-)) In a right triangle, a and b are the lengths of the legs and c is the length of the
hypotenuse. If b = 5.4 millimeters and c = 8.3 millimeters, what is a? If necessary, round to
the nearest tenth

Answer: 2.6

Step-by-step explanation:

Step 1: Calculate the mean of Shade's plant heights.

= 7+12+12+8+9+8+8+8/8

= 72/8

=9

Step 2: Calculate the range of Shade's plant heights. Range is highest minus lowest number. This will be:

12 - 7 = 5

Step 3: Calculate the mean of Sun plant heights.

19+24+20+23+24+23+23+20/8

= 176/8

= 22

Step 4: Find the range of Sun plants height.

= 24 - 19 = 5

Step 5: Find the difference of means

= 22 - 9

= 13

Step 6: Divide the difference of means by the range.

= 13 ÷ 5

= 2.6

The difference in mean and range are 13 and 0 respectively.

We are to find the difference in mean and range of the plant height.

Given the Shade plant heights expressed as 7 12 12 8 9 8 8 8

Mean =  7 + 12+12+ 8+ 9+ 8+ 8+ 8

Mean = 72

Sample size = 8

Range = Highest value - Lowest value

Range = 21 - 7

Given the Sun plant heights expressed as 19 24 20 23 24 23 23 20

Mean =  19+ 24+ 20+ 23+ 24+ 23+ 23+ 20

Mean = 176

Sample size = 8

Range = Highest value - Lowest value

Range = 24 - 19

Evaluate the difference in mean

Difference in mean = 22 - 9

Difference in mean = 13

Evaluate the difference in range

Difference in range = 5 - 5

Difference in range = 0

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We are given

[tex]2ab + 2bc + 2ac = 350 \iff ab + bc + ac = 175[/tex]

We are also given [tex]a=b[/tex] and [tex]c=9[/tex], which allows us to rewrite the equation as

[tex]a^2 + 9a + 9a = 175 \iff a^2+18a-175=0[/tex]

(I substituted every "b" with "a" and every "c" with "9").

The solutions to this quadratic equation are -25 and 7. We discard -25 because a side with negative length would make no sense.

The length of sides a and b of a rectangular prism, given a surface area of 350 square meters and side c measuring 9 meters, is approximately 12.75 meters each.

In this question, we have a rectangular prism whose surface area is 350 square meters, with side c measuring 9 meters and sides a and b of equal lengths. The formula for the surface area of a rectangular prism is SA = 2ab + 2bc + 2ac. Since a = b, we can rewrite the equation as SA = 2a^2 + 2ac. Therefore, inserting the given measurements into the formula and solving for a we get:

So, the length of side a (or b) is approximately 12.75 meters.

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Answer:

2249 dollars more

Step-by-step explanation:

52 weeks in one year so divide by 2 and then multiply by 721 and then take that amount and dubtract the new salary 20.995 and subtract the previous annual amount and then boom 2295 more

Final answer:

Roger will make $2,249.00 more money next year than he did this year.

Explanation:

To determine how much more money Roger will make next year compared to this year, we need to find the difference between his new annual salary and his current biweekly salary.

To calculate the annual salary, we can multiply the biweekly salary by the number of biweekly periods in a year. There are 26 biweekly periods in a year (52 weeks / 2). So, Roger's current annual salary is $721.00 x 26 = $18,746.00.

The difference between his new annual salary and his current annual salary is $20,995.00 - $18,746.00 = $2,249.00. Therefore, Roger will make $2,249.00 more money next year than he did this year.

Answer:

The answer is C.

Step-by-step explanation:

(n-2) * 180

(8-2) * 180

(6) * 180

1080

Answer:

D

Step-by-step explanation:

This function resembles that of the absolute value function, never going into the negative y values. Hope this helps!

