Find the compound interest and the total amount after eight years if the interest is compounded every two years.
Principal = ₹10,000
Rate of interest = 20%
Total amount = (find)
Total interest = (find)

The null hypothesis is that the average speed of motorists on a highway with a speed limit of 55 mph is equal to 55 mph.Given statement is false.

A statistical hypothesis test is a technique for determining whether the available data are adequate to support a specific hypothesis. We can make probabilistic claims about demographic parameters through hypothesis testing.

The null hypothesis should be a statement of no difference or no effect. In this case, the null hypothesis would be that the average speed of motorists on the highway is equal to 55 mph.

So the correct statement would be:

The null hypothesis is that the average speed of motorists on a highway with a speed limit of 55 mph is equal to 55 mph.

Thus, Given statement is false.

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Answer:

Step-by-step explanation:

only the 1st and 5th statements are true

Answer:

m= 1/14

Step-by-step explanation:

If the slope is perpendicular, the rule say that it must be reciprocal (turned around) and with the opposite sign.

Therefore, if the original slope is -14/1.

It must be changed to positive, and swap numerator and denominator.

m2= 1/14

[tex]\textit{volume of a pyramid}\\\\ V=\cfrac{Lwh}{3} ~~ \begin{cases} L=\stackrel{base's}{length}\\ w=\stackrel{base's}{width}\\ h=height\\[-0.5em] \hrulefill\\ L=6L\\ w=6w \end{cases}\implies V=\cfrac{(6L)(6w)h}{3}\implies \stackrel{ \textit{36 times the volume} }{V=\cfrac{Lwh}{3}(36)}[/tex]

Answer:

D) $28,224.00

Step-by-step explanation:

1st hour: 480 ticket sales

2nd hour: 480 + 40% of 480 = 480 + 0.4 × 480 = 480 + 192 = 672

Total ticket sales in first 2 hours: 480 + 672 = 1152

Ticket price: $24.50

Total sales: 1152 × $24.50 = $28,224

The total amount of paint Aubrey used is more than 1/2 liter but less than 1 liter

To estimate the total amount of paint that Aubrey used for both the mural and the wall, we can add the fractions of paint used

So, we have

Total = 4/7 + 2/10

Evaluate the sum in decimals

This gives

Total = 0.77 (approximated)

This value is between 0.5 liters and 1 liter

Hence, the estimate is between 0.5 liters and 1 liter

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Complete question

Aubrey used 4/7 liter of paint for a mural in her room and 2/10 for a wall in her bathroom.

Determine a reasonable estimate for the total amount of paint Aubrey used

Answer: B or the one that is more than 1/2 but it is less than 1

Step-by-step explanation: Took quiz on khan

Answer:

can you give me the answer to this question sin y minus cos (y + 20), sin theta minus cos theta equals to 0 cos theta equals to sin theta - 10​

Step-by-step explanation:

To solve sin y - cos (y + 20) = 0, we can rearrange it as sin y = cos (y + 20).

Then, we can use the identity sin (90 - x) = cos x to rewrite the right side as cos (y + 20) = sin (70 - y).

Substituting this into the equation, we get sin y = sin (70 - y).

Now, there are two possibilities:

y = 70 - y, which gives y = 35 degrees.

y = 180 - (70 - y), which gives y = 105 degrees.

To solve cos theta = sin theta - 10, we can rearrange it as cos theta - sin theta = -10 and then use the identity cos (x - 90) = sin x to rewrite it as -sin (theta - 90) = -10.

Taking the inverse sine of both

the statement "A Triangle with side lengths 20,21, and 28 is a right triangle" is invalidated.

As, You may simply rule out the first three options if you are familiar with specific Pythagorean triples and other triangle relationships.

Pythagorean triples consist of the three positive numbers a, b, and c, where a2+b2 = c2. The symbols for these triples are (a,b,c). Here, a represents the right-angled triangle's hypotenuse, b its base, and c its perpendicular. The smallest and most important triplets are (3,4,5).

So,

20² +21² = 400 +441 = 841 = 29²

The appropriate choice is  20, 21, and 29

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There are two possible outcomes where a red counter and a vowel are spun: a)red, A and b) red, E.

To see why, we can make a table listing all the possible outcomes of flipping a red or yellow counter and spinning a spinner labeled A-E:

A B C D E

Red A B C D E

Yellow A B C D E

We can then circle the outcomes that satisfy the condition of spinning a red counter and a vowel: red, A and red, E.

Therefore, the selected outcomes are:

red, A

red, E

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D: "[tex]c_{1} = 10[/tex] and [tex]c_{2} = 2[/tex]" are programmer-defined constants for quadratic probing that cannot be used in a quadratic probing equation. Option D is correct answer.

