Find all angle measures in the diagram.
The measure of ZKJL =
The measure of ZNJM =
The measure of ZMJL=

Using the definition of the derivative, we have:
f'(a) = lim (h -> 0) [(f(a+h) - f(a)) / h]

We're asked to use the definition of the derivative, which includes the terms:

limit, h, f(a+h), f(a), and the fraction f(a+h) - f(a) / h.
The definition of the derivative of a function f(x) at a specific point x=a is given by:
f'(a) = lim (h -> 0) [(f(a+h) - f(a)) / h]
f(a+h) represents the value of the function f(x) at the point (a+h).
f(a) represents the value of the function f(x) at the point a.
f(a+h) - f(a) calculates the difference in the function values at these two points.
h is the small change in the x-coordinate (x-axis) between these two points, and we let h approach 0 to ensure we're finding the instantaneous rate of change.
(f(a+h) - f(a)) / h represents the average rate of change between the points (a, f(a)) and (a+h, f(a+h)).
By taking the limit as h approaches 0, we find the instantaneous rate of change at the point x=a, which is the derivative of the function f(x) at x=a.

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We can start by drawing a diagram of the situation:

The simplified ratio is 3 light bulbs for every 1 chandelier.

It should be noted that to find equivalent ratios, we need to multiply or divide both the numerator and denominator of the ratio by the same number.

In this case, the ratio is 9 light bulbs for every 3 chandeliers, which can be simplified by dividing both the numerator and denominator by 3:

9 light bulbs ÷ 3 = 3 light bulbs

3 chandeliers ÷ 3 = 1 chandelier

So the simplified ratio is 3 light bulbs for every 1 chandelier.

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Stacia needs 9 light bulbs for every 3 chandeliers she makes Complete the table using equivalent ratios.

The bacterial count after 48 hours decreases. A correlation coefficient of 0 would indicate no relationship between the two variables.

To find the correlation between the bacterial count after 24 hours and 48 hours, we would need the actual numerical values of the bacterial counts for each strain. Without that information, we cannot calculate the correlation coefficient. However, it is important to note that a positive correlation would indicate that as the bacterial count after 24 hours increases, the bacterial count after 48 hours also increases. A negative correlation would indicate that as the bacterial count after 24 hours increases, the bacterial count after 48 hours decreases. A correlation coefficient of 0 would indicate no relationship between the two variables.

The complete question is-

Five strains of the Staphylococcus aureus bacteria were grown for 24 hours either at 35 degrees Celsius or at 43 degrees Celsius. Here are the resulting bacterial counts for each condition:

24 hr: 66, 71, 93, 102, 62

48hr: 110,123,146,136,113

If we had plotted bacterial count at 35 degrees Celsius on the y-axis instead of the x-axis, the value of the correlation coefficient would be

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Answer:

DE = √21

x = 10

Step-by-step explanation:

4)

AC is bisected by BX

AC/2 = 8/2 = 4 = AB

BX² + AB² = AX²

3² + 4² = AX²

AX = 5 = radius of the circle

DE² = DX² - EX²

DE² = 5² - 2² = 25 - 4 = 21

DE = √21

6)

x² = (11-5)² + 8² = 36 + 64 = 100

x = √100 = 10

x = 10

Answer:The discount would be 25%.

Step-by-Step explanation:

1.In order for us to find out the discount we need to find how much the original price got cut off.Let’s use 86.88-65.16 the answer would be 21.72.

2.Now for us to find the discount we need to find out what part of a hundred is the discount.Let’s use 86.88/21.72 the answer would be 4.

3.So now we have a fourth of a hundred and a fourth of a hundred would be 25%.

Discount given=25%=21.72

Using the given percentage we can see that the minimum and maximum numbers are:

N-  = 967

N+ = 1,150

The total number of students is 3,650, and we know that the average percentage is 29% ± 2.5%

The minimum value is what we get when we use the minus sign:

29% - 2.5% = 26.5%

The 26.5%  of 3,650 is:

N- = (0.265)* 3,650 = 967

The maximum value is what we get when we use the plus sign:

29% + 2.5% = 31.5%

The 31.5% of  3,650 is:

N+ = (0.315)*3,650 = 1,150

These are the two values.

