A student tosses a coin and then draws a card from a stack of 4 cards labeled 1 through 4

What is the sample space for this compound event?

{H, T, 1, 2, 3, 4}

{H1, T1, H4, T4}

{HT1, HT2, HT3, HT4}

{H1, T1, H2, T2, H3, T3, H4, T4}

So we want to know how many out of 1000 people did not listen to any type of the three music types that were surveyed If 30% of people listened to pop, 26% of people listened to rock and 20% of people listened country music. So first lets see how many people liked the three types of music: 30%+26%+20%=76%. So 24% of people did not like the three types of music that were surveyed. Finally we need to see how many people in 1000 is 24%. 24% out of 1000 people is 0.24*1000=240 people. So 240 people didn't like the 3 types of music.

Answer:

The answer is D

Step-by-step explanation:

The solution is in the file

Answer:

A. and B.

Step-by-step explanation:

Answer:

Step-by-step explanation:

First things first, let's explain what a right triangle is. The definition is very simple and might even seem obvious for those who already know it: a right-angled triangle is a triangle where one and only one of the angles is exactly 90°. The other two angles will clearly be smaller than the right angle because the sum of all angles in a triangle is always 180°. In a right angled triangle the sides are defined in a special way. The side opposing the right angle is always the biggest in the triangle and receives the name of "hypotenuse". The other two sides are called catheti. The hypotenuse is opposite the right angle and can be solved by using the Pythagorean theorem. In a right triangle with cathetus a and b and with hypotenuse c, Pythagoras' theorem states that: a² + b² = c².

To solve for c, take the square root of both sides to get c = √(b²+a²). This extension of the Pythagorean theorem can be considered as a "hypotenuse formula".

Steps to solve:

[tex]c=\sqrt{a^{2} +b^{2} } \\c=\sqrt{1.3^{2} +6.1^{2} } \\c=\sqrt{1.69+37.21} \\c=\sqrt{38.9} \\c=6.236986[/tex]

Answer:

the answer is C I hope this helps

The expression after simplifying is -12x² + 6x + 6.

Option A is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

5x - 4x² - 1 + x - 8x² + 7

Add like terms.

6x - 12x² + 6

-12x² + 6x + 6

Thus,

The final expression is -12x² + 6x + 6.

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Answer:

-9

Step-by-step explanation:

We are given the value of "a", which is 6. Let us substitute the value of "a" into the expression to determine a numerical value of 3(a - 9).

Open the parentheses to simplify the expression inside the long brackets [ ].

Subtract the expression inside the long brackets [ ]

Finally, simplify the product of 3 and -3.

Therefore, -9 is the value of 3(a - 9) when a = 6.

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{3(a - 9)}\\\\\mathsf{= 3(\bold{6} - 9)}\\\\\mathsf{= 3(6) + 3(-9)}\\\\\mathsf{= 18 - 27}\\\\\large\text{OR EVEN \rm{3(-3)}}\\\\\mathsf{= 3(-3)}\\\\\mathsf{= -9}\\\\\\\\\huge\text{Therefore, the answer is: \boxed{\mathsf{-9}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Given the ODE

(x - 1) y'' + y' = 0

we assume a solution of the form

[tex]y(x) = \displaystyle \sum_{n=0}^\infty c_n x^n[/tex]

with derivatives

[tex]y'(x) = \displaystyle \sum_{n=0}^\infty n c_n x^{n-1} = \sum_{n=0}^\infty (n+1) c_{n+1} x^n[/tex]

[tex]y''(x) = \displaystyle \sum_{n=0}^\infty (n+1) n c_{n+1} x^{n-1} = \sum_{n=0}^\infty (n+2)(n+1) c_{n+2} x^n[/tex]

Substituting these series into ODE gives

[tex]\displaystyle (x - 1) \sum_{n=0}^\infty (n+2)(n+1) c_{n+2} x^n + \sum_{n=0}^\infty (n+1) c_{n+1} x^n = 0[/tex]

[tex]\displaystyle \sum_{n=0}^\infty (n+2)(n+1) c_{n+2} x^{n+1} - \sum_{n=0}^\infty (n+2)(n+1) c_{n+2} x^n + \sum_{n=0}^\infty (n+1) c_{n+1} x^n = 0[/tex]

[tex]\displaystyle \sum_{n=1}^\infty (n+1)n c_{n+1} x^n - \sum_{n=0}^\infty (n+2)(n+1) c_{n+2} x^n + \sum_{n=0}^\infty (n+1) c_{n+1} x^n = 0[/tex]

[tex]\displaystyle \sum_{n=1}^\infty \bigg((n+1)n c_{n+1} - (n+2)(n+1) c_{n+2} + (n+1) c_{n+1}\bigg) x^n - 2c_2 + c_1 = 0[/tex]

[tex]\displaystyle \sum_{n=1}^\infty \bigg((n+1)^2 c_{n+1} - (n+2)(n+1) c_{n+2}\bigg) x^n - 2c_2 + c_1 = 0[/tex]

[tex]\displaystyle \sum_{n=0}^\infty \bigg((n+1)^2 c_{n+1} - (n+2)(n+1) c_{n+2}\bigg) x^n = 0[/tex]

Then the coefficients [tex]c_n[/tex] are given recursively by

[tex](n+1)^2 c_{n+1} - (n+2)(n+1) c_{n+2} = 0[/tex]

for all n ≥ 0, or equivalently,

[tex]c_{n+2} = \dfrac{n+1}{n+2} c_{n+1}[/tex]

which most closely resembles the second choice.

