A box contains 14 scarves in unique colors. If 4 scarves are picked randomly from the box,__________ different combinations are possible if the order doesn't matter.

Answer:

y > 2x - 4 and y ≤ [tex]\frac{x}{2}-1[/tex]

Step-by-step explanation:

In this question we will find the equations of the lines first then decide the inequality sign.

Dotted line in the graph passes through two points (2, 0) and (0, -4)

Let the equation of the line is y = mx + c

Where m = slope and c = y-intercept

Slope (m) of the line will be = [tex]\frac{y-y'}{x-x'}[/tex]

m = [tex]\frac{0+4}{2-0}[/tex]

m = 2

y-intercept of the line = (-4)

So, equation of the line will be y = 2x - 4

Now we see the shaded area is above the dotted line so inequality will be

y > 2x - 4

Now for the bold line

Let the equation of this line is y = m'x + c'

This line passes through points (2, 0) and (0, -1)

then slope of the line m' = [tex]\frac{y-y'}{x-x'}[/tex]

m = [tex]\frac{0+1}{2-0}[/tex] = [tex]\frac{1}{2}[/tex]

y-intercept = c = -1

Then equation of the line will be

y = [tex]\frac{x}{2}-1[/tex]

Since shaded area is below the bold line therefore, inequality sign will be "less than equal to"

Inequality of the bold line will be y ≤ [tex]\frac{x}{2}-1[/tex]

System of the linear inequalities will be

y > 2x - 4 and y ≤ [tex]\frac{x}{2}-1[/tex]

The probability that one number is twice the other number when two different cards are chosen at random is 1/49.

To find the probability that one number is twice the other number when two different cards are chosen at random from a set of 50 cards numbered from 1 to 50, we need to determine the number of favorable outcomes and the total number of possible outcomes.

The favorable outcomes occur when one card is twice the value of the other card. Let's consider the smaller number as 'x'. In that case, the larger number would be '2x'. We can see that 'x' can take any value from 1 to 25, since the larger number '2x' should be less than or equal to 50.

So, the number of favorable outcomes is 25. The total number of possible outcomes is the number of ways to choose 2 cards out of 50, which is given by the combination formula: C(50, 2) = 50! / (2! * (50-2)!), which simplifies to 50 * 49 / 2 = 1225.

Therefore, the probability is given by the ratio of the favorable outcomes to the total number of possible outcomes: 25/1225 = 1/49.

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it will be simplified as  [tex]\( -5a^2b^5c^3 \).[/tex]

Sure, let's simplify the expression step by step:

Given expression: [tex]\( (5ab^4c)(-abc^2) \)[/tex]

Step 1: Multiply the coefficients (numbers) together:[tex]\( 5 \times -1 = -5 \)[/tex]

Step 2: Multiply the variables with the same base together and add their exponents. Start with 'a': [tex]\( a \times a = a^{1+1} = a^2 \)[/tex]

Step 3: For 'b', multiply[tex]\( b^4 \) with \( b^1 \) which gives \( b^{4+1} = b^5 \).[/tex]

Step 4: For 'c', multiply[tex]\( c^1 \) with \( c^2 \) which gives \( c^{1+2} = c^3 \).[/tex]

Combine all these results together:[tex]\( -5a^2b^5c^3 \)[/tex]

So, the simplified expression is [tex]\( -5a^2b^5c^3 \).[/tex]

1. Start by multiplying the coefficients (numbers) together. In this case,[tex]\( 5 \times -1 = -5 \).[/tex]

2. Next, multiply the variables with the same base together and add their exponents. For 'a',[tex]\( a^1 \) times \( a^1 \) gives \( a^{1+1} = a^2 \). Similarly, for 'b', \( b^4 \) times \( b^1 \) gives \( b^{4+1} = b^5 \), and for 'c', \( c^1 \) times \( c^2 \) gives \( c^{1+2} = c^3 \).[/tex]

3. Combine all these results together to get [tex]\( -5a^2b^5c^3 \).[/tex]

This process ensures that each term in the expression is simplified according to the rules of exponents and multiplication of coefficients.

complete question

Simplify (5ab4c)(-abc2). 4b3c -5a2b5c3 -5ab4c2

The measure of ∠DCE is 100° so option (B) will be correct.

