Andy rode his bicycle 2
3
miles on Monday and 1
10
miles on
Tuesday

There are 26.24 cubic feet of sand in the rectangular container based on volume.

We must determine the volume of sand in the rectangular container in order to determine how much is there.

Let's start by determining the container's volume:

Container volume equals length, width, and height

Container volume: 6.5 feet by 3.2 feet by two feet

Container volume is 41.6 cubic feet.

The amount of sand in the container's volume must then be determined. We can determine the volume of sand by using the following formula because it fills the container to a depth of 1.3 feet:

Sand volume is determined by its length, width, and depth.

Sand volume = 6.5 feet by 3.2 feet by 1.3 feet

Sand volume = 26.24 cubic feet

As a result, the container contains 26.24 cubic feet of sand.

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The value of the standard deviation depends on the value of the mean.

As per the given data, we have to determine that the value of the standard deviation depends on the value of the mean

Yes, the value of the standard deviation depends on the value of the mean.

Because you have to know the mean to calculate the standard deviation.

The size of the standard deviation of a data set depends on what the mean is because the calculation of the mean is essential for calculating Standard Deviation.

The standard deviation determines how much the values deviate from the mean.

Besides, Standard deviation in simple terms means the deviation of data from the Mean.

The most popular way to assess dispersion is standard deviation, which is based on all values. As a result, even a small change in one value can modify the standard deviation's value.

Hence, Standard Deviation depends on the Mean.

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Answer:

A)2x+7

Step-by-step explanation:

-x+5+3x+2

2x+7

Answer:

50

Step-by-step explanation:

You would do 600/12 which is the 600 miles driven divided by the 12 gallons put in the tank!

34 inches have the same length of 0.0008636 kilometers.

The hypotenuse of 4th triangle be \(2\sqrt{2}\\\)

The hypotenuse of 100th triangle be \(2\sqrt{26}\\\)

The hypotenuse of nth triangle be \(\sqrt{4+n}\\\)

Given, that Triangles be drawn according to the spiraling pattern

let hypotenuse of 1st triangle be \(h_{1}\), hypotenuse of 2nd triangle be \(h_{2}\) and so on.

as, we know Pythagoras theorem i.e.

\(hypotenuse^{2} = base^{2} + perpendicular^{2}\)

In 1st triangle,

base = 2 units and perpendicular = 1 unit

On applying Pythagoras theorem in 1st triangle, we get

\(h_{1}^{2}=2^2 +1^2\)

\(h_{1}^2=5\\ h_{1} = \sqrt{5}\) ... (1)

Now, hypotenuse of 1st triangle will be the base of 2nd triangle

so, In 2nd triangle,

base = \(\sqrt{5}\) units and perpendicular = 1 unit

On applying Pythagoras theorem in 2nd triangle, we get

\(h_{2}^2 = \sqrt{5}^2 + 1^2\)

\(h_{2}^2=5+1\\h_{2}^2=6\\ \\h_{2}=\sqrt{6} \\\)... (2)

Now, observing Eq (1) and Eq (2) we can define a rule to find the hypotenuse of nth triangle i.e.

\(h_{n}=\sqrt{4+n}\)

So, the hypotenuse of the 4th triangle be

\(h_{4}=\sqrt{4+4}\\ h_{4}=\sqrt{8}\\ h_{4}=2\sqrt{2}\)

Also, the hypotenuse of the 100th triangle be

\(h_{100}=\sqrt{100+4}\\ h_{100}=\sqrt{104}\\ h_{100}=2\sqrt{26}\)

The hypotenuse of 4th triangle be \(2\sqrt{2}\\\)

The hypotenuse of 100th triangle be \(2\sqrt{26}\\\)

The hypotenuse of nth triangle be \(\sqrt{4+n}\\\)

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answer is b Answer:

Step-by-step explanation:

When we identify a nonsignificant finding, p relates to alpha in the following way:

b. p is less than or equal to alpha.

Explanation:

In hypothesis testing, a p-value is the probability of obtaining a test statistic as extreme or more extreme than the one observed, assuming the null hypothesis is true. On the other hand, alpha is the level of significance or the probability of rejecting the null hypothesis when it is true.

The common convention is to set the level of significance at 0.05 or 0.01, which means that if the p-value is less than alpha, we reject the null hypothesis. On the other hand, if the p-value is greater than alpha, we fail to reject the null hypothesis.

Therefore, when we identify a nonsignificant finding, it means that the p-value is greater than the alpha, and we fail to reject the null hypothesis. Hence, option (b) is the correct answer.

Answer:

True

Step-by-step explanation:

The best buy will be;

''28 pounds for $49.56''

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The two options are,

16 pounds for $31.68

28 pounds for $49.56

Now,

Since, The two options are,

16 pounds for $31.68

28 pounds for $49.56

Hence, The unit rate for each are;

Since, The cost of 16 pounds = $31.68

Hence, The cost of 1 pounds = $31.68/16

                                            = $1.98

And, The cost of 28 pounds = $49.56

Hence, The cost of 1 pounds = $49.56/28

                                            = $1.77

Thus, The best buy will be;

''28 pounds for $49.56''

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Answer:

...

Step-by-step explanation:

Selecting all students with last names beginning with the letter M would not produce a random sample of a school population of 1000 students. Hence the answer is no.

A random sample is obtained by selecting individuals from a population in a way that ensures every member of the population has an equal chance of being included in the sample.

By choosing only students with last names beginning with the letter M, you are introducing a bias and not providing an equal chance for all students to be selected.

To obtain a random sample of 1000 students from a school population, you would need to use a random selection method that ensures each student has an equal probability of being chosen.

This could be achieved through techniques such as random number generators, random sampling software, or random sampling techniques like stratified or cluster sampling.

Selecting all students with last names beginning with the letter M would not meet the requirements of a random sample, as it would not provide an equal chance for all students in the population to be included.

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\(f(x) = x + 7\)

\(h(x) = - 2x + 1\)

Add them up :

\(f(x) + h(x) = x + 7 - 2x + 1 \\ \)

Collect like terms

\(f(x) + h(x) = - x + 8\)

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Answer: 5°

Step-by-step explanation:

You can use a right triangle to solve

Hypotenuse would be the flight path

One leg (opposite) is the tree     65 ft

Tan (Θ) = opposite/ adjacent = 65/750  

Θ = arctan (65/750)

Θ = 5°

On solving the provided question, we can say that Considering that the test statistic inside the lower tail the rejection zone, the null hypothesis should be rejected.

A null hypothesis is a kind of statistical hypothesis that asserts that a specific set of observations has no statistical significance. Using sample data, hypotheses are tested to determine their viability. Sometimes known as "zero" and symbolized by H0. Researchers start off with the presumption that there is a link between the variables. In contrast, the null hypothesis claims that there is no such association. Although the null hypothesis may not appear noteworthy, it is a crucial component of research.

\(H0:p=0.25\) (null hypothesis)

\(H0:p \neq 0.25\) (alternative hypothesis)

Do not reject the null because the test statistic\((-1.2) is >\) \(the critical value (-1.7531)\)

Considering that the test statistic is inside the lower tail of the rejection zone, the null hypothesis should be rejected.

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Answer: Maybe first give an equation

Step-by-step explanation:

Answer:

Step-by-step explanation:

In numerical order:

      \(1\frac{2}{3},1\frac{3}{4}\)

Since there are only 2 scores the median(middle score)  will be the same as the mean:

     \((1\frac{2}{3}+ 1\frac{3}{4}) \div 2=(\frac{20}{12}+ \frac{21}{12}) \div 2=\frac{41}{12} \times \frac{1}{2} =\frac{41}{24}=1\frac{17}{24}\)

Answer:

\(m=4\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Point (-2, 1)

Point (-3, -3)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Answer: 2.4

Step-by-step explanation: just use a calculator???

Answer:

2.4

Explanation:

From the calculation, all three inequalities are satisfied, which means that the given measurements produce one triangle.

To determine whether the given measurements produce one triangle, two triangles, or no triangle at all, we can use the Law of Sines and the Triangle Inequality Theorem.

Given:

a = 10

b = 13.6

A = 33°

Determine angle B:

Angle B can be found using the equation: B = 180° - A - C, where C is the remaining angle of the triangle.

B = 180° - 33° - C

B = 147° - C

Apply the Law of Sines:

The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

a/sin(A) = b/sin(B) = c/sin(C)

We can rearrange the equation to solve for side c:

c = (a * sin(C)) / sin(A)

Substituting the given values:

c = (10 * sin(C)) / sin(33°)

Determine angle C:

We can use the equation: C = arcsin((c * sin(A)) / a)

C = arcsin((c * sin(33°)) / 10)

Apply the Triangle Inequality Theorem:

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.

In this case, we need to check if a + b > c, b + c > a, and c + a > b.

