Determine if 7x – 4 and 2x + 1 are factors of
k (2) = 7x4 – 423

Answer:

r = \(\sqrt{29}\)

Step-by-step explanation:

The distance from the centre to a point on the circle is the radius r

Calculate r using the distance formula

r = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = (0, 0 ) and (x₂, y₂ ) = (2, 5 )

r = \(\sqrt{(2-0)^2+(5-0)^2}\)

  = \(\sqrt{2^2+5^2}\)

  = \(\sqrt{4+25}\)

  = \(\sqrt{29}\)

Answer:

B. 2.2 kilometers

Step-by-step explanation:

⭐What is the change in the cyclist's elevation?

Thus, we need to solve for the value of the height (x) of the hill.

Notice that the hill is in the shape of a right triangle. In order to find an unknown side length for right triangles, we need to use a trigonometric function.

⭐What is a trigonometric function?

First, let's see what kind of side lengths we are given (opposite, hypotenuse, or adjacent).

We are given a side length of 10km, which is the hypotenuse of the triangle, and we are given a side length of x, which is the opposite of θ (13°).

Therefore, we will use the trigonometric function sin(θ) to solve for x.

Substitute the side lengths and angle measures we are given:

\(sin(13) = \frac{x}{10}\)

Set the equation equal to x:

\(10sin(13) = x\)

Solve for x. I recommend using a scientific calculator (e.g. Desmos Scientific Calculator):

\(2.2 = x\)

∴ The cyclist's change in elevation is 2.2 kilometers.

Answer:

Sampling bias

Step-by-step explanation:

Sampling bias is due to the mistaken manner of selection of the respondents for the survey when conducting market research or similar survey. The sampling bias error is said to have occurred when the sample selection procedure, methodology, or process focuses on part of the population with a particular attribute, rather than being a random sample. Such that a given subset of the of the population are selected for the survey, which results in a biased sample.

When a stone is dropped into a lake, it generates a circular ripple that travels outward at a velocity of 60 cm/s. We need to find the value of A ∘ r. When solving such a problem, the wave equation is used.

A general wave equation is given as follows: A(x, t) = f(x - vt) + g(x + vt)where A is the amplitude of the wave, v is the speed of the wave, and f and g are functions that depend on the shape of the wave. Initially, the stone is dropped into the lake, and the ripple starts to propagate outward.

We assume that the shape of the ripple is circular; thus, we can say that the function that represents the ripple is: A(x, t) = A∘r(x, t)where r is the distance from the center of the ripple to any point on the circumference of the ripple. Since the ripple is circular, r will be constant at any given point on the circumference of the ripple. Also, we can assume that the amplitude of the ripple is constant; therefore, A is also constant at any point on the ripple circumference. The wave speed is given as 60 cm/s, and the ripple is circular, so the equation that represents the ripple can be written as: A(x, t) = A∘r(x - vt)For a circular ripple, the distance r from the center of the ripple to any point on the circumference can be expressed in terms of the angle θ between the radius vector and the x-axis. Hence, we can write: r = Rsin(θ)where R is the radius of the circle. The wave equation is given as:A(x, t) = A∘r(x - vt) Substitute r into the wave equation and we get: A(x, t) = A∘ Rsin(θ) (x - vt) From the initial point of the ripple, t = 0. Hence, the wave equation becomes: A(x, 0) = A∘Rsin (θ) x We can now solve for A ∘ R by using the following equation:A(x, 0) = A∘Rsin(θ) x.Thus, the value of A ∘ R is given as: A ∘ R = A(x, 0) / sin(θ)The final answer will be (A ∘ r)(t) = (A ∘ R)sin(θ) (x - vt).

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Answer: 42.8º

Explanation

Using a scientific calculator, we can get the inverse of the sine function on both sides:

Simplifying:

The formula for calculating the confidence interval of a sample mean is sample mean ( /-) critical value z-score times the standard error of the sampling distribution of the mean.

Confidence interval is a range of values that enclose the true value of a population parameter with a specified level of confidence. It is used in inferential statistics to estimate an unknown parameter using a sample. The value of the confidence interval depends on the level of confidence chosen by the researcher which is usually 90%, 95%, or 99%.The correct answer is b which is the formula for calculating the confidence interval of a sample mean.

