Randy worked 18 hours each week for four weeks. for each of the next four weeks, he worked 1/3 fewer hours as the previous four weeks. what was the total number of hours he worked for the eight weeks

Answers

Answer 1

from 1st week to 4th: 18 x 4= 72 hours
from 5th week to 8th week: 18 x 1/3 x 4 = 48 hours
72 + 48 = 120 hours

Related Questions

What are the missing pieces to the steps? –27 = 4x2 – 24x –27 = 4(x2 – 6x) –27 + = 4(x2 – 6x + 9) 9 = 4(x – 3)2 = (x – 3)2 ± = x – 3 = x

Answers

i think the 4 wasn't distributed correctly. it should be one of the first steps.

Answer:

We can find out the missing pieces by the below explanation,

Here, the given equation,

[tex]-27 = 4x^2 - 24x[/tex]

Step 1 :

[tex]-27=4(x^2-6x)[/tex]

Step 2 :

[tex]-27+36=4(x^2-6x+9)[/tex]

Step 3 :

[tex]9=4(x-3)^2[/tex]

Step 4 :

[tex]\frac{9}{4}=(x-3)^2[/tex]

Step 5 :

[tex]\pm \frac{3}{2}=x-3[/tex]

Step 6 :

[tex]x=3\pm \frac{3}{2}[/tex]

What is the sum of the first 35 terms in the series 7 + 9 + 11 + ...?

a.

29

c.

1645

b.

1399

d.

1435

Answers

The answer is d
Hope this helps :)

First find the 35th number in the series using the formula:
an = a1 + (n - 1)d
a1 = first number in the series
d = difference between successive number
n = number of terms
a35 = 7 + (35 - 1)2
a35 = 7 + (34)2
a35 = 7 + 68 = 75.
Therefore, the 35th term is 75.
To find the sum of the first 35 numbers, use the formula:
Sn = n(a1 + an) / 2
Sn = 35(7 + 75) / 2
Sn = 2870 / 2 = 1,435.
Therefore, the sum of the first 35th term is 1,435.
The correct answer is D.

Lana is trying to find an equation for a line that passes through (5, 2) and is parallel to 3x + 2y = 15. explain the steps that lana could take to determine the equation.

Answers

We have the following equation:
3x + 2y = 15

Step 1:
Rewrite given equation:
2y = 15 - 3x
y = 15/2 - (3/2) x

Step 2:
Parallel lines have the same slope:
y = mx + b
m = -3 / 2
y = (- 3/2) x + b

Step 3:
Find b, for this we evaluate the point (5, 2) in the equation:
2 = (- 3/2) (5) + b
2 = (- 15/2) + b
2 + 15/2 = b
19/2

Step 4:
The parallel line is:
y = (- 3/2) x + 19/2

Question part points submissions used use the gram-schmidt process to find an orthogonal basis for the column space of the matrix. (use the gram-schmidt process found here to calculate your answer. let xi be the ith column of the matrix.) 0 1 1 1 0 1 1 1 0

Answers

Assuming your unformatted string of numbers at the end is a 3x3 matrix, {(0, 1, 1), (2, - 1, 1), (1, 1, - 1)} is an orthogonal basis for its column space.

Hugo is a veterinarian. He knows the following information about his 41 patrons: 20 patrons in total do not have a dog. 17 patrons in total have a cat. 7 patrons have neither a dog nor a cat. Can you help Hugo organize the results into a two-way frequency table?

Answers

Answer:

4,17,13,7

Step-by-step explanation:

i got it right :)

Final answer:

To assist Hugo in organizing patron pet ownership into a two-way frequency table, calculations were made to determine the number of patrons with both a dog and a cat, leading to a complete frequency table illustrating pet ownership among 41 patrons.

Explanation:

Hugo, the veterinarian, is attempting to organize patron pet ownership information into a two-way frequency table. First, let's establish the total number of patrons which is 41. Since 20 patrons do not have a dog, it implies that 41 - 20 = 21 patrons have a dog. Of the 41 patrons, we know that 17 have a cat. Also, 7 patrons have neither a dog nor a cat. To create the two-way frequency table, we need to figure out how many patrons have both a dog and a cat.

To find the number of patrons with both pets, we add the number of patrons without pets to those with dogs and then subtract from the total number of patrons, which gives us 41 - 20 + 7 = 28. However, since this number includes all dog owners, we need to subtract those who only have dogs and no cats, which gives us 28 - (41 - 17) = 28 - 24 = 4 patrons with both a dog and a cat.

