witch table shows exponential decay

Answer:

300

Step-by-step explanation:

You simply multiply 50 and 6.  I hope you have a nice day.  :)

Answer:

300 :3

Step-by-step explanation:

6 x 1 = 6

6 x 2 = 12

6 x 3 = 18

6 x 50 = 300

The width of the model is 13 inches as per the given information.

A ratio in mathematics represents the number of times one number contains another. For instance, if a dish of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the lemon-to-orange ratio is 6:8 (or 3:4), while the orange-to-fruit ratio is 8:14. (or 4:7).

Ratios are mathematical expressions that compare two numbers by dividing them. If you want to compare one data point (A) to another (B), your formula is A/B.

Given,

Width of Sarah dog house=39 inches

Height of Sarah dog house=24 inches

The ratio of width: Height is,

39:24

=13:8

If the height of the model is 8 inches then,

13/8=x/8

x=13

Therefore, the width of the model is 13 inches.

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The derivative of the function is

A) dw/dz=z^5 (7z-18)

B) dh/dx=192x^11+36x^5-6x^2+19

C) dy/dx=24x^2-38x-15

In mathematics, the derivative of a function measures the sensitivity to change of the function value with respect to a change in its argument. It is the rate of change of a function with respect to a variable.

A) w = z^7 – 3z^6 + 14

dw/dz=7z^6-18z^5

dw/dz=z^5 (7z-18)

B) h(x) = 16x^12 + 6x^6 – 2x^3 + 19x – 7

dh/dx=192x^11+36x^5-6x^2+19

C) y = (8x + 5)(x^2 – 3x)

dy/dx=  d/dx  [8x+5]*〖(x〗^2-3x)+(8x+5)*d/dx[x^2-3x]

dy/dx=(8*  d/dx  [x}+d/dx[5])*〖(x〗^2-3x)+(8x+5)*(d/dx[x^2]-3 d/dx[x])

dy/dx=(8*1+0)(x^2-3x)+(8x+5)(2x-3*1)

dy/dx=8(x^2-3x)+(2x-3)(8x+5)

dy/dx=24x^2-38x-15

Note: The question is incomplete. The complete question probably is: Find the derivative of the following function: A) w = z^7 – 3z^6 + 14 B) h(x) = 16x^12 + 6x^6 – 2x^3 + 19x – 7 C) y = (8x + 5)(x^2 – 3x).

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The cubic centimeter (cm³ or cc) is a unit of volume that is equivalent to a cube with sides measuring one centimeter each. It is commonly used to measure the volume of small objects or substances.

The term "cc" is often used in medical and automotive contexts to denote engine displacement or medication dosages. The cubic centimeter is a convenient unit for expressing small volumes due to its relation to the metric system and its ease of conversion. The cubic centimeter, denoted as cm³ or cc, is a unit of volume in the metric system. It represents the volume of a cube with sides measuring one centimeter each. This unit is widely used to measure the volume of small objects or substances, especially in scientific, medical, and engineering fields. In the medical field, the term "cc" is often used interchangeably with ml (milliliter) to express medication dosages. For example, a doctor may prescribe a certain medication to be administered in 5 cc or 5 ml doses. In the automotive industry, cc is used to denote engine displacement, which represents the total volume swept by all the pistons in an internal combustion engine. It is commonly used to categorize and compare the sizes and capacities of different engines. The cubic centimeter is a convenient unit for measuring small volumes due to its relation to the metric system. It is easily convertible to other metric units of volume, such as liters or milliliters, by using the appropriate conversion factors. For example, 1 cm³ is equivalent to 0.001 liters or 1 milliliter. Overall, the cubic centimeter serves as a practical unit for quantifying small volumes in various fields, providing a common measurement standard and facilitating easy conversions within the metric system.

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Answer:

The awnser would be m= 2/3

Step-by-step explanation:

Answer:

-5

Step-by-step explanation:

10-15=-5

Answer:

y - 1 = 3/4 * (x + 6)

Step-by-step explanation:

Answer:15

Step-by-step explanation:

The solution to the system of equations in the graph is (2,1) because it is the coordinate of the intersection of the lines.

