1 A, B and C are points on a circle with centre O.
8 cm A-B

15 cm B-C

B
AOC is a diameter of the circle.
AB= 8 cm
BC= 15 cm
Angle ABC = 90°
Work out the total area of the regions shown shaded in the diagram.
Give your answer correct to 3 significant figures.
Diagram NOT
accurately drawn

Answer:

a₁₁₀ = 1083

Step-by-step explanation:

there is a common difference between consecutive terms, that is

3 - (- 7) = 13 - 3 = 23 - 13 = 10

this indicates the sequence is arithmetic with nth term

\(a_{n}\) = a₁  + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = - 7 and d = 10 , then

a₁₁₀ = - 7 + (109 × 10) = - 7 + 1090 = 1083

Answer:

a=12

Step-by-step explanation:

7a+18=102

first, subtract 18 FROM BOTH SIDES!

then you get 7a=84.

next, divide BOTH SIDES by 7

and you get a =12 :)

Frequency polygon A frequency polygon is a graph that displays the distribution of data.

It shows the number of occurrences (frequency) of each data value, which is represented by a dot plotted above the corresponding value on the horizontal axis.

The dots are then connected by straight lines to form the polygon. In the context of Molly's Candle Shop, the chart would show the number of packages shipped per day for the last 100 days.

a diagram that shows how a variable's variation compares to that of one or more other variables, such as a collection of points, lines, line segments, curves, or regions. the grouping of all locations whose coordinates fit into a certain pattern (like a function).

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Answer:

B

Step-by-step explanation:

A function cannot have more than one point on the same x coordinate. So, B is the only option that works.

An infinite amount

When you are only given angles, then that means that the sides could be anything. 1, 2, 3, 1298371823, they are all possible.

Answer:

only 1

Step-by-step explanation:

Because I'm smart

Sry for the bad explanation but the answer is correct.

The probability that the arrival time between vehicles is 12 seconds or less is approximately 0.573.

Given that the time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 14 seconds.

We know that the exponential probability distribution function is given by

f(x) = λ e^(-λx)

Where λ is the rate parameter of the distribution and is equal to 1/mean in this case. So, λ = 1/14.

Now, we need to find the probability that the arrival time between vehicles is 12 seconds or less. Mathematically, we can express this as:

P(X ≤ 12) = \(\int\limits^{12}_0\) λ e^(-λx) dx

Integrating this expression, we get:

P(X ≤ 12) = [-e^(-λx)]_[0,12] = -e^(-λ12) + e^(-λ0)

Since e^(-λ×0) is equal to 1, we have:

P(X ≤ 12) = 1 - e^(-λ×12)

Substituting the value of λ, we get:

P(X ≤ 12) = 1 - e^(-12/14)

P(X ≤ 12) ≈ 0.573

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The given question is incomplete, the complete question is:

The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 14 seconds . What is the probability that the arrival time between vehicles is 12 seconds or less?

To draw the horizontal alignment for the curve on that shape on 12D, follow these steps:

Step 1: First of all, we have to determine the horizontal alignment for the curve. The horizontal alignment consists of a series of tangents, curves, and spirals.

Step 2: After that, we have to select the appropriate curve radius for the design speed, the superelevation, and the allowable sight distance.

Step 3: Next, plot the vertical curves with the curve layout. A design speed of 50 mph and a curve radius of 1200 ft will be used in this example.

Step 4: Next, we have to calculate the curve length using the formula Lc = Rθ. Here, Lc is the curve length, R is the radius, and θ is the curve angle. In this case, the curve angle is 4 degrees, so the curve length will be 83.775 ft.

Step 5: Then, we will plot the curve using a tangent-tangent-radius (TTR) method. The TTR method involves drawing a tangent to the curve's point of intersection, then drawing another tangent to the next point of intersection, and finally drawing the curve's arc with the given radius. This process is repeated until the curve's entire length is completed.

Step 6: Finally, label the horizontal and vertical curves, including the stationing and curve radius.

That's how we draw the horizontal alignment for the curve on that shape on 12D.

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Answer:

74 inches

Step-by-step explanation:

1ft = 12 inches

6* 12 = 72

72 + 2 = 74 inches

Answer: This is what I got??  It doesn't feel right.

X = -5.7

Step-by-step explanation:

Let B = 12/C

Solve the other two equations for A.

Then set both equations, solved for A, equal to each other.

Substitute 12/C for B.

Cross Multiply.

Answer:

-3

Step-by-step explanation:

for this function you have to replace -1 were there's x in the function h(x)=2x-1

h(-1)=2(-1)-1

=-2-1

=-3

hope this helps

The value of x is 4 for the isosceles triangle has a base that measures x+2 with legs that measure 4x-3 and 2x+5.

Therefore, an isosceles triangle has two equal sides as well as two equal angles. An equilateral triangle is one in which all of its sides are equal, and a scalene triangle is one in which none of its sides are equal. The characteristics of an isosceles triangle are as follows: There is agreement between two sides. The base of an isosceles triangle refers to the third side of the triangle, which is unequal to the other two sides. The two angles that are opposite the equal sides line up perfectly.

