Nendell saw the following sign at
a diner. If he bought one of each item
and spent $7.50, how much did the
drink cost?

Answer:

78.5 m²

Step-by-step explanation:

Area formula: πr²

Plug it in: (3.14)(5m)²

Answer: 78.5 m²

Therefore, based on the given information, the estimated age of the tomb is approximately 3,970 years.

To estimate the age of the tomb based on the radioactive carbon-14 (C-14) content in the cypress beam, we can use the decay equation:

A = A₀ * e*(kt)

Where:

A = Final amount of radioactive substance (55% of the original C-14 content)

A₀ = Initial amount of radioactive substance (100% of the original C-14 content)

k = Decay constant (ln(2) / half-life of C-14)

t = Time (age of the tomb)

Given that the half-life of C-14 is approximately 5600 years, we can calculate the decay constant:

k = ln(2) / 5600 years

Now we can plug in the values:

0.55A₀ = A₀ * e*((ln(2) / 5600 years) * t)

Dividing both sides by A₀:

0.55 = e*((ln(2) / 5600 years) * t)

Taking the natural logarithm of both sides:

ln(0.55) = (ln(2) / 5600 years) * t

Now we can solve for t, the age of the tomb:

t = (ln(0.55) * 5600 years) / ln(2)

Evaluating the expression:

t ≈ 3,970 years

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Answer: 32

Step-by-step explanation:add 14 to 18

Answer:

32

Step-by-step explanation:

32 is the answer because 18 plus 14 equals 32. And so the number 32 decreased by 14 is 18.

The total number of sides of a regular polygon with each exterior angle of measure 30 degrees is equal to 12.

Let us consider 'n' be the number of sides of the regular polygon.

Let 'y' be the measure of each of the exterior angle of regular polygon.

y = 30 degrees

Measure of each of the exterior angle of regular polygon 'y'

= ( 360° ) / n

⇒ n = ( 360° / y )

Substitute the value we get,

⇒ n = ( 360° / 30° )

⇒ n = 12

Therefore, the number of sides of a regular polygon with each of the exterior angle 30 degrees is equal to 12.

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The above question is incomplete, the complete question is:

How many sides does a regular polygon have when each exterior angle measures 30 degrees?

Answer:

$ 142100

Step-by-step explanation:

Profit is the difference between the revenue and the cost

        P(x) = R(x) - C(x)

                = 820x - x² - (2300 + 60x)

                = 820x - x² - 2300 - 60x

                = -x² + 820x - 60x - 2300

         P(x) = -x² + 760x - 2300

a =  -1   ; b = 760  and c = -2300

       \(\sf \boxed{P_{max} = c - \dfrac{b^2}{4a}}\)

                  \(\sf = -2300 - \dfrac{760^{2}}{4*(-1)}\)

                  \(\sf = -2300 +\dfrac{577600}{4}\\\\ = -2300 + 144400\\= 142100\)

\(\sf \boxed{P_{max}= \$ 142100}\)

One example of a quantitative, continuous variable is height. Height can be measured on a continuous scale, with infinite possible values between any two points. For example, an individual's height may be measured as 5 feet and 8 inches, but it could also be expressed as 5.75 feet or 68 inches.

One example of a quantitative, discrete variable is the number of children in a family. This variable can only take on whole number values, such as 0, 1, 2, 3, etc., and cannot be divided into smaller units or fractions.

Height is an example of a quantitative, continuous variable because it can be measured on a continuous scale, which means there are infinite possible values between any two points. For instance, if we take two people who are both 5 feet tall, one person may be slightly taller than the other if we measure their height more precisely, such as to the nearest centimeter or millimeter.

Furthermore, height can take on decimal or fractional values, like 5.75 feet or 68 inches, which allows for even greater precision in measurement. This is why height is considered a continuous variable rather than a discrete variable, where only whole number values are possible.

Quantitative, continuous variables are often measured using tools that allow for precise measurement, such as measuring tapes or rulers. They can also be analyzed using statistical methods like regression and correlation analysis to understand the relationship between this variable and other factors of interest.

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Step-by-step explanation:

9.1x−0.8=−1.71 = 251/910 pic for answering

Answer:

165

Step-by-step explanation:

its the answer trust me rank me brainiest

Answer:

B. 165

Step-by-step explanation:

Table: x = 11 and y = 770

Graph: x = 11 and y = 605

770 - 605 = 165

The required graph of the solution to the given inequality y>3 x-4 has shown.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
Given inequality,
y > 3x-4

Illustrating the above inequality on the coordinate plane, the yellow shaded region shows the solution of the given inequality y > 3x-4.

Thus, the required graph of the solution to the given inequality y>3 x-4 has shown.

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Answer:

i can't see the pic clearly

Step-by-step explanation:

(y÷7)+5

jdkscnkfggjfnznsogsops hexa

Answer:

see explanation

Step-by-step explanation:

\(\frac{y}{7}\) + 5 ← algebraic expression

Answer:

cos²x+sinx = 1

sinx = 1 - cos²x

sinx = sin²x

sinx = 1

x = 90

Answer:

x = 90° or π/2 radians

Step-by-step explanation:

We are given
cos²(x) + sin(x) = 1    [1]

The following identity is true:
cos²(x) + sin²(x) = 1    [2]

Subtract [1] from [2]
cos²(x) + sin²(x) - (cos²(x) + sin(x)) = 1 - 1

cos²(x) + sin²(x)  - cos²(x)  - sin(x) = 0

==> sin²(x) - sin(x) = 0

==> sin²(x)  = sin(x)

Divide both sides by sin(x) to get

sin²(x)/sin(x) = sin(x)/sin(x)

==> sin(x) = 1

x = sin⁻¹(1)

x = 90° or π/2 radians

The volume of the model to the nearest cubic foot is 137 ft³

Volume of a sphere = 4/3πr³

Radius, r = diameter / 2

= 6.4 ft / 2

= 3.2 ft

Volume of a sphere = 4/3πr³

= 4/3 × 3.14 × 3.2³

= 4/3 × 3.14 × 32.768

= 411.56608 / 3

= 137.188693333333

Approximately,

Volume of the sphere = 137 ft³

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a. using Excel we get:

the equation of best fit is:

y = 12.165x + 31.335

where y represents the account balance and x the days.

b. The slope represents how much the balance increase from one day to the next one. The y-intercept represents the balance at day zero, that is before they started the store.

c. Their goal is to reach $900. Replacing y = 900 into the equation:

900 = 12.165x + 31.335

900 - 31.335 = 12.165x

868.665/12.165 = x

71.4 days = x

That is, they will need 72 days to reach their goal.

d. using Excel we get:

The difference between this correlation and the previous one is caused by the inclusion of new data. After the addition of new points is hardly impossible that the new line remains equal to the previous one.

with this new correlation, they will reach their goal after:

900 = 10.333x + 36.433

900 - 36.433 = 10.333x

863.567/10.333 = x

83.6 days = x

That is, they will need 84 days to reach their goal.

e. The second prediction is more reliable, because the line of best fit was gotten using more points.

Answer:

  C.  The point where the perpendicular bisectors of the three sides of the triangle intersect.

Step-by-step explanation:

A number of centers of a triangle are defined. The circumcenter is the center of the circumscribing circle. The incenter is the center of an inscribed circle. The centroid is the center of balance of a triangle of uniform mass density.

The centers defined by descriptions A through D are ...

  A. centroid -- coincident point of medians

  B. incenter -- coincident point of angle bisectors

  C. circumcenter -- coincident point of side perpendicular bisectors

  D. orthocenter -- coincident point of altitudes

sin^2(4x) cos^2(4x) can be written in terms of first powers of the cosines of multiple angles as: 1/4 [cos^2(4x) - cos^3(4x) - cos(4x) + 1].

Using the power-reducing formula for cosine:

cos(2x) = cos²(x) - sin²(x)

We can write:

cos²(x) = 1/2 [cos(2x) + 1]

sin²(x) = 1/2 [1 - cos(2x)]

Using these formulas, we can rewrite the expression:

sin^2(4x) cos^2(4x) = [sin²(2(2x))] [cos²(2(2x))]

= [1/2 (1 - cos(4x))] [1/2 (cos(4x) + 1)]

= 1/4 [cos^2(4x) - cos^3(4x) - cos(4x) + 1]

= 1/4 [cos^2(4x) - cos^3(4x) - cos(4x) + cos^2(0)]

= 1/4 [cos^2(4x) - cos^3(4x) - cos(4x) + 1]

Therefore, sin^2(4x) cos^2(4x) can be written in terms of first powers of the cosines of multiple angles as: 1/4 [cos^2(4x) - cos^3(4x) - cos(4x) + 1]

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The probability of any plant surviving in Kerry's garden is 0. 8.  If she plants 19 new plants this year then the probability of at least 14 out of 19 plants surviving is 0.1082.

The probability of any plant surviving in Kerry's garden is 0.8. Suppose she plants 19 new plants this year.

A) What is the probability that at least 14 of them survive?

To find the probability of at least 14 plants surviving out of 19 new plants, we need to find the probability of 14, 15, 16, 17, 18, and 19 plants surviving and add them up.

P(X ≥ 14) = P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19)where X is the number of new plants that survive out of 19.

From the question, the probability of any plant surviving is 0.8, therefore, the probability of any plant dying is 1 - 0.8 = 0.2.

So, the probability that exactly x plants out of 19 survive is given by: P(X = x) = \binom{19}{x}(0.8)^x(0.2)^{19 - x}

Substitute x = 14, 15, 16, 17, 18, and 19 into the above equation and sum the terms. P(X ≥ 14) = P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) = 0.2028 + 0.2857 + 0.2864 + 0.2013 + 0.0881 + 0.0229 = 0.1082

Therefore, the probability of at least 14 out of 19 plants surviving is 0.1082 (rounded to four decimal places).

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Answer:

6. No. See explanation below.

7. 18 months

8. 16

Step-by-step explanation:

6. To rewrite a sum of two numbers using the distributive property, the two numbers must have a common factor greater than 1.

Let's find the GCF of 85 and 99:

85 = 5 * 17

99 = 3^2 + 11

5, 3, 11, and 17 are prime numbers. 85 and 99 have no prime factors in common. The GCF of 85 and 99 is 1, so the distributive property cannot be used on the sum 85 + 99.

Answer: No because the GCF of 85 and 99 is 1.

7.

We can solve this problem with the lest common multiple. We need to find a number of a month that is a multiple of both 6 and 9.

6 = 2 * 3

9 = 3^2

LCM = 2 * 3^2 = 2 * 9 = 18

Answer: 18 months

We can also answer this problem with a chart. We write the month number and whether they are home or on a trip. Then we look for the first month in which both are on a trip.

Month                Charlie          Dasha

1                          home             home

2                          home             home

3                          home             home

4                          home             home

5                          home             home

6                         trip                home

7                          home             home

8                          home             home

9                          home             trip

10                         home             home

11                         home             home

12                         trip               home

13                         home             home

14                         home             home

15                         home             home

16                         home             home

17                         home             home

18                         trip                 trip

Answer: 18 months

8.

First, we find the prime factorizations of 96 an 80.

96 = 2^5 * 3

80 = 2^4 *5

GCF = 2^4 = 16

Answer: 16

The measure of the length r (SQ) of the triangle ΔQRS will be 2.40 inches.

The Law of Sines The law of trigonometric functions, sine law, sine formula, or sinusoidal rule is a trigonometric equation that relates the sizes of any triangle's edges to the sines of its orientations.

The sine law in the triangle ΔQRS is given as,

QR / sin S = SQ / sin R = SR / sin Q

The third angle of the triangle ΔQRS is given as,

∠Q + ∠R + ∠S = 180°

∠R + 30° + 129° = 180°

∠R = 21°

Then the measure of the length r (SQ) will be calculated as,

5.2 / sin 129° = SQ / sin 21°

SQ = 2.40 inches

The measure of the length r (SQ) of the triangle ΔQRS will be 2.40 inches.

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The best interpretation of the statement "the chances of winning a prize are 1 out of 10" is that if many people buy a ticket, about 1 in 10 will win.

This statement means that for every 10 tickets sold, on average, only one ticket will win a prize. It does not guarantee that you will win a prize if you buy a single ticket or even several tickets. The probability of winning a prize remains the same for every ticket purchased. It is important to note that winning a prize in a lottery is largely a matter of luck, and the odds are always against the player. While buying more tickets may increase your chances of winning, it does not guarantee a win.

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The two lines are:x=3+2s,y=2+8s,z=1−sandx=2−3t,y=−3+4t,z=1+tThe two lines are neither parallel nor skew.

To find their point of intersection we need to equate their x,y,z coordinates:

3+2s = 2 - 3ty = 2 + 8s = -3 + 4tz = 1 - s = 1 + t3 + 2s - 2 = -3ty - 8s = -5tz + s = t1. 2s = -5t + 1t = s + 13. -8s = -8t - 11t = s + 1

We can now find the x, y, and z coordinates of the point of intersection of the two lines by substituting t = s + 1 into one of the equations:x = 3 + 2s = 3 + 2 (t - 1) = 2t + 1 = y = 2 + 8s = 2 + 8 (t - 1) = 8t - 6z = 1 - s = 1 - (t - 1) = -t + 2The point of intersection is (3,2,1).The shortest distance between two skew lines is the distance between their closest points. We can take an arbitrary point on each line, say A(x1,y1,z1) and B(x2,y2,z2), then find the line between these two points and take its shortest distance to both lines.The line between A and B is given by:x = x1 + (x2 - x1)t,y = y1 + (y2 - y1)t,z = z1 + (z2 - z1)tWe need to find the value of t such that this line is perpendicular to both given lines. Let's call the point on the first line P and the point on the second line Q:

P = (3 + 2s, 2 + 8s, 1 - s)Q = (2 - 3t, -3 + 4t, 1 + t)

To find the value of t we need the dot product between the vector PQ and the vector of each line to be zero:

(3 + 2s - 2)(2 - 3t - (3 + 2s)) + (2 + 8s + 3)(-3 + 4t + 2) + (1 - s - 1)(1 + t - 1) = 0

Simplifying this expression gives:

20s - 13t - 17 = 0t = (20s - 17)/13

Substituting this value of t into the equation of the line between A and B gives the point of closest approach between the two lines:

(x,y,z) = (3 + 2s + (5/13)(2 - 3t - (3 + 2s)), 2 + 8s + (5/13)(-3 + 4t + 2), 1 - s + (5/13)(1 + t - 1)) = (19/13, -29/13, 38/13)

The distance between this point and any point on either line is the shortest distance between the two lines. For example, the distance between this point and the first line is:

(19/13 - 2, -29/13 + 12, 38/13 - 1) · (1, 4, 1) / sqrt(1² + 4² + 1²) = 6 sqrt(2)/13.

The two lines intersect at (3,2,1). They are not parallel or skew lines. Therefore, we need to find the distance between the two lines. We used an arbitrary point on each line to determine the closest point between the two lines. The shortest distance is the distance between this point and any point on either line, and this value was calculated to be 6 sqrt(2)/13.

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We can conclude that Kadoka, Rapid City, Sioux Falls, and Alexandria are all connected by Interstate 90, as shown in the diagram.

What are the attributes of a good conclusion?

The key argument raised throughout the argument's discussion must be summarized in the good conclusion.

a. In below diagram, each city is represented by a point, and the distances between the cities are shown as line segments with the distance in miles labeled above the segment. The distances are labeled in the order in which they appear in the diagram, so for example, the distance between Kadoka and Rapid City is labeled as 96 because that is the distance between the two cities as you move from Kadoka to Rapid City.

b. To support the conclusion that Kadoka, Rapid City, Sioux Falls, and Alexandria are all connected by Interstate 90, we can use the distances given in the problem to show that it is possible to travel from any one city to any other city using only Interstate 90.

First, we note that Kadoka is connected to Rapid City by Interstate 90, because the distance between them is given as 96 miles and no other route is mentioned. Similarly, Rapid City is connected to Alexandria by Interstate 90, because the distance between them is given as 292 miles and no other route is mentioned.

Finally, to show that Alexandria is connected to all the other cities by Interstate 90, we note that the distance between Alexandria and Rapid City is given as 292 miles, and the only way to travel between the two cities is on Interstate 90. Also, since Kadoka is connected to Rapid City by Interstate 90 and Rapid City is connected to Alexandria by Interstate 90, it follows that Kadoka is connected to Alexandria by Interstate 90.

Therefore, we can conclude that Kadoka, Rapid City, Sioux Falls, and Alexandria are all connected by Interstate 90, as shown in the diagram.

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Answer:

1.2

Step-by-step explanation:

\(s/1.5 = .8\\s = 1.5 * .8\\s = 1.5 *4/5\\s = 6 /5\\s=1.2\)

Answer: 15

Step-by-step explanation:

The perimeter of the square patio is the sum of its side lengths

The length of the patio is: 8x + 2

The given parameters are:

\(\mathbf{Shape = Square}\)

\(\mathbf{Perimeter = 32x + 8}\)

The perimeter of a square is:

\(\mathbf{Perimeter = 4 \times Length}\)

So, we have:

\(\mathbf{4 \times Length = 32x + 8}\)

Divide both sides by 4

\(\mathbf{Length = 8x + 2}\)

Hence, the length of the patio is: 8x + 2

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Given dataAn element with mass 310 grams decays by 5.7% per minute. We need to find how much of the element is remaining after 9 minutes, to the nearest 10th of a gram.Solution

Let P be the amount of the element remaining after 9 minutes. Then, the amount of the element that decayed in 9 minutes is:Q = 310(1 - 0.057)^9= 310(0.943)^9≈ 174.24 gramsTherefore, the amount of the element remaining after 9 minutes is:P = 310 - Q≈ 135.76 grams.So, the amount of the element remaining after 9 minutes is approximately 135.76 grams, rounded to the nearest 10th of a gram.

Let x be the number of ounces of the 40% alloy Dr. Hamilton used.Then (80 - x) would be the number of ounces of the 60% alloy he used. Therefore, the equation is:0.4x + 0.6(80 - x) = 0.45(80)Simplify this equation to solve for x as follows:0.4x + 48 - 0.6x = 36Add like terms:-0.2x + 48 = 36Subtract 48 from both sides of the equation:-0.2x = -12Solve for x by dividing both sides of the equation by -0.2:x = 60Therefore, Dr. Hamilton used 60 ounces of the 40% alloy.

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Answer:

\(\displaystyle y=\frac{1}{2}x-2\)

Step-by-step explanation:

The equation of the line in slope-intercept form is:

y=mx+b

Being m the slope and b the y-intercept.

Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:

\(\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\)

The points are (-6,-5) and (-4,-4), thus:

\(\displaystyle m=\frac{-4+5}{-4+6}=\frac{1}{2}\)

Knowing the value of the slope, the equation of the line is:

\(\displaystyle y=\frac{1}{2}x+b\)

The value of b can be found using any of the points in the equation and solving for b. Let's pick the point (-6,-5):

\(\displaystyle -5=\frac{1}{2}(-6)+b\)

Operating:

-5=-3+b

Solving:

b=-2

The equation of the line is:

\(\boxed{\displaystyle y=\frac{1}{2}x-2}\)