Suppose a radioactive substance decays at a rate of 4% per hour. How long does it take until the substance is half of its original weight?

7 days and 5 hours
1713 hours
712 hours
17 days and 8 hours

also have a few questionsmore.

Answer:

Step-by-step explanation:

2x + 4 = -42         subtract 4 from both sides

2x + 4 - 4 = -42 - 4

2x = -46         divide both sides by 2

2x/2 = -46/2

x = -23

Steps To Solve:

2x + 4 = -42.

2x + 4 - 4 = -42 - 4

2x = -46

2x/2 = -46/2

x = -23 (Answer)

______

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Answer:

Option B is the correct choice.

Step-by-step explanation:

The graph is attached below.

We have to find the [tex]x[/tex] intercept meaning the value of the point on[tex]x-axis[/tex] when [tex]y=0[/tex]

So we will put the value of zero [tex](0)[/tex] instead of [tex]y[/tex] in our given equation.

So here we have solved it algebraically.

[tex]y=\frac{3}{4}x-3[/tex]

Putting [tex]y=0[/tex]

[tex]0=\frac{3}{4}x-3[/tex]

[tex]0=\frac{3x-12}{4}[/tex]

Multiplying [tex]4[/tex] both sides.

[tex]0=3x-12[/tex]

Adding [tex]12[/tex]both sides.

[tex]12=3x[/tex]

Dividing with [tex]3[/tex] both sides.

[tex]x=\frac{12}{3}=4[/tex]

So the x-intercept of the given equation is [tex]4[/tex] which can be written as [tex](4,0)[/tex] in terms of coordinates.

Option B [tex](4,0)[/tex] is the correct choice.

Answer:

The second option

Step-by-step explanation:

The second option because it is the one in which if you multiply f4 to the values of x, you would get y.

And that is why it is the second option.

To solve this, subtract 2 from both sides, and you end up with x = 8. :)

Answer:

It's C and D

Step-by-step explanation:

The points on the graph in which this was occurring is between points C and D.

This refers to the representation of data on an x-y plane showing the various cardinal points.

Hence, based on the fact that Carol's car is punctured by a nail and she had to drive slowly and then let off all the air in the tire, these actions most likely occurred between points C and D based on the fact that there is a change in speed.

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Answer:

A.) -9

Step-by-step explanation:

it is observed that triangles ABL and KML are similar triangles

hence the following ratios are valid:

LA / LK = LB/LM = AB/KM

we can see that LA/LK = LB/LM = 1/2

hence the above ratio becomes

1/2 = AB/KM  (rearranging)

KM = 2AB

We are given that KM = (x + 21) and AB = (x + 15)

hence

KM = 2AB

(x + 21) = 2 (x + 15)

x + 21 = 2x + 30

x - 2x = 30 - 21

-x = 9

x = -9

Answer: -9

Step-by-step explanation: When your adding and subtracting positives and negatives, it's a good idea to use a number line to visualize what's going on.

When you're simplifying a problem like (+4) + (-13) we start at zero and +4 moves us 4 units to the right along our number line.

From there, -13 then moves us 13 units back to the left so we end up at -9.

Image provided.

Therefore, (+1) + (-13) = -9

Essentially, the slope that is parallel to the pair is the the slope of the pair of points.

Using the formula [tex]\frac{y_1-y_2}{x_1-x_2}[/tex], the answer is [tex]\frac{-2}{-12}=\frac{1}{6}[/tex]

Assuming first number is (2^3)(3^2), second number is (2^2)(3^1).

First number:         2 * 2 * 2 * 3 * 3

Second number:   2 * 2 * 3

Both numbers have at least two factors for 2 and one factor for 3.

Their greatest common factor is (2^2)(3).

Answer:

Length of new radius 4 cm.

Step-by-step explanation:

Given radius of circle = 16 cm

Circle is dilated with scale factor 1/4

We need to find the new radius

To calculate New radius we need  to multiply radius of the circle with the dilated factor.

Hence new radius = [tex]16 \times \frac{1}{4}= 4\cm[/tex]

Hence Length of new radius is 4 cm.  

