The sum of the angle measures of any triangle is 180°. Find each of the angle measure of a triangle if the second angle measure 10º more than twice the first, and the third angle measures 10° more
than the second.

Answer:

4,000

_______

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The series converges by the ratio test.

To determine whether the series converges or diverges, we can use the ratio test:

lim(n->∞) |(n+1+5)/(n+5)| * |((n+1)+4)^4/(n+4)^4|

Simplifying this expression, we get:

lim(n->∞) |(n+6)/(n+5)| * |(n+5)^4/(n+4)^4|

= lim(n->∞) (n+6)/(n+5) * (n+5)/(n+4)^4

= lim(n->∞) (n+6)/(n+4)^4

Since the limit of this expression is finite (it equals 1/16), the series converges by the ratio test.

The ratio test is a method used to determine the convergence or divergence of an infinite series. It is particularly useful for series involving factorials, exponentials, or powers of n.

The ratio test states that for a series ∑(n=1 to infinity) aₙ, where aₙ is a sequence of non-zero terms, if the limit of the absolute value of the ratio of consecutive terms satisfies the condition:

lim(n→∞) |aₙ₊₁ / aₙ| = L

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According to the figure the value of B is

The value of B is solved using the principles of segments of chords secants and tangents

The principle is such that

10^2 = 5 * (5 + b)

100 = 25 + 5b

gathering like terms

5b = 100 - 25

5b = 75

isolating b

b = 75 / 5

b = 15

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If Marcus monthly salary is $1,500 plus 10% of sale, then he could earn 1500 + 0.09x per month with salary and 9% sales

Monthly salary of Marcus = $1500

The percentage incentives for sales = 10%

If the percentage of incentive for sales is 9 %

Consider the amount of sales is $x

Therefore the monthly salary of Marcus = Monthly salary of Marcus + (The amount of sales × 9/100)

Substitute the values in the equation

The monthly salary of Marcus = 1500 + (x×9/100)

Divide the numbers in the equation

= 1500 + (x × 0.09)

Multiply the numbers the numbers

= 1500 + 0.09x

Therefore, the monthly salary of Marcus will be 1500 + 0.09x

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Answer:

To the nearest 100 miles, Jessica drove about 300 miles since we haven't reached 350 miles.  If we have a number that is greater than 350 miles than we would've rounded it up to 400 but since ours is less than that we round down to the nearest hundred which is 300 miles.

Answer:

4.1x + 29

Step-by-step explanation:

So the perimeter would be the sum of all of the sides, so:

\(2.3x + 14 + 2x - 0.2x + 15\\= 4.1x + 29\)

Answer: 4.5x+ 29 which is 3, so 3 is correct.

Step-by-step explanation:

P = a+b+c

First do the ordered pairs ( add the numbers with the x to the end, then add the other numbers with no x's)

Answer:

x°=48°

Step-by-step explanation:

angle Y=x°

angle Z= angle y, because equal side of the angles are equal.

so, angle X +angleY+ angle Z=180° ( angle sum property of triangles)

therefore 84°+x°+x°=180°

2x°=180° -84°

2x°=96°

x°=48°

For Adan's car, equation which can be used to determine average number of miles that the car traveled on each gallon of gallon is,

\(16.5x=465.3\)

Average mileage of a vehicle is the ratio of distance traveled by a vehicle to the total number of fuel it used to cover that distance.

It can be given as,

\(m=\dfrac{d}{n}\)

Here, (d) is the distance traveled and (n) is the amount of fuel used.

Suppose the mileage of Adam's car is x miles per gallon.

Adam’s car traveled 465.3 miles on 16.5 gallons of gas. Thus, the mileage of Adam's car is,

\(x=\dfrac{465.3}{16.5}\\\)

Simplify it further,

\(16.5x=465.3\)

Thus, For Adan's car, equation which can be used to determine average number of miles that the car traveled on each gallon of gallon is,

\(16.5x=465.3\)

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The number of bags of fiber stuffing needed to fill the cones is 52 bags.

Given:

Height (h) = 10 inches

Radius (r) = 4 inches

To calculate the number of bags of fiber stuffing needed to fill the ice cream cones, we first need to calculate the volume of a single cone ( cone + hemisphere) using its height and radius.

