The lengths of text messages are normally distributed with a population standard deviation of 6 characters and an unknown population mean. If a random sample of 27 text messages is taken and results in a sample mean of 25 characters, find a 95% confidence interval for the population mean. Round your answers to two decimal places. z0.10 z0.05 z0.04 z0.025 z0.01 z0.005 1.282 1.645 1.751 1.960 2.326 2.576 You may use a calculator or the common z-values above.

Answer:

Research that verifies the number of people who preferred the pillow.

Sorry, if I'm wrong.

The solution for 4ˣ⁺³ = 7 using change of base formula is -1.596

To solve 4ˣ⁺³ = 7 using change of base formula log base b of y equals log y over log b, we are going to use logarithm rules.

If f(x) = g(x), then ln(f(x)) =  ln(g(x)). Thus,

ln( 4ˣ⁺³) = ln(7)

Using log rule:

[tex]\log _{a} x^{b} = b \log _{a}(x)[/tex]

ln (4ˣ⁺³) = ln(7)

(x+3) · ln(4) = ln(7)

(x+3) · ln(2²) = ln(7)

(x+3) · 2ln(2) = ln(7)

x+3 = ln(7) / (2ln(2))

x  = [ln(7) / (2· ln(2))] - 3

x = -1.596

Thus, the solution is x = -1.596

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Answer:

Did he round up?

Step-by-step explanation:

To do simple subtraction, use the - (minus sign) arithmetic operator.

6N + 10

---------- - 5  =

  2

3N + 5 - 5

3N

so yes, you will always get triple the original number. or 3N.

A final step should be to divide the last difference by 3, which gets you

the original number back.

Two positive integers added together are always positive.
When two negative integers are added together, the result is always negative.
The result of subtracting two positive integers might be either positive or negative.
The result of subtracting two negative integers might be either positive or negative.

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The new substitution rule states teams will be able to make five substitutes instead of the traditional three during each match.

Teams have decided to allow more substitutions after voting in favor of the change. Teams will now be permitted to use five substitutions instead of the customary three throughout each game starting in the 2022/2023 season.

The primary motivation for this choice is to lessen the negative impacts of increased match intensity and fixture congestion, which are thought to have a direct influence on player health and well-being. Over time, it will become clear how an increase in substitutes would affect player health and happiness.

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The measure of angle B crossing the river perpendicularly is 110°.

When the sum of the two angles is 180° they are said to be supplementary.

When the sum of the two angles is 90° they are said to be complementary.

Given, Bridge A crosses the river at an exterior angle of (2x),  Bridge B crosses at an angle of (4x-6) and these two angles are supplementary.

So, The sum of these two angles are 180°.

Therefore,

4x - 6 + 2x = 180°.

6x = 174°.

x = 174°/6.

x = 29°.

So, The measure of the angle B is (4(29) - 6)°.

= 116 - 6.

= 110°.

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Answer:

15

Step-by-step explanation:

x/3+10=15

(x+30)/3=15

x+30=15×3

x+30=45

x=45-30

x=15

Answer:

First you need to put the variable, x, in a fraction

     [tex]\frac{x}{3} + 10=15[/tex]

In this case, 10, is a positive integer, so because its a whole number, we put it with 15 on the other side of the equal sign. Then the +10 will become -10.

   [tex]\frac{x}{3} =15-10[/tex]

Then its easier to calculate, 15 - 10 is 5.

     [tex]\frac{x}{3} =5[/tex]

After that you put 5 over 1 and crisscross the equation.

    [tex]\frac{x}{3} =\frac{5}{1}[/tex]

x times 1 is x itself, and 3 times 5 is 15

   [tex]x=15[/tex]

So in the end x = 15

Have a wonderful day! :-)

The amount of time he spent on the bicycle is 5.5 hours.

Jim began a 167​-mile bicycle trip to build up stamina for a triathlete competition.​ Unfortunately, his bicycle chain​ broke, so he finished the trip walking.

The whole trip took 6 hours. Jim walks at a rate of 4 miles per hour and rides at 30 miles per​ hour.

The amount of time he spent on the bicycle can be calculated as follows;

speed = distance / time

distance = speed × time

Therefore, total distance is as follows:

let

x = time spent walking

167 = 4x + 30(6 - x)

167 = 4x + 180 - 30x

167 = -26x + 180

167 - 180 = -26x

x = -13 / -26

x = 1 / 2

Time spent on bicycle = 6 - 0.5 = 5.5 hours.

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The three numbers are: 23, 25, 27, The boy is 140 cm tall, the father is 140 + 30 = 170 cm, and the sister is 70 cm tall.

In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions.

The terms 3x + 5 and 14 are separated by the word "equal" in the equation 3x + 5 = 14. The three main formats for linear equations are the slope-intercept form, standard form, and point-slope form.

Two expressions are combined with an equal sign to form a mathematical statement known as an equation. An equation is, for instance, 3x - 5 = 16. It is possible to solve this equation, and the answer reveals that the value of the variable x is 7.

Let the the first number is : x

So, the other two numbers are :x+2, x+4

a) x+(x+2)+(x+4)=75

3x+6=75

3x=69

X=23

The three numbers are: 23, 25, 27

b)The sister's height is denoted as x. Two times, since the boy is twice as tall. His height is 2x + 30 because the father is 30 centimeters taller than the boy. The total height is 3.8 meters, or 380 centimeters. You can now create an equation.

x + 2x + 2x + 30 = 380

assemble similar terms

5x = 350

x = 70

The boy is 140 cm tall,

the father is 140 + 30 = 170 cm,

and the sister is 70 cm tall.

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The y-intercept indicates the y-value when the x-value is 0.

What does the y-intercept look like?

When a linear equation is expressed in slope-intercept form (y=mx+b), the constant variable b stands in for the y-intercept. As an illustration, the variable b corresponds to the number 8 in the equation y=6x+8. The y-intercept is shown here.

In regression, what does the y-intercept stand for?

In regression analysis, the point at which the regression line crosses the y-axis is known as the constant term. The y-intercept is another name for the constant.

                       The easiest way to depict the overall picture of what the collected data is indicating is with a straight line, which is what a linear regression does. It aids in our ability to determine whether the two things under investigation are related or have a correlation.

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The value of the expression of the percentage as the friend details is; 0.04888....... and as such the friend is not correct

Percentages are usually calculated by dividing the value by the total value, and then multiplying the result by 100. It is given by:

Percentage = (value / total value) * 100%

Now, we are given the number 4.8% with 8 having a bar over it.

A bar over a number is called  vinculum  and it means that the number is being repeated indefinitely after a decimal point.

This tells us that our given number can now be expressed as;

4.888.....%

This is because from the definition of  vinculum , 8 is repeated indefinitely. Thus, this can be simplified as;

4.888...../100 = 0.04888.......

Thus, the friend is not correct in conclusion.

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The equations in the slope intercept form are,

                     y = -5x + 87

                    y = 8x + 13

What is slope intercept form?

The equation of the line can be written in different ways. One of the methods of writing equations of a line is slope intercept form.

The line with m as the slope, and c as the y-intercept is the graph of the linear equation y = mx + c. This form of linear equation is known as slope intercept form. The values of m and c are real integers in the slope-intercept form of the linear equation.

The slope, m, is a measure of how steep a line is. A line's y-intercept, c, denotes the y-coordinate of the location where the line's graph crosses the y-axis.

For farmer Dubble,

      Number of elentires in beginning c = 87

      Number of elentires destroyed every month m = -5

     Linear equation in slope intercept form

              y = -5x + 87

For farmer Gespil,

      Number of elentires in beginning c = 13

      Number of elentires bought every month m = 8

     Linear equation in slope intercept form

           y = 8x + 13

Therefore the system of equations in slope intercept form  are,

    y = -5x + 87

    y = 8x + 13

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The zeros of the polynomial x3 + 2x2 - x - 2 are -1, -2 and 4.

The given polynomial is x3 + 2x2 - x - 2. To find the zeros of this polynomial, we need to solve the equation x3 + 2x2 - x - 2 = 0.

Rewrite the equation as x3 + 2x2 - x - 2 = 0.

Factor the equation.

Set each factor equal to zero and solve for x.

(x + 2)(x2 - x - 1) = 0

x + 2 = 0

x = -2

(x2 - x - 1) = 0

x2 - x - 1 = 0

x2 - 1x - 1 = 0

Apply the quadratic formula to solve for x.

x = [-b ± √(b2 - 4ac)] / 2a

x = [(-1) ± √(1 - 4*1*(-1))] / 2*1

x = [(-1) ± √(5)] / 2

x = [-1 ± √5] / 2

x = [(-1 + √5) / 2] and [(−1 - √5) / 2]

Simplify the solutions and find the zeros of the polynomial.

x = (-1 + √5) / 2  and x = (-1 - √5) / 2

Therefore, the zeros of the polynomial x3 + 2x2 - x - 2 are -1, -2 and 4.

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The final velocity in the given equation is −0.5, when the acceleration is -5.

The distance covered by a body in one unit of time in a specific direction is referred to as velocity. M/s is always the only metric unit of velocity.

