The ratio of top dogs to fat cats was 24 to 19. if they were 152 fat cats, how many top dogs were there?

Therefore, the probability of the first case : 94.5% and second case:9.7%

the likelihood that an event will take place. The proportion of feasible outcomes to outcomes in an exhaustive set of equally likely outcomes that result in a particular event. a field of mathematics that focuses on the investigation of probability.

Here,

Thus, the probabilities of following cases comes out to be:

1) The odds that either the pedestrian or the driver weren't are

=>(246+603+83)*100/986

=>(932/986)*100 =94.5%

2) The likelihood that both incidents involved inebriated pedestrians is equal to

=>(305/978)*(304/977)*100 = 9.7%

Therefore, the probability of the first case : 94.5% and second case:9.7%

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1. We can prove these triangles are congruent through J. SSS.

2. A triangle with 3 congruent angles is called an equilateral triangle.

If all three corresponding sides are equal and all three corresponding angles are equal in measure, two triangles are said to be congruent. These triangles can be moved, rotated, flipped, and turned to look exactly the same. They coincide if they are repositioned.

SSS rule states that two triangles are congruent if all three sides of one triangle are equivalent to the corresponding three sides of the other triangle.

An equilateral triangle has all three sides and angles equal.

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Answer:

A circle is formed.

Step-by-step explanation:

When a plane, parallel to the base of a cone, slices a cone, a circle is formed

and for proof:

In linear equation ,The correct order from least time to greatest time is: Andy, Beth, Cindy.

Describe a linear equation using an example.

An equation with only one variable is referred to as a linear equation in one variable.

                   It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value. One such linear equation in one variable is 9x + 78 = 18.

Consider the provided information,

Andy walked [tex]2\frac{3}{4}[/tex]  mi at a constant speed of [tex]2\frac{1}{2}[/tex] mi/h.

As we know

       Time = distance/speed

           = [tex]\frac{2\frac{3}{4} }{2\frac{1}{2} }[/tex]

            =  [tex]\frac{11/4}{5/2}[/tex]

           = 11/40

Therefore, Andy takes 1.1 hours.

Beth walked 1 1/2 mi at a constant speed of 1 1/8 mi/h .

  time = [tex]\frac{1 1/2}{ 1 1/8}[/tex]

           = 3/2/ 9/8

           = 4/3

Therefore, Beth takes 1.33 hours.

Cindy walked for 1 h and 24 min at a constant speed of 1[tex]\frac{1}{4}[/tex] mi/h.

   1  hour 24 min   =  1 + 24/60   = 1.4 hours

    Therefore Cindy takes 1.4 hours.

Andy spent least time i.e 1.1 hours and Cindy spent greatest time i.e 1.4 hours.

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a) The velocity of the particle is described by v(t) = - 3 · t² + 12 · t - 9.

b) The particle is at rest when t = 1 s. and t = 3 s.

c) The particle changes its direction when t = 1 s. and t = 3 s.

d) The particle is moving right when 0 s < t < 1 s and t > 3 s and left when 1 s < t < 3 s.

e) The acceleration of the particle is described by a(t) = a(t) = - 6 · t + 12.

f) The velocity increases at t = 1 s.

g) The particle has a total distance of 54 meters.

In the statement we find the function of a particle that describes its position (y), measured in meters, in time (t), in seconds. Herein we shall analyze the function to determine all important features.

a) The velocity of the particle (v), in meters per second, is the first derivative of the function position:

v(t) = - 3 · t² + 12 · t - 9

b) The particle is at rest when v(t) = 0. Now we proceed to determine the roots of the resulting polynomial:

- 3 · t² + 12 · t - 9 = 0

t = 3 s. or t = 1 s.

c) The particle changes its direction when v(t) = 0. Then, this change happens in t = 1 s and t = 3 s.

d) The particle is moving right when v(t) > 0, then:

(t - 1) · (t - 3) > 0

There are two possible intervals: (i) 0 s < t < 1 s, (ii) t > 3 s. The particle is moving left when 1 s < t < 3 s.

e) The acceleration is the second derivative of function position, thus:

a(t) = - 6 · t + 12

f) The velocity increases when a(t) > 0. Then, the acceleration at t = 1 s is:

a(1) = - 6 · 1 + 12

a(1) = 6

The velocity is increasing at t = 1 s.

g) The total distance (s), in meters, traveled is determined by the following expression:

s = |x(1) - x(0)| + |x(3) - x(1)| + |x(6) - x(3)|

s = |7 - 11| + |11 - 7| + |- 43 - 11|

s = |- 4| + |4| + |- 54|

s = 54

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a) The percentage reduction in the price of the television each time is as follows:

b) The absolute change after the two reductions amounting to $100 is that the price of the television is now $380.

c) The overall percentage decrease in the price of the television is 20.83%.

