Write the word sentence as an inequality.
3.2 less than a number t is at most 7.5

Answer:

City A and city B will have equal population 25years after 1990

Step-by-step explanation:

Given

Let

[tex]t \to[/tex] years after 1990

[tex]A_t \to[/tex] population function of city A

[tex]B_t \to[/tex] population function of city B

City A

[tex]A_0 = 10000[/tex] ---- initial population (1990)

[tex]r_A =3\%[/tex] --- rate

City B

[tex]B_{10} = \frac{1}{2} * A_{10}[/tex] ----- t = 10 in 2000

[tex]A_{20} = B_{20} * (1 + 20\%)[/tex] ---- t = 20 in 2010

Required

When they will have the same population

Both functions follow exponential function.

So, we have:

[tex]A_t = A_0 * (1 + r_A)^t[/tex]

[tex]B_t = B_0 * (1 + r_B)^t[/tex]

Calculate the population of city A in 2000 (t = 10)

[tex]A_t = A_0 * (1 + r_A)^t[/tex]

[tex]A_{10} = 10000 * (1 + 3\%)^{10}[/tex]

[tex]A_{10} = 10000 * (1 + 0.03)^{10}[/tex]

[tex]A_{10} = 10000 * (1.03)^{10}[/tex]

[tex]A_{10} = 13439.16[/tex]

Calculate the population of city A in 2010 (t = 20)

[tex]A_t = A_0 * (1 + r_A)^t[/tex]

[tex]A_{20} = 10000 * (1 + 3\%)^{20}[/tex]

[tex]A_{20} = 10000 * (1 + 0.03)^{20}[/tex]

[tex]A_{20} = 10000 * (1.03)^{20}[/tex]

[tex]A_{20} = 18061.11[/tex]

From the question, we have:

[tex]B_{10} = \frac{1}{2} * A_{10}[/tex]  and  [tex]A_{20} = B_{20} * (1 + 20\%)[/tex]

[tex]B_{10} = \frac{1}{2} * A_{10}[/tex]

[tex]B_{10} = \frac{1}{2} * 13439.16[/tex]

[tex]B_{10} = 6719.58[/tex]

[tex]A_{20} = B_{20} * (1 + 20\%)[/tex]

[tex]18061.11 = B_{20} * (1 + 20\%)[/tex]

[tex]18061.11 = B_{20} * (1 + 0.20)[/tex]

[tex]18061.11 = B_{20} * (1.20)[/tex]

Solve for B20

[tex]B_{20} = \frac{18061.11}{1.20}[/tex]

[tex]B_{20} = 15050.93[/tex]

[tex]B_{10} = 6719.58[/tex] and [tex]B_{20} = 15050.93[/tex] can be used to determine the function of city B

[tex]B_t = B_0 * (1 + r_B)^t[/tex]

For: [tex]B_{10} = 6719.58[/tex]

We have:

[tex]B_{10} = B_0 * (1 + r_B)^{10}[/tex]

[tex]B_0 * (1 + r_B)^{10} = 6719.58[/tex]

For: [tex]B_{20} = 15050.93[/tex]

We have:

[tex]B_{20} = B_0 * (1 + r_B)^{20}[/tex]

[tex]B_0 * (1 + r_B)^{20} = 15050.93[/tex]

Divide [tex]B_0 * (1 + r_B)^{20} = 15050.93[/tex] by [tex]B_0 * (1 + r_B)^{10} = 6719.58[/tex]

[tex]\frac{B_0 * (1 + r_B)^{20}}{B_0 * (1 + r_B)^{10}} = \frac{15050.93}{6719.58}[/tex]

[tex]\frac{(1 + r_B)^{20}}{(1 + r_B)^{10}} = 2.2399[/tex]

Apply law of indices

[tex](1 + r_B)^{20-10} = 2.2399[/tex]

[tex](1 + r_B)^{10} = 2.2399[/tex] --- (1)

Take 10th root of both sides

[tex]1 + r_B = \sqrt[10]{2.2399}[/tex]

[tex]1 + r_B = 1.08[/tex]

Subtract 1 from both sides

[tex]r_B = 0.08[/tex]

