in right trapezoid abcd the area of one of the shaded triangles is 54 sq units more than the area of the other one. the length of the shorter leg is 12. find the length of the other leg.
rsm problem pls help

Therefore, the probability that the mean tariff rate of 600 randomly selected railroad-car shipments of ethanol will be within $90 of the mean tariff rate of all railroad-car shipments of ethanol is approximately 0.9732 or 97.32%.

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability theory is widely used in many fields, including mathematics, statistics, physics, engineering, economics, and social sciences. It provides a framework for analyzing and understanding uncertain events and making predictions based on available information. Probability theory is also used in decision-making, risk management, and game theory, among other applications.

Here,

Let μ be the mean tariff rate of all railroad-car shipments of ethanol, and let x be the mean tariff rate of a random sample of 600 railroad-car shipments of ethanol. We want to find the probability that x will be within $90 of μ.

The standard error of the mean (SE) can be calculated as:

SE = σ / √(n)

where σ is the standard deviation of the population, n is the sample size.

Substituting the given values, we get:

SE = 1150 / √(600)

≈ 47.03

The probability that x will be within $90 of μ can be calculated by standardizing x using the standard error and the z-score formula:

z = (x - μ) / SE

z = ($90) / 47.03

≈ 1.915

Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score less than 1.915 is approximately 0.9732.

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\( \huge \pink{ \underline \mathfrak{ \green{Answer}}} \: \\ \\ \: \: \rightarrow \fbox{ a). \blue{ \: 54 \: }}\)

Step-by-step explanation:

\( \bf{Given} \: \colon 4w² + w-6, when \: \: w = -4 \\ \\ \tt \underline \red{Solution} \colon \\ \\ \rightarrow \: 4w {}^{2} + w \: - 6 \\ \\ \: put \: \: value \: \: of \: \: w \: \: in \: \: given \: \: equation \\ \\ \rightarrow \: 4( - 4) {}^{2} + \: (- 4 )\: - 6 \\ \\ \rightarrow \: 4(16) \: - 4 \: - 6 \\ \\ \rightarrow \: 64 \: - 10 \\ \\ \bf \rightarrow54\)

Please find attached photograph for your answer. The answer will be option B.

Answer:

oooo lucky for you

Step-by-step explanation:

answer

64/729

Step-by-step explanation:

Greetings !

Firstly, find the class-midpoints (X) to solve for the mean.

Thus, mid points of each classes are

\(5.15.25.35.45\)

Solve, for p using mean grouped data formula

\( \frac{5(3) + 15(4) + 25(p) + 35(3) + 45(2)}{3 + 4 + p + 3 + 2} = 24\)

multiply each values add them and solve for p.

\( \frac{15 + 60 + 25p + 105 + 90}{12 + p} = 24\)

make a cross multiplication

\(270 + 25p = 24(12 + p) \\ 270 + 25p = 288 + 24p\)

subtract 270 from both sides

\(270 + 25p - 270 = 288 + 24p - 270 \\ 25p = 24p + 18\)

subtract 24p from both sides

\(25p - 24p = 24p + 18 - 24p \\ p = 18\)

Also refer the attached image for further details

Hope it helps!

Answer:

See Explanation

Step-by-step explanation:

Given

\(7.5d = 2.5d\)

Analyzing Lin's

\(\frac{7.5d}{2.5d} = \frac{2.5d}{2.5d}\)

\(3 = 1\)

This isn't a solution because \(3 \neq 1\)

Analyzing Elena's

\(7.5d - 2.5d= 2.5d-2.5d\)

\(5d = 0\)

Divide through by 5

\(d = 0\)

Hence;

Going by the analysis above; only Elena's  move will lead to a solution

The correct answer is 520 square units that is option D.

What is the formula for surface area of prism?

The formula used to find the surface area S of right prism is S=bh+pH.

In the formula b is the base, h is the height of the right angle triangle formed in the prism and p is the perimeter of the triangle, H is the width of the prism.

Let x be the hypotenuses of the right angle triangle of the prim.

Use Pythagoras theorem in the right angle triangle to find the value of x.

\(15^{2} +8^{2} =x^{2}\)

\(x^{2} =289\)

On solving this we will get x=17.

On adding all the sides of the triangle the perimeter of the triangle is 8+15+17=40.

By calculation and given information, we have b=8, h=15, p=40 and H=10.

Now we will substitute all the values in the formula to find the surface area.

S=(8)(15)+(40)(10)=120+400=520 Square units.

Therefore, the correct option is D.

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Answer:Michelle paid $56.15 for her shoes

Step-by-step explanation:

Answer:Michelle paid $56.15 for her shoes

Step-by-step explanation:

Since Michelle paid $3.89 more for her shoes compared to Conrad, who paid $52.26. This means you have to add $3.89 to $52.26.

