On the standard coordinate grid at initial moment, ship Tiger is at the position (0, 795), ship Lion is at the position (985, 0). Tiger sails along the straight line to the position (1229, 0). At the same time, Lion sails along the straight line to the position (0, 1039). Lion will reach her destination in one hour, Tiger – in two hours.
a) Find the point of intersection of the paths of the ships.
b) At what time from the moment of departure each of the ships will pass the point of intersection of the paths.
c) At what time (in minutes after departure) the distance between Lion and Tiger will be the shortest?
d) What is the shortest distance between Lion and Tiger?
e) What will be the positions of both ships at the moment when the distance between them is the shortest?

Answer:

2/3 of a pound.

Step-by-step explanation:

10 pounds per 15 bowls = 2 pounds per 3 bowls, this is equal to 2/3 of ice cream a pound in a single bowl.

Answer: The one-day SAT prep class is associated with statistically significant improvements in SAT writing performance.

Step-by-step explanation: just took the quiz

The correct conclusion about the situation is, the one-day SAT prep class produces statistically significant improvements in SAT writing performance, which is option (e).

Given that:

It is assessing the performance of the students in the SAT writing exam before and after SAT prep class.

The hypothesis is:

H₀: μ = 0

H₁: μ > 0

This is a one-tailed test.

Here, the T-test is used.

Now, the significance level is, α = 0.05

p-value = 0.028

Since, the p-value, 0.028 is less than the significance level 0.05, the null hypothesis is rejected.

So, the mean of the difference in SAT scores is greater than 0.

That is, there is a significant effect in SAT exam by the prep class.

Hence, the correct conclusion is, The one-day SAT prep class produces statistically significant improvements in SAT writing performance, which is option (e).

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Answer:

f( - 2) =12

Step-by-step explanation:

[tex]f(x) = x^2-3x+2 \\ plugging \: x = - 2 \\ f( - 2) = ( - 2)^2-3( - 2)+2 \\ f( - 2) =4 + 6+2 \\ f( - 2) =12 \\ [/tex]

Answer:

a) P(x=108)=0.0020

b) P(x≥108)=0.9980

c) P(x<124)=0.7794

d) P(124≤x≤128)=0.1925

Step-by-step explanation:

We know the population proportion, that is p=0.84.

We take a sample of size n=143.

We will use the normal approximation to the binomial distribution to model this problem.

The mean and standard deviation of the normal approximation to the binomial distribution will be:

[tex]\mu=np=143*0.84=120.12\\\\\sigma=\sqrt{np(1-p)}=\sqrt{143*0.84*0.16}=\sqrt{19.22}=4.38[/tex]

a) We have to calculate the probability that exactly 108 flights are on time.

As the normal distribution considers the random variable to be continous, we have to apply the continuity correction factor.

In this case, the probability of 108 flights on time can be calculated as P(107.5<x<108.5):

[tex]P(x=108)=P(107.5<x<108.5)=P(x<108.5)-P(x<107.5)\\\\\\ z_1=(x_1-\mu)/\sigma=(107.5-120.12)/4.38=-12.62/4.38=-2.88\\\\z_2=(x_2-\mu)/\sigma=(108.5-120.12)/4.38=-11.62/4.38=-2.65\\\\\\P(x<108.5)-P(x<107.5)=P(z<-2.65)-P(z<-2.88)\\\\P(x<108.5)-P(x<107.5)=0.0040-0.0020=0.0020[/tex]

b) Now we have to calculate that at least 108 flights are on time.

As the probability includes 108, the continuity factor will indicates that we calculate P(x>107.5). The z-value for x=107.5 has been already calculated in point a:

[tex]P(x\geq108)=P(x>107.5)=P(z>-2.88)=0.9980[/tex]

c) We have to calculate the probability that fewer than 124 flights are on time. According to the continuity factor, we have to calculate the probability P(x<123.5), as the flight number 124 is not included in the interval.

