Choose the correct answer below

A triangle is a plane figure that consists of three sides and three internal angles. Thus m<FHG is [tex]122^{o}[/tex].

A triangle is a family of polygon which is bounded by three straight sides, thus forming three internal angles. The sum of the internal angles of a trigon is [tex]180^{o}[/tex]. While exterior angles are angles which are outside the edges of a triangle.

From the given question;<IGH = <BGD = 42°   (vertically opposite angles)<HIG = 180 - <CIH         = 180 - 100<GIH = [tex]80^{o}[/tex]

Thus, we can conclude that;<IGH + <GIH + <GHI =   [tex]180^{o}[/tex]42 + 80 + <GHI =  [tex]180^{o}[/tex]<GHI =  [tex]180^{o}[/tex] - 122         = 58<GHI = [tex]58^{o}[/tex]So that;m<FHG

=  [tex]180^{o}[/tex] - M<GHI             =  [tex]180^{o}[/tex] - 58            

= [tex]122^{o}[/tex]m<FHG

= [tex]122^{o}[/tex]

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Gregory has 10 ways to choose 3 boxes of cereal.

What do you mean by purchase?

A corporation or organization uses the purchasing process to buy products or services in order to achieve its objectives. Although many organizations make an effort to establish standards for the purchasing process, procedures can differ significantly between organizations.

According to data in the given question,

We have :

The purchase of 3 boxes and the store has 5 different varieties of munchie brand cereal.

The order in which the boxes of cereal are chosen is not important as Gregory can randomly choose any 3 different varieties. So, this is a combination problem.

Use the combination formula:

[tex]_nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

Putting n=5 (5 different varieties) and r=3 (3 different varieties). So, the number of ways Gregory choose 3 boxes of cereal is:

[tex]_{5}C_3=\dfrac{5!}{3!(5-3)!}=\dfrac{5!}{3!2!}= \frac{5.4.3.2.1}{3.2.1.2.1} _{5}C_3=\dfrac{5\cdot 4}{2\cdot 1}=10[/tex]

Therefore, the required answer is 10 ways.

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If she records the liquid volume using milliliter and deciliter, then the deciliter gives more precise measure

The total capacity = 3 gallon

Convert the gallon to milliliter

We know

1 gallon = 3.785 ml

The total capacity in milliliter = The total capacity × 3.785

Substitute the values in the equation

= 3 × 3.785

= 11.355 milliliter

Convert the gallon to deciliter

We know,
1 gallon = 37.854 deciliter

Total capacity in deciliter = The total capacity × 37.854

Substitute the values in the equation

= 3 × 37.854

= 113.562 deciliter

Here deciliter is much smaller than millimeter

Therefore, deciliter gives more precise measure

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The distance, in feet, on Main Street between First Avenue and Canal Street, using relations in a right triangle, is of:

319.25 ft.

The situation is represented by a right triangle, hence the three trigonometric measures are defined as follows:

From the image given at the end of the answer, the parameters are given as follows:

Hence the distance of the Main Street is found using the sine of the angle of 70º, as follows:

sin(70º) = 300/x

x = 300/sin(70º)

x = 319.25 ft.

The right triangle is given by the image shown at the end of the answer.

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The number of cards in the deck are either a jack or a heart are 17.

What is card deck?

A playing card is a specially made piece of card stock, heavy paper, thin cardboard, paper coated with plastic, cotton-paper blend, or thin plastic that is imprinted with distinctive motifs. To make handling easier, each card frequently has a finish on the front and back.

Given:

A standard deck of cards consists of four suits (clubs, diamonds, hearts, and spades), with each suit containing 13 cards (ace, two through ten, jack, queen, and king) for a total of 52 cards in all.

We have to find the number of cards in the deck are either a jack or a heart.

Since, there are four Jack in a 52 card deck.

So, one jack can be chosen by 4C1 ways.

Also there are 13 cards of hearts in a 52 card deck.

So, one heart can be chosen by 13C1 ways.

The number of ways = 4C1 + 13C1 = 4 + 13 = 17.

Hence, the number of cards in the deck are either a jack or a heart are 17.

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Answer:

4/45

Step-by-step explanation:

Answer:

can u see when i do this????

Step-by-step explanation:

A car travels 500/3 meters in 2 seconds.

