Under certain conditions the pressure of a gas varies directly with the temperature. When the - pressure is 800 psi, the temperature is 400°. What is the temperature when the pressure is 450​

Answer:  8

Step-by-step explanation:

5-1

3 out of 4 = 1/4

Answer:

Green Pens : 21

Step-by-step explanation:

Let the number of
green pens = x

Three more blue pens than green pens translates to
=> number of blue pens = number of green pens + 3
=> blue pens  = x + 3

Total number of pens = blues + green = x + 3 + x = 2x + 3

Probability of taking 2 green pens:
The first time a green pen is taken out, the probability
P( 1s green pen) = Number of green pens/Total number of pens

= [tex]\dfrac{x}{2x + 3}[/tex]

After the first green pen is removed, the number of green pens will be one less and so will the total number of pens

Number of green pens = x - 1
Total number of pens = 2x + 3 - 1 = 2x + 2

P(second green pen | first green pen)

[tex]=\dfrac{x-1}{2x + 2}[/tex]

P(2 green pens) = P(first green pen) x P(second green pen)
[tex]= \dfrac{x}{2x + 3} \times \dfrac{x-1}{2x + 2}\\\\=\dfrac{x(x -1)}{(2x +3)(2x+2)}[/tex]          [1]

Probability of 2 blue pens

P( 1st blue pen) = number of blue pens/total number of pens
[tex]=\dfrac{x + 3}{2x + 3}[/tex]

P(second blue pen = (number of pens remaining if first was blue) ÷ total number of pens - 1

If the first pen taken was blue then there will be 2x + 3 - 1 blue pens out of a total of 2x + 3 - 1 pens

P(2nd blue pen | first blue pen)

[tex]=\dfrac{x + 2}{2x + 2}[/tex]

[tex]\text{P(2 blue pens)} =\dfrac{x + 3}{2x + 3} \times \dfrac{x + 2}{2x + 2}[/tex][tex]=\dfrac{(x + 3)(x+2)}{(2x + 3)({2x + 2})}[/tex]  [2]

The probability of either 2 green pens or 2 blue pens is the sum of the two probability expressions [1] and [2]

[tex]= \dfrac{x(x -1)}{(2x +3)(2x+2)} + \dfrac{(x + 3)(x+2)}{(2x + 3)({2x + 2})}[/tex]

[tex]= \dfrac{x(x - 1)+ (x + 3) (x +2)}{(2x + 3)(2x + 2)}\\\\\\= \dfrac{2x^2+4x+6}{(2x + 3)(2x + 2)}\\\\\\\\[/tex]

Numerator: factor out 2 to get 2(x² + 2x + 3)

denominator = 4x²+10x+6 = 2 (2x² + 5x + 3)

2 of numerator and 2 of denominator cancel out to give the final expression:

[tex]\dfrac{x^2\:+\:2x\:+\:3}{2x^2+\:5x\:+\:3}[/tex]

But we are given that the probability of picking 2 pens of the same color = 27/55

This will give us:
[tex]\dfrac{x^2\:+\:2x\:+\:3}{2x^2+\:5x\:+\:3} = \dfrac{27}{55}[/tex]

Cross-multiplying we get

[tex]55\left(x^2+\:2x\:+\:3\right)=27\left(2x^2+\:5x\:+\:3\right)[/tex]

=> [tex]55x^2+110x+165 = 54x^2+135x+81[/tex]

Grouping like terms and simplifying gives
[tex]x^2-25x+84=0[/tex]

This is a quadratic equation which can be solved using a scientific calculator (as I did)

The solution set is

x = 21, x = 4

Remember x = number of green pens. We can ignore x = 4 because the total number of pens given by the expression 2x + 3 will be less than 12 and we are told there are more than 12 pens total

So the solution is x = 21 (number of green pens)
Number of blue pens = x + 3 = 21 + 3 = 24

Answer: Green Pens : 21   and Blue Pens: 24

The obtained decimal number is 0.155.

To solve the question  [tex]\frac{3.1 * 10}{2.0 * 10^{2}}[/tex].

Canceling out 10 from the denominator and numerator

= [tex]\frac{3.1 }{2.0 * 10}[/tex]

= 3.1 / 20

Remove the decimal point from the numerator and add one zero in the denominator

= 31/ 200

As we divide the numbers using the long division method we get the decimal number as a result,

= 0.155

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The values of p and q if x-1 is a common factor of f(x)=x⁴-px³ +7qx+1, and g(x)=x²-4x² + px² +qx-3,​are 13/2 and -1/2 respectively.

In Mathematics, factors are positive integers that can divide a number evenly.  Suppose we multiply two numbers to get product. The number that is multiplied are the factors of the product. Each number is factor of itself.  Factors have many real-life examples, such as arranging sweets in box, arranging numbers in pattern, distributing chocolates among children, etc. To find the factors of number, we need to use the multiplication or division method.

