Write each of the following word names as mixed decimals. a. six and two tenths b. seventeen and four hundredths c. four hundred, and thirty-five thousandths d. fifty-six, and two hundred seventy-eight thousandths

ANSWER

The population in 2000 is 525.5

EXPLANATION

The population is modeled by the equation:

[tex]y=525.5e^{-0.01t}[/tex]

Where y=population (in thousands)

t=the time (in years) with t=0 for the year 2000.

To find the population in the year 2000, we substitite t=0 into the equation to get:

[tex]y=525.5e^{-0.01 \times 0}[/tex]

Perform the multiplication in the exponent:

[tex]y=525.5e^{0}[/tex]

Note that any non-zero number exponent zero is 1.

[tex]y=525.5(1)[/tex]

Any number multiplied by 1 is the same number;

[tex]y=525.5[/tex]

The population in 2000 is 525.5

Answer:

Step-by-step explanation:

[tex]4x+2y=8\qquad\text{subtract 4x from both sides}\\\\4x-4x+2y=-4x+8\\\\2y=-4x+8\quad\text{divide both sides by 2}\\\\\dfrac{2y}{2}=\dfrac{-4x}{2}+\dfrac{8}{2}\\\\y=-2x+4[/tex]

Answer:

The probability that it will snow and Amy will be late for school is 6%

Step-by-step explanation:

The answer is:

The probability that it will snow and Amy will be late for school is 6%

Step-by-step explanation:

I did the question in the quiz and I got it right soo… ^0^

Answer:

h(height)= 40cm

Step-by-step explanation:

V= h x w x l

(10000)= h x (25) (10)

h= (10000)/ ((25) (10))

h= (10000)/ ((250))  

h=40

You can verify if this is right by working the problem backwards.

V= (25) (10) (40)

V= 10, 000 cm^3

Answer:

h = 40 cm

Step-by-step explanation:

the formula for the volume of a rectangular box of width w, height h and depth d is V = w·h·d (the order in which you write these doesn't matter).

We want to find out how tall this box is.  Thus, we solve V = w·h·d for h:

            V

h = -------------

          w·d

Here, h = vertical measurement of box = ( 10000 cm³) / [ (25 cm)(10 cm) ], or

h = 40 cm

Answer:

16 cm

Step-by-step explanation:

Consider isosceles triangle ABC with vertex angle ACB of 120° and legs AC=CB=8 cm.

CD is the median of the triangle ABC. Since triangle ABC is isosceles triangle, then median CD is also angle ACB bisector and is the height drawn to the base AB. Thus,

∠DCB=60°

Consider triangle OBC. This triangle is isoscels triangle, because OC=OB=R of the circumscribed about  triangle ABC circle. Thus,

∠OCB=∠OBC=60°

So, ∠COB=180°-60°-60°=60°.

Therefore, triangle OCB is equilateral triangle.

This gives that

OC+OB=BC=8 cm.

The diameter of the circumscribed circle is 16 cm.

Answer:

16 cm

Step-by-step explanation:

Answer:

either 76 or 19

Step-by-step explanation:

76 if it's 1/5 of the original amount as well as 3/4 the original amount

1/5+3/4=19/20

3.80=1/20x

3.80+19/20x=76

3.8*20=76

19 if it's 1/5 of the original amount and 3/4 of the new amount

3.80=1/4y

3.80+3/4y=15.20

15.20=4/5x

15.20+1/5x=19

Answer:

i belive its 100

Step-by-step explanation:

Answer:

hes right its 100

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

Plot the points on the given graph. The ones that fall in on a solid line at the edge of the doubly-shaded area, or fall in the doubly-shaded area, are part of the solution set.

(0, 4) on the dashed line — not a solution

(-2, 4) on red line in blue area — solution

(0, 5) in doubly-shaded area — solution

(–2, 7) in doubly-shaded area — solution

(–4, 1) in blue area — not a solution

(–1, 1) on red line outside blue area — not a solution

(–1.5, 3.5) in doubly-shaded area — solution

Answer:

  f(x) = (x -(-3))(x -(-4))

Step-by-step explanation:

The function can be written as the product of binomial terms whose values are zero at the given zeros.

  (x -(-3)) is one such term

  (x -(-4)) is another such term

The product of these is the desired quadratic function. In the form easiest to write, it is ...

  f(x) = (x -(-3))(x -(-4))

This can be "simplified" to ...

  f(x) = (x +3)(x +4) . . . . simplifying the signs

  f(x) = x^2 +7x +12 . . . . multiplying it out

Answer:

c. zero

Step-by-step explanation:

The expression on the left of the equal sign is a polynomial of degree 2. (The highest power of x is 2.) A polynomial of degree 2 is called a "quadratic." Values of the variable (x, in this case) that make the value of the quadratic be zero are called "zeros" or "roots" of the quadratic.

Every polynomial has as many roots as its degree. So, a second degree polynomial (quadratic) will have two roots. The roots may be real numbers, or they may be complex numbers. For polynomials of degree higher than 2, there may be some roots of each kind.

This question is asking, "How many roots of this quadratic are real numbers?"

___

There are several different ways you can figure out the answer to this question. One of the simplest is to graph the quadratic. (See attached.) You can see that the graph of the quadratic never has a y-value of zero, so there are no (real) values of x that will be solutions to this equation.

The two solutions are -0.25±i√1.1875. The "i" indicates that portion of the number is imaginary, and the entire number (real part plus imaginary part) is called a "complex" number. Both solutions for this quadratic are complex, not real.

__

Another way you can answer this question is to compute what is called the "discriminant." The roots of every quadratic of the form ax^2+bx+c can be found using the formula ...

x = (-b±√(b^2-4ac))/(2a)

For this quadratic, the values of a, b, and c are 4, 2, and 5, respectively. Then the formula becomes ...

x = (-2±√(2^2 -4·4·5))/(2·4) = (-2±√-76)/8

The value under the radical sign is the "discriminant." When it is negative, as here, the value of the square root is an imaginary number (not a real number), so the roots are complex. When the discriminant is zero, the two roots have the same value; when it is positive, there are two distinct roots.

There are zero real number solutions to this equation.

Answer:

0.19

Step-by-step explanation:

μ = 160 and σ = 50.  Find the z scores for 180 and 210.

z = (x - μ) / σ

z = (180 - 160) / 50 = 0.40

z = (210 - 160) / 50 = 1.00

So we want P(0.40<z<1.00).  This can be found as:

P(0.40<z<1.00) = P(z<1.00) - P(z<0.40)

Now use a calculator or table to find each probability:

P(0.40<z<1.00) = 0.8413 - 0.6554

P(0.40<z<1.00) = 0.1859

Rounded to the nearest hundredth, P ≈ 0.19.

Final answer:

The probability of a Major League Baseball game lasting between 180 and 210 minutes is approximately 0.19 when assuming normal distribution with a mean of 160 minutes and a standard deviation of 50 minutes.

Explanation:

The probability of a Major League Baseball game duration being between 180 and 210 minutes can be calculated using the Z-score formula, which is Z = (X - μ) / σ, where X is the value in question, μ is the mean, and σ is the standard deviation. In this case, the mean (μ) is 160 minutes, and the standard deviation (σ) is 50 minutes.

First, we find the Z-score for 180 minutes:

Z1 = (180 - 160) / 50 = 0.4

Then, we find the Z-score for 210 minutes:

Z2 = (210 - 160) / 50 = 1.0

Using a Z-table or a calculator with normal distribution functions, we can find the probabilities corresponding to these Z-scores:

P(Z < Z1) = P(Z < 0.4)

P(Z < Z2) = P(Z < 1.0)

To find the probability of a game duration between 180 and 210 minutes, subtract the probability of Z1 from the probability of Z2:

P(180 < X < 210) = P(Z < Z2) - P(Z < Z1)

Assuming the probabilities from Z-table or calculator:

P(Z < Z2) = 0.8413 (approximately)

P(Z < Z1) = 0.6554 (approximately)

Therefore:

P(180 < X < 210) = 0.8413 - 0.6554 = 0.1859

So the probability, rounded to the nearest hundredth, that a game will last between 180 and 210 minutes is approximately 0.19.

When you mark up a price, multiply the original price by 1 plus the amount of the mark up as a decimal.

15% = 0.15 + 1 = 1.15

$60 x 1.15 = $69

The correct answer is $69 Start by putting 15 into a decimal

Answer:

D. -1

Step-by-step explanation:

We have been given a set of data points and the slope of the line of best fit as 2.5.

The equation of the line of best fit, in slope-intercept form, can be thus written as;

y = 2.5x + c

where c is the  y-intercept of this line.