1. Positive but not perfect: Figure 4

2. Correlation coefficient equal to 1:

3. Strongest linear relationship: Figure 2

Step-by-step explanation:

"Correlation is the link between two quantities"

The relationship is said to be positive if both are increasing and said to be negative if both are opposite i.e. one is increasing and one is decreasing.

In the Given figures

1. Positive but not perfect linear relationship:

The perfect positive relationship is when both the quantities are increasing and the scatter points are in a line that grows linearly. Here, The data set in figure 4  has positive correlation but as the points are scattered around a line so the correlation is positive but not perfect.

2. Correlation equal to 1

The correlation in figure 1 is the perfect correlation as the data points follow a straight line and both the quantities are increasing.

3. Strongest linear relationship:

The relationship in figure 2 has the strongest in figure 2 as the data points are more close to the best fit line

Keywords: Correlation, Scatter Plot

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Answer:

37 and  29

Step-by-step explanation:

x + y = 66

x - y = 8

*******************************************

solve second equation for x

x = y + 8

substitute for x in first equation

y+8 +y = 66

2y = 58

y = 29

*******************************************

x - 29 = 8

x = 37

******************************************

x = 37 and y = 29

Final answer:

To solve for the two numbers, set up equations based on the sum and difference provided. By solving these equations, we find that the numbers are 52 and 14.

Explanation:

The sum of two numbers is 66, and their difference is 38. This problem can be solved using a system of equations. Let's denote the two numbers as x and y.

According to the information given:

Now, we can solve these equations simultaneously.

The two numbers that satisfy the conditions of the problem are 52 and 14.

Answer:

Part 1: Less.

Part 2: Greater.

Part 3: Greater.

Part 4: Less.

Part 5: Equal.

Step-by-step explanation:

Part 1: Assume that the value is x initially.

So, 55% decrease of value of x will give [tex]x(1 - \frac{55}{100}) = 0.45x[/tex].

Again, 25% increase of the value obtained will give [tex]0.45x(1 + \frac{25}{100}) = 0.45 \times 1.25 \times x = 0.5625x[/tex]

So, it is less than x. (Answer)

Part 2: Assume that the value is x initially.

So, 75% increase followed by [tex]33\dfrac{1}{3}  = 33.33[/tex]% decrease will give [tex]x \times (1 + 0.75) \times (1 - 0.333) = x \times 1.75 \times 0.667 = 1.167x[/tex]

So, it is greater than x.

Part 3: Assume that the value is x initially.

So, 20% decrease followed by 40% increase will give [tex]x \times (1 - 0.2) \times (1 + 0.4) = x \times 0.8 \times 1.4 = 1.12x[/tex]

So, it is greater than x.

Part 4: Assume that the value is x initially.

So, 30% increase followed by 30% decrease will give [tex]x \times (1 + 0.3) \times (1 - 0.3) = x \times 1.3 \times 0.7 = 0.91x[/tex]

Hence, it is less than x.

Part 5: Assume that the value is x initially.

So, 100% increase followed by 50% decrease will give [tex]x\times (1 + 1) \times (1 - 0.5) =x \times 2 \times 0.5 = x[/tex]

Hence, the final value is same as x. (Answer)

Answer:

the pictures uppppppppp

Answer:

See explanation

Step-by-step explanation:

Which display is more useful for approximating the minimum distance?

More useful is box-and-whisker plot (second display) because there you can exactly see that the minimum distance is 10 km (left point at the plot).

Which display can be used to find that there were 23 vehicles at Nam’s Used Car Lot?

More useful is first display, because you see the following information:

Distance           Number of vehicles

0 - 50                              3

50 - 100                          4

100 - 150                         5

150 - 200                        6

200 - 250                       3

250 - 300                       2

Total number of vehicles = 3 + 4 + 5 + 6 + 3 + 2 = 23

Answer:

23 vehicles

I'm on khan academy right now and its 23

Answer:

The graph will show what the line is.

Step-by-step explanation:

y-3 = -5/6(x+3)

Distribute first:

y-3= -5/6x - 15/6

-15/6 is negative because when disributing, -5/6, the negative sign will follow it.

Single out the y:

this means to make the y alone! by doing this, just add 3 to the other side

y-3= -5/6x - 15/6

+3             +3

______________

y= -5/6x + 3/6

Simplify:

y= -5/6 +1/2

-> 3/6 can be simplified to 1/2

Find the Y-intercept on the graph

1/2 on the graph is between 0 and 1

Graph the slope:

from the Y-intercept, go down 5 units, and to the right 6 units.

