Find the area. Round your answer to the nearest tenth. Use 3.14 for pi.
19 cm

Answer:

Step-by-step explanation:

Step one:

given data

the brown family has 5 liters of lemonade that weighs 1 kg per liter

this implies that they have 5kg of lemonade.

convert 5kg to grams we have 5*1000= 5000grams

(because 1000g is equal to 1kg)

Step two:

if at the end of the day there was 290grams left, then they drank

=5000-290

=4710

They drank 4710grams of lemonade.

Answer:

1.55s

Step-by-step explanation:

The height equation of the projectile is given as;

h = -16t^2 + vt + s .......1

where;

t is the time in seconds,

v is the upward velocity at the start,

s is the starting height.

Given;

v = 70 ft/s

s = 5 ft

Substituting the values equation 1 becomes;

h = -16t^2 + 70t + 5

For the ball to reach 75 ft, h = 0

75 = -16t^2 + 70t + 5

-16t^2 + 70t + 5 - 75 = 0

-16t^2 + 70t - 70 = 0

solving the quadratic equation;

Time t = 2.83 s and t = 1.55s

Therefore, the ball will first reach 75 ft after 1.55 seconds.

P (A ∩ B) is (e) 0.63. It is the product of their individual probabilities.

If the event A and B are independent, the probability of both A and B is happening is

P (A ∩ B) = P(A) . P(B)

We have

A and B are independent events.

Find P(A ∩ B)!

Since the events are independent, we use the formula above and we get

P (A ∩ B) = 9/10 . 7/10

P (A ∩ B) = 0.63

Hence, the probability of both A and B is happening 0.63.

The correct option is (e).

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No, the plan will not work because tan B = 8/5; B ≈ 58°

There are three primary trigonometric ratios for a right angle triangle and they are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

To get angle B, we will make use of trigonometric ratios to get:

tan B = 8/5

tan B = 1.6

B = tan⁻¹1.6

B = 58°

From the ramp, we can see that the angle is greater than what Gael wants to build and as such we can say it will not work.

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Answer:

10

Step-by-step explanation:

18-7=11 then you subtract 1 because 9*2=18 so the answer is 1o

Answer:

Step-by-step explanation:

Answer:

\(b = \frac{(d-c)}{a}\)

Step-by-step explanation:

ab + c = d

Subtract c from both sides

ab + c - c = d -c

         ab = d - c

Divide both sides by 'a'

\(\frac{ab}{a}=\frac{d-c}{a}\\\\b = \frac{(d-c)}{a}\)

Answer:

b = (d - c)/a

Step-by-step explanation:

just took this test

You must divide by the coefficient (a number before a variable)

Hope this helps you! :)

~Just a joyful teen

\(GraceRosalia :)\)

Answer:

8 like I'm trying maybe I'll be good at math someday

Step-by-step explanation:

hehe

We can start by using the formula for a geometric series:

S = a + ar + ar^2 + ...

where S is the sum of the series, a is the first term, r is the common ratio.

Let's choose a = e and r = e. Then we have:

S = e + ee + eee + ... = e(1 + e + e^2 + ...)

Now we can use the formula for the sum of an infinite geometric series with |r| < 1:

S = a / (1 - r)

Substituting our values, we get:

e(1 + e + e^2 + ...) = e / (1 - e)

Multiplying both sides by (1 - e), we get:

e(1 + e + e^2 + ...) (1 - e) = e

Simplifying the left side using the distributive property, we get:

e - e^2 + e^2 - e^3 + e^3 - ... = e

All the terms after the first two cancel out, leaving us with:

e - e^2 = e(1 - e)

Dividing both sides by e(1 - e), we get:

1 = 1/(1 - e) + 1/e

Multiplying both sides by e(1 - e), we get:

e(1 - e) = (1 - e) + e(1 - e)/e

Simplifying the right side, we get:

e(1 - e) = 1

So we have:

ex = Px(1 + ex+1)

Multiplying both sides by e, we get:

ex+1 = Pe(x+1) + e^(x+1)

Substituting x = 59, we can use the table to find P60:

e60 = P60(e61 + 1)

15.96 = P60(15.27 + 1)

15.96 = P60(16.27)

P60 = 15.96/16.27

P60 ≈ 0.98

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Answer:

4 1/4.

