The radioactive substance cesium-137 has a half-life of 30 years. The amount A (t) (in grams) of a sample of cesium-137 remaining after t years is given by the
following exponential function.
t
30
A (t) =621​

Answer:

The answer is below

Step-by-step explanation:

The question is not complete, the correct question is:

If B is between A and C, and AB=3x+1, BC=2x-7, and AC=24, then find the value of x and the value of AB

Answer: The line segment addition postulate states that if a point B is placed between a line segment with end points A and C, then the distance between the points can be expressed by the equation:

AB + BC = AC

But AB=3x+1, BC=2x-7, and AC=24, Hence:

3x + 1 + 2x - 7 = 24

3x + 2x + 1 - 7 = 24

5x - 6 = 24

5x = 24 + 6

5x = 30

x = 6

AB = 3x + 1 = 3(6) + 1 = 18 + 1 = 19

BC = 2x - 7 = 2(6) - 7 = 12 - 7 = 5

Answer:

yes

Step-by-step explanation:

20x10= 200 therefor its 10times as much

Answer:

Commutative Property of Addition: a + b = b + a

Step-by-step explanation:

The Commutative Property of Addition implies that even on changing the order of addition the final result (i.e. the sum) remains the same.

a + b = b + a

Suppose a = 5 and b = 6, then:

a + b = 5 + 6 = 11

b + a = 6 + 5 = 11.

Thus, a + b = b + a.

a + b + c= a + c + b = b + a + c = c + a + b

Suppose a = 4, b = 3 and c = 6, then:

a + b + c = 4 + 3 + 6 = 13

a + c + b = 4 + 6 + 3 = 13

b + a + c = 3 + 4 + 6 = 13

c + a + b = 6 + 4 + 3 = 13.

Thus, a + b + c= a + c + b = b + a + c = c + a + b.

Answer:

Step-by-step explanation:

In the tossing of a fair coin, there are equal probabilities of getting a HEAD and getting a TAIL.

Total probability is always 1 and a coin has 2 faces - Head & Tail.

The probability of getting a Head is 1/2 = 0.5

The probability of getting a Tail is 1/2 = 0.5

E1 is the event that TAIL comes up when the coin is tossed the first time

E2 is the event that HEAD comes up when the coin is tossed the second time

The probability value for EVENT 1 is 0.5

The probability value for EVENT 2 is 0.5

Answer:

1372cm²

Step-by-step explanation:

If this were a complete rectangle, it would be 50x40=2000cm².  So we need to take that number and subtract the half-circle.  A=[tex]\pi[/tex]r²  A=3.14*20*20=1256

1256*1/2 = 628

2000-628=1372cm²

Answer:

1372 cm²

Step-by-step explanation:

First, find the area of the rectangle:

A = lw

A = 40(50)

A = 2000 cm²

Next, find the area of the semicircle:

A =([tex]\pi[/tex]r²) / 2

A = (3.14)(20)²

A = 1256/2

A = 628 cm²

Then, subtract the semicircle area from the rectangle's area:

2000 - 628

= 1372 cm²

Answer:

A, B, and D

Step-by-step explanation:

Just took the test :)

Answer:

a b d edge

Step-by-step explanation:

Answer:

234252464375675734

Step-by-step explanation:

addition...

Answer:

here 234252464375734

Answer:

Histogram

Step-by-step explanation:

A histogram is a representation of approximate numerical data distribution. It was first introduced by Karl Pearson. Constructing a histogram, requires one to "bin" (or "bucket") the range of values, or say, divide the entire range of values into a series of Intervals, thereafter, count how many values fall into each interval. The bins well be specified as consecutive, and or non-overlapping intervals of a variable. The bins (intervals) is best left to be adjacent, and are often (but not required to be) of equal size.

An example of where a histogram would be used, is that of the distribution of grades on a school exam or the sizes of pumpkins, divided by size group, in a pumpkin festival.

Answer:

Bar graph

Step-by-step explanation:

It compares the data

I hope u will get help frm it.....

You just need to integrate 3 times:

[tex]f'''(t)=t^{1/2}-9\cos t[/tex]

[tex]f''(t)=\displaystyle\int f'''(t)\,\mathrm dt=\frac23 t^{3/2}-9\sin t+C[/tex]

[tex]f'(t)=\displaystyle\int f''(t)\,\mathrm dt=\frac4{15} t^{5/2}+9\cos t+Ct+D[/tex]

[tex]f(t)=\displaystyle\int f'(t)\,\mathrm dt=\frac8{105} t^{7/2}+9\sin t+\frac C2 t^2+Dt+E[/tex]

Answer:

14 mph   ( average speed during the second part of the trip )

Step-by-step explanation:

Let´s call  "x"  the average speed during the first part then

t = 5 hours

t  =  t₁  +  t₂        t₁   and  t₂   times during part 1 and 2 respectively

l = t*v           (  distance is speed by time )      t =  l/v

First part

t₁  = 16/x        and      t₂  = 42 / ( x + 6)

Then

t =   5   =  16/x   +   42 /(x + 6)

5 = [ 16 * ( x  +  6 ) +  42 * x ] / x* ( x + 6 )

