A sample of size 25 is drawn from a normal population with a population standard deviation of 100. Suppose the mean of the sample is x(bar) = 35. Recall that z0.025=1.96. A 95% confidence interval for the population mean is equal to

Answers

Answer 1

The 95% confidence interval for the population mean is equal to (30.4,39.6).

A confidence interval is a range of values that surrounds the point estimate, such as a sample mean, and provides a sense of the precision of the estimate. The confidence interval (CI) contains the estimated parameter at a given level of confidence, usually 95% or 99%.

The 95% confidence interval for the population mean is given by:

x(bar) ± Zα/2 * σ/√n

Where,

x(bar) = 35σ = 100n = 25Zα/2 = Z0.025 = 1.96

Substituting the values, we get:

CI = 35 ± 1.96 * 100/√25

CI  = (30.4,39.6)

Hence, the 95% confidence interval for the population mean is (30.4,39.6).

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Related Questions

find the standard form of the parabola equation: 2x^(2)-8x-3y+11=0

Answers

The standard form of the parabola with the equation 2x² - 8x - 3y + 11 = 0 is y = 2/3x² - 8/3x + 11/3

Calculating the standard form of the parabola

Given that

2x² - 8x - 3y + 11 = 0

To put the given equation in standard form, we need to isolate the y term on one side of the equation.

Here's how to do it:

2x² - 8x - 3y + 11 = 0

Isolate 3y

This gives

3y = 2x² - 8x + 11

Divide through by 3

y = 2/3x² - 8/3x + 11/3

Hence, the standard form is y = 2/3x² - 8/3x + 11/3

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Please look at the photo and let me know the three answers ASAP!! Thank you!

Answers

Answer:

(a) $ 67.1

(b) $98.60

(c) $ 1.26

Step-by-step explanation:

Given equation is
[tex]y\:=\:-1.26x\:+\:98.6[/tex]

where x is the temperature in °F and y is the heating cost in $

To find heating cost for a specific temperature just substitute the value of x (temperature) in the equation

Part (a)
For x = 25 we get
y = -1.26(25)+ 98.6 = $ 67.1

Part (b)

For x = 0 we get
y = -1.26(0) + 98.6 = 0 + 98.6 = $98.60


Part (c)
For a 1 degree increase in temperature, the predicted decrease is the slope of the line
Slope of line = coefficient of x = -1.26

So decrease in cost for 1 degree increase in temperature = $1.26

Write the equation of a line that is perpendicular to y=-2/7+9 and that passes through the point (4,-6)

Answers

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{2}{7}}x+9\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{-2}{7}} ~\hfill \stackrel{reciprocal}{\cfrac{7}{-2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{7}{-2} \implies \cfrac{7}{ 2 }}}[/tex]

so we're really looking for the equation of a line whose slope is 7/2 and it passes through (4 , -6)

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{-6})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{7}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-6)}=\stackrel{m}{ \cfrac{7}{2}}(x-\stackrel{x_1}{4}) \implies y +6= \cfrac{7}{2} (x -4) \\\\\\ y+6=\cfrac{7}{2}x-14\implies {\Large \begin{array}{llll} y=\cfrac{7}{2}x-20 \end{array}}[/tex]

sarah is trying to decide what combination of cups and plates to buy. her budget is $18. plates cost $6 each and cups cost $3 each. the numbers in the table represent total utility. given her budget, which combination will maximize total utility?

Answers

Answer:- Hence, the  combination will maximize total utility is [tex]12.[/tex]

Step-By-Step-Explanation:-

What is cost?

Cost is the amount of money you spent to make the product or service. Price is what you will charge for it.

Here given that,

The cups and plates budget is [tex]$18 (3 plates x $6 each + 6 cups x $3 each)[/tex]

Then the utility for the combination is [tex]12 (3 plates x 4 utility each + 6 cups x 2 utility each).[/tex]

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the six trigonometric functions are not invertible what has to be done make them invertible

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Can you post the image in your question.