The quadratic probing equation is defined as:

h (k, i) = (h′(k) + [tex]c_{1}[/tex] * i + [tex]c_{2}[/tex] * i^2) mod m,

where h′(k) is the hash value of key

k and m is the size of the hash table.

The constants [tex]c_{1}[/tex] and [tex]c_{2}[/tex] are programmer-defined constants that are used to compute the new hash index when a collision occurs in the hash table.

The given hash function is h(k) = k % 10.

Therefore, the hash value of any key will be between `0` and `9`.Now, let's check which of the given programmer-defined constants for quadratic probing cannot be used in a quadratic probing equation:

Option A: `c1 = 1 and c2 = 0`This option can be used in the quadratic probing equation. It means that linear probing is being used.

Option B: [tex]c_1 = 5[/tex] and [tex]c_2 = 1[/tex] This option can be used in the quadratic probing equation. It means that the new index is being computed as `h(k, i) = (h′(k) + 5i + i^2) mod m`.

Option C: [tex]c_1 = 1[/tex] and [tex]c_2 = 5[/tex] This option can be used in the quadratic probing equation. It means that the new index is being computed as `h(k, i) = (h′(k) + i + 5i^2) mod m`.

Option D: [tex]c_1 = 10[/tex] and [tex]c_2 = 2[/tex] This option cannot be used in the quadratic probing equation. It means that the new index is being computed as `h(k, i) = (h′(k) + 10i + 2i^2) mod m`.

Since [tex]c_{1}[/tex] is greater than or equal to `m`, this equation will always result in a hash index that is greater than or equal to `m`. Therefore, it is not possible to use `[tex]c_{1}[/tex]= 10` in the quadratic probing equation. Hence, the correct option is D.

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Answer:

103

Step-by-step explanation:

57° + 46° =103°

This shows that the third angle in the triangle is 180°-103°=77°

Therefore the largest exterior angle is 180°-77°=103°

Answer:

The perimeter of the shape is 53km.

Answer : 53km

Step-by-step explanation: To find the perimeter you need to add all the sides so 8+18+18+9=53 and dont forget the unit km! Have a great day! And good luck!

The classification of student class designation (freshman, sophomore, junior, senior) is an example of a categorical random variable.  The correct option is A.

A random variable is a numerical or categorical quantity whose value is unknown but whose behavior can be forecast based on data that has been measured or observed. Random variables are typically used to represent quantities that fluctuate over time or are subject to chance occurrences.

The types of random variables are as follows:

i) Categorical random variable: This type of variable contains categorical data or data that are descriptive in nature. It is used to classify items or events into categories, which can be named or identified. For example, a set of data that includes categories like gender, eye color, or country of origin.

ii) Discrete random variable: This type of variable takes on discrete values, which means it can only take on whole numbers. For example, the number of cars sold at a dealership on any given day is a discrete random variable because it can only take on integer values.

iii) Continuous random variable: This type of variable takes on continuous values, which means it can take on any value within a given range. For example, the temperature in a room can take on any value between a certain minimum and maximum value.

Therefore, the correct option is A.

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Answer:

the value of x is approximately 0.382 cm.

Step-by-step explanation:

The upper bound for the rate at which the water could have flowed into lake is 8.2 liters per second.

An upper limit is a value that is larger than or equal to all the values in a set. In mathematics, it is used to specify a cap or a maximum value for a collection of data. For instance, an upper bound is frequently employed in optimization issues to place a cap on the highest value that a function or variable may take. Upper limits are used in statistics to specify a data set's maximum range which may be used to spot outliers or other abnormalities in the data. In calculus, upper bounds are used to specify a sequence's or series' limit, or the highest number that it may possibly approach.

Given that, 400 liters of water flowed into the lake in 1 minute.

The upper bound of water flow will be the maximum amount of water.

For the nearest measures taken by Grace the amount of water needs to ne more than 400, while the time must be less than 10 seconds from the recorded 1 min.

That is time must be 60 - 10 = 50 seconds.

Approximating the values we have:

410/50 = 8.2 liters per second.

Hence, the upper bound for the rate at which the water could have flowed into lake is 8.2 liters per second.

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Answer:

Step-by-step explanation:

Let P be the point C with position vector 2i + 3j and Q be the point D with position vector 7i + 5j. We want to find the position vector of point H which divides PQ in the ratio 2:3.

