30 POINTS! Solve the following equation for l. A = 2πr + πrl. Explain each step.

Answer:

circle b

Step-by-step explanation:

Answer:

Step-by-step explanation:

amosc: marcos62280 ( ;

Answer:

The coordinates of the point that partitions the directed line segment PT in a 3:2 ratio will be (5, 11).

Step-by-step explanation:

Given the points

What are the coordinates of the point that partitions the directed line segment PT in a 3:2 ratio?

Let D be the Divided point of the directed line segment PT.

SECTION FORMULA

The point (x, y) which partitions the line segment of the points (x₁, y₁) and

(x₂, y₂) in a ratio [tex]m:n[/tex] will be:

                                            [tex]\left(\frac{m\:x_2+n\:x_1}{m+n},\:\frac{m\:y_2+n\:y_1}{m+n}\right)[/tex]

Here,

Substituting the values in the above formula

[tex]D\left(x\right)=\left(\frac{3\times \:7\:+\:2\times 2}{3+2},\:\frac{3\times 17\:+\:2\times 2}{3+2}\right)[/tex]

[tex]D\left(x\right)=\left(\frac{21\:+\:4}{5},\:\frac{51\:+\:4}{5}\right)[/tex]

[tex]D\left(x\right)=\left(\frac{25}{5},\:\frac{55}{5}\right)[/tex]

As

[tex]\frac{25}{5}=5,\:\frac{55}{5}=11[/tex]

So

[tex]$D(x)=(5, 11)[/tex]

Therefore, the coordinates of the point that partitions the directed line segment PT in a 3:2 ratio will be (5, 11).

Answer:

Work done is 1.02J

Step-by-step explanation:

Work (W) done in stretching a spring = 1/2Fe

F (force) = 6 lb = 6×4.4482N = 26.6892N

e (extension) = 11in - 8in = 3in = 3×0.0254m = 0.0762m

W = 1/2 × 26.6892 × 0.0762 = 1.02J

Answer:

880 in³

Step-by-step explanation:

L = 20, W = 10, H = 8

2(h × W) + 2(h × L) + 2(W × L)

= 2(8*10) + 2(8*20) + 2(10*20)

= 2(80) + 2(160) + 2(200)

= 160 + 320 + 400

= 880 in³

Answer:

1.2 gallons

Step-by-step explanation:

We assume that each room is rectangular with four walls and no doors. If the dimensions are length l, by width w with height h, then there are two walls with area l*h and two walls with w*h.

The total area of the room is thus: 2lh + 2wh = 2h(l+w).

l = 12ft, w = 12ft, h = 10ft  (all given)

Area of walls = 2h(l+w) = 2*10(12+12)

Area = 2*10*24 = 480 square feet

Each gallon of paint covers 400 square feet. So, you will need to buy

480 / 400 = 1.2 gallons

You will need to buy 2 gallons

Answer:

Step-by-step explanation:

Let x represent the amount that she needs to save each month for the next year.

Stephanie is saving money to buy a new computer. So far she has saved $200. This means that the total amount that she would have saved in y months is

200 + xy

Since there are 12 months in a year,

an inequality to show how much she needs to save each month for the next year so she has at least $1200 to spend on the computer is

200 + 12x ≥ 1200

12x ≥ 1200 - 200

12x ≥ 1000

x ≥ 1000/12

x ≥ 83.33

Answer:

The probability that n of the cars tested turn out to be lemons is [tex]{m\choose n}\times\frac{k^{m}(100-k)^{(m-n)}}{100^{m}}[/tex].

Step-by-step explanation:

Let X = a car is lemon

There are 100 cars in a parking lot.

The probability that a car is a lemon is:

[tex]P (A\ car\ is\ lemons) = \frac{Number\ of\ cars\ that\ are\ lemons}{Total\ number\ of\ cars} =\frac{k}{100}[/tex]

The random variable [tex]X\sim Bin (100, \frac{k}{100})[/tex]

The probability function of a Binomial distribution is:

[tex]P(X=a)={a\choose b}\times p^{b}\times (1-p)^{a-b}[/tex]

Number of cars selected is a = m.