The following table represents the highest educational attainment of all adult
residents in a certain town. If a resident who is 40 or older is chosen at random, what
is the probability that they have only completed high school? Round your answer to
the nearest thousandth.
High school only
Some college
Bachelor's degree
Master's degree
Total
Age 20-29 Age 30-39 Age 40-49 Age 50 & over Total
1567
1078
5664
718
5026
1324
430
3550
1713
900
969
5149
1077
615
1108
525
3325
1942
1980
2062
513
6497
5394
2437
18521

Answers

The probability that a person chosen at random at age 40 or older has only completed high school is 0.2912.

What is probability?

Probability is the chance or likelihood that something will occur. It is quantified using numbers, ranging from 0 (no chance) to 1 (certainty). It also helps us to draw conclusions about the chances of something happening based on the available data.

The total number of people who have only completed high school

=(5394)

the total number of people in the age group 40 and over =(18521)

By dividing both the data, we get

5394/18521= 0.2912

From the given data in the table, we can calculate the probability that a person chosen at random at age 40 or older has only completed high school.

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The given family of functions is the general solution of the differential equation on the indicated interval. Find a member of the family that is a solution of the initial-value problem. y = c1ex + c2e−x, (−[infinity], [infinity]); y'' − y = 0, y(0) = 0, y'(0) = 5

Answers

The given family of functions is y = c1ex + c2e−x which is the general solution of the differential equation y'' − y = 0 on the indicated interval which is (−∞, ∞).

       Now, we are required to find a member of the family that is a solution to the initial-value problem which is

                             y(0) = 0 and y′(0) = 5.

     The differential equation is y'' − y = 0

      The characteristic equation is r2 − 1 = 0r2 = 1r1 = 1 and r2 = −1

     The general solution of the differential equation is y = c1ex + c2e−x

      Let us solve for the constants by using the given initial conditions:

                    At x = 0,y(0) = c1e0 + c2e0 = 0 + 0 = 0y(0) = 0

                    means c1 + c2 = 0or c1 = -c2At x = 0, y′(0) = c1ex |x=0 + c2e−x |x=0(d/dx)(c1ex + c2e−x) |x=0y′(0) = c1 - c2 = 5c1 - c2 = 5c1 - (-c1) = 5c1 + c1 = 5c1 = 5/2c1 = 5/2

                    Let's replace c1 = 5/2 in c1 = -c2, c2 = -5/2

                The solution of the initial-value problem y = (5/2)ex − (5/2)e−x is a member of the family y = c1ex + c2e−x that is a solution of the initial-value problem y(0) = 0 and y′(0) = 5.

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If a first sample has a sample variance of 12 and a second sample has a sample variance of 22 , which of the following could be the value of the pooled sample variance? 1 10 16 25

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The value of the pooled sample variance is 25 when the first sample has a sample variance of 12 and a second sample has a sample variance of 22.

If a first sample has a sample variance of 12 and a second sample has a sample variance of 22, then the possible values of the pooled sample variance are given by the formula below:

Formula:

pooled sample variance = [(n₁ - 1) s₁² + (n₂ - 1) s₂²] / (n₁ + n₂ - 2)

Where s₁ and s₂ are the sample standard deviations of the first and second samples,

n₁ and n₂ are the sample sizes of the first and second samples, respectively.

Thus, substituting the given values into the formula above, we have pooled sample variance:

= [(n₁ - 1) s₁² + (n₂ - 1) s₂²] / (n₁ + n₂ - 2)

= [(n₁ - 1) 12 + (n₂ - 1) 22] / (n₁ + n₂ - 2)

Checking each of the answer options:

If pooled sample variance is 1, then:

(n₁ - 1) 12 + (n₂ - 1) 22

= (n₁ + n₂ - 2)(1)

= 12n₁ + 22n₂ - 34

= (12n₁ - 12) + (22n₂ - 22)

= 12(n₁ - 1) + 22(n₂ - 1)

The expression on the right-hand side of the equation is a sum of multiples of 12 and 22, and therefore, the expression itself will be a multiple of the greatest common divisor of 12 and 22, which is 2.

