Find the value of x using the measures of the two given adjacent supplementary angles. The figure is not drawn to scale. The two angles are 3x and 54

Answer:

10: D  11: C  12:B

Step-by-step explanation:

In the production possibilities framework, economic growth is depicted by the PPF (Production Possibilities Frontier) shifting rightward (away from the origin). This indicates an increase in the economy's capacity to produce goods and services.

The production possibilities framework represents the different combinations of goods and services that an economy can produce given its resources and technology.

The PPF is typically depicted as a curve, showing the trade-off between producing different goods or allocating resources between different sectors of the economy.

When the PPF shifts rightward, it means that the economy's production capacity has increased.

This can happen due to various factors such as technological advancements, increased capital investment, improved infrastructure, or an expansion of the labor force.

As a result, the economy can produce more goods and services at each point along the PPF.

The shift of the PPF rightward indicates economic growth because it signifies an expansion of the production possibilities.

With a larger production capacity, the economy has the potential to achieve higher levels of output, leading to increased living standards, higher incomes, and greater overall economic prosperity.

On the other hand, if the PPF became a straight line or shifted leftward (toward the origin), it would indicate a decrease in the economy's production capacity or a decline in resources or technology.

In such cases, the economy would experience a contraction in its production possibilities and potentially face challenges in meeting the needs and wants of its population.

Therefore, the correct answer is that economic growth in the production possibilities framework is depicted by the PPF shifting rightward (away from the origin).

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Significant zeros are zeros that contribute to the precision of a number, while nonsignificant zeros are placeholders or indicate the magnitude of a number.

Significant zeros are zeros that are considered significant and contribute to the precision of a number. They are located between nonzero digits or at the end of a number with a decimal point.

For example:

In the number 4,503, the zeros between 4 and 3 are significant.

In the number 0.00856, the zeros after the decimal point and before the 8 are significant.

Nonsignificant zeros, on the other hand, are zeros that do not contribute to the precision of a number and are used for placeholders or to indicate the magnitude of a number. They are typically located at the beginning or end of a number without a decimal point. Examples include:

In the number 0420, the zero at the beginning is nonsignificant.

In the number 0.003, the zeros before the decimal point is nonsignificant and serve as placeholders.

It's important to note that the significance of zeros can vary depending on the context and the rules of significant figures or decimal places being used in a specific calculation or measurement.

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1. When t = 0, the position (displacement) of the object can be found by substituting t = 0 into the given equation of motion:d = 3sin(8π(0)) - 2 = 0 - 2 = -2 meters.2. The maximum displacement of the object from its t=0 position can be found by taking the amplitude of the displacement function. Since the function is of the form d = Asin(ωt) - B, where A is the amplitude, ω is the angular frequency and B is the vertical shift, it can be seen that the amplitude in this case is A = 3 meters. So, the maximum displacement is 3 meters.3. The time taken for one oscillation can be found by dividing the period, T, of the oscillation by the number of oscillations in that period. The period of the oscillation is the time taken for one complete cycle of the sine wave, which is 1/8 seconds. Thus, the time taken for one oscillation is:1 oscillation = T/1/8 s = 8T s4. The frequency of the oscillation is the reciprocal of the period, which is f = 1/T. Thus, the frequency is:f = 1/T = 1/(1/8) Hz = 8 Hz.

Given the function F0(x) = 1 - 1/(1+x) for x ≥ 0, we can find expressions for the requested terms:

(a) S0(x) is the survival function, which is the complement of the cumulative distribution function F0(x). Therefore, S0(x) = 1 - F0(x). Substituting F0(x) into the equation, we get:
S0(x) = 1 - (1 - 1/(1+x)) = 1/(1+x)
(b) f0(x) is the probability density function (pdf) and can be found by taking the derivative of the cumulative distribution function F0(x) with respect to x:
f0(x) = dF0(x)/dx = d(1 - 1/(1+x))/dx = 1/(1+x)^2
(c) To find Sx(t), we need to find the survival function for an individual aged x at time t. Since we know S0(x), we can find Sx(t) using the following relationship:
Sx(t) = S0(x+t)/S0(x)
By substituting S0(x) into the equation, we get:
Sx(t) = (1/(1+x+t))/(1/(1+x)) = (1+x)/(1+x+t)
Now we can calculate the requested values:
(d) p20 is the probability of surviving one more year for an individual aged 20. It is given by:
p20 = S20(1)/S20(0)
Substitute 20 for x and 1 for t in Sx(t):
p20 = (1+20)/(1+20+1) = 21/22
(e) The term 10|5q30 does not follow the standard notation used in survival analysis. Please provide more context or clarify the term to receive an appropriate answer.

