draw in all lines of symmetry of the blue square

The sample upper quartile of the data set is 91 and the lower quartile is 67 for the students of the given examination.

The median and quartiles of a data set:

The data set's median, or 50th percentile, separates the bottom half from the higher half.

The first quartile is the median of the data set's first half.

The third quartile is the median of the data set's second half.

Because there are an even number of items 60, the median is the mean of the31st element elements, with the first half consisting of 30 elements ranging from 1 to 29, and the second half consisting of 12 elements ranging from 31 to  60.

The first quartile is the mean of the elements, 67 and 68, respectively, therefore Q1 = 60/4 =15th element =  67

The third quartile is defined as the mean of the sixth and seventh elements of the second half, hence Q3 = 3×60 / 4 = 91.

Hence the quartiles are at 67 and 91 respectively.

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The derivative of the function [tex]y = 5^x + e^7[/tex] with respect to 'x'

is  [tex]\frac{dy}{dx} = 5^xln5 + 0[/tex].

Differentiation, in mathematics, process of finding the derivative, or rate of change, of a function also known as the slope.

We know, [tex]\frac{dy}{dx} a^x = a^xlna[/tex], where 'a' is a constant.

Given, [tex]y = 5^x + e^7[/tex].

Now, The derivative of the function with respect to 'x' is,

[tex]\frac{dy}{dx} = 5^xln5 + 0[/tex], As [tex]e^7[/tex] is a constant, and the derivative of any constant term is zero because the slope of a constant term is zero.

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The correlation coefficient of r measures how closely the two variables, x and y, are related. If the coefficient is close to 1, it means that the two variables are strongly related, whereas if it is close to 0, it means that there is no relation between them.

The correlation coefficient of r is a measure of how closely related two variables are to each other. It is calculated by taking the covariance of the two variables and dividing it by the product of their standard deviations. The coefficient ranges from -1 to +1, with -1 indicating a perfectly negative linear relationship, 0 indicating no relationship, and +1 indicating a perfectly positive linear relationship. In the case of the sales manager analyzing the sales of snow shovels compared to the outside temperature, the correlation coefficient of r can be used to measure the strength of the relationship between the two variables. If the coefficient is close to 1, it indicates that the two variables are strongly related, while a coefficient close to 0 indicates that there is no relation between them.

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Answer: 48

Step-by-step explanation: Use this to help you!

at least 24 people must be in the party to guarantee that at least 3 people have the same date of birth, date of birth, date of birth.

To warrant that at least three people have the same date, month, and year of birth, we need to find the minimum number of people such that there is a probability that at least three people have the same date, month, and year. there is. Birth year she is 1 or more. Non-leap years have 365 days, and leap years have her 366 days. The birth year range includes two leap years, so there are 3652 + 3662 = 2,922 possible births. This means that the probability that a particular person's birthday is unique is (2922-1)÷2922 = 1÷2922.

Now we can use the birthday puzzle to calculate the probability that at least three people have the same birthday. The probability that no one has the same birthday is (1 - 1÷2922)^n, where n is the number of people in your party. At least he has 1-(1-1÷2922)^n probability that 3 of them have the same birthday. You can set this probability to 1 or more and solve for n.

1 - (1 - 1÷2922)^n >= 1

(1 - 1÷2922)^n <= 0

n >= log(0) ÷ log(1 - 1÷2922)

The logarithm of 0 is not defined, so you can use a small value on the right hand side instead. B. 10^-6. This will tell you:

n >= log(10^-6) ÷ log(1 - 1/2922)

n >= log(10^-6) ÷ log(2921/2922)

n >= log(10^-6) ÷ log(2921) - log(10^-6) / log(2922)

n >= log(10^-6) × log(2922) ÷ log(2921) - log(10^-6)

n >= log(10^-6) × log(2922) ÷ log(2921) - log(10^-6)

n >= 23.

Hence, at least 24 people must be in the party to guarantee that at least 3 people have the same date of birth, date of birth, date of birth.

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the tension in each wire will be equal. The tension in each wire, T ,the tension in each wire is 85.36 N with its weight.

Assuming that the tool has negligible mass so that its weight does not contribute to the tension in the wires, the tension in each wire will be equal. The tension in each wire, T, can be calculated using the equation:

T = (W/2) + (L/2)*sin(θ),

where W is the weight of the shelf and L is the length of the shelf. The angle θ is the angle between the ceiling and the shelf.

In this case, W = 50 N, L = 50 cm and θ = 45°. Therefore, T = (50/2) + (50/2)*sin(45) = 50 + 35.36 = 85.36 N.

So, the tension in each wire is 85.36 N.