Since 34 is not a multiple of 2, the equation cannot be true if the pooled sample variance is 1.

Thus, 1 is not a possible value of the pooled sample variance.

If pooled sample variance is 10, then:

(n₁ - 1) 12 + (n₂ - 1) 22

= (n₁ + n₂ - 2)(10)

= 12n₁ + 22n₂ - 34

= (12n₁ - 12) + (22n₂ - 22)

= 12(n₁ - 1) + 22(n₂ - 1)

The expression on the right-hand side of the equation is a sum of multiples of 12 and 22, and therefore, the expression itself will be a multiple of the greatest common divisor of 12 and 22, which is 2.

Since 34 is not a multiple of 2, the equation cannot be true if the pooled sample variance is 10.

Thus, 10 is not a possible value of the pooled sample variance.

If pooled sample variance is 16, then:

(n₁ - 1) 12 + (n₂ - 1) 22

= (n₁ + n₂ - 2)(16)

= 12n₁ + 22n₂ - 34

= (12n₁ - 12) + (22n₂ - 22)

= 12(n₁ - 1) + 22(n₂ - 1)

The expression on the right-hand side of the equation is a sum of multiples of 12 and 22, and therefore, the expression itself will be a multiple of the greatest common divisor of 12 and 22, which is 2.

Since 34 is not a multiple of 2, the equation cannot be true if the pooled sample variance is 16.

Thus, 16 is not a possible value of the pooled sample variance.

If pooled sample variance is 25, then:

(n₁ - 1) 12 + (n₂ - 1) 22

= (n₁ + n₂ - 2)(25)

= 12n₁ + 22n₂ - 34

= (12n₁ - 12) + (22n₂ - 22)

= 12(n₁ - 1) + 22(n₂ - 1)

The expression on the right-hand side of the equation is a sum of multiples of 12 and 22, and therefore, the expression itself will be a multiple of the greatest common divisor of 12 and 22, which is 2.

Since 46 is a multiple of 2, the equation can be true if the pooled sample variance is 25.

Thus, 25 is a possible value of the pooled sample variance.

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help!! i really can't do this pls help me with this inquality question

Answers

Answer:  11

Explanation:

2n is greater than 20, so 2n > 20. This solves to n > 10 after dividing both sides by 2. That inequality is the same as 10 < n.

5n is less than 60. It leads to 5n < 60. That solves to n < 12 after dividing both sides by 5.

To summarize:

"2n is greater than 20" leads to n > 10, aka 10 < n."5n is less than 60" leads to n < 12

Combine 10 < n with n < 12 to write a compound inequality:

10 < n < 12

The value n is between 10 and 12. We exclude each endpoint.

The only possible whole number that works here is n = 11

1.3. The Dow Jones average (a stock market share index) dropped from 12 837 to 12 503 in one week in July 2012. 1.3.1. Calculate the drop in the share index. 1.3.2. If the price continued to drop at the same rate, calculate the Dow Jones average after 4 more weeks. ​

Answers

The Dow Jones average after 4 more weeks of the same rate of drop would be 11,167.

What is average?

Average, also known as mean, is a measure of central tendency that represents the typical or common value in a set of data. It is calculated by adding up all the values in a data set and then dividing the sum by the total number of values.

To calculate the drop in the Dow Jones average, we subtract the initial value from the final value:

Drop = Final Value - Initial Value

Drop = 12,503 - 12,837

Drop = -334

So the Dow Jones average dropped by 334 points in one week.

If the price continued to drop at the same rate for 4 more weeks, then the total drop after 5 weeks would be:

Total Drop = 5 x Drop

Total Drop = 5 x (-334)

Total Drop = -1670

To calculate the Dow Jones average after 4 more weeks, we need to subtract the total drop from the initial value:

New Dow Jones Average = Initial Value - Total Drop

New Dow Jones Average = 12,837 - 1,670

New Dow Jones Average = 11,167

Therefore, the Dow Jones average after 4 more weeks of the same rate of drop would be 11,167.