Compute the probability that out of m cars n turn out to be lemons as follows:

[tex]P(X=n)={m\choose n}\times [\frac{k}{100}] ^{n}\times (1-\frac{k}{100} )^{m-n}={m\choose n}\times\frac{k^{m}(100-k)^{(m-n)}}{100^{m}}[/tex]

Thus, the probability that out of m cars n turns out to be lemons is [tex]{m\choose n}\times\frac{k^{m}(100-k)^{(m-n)}}{100^{m}}[/tex].

Answer:

Step-by-step explanation:

Finding the average velocity for time t=1 and t= 5

For t^2+ 5t+ 2

Putting 5 and 1 in to the equation

= (5^2)-(1^2) + 5(5-1)+ 2

= 25-1+ 5*4+2

=24+20+2

=46m/s

For instantaneous velocity

ds/dt is found

Which gives 2t+ 5

Putting t= 5 15

Putting t= 1. 7

Subtracting the answer 8m/s.

the average velocity between [tex]\( t = 1 \)[/tex] and [tex]\( t = 5 \)[/tex] is 11 units/time, and the instantaneous velocities at [tex]\( t = 1 \)[/tex] and [tex]\( t = 5 \)[/tex] are 7 units/time and 15 units/time, respectively.

To find the average velocity between t = 1 and t = 5, we use the formula for average velocity:

[tex]\[ \text{Average Velocity} = \frac{\text{Change in Position}}{\text{Change in Time}} \][/tex]

a) Average velocity between t = 1 and t = 5 :

First, we find the position at t = 1 and t = 5 by plugging the values into the position function [tex]\( s(t) = t^2 + 5t + 2 \)[/tex]:

At t = 1:

[tex]\[ s(1) = (1)^2 + 5(1) + 2 = 1 + 5 + 2 = 8 \][/tex]

At t = 5:

[tex]\[ s(5) = (5)^2 + 5(5) + 2 = 25 + 25 + 2 = 52 \][/tex]

Now, we calculate the change in position:

[tex]\[ \text{Change in Position} = s(5) - s(1) = 52 - 8 = 44 \][/tex]

The change in time is \( 5 - 1 = 4 \).

[tex]\[ \text{Average Velocity} = \frac{44}{4} = 11 \, \text{units/time} \][/tex]

b) Instantaneous velocity at t = 1 and t = 5 :

The instantaneous velocity at any time t is given by the derivative of the position function [tex]\( s(t) \)[/tex] with respect to t, denoted as [tex]\( s'(t) \)[/tex] or [tex]\( \frac{ds}{dt} \)[/tex].

[tex]\[ s(t) = t^2 + 5t + 2 \][/tex]

Taking the derivative with respect to [tex]\( t \)[/tex]:

[tex]\[ s'(t) = \frac{ds}{dt} = 2t + 5 \][/tex]

Now, we can find the instantaneous velocities at [tex]\( t = 1 \)[/tex] and [tex]\( t = 5 \)[/tex] by plugging these values into [tex]\( s'(t) \)[/tex]:

At t = 1:

[tex]\[ s'(1) = 2(1) + 5 = 2 + 5 = 7 \, \text{units/time} \][/tex]

At t = 5:

[tex]\[ s'(5) = 2(5) + 5 = 10 + 5 = 15 \, \text{units/time} \][/tex]

So, the average velocity between [tex]\( t = 1 \)[/tex] and [tex]\( t = 5 \)[/tex] is 11 units/time, and the instantaneous velocities at [tex]\( t = 1 \)[/tex] and [tex]\( t = 5 \)[/tex] are 7 units/time and 15 units/time, respectively.

Answer:

200-50-40=B

B =110 blue pieces

Step-by-step explanation:

[tex]\bf (\stackrel{x_1}{-1}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{-9}~,~\stackrel{y_2}{-2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{(-7)}}}{\underset{run} {\underset{x_2}{-9}-\underset{x_1}{(-1)}}}\implies \cfrac{-2+7}{-9+1}\implies -\cfrac{5}{8}[/tex]

Answer:

The answer to your question is m = [tex]\frac{5}{8}[/tex]

Step-by-step explanation:

Data

A (-1, -7)

B (-9, -2)

Formula

slope = m = [tex]\frac{y2 - y1}{x2 - x1}[/tex]

Use the slope formula to find the answer. Just substitute the values and simplify them.

