The Pythagorean Theorem Part 2 Quiz

Answer: 28

Step-by-step explanation:

16% = 0.16

Percents are just decimals!

Now you can put this in your calculator, and you will get 28.

However:

It might help you later to know that x% of y = y% of x

In other words, 16% of 175 is the same thing as 175% of 16

This problem is easier, since we can break 175% into 1 and 3/4th. 3/4th of 16 is easy to calculate, (its 12), and so we can add 12 to 16 to find the answer, which is still 28 :)

No calculator needed!

Answer:

NO

Step-by-step explanation:

no she cannot. you do not need to do any math for this, none of these measurements are equal to or greater than 6 feet, and i dont think lily's gonna snap her fishing pole in half 6>4, 4=the longest thing about this box, aka the length

Answer: No, she can not store the fishing pole in the box.

No, Lily can not store the fishing pole into the box. The pole is 6 feet long, while the box is 4 feet long. Even if you tried to insert the pole into the box vertically it would not fit. Therefore, no Lily cannot fit the box.

I hope this helped & Good Luck <3 !!!

The dot product a . b is -22

The dot product, also known as scalar product or inner product, is a binary operation that takes two vectors and returns a scalar (single-valued) quantity. The dot product of two vectors is equal to the product of the magnitude (length) of the vectors and the cosine of the angle between them.

Given two vectors, A and B, the dot product is defined as:

A ∙ B = |A| * |B| * cos(θ)

where |A| and |B| are the magnitudes of vectors A and B, and θ is the angle between them.

a = <3, -2>

b = <-2, 8>

a . b = (3 * -2) + (-2 * 8)

a . b = -6 + - 16

a . b = -22

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The angle of depression from the top of the taller building and the angle of elevation from the top of the shorter building are alternate interior angles.

Alternate interior angles are the angles formed when a transversal intersects two coplanar lines. They lie on the inner side of the parallel lines but on the opposite sides of the transversal. The transversal crosses through the two lines which are Coplanar at separate points.

The angles of elevation and depression are formed by the line of sight and the horizontal line. When the line of vision is above the horizontal line, the angle is of elevation, and if the line of sight is below the horizontal, the angle is of depression.

If the angle of depression of the taller building is 15° the angle of elevation of the shorter building is 15° too.

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The question that can be answered using the expression 3 ÷ 1 is "How many 1-pound pieces of fudge are in a 3-pound fudge?". The correct option is B.

The expression "3 ÷ 1" is a mathematical expression that represents a division operation. In this case, the operation is "3 divided by 1".

To understand what this expression means, we can think of it in terms of a real-world scenario. For example, we can think of it as dividing 3 pounds of fudge into 1-pound pieces.

If we divide 3 pounds of fudge into 1-pound pieces, we can ask the question "How many 1-pound pieces of fudge are in 3 pounds of fudge?" This is the question that can be answered using the expression "3 ÷ 1".

To solve this division problem, we simply divide 3 by 1. The result is 3. This means that there are 3 one-pound pieces of fudge in 3 pounds of fudge.

So, to summarize, the expression "3 ÷ 1" means "3 divided by 1" and can be interpreted as dividing 3 pounds of fudge into 1-pound pieces. The answer to the question "How many 1-pound pieces of fudge are in 3 pounds of fudge?" is 3.

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The total number of strings that satisfy the given conditions is 24.

Let us count the number of strings where the two ones that are next to each other are in the first two positions, and the third one is in the fifth position. There are two choices for the value of the fourth digit (0 or 1), and two choices for the value of the last digit (0 or 1). Therefore, there are 2 \cdot 2 = 4 strings with this property: 110010, 110100, 111010, and 111100.

We can obtain the same number of strings by considering the case where the two ones that are next to each other are in the last two positions, and the third one is in the fifth position.

Now, let us count the number of strings where the two ones that are next to each other are in the first two positions, and the third one is in the sixth position. There are two choices for the value of the third digit (0 or 1), and two choices for the value of each of the other digits (digits 4 and 5 must be different from each other and from digit 3). Therefore, there are 2 \cdot 2 \cdot 2 = 8 strings with this property: 1100010, 1101010, 1110010, 1111010, 1000110, 1001110, 1010110, and 1011110.

Again, we can obtain the same number of strings by considering the case where the two ones that are next to each other are in the last two positions, and the third one is in the sixth position.

Thus, the total number of strings that satisfy the given conditions is 4+4+8+8=24.

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The initial amount A is 1 and the growth factor B is 1.4 in the Exponential function f(t)=14^x.

Given,

f(x) = 1.4^x

It is an exponential function.

y = a.b^x

where a is the initial quantity and b is the growth/ decay component.

Now we are able to examine the given feature with

A = 1

B = 1.4

An exponential function is a mathematical function that has the form f(x) = a^x, where a is a constant greater than zero and not equal to one, and x is a variable. This function is widely used in a variety of fields, such as finance, physics, and biology, due to its ability to model growth, decay, and change over time.

Exponential functions are essential in understanding various natural phenomena, from population growth to radioactive decay, and they play a crucial role in the advancement of scientific research.The exponential function has several unique properties, such as exponential growth, where the function grows at an increasing rate as x increases. Additionally, the function has an asymptotic relationship with the x-axis, meaning it never actually touches the x-axis but gets infinitely close to it.

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If the measure of <2 is 5 less than 4 times the measure of <1. The measure of angle <1 is 37 degrees, and the measure of angle <2 is   143 degrees. The measure of angle <3 is 55 degrees.

Let's call the measure of angle <1 "x".

From the problem, we know that:

4 times the measure of angle <1 is equal to the measure of angle <2 plus 5:

4x = measure of angle <2 + 5

So the measure of angle <2 is 4x - 5.

Next, we know that the measures of all angles in a triangle must add up to 180 degrees.

Therefore, we have:

x + (4x - 5) + measure of angle <3 = 180

Expanding and simplifying:

5x - 5 + measure of angle <3 = 180

5x + measure of angle <3 = 185

5x = 185

Finally, solving for x:

x = 37

So the measure of angle <1 is 37 degrees, and the measure of angle <2 is 4 * 37 - 5 = 143 degrees. The measure of angle <3 is 185 - 5x = 185 - 5 * 37 = 55 degrees.

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the probability of getting (a, b), i.e. the first card is a and the second card is b is 2/3 by conditional probability.

The potential of an event or outcome occurring based on the existence of a prior event or outcome is known as conditional probability. It is computed by dividing the likelihood of the earlier occurrence by the likelihood of the subsequent, or conditional, event.

This is where the independent event and dependent event notion is used. Consider a student who misses class twice each week, omitting Sunday. What are the possibilities that he will take a leave of absence on Saturday of the same week if it is known that he will be absent from school on Tuesday? It has been noted that situations where the outcome of one event influences the outcome of a subsequent event are termed as conditional probability

We can work this out directly from the definition of conditional probability,

[tex]P(G_1|G_2)=P(G_1nG_2)/(P(G_1)[/tex]

Exactly one of the three cards has sides, so

P(G1∩G2)=1/3

and P(G1)=1/2

THEN

the probability of getting (a, b), i.e. the first card is a and the second card is b IS = 1/3÷1/2 = 2/3

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A manufacturer working at the 430 gram setting, and a 21 bag sample had a mean of 421 grams with a standard deviation of 15. The p-value of test statistic is 0.0074.

To test whether the bag filling machine works correctly at the 430 gram setting, we can conduct a one-sample t-test. The null hypothesis is that the true mean weight of the bags filled by the machine is equal to 430 grams, and the alternative hypothesis is that the true mean weight is less than 430 grams.

The test statistic is calculated as:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

Plugging in the values given in the problem, we get:

t = (421 - 430) / (15 / sqrt(21)) = -2.77

The degrees of freedom for the t-distribution are n - 1 = 20.

Using a t-table or calculator, we can find the p-value associated with a t-score of -2.77 and 20 degrees of freedom. The p-value turns out to be 0.0074 (rounded to four decimal places).

Since the p-value is less than the level of significance of 0.1, we can reject the null hypothesis and conclude that the bag filling machine is underfilling the bags at the 430 gram setting.

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Answer:

A Y=10

Step-by-step explanation:

Answer:

Option B is the right answer.

Step-by-step explanation:

See Attachment

The probability of randomly selecting one of these coded items with the first letter a vowel and the last digit even is 5/52

probability is an occurence of a particular events. This particular problem can be solved using permutations and combinations.

Given that, if each coded item in a catalog begins with 4 distinct letters followed by 4 distinct nonzero digits

Like the 4 distinct letters be A,B,C,D

4 distinct nonzero digits are 2,3,4,5

The probability of randomly selecting one of these coded items with the first letter a vowel and the last digit even is approximately equals to the 10/104 = 5/52

Here the probability is an occurence of a particular events. This particular problem can be solved using permutations and combinations and the probability of randomly selecting one of these coded items with the first letter a vowel and the last digit even is approximately equals to 5/52

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Answer:

x = 59.036°

Step-by-step explanation:

tan (BÂC) = BC/AB

tan= opposite/ adjacent

Then subs AB = 3 BC= 5 BÂC= x into tan (BÂC) = BC/AB

tan(x)=5/3

x= tan^-1 (5/3)

x= 59.036°

The value of x by using the addition postulate of an acute angle is 36.

Acute angles are those between 0 and 90 degrees, and those angles are less than 90 degrees. When two rays intersect at a vertex, an angle is created.

An acute angle is one that is smaller than 90 degrees in length and has all internal angles that are less than 90 degrees.

Here, we have an acute angle NCQ that is 70 degrees. Using the addition postulate to determine the value of x, we have:

x + 34 = 70

x = 70 + (-34)

x = 70 - 34

x = 36

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Answer: $135

Step-by-step explanation:

We have the ratio 1 : 3.

Kim gets $90 more than Jake.

So 1 : 3 can also be written as x : x+90

If x * 3 equals x+90, we can create the equation 3x=x+90. Solving this results in x being equal to 45

Kim gets $135 (x+90=45+90=135)

Using the gradient of the curve given, the value of a is 6

The stationary point of a curve is a point where the slope of the curve is equal to zero. So, to find the value of a, we need to set the derivative of the curve equal to zero and solve for x.

dy/dx = 2(x + 3)^(1/2) - x

Setting this equal to zero, we have:

2(x + 3)^(1/2) - x = 0

Expanding the square root and rearranging, we get:

x = 2(x + 3)^(1/2)

Squaring both sides of the equation, we have:

x^2 = 4(x + 3)

Expanding the right side and rearranging, we have:

x^2 - 4x - 12 = 0

Using the quadratic formula, we can find the values of x that satisfy this equation:

x = [-(-4) ± √((-4)^2 - 4(1)(-12))] / 2(1)

x = [4 ± √(16 + 48)] / 2

x = [4 ± √64] / 2

x = [4 ± 8] / 2

So, the two possible values of x are:

x = 6, x = -2

Since we are looking for a positive value of x, the only solution that works is x = 6.

Therefore, the value of a is equal to 6.

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The Linear Equation for the line with slope as -1/3 and the point (-9,-1) is y = (-1/3)x - 4   .

We use the point slope form of a linear equation to write the equation of a line with its slope and a point on the line.

The point-slope form is ⇒ y - y₁ = m(x - x₁)  ;

Where m is = slope of line, and (x₁, y₁) is a point on line.

The Slope (m) of line  is  = -1/3 and point on line (x₁, y₁) is = (-9, -1),

Now , we substitute  these values ;

we get ;

⇒ y - (-1) = (-1/3)(x - (-9)) ;

⇒ y + 1 = (-1/3)(x + 9)  ;

Simplifying further ,

we get ;

⇒ y + 1 = (-1/3)x - 9/3  ;

Subtracting 1 from both sides, we get:

⇒ y = (-1/3)x - 4

Therefore, the equation of the line is y = (-1/3)x - 4  .

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Answer:

4 and -2

Step-by-step explanation:

4 + -2 = 2

4 x -2 = -8

Final Answer:

There are 0.036 decimeters in 3.6 millimeters.

Explanation:
To convert from millimeters to decimeters, we can use the following measurement conversion:

1 millimeter = 0.01 decimeters

So, to find out how many decimeters are in 3.6 millimeters, we can multiply 3.6 by 0.01:

3.6 * 0.01 = 0.036

Therefore, there are 0.036 decimeters in 3.6 millimeters.

The probability of 3 students arriving at a randomly selected office hour is 0.27(27%). This can be calculated by using the Poisson distribution equation which is P(x)=e^(-λ)*(λ^x/x!).

In the above equation, λ is equal to the average number of arrivals which is 3.3. Plugging these values into the equation gives us  P(3)= e^(-3.3)*(3.3^3/3!) = 0.27, this means that the probability of 3 students arriving in randomly selected office hours is 0.27.The Poisson distribution is used to calculate the probability of a certain number of events occurring in a fixed interval of time or space. It is commonly used in engineering, economics, and other fields.

This equation is especially useful in situations like this one where the arrival rate is known and the probability of a certain number of arrivals needs to be determined.

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A statistics professor finds that when she schedules an office hour for student help, an average of 3.3 students arrive. Find the probability that in a randomly selected office hour, the number of student arrivals is 3.

Answer:

Step-by-step explanation:

You want to know the meaning of D(2.60) = 159 if D(p) tells you the number of toys demanded at price p in hundreds.

Compare D(p) to D(2.60) and you see that p=2.60. The problem statement tells you p is the price. This means ...

The problem statement tells you that D(p) is the number of toys in hundreds. When D(p) is 159, the demand is 159 hundred toys.

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The scale of the blueprint is 1 in : 4 ft.

A map scale is the relationship between a distance on a map and the corresponding distance on the earth.

Given that, on a blueprint of a house, the kitchen is 5 inches long, the actual kitchen is 20 feet long, we are asked to find the scale of the blueprint.

Since, the kitchen in the map is 5 in long whereas n earth it is 20 ft long.

Therefore, the ratio =

5 in / 20 ft = 1 in / 4 ft

Hence, the scale of the blueprint is 1 in : 4 ft.

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Answer:

ray ts

Step-by-step explanation:

         a = amount given to the 1st share, ratio of 5.

a + 122 = amount given to the 2nd share, ratio of 7.

        T = total amount

so the total amount is really "T", and we'll be splitting that into a 7 : 5 ratio, that is, we'll be dividing "T" by (7 + 5) and distribute accordingly.

[tex]\stackrel{\textit{total split by 7 + 5}}{\cfrac{T}{7+5}\implies \cfrac{T}{12}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{we know the 1st share is}}{a= 5\cdot \cfrac{T}{12}}\implies a=\cfrac{5T}{12} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{we know the 2nd share is}}{a+122= 7\cdot \cfrac{T}{12}}\implies a+122=\cfrac{7T}{12}\implies \stackrel{\textit{substituting from above}}{\left( \cfrac{5T}{12} \right)+122=\cfrac{7T}{12}} \\\\\\ 122=\cfrac{7T}{12}-\cfrac{5T}{12}\implies 122=\cfrac{2T}{12}\implies 122=\cfrac{T}{6}\implies \boxed{732=T}[/tex]

The set of the numbers are all integers from 9 to 21 inclusive

It is the collection of items to form a group

All  the members of:

P={odd numbers}

P={9,11,13,15,17,19,21}

Q={Even numbers}

Q= {10,12,14,16,18,20}

U={ positive integer between 9 and 21}

This means that U = {9,10,11,12,13,14,15,16,17,18,19,20,21}

Therefore,  P1 and Q1​

P prime include all the elements in the universal set that are not in the subset P  = {10,12,14,16,18,20}

and Q prime include all the elements in the universal set that are not in subset Q =  P={9,11,13,15,17,19,21}

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Peter the rabbit have  51 carrots are left.

one fourth means A quarter is represented in mathematics using fractions. Mathematically, a quarter fraction is a whole divided into four equal parts. where 1 indicates the part being referenced and 4 indicates the number of parts the whole is divided into. In numeric format, it is written as ¼.

so total carrot is 84

and he ate one fourth on that day

so remaining are

84*1/4= 21

21 he eat on that the then remaining =

84 - 21  = 63

63 carrots are remain for next day and

he eat 12 carrot on next day

so remaining = 63 - 12 = 51

so 51 carrot left .

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The distance between these two points (2,0) and (2,−5) is 5 unit.

The distance between two points is the length of the line segment connecting the two points on the plane. The formula for finding the distance between two points is usually d=√((x2 – x1)² + (y2 – y1)²). This formula is used to find the distance between any two points on the coordinate or x-y plane.

d=√((2 – 2)² + (-5 – 0)²)

d = √(0+25)

d = 5 unit

if the coordinates of two points P and Q are such that, (x1, 0) and (x2, 0), the distance between PQ will be given by:

PQ = |x2 – x1|

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Answer:

It would be 180 - 136 = 44

Step-by-step explanation:

Answer:

yes you are correct

Step-by-step explanation:

180-136=44