Here,

Since the adjacent sides of isosceles triangles are equal,

4x-3=2x+5

4x-2x=5+3

2x=8

x=4

The isosceles triangle has a base that measures x+2 and legs that measure 4x-3 and 2x+5, so x is equal to 4.

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The first partial derivative of f(x,y) with respect to x is:

∂f/∂x = a(bx - ad) + c(cx + dy)

The first partial derivative of f(x,y) with respect to y is:

∂f/∂y = b(cx + dy) + c(cx + dy)

Answer:

A

Step-by-step explanation:

There is a 50% chance of this correct

Answer:

the base must have a minimum of 3 sides

Step-by-step explanation:

Answer:

It's 3

Step-by-step explanation:

333333333333333333333333333333333333333333333333333333333333333333333333333333

Answer:

1:3

Step-by-step explanation:

9:3=3

3.6:1.2=3

A is 3 times greater than B. It means that the scale factor from A to B is 1:3

Answer:

y = 8

RS = 60

ST = 46

Step-by-step explanation:

RS + ST = RS

7y + 4 + 5y + 6 = 106

12y + 10 = 106

12y = 96

y = 8

RS = 7y + 4 = 7*8+4 = 60

ST = 5y + 6 = 5*8+6 = 46

The solutions (or roots) of 2x^2 + 8x + 26 = 0 are -2 + 3i and -2 - 3i.

To find the solutions of 2x^2 + 8x + 26 = 0, we can use the quadratic formula which states that for an equation of the form ax^2 + bx + c = 0, the solutions (or roots) are given by:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 2, b = 8, and c = 26. Substituting into the formula, we get:

x = (-8 ± sqrt(8^2 - 4(2)(26))) / 2(2)

Simplifying inside the square root:

x = (-8 ± sqrt(8^2 - 208)) / 4

x = (-8 ± sqrt(-144)) / 4

Since the square root of a negative number is not a real number, we can say that the solutions to this equation are complex numbers. Specifically, the solutions are:

x = (-8 + 12i) / 4 = -2 + 3i

x = (-8 - 12i) / 4 = -2 - 3i

Therefore, the solutions (or roots) of 2x^2 + 8x + 26 = 0 are -2 + 3i and -2 - 3i.

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An identification and interpretation of the slope in this scenario is: The slope is −0.1. Starting at 3.9, the GPA will decrease by 0.1 for every text sent in class.

Mathematically, the slope-intercept form of a line can be calculated by using this equation:

y = mx + c          .......equation 1.

Where:

From the information provided, we have the following equation:

y = 3.9 - 0.1x

Rewriting the equation in slope-intercept form, we have:

y = -0.1x + 3.9         .......equation 2.

Comparing equation 1 and equation 2, we have:

Slope, m = -0.1

y-intercept, c = 3.9, which also represents the initial value.

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Answer:

No , because The Pythagorean equation isn't true.

Step-by-step explanation:

a² = b² + c²

14² = 11² + 8²

196 = 121 + 64

196 ≠ 185

Answer: 108 degrees.

Step-by-step explanation: If you multiply 108 by 5, you'll get 540. If you divide 540 by 5, you'll get 108.

Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path. This is formalized by using the →(if-then) and ∧(logical and) operators.

Given information and corresponding atomic propositions:

We need to formalize the given statements in terms of atomic propositions r, b, and w, which are defined as follows:

r: Rabbits have been seen in the area.

b: Berries are ripe along the path.

w: Walking on the path is safe.

Now, let us formalize each of the given statements in terms of these atomic propositions:

a) Berries are ripe along the path, but rabbits have not been seen in the area.

b: Rabbits have not been seen in the area, and walking on the path is safe, but berries are ripe along the path.

c: If berries are ripe along the path, then walking is safe if and only if rabbits have not been seen in the area.

d: It is not safe to walk along the path, but rabbits have not been seen in the area, and the berries along the path are ripe.

e) For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.

Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path.

The formalizations in terms of atomic propositions are:

a) b ∧ ¬r.b) ¬r ∧ w ∧

b.c) (b → w) ∧ (¬r → w).

d) ¬w ∧ ¬r ∧

b.e) (¬r ∧ ¬b) → w.b ∧

Berries are ripe along the path, but rabbits have not been seen in the area.

This is formalized by using the ∧(logical and) operator.

(¬r ∧ ¬b) → w: It means For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.

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Given:

A scale model of a building having the dimensions of 3 inches in length and 4 inches in width.

Here, 1 inch = 40 feet.

To find the actual dimensions of the base of the building:

Since 1 inch = 40 feet,

So we have,

Thus, the length of the base of the building is 120 feet and the width of the base of the building is 160 feet.

H0: The distribution of lunch preferences is 70% cafeteria, 10% hut, 10% taco wagon, and 10% pizza.

Ha: The distribution of lunch preferences is not 70% cafeteria, 10% hut, 10% taco wagon, and 10% pizza place.