[tex]P(x<124)=P(x<123.5)=P(z<0.77)=0.7794\\\\\\z=(x-\mu)/\sigma=(123.5-120.12)/4.38=0.77[/tex]

d) We have to calculate the probability that between 124 and 128 flights, inclusive, are on time.

This interval corresponds to the probability P(123.5<x<128.5)

[tex]P(123.5<x<128.5)=P(x<128.5)-P(x<123.5)\\\\\\ z_1=(x_1-\mu)/\sigma=(128.5-120.12)/4.38=8.38/4.38=1.91\\\\z_2=(x_2-\mu)/\sigma=(123.5-120.12)/4.38=0.77\\\\\\P(x<128.5)-P(x<123.5)=P(z<1.91)-P(z<0.77)\\\\P(x<128.5)-P(x<123.5)=0.9719-0.7794=0.1925[/tex]

Answer:

a) Null hypothesis: [tex]\mu_d= 0[/tex]

Alternative hypothesis: [tex]\mu_d \neq 0[/tex]

b) [tex]t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{850 -0}{\frac{1123}{\sqrt{42}}}=4.905[/tex]

The next step is calculate the degrees of freedom given by:

[tex]df=n-1=42-1=41[/tex]

Now we can calculate the p value, since we have a left tailed test the p value is given by:

[tex]p_v =2*P(t_{(41)}>4.905) =0.000015[/tex]

So the p value is lower than any significance level given, so then we can conclude that we can reject the null hypothesis that the difference between he two groups are equal.

Step-by-step explanation:

Assuming the following questions:

We assume the following data: [tex] n = 42 ,\bar d= 850 , s_d = 1123[/tex]

Previous concepts

A paired t-test is used to compare two population means where you have two samples in  which observations in one sample can be paired with observations in the other sample. For example  if we have Before-and-after observations (This problem) we can use it.  

a. Formulate the null and alternative hypotheses to test for no difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out.

The system of hypothesis for this case are:

Null hypothesis: [tex]\mu_2- \mu_1 = 0[/tex]

Alternative hypothesis: [tex]\mu_2 -\mu_1 \neq 0[/tex]

Or equivalently

Null hypothesis: [tex]\mu_d= 0[/tex]

Alternative hypothesis: [tex]\mu_d \neq 0[/tex]

b. Use a .05 level of significance. Can you conclude that the population means differ? What is the p-value?

[tex]t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{850 -0}{\frac{1123}{\sqrt{42}}}=4.905[/tex]

The next step is calculate the degrees of freedom given by:

[tex]df=n-1=42-1=41[/tex]

Now we can calculate the p value, since we have a left tailed test the p value is given by:

[tex]p_v =2*P(t_{(41)}>4.905) =0.000015[/tex]

So the p value is lower than any significance level given, so then we can conclude that we can reject the null hypothesis that the difference between he two groups are equal.

Answer:

There is a 1/2 chance the coin will land on heads and there is a 1/6 chance that the number cube will land on 6. hope this helps

Answer:

work and answer are shown in the picture

Step-by-step explanation:

if you have any questions about my work please let me know

Answer:

0.4801

Step-by-step explanation:

This is a binomial distribution question.

It can be approximated using normal distribution if the following conditions are met:

np > 10

n(1-p) > 10

Here,

n = 29

p = 0.487

So,

np = 14.12

n(1-p) = 14.88

So, we can use normal approximation here:

Binomial:  X ~ B(n,p)  becomes

Normal Approx:  X~ N([tex]np,\sqrt{np(1-p)}[/tex])

Mean is:

[tex]\mu=np=14.123[/tex]

Standard Deviation is:

[tex]\sigma=\sqrt{np(1-p)} =2.69[/tex]

We need probability of less than or equal to 14, so we can say:

P(x ≤ 14)

Using  [tex]z=\frac{x-\mu}{\sigma}[/tex], we have:

P(x ≤ 14) = [tex]P(\frac{x-\mu}{\sigma} \leq \frac{14-14.123}{2.69})\\=P(z \leq -0.05)\\=0.4801[/tex]

Note: We used z table in the last line

So the probability is 0.4801

Answer:

its A

Step-by-step explanation:

Answer:

all sides are congruent

Step-by-step explanation:

its talking about sides

I believe A is correct

Good luck!

