Four children randomly line up, single file. What is the probability that they are in height order, with the shortest child in front? All of the children are of different heights.

A 1/4
B 1/256
C 1/16
D 1/24

The cost price of this television set is equal to $447.87.

Given the following data:

To calculate the cost price:

In this exercise, you're required to determine the cost price of a television set that was sold for $421.

Mathematically, cost price is given by this formula:

\(Cost\;price = \frac{Selling\;price \times 100}{100-Percentage\;loss}\)

Substituting the given parameters into the formula, we have;

\(Cost\;price = \frac{421 \times 100}{100-6}\\\\Cost\;price = \frac{42100}{94}\)

Cost price = $447.87.

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The chocolate for 140 bon-bons would cost approximately $6.13.

1. Calculate the volume of each chocolate bon-bon using the formula for the volume of a sphere: V = (4/3)πr³, where r is the radius.

  V = (4/3)π(0.7 cm)³

  V ≈ 1.437 cm³

2. Determine the mass of each chocolate bon-bon using the density formula: density = mass/volume.

  density = 1.27 g/cm³

  mass = density * volume

  mass ≈ 1.27 g/cm³ * 1.437 cm³

  mass ≈ 1.826 g

3. Calculate the total mass of chocolate needed for 140 bon-bons.

  total mass = mass per bon-bon * number of bon-bons

  total mass ≈ 1.826 g * 140

  total mass ≈ 255.64 g

4. Determine the cost of the chocolate by multiplying the total mass by the cost per gram.

  cost = total mass * cost per gram

  cost ≈ 255.64 g * $0.04/g

  cost ≈ $10.2256

5. Round the cost to the nearest cent.

  cost ≈ $10.23

Therefore, the chocolate for 140 bon-bons would cost approximately $6.13.

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Answer:

d=1/6

Step-by-step explanation:

hope this help, good day.

Answer:

right now in Bonny

Step-by-step explanation:

am so sorry for your prayers

hope it helps

Statistical power is a measure of the ability to reject the null hypothesis when it is false. It represents the probability of correctly identifying a true effect or relationship in a statistical hypothesis test.

A high statistical power indicates a greater likelihood of detecting a significant result if the null hypothesis is indeed incorrect. The power of a statistical test depends on several factors, including the sample size, the effect size (the magnitude of the true effect or difference), the chosen significance level (often denoted as α), and the variability or noise in the data. Increasing the sample size or effect size generally increases the statistical power, while a lower significance level or higher variability decreases it.

Power analysis is commonly used to determine an appropriate sample size for a study, ensuring that it is adequately powered to detect the desired effect. A higher power is desirable as it reduces the chances of a Type II error (failing to reject the null hypothesis when it is false) and increases the chances of correctly detecting real effects or relationships.

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Answer: 127 to the nearest whole number is 130

Step-by-step explanation:

Since 7 is more than 5, we add 1 to the tenth place (2) which becomes 3 and add that to the original number (7) which gets you 10. After that you add 120 to 10 which gets you 130, therefore, the nearest whole number is 127.

We could expect $30.00 to gain after 20 tosses.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of sample

The probability of all the events occurring need to be 1.

if the toss of a coin comes down heads, you win a dollar. if it comes down tails, you lose fifty cents.

We need to find out How much would you expect to gain after 20 tosses (in $ dollars).

Because if you think about it, you will see that about half of them are going to be heads and the other half are going to be tails.

Therefore, We could expect $30.00 to gain after 20 tosses.

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Lamento comentar en esto pero necesito puntos

The equation for the line of symmetry for the function defined by f(x) =-3x² +6x - 9 is x = 1.

Given the function in the question;

f(x) = -3x² + 6x - 9

To find the equation for the line of symmetry, we need to use the formula:

x = -b/2a,

Where a and b are the coefficients of x² and x in the quadratic equation, respectively.

Given the function:

f(x)= -3x² +6x - 9

We have:

a = -3 and b = 6.

Hence, the equation for the line of symmetry is:

x = -b/2a

x = -6 / ( 2(-3))

x = -6/(-6)

x = 1

The equation for the line of symmetry is x = 1.

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Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

The mean average deviation (MAD) shows the average of the deviation of all the values from their average/mean.

It is calculated as follows;

Next step, we find the difference of each given value from the mean. The result is now divided by the number of data which is 7.

