Elizabeth, Frank, Gary, and Helen are getting in line to buy lunch in the cafeteria. How many different ways could they line up so that Helen is first in line?

Answer:

2.5%

Step-by-step explanation:

656 / 640 = 1.025

1.025 into percent is 102.5%

102.5% - 100% = 2.5

640 + 2.5% of 640 = 656

BOOM

The required value of increase in price is 2.5%.

A percentage is a value that indicates 100th part of any quantity.

A percentage can be converted into a fraction or a decimal by dividing it by 100.

Given that,

The cost of ticket at present is £656.

Its cost last year was £640.

Then, the difference between the costs is given as,

656 - 640 = £16

Now, the increase in percentage can be found by taking the ratio of the difference to the last year price and multiplying it by 100 as below,

Percentage increase = 16/640 × 100%

                                   = 2.5%

Hence, the percentage increase in price is 2.5%.

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Seriousness is what is being portrayed by the oxymoron and paradox in this excerpt.
Simply put, a serious relationship is one in which you are fully committed to your partner. You are completely open and honest with each other. You trust each other deeply. And you are on the same page together not only from your values ​​and ethics perspective, but also from your future perspective.

Monks do not claim that "moderate" love is more wise than fleeting love, but they guide Romeo to understand the reason for his wisdom and explore their relationship.

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:x = 7° [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

Since the two triangles are congruent, their corresponding sides and angles should be equal to one another too.

That means : Angle ADB = Angle CDB.

[tex]\large \textsf{Solve for x } [/tex]

[tex]\qquad \tt \rightarrow \:7x = 49 \degree[/tex]

[tex]\qquad \tt \rightarrow \:x = \cfrac{ 49 \degree}{7}[/tex]

[tex]\qquad \tt \rightarrow \:x = { 7 \degree}{}[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

Proof explained below

Step-by-step explanation:

Tan trigonometric ratio

[tex]\sf \tan(\theta)=\dfrac{O}{A}[/tex]

where:

Draw a diagram to help visualize the scenario (see attached).

If the angles are complementary, their sum is 90°.

Therefore, let one of the angles be [tex]x[/tex] and the other angle be [tex]90^{\circ}-x[/tex].

Use the tan trig ratio to create two equations with the missing side length.

Right triangle ACD

Given:

Substituting the given values into the tan trig ratio:

[tex]\implies \tan (x)= \dfrac{\textsf{CD}}{9}[/tex]

Right triangle BCD

Given:

Substituting the given values into the tan trig ratio:

[tex]\implies \tan (90^{\circ} - x)= \dfrac{\textsf{CD}}{4}[/tex]

[tex]\textsf{As }\:\tan(90^{\circ} - x)= \cot (x):[/tex]

[tex]\implies \cot(x)= \dfrac{\textsf{CD}}{4}[/tex]

[tex]\implies \dfrac{1}{\tan(x)}= \dfrac{\textsf{CD}}{4}[/tex]

[tex]\implies \tan(x)= \dfrac{4}{\textsf{CD}}[/tex]

Therefore, the two equations are:

  [tex]\textsf{Equation 1}: \quad \tan (x)= \dfrac{\textsf{CD}}{9}[/tex]

  [tex]\textsf{Equation 2}: \quad \tan(x)= \dfrac{4}{\textsf{CD}}[/tex]

Substitute one equation into the other and solve for CD:

[tex]\implies \sf \dfrac{CD}{9}=\dfrac{4}{CD}[/tex]

[tex]\implies \sf CD \cdot CD= 4 \cdot 9[/tex]

[tex]\implies \sf CD^2=36[/tex]

[tex]\implies \sf CD=\sqrt{36}[/tex]

[tex]\implies \sf CD= \pm 6[/tex]

As distance cannot be negative, CD = 6 m only, thus proving that the height of the tower is 6 m.

