11 m
The figure shows a diver diving from a platform. The diver reaches a depth of 4 meters. What is the change in elevation of the diver?
The change in the elevation of the diver is meter(s).


Sorry ik the pic is blurry

Answer:

42 miles per gallon

Step-by-step explanation:

First, Convert it into a decimal to make it easier, 26.25 miles on .625 gallon. Now we Divide the two numbers 26.25 ÷ .625 = 42.

Hope this helps :D

A sequence is a geometric sequence if all the numbers of a list are found by multiplying the preceding term by the common ratio r of that sequence. Sigma notation can represent the sum of a finite number of terms (although higher mathematics will tell you how it works for infinite numbers as well).

Now the given problem is,

calculate ∑ n=1, 4, 2n

∑n=1 , 4 , 2n

Since the bounds are finite, the number of terms is finite as well, and we just calculate the sum by summing up the terms.

(∑n=1 4 ,2n) = (2+4+8+16) (∑n=1 4, 2n) = (2+4+8+16)

(∑n=1 4 ,2n) = (30) (∑n=1 4, 2n) = (30)

Hence,

∑n=1 4, 2n=30 ∑n=1 4, 2n=30

Answer:

∑n=1 4, 2n=30

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Answer: sinW≈0.75

Step-by-step explanation:

[tex]m\angle X=90^0\ \ \ \ XV=48\ \ \ \ \ WV=73\ \ \ \ \ VX=55\ \ \ \ sinW=?[/tex]

The sine theorem: The sides of a triangle are proportional to the sines of the opposing angles

Hence,

[tex]\displaystyle\\\frac{WV}{sinX} =\frac{VX}{sinW} \\\\\frac{73}{sin90^0} =\frac{55}{sinW} \\\\\frac{73}{1} =\frac{55}{sinW} \\\\sinW=\frac{55}{73} \\\\sinW\approx0.75[/tex]

The expanded form of 0.68 is written as 0 x 1 + 6 x 0.1 + 8 x 0.01.

To express decimal numbers in their expanded form simply means writing each number according to its place value. It can be done by multiplying each digit of the decimal by its place value and adding it all together.

Given the decimal 0.68 or sixty eight hundredths in words, first, multiply the digit 0 by its place value, which is 1.

0 x 1

Multiply the digit 6 by its place value, which is 0.1.

6 x 0.1

Multiply the digit 8 by its place value, which is 0.01.

8 x 0.01

Add it all together.

0 x 1 + 6 x 0.1 + 8 x 0.01

Hence, the expanded for of the decimal 0.68 is written as 0 x 1 + 6 x 0.1 + 8 x 0.01.

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Answer:

Yes

Step-by-step explanation:

We can check using pythagoras theorem, setting a and b equal to the shorter sides.

[tex]51^2+68^2=85^2\\2601+4624=7225\\7225[/tex]

The expression (128 + 32) when rewritten using factoring is 4 * (32 + 8)

The expression in the question s given as

(128 + 32)

Express the numbers 128 and 32 as the product of their factors

i.e. we factor out 4 from the expression

So, we have

(128 + 32) = (4 * 32 + 4 * 8)

Next, we factor out the common factor (i.e. 4) from the expression

So, we have

(128 + 32) = 4 * (32 + 8)

Rewrite the above expression as follows

(128 + 32) = 4(32 + 8)

Hence, the expression (128 + 32) when rewritten using factoring is 4 * (32 + 8)

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The distance between the given 2 points using the distance formula is 4√2.

So, the Distance formula: [tex]d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]

Substitute values in the distance formula as follows:
[tex]d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\\d=\sqrt{\left(0-(-4)\right)^2+\left((-2)-2\right)^2}\\d=\sqrt{\left(4\right)^2+\left(-4\right)^2}\\\\d=\sqrt{16+16}\\d=\sqrt{32}\\\\d=\sqrt2*2*2*2*2\\d=2*2\sqrt2\\\\d=4\sqrt2[/tex]

Therefore, the distance between the 2 points is 4√2.

