divide 25/1658 To find the quotient, start by dividing _
into _.

Completing the equalities using the given options, we have:

\(a) sin^(-1)(1) = 90°\\b) cos^(-1)(1/2) = 60°\\c) tan^(-1)(√3) = 60°\)

a) \(sin^(-1)(1) = 90°\)

The inverse sine function, \(sin^(-1)(x)\)gives the angle whose sine is equal to x. In this case, we are looking for the angle whose sine is equal to 1. The angle that satisfies this condition is 90 degrees, so\(sin^(-1)(1) = 90°\).

b) \(cos^(-1)(1/2) = 60°\)

The inverse cosine function, cos^(-1)(x), gives the angle whose cosine is equal to x. Here, we are looking for the angle whose cosine is equal to 1/2. The angle that satisfies this condition is 60 degrees, so \(cos^(-1)(1/2)\)= 60°.

c) \(tan^(-1)(√3) = 60°\)

The inverse tangent function, tan^(-1)(x), gives the angle whose tangent is equal to x. In this case, we are looking for the angle whose tangent is equal to √3. The angle that satisfies this condition is 60 degrees, so tan^(-1)(√3) = 60°.

Completing the equalities using the given options, we have:

\(a) sin^(-1)(1) = 90° b) cos^(-1)(1/2) = 60°c) tan^(-1)(√3) = 60°\)

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a) The completed equalities are:

sin-¹(x) = 30°, sin-¹(x) = 45°, sin-¹(x) = 60°

b) The completed equalities are:

cos-¹(x) = 30°, cos-¹(x) = 45°, cos-¹(x) = 60°

c) The completed equalities are:

tan-¹(x) = 30°, tan-¹(x) = 45°, tan-¹(x) = 60°. C.

a) sin-¹(x) = 30°, 45°, 60°

The inverse sine function, sin-¹(x), gives the angle whose sine is equal to x.

Let's find the angles for each option given:

sin-¹(x) = 30°:

If sin-¹(x) = 30°, it means that sin(30°) = x.

The sine of 30° is 0.5, so x = 0.5.

sin-¹(x) = 45°:

If sin-¹(x) = 45°, it means that sin(45°) = x.
The sine of 45° is √2/2, so x = √2/2.

sin-¹(x) = 60°:

If sin-¹(x) = 60°, it means that sin(60°) = x.

The sine of 60° is √3/2, so x = √3/2.

The completed equalities are:

b) cos-¹(x) = 30°, 45°, 60°

The inverse cosine function, cos-¹(x), gives the angle whose cosine is equal to x.

Let's find the angles for each option given:

cos-¹(x) = 30°:

If cos-¹(x) = 30°, it means that cos(30°) = x.

The cosine of 30° is √3/2, so x = √3/2.

cos-¹(x) = 45°:

If cos-¹(x) = 45°, it means that cos(45°) = x.
The cosine of 45° is √2/2, so x = √2/2.

cos-¹(x) = 60°:

If cos-¹(x) = 60°, it means that cos(60°) = x.

The cosine of 60° is 0.5, so x = 0.5.

Therefore, the completed equalities are:

c) tan-¹(x) = 30°, 45°, 60°

The inverse tangent function, tan-¹(x), gives the angle whose tangent is equal to x.

Let's find the angles for each option given:

tan-¹(x) = 30°:

If tan-¹(x) = 30°, it means that tan(30°) = x.

The tangent of 30° is 1/√3, so x = 1/√3.

tan-¹(x) = 45°:

If tan-¹(x) = 45°, it means that tan(45°) = x.

The tangent of 45° is 1, so x = 1.

tan-¹(x) = 60°:

If tan-¹(x) = 60°, it means that tan(60°) = x.

The tangent of 60° is √3, so x = √3.

The completed equalities are:

tan-¹(x) = 30°, tan-¹(x) = 45°, tan-¹(x) = 60°. c)

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Using sinusoid we see since 193° < 205°, sin (193°) > sin (205°), sin 193° is greater.

