Jamie receives 15% commission on magazine subscriptions. One week her sales totaled $860. What was her commission?

Answer:

16ft

Step-by-step explanation:

use pythagreom thereom

12^2+b^2=20^2 solve

144+b^2=400

b^2= 256 square it

b= 16

Answer:

b=16

Step-by-step explanation:

Answer:

33cm^2

Step-by-step explanation:

Add the areas of the individual shapes so one rectangle and a square.

4*2 + 5*5 > 8 + 25 = 33

Answer:

31 cm²

Step-by-step explanation:

The area of the large figure is the sum of the areas of the smaller rectangles, the 4 cm x 2 cm one and the 5 cm x 5 cm one.

Area of the 4 x 2: 4 x 2 = 8 cm²

Area of the 5 x 5: 5 x 5 = 25 cm²

Sum of the two: 8 cm² + 25 cm² = 31 cm²

If z is a standard normal random variable , then the value of z for which P(Z≤z)=0.2580 is -0.65 .

A standard normal random variable is a continuous random variable that follows a normal distribution with a mean of 0 and a standard deviation of 1.

We can use a standard normal distribution table to find the value of z for which P(Z ≤ z) = 0.2580.

By using the standard normal distribution table, we can find the value that is closest to 0.2580, which is 0.2580 itself, and locate the corresponding z-value in the table,

Which is approximately z = -0.649523 ,

⇒ z ≈ -0.65 .

Therefore , the required value of z is -0.65 .

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The given question is incomplete , the complete question is

Given that z is a standard normal random variable, the value z for which P(Z≤z)=0.2580 is

assume the point (10,20) belongs to the graph of f of x what point belongs to the graph of y equals f (x )minus 5 ​

In this problem we have a transformation with the dollowing rule

(x,y) ------> (x,y-5)

so

(10,20) --------> (10, 20-5)

(10,20) --------> (10, 15)

therefore

The answer is

(10, 15)

Answer:

20$ is the answer of your question

The numerical length of the line segment FG is 10 units.

An equation is an expression that shows the relationship between two or more numbers and variables. An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.

Point G is on FH, hence:

FH = FG + GH

Given that GH = 8, FH = 3x + 3, FG = 2x, hence:

3x + 3 = (2x) + 8

x = 5

FG = 2x = 2(5) = 10

The numerical length of the line segment FG is 10 units.

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Answer:

4

Step-by-step explanation:

put in a calculator 2 + 2= 4

Answer:

Legally, it's 4

Step-by-step explanation:

2+2 = 4

However! Kim-jun-un as been quoted to say 1+1=1, so by that FALSE logic 2+2=2

The equation of the quadratic function is OB. y=x²-2x+1.
To determine which equation matches the given quadratic function, let's compare each option with the function:

Given function: y = -x² + 2x - 1

Option A: y = -x² + 2x - 1
Comparing this with the given function, we can see that they are identical.

Option B: y = x² - 2x + 1
This does not match the given function since the coefficient of x² is positive here, but it is negative in the given function.

Option C: y = x² + 9x - 18
This does not match the given function since the coefficients of both x² and x are different.

Option D: y = x² - 9x + 18
This does not match the given function since the coefficient of x² is positive here, but it is negative in the given function.

Based on the comparison, the correct answer is:

Option A: y = -x² + 2x - 1

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To find the average number of bits required to encode this source using a Huffman code, we need to first construct the Huffman code for the given probabilities. The Huffman code assigns shorter codes to more probable values and longer codes to less probable values. We can start by listing the probabilities in descending order:

0.2, 0.15, 0.15, 0.15, 0.15, 0.1, 0.1

Next, we group the two least probable values and assign them a code of 0. We then repeat this process, grouping the next two least probable values and assigning them a code of 10. We continue until we have assigned codes to all values:

7: 0
1: 1000
2: 1001
3: 1010
4: 1011
5: 110
6: 111

We can see that the average number of bits required to encode this source using the Huffman code is:

(0.2 x 1) + (0.1 x 4) + (0.1 x 4) + (0.15 x 4) + (0.15 x 4) + (0.15 x 3) + (0.2 x 3) = 2.771 bits

Therefore, the correct answer is b) 2.771 bits.
To find the average number of bits required to encode this source using a Huffman code, follow these steps:

1. Arrange the probabilities in descending order: 0.2, 0.15, 0.15, 0.15, 0.15, 0.1, 0.1.

2. Build the Huffman tree:
- Combine the two smallest probabilities (0.1 and 0.1) into a single node with a probability of 0.2.
- Combine the next two smallest probabilities (0.15 and 0.15) into a single node with a probability of 0.3.
- Combine the next smallest probability (0.2) with the previously created 0.2 nodes to create a node with a probability of 0.4.
- Combine the remaining 0.3 and 0.4 nodes to create the root node with a probability of 0.7.

