PLEASE HELP! Why did Southern states feel betrayed by President Zachary Taylor? He wanted popular sovereignty for new states, and Southerners did not trust their votes. He was from the South, and Southerners thought he should support their cause. He was from the South, and Southerners thought he favored California over his home state. He was a slaveholder, but did not want to bring his enslaved workers to California.

The required interval of domain for the composite function is  [-2, 3].

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

The domain of fog(x) is the set of all values of x for which the composition function fog(x) is defined.

fog(x) means that we plug g(x) into f(x), so we have:

fog(x) = f(g(x)) = f(x^2 - x) = √(6 - (x^2 - x))

= √(6 - x^2 + x)6

For the expression under the square root to be defined, we must have 6 - x^2 + x ≥ 0. This is a quadratic inequality that can be factored as:

-(x - 3)(x + 2) ≤ 0

The solutions of this inequality are -2 ≤ x ≤ 3.

However, we also need to check that the expression under the square root is non-negative, so we need to exclude the values of x that make 6 - x^2 + x < 0. This inequality holds for x < -2 or x > 3.

Therefore, the domain of fog(x) is [-2, 3].

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Answer:

There is no sufficient evidence to support the claim

Step-by-step explanation:

From the question we are told that

     The level of significance is  \(\alpha = 0.05\)

     The  sample proportion is  \(\r p = 0.08\)

     The  sample size is  \(n = 250\)

Generally for normal sampling distribution can  be used

     \(n * p > 5\)

So  

     \(n* p = 250 * 0.12 = 30\)

Since  

     \(n * p > 5\) then  normal sampling distribution can  be used

The null hypothesis is  \(H_o : p = 0.12\)

  The alternative hypothesis is  \(H_a : p > 0.12\)

The  test statistic is evaluated as

            \(t = \frac{\r p - p }{ \sqrt{ \frac{p(1- p)}{n} } }\)

substituting values

            \(t = \frac{0.08 - 0.12 }{ \sqrt{ \frac{0.12 (1- 0.12)}{250 } } }\)

            \(t = -1.946\)

The  p-value is obtained from the z  table and the value is

        \(p-value = P(t > -1.9462) =0.97512\)

Since the \(p-value > \alpha\)

    Then we fail to reject the null hypothesis

Hence it means there is no sufficient evidence to support the claim

the equations are,

3x - 5y = 2

4x + 5y = 33

sum the equations,

7x = 35

x = 35/7

x = 5

put x = 5 in equation 3x - 5y = 2

3(5) - 5y = 2

15 - 2 = 5y

5y = 13

y = 13/5

thus, the answer is x = 5 and y = 13/5

i have solved your problem in the answer tab.

if you have any doubt with this solution then let me know.

Answer:

6cm

Step-by-step explanation:

\(y \leqslant 2\)

Using a calculator, the value of  csc (203°) is -1.086

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

Since csc (203°) = 1/[sin (203°)]

Press 1/ [sin (203°)] and then the equal to button on your calculator. We have:

1/[sin (203°)] = -1.086

Note: If you calculator have "cosec" or "csc" button, you can simply press cosec (203°) or csc (203°) to get the answer.

Thus, the value of  csc (203°) is -1.086

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Answer: x = 2.

Step-by-step explanation:

By an online search, i found that the question is:

"Given that x satisfies the inequality 20*x > 33,  find the smallest value of x if x is a prime number."

To find the smallest value of x we need to input different possible values of x (where we have the condition that x must be a prime number) and see which one is the first one that makes the inequality true.

The prime numbers are:

2, 3, 5, ....

Let's start with the smaller one, x = 2

So we input it in the inequality and get:

20*2 > 33

40 > 33

this is true.

Then we can have x = 2, which is the smaller prime number that satisfies the inequality.

Answer:

D. 1/15

Step-by-step explanation:

Actual tree = 10 ft = 12 × 10 = 120 in.

Model tree = 8 in.

