Make a 3-by-6 logic grid on your own paper. Use it to help you solve the logic
puzzle and answer the question given below.
Davis, Roy, and Tom are on the rowing team. Each sits in a different position
(front, middle, and end) and is a different age (18, 19, and 20).
• Tom and the 19-year-old do not sit in the rear.
.
The person who sits in the rear is 20 years old.
Neither Tom nor Roy sits in the front.
Who sits in the middle, and how old is he? Be sure to check both answers.

Answer: 5/2

To convert 2.5 into a fraction, firstly we will write the number in x/y form, where x and y are positive integers. So, 2.5 can be written as 2.5/1. For the removal of the decimal, we multiply and divide by 10. And we get, 2.5/1 x 10/10 = 25/10 = 5/2.

Answer: 6 feet describes the center, and 9 feet describes the spread

Step-by-step explanation:

The center of a data set is mostly considered as the median or the mean

Here mean is 6 (given). And median is also 6. As 6 is exactly at the middle of the data set. (When arranged in ascending order)

Now, one of the way of calculating the spread is calculating the range, here it's given that the range is 9.

Therefore, 6 feet describes the center, and 9 feet describes the spread is correct.

Answer: 2,-2

Step-by-step explanation: 9-7 is 2 and -9 minus -7 is minus 2.

Answer:

it will depend on what state you are in

Step-by-step explanation:

depending on what state you are in will depend on the voting polls. and it would most likely be democratic

Answer:

The length of the hypotenuse ≈ 39.7 cm

Explanation:

Since the given triangle is a right-angled triangle, this means that we can apply the Pythagorean theorem.

The equation for Pythagorean calculation is:

(hypotenuse)² = (first leg)² + (second leg)²

In the given, we have:

first leg = 30 cm

second leg = 26 cm

Substitute with the givens in the above equation to get the hypotenuse as follows:

(hypotenuse)² = (30)² + (26)²

(hypotenuse)² = 1576

This means that:

either hypotenuse = √1576 = 39.69 ≈ 39.7 cm ..........> accepted

or hypotenuse = -√1576 = -39.69 ......> rejected as length can't be negative

Hope this helps :)

Answer:

51

Step-by-step explanation:

5x^2 - x + 9

5(3^2) - 3 + 9

5(9) + 6

45 + 6

= 51

Answer:

Domain is all real #s

Range is (-∞, 4]  or y < 4

Step-by-step explanation:

Answer:

[tex]y = 2x -4[/tex]

Step-by-step explanation:

[tex]y = -\frac{1}{2}x - 2\ \ \ \ \ \ (0, -4)[/tex]

To find the perpendicular equation of a line,

You need the product of their gradients to be -1

[tex]-\frac{1}{2} \times ? = -1[/tex]

Divide both sides by [tex]-\frac{1}{2}[/tex]

? = 2

The gradient of the perpendicular line is 2

Straight line formula is in the form [tex]y = mx + c[/tex]

[tex]y = 2x + c[/tex]

We're nearly there, we just need to find out c.

Luckily, we're given a point [tex](0, -4)[/tex]

[tex](x, y) = (0, -4)[/tex]

[tex]y = 2x + c[/tex]

[tex]-4 = 2(0) + c\\-4 = 0 + c\\c = -4[/tex]

We then end up with...

[tex]y = 2x -4[/tex]

The total amounts of money which Mrs. Reynolds now has according to the descriptions in the task content is; $68.

It follows from the task content that;

On this note;

Hence, it follows that the amount of money, s she has now is;

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Answer: 1500

Hope this helps! :)

Please mark brainliest.

Answer:

4:9

Step-by-step explanation:

Find the area in inch first:

20 inch × 10 inch = 200 inch

Area in feet:

(20×15) + (10×15) = 450 inch

Area of the drawing : Area of the actual playground

200:450

Simplify it by dividing by 5

Last answer =4:9

Answer:

6825 in^3

Step-by-step explanation:

First break the shape into two shapes a square prism and triangular prism

the volume of a square prism is equal to s^2 * h

and the volume of a triangular prism is 1/2 b * l *h

square prism:

v = s^2 * h

v = 13^2 * 30

v = 5070 in^3

triangular prism:

v = 1/2 b * l * h

v = 1/2 * 9 * 30 * 13

v = 1755 in^3

then you add the two volumes to get the total volume

5070 + 1755 = 6825 in^3

Answer:

45 degrees      

right angle =90 degrees

remaining :90

angles are equal

so 45 each

Answer:

The answer is e. (x - 10 * y^2 * z) (x + 10 *y^2 *z)

Step-by-step explanation:

To explain it test all the options by distributing them.

Using an online website that I plugged into the calculator to factory gets answer e.

Answer:

x=24

Step-by-step explanation:

you need 300.

10x + 60?

10 x 3 = 300

300 - 60 = 240

300 = (10 x 24) + 60

Answer:

[tex]\sqrt{28}[/tex]

Step-by-step explanation:

the point lies between 5 and 6 , that is between

[tex]\sqrt{25}[/tex] and [tex]\sqrt{36}[/tex]

therefore the poi nt approximates to the [tex]\sqrt{28}[/tex]

Answer:

  C.  16π

Step-by-step explanation:

You want to know the area of a circle whose radius is twice the edge of a cube that has a surface area of 24 square units.

The relevant area formulas are ...