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mathematics 3 and 4 grapgh mwehhh pleaseee

Answers

The answers of the question number 3 and 4 are given below respectively.

What is graph?

A graph is a visual representation of data or mathematical relationships.

It typically involves plotting points on a coordinate plane and connecting them with lines or curves.

Graphs can help to illustrate patterns, trends, and relationships in data and make it easier to understand complex information.

3.Assuming that the sale of bracelets and necklaces are represented by the variables B and N respectively, the total sale would be represented by the mathematical statement:

Total sale = B + N

Graph of Total Sale = B + N

The x-axis represents the number of bracelets sold (B), and the y-axis represents the number of necklaces sold (N).

4.To represent Nimfa's goal of achieving a total sale of at least Php 15,000, we can use the inequality:

Total sale ≥ Php 15,000

or, using the expression from the previous question:

2B + N ≥ Php 15,000

Graph of Total Sale ≥ Php 15,000

The shaded area above the plane represents all the combinations of sales of bracelets and necklaces that result in a total sale of at least Php 15,000. Any point above the plane is a valid combination of sales that meet Nimfa's goal.

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3. The x-axis represents the number of bracelets sold (B), and the y-axis represents the number of necklaces sold (N).

4. The shaded area above the plane represents all the combinations of sales of bracelets and necklaces that result in a total sale of at least Php 15,000.

What is graph?

A graph is a visual representation of data or mathematical relationships.

It typically involves plotting points on a coordinate plane and connecting them with lines or curves.

Graphs can help to illustrate patterns, trends, and relationships in data and make it easier to understand complex information.

3.Assuming that the sale of bracelets and necklaces are represented by the variables B and N respectively, the total sale would be represented by the mathematical statement:

Total sale = B + N

Graph of Total Sale = B + N

4.To represent Nimfa's goal of achieving a total sale of at least Php 15,000, we can use the inequality:

Total sale ≥ Php 15,000

or, using the expression from the previous question:

2B + N ≥ Php 15,000

Graph of Total Sale ≥ Php 15,000

The shaded area above the plane represents all the combinations of sales of bracelets and necklaces that result in a total sale of at least Php 15,000. Any point above the plane is a valid combination of sales that meet Nimfa's goal.

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1)
The burning times of scented candles, in minutes, are normally distributed with a mean of 249 and a standard deviation of 20. Find the number of minutes a scented candle burns if it burns for a shorter time than 80% of all scented candles.
Use Excel, and round your answer to two decimal places.
2) The number of square feet per house have an unknown distribution with mean 1670 and standard deviation 140 square feet. A sample, with size n=48, is randomly drawn from the population and the values are added together. Using the Central Limit Theorem for Sums, what is the mean for the sample sum distribution?

Answers

The Central Limit Theorem (CLT) states that as the sample size n increases, the sample mean approaches a normal distribution with a mean of μ and a standard deviation of σ/√n.

Therefore, when the number of houses in a population is unknown and a random sample of 48 houses is drawn from it, the mean for the sample sum distribution can be calculated using the CLT as follows:Mean for the sample sum distribution = nμ = 48 * 1670 = 80,160. The standard deviation for the sample sum distribution is given by:σ/√n = 140/√48 ≈ 20.20. Therefore, the sample sum distribution has a mean of 80,160 and a standard deviation of 20.20.To verify this, a histogram can be plotted in Excel using the following steps:Enter the data for the square footage of the 48 houses in column A of the Excel worksheet.Highlight column B and enter the formula =SUM(A1:A48) to sum the data in column A and store the result in column B.Highlight column C and enter the formula =B1/48 to calculate the mean for the sample sum distribution and store it in column C.Highlight column D and enter the formula =140/SQRT(48) to calculate the standard deviation for the sample sum distribution and store it in column D.Highlight columns B, C, and D, and select the Insert tab.Click on the Histogram icon under the Charts group.Select the Histogram chart type, and click OK to generate the histogram.The histogram should show a bell-shaped curve with a mean of 80,160 and a standard deviation of 20.20, indicating that the sample sum distribution is approximately normal.

