12. Name the theorem or postulate that can be used to prove that these triangles
are similar.

Answer:

Step-by-step explanation:

quit

Answer:

10 meters

Step-by-step explanation:

Use the pythagorean theorem. 'c' represents the length of the hypotenuse of a right triangle.

[tex]a^{2} +b^{2} =c^{2}[/tex]

[tex]6^{2} +8^{2} = 100\\[/tex]

[tex]c^{2} =100\\c=10[/tex]

Take the sq rt of 100 which is 10

Answer:

10 meters

Step-by-step explanation:

hypotenuse = √(6² + 8²)

hypotenuse = √(36 + 64)

hypotenuse = √100

hypotenuse = 10 m

Answer:√(9) is a rational number.

Step-by-step explanation:

Answer:This is a rational numer because it can be expressed in the form of p/q

Step-by-step explanation:If a number can be expressed int he form of p/q then its rational.

to calculate the total price for car wash services. A base car wash is $10. A dictionary with each additional service and the corresponding cost has been provided. Two additional services can be selected. A '-' signifies an additional service was not selected. Output all selected services, according to the input order, along with the corresponding costs and then the total price for all car wash services.

"""

Python version: 3.6

Python program to calculate the total price for car wash services

"""

# dictionary containing the services as keys and their price as values

services = {'Air freshener' : 1, 'Rain repellent' : 2, 'Tire shine' : 2, 'Wax' : 3, 'Vacuum' : 5}

# variable to store the base car wash price

base_wash = 10

# variable to store the total price

total = 0

# read the 2 services

service_choice1 = input()

service_choice2 = input()

print("ZyCar Wash")

# display the base wash price

print("Base car wash -- ${}".format(base_wash))

total += base_wash # add base_wash to total

# first service read is in services dictionary

if service_choice1 in services:

   total += services[service_choice1] # add the price for the service to total

   # display the service and its price from dictionary

   print("{} -- ${}".format(service_choice1, services[service_choice1]))

# second service read is in services dictionary    

if service_choice2 in services:

   total += services[service_choice2] # add the price for the service to total

   # display the service and its price from dictionary

   print("{} -- ${}".format(service_choice2, services[service_choice2]))

# display the total price  

print("----")

print("Total price: ${}".format(total))    

# end of program

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The given function is continuously decreasing for x = (-∝, 1).

Given function,

f(x) = | 4(x - 1) | + 2

⇒ f(x) = |4||x-1| + 2

⇒ f(x) = 4|x - 1| + 2

If x ≥ 1, |x - 1| = x - 1

⇒ f(x) = 4(x - 1) + 2 = 4x - 4 + 2

⇒ f(x) = 4x - 2

On differentiating on both sides:

f'(x) = 4 > 0

⇒ Function is continuously increasing for x ≥ 1.

If x < 1, |x - 1| = -(x - 1) = 1 - x

⇒ f(x) = 4(1 - x) + 2 = 4 - 4x + 2

⇒ f(x) = 6 - 4x

On differentiating on both sides:

f'(x) = -4 > 0

⇒ Function is continuously decreasing for x < 1.

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Part A: The length (number of hours) of each CD is 0.875 hours.

Part B: The Hernandez family can listen each for 0.875 hours

Given that,

The Hernandez family is on a road trip. They have been driving for 3 1/2 hours. They have listened to 4 CDs of equal length.

What is an equation?

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Part A

Let the length (number of hours) of each CD be x.

Now, x = 7/2 = 3.5/4 = 0.875

= 0.875 hours

Part B

If the family has 1 hour of their drive left, still they can listen 4 CDs.

Therefore, the Hernandez family can listen each for 0.875 hours.