A sinusoid is a curve with similar characteristics to the sine or cosine function. A sinusoidal wave is a wave that has the same pattern as a sine or cosine wave when it oscillates over time. It's characterized by the wave's wavelength, period, and amplitude. Using the sinusoid, determine which value is greater, sin 351° or sin 357°. Sin 351° and sin 357° have the same values; therefore, neither of them is greater. The sine function is periodic, meaning that it repeats after 360°. Furthermore, sin(x) = sin(360° - x); therefore, sin(351°) = sin(360° - 9°) = sin(9°), and sin(357°) = sin(360° - 3°) = sin(3°).Both sine functions are equal; therefore, neither of them is greater. b) sin (−205) or sin193∘. The answer is sin 193° since sin(x) = sin(- x), which implies that sin(-205°) = sin(205°). Now, sin 193° and sin 205° both fall in the third quadrant. In the third quadrant, sin is negative. Since 193° < 205°, sin (193°) > sin (205°). Therefore, the answer is that sin 193∘ is greater.

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Complete question :

The Cozy Inn wants to gather information about customer satisfaction concerning the cleanliness of its rooms upon check-in. This Inn has 100 rooms, and the manager decides to start with the first room and place surveys in this room and every 5th room thereafter (room 6, room 11. room 16, etc.). This is an example of a :

Answer: Systematic sampling

Step-by-step explanation: Systematic sampling usually takes an ordered technique or process in dealing with samples. Systematic sampling could assume a randomized start point in selecting observations, However, every other successive points usually follow a fixed order or selection process. In the scenario above, the manager sampling choice involves an ordered and fixed selection process whereby every fifth sample after the initial point is considered. Hence, resulting in predictable points, such as 6th, 11th, 16th, 21st, 26th, 31st,...and so on.

Answer:

\(\csc(\theta)=\sqrt{2}\)

Step-by-step explanation:

Please refer to the attachment below.

We have:

\(5\cos^2(\theta)+6\sin^2(\theta)=11/2\)

Remember that cosine is the ratio of the adjacent side to the hypotenuse. Therefore:

\(\cos(\theta)=\frac{b}{c}\)

And sine is the ratio of the opposite side to the hypotenuse. Therefore:

\(\sin(\theta)=\frac{a}{c}\)

Substitute into our original equation:

\(5(\frac{b}{c})^2+6(\frac{a}{c})^2=11/2\)

Square:

\(\frac{5b^2}{c^2}+\frac{6a^2}{c^2}=\frac{11}{2}\)

Multiply both sides by c squared:

\(5b^2+6a^2=\frac{11}{2}c^2\)

Let’s also multiply both sides by 2 to eliminate the fraction:

\(10b^2+12a^2=11c^2\)

Remember that according to the Pythagorean Theorem:

\(c^2=a^2+b^2\)

Hence, we can make another substitution:

\(10b^2+12a^2=11(a^2+b^2)\)

Distribute:

\(10b^2+12a^2=11a^2+11b^2\)

Subtract 10b² from both sides:

\(12a^2=11a^2+b^2\)

Subtract 11a² from both sides:

\(a^2=b^2\)

Take the square root of both sides:

\(a=b\)

Hence, a is equivalent to b.

Then, we must have a 45-45-90 Triangle.

Therefore, our angle θ is 45°.

We can substitute this back into our original equation to make sure. Remember that cos(45)=sin(45)=√2/2:

\(\begin{aligned} 5\cos^2(45)+6\sin^2(45)&=11/2 \\ 5(\frac{\sqrt{2}}{2}})^2+6(\frac{\sqrt{2}}{2})^2&=11/2 \\ 5(2/4)+6(2/4)&=11/2 \\ 5(1/2)+6(1/2)&=11/2 \\ 5/2+6/2&=11/2 \\ 11/2&=11/2 \;\checkmark \end{aligned} \\\)

Hence:

\(\begin{aligned} \sin(45)&=\frac{1}{\sqrt{2}} \\ \Rightarrow \csc(\theta)&=\sqrt{2} \end{aligned}\)

From the problem, the cost of 12 oz honey is $5.40

a. the cost of honey per ounce will be :

The answer is $0.45 per ounce.

b. the amount of honey per dollar will be :

The answer is 2.22 oz per dollar

c. when h = ounces of honey and c = cost in dollar

The equation will be :

For the cost of honey per ounce :

For the amount of honey per dollar :

d. Graphing one equation, we will graph c = 0.45h

A line with points (0, 0) and (12, 5.40)

x-axis will be the amount of honey

y-axis will be the cost in dollar.

