The question is present in the image

The value of x in the given arrangement of equilateral triangle and isosceles triangle is 88°

An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.

Given that,

A arrangement which contains,

one equilateral triangle ABE &

one isosceles triangle CDE

It is known that sum of all the angles in each direction is 180°.

ΔAEB is equilateral triangle,

so angle will be of 60°

∠AEB = 60°

And in isosceles triangle,

∠EDC = ∠ECD

∠ADC = 90°

∠ADC = ∠ADE + ∠EDC

90°  =  62°  + ∠EDC

∠EDC  = 28°  = ∠ECD

It is known that sum of all the interior angles of the triangle is 180°.

∠EDC  + ∠ECD + ∠DEC   = 180°

28° + 28° + ∠DEC   = 180°

∠DEC   = 124°

Now sum of all the angles around point E is 360°

∠AED + ∠DEC + ∠BEC + ∠AEB  = 360°

x   +  124°  + x  + 60°  = 360°

2x  = 176°

x = 88°

Hence, the value of x is 88°

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The table that can be constructed with the following equation has vales x: 0, 1, 2, 3 and y = 0, 8, 16, 24.

When the greatest power of the variable is consistently 1, an equation is considered to be linear. A one-degree equation is another name for it. The typical form of a linear equation with one variable is Ax + B = 0.

The slope of the linear relationship is eight. The solution is below, along with a picture of the line.

Substitute different values of x to obtain value of y:

The table is given below:-

x  I  y

-------

0  I  0

1  I  8

2  I 16

3  I 24

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The complete question is:

Answer: B. 50

Step-by-step explanation:

  To solve this, we will isolate the variable b.

   Given:

[tex]\frac{1}{5}[/tex]b + 4 = 14

   Subtract four from both sides of the equation:

[tex]\frac{1}{5}[/tex]b = 10

   Multiply both sides of the equation by 5:

b = 50

        B. 50

Answer:whoops it’s b

Answer:

Its A I think

Step-by-step explanation:

On solving the provided question we can say that value equation is

y = mx => -7 = m * 4 => m = -7/4 and x² + y² = 13 => x² + (-7)² = 13 => x

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence.

here, we have,

Squaring both sides and simplifying we get:

3m² + 56m + 36 = 0

The coordinates of the points A and B are (-12,103) and (-3,-89) respectively.

y = mx => -7 = m * 4 => m = -7/4

x² + y² = 13 => x² + (-7)² = 13 => x

So the equation of the tangent line is y = m(x - 0) + 0,

where m = -(x+4)/(y-7)

Now we can substitute the coordinates of the center of the circle into the equation of the tangent line to get y = -(x+4)/(y-7) * x

Squaring both sides and simplifying we get:

3m² + 56m + 36 = 0

b) To find the coordinates of the points A and B, we can use the equation of the tangent line and the equation of the circle.

We know that the equation of the tangent line is y = -(x+4)/(y-7) * x and the equation of the circle is (x+4)² + (y-7)² = 13.

We can substitute y = -(x+4)/(y-7) * x into the equation of the circle and solve for x.

This equation simplifies to 3x² + 56x + 36 = 0, which factors to

(x+12)(x+3) = 0

y = -(-12+4)/(y-7) * -12 = 8/(y-7) * 12 = 96/(y-7)

y = 96 + 7 = 103 and y = -96 + 7 = -89

The coordinates of the points A and B are (-12,103) and (-3,-89) respectively.

We know that the equation of the tangent line is y = mx and the equation of the circle is x² + y² = 13.

We can substitute the point (4, -7) for x and y in the equation of the tangent line and the equation of the circle and solve for m and x,y respectively.

y = mx => -7 = m * 4 => m = -7/4

x² + y² = 13 => x² + (-7)² = 13 => x

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Answer:

x = 8

Step-by-step explanation:

[tex]15 + x = 23[/tex]

[tex]x = 23 - 15[/tex]

∴[tex]x = 8[/tex]

This is happening because the standard deviation of the scores is 12.