It is the sample mean plus or minus the critical value z-score times the standard error of the sampling distribution of the mean. The standard error of the sampling distribution of the mean is the standard deviation of the sample mean and is estimated using the formula, standard deviation of the population divided by the square root of the sample size.The critical value of the z-score depends on the level of confidence chosen by the researcher.

A 90% confidence interval has a critical value of 1.645, a 95% confidence interval has a critical value of 1.96, and a 99% confidence interval has a critical value of 2.58. Therefore, the formula for calculating the confidence interval of a sample mean is sample mean ( /-) critical value z-score times the standard error of the sampling distribution of the mean.

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Answer:

$936.18

Byehave fun k bye

Answer:

1

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

(1,0)

(x,y)

x-intercept is 1

Answer:

90 degrees

I hope this helps!

Based on the p-value, we make a decision:

Since the p-value is greater than 0.05, we fail to reject H₀.

What is probability?

Probability is a measure or quantification of the likelihood of an event occurring. It is a numerical value assigned to an event, indicating the degree of uncertainty or chance associated with that event. Probability is commonly expressed as a number between 0 and 1, where 0 represents an impossible event, 1 represents a certain event, and values in between indicate varying degrees of likelihood.

To test whether Utah had a higher proportion of identity theft complaints than the overall proportion of 26%, we can perform a hypothesis test using the proportion of identity theft complaints in Utah.

The hypotheses are as follows:

H₀: p ≤ 0.26 (The proportion of identity theft complaints in Utah is less than or equal to 26%)

Hₐ: p > 0.26 (The proportion of identity theft complaints in Utah is greater than 26%)

To calculate the test statistic, we can use the formula for a test of a single proportion:

z = (P - p₀) / √(p₀(1-p₀)/n)

Where P is the sample proportion, p₀ is the hypothesized proportion, and n is the sample size.

Given that Utah had 924 complaints of identity theft out of 3460 consumer complaints, we can calculate the sample proportion as P = 924 / 3460 = 0.267.

Plugging in the values, we have:

z = (0.267 - 0.26) / √(0.26(1-0.26)/3460)

Calculating this expression:

z ≈ 0.007 / √(0.26(0.74)/3460) ≈ 0.007 / 0.0082 ≈ 0.854

Rounding to three decimal places, the standardized test statistic is z ≈ 0.854.

To find the p-value, we need to calculate the probability of observing a test statistic as extreme as the one we obtained (0.854) under the null hypothesis.

The p-value is the probability of getting a z-value greater than or equal to the observed test statistic of 0.854. Since the alternative hypothesis is one-sided (p > 0.26), we look for the area to the right of the observed test statistic on the standard normal distribution.

Using a standard normal distribution table or statistical software, we find that the p-value ≈ 0.1977.

Rounding to four decimal places, the p-value is approximately 0.1977.

Hence, Based on the p-value, we make a decision:

Since the p-value is greater than 0.05, we fail to reject H₀.

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The correct expressions are;

B). 2/2 + 2/2 + 1/2 = 2.5

D). 1 1/2 + 1/2 + 1/2 = 2.5

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

Given:

Danny has 2 1/2 pounds of coffee grounds.

2 1/2 = 2.5

The choices are given in the image.

A). 3/2 + 2/2 + 1/2 = 6/2 = 3 ≠ 2.5.

B). 2/2 + 2/2 + 1/2 = 2.5

C).  1 + 1 + 1/2 + 1/2

But this shows the situation for four days,

So, this option is discarded.

D). 1 1/2 + 1/2 + 1/2 = 2.5

Therefore, B and D are the correct options.

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According to the information, the 95% confidence interval for the proportion of Americans who drink tea daily is approximately (0.2485, 0.2766). The margin of error is approximately 0.0140.

To construct a confidence interval for the proportion of Americans who drink tea daily, we can use the formula:

Where,

p = the sample proportion

Z = the critical value corresponding to the desired confidence level

n = the sample size

Given:

Now, let's calculate the confidence interval and margin of error:

According to the information, the 95% confidence interval for the proportion of Americans who drink tea daily is approximately (0.2485, 0.2766), with a margin of error of approximately 0.0140.