(a) The mean is expected to be less than the median. (b) Approximately 1.98% of individuals live between 65.38 years and 83.04 years. (c) The smallest interval guaranteed to capture at least 92% of all life expectancies is approximately 5.43 years.

(a) In a skewed-left distribution, the tail of the distribution is elongated to the left, meaning that there are some low values that pull the mean towards the left side of the distribution. In such cases, the mean is usually less than the median.

This happens because the mean is sensitive to extreme values, and when there are a few very low values, they can significantly affect the mean. On the other hand, the median represents the middle value of the data, so it is less affected by extreme values and is generally a better measure of the central tendency in skewed distributions.

Therefore, in this case, we would expect the mean (74.21 years) to be less than the median.

(b) To find the percentage of individuals living between 65.38 years and 83.04 years, we can calculate the z-scores for these values and use the standard normal distribution table. The z-score is calculated as (x - mean) / standard deviation.

For 65.38 years:

z1 = (65.38 - 74.21) / 3.87 = -2.27

For 83.04 years:

z2 = (83.04 - 74.21) / 3.87 = 2.27

Using the standard normal distribution table or a calculator, we can find the area under the curve between these two z-scores. Since the standard normal distribution is symmetric, the area between -2.27 and 2.27 is the same as the area between -2.27 and -(-2.27), which is 2 * P(z < 2.27).

Using the standard normal distribution table or a calculator, we find that P(z < 2.27) is approximately 0.9884.

Therefore, the percentage of individuals living between 65.38 years and 83.04 years is approximately 2 * 0.9884 = 1.9768, which is approximately 1.98% (rounded to two decimal places).

(c) To find the smallest interval guaranteed to capture at least 92% of all life expectancies, we need to find the z-score corresponding to the cumulative probability of 0.92.

Using the standard normal distribution table or a calculator, we find that the z-score corresponding to a cumulative probability of 0.92 is approximately 1.4051.

We can then calculate the interval using the formula:

Interval = z * standard deviation

Interval = 1.4051 * 3.87 = 5.43 (rounded to two decimal places)

Therefore, the smallest interval guaranteed to capture at least 92% of all life expectancies is approximately 5.43 years.

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The eigenvalues of the matrix H are λ₁ = 1 + 3i, λ₂ = 1 - 3i, and λ₃ = 5. The corresponding eigenvectors are v₁ = [7i, 0, 1], v₂ = [-7i, 0, 1], and v₃ = [0, 1, 0].

To find the eigenvalues and eigenvectors of the given matrix H, we will first perform block diagonalization. The matrix H can be written as:

H =\(BDB^(^-^1^)\),

where D is the diagonal matrix of eigenvalues and B is the matrix of eigenvectors. We can find B by solving the equation H·B = B·D.

Finding the eigenvalues

To find the eigenvalues, we solve the secular equation |H - λI| = 0, where I is the identity matrix. Substituting the values of H, we have:

|1 - λ   0      7i  |

|0       3 - λ   0   | = 0

|-7i     0       5 - λ|

Expanding the determinant, we get:

(1 - λ)[(3 - λ)(5 - λ) + 7i·(-7i)] - 7i[0 - (-7i)·(7i)] = 0

Simplifying further, we obtain:

(1 - λ)[(3 - λ)(5 - λ) + 49] + 49 = 0

Expanding and collecting terms, we get:

(λ - 1)λ² - 8λ - 250 = 0

Solving this quadratic equation, we find the eigenvalues λ₁ = 1 + 3i, λ₂ = 1 - 3i, and λ₃ = 5.

Finding the eigenvectors

To find the eigenvectors, we substitute each eigenvalue into the equation H·v = λv, where v is the eigenvector corresponding to the eigenvalue.

For λ₁ = 1 + 3i:

(1 - (1 + 3i))v₁₁ + 0v₁₂ + (7i)v₁₃ = 0

(0)v₁₁ + (3 - (1 + 3i))v₁₂ + (0)v₁₃ = 0

(-7i)v₁₁ + (0)v₁₂ + (5 - (1 + 3i))v₁₃ = 0

Simplifying each equation, we get:

-3iv₁₁ + 7iv₁₃ = 0

2v₁₂ = 0

-4iv₁₁ + 4iv₁₃ = 0

Solving these equations, we find v₁ = [7i, 0, 1].