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.

In another word, the angle is the measurement of the angular distance for example for linear motion we have a meter inch but for angular rotation, we don't have the measurement so the angle is useful to measure the angular rotation.

Given the angle,

∠DCG = ∠DCE + 20 + 25

145° = ∠DCE + 20 + 25

∠DCE = 100°

Hence "The measure of ∠DCE is 100°

For more about the angle,

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To find the speed of each car, we set up and solve an equation based on the given information. The slower car's speed is 35 mph and the faster car's speed is 45 mph.

To solve this problem, we need to set up an equation based on the given information. Let's assume that the slower car's speed is x mph, so the faster car's speed would be (x + 10) mph. Since they meet at 5:00 p.m. and start at 2:00 p.m., they have been traveling for 3 hours.

Using the formula: speed = distance/time, we can write the equation:

x * 3 + (x + 10) * 3 = 240

Simplifying the equation, we get:

3x + 3(x + 10) = 240

6x + 30 = 240

6x = 210

x = 35

So, the slower car's speed is 35 mph and the faster car's speed is (35 + 10) = 45 mph.

[tex]n+n+1+n+2=3n+3=3(n+1)[/tex]

The product of all positive divisors of the number 100 is 1,000,000, using the property that the product of an integer's positive divisors is equal to the integer raised to the power of half its total number of divisors.

The product of all positive divisors of 100 can be found using a special property. This property states that for any positive integer n, the product of all its positive divisors will be equal to n raised to the power of half its total number of divisors. Now, factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. So, there are 9 divisors, and the product of all positive divisors will be 100^((9/2)). The answer is 1,000,000.

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Answer:

x=18 degrees

Step-by-step explanation:

Hello

by definition, two angles are called complementary angles, if the sum of their degree measures is 90. Each angle is called complement of the other.

A = angle 1=x

B=angle 2 =4x

A and B are complementary angles,hence

A+B=90

replacing

[tex]x+4x=90\\\\5x =90\\x=\frac{90}{5} \\x=18\ degrees[/tex]

A=18 degrees

B=4*x

B=72 degrees

x=18 degrees

Answer:

D) 23.6 cm

Step-by-step explanation:

We first find the circumference of the circle. Circumference is given by the formula

C = 2πr, where π = 3.14 and r is the radius.  The radius of our circle is 15 cm; this gives us

C = 2(3.14)(15) = 94.2.

Next we find the portion of the circumference associated with the given arc.  The measure (in degrees) of the arc is 90°; this makes it 90/360 of the circle.  90/360 simplifies to 1/4; this means this arc is 1/4 of the circumference:

1/4(94.2) = 23.55

This rounds to 23.6.

Final answer:

S5 represents Wen's salary in the fifth year after receiving a 3% annual raise from a starting salary of $100,000. Fifth year salary is $112,550.

Explanation:

The student is asking about an arithmetic sequence or a geometric sequence involving a salary increase. In this case, S5 represents the salary Wen will earn in the fifth year of her employment, assuming a 3% annual salary increase from a starting salary of $100,000. To calculate S5, we use the formula for the sum of a geometric sequence because a constant percentage change implies exponential growth. The first term (a) is her starting salary, the common ratio (r) is 1.03 (reflecting the 3% increase), and the term we want to calculate is the fifth term (n=5).

The formula for the nth term of a geometric sequence is Tn = a × r^(n-1), where Tn is the nth term, a is the first term, and r is the common ratio. Applying the formula:

Therefore, S5 calculates the salary Wen will earn in year five after receiving a 3% raise each year from the starting salary of $100,000 to $112,550.