The percentage is the ratio.

The percentage is computed as the quotient of the smaller value (numerator) over the larger value (denominator), between two values.

Percentages are depicted using the percentage sign (%) to show that the value is expressed over 100.

Price of the television = $480

First price reduction = $50

New price after the first price reduction = $430 ($480 - $50)

Percentage reduction in price = 10.42% ($50/$480 x 100)

Second price reduction = $50

New price after the second price reduction = $380 ($430 - $50)

Percentage reduction in price = 11.63% ($50/$430 x 100)

Overall percentage decrease = 20.83% ($100/$480 x 100)

Thus, overall, the price of this television decreased by 20.83 percent.

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2.1m/s is the tip of his shadow moving when he is 15 m from the pole

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

x is the distance from the man to the pole, and y is the distance from the tip of the man's shadow to the pole. i assume the man and pole are standing straight up, which means the 2 triangles are similar.

(y-x)/y=2/6

(y-x)/y=1/3

Apply cross multiplication

3(y-x)=y

3y-3x=y

2y=3x

y=3/2x

differentiate both sides with respect to t or time.

dy/dt=3/2dx/dt

By given dx/dt=1.4m/s

dy/dt=3/2×1.4

dy/dt=2.1m/s

Hence, 2.1m/s is the tip of his shadow moving when he is 15 m from the pole

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Answer:Yes

Step-by-step explanation:It changes the answer,

Answer:

Step-by-step explanation:

nope

Example:

5+(6+3)                   (+)  (+) = +

5+9= 14

Answer:

D

Step-by-step explanation:

x=9 and y=4 is given in the graph, this makes the answer between B and D

Since y=-⅔x+10 and y=x-5, 4=-⅔(9)+10 and 4=9-5

So the answer is D

To find the domain of the expression 24^(sqrt(5x^2-8x)+1)+4=332^(sqrt(5x^2-8x)), we need to consider the values of x for which the expression is defined.

First, we need to consider the square root term, sqrt(5x^2-8x). The square root of a number is only defined for nonnegative values, so we need to find the values of x for which 5x^2-8x is nonnegative. We can do this by setting 5x^2-8x equal to 0 and solving for x:

5x^2-8x=0

5x(x-8)=0

We can see that x=0 and x=8 are the solutions to this equation. Since the square root of a negative number is not defined, the expression 24^(sqrt(5x^2-8x)+1)+4=332^(sqrt(5x^2-8x)) is only defined for x values that are greater than or equal to 0 and less than or equal to 8. This means that the domain of the expression is x ∈ [0, 8].

To solve the equation 24^(sqrt(5x^2-8x)+1)+4=332^(sqrt(5x^2-8x)), we can start by isolating one of the exponential terms on one side of the equation. Let's isolate the term 2^(sqrt(5x^2-8x)):

24^(sqrt(5x^2-8x)+1)+4=332^(sqrt(5x^2-8x))

22^(2sqrt(5x^2-8x)+1)=332^(sqrt(5x^2-8x))

2^(2sqrt(5x^2-8x)+1)=16.52^(sqrt(5x^2-8x))

2sqrt(5x^2-8x)+1=4.5+sqrt(5x^2-8x)

sqrt(5x^2-8x)=3.5

5x^2-8x=12.25

5x^2-8x-12.25=0

We can use the quadratic formula to solve this equation for x:

x = (-(-8) ± sqrt((-8)^2 - 45(-12.25))) / (2*5)

x = (8 ± sqrt(64 + 97)) / 10

x = (8 ± sqrt(161)) / 10

x = (8 ± sqrt(289)) / 10

x = (8 ± 17) / 10

x = -9/10 or 25/10

Since x must be greater than or equal to 0 and less than or equal to 8, the only solution that is within the domain of the expression is x=25/10, or x=2.5.

Therefore, the solution to the equation 24^(sqrt(5x^2-8x)+1)+4=332^(sqrt(5x^2-8x)) is x=2.5.

what do you mean by domain of a function?

The domain of a function is the set of all input values for which the function is defined. In other words, it is the set of all values that can be plugged into the function as an argument, or input, and produce a valid output

For example, consider the function f(x) = x^2. The domain of this function is all real numbers, since the function is defined for any value of x. However, some functions may not be defined for certain values of x. For example, the function g(x) = 1/x is not defined for x=0 because division by zero is not allowed. In this case, the domain of the function g(x) would be all real numbers except for x=0.

