If FD = 45 units and DE = 60 units , what is the value of a? round the solution to the nearest hundredth

a) P(10.99 ≤ X ≤ 11.01) = 0.9544

b) Probability that the sample mean diameter exceeds 11.01 when n = 25 is 0.0062.

We are given the following in the question:

Mean, μ = 11 cm

Standard Deviation, σ = 0.02 cm

We are given that the distribution of diameter is a bell-shaped distribution that is a normal distribution.

Formula: z = (x - μ)/σ

a) P(10.99 ≤ X ≤ 11.01 when n = 16)

Standard error due to sampling = σ/n = 0.02/√16 = 0.005

P(10.99 ≤ X ≤ 11.01) = P((10.99 - 11)/0.005 ≤ z ≤ (11.01 - 11)/0.005)

                              = P(-2 ≤ z ≤ 2) = 0.9772-0.0228

                              = 0.9544 = 95.44%

b) P(sample mean diameter exceeds 11.01 when n = 25)

Standard error due to sampling =  σ/n = 0.02/√25 = 0.004

P(x > 11.01) = P(z > (11.01 - 11)/0.004) = P(z > 2.5)

                 = 1 - P(z ≤ 1) = 1 - 0.9938 = 0.0062 = 0.62%

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Answer:

The product of (4 + 3i)(5 - 2i) can be calculated using the distributive property:

(4 + 3i)(5 - 2i) = 4 × 5 + 4 × -2i + 3i × 5 + 3i × -2i

= 20 - 8i + 15i - 6i^2

= 20 + 7i - 6(-1)

= 26 + 7i

So the answer is (4) 26 + 7i.

I believe the answer is (d) 26 + 7i.

Only Equation I is a linear equation. A linear equation is defined as an equation where the highest power of the variable is 1, and the relationship between the variables is a straight line.

What is Straight line?

A straight line is a type of geometric shape that is defined as a line with no curvature, extending infinitely in both directions. In other words, it is a one-dimensional object that extends indefinitely without bending or curving. Straight lines are often represented mathematically as y = mx + b, where m is the slope (or gradient) of the line and b is the y-intercept.The slope determines the steepness of the line, and the y-intercept determines where the line crosses the y-axis. Straight lines play a crucial role in mathematics, especially in geometry and linear algebra.

Only Equation I is a linear equation.

A linear equation is defined as an equation where the highest power of the variable is 1, and the relationship between the variables is a straight line. In Equation I, P is equal to 4 times s, so the highest power of the variable (s) is 1, making this a linear equation.

In Equation II, the right-hand side of the equation contains a single constant ($3), not a variable, and therefore it is not a linear equation.

Equation III is not a linear equation because it is just a constant equal to 2 and does not contain a variable.

So the answer is: 1. Equation I, only.

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133 days saw either rain or high winds.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

Example: If an experiment has 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event will be as follows:

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

P(r) = 66 days

P(w) = 98 days

P(both) = 31 days

P(r or w) = P(r) + P(w) - P(both)

P(r or w) = 66 + 98 - 31

P(r or w) = 133 days

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The approximate angle of elevation if Brendan looks up at the tower is 20.03°

The angle of elevation in math is "the angle formed between the horizontal line and the line of sight when an observer looks upwards is known as an angle of elevation".

We know that, sinθ = opposite/hypotenuse

Here, sinx° = 50/146

sinx° =0.34246575342

x = sin⁻¹(0.34246575342)

x = 20.0271724581

x = 20.03°

Therefore, the approximate angle of elevation if Brendan looks up at the tower is 20.03°

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"Your question is incomplete, probably the complete question/missing part is:"

Amelia and Brendon are both on the ground looking at The top of a tower point D. Amelia is at point A and Brendan is at point B.

What is the approximate angle of elevation in Brendan looks up at the tower explain your reasoning.

The two possible locations of the fourth vertex are (4, -1) and (-6, 9). The solution has been obtained by using the properties of parallelogram.