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Answer:

B (-4,-4)

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Since it is currently at (4,2), reflecting it across y=-1 will bring the y-coordinate down to -4. After that, reflecting it across the y-axis will flip the sign in front of the x-coordinate, so 4 to -4. Therefore, your answer is (-4,-4).

Answer:

False, 82 inches is not greater than 5 feet and 10 inches

Step-by-step explanation:

1 feet = 12 inches

5x12=60+10=70

82 is greater than 70.

Answer:

pi r^2

Step-by-step explanation:

Take the radius and square it (multiply it by itself) and then multiply by pi (3.14)

Answer:

A = πr²

Step-by-step explanation:

The area of a circle is equal to A = πr²

π = 3.14159 ...

       -> it is a value that goes on forever, most calculators will have a button for this, it is called "Pi" or "π"

r = the radius

       -> this is the distance of half the width of the circle. You can see the parts of a circle attached

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

Step-by-step explanation:

We divide the number by 8 and write the remainder in reverse order to get the equivalent octal number.

Answer:

Let's write down the base of each one:

- Decimal is base 10 (0 to 9)

- Octal is base 8 (0 to 7)

So, if we want to convert decimal to octal, we need to divide the decimal number by 8 and hold onto the remainder.

Then once your quotient becomes 0, from the last remainder to the first, write your numbers.

For example here is 437 base 10.

437 / 8 = 54 R 5

54 / 8 = 6 R 6

6 / 8 = 0 R 6

So, the answer is 665 base 8.

The factor that does NOT control the stability of a slope is the angle of repose for intact bedrock. The angle of repose refers to the steepest angle at which a pile of loose material remains stable without sliding. It is mainly applicable to loose materials like soil and granular substances, not intact bedrock.

Bedrock stability depends on factors such as its strength, fracturing, and geological properties, rather than the angle of repose. Factors that control the stability of a slope include whether the slope is rock or soil. Rock slopes tend to be more stable than soil slopes due to the cohesive nature of intact rock.

The amount of water in the soil also affects slope stability, as excessive water can increase pore pressure and reduce the shear strength of the soil, leading to slope failure. Additionally, the orientation of fractures, cleavage, and bedding in the rock can influence slope stability by creating planes of weakness or strength.

To summarize, while the angle of repose is a significant factor in slope stability, it is not applicable to intact bedrock. The stability of a slope is influenced by the type of material (rock or soil), the presence of water, and the orientation of fractures and bedding.

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Question: In a sale, the price of a book is reduced by 25%. The price of the book in the sale is £12. Work out the original price of the book

Answer: £16

Step-by-step explanation:

To determine the original price of the book, we can use the fact that the sale price is 75% (100% - 25%) of the original price. Let's denote the original price as x.

75% of x = £12

To solve for x, we can set up the equation:

0.75x = £12

To isolate x, we divide both sides of the equation by 0.75:

x = £12 / 0.75

x = £16

Therefore, the original price of the book was £16.

The surface area of the regular square pyramid is approximately 212.932 square yards.

To find the surface area of a regular pyramid, we need to calculate the area of each face and then sum them up. In the case of a square pyramid with a base side length of 6.8 yards and a height of 10.2 yards for each face, we can follow these steps:

(1) Calculate the area of the base: Since the base is a square, its area can be found by multiplying the length of one side by itself. Thus, the area of the base is 6.8 yards multiplied by 6.8 yards, which equals 46.24 square yards.

(2) Calculate the area of the triangular faces: Each triangular face of the pyramid is an isosceles triangle, with one side being the height (10.2 yards) and the other two sides being the slant height. To find the slant height, we can use the Pythagorean theorem. The slant height is the hypotenuse, and the height and half of the base form the legs of the right triangle. Thus, the slant height can be calculated as sqrt((6.8/2)^2 + 10.2^2), which is approximately 11.594 yards.

Now, we can calculate the area of each triangular face using the formula: (1/2) * base * height, where the base is the length of the side (6.8 yards) and the height is the slant height (11.594 yards). Thus, the area of each triangular face is (1/2) * 6.8 * 11.594, which is approximately 39.548 square yards.

(3) Calculate the total surface area: The pyramid has one base and four triangular faces. Therefore, the total surface area is the sum of the areas of the base and the four triangular faces. Adding up the numbers obtained above, we get 46.24 + 4 * 39.548, which equals approximately 212.932 square yards.

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Answer: x=8

Step-by-step explanation: 8+14x+8x-4=180

The sum of a triangle will always be 180 degrees so you put 8+14x + 8x-4 equal to 180 and solve the equation, the answer is x=8

Answer:

(a) (300+2x)(4x+40)=8x^2+1280x+12000

(b) 300+2x=360, x=30. Then width = 4*30+40=160. 360*160=57600 ft squared.

The statistical analysis method known as analysis of variance (ANOVA) divides the observed aggregate variability within a data set into two parts:

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hi

3/5 *20= 60/5 = 12  

12 block are green

Answer:

a. x = 2 , x = -5

b. no real roots

Step-by-step explanation:

a. x² + 3x – 10

= x² - 2x + 5x - 10

= x (x²/x - 2x/x) + 5 (5x/5 - 2*5/5)

= (x - 2) (x + 5)

x - 2 = 0                            x + 5 = 0

 + 2    +2                             -5     -5

--------------                         ---------------

x = 2                                   x = -5

x = 2 , x = -5

b. 2x² - 4x + 3

This can't be solved because the equation has no real roots, and also the discriminant is negative.

To use the Midpoint Rule with n = 4 to approximate the integral of x^2 + 5dx from 10 to 2, we first need to find the width of each subinterval.

The width is given by (b - a)/n, where a is the lower limit of integration (2), b is the upper limit of integration (10), and n is the number of subintervals (4).
Therefore, the width of each subinterval is (10 - 2)/4 = 2.
Next, we need to find the midpoint of each subinterval. The first midpoint is 2 + 1(2) = 4, the second midpoint is 4 + 1(2) = 6, the third midpoint is 6 + 1(2) = 8, and the fourth midpoint is 8 + 1(2) = 10.
Now, we can use the Midpoint Rule formula:
Δx/2 [f(x1) + f(x2) + f(x3) + f(x4)]
where Δx is the width of each subinterval and f(xi) is the function evaluated at the midpoint of the ith subinterval.
Plugging in the values, we get:
2/2 [(4^2 + 5) + (6^2 + 5) + (8^2 + 5) + (10^2 + 5)] = 80
Rounding to four decimal places, the approximate integral value is 80.0000.

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Answer:

31.5 (rounded)

Step-by-step explanation:

Answer:

5 ∛249

≈ 31.45597 (In decimal form)

Step-by-step explanation:

The correct answer is (b) all real numbers except odd multiples of π/2. The domain of validity for cscθ (cosecant) is restricted because cosecant is undefined when the sine of an angle is zero.

In the trigonometric identity cscθ = 1/sinθ, the denominator sinθ becomes zero at odd multiples of π/2 (such as π/2, 3π/2, 5π/2, etc.), resulting in a division by zero error. Therefore, the cosecant function is not defined for these values of θ.

For all other real numbers θ, the sine function is non-zero and well-defined, allowing us to calculate the reciprocal of the sine and determine the value of the cosecant. Hence, the domain of validity for cscθ is all real numbers except odd multiples of π/2, as stated in option (b).

It's important to note that in trigonometry, the domain of validity is determined by avoiding any values that would lead to undefined expressions or division by zero errors.

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The domain of validity for csc θ = 1/sin θ is all real numbers except multiples of π, because at these points the sine function equals zero, and division by zero is undefined.

In mathematics, the cosecant function (csc), is defined as the reciprocal of the sine function, or 1/sinθ. The domain of a function are all the possible input values that will yield real numbers (output). For the csc function, its domain includes all real numbers except where the denominator is zero because division by zero is undefined.

In the unit circle context, sine equals zero at 0, π, 2π, ..., and the negative counterparts. Basically, these are the multiples of π. Thus, for the csc function, the domain is all real numbers except multiples of π, which matches option d in your choices.

The domain of validity for csc θ = 1/sin θ is all real numbers except multiples of π.

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