What is speed?

The speed at which an object's location changes in any direction. The distance traveled in relation to the time it took to travel that distance is how speed is defined. Given that it just has a direction and no magnitude, speed is a scalar number.

Here, we have

Speed of car  = 100 KM/ hour

1 km= 1000m

1 hour = 3600 seconds

Let's find the speed of the car in Meters/second

Speed of car in m/sec = 100*1000 m/3600 second

Here we have taken 1000 for km and 3600 for an hour

Speed of car in m/sec = 100*1000 m/3600 second = 500/18 m/second

Speed of car in m/sec = 250/9  m per sec

We know that

Distance = speed*time

Speed = 250/9  m per sec

Time = 2 second

Distance = 250/9 * 2 meters = 500/3 meters

Hence, a car travels 500/3 meters in 2 seconds.

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So when parent population is right-skewed and the sample size is small, the percentage of intervals that include population mean is (above, below, equal to) 0.95 when building 95% confidence intervals for said mean.

A confidence level of both the CI refers to the likelihood that its confidence interval contains the actual population mean value.

Thus, when parent population is right-skewed and the sample size is small, the percentage of intervals that include population mean is (above, below, equal to) 0.95 when building 95% confidence intervals for said mean.

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A ball must be fast rolled is 185.2cm/sec, according to the question.

What do you mean by distance?

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

According to the given question,

We have the given information:

Table height = h = 70cm

Distance = s = 70cm

g = 9.8[tex]ms^{-1}[/tex]

Now, we have to find the time of falling,

[tex]t=\sqrt{\frac{2h}{g} }=0.378c[/tex]

Horizontal velocity,

[tex]v=\frac{s}{t}=\frac{70cm}{0.378s}=185.2cm/s[/tex]

Therefore, the required answer is 185.2cm/sec.

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The rate in the height of water changing for the given cylinder is equal to 0.318m/s.

As given in the question,

Change in volume represent the decrease in rate of change of water height in the cylinder in time t

dV/dt = 4m³/sec.

Decrease in volume represent the change in the height of the water

Let 'h' be the height

h = 10m

radius 'r' = 2m

V = πr²h

Rate of change of leaking water only change the height radius remain constant.

⇒V = (3.14)(2²) h

Differentiate both the side with respect to 't' to get the rate of change

dV/dt = (3.14)(4)dh/dt

⇒4 =(3.14)(4)dh/dt

⇒dh/dt = 4/ (3.14)(4)

⇒dh/dt = 0.318 m/s

Therefore, the rate of change of height is equal to 0.318m/s.

The complete question is:

A vertical cylinder is leaking water at a rate of 4m3/sec. If the cylinder has a height of 10m and a radius of 2m, at what rate is the height of the water changing when the height is 3m?

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The distance between two points (4, 0) and (2, -9) is √85 units in the simplest radical form.

The length of the line segment connecting two points in a plane is defined as the distance between them. The formula for calculating the distance between two points is commonly presented as √(x₂-x₁)²+(y₂-y₁)².

Distances in geometry are usually positive, unless when the points coincide. We consider two points A(a, b) and B to obtain the formula for the distance between two points in the plane (c, d).

The given two points are (4, 0), (2, -9).

Distance between two points is given by,

Distance=√(x₂-x₁)²+(y₂-y₁)²

Where x₁, x₂, y₁, y₂ are the points.

So, the distance between (4, 0) and (2, -9)

=√(2-4)²+(-9-0)²

=√4+81

=√85 units

Therefore, the distance between two points (4, 0) and (2, -9) is √85 units in the simplest radical form.

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Answer:

5 people total including Mark. So, 4 friends.

Step-by-step explanation:

$67 total - $22 concession stands

$45 spent on tickets

45/$9per ticket

5 tickets were purch

At 0.01 significance level the hypothesis is rejected.

Null Hypothesis (H₀): The sample data occurs purely from chance.

Alternative Hypothesis (H₁): The sample data is influenced by some non-random cause.

If the p-value of the hypothesis test is less than some significance level (e.g. α = .01), then we can reject the null hypothesis and conclude that we have sufficient evidence to say that the alternative hypothesis is true.