With these calculations, we can now fill out the two-way frequency table:

Patron\PetDogNo DogTotalCat41317No Cat17724Total212041

Note: The sum of the numbers for dog owners and non-dog owners must equal the total number of patrons, and the same applies for cat ownership.

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Hey can you please help me out posted picture

Answers

A because you have to do 3+2+6+5+4+8

For each language we have:
Number of people who speak Spanish:
Spanish = 8 + 4 = 12
Number of people who speak Chinese:
Chinese = 5 + 6 = 11
Number of people who speak both languages:
Both = 3 + 2 = 5
Adding we have:
12 + 11 + 5 = 28
Answer:
28
option A

A right angle has a league of 13 cm in the hypotenuse of 21 cm what is the length of the other leg

Answers

For a Right Angled Triangle, according to the Pythagoras Theorem, the square of hypotenuse is equal to the sum of squares of its two legs.

One leg is 13cm long, hypotenuse is 21cm long. Let the other leg be x cm. So, we can write:

[tex]21^{2} =13^{2} + x^{2} \\ \\ 272= x^{2} \\ \\ x= \sqrt{272} \\ \\ x=16.49 [/tex]

Rounding of to nearest hundredth, the length of other leg of the Triangle is 16.49

You can use c^2 = a^2 + b^2 to solve for the length of the other leg. Just substitute the values to the variable then transpose to get the value of the missing variable.

Given: a = 13; c = 21
Required: b - other leg
Solution:
c^2 = a^2 + b^2
21^2 = 13^2 + b^2
441 = 169 + b^2
b^2 = 272
√b = 16.49
b = 16.49 cm

Find the absolute maximum of f(x,y) = e^(-x^2-y^2)(x^2+2y^2) on x^2 + y^2 < 2

Answers

[tex]f(x,y)=e^{-x^2-y^2}(x^2+y^2)[/tex]

Notice that converting to polar coordinates, setting
[tex]x=r\cos\theta[/tex]
[tex]y=r\sin\theta[/tex]
[tex]\implies r^2=x^2+y^2[/tex]

allows us to consider [tex]f(x,y)[/tex] as a function of one variable; let's call it [tex]F(r)[/tex], where

[tex]f(x,y)\equiv F(r)=re^{-r}[/tex]

Then

[tex]F'(r)=e^{-r}(1-r)=0\implies r=1[/tex]

We have [tex]F'(r)>0[/tex] for [tex]r<1[/tex], and [tex]F'(r)<0[/tex] for [tex]r>1[/tex], which means [tex]F[/tex] is increasing, then decreasing as [tex]r[/tex] exceeds 1. This suggests that extrema occur for [tex]f(x,y)[/tex] wherever [tex]r^2=x^2+y^2=1[/tex], i.e. along the intersection of the cylinder [tex]x^2+y^2=1[/tex] and [tex]f(x,y)[/tex].

Computing the second derivative of [tex]F(r)[/tex] and setting equal to 0 gives

[tex]F''(r)=-e^{-r}(2-r)=0\implies r=2[/tex]

as a possible point of inflection. We have [tex]F''(r)<0[/tex] for [tex]r<2[/tex], and namely when [tex]r=1[/tex], which means [tex]F(r)[/tex] is concave downward around this point. This confirms that [tex]r=1[/tex] is a site of a maximum. Along this path, we have a maximum value of [tex]F(1)=e^{-1}\approx0.368[/tex].

Next, to check for possible extrema along the border, we can parameterize [tex]f(x,y)[/tex] by [tex]x=\sqrt2\cos t[/tex] and [tex]y=\sqrt2\sin t[/tex], so that

[tex]x^2+y^2=(\sqrt2\cos t)^2+(\sqrt2\sin t)^2=2[/tex]

and we can think of [tex]f(x,y)[/tex] as a function a single variable, [tex]F(t)[/tex], where

[tex]F(t)=2e^{-2}\approx0.271[/tex]

In other words, [tex]f(x,y)[/tex] is constant along its boundary [tex]x^2+y^2=2[/tex], and this is smaller than the maximum we found before.

So to recap, the maximum value of [tex]f(x,y)[/tex] is [tex]\dfrac1e\approx0.368[/tex], which is attained along the surface above the circle [tex]x^2+y^2=1[/tex] in the [tex]x-y[/tex] plane.