Similarly, for λ₂ = 1 - 3i, we find v₂ = [-7i, 0, 1].

For λ₃ = 5, we find v₃ = [0, 1, 0].

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Answer: 40k⁶-15k⁴

Step-by-step explanation:

\((8k^4-3k^2)(5k^2)=\\\\8k^4(5k^2)-3k^2(5k^2)=\\\\8(5)(k^{4+2})-3(5)(k^{2+2})=\\\\40k^6-15k^4\)

Result of \(8k^{4} -3k^{2}\) multiplied by \(5k^{2}\) is \(40k^{6}-15 k^{4}\)

Algebra and Exponent

To answer this question you need to know about algebra and exponent rule.

\(8k^{4} -3k^{2}\) multiplied by \(5k^{2}\)

It means the operation will become:

\(5k^{2} (8k^{4} -3k^{2} )=\)

The way to calculate algebraic multiplication with 2 or more variables is the way I call 'rainbow'.

\(5k^{2} (8k^{4} -3k^{2} )=\)

\(5k^{2}\) multiplied by \(8k^{4}\),  \(5k^{2}\) multiplied by \(-3k^{2}\) first, then the two are added.

\((5k^{2}) (8k^{4} )=\)

The way to multiply this is by: numbers multiplied by numbers and letters multiplied by letters

\(=5k^{2} (8k^{4} -3k^{2} )\\=((5)(8))((k^{2} )(k^{4} ))\\=40((k^{2} )(k^{4} )\)

Then how to multiply the letters, this uses the rule of exponents. If there are 2 same variables are multiplied, then the result is a variable with the power of the sum of the two powers.

\(a^{m} a^{n} =a^{m+n}\)

Which means,

\(k^{2}k^{4} =k^{6}\)

Then,

\(=5k^{2} (8k^{4} -3k^{2} )\\=((5)(8))((k^{2} )(k^{4} ))\\=40((k^{2} )(k^{4} )\\=40k^{6}\)

Also same with above,

\(=(5k^{2} )(-3k^{2} )\\=((5)(-3))((k^{2} )(k^{2} )\\=-15k^{4}\)

\(=5k^{2} (8k^{4} -3k^{2} )\\=((5k^{2})(8k^{4})+((5k^{2})(-3k^{2})\\=(40k^{6})+(-15k^{4} )\\=40k^{6}-15k^{4}\)

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the area of the circle with a radius of 279 inches is approximately 245203.86 square inches.

What is circumference of a circle?

The measurement of the circle's boundaries is called as the circumference or perimeter of the circle. whereas the circumference of a circle determines the space it occupies. The circumference of a circle is its length when it is opened up and drawn as a straight line. Units like cm or unit m are typically used to measure it. The circle's radius is considered while calculating the circumference of the circle using the formula. As a result, in order to calculate the circle's perimeter, we must know the radius or diameter value.

Substituting the given value of r, we get:

C = 2 × 3.14 × 279

C = 1750.92 inches (rounded to two decimal places)

Therefore, the circumference of the circle with a radius of 279 inches is approximately 1750.92 inches.

To find the area of a circle with a radius of 279 inches, we use the formula:

A = πr²

Substituting the given value of r, we get:

A = 3.14 × (279)²

A = 245203.86 square inches (rounded to two decimal places)

Therefore, the area of the circle with a radius of 279 inches is approximately 245203.86 square inches.

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Answer:

12/10 simplified is 1 2/10 or 1 1/5

Step-by-step explanation:

Answer:

132

100% correct

Therefore, the compound interest of the annuity due of BD 400 paid each 4 months for 6.2 years at a nominal rate of 3% per annum is BD 40,652.17.

Compound interest of an annuity due can be calculated using the formula:A = R * [(1 + i)ⁿ - 1] / i * (1 + i)

whereA = future value of the annuity dueR = regular paymenti = interest raten = number of payments First, we need to calculate the effective rate of interest per period since the nominal rate is given per annum. The effective rate of interest per period is calculated as

:(1 + i/n)^n - 1 = 3/1003/100 = (1 + i/4)^4 - 1

(1 + i/4)^4 = 1.0075i/4 = (1.0075)^(1/4) - 1i = 0.0303So,

the effective rate of interest per 4 months is 3.03%.Next, we can substitute the given values in the formula:

A = BD 400 * [(1 + 0.0303)^(6.2 * 3) - 1] / 0.0303 * (1 + 0.0303)A = BD 400 * [4.227 - 1] / 0.0303 * 1.0303A = BD 400 * 101.63A = BD 40,652.17

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To calculate the cash balance at the end of the period, we need to consider the cash inflows and outflows.

