Two planes start from the same point and fly in opposite directions. The first plane is flying 30 mph slower than the second plane. In 3 h, the planes are 810 mi apart. Find the rate of each plane.

The water pressure on a submerged object is given by P = 64d, then the

a. The answer to the subject of the formula, "d," is d = P/64.

b. A submerged object will be 10. 5 feet deep at a pressure of 672 pounds per square foot.

A function can be defined as an expression, law or rule that shows the relationship between two variables.

These variables are namely;

given the role as;

P = 64d

Where;

P stands for pounds per square foot of pressure.

d represents the object's depth in feet.

Let's now make the variable "d" the focus of the formula.

The coefficient of the variable "d," which is 64, is used to divide both sides of the equation. So that the variable can stand on its own, this is done.

We get,

P/64 = 64d/64

d = P/ 64

P equals 672 pounds per square foot if there is pressure.

When the variable's value is substituted into the formula, we get;

d = P/64

Then,

d = 672/64

Discover the quotient.

d = 10. 5 ft.

The value is 10.5 feet.

Therefore,

a. The answer to the subject of the formula, "d," is d = P/64.

b. A submerged object will be 10. 5 feet deep at a pressure of 672 pounds per square foot.

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Based on the direct variation between x and y, the value of y is 48

The given statements are:

From the above points, we understand that:

The variation is a direct variation

A direct variation is represented as

y = kx

Where k represents the constant of variation

The above equation is a linear equation

As a general rule, linear equations are equations that have constant average rates of change.

So, we have

y = kx

y is 120 when x is 15

This means that

120 = 15k

Divide by 15

k = 8

So, we have

y = 8x

The value of y when x is 6 is

y = 8 x 6

Evaluate

y = 48

Hence, the value of y when the value of x is 6 is 42

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The angle not congruent to the angle 4 in the options is angle 7(∠7)

When parallel lines are cut by a transversal, angle relationships are formed such as corresponding angles, alternate angles, vertically opposite angles etc.

Therefore, corresponding angles are equal, alternate angles are equal and vertically opposite angles are equal.

Therefore,

∠4≅∠6(vertically opposite angles)

∠4≅∠2(corresponding angles)

∠4≅∠8(alternate exterior angles)

Therefore the angle not congruent to ∠4 among the option is ∠7

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In linear relationship, 199.333 million dollers per year is the percent growth rate.

What is linear relationship in math?

Given , t Rs numbers of year since 1997 .

t = 0 corresponds to year 1997

t = 6 corresponds to year 2003

Let  s(t) = sales of the year

So, given that

 sales in 19997 is  $2503 millions

so    s(0) = 2503  million dollers

Sales in 2003 is $3699 millions

so  s(6) = 3699  million dollers

Now apply formula of linear relation ship

               s - s(0) = s(6) - s(0)/6 - 0 ( t - 0)

               s - 2503 = 3699 - 2503/6 (t)

                s = 1196* t /6 + 2503

  so         s(t) = 598t/3 + 2503

 so now average rate of change of function over on interval is given by

                 =     s(b) - s(a)/b - a

                 = s(6) -  s( 0)/6 - 0

                 = 3699 - 2503/6

                 = 598/3

                 = 199.333 million dollers per year .

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The length of the bridge that connect the two cities separated by the lake is 3.4 miles.

The mathematical operation that would be used to convert yards to miles is division. Division is the process of putting a number into equal groups using another number. For example, when 6 is divided by 3, 3 divides 6 into 2 equal groups.

In order to convert yards to miles, divide the given length in yards by 1760.

1 yard = 1 / 1760 miles

5927.61 / 1760  = 3.36796 miles

= 3.4 miles

To round off to the nearest tenth, since the hundredth digit is greater than 5, 1 is added to the tenth digit and the digits less than the tenth digit is replaced with zero.

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Answer:

The top set does not represent a function because -4 corresponds to two y-values.

he Solution:

iven in the question that if

We are required to give a counterexample to the given conditional statement above.

Solving each of the equations above, we get

So, the counterexample to the given conditional statement is x = 4.

EXPLANATION

Since we have four given scenarios, the only viable option is the third one because It's the only statement where we take a sample (1000 individuals of 1883 participants).

⇒Parallel line have the same gradient if the gradient of the given equation is m=-6  it means that the gradient of the new equation is also m=-6

The general equation of a straight line is y=mx+c

⇒plug in the points and find the value of the unknown c

[tex]6=-6(9)+c\\6=-54+c\\c=6+54\\c=60[/tex]

⇒This means that the new equation parallel to the given equation is⇒

[tex]y=-6x+60[/tex]

Answer: 3

Step-by-step explanation:

1. 2 packs of 6

2. 6 packs of 2

3. 3 packs of 2 and one pack of 6

the multiplication of 2 matrices A and B

a11 a12 a13 ...

a21 a22 a23 ...

a31 a32 a33 ...

...

b11 b12 b13 ...

b21 b22 b23 ...

b31 b32 b33 ...

is

a11×b11+a12×b21+a13×b31+... a11×b12+a12×b22+a13×b32 ...

a21×b11+a22×b21+a23×b31+... a21×b12+a22×b22+a23×b32

a31×b11+a32×b21+a33×b31+... a31×b12+a32×b22+a33×b32

...

in other words, we combine the rows of the first matrix with the columns of the second matrix.

the rows of the result matrix are driven by the rows of the first matrix and the columns of the second matrix.

formally :

we can multiply a m×n matrix only with a n×o matrix.

the number of columns in the first matrix must be equal to the number of rows in the second matrix.

the result matrix is then sized m×o.

the first element (first row first column) of the result matrix is the sum of the products of the elements of the first row of the first matrix with the elements of the first column of the second matrix.

the element in the (x,y) position in the result matrix is the sum of the products of the elements of the xth row of the first matrix with the elements of the yth column of the second matrix.

so, when multiplying 2 2×2 matrices, the condition is automatically fulfilled : m = n = o = 2

ST =

4×0+1×-4 4×4+1×3

-3×0+-2×-4 -3×4+-2×3

=

-4 19

8 -18

and TS =

0×4+4×-3 0×1+4×-2

-4×4+3×-3 -4×1+3×-2

=

-12 -8

-25 -10

as we can see, the 2 results are completely different.

The amount of IRA when he will retire at age 65 = $83448.27

And the total deposits made over the time period is less than the the amount of IRA

We have been given, at age 19​, someone sets up an IRA​ (individual retirement​ account) with an APR of7 ​%. At the end of each month he deposits ​$20.00 in the account.

We need to find the IRA when he retires at age​ 65.

here, 65 - 19 = 46 years

So, the period would be,

46 × 12 = 552 months

Monthly deposit= $20

And the interest rate would be,

Interest = 0.07/12

             = 0.0058

To calculate the future value, we need to use the following formula:

FV= {A × [(1 + i)^n-1]} / i

A= monthly deposit

i = interest rate

n = period

So, the Future Value of Annuity

= 20 × ([1 + 0.0058]^552 - 1 ) / (0.0058)

= 20 × 24.2 / 0.0058

= $83448.27

So, the amount of IRA when he will retire = $83448.27

Deposits made over the time period = 20 × 46 × 12 = $‭11040

Difference = 83448.27 - 11040

= $72408.27

This means, the total deposits made over the time period is less than the the amount of IRA he will get when he retires at age 65.

Therefore, the amount of IRA when he will retire at age 65 = $83448.27

And the total deposits made over the time period is less than the the amount of IRA

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Answer:

When making homemade ice cream in a hand-cranked freezer, the tub containing the ice cream mix is surrounded by a brine (water/salt) solution. To freeze the ice cream mix rapidly so that smooth and creamy ice cream results, the brine solution should combine crushed ice and rock salt in a ratio of 5 to 1.