Step-by-step explanation:

First convert to improper fractions:

1 3/4 = (4*1 + 3)/4 = 7/4

2 1/2 = (2*2 + 1)/2 = 5/2

So it becomes:

7/4 + 5/2

The LCM of 2 and 4  is 4 so we write:

7/4 + 10/4

= 17/4

Now convert this to a mixed number:

17 / 4 = 4 remainder 1

So the answer is 4 1/4.

Answer:

4¼ is the answer

Step-by-step explanation:

\( \\ 1 \frac{3}{4} + 2\frac{1}{2} \)

\( \\ \rightarrow \frac{7}{4} + \frac{5}{2} \)

\( \\ \rightarrow\frac{7 + 10}{4} \)

\( \\ \rightarrow \frac{17}{4} \)

\( \\ \rightarrow 4\frac{1}{4} \)

As we can see 17/4 is not divisible by 4 so if we divide it we will get decimal number or mixed number and we need the answer in mixed number so the number 4¼ is in the simplest form and is the answer.

Hope it's helpful!

We have the following function given:

We want to apply a dilation with a scale factor k centered at the origin

Assuming that the scale factor is k, then we just need to do the following :

And with this we preserve the condition of centered at the origin and with the dilation factor

The cost of installing a bush is $7 and the cost of installing a tree is $28

Represent the trees with t and the bushes with b.

So, we have the following equations:

13b + 7t = 287

8b + 12t = 392

Make t the subject in 13b + 7t = 287

t = (287 - 13b)/7

Substitute t = (287 - 13b)/7 in 8b + 12t = 392

8b + 12 * (287 - 13b)/7 = 392

Multiply through by 7

56b + 12 * (287 - 13b) = 2744

Expand

56b + 3444 - 156b = 2744

Collect like terms

56b - 156b = 2744 - 3444

-100b = -700

Divide both sides by -100

b = 7

Substitute b = 7in t = (287 - 13b)/7

t = (287 - 13*7)/7

Evaluate

t = 28

Hence, the cost of installing a bush is $7 and the cost of installing a tree is $28

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If he puts away 10% of his $32,000 salary every year, The total of his 401(k) be in 10 years is: a. $67,266.16.

First step

Contribution=(10% ×$32,000)+ 50% from employer

Contribution=$3,200+ ($3,200×50%)

Contribution=$3,200+$1,600

Contribution=$4,800

Second step

Future value= 4800 (1 + 0.073)^10 – 1/ 0.073

Future value= 4800 (1 .073)^10 – 1/ 0.073

Future value= 4800 (2.0230062274104 – 1) / 0.073

Future value= 4800 (1.0230062274104) / 0.073

Future value=$4,910.42989157/0.073

Future value=$67,226.16

Therefore the total of his 401(k) be in 10 years is: a. $67,266.16.

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Answer:a. $67,266.16.

Step-by-step explanation:edge

Answer:

8h

Step-by-step explanation:

8 miles per hour

h hours

plug in h for how many hours

8 divided by 6 is 1.3

1.3 hours to run 6 miles

Rounded to the nearest cent, each member should still raise approximately $39.96 on average to meet the goal.

To determine how much each member should still raise on average to meet the goal, we need to find the remaining amount that needs to be raised and divide it by the number of team members.

The total amount needed to meet the goal is $1460.00, and they have already raised $461.00. Therefore, the remaining amount to be raised is:

Remaining amount = Total amount needed - Amount already raised

Remaining amount = $1460.00 - $461.00

Remaining amount = $999.00

Now, to find out how much each member should raise on average, we divide the remaining amount by the number of team members:

Average amount per member = Remaining amount / Number of team members

Average amount per member = $999.00 / 25

Average amount per member = $39.96

Note: In practice, some members may raise more or less than the average amount, depending on their individual fundraising efforts and capabilities. The average amount per member serves as a guideline for the overall target, but individual contributions may vary.

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Answer:

New price = 0.06 x Original price

New price $1,968

We are given a graph of a line and asked to write the equation in the form below.

Where m is the slope and b is the y-intercept of the line.

The y-intercept is the point where the line intersects the y-axis.

From the graph, we see that the line intersects the y-axis at -2

So, the y-intercept is -2

The slope of the line is given by

The rise is the vertical distance between the two points on the line.

The run is the horizontal distance between the two points on the line.

As you can see, we selected two points on the line and we have got a rise of 8 units and a run of 4 units

So, the slope of the line is 2

Therefore, the equation of the line is

The closed formula of h(t) and f(t) for

h(0)=f(0)=100b => h(t) = 100(2t+1), f(t) = 100(2t-1) ,

h(0)=200, f(0)=100 => h(t) = 200(2t+1), f(t) = 100(2t-1)

h(0)=600, f(0)=500 =>h(t) = 300 + 200(2t+\((-1)^{t}\)), f(t) = 200 - 100\((-1)^{t}\)

The recursive equations for the given two interacting population of hares and foxes are

h(t+1)=4h(t)-2f(t)

f(h+1)=h(t)+f(t)

for the given initial population in parts from a to c we need to create a close formula for h(t) and f(t)

h(t) = 100(2t+1)

f(t) = 100(2t-1)

h(t) = 200(2t+1)

f(t) = 100(2t-1)

h(t) = 300 + 200(2t+\((-1)^{t}\))

f(t) = 200 - 100\((-1)^{t}\)

The closed formula of h(t) and f(t) for

h(0)=f(0)=100b => h(t) = 100(2t+1), f(t) = 100(2t-1) ,

h(0)=200, f(0)=100 => h(t) = 200(2t+1), f(t) = 100(2t-1)

h(0)=600, f(0)=500 =>h(t) = 300 + 200(2t+\((-1)^{t}\)), f(t) = 200 - 100\((-1)^{t}\)

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The standard deviation of the given data set, {12, 12, 12, 12, 12, 12, 12}, is zero. This is because the deviation of every value from the mean is zero. Therefore, the standard deviation of the given data set is zero.

In statistics, the standard deviation (SD) is a measure of how much the data is spread out from the mean, or how much the data deviates from the average value. It is calculated by finding the square root of the variance.Variance (σ2) is a measurement of the degree to which a set of data deviates from the mean. In other words, variance is a measure of how much the data is spread out. It is defined as the average of the squared differences from the mean.The formula for calculating the variance is

:σ2 = Σ(x - μ)2/N

where Σ represents the sum, x is the value of the observation,

μ is the mean of the observations, and

N is the total number of observations.

The standard deviation formula is the square root of the variance.

Therefore,σ = √σ2 = √Σ(x - μ)2/N

The given data set is {12, 12, 12, 12, 12, 12, 12}.

The mean of this data set is:(12+12+12+12+12+12+12) / 7 = 12

The deviation of every value from the mean is zero. Therefore, the variance of the given data set is zero. The standard deviation formula is the square root of the variance. Therefore, the standard deviation of the given data set is zero.

The standard deviation of the given data set, {12, 12, 12, 12, 12, 12, 12}, is zero.

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we know that 76% of the specialty soaps are made with fresh herbs, and we also know that there are a total of 350 specialty soap bars, so how many are made with fresh herbs?  well, just 76% of those 350

\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{76\% of 350}}{\left( \cfrac{76}{100} \right)350}\implies 266\)

The multiple of 2 means any number that is completely divisible by 2.

A multiple in mathematics is basically that number which is formed by multiplying a particular number and it is completely divisible by that number.

If we talk about the number 2, then the multiple of 2 will mean that any number that is formed by multiplying 2 into it.

For example, 6 is a number which can be written as 2 x 3.

Here, 3 is multiplying two times and it becomes 6, so, it is a multiple of 2. Also, if any number is appearing in the table of 2 then it is a multiple of 2.

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The length of the line segment AB such that PQ is the reflection of AB will be 6 units.

A line section that can connect two places is referred to as a segment.

A line segment is just part of a big line that is straight and going unlimited in both directions.

If we reflect any curve about the x-axis then only the y coordinate changes its sign (x,y) → (x,-y).

Given PQ is a reflection of AB and P(2,-2) and Q (8,-2)

Therefore, A(2,2) and B(8,2).

The length of AB will be,

AB = √(8 - 2)² + (2-2)² = 6

Hence "The length of the line segment AB such that PQ is the reflection of AB will be 6 units".

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Answer:

3/9 + 5/9 and 4/9 + 4/9 are both equal to 8/9.

Answer:

Second option and fifth option

Step-by-step explanation:

Since they are all with a denominator of 9 we do not need to do anything else except add them up.

The first one is equal to 7/9

Second is 8/9

Third is 6/9

Fourth is 9/9

Fifth is 8/9

Transition matrix We are given that the proportion of customers who shop at store 1, store 2 and store 3 on January 1 are respectively 0.3, 0.33 and 0.4166666666666667. Therefore, the equilibrium has been reached.

In other words, we have to find a vector x such thatAx = xwhere A is the transition matrix.

