The temperature outside was -10°F. During the
night the temporadurre dropped another 120F
What was the lowest temperature that night

Step-by-step explanation:

The circle equaiton is

(x-h)^2+(y-k)^2=r^2

(h,k)=center

r=radius

so just insert the center being (5,2) and the radius being 3

(x-5)^2+(y-2)^2=9

Hope that helps :)

Answer:

Step-by-step explanation:

acceleration, a = 20 m/s^2

initial velocity, u = 0 since it starts from rest

final velocity, v = 400 m/s

v = u + at

400 = 0 + 20 t

400 = 20 t

t = 400 / 20

t = 20 sec

Hope this helps

plz mark as brainliest!!!!

It will take 20 sec the rocket reach a velocity of 400 m/s

There are three equation of motions that can be used when motion of the object is under constant acceleration and on a straight path.

They are listed below as:

\(v = u + at\\\\s = ut + \dfrac{1}{2} at^2\\\\v^2 = u^2 + 2as\)

We are given that manned rocket accelerates at a rate of 20 m/s2 during launch

The acceleration, a = 20 m/s^2

The initial velocity, u = 0 since it starts from rest

The final velocity, v = 400 m/s

Therefore, v = u + at

400 = 0 + 20 t

400 = 20 t

t = 400 / 20

t = 20 sec

Hence, It will take 20 sec the rocket reach a velocity of 400 m/s

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You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.

When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.

A cuboid has six faces, but each face has a pair that is identical in size and shape.

Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.

To find the surface area of a cuboid, you can add up the areas of all its faces.

However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:

(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.

By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.

Essentially, you are considering one face from each pair and then summing their areas.

Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.

When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.

Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.

Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.

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Answer:

it's c

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

A

AAAAAAAAAAAAAAZSAAAAAAA

3 tables of 200-miligram of medicine are needed daily for the patient.

According to the statement, we need to determine the amount of medicine (m), in miligrams, in proportion with the weight of the patient (M), in kilograms. Since there is a case of direct variation, we can determine the required amount by means of this expression:

m = r · M

Where r is the constant of proportionality, in miligrams per kilogram.

If we know that r = 10 mg / kg and M = 130 · 0.45 = 58.5 kg, then the required amount is:

m = 10 · 58.5

m = 580.5 mg

And the number of 200-miligram tablets is:

n = 580.5 mg / 200 mg

n = 2.90

n = 3

3 tables of 200-miligram of medicine are needed daily for the patient.

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the 95% confidence interval for the mean number of years of education for lower-class respondents is (9.6032, 10.3968).

what is  mean number ?

In mathematics and statistics, the "mean" typically refers to the arithmetic average of a set of numbers. To find the mean of a set of numbers, you add up all the numbers in the set and divide the total by the number of numbers in the set.

In the given question,

To calculate the 95% confidence interval for the mean number of years of education for lower-class respondents, we need the sample mean, sample standard deviation, sample size, and the t-value for the 95% confidence level with (n-1) degrees of freedom. Here are the steps to calculate the interval:

Collect the sample data of the number of years of education for lower-class respondents.

Calculate the sample mean  and the sample standard deviation (s) of the data.

Determine the sample size (n) of the data.

Look up the t-value for the 95% confidence level with (n-1) degrees of freedom. For example, if the sample size is 50, then the degrees of freedom are 49, and the t-value for a 95% confidence level is 2.009 (using a t-distribution table or software).

Calculate the margin of error (ME) using the formula:

ME = t-value x (s / √(n))

Calculate the lower and upper bounds of the confidence interval using the formulas:

Lower bound = x- ME

Upper bound = x + ME

For example, suppose we have a sample of 100 lower-class respondents with a mean of 10 years of education and a standard deviation of 2 years. The degrees of freedom are 99, and the t-value for a 95% confidence level is 1.984 (using a t-distribution table or software).

ME = 1.984 x (2 / √(100)) = 0.3968

Lower bound = 10 - 0.3968 = 9.6032

Upper bound = 10 + 0.3968 = 10.3968

Therefore, the 95% confidence interval for the mean number of years of education for lower-class respondents is (9.6032, 10.3968). We can interpret this interval as follows: we are 95% confident that the true mean number of years of education for all lower-class respondents is between 9.6032 and 10.3968 years.

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The given statement is false. If the characteristic polynomial of a matrix A factors into a product of linear factors, then A is not necessarily diagonalizable.

By definition, a matrix A having characteristic F is diagonalizable if and only if the following 2 conditions are met-

Hence, we can conclude that the given statement is false. If the characteristic polynomial of a matrix A factors into a product of linear factors, then A is not necessarily diagonalizable.

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The tangents of triangle DEF are Tan D = 0.28 and Tan F = 0.96  

The tangents of triangle JLK are Tan J = 0.8574 and Tan K = 0.5388  

In a right-angled triangle, the tangent of one of the non-right angles is defined as the ratio of the length of the opposite side to the length of the adjacent side.  

where θ is the angle between the hypotenuse and the adjacent side.          

Here we have

Two right-angled triangles

From triangle DEF,

DE = 24, EF = 7 about FD = 25  

From triangle JLK,

JL = 3, LK = 5,  JK = √34  

Using the formula, Tan(θ) = opposite/adjacent

From triangle DEF,

Tan D = EF/DF = 7/25 = 0.28

Tan F = DE/DF = 24/25 = 0.96

From triangle JLK,

Tan J = LK/JK = 5/√34 = 0.8574

Tan K = JL/JK = 3/√34 = 0.5388  

Therefore,

The tangents of triangle DEF are Tan D = 0.28 and Tan F = 0.96  

The tangents of triangle JLK are Tan J = 0.8574 and Tan K = 0.5388  

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The triangles are given in picture

Answer:

Step-by-step explanation:

The Order of Operations is very important when simplifying expressions and equations. The Order of Operations is a standard that defines the order in which you should simplify different operations such as addition, subtraction, multiplication and division.

This standard is critical to simplifying and solving different algebra problems. Without it, two different people may interpret an equation or expression in different ways and come up with different answers. The Order of Operations is shown below.

Parentheses and Brackets -- Simplify the inside of parentheses and brackets before you deal with the exponent (if any) of the set of parentheses or remove the parentheses.

Exponents -- Simplify the exponent of a number or of a set of parentheses before you multiply, divide, add, or subtract it.

Multiplication and Division -- Simplify multiplication and division in the order that they appear from left to right.

Addition and Subtraction -- Simplify addition and subtraction in the order that they appear from left to right.

Before we begin simplifying problems using the Order of Operations, let's examine how failure to use the Order of Operations can result in a wrong answer to a problem.

Without the Order of Operations one might decide to simplify the problem working left to right. He or she would add two and five to get seven, then multiply seven by x to get a final answer of 7x. Another person might decide to make the problem a little easier by multiplying first. He or she would have first multiplied 5 by x to get 5x and then found that you can't add 2 and 5x so his or her final answer would be 2 + 5x. Without a standard like the Order of Operations, a problem can be interpreted many different ways

We cannot combine the variable terms before using the distributive property when solving the equation as it will results in wrong answer.

What is distributive property of multiplication over addition ?

If we multiply a number by the sum of more than two, we use the distributive property of multiplication over addition.

Here the expression given is :

7(x+5)-x=42

The Order of Operations is very important when simplifying expressions and equations. The Order of Operations is a standard that defines the order in which you should simplify different operations such as addition, subtraction, multiplication and division.

Parentheses and Brackets -- Simplify the inside of parentheses and brackets before you deal with the exponent (if any) of the set of parentheses or remove the parentheses.

Exponents -- Simplify the exponent of a number or of a set of parentheses before you multiply, divide, add, or subtract it.

Multiplication and Division -- Simplify multiplication and division in the order that they appear from left to right.

Addition and Subtraction -- Simplify addition and subtraction in the order that they appear from left to right.

Without the Order of Operations one might decide to simplify the problem working left to right. He or she would add two and five to get seven, then multiply seven by x to get a final answer of 7x. Another person might decide to make the problem a little easier by multiplying first. He or she would have first multiplied 5 by x to get 5x and then found that you can't add 2 and 5x so his or her final answer would be 2 + 5x. Without a standard like the Order of Operations, a problem can be interpreted many different ways.