Answer:

[tex]composite \: function \: is \: given \: as \: in \: two \: forms \\ \\ f(g(x))and \: g(f(x)) \: therefore \: f(g(x)) =( x {}^{2} ) {}^{2} + 2 \\ whereas \: g(f(x)) = (x {}^{2} + 2) {}^{2} \\ domain of \: f(x) = x {}^{2} is( \infty - \infty ) \: and \: domain \: of \: g(x) = x {}^{2} + 2 \: is \: also \: ( \infty - \infty )[/tex]

The range of the function on the graph is (c) all real numbers less than or equal to 3

The missing graph is added as an attachment

From the graph, we have the following highlights

This means that the range is (c) all real numbers less than or equal to 3

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Answer:

12

Step-by-step explanation:

3(4)=12

The 4th term of the sequence is 12.

A grouping of numbers in a specific order is known as a sequence. On the other hand, a series is described as the accumulation of a sequence's constituent parts.

In the sequence 1, 3, 5, 7, 9, …, 1 is the first term, 3 is the second term, 5 is the third term, and so on.

Given:

sequence, S(n): 3n

Now, to find the 4th term of sequence we have to put n= 4.

So, the term of sequence

S(4) = 3(4)

s(4) = 12

Hence, the 4th term is 12.

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Answer:

There is a negative correlation.

Step-by-step explanation:

The point on the scatter plot are downwards sloping. This implies that there is a negative relationship between the variables temperature and sales. Thus, there is a negative correlation.

The value of  x is 3.711 yd

area = √(s * (s - a) * (s - b) * (s - c))

where

s is the semi perimeter - half of triangle perimeter:

s = (a + b + c) / 2

Using Heron's Formula

area = √(s * (s - a) * (s - b) * (s - c))

area = √(14* (15- 6) * (15 - 14) * (15 - 10))

area = √(14* 9 * 1 * 5))

area = √ 630

area = 25.981 yd²

Now,

area of triangle= 1/2 * b * h

25.981 = 1/2 * 14 *h

51.962 = 14h

h= 3.711 yd

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Answer:

84/400

Step-by-step explanation:

First, divide 35 by 100 to get the decimal, 0.35. Then, multiply 0.35 x 400. You should get 140. Now the question says 2/5 of the remaining are blue. You need to multiply 2/5 x 140 to get 56. 56 are blue. So now subtract 56 from 140 to get 84. The answer (not in simplest form) is 84/400.

The day of the month that was 75% of the pond algae-free is: on day 28 or third day.

Since we were told the algae  doubled every day until it was  covered in algae on day 30 of the month.

Hence:

Day 30 (First day)= It was 100% covered.

Day 29 (Second day)=It was 50% covered.

Day 28 (Third day )=it was 25% covered, which will be the same as 75% pond algae-free.

Therefore the day of the month that was 75% of the pond algae-free is: on day 28 or third day.

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The complete question is:

amount of algae covering the Smith's backyard pond doubled every day until it was completely covered in algae on day 30 of the month. On what day of that month was 75% of the pond algae-free?

The height of the tower is 452.66 ft

The angle formed by the line of sight and the horizontal plane for an object above the horizontal.

The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line.

Given:

we have two angles one of which is angle of elevation and another angle depression.

Using trigonometric ratio,

tan ∅ = P / B

tan 32° = h / 425

0.624= h /425

h= 265.569 ft

again,

tan 29° = h(bottom of the tower) / 425

h(bottom of the tower) = 425 × tan 29°

h(bottom of the tower)  = 235.581 ft

Thus, Height of tower = h(top of the tower) + h(bottom of the tower)

Height of tower = 265.569  + 235.581

Height of tower = 501.15 ft

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Answer: C slope= 1/2 y-intercept =2

Step-by-step explanation:

The triangle ABC was dilated with a scale factor of 5 to form a figure with new coordinates at A'(-15, -5), B'(10, -10) and C'(-5, -20).

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

The triangle ABC was dilated with a scale factor of 5 to form a figure with new coordinates at A'(-15, -5), B'(10, -10) and C'(-5, -20).

