I need help with all of these ☹️

=50

Step-by-step explanation:

=1/2×100

=1×50

=50

In linear equation, £ 8.4 much does a ticket cost.

What are a definition and an example of a linear equation?

They each pay £ 6.30

the total they pay is

6.3 × 4 = £ 25.2

buy three tickets and get a free ticket

3 tickets is £ 25.2

25.2/3 = £ 8.4

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From the given stem-and-leaf plot, we have that:

a) 80.65% of days in this month were hotter than 100 ºF.

b) The shape of the distribution is negatively skewed.

c) The value of 84, with key 8|4, appears to be an outlier in this data-set.

The stem-and-leaf plot lists all the measures in a data-set, with the first number as the key, for example:

4|5 = 45.

From the plot in this problem, the 31 observations are given as follows:

84, 93, 97, 99, 100, 101, 101, 102, 102, 103, 104, 104, 104, 105, 105, 106, 106, 106, 107, 107, 108, 108, 109, 109, 109, 110, 111, 111, 113, 115.

For item a, we have that of the 31 observations, 25 were hotter than 100 ºF, hence:

25/31 = 80.65%.

80.65% of days in this month were hotter than 100 ºF.

For item b, using a calculator, we have that:

Since the mean is less than the median, the shape of the distribution is negatively skewed.

For item c, we have that:

Outliers are values that are more than 1.5IQR from the quartiles, hence:

84 < 91.5, hence the value of 84, with key 8|4, appears to be an outlier in this data-set.

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The coordinates are  A'(14, 3), B'(-6. 2) and C'(-8, 6)

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.

given rule:

(x,y) -> (2x,y-3)

Also, we have

A(7,6), B(-3,5), and C(-4,9)

so, after applying the rule we have the coordinates

A'(14, 3)

B'(-6. 2)

C'(-8, 6)

Hence, the coordinates are A'(14, 3), B'(-6. 2) and C'(-8, 6)

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The interquartile range of the players' weights = 48 pounds.

The boxplot attached to this question is missing. It was obtained online and is attached to this solution of the question.

It should be noted that the following is true for a boxplot.

A box plot gives a visual representation of the distribution of the data, showing where most values lie and those values that greatly differ from the rest, called outliers.

The elements of the box plot are described thus;

The bottom side of the box represents the first quartile, and the top side, the third quartile. Therefore, the width of the central box represents the inter-quartile range.

The horizontal line inside the box is the median.

The lines extending from the box reach out to the minimum and the maximum values in the data set, as long as these values are not outliers. The ends of the whiskers are marked by two shorter horizontal lines.

Variables in the dataset, higher than Q3+(1.5×IQR) or lower than Q1-(1.5×IQR) are considered outliers and are usually shown using dots above the top whisker or below the bottom whisker.

So, it is evident that for this question,

First quartile = 174 pounds

Third quartile = 222 pounds

Inter Quartile Range = (Third quartile) - (First quartile)

= 222 - 174

= 48 pounds.

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The probability that a hand of five cards chosen at random and without replacement from a standard 52 card deck will have a king of spades, exactly one other king, and exactly two queens = 0.000332

A deck of cards consist of 52 cards in which each 13 cards are from 4 suits: Spades, Hearts, Diamonds and Clubs.

Each suit consist of cards Ace, King, Queen, Jack and other 9 cards.

So in 52 cards there is 4 kings and 4 queens each.

Five cards are selected at random and without replacement.

Five cards from a 52 deck cards can be chosen in 52C5 ways.

A spade king can be chosen in 1C1 way. [ Since there is only one spade king]

Exactly one other king can be chosen in 3C1 ways. [Since now only 3 kings are remaining after choosing 1 spade king]

Exactly 2 queens can be chosen in 4C2 ways.

Now 4 cards are selected out of 5. The remaining 1 card is chosen out in 48C1 ways.

So the probability that the five cards chosen will have a king of spades, exactly one other king, and exactly two queens

                           = (1C1 x 3C1 x 4C2 x 48C1) /52C5 = 18/54145 =0.000332

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Answer:

3 3/5

Step-by-step explanation:

Answer:

[tex]y _{ \rm parallel} = - 5x +27[/tex]

Step-by-step explanation:

The equation of line p is in point-slope form , that's

[tex]y-y_1=m(x-x_1)[/tex]

Where:

Since line I is parallel to the line p , line I has the same slope as p. From the given equation of p , we can consider the slope of line p -5. Hence the slope of line I is also -5.