A system of equations is the given term of math for two or more equations with the same variables. The solution of these equations represents the point of the intersection.

You can solve a system of equations algebraically or graphically.When you solve algebraically, you can apply the substitution or addition methods. In the addition method, you eliminate a variable, on the other hand, in the substitution method you replace a variable for the other. When you solve graphically, the solution is given from the intersection point coordinates.

The question shows two lines, the solution of the system of equations will be the intersection point coordinates between these lines. Therefore, the solution is x=2 and y=1 (2,1).

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Answer:

TV = 9.71

Step-by-step explanation:

sin 47° = TV/13.28

0.7314 = TV/13.28

TV = 9.71

Step-by-step explanation:

large is 3 times larger than medium.

2 1/4 × 3 = 6 3/4

large is 6 times larger than small.

1 1/8 × 6 = 6 6/8 = 6 3/4

medium is 2 times larger than small.

1 1/8 × 2 = 2 2/8 = 2 1/4

The required measures of the angle A, L, and J is 40.8°, 83°, and 95° respectively.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
1.

The sum of the vertical angle is 180°. So,
∠A + ∠B = 180
Substitute value in the above equation,
x + 4x - 24 = 180
5x - 24 = 180
5x = 204
x = 204 / 5
x = 40.8°
∠A = 40.8°
Similarly,
2. ∠L = 83°
3. ∠J = 95°

Thus, the required measures of the angle A, L, and J is 40.8°, 83°, and 95° respectively.

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Answer:

A

Step-by-step explanation:

negative times a postive is always negative unless squared

Answer:

A. -21

Step-by-step explanation:

Note that when you multiply a negative with a positive number, your answer will be negative. Multiply as usual:

-3 * 7 = -21

A. -21 is your answer.

~

Answer:104.06

Step-by-step explanation:

The area of the shaded region is 123.84 cm²

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

The side length of the square is a= 24 cm

Area of square = a²

=24²

=576 cm²

Now let us find the area of circle

Diameter of circle is 24cm

Radius=24/2=12 cm

Area of circle=πr²

=3.14×12²

=3.14×144

=452.16cm²

the area of the shaded region = 576-452.16

=123.84 cm²

Hence, the area of the shaded region is 123.84 cm²

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The mean of the data is X = 85. The variance is 187.5. The standard deviation is σ = 13.7

Standard deviation is a measure of the amount of variability or dispersion of a set of data points from the mean value. It is calculated by finding the square root of the variance, which is the average of the squared differences between each data point and the mean. The standard deviation indicates how far the data points are from the mean on average, with larger values indicating greater variability and smaller values indicating less variability. The standard deviation is a commonly used measure of spread in statistics and is often used to describe the distribution of a dataset. It is denoted by the symbol σ (sigma) for a population and s for a sample.

To find the mean of the data, we add up all the values and divide by the total number of values:

X = (90 + 75 + 60 + 85 + 65 + 80 + 70 + 75) / 8

= 680 / 8

= 85

So the mean of the data is X = 85.

To find the variance, we need to first find the deviation of each value from the mean, square each deviation, and then take the average of the squared deviations:

deviation of 90 from mean = 90 - 85 = 5

deviation of 75 from mean = 75 - 85 = -10

deviation of 60 from mean = 60 - 85 = -25

deviation of 85 from mean = 85 - 85 = 0

deviation of 65 from mean = 65 - 85 = -20

deviation of 80 from mean = 80 - 85 = -5

deviation of 70 from mean = 70 - 85 = -15

deviation of 75 from mean = 75 - 85 = -10

Now, we square each deviation and find the average:

variance = [(5)² + (-10)² + (-25)² + (0)² + (-20)² + (-5)² + (-15)² + (-10)²] / 8

= (25 + 100 + 625 + 0 + 400 + 25 + 225 + 100) / 8

= 1500 / 8

= 187.5

So the variance is 187.5.

Finally, the standard deviation is the square root of the variance:

σ = √(187.5)

= 13.7 (rounded to the nearest tenth)

Therefore, the standard deviation is σ = 13.7 (rounded to the nearest tenth).

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Answer:

4739 CDs

Step-by-step explanation:

Given the function that models the rate at which the disc is sold expressed as;

R(t)=20,000e^−0.12t

t is the number of weeks since the CD was first released

We are to look for the number of CDs that are expected to be sold during the first 12 weeks after the release. To do this, you will simply substitute t = 12 into the modeled function and get R(12) as shown;

R(t)=20,000e^−0.12t

R(12)=20,000e^−0.12(12)

R(12)=20,000e^−1.44

R(12)=20,000(0.2369)

R(12) = 4738.56

Hence the total number of CDs expected to be sold to nearest thousand is 4739 CDs

Answer:

127,000

Step-by-step explanation:

you take the integral from 0 to 12 of R(t)

Answer:

The sum of interior angles of a triangle is 180°

In a right triangle, one of the three angles is 90°.  Therefore, the sum of the other two angles is 90°.

Let a = one unknown angle

Let b = the other unknown angle

As the sum of the angles is 90°:

⇒ a + b = 90°

As the difference between the two angles is 20°:

⇒ a - b = 20°

Rewriting the first equation to make a the subject:

⇒ a = 90° - b

Substituting this into the second equation and solving for b:

⇒ 90° - b - b = 20°

⇒ 90° -2b = 20°

⇒ 70° = 2b

⇒ b = 35°

Substituting found value for b into  a = 90° - b  and solving for a:

⇒ a = 90° - 35°

⇒ a = 55°

Therefore, the two unknown angles are 35° and 55°

The intervals [-5,-1], [-4,-1], [-3,1],[-2,1] match with -8,-7,4,-3.

Given the value of function at x=-5 is 35, at x=-4 is 24, at x=-3 is 15,at x=-2 is 8,at x=-2 is 8,at x=-1 is 3, at x=0 is 0, at x=1 is -1.

Average rate of change of values refers to the average of differences in the values divided by the difference of values of x.

First finding the average rate of change of interval [-5,-1]

Average rate of change={f(-1)-f(-5)}/(-1+5)

=(3-35)/4

=-32/4

=-8

Finding the average rate of change of interval [-4,-1]

Average rate of change={f(-1)-f(-4)}/(-1+4)

=(3-24)/3

=-21/3

=-7

Finding the average rate of change of interval [-3,1]

Average rate of change={f(1)-f(-3)}/(-3-1)

=(-1-15)/-3-1

=-16/-4

=4

Finding the average rate of change of interval [-2,1]

Average rate of change={f(1)-f(-2)}/(1+2)

=(-1-8)/3

=-9/3

=-3

Hence the values which are to be filled in the boxes are -8,-7,4,-3.

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Answer: there are 20 pieces of bread.

Step-by-step explanation:

Well, 12*1.5= 18, and 18*1.1111 = 20.

Answer:

On the circle

Step-by-step explanation:

The distance between D and G is:

\(\sqrt{(-1-(-10))^2+(3-1)^2}=\sqrt{9^2+2^2}=\sqrt{81+5}=\sqrt{86}\)

If point J is not exactly this far, then it is not on the circle.

\(\sqrt{(-1-(-3))^2+(12-3)^2}=\sqrt{2^2+9^2}=\sqrt{5+81}=\sqrt{86}\)

Therefore, it is on the circle. Hope this helps!

There are no values of $b$ for which the base-$b$-representation of $2013$ ends in the digit $3$. For a number to end in the digit $3$ in base-$b$ representation, it must be congruent to $3$ modulo $b$.

We can rewrite $2013$ as $2 \cdot 10^3 + 0 \cdot 10^2 + 1 \cdot 10^1 + 3 \cdot 10^0$. Now, if $2013$ is congruent to $3$ modulo $b$, it means that $2 \cdot 10^3 + 0 \cdot 10^2 + 1 \cdot 10^1 + 3 \cdot 10^0$ is also congruent to $3$ modulo $b$.