Scale factor = model tree/actual tree

Scale factor = 8/120

Scale factor = 1/15

Answer:

In line 4, he did the mistake. He should have square rooted the other side as changing sides changes square to square root.

explanation:

line 1:   \(\sf p^2 - 10p - 11 = 0\)

\(\sf p^2 - 10p = 11\)

line 2:   \(\sf p^2 - 10p + 25 = 11 + 25\)

\(\sf p^2 - 5p -5p+ 25 = 36\)

\(\sf p(p-5)-5(p-5) = 36\)

line 3:   \(\sf (p-5)^2 = 36\)

line 4:   \(\sf p - 5 = \pm \sqrt{36}\)

\(\sf p-5 = 6\)   or   \(\sf p-5 = -6\)

line 5: \(\sf p = 11\)  or   \(\sf p = -1\)

line 6: The solution is p = 11 or p = -1

Answer:

26

Step-by-step explanation:

to get from -6 to a 0, you add 6. 0+20 is 20, so that is how you get it

Answer:

Wii 467847585848584585869t8569

Answer: 0.03

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let's call the number of hot dogs Mr. Macho ate on the first day "h". On the second day, he ate h + 7 hot dogs, on the third day he ate h + 7 + 7 = h + 14 hot dogs, and so on. After five days, the total number of hot dogs he ate would be h + (h + 7) + (h + 14) + ... + (h + 28) = 125 hot dogs.

Expanding the expression for the total number of hot dogs, we get:

5h + 28 + 21 + 14 + 7 = 125

Solving for h:

5h = 75

h = 15

Therefore, Mr. Macho ate 15 hot dogs on the first day.

Answer:

12 hot dogs on the first day

Step-by-step explanation:

28+21+14+7=70

125-70=55

55/5=11

The surface area of the right triangular prism is 270 sq ft

The total surface area of the prism is the  sum of all the area of its faces

For the two triangles

A = 2(0.5bh)

A = bh

A = 7 * 12 = 84 sq.ft

For the two rectangles

A = 2lw

A = 2(6*12)

A = 2 * 72 = 144 sq.ft

For the third triangle;
Area  6ft * 7ft

Area = 42 sq.feet

Taking the sum of the areas

TSA = 84 + 144 + 42

TSA  = 270 sq ft

Hence the surface area of the right triangular prism is 270 sq ft

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the left side of this equation equal the right side through the process of completing the square that establishes the equality between the left side and the right side of the Gaussian integral equation.

using  completing the square method:

Starting with the left side of the equation:

∫\(e^(^-^x^2)\) dx

\(e^(^-^x^2) = (e^(^-x^2/2))^2\)

∫\((e^(^-^x^2/2))^2 dx\)

let  u = √(x²/2) =  x = √(2u²).

dx = √2u du.

∫ \((e^(^x^2/2))^2 dx\)

= ∫ \((e^(^-2u^2)\)) (√2u du)

The integral of \(e^(-2u^2)\)= √(π/2).

∫ \((e^(-x^2/2))^2\) dx

= ∫  (√2u du) \((e^(-2u^2))\\\)

= √(π/2) ∫ (√2u du)

We substitute back  u = √(x²/2), we obtain:

∫ \((e^(-x^2/2))^2\)dx

= √(π/2) (√(x²/2))²

= √(π/2) (x²/2)

= (√π/2) x²

A comparison  with the right side of the equation  shows that they are are equal.

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Hello!

YH // YV

so Thalès !!

YA/YH = YB/YV

17/YH = 16/(16+22)

17/YH = 16/38

YH = 17 x 38 ÷ 16 = 40.375

YH = x = 40.375

Answer:

Well it’s 2d and how many tiles in the rectangle is an area question

In this case we just multiply since w*l is area but in this case width is 6 and length (height) is 12

so 6*12= 72

Answer:

72 tiles

Step-by-step explanation:

Here you have to multiply. Why?

Think of a graph. To find the area we need to use the formula length times width. (a = l x w)  So we use 6 tiles wide and 12 tiles high as out length and width.