Factors are numbers that can divide a number exactly.  Hence, after the division, there is no remainder left. Factors are numbers you multiply together to get the another number. Thus, factor is the divisor of another number.

f(x)=[tex]x^{4}-px^{3}+7qx+1[/tex]

    = 1-p+7q+1

     = p-7q=2---------1

g(x)= [tex]-3x^{2} +px^{2} +qx-3[/tex]

      = -3+p+q-3

      =p+q= 6----------2

p-7q=2

p+q=6

-----------------

By subtracting 2 from 1

-8q=4

q=-1/2

putting value of q in equation 2 we get,

p+(-1/2)=6

p=6+[tex]\frac{1}{2}[/tex]

p=13/2

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Answer:

[tex]x=\boxed{13}\\\\y=\boxed{20}[/tex]

Step-by-step explanation:

Vertical Angle Theorem

When two straight lines intersect, they form two pairs of angles.  The vertically opposite (non-adjacent) angles are congruent.

Solving for x:

[tex]\boxed{\begin{aligned}(6x-26)^{\circ}&=4x^{\circ}\\6x-26&=4x\\6x-26+26&=4x+26\\6x&=4x+26\\6x-4x&=4x+26-4x\\2x&=26\\2x \div 2&=26 \div 2\\x&=13\\\end{aligned}}[/tex]

Solving for y:

[tex]\boxed{\begin{aligned}(7y-12)^{\circ}&=(6y+8)^{\circ}\\7y-12&=6y+8\\7y-12-6y&=6y+8-6y\\y-12&=8\\y-12+12&=8+12\\y&=20\end{aligned}}[/tex]

Therefore:

[tex]x=\boxed{13}\\\\y=\boxed{20}[/tex]

               8 square = 64

               5 cube = 125

Step-by-step explanation:

               =8² + 5³

            =64 + 125

                   =189

What are square and cube ?

The square of a number is the multiplication by itself. That means, for any integer, we can obtain the square by multiplying the integer itself. For example, the square of an integer 4 will be: 4 × 4 = 16, i.e., the square of 4 is equal to 16.

The cube of a number is the multiplication by itself thrice. That means, for any integer, we can obtain the cube by multiplying the integer by its square. For example, the cube of an integer 5 will be: 52 × 5 or 5 × 5 × 5, i.e., the cube of 5 is equal to 125.

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The line that passes through the point -1, four and is parallel to the line 2 X plus Y equals one is y + 2x = 2.

Slope is measure of steepness of a line.

The Equation of line is y = mx + c

where,

m is slope

c is y intercept

To find equation of the parallel line we must first find the slope of the original line

The original line is 2x + y = 1

We must first write equation in the general form above

That's

y = - 2x + 1

Comparing with general equation above

Slope = - 2

Since lines are parallel their slope are also same

Slope of parallel line = - 2

So the equation of line using point

( - 1 , 4) and the slope - 2 is

y-4= -2(x+1)

y-4= 2x-2

y+2x= -2+4

We have final answer as

y + 2x = 2

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The special angle pair relationship between the given angles are:

1. Corresponding angles

2. Alternate exterior angles

3. Consecutive

The following are some special angle pair relationships:

1. Angles 1 and 3 form a special angle pair relationship known as: corresponding angles.

2. Angles 8 and 4 form a special angle pair relationship known as: alternate exterior angles.

3. Angles 2 and 3 both lie on the same side of the given transversal, therefore, the special angle pair relationship between angle 2 and angle 3 is: consecutive interior angles.

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one is the pmf or probability mass function of X = number of children in the family

The Probability Mass Function (PMF) is also called a probability function or frequency function which characterizes the distribution of a discrete random variable.

X takes values: { 3, 4, 5 }

where:  P ( X = 3 ) + P ( X = 4 ) + P ( X = 5 ) = 1

For X = 3 we have : BBB or GGG.

P ( X = 3 ) = ( 1/2 * 1/2 * 1/2 ) * 2 = 1/8 * 2 = 2 / 8 = 1/4

P ( X = 4 ) = ( 1/2 * 1/2 * 1/2 * 1/2 ) * 6 = 6 /16 = 3/8

P ( X = 5 ) = ( 1/2 * 1/2 * 1/2 * 1/2 * 1/2 ) * 12 = 12 / 32 = 3/8

1 / 4 + 3 / 8 + 3 / 8 = 8 / 8 = 1

the complete question is

A family decides to have children until it has three kids of the same gender. Assuming P(B) = P(G) = 0.5, what is the pmf of X = number of children in the family?

