2. Is -1/3-4/5 positive,negative, or zero ?

Answer:

56 and 42

Step-by-step explanation:

3:4

3 + 4 = 7

98 / 7 = 14

14 x 3 = 42

14 x 4 =  56

56 + 42 = 98

The dimensions of the pool can be categorized as below:

Length equals 28 feet

Width equals 21 feet

The perimeter of a rectangle is the outside length of the rectangle. To find the perimeter we add all the 4 sides of the rectangle.

Perimeter = 2(length) + 2 (width )

The ratio of the width to the length is 3:4. The width of the rectangle is 3x  

We know,

Length of the rectangle is 4xWidth =3x  

Length = 4x

Substitute it in the perimeter formula and solve for x.

Given that,

Perimeter of a rectangle = 98 feet

Perimeter = 2(length )+2(width)

98 = 2(4x)+2(3x)

98 = 8x+6x

98 = 14x

∵ x = 7

Now, we will find out the length and width of the pool.

Length = 4x

= 4(7)

= 28 ft.

and,

Width = 3x

= 3(7)

= 21 ft.

Thus, the length of the pool is 28 feet and the width of the pool is 21 feet

Learn more information about 'Perimeter' here: brainly.com/question/89866

Answer:

(C) 18cm, 39cm, 21cm and 45cm.

Step-by-step explanation:

The quadrilateral HIJK has sides measuring 12 cm, 26 cm, 14 cm, and 30 cm.

When HIJK is dilated with a scale factor of 1.5, the side lengths becomes:

12 X 1.5 =18 cm

26 X 1.5 =39 cm

14 X 1.5 =21 cm

30 X 1.5 =45 cm

A dilation of HIJK with a scale factor of 1.5 will give us the side lengths:

18cm, 39cm, 21cm and 45cm.

The correct option is C.

Answer:

140672

Step-by-step explanation:

formula for cone volume=pi*r^2*h*1/3

80^2*3.14*21=422016

422016*1/3

=140672

Answer:

22+2[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Expanded it is

24-4[tex]\sqrt{2}[/tex]+6

This simplified leads to 22+2[tex]\sqrt{2}[/tex]

Hope this helps

Answer:

608 (D)

Step-by-step explanation:

To find the area of the prism, just add all the areas in the nets together.  

The rectangle in the middle has an area of 192 because it is a 12x16 triangle so you multiply the sides.

Both the rectangles on the top and bottom have an area of 160 because they are both a 10x16.  The total of the 2 rectangles would be 320 because 160+160=320.

The triangles on the right each have an area of 48 because the Base=12 and the Height= 8.  The formula for finding the area of a triangle is 1/2(BH).  1/2(12*8)= 1/2(96)= 48.  There are 2 triangles like this so the totla area of both triangles is 96.

To find the surface area, you just add them all up.  96+320+192= 608

Answer:

a) The observed proportion of wallets that were returned

  p = 0.45625

b) 95% of confidence intervals for Population proportion

 0.40168  , 0.51082)

c) The lower bound of the 95% confidence interval = 0.40168

d) The upper bound of the 95% confidence interval = 0.51082

Step-by-step explanation:

Step(i):-

a)

Given data the  researchers left a total of 320 wallets around Edinburgh, as though the wallets were lost. Each contained contact information including an address. Of the wallets, 146 were returned by the people who found them

Given sample size 'n' = 320

  Given data          'x ' = 146

Sample proportion

              [tex]p = \frac{x}{n}[/tex]

             [tex]p = \frac{x}{n} = \frac{146}{320} = 0.45625[/tex]

Step(ii):-

b) 95% of confidence intervals for Population proportion

Level of significance = 95% or 0.05%

[tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.05}{2} } = Z_{0.025} = 1.96[/tex]

95% of confidence intervals for Population proportion are determined by

[tex](p - Z_{0.025} \frac{\sqrt{p(1-p)} }{\sqrt{n} } , p + Z_{0.025} \frac{\sqrt{p(1-p)} }{\sqrt{n} })[/tex]

[tex](0.45625 - 1.96\frac{\sqrt{0.45625(1-0.45625)} }{\sqrt{320} } , 0.45625 + 1.96\frac{\sqrt{0.45625(1-0.45625)} }{\sqrt{320} })[/tex]