Then you have your graph!

Answer:x=1

Step-by-step explanation:

fist add like- terms in either side of the equation:

4x=2x+2.

next, you want to get both the X's on the same side of the equation. this means you need to subtract 2x from the left side of the equation and bring it to the right side of the equation. this means you have to subtract 2x from 4x. because what you do on one side of the equation you have to do on the other.

2x=2

next divide each side of the equation to get x alone.

x=1.

Answer:

This is only if you are looking to find the Arch AED        11pi/4

Step-by-step explanation:

See photo

Arc length AED of a given circle with a radius of 3 units is 11π/4.

According to the given diagram,

The angle subtended by arc AED or central angle = 360°-120°-45°-30° = 165°

The radius of the circle = 3 units

Arc length = Central angle(in radians) * Radius

So, arc length AED = 165 *π/180 * 3

Arc length AED = 11π/12 * 3 = 11π/4

Therefore, the Arc length AED of a given circle with a radius of 3 units is 11π/4.

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Answer:

1)121.5 sq.yards

2)157.92 m²

3)5.434 ft²

4)147.4513 cm²

5)147 cm²

6)56 in²

Step-by-step explanation:

1) Area of shaded region= Area of rectangle-Area of triangle

Area of rectangle= Length*Breadth=18*9 sq.yards=162 sq.yards(length=18 yards and breadth=9 yards)

Area of triangle= [tex]\frac{1}{2}*Base*Height[/tex]=[tex]\frac{1}{2}*9*9[/tex]=40.5 sq.yards(base=9 yards and height= 9 yards)

Therefore,Area of shaded region=162-40.5=121.5 sq.yards

2) In the following figure,

Length of rectangle, l= 21 m

breadth of rectangle, b= 15 m

Radius of circles, r= 5 m

Area of rectangle=l*b=21*15=315 m²

Area of circle= π[tex]r^{2}[/tex]=π*[tex]5^{2}[/tex]=78.54 m²

Therefore,Area of shaded region= Area of rectangle-2*Area of circle

                                                       =315-2*78.54=157.92 m²

3) In the following figure,

Radius of circle, r= 2 ft

Base of triangle, b= 6 ft

Height of triangle, h=6 ft

Area of circle= π[tex]r^{2}[/tex]=π*[tex]2^{2}[/tex]=12.566 ft²

Area of triangle= [tex]\frac{1}{2}*Base*Height[/tex]

                         =[tex]\frac{1}{2}*6*6[/tex]=18 ft²

Therefore,Area of shaded region= Area of triangle- Area of circle

                                                       = 18-12.566=5.434 ft²

4) In the following figure,

Radius of circle, r= 6 cm

Length of rectangle, l= 17 cm

breadth of rectangle, b= 2*r= 12 cm

Area of semi-circle= π[tex]\frac{r^{2}}{2}[/tex]=π*[tex]\frac{6^{2}}{2}[/tex]

                               =56.5487 cm²

Area of rectangle=l*b=17*12=204 cm²

Therefore,Area of shaded region= Area of rectangle- Area of semi-circle

                                                       = 204-56.5487=147.4513 cm²

5) In the following figure,

Side of bigger square, a=14 cm

Side of smaller square, b=7 cm

Area of bigger square= [tex]a^{2}[/tex]=[tex]14^{2}[/tex]=196 cm²

Area of smaller square= [tex]b^{2}[/tex]=[tex]7^{2}[/tex]=49 cm²

Therefore,Area of shaded region= Area of bigger square- Area of smaller                                                                                              square

                                                       =196-49=147 cm²

6) In the following figure,

Length of rectangle, l= 10 in

breadth of rectangle, b= 8 in

Base of triangle, b= 8 in

Height of triangle, h=6 in

Area of rectangle=l*b=10*8=80 in²

Area of triangle= [tex]\frac{1}{2}*Base*Height[/tex]

                         =[tex]\frac{1}{2}*8*6[/tex]=24 in²

Therefore,Area of shaded region= Area of triangle- Area of circle

                                                       = 80-24=56 in²

Answer:

5,470,000

do the multiplication first and then add

When adding numbers in scientific notation, align the exponents and then add the coefficients. The sum of 1.2 x 10^5 and 5.35 x 10^6 is 5.47 x 10^6.