Substitution

x1 = -1

x2 = -9

y1 = -7

y2 = -2

                 m = [tex]\frac{-2 + 7}{-9 + 1}[/tex]

Simplification

                 m =- [tex]\frac{5}{8}[/tex]

Result

                  m =- [tex]\frac{5}{8}[/tex]

Abby's final grade average is 69.14, which is less than 80%. Therefore, she did not get a "B".

To calculate Abby's final grade average, we first need to find the average of her three test scores: 85 + 90 + 75 = 250. Then we need to add her final exam score, which counts as three test scores. 78 x 3 = 234. So the total score for Abby's tests and final exam is 250 + 234 = 484. Since there are a total of 7 test scores (3 tests + 3 tests for the final exam + 1 final exam), we divide the total score by 7 to get 484/7 = 69.14. Abby's final grade average is 69.14, which is less than 80%, so she did not get a "B".

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Answer:

B. [-1, ∞).

Step-by-step explanation:

g(x) = 3|x − 1| − 1

When x = 1  g(x) = 3(0) - 1 = -1.

As all negative vales of x will give positive values of  |x - 1| then  g(x) = -1 is its minimum value. The graph will be shaped like a letter V with the vertex at (1,-1).

Therefore the range is  [-1, ∞).

The range of g(x)=3|x-1|-1 is [-1,∞) i.e. option B is correct.

The set of all the outputs of a function is known as the range of the function .

According to the given question

we have,

A function, g(x) = 3|x-1| - 1

Lets, find the value of g(x) for the different values of "x"

when,

x=0 ⇒ g(0) = -1

x=1 ⇒ g(1) = -1

x=2 ⇒g(2) = 2

Similarly, we can check for the negative values of x.

So, for all the negative values of x we will gives only positive values for g(x) and  only at x=0, g(x) = -1 , which is its minimum value .

⇒ The range of given function g(x) is {-1,∞).

Hence , option B is correct.

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Answer:

Acceleration (a) [tex]=5.29\ m\./s^2[/tex]

Step-by-step explanation:

Given that

final velocity (v) [tex]=45\ m/s[/tex]

Initial velocity (u) [tex]=0\ m/s[/tex]

Time (t) [tex]=8.5\ seconds[/tex]

Then

[tex]v=u+at\ ...................................... (1)[/tex]

Where [tex]a[/tex] is acceleration.

put the value in equation [tex](1)[/tex]

[tex]45=0+a\times8.5\\a\times8.5=45[/tex]

dividing [tex]8.5[/tex] both sides

[tex]\frac{a\times8.5}{8.5}=\frac{45}{8.5}\\\\a=\frac{45}{8.5}\\\\a=\frac{450}{85}\\\\a=5.29\ m/s^2[/tex]

To find out how many students answered at least one bonus question out of 50, we subtract the number who didn't answer any from the total, resulting in 48 students.

To determine how many students answered at least one of the bonus questions in a midterm psychology exam, we can use the principle of inclusion-exclusion.

Given that 26 students answered the first bonus question,

3 students answered the second bonus question,  

2 students didn't answer either, we can find the total number of students who attempted at least one bonus question.

First, add the number of students who answered each question: 26 + 33 = 59.

However, this count includes the students who answered both questions twice.

Since the total number of students is 50, and 2 didn't answer any bonus questions, 48 students must have attempted at least one bonus question.

The apparent excess (59) suggests overlaps, indicating students answered both questions.

To find the exact number of students who answered at least one bonus question, we subtract the total number of students by those who didn't attempt any: 50 - 2 = 48.

Therefore, 48 students answered at least one of the bonus questions.

The Complete Question is:

out of 50 students taking a mid-term psychology exam, 23 answered the first of two bonus questions, 36 answered the second bonus question, and 2 didn't with either one. round your answer to the nearest percent.

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse's length equals the sum of the squares of the other two sides' lengths. This can be proven via the areas of squares with sides corresponding to the triangle's sides, demonstrating that a²+b²=c².

