ABCD is a trapezium.
EBC is a straight line.
F is the point on AB so that DFE is a straight line.
Angle BEF = 45°
Angle FBC = 100°
Work out the value of angle ADF.
Give a reason on the same line of each
stage of your working.
+
F
Answer: angle ADF =
E
45°
100°
B
Diagram not drawn to scale
C
Total marks: 4

The probability that a sample of size n=48 has a mean between 182.3 and 198.6 is approximately 0.9474.

The behaviour of sample means and sums in sizable random samples is described by the central limit theorem, a statistical concept. It asserts that regardless of how the underlying population is distributed, as the sample size grows, the distribution of the sample means and sums will converge to a normal distribution. This theorem is crucial because it enables us to extrapolate population parameters from sample data. Because sample means and variances are simpler to gather and evaluate, we may use them to estimate population means, variances, and other characteristics. Several study fields, including the social sciences, the natural sciences, and business, frequently employ the central limit theorem.

Given that the sample size n = 48.

The mean between 182.3and 198.6 is calculated using the central limit theorem.

The sample mean is given as:

Z = (M - μ) / (σ / √(n))

Substituting the values we have:

Z = (198.6 - 178) / (75.2 / √(48)) - (182.3 - 178) / (75.2 / √(48))

Z = 1.62

Now, Z-score less than 1.62 is approximately 0.9474.

Hence, the probability that a sample of size n=48 has a mean between 182.3 and 198.6 is approximately 0.9474.

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Answer:

Triangular base

Step-by-step explanation:

It possesses all attributes except from triangular base

The trigonometric ratios for cosines indicates that the measure of angle B, m∠B, in the right triangle with hypotenuse side length of 15 units and adjacent leg to ∠B of 12 units, obtained using the trigonometric ratios for cosines is; m∠B ≈ 36.9°

Trigonometric ratios relate the lengths of two side lengths of a right triangle and the interior angles of the right triangle.

The cosine of an angle can be obtained from the ratio of the adjacent side to the angle to the hypotenuse side of the right triangle in which the angle is an acute angle, therefore;

cos(θ) = Adjacent side to the angle ÷ Hypotenuse side of the angle

The measure of the length of the adjacent side to the angle x = 12 units

The measure of the hypotenuse side of the right triangle = 15 units, therefore;

cos(x°) = 12/15 = 4/5 = 0.8

The measure of the angle x therefore can be obtained using the arccos function, (cos⁻¹ function) in a scientific calculator as follows;

x = arccos(0.8) ≈ 36.9°

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Nikki applied to 3x colleges.

To determine the number of colleges Nikki applied to, we need to multiply the number of colleges Diego applied to by 3. Hence, the answer is represented by the mathematical expression 3x.

In this problem, 'x' represents the number of colleges Diego applied to. Nikki, on the other hand, applied to 3 times as many colleges as Diego did.

So, to find out the total number of colleges Nikki applied to, we multiply the number of colleges Diego applied to ('x') by 3.

Hence, the correct mathematical expression for the number of colleges Nikki applied to would be 3x.

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The interval of the expression x ≤ 3 and x ≥ -3 is (-3, 3).

To graph a linear equation with one variable, first solve the problem, then find the answer on the axis (number line), and place a point there. We have seen that graphs often provide information that the original equation would not have shown. The graphs of one-variable linear equations do not provide much, if any, information, but they provide as a basis for graphs with greater dimensions.

The given inequality is x ≤ 3 and x ≥ -3.

Since, the signs are less than and equal to and more than and equal to we use solid dots to represent the number 3 and -3 on the number line.

Also, the expression requires all the numbers between 3 and -3. Thus, the interval is:

(-3, 3).

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The end behavior of a polynomial function is to decrease without bound as x approaches negative infinity, and to increase without bound as x approaches positive infinity.

If the degree of a polynomial function is odd and the leading coefficient is negative, then the end behavior of the function is as follows:

As x approaches negative infinity, the value of the function decreases without bound.