What is a parallelogram?

A parallelogram has two sets of parallel sides, making it a quadrilateral. A parallelogram's opposing sides and angles are both the same length.

Finding the vector that depicts the shift from one of the given vertices to another is necessary in order to determine the fourth vertex of a parallelogram.

The third given vertex must then be added to the vector.

We know that the opposite sides of a parallelogram are parallel and equal in length, we may determine the coordinates of the other two vertices by adding the same displacement vector to two of the given vertices.

The difference between the first and second provided vertices i.e.

(1 - (-4), -2 - 3), is one potential displacement vector which is (5, -5).

On adding this vector to the third vertex, we get the fourth vertex as (4,-1).

Similarly, the difference between the second and third vertices i.e.

(-1 - 1, 4 - (-2))  is another potential displacement vector which is (-2, 6).

On adding this vector to the third vertex, we get the fourth vertex as

(-6, 9).

Hence, the two possible locations of the fourth vertex are (4, -1) and

(-6, 9).

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Answer:

x = 9.75

Step-by-step explanation:

1 / 4 * ( 8x + 2) = 20

( 8x + 2) = 20 / (1/4)

8x + 2 = 20 * 4

8x + 2 = 80

8x = 78

x = 9.75

Answer:

x=39/4  (39 over 4 as a fraction)

The graph of the quadratic function is on the image at the end.

Here we want to graph the quadratic function:

f(x) = -x² - 2

To do so, we can complete the table of values by evaluating the function.

if x = ±2 then:

f(±2) = -(±2)² - 2 = -4 - 2 = -6

if x =  ±1

f(±1) = -(±1)² - 2 = -1 - 2 = -3

if x = 0

f(0) = -(0)² - 2 =  - 2 = -2

Then we have the points:

(-2, -6), (-1, -3), (0, -2), (1, -3), (2, -6)

Now just graph these points and connect them with a curve. The graph of the parabola is below.

Answer:

No. The length of the ramp is [tex]\sqrt{226[/tex] The rubber mat will be too short

Step-by-step explanation:

[tex] \large \blue{ \large\tt{C ) \$500}}[/tex]

_____________

[tex] \: [/tex]

Given:-

[tex] \: [/tex]

By using formula:-

[tex] \boxed{ \rm{ \pink{Simple \: interest= \frac{Principal × Time × Rate}{100}}}}[/tex]

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

hope it helps!:)

Answer: the answer is c.$500 hope that helps !

Step-by-step explanation: I took the test

The values are a = 16.69, c=16.68 ad m∠C = 22.07°.

What are trigonometric ratios?

Trigonometric ratios are mathematical functions that describe the relationship between the angles and sides of a right triangle. The three main trigonometric ratios are the sine, cosine, and tangent.

In the given figure, by using trigonometric ratios, we can find

sin68° = a/18

18 sin 68° = a

Using a calculator, we can find that sin 68° is approximately 0.9272. Multiplying 18 by 0.9272 gives us:

a ≈ 16.69

Therefore, a is approximately 16.69.

cos68° = c/18

18 cos 68° = c

Using a calculator, we can find that cos 68° is approximately 0.3714. Multiplying 18 by 0.3714 gives us:

c ≈ 6.68

Now

sinC = c/18

[tex]C = sin^{-1}(\frac{6.68}{18})\\\\C = sin^{-1}(0.3714)\\\\C = 22.07\degree[/tex]

Hence, the values are a = 16.69, c=16.68 ad m∠C = 22.07°.

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Answer:

a. The probability that a married couple watches the show can be calculated by multiplying the probabilities that each spouse watches the show:

P(Married couple watches the show) = P(Husband watches the show) * P(Wife watches the show) = 0.4 * 0.5 = 0.2

Step-by-step explanation:

b. The probability that a wife watches the show, given that her husband does, can be calculated using Bayes' theorem:

P(Wife watches the show | Husband watches the show) = P(Husband watches the show | Wife watches the show) * P(Wife watches the show) / P(Husband watches the show)

P(Wife watches the show | Husband watches the show) = 0.7 * 0.5 / 0.4 = 0.875

c. The probability that at least one member of a married couple will watch the show can be calculated as the sum of the probabilities that either the husband or the wife watches the show:

P(At least one member of a married couple watches the show) = P(Husband watches the show) + P(Wife watches the show) - P(Married couple watches the show) = 0.4 + 0.5 - 0.2 = 0.7

Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ

Weighed averages show that the student has a grade point average of 2.33.

The grade point average (GPA) is calculated by multiplying the unit value for each course in which a student receives one of the aforementioned grades by the grade point total for that grade. Divide the total of these products by the total number of units. By dividing the total grade points by the total number of units, the cumulative GPA is determined.

A. The student's weighted mean grade point score is (3 classes) × (3 credits per class) × (3 points for a B) ÷ (9 total credits) = 3.00.

B. The student's weighted mean grade point score is (1 class) × (3 credits) × (1 point for a D) ÷ (3 total credits) = 1.00.

C. The student's weighted mean grade point score is (1 class) × (4 credits) × (2 points for a C) ÷ (4 total credits) = 2.00.

D. The student's weighted mean grade point score is (1 class) × (2 credits) × (2 points for a C) ÷ (2 total credits) = 2.00.

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Answer: 2 hours babysitting

Step-by-step explanation:

18 x 9 = 162

180-162= 18

meaning he'd have to work 2 hours babysitting to get to meet his requirement.

hours used = 11

hours left= 3

Answer:

(C) 29

Step-by-step explanation:

Answer:

the least possible number of marbles in the bag is 12.

Step-by-step explanation:

As for the question about the marbles, let's call the number of red marbles "x". Then the number of white marbles is 4x, the number of blue marbles is 5x, and the number of green marbles is (1/2) * 5x = 2.5x.

The total number of marbles in the bag is x + 4x + 5x + 2.5x = 12.5x.

To find the least possible number of marbles, we need to find the smallest possible value of x, which will give us the smallest total number of marbles. Since x represents the number of red marbles, it must be a positive integer. The smallest positive integer value of x is 1.

So, if there is one red marble, there are 4 white marbles, 5 blue marbles, and 2.5 green marbles. The total number of marbles in the bag is 1 + 4 + 5 + 2.5 = 12.5.

Therefore, the least possible number of marbles in the bag is 12.

After 40 years, the account has a total balance of $49.450.80.

Any loans or borrowings come with interest. the portion of the loan's value that lenders use to calculate interest. By lending money (via a bond or certificate of deposit, for instance), or by depositing funds into an interest-bearing bank account, consumers can earn interest.

here, we have,

Let's assume that he starts with $0 in the account and makes a monthly contribution of $100 for 40 years, which is equal to 40 x 12 = 480 months.

The total contributions would be $100 x 480 = $48,000.

The interest earned on the account balance can be calculated as follows:

Interest = Account balance * Interest rate

At the end of each year, the interest is added to the account balance. So, after 40 years, the balance would be:

Year 1: $48,000 * 1.5% = $720

Balance = $48,000 + $720 = $48,720

Year 2: $48,720 * 1.5% = $730.80

Balance = $48,720 + $730.80 = $49,450.80

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Answer:

Step-by-step explanation:

To find the value of x such that f(x) = g(x), we need to set the two functions equal to each other and solve for x.

First, let's define the variables:

f(x) = 2x² - x - 6 is a quadratic function with x as the variable.

g(x) = x² - 4 is also a quadratic function with x as the variable.

Now, to find the value of x such that f(x) = g(x), we set the two functions equal to each other:

2x² - x - 6 = x² - 4

Next, we simplify this equation by subtracting x² from both sides:

x² + x - 10 = 0

This is a quadratic equation, which we can solve for x using either the quadratic formula or by factoring.