Numerical variables are the subject of quantitative data. Qualitative data can be represented by a name, symbol, or number code and are measures of "types."

Numerical variables are the subject of quantitative data. Qualitative data can be represented by a name, symbol, or number code and are measures of "types." Data concerning categorical variables make up qualitative data.

Quantitative Variables with values obtained through measurement or counting. Variables that exists not measurement variables are referred to as qualitative variables. Their values are not determined by counting or measuring. Values that are used to identify people in a table are called designators. While qualitative research focuses on words and meanings, quantitative research deals with figures and statistics.

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We know that

1 m = 100 cm

Then to change from meter to centimeter, multiply by 100

Since the tree in Bob's backyard is 8.5 m

Then to change it to cm, multiply 8.5 by 100

The height of the tree is 850 cm

Answer:

−1≤x<3

Step-by-step explanation:

−4≤3x−1<8

−4≤3x−1and3x−1<8

3x−1≥−4and3x−1+1<8+1

3x≥−3and3x<9

x≥−1andx<3

−1≤x<3

Answer: $-75

Step-by-step explanation:

She took out money therefore the balance will go down. If we take 43 dollars from $-32 then we will get -75.

Based on the interest compounded by the bank monthly, and the amount deposited by Sean in the account, the amount of money that will be in that account in a year is $3,668.09

First, find the monthly rate because the interest is compounded monthly:
= 4.7% / 12

= 4.7/12 %

The number of periods would be:

= 1 x 12 months a year

= 12 periods

The amount that Sean will have in a year can be found by the formula:

= Amount invested x (1 + periodic rate) ^ number of periods

Solving for the amount in the account after 1 year gives:
= 3,500 x (1 + 4.7%/12) ^ 12

= 3,500 x 1.0480257937581146250656044647993

= $3,668.09

In conclusion, the amount that Sean will have after saving for a year in the account would be $3,668.09

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For the following relations, using the condition for a relation to represent a function, we have that:

A relation represents a function if each value of the input is mapped to only one value of the output, that is, one input cannot be mapped to multiple outputs.

The input may also be called domain, while the output may also be called range.

For a point in the standard format (x,y), we have that:

Hence, in the context of this problem, we have that:

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Answer:  3 ≥ W > -5

Step-by-step explanation:

Just look at the way the question is asked, that is the best I can explain. Sorry.

Answer:

6[tex]x^{2}[/tex]y

Step-by-step explanation:

If I ready your explanation correctly it is

2x3xy  We multiply the 2 and 3 and the xx would be [tex]x^{2}[/tex]

Here, we want to get the value of x

We can get this by isolating x

We start by bringing like terms together

The cost of the watch which sold at 130% of its cost and sale price is $39 is equal to $30.

As given in the question,

Sale price of the watch for which dealer sold = $39

Let $'x' be the cost of the watch with which dealer purchase

A dealer sold a watch 130% of its cost

Required expression to show the given condition of a dealer is given by:

   130% of x = $39

⇒ (130 /100) × x = $39

⇒ x = ( 39 × 100 ) / 130

⇒ x = $30

Therefore, the cost of the watch which sold at 130% of its cost and sale price is $39 is equal to $30.

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First, we need to calculate the median

13, 14, 14, 14, 15, 15, 15, 16, 16, 21, 23

we have 11 values the media is the 6th value in this case 15.

the lower extreme is 13 the upper extreme is 23.

The lower quartile is 14 and upper quartile is 16

the box plot is

Answer:

Step-by-step explanation:

3x−(12x−6)−42=0

−9x+6−42=0

(−9)⋅x+(−36)=0

x=−(−36)/−9

x=-4

To solve the given system of equation by graphing you only have to graph both lines. The solution is the intersection between the lines.

According to this, the intersection of the two lines is (-2, -2). It means that the solution is (-2, -2).

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

plants have developed seeds = 71

total plants = 200

Step 02:

% = part / whole * 100

% = 35.5

The answer is:

35.5 %