Use the Distributive Property to solve the equation.
Apply the Distributive Property and simplify.
-5(x+2)=20
-5x+___=20

Answer:

12 ten inch pieces

Step-by-step explanation:

you do 120 divided by 10 to get an answer of 12

hope this helped =)

Since the test statistic (-2.24) falls outside the range of the critical values (-1.96 to 1.96), we reject the null hypothesis.

What is sign test?

The sign test is a non-parametric statistical test used to determine whether the median of a distribution is equal to a specified value. It is a simple and robust method that is applicable when the data do not meet the assumptions of parametric tests, such as when the data

The given problem can be solved using the one-sample sign test to test the null hypothesis that the mean of the population is 19.4 minutes against the alternative hypothesis that it is not 19.4 minutes.

(a) Using Table I:

Step 1: Set up the hypotheses:

Null hypothesis (H0): The mean of the population is 19.4 minutes.

Alternative hypothesis (H1): The mean of the population is not 19.4 minutes.

Step 2: Determine the test statistic:

We will use the sign test statistic, which is the number of positive or negative signs in the sample.

Step 3: Set the significance level:

The significance level is given as 0.05.

Step 4: Perform the sign test:

Count the number of observations in the sample that are greater than 19.4 and the number of observations that are less than 19.4. Let's denote the count of observations greater than 19.4 as "+" and the count of observations less than 19.4 as "-".

In the given sample, there are 5 observations greater than 19.4 (18.1, 20.3, 19.3, 19.5, and 20.0), and 15 observations less than 19.4 (18.3, 15.6, 16.8, 17.6, 16.9, 17.0, 16.5, 18.6, 18.8, 19.1, 17.5, 18.5, and 18.0).

Step 5: Calculate the test statistic:

The test statistic is the smaller of the counts "+" or "-". In this case, the test statistic is 5.

Step 6: Determine the critical value:

Using Table I, for a significance level of 0.05 and a two-tailed test, the critical value is 3.

Step 7: Make a decision:

Since the test statistic (5) is greater than the critical value (3), we reject the null hypothesis.

(b) Using the normal approximation to the binomial distribution:

Alternatively, we can use the normal approximation to the binomial distribution when the sample size is large. Since the sample size is 20 in this case, we can apply this approximation.

Step 1: Set up the hypotheses (same as in (a)).

Step 2: Determine the test statistic:

We will use the z-test statistic, which is calculated as (x - μ) / (σ / √n), where x is the observed number of successes, μ is the hypothesized value (19.4), σ is the standard deviation of the binomial distribution (calculated as √(n/4), where n is the sample size), and √n is the standard error.

Step 3: Set the significance level (same as in (a)).

Step 4: Calculate the test statistic:

Using the formula for the z-test statistic, we get z = (5 - 10) / (√(20/4)) ≈ -2.24.

Step 5: Determine the critical value:

For a significance level of 0.05 and a two-tailed test, the critical value is approximately ±1.96.

Step 6: Make a decision:

Since the test statistic (-2.24) falls outside the range of the critical values (-1.96 to 1.96), we reject the null hypothesis.

Rework Exercise 16.16 using the signed-rank test based on Table X:

To provide a more accurate solution, I would need additional information about Exercise 16.16 and Table X.

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If the jar of olives had a circumference of 11. 99 cm, the approximate diameter of the jar is 3.82 cm

The circumference of a circle is given by the formula C = 2πr, where C is the circumference, π is the constant pi (approximately equal to 3.14), and r is the radius. The diameter is twice the radius, so we can also write the formula as C = πd, where d is the diameter.

In this case, the circumference is 11.99 cm, so we can set up the equation

11.99 = πd

To solve for d, we can divide both sides by π

d = 11.99/π

Using a calculator, we get

d ≈ 3.82 cm

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Answer:

third one

Step-by-step explanation:

Answer: it would be the third option, (2/5)^4

Step-by-step explanation:

sure thing! so, when all of those fractions in parenthesis, it means they are all going to be multiplied. and, this gets easy! that third option means that all of them are getting multiplied 4 times, which is exactly what the original problem means. hope this helps!

Answer:

The correct option is;

y = 12·cos[π/2·(x- 2)] + 18

Step-by-step explanation:

The general equation for the motion of a Ferris wheel as a function of time, t, can be presented as follows;

f(t) = A·cos(B·x + C) + D

Where;

A = The amplitude = Diameter/2 = 24/2 = 12 meters

The period = 4 minutes

B = 2·π/Period = 2·π/4 = π/2

D = The midline = 6 + 12 = 18 meters

Substituting the values gives;

f(x) = 12·cos(π/2·x + C) + 18

At x = 0, we have

f(x) = 6 = 12·cos(π/2×0 + C) + 18

cos( C) = (6 - 18)/12 = -1

∴ C = -π

We therefore have;

f(t) = y = 12·cos(π/2·t - π) + 18 =  12·cos[π/2·(x- 2)] + 18

y = 12·cos[π/2·(x- 2)] + 18.

