9.50

  2a +4o +5v = 14.00

__

Dividing the first equation by 6 makes it ...

  a +o +v = 3.25

Subtracting this from the second equation gives ...

  (12a +2o +v) -(a +o +v) = (9.50) -(3.25)

  11a +o = 6.25

Subtracting the third equation from 5 times the reduced first equation gives ...

  5(a +o +v) -(2a +4o +5v) = 5(3.25) -(14.00)

  3a +o = 2.25

The difference of these last two equations is ...

  (11a +o) -(3a +o) = (6.25) -(2.25)

  8a = 4.00

  a = 0.50

Then the other values are ...

  o = 2.25 -3(a) = 0.75

  v = 3.25 -a -o = 2.00

The unit prices are:

  apples -- $0.50

  oranges -- $0.75

  avocados -- $2.00

_____

Additional comment

Most graphing or scientific calculators will solve systems of equations like these. Using an appropriate tool, it takes less time to find the solution than to read this one.

Note that the last purchase description in the problem statement has the items in a different order than in the first two descriptions. Care must be taken to make sure the correct equations are written.

Answer:

2.75 m²  

Step-by-step explanation:

From the information given:

the thickness of the paint = 0.07 cm = (0.07/100) m

= 0.0007 m thick

the diameter hemispherical dome = 50 m

∴

radius of the dome = 50m /2 = 25 m

The volume of a hemispherical dome is expressed as:

[tex]V = \dfrac{2}{3}\pi r^3[/tex]

Thus, the change in the volume now is:

[tex]\dfrac{dV}{dr} = \dfrac{2}{3}\pi *3 r^2[/tex]

[tex]{dV} = \dfrac{2}{3}\pi *3 r^2 (dr)[/tex]

[tex]{dV} = 2 \pi r^2 (dr)[/tex]

∴

dV = 2π × (25)² (0.0007)

where;

dr = 0.0007

dV = 2π × (25)² (0.0007)

dV = 2.75 m²  

Answer:

A child who weighs 84 pounds should be given 94.5 milligrams of the drug.

Step-by-step explanation:

Givens:

1kg=2.5 milligrams of dosage

Weight of child = 84 pounds

1 pound = 0.45 kg

Solution:

Convert pounds to kilograms --> 84lbs*0.45kg = 37.8 kg

Convert weight to dosage --> 37.8kg * 2.5 mg = 94.5 mg of dosage.

Answer:

Step-by-step explanation:

triangol BCD = triangle BDA

so

3x - 1 = 34 - 2x

5x = 35

x = 35 : 5

Answer:

x = 7

Step-by-step explanation:

BD is an angle bisector , so

∠ ABD = ∠ DBC , that is

3x - 1 = 34 - 2x ( add 2x to both sides )

5x - 1 = 34 ( add 1 to both sides )

5x = 35 ( divide both sides by 5 )

x = 7

Answer:

here's the answer to your question

Answer:

Hello,

Answer is (x+1)(x+3)(2x+1)

Step-by-step explanation:

[tex]p(x)=2x^3+9x^2+10x+3\\p(-1)=2*(-1)^3+9*(-1)^2+10*(-1)+3=-2+9-10+3=0\\p(x)\ is\ divisible\ by\ (x+1)We\ arrange\ to\ put\ a\ factor\ of\ x+1\\\\2x^3+9x^2+10x+3\\\\=2x^3+2x^2+7x^2+7x+3x+3\\\\=2x^2(x+1)+7x(x+1)+3(x+1)\\\\=(x+1)(2x^2+7x+3)\\\\=(x+1)(2x^2+6x+x+3)\\\\=(x+1)(2x(x+3)+1(x+3))\\\\=(x+1)(x+3)(2x+1)\\[/tex]

Answer:

2x^2+x-15

Step-by-step explanation:

foil

Answer:

2x^2 + x - 15

Step-by-step explanation:

using FOIL

(2x - 5)(x + 3)

[(2x ⋅ x) + (2x ⋅ 3) + (-5 ⋅ x) + (-5 ⋅ 3)]

[2x^2 + 6x - 5x - 15]

2x^2 + x - 15

Answer:

x=  $6,284.15

Step-by-step explanation:

7300 = x(1 + .025/12)^72

x = [tex]\frac{7300}{(1 + \frac{.025}{12} )^{72} }[/tex]

x=  $6,284.15  

Answer:

C

Step-by-step explanation:

the answer is C because only C contained it's correct root and power

Answer:

t = 22 s

Step-by-step explanation:

If n is the number of strobe pulses

The first strobe pulse occurs at t = 0

t = 2(n - 1)

t = 2(12 - 1)

t = 2(11)

t = 22 s

Answer:

Option (C)

Step-by-step explanation:

Coordinates of the point representing the location of Miya → (1, 10)

Coordinates of the point representing the location of Drea → (13, 1)

Coordinates of the point representing the location of Francine → (16, 1)

Coordinates of the point representing the location of Beach → (19, 4)

Distance between Miya and Drea = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

                                                        = [tex]\sqrt{(13-1)^2+(1-10)^2}[/tex]

                                                        = [tex]\sqrt{144+81}[/tex]

                                                         = 15 miles

Distance between Drea and Francine = [tex]\sqrt{(16-13)^2+(1-1)^2}[/tex]

                                                               = 3 miles

Distance between Francine and Beach = [tex]\sqrt{(19-16)^2+(4-1)^2}[/tex]

                                                                  = [tex]\sqrt{9+9}[/tex]

                                                                  ≈ 4.2 miles

Total distance between Miya and the beach = 15 + 3 + 4.2

                                                                          = 22.2 miles

Option (C) is the answer.