To calculate [tex]B_0[/tex], we have:

[tex]B_0 * (1 + r_B)^{10} = 6719.58[/tex]

Recall that: [tex](1 + r_B)^{10} = 2.2399[/tex]

So:

[tex]B_0 * 2.2399 = 6719.58[/tex]

[tex]B_0 = \frac{6719.58}{2.2399}[/tex]

[tex]B_0 = 3000[/tex]

Hence:

[tex]B_t = B_0 * (1 + r_B)^t[/tex]

[tex]B_t = 3000 * (1 + 0.08)^t[/tex]

[tex]B_t = 3000 * (1.08)^t[/tex]

The question requires that we solve for t when:

[tex]A_t = B_t[/tex]

Where:

[tex]A_t = A_0 * (1 + r_A)^t[/tex]

[tex]A_t = 10000 * (1 + 3\%)^t[/tex]

[tex]A_t = 10000 * (1 + 0.03)^t[/tex]

[tex]A_t = 10000 * (1.03)^t[/tex]

and

[tex]B_t = 3000 * (1.08)^t[/tex]

[tex]A_t = B_t[/tex] becomes

[tex]10000 * (1.03)^t = 3000 * (1.08)^t[/tex]

Divide both sides by 10000

[tex](1.03)^t = 0.3 * (1.08)^t[/tex]

Divide both sides by [tex](1.08)^t[/tex]

[tex](\frac{1.03}{1.08})^t = 0.3[/tex]

[tex](0.9537)^t = 0.3[/tex]

Take natural logarithm of both sides

[tex]\ln(0.9537)^t = \ln(0.3)[/tex]

Rewrite as:

[tex]t\cdot\ln(0.9537) = \ln(0.3)[/tex]

Solve for t

[tex]t = \frac{\ln(0.3)}{ln(0.9537)}[/tex]

[tex]t = 25.397[/tex]

Approximate

[tex]t = 25[/tex]

Answer:

2x^2 +11

Step-by-step explanation:

(x) = 3 x^2 + 2

g(x) = x^2 - 9

(f - g)(x) =3 x^2 + 2 - (x^2 - 9)

Distribute the minus sign

             = 3x^2 +2 - x^2 +9

Combine like terms

             = 2x^2 +11

Answer:

65

Step-by-step explanation:

Answer:

they just go straight what does it mean?

Answer:

VPQ = 83°

Step-by-step explanation:

You can draw a circle around the point P, and a circle have 360°, so it means that the sum off all the angles have ro be 360°. Some of these angles have the same measure, because they're formed by the same lines segments, they are:

SPR = UPV; TPU = RPQ; TPS = VPQ

360 - SPR - UPV - RPQ - TPU = VPQ + TPS

As some of they are equal, we can just multiply they by 2:

360 - 2×SPR - 2×RPQ = 2× VPQ

360 - 2×35 - 2×62 = 2×VPQ

360 - 70 - 124 = 2×VPQ

2 VPQ = 166

VPQ = 166/2

VPQ = 83°

[tex] \frac{2x - 20}{ {x}^{2} + 6x - 40 } [/tex]

This is the right answer.

Refer to the attachment for the complete work.

Answer:

x> 17/8

Step-by-step explanation:

add the numbers

17-8x<0

move the constant to the right-hand side and change its sign

-8x<-17

Divide both side of the inequality by -8 and flip the inequality sign

x>17/8

Answer:

[tex]160[/tex]

Step-by-step explanation:

A rectangular prism's surface area is [tex]2(wl+hl+hw)[/tex].

2·(10·5+2·5+2·10)=160.

Answer:

a or c

Step-by-step explanation:

surry if im wrong

Answer:

the next three terms, 0.075,0.0375,0.01875 (common ratio 0.5)

the formula is 0.3*0.5^n-1

the formula for finding the nth term of a geometric sequence preset would be

a*r^n-1

a is first term

r is common ratio

Step-by-step explanation:

Answer:

30 cookies

Step-by-step explanation:

Reeba sells [tex]\frac{2}{3}[/tex] of [tex]3\frac{3}{4}[/tex] of 12 chocolate chip cookies.