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Answer:

[tex]{ \tt{slope = \frac{y _{2} - y _{1} }{x _{2} - x _{1} } }} \\ \\ { \tt{ - 3 = \frac{ - 3 - ( - 6)}{s - 5} }} \\ \\ { \tt{ - 3(s - 5) = 3}} \\ \\ { \tt{s - 5 = - 1}} \\ \\ { \tt{s = 4}}[/tex]

7 × 12 = 72 satisfies the closure property of multiplication, the other integer when the sum is - 38 and one integer is - 22 will be - 16 and the total score for Gopi will be 112 marks.

1)

Closure property of multiplication:

It states that if  two real numbers a and b are multiplied, then the product will be a real number as well.

We have 7 × 12 = 72

7, 12 and 72 all are real numbers.

So, it is a closure property under multiplication.

2)

Sum = - 38

a = - 22

We need to find b

a + b = - 38

- 22 + b = - 38

b = - 38 + 22

b = - 16

3)

1 correct answer = 4 marks

1 incorrect answer = - 2 marks

Number of correct answers = 32

Number of incorrect answers = 8

Total score = 32 × 4 + (- 2) × 8

= 128 - 16

= 112 marks.

Therefore, we get that, 7 × 12 = 72 satisfies the closure property of multiplication, the other integer when the sum is - 38 and one integer is - 22 will be - 16 and the total score for Gopi will be 112 marks.

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The estimate of 24% of 289 is 69.36

From the question, we are to determine the estimate the given rate

The given rate is

24% of 289

This can be expressed as

24% × 289

Now, we will evaluate the percentage

To evaluate the percentage, we will divide the number by 100.

That is,

24% = 24/100

Thus,

The expression can further be expressed as

24/100 × 289

= 0.24 × 289

=  69.36

Hence, the estimate is 69.36

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From the word problem given, the number of pizzas each that were delivered are:

Step I

Let a = number of small pizzas delivered

Let b = number of medium pizzas delivered

Let c = number of large pizzas delivered

Step 2 - Creating relevant expressions based on number and type ordered, we have:

a + b + c = 8.............................1

3a + 5b + 11c = 56..................2
4a + 9b + 12C = 4 * 8 + 12.....3a

We can rewrite (3) as
4a + 9b + 12C = 44 ....3b

Step 3

Multiply both sides of (1) by 4

We have

4a +4b +4c = 32

-
4a +4b +4c = 32
5b +8C = 12......................(4)

Multiply both sides of (1) by 3 and subtract from (2), and we have:

3a + 3b + 3c = 24, removing this from (2) we have

3a + 5b + 11c = 56

-
3a + 3b + 3c = 24
2b + 8c = 32.....................(5)

Step 4 - Subtract (4) from (5)

2b + 8c = 32
-
5b + 8c = 12
-3b = 20

b = - 20/3

= - 6.67
Since we cannot have negative values, we work with absolute value to get:

b [tex]\approx[/tex] 7

Since b = 7

2(7) + 8c = 32
8c = 32 - 14
c = 18/8

c [tex]\approx[/tex] 2


Plug in that back into a we have

a + b + c = 8
a + 7 + 2 = 8

a = 8-9
a = -1 (recall we must have absolute values)
a therefore = 1.

Hence the number of pizzas that were ordered are:

1 small
7 medium; and

2 large.

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Answer:

10.5:12:13.5

Step-by-step explanation:

The only two values you know and can compare are 8 and 12, so you have to find the relationship between them. 12/8 = 1.5. To get the two unknown values, you multiply 1.5 by the ones you do know.

7 * 1.5 = 10.5

9 * 1.5 = 13.5

So, you get 10.5:12:13.5

Step-by-step explanation:

Use the Pythagorean Theorem.

a^2+b^2=c^2

a^2 + 5^2 = 16^2

a^2 + 25 = 256

a^2 = 231

a = square root of 231

a= 15.20

Answer:15.20

Step-by-step explanation:

a) The problem is in the second step, the square root can't be distributed under sum.

b) 10*√41

a) The incorrect step is the second one, the square root can't be distributed like that.

Here we have the numeric expression:

5*√164

And we want to simplify it.

We can write:

5 = √25

Then:

5*√164 = √25*√164 = √(164*25) = √4,010

Now we can decompose this as a product of square numbers:

4,010 = 4*1,025 = 4*25*41

Then we rewrite:

√4,010 = √4*√25*√41 = 2*5*√41 = 10*√41

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The first term of the arithmetic progression is 5

An arithmetic sequence can simply be defined as a sequence of numbers or terms in which the differences between successive or consecutive terms are always equal.

The formula for the nth term of an arithmetic sequence is expressed as;

Tn = a + (n-1)d

Where;

Given that the first term of the sequence is a, the 43rd term is 26 and the common difference is 1/2

Substitute the values into the formula

26 = a + (43 -1)1/2

expand the bracket

26 = a + (42)1/2

Multiply through

26 = a + 21

collect like terms

a = 26 - 21

a = 5

Thus, the value is 5

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Answer: Multiplicative inverses or reciprocal, is a number that when multiplied by the given number gives the product as 1.