The first one is KL and the second one is FG

Side GE corresponds to side EJ, which is 24 meters long and side JK corresponds to side LK, which is 60/7 meters (or approximately 8.57 meters) long.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

To determine which side of triangle EFG corresponds to side GE

we need to find the ratio of the lengths of corresponding sides.

The sides that share vertex E are EF and EJ, so we can write:

EF / EJ = FG / FJ = EG / EK

Substituting the given values, we get:

6 / ? = 5 / ? = 7 / 20

To solve for the missing value, we can cross-multiply and simplify:

6 × 20 = 5 × x

x = 24

To determine which side of triangle KLJ corresponds to side JK, we can use the same approach.

The sides that share vertex J are JL and JF, so we can write:

JL / JF = LK / EF = LJ / FG

Substituting the given values, we get:

24 / ? = 20 / 6 = 28 / 5

Cross-multiplying and simplifying:

24 × 5 = x × 28

x = 60 / 7

Therefore, side GE corresponds to side EJ, which is 24 meters long and side JK corresponds to side LK, which is 60/7 meters (or approximately 8.57 meters) long.

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Answer:

a)  3.6%

Step-by-step explanation:

The given question mixed up, below is the correct question:

The bumper car ride at the state fair has 2 red cars, 4 green cars, and 2 blue cars. Garth is first in line for the ride and is assigned a car at random.  Patty is next in line and is randomly assigned a car. Find the probability that both events A and B occur. Express your answer as a percent. If necessary, round your answer to the nearest tenth.

Calculation:

Given that the state fair has 2 red cars, 4 green cars and 2 blue cars.

There are therefore 2+4+2 = 8 cars in total.

Probability that Events A occurs P(A) = [tex]\frac{2}{8}[/tex] = 4

Probability that Events B occurs P(B) = [tex]\frac{1}{7}[/tex]

Probability that Events A and B occur P(A ∩ B) = [tex]\frac{2}{8}[/tex] × [tex]\frac{1}{7}[/tex] = [tex]\frac{2}{56}[/tex] = 0.0357 = 3.57%  ≈ 3.6%

Therefore, the probability that both events A and B occur is 3.6%

Final answer:

The probability that both Garth and Patty will drive a red bumper car is found by multiplying the probability of Garth picking a red car (1/4) by the probability of Patty picking a red car after Garth (1/7), resulting in 1/28 or approximately 3.6%.

Explanation:

To solve the problem, we need to calculate the probability that both events A and B happen, which involves Garth and Patty both getting a red bumper car. Initially, there are 2 red cars, 4 green cars, and 2 blue cars, totaling 8 cars.

Event A: Garth picks a red car. The probability of this happening is the number of red cars over the total number of cars. So P(A) = 2/8 = 1/4.

After Garth picks a red car, there is 1 red car, 4 green cars, and 2 blue cars left, totaling 7 cars.

Event B: Patty picks a red car after Garth has already picked one. The probability of this happening is the number of remaining red cars over the total number of remaining cars. So P(B after A) = 1/7.

The probability that both A and B occur is the product of the probability of A and the probability of B given A has occurred. So P(A and B) = P(A) × P(B after A) = (1/4) × (1/7).

P(A and B) = 1/28. To express this as a percent, we multiply by 100%: (1/28) × 100% ≈ 3.6%.

Therefore, the probability that both Garth and Patty will drive a red bumper car is approximately 3.6%, which corresponds to option d.