  As = 6s² . . . . . . area of cube with edge s

  Ac = πr² . . . . . . area of circle with radius r

Here, we have r = 2s, so the area of the circle is ...

  Ac = π(2s)² = 4πs²

And we have the area of the square as 24, so the value of s² is ...

  As = 24 = 6s²

  24/6 = 4 = s²

Using this in the circle area expression, we have the area of the circle as ...

  Ac = 4π(4) = 16π . . . . . square units

The area of the circle is 16π square units.

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Answer:

11 years

Step-by-step explanation:

x = years to equal

45 + 10x  =  23 + 12x

22 = 2x

x = 11 years

It will take 11 years for Dean to read as many books as Lillie.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given that,

Number of books read by Lillie every year = 10 books

Total number of books already read = 45 books

The number of books, n, read by Lillie in t years,

n = 45 + 10t

Number of books read by Dean every year = 12 books

Total number of books already read = 23 books

The number of books, n, read by Lillie in t years,

n = 23 + 12t

Dean read as many books as Lillie, when,

23 + 12t = 45 + 10t

12t - 10t = 45 - 23

2t = 22

t = 11

Hence the number of books read by both will be same in 11 years.

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The center and shape of the distribution are 2.5 and symmetric. Then the correct option is B.

Binomial distributions consist of n independent Bernoulli trials.

Bernoulli trials are those trials that end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining to a binomial distribution with parameters n and p, then it is written as

[tex]X \sim B(n,p)[/tex]

The probability that out of n trials, there'd be x successes is given by

[tex]\rm P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]

Then the center and shape of the distribution will be 2.5.

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Answer:

Center : 2.5 Shape: Symmetric

Step-by-step explanation:

Trust Fam

Answer:

The equation of the tangent line is given by the following equation:

[tex]\displaystyle y - \frac{1}{e} = \frac{-1}{e} \bigg( x - 1 \bigg)[/tex]

General Formulas and Concepts:

Algebra I

Point-Slope Form: y - y₁ = m(x - x₁)

Calculus

Differentiation

Derivative Property [Multiplied Constant]:
[tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Derivative Rule [Basic Power Rule]:

Derivative Rule [Chain Rule]:
[tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

*Note:

Recall that the definition of the derivative is the slope of the tangent line.

Step 1: Define

Identify given.

[tex]\displaystylef(x) = e^{-x} \\x = -1[/tex]

Step 2: Differentiate

Step 3: Find Tangent Slope

∴ the slope of the tangent line is equal to  [tex]\displaystyle \frac{-1}{e}[/tex].

Step 4: Find Equation

∴ our point is equal to  [tex]\displaystyle \bigg( 1, \frac{1}{e} \bigg)[/tex].

Substituting in our variables we found into the point-slope form general equation, we get our final answer of:

[tex]\displaystyle \boxed{ y - \frac{1}{e} = \frac{-1}{e} \bigg( x - 1 \bigg) }[/tex]

∴ we have our final answer.

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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Answer:

12

Step-by-step explanation:

n(AUB) = n((A) + n(B) – n(AnB)

Step 1:

Identify the values for each function of the formula. n(A) = 10, n(B) = 5, n(AnB) = 3

Step 2:

Replace each function with its values

n(AUB) = n(A) + n(B) – n(AnB)

n(AUB) = 10 + 5 – 3

Step 3:

Carry on the simple arithmetic

n(AUB) = 10 + 5 – 3 (follow the BODMAS method)

= 15–3

= 12

Therefore, the n(AUB) is 12

Answer:

See below.

Step-by-step explanation:

1) We know that the circumference of a circle can be found using the formula [tex]c=\pi d[/tex], so for this circle the circumference will be [tex]c=3.14 \times 40=125.6 \text{ yards}[/tex]. The formula for the area of a circle is [tex]A=\frac{1}{4}\pi d^2[/tex], so the area of this circle will be [tex]A=\frac{1}{4} \times 3.14 \times 40^2=1256 \text{ yards}[/tex].

2) First we'll work out the length of the curved side of the shape. That's [tex]\frac{1}{2}\times\pi d =\frac{1}{2} \times 3.14 \times 12=18.84 \text{ mm}[/tex]. Then, we'll add the length of the other two straight sides to get [tex]10.82 \times 2 + 18.84=40.48 \text{ mm}[/tex]. Next: the area of the semi-circle is [tex]\frac{1}{2} \times \frac{1}{4} \pi d^2 = \frac{1}{8} \times 3.14 \times 144 = 56.52 \text{ mm}[/tex]. Adding this to the areas of the two triangles: [tex]56.52+2 \times \frac{1}{2}bh=56.52+(\sqrt{10.82^2-9^2)}\times9 \approx 110.57 \text{ to 2 d.p.}[/tex]

Answer:

25

Step-by-step explanation:

ABC is a right angle so ABD and DBC are complementary angles and their sum is equal to 90:

x + 55 = 90 subtract 55 from both sides

x = 25

Answer:

6.3

Step-by-step explanation:

151.2/24 in order to find out how many miles he drove per day

the answer is 6.3 miles per day

Answer:

6.3 Miles

Step-by-step explanation:

just divide 151.2 by 24.

To determine if you have enough money to buy this product, calculate the sales tax and the final price of the product.

Sales tax is usually expressed as a percentage. Moreover,  this percentage can slighly change depending on the state where you live.

Here is an example:

Final price = 138.12

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