Answer:

no,

Step-by-step explanation:

1/4 of 40 is 10

40-10=30

It depends. The actual price would be $31.35. So it is not really reasonable since it is closer to the original price than it is to the discounted one... Just use your best judgement...

Answer:14In

Step-by-step explanation:

volume(v)=768π

height(h)=3

Radius=√(v ➗ πxh)

Radius=√(768π ➗ 3π)

Radius=√(256)

Radius=14 In

Answer:

She still has 166.67 square feet does she have left to plant flowers

Step-by-step explanation:

The sum of total area planted, and the remaining area left to plant, is 100% = decimal 1.

She has planted 1/3 of the area. So

[tex]\frac{1}{3} + p = 1[/tex]

[tex]p =  1 - \frac{1}{3}[/tex]

[tex]p = \frac{3-1}{3}[/tex]

[tex]p = \frac{2}{3}[/tex]

So she still has to paint two thirds of the area.

The area is of 250 square feet.

2/3 of 250

[tex]250\frac{2}{3} = 166.67[/tex]

She still has 166.67 square feet does she have left to plant flowers

Answer:

-7<x<6

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variables

Mark me brainliest please!

Step-by-step explanation:

I think common factors are

18 = 1 2 3 6 9 18

30 = 1 2 3 10 15 30

So highest common factor is 3

18x + 30x2

3x (6 + 10x)

Answer:

The answer is 6x

Step-by-step explanation:

Answer:

P(hh) = 0.2209

P(ht) = 0.2491

P(th) = 0.2491

P(tt) = 0.2809

John von Neumann suggested that if both tosses results in same outcome then discard the result and start again. If each result is different then accept the first one

Step-by-step explanation:

We are given that a coin is unfair and the probabilities of getting a head and tail are

P(h) = 0.47

P(t) = 0.53

John von Neumann suggested a way to make perfectly fair​ decisions, even with a possibly biased coin.

He suggested to toss the coin twice, so the possible outcomes are

Sample space = {hh, ht, th, tt}

The probabilities of these outcomes are

P(hh) = P(h)*P(h)

P(hh) = 0.47*0.47

P(hh) = 0.2209

P(ht) = P(h)*P(t)

P(ht) = 0.47*0.53

P(ht) = 0.2491

P(th) = P(t)*P(h)

P(th) = 0.53*0.47

P(th) = 0.2491

P(tt) = P(t)*P(t)

P(tt) = 0.53*0.53

P(tt) = 0.2809

He suggested that if both tosses results in same outcome then discard the result and start again.

If each result is different then accept the first one, for example,

if you get heads on the first toss and tails on the second toss then result is heads.

if you get tails on the first toss and heads on the second toss then result is tails.

If you notice the probability of P(ht) and P(th) are same therefore, this strategy allows to make fair decision even when the coin is biased.

Answer:

108

Step-by-step explanation:

As per the given question the solution of items need to be counted each day is provided below:-

Here to reach the items needs to be counted each day first we need to find out the number of items which are as follows:-

[tex]For\ item\ A\ = Inventory\ A\ Percentage \times \ Number\ of\ inventory\ items[/tex]

[tex]= 10\% \times \ 7,000[/tex]

[tex]= 0.1 \times \ 7,000[/tex]

[tex]= \ 700[/tex]

[tex]For\ item\ B\ = Inventory\ B\ Percentage \times \ Number\ of\ inventory\ items[/tex]

[tex]= 35\% \times \ 7,000[/tex]

[tex]= 0.35 \times\ 7,000[/tex]

[tex]= \ 2,450[/tex]

[tex]For\ item\ C\ = Inventory\ C\ Percentage \times \ Number\ of\ inventory\ items[/tex]

[tex]= 55\% \times \ 7,000[/tex]

[tex]= 0.55 \times\ 7,000[/tex]

[tex]= 3,850[/tex]

Now, we will find out the items to be counted each day

[tex]Items\ to\ be\ counted\ each\ day\ = \frac{Item\ A}{Working\ Days\ of\ A} \ + \frac{Item\ B}{Working\ Days\ of\ B} \ + \frac{Item\ C}{Working\ Days\ of\ C}[/tex]

[tex]= \frac{700}{20} \ + \frac{2,450}{60}\ + \frac{3,850}{120}[/tex]

[tex]= \ 35\ + \ 40.83\ + \ 32.08[/tex]

[tex]= \ 107.92[/tex]

or

= 108

So, we have calculated the items to be counted for each day by using the above formula.