The mean average deviation is 0.5 minutes

Please note that when computing the MAD (mean average deviation, we take absolute values only, that is no negative values. Rather all negative values would be taken as positive. That is why we insert the absolute sign { | | } into the formula.

Answer:

$15,539.67

Step-by-step explanation:

Compound Interest Formula

\(\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}\)

where:

Given:

Substitute the given values into the formula and solve for A:

\(\implies \sf A=11000\left(1+\frac{0.058}{4}\right)^{(4 \times 6)}\)

\(\implies \sf A=11000(1.0145)^{24}\)

\(\implies \sf A=15539.67451...\)

Therefore, the value of the investment after 6 years will be $15,539.67 to the nearest cent.

The total number of bushels the farmer has for sale at the farmers market is 9.75 bushels.

The given parameters;

The actual amount of the bushel sold in per day;

\(= \frac{15.75}{1 \ day}\)

After 7 days the amount of the bushel sold is calculated as;

\(= \frac{15.75}{1 \ day} \times 7\ days= 110.25 \ bushels\)

The amount of the bushel left after the 7 days;

\(= 120 - 110.25\\\\= 9.75 \ bushels\)

Thus, the total number of bushels the farmer has for sale at the farmers market is 9.75 bushels.

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To determine the exposure from a radioactive substance at a different distance, we can use the inverse square law. The exposure at a distance of 20 cm is 11,250 mR.

The inverse square law states that the intensity of radiation is inversely proportional to the square of the distance from the source. In this case, we have the initial distance of 100 cm and the corresponding exposure of 450 mR.

Using the inverse square law equation, we can set up a proportion to find the new exposure at a distance of 20 cm. The equation can be written as:

(Exposure at initial distance) / (Exposure at new distance) = (Square of new distance) / (Square of initial distance)

Substituting the given values, we have:

450 mR / X = \((20 cm)^2 / (100 cm)^2\)

Simplifying the equation, we get:

450 mR / X = 1/25

Cross-multiplying, we have:

X = (450 mR) * (25)

Calculating the value, we find:

X = 11,250 mR

Therefore, the exposure at a distance of 20 cm is 11,250 mR.

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Answer:

c

Step-by-step explanation:

Answer:

420-20w = 240

Step-by-step explanation:

She starts with $420 and is taking out $20 a week so in the equation the 20 has to be negative because she is withdrawing instead of adding.

The number of possible social security numbers will be one billion.

There are 10 digits (0-9) that can be used for each position in a social security number.

The first position can be any digit from 0 to 9, so there are 10 choices for the first digit. The same is true for the second and third positions.

The fourth position is a dash, so there is only one choice for that position.

The fifth and sixth positions can each be any digit from 0 to 9, so there are 10 choices for each of those positions.

The seventh position is another dash, so there is only one choice for that position.

The last four positions can each be any digit from 0 to 9, so there are 10 choices for each of those positions.

Therefore, the total number of possible social security numbers is:

10 × 10 × 10 × 1 × 10 × 10 × 1 × 10 × 10 × 10 × 10 = 1,000,000,000

So there are 1 billion possible social security numbers.

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The frequency of A allele after a single generation of mutation can be found as follows: Frequency of A allele after a single generationp(A) = p(A) x (1 - m) + q(a) x m

where,
m = mutation rate = 10^-6p(A) = frequency of A allele in initial generation = 0.75q(a) = frequency of a allele in initial generation = 0.25Thus,p(A) = 0.75 x (1 - 10^-6) + 0.25 x 10^-6 = 0.74999925

And the frequency of a allele will beq(a) = 1 - p(A) = 1 - 0.74999925 = 0.25000075

Therefore, the frequency of the A and a alleles in the next generation will beA: 0.74999925 and a: 0.25000075.

This is option D.

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According to the isosceles triangle theorem, if two sides of a triangle are congruent, the angles across from those sides are likewise congruent.

According to the isosceles triangle theorem, if two sides of a triangle are congruent, the angles across from those sides are likewise congruent.

∆ABC is an isosceles triangle with AB = AC.

Construction: Altitude AD from vertex A to the side BC.

Proof: We know, that the altitude of an isosceles triangle from the vertex is the perpendicular bisector of the third side. Thus, we can conclude that,

∠ADB = ∠ADC = 90º ----------- (1)

BD = DC ---------- (2)

Consider ∆ADB and ∆ADC

AB = AC [Given]

AD = AD [common side]

BD = DC [From equation (2)]

Thus, by SSS congruence we can say that,

∆ADB ≅ ∆ADC

By CPCT, ∠B = ∠C.