Answer:

⁴ˣ√16³

Step-by-step explanation:

The equivalent to 16^(3/4x) is ⁴ˣ√16³. It reads, 4x root of 16 raised to the power of 3. 1/4x as an exponent means the 4x root of the base number. 3 as an exponent simply means that the base number is raised to the third power.

To prove the statement (A − B) ∪ (A ∩ B) = A, we can use the property of set difference, distribution, and identity from Theorem 6.2.2.

To construct an algebraic proof for the statement (A − B) ∪ (A ∩ B) = A, we can use the property of set difference, distribution, and identity from Theorem 6.2.2.

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Answer:

  E(3, -5)

Step-by-step explanation:

In a rectangle, the diagonals are the same length and bisect each other. That means their midpoints are the same. Then ...

  (F +C)/2 = (A +E)/2

  E = F +C -A

  E = (-5, 1) +(6, -1) -(-2, 5) = (-5+6+2, 1-1-5)

  E = (3, -5) . . . . . . . E is chosen so that the midpoint of AE is that of FC

__

To prove the figure is a rectangle, we can show the lengths of the diagonals are the same. Using the distance formula, ...

  FC = √((6-(-5))^2 +(-1-1)^2) = √(11^2 +2^2) = √125

  AE = √((3-(-2))^2 +(-5-5)^2) = √(5^2 +10^2) = √125

The diagonals are the same length and have the same midpoint, so the figure is a rectangle.

Answer:

a) True

Step-by-step explanation:

Repeated samples are a type of samples that are used to determine the features or characteristics or a given set of data.

In repeated samples, statistical techniques are applied whereby two samples that have similar characteristics are tested or analysed under different conditions.

Repeated samples can also be called matched or paired samples.

In repeated samples , we have what we refer to as confidence intervals. These are intervals whereby the true and correct value of certain parameters such as mean, the standard deviation of a given data or distribution is determined. We have confidence interval levels of 90%, 95% and 99%.

In repeated samples, approximately 99% of all differences in sample means will fall within the bounds of the interval already computed.

Answer:

157,286,400 bacteria.

Step-by-step explanation:

We have been given that a certain type of bacteria, given favorable growth medium, quadruples in population every 6 hours. Given that there were 150 bacteria to start with.

We will use exponential growth function to solve our given problem.

[tex]y=a\cdot b^x}[/tex], where

y = Final value,

a = Initial value,

b = Growth factor.

x = Time.

Quadruples meaning 4 at a time, so growth factor is 4.

We are also told that population becomes 4 times every 6 hours, so time would be [tex]\frac{1}{6}x[/tex].

Initial value is given as 150.

Upon substituting these values in above formula, we will get:

[tex]y=150(4)^{\frac{1}{6}x}[/tex]

Let us convert two and a half days into hours.

1 day = 24 hours.

2.5 days = 2.5*24 hours = 60 hours.

To find the bacteria population in two and half days, we will substitute [tex]x=60[/tex] in our formula as:

[tex]y=150(4)^{\frac{1}{6}(60)}[/tex]

[tex]y=150(4)^{10}[/tex]

[tex]y=150(1048576)[/tex]

[tex]y=157,286,400[/tex]

Therefore, there will be 157,286,400 bacteria in two and a half days.

Answer:

[tex]t=52.39[/tex]

Step-by-step explanation:

Answer:

30.0

Step-by-step explanation:

Given our data is normally distribute with [tex]\mu=21.3[/tex] and [tex]\sigma=5.9[/tex]

-Top 7% is given by find the z-value corresponding to p=(1-0.07)=0.93

-We substitute our values in the equation below;

[tex]z=\frac{\bar X-\mu}{\sigma}\\\\\\=\frac{X-21.3}{5.9}, z_{0.035}=1.476\\\\\therefore 1.476=\frac{X-21.3}{5.9}\\\\X=5.9\times 1.476+21.3\\\\=30.0084\approx30.0[/tex]

Hence, the minimum score required for the scholarship is 30.0

The minimum ACT Reading score required for a university scholarship awarded to the top 7% is approximately 30.0.

