4. Round each fraction to help you estimate the solution for the following equation:
one-sixth plus five-sixths equals
1. 0
2. one half
3. 1
4. 2

5. Round each fraction to help you estimate the solution for the following equation:
seven twelfths plus two-twelfths equals
1. one half
2. 1
3. one and one half
4. 2



6. Round each fraction to help you estimate the solution for the following equation:
nine-tenths minus four-tenths equals
1. 0
2. one half
3. 1
4. one and one half

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: \sqrt{250 {h}^{4} {k}^{5} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{(2 \times 5 \times 5 \times 5) \times (h \times h \times h \times h )\times (k \times k \times k \times k \times k} )[/tex]

[ take out one of the pair ~ ]

[tex]\qquad \sf  \dashrightarrow \: 5 \times h \times h \times k \times k \sqrt{2 \times 5 \times k} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 5 {h}^{2} {k}^{2} \sqrt{10k} [/tex]

That's our simplified answer ~

Answer:

<--> V 250h4k5

√(2 × 5 × 5 × 5) × (h×h×h×

[ take out one of the pair ~]

5 xhxhxkx k√2 × 5 × k

--> 5h2k2✓10k

The difference of the fractions 8/2 and 3/5 is given as follows:

17/5.

The difference operation for this problem is defined as follows:

8/2 - 3/5.

8 is divisible by 2, with a quotient of 4, hence the subtraction can be simplified as follows:

4 - 3/5.

With a common denominator of 5, we have that 4 x 5 = 20, hence:

20/5 - 3/5.

As the fractions now have a common denominator, we can subtract the numerators while keeping the denominator constant, thus the subtraction is given as follows:

(20 - 3)/5 = 17/5.

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Answer:

Option C

Step-by-step explanation:

2*-1 = -2

2*0 = 0

Exponents, terms in parenthesis, multiplication, division, addition, and finally subtraction. You can use PEMDAS as a helpful acronym to help you remember this.

[tex]$\frac{4 x^2+12 x-16}{\frac{2 x+10}{\frac{6 x+24}{x^2+9 x+20}}}$[/tex]

Here we have two fractions top and bottom

[tex]$\frac{4 x^2+12 x-16}{2 x+10}$ divide by $\frac{6 x+24}{x^2+9 x+20}$[/tex]

We have division in between . we reverse the second fraction and multiply it with first fraction.

[tex]$\frac{4 x^2+12 x-16}{2 x+10} * \frac{x^2+9 x+20}{6 x+24}$[/tex]

Now we factor both numerator and denominator

[tex]$\begin{aligned} & 4 x^{\wedge} 2+12 x-16=4(x+4)(x-1) \\ & 2 x+10=2(x+5) \\ & x^{\wedge} 2+9 x+20=(x+5)(x+4) \\ & 6 x+24=6(x+4)\end{aligned}$[/tex]

Replace the factors,

[tex]$\frac{4(x+4)(x-1)}{2(x+5)} * \frac{(x+5)(x+4)}{6(x+4)}$[/tex]

We cancel out same factors at the top and bottom

So it becomes ,[tex]$\frac{(x-1)(x+4)}{3}$[/tex]

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Answer:

12

Step-by-step explanation:

If 113 divided by a number leaves a remainder of 5, then we need to find the prime factorization of 108.

If 135 divided by a number leaves a remainder of 3, then we need to find the prime factorization of 132.

If 160 divided by a number leaves a remainder of 4, then we need to find the prime factorization of 156.

108 = 2² × 3³

132 = 2² × 3 × 11

156 = 2² × 3 × 13

The GCF of 108, 132, and 156 is common factors with lower exponent.

GCF = 2² × 3 = 12

Answer: 12

The school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets.The price of a senior citizen ticket is $17.33 and the price of a child ticket is $5.01.

What is Word Problem?

A word problem is a mathematical problem that is presented in the form of a story or scenario, often using words and symbols to describe a real-world situation. Word problems require the solver to read and understand the problem, identify the relevant information, translate the information into mathematical expressions or equations, and then solve for the unknown quantity.

Word problems can involve a wide range of mathematical concepts, including arithmetic, algebra, geometry, statistics, and calculus, and are often used to test students' problem-solving abilities and mathematical reasoning skills.

Let's call the price of a senior citizen ticket "s" and the price of a child ticket "c".

From the information given, we know:

3s + c = 38 (equation 1)

3s = 52 (equation 2)

Using equation 2, we can solve for s:

3s = 52

s = 17.33 (rounded to two decimal places)

Now we can substitute this value of s into equation 1 and solve for c:

3s + c = 38

3(17.33) + c = 38

c = 38 - 3(17.33)

c = 5.01 (rounded to two decimal places)

So the price of a senior citizen ticket is $17.33 and the price of a child ticket is $5.01.

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Answer:

73°

Step-by-step explanation:

Vertical angles are congruent.  They have the same measurement.

i don't know sorry i have no idea sorry i don't know sorry sir

PLEASE GIVE BRAINLIEST!

thank you and have a good day :)

Answer:

b^5

Step-by-step explanation:

When you are multiplying exponents with the same letter base, you simply just add the exponents.

for example, x^2 * x^3 = x^5

another example, y^6 * y^8 = y^14

An expression equivalent to b^3 * b^2 would be b^5

I hope this helps!

There are 5,760 ways to arrange the books on the bookshelf.

A permutation is an ordered arrangement of objects, and it can be calculated as follows:

ⁿPₓ = n! / (n - x)!

where n is the total number of objects and r is the number of objects that we are arranging.

To determine the total number of ways in which we can arrange the books on a bookshelf, we need to first calculate the total number of possible arrangements. We can do this by using the fundamental principle of counting, which tells us that the total number of possible arrangements is equal to the product of the number of ways in which each book can be arranged.

Therefore, the total number of possible arrangements can be calculated as follows:

Total number of possible arrangements = Number of ways to arrange math books × Number of ways to arrange history books × Number of ways to arrange science books

In our case, we have 4 math books, 5 history books, and 2 science books, so we can calculate the number of permutations for each type of book as follows:

Number of ways to arrange math books = ⁴P₄ = 4! / (4-4)! = 4! / 0! = 24

Number of ways to arrange history books = ⁵P₅ = 5! / (5-5)! = 5! / 0! = 120

Number of ways to arrange science books = ²P₂ = 2! / (2-2)! = 2! / 0! = 2

Now, we can substitute these values in the formula for the total number of possible arrangements:

Total number of possible arrangements = 24 × 120 × 2 = 5,760

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Step-by-step explanation:

First things first, we are rotating about a point so the first we do is the move the clockwise rotation to the origin.

Since a rotation is a rigid transformation, we must move all the other points as well.

So move every point using the rotation vector

R(-6,-8), move every point to

D(1-6,4-8)=D'(-5,-4)

E(5-6,5-8)=E'(-3,-5)

F(4-6,1-8)=F'(-2,-7)

G(0-6,0-8)=G'(-6,-8)

So know since the center of rotation is middle at (0,0) , we can apply the rotation rules

For a 270 clockwise rotation, we apply this rule

(-y,x)

So for the points we know get

D''(5,-4)

E''(3,-5)

F''(2,-7)

G"(6,-8)

Know since we done our rotation, we undo what we did in step 1, we add 6 to the x coordinates and 8nto the y coordinate

D"'(11,8)

E"'(9, 3)

F"(8,1)

G"'(12,0)

So those are our new coordinates.

Step-by-step explanation:

This is a family of curves represented by the equation:

y = a (x + 4) (x − 2)

Different values of the a coefficient result in different quadratic functions.

The vertex of the parabolas is halfway between the zeros, at x = -1.

y = a (-1 + 4) (-1 − 2)

y = -9a

So to find the value of a, divide the y-coordinate of the vertex by -9. For example, curve A has a vertex at (-1, -3), so the value of the a coefficient is -3 / -9 = ⅓.

A. y = ⅓ (x + 4) (x − 2)

B. y = (x + 4) (x − 2)

C. y = 2 (x + 4) (x − 2)

D. y = -⅓ (x + 4) (x − 2)

E. y = -2 (x + 4) (x − 2)

The second year's interest rate is 1.80%.

Compound interest is defined as Since compound interest accrues and is added to the accrued interest from earlier periods, borrowers are expected to pay interest on interest in addition to principal.

We are aware that the compound interest formula is,

A = P(1 + r/100)ⁿ.

Where A is the amount, P is the principle, r is the rate, and n is the number of years.

Given, Katy places $2000 over a three-year period in a savings account.

For the first year, the account offers compound interest at a 2.5% annual rate.

∴ A = 2000(1 + 2.5/100)¹.

A = 2000(1.025). (1.025).

A = 2050.

It now earns x% for the second year.

∴ 2050(1+x/100)² = 2124.46

(1+x/100)² =2124.46/2050

1+x/100 =√(2124.46/2050)

x/100 = √(2124.46/2050) -1

x = (√(2124.46/2050) -1)*100

x = 1.80%.

the interest is 1.80 percent

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Answer:

D. 2x^3−6x^2−x

Step-by-step explanation:

Factor the numerator and denominator and cancel the common factors.

Hope this helps.

A function rule, if a carnival charges $6 to enter and $. 75 per ticket is f(x) = $6 + .75x

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input

According to the question,

carnival charges is $6

cost per ticket is $0.75

Let the number of person/tickets be x

and f(x) be the total cost

therefore the function is f(x) = $6 + 0.75x

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A hypothesis that there is some sort of relationship between the variables is where scientists start their inquiry. The alternative, or null hypothesis, asserts that there is no such relationship. Although the null hypothesis may not appear fascinating, it is a crucial component of research.

The claim can be supported by either the null hypothesis or the alternative hypothesis. The null hypothesis states that the population proportion is the same as the value specified in the claim. If the null hypothesis is the assertion, then the alternative hypothesis statement is the antithesis of the null hypothesis. A hypothesis is a well-informed, logically-supported guess about the answer to a scientific question. Although it is the experiment's anticipated outcome, it does not constitute experimental proof. The information obtained may or may not be supported, depending on the information received. Simple hypotheses simply state the relationship between two independent and dependent variables. Examples: If you stay up late, you will feel fatigued the next day.

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The original polynomial, [tex]x^2 + 7x + 12[/tex], it can be seen that the two are the same, thus confirming that the polynomial was correctly factored.

To check the result after factoring a polynomial, one can use the FOIL method to ensure that the factored polynomial is equivalent to the original polynomial. The FOIL method stands for First, Outer, Inner, Last, and is used to multiply two binomials. To check the result, one would use the FOIL method to multiply the factored polynomial, and compare the result to the original polynomial. For example, let’s consider the polynomial[tex]x^2+7x+12[/tex]. After factoring, this can be written as (x+4)(x+3). To check the result, one would multiply the two binomials together, (x+4)[tex](x+3) = x^2 + 3x + 4x + 12[/tex]. Comparing this to the original polynomial, [tex]x^2 + 7x + 12[/tex], it can be seen that the two are the same, thus confirming that the polynomial was correctly factored.

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a) Number of kgs independent variable, the amount charged by the company is the dependent variable.

b) The equation is y= 400+ 0.04x.

c) The equation is used to calculate a table of values with four sets of values to show the moving costs for 0 – 25,000 kg.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

It is given that a moving company charges $400 plus 0.04 per kg to move a family from Toronto to Windsor.

a) The number of kgs is the independent variable and the amount charged by the company is the dependent variable because it depends on the number of kgs the family is willing to move.

b) The equation that represents the given data is y= 400+ 0.04x

where y is the total amount charged by the company, and x is the number of kgs.

c) For 4 different values of x between 0 - 25,000 we will find values of y.

x                      y= 400+ 0.04x

6250               650

12500             900

18750              1150

25000             1400

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This means that  for part of 19.16 is 0.24% of the total number 7990.Percentage is a way of expressing a number as a fraction of 100. It is commonly used to describe a portion or share of a total quantity.

To find the percentage of a number, we need to multiply the number by the percentage as a decimal and then express the result as a percentage.

In the case of 7990 and 19.16, 19.16 is the part of the whole number 7990. To find the percentage, we need to divide the part by the whole and then multiply by 100.

So, the percentage of 19.16 of 7990 is:

19.16 ÷ 7990 × 100 = 0.24%

This means that 19.16 is 0.24% of the total number 7990.

Percentages are often used in various applications, including calculating interest on loans, determining grades in school, and comparing data between different sets of information. In addition, they are used in various business applications, such as computing taxes, discounts, and determining profits and losses. In conclusion, understanding the concept of percentage is important in various areas of our daily lives and in various professions, as it helps us to make informed decisions and communicate information effectively.

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Probability that exactly one doesn't grow is 0.004

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x. The probability of an event can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

If a seed is planted, it has a 60% chance of growing into a healthy plant.

the probability of growing is 60/100 = 0.6

the probability of not growing is 1-0.6 = 0.4

eleven seeds are planted,

and 10 should grow and exactly one doesn't grow

so probability = 0.6*0.6*0.6*0.6*0.6*0.6*0.6*0.6*0.6*0.4=0.004031

= 0.004

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Answer:

linear

Step-by-step explanation:

when you graph x/2 it is a straight line, therefore it is linear

To evaluate the multiplication expression 7*38, we simply multiply 7 and 38 together and the result after multiplication is 266.

Multiplication is a basic arithmetic operation that involves combining two or more numbers to obtain a product. In this case, we are given the expression 738, which involves multiplying the number 7 by the number 38 to obtain a product. To do this, we can use the multiplication operation, which involves adding 7 to itself 38 times.

This can be a time-consuming process when dealing with large numbers, but it is a fundamental skill in mathematics and is used in a wide range of applications, including engineering, science, finance, and computing. In this case, we have evaluated the expression 738 to be equal to 266, which is the product of 7 and 38.

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By inspection, the following products which are multiples of 30 are:

This is referred to as a number that may be divided by another a certain number of times without a remainder.

The multiple of 30 in the options are those who have 2, 3 and 5 as the common values and is therefore the reason why options A, C and D  were chosen as the correct choice.

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The explanation of each statement in each given situation is given below:

a. B(0) = 0

depth in inches 0 minutes after filling began is 0; that is at time =0; depth =0

b. B(1) < B(7)

B(1) represents the function one minus after filling began

c. B(9) = 11

depicts that the depth in inches of water 5 minutes after filling is 11

d. B(10) = B(22)

depicts that the depth in inches of water 10 minutes after filling began is 22.

e. B(20) > B(40)

represents the function 20 minutes after filling began

These are the required answers

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The question translated in English is: "#7. Tyler filled his tub, took a shower, and then drained the tub. Function B gives the depth of the water,

inches, t minutes after Tyler started filling the tub.

Explain the meaning of each statement in this situation.

to. B(0) = 0

b. B(1) C.B(9) = 11

d. B(10) = B(22)

and. B(20) > B(40)"

Answer:

yes

Step-by-step explanation:

The formula to calculate the new value after an increase is to multiply the original value by the percentage of the increase.

The formula to calculate the new value after an increase is to multiply the original value by the percent of the increase. For example, if the original value is $100 and the increase is 10%, the new value would be $100 x 1.10 = $110. This formula can be applied to any original value and any percentage increase. It is useful for calculating the new value after applying a percentage increase, such as when calculating a pay raise or the cost of goods after a price increase. The formula can also be applied to calculate the new value after a percentage decrease, by multiplying the original value by 1 minus the percentage of the decrease.

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The complete question is

the formula for calculating the value after an increase by multiplying the original value by the percent for a new value is: value after increase  by multiplying the original value by the percent for a new value?

The probability at least one of the two television does not work will be 7/9.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Suppose you just received a shipment of ten television. Five of the televisions are defective. If two televisions are randomly selected. Then the probability is given as,

P = (5/10) x (5 / 9) + (5/10) x (5/9) + (5/10) x (4/9)

P = 25/90 + 25/90 + 20/90

P = 70 / 90

P = 7/9

The probability at least one of the two television does not work will be 7/9.

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