As x approaches positive infinity, the value of the function increases without bound.

To understand why this is the case, consider a polynomial function of the form:

f(x) = a_n x^n + a_{n-1} x^{n-1} + ... + a_1 x + a_0

where n is odd and a_n < 0.

As x approaches negative infinity, the dominant term in the polynomial is a_n x^n, and since n is odd and a_n is negative, the value of the dominant term approaches negative infinity as x approaches negative infinity.

Similarly, as x approaches positive infinity, the dominant term in the polynomial is again a_n x^n, but this time the value of the dominant term approaches negative infinity as x approaches positive infinity.

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Based on the information provided, the true sentences are that route B has a more consistent number of rides (B), and the typical number of riders is greater on route A (D).

To begin, these whisker plots compare the number of riders in two routes. In this context, the graph shows the median for route A is 40 and for the route, B is 35, which means the "typical number of riders is greater on route" (option D). Besides this, it can be observed that the number of riders varies more for route A than for route B, which makes B to be true.

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Answer:

105° is the largest angle

Step-by-step explanation:

All angles add up to 180°

Find the value of x

105 + 6x + 17 + 5x + 14 = 180

Combine like terms

136 + 11x =180

Isolate the x ( subtract 136 from both sides)

11x = 44

Divide both sides by 11

x = 4

Now substitute the value of x into each expression to find the largest angle

5(4) + 14 = 20 + 14 = 34°

6(4) + 17 = 24 + 17 = 41°

105 > 41 > 34

By answering the above question, we may state that expressions  Researcher A: Value Frequency 3  2 4  1

In mathematics, you can multiply, divide, add, or take away. The following is how an expression is put together: Numeric value, expression, and math operator The elements of a mathematical expression include numbers, parameters, and functions. It is feasible to use contrasting words and expressions. Any mathematical statement containing variables, numbers, and a mathematical action between them is known as an expression, often known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.

Researcher A:

Value Frequency

3                 2

4                 1

8                  1

10               2

12              1

13                1

14               2

16                 2

17               2

19                 1

21                 1

22               2

24                2

25               2

26                   2

27             2

29               3

31                 2

32                    1

33                  2

34                    2

35                   1

37                   1

40                 1

44                 2

47                   1

Researcher B:

Value Frequency

3                 2

4                 1

6                      1

8               2

13              1

14               3

16             2

17                 1

18                  2

21                 3

22                 2

23              2

24              2

25              2

26            1

28                  1

29                 2

31              2

33                2

34               1

35                   1

41                2

42             1

44                   1

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The standard deviation of her total weekly pay is approximately $262.25 and the mean is $1075

Let X be the number of cars the salesperson sells in a week. Then, X follows a normal distribution with mean μ = 3.1 and standard deviation σ = 1.1.

The total weekly pay Y is given by the equation:

Y = $300 + $250X

Using the properties of means and variances of linear combinations of random variables, we can find the mean and standard deviation of Y as follows:

Mean of Y:

E(Y) = E($300 + $250X) = $300 + $250E(X) = $300 + $250(3.1) = $1075

Therefore, the mean of her total weekly pay is $1075.

Standard deviation of Y:

Var(Y) = Var($250X) = $250^2Var(X) = $250^2(1.1^2) = $68,750

Since the standard deviation is the square root of the variance, we have:

SD(Y) = sqrt($68,750) ≈ $262.25

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As a result, the answer to the following question, When we round to the area nearest hundredth, we get: 42.84 square units in total.

An area is the size of a surface area. The surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a planar region or planar region refers to the area of a form or flat layer. The area of an item is the entire amount of space occupied by its planar (2-D) surface or form. Using a pencil, draw a square on a sheet of paper. A two-dimensional character. The area of a form on paper is the amount of space it occupies. Assume that the square is made up of smaller unit squares.  