The volume of a cone can be calculated using the formula:

= (1/3) πr²h

The volume of a hemisphere can be calculated using the formula:

= (2/3) πr³

Substituting these values into the formula, we can find the volume of a single cone:

V = (1/3) π × 4² × 10 + (2/3)π × 4³

V = 167.5 + 134.04

V = 301.54

V ≈ 167.5516 cubic inches (rounded to 4 decimal places)

Now, to determine the number of bags of fiber stuffing needed, we divide the total volume of the cones by the volume that can be filled by a single bag of fiber stuffing:

Number of bags = Total volume of cones / Volume filled by a single bag

Total volume of cones = Volume of a single cone x Number of cones

Total volume of cones = 167.5516 cubic inches x 125 cones

Total volume of cones ≈ 37692.66 cubic inches (rounded to 2 decimal places)

Number of bags = 37692.66 cubic inches / 720 cubic inches (per bag)

Number of bags ≈ 52 (rounded to nearest whole number)

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9 is the  common factor of 9x + 36.

A number system is defined as a system of writing to express numbers.

The given expression is 9x+36

Factor is a number or algebraic expression that divides another number or expression evenly i.e., with no remainder.

The factors of 9 are 1,3,9

The factors of 36 are 1,2,3,4,6,9,12 and 18

The highest common factor is 9.

Take 9 as common from the expression.

9(x+4)

Hence, 9 is the  common factor of 9x + 36.

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Answer:

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

Use Pythagorean theorem and find the length of the hypotenuse r:

The value of r is 9.43 units.

Let's denote the length of one side of the rectangle as L and the width as W. Given that the area of the rectangle is 36 m², we have the equation:

Area = Length × Width

36 = L × W

To express the perimeter of the rectangle as a function of the length (L), we need to find the relationship between the length and the width.

Solving the equation for W, we get:

W = 36 / L

The perimeter (P) of the rectangle is given by the formula:

P = 2L + 2W

Substituting the value of W, we have:

P(L) = 2L + 2(36 / L)

Simplifying further:

P(L) = 2L + 72 / L

Therefore, the perimeter of the rectangle, expressed as a function of the length (L) of one of its sides, is given by P(L) = 2L + 72 / L.

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Answer:

61.5°

Step-by-step explanation:

The triangle is isosceles , the radii are congruent , then the 2 base angles are congruent.

The vertex = 360° - 303° = 57

shaded angle = \(\frac{180-57}{2}\) = \(\frac{123}{2}\) = 61.5°

The probability for a data point is less than is 0.8413.

The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event.

The mean(μ)=4

Standard deviation(σ)=1

(P<5)

From the figure, standard normal distribution curve probability which we have to find P<5

It is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

P(x=4)=x-μ/σ

=4-4/1=0

P(x=4)=50%

P(x<5)=P(x=4)+P(x=1)

=50%+34.13%

=0.8413

P(x<5)=0.8413

Therefore, the probability a data point is less than 5 is 0.8413.

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There are eight possible states, and the transition probabilities can be estimated based on historical data or observations.

To analyze the given weather system using a Markov chain, we need to identify the different possible states that the system can be in.

In this case, the states would correspond to the different combinations of weather conditions over the last three days. There are eight possible states, as each day can either be rainy or not rainy, resulting in 2^3 = 8 possible combinations.

Next, we would need to determine the probability of transitioning from one state to another. For example, if it rained for the past three days, the probability of it raining again tomorrow might be high,

while if it was sunny for the past three days, the probability of rain might be low. These transition probabilities can be estimated based on historical weather data or by observing the system for a period of time.

Once we have determined the transition probabilities, we can create a transition matrix that describes the probabilities of moving from each state to every other state. This matrix can then be used to calculate the long-term probabilities of being in each state, and to make predictions about the likelihood of rain in the future.

In summary, to analyze the given weather system using a Markov chain, we need to identify the possible states based on the weather conditions over the last three days,

determine the transition probabilities between states, create a transition matrix, and use it to calculate long-term probabilities and make predictions.

In this case, there are eight possible states, and the transition probabilities can be estimated based on historical data or observations.

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The length of the long piece of wood is 17.15m

Dimensions in mathematics are the measure of the size or distance of an object or region or space in one direction. In simpler terms, it is the measurement of the length, width, and height of anything. Dimensions are generally expressed as: Length. Breadth.

The dimension of a shape is expressed in the form Length by breadth.

The dimension of the first stick is 17m by 28mm, therefore the length is 17m

The dimension of the second stick is 15cm by 37mm, therefore the length is 15cm = 0.15m

The length of the long stick = 17+0.15 = 17.15m

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Answer:on the circle

Step-by-step explanation:

Point J(-3, 12) is lying on the circle whose center is located at point D(-1, 3).

It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the center of a circle).

We have a center of the circle at D(-1, 3)

And point G(-10, 1) is on the circle.

We know the standard equation of the circle when a center is given:

\(\rm (x-h)^2+(y-k)^2=r^2\)

Where r is the radius of the circle and (h, k) is the center of the circle.

Here (h, k) ⇒ (-1, 3)

The circle equation becomes:

\(\rm (x+1)^2+(y-3)^2=r^2\)

Put the point on the circle equation to get the radius of the circle:

\(\rm (-10+1)^2+(1-3)^2=r^2\)

\(\rm (-9)^2+(-2)^2= r^2\\\\\rm 81+4 = r^2\\\\ \rm r = \sqrt{85} \ units\)

Equation of circle is:

\(\rm (x+1)^2+(y-3)^2=85\)

Now put the point J(-3, 12 ) in the circle equation:

\(\rm (-3+1)^2+(12-3)^2=85\)

4+ 81 ⇒ 85

It means point J is lying on the circle.

Thus, point J(-3, 12) is lying on the circle whose center is located at point D(-1, 3).

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Answer:

8.8 hours or 528 minutes

Step-by-step explanation:

110 miles in 2 hours

divide both by 2

55 miles in 1 hour

484/55 = 8.8 hours

If you need it in minutes there are 60 minutes in an hour so multiply 8.8 by 60

8.8*60=528 minutes

Answer:Andrew tarda 19 minutos en ducharse y desayunar

Explicación paso a paso:

720 seg de ducharse + 420 segundos de su desayuno dan igual a 1140 segudnos

a este numero de segundos hay que pasarlo a minutos. El resultado es 19 minutos que son 1140 segundos

Step-by-step explanation:

Based on the fact that the two numbers multiply to 2,400 and add up to -16, the numbers are undefined.

Assume that one of the numbers is x and the other number is y, the system of equations to represent this is given that the two numbers add up to -16 and multiplying to 2,400:
x + y = -16

xy = 2,400

Expressing y in terms of x :

xy = 2,400

y = 2,400 / x

Solving for x gives:

x + y = -16

x + (2,400 / x) = -16

x = 0

y = 0

The problem given in the question is wrong because the results of x and y are undefined.

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Answer:

(x1y1)= (-8,-4)

(x2y2)= (4,-4)

here

slope= (y2-y1)/ (x2-x1)

= 0/ 12

= 0

Step-by-step explanation:

0

Answer:

10/(2/5)

Step-by-step explanation:

If you want to find how much of something is in another thing, you divide.

Answer:

The answer is A 10 divided by 2/5=25. I just took the test on Ed

Step-by-step explanation:

Answer:

1. 4π/3 in³

2. 2.6 ounces

3. 1081.5 ft³

Step-by-step explanation:

1. A soap manufacturing company changes the design of their soap from a cone to a sphere shape. The cone had a height of 4 inches and radius of 3 inches. The sphere has a diameter of 4 inches. In cubic inches, how much less soap is in the new design than the old design? Leave answer in terms of π and as a simplified fraction.

We find the volume of the cone and sphere to know the quantity of soap in each of them.

Volume of cone of soap, V = πr²h/3 where r = radius of cone = 3 inches and h = height of cone = 4 inches

So, V = πr²h/3

= π(3 in)² × 4 in/3

= 9π in² × 4 in/3

= 3π in² × 4 in

= 12π in³

We now find the volume of the sphere, V' = 4πR³/3 where R = radius of sphere = d/2 where d = diameter of sphere = 4 inches. So. R = d/2 = 4 in/2  = 2 in.