The Pythagorean theorem is a fundamental principle in geometry, named after the Greek mathematician Pythagoras. It states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a²+b²=c².

To prove this, we can begin with a right-angled triangle with sides a, b, and hypotenuse c. If we square the length of c (i.e., c²), this is equivalent to the area of a square with side length c. Similarly, a² and b² represent the areas of squares with side lengths a and b, respectively.

If we add together the areas of the two smaller squares (a²+b²), this equals the area of the larger square (c²). This proves the Pythagorean theorem. For instance, consider a right triangle with sides of lengths 3, 4, and 5. The squares would have areas 9 and 16, which add up to 25 - the area of the square on the hypotenuse.

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The Pythagorean Theorem states that a² + b² = c². A step-by-step proof involves constructing a square with the right-angled triangle and equating the areas. This logical deduction confirms the theorem's correctness.

The Pythagorean Theorem is one of the fundamental results in Geometry, which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): a² + b² = c². Here is a step-by-step proof:

Thus, we have proven that the theorem holds true using logical deductions.

Answer:

f'(x) = [tex]-\frac{9}{x^2}[/tex]

Step-by-step explanation:

i) f(x) = 9 / x

ii) f'(x)  = [tex]$\lim_{h\to 0} \frac{f(x+h) - f(x)}{h} $ \hspace{0.2cm}[/tex]

        [tex]= $\lim_{h\to 0} \frac{\frac{9}{x+h} - \frac{9}{x} }{h} = \hspace{0.1cm} $\lim_{h\to 0} \frac{9x - 9(x+h)}{hx(x+h)} $ \hspace{0.1cm} = \hspace{0.1cm}$\lim_{h\to 0} \frac{-9h}{hx(x+h)} = $\lim_{h\to 0} \frac{-h}{x(x+h)} = \frac{-9}{x^2}$[/tex]

Answer:

[tex]7p\leq 40[/tex]

Jamie can buy lunch for 5 person.

Step-by-step explanation:

Given:

Jamie has $40.

Lunch cost per person = $7

Solution:

Jamie wants to treat some friends to lunch.He has $40 and knows that lunch will cost about $7 per person, p.

So, an inequality to represent this situation is written as:

[tex](Lunch\ cost\ per\ person)p\leq Total\ amount[/tex]

[tex]7p\leq 40[/tex]

[tex]p\leq \frac{40}{7}[/tex]

[tex]p\leq 5.71[/tex]

Hence, the answer is 5

Therefore, Jamie can buy lunch for 5 persons.

Step-by-step explanation:

0

Answer: B) 4.963±0.019.

Step-by-step explanation:

Confidence interval for population mean ( when population standard deviation is not given) is given by :-

[tex]\overline{x}\pm t^*\dfrac{s}{\sqrt{n}}[/tex]

, where [tex]\overline{x}[/tex] = Sample  mean

n= Sample size

s= sample standard deviation

t* = critical t-value.

As per given:

n= 50

Degree of freedom = n-1 =49

[tex]\overline{x}= 4.963\ lb[/tex]

s= 0.067 lb

For df = 49 and significance level of 0.05 , the critical two-tailed t-value ( from t-distribution table) is 2.010.

Now , substitute all values in the formula , we get

[tex]4.963\pm (2.010)\dfrac{0.067}{\sqrt{50}}\\\\ 4.963\pm (2.010)(0.0094752)\\\\ 4.963\pm0.019045152\approx4.963\pm0.019[/tex]

Hence,  a 95% confidence interval for the mean weight (in pounds) of the mulch produced by this company is [tex]4.963\pm0.019[/tex].

Thus , the correct answer is B) 4.963±0.019.

Answer:

the correct answer is B) 4.963±0.019.

Step-by-step explanation:

The only three-digit number meeting all the conditions is 234, where 2, 3, and 4 are consecutive numbers the tens digit is an odd number, and the sum of each pair of digits is more than 4 and less than 10.