6 = width

12 = length

Now multiply

6 x 12 = 72

Hope this helps! Please comment if it does or not and if it needs adjustment. :)

Anna's total profit was $6000 + $16000 - $4000 = $14000.

How did Anna earn profit

Anna bought $4000 of company stock. The value of the stock doubled when she sold 75% of it, which means she sold 0.75 * $4000 = $3000 worth of stock when its value doubled.

Since the value of the stock doubled, Anna sold the $3000 worth of stock for 2 * $3000 = $6000.

Anna then sold the remainder of the stock (25% of the original amount) for four times the purchase price. Since she originally bought the stock for $4000, the remainder was worth 0.25 * $4000 = $1000.

Selling this remainder for four times the purchase price means that Anna sold it for 4 * $4000 = $16000.

Answer:

Step-by-step explanation:

So we know he arrived at 8:11 am. He should've arrived at 8:05 am if he rode the bus. So, we know that it took 27 minutes for him to get to school by walking. If he arrived at 8:11, then he started walking at 7:44 am. Since the school bus arrived 2 minutes before he started walking, we can say that the school bus arrived at 7:42 am.

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The correct interpretation of the confidence interval is: "We are 95% confident that between 50.6% and 55.4% of California adult residents say that marijuana should be legal." (Option A)

The confidence interval represents the range of values within which we are 95% confident that the true population parameter (in this case, the percentage of California adult residents who say that marijuana should be legal) lies. It is specific to the population of California adult residents that was surveyed, and cannot be generalized to other states or to all American adults.

Therefore, Option A is the correct answer that we are 95% confident that between 50.6% and 55.4% of California adult residents say that marijuana should be legal.

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The confidence interval denotes the range of values within which we are 95% certain that the true population parameter (in this case, the proportion of adult Californians who support marijuana legalization) resides. It cannot be extrapolated to adults in other states or to all Americans as a whole because it is specific to the demographic of adult inhabitants of California who were polled.

Accordingly, Option A is the right response, and we are 95% certain that between 50.6% and 55.4% of adult inhabitants of California agree that marijuana should be legal.

Answer: The answer is x²+3x

Step-by-step explanation:

hope that helps.

The formula for the centripetal force, as a function of the radius, is given as follows:

F = 896/r.

The equation that defines a direct proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality.

For an inverse proportional relationship, the equation is given as follows:

y = k/x.

The centripetal force varies inversely with the radius, hence the equation is given as follows:

F = k/r.

When F = 56, r = 16, hence the constant k is obtained as follows:

56 = k/16

k = 56 x 16

k = 896.

Hence the equation is given as follows:

F = 896/r.

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The dimensions of the room are approximately 7 meters by 10.5 meters.

In Mathematics, dimensions are referred to as measures of size such as length, width, and height of an object or a shape. A rectangle has length and width as its dimensions that define the area of a rectangle.

Let's start by using algebra to represent the information given in the problem. Let x be the width of the rectangular room, then the length is 1.5 times the width or 1.5x.

The perimeter of a rectangle is the sum of the lengths of all its sides, which can be expressed as:

\(\text{Perimeter} = 2(\text{length} + \text{width})\)

Substituting the values we have for length and width, we get:

\(\rightarrow35 = 2(1.5\text{x} + \text{x})\)

Simplifying the equation, we get:

\(\rightarrow35 = 2(2.5\text{x})\)

\(\rightarrow35 = 5\text{x}\)

\(\rightarrow\text{x}=\dfrac{35}{5}\)

\(\rightarrow\bold{x\thickapprox7}\)

So the width of the room is 7 meters.

To find the length, we can substitute x into the expression we have for the length:

\(\rightarrow\text{Length} = 1.5\text{x}\)

\(\rightarrow\text{Length} = 1.5(7)\)

\(\rightarrow\bold{Length=10.5}\)

So the length of the room is 10.5 meters.

