4 Isabel is designing a new fish tank that is shaped like a triangular prism with lateral faces made of glass. A model of the fish tank and its dimensions are shown below. 10 in 8 in 1 6 in 8 in What is the lateral surface area of Isabel's fish tank? ​

A quadrilateral is a polygon with four sides and four angles. It is a geometric shape that consists of four straight sides connected by four vertices or corners. The maximum value of x is 11 cm.

To find the value of x, we can use the information given in the question.

We have the lengths of three sides of a quadrilateral:

12 cm, 6 cm, 5 cm, and x cm.

In order to find the value of x, we need to use the fact that the sum of the lengths of any two sides of a quadrilateral must be greater than the length of the remaining two sides.

Let's check if this condition is met:

12 cm + 6 cm = 18 cm

Since 18 cm is greater than both 5 cm and x cm, this condition is satisfied.

6 cm + 5 cm = 11 cm

Again, 11 cm is greater than both 12 cm and x cm, so this condition is also satisfied.

12 cm + 5 cm = 17 cm

Here, 17 cm is less than the sum of 6 cm and x cm. Therefore, this condition is not satisfied.

Based on this, we can conclude that the value of x must be such that 17 cm is less than 6 cm + x cm.

To find the maximum value of x, we subtract 6 cm from 17 cm:

17 cm - 6 cm = 11 cm

Therefore, the maximum value of x is 11 cm.

Hence, x = 11 cm.

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Answer:

£10.40

Step-by-step explanation:

Latte = £2.60
2 Hot Chocolates = £6.00
Tea = £1.80
Total = £2.60 + £6.00 + £1.80 = £10.40

Answer:

£10.40

Step-by-step explanation:

Add the cost of the drinks together to find the total cost:

\(\begin{tabular}{r r}Latte & \£2.60\\Hot Choc & \£3.00\\ Hot Choc & \£3.00\\Tea & \£1.80\\\cline{1-2} Total & \£10.40\\\cline{1-2}\end{tabular}\)

Answer:

$0.80

Step-by-step explanation:

Given:

To find the unit price in dollars per centimeter, divide the total amount by the number of centimeters:

\(\implies \dfrac{16.40}{20.5}=\dfrac{164}{205}=\dfrac{41 \times 4}{41 \times 5}=\dfrac{4}{5}=0.8\)

Therefore, the unit price in dollars per centimeter is $0.80.

Answer:4th one

Step-by-step explanation:

Answer: A

Step-by-step explanation:

The total number of ways to achieve a Straight is 10,240.

The total number of ways to achieve a Flush is 5148.

The total number of ways to achieve a Full House is 312.

The total number of ways to achieve a Straight Flush is 40.

What is number of ways?

The term "number of ways" refers to the total count of possible arrangements or combinations of a set of objects or events. It is often used in combinatorics, which is the branch of mathematics concerned with counting and arranging objects.

a) A Straight: There are 10 possible sequences of 5 cards of sequential rank (e.g., 2, 3, 4, 5, 6 or 10, J, Q, K, A), and for each sequence, there are \(4^5\) = 1024 ways to choose the suits of the cards. Therefore, the total number of ways to achieve a Straight is 10 * 1024 = 10,240.

b) A Flush: There are 4 suits in the deck, and for each suit, there are (13 choose 5) ways to choose 5 cards of that suit. Therefore, the total number of ways to achieve a Flush is 4 * (13 choose 5) = 5148.

c) A Full House: There are 13 ranks in the deck, and for the 3 cards of one rank, there are (4 choose 3) = 4 ways to choose the suits, and for the 2 cards of another rank, there are (4 choose 2) = 6 ways to choose the suits. Therefore, the total number of ways to achieve a Full House is 13 * 4 * 6 = 312.

d) A Straight Flush: There are 10 possible sequences of 5 cards of sequential rank (as in part a)), and for each sequence, there are 4 ways to choose the suit of the cards. Therefore, the total number of ways to achieve a Straight Flush is 10 * 4 = 40.

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The equation for the tangent line at (0, 8) is y = 8x + 8.

A tangent line is a line that touches a curve at a single point, and has the same slope as the curve at that point. The slope of the tangent line is equal to the derivative of the function at the point of tangency.

The tangent line at (0, 8) is the same as the slope of the curve evaluated at x = 0.
To determine the slope, we take the derivative of y with respect to x:
y' = 8e^x(cosx - sinx)
At x = 0, the derivative simplifies to y' = 8cos0 - 8sin0 = 8(1 - 0) = 8.
Thus, the equation for the tangent line at (0, 8) is y = 8x + 8.

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The required probability that she'll use a cab exactly one time is  4/9.

probability is a part of math that arrangements with figuring out the probability of the event of an occasion.

Elizabeth lives in San Francisco and works in Mountain View.