Standard deviation is a measure of how spread out a set of data is. It is a measure of how far each data point is from the mean of the data set. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean. Standard deviation is an important concept in statistics and is used to measure the variability of a data set. It is used to assess the risk associated with investments, as well as to determine the accuracy of an estimate.

(a) Approximately 68% of the students scored between blank and blank.
39 and 63
(b) Approximately 95% of the students scored between blank and blank.
27 and 75

This is happening because the standard deviation of the scores is 12. When the scores are normally distributed, roughly 68% of them will fall within 1 standard deviation of the mean, which is between 39 and 63. Similarly, 95% of the scores will fall within 2 standard deviations of the mean, which is between 27 and 75.

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The new total after the 13% discount has been applied to a bill of £39 is £33.93.

percentage, a relative value indicating hundredth parts of any quantity.

To calculate the new total after the discount, we need to first find the amount of discount applied to the original bill.

We can do this by multiplying the original bill by the discount rate (as a decimal):

Discount = 0.13 * £39 = £5.07

Therefore, the amount of the discount is £5.07.

To find the new total, we need to subtract the discount from the original bill:

New total = £39 - £5.07 = £33.93

Therefore, the new total after the 13% discount has been applied to a bill of £39 is £33.93.

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The correct sample space is given in option C.

What exactly is a sample space?

In probability theory, a sample space is the set of all possible outcomes or results of an experiment or random phenomenon. It is denoted by the symbol "S". For example, when rolling a fair six-sided die, the sample space would be {1, 2, 3, 4, 5, 6} because those are the only possible outcomes. The sample space can be finite, countably infinite, or uncountably infinite, depending on the experiment being considered. The concept of a sample space is fundamental to probability theory, as all probabilities of events are defined in terms of the sample space.

Now,

To determine the sample space for spinning the spinner two times, we need to consider all possible outcomes for each spin and then combine them.

For one spin of the spinner, there are three possible outcomes: blue, orange, and red.

For two spins of the spinner, we need to consider all possible combinations of outcomes from the first and second spin. This can be done by creating a table

            1st spin      2nd spin

1       blue                  blue

2       blue                  orange

3            blue                  red

4       orange               blue

5       orange          orange

6      orange           red

7      red                   blue

8      red                   orange

9      red                   red

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Answer:

7 minutes

Step-by-step explanation:

It is 7 minutes because the bank it the top straight line and it elapses for 7 minutes

Im not fully sure but it might be the 3rd one!

Answer:521.32

Step-by-step explanation:

.3 represents your tenths

the 2 in .32 represents your hundredths

to round, you look at the number next to your two on the right which is 1

since 1 is less than 5 you leave it the same and eliminate the rest of the numbers that follow it

The answer of the given question based on the addition of

((( 56)x)78)9)24 the answer is the  943488.

A expression is  combination of numbers, variables, and mathematical operations like addition, subtraction, multiplication, and division. It is  as simple as single number, variable or  combination of them, or it can be complex combination of various terms connected by mathematical operators. Expressions are used to represent the mathematical relationships, formulas, and calculations

To add the expression (((56)x)78)9)24, you would need to simplify it using the order of operations (PEMDAS):

First, simplify the innermost parentheses:

The expression (56)x evaluates to 56 times x.

The expression 78 with the result of (56)x in parentheses evaluates to 78 times the result of (56)x, or 78(56x).

The expression 9 with the result of the previous step in parentheses evaluates to 9 times the result of the previous step, or 9(78(56x)).

The expression 24 with the result of the previous step in parentheses evaluates to 24 times the result of the previous step, or 24(9(78(56x))).

Next, multiply from left to right to simplify further:

78 times 56 is 4368.

9 times 4368 is 39312.

24 times 39312 is 943488.

Therefore, the simplified value of the expression (((56)x)78)9)24 is 943488.