In solving this problem, we need to apply logic based on the given conditions. The number is a three‐digit number. The digits are consecutive whole numbers in increasing order and the tens digit is an odd number. Given the sum of each pair of digits should be more than 4 and less than 10, the only possible digits that can be put in a row and satisfy these conditions are 2, 3, and 4 or 4, 5, and 6. From these options, only 2, 3, and 4 have the tens place occupied by an odd number. So, the correct number is 234.

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Final answer:

The three-digit number that meets all the given conditions, including having consecutive digits in increasing order with an odd middle digit and each pair's sum between 4 and 10, is 345.

Explanation:

To find a three-digit number that meets the given conditions, we first identify the critical factors: The digits are consecutive whole numbers in increasing order, each pair of digits' sum must be greater than 4 and less than 10, and the tens digit is an odd number. Therefore, we proceed with a logical approach to solve this.

Since the tens digit must be odd, possible options for the tens digit are 1, 3, 5, 7, or 9.

Considering the sum of each pair must be greater than 4 and less than 10 limits our options. If we start with 1, the consecutive numbers don't satisfy the sum condition strictly. Similarly, higher starting digits will not fit the conditions.

Realizing the only sequence of three consecutive numbers, among which the middle one is odd and every pair's sum falls within the required range, is 3, 4, and 5. Hence, 345 is the only number that satisfies all the given conditions.

Answer:

Question 1: Are the footprints of the two sheds similar?

Question 2: Tell whether the footprint of the least expensive shed is an enlargement or a reduction,

Question 3: Find the scale factor from the most expensive shed to the least expensive shed

Explanation:

Question 1: Are the footprints of the two sheds similar?

The footprints of the two sheds will be similar if their measures are proportional.

The ratio of the measures of the footprint of the most expensive shed is:

The ratio of the measures of the footprint of the least expensive shed is:

Since, the two ratios are equal, you conclude that the corresponding dimensions are proportional and the two sheds are similar.

Question 2: Tell whether the footprint of the least expensive shed is an enlargement or a reduction.

A reduction is a similar transformation (the image and the preimage are similar)  that maps the original figure into a smaller one.

Since the dimensions of the foot print of the least expensive shed, 10 feet wide by 14 feet long, are smaller than the dimensions of the most expensive shed, 15 feet wide by 21 feet long the you conclude that the former is a reduction of the latter.

Question 3: Find the scale factor from the most expensive shed to the least expensive shed.

To find the scale factor from the most expensive shed to the least expensive shed, you divide the measures of the corresponding dimensions. You can do it either with the widths or with the lengths.

Using the widths, you get:

That means that the scale factor from the most expensive shed to the least expensive shed is 3/2.

Using the lenghts, you should obtain the same scale factor:

Answer:i dont knowStep-by-step explanation:

Answer:

hot dogs sold=110

sodas sold=36

Step-by-step explanation:

146-36=110

110+36=146

Answer:91 Sodas and 55 hot dogs were sold.

Step-by-step explanation:

Let x represent the number of Sodas that were sold at the basketball game.

Let y represent the number of hot dogs that were sold at the basketball game.

At the basketball game a vendor sold a combined total of 146 sodas and hotdogs. This means that

x + y = 146 - - - - - - - - - - - - - - -1

The number of Sodas was 36 more than the number of hotdogs sold. This means that

x = y + 36

Substituting x = y + 36 into equation 1, it becomes

y + 36 + y = 146

2y + 36 = 146

2y = 146 - 36 = 110

y = 110/2 = 55

x = y + 36 = 55 + 36

x = 91

Answer:

the selling price of the house is estimated as $137,000

Step-by-step explanation:

Given data:

clear amount is $128,000

closing cost is $780

sales commission rate is 6%

let S be the selling price of house

from the information given in the question we have  following relation

[tex]128,000 \leq S - 0.06S - 780[/tex]

[tex]128,000 \leq 0.94S - 780[/tex]

adding 780 on both side, we get

[tex]128,000 - 780 \leq 0.94S[/tex]

divide the both side by 0.94, we get

[tex]137,000 \leq S[/tex]

therefor the selling price of the house is estimated as $137,000

Answer:

  $5.25

Step-by-step explanation:

The two purchases can be described by the equations ...