Step-by-step explanation:

number of apartments = 4

1 apartment = 3 hours

4 apartments = 12 hours

Answer:

w=V/Ih

Step-by-step explanation:

The formula for the volume of a rectangular prism is given as V = lwh.

✓ we are required to solve for "w" and this can be done by making "w" subject of the formula.

w=V/Ih

Hence, formula for " w" is w=V/Ih

The proposition states several properties related to neighborhoods and open sets in a space X. The proof of these properties is based on the MI 3.4 theorem, which establishes the equivalence of different conditions for continuity of a function between two spaces. The properties involve concepts like openness, closedness, and the behavior of functions on subsets. The proof demonstrates the interplay between these concepts and establishes their equivalence in the given context.

The proposition consists of several properties that are proven using the MI 3.4 theorem, which establishes the equivalence of different conditions for continuity of a function between two spaces, in this case, X and Y.

Property (i) states that if U is a neighborhood of x in X, then x must be an element of U. This property essentially says that every point in a neighborhood is contained within that neighborhood.

Property (ii) states that for any neighborhoods U and V in X, if U intersects V, then there exists a neighborhood W that is contained in both U and V. This property highlights the concept of neighborhoods being closed under intersections.

Property (iii) states that if x is an element of a set U, and U is a subset of a set V, then x must be an element of V. This property asserts that if a point belongs to a set U, which is a subset of V, then that point must also belong to V.

Property (iv) states that a set G is open in X if and only if for every point x in G, there exists a neighborhood N such that N is contained within G. This property characterizes openness in terms of neighborhoods, stating that a set is open if every point has a neighborhood completely contained within the set.

Property (v) states that if a point x belongs to a set U, then there exists a neighborhood V of x such that V is contained within U. This property confirms that every point in a set has a neighborhood contained within the set.

The proof of these properties utilizes the MI 3.4 theorem, which states several equivalent conditions for continuity of a function. By establishing the equivalence between these conditions, the properties of neighborhoods and open sets in X are proven.

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Answer:

It can be described as d. having no maximum and a minimum of 3.

Step-by-step explanation:

It can be described as d. having no maximum and a minimum of 3. The reason is because the dot is on 3, and doesn't have an arrow telling you that there is not minimum. The right has an arrow telling you that it doesn't have a maximum.

The derivative of the function f(x) = (9\(x^{6}\) + 8x³)³ is f'(x) = 4(9\(x^{6}\) + 8x³)³(54x³ + 24x²).

To find the derivative of the function f(x) = (9x² + 8x³)³, you need to apply the Chain Rule. The Chain Rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function. In this case, let u = 9x + 8x.

First, find the derivative of the outer function with respect to u: d( u³ )/du = 4u³.
Next, find the derivative of the inner function with respect to x: d(9x² + 8x³)/dx = 54x³ + 24x².

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Question 1

\(\sqrt{(3-8)^2 +(2-14)^2}=13\)

Question 2

\(\left(\frac{3+8}{2}, \frac{2+14}{2} \right)=(5.5, 8)\)

Question 3

\(M=\left(\frac{1+9}{2}, \frac{5+7}{2} \right)=(5, 6) \\ \\ N=\left(\frac{9+7}{2}, \frac{7+13}{2} \right)=(8, 10) \\ \\ MN=\sqrt{(8-5)^2 + (10-6)^2}=5\)

Answer: The answer is 9

Step-by-step explanation: Because if 3 is a third then do 3 3 3 and the whole would be 9

Answer: 9

Step-by-step explanation:

If 3 is only = 1/3, then multiply 3 by 3 to get a whole and you get 9

Assume all of the statistics used have a normal sampling distribution. Use 3 decimal places. Below are the steps of calculation:(a) For a 98% confidence interval for a population mean based on n = 11 observations with known: We know that margin of error formula = Zα/2 σ/√n, Where Zα/2 is the quantile of the normal distribution at α/2, σ is the population standard deviation and n is the sample size. In this case, α = 0.02, n = 11 and Zα/2 = 2.326. The sample size is small, and therefore we assume a normal distribution. Using the formula above, we obtain: margin of error = Zα/2 σ/√n = 2.326 σ/√11(b) For a 98% confidence interval for a population mean based on n = 11 observations with unknown. We know that margin of error formula = tα/2 s/√n. Where tα/2 is the quantile of the t-distribution at α/2, s is the sample standard deviation and n is the sample size. In this case, α = 0.02, n = 11 and tα/2 = 2.718. The sample size is small, and therefore we assume a normal distribution.