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The required area of the given parallelogram is 9yd² respectively.

A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry.

A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.

If one of the angles in a parallelogram is a right angle, then all four angles must also be right angles.

A four-sided figure is a trapezoid if it has at least one angle of a different measure in addition to at least one right angle.

So, the formula for the area of a parallelogram is:

A=bh

Now, insert values as follows:
A = bh

A = 9/2 * 2

A = 4.5*2

A = 9yd²

Therefore, the required area of the given parallelogram is 9yd² respectively.

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Answer: 14

Step-by-step explanation:

Answer: x^2 + 17x/2 + 15

Step-by-step explanation:

i promise this is right

Answer: x=0 and x=-9

Step-by-step explanation:

Answer:

Step-by-step explanation:

Average rate of change = (Ending value - Beginning value) / Time elapsed

Using the formula for the average rate of change, we get:

(1824 - 1140) / 1095 = $0.55 per day

(1824 - 1140) / 36 = $19 per month

(1824 - 1140) / 12 = $54 per quarter

(1824 - 1140) / 3 = $228 per year

Therefore, the average rate of change for Tony's investment was $19 per month.

The capacity of 1 thumb drive is 4 gigabytes and the capacity of 1 compact disk is 2 gigabytes.

The first step is to form the system of equations that represent the information in the question:

4x + y = 18 equation 1

4x + 3y = 22 equation 2

The elimination method would be used to determined the required values.

Subtract equation 1 from equation 2

2y = 4

y = 4/2

y = 2

Substitute for y in equation 1: 4x + 2 = 18

4x = 18 - 2

4x = 16

x = 16/4

x = 4

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The expression -20 + 18.5u, when u is 0.6, in a decimal or whole number is equal to -8.9.

To evaluate the expression -20 + 18.5u when u = 0.6, we simply substitute 0.6 in place of u and simplify using the order of operations (PEMDAS).

-20 + 18.5u = -20 + 18.5(0.6) (substitute 0.6 for u)

-20 + 11.1 = -8.9 (simplify using multiplication first and then addition/subtraction)

Therefore, the value of the expression when u = 0.6 is -8.9.

The order of operations is a set of rules that dictate the order in which mathematical operations should be performed to avoid ambiguity and ensure that calculations are carried out correctly. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (performed from left to right), and Addition and Subtraction (also performed from left to right).

In this case, we first multiply 18.5 and 0.6, giving us 11.1. Then, we subtract 20 from 11.1, resulting in -8.9.

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Answer:

1.8

Step-by-step explanation:

5x+3(8-1)=30

5x+24-3=30

5x+21=30

5x=9

x=9/5 or 1 4/5 or 1.8

The area of the polygon containing the given triangle and rectangle is 45 square units.

What exactly is a rectangle?

A rectangle is a quadrilateral having four straight sides, four right angles, and parallel and equal-length opposing sides. A rectangle's opposing sides are also congruent, which implies they have the same length.

The formula A = lw gives the area of a rectangle, where A is the area, l is the length, and w is the width. A rectangle's perimeter is determined by the formula P = 2l + 2w, where P is the perimeter.

Now,

To find the area of the polygon containing the triangle and rectangle, we need to find the individual areas of the triangle and rectangle, and then add them together.

The area of a triangle

A = (1/2)bh

where b= base and h = height. Substituting the given values, we get:

A_triangle = (1/2)(9)(6) = 27 square units

The area of a rectangle is

A = lw

where l = length and w = width. Substituting the given values, we get:

A_rectangle = (9)(2) = 18 square units

Therefore, the total area of the polygon is:

A_polygon = A_triangle + A_rectangle

A_polygon = 27 + 18

A_polygon = 45 square units

Therefore, the area of the polygon containing the given triangle and rectangle is 45 square units.

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Based on the given information, the correct statement is: The area of the rectangle is twice the area of the shaded triangle.