Starting cash balance: $4,520

Cash inflows: $1,654 (receivables collected)

Cash outflows: $1,961 (payments to suppliers) + $500 (cash expenses)

Total cash inflows: $1,654

Total cash outflows: $1,961 + $500 = $2,461

To calculate the cash balance at the end of the period, we subtract the total cash outflows from the starting cash balance and add the total cash inflows:

Cash balance at the end of the period = Starting cash balance + Total cash inflows - Total cash outflows

Cash balance at the end of the period = $4,520 + $1,654 - $2,461

Cash balance at the end of the period = $4,520 - $807

Cash balance at the end of the period = $3,713

Therefore, the cash balance at the end of the period is $3,713.

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Answer: D.) 14

Step-by-step explanation:

First, you first calculate the square root of 64 , this gives you 8

Next, you calculate the square root of 36, which gives you 6

Then, since you are asked to add the two, you add 8 + 6 since this is the simplified version of the original equation.

8 + 6 = 14

Therefore, your answer is D.) 14

Centering x values before squaring eliminates the correlation between x and its square term, reducing multicollinearity. This helps to determine independent effects of predictor variables, and can also straighten the curve of a scatterplot.

Centering the x values before squaring is important because it helps to eliminate the correlation between the x variable and its square term. When we square a variable without centering it, we are essentially capturing the effect of both the linear and the quadratic terms.

This can lead to multicollinearity, which occurs when two or more predictor variables are highly correlated with each other.

Multicollinearity can create problems in statistical analyses because it can make it difficult to determine the independent effects of each predictor variable on the outcome variable. Centering the x values before squaring helps to reduce the effects of multicollinearity by eliminating the correlation between the x variable and its square term.

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The hospital must cut the number of overtime hours by approximately 2.91% in order to stay within budget.

To determine the required percentage reduction in overtime hours, we need to consider the impact of the nurses' hourly rate increase and the limited budget increase for overtime wages.

Let's assume the current budget for nurses' overtime wages is denoted by B, and the total number of overtime hours worked is denoted by H. The current overtime rate per hour is R.

With the 5% hourly rate increase, the new overtime rate per hour becomes 1.05R. Considering the limited budget increase of 3%, the new budget for overtime wages is 1.03B.

To calculate the required percentage reduction in overtime hours, we can set up the following equation:

(1.05R) * (1 - x) * H = 1.03B

where x represents the required percentage reduction in overtime hours.

Simplifying the equation, we have:

(1 - x) * H = (1.03B) / (1.05R)

Now, let's solve for x:

1 - x = (1.03B) / (1.05R * H)

x = 1 - [(1.03B) / (1.05R * H)]

Here, we can see that the required percentage reduction in overtime hours, represented by x, depends on the values of B, R, and H.

It's important to note that without knowing the specific values of B, R, and H, we cannot calculate the exact percentage reduction. However, based on the provided information, we can determine the maximum percentage reduction that the hospital must make to stay within budget.

By assuming that B, R, and H are constant, we can use the given constraints to calculate an approximate percentage reduction. Based on the constraints of a 3% budget increase and a 5% hourly rate increase, the hospital would need to reduce the number of overtime hours by approximately 2.91% to maintain a balanced budget.

Please keep in mind that this approximation may vary depending on the specific values of B, R, and H.

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the third-degree polynomial function with real coefficients, having the zeros 6 + i, 6 - i, and 7, is:

f(x) = (x² - 12x + 37)(x - 7)

To form a third-degree polynomial function with real coefficients such that the complex number 6 + i and the real number 7 are zeros, we can use the fact that complex zeros come in conjugate pairs.

Given that 6 + i is a zero, its conjugate 6 - i will also be a zero. Thus, the zeros of the polynomial are 6 + i, 6 - i, and 7.

