Kevin is 3 years older then Daniel. Two years ago, Kevin was 4 times as old as Daniel. How old is Kevin now

Start with y: [tex]y[/tex]

Subtract 4: [tex]y-4[/tex]

Multiply by 9: [tex]9(y-4)=9y-36[/tex]

Answer:

[tex]9(y - 4) \\ = 9y - 36[/tex]

Step-by-step explanation:

[tex]start \: \: \: \: \: \: \: \: \: \: = y \\ subtract \: = y - 4 \\ times \: \: 9 \: \: \: = 9(y - 4) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 9y - 36[/tex]

Answer:

Step-by-step explanation:

By using j, s ,h to represent the number of jerseys,shorts and hats respectively.

System of Equations:

j + s + h = 40

j = s + h

50j + 20s + 15h = 1350

(s + h) + s + h = 40

2s + 2h = 40

s + h = 20

s = 20 – h

50[(20 – h) + h] + 20(20 – h) + 15h = 1350

50(20) + 400 – 20h + 15h = 1350

1400 – 5h = 1350

5h = 50h

h = 10

s = 20 – 10

s = 10

j = 10 + 10

j = 20

20 jerseys, 10 shorts, 10 hats

They order 20 jerseys, 10 shorts, 10 hats

A system of equations, also known as a set of simultaneous or equation system, is a finite set of equations for which we sought the common solutions.

According to the question

By using j, s ,h to represent the number of jerseys ,shorts and hats respectively.

System of Equations:

j + s + h = 40.   .   .   .   . Equation (1)

j = s + h.   .   .   .   .   .   .Equation (2)

50j + 20s + 15h = 1350 .    .    .    .     .      .     Equation (3)

By putting the value of j = s + h in equation (1)

(s + h) + s + h = 40

2s + 2h = 40

s + h = 20

s = 20 – h.   .   .   .   .   .   .   .Equation (4)

By putting the value of j = s + h and s = 20 - h in equation (3) we get

50[(20 – h) + h] + 20(20 – h) + 15h = 1350

50(20) + 400 – 20h + 15h = 1350

1400 – 5h = 1350

5h = 50h

h = 10

s = 20 – 10

s = 10

j = 10 + 10

j = 20

Hence , 20 jerseys, 10 shorts, 10 hats

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The Euclid's mug holds the most root beer.

Step-by-step explanation:

Euclid's mug :

Height = 8 inches

Radius = 3 inches

Volume = π(r x r) h

= (3.14) (9) 8

= 226.08 cubic inches

Aristotle's mug:

Height = 18 inches

Diameter = 4 inches

Radius = 2 inches

Volume = (1/3) π(r x r) h

= (1/3) (3.14) (4) 18

= 37.68 cubic inches

The Euclid's mug holds the most root beer.

9514 1404 393

Answer:

  43.1

Step-by-step explanation:

The perimeter is the sum of the lengths of the two straight edges, each of which is 9 units long, and the circumference of the full circle of diameter 8 units. The circumference is pi times the diameter.

  P = 2(9) +8π = 18 +25.13

  P ≈ 43.1 . . . units

The perimeter of the combination of a rectangle and two semicircles is found by adding the straight sides of the rectangle and the circumference of the resulting full circle formed by the semicircles. In this case, it's 43.1 units.

To find the perimeter of the combined shape consisting of a rectangle and two semicircles, we need to consider the lengths of the straight parts as well as the circumference of the circles. The perimeter is the sum of the lengths of the straight sides of the rectangle, each of which is 9 units long, and the circumference of the full circle with a diameter of 8 units.

Using the formula for the circumference of a circle (C = πd) where d is the diameter, the circumference of the full circle would be 8π. So, the total perimeter of the shape is:

P = 2*(9) + 8π

That gives us:

P = 18 + 25.13 approximately

So, P ≈ 43.1. . . units

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Answer:

the domain is anything with the x-axis and range the y-axis

Answer:

Domain- is the set of all possible x-values or "input" for the function that gets you to the "output" or y-values. Range- is the difference between the highest and the lowest values.

Step-by-step explanation:

Answer: 12 cupcakes will get chocolate frosting

Step-by-step explanation: John started with 30 cupcakes and spresd mint icing on 1/5 of these. That means he did the following

Mint icing = 30 x 1/5

Mint icing = 6

That leaves him with a total of 30 minus 6 cupcakes which equals 24 cupcakes.

