Select the correct answer.
Of a group of 500 people, 60 are fit enough to climb Mount Shasta in California. The group has 300 women and 200 men. 12% of the men are fit to climb the mountain. What is
the probability that a person picked at random from the group is a male or is fit to climb Mount Shasta?

The pair of 1st line is vertical opposite angle and 2nd one is adjacent angles.

What is vertical opposite angle ?

When 2 lines meet one another, then the other angles, shaped thanks to intersection ar known as vertical angles or vertically opposite angles. A try of vertically opposite angles ar continuously adequate to one another. Also, a angle and its adjacent angle are supplementary angles, i.e., they add up to a hundred and eighty degrees.

Main body:

1st pair of line intersect each other , so ∠1 = ∠2 by using vertical opposite angle.

2nd pair of line also intersect each other , so ∠3 ,∠4 are adjacent angles.

Hence ,pair of 1st line is vertical opposite angle and 2nd one is adjacent angles.

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4/7 is probability a two-way table to model this chance process.

What are examples and probability?

A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

                                The likelihood of an event occurring increases as its probability increases. The flip of a fair (impartial) coin serves as a straightforward illustration.

No events getting thick crust pizza and getting pizza with mushrooms are not disjoint as we can have pizza that has thick crust and mushroom both.

No events are not independent as

P(thick and having mushroom) is not equal to P(thick crust)*P(having mushroom)

P( thick and having mushroom) = 2/7

P(thick crust) = 3/7

P( having mushroom) = 4/7

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Answer: when y = -64 and x = 16 is y = -4x. This equation states that for every value of x, the corresponding value of y is equal to -4 times the value of x.

The angle of elevation is 72.5° and the height at which the ladder will elevate on the building is 19.06 ft.

Here we have to find the angle of elevation of the ladder and the height the ladder will reach on the building if the ladder is leaned against a building.

Data given:

length of the ladder = 20 ft

the base of the ladder = 6ft

we have to find the angle of elevation.

cos Ф = base/ hypotenuse

= 6/20

Ф = [tex]cos^{-1}[/tex] ( 6/20)Ф

    = 72.5°

Now we have to find how high the ladder reaches on the building when leaned against a building.

sin(72.5°) = x/ 20

x = 0.953 ×20

x = 19.06 ft

Therefore the angle of elevation is 72.5° and the ladder will elevate to 19.06.

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The measurement of side DF is 4cm.

Here in the figure attached below,

Given two triangles ΔABC and ΔDEF

Also given that,

ΔABC and ΔDEF are congruent to each other.

Given AC = 4cm

Since both triangles are congruent ,

Side AC is congruent to DF

Therefore DF = 4cm (based on SSS theorem).

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The measure of DF is 4cm.

What is congruent triangle?

When two triangles are congruent, their three sides and their three angles match precisely.

If there is a turn or a flip, the equal sides and angles might not be in the same place, but they are still present.

Here in the figure attached below,

There are two triangles ΔABC and ΔDEF and it is given that ΔABC and ΔDEF are congruent to each other.

From the figure, side AC = 4cm

The side DF = AC = 4cm, because the triangles  ΔABC and ΔDEF are congruent to each other and based on Side-Side-Side Theroem, we can confirm that.

Hence, DF = 4cm.

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The full expansion of the expression (2x - 1) (x + 5) is 2x² + 9x - 5

From the question, we have the following parameters that can be used in our computation:

(2x - 1) (x + 5)

Combine the factors of the expression using the product sign

So, we have

(2x - 1) (x + 5) = (2x - 1)*  (x + 5)

Evaluate the products

This gives

(2x - 1) (x + 5) = 2x² - x + 10x - 5

Evaluate the like terms in the expression

(2x - 1) (x + 5) = 2x² + 9x - 5

Hence, the expanded expression is 2x² + 9x - 5

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Answer:

(x-1)(2x+5)

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The upper bound of the length of the line is 12.34 cm

From the question, we have the following parameters that can be used in our computation:

Length of the line = 12.3 cm

From the question, we understand that

Time = rounded to the nearest one decimal place

The highest number that can be rounded to 12.3 to the nearest one decimal place is 12.34

This means that

Upper bound = 12.34

Hence, the upper bound is 12.34 cm

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So, the half of [tex]7\frac{3}{4}[/tex] is [tex]3\frac{7}{8}[/tex]. An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

A fraction is a numerical value that represents a part of a whole. It is typically written as a ratio of two numbers, with a line separating the numerator and the denominator. For example, the fraction one-half can be written as 1/2. Fractions are often used to represent a part of a whole number or a part of a whole object, such as a pie that has been cut into several pieces.

