What is [tex]3^2*3^5[/tex]?

Answer:

The regular bottle holds 9 fl oz less

Step-by-step explanation:

Given

Family Size =  12 fl oz

Required

Determine the size held less by the regular bottle

From the question, we have that the regular bottle holds 75% less;

[tex]Regular\ Size = 75\% * Family\ Size[/tex]

Substitute 12 fl oz for Family Size

[tex]Regular\ Size =75\% * 12\ fl\ oz[/tex]

Convert percentage to fraction

[tex]Regular\ Size = \frac{75}{100} * 12\ fl \oz[/tex]

[tex]Regular\ Size = \frac{75 * 12\ fl\ oz}{100}[/tex]

[tex]Regular\ Size = \frac{900\ fl\ oz}{100}[/tex]

[tex]Regular\ Size = 9\ fl\ oz[/tex]

Hence, the regular bottle holds 9 fl oz less

Answer:

48 girls tried out for the team.

Step-by-step explanation:

The phrase "2 out of every 9" can be written as the fraction 2/9. To find our answer, all we have to do is 2/9 * 216 = 48 girls.

we can subtract the trapezium (white part) formed after from the trapezium (including white and grey) to get area of striped part

area of trapezium is [tex]\frac H2(a+b)[/tex] where $a$ and $b$ are parallel sides.

for bigger trapezium, $h=4$ parallel sides are $5$ and $5$

hence area is $\frac{4(5+5)}{2}=20$

similarily area of white trapezium, $\frac{4(3+3)}{2}=12$

and area of striped part is $20-12=8$

Answer:

A. 4y + 3 = 15

B. y = 3

Step-by-step explanation:

Three is added to four times a number, the result is 15

A. Equation to represent the above information:

Let the unknown number= y

4 * y + 3 = 15

4y + 3 = 15

B. Solve your equation in (a)​

4y + 3 = 15

Collect like terms

4y = 15 - 3

4y = 12

Divide both sides by 4

4y / 4 = 12 /4

y = 3

Therefore, the unknown number is 3

Answer:

Step-by-step explanation:

Given the functions  f(x) =  3x² + 4 and g(x) = 2x − 3, to know that statements that is  true about f+g, we will need to add the functions together first.

f(x)+g(x) = 3x² + 4 + 2x - 3

f(x)+g(x) = 3x²+2x +4 - 3

f(x)+g(x)  = 3x²+2x + 1

The highest degree of a quadratic function is 2 and since the highest degree of the resulting function is 2, hence the resulting sum of the equations is quadratic.

Also the range of the values is all real numbers because the presence of x² in the function will always return a positive value greater than x.

Hence the correct statements are 'the range is all real numbers and it is a quadratic function'

Answer:

B AND D

Step-by-step explanation:

It is an equilateral triangle so its angles are equal 60°. From the definition, we know that:

[tex]\sin60^\circ=\dfrac{h}{4}[/tex]

and

[tex]\sin60^\circ=\dfrac{\sqrt{3}}{2}[/tex]

so

[tex]\dfrac{\sqrt{3}}{2}=\dfrac{h}{4}\quad \Big|\cdot4\\\\\\h=\dfrac{4\cdot\sqrt{3}}{2}\\\\\boxed{h=2\sqrt{3}}\\[/tex]

Answer:

h = √12

Step-by-step explanation:

use the Pythagorean

h² = 4² - 2²

h² = 16 - 4

h = √12

Answer: The answer is C.

Step-by-step explanation:

Because in the theory of the outcome is a 50/50 chance landing heads or tails.  So, the theorectical probability is 1/2.  Now the experimental must be 11/20.

Answer:

theory=1/2, experimental=11/20

Step-by-step explanation:

so when talking about theoretical probability you only consider the only possible outcomes which are either head or tail and since you haven't carried out any sort of experiment yet (many flips) you consider the number of outcomes of tossed once since it's theory which are two therefore the probability of each will be 1/2

but in experimental probability you now consider the number of times tossed and the outcomes of each side which is this case of heads will be 55/100 but in the answers they have simplified so it will be 11/20

Answer:

a) 7b+6=97

b)b=13

Step-by-step explanation:

Total cost = $97

Cost of each book = $7

Cost of shipping =$6

Therefore ,

Cost of the total no. of books+ Cost of shipping = Total Cost

=>7b+6= 97   <------- Answer to part(a)

=>7b=97-6

=>7b=91

=>b=13

No. of books = 13 <--------- Part (b)

Answer:

1,080 meters squared.