The shaded triangle is a part of the rectangle, as indicated by the given dimensions of 10 in. and 4 in. The shaded triangle is formed by one of the shorter sides of the rectangle and a diagonal line connecting the opposite corner of the rectangle to the midpoint of that shorter side.

Since the area of the rectangle is given by the formula length × width, the area of the rectangle is 10 in. × 4 in. = 40 square inches.

On the other hand, the area of the shaded triangle is given by the formula 1/2 × base × height, where the base is the length of the shorter side of the rectangle (4 in.) and the height is the length of the longer side of the rectangle (10 in.) divided by 2, since the triangle only occupies half of the height of the rectangle.

So, the area of the shaded triangle is 1/2 × 4 in. × (10 in./2) = 1/2 × 4 in. × 5 in. = 10 square inches.

Comparing the area of the rectangle (40 square inches) to the area of the shaded triangle (10 square inches), we can see that the area of the rectangle is indeed twice the area of the shaded triangle. Therefore, the correct statement is "The area of the rectangle is twice the area of the shaded triangle."

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Answer: 1.2

Step-by-step explanation:

0.2 times 6 is 1.2

1/ 3 is the difference in the gierls that have blue eyes and brown eyes

Let's first find the difference in fractions between the number of girls with brown eyes and the number of girls with blue eyes.

Brown eyes: 7/12

Blue eyes: 1/4

To subtract these fractions, we need to find a common denominator, which in this case is 12. So, we'll convert the fractions to have the same denominator:

7/12 - (3/3)*(1/4) = 7/12 - 3/12

Now, subtract the fractions:

(7 - 3)/12 = 4/12

Simplify the fraction:

4/12 = (1/3)*(4/4) = 1/3

So, 1/3 more girls have brown eyes than blue eyes.

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Answer: The sum of the exterior angles of any polygon is 360 degrees.

The measure of one exterior angle of a regular polygon with n sides is given by the formula:

360/n

For a polygon with 26 sides, the measure of one exterior angle is:

360/26 = 13.8 degrees (rounded to one decimal place)

Step-by-step explanation:

The value of cos (2tetha) is 161/289

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

Therefore if tan(tetha) = -8/15, therefore opposite is 8 and adj is 15

hyp = √8²+15²

= √ 64+225

= √ 289

= 17

therefore cos (tetha) = 8/17 and since theta is in second quadrant, cos tetha will be negative

cos (tetha) = -15/17

cos²(tetha) = 225/289

sin(tetha) = 8/17

sin²(tetha) = 64/289

cos(2tetha) = cos²(tetha) -sin²(tetha)

= 225/289 - 64/289

= 161/289

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To find the values of c that make f continuous everywhere, Finally, from the graph above, it looks like the slope of the tangent at x = 2 is around 1.

For x < 15, the function is given by x² - c*x + 9. To ensure continuity at x = 15, we need to find the limit of the function as x approaches 15 from both sides:
lim x→15- (x² - c*x + 9) = 15² - c*15 + 9 = 201 - 15c
lim x→15+ (x² - c*x + 9) = 15² - c*15 + 9 = 201 - 15c

For continuity at x = 15, we need these two limits to be equal, so we set them equal to each other:
201 - 15c = 201 - 15c

Solving for c, we get c = 13.4 (rounded to 3 decimal places).
For x > 15, the function is given by x² - c*x + 9. To ensure continuity at x = 15, we need to find the limit of the function as x approaches 15 from both sides:
lim x→15- (x² - c*x + 9) = 15² - c*15 + 9 = 201 - 15c
lim x→15+ (x² - c*x + 9) = 15² - c*15 + 9 = 201 - 15c

For continuity at x = 15, we need these two limits to be equal, so we set them equal to each other:
201 - 15c ≤ 15 Solving for c, we get c ≥ 12.9 (rounded to 3 decimal places).

Therefore, the values of c that make f continuous everywhere are 13.4 ≤ c ≤ 12.9.
To estimate the value of f'(-2), we can look at the slope of the tangent line at x = -2 on the graph. From the graph, it looks like the slope of the tangent at x = -2 is around -2.5. Rounding to one decimal place, we estimate f'(-2) to be -2.5.