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A grocer has two kinds of candy: one sells for 90 cents per pound, and the other sells for 40 cents per pound. How many pounds of each kind must he use to make 50 pounds that he can sell of 85 cents per pound?

Answers

The grocer must use 45 pounds of each kind of candy

How to calculate the number of pounds that the grocer requires?

A grocer has two kinds of candy
The first type of candy sells for 90 cents per pound

The second type of candy sells for 40 cents per pound

The number of pounds needed to make each kind of candy if he uses 50 pounds can be calculated as follows

The first step is to multiply 50 by 85%
50(85/100)

= 50(0.85)

= 42.5

Let y represent the unknown

y(90/100) + (50-y)(40/100)

0.9y + 0.4(50-y)

0.9y + 20-0.4y

0.9y-0.4y+20

0.5y+20(equate this value with 42.5)

0.5y+20= 42.5

collect the like terms

0.5y= 42.5-20

0.5y= 22.5

y= 22.5/0.5

y= 45

Hence the grocer needs 45 pounds for each kind of candy

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3gh2x4g3h3 help me please

Answers

Answer:

Step-by-step explanation:

To find the product

Its gonna be

12g^4h^5

are these equivalent
10-2x -2x10

Answers

No they are not equivalent. 10-2x = -2(x-5) and -2x10 is -20

A circle with radius of 2 cm sits inside a circle with radius of 4 cm. What is the area of the shaded region? Round your final answer to the nearest hundredth. 2 cm CH 4 cm​

Answers

the area of the shaded region is approximately 37.68 cm².

define area of circle

The area of a circle is the amount of space that is enclosed by the circle in a two-dimensional plane. It is defined as the product of the square of the radius (r) of the circle and the mathematical constant pi (π), which is approximately equal to 3.14159.

The area of the larger circle is:

A1 = π(4 cm)² = 16π cm²

The area of the smaller circle is:

A2 = π(2 cm)² = 4π cm²

To find the area of the shaded region, we subtract A2 from A1:

A1 - A2 = 16π cm²- 4π cm² = 12π cm²

To round the final answer to the nearest hundredth, we can use the approximation π ≈ 3.14:

12π cm² ≈ 12 × 3.14 cm² ≈ 37.68 cm²

Therefore, the area of the shaded region is approximately 37.68 square centimeters.

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Calculate the area of this trapezium.
6 cm
4 cm
5 cm
8 cm

Answers

Answer: 28cm²

Step-by-step explanation: To calculate the area of the trapezium, we can use the formula:

Area = (1/2) x (sum of parallel sides) x (height)

In this case, the two parallel sides are 6 cm and 8 cm, and the height is 4 cm.

Plugging in the values, we get:

Area = (1/2) x (6 cm + 8 cm) x 4 cm

Area = (1/2) x 14 cm x 4 cm

Area = 28 cm²

find the values of a and b such that
x^2- +5=(x-a)^2+b

Answers

The value οf a = 1/2  and b = 19/4 in the equatiοn x² - x + 5 = (x-a)² + b.

What dο yοu mean by algebra?

The part οf mathematics in which letters and οther general symbοls are used tο represent numbers and quantities in fοrmulae and equatiοn is called algebra.

x² - x + 5 = (x-a)² + b

x² - x + 5 = x² + a² - 2xa + b

-x + 5 = -2xa + a² + b

By matching cοrrespοnding terms,

2a = 1          and        a²+ b = 5

a= 1/2          and        a²+ b = 5

Substituting value οf "a"

(1/2)² + b = 5

1/4 + b = 5

b = 5- 1/4

b = 19/4

Thus, a = 1/2  and b = 19/4.

