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Explanation

From the question, the winning door number must be selected from 1 to 150.

Recall that the formula for the probability of an event is given as

The total possible numbers is from 1 to 150 which gives 150 numbers. We can then find the favorable outcomes for each of the questions.

Part A

When you multiply an integer (a “whole” number, positive, negative or zero) times itself, the resulting product is called a square number, or a perfect square or simply “a square.” So, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 are the square numbers from 1 to 150.

In total, we have 12 square numbers. Therefore, the probability is given as

Answer:

Part B

At least 100 implies from 100 to 150. This gives 51 favorable numbers.

Answer:

Part C

The numbers divisble by 5 are 5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100,105,110,115,120,125,130,135,140,145,150. This gives a total of 30 favorable numbers.

Answer:

Part D

The numbers no more than 11 are 11 favorable numbers

Answer:

49 is the smallest possible value of x.

Given: x, y, and z are three perfect square numbers.

What is the least x that can be?

Currently, we have three numbers by the stipulation:

x > y > z > 0

and AP has these figures.

Let's now list every perfect square from 1 to 10 in the following order: 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.

As a result, we can observe that 25 is equal to the product of 1 plus 49.

The possible outcomes are 1, 25, and 49.

If x = 49 and z = 1, then

x + z / 2 = y

49 + 1 / 2 = y

y = 50 / 2

y = 25

Y is therefore 25 and X is 49.

As a result, 49 is the lowest value of x that can exist.

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Answer:

Just wanted to say that i wish you good luck!

Step-by-step explanation:

Answer:

To divide fractions, you need to follow these steps:

Flip the second fraction (the one you want to divide by) upside down (this is called taking the reciprocal).

Multiply the first fraction by the reciprocal of the second fraction.

Simplify the resulting fraction if possible.

Here is an example:

1/3 ÷ 2/5

Step 1: Flip the second fraction: 2/5 becomes 5/2.

Step 2: Multiply the first fraction by the reciprocal of the second fraction: 1/3 x 5/2 = 5/6.

Step 3: Simplify the resulting fraction if possible: 5/6 is already in its simplest form.

For more examples and explanatTo divide fractions, you need to follow these steps:

Flip the second fraction (the one you want to divide by) upside down (this is called taking the reciprocal).

Multiply the first fraction by the reciprocal of the second fraction.

Simplify the resulting fraction if possible.

Here is an example:

1/3 ÷ 2/5

Step 1: Flip the second fraction: 2/5 becomes 5/2.

Step 2: Multiply the first fraction by the reciprocal of the second fraction: 1/3 x 5/2 = 5/6.

Step 3: Simplify the resulting fraction if possible: 5/6 is already in its simplest form.

Step-by-step explanation:

brainliest pls

Answer:

Step-by-step explanation:

For dividing fractions:

Remember:

Keep Change Flip

Keep the first the same

Change the sign to multiplication

Flip the second fraction.

EX.

\(\frac{4}{5}\) ÷ \(\frac{1}{2}\)                           >Keep, Change Flip

=\(\frac{4}{5}\) * \(\frac{2}{1}\)                          >Now it's multiplication, reduce first if you can

                                    (nothing reduces in this problem), so mulitply

                                    across

= \(\frac{8}{5}\)

The location which is in the region for plants receiving the maximum amount of water is "(-3,-1)". The Option A is correct.

Water flows into the open pore spaces in the soil by gravity, and the size and spacing of the soil particles determine how much water can flow in. Because coarse soils have larger pore spacing at the soil surface, they have a higher infiltration rate than fine soils.

Based on the graph, we observed that the point of location in which is in the region for plants receiving the maximum amount of water is the point (-3,-1). Therefore, we agree that Option A is correct.

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=

3

3

2

hope it's helpful for you

Answer:

x=33/2

Step-by-step explanation:

\(\frac{2x-7}{4}\)=\(\frac{x+3}{3}\)

do cross multiplication

4(x+3)=3(2x-7)

4x+12=6x-21

12+21=6x-4x

33=2x

33/2=x

Answer:

11. Not enough information

12. You can say DB = DC by SAA congruence rule and CPCTC (Corresponding parts of congruent triangles are congruent)

Step-by-step explanation:

For 12, you can say ΔABD≅ΔACD because they have a side in common (AD) and they have 2 congruent angles. Thus, you can use the SAA congruence criterion. Then, you can use CPCTC (Corresponding parts of congruent triangles are congruent) to say that DB = DC.

Hope this helps :)

Answer:

Step-by-step explanation:

But we know that √5 is an irrational number. So, {(a - 3b)/b} should also be an irrational number. Hence, it is a contradiction to our assumption. Thus, 3 + √5 is an irrational number.

Answer:

A  -4a(3 + 2a)

Step-by-step explanation:

-12a - 8a^2) factor out a -4

-4(3a + 2a^2) factor out an a

-4a(3 + 2a)

The length of the two segments, written as radicals, are:

AB = √117

PQ = √244

Remember that for a segment whose endpoints are (x₁, y₁) and (x₂, y₂), the length of the segment is:

L = √( (x₂ - x₁)² + (y₂ - y₁)²)

First, for the segment AB the endpoints are:

A = (-4,  -4)

B = (2, 5)

Then the length is:

L =  √( (-4 - 2)² + (-4 - 5)²)

L = √117

For the segment PQ the endpoints are:

P = (-6, 8)

Q = (6, -2)

The length is:

L =  √( (-6 - 6)² + (8 + 2)²)

L = √244

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Answer:

Area of triangle AED = \(\frac{1}{2}\) × AE × DE

Step-by-step explanation:

The area of a triangle is \(\frac{bxh}{2}\)

Answer:

Other person is right, i took the test

Step-by-step explanation:

The left side of the expression has a denominator of 4 while the right side has a denominator of 1.

To start with, we have to find the LCM (lowest common multiple) for both sides of the expression

The LCM of 4 and 1 is 4.

When dealing with fractions, the first step after finding the LCM is;

Left side:LCM divided by left denominator times left numerator PLUS

Right side:LCM divided by right denominator times right numerator.

Thus we now have the following;

(4/4) * (-2 + 2*3) + (4/1) * 4*(-2)

1 * (-2 + 6) + 4 * (-8)

4 + (-32)

-28

Answer:

The middle 90% of all freshman biology majors' GPAs lie between 2.31 and 3.43.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean 2.87 and standard deviation .34.

This means that \(\mu = 2.87, \sigma = 0.34\)

Middle 90% of scores:

Between the 50 - (90/2) = 5th percentile and the 50 + (90/2) = 95th percentile.

5th percentile:

X when Z has a pvalue of 0.05. So X when Z = -1.645.

\(Z = \frac{X - \mu}{\sigma}\)

\(-1.645 = \frac{X - 2.87}{0.34}\)

\(X - 2.87 = -1.645*0.34\)

\(X = 2.31\)

95th percentile:

X when Z has a pvalue of 0.95. So X when Z = 1.645.

\(Z = \frac{X - \mu}{\sigma}\)

\(1.645 = \frac{X - 2.87}{0.34}\)

\(X - 2.87 = 1.645*0.34\)

\(X = 3.43\)

The middle 90% of all freshman biology majors' GPAs lie between 2.31 and 3.43.

Answer:

Step-by-step explanation:

Area of a triangle is given by

\(A = \frac{1}{2} bh\)

Where

b is the base of the triangle

h is the height

From the question

\(base = 4 \frac{1}{2} \: in = \frac{9}{2} \: in \\ \\ height = 2 \frac{1}{4} \: in \: = \frac{9}{4} \: in\)

Substitute the values into the above formula and solve for the area

We have

\(A = \frac{1}{2} \times \frac{9}{2} \times \frac{9}{4} = \frac{81}{16} \\ = 5.0625\)

We have the final answer as

Area = 5.06 in² to the nearest hundredth

Hope this helps you

Answer:

5.06 in^2

Step-by-step explanation:

Triangle Area: (b*h)/2

4 1/2=9/2

9/2=4.5

2 1/4=9/4

9/4=2.25

4.5*2.25=10.125

10.125/2=5.0625

5.0625 rounded to the nearest hundredth is 5.06

Answer:

4.19

Step-by-step explanation:

Find the mean:

\(\text{Mean}=\frac{12+19+9}{3}=\frac{40}{3}\)

Find the standard deviation:

\(\text{Standard Deviation}=\sqrt{\frac{(12-\frac{40}{3})^2+(19-\frac{40}{3})^2+(9-\frac{40}{3})^2}{3}}=\sqrt{\frac{158}{9}}\approx4.19\)

Answer:

A

Step-by-step explanation:

1 cm = 10 miles

7.5 cm = x

Cross multiply

x*1 cm = 10 miles * 7.5 cm

x = 75 miles cm / cm

x = 75 miles

A

Given statement solution is :- Math Proficiency conceptual knowledge involves understanding the fundamental concept of division and its relationship to fractions, enabling flexibility in solving division problems with different fractions. Procedural knowledge, on the other hand, focuses on following a specific set of steps to achieve a correct solution without necessarily comprehending the underlying concept.

3.1 Activity: Procedural and Conceptual Understanding in Action

Content Area: Fractions

Problem: Comparing Fractions

Objective: Students will demonstrate both procedural and conceptual understanding of comparing fractions.

Activity Steps:

Begin by introducing the concept of fractions and reviewing the basic procedures for comparing fractions (e.g., finding a common denominator, cross-multiplying).

Provide students with a set of fraction comparison problems (e.g., 2/3 vs. 3/4, 5/8 vs. 7/12) and ask them to solve the problems using the traditional procedural approach.

After students have solved the problems procedurally, engage them in a group discussion to explore the underlying concepts and relationships between fractions. Ask questions such as:

What does it mean for one fraction to be greater than or less than another?

Can you explain why we need a common denominator when comparing fractions?

How can you visually represent and compare fractions to better understand their relative sizes?

Introduce visual aids, such as fraction bars or manipulatives, to help students visualize the fractions and compare them conceptually. Encourage students to reason and explain their thinking.

Have students revisit the fraction comparison problems and solve them again, this time using the conceptual understanding gained from the group discussion and visual aids.

Compare the students' procedural solutions with their conceptual solutions, and discuss the similarities and differences.

Conclude the activity by emphasizing the importance of both procedural and conceptual understanding in solving fraction comparison problems effectively.

By incorporating both procedural and conceptual approaches, this activity allows students to develop a deeper understanding of comparing fractions. The procedural approach provides them with the necessary steps to solve problems efficiently, while the conceptual approach helps them grasp the underlying principles and relationships involved in fraction comparison.

3.2 Example: Conceptual Knowledge vs. Procedural Knowledge

Conceptual knowledge refers to the understanding of underlying concepts, principles, and relationships within a domain, whereas procedural knowledge focuses on knowing the specific steps or procedures to perform a task without necessarily understanding the underlying concepts.

Example: Division of Fractions

Conceptual Knowledge: Understanding the concept of division as the inverse operation of multiplication, and recognizing that dividing fractions is equivalent to multiplying by the reciprocal of the divisor. This understanding allows for generalization and application of division concepts to various fractions.

Procedural Knowledge: Following the specific steps to divide fractions, such as "invert the divisor and multiply" or "keep-change-flip" method. This knowledge involves applying the procedure without necessarily grasping the underlying concept or reasoning behind it.

In this example, Math Proficiency conceptual knowledge involves understanding the fundamental concept of division and its relationship to fractions, enabling flexibility in solving division problems with different fractions. Procedural knowledge, on the other hand, focuses on following a specific set of steps to achieve a correct solution without necessarily comprehending the underlying concept.

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Answer:

41.1

Step-by-step explanation:

It was decreased by 26.7 between noon and midnight.

If it was -14.4 at midnight, which i after noon, you minus 26.7 and -14.4.

26.7--14.4 is 41.1.

(- and - = +)

Answer:

The temperature was 12.3°F at noon.

Step-by-step explanation

12.3

Answer:

(C) 12

Step-by-step explanation:

To solve this problem, we can use the following steps:

Find half of 80: 80/2 = 40

Add 20 to half of 80: 40 + 20 = 60

Find one fifth of the result: 60/5 = 12

Therefore, one fifth of twenty more than half of 80 is equal to 12. The correct answer is (C) 12.

Answer:

(C) 12

Step-by-step explanation:

What is one fifth of twenty more than half of 80

0.5 × 80 = 40

What is one fifth of twenty more than half of 80

40 + 20 = 60

What is one fifth of twenty more than half of 80

1/5 × 60 = 60/5 = 12

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the

10

. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

6.11/104

Answer:

(48, 3), (80, 5), (160, 10)

Answer:

Dilate circle A by a scale factor of 4.

Step-by-step explanation:

To show that two circles are similar, use transformations to map one to the other.

Step 1

Translate circle A so that its center is the same as circle B.

Translate circle A using the rule (x - 4, y - 3)

Step 2

Find the scale factor needed to dilate circle A to the size of circle B using the radii of the circles.

⇒ scale factor = 16 ÷ 4 = 4

Dilate circle A by a scale factor of 4.

Therefore, the only answer option that is correct is:

Dilate circle A by a scale factor of 4.

Answer:

y = 12 x = 12\(\sqrt{3}\)

Step-by-step explanation:

This is a 60, 90, 30. It's a special triangle.

2z = 24

z = 12

If x = z\(\sqrt{3}\)

then x = 12\(\sqrt{3}\)

y = z itself

So y = 12

Answer:

8 hours

Step-by-step explanation:

when sheʻs helping him theyʻre working together so 8/2= 4

when sheʻs working alone itʻll be 4 x 2 =8

Explanation:

Let's say we measure the job in terms of square feet. So let's say the house is 320 square feet.

If Dan can dust the house in 8 hours on his own, then his unit rate is 320/8 = 40 sq ft per hour.

After 4 hours, he can dust 4*40 = 160 sq ft of the house. This leaves 320-160 = 160 sq ft for Mary to handle.

Her unit rate is (160 sq ft)/(4 hrs) = 40 sq ft per hour. It's a coincidence that the two people happen to have the same unit rate (that won't always be the case). Because her unit rate is identical to Dan's rate, this means she takes the same amount of time to get the job done if she works alone.

Side note: this all assumes that the two workers do not hinder one another, or get in each others way, in any fashion. So in a sense, they split up the house down the middle.

Answer:

51

Step-by-step explanation:

I'm not sure which is the nth term, but the next term would be 51 because the numbers are going up by nine.