PLZ HELP NNOOOOOOOWW!! 15 points!!

What is the midpoints of the line segment with endpoints (-3,7) and (9,-2)?

Answers

the midpoint of the line having the endpoints [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is [tex](\frac{x_{1}+_x_{2}}{2}, \frac{y_{1}+_y_{2}}{2})[/tex]
basically average them

so given that the line has the endpoints of (-3,7) and (9,-2)
x₁=-3
y₁=7
x₂=9
y₂=-2

so the midpoint can be found by doing
[tex](\frac{-3+9}{2}, \frac{7+(-2)}{2})=[/tex]
[tex](\frac{6}{2}, \frac{7-2}{2})=[/tex]
[tex](3, \frac{5}{2})[/tex]

the midpoint is [tex](3,\frac{5}{2})[/tex]

2.
Find the amount of the annuity.

Amount of Each Deposit: $295

Deposited: Quarterly

Rate per Year: 10%

Number of Years: 6

Type of Annuity: Due

$9,671.28

$9,542.97

$10,076.54

$9,781.54

Answers

To solve this we are going to use the future value of annuity due formula: [tex]FV=(1+ \frac{r}{n} )*P[ \frac{(1+ \frac{r}{n} )^{kt} -1}{ \frac{r}{n} } ][/tex]
where
[tex]FV[/tex] is the future value [tex]P[/tex] is the periodic payment [tex]r[/tex] is the interest rate in decimal form [tex]n[/tex] is the number of times the interest is compounded per year [tex]k[/tex] is the number of payments per year [tex]t[/tex] is the number of years

We know for our problem that [tex]P=295[/tex] and [tex]t=6[/tex]. To convert the interest rate to decimal for, we are going to divide the rate by 100%:
[tex]r= \frac{10}{100} [/tex]
[tex]r=0.1[/tex]
Since the payment is made quarterly, it is made 4 times per year; therefore, [tex]k=4[/tex].
Since the type of the annuity is due, payments are made at the beginning of each period, and we know that we have 4 periods, so [tex]n=4[/tex].
Lets replace those values in our formula:

[tex]FV=(1+ \frac{r}{n} )*P[ \frac{(1+ \frac{r}{n} )^{kt} -1}{ \frac{r}{n} } ][/tex]
[tex]FV=(1+ \frac{0.1}{4} )*295[ \frac{(1+ \frac{0.1}{4} )^{(4)(6)} -1}{ \frac{0.1}{4} } ] [/tex]
[tex]FV=9781.54[/tex]

We can conclude that the amount of the annuity after 10 years is $9,781.54

If rain is falling at a rate of ¼ inch per hour, how much rain would you expect after 6 hours

Answers

1 hour = 1/4 inch

6 hours = 1/4 x 6 = 6/4 = 1 1/2 inches

Answer: 1 1/2 inches

Costs for standard veterinary services at a local animal hospital follow a normal distribution with a mean of $88 and a standard deviation of $24. what is the probability that one bill for veterinary services costs between $42 and $133?

Answers

the probability that one bill for veterinary services costs between $42 and $133 will be given as follows
P(42<x<133)
z=(x-μ)/σ
where:
μ-mean
σ-standard deviation
thus
when x=42:
z=(42-88)/24=-1.92
thus
P(x<42)=0.0281

when x=133
x=(133-88)/24=1.875
thus
P(x<133)=0.9699
Thus
P(42<x<133)
=0.9699-0.0281
=0.9418

Answer: 0.9418

Final answer:

There is a 94.25% probability that a bill for veterinary services costs between $42 and $133 in this local animal hospital, based on calculating Z-scores for $42 and $133 and finding the difference between probabilities.

Explanation:

The question pertains to the concepts of statistics, specifically the normal distribution which often appear in situations describing natural phenomena and social behavior. To solve this, we need to calculate the Z-scores for both values given and then look those Z-scores up in a standard normal distribution table, or use a calculator or software that can do this.

A Z-score is a statistical measurement that describes a value's relationship to the mean of a group of values. It's measured in terms of standard deviations from the mean.

If X is a random variable from a normal distribution with mean (µ) and standard deviation (σ), the Z-score is calculated by the formula Z = (X - µ)/σ.

For X =$42, Z1 = ($42 - $88)/$24 = -1.92 and for X=$133, Z2=($133-$88)/$24 = 1.88.