Next he spreads chocolate icing on half of the remaining, that is half of 24. That means he did the following;

Chocolate icing = 24 x 1/2

Chocolate icing = 12

Therefore 12 cupcakes will get chocolate frosting

Answer:

[tex]log(10a)[/tex]

Step-by-step explanation:

[tex]log(a\sqrt{44})+log(a \sqrt275)-log(11a)[/tex]

We can simplify this using these log laws:

[tex]log(a)+log(b)=log(ab)\\log(a)-log(b)=log(\frac{a}{b})[/tex]

[tex]log(\frac{a^2\sqrt{44} \sqrt{275}}{11a})[/tex]

We also have laws to simplify square roots

[tex]\sqrt{a}*\sqrt{b} = \sqrt{ab}[/tex]

So this becomes

[tex]log(\frac{a^2\sqrt{12100}}{11a})[/tex]

[tex]\sqrt{12100} = 110[/tex]

so this becomes

[tex]log(\frac{110a^2}{11a})=log(10a)[/tex]

Answer:

[tex]2x^4\sqrt{5}[/tex]

Step-by-step explanation:

[tex]\sqrt{20x^8}[/tex] = [tex]\sqrt{4*5*(x^4)^2}[/tex] = [tex]2x^4\sqrt{5}[/tex]

The solution of the equation after remove all perfect squares from inside the square root is,

⇒ 2x⁴√5

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ √20x⁸

Now, We can simplify and remove all perfect squares from inside the square root as;

⇒ √20x⁸

⇒ √2 × 2 × 5 × (x⁴)²

⇒ 2x⁴√5

Thus, The solution of the equation after remove all perfect squares from inside the square root is,

⇒ 2x⁴√5

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Answer:

3 1/5 ft

Step-by-step explanation:

We can set up a proportion:

[tex]\frac{1}{2\frac{2}{7} } =\frac{1\frac{2}{5} }{x}[/tex] , where x is how long the pants are in real life

Cross multiply:

x = (2 2/7) * (1 2/5)

It's easier if we have improper fractions, so convert the mixed numbers into improper fractions:

2 2/7 = 16/7

1 2/5 = 7/5

Now, put these back in:

x = (16/7) * (7/5) = 16/5 = 3 1/5

Thus, in real life, the pants would be 3 1/5 ft long.

Hope this helps!

Answer:

3⅕ ft

Step-by-step explanation:

1 in --> 2 2/7 ft

2 2/7 = 16/7

1 2/5 in = 7/5 in

7/5 × 16/7 = 16/5 ft

3 1/5 ft

Answer:

2 pounds of turkey?

Step-by-step explanation:

Margot will therefore need 3 pounds of turkey to make 4 liters of her turkey chili.

To find out how many pounds of turkey Margot will need to make 4 times her turkey chili recipe for 1 liter, we first identify the amount needed for 1 liter based on the given ratio, and then multiply that amount by 4.

Margot uses 1/2 pounds of turkey for 2/3 liters of turkey chili. If we need to find out the amount for 1 liter, we can set up a proportion:

1/2 pounds turkey / (2/3 liters) = x pounds turkey / 1 liter

We cross multiply to solve for x:

(1/2) * 1 = x * (2/3)

Now we solve for x:

x = (1/2) * (3/2)

x = 3/4 pounds of turkey for 1 liter of chili

For 4 liters of chili (4 times the recipe), we would multiply:

4 * (3/4 pounds) = 3 pounds of turkey

Answer:

39.6x +26.4

Step-by-step explanation:

The area of a rectangle is given by

A = l*w

A = 13.2 * (3x+2)

Distribute

    39.6x +26.4

Answer: (x+3)2 + (y+5)2 =36

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

The answer is 8. And for the love of God people if you don't know the answer don't waste an answer space just for the points. It makes everyone mad. Stop. Just cut it out.

Step-by-step explanation:

The equation of the line that passes through the point (6,-5)and has a slope of [tex]-\dfrac{3}{2}[/tex] is y+5 = -3/2(x+6).

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Which is the required equation of a line in a point-slope form.

WE need to find the equation of the line that passes through the point (6,-5)and has a slope of [tex]-\dfrac{3}{2}[/tex].

Given:  m=-3/2  and  x_1 = -6  and  y_1 =-5

So the required equation of a line in a point-slope form;

y+5 = -3/2(x+6)

Hence, The equation of the line that passes through the point (6,-5)and has a slope of [tex]-\dfrac{3}{2}[/tex] is y+5 = -3/2(x+6).

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The equation of the line that passes through the point (6, -5) and has a slope of -3/2 is y = -3/2x + 4.

To find the equation of the line, we can use the point-slope form of a linear equation, which is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. In this case, the point is (6, -5) and the slope is -3/2. Plugging these values into the equation, we get y - (-5) = -3/2(x - 6), which simplifies to y + 5 = -3/2(x - 6).

Expanding the equation further, we get y + 5 = -3/2x + 9. To isolate y, we can subtract 5 from both sides of the equation, resulting in y = -3/2x + 4. Therefore, the equation of the line that passes through the point (6, -5) and has a slope of -3/2 is y = -3/2x + 4.

Answer:

Im pretty sure its A

Step-by-step explanation:

Therefore, the option (A) is the correct answer.

What is the scatter plot?

Scatter plots are the graphs that present the relationship between two variables in a data-set. It represents data points on a two-dimensional plane or on a Cartesian system.

As per the given information, the correct graph is in option (A) because in this graph it is moving upward with respect to the line of curve.

Hence, the option (A) is the correct answer.

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Answer:

Step 2 is where this person went wrong

Step-by-step explanation:

Should be

11 + (9)(3)= x

11 + 27= x

x = 38

Answer:

Step 2 is where the error started. You can see the person did the order of operations wrong. The person was supposed to multiple (9)(3) first because of PEMDAS; (9)(3)=27 and then you add the 27 to 11 and get 38

Step-by-step explanation:

Answer:

a = -1  b = -9   c = -20

x1 = [--9 +- (sq root -9^2 - 4 * -1 * -20)] / 2 * -1

x1 = 9 +sq root (81 - 80) / -2

x1 = [9 + 1 ] / -2

x1 = -5

x2 = 9 -sq root (81 - 80) / -2

x2 = 8 / -2

x2 = -4

Step-by-step explanation:

Answer:

3/9 or 33.33%

Step-by-step explanation:

there are 9 total cans and 3 pink cans. So, that'd be 3/9 or 33.33%

hope this helps!

Answer:

1/3

Step-by-step explanation:

Answer:

6.5 units

Step-by-step explanation:

In circle with center O, AB is diameter.

[tex] \therefore m\angle ACB = 90°\\[/tex]

(Angle inscribed in a semicircle)

[tex] \therefore \: in\: \triangle ABC, \:AB \: is\: hypotenuse \\[/tex]

By Pythagorean theorem:

[tex]AB = \sqrt{ {12}^{2} + {5}^{2} } \\ = \sqrt{144 + 25} \\ = \sqrt{169} \\ AB \: = 13 \\ r = \frac{13}{2} = 6.5 \: units[/tex]

Answer: A

Step-by-step explanation:

Answer:

[tex]V(x) = 4x^3 - 54x^2 + 180x[/tex]  

Step-by-step explanation:

We are given the following in the question:

A rectangular piece of cardboard of side 15 inches by 12 inches is cut in such that a square is cut from each corner.

Let x be the side of this square cut. When it was folded to make the box.

The height of box =

[tex]x\text{ inches}[/tex]

The length becomes

[tex](15-2x)\text{ inches}[/tex]

The width becomes

[tex](12-2x)\text{ inches}[/tex]

Volume of box =

[tex]V =l\times w\times h[/tex]

Putting values, we get

[tex]V(x) = (15-2x)(12-2x)x\\V(x) = (180-30x-24x+4x^2)(x)\\V(x) = (4x^2 - 54x + 180)(x)\\V(x) = 4x^3 - 54x^2 + 180x[/tex]

is the required polynomial for volume of box formed.

Answer:

The Length , width and height of solid are 4 feet , 3 feet and 7 feet respectively.

Step-by-step explanation:

Let the width of rectangular solid be x

We are given that the length of the container must be one meter longer than the width

So, Length of solid = x+1

We are also given that height must be one meter greater than twice the width

So, Height of solid = 2x+1

So, Volume of solid = [tex]Length \times Width \times height[/tex]

Volume of solid = [tex](x+1) \times x \times (2x+1)[/tex]

Volume of solid =[tex](x^2+x)(2x+1)[/tex]

Volume of solid =[tex]2x^3+x^2+2x^2+x=2x^3+3x^2+x[/tex]

We are given that  a rectangular solid must have a volume of 84 cubic meters

So, [tex]2x^3+3x^2+x=84\\2x^3+3x^2+x-84=0\\(x-3)(2x^2+9x-28)=0\\[/tex]

On equating

x-3=0

x=3

So, Length of solid = x+1=3+1 = 4 feet

Height of solid = 2x+1 =2(3)+1=7 feet

Width of solid = 3 feet

Hence The Length , width and height of solid are 4 feet , 3 feet and 7 feet respectively.

The volume of a rectangular solid shipping container = 84 cubic meters

The width of the container = 3m

The length of the container = (x + 1) = (3+1) = 4m

The height of the container = (2x + 1) = (2 x 3 + 1) = 7m

Given:

The volume of a rectangular solid shipping container = 84 cubic meters

Let: The width of the container be x

The length of the container must be one meter longer than the width.

So, The length of the container be (x + 1)

The height must be one meter greater than twice the width.

So, The height of the container be (2x + 1)

To find the dimensions of the container

The Volume of the container = Length x Width x Height

[tex]84=x(x+1)(2x+1)[/tex]

[tex]84=(x^{2} +x)(2x+1)[/tex]

[tex]84=2x^{3} +3x^{2} +x[/tex]

[tex]2x^{3} +3x^{2} +x-84=0\\(x-3)(2x^{2} +9x+28)=0\\x-3=0\\x=3[/tex]

So, The width of the container = 3m

The length of the container = (x + 1) = (3+1) = 4m

The height of the container = (2x + 1) = (2 x 3 + 1) = 7m

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Answer:

Step-by-step explanation:

Confidence interval is written as

Sample proportion ± margin of error

Margin of error = z × √pq/n

Where

z represents the z score corresponding to the confidence level

p = sample proportion. It also means probability of success

q = probability of failure

q = 1 - p

p = x/n

Where

n represents the number of samples

x represents the number of success

a) From the information given,

Margin of error = 0.02

p = 0.3

q = 1 - 0.3 = 0.7

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.5 = 0.05

α/2 = 0.05/2 = 0.025

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.05 = 0.975

The z score corresponding to the area on the z table is 1.96. Thus, confidence level of 95% is 1.96

Therefore,

0.02 = 1.96 × √(0.3 × 0.7)/n

0.02/1.96 = √0.21/n

0.0102 = √0.21/n

Taking square of both sides, it becomes

0.00010404 = 0.21/n

n = 0.21/0.00010404

n = 2018

Sample size = 2018

b) if n = 2018

x = 520

Then

p = 520/2018 = 0.26

Point estimate of the proportion of smokers in the population is 0.26

c) q = 1 - 0.26 = 0.74

the 95% confidence interval for the proportion of smokers in the population is

0.26 ± 1.96 × √(0.26)(0.74)/2018

= 0.26 ± 0.019

Answer:

a) n = 2017

b) Point estimate is 0.2578

c) 95% Confidence Interval is Minimum = 0.2387,  Maximum  0.2769

Step-by-step explanation:

Here we have

At 95%, we have

[tex]z_{\alpha /2}[/tex] =  1.96

To determine sample size, we have

[tex]n = \frac{(z_{\alpha /2})^2 \hat p \hat q}{E^2}[/tex]

Where:

[tex]\hat p[/tex] = 0.3

[tex]\hat q[/tex] = [tex]1-\hat p[/tex] =  0.7

E = 0.02

Therefore, n = 2016.84 ≈2017

b) The point estimate is given by

[tex]\hat p =\frac{x}{n} = \frac{520}{2017}[/tex] = 0.2578

c) The confidence interval is given by;

[tex]CI=\hat{p}\pm z\times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex]

Which gives

[tex]CI=0.2578\pm 1.96\times \sqrt{\frac{0.2578(1-0.2578)}{2017}}[/tex]

Hence CI = Min = 0.2387 to Max = 0.2769

Answer:

18,500  , 1 , 1.03

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.  

f(t) =18,500(1.03)^t  

1st blank:

19,055

1.03

3

18,500

2nd blank:

t years

2 years

3 years

1 year

3rd blank:

19,055

3

18,500

1.03

My answer:

Given that:  f(t) =18,500*[tex]1.03^{t}[/tex]

1st blank:

Initial value when t = 0, so we have:

f(0) =18,500*[tex]1.03^{0}[/tex]

[tex]f(0) =18,500(1)\\ f(0) =18,500[/tex]

So we choose D for 1st blank

2nd and 3rd blank:

Because it's an exponential function f(t) =18,500*[tex]1.03^{t}[/tex]  , with every value of t increment f(t) increase by a factor of 1.03 . So  Every  1 year the number of students who enroll at the university increases by a factor of 1.03

=> 2nd blank: 1

=> 3rd blank: 1.03

Hope it will find you well.

Answer:

The first blank this is 18,500. Second blank is 1. The third blank is 1.03. hope this helps

Step-by-step explanation:

Answer:

Probability thay the next page she turns to will have an advert = 0.4042

Step-by-step explanation:

In the last 12 issues of the magazine, 384 out of 950 pages contain an advertisement.

We now need to find the probability that the next page has an advertisement.

Probability of an event

= n(of that event) ÷ n(total sample spaces)

n(of the event of an advert) = number of pages with adverts in those issues = 384

n(total sample spaces) = total number of pages = 950

Probability that the next page or any page at all will have an advert = (384/950) = 0.4042

Hope this Helps!!!

Answer:

[tex]4(x+4)=4x+16[/tex]

Step-by-step explanation:

a) The Greatest Common Factor, of both terms 4x and 16 is 16.

4,16|2

2,8|2

1,4|2

1,2|2

1,1| = 2*2*2*2=16

b) Let's divide each term by 4 their

4x+16

[tex]\frac{4x}{4}=x\\\\\frac{16}{4}=4[/tex]

Placing their common divisor outside the parentheses, and inside the sum of this result:

[tex]4(x+4)=4x+16[/tex]

The equivalent expression after factoring out the GCF is [tex]\(4(x + 4)\)[/tex].

To apply the distributive property to the expression \(4x + 16\), we can factor out the greatest common factor (GCF) of the two terms. In this case, the GCF of 4 and 16 is 4. By dividing each term in the expression by 4, we can factor out the GCF.

\(4x\) divided by the GCF (4) is \(x\), and \(16\) divided by the GCF (4) is \(4\). Therefore, the expression \(4x + 16\) can be factored as \(4(x + 4)\) using the distributive property.

To summarize:

- GCF of 4 and 16 is 4.

- \(4x\) divided by the GCF (4) is \(x\).

- \(16\) divided by the GCF (4) is \(4\).

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Answer:

240

Step-by-step explanation:

Multiply everything together. 6*4*5 is 240.

Answer:

Amount of sand=Area of triangle(ABC)=1/2*AB*BC

Dimension of rectangle as  length=BC and breadth=AB

Step-by-step explanation:

Given:

Pedro building a playground in shape of right angled triangle.

To Find:

How much sand he need to buy

And if playground changed to rectangle what will be the dimensions.

Solution:

Consider a ΔABC be the play ground vertex of playground,

And AB and BC be the sides making right angle.

The sand required to fill ground will be the amount of are covered by the ABC triangle.

So,

Area Of triangle(ABC)=1/2* base* height

Here base will be BC and height =AB

Therefore Area of Triangle(ABC)=1/2*BC*AB

Depending on the lengths of base and height amount of sand will be decided.

Now,

For Rectangle dimensions,

We know that if same sized triangles composes each other forms a rectangle.

It requires two triangle to form one rectangle as follows

(Refer the attachment)

Same sized Triangle ACD is imposed on it  to from rectangle ABCD.

So dimension for rectangle will be same as the triangle

Dimension=length and breadth

i.e. length=base of triangle=BC

Breadth=Height of triangle=AB

i.e Breadth =AB.