We can then use any of the points given to determine c. Using the point

( 2, 4);

4 = 2.5(2) + c

4 = 5 +c

c = 4-5 = -1

The answer will be -1

Answer:4

Step-by-step explanation:

The equation of a vertical parabola is:

y = a (x − h)² + k,

where (h, k) is the vertex and a is the coefficient.

We know the vertex is (-5, -2), so:

y = a (x − (-5))² + (-2)

y = a (x + 5)² − 2

We also know the parabola passes through (-4, 2).

2 = a (-4 + 5)² − 2

2 = a (1)² − 2

2 = a − 2

a = 4

So the coefficient of the squared expression is 4.

Answer:

5676.16 cm^3

Step-by-step explanation:

The volume of any prism is given by the formula ...

V = Bh

where B is the area of one of the parallel bases and h is the perpendicular distance between them. Here, the base is a triangle, so its area will be ...

B = 1/2·bh

where the b and h in this formula are the base and height of the triangle, 28 cm and 22.4 cm.

Then the volume is ...

V = (1/2·(28 cm)(22.4 cm))·(18.1 cm) = 5676.16 cm^3

_____

You will note that this is half the product of the three dimensions, so is half the volume of a cuboid with those dimensions. Perhaps you can see that if you took another such prism and placed the faces having the largest area against each other, you would have a cuboid of the dimensions shown.

Answer:

[tex]V=5,676.16\ cm^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the triangular prism is equal to

[tex]V=BL[/tex]

where

B is the area of the triangular face

L is the length of the triangular prism

Find the area of the triangular face B

[tex]B=\frac{1}{2}(28*22.4)= 313.6\ cm^{2}[/tex]

we have

[tex]L=18.1\ cm[/tex]

substitute the values

[tex]V=313.6*18.1=5,676.16\ cm^{3}[/tex]

Answer:

[tex]\frac{1}{15}[/tex]

Step-by-step explanation:

Multiples of 3 (from 1 to 10) are 3, 6, and 9.

Multiples of 4 (from 1 to 10) are 4 and 8.

First,

Probability of selecting multiple of 3 from 10 total slips are 3/10

now since it is not replaced, we have to now think that there are 9  total slips.

Second,

Probability of selecting multiple of 4 from 9 total slips are 2/9

in probability "AND" means multiplication. Hence,

selecting 3 "AND" then selecting 4 means, we need to multiply the individual probabilities found.

So,

3/10 * 2/9 = 1/15

Answer:

1/15

Step-by-step explanation:

I just took the test

Answer:

The flux of F across S is 8.627.

Step-by-step explanation:

Given,

F(x, y, z) = xy i + yz j + zx k

or F=(xy, yz, zx)

S is the part of the paraboloid [tex]z=8-x^{2} -y^{2}[/tex] above the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1

By differentiating z with respect to x we get:

fx=-2x

By differentiating z with respect to y we get:

fy=-2y

So, Surface integral is given by:

[tex]=\int\limits^1_0\int\limits^1_0( {(xy)*(2x)+y(8-x^{2} -y^{2} *(2y)+x(8-x^{2} -y^{2})} \, )dx \, dy[/tex][tex]=\int\limits^1_0\int\limits^1_0 (2x^{2} y+16y^{2} -2x^{2} y^{2} -2y^{4}+8x-x^{3}-xy^{2} } \,) dx \, dy[/tex]

Integrating with respect y:

[tex]=\int\limits^1_0(x^{2} y^{2} +\frac{16}{3} y^{3} -\frac{2}{3} x^{2} y^{3} -\frac{2}{5} y^{5}+8xy-x^{3}y-\frac{1}{3} xy^{3} } \, )dx \,[/tex]

After Substituting limits of y, we get:

[tex]=\int\limits^1_0(x^{2} +\frac{16}{3} -\frac{2}{3} x^{2} -\frac{2}{5}+8x-x^{3}-\frac{1}{3} x } \,) dx \,[/tex]

Integrating with respect x:

[tex]=(\frac{1}{3} x^{3} +\frac{16}{3}x -\frac{2}{9} x^{3} -\frac{2}{5}x+4 x^{2} -\frac{1}{4} x^{4}-\frac{1}{6} x^{2} } \,)[/tex]

After Substituting limits of x, we get:

[tex]=(\frac{1}{3} +\frac{16}{3} -\frac{2}{9} -\frac{2}{5}+4 -\frac{1}{4} -\frac{1}{6} } \,)\\\\=\frac{1553}{180}[/tex]

[tex]= 8.627[/tex]

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To evaluate the surface integral of the given vector field F across the given surface S, we need to use the formula: Φ = ∫∫S F · dS. In this case, the vector field F(x, y, z) = xy i + yz j + zx k and the surface S is the part of the paraboloid z = 8 - x^2 - y^2 that lies above the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, with upward orientation. We can parametrize the surface S and calculate the normal vector to evaluate the surface integral using the given formula.

To evaluate the surface integral of the given vector field F across the given surface S, we need to use the formula:

Φ = ∫∫S F · dS

In this case, the vector field F(x, y, z) = xy i + yz j + zx k and the surface S is the part of the paraboloid z = 8 - x2 - y2 that lies above the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, with upward orientation.

We can parametrize the surface S as r(u, v) = (u, v, 8 - u2 - v2), where 0 ≤ u ≤ 1 and 0 ≤ v ≤ 1.

Next, we calculate the normal vector to S by taking the cross product of the partial derivatives of r(u, v) with respect to u and v: N = (-∂r/∂u) x (-∂r/∂v) = (2u, 2v, 1).

Now, we can evaluate the surface integral using the formula:

Φ = ∫∫S F · dS = ∫∫R F(r(u, v)) · (N · (∂r/∂u) x (∂r/∂v)) du dv

Substituting the values for F and N, we get:

Φ = ∫∫R (u2v + 4uv + 4uv) (2u, 2v, 1) · (2u, 2v, 1) du dv

Calculating this integral over the region R: 0 ≤ u ≤ 1 and 0 ≤ v ≤ 1, we find the flux of F across S.

Answer:

  D)  y = 1/4 x^2

Step-by-step explanation:

For these functions, the leading coefficient can be considered to be either ...

  the vertical scale factor (larger ⇒ narrower)

  the square of the inverse of the horizontal scale factor.

In the latter case, the horizontal scale factor will be larger (wider) when its inverse and the square of its inverse are smaller.

Either way, you're looking for the smallest leading coefficient: 1/4.

Answer:

3 v (v - 7) (w - 1) thus the answer is B:

Step-by-step explanation:

Factor the following:

3 v^2 w - 21 v w - 3 v^2 + 21 v

Factor 3 v out of 3 v^2 w - 21 v w - 3 v^2 + 21 v:

3 v (v w - 7 w - v + 7)

Factor terms by grouping. v w - 7 w - v + 7 = (v w - 7 w) + (7 - v) = w (v - 7) - (v - 7):

3 v w (v - 7) - (v - 7)

Factor v - 7 from w (v - 7) - (v - 7):

Answer:  3 v (v - 7) (w - 1)

Answer:

Sheridan is correct.

Step-by-step explanation:

She is correct because there is no B squared listed only A and C are provided, Jayden put 13 cm as B instead of listing it as C but she listed it correctly and answered everything else correctly.

Hope this helps!

Explanation:

By checking the table for when y=0, Jose was looking for the number of rows such that the total number of seats is zero. Jose needed to check the table for when y = 416.

Doing that, Jose would find the number of rows to be -13 or +16. He would determine that the auditorium has 16 rows of seats.

Let's analyse the function

[tex]y = f(x) = A\sin(\omega x)[/tex]

The amplitude is A, so we want A=1.5

Now, we start at x=0, and we have [tex]1.5\sin(0)=0[/tex]

After one second, i.e. x=1, we want this sine function to make 330 cycles, i.e. the argument must be [tex]330\cdot 2\pi[/tex]

So, we have

[tex]f(1)=1.5\sin(\omega) = 1.5\sin(660\pi)[/tex]

so, the function is

[tex]f(x) = 1.5\sin(660\pi x)[/tex]

Answer:

f(x) = 1.5\sin(660\pi x)

Step-by-step explanation:

Answer:

The measure of arc DC is [tex]11\°[/tex]

Step-by-step explanation:

we know that

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.

[tex]m\angle ATB=\frac{1}{2}[arc\ AB+arc\ DC][/tex]

substitute the given values

[tex]63\°=\frac{1}{2}[115\°+arc\ DC][/tex]

[tex]126\°=[115\°+arc\ DC][/tex]

[tex]arc\ DC=126\°-115\°=11\°[/tex]

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite. Then the arc DC will be 11°.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.

 ∠ATB = 1/2 [arc AB + arc DC]

     63° = 1/2 [115° + arc DC]

arc DC = 11°

More about the angled link is given below.

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Answer:

6

Step-by-step explanation:

If we are raising to the 5th power we have to allow for the constant at the end of it all.

Answer:

The answer is 6.

Answer:h

Step-by-step explanation:

Answer:

the left curve is: y=(x+2)³-1;

the right curve is: y=3(x-2)³-1

Answer:

g(x) is translated down 2 units from f(x)

Step-by-step explanation:

Adding -2 to the function value moves it down 2 units.

Answer:

The graph of f(x) is shifted to right by 2 units to get graph of g(x).

Step-by-step explanation:

We have been given two functions [tex]f(x)=4^x[/tex] and [tex]g(x)=4^{x-2}[/tex]. We are asked to find the graph of g(x) is related to the parent function f(x).

Let us recall transformation rules.

[tex]f(x)\rightarrow f(x-a)=\text{Graph shifted to right by a units}[/tex]

[tex]f(x)\rightarrow f(x+a)=\text{Graph shifted to left by a units}[/tex]

[tex]f(x)\rightarrow f(x)-a=\text{Graph shifted downwards by a units}[/tex]

[tex]f(x)\rightarrow f(x)+a=\text{Graph shifted upwards by a units}[/tex]

Upon comparing the graph of f(x) to g(x), we can see that [tex]g(x)=f(x-2)[/tex], therefore, the graph of f(x) is shifted to right by 2 units to get graph of g(x).

Answer:

The triangle should be 4 inches tall

Step-by-step explanation:

We can write a proportion to solve.  Put the height over the width

20           x

------- = -----------

5              1

Using cross products

20*1 = 5*x

20 = 5x

Divide by 5

20/5 = 5x/5

4 =x

The triangle should be 4 inches tall

To find the new height when the width of a triangle is reduced, you can use the concept of similar triangles and ratios.

To determine the new height of the triangle, we can use the concept of similar triangles. Similar triangles have proportional sides. So, if the width of the triangle is reduced from 5 in to 1 in, the height will also be reduced proportionally. Using the ratio of the new width to the original width, we can find the new height:

New height = (new width / original width) * original height = (1 / 5) * 20 = 4 in

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Answer:

b = 29.4 units , m∠A = 122.9 , m∠C = 21.1°

Step-by-step explanation:

* To solve a triangle we can use cosine rule and sin rule

* In ΔABC

- If a, b, c are the lengths of its 3 sides, where

# a is opposite to angle A

# b is opposite to angle B

# c is opposite to angle C

- By using the cosine rule:

# a² = b² + c² - 2bc cos(A)

# b² = a²² + c² - 2ac cos(B)

# c² = a² + b² - 2ab cos(C)

- By using sin rule

# c/sinC = a/sinA = b/sinB

* Lets solve the problem

∵ a = 42 , c = 18 , m∠B = 36°

* We will use the cosine rule

∴ b² = (42)² + (18)² - 2(42)(18) cos(36) =864.766 ⇒ take √ for both sides

∴ b = 29.4

* Now we will use the sin rule to find m∠C

∵ 29.4/sin(36) = 18/sin(C) ⇒ by using cross multiplication

∴ sin(C) = 18 × sin(36°)/29.4 = 0.3598685

∴ m∠C = 21.1°

* The sum of the measure of the interior angle of a triangle is 180°

∴ m∠A = 180° - (36° + 21.1°) = 122.9°

* b = 29.4 units , m∠A = 122.9 , m∠C = 21.1°

Answer: Last Option

[tex]4x^5\sqrt[3]{3x}[/tex]

Step-by-step explanation:

To make the product of these expressions you must use the property of multiplication of roots:

[tex]\sqrt[n]{x^m}*\sqrt[n]{x^b} = \sqrt[n]{x^{m+b}}[/tex]

we also know that:

[tex]\sqrt[3]{x^3} = x[/tex]

So

[tex]\sqrt[3]{16x^7}*\sqrt[3]{12x^9}\\\\\sqrt[3]{16x^3x^3x}*\sqrt[3]{12(x^3)^3}\\\\x^2\sqrt[3]{16x}*x^3\sqrt[3]{12}\\\\x^5\sqrt[3]{16x*12}\\\\x^5\sqrt[3]{2^4x*2^2*3}\\\\x^5\sqrt[3]{2^6x*3}\\\\4x^5\sqrt[3]{3x}[/tex]