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The equivalent expression of -6(b + 2) + 8 is -6b - 4

The expression is given as

-6(b + 2) + 8

Expand

-6b - 12 + 8

Evaluate the like terms

-6b - 4

Hence, the equivalent expression of -6(b + 2) + 8 is -6b - 4

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Answer:

x ≈ 25.73

Step-by-step explanation:

using the tangent ratio in the right triangle

tan25° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{12}{x}[/tex] ( multiply both sides by x )

x × tan25° = 12 ( divide both sides by tan25° )

x = [tex]\frac{12}{tan25}[/tex] ≈ 25.73 ( to 2 dec. places )

The value of the line segment in the right-angle triangle 'x' will be 25.75 units.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The measure of the length 'x' is calculated by the tangent of angle 25°. The tangent of an angle is the ratio of the perpendicular to the base of the right-angle triangle. Then we have

tan 25° = 12 / x

x = 12 / tan 25°

x = 12 / 0.466

x = 25.75 units

The value of the line segment in the right-angle triangle 'x' will be 25.75 units.

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The profit of the concession is $350.

So, c - e:

Substitute the values in the expression:

Therefore, the profit of the concession is $350.

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The amounts left after: 1 hour = 642g, 3 hours = 160.6g, 4 hours = 80.3g, as calculated by the formula of radioactive decay.

The formula so used: A = [tex]\frac{-dN}{dt}[/tex]

=> N = A ([tex]e^{-kt}[/tex]), where:

Now,

AS shown in the table (refer to the image attached), for k:

=> 322 = 1284[tex]e^{-2k}[/tex]

=> [tex]\frac{322}{1284}[/tex] = [tex]e^{-2k}[/tex]

=> 0.25 = [tex]e^{-2k}[/tex]

Taking natural logarithm on both sides.

=> ln(0.25) = ln([tex]e^{-2k}[/tex])

=> ln(0.25) = (-2k) ln(e)

As ln (e) = 1,

=> ln (0.25) = -2k

=> -1.386 = -2k

=> k = 0.693

Now, for t = 1 and k = 0.693, in the original formula, we get:

=> N = 1284 ([tex]e^{-0.693(1)}[/tex])

=> N =  1284 (0.5)

=> N = 642

For t = 3 and k = 0.693, in the original formula, we get:

=> N = 1284 ([tex]e^{-0.693(3)}[/tex])

=> N =  1284 (0.125)

=> N = 160.6g

For t = 4 and k = 0.693, in the original formula, we get:

=> N = 1284 ([tex]e^{-0.693(4)}[/tex])

=> N = 1284(0.0625)

=> N  = 80.3g

Thus, The amounts left after: 1 hour = 642g, 3 hours = 160.6g, 4 hours = 80.3g, as calculated by the formula of radioactive decay.

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The six rational number between 7 and 8 are 7.5 ,7.75, 7.875 , 7. 9375 ,7.9675 and 7.98375

Answer:

55

Step-by-step explanation:

[tex]\sqrt{3025} =55^2\\\sqrt{55^2}\\\sqrt{55^2}=55\\=55[/tex]

Hope this helps.

Answer For Question 2: Associative property. The associative property says that even if you rearrange the parenthesis () the result will still be the same. And that is what is happening in question 2
Answer For Question 3: Commutative property of addition. This is the BEST choice because you will first want to add 3/5 + 2/5. And since the Commutative property says that no matter the order of the addends, you can add what ever you think is the best choice.

Here are some answers. I couldn't really understand Question 1 so i didn't want to give you an incorrect answer. Also are the pictures questions too? Im not too sure but here you go hope this helps you in some way

The equation of the line in point-slope form, which passes through the pair of points located at (7 , 11) and (13 , 17), is y - 11 = (x - 7).

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Getting the slope of the two points: (7 , 11) and (13 , 17).

m = (y2 - y1)/(x2 - x1)

m = (17 - 11)/(13 - 7)

m = 6/6

m = 1

Using the point slope form, plug in the values of the slope and one point to set up the equation.

(y - y1) = m(x - x1)

where m = 1 and (x1 , y1) = (7 , 11)

(y - 11) = 1(x - 7)

y - 11 = (x - 7)

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 The given function

f(x) = y = 4x(7 - 2x) , is a Quadratic function

 where its quadratic term is -8x².

 Its linear term is 28x

 Constant 0

 A function is a mathematical expression or equation that allows us to visualize graphically the behavior of a function. A function is not real when it cuts the vertical axis at the same point of x.

   A function can be linear or quadratic, this is evidenced by the higher exponential degree, in our case we have the following function:

f(x) = -2(3+x)²+2x² we solve the function that seems to be quadratic because it has the highest degree the number "2" in the variable, however we will solve its reduction.

4x (7 - 2x)  we apply the distributive property

28x - 8x²   is a quadratic function

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Answer:

The equation for new function is

Step-by-step explanation:

We have been given the absolute value parent function f(x) = |x| and this function is vertically compressed by a factor 3.

If we multiply the function with a constant (say a) then the parent function will get stretch/compressed vertically.

We have below conditions for vertical stretch and compression.

a > 1 => vertically stretch

0 < a < 1 => vertically compression

Hence, in order to vertical compression by a factor 3, we have to multiply the whole function by 1/3

Therefore, the equation for new function is

Step-by-step explanation:

g(x) = 1/3 |x| !

the reflection of coordinates ( -6, -3 ) on y-axis has coordinates ( 6, -3 ).

The reflection transformation can be with respect to x-axis and y-axis. When a point is reflected about the x-axis, the x-coordinates stay the same and y-coordinates are transformed and written with their opposite signs.

For example, the reflection of the point with coordinates (x, y) across x-axis is (x, -y).

When a point is reflected about the y-axis, the y-coordinates stay the same and the x-coordinates are transformed and written with their opposite signs.

For example, the reflection of the point (x, y) across y-axis is (-x, y).

As we can see that the point with coordinates ( -6, -3 ) lies in the third quadrant and thus the reflection of this point on y-axis lies in fourth quadrant. We know that in fourth quadrant  the x coordinate is positive and y coordinate is negative.  

By changing the signs according to the above rules, we get

from ( -6, -3 ) to  ( 6, -3 ).

Therefore, we can conclude that the reflection of coordinates ( -6, -3 )  on y-axis has coordinates ( 6, -3 ).

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Answer:

x = 2 11/12

Step-by-step explanation:

First of all, on the right you have to combine 15x+3/7x which equals 15 3/7x.

9x + 45 = 15 3/7x

-9x              -9x             Next step is to subtract 9x from both sides.

45 = 15 3/7x

/              /

15 3/7   15 3/7        Third step is to divide 15 3/7 on both sides to leave x          

                              by itself.

35/12 = 2 11/12 = x

x = 2 11/12

The downloads of the standard version are 1127.25.

So, let the download of the standard version be 'x'.

Then, automatically the download of the high-quality version becomes '3x'.

Now,

Therefore, the downloads of the standard version are 1127.25.

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Answer: mean = 34

median = 33

mode = 33

Step-by-step explanation:

To figure out the mean you add every number and divide them by the number of values you added together so 27 + 31 + 33 + 33 + 35 + 45 = 204 then we would divide that by 6 = 34

To find the median you put all the numbers into order so which it already is meaning now you find the number in the middle which is 33 and 33 if there were two more values you would have to find the mean of them, but in this case its 33

The mode is the number which appears the most which is 33 as it appeared more than 2 times.

The circumference of ®B is 36 units.

A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object.

