The following set of numbers
has a mean of 38.8.
What would be the mean if 29
was added to the list?
75, 21, 45, 39, 14

The rest wavelength of the emission line observed at 2148 nanometers in the galaxy 100 million light-years away is approximately 2103 nanometers.

The rest wavelength of an emission line can be determined by applying the concept of redshift, which is a phenomenon observed in astrophysics where light from distant objects is shifted towards longer wavelengths due to the expansion of the universe.

In this case, the emission line is observed at 2148 nanometers (or 2.148 micrometers) in a galaxy located 100 million light-years away. To calculate the rest wavelength, we need to consider the redshift factor. Redshift, denoted by z, is defined as the observed wavelength divided by the rest wavelength minus 1.

Given that the observed wavelength is 2.148 micrometers and the galaxy is located 100 million light-years away, we need to convert the distance into a redshift factor using the cosmological relationship between redshift and distance. Assuming a standard cosmological model, we can use the Hubble constant to estimate the redshift.

The Hubble constant represents the rate at which the universe is expanding. Taking a typical value of the Hubble constant as 70 kilometers per second per megaparsec, we find that the redshift factor, z, is approximately 0.021.

To determine the rest wavelength, we rearrange the redshift equation as \((observed wavelength) = (1 + z) \times (rest wavelength)\). Substituting the values, we get \((2.148 micrometers) = (1 + 0.021) \times (rest wavelength).\)

Simplifying the equation, we find the rest wavelength to be approximately 2.103 micrometers or 2103 nanometers.

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The value of x for the chord is:

x = 12

A chord of a circle is a straight line segment whose endpoints both lie on a circular arc.

Recall that: If two chords intersect inside the circle, then they cut each other in such a way that the product of the lengths of the parts is the same for the two chords.

Using the above principle, we can say:

3 * x = 4 * 9

3x = 36

x = 36/3

x = 12

Thus, the value of x for the chord is 12.

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Answer: a= 0.0231

Step-by-step explanation:

n=8

p=0.75

q=1 - 0.75 = 0.25

(p=x)

p(5) = 8C5 (0.25)^5 (0.75)^8-5

p(5)= 0.0231

Or 2.31%

The probability that exactly 3 people  from that group will go to Ches Tahoe restaurant is 2.11%

The probability that at least 35 people will go to Ches Tahoe  the restaurant is -1.88.

Given that,

When you select a random person, the probability that this person will go to Ches Tahoe restaurant is 75%,

We have to determine,

You randomly select 8 people. What is the probability that exactly 3 people

from that group will go to Ches Tahoe restaurant.

You randomly select 50 people. Use the normal approximation to the binomial distribution to find the probability that at least 35 people will go to Ches Tahoe restaurant.

According to the question,

When you select a random person, the probability that this person will go to Ches Tahoe restaurant is 75%,

You randomly select 8 people.

Then,

The probability that exactly 3 people

from that group will go to Ches Tahoe restaurant is,

\(P(x) = ^nC_x \times q^x \times p^{n-x}\)

Where n = 8, x = 5, q = 1 - 0.75 = 0.25, and p = 0.75

Substitute all the values in the expression,

\(P(5) = ^8C_5 \times (0.25)^5 \times (0.75)^{8-5}\\\\P(5) = \dfrac{8!}{(8-5)!. 5!} \times 0.00097 \times (0.75)^3\\\\P(5) = \dfrac{8 \times 7 \times 6}{3 \times 2} \times 0.00097 \times 0.42\\\\P(5) = 0.2118\\\\P(5) = 2.11 \ Percent\)

The probability that exactly 3 people from that group will go to Ches Tahoe restaurant is 2.11%.

You randomly select 50 people. Use the normal approximation to the binomial  distribution

Then, the probability that at least 35 people will go to Ches Tahoe  restaurant is,

Mean for that at least 35 people will go to Ches Tahoe  restaurant is,

\(\mu = n \times p \\\\\mu = 8 \times 0.75\\\\\mu = 6\)

And standard deviation that at least 35 people will go to Ches Tahoe  restaurant is,

\(\sigma = \sqrt{n \times p \times q} \\\\\sigma = \sqrt{0.75 \times 0.25 \times 8}\\\\\sigma = \sqrt{1.5}\\\\\sigma = 0.53\)

Normal approximation to the binomial distribution is,

\(z = \dfrac{x-\mu}{\sigma}\\\\z = \dfrac{5-6}{0.53}\\\\z = \dfraac{-1}{0.53}\\\\z = -1.88\)

The probability that at least 35 people will go to Ches Tahoe  the restaurant is -1.88.

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1)

The axis of symmetry is x = -6.

2)

Vertex is (-6, 26).

3)

f(x) has a maximum value.

4)

f(x) is concave down.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 7 is an equation.

We have,

f(x) = -x² - 12x - 10

This is in the form of ax² + bx + c.

a = -1, b = -12, c = -10

The axis of symmetry is x = -b/2a

x = 12/(-2)

x = -6

Now,

f(x) = -x² - 12x - 10

f(x) = -(x² + 12x + 10)

f(x) = - { (x² + 12x + 36) - 36 + 10}

f(x) = -(x + 6)² + 26

This is in the form of f(x) = a (x - h)² + k

a = -1, h = -6, k = 26

Vertex = (h, k) = (-6, 26)

Now,

f(x) = -x² - 12x - 10

f'(x) = -2x - 12

f''(x) = -2

It is a negative value.

This means f(x) has a maximum value.

Now,

From the graph, we see that f(x) is concave down.

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Answer:

85 mi

Step-by-step explanation:

Let d = the distance in miles traveled

Let M = the time in hours for Maria to travel d miles

\(m+\frac{3}{4} =\) time in hours for Ricky to travel d miles

(Note that \(\frac{3}{4}\) hrs = 45 min)

----------------------

Maria's equation:

d = 51m

Ricky's equation:

d = 24 · \((m+\frac{3}{4} )\)

----------------------

Substitution:

51m = 24 · \((m+\frac{3}{4} )\)

51m = 24m + 45

6m = 10

m = \(\frac{5}{3}\)

----------------------

d = 51m

d = 51 · \((\frac{5}{3})\)

d = 85

----------------------

The distance traveled is 85 mi

If it takes Ricky, traveling at 24 mph, 45 minutes longer to go a certain distance than it takes Maria traveling at 51 mph, the distance traveled is 85 miles

Speed is the ratio of distance traveled to time taken. Mathematically:

Distance = Speed/Time

According to the given question:

Set up the Maria equation:

d = 51m

Set up Ricky's equation:

d = 24 · (m+3/4)

Substitute

51m = 24 · (m+3/4)

51m = 24m + 45

6m = 10

m = 5/3

Determine the required distance

d = 51m

d = 51 · 5/3

d = 85

Hence the distance traveled is 85 mile

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Answer:

Grogg's dad is 22

Step-by-step explanation:

Let D = dad's current age

Let g = Grogg's current age

6(d - 7) = g - 7 → 6d - 42 = g - 7 → 6d -35 = g

4(d - 3) = g - 3 → 4d -12 = g - 3 → 4d -9 = g

Set the two equations equal to each other and solve for d

6d - 35 = 4d - 9  Subtract 4d from both sides

2d -35 = -9  Add 35 to both sides

2d = 44  Divide both sides by 2

d = 22

Helping in the name of Jesus.

Answer:

Step-by-step explanation:

d = current dad age

g = current grogg age

d-7 = 6(g-7)

d-3 = 4(g-3)

Let's solve the first equation first:

Add 7 to both sides: d - 7 +7 = 6g - 42 + 7 so d = 6g - 35

Substitude d = 6g - 35 for d in d - 3 = 4g - 12

(6g-35)-3 = 4g-12 = 6g-38 = 4g-12

Subtract 4g from both sides: 2g - 38 = -12

Add 38 to both sides: 2g = 26

Easy: g = 13

And now substitude g in for any equations.

d-3 = 52-12

d = 43

Answer:

ABC is translated right 5 units and down 5 units

Step-by-step explanation:

The vertices of the original and new triangles haven't moved. Only the triangle as a whole moved from one place to another. The other choices involved reflecting the triangle in which the vertices change locations that are different from their original locations. Hope this helps!

A' ( 0,0)

B' (4,0)

C' (4, 8)

D' (0,8)

Given the transformation rule, we want to get the coordinates of the transformed point

The transformation rule is that;

(x,y) to (x,2y)

Thus we have;

A (0,0) to (0 , 2(0))

A' (0,0)

For B (4,0)

WE have

(4, 2(0)) = (4,0)

For C (4,4)

WE have;

(4, 2(4)) = (4,8)

For (0,4)

We have

(0, 2(4)) = (0,8)

The required cost of the dinner not including sales tax was $34.28.