To find the minimum ACT Reading score required for a scholarship awarded to students in the top 7%, we need to determine the z-score that corresponds to the top 7% of a normal distribution. We can then use this z-score to find the corresponding ACT score.

The z-score for the top 7% of a standard normal distribution is approximately 1.475. Since the ACT Reading scores have a mean (μ) of 21.3 and a standard deviation (σ) of 5.9, we can use the z-score formula to find the minimum score 'x' required for the scholarship: z = (x - μ) / σ.

Solving for 'x', we get: x = zσ + μ = 1.475(5.9) + 21.3 ≈ 30.0. Therefore, the minimum ACT Reading score required for the scholarship is approximately 30.0.

Answer:

  0

Step-by-step explanation:

The slope formula is ...

  m = (y2 -y1)/(x2 -x1)

Filling in the given point values, we find the slope to be ...

  m = (-4 -(-4))/(9 -5) = 0/4 = 0

The slope is 0.

_____

The y-values are the same at -4, the equation of the line is y = -4. It is a horizontal line with zero slope.

Final answer:

Oscar's balloon, which has an 8-inch diameter, will hold approximately 268.1 cubic inches of helium, calculated using the volume formula for a sphere.

Explanation:

Oscar needs to calculate the volume of a sphere-shaped balloon to determine how much helium it can hold. To find the balloon's volume, we use the formula for the volume of a sphere, which is V = ⅓πd³, where V is the volume, π is approximately 3.14159, and d is the diameter of the sphere. Since the balloon has a diameter of 8 inches, its radius r is 4 inches (which is half of the diameter).

Plugging the radius into the formula, we get: V = ⅓π(4 inches)³ = ⅓π(64 inches³) = 268.0826 inches³. Therefore, Oscar's balloon will hold approximately 268.1 cubic inches of helium to the nearest tenth, making the correct answer C. 268.1 in.³

Answer:

Hello

The answer is  30% increase in texts since last month.

IF you feel any problem in understanding , do comment pls.

Step-by-step explanation:

Let

X = last month sent texts

y = this month sent texts

First of all find the no. of increased texts,

by subtracting x from y

=> y-x= 7085- 5450

        = 1635

We want to find these 15 texts % with respect to 5450 texts

i.e.    1635/X

=0.30

for answer in % multiply with 100

i.e. 30%

Answer: There are 4 more wrenches in the toolbox then the screwdrivers.

Step-by-step explanation: Add the 6 wrenches Sid put in the toolbox with the 8 wrenches Bella added to get 14 wrenches in total. Then, subtract the 10 screwdrivers from the 14 wrenches to get 4 wrenches.

Final answer:

Bella added 8 wrenches to the toolbox, making a total of 14 wrenches. There were initially 10 screwdrivers, so there are now 4 more wrenches than screwdrivers.

Explanation:

Calculating the Difference Between Wrenches and Screwdrivers in a Toolbox

Initially, there are 10 screwdrivers and 6 wrenches in the toolbox. Bella adds 8 more wrenches, which brings the total number of wrenches to 6 + 8, which equals 14 wrenches. The question asks how many more wrenches there are than screwdrivers. To find this, we subtract the number of screwdrivers from the number of wrenches:

14 wrenches - 10 screwdrivers = 4 more wrenches than screwdrivers in the toolbox.

Answer: C

Step-by-step explanation:

The answer is 7 feet

Answer:

c. 7ft

good luck, i hope this helps :)

Answer:

C: 12.56 inches

Step-by-step explanation:

We know that the minute hand can move an equivalent of 60 minutes in any one revolution.

