Leo dug up 6 4/5 pounds of
treasure on his first dig. Anne dug
up 4 1/2 pounds of treasure. How
much more treasure did Leo dig
up than Anne?

We can conclude that approximately 2.5% of students are likely to get a score below 275 on the GRE.

According to the empirical rule, approximately 68% of the data falls within one standard deviation of the mean, 95% of the data falls within two standard deviations of the mean, and 99.7% of the data falls within three standard deviations of the mean.

Given that the mean GRE score is 500 and the standard deviation is 75, we can calculate that a score of 275 is 2.33 standard deviations below the mean

z-score = (275-500) ÷75 = -2.33.

Using the empirical rule, we can determine that approximately 2.5% of students are expected to score lower than 275 on the GRE. This is because the area under the normal distribution curve beyond 2.33 standard deviations below the mean (i.e., to the left of z-score = -2.33) is about 0.01, and this area is multiplied by 2 to account for both tails of the distribution, giving a total probability of 0.025 or 2.5%.

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The perimeter of the figure is 58 m.

To find the perimeter of the given figure we can divide the figure in three rectangles.

Rectangle 1:

Perimeter= 2 (l + w)

= 2(5 + 2)

= 2 x 7

= 14 m

Rectangle 2:

Perimeter= 2 (l + w)

= 2(5 + 1)

= 2 x 6

= 12 m

Rectangle 3:

Perimeter= 2 (l + w)

= 2(14 + 2)

= 2 x 16

= 32 m

So, the perimeter of the figure is

= 14 + 12 + 32

= 58 m

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Answer:

1/3

Step-by-step explanation:

thats the slope so im assuming :/

Answer:

x = 24°

z = 117°

Step-by-step explanation:

I added a photo of my solution

Answer:x = 24°

Step-by-step explanation:z =

Step-by-step explanation:

please mark me as brainlest

Answer:

4.25 I think but I hoped that helped

We have to find which got a better deal.

We consider it a better deal when it has a lower value in respect to the possible prices of that specific brand.

We can compare the relative position of each deal by calculating the z-score. This z-score will give us the distance, as a proportion of the standard deviation, of the deal to the mean of the population.

Mr. X bought a Ford for $24,000. The mean and standard deviation of Ford prices is $25,000 and $1,000.

Then, we can calculate the z-value as:

We can visualize this as: there is 15.87% chances of getting a better deal with a Ford, as 15.87% of the prices are below $24,000.

NOTE: the z-score of -1 in this case means that $24,000 is one standard deviation to the left from the mean. The z-score gives us the relative position of a data point in a normal distrubution, letting us use a standard normal distribution to calculate the probabilities.

Miss Y bought a BMW for $65,000. The prices of BMW are normally distributed with a mean of $70,000 and a standard deviation of $3,000.

Then, we can calculate the z-score for this deal as:

The value of the z-score is lower than the one from Mr. X. We can see that in this case, the proportions of BMW's that cost less than $65,000 is 4.75%.

Then, the deal of Miss Y is better that the deal done by Mr X: there are less better deals for a BMW for Miss Y with the proce of $65,000 than the deals for less than $24,000 for a Ford.

Answer:

Z-score for Mr. X: -1

Z-score for Miss Y: -1.67

Miss Y got a better deal.

Step-by-step explanation:

-1 - root3

The value of the given expression 2cos2(105⁰) − 1 is,

⇒ - 1 - √3

A right-angled triangle's angle can be related to side length ratios using trigonometric functions, which are real functions in mathematics. They are extensively used in all geosciences, including navigation, solid mechanics, celestial mechanics, geodesy, and many others.

We have to find the value of;

⇒ 2cos2(105⁰) − 1

Now, We can Plug 105° = θ

So, the expression becomes,

⇒ 2cos2θ - 1

Using the formula;

cos2θ = 1 - 2sin^2θ

We get;

⇒ 2cos2θ - 1 = 2(1-2sin^2θ) - 1

                    = 2 - 4sin^2θ - 1

⇒ 2cos2θ - 1 = 1 - 4sin^2θ

Now, Again plug θ = 105°

⇒ 2cos2(105°) - 1  = 1 - 4sin¹⁰⁵

⇒ 2cos2(105°) - 1  = -1 - √3

Hence, The value of the given expression is,

⇒ (-1 - √3)

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Answer:

u=32

Step-by-step explanation:

Hey There!

Those are a pair of complementary angles we can tell because it has a square at the angle.

When angles are complementary they add up to 90

So given one angle we subtract that by 90 to find the missing angle

90-58=32

therefore u = 32

Answer:

The null hypothesis is  \(H_o : \mu_1 = \mu_2\)

The alternative hypothesis is   \(H_a : \mu_1 < \mu_2\)

The test statistics is   \(t =  -2.65\)

Reject the null hypothesis

There is  sufficient evidence to conclude that the weight of the old aluminium package pills is less than the new aluminium pills.

Step-by-step explanation:

From the question we are told that

The data for X is  373.2 , 376.7  , 381.6 , 382.1  , 388.7 ,  384.0 ,  397.9 , 389.8 ,385.1 , 371.3 , 383.5

The data for Y is 395.5 ,  384.8 , 383.5  , 386.5  ,394.8

, 391.6  , 397.7 , 384.0 , 391.7 , 398.8

Generally the sample mean for X is mathematically represented as

          \(\= x = \frac{\sum x_i }{n}\)

=>       \(\= x = \frac{373.2 +376.7 +\cdots + 383.5}{11}\)

=>       \(\= x = 383.08 \)

Generally the sample mean for Y is mathematically represented as

          \(\= y = \frac{\sum y_i }{n}\)

=>       \(\= y = \frac{395.5 +384.8 +\cdots + 398.8}{10}\)

=>       \(\= y = 390.89 \)

Generally the standard deviation for  X is mathematically represented as

     \(\sigma_1 = \sqrt{\frac{\sum (x_i - \= x_1 )^2}{n} }\)

=>   \(\sigma_1 = \sqrt{\frac{( 373.2 - 383.08)^2 +( 376.7 - 383.08)^2 +\cdots + ( 383.5 - 383.08)^2 }{11} }\)

=> \(\sigma_1 = 7.63 \)  

Generally the standard deviation for  Y is mathematically represented as

     \(\sigma_2 = \sqrt{\frac{\sum (y_i - \= y )^2}{n} }\)

=>   \(\sigma_2 = \sqrt{\frac{( 395.5 - 390.89)^2 +( 384.8 - 390.89)^2 +\cdots + ( 398.8 - 390.89)^2 }{10} }\)

=> \(\sigma_2 = 5.82 \)  

The null hypothesis is  \(H_o : \mu_1 = \mu_2\)

The alternative hypothesis is   \(H_a : \mu_1 < \mu_2\)

Generally the test statistics is mathematically represented as

     \(t = \frac{\= x - \= y}{ \sqrt{\frac{\sigma_1^2 }{ n_1 } +\frac{\sigma_2^2 }{ n_2 } } }\)

=>   \(t = \frac{383.08 - 390.89}{ \sqrt{\frac{7.63^2 }{ 11 } +\frac{5.82^2 }{10} } }\)

=>   \(t = -2.65\)

Generally the level of significance is \(\alpha = 0.05\)

Generally the degree of freedom is mathematically represented as

      \(df = n_1 + n_2 - 2\)

=>   \(df = 11 + 10 - 2\)

=>   \(df = 19\)

Generally from the student t- distribution table the critical value of   \( \alpha \) at a df = 19 is      

    \(t_{\alpha ,df} =t_{0.05 ,19} = -2.093\)

Now comparing the critical value  obtained with test statistic calculated we see that the critical value is the region of the calculated test statistic( i.e  between  -2.65 and  2.65) hence we reject the null hypothesis

Therefore there sufficient evidence to conclude that the old aluminium package pills weight is less than the new aluminium pills

Answer: The area is going to be 0.8

Step-by-step explanation:  The diameter is 1

You need the radius of the circle which is half the diameter. So the Radius(R) is 0.5.

After you find the radius of the circle to find the area of the circle you use the formula pie (R)^2. You are using 3.14

3.14(0.5)^2= 0.785

you then want to round your answer to the nearest tenth so the 8 turns the 7 into an 8.