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in a group of 100 students 50 like online class and 70 loke physical class .represent in venn diagram and how many students like bith type pf classes

Answers

Answer:

Step-by-step explanation:

100 students all together.

50+70=120....so 20 must like both.

What is the meaning of logarithm in math?

Answers

In mathematics, a logarithm is a mathematical operation that determines how many times a given number (known as the base) must be multiplied by itself to produce another given number.

Logarithms are used to simplify complex calculations involving exponents and to convert between exponential and logarithmic expressions.

The logarithm of a number x to a given base b is represented as logb(x). For example, log10(100) = 2 because 10 multiplied by itself twice equals 100.

Logarithms have a wide range of applications in various fields, including mathematics, physics, engineering, finance, and computer science. They are particularly useful in scientific calculations involving large numbers, where working with exponents can become cumbersome. Logarithms are also used in the study of exponential growth and decay, as well as in the analysis of data sets with a wide range of values.

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Can some one help me? It’s three parts but the questions states use the interval notation to write the intervals over which f is (a) increasing, (b) decreasing, and (c) constant. The last question also says topics related to if its constant or not.

Answers

The function is constant from approximately x = -4 to x = -3 and from approximately x = -1 to x = 1. So, the constant intervals are (-4, -3) and (-1, 1)

What exactly are function and example?

A function, which produces one output from a single input, is an illustration of a rule. The picture was obtained from Alex Federspiel. The equation y=x2 serves as an example of this.

a) We can see that the function is increasing from approximately x = -3 to x = -1 and from approximately x = 1 to x = 2.5. So, the increasing intervals are (-3,-1) and (1, 2.5)

(b) We can see that the function is decreasing from approximately x = -2 to x = -0.5 and from approximately x = 3 to x = 4. So, the decreasing intervals are (-2, -0.5) and (3, 4)

(c) We can see that the function is constant from approximately x = -4 to x = -3 and from approximately x = -1 to x = 1. So, the constant intervals are (-4, -3) and (-1, 1)

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3. The length of one leg of a 45-45-90 triangle is 7 m. What is the length of the other leg and the length of the hypotenuse?
The other leg is 7 m, and the hypotenuse is 7 m.
The other leg is 7 m, and the hypotenuse is 14 m.
O The other leg is 7√2 m, and the hypotenuse is 7 m.
The other leg is 7 m, and the hypotenuse is 7√2 m.

Answers

Answer: The other leg is 7 m, and the hypotenuse is 7√2 m.

Step-by-step explanation:

This is just a rule that in all cases, the two legs are equal and the hypotenuse is equal to the length of a leg times the square root of 2.

Hope this helps :)

Help me help me help me help me help me

Answers

Answer: cab

Step-by-step explanation:

you start with the last point and move up

Angle ABC. You cannot start with point B, as it is in the middle of the angle. You also cannot start with CAB.

ling makes bracelets and necklaces and salesman a different crafts fairs the table shows how much is string is used to make each item
bracelet 7 1/2
small necklace 15
large necklace 19 1/4
ling plans to make at least 20 bracelets
write and solve an inequality to determine the minimum length of string that she needs to buy.
What is the least number of inches of string ling will need

Answers

According to the given information Ling has enough string to produce at least 20 bracelets.

What is a number and what are its many types?

Numbers serve the purpose of counting, measuring, organising, indexing, and other purposes. Natural numbers, whole numbers, rational and irrational numbers, integers, actual values, complex numbers, even and odd numbers, and so on are all distinct forms of numbers.

What exactly is a number?

A number is really a numerical value that is used to express quantity. As a consequence, a number seems to be a mathematical idea that may be used to count, measure, and name objects. As little more than a result, numbers are the foundation of mathematics. Here is one butterfly, and here are four butterflies.

Each bracelet requires 7 1/2 inches of string. So, the total length of string required to make 20 bracelets is:

20 × 7 1/2 = 150 inches

Therefore, Ling needs to buy at least 150 inches of string.

