Round 473,615 to the nearest hundred

Answer:

10

Step-by-step explanation:

the side is 13 and 3 so the difference is 10 on that side

on the bottom side it's 3 and if it's the same it's 10

Answer:

$3,080 for each person

Step-by-step explanation:

9,240 / 3 = 3,080

Answer:

Step-by-step explanation:

12

Answer:

get help from a tutor if you need help really fast :)

Step-by-step explanation:

The data is best described by an increasing function. The regression equation is y =0.0965x - 0.61.

Here is a table of the data:

Temperature (K) Gas Volume (cm³)

173     16

223     21

273     26

323     30

373     36

423     40

The data is best described by an increasing function, and it is likely to be linear since the volume of the gas increases uniformly with the temperature.

Let x be the temperature and y be the volume of the gas.

The slope is given by (nΣxy - ΣxΣy) / (nΣx² - (Σx)²),

where n is the number of data points, Σxy is the sum of the products of x and y, Σx is the sum of x, Σy is the sum of y, and Σx² is the sum of the squares of x.

The y-intercept is given by (Σy - bΣx) / n, where b is the slope.

Using the data, we have n = 6, Σx = 17788, Σy = 169, Σxy = 4225, and Σx² = 43750.

Substituting these values into the formulas gives the slope b = 0.09657 and the y-intercept a = -0.61.

Therefore, the regression equation is y =0.0965x - 0.61.

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The perimeter of the sandbox is 28 feet. a.

The width of the rectangular sandbox using the given area and length and then use the formula for the perimeter of a rectangle to find the perimeter.

Let's start by using the formula for the area of a rectangle to find the width:

Area = length × width

The area of the sandbox is 45 square feet and the length is 5 feet can substitute these values into the formula and solve for the width:

45 = 5 × width

Dividing both sides by 5, we get:

width = 9 feet

Now that we know the width and length of the sandbox can use the formula for the perimeter of a rectangle:

Perimeter = 2 × length + 2 × width

Substituting the values we found earlier get:

Perimeter = 2 × 5 + 2 × 9

Simplifying, we get:

Perimeter = 10 + 18

Perimeter = 28 feet

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The area of the rectangle is 1632/3 square feet.

To calculate the area, we need to multiply the length and width of the given rectangle. The length is 51 feet, and the width is 10 2/3 feet, which can be expressed as an improper fraction as 32/3 feet.

Multiplying these values, we have:

Area = length × width

= 51 ft × (32/3) ft

= (51 × 32)/(3)

= 1632/3 square feet

So, the area of the rectangle is 1632/3 square feet.

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The domain and range of a function for the area of a rectangle indicates;

(a) Range; 0 ≤ y < ∞

(b) Domain; 0 ≤ x < ∞

A function is a definition or rule that maps the values of an input unto the values of the output variables.

The area of a rectangle, A = Length, L × Width, W

Therefore;

The area of a rectangle is directly proportional to the width of a rectangle

A ∝ W

The graph of the area to the length of the width of the rectangle indicates that we get;

(a) The domain is the set of the possible x-values of the function

The proportional relationship between the area and the width of a rectangle indicates;

The domain is; 0 ≤ x < ∞

(b) The range is the set of the possible output values of the graph, which is the set of the y-values

The proportional relationship between the area, y and the width, x , the range is; 0 ≤ y < ∞

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Answer:

  80°

Step-by-step explanation:

You want the sum of angles 1 and 2 in the attached figure where line m ║ line n.

Vertical angles are congruent. This means angle 1 is 60°, and the unnumbered angle in triangle ABC at vertex A is 20°.

Where a transversal crosses parallel lines, alternate interior angles are congruent. This means angle 2 is congruent with the unnumbered interior angle at A, which we know is 20°.

Angle 1 is 60° and angle 2 is 20°. Their sum is ...

  ∠1 +∠2 = 60° +20° = 80°

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The length of side x to the nearest tenth is equal to 2.4 units.

In Mathematics and Geometry, an isosceles triangle simply refers to a type of triangle with two (2) sides that are equal in length (side lengths) and two (2) equal angles.

This ultimately implies that, an isosceles triangle comprises two (2) side lengths that are equal and two (2) angles with the same magnitude.

Therefore, we would apply Pythagorean theorem in order to find the length of side x as follows;

x² + x² = (√11)²

2x² = 11

x² = 11/2

x² = 5.5

x = 2.4 units.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

third option represents a function.

Step-by-step explanation:

for the ordered pairs to represent a function.

each value of x must only map to one unique value of y

in the first option

(- 2, 0 ) and (- 2, 2 )

the same x- coordinate maps to 2 different values of y

thus not a function.

in the second option

every value of x = - 5 maps to 5 different values of y

thus not a function.

in the third option

each value of x maps to a unique value of y.

thus a function.

in the fourth option

(- 6, - 3 ) and (- 6, - 2 )

the same x value maps to 2 different values of y

thus not a function.

Answer: Infinity

Step-by-step explanation: Since 0 doesn't have a measurable amount of times it can go into 28 the answer is infinity.

Answer:

$27.69

Step-by-step explanation:

39 - (39)(0.29) = 39 - 11.31 = 27.69

The location of the center and the radius will be (-1.5. -2) and 3, respectively. Thus, the correct option is A.

Given that:

Equation: (x + 1.5)² + (y + 2)² = 9

Let r be the radius of the circle and the location of the center of the circle be (h, k). Then the equation of the circle is given as,

(x - h)² + (y - k)² = r²

Compare the equation, then we have

Center: (-1.5, -2)

Radius: r² = 9 ⇒ r = 3

Thus, the correct option is A.

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Answer:

7.7

Step-by-step explanation:

Find the third angle that is not given:

180 - (120 + 37) = 23.

Draw a line that cuts the 120 degree angle and makes two 90 degree angles with the opposite side. We will call this line h.

You can find the length of h by using sine of 37 degrees. We get:

sin(37 deg) = h/5

h = 3.01

Because we have already found the third angle, 23 degrees, we can use sine of 23 degrees to find the missing side length (x):

sin(23 deg) = 3.01/x

x = 7.7

Answer is 7.7

The reduced row echelon form of the matrix is:

[tex]\left[\begin{array}{ccc}-1144/259&\\-321/259\\25/74\end{array}\right][/tex]

Given the matrix below

[tex]\left[\begin{array}{ccc}7&-1&-3 |-63\\0&-6&-2 |-20\\0&1&1 | 6\end{array}\right][/tex]

Divide the first row by 7:

[tex]\left[\begin{array}{ccc}1&-1/7&-3/7 |-9\\0&-6&-2 |-20\\0&1&1 | 6\end{array}\right][/tex]

Add 1/7 times the first row to the second row:

[tex]\left[\begin{array}{ccc}1&-1/7&-3/7 |-9\\0&-37/7&-17/7 |-107/7\\0&1&1 | 6\end{array}\right][/tex]

Add 3/7 times the second row to the first row:

[tex]\left[\begin{array}{ccc}1&0&-16/37 |-296/37\\0&-37/7&-17/7 |-107/7\\0&1&1 | 6\end{array}\right][/tex]

Add 17/37 times the second row to the third row:

[tex]\left[\begin{array}{ccc}1&0&-16/37 |-296/37\\0&-37/7&-17/7 |-107/7\\0&0&20/37 | 25/37\end{array}\right][/tex]

Multiply the third row by 37/20:

[tex]\left[\begin{array}{ccc}1&0&-16/37 |-296/37\\0&-37/7&-17/7 |-107/7\\0&0&1 | 25/74\end{array}\right][/tex]

Add 3/7 times the third row to the second row:

[tex]\left[\begin{array}{ccc}1&0&-16/37 |-296/37\\0&-37/7&0 |-321/259\\0&0&1 | 25/74\end{array}\right][/tex]

Add 16/37 times the third row to the first row:

[tex]\left[\begin{array}{ccc}1&0&0 |-1144/259\\0&-37/7&0 |-321/259\\0&0&1 | 25/74\end{array}\right][/tex]

Multiply the second row by -7/37:

[tex]\left[\begin{array}{ccc}1&0&0 |-1144/259\\0&1&0 |321/259\\0&0&1 | 25/74\end{array}\right][/tex]

This is the reduced row echelon form of the given matrix.

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The required length is 11 units for the given triangle.

The sine rule defines the side length ratios of triangles to their opposing angles. This proportion is true for all three sides and opposing angles.

a/sinA = b/sinB = c/sinC

The triangle is given in the question, as follows:

In ΔABC, ∠A=120°, ∠B=37°, and c = 5 units

Here, ∠C= 180° - 120° - 37° = 23.

We have to determine the length of a.

As per the sine rule, the required solution would be as:

a/sin∠A = c/sin∠C

Substitute the known values and we get

a/sin 120° = 5/sin 23°

a = (18/sin 1240°) × sin 23°

k ≈ 11

Thus, the length of c is 11 units.

Hence, the number that belongs in the green box is 11.

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Answer:

Step-by-step explanation:

let m = mean

s= standard deviation

to find zscore = (value-m)/s

1.)

((m-1.5s)-m)/s = -1.5

in fact, if it's n standard deviations ABOVE the mean, your zscore is n

if it's n standard deviations BELOW the mean, your zscore is -n

2.)

((m+1.7s)-m)/s= 1.7

3.)

(m-m)/s= 0

Answer: the approximate circumference of the circle with a radius of 2.5 meters is 15.70 meters.

Step-by-step explanation:

The circumference of a circle can be calculated using the formula C = 2πr, where C is the circumference and r is the radius.

Given a radius of 2.5 meters and using an approximation of π = 3.14, we can calculate the circumference as:

C = 2 * 3.14 * 2.5

C ≈ 15.70 meters

Answer:

15.70 meters

Step-by-step explanation:

Use the formula: [tex]\\\sf{C = 2\pi r}[/tex]

C = circumference, R = radius, [tex]\pi[/tex] = pi (3.14)

C = 2(3.14)(2.5)

C ≈ 15.70

-----------------------------------≈

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Hoped this helped! :)

Answer:

121

Step-by-step explanation:

firstly you arrange the numbers in ascending order the number in the middle is considered to be the median

Answer: 15/38 or 0.39473684210526315789473684210526

Step-by-step explanation:

Sorry if I'm wrong but I hope this helps! :)

The cost per pound of sausage, s, and brisket, b is 10s + 14b = 100.5

We are given that;

First customer order= $21

Second customer order= $100.50

Now,

The two equations that can be used to create a system of equations are:

2s + 3b = 21 10s + 14b = 100.5

These equations are obtained by multiplying the cost per pound of sausage and brisket by the number of pounds ordered by each customer and setting them equal to the total cost for each customer. The variables s and b represent the cost per pound of sausage and brisket, respectively.

Therefore, by the equation the answer will be 10s + 14b = 100.5

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Answer:

710

Step-by-step explanation:

The assumption of a decay constant of k = 0.1, we estimate that there would be approximately 36.788 fossils per cubic meter after 10 years.

To estimate the number of fossils after 10 years, we need to solve the given equation. However, since the equation is not provided, we'll assume a simple exponential decay model for the population of fossils.

Let's assume the equation for the population of fossils is:

N(t) = N0 * e^(-kt)

where:

N(t) is the number of fossils after t years,

N0 is the initial number of fossils,

k is a decay constant, and

e is the base of the natural logarithm (approximately 2.71828).

Since the initial number of fossils is given as 100, we have N0 = 100. Now, we need to find the value of the decay constant (k) to estimate the number of fossils after 10 years.

Without further information, it's challenging to determine the exact decay constant. However, let's assume a hypothetical value of k = 0.1 for this example.

Plugging the values into the equation, we get:

N(10) = 100 * e^(-0.1 * 10)

= 100 * e^(-1)

≈ 100 * 0.36788

≈ 36.788

So, with the assumption of a decay constant of k = 0.1, we estimate that there would be approximately 36.788 fossils per cubic meter after 10 years.

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Answer:

B. 2333.59

Step-by-step explanation:

We have been given the following differential equation:

[tex]\dfrac{dN}{dt}=\dfrac{5000}{6+5t}[/tex]

To find the number of fossils N(t) after t = 10 years, we first need to solve the differential equation using integration and the given parameters to create an equation for N(t) in terms of t.

Solving a differential equation means using it to find an equation in terms of the two variables, without a derivative term.

Rearrange the equation so that all the terms containing N are on the left-hand side, and all the terms containing t are on the right-hand side:

[tex]1\;dN=\dfrac{5000}{6+5t}\; dt[/tex]

Integrate both sides:

[tex]\displaystyle \int 1 \;dN=\int \dfrac{5000}{6+5t}\; dt[/tex]

Use the following integration rules:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Integration rulest}\\\\\\$\displaystyle \int n\:\text{d}x=nx+\text{C}$\;\;(where $n$ is any constant value)\\\\\\$\displaystyle \int \dfrac{n}{a+bx}\:\text{d}x=\dfrac{n}{b}\ln |a+bx|+\text{C}$\\\\ \end{minipage}}[/tex]

Therefore:

[tex]\begin{aligned}\displaystyle \int 1\;dN&=\int \dfrac{5000}{6+5t}\; dt\\\\\implies N&=\frac{5000}{5}\ln \left|6+5t\right|+C\\\\N&=1000\ln \left|6+5t\right|+C\end{aligned}[/tex]

As the initial number of fossils is 100, then N = 100 when t = 0.

Substitute these values into the equation and solve for C:

[tex]100=1000\ln \left|6+5(0)\right|+C[/tex]

[tex]C=100-1000\ln (6)[/tex]

Therefore, the equation for N in terms of t is:

[tex]N=1000\ln \left|6+5t\right|+100-1000\ln(6)[/tex]

Use the quotient log rule to simplify:

[tex]N=1000\ln \left|6+5t\right|-1000\ln(6)+100[/tex]

[tex]N=1000\ln \left(\dfrac{\left|6+5t\right|}{6}\right)+100[/tex]

To estimate the number of fossils after 10 years, substitute t = 10 into the equation:

[tex]N=1000\ln \left(\dfrac{\left|6+5(10)\right|}{6}\right)+100[/tex]

[tex]N=1000\ln \left(\dfrac{56}{6}\right)+100[/tex]

[tex]N=2333.59\; \sf (2\;d.p.)[/tex]

Therefore, the number of fossils after 10 years is 2333.59.

The area of the regular decagon with a radius of 14 units is approximately [tex]195.7 unit^{2}[/tex]

To find the area of a regular decagon, we need to know either the side length or the apothem (the perpendicular distance from the center to a side). In this case, you have provided the radius of the decagon, which is 14 units.

For a regular decagon, the apothem (a) is related to the radius (r) by the formula:

[tex]a = r * cos(\pi/10)[/tex]

Let's calculate the apothem using the given radius:

[tex]a = 14 * cos(\pi/10) =12.149[/tex]

Now, we can calculate the area (A) of the regular decagon using the formula:

[tex]A = (5/2) * a^2 * tan(\pi/10)[/tex]

[tex]A = (5/2) * (12.149)^2 * tan(\pi/10) =195.7[/tex]

Rounding to the nearest tenth, the area of the regular decagon with a radius of 14 units is approximately [tex]195.7 unit^{2}[/tex].

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Answer: median = 8.5

mean=

9.7

total = 58

Answer:

median=8.5 hours Mean=9.7 hours

Step-by-step explanation:

First you take the values and add them together, find the sum.
20+4+7+7+10+10=x
x=58
now take 58 and divide it by the number of students
58/6=9.66666
the mean would be 9.7 hours since it asks to round to the nearest 10th
and for the median sort it from lowest to highest
4,7,7,10,10,20
now since in the middle are 7 and 10, add those together and divide by 2
10+7=17
17/2=8.5
the median is 8.5

Using the model, at 150°F they can sell 304 cups.

We can see that the line that models this passes through (65, 35) and (80, 75)

Then the slope of the line is:

a = (75 - 35)/(80 - 65)

a = 2.66

y = 2.66*x + b

To find the value of b, we can use the fact that y = 35 when x = 65

35 = 2*65 + b

35 - 2*65 = b

-95

y = 2.66*x -95

IF the tempererature is 150°F, then:

y = 2.66*150 - 95

y = 304

They can expect to sell 304 cups.

And no, the 150° don't make sense, that is equivalent to 66°C.

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The batting average for Brett is of 0.25 = 25%.

The batting average is obtained applying the proportions in the context of the problem.

A proportion is applied as the batting average is given by the division of the number of hits by the number of at bats.

Brett got 10 hits in 40 at bats, hence his batting average is calculated as follows:

10/40 x 100% = 0.25 x 100% = 25%.

From the image given at the bottom, we have that he got 10 hits on 40 at bats, hence the batting average calculated above is of 25%.

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At the end of 2 years, Jackson's account balance is $700.40.

We have,

The formula for calculating simple interest is:

I = Prt

Where:

I is the interest earned

P is the principal amount

r is the interest rate

t is the time period

In this case,

Jackson invested $680.00 at an annual interest rate of 1.5% for 2 years. Therefore:

P = $680.00

r = 1.5% = 0.015

t = 2 years

Plugging these values.

I = Prt = $680.00 x 0.015 x 2 = $20.40

So,

Jackson earned $20.40 in interest over 2 years.

To find his total account balance at the end of 2 years, we need to add the interest earned to the initial principal:

Total balance

= $680.00 + $20.40

= $700.40

Therefore,

At the end of 2 years, Jackson's account balance is $700.40.

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