-10 minutes movement is equal to 1/6 the total distance and the circumference covered in that time is calculated as:

[tex]C=\pi D\\\\=\frac{1}{6}\pi \times (12\times 2)\\\\\\=12.56\ in[/tex]

Hence, over 10 minutes the minutes hand moves 12.56 inches away.

The tip of a 12 inch minute hand will move approximately 12.56 inches over the course of 10 minutes, which aligns with option C in your given choices.

The subject of this question is Mathematics, specifically geometry and involves calculating the length of an arc within a circle. The minute hand of a clock can be thought of as the radius of a circle, with a full rotation of the hand representing a complete circle. The minute hand moves 360 degrees in 60 minutes (or 6 degrees per minute), so over 10 minutes, the minute hand will move 60 degrees.

Now, the length of that portion of the circle (the arc length) is calculated using the formula: (2πr)(θ/360), where r is the radius (half of the diameter, or 12 inches in this case), and θ is the angle in degrees. When you plug in the respective values, you will find that the minute hand of the clock moves an approximate distance of 12.56 inches, which corresponds to option C in your given choices.

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Answer:= (504, 516)

Therefore, the 90% confidence interval (a,b) = ( 504, 516)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean gain x = 510

Standard deviation r = 37

Number of samples n = 95

Confidence interval = 90%

z(at 90% confidence) = 1.645

Substituting the values we have;

510+/-1.645(37/√95)

510+/-1.645(3.796)

510+/-6.24

510+/-6

= (504, 516)

Therefore at 90% confidence interval (a,b) = ( 504, 516)

Answer:

i need points.

Step-by-step explanation:

Answer:

a = 1/3

b = -3

c = 26/3

d = -6

e = 0

Step-by-step explanation:

Given the quartic polynomial

p(x)=ax⁴+bx³+cx²+dx+e and

p(i) =2i when i=0,1,2,3,4

If i = 0:

p(0) = 2(0)

p(0) = 0

0 = 0+0+0+0+0++e

e = 0

When i = 1

p(1) = 2(1) = 2

2 = a(1)⁴+b(1)³+c(1)²+d(1)+e

2 = a+b+c+d+0

a+b+c+d = 0... (1)

When i = 2, p(2) = 2(2)

p(2) = 4

4 = a(2)⁴+b(2)³+c(2)²+d(2)+e

4 = 16a+8b+4c+2d+0

16a+8b+4c+2d = 4

8a+4b+2c+d = 2... (2)

When i = 3

p(3) = 8

8 = a(3)⁴+b(3)³+c(3)²+d(3)+0

8 = 81a+27b+9c+3d..(3)

When i = 4

p(4) =16

16 = a(4)⁴+b(4)³+c(4)²+d(4)+0

16 = 256a+64b+16c+4d

64a+16b+4c+d = 4...(4)

Solving equation 1 to 4 simultaneously.

Check the attachment for solution.

The problem here is to determine the coefficients of a quartic polynomial to match the given conditions. This results in a system of linear equations which can be solved to find the desired coefficients.

This question is a

polynomial problem

and involves finding the coefficients of a

quartic polynomial

, and for that we form a system of linear equations. Using the given conditions, we get the following equations:

By solving the above system of equations, we can find the values of a, b, c, d and e that satisfy those equations simultaneously.

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Answer:

Circle

Step-by-step explanation:

I don't know if there is a more "professional" way to solve this, but I wrote out the pattern until I got to the twentieth shape and it ended up being a circle :)

The 20th shape in the pattern is a circle.

To determine the 20th shape in the pattern of triangle, circle, circle, we need to analyze the pattern. The pattern starts with a triangle and is followed by two circles. This sequence repeats - triangle, circle, circle. To find the 20th shape, we need to determine how many times this sequence repeats within the first 20 shapes. Each complete sequence consists of 3 shapes (triangle, circle, circle), so we divide 20 by 3 to get 6 complete sequences. The 6th complete sequence ends with a circle, so the 20th shape in the pattern is also a circle.

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