Answer:

C. 98

Step-by-step explanation:

The proposed regression equation is weight = b + width * m

R2 = 0.423

A.) What is the regression equation for this example?

The estimate for the y-intercepts is b= 2.3013 and the estimate for the slope is m= 0.7963

In general, we can symbolize the estimated regression equation as ^Y= b + m*Xi. For this example you have to replace it with the calculated values of the regression coefficients to obtain the estimated regression equation:

^Y= 2.3013 + 0.7963Xi

B.) What is the explanatory, or predictor, variable in this study?

The explanatory or predictor variable is the variable that is suspected to have an effect over the response variable. In this example the predictor variable is:

X: Width of a horseshoe crab (cm)

C.) If the researcher wanted to test whether there is a statistically significant relationship between these two variables, what would the test statistic be? Calculate it from the table above.

To test if the regression is significant, the parameter of study will be the slope of the regression equation, symbolically: β. If the slope is equal to zero "β=0" then there is no linear regression between the response and explanatory variable. If the slope is different from zero "β≠0" then the regression is significant and the explanatory variable affects the response variable.

The hypotheses are:

H₀: β=0

H₁: β≠0

α: 0.05

The value of the statistic under the null hypothesis is t= 8.48

D.) What can we say about the p-value?

This test is two-tailed and so is the p-value, remember that the p-value is the probabulity of obtaining a value as extreme as the value of the statistic under the null hypothesis. The distribution for this test is a t with n-2= 100-2= 98 degrees of freedom. You can calculate the p-value as:

P(t₉₈≤-8.48) + P(t₉₈≥8.48)= P(t₉₈ ≤ -8.48) + (1 - P(t₉₈ < 8.48) ≅ 0.00001

E.) Ultimately, the reason that we find test statistics is so that we can compare them to a null distribution. For regression, that is a t-distribution based on the degrees of freedom. With 98 degrees of freedom (100-2), we can safely say that the critical t (or the confidence multiplier) is what?

As mentioned before, this test is two tailed, meaning that the rejection region is divided in two:

Critical values ± = ± = ± 1.984

This means that you'll reject the null hypothesis when the statistic is t ≤ -1.984 or if the statistic is t ≥ 1.984-

F.) Find the confidence interval for the slope.

Using a 95% confidence level, the interval for the slope is:

[m ± Sm]

[0.7963 ± 1.984 * 0.0939]

[0.61; 0.98]

G.) Is there a statistically significant relationship? Answer with the test statistic and the confidence interval.

Yes, there is a significant relationship between the width and weight of the horseshoe crabs.

Using the critical value approach:

The calculated statistic is 8.48 and the critical value is ± 1.984, since the statistic is greater than the positive critical value, the decision is to reject the null hypothesis.

If you pay attention to the confidence interval, which was made at a confidence level complementary to the significance level of the hypothesis test, this interval [0.61; 0.98] doesn't include the "zero". Since the interval doesn't include the value of the parameter stated in the null hypothesis, you can conclude that this hypothesis is not true and therefore reject it.

Answer:

82

Step-by-step explanation:

1/3( x+9/7) + 3^4

Let x = 12/7

1/3( 12/7+9/7) + 3^4

PEMDAS says parentheses first

1/3( 21/7) + 3^4

1/3(3) +3^4

Then exponents

1/3(3)+81

Then multiply

1+81

82

Answer:

Your equation would be

y=4x-12

Step-by-step explanation:

So an easy way to figure this out is graph the points and look at the distance the points are away from each other. In this case it was 12 up and 3 right. This is your slope. Simplify the fraction to 4/1. Then from (2,-4) use the given slope to work back to a point that is on the y axis, which is (0,12). Plug all of the given information you found into y=mx+b and you get the given formula.

Answer:

b = h*D +hg^3

Step-by-step explanation:

b/h = D +g^3

Multiply each side by h

h* b/h = h*D +hg^3

b = h*D +hg^3

Answer:

Hi Keke,

Let Amy have x dollars. Then Jose has x - 8 dollars and Milan has 4(x - 8) dollars.

x + (x-8) + 4(x-8) = 152

6x - 40 = 152

6x = 192

x = 32

Amy has $32

Jose has 32 - 8 = $24

Milan has 4*24 = $96