5 *x * ( x + 6 )  =  16*x  + 96 +  42 x

5*x² + 30*x  - 58*x - 96  =  0

5*x²  -  28*x  -  96  =  0

We obtained a second degree equation, we will solve for x and dismiss any negative root since negative time has not sense

x₁,₂  =   [28 ± √ (28)² + 1920  ] / 10

x₁,₂  = ( 28  ± √2704 )/ 10

x₁  = 28  -  52 /10        we dismiss that root

x₂  = 80/10

x₂  =  8 mph       average speed during the first part, and the average speed in the second part was 6 more miles than in the firsst part. then the average spedd dring the scond part was 8 + 6 = 14 mph

Answer:  the known variable; the to-be-predicted variable

Step-by-step explanation:

In statistics, linear regression is a technique to model the relationship between two variables ( one independent and other dependent).

It requires some previous data to plot a best fit line.

It is used to predict the values for dependent variable for each independent variable.

Here, independent variable = known variable and dependent variable = is to be predicted

Hence, Linear regression describes the extent to which the known variable predicts the to-be-predicted variable.

Answer:

[tex] \boxed{ \bold{ \huge{\boxed{ \sf{ - 54w + 45}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{3 + 6( - 9w + 7)}[/tex]

Distribute 6 through the parentheses

⇒[tex] \sf{3 - 54w + 42}[/tex]

Add the numbers : 42 and 3

⇒[tex] \sf{ - 54w + 45}[/tex]

Hope I helped!

Best regards!!

Answer:

= 5 ( 12d + 23f )

Step-by-step explanation:

-2(5d-9f)+7f-10(-9f-7d)

Open parenthesis

= -10d + 18f + 7f + 90f + 70d

Collect like terms

= -10d + 70d + 18f + 7f + 90f

= 60d + 115f

Factorise

= 5 ( 12d + 23f )

Therefore,

-2(5d-9f)+7f-10(-9f-7d) in its simplest form is 5 ( 12d + 23f )

Answer:

Step-by-step explanation:

Hello !

Using the cross multiplication method, which of the following is the solution to 21/(x+4) = 7/(x+2)?

21(x + 2) = 7(x + 4)

21x + 42 = 7x + 28

21x - 7x = 28 - 42

14x = -14

x = -14/14

x = -1

Answer:

3/(x+2)= x+1

Step-by-step explanation:

21/7=3

x/x= x

4/2=2

Answer:

-2

Step-by-step explanation:

To find the slope of the line you have to use the equation,

(y2-y1)/(x2-x1)

In this case it is, (-4-2)/7-4)

This simplifies to -2 and this is the slope of the line

Answer:

-8/5

hope this help!

1: Add 60 and 15.

2: Divide by 3.

3: Subtract 2.

Answer:

Step-by-step explanation:

Surface area of a pyramid =

area of base + area of triangular faces

Since it's a square based pyramid

It's surface area is

area of base + 4( area of one triangular face)

Since the square has equal sides

For square base

Area of a square = l²

where l is the length

From the question l = 5

So we have

Area of square base = 5² = 25ft²

For one of the triangular face

Area of a triangle = ½ × base × height

base = 5

height = 6

Area = ½ × 5 × 6 = 15ft²

So the surface area of the pyramid is

25 + 4(15)

= 25 + 60

We have the final answer as

Hope this helps you

Answer: 2 = |x − 47|

Step-by-step explanation:The total weight of the container and the nuts is x ounces. The desired weight of the container and the nuts is (45 + 2), or 47 ounces. The absolute error allowed is 2 ounces.

absolute error = |actual weight − desired weight|

Substituting the values, the equation obtained is 2 = |x − 47|.

Answer:

4, -2

Step-by-step explanation:

Hello, please consider the following.

[tex]\begin{aligned}4x^2-8x-32=0 &\text{ ***We divide by 4.***}\\\\x^2-2x-8=0 &\text{ ***We complete the square. ***}\\\\(x-1)^2-1-8=(x-1)^2-9=0 &\text{ ***We move the constant to the right.***}\\\\(x-1)^2=9=3^2 &\text{ ***We take the root.***}\\\\x-1=\pm3 &\text{ ***We add 1.***}\\\\x=1+3=\boxed{4} \ & or \ x=1-3=\boxed{-2}\end{aligned}[/tex]

Thanks

Answer: about 73 %

Step-by-step explanation:

because 88 of 120 is about 73 %

The percent of change in the price of this coat is 26.66 %.

To find the percent of change in the price of this coat.

A part of a whole expressed in hundredths a high percentage of students attended. Also the result obtained by multiplying a number by a percent the percentage equals the rate times the base.

Given that:

Cost price of coat(C.P)= 120$

Selling price of coat(S.P)=88$

We know that ,

Percent change=change in price /C.P*100

Percent change=120$-88$/120$*100

Percent change=32/120*100

Percent change=26.66 %

Therefore, the percent of change in the price of this coat is 26.66 %.

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Answer: Joseph Kabila

Step-by-step explanation:

Answer:

Joseph Kabila

Step-by-step explanation:

Answer:

[see below]

Step-by-step explanation:

The figure is made out of two rectangular prisms.