Let us start by finding [tex]3\frac{3}{4}[/tex] of 12. We simply have to multiply the two numbers. However, it would be much easier if we had an improper fraction than a mixed number. Let us make [tex]3\frac{3}{4}[/tex]  an improper fraction first.

[tex]3\frac{3}{4} =\frac{15}{4}[/tex]

Ok! Let's multiply.

[tex]\frac{15}{4} *\frac{12}{1} =\\15*3\\=45[/tex]

Ok, Reeba baked 45 cookies in total. We know that she sells  [tex]\frac{2}{3}[/tex]  of her baked cookies, so we can again multiply the two numbers.

[tex]\frac{2}{3} *\frac{45}{1} =\\2*15=\\30[/tex]

Therefore, Reeba sold 30 cookies.

I hope this helps! Let me know if you have any questions :)

Answer:

Area of the bookmark = 52.56 cm²

Step-by-step explanation:

The two semicircles attached at both end of the rectangle will give us a full circle.

Therefore,

Area of the bookmark = area of rectangle + Area of a circle

Area of the bookmark = L × W + πr²

Length (L) = 10 cm

Width (W) = 4 cm

radius (r) = ½(4) = 2 cm

π = 3.14

Plug in the values into the equation

Area of bookmark = 10 × 4 + 3.14 × 2²

= 40 + 12.56

= 52.56 cm²

Answer:

Amount won : $3,000,000

Step-by-step explanation:

Let the amount won be =100 x

Amount spent on house :

                                     [tex]\frac{4}{5} \ of \ 100 x = 80 x[/tex]

Remaining amount = 100x - 80x = 20x

Amount spent on yacht :

                                    [tex]\frac{3}{4} \ of \ 20x = 15x[/tex]

Remaining amount = 20x - 15x = 5x

Amount spent on a trip :

                                   [tex]\frac{2}{3} \ of \ 5x = \frac{10}{3}x[/tex]

Remaining amount =

                         [tex]5x - \frac{10}{3}x = \frac{15x -10x}{3} = \frac{5x}{3}[/tex]

This amount is given for charity :

                                                     [tex]\frac{5}{3}x[/tex]

But given :

           Amount given to charity is  50000

Therefore ,

                 [tex]\frac{5}{3}x = 50000[/tex]

                [tex]5x = 3 \times 50000\\\\5x = 150000\\\\x = 30000[/tex]

Therefore , the amount won on lottery is = 100x = 100 ( 30000) = 3,000,000

The amount of money he won

Answer:

The answer is A, 86 sections.

Step-by-step explanation:

Step one : Add the 130 feet on to the 300 feet to find the new length of the fence.

130 + 300 = 430

Step two : find how many 5 foot sections he has now, divide 430 by 5.

430/5 = 86

Mr. Jackson can divide the new fence into 86 5-foot sections.

The answer is A, 86 sections.

Answer:

Below:

Step-by-step explanation:

A) 0.15 (0.35 + 0.40 + 0.10 + 0.15 = 1)

B) 0.45

C) 0.40

A) the total probability has to equal 1.

To find the probability of rat subtract the other animals from1:

Rat = 1 - 0.35-0.4-0.1 = 0.15

Rat = 0.15

B) probability of cat or hamster equals the sum of their probabilities:

Cat = 0.35 + hamster = 0.1 = 0.45

Answer = 0.45

C) the probability of them both picking the same = dog x dog = 0.4 x 0.4 = 0.16

Answer = 0.16

Answer:

20 degree

Step-by-step explanation:

x + x + 70 = 110 degree (sum of two opposite interior angle equal to the exterior angle formed)

2x = 110 - 70

x = 40/2

x = 20 degree

Answer:

f(x) = (x+5)^2 +12

The minimum value is 12

Step-by-step explanation:

f(x)=x^2+10x+37

The vertex will be the minimum value since this is an upwards opening parabola

Completing the square by taking the coefficient of x and squaring it adding it and subtracting it

f(x) = x^2+10x  + (10/2) ^2 - (10/2) ^2+37

f(x) = ( x^2 +10x +25) -25+37

    = ( x+5) ^2+12

Th is in vertex form y = ( x-h)^2 +k  where (h,k) is the vertex

The vertex is (-5,12)

The minimum is the y value or 12

Step-by-step explanation:

kayo na po bahala mag calculate

The value of function f (- 2) would be,

⇒ f (- 2) = 3 / 4

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The value of function is,

⇒ f (x) = 3 × 2ˣ

Now,

At x = - 2;

The value of function f (- 2) would be,

⇒ f (x) = 3 × 2ˣ

⇒ f (- 2) = 3 × 2⁻²

⇒ f (- 2) = 3 × 1 / 4

⇒ f (- 2) = 3 / 4

Thus, The value of function f (- 2) would be,

⇒ f (- 2) = 3 / 4

Learn more about the function visit:

https://brainly.com/question/11624077

#SPJ2

Answer:

43.2 meters

Step-by-step explanation:

Multiply the length of one piece of ribbon by 8 to determine the total length

5.4 * 8 =43.2 meters

Answer:

The answer is "The second choice".

Step-by-step explanation:

[tex]r=6\\\\h=13 \\\\[/tex]

Formula:

[tex]A=2\pi rh[/tex]

[tex]=2\times 3.14 \times 6 \times 13\\\\=2\times 3.14 \times 78\\\\=3.14 \times 156\\\\=3.14 \times 156\\\\=489.84 \approx 489.8 ft^2[/tex]

===========================================================

Explanation:

Each square has a side length of 5 inches, so each square has area 5*5 = 25 square inches. We have 6 such squares to give a total surface area of 6*25 = 150 square inches.

Effectively, this is the same as using the formula below

S = 6x^2

S = 6*5^2

S = 6*5*5

S = 150

x = 5 refers to the side length and S is the surface area. It might help to cut the figure from the paper, and fold it up and you should find that a 3D box will form. There are 6 faces with area of 5*5 each, hence the 6*5*5

Answer:

good luck man

Step-by-step explanation:

you will get answers after some time

f(x) = 3/x+2 - √x - 3

f(3) = 3/3 + 2 - √3 - 3

f(3) = 3/3 + 2 - √0

f(3) = 3/5 - 0

f(3) = 3/5

You can let x be any value of your choice.

Answer:

the answer is the alphabet A at the picture

The circle must be on -5 and arrow drawn to the right. Hence the correct answer is number line A

Given the inequality expression

-4(x+3) <= -2-2x

Expand the inequality

-4x - 12 <= -2-2x

Collect the like terms

-4x + 2x <= -2+12

-2x <= 10

Divide both sides by -2

-2x/-2 >= 10/-2

x >= -5

For the number line, the circle must be on -5 and arrow drawn to the right. Hence the correct answer is number line A.

Learn more on inequality expression: https://brainly.com/question/24372553

Answer:

18

Step-by-step explanation:

f(x) = 2x^2

Let x = -3

f(-3) = 2 * (-3)^2

Exponents first

f(-3)=2 *9

f(3) = 18

Answer:

f ( - 3 ) = 18

Step-by-step explanation:

f ( x ) = 2x²

Find f ( - 3)

let , x = - 3

lf ( - 3 ) = 2 ( -3 )²

f ( - 3 ) = 2 × ( - 3 )²

Evaluate the power

f ( -3) = 2 × 9

multiply the numbers

f ( - 3 ) = 18

Answer:

-4z^3 + 5z^2 + 29z -24

Step-by-step explanation:

(4z^2 + 7z-8) (-z+3)

would equal -4z^3 + 12z^2 - 7z^2 + 21z + 8z - 24

and simplified to -4z^3 + 5z^2 + 29z -24

Answer:

5

29

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

135-75 = 60

HOPE IT HELPS

Answer:

1 gallon

Step-by-step explanation:

gallons of paint needed; 4

gallons used: (3/4)*4

= 1 gallon was used

Answer:

Answer is 3 gallons

Step-by-step explanation:

1 gallon= 25%

2 gallons=50%

3 gallons=75%

3/4 is equivalent to 75%

Hope this helped!