The volume of the cone will be multiplied by a factor of [tex]\(3^1 = 3\).[/tex]

The volume of a right circular cone is given by the formula:

[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]

where [tex]\( r \)[/tex] is the radius and [tex]\( h \)[/tex] is the height of the cone.

Given that the height of the cone is multiplied by 3, the new height [tex](\( h' \))[/tex] becomes 3 times the original height [tex](\( h \))[/tex]:

[tex]\[ h' = 3h \][/tex]

Now, let's find the volume of the new cone with the updated height:

[tex]\[ V' = \frac{1}{3} \pi r^2 (3h) \][/tex]

[tex]\[ V' = \pi r^2 (h) \times 3 \][/tex]

So, the volume of the new cone is three times the original volume.

Now, let's dive into the explanation:

When the height of a cone is multiplied by a factor, the volume of the cone is directly proportional to the cube of that factor. This is because the volume formula contains the height term raised to the power of 3. So, if the height is tripled, the volume will be multiplied by[tex]\(3^3 = 27\).[/tex]

Alternatively, we can calculate it directly:

Original Volume: [tex]\(V = \frac{1}{3} \pi r^2 h\)[/tex]

New Volume:[tex]\(V' = \frac{1}{3} \pi r^2 (3h) = \pi r^2 h \times 3\)[/tex]

Therefore, the volume of the cone will be multiplied by a factor of [tex]\(3^1 = 3\).[/tex]

Complete question:

The height of a right circular cone is multiplied by 3, but its radius remains fixed. By what factor will the volume of the cone be multiplied?

There are a total of 36 outcomes if you rolled a fair single die twice.

The sample space for this event would be: (check in the attached file)

The area of the flower bed is approximately 132.73 square feet. Each bag of fertilizer covers 10 square feet, so we'd need 13.27 bags. Rounding up, we'll need to buy 14 bags.

The question involves the calculation of the area of a circular flower bed and determining the amount of fertilizer needed for that area. The area of a circle can be calculated using the formula πr², where 'r' (radius) is half of the diameter. In this case, the diameter of the flower bed is 13 feet, so the radius is 13/2 = 6.5 feet. We then square the radius (6.5²) which gives us 42.25 and multiply by π (approximately 3.14), resulting in an area of approximately 132.73 square feet. Given that each bag of fertilizer covers 10 square feet, we would need 13.27 bags of fertilizer. Since we cannot buy a fraction of a bag, we would need to buy 14 bags to fully cover the flower bed.

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Answer:

A magazine has a special offer of 18 issues for $28.44. Each issue costs $1.58. Solution: 28.44 / 18 = 1.58.

Answer:its c

Step-by-step explanation:

cccccccccccccccccccccccccccccccccccccccccccc

Given that an isosceles triangle has an exterior angle  of its base angle that is 130°​, the two possible sets of angles obtainable in the triangle are:

Recall:

Thus:

The isosceles triangle has been given in the image attached below to show the possible angle measures we can get.

In figure 1, we see that when the exterior angle of the bases is 130°​, the measure of each of the base angles would be:

[tex]\mathbf{180 - 130 = 50^{\circ}}[/tex]

The vertex angle would be:

[tex]\mathbf{180 - (50 + 50) = 80^{\circ}}[/tex]

Therefore, given that an isosceles triangle has an exterior angle  of its base angle that is 130°​, the two possible sets of angles obtainable in the triangle are:

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Answer: After doing the order of operations and round the decimal to tenths the result is - 15.5

Solution:

1/3(-32.48-14.02)

1. Operations inside the parentheses: Add numbers with the same sign:

1/3(-46.50)

2. Multiplication:

1/3(-46.50/1)=[(1)(-46.50)] / [(3)(1)]=(-46.50)/(3)

3. Dividing:

(-46.50)/(3) = - 15.50

4. Rounding decimal to tenths:

- 15.50 = - 15.5

Answer: First one

Step-by-step explanation:

Due to slope form which is y=mx + b.

-1 = x and y = 4.

It does not show the one because it would be equal to X, but it does show the negative