The probability that one bill for veterinary services costs between $42 and $133 equals the probability for Z values falling between -1.92 and 1.88. Refer to the standard normal distribution table or a calculator for the corresponding probabilities. The probability for Z1 equals approximately 0.0274, probability for Z2 equals approximately 0.9699. The required probability is then P(Z1

So, "there's a 94.25% chance that a bill for veterinary services costs between $42 and $133 in this local animal hospital".

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Hey can you please help me out posted picture

Answers

We have for this case:
For each language we have:
Number of people who speak Spanish:
Spanish = 8 + 4 = 12
Number of people who speak Chinese:
Chinese = 5 + 6 = 11
Number of people who speak both languages:
Both = 3 + 2 = 5
Adding we have:
12 + 11 + 5 = 28
Answer:
28
option A

Number of employees who speak only Spanish = 8
Number of employees who speak only Chinese = 6
Number of employees who speak Spanish and Russian = 4
Number of employees who speak Spanish and Chinese = 3
Number of employees who speak all three languages = 2
Number of employees who speak Chinese and Russian = 5

The number of employees who speak Spanish or Chinese or both will be the sum of all above values. The sum is = 28

Thus the correct answer is option A

the following shows the correlation between the length of a person's handspan and how many jolly ranchers they can pick up with one hand.
Which of the following does the data suggest?
a. strong positive
b. strong negative
c. no relation
d.weak negative
( please help)

Answers

It is A) strong positive, because the slope is graphing up

Answer:

a. strong positive is the answer.

Step-by-step explanation:

The following shows the correlation between the length of a person's hand span and how many jolly ranchers they can pick up with one hand.

There is a strong positive correlation between the two things. We can see the scatter plot moving up as the hand span increases, the number of jolly ranchers they can pick up also increases.

Write an expression that represents the difference of 32 and N multiplied by 10

Answers

(32-n)10________________

So, we first find the difference:
32-n
we multiply it by 10:
10(32-n)
If you want it to be distributed:
320 - 10n

Use the word BULLDOG to answer the question. If the letters of this word are written on paper and then cut into squares with one letter per square, what is the probability of selecting a C or a Z?

Answers

There is a 0% chance of selecting either of those letters as they do not appear in the work BULLDOG.

hey can you please help me posted picture of question

Answers

The correct answer for the problem shown in the figure atttached is the last option (option D), which is shown below:

D. (-3x+6i)(x+2i)
It is impotant to know that if you want to verify that the option D. (-3x+6i)(x+2i) is the correct answer, you can apply the distributive property to (-3x+6i)(x+2i).
Therefore, when you apply the distributive property, you obtain that the result is:
-3x²-12

Which is correct

Therefore, you can be sure that the correct answer is the option D. (-3x+6i)(x+2i).

Find the surface area of the part of the surface z = x y that lies within the cylinder

Answers

A surface area, r radius, and h height

A=2πr²+2πrh

xy should be like a rectangle so x is r and y is h

A=2πx²+2πxy

Find the horizontal or oblique asymptote of f(x) = negative 3 x squared plus 7 x plus 1, all over x minus 2

Answers

Find the horizontal or oblique asymptote of f(x) = negative 3 x squared plus 7 x plus 1, all over x minus 2

Finding the horizontal and oblique asymptote of
f(x)= (-3x^2+7x+1)/(x-2)

Solution:

For Horizontal Asymptote:
Line y=L is a horizontal asymptote of the function y=f(x), if either limx→∞f(x)=Llimx→∞f(x)=L or limx→−∞f(x)=Llimx→−∞f(x)=L, and LL is finite.

Calulate limits:

limx→∞(1x−2(−3x2+7x+1))=−∞

limx→−∞(1x−2(−3x2+7x+1))=∞

Thus, there are no horizontal asymptotes.

For Oblique Asymptote:

Do polynomial long division (−3x2+7x+1)/(x-2)=−3x+1+3/(x−2)

The rational term approaches 0 as the variable approaches infinity.

Thus, the slant asymptote is y=−3x+1y=−3x+1.

At the deli Jennifer bought roasted turkey and provolone cheese. The turkey costs $6.35 per pound and the cheese costs $4.75 per pound. In total, she bought 3 pounds and the price was $17.13 How many pounds of each did she buy?

Answers

She bought two pounds of turkey and one pound of cheese

Let the amounts of Turkey Jennifer bought be [tex] T [/tex] pounds and that of Cheese be [tex] C [/tex] pounds.

From the given information,

[tex] 6.35T+4.75C=17.13\\
T+C=3 [/tex]

Solving the above two equations together,

[tex] 6.35T+4.75(3-T)=17.13\\
(6.35-4.75)T+4.75*3=17.13\\
1.6T=2.88\\
T=\frac{2.88}{1.6}\\
T=1.8
[/tex]

Thus, Jennifer bought [tex] 1.8\;pounds [/tex] of Turkey and [tex] 3-1.8=1.2\;pounds [/tex] of Cheese.

Determine the mean ,median,modes ,IQR,and rage for the data 3,8,6,6,4,6,9,9,12

Answers

Mean:

Add all the numbers:

3 + 8 + 6 + 6 +4 + 6 + 9 + 9 + 12 = 63

There are 9 numbers.

63 / 9 = 7

Mean = 7

Median:

Order all the numbers:

3, 4, 6, 6, 6, 8, 9, 9, 12

The median is 6.

Mode:

The number that appears the most is 6.

The mode is 6.

Inter-Quartile Range :

Median of 2nd part = 9

Median of 1st part = 5

Subtract:

9 - 5 = 4

The IQR is 4.

Range:

The highest number is 12. The lowest is 3

Subtract:

12 - 3 = 9

The range is 9.

Hope this helped☺☺

Mean=Average/add all the numbers and divide it by how many numbers there are

3+8+6+6+4+6+9+9+12

=63

63/9

=7 is your mean

Median=The middle number in a set of ordered numbers

first place all the numbers from least to greatest

3,4,6,6,6,8,9,9,12

The middle number of this set is 6 so 6 is your median

Mode is the most numbers repeated so if no numbers are repeated there is no mode

6 is repeated 3 times so 6 is your mode

Range: greatest number minus least number

12-3

=9 is your range

IQR=since the median is 6 we would split it and then minus it

so 3,4,6,6,6,8,9,9,12

It would be 9-5

=4is your IQR I am pretty sure that is correct!

^o^

the speed limit is 55 minutes per hr. write an inequalit to represent the speed limit.

Answers

Answer: Either [tex]x \le 55[/tex] or [tex]0 \le x \le 55[/tex] depending on your teacher's preference. See the note at the bottom for more info.

=====================================

Let x be the speed limit. It is simply a placeholder. Think of it as a box with the number inside. We don't know what the number is, but we know that the largest it can be is 55. It cannot be larger than 55.

So x can be equal to 55 or it can be smaller

Put another way, x is less than or equal to 55 which is written as [tex]x \le 55[/tex] (on the keyboard you would type " x <= 55 " without quotes).

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

Note: since negative speeds make no sense, we also must imply that x can't be negative. Your teacher may want you to write this in to clearly state it. If so, then you would also have [tex]x \ge 0[/tex] which when combined with the first inequality, you get this compound inequality [tex]0 \le x \le 55 [/tex] (basically saying "x is some speed between 0 and 55 mph"). This very clearly states the boundaries on what x can be. Though your teacher may want you to stick to the first format as its simpler.

The quantity demanded each month of the walter serkin recording of beethoven's moonlight sonata, manufactured by phonola media, is related to the price per compact disc. the equation p = −0.00054x + 9 (0 ≤ x ≤ 12,000) where p denotes the unit price in dollars and x is the number of discs demanded, relates the demand to the price. the total monthly cost (in dollars) for pressing and packaging x copies of this classical recording is given by c(x) = 600 + 2x − 0.00002x2 (0 ≤ x ≤ 20,000)

Answers

We can get the Profit function P(x) from the Hint.

the Profit function is: P(x) = xp(x) - C(x) = -0.00041 x2 + 4x - 600
Attention: don't get confuse by the big P of the profit with the small p of the price To calculate the maximum profit, we need to find the derivative of P(x) then set it to 0 then find x: dP(x)/dx = -0.00082 x + 4 = 0 , so x = 4/0.00082 = 4,878 copies each month.

Final answer:

To find the equilibrium price and quantity, we set the demand to be equal to the supply, solve for x, and substitute the value back into the demand equation to find the equilibrium price.

Explanation:

The given equation is:

p = -0.00054x + 9, where p is the unit price in dollars and x is the number of discs demanded.