In hypothesis testing, we have a null hypothesis (H0) and an alternative hypothesis (Ha). The null hypothesis represents the claim or assumption we want to test, while the alternative hypothesis represents the opposite or alternative claim.

In this case, the null hypothesis (H0) states that the distribution of lunch preferences is 70% cafeteria, 10% hut, 10% taco wagon, and 10% pizza place. The alternative hypothesis (Ha) states that the distribution of lunch preferences is not 70% cafeteria, 10% hut, 10% taco wagon, and 10% pizza place.

To test these hypotheses, a random sample of 150 students is selected, and their lunch preferences are recorded. The goal is to determine if the observed distribution of lunch preferences in the sample provides enough evidence to reject the null hypothesis in favor of the alternative hypothesis.

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3 yards 5 feet 6 inches X 7 is 33.833333 yards. The correct option is K- none of these.

First step

One yard is 36 inches hence:

3 yards 6 inches=(36 inches×3)+6 inches

3 yards 6 inches=108 inches+6 inches

3 yards 6 inches=114 inches

Second step

5 Feet to inches=5 ft×12

5 feet to inches=60 inches

Third step

Yards=[(114 inches+60 inches)×7]/ 36 inches

Yards=(174 inches×7)/ 36 inches

Yards=1,218 /36 inches

Yards=33.833333

Therefore the correct option is K- none of these.

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Answer:

55 and 91 are not prime.

Step-by-step explanation:

\(12(1) -5=7\\12(2) -5=19\\12(3) -5=31\\ 12(4) -5=43\\12(5) -5=55\\12(6) -5=67\\12(7) -5=79\\12(8) -5=91\\12(9) -5=103\)

The two digits numbers in the sequence that are not prime: 55 and 91

"It is a list of numbers in particular order."

"A natural number that are divisible by only 1 and the number itself."

For given example,

The nth term of a sequence is 12n -5.

The numbers in the sequence that have two digits and are not prime.

The two digit numbers have range: [10, 99]

Assuming n be a positive natural number,

⇒ 10 ≤ 12n - 5 ≤ 99

⇒ 10 + 5 ≤ 12n - 5 + 5 ≤ 99 + 5

⇒ 15 ≤ 12n ≤ 104

⇒ 15/12 ≤ 12n/12 ≤ 104/12

⇒ 1.25 ≤ n ≤ 8.67

This means, 'n' can take values 2, 3, 4, 5, 6, 7, and 8

For n = 2,

12n -5

= 12(2) - 5

= 19 which is a prime number.

For n = 3,

12n -5

= 12(3) - 5

= 31 which is a prime number.

For n = 4,

⇒ 12n -5

= 12(4) - 5

= 43 which is a prime number.

For n = 5,

⇒ 12n -5

= 12(5) - 5

= 55 which is not prime.

For n = 6,

⇒ 12n -5

= 12(6) - 5

= 67 which is a prime number.

For n = 7,

⇒ 12n -5

= 12(7) - 5

= 79 which is a prime number.

For n = 8,

⇒ 12n -5

= 12(8) - 5

= 91 which is not prime.

From above, the two digits numbers in the sequence that are not prime: 55 and 91

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Answer:

The answer lies in the gradient.

Step-by-step explanation:

The gradient in this equation is -5/8. If any line has the same gradient as the equation above they are parallel because they have the same slant or tilt. Gradient determines if a line is parallel between linear line graphs. If the gradient between two linear line graphs are equal that means that they are parallel.

First identify what is the gradient of a line. The gradient is usually the number that is multiplied with x. In this case (-5/8x), -5/8 is the gradient.

Hope this help.

Answer: ummm B

Step-by-step explanation:

Answer: B

Step-by-step explanation: To make his special energy drink Jerome uses 8 cups of water and 3 cups of drink mix. So the ratio of drink mix to water is 3:8.

Answer:

14,508

I hope this helps!

The length of the curve can be found using the arc length formula and is equal to  approximately 2.312 units

In this case, the curve is given by y = sec(x) over the interval [-π/3, π/3]. To find the length of this curve, we need to compute the integral of the square root of the expression (1 + y'²) with respect to x, where y' denotes the derivative of y with respect to x.

First, we find the derivative of y as follows:

y' = sec(x) tan(x)

Then, we substitute this expression into the integrand and simplify:

L = ∫ √(1 + (sec(x) tan(x))²) dx

= ∫ √(sec²(x)) dx

= ∫ sec(x) dx

Using the trigonometric identity ∫ sec(x) dx = ln|sec(x) + tan(x)| + C, where C is the constant of integration, we can integrate to obtain:

L = ln|sec(π/3) + tan(π/3)| - ln|sec(-π/3) + tan(-π/3)|

= ln(2 + √3) - ln(2 - √3)

= ln[(2 + √3)/(2 - √3)]

≈ 2.312

Therefore, the length of the curve y = sec(x) over the interval [-π/3, π/3] is ln[(2 + √3)/(2 - √3)], or approximately 2.312 units.

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