In the first part of the day she has 3 transportation choices  (bus, cab, train) to work, and at night she has similar 3 options for her outing home.

All transportation  (bus, cab, train) are comparably liable to be chosen, and 1 of them should be chosen in the first part of the day and night, so we get:

P (bus) = P (taxi) = P (train) = 1/3.

We additionally have P(no taxi in night) = P(no taxi at morning) = 2/3

Presently, P(using taxi precisely once) = P(cab at morning and no taxi at night) + P(no taxi at morning and taxi at night)

= P(cab, no taxi) + P(no taxi, taxi)

= 1/3 × 2/3 + 2/3 × 1/3

= 2/9 + 2/9

= 4/9

Consequently, the probability that Elizabeth utilizes a taxi just once is 4/9.

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Answer: y=5/2x+3

Step-by-step explanation:

y=mx+b

-7=(5/2)(-4)+b

b=3

y=5/2x+3

Answer:

x=37 CD=20

Step-by-step explanation:

We know this becuase the two triangles are congruent.

To find the Depth you need to substitute the values of x and y into the equation: depth = y - x.

To determine the depth of the satellite dish, we need to calculate the distance from the receiver to the vertex of the dish. Given that the receiver is located inches above the vertex, we can subtract this distance from the dish's width to find the depth.

Let's assume the distance from the receiver to the vertex is x inches. We know that the width of the dish is y inches. It may be a parabola. Therefore, the depth of the dish can be calculated as y - x inches.

However, since you haven't provided specific values for the receiver's distance or the dish's width, it is not possible to give an exact answer. To find the depth, you need to substitute the values of x and y into the equation: depth = y - x.

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Answer:

y=2x-7

Step-by-step explanation:

first you find the slope by using point slope form.

then you use slope formula

Answer:

C

∠L and∠Q

Step-by-step explanation:

in the congruence statementit shows

A. JL and PR

JKL≅PQR

THEY MATCH-not this one

B. ∠K and ∠Q

JKL≅ PQR

THEY MATCH-not this one

C.∠L and ∠Q

JKL≅PQR

THEY DO NOT MATCH

D. ∠J and ∠P

JKL≅PQR

THEY MATCH-not this one

Answer:

Step-by-step explanation:

Use the formule V=4/3 *Pi*R^3

where R =10

so V=4/3*Pi*10^3

v= 4000Pi/3 =4188.7902

Answer: -3/2/3

Step-by-step explanation:

The given categories of variables that are mutually exclusive and exhaustive are weekdays and weekend and vowels and consonants.

Mutually exclusive and exhaustive variables: A variable is mutually exclusive and exhaustive if it includes all possible outcomes and each outcome can only be assigned to one variable category.a. Days: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, and Sunday - Mutually exclusive and exhaustiveb. Days: Weekday and Weekend - Mutually exclusive and exhaustive c. Letters: Vowels and Consonants - Mutually exclusive and exhaustive. Letters: Alphabets and Consonants - Not mutually exclusive and exhaustiveThe given categories of variables that are mutually exclusive and exhaustive are weekdays and weekend and vowels and consonants. Hence, the options a and c are correct.

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Given that the screw is a regular hexagon with side length 6 mm, the area of the screw is 93.5 mm^2

The area of an hexagon can be found using the following equation;

\(A = \mathbf{ \frac{3 \cdot \sqrt{3} }{2} \times {a}^{2}} \)

Where a = The side length

However the side lengths are not equal, and the figure is a composite figure with two triangles and one rectangle;

Base length of the triangles = 12

Height of the triangles = 3

Area of each triangle = 0.5 × 12 × 3 = 18

Width of the rectangle = 12

Height of the rectangle = 6

Area of the rectangle = 12 × 6 = 72

Area of the screw = 18 + 18 + 72 = 108

However taking the screw as a regular hexagon, with side length a = 6, we have;

\(A = \frac{3 \cdot \sqrt{3} }{2} \times {6 \: mm}^{2} = 93.5 \: mm^2 \)

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Answer:

Step-by-step explanation:

Given

Area of the rectangle =Length × width

Given

The desired length of the lot is 6 m longer than its width, then L = 6+W

A = LW

40 = (6+W)W

40= 6W+W²

W²+6W -40 = 0

W²+10W-4W-40 = 0

W(w+10)-4(w+10) = 0

W+10 = 0 and w-4 = 4

W = -10 and w = 4

Width can't be negative

W = 4m

Since L = 6+w

L = 6+4

L = 10m

Hence the possible dimension s 4m by 10m

9514 1404 393

Answer:

  6x -7 units

Step-by-step explanation:

Let c represent the length of the third side. The perimeter is the sum of the three side lengths.

  P = a + b + c

  (17x -5) = (3x +5) +(8x -3) +c

 17x -5 = 11x +2 + c . . . . . . . . . . . . collect terms

  6x -7 = c . . . . . . . . . . . . . . subtract 11x+2

The third side is 6x -7 units.

