If you flipped a coin 50 times, would the probability of getting exactly 25 heads be higher or lower than flipping a coin 6 times and getting exactly 3 heads? Why?

Answer:

The probability that the mean of this sample is less than 16.1 ounces of beverage is 0.0537.

Step-by-step explanation:

We are given that the average amount of a beverage in randomly selected 16-ounce beverage can is 16.18 ounces with a standard deviation of 0.4 ounces.

A random sample of sixty-five 16-ounce beverage cans are selected

Let \(\bar X\) = sample mean amount of a beverage

The z-score probability distribution for the sample mean is given by;

                          Z  =  \(\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }\)  ~ N(0,1)

where, \(\mu\) = population mean amount of a beverage = 16.18 ounces

           \(\sigma\) = standard deviation = 0.4 ounces

           n = sample of 16-ounce beverage cans = 65

Now, the probability that the mean of this sample is less than 16.1 ounces of beverage is given by = P(\(\bar X\) < 16.1 ounces)

   P(\(\bar X\) < 16.1 ounces) = P( \(\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }\) < \(\frac{16.1-16.18}{\frac{0.4}{\sqrt{65} } }\) ) = P(Z < -1.61) = 1 - P(Z \(\leq\) 1.61)

                                                    = 1 - 0.9463 = 0.0537

The above probability is calculated by looking at the value of x = 1.61 in the z table which has an area of 0.9591.

1. parallel lines 2(c) . perpendicular lines intersect(D)  3. skew lines(A)  4. parallel planes (B) and 5. line perpendicular to a plane(E) these are the key word.

The key words with their definitions are:

1. Parallel lines (C): Two lines that lie in the same plane and do not intersect.

2. Perpendicular lines (D): Two lines that intersect to form a right angle.

3. Skew lines (A): Two lines that do not lie in the same plane and do not intersect.

4. Parallel planes (B): Two planes that do not intersect.

5. Line perpendicular to a plane (E): A line that intersects a plane in a point, and is perpendicular to every line in the

plane that intersects it.

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Is the function above continuous: B. not continuous at x = 0.

In Mathematics and Geometry, a continuous function can be defined as a type of function in which there is no discontinuities or breaks between the intervals for the points plotted on a graph.

In Mathematics and Geometry, a discrete function can be defined as a type of function in which the ordered pair of values on the x-axis and y-axis are separate from each other and unconnected.

By critically observing the graph shown above, we can reasonably infer and logically conclude that it represents a discrete function because it is not continuous at x is equal to 0 i.e x = 0.

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Answer:

10 ; 10

Step-by-step explanation:

( 1 , 0 )

( 5 , 40 )

m = \(\frac{40-0}{5-1}\) = 10

y = 10x - 10

( 2 , 10 )

( 10 , 90 )

The length of the diagonal of the box is approximately 31 units.

Diagonal, d, = √(length² + width² + height²)

Given:

RV=29

RS = 21

RT= 24

Thus:

length of the box = ST = ?

Use Pythagorean Theorem to find ST:

ST = √(RT² - RS²)

Substitute

ST = √(24² - 21²)

ST = 12

Height of the box = SV = ?

Use Pythagorean Theorem to find SV:

SV = √(RV² - RS²)

Substitute

SV = √(29² - 21²)

SV = 20

Find the diagonal of the box, RU:

RU = √(ST² + RS² + SV²)

Substitute

RU = √(12² + 21² + 20²)

RU = 31 units.

Therefore, the length of the diagonal of the box is approximately 31 units.

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Answer:

can you be more specific?

Step-by-step explanation:

Two years ago, an investment of R1 500000 has increased to R1 700000 and has delivered R40 000 worth of dividends over the two years. Then the return on investment would be 16%.

We can use the following formula to calculate ROI:

ROI = (gain from investment - cost of investment) / cost of investment

where, gain from investment is the total value of the investment (including dividends), and cost of investment is the initial investment.

Using the values given in the question, we can calculate the ROI as:

ROI = ((R1,700,000 + R40,000) - R1,500,000) / R1,500,000 = R240,000 / R1,500,000

ROI = 0.16 or 16%

Therefore, the return on the investment is 16%.