(0.45625 - 0.05457 , 0.45625 + 0.05457)

(   0.40168  , 0.51082)

c) The lower bound of the 95% confidence interval = 0.40168

d) The upper bound of the 95% confidence interval = 0.51082

Answer:

The Sum of two number is 15: x + y = 15

One of the numbers is 12 times the other: x = 12y:

System of equations:

x + y = 15

x = 12y

Plug x = 12y into equation one(x + y = 15)

12y + y = 15

13y = 15

y = 15/3

y ≈  1.15

Now we know x = 12y

x = 12(15/13) = 180/13

x = 180/13

x ≈ 13.85

The biggest number is x = 180/13.

Answer:

1385.622

Step-by-step explanation:

A=πr2=π·212≈1385.622

hope this helped

Volume of the bottom rectangle:

12 x 4.5 x 5.5 = 297 cubic cm

Volume of triangle:

1/2 x 12 x 5 = 30 x 4.5 = 135 cubic cm

Total volume = 297 + 135 = 432 cubic cm

Answer:

A) The linear relation between price and demand is:

[tex]d=-550x+2750[/tex]

The revenue R is:

[tex]R=-550x^2+2750x[/tex]

B) The profit functionP is:

[tex]P=-550x^2+2750x-30[/tex]

C) The largest monthly profit is obtained with a log-on fee of $2.5 per month. This corresponds to a profit of $3407.5.

Step-by-step explanation:

We have a site where the number of log-ons depends on our monthly fee. A linear relation is established between the price (log-on fee) and the number of log-ons.

We have two points for this linear relationship:

We will model the relation:

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

We can calculate the slope m as:

[tex]m=\dfrac{\Delta d}{\Delta x}=\dfrac{d_2-d_1}{x_2-x_1}=\dfrac{1375-1100}{2.5-3}\\\\\\m=\dfrac{275}{-0.5}=-550[/tex]

Then, replacing one point in the linear equation, we can calculate the intercept b:

[tex]d_1=mx_1+b\\\\1100=(-550)\cdot 3+b\\\\1100=-1650+b\\\\b=1100+1650=2750[/tex]

Then, the linear relation between demand and price is:

[tex]d=-550x+2750[/tex]

The revenue R can be expressed as the multiplication of the price and the demand:

[tex]R=x\cdot d=x(-550x+2750)=-550x^2+2750x[/tex]

If we have a fixed cost of $30 per month, the profit P is:

[tex]P=R-FC=-550x^2+2750x-30[/tex]

We can maximize the profit by deriving the profit function and making it equal to zero.

[tex]\dfrac{dP}{dx}=0\\\\\\\dfrac{dP}{dx}=-550(2x)+2750(1)=0\\\\\\-1100x+2750=0\\\\x=\dfrac{2750}{1100}=2.5[/tex]

This corresponds to a profit of:

[tex]P(2.5)=-550(2.5)^2+2750(2.5)-30\\\\P(2.5)=-550\cdot 6.25+6875-30\\\\P(2.5)=-3437.5+6875-30\\\\P(2.5)=3407.5[/tex]

Answer:

calculate the area of a square using the length * width formula, and then add the areas of the other triangles, of which you can calculate by using the base * height formula

Step-by-step explanation:

Answer:

Multiply the side length of the base by the slant height and divide by two. Then, multiply by 4. This will give you the lateral surface area of the pyramid.Step-by-step explanation:

Answer: D with the open circles at -10 and 10 with a line in between them.

Step-by-step explanation:

Since x has an absolute value sign around it this means that all the values will be positive which includes negative numbers.

Since the solution must be less than 10 we need all values under 10 which is 1-9.9 repeating. we can show the 9.9 repeating with an open circle on the value of 10. This also goes for the negative values for x as we can go up to -9.9 repeating because it will become positive.

The only graph that shows these values is D with the open circles at -10 and 10 with a line in between them.

Answer:

D

Step-by-step explanation:

Hope this helps

Answer:

x = 5

Step-by-step explanation:

Since TV bisects (equally divides) EF hence <EKT = 90°

Also <EKT = 5x+65

So

5x+65 = 90

5x = 90-65

5x = 25

Dividing both sides by 5

x = 5

Step-by-step explanation:

To find the inverse we just switch f(x) and x so we get :

x = 2f(x) + 1

2f(x) = x - 1

h(x) = 1/2x - 1/2

Hope this helps!

