16 There are some children in a classroom.
The ratio of boys to girls is 3:1
(a) Work out the fraction of the children that are boys.

The Equivalent expressions of  4x+1/2+2x-3 is  6x × 1/2 - 3 .

Expressions that perform similarly but differ in appearance are said to be equivalent expressions. When the same value(s) for the variable are entered, two algebraic expressions that are equivalent will have the same value (s). An expression that is equivalent to another expression but does not share its visual characteristics has the same value or worth. According to algebra, the equivalent formulae 2(2x - 3y + 6) and 4x -6y + 12 are the same. When two expressions can be written similarly or when they can be combined into a single, simpler expression, they are said to be equivalent. Furthermore, if values are replaced for the variable in two expressions and they both yield the same result, you can tell if the expressions are similar.

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Answer:

50

Step-by-step explanation:

    [tex]\sf 2\sqrt{5}*5*\sqrt{5} = 2*5* \sqrt{5*5}[/tex]

                          = 10 * 5

                           = 50

Multiply the rational numbers and multiply the radicals.

The inequality for the given statement is y > -8x+9.

inequality, In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Given that,

The statement is "The value of y is greater than the sum of negative eight times the value of x and 9".

According the given statement

First taking the sum of negative eight times the value of x and 9.

-8x+9

Then,

y is greater than -8x+9.

y > -8x+9

Hence, The inequality for the given statement is y > -8x+9.

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It should be noted that (6 ten thousands 3 hundreds) x 10 will give a value of 603000

Based on the information given, it should be noted that we want to calculate (6 ten thousands 3 hundreds) x 10

It should be noted that 6 ten thousands is 60000.

It should be noted that 3 hundreds will be 300.

Therefore, 6 ten thousands 3 hundreds x 10 will be:

= (60000 + 300) × 10

= 60300 × 10

= 603000

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The following linear equation gives Johnny's savings w weeks after her opened the account.

S(w) = $95 + $15*w

We know that initially, Johnny deposits an amount of $95, and then he saves $15 per week.

So, after w weeks, the amount in that savings account will be:

S(w) = $95 + $15*w

This linear equation gives the bank account balance w weeks after her opened the account.

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The values ​​of the trigonometric functions of the 0° angle are, cos 0° = 1, sin 0° = 0 ,tan 0° = 0, cot 0° = ∞, sec 0° = 1 , cosec 0° = ∞.

The simplest definition of a trigonometric function is the function of an angle in a triangle, also known as a circular function. It implies that these trigonometric functions can be used to determine the relationship between a triangle's angles and sides. The fundamental trigonometric operations include sine, cosine, tangent, cotangent, secant, and cosecant.

Now given degree is 0 ,

So, we know that sin 0° = 0,

And cos 0° = 1,

⇒tanθ=sinθ/cosθ,

Here θ = 0°

⇒tan 0° = 0/1,

⇒tan 0° = 0,

Now as cot θ is the inverse of tan θ, we get,

⇒cot θ = 1/tan θ,

⇒cot 0°= 1/0,

⇒cot 0° = ∞,

Now we know that cosec θ is the inverse of sin θ, we get,

⇒cosec θ = 1/sin θ,

⇒cosec 0° = 1/0,

⇒cosec 0° = ∞

And we know that sec θ is the inverse of cos θ we get,

⇒sec θ = 1/cos θ,

⇒sec 0° = 1/1,

⇒sec 0° = 1.

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Step-by-step explanation:

soz bro I need the points but that guy too be moving madd

Hello!

The product of something is the outcome of ADDITION.

This means we will have to add 7 and 13.

7+13=20.

It says the subtract 18.

20-18=2.

2 is your answer!!
---------------------------------

this is a pretty simple concept so I hope you understood. just remember product=addition. much love!! <3

Answer:

1/5

Step-by-step explanation:

we know that

To find the scale factor divide the circumference of the dilated circle by the circumference of the original circle

so

Scale factor= 4/20=1/5

Answer:

64

hope it helps

The graph of the continuous exponential function f(x) has been plotted and there is no y intercept in the graph

The  domain is the set of all possible inputs of the given function.

The range is the set of all possible outputs of the given function

Here values of the x is the set of all possible inputs of the function and the values of (x) is the set of all possible outputs of the function.

Draw the graph using the given domain and range

From the given graph

We can see that there is no y intercept and x intercept

Hence, the graph of the continuous exponential function f(x) has been plotted and there is no y intercept in the graph

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The measures of the unknown angles are as follows:

The measures of each angles can be found as follows:

Therefore,

∠AEB = ∠CED (vertically opposite angle)

∠DEA = ∠BEC (vertically opposite angle)

Vertically opposite angles are equal.

Therefore,

4x = 75 - x

4x + x = 75

5x = 75

x = 75 / 5

x = 15

Therefore,

∠DEA = ∠BEC = 4(15) = 60°

∠AEB = ∠CED  = 360 - 120 / 2 = 240 / 2 = 120°

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When the compass setting is changed in the next step of perpendicular bisector setting the construction line that suppose to be the perpendicular bisector will:

When a line say AB requires a perpendicular bisection by another line say CD, the following will happen

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As we can see

A. The figures have the same shape. TRUE

B. The figures have the same size. FALSE

figure 1 is smaller than figure 2

C. Corresponding angles have the same measure. TRUE

as we can see in the image they have the same measure

D. Corresponding sides have the same length. FALSE

figure 1 is smaller than figure 2

E. Corresponding side lengths have the same ratio. TRUE

two figures are similar, the ratios of the lengths of their corresponding sides are equal.

F. The figures are similar. TRUE

because they have the same shape but the size is different

[tex]4x=8\\\frac{4x}{4} =\frac{8}{4} \\x=2[/tex]

simplified it is x=2

Answer:

x = 2

Step-by-step explanation:

4 x 2 = 8

The probability of rolling an even number or a multiple of 3 is 3/4.

Probability determines the odds that a random event would happen. The probability the event takes place is 1 and the probability that the event does not happen is 0.

An even number is a number that is perfectly divisible by 2.

Probability of rolling an even number = number of sides that are even / total number of sides

Sides that are even = 2, 4, 6

Probability of rolling an even number = 3/6 = 1 / 2

Probability of rolling a multiple of 3 = number of sides that are multiples of 3  / total number of sides

Sides that are multiples of 3 = 3, 6

Probability of rolling a multiple of 3 = 2/6 = 1/2

The probability of event B or C = 1/4 + 1/2 = 3/4

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A certain plant grows 1 1/6 inches each week. it will rake the plant to grow 6 1/6 inches is 5 weeks 2 days.

Time is ongoing progression of existence and things that happen in what seems to be an irrevocable order from the past, present, and forward into the future. It is a quantity that is part of several measurements that are used to compare the length of events or the gaps between them, to compare how long they last, to order events, and to measure how quickly the things change in the real world or in our conscious experience. Along with the three spatial dimensions, time is frequently referred to as a fourth dimension.

Time has long been an important subject of study in religion, philosophy, and science, but defining it in a manner applicable to all fields without the circularity has consistently eluded scholars. Nevertheless, diverse fields such as the business, industry, sports, sciences, and the performing arts all incorporate some notion of time into their respective measuring systems.

A certain plant grows every week = [tex]1\frac{1}{6}[/tex] = [tex]\frac{7}{6}[/tex] inches

1 week = 7 days

Therefore in 1 day plant grows = [tex]\frac{\frac{7}{6} }{7}[/tex]

                                                        = [tex]\frac{1}{6}[/tex] inch

Now we have to calculate the number of days in which the plant grows [tex]6\frac{1}{6}[/tex]  inches ≈ [tex]\frac{37}{6}[/tex] inch

Number of days = [tex]\frac{Total growth}{growth in one day}[/tex]

                          = [tex]\frac{37}{6}[/tex] ÷ [tex]\frac{1}{6}[/tex]

                          = [tex]\frac{37}{6}[/tex]  × 6

                          = 37 days ≈ 5 weeks and 2 days

It will take plant 5 weeks 2 days to grow [tex]6\frac{1}{6}[/tex] inches.

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The probability that the amount dispensed per box will have to be increased is 0.0062.

Consider the provided information.

Sample of 16 boxes is selected at random.

If the mean for 1 hour is 1 pound and the standard deviation is 0.1

1 Pound = 16 ounces , then 0.1 Pound = 16/10 = 1.6 ounces

Thus: μ = 16 ounces and σ = 1.6 ounces.

Compute the test probability

z= x−μ/σ/[tex]\sqrt{n}[/tex]

z= 15-16/ 1.6/[tex]\sqrt{4}[/tex]

z= -1/ 0.4

z= -2.5

By using the table.

Probability p value = P(Z<-2.50) = 0.0062

Thus, the probability that the amount dispensed per box will have to be increased is 0.0062.

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The polynomial is

[tex]10x + y[/tex]

The length of a corresponding line segment in the image is; Nz

We know that;

Slope is the ratio of change in y-value and change in x-value.

Thus, dilation does not change the slope of any line.

Now, after dilation; M---->M

Length of line:

We know that a dilation has the effect of stretching or shrinking the line segment by the factor of N units

We are given

Length of line = z

Thus, the length after dilation will become

= N * z

= Nz which is the length of a corresponding line segment

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Ava's age is 26 years when Ava and Olivia's ages are consecutive even integers and the sum of Ava's age and 2 times Olivia's age is 74.

According to the question,

Ava and Olivia's ages are consecutive even integers.

Now, let's take Olivia's age to be x years.

So, Ava's age would be (x+2) years because their ages are consecutive even integers. (Even numbers are the number which are divisible by 2.)

We have the sum of Ava's age and 2 times Olivia's age is 74.

So, we have the following expression:

(x+2+2x) = 74

3x+2 = 74

3x = 74-2

3x = 72

x = 72/3 (3 was in multiplication on the left hand side. So, it is in the division on the right hand side.)

x = 24 years

So, Olivia's age is 24 years.

Now, we have:

Ava's age = (x+2) years

Ava's age = (24+2) years

Ava's age = 26 years

Hence, Ava's age is 26 years.

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The greatest number of identical arrangements the florist can make is .12 arrangements with 5 lilies and 3 daisies.

The greatest number of identical arrangements with the lilies and the daisies the florist can make would be equivalent to the highest common factor of the number of lilies and daisies.

The highest common factor of two or more numbers is the highest number that can divide the numbers evenly without leaving any remainder. For example, the highest common factor of 4 and 8 is 4.

Factors of 60=  1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, and 36.

Common factors = 1, 2, 3, 4, 6, 12

Highest common factor = 12

Number of daisies = 36 /12 = 3

Number of  lilies = 60 / 12 = 5

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Answer:

20.8 cm^2.

Step-by-step explanation:

Area = 1/2 * base * height

         = 1/2 * 8 * 5.2

Answer:

A = 20.8 cm²

Step-by-step explanation:

We have just to use the following expression:

A = (Base x height) / 2

So:

A = (8 x 5.2) / 2

A = 4 x 5,2

A = 20.8 cm²

The expression of b over negative 5.6 is less than or equal to negative 4.9 for b ≤ 0.7 ( b less than or equal to 0.7 ).

Based on the given conditions,

Negative 5.6 means = -5.6

Negative 4.9 means = -4.9

Negative 5.6 means ≤ Negative 4.9 means

Then,

-5.6  ≤  -4.9

But,

Let the number b is over negative 5.6,

It means,

We can write,

b + (-5.6)      (Equation-1)

This equation-1 is write into,

b + (-5.6) ≤  -4.9

b - 5.6 ≤  -4.9

b ≤ (-4.9) + 5.6

We can sum or difference the products,

b ≤ 0.7

Therefore,

The expression b over negative 5.6 is less than or equal to negative 4.9 for b ≤ 0.7

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Answer: The expression b over negative 5.6 is less than or equal to negative 4.9 for b ≤ 0.7

Step-by-step explanation:

Answer:

Step-by-step explanation:

I guess you want to draw the graph.

The graph is a straight line

-6x - 20 = 4y

When x = 0:

-6(0) - 20 = 4y

y = -20/4 = -5

So, one point on the graph

= (0, -5)

When y = -2:

Plugging y = -2 into the equation:

-6x - 20 = 4(-2)

-6x = -8 + 20 = -12

x = -2

So, another point is (-2, -2)

Mark these 2 points on the graph paper

and draw a line passing through them.

Step-by-step explanation:

4(x - 3) + 5x - x²

If x = 2,

= 4(2 - 3) + 5(2) - (2)²

= 4(-1) + 10 - 4

= -4 + 10 - 4

= 6 - 4

= 2.

Therefore, it is confirmed that x = 2.

He will pay $24.055 after discount and sales tax.

A sales tax is a fee that is paid to the government when specified goods and services are sold. Typically, laws permit the vendor to charge the customer the tax at the time of purchase. Use taxes are typically used to describe taxes on goods and services that consumers pay directly to a governing authority.

Given Data

Car cost = $24.211

Discount = 8%

Car cost after discount:

= 24.211 - 8%

= 22.274

Car cost after sales tax:

= 22.274(8%)

= 22.274 (0.08)

= 1.781

Cost of car =  22.274 + 1.781

Cost of car = 24.055

He will pay $24.055 after discount and sales tax.

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Answer:

1. x2-2x-24=0

break middle term

= x2-6x+4x-24=0

factorise:

x(x-6)+4(x-6)=0

=(x+4)(x-6)=0

x+4=0

x= -4

x-6=0

x= 6

2. x2-11x+18=0

break middle term

x2-9x-2x+18=0

Factorise

x(x-9)-2(x-9)=0

(x-2)(x-9)=0

x-2=0

x=2

x-9=0

x=9

Ask me if u don't know how to break middle term

The value of c is -3.

The factorization of the polynomial is [tex](x+3)(x^3-3x+2)[/tex].

Given that:-

Polynomial P(x) = x⁴ + 3x³ + cx² - 7x + 6 is divisible by (x + 3).

We have to determine the value of c and factorize the polynomial.

Using remainder theorem, putting x = -3 in the given polynomial, we get

[tex]P(-3)= (-3)^4+3(-3)^3+c(-3)^2-7(-3)+6=0[/tex]

P(-3) = 81 -81 +9c +21 +6 = 0

9c + 27 = 0

9c = -27

c = -27/9 = -3

Dividing the given polynomial  x⁴ + 3x³ -3x² - 7x + 6  by (x + 3), we get,

[tex]x^3-3x+2[/tex]

Hence, the factorization of the polynomial is given by:-

[tex](x+3)(x^3-3x+2)[/tex]

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