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The vertex and the range of y = |2x + 6| + 2 are (c) (-3, 2); 2 ≤ y < ∞

The equation is given as

y = |2x + 6| + 2

The above equation is an absolute value function

An absolute value function represented as

y = a|x - h| + k

Where

Vertex = (h, k)

So, we have

y = |2x + 6| + 2

This gives

y = 2|x + 3| + 2

This means that the vertex is

Vertex = (-3, 2)

Remove the x value

y = 2

Because the leading coefficient is positive, then the vertex is a minimum

i.e.

y ≥ 2

So, the range is 2 ≤ y < ∞

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Answer:

Step-by-step explanation:

the figure is a parallelogram, therefore the sum of angle A and angle B is 180°, we solve with an equation

180 = 5x + 5 + 4x - 5

180 = 9x

x = 180 : 9

x = 20

------------------------

check

180 = 5x + 5 + 4x - 5

180 = 5 × 20 + 5 + 4 × 20 - 5  (remember PEMDAS)

180 = 180

the answer is good

Answer:

The angle x is equal to 20 degrees

Answer:

$70

Step-by-step explanation:

x = 200 - 10 · 13

x = 200 - 130

x = 70

According to the facts provided in the question and we know that the derivative of the function f(x) is f'(x) which refers to the slope at the point. The answer is f(x) is always increasing.

The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. Calculus's core tool is the derivative. The rate at which a function changes in relation to a variable Calculus and differential equations issues must be solved using derivatives.

A line's steepness can be determined by looking at its slope. The ratio of the change in the y-value to the change in the x-value can also be used to determine slope.

f(x) is the function.

f'(x) is the derivative of the function.

f'(x) is always positive which explains that the line has positive slope that is moving upwards in graph.

So, f(x) is always increasing.

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Marcus' overtime pay for the week is $67.50.

The overtime pay is paid at the hourly rate and a half.

This translates to the regular rate of pay x 1.5 x overtime hours worked.

The total hours worked this week = 45 hours

Normal working hours per week = 40 hours (5  days x 8 hours)

Overtime hours = 5 hours (45 - 40)

Hourly rate = $9.00

Overtime rate = $13.50 ($9 x 1.5)

Overtime pay = $67.50 ($13.50 x 5)

Thus, for this week, Marcus has earned overtime pay of $67.50 above his normal weekly pay of $360.

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Answer:

75%

Step-by-step explanation:

42/56 * 100% = 0.75 * 100

= 75%

Answer:

point-slope form: [tex]y+5=-\frac{1}{10}(x-5)[/tex]

slope-intercept form: [tex]y = -\frac{1}{10}x - \frac{9}{2}[/tex]

Step-by-step explanation:

We can express any one-variable linear equation as: [tex]y-y_1=m(x-x_1)[/tex], where "m" is the slope, and [tex](x_1, y_1)[/tex] is some point on the graph.

We're given the equation in point-slope form: [tex]y-1=-\frac{1}{10}(x+8)[/tex], and if we want to make a line parallel to this line, we just need the slopes to be the same. So let's just look at the value in front of the parenthesis. This is given to be: [tex]-\frac{1}{10}[/tex]

We can use this same form, to develop an equation parallel to the given line, and passing through: [tex](-5, 5)[/tex]

Plugging the values into the point-slope formula, we get:
[tex]y-(-5)=-\frac{1}{10}(x-5)\\\\y+5=-\frac{1}{10}(x-5)[/tex]

From here we can also convert this into slope-intercept form, where "y" is isolated.

[tex]\\y+5=-\frac{1}{10}(x-5)\\\\y+5=-\frac{1}{10}x + \frac{5}{10}\\\\y + \frac{10}{2} = -\frac{1}{10}x + \frac{1}{2}\\\\y + \frac{10}{2} - \frac{10}{2} = -\frac{1}{10}x + \frac{1}{2} - \frac{10}{2}\\\\y = -\frac{1}{10}x - \frac{9}{2}[/tex]

Answer:

Step-by-step explanation:

23

Answer:$2400 invested at $9% $3000 invested at $11%

Step-by-step explanation:

The measure of angle B is 121°

The correct option is B) 121° doing the Nae Nae

"Information available from the question"

In the question:

In ΔA B C, if m ∠C is nine less than m ∠A and m ∠B is fifteen less than four times m ∠A,

To find the measure of ∠B.

Now, According to the question:

We know that:

The sum of the measures of the angles of a triangle are 180

m<A + m<B + m<C = 180°

m<C = m<A - 9

m<B = 4*m<A - 15

m<A + 4*m<A - 15 +  m<A - 9 = 180°

6m<A - 24 =  180°

6m<A = 204

m<A = 34°

Now, To find the measure of ∠B

m<B = 4*m<A - 15

m<B = 4* 34 - 15

m<B = 121°

The correct option is B) 121° doing the Nae Nae

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Answer:

√3√ab

Step-by-step explanation:

Please look in the attachment! Hope this helps! :D

D flip flop stands for a delay flip flop that produces output that is identical to input after a brief delay. The flip flop's input and next state are equal.

