Myra is taking her first hot-air balloon ride! The balloon was at an altitude of 288 meters until an air current caused it to rise another 36 meters.
What is the altitude of the balloon now?

Linear equations - each backpack costs $14 and 5 cents .

What are linear equations with one variable?

A linear equation is a one-variable equation of a straight line. The variable only has one power, which is 1. Simple algebraic operations are used to solve linear equations in one variable, which can have the form ax+b=0.

First, we categorise one-variable linear equations into one of three categories: identity, conditional, or inconsistent. The variable's identity equation holds true for all possible values.

let us assume that the backpack costs $x.
We are informed that each kit included a backpack and school supplies totaling $18.
there are 4 school supply kits in total,
according to the above conditions we have,

4(18+x)

we are also given that she spent a total of $130, thus,

4 (18+x) = 130

72 + 4x = 130

4x = 130 - 72

4x = 58

dividing both the sides with 4,

x = 58/4

thus, x = 14.5

therefore each backpack costs $14 and 5 cents

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To describe the transformation, dilation by a scale factor of 4 with center of dilation at origin the rule is (x,y)→(4x,4y) and , the coordinates of rectangle Q'R'S'T  will be Q'(-32,20) , R'(-32,28) , S'(-20,28) , T'(-20,20) .

In the question ,

the coordinates of the rectangle QRST are given as Q(-8,5), R(-8,7), S(-5,7), and T(-5,5)  .

we have to to dilate the rectangle by a scale factor of 4 with center of dilation at the origin.

So , to dilate the rectangle by a scale factor of 4 with center of dilation at the origin  we multiply coordinates of the original shape with the dilation factor .

So , the rule of transformation becomes

(x,y)→(4x,4y)

Using the above rule to find the coordinates of the rectangle Q'R'S'T' .

given Q = (-8,5)

So, Q' = (4*(-8),4*5)

Q' = (-32,20)

Given R = (-8,7)

So, R' = (4*(-8),4*7)

R' = (-32,28)

Given S = (-5,7)

So, S' = (4*(-5),4*7)

S' = (-20,28)

Given T= (-5,5)

So, T'  = (4*(-5),4*5)

T' = (-20,20)

hence , the rectangle Q'R'S'T' coordinates are  Q' = (-32,20) , R' = (-32,28) , S' = (-20,28) , T' = (-20,20) .

Therefore , to describe the transformation, dilation by a scale factor of 4 with center of dilation at  origin the rule is (x,y)→(4x,4y) and , the coordinates of rectangle Q'R'S'T will be Q'(-32,20) , R'(-32,28) , S'(-20,28) , T'(-20,20) .

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Multiplying the expression 9x² - (x² - 4)² . 4 + 3x - x² will give -4x⁴ + 40x² + 3x - 64

From the information given, we want to multiply the expression 9x² - (x² - 4)² . 4 + 3x - x². This will be illustrated thus:

Distribute

9x² - (x² - 4)² . 4 + 3x - x².

9x² - (x² - 4)(x² - 4) . 4 + 3x - x².

Now we can open the parentheses. This will be illustrated as:

9x² - 2(x⁴ - 4x² - 4(x² - 4) . 4 + 3x - x³

= -4x⁴ + 40x² + 3x - 64

The value of the expression is -4x⁴ + 40x² + 3x - 64.

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Multiply the expression 9x² - (x² - 4)² . 4 + 3x - x²

The unit rate of the graph is is inches per hour

A graph will hold as many information as the plotter will wish to give it. The information the graph has the more compicated wit will be

The graph plotted is a graph of snowfall in inches against time in hours. The input values of the graph is the time in hours while the snow fall in inches is the output values

The unit rate of graphs is gotten from the the units plotted against the other unit. Here it is inches against hours

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Error might the student have made was in angle 147 as acute angle means angle less than 60°

Acute angles are those that range in size from 0 to 90 degrees and are smaller than 90 degrees. Examples include 60, 30, 45, and other angles. An acute triangle is a triangle with all of its internal angles smaller than 90 degrees. An equilateral triangle, for instance, is an acute triangle because the internal angles are 60°.