Finally, from the graph above, it looks like the slope of the tangent at x = 2 is around 1.

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Answer:

B

Step-by-step explanation:

Its easy

The areas and the surface areas of the figures are calculated below

The area of a figure is the amount of space it occupies in a plane, measured in square units.

So, we have

Figure 1

For the first figure, we have

Area = (2a)² - 1/2 * b² * sin(B)

Evaluate

Area = 4a² - b²sin(B)/2

For the second figure, we have

Area = 18 * 10 + 1/2 * 10 * √(4 * 15² + 18²) + 1/2 * 18 * √(4 * 15² + 10²)

Evaluate

Area = 639.53 square units

Figure 2

Here, we have

Area = 2 * 2 * 2.5 + 2 * 1/2 * 3 * √(3² - 2.5²) + 3 * 2

Evaluate

Area = 20.97

Figure 3 (Stairs)

Here, we have

Area = 8 * 4 + 8 * 8 + 8 * 4 + 8 * 8 + 2 * 16 * 4 + 2 * 8 * 4

Evaluate

Area = 384

Figure 3 (Semi-circular)

Here, we have

Area = 4 * 4 * 6 + 6 * 6 + 2 * 1/2 * (22/7 * (6/2)²) + 1/2 * 2 * 22/7 * (6/2) × 6

Evaluate

Area = 216.86

Figure 3 (Cylinder-Hemisphere-Cone)

Here, we have

Area = 2 * 22/7 * (10/2) * 12 + 22/7 * (10/2) * √(8² - 5²) + 2 * 22/7 * (10/2)²

Evaluate

Area = 632.42

Figure 3 (Cylinder-Cylinder)

Here, we have

Area = 2 * 22/7 * 8 * (8 + 3) + 2 * 22/7 * 2 * (2 + 7) - 22/7 * 2²

Evaluate

Area = 653.71

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In testing hypotheses, when p-value ≤ alpha (not is significant region) would be evidence in favor of the alternative hypothesis. So, option( a) is right answer.

Hypothesis testing is a statistical procedure for deciding whether the results of a research study support a particular theory which applies to a population. Steps to do hypothesis testing are

Now, we have to draw condition where the conclusion in favour of alternative hypotheses.

Hence, option(a) is right answer for favour alternative hypothesis.

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For a survey to put an estimate the proportion of voters who support gun control, the minimum sample size is 752 that is minimum 752 people need to be included in the sample.

We have a survey which is planned to estimate the proportion of voters who support gun control. Margin of error, MOE = 3% = 0.03

Confidence level = 90% = 0.90

No information about the proportion of the voters that is p,so let's assume, p= 0.5

Level of significance, α = 1 - CI

= 1 - 0.90 = 0.10

We have to determine the sample size of people. Using the following formula for computes minimum sample size required to estimate population proportion within the required margin of error, [tex]n ≥ p( 1-p) (\frac{z_c}{MOE})²[/tex]

where, n --> sample size

[tex]z_c[/tex]--> critical value of z

using the Z-distribution table, the value of z for 90% confidence interval is 1.64.

Substitute all known values in above formula, [tex]n ≥ 0.5( 1- 0.5) (\frac{1.64}{0.03})²[/tex]

= 751.54 ~ 752( people must be a integer no.)

Hence, required minimum sample size is 752.

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Answer: Hi! Read the explanation below:

Brainliest?

Step-by-step explanation:

Let's use the variables x and y to represent the number of bags of soil and plants, respectively, that Katte will buy.

The cost of x bags of soil is $4x, and the cost of y plants is $10y. Therefore, the total cost of Katte's purchases is:

$4x + $10y

We want to make sure that she doesn't spend more than $100, so we can write:

$4x + $10y ≤ $100

We also want to make sure that she buys at least 5 plants, so we can write:

y ≥ 5

Finally, we want to make sure that both x and y are non-negative, since you can't buy negative bags of soil or plants. Therefore, we can write:

x ≥ 0

y ≥ 0

Putting it all together, the system of linear inequalities is:

4x + 10y ≤ 100

y ≥ 5

x ≥ 0

y ≥ 0

To graph this system, we can start by graphing the boundary lines for each inequality. The boundary for 4x + 10y ≤ 100 is the line 4x + 10y = 100, which we can graph by finding two points on the line:

When x = 0, we have 10y = 100, so y = 10. Therefore, one point on the line is (0, 10).