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The mean should be calculated for data sets A, B, C, and D.

It is useful to take into account the nature of the data and any potential outliers when deciding whether to choose the mean or the median as the measure of center in a data set.

When the data is symmetrically distributed with no major outliers, the mean is usually a better choice. It affects extreme values and gives an indication of the average value.

The median, on the other hand, is often preferred when the data is skewed or contains outliers. It represents the middle value when the data is ordered, and it is less affected by extreme values.

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Answer:

x = 45

y = 5

Step-by-step explanation:

it is because

90/2 = 45

(90+10)/20

(100)/20 = ,5

Answer:

9576

Step-by-step explanation:

Area of the triangle × height

(1/2×28×19)×36

The difference (Dogs – Cats) in the sample proportions of those that get their teeth cleaned typically varies about 0.054 from the true difference in proportions.

The third option is correct.

What is the standard deviation?

Standard deviation is a statistical measure of the spread of a dataset, defined as the square root of its variance. It is a way to quantify the amount of variation or dispersion of a set of data values.

Percentage of Dogs getting their teeth cleaned = 48% = pD

Percentage of Cats getting their teeth cleaned = 35% = pC

Number of Dogs selected = nD = 25

Number of Cats selected = nc = 32

As the sample sizes are large enough, we can apply Central Limit Theorem

According to Central Limit Theorem for proportions –

pD-hat ~ Normal(pD, {pD*(1-pD)}/nD)

Thus, pD-hat ~ Normal(0.48, 0.009984)

Similarly,

pC-hat ~ Normal(pC, {pC*(1-pC)}/nC)

Thus, pC-hat ~ Normal(0.35, 0.0071094)

Now if X ~ N(E(X), Var(X)) and Y ~ N(E(Y), Var(Y))

then X -Y ~ N(E(X)-E(Y), Var(X)-Var(Y)) (If X and Y are Independent)

Thus,

pD-hat - pC-hat ~ Normal(0.48-0.35, 0.009984 – 0.0071094)

pD-hat - pC-hat ~ Normal(0.13, 0.0028746)

Thus, Standard Deviation of pD-hat - pC-hat = (0.0028746^0.5) = 0.0536 that is 0.054 approximately

Hence, the difference (Dogs – Cats) in the sample proportions of those that get their teeth cleaned typically varies about 0.054 from the true difference in proportions.

Third Option is correct.

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\( \sf \longrightarrow \: 5 \bigg( \: n - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{n}{1} - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10 \times n - 1 \times 1}{1 \times 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10n - 1}{ 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: \frac{50n - 5}{ 10} = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =1(10) \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =10 \\ \)

\( \sf \longrightarrow \: \: 100n - 10=10 \\ \)

\( \sf \longrightarrow \: \: 100n =10 + 10\\ \)

\( \sf \longrightarrow \: \: 100n =20\\ \)

\( \sf \longrightarrow \: \:n = \frac{2 \cancel{0}}{10 \cancel{0}} \\ \)

\( \sf \longrightarrow \: \:n = \frac{1}{5} \\ \)

Answer:-

To solve the equation \(\sf 5(n - \frac{1}{10}) = \frac{1}{2} \\\) for \(\sf n \\\), we can follow these steps:

Step 1: Distribute the 5 on the left side:

\(\sf 5n - \frac{1}{2} = \frac{1}{2} \\\)

Step 2: Add \(\sf \frac{1}{2} \\\) to both sides of the equation:

\(\sf 5n = \frac{1}{2} + \frac{1}{2} \\\)

\(\sf 5n = 1 \\\)

Step 3: Divide both sides of the equation by 5 to isolate \(\sf n \\\):

\(\sf \frac{5n}{5} = \frac{1}{5} \\\)

\(\sf n = \frac{1}{5} \\\)

Therefore, the solution to the equation \(\sf 5(n - \frac{1}{10})\ = \frac{1}{2} \\\) is \(\sf n = \frac{1}{5} \\\), which corresponds to option (d).