Given that,

x = 28

s = 2.9

μ = 31

n = 8

α = 0.01

Then, the Null Hypothesis : H₀ = 31

          The Alternate Hypothesis : H₁ < 31

The average number of cigeratte smoker  per day is less than 31.

Test Statistics:

t = x -μ / s√n

   = 28 - 31/ 2.9√8

   = -3/ 8.41

   = -0.356

Since the p-value of 0.0046 is less than the significance level of 0.01, the auditor rejects the null hypothesis.

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Your answer is 8.

[tex]2x2x2=8[/tex]

The number of songs that were originally on the player is 41.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

In this situation, a DJ added 20 more songs to his MP3 player, making the total more than 61. The number of songs will be the subtraction of the value.

This will be:

= 61 - 20

= 41

The original songs are 41.

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An equation to represent this situation is 16x - 5 = 14x + 1. The value of x is equal to 3.

The perimeters of the rectangle and triangle are equal to 43 units.

Mathematically, the perimeter of a rectangle can be calculated by using this equation;

P = 2(L + W)

Where:

An equation for the perimeter of this rectangle is given by:

P = 2[(5x - 2) + (3x - 0.5)]

P = 2(8x - 2.5)

P = 16x - 5.

Mathematically, the perimeter of a triangle can be calculated by using this equation:

P = a + b + c

Where:

P = (2x + 3) + (2x + 3) + (10x - 5)

P = 14x + 1

Since the perimeter of both geometric figures are the same, we can calculate the value of x as follows:

16x - 5 = 14x + 1

2x = 6

x = 3

For the perimeter of this rectangle, we have:

P = 16x - 5.

P = 16(3) - 5.

P = 43 units.

For the perimeter of this triangle, we have:

P = 14x + 1.

P = 14(3) + 1.

P = 43 units.

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28.9641 ≤ x-bar(t) ≤ 39.0359.

Knowing that we have 10 different values of speed, the size of the sample is 10; n=10. Therefore, this sample is considered statistically small because n < 30.

Arithmetic mean= (Sum of all values) / (Amount of values)

x-bar= (340) / (10)

x-bar= 34.0000.

x-bar= arithmetic mean.

We're going to use the Microsoft Excel tool for the standard deviation for samples (check attached image 1).

Standard deviation for samples (s)= 7.0396.

Check attached image 2.

σ(x-bar)= 2.2261.

α is the error that the confidence interval will have. Given a 95% confidence level, we know that the error is 5%; Error= 1 - Confidence.

α/2= 5%/2= 0.05/2= 0.025.

You can either use the probability tables or the Microsoft Excel tools to find the inverse of a t-student distribution for this α/2 value (check attached image 3).

In this case we use the t-student distribution instead of the normal distribution because the sample size is small and the standard deviation of the population is unknown.

T-student value= -2.2622

Absolute t value= 2.2622.

Check attached image 4 to see the formulas.

Lower limit = (34) - (2.2622*2.2261) = 28.9641

Upper limit = (34) + (2.2622*2.2261) = 39.0359

28.9641 ≤ x-bar(t) ≤ 39.0359

This result means that the value of speed could be any value between 28.9641 and 39.0359, including, with a 95% confidence level. There's a 5% chance that a newly measured value of speed is outside this interval.

The required reciprocal of 3 would be 1/3.

The reciprocal of a number multiplied by a number is 1.

The coefficient of the inverse of the function f(x)=nx is the reciprocal of a number n. A function's inverse is the function with its points flipped.

The reciprocal of a number is the same as its multiplicative inverse.

(The multiplying opposite) It is the number 'turned upside down.

The product of a number and its reciprocal is always 1

So in this case, we can write 3 as: 3/1

The reciprocal is 1/3.

Therefore, the required reciprocal of 3 would be 1/3.

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1/3 Answer:

this is a random answer

Step-by-step explanation:

Answer: When multiplying a whole number by a PROPER fraction (always less then 1), the product is always less than a whole number. So yes, i agree with jenny when using proper fractions.

The confidence interval for the one-way analysis of variance experiment be, (138.94 , 181.06) and the margin of error of the poll be,

±31.06.

On Subtracting 1 from your sample size, we get

330 – 1 = 229.

On Subtracting confidence level from 1, and then divide by two.

(1 – .95) / 2 = 0.025

Now, df = 229 and α = 0.025

from the table at df = 999 we got 2.262.