When y = 0, we have 4x = 100, so x = 25. Therefore, another point on the line is (25, 0).

Plotting these two points and connecting them with a line gives us the boundary for 4x + 10y ≤ 100:

       |

   11  |      o

       |

   10  |           o

       |

    9  |              o

       |

    8  |                 o

       |

    7  |                    o

       |

    6  |                       o

       |

    5  |                          o

       |

--------|-----------------------------    

       0    25

The boundary for y ≥ 5 is the horizontal line y = 5. We can graph this line by plotting two points on the line:

When x = 0, we have y = 5, so one point on the line is (0, 5).

When x = 100/4 = 25, we still have y = 5, so another point on the line is (25, 5).

Plotting these two points and connecting them with a line gives us the boundary for y ≥ 5:

lua

       |

       |    

       |

       |    

       |

       |    

    5  |-----------------------

       |

       |

       |

       |

       |

--------|-----------------------------    

       0    25

Finally, the boundaries x ≥ 0 and y ≥ 0 are simply the x and y axes, respectively. We can graph them as:

diff

       |

       |    

       |

       |    

       |

       |    

       |

       |

       |

--------|-----------------------------    

       0    25

Putting it all together, the graph of the system of linear inequalities looks like:

       |

   11  |      o

       |

   10  |           o

       |

    9  |              o

       |

    8  |                 o

       |

    7  |                    o

       |

    6  |                       o

       |

    5  | o----------------------

       |

       |    

       |

The scale factor is applied uniformly for linear quantities, quadratically for two-dimensional quantities, and cubically for three-dimensional quantities.

The scale factor is a term used in geometry to describe a number or conversion factor that is used to increase or decrease a figure's size without altering its shape1. It is used to increase or decrease the size of an object1. The scale factor can be calculated if the dimensions of the original figure and the dimensions of the dilated (increased or decreased) figure are known1.

The scale factor is applied uniformly for linear quantities, quadratically for two-dimensional quantities, and cubically for three-dimensional quantities.

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a) The appropriate hypothesis testing are states as [tex]H_0 : p = 0.50[/tex]

[tex]H_a : p > 0. 50 [/tex]

b) The p-value for z-test is equals to the 0.000. Also, p-value < α.

c) Conclusion: Null hypothesis is rejected and there is evidence to support that more than 50% do not belief that such software unfairly targets students.

We have a sample of at an australian university that introduced the use of plagiarism-detection software.

Sample size = 178

Number of students who belief that such software unfairly targets student = 53

a) Null and alternative hypothesis are stated here as for right tailed t test.

[tex]H_0 : p = 0.05 [/tex]

[tex]H_a : p > 0.05[/tex]

sample proportion for students who does not belief that such software unfairly targets student [tex]\hat p = \frac {178- 53 }{178} [/tex] = 0.71

Now, test-statistic : [tex]t = \frac { \hat p - p} {\sqrt{ \frac{ p( 1- p)}{n}}}[/tex]

Substitute all the known values in above formula, [tex]= \frac {0.71 - 0.05} {\sqrt{ \frac{ 0.05( 1- 0.05)}{178}}}[/tex]

=> t = 41.25

b) Now, using Excel, the p-value for z

= 41.25 is 0.000. So, p-value < 0.05

Therefore, the Null hypothesis is rejected here.

c) Conclusion: there is evidence to support the claim that more than 50% do not belief that such software unfairly targets students.

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Complete question:

in a sample of 178 students at an australian university that introduced the use of plagiarism-detection software in a number of courses, 53 students indicated a belief that such software unfairly targets students. does this suggest that a majority of students at the university do not share this belief? test appropriate hypotheses at level 0.05.

a) State appropriate hypothesis

b) find p-value

c) draw conclusion