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Answer:

Class A: 87, 93, 96, 88, 92, 90, 100, 93, 91, 96

Mean: 92.6

Median: 92.5

Mode: 93 and 96

Class B: 72, 69, 54, 66, 63, 74, 59, 64, 70, 68

Mean: 65.9

Median: 67

Mode: No mode or 0

Step-by-step explanation:

You're welcome.

For the differential equation y = [(x² - 1) sin x] / (sin x + 1), the derivative is   dy/dx = [(x² + 2x) sin² x] / (sin x + 1)².

What is differential equation?

Any equation with one or more terms and one or more derivatives of the dependent variable with respect to the independent variable is referred to as a differential equation.

To find dy/dx, we need to use the quotient rule of differentiation, which states that -

d/dx [f(x)/g(x)] = [g(x) × f'(x) - f(x) × g'(x)] / [g(x)]²

Applying this rule to the given function, we get -

y = [(x² - 1) sin x] / (sin x + 1)

y' = [(sin x + 1) d/dx[(x² - 1) sin x] - (x² - 1) sin x d/dx[sin x + 1]] / (sin x + 1)²

Now we need to find the derivatives of the two terms in the numerator separately -

d/dx[(x² - 1) sin x] = (2x sin x + (x² - 1) cos x) sin x

d/dx[sin x + 1] = cos x

Substituting these values in the formula for y', we get -

y' = [(sin x + 1) * (2x sin x + (x² - 1) cos x) - (x² - 1) sin x * cos x] / (sin x + 1)^2

Simplifying this expression, we get -

y' = [(x² + 1) sin² x + 2x sin x cos x - (x² - 1) sin x cos x - (x² - 1) sin x cos x] / (sin x + 1)²

y' = [(x² + 2x) sin² x] / (sin x + 1)²

Therefore, the derivative of y with respect to x (dy/dx) is -

dy/dx = [(x² + 2x) sin² x] / (sin x + 1)²

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Answer:

x^2 - 9 = 0

Step-by-step explanation:

its right one.......

The expression of the length of the arc is  4πb⁵

The circle has a radius of 9b³. An arc subtend an angle at the centre of 80b² degrees. Therefore, the expression for the length of the arc can be solved as follows:

length of arc = ∅ / 360 × 2πr

where

Therefore,

length of arc = 80b² / 360 × 2 × π × 9b³

length of arc = 144b⁵π / 36

Therefore,

length of arc = 4πb⁵

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Answer:

To determine whether the shaded triangle is a right triangle, we need to use the fact that the three right triangles together form a rectangle.

Let's label some of the dimensions as shown in the diagram:

[asy]

unitsize(0.25cm);

pair A = (0,0), B = (10,0), C = (8,6), D = (6,0), E = (8,0), F = (10,6), G = (8,2);

draw(A--B--F--C--cycle);

draw(D--E);

draw(C--G);

label("$10$", (A+B)/2, S);

label("$6$", (C+F)/2, N);

label("$8$", (B+E)/2, E);

label("$2$", (C+G)/2, E);

label("?", (D+G)/2, NE);

label("$?$", (G+E)/2, S);

fill(C--G--D--cycle, gray(0.7));

[/asy]

The dimensions of the rectangle are 12 units by 14 units, so we know that:

\begin{align*}

10 + 8 &= 18 \\

6 + 2 + ? &= 14

\end{align*}

Simplifying the first equation, we get $8 = 14 - 6$. Substituting this into the second equation, we get:

$$2 + ? = 8$$

Therefore, the length of the shaded side of the triangle is 6 units. Now we can use the Pythagorean theorem to determine whether the shaded triangle is a right triangle. Letting $x$ be the length of the other leg of the shaded triangle, we have:

\begin{align*}

x^2 + 6^2 &= 8^2 \\

x^2 + 36 &= 64 \\

x^2 &= 28 \\

x &= 2\sqrt{7}

\end{align*}

Since $2\sqrt{7}$ is not an integer, we can conclude that the shaded triangle is not a right triangle.