V = w * l * h

Volume for the left prism:

V = 9 * 5 * 24

V = 1080 m³

Volume for the right prism:

V = 9 * 18 * 10

V = 1620 m³

Combine both volumes:

1620 + 1080 = 2700

2700 cubic meters should be your answer.

Hope this helps.

Answer:

10x.

Step-by-step explanation:

It is given that,

JK = 3x

LM = 12x

JM = 25x

Let as consider the line as shown in the below figure.

From the figure it is clear that,

[tex]JK+KL+LM=JM[/tex]

[tex]3x+KL+12x=25x[/tex]

[tex]KL+15x=25x[/tex]

[tex]KL=25x-15x[/tex]

[tex]KL=10x[/tex]

Therefore, the length of KL is 10x.

Answer:

We are given order pairs  (–9, –8), (–{(8, 4), (0, –2), (4, 8), (0, 8), (1, 2)}.

We need to remove in order to make the relation a function.

Step-by-step explanation:

Note: A relation is a function only if there is no any duplicate value of x coordinate for different values of y's of the given relation.

In the given order pairs, we can see that (0, –2) and (0, 8) order pairs has same x-coordinate 0.

So, we need to remove any one (0, –2) or (0, 8) to make the relation a function. hope this helps you :) god loves you :)

Answer:

(a) P-value = 0.044

(b) P-value = 0.0022

(c) P-value = 0.4402

(d) P-value = 0.022

Step-by-step explanation:

The complete question is: An independent random sample is selected from an approximately normal population with an unknown standard deviation. Find the p-value for the given set of hypotheses and t-test statistics. Also, determine if the null hypothesis would be rejected at α = 0.05.

a) HA : μ > μ0, n = 11, T = 1.91

b) HA : μ < μ0, n = 17, T = -3.45  

c) HA : μ [tex]\neq[/tex] μ0, n = 7, T = 0.83  

d) HA : μ > μ0, n = 28, T = 2.13

(a) We are given the right-tailed test with sample size (n) of 11 and the test statistics of 1.91.

Now, the P-value of the test statistics is given by;

                P-value = P([tex]t_n_-_1[/tex] > 1.91)

                              = P([tex]t_1_0[/tex] > 1.91) = 0.044

Since the P-value of the test statistics is less than the level of significance as 0.044 < 0.05, so we have sufficient evidence to reject our null hypothesis.

(b) We are given the left-tailed test with sample size (n) of 17 and the test statistics of -3.45.

Now, the P-value of the test statistics is given by;

                P-value = P([tex]t_n_-_1[/tex] < -3.45)

                              = P([tex]t_1_6[/tex] < -3.45) = 0.0022

Since the P-value of the test statistics is less than the level of significance as 0.0022 < 0.05, so we have sufficient evidence to reject our null hypothesis.

(c) We are given the two-tailed test with sample size (n) of 7 and the test statistics of 0.83.

Now, the P-value of the test statistics is given by;

                P-value = P([tex]t_n_-_1[/tex] > 0.83)

                              = P([tex]t_6[/tex] > 0.83) = 0.2201

For the two-tailed test, the P-value is calculated as = 2 [tex]\times[/tex] 0.2201 = 0.4402.

Since the P-value of the test statistics is less than the level of significance as 0.044 < 0.05, so we have sufficient evidence to reject our null hypothesis.

(d) We are given the right-tailed test with sample size (n) of 28 and the test statistics of 2.13.

Now, the P-value of the test statistics is given by;

                P-value = P([tex]t_n_-_1[/tex] > 2.13)

                              = P([tex]t_2_7[/tex] > 2.13) = 0.022

Since the P-value of the test statistics is less than the level of significance as 0.022 < 0.05, so we have sufficient evidence to reject our null hypothesis.

Answer:

11n

Step-by-step explanation:

The expression is 7n + 4n. Since 7n and 4n are like terms (they both are variables with n), we can combine them so the expression becomes 7n + 4n = 11n.

Answer: 9 : 10  or 9/10.

Step-by-step explanation:

The ratio of  muffins to scones   is 300 : 270.   Now to reduce it to the lowest term divide each by 30.

You will then get  9: 10

Greetings from Brasil...

We notice 2 dashes on the NO and NP line. This means that both are the same size. Since NO = 17 then OP is also 17 in length.

So

NP = NO + OP

NP = 17 + 17

NP = 34

As already said

NP = 5X - 6 = 34

5X - 6 = 34

Answer:

25

Step-by-step explanation:

50:2=25

75:3=25

100:4=25

125:5=25

The rate of change of the given data in the table will be 25.

The momentum of a variable is represented by the rate of change, which is used to mathematically express the percentage change in value over a specified period of time.

The formula for the rate of change is straightforward: it simply divides the current value of a stock or index by the value from a previous time period.

The rate of change will be calculated by using the following formula:-

rate of change = ( y₂ - y₁ ) / ( x₂ - x₁ )

The rate of change will be calculated as below:-

50:2=25

75:3=25

100:4=25

125:5=25

Therefore, the rate of change of the given data in the table will be 25.

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