To find the polynomial function, we start by forming the factors corresponding to each zero:

(x - (6 + i))   --> This corresponds to the zero 6 + i

(x - (6 - i))   --> This corresponds to the zero 6 - i

(x - 7)        --> This corresponds to the zero 7

To simplify the factors, we multiply them out:

(x - (6 + i))(x - (6 - i))(x - 7)

= ((x - 6) - i)((x - 6) + i)(x - 7)

= ((x - 6)² - i²)(x - 7)

= ((x - 6)² + 1)(x - 7)

Expanding the squared term:

= (x² - 12x + 36 + 1)(x - 7)

= (x² - 12x + 37)(x - 7)

Therefore, the third-degree polynomial function with real coefficients, having the zeros 6 + i, 6 - i, and 7, is:

f(x) = (x² - 12x + 37)(x - 7)

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Answer:

d Because I just took the test and got it right

The given number is a solution of 2(3x + 1) 2 7x + 4 is 0.

Analyze a number to see if it is an equation's solution.

For the variable in the equation, substitute the integer.

On both sides of the equation, simplify the expressions.

Check the equation to see if it's correct. The number provides a solution if it is accurate. The figure isn't a solution if it's false.

Equations with just one solution. If you solve an equation and the result is a variable equal to a number, the problem only has one solution.

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Answer: \(9\times 11\ ft^2\)

Step-by-step explanation:

Given

Height is \(2\ ft\) more than its width

Suppose the width is \(x\). So, height becomes \(x+2\)

Area of the painting is \(99\ ft^2\)

Area is the product of width and height

\(\therefore 99=x(x+2)\\\Rightarrow 99=x^2+2x\\\Rightarrow x^2+2x-99=0\\\Rightarrow x^2+11x-9x-99=0\\\Rightarrow (x+11)(x-9)=0\\\Rightarrow x=-11,9\)

Neglect the negative values

\(\text{Width =}9\ ft\\\text{height =}9+2=11\ ft\)

Answer:

Consecutive terms are numbers which follow each other in order, without gaps, from smallest to largest.

Example:

12, 13, 14 and 15

or

2, 24, 26, 28 and 30 (Even Consecutive)

or

40, 45, 50 and 55 (Consecutive Multiples of 5)

SOURCE/GOOGLE

Answer:

Consecutive numbers are numbers that follows one other in their counting order. Each number in the order will be higher than the previous number by 1.

They are always ordered from the smallest to the largest value.

Step-by-step explanation:

Example :

7, 8, 9, 10 are consecutive numbers.

23, 24, 28, 29 are not consecutive numbers.

As long as the measures of the three angles of a triangle add up to less than 180 degrees, and none of the angles measures more than 90 degrees, the triangle will be acute.

An acute triangle is a triangle that has three acute angles, which are angles that measure less than 90 degrees. All three angles of an acute triangle must be acute, so they must measure less than 90 degrees. The measures of the three angles of an acute triangle can be any combination of angles that add up to less than 180 degrees.

Here are some examples of the measures of the three angles of an acute triangle:

45 degrees, 45 degrees, 90 degrees

30 degrees, 60 degrees, 90 degrees

35 degrees, 40 degrees, 105 degrees

60 degrees, 60 degrees, 60 degrees (this would be an acute equilateral triangle)

As long as the measures of the three angles of a triangle add up to less than 180 degrees, and none of the angles measures more than 90 degrees, the triangle will be acute.

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Any algebraic expression can be represented graphically. The given problem can be solved as shown in the image attached.

A polynomial in one variable is also an algebraic expression. It can be written in the form aˣn. Here, n is a non-negative integer and a is a real number. The a is also called the coefficient of the term.

The given problem also consists of a polynomial in one variable. It can be solved as such.

We have been told that = y = -3x+7

We need to graph this. For this, we plot at least two values for x and y -

x  = 0 and y = 7

x = 1 and y = 4

We plot both these coordinates on the graph which has been attached below.

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The data which is given by the historian is used to find the population, variable, parameter, sample, data, and statistic. He estimated the mean number of children per household in New York City in 1900.

Population - all of the households in New York City in 1900.

Variable - a quantity equivalent to the number of children in a randomly selected household

Parameter -  the mean number of children per household in New York City in 1900

Sample - the 200 households selected by the historian

Data - the 200 records collected by the historian

Statistic -  the mean number of children per household in the historian's sample.