Now To determine the equation of I.

We have

So, the equation of line l is

[tex] y - 47 = - 5(x - ( - 4)) \\ \implies y - 47 = - 5 x- 20 \\ \implies \boxed{y _{ \rm parallel} = - 5x + 27}[/tex]

And we're done!

There are [tex]Three[/tex] planes in the diagram containing point "W".

As per the question statement, We are given a diagram comprising of various planes and we are supposed to find out the number of planes comprising of point "W".

To solve this question, we should have the knowledge of what exactly is a plane.

In the given diagram, we can see that the point "W" lies on the plane formed by the following points:

As Point "W" is common is all the given [tex]Three[/tex] planes hence "3" is the correct answer.

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Answer: D

Step-by-step explanation:

i did the test

Answer:

Step-by-step explanation:

subsitute x with value given in bracket

a) f(1) = (1)²  + 1 = 2

b) f(-3) = (-3)² + 1 = 10

c) f(b³) = (b³)² + 1 = b^6 + 1

d) f(x-1) = (x-1) +1 = x

Answer:

n = -0.4, or n = -2/5.

Step-by-step explanation:

They are the same btw.

Answer:

The answer is 2, and thanks for asking my day's good :D
How's your day?

Step-by-step explanation:

The solution to the inequality where the inequality expression is given as: -1 < x + 3 < 5 is -4 < x < 2

The inequality expression is given as:

-1 < x + 3 < 5

Subtract 3 from all parts of the inequality expression

So, we have:

-3 -1 < x + 3 -3 < 5 - 3

Evaluate the difference and sum

So, we have:

-4 < x < 2

Hence, the solution to the inequality where the inequality expression is given as: -1 < x + 3 < 5 is -4 < x < 2

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By graphing the equation y = 0.2x, we find that x is equal to -10 when y is -2, x is equal to 0 when y is 0, and x is equal to 10 when y is 2.

To graph the equation y = 0.2x, we can plot a few points and then connect them to create the line.

Let's calculate the corresponding values of x when y takes on the values of -2, 0, and 2:

When y = -2:

-2 = 0.2x

x = -2 / 0.2

x = -10

When y = 0:

0 = 0.2x

x = 0 / 0.2

x = 0

When y = 2:

2 = 0.2x

x = 2 / 0.2

x = 10

Using these values, we can plot the points (-10, -2), (0, 0), and (10, 2) on the coordinate plane. Drawing a line passing through these points, we obtain the graph of the equation y = 0.2x.

The graph will be a straight line that passes through the points (-10, -2), (0, 0), and (10, 2). The line will have a positive slope, indicating that as x increases, y increases at a slower rate.

The graph visually represents the relationship between x and y according to the equation y = 0.2x. It shows that for every increase of 1 unit in x, y increases by 0.2 units.

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The variable in the expression is g.

The coefficient of g is 10.

The constant term is 12.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

g + 12 + 9g

Add the like terms.

10g + 12

Now,

The variable in the expression is g.

The coefficient of g is 10.

The constant term is 12.

Thus,

The coefficient is 10.

The constant is 12.

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Answer:

3(c+30)+4(c+30), 7c + 210, 3c+90+4c+120

Step-by-step explanation:

I this helps :D

Answer:

I think it's the first one

Step-by-step explanation:

because he went to class 3 times a week and u would need to multiply 3 by c minutes + 30 minutes ( u have to add them to find the total amount of minutes he exercised during one class and multiply that by 3 after adding them together bc he did that class 3 times which means he did the exercise 3 times so u multiply) then u add that with next week where he went 4 times and did c minutes+ 30 minutes. HOPE THIS HELPS!

Answer:

(i)  2² · 3 · 7

(ii)  3024

(iii) k = 16

(iv) 12 cm

Step-by-step explanation:

The first few prime numbers are:  2, 3, 5, 7, 11, 13, 17, ...

To find which prime numbers multiply together to make 84, start by dividing 84 by the first prime number, 2:

⇒ 84 ÷ 2 = 42

As 42 is not a prime number, we need to divide again:

⇒ 42 ÷ 2 = 21

As 21 is not a prime number, we need to divide again.  

21 is not divisible by 2, so let's try dividing by the next prime number, 3:

⇒ 21 ÷ 3 = 7

As 7 is a prime number, we can stop.

Therefore, 84 is the product of:

⇒ 84 = 2 · 2 · 3 · 7

As 2 appears two times, we can write this using exponents:

⇒ 84 = 2² · 3 · 7

Lowest Common Multiple (LCM):  The lowest multiple shared by two or more numbers.