  3s +2p = 29.75

  4s +3p = 42.00

If you multiply the first equation by 3 and subtract 2 times the second equation, the cost of a shirt pops out.

  3(3s +2p) -2(4s +3p) = 3(29.75) -2(42.00)

  9s +6p -8s -6p = 89.25 -84.00 . . . . . . . eliminate parentheses

  s = 5.25 . . . . . . . . . . collect terms

One shirt costs $5.25.

Answer:

W = 650000 ftlb

Step-by-step explanation:

Parameters given:

Weight of the cable = 2 lb/ft

Weight of the coal = 800 lb

Depth of the shaft, x = 500 ft

The total work done in this system is given by the sum of the work done on the coal and the work done on the shaft.

WORK DONE ON THE COAL

The work done on the coal is given as:

[tex]W_{coal}[/tex] = Weight of coal * distance

[tex]W_{coal}[/tex] = 800 * 500

[tex]W_{coal}[/tex] = 400000 ftlb

WORK DONE ON THE SHAFT

If we partition the cable into several segments of depth Δx, we can find the work done on the cable.

The work done on the shaft is given as:

[tex]W_{shaft}[/tex] = 2Δx * x

[tex]W_{shaft}[/tex] = 2xΔx

=> [tex]W_{shaft}[/tex] = [tex]\int\limits^{500}_{0} {2x} \, dx[/tex]

[tex]W_{shaft}[/tex] = [tex]\frac{2x^{2}}{2} \left \{ {{500} \atop {0}} \right.[/tex]

[tex]W_{shaft}[/tex] = [tex]500^{2} - 0^{2}[/tex]

[tex]W_{shaft}[/tex] = 250000 ftlb

Therefore, total work done is:

[tex]W_{total} = 250000 + 400000[/tex]

[tex]W_{total} = 650000 ftlb[/tex]

The work done to lift the coal up the mine shaft is 900,000 ft-lbf.

To find the work done, we can use the formula:

Work = Force x Distance

First, we need to calculate the force. The cable weighs 2 lbf/ft, so the total weight of the cable is 2 lbf/ft x 500 ft = 1000 lbf. The force to lift the coal is 800 lbf. Therefore, the total force is 1000 lbf + 800 lbf = 1800 lbf.

Next, we can calculate the work done by multiplying the force by the distance: Work = 1800 lbf x 500 ft = 900,000 ft-lbf.

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(A) Probability of the black card is 1 /2.
(B) Probability of a red card is 26/51.
(C) Probability of selecting a black card and then selecting a red card is 13/51.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
Total number of cards in the deck = 52
Total number of black cards = 26
Total number of red cards = 26
Probability of selecting a black card = 26 / 52 = 1 / 2
Now, the total number of card become after selecting 1 black card = 51
Probability of selecting a red card = 26 / 51
Now,
The probability of selecting a black card and then selecting a red card is,
= 1 / 2 * 26 / 51
= 13 / 51

Thus, (A) the Probability of a black card is 1 /2.
(B) Probability of a red card is 26/51.
(C) Probability of selecting a black card and then selecting a red card is 13/51.

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The probability of selecting a black card first and then a red card is [tex]\(\frac{13}{51}\).[/tex]

To find the probability of selecting a black card and then selecting a red card from a standard deck of 52 playing cards without replacement, we need to follow these steps:

1. Calculate the probability of selecting a black card first:

  - There are 26 black cards in a standard deck (13 spades and 13 clubs).

  - The probability of selecting a black card first is:

  [tex]\[ P(\text{Black card first}) = \frac{26}{52} = \frac{1}{2} \][/tex]

2. Calculate the probability of selecting a red card second, given that the first card was black:

  - After drawing the first black card, there are 51 cards left in the deck.

  - There are still 26 red cards in the deck (since the black card was not replaced).

