select all equations that are equivalent to (5x+6)/2=3-(4x+12)

The probability of of a random student having blue eyes and dark hair

 is 35% .

let consider the total students in the school be (U) = 100%

out of them ,

students having blue eyes (A) = 60%

students having  dark hair (B) = 55%

students with neither blue eyes nor dark hair (A∪B)' = 20%

let the students with blue eyes and dark hair be (A∩B) = x %

Then according to the set theorem

U = n(A∪B) + n(A∪B)'

U = n(A) + n(B) - n(A∩B) + n(A∪B)'

100 = 60 + 55 - x +20

∴ x = 60 + 55 +20 - 100

x = 35 %

So the probability of random student having blue eyes and dark hair is 35% .

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Answer: [tex]x^{26}[/tex]

Step-by-step explanation:

The [tex]x^2[/tex] appears 13 times. Using the exponent rule [tex]x^a x^b=x^{a+b}[/tex], we get that:

[tex]x^2x^2x^2x^2x^2x^2x^2x^2x^2x^2x^2x^2x^2=x^{2(13)}=x^{26}[/tex]

Answer:

1. 130/6

2. 240/3

Step-by-step explanation:

make the whole numbers into a fraction by putting 1 as the denominator.

48/1.

then multiply together.

48 x 5 = 130

6 x 1 = 6

130/6

do the same with the other

120 x 2 = 240

1 x 3 = 3

240/3

Answer:

40

80

Step-by-step explanation:

5/6 × 48

5 × 48 = 240

240/6

= 40

120 × 2/3

120 × 2 = 240

240/3

= 80

Answer: x=10

Step-by-step explanation:

Images below

Help this helps

Answer:

  ∆JGF ≅ ∆GJH by the SAA Postulate

Step-by-step explanation:

Given a figure showing two triangles with a common side, and two marked angles not at either end of that side, you want to know the applicable congruence postulate.

The letters S and A in the congruence postulate references refer to "Side" and "Angle". The sequence of the letters corresponds to the sequence of corresponding parts in the triangles.

In the given figure, two angles in each triangle are marked with a single arc and a double arc. The triangles share a side that has the double-arc angle at one end. Hence, the sequence of corresponding parts can be seen to be (common) Side - (double-arc) Angle - (single-arc) Angle. The SAA congruence postulate applies.

  ∆JGF ≅ ∆GJH by the SAA Postulate

Answer:

B

Step-by-step explanation:

∠ ADB and ∠ AOB sum to 180° , that is

56° + ∠ AOB = 180° ( subtract 56° from both sides )

∠ AOB = 124°

An angle on the circle is half the central angle subtended on the same arc , so

∠ BCA = [tex]\frac{1}{2}[/tex] ∠ AOB = [tex]\frac{1}{2}[/tex] × 124° = 62°

The probability that the second ball drawn is a purple ball  is (e) 0.5833

From the question, we have the following parameters that can be used in our computation:

Green balls = 10

Purple balls = 14

This means that the total number of balls is

Total = 10 + 14

Evaluate the equation

So, we have

Total = 24

From the question, we understand that the ball is replaced

So, the probability that the second ball is purple ie

P(second purple) = purple/total

This gives

P(second purple) = 14/24

Evaluate

P(second purple) = 0.5833

Hence, the probability is (e) 0.5833

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250 bicycles must be manufactured to minimize the cost.

The cost C in dollar of manufacturing x bicycles at a production plant is given by:

C(x) = 3x² - 1500x + 198,500

a. To find number of bicycle that can minimize the cost

differentiate C(x) with respect to x

C'(x) = 6x - 1500

equating C'(x) = 0

6x - 1500 = 0

x = 1500/6

x = 250 , is our stationary point

Differentiate C'(x) = 6x - 1500 again and put x = 250,

C''(x) = 6 (positive)

At x = 250 , cost is minimum

Therefore , 250 bicycles must be manufactured to minimize the cost.

b. C(x) = 3x² - 1500x + 198,500

putting x = 250,

C(x) = 3(250)² - 1500(250) + 198,500
= 187,500 - 375 ,000 + 198,500

= $11,000 is the minimum cost

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The number of buttons A will be 11. And the number of buttons B will be 11.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

A container of buttons contains a similar number of each kind of button it contains 220g of buttons. The weight of the button is given as,

Let x be the number of each button. Then the equation is given as,

8x + 12x = 220

20x = 220

x = 11

The number of buttons A will be 11. And the number of buttons B will be 11.

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Answer:

Step-by-step explanation:

It is assumed 30% is the discount.

Original price is $150.99, discount is 30%, sale price is:

An equation of the form P=0 is referred to as a polynomial equation. P is a polynomial with coefficients in some field, typically the field of the rational numbers. A polynomial equation, on the other hand, can include a number of variables. The phrase polynomial equation is typically preferred over algebraic equation when discussing situations with multiple variables.

One or more variables, coefficients, and non-negative integer exponents of variables make up a polynomial, which is an expression. A mathematical statement that has a "equal to" symbol between two algebraic expressions with equal values is called an equation.

Sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials.

4x² + 6x + 21=0 where 4x²+6x+21 is considered as a polynomial expression which is written on the left side and has been fixed to make the polynomial expression equal to zero to form a complete polynomial equation.

1 Already answered

2 Degree:1 Real Roots of an equation:8 Number of Real Roots:1

3 Degree:2 Real Roots of an equation:2,-2 Number of Real Roots:2

4 Degree:5 Real Roots of an equation:-1,1-3,-3,-3 Number of Real Roots:5

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Answer: 695.52

Step-by-step explanation:

The area of each triangle is [tex]\frac{1}{2}(12)(14.49)[/tex].

There are 8 triangles in the figure, so the area is [tex]8(1/2)(12)(14.49)=695.52[/tex].

Answer:

x = 5

Step-by-step explanation:

3x + 5 = 2x + 10

subtract 5 from both sides:

3x + 5 - 5 = 2x + 10 - 5

3x = 2x + 5

subtract 2x from both sides:

3x - 2x = 2x + 5 - 2x

x = 5

The level of water in the swimming pool after a specified duration of the water draining at a constant rate is found as follows;

10. a. The water level is changing (reducing) at a rate of 1.75 inches per hour.

b. After 9 hours, the change in the water ls 15.75 inches

c. The change in the water level after 23 hours is 40.25 inches

A constant rate is a rate that is fixed or steady and does not vary following a change of the other variables?

The table of values for the draining swimming pool obtained from a similar question on the internet is as follows;

Hours Draining  [tex]{}[/tex]           Change in Water Level (inches)

2   [tex]{}[/tex]                                   -35

9  [tex]{}[/tex]                                     ?

17  [tex]{}[/tex]                                    -29.75

23  [tex]{}[/tex]                                    ?

The relationship between the hours the swimming pool drains and the water level is a proportional relationship., such that the ratio of each coordinate pair in the table is a constant.

Let H represent the hours draining and let C represent the change in water level, we have;

C ∝ H

C = k·H
[tex]k = \dfrac{C}{H}[/tex]

Where;

k = The constant of proportionality, which is the rate at which the water level is changing per hour

a. The rate at which the water level changes per hour can be found from the first pair of points on the table as follows;

The first pair of points = (2, -3.5)

[tex]k = \dfrac{-3.5}{2} = -1.75[/tex]

The rate at which the water level is changing per hour is -1.75 inches per hour

The water level is decreasing at 1.75 inches per hour

b. The change in water level after 9 hours is found by using the formula;

C = k × H

Where, H = 9, we have;

Change in water level, C = -1.75 × 9 = -15.75

The change in water level after 9 hours is 15.75 inches

c. The change in water level after 23 hours is found by plugging in H = 23 as follows;

C = -1.75 × 23 = -40.25

The change in water level after 23 hours is -40.25 inches

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Step-by-step explanation:

15t + 30 = 20t | -15t

30 = 5t

t = 30/5 = 6

20 + 5t = -6t + 86 | + 6t

20 + 11t = 86 | -20

11t = 66

t = 6

18t + 20 = 24t + 50 | -18t

20 = 6t + 50 | -50

-30 = 6t

t = -30/6 = -5

18t - 2 = 10t + 54 | -10t

8t - 2 = 54 | +2

8t = 56

t = 56/8 = 7

7t - 5 = 15t + 91 | -7t

-5 = 8t + 91 | -91

-96 = 8t

t = -96/8 = -12

Using the given expression, the number of tiles Mr. Grants will need to buy is 48

From the question, we are to use the given expression to determine the number of tiles Mr. Grant would have to buy

From the given information,

The given expression is,

27 ÷ s²

and

Mr. Grants decides to buy square tiles that have side lengths of 3/4 foot

That is,

s = 3/4

Now,

Using the given expression

27 ÷ s²

We get

27 ÷ (3/4)²

27 ÷ 9/16

= 27 × 16 / 9

= 3 × 16
= 48

Hence, he will need to buy 48 of the tiles

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The required value of a₄ is 10,202 to the given recursive formula.

An arithmetic sequence is defined as an arrangement of numbers that is in a particular order.

The given recursive formula in the question as:

aₙ = (aₙ ₋₁ )² + 1 ....(i)

And, a₁ = 3

Substitute the value of a₁ = 3 in equation (i), and solve for n = 2

a₂ = (a₁)² + 1

a₂ = (3)² + 1

a₂ = 9 + 1 = 10

Substitute the value of a₂ = 10 in equation (i), and solve for n = 3

a₃ = (10)² + 1

a₃ = 100 + 1 = 101

Substitute the value of a₃ = 101 in equation (i), and solve for n = 4

a₄ = (101)² + 1

a₄ = 10,201 + 1

a₄ = 10,202

Therefore, the required value of a₄ is 10,202.

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The linear programming model for this problem is Max 1000F + 1000T

Given that,

If the quantity of flip top pens to be produced is f and the quantity of tiptop pens to be produced is t, then

Number of lots of Flip top pens to produce = F

Number of lots of Tip top pens to produce = T

Therefore, The linear programming formulation is given by:

Max 1000F + 1000T

s.t.

Plastic: 3F + 4T <= 39

Ink Assembly:  5F + 4T <= 45

Molding time: 5F + 2T <= 37

F, P >= 0

Hence, the linear programming model for this problem is Max 1000F + 1000P

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The fifth graders are read for total 180 minutes.

What do you mean by minutes?

A 60-second interval of time. In an hour, there are 60 minutes. For illustration, the time 10:35 is 35 minutes after 10 o'clock. A minute is equivalent to 1/60th of a degree in terms of angles.

According to the given question,

First 5 students read for 100 minutes.

Then, next 25 studenda read for 50 minutes.

And the rest of the fifth graders read for 30 minutes.

Now, we will adding all the minutes to obtain the answer or total minutes of fifth grader read,

Total minutes of fifth graders read= 100+50+30

                                                        =180 minutes.

Therefore, the fifth graders take 180 minutes to read.

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What is Angle?

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

From the figure, we can tell that a transversal is passing through the two parallel lines which makes corresponding angles.

In the given figure 14x+7 and 10x+5 are the two angles formed by the transversal.

14x+7=10x+5

Now take all the variable terms to one side

14x-10x=5-7

4x=-2

Divide both sides by 4

x=-2/4

Divide numerator and denominator by 4

x=-1/2

Hence the value of x is -1/2

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Answer:

Step-by-step explanation:

It will be 115$

Answer:  the answer is $21.7391304348 or round to $21.74 is the cost for 50 gallons

Step-by-step explanation: I did the calculations and it costs $2.30  a gallon

For the parallel lines (l//m), the value of x is equal to 25 and the converse used is the alternate exterior angle theorem.

Parallel lines simply refers to two (2) lines that always have the same or equal distance apart and never meet.

The alternate exterior angle theorem states that when two (2) parallel lines are cut through by a transversal, the alternate exterior angles that are formed are congruent or angles of equal measure and magnitude.

By applying the alternate exterior angle theorem to parallel lines (l//m), we have:

4x - 13 = 2x + 37

4x - 2x = 37 + 13

2x = 50

x = 50/2

x = 25

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The total quantity of diesel fuel is 15.75 gallons.

The total quantity of diesel fuel can be calculated by summing up all the values. But, firstly converting quarts and pint into gallons.

1 quart = 0.25 gallon

For first container, 3 quarts = 0.25 × 3

3 quarts = 0.75 gallon

For second container, 2 quarts = 0.25 × 2

2 quarts = 0.5 gallon

For third container, it has 0.25 gallon

1 pint = 0.125 gallon

For first and third container, it has 0.125 gallon

So, amount of diesel fuel in first container = 3 + 0.75 + 0.125

Amount of diesel fuel in first container = 3.875 gallons

Amount of diesel in second container = 5 + 0.5

Amount of diesel in second container = 5.5 gallons

Amount of diesel in third container = 6 + 0.25 + 0.125

Amount of diesel in third container = 6.375 gallons

So, the total quantity of diesel fuel = 3.875 + 5.5 + 6.375

The total quantity of diesel fuel = 15.75 gallons

Hence, the total quantity is 15.75 gallons.

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The value of test statistic is  -1.14

Define Standard error.

The standard error (SE)of a statistic (usually an estimate of a parameter) is the standard deviation of its sampling distribution or an estimate of that standard deviation. If the statistic is the sample mean, it is called the standard error of the mean (SEM).

Null Hypothesis

P = 0.54

Alternate Hypothesis

P < 0.54

For 0.05 level , the value of Z = 1.645

Decision rule ,

reject null Hypothesis if test statistic Z < -1.645

sample size (n) = 200

sample success (x) = 100

Standard error SE = √(p * (1 - p) / n

                         = √0.54 * (1 - 0.54) / 200

Standard error SE= 0.0352

Sample proportion (р)  = x/n

                               = 100 / 200 ⇒ 0.5

test statistic  Z = (р - P) / SE

                         = (0.5 - 0.54) / 0.0352

test statistic  Z = -1.136 or -1.14

Therefore, the value of test statistic is  -1.14

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There are 96 basketball conference games are scheduled.

For the given question;

There are N games on the schedule because there are two teams in each game.

N = 12×16/2

N = 96

Thus, there are 96  basketball conference games are scheduled.

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Step-by-step explanation:

In Peter class three times as many students who wear glasses are those who do not.there are 28 students in the class. How many students do not wear glasses?

with glasses: x
without glasses: 3x

x + 3x = 28

4x = 28

x = 7 with glasses

7 * 3 = 21 without glasses

Answer: n=895

Step-by-step explanation:

Answer:

n = 895

Step-by-step explanation:

Here we want to find n , 1st form the Equation then solve it for n

0.1 times n = 0.1n

0.1 times n equal 89.5

Then 0.1n = 89.5

Solve for n , b dividing both sides by 0.1

n = 89.5 / 0.1 = 895

The least possible value of n, where the product of 180 and the positive integer n is a perfect cubic number is 150.

so, by the question,

n×180 is a perfect cube

on the prime factorization of 180, we get

180 = 2²×3²×5

so the number should be

n = 2 × 3 × 5² =150

when we multiply both of them we get

180×n = (2²×3²×5)×(2 × 3 × 5²)

          = (2³×3³×5³)

          =(2×3×5)³

          =(30)³

          =27000

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Answer:

D

Step-by-step explanation:

f(-5) = 2|-5-5|

f(-5) = 2|-10|

f(-5) = 2 * 10

f(-5) = 20

f(0) = 2|0-5|

f(0) = 2|-5|

f(0) = 2 * 5

f(0) = 10