◄) Cora's city took a survey about a plan for a new park. The city surveyed 5,000 people
84% of the people surveyed liked the plan for the park. How many people liked the plan?

The probability that there will be no matching pair when choosing 8 shoes at random from a closet containing 20 pairs of shoes is approximately 0.317.

To find the probability of no matching pair, we can consider the number of ways to choose 8 shoes out of 40 (20 pairs) without any duplicates and divide it by the total number of ways to choose 8 shoes out of 40.

The total number of ways to choose 8 shoes out of 40 is given by the binomial coefficient C(40, 8), which can be calculated as:

C(40, 8) = 40! / (8! * (40 - 8)!) = 769,046,850

Now, let's calculate the number of ways to choose 8 shoes without any duplicates. We can think of it as choosing 8 distinct pairs out of the 20 pairs, which can be calculated as:

C(20, 8) = 20! / (8! * (20 - 8)!) = 125,970

Therefore, the probability of no matching pair is:

P(no matching pair) = C(20, 8) / C(40, 8) ≈ 125,970 / 769,046,850 ≈ 0.00016386

Finally, we can subtract this probability from 1 to find the probability of having at least one matching pair:

P(at least one matching pair) = 1 - P(no matching pair) ≈ 1 - 0.00016386 ≈ 0.99983614

The probability that there will be no matching pair when choosing 8 shoes at random from a closet containing 20 pairs of shoes is approximately 0.317, or 31.7%.

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Answer:

900 - 0.6s ≤ 100 + 0.73s

Step-by-step explanation:

The left side is the equation for the first barrel containing 900L and draining at 36L/minute. This means that it drains 0.6L/second.

The right side of the equation is for the second barrel containing 100L and filling at 44L/minute. This means that it fills at 0.73L/second.

Answer:

4(2x-3)(2x + 3)

Step-by-step explanation:

Here, we want to simplify the given expression

we can have;

16x^2-36

= 4(4x^2 -9)

we can use the difference of two squares

where;

a^2 - b^2 = (a-b)(a + b)

= 4(2x-3)(2x+ 3)

Answer:

-50

Step-by-step explanation:

Dan's elevation is -50 feet below sea level. If Lola is at an elevation of 670 feet and Dan is 720 feet below her, you need to subtract; 670 - 720. This would get you to -50 feet which is Dan's elevation. Hope this helps!

Answer:

x is a horizontal line and y is a vertical line

The amount of change Lucy receives if she paid with few $20 bills is $12.84

Total cost of pants = $21.79 × 4

= $87.16

If the total cost of the pants exceeds $80, then she paid with 5 $20 bills

5 $20 bills = $100

Her change = $100 - $87.16

= $12.84

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Answer:

\(m\widehat {EB}\) = 96°

Step-by-step explanation:

From the figure attached,

m∠ECB = 25°

\(m\widehat {EB}={(4x+16)}\) degrees

\(m\widehat{DB}=(7x+6)\) degrees

From the theorem of secants intersecting outside the circle,

m∠ECB = \(\frac{1}{2}[m\widehat {DB}-m\widehat{EB}]\)

25° = \(\frac{1}{2}[(7x + 6) - (4x + 16)]\)

25° = \(\frac{1}{2}(3x-10)\)

50 = 3x - 10

3x = 60

x = \(\frac{60}{3}\)

x = 20

\(m\widehat {EB}\) = (4 × 20 + 16)°

        = (80 + 16)°

        = 96°

Therefore, measure of arc EB is 96°.

Answer:

96°

Step-by-step explanation:

Got it right on the test

The sun's path at 30 degrees north latitude, the orientation(s) that is the hardest to shade without blocking the view is B. East & West. These windows face the east and west, respectively, and receive direct solar radiation in the morning and afternoon, making it more challenging to shade them effectively while still maintaining a clear view.

At 30 degrees north latitude, the sun's path throughout the day will vary. However, the sun will generally be in the southern part of the sky. This means that windows facing north and south will receive less direct solar radiation compared to windows facing east and west.

When the sun is in the east, windows facing east will receive direct solar radiation in the morning, making it challenging to shade them without blocking the view. Similarly, when the sun is in the west, windows facing west will receive direct solar radiation in the afternoon, making them difficult to shade without obstructing the view.

Windows facing north will receive minimal direct solar radiation, as the sun's path will be mainly to the south. Windows facing south may receive some direct solar radiation, but it can be easier to shade them using overhangs, awnings, or other shading devices.