Hence, we have proved that if two sides of a triangle are congruent, then the angles opposite to the congruent sides are equal.

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Rounding to the nearest degree, the angle of depression is approximately 27.5 degrees.

The angle of depression is an angle formed by a horizontal line and a line of sight from a higher point to a lower point. The angle of depression is measured in degrees and is always a positive value. It is typically used in navigation and surveying, as well as in other fields such as architecture and engineering.

In a common scenario, an observer is located at a higher point and is looking down at an object on the ground. The angle of depression is the angle formed by an imaginary line extending horizontally from the observer's position to the point on the ground directly below the observer, and a line extending from the observer's position to the object.

It is complementary to angle of elevation which is formed by observer looking up to an object above the observer's position.

To find the angle of depression, we can use the tangent function of the angle of depression.

tan(θ) = opposite / adjacent

where opposite is the distance from the plane to the building, and adjacent is the distance from the plane to the building (800 ft)

tan(θ) = \(\frac{463}{800}\)

To find the angle of depression in degrees, we need to use the inverse tangent function (arctan)

θ = arctan(\(\frac{463}{800}\))

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Answer:

7.1 yard per min

Step-by-step explanation:

The unit rate in teaspoons per pound would be 1/2 teaspoons per pound.

What is the unit rate?

A unit rate means a rate for one or something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.

The number of teaspoons:

                                      \(=1\frac{3}{4}\\\\=\frac{4+3}{4}\\\\=\frac{7}{4}\)

Amount of pasta:

                              \(=3\frac{1}{2}\\\\=\frac{6+1}{2}\\\\=\frac{7}{2}\)

Now the unit rate = number of teaspoons/ amount of pasta

                             \(=\frac{7/4}{7/2}\\\\=\frac{1}{2}\\\)

Hence, the unit rate in teaspoons per pound would be 1/2 teaspoons per pound.

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Answer:

Step-by-step explanation:

1/2

Margin of error = 1.96 * 0.038 = 0.0745 ≈ 0.075 (to 3 decimal places)

a) To calculate the margin of error for the first high school student, we can use the formula:

Margin of error = z* (standard error)

where z* is the critical value of the standard normal distribution corresponding to the desired level of confidence, and the standard error is given by:

standard error = sqrt[(p-hat * (1-p-hat))/n]

where p-hat is the sample proportion, and n is the sample size.

Given that the sample size is n=178, and the sample proportion is p-hat = 0.69, the standard error is:

standard error = sqrt[(0.69*0.31)/178] = 0.042

To find the critical value z* for a 95% confidence interval, we can look up the value in the standard normal table. Since we want a two-tailed confidence interval, we need to divide the level of significance (1 - 0.95 = 0.05) by 2, resulting in an alpha level of 0.025. Looking up the corresponding z-score, we find:

z* = 1.96

Therefore, the margin of error for the first high school student is:

Margin of error = 1.96 * 0.042 = 0.0828 ≈ 0.083 (to 3 decimal places)

b) To calculate the margin of error for the second high school student, we can follow the same procedure as above, using the sample size n=178 and the sample proportion p-hat = 0.83. The standard error is:

standard error = sqrt[(0.83*0.17)/178] = 0.038

The critical value z* for a 95% confidence interval is still 1.96, so the margin of error is:

Margin of error = 1.96 * 0.038 = 0.0745 ≈ 0.075 (to 3 decimal places)

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Answer:

h(x)=24X^2+40x+14

Answer:

x=5 , y= -1

Step-by-step explanation:

You can see that one of the y's is negative while the other is positive, so you can add them together.

Now, negative 1 + positive 1 = 0, so the y's cancel out leaving only the x's.

Remember you can't add one part without adding the other so x+x = 2x, and 4+6=10. This makes the final equation 2x=10.

You can simplify that into x=5. This gives you the answer for x

Then substitute x=5 into any of the two equations (doesn't matter) I'll use the first one. So if you substitute it you get 5+y=4.

Simplified, y= -1

Therefore, x= 5 and y=-1

Answer:

(5,-1)

Step-by-step explanation:

Got it right on edge cause of the guy above me

Answer: 20.52

Step-by-step explanation:

Your welcome