The half-life of silicon-32 is 710 years. If 30 grams is present now, how much will be present in 300 years? Round answer to three decimal places. Using A(t)=A0e^(ln(0.5)/T)t

Answer:

(2, 2)

Step-by-step explanation:

To determine which ordered pair is a solution to the equation.

Substitute the x- coordinate into the left side and the y- coordinate into the right side and if both sides are equal then that is the solution.

(2, 2)

3 × 2 = 6 and 8 - 2 = 6 → hence (2, 2) is a solution

(8, 0)

3 × 8 = 24 and 8 - 0 = 8 → hence (8, 0) is not a solution

(3, 1)

3 × 3 = 9 and 8 - 1 = 7 → hence (3, 1) is not a solution

Answer:

C

Step-by-step explanation:

4 divided is said first, so it comes first in the equation. Difference means subtraction, meaning h - 7

Answer:

(-6,-4)

Step-by-step explanation:

The first endpoint of the line is (-6,8), we can call

x_1 = -6

and

y_1 = 8

Let the last endpoint have coordinates (x_2,y_2)

Also, the midpoint formula is:

(x_1+x_2)/2 , (y_1+y_2)/2

Now, plugging these values is the formula, we get:

(-6+x_2)/2 = -6

-6+x_2=-12

x_2=-12+6 = -6

x_2 = -6

Also

(8+y_2)/2=2

8+y_2=4

y_2=4-8=-4

y_2 = -4

The coordinates of the other endpoint is (-6,-4)

Rounding to the nearest tenth, the area of the regular pentagon is approximately 175.1 square centimeters.

To find the area of the regular pentagon, we can use the formula:

Area = (5/2) * s * r

Where s is the length of one side of the pentagon and r is the distance from the midpoint of the pentagon to one of its vertices.

We are given that s = 8.37 cm and r = 8.37 cm.

Plugging these values into the formula, we get:

Area = (5/2) * 8.37 * 8.37

Area = (5/2) * 70.0569

Area = 175.14225

Rounding to the nearest tenth, the area of the regular pentagon is approximately 175.1 square centimeters.

Answer is D and E

Since 9 divided by 3 is three it would be correct and 4 multiplied by 9 is E would be correct. The others just don’t add up.

The equation where c = 9 should be option D and option E.

C = 9

If [tex]C \div 3 = 3\\\\[/tex]

So this should be correct as 3 = 3

And,

36 = 4c

c = 9

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Answer:

That is an octagon (eight sides).

Interior Angle Total = 1,080

EACH interior angle = 180 - (360 / 8) = 135

n + 161 + (n -12) +(n + 30) + n + 134 + (n+16) + 126 = 1,080

5n + 455 = 1,080

5n = 625

n = 78.125

Step-by-step explanation:

So C= dxpi or rx2xpi= c in this case 7x 2 = 14 is diameter do E D and A finds the diameter and the rest do not

Answer:

5 + 5 + 5 + 5 + 5 + 5 = 30

6 + 6 + 6 + 6 + 6 = 30

5 = 30 ÷ 6

6 = 30 ÷ 5

Answer:

[tex](-5,0)[/tex] and [tex](3,0)[/tex]

Step-by-step explanation:

Think about it.

What two numbers multiply to -15 and add up to 2?

The answers are 5 and -3.

So plug that into the factored form of a parabola.

[tex]y=(x+5)(x-3)[/tex]

To find the x-intercepts, plug in 0 for [tex]y[/tex].

[tex](x+5)(x-3)=0[/tex]

Since we are multiplying, at least one of the terms has to equal 0.

[tex]x+5=0 \\ x-3=0 \\ \\ x=-5,3[/tex]

So the x-intercepts are [tex](-5,0)[/tex] and [tex](3,0)[/tex].

Answer:

b. 1.5 hope it helps

Answer:

[tex]a_0 = -6[/tex]

[tex]a_1=8[/tex]

[tex]x^2 +y^2 -6x + 8y = 0[/tex]

Step-by-step explanation:

The equation of the circle has the following form

[tex]x^2 + y^2 + a_0x + a_1y=0[/tex]

The equation of the circle has the following form

We know that the circle goes through the following points

(0, 0)

(6, 0)

(0, -8).