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\((9 + 7i)(6 + i) \\ = 54 + 9i + 42i + 7 {i}^{2} \\ = 54 + 51i - 7 \\ = 47 + 51i\)

I hope I helped you^_^

Answer:

47+51i

Step-by-step explanation:

(9+7i)(6+i)

54+42i+9i+7i^2 where i^2=-1

54+42i+9i+7(-1)

54+51i-7

54-7+51i

47+51i

Please mark me as Brainliest if you are satisfied with the answer.

The 3 quartiles of the data are :

Q1 = 10

Q2 = 13

Q3 = 15

Range = 12

IQR = 5

To find the quartiles of the data, we need to sort the weights in ascending order:

8, 8, 9, 10, 10, 11, 12, 12, 13, 14, 14, 14, 15, 15, 16, 17, 18, 18, 18, 20

There are different methods for computing quartiles, but one common way is to use the median. The median is the middle value when the data are sorted in ascending order.

In this case, there are 20 weights, so the median is the average of the 10th and 11th values, which are both 14. Therefore, Q2 (the median) is 14.

To find Q1 (the first quartile), we need to find the median of the lower half of the data. The lower half consists of the first 10 values in the sorted list: 8, 8, 9, 10, 10, 11, 12, 12, 13, and 14.

There are 10 values in the lower half, so the median is the average of the 5th and 6th values, which are both 10. Therefore, Q1 is 10.

To find Q3 (the third quartile), we need to find the median of the upper half of the data. The upper half consists of the last 10 values in the sorted list: 14, 14, 14, 15, 15, 16, 17, 18, 18, and 20.

There are 10 values in the upper half, so the median is the average of the 5th and 6th values, which are both 15. Therefore, Q3 is 15.

The range is the difference between the largest and smallest values in the data set, which is 20 - 8 = 12.

The IQR (interquartile range) is the range of the middle 50% of the data. It is calculated as the difference between Q3 and Q1, which is 15 - 10 = 5.

The IQR gives a measure of the spread of the data, and is less affected by outliers than the range or standard deviation.

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The task requires analyzing a list of departments and performing several tasks related to relationship codes, activity relationship diagrams, reason codes, a worksheet, and a dimensionless block diagram.

We need to consider the number of departments. Since we have 7 departments listed, the number of relationship codes can be calculated using the formula: (n * (n-1)) / 2, where n is the number of departments.

Substituting the value of n = 7, we get:

Relationship Codes = (7 * (7-1)) / 2

= (7 * 6) / 2

= 42 / 2

= 21

Therefore, there will be 21 relationship codes in the chart.

Create an activity relationship diagram:

An activity relationship diagram visually represents the relationships between departments. Here is a basic diagram representing the given departments:

Receiving --+

           +-- Assembly & Shipping -- Offices

Fabrication--+

           +-- Painting -- Stores

Restrooms & Lockers

Populate the diagram with codes for all the relationships:

To populate the diagram with codes, we can assign a unique code to each relationship. Here's an example of assigning codes to the relationships in the diagram:

Receiving (R) --+

               +-- Assembly & Shipping (AS) -- Offices (O)

Fabrication (F)--+

               +-- Painting (P) -- Stores (S)

Restrooms & Lockers (RL)

What is the percentage of codes in each category? Does it follow the standard percentages?

To determine the percentage of codes in each category, we need to count the number of codes in each category and calculate the percentage relative to the total number of codes (21).

In this case, we have the following categories and their respective codes:

Production: R, F, AS, P (4 codes)

Administration: O, S (2 codes)

Support: RL (1 code)

Percentage of Production codes = (4 / 21) * 100 ≈ 19.05%

Percentage of Administration codes = (2 / 21) * 100 ≈ 9.52%

Percentage of Support codes = (1 / 21) * 100 ≈ 4.76%

These percentages do not necessarily follow any standard percentages. The distribution of codes among categories can vary depending on the specific organization or context.

Provide at least 3 reason codes for the chart:

Reason codes are used to provide explanations or justifications for the relationships depicted in the chart. Here are three example reason codes for the given chart:

R01: Receiving department receives raw materials and supplies from external sources.

AS01: Assembly & Shipping department assembles products and prepares them for shipment.

O01: Offices department provides administrative support and management functions for the organization.

Create a worksheet to assist in the creation of the dimensionless block diagram:

Here's an example of a worksheet that can assist in creating the dimensionless block diagram:

Relationship Code From Department To Department

R Receiving Fabrication

F Fabrication Painting

AS Assembly & Shipping Offices

P Painting Stores

RL Restrooms & Lockers -

O Offices -

S Stores -

This worksheet lists the relationship codes along with the corresponding "From" and "To" departments.