Prime Factors Method of finding LCM

Step 1

Find the prime factorization of each number.

From part (i):            84 = 2² · 3 · 7

Given in part (ii):    432 = 2⁴ · 3³

Step 2

Write each number as a product of primes, matching primes vertically where possible:

[tex]\begin{array}{ r c c c c c c c ccccccccc}84&=& 2 & \cdot & 2 & \cdot & & & & & 3& \cdot & & & && 7\\\\432 &=& 2 & \cdot & 2 &\cdot & 2& \cdot & 2& \cdot & 3& \cdot & 3& \cdot & 3\\\\\cline{1-17} \\\sf LCM & = & 2 & \cdot & 2 &\cdot & 2& \cdot & 2& \cdot & 3& \cdot & 3& \cdot & 3 &\cdot & 7\end{array}[/tex]

Step 3

Bring down the primes in each column then multiply the factors to get the LCM:

⇒ LCM = 2 · 2 · 2 · 2 · 3 · 3 · 3 · 7

⇒ LCM = 2⁴ · 3³ · 7

⇒ LCM = 3024

From part (ii) we know that the prime factorization of 432 is:

432 = 2⁴ · 3³

A perfect cube is a number multiplied by itself three times.

One of the factors of 432 is a perfect cube → 3³.

Therefore,

[tex]\begin{aligned}432 & = 2^4 \cdot 3^3\\\\\implies \dfrac{432}{2^4} & = 3^3\\\\\dfrac{432}{16} & = 3^3\end{aligned}[/tex]

So we need to divide 432 by 2⁴ to get the perfect cube 3³.

Therefore,

⇒ k = 2⁴

⇒ k = 2 · 2 · 2 · 2

⇒ k = 16

To find the largest possible length of the side of the square, we need to find the greatest common factor of 432 and 84.

Prime Factors Method of finding GCF

Step 1

Find the prime factorization of each number.

From part (i):            84 = 2² · 3 · 7

Given in part (ii):    432 = 2⁴ · 3³

Step 2

Write each number as a product of primes, matching primes vertically where possible:

[tex]\begin{array}{ r c c c c c c c ccccccccc}84&=& 2 & \cdot & 2 & \cdot & & & & & 3& \cdot & & & && 7\\\\432 &=& 2 & \cdot & 2 &\cdot & 2& \cdot & 2& \cdot & 3& \cdot & 3& \cdot & 3\\\\\cline{1-17} \\\sf GCF & = & 2 & \cdot & 2 & \cdot & & & & & 3& & & & && \end{array}[/tex]

Step 3

Bring down the primes in the columns where both numbers have the factor, then multiply the factors to get the GCF:

⇒ GCF = 2 · 2 · 3

⇒ GCF = 12

Therefore, the largest possible length of the side of the square is 12 cm.

Answer:

True.

Step-by-step explanation:

(LHS) cos 6∘ cos 42∘ cos 66∘ cos 78∘

1/4 [cos(66∘+6∘) = cos(66∘-6∘)] • [cos(78∘+42∘)+cos(78∘-42∘)]

= 1/4(sin18∘+12)(-12+cos36∘)

[∵cos72∘ = cos(90∘−18∘) = sin18∘]

1/4[(5-√-1)/4+1/2][−1/2+(5-√+1)/4]

[∵sin(18∘ = (5-√-1)/4, and, cos 36∘ = (5-√+1)/4]

1/4(5-√+1)/4(5-√-1)/4 = (5-1)/64

= 4/64 = 1/16 (RHS)

Therefore, the cosine is equal to 1/16.

Answer:

Step-by-step explanation:

The midpoint and length of the points J(4,3) and K(2,-3) is calculated as (1,0) and 40.

The midpoint and length of the points L(-4,5) and N(5,-3) is calculated as (-12,1) and 145.

Given : The endpoints J(4,3) and K(2,-3) and L(-4,5) and N(5,-3)

We need to find the midpoint and length of these endpoints.

