Look at the shape below, find the length of the side pointed with the arrow:
T

7 in
8
s
6 in
3 in
4 in
X
Length (inches)
Check Answer
X

Look At The Shape Below, Find The Length Of The Side Pointed With The Arrow:T7 In8s6 In3 In4 InXLength

Answers

Answer 1

The length of the segment indicated in the figure is 4.21 in.

Given are two right triangles with one having base and perpendicular on 6 in and 7 in respectively and the other one is having base and perpendicular on 3 in and 4 in respectively joined their hypotenuse,

we need to find the length of the segment indicated in the figure,

So to find the same we will find the length of the hypotenuse of both and subtract the smaller one from the larger one,

So, the hypotenuse of the rt. triangle with base and perpendicular on 6 in and 7 in = √6²+7² = √36+49 = 9.21

the hypotenuse of the rt. triangle with base and perpendicular on 3 in and 4 in = √3²+4² = 5

Therefore, the length of the segment indicated in the figure = 9.21-5 = 4.21 in

Hence the length of the segment indicated in the figure is 4.21 in.

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Related Questions

What is the additive inverse of 4 /- 9?

Answers

The additive inverse of 4 /- 9 is 9 /- 4. This means that if you add 4 /- 9 and 9 /- 4 together, the result is 0.

The additive inverse of a number is the number that, when added to the original number, will result in a sum of 0. In other words, it is the opposite of the original number. For example, the additive inverse of 4 /- 9 is 9 /- 4. Adding 4 /- 9 and 9 /- 4 together will result in a sum of 0. This is because 4 /- 9 means -4 + 9 and 9 /- 4 means -9 + 4. When these two numbers are added together, the result is -4 + 4 which is 0. Additive inverses are often used in algebra and calculus to simplify equations and find solutions to problems. For example, if you have an equation with two unknowns and you know the value of one of the unknowns, you can use the additive inverse to find the value of the other unknown. This is because adding the two unknowns together will result in 0, and subtracting the known value from 0 will give you the value of the unknown.

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"subtract 7 from the sum of 34 and 3"​

Answers

Answer: 30

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

(34 + 3) -7

37 - 7

30

Two identical springs (x and y) are stretched to different lengths and held there.

Answers

The illustration shows that (A) spring x has a higher elastic potential energy.

What is elastic potential energy?

The energy that is stored when a force is used to deform an elastic object is known as elastic potential energy.

Until the force is released and the object springs back to its original shape, doing labor in the process, the energy is retained.

Kinetic energy is the power that an object has while in motion.

For instance, a stretched rubber band contains elastic potential energy because, when released, it will spring back to its resting position, converting the potential energy to kinetic energy.

So, according to the given image, spring x has more elastic potential energy.

Therefore, the illustration shows that (A) spring x has a higher elastic potential energy.

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Correct question:

Two identical springs ( x and y ) are stretched to different lengths and held there

Which of the following statements is true

A) spring x has more elastic potential energy

B) spring y has more elastic potential energy

C) spring x has more kinetic energy

D) spring y has more kinetic energy

Find the perimeter of the given triangle

Answers

The perimeter of triangle DEF is 10.8 units.

What is perimeter of triangle?

The area around any two-dimensional figure determines its perimeter. We can calculate the perimeter of any closed shape by adding the lengths of its sides.

We are given that triangle ABC is similar to triangle DEF

So,

⇒AB/DE = BC/EF = AC/DF

We are given AB=5, BC=6 and DE = 3

Therefore,

⇒AB/DE = BC/EF

⇒5/3 = 6/EF

EF = 3.6

Similarly, we are given AC =7

So,

⇒AB/DE  = AC/DF

⇒5/3  = 7/DF

DF = 4.2

Perimeter of triangle = DE + EF + DF

⇒Perimeter of triangle = 3 + 3.6 + 4.2

⇒Perimeter of triangle = 10.8 units

Hence, the perimeter of triangle DEF is 10.8 units.

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Analyze and Persevere Susan bought
3 plants that cost $2.75 each. She wants
to buy 3 clay pots that cost $4.15 each.
If Susan had $20 to start, does she have
enough money to also buy the clay pots?
Explain. Bc

Answers

Using arithmetic operations it can be seen that if Susan had $20 to start, she does not have enough money to buy 3 clay pots pricing $4.15 each after buying plants costing $2.75 each. She can buy 2 clay pots.

What are the types of arithmetic operation?

The four basic arithmetic operations in Maths, for all real numbers, are -

Addition (Finding the Sum; ‘+’)

Subtraction (Finding the difference;  ‘-’)

Multiplication (Finding the product; ‘×’ )

Division (Finding the quotient; ‘÷’)

Susan bought 3 plants that cost $2.75 each.

Using arithmetic operation of multiplication -

Total cost of the plants = number of plants bought × cost of each plant

Total cost of the plants = 3 × 2.75

Total cost of the plants = $8.25

Susan wants to buy 3 clay pots that cost $4.15 each.

Using arithmetic operation of multiplication -

Total cost of the clay pots = number of clay plots × cost of each clay pot

Total cost of the clay pots = 3 × 4.15

Total cost of the clay pots = $12.45

The total amount of money Susan has is $20.

She has already bought the plants.

So, the money left with her after buying the plants is -

Using arithmetic operation of subtraction -

Money left with Susan = Total money - Total cost of the plants

Money left with Susan = 20 - 8.25

Money left with Susan = $11.75

Therefore, Susan has enough money to buy only 2 clay pots and not 3.

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help me, please i need this by tomorrow and I'm in school

Answers

Answer:

1/3

Step-by-step explanation:

please give me brainliest

Answer:

4/16

Step-by-step explanation:

The answer is actually 4/16 because you cannot either divide or multiple by any number to get 4/16.

Alec and Ardella graphing soccer plays. They call The center of soccer field (0,0). they both Start at point (2,3). Alec runs four units to the left and two units up. Ardella Runs four units to the left and seven units down which graph below shows the position after a run?

Answers

Graph B shows the position of Alec and Ardella after a run.

What is Translation?

Translation is a type of transformation of geometrical figures. After translation, the original figure is shifted from a place to another place without affecting it's size.

Translation can be done upwards or downwards which changes the value of y. And if the translation is towards left or right, x coordinate changes.

Starting point of both Alec and Ardella = (2, 3)

Alec runs four units to the left and two units up.

(2, 3) becomes (2 - 4, 3 + 2) = (-2, 5)

Ardella runs four units to the left and seven units down.

(2, 3) becomes (2 - 4, 3 - 7) = (-2, -4)

These points are marked on graph B.

Hence the position of Alec and Ardella after the run are marked in graph B.

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How do you write 3 exponents?

Answers

To write 3 exponents, you can use the following format: base^exponent.

An exponent is a small number that is written slightly above and to the right of a base number. The base is the number being multiplied, and the exponent tells you how many times the base is being multiplied by itself.

For example, to write 3 raised to the power of 2, you would write it as 3^2, which means 3 multiplied by itself 2 times, which is equal to 9.

It's important to note that the exponent is also known as the power, so 3^2, 3^3 and 3^4 are also read as 3 to the power of 2, 3 to the power of 3, 3 to the power of 4.

In summary, to write 3 exponents, you can use the format: base^exponent, where the base is the number being multiplied and the exponent tells you how many times the base is being multiplied by itself. In this case, 3^2, 3^3, and 3^4 represent 3 multiplied by itself 2, 3, and 4 times respectively.

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. Temoso borrowed R1 000 from the bank for 3 years at 8% compound interes Without using a formula, calculate how much Temoso owes the bank at the end of three years.​

Answers

Answer:initial balance: 1000

interest rate:8%

term 20 years

how often: never

The final balance is $4,926.8.

The total compound interest is $3,926.8.

Step-by-step explanation:

Identify the center of dilation.
-8 -4
8
-4
-8
ty
8
x₁
X

Answers

Therefore , the ratio of the triangles ABC and XYZ's corresponding sides will therefore be the same.

Describe the triangle.

A triangle is regarded as both a polygon since it has 4 elements or segments. It is a basic geometric form. Triangle ABC denotes a triangle having angles A, B, or C. Therefore, in Euclidean geometry, a single planes and square are produced whenever sides are not collinear. A triangle is a polygon if it has three parts and three corners. The points where a triangle's three sides come together are at its corners. The three triangular angles add up to 180 degrees.

Here,

An dilation is a change that produces an image that is smaller but still exactly the same shape also as original. A particular degree of stretching or contraction is possible for the initial figure.

We can see that in the problem, a 5x dilatation causes ABC to constrict to produce XYZ.

As a result, the triangles ABC or XYZ will have the same ratio of their corresponding sides.

A/B/C/D = A/C/X/Y/Z = 5

The ratio of the adjacent angles of the triangle ABC and XYZ will therefore be the same.

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What to do if the bases and exponents are different?

Answers

If the bases of two exponential expressions are different, they cannot be directly compared or combined.

THE BASE AND EXPONENTS

You can convert one of the bases to match the other by using logarithm properties. For example, if you want to compare or combine 2³ and 3², you can convert the base of one of them to match the other by using the logarithm property log3(3²) = 2, so 3² can be rewritten as 2^(log3(3²)) = 2².

If you want to add or subtract exponential expressions with different bases, you can convert one of the bases to match the other by using logarithm properties, then combine the exponents. For example, if you want to add 2³ and 3², you can convert the base of one of them to match the other by using the logarithm property log2(3) = 1.58496, so 3² can be rewritten as 2^(log2(3)*2) = 2^3.18992. Now you can add the two exponents: 2³ + 2^3.18992 = 2³ (1 + 2^0.18992).

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A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 447 gram setting. Based on a 24 bag sample where the mean is 444 grams and the standard deviation is 10, is there sufficient evidence at the 0.1 level that the bags are underfilled or overfilled? Assume the population distribution is approximately normal.
Step 2 of 5: Find the value of the test statistic. Round your answer to three decimal places.

Answers

The value of the test statistic is given as 1.341

How  to solve for the test statistic

We will solve for the test statistic through the use of the following data. We have the level of significance as 0.1, the standard deviation is given as 10, sample = 24, mean = 444

test statistic is solved with the formula: (x - µ )/SE =

hence we would have: ( 447 - 444 ) / 2.2371 = 1.341

Therefore the test statistics is given as 1.341

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evaluate the expression

Answers

Decimal Form:

2.52185454

Can someone solve the very first one under the pencil line solve that equation ASAP please

Answers

Answer:19.28   or 125/7

Step-by-step explanation:

first, replace all the a's with 1's, the b's with 2's, and the c's with 4's. you end up with  (-3(1)+4(2))  ³/2(4)-1

then you would solve that until you get,   (-3+8)³/8-1

then,  (5)³/7

and once you've solved that you get 19.28 or 125/7

use pascal’s triangle to expand (z+1)^6

Answers

The expansion of  (z+1)⁶ = z⁶ + 6z⁵+ 15z⁴ + 20z³+ 15z² + 6z + 1

Pascal's Triangle:

A type of number pattern is Pascal's Triangle. The triangle-shaped arrangement of integers known as Pascal's Triangle provides the coefficients for the expansion of any binomial statement.

The arrangement of the numerals creates a triangle when they are reflected. The number 1 is first placed at the top, and then the numbers are arranged in a triangle design.

The expansion of (x + y)ⁿ is is given by

(x + y)ⁿ = a₀xⁿ + a₁xⁿ⁻¹y + a₂xⁿ⁻²y² + … + a[tex]_{n -1}[/tex] xyⁿ⁻¹ + a[tex]_{n}[/tex]yⁿ  

Here we have (z+1)⁶

Write out Pascal's triangle starting from 1 and up to 6 rows

                                1

                           1         1    

                      1         2         1      

                 1         3         3        1          

            1        4          6         4       1    

      1         5        10         10      5        1  

1          6         15         20      15      6        1    

So coefficients of expansion are 1, 6, 15, 20, 15, 6, and 1  

(z+1)⁶ =  (1)z⁶ + (6)z⁵(1)+ (15)z⁴(1)² + 20z³(1)³ + 15z²(1)⁴ + 6z¹(1)⁵ + (1)z⁰(1)⁶

=> (z+1)⁶ = z⁶ + 6z⁵+ 15z⁴ + 20z³+ 15z² + 6z¹ + 1

Therefore,

The expansion of  (z+1)⁶ = z⁶ + 6z⁵+ 15z⁴ + 20z³+ 15z² + 6z + 1

       

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-91x-13x= 276.50
Show work

Answers

Answer:

x = -2.65865384615

Step-by-step explanation:

-91x - 13x = 276.50

First, Combine Like Terms

-91x + (-13x) = -104x

-104x = 276.50

Second, divide

276.50 / -104 = x

x = -2.65865384615

Sergio has p paintings in his art collection. He and other local painting collectors agreed to donate a total of 48 paintings to the local museum. Each of the 12 collectors will donate the same number of paintings How many paintings will Sergio have in his art collection after his donation?

Answers

Step-by-step explanation:

The question is a bit confusing, so I am going to reword it to what I assume it means, which is, “Sergio initially has “p” paintings. There are 12 art collectors total, including Sergio. All the art collectors together donate a total of 48 paintings, and each art collector donates the same number of paintings. How many paintings does Sergio have left?”

p = number of Sergio’s paintings at the start.

p-X = the number of Sergio’s paintings at the end.

48 = the total number of paintings donated by all art collectors

12 = number of art collectors

48/12 = 4 = the number of paintings that each art collector donated

4 = X = the number of paintings that Sergio donated

p-4 = the number of paintings Sergio has left (answer)

(My regrets if my understanding of the question was something other than the above.)

Which of the following tables represents a linear relationship that is also proportional? x y 0 3 3 6 6 9 x y 0 4 2 6 4 8 x y 0 0 6 3 12 6 x y 0 3 5 5 10 7

Answers

Choice B, with a y-intercept of 0, is the correct response and provides a table that depicts a linear and proportionate relationship that is

x y

0 0

2 1

4 2

What do you mean By graph Intercept function?

The graph's intercept is the location where the line or curve crosses the axis. The term "x-intercept" refers to a point that crosses the x-axis. The y-intercept is the location where a point crosses the y-axis. Here is a y-intercept illustration. Suppose the line y = x+ 3 exists. This graph's y-axis intersects at this location (0,3). So, the line y = x+3's y-intercept is (0,3). By changing Y to 0 and solving for X, you can always discover the X-intercept. Likewise, you may always solve for Y while holding X equal to 0 in the equation to determine the Y-intercept.

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Shannon babysits and charges a flat fee of $10 plus $2 for very hour she babysits. She needs to make $72 this week. How many hours can Shannon babysit

Answers

Answer:

72 divided by 12 is 6 so 6 hours she needs to babysit

7 of 8

The area of a circle, in terms of π, is 100
π m².
Find the value of the diameter.
d = 0
m

Answers

Answer:

look it up broski

Step-by-step explanation:

Which sets of three numbers could represent the lengths of the sides of a right triangle? Choose the two correct answers. A. 27,35,37 - B. 20,21,29 - C. 7,24,25 - D. 8,12,14

Answers

Using the Pythagorean theorem we know that (B) 20,21,29 can represent the length of sides of the right triangle.

What is the Pythagorean theorem?

According to the Pythagorean Theorem, the squares on the hypotenuse of a right triangle, or, in conventional algebraic notation, a2 + b2, are equal to the squares on the legs.

Now, calculate using the Pythagorean theorem as follows:

A. 27,35,37

37² = 27² + 35²

1,369 ≠ 729 + 1,225

FALSE

B. 20,21,29

29² = 21² + 20²

841 = 441 + 400

841 = 841

TRUE

*(We don't need to solve further as we got the answer.)

Therefore, using the Pythagorean theorem we know that (B) 20,21,29 can represent the length of sides of the right triangle.

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[Algebra, polynomials] I'd like help with further explanation with what the image is telling me. I understand that you find the GCF of each term, but for the question I don't know why the GCF of the exponents are 3. I thought 4 would be the GCF. I don't think I learned how to find GCF properly.

As for the second image, I just have no clue on how to do it. I don't want just the answer. Anyone good with math please help :)

Answers

Answer: For the GCF one, the GCF would be [tex]3y^{3}[/tex] because you are factoring from both [tex]15y^{4}[/tex] and [tex]12y^{3}[/tex], the reason it cannot be [tex]3y^{4}[/tex] is because that exponent value exceeds the exponent value of [tex]12y^{3}[/tex].

Step-by-step explanation:

So when you find a greatest common factor (GCF) you are basically trying to simplify the expression by extracting numbers to put it into its simplest form. The GCF of 15 and 12, is 3. And the GCF of the exponents would be [tex]y^{3}[/tex] .

What are coordinates Class 9?

Answers

A series of numbers known as coordinates can be used to display a point's precise location on a coordinate plane. Coordination Plane Definition. The intersection of the x-axis and y-axis, two perpendicular lines that create a 2D plane known as a coordinate plane.

Which coordinate system is used?

There are three types of co-ordinates are:

(i) Cartesian co-ordinates

(ii) cylindrical co-ordinates

(iii) spherical co-ordinates

The Cartesian coordinate system is a prime example of a coordinate system. Two perpendicular lines are picked in the plane, and a point's coordinates are assumed to be the signed distances between the lines.

Coordinates are a pair of integers (also known as Cartesian coordinates), or occasionally a letter and a number, that identify a specific point on a grid, also known as a coordinate plane. Two axes, the x (horizontal) and y (vertical), and four quadrants make up a coordinate plane (vertical).

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Express 12^{\frac{1}{2}}12
2
1


in simplest radical form.

Answers

25/2 is simplest form of fraction.

In math, what is a fraction?

An element of a whole is a fraction. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction.

                      Whether it is in the numerator or denominator, a complex fraction contains a fraction. The numerator and denominator of a correct fraction are opposite each other. The Latin word fraction, which meaning "to break," is where we get the English word fraction.

Fraction = 12  1/2

              =   25/2

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How do you write a polynomial function with factors?

Answers

So on provided question we cans ay that Take the common binomial into account. Note that when we multiply our response by itself, the original polynomial results.

what are polynomials?

A mathematical expression made up of coefficients and uncertainty that only makes use of additions, subtractions, multiplications, and positive integer powers of variables is known as a polynomial. The formula x2 4x + 7 denotes a single indeterminate x polynomial. An expression in mathematics known as a polynomial is made up of variables (also known as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. An algebraic statement with variables and coefficients is called a polynomial. An expression can only contain the operations addition, subtraction, multiplication, and non-negative integer exponents. Polynomials are the name for these expressions.

here,

Group the first two terms first, followed by the last two terms. Remove a GCF from each each binomial. Take the common binomial into account. Note that when we multiply our response by itself, the original polynomial results.

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Please help with this question ASAP

Answers

Answer:

x=8

Step-by-step explanation:

5(2)=10

4(2)=8

What equation is solved by the graphed systems of equations?

Answers

equation of first line -> y = x - 3

equation of second line -> y = 7x + 3

to get intersection, equate both equation

-> y = y

-> 7x + 3 = x - 3

PLEASE HELP ME! :(………..

Answers

Therefore, as a result of congruency along the line DE, one triangle is simply the other triangle reflected and DE = 1/2CB is proven.

What is Congruency?

When two shapes or items are similar in shape, or when one is a perfect mirror of another and is similar in size and shape, they are said to be congruent in geometry. Two forms are congruent if their dimensions match. It is also true that mirror representations of two forms are the same if different systems are congruent. Objects with exact matching dimensions and shapes are referred to be matches. The forms hold true regardless of rotation, flipping, or reversal. Use the to create two circles.

Here,

When ΔABC and ΔDEF are used,

∠ABC = ∠ DEF (given)

AB = DE, and (same length)

∠BAC = ∠FED (same angle)

The  ΔABC and ΔDEF triangle is similar

Thus , as there are similar we can say that:

=> DE = 1/2CB

As a result, along the line DE, one triangle is simply the other triangle reflected and DE = 1/2CB is proven.

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A rectangle has a perimeter of 38.6 kilometers and a base of 16.2 kilometers. What is the height?

Answers

The height of the rectangle is 3.1 kilometers.

What is the height?

A rectangle is a 2-dimensional quadrilateral with four right angles and two diagonals which bisect each other . The perimeter of a rectangle is the distance round the rectangle. It is the sum of the four sides of the rectangle.

Perimeter of a rectangle = 2 x (height + width)

38.6 = 2 x (16.2 + height)

In order to determine the height, take the following steps:

38.6 / 2 = 16.2 + height

19.3 = 16.2 + height

height = 19.3 - 16.2 = 3.1 kilometers

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Lines AE and GH are parallel in the image below. The image will be used to prove that the sum of the measures or the
interior angles of ACGH is 180°.

Which statement would be included in a proof of why m/C+m/G+mZH= 180

Answers

Angles F and C are congruent. An angle inside a form is called an interior angle.

What is interior angle?An angle inside a form is called an interior angle. The closed shape with vertices and sides is called a polygon. Every interior angle of a regular polygon is equal to every other interior angle. For instance, the inner angles of a square are all equal to the right angle, or 90 degrees. A set's interior is comprised of all of its open subsets. The area of a region that is "within" a given border is more often referred to as the interior of a geometric structure. For instance, the interior of a circle and a sphere, respectively, is a (open) disk. Interior angles are the angles created within or inside of a shape. In this case, the interior angles ABC, BCA, and CAB.

From the figure, it can be seen that Angles F and C are opposite angles. Opposite angles are non-adjacent angles formed by two intersecting lines. Opposite angles are congruent .

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Angles F and C are congruent. An angle inside a form is called an interior angle.

What is interior angle?

An angle inside a form is called an interior angle. The closed shape with vertices and sides is called a polygon. Every interior angle of a regular polygon is equal to every other interior angle. For instance, the inner angles of a square are all equal to the right angle, or 90 degrees.

A set's interior is comprised of all of its open subsets. The area of a region that is "within" a given border is more often referred to as the interior of a geometric structure. For instance, the interior of a circle and a sphere, respectively, is a (open) disk. Interior angles are the angles created within or inside of a shape. In this case, the interior angles ABC, BCA, and CAB.

From the figure, it can be seen that Angles F and C are opposite angles. Opposite angles are non-adjacent angles formed by two intersecting lines. Opposite angles are congruent .

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4.Describe the correct use of any equipment used to protect the health and safety of themselves andtheir colleagues What happens to plants in the absence of light? Select the TWO answers that are correct. O Chemical energy is produced using only water and carbon dioxide. O Chloroplasts use the energy in glucose to photosynthesize. O The process of photosynthesis shuts down.O Plants stop generating chemical energy from light O Plants begin converting sugars into fats and proteins. How do you find the equation of a line with 2 points in Class 10? What does lady Macbeth believe about her husbands character, according to this speech Evaluate mamas words of wisdom - do you agree with her? Why or why not? Who can you think of in your own life who needs to be measured right - things need to be known and considered about their life before judging them? Suppose that 60 percent of 1,000 randomly selected U.S. adults say that they take part in some form of daily activity to keep physically fit. Based on this finding, find a 95 percent confidence interval for the proportion of all U.S. adults who would say they take part in some form of daily activity to keep physically fit. Based on this interval, is it reasonable to conclude that more than 50 percent of all U.S. adults would say they take part in some form of daily activity to keep physically fit? What is the exponential form of 8 * 8 * 8 * 8? What is the value of the missing angle? Yesterday a chef used 30 eggs to make 6 chocolate souffles and 6 lemon meringue pies. The day before, he made 4 chocolate souffles and 8 lemon meringue pies, which used 24 eggs. How many eggs does each dessert require? How do you describe transformations from the parent function? Emergency treatment of cardiac arrest victims sometimes involves injection of a calcium chloride solution directly into the heart muscle.How many grams of CaCl2 are administered in an injection of 5.0mL of a 5.0% (w/v) solution and how many milliequivalents of Ca2+? According to philosopher Immanuel Kant, what did the Enlightenment encourage people to do?be careful and cautiousthink for themselvesrely on past ideas and principlesfollow decisions made by others Picture 1: is the function described by the points linear or nonlinear? Picture 2: which table could be a partial set of values for a linear function? Picture 3: is this function linear or nonlinear? Picture 4: select linear or nonlinear to correctly classify each function. Picture 5: a function is represented by values in the table. The function represented in the table is linear or is not linear. ANALYZE What tone does the author deve 6 and 7? How does word choice help shape that tone.? Which word best completes the blank. 4x + 4 = 4x + h This equation will have __________many solutions when h = 4 because you get _______ solutions when you have the same number of x's on each side and the same constant Question 2 options: a) none b) zero c) one d) infinite Lisa worked 26 hours last month and earn seven dollars per hour she spent $17 on her earring since then how much money does she have left? When did Cosimo de Medici live? what is a definition of a circle What are the three main purposes of a labor union? in what ways did trade routes impact the gupta empire?