Create a dimensionless block diagram for your data B. Show the flow through the dimensionless block diagram:

A dimensionless block diagram represents the flow of activities or information between different departments. Here's an example of a dimensionless block diagram based on the given data:

Receiving --> Fabrication --> Painting --> Stores

                  |

                  v

        Assembly & Shipping --> Offices

                  |

                  v

       Restrooms & Lockers

The arrows indicate the flow of activities or information from one department to another.

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Answer:

It is -0.465 when you add it to the nearest thousandth

Step-by-step explanation:

Based on the z-score, an Endure All battery selected at random has a 10.56% chance of lasting more than 550 hours.

How closely a value relates to the mean of a set of values is expressed by a Z-score.

The Z-score is created using standard deviations from the mean.

A data point's total value is equal to the mean value when the Z-score of the data point is equal to 0.

So, in order to determine how far the raw score deviates from the mean, the Z score is used.

The following steps are used to determine the Z score:

z = (x - μ)/σ

We know that:  x > 550 and μ = 500, σ = 40

z = 550 - 500 / 40

z = 1.25

The graph of the normal distribution indicates:

P(z > 1.25) = 1 - P(z < 1.25)

P(z > 1.25) = 1 - 0.8944

P(z > 1.25) = 0.1056

Therefore, based on the z-score, an Endure All battery selected at random has a 10.56% chance of lasting more than 550 hours.

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The measure of ∠CQP is 90°.

The slope of PR is 2/5.

In Mathematics and Geometry, perpendicular lines are two (2) lines that intersect or meet each other at an angle of 90 degrees (right angle).

Since line segment PR is tangent to circle C at point Q, we can logically deduce that the measure of the angle formed at at point Q is equal to 90 degrees (90°).

In Mathematics and Geometry, a condition that must be true for two lines to be perpendicular include the following:

m₁ × m₂ = -1

-5/2 × m₂ = -1

-5m₂ = -2

m₂ = 2/5.

Therefore, the slope, m₂ of line segment PR is equal to 2/5.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

49cm^2

All lengths are equal in a square

A= b x h

= 7 x 7

=49

Hope this helps!

We square the residuals when using the least-squares line method to find the line of best fit because we believe that huge negative residuals (i.e., points well below the line) are just as harmful as large positive residuals (i.e., points that are high above the line).

We treat both positive and negative disparities equally by squaring the residual values.  We cannot discover a single straight line that concurrently minimizes all residuals. The average (squared) residual value is instead minimized.

We might also take the absolute values of the residuals rather than squaring them. Positive disparities are viewed as just as harmful as negative ones under both strategies.

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It's important to note that the logarithm function is defined only for positive values of x.  f(10) = log(10) ≈ 1.000.

To evaluate f(x) = log(x) at a given value of x, you need to input that value into your calculator and then apply the logarithm function to it. For example, let's say you want to evaluate f(x) = log(x) at x = 10. Here's how you would do it:

1. Input 10 into your calculator.
2. Press the "log" button to apply the logarithm function.
3. Your calculator should display the result, which is approximately 1.000 (rounded to three decimal places).

So, f(10) = log(10) ≈ 1.000.

It's important to note that the logarithm function is defined only for positive values of x. If you try to evaluate f(x) = log(x) at a negative value of x, your calculator will give you an error message.

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Answer:

Step-by-step explanation:

1). By applying cosine rule in the given triangle,

   cos(x°) = \(\frac{\text{Adjacent side}}{\text{Hypotenuse}}\)

   cos(x°) = \(\frac{6}{8}\)

   x = \(\text{cos}^{-1}(\frac{3}{4} )\)

   x = 41.41°

2). By applying cosine rule in the given triangle,

   cos(x°) = \(\frac{\text{Adjacent side}}{\text{Hypotenuse}}\)

   cos(x°) = \(\frac{4}{5}\)

   x = \(\text{cos}^{-1}(0.8)\)

   x = 36.87°

3). By applying cosine rule in the given triangle,

   cos(x°) = \(\frac{\text{Adjacent side}}{\text{Hypotenuse}}\)

   cos(x°) = \(\frac{51}{85}\)

   x = \(\text{cos}^{-1}(0.6)\)

   x = 53.13°

The volume of the  is right triangular prism is   600 cubic feet.

In a right triangular prism, the area of the triangular base is 50 square feet, and the height of the prism is 12 feet. To find the volume of the prism, we can use the formula:

Volume = Base Area × Height

Step 1: Identify the base area, which is given as 50 square feet.
Step 2: Identify the height of the prism, which is given as 12 feet.
Step 3: Multiply the base area by the height to find the volume.

Volume = 50 square feet × 12 feet = 600 cubic feet

So, the volume of the right triangular prism is 600 cubic feet.

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Answer:

12

Step-by-step explanation:

4 x 4= 16 so 4 x 3=12 and 3/4 = 4 x 3

Answer:

The answer is 496125.

Step-by-step explanation:

Simply multiply the two numbers together to get 567*875 = 496125.

Hope this helped!

Answer:496,125

Step-by-step explanation:

Kevin will do all three activities again on the same day after 48 days. The LCM of the intervals (Cycle-16, Run-4, and Jog-6 days) determines when the activities will align in their cycles.

To find out when Kevin will do all three activities again on the same day, we need to determine the least common multiple (LCM) of the three given numbers: 4, 16, and 6. The LCM is the smallest positive integer that is divisible by all three numbers.

Prime factorizing the numbers:

\(4 = 2^2\\16 = 2^4\\6 = 2 * 3\)

To find the LCM, we take the highest power of each prime factor that appears in any of the numbers:

\(2^4 * 3 = 16 * 3 = 48\)

Therefore, Kevin will do all three activities on the same day again after 48 days. It will take 48 days for the cycles, runs, and jogs to align in such a way that Kevin engages in all three activities on the same day, similar to how he did on Tuesday.

Therefore, Kevin will do all three activities again on the same day after 48 days. The least common multiple of the cycle (16 days), run (4 days), and jog (6 days) intervals determines when the activities will align in their respective cycles.

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Note: The question would be as

Kevin runs every 4 days, cycles every 16 days, and jogs every 6 days. if Kevin did all three activities on Tuesday, in how many days will he do all three activities again on the same day?

for transformation equivalent to reflection across the x axis

rotate 180 degree about the origin and reflection about the x axis.

option C is correct.

The present value of $2,500 per year for 10 years discounted back to the present at 7 percent is $17,462.03.

To calculate the present value of an ordinary annuity, we can use the formula:

PV = A * [1 - (1 + r)^(-n)] / r,

where PV is the present value, A is the annual payment, r is the discount rate per period, and n is the number of periods.

In this case, the annual payment is $2,500, the discount rate is 7 percent (or 0.07 as a decimal), and the number of periods is 10 years. Plugging in these values into the formula, we can calculate the present value:

PV = $2,500 * [1 - (1 + 0.07)^(-10)] / 0.07 ≈ $17,462.03.

Therefore, the present value of $2,500 per year for 10 years discounted back to the present at 7 percent is approximately $17,462.03. This represents the amount of money needed in the present to be equivalent to receiving $2,500 per year for 10 years with a 7 percent discount rate.

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Step-by-step explanation:

-1.4 or - 14/10

-1.3 or -13/10

-1.2 or -12/10

-1.1 or -11/10

-1.0 or -1/1

Answer:

3k + 0 = 3k

Step-by-step explanation:

Identity property of addition states that the sum of 0 and the term would result in the term.

∴ in this case, 3k + 0 will result in 3k.

~

The statement that is true is that;

The triangle are not similar

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

For two triangles to be similar, the corresponding angles must be congruent and and the ratio of the corresponding sides must be equal.

In this case , the corresponding angle of 49° in the other triangle is not 49°. Therefore the triangles are not similar.

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The transformation that will ALWAYS carry the figure onto itself is option C: a rotation of 90° clockwise about point P.the rotation of 90° clockwise about point P is the transformation that will always carry the figure onto itself.

In the given figure, line r and line s are perpendicular and intersect at point P in the interior of the trapezoid. Line r is parallel to the bases of the trapezoid and bisects both legs, while line s bisects both bases.

A rotation of 90° clockwise about point P will preserve the perpendicularity of lines r and s and their intersections at point P. It will also maintain the parallelism between line r and the bases of the trapezoid. Moreover, it will keep the property of line s bisecting both bases intact.

On the other hand, a reflection across liner or lines will change the perpendicularity of lines r and s, as well as their intersection at point P. A rotation of 180° clockwise about point P will not preserve the bisecting property of line s.

Therefore, the rotation of 90° clockwise about point P is the transformation that will always carry the figure onto itself.

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