Using the formula above, we obtain: margin of error = tα/2 s/√n = 2.718 s/√11(c) For a 90% confidence interval for a population proportion, p, based on n = 11 observations. We know that margin of error formula = Zα/2 √((p(1-p))/n)Where Zα/2 is the quantile of the normal distribution at α/2, n is the sample size, and p is the sample proportion. In this case, α = 0.1, n = 11 and Zα/2 = 1.645.Using the formula above, we obtain: margin of error = Zα/2 √((p(1-p))/n) = 1.645 √((p(1-p))/11)(d) For a 92% confidence interval based on n = 14 observations for the slope parameter. We know that margin of error formula = tα/2 * SE. Where tα/2 is the quantile of the t-distribution at α/2, and SE is the standard error of the estimate. In this case, α = 0.08, n = 14 and tα/2 = 1.771.

Using the formula above, we obtain: margin of error = tα/2 * SE = 1.771 * SE. Therefore, the correct quantile for the margin of error of each confidence interval is as follows:(a) 2.670(b) 2.570(c) 0.512(d) 1.564.

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The value of both variables is equal to 23.

The angle measures are 45 degrees and 135 degrees respectively.

In Mathematics and Geometry, a supplementary angle simply refers to two (2) angles or arc whose sum is equal to 180 degrees.

Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can reasonably infer and logically deduce that the sum of the given angles are supplementary angles:

(2x - 1)° + (4x + 43)° = 180°

By rearranging and collecting like-terms, the value of y is given by:

6x + 42 = 180

6x = 180 - 42

x = 138/6 = 23

(2x - 1)° = 2(23) - 1 = 45°

(4x + 43)° = 4(23) + 43 = 135

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A translation there is a reflection across the x-axis, 2 units down and 2 units to the left. As a result, choice C is the right option.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

As seen on the graph, the square PQRS is translated 2 units to the left and 2 units to the right before being reflected on the x-axis.

A translation after a reflection across the x-axis, there are 2 units down and 2 units to the left. As a result, choice C is the right option.

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Complete Question:

Squares PQRS and TUVW are shown below. Which sequence of transformations of squarePQRS shows that square PQRS is congruent to square TUVW?a) A translation 2 units up and 2 units to theright, then a reflection over the x-axisb) A translation 2 units up and 2 units to theright, then a reflection over the y-axisc) A translation 2 units down and 2 units to theleft, then a reflection over the x-axisd) A translation 2 units down and 2 units to theleft, then a reflection over the y-axis

Answer:

x = -\(\frac{2}{3}\)

y = 2

Step-by-step explanation:

The process of elimination is a method of solving a system of equations. One must first manipulate one of the equations such that one of the variables shared between the two equations has the inverse coefficient of the same variable in the other equation. Therefore, when one adds the equations, the variable cancels. One can solve for the variable using inverse operations, and then backsolve to find the value of the first variable.

When given the following system:

y = 3x + 4

y + 6x = 3x

Use inverse operations so that both equations are solve for one variable,

y = 3x + 4

y = -3x

Add the systems so that one of the variables (x) cancels, this process is called the process of elimination;

y = 3x + 4

y = -3x

_________

2y = 4

Inverse operations,

2y = 4

y = 2

Now backsolve, find the value of (x) by substituting the value of (y) into the equation:

y = -3x

2 = -3x

x = -\(\frac{2}{3}\)

Answer: No solution.

Step-by-step explanation:

Answer:

.14

Step-by-step explanation:

The relative frequency that favors football is around 0.14, or 14%.

Given that Phoebe took a survey of her classmates' favorite sport.

We need to find the relative frequency of survey members who prefer football,

Preferred sports =

Football    baseball     basketball    tennis       others     total

     4              5                     8                 7              4          28

To calculate the relative frequency of survey members who prefer football, you need to divide the number of people who prefer football by the total number of survey respondents.

According to the table, the number of people who prefer football is 4, and the total number of respondents is 28.

Relative Frequency = Number of people who prefer football / Total number of respondents

= 4 / 28

≈ 0.14

Therefore, the relative frequency of survey members who prefer football is approximately 0.14 or 14%.

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9514 1404 393

Answer:

  8 lb

Step-by-step explanation:

The original weight W increased by 12% is ...