Answer:

x = 2f(x) + 1

2f(x) = x - 1

h(x) = 1/2x - 1/2

Step-by-step explanation:

Answer:

It is B I think

Step-by-step explanation:

D is incorrect

Answer:

Ariana is going to invest P($) in an account paying an interest rate of 3.4% compounded monthly.

After 14 years, the amount of money in Adrina's account is calculated by:

A = P x (1 + rate)^(time)

or

A = P x (1 + 3.4/12)^(14 x 12)

or

9200 = P x (1 + 3.4/12)^(14 x 12)

=> P = 9200/[(1 + 3.4/12)^(14 x 12)]

=> P = 5791.044$

Hope this helps!

:)

The value of the account to reach $9,200 in 14 years is $5,791.

Since interest rate of 3.4% compounded monthly. And, the amount is  $9,200 in 14 years

So, the value should be

[tex]A = P \times (1 + rate)^{(time)}\\\\A = P \times (1 + 3.4/12)^{(14 \times 12)}\\\\9200 = P \times (1 + 3.4/12)^{(14 \times 12)}\\\\ P = 9200\div [(1 + 3.4/12)^{(14 \times 12)]}[/tex]

P = $5791

hence, The value of the account to reach $9,200 in 14 years is $5,791.

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Answer:

A and A that is the answer

Answer:

a) 59.10% probability that 12 or fewer fish were caught.

b) 99.74% probability that 5 or more fish were caught.

c) 58.84% probability that between 5 and 12 fish were caught.

Step-by-step explanation:

I am going to use the normal approximation to the binomial to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

In this problem, we have that:

[tex]n = 29, p = 0.41[/tex]

So

[tex]\mu = E(X) = np = 29*0.41 = 11.89[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = 2.6486[/tex]

Find the following probabilities.

a) 12 or fewer fish were caught.

Using continuity correction, this is [tex]P(X \leq 12 + 0.5) = P(X \leq 12.5)[/tex], which is the pvalue of Z when X = 12.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{12.5 - 11.89}{2.6486}[/tex]

[tex]Z = 0.23[/tex]

[tex]Z = 0.23[/tex] has a pvalue of 0.5910

59.10% probability that 12 or fewer fish were caught.

b) 5 or more fish were caught.

Using continuity correction, this is [tex]P(X \geq 5 - 0.5) = P(X \geq 4.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 4.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{4.5 - 11.89}{2.6486}[/tex]

[tex]Z = -2.79[/tex]

[tex]Z = -2.79[/tex] has a pvalue of 0.0026

1 - 0.0026 = 0.9974

99.74% probability that 5 or more fish were caught.

c) between 5 and 12 fish were caught.

Using continuity correction, this is [tex]P(5 - 0.5 \leq X \leq 12 + 0.5) = P(4.5 \leq X \leq 12.5)[/tex], which is the pvalue of Z when X = 12.5 subtracted by the pvalue of Z when X = 4.5. So.

From a), when X = 12.5, Z has a pvalue of 0.5910

From b), when X = 4.5, Z has a pvalue of 0.0026.

So

0.5910 - 0.0026 = 0.5884

58.84% probability that between 5 and 12 fish were caught.

Answer:

The y-intercept of the line is 2

Step-by-step explanation:

You could try to find the slope of the line and then find the intercept with y axis by sloving b = y - ax

But here it seems easy enough once you see that the x values in the table increase by a factor of 8 and the y values in the table increase by a factor of 20.

(By the way, this is enough to give you the slope, because it is 8/20 ). But why bother?

Just extrapolate the table to the left, and you will find the y value where x = 0

x 0 8 16 24 32

y 2 22 44 64 84

So the y-intercept of the line is 2.

Extra:

The full equation of the line is:

y = 8/20x + 2

Answer:

(0,4)

Step-by-step explanation:

Answer:

The slope is 2, while the y-intercept is 4. This equation represents starting with  4 cards and adding  2 cards each week.

Step-by-step explanation:

Given the equation which describes the number of cards, y, you have after x weeks: y=2x+4

Comparing this with the slope intercept form of the equation of the line: y=mx+b, where:

We have that:

Slope

Slope, m=2.

