4) Every 10 years in April, the population of Boston is recorded. In 1990, Boston had a
population of 4,500 people. From 1990 to 2000, the population increased by 15%. From 2000
to 2010, the population decreased by 4%. That was Boston's population in 2010?
A
4,527
B
4,968
с
4,995
D
5,382

Answer:

There is a 9 out of 14 chance that the marble will be white or there is a 3 out of 5 chance along with a 6 out of 9 chance.

Step-by-step explanation:

Since there's a total of 14 marbles from both bags and there are a possible 9 white marbles, it would be a total of 9 out of 14, or it would be separate and be a 3 out of 5 chance with a 6 out of 9 chance.

Answer:

First number: 6

Second number: 16

Third number: 32

Step-by-step explanation:

x + y + z = 54

z = 2y

y = x + 10

Now you can substitute y = x + 10 into z = 2y

The equation becomes z = 2x + 20

Now plug it into the main equation.

x + x + 10 + 2x + 20 = 54

4x + 30 = 54

4x = 24

x = 6

y = 16

z = 32

Answer:

The triangle is an acute scalene triangle

Step-by-step explanation:

None of the sides have the same length so the triangle is scalene

All of the angles are less than 90 degrees so all of the angles are acute

The triangle is an acute scalene triangle

Answer:

A.) 4991/157216

B.) 2401/1336336

C.) 16399/314432

Step-by-step explanation:

Given the following :

Granny Smith = 23

Honey crisp = 14

Red delicious = 31

Probability = (number of required outcome / number of possible outcomes)

Number of possible outcomes = 23 + 14 + 31 = 68

With replacement :

A.) one of each :

P(granny Smith) × P(Honey crisp) × P(Red delicious)

P(granny Smith) = 23/68

P(Honey crisp) = 14/68 = 7/34

P(red delicious) = 31/68

(23/68 × 7/34 × 31/68) = 4991/157216

B) 4 honey crisp:

P(4 Honey crisp) = P(honey crisp) × P(honey crisp) × P(honey crisp) × P(honey crisp)

7/34 × 7/34 × 7/34 × 7/34 = 2401/1336336

C.) 2 granny Smith and 1 red delicious

P(granny Smith) × P(granny Smith) × P(red delicious)

23/68 × 23/68 × 31/68 = 16399/314432

Answer: The slope is infinite

Step-by-step explanation:

An infinite slope is simply a vertical line. When you plot it on a line graph, an infinite slope is any line which runs parallel to the y-axis. You can also describe this as any line that doesn't move along the x-axis but stays fixed at one constant x-axis coordinate, making the change along the x-axis.

Answer:

graph a: $10 dollars an hour

graph b: 10

Step-by-step explanation:

slope is calculated by rise over run ([tex]\frac{rise}{run}[/tex]) which means how many the line goes up divided by how many the line goes over (to the right)

negative slope is how many the line goes down divided by how many the line goes over (to the right)

Answer:

C

Step-by-step explanation:

to add the two equations, you have to make sure that the y's are the same. you would do this by multiplying each equation by the other equation's y variable

A prism is a three-dimensional shape with the same cross-section all the way through.

A prism is a solid shape that is bound on all its sides by plane faces.

A prism is a type of three-dimensional (3D) shape with flat sides. It has two ends that are the same shape and size (and look like a 2D shape).It has the same cross-section all along the shape from end to end; that means if you cut through it you would see the same 2D shape as on either end.

Hence, a prism is a three-dimensional shape with the same cross-section all the way through.

Learn more about prisms, click;

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[tex]\frac{30}{6+4}[/tex]

[tex]\frac{30}{10}[/tex]

[tex]=3[/tex]

[tex]3*6:3*4[/tex]

[tex]18:12[/tex]

Answer:

4

Step-by-step explanation:

10÷2.5

Answer:

4 plants

Step-by-step explanation:

She can grow 4 plants because 10/2.5 is equal to 4. So, the answer is 4 plants.

Answer:

2

Step-by-step explanation:

We can find the slope between two points by using

m= (y2-y1)/(x2-x1)

   = (3 - -3)/(0 - -3)

   = (3+3)/(0+3)

   = 6/3

   =2

Answer:

The slope of the line is 2

Step-by-step explanation:

using rise/run will help you figure this out :)

Answer:

Subtract  12  from  7 = -5

Answer:

8 - 35

a. 350 unit²

b. 81.23  unit²

c. 41.57 unit²

8 - 36

Beth should buy 3 bags of fertilizer

Step-by-step explanation:

8 - 35

a. The figure consists of 9 isosceles triangles of side lengths 11 and vertex angle = 360/9 = 40°

Hence base angles = (180 - 40)/2 = 70°

Therefore, the base of the triangles = sin(40) × 11/sin(70) = 7.52

Hence area of figure = 9 × 0.5 × 7.52 × √(11² - (7.52/2)²) =349.99 ≈ 350 unit²

b. Area of a decagon

We note that the vertex angle = 36°

∴ Half the base = tan(18) × 5 = 1.62

Area = 10 × 1.62 × 5 = 81.23  unit²

c. The area of a hexagon = [tex]s^2 \times \dfrac{3\sqrt{3} }{2}[/tex]

s = 4 therefore, the area = [tex]4^2 \times \dfrac{3\sqrt{3} }{2} = 41.57 \, unit^2[/tex]

8 - 36

Area, A of a regular pentagon = [tex]A = a^2 \times \dfrac{1}{4} \sqrt{5(5 + 2\sqrt{5} )}[/tex]

a = 15 ft., therefore, A = [tex]15^2 \times \dfrac{1}{4} \sqrt{5(5 + 2\sqrt{5} )}[/tex] = 387.11 ft.²

Therefore, since a bag of fertilizer can fertilize 150 ft.², the number of bags of fertilizer that will fertilize 387.11 ft.² will be 387.11/150 = 2.58 bags

Therefore, since 2 bags of fertilizers will not be enough, Beth should buy 3 bags of fertilizer.

Answer:

see explanation

Step-by-step explanation:

Given

f(x) = 2x + 1

(a)

To evaluate f(2) substitute x = 2 into f(x), that is

f(2) = 2(2) + 1 = 4 + 1 = 5

(b)

let y = f(x) and rearrange making x the subject

y = 2x + 1 ( subtract 1 from both sides )

y - 1 = 2x ( divide both sides by 2 )

[tex]\frac{y-1}{2}[/tex] = x

change y back into terms of x and x = [tex]f^{-1}[/tex] (x) , thus

[tex]f^{-1}[/tex] (x ) = [tex]\frac{x-1}{2}[/tex]

(c)

To evaluate the inverse function substitute x = 7, that is

[tex]f^{-1}[/tex] (7) = [tex]\frac{7-1}{2}[/tex] = [tex]\frac{6}{2}[/tex] = 3

Answer:

x^2 + {a/(a + b) + (a + b)/a}x + 1 = 0

Delta =  {a/(a + b) + (a + b)/a}^2 - 4

         =  {a/(a + b)}^2 + {(a + b)/a}^2 + 2 - 4

         =  {a/(a + b)}^2 + {(a + b)/a}^2  - 2

         =  {a/(a + b) - (a + b)/a}^2

If a is not equal to zero and a is not equal to -b => delta is always larger than 0

=>  Solution 1 =  - [ {a/(a + b) + (a + b)/a} + |{a/(a + b) - (a + b)/a}| ]/2

=>  Solution 2 = - [ {a/(a + b) + (a + b)/a} - |{a/(a + b) - (a + b)/a}| ]/2

Hope this helps!

:)

Answer:

if the marble slab is 1 cm³ in volume the mass is 2.7 g but u did not put a volume

Answer:

The answer to your question: Similar

Step-by-step explanatioN

i picked this answer because they have one comparison- same shape

what is comparison- the same features in something  between 2 objects or more

this also means similar

so it is similar

Answer:

Similar

Step-by-step explanation:

Answer:Week 1:  $35.40

              Week 2: $40.90

              Week 3: $46.40

               Week 4: $51.90

Step-by-step explanation:

29.90 + 5.50(x) = y

replace x with 1, 2, 3, or 4 for each week.

Answer:

[tex]z = 362\,botellas[/tex]

Step-by-step explanation:

(This exercise has been presented in Spanish and for that reason explanation will be held in Spanish)

La cantidad de botellas de 0,25 litros que se llenan con 49 litros de yogurt es:

[tex]x = \frac{49\,L}{0.25\,\frac{L}{botella} }[/tex]

[tex]x = 196\,botellas[/tex]

La cantidad remanente de yogurt es:

[tex]V_{r} = 132\,litros - 49\,litros[/tex]

[tex]V_{r} = 83\,litros[/tex]

Ahora, la cantidad de botellas de 0,5 litros que se llenan con el volumen remanente es:

[tex]y = \frac{83\,litros}{0.5\,\frac{litros}{botella} }[/tex]

[tex]y = 166\,botellas[/tex]

Finalmente, el total de botellas a llenar es:

[tex]z = 196\,botellas + 166\,botellas[/tex]

[tex]z = 362\,botellas[/tex]

Answer:

£1.6

Step-by-step explanation:

£20 ÷ £2.3= 8 remainder 1.6

change= £1.6

Answer:

1.60 euros

Step-by-step explanation:

2.30 times 8 = 18.40

20-18.40 = 1.60

Answer: x = 3

Step-by-step explanation:

From the question,

5x² – 18 = 27

Collect the like terms

5x² = 27 + 18

5x² = 45

We can th n divide both side by 5 which is the coefficient of x²

5x²/5 = 45/5

x² = 9

To get the value of x, we find the square root of 9

x² = 9

x =✓9

x = 3

The value of x is 3

Answer:

Step-by-step explanation:

I used Cramer's Rule to find y, since we can isolate and solve for individual variables using Cramer's Rule.  Do that by finding the determinant of the matrix, |A|.  The matrix A looks like this:

2   -2   1

-1     3   2

1    -4   -3

and we find the determinant of a 3x3 by expanding it.  Do that by picking up the first 2 columns and throw them on at the end, like this:

2   -2    1     2   -2

-1     3    2    -1    3

1    -4    -3    1    -4

and find the determinant by multiplying along the 3 major axes and subtract from that the product of the 3 minor axes:

[(2*3*-3)+(-2*2*1)+(1*-1*-4)] - [(1*3*1)+(-4*2*2)+(-3*-1*-2)] which simplifies to

-18 - (-19) = 1

So the determinant of the matrix A is |A| = 1.

Now to find the determinant of Ay, we replace the y column with the solutions and so the same thing by expansion and then multiplying and subtracting:

2    -7     1     2     -7

-1      0     2    -1     0

1      1     -3     1      1

and find the determinant of y:

[(2*0*-3)+(-7*2*1)+(1*-1*1)] - [(1*0*1)+(1*2*2)+(-3*-1*-7)] which simplifies to

-15 - (-17) = 2

So the detminant of y is |Ay| = 2

We can solve for the variable now by dividing Ay by A:

2 / 1 = 2

So the solution for y = 2

Answer:

[tex]75^{\circ}[/tex]

Step-by-step explanation:

Given: [tex]\csc (x) = 1.0353[/tex]

To find: angle to the nearest degree

Solution:

A triangle is a polygon that has three sides, three angles ,and three vertices.

Trigonometry explains the relationship between the sides and angles of the triangle.

The angle can be expressed in two forms: degrees or radians.

[tex]\csc (x) = 1.0353\\x=74.995\approx 75^{\circ}[/tex]

Answer:

Two real solutions

Step-by-step explanation:

We have the equation [tex]u^2=80[/tex]

To get a solution, we must solve for u.

When we solve for u, we need to square root each side, but when we do this, we must add a ± to the side that opposite to the u in order to compensate. This is because you could get 80 in two different ways:

[tex](\sqrt{80} )(\sqrt{80})=80 \\\\(-\sqrt{80} )(-\sqrt{80})=80[/tex]

This would mean that when we solve for u, we would get [tex]u=[/tex] ± [tex]\sqrt{80}[/tex]

Which is the same thing as [tex]u=\sqrt{80}[/tex] and [tex]u=-\sqrt{80}[/tex]

Which are two real solutions.

Answer:

2 real solutions

Step-by-step explanation:

u^2=80 is worked out as u as a variable times 2/u 2 times and when u do that you have to find the value of u and the result should be equal to 80. plz rate as the brainliest

Answer:

100 children

150 adults

Step-by-step explanation:

c- children

a- adults

---------------

we get equations as per question:

Children 100, adults 150

Answer:

96

Step-by-step explanation:

Triangles (front and back)

There are two right triangles -- front and back.

One triangle = 1/2*h*b

h = 3

b = 4

One triangle = 1/2 * 3 * 4

One triangle = 6

two triangles = 2*6 =12

Rectangle using the Net

Area = L * W

L = 3 + 4 + 5 = 12

W = 7

Area = 12 * 7 = 84

Total Area

Area = 12 + 84

Area = 96