Find the missing side length

Answer:

Translation (3 right)

then a rotation 90 degrees clockwise

Or

Rotation of 90 degrees clockwise

Then translation (3 right)

Either one

The estimate of average sat score is between (1440.91, 1559.09) and the number of students to sample in next case is 553.

The margin of Error is a statistical expression that is used to determine the percentage point by which the result arrived will differ from the value of the entire population, and it is calculated by dividing the standard deviation of the population by the sample size and lastly multiplying the resultant with the critical factor.

A higher error indicates a high chance that the result of the sample reported may not be the true reflection of the whole population.

n = 99

Mean = μ = 1500

Standard deviation = σ = 300

Confidence interval = μ ± zσ/√n

= 1500 ± 1.96×300/√99

= 1500 ± 59.09

= (1440.91, 1559.09)

Now, if margin of error is 25 with 95% confidence interval,

Margin of error = z × σ/√n

∴ 25 = 1.96 × 300/√n

⇒ √n = 23.52

⇒ n = 553.19 ≅ 553

Thus, the estimate of average sat score is between (1440.91, 1559.09) and the number of students to sample in next case is 553.

To learn more about confidence interval, visit brainly.com/question/24131141

#SPJ4

Answer: 4 times 3 equals 12, and that plus 6 is 18.  18 divided by 5 is not 4, sorry if i interpreted your statement wrong, but that is incorrect, or my brain is melting. Help.

Step-by-step explanation:

The answer is (3,0)

Sure hope this helps you

The statement that best describes what the quotient represents in the situation above is: "Maddy made 4 bows from the piece of ribbon and had 2/3 yards of a yard left." (Option C)

Note that the length of the piece of ribbon Maddy used is 31/2 yards or 7/2 yards.

We also know that the length of the ribbon required to make a bow is 3/4.

Hence the number of bows made is:

7/2 ÷ 3/4

= 7/2 * 4/3

= 28/6

= 14/3

= 4 2/3

Thus it is correct to state that Maddy made 4 bows from the piece of ribbon and had 2/3 of a yard remaining.

Learn more about quotient:
https://brainly.com/question/16134410
#SPJ1

Full Question:

Maddy had a piece of ribbon that was  31/2 yards long. She used this ribbon to make bows. Each bow was made from a piece of ribbon that was 3/4 yard long. This situation can be represented by the equation 31/2 ÷ 3/4 - 42/3. Which statement best describes what the quotient represents in the situation above?

A Maddy had bows that were each 42/3 yards long.

B Maddy had 42/3 yards of ribbon left after making the bows.

C Maddy made 4 bows from the piece of ribbon and had 2/3 yards of a yard left.

D Maddy made 4 bows from the piece of ribbon and had enough left for   2/3 of a bow.

Answer:

x = 1

Step-by-step explanation:

\(\frac{2}{3}\) (9x - 6) = \(\frac{1}{4}\) (12 - 4x) ← distribute parenthesis on both sides

6x - 4 = 3 - x ( add x to both sides )

7x - 4 = 3 ( add 4 to both sides )

7x = 7 ( divide both sides by 7 )

x = 1

we must use trigonometric ratios to solve the right triangle

i will use the cosine

where alpha is the angle, a the adjacent side and H the hipotenuse,

so replacing

now solve for x

so the right option is I

Answer:

1) 2 nonreal complex roots

2) 1 Real Solution

3) 16

4) Reflected, narrower by a factor of 2/5, slides right 4 units and slides up 6 (units)

Step-by-step explanation:

1) The graph does not intercept the x-axis, therefore, there are no real solutions at the point y = 0

We get;

y = a·x² + b·x + c

At y = 6, x = -2

Therefore;

6 = a·(-2)² - 2·b + c = 4·a - 2·b + c

6 = 4·a - 2·b + c...(1)

At y = 8, x = 0

8 = a·(0)² + b·0 + c

∴ c = 8...(2)

Similarly, we have;

At y = 8, x = -4

8 = a·(-4)² - 4·b + c = 16·a - 4·b + 8

16·a - 4·b = 0

∴ b = 16·a/4 = 4·a

b = 4·a...(3)

From equation (1), (2) and (3), we have;