A slope of 2 indicates that you buy 2 cards per week.

The y-intercept

The y-intercept of the line, b=4.

This is the starting value. In this case, it represents the number of cards you were given by your friend.

The slope is 2, while the y-intercept is 4. This equation represents starting with  4 cards and adding  2 cards each week.

Answer:

10.60%

Step-by-step explanation:

We have to solve the above we have to apply bimonial and add each one, like this:

p (x <= 3) = p (x = 0) + p (x = 1) + p (x = 2) + p (x = 3)

p (x <= 3) = 8C0 * (0.65) ^ 0 * (0.35) ^ 8 + 8C1 * (0.65) ^ 1 * (0.35) ^ 7 + 8C2 * (0.65) ^ 2 * (0.35) ^ 6 + 8C3 * (0.65) ^ 3 * (0.35) ^ 5

p (x <= 3) = 8! / (0! (8-0)!) * (0.65) ^ 0 * (0.35) ^ 8 + 8! / (1! (8-1)!) * (0.65 ) ^ 1 * (0.35) ^ 7 + 8! / (2! (8-2)!) * (0.65) ^ 2 * (0.35) ^ 6 + 8! / (3! (8-3)!) * (0.65) ^ 3 * (0.35) ^ 5

p (x <= 3) = 0.1060

therefore the probability is 10.60%

Answer:

The probability that at most 3 of the southerners believe in angels is 10.61%

Step-by-step explanation:

Given;

65% believe in angels = p

then, 35% will not believe in angel = q

total sample number, n = 8

The probability that at most 3 southerners believe in angels is calculated as;

= p( non believe in angel) or p( 1 southerner believes and 7 will not believe) or p( 2 southerner believe and 6 will not believe) or p( 3 southerner believe and 5 will not believe)

= 8C₀(0.65)⁰(0.35)⁸ + 8C₁(0.65)¹(0.35)⁷ + 8C₂(0.65)²(0.35)⁶ + 8C₃(0.65)³(0.35)⁵

= 1(1 x 0.000225) + 8(0.65 x 0.000643) + 28(0.4225 x 0.00184) + 56(0.2746 x 0.00525)

= 0.1061

= 10.61%

Therefore, the probability that at most 3 of the southerners believe in angels is 10.61%

Answer:

52

Step-by-step explanation:

24+28 = 52

52 - 24 = 28

Answer: Rectangular pyramid

Step-by-step explanation:

When you think about it, a pyramid has 3 faces that are triangular!

If you found this answer helpful, give it a five-star rating and a thanks! I would really appreciate it!

You can even give it a brainliest if you want! ;)

Answer:

the mean is 20.8.

Step-by-step explanation:

Add all the numbers to get 104. Then, divide it by how many score there were, 5. 104/4= 20.8

Solution,

Given data: 17,19,19,23,26

summationfX=104

N(total no.of items)=5

Now,

Mean=summation FX/N

=104/5

=20.8

hope it helps

Good luck on your assignment

Answer:

About 0.642

Step-by-step explanation:

Answer: 0.5

Step-by-step explanation: I think that the answer.

Answer: A

Step-by-step explanation:

First, the problem is g(f(x)). You would plug in f(x) wherever you see an x in g(x). To find the domain, you take the bottom function, and set it equal to 0.

[tex]\sqrt{x-2} =0[/tex]

When you solve that, you get x=2. You know your domain is x≥2, but there is as asymptote at x=11. That means the graph never reaches x=11, but gets very close. You find that by setting the entire equation equal to 0 and solve from there.

Answer:

Length of segment PZ = 6 units

Step-by-step explanation:

As per theorem of intersecting chords in a circle ;

"Product of lengths of line segments on each chord are equal".

From the figure attached,

Chords XY and WZ are intersecting at point P in a circle.

By theorem;  XP × PY = WP × PZ

7 × 12 = 14 × PZ

PZ = [tex]\frac{84}{14}[/tex]

PZ = 6 units

Therefore, length of the segment PZ = 6 units.

Answer:

2x - 5y = 9 // standard form

y + 6 = -3 (x-1) // point slope form

y = -x + 8 // slope intercept form

Step-by-step explanation: