O and R are the subsets of a Universal set, U, such that U={22,23,24,25,26,27,28,29,30} 0={ prime numbers } {R}={ even numbers } a) Draw a Venn diagram to represent this information.
b) List the elements of.
i) ( O U R )'
ii) ( O ∩ R)'
iii) O ∩ R

The amount spent for other than groceries is $246.36.

Given that the money to spend this month = $410.60

Theresa uses 2/5 of the money to groceries.

So she spent on groceries = 410.60*(2/5) = 164.24

We have to subtract the spending on groceries from the total spending in order to find the required.

Then the amount spend other than groceries = 410.60-164.24 = 246.36

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Answer:

Step-by-step explanation:

Now, to complete the sentences assume the missing value is x.

1) 1 box, x bags and 9 single marbles:

2) 2 boxes, 2 bags and x single marbles:

Answer: Let 5/9=□/54

Clearly shows 54=(9×6)

Now multiply the numerator by 6 also

∴5 / 9 = (5 \times 6) / (9 \times 6) = 30 /54$$

Hence, 30/54 is the equivalent fraction of 5/9 having denominator 54

(ii) Let 5/9=35/□

Clearly shows 35=(5×7)

Now multiply the denominator by 7 also

∴5/9=(5×7)/(9×8)=35/63

Hence, 35/63 is the equivalent fraction of 5/9 having numerator 35

Step-by-step explanation:

All integer values of x in the interval [0, 7] are  0,1

What is an integer?

A full number, not a fraction, that can be positive, negative, or zero is called an integer (pronounced IN-tuh-jer). Integer examples include: -5, 1, 5, 8

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

−5x+3>-4

-5x > -4-3

-5x > -7

Divide by -5 on both sides

x< -7/-5

x< 7/5

x< 1.4

So, all integer values of x in the interval [0, 7] are  0,1

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Answer:

Step-by-step explanation:

False. They have one point in common meaning there is only 1 solution.

As per the proportionally concept, the missing value in the table is 240

and in 18 minute Kenny type 720 words.

Proportionality:

If two objects are proportional to each other, then it means that as one object increases the other will also increase and the ratio of the quantities is the same for all values.

Given,

Kenny is practicing for a typing test to obtain a job as paralegal. The number of words he can type is proportional to the number of minutes he types.

Here we need to find if the test is 18 mins long how many word will Kenny be able to type and the missing value in the table.

Here we have assume that if number of words typed is proportional to number of minutes

So, it can be written as Word typed α number of minutes

As in the equation form of the relation is,

Word typed = k * number of minutes

where k refers constant of proportionality

So, first we have to find the value of k, in order to solve this,

For, that we have to take the following,

=> 120 = k * 3

=> k = 120/3

Therefore, k = 40

So, if test is 18 minutes long, then the number of words is calculated as,

=> Word typed = k * 18

=> Word typed = 40 * 18

=> Word typed = 720

And the missing value of the table is,

=> words = 40 * 6

=> words = 240

Therefore, the number of words in 6 minutes is 240.

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Proportional reasoning can be used to solve a problem in which one quantity is a constant multiple of the other.

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".

Proportional reasoning is the reasoning based on the cognition that a relationship exists between the multiples of the variables in the problem, such that the magnitude of a variable can implied from the changes made to the relationships connecting the variables.

An example of proportional reasoning is the distance travelled, d, after a given time, t, at a constant velocity, v;

d = v·t

To judge the distance travelled, a constant, v,  multiplies the time, t, such that, at a longer time, it can be reasoned that the distance travelled is much further.

Therefore, proportional reasoning can be used to solve a problem in which one quantity is a constant multiple of the other.

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Answer:

32000 bacteria

Step-by-step explanation:

because it doubles every half hour and it has 200 then it would be 32000 bacteria

The distance 170.4 is 24% of 710 miles, 86.1% is the percent of 62 hours of 3 days and 50 is the 16% of the 8.

What is percentage?

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

1) given, 24% and 710 miles,

24/100×710= 170.4

2) first convert 3 days into hours.

=(3)(24) = 72 hours.

62/72×100=86.1%

3) let x be that number,

16%of x = 8

16/100×x = 8

x = 800/16

x =15

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Answer:

x=1/2

Step-by-step explanation:

x^2+5x-9=0

Plus 9: x^2+5x=9

square root: x+5x=3

6x=3 so x=1/2

Answer:

  (f∘g)(x) = 5x -16

Step-by-step explanation:

You want the simplified form of the composition (f∘g)(x) when f(x)=5x-6 and g(x)=x-2.

The notation (f∘g)(x) is a shorthand way to write f(g(x)). The composition operator (ring operator) works right to left, meaning that g(x) is evaluated first, then the result is used as an argument to the function f.

Functions are evaluated in the usual way.

  f(g(x)) = f(x-2) = 5(x-2) -6 = 5x -10 -6 = 5x -16

  (f∘g)(x) = 5x -16

(x+2)(x+5)(x-3) These are the factor of x³+4x²-11x-30
Hence x+3 is not the factor of this equation

What in mathematics is a binomial equation?

A polynomial with only terms is a binomial. An illustration of a binomial is x + 2, where x and 2 are two distinct terms. Additionally, in this case, x has a coefficient of 1, an exponent of 1, and a constant of 2. As a result, a binomial is a two-term algebraic expression that contains a constant, exponents, a variable, and a coefficient.

factor the equation

x³+(2x²+2x²)-(-4x+15x)-30

x³+2x²+2x²+4x-15x-30

x²(x+2)+2x(x+2)-15(x+2)

(x+2)(x²+2x-15)

(x+2)(x+5)(x+3)

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Answer:

147 degrees

Step-by-step explanation:

a straight line is always 180 degrees so the sum of these 2 angles equal 180 degrees so we pop it into an equation to solve for a

33+a=180

-33.      -33

a=147

Hopes this helps please mark brainliest

Answer:

a = 147°

Step-by-step explanation:

33°   +    a   form a straight line which is 180 °

33  + a  = 180

a = 147°

Answer:

Step-by-step explanation:

Option D

The graph using the direction, vertex, focus, and axis of symmetry is shown below.

The given equation is y=x²-4x.

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.

Put x=0, 1, 2, 3, 4,....in the given equation, we get

When x=0

y=0

When x=1

y=-3

When x=2

y= -4

When x=3

y= -3

When x=4

y=0

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex: (2, -4)

Focus: (2, -15/4)

Axis of Symmetry: x=2

Directrix: y= -17/4

Hence, the graph using the direction, vertex, focus, and axis of symmetry is shown below.

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Answer:

[tex]x - 1 \geqslant 3[/tex]

Simplifying

-7x2 + 5x + -18 = 0

Reorder the terms:

-18 + 5x + -7x2 = 0

Solving

-18 + 5x + -7x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by

-7 the coefficient of the squared term:

Divide each side by '-7'.

2.571428571 + -0.7142857143x + x2 = 0

Move the constant term to the right:

Add '-2.571428571' to each side of the equation.

2.571428571 + -0.7142857143x + -2.571428571 + x2 = 0 + -2.571428571

Reorder the terms:

2.571428571 + -2.571428571 + -0.7142857143x + x2 = 0 + -2.571428571

Combine like terms: 2.571428571 + -2.571428571 = 0.000000000

0.000000000 + -0.7142857143x + x2 = 0 + -2.571428571

-0.7142857143x + x2 = 0 + -2.571428571

Combine like terms: 0 + -2.571428571 = -2.571428571

-0.7142857143x + x2 = -2.571428571

The x term is -0.7142857143x.  Take half its coefficient (-0.3571428572).

Square it (0.1275510204) and add it to both sides.

Add '0.1275510204' to each side of the equation.

-0.7142857143x + 0.1275510204 + x2 = -2.571428571 + 0.1275510204

Reorder the terms:

0.1275510204 + -0.7142857143x + x2 = -2.571428571 + 0.1275510204

Combine like terms: -2.571428571 + 0.1275510204 = -2.4438775506

0.1275510204 + -0.7142857143x + x2 = -2.4438775506

Factor a perfect square on the left side:

(x + -0.3571428572)(x + -0.3571428572) = -2.4438775506

Answer:

52 degrees

Step-by-step explanation:

first solve for x

9x-20=2x+36

9x=2x+56

7x=56

x=8

Now we find angle PTU

9(8)-20

72-20

52

Hopes this helps please mark brainliest

The image vertices for a dilation with center (0,0) and a scale factor of 4 are A'(-12,4), B'(16,-12), C'(8,12), and D'(-4,16).

What are dilation and scale factors?

A figure or point that has undergone a change in size and location is known as dilation.

The amount by which the figure is stretched or contracted in a dilation is known as the scale factor.

The coordinates of the points in the pre-image can be multiplied by the scale factor to get the points in the picture if we are dilating a figure that is centered at the origin.

Given, vertex A = (-3,1), vertex B = (4,-3)

vertex C = (2,3), vertex D = (-1,4)

scale factor = 4 and center = (0,0)

Now, we need to find the image of the given vertices for dilation with center (0,0) and scale factor 4, then we have to multiply the given vertices with scale factor 4

A' = (-3*4,1*4) = (-12,4)

B' = (4*4,-3*4) = (16,-12)

C' = (2*4,3*4) = (8,12)

D' = (-1*4,4*4) = (-4,16)

Hence, the image of the given vertices are A'(-12,4), B'(16,-12), C'(8,12) and D'(-4,16).

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Answer:

Step-by-step explanation:

[tex]\sf \cfrac{x}{3}+2=16[/tex]

First, subtract 2 from both sides:-

[tex]\sf \cfrac{x}{3}+2-2=16-2[/tex]

Simplify:-

[tex]\sf \cfrac{x}{3}=14[/tex]

Now, let's multiply both sides by 3:-

[tex]\sf \cfrac{3x}{3}=14\times\:3[/tex]

Simplify:-

[tex]\sf x=42[/tex]

Hope this helps!

Have a great day! :)

Answer:

delete

Step-by-step explanation:

ok this is wrong pls delete

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$300\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &2 \end{cases}[/tex]

[tex]A=300\left(1+\frac{0.04}{12}\right)^{12\cdot 2} \implies A=300\left( \frac{301}{300} \right)^{24}\implies A \approx 324.94[/tex]

Answer:

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

Answer:

x = 1

Step-by-step explanation:

k is the constant of proportionality

Answer:

Step-by-step explanation:

Answer:she is correct i dont really get the formula but if -9 - 8 = -17

Step-by-step explanation:

The number of days which it would take 1000 people to sign the petition as required in the task content is; 4.35 days.

It follows from the task content that the number of days which it would take Jan to get 1000 signatures on the petition be determined.

Since it is given in the task content that 230 people sign the petition each day.

It therefore follows from proportion that the number of days needed for 1000 people to sign the petition is;

= 1000/230

= 4.3478 days.

Hence, the number of days which it would take 1000 people to sign the petition is approximately; 4.35 days.

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The other rational number is -23/60.

So, the other rational number is:

We know that,

Now, get the other number as follows:

Therefore, the other rational number is -23/60.

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The length of AB = b - a, MN = 3a - b/2 and MP = b/2 + (k + 1)(b - a).

A triangle is defined as a two-dimensional shape with three sides, three interior angles, and three vertices.

Given that OB = b and OA = a

From ΔAOB we have

OB + BA + AO = 0

b + (- AB) -a = 0

AB = b - a

Now from ΔMNO we get

MN + NO + OM = 0

MN + (-ON) + OB/ 2 = 0

MN - (OA + AN) + b/2 = 0

MN - (a + 2a) + b/2 = 0

MN = 3a - b/2

Now from ΔMBP, we have

MB + BP + PM = 0

OB/2 + (BA - PA) + PM = 0

b/2 + (- AP/k + AP) + PM = 0

b/2 + (-kAB /k + kAB) + PM = 0

b/2 + (k AB + AB) + PM = 0

PM = -b/2 - (k + 1) (b - a)

MP = b/2 + (k+1) (b - a)

Hence, The length of AB = b - a, MN = 3a - b/2 and MP = b/2 + (k + 1)(b - a).

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According to the given square root value, the resulting value of the expression 2√4 × √9 is 12

Square root:

Square root refers any number that is equal to a number, which when squared gives the original number.

Given,

Here we have the expression 2√4 × √9.

Now, we have to find the value of the expression.

While we looking the given expression we have identified that the value of the square roots are

√4 = √(2 x 2) = 2

Similarly, the value of

√9 = √(3 x 3) = 3

So, now we have to replace the root with these values, then we get,

=> (2 x 2) x 3

=> 4 x 3

=> 12

Therefore, the resulting value is 12.

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Answer:

10

Step-by-step explanation:

line LF divides the triangle into two equal parts

since LH is 5

therefore, GH is 5*2=10