2 quart of blue paint and 5/4 quart of red paint is needed to make 3 1/4 quart purple paint

An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.

2/5 quart of blue paint is mixed with 1/4 quart of red paint to make purple paint. Hence:

Ratio of blue paint to red paint = (2/5) : (1/4) = 8 : 5

Therefore for 3 1/4 quart of purple paint:

Amount of blue paint = (8/13) * 3 1/4 = (8/13) * 13/4 = 2 quart

Amount of red paint = (5/13) * 3 1/4 = (5/13) * 13/4 = 5/4 quart

2 quart of blue paint and 5/4 quart of red paint is needed to make the purple paint

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Answer:

Step-by-step explanation:

To convert a degree of likelihood to a probability value, we use the formula:

probability = number of favorable outcomes / total number of possible outcomes

In this case, the chances of encountering a car crash on the road are stated as "5 in 17", which means there are 5 favorable outcomes (encountering a car crash) out of 17 possible outcomes (driving on the road).

So, the probability of encountering a car crash can be calculated as:

probability = 5/17

This fraction can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 1 in this case. Therefore, the probability of encountering a car crash on the road is:

probability = 5/17 ≈ 0.2941

Since the probability value is between 0 and 1 inclusive, we can express the indicated degree of likelihood as a probability value of approximately 0.2941.

Disjunctive Syllogism is the logical form of the given argument. Therefore, the correct option is option A.

An argument seems to be a statement or set of claims, known as premises, that seeks to assess the plausibility or acceptance of a conclusion. The logical, dialectical, and rhetorical perspectives are the three basic areas of study for arguments.

An argument in logic can be defined as a collection of propositions whereby a single one is tried to claim to follow the rest through deductively obtain reasonable that maintain truth from either the premises towards the conclusion. Disjunctive Syllogism is the logical form of the given argument.

Therefore, the correct option is option A.

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We are 95% confident that the true mean hearing loss of senior citizens is between 3.5249 and 4.8751

A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. The 95% confidence level is the most usual, but other levels, such 90% or 99%, are occasionally used to generate a confidence range.

How to calculate:

From the given data:

n= 30

x = 4.2

s = 1.808

d.f = n-1 = 30-1 = 29

At 95% confidence interval:

t[tex]\alpha /2[/tex] = 2.0452

The 95% C.I for the mean is:

x ± t[tex]\alpha /2[/tex]

= 4.2 ± 2.045 [tex]\frac{1.808}{\sqrt{30} }[/tex]

= 4.2 ± 0.6751

( 3.5249, 4.8751)

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Therefore , the solution of the given problem of graph comes out to be the graph is a symmetric wave that oscillates between 5 and 5.

Mathematicians use graphs to logically chart or illustrate claims rather than values in an interesting visual way. Usually, a graph point shows the connection between two or more objects. A graph is a particular kind of non-linear railway assembly composed of nodes and lines. The nodes, also known as the borders, should be joined together with glue. The node numbers in this network included 1, 2, 3, and 5, while the edge numbers included 1, 2, 3, and 4, along with (2.5), (3.5), (4.5), but also (4.5). (4.5).

Here,

Plotting a few important spots will help us later when we sketch the graph of f(t) = 5 cos(t).

Since the function has a phase of 2, we can concentrate on the range from 3/2 to 3/2. We possess

=> f(−3/2) = 5 cos(−3/2) ≈ 4.515

=> f(−π) = 5 cos(−π) = −5

=> f(−1/2) = 5 cos(−1/2) ≈ 4.045

=> f(0) = 5 cos(0) = 5

=> f(1/2) = 5 cos(1/2) ≈ 4.045

=> f(π) = 5 cos(π) = −5

=> f(3/2) = 5 cos(3/2) ≈ 4.515

Using these coordinates, we can create the following f(t) graph:

With maximum positions at t = /2 and t = /2, and minimum points at t = 3/2, t = 1/2, t = 1/2, and t = 3/2,

the graph is a symmetric wave that oscillates between 5 and 5.

