Which numbers have a digit in the ones place that is 1/10 the value of the digit in the tens place? select all that apply
a. 6,044.7
b 6,339.99
c. 8,101.13
d. 8,066.51
e. 9,777.1​

Answer:

a) 99% of the sample means will fall between 0.933 and 0.941.

b) By the Central Limit Theorem, approximately normal, with mean 0.937 and standard deviation 0.0015.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

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 zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

(a) If the true mean is 0.9370 with a standard deviation of 0.0090 within what interval will 99% of the sample means fail?

Samples of 34 means that \(n = 34\)

We have that \(\mu = 0.937, \sigma = 0.009\)

By the Central Limit Theorem, \(s = \frac{0.009}{\sqrt{34}} = 0.0015\)

Within what interval will 99% of the sample means fail?

Between the (100-99)/2 = 0.5th percentile and the (100+99)/2 = 99.5th percentile.

0.5th percentile:

X when Z has a pvalue of 0.005. So X when Z = -2.575.

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

By the Central Limit Theorem

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

\(-2.575 = \frac{X - 0.937}{0.0015}\)

\(X - 0.937 = -2.575*0.0015\)

\(X = 0.933\)

99.5th percentile:

X when Z has a pvalue of 0.995. So X when Z = 2.575.

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

\(2.575 = \frac{X - 0.937}{0.0015}\)

\(X - 0.937 = 2.575*0.0015\)

\(X = 0.941\)

99% of the sample means will fall between 0.933 and 0.941.

(b) If the true mean 0.9370 with a standard deviation of 0.0090, what is the sampling distribution of ¯X?

By the Central Limit Theorem, approximately normal, with mean 0.937 and standard deviation 0.0015.

Answer:

AC = 28

Step-by-step explanation:

Ok, we know that:

Points A, B, and C are collinear.

Point B is between A and C.

We want to find the length AC (distance between A and C), if we know that:

AB = 16

BC = 12

Ok, knowing that B is between the other points, we know that:

AB + BC

defines the total length of the segment that connects the 3 points.

Thus, if we define this segment as a length, we only use the endpoints, A and C.

Then we have that:

AB + BC = AC

now we can solve this:

16 + 12 = AC

28 = AC

Answer: x= 2/5, 20

Step-by-step explanation:

5x+8=10

1. subtract 8 on both sides

   5x = 2

2. divide 5 on both sides

    x  = 2/5

10x+16

x = 2/5

1. substiuite x for 2/5

10 times 2/5 +16

4 + 16

= 20

The side length of 6 units for the intermediate large square and 4 units for the smallest square, give the area of the shaded region as 32 square unites.

The area of a shape or figure is the two dimensional space occupied by the boundary line of the shape.

Please find attached a possible drawing of the figure in the question created with MS Word

From the drawing, we have;

Side length of the ;large square containing the other squares = 6 + 4 = 10

Area of the largest square, A₁ = 10 × 10 = 100

Side length of the second largest square = 6

Area of the second largest square, A₂ = 6 × 6 = 36

Side length of the two small squares = 4

Area of the two small squares, A₃ = 4 × 4 = 16

Therefore;

Area of the shaded region = A₁ - A₂ - 2·A₃

Which gives;

Area of the shaded region = 100 - 36 - 2×16 = 32

The area of the shaded region is 32

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Answer: \(5\sqrt 5\)

Step-by-step explanation:

Sol \(\sqrt 125\) = \(\sqrt{25.5}\)

= \(\sqrt{25}\)  x  \(\sqrt{5}\)

\(5 \sqrt{5}\)

The capacity of the tank is 7234.56litres

Capacity refers to the amount of fluid a container can hold. It expressed in units like litres (l), millilitres (ml). Capacity is also known as volume of a substance.

The capacity of the cylindrical pipe is

V = πr²h

r = 8cm

if it takes the pipe 2m per second

then it's volume in one second is

V = 3.14 ×8 × 2× 100

V = 5024cm³/s

if it takes 24 minutes

24 minutes = 24 × 60 s

= 1440s

therefore volume of the tank = 1440 × 5024

= 7234560cm³

in litres = 7234560/1000

= 7234.56litres

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The correct equation of the circle with center (0,0) that passes through the point (-6,-6) is:

(x + 6)² + (y + 6)² = 72

Please note that the equation represents the circle with center (0,0) and radius √72.\(\)

Answer:

The equation of a circle with center (0,0) that passes through the point (-6,-6) is:

(x - 0)² + (y - 0)² = r²

where r is the radius of the circle. Since the center of the circle is (0,0), we can use the distance formula to find the radius:

r = √(0 - (-6))² + (0 - (-6))² = √(6² + 6²) = √72

Therefore, the equation of the circle is:

x² + y² = 72

Answer:

28. B

29. D

30. A

Step-by-step explanation:

28.

2 5/8 yd × 5/6 yd =

= 21/8 × 5/6 yd²

= 105/48 yd²

= 35/16 yd²

= 2 3/16 yd²

Answer: B

29.

2641 becomes 6241.

In 6241, the 6 is in the thousands place.

6 × 1000 = 6000

Answer: D

30.

90 + 7 × (7 - 1) =

Use the correct order of operations.

= 90 + 7 × 6

= 90 + 42

= 132

Answer: A

Using double angle identity, we are able to prove tan(x)(1 + cos(2x)) = sin(2x).

To prove the identity tan(x)(1 + cos(2x)) = sin(2x), we can start by using trigonometric identities to simplify both sides of the equation.

Starting with the left-hand side (LHS):

tan(x)(1 + cos(2x))

We know that tan(x) = sin(x) / cos(x) and that cos(2x) = cos²(x) - sin²(x). Substituting these values, we get:

LHS = (sin(x) / cos(x))(1 + cos²(x) - sin²(x))

Next, we can simplify the expression by expanding and combining like terms:

LHS = sin(x) / cos(x) + sin(x)cos²(x) / cos(x) - sin³(x) / cos(x)

Simplifying further:

LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)

Now, let's work on the right-hand side (RHS):

sin(2x)

Using the double angle identity for sine, sin(2x) = 2sin(x)cos(x).

Now, let's compare the LHS and RHS expressions:

LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)

RHS = 2sin(x)cos(x)

To prove the identity, we need to show that the LHS expression is equal to the RHS expression. We can combine the terms on the LHS to get a common denominator:

LHS = [sin(x) - sin³(x) + sin(x)cos²(x)] / cos(x)

Now, using the identity sin²(x) = 1 - cos²(x), we can rewrite the numerator:

LHS = [sin(x) - sin³(x) + sin(x)(1 - sin²(x))] / cos(x)

    = [sin(x) - sin³(x) + sin(x) - sin³(x)] / cos(x)

    = 2sin(x) - 2sin³(x) / cos(x)

Now, using the identity 2sin(x) = sin(2x), we can simplify further:

LHS = sin(2x) - 2sin³(x) / cos(x)

Comparing this with the RHS expression, we see that LHS = RHS, proving the identity.

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We can iterate through a list using two nested loops to check for pairs that add up to the target.

The formula for finding pairs that add up to the target is as follows:

For each element (x) in the list, loop through the rest of the list (y) and check if x + y = target

Let's say we have a list of numbers [1,2,3,4] and the target is 5.

We will start by checking if 1 + 4 = 5. Since it does, we have found our first pair.

Then, we will move on to 2 + 3 = 5. This is also true, which gives us our second pair.

We have now looped through the entire list and found all pairs that add up .

By using a formula and calculation, we can iterate through a list using two nested loops to check for pairs that add up to the target.

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The adjusted balance, considering the new account balance, payments/credits, new purchases, and finance charge, is $489.61.

To calculate the adjusted balance, we need to consider the new account balance, payments/credits, new purchases, and finance charges.

Starting with the new account balance of $435.92, we subtract the payments/credits of $68.50. This represents the amount that has been paid or credited to the account, reducing the balance.

Next, we add the new purchases of $118.49. These are additional charges made to the account, increasing the balance.

Finally, we add the finance charge of $3.70. This charge is typically applied as interest on the outstanding balance.

To calculate the adjusted balance, we can follow these steps:

Start with the new account balance: $435.92

Subtract the payments/credits: $435.92 - $68.50 = $367.42

Add the new purchases: $367.42 + $118.49 = $485.91

Add the finance charge: $485.91 + $3.70 = $489.61

Therefore, the amount of the adjusted balance is $489.61.

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The solution to the system of linear equations by substitution is (1, 5)

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

-3x+y=2

-x+y-4=0

Rewrite as

-3x + y = 2

-x + y - 4 = 0

Make y the subject in -x + y - 4 = 0

So, we have

y = x + 4

Substitute y = x + 4 in -3x + y = 2

-3x + x + 4 = 2

Evaluate the like terms

-2x = -2

So, we have

x = 1

Substitute x = 1 in y = x + 4

y = 1 + 4

Evaluate

y = 5

Hence, the solution is  x = 1 and y = 5

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9514 1404 393

Answer:

  d)  x = 3

Step-by-step explanation:

The given equation resolves to a quartic equation in (3^x). It has a solution near ...

  x = 0.541770946714

__

Perhaps you want the solution to ...

  3^(x+9) = 81^(x)

Rewriting in powers of 3, this is ...

  3^(x+9) = (3^4)^x = 3^(4x)

Taking logarithms base 3 gives ...

  x +9 = 4x

  9 = 3x . . . . . . subtract x

  3 = x . . . . . . . divide by 3 . . . . matches choice D

_____

Additional comment

The Order of Operations requires that exponential terms be evaluated before addition and subtraction. That means (3^x) must be evaluated before the sum (3^x) + 9. If you want the sum of x and 9 to be evaluated first, it must be in parentheses: 3^(x+9).

In typeset equations, the superscript font serves to group parts of the exponent. In plain text, a grouping symbol (parentheses) must be used.

Answer:

15%

Step-by-step explanation:

Convert this into 12/80, and we can convert THAT into a percentage, which would be 15%.

Please give brainliest.

The figure shown can be divided into three rectangles , the two yellow ones and the blue one.

As the width of the yellow triangles is 1 unit and the length of the entire shape is 8 units , it can be calculated that the length of the blue triangle is 6 units ( as shown in second picture )

\(\therefore \: area \: of \: figure \: = \: area \: of \: two \: yellow \: triangles \: \times area \: of \: blue \: triangle\)

\(area \: of \: figure \: = 2( \: l \times b \: ) + ( \: l' \times b' \: ) \\ \dashrightarrow \: area \: = 2(5 \times 1) + (6 \times 1) \\ \dashrightarrow \: area = 10 + 6 \\ \dashrightarrow \: \boxed{area \: = 16 \: {units}^{2} }\)

hope helpful! :)

Answer:

the slope intercept form is   y = (1/2)x - 1

Step-by-step explanation:

The slope-intercept form is, y = mx + b

We see from looking at the graph that,

at x = 0, y = -1

So, from this we find that b = -1

at x = 2, y = 0,

now, we find the slope m,

using,

\(m = \frac{y_{2} -y_1}{x_2-x_1}\)

Using x_2 = 2, y_2 = 0,

x_1 = 0, y_1 = -1, we get,

m = (0-(-1))/(2-0)

m = 1/2

So, the slope intercept form is,

y = (1/2)x - 1

Given the triangles NSQ and NPQ, you need to remember that two triangles are congruent if their corresponding sides are equal and if their corresponding angles have the same measure.

In this case, you can identify that:

- Sides NS and PQ have the same indicator mark. That indicates that they are equal.

- Angles S and P have the same indicator mark. That indicates that they have the same measure.

- Both triangles have the side NQ in common.

According to one of the Congruence Theorems for Triangles called Side-Angle-Side (SAS), if the included angle and the two included sides of two triangles are equal, the triangles are congruent.

In this case, you know that both sides have two equal corresponding sides. But since the angle is not formed by the included sides that are equal, you cannot apply the SAS rule to prove they are congruent. You do not have enough data to prove they are congruent.

Hence, the answer is: These triangles cannot be proven congruent.

If you have any specific questions or need assistance, feel free to ask, and I'll do my best to provide a helpful response within the scope of my training

As an AI language model my understanding of subjects and skills is based on the information and data available to me up until my last training update in September 2021. I can provide accurate and comprehensive responses within the limits of my training, but please keep in mind that I may not have knowledge of events or developments that have occurred after that cutoff date.

With a wide range of general knowledge, I can understand and generate responses on various topics such as science, history, literature, mathematics, and more. I can also assist with specific skills like writing, editing, brainstorming ideas, offering explanations, and providing recommendations.

However, it's important to note that while I strive to be helpful, I am still an AI and may not always provide perfect answers. I do not possess personal experiences or opinions, and I am not able to perform physical actions. My responses are generated based on patterns and examples from my training data.

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.

Answer:

d = 3.2

Step-by-step explanation:

1 * 3.2 = 3.2

Hence,

d = 3.2

Answer:

the correct answer is -1/16 i believe

The dimensions of the room are approximately 5.87 meters by 7.63 meters.

Let's assume the width of the room is "x" meters.

According to the problem, the length of the room is 1.3 times the width, so the length would be 1.3x meters.

The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 27 meters.

Perimeter = 2(length + width)

Substituting the values we know:

27 = 2(1.3x + x)

Simplifying:

27 = 2(2.3x)

27 = 4.6x

Dividing both sides by 4.6:

x = 27 / 4.6

x ≈ 5.87

The width of the room is approximately 5.87 meters.

To find the length, we can multiply the width by 1.3:

Length = 1.3 * 5.87 ≈ 7.63

The length of the room is approximately 7.63 meters.

Therefore, the dimensions of the room are approximately 5.87 meters by 7.63 meters.

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Answer:

The answer is below

Step-by-step explanation:

The complete question is:

In 1960​, there were 237,794 immigrants admitted to a country. In 2001, the number was 1,150,729.

a. Assuming that the change in immigration is​ linear, write an equation expressing the number of​ immigrants, y, in terms of​ t, the number of years after 1900.

b. Use your result in part a to predict the number of immigrants admitted to the country in 2013.

c. Considering the value of the​ y-intercept in your answer to part a​, discuss the validity of using this equation to model the number of immigrants throughout the entire 20th century.

Answer:

a) From the question, we can get two ordered pairs which are \((t_1,y_1)=(60,237794)\ and\ (t_2,y_2)=(101,1150729)\)

Using the equation of a line given two points:

\(y-y_1=\frac{y_2-y_1}{t_2-t_1}(t-t_1)\\ \\y-237794=\frac{1150729-237794}{101-60}( t-60)\\\\y-237797=22266.71(t-60)\\\\y=22266.71t-1098205.44\)

b) In 2013, t = 2013 - 1900 = 113.

Hence:

\(y=22266.71t-1098205.44\\\\y=22266.71(113)-1098205.44\\\\y=1417932.488\\\\y=1417933\)

c)

\(y=22266.71t-1098205.44\\\\the\ y\ intercept\ is\ at\ t=0,hence:\\\\y=22266.71(0)-1098205.44\\\\y=-1098205.44\)

Since the y intercept is negative, that is in 1900 the number of immigrants was -1098206 which can not be possible. Hence this equation is not valid and the growth may or may not be linear.

Answer:

7 grams

Step-by-step explanation:

cause 1 gram is 1000 milligrams and therefore 7 grams is more than 6,999 nilligrams

Answer:

63/3 m/7

Step-by-step explanation:

i dont have time to exlplain lol just trust

Answer:is this actually a question!

Step-by-step explanation:

Answer:

Between 82.2 and 90

Between 90 and 97.8

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 90

Standard deviation = 7.8.

According to the Empirical Rule, 34% of test scores fall into what range?

68% of the measures are within 1 standard deviation of the mean.

The normal distribution is symmetric, which means that 68/2 = 34% fall between one standard deviation of the mean and the mean and 34% fall within the mean and one standard deviation above the mean.

90 - 7.8 = 82.2

90 + 7.8 = 97.8

34% between 82.2 and 90

34% between 90 and 97.8

So the correct options are:

Between 82.2 and 90

Between 90 and 97.8

Answer:

(a)

\(3b + 4g =10.25\)

\(2b + 2g = 5.50\)

(b)

1 pound of banana = $0.75

1 pound of grape = $2.00

Step-by-step explanation:

Given

Represent banana with b and grapes with g.

From the first statement, we have:

\(3b + 4g =10.25\)

From the second, we have:

\(2b + 2g = 5.50\)

Solving (a): The equations

This has been solved above.

The equations are:

\(3b + 4g =10.25\)

\(2b + 2g = 5.50\)

Solving (b):

\(3b + 4g =10.25\) --- (1)

\(2b + 2g = 5.50\) --- (2)

Multiply (2) by 2

\(2b + 2g = 5.50\) * 2

\(4b + 4g = 11\) ----- (3)

Subtract (3) from (1)

\(3b - 4b + 4g - 4g = 10.25 - 11\)

\(-b =-0.75\)

\(b =0.75\)

Substitute 0.75 for b in (2)

\(2b + 2g = 5.50\)

\(2 *0.75 + 2g = 5.5\)

\(1.5 + 2g = 5.5\)

Collect Like Terms

\(2g = 5.5 - 1.5\)

\(2g = 4\)

\(g = 2\)

Answer:

1 5/7

Step-by-step explanation:

Divide using long division. The whole number portion will be the number of times the denominator of the original fraction divides evenly into the numerator of the original fraction, and the fraction portion of the mixed number will be the remainder of the original fraction division over the denominator of the original fraction.

Answer:

\( \frac{12}{7} = 1 \frac{5}{7} \)