The formula for midpoint is x1+x22, y1+y22

From the first endpoints,  x1=4 , y1=3 , x2=2 , y2=-3

4+22, 3-32 => (22,02) => (1,0)

So, the midpoint for the endpoints is (1,0)

The formula to find the length is (x2-x1)2+(y2-y1)2

From the first endpoints , the length becomes

(2-4)2+((-3)-3)2=> (-2)2+(-6)2 => 4+36 => 40

The formula for midpoint is x1+x22, y1+y22

From the first endpoints,  x1=-4 , y1=5 , x2=5 , y2=-3

-4+52, 5-32 => (-12,22) => (-12,1)

So, the midpoint for the endpoints is (-12,1)

The formula to find the length is (x2-x1)2+(y2-y1)2

From the first endpoints , the length becomes

(5+4)2+((-3)-5)2=> (9)2+(-8)2 => 81+64 => 145

Hence, the midpoint and the length from the endpoints is calculated and determined.

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Answer:

53.7 degrees.

Step-by-step explanation:

The number of movies that would make the monthly cost equal is 4.

The total monthly cost is a function of the cost per month, total movies watched and the cost per movie.

The equations that represent the total cost of using the streaming sites would be in the form:

Total cost = cost per month + (number of movies watched x cost per movie)

Plan 1: $22 + ($x)

Plan 2: $14 + (3x)

When both plans have the same monthly cost, the two above equations would be equal

$22 + x =$14 + 3x

In order to determine the value of x, take the following steps:

Combine similar terms: $22 - $14 = 3x -x

Add similar terms together: $8 = 2x

Divide both sides of the equation by 2: $8 /$ 2 = x

x = 4

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Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. The person has invested $35,000 in the fund returning at a rate of 6.5%.

Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,

SI = PRT = (R% of P)T

where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.

Let the amount invested in the first fund be represented by x, then the amount invested in the second fund will be ($50,000 - x).

Now, if the 2 funds earn 6.5% and 9% simple interest. Also, in the first year, they earned a total of $3625 from the interest. Therefore, we can write the equation to represent the given situation as,

6.5% of x + 9% of ($50,000 - x) = $3625

0.065x + 0.09(50,000 - x) = 3625

0.065x + 4,500 - 0.09x = 3,625

0.065x - 0.09x = 3625 - 4500

0.025 = 875

x = 875/0.025

x = 35,000

Therefore, the person has invested $35,000 in the fund returning at a rate of 6.5%.

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If we reflect the point (-5,2) (five, -two) over the x-axis (line of symmetry) the reflected point is (-5,-2). If we reflect the point (-5,2) (five, - two) over the y-axis (line of symmetry) the reflected point is (5,2).

What are the x-axis, and y-axis?

The point (-5,2) is plotted as red in the picture attached.

To reflect a point over the x(ax)-axis, the x(ax) value must be the same and the y value must be the opposite.

To reflect a point over the x(ax)-axis, the y(y) value must be the same and the x(ax) value must be the opposite.

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The expressions that represents the vertical distance between the top of the mango tree and the tips of its roots is C. None of the above.

It should be noted that the mango tree stands 2.6 meters above the ground. Its roots extend 7/5 meters below the ground.

In this case, the vertical distance will simply be the difference between the values that are given.

This wasn't written on this case.

Therefore, the correct option is C.

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Answer:

[tex]a_{n}[/tex] = 1 [tex](5)^{n-1}[/tex]

Step-by-step explanation:

the explicit formula for a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

here a₁ = 1 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{5}{1}[/tex] = 5 , then

[tex]a_{n}[/tex] = 1 [tex](5)^{n-1}[/tex]

Answer: 3

Step-by-step explanation:

3 * 3 * 3 = 27

Answer:

3

Step-by-step explanation:

The expression is cube root.

The root function essentially wants to find a number that when multipled n times will give the input to the function.

In this case n = 3

We need a number when multiplied by itself 3 times will give us 27.

In other words we need [tex]x^{3}[/tex] = 27

If u rearrange u simply get the expression given and u can solve simply by way of calculator.

The conditional operator creates a compound statement that sets up a condition for something to be true. Therefore, if the condition is met, the statement is true. The parts of the conditional statements are two, the first simple statement in a conditional is called the antecedent  and the second simple statement is called the consequent. So, for two statements A (antecedent) and B (consequent) we will have that:

A → B that means: If A then B

In this problem:

A:  A number is even.

B: The number is divisible by 2.

Thus:

A → B: If a number is even, then the number is divisible by 2.

So, the conclusion of this conditional statement is the consequent, that is,  the number is divisible by 2.

Accordingly, the right answer is D. The number is divisible by 2.

the complete question is

What is the conclusion of the following conditional? A number is divisible by 2 if even.

A. The sum of the digits of the number is divisible by 2.

B. If a number is even, then the number is divisible by 2.

C. The number is even.

D. The number is divisible by 2.

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