To find half of 7 3/4 on a tape measure, we need to follow these steps:

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The necessarily simplified answer to the provided experiment is given as x = 1 ± √2.

A mathematical expression is simplified when it is replaced with a simpler, usually shorter, equivalent expression.

So, for the given phrase (x + 1)2 - 4(x + 1) + 2 = 0, find the simple answer as follows:
The expression is:  (x + 1)² – 4(x + 1) + 2 = 0

Replace x + 1 = u in the preceding equation:

u² - 4u + 2 = 0

u² - 4u +4 - 4 + 2 = 0

(u - 2)² = 2

u - 2 = ±√2

replace with u = x + 1:

x + 1 - 2 = ±√2

x - 1 = ±√2

x = 1 ± √2

Therefore, the necessarily simplified answer to the provided experiment is given as x = 1 ± √2.

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Correct question:
Solve (x + 1)2 – 4(x + 1) + 2 = 0 using substitution. u = Select the solution(s) of the original equation.

The maximum possible change in the money supply is $1000.

In the given question, if the required reserve ratio is 10% and the Fed conducts an open market purchase of $100, we have to find the maximum possible change in the money supply.

The required reserve ratio is 10%.

The Fed conducts an open market purchase of $100.

So the maximum possible change in the money supply is

money multiplier=1/RRR

money multiplier=100/10

money multiplier=10

Open market purchase of $100

Change in money supply is 10*100=$1000

So, the maximum possible change in the money supply is $1000.

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The solution of the inequality 3r ≤ 4r - 6 is  r ≥ 6.

In Mathematics, the relationship between two values that are not equal is defined by inequalities.

An inequality have the symbol <, >, ≤ and ≥. Hence, the inequality can be solved as follows:

3r ≤ 4r - 6

subtract 4r from both sides of the inequality,

3r ≤ 4r - 6

3r - 4r ≤ 4r - 4r - 6

3r - 4r ≤ - 6

- r ≤ -6

divide both sides of the inequality by -1

Therefore, the solution is r ≥ 6

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Answer:

6.25h

Step-by-step explanation:

The required coordinates of point B will be (2/9, -14/9).

Point A is at ( -3,4) and Point C is at ( 2,-6 )

Given that point B on line, AC suck as the ratio of AB to AC is 4:5

The coordinates of point B will be,

{[(mx2+nx1)/(m+n)],[(my2+ny1)/(m+n)]}

Breaking it down, the x coordinate is (mx2+nx1)/(m+n) and the y coordinate is (my2+ny1)/(m+n)

As per the question, m = 4 and n = 5

The coordinates of point B :

⇒ {[(4×-3+5×2)/(4+5)],[(4×4+5×-6)/(4+5)]}

⇒ {[(-12+10)/(9)],[(16-30)/(9)]}

⇒ (2/9, -14/9)

Thus, the required coordinates of point B will be (2/9, -14/9).

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The graph crosses the x-axis at x = 0 and touches the x-axis at x = –5.

Option (C) is correct.

What is a function in mathematics?

In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. The set of inputs is called the domain of the function, and the set of possible outputs is called the range of the function.

First, factorize the function f(x):

[tex]f(x)=4x^7+40x^6+100x^5\\\\f(x)=4x^5(x^2+10x + 25)\\\\f(x)=4x^5(x+5)^2[/tex]

When f(x)=0, you get that

[tex]4x^5(x+5)^2 = 0\\\\x=0 $ or $ x = -5[/tex]

This means that the graph intersects the x-axis at points (0,0) and (-5,0). But:

1. since the degree at term [tex]x^5[/tex] is odd, point (0,0) is x-intercept;

2. since the degree at term [tex](x+5)^2[/tex] is even, point (-5,0) is the tangent point (see the attached graph of the function).

Hence, The graph crosses the x-axis at x = 0 and touches the x-axis at x = –5.

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Answer: 18%

Step-by-step explanation:

I gogled

The shape will be rectangular.

In statistics, uniform distribution refers to a type of probability distribution in which all outcomes are equally likely. A deck of cards has within it uniform distributions because the likelihood of drawing a heart, a club, a diamond, or a spade is equally likely. A coin also has a uniform distribution because the probability of getting either heads or tails in a coin toss is the same.The uniform distribution can be visualized as a straight horizontal line, so for a coin flip returning a head or tail, both have a probability p = 0.50 and would be depicted by a line from the y-axis at 0.50.

From the definition of a uniform probability distribution, since it has a constant probability across a given interval, then it has a rectangular shape. Note also that another term for the uniform probability distribution is the rectangular distribution. Therefore, the correct answer is c.

Thus, option (c) will be the correct option.