The formula for a sector's area is:

Sector area = (central angle/360) x pi x radius2

When we plug in the values we know, we get:

Sector area = (60/360) x 3.14 x 62

Sector area = 18.84 square units

Triangle area = (base x height)/2

When we plug in the values we know, we get:

Triangle area = (8 x 6)/2 Triangle area = 24 square units

Total area Equals sector area + triangle area

18.84 + 24 = total area

42.84 square units in total

When we round to the nearest hundredth, we get:

42.84 square units in total.

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The length of the x is 9 units.

Triangles can be classified based on the lengths of their sides and the sizes of their angles. The three most common types of triangles are equilateral, isosceles, and scalene. In an equilateral triangle, all sides and angles are equal. In an isosceles triangle, two sides and two angles are equal. In a scalene triangle, all three sides and angles are different.

Let's call the two sides of the triangle that the median divides into 9 and 10 "a" and "b", respectively. Then, we can use the formula for the length of a median in a triangle:

median = 1/2 * √(2a² + 2b² - c²)

where c is the length of the third side of the triangle. However, we don't know the length of the third side, so we need to find it. We can use the fact that the median divides the third side into two equal parts:

c/2 = (a + b)/2

c = a + b

Now we can substitute this into the formula for the length of the median:

x = 1/2 * √(2a² + 2b² - (a + b)²)

Simplifying:

x = 1/2 * √(2a² + 2b² - a² - 2ab - b²)

x = 1/2 * √(a² + 2ab + b²)

x = 1/2 * √((a + b)²)

x = 1/2 * (a + b)

x = 1/2 * (9 + 10)

x = 9

So the length of the median is 9 units.

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The surface area οf the cube with sides οf 25 cm is 3750 square centimeters.

Surface area is the measure οf the tοtal area that the surface οf a three-dimensiοnal οbject οccupies, including all οf its faces, sides, and curves. It is οften expressed in square units such as square meters οr square feet, and is an impοrtant parameter fοr determining prοperties such as heat transfer, frictiοn, and οptical prοperties οf an οbject.

The surface area οf a cube with sides οf length "a" can be fοund by using the fοrmula:

Surface area[tex]= 6a^2[/tex]

Substituting the given value οf "a" intο the fοrmula, we get:

Surface area [tex]= 6(25 cm)^2[/tex]

Surface area[tex]= 6(625 cm^2)[/tex]

Surface area [tex]= 3750 cm^2[/tex]

Therefοre, the surface area οf the cube with sides οf 25 cm is 3750 square centimeters.

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The question was incomplete, the complete question is mentioned here:

Find the surface area of the cube with side 25cm?

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\pounds 2000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases} \\\\\\ A = 2000\left(1+\frac{0.03}{1}\right)^{1\cdot 2}\implies A=2000(1.03)^2 \implies A = 2121.8[/tex]

Answer:

If Benny makes $20 an hour babysitting, his 35% increase would be:

35% of $20 = 0.35 x $20 = $7

This means that Benny could make an extra $7 per hour if he babysits an extra kid. Therefore, his new hourly wage would be:

$20 + $7 = $27

So, if Benny babysits an extra kid, he could make $27 per hour.

Step-by-step explanation:

The half-life of the radioactive substance,1/2 = 18.905 years.

The half-life of a radioactive atom or substance

A radioactive element's half life is the amount of time it takes for its atoms to split in h-alf from their initial number.

nuclear decay

The process of a heavy radioactive element's nucleus disintegrating and emitting alpha, beta, and gamma rays is known as radioactive decay.

Radioactivity law

According to the law, when a radioactive element decays or disintegrates, a new element two places below the original element in the periodic table with alpha particle emission or two places above the original element with beta particle emission results.

Hence, The half-life of the radioactive substance,1/2 = 18.905 years.

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Using the angle of intersecting chords theorem, the measure of x = 175°.

The angle of intersecting chords theorem states that when two chords intersect within a circle, the angle that they form is equal to half the sum of the measures of the intercepted arcs and the vertical angle opposite to the angle.