Then we substitute the values of x and y in the equation

For (0, 0)

[tex]0^2 + 0^2 + a_0(0) + a_1(0)=0[/tex]

[tex]0=0[/tex]

For  (6, 0)

[tex]6^2 + 0^2 + a_0(6) + a_1(0)=0[/tex]

[tex]36 + 6a_0=0[/tex]

[tex]a_0 = -\frac{36}{6}\\\\a_0 = -6[/tex]

For (0, -8)

[tex]0^2 + (-8)^2 + a_0(0) + a_1(-8)=0[/tex]

[tex](-8)^2 - 8a_1=0[/tex]

[tex](-8)^2 = 8a_1[/tex]

[tex]a_1=8[/tex]

Finally the equation is:

[tex]x^2 +y^2 -6x + 8y = 0[/tex]

Answer:

120 pounds

Step-by-step explanation:

1. divide 45 by 15

45 / 15 = 3

2. Each box costs 3 pounds each

3. multiple 3 by 40.

4. 40 x 3 = 120

1,2 cause of the o and y axis

The vertex is where the parabola changes directions, or in simpler terms, at the parabolas lowest point. Unless the parabola is upside down, then the vertex is where the highest point is.

The acid of symmetry is the line where the parabola can be divided evenly. This is almost always where the vertex is, except it continues on.

The y-intercept is where the parabola intersects with the y-axis.

I’ve answered the question below in the picture (my graph is not to scale but the answers are correct for yours)

Hope this helped and good luck!!

Answer:

Same:

A 50% decrease followed by a 100% increase.

A 33 1/3% decrease followed by a 50% increase.

Less:

A $25 increase followed by a $30 decrease.

A 20% increase followed by a 25% decrease.

Greater:

An 80% increase followed by a 40% decrease.

IN ORDER TO FIGURE OUT THE ANSWER CHOOSE A NUMBER AND APPLY WHAT IT IS TELLING YOU. FOR EX: on #1: I chose the number 100 then multiplied it by 1.8 then multiplied that number by 0.6 to get 108 which is greater than 100

80% increase followed by 40% decrease=greater

50% decrease follow by 100% increase=greater

20% increase followed by a 25% decrease=less

$25 increase followed by $30 decrease= less

33 1/3% decrease followed by 50% increase= same

Answer:

one solution

Step-by-step explanation:

9x+16=4x

16=4x-9x

16/-5=x

x=-3.2

The phrase 'Eight less than the product of two and a number x' translates to the algebraic expression 2x - 8.

The student's question is about writing an algebraic expression to represent a phrase. In this case, 'Eight less than the product of two and a number x' can be translated into algebraic expression. The 'product of two and a number x' is simply, 2x. 'Eight less than' is subtracting 8 from something. Therefore, this phrase is written as 2x - 8 in algebraic expression.

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Withdrawing money from an account is a negative value, losing yards in a game would also be a negative value.

A rise in temperature would be a positive value.

Both 1 and 2 could be written as -17.

The answer is C.

Answer:

50 miles

Step-by-step explanation:

Addition:

7/8 + 9/4 = 7/8 + 18/8 = 25/8 inches.

Now we have to convert to miles:

25/8 inches *16

Answer = 50 miles.

Answer: 3 7/10

Let's rewrite our equation with the parts separated

= 1 + 2/5 + 2 + 3/10

Now, let's add the whole numbers

1 + 2 = 3

Now, let's figure out how to solve the fraction parts

2/5 + 3/10 = ?

You'll need to find the LCD (Lowest Common Denominator) of 2/5 and 3/10.

If you don't know, the LCD is 10

Since 3/10 already has a denominator of 10, we don't need to do anything with it.

However, we need to multiply the numerator and denominator of 2/5 by 2

Why? We need the LCD, which is 10. Also, we can only add fractions if they have the same denominators

Numerator: 2 x 2 = 4

Denominator: 5 x 2 = 10

Fraction: 4/10

Now add the fractions

4/10 + 3/10 = 7/10

Finally, combine the whole numbers with the fractions

3 + 7/10 = 3 7/10

Answer:

DF = 458

Step-by-step explanation:

In statistics, T-test have an extensive application. T-tests are used in hypothesis testing or inference about the population mean when the population standard deviation is not known. Nevertheless, they are used in making inference in paired samples or dependent samples t-test as well as independent samples.