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Answer:

length of rectangular prism: 9 feet

width of rectangular prism: 9 feet

Step-by-step explanation:

volume= length x width x height

567/7=81

Since 81 cubic feet squared is the area of the base; the square bottom, you will need to find the square root of 81 which is 9 since 9 times 9 equals 81.

Answer:

300

Step-by-step explanation:

because you do it for 1 hundred years you multiply it by 100 and it would be 3x100=300

Answer:42

Step-by-step explanation: 42x0=42

Answer:

It seems like there is a mistake in the variable provided. The variable mentioned is "Gender" but the data provided is about "Age" and "f" (frequency). Assuming that "f" is the frequency of participants at each age, here are the answers to your questions:

For the variable "f", the most appropriate measure of central tendency would be the mode, which represents the most frequently occurring value. For the variable "Age", the most appropriate measure of central tendency would be the median, as it is less affected by outliers than the mean.

Mode = 8; Median = 11; Mean = 10.11 (rounded to two decimal places)

Range = 15 - 7 = 8; Variance = 8.99 (rounded to two decimal places); Standard deviation = 2.99 (rounded to two decimal places)

To calculate the age range that reflects 68% of the sample, we need to find the mean age and the standard deviation. The mean age is 10.11, and the standard deviation is 2.99. 68% of the data falls within one standard deviation of the mean. Using the empirical rule, we can say that the ages of participants that reflect 68% of the sample are between (10.11 - 2.99) and (10.11 + 2.99), which is between 7.12 and 13.10.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Since the variable Gender is not given in the data, we cannot compute any measure of central tendency for it. For the variable Age, the most appropriate measure of central tendency would be the mode, since all the observations have the same value for this variable.

To calculate the mode, median and mean for Age, we can first arrange the data in ascending order of age:

7, 2

8, 2

9, 0

10, 1

11, 1

12, 1

13, 1

14, 1

15, 1

The mode is the most frequently occurring value, which is 1 for all ages. The median is the middle value when the data is arranged in ascending order. Since there are 9 observations, the median is the average of the 5th and 6th values, which are 12 and 13. So, the median is (12+13)/2 = 12.5. The mean is the sum of all the values divided by the number of observations, which is:

(72 + 82 + 90 + 101 + 111 + 121 + 131 + 141 + 15*1) / 9 = 11.44 (rounded to two decimal places)

Therefore, the mode is 1, the median is 12.5 and the mean is 11.44.

To calculate the range, variance and standard deviation for Age, we can use the following formulas (assuming the data is a population):

Range = maximum value - minimum value = 15 - 7 = 8

Mean = 11.44 (computed in step 2)

Variance = Σ(x - μ)^2 / N, where μ is the mean, x is each value, and N is the number of observations. Plugging in the values, we get:

Variance = [(7-11.44)^2 + (8-11.44)^2 + (9-11.44)^2 + (10-11.44)^2 + (11-11.44)^2 + (12-11.44)^2 + (13-11.44)^2 + (14-11.44)^2 + (15-11.44)^2] / 9 = 5.72 (rounded to two decimal places)

Standard deviation = square root of variance = √5.72 = 2.39 (rounded to two decimal places)

Therefore, the range is 8, the variance is 5.72, and the standard deviation is 2.39.

Since the data is approximately normally distributed, we can use the empirical rule to estimate the ages that reflect 68% of the sample. According to the empirical rule, 68% of the data falls within one standard deviation of the mean. So, we can compute the lower and upper limits of this range by subtracting and adding one standard deviation from the mean, respectively:

Lower limit = mean - standard deviation = 11.44 - 2.39 = 9.05 (rounded to two decimal places)

Upper limit = mean + standard deviation = 11.44 + 2.39 = 13.83 (rounded to two decimal places)

Therefore, the ages of participants that reflect 68% of the sample are between 9.05 and 13.83 years old.