$3.89+$52.25= $56.15

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Answer:

$6.88

Step-by-step explanation:

16Tbs. =1 cup,

4 pies =2 cups of lemon juice, so you need 32 Tbs. of lemon juice

32/2=16

16*0.43=$6.88

Answer: $ 6.88

Step-by-step explanation:

In one cup there is 16 tablespoons.

each lemon costs .43 and gives 2 tablespoons

Half a cup would give us 8 tablespoons = 4 lemons at the cost of 1.72

1.72 times 4 pies

Making the whole thing of 4 pies cost 6.88

Giving us the answer of 6.88.

(correct me if i'm wrong)

Answer:

a number that is divisible only by itself and 1 (e.g. 2, 3, 5, 7, 11).

The mean is 27.3. and the median is 24.5.

A data set's mean (average) is calculated by summing all οf the numbers in the set, then dividing by the tοtal number οf values in the set. When a data cοllectiοn is ranked frοm least tο greatest, the median is the midpοint. The number that appears mοst frequently in a data set is called the mοde.

Part A:

Tο calculate the mean, we need tο add up all the values and divide by the tοtal number οf values:

15 + 20 + 22 + 24 + 25 + 26 + 30 + 35 + 36 + 60 = 273

273 / 10 = 27.3

Therefοre, the mean is 27.3.

Tο find the median, we need tο find the middle value when the data is οrdered frοm smallest tο largest.

Median = (24 + 25) / 2 = 24.5

Therefοre, the median is 24.5.

Part B:

The measure οf centre that the student shοuld give tο their teacher depends οn the teacher's preference. The median is a mοre rοbust measure οf center that is nοt as affected by οutliers οr extreme values. The median alsο gives a better sense οf the typical value in the data.

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Here, we just need to add x and y and subtract it from 180.

x + y = 91 + 42 = 133.

180 - 133 = 47.

Hence, z = 47 degrees.

Answer:

Step-by-step explanation:

straight line = 180° we remove the angles x and y and find z

180 - 91 - 42 =

47°

Answer:

what is sin^3A=3sinA-4sin^3A

Answer:

y = -3x + 9

Step-by-step explanation:

pretty much the slope is what is in front of the x.
the slope is rise of run and since it goes down by 3 every time x goes up by 1, the slope is -3.

The +9 is just what y is equal to when x is 0

Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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Answer:

(100/500) *200 =40%

Step-by-step explanation:

The number of standard deviations from the mean that include all

data values is two.

From the gathering of information, we will see that the minimum worth is $19.95 and also the most worth is $29.95. So , we would like to seek out the amount of normal deviations, let's decision it "a" , such that\(\overline x $\color \ - a\cdot\sigma \le 19.95}\) and   \(\overline x $\color \ +a\cdot\sigma \geq 29.95}\)

Use the given values of mean  \(\overline x\) and normal deviation (σ) to notice the worth of "a".

         \(\overline x $\color \ - a\cdot\sigma \le 19.95}\\25.07\ - 2.62a \leq 19.95\\5.12\leq 2.62a\\1.9541\leq a\)

On rounding off we get a = 2

Checking another inequality

         \(\overline x $\color \ + a\cdot\sigma \geq 29.95}\\25.07 \ + 2(2.62) \geq 29.95\\25.07 + 5.24 \geq 29.95\\30.31\geq 29.95\)

Thus , 2 standard deviation include the all values from the given set of data .

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Answer:

\(P_{B}\) = 80

Step-by-step explanation:

given 2 similar figures with ratio of sides = a : b

then ratio of perimeters is also a : b

here ratio of sides = 24 : 15 = 8 : 5

the ratio of perimeters is also 8 : 5

then by proportion

\(\frac{ratioA}{P_{A} }\) = \(\frac{ratioB}{P_{B} }\) , that is

\(\frac{8}{128}\) = \(\frac{5}{P_{B} }\) ( cross- multiply )

8 \(P_{B}\) = 5 × 128 = 640 ( divide both sides by 8 )

\(P_{B}\) = 80

Answer:

Step-by-step explanation:

it is y

Answer: Y=0x +5

Step-by-step explanation

its going up by 0 so 0x and you start at 5 so plus 5

Answer:

The Answer is x=2

Step-by-step explanation:

Hope this helps!!!!

Answer:

x=2  

Step-by-step explanation:

4x+3=11

4x=11-3      ( subtract 3 on both sides)

4x=8

x=2            ( divide 4 on both sides)

9.  The stamp duty payable on a property with a purchase price of K45,000 is K1,350.

10. The stamp duty payable on a property with a purchase price of K150,000 is K7,500.

To calculate the stamp duty payable on properties with a purchase price of K45,000 and K150,000, we need to apply the corresponding rates of stamp duty based on the given information.