So, the Area is 0.785 but after rounding it is 0.8.

Hope that helped :)

The approximate area to the left of z= 2​ is 0.978

From the question, we have the following parameters that can be used in our computation:

The left of z= 2​

The area to the left of z is calculated by calculating the probability that the z-score is less than 2

In other words, this is represented as

Area = (z < 2)

This can then be calculated using a statistical calculator or a table of z-scores,

Using a statistical calculator, we have the area to be

Area =  0.97725

When this value is approximated, we have the approximated area to ve

Area =  0.978

Hence, the area is 0.978

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The value of the given summation is:

\(\sum (29a_i - 13b_i) ]= -30\)

Here we know that the sums are:

\(\sum a_i = -10\\\\\sum b_i = -20\)

And we want to find the value of the sum:

\(\sum (29a_i - 13b_i)\)

First we can distribute the sum to get:

\(\sum 29a_i + \sum - 13b_i\)

And take the coefficients out of the sum:

\(29\sum a_i -13\sum b_i\)

Now replace the known values:

\(29\sum a_i -13\sum b_i = 29*-10 - 13*-20 = -290 + 260 = -30\)

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Answer:

9%

Step-by-step explanation:

To find the increased amount, subtract this month sales from the last month sales.      

Increased amount = 196200 - 180000

                              = £ 16,200

Now, find the increased percentage using the formula,        

\(\boxed{\bf Increased \ percentage = \dfrac{Increased \ amount}{Original \ amount}*100}\\\\\)

                                        \(= \dfrac{16200}{180000}*100\\\\= 9\%\)

Answer: The equation of a line perpendicular to 2x + 2y = - 10 that passes through the point (6, 2) is y = x - 4

Answer:

the bag contains $10.89.

Step-by-step explanation:

Let's start by using algebra to represent the number of coins in terms of one variable. Let x be the number of pennies in the bag. Then:

The number of nickels is 4 more than the number of pennies, so there are x + 4 nickels.

The number of dimes is 30% of the total, so there are 0.3 * 50 = 15 dimes.

The number of quarters is the remaining coins: 50 - (x + x + 4 + 15) = 31 - 2x.

To find the total amount of money, we need to multiply the number of each type of coin by its value and add them up. Using the values of the coins:

Pennies: x * $0.01

Nickels: (x + 4) * $0.05

Dimes: 15 * $0.10

Quarters: (31 - 2x) * $0.25

Adding these expressions and simplifying, we get:

Total = 0.01x + 0.05(x + 4) + 0.10(15) + 0.25(31 - 2x)

= 0.01x + 0.05x + 0.20 + 1.50 + 7.75 - 0.50x

= 0.06x + 9.45

Now we need to find x, the number of pennies. We know that 14% of the coins are pennies, so:

0.14 * 50 = 7 = x + (x + 4) + 15 + (31 - 2x)

Solving for x, we get:

7 = 50 - x - 19

x = 24

So there are 24 pennies, 28 nickels, 15 dimes, and 3 quarters in the bag. The total amount of money is:

Total = 0.06(24) + 9.45 = $10.89

Therefore, the bag contains $10.89.

The values of {m} that is greater than 4.6 represent the solution of the given inequality.

An inequality is used to compare two or more expressions or numbers.

For example -

2x > 4y + 3

x + y > 3

x - y < 6

The given inequality is -

5m - 7 > 16

Adding 7 on both sides, we get -

5m - 7 + 7 > 16 + 7

5m > 23

m > 23/5

m > 4.6

Therefore, the values of {m} that is greater than 4.6 represent the solution of the given inequality.

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Answer:

B. [[0,4]

   [-6,1]

  [3,-4]]

Step-by-step explanation:

If you multiply the matrices, you get the answer.

Answer:

The highest you could reach with this ladder is 30 feet or 9.14 meters.

The true statement about the parallelogram is (c) Yes, because adjacent sides are congruent.

Given that

Figure ABCD is a parallelogram

Such that

Side lengths = 5 cm

This means that

The figure is a square

As a general rule

All squares can be classified as rhombus

This is because a rhombus is a quadrilateral with all four sides of equal length and square is a type of rhombus in which all four sides are equal in length

Hence, the true statement is (c)

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On solving the provided question, we can say that - Surface area of the following will be 20 sq unit sq.

A three-dimensional shape's surface area is the total amount of space that surrounds it. Additional distinctions between interface types include: The area that includes the base and curving section is referred to as the gross area. The curved area is the section of the curved portion that is devoid of a base. A plane is a two-dimensional object that occupies space. square units of measurement. The surface area of a three-dimensional object refers to the space it takes up on its outside surface.

Given plane:

\(-\sqrt{20} + 2y + z = 82\\ z = 82 + \sqrt{20} -2y\\\frac{dx}{dy} = \frac{d}{dy}(82 + \sqrt{20} -2y) \\= -2\)

Surface area =

\(\sqrt{1 + (\sqrt{20} )^2 + (-2)^2}\\ \sqrt{(1 + 20 + 2} \\5\)

5 X Area of the Porth

5 X 6

30 unit sq

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The number that belongs in the green box using sine rule is 13.96.

The rule of sine or the sine rule states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.

To calculate the number that belongs in the green box, we use the formula below

Formula:

From the diagram,

Given:

Substitute these values into equation 1

Solve for x

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Answer:

12

Step-by-step explanation:

In four acres there are 3 gardens so you just have to multiply 4x3=12

A total of 7 Cyclists traveled more than 45 miles. 4 cyclists traveled 50 miles or more, and 3 cyclists traveled more than 54 1/4 miles.

A line plot is drawn with the cyclists' names plotted on the x-axis and their corresponding distances covered plotted on the y-axis.

The dots are then joined to form a line, revealing the relationship between the cyclist's names and their corresponding distance traveled. The cyclist names and their corresponding distances are given in the table below.

Name Distance (in miles) Gina 40 1/2 Rey 50 Faye 35 3/4 Mark 60 John 45 1/2 James 40 1/2 Albert 40 1/4 William 54 1/4 Nathan 40 Kate 40 1/4 Mary 60 Risa 40 Abi 35 3/4 Joan 50 1/2 1. The number of cyclists is 14. 2. The longest distance covered by a cyclist is 60 miles.

Mary and Mark both covered this distance.3. A total of 7 cyclists traveled less than 50 miles. 4. The most common distance traveled by cyclists is 40 1/2 miles. Gina, James, and Albert covered this distance. 5. 2 more cyclists traveled 45 miles than 55 1/4 miles. Only William traveled 55 1/4 miles, while John and James both traveled 45 1/2 miles.6.

A total of 7 cyclists traveled more than 45 miles. 4 cyclists traveled 50 miles or more, and 3 cyclists traveled more than 54 1/4 miles.

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Answer:

2

Step-by-step explanation:

-4(2x-7)=12

(2x-7)=12/(-4)

2x-7=-3

2x= -3+7

2x= 4

x= 4/2

x=2

Given data:

The given expression is y= -1/2 (x+4)^2 +3.

The standard expression for the parabola is,

y=x^2

Shift the parabola by 4 units on y-axis.

y=(x^2 +4)

Then multiply with negattive sign, means the parabola is open downward.

y=-(x^2+4)

Mulltiply by 1/2 means the verrtical scale is reduced by 1/2 units.

y= -1/2 (x^2 +4)

Now add 3 units means the parabola shifts 3 units in vertical upward direction.

y= -1/2 (x^2 +4) +3.

The final parabola is open downward, passing (0,1).

Answer:

Jenny is farther from the finish line.

Step-by-step explanation:

If jenny is 8.5 yards away and Tracy is 3.75 yards away, that means that jenny is farther.

The quotient is 32 and the remainder is 6.

i.e,

32 R6

Option A is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

774 ÷ 24

24 ) 774 ( 32

      768

           6

The quotient is 32 and the remainder is 6.

Now,

We can write in this form,

(Quotient) R(remainder)

Thus,

The quotient is 32 and the remainder is 6.

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Answer:

1650

Step-by-step explanation:

66% = 66/100

66/100 times 2500 = 0.66 times 2500 = 1650

There were 1650 students