Complete question:

Suppose a historian wants to estimate the true mean number of children per household in New York City in 1900. The historian randomly selects 200 household census records from New York City. She records the number of children residing in each household. The historian then computes the mean number of children per household among these 200 households. Classify each description as one of a parameter, variable, population, sample, data, or statistic.

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The equation of the perpendicular line to the given line is: y = -5/4x - 30.

The slope values of two perpendicular lines are negative reciprocal of each other.

Given that the line is perpendicular to y = 4/5x+23, the slope of y = 4/5x+23 is 4/5. Negative reciprocal of 4/5 is -5/4.

Therefore, the line that is perpendicular to it would have a slope (m) of -5/4.

Plug in m = -5/4 and (x, y) = (-40, 20) into y = mx + b to find b:

20 = -5/4(-40) + b

20 = 50 + b

20 - 50 = b

b = -30

Substitute m = -5/4 and b = -30 into y = mx + b:

y = -5/4x - 30

The equation of the perpendicular line is: y = -5/4x - 30.

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Answer:

Let Ji and Bi represent the initial amounts that Joe and Bill have at the start.  Number after J and B will be used to indicate subsequent steps in the problem.

We are told that "Joe has five times as much money as Bill," which we can write as:

   1)  Ji = 5Bi

We learn that "Joe pays Bill $5," which we can represent as:

   2)  J1 = Ji - 5

This would mean that Bill has added $5:

   3)  B1 = Bi + 5

We are then told that "Joe has just twice the amount Bill now has," which we can write as:

   4)  J1 = 2B1

===

We can rearrnage and substitute the above relationships to eliminate one of the two variables (B1 or J1)

J1 = Ji - 5                [from 2]

2B1 = Ji - 5              [Substitute 4 to eliminate J1]

Ji = 5Bi                    [from 1]

2B1 = 5Bi - 5           [Substitute 1 to eliminate Ji]

B1 = Bi + 5               [Rearrange]

2(Bi + 5) = 5Bi - 5    [Use the above expression in the previous equation to eliminate B1]

2Bi + 10 = 5Bi - 5    [Simplify]

-3Bi = -15                  [Simplify]

Bi = $5                       [Solve]

Ji = 5Bi                    [from 1]

Ji = 5*(5)                  [Since Bi = $5]

Ji = $25                    [Solve]  

===

CHECK:

Does Joe has five times as much money as Bill?

Ji = $25 and Bi = $5  YES

When Joe pays Bill $5 he owes him, does Joe has just twice the amount Bill now has?

J1 = $25 - $5 = $20

B1 = $5 + $5  = $10    YES

If the area above the line is shaded, it means that the inequality consists in all values of y greater than a certain expression.

If the line is solid, it means that the values of y are greater or equal to a certan expression.

If the line has a slope of 3/2 and a y-intercept of 8, the equation of the line si:

y = 3/2x + 8

adnd consider that the solution are all values of y greater or equal to 3/2x + 8:

y ≥ 3/2x + 8

Answer:

33.33%

Step-by-step explanation:

We take

3 divided by 2.25, time 100 = 133.33%

Then We Take

133.33 - 100 = 33.33%

So, the percent increase is 33.33%

Answer:

Operations Inverse operations

Addition             Subtraction

Subtraction      Addition

Multiplication      Division

Division           Multiplication

Step-by-step explanation:

i hope this will help you

The probability of finding such people will get closer to 0.61 as the sample gets bigger.

a) This means that if you were to take a large sample of US adults and inquire them about having breakfast, about 61%(i.e. 0.61) will say that they usually have breakfast.

b) It is, for sure, expected that if we take a sample of 100, around 61% of these americans will say that they usually eat breakfast. But if the number will be 61 exactly is not a certainty and it will vary from sample to sample.

The probability of finding such people will get closer to 0.61 as the sample gets bigger.

Explanation has been provided in the answers above due to their descriptive nature.

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The number of calories that Darrell will burn in 1 minute while kayaking is given as follows:

4 calories.

The number of calories that Darrell will burn in 1 minute while kayaking is obtained applying the proportions in the context of the problem.

For each input-output pair in the table, the constant of proportionality is of 4, hence the number of calories that Darrell will burn in 1 minute while kayaking is given as follows:

4 calories.

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