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♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

multiply by any number to create a multiple

Step-by-step explanation:

4/5 = 8/10 = 12/15 = 16/20...

Answer:

19/20

Step-by-step explanation:

Make the denominators of 7/10 and 1/4 the same => 14/20 + 5/20 = 19/20

Answer:

Alternate interior

Step-by-step explanation:

They are inside making them interior angles and they are on opposite sides making them alternate angles as well.

Hope this helps!

Answer:

Step-by-step explanation:

alternate interior angles are congruent if and only lines are parallel.

∠4 ≅ ∠5

\( \sf= \frac{100}{100 + 25} \times 4000 \\ = \frac{100}{125} \times 4000 \\ = \frac{4}{5} \times 4000 \\ = 4 \times 800 \\ = 3200\)

\( \huge \sf \: Answer\)

The cost price is 3200.

Hope you could get an idea from here

Doubt clarification- use comment section.

12:14❤

21:18

The area that will be painted grey is approximately 38 ft².

The circumference of the free-throw circle is given as 30.77 feet, and we know that the free-throw circle is a perfect circle. We can use the formula for circumference to find the radius of the circle, which will be necessary to calculate its area.

Circumference of a circle = 2πr

30.77 = 2 x 3.14 x r

r = 30.77 / (2 x  3.14) = 4.9 feet

Half of the circle will be painted grey. Find the area of half the circle using the formula for the area of a circle.

Area of a circle = π x r²

Area of half the circle = 0.5 x  π x r²

Area of half the circle = 0.5 x 3.14 x 4.9²

Area of half the circle = 37.73 ft²

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The equation for the plane passing through Q and perpendicular to line PQ is r (2 i + 3 j + 6 k) + 28 = 0.

Let position vector of point P be:

p = 3 i + j + 2 k

Let position vector of point Q be:

q = i - 2 j - 4 k

So, PQ = Q - P

PQ = n = i - 2 j - 4 k - (3 i + j + 2 k)

n = i - 2 j - 4 k - 3 i - j - 2 k

n = - 2 i - 3 j - 6 k

The Equation of plane passing through point Q and perpendicular to PQ will be:

(r - q).n = 0

r n = q n

q n = (i - 2 j - 4 k) . (- 2 i - 3 j - 6 k)

q n = - 2 + 6 + 24

q n = 28

r n = 28

r (- 2 i - 3 j - 6 k) = 28

r (2 i + 3 j + 6 k) + 28 = 0

Therefore the equation for the plane passing through Q and perpendicular to line PQ is r (2 i + 3 j + 6 k) + 28 = 0.

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Answer:

The number: 13,226

Step-by-step explanation:

1. The smallest 5-digit number possibile is: 10,000

2. The smallest 5-digit number being odd should be: 10,001

3. All factors of 6 are {1, 2, 3, 6} so that the smallest possible way to arrange these numbers would be: 11,236

4.  Now this number contains 3 prime numbers, 2 being {2 and 3}. If we were to consider another prime number, still being a factor of 6, that would be: 2. That would mean instead of the 1 being the second digit of the value 11,236 it could be 2: 12,236.

5. The digit in the thousands place (2) should be greater than the digit in the tens place (3). Let's swap these digits for now so that condition is satisfied: 13,226. 2 is the only number that has a number greater than it, besides 1, but 1 can't be a digit in the tenth place as it would make a greater 5 digit-number. Thus, provided the conditions are still satisfied, the number 13,226 is the smallest number possible.

Answer

Measure the shape yourself and follow the explanation.

Step-by-step explanation:

Measure each side of the Triangles with your ruler. Record it.

For example,

I measured and got 3cm, 3.5cm, 3.5cm.

Multiply by scale factor r 2.

for example, 3cm × 2 = 6cm

3.5cm × 2 = 7.0cm

3.5cm × 2 = 7.0cm

Use your pencil to draw your new numbers to form the new Triangle.

As for the second shape, measure each four sides using ruler

for example, I measured and had 4cm, 6cm, 4cm, 6m.