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The area of a triangle whose sides are 4.5 cm and 1 cm and perimeter 10.5 cm is 2.045 square cm

The area for the triangle whose perimeter and side is given is solved by the formula

A= √(s(s ﹣ a) (s ﹣ b) ( s ﹣ c))

where:

a, b, and c are the sides of the triangle

s = perimeter / 2

perimeter = a + b + c

10.5 = 4.5 + 1 + c

c = 10.5 - 5.5

c = 5

s = (a + b + c) /2

s = 10.5/2

s = 5.25

substituting for s a b and c

A= √(s(s ﹣ a) (s ﹣ b) ( s ﹣ c) )

A= √(5.25 (5.25 ﹣ 4.5) (5.25 ﹣ 1) (5.25 ﹣ 5) )

A = √4.18358

A = 2.045 square cm

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The Theoretical yield of solid precipitate is 1.42g/mol

Now, consider solid precipitate as cacl2

let us take the mass of cacl2 and calculate the moles of cacl2.

Mass of CaCl2 =2.0 g

By, default the molar mass of CaCl2 =110.98 g/mol

To calculate the Moles we have a formula:

Moles=Given mass*1 mol/Molar mass of a precipitate.-----(1)

substitute the values in equation (1)

Moles of CaCl2 =2.0 g * 1 mol/110.98g

                           = 0.018 mol

Take another solid precipitate:

Mass of K2Co3=2.0 g

The molar mass of K2Co3 =138.205 g/mol

Now calculating the moles of K2Co3

substitute the values in equation(1)

Moles of K2Co3 =2.0 g * 1 mol/ 138.205g

                             =0.0145 moles

According to balanced equation 1mole of CaCl2 reacts with 1 mole of K2CO

Thus, 0.018 moles of CaCl2 will react with 0.018 moles of K2CO3

And,0.0145 moles of K2CO3 will produce 0.0145 moles of CaCO3

Molar mass of CaCO3 =100.0869 g/mol

Theoretical yield of CaCO3 =moles of CaCO3 *molar mass of CaCO3

                                                =0.0145 moles * 100.0869 g/mol

                                                 =1.45g/mol

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Answer:D

Step-by-step explanation: 610/488= 1.25 or 5/4

A system of equation is 1680mi3hr = p−w×600×2hr -p + w  for a jet airliner travels 1680 miles in 3hours with a tail wind.

Let p be  the speed of the jet airliner

and w  be the speed of the tail wind

It takes the plane 3 hours to go 1680 miles when a jet airliner travels with a tail wind and and 3.5 hours to go 1680 miles against the wind.. So, using system of equations we get

1680mi3hr = p−w×600×2hr = p + w

Solving for the left sides we get:

200mph = p - w

300mph = p + w

Now solve for one variable in either equation, we use

200mph = p - w

Add w to both sides:

p = 200mph + w

Using the value of x, we can found the value of w using system of equations.

300mph = (200mph + w) + w

Combine like terms:

300mph = 200mph + 2w

Subtract 200mph on both sides:

100mph = 2w

On dividing by 2:

50mph = w

So the speed of the tail wind is 50mph.

Therefore, 200mph = p - 50mph

Add 50mph on both sides:

250mph = p

Hence, speed of jet airliner is 250mph.

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Hence,  when [tex]n=10[/tex] the given inequality is true.

What is the inequality?

An inequality is said to be sharp if it cannot be relaxed and still be valid in general.

Here given that,

Which integer will make the inequality [tex]2(n + 2) < 5(n -1)[/tex] true.

So,

[tex]2(n + 2) < 5(n-1)[/tex]

When

[tex]n=10\\\\\\2(10+2) < 5(10-1)\\\\2(12) < 5(9)\\\\24 < 45[/tex]

Hence,  when [tex]n=10[/tex] the given inequality is true.

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The alkali metals, which are located in Group 1A of the periodic table, are the most reactive metals.

The blue column on the left of the periodic table contains the alkali metals, which are the most reactive metals. As we move down column (group) one, which is depicted in blue, their responsiveness improves.

What are Alkali metals ?

Alkali metals are those that react with water to produce strong bases.

It is composed of six elements collectively referred to as the lithium family. These metals have one electron in their outermost shell, making them extremely reactive elements of the periodic table.

A few instances of alkali metal

lithium (Li), sodium (Na), rubidium (Rb), potassium (K), francium (Fr) and  Caesium  (Cs).

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Answer:

y - 2 = - [tex]\frac{3}{4}[/tex] (x + 8)

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = - [tex]\frac{3}{4}[/tex] and (a, b ) = (- 8, 2 ) , then

y - 2 = - [tex]\frac{3}{4}[/tex] (x - (- 8) ) , that is

y - 2 = - [tex]\frac{3}{4}[/tex] (x + 8)

Answer:

  y = 90°

Step-by-step explanation:

You want the value of y in the diagram showing y as the angle at the base where the isosceles triangle a.pex angle bisector meets the base.