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Step-by-step explanation:

I think you mean the sun's mass is 1.99 × 10³⁰ kg.

70% of that is hydrogen :

1.99 × 10³⁰ × 0.7 = 1.393 × 10³⁰ kg

a.

13% of that is in the core :

1.393 × 10³⁰ × 0.13 = 0.18109 × 10³⁰ = 1.8109 × 10²⁹ kg

b.

600 000 000 000 kg = 6.0 × 10¹¹ kg/s

so, 1.8109 × 10²⁹ kg will last

1.8109 × 10²⁹ / (6.0 × 10¹¹) = 0.301816666... × 10¹⁸ =

= 3.01816666... × 10¹⁷ seconds

60 seconds per minute.

60 minutes per hour.

24 hours per day.

365 days per year.

1 000 000 000 years.

that is

31,536,000,000,000,000 seconds in 1 billion years =

= 3.1536 × 10¹⁶ seconds in 1 billion years

so, this will go on for

3.018166666... × 10¹⁷ / 3.1536 × 10¹⁶ billion years =

= 0.957054372... × 10¹ = 9.57054372... billion years.

c.

the sun has already "spent" 4.6 billion years, so, that leaves about

9.6 - 4.6 = 5 billion years

According to the information, the total mass of hydrogen available for nuclear fusion in the Sun's core is 10^29 kg, the duration of the oroginal supply of hydrogen of the sun is 3.02 × 10^17 seconds, and the left time of the sun is 4.98 billion years.

a. The total mass of hydrogen available for nuclear fusion in the Sun's core is:

0.7 × 1.99 × 10^30 kg × 0.13 = 1.81 × 10^29 kg

How long the sun's original suply of hydrogen can last?

t = (1.81 × 10^29 kg) / (6 × 10^11 kg/s) = 3.02 × 10^17 seconds

Converting to billions of years:

t = (3.02 × 10^17 s) / (3.15 × 10^16 s/billion years) = 9.58 billion years

c. The Sun has already burned for 4.6 billion years, so the amount of time it has left before it runs out of fuel is:

9.58 billion years - 4.6 billion years = 4.98 billion years

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Answer:

Step-by-step explanation:

Vertical angles are equal

<A = <B

5x + 6 = 6x - 25                    Add 25 to both sides

5x + 6 + 25 = 6x                   Combine

5x + 31 = 6x                           Subtract 5x from both sides

31 = 6x - 5x

x = 31

Hi there!

\(\large\boxed{cos(\frac{\theta}{2} )= \frac{3}{\sqrt{7}}}\)

\(\large\boxed{tan(\frac{\theta}{2}) = \frac{\sqrt{5}}{3}}\)

Begin by recalling that:

sin(θ) = O/H,  so:

Opposite side = 3√5

Hypotenuse = 7

We can solve for the adjacent sign using the Pythagorean Theorem:

7² = (3√5)² + b²

49 = 45 + b²

b² = 4

b = 2.

Thus, cosθ = 2/ 7

Use the half angle identity to solve for cos(θ/2):

cos(θ/2) = √(1 + cosθ)

Plug in the value of cosθ:

= √(1 + 2/7) = √9/7, or 3 /√7

Thus:

\(cos(\frac{\theta}{2}) = \frac{3}{\sqrt{7}}\)

Calculate tan(θ/2) using the same process but with a different formula:

tan(θ/2) = √(1 - cosθ / 1 + cosθ)

Substitute in the value of cosθ:

tan(θ/2) = √(1 - 2/7)/(1 + 2/7)

= √(5/7)/(9/7) = √5/9 = √5/3

Answer:

3/16

Step-by-step explanation:

16 pupils, 11 play both, 1 plays piano only and 1 flute only

⇒ 11 + 1 + 1 = 13 pupils who play at least one instrument

⇒ 16 - 13 = 3 pupils who don't play either instrument

⇒ Out of the 16 total pupils, 3 play neither, putting this into numbers:

\(\frac{3}{16}\) which is then also the answer.