To add these two numbers in scientific notation, we need to first align the exponents. In this case, we can rewrite the first number as 0.12 x 10^6 and the second number as 5.35 x 10^6. Now, we can add the numbers together:

0.12 x 10^6 + 5.35 x 10^6 = 5.47 x 10^6. Thus, the sum of 1.2 x 10^5 and 5.35 x 10^6 is 5.47 x 10^6.

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Answer:

-7/6x+y=5

Step-by-step explanation:

y=7/6x+5

y-7/6x=5

-7/6x+y=5

If the measure of the supplement of an angle is 60 degrees less than four times the measure of the complement of the angle, the required angle will be 40degrees.

Let the measure of the required angle be x

Supplement of the angle = 180 - x ....................1

Complement of the angle = 90 - x

four times the measure of the complement of the angle = 4(90-x)

60 degrees less than four times the measure of the complement of the angle = 4(90-x) - 60 ................................ 2

Equate 1 and 2 to get the unknown value 'x'

180 - x = 4(90-x) - 60

180 - x = 360-4x-60

180 - x = 300 - 4x

Collect the like terms

-x + 4x = 300 - 180

3x = 120

Divide both sides by 3

3x/3 = 120/3

x = 40

Hence the measure of the required angle is 40 degrees

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The measure of the angle is found to be 40 degrees. This was determined by setting up and solving the equation based on the given relationships between the angle's supplement and complement. Therefore, the angle measures 40 degrees.

To find the measure of the angle, let's denote the angle as x. We know the following:

According to the problem, the supplement of the angle is 60 degrees less than four times the complement of the angle. Therefore, we have the equation:

(180 - x) = 4(90 - x) - 60

First, expand and simplify the right-hand side:

180 - x = 360 - 4x - 60

Combining like terms, we get:

180 - x = 300 - 4x

Next, add 4x to both sides to start isolating x:

180 + 3x = 300

Then, subtract 180 from both sides:

3x = 120

Finally, divide both sides by 3:

x = 40

Thus, the measure of the angle is 40 degrees.

Answer:

The perimeter is 37

Step-by-step explanation:

there you go

The perimeter of the triangle is 37 units.

Perimeter is given by the sum of all the sides of any figure.

Given that, ABC, DE is a midsegment of Δ ABC, DE = 7, AB = 10, and BC = 13.

According to the midpoint theorem states that “The line segment in a triangle joining the midpoint of any two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”

Therefore, AC = 2DE

AC = 14

Therefore, perimeter = sum of all sides,

= 10+13+14

= 37

Hence. the perimeter of the triangle is 37 units.

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Answer:

81 and -31

Step-by-step explanation:

x + (x - 112) = 50

2x - 112 = 50

2x = 162

x = 81

the other number is x-112 = 81 - 112 = -31

Final answer:

To find the two numbers, set up a system of equations based on the given information. Solve the system of equations to find the values of the two numbers, which are -31 and 81.

Explanation:

To find the two numbers, we can set up a system of equations based on the given information.

Let's assume one number is x, and the other number is y.

According to the problem, the sum of the two numbers is 50, so we can write the equation:

x + y = 50

We are also told that one number is 112 less than the other, so we can write another equation:

x = y - 112

Now we can solve this system of equations to find the values of x and y.

Substituting the value of x from the second equation into the first equation, we have:

(y - 112) + y = 50

Combining like terms, we get: 2y - 112 = 50

Adding 112 to both sides of the equation, we have: 2y = 162

Dividing both sides by 2, we get: y = 81

Substituting this value of y into the second equation, we have: x = 81 - 112

Simplifying, we get: x = -31

Therefore, the two numbers are -31 and 81.

Answer:

C = 6500 + 225n

Step-by-step explanation:

It will cost $6500 to rent a truck plus $225 for each ton of sugar transported.

So, in the equation which relates the total cost for transporting sugar in a truck, $6500 will be the initial value and $225 will be the rate of transporting sugar per ton.

