If we use a × b, then it means that a is b times more than a and if we use a/b it means that we are making parts of a by the factors of b.
What is meant by multiplication and division?A mathematical expression that specifies the objects to be multiplied, known as a factor, produces a product. The other operations are multiplication, addition, and subtraction. When two natural numbers are divided with a remainder, or in the Euclidean method, the result is an integer quotient, which is the number of times the second number is entirely contained in the first number, and a remainder, which is the portion of the first number that remains after computing the quotient.
Rule of Division and Multiplication of Integers
Multiplication:
Rule 1: A positive integer and a negative integer cannot be added together.
Rule 2: A positive number is the result of two positive integers.
Rule 3: It states that the sum of two negative integers is positive.
Examples:
Rule 1: 1. (+4) x (-2) = -8 2. (-2) x (+5) = -10
Rule 2: 1. (+6) x (+8) = +48 2. (+6) x (+2) = +12
Rule 3: 1. (-6) x (-8) Equals +48 2. (-2) x (-4) = +8
Division:
Rule 1: A positive integer and a negative integer cannot be multiplied together.
Rule 2: A positive number is the quotient of two positive integers.
Rule 3: A positive number is the quotient of two negative integers.
Examples:
Rule 1: 1. (-8) / (+4) = -2 2. (-12) / (+6) = -2
Rule 2: 1. (+6) / (-3) = -2 2. (+24) / (-6) = -4
Rule 3. 1. (+9) / (+3) = +3 2. (+16) / (+4) = +4
Rule 4: 1. (-6) / (-2) = +3 2. (-42) / (-7) = +6
This is the summary of multiplication and division rules.
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If the two triangles below are similar and the area of the larger triangle is 36, what is the area of the smaller triangle?
The area of the smaller triangle is 18 squared units which is determined by the property of similar triangles.
The area of the larger triangle is 36.
The two triangles are similar which is given in the question
We know that the corresponding sides of similar triangles are being in the same ratio.
As per the property of similar triangles,
A₁ : S₁ = A₂ : S₂
Here A₁ is area of the larger triangle, A₂ is area of the smaller triangle
S₁ is side of the larger triangle, and S₂ is side of the smaller triangle,
⇒ A₁ / S₁ = A₂ / S₂
⇒ 36 / 12 = A₂ / 6
⇒ 3 = A₂ / 6
⇒ A₂ = 18
Therefore, the area of the smaller triangle is 18 squared units.
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What is the explicit formula for this sequence?
6, 2, -2, -6, ...
A. an = -6+ (n − 1)(-4)
B. a = -4+ (n-1)6
C. an= 6+ (n-1)(-4)
D. an = 6+ (n-1)4
SUBV
Explicit formula for this sequence is (C) an= 6+ (n-1)(-4)
Given sequence,
6, 2, -2, -6.....
First term = a = 6
Difference = d = 2 - 6
= -4
No. of terms = n
Therefore, an = a + (n-1)d
= 6 + (n-1)(-4)
Hence, an= 6+ (n-1)(-4).
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the product of two consecutive nonnegative integers is 240 find the integers and separate them with a comma
The product of two consecutive non-negative integers is 240 and the integers are 15,16.
What are consecutive integers?
The numbers that come after one another are known as consecutive integers. They proceed sequentially or alphabetically. For instance, a group of natural numbers is a sequence of integers. In mathematics, the term "consecutive" refers to an uninterrupted succession or a continuous flow of numbers, so that successive integers follow a sequence in which each succeeding number is one more than the one before it. The mean and median in an array of successive integers (or in numbers) are both identical. In the event that x is an integer, then x + 1 and x + 2 are also integers.Let the numbers be x, x+1
Product is x(x+1)=240
x² + x = 240
x² + x − 240 = 0
x² + 16x − 15x − 240 = 0
x(x+16) − 15(x+16) = 0
(x+16)(x−15)=0
x = 15,−16
So, the product of two consecutive non-negative integers is 240,then numbers are 15, 16.
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Which is the better buy?
37-ounce bottle of barbeque sauce for
$35.15
2-pound bottle of barbeque sauce for
$23.36
Answer:
2 pound bottle
Step-by-step explanation:
convert ounce to pounds:
37/16=2.3125
find price of 1 pound of bbq sauce:
35.15/2.3125=$15.2
23.36/2=$11.68
$11.68 is more cheaper so 2 pound bottle is better to buy
what is the goal of a hypothesis test? select one: a. to give a strong statement about a statistic b. to determine if the data can refute an assumption about a parameter or population c. to create a larger sample d. to provide a range of values that are reasonable for the parameter of interest
The goal of a hypothesis test is to determine if the data can refuse an assumption a parameter or a population.
Statistical hypothesis test:
A statistical hypothesis test is a technique for determining whether the available data are sufficient to support a specific hypothesis. We can make probabilistic claims about population parameters through hypothesis testing.
The purpose of a hypothesis test is to ascertain whether the data can refute a parameter or population assumption.
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Which is the better buy?
5,149 pounds of sawdust for $1,132.78
4 tons of sawdust for $2,800.00
Answer:5,149 pounds of sawdust for $1,132.78
Step-by-step explanation:
Step 1 is to convert 4 tons into pounds is:
4 tons * 2000 pounds per ton = 8000 pounds
Step 2 is to find the cost of saw dust per pound in each scenario:
Scenario 1: $1132.78 / 5149 = .22 dollars per pound
Scenario 2: $2800 / 8000 = .35 dollars per pound
Step 3 is just comparing which one is the cheapest per pound based on step 2:
.22 per pound is less than .35 per pound. So the answer is scenario 1 (5149 pounds for 1132.78) is the better buy
92.3- (3.2 ÷ 0.4) × 2³
Answer:
28.3
Step-by-step explanation:
To solve this problem, we must follow PEMDAS, which must be used in solving all mathematical equations and expressions.
PEMDAS is the order you solve the equation/expression in. It is an acronym for:
P: Parenthesis
E: Exponents
M: Multiplication
D: Division
A: Addition
S: Subtraction
Keep in mind that multiplication and division are too be done left and right. You do not do multiplication first and division last, read left to right. Same goes with addition and subtraction.
This is the less confusing notation of PEMDAS.
P: Parenthesis
E: Exponents
M: Multiplication D: Division
A: Addition S: Subtraction
Now, lets solve the problem.
92.3 - (3.2 ÷ 0.4) × 2³
What do we do first? Well since parenthesis is first according to PEMDAS, we must solve the division in side of the parenthesis first.
3.2/0.4 = 8
Now we have:
92.3 - (8) × 2³
Remove the parenthesis as there is only one term inside and therefore not needed.
92.3 - 8 × 2³
What do we do next?
We have:
Subtraction: 92.3 - 8
Multiplication: -8 × 2³
Exponent: 2³
Because PEMDAS states exponents is to be solved in front of multiplication/division and addition/subtraction, we must do that.
What is an exponent?
2³
2 is the base, 3 is the exponent.
2³
Means multiplying 2 by itself 3 times:
2 × 2 × 2
8
Now we have:
92.3 - 8 × 8
Because PEMDAS states solving multiplication/division is prioritized over addition/ subtraction, we must solve 8 × 8
8 × 8 = 64
Now we have: 92.3 - 64
Solve.
28.3
Jake completes two trails and hikes less than 10 km. Which two trails did Jake hike? Explain.
Step-by-step explanation:
Great Meadow Loop and Jordan Pond Path
Mo puts $290000 into savings bonds that pay a simple interest rate of 5.2%. How much money will the bonds be worth at the end of 6 years
Answer:
in six years, Mo will have roughly $393090.4 in savings bonds.
Step-by-step explanation:
(This might not be the most efficient way to do it.)
year one - 290000 x 1.052 = 305080
year two - 305080 x 1.052 = 320944.16
year three - 320944.16 x 1.052 = 337633.256
year four - 337633.256 x 1.052 = 355190.185
year five - 355190.185 x 1.052 = 373660.075
year six - 373660.075 x 1.052 = 393090.399
in six years, Mo will have roughly $393090.4 in savings bonds.
Given ∠11≅∠13. Which lines, if any, must be parallel based on the given information? Justify your conclusion.
Based on the information given: A. c║d; converse of alternate exterior angles theorem.
What is the Converse of Alternate Exterior Angles Theorem?Exterior alternate angles are congruent based on the alternate exterior angles theorem. Conversely, it can also be stated that if two angles, which are exterior alternate angles, are congruent to each other, therefore the lines they lie on that is crossed by a transversal are proven to be parallel to each other based on the converse of alternate exterior angles theorem.
Given that angles 11 and 13 are congruent angles, the diagram also shows that they are alternate exterior angles. They lie on each lines, c and d, that are crossed by transversal a.
Therefore, based on the converse of alternate exterior angles theorem, lines c and d are parallel.
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HELP NEEDED ASAP THANKS
Answer:
{A) X=5} {B) X=2.75}
Step-by-step explanation:
A) (2)4x-1/2=x+7(2) - multiply each side by denominator
4x-1=x+14
-x + 1 -x +1
3x=15
÷3. ÷3
x=5
B) (2)3x+2=2x+13/2(2)
6x+2=2x+13
-2x -2. -2x -2
4x=11
÷4. ÷4
x=2.75
Answer:
x = 7.5 , x = 1
Step-by-step explanation:
(a)
[tex]\frac{4x-1}{2}[/tex] = x + 7 ( multiply both sides by 2 to clear the fraction )
4x - 1 = 2(x + 7)
4x - 1 = 2x + 14 ( subtract 2x from both sides )
2x - 1 = 14 ( add 1 to both sides )
2x = 15 ( divide both sides by 2 )
x = 7.5
(b)
3x + 2 = [tex]\frac{2x+13}{3}[/tex] ( multiply both sides by 3 to clear the fraction )
3(3x + 2) = 2x + 13
9x + 6 = 2x + 13 ( subtract 2x from both sides )
7x + 6 = 13 ( subtract 6 from both sides )
7x = 7 ( divide both sides by 7 )
x = 1
imagine that you are a researcher conducting a survey for a client. you are trying to decide what sample size you need. what would the main advantage be of a larger sample size?
Large sample size gives more accurate information about population.
The main advantages of Large sample size is :
1. Large sample size provide stronger and more reliable information about parent population.
2. It will help researcher to capture outliers and sweeping out in sample.
3. Measuring large sample size allows one to divide the sample into segments .
4. Large sample size helps in obtaining a quality and precise mean .
Some disadvantages of Large sample size is :
1. Large sample size will be time consuming and more expensive to work with
2. It require higher financial involvement to complete the survey.
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Which of the following is a correct interpretation of the expression -7 - (-11)−7−(−11)minus, 7, minus, left parenthesis, minus, 11, right parenthesis?
The correct interpretation of the expression "minus, 7, minus, left parenthesis, minus, 11, right parenthesis" is 8.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
We have to write the correct interpretation of the expression "minus, 7, minus, left parenthesis, minus, 11, right parenthesis".
We have to subtract when two different signs appear next to each other (-+ or +-)
Similalry We have to add when two of the same signs appear next to each other (++ or --)
So:
-7 - (-11)−7−(−11)
-7 + 11 - 7 + 11
-14 + 22
8
Therefore, the correct interpretation of the expression "minus, 7, minus, left parenthesis, minus, 11, right parenthesis" is 8.
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a tree t with 50 end-vertices has an equal number of vertices of degree 2, 3, 4 and 5 and no vertices of degree greater than 5. what is the order of t?
The order of T is 82.
Let n and e be the order and number of edges of T respectively.
Also, let a, b, c and d be the number of vertices of degree 2, 3, 4 and 5 respectively.
Then, 50+a+b+c+d = n
And by the Handshake Lemma, the sum of the degrees of all the vertices of T is twice the number of edges, so we have
50+2a+3b+4c+5d = 2e
Since a=b=c=d then we have the following two equations,
50+4a = n
50+14a = 2e
But, T is a tree so e=n=1, then the two equations become,
50+4a = n ...............(1)
50+14a = 2(n-1) .............(2)
Solving for a in (1) we get,
a = [tex]\frac{n-50}{4}[/tex]
Plugging a into (2) we get,
50+14([tex]\frac{n-50}{4}[/tex]) = 2(n-1)
50+3.5n-175 = 2n-2
3.5n-2n = 175-50-2
1.5n = 123
n = [tex]\frac{123}{1.5}[/tex] = 82
Therefore, the order of T is 82.
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A chunk meat weighs 8kg.After reducing it a bit a bit,it weighs 6 1/2kg. Find the percentage decrease
Answer: 18.75%
Step-by-step explanation:
To find the percentage decrease, the formula is shown below.
Plug in the values and calculate:
[tex]\frac{8-6.5}{8} *100=18.75%[/tex]
So, the chunk of meat lost 18.75% of its initial weight.
What is the sale price of the oil change after the discount
The sale price of the oil change after the discount can be found to be $25.50.
How to find the sale price?When given a discount, the selling price of an item is found by the formula:
= Price of item before discount - Discount
The discount on the oil change, given the price of the oil change and the coupon is:
= Price of oil change x Coupon rate
= 30 x 15%
= $4.50
The sale price after the oil change is:
= Price of oil change before discount - discount
= 30 - 4.50
= $25. 50
The first part of the question is:
An oil change at city auto is regularly $30. Mr Allen has a coupon for 15% off.
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an overhead wire stretches from the service drop that is 20 ft from the ground, on a building to an insulator on a pole 35 ft from the ground. how long is the wire if the pole and building are 48 ft apart? (assume ground is level.) round answer to tenths.
Answer:
50.6 ft
Step-by-step explanation:
We can use the pythagoreas theorem to solve this problem.
If the service drop is 20 ft from the ground and the insulator is 35 ft, that means that the insulator is 15 ft higher than the service drop.
a² + b² = c²
15² + 48² = c²
255 + 2304 = c²
2559 = c²
√2559 = c
50.6 ≈ c
a pet boarder keeps a dog-to-cat ratio of 5:2.if the boarder has room for 98 animals,then how many of them can be dogs
Answer:
70 dogs
Step-by-step explanation:
total animal is 98
total ratio is 5+2 = 7
calculate how much each ratio has
98/7 = 14
5 ratio are dogs, so multiply 14 with 5 to get 70 dogs
you can also do:
5/7 × 98 = 70
A line make an alpha beta and delta with four diagonal of a cube. A) Find direction ratio of any two diagonal in vector form. B) Find angle between two diagonal of a cube. C) Prove that: co quare alpha co quare beta co quare gamma co quare delta = 4/3
B) direction ratio of any two diagonals in vector form is 60°.
C) cos²α+cos²β+cos²γ+cos²δ= [tex]\frac{4}{3}[/tex]
In Euclidean geometry, a perspective is a parent created by rays, often referred to as the angle's perimeters, sharing a single endpoint known as the perspective's vertex. Angles created by rays are located in the plane that contains the rays. Angles can also be created by intersecting two planes. They are referred to as dihedral angles. Curves that cross may also define an angle, which is the angle formed by rays that are perpendicular to the individual curves at the point of junction.
The degree of an angle or rotation is also expressed in terms of perspective. This metric represents the relationship between a circular arc's length and radius.
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Two sides of a triangle are 30in and 30in, what are the possible lengths of the third side
Answer:
[tex]0 < x < 60[/tex]
Step-by-step explanation:
By the Triangle Inequality Theorem:
30 + 30 > x, so 60 > x ----> x < 60
30 + x > 30, so x > 0
x + 30 > 30, so x > 0
Putting these inequalities together, we have 0 < x < 60. So the length of the third side can be greater than 0 inches but less than 60 inches.
how many ordered pairs ( m , n ) of positive integers, such that m > n , have the property that their squares differ by 96 ?
Answer:
4 pairs
Step-by-step explanation:
You want the number of pairs of integers (m, n) such that m > n and m² -n² = 96.
Difference of squaresThe difference of squares is factored as ...
m² -n² = (m -n)(m +n)
In order for the difference to be 96, these factors must be factors of 96.
Factors of 96The prime factorization of 96 is ...
96 = 2^5 · 3
The number of divisors of 96 is the product of the exponents of these factors, each increased by 1:
(5+1)(1+1) = 12
That is, there are 12/2 = 6 factor pairs ab such that a<b. They are ...
96 = 1·96 = 2·48 = 3·32 = 4·24 = 6·16 = 8·12
SolutionThe values of m and n relate to the values of 'a' and 'b' by ...
m = (a+b)/2
n = (b-a)/2
In order for m and n to be integers, the values of 'a' and 'b' must both have the same parity. That is, they must both be even, or both be odd. This eliminates the factor pairs 1·96 and 3·32, leaving 4 (a, b) pairs, hence 4 (m, n) pairs. Possible ordered pairs are ...
(m, n) ∈ {(25, 23), (14, 10), (11, 5), (10, 2)} . . . . . 4 pairs
Which choice is the value of two over five raised to the second?
four over twenty-five
two over twenty-five
two over ten
four over seven
powers of negative integers are always negative. (T OR F)
Answer:
False
Step-by-step explanation:
[tex]10^{-2}[/tex] id not a negative number it means
[tex]\frac{1}{10^{2} }[/tex] or [tex]\frac{1}{100}[/tex] Which is a number with a lesser value than 1, but it is not a negative number.
it is desired to estimate the mean number of chocolate chips in a chocolate chip cookie. how many cookies need to be sampled to estimate the true mean number of chocolate chips per cookie to within 2 chocolate chips with 99% confidence. assume that the population standard deviation is 3.7 chocolate chips.
According to the given standard deviation, the true mean number of chocolate chips per cookie to within 2 chocolate chips with 99% confidence is 10.6
Standard deviation:
Basically, the standard deviation refers a quantity expressing by how much the members of a group differ from the mean value for the group.
Given,
It is desired to estimate the mean number of chocolate chips in a chocolate chip cookie.
Here we need to find how many cookies need to be sampled to estimate the true mean number of chocolate chips per cookie to within 2 chocolate chips with 99% confidence and assume that the population standard deviation is 3.7 chocolate chips.
From the given question we have identified the following details,
Confidence interval = 99%
Standard deviation = 3.7
So, the critical value is calculated as,
=> 1 - 0.99
=> 0.01
So, the z scores is 2.576.
Now, the formula to confidence interval is given by : -
=> 10.6 ± 2.576 (0.01)/ √3.7
=> 10.6
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6. Jason states that -8.0 is not an integer because it has a decimal. Is he correct? Why or why not
Answer: He is incorrect.
Step-by-step explanation:
Since we are talking about -8.0, we can "ignore" the .0 because 0 has no value. An integer is a whole negative number, whole positive number, or zero. -8 is a whole negative number, since .0 means "nothing" here, so it is an integer.
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The force of attraction, F of a body varies directly as its mass (m) and inversely as the square of the distance (d) from the body. When m=8kg and d=5meters, F=100 Newtons. Find F when m=2 kilograms and d=15 meters.
The force of attraction is 2.78 Newton when m = 2 kilograms and d = 15 meters.
According to the question,
We have the following information:
The force of attraction, F of a body varies directly as its mass (m) and inversely as the square of the distance (d) from the body. And when m=8kg and d=5meters then F=100 Newtons.
Now, let's take the constant for this case to be k.
We have the following expression:
F = km/[tex]d^{2}[/tex]
Putting the values in this expression to find the value of k:
100 = 8k/(5*5)
Using the cross multiplication method:
2500 = 8k
k = 2500/8
k = 312.5
Now, we have the following value of F:
F = 312.5*2/15*15
F = 625/225
F = 2.78 Newton
Hence, the force of attraction is 2.78 Newton when m = 2 kilograms and d = 15 meters.
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Write the equation of the function in
slope-intercept form:
A line with a slope of 2 and passes through (-8, 3)
The equation of the function in slope-intercept form with slope of 2 is y = 2x+19.
According to the question,
We have the following information:
Slope = 2 (Note that slope of a line is denoted by m.)
Points through which function is passing = (-8,3)
So, we have x' = -8 and y' = 3.
We know that the following equation is used to find the equation of the function or line:
(y-y') = m(x-x')
y-3 = 2{x-(-8)}
y-3 = 2(x+8)
y-3 = 2x+16
y = 2x+16+3
y = 2x+19
Hence, the equation of the function in slope-intercept form with slope of 2 is y = 2x+19.
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The amounts below show the change (measured in feet) in water
level over four months. What is the average monthly change in
water level?
-2.54, -3.16, -2.82, 1.6
Answer: -1.73 ft
Step-by-step explanation:
(-2.54 - 3.16 - 2.82 + 1.6) / 4 = -1.73
Find the missing values for the exponential function represented by the table below.
The missing values for the exponential function are y = 16.875 and y = 25.3125
How to find the missing values for the exponential function?The general form of the exponential function is y = abˣ
From the table, when x = 0, y = 11.25. Substitute the values into the function:
y = abˣ
11.25 = ab⁰ (Note: b⁰ = 1)
11.25 = a(1)
11.25 = a
a = 11.25
Also, from the table, when x = -1, y = 7.5. Substitute the values into the function:
7.5 = 11.25b⁻¹
7.5 = 11.25/b (Note: b⁻¹ = 1/b)
7.5b = 11.25
b = 11.25/7.5 = 1.5
We can now write the exponential function for this case:
y = abˣ
y = 11.25(1.5)ˣ
We can find the missing values now:
when x = 1:
y = 11.25(1.5)ˣ
y = 11.25(1.5)¹
y = 16.875
when x = 2:
y = 11.25(1.5)ˣ
y = 11.25(1.5)²
y = 25.3125
Therefore, the missing values are 16.875 and 25.3125. Option c is the correct answer
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john recently bought a used car for $\$5000$ for his pizza delivery job. he gets $\$10$ for each pizza he delivers, but he has to spend $\$3$ on gas for each pizza he delivers. what is the minimum whole number of pizzas john must deliver in order to earn back the money he spent on the car he bought?
The minimum number of pizzas that john must deliver to earn back the money he spent on the car he bought is 715 pizzas .
In the question,
it is given that ,
the amount for which John bought the used car for pizza delivery = $5000
the amount John gets for 1 pizza he delivers = $10
the amount John spend on gas for 1 pizza he delivers = $3
So , the amount that John earned for 1 pizza delivered is = 10 - 3 = $7 .
the number of pizza required to sell = (price of car)/(amount earned from 1 pizza)
Substituting the values , we get
number of pizza required to sell = 5000/7 = 714.2857
rounding the answer to whole number ,
we get
= 715 pizzas
Therefore , The minimum number of pizzas that John must deliver to earn back the money he spent on the car he bought is 715 pizzas .
The given question is incomplete , the complete question is
John recently bought a used car for $5000 for his pizza delivery job. he gets $10 for each pizza he delivers, but he has to spend $3 on gas for each pizza he delivers. what is the minimum whole number of pizzas john must deliver in order to earn back the money he spent on the car he bought ?
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