Now it is given that,

The scale factor from  ®A to ®B = 1/3

⇒Ks = 1/3

∵ Ks = A/B

By comparison we get,

A = 1

and B = 3

Thus, circumference (CA) of ®A = 12

⇒ Since scale factor for A = 1

⇒ 2πr = 12

⇒ r = 6/π

Now, circumference (CB) of ®B = 2πr = 2π* 6/π

⇒ circumference (CB) of ®B = 12

Since scale factor for B = 3

⇒ circumference (CB) of ®B = 3 * 12

⇒ circumference (CB) of ®B = 36 units.

Thus, the circumference of ®B is 36 units.

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A percentage in mathematics is a number or ratio that can be expressed as a fraction of 100.

The percent of the given number 92% of 90 is 82.8.

A percentage in mathematics is a number or ratio that can be expressed as a fraction of 100. The term percent comes from the Latin "per centum" which means per hundred. The symbol percentage is used to represent percentage.

Let the equation be 92% of 90

Percentage = (value/total value) × 100 %.

Since, finding the fraction of a number is same as multiplying the fraction with the number, we have

92% of 90 = 92/100 of 90

92/100 × 90 = 82.8

Therefore, the percent of the given number 92% of 90 is 82.8.

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The results of the operations between the sets are given as follows:

1. U = {a, d, e, i, l, o, n, p, y}

2. E ∪ I = {d, o, l, e, p, i, n, a, y}.

3. E ∩ I = ∅.

4. J' = {d, a, l, e}

5. I ∪ J = {p, i, n, a, y, o}

6. (J ∩ I) ∪ E = {p,i,n,y,d,o,l,e}

7. E = {p, i, n, a, y}

8. I' ∪ J = {p, i, n, y, d, o, l, e}

9. (E ∪ I) ∩ (I ∪ J) = {p, i, n, a, y, o}

10. (J ∪ I)' = {d, l, e}

The universal set is the set that contains all elements that belong to at least one of the sets E, I and J, hence:

U = {a, d, e, i, l, o, n, p, y}

The union operation between two sets is the set of elements that belong to at least one of the sets.

Hence, in item 2, we have that:

E ∪ I = {d, o, l, e, p, i, n, a, y}

In item 5, we have that:

I ∪ J = {p, i, n, a, y, o}

The negation operation of a set X is the set that contains all elements that belong to the universe U but do not belong to X.

Hence, for item 4, we have that:

J' = {d, a, l, e}

For item 7, we have that:

E = {p, i, n, a, y}

Item 8 involves a negation then a union, hence:

I' = {d,o,l,e}

I' ∪ J = {p, i, n, y, d, o, l, e}

Item 10 involves an union then a negation, just different precedence of 8, hence:

I ∪ J = J ∪ I = {p, i, n, a, y, o}

(J ∪ I)' = {d, l, e}

The union operation between two sets is the set of elements that belong to both of the sets.

Hence, in item 3, we have that:

E ∩ I = ∅ (no element belongs to both sets).

For item 6, we have an intersection then an union, hence:

J ∩ I = {p,i,n,y}

(J ∩ I) ∪ E = {p,i,n,y,d,o,l,e}

For item 9, we have the intersection of two unions, hence:

E ∪ I = {d, o, l, e, p, i, n, a, y}

I ∪ J = {p, i, n, a, y, o}

(E ∪ I) ∩ (I ∪ J) = {p, i, n, a, y, o}

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Answer:                 x= negative 3

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

-3(-3+3)=0

-3(0)=0

0=0

Answer: 28 miles per hour

Step-by-step explanation:

224 miles / 8 hours=

224/8= 28 miles per hour

Answer:

5.5 = 5 5/10 = 5 1/2 (simplified)

Hope this helps in any way :)

Answer:

  d: {-5, 0, 8}

  r: {-6, -3, 1, 8}

Step-by-step explanation:

You want the domain and range of the relation T= {(-5, -3), (8, -6), (-5, 1), (0,8)}.

The domain is the set of first values. We usually like to see duplicates eliminated and the values written in increasing order:

  {-5, 0, 8}

The range is the set of second values. Again, we like them in order:

  {-6, -3, 1, 8}

__

Additional comment

If there are duplicates among the domain values (as here), the relation is not a function.