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Answer:

Step-by-step explanation:

oh wow

Step-by-step explanation:

since AD is an altitude (height) of ABC, the angle at D must be 90° (that is the definition of an altitude or height).

so,

90 = x² + 6x + 18

72 = x² + 6x

0 = x² + 6x - 72

the general solution to such a quadratic equation

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = (-6 ± sqrt(6² - 4×1×-72))/(2×1) =

= (-6 ± sqrt(36 + 288))/2 = (-6 ± sqrt(324))/2 =

= (-6 ± 18)/2 = -3 ± 9

x1 = -3 + 9 = 6

x2 = -3 - 9 = -12

so, the 2 solutions are

x = 6

x = -12

Answer: 28055

Step-by-step explanation:

One of the interior angles of the triangle, angle y is equal to 67° and the exterior angle x is equal to 113°.

The interior angles of a triangle have a total sum of 180°.

Considering the triangle with interior angles: y, 51°, and 62° we have that;

y + 51° + 62° = 180°

y + 113° = 180°

y + 113° - 113° = 180° - 113° {subtract 113° from both sides}

y = 67°

the exterior angle x and the angle y lie on a straight line, so they sum up to 180°.

x + 67° = 180°

x + 67° - 67° = 180° - 67° {subtract 67° from both sides}

x = 113°

Therefore, the interior angle y = 67° and the exterior angle x = 113°.

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The length of side DE of the rectangle ABCD is 11/5 units .

What is rectangle?

In euclidean plane geometry, a rectangle may be a quadrilateral with four right angles. It also can be outlined as: an angular quadrilateral, since angular means all of its angles square measure equal; or a tetragon containing a right angle.

Main body:

given:

AE = 4x+8       -----------(1)

CE = 7x - 3      -----------(2)

as we know diagonal of rectangle bisect each other , which means AE = CE

using the property , we get

4x+ 8 = 7x -3

taking like terms to one side,

7x - 4x = 8+3

3x = 11

x = 11/3

put the value of x in any equation,

AE = 4(11/3) +8

AE = 44/3 +24/3

AE = 68/3

as AE = DE

Hence the value of DE is 68/3 units.

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Answer:

third option

Step-by-step explanation:

sinX = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{YZ}{XY}[/tex] = [tex]\frac{3}{\sqrt{34} }[/tex]

tanY = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{XZ}{YZ}[/tex] = [tex]\frac{5}{3}[/tex]

The largest 15-year term policy he can buy without spending more than $800 per annum is $148,699.

What is insurance?

An agreement to pay compensation to another party in the event of a specific loss, damage, or injury is known as insurance, and it is a way to protect against financial loss. It is a type of risk management that is mostly applied to protect against the risk of a potential or unforeseen loss.

The terms "insurer," "insurance company," "insurance carrier," and "underwriter" all refer to organizations that offer insurance.

Given: Justin, age 52, wants to pay no more than $800 a year in life insurance. If the annual life insurance premium rate (per $1000 of face value) is $5.38.

Annual life insurance premium rate = $5.38 per $1000 of the face value.

Largest 15-year term policy possible

= [tex]\frac{800}{5.38}*1000 = 148,698. 885 = 148, 699[/tex]

Therefore, the largest 15-year term policy he can buy without spending more than $800 per annum is $148,699.

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Answer: 24. The remainder is 7

Step-by-step explanation:

We are told that 6 is two-fifths of the brownies. So we can figure it out as such:

[tex]\frac{6}{x} = \frac{2}{5}[/tex]

Cross multiply

6 * 5 = x * 2

30 = 2x

Divide both sides of the equal sign by 2 to get x by itself

[tex]\frac{30}{2} =\frac{2x}{2}[/tex]

15 = x

15/5 = 3. Every third piece is 1/5 of the pan.

Total amount payable including sales tax and tip =  $68.12

A sales tax is a tax levied by a government on the sale of certain goods and services. Generally, laws allow the seller to collect tax funds from the consumer at the point of sale. A use tax is a tax on goods or services paid directly to a governing body by a consumer.

Given:

Bill at dinner was before tax and tip = $58.24

Sales tax = 6%

Tip = 18%

As per the question:

first, we will calculate the amount payable after adding tax.

The amount payable after adding sales tax = bill + 6% sales tax of the bill

The amount payable after adding sales tax = 58.24 + [tex]\frac{6}{100} 58.24[/tex]

Amount payable after adding sales tax = A = $57.73

Now we will calculate the total amount payable after adding the tip.

Total amount payable = A + 18% of A

Total amount payable = $57.73 + 18% of $57.73

Total amount payable =  57.73 + 10.40

Total amount payable including sales tax and tip =  $68.12

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Total amount payable including sales tax and tip =  $68.12

A sales tax is a tax levied by a government on the sale of certain goods and services. Generally, laws allow the seller to collect tax funds from the consumer at the point of sale. A use tax is a tax on goods or services paid directly to a governing body by a consumer.