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Answer:

\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)

Step-by-step explanation:

Use Quotient Rule to find f'(x)

\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)

Find f'(1) using f'(x)

\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)

Answer:

\(f'(1)=-\dfrac{9}{e^{3}}\)

Step-by-step explanation:

Given rational function:

\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)

To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)

\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)

\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)

Therefore:

\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)

\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)

\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)

To find f'(1), substitute x = 1 into f'(x):

\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)

\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)

\(f'(1)=-\dfrac{9}{e^{3}}\)

Answer:             \(*****************\)

8

Step-by-step explanation:                       \(********************\)

x=12-4

x=8

Mental Math! (:

Answered by

\(***Rosalind*Cordelia***\)

Step-by-step explanation:

X + 4 = 12

X + 4 - 4 = 12 - 4

X = 8

That means X is eight

Answer:

55

Step-by-step explanation:

\(\displaystyle MOE = z\biggr(\frac{\sigma}{\sqrt{n}}\biggr)\\\\4=1.96\biggr(\frac{15}{\sqrt{n}}\biggr)\\\\4=\frac{29.4}{\sqrt{n}}\\\\\sqrt{n}=\frac{29.4}{4}\\\\\sqrt{n}=7.35\\\\n=54.0225\\\\n\approx55\uparrow\)

Make sure to always round up the required sample size to the nearest integer!

Answer:

I think its 13/35 it cant be divided

Answer: See below

Step-by-step explanation:

The first is a beaker, it's used to measure liquid volume

The second is a ruler, it's used to measure length.

Last is a thermometer, it's used to measure temperature.

The value of the equation f ( x ) is

f ( x ) = x³ + x² - 8x - 12

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

f ( x ) = ( x + 2 )²( x -3 )   be equation (1)

Now , on simplifying the equation , we get

f ( x ) = ( x + 2 )²( x -3 )

f ( x ) = ( x² + 4x + 4 ) ( x - 3 )

Now , multiplying each term with ( x - 3 ) , we get

f ( x ) = ( x - 3 ) x² + ( x - 3 ) 4x + ( x - 3 ) 4

f ( x ) = x³ - 3x² + 4x² - 12x + 4x - 12

On simplifying the equation ,we get

f ( x ) = x³ + x² - 8x - 12

Now , the value of the equation f ( x ) = x³ + x² - 8x - 12

On graphing the equation , we get

The graph of the equation f ( x ) = x³ + x² - 8x - 12 is shown below

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Answer:

x<-9

Step-by-step explanation:

subtract the 7x from the right side to bring it over to the left side to get:

2x-7<-25

then add the 7 from the left side to bring it over to the right side to get:

2x<-18 and then divide both sides by 2 to get the final inequality to be:

x<-9

Therefore, the solved inequality is x < -9.

Hoped this helped.

\(BrainiacUser1357\)

Answer:

=197060718

Step-by-step explanation:

51661−61661+(611)(5561)(58)

=−10000+(611)(5561)(58)

=−10000+(3397771)(58)

=−10000+197070718

=197060718

The equation explaining the relationship between line segment AC and line segment A"C" is: y_A"C" = y_AC.

To determine the relationship between line segment AC and line segment A"C" in the given transformation, let's consider the properties of translation and dilation.

Translation:

A translation moves an object in a specific direction by a given distance. In this case, the translation (x + 0, y + 2) means that every point of the original triangle A'B'C' is shifted vertically upward by 2 units. So, A' becomes A" when shifted vertically by 2 units.

Dilation:

A dilation scales an object by a certain factor while keeping the same center of dilation. The scale factor of 2 means that every point is multiplied by 2 in both the x and y coordinates. Since the center of dilation is the origin (0, 0), the origin remains fixed.

Considering these transformations, we can deduce the following:

1. Translation: (x, y) ⟼ (x, y + 2)

2. Dilation: (x, y + 2) ⟼ (2x, 2(y + 2))

Applying the dilation to the translated point A", we get:

A" = (2x, 2(y + 2))

Now, we can determine the equation that relates line segment AC and line segment A"C" by comparing their coordinates:

The coordinates of A are (x, y), and the coordinates of C are (0, y) since it is a vertical line segment.