3. Assign binary codes to each value based on the Huffman tree:
- Value 1: 111
- Value 2: 110
- Value 3: 101
- Value 4: 100
- Value 5: 011
- Value 6: 010
- Value 7: 00

4. Calculate the average number of bits required to encode the source using the assigned binary codes and their probabilities:
- (3 * 0.1) + (3 * 0.1) + (3 * 0.15) + (3 * 0.15) + (3 * 0.15) + (3 * 0.15) + (2 * 0.2) = 0.9 + 0.9 + 1.35 + 1.35 + 0.4 = 2.771 bits

So, the average number of bits required to encode this source using a Huffman code is 2.771 bits, which corresponds to option (b).

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Step-by-step explanation:

well, we have 1 4/5 miles in 1/4 hour, that means we have one quarter of the time unit of the requested speed unit.

so, we need to multiply everything by 4 to get to miles per hour :

(1 4/5) × 4 / 1 hour = (5 + 4)/5 × 4 = 9/5 × 4 = 36/5 =

= 7 1/5 mph = 7.2 mph

Answer:

Step-by-step explanation:

Angle ABE = 90°

Angle CBE = 37° (opposite angle)

90 - 37 = 53°

The required whole number, is either -19/3 or 7 which satisfied the given conditions

let us consider the whole number be x .

we have given the following

the twice a certain whole number i.e x and subtracted it from 3 times the square of the number leaves 133. Mathematically ,

3x^2 - 2x = 133

=> 3x^2 - 2x - 133 = 0

Factorize the above formula we get

=> (3x + 19)(x - 7)= 0

=> 3x + 19 = 0

=> 3x = -19

=> x = -19/3

=> x - 7 = 0

=> x = 7

Hence, possible value of x a whole number is either equal -19/3 or 7.

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Answer:

See below

Step-by-step explanation:

Period = 1 day      

Periodic interest = .045 / 365       (since there are 365 days in a year)

V(t) = 6000 *  ( 1 + .045/365)^t      where t is in days

V(t) = 6000 * (1+.045/365)^(t * 365)       where t is in years

The 15 and 9 units side lengths of the parallelogram ABCD, and the 36° measure of the acute interior angle, A indicates the values of the ratios are;

1. AB:BC = 5:3

2. AB:CD = 1:1

3. m∠A : m∠C= 1 : 4

4. m∠B:m∠C = 4:1

5. AD: Perimeter ABCD = 3:16

A ratio is a representation of the number of times one quantity is contained in another quantity.

The shape of the quadrilateral ABCD in the question = A parallelogram

Length of AB = 15

Length of BC = 9

Measure of angle m∠A = 36°

Therefore;

1. AB:BC = 15:9 = 5:3

2. AB ≅ CD (Opposite sides of a parallelogram are congruent)

AB = CD (Definition of congruency)

AB = 15, therefore, CD = 15 transitive property

AB:CD = 15:15 = 1:1

3. ∠A ≅ ∠C (Opposite interior angles of a parallelogram are congruent)

Therefore; m∠A = m∠C = 36°

∠A and ∠D are supplementary angles (Same side interior angles formed between parallel lines)

Therefore; ∠A + ∠D = 180°

36° + ∠D = 180°

∠D = 180° - 36° = 144°

∠D = 144°

m∠A : m∠C = 36°:144° =1:4

m∠A : m∠C = 1:4

4. ∠B = ∠D = 144° (properties of a parallelogram)

m∠B : m∠C = 144° : 36° = 4:1

5. AD ≅ BC (opposite sides of a parallelogram)

AD = BC = 9 (definition of congruency)

The perimeter of the parallelogram ABCD = AB + BC + CD + DA

Therefore;

Perimeter of parallelogram ABCD = 15 + 9 + 15 + 9 = 48

AD:Perimeter of the ABCD  = 9 : 48  = 3 : 16

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Answer: -1 (x-1) (3x+4)

Step-by-step explanation: You have to dristibute, combine Like terms, find the common factors, use the sum- product pattern, common factor from 2 pairs,  re-write in correct form then you got your answer

Answer:

c = -72

Step-by-step explanation:

Subtract 6 from both sides (14 - 6 = 8)

c/-9 = 8

Multiply -9 to both sides to isolate c (8 * -9 = -72)

c = -72

Answer:

Bigger number = 42

Smaller number = 10

Step-by-step explanation:

Step 1: Define variables

x = larger number

y = smaller number

Step 2: Write systems of equations

x + 2y = 62

3x = y + 116

Step 3: Rewrite 1st equation

x = 62 - 2y

Step 4: Substitution

3(62 - 2y) = y + 116

186 - 6y = y + 116

186 = 7y + 116

70 = 7y

y = 10

Step 5: Plug in y to find x

x + 2(10) = 62

x + 20 = 62

x = 42

Answer:

  It is the 3rd one

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

x-6-6/x+4

Answer: 10

Step-by-step explanation:

6-5 = 1

-2 x 1 = -2

-2 x -5 = 10

It is a true statement that when rainfall increases, the water level in the lake goes up. The rainfall is the independent variable in the situation.

The answer is yes because independent variable is the one that is manipulated or changed in an experiment. The dependent variable is the one that is observed or measured.

In this situation, rainfall is independent variable because it is what is being manipulated or changed. The water level in the lake is the dependent variable because it is what is being observed or measured.

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The point of intersection of the equations (1, 3)

From the question, we have the following parameters that can be used in our computation:

Y=2x+1

Y=4x-1

So, we have

2x + 1 = 4x - 1

Evaluate the like terms

2x = 2

So, we have

x = 1

This means that

y = 2(1) + 1

So, we have

y = 3

Hence, the intersection is (1, 3)

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Answer:

9- 8

Step-by-step explanation:

Answer:

The slope is \(\frac{1}{2}\).

Step-by-step explanation:

The formula for finding the slope is rise over run.

The "rise" is change in y.

The "run" is change in x.

Here, the change in y is 1, while the change in x is 2.

So, the rise over run would be 1 over 2.

Hence, the answer is \(\frac{1}{2}\).

Answer:

15625

Your welcome. Have a great day :D

Answer:

2.9

Step-by-step explanation:

and yw i saw that u put thx in the comments

Answer:

the answer is 83°

Step-by-step explanation:

by the sum of iner and outer angle=180°

180-126= 54°

x=180-43+54

x=180-97

x=83°

The measure of angle x is 43°.

What is Triangle?

A triangle is a three sided polygon , which has three vertices.

Given that;

In triangle, The value of interior angles are 43° and x°.

And, An exterior angle is 126°.

Since, The sum of two interior angles is equal to the exterior angle of same triangle.

Hence, We can formulate;

43° + x = 126°

Subtract 43° both side;

43° + x - 43° = 126° - 43°

x = 83°

Thus, The measure of angle x is 43°.

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After reducing all the book prices by 50%, the new median price is determined to be $7.70 (B)

To find the new median price after reducing all the book prices by 50%, we first need to calculate the reduced prices. By reducing each given price by 50%, we get $6.375, $7.40, $9.995, $4.975, $8.00, and $8.975 respectively.

Next, we arrange these reduced prices in ascending order: $4.975, $6.375, $7.40, $8.00, $8.975, and $9.995. The median is the middle value in this ordered list. Since there are six prices, the middle two values are $7.40 and $8.00.

To find the median, we take the average of these two values, which gives us ($7.40 + $8.00) / 2 = $7.70.

Therefore, the new median price, after reducing all the book prices by 50%, is $7.70 (B). This means that the median price of the books, after the reduction, is $7.70.

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To calculate the probabilities, we need to use the concept of binomial probability.

For a fair coin being tossed 5 times:

(a) Probability of getting five heads:

The probability of getting a head in a single toss is 1/2.

Since each toss is independent, we multiply the probabilities together.

P(Head) = 1/2

P(Tails) = 1/2

P(Five Heads) = P(Head) * P(Head) * P(Head) * P(Head) * P(Head) = \((1/2)^5\) = 1/32 ≈ 0.03125

So, the probability of obtaining five heads is approximately 0.03125 or 3.125%.

(b) Probability of getting four heads:

There are five possible positions for the four heads.

P(Four Heads) = (5C4) * P(Head) * P(Head) * P(Head) * P(Head) * P(Tails) = 5 * \((1/2)^4\) * (1/2) = 5/32 ≈ 0.15625

So, the probability of obtaining four heads is approximately 0.15625 or 15.625%.

(c) Probability of getting one head:

There are five possible positions for the one head.

P(One Head) = (5C1) * P(Head) * P(Tails) * P(Tails) * P(Tails) * P(Tails) = 5 * (1/2) * \((1/2)^4\) = 5/32 ≈ 0.15625

So, the probability of obtaining one head is approximately 0.15625 or 15.625%.

