Jose has $25 to spend on gas. Gas cost $1.25 per gallon. This situation is modeled by the function, M(g) = 25 -1.25g, where Mg) represents the amount of money Jose has remaining as a function of the number of gallons of gas, g he pumped. Which inequality represents the situational domain and range?

Answer:

the answer is 3

Step-by-step explanation:

21 x 3 =7

hope it helps

Answer:

21/7

Step-by-step explanation:

Move 7 to next side with opposite process it is multiple after move it will be divided so 21x (21/7) it will be 7 although (21/7)equivalent to 1/3

The definite integral for this problem has the result given as follows:

\(\int_1^5 x^2 + 2x - \tan{x} dx = 212 - \ln{|\sec{5}|} + \ln{|\sec{1}|}\)

The definite integral for this problem is defined as follows:

\(\int_1^5 x^2 + 2x - \tan{x} dx\)

We have an integral of the sum, hence we can integrate each term, and then add them.

For the first two terms, applying the power rule, the integrals are given as follows:

The integral of the tangent is given as follows:

ln|sec(x)|

Then the integral is given as follows:

I = x³/3 + x² - ln|sec(x)|, from x = 1 to x = 5.

Applying the Fundamental Theorem of Calculus, the result of the integral is obtained as follows:

I = 5³/3 + 5² - ln|sec(5)| - (1³/3 + 1² - ln|sec(1)|)

I = 625/3 - 1/3 + 5 - 1 - ln|sec(5)| + ln|sec(1)|

I = 208 + 5 - 1 - ln|sec(5)| + ln|sec(1)|

I = 212 - ln|sec(5)| + ln|sec(1)|.

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Answer:

A)H0: μ1 − μ2 = 0

Ha: μ1 − μ2 ≠ 0

(b)  Means

Company A___50.6___ min.

Company B___52.75___ min.

c)The t-value is -0.30107.

The p-value is 0 .764815.

C) Do not reject H0. There is no statistical evidence that one airline does better than the other in terms of their population mean delay time.

Step-by-step explanation:

A)H0: μ1 − μ2 = 0

i.e there is no difference between the means of delayed flight for two different airlines

Ha: μ1 − μ2 ≠ 0

i.e there is a difference between the means of delayed flight for two different airlines

(b)

Company A___50.6___ min.

Company B___52.75___ min.

Mean of Company A = x`1= ∑x/n =34+ 59+ 43+ 30+ 3+ 32+ 42+ 85+ 30+ 48+ 110+ 50+ 10+ 26+ 70+ 52+ 83+ 78+ 27+ 70+ 27+ 90+ 38+ 52+ 76/25

= 1265/25= 50.6

Mean of Company B = x`2= ∑x/n =

=46+ 63+ 43+ 33+ 65+ 104+ 45+ 27+ 39+ 84+ 75+ 44+ 34+ 51+ 63+ 42+ 34+ 34+ 65+ 64/20

= 1055/20= 52.75

Difference Scores Calculations

Company A

Sample size for Company A= n1= 25

Degrees of freedom for company A= df1 = n1 - 1 = 25 - 1 = 24

Mean for Company A= x`1=  50.6

Total Squared Difference (x-x`1) for Company A= SS1: 16938

s21 = SS1/(n1 - 1) = 16938/(25-1) = 705.75

Company B

Sample size for Company B= n1= 20

Degrees of freedom for company B= df2 = n2 - 1 = 20 - 1 = 19

Mean for Company B= x`2=  52.75

Total Squared Difference (x-x`2) for Company B= SS2=7427.75

s22 = SS2/(n2 - 1) = 7427.75/(20-1) = 390.93

T-value Calculation

Pooled Variance= Sp²

Sp² = ((df1/(df1 + df2)) * s21) + ((df2/(df2 + df2)) * s22)

Sp²= ((24/43) * 705.75) + ((19/43) * 390.93) = 566.65

s2x`1 = s2p/n1 = 566.65/25 = 22.67

s2x`2 = s2p/n2 = 566.65/20 = 28.33

t = (x`1 - x`2)/√(s2x`1 + s2x`2) = -2.15/√51 = -0.3

The t-value is -0.30107.