Multiply by scale factor r 2.

for example, 4cm × 1/4 = 1 cm

6cm × 1/4 = 1.5cm

4cm × 1/4 = 1 cm

6cm × 1/4 = 1.5cm

Use your ruler to measure 1cm, 1.5cm, 1cm and 1.5cm, then to draw your new shape

It is not possible to find a combination using addition and multiplication of the given single-digit numbers that totals exactly 100 while keeping the same order.

To combine the single-digit numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 using only addition and multiplication so that they total 100 while keeping the same order, we can form the following expression:

1 + 2 + 3 + 4 + 5 + 6 + 78 + 9

In this expression, we group the numbers 7 and 8 together to form 78. Then, we add all the other numbers from 1 to 6 and the number 9. Adding them up, we get:

1 + 2 + 3 + 4 + 5 + 6 + 78 + 9 = 108

Unfortunately, the sum obtained from this expression is 108, not 100 as required.

It is not possible to obtain a sum of exactly 100 by combining the single-digit numbers 1 to 9 in the given order using only addition and multiplication. This is because the largest single-digit number, 9, is relatively small compared to the desired total of 100.

Adding all the single-digit numbers in order without any multiplication would result in a sum of 45, which is significantly lower than 100. Multiplication can only further decrease the sum, making it even more difficult to reach 100.

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The required value of t is (-∞, -6) U (4, ∞).

What is a linear inequality and how is it solved?
Expressions with linear inequalities compare any two values using inequality symbols like "<" and ">." The mathematical expression with unequal sides is known as an inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. Polynomial inequality, rational inequality, and absolute value inequality are the several types of inequalities that exist in mathematics.
First, create an equation for the inequality. The given equation must be solved for one or more values. Represent all of the values that you found on the number line now. On the number line, use open circles to symbolize the excluded values. the interval, then. To determine whether the values satisfy the inequality equation, substitute any random value from the interval into the inequality equation. The solutions of the given inequality equation are intervals that fulfil the inequality equation.

Given, the linear inequalities are t + 1 < -5 and t + 1 > 5
Solving the first inequality, t + 1 < -5 ⇒ t < -5 -1 ⇒ t < -6
Again, solving second inequality, t + 1 > 5 ⇒ t > 5 - 1 ⇒ t > 4
Combining the solution of both the inequalities, we have;
the value of t can take any value in (-∞, -6) U (4, ∞).
Therefore, the required value of t is (-∞, -6) U (4, ∞).

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Answer:

4pqr

Step-by-step explanation:

because pqr is 1pqr

so 1pqr + 3pqr is

4pqr

Answer:

4<x<10

Step-by-step explanation:

-2x<-4

Divide by 2

-x<-4

Divide by -1 (remember if you divide by -1, flip the direction of the sign)

x>4

x-4<6

Add 4 to both sides

x<10

Combine these

4<x<10

Answer:

To one decimal place,

y = 16.3 m

Step-by-step explanation:

Using SOHCAHTOA,

In this case we need to use CAH,

WE know the angle = 25 and the hypotenuse H = 18,

so,

y = adjacent

\(cos(angle) = y/H\\y = (18)(cos(25))\\y = 16.3135\\y = 16.3\)

Answer: 16.3 in.

Step-by-step explanation:

use SOH CAH TOA

cos x = adj/hyp

cos 25  = y/18

18 cos 25  = y

y= 16.3

Answer:

I think its 90°

Step-by-step explanation:

I dont know foe suee

Answer:

a = 98⁰

Step-by-step explanation:

According to the the triangle sum thereom, all angles in triangle add up to 180⁰.

m<a + m<b + m<c = 180⁰

m<a + 34⁰ + 48⁰ = 180⁰

m<a + 82⁰ = 180⁰

m<a + 82⁰ - 82⁰ = 180⁰ - 82⁰

m<a = 98⁰

Hope this helps, thank you :) !!

Answer:

A

Step-by-step explanation:

If g is equal to 8, then we can rewrite the fraction as 8/2+3. We can simplify this to 8/5. That means A is correct.