Given:

Bill at dinner was before tax and tip = $58.24

Sales tax = 6%

Tip = 18%

As per the question:

first, we will calculate the amount payable after adding tax.

The amount payable after adding sales tax = bill + 6% sales tax of the bill

The amount payable after adding sales tax = 58.24 +

Amount payable after adding sales tax = A = $57.73

Now we will calculate the total amount payable after adding the tip.

Total amount payable = A + 18% of A

Total amount payable = $57.73 + 18% of $57.73

Total amount payable =  57.73 + 10.40

Total amount payable including sales tax and tip =  $68.12

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The Inequality expression that shows the above situation is x ≥ 75.

The word "inequality" describes the state of being unequal, In Inequalities like in equations, we compare two values but not with the equal signs here we use signs like Not equal, less than, less than or equal to; greater than or greater than or equal to, etc.

Here we have,

The minimum amount required to open a new checking account is $ 75        

Let us assume that we used $ x dollars to open a bank account

By the given data,

The amount is a minimum of $ 75  

=> x ≥ 75      [ x is less than or equal to $ 75 ]

Therefore,

The Inequality expression that shows the above situation is x ≥ 75.  

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You will able to deposit  X=7000.182500⁴⁷⁴⁵/182537⁴⁷⁴⁵now under the scenario Below.

A minimum deposit or initial  deposit is the lowest minimum  amount of the  money required to open an object account with all the  financial institution, such as the bank or the brokerage firm.

Based on the given scenario the formulate is-

X×(1+7.4%÷ 365)¹³×365 = 70000

Now we have to solve the equation -

X×(1+0.074/365)¹³×365=70000

Convert the number

X× 1+ (74/365000)¹³×365=70000

Now reduce

X×(1+37/182500)¹³×365=70000

Now we have to calculate=

X× (1+ 37/182500)⁴⁷⁴⁵=70000

We have to transfer the edition

X× (1+ 37/182500)⁴⁷⁴⁵=70000

Devide both side

X= 70000/ ( 182537/182500)⁴⁷⁴⁵

By Calculation we can get

X= 70000×182500^4745/182537⁴⁷⁴⁵

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The required unit rate for the dollars per class is 16 dollars per class,

Given that,
The "constant of proportionality" between to cost and the number of classes is 16. The unit rate for dollars per class is to be determined.

proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

Here,
Let, y be the dollars is directly proportional to the x classes,
According to the question,
y = kx
k = 16
y = 16x
Now,
y/x = 16 dollars per class

Thus, the required unit rate for the dollars per class is 16 dollars per class,

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Answer:

asa

Step-by-step explanation:

there Is angle

there is side

there is angle but not shown

When the truck cost 60,000 it depreciate in value 4000 per year, the model is 60000 - 4000x

Equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario

In this case, the truck cost 60,000 it depreciate in value 4000 per year.

Let the number of years be x.

The linear model in the representation will be:

60000 - 4000(x)

= 60000 - 4000x

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The point estimate proportion that they would seriously consider purchasing an electric-powered vehicle is 0.468.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

let y be 2326 said that they would seriously consider purchasing an electric-powered vehicle and x be the sample of 4972 car owners.

∴ The point estimate proportions is y = px.

2326 = 4972p.

p = 2326/4972.

p = 0.468.

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The two column proof is written as follows

Statement                                                           Reason

line UT ≅ line GH                                     given

line UV ≅ line GH                                     given

< U ≅ < G                                                  given

Δ TUV  ≅  Δ BEC                                     Congruent triangles by SAS

< F ≅ < V                                                  CPCTC theorem

Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules

Some of the rules include

Side -  Side - Side = SSS

Side - Angle - Side = SAS

Angle - Side - Angle = ASA

Angle - Angle - Side = AAS

Hypotenuse and one leg = HL

The problem requires the prove by Side - Angle - Side = SAS to ensure that the the triangles are congruent

The SAS have it that the two sides of the triangles being compared should be equal and the included angles are equal

The given sides and the included angle are

line UT ≅ line GH    Side

< U ≅ < G                  included angel

line UV ≅ line GH    Side

< F ≅ < V                  CPCTC theorem

According to the CPCTC theorem, whenever two triangles are congruent, then each of their corresponding parts are also congruent. In other words, if two or more triangles are congruent, then their corresponding sides and angles are also congruent or equivalent in size.

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Answer:

50

Step-by-step

Answer:

clap

Step-by-step explanation:

since the rhythm repeats every 5, then you will be clapping on the fifty first beat.  on the 6th beat in the rhythm, its a clap, so since 50/5 is 10 then the next will be clap