Hence, for transporting n tons of sugar, the total cost C in dollars is given by the following equation  

C = 6500 + 225n (Answer)

Answer:

(-1, 5)

(0, 3)

(2, -1)

Step-by-step explanation:

we have

[tex]f(x)=3-2x[/tex]

Remember that

If a ordered pair is a solution of the given function, then the ordered pair must satisfy the given function

Verify each case

case a) (-2, -1)

substitute the value of x and the value of y in the given function and compare the result

[tex]-1=3-2(-2)[/tex]

[tex]-1=7[/tex] ---> is not true

therefore

Is not a ordered pair of the given function

case b) (-1, 5)

substitute the value of x and the value of y in the given function and compare the result

[tex]5=3-2(-1)[/tex]

[tex]5=5[/tex] ---> is true

therefore

Is a ordered pair of the given function

case c) (0, 3)

substitute the value of x and the value of y in the given function and compare the result

[tex]3=3-2(0)[/tex]

[tex]3=3[/tex] ---> is  true

therefore

Is a ordered pair of the given function

case d) (1,0)

substitute the value of x and the value of y in the given function and compare the result

[tex]0=3-2(1)[/tex]

[tex]0=1[/tex] ---> is not true

therefore

Is not a ordered pair of the given function

case e) (2, -1)

substitute the value of x and the value of y in the given function and compare the result

[tex]-1=3-2(2)[/tex]

[tex]-1=-1[/tex] ---> is true

therefore

Is a ordered pair of the given function

Answer:

θ = π n + π/2 for n element Z

Step-by-step explanation:

Solve for θ:

1 + 2 cos(2 θ) + cos^2(2 θ) = 0

Write the left hand side as a square:

(cos(2 θ) + 1)^2 = 0

Take the square root of both sides:

cos(2 θ) + 1 = 0

Subtract 1 from both sides:

cos(2 θ) = -1

Take the inverse cosine of both sides:

2 θ = 2 π n + π for n element Z

Divide both sides by 2:

Answer:  θ = π n + π/2 for n element Z

Answer:

16 servings

Step-by-step explanation:

To calculate the servings of chicken, we need two pieces of information. We need to know how much money the food bank has and how many ounces of chicken is available. This information is given. Therefore, we can work out the servings of chicken by dividing the ounces of by the amount of money.

[tex]=1774.4/110.9=16[/tex]

So 16 servings of chicken can be provided for 110.9 pounds.

Answer:The greater value is 600 x 10⁻⁸. And the lesser value is 2 x 10⁻⁸. The number 600 x 10⁻⁸ is 300 times greater number 2 x 10⁻⁸.

Step-by-step explanation:⇒ 6 x 10⁻⁶ and 2 x 10⁻⁸⇒ 600 x 10⁻⁸ and 2 x 10⁻⁸The number  600 x 10⁻⁸ times greater than the number 2 x 10⁻⁸ will be ⇒ 600 x 10⁻⁸ / 2 x 10⁻⁸⇒ 300

Final answer:

The circumference of Saturn is not greater than that of Earth; Earth's circumference is greater. Saturn's circumference at 40,100 km is approximately 0.11 times that of Earth. Also, 0.037854921 rounded to the nearest hundredth is 0.04, and 6 x 10⁻⁶ is larger than 2 x 10⁻⁸.

Explanation:

To answer how many times greater the circumference of Saturn is than the circumference of Earth, we need to compare the two given circumferences. The circumference of Earth is 365,882 km, and the circumference of Saturn is given as 4.01 x 10⁴ km.

First, we convert Saturn's circumference to a standard numerical form: 4.01 x 10⁴ is 40,100 km. Now, we can divide the circumference of Saturn by the circumference of Earth: 40,100 km / 365,882 km which roughly equals 0.11. This means that Saturn's circumference is about 0.11 times the circumference of Earth, which indicates that Earth's circumference is actually greater, not Saturn's.

For the second part, estimating 0.037854921 to the nearest hundredth would result in 0.04 because the third digit after the decimal is 7, which rounds the second digit up to 4.

Comparing the numbers 6 x 10⁻⁶ and 2 x 10⁻⁸, 6 x 10⁻⁶ is larger because it is only 10⁻⁶ compared to 2 x 10⁻⁸ which is much smaller being 10⁻⁸.