The degrees of freedom, DF, is a characteristic of the student's t distribution which is used in T-tests. In a simple T-test;

DF = n - 1

where n is the sample size

Given n is 459, DF = 459 - 1 = 458

Therefore, DF = 458

The range of the piecewise defined function is:

                  y= -6 , y= -4 , y= -3 , y=0

The piecewise function is defined by:

f(x)  =    2x+2   when  x < -3

              x       when  x = -3

  and  -x-2      when  x > -3

Then the graph of the function is a strictly increasing function and is a line with a slope of 2.

The function increases continuously from -∞ to -4

i.e. it takes all the value in the interval (-∞,-4)

There is a open circle at (-3,-4)

The graph of the function f(x) is strictly decreasing .

Since the graph is a line with slope -1.

Also, there is a open circle at (-3,1)

and the function starts decreasing continuously and will take all the values strictly less than 1.

i.e. the range for x > -3 is:  (-∞,1)

The range of the whole function f(x) is:

                            (-∞,1)

The coefficient of 'a' is 5.

The coefficient of 'b' is 9.

The coefficient of the constant term '-4' is -4 (or you can think of it as -4 times '1').

The coefficient in the expression 5a + 9b - 4 is the number that multiplies or is associated with a variable. In this expression:

The coefficient of '5a' is 5.

The coefficient of '9b' is 9.

The constant term '-4' does not have a variable and can be considered as a coefficient of '1' for the constant.

So, in summary:

The coefficient of 'a' is 5.

The coefficient of 'b' is 9.

The coefficient of the constant term '-4' is -4 (or you can think of it as -4 times '1').

for such more question on coefficient

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In the expression 5a+9b-4, 5 and 9 are the coefficients, representing the magnitude and direction of the variables 'a' and 'b'. The '-4' is a constant.

In the algebraic expression 5a+9b-4, the coefficients are the numbers in front of the variables. So in this case, 5 is the coefficient of a and 9 is the coefficient of b. A coefficient provides information about the magnitude and direction of a certain variable. In the absence of a variable, such as with the -4 in this expression, we don't refer to it as a coefficient, but rather as a constant.

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2\xy³z⁴ is the simplification.

Answer:

Part 11) The cyclist stops for a time during the section B

Part 12) He traveling slowest in section A

Part 13) He traveling fastest in section C

Part 14) The speed in section D is 20 km/h

Part 15) The cyclist was 60 km from home when he turned around

Step-by-step explanation:

we know that

The speed is the ratio of the distance by the time

s=d/t

The slope of the graph is equal to the speed of the cyclist

Part 11. During the trip the cyclist stops for a time. During which labeled section-A, B, C, or D- did he stop?

The cyclist stops for a time during the section B

Because, during section B the distance is a constant (d=30 km)

therefore

The speed is equal to zero (Remember that the slope of a horizontal line is equal to zero)

Part 12. During which labeled section was he traveling the slowest?

Find the slope (speed) in each section

Find the slope in section A

Let

A(0,0) and B(4,30)

the slope is equal to

m=(30-0)/(4-0)=7.5 km/h

Find the slope in section B

Is a horizontal line

therefore

the slope is equal to

m=0 km/h

Find the slope in section C

Let

C(6,30) and D(7,60)

the slope is equal to

m=(60-30)/(7-6)=30 km/h

Find the slope in section D

Let

E(7,60) and F(10,0)

the slope is equal to

m=(0-60)/(10-7)=-20 km/h ---> is negative because in this section he turned around

therefore

He traveling slowest in section A

Part 13. During which labeled section was he traveling the fastest?

Remember part 12)

Slope in section C

Let

C(6,30) and D(7,60)

the slope is equal to

m=(60-30)/(7-6)=30 km/h ----> is the greater slope

therefore

He traveling fastest in section C

Part 14. Calculate the speed of the cyclist during section D

Remember part 12)

Slope in section D

Let

E(7,60) and F(10,0)

the slope is equal to

m=(0-60)/(10-7)=-20 km/h ---> is negative because in this section he turned around

therefore

The speed in section D is 20 km/h

Part 15. How far away was the cyclist when he turned around and headed home

Observing the graph

we know that the cyclist turned around at point (7,60)

therefore

The cyclist was 60 km from home when he turned around

Answer:

80%

Step-by-step explanation:

4/5 is equal to 0.8, and 0.8 is equal to 80%

Answer:

[tex]\large\boxed{\dfrac{4}{5}=80\%}[/tex]

Step-by-step explanation:

[tex]n\ to\ a\ percent:\ n=n\cdot100\%\\\\======================\\\\\dfrac{4}{5}=\dfrac{4}{5}\cdot100\%=\dfrac{400}{5}\%=80\%[/tex]

Answer:

1/182 or 0.55%

Step-by-step explanation:

There are 2 ways to approach this problem (and both give the same answer!).