Answer:

6

Step-by-step explanation:

I did it

Answer:

9.76

Step-by-step explanation:

I am very smart

Tbe confidence interval marked the range of values for which the true population mean is estimated to be given a certain level of confidence. Hence, the confidence interval is (0.6523, 0.7477)

Since the sample size is large enough, we use the the Z distributuon :

Confidence interval is defined thus :

Margin of Error :

Hence,

Lower confidence boundary = 0.7 - 0.0290 = 0.6523

Upper confidence boundary = 0.7 + 0.0290 = 0.7477

Therefore, the confidence interval is (0.6523, 0.7477)

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To construct a 90% confidence interval for the population proportion, calculate the sample proportion, the standard error, and use the confidence interval formula.

Step 1:

Calculate the sample proportion, which is X divided by n. In this case, it is 175 divided by 250, which gives us 0.7.

Step 2:

Calculate the standard error, which is the square root of (p*(1-p))/n, where p is the sample proportion. In this case, it is the square root of (0.7*(1-0.7))/250, which is approximately 0.0266.

Step 3:

Construct the confidence interval using the formula p ± z*(standard error), where p is the sample proportion and z is the z-score corresponding to the desired level of confidence. For a 90% confidence interval, the z-score is approximately 1.645. Therefore, the 90% confidence interval is 0.7 ± 1.645*0.0266, which becomes (0.658, 0.742).

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Answer:

5

Step-by-step explanation:

f(x) = x^2 -6x+13

Let x=4

f (4) = 4^2 -6(4) +13

       = 16 -24 +13

       = 5

The value of f(4) for the function f(x) = x^2 - 6x + 13 is 5.

In order to find f(4) for the function f(x) = x2 - 6x + 13, we replace each x in the equation with 4. So, f(4) = (4)2 - 6(4) + 13. Squaring 4 gives us 16, and 6 times 4 gives us 24.

Therefore, our equation is now f(4) = 16 - 24 + 13. Solving for f(4), we subtract 24 from 16 to get -8, and then add 13 to get 5.

Thus, f(4) = 5.

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9514 1404 393

Answer:

  2.6 cm

Step-by-step explanation:

The full circle is 360°, so an arc of 30° will have 30/360 = 1/12 of the measure of the circumference of the circle.

  arc length = πd/12 = π(10/12) ≈ 2.6 cm

Answer:

Rotation

Step-by-step explanation:

Given:  

Triangle DEF is congruent to Triangle GHJ by the SSS theorem

To find: transformation required to map Triangle DEF onto Triangle GHJ

Solution:

Two figures are said to be congruent if they overlap each other.

Two polygons are said to be congruent if they have same size and shape.

A rotation is a transformation that turns a figure about  the center of rotation.

Rotation transformation is required to map Triangle DEF onto Triangle GHJ

Answer:

translation

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

edge

The positive slope of the asymptote of a hyperbola is a straight line with positive slope.

The positive slope of the asymptote of a hyperbola is a straight line with positive slope (option b). A positive slope indicates that the line moves up the y-axis as the x-value increases, while a negative slope means that the line moves down the y-axis. The appearance of positive slope differs from negative slope and zero slope in that it moves up the y-axis as the x-value increases, while negative slope moves down the y-axis and zero slope means a horizontal line.

Answer:

Blake has 2 dimes and 4 nickels

Step-by-step explanation:

2 dimes = 20 cents

4 nickels = 20 cents

20 + 20 = 40 cents

2 × 2 = 4 dimes

Final answer:

Explanation of the relationship between the number of nickels and dimes in a coin collection yielding a total value of 40 cents.

Explanation:

Problem Statement:

Blake has only nickels and dimes. He has twice as many nickels as dimes. The total value of his coins is 40 cents.

Solution:

Let the number of dimes be 'x', so the number of nickels is '2x'.

Value of dimes = 10x cents, value of nickels = 5(2x) = 10x cents.

Given total value is 40 cents, so 10x + 10x = 40.

Solving the equation, x = 2. Therefore, Blake has 2 dimes and 4 nickels.

Answer:

(x-4)

Step-by-step explanation:

Since a square has 4 equal sides, the perimeter of a square is 4 times one of the sides (which is equal to adding all the sides together). So:

Perimeter = 4(a side) = 4x-16

a side = (4x-16)/4 = (x-4)

The length of a side of a square with perimeter 4x - 16 is x - 4.  

perimeter of a square is represented as follows:

where

l = length

Therefore,

4l = 4x - 16

divide both sides by 4

l = x - 4

The length = x - 4

Note a square have all its side equal to each other.

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Answer:

95.

Step-by-step explanation:

Step one: the first step here is to find the mean or average of the data for the six(6) weeks of total entrees. That is, we will have;

Average = (444 + 447 + 423 + 437 + 444 + 429)/ 6 = 2,624 / 6 = 437.3.

Average = 437.3.

Step two: the next step here is to determine the popularity index for the roast beef roast beef will be forecasted and that will be;

popularity index = 96 / 444.

popularity index = 21.6%.

Step three: the quantity of roast beef that should be forecasted for next Friday will be;

Popularity index × Average.

0.216 × 437.3 = 95.

Hence, the quantity of roast beef that should be forecasted for next Friday will be 95.

To forecast the number of roast beef portions, we first determine the proportion of roast beef sold the last time this menu was offered, then average the total meal counts from the past five Fridays, and apply the proportion to this average to get the forecasted demand.

To forecast the number of portions of roast beef for next Friday, we can apply a demand ratio approach, which uses historical sales data to predict future demand.

Since we have the last time sales data for the entrées, and the counts of total meals sold for the past five Fridays, the first step is to calculate the proportion of each entrée sold relative to the total sales from the last time this menu was offered.

The number sold for each entrée the last time was: BBQ ribs - 76, seafood platter - 118, roast beef - 96, and filet mignon - 154, summing up to a total of 444 entrées.

The proportion for roast beef is calculated by dividing the number of roast beef meals sold by the total number of entrées sold: 96/444. This gives us the portion of meals that were roast beef.

To forecast the demand for roast beef for next Friday, we need to apply this proportion to an estimate of the total number of meals to be served. We can get this estimate by averaging the total meal counts from the past five Fridays: (447 + 423 + 437 + 444 + 429)/5 which equals 436 meals on average (rounded to the nearest whole number).

Multiplying this average by the roast beef proportion (96/444), we get the forecast for roast beef portions: 436 * (96/444) ≈ 93 portions.

Answer:

The proportion of defective chips produced by the machine is more than 4% so the machine needs an adjustment.

Step-by-step explanation:

In this case we need to test whether the proportion of defective chips produced by the machine is more than 4%.

The hypothesis can be defined as follows:

H₀: The proportion of defective chips produced by the machine is not more than 4%, i.e. p ≤ 0.04.

Hₐ: The proportion of defective chips produced by the machine is more than 4%, i.e. p > 0.04.

The information provided is:

X = 12

n = 200

α = 0.025

The sample proportion of defective chips is:

[tex]\hat p=\frac{X}{n}\\\\=\frac{12}{200}\\\\=0.06[/tex]

Compute the test statistic as follows:

[tex]z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}\\\\=\frac{0.06-0.04}{\sqrt{\frac{0.04(1-0.04)}{200}}}\\\\=1.44[/tex]

The test statistic value is 1.44.

Decision rule:

We reject a hypothesis if the p-value of a statistic is lower than the level of significance α.

Compute the p-value of the test:

[tex]p-value=P(Z>1.44)\\=1-P(Z<1.44)\\=1-0.92507\\=0.07493\\\approx 0.075[/tex]

The p-value of the test is 0.075.

p-value = 0.075 > α = 0.025

The null hypothesis was failed to be rejected at 2.5% level of significance.

Thus, it can be concluded that the proportion of defective chips produced by the machine is more than 4% so the machine needs an adjustment.

To test the hypothesis whether or not the machine needs an adjustment, we can use a one-sample proportion test. Calculate the sample proportion, the standard error of the proportion, and the test statistic. Find the p-value and compare it to the significance level to make a conclusion.

To test the hypothesis whether or not the machine needs an adjustment, we can use a hypothesis test. The null hypothesis (H0) is that the machine is working properly and the alternative hypothesis (Ha) is that the machine needs an adjustment. We can use a one-sample proportion test since we are testing the proportion of defective chips.

If the p-value is less than the significance level (2.5%), we reject the null hypothesis and conclude that the machine needs an adjustment. If the p-value is greater than or equal to the significance level, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the machine needs an adjustment.

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Answer:

[tex]V(t) = 35000(0.92)^{t}[/tex]

Decay function

The value of the car in 2015 is $19,525.

Step-by-step explanation:

A exponential value function has the following format:

[tex]V(t) = V(0)(1+r)^{t}[/tex]

In which V(t) is the value after t years, V(0) is the initial value and 1+r is the yearly variation rate.

If 1+r>1, the function is a growth function.

If 1-r<1, the function is a decay function.

Mark bought a brand new car for $35,000 in 2008.

This means that [tex]V(0) = 35,000[/tex]

If the car depreciates in value approximately 8% each year

Depreciates, then r is negative. So [tex]r = -0.08[/tex]

Then

[tex]V(t) = V(0)(1+r)^{t}[/tex]

[tex]V(t) = 35000(1-0.08)^{t}[/tex]

[tex]V(t) = 35000(0.92)^{t}[/tex]

0.92 < 1, so decay function.

Then, find the value of the car in 2015.

2015 is 2015-2008 = 7 years after 2008. So this is V(7).

[tex]V(t) = 35000(0.92)^{t}[/tex]

[tex]V(7) = 35000(0.92)^{7}[/tex]

[tex]V(7) = 19525[/tex]

The value of the car in 2015 is $19,525.

Answer:

11> x

Step-by-step explanation:

-5 > x-16

Add 16 to each side

-5+16 > x-16+16

11> x

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached image below to see the step by step explanation to the question above.

Answer:

19

Final answer:

The class set up 19 full rows of chairs for the graduation ceremony by dividing the total number of chairs, 418, by the number of chairs in each row, 22.

Explanation:

To determine how many rows of chairs the fifth grade class set up for a graduation ceremony, we divide the total number of chairs by the number of chairs in each row. They have set up a total of 418 chairs, and each row contains 22 chairs.

Divide the total number of chairs (418) by the number of chairs per row (22).

Perform the division: 418 ÷ 22 = 19.

The result is that they set up 19 full rows of chairs.

Answer:

Perimeter =

[tex]2(length + width) \\ 2(5x + 1 + 4x - 1) \\ 2(5x + 4x + 1 - 1) \\ 2(9x ) \\ 9 \times 2 \\ = 18[/tex]

Answer:121

Step-by-step explanation:

11 times 11.

Answer:

[tex]121[/tex]

Step-by-step explanation:

[tex]11^{2} \\ write \: the \: exponentiation \: as \\ multiplication. \\ \\ 11 \times 11 \\ multiply \\ \\ 121[/tex]