For a fair die being thrown eight times:

(a) Probability of a 6 occurring six times:

The probability of rolling a 6 on a fair die is 1/6.

Since each roll is independent, we multiply the probabilities together.

P(6) = 1/6

P(Not 6) = 1 - P(6) = 5/6

P(Six 6s) = P(6) * P(6) * P(6) * P(6) * P(6) * P(6) * P(Not 6) * P(Not 6) = \((1/6)^6 * (5/6)^2\) ≈ 0.000021433

So, the probability of rolling a 6 six times is approximately 0.000021433 or 0.0021433%.

(b) Probability of a 6 never happening:

P(No 6) = P(Not 6) * P(Not 6) * P(Not 6) * P(Not 6) * P(Not 6) * P(Not 6) * P(Not 6) * P(Not 6) = \((5/6)^8\) ≈ 0.23256

So, the probability of not rolling a 6 at all is approximately 0.23256 or 23.256%.

(c) Probability of an odd number of 6s:

To have an odd number of 6s, we can either have 1, 3, 5, or 7 6s.

P(Odd 6s) = P(One 6) + P(Three 6s) + P(Five 6s) + P(Seven 6s)

\(P(One 6) = (8C1) * P(6) * P(Not 6)^7 = 8 * (1/6) * (5/6)^7P(Three 6s) = (8C3) * P(6)^3 * P(Not 6)^5 = 56 * (1/6)^3 * (5/6)^5P(Five 6s) = (8C5) * P(6)^5 * P(Not 6)^3 = 56 * (1/6)^5 * (5/6)^3P(Seven 6s) = (8C7) * P(6)^7 * P(Not 6) = 8 * (1/6)^7 * (5/6)\)

P(Odd 6s) = P(One 6) + P(Three 6s) + P(Five 6s) + P(Seven 6s)

Calculate each term and sum them up to find the final probability.

After performing the calculations, we find that P(Odd 6s) is approximately 0.28806 or 28.806%.

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The given function f does not have a one-to-one correspondence between its domain and the range.

Set A, B, and C, prove that the given function f is not one-to-one: Let F(IR, R) be the set of all functions from I. We have to prove that FR, 2¹ > 2¹⁰¹. Here, I = {A, B, C}, i.e. the set of elements is {A, B, C}.To prove the function f is not one-to-one, consider the following steps:Step 1: Consider a function f ∈ F(2, 1) defined as: $f(A) = x$ and $f(B) = y$, where $x, y \in \{0, 1\}$.Step 2: Also, consider A, B $\in$ 2¹ such that A = $\{x, y\}$ and B = $\{y, z\}$. Here, x $\ne$ y, y $\ne$ z, and x $\ne$ z. Thus, we have A $\ne$ B.Step 3: Now, assume that f(A) = f(B). Hence, we have: $f(A) = f(B) \Rightarrow x = y$ and $y = z \Rightarrow x = z$Step 4: This contradicts the assumption that x $\ne$ z. Hence, the given function f is not one-to-one, i.e. it is many-to-one.Inference: Thus, the given function f does not have a one-to-one correspondence between its domain and the range.

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Solution,

Principal=£ 500

Time=2 years

Interest=£40

Rate=?

Now,

R=I*100/P*T

= 40*100/500*2

=4000/1000

=4%

Hope it helps

Good luck on your assignment

Answer:

\(4\%\)

Step-by-step explanation:

\(p = 500 \\ r = x \\ t = 2\)

\(simple \ \: \: \: = \frac{prt}{100} \\ interest \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 40= \frac{500 \times x \times 2}{100} \\ \: \: \: \: \: \: \: 40 \: \: \: \: \: \: \: \: \: = \frac{1000x}{100} \\ \frac{40 \times 100}{1000} = x \\ x = 4\)

The radius of Deimos to one significant digit in meters is approximately 9.4 m

.

Given the ratio of the Sun-from-Mars distance to Deimos-from-Mars distance is 365,000, the distance between Mars and Deimos can be found to bedeimos distance = Sun-Mars distance / 365,000

Next, we can find the diameter of Deimos by noting that 550 of its diameters is equal to the distance it takes to transit the shadow of Mars during a lunar eclipse.

Let's call the diameter of Deimos "d", so we can

diameter = 1/550 * deimos distance

Finally, the Sun appears about 8.4 times as large as Deimos in the Martian sky. If we call the radius of Deimos "r", then the radius of the Sun is 8.4r.

Using the information given, we can set up the following equation:

deimos distance / (3,000,000 + r) = 8.4r / (3,000,000)Simplifying and solving for r,

we get:r = 9.39 m (rounded to one significant digit)

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