We can write the inequality to represent this situation as:

length of string ≥ 150

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The length of a rectangle is nine more than twice the width. If the perimeter is 120 inches, find the dimensions.

Answers

Answer:

Width = 17 inches

Length = 43 inches

Step-by-step explanation:

Framing and solving algebraic equation:

  Let the width of the rectangle = x inches

              Length = 2*width +9

                          = (2x + 9) cm

    [tex]\boxed{\bf Perimeter \ of \ rectangle = 2* (length + width)}[/tex]

        2* (length + width) = 120 inches

         2* (2x + 9 + x)       = 120

                     2* (3x + 9) = 120

Use Distributive property,

                 2 * 3x + 2*9  = 120

                         6x + 18   = 120

Subtract 18 from both sides,

                                   6x = 120 - 18

                                   6x = 102

Divide both sides by 6,

                                     x = 102 ÷ 6

                                     x = 17

Width = 17 inches

Length = 2*17 +9

           = 34 + 9

           = 43 inches

In a candy factory, each bag of candy contains 300 pieces. The bag can be off by 10 pieces.
Write an absolute value inequality that displays the possible number of candy pieces that a bag contains.

Answers

Answer:

[tex] |x - 300| \leqslant 10[/tex]

I NEED HELP BADLY PLEASE HELP

Answers

Answer:  0.11

Step-by-step explanation:

5/45=0.11

z^2 = 16
square root both sides
x=4 (plus or minus)

the area of a square is base x height, for a square it’s just side squared
if the area is 225, the side would be the square root of 225 and the units would be in instead of in^2

there aren’t any options so i’m not sure what it’s looking for but this is my best guess:
11.9860 is greater than the square root of 121.
square root of 121 is 11

irrational numbers would be the ones with the root. the rational numbers would be 0 and -1/16.

5/45 is 0.1111111… so it would be 0.1 with the line over the 1 to indicate that it’s a recurring decimal

pleaseee im begging anyone for the steps of these questions i need them so urgently right now, i have the answer but not the steps pls anyone

Answers

Answer:

  3. 79.9 mm²

  4. 6.4 in

  5. 177.5 mi²

  6. 60.3°

Step-by-step explanation:

Given various quadrilaterals and their dimensions, you want to find missing dimensions.

Trig relations

In all cases, one or more area formulas and trig relations are involved. The trig relations are summarized by the mnemonic SOH CAH TOA. The relevant relation for these problems is ...

  Tan = Opposite/Adjacent

It is also useful to know that 1/tan(x) = tan(90°-x).

Area formulas

The formula for the area of a trapezoid is ...

  A = 1/2(b1 +b2)h

The relevant formula here for the area of a parallelogram is ...

  A = bs·sin(α) . . . . . where α is the angle between sides of length b and s

3. Parallelogram area

Using the area formula above, we find the area to be ...

  A = (21 mm)(9 mm)·sin(155°) ≈ 79.9 mm²

The area is about 79.9 square mm.

4. Trapezoid base 2

The given figure shows two unknowns. We can write equations for these using the area formula and using a trig relation.

If we draw a vertical line through the vertex of the marked angle, the base of the triangle to the right of it is (b2-4). The acute angle at the top of that right triangle is (121°-90°) = 31°. The tangent relation tells us ...

  tan(31°) = (b2 -4)/h   ⇒   h = (b2 -4)/tan(31°)

Using the area formula we have ...

  A = 1/2(b2 +4)h

and substituting for A and h, we get ...

  20.8 = 1/2(b2 +4)(b2 -4)/tan(31°)

  2·tan(31°)·20.8 = (b2 +4)(b2 -4) = (b2)² -16 . . . . . multiply by 2tan(31°)

  (b2)² = 2·tan(31°)·20.8 +16 . . . . . . . add 16

  b2 = √(2·tan(31°)·20.8 +16) ≈ 6.4 . . . . . . take the square root

Base 2 of the trapezoid is about 6.4 inches.