First method: probability for each test.

First test, worms: There's 1/14 chances for bear #3 to be selected, since there are 14 bears total.

Second test, ticks: There's 1/13 chances for bear #5 to be selected, since only 13 bears remain (#3 cannot be tested for both ticks and worms).

So, to obtain the total probability, we multiply 1/14 with 1/13 = 1/182

Second method: permutations

We can see the problem from a permutations perspective.  How many permutations can we have for 2 bears to be tested? It's a permutation since the order is important. (#3 ticks + #5 worms ≠ #3 worms + #5 ticks)

[tex]P(14,2) = \frac{14!}{(14 - 2)!} = 182[/tex]

There are 182 permutations possible, ONE of which is bear #3 is tested for worms and bear #5 is tested for ticks.

So, once again, 1/182.

ANSWER

[tex]r = 2 \sqrt{29} ( \cos(292 \degree) + \sin(292 \degree)) [/tex]

EXPLANATION

The polar form of a complex number ,

[tex]z = x + yi[/tex]

is given by:

[tex]z = r( \cos( \theta) + i \sin( \theta) )[/tex]

where

[tex]r = \sqrt{ {x}^{2} + {y}^{2} } [/tex]

The given complex number is:

[tex]z = 4 - 10i[/tex]

[tex]r = \sqrt{ {4}^{2} + {( - 10)}^{2} } [/tex]

[tex]r = \sqrt{16 + 100} [/tex]

[tex]r = \sqrt{116} = 2 \sqrt{29} [/tex]

And

[tex]\theta= \tan^{ - 1}(\frac{ y}{x} )[/tex]

[tex]\theta= \tan^{ - 1}(\frac{ - 10}{4} )[/tex]

[tex]\theta= 292 \degree[/tex]

Hence the polar form is :

[tex]r = 2 \sqrt{29} ( \cos(292 \degree) + \sin(292 \degree)) [/tex]

Answer:

12

Step-by-step explanation:

He can take one of the 2 shirts, so he has 2 choices.

He can take any one of the 3 pair of pants, so he has 3 choices.

He can choose any one of the 2 caps he has, thus he has 2 choices.

To find the number of different outfits possible, we simply multiply the number of choices available for each.

2 * 3 * 2 = 12 different outfits

Answer:

he can only make 2 outfits and have 1 pair of pants and one cap left byebye tell me if i am rightor wrong plz

stay safe

Step-by-step explanation:

Answer:

4 3/4 or 19/4

Step-by-step explanation:

To answer this question, you must add the values of all of the x's on the line plot. There is 1 x on 1/4 and 2 x's on 3/8. So, add 1/4 + 3/8 + 3/8 to get 1. Next, there are 3 x's on 1/2. So, add 1 + 1/2 + 1/2 + 1/2 to get 2 1/2. Lastly, there's 1 x on 5/8, 1 x on 3/4, and 1 x on 7/8. So add 2 1/2 + 5/8 + 3/4 + 7/8 to get  4 3/4 of 19/4 as your final answer. I hope this helps!!!

Answer:

• 9(sin 42°)

_______

sin 29°

Step-by-step explanation:

The value of x is calculated by the sine rule is 9(sin 42°)/sin 29°. Then the correct option is B.

Trigonometry deals with the relationship between the sides and angles of a triangle.

We know that the sine rule is given as

[tex]\rm \dfrac{a}{sin A} =\dfrac{b}{sin B}=\dfrac{c}{sin C}[/tex]

Then put the values and we have

[tex]\begin{aligned} \rm \dfrac{x}{sin 42^o} &= \rm \dfrac{9}{sin 29^o}\\\\\\\rm x &= \rm \dfrac{9*sin 42^o}{sin 29^o} \end{aligned}[/tex]

More about the trigonometry link is given below.

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