Determine the truth value of the given conditional statement. If true, explain your reasoning. If false, give a counterexample.

If {x⁴=16}, then x=2.

Answer:

3.75 dollars for the boys and 7.5 for girls

Step-by-step explanation:

Boys get x amount.

Girls get 2x

6x+2x=8x

30/8=3.75

Each boy receive the amount of $3.75 and Each girl receive the amount of $7.5

An equation is an expression that shows the relationship between two or more numbers and variables.

Let consider that each boy gets $x

It is given that each of the girls receives twice as much each of the boys

So, each girl receive the amount of 2x

Since there are 3 girls .

So, Three girls received the amount = 3(2x)=6x

2 boys get amount of 2x

Therefore,

6x+2x=8x

30/8

=3.75

Hence Each boy receive the amount of $3.75 and Each girl receive the amount of $7.5

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The volume of a cone that has a radius of 1 cm and a height of 3.4 cm is 3.56 cm³.

Volume of a cone is the space occupied by it in a three - dimensional space.

Volume of a cone is calculated using the formula:

[tex]V = \frac{1}{3} \pi r^{2} h[/tex]

where r is the radius of the base of the cone

[tex]\pi[/tex] is a constant having value 3.14

h is the height of the cone. It is the perpendicular height from the base.

According to the given condition,

r = 1 cm and h = 3.4 cm

Substituting these values in the equation above,

[tex]V = \frac{1}{3} \pi (1^{2}) (3.4)[/tex]

∴ V = 3.56 cm³.

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Answer:

x=100

Step-by-step explanation:

√x-6+2=6

√x -4 =6

√x =6+4

√x = 10

squere both sides of the equation

x =100

According to the given data the value of the  triangle's angle is m ∠ A =30

A triangle's inner angles always add up to 180°, whereas its outside angles are equivalent to the sum of its two inside angles. equal toward the combination of the two nearest interior angles Another method for calculating a triangle's exterior angle is to subtract overall angle of something like the vertex of concern from 180°.

m ∠ R=41

m ∠S=109

find m∠ A

We know that the total of the triangle's angles must equal 180°.

So ,

(​substitute given values)

m ∠R+ m ∠S +m ∠A =180

(add)

41 + 109 + m ∠A =180

(subtract 150 from both side)

150+m∠A =180

m ∠ A =30

According to the given data the value of the  triangle's angle is m ∠ A =30

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Answer:

Step-by-step explanation:

x=72+23

x=95

Answer: x = 95

Step-by-step explanation:

Add 23 to both sides to isolate x

x - 23 + 23 = 72 + 23

x = 95

Answer:

- 1 [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

substitute x = - 5 into f(x)

f(- 5) = [tex]\frac{1}{4}[/tex] × - 5 = - [tex]\frac{5}{4}[/tex] = - 1 [tex]\frac{1}{4}[/tex]

The slope of the line of each pair of points 3/2 , - (1/2) and -(2/3) , 1/3 is zero

A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.

The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.  

Therefore,

m =  y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.

Be aware that tan ∅ = y/x.

We also refer to this tan as the line's slope.

We know that slope, slope = m =  [tex]\frac{y_2 -y_1}{x_2 -x_1}[/tex]

For the pair of points 3/2 , - (1/2)

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

   = 0/(-4)

Hence the slope is zero for these points.

For the pair of points -(2/3) , 1/3

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

   = 0/3

Hence the slope is zero for these points.

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The equation of line parallel to the given equation and goes through the given point is y = 7x - 26.

Given the data in the question;

First, we determine the slope by comparing the equation with the slope intercept formula ( y = mx + b )

y = 7x + 3

Hence,

Slope m = 7

Next, we use the point-slope formula y-y₁ = m( x-x₁ ) to determine the equation of the line parallel.

Note that, the slopes must equal.

Given that; slope m = 7, Point: (-4,-2)

Plug into the point-slope formula and simplify.

y-y₁ = m( x-x₁ )

y - (-2) = 7( x - (-4) )

y + 2 = 7( x + 4 )

y + 2 = 7x + 28

y = 7x + 28 - 2

y = 7x - 26

Therefore, the equation of line parallel to the given equation and goes through the given point is y = 7x - 26.

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The value of a in the expression is 15.

It should be noted that an expression shows that relationship that exists between variables.

In this case, we are given the expression that 1/3a = -5

To find the value of a will be:

a/3 = 5

Cross multiply

a = 3 × 5.

a = 15

Therefore, the value of a in the expression is 15.

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1/3a = -5. Find the value of a.

Based on the graph, the expected total value of the donations in October would be $460.

When donations were 5 in number, the expected value was £30.

When donations were 8, the expected value was £50.

When donations were 15, the expected value was £90.

The slope of the line is:

= (90 - 50) / (15 - 8)

= 5.71

The y-intercept as seen on the graph is 0.

The equation of the line is therefore:

y = 5.71x

The expected value of £80 in donations is therefore:

y = 5.71 x 80

= $460

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The summation notation for the series 500+490+480+ . . . . . . . +20+10 is

[tex]25500-10\sum\limits^{50}_{n=1} {n}[/tex]

A summation notation is used to express a long summation into a single notation.

The given series is:

    500+490+480+ . . . . . . . +20+10

This is an arithmetic series with:

a(1) = 500, and

d = 490 - 500 = -10

The last term is a(n) = 10. Find n first by using the nth term formula of an arithmetic sequence:

a(n) = a(1) + (n-1) . d

10 = 500 + (n-1) . (-10)

10 = 500 -10n + 10

10 n = 500

n = 50

Write the explicit formula for the nth term:

a(n) = a(1) + (n-1) . d

a(n) = 500 + (n-1) . (-10)

a(n) = 500 -10n + 10

a(n) = 510 - 10n

The series is the summation notation from n=1 to n = 50

[tex]=\sum\limits^{50}_{n=1} {a(n)}[/tex]

[tex]=\sum\limits^{50}_{n=1} {(510-10n)}[/tex]

[tex]=\sum\limits^{50}_{n=1} {510} -\sum\limits^{50}_{n=1} {10n}[/tex]

[tex]=510\times50-10\sum\limits^{50}_{n=1} {n}[/tex]

[tex]=25500-10\sum\limits^{50}_{n=1} {n}[/tex]

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A solution to an equation that appears in the process of solving other equations is known as a extraneous solution.

The value of x = 2 then L.H.S = R.H.S, this equation has no extraneous solutions.

A solution to an equation that appears in the process of solving other equations is known as a extraneous solution.

To determine if a solution exists extraneous, we simply plug the solution into the original equation.

If it makes a true statement, then it exists not an extraneous solution, but if it makes a false statement, then it is an extraneous solution

Let the equation be,

√5x - 3 = √2x+3

squaring on both sides of the equation, we get

⇒ 5x - 3 = 2x + 3

⇒ 5x - 2x = 3 + 3

simplifying the above equation, we get

⇒ 3x = 6

Divide both sides of the equation by 3,

⇒ x/3 = 6/3

⇒ x = 2

The value of x = 2.

Substituting x = 2 in L.H.S

[tex]$\sqrt{5x-3} =\sqrt{10-3} =\sqrt{7}[/tex]

Substituting x = 2 in R.H.S

[tex]$\sqrt{2x+3} =\sqrt{4+3} =\sqrt{7}[/tex]

Since, L.H.S = R.H.S, this equation has no extraneous solutions.

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The expression for 7(2+9) IS A(B+C) which is distributive property of addition over multiplication.

Only two arithmetic procedures are subject to the commutative property: Multiplication and Addition

 A + B = B + A Which is Commutative property of addition

A.B = B.A, which is a commutative property of multiplication.

Distributive property is A(B+C) =AB+AC

The operation on numbers that are available in brackets can be distributed for each number outside the bracket, according to the distributive property. It is one of the mathematical properties that is used the most. Commutative and associative qualities are the other two important features.

from the given data 7(2+9) =7*2+7*9

                                                =14+63

                                                =77

Now, we can clear that 7(2+9) =7(9+2)

Hence, the expression for commutative property of addition is A(B+C) = AB+AC.

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So 1st off you divide 25.2 by 36 since it miles is the x and the cost is y

the unit rate is 0.7 since i divided those 2 numbers

now i just have to do 0.7 times 47

The answer is $ 32.9

sorry if its wrong?

☞ user58580~ ♥

If 37 kids stayed home, the daycare normally has 143 kids.

We can use algebra to solve the problem.

Let's call the total number of kids in the daycare "x".

We know that 74% of the kids were absent, which means that 26% (100% - 74%) of the kids came to the daycare.

Note:  37 kids stayed home.

Set up the following equation:

0.26x = 37

To solve for x,  divide both sides by 0.26:

x = 37 / 0.26

x ≈ 142.31

Therefore, the daycare normally has approximately 143 kids.

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Answer:

w = 3,−5

Step-by-step explanation:

If ur solving for w then that i presume.

Answer:14

Step-by-step explanation:X+8=asher's age X=Asher's sisters age

x+x+8 =20
2x+8=20
2x+8-8=20-8
2x=12
2x/2=12/2
x=6
x+8=asher's age
6+8=14

Given statement 'The component form of a vector describes the vector in terms of change in x and change in y.' is True.

For a vector V whose initial point is (x1, y1) and the terminal point is (x2, y2), the component form of a vector V is given as:  < x₂ – x₁, y₂ – y₁ >

The coordinates of the component form of vector are nothing but the ordered pair that describes the changes in the x-values and y-values.

Consider a vector v whose initial point is (1, 3) and the terminal point is   (3, 6).

The component form of vector v is:

<3 - 1, 6 - 3>

= <2, 3>

Here, 2 is the change in the x-values from initial point to terminal point and 3 is the change in the y-values  from the initial point to the terminal point.

Therefore, given statement 'The component form of a vector describes the vector in terms of change in x and change in y.' is True.

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The equation to represent the given situation is 1/2X-5=11-5/6 using X as the variable.

What is an equation and how it can be formed?

Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.

When we are given a mathematical problem that is or may be described using algebraic expressions, we form and solve equations. The information from the situation and the algebraic expressions can be used to create an equation. The equation can then be solved to obtain the answer.

Given the situation: If 5 is lessened by 1/2 of a number the result is the same as subtracting 5/6 from 11.

To write an equation for the given situation.

Let the number be X.

If 5 is lessened by 1/2 of the number, we get the expression 1/2X-5

Subtracting 5/6 from 11 gives the expression 11-5/6

Now, it is given that both the situations are same so equating both the expressions we get,

1/2X-5=11-5/6

⇒1/2X-5=61/6

Hence, the equation to represent the situation is 1/2X-5=11-5/6.

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Compare the two numbers 12,-√150

[tex]-\sqrt{150} =-12.24[/tex]

So,12  >  -√150

What is a square root?

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Answer:

Step-by-step explanation:

M(6,3)

A(4,-2)⇒A(x1,y1) just incase you understand

B(x2,y2),Now I will use the midpoint formula

[tex]M(\frac{x1+x2}{2} ,\frac{y1+y2}{2} )\\=(\frac{4+x2}{2} ,\frac{-2+y2}{2} )\\=separate(x)\\\frac{4+x2}{2} =6\\4+x2=12\\x2=12-4\\x2=8\\\\\frac{-2+y2}{2} =3\\-2+y2=6\\y2=3+2\\y2=5[/tex]

B(8,5)

Answer:

3 hours i believe

Step-by-step explanation:

i did 11.25 (11 1/4) divided by 3.75 (3 3/4)

The total number of hours in a single shift is 3 hours

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total number of hours in a single shift be = A

Now , The total length of equal shifts Skylar worked last week = 3 3/4 shifts

The total length of equal shifts Skylar worked last week = 15 / 4 shifts

The total number of hours Skylar worked in the week = 11 1/4 hours

The total number of hours Skylar worked in the week = 45 / 4

Now , the equation will be

Total length of equal shifts Skylar worked last week = total number of hours Skylar worked in the week

So ,

Total length of one shift of Skylar = total number of hours Skylar worked in the week / Total length of equal shifts Skylar worked last week

On substituting the values in the equation , we get

Total length of one shift of Skylar A = ( 45/4 ) / ( 15/4 )

On simplifying the equation , we get

A = ( 45/4 ) / ( 15/4 )

A = 45 / 15

A = 3 hours

Therefore , the value of A is 3 hours

Hence , The total number of hours in a single shift is 3 hours

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The probability of selecting that both chips are purple is 3/40

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

It is Given that A bag contains 3 red chips, 5 green chips, 2 yellow chips, 4 brown chips, and 6 purple chips. One chip is chosen at random, the color noted, and the chip returned to the bag.

The probability of selecting that both chips are purple

= 6/20 x 5/20

= 30/400

= 3/40

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Answer:

I think the answer is ∞ which is the third option, undefined.

Answer:

Step-by-step explanation:

Hey there!

(3^2)^4

= (3 * 3)^4

= (9)^4

= 9^4

= 9 * 9 * 9 * 9

= 81 * 81

= 6,561

Therefore, your answer should be:

6,561

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

The last one is incorrect

Step-by-step explanation:

Answer:

A. Jake made a mistake in step 2

Step-by-step explanation:

If you subtract a number from one side, you should do the same for the other. In step 2 Jake subtracted 7 from one side but not from another.

Answer:

s = 5

Step-by-step explanation:

V=s^3

125 = s^3

s = 125^(1/3) (cube root)

s = 5

Never mind got it wrong

Answer:

Step-by-step explanation:

So it gives us the equation y=2x+3

Thinking process

1. What you want to do is remove the 3 from the equation so you just get y=2x

How to solve(example)

For the first row to find x first minus 3 from 9 which is 6

9-3=6

Then six divided by two so you can find x.

2x=6

x=3

Answer:

Step-by-step explanation:

x + 80° = 5x ( being corresponding angle )

80° = 5x - x

4x = 80°

x = 80° / 4

x = 20°

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