Divide your sample standard deviation by the square root of your sample size.

150 / √(330) = 1.37

Now, 2.262 × 1.37 = 31.06

So, the confidence interval be,

(150 - 31.06 , 150 + 31.06) = (138.94 , 181.06)

Hence, the confidence interval for the one-way analysis of variance experiment be, (138.94 , 181.06) and the margin of error of the poll be,

±31.06.

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The value of x is 35 and the value of y is 82.

In geometry, an isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.

Given that the three angles of the triangle are 40, 2x and y-12. The value of x and y will be calculated as,

2x = y-12

2x + y-12 + 40 = 180

2x + y =180-40+12

2x + y = 152

2x - y = -12

___________

4x = 140

x = 35

y = 2x + 12

y = 2 x 35 + 12

y = 82

Therefore, the value of x is 35 and the value of y is 82.

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Answer:

x=3,x=4

Step-by-step explanation:

(x-3)(x-4)=0

x=3, 4

Answer:

x = 3

x = 4

Step-by-step explanation:

"find the roots" means to find the solutions to the equation.

Roots are solutions are zeros are x-intercepts.

You are being asked to solve the equation.

First, factor the quadratic.

x^2 -7x + 12 = 0

(x - 3)(x - 4) = 0

This works because -3 × -4 is 12 and

-3 + -4 is -7

You see the 12 in the equation is the constant and the -7 is the middle term, the x-term in the trinomial.

So we have

(x - 3)(x - 4) = 0

Separate the two factors into two separate tiny, one-step equations.

x - 3 = 0 , x - 4 = 0

Solve.

x = 3 , x = 4

These are the roots (solutions, zeros and x-intercepts)

The amount of the salmon left after Mr Jones used some part is

Total amount of salmon  bought is 6 and 2/7 lb = 6 2/7 lb

The amount used is 1/5 of the amount Mr Jones bought

= 1/5 * 6 2/7

= 44 / 35

= 1 9/35

= 1.257

The amount left is calculated by subtraction

= 6 2/7 - 1 9/35

= 176 / 35

= 5 1/35

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Answer:

[tex]1\frac{1}{2}[/tex]

Step-by-step explanation:

we multiply the fractions

1/8 x 12/1

12/8

1 4/8

1 1/2

Hopes this helps please mark brainliest

Answer:

ypotheses:

H0: μ = 2000

H1: μ < 2000

Claim: The average number of acres in the State Park is less than 2000.

Critical Value (s): -1.645 (z-score)

Acceptance Region: z < -1.645

Rejection Region: z ≥ -1.645

Test Value: z = -3.537

Conclusion: Since -3.537 is less than -1.645, we reject the null hypothesis and accept the alternate view. There is enough evidence to support the claim that the average number of acres in the State Park is less than 2000.

Step-by-step explanation:

The length of a human's femur, x, and the length of a human's humerus, Y would ,positive correlation.

A statistical measure known as correlation expresses how closely two variables are related linearly (meaning they change together at a constant rate). It's a typical technique for describing straightforward connections without explicitly stating cause and consequence.

A scale from + 1 to -1 is used to calculate the correlation coefficient. Either + 1 or -1 represents a variable's complete connection with another. The correlation is positive when one variable rises as the other rises; it is negative when one variable falls as the other rises.

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The value of f(0) is f(0) = 3 and the value of f(-4) is f(-4) = 1

From the question, we are to determine the value of the given functions

The functions are

f(0) and f(-4)

First, we will determine the value of f(0)

Since 0 ≥ -2, we will use the function

f(x) = x² + 2x + 3

Thus,

f(0) = (0)² + 2(0) + 3

f(0) = 0 + 0 + 3

f(0) = 3

Now, we will determine the value of f(-4)

Since -4 < -2, we will use the function

f(x) = x + 5

Thus,

f(-4) = -4 + 5

f(-4) = 1

Hence, f(0) = 3 and f(-4) = 1

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[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-5)}}} \implies \cfrac{-3 +5}{1 +5} \implies \cfrac{ 2 }{ 6 } \implies \cfrac{1 }{ 3 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{ \cfrac{1 }{ 3 }}(x-\stackrel{x_1}{(-5)}) \implies y +5 = \cfrac{1 }{ 3 } ( x +5)[/tex]