The angle sum theorem tells you the sum of angles in a triangle is 180°.

Consider the large outside triangle. The sum of its angles is ...

  60° +2x +60° = 180°

  2x = 60° . . . . . . . . . . . . subtract 120°

  x = 30° . . . . . . . . . . divide by 2

Now, consider the left smaller triangle. The sum of its angles is ...

  60° +x +y = 180°

  60° +30° +y = 180° . . . . . . use the known value of x

  y = 90° . . . . . . . . . . . . subtract 90°

__

Additional comment

The a.pex angle bisector of an isosceles triangle is always an altitude that meets the base at right angles. The meeting point is the midpoint of the base, so that segment is also a median.

The halves of the isosceles triangle are congruent right triangles, so the base angle is complementary to the angle marked x.

The ratio of basketballs to soccer balls is 2 : 1

The quantity which would be written first if basketballs to soccer balls is 2 : 1 is basketball

This refers to a number representing a comparison between two or more named things.

If the ratio of basketballs to soccer balls = 2 : 1

This means,

Basketball : soccer ball = 2 : 1

Therefore, Basketball is the quantity which would be written first because it comes first in the given expression.

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Answer:

There are 1,680 possible committees if there have to be at least two housekeepers.

Step-by-step explanation:

The angular velocity of the sphere at the bottom of the incline is 88.1 rad/s.

In physics, angular velocity or angular speed, also recognized as angular frequency vector, is a pseudovector portrayal of how fast the angular position or orientation of an object changes over time.

So, angular velocity will be:

mg(h sinθ) = 1/2 Iω² + 1/2mv²

I of solid sphere = 2/5 mr²

Hence,

mg(h sinθ) = 1/2 (2/5 mr²) ω² + 1/2 mv²

Now remove the mass:

g h sin θ = 1/5 r² ω² + 1/2 v²

ω = v/r, v = ωr

Now, calculate angular velocity as follows:
g h sin θ = 1/5 r² ω² + 1/2 (ωr)²

g h sin θ = (7/10) r² ω²

ω² = 10 g h sin θ/7 r²

ω = √10 g h sin θ/7 r²

  = √10 (9.8) (2.1) sin 25° / 7 (0.04)²

  = 88.1 rad/s

Therefore, the angular velocity of the sphere at the bottom of the incline is 88.1 rad/s.

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Complete question:
An 8.0 cm diameter, 400 g sphere is released from rest ta the tip of a 2.1 m long, 25-degree incline. It rolls, without slipping, to the bottom. What is the sphere's angular velocity at the bottom of the incline?

Answer:

original fraction = [tex]\frac{4}{5}[/tex]

Step-by-step explanation:

let the denominator of the fraction be x then the numerator is x - 1 , so

original fraction is

[tex]\frac{x-1}{x}[/tex]

if 1 is added to the numerator and 5 to the denominator , then fraction is

[tex]\frac{-1+1}{x+5}[/tex] = [tex]\frac{x}{x+5}[/tex]

equate this to [tex]\frac{1}{2}[/tex]

[tex]\frac{x}{x+5}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

2x = x + 5 ( subtract x from both sides )

x = 5

then original fraction is

[tex]\frac{x-1}{x}[/tex] = [tex]\frac{5-1}{5}[/tex] = [tex]\frac{4}{5}[/tex]

Answer:

Below

Step-by-step explanation:

Original fraction   (x-1) / x          <====given   (use in final step below)

Altered fraction   (x-1  +1) / (x+5)  = 1/2     <====solve this  for 'x'

                                   x / (x+5) = 1/2      cross multiply

                                        2x = x+5

                                           x = 5

So original fraction was   4/5

Answer: (3, -3) and (18, -3) is 0

Step-by-step explanation:

The slope of a line is a measure of the line's steepness, and it is calculated by taking the difference in the y-coordinates of two points on the line, divided by the difference in their x-coordinates. In this case, the line passes through the points (3, -3) and (18, -3), and the y-coordinates of both points are -3. Therefore, the difference in the y-coordinates is 0, and the slope of the line is 0.

To write this answer in simplest form, we can simply express the slope as 0/1, which can be simplified to 0. Therefore, the slope of the line that passes through the points (3, -3) and (18, -3) is 0.

Answer:

0

Step-by-step explanation:

We can find the slope of the line given two points

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

    = ( -3 - -3)/(18 -3)

    = (-3+3)/(15

   = 0/15

   = 0