6 = 4·a - 2·b + c

∴ 6 = b - 2·b + 8 = -b + 8

6 - 8 = -b

∴ -b = -2

b = 2

b = 4·a

∴ a = b/4 = 2/4 = 1/2

The equation is therefor;

y = (1/2)·x² + 2·x + 8

Solving we get;

x = (-2 ± √(2² - 4 × (1/2) × 8))/(2 × (1/2))

x =( -2 ± √(-12))/1 = -2 ± √(-12)

Therefore, we have;

2 nonreal complex roots

2) Give that the graph of the function touches the x-axis once, we have;

1 Real Solution

3) The given function is f(x) = 2·x² + 8·x + 6

The general form of the quadratic function is f(x) = a·x² + b·x + c

Comparing, we have;

a = 2, b = 8, c = 6

The discriminant of the function, D = b² - 4·a·c, therefore, for the function, we have;

D = 8² - 4 × 2 × 6 = 16

The discriminant of the function, D = 16

4.) The given function is g(x) = (-2/5)·(x - 4)² + 6

The parent function of a quadratic equation is y = x²

A vertical translation is given by the following equation;

y = f(x) + b

A horizontal to the right by 'a' translation is given by an equation of the form; y = f(x - a)

A vertical reflection is given by an equation of the form; y = -f(x) = -x²

A narrowing is given by an equation of the form; y = b·f(x), where b < 1

Therefore, the transformations of g(x) from the parent function are;

g(x) is a reflection of the parent function, with the graph of g(x) being narrower by 2/5 than the graph of the parent function. The graph of g(x) is shifted right by 4 units and is then slides up by 6 units.

The positive even integers whose sum of reciprocals is 7/24 are 6 and 8.

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

Let the two consecutive even integers be 2x and 2x+2 then there sum of reciprocal will be 7/24 that is now solving for positive value of x by finding roots of quadratic equation :

\(\begin{aligned}\frac{1}{2x}+\frac{1}{2x+2}&=\frac{7}{24}\\\frac{1}{x}+\frac{1}{x+1}&=\frac{7}{12}\\\frac{2x+1}{x^2+x}&=\frac{7}{12}\\24x+12&=7x^2+7x\\7x^2-17x+12x&=0\\x&=3, \frac{-4}{7} \end{aligned}\)

Consider only positive value of x that is 3

Therefore, The positive even integers whose sum of reciprocals is 7/24 are 6 and 8.

check and know more about equations here :

https://brainly.com/question/10003183

#SPJ1

Answer:

$200

Step-by-step explanation:

30 * 5=150 +50=200

The 25th battery replacement will occur in October.

What is Rate of change?

A rate is anything that can be measured over time. Common rates include velocity (which is the rate of distance traveled), power (rate of work being done), etc. All these have one thing in common which is that they are all divided by the amount of time it took to obtain a certain measurement.

The last time he changed his batteries was in May, so we know he needs to change them every 5 months. So we can figure out when he has to replace them for the 24th time. The first thing we need to do is figure out how many months have passed since he has to replace them 24 times a year.

\(\begin{aligned}5\text{ months}\cdot 24\text{ replacement}&= 120\text{ months}\end{aligned}\)

From the amount of months we can calculate the amount of years that will pass.

120 months x  (12 months/ 1 year ) = 10 year

Adding 10 years to May results in 10 years later May, which is the month of the 24th replacement.

That is the 24th battery replacement will occur in May and therefore, the 25th battery replacement will occur in October.

Read more about unit rates at:

brainly.com/question/19493296

#SPJ4

Answer:

constant.

Step-by-step explanation:

like natural constants like pi or e.

Answer:

pi

Step-by-step explanation:

it stays the same 3.14 and so on

Answer:

axis of symmetry=(1.5,6.5)

x intercept= (-1,1.5)

y intercept=(4,0)

Step-by-step explanation:

2 objects and their shadows create 2 similar right-angled triangles.

that means all angles are the same, and the side lengths of one triangle correlate to the corresponding side lengths of the other triangle via the same factor.

so,

122 × f = 2

f = 2/122 = 1/61

therefore, Ryan is

305 × f = 305 × 1/61 = 5 ft

tall.

If the Statue of Liberty is 305 feet tall, Ryan is 5 feet tall.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio.

Given that,

The length of shadow of Statue of Liberty = 122 foot.

The length of shadow of Ryan = 2 foot.

Also, the height of Statue of Liberty = 305 feet.

Let the height of Ryan = x

To find the value of x,

Use ratio and proportion method,

122 / 305 = 2 / x

x = 2 x 305 / 122

x = 305 / 61

x = 5

The height of Ryan is 5 feet.

To know more about Proportion on:

https://brainly.com/question/7096655

#SPJ5

Answer:

c is 1

o is q

h is 2

in ch3

c is 2 h is 3

and finally o is 1

Answer:

the first one

Step-by-step explanation:

the others don't make any sense and also the first one's the only one that's in inequality form.

The inequality that represents the ages is 12 ≤ a ≤ 18.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

The inequality graphed below is shown.

The number line includes the numbers 12 and 18.

So,

The ages of the baseball team are 12 to 18.

This can be written as,

12 ≤ a ≤ 18

Thus,

The inequality that represents the ages is 12 ≤ a ≤ 18.

Learn more about inequalities here:

https://brainly.com/question/20383699

#SPJ7

Data that are accurate, consistent, and available in a timely fashion are considered C) high-quality.

High-quality data is characterized as being reliable, consistent, and timely. High-quality data offers a strong foundation for analysis and decision-making because it is accurate, error-free, and consistent.

It is a valuable asset for organizations because it promotes accurate reporting and analysis, increases operational efficiency, and allows for informed decision-making. Although database management systems like Oracle and Microsoft SQL Server can assist with managing and storing data, the quality of the data is unrelated to the particular technology or program employed.

Learn more about Data:

brainly.com/question/28285882

#SPJ4

Answer: answer D

Step-by-step explanation:

i am pretty sure it is D. not 100%, but like 90%. they are both on the outside of the lines, so that is why i know they are exterior. and, they are on opposite sides, so that makes them alternate.

frustum of a cone is: = pi * l(R + r)

(l) = slant height of the frustum.

from 2929.645714 - 506.1257143

= 2423.52

= 2423.5cm

Answer:

from 2929.645714 - 506.1257143

= 2423.52

= 2423.5cm

Answer:

C

Step-by-step explanation:

negative four raised to the sixth power divided by negative four raised to the fourth power

because  negative four raised to the fourth power divided by negative four raised to the second power = negative four raised to the second power

negative four raised to the sixth power divided by negative four raised to the fourth power also = negative four raised to the second power

The answer is A: negative four raised to the second power divided by negative four raised to the fourth power. This is obtained by applying the rules of exponents, specifically, when dividing with the same base, subtract the exponents.

This question pertains to exponents division rules. According to the rule of Power of a Power in exponents, when you divide expressions with the same base, you subtract the exponents. So if you have negative four raised to the fourth power (-4⁴) and you want to divide it by negative four raised to the second power (-4²), you subtract 2 from 4 to get an exponent of 2. This results in a negative four raised to the second power (-4²). So, the correct option from the given choices in your question is A: negative four raised to the second power divided by negative four raised to the fourth power.

Learn more about Exponents here:

https://brainly.com/question/5497425

#SPJ2

The population of Mayville from the obtained equation is 41370.

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

Given that, the population of Clayton is 6,370 less than the population of Mayville.

Let x be the population of Mayville.

x-6,370=35,000

⇒ x=35,000+6,370

⇒ x=41370

Therefore, the population of Mayville is 41370.

To learn more about an equation visit:

https://brainly.com/question/14686792.

#SPJ2

Answer:

no

Step-by-step explanation:

i hope this helps :)

Answer:

x = -33, y= -46

Step-by-step explanation:

0.4(x - 2) = -14

0.4x - 0.8 = -14

0.4x = -13.2

x = -33

-2/5(y + 6) = 16

-2/5y - 2 2/5 = 16

-2/5y = 18 2/5

y = -46

Answer && Step-by-step explanation:

divide both sides by .4

.4/.4(x-2)=-14/.4 == x-2=-35

add 2 to both sides

x-2+2=-35+2 ==x=-33

x=-33 is your answer

Use the same methodology for finding y

\( \: \: \: \: \: \)

\((x,y) = ( - 8,0)\)

\( \: \: \: \: \)

Here is the solution to your given problem:1. Using the partial fraction method, we can write:F(s) = 10/s4 + 5/(s – 3) = (A/s) + (B/s2) + (C/s3) + (D/(s – 3))For s = 0,

the value of A can be obtained as:A = [s × F(s)]s=0 = [10/s3]s=0 = ∞For s = 3, the value of D can be obtained as:D = [s × F(s)]s=3 = [5/(s – 3)]s=3 = 5/0 = ∞

Using the same procedure as above, we can obtain the values of B and C as:B = -∞ and C = ∞Hence, the partial fraction representation of F(s) is:F(s) = (∞/s) + (-∞/s2) + (∞/s3) + (∞/(s – 3))

Taking the inverse Laplace transform, we have:f(t) = ∞ – t + ∞t2 – ∞e3t2. We can express the final solution in terms of a single equation as follows:f(t) = 2 - 2t2 + e3t/2 2. Using partial fractions, we can write:F(s) = (8s – 9)/(s2 + 9) = (As + B)/(s2 + 9) + (Cs + D)/(s2 + 9)

For s = 0,

the value of B can be obtained as:B = [s × F(s)]s=0 = [-9/(s2 + 9)]s=0 = -1For s = 0, the value of A can be obtained as:A = F(0) – B = (8 × 0 – 9)/(02 + 9) + 1 = -1/9For s = 3i,

the value of D can be obtained as:D = [s × F(s)]s=3i = [(8s – 9)/(s2 + 9)]s=3i = [(-9 + 24i)/(–18i)] = (3 – 4i)/3For s = -3i, the value of C can be obtained as:C = [s × F(s)]s=-3i = [(8s – 9)/(s2 + 9)]s=-3i = [(-9 – 24i)/(18i)] = (3 + 4i)/

, the partial fraction representation of F(s) is:F(s) = (-1/9) + (s – 1)/((s2 + 9)) + [(3 – 4i)/(3(3i + s))] + [(3 + 4i)/(3(-3i + s))]Taking the inverse Laplace transform, we have:f(t) = (-1/9) δ(t) + (1/3)cos3t + (4/9)sin3t – (1/3)e-t3sin3t3.

Using partial fractions, we can write:F(s) = 6/s + 7/(s + 4)Taking the inverse Laplace transform, we have:f(t) = 6 – 7e-4t4. Using partial fractions, we can write:F(s) = (2s + 3)/(s2 – 4) = (As + B)/(s + 2) + (Cs + D)/(s – 2)For s = 2, the value of C can be obtained as:C = [s × F(s)]s=2 = [(2s + 3)/(s2 – 4)]s=2 = 1For s = -2,

the value of A can be obtained as:A = [s × F(s)]s=-2 = [(2s + 3)/(s2 – 4)]s=-2 = 1For s = 0, the value of B can be obtained as:B = [s × F(s)]s=0 = [(2s + 3)/(s2 – 4)]s=0 = 3/(-4) = -3/4For s = 0, the value of D can be obtained as:D = F(0) – A – B = [(2s + 3)/(s2 – 4)]s=0 – 1 – (-3/4) = -1/4

Thus, the partial fraction representation of F(s) is:F(s) = [(s + 2)/4] – [(s – 2)/4]Taking the inverse Laplace transform, we have:f(t) = (1/4)(e2t – e-2t) + δ(t)

Thus, we have found the inverse transformation of Laplace for the given expressions. The solution for each question is as follows:1. \( f(t)=2-2t^{2}+\frac{1}{2}e^{\frac{3}{2}t} \)2. \( f(t)=\frac{1}{3}e^{-3t}\sin 3t+\frac{1}{3}\cos 3t+\frac{4}{9}\sin 3t-\frac{1}{9}\delta (t) \)3. \( f(t)=6-7e^{-4t} \)4. \( f(t)=\frac{1}{4}(e^{2t}-e^{-2t})+\delta (t) \).

To know more about inverse transformation, click here

https://brainly.com/question/30404106

#SPJ11