Therefore, based on the theorem, we would have:

180 - 60 = 1/2(x + 65)

120 = 1/2(x + 65)

Multiply both sides by 2:

240 = x + 65

subtract 65 from both sides:

240 - 65 = x

x = 175°

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Answer: what's the queston?

Step-by-step explanation:

Answer:

um question ?

Step-by-step explanation:

Answer: We can simplify 27 as 3^3 and 9 as 3^2. Then, we have:

27^2/9^4 = (3^3)^2/(3^2)^4

Using the power of a power rule, we can simplify:

= 3^(3x2)/(3^2x4)

= 3^6/3^8

Using the quotient rule, we can subtract the exponents:

= 3^(6-8)

= 3^-2

Therefore, 27^2/9^4 can be expressed as 3^-2 in terms of a power of 3.

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The fraction 1/6 is closer to 0, while the fraction 5/6 is closer to 1.

A horizontal bar between two numbers and, on occasion, the symbol "/" can be used to identify a fraction. The term "fractional bar" refers to this bar or symbol. The "denominator" is the number below the fractional bar, while the "numerator" is the number at the top.

Indeed, the following number line displays positive proper fractions with the denominator 6:

0            1             2             3            4             5

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

0          1/6          1/3           1/2         2/3         5/6

The complete numbers are represented by tick marks, while the fractions are displayed in between. The fractions 1/6 and 5/6 are closer to the numbers 0 and 1, respectively.

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Answer: The volume of a rectangular prism is given by the formula V = lwh, where l, w, and h are the length, width, and height, respectively.

For the first rectangular prism, we have:

V1 = 5 x 7 x 1 = 35 cubic inches

For the second rectangular prism, we have:

V2 = 9 x 7 x 4 = 252 cubic inches

To find the total volume of the figure, we add the volumes of the two rectangular prisms:

V = V1 + V2 = 35 + 252 = 287 cubic inches

Therefore, the volume of the figure is 287 cubic inches.

Step-by-step explanation:

Answer:

yes because it is a right triangle

Step-by-step explanation:

if you apply the pythagorean theorem a squared plus b squared equals c squared. c being the hypotenuse, the longest side. so 3x3 + 4x4 = 25 and 5x5 is 25. This confirms that it is a right triangle because pythagoras's theorem only works with right triangles. Also, every angle of a rectangle is a right angle (90 degrees) meaning that the triangle will fit in any and every corner! Hope this helped!

The value of the required number is - 10  

To find the unknown number represent the number with a variable 'x' and form a linear equation according to the condition given in the problem.

Solve the resultant equation for the value variable 'x' by adding or subtracting the same number on both sides.

Here we have

A number decreased by 16 and the result was -26.

Let 'x' be the number

According to the given data,

=> x - 16 = - 26

Add 16 on both sides

=> x - 16 + 16 = - 26 + 16

=> x = - 10

Hence,

The value of the required number is - 10  

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Answer: For each increase in budget by $1 million, the predicted score increases by 0.145 points.

Answer:

x²+5x+6 can be factored as (x+2)(x+3)

x²-4 can be factored as (x+2)(x-2)

x³+8 can be factored as (x+2)(x²-2x+4)

The common factor of all three expressions is (x+2). Therefore, the HCF of x²+5x+6, x²-4, and x³+8 is (x+2).

Step-by-step explanation:

Answer: To find the highest common factor (HCF) of these three polynomials, we can factor each polynomial and then look for the factors that they have in common.

First, let's factor each polynomial:

x² + 5x + 6 = (x + 2)(x + 3)

x² - 4 = (x + 2)(x - 2)

x³ + 8 = (x + 2)(x² - 2x + 4)

Now, we can see that all three polynomials have a factor of (x + 2). Therefore, the HCF of these three polynomials is (x + 2).

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The ratio of boys to girls is 4:3  boys are there of 5 boys were more than girls.

Most of the explanations for ratios and proportions use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion.

We apply the concepts of ratio and proportion every day, for example, while dealing with money in business or when preparing any meal, etc. Students occasionally struggle to understand the difference between ratio and proportion.