If all three inequalities are satisfied, it means that the measurements produce one triangle. If one of the inequalities is not satisfied, it means no triangle can be formed.

Now, let's perform the calculations:

B = 147° - C (from step 1)

c = (10 * sin(C)) / sin(33°) (from step 2)

C = arcsin((c * sin(33°)) / 10) (from step 3)

Using a calculator, we find that C ≈ 34.65° and c ≈ 6.16.

Now, let's check the Triangle Inequality Theorem:

a + b > c:

10 + 13.6 > 6.16

23.6 > 6.16 (True)

b + c > a:

13.6 + 6.16 > 10

19.76 > 10 (True)

c + a > b:

6.16 + 10 > 13.6

16.16 > 13.6 (True)

All three inequalities are satisfied, which means that the given measurements produce one triangle.

In summary, with the given measurements of a = 10, b = 13.6, and A = 33°, we can determine that one triangle can be formed. The measures of the angles are approximately A = 33°, B ≈ 147° - C, and C ≈ 34.65°, and the lengths of the sides are approximately a = 10, b = 13.6, and c ≈ 6.16.

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Answer:

70%

Step-by-step explanation:

Given data

Last years worth of vanishing potion= $82

This years worth of vanishing portion= $118

Note: Another way of asking this question is "what percent of $82 is $118"

So

=82/118*100

=0.69*100

=69%

=70% approx

Hence last years sale is 70% of this year's sales

Answer:

\(m \ge 45\)

She must practice for at least 45 minutes each night

Step-by-step explanation:

Given

\(Practice = 225\ minutes\) --- at least

\(Nights = 5\) --- each week

Required

Write an inequality

Let the number of minutes in a night be m.

At least means \(\ge\)

So, we have:

\(Nights * m \ge Practice\)

\(5* m \ge 225\)

Divide both sides by 5

\(m \ge 45\)

A vector space, or linear space, is a set of objects called vectors that are added and multiplied ("scaled") by numbers called scalars.

We claimed that set of all points in R² lying on a line is a vector space with respect to the standard operations of vector addition and scalar multiplication if and only if the line passes through the origin i.e c = 0 .

Vector spaces must be closed under addition and scalar multiplication.

closed in addition -: if vectors v and w are in the space, so is v+w also in space.

closed in scalar multiplication :- if vector v is in the space, so is rv∈V, where r is a real number.

a) An equation of a line in R² is ax + by = c.

Let (x₁,y₁) and (x₂,y₂) be 2 points on the line and r be a real number.

Then ax₁+ by₁= c and ax₂+ by₂= c so, we have vectors v = [x₁, y₁] and w = [x₂, y₂]

add them v+w = [x₁+x₂,y₁+y₂]

The coordinates of the vector must satisfy

ax+by=c so, a(x₁+x₂) + b(y₁+y₂) = c

But if we add ax₁+by₁ = c and ax₂+by₂ = c we get a(x₁+x₂)+b(y₁+y₂) = 2c

Thus 2c = c or c=0.

Now, rv = [rx₁, ry₁]

The coordinates of the vector must satisfy ax+by=c so, a(rx₁) + b(ry₁) = c

But if we multiply ax₁+by₁= c by r we get arx₁+bry₁= rc

=> rc = c or c=0.

Thus, it is a vector space if and only if c=0. Thus our line is ax+by=0, a line which passes through the origin.

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Answer:

-7

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

-2 +(-5) is basically -2 - 5

Don't let it confuse you.

Answer:

3744:\p=11756.16 m^2

Step-by-step explanation:

\( {12}^{2} \pi(18 + 9) - {4}^{2} \pi \times 9 = 3744\pi \: \: {m}^{2} \)

The probability of the arrow landing on an odd number is the number of odd numbers divided by the total number of possible outcomes. Therefore, the probability of the arrow landing on an odd number is  0.5 or 50%.


To find the probability that the arrow will point at an odd number on a circular board with 8 equal parts, we'll first determine the total number of odd numbers present and then divide that by the total number of possible outcomes.

Step 1: Identify the odd numbers on the board. They are 1, 3, 5, and 7. The game consists of spinning the arrow on a circular board with 8 equal parts, which means there are 8 possible outcomes or numbers. Since we want to know the probability of landing on an odd number, we need to count how many odd numbers are on the board. In this case, there are four odd numbers: 1, 3, 5, and 7.

Step 2: Count the total number of odd numbers. There are 4 odd numbers.

Step 3: Count the total number of possible outcomes. Since the board is divided into 8 equal parts, there are 8 possible outcomes.

Step 4: Calculate the probability. The probability of the arrow pointing at an odd number is the number of odd numbers divided by the total number of possible outcomes.

Probability = (Number of odd numbers) / (Total number of possible outcomes)
Probability of landing on an odd number = Number of odd numbers / Total number of possible outcomes
Probability of landing on an odd number = 4 / 8

Step 5: Simplify the fraction. The probability of the arrow pointing at an odd number is 1/2 or 50%.

So, the probability that the arrow will point at an odd number is 1/2 or 50%.

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The number of jelly beans that fit in a 2001 Chevy Suburban can be calculated by finding the volume of the car's interior and dividing it by the volume of a single jelly bean.

To find the number of jelly beans that fit in a 2001 Chevy Suburban, we first need to calculate the volume of the car's interior. The volume of a rectangular prism is calculated by multiplying its length, width, and height. In this case, the length of the Suburban is 219.3in, the width is 78.8in, and the height is 75.4in.

Using the formula V = lwh, we can calculate the volume:

V = 219.3in * 78.8in * 75.4in

Next, we need to find the volume of a single jelly bean. Since the question does not provide this information, we will assume a standard jelly bean size.

Once we have the volume of the car and the volume of a single jelly bean, we can divide the car's volume by the jelly bean's volume to find the number of jelly beans that fit.

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In 0.75lb (340g) of 85% lean ground beef, there are approximately 72 grams of fat.

To calculate the grams of fat in 0.75lb of 85% lean ground beef, we need to determine the fat content based on the percentage given. The term "85% lean" indicates that 85% of the weight of the ground beef is lean meat, while the remaining 15% is fat.

First, we convert 0.75lb to grams. Since 1lb is equal to 454g, multiplying 0.75lb by 454g/lb gives us 340g.

Next, we calculate the fat content by multiplying the weight of the ground beef (340g) by the percentage of fat (15%).

340g * 0.15 = 51g

Therefore, in 0.75lb (340g) of 85% lean ground beef, there are approximately 51 grams of fat.

However, the question asks for the fat content, so we subtract this value from the total weight to find the grams of fat:

340g - 51g = 289g

Therefore, there are approximately 72 grams of fat in 0.75lb (340g) of 85% lean ground beef.

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Answer:

3 + 2 = 5

Step-by-step explanation:

Remember Commutative Property by thinking about what happens when someone has to "commute" (driving back and forth to work or school) If the numbers in the addition MOVE then it is Commutative Property.

The value of "a" is approximately 1.83 given that the absolute value of the difference of the two roots of the quadratic equation "ax squared plus 5x minus 3 equals 0" is the square root of 61 divided by 3, and "a" is positive.

We are given that the absolute value of the difference between the two roots of the quadratic equation "ax squared plus 5x minus 3 equals 0" is the square root of 61 divided by 3, and "a" is positive. We need to find the value of "a".

Let the two roots of the equation be r1 and r2, where r1 is not equal to r2. Then, we have:

|r1 - r2| = √(61) / 3

The sum of the roots of the quadratic equation is given by r1 + r2 = -5 / a, and the product of the roots is given by r1 × r2 = -3 / a.

We can express the difference between the roots in terms of the sum and product of the roots as follows:

r1 - r2 = √((r1 + r2)² - 4r1r2)

Substituting the expressions we obtained earlier, we have:

r1 - r2 = √(((-5 / a)²) + (4 × (3 / a)))

Simplifying, we get:

r1 - r2 = √((25 / a²) + (12 / a))

Taking the absolute value of both sides, we get:

|r1 - r2| = √((25 / a²) + (12 / a))

Comparing this with the given expression |r1 - r2| = √(61) / 3, we get:

√((25 / a²) + (12 / a)) = √(61) / 3

Squaring both sides and simplifying, we get:

25 / a² + 12 / a - 61 / 9 = 0

Multiplying both sides by 9a², we get:

225 + 108a - 61a² = 0

Solving this quadratic equation for "a", we get:

a = (108 + √(108² + 4 × 61 × 225)) / (2 × 61)

Since "a" must be positive, we take the positive root:

a = (108 + √(108² + 4 × 61 × 225)) / (2 × 61) ≈ 1.83

Therefore, the value of "a" is approximately 1.83.

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The question is -

Given that the absolute value of the difference of the two roots of the quadratic equation "ax squared plus 5x minus 3 equals 0" is the square root of 61 divided by 3, and "a" is positive, what is the value of "a"?