The multiplication problem represented by this grid is 0.7 x 0.4 = 0.28

Sure hope this helps you

Answer:

The perimeter of the rectangle is 28 units

Answer:

$310.05

Step-by-step explanation:

Method 1: Find the amount of 22% discount and subtract from original price, and find the amount of 6% tax and add to discounted price.

Original price: $375

Discount of 22%

22% of $375 = 0.22 × $375 = $82.50

Price after discount (but before tax): $375 - $82.50 = $292.50

Sales tax of 6%

6% of $292.50 = 0.06 × $292.50 = $17.55

Price after discount and tax: $292.50 + $17.55 = $310.05

Method 2: Add and subtract the discount percent and the tax percent first, then multiply.

Original price: $375

The discount is 22%.

The original price is 100%.

Subtract 22% from 100%: 100% - 22% = 78%

The discounted price is 78% of the original price.

Once you have the discounted price, tax is 6%.

The new discounted price is 100%. Add 6% to get 106%.

The price with tax is 106% of the discounted price.

106% of 78% of $375 = 1.06 × 0.78 × $375 = $310.05

Answer: $310.05

Answer:

= 25√3/3

Step-by-step explanation:

x/25 = tan 30o

x = 25/√3

= 25√3/3

Part A: The total length of the two sides, 1 and 2, of the triangle is 10x² + 14x - 8

Part B: The length of the third side of the triangle is 10x³ -2x²  - 16x + 2

From the given information,

The length of side 1 is

6x² - 4x - 2

and the length of side 2 is

18x + 4x² - 6

Part A

The total length of the two sides, 1 and 2, of the triangle will be

Length of side 1 + Length of side 2

That is,

6x² - 4x - 2 + 18x + 4x² - 6

This becomes,

6x² + 4x² + 18x - 4x - 2   - 6

10x² + 14x - 8  

Therefore, the total length of the two sides, 1 and 2, of the triangle is 10x² + 14x - 8

Part B

The length of the third side will be

Perimeter of the triangle - the total length of sides 1 and 2

From the given information,

The perimeter of the triangle is 10x³ + 8x² - 2x - 6

Then,

Length of third side = 10x³ + 8x² - 2x - 6 - (10x² + 14x - 8)

Length of third side = 10x³ + 8x² - 2x - 6 - 10x² - 14x + 8

Length of third side = 10x³ + 8x² - 10x²  - 2x - 14x - 6  + 8

Length of third side = 10x³ -2x²  - 16x + 2

Hence, the length of the third side of the triangle is 10x³ -2x²  - 16x + 2

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The two coterminal angles in radian measure (one positive and one negative) for each angle for figure 1 and 2 are,[(13π/4),(-π/4) and [(7π/4),(-17π/4) rad] respectively.

Angles having the same terminal side at standard position are called coterminal angles.

Although the magnitudes of coterminal angles varies, they all have the same sides and vertices.

Positive or negative coterminal angles are possible. The positive coterminal is obtained by adding 2 rad or 360° to the negative coterminal, while the negative coterminal is obtained by removing 2 rad or 360°.

For figure 1;

The positive coterminal angle is found as;

[tex]\rm \rightarrow \theta + 2 \pi \\\\ \rightarrow \frac{5 \pi}{4} + 2 \pi \\\\ \rightarrow\frac{13 \pi}{4} \ rad[/tex]

The negative coterminal angle is found as;

[tex]\rm \rightarrow \theta - 2 \pi \\\\ \rightarrow \frac{5 \pi}{4} - 2 \pi \\\\ \rightarrow\frac{-3 \pi}{4} \ rad[/tex]

For figure 2;

The positive coterminal angle is found as;

[tex]\rm \rightarrow \theta + 2 \pi \\\\ \rightarrow \frac{-9\pi}{4} + 2 \pi \\\\ \rightarrow\frac{7 \pi}{4} \ rad[/tex]

The negative coterminal angle is found as;

[tex]\rm \rightarrow \theta - 2 \pi \\\\ \rightarrow \frac{-9 \pi}{4} - 2 \pi \\\\ \rightarrow\frac{-17 \pi}{4} \ rad[/tex]

Hence,the two coterminal angles in radian measure (one positive and one negative) for each angle for figure 1 and 2 are,[(13π/4),(-π/4) and [(7π/4),(-17π/4)] respectively.

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Answer:

the answer is letter E.

see the attachment.