This is equivalent to solving the system of equations:(0.3716666666666667)x1 + 0.29625x2 + 0.25333333333333335x3

= x1(0.9) + x2(0.05) + x3(0.1)(0.05)x1 + 0.85x2 + 0.4x3

= x1(0.1) + x2(0.85) + x3(0.05)(0.05)x1 + 0.1x2 + 0.5x3

= x1(0.5) + x2(0.1) + x3(0.4)

Solving this system of equations,

we getx1

= 0.33027522935779817x2

= 0.30184331797235023x3

= 0.3678814526698518.

Therefore, the long-run distribution of customers among the three stores is

[0.33027522935779817 0.30184331797235023 0.3678814526698518].d)

Prove that an equilibrium has been reached The equilibrium has been reached if the proportion of customers who will shop at each store in the long-run is unchanged when multiplied by the transition matrix.

We can check if this is true by multiplying the long-run distribution vector by the transition matrix and verifying that it is equal to the long-run distribution vector.

We have

A[0.33027522935779817 0.30184331797235023 0.3678814526698518]

= [0.33027522935779817 0.30184331797235023 0.3678814526698518].

Therefore, the equilibrium has been reached.

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Answer:

It is called an isosceles trapezoid/ trapezium

Step-by-step explanation:

The translation rule for these circles is C): (x-1),(y+4), with a scale factor of 1/4. This means that when transforming Circle A to Circle B, each x-coordinate is decreased by 1 and each y-coordinate is increased by 4.

Circle is a two-dimensional shape with no sides or corners. Its defining feature is its curved line, which forms a continuous loop. The circle has no beginning or end, which symbolizes eternity, completeness and unity. Circles are often used in various designs, logos and artwork, as well as in mathematics, science, engineering and architecture.

The translation rule for these circles is C): (x-1),(y+4). We can calculate the scale factor by determining the difference between the coordinates of the two circles.

The coordinates of Circle A are (x,y). The coordinates of Circle B are (x-1, y+4). Therefore, the difference between the two is (1,4).

The scale factor is the ratio of the differences. Therefore, the scale factor is 1/4.

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Therefore, the translation rule for these circles is C): (x-1),(y+4), and the scale factor is 1/4.

In conclusion, the translation rule for these circles is C): (x-1),(y+4), with a scale factor of 1/4. This means that when transforming Circle A to Circle B, each x-coordinate is decreased by 1 and each y-coordinate is increased by 4.

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The probability of the Bob arrived before 1.30 P.M is 1/2 if the Alice arrives after Bob.

According to the question,

Alice and Bob each arrive at a party at a random time between 1.00 P.M and 2.00 P.M.

In probability theory, the sample space(s) of a random trial is the set all possible results of that trial.

Let 'x' be the arrival time of Alice and 'y' be the arrival time of Bob.

s = {(x, y) /1≤x≤2 and 1≤y≤2}

In order to find the probability of the Bob arrived before 1.30 P.M, if the Alice arrives after Bob.

Formula for Probability = \(\frac{Number of favorable events}{Total number of events}\)

= 1/2

Hence, the probability of the Bob arrived before 1.30 P.M is 1/2 if the Alice arrives after Bob.

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Answer:

Bus 18 is more consistent than Bus 47 based on the IQR, which is smaller for Bus 18 (16) compared to Bus 47 (24), indicating less spread of data between the 25th and 75th percentiles.

Step-by-step explanation:

Answer: The correct option regarding which bus has the least spread among the travel times is given as follows:

Bus 14, with an IQR of 6.

How to obtain the measures of spread?

First, we consider the dot plot, which shows the number of times that each observation appears in the data set.

Then we consider the interquartile range, which gives the difference between the third quartile and the first quartile of the data set.

The interquartile range is a better measure of spread compared to the range of a data set, as it does not consider outliers.

For groups of 15 students, we have that:

The first half is composed of the first seven students, hence the first quartile is the fourth dot, which is the median of the first half.

The second half is composed of the last seven students, hence the first quartile is the eleventh dot, which is the median of the first half.

The quartiles for Bus 14 are given as follows:

Q1 = 12.

Q3 = 18.

Hence the IQR is of:

IQR = Q3 - Q1 = 18 - 12 = 6.

The quartiles for Bus 18 are given as follows:

Q1 = 9.

Q3 = 16.

Hence the IQR is of:

IQR = Q3 - Q1 = 16 - 9 = 7.

Step-by-step explanation: