HURRY GETTING TIMED
Which expression is equivalent to 20 n=3
20 n=3 + 20n=3

Answer:

Step-by-step explanation:

If to lines are parallel then they could go on forever without touching at any given point.

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

Read the values from the graph in the usual way: find the x-coordinate, then locate the point on the graph and find its y-coordinate.

You find the y-coordinate by following the horizontal line to the y-axis, where the numbers are.

Answer:

Step-by-step explanation:

Jill needs to make 2 full glasses of orange drink for each of the 50 people, which means she needs to make a total of 100 glasses of orange drink. Since each glass requires 250 millilitres of orange drink, Jill needs a total of 25 litres (100 glasses x 250 millilitres per glass) of orange drink.

According to the instructions, Jill needs to mix 1 part of orange squash with 4 parts of water. This means that for every 5 parts of drink, 1 part is orange squash and 4 parts are water. Therefore, Jill needs to use 5 times the amount of water as the amount of orange squash.

If Jill needs to make 25 litres of orange drink, then she needs to use 1/5th of that amount (5 parts) or 5 litres of orange squash.

A one litre bottle of orange squash costs £2. Therefore, Jill needs to buy 5 bottles of orange squash at a total cost of £10.

I hope this helps you with your calculations!

Answer:

107.5

Step-by-step explanation:

Make sure you use PEMDAS! (parentheeses, exponets, multiplication, divison, addition, and subtraction!)

So, 5/2 is 2.5 plus 100 is 102.5 plus another 5 is 107.5! Hope this helped :)

Answer:

64 square centimeters

Step-by-step explanation:

The surface are of a pyramid is found by finding the sum of the area of the four sides and the base.

Finding the triangular face:

Area of triangle = \(\frac{1}{2} b h\) = \(\frac{1}{2}*4*6 = 12\)

12 * 4 (4 sides) = 48 square cm

Finding the Base = \(w * l = 4 * 4 = 16\)

Finally, we add it together. 48 + 16 = 64

The correct option for the approximate value of -12 + √32  is -6.3 to the nearest tenth.

An approximation is anything that is similar, but not exactly equal, to something else.

The given expression is  −12 + √32

The value of √32 is given as 5.656

Since,after decimal 6 to the right of 5 is greater than 5

To the nearest tenth, we can write as 5.66

∴ √32 = 5.66

For the required value of the expression we can write,

−12 + √32

Put the value of √32  = 5.66

Putting values in expression we have,

-12 + √32 = -12 + 5.66

Solving them

⇒ -12 + √32 = -6.34

Hence,the approximate value of -12 + √32  is -6.3 to the nearest tenth.

So, the correct option is -6.3.

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Answer:

Step-by-step explanation:

1/3

The lateral surface area of a cone can be less than or greater than half the lateral surface area of a cylinder, depending on the specific dimensions of each shape. The given statement is true.

It depends on the specific dimensions and measurements of cone A and cylinder B. In general, however, it is not true that the lateral surface area of a cone is exactly half the lateral surface area of a cylinder with the same base and height.

The lateral surface area of a cone is given by πrl, where r is the radius of the base and l is the slant height of the cone. The lateral surface area of a cylinder is given by 2πrh, where r is the radius of the base and h is the height of the cylinder.

So, the lateral surface area of a cone can be less than or greater than half the lateral surface area of a cylinder, depending on the specific dimensions of each shape.

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This results in the systematic measurement error as the deviation is consistently in one direction. Hence, this is an

example of systematic measurement error.

In the given scenario, the researcher reviews study data about head circumference in newborns and notes that study

personnel are measuring from the end of the measuring tape and not from the zero point, which is 1 cm from the end.

This is an example of systematic measurement error.

Systematic measurement error refers to a consistent deviation from the true value in a particular direction in a series of

measurements.

This error is also referred to as bias. In the given scenario, the personnel are measuring from the end of the measuring

tape and not from the zero point, which is 1 cm from the end.

This results in the systematic measurement error as the deviation is consistently in one direction. Hence, this is an

example of systematic measurement error.

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Answer:

?wdym

Step-by-step explanation:

By application of the combination formula, there are 210 ways for distributing 10 indistinguishable candies among 4 children.

Combination is the arrangement of objects in which order is not taken into account.

The applicable formula is:

n combination r = n!/[(n - r)!r!]

where n is the number of indistinguishable items (10 candies), and r is the possible number of recipients (4 kids).

Hence;

10 combination 4 = 10!/[(10 - 4)!4!] ways

10 combination 4 = 10!/(6! × 4!) ways

10 combination 4 = (10 × 9 × 8 × 7 × 6!)/(6! × 4 × 3 × 2 × 1) ways

10 combination 4 = 10 × 3 × 7 ways

10 combination 4 = 210 ways

Therefore, there are 210 ways for the 10 indistinguishable candies to be distributed among the 4 children by with the application of combination formula.

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Answer:

30°, 60° and 90°

Step-by-step explanation:

Given the expression Arccos (√3/2)=β, we can use the expression to calculate one of the acute angles in a right angled triangle.

Note that a right angled triangle is made up of two acute angles and a right angled (90°)

Let's get one of the acute angles first

If Arccos (√3/2)=β

β = cos^-1 √3/2

β = 30°

This shows that one of the acute angles is 30°

To get the third angle, we know that sum of angles in a triangle is 180° and since we already know two of the angles, i.e 90° and 30°, we can get the third angle.

90+30+x = 180

120+x = 180

x = 180-120

x = 60°

All the angle measurement for the right angled triangle are 30°, 60° and 90°

The area of one of the base of the pentagonal prism is 35 square units.

What is a pentagonal prism?

A prism having two top and bottom pentagonal bases and five rectangular sides is called a pentagonal prism. It is a special kind of heptahedron with 7 faces, 10 vertices, and 15 edges. Because of its pentagonal bases, a pentagonal prism can have five sides. Another name for a pentagonal prism is a five-sided polygon prism.

We are given that a pentagonal prism has a height of 5 units and the volume of the prism is 175 cubic units.

We know that volume of pentagonal prism is the product of the area of base and the height.

So, from this we get

⇒ Volume = Area of base * Height

⇒ 175 = Area of base * 5

⇒ Area of base=  35 square units

Hence, the area of one of the base of the pentagonal prism is 35 square units.

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Answer:

Question 1: ∠3 and ∠7 are corresponding angles.

Question 2: ∠2 and ∠8 are alternate interior angles.

Question 3: ∠4 and ∠6 are alternate exterior angles.

Question 4: ∠2 is congruent to ∠6.

Question 5: ∠8 is not congruent to ∠1.

Question 6: If ∠2 measures 132°, the measure of ∠7 would be 48°.

The correct statements about given synthetic division are C, D, and F

"It is a polynomial with degree 2."

"It is defined as a way of dividing one polynomial by another polynomial of first degree."

For given question,

We have been given a quadratic polynomial \(F(x)=4x^{2} -17x-15\)

We can factorize above quadratic polynomial as,

\(F(x)\\=4x^{2} -17x-15\\=4x^{2} -20x+3x-15\\=4x(x-5)+3(x-5)\\=(x-5)(4x+3)\)

This means the factors of \(4x^{2} -17x-15\) are (x - 5) (4x + 3)

And the roots of the polynomial would be,

\(\Rightarrow F(x)=0\\\Rightarrow 4x^{2} -17x-15=0\\\Rightarrow (x-5)(4x+3)=0\\\Rightarrow x-5=0~~,~~4x+3=0\\\Rightarrow x=5~~,~~x=-\frac{3}{4}\)

This means, the roots of \(4x^{2} -17x-15\) are 5 and \(\frac{-3}{4}\)

Therefore, the correct statements about given synthetic division are C, D, and F

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Amy has $ 27, Bob has $ 80 and Ravi has $ 20 amounts in their wallets.

Finding unknown quantity using Linear Equation:

A mathematical statement used to find an unknown quantity in a given problem is known as a Linear Equation. Here to represent the unknown quantity we will use variables like x, y, and so on.  

Here we have,

Amy, Ravi, and Bob have a total of $127 in their wallets.  

Since we don't know the amount of each person we represent them with different variables

Let 'a' be Amy's amount

'b' be Bob's amount

'r' be Ravi's amount  

Then the total amount a + b + r = 127 -----(1)  

Given that,

Bob has 4 times what Ravi has

=> b = 4r ----(2)

Ravi has $7 less than Amy

=> r = a - 7 ----(3)

From (2) and (3)

b = 4(a - 7)

b = 4a - 28 ----(4)

Now substitute (3) and (4)  

=> a + 4a - 28 + a - 7 = 127

=>  6a - 35 = 127

=> 6a = 162

=>  a = 27

From (3)    

r = a - 7 = 27 - 7 = 20

From (2)

b = 4r = 4(20) = 80  

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Answer:

E = 4.5, F = -6.25, D = -3.25

Step-by-step explanation:

The problem does not mention the height of S. Mr. Watkins, so we are just going to assume its from his feet.  

So, i made this drawing to represent him and the tree, at a distance of 10 meters looking up at a 25* angle.

I marked the opposite side, adjacent side, and hypotenuse.

x is angle where you are "looking" from.  I.E., from the POV of mr watkins.

sin(x) = opposite/hyp

cos(x) = adj/hyp

tan(x) = opp/adj

So, we have an unknown side which is the opposite side, represented by length x.

The side adjacent is 10 meters.

The angle from him is 25 degrees.

What deals with adjacent and opposite?  Tangent.

Tan(25) = x/10

Solve for x.

10tan(25) is the height of the tree = 4.66

The height of the tree is 5 meters.

Answer:

V = 108

Step-by-step explanation:

B = 9 x 4 = 36 Height of Triangular prism is 3 so 36 x 3 = 108

To construct an interval, estimate for mu with 95% confidence for the first question, we use the formula:
Interval estimate = x ± (zα/2 * σ/√n)

where x is the sample mean, σ is the known population standard deviation, n is the sample size, zα/2 is the z-score corresponding to the desired confidence level (in this case, 1.96 for 95% confidence). Plugging in the values, we get:

Interval estimate = 850 ± (1.96 * 50/√100) = 850 ± 9.8
So the 95% confidence interval is from 840.2 to 859.8.

For the second question, where sigma is assumed to be 100, we use the same formula but with σ = 100:

Interval estimate = 850 ± (1.96 * 100/√100) = 850 ± 19.6
So the 95% confidence interval is from 830.4 to 869.6.

For the third question, where sigma is assumed to be 200, we again use the same formula but with σ = 200:

Interval estimate = 850 ± (1.96 * 200/√100) = 850 ± 39.2
So the 95% confidence interval is from 810.8 to 889.2.

As we can see, the confidence interval gets wider as sigma increases. This is because a larger standard deviation indicates greater variability in the population, which means there is more uncertainty in the sample mean as an estimate of the true population mean. Therefore, a wider interval is needed to account for this increased uncertainty.

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The correct statement about the two data is: C. upper quartile of A (7.5) < upper quartile of B (8.75).

Median, Range, Upper and Lower Quartiles of A:

Median, Range, Upper and Lower Quartiles of B:

The correct answer is: C. upper quartile of A (7.5) < upper quartile of B (8.75).

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Answer:

(6, 5) will be the point after the rule is applied

The required translation as of the given condition is (6, 5).

Given that,
To apply the following rule to the point (-5,6): (x,y)-->(y, -x).

Coordinate, is represented as the values on the x-axis and y-axis of the graph

Translation of a point is defined as changing the location of the point on an arbitrary space with the help of any function and instructions.

Here,
In the question, a rule is mentioned for the transposition of the coordinates,
(x,y)-->(y,-x)
we just need to simply poor the coordinate in the given translation equation,
(-5, 6) - - -> (6, -(-5))
(-5, 6) - - -> (6, 5)

Thus, the required translation as of the given condition is (6, 5).

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Answer:

3

Hope it helps you, tell me if im wrong pls, BE SAFE! :D

Answer:

d = 48

Step-by-step explanation:

The values of p and q, if Expression 10x – x² can be written as p – (x – q)² are 25 and 5.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

Given:

Expression 10x – x²

The expression can be written as

10x – x² = p – (x – q)²

10x – x² = p - x² - q² + 2xq

10x – x² = - x² + 2xq + p - q²

Compare the quantities on both sides,

10x = 2xq and 0 = p - q², p = q²

q = 10x / 2x = 5

p = 5² = 25

Therefore, the values of p and q, if Expression 10x – x² can be written as p – (x – q)² are 25 and 5.

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From the amounts found using simple and compound interest formulas, we found that Carlie earns more interest than Jack by $1009.45.

What is the difference between simple and compound interests?

Simple interest is based on the principal amount, which is the main distinction between it and compound interest. Contrarily, compound interest is calculated using the principle sum and interest that has been compounded over the course of a period. Simple interest is a predetermined proportion of the principal amount borrowed or lent that is paid or received over a set period of time. Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.

The complete question is given below.

Given,

  The principal amount deposited by both Jack and Carlie  P = $17,250

The rate of interest r = 6% = 0.06

The time period = 6.5

Jack's account earns annual simple interest and Carlie's account earns annual compound interest.

So the amount in each person's account after a time period of t = 6 years.

Jack:

Amount = P(1+rt) = 17250 ( 1 + 0.06*6) = $23,460

Carlie:

number of times compounded in a year n = 1

Amount = \(P(1 + \frac{r}{n})^{nt}\) = 17250 ( 1+0.06)⁶ = $24,469.45

Therefore from the amounts found using simple and compound interest formulas, we found that Carlie earns more interest than Jack by $1009.45.

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Probability that the second card is an ace, given that the first card is an ace is 1/ 221

Without replacement means drawing the card first but not putting back to the deck and then drawing again.

Total number of cards in a deck = 52

Number of an ace in whole deck = 4

let event of getting an ace in first draw be A

and event of getting an ace in second draw be B

P(A) = 4 / 52 = 1 /13

drawing without replacement

P(B) = 3 / 51 = 1 / 17

Probability that second card is an ace given that first card is an ace is

P(A).P(B) =

1/13 × 1/ 17 = 1 / 221

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