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\[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{What is the formula for finding slope?}[/tex]

[tex]\mathbf{\dfrac{y_2 - y_1}{x_2 - x_1} = slope}[/tex]

[tex]\huge\textbf{Often people understand it better by:}[/tex]

[tex]\mathbf{\dfrac{rise}{run} = slope}[/tex]

[tex]\huge\textbf{Answering the given question:}[/tex]

[tex]\mathbf{y_2 \rightarrow 11}\\\\\\\mathbf{y_1 \rightarrow 5}\\\\\\\mathbf{x_2 \rightarrow 0}\\\\\\\mathbf{x_1 \rightarrow 3}[/tex]

[tex]\huge\textbf{Now, that we have that information out}\\\huge\textbf{the way, we can answer the question.}[/tex]

[tex]\huge\textbf{Your equation should look like this:}[/tex]

[tex]\mathbf{\dfrac{11 - 5}{0 - 3} = slope}[/tex]

[tex]\huge\textbf{Solving for the answer:}[/tex]

[tex]\mathbf{\dfrac{11 - 5}{0 - 3} = slope}[/tex]

[tex]\mathbf{\rightarrow \dfrac{6}{-3} = slope}[/tex]

[tex]\mathbf{\rightarrow 6 \div -3 = slope}[/tex]

[tex]\mathbf{\rightarrow -2}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\textsf{S}\frak{lope \rightarrow -2}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

90 inches tall

Step-by-step explanation:

7x12=84

84+6=90

The condition that must not be met before usage us that the coefficient of the x²-term must be positive.

The standard quadratic function is given as;

ax²+bx + c = 0

From the equation shown above, the leading degree of the equation is 2. The following are condition that must be met before you can use

the quadratic formula to find the solutions of an equation.

The condition that must not be met before usage us that the coefficient of the x²-term must be positive.

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The value of x in the triangle is (a) 22

The complete question is in the attached image.

From the attached image of the triangle, we have:

[tex]\sin(45) = \frac{x}{22\sqrt 2}[/tex]

Evaluate sin(45)

[tex]\frac{1}{\sqrt 2} = \frac{x}{22\sqrt 2}[/tex]

Solve for x

[tex]x = \frac{22\sqrt 2}{\sqrt 2}[/tex]

Divide

x = 22

Hence, the value of x is (a) 22

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the probability that a positive integer less than 100 picked at random has all distinct digits is 90.

He has 99 positive integers less than 100.

The integers that do not have all distinct digits have the same digit twice.

11, 22, 33, 44, 55, 66, 77, 88, 99

There are 9 integers that do not have distinct digits, therefore there are 99-9 integers that do.

Probability is without a doubt how probable something is to show up. whenever we are uncertain about the final results of an occasion, we can talk about the possibilities of sure outcomes and how probable they are. The analysis of events governed by opportunity is referred to as records.

A chain of moves in which the results are usually unsure. The tossing of a coin, selecting a card from a deck of playing cards, throwing a cube. occasion. it is a single final results of an experiment. Getting a Heads whilst tossing a coin is an event.

Simple probability is the calculation of an outcome or the chance of an event ever taking place. coverage companies use possibility statistics to determine the possibilities of having to pay out a declare. A simple chance is calculated by way of dividing a particular outcome through all of the feasible outcomes.

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Answer:

[tex]p = 52.942259755149776[/tex]

Step-by-step explanation:

This is basic trigonometry.

[tex] \cos(39) = \frac{e}{22} [/tex]

[tex]e = \cos(39) \times 22[/tex]

[tex] \sin(39) = \frac{d}{22} [/tex]

[tex]d = \sin(39) \times 22[/tex]

And finally perimeter (p):

[tex]p = 22 + e+ d[/tex]

Answer:

[tex]25a^6-4[/tex]

Step-by-step explanation:

So if you look at the equation, you'll notice it's being multiplied by it's conjugate which can be expressed as: x+a and x-a. See how only the sign changes? Well if remember the differences of squares, it looks like that, because it is. Essentially the difference of squares says that: [tex]a^2-b^2=(a-b)(a+b)[/tex]. So expanding this out will result in [tex](5a^3)^2-(2)^2[/tex] which simplifies to: [tex]25a^6-4[/tex]. If you're confused on how I got 25a^6. Try to think of a^3 as three a's rather than simply an exponent. and since it has a coefficient of 5. 5a^3 is the same as (5 * a * a * a). Now if you square this you have (5 * a * a * a) * (5 * a * a * a). So if you group like terms you'll end up with 6 a's being multiplied by each other (which can be expressed as a^6) and 5 * 5 which is 25.