So, V = 4πR³/3

= 4π(2 in)³/3

= 4π × 8 in³/3

= 32π in³/3

So the amount of soap less used in the new design than the old design is the old volume - new volume = V - V' = 12π in³ - 32π in³/3 = (36π in³ - 32π in³)/3 = 4π/3 in³

2. Austin uses a mold to make cone shaped cupcakes. The diameter of the mold is 3 inches, and the height of the mold is 2 inches. If 1 cubic inch is about 0.55 ounce, how many ounces will ten cupcakes weigh? Use 3.14 for pi. Round to the nearest tenth of an ounce.

Since the cake is a cone, we find its volume to know its quantity.

So,  Volume of cone of cupcakes, V = πr²h/3 where r = radius of cone = d/2 where d = diameter = 3 inches. So r = d/2 = 3/2 = 1.5 in and h = height of cone = 2 inches

So, V = πr²h/3

= π(1.5 in)² × 2 in/3

= 2.25π in² × 2 in/3

= 4.5π in³/3

= 4.5(3.14) in³/3

= 14.13 in³/3

= 4.71 in³

Now since 1 cubic inch = 0.55 ounces,

4.71 in³ = 4.71 × 1 in³

= 4.71 × 0.55 ounces

= 2.591 ounces

≅ 2.6 ounces to the nearest tenth of an ounce.

3. Walden is planning to install an above ground pool in he backyard. The pool has a diameter of 18 feet and depth of 5 feet. He is going to fill it to 85% capacity. How much water will be in the pool when he is finished?

We need to find the volume of the empty pool, V.

Since the pool has a diameter, d = 18 feet, it has a circular cross-section whose area, A = πd²/4.

Since the depth of the pool, h = 5 feet, the volume of the pool is V = Ah = πd²h/4.

So, V = πd²h/4

= π(18 ft)² × 5 ft/4

= 324π ft² × 5 ft/4

= 81π ft² × 5 ft

= 405π ft³

= 1272.35 ft³

Since Walden fills the pool to 85 % capacity, the volume of water would thus be V' = 85% of V

= 0.85V

= 0.85 × 1272.35 ft³

= 1081.5 ft³

Answer:

Answer is – 3

Step-by-step explanation:

expand the expression using ( a – b) ( a + b) = a² –b²

( 3 ) ² – ( 6) ² *remember to place your square roots inside the brackets my phone doesn't have one*

then simplify the radical

3–6 = – 3

Answer:

6.volume=

\(4 \times 3 \times 11 = 132 \)

surface area

\(2(4 \times 3 + 11 \times 3 + 4 \times 11) = 172in \\\)

Answer:

6.

volume=l×b×h=11×3×4=132in³

surface area =2(lb+bh+lh)=2(11×3+3×4+11×4)=178in²

7.

lateral surface area of traingular prism=perimeter of traingle ×length=[5+3+4]×6=72cm²

curved surface area=2[area oftraingle]=2×1/2×4×3

=12cm²

now

total surface area=72cm²+12cm²=84cm²

8.

volume of traingular prism=area of traingle ×length

=1/2×12×3.4×4=81.6in³

Options a, d, and e could describe a binary search tree while the rest doesn't.

In a binary search tree (BST), every element 'a' has certain properties regarding its position relative to other elements in the tree. Let's analyze it:

a. "Lesser than all elements in its left subtree": This statement would hold true in a BST. In a BST, the left subtree contains elements that are smaller than the current element.

b. "Greater than all elements in its left subtree": This statement would not hold true in a BST. In a BST, the left subtree contains elements that are smaller than the current element, so 'a' cannot be greater than all elements in its left subtree.

c. "Lesser than all elements in its right subtree": This statement would not hold true in a BST. In a BST, the right subtree contains elements that are greater than the current element, so 'a' cannot be lesser than all elements in its right subtree.

d. "Greater than all its descendants": This statement would hold true in a BST. In a BST, all elements in the left subtree are smaller than the current element, and all elements in the right subtree are greater. Therefore, 'a' would be greater than all its descendants.

e. "Greater than all elements in its right subtree": This statement would hold true in a BST. In a BST, the right subtree contains elements that are smaller than the current element, so 'a' can be greater than all elements in its right subtree.

In summary, options a, d, and e could describe a binary search tree, while options b and c would not accurately describe a binary search tree.

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