  W + 12%·W = 8.96

  1.12W = 8.96

  W = 8.96/1.12 = 8.00

The kitten's weight a month ago was 8.0 pounds.

Amanda would use 3 planks of lengths 3 feet, 5 feet, and 6 feet.

To determine which planks Amanda should use to build the triangular-shaped kennel:

Therefore, Amanda would use 3 planks of lengths 3 feet, 5 feet, and 6 feet.

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Answer:

4.57

Step-by-step explanation:

Answer:

B.  

Step-by-step explanation:

Personally is the adverb of the noun person.

Answer:

Find the volume of this prism.

Answer:

24% or d

Step-by-step explanation:

Answer:

6 package

Step-by-step explanation:

Given:

Amount of cheese needs = 3 KG = 3,000 gram

Assume;

1 package of cheese = 500 gram

Find:

Number of package need

Computation:

Number of package need = Amount of cheese needs / 1 package of cheese

Number of package need = 3,000 / 500

Number of package need = 6 package

I can help you with that problem i just did that on my own.

Answer:

hey what up

Step-by-step explanation:

Answer:

ff

Step-by-step explanation:

fff

Answer: 745

Step-by-step explanation:

\(7.45 \times 10^{3}=7.45(1000)=\boxed{745}\)

Answer:

84%

Step-by-step explanation:

correct answers = 42

incorrect answers =8

total mark=50

% of the correct =

\( \frac{42}{50} \times 100 = 84\)answer is 84%

The length of the hypotenuse is approximately 6.802 units and the length of the adjacent side is approximately 5.5 units in the right triangle where one angle measures 36 degrees and its opposite side measures 4 units.

To find the sides of a right triangle where one angle measures 36 degrees and its opposite side measures 4 units, we can use trigonometric ratios.

Let's label the sides of the triangle:
- The side opposite the angle of 36 degrees is called the opposite side and has a length of 4 units.
- The side adjacent to the angle of 36 degrees is called the adjacent side.
- The hypotenuse is the longest side of the right triangle and is opposite the right angle.

Using the trigonometric ratio for the sine function, we can find the length of the hypotenuse:

sin(angle) = opposite / hypotenuse

Plugging in the values we know:

sin(36 degrees) = 4 / hypotenuse

Now, we can solve for the hypotenuse by isolating it:

hypotenuse = 4 / sin(36 degrees)

Using a calculator, we find that sin(36 degrees) is approximately 0.5878.

hypotenuse ≈ 4 / 0.5878 ≈ 6.802

So, the length of the hypotenuse is approximately 6.802 units.

To find the length of the adjacent side, we can use the Pythagorean theorem:

adjacent^2 + opposite^2 = hypotenuse^2

Plugging in the values we know:

adjacent^2 + 4^2 = 6.802^2

Simplifying the equation:

adjacent^2 + 16 = 46.2496

Subtracting 16 from both sides:

adjacent^2 = 30.2496

Taking the square root of both sides:

adjacent ≈ √30.2496 ≈ 5.5

So, the length of the adjacent side is approximately 5.5 units.

In summary, the length of the hypotenuse is approximately 6.802 units and the length of the adjacent side is approximately 5.5 units in the right triangle where one angle measures 36 degrees and its opposite side measures 4 units.

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Answer:

The least degree of the polynomial that assures an error smaller than 0.001 is 4.

The Lagrange error bound for the Taylor polynomial of degree n centered at x=2 for e^x is given by:

```

|e^x - T_n(x)| < \frac{e^2}{(n+1)!}|x-2|^{n+1}

```

where T_n(x) is the Taylor polynomial of degree n centered at x=2.

We want the error to be less than 0.001, so we have:

```

\frac{e^2}{(n+1)!}|x-2|^{n+1} < 0.001

```

We can solve for n to get:

```

n+1 > \frac{e^2 \cdot 1000}{|x-2|}

```

We know that |x-2| = 0.45, so we have:

```

n+1 > \frac{e^2 \cdot 1000}{0.45} \approx 6900

```

Therefore, n > 6899.

The least integer greater than 6899 is 6900, so the least degree of the polynomial that assures an error smaller than 0.001 is 4.

The fourth-degree Taylor polynomial centered at x=2 for e^x is given by:

```

T_4(x) = 1 + 2x + \frac{x^2}{2} + \frac{x^3}{6} + \frac{x^4}{24}

```

We can use this polynomial to estimate e^1.45 as follows:

```

e^1.45 \approx T_4(1.45) = 4.38201

```

The actual value of e^1.45 is 4.38202, so the error in this approximation is less than 0.001.

Step-by-step explanation: