1. Simplify each of the following.
a^4 divided by a^-2 multiplied by a^7

Answer:

Step-by-step explanation:

A contrapositive is a logical equivalent of the original statement that has the opposite direction and negated conclusion. It can be proven by using the following steps:

Start with the original statement in the form of "If P, then Q".

Negate both the hypothesis (P) and the conclusion (Q) of the original statement.

Conjoin the negated hypothesis and the negated conclusion to form a new statement.

Show that the contrapositive is logically equivalent to the original statement, meaning that it has the same truth value as the original statement for all possible cases.

For example, consider the statement: "If it rains, the roads will be wet." The contrapositive of this statement is "If the roads are not wet, it did not rain." To prove the contrapositive, we can use the following steps:

Start with the original statement "If it rains, the roads will be wet."

Negate both the hypothesis and the conclusion: "It does not rain" and "The roads are not wet".

Conjoin the negated hypothesis and the negated conclusion: "It does not rain and the roads are not wet."

Show that the contrapositive is logically equivalent to the original statement by considering all possible cases:

If it rains, the roads will be wet (as stated in the original statement), and the contrapositive "It does not rain and the roads are not wet" is false.

If it does not rain, the roads will not be wet (as stated in the contrapositive), and the original statement "If it rains, the roads will be wet" is false.

This shows that the contrapositive is logically equivalent to the original statement, and we can use it to draw the same conclusion with a different proof.

The area of Andrea’s backyard, not including the swimming pool, is 340 feet²

The Area of rectangle is the product of its length to its width.

i.e., Area of rectangle = length x width.

Given:

A rectangular swimming pool has 10 feet long and 6 feet wide.

The area of a rectangle is:

A= L x W

A = 10 x 6

A = 60 ft²

Now, the area of the Andrea’s backyard (A2) is 400 ft²,

So, area of backyard not including the swimming pool​

Area = Area of backyard - area of pool

A =400 ft²-60 ft²

A =340 ft²

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62kg is equivalent to approximately 136.7 pounds and both are unit of measurement of weight.

The conversion factor from kilograms to pounds is 2.20462. To convert kilograms to pounds, you simply multiply the weight in kilograms by this conversion factor.

Therefore, to convert 62kg to pounds, we can multiply 62 by 2.20462, which gives us approximately 136.7 pounds.

It's important to note that kilograms and pounds are both units of weight, but they are used in different parts of the world. Kilograms are the standard unit of weight in most countries, while pounds are commonly used in the United States and some other countries.

When traveling or communicating with people from different countries, it's important to be able to convert between different units of measurement.

Online converters or calculators can be useful tools to quickly and accurately convert between kilograms and pounds, or other units of measurement, as needed.

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Answer: y = 4 + 2.50(x > 2)

Step-by-step explanation: y is the outcome, the fixed cost is 4, and the variable cost is 2.50 × (x > 2).

The fraction of the box she puts in each bowl is, 1/10

Fraction is a mathematical term, which represents the portion or sub-parts of the whole thing. Basically, It has two parts: numerator and denominator.

Numerator is a number which lies on the top side, it indicates the number of equal parts taken and denominator is on the bottom side, it indicates the equal parts of the whole number.

To find the fraction of the box that Evangeline puts in each bowl, we need to divide the total amount of nuts in the box by the number of bowls.

The amount of nuts she has is 3/5 of a box.

To find the amount of nuts in each bowl, we need to divide 3/5 by 6:

(3/5) ÷ 6

To divide by a fraction, we can multiply by its reciprocal:

= (3/5) ÷ (6/1)

= (3/5) x (1/6)

Multiplying across, we get:

= (3/5) x (1/6)

= 3/30

= 1/10

Therefore, Evangeline puts 1/10 of the box in each bowl.

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The complete question:

Evangeline has 3/5 of a box of nuts. She uses it to fill 6 bowls. What fraction of the box does she put in each bowl.

Answer:

Step-by-step explanation:

C=[tex]2\pi R=\pi d[/tex]

if [tex]\pi = 3.14[/tex]

c=3.14*7=21.98

The value of x or length of FD int the figure is  75.

image attached below,

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

In a right triangle, the hypotenuse is the longest side, an "opposite" side is the one across from a given angle, and an "adjacent" side is next to a given angle.

This is similarities in sides questions. To solve make equation.

JY = 42

JS = 42 + 63 = 105

JD = 50

JF = 50 + x

Using the sides,

52/105 = 50/50+x

(42)(50+x) = (50)(105)

2100 + 42x = 5250

42x = 5250 - 2100

42x = 3150

x = 3150/42

x = 75.

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Answer:

12 carrots

Step-by-step explanation:

If there is 3 times as much cabbages as there is carrots, and there is 36 cabbages then you would do 36/3 because of the 3 times as much.  The answer would be 12 carrots.

36/3=12

The steps to explain and show how to evaluate a·b for a = 5 and b = 8 include the following:

Steps                                  a·b___

Substitute 5 for a              5·b

Substitute 8 for b              5·8

Multiply                              40

In Mathematics, an expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).

Based on the information provided above, we have the following mathematical expression:

Expression = a·b

Expression = 5 × 8 (Substitute 5 for a and substitute 8 for b)

Expression = 40 (multiply).

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If the measure of one interior angle of a parallelogram is 0.25 times the measure of another angle, let's call the measure of the larger angle "x". Then, the measure of the smaller angle would be 0.25x.

In a parallelogram, opposite angles are equal in measure. So, if one angle measures x, the opposite angle would also measure x. And if one angle measures 0.25x, the opposite angle would also measure 0.25x.

Therefore, the sum of the measures of the angles in a parallelogram would be x + x + 0.25x + 0.25x = 2x + 0.5x = 2.5x.

Since the sum of the measures of the interior angles in a parallelogram must equal 360 degrees, we can set up the following equation:

2.5x = 360

Solving for x, we get:

x = 144

0.25x = 0.25*144

         = 36

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1. The area of the mat is 1 in² and the cost is $0.05

2. The area of the mat is 4 in² and the cost is $0.2

The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units like cm² and m².

The area of a square = l²

1. the area = 1×1 = 1 in²

since $0.05 is the cost per in²

therefore the cost of the mat is $0.05

2. the area = 2× 2 = 4 in²

therefore the cost = 4 × 0.05

= $0.2

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The reason [tex]26^{23[/tex] x [tex]26^{15[/tex]  can be written as  [tex]26^{38[/tex] because both have same base and power get added.

Exponents and powers can be used to represent extremely big or extremely small numbers in a more straightforward fashion.

For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as [tex]3^4[/tex], where 4 is the exponent and 3 is the base.

Given:

We have [tex]26^{23[/tex] x [tex]26^{15[/tex]

Now, using the property of exponents and power if the base of number same and in relation of multiplication then the power get added.

So,  [tex]26^{23[/tex] x [tex]26^{15[/tex]

= [tex]26^{23 + 15[/tex]

and, 23+ 15 = 38

= [tex]26^{38[/tex]

So, the exponent can written with power of 38 as the power gets added.

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The probability of the parents having a child who is homozygous dominant for this trait is 25%

In the given question, there is a particular character that has two alleles Y dominant allele and y recessive allele. Both parents are heterozygous for the trait that is encoded as Yy cross with Yy.

                                   (1/4)x100 = 25%

Thus, the correct probability would be 25%

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Answer:

58.2677

Step-by-step explanation:

148 divide the length value by 2.54

Answer:

1 inch = 2.54 cm

148 / 2.54 = 58.2677165354 inches

Step-by-step explanation:

Answer:(x,y)=(8/3+y/3,-3-y/2

Step-by-step explanation:

y=3x-8            3x+2y=2         next simplify

8/3+y/3           -x-2/3y=-2/3   multiply both sides by -1/3

x=8/3+y/3       -x-2/3y=-2/3   eliminate at least 1 variable

y=-3-y/2

ordered pair to the solution 0=0 & 2=2

Answer:

10 minutes

Step-by-step explanation:

21/6 will give us how much hot dogs in 1 minute

You then get 3.5 hot dogs per minute.

For 35 hot dogs do 35/3.5 which gives us the amount of time it wil take for Mika to eat 35 hot dogs

Answer:

x = 30

Step-by-step explanation:

ΔABC is a right-angled triangle where:

∠C = 90°

Sum of interior angles in any triangle = 180°

Therefore:

x° + 2x° + 90°= 180°

3x° + 90° = 180°

3x° = 180° - 90°

3x° = 90°

x = [tex]\frac{90}{3}[/tex]

∴Value of x = 30

Answer:

[tex]x[/tex] is equal to [tex]30\textdegree[/tex]

Step-by-step explanation:

The sum of the interior angles in a triangle is 180 degrees. This is because a triangle is a polygon with three sides and three angles, and the sum of the angles in any polygon can be found by using the formula:

sum of interior angles = (n - 2) x 180 degrees

Note: n is the number of sides.

A triangle has 3 sides. So substituting 3 in for n gives us

(3 - 2) x 180 degrees = 180 degrees

So the sum of the interior angles in a triangle is always 180 degrees.

In this example we can say that  [tex]\angle A +\angle B+ \angle C=180\textdegree[/tex]

We are given a right triangle. A right angle is equal to 90 degrees.

We can conclude that

[tex]x+2x+90=180[/tex]

Lets solve for [tex]x[/tex].

Subtract 90 from both sides.

[tex]x+2x=180-90[/tex]

[tex]x+2x=90[/tex]

Add [tex]x[/tex] and [tex]2x[/tex].

[tex]3x=90[/tex]

Divide both sides by 3.

[tex]x=\frac{90}{3}[/tex]

[tex]x=30[/tex]

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The proportional symbol in statistics is to express the percentage of a population that possesses a particular feature.

To express the percentage of a population that possesses a particular feature, the proportion symbol in statistics, abbreviated "p," is employed. The number of people in a population who share an interest feature divided by the total number of people in the population is represented as a proportion, which is a fraction or ratio.

We can select a random sample of people from the population and count the number of people who own cars, for instance, if we are interested in the percentage of residents of a city who drive. In our sample, let "x" represent the number of car owners, and "n" represent the total number of participants. The sample percentage of cars is thus to express the percentage of a population that possesses a particular feature, the proportion symbol in statistics, abbreviated "p," is employed. The number of people in a population who share an interest feature divided by the total number of people in the population is represented as a proportion, which is a fraction or ratio.

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Answer:v = y(1-n)dv/dx = (1-n)y-n dy/dxso dy

Step-by-step explanation:

Answer:

Step-by-step explanation:

to answer the questions.

Part A

To the nearest inch, how many inches is the height of the cylindrical package?

Part B

The company decides to keep the radius the same and double the height. Rounded to the nearest hundredth, how many cubic inches is the new volume of the package?

The sum of the 10th square number and the 9th square number is, 181

A number is multiplied by itself when it is squared. For instance, when you square the number 3, you get the result 9 (3 x 3). Superscript "2" is the symbol for squaring a number. For instance, 32 = 9 can be used to represent the square of 3.

Numerous crucial mathematical properties and applications of squaring a number can be found in number theory, algebra, and geometry. Squaring, for instance, can be used to solve quadratic equations or to determine the area of a square, the distance between two points, or both. A number's ability to form a perfect square can also be determined by squaring it.

The 10th square number is 10² = 100

and the 9th square number is 9² = 81.

So, the sum of the 10th square number and the 9th square number is:

= 100 + 81

= 181

Therefore, the sum of the 10th square number and the 9th square number is 181.

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Answer:

cost of television + cost of DvD =1140

cost of television =3×cost of DVD

3×cost of DVD+cost of DVD =1140

4×cost of DVD =1140

cost of DVD =285$

Step-by-step explanation:

the 3rd, 5th and 6th answers are correct.

Answer:

3, 5, 6

Step-by-step explanation:

For every change in x of 1, there is a change in y of -2.

For an equation to be linear, equal changes in x must produce equal changes in y.

Since that is true here, it is a linear equation.

Point (0, 5) gives you the y-intercept, b = 5.

From (0, 5) to (1, 3), you can calculate the slope:

slope = m = (3 - 5)/(1 - 0) = -2

The equation is y = -2x + 5

The true statements are: 3, 5, 6

The coefficient  of 6x is 6.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

We have to write the coefficient of 6x.

As, coefficient is the number which is just before the variable like in 2x 'x' is the variable and '2' is the coefficient.

So, the coefficient 6x is 6.

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Answer:

Step-by-step explanation: umm i'm a middle schooler so i tried i'm sorry.

The constant of proportionality between 3.56 and 13.35 is 3.75 using the formula C = y/x.

If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.

When two variables are directly or indirectly proportional to one another, their relationship can be expressed using the formulas y = kx or y = k/x, where k specifies the degree of correspondence between the two variables.

The proportionality constant, k, is often used.

So, the Constant of Proportionality is as follows:

C = y/x

Now, insert values as follows:
C = y/x

C = 13.35/3.56

C = 3.75

Therefore, the constant of proportionality between 3.56 and 13.35 is 3.75 using the formula C = y/x.

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Correct question:

Proportionality constant between 3.56 and 13.35?

A B C D E F G H I J K L M N O P Q R S T U V W X Y AND Z NOW I KNOW MY ABCS NEXT TIME WONT YOU SING WITH MEEEEEEEEE

To determine which expression has a greater value for Y + 6, we need to isolate Y + 6 on one side of the equation and compare the two expressions.

Starting with 4(y + 6) = 48, we can distribute the 4 to get 4y + 24 = 48. Subtracting 24 from both sides gives us 4y = 24, and then dividing both sides by 4 gives us y = 6. So, for this expression, the value of Y + 6 is 6 + 6 = 12.

Next, for 12(y + 6) = 48, we can distribute the 12 to get 12y + 72 = 48. Subtracting 72 from both sides gives us 12y = -24, and then dividing both sides by 12 gives us y = -2. So, for this expression, the value of Y + 6 is -2 + 6 = 4.

Therefore, the value of Y + 6 is greater in 4(y + 6) = 48 than in 12(y + 6) = 48.

Answer:

The value of y + 6 is greater in the first equation.

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

Divide both sides of the first equation by 4:

Divide both sides of the second equation by 12:

As we see the first expression has greater value since 12 > 4.

False: The decrease in sample size will increase the margin of error and decrease the confidence interval.

Interval is a set of values that are located between two specific points on a line. It can be used to measure the amount of time between two events, the difference between two numbers, or the distance between two points. Intervals can also be used in data analysis to identify patterns or trends. In mathematics, intervals are often represented as a pair of numbers, such as (1, 5).


The decrease in sample size will decrease the margin of error and increase the confidence interval. This is because when the sample size is decreased, the margin of error is increased and the confidence interval is decreased since the precision of the estimate is lower. This means that the range of the confidence interval is wider and the estimates are less precise.

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