Speed and velocity are different in that:

v = u + at

here,

a = average acceleration

v = final velocity

u = initial velocity

t = time

given,  u = 2

a = -5

t = 1/2 = 0.5

putting the values

v = 2 + (-5)(0.5)

v = 2 - 2.5

v = −0.5

Thus, The final velocity in the given equation is −0.5, when the acceleration is -5.

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As a result, the answer to the provided coordinate plane problem is only choice C), which is the right answer.

The term "coordinate plane" refers to a two-dimensional region that consists of two number lines. It emerges when the X-axis & Y-axis intersect at a location known as the origin. Using the numbers on a coordinate grid, one can locate points.

Here,

Since, If there is a coordinate plane with both parallel lines, go with option A.

Therefore, there is no cure.

There are hence a finite number of solutions that could be found.

If two lines cross, there is only one potential result for Option B. Consequently, the quantity of potential solutions is.

According to Option C, there must be an endless number of solutions to the system because there are two coinciding lines that provide us an infinite number of junction sites.

The difference between Option D) and Option B) is noted.

Only choice C) is hence the proper one.

Therefore , the solution to the given problem of coordinate plane comes out to be Only choice C) is hence the correct one.

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The measure of angle B in the given triangle is 41°

From the question, we are to calculate the measure of angle B.

From the exterior angle theorem of a triangle which states that if a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.

Then,

We can write that

∠B + 72° = 113°'

∠B = 113° - 72°

∠B = 41°

Hence, the measure is 41°

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To solve the inequality -1/2 > 3/5, we can start by multiplying both sides of the inequality by the least common multiple of the denominators, which is 10, to get rid of the fractions. This gives us:

-1/2 * 10 > 3/5 * 10

-5 > 6

This inequality is not true, since -5 is not greater than 6. So the solution set is the empty set, or { }.

The method of solving "by substitution" works by solving one of the equations for one of the variables, and then plugging this back into the other equation, "substituting" for the chosen variable and solving for the other. Then you back-solve for the first variable.

A quadratic equation is a second-order equation written as ax² + bx + c = 0 where a, b, and c are coefficients of real numbers and a ≠ 0.

To solve two order system of equations using substitution, follow these steps:

Step 1. Choose one equation and solve it for either of the one variables.

Step 2. In the other equation, substitute the value get from step 1.

Step 3. Solve the new equation.

Step 4. Substitute the value found into any equation involving both variables and solve for the other variable.

Step 5. Check the solution in both original equations.

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Answer: 9.42 Feet or 9 Feet 5.04 Inches

Step-by-step explanation: To solve for the circumference, the equation you must use is C = 2πr (Circumference = 2pi(3.14)radius(half of the diameter)).

Students have 52.5 lb. weight in water.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

A student weighs = 70 lb.

And, About 3/4 of a person's weight is water.

Since, A student weighs = 70 lb.

Hence, Students weighs in water = 3/4 of 70 lb.

                                                   = 3/4 × 70

                                                   = 52.5 lb.

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Gender inequality refers to the unequal distribution of rights, opportunities, and resources between individuals based on their gender. There are many forms of gender inequality, but some common ones include economic inequality, educational inequality, health inequality, political inequality, violence against women, social inequality and intersectionality.

Economic inequality: This refers to the unequal distribution of wealth, income, and resources between men and women. This can manifest in various forms, such as the gender pay gap and lack of representation in leadership positions.

Educational inequality: This refers to the unequal access to education and the resulting disparities in literacy rates and educational attainment between men and women.

Health inequality: This refers to the unequal access to healthcare and the resulting disparities in health outcomes between men and women.

Political inequality: This refers to the underrepresentation of women in politics and leadership positions, as well as the lack of policies and laws that promote gender equality.

Violence against women: This refers to the widespread problem of physical, sexual, and emotional abuse against women.

Social inequality: This refers to the unequal distribution of social status, power, and privilege between men and women, which can manifest in various forms of discrimination, prejudice, and bias.

Intersectionality: This refers to the ways in which gender inequality intersects with other forms of inequality, such as race, class, and sexuality, creating complex and interconnected forms of disadvantage for certain individuals and groups.

It's important to note that Gender inequality can manifest in various forms and it can have a significant impact on individuals and groups, leading to reduced opportunities, access to resources, and lower quality of life. Therefore, it's crucial to understand and address gender inequality in all its forms.

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Answer:

Step-by-step explanation:

the 3rd

Answer: The measure of the third side of a triangle, when the measures of the other two sides are 13 in and 27 in, must be greater than the difference between the measures of the other two sides (which is 27 in - 13 in = 14 in) and less than the sum of the measures of the other two sides (which is 27 in + 13 in = 40 in).

This is because according to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So the measure of the third side must be between the difference of the two given sides and the sum of the two given sides.

Therefore the range of the measure of the third side of a triangle with side lengths 13 in and 27 in is:

(14 in < x < 40 in)

or

[x > 14 in and x < 40 in].

It is also important to note that any value of x within this range will produce a valid triangle, however any value less than 14 in or greater than 40 in will not.

Step-by-step explanation:

I recommend that Tammy create a budget to keep track of her income and expenses. She should also set up automatic payments for her International Club advisor so she doesn't miss any payments. Additionally, Tammy should create a savings plan for the trip to make sure she has enough money for it. Finally, she should start the habit of setting aside money from each paycheck for the trip, so she has a consistent source of funds when she needs them.

The line that passes through (12, 5) and (12, 9) is a vertical line, and its equation is:

x = 12

We know that we have a line that passes through points (12, 5) and (12, 9).

Notice that the x-value of the two points is the same one, then we will have a vertical line of the form:

x = a

The x-value in both points is 12, then the constant value of the line is 12, thus the equation for the line that passes through these two points is:

x = 12.

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Constant variance, also known as homoscedasticity, is a statistical property where the variance of a variable is equal across all values of the variable.

This means that the variability of the variable is consistent, no matter what the value of the variable is. Mathematically, this is expressed by the formula:

Var(X) = σ^2

where Var(X) is the variance of the variable X, and σ^2 is the same across all values of X.

For example, if we look at the heights of a group of people, we may find that the variance of their heights is equal to 25 cm, no matter what the heights are. In this case, the variance of the heights is 25 cm, and this variance (25 cm) is the same for all the heights in the group.

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The resulting quadrilateral have the following vertices: A'(x, y) = (- 1, 1.5), B'(x, y) = (- 0.5, 0.5), C'(x, y) = (1, - 0.5), D'(x, y) = (1, 1). (Correct choice: B)

Herein we have the case of a quadrilateral, that is, a polygon with four vertices: A(x, y) = (- 4, 6), B(x, y) = (- 2, 2), C(x, y) = (4, - 2), D(x, y) = (4, 4), whose image is the result of a dilation with a scale factor of 1 / 4 about the origin on Cartesian plane. The polygon is contracted by contracting each of five vertices, whose formula is shown below:

P'(x, y) = k · P(x, y)

Where:

If we know that k = 1 / 4, A(x, y) = (- 4, 6), B(x, y) = (- 2, 2), C(x, y) = (4, - 2) and D(x, y) = (4, 4), then the coordinates of the resulting polygon:

A'(x, y) = 0.25 · (- 4, 6)

A'(x, y) = (- 1, 1.5)

B'(x, y) = 0.25 · (- 2, 2)

B'(x, y) = (- 0.5, 0.5)

C'(x, y) = 0.25 · (4, - 2)

C'(x, y) = (1, - 0.5)

D'(x, y) = 0.25 · (4, 4)

D'(x, y) = (1, 1)

The vertices of the resulting quadrilateral are A'(x, y) = (- 1, 1.5), B'(x, y) = (- 0.5, 0.5), C'(x, y) = (1, - 0.5) and D'(x, y) = (1, 1).

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The value of x in the square is 5√2 centimetres.

A square is a quadrilateral with 4 sides equal to each other. The square has side length 5 times x centimetres and the diagonal length is 50 centimetres.

Therefore, the side x can be found using Pythagoras's theorem as follows:

c² = a² + b²

where

Therefore,

50² = (5x)² + (5x)²

2500 = 25x² + 25x²

2500 = 50x²

divide both sides by 50

x² = 2500 / 50

x² = 50

square root both sides of the equation

x = √50

x = √25 × 2

x = 5√2 centimetres

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Answer:

Step-by-step explanation:

second one

The exponential value of 3, also known as [tex]e^3[/tex]  is the value of the mathematical constant e (approximately equal to 2.71828) raised to the power of 3.

To calculate [tex]e^3[/tex] , we would use the following formula:

[tex]e^3[/tex]= e x e x e = 2.71828 x 2.71828 x 2.71828 = 20.0855

So, the exponential value of 3 is approximately 20.0855.

It's important to note that the exponential value of any number is a real number, the value of e is raised to the power of that number. The mathematical constant e, also known as Euler's number, is an important number in mathematics and is used in various branches such as calculus, statistics and probability. It has also been used in physics and engineering, it appears naturally in many processes such as radioactive decay, natural growth and decay of populations, and more.

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