A population of bacteria can be modeled by the function f(t) = 1000(0,98)", where t represents
the time since the population started decaying, and f (t) represents the population of the
remaining bacteria at time t. What is the rate of decay for this population?

Answer:

Measure of angle K is 52.5 degrees

Step-by-step explanation:

Here, we have a case of two sides being congruent

mathematically when two sides are congruent, then we have an isosceles triangle

For an isosceles triangle, the base angles are equal

LM faces K , while M faces KL

What this mean is that L faces KM

From above, we can see that K = M = ?

Let us call this x

Mathematically, the sum of angles in a triangle is 180 degrees

75 + x + x = 180

2x = 180-75

2x = 105

x = 105/2

x = 52.5

Answer:

The x-intercept = -3/2

Step-by-step explanation:

Set y = 0 to find the x-intercepts;

=> y = 4x + 6

=> 0 = 4x + 6

=> 0 - 6 = 4x

=> -6 = 4x

=> -6/4 = x

=> -3/2 = x

Therefore the x-intercept = -3/2

Hope this helps!

Answer:

So , 41 years ago, Mothers age is 3 times of Sally's age. When Sally's age was 13 , and her mom age was 39 (

Given:

The length of field is n yards.

The length of a field in feet is a function f(n).

To find:

The function rule for this situation.

Solution:

We know that,

1 yard = 3 feet

Using this conversion, we get

n yard = 3n feet

The length of field is n yards. So, the length of the field is 3n feets.

The length of a field in feet is a function f(n). So,

[tex]f(n)=3n[/tex]

Therefore, the required function rule for this situation is [tex]f(n)=3n[/tex].

Answer:

133,300

Step-by-step explanation:

3100 x 43 = 133,300

Answer: 133,300

Step-by-step explanation: 3100 x 43= 133300

Answer:

6 units

Step-by-step explanation:

E(-2 , -1) = (x1 , y1)

F(-2 , -5) = (x2 , y2)

distance = [tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex]

=[tex]\sqrt{(-2 - (-2))^2 + (-5 - (-1))^2}[/tex]

=[tex]\sqrt{(-2 + 2)^2 + (-5 + 1)^2[/tex]

=[tex]\sqrt{0^2 + 6^2}[/tex]

=[tex]\sqrt{36}[/tex]

= 6 units

Answer:

D

Step-by-step explanation:

All parts of the circle have a star, meaning that Andrea has a 4/4 or 1 probability of landing on a part that has a star.

Answer:

2703

explanation:

12×189=2268

2268+435=2703

Darrel earned 1503 dollars that week.

Suppose we are given how many no. are there from 224 to 358.

To find do the following (358 - 224 + 1) = 135 numbers.

According to the question Darrel receives a weekly salary of 435 dollars. In addition, 12 dollars is paid for every item sold in excess of 100 items.

Here excess of 100 items means after 100 which is 101.

He sold 189 items so his addition earning is for (189 - 101 + 1) = 89 items.

Given for each item he is paid 12 dollars.

∴ For 89 items he is paid (89 × 12) dollars which is

= 1068 dollars.

So in that week Darrel earns total of (435 + 1068) dollars.

= 1503 dollars.

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Answer:

The cost price = GHc 16.00

Step-by-step explanation:

Selling price = GHC 20.00

Profit Percent = 25%

Cost price = ?

Formula for finding cost price =

[tex] \frac{100}{100 + profit \: percent} \times selling \: price[/tex]

Let's insert the numbers

[tex] \frac{100}{100 + 25} \times 20 \\ = \frac{100}{125} \times 20 \\ = \frac{4}{5} \times 20 \\ = \frac{4 \times 20}{5} \\ = \frac{80}{5} \\ = 16[/tex]

So therefore ; the cost price is GHC 16.00

Answer:

D. 2

Step-by-step explanation:

The degree is the biggest exponent. In this case, it is 2.

Answer:

2

Step-by-step explanation:

The highest exponent is 2

therefor this is a 2nd degree polynomial

Answer:

The answer is 4x+7

Step-by-step explanation:

3x+7+x

= 3x+x+7

= 4x+7

(I used symbolab)

Answer:

12[tex]\sqrt{3}[/tex] / 24

Step-by-step explanation:

ΔXZW is a 30-60-90 triangle whose sides are in the ratio of 1 : [tex]\sqrt{3}[/tex] : 2, respectively

also, ΔXZW ≅ ΔYZW

so XW = 12

XZ = 24

WZ = 12[tex]\sqrt{3}[/tex]

cos ratio of ∡XZW is WZ/XZ which is:

12[tex]\sqrt{3}[/tex] / 24

Answer:

x=2.5 cups are needed  for 2 pies

Step-by-step explanation:

4/5 or 0.8

Fraction form: 4/5x = 2   x= 5/4

Decimial form: 0.8x = 2   x = 2.5

Mixed number form: 2 1/2

Hope that helped :)

Answer:

5x^2 - 3x -5

Step-by-step explanation:

You simplify the like terms

Remember to use distributive property to do the (7x-3x^2+5) part

Answer:

4.25 meters

Step-by-step explanation:

425/100 = 4.25

or move the decimal to the left 2 places. One place for each zero in 100.

answer:

N(t)=2×[tex]1.7^{t}[/tex]

17

15

step by step explain:

before lesson (t=0), she knows 2 words.

after a week (t=1), she knows

2×(1+70%)=3.4 words

after one more week (t=2), she knows

3.4×(1+70%)=5.78 words

one more week later (t=3), she knows

5.78×(1+70%)=9.826 words

and so on ...

from pattern shown above, we know that she knows

2×[tex]1.7^{t}[/tex] words after t weeks

so N(t)=2×[tex]1.7^{t}[/tex]

after 4 weeks (t=4), she knows 2×[tex]1.7^{4}[/tex]=16.7042≈17 words

for learning 5000 words, she need:

2×[tex]1.7^{t}[/tex]=5000

   [tex]1.7^{t}[/tex]=2500

t log(1.7)=log(2500)

         t=[tex]\frac{log(2500)}{log(1.7)}[/tex]

          =14.7448727

          ≈15 (round up)

Answer:

(a) N(t) = 2(1.7)^t

(b) 17

(c) 15

Step-by-step explanation:

(a) N(t) = 2(1.7)^t

There is a 2 because she starts with 2 words. The 1.7 is since her vocabulary grows by 70%. Finally, t represents the weeks. (it is an exponent)

(b) Just plug in the equation

N(4) = 2(1.7)^4

N(4) = 2(8.3521)

N(4) = 16.7042

Round, so it is 17

(c) Once again, plug in the equation

5000 = 2(1.7)^t

2500 = (1.7)^t

use a calculator for the part below

log1.7(2500) = log1.7(1.7)*t

t = log1.7(2500)

t = 14.7448

Round, so it is 15

Multiply the number of days (x) by the amount per day (80) to get 80x.

She is driving 150 miles at 0.10 per mile so multiply to get the mileage cost: 150 x 0.10 = 15

Add this to the daily amount:

80x+15

She can spend up to 300, so less than or equal to 300:

80x +15 <=300

Answer:

3

Step-by-step explanation:

5(2x + 1) = 35

10x + 5 = 35

10x = 30

x = 3

Answer:

Step-by-step explanation:

Distribute the Negative Sign:

=−9x+32+−1(15x+41)

=−9x+32+−1(15x)+(−1)(41)

=−9x+32+−15x+−41

Combine Like Terms:

=−9x+32+−15x+−41

=(−9x+−15x)+(32+−41)

=−24x+−9

Answer:

-24x - 9

Step-by-step explanation:

Combine like terms.

Answer:

20 degrees

Step-by-step explanation:

The sum of inner angles of a triangle is 180 degrees

120 + 40 + x = 180

160 + x = 180

x = 20

Answer:

A + 120 + 40 = 180 (interior angles of a triangle equal to 180°)

A = 180-120-40

A = 20°

Answer:

∠ B = 61°

Step-by-step explanation:

The inscribed angle B is half the measure of its intercepted arc, then

∠ B = [tex]\frac{1}{2}[/tex] × 122° = 61°

Answer:

123

Step-by-step explanation:

100 ÷ 5 x 4 + 43

20 x 4 + 43

80 + 43

123

Answer:

C    Zero

Step-by-step explanation:

[tex] -9 \times (\dfrac{0}{-3}) = [/tex]

[tex] = -9 \times 0 [/tex]

[tex] = 0 [/tex]

Answer: C  Zero

Answer:

options number 1 is the answer

Answer:

Mass of piece of marble  = 0.27 kilogram

Step-by-step explanation:

Given:

Dimensions of cuboid = 1 x 0.2 x 0.5

Density of marble = 2.7

Find:

Mass of piece of marble

Computation:

Volume of cuboid = (l)(b)(h)

Volume of marble = 1 x 0.2 x 0.5

Volume of marble = 0.1

Mass = Density x Volume

Mass of piece of marble  = Density of marble x Volume of marble

Mass of piece of marble  = 2.7 x 0.1

Mass of piece of marble  = 0.27 kilogram

Answer:

......

Step-by-step explanation:

Length of diagonal of the rectangle=

√( length) ²+( breadth) ²

=√(20) ²+(12) ²

=√400+144

√544 m

. '. Length of fence= √544 m

Perimeter of the triangle formed by the diagonal of the rectangle =(12+20+√544)

=(32+√544) m

Answer:

37.3 ft

Step-by-step explanation:

tan A = opp/adj

tan 31° = x/62

x = 62 * tan 31°

x = 37.3 ft

The height of the tree is 37.25 ft if the point on the ground is 62 feet from the tree.

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

Trigonometric ratios are used to demonstrate the connection between the sides and angles of a right-angled triangle.

Let h denote the tree if the point on the ground is 62 feet from the tree.

The angle of elevation = 31°. Hence:

tan 31° = h/62

h = 62 × tan 31°

h = 37.25 ft

Thus, the height of the tree is 37.25 ft if the point on the ground is 62 feet from the tree.

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Given:

The equation is:

[tex](2x+3y)(2x-3y)=4x^2+6y^2[/tex]

To find:

The error in the given equation and correct it.

Solution:

We have,

[tex](2x+3y)(2x-3y)=4x^2+6y^2[/tex]

Taking left-hand side, we get

[tex]L.H.S.=(2x+3y)(2x-3y)[/tex]

[tex]L.H.S.=(2x)^2-(3y)^2[/tex]                 [tex][\because a^2-b^2=(a-b)(a+b)][/tex]

[tex]L.H.S.=(2)^2(x)^2-(3)^2(y)^2[/tex]       [tex][\because (ab)^x=a^xb^x][/tex]

[tex]L.H.S.=4x^2-9y^2[/tex]

It is not equal to right-hand side [tex]4x^2+6y^2[/tex]. In the right hand side, there must be a negative sign instead of positive sign.

Therefore, [tex](2x+3y)(2x-3y)=4x^2-6y^2[/tex].