To have a more realistic picture of a typical salary, it is true that using multiple measures of central tendency, such as the mean, median, and mode, can provide a comprehensive understanding of the salary distribution.

When examining salaries, relying solely on one measure of central tendency may not capture the full range and distribution of salaries within a dataset. Each measure of central tendency provides different insights into the typical salary and can help paint a more realistic picture.

The mean, or average, is calculated by summing all salaries and dividing by the number of data points. It provides an overall measure of central tendency, but it can be influenced by extreme values or outliers. Therefore, it may not accurately represent a typical salary if there are a few extremely high or low salaries in the dataset.

The median is the middle value when salaries are arranged in ascending or descending order. It is less sensitive to extreme values and provides a better representation of a typical salary when there are outliers present. By identifying the middle value, it considers both higher and lower salaries, offering a more balanced view.

The mode represents the most frequently occurring salary. It can be useful when there are distinct peaks or clusters in the salary distribution. If there are multiple modes, it suggests different salary groups or categories within the dataset.

By considering multiple measures of central tendency, such as the mean, median, and mode, analysts can obtain a more comprehensive understanding of the salary distribution. This approach allows for a more realistic and nuanced picture of the typical salary, taking into account different aspects of the dataset.

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Part b

From the given information, we can to note that the class width is 10. The class width refers to the difference the upper and lower boundaries of any class. Therefore, the answer fo part b is. Class widh = 10

Part c

Now, lets complete the relative frequency table.

The classes are given by:

For the first class (49.5, 59.5), there are 10 numbers.

For the second class (59.5,69.5), there are 8 numbers.

For the third class (69.5,79.5), there are 4 numbers

For the fourth class (79.5,89.5) there are 2 numbers

For the fifth class (89.5,99.5) there is 1 number.

Then, the frequency column is given by:

On the other hand, the relative frequency is defined as the frequency divided by the total number of events ocurring. In our case, the total number is 10+8+4+2+1= 25. Then, the relative frequency for the first row is:

For the second row

3rd row:

4th row:

and 5th row:

Then, the complete table is:

Therefore, the histrogram representing this table is:

corresponding to the third option from top to bottom.

As we can note from the histogram, its shape is right skewed because has a long right tail. So, the answer for part d is: Right skewed

Answer:

oh god

Step-by-step explanation:

Explanation

Step 1

subtract m in both sides

Step 2

multiply each side by k

Step 3

finally, add j in both sides

I hope this helps you

The null and alternative hypotheses for the researcher's study on the effect of a stress-reduction program on people's levels of cortisol. None of the options you provided match these hypotheses.

The null hypothesis (H0) is that the stress-reduction program has no effect on cortisol levels, while the alternative hypothesis (H1) is that the program reduces cortisol levels. In this case, the null and alternative hypotheses can be represented as follows:

Null hypothesis (H0): Δcortisol = 0 (no difference in cortisol levels before and after the program)
Alternative hypothesis (H1): Δcortisol < 0 (cortisol levels are lower after the program)

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Answer:

5x + 16

Step-by-step explanation:

First you have to distribute the 2 into the parentheses

2 times x is 2x

2 times 6 is 12

so now the equation is

2x + 12 + 3x + 4

add the 2x and 3x and that is 5

so now the equation is...

5x + 12 + 4

add 12 + 4 and that is 16

so now the answer is

5x + 16

Without specific information about the data set, it is not possible to determine which equation is the best fit.

To determine the linear function equation that best fits the data set, we need more information about the data set itself. Without the data points or any other details, we cannot accurately determine which linear function equation is the best fit.

However, I can provide a general explanation of the four options:

y = -2x + 5: This is a linear equation with a negative slope of -2. It represents a line that decreases as x increases. The y-intercept is 5.

y = 2x + 5: This is a linear equation with a positive slope of 2. It represents a line that increases as x increases. The y-intercept is 5.

y = -1/2x + 5: This is a linear equation with a negative slope of -1/2. It represents a line that decreases at a slower rate as x increases. The y-intercept is 5.

y = 1/2x - 5: This is a linear equation with a positive slope of 1/2. It represents a line that increases at a slower rate as x increases. The y-intercept is -5.

Without specific information about the data set, it is not possible to determine which equation is the best fit. The best fit would depend on how well the equation aligns with the actual data points.

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Answer:

I think it's

Step-by-step explanation:

usually involves reading the pattern on the table while keeping in mind that x goes on top and y on

Answer:

Step-by-step explanation:

Profit = 5907.51  - 3663.98 = 2243.53

\(Profit \ percent = \dfrac{Profit}{CP}*100\\\\=\dfrac{2243.53}{3663.98}*100\)

=61.23

= 61%

Answer:

(x + 2)² - 11, so a = 2 and b = 11