A sales tax is a fee that is paid to the government when specified goods and services are sold. Typically, laws permit the vendor to charge the customer the tax at the time of purchase. Use taxes are typically used to describe taxes on goods and services that consumers pay directly to a governing authority.

To find out how much the dinner cost before sales tax, we need to subtract the sales tax amount from the total cost.

We know that the sales tax rate is 8%. To find the sales tax amount, we can multiply the total cost by 8% (or 0.08):

Sales tax = 0.08 * $37.26 = $2.98

To find the cost of the dinner before sales tax, we can subtract the sales tax amount from the total cost:

Cost before sales tax = $37.26 - $2.98 = $34.28

Therefore, the cost of the dinner not including sales tax was $34.28.

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The length of the shadow would be approximately 41.7 feet if the angle of elevation from the horizontal to the sun is 38° at this time.

If the angle of elevation from the horizontal to the sun is 38°, then the tangent of that angle is equal to the opposite side (the height of the tree) divided by the adjacent side (the length of the shadow).

Therefore, we can set up the equation using trigonometric function tangent as,
tan(38°) = height of tree / length of shadow

Solving for the length of the shadow, we get:
length of shadow = height of tree / tan(38°)

Plugging in the given height of the tree (32 feet) and using a calculator to find the tangent of 38°, we get:
length of shadow = 32 / tan(38°) = 41.7 feet (rounded to one decimal place)

Therefore, the length of the shadow would be approximately 41.7 feet at this time.

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The estimated regression equation for these data is Ŷ = 23.194 + 0.318x for every i=1,...,6.

What is meant by regression equation?

In math, the linear regression analysis output delivers some important information, which helps the researcher to predict the estimation, accuracy, and efficiency of the model.

Here we have the data on price and the overall score for stereo headphones that were tested by consumer reports were as follows.

And we need to find the estimated regression equation for these data.

Here let us consider x be the price in dollars of the stereo headphones of brand ii (the independent variable). and let y be the overall score of the stereo headphones of brand ii (the dependent variable).

Here first, we will compute the value of SSE.

The formula is given by

= > SSE = 1∑n​ (yi ​− y​)²

Therefore, we will show the table of values of xi​, Ŷ​, Ŷ​​, (yi​−Ŷ​​) and (yi​−Ŷ​)².

Now, we have to calculate the value of yi​^​, plug in the value of xi​ in the equation 

=> Ŷ = 23.194 + 0.318x for every i=1,...,6.

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To match the graphs of cylinders a and b to cylinders P and Q, we need to analyze the relationship between the height of the water and the volume of water in each cylinder.

Cylinder P would correspond to graph b, while Cylinder Q would correspond to graph a.

The reasoning behind this is as follows:

Cylinder P, corresponding to graph b, shows a steeper increase in height with increasing volume. This indicates that the water level rises quickly as more volume is added, suggesting that the cylinder has a smaller cross-sectional area. Since height is directly proportional to volume for a cylinder, a smaller cross-sectional area would result in a higher rise in height for the same volume of water.

Cylinder Q, corresponding to graph a, shows a slower increase in height with increasing volume. This implies that the water level rises more gradually as more volume is added, indicating a larger cross-sectional area. A larger cross-sectional area would result in a smaller increase in height for the same volume of water.

In summary, the steeper graph b matches Cylinder P with a smaller cross-sectional area, while the gentler graph a matches Cylinder Q with a larger cross-sectional area.

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Answer:

D. A pair of intersecting lines

Step-by-step explanation:

A conic section is a fancy name for a curve that you get when you slice a double cone with a plane. Imagine you have two ice cream cones stuck together at the tips, and you cut them with a knife. Depending on how you cut them, you can get different shapes. These shapes are called conic sections, and they include circles, ellipses, parabolas and hyperbolas. If you cut them right at the tip, you get a point. If you cut them slightly above the tip, you get a line. If you cut them at an angle, you get two lines that cross each other. That's what happened in your question. The plane cut the cone at an angle, so the curve is two intersecting lines. That means the correct answer is D. A pair of intersecting lines.

I hope this helps you ace your math question.

Answer:

796871

Step-by-step explanation:

Based on the given conditions, formulate:

5000 x (1 - (1 + 10%) 10)

-------------------------------                                                                  

           1 - (1 + 10%)                                                                          

Evaluate the equation/expression:

796871.23005

Find the closest integer to

798871.23005

=  796871

Answer:

Step-by-step explanation:

Let the length is x, then the width is 1/4x.

Find the perimeter of rectangle:

Answer:

I think it's d, but it could also be b. I'm sorry if I'm wrong!

Step-by-step explanation:

Answer:

the area of the rectangle is A=L•W

The length is 3m less than twice its width W: L+ 3m=2W...->, L=2W-3m

A=L-W

27m²=(2W-3m)-W

27m2=2w2-3m-W

2w2-3wm-27m2=0

....use quadratic formula -(-3m)+ (-3m)²-4-2-(-27m²)

W=

2-2

w=(3m± √9m²+216m²)

w=(3m+ √225m²)

W=(3m± 15m...you need only positive root because width cannot be negative

W= 3m+15m

4

W=. 4

18m

W=4.5m ......now find the L

L=2.4.5m-3m

L=9m-3m

L=6m

Answer:

W = 4.5cm

L = 6cm

Step-by-step explanation:

Answer:

The caterer served 5 hours. x = 5

Step-by-step explanation:

25x + 225 = 350

We must use inverse operations to get x

25x + 225 - 225 = 350 - 225

25x = 125

25x ÷ 25 = 125 ÷ 25

x = 5

the caterer served 5 hours.

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Answer:

the top empty box is 5 the second down box is 4 the box under 6 is 8

Step-by-step explanation:

Answer:

Step-by-step explanation:

23.06, 23.3, 23.7, 24.269

Answer:

question 1(2)

answer 4

question 2(3)

answer 1

question 3(4)

(a)6; factored

(b)7; factored

c(8); factored

The whole number that can be substituted for z is 1.

To order these numbers from least to greatest, we need to first find a value for x that makes the expressions comparable.

1/x can be rewritten as 0.01/x

80% can be written as 0.8

So, the list becomes:

0.01/x, x/3, 0.8

To compare 0.01/x and x/3, we can cross-multiply and simplify:

0.01/x < x/3

0.01*3 < x^2

0.03 < x^2

x > sqrt(0.03)

Since x has to be a whole number, the smallest possible value for x is 1.

So, substituting x = 1, the list becomes:

0.01, 1/3, 0.8

Ordering these from least to greatest, we get:

0.01, 0.8, 1/3

Therefore, the whole number that can be substituted for z is 1.

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Answer:

20%

Step-by-step explanation:

The multiples of 4 and 4 and 8

The total number of spaces = 10

The probability is

P( multiples of 4) = number of multiples of 4/ total

                            = 2/10

                            = 20/100

                            =20%

Answer:

6 × Y, 3=2 should be the answer to that

Amplitude of  f(x)=5cosx

= 5

The amplitude of a periodic variable is a measure of its change in a single period. The amplitude of a non-periodic signal is its magnitude as compared with a reference value. there are numerous definitions of amplitude, which can be all functions of the magnitude of the differences between the variable's extreme values.

It refers to most displacement from the equilibrium that an object in periodic motion show. as an example, a pendulum swings through its equilibrium point (straight down), and then swings to a maximum distance away from the center.

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Result is x = - 2 and y = 1.6 so the ordered pair ( -2, 1.6) is the solution of the system equations.

It is a mathematical expression that shows the equalities between two or more terms. There are different types of equation such as linear equation, quadratic equation, exponential equation and so on.

Given, the two systems of equation.

y = - 0.5x + 0.6

and y = x + 3³₅

rewrite the second equation and get y = x +18/5

                                                       5y = 5x + 18 ....  equation 2

                   the first equation is multiplied by 5 and we get.

                                               5y = - 2.5 x + 3

                                               5y = 5x +18

                                            -          -     -

                        we will now solve the above equations by addition method.

                                       0 = - 7.5 x - 15

                                    7.5 x = - 15

                                     x = -2

        putting the value of x in any equation, we get the value of y = 1.6

    x = - 2 and y =1.6

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Answer:

$32.48

Step-by-step explanation:

Find 116% of $28.(sorry if this sentence was confusing)

x = 116% of $28

    x                116%

_______=_______

 $28            100%

116 x 28 = 3,248

3,248/100= 32.48

= 32.48

Answer:

A.

Explanation:

Use the midpoint formula to find the midpoint of this line segment.

Answer:

A.

Step-by-step explanation:

count