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Answer:

D.  8

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}\dfrac{1}{3}x+\dfrac{1}{4}y=1\\\\2x-4y=-30\end{cases}[/tex]

Multiply the first equation by -6:

[tex]\implies -6 \cdot \dfrac{1}{3}x+-6 \cdot \dfrac{1}{4}y=-6 \cdot 1[/tex]

[tex]\implies -2x-\dfrac{3}{2}y=-6[/tex]

Add this to the second equation to eliminate x:

[tex]\begin{array}{rrcccl}&2x &- &3y& = &-30\\\phantom{\dfrac12}+ &(-2x& - &\frac{3}{2}y &= &\;\;-6)\\\cline{2-6} \phantom{\dfrac12}&0&-&\frac{9}{2}y&=&-36\\ \cline{2-6}\end{array}[/tex]

Solve the equation for y:

[tex]\implies -\dfrac{9}{2}y=-36[/tex]

[tex]\implies \dfrac{9}{2}y=36[/tex]

[tex]\implies 9y=72[/tex]

[tex]\implies y=\dfrac{72}{9}[/tex]

[tex]\implies y=8[/tex]

The factors of the given expression are [tex]\frac{(x-1)^{2}}{x^{\frac{3}{2} }}[/tex]  .

In mathematics, a factor is a divisor of a given integer that divides it exactly, leaving no leftovers. We may employ a variety of techniques, including the division method and the multiplication method, to determine the factors of a given integer. When we need to split anything into equal rows and columns, compare prices, exchange money, and other real-world scenarios, we employ factors.

The given expression is [tex]x^{\frac{-3}{2}} -2x^{\frac{-1}{2} }+ x^{\frac{1}{2} }[/tex]

Apply the exponential rule [tex]a^{b+c}= a^{b}a^{c}[/tex], so we can write

= [tex]x^{\frac{-3}{2}} -2x^{\frac{-1}{2} }+ x^{\frac{-1}{2}}(x^{2\times\frac{1}{2}})[/tex]

Factor out the common term [tex]x^{\frac{-1}{2} }[/tex]

= [tex]x^{\frac{-3}{2}} + x^{\frac{-1}{2}}(-2+x^{2\times\frac{1}{2}})[/tex]

Apply the exponential rule [tex]a^{b+c}= a^{b}a^{c}[/tex],

= [tex]x^{\frac{-3}{2}}-2 x^{1}x^{\frac{-3}{2} }+ x^{2}x^{\frac{-3}{2}}[/tex]

Factor out the common term [tex]x^{\frac{-3}{2} }[/tex]

= [tex]x^{\frac{-3}{2} }(1-2x+x^{2})[/tex]

= [tex]x^{\frac{-3}{2} }(x-1)^{2}[/tex]

= [tex]\frac{(x-1)^{2}}{x^{\frac{3}{2} }}[/tex]

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The equation to represent the area of the.large office is 3.5l = 42.

An equation is simply used to illustrate the relationship between the variables given.

In this case, the large office desk has an area of 42ft² anz the width is 3.5 feet. It should be noted that the area is calculated as:

= Length × Width

Therefore, l × w = 42

where w = 3.5

l × 3.5 = 42

3.5l = 42

Therefore, the equation is 3.5l = 42

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Answer:

=====================

Use identities:

Answer:

[tex]\textsf{11.} \quad 4x^2+ \sqrt{1-16x^2}\sqrt{1-x^2}[/tex]

[tex]\textsf{12.} \quad \dfrac{1 - \sqrt{x}}{1 + \sqrt{x}}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6 cm}\underline{Sine Double Angle Identity}\\\\$\sin (A \pm B)=\sin A \cos B \pm \cos A \sin B$\\\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{5 cm}\underline{Inverse Trigonometric Identities}\\\\$\sin(\cos^{-1}x)=\sqrt{1-x^2}$\\\\$\cos(\sin^{-1}x)=\sqrt{1-x^2}$\\\end{minipage}}[/tex]

Given trigonometric expression:

[tex]\sin ( \sin^{-1} 4x + \cos^{-1} x)[/tex]

Using the Sine Double Angle Identity:

Therefore:

[tex]\begin{aligned}\sin ( \sin^{-1} 4x + \cos^{-1} x)&=\sin(\sin^{-1}4x) \cos (\cos^{-1}x)+ \cos(\sin^{-1}4x) \sin(\cos^{-1}x)\\&=4x \cdot x+ \cos(\sin^{-1}4x) \sin(\cos^{-1}x)\\&=4x^2+ \cos(\sin^{-1}4x) \sin(\cos^{-1}x)\\&=4x^2+ \sqrt{1-(4x)^2}\sqrt{1-x^2}\\&=4x^2+ \sqrt{1-16x^2}\sqrt{1-x^2}\end{aligned}[/tex]

[tex]\boxed{\begin{minipage}{5 cm}\underline{Tan Double Angle Identity}\\\\$\tan (A \pm B)=\dfrac{\tan A \pm \tan B}{1 \mp \tan A \tan B}$\\\end{minipage}}[/tex]

Given trigonometric expression:

[tex]\tan(\tan^{-1}1-\tan^{-1}\sqrt{x})[/tex]

Using the Tan Double Angle Identity:

Therefore:

[tex]\begin{aligned}\tan(\tan^{-1}1-\tan^{-1}\sqrt{x})&=\dfrac{\tan (\tan^{-1}1) - \tan (\tan^{-1}\sqrt{x})}{1 + \tan (\tan^{-1}1) \tan (\tan^{-1}\sqrt{x})}\\\\&=\dfrac{1 - \sqrt{x}}{1 + 1 \sqrt{x}}\\\\&=\dfrac{1 - \sqrt{x}}{1 + \sqrt{x}}\\\\\end{aligned}[/tex]

You could use

2x((2x5)+5+2)+1

The margin of error is approximately 0.3

To answer the question, we must figure out what margin of error corresponds to a 90% confidence level. The definition of the margin of error used to create confidence intervals for the population mean is as follows;

Mean = μ = 20.6

Standard deviation = σ = 2.7

Number of students = n = 225

the result of the sample mean's standard error and the accompanying z-score. The formula used to compute the sample mean's standard error is;

⇒  σ / √n

The z-score associated with a 90% confidence level:

From the given table z-score is 1.645

Therefore, the margin of error;

σ / √n * 1.645 = 2.7/√225 * 1.645

                      = 0.296

Hence, the margin of error is approximately 0.3

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Answer:

Approximately 0.3 of an error is allowed.

Given data in question

Confidentialevel=90%

Mean = μ = 20.6

2.7 as the standard deviation

N = 225 students are enrolled.

the outcome of the standard error of the sample mean and the corresponding z-score. The formula used to determine the standard error of the sample mean is;

⇒ σ / √n

The z-score for a 90% degree of confidence is:

Z-score for the provided table is 1.645.

Consequently, the error margin;

σ / √n * 1.645 = 2.7/√225 * 1.645

= 0.296

Consequently, the margin of error is roughly 0.3.

Convenience sampling is not a type of statistical sampling.

What is statistical sampling?

Sampling techniques in a statistical study refer to how participants are chosen from the population to participate in the study.

If a sample isn't chosen at random, it will likely be skewed in some way, and the results might not be generalizable.

Main body:

Simple random sample:

Each individual and group of individuals have the same chance of being selected for the sample. To obtain a basic random sample, one needs technology, random number generators, or some other type of chance mechanism.

stratified Random sample :

The population is first divided into sections. There are some people from each group in the overall sample. Each group's participants are chosen at random.

Cluster sampling:

Grouping the population first, a cluster random sample is taken. Every member of some of the groups makes up the overall sample. The selection of the groups is random.

Hence Convenience sampling is not a type of statistical sampling.

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Answer:

534,000

Step-by-step explanation:

12 days pass from may 10 to may 22 so we replace x with 12

190,000(1.09)^12
190,000(2.81266)

534406.309

But rounded to the nearest thousands

534,000

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We can see that the p-value for above test is less than α=0.05 and it indicates that we have very strong evidence against H(0) to reject it and we can conclude that there is highly significant relationship between money spent on advertising and sales.

In the given question we have to find is there a statistically significant relationship between money spent on advertising and sales.

Here we have Sales(in $1000) as dependent variable (y) and spend on Advertising (in $1000) as independent variable (x).

The significance of relationship between x and y is given by the significance of regression coefficient of regression of y of x.

So we have to test

H(0): β1=0

H(1): β1≠0

From the table that is given below, we have;

b(1)=3.778221987

se(b(1)) =0.563520732

The test statistic to test the above hypothesis is

t=b(1)/se(b(1))

From the given output, we already have

t=6.704672556

p-value=0.0000146

We can see that the p-value for above test is less than α=0.05 and it indicates that we have very strong evidence against H(0) to reject it, so we reject the H(0) and we can conclude that there is highly significant relationship between money spent on advertising and sales.

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Answer:

Step-by-step explanation:

The slope is determined with two points.

Take the pairs (0, - 9) and (1, - 5).

The slope is:

Answer:

Slope = 4

Step-by-step explanation:

Formula we use,

→ Slope = (y2 - y1)/(x2 - x1)

Then required slope will be,

→ (y2 - y1)/(x2 - x1)

→ (-5 -(-9))/(1 - 0)

→ (-5 + 9)/(1 - 0)

→ 4/1 = 4

Therefore, the slope is 4.

The coordinates of the midpoints of GH are M (4,3) and the coordinates of one endpoints are G (5,-6) the coordinates of the other endpoints are

The co - ordinates of another end point is

(x,y) = (3, 12)

mid point formula:-

Let [tex](x_{1}, y_{1}) and (x_{2}, y_{2})[/tex] be any two end points

Mid point of two given points are

[tex](\frac{x_{1}+ x_{2}}{2}, \frac{y_{1}+ y_{2}}{2} )[/tex]

let (x,y ) be the another end point

given one end point is (5,-6)

now by using mid-point formula , we get

 [tex](\frac{x+5}{2} ,\frac{y-6}{2})[/tex]  this is equating to given mid-point is M(4,3)

now [tex](\frac{x+5}{2}, \frac{y-6}{2}) = (4,3)[/tex]

simplify , we get

[tex]\frac{x+5}{2} = 4 and \frac{y-6}{2} = 3[/tex]

cross multiplication and simplify

x+5 = 8 and y-6 = 6

so x = 3 and y = 12

Hence the another point is (x,y) = (3,12)

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The car is about a year old if it depreciates exponentially at a rate of 9% per year 0.62

In order to know how old the car is, we will use the depreciation formula expressed below:

[tex]P_{t}=P_{0}e^{rt}[/tex]

[tex]P_t[/tex] is the final price = 16000

[tex]P_0[/tex]  is the initial price = 28000

Given the rate of 0.09

Substitute the given parameters into the formula to get the time "t"

[tex]16000 = 28000e^{0.09t}[/tex]

[tex]\frac{16000}{28000} = e^{0.09t}[/tex]

t=0.5714/0.9139

This shows that the car is about a year old if it depreciates exponentially at a rate of 9% per year

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Answer:

How I got the answer:

93 doesn't have an exact square root. So, we need to try numbers that fit with the equation.

x will be less than the square root of 93. Since the square root of 93 is between 9 and 10. The largest perfect square that we can try is 9. Let us see if that number works.

x + x² + √x = 93

9 + 9² + √9 = 93

9 + 81 + 3 = 93

93 = 93 ✔

It does work.

So the number is 9.

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1. When Alice shrank, the height will be 12.05cm.

2. When she grew 10 times, the height will be 1205cm.

1. Since Alice's actual height was 120.5 cm and she shrank to 1/10 of her height, the height will be:

= 1/10 × 120.5

= 12.05 cm

2. If Alice grew to 10 times her normal size, the height will be:

= 120.5 × 10

= 1205cm

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The compression work if the final state is 500 kpa will be 44.32KJ

Step-by-step explanation:

The stated circumstance is;

P₁= 1.0 MPa

T₁ = 250°C

M=0.6 Kg

v₂=0.4v₁

v₁=0.30661 m/sec

P₂=1 Mpa

T₂=250°C

repairs made to the piston;

 W= mP(V2-V1),

W= 0.6*1,000(0.232-0.30661)

W= -44.32\J

illustrates the compression work using (- ve)

Since there is pressure in the final condition, the compression work is 44.32. (KJ)

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Answer:

She purchased 5 boxes

Step-by-step explanation:

17.40 ÷ 3.48 = 5

The largest length each square can be in order to have the least amount of waste from the fabric will be 34.5.

It is defined as a two-dimensional geometry that has four sides and four vertices. The sides of the square are equal in length. It is a regular quadrilateral.

It is given that, Jordan and her grandma are creating a quilt as a result. To make their quilt, they will cut square pieces of cloth. They have already bought three fabric lengths. 30 inches, 48 inches, and 60 inches are the lengths.

The total length of the fabric is,

=30+48+60

=138 inches

The perimeter of a square is,

P = 4a

138 = 4a

a=138/4

a=34.5 inches

Thus, the largest length each square can be in order to have the least amount of waste from the fabric will be 34.5.

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Answer:

The answer is [tex]\frac{4}{13}[/tex].

Step-by-step explanation:

Additive rule:

According to this rule, the probability that events A or B will occur is given by the formula,

[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]

Here,

We know that there are 13 spades and 4 queens in a deck of 52 cards. Also, there is only one queen of a spade.

Then,

[tex]\begin{aligned}P(S)&=\frac{13}{52}\\P(Q)&=\frac{4}{52}\\P(S\cap Q)&=\frac{1}{52}\end{aligned}[/tex]

Therefore, the probability that the card you select is a spade or queen is given by,

[tex]\begin{aligned}P(S\cup Q)&=P(S)+P(Q) -P(S\cap Q)\\&=\frac{13}{52}+\frac{4}{52}-\frac{1}{52}\\&=\frac{16}{52}\\&=\frac{4}{13}\end{aligned}[/tex]

Therefore, the answer is [tex]\frac{4}{13}[/tex].

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The distance covered by bicycle is 1.885 km.

What is distnace?

Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in ordinary language.

Given:  A bicycle wheel with radius 30cm made 1000 revolutions.

We have to find the total distance covered by bicycle.

First to find the circumference of the bicycle wheel.

Circumference = 2πr

where, r is the radius.

Here r = 30.

So,

Circumference = 2 x π x 30 = 60π

Now to find the total distance,

D = circumference x number of revolutions.

D = 60π x 1000

D = 188,495.5592 cm

D = 188,495.5592 /1000 km

D = 1.88 km

Therefore, the distance covered by bicycle is, 1.885 km.

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As per the statement the function which is best suited for this calculation is averageif.

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Caspian Sea is elevated at 92 feet (or 28 meters) below sea level. (globally preferred unit is meters)

On the scale of sea levels, a certain height has been assigned zero elevation. This acts as a reference point for rest of the measurements and is called Mean Sea Level (MSL). It is also known as still water level.

Caspian Sea at 92 feet below sea level means it is 92 feet below MSL. Thus, its elevation is considered 92 feet below sea level.

Global MSL is calculated using the spatial average of the complete ocean's level.

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The required equation of a parabola expressed in vertex form is f(x) = (x + 2)² - 1.

The equation of a parabola expressed in vertex form is

y = a(x - h)² + k

Where a is a multiplier and (h, k) are the coordinates of the vertex

The expression is given in the question as

f(x) = x² + 4x + 3

To complete the perfect square:

We have to add/subtract ( half the coefficient of the x- term )² to x² - 4x

f(x) = x² + 2(2)x + 4 - 4 + 3

f(x) = (x + 2)² - 1

Thus, the required equation of a parabola expressed in vertex form is f(x) = (x + 2)² - 1.

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The instance in question was chosen at random assignment.

Given statement;

Participants should be selected by chance for an experimental or control group so each has an equal probability of being assigned to any of the groups.

The given case is done by Random assignment.

In Mathematical experiments, random assignment refers to the use of chance processes to ensure that each participant has an equal chance of being assigned to any particular group. Participants in studies are divided into several groups at random, such as the experimental group or the treatment group.

It is known as random assignment.

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Answer:

A: $7.50 per cap

Step-by-step explanation:

IM BACCCCKKKKK XD

we use the slope formula of y2-y1/x2-x1

37.5-22.5/5-3

15/2

7.5

So he gets $7.50 per cap

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Answer: He gets $7.50 per cap.

Step-by-step explanation:

If at 3 caps he got $22.50, we'll need to divide $22.50 by 3 to get the cost for a single cap.

$22.50/3 = $7.50

This means that he gets $7.50 per cap.