The total degrees of freedom is = n1+n2- 2= 25+20-2=43

The critical region for two tailed test at significance level ∝ =0.05 is

t(0.025) (43) = t > ±2.017

Since the calculated value of t=  -0.30107.  does not fall in the critical region t > ±2.017, null hypothesis is not rejected that is there is no difference between the means of delayed flight for two different airlines.

The p-value is 0 .764815. The result is not significant at p < 0.05.

In this exercise, it is necessary to use the knowledge given by the airlines and the flights, having as a solution:

a)\(H_0: \mu_1 -\mu_2 = 0\\H_a:\mu_1 -\mu_2\neq 0\)

b)  Means: Company A 50.6 min.

Company B 52.75 min.

c)The t-value is -0.30107.

The p-value is 0 .764815.

C) Do not reject H0. There is no statistical evidence that one airline does better than the other in terms of their population mean delay time.

A)\(H_0: \mu_1 -\mu_2 = 0\)

There is no difference between the means of delayed flight for two different airlines:

\(H_a:\mu_1 -\mu_2\neq 0\)

There is a difference between the means of delayed flight for two different airlines.

(b) Mean of Company A\(= x_1= \sum{x/n} = 1265/25= 50.6\)

Mean of Company B \(= x_2= \sum{x/n} =1055/20= 52.75\)

C) Difference Scores Calculations:

Company A:

Sample size for Company \(A= n1= 25\)

Degrees of freedom for company \(A= df1 = n1 - 1 = 25 - 1 = 24\)

Mean for Company \(A= x_1= 50.6\)

Total Squared Difference for Company \(A= SS1: 16938\\s21 = SS1/(n1 - 1) = 16938/(25-1) = 705.75\)

Company B:

Sample size for Company \(B= n1= 20\)

Degrees of freedom for company \(B= df2 = n2 - 1 = 20 - 1 = 19\)

Mean for Company\(B= x_2= 52.75\)

Total Squared Difference for Company \(B= SS2=7427.75\\s22 = SS2/(n2 - 1) = 7427.75/(20-1) = 390.93\)

T-value Calculation

Pooled Variance= Sp²

\(Sp^2= ((df1/(df1 + df2)) * s21) + ((df2/(df2 + df2)) * s22)\\Sp^2= ((24/43) * 705.75) + ((19/43) * 390.93) = 566.65\\s2x_1 = s2p/n1 = 566.65/25 = 22.67\\s2x_2 = s2p/n2 = 566.65/20 = 28.33\\t = (x_1 - x_2)/\sqrt{s2x_1 + s2x_2} = -2.15/\sqrt{51} = -0.3\)

The t-value is -0.30107.

The total degrees of freedom is \(= n1+n2- 2= 25+20-2=43\)

The critical region for two tailed test at significance level ∝ =0.05 is \(t(0.025) (43) = t > 2.017\)

Since the calculated value of t=  -0.30107.  does not fall in the critical region t > ±2.017, null hypothesis is not rejected that is there is no difference between the means of delayed flight for two different airlines.

The p-value is 0 .764815. The result is not significant at p < 0.05.

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The functions that have a range of all real numbers include the following:

Option 1; f(x) = -x + 2

Option 3; \(h(x) = 2^x +1\)

In Mathematics and Geometry, a range can be defined as the set of all real numbers that connects with the elements of a domain.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following range for f(x) and h(x):

Range = {-∞, ∞}, y|y ∈ R, or all real numbers.

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x^2 - 2x + 1 is the required quadratic equation using the completing the square

Given the quadratic expression below

x^2 - 2x

We need to determine the constant that will make the expression a perfect square.

The constant will be the half of the square of coefficient of 'x'

Coefficient of 'x' = -2

Half of the coefficient of 'x' = -2/2 = -1

Square of the coefficient = (-2/2)^2

Square of the coefficient = 1

Hence the complete quadratic expression using the completing the square is x^2 - 2x + 1

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Answer:

because you have to distrubute the 2 to the letters inside the () or else youll get a diff answer thats wrong

Step-by-step explanation:

Answer:

I have solved it and attached in the explanation.

Step-by-step explanation:

The probability of randomly selecting a score greater than X = 65 is approximately 0.4013 or 40.13%.

What is a normal distribution?

Normal distribution, also known as Gaussian distribution or bell curve, is a probability distribution that describes the random variation of a continuous variable in a population. The distribution is symmetrical and bell-shaped, with the majority of the values clustered around the mean or average value, and the frequency decreasing as the distance from the mean increases.

To solve this problem, we need to standardize the X value using the formula:

z = (X - μ) / σ

where X is the raw score we want to convert to a z-score, μ is the population mean, and σ is the population standard deviation.

Substituting the given values, we get:

z = (65 - 61) / 16 = 0.25

Now, we can use a standard normal distribution table (or a calculator) to find the probability of selecting a score greater than z = 0.25. The area to the right of z = 0.25 represents the probability of selecting a score greater than X = 65.

Using a standard normal distribution table, we find that the probability of selecting a score greater than z = 0.25 is approximately 0.4013. Therefore, the probability of randomly selecting a score greater than X = 65 is approximately 0.4013 or 40.13%.

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The constants A and B for the differential equation are given as follows:

The solutions to the differential equation are given as follows:

This means that the roots of the characteristic equation are given as follows:

r = -8 and r = 8.

Considering that the leading coefficient is of 1, as 1 multiplies y'', the characteristic equation is given as follows:

(r + 8)(r - 8) = r² - 64.

Hence the differential equation is given as follows:

y'' - 64y = 0.

Hence the constants are given as follows:

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Answer:

D

Step-by-step explanation:

\(m\angle BCA+m\angle ACD=180^{\circ} \\ \\ 2x-5+3x+10=180 \\ \\ 5x+5=180 \\ \\ 5x=175 \\ \\ x=35 \\ \\ \\ m\angle ACD=3(35)+10=115^{\circ}\)

The transfοrmatiοn f(x)↦f(-x) , the graph οf f(x) reflects it acrοss the y-axis

Optiοn B

In mathematics, a functiοn is a rule that maps each element in οne set, called the dοmain, tο exactly οne element in anοther set, called the range. A functiοn can alsο be thοught οf as a set οf οrdered pairs, where the first element in each pair belοngs tο the dοmain, and the secοnd element belοngs tο the range.

Functiοns are cοmmοnly denοted by symbοls such as f(x), g(x), οr h(x), where x represents the input variable οr independent variable, and the functiοn prοduces an οutput value οr dependent variable, which is denοted by f(x), g(x), οr h(x), respectively.

Functiοns are impοrtant in many areas οf mathematics, science, and engineering, as they prοvide a way tο describe relatiοnships between variables and make predictiοns abοut the behaviοr οf systems. They are used tο mοdel physical phenοmena, analyze data, and sοlve equatiοns, amοng οther applicatiοns.

Given :

The transfοrmatiοn f(x) -> f(-x)

Fοr example , lets take a pοint οn f(x)

Let (x,y) be a pοint οn f(x)

given f(x)- > f(-x) it means x is replaced by -x

f(x) is nοt multiplied with -1  sο y value remains the same

(x,y) be a pοint οn f(x) .

After transfοrmatiοn f(x)-> f(-x) , the pοint (x,y) ---> (-x,y)

When x is multiplied by -1 then there is a reflectiοn acrοss the y axis

Sο, the graph οf f(x) reflects it acrοss the y axis.

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Complete Question:

What does the transformation f(x)↦f(-x) do to the graph of f(x)?

a) stretches it horizontally

b) reflects it across the y-axis

c) shrinks it horizontally

d) reflects it across the x-axis

e) Submit

The sum of the elements of S is 360

Let S be the set of real numbers that can be represented as repeating decimals

The form of the repeating decimal is 0.abc cap

Where a, b and c are distinct digits

If x = 0.abcabc

1000x = abc.abc

1000x - x = abc

999x = abc

x = abc/999

a, b, c are distinct digits

Number of combinations possible = 10 × 9 × 8

= 720 combinations

Therefore each value appear is each place value = 720/10

= 72

Sum of the digits from 0 to 9 = 45

Sum of the elements of S = (45 × 72 × 111 / 999)

= 360

Therefore, the sum of the element is 360

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Answer:

50.75

Step-by-step explanation:

We have:

\(E[g(x)] = \int\limits^{\infty}_{-\infty} {g(x)f(x)} \, dx \\\\= \int\limits^{1}_{-\infty} {g(x)(0)} \, dx+\int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx+\int\limits^{\infty}_{6} {g(x)(0)} \, dx\\\\= \int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x+3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x)\frac{2}{x} } \, dx + \int\limits^{6}_{1} {(3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {8} \, dx + \int\limits^{6}_{1} {\frac{6}{x} } \, dx\\\\\)

\(=8\int\limits^{6}_{1} \, dx + 6\int\limits^{6}_{1} {\frac{1}{x} } \, dx\\\\= 8[x]^{^6}_{_1} + 6 [ln(x)]^{^6}_{_1}\\\\= 8[6-1] + 6[ln(6) - ln(1)]\\\\= 8(5) + 6(ln(6))\\\\= 40 + 10.75\\\\= 50.74\)

The two relations to change the units of temperatueres are:

a) C = (5/9)*(F - 32°)

b) F = (9/5)*C + 32°

We start knowing that:

32°F = 0°C

212°F = 100°C

Taking the difference we can get the relation:

212°F - 32°F = 100°C - 0°C

180°F = 100°C

1.8°F = 1°C

(9/5)*F = 1°C

Then the relation to go from Farhenheit to Celcius is:

C = (5/9)*(F - 32°)

b) To get the other relation, we just need isolate F in the above one, so we get:

C = (5/9)*(F - 32°)

(9/5)*C = F - 32°

(9/5)*C + 32° = F

Then the other relation is:

F = (9/5)*C + 32°

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Answer:5

Step-by-step explanation:

5098

Answer:

C. I,II,III

Step-by-step explanation:

Absolute value is the distance of a number from 0 on a number line. 6 is 6 units from 0, therefore this option is correct. -6 is 5 units to the left of 0, but it is still 6 units away, therefore this option is correct. 6 is 6 units away from 0, therefore, III is correct. But 0 is 0 units away from 0, therefore this option is incorrect.

Answer:

Step-by-step explanation:

1. is 0.125x – 3.375

2.  0.6x – 5

3. 0.89x-5

Just use a slope calculator and desmos to see if your answer is right. Also a rounding calculator if the answer for one is too long, example: the third one said 0.88888888888889 for the first number so i rounded that to 0.89 to make sure it doesnt look like a computer did it

Step-by-step explanation:

when it is phrased like that it should mean that we apply the scale factor to the original images to create the new ones.

and that means the new images will in our case be bigger by the factor of 2.

therefore, the 4th answer option is correct.

2 cm turn into 2×2 = 4 cm

1.5 cm turn into 2×1.5 = 3 cm

3 cm turn into 2×3 = 6 cm

Answer:

20991

Step-by-step explanation:

Answer:

All of the above they are multiples

Step-by-step explanation:

(i) False. If two lines are parallel, then they never intersect.

(ii) True. We can draw infinitely many different lines through a single point. We can think of rotating a line around a single point to form a circular fan of lines.

(iii) True. Any line is defined uniquely by two distinct points.

Greetings from Brasil...

F(V) = - 11V² - 8

F(a + h) - F(a)]/h

let's do it by steps

F(a + h) = - 11 · (a + h)² - 8

F(a + h) = - 11 · (a² + 2ah + h²) - 8

F(a + h) = - 11a² - 22ah - 11h² - 8

and

F(a) = - 11 · (a)² - 8

F(a) = - 11a² - 8

Then

F(a + h) - F(a)]/h

{- 11a² - 22ah - 11h² - 8 - [- 11a² - 8]}/h

[- 11a² - 22ah - 11h² - 8 + 11a² + 8]/h

[- 22ah - 11h²]/h

h · [- 22a - 11h]/h

Answer:

to solve the equation you first need to bring it to factors and by doing that you first need to let the equation equal 0 hence you need to minus 2 on both sides of the equation therefore

x^2 + 10x + 25 - 2 =2 - 2

therefore

x^2 + 10x +23 = 0

now since the equation cannot be factored, we use the formula.

x= \(\frac{-b +- \sqrt{b^{2}-4ac } }{2a}\)

where

a=1

b=10

c=23

note we use the coefficients only.

therefore x = \(\frac{-10 -+ \sqrt{10^{2}-4(1)(23) } }{2(1)}\)

=\(\frac{-10-+\sqrt{100-92} }{2}\)

=\(\frac{-10-+\sqrt{8} }{2}\)

then we form two equations according to negative and positive symbols

x=\(\frac{-10+\sqrt{8} }{2} or x =\frac{-10-\sqrt{8} }{2}\)

therefore x = \(-5+\sqrt{2}\)   or x=\(-5-\sqrt{2}\)

The utility can be used to quantify and compare preferences in decision-making scenarios where performance is not measured by monetary value.

The utility can be used as a measure of preference or satisfaction in decision-making situations where performance is not directly measured by monetary value. Utility refers to the subjective value or desirability that an individual assigns to different outcomes or options.

In such cases, utility can be quantified using a utility function, which maps the outcomes or attributes of the decision problem to a numerical representation of the individual's preferences. This function allows for the comparison and evaluation of different options based on their utility values.

For example, consider a decision involving healthcare treatments. The performance of different treatments may not be easily measured in monetary terms, but individuals may have preferences based on factors such as effectiveness, side effects, or quality of life impact.

Utility can be used to capture these preferences and make a decision that maximizes the overall satisfaction or well-being of the individual.

To use utility in decision-making, it is necessary to understand and quantify individual preferences through techniques like surveys, interviews, or experimental methods. By assigning utility values to different outcomes or attributes, decision-makers can then compare options and select the one that maximizes utility.

However, it's important to note that utility is subjective and varies among individuals. Different people may have different utility functions and weigh attributes differently. Therefore, utility-based decision-making requires taking into account the preferences of the specific individual or group involved.

In summary, utility can be employed in decision-making scenarios where performance is not directly measured in monetary terms. It quantifies subjective preferences and allows for the comparison and selection of options based on the utility values assigned to different outcomes or attributes.

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Answer:

To find the effective annual rate (EAR) of an account that pays interest at the nominal rate of 7% per year, compounded daily, we can use the following formula:

EAR = (1 + r/n)^n - 1

where r is the nominal annual interest rate (expressed as a decimal), and n is the number of times the interest is compounded in a year.

For daily compounding, n = 365 (since there are 365 days in a year), so we have:

EAR = (1 + 0.07/365)^365 - 1 = 0.0725 or 7.25%

To find the effective annual rate for hourly compounding, we need to adjust the value of n to account for the fact that interest is compounded more frequently. There are 365 days * 24 hours = 8,760 hours in a year, so we can use n = 8,760:

EAR = (1 + 0.07/8760)^8760 - 1 ≈ 0.0727 or 7.27%

Therefore, the effective annual rate for hourly compounding is approximately 7.27%.

Answer:

1) the most direct way is to use the normal volume formula for cubes/rectangular prisms

2)60 inches cubed

Step-by-step explanation:

Volume=length x width x height

V=4x5x3

V=20x3

V=60

therefore the volume is 60 inches ^3

5 because the value of pi is 3.14 and therfore the graph must be a rational and a multiple of 3