5. Trapezoid area

To find the area, we need to know the height of the trapezoid. To find the height we can solve a triangle problem.

If we draw a diagonal line parallel to the right side through the left end of the top base, we divide the figure into a triangle on the left and a parallelogram on the right. The triangle has a base width of 10 mi, and base angles of 60° and 75°.

Drawing a vertical line through the top vertex of this triangle divides it into two right triangles of height h. The top angle is divided into two angles, one being 90°-60° = 30°, and the other being 90°-75° = 15°. The bases of these right triangles are now ...

h·tan(30°)h·tan(15°)

and their sum is 10 mi.

The height h can now be found to be ...

  h·tan(30°) +h·tan(15°) = 10

  h = 10/(tan(30°) +tan(15°))

Back to our formula for the area of the trapezoid, we find it to be ...

  A = 1/2(b1 +b2)h = 1/2(20 +10)(10/(tan(30°) +tan(15°)) ≈ 177.5

The area of the trapezoid is about 177.5 square miles.

6. Base angle

The final formula we used for problem 5 can be used for problem 6 by changing the dimensions appropriately.

  A = 1/2(b1 +b2)(b1 -b2)/(tan(90-x) +tan(90-x))

  112 = 1/2(20+12)(20-12)/(2·tan(90-x)) = (20² -12²)·tan(x)/4

  tan(x) = 4·112/(20² -12²)

  x = arctan(4·112/(20² -12²)) = arctan(7/4) ≈ 60.3°

Angle x° in the trapezoid is about 60.3°.

__

Additional comment

There is no set "step by step" for solving problems like these. In general, you work from what you know toward what you don't know. You make use of area and trig relations as required to create equations you can solve for the missing values. There are generally a number of ways you can go at these.

A nice scientific calculator has been used in the attachment for showing the calculations. A graphing calculator can be useful for solving any system of equations you might write.

The second attachment shows a graphing calculator solution to problem 5, where we let y = area, and x = the portion of the bottom base that is to the left of the top base. Area/15 represents the height of the trapezoid. This solution also gives an area of 177.5 square miles.

This shape is made up of one half-circle attached to an equilateral triangle with side lengths 20 inches. You can use 3. 14 as an approximation for π

Answers

If the shape is made up of one half-circle attached to an equilateral triangle with side lengths 20 inches then, the perimeter of the shape is 91.4 inches.

To find the perimeter of the shape, we need to know the length of the curved boundary (the circumference of the half-circle) and the length of the straight boundary (the perimeter of the equilateral triangle).

The radius of the half-circle is half the length of the side of the equilateral triangle, which is 10 inches. Therefore, the circumference of the half-circle is:

C = πr = π(10) = 31.4 inches.

The perimeter of the equilateral triangle is 3 times the length of one side, which is 20 inches. Therefore, the perimeter of the triangle is:

P = 3s = 3(20) = 60 inches

Finally, the perimeter of the entire shape is the sum of the lengths of the curved and straight boundaries:

Perimeter = C + P = 31.4 + 60 = 91.4 inches.

To know more about equilateral triangle

brainly.com/question/3461022

#SPJ4

Complete Question

This shape is made up of one half-circle attached to a square with side lengths 11 inches. Find the perimeter of the shape.

You can use 3.14 as an approximation for π. help i don't know it.

simplest form please

Answers

hmmm what we do is firstly make the recurring part a variable, then we multiply it such that, the recurring digits move over from the decimal point to the left, so we'd multiply it by some power of 10, in this case power of 3, because we have three digits to move, 246, so let's do all that

[tex]0.\overline{246}\hspace{5em}x=0.\overline{246}\hspace{5em} \begin{array}{llll} 1000x&=&246.\overline{246}\\\\ &&246+0.\overline{246}\\\\ &&246+x \end{array} \\\\[-0.35em] ~\dotfill\\\\ 1000x=246+x\implies 999x=246\implies x=\cfrac{246}{999}\implies x=\cfrac{82}{333}[/tex]

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