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Answer:

Step-by-step explanation:

Step one:

given data

hyp=16cm

say the adjecent= 15

let the hypotenuse be z

and the adjacent be x, while the missing side, the opposite be y

by Pythagoras theorem

\(z^2=y^2+x^2\)

\(z=\sqrt{x^2+y^2}\)

substitute the values we have

\(16^2=y^2+15^2\\\\256=y^2+225\\\\256-225=y^2\\31=y^2\\\\y=\sqrt{31}\)

\(y=5.56cm\)

The other side is 5.56cm

Answer:

No because the slopes arent the same (I’m guess it was -4y and not -4)

Step-by-step explanation:

Answer: A. 2,

B. -11,

C. -25

D. 43

e. -3/2

Step-by-step explanation:

Answer:

p =43

Step-by-step explanation:

Finding the angle in a triangle

The angle next to 133, angle a,  is 180-133 = 47 because the angles form a straight line

The angle next to 90, angle b, is 180-90 = 90,  because the angles form a straight line

We have a triangle.  The angles in a triangle equal 180 degrees

a+b+ p =180

47+90+p = 180

137 + p = 180

p = 180-137

p =43

After the conversion of $500 in japanese yen Ben will have 61,650 yen.

According to the question.

The amount of money in US dollars Ben wishes to convert in Japanese yen is $500.

Also, it is given that

$1 = 123.3yen

Therefore,

The number of yen Ben have after the conversion of dollars in yen

= 500 × 123.3

= 61,650

Hence, after the conversion of $500 in japanese yen Ben will have 61,650 yen.

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Answer i cant read it..

Step-by-step explanation:

The cost of constructing the box will be = $81.77

Since the question gives us information about the rectangle,

so the area of the rectangle is shown by,

Area = 2 x (length + width)

So we have the area as,

Area = 2(lh + wh) +lw

(since the area per square meter is also given so we added l x w)

Since the cost of the base is = $5 per square meter and the cost of the sides is = $3 per square meter, so area in terms of the cost function,

⇒ C = 3 x 2(lh + wh) + 5 x l x w

⇒ C = 6(lh + wh) +5lw ---------equation 1

According to the question, the length of the rectangular container is twice that of the width of the container,

⇒ l = 2w

Substituting the new value of l in equation 1,

⇒ C = 6(2wh + wh) + 10 \(w^{2}\)

⇒ C = 18wh + 10 \(w^{2}\) ---------- equation 2

To calculate the volume of the rectangle,

V = length x width x height ( lwh )

substituting v = 10 and 2w = l,

2\(w^{2}\)h = 10

h = \(\frac{5}{w^{2} }\)

Substitute the value of h in equation 2,

⇒ C = 18w x \(\frac{5}{w^{2} }\) + 10\(w^{2}\)

⇒ C = \(\frac{90}{w}\) + 10\(w^{2}\) --------- equation 3

Differentiating the above equation we get,

⇒ C* = - \(\frac{90}{w^{2} }\) + 20w

⇒ 20w = \(\frac{90}{w^{2} }\)

Multiply both sides by \(w^{3}\)

⇒ \(20w^{3}\) = 90

⇒ \(w^{3}\) = 4.5

w = 1.65

Put the value of w in equation 3,

⇒ C = \(\frac{90}{1.65}\) + 10 x \(1.65^{2}\)

⇒ C = 81.77

Therefore, The cost of constructing the box will be = $81.77

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Answer:

2500 gallons or water.

Step-by-step explanation:

Atlantic ocean contains 2 x 10¹⁶ gallons of water.

lake Ontario has approx 8 x 10¹² gallons of water.

req'd:

how many lake ontarios would it take to fill the Atlantic ocean in gallons of water?

= 2 x 10¹⁶ gallons of water

  8 x 10¹² gallons of water

= 2500 Lake Ontarios to fill The Atlantic Ocean

2500 times the gallons of water Lake Ontarios will take to fill the Atlantic Ocean region.

Given that,
The Atlantic Ocean region contains approximately 2 × 10^16 gallons of water.
Lake Ontario has approximately 8,000,000,000,000 gallons of water or 8 * 10¹².
To determine how many Lake Ontarios would it take to fill the Atlantic Ocean region in terms of gallons of water

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Here,
Lake Ontarios would it take to fill the Atlantic Ocean region
= 2 × 10¹⁶ / 8 * 10¹²
= 0.25 * 10⁴
= 2500 times the  gallons of water Lake Ontarios

Thus, 2500 times the gallons of water Lake Ontarios will take to fill the Atlantic Ocean region.

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Answer:

See answers below

Step-by-step explanation:

A. 3/4 * 3 = 2.25 <= 4 = YES

B. 11/12 * 4 = 3.67 <= 4 = YES

C. 7/8 * 5 = 4.38 >= 4 = NO

D. 5/6 * 6 = 5 >= 4 = NO

E. 1/2 * 8 = 4 <= 4 = Yes

Mark brainliest if this helped

Mark brainliest if this helped

1) 47

2) 6/11

3) 5x + 13

4) 8x - 3

5) x = 98

6) x = 3

7)

a) Slope = 4

b) The slope-intercept form is y = 4x - 17.

c) Distance = √272

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

1)

(15 - 7)² - 3.4  - 5

= 8² - 12 - 5

= 64 - 17

= 47

2)

6(8 - 4) / 6.8 - 4

= 6 x 4 / (48 - 4)

= 24/44

= 6/11

3)

Number = x

Expression = 5x + 13

4)

Number = x

Expression = 8x - 3

5)

x/7 - 9 = 5

x/7 = 5 + 9

x/7 = 14

x = 14 x 7

x = 98

6)

8(2x - 5) + 3x = 4x + 5

16x - 40 + 3x = 4x + 5

19x - 4x = 5 + 40

15x = 45

x = 3

7)

A = (3, -5)

B = (7, 11)

a)

Slope = (11 + 5)/(7 - 3) = 16/4 = 4

b)

m = 4

(3, -5) = (x, y)

-5 = 4 x 3 + c

-5 = 12 + c

c = -5 - 12

c = -17

So,

y = 4x - 17

The slope intercept form is y = 4x - 17.

c)

Distance between A and B.

= √(7 - 3²) + (11 + 5)²

= √(16 + 256)

= √272

Thus,

Each statement is given above.

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Answer:

55 stamps, 24 girls, and 60cm

Step-by-step explanation:

Big Brain

Answer: A

Step-by-step explanation:

To add fractions, we want to make sure there is a common denominator. After that, we can add the numerator.

\(\frac{8}{z^2+6z+9} +\frac{5}{z^2-9}\)                 [factor denominator]

\(\frac{8}{(z+3)(z+3)} +\frac{5}{(z+3)(z-3)}\)      [multiply first fractioni by z-3 and second by z+3]

\(\frac{8(z-3)}{(z+3)^2(z-3)} +\frac{5(z+3)}{(z+3)^2(z-3)}\)   [distribute by FOIL]

\(\frac{8z-24}{(z+3)^2(z-3)} +\frac{5z+15}{(z+3)^2(z-3)}\)   [add]

\(\frac{13x-9}{(z+3)^2(z-3)}\)

This is the same as A. Therefore, A is our answer.

Driving a personal car would be the most cost-effective mode of transportation for this commute, with a total daily cost of approximately $4.60 ($3.60 for gas + $1 for travel time).

Based on the given information, the most cost-effective mode of transportation for this commute would be to drive a personal car. Taking public transportation or carpooling may be more environmentally friendly options, but they may not save as much money as driving alone.

Assuming an average speed of 60 miles per hour on the highway, the commute would take approximately 20 minutes each way, or 40 minutes round-trip. This means the total cost of travel time for each workday would be $40 ($60/hour x 2/3 hour).

Using a cost calculator such as GasBuddy, we can estimate that the cost of driving 20 miles per day (round-trip) would be around $3.60 per day, assuming an average fuel efficiency of 25 miles per gallon and a gasoline price of $2.50 per gallon.

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Answer:

(15/4)4^x

Step-by-step explanation:

Substituting the x and y values of the first point, we get:

y = ab

60 = ab^(2)

Substituting the x and y values of the second point, we get:

y = ab

960 = ab^(4)

Now we can solve for a and b by eliminating one of the variables. One way to do this is to divide the second equation by the first equation:

960/60 = (ab^(4))/(ab^(2))

16 = b^(2)

Taking the square root of both sides, we get:

b = ±4

Since an exponential function can only have positive values for b, we choose b = 4. Now we can solve for a by substituting b = 4 into one of the original equations:

60 = a(4^(2))

60 = 16a

a = 60/16

a = 15/4

Therefore, the values of a and b are a = 15/4 and b = 4, and the exponential function is y = (15/4)4^x.

Answer:

35°

Step-by-step explanation:

angle3 = 3x-7

the two angles are complementary  ( they sum to 90)

4x-1     +     3x-7      = 90

7x - 8 = 90

7x = 98

x = 14        then angle3 = 3x-7 = 35°

Answer:

refer to the above attachment

We will have the following:

So, the point (2, -1) is one of the many solutions.

Answer:

y = 3x + 3

Step-by-step explanation:

As x increases, y increases by 3. Therefore, the slope of the function is 3.

Setting x = 0 will give an output of 3. Therefore, the y-intercept is (0, 3).

Overall, the function rule for the given data set is y = 3x + 3.

Answer:

(4, -3)

Step-by-step explanation:

Rewrite equations:

x−2y=10;6x+3y=15

Step: Solvex−2y=10for x:

x−2y=10

x−2y+2y=10+2y(Add 2y to both sides)

x=2y+10

Step: Substitute2y+10forxin6x+3y=15:

6x+3y=15

6(2y+10)+3y=15

15y+60=15(Simplify both sides of the equation)

15y+60+−60=15+−60(Add -60 to both sides)

15y=−45

15y

15

=

−45

15

(Divide both sides by 15)

y=−3

Step: Substitute−3foryinx=2y+10:

x=2y+10

x=(2)(−3)+10

x=4(Simplify both sides of the equation)

Therefore answer: is

x=4 and y=−3

Hope it helps!

The lower and upper values of the confidence interval of the population mean for the minutes spent getting to work is (31.74,38.4)

What is Standard Deviation?

The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean. By calculating the departure of each data point from the mean, the standard deviation may be determined as the square root of variance. The bigger the deviation within the data collection, the more the data points deviate from the mean; Hence, the higher the standard deviation, the more dispersed the data.

We know that:

\(\text { Standard Deviation }=\sqrt{\frac{\sum\left(x_i-\bar{x}\right)^2}{n-1}}\)

where \(x_{i}\)  is the mean and n is the number of observations.

\(\text { Standard Deviation }=\sqrt{\frac{\sum\left(x_i-\bar{x}\right)^2}{n-1}}\)

98% Confidence interval:  

\(\bar{x} \pm t_{\text {critical }} \frac{s}{\sqrt{n}}\)

Putting the values, we get,  

\(t_{\text {critical }} \alpha_{0.02}\\=\pm 2.14535.07 \pm 2.145\left(\frac{6.02}{\sqrt{15}}\right)\\=35.07 \pm 3.33\\=(31.74,38.4)\)

Hence, The lower and upper values of the confidence interval of the population mean for the minutes spent getting to work is (31.74,38.4)

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To find the distance between centers of circles W and Y, draw segments WY- and WS-, but lack information on YS, SZ, and angles, resulting in insufficient calculations.

To find the distance between the two centers of circles W and Y, we can use the hint provided.

1. Draw segment WY- connecting the centers of the two circles.
2. Draw segment WS- such that YS + SZ = YZ and WS- is perpendicular to YZ-.

Now, we have formed a right triangle WSY- with WS- as the hypotenuse and YS as one of the legs.

To find the distance between the two centers, we need to calculate the length of the hypotenuse WS-.

Unfortunately, we don't have enough information to determine the lengths of YS and SZ, or the measures of any angles. Therefore, we cannot determine the length of WS- or the distance between the two centers of the circles.

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To find the measure of angle BOC, set the expressions for m∠AOD and m∠BOC equal and solve for x. Then substitute the value of x back into the expression for m∠BOC to find its measure, which is 30°.

To find the measure of angle BOC, we can set the expressions for m∠AOD and m∠BOC equal to each other and solve for x.

7x - 5 = 3x + 15

Subtract 3x from both sides: 4x - 5 = 15

Add 5 to both sides: 4x = 20

Divide both sides by 4: x = 5

Now that we know x = 5, we can substitute it back into the expression for m∠BOC to find its measure.

m∠BOC = (3x + 15)° = (3*5 + 15)° = 30°

Therefore, the measure of ∠BOC is 30°, which corresponds to option B.

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if the sample size is small and the population distribution is significantly skewed, then the sample means may not follow a normal distribution. In this case, other methods such as non-parametric tests may need to be used.

No, the sample means will not necessarily follow a normal distribution if the population is skewed right. The distribution of the sample means is dependent on the size of the sample and the shape of the population distribution. If the sample size is large enough, then the Central Limit Theorem states that the distribution of the sample means will tend to follow a normal distribution regardless of the shape of the population distribution. However, if the sample size is small and the population distribution is significantly skewed, then the sample means may not follow a normal distribution. In this case, other methods such as non-parametric tests may need to be used.

 If you have a population that is skewed right and you take samples with measurements each (assuming the sample size is large enough, generally n > 30), your sample means will follow a normal distribution according to the Central Limit Theorem.

The Central Limit Theorem states that when you have a large enough sample size (n > 30), the distribution of the sample means will approximate a normal distribution, regardless of the shape of the original population. This is true even for populations that are not normally distributed or are skewed, like the one in your question. The key is to have a large enough sample size so that the theorem can apply.

In summary, even though your population is skewed right, the sample means will follow a normal distribution as long as your sample size is large enough.

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Answer:

200g:300g

Step-by-step explanation:

2+3=5

500g/5=100g

100x2=200g

100x3=300g