Let the position vector of point H be r. Then we have:

PH/PQ = 2/3

(P - r)/(Q - r) = 2/3

Multiplying both sides by (Q - r), we get:

P - r = (2/3)(Q - r)

Expanding the brackets and rearranging, we get:

r = (2Q + 3P)/5

Substituting the position vectors of P and Q, we get:

r = (2(7i + 5j) + 3(2i + 3j))/5

= (14i + 10j + 6i + 9j)/5

= (20i + 19j)/5

= 4i + 3.8j

Therefore, the position vector of point H is 4i + 3.8j.

Step-by-step explanation:

You are given miles ( 546) and gallons (14)  and you

   want miles / gal     this is just     546 miles / 14 gallons  = 39  mpg

Answer:

39

Step-by-step explanation:

14 is the main number here.

assuming 1 tank = 14gallons. / 546 miles

a = gallons

b = miles

b / a = mpg (miles per gallon)

so: 546 / 14 = 39

Answer:

25 computers per hour

Step-by-step explanation:

look ate the point 2 hours corresponding to 50 computers

50/2 = 25/1 or 25 computers per hour

Most correlational studies use d)relative data, which compares two variables.

This means that one variable is being measured against another, often in the form of ratios or percentages. For example, one might compare the number of people who smoke cigarettes with the number of people who develop lung cancer, in order to determine whether there is a correlation between the two.

Relative data allows researchers to examine the relationship between variables, allowing them to assess the strength of the relationship between them.

In order to compare variables, correlational studies rely on either primary or secondary data. Primary data is collected through direct observation and experimentation, while secondary data is obtained from existing sources.

In most cases, correlational studies use secondary data, such as survey results or statistics from public databases. This data is often in the form of relative data, such as percentages or ratios.

By using relative data, correlational studies can determine the strength of the relationship between two variables. This information can be used to better understand how the variables are related, as well as to draw conclusions about their relationship. For example, the relationship between smoking and lung cancer can be examined using relative data, allowing researchers to identify patterns and draw conclusions about the correlation between the two variables.

Hence Option D is correct.

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Answer:

b = [tex]\frac{S-2la}{h+l}[/tex]

Step-by-step explanation:

S = bh + lb + 2la ( reversing the equation )

bh + lb + 2la = S ( subtract 2la from both sides )

bh + lb = S - 2la ← factor out b from each term on the left side

b(h + l) = S - 2la ← divide both sides by (h + l)

b = [tex]\frac{S-2la}{h+l}[/tex]

Answer: 36% passed the science test, while 25% passed the history test.

In order to find a percentage we divide our two know numbers

Science Class- 9/25 is a fraction with / standing for divided by. 9 divided by 25 is .36   This means 36% of the class passed the science test.

History Class- 4/16 is a fraction with / standing for divided by. 4 divided by 16 is .25   This means 25% of the class passed the science test.

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

Answer:

D

Step-by-step explanation:

sub y into the 2nd equation and find x

Lin's statement is correct. The incorrect answer is obtained due to inaccurate calculations of the new area of triangle.

A geometric modification called a dilation alters a figure's size. Each coordinate in the graphic is multiplied by a preset scale factor k to obtain it. The same element causes the figure to be stretched or contracted in all directions, creating a new figure that resembles the original but is smaller. Both two-dimensional (2D) and three-dimensional (3D) dilations are possible (3D). They are frequently employed in geometry to generate analogous figures and compute scale factors.

Mai's statement is incorrect. When a triangle is dilated by a factor of k, its area is multiplied by k².

When the given area of 100 square inches is dilated by a factor of 0.25 the new area is 6.25.

Hence, Lin's statement is correct. The incorrect answer is obtained due to inaccurate calculations of the new area.

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The number of toy soldiers Leo has is 48.

To solve this problem, we need to find a number that satisfies the three given conditions:

The number is between 27 and 54.

When the number is divided by 4, there is no remainder.

When the number is divided by 7, the remainder is 6.

When the number is divided by 5, the remainder is 3.

Let's start by finding a number that satisfies the first two conditions. We can do this by listing the multiples of 4 between 27 and 54:

28, 32, 36, 40, 44, 48, 52

Next, we need to find which of these numbers also satisfies the third condition, that is, leaves a remainder of 6 when divided by 7. We can go through each of these numbers and check:

28 divided by 7 leaves a remainder of 0.

32 divided by 7 leaves a remainder of 4.

36 divided by 7 leaves a remainder of 1.

40 divided by 7 leaves a remainder of 5.

44 divided by 7 leaves a remainder of 2.

48 divided by 7 leaves a remainder of 6.

52 divided by 7 leaves a remainder of 3.

So, the only number that satisfies the first three conditions is 48.

Finally, we need to check if 48 also satisfies the fourth condition, that is, leaves a remainder of 3 when divided by 5. Indeed, 48 divided by 5 leaves a remainder of 3.

Therefore, the number of toy soldiers Leo has is 48.

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In the following question, among the conditions given, the statement is said to be, the exact molarity of the NaOH solution is 0.0960 M.

The question is asking to calculate the exact molarity of the sodium hydroxide from Experiment 1.
KHP stands for potassium hydrogen phthalate, and one mole of sodium hydroxide (NaOH) will neutralize one mole of KHP. To solve the problem, use the mass of KHP and a stoichiometry problem.
First, calculate the number of moles of KHP:
Moles KHP = (Mass KHP (g) / Molar Mass KHP (g/mol))
Then, calculate the moles of NaOH:
Moles NaOH = (Moles KHP * Mole Ratio NaOH/KHP)
Finally, calculate the molarity of NaOH:
Molarity NaOH = (Moles NaOH / Volume NaOH (L))

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Hence, the cost of fencing the garden is ₹9485. Hence, the cost of plowing the garden is ₹756.

Perimeter is the total distance around the outside of a closed two-dimensional shape. It is the sum of the lengths of all the sides of the shape. For example, the perimeter of a rectangle is found by adding the lengths of all its four sides, whereas the perimeter of a circle is found by multiplying the diameter by π (pi). Perimeter is usually expressed in units of length, such as meters, centimeters, feet, or inches.

Here,

The perimeter of the rectangular garden is twice the sum of its length and width. So, the length of the fence needed to enclose the garden is:

2 × (length + width) = 2 × (175 m + 96 m) = 542 m

Therefore, the cost of fencing the garden at 17.50 per meter is:

Cost of fencing = length of fence × cost per meter

= 542 m × 17.50

= 9485

Hence, the cost of fencing the garden is ₹9485.

To find the cost of plowing the garden, we need to first calculate its area, which is given by:

Area = length × width

= 175 m × 96 m

= 16800 m²

Therefore, the cost of plowing the garden at 4.50 paise per square meter is:

Cost of plowing = area of garden × cost per square meter

= 16800 m² × 0.045

= 756

Hence, the cost of plowing the garden is ₹756.

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Total number of seats that remain unsold are 168.

What is statistics?

The branch of mathematics dealing with data collection, organization, analysis, interpretation and presentation.

Let's start by defining some variables to represent the unknowns in the problem:

From the problem, we know that:

We also know that the total revenue collected is $34,650:

27x + 45y = 34650

Now we can substitute y = 0.5x from the second equation into the third equation and simplify:

27x + 45(0.5x) = 34650

27x + 22.5x = 34650

49.5x = 34650

x = 700

So there were 700 $30-seats and 350 $50-seats.

The number of sold $30-seats is 0.9(30x) = 567, and the number of sold $50-seats is 0.9(50y) = 315.

Therefore, the total number of seats sold is 882, and the number of unsold seats is:

1050 - 882 = 168

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He mean salary at a local industrial plant is $27,600 with a standard deviation of $5400 . the median salary is $25,200 and the 61st percentile is $29,100, The amount Tom earns (in dollars) is $31,590.

Given that, the mean salary at a local industrial plant is $27,600The standard deviation of salary is $5400The median salary is $25,200The 61st percentile is $29,100We have to find the amount that Tom earns (in dollars) if Tom's salary has a z-score of 0.7.

We need to calculate the z-score using the formula,[tex]Z = (X - \mu) / \sigma[/tex], where X is the value, μ is the mean and σ is the standard deviation. [tex]z = (X - \mu) / \sigma 0.7 = (X - 27,600) / 5,400[/tex] Multiplying both sides by 5,400, we get,0.7 × 5,400 = X - 27,600 Add 27,600 on both sides, we get, [tex]X = (0.7 * 5,400) + 27,600= 3,780 + 27,600= $31,590[/tex] Therefore, The amount Tom earns (in dollars) is $31,590.

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The height of water in the tank in feet after t seconds can be expressed as h(t) = H - (Aw/Ah) 2gh t2, where Aw and Ah are the cross-sectional areas of the water and the hole in square feet respectively,

and g is the gravitational acceleration (32 ft/s2). The interval of definition for h(t) is 0 ≤ t ≤ H/2gh.

The graph of h(t) is a parabola with its vertex at (H/2gh, H) and is symmetric about the line t = H/2gh. It starts at (0, H) and gradually decreases to (H/2gh, 0).

Given the tank is 11 ft high, has radius 2 ft and the circular hole has radius in, and it is initially full, the time it will take to empty can be calculated as: t = √(2H/gAh) = √(22/(32 x π(0.52))) = 3.87 seconds. Therefore, it will take approximately 3.87 seconds to empty.

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