Step-by-step explanation:

expression :

[tex]\sqrt{5} \sqrt{5}[/tex] = [tex]\sqrt{5X5} = \sqrt{25} = 5[/tex].

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1. The value of t in the triangle is 50°

2. The value of x in the triangle is 107°

It should be noted that the total sum of the angles that are in a triangle is 180°.

Therefore, the calculation of the angles will be illustrated thus:

1. 2t + 12 + t + 18 = 180°

3t + 30 = 180°

Collect like terms

3t = 180° - 30°

3t = 150°

Divide through by 3

3t/3 = 150° / 3

t = 50°

2. x + 30° + 43° = 180°

x + 73° = 180°

Collect like terms

x = 180° - 73°

x = 107°

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By solving using given linear equation f(x)=x2-7 and g(x) = 2x + 9 we get  the desired value as ( g - f )(-2) = 32 .

An equation is deemed to be linear when the maximum power of the variable is consistently 1. It is also known as a one-degree equation. A linear equation with one variable usually has the form Ax + B = 0. In this scenario, the variables x and A are variables, whereas B is a constant.

A linear equation in two variables is of the form Ax + By + C = 0, in which A and B are the coefficients, C is a constant term, and x and y are the two variables, each with a degree of 1.

For example, 7x + 9y + 4 = 0 is a linear equation in two variables. If we consider two such linear equations, they are called simultaneous linear equations.

Simplification:

f(x)  = x2 - 7

g(x) = 2x + 9

( g - f )(-2) = (2x-7-2x -9)(-2)

                = -16 * -2

                = 32 .

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1) [tex]\angle A \cong \angle D, \angle C \cong \angle E, \overline{AB} \cong \overline{DF}[/tex] (given)

2) [tex]\triangle ABC \cong \triangle DFE[/tex] (AAS)

3) [tex]\angle ACB \cong \angle DEF[/tex] (CPCTC)

The number of animals that are on the farm is 48.

A fraction is a non-integer that is made up of a numerator and a denominator. An example of a fraction is 2/3.

The first step is to determine the fraction of the animals that are chickens.

Fraction that are chickens = 1 -  fraction that are pigs and horses.

[tex]\frac{1}{8} + \frac{2}{3}[/tex]

[tex]\frac{3 + 16}{24}[/tex] = [tex]\frac{19}{24}[/tex]

Fraction that are chickens = 1 - 19/24 = 5/24

The next step is to divide the number of chickens by the fraction of the chickens.

Number of animals = number of chickens ÷ fraction of chickens

10 ÷ 5/24

10 x 24/ 5 = 48

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Answer:

slope of perpendicular line = - [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

calculate the slope m of the given line using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (1, 0) and (x₂, y₂ ) = (3, 3) ← 2 points on the line

m = [tex]\frac{3-0}{3-1}[/tex] = [tex]\frac{3}{2}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{3}{2} }[/tex] = - [tex]\frac{2}{3}[/tex]

The value of a negative number such that the sum of that number and its square is 42 is -7.

Let the negative number be -x.

According to the question, the sum of the negative number and its square is 42.

So, we form an equation

- x + (-x)² = 42

x² - x - 42 = 0

Solving the quadratic equation,

x² - 7x + 6x - 42 = 0

x(x - 7) + 6(x - 7) = 0

(x - 7)(x + 6) = 0

x = -6 and x = 7

We have taken the number -x to be negative.

So, -x = -6 and -x = 7

x = 6 and x = -7

Hence, the value of the negative number is -7.

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The correct question is: "Determine the value of a negative number such that the sum of that number and its square is 42."

The Solution:

Given the function:

Required:

To determine the domain and the range of the function.

Below is the graph of the function:

Step 1:

The domain of the function is:

Step 2:

The range of the function is:

Therefore, the correct answer is :

Answer:

1. X+3x8=24
2.X+3x5=15

Step-by-step explanation:

Hello! So...

We are given the following to simplify:

[tex]\frac{(x+3)^8}{(x+3)^5}[/tex]

_______________________________

1. Apply the exponent rule ([tex]a^b^+^c=a^b * a^c[/tex]).

[tex](x+3)^8=(x+3)^5(x+3)^3[/tex]

=[tex]\frac{(x+3)^5(x+3)^3}{(x+3)^5}[/tex]

________________

2. Cancel out the common factor, given us our solution: [tex](x+3)^5[/tex].

________________________________________________________

Hope this helps! If so, please lmk! Thanks and good luck!

Write an algebraic expression to represent each statement.

the number, b, divided by thirty-six

b/36