Let's try factoring:

x² + x - 10 = (x + 5)(x - 2) = 0

So either x + 5 = 0 or x - 2 = 0. Solving for x, we find that:

x = -5 or x = 2

These are the two values of x such that f(x) = g(x).

Answer:

0.075 is a hundred times smaller than 7.5

Step-by-step explanation:

The perimeter of the parallelogram is 10units

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure. Also, the interior angles on the same side of the transversal are supplementary. The Sum of all the interior angles equals 360 degrees.

To obtain the perimeter of the parallelogram , we add all the sides together.

P = 2(l+b)

P= 2( c-2+12-c)

P = 2( c-c -2 +12 )

P = 2( 10)

P = 20

therefore the perimeter of the parallelogram is 20

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The total optimal solution based on the information will be 49 rupees.

Here, four jobs and four machines are given, with the assignment matrix.

Find out the each row minimum element and subtract it from that row

Find out the each column's minimum element and subtract it from that column.

This assignment problem is being solved using Hungerian Method as the optimal solution is:

J1 to M2, J2 to M4, J3 to M1 and J4 to M3. The total optimal cost is:

= 11 + 13 + 14 + 11

= 49 rupees

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Step-by-step explanation:

The average rate of change of a function on an interval [x, x + h] is given by the formula:

(F(x + h) - F(x)) / h

For the function F(x) = 6x^2 + 5, the average rate of change on the interval [x, x + h] is:

(F(x + h) - F(x)) / h = (6(x + h)^2 + 5 - (6x^2 + 5)) / h = (6(x^2 + 2xh + h^2) - 6x^2 + 5) / h = (6(2xh + h^2)) / h = (12xh + 6h^2) / h

So the average rate of change of the function on the interval [x, x + h] is (12xh + 6h^2) / h for a real number h.

Answer:

  27.5 square units

Step-by-step explanation:

You want to know the area of the composite shape shown in the graph.

The shape can be decomposed into a parallelogram and a triangle. Each has the same base, 5 units.

The parallelogram has a height of 3 units, so its area is ...

  A = bh

  A = (5)(3) = 15 . . . . square units

The triangle has a height of 5 units, so its area is ...

  A = 1/2bh

  A = 1/2(5)(5) = 12.5 . . . . square units

The total area of the figure is the sum of the areas of its parts:

  total area = (15 units²) +(12.5 units²) = 27.5 units²

The area of the polygon is 27.5 square units.

The number of times it is not land on the blue color sector is 7-1 = 6

A probability is defined as the ratio to the number of required outcomes to the total number of outcomes of an event.

The spinner is divided into 7 sectors, in which each sector is equal in size.

Among 7 sectors two of of them are blue in color.

We have to calculate that how many times the spinner not landing on the blue color sector.

For that we have to calculate the possible outcome for the blue color sector for 1 spin.

For 1 spin , the number of possible outcomes = 7.

Number of required outcomes = 2.

Probability of number of spins on blue sector for 1 spin = 2/7.

Probability of number of spins on blue sector for 7 spin = 7*(2/7) = 2.

Standard deviation = [tex]\sqrt{\frac{2}{7} *\frac{5}{7} }[/tex]= 0.4518.≅0.452.

Standard error=root(7)*0.452= 1.19≅1.2

Expected value =2-1.2 = 0.8 ≅1

Therefore the expected value is 1.

Number of times it will land on the blue color sector is 1.

Hence, the number of times it is not land on the blue color sector is 7-1 = 6.

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Answer:

m = -4

Step-by-step explanation:

-2 ( m + 1 ) = 10

( m + 1 ) = 10 / -2

m + 1 = -5

m = -4

Answer:

Step-by-step explanation:

18-5=13

18-9=9

If a value of "y" is greater than 10, then it is a solution to the inequality 10 < y. If it is less than or equal to 10, then it is not a solution.