The statement that is true about the cost of haircuts is "On Average, the cost of a man's haircut is $16 less than the cost of a women's haircut".

A mean is an arithmetic average of a set of observations. it is given by the formula,

Mean = (Sum of observations)/Number of observations

Given that the mean cost of a haircut for a man is $28 and the mean cost of a haircut for a woman is $44. Therefore, the statement that is true about the cost of haircuts is "On Average, the cost of a man's haircut is $16 less than the cost of a women's haircut".

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Answer:

You need 443.2 square inches of wrapping paper to completely cover the prism.

Step-by-step explanation:

Calculate the area of each side.

Triangles:

Base * Height * 1/2

10 in. * 8.7 in. * 1/2

87 in.^2 * 1/2

43.5 in.^2

There are two sides with the triangle so we multiply the 43.5 in.^2 by two

(43.5 in.^2) * 2

87 in.^2

Side Rectangles:

Length * Width

13 in. * 8.7 in.

113.1 in.^2

There are two sides with this size rectangle so we multiply the 113.1 in.^2 by two

(113.1 in.^2) * 2

226.2 in.^2

Bottom Rectangle

Length * Width

13 in. * 10 in.

130 in.^2

There is only one side with the bottom rectangle.

Add up all the calculate areas.

Triangles + Side Rectangles + Bottom Rectangle

87 in.^2   +     226.2 in.^2      +     130 in.^2

443.2 in.^2

Answer:

11

Step-by-step explanation:

if the other things are the XY and XY, then the other one needs to measure 11.

Answer:

x = 13.83

Step-by-step explanation:

[tex]sin(70^{o}) =\frac{13}{x}[/tex]

[tex]x=\frac{13}{sin(70^{o} )} =13.83[/tex]

Hope this helps

Answer:

The common denominator is 4.

Step-by-step explanation:

4/8 simplified is 2/4.

Therefore, we can now add them together.

2/4 + 2/4 = 1.

Hope this helps:) Goodluck!

Answer:

hello!!!

the answer is 1916.6

please read the explanation it always helps... trust me!

Step-by-step explanation:

alrighty so....

we what to find the number that when we take 12% of we get 230...

okay we have to switch things up in the percent formula since we dont have the total number just the percentage and the percent number itself (i hope that isnt confusing.. the math is easier tho)

230 x 100= 23000 --> 23000/12= 1,916.6

Answer:

1,916.67

Step-by-step explanation:

1230/12 = x/100.

12x= (230)(100).

12x=23000.

x= 23000/100

x = 1,916.67

Answer:

8 feet

Step-by-step explanation:

3 + 5 = 8

..................................................

Answer:

15 gallons per hour

Step-by-step explanation:

So, what is given in the equation is that 1/4 of a gallon is leaking per minute. We have to change this to gallons per hour. Set it up like this:

[tex]\frac{\frac{1}{4}gallon }{1 minute} *\frac{60 min}{1 hour}[/tex]

Use a calculator and multiply 1/4 by 60.

After doing this, you should get:

[tex]\frac{15 gallons}{1 hour}[/tex]

Thus, the answer is the pool will leak 15 gallons per hour.

Hope this helps!! Ask questions in comments if needed!

Answer: 20:21

Step-by-step explanation: The Greatest Common Factor is 4, 80 divided by 4 is 20 and 84 divided by 4 is 21

Hope this helps

Answer:

20:21

Step-by-step explanation:

Expressing a number or more in their simplest form simply means expressing them to their lowest terms. You can divide 80:84 with 2 or 4. To make it faster, just divide both by 4 and you'll get 20:21 which is the final answer, no other number can divide 20:21.

I hope this helps.

Answer:

63/8

Step-by-step explanation:

For this question all you have to do is times the 9 and 7 and put the denominator(in this case 8) underneath to make a fraction. The answer totals as 63/8 or 7 and 7/8.

The selection of a random number from 1 - 72 is an illustration of probability, and the probability of selecting a multiple of 9 is 1/8

The sample size is given as:

n = 72

There are 8 multiples of 9 from 1 to 72.

So, the probability that a multiple of 9 is selected is:

P(Multiple of 9) = 8/72

Simplify

P(Multiple of 9) = 1/9

Hence, the probability of selecting a multiple of 9 is 1/8

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Answer:

A = 2700   M = 2100 dollars

Step-by-step explanation:

9 + 7 = 16 shares

  2 shares more = 600

       1 share = 300

9 shares * 300 = 2700

7 shares x 300 = 2100

Answer:

(y-3)^2=4p(x-2)

Step-by-step explanation:

C(h,k)

The equation is (y-k)^2=4p(x-h)

Answer:

(x-2)² + (y-3)² = 9

Explanation:

Circle Formula: (x - h)² + (y - k)² = r²

As touches x axis, coordinates: (2, 0)

radius: √(2-2)² + (3 -0)² = 3

Now find equation:

= (x-2)² + (y-3)² = 3²

= (x-2)² + (y-3)² = 9