Simplifying the expression, we have $2000 + 0 + 10 + 3$. Since the base-$b$-representation is formed by multiplying each digit by the corresponding power of $b$, we can rewrite the expression as $2 \cdot b^3 + 1 \cdot b^1 + 3 \cdot b^0$. We can now observe that the constant term $3 \cdot b^0$ will always be congruent to $3$ modulo $b$. However, the other terms $2 \cdot b^3$ and $1 \cdot b^1$ will not be congruent to $3$ modulo $b$ for any positive value of $b$. Therefore, the base-$b$-representation of $2013$ cannot end in the digit $3$ for any value of $b$.

Hence, there are no values of $b$ for which the base-$b$-representation of $2013$ ends in the digit $3$.

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\(~~~~~x^2 -2 = 47\\\\\implies x^2 = 47 +2 \\\\\implies x^2 = 49\\\\\implies x = \pm\sqrt{49}\\\\\implies x = \pm 7\\\\\text{Hence, }~ x = 7,~~ x = -7\)

Three students want to estimate the mean backpack weight of their schoolmates. To do this, they each randomly chose 8 schoolmates and weighed their backpacks. Then as per the given sample data,

(a) The sample means of the backpacks are: 6.375,6.375,6.625

(b) Range of sample means: 0.25

(c)The true statement is: The closer the range of the sample means is to 0, the less confident they can be in their estimate.

For the first sample, mean= 6.375

For the second sample, mean= 6.375

For the third sample, mean= 6.625

Range of sample means=Maximum Mean- Minimum Mean

                                        = 6.625 - 6.375

                                        = 0.25

The students will estimate the average backpack weight of their classmates using sample means, the true statement is:

The closer the range of the sample means is to 0, the more confident they can be in their estimate.

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Answer:

E

Step-by-step explanation:

1.234 is most definitely a rational number!!

Answer:

X=8

Hope I helped

Answer:

8

Step-by-step explanation:

I hope this helps!

Answer: y = 2(x + 2)² - 5

Step-by-step explanation:

          We are going to use the completing the square method to transform this quadratic equation from standard form to vertex form.

Given:

     y = 2x² + 8x + 3

Factor the 2 out of the first two terms:

     y = 2(x² + 4x) + 3

Add and subtract \(\frac{b}{2} ^2\):

     y = 2(x² + 4x + 4 - 4) + 3

Distribute the 2 into -4 and combine with the 3:

     y = 2(x² + 4x + 4) - 5

Factor (x² + 4x + 4):

     y = 2(x + 2)² - 5

Answer:

Sum less than: 7 (1,1), (1,2), (1,3), (1,4), (1,5), (2,1), (2,2), (2,3), (2,4), (2,5), (3,1), (3,2), (3,3), (3,4), (3,5), (,4,1), (4,2), & (5,1)

Sum divisible by 5 (1,4), (2,3), (3,2), (4,1)

Answer: $20.78

Step-by-step explanation:

The exchange rate in 2010 should be $0.66/riyal. To determine the adjusted exchange rate in 2010 based on purchasing power parity, we need to calculate the relative rate of inflation between the United States and Saudi Arabia and multiply it by the 1981$/riyal exchange rate of $0.42.

The formula for calculating the relative rate of inflation is:

Relative Rate of Inflation = (Saudi Arabian Price Level / U.S. Price Level) - 1

Given that the Saudi Arabian price level in 2010 is 240 and the U.S. price level in 2010 is 100, we can calculate the relative rate of inflation as follows:

Relative Rate of Inflation = (240 / 100) - 1 = 1.4 - 1 = 0.4

Next, we multiply the relative rate of inflation by the 1981$/riyal exchange rate:

Adjusted Exchange Rate = 0.4 * $0.42 = $0.168

Finally, we add the adjusted exchange rate to the original exchange rate to obtain the exchange rate in 2010:

Exchange Rate in 2010 = $0.42 + $0.168 = $0.588

Rounding the exchange rate to 2 decimal places, we get $0.59/riyal.

Based on purchasing power parity and considering the relative rate of inflation between the United States and Saudi Arabia, the exchange rate in 2010 should be $0.66/riyal. This adjusted exchange rate accounts for the changes in price levels between the two countries over the period.

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