What is inequality?

In mathematics, an inequality is a statement that describes a relationship between two values, expressing that one value is greater than, less than, or equal to the other value. Inequalities are denoted by symbols such as "<" (less than), ">" (greater than), "≤" (less than or equal to), "≥" (greater than or equal to), or "≠" (not equal to).

The inequality 10 < y means that "y" is greater than 10. To determine whether a given value of "y" is a solution to this inequality, we simply need to check whether that value is indeed greater than 10.

For example:

If y = 11, then 10 < y is true, because 11 is greater than 10.

If y = 10, then 10 < y is false, because 10 is not greater than 10 (they are equal).

If y = 9, then 10 < y is false, because 9 is not greater than 10.

Hence, if a value of "y" is greater than 10, then it is a solution to the inequality 10 < y. If it is less than or equal to 10, then it is not a solution.

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The distance at which Allison should stand to catch the ball will be 8.32 m.

What is speed?

Speed of an object is defined as the ratio of distance covered by the object to the time taken by the object to cover that distance. In other words its tell how much times an object takes to cover a particular distance.

Now for the given question:

Emily throw the ball at 30° below the horizontal towards Allison at a speed of 12m/s. So here we will calculate the Horizontal and Vertical components of the speed.

[tex]v_{x}[/tex]=12cos30°=10.4 m/s

[tex]v_{y}[/tex]=12sin30°=6 m/s

Vertical distance between Alice and Emily according the question is 8 m.

s= 8 m.

Now by applying Second equation of motion to calculate time take by ball to move from Emily to Allison.

s=[tex]v_{y}[/tex]×t+[tex]\frac{1}{2}[/tex]×a×[tex]t^{2}[/tex]

4= 6×t+[tex]\frac{1}{2}[/tex]×9.8×[tex]t^{2}[/tex]           (a=9.8 m/[tex]s^{2}[/tex] acc. due to gravity a constant)

By solving above quadratic equation we get

t= 0.8 s

To find horizontal distance

d= [tex]v_{x}[/tex]×t

d=10.4×0.8

d= 8.32 m

Hence Allison should stand at a distance of 8.32 m to catch the ball.

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The function g(x) = (x - 3)³ is shown in the graph. The solution has been obtained by using the concept of transformation.

What is transformation?

Any action that moves a polygon or other two-dimensional object on a plane or coordinate system is referred to as a transformation.

Translation, rotation, reflection, and dilation are all methods of transformation.

We are given a graph, from which we can say that when x = 3, then y = 0

The function must satisfy these values.

The functions g(x) = (x + 3)³ , g(x) = x³ + 3 and g(x) = x³ − 3 does not satisfy the point (3,0).

Also, the translation is 3 units to the right.

So the function shown in the graph is g(x) = (x - 3)³.

Hence, the transformed function is g(x) = (x - 3)³.

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Question: If the parent function is f(x) = x³, which transformed function is show in the graph?

g(x) = (x − 3)³ , g(x) = (x + 3)³ , g(x) = x³ + 3 , g(x) = x³ − 3

Answer:

Step-by-step explanation:

here's a step-by-step explanation with more detail:

The equation X^2 + X + 8 = 0 can be solved using the Quadratic Formula:

X = (-b ± √(b^2 - 4ac)) / 2a,

where a = 1, b = 1, and c = 8.

Plugging in the values, we get:

X = (-1 ± √(1^2 - 4 * 1 * 8)) / 2 * 1

X = (-1 ± √(-31)) / 2

Since the square root of a negative number is not a real number, the solution to the equation must be expressed using complex numbers. In this case, the square root of -31 can be expressed as the imaginary unit i times the square root of 31.

X = (-1 ± i * √31) / 2

So, the two solutions to the equation are:

X = (-1 + i * √31) / 2 and X = (-1 - i * √31) / 2

And these are the two solutions expressed in terms of the imaginary unit i.