Formula used:

No. of Object= Total No of abject. x Given ratio/Sum of ratios

No. of Boys = 35 x 4 /7

No. of Boys = 140 / 7

No of Boys = 20

And No. of Girls = 35 x 3/7

No. of Girls = 105 /7

No. of Girls = 15

Final answer:

No. of boys - No. of girls

20-15= 5

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Jerimiah's finger is longer. A number line can be drawn from 0 to 8 inches with 2 inches marked for Alex's finger and 7/4 inches marked for Jerimiah's finger. Since 7/4 is greater than 2, Jerimiah's finger is longer.

To prove that Jerimiah's finger is longer than Alex's, we can use a number line. On this number line, we start with 0 inches at one end and 8 inches at the other. We mark 2 inches for Alex's finger and 7/4 inches for Jerimiah's finger. Since 7/4 inches is greater than 2 inches, Jerimiah's finger is longer than Alex's. To further prove this, we can convert the fraction 7/4 into a decimal. 7/4 = 1.75, which is greater than 2. Therefore, Jerimiah's finger is longer than Alex's.

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The statements that are cοrrect based οn unit cοnversiοn is -

A - One milliliter is 100 times smaller than οne liter.

C - Milliliters are smaller units than liters.

D - One liter is 1,000 times larger than οne milliliter.

Unit cοnversiοn is a prοcess with multiple steps that invοlves multiplicatiοn οr divisiοn by a numerical factοr οr, particularly a cοnversiοn factοr. The prοcess may alsο require selectiοn οf the cοrrect number οf significant digits, and rοunding.

On the basis οf unit cοnversiοn methοds -

These three statements are true -

One milliliter is 100 times smaller than οne liter.

Milliliters are smaller units than liters.

One liter is 1,000 times larger than οne milliliter.

The οther statements are incοrrect -

Liters are nοt smaller units than milliliters.

One milliliter cannοt be 100 times larger than οne liter, as it is a smaller unit οf vοlume.

One liter cannοt be 1,000 times smaller than οne milliliter, as it is a larger unit οf vοlume.

Therefοre, the statements A, C and D are cοrrect.

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Which statements about liquid volume are true?

Select each correct answer.

One milliliter is 100 times smaller than one liter.

Liters are smaller units than milliliters.

Milliliters are smaller units than liters.

One liter is 1,000 times larger than one milliliter.

One milliliter is 100 times larger than one liter.

One liter is 1,000 times smaller than one milliliter.

The maximum height of the coin is approximately 14.825 meters.

To find the maximum height of the coin, we need to find the vertex of the parabolic function. The x-coordinate of the vertex is given by:

x = -b/2a

where a = -5 and b = 13 are the coefficients of the quadratic function f(x) = -5x^2 + 13x + 6.

Plugging these values into the formula, we get:

x = -13/(2×(-5)) = 13/10

Now we can find the y-coordinate of the vertex by plugging in x = 13/10 into the function:

f(13/10) = -5(13/10)^2 + 13(13/10) + 6

Do the arithmetic operations

≈ 14.825 meters

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In the given triangle the value of the ratios are Sin (P) = 5/13. tan (T) = 12 /5. cos (T) = 5/13.

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are several distinctive trigonometric identities that relate a triangle's side length and angle. Only the right-angle triangle is consistent with the trigonometric identities.

The six trigonometric ratios serve as the foundation for all trigonometric identities. Sine, cosine, tangent, cosecant, secant, and cotangent are some of their names. The adjacent side, opposite side, and hypotenuse side of the right triangle are used to determine each of these trigonometric ratios. The six trigonometric ratios are the source of all fundamental trigonometric identities.

Using the trigonometric identities we can write the ratios as follows:

Sin (P) = Opposite side to P / Hypotenuse= 5/13

tan (T) = Opposite side to T / Adjacent side to T = 12 /5

cos (T) = adjacent side to T / Hypotenuse = 5/13.

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