  - The probability of selecting a red card given that the first card was black is:

   [tex]\[ P(\text{Red card second} \mid \text{Black card first}) = \frac{26}{51} \][/tex]

3. Calculate the combined probability of both events occurring:

  - The probability of both events happening (selecting a black card first and then a red card) is the product of the individual probabilities:

    [tex]\[ P(\text{Black card first and Red card second}) = P(\text{Black card first}) \times P(\text{Red card second} \mid \text{Black card first}) \][/tex]

    Substituting the values we found:

    [tex]\[ P(\text{Black card first and Red card second}) = \left(\frac{1}{2}\right) \times \left(\frac{26}{51}\right) = \frac{26}{102} = \frac{13}{51} \][/tex]

Therefore, the probability of selecting a black card first and then a red card is [tex]\(\frac{13}{51}\).[/tex]

Answer:

There were 6 people against the bill.

Step-by-step explanation:

Given:

In a recent poll,only 8% of the people surveyed were against a new bill making it mandatory to recycle.

Now, to find of the 75 people surveyed were against the bill.

Total number of people = 75.

Percent of the people surveyed were against the bill = 8%.

Now, to get the number of people who were against the bill:

8% of 75

[tex]=\frac{8}{100}\times 75[/tex]

[tex]=0.08\times 75[/tex]

[tex]=6.[/tex]

Therefore, there were 6 people against the bill.

Answer:

Step-by-step explanation:

Triangle GHI is a right angle triangle.

From the given right angle triangle,

GH represents the hypotenuse of the right angle triangle.

With m∠H as the reference angle,

HI represents the adjacent side of the right angle triangle.

GI represents the opposite side of the right angle triangle.

To determine m∠H, we would apply

the Sine trigonometric ratio.

Sin θ = adjacent side/hypotenuse. Therefore,

Sin m∠H = 7/10 = 0.7

m∠H = Sin^-1(0.7)

m∠H = 44.4° to the nearest tenth.

Answer: gayness

Step-by-step explanation:

Answer: the weight of each bags are 1.85kg, 1.85kg and 3.05 kg

Step-by-step explanation:

Total weight of the three bags is

6 3/4 kg. Converting to decimal, it becomes 6.75 kg.

Two of them have the same weight. Let x represent the bags of equal weight. Their total weight would be 2x. The third bag is heavier than each of the bags of equal weight by 1 1/5 kg. Converting to decimal, it becomes 1.2kg. It means that the weight of the third bag would be

x + 1.2

Therefore, for the three bags,

2x + x + 1.2 = 6.75

3x = 6.75 - 1.2 = 5.55

x = 5.55/3 = 1.85

Weight of the third bag is

1.85 + 1.2 = 3.05kg

To solve for the weights of the bags, we set up an equation and find that the weight of each of the lighter bags is 1 17/20 kg, and the weight of the heavier bag is 3 1/20 kg.

The question asks us to calculate the weight of each bag of sweets when given the total weight and the additional weight of the heavier bag. Let's denote the weight of the two equal bags as 'x' kilograms each. According to the problem, the third bag weighs 'x + 1 1/5' kg, which is heavier by 1 1/5 kg than each of the other two bags. The total weight of the three bags is 6 3/4 kg.

Starting with this information, we can set up an equation to find the value of 'x': 2x + (x + 1 1/5 kg) = 6 3/4 kg. To solve for 'x', first simplify the right side of the equation by converting the mixed fraction to an improper fraction: 6 3/4 kg = 27/4 kg. Now, convert 1 1/5 kg to an improper fraction as well: 1 1/5 kg = 6/5 kg. The equation now is: 2x + x + 6/5 = 27/4 kg.

Combining like terms, we have: 3x = 27/4 kg - 6/5 kg. To combine these fractions, we need a common denominator, which would be 20 in this case. This changes the equation to: 3x = (27/4) * (5/5) - (6/5) * (4/4) = 135/20 kg - 24/20 kg = 111/20 kg. To find 'x', divide both sides by 3: x = (111/20 kg) / 3 = (111/20) * (1/3) kg = 37/20 kg = 1 17/20 kg. This is the weight of each of the lighter bags.

Subsequently, the weight of the heavier bag can be found by adding the additional weight: x + 6/5 kg = (37/20 kg) + (6/5 kg) = (37/20) + (24/20) = 61/20 kg = 3 1/20 kg.

Therefore, the weight of the two bags with equal weight is 1 17/20 kg each, and the weight of the heavier bag is 3 1/20 kg.