Step-by-step explanation:

Let's say the breadth of the rectangle is x. That means the length of it is 6/5x.

The perimeter is 132 meters. The formula for the perimeter is 2 times the breadth plus two times the length.

2(x) + 2(6/5x) = 132

2x + 12/5x = 132

10/5x + 12/5x = 132

22/5x = 132

22x = 660

x = 30.

That means that the breadth of the rectangle is 30 meters, and the length is (6/5) * 30 = 6 * 6 = 36 meters.

The formula for the area of the rectangle is the breadth times the length, so the area is 36 * 30 = 1,080 meters squared.

Hope this helps!

Answer: [tex]\dfrac{1}{5}+\dfrac{1}{2}=\dfrac{7}{10}[/tex]

Step-by-step explanation:

A or B = A+B

Given: In a fish tank, [tex]\dfrac15[/tex] of the fish are guppies and [tex]\dfrac{1}{12}[/tex] of the fish are goldfish.

Then,  the fraction of the fish that are guppies or goldfish in the tank=[tex]\dfrac{1}{5}+\dfrac{1}{2}=\dfrac{2+5}{5\times2}[/tex]

[tex]\dfrac{7}{10}[/tex]

Hence, the equation most closely estimates the fraction of the fish that are guppies or goldfish in the tank:

[tex]\dfrac{1}{5}+\dfrac{1}{2}=\dfrac{7}{10}[/tex]

Answer:

The x coordinate of P is [tex]\frac{4}{3}[/tex].

Step-by-step explanation:

Let is find the rate of change of the equation in time, which consists in a composite differentiation. That is:

[tex]\frac{dy}{dt} = 2\cdot x \cdot \frac{dx}{dt} -2\cdot \frac{dx}{dt}[/tex]

According to the statement of the problem, these variables are known:

[tex]\frac{dx}{dt} = 6[/tex] and [tex]\frac{dy}{dt} = 4[/tex]

Hence, the x coordinate of P is found by direct substitution:

[tex]4 = 2\cdot x \cdot (6)-2\cdot (6)[/tex]

[tex]4 = 12\cdot x -12[/tex]

[tex]x = \frac{4}{3}[/tex]

The x coordinate of P is [tex]\frac{4}{3}[/tex].

Answer:

10

Step-by-step explanation:

d is the variable for distance

√(0−8)2+(−3−3)2=

√(−8)2+(−6)2=

√64+36=

√100=

10

Answer:

10

Step-by-step explanation:

Answer:

no solution

Step-by-step explanation:

1/3(12-6x)=4-2x

4-1.3x=4-2x

4=4-0.7x

0=0.7x

ns

Answer:

A.

Step-by-step explanation:

All of those graphs represent functions. You are able to tell because they all pass the vertical line test. The vertical line test is conducted by drawing a line that goes vertically and intercepts any point of the line in question. If the function crosses the vertical line twice, it is not a function. If it only intercepts once, it is a function. In this case, every graph is a function because they would intercept a vertical line once.  

Answer:

y = x + 15

Step-by-step explanation:

My friend swims x minutes.

I swim 15 minutes more than my friends, so I swim x + 15 minutes.

I swim y minutes, so y equals x + 15

Answer: y = x + 15

Step-by-step explanation:

why did u add the 5 in the question?.

Answer:

Step-by-step explanation:

Area of a circle = πr²

where

r is the radius

From the question

Area = 6.76 cm²

To find the radius substitute the value of the area into the above formula and solve for the radius

That's

[tex]6.76 = \pi \: {r}^{2} [/tex]

Divide both sides by π

We have

[tex] {r}^{2} = \frac{6.76}{\pi} \\ r = \sqrt{ \frac{6.76}{\pi} } [/tex]

r = 1.46689291

We have the final answer as

radius = 1.47 cm

Hope this helps you

Answer:

Era

Step-by-step explanation:

Century, Decade and Millennium have something in common and that which they have in common is that they are all measurement of time.

The keyword measurement implies that they are units of time just like seconds, minutes, hours, etc.

Century -> 100 years

Decade -> 10 years

Millennium -> 1000 years

However, era is used to describe events in history;

Take for instance; the era of the first generation of computer;

So, from the list of given options; Era best answers the question

An era describes a time period marked by a change that begins a new period.

An era :

Examples of eras include:

All the eras mentioned above were distinct in how people behaved so in conclusion we can say that an era is a time period that begins a new period of development.

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Answer:

Step-by-step explanation:

Number of class intervals = 7

Class width = 5

Class intervals (heights)        Frequency (Number of boys)

130 - 135                                                     3                        

136 - 140                                                     5

141 - 145                                                      3

146 - 150                                                     5

151 - 155                                                      2

156 - 160                                                     1

161 - 165                                                      1

Therefore, frequency table given above will represent the distribution of the heights and number of students.

Answer:

5/8

Step-by-step explanation:

(10 +/- √100-104)/4

(10 +/- 2i)/4

5/4 +/- 1/2i

5/4 * 1/2 = 5/8

Answer:

t = 0.75n - 0.25

t represents your total

Step-by-step explanation:

So lets start by writing our total variable.

t =

Now each candy is 0.75 so lets write that down too.

t = 0.75

Since we don't know how much candy we buy, lets multiply 0.75 by n.

t = 0.75n

Now we have a $0.25 coupon so now subtract the 0.25 from the cost.

t = 0.75n - 0.25

There you go.

Answer:

Isabelle spent $52.50 more on Erasers than rulers.

Step-by-step explanation:

Step 1

Find the quantity of each stationery bought in fraction

Let us represent the total fraction of what Isabelle bought as: x

1/3x = quantity of pencils bought

5/8 of the remainder = quantity of erasers bought

The remainder = x - 1/3x = 2/3x

5/8 of 2/3x = 5/8 × 2/3x = 5/12x

Hence, 5/12x = quantity of erasers bought

The rest is rulers

1 - (1/3 + 5/12)

1 - (4 + 5/12)

1 - 9/12

1 - 3/4

= 1/4x

Hence, 1/4 = quantity of rulers bought.

Step 2

We find the number of stationeries that Isabelle bought.

The cost of the stationery is

a Pencil: $1.20

an eraser: $1

a ruler: $0.50.

Total amount spent on stationery = 169.50

We have this equation

1.20 × 1/3x + 1 × 5/12x + 0.50 × 1/4x = 169.50

0.4x + 0.4166666667x + 0.125x =

169.50

0.9416666667x = 169.50

x = 169.50 /0.9416666667

x = 179.99999999

Approximately , the number of stationeries that Isabelle bought = x = 180

Step 3

Find the number and the amount spent on each stationery that Isabelle bought

a) i) Quantity of pencils bought = 1/3 x

x = 180

= 1/3 × 180

= 60 pencils

ii) Amount spent on pencils

If 1 pencil = $1.20

60 pencils =

60 × 1.20 = $72

b) i) Quantity of Erasers bought = 5/12x

x = 180

= 5/12 × 180

= 75 pencils

ii) Amount spent on Eraser

If 1 pencil = $1

75 pencils =

75 × 1 = $75

c) i) Quantity of rulers bought = 1/4 x

x = 180

= 1/4 × 180

= 45 pencils

ii) Amount spent on pencils

If 1 pencil = $0.50

45 pencils =

45 × 0.50 = $22.50

Step 4

We were asked to calculate how much more did she spend on erasers than rulers.

In step 3, the amount spent on Erasers = $75

the amount spent on ruler = $22.5

The difference in the amount spent = $75 - $22.5

= $52.5

Therefore, Isabelle spent $52.50 more on Erasers than rulers.

Answer:

third option

Step-by-step explanation:

Given

f(x) = [tex]\frac{5x+5}{x^2+x-2}[/tex]

The denominator cannot be zero as this would make f(x) undefined.

Equating the denominator to zero and solving gives the values that x cannot be and if the numerator is non zero for these values then they are vertical asymptotes.

solve x² + x - 2 = 0 ← in standard form

(x + 2)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x - 1 = 0 ⇒ x = 1

The vertical asymptotes are x = 1 and x = - 2

Answer:

hey here is the answer

Step-by-step explanation:

Subject of the formula:

It is a variable which is expressed in terms of other variables involved in the formula.

Formulas are written so that a single variable, the subject of the formula is on the L.H.S. of the equation. Everything else goes on the right side of the equation. We evaluate the formula by substituting for the literal numbers on the right hand side.

For example:

In the formula v = u + at, v is the subject.

To find v in the example, we substitute the values u, a and t in the R.H.S. of the equation.

Changing the subject of the formula:

To change the subject of a formula, begin with the variable to become the new subject, and apply inverse operation as for solving equations in the opposite order to the order conventions.  

1. To make ‘u’ the subject of the formula in v = u + at,  

  [subtract at from both sides]

v - at = u

or, u = v - at

2. To make ‘t’ the subject of the formula, v = u + at,

 [subtract u from both sides]

v - u = at

or, (v - u )/a = t

or, t = (v - u)/a

Change the Subject of a Formula

The value of the equation is v = 96 when u = 6 and t = 9

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 equation be represented as A

Now , the value of A is

v = u + 10t   be equation (1)

when u = 6 and t = 9

Substitute the value of u and t in the equation , we get

v = 6 + 10 ( 9 )

On simplifying the equation , we get

v = 6 + 90

v = 96

Therefore , the value of v is 96

Hence , the equation is v = 96

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Answer:

pattern A is going by 3

pattern B is going by 12

Step-by-step explanation:

so you basically just have to add 3 for pattern a and add 12 for pattern B for each number

Answer: Yes, because the results are unlikely to occur by chance.

Step-by-step explanation: apparently, the weight loss program has a statistical significance, because the results are likely to also occur by chance. because it occurrs by chance, this applits to a happening which has occurred without an intent, volition, or plan. an event or encounter that occurs by chance usually implies an occurrence of some importance.

Answer:

98

Step-by-step explanation:

So we have the two functions:

[tex]g(x)=-2x-2\text{ and } r(x)=x^2-2[/tex]

And we want to find the value of r(g(4)).

To do so, first find the value of g(4):

[tex]g(x)=-2x-2\\g(4)=-2(4)-2\\[/tex]

Multiply:

[tex]g(4)=(-8)-2[/tex]

Subtract:

[tex]g(4)=-10[/tex]

Now, substitute this into r(g(4)):

[tex]r(g(4))\\=r(-10)[/tex]

And substitute this value into r(x):

[tex]r(-10)=(-10)^2-2[/tex]

Square:

[tex]r(-10)=100-2[/tex]

Subtract:

[tex]r(-10)=98[/tex]

Therefore:

[tex]r(-10)=r(g(4))=98[/tex]

Answer:

Step-by-step explanation:

Answer:

f(x) = - 3x + 4

Step-by-step explanation:

Note that y = f(x)

Rearrange making y the subject

9x + 3y = 12 ( subtract 9x from both sides )

3y = - 9x + 12 ( divide all terms by 3 )

y = - 3x + 4 , that is

f(x) = - 3x + 4

Answer:

It is reduced to the equation of the Theorem of Pythagoras.

Step-by-step explanation:

Any triangle can be modelled by this formula under the Law of Cosine:

[tex]b = \sqrt{a^{2}+c^{2}-2\cdot a\cdot c\cdot \cos B}[/tex]

Where:

[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Side lengths, dimensionless.

[tex]B[/tex] - Angle opposed to the side [tex]b[/tex], measured in sexagesimal degrees.

Now, let suppose that angle B is a right angle (90º), so that b is a hypotenuse and a and c are legs. Hence:

[tex]\cos B = 0[/tex]

And the equation is reduced to the form of the Theorem of Pythagoras, that is to say:

[tex]b = \sqrt{a^{2}+c^{2}}[/tex]