Find the equation of the line through the points (-3,-3) and (2,-1) using point-slope form. Then rewrite the
equation in slope-intercept form.

Answer:

a) [tex]t=\frac{18.4-17.5}{\frac{2.2}{\sqrt{45}}}=2.744[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=45-1=44[/tex]  

The critical value for this case is [tex]t_{\alpha}=1.68[/tex] since the calculated value is higher than the critical we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 18.4

b) [tex]p_v =P(t_{(44)}>2.744)=0.0044[/tex]  

Step-by-step explanation:

Information given

[tex]\bar X=18.4[/tex] represent the sample mean

[tex]s=2.2[/tex] represent the sample standard deviation

[tex]n=45[/tex] sample size  

[tex]\mu_o =17.5[/tex] represent the value to verify

[tex]\alpha=0.05[/tex] represent the significance level

t would represent the statistic

[tex]p_v[/tex] represent the p value

Part a

We want to test if the true mean is higher than 17.5, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 17.5[/tex]  

Alternative hypothesis:[tex]\mu > 17.5[/tex]  

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

And replacing we got:

[tex]t=\frac{18.4-17.5}{\frac{2.2}{\sqrt{45}}}=2.744[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=45-1=44[/tex]  

The critical value for this case is [tex]t_{\alpha}=1.68[/tex] since the calculated value is higher than the critical we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 18.4

Part b

The p value would be given by:

[tex]p_v =P(t_{(44)}>2.744)=0.0044[/tex]  

Answer:

a) 10.08 gallons and $32.66 of gas

b) gallons used = n/25

c)cost of the gasoline = [tex]\frac{n}{25}(3.24)[/tex]

Step-by-step explanation:

a) We know that Kimberly has traveled 252 miles and we also know that her car gets 25 miles per gallon. We can apply proportions and rule of three:

25 miles ------ 1 gallon

252 miles ----- x gallons

Solving for x:

x gallons = 252 miles(1 gallon)/25 miles= 10.08 gallons.

Thus, she has used 10.08 gallons since she started driving.

Now we need to know the cost of the gasoline that she has used.

We know that each gallon of gas costs $3.24 and she has used 10.08 gallons. Again, we can apply proportions and rule of three:

1 gallon ------ 3.24 dollars

10.08 gallons---- x dollars.

Solving for x we get:

[tex]x=(10.08)(3.24)[/tex]= 32.659=32.66 dollars.

Thus, she has used $32.66 of gas since she started driving.

b) Write an expression in terms of n that represents the number of gallons of gasoline she has used since she started driving.

If we know that n is the number of miles that she drives, from what we wrote above, an expression to know the number of gallons she has used would be:

Gallons used = n/25 (since her car gets 25 miles per gallon) where n is the number of miles.

c) Write an expression in terms of n that represents the cost of the gasoline that she has used since she started driving.

Again, to know the cost of the gasoline we first need to know how many gallons she has used. From b) we know that the expression to know how many gallons she has used is n/25. Since each gallon costs $3.24 we will multiply this number by n/25 and we will get the cost (like we did in a))

Therefore, the cost of the gasoline = [tex]\frac{n}{25}(3.24)[/tex] where n is the number of miles.

Answer:

326

Step-by-step explanation:

l x w

7x8

25x6

4x30

326

Answer:

123.7 meters

Step-by-step explanation:

If you draw a diagram, this will be a rectangle and the line across cuts it into a right triangle, with a base of 120 and a height of 30. The need to know the length of the hypotenuse of the triangle, so we can use the pythagorean theorem.

30^2 + 120^2 = c^2

c=123.7

Answer:

Step-by-step explanation:

Consider the calculations in the table below with the respective columns being: Name | Laps | Time | Time(in hours) |Total Distance | Unit Rate

[tex]\left|\begin{array}{c|c|c|c|c|c}---&---&---&----&----&---\\Amber&3&40&\frac{40}{60}&3*\frac{3}{4}=2.25&2.25 \div \frac{40}{60}= 3\frac{3}{8} \\\\Bruno&4&54&\frac{54}{60}&4*\frac{3}{4}=3&3 \div \frac{54}{60}= 3\frac{1}{3}\\\\Cady&5&75&\frac{75}{60}&5*\frac{3}{4}=3.75&3.75 \div \frac{75}{60}= 3 \\\\Drake&6&72&\frac{72}{60}&6*\frac{3}{4}=4.5&4.5 \div \frac{72}{60}= 3\frac{3}{4} \end{array}\right|[/tex]

We can then match each walker to their respective unit rates in miles per hour.

Answer:

160 off 20p coins

Step-by-step explanation:

20 p coins= 640 - 640*(3/8+3/8)= 640*(1- 6/8)= 640 * 2/8= 640* 1/4= 160

Answer:

a.

Number:      0,    1,       2,     3,      4,       5,    6,    7,     8

Frequency:  6,    12,     13,     15,     5,      3,     3,    1,    1

b. The proportion of the batches that have at most is 0.864

Step-by-step explanation:

a. The given data are;

2 1 2 3 1 1 3 2 0 5 3 3 1 3 2 4 7 0 2 3

0 4 2 1 3 1 1 3 4 1 2 3 2 2 8 4 5 1 3 1

5 0 2 3 2 1 0 6 4 2 1 6 0 3 3 3 6 2 3

The frequencies are;

x     fx  

0     6

1      12

2     13

3      15

4      5

5      3

6      3

7       1

8       1

The relative frequency are;

x     Rfx  

0   0.102

1   0.203

2   0.220

3   0.254

4   0.085

5   0.051

6   0.051

7   0.017

8   0.017

b. The proportion of the batches that have at most 4 is given as follows;

The number of the batches that have at most 4 = 6 + 12 + 13 + 15 + 5 = 51

Therefore, the proportion of the batches that have at most 4 = 51 / 59 = 0.864.

Answer:

A) y = -2/3x + 1

Step-by-step explanation:

Slope - intercept form is y = mx + b, where m is the slope and b is the y - intercept.

The line is falling from left to right, so it has a negative slope.

    y = -mx + b

The line has a slope of -2/3.

    y = -2/3x + b

The line has a y - intercept of 1.

    y = -2/3x + 1

I hope this helps :)

A) y = -2/3x + 1, the equation of the line shown in the graph above in slope-intercept form.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

Slope - intercept form is y = mx + b,

where m is the slope and b is the y - intercept.

The line is falling from left to right, so it has a negative slope.

 y = -mx + b

As, the line passes through (0,1) and (1.5,0)

The line has a slope of -2/3.

 y = -2/3x + b

The line has a y - intercept of 1.

y = -2/3x + 1

hence, A) y = -2/3x + 1, the equation of the line shown in the graph above in slope-intercept form.

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Answer:

(See explanation below for further detail/Véase la explicación abajo para mayores detalles)

Step-by-step explanation:

(This exercise is written in Spanish and explanations will be held in such language)

a) Las temperaturas quedan representadas a continuación:

Quito - Temporada Fría

Intervalo

[tex]5 ^{\circ}C \leq t \leq 18^{\circ}C[/tex] (Este intervalo indica si el dato puede pertenecer a la temporada fría)

Conjunto

[tex]C = \{\forall t \in \mathbb {R}| 5 \leq t \leq 18\}[/tex] (Este conjunto acumula todo el registro de las temperaturas de la temporada fría)

Quito - Temporada Cálida

Intervalo

[tex]4 ^{\circ}C \leq t \leq 30^{\circ}C[/tex] (Este intervalo indica si el dato puede pertenecer a la temporada cálida)

Conjunto

[tex]H = \{\forall t \in \mathbb {R}| 4 \leq t \leq 30\}[/tex] (Este conjunto acumula todo el registro de las temperaturas de la temporada cálida)

b) La temperatura de la ciudad de Quito pertenece esencialmente a dos intervalos:

Intervalo de Temporada Fría:

[tex]5 ^{\circ}C \leq t \leq 18^{\circ}C[/tex]

Intervalo de Temporada Cálida:

[tex]4 ^{\circ}C \leq t \leq 30^{\circ}C[/tex]

c) Toda temperatura mayor o igual que 4 °C y menor o igual que 30 °C.

d) Temperaturas mayores o iguales a 5 °C y menores o iguales a 18 °C.

e) Temperaturas mayores o iguales a 4 °C y menores o iguales a 30 °C.

Answer:

1st : 8

2nd: 8

3rd: equal to

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

The remainder of the polynomial when divided by x + 2 is -60.

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

2[tex]x^{4}[/tex] - 4x³ - 11x² + 3x - 6 divide by x + 2.

Now,

x + 3 ) 2[tex]x^{4}[/tex] - 4x³ - 11x² + 3x - 6 ( 2x³ - 2x² - 5x + 18

          2[tex]x^{4}[/tex] + 6x³

      (-)       (-)                            

                  -2x³ - 11x² + 3x - 6

                  -2x³ - 6x²

              (+)        (+)                  

                           - 5x² + 3x - 6

                          -5x²  - 15x      

                        (+)        (+)

                                      18x - 6                      

                                      18x + 54

                                    (-)      (-)    

                                               -60

We see that,

The remainder is -60.

f(-2) = 2[tex]x^{4}[/tex] - 4x³ - 11x² + 3x - 6

f(-2) = 2 x 16 + 32 - 44 - 6 - 6 = 32 + 32 - 44 - 12 = 64 - 56 = 8

Thus,

The remainder of the polynomial when divided by x + 2 is -60.

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Answer:

Step-by-step explanation:

Let x be a random variable representing the number of guesses made for the sat questions.

Since the probability of getting the correct answer to a question is fixed for any number of trials and the outcome is either getting it correctly or not, then it is a binomial distribution. The probability of success, p = 0.2

Probability of failure, q = 1 - p = 1 - 0.2 = 0.8

the probability that the number x of correct answers is fewer than 4 is expressed as

P(x < 4)

From the binomial distribution calculator,

P(x < 4) = 0.97

Answer: Y is less than or equal to 65 and X + y= less than or equal to 95

Answer:

For this problem we can use the following proportional rule:

[tex] \frac{73 mi}{25 gal}= \frac{x}{75 gal}[/tex]

Where x represent the number of miles that we can travel with 75 gallons. For this case we can use this proportional rule since by definition [tex] D=vt[/tex]. If we solve for x we got:

[tex] x =75 gal (\frac{73 mi}{25 gal}) =219mi[/tex]

And the best answer would be:

219 mi

Step-by-step explanation:

For this problem we can use the following proportional rule:

[tex] \frac{73 mi}{25 gal}= \frac{x}{75 gal}[/tex]

Where x represent the number of miles that we can travel with 75 gallons. For this case we can use this proportional rule since by definition [tex] D=vt[/tex]. If we solve for x we got:

[tex] x =75 gal (\frac{73 mi}{25 gal}) =219mi[/tex]

And the best answer would be:

219 mi

Answer:

12 45

Step-by-step explanation:

plane leaves London at 09 35

plane arrives in Los Angeles after 11 hrs and 10 min

considering time difference:

local arrival time:

Answer:

Step-by-step explanation:

The question tells us that;

Given F1 = ∑ m(0,2,5,7,9) and F1 = ∑ m(2, 3,4,7,8) find the minterm expression for F1+F2. State a general rule for finding the expression for F1+F2 given the minterm expansions for F1 and F2. Prove your answer by using the general form of the minterm expansion.

Note: The answer is provided in the image uploaded below

cheers i hope this helped !!!

Answer:

Distance between 2 boats= 5.86m (3 s.f.)

Actual distance from farther boat from top of cliff= 16m

Step-by-step explanation:

Please see the attached pictures for full solution.

Answer:

1/2(n+7)

the sum of n and 7 is (n+7). to half it just put 1/2 in front of the parentheses. :)

Answer:

We use the binomial distribution to describe this situation.

The mean number of phone sales is 749.7 with a standard deviation of 15.

Step-by-step explanation:

For each shopper, there are only two possible outcomes. Either they plan to purchase the newly released smart phone, or they do not. Each customer is independent of other customers. So we use the binomial distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Fifty random shoppers at an electronics store have been interviewed and 35 of them intend to purchase a newly released smart phone.

This means that [tex]p = \frac{35}{50} = 0.7[/tex]

What are its mean and standard deviation of phone sales if we are concerned about 1071 shoppers that day

1071 shoppers, so [tex]n = 1071[/tex]

Mean

[tex]E(X) = 1071*0.7 = 749.7[/tex]

Standard deviation

[tex]\sqrt{V(X)} = \sqrt{1071*0.7*0.3} = 15[/tex]

The mean number of phone sales is 749.7 with a standard deviation of 15.

Answer:

There are 55 sweets in total.

Step-by-step explanation:

The total number of sweets is t.

Henry, Brian and Colin share some sweets in the ratio 6:4:1.

This means that Henry earns [tex]\frac{6}{6+4+1} = \frac{6}{11}[/tex] of the total(t).

Brian earns [tex]\frac{4}{11}[/tex] of the total.

Colin earns [tex]\frac{1}{11}[/tex] of the total

Henry gets 25 more sweets than Colin.

Henry earns [tex]\frac{6t}{11}[/tex]

Colin earns [tex]\frac{t}{11}[/tex]

So

[tex]\frac{6t}{11} = \frac{t}{11} + 25[/tex]

Multiplying everything by 1

[tex]6t = t + 275[/tex]

[tex]5t = 275[/tex]

[tex]t = \frac{275}{5}[/tex]

[tex]t = 55[/tex]

There are 55 sweets in total.

Answer:

12.08

Step-by-step explanation:

For each sunflower, there are only two possible outcomes. Either it germinates, or it does not. The probability of a sunflower germinating is independent of other sunflowers. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Seventy-six percent of sunflower seeds will germinate into a flower

This means that [tex]p = 0.76[/tex]

Samples of 800:

This means that [tex]n = 800[/tex]

The standard deviation for the number of sunflower seeds that will germinate in such samples of size 800 is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{800*0.76*0.24} = 12.08[/tex]

Answer: 400

Step-by-step explanation:

25% is equal to one quarter (1/4). If theres 100 red gumballs then there must be 300 more gumballs in the machine because a quarter of a number is always even.

The right answer is 100 units^2

please see the attached picture for full solution

Hope it helps

Good luck on your assignment,

Answer:

P = 0.5207

Step-by-step explanation:

First, we have three options: Just the first card is a diamond or an ace, Just the second card is a diamond or an ace and both cards are diamonds or aces.

Additionally, there are 16 cards that are diamond or aces in a standard deck of 52 cards (13 diamonds and 3 aces that are not diamonds). It means that there are 36 cards that are not diamond or aces (52 - 16 = 36).

So, the probability that just the first card is a diamond or an ace is calculated as:

[tex]P_1=\frac{16}{52}*\frac{36}{52}=0.2130[/tex]

At the same way, the probability that just the second card is a diamond or an ace is:

[tex]P_2=\frac{36}{52}*\frac{16}{52}=0.2130[/tex]

Finally, the probability that both cards are diamonds or aces is:

[tex]P_3=\frac{16}{52}*\frac{16}{52}=0.0947[/tex]

Therefore, the probability that at least one of the cards is a diamond or an ace is:

[tex]P=P_1+P_2+P_3\\P=0.2130+0.2130+0.0947\\P=0.5207[/tex]

Answer:

  5 and 13

Step-by-step explanation:

Let x represent the smaller number. Then the larger number is 2x+3, and the difference is ...

  (2x+3) -(x) = 8

  x = 5

The two numbers are 5 and 13.

_____

Check

Twice the smaller number is 10. 3 more than that is 13, the larger number. Their difference is 13 -5 = 8.

Answer:

[tex]t \approx 17.690\,min[/tex]

Step-by-step explanation:

This differential equation is a first order linear differential equation with separable variables, whose solution is found as follows:

[tex]\frac{dy}{dt} = - \frac{1}{53} \cdot (y - 17)[/tex]

[tex]\frac{dy}{y-17} = -\frac{1}{53} \, dt[/tex]

[tex]\int\limits^{y}_{y_{o}} {\frac{dy}{y-17} } = -\frac{1}{53} \int\limits^{t}_{0}\, dx[/tex]

[tex]\ln \left |\frac{y-17}{y_{o}-17} \right | = -\frac{1}{53} \cdot t[/tex]

[tex]\frac{y-17}{y_{o}-17} = e^{-\frac{1}{53}\cdot t }[/tex]

[tex]y = 17 + (y_{o} - 17) \cdot e^{-\frac{1}{53}\cdot t }[/tex]

The solution of the differential equation is:

[tex]y = 17 + 74\cdot e^{-\frac{1}{53}\cdot t }[/tex]

Where:

[tex]y[/tex] - Temperature, measured in °C.

[tex]t[/tex] - Time, measured in minutes.

The time when the cup of coffee has the temperature of 70 °C is:

[tex]70 = 17 + 74 \cdot e^{-\frac{1}{53}\cdot t }[/tex]

[tex]53 = 74 \cdot e^{-\frac{1}{53}\cdot t }[/tex]

[tex]\frac{53}{74} = e^{-\frac{1}{53}\cdot t }[/tex]

[tex]\ln \frac{53}{74} = -\frac{1}{53}\cdot t[/tex]

[tex]t = - 53\cdot \ln \frac{53}{74}[/tex]

[tex]t \approx 17.690\,min[/tex]

Answer:

2,808

Step-by-step explanation:

since 117 = d then we would just plug that into the equation of s = 24d and get s = 24(117), after that you would just solve.

Answer:

53

Step-by-step explanation:

The image of the ramp with dimensions is missing, so i have attached it.

Answer:

680 in² of wood is needed.

Step-by-step explanation:

The way to find how much wood would be needed by devon would be to find the total surface area of the ramp.

From the attached image,

Let's find the area of the 2 triangles first;

A1 = 2(½bh) = bh = 15 x 8 = 120 in²

Area of the slant rectangular portion;

A2 = 17 x 14 = 238 in²

Area of the base;

A3 = 15 × 14 = 210 in²

Area of vertical rectangle;

A4 = 8 × 14 = 112 in²

Total Surface Area = A1 + A2 + A3 + A4 = 120 + 238 + 210 + 112 = 680 in²

Answer:

44°

Step-by-step explanation:

A pair of angles formed from the intersection of two lines opposite to each other at the point of intersection (vertex) is called vertically opposite angles. These vertically opposite angles are congruent to each other (that means they are equal).

Since opposite angles are equal, the equation needed to calculate w is given as:

80° = 36° + w

w = 80° - 36°

w = 44°

Answer:

  too much caramel

Step-by-step explanation:

3 ounces : 5 scoops = 3·2 ounces : 5·2 scoops = 6 ounces : 10 scoops

If the Freeze Zone shakes have 6 ounces : 8 scoops, then Ari will think they need more ice cream (2 scoops per shake) or less caramel.

As is, the ratio of caramel to ice cream is too high.

Answer:

Step-by-step explanation:

We can write some equations to describe the given relationships:

  A = B - 2 . . . . . A is 2 kg lighter than B

  A = C/5 . . . . . . A is 1/5 the weight of C

  A+C = 3B . . . . together, A and C are 3 times the weight of B

__

Let's solve for A.

  B = A+2 . . . from the first equation

  C = 5A . . . . from the second equation

  A +5A = 3(A+2) . . . . substituting for B and C in the third equation

  6A = 3A +6

  3A = 6

  A = 2

__

  B = A+2 = 4

  C = 5A = 10

Watermelon A weighs 2 kg; B weighs 4 kg; and C weighs 10 kg.

Answer:

2 kg 4 kg 10 kg

I BLESS THE EYES!