The total monthly cost for pressing and packaging x copies is given by:

c(x) = 600 + 2x - 0.00002x^2

To find the equilibrium price and quantity, we need to find the point where the demand equals the supply. In this case, the demand is represented by the equation p = -0.00054x + 9 and the supply is represented by the equation c(x) = 600 + 2x - 0.00002x^2.

To solve for the equilibrium price and quantity, we set the demand equals the supply:

-0.00054x + 9 = 600 + 2x - 0.00002x^2

This equation can be solved by rearranging and solving for x:

0.00002x^2 + 2.00054x - 591 = 0

Using the quadratic formula, we can find the values of x that satisfy this equation:

x = (-2.00054 ± sqrt(2.00054^2 - 4*0.00002*(-591))) / (2*0.00002)

After calculating, we find two possible values for x, which are approximately x_1 = 13727.927 and x_2 = -0.036. However, since the quantity demanded cannot be negative, we discard the negative value.

The equilibrium quantity is approximately 13728.

To find the equilibrium price, we substitute the value of x into the demand equation:

p = -0.00054(13728) + 9

p is approximately equal to $1.53.

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4.
Find the present value of the annuity.

Amount Per Payment: $4,725

Payment at End of Each: 6 months

Number of Years: 15

Interest Rate: 10%

Compounded: Semiannually

$72,634.83

$35,938.73

$32,242.03

$68,951.03

Answers

To solve this we are going to use the present value of annuity formula: [tex]PV=P[ \frac{1-(1+ \frac{r}{n})^{-kt} }{ \frac{r}{n} } ][/tex]
where
[tex]PV[/tex] is the present value
[tex]P[/tex] is the periodic payment
[tex]r[/tex] is the interest rate in decimal form
[tex]n[/tex] is the number of times the interest is compounded per year
[tex]k[/tex] is the number of payments per year
[tex]t[/tex] is the number of years

We know from our problem that [tex]P=4725[/tex] and [tex]t=15[/tex]. To convert the interest rate to decimal form, we are going to divide it by 100%:
[tex]r= \frac{10}{100} [/tex]
[tex]r=0.1[/tex]
Since the interest is compounded semiannually, it is compounded 2 times per year; therefore, [tex]n=2[/tex]. Similarly, since the payment is made at the end of each 6 months, it is made 2 times per year; therefore, [tex]k=2[/tex].
Lest replace the values in our formula:

[tex]PV=P[ \frac{1-(1+ \frac{r}{n})^{-kt} }{ \frac{r}{n} } ][/tex]
[tex]PV=4725[ \frac{1-(1+ \frac{0.1}{2})^{-(2)(15)} }{ \frac{0.1}{2} } ][/tex]
[tex]PV=72634.83[/tex]

We can conclude that the correct answer is $72,634.83

When 415 junior college students were surveyed, 150 said they have a passport. constructa 95% confidence interval for the proportion of junior college students that have apassport. round to the nearest thousandth?

Answers

Solution:
The 95% confident interval will be estimated as follows:

sample proportion: 150/415=0.362

ME=1.96*[0.362*0.638/415]=0.0011
thus
95% CI
0.362-0.0011<p<0.362+0.0011

Answer:

[tex]0.362-0.045<p<0.362+0.045[/tex]

Step-by-step explanation:

It is given that When 415 junior college students were surveyed, 150 said they have a passport, then sample proportion will be:

Sample proportion=[tex]\frac{150}{415}=0.362[/tex]

Then, [tex]ME=1.96\sqrt{\frac{0.362{\times}0.638}{415}}[/tex]

=[tex]1.96\sqrt{\frac{0.230}{415}[/tex]

=[tex]1.96(0.023)[/tex]

=[tex]0.045[/tex]

Therefore, at 95% confidence interval, the proportion of junior college students that have a passport is:

[tex]0.362-0.045<p<0.362+0.045[/tex]

The price C, in dollars per share, of a high-tech stock has fluctuated over a twelve-year period according to the equation C= 14 +12x – x2, where x is in years. The price C, in dollars per share, of a second high-tech stock has shown a steady increase during the same time period according to the relationship C = 2x + 30. For what values are the two stock prices the same?

Answers

For this case we have the following equations:
C = 14 + 12x - x2
C = 2x + 30
Equating the equations we have:
14 + 12x - x2 = 2x + 30
Rewriting we have:
-x2 + 10x - 16 = 0
Solving the polynomial we have:
x1 = 2
x2 = 8
Answer:
the two stock prices are the same for:
x1 = 2
x2 = 8

Final answer:

The values for which the two stock prices are the same are approximately x ≈ -1.405 and x ≈ 11.405.

Explanation:

To find the values for which the two stock prices are the same, we need to set the equations for the prices equal to each other and solve for x.

Equation for the first stock: C = 14 + 12x - x^2

Equation for the second stock: C = 2x + 30

Setting the two equations equal: 14 + 12x - x^2 = 2x + 30

Rearranging the equation and combining like terms: x^2 - 10x - 16 = 0

Using the quadratic formula to solve for x: x = (-b ± sqrt(b^2 - 4ac))/(2a)

Plugging in the values: x = (-(-10) ± sqrt((-10)^2 - 4(1)(-16)))/(2(1))

Simplifying: x = (10 ± sqrt(100 + 64))/2

Calculating: x = (10 ± sqrt(164))/2

Approximate values: x ≈ (10 ± 12.81)/2

Therefore, the two stock prices are the same for x ≈ -1.405 and x ≈ 11.405.

number of per month__number of moviegoers
more than 7____________96
5-7_______________ ___180
2-4__________________219
less than 2____________205
total _________________700

Use the frequency table. Find the probability that a person goes to the movies at least 2 times a month. Round to the nearest thousandth.

A. 0.138

B. 0.707

C. 0.137

D. 0.394

sorry for the poor graph up top,,,,:/

Answers

Leave out those who went less than twice to get those who went at least twice
pr = (700 - 205)/700 = 0.7071 <-------

So answer is B

Answer:

B. 0.707

Step-by-step explanation:

The frequency table is given by,

Number of months Number of movie goers

More than 7 96

5 - 7 180

2 - 4 219

Less than 2 205

Total 700

Since, Probability of an event is the ratio of favorable events to the total number of events.

As, the number of people going to movies atleast 2 times a month = 96 + 180 + 219 = 495

The probability that a person goes to the movies atleast 2 times a month = [tex]\frac{495}{700}=0.707[/tex].

Thus, option B is correct.

A mountain climber is at an altitude of 2.9 mi above the earths surface. From the climbers viewpoint what is the distance to the horizon

Answers

we know that
applying the Pythagorean theorem
(3959+2.9)²=x²+3959²
x²=(3959+2.9)²-3959²
x²=3961.9²-3959²
x²=22970.61
x=√22970.61
x=151.56 mi

the answer is
x=151.56 mi

50 POINTS...Which equation would best help solve the following problem? Tania releases a javelin 1.6 meters above the ground with an initial vertical velocity of 25 meters per second. How long will it take the javelin to hit the ground?

Answers

Let [tex]x(t)[/tex] be the vertical position of the javelin at time [tex]t[/tex]. Once it's thrown in the air, the only force acting on it is gravity, so the javelin would be subjected to a constant downward acceleration of approx. 9.8 meters per second per second. So

[tex]x''(t)=-9.8[/tex]

Integrating once with respect to [tex]t[/tex], we get

[tex]x'(t)=-9.8t+C_1[/tex]

where [tex]x'(t)[/tex] is the velocity of the javelin. We're told that [tex]x'(0)=25[/tex], so

[tex]25=-9.8\cdot0+C_1\implies C_1=25[/tex]

Integrating again with respect to [tex]x[/tex] to get

[tex]x(t)=-4.9t^2+25t+C_2[/tex]

and we know the javelin was initially thrown 1.6 meters above the ground, or [tex]x(0)=1.6[/tex], so we get

[tex]1.6=-4.9\cdot0^2+25\cdot0+C_2\implies C_2=1.6[/tex]

So the javelin's position at any time [tex]t[/tex] is given by

[tex]x(t)=-4.9t^2+25t+1.6[/tex]

It will hit ground when [tex]x(t)=0[/tex]. Solve this however you want; you'll find that this will happen at about [tex]t=5.165[/tex] seconds after the javelin has been thrown.

im doing the same quiz anyone know number 1 with the base of a traingle or something

one more question please help me!!!

Answers

a = (9/6)*10 mm = 15 mm

b = (35/10)*6 mm = 21 mm

The ratio in parentheses is the ratio of corresponding sides in the respective rectangles, so is the scale factor. The unknown dimension is that scale factor applied to the corresponding known dimension.

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