Z is an output, and x and x inputs.

x'y + xA = DA= A*

B* = x'B + xA

z=A (output is independent of input) (output is independent of input)

The next states are A(t+1) and B(t+1). We must provide the next state value to D of the D flip flop in order to obtain the next states A(t+1), and B(t+1) for A, B(present state). So the sequential circuit will be:

To get the next state as A(t+1)= x’A + xA, B(t+1)= x’B + xA, we have to give them to DA, DB of D flip flop because for D flip flop whatever is given to DA, DB will appear at output A, B.

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Answer:

---------------------------

Let the number of total parts be x.

12% of x were defective and it is 48 in number.

Find x:

Correct choice is A.

1716 is the probability that a sophomore, the second is a freshman, and the third is a sophomore.

What is probability explained with an example?

A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty. The likelihood that an event will occur increases with its probability.

                        The flip of a fair (impartial) coin serves as a straightforward illustration. The probability of an event occurring, or P(E), is defined as the ratio of the number of favorable outcomes to the total number of outcomes in the probability formula.

The total number of ways in which 3 students can be arranged for speech out of total 13 students is,

       P(13,3) = 13 * 12 * 11

                 = 1716

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Answer: The answer should be 31.42 in

The equation for a parabola with x-intercept is y = 4/3x² + 8/3x - 20.

What is equation?

In arithmetic, an equation could be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.

Main body:

The equation has the form y = Ax² + Bx + C

Since (3,0), (-1,0), (1,-16) are points on the graph, we get the following system of equations:

9A + 3B + C = 0

A - B + C = 0

A + B + C = -16

Subtracting the first 2 equations and subtracting the 3rd equation from the first, we obtain:

8A - 4B = 0

8A + 2B = 16

Since 8A - 4B = 0, 8A = 4B.  So, A = 1/2B.

Therefore, 8A + 2B = 16

6B = 16  So , B = 8/3  and A = 8/6

Since A + B + C = -16 and A = 8/6 , B = 8/3, we have 4 + C = -16.  So, C = -20.

An equation of the parabola is y = 4/3x² + 8/3x - 20

Hence , the equation for a parabola with x-intercept is y = 4/3x² + 8/3x - 20.

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Based on the graph of the function g(x) = −2x − 8, the x-intercept is equal to -4.

In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively.

In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" is equal to zero (0).

By critically observing the graph of g(x) = −2x − 8, the x-intercept is -4. This ultimately implies that, the function g(x) = −2x − 8 would cross the x-coordinate (x-axis) at point (-4, 0.

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The total weight of the 4 boxes was -  18.382 pounds.

A company shipped 3 boxes which each weighed 3.894 pounds.

As per the rule, we shall have to multiply the weight of the boxes of similar weight into 3 followed by the addition of the weight of the other box.

Then, we can get the final answer.

one box weighed  = 3.894 pounds

Three boxes weighed  = 3 * 3.894 pounds

                                       = 11.682 pounds

Another box weighed  = 6.7 pounds

The total weight of the 4 boxes was = ( 11.682 + 6.7 ) pounds

                                                             = 18.382 pounds

Hence, The total weight of the 4 boxes was -  18.382 pounds.

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Answer:

Step-by-step explanation:

you times 13 times 45 degrees and that equals to 585

Answer:

4 days

Step-by-step explanation:

If Rachel has 7/15 of her project done, then she has 8/15 of her project left to complete.

Convert 8/15 and let it have a denominator of 45, and you get 24/45. If she can finish the rest of her project 7/45 each day, and she has 24/45 left to go, then divide 24 by 7, and you get 3 R3.

Afterwards round that to 4, because Rachel can't leave 3/45 of her project unfinished, she just doesn't have as much work the last day.

So then Rachel can finish her project in 4 days.

Hope this helps!

Answer:

4 days

Step-by-step explanation:

7/15 done ...then 8/15 to go

8/15 = 24 / 45      if she can do 7/45 per day, she will need 4 more days

(24/7) = 3.4 =~ 4 days

The probability that there are two such couples given that there is at least one is 1 - (4999999/12000000) = 4/12 = 1/3.

Probability is the measure of the likelihood that a given event will occur. It is expressed as a number between 0 and 1 (or 0% to 100%). A probability of 1 indicates that the event is certain to occur, while a probability of 0 indicates that it is impossible for the event to occur. Probability is used in a wide range of disciplines including mathematics, science, engineering, finance, and philosophy. Probability can be used to make predictions and help inform decision-making. By understanding probability, we can better understand the chances of certain outcomes and make more informed decisions.

This is because the probability that the first couple matches the description is 1/12000000, and the probability that the second couple matches the description, given that the first couple does, is 1/(12000000-1). Since there are 4999999 other couples, the probability that the second couple matches the description is (4999999/12000000). Thus, the probability that there are two such couples is 1 minus the probability that the second couple does not match the description, which is 1 - (4999999/12000000) = 4/12 = 1/3.

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