Exercise #1: The amount of money in Nicole's bank account can be represented by the function f(x) = 32.50x + 200,
where f(x) is the amount of money in dollars after x days. State the meaning of the slope and y-intercept of this function in
the given context

Answer:

(A)He only accepts jobs that last 4 or more hours.

Step-by-step explanation:

Deepak charges $30 for each job plus an additional $15 for each hour he works.

Let the number of hours =x

Deepak's Total Income for x hours =30+15x

Since he only accepts jobs if he will earn at least $90 the job.

[tex]\text{Total Income}\geq 90[/tex]

[tex]30+15x\geq 90[/tex]

We then solve the inequality for x

[tex]30+15x\geq 90\\$Subtract 30 from both sides\\30-30+15x\geq 90-30\\15x\geq 60\\$Divide both sides by 15\\15x\div 15\geq 60 \div 15\\x\geq 4[/tex]

We therefore conclude that Deepak only accepts jobs that last 4 or more hours.

The correct option is A.

Answer:

A) He only accepts jobs that last 4 or more hours.

Step-by-step explanation:

Correct me if i'm wrong sorry if i am :)

Answer:

1 / 15

Step-by-step explanation:

The vertical change (rise) is 6 - 3, or just 3.  The horizontal change (run) is 0.4 - 0.2, or 0.2.  Thus the slope of this line is m = rise / run = 0.2 / 3 = 2 / 30 = 1 / 15

Answer: option (g)

Step-by-step explanation:

So the question says :

The study ran for several weeks during the semester. About a week after it started, the university announced that they would be holding training sessions for faculty and staff about how to handle situations involving a gunman on campus. This shut down the study for several days as the university needed the lab building for training. The study then resumed according to script after the training. The researchers found that those in the experimental group did not differ in their memories regarding the presence of a gun compared to those in the control condition. That is, the mean score that a gun was present was similar for the experimental group (M = 65%, SD = 11.4%) and the control group (M = 63%, SD = 13.26%). a. Maturation b. Regression to the mean c. Selection d. Mortality e. Instrumentation f. Testing g. History h. Interactions i. Diffusion j. No Threat

ANS ⇒  The correct answer to this question is option G.

We can confirm here that History is the biggest threat to internal validity in the study as a significant period of time was allowed to pass between the testing conditions.

cheers i hope this helped !!!

Answer:

[tex]x^2+8[/tex]

Step-by-step explanation:

[tex]f(x)=2x^2+1 \\\\g(x)=x^2-7 \\\\(f-g)(x)= (2x^2+1)-(x^2-7)=x^2+8[/tex]

Hope this helps!

Answer:

x ≥ -1

Step-by-step explanation:

Divide everything by 7 to isolate x and you have your answer!

Answer:

x ≥ –1

Step-by-step explanation:

7x ≥ –7

Divide by 7

7x /7≥ –7/7

x ≥ –1

Answer:

Volume = PI * radius^2 * height / 3

Volume = 4,712.39 cubic feet

Lateral Area = PI * radius * slant height

slant height^2 = 20^2 + 15^2

slant height ^2 = 625 slant height = 25

Lateral Area = PI * 15 * 25 = 1,178.1 square feet

Surface Area = PI * radius^2 = 706.86 square feet

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\sqrt{(5-1)^{2} +(10-7)^{2}\\\\\sqrt{4^{2} + 3^{2} \\\\\sqrt{16+9} = \sqrt{25} = 5[/tex]

Answer:

I had $10

I have $150

Step-by-step explanation:

This is a riddle and not a math question

So

The answer to the question how much I had is:

The answer to the question how much I have is:

Here we need to perform an addition of several numbers.

We will find that the total amount of money that you have is $150.

We know that:

You had $5.00

Your mom gave you $10.00

Your dad gave you $30.00

Your aunt and uncle gave you $100.00

You had another $5.00

Now you want to find how much money do you have, so you just need to add these numbers.

We can add it as:

$5 + $10 + $30 + $100 + $5

We can perform the addition in any order we want, for example:

($5 + $5) + $10 + $30 + $100

$10 + $10 + $30 + $100

($10 + $10) + $30 + $100

$20 + $30 + $100

($20 + $30) + $100

$50 + $100 = $150

You have $150.

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Answer:

5 boxes of diaries

6 boxes of pencils

10 boxes of rulers

Step-by-step explanation:

In order to find the smallest number of units that would be possible to buy, find the least common multiple between the number of units in each box:

[tex]12\ \ 10\ \ 6\ |2\\6\ \ \ \ 5\ \ \ 3\ |2\\3\ \ \ \ 5\ \ \ 3\ |3\\1\ \ \ \ 5\ \ \ 1\ |5\\1\ \ \ \ 1\ \ \ 1\ | = 2*2*3*5=60[/tex]

The number of boxes required for each item to get 60 units is:

[tex]d=\frac{60}{12} = 5\ boxes \\p=\frac{60}{10} = 6\ boxes \\r=\frac{60}{6} = 10\ boxes[/tex]

the smallest number of boxes of each item he could buy is:

5 boxes of diaries

6 boxes of pencils

10 boxes of rulers

Answer:

The 90% confidence interval for the difference between means is (-161.18, 205.18).

Step-by-step explanation:

Sample mean and standard deviation for Region I:

[tex]M=\dfrac{1}{12}\sum_{i=1}^{12}(438+1013+1127+737+...+1075+500+340)\\\\\\ M=\dfrac{8424}{12}=702[/tex]

[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{12}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{11}\cdot [(438-(702))^2+(1013-(702))^2+...+(500-(702))^2+(340-(702))^2]}\\\\\\[/tex]

[tex]s=\sqrt{\dfrac{1}{11}\cdot [(69696)+(96721)+...+(131044)]}\\\\\\s=\sqrt{\dfrac{1174834}{11}}=\sqrt{106803.1}\\\\\\s=326.8[/tex]

Sample mean and standard deviation for Region II:

[tex]M=\dfrac{1}{15}\sum_{i=1}^{15}(778+464+563+...+479+710+389+826)\\\\\\ M=\dfrac{10204}{15}=680[/tex]

[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{15}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{14}\cdot [(778-(680))^2+(464-(680))^2+...+(389-(680))^2+(826-(680))^2]}\\\\\\[/tex]

[tex]s=\sqrt{\dfrac{1}{14}\cdot [(9551.804)+(46771.271)+...+(84836.27)+(21238.2)]}\\\\\\ s=\sqrt{\dfrac{545975.7}{14}}=\sqrt{38998}\\\\\\s=197.5[/tex]

Now, we have to calculate a 90% confidence level for the difference of means.

The degrees of freedom are:

[tex]df=n1+n2-2=12+15-2=25[/tex]

The critical value for 25 degrees of freedom and a confidence level of 90% is t=1.708

The difference between sample means is Md=22.

[tex]M_d=M_1-M_2=702-680=22[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{326.8^2}{12}+\dfrac{197.5^2}{15}}\\\\\\s_{M_d}=\sqrt{8899.853+2600.417}=\sqrt{11500.27}=107.24[/tex]

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_{M_d}=1.708 \cdot 107.24=183.18[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M_d-t \cdot s_{M_d} = 22-183.18=-161.18\\\\UL=M_d+t \cdot s_{M_d} = 22+183.18=205.18[/tex]

The 90% confidence interval for the difference between means is (-161.18, 205.18).

Answer:

6^-2

6^3/6^5

6^-9 *6^ 7

Step-by-step explanation:

We want the fractions equal to 1/36

We know that a^-b = 1/a^b

We also know that a^b / a^c = a^(b-c)

We also know that a^b * a^c = a^(b+c)

3^ -6 = 1/3^6 = 1/729

6^-2 = 1/6^2 = 1/36

6^3/6^5 = 6^(3-5) = 6^-2 = 1/6^2 = 1/36

6^2 / 6^-1 = 6^(2- -1) = 6^3 = 216

6*6^-2 = 6^(1-2) = 6^-1 = 1/6

6^-9 *6^ 7 = 6^(-9+7) = 6^ -2 = 1/6^2 = 1/36

Answer:

B C and F

Step-by-step explanation:

Answer:

  21,504

Step-by-step explanation:

This is the usual method multiplication is done "by hand."

  6 × 3584 = 6 × (3000 +500 +80 +4)

  = 6×3000 +6×500 +6×80 +6×4

  = 18000 +3000 +480 +24

  = 21000 +504

  = 21,504

_____

Many of us are taught in grade school to do the multiplication right to left:

  = 6×4 +6×80 +6×500 +6×3000

... writing down the digit corresponding to the place value of the product, and "carrying" any more significant digits to add to the next product.

Here, that looks like 6×4 = 24, write down 4, carry 2. 6×8 = 48, add 2 to get 50, write down 0, carry 5. 6×5 = 30, add 5 to get 35, write down 5, carry 3. 6×3 = 18, add 3 to get 21, write down 21. Then the product is 21504.

__

When doing mental calculation, or using an abacus or soroban, it often works better to do the multiplication left to right, as shown in the answer above.

Answer:

both fireworks will explode 4.5 seconds after  Firework B launches

Step-by-step explanation:

Given;

speed of firework A, [tex]V_A[/tex]= 360 ft/s

speed of firework B, [tex]V_B[/tex] = 340 ft/s

If the two fireworks explodes at the same height, then the height attained by the two fireworks are equal.

let the distance traveled by each firework before explosion = d

Distance = speed x time

Distance A = Distance B

speed A x time = speed B x time

let the time both fireworks explodes after Firework B launches = t

([tex]V_A[/tex]) t = ([tex]V_B[/tex] ) t

360t = 340t

if firework B is launched 0.25 s before Firework A, for the time of the two fireworks to be equal since we are considering time (t) after 0.25 seconds, we will have;

360(t-0.25) = 340t

360t  - 90 = 340t

360 t - 340 t = 90

20 t = 90

t = 90/20

t = 4.5 seconds

Therefore, both fireworks will explode 4.5 seconds after  Firework B launches

Answer:

105 cm ^ 2 / s

Step-by-step explanation:

We have that the area of a rectangle is given by the following equation:

A = l * w

being the length and w the width, if we derive with respect to time we have:

dA / dt = dl / dt * w + dw / dt * l

We all know these data, l = 15; w = 12; dl / dt = 5; dw / dt = 3, replacing we have:

dA / dt = 5 * 12 + 3 * 15

dA / dt = 105

Which means that the area of the rectangle increases by 105 cm ^ 2 / s

Answer:

210 in²

Step-by-step explanation:

6*2.5+6*6*2+(8+6)*2.5+10*2.5+1/2*6*8*2+6*2.5= 210 in²

Answer:

A) periodic rate

Step-by-step explanation:

Because a percentage that is charged or added to the credit card we assume that it is an interest rate, they also tell us that it is charged every month, that is, it has a known collection frequency, which means that it is Newspaper.

therefore, the answer in this case is A) periodic rate since it complies with the premise of the statement

Answer:

C) For each hour worked the dollars earned increases by $5

Step-by-step explanation:

I don't have the context of the problem.

However, we do know that in math, when we have an equation of the form [tex]y=mx+b[/tex], the slope m represents the rate of change. This means, how much one quantity changes in regards to other quantity (from the options I can assume that we are talking about amount earned and hours worked).

Thus, in this case we have [tex]m=5[/tex] and this tells us how much the payment increase in terms of hours worked. Thus, we can say that for each work we work the payment increases by $5.

Thus, the correct answer is c) For each hour worked the dollars earned increases by $5

Answer:

hi your question options is not available but attached to the answer is a complete question with the question options that you seek answer to

Answer:  v = 5v + 4u + 1.5sin(3t),

Step-by-step explanation:

u" - 5u' - 4u = 1.5sin(3t)        where u'(1) = 2.5   u(1) = 1

v represents the "velocity function"   i.e   v = u'(t)

As v = u'(t)

u' = v

since u' = v

v' = u"

v'  = 5u' + 4u + 1.5sin(3t)   ( given that u" - 5u' - 4u = 1.5sin(3t) )

    = 5v + 4u + 1.5sin(3t)  ( noting that v = u' )

so v' = 5v + 4u + 1.5sin(3t)

d/dt [tex]\left[\begin{array}{ccc}u&\\v&\\\end{array}\right][/tex]= [tex]\left[\begin{array}{ccc}0&1&\\4&5&\\\end{array}\right][/tex]  [tex]\left[\begin{array}{ccc}u&\\v&\\\end{array}\right][/tex] + [tex]\left[\begin{array}{ccc}0&\\1.5sin(3t)&\\\end{array}\right][/tex]

Given that u(1) = 1 and u'(1) = 2.5

since v = u'

v(1) = 2.5

note: the initial value for the vector valued function is given as

[tex]\left[\begin{array}{ccc}u(1)&\\v(1)\\\end{array}\right][/tex]  = [tex]\left[\begin{array}{ccc}1\\2.5\\\end{array}\right][/tex]

Answer:

the range for this problem is the first one

The range of  f(x) =(3/4)ˣ- 4 function is {yly>-4}, Option A is correct.

A relation is a function if it has only One y-value for each x-value.

The function f(x) = (3/4)ˣ- 4 is an exponential function with a base of 3/4. The base is between 0 and 1, which means that the function is decreasing as x increases.

The function has a vertical asymptote at x = infinity, since the base is between 0 and 1, and the function approaches 0 as x approaches negative infinity.

As the exponential function (3/4)ˣ approaches 0 as x approaches infinity, we have:

lim((3/4)ˣ) = 0 as x -> infinity

So, the range of the given function is all real numbers greater than -4.

Hence, the range of function f(x) =(3/4)ˣ- 4  is {yly>-4}, Option A is correct.

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Answer: 6/14 or 3/7

Step-by-step explanation:

There are a total of 14 employees hired so it would like like this: 1/14 if you were to chose one of all 6 women and 8 men hired.

There are 6 women that may be chosen out of all 14 employees of which 8 are men, now what this would look like is : 6?14 or simplified, (3/7).

This means there is a 6/14 chance of choosing a woman instead of a man in these 14 hired employees. just because the question asks, "what is the chance of a woman getting chosen", of the other 5 women and 8 men hired, so the answer is 6/14 or 3/7 to chosen as a women instead of men in all the 14 employees that may/might be chosen. hope this helps love yawl!!

                  STAY SAFE !!!             LOVE YOU !!!         <3 <3 <3 <3

                                         ..... <3 <3 <3 <3 <3 <3 <3 .....

Answer:

[tex] 16C5= \frac{16!}{5! (16-5)!}= \frac{16!}{5! 11!}= \frac{16*15*14*13*12*11!}{5! 11!}[/tex]

If we simplify we got:

[tex] 16C5 = \frac{16*15*14*13*12}{5*4*3*2*1}=4368[/tex]

And the best option would be:

4368

Step-by-step explanation:

For this case we have a total of 16 IT specialists and we want to select 5 IT specialists from the total of 16 so we can use the combination formula given by:

[tex] nC x= \frac{n!}{x! (n-x)!}[/tex]

And replacing we got:

[tex] 16C5= \frac{16!}{5! (16-5)!}= \frac{16!}{5! 11!}= \frac{16*15*14*13*12*11!}{5! 11!}[/tex]

If we simplify we got:

[tex] 16C5 = \frac{16*15*14*13*12}{5*4*3*2*1}=4368[/tex]

And the best option would be:

4368

the problaty of getting Gray tile is 6 time

Answer:

240 table tops or none

Step-by-step explanation:

p(x) = 480x- 2x^2

For profit to be 0, it means;

p(x)= 0

Therefore 480x- 2x^2 = 0

Dividing through by 2 we have ;

240x - x^2 = 0

By factorisation of x we have ;

(240-x) x = 0

x = 0 or 240-x= 0; x= 240( by moving x to the right of the expression:240-x= 0; we have 240=x => x=240).

So the company needs to produce 240 table tops or none in order not to make a profit.

The company need to make a profit of zero dollars will be 240.

A monetary profit, particularly the distinction between the amount gained and the actual cost of purchasing, running or creating anything.

The profit a company makes from producing x tabletops is modeled by the equation is given as,

p(x) = 480x – 2x²

Then the company need to make a profit of zero dollars will be

p(x) = 0

480x – 2x² = 0

2x(240 – x) = 0

                x = 0, 240

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Answer:

a.    [tex]\hat{amount} \ \hat{ spent} = -91.67 - (229.47* ownhome)-(604.90 * close) +(0.02216 * salary) + (42.62 * catalogs)[/tex]

b.    the expected amount spent by Amy is $1144.47

c.    the expected amount that Brenda is going to spend is $1749.37

Step-by-step explanation:

(a)

From the regression output; the equation for the regression model can be written as:

[tex]\hat{amount} \ \hat{ spent} = -91.67 - (229.47* ownhome)-(604.90 * close) +(0.02216 * salary) + (42.62 * catalogs)[/tex]

From the information given in the question;

(b)

Amy does not own a home but rent; the variables given also stated that ;

Own Home = 1 if customer owns home, 0 if renting

So for Amy ; Own Home = 0 (since it is rented)

Close = Yes(1)

Salary = $60,000

Catalogs = 12

Therefore;

the mean amount spent by Amy is by using the regression model is  ;

[tex]\hat{amount} \ \hat{ spent} = -91.67 - (229.47* 0)-(604.90 * 1) +(0.02216 * 60000) + (42.62 * 12)[/tex]

[tex]\hat{amount} \ \hat{ spent} = -91.67 -0-604.90 +1329.6 + 511.44[/tex]

[tex]\hat{amount} \ \hat{ spent} =1144.47[/tex]

Thus;  the expected amount spent by Amy is $1144.47

(c)

If Brenda has the same characteristics as Amy but does not live close to store with similar merchandise.

Then the Close for Brenda will be = No (0)

Thus; the amount spent by Brenda will be:

[tex]\hat{amount} \ \hat{ spent} = -91.67 - (229.47* 0)-(604.90 * 0) +(0.02216 * 60000) + (42.62 * 12)[/tex]

[tex]\hat{amount} \ \hat{ spent} = -91.67 -0-0 +1329.6 + 511.44[/tex]

[tex]\hat{amount} \ \hat{ spent} = 1749.37[/tex]

Thus, the expected amount that Brenda is going to spend is $1749.37

Answer:

60.85% probability that the sample mean is between $1.4 million and $1.5 million per year

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

In millions of dollars.

[tex]\mu = 1.47, \sigma = 0.3, n = 30, s = \frac{0.3}{\sqrt{30}} = 0.0548[/tex]

What is the probability that the sample mean is between $1.4 million and $1.5 million per year?

This is the pvalue of Z when X = 1.5 subtracted by the pvalue of Z when X = 1.4. So

X = 1.5

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1.5 - 1.47}{0.0548}[/tex]

[tex]Z = 0.55[/tex]

[tex]Z = 0.55[/tex] has a pvalue of 0.7088

X = 1.4

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1.4 - 1.47}{0.0548}[/tex]

[tex]Z = -1.28[/tex]

[tex]Z = -1.28[/tex] has a pvalue of 0.1003

0.7088 - 0.1003 = 0.6085

60.85% probability that the sample mean is between $1.4 million and $1.5 million per year

Answer:

[tex] z= \frac{1.4-1.47}{\frac{0.3}{\sqrt{30}}}= -1.278[/tex]

[tex] z= \frac{1.5-1.47}{\frac{0.3}{\sqrt{30}}}= 0.548[/tex]

And we can find the probability with this difference:

[tex] P(-1.278<z<0.548) = P(z<0.548) -P(z<-1.278) =0.708-0.101= 0.607[/tex]

So then the probability that the sample mean is between $1.4 million and $1.5 million per year is 0.607

Step-by-step explanation:

For this case we have the following info given:

[tex] \mu = 1.47[/tex] the true mean for the problem

n =30 represent the sample size

[tex] \sigma = 0.3 millions[/tex] represent the population deviation

And we want to find this probability

[tex] P(1.4< \bar X <1.5)[/tex]

And we can use the z score given by:

[tex] z= \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

And if we find the z scores for the limits we got:

[tex] z= \frac{1.4-1.47}{\frac{0.3}{\sqrt{30}}}= -1.278[/tex]

[tex] z= \frac{1.5-1.47}{\frac{0.3}{\sqrt{30}}}= 0.548[/tex]

And we can find the probability with this difference:

[tex] P(-1.278<z<0.548) = P(z<0.548) -P(z<-1.278) =0.708-0.101= 0.607[/tex]

So then the probability that the sample mean is between $1.4 million and $1.5 million per year is 0.607

Answer:

28

Step-by-step explanation:

operating loss is loss when value of operating loss is more than gross profit.

In the given problem

cost: 284

price : 299

profit = 299 - 284 = 15

but given that there is operating expense as well.

operating expenses = 43

as expense is greater than profit there is loss which is called operating loss.

operating loss = operating expense - profit = 43 - 15 = 28

Thus, operating loss is 28.

Answer:

Isolate the variable using inverse operations.

You would divide each side by 52.

Answer:

  1102.8 mm^2

Step-by-step explanation:

We presume your equation is intended to be ...

  y = 112(1.58)^t

Since t is in minutes, fill in the given value and do the arithmetic:

  y = 112(1.58)^5 = 112(9.84658) ≈ 1102.8

The approximate size of the bacteria strain will be 1102.8 mm^2 after 5 minutes.

Answer:

Explanation:

To find the size of bacteria in five minutes, substitute 5 for t in the equation and simplify:

y = 112(1.58)5

  = 112 ∙ 9.85

  = 1,103.2.

Round the answer to the closest integer to get 1,103.

Step-by-step explanation:

Answer:

h(x-11)=-5

Step-by-step explanation:

just put the equetion from the top

h(x-11)=-5