Less than 90° of an angle is referred to be an acute angle. An acute angle, for instance, is formed when the time is 11 o'clock between the hour hand and the minute hand. Consequently, acute angles include 30°, 40°, 57°, and others.

Given that : The students are guvena right triangle. One of the acute angles has a measure of 33°. One student saha tbe measure kf the other acute angle is 147°.

As the acute angles are angles less than 90°

and they have measure as 147°

So the error was in measure angle as 147°

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Check the picture below.

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{9})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~7 - (-2)~~)^2 + (~~9 - 7~~)^2} \implies d=\sqrt{(7 +2)^2 + (9 -7)^2} \\\\\\ d=\sqrt{( 9 )^2 + ( 2 )^2} \implies d=\sqrt{ 81 + 4 } \implies d=\sqrt{ 85 }[/tex]

[tex](\stackrel{x_1}{-8}~,~\stackrel{y_1}{-9})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-4}-\stackrel{y1}{(-9)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-8)}}} \implies \cfrac{-4 +9}{3 +8} \implies \cfrac{ 5 }{ 11 }[/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}{(-9)}=\stackrel{m}{ \cfrac{ 5 }{ 11 }}(x-\stackrel{x_1}{(-8)}) \implies {\large \begin{array}{llll} y +9= \cfrac{ 5 }{ 11 } (x +8) \end{array}}[/tex]

The sum of the expression 10,000 + 2,000 + 60 + 1 is 12061

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

10,000 + 2,000 + 60 + 1

The sum of the expression can be calculated using a calculator

So, we have

10,000 + 2,000 + 60 + 1 = 12061

Hence, the value of the sum 10,000 + 2,000 + 60 + 1 is 12061

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Answer:

d. 3.8 m

Step-by-step explanation:

The figure is omitted.

tan(70°) = h/1.4

h = 1.4 tan(70°) = 3.8

You can confirm this by drawing and labeling a right triangle.

Additionally, make sure your calculator is in degree mode.

The correct option regarding the central limit theorem is given as follows:

The average survival time of a large number of guinea pigs has a distribution that is close to normal.

It states that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean given by [tex]\mu[/tex] and standard deviation given by [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, as is the case in this problem, the sampling distribution is also approximately normal, as long as n is at least 30.

For this problem, we have that the distribution is strongly skewed, hence it will only be normal for large sample sizes, and the last option is correct.

The options are given by the image at the end of the answer.

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Answer:

2600 meters

Step-by-step explanation:

2.6x1000

The power of the kettle if it takes 70 seconds to boil is 4 kilowatts.

It is given in the question that the  number of seconds that it takes for a kettle to boil, n, is inversely proportional to its power in kilowatts, p.

Also, The equation of proportionality is n = 280/p.

We have to find the power of the kettle if it takes 70 seconds  to boil.

According to the data given in the question, we can write,

n ∝ 1/p

n = k/p

Where k is the constant of proportionality.

Hence, k = 280

n = 280/p

Putting n = 70 seconds in the equation, we get,

70 = 280/p

p = 280/70

p = 4 kilowatts.

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Answer: 11x-27

Step-by-step explanation:

1- 3[2x-6+2] + 5(x-3)

2- 3[2x-4] + 5x-15

3- 6x-12+5x-15

4- 11x-27

Answer: $3.25 an hour.

Step-by-step explanation: If the server wants to make 184 dollars and they already made 164.50, you subtract 184 by 164.50. 184-164.50= 19.50

That is how much the server made without tips over the course of 6 hours, and we want the amount they made in 1 hour. So we now divide 19.50 by 6. 19.50/6=3.25

Answer: The answer 1/2(p+24)=21

Step-by-step explanation:
The answer could be found by solving each of the equations but that would have been time consuming so it is better to fine the answer through the word problem.

the sunglasses and flip flops were bought at a half-off sale, which means that each of their prices were reduced by 1/2. So the new price was 1/2 of the original price for each of the items. $21 was spent by adding the new price of both the items.
let, 1/2 of original price of sunglasses = p
therefore we get the equation,
new price for sunglasses = 1/2p

therefore
1/2p + 1/2(24) = 21
if we take 1/2 common,
1/2(p+24)=21

RMSE =  (nΣt=1 (At-Ft)²/n is the formula .

What is Root Mean Square Error (RMSE)?

What makes a good RMSE?

Identify the formula used to calculate the root mean square error over a range of forecasted values, if the actual value of the time series at time t and the forecast value for time t are denoted by A t and F t respectively.

RMSE = [ (nΣt=1 (At-Ft)2) / n ]0.5

MSE = (nΣt=1 (At-Ft)²/n

RMSE = Root of MSE

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for the different values of x, we have found the values of the function f (x) = x² + 2 x + 1.

We are given the function:

f (x) = x² + 2 x + 1

We need to complete the given table of values for x and f (x)

For x = - 3:

f (- 3) = (- 3)² + 2 (- 3) + 1

f (- 3) = 9 - 6 + 1

f (- 3) = 4

For x = - 2:

f (- 2) = (- 2)² + 2 (- 2) + 1

f (- 2) = 4 - 4 + 1

f (- 2) = 1

For x = - 1:

f (- 1) = (- 1)² + 2 (- 1) + 1

f (- 1) = 1 - 2 + 1

f (- 1) = 0

For x = 0:

f (0) = (0)² + 2 (0) + 1

f (0) = 0 + 0 + 1

f (0) = 1

For x = 1:

f (1) = (1)² + 2 (1) + 1

f (1) = 1 + 2 + 1

f (1) = 4

For x = 2:

f (2) = (2)² + 2 (2) + 1

f (2) = 4 + 4 + 1

f (2) = 9

For x = 3:

f (3) = (3)² + 2 (3) + 1

f (3) = 9 + 6 + 1

f (2) = 16

Table:

x     - 3      - 2      - 1      0      1      2      3

y       4         1        0      1      4      9     16

Therefore, for the different values of x, we have found the values of the function f (x) = x² + 2 x + 1.

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Answer:-60

Step-by-step explanation:

Answer:

all those that give 12p as a result (look at the examples)

Step-by-step explanation:

Which expression is equivalent to 5p+7p

5p + 7p = 12p

Answer:

211a+9x

Step-by-step explanation:

first, calculate the exponents (the number times itself) of each number

9a +81a +121a+9x

the reason they are positive is that a negative times a negative equals a positive ex: -3 x -3 = 9

next, combine the coefficients

starting with the variable for a

9a+81a+121a= 211a

x has no other coefficients so it would remain 9x

so the simplified answer would be

211a+9x

The rule that can also model the function is f(x)= 4 + 3x.

The initial population of fruit flies = 4 and the population of fruit flies triple every week

Let x represent number of weeks

Therefore function can be modelled as:

f(x)= 4 + 3x

Now assume population grows for two weeks, using the function:

f(x)= 4 + 3x

f(2)= 4+3×2

f(2)= 10

Therefore population grows to 10 fruit flies in 2 weeks based on our function

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Sarah is conducting a science experiment where she initially has a population of 4 fruit flies. Every week the population triples. She writes the function f(x)=4(3)x to predict the population growth. Which rule can also model the function?

The total amount received at the end of 1 year will be 242000

The amount available in Austin's saving account: $100,000

Rate of interest = 142% per year

Simple interest: Simple interest is a quick and simple formula for figuring out how much interest will be charged on loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.

The formula for simple interest is given:

Simple Interest = P*R*T/100

where P = principal amount invested

R = rate of interest per year

T = time in years for which the amount is invested

Substituting the values in the formula we get:

Simple interest = 100000*142*1/100

= 142000

Total amount after 1 year = Principal invested + Simple interest earned

= 100000 + 142000

= 242000

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The value of x in the triangle extended through W to X is 39.5°.

It should be noted that a triangle has a total angle of 180° and also has three sides. Based on the information given, the following can be deduced:

Angle 1 = 3x - 4.

Angle 2 = 6x + 6

Angle 3 = x + 20

Therefore, the value of x will be gotten by adding the values and equating to 180°. This will be:

3x - 4 + 6x + 6 + x + 20 = 180

4x + 22 = 180

Collect like terms

4x = 180 - 22

4x = 158°

Divide

x = 158/4

x = 39.5°

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Answer: 39.5°

Step-by-step explanation:

The given exponential function represents the growth in function with a percentage increase as 57.3%.

Given we have the exponential function as :

y=8800(1.573)ˣ

it is in the form of: y=k.aˣ

therefore, if a>2 then the function represents growth.

and if a<1 then the function represents decay.

now, x=1.573

1.573 > 1

so, the function represents change in growth.

therefore, 1.573 - 1

= 0.573

= 57.3%

hence the change in growth of the function is increased by 57.3%.

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Answer:

Step-by-step explanation: the answer is .75. your welcome

the answer is 3/4 or 0.75

Answer: C

Step-by-step explanation:

First, take the square root of both the numerator and denominator. The numerator would then be equal to 6 a^4 b^2 and the bottom would just be sqrt7c. Since you still have a sqrt in the denominator, rationalize the fraction by multiplying sqrt7c to both the numerator and denominator to get rid of the sqrt. This would leave you with answer choice C.

Answer:

[tex]\frac{6a^4b^2\sqrt{7c}}{7c}[/tex]

Step-by-step explanation:

You can distribute radicals across division such that: [tex]\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}[/tex]

So you get the expression: [tex]\frac{\sqrt{36a^8b^4}}{\sqrt{7c}}[/tex]

Similarly with division, you can distribute radicals across multiplication such that: [tex]\sqrt{ab}=\sqrt{a}*\sqrt{b}[/tex], and you can do this multiple times

So our expression on top becomes: [tex]\frac{\sqrt{36}*\sqrt{a^8}*\sqrt{b^4}}{\sqrt{7c}}[/tex]

Whenever we take the square root of a base to an exponent, we simply divide the exponent by two. In general if you take the "nth" root of any base to an exponent, you divide the exponent by n, since: [tex](x^a)^b=x^{a*b}[/tex] and radicals such as: [tex]\sqrt[n]{x}=x^{\frac{1}{n}}[/tex], so you're just multiplying the two, which results in a division of "n" which in this case is 2.

So the square root of a^8 simplifies to a^4 after dividing the exponent by 2, which makes since: [tex]a^4*a^4=a^{4+4}=a^8[/tex] which exemplifies the very definition of a square root.

Applying this same logic to b^4 and just simplifying sqrt(36) regularly we get the following expression:

[tex]\frac{6a^4b^2}{\sqrt{7c}}[/tex]

We generally don't want square roots in the denominator, so we rationalize it by multiplying by the sqrt(7c)/sqrt(7c) which just simplifies to one, so we're not actually changing the value but it removes the sqrt(7c) from the denominator

[tex]\frac{6a^4b^2}{\sqrt{7c}} *\frac{\sqrt{7c}}{\sqrt{7c}}\\\\\frac{6a^4b^2\sqrt{7c}}{7c}[/tex]

and this turns out to be our solution!

Answer: $47,000 at 10% annually is ≈ $77,297.70 and $47,000 at 5% monthly is ≈ $569,611.01

Step-by-step explanation:

Use the compound interest formula. A=P(1+r/n)^nt

The values of the expressions are

Expression 1

5-(-1 - 2)^2

Evaluate the difference in the expression

So, we have

5 - (-1 - 2)^2 = 5 - (-3)^2

Evaluate the exponent in the expression

So, we have

5 - (-1 - 2)^2 = 5 - 9

Evaluate the difference in the expression

So, we have

5 - (-1 - 2)^2 = -4

Expression 2

|x/x+y| - x^2 + y

When x = 2 and y = -3

Substitute x = 2 and y = -3 in |x/x+y| - x^2 + y

So, we have

|x/x+y| - x^2 + y = |2/2 - 3| - 2^2 - 3

Evaluate the difference in the expression

So, we have

|x/x+y| - x^2 + y = |2/-1| - 2^2 - 3

Evaluate the quotient and the exponent in the expression

So, we have

|x/x+y| - x^2 + y = |-2| - 4 - 3

Remove the absolute bracket

|x/x+y| - x^2 + y = 2 - 4 - 3

Evaluate the difference in the expression

So, we have

|x/x+y| - x^2 + y = -5

Hence, the solutions to the expressions are -4 and -5

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