The multiplication can be transformed into the difference of squares using the rule:(a−b)(a+b)=a²-b² . Gets the square of 2.

(5a³)²-4

Expand (5a³)².

5² (a³)² -4

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

5²a⁶-4

25a⁶-4 ====> Answer

Answer:

$2.20

Step-by-step explanation:

100 cents= $1

70+60= 130. Move the decimal to the left twice to get $1.30.

50+40= 90 cents

90+30= $1.20+ the 1 dollar from before and you get $2.20

Answer: 220

Step-by-step explanation:

40+50+60+70= 220

Because the questions says in all we have to add it all together.

2x-15y = 117 is the simplified form of the equation.

Equation : In a mathematical sentence, if two expressions are present in left and right side of an equal sign, then the mathematical sentence is called an equation.

If, a, b, c be integers and x is x-intercept & y is y-intercept, then ax+by=c is called equation of line.

Given that, the equation of the line that passes through the points (-9,-9)(−9,−9) and (6,-7)(6,−7).

Now, (-9,-9) & (6, -7) have a line through them with slope = (-9+7)/(-9-6) = 2/15

Therefore, (y+7) = 2/15×(x-6)

⇒ y+7 = 2x/15 - 4/5

⇒ y = 2x/15 - 4/5 - 7

⇒ y = 2x/15 -39/5

This is the equation in slope intercept form.

Multiplying the equation with 15, we get,

⇒ 15y = 2x-117

⇒ 2x-15y = 117 , which is the simplified form of the equation.

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Answer:

if you divide 10 by 8 it should be 10/8 so a

Hope This Helps!!!

Answer: A

Step-by-step explanation: Step 3 is incorrect as it should be 10/8 (or 5/4 simplified.) When we have 8x = 10, we are looking at what number "x" multiplied by 8 gives 10. Meaning we need to have 8(?) = 10. So, to find out what x is, we just divide by 8 from both sides. Since 8x/8 cancels out and becomes just x, we get x = 10/8 since we are dividing 10 by 8. We get 5/4 simplified or 10/8 unsimplified.

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jill is 24 years old.

The ratio of vina's age to jill is 7:6 .

      Let vina's age =7x

      let jill's age = 6x

If vina is 4 years older than jill.

Then ,                   7x - 6x = 4

                                  x = 4

Now  vina's age = 7x = 7 * 4 = 28 years

          jill's age = 6x = 6 * 4 = 24 years.

Therefore, jill is 24years old.

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there are total 64 is the answer if she puts 2 cookies in each packet

hope this helps u :)

Using the margin of error for the z-distribution, the sample sizes are given as follows:

a) 822.

b) 1068.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

We have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

Item a:

The estimate is of [tex]\pi = 0.26[/tex], hence we solve for n when M = 0.03.

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.03 = 1.96\sqrt{\frac{0.26(0.74)}{n}}[/tex]

[tex]0.03\sqrt{n} = 1.96\sqrt{0.26(0.74)}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.26(0.74)}}{0.03}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.26(0.74)}}{0.03}\right)^2[/tex]

n = 821.2

A sample of 822 is needed.

Item b:

No prior estimate, hence [tex]\pi = 0.5[/tex].

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.03 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.03\sqrt{n} = 1.96\sqrt{0.5(0.5)}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.5(0.5)}}{0.03}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.5(0.5)}}{0.03}\right)^2[/tex]

n = 1067.11

A sample of 1068 is needed.

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The simulation design regarding the probability is:

Let 1, 3 = fiction.

Let 2, 4 = non fiction.

Let 5,6 = poetry

It should be noted that a simulation design us used to make a particular prediction.

In this case, a number cube can be used to estimate the probability.

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