The coordinates of A" are (2x, 2(y + 2)), and the coordinates of C" are (0, 2(y + 2)).

The slope between A and C is given by:

m_AC = (y - (y + 2)) / (x - 0) = -2 / x

The slope between A" and C" is given by:

m_A"C" = (2(y + 2) - (2(y + 2))) / (2x - 0) = 0

Since the slope between A" and C" is zero, it indicates that line segment A"C" is a horizontal line. There is no change in the y-coordinate, implying that the y-value of A" and C" remains the same.

In other words, the y-coordinate of A"C" is equal to the y-coordinate of AC.

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The probable question may be:
Triangle A″B″C″ is formed using the translation (x + 0, y + 2) and the dilation by a scale factor of 2 from the origin. Which equation explains the relationship between line segment AC and line segment A"C"?

Answer:

----------------------

Given:

To find the arc measure (θ) in radians, we can use the formula:

Now, plug in the given values:

To solve for θ, divide both sides by 4:

Simplify the expression:

So, the arc measure (θ) is 2π/3 radians

Answer:

Option E

The answer is (x - 4) (x - 6)

Step-by-step explanation:

x² - 10x + 24

x² - 6x - 4x + 24

x(x - 6) - 4(x - 6)

(x - 4) (x - 6)

Thus, The answer is (x - 4) (x - 6)

-TheUnknownScientist

Degree 7

Other zeros -i and -3-i (option A)

Here, we want to give the degree of the polynomial

The degree of a polynomial simply refer to the number of roots that the polynomial have

With respect to this question, we have the following roots

-4, since it is with a multiplicity of 2, it means we have two roots here (-4,-4)

20

i

-3+i

The other complex roots are simply the conjugates of the given complex roots

This should be -i and -3-i

So the total number of roots are 7 and also, the degree which is the number of roots is also seven; meaning we have a polynomial of degree 7

STEP1:

Simplify

\( \frac{x + 4}{x - 2} \\ \)

Equation at the end of step1:

\( \frac{ ((x {}^{2} ) - 4) }{x} \times \frac{(x + 4)}{x - 2} \\ \)

Factoring: x2 - 4

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A² - AB + BA - B² =

A² - AB + AB - B² =

A² - B²

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 4 is the square of 2

Check : x2 is the square of x1

Factorization is : (x + 2) • (x - 2)

Polynomial Long Division :

2.2 Polynomial Long Division

Dividing : x + 2

("Dividend")

By : x ("Divisor")

dividend x + 2

- divisor * x⁰ x

remainder 2

Quotient : 1

Remainder : 2

Equation at the end of step 2:

\( \frac{(x + 2) \times (x - 2)}{x} \times \frac{(x + 4)}{x - 2} \\ \)

Cancel out (x-2) which appears on both sides of the fraction line.

Final result :

\(⇒ \frac{(x + 2) \times (x + 4)}{x} \\ \)

Answer:

\(a=-\frac{c-b}{2}\)

Step-by-step explanation:

Solving for the variable \(a\), given that :

\(b-2a=c\)

We can first start start by subtracting \(b\) from both sides of the equation:

\(-2a=c-b\)

Now, we can divide both sides of the equation by the coefficient of \(a\), which would be \(-2\):

\(a=\frac{c}{-2}-\frac{b}{-2}\)

Applying the fraction rule \(\frac{a}{c}\pm\frac{b}{c} =\frac{a\pm b}{c}\):

\(a=\frac{c-b}{-2}\)

Then, apply the fraction rule \(\frac{a}{-b} =-\frac{a}{b}\)

\(a=-\frac{c-b}{2}\)

a. The probability of no insect contaminants in a 225-gram bar from a brand at the mean contamination level can be found using the Poisson probability formula:

\(P(X = 0) = \frac{ (e^{-λ})(λ^0)}{0!} = \frac{(e^{-14.4})(14.4^0)}{0!}= 0.000000831\)

b. If you consume a bar that is one-fifth the size tested (45 grams) from a brand at the mean contamination level, the mean number of insect fragments would be one-fifth of 14.4, or 2.88. The probability of no insect contaminants can be found using the Poisson probability formula:

\(P(X = 0) = \frac{(e^-λ)(λ^0)}{0!} = \frac{(e^-2.88)(2.88^0)}{0!} = 0.056032\)

c. If you consume seven 28.35 gram (one-ounce) bars this week from a brand at the mean contamination level, the mean number of insect fragments would be (7 * 28.35/225) * 14.4 = 5.4336.

The probability of consuming one or more insect fragments in more than one bar can be found using the Poisson probability formula and the complement rule:

\($$\begin{aligned}& P(X>1) \\& =1-P(X \hat{a} 1) \\& =1-\left[\left(e^{-} \hat{I}\right)\left(\hat{I}^0\right) / 0 !+\left(e^{-} \hat{I}\right)\left(\hat{I}^1\right) / 1 !\right] \\& =1-\left[\left(e^{-} 5.4336\right)\left(5.4336^0\right) / 0 !+\left(e^{-} 5.4336\right)\left(5.4336^1\right) / 1 !\right] \\& =0.994784\end{aligned}$$\)

d. The probability of contamination more than twice the mean of 14.4 can be found using the Poisson probability formula and the complement rule:

\(P(X > 28.8) = 1 - P(X ≤ 28.8) \\= 1 - ∑(e^-λ)(λ^x)/x!\\ = 1 - 0.999999999999999 \\= 0.000000000000001\)

This probability is extremely small, so it can be considered unusual and not typical variation.

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The dataset represented by the given box plot is 12, 15, 15, 17, 19, 19, 20, 22, 24 option B.

A box plot, sometimes called a box whisker plot, shows the distribution of a dataset graphically. The minimum value, the first quartile (25th percentile), the median (50th percentile), the third quartile (75th percentile), and the maximum value are the five main values used to standardise this method of displaying the distribution of data.

Two whiskers that extend from a rectangular box make up a box plot. The range of values between the first and third quartiles is represented by the box, which is known as the interquartile range (IQR).

From the given box plot we observe that the minimum value is 12 and the maximum value is 24.

Here, the median is 19.

From the information the two data set that have the corresponding values are:

12, 15, 15, 17, 19, 19, 20, 22, 24

12, 15, 17, 17, 19, 19, 22, 22, 24

The lower quartile is 15.

The upper quartile is 21.

Calculating the lower quartile for the data sets:

12, 15, 15, 17, 19, 19, 20, 22, 24

Lower quartile = 15

Hence, the dataset represented by the given box plot is 12, 15, 15, 17, 19, 19, 20, 22, 24 option B.

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a) Comparing the two functions, Scooter's business has a lower slope of 15 compared to Karissa's business with a slope of 35. b) Both Scooter and Karissa earned a total of $500 in that month. Therefore, they had an equal month in terms of total money earned.

a) In the context of Scooter's business, the slope of the function f(x) = 200 + 15x represents the rate at which the total money earned increases with each additional sale. Each unit increase in x (number of sales) results in an increase of $15 in total money earned. The y-intercept of 200 represents the initial amount of money Scooter already had before making any sales.

In the context of Karissa's business, the slope of the function f(x) = 80 + 35x represents the rate at which the total money earned increases with each additional repair job. Each unit increase in x (number of repairs) results in an increase of $35 in total money earned. The y-intercept of 80 represents the initial amount of money Karissa already had before doing any repair jobs.

Comparing the two functions, Scooter's business has a lower slope of 15 compared to Karissa's business with a slope of 35. This means that Karissa's business earns more money per repair job compared to Scooter's business per t-shirt sale.

b) To determine who had the better month, we need to calculate the total money earned by each individual based on the given sales/repairs.

For Scooter, with x = 20 (number of shirts sold):

f(x) = 200 + 15x

f(20) = 200 + 15 * 20

f(20) = 200 + 300

f(20) = 500

For Karissa, with x = 12 (number of repairs):

f(x) = 80 + 35x

f(12) = 80 + 35 * 12

f(12) = 80 + 420

f(12) = 500

Both Scooter and Karissa earned a total of $500 in that month. Therefore, they had an equal month in terms of total money earned.

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Option A

A large naturally occurring community of flora and fauna occupying a major habitat, e.g. forest or tundra. A biome is a large area characterized by its vegetation, soil, climate, and wildlife.