Given:

Value of Property:

Up to K35,000: Stamp Duty Rate - 2%

K35,000 to K70,000: Stamp Duty Rate - 3%

K70,000 to K140,000: Stamp Duty Rate - 4%

Over K140,000: Stamp Duty Rate - 5%

9. Calculate the stamp duty payable on properties whose purchase price is K45,000:

Since the purchase price of K45,000 falls within the range of K35,000 to K70,000, the stamp duty rate applicable is 3%.

Stamp Duty Payable = Purchase Price * Stamp Duty Rate

= K45,000 * 3%

= K45,000 * 0.03

= K1,350

Therefore, the stamp duty payable on a property with a purchase price of K45,000 is K1,350.

10. Calculate the stamp duty payable on properties whose purchase price is K150,000:

Since the purchase price of K150,000 is above K140,000, the stamp duty rate applicable is 5%.

Stamp Duty Payable = Purchase Price * Stamp Duty Rate

= K150,000 * 5%

= K150,000 * 0.05

= K7,500

Therefore, the stamp duty payable on a property with a purchase price of K150,000 is K7,500.

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The cosine function that could model the block's height in inches above the ground at time t seconds is:

h(t) = 9cos(1.67π(x - 2.1)) + 39.

The cosine function is defined as follows:

g(x) = acos(bx+c)+d.

The coefficients have these following roles:

In this problem, we have that the maximum value is of 48 and the minimum value is of 30(difference of 18), hence the amplitude is given as follows:

2a = 18

a = 9.

A standard cosine function with amplitude 9 would vary the between -9 and 9, while this one varies between 30 and 48, hence the vertical shift is of d = 39.

The minimum and maximum values form half the period, hence:

π/B = 2.7 - 2.1

B = π/0.6

B = 1.67π.

The maximum value in the standard function is at x = 0, while at this function is at x = 2.1, hence the phase shift is of 2.1 units to the right, that is, c = -2.1.

Hence the cosine function is:

h(t) = 9cos(1.67π(x - 2.1)) + 39.

This function is graphed at the end of the answer, showing that the minimum and the maximum values are as desired.

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Answer:

x=-4 is true, x=6 is not

Step-by-step explanation:

5x + 7 < 22

Plug in our X values

5(-4) + 7 < 22 ?

solve

-20 + 7 < 22

-13 < 22 ?

x=-4 is true.

Repeat steps from ^

5(6) + 7 < 22

30 + 7 < 22

37 < 22 ?

x=6 is not true.

Hope this helped

Answer:

False

Step-by-step explanation:

5(-4) + 7 < 22

-20 + 7 < 22

-14 < 22

5(6) + 7 < 22

30 + 7 < 22

37 < 22

The statement would be false because when applying 6 to the equation, the equation becomes false.

On the other hand, when applying -4 to the equation, the equation becomes true, but since both -4 and 6 HAVE to be BOTH solutions to the equation, the statement becomes false.

Answer:

it is 10 rounded hope it help

Answer: A proper subset is a subset that is not identical to the original set—it contains fewer elements. You can see that there are 16 subsets, 15 of which are proper subsets. Listing the sets is fine if you have only a few elements.

Answer:

5-4=12x+x

1=13x

1/13=×

Answer:

y = (1/2)x - (15/2)

Step-by-step explanation:

goal: to rearrange the expression such that it is in the form

y = f(x); where f(x) is an expression in terms of x

given:

x - 2y = 15      (subtract x from both sides)

-2y = 15 - x    (multiply both sides by -1 to make left side positive)

2y = -15 + x   (divide both sides by 2 and rearrange)

y = (1/2)x - (15/2)

Answer:

\(\sqrt{75} =\sqrt{25*3} =5\sqrt{3}\)

Step-by-step explanation:

Answer:

1882

Step-by-step explanation:

46x42=1932 1932-50=1882

Answer:

The heavier an object the harder it is to move.

Step-by-step explanation:

I'm pretty sure this is it

Answer:

C. Gravity and Friction combine to make a train hard to move.

Step-by-step explanation:

This option makes the most sense based off of the text. In the text it says "Since gravity and friction make trains harder to move...." None of the other options really match the text either.

Hope it helps!

In order to make the question true the length should be 45cm not 4.5 cm , Solving accordingly

The equation is

As 45 is base amount we used it as y intercect

This means that the length of the scarf after x nights can be represented by the equation y = 4.5 + 5x.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

To create an equation that shows the relationship between the number of nights Madelyn spends knitting, x, and the length of the scarf in centimeters, y, we need to consider the information given.

We know that the scarf is currently 4.5 centimeters long, and Madelyn plans to add 5 centimeters per night.

This means that the length of the scarf after x nights can be represented by the equation:

y = 4.5 + 5x

In this equation,

x represents the number of nights Madelyn spends knitting and y represents the length of the scarf in centimeters after x nights.

Thus,

The initial length of the scarf, 4.5 centimeters, is added to the length of the scarf Madelyn knits in x nights, which is represented by the product of 5 and x.

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