Answer:
The distance between the boats is [tex]50\ mi[/tex]
Step-by-step explanation:
we know that
The Pythagoras Theorem states that
In a right triangle
[tex]c^{2}=a^{2}+b^{2}[/tex]
where
c is the hypotenuse
a and b are the legs
In this problem
Let
c ----> the distance between the boats
a -----> the horizontal distance between the boats
b -----> the vertical distance between the boats
[tex]a=12+18=30\ mi[/tex]
[tex]b=16+24=40\ mi[/tex]
substitute the values
[tex]c^{2}=30^{2}+40^{2}[/tex]
[tex]c^{2}=2,500[/tex]
[tex]c=50\ mi[/tex]
Final Answer:
The distance between the two boats is 50 miles.
Explanation:
To find the distance between the two boats after they have traveled, we need to determine the final position of each boat relative to the island, and then use the Pythagorean theorem to find the distance between these two positions. Let's go through the calculations step-by-step:
Step 1: Determine the final position of each boat relative to the island.
- Boat 1 travels 12 miles east and then 16 miles north. Let’s define east as the positive x-direction and north as the positive y-direction. So, the final coordinates of Boat 1 relative to the island are (12, 16).
- Boat 2 travels 24 miles south and then 18 miles west. Let’s define south as the negative y-direction and west as the negative x-direction. So, the final coordinates of Boat 2 relative to the island are (-18, -24).
Step 2: Determine the differences in the x and y coordinates between Boat 1 and Boat 2.
- The difference in x-coordinates dx is the x-coordinate of Boat 1 minus the x-coordinate of Boat 2:
[tex]\( dx = 12 - (-18) = 12 + 18 = 30 \)[/tex] miles.
- The difference in y-coordinates dy is the y-coordinate of Boat 1 minus the y-coordinate of Boat 2:
[tex]\( dy = 16 - (-24) = 16 + 24 = 40 \)[/tex] miles.
Step 3: Use the Pythagorean theorem to calculate the distance between the two boats.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse c (the side opposite the right angle) is equal to the sum of the squares of the other two sides a and b:
[tex]\[ c^2 = a^2 + b^2 \][/tex]
Here, dx and dy can be considered the lengths of the sides of a right triangle, and the distance between the boats d is the hypotenuse of this triangle. So:
[tex]\[ d = \sqrt{dx^2 + dy^2} \\\\\[ d = \sqrt{30^2 + 40^2} \\\\\[ d = \sqrt{900 + 1600} \\\\\[ d = \sqrt{2500} \\\\\[ d = 50 \][/tex]
Therefore, the distance between the two boats is 50 miles.
The sum of two numbers is 16 and their difference is 20. What are the two numbers?
Final answer:
To find the two numbers whose sum is 16 and difference is 20, we set up two equations from the given conditions and solve them simultaneously, yielding the numbers 18 and -2.
Explanation:
The student has asked about solving a system of equations where the sum of two numbers is 16 and their difference is 20. We can set up two equations based on the given information:
x + y = 16 (Equation 1, where x and y are the two numbers)
x - y = 20 (Equation 2, because the difference between the two numbers is 20)
To find the two numbers, we can solve this system of equations by adding both equations to eliminate the 'y' variable:
2x = 36
Dividing both sides by 2 gives us x = 18. We then substitute x back into Equation 1 to find y:
18 + y = 16 => y = 16 - 18 => y = -2
Therefore, the two numbers are 18 and -2.
Lata has collected 75 pennies. Lata's father says that if she arranges the pennies in 15 rows, Lata will be able to make a rectangle using all of her pennies. Is her father correct?
Answer:
Yes - he is correct
Step-by-step explanation:
If she has 75 pennies, she would have 15 rows with 5 pennies in each row with a 3:5 ratio for the rectangle.
Lata's father is correct.
What is a rectangle?Rectangle is a type of quadrilateral having two opposite sides that are equal in measurement.All the angles of Rectangle are of 90°.
Area of rectangle = Length * Width
Perimeter of rectangle =2(length + width)
Given,
Total number of pennies Lata have = 75
If she arranges the pennies in 15 rows with 5 pennies in each row.
i.e; 15 * 5 = 75
Then she will get Rectangle of side of length 15 and width 5
So, her father is correct.
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A triangle has a perimeter of 206 inches. if the two sides of the triangle measure 59 inches and 94 inches, determined the length of other side.
➷ The perimeter is the sum of all the lengths
206 - (59 + 94) = 53
It is 53 inches.
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Answer:
53 inches.
Step-by-step explanation:
Perimeter = sum of the 3 sides so the third side
= 206 - 94 - 59 = 53.
The service time distribution describes the probability P that the service time of the customer will be no more than T hours. If m is the mean number of customers serviced in an hour, then P=1-e^mt
Answer: option d.
Step-by-step explanation:
You have the following formul given in the problem:
[tex]p=1-e^{-mt}[/tex]
You know that:
The number of customers serviced in an hour by the technical support representative is 6 costumbers, therefore:
[tex]m=6[/tex]
As the problem asked for the probability that a costumber will be on hold less than 30 minutes, we know that:
[tex]t=0.5[/tex]
Substitute the values above into the formula.
Then, you obtain:
[tex]p=1-e^{-(6)(0.5)}=0.95[/tex] or 95%
A circle is divided into 9 equal parts. What is the angle measured of two of those parts?What is the degrees
Answer:
Angle of 1 part: 40°
Angle of 2 parts: 80°
Step-by-step explanation:
Angles in a circle / Equal parts of a circles = Angle of 1 part
360/9 = 40°
40 x 2 = 80
Use the figure below to find the Measure of Angle BEH
Explain/Show how you got your answer please
Answer:
The answer is ; m∠BEH = 55°
Step-by-step explanation:
You estimate you can do 12 math problems in 45 minutes. How long should it take you to do 20 math problems?
[tex]\bf \begin{array}{ccll} problems&minutes\\ \cline{1-2} 12&45\\ 20&x \end{array}\implies \cfrac{12}{20}=\cfrac{45}{x}\implies \cfrac{3}{5}=\cfrac{45}{x}\implies 3x=225 \\\\\\ x=\cfrac{225}{3}\implies x=75[/tex]
It takes 75 minutes to solve 20 math problems.
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here it takes 45 minutes to solve 12 math problems thus to solve 1 math problem it will take t= 45/12
=3.75 minutes
Thus to solve 20 math problems it will take t₂₀=3.75×20
=75 minutes
Hence, It takes 75 minutes to solve 20 math problems.
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A student needs to collects at least 10 flowers for a science project the student has already collected 3 flowers the inequality shown can be useed to find n the number of flowers the student still needs
he is still looking for seven more flowers
Answer:
The answer is n, greater than or less than 13.
The equation of the line of best fit of a scatter plot is y = −5x − 2. What is the slope of the equation?
Answer:
SLOPE = -5
Step-by-step explanation:
Because that's what x is.
In Amy's garden the ratio of herbs to plants is 5:2. If there are 40 herb plants, how many vegetable plants are in her garden?
Please help me with this problem
Diagonal = SQRT(8^2 + 12^2 + 30^2)
Diagonal = SQRT(64 + 144 + 900)
Diagonal = SQRT(1108)
Diagonal = 33.3 feet
Evaluate the log.
[tex]log\frac{1}{27} 81[/tex]
Answer:
−115.940465
Step-by-step explanation:
Simplified = −115.940465
Answer:
-4/3.
Step-by-step explanation:
Using the change of base formula convert to log 3:
logb x = loga x / loga b
log(1/27) 81 = log3 81 / log3 1/27
log3 81 = 4 ( because 3^4 = 81) and log3 1/27 = -3 (because 3^-3 = 1/27)
So log(1/27) 81 = 4/-3 = -4/3.
Find the difference between the fastest girls time and the slowest girl time. Barbra ran 3 3/10, Donna ran 2 4/5 , Cindy ran 4 3/5 and Nicole ran 2 1/10
Answer: 2.5 or 2 1/2
Step-by-step explanation:
You can convert the mixed fractions to decimal numbers:
- Divide the numerator by the denominator of the fraction.
- Add the result to the whole number.
Thenyou have:
Barbara's time: [tex]3\ 3/10=3+0.3=3.3[/tex]
Donna's time: [tex]2\ 4/5=2+0.8=2.8[/tex]
Cindy's time: [tex]4\ 3/5=4+0.6=4.6[/tex]
Nicole's time: [tex]2\ 1/10=2+0.1=2.1[/tex]
As you can see, the fastest girl is Cindy and the slowest girl is Nicole.
Then, you must make the following subtraction to calculate the difference:
[tex]4.6-2.1=2.5[/tex] or 2 1/2
Answer:
Cindy's correct time is 3 2/5 (for the portfolio assignment that this question goes with).
Step-by-step explanation:
Formulate the quadratic function that contains the points (-1,2), (0,-1) and (2,5).
1.) f(x) = 2x^2 + x + 1
2.) f(x) = 2x^2 - x - 1
3.) f(x) = 2x^2 - x + 2
4.) f(x) = 2x^2 - x - 2
Answer:
option 2
2x²- x - 1
Step-by-step explanation:
We are given points: (-1,2), (0,-1) and (2,5)
Substitute each point one by one in the quadratic equation to check if the quadratic equation contains all points mention.
2) f(x) = 2x²- x - 1
Point(-1,2)
f(-1) = 2(-1)² -(-1) -1
2 = 2 + 1 - 1
2 = 2
Point(0,-1)
f(0) = 2(0)² -(0) -1
-1 = 0 - 0 -1
-1 = -1
Point(2,5)
f(2) = 2(2)² -(2) -1
5 = 8 - 2 -1
5 = 6 - 1
5 = 5
Twice Jack's age plus 5 is 21. Write and solve an equation. How old is Jack? A) 8 B) 13 C) 32 D) 52
Answer:
A - 8
Step-by-step explanation:
(21-5)/2
16/2 = 8
Answer: Jack is 8 years old (option A)
Step-by-step explanation:
Hi, to answer this question we have to write an equation using the information given:
Twice Jack's age plus 5 is 21Twice : Means that the age of jack (j) is multiplied by 2 (2j),
Plus 5: we have to add 5 (2j+5).
Is 21: all is equal to 21.
Mathematically speaking:
2j +5 =21
Solving:
2j =21-5
2j =16
j= 16/2
j=8
Option A). 8
Feel free to ask for more if needed or if you did not understand something.
Every year 39 million cars cross the Golden Gate Bridge in San Francisco. Which kind of function best models the relationship between time and the cumulative number of cars that have crossed the Golden Gate Bridge, exponential or linear?
Answer:
Linear
Step-by-step explanation:
Hello
Is linear
Best regards
Answer:
Linear
Step-by-step explanation:
Linear function : if the value increases with the constant value per period,
It can written as y = a + bx
Where, a = initial value, b = constant value per period,
Exponential function : if the value increases with the constant rate per period,
It can be written as,
[tex]y=ab^x[/tex]
Where, a = initial value, b = growth factor per period.
∵ Every year 39 million cars cross the Golden Gate Bridge in San Francisco.
Then after x years, the number of cars ( in million )
f(x) = 39x
⇒ f(x) = 0 + 39x
By the above explanation,
Hence, the function that represents the number of cars that have crossed the Golden Gate Bridge is linear.
What is the measure of EFG?
Answer: [tex]149^{\circ}[/tex]
Step-by-step explanation:
From the given figure, the measure of central angle FDG is given by :-
[tex]\angle{EDG}=\angle{EDF}+\angle{FDG}\\\\=83^{\circ}+66^{\circ}\\\\=149^{\circ}[/tex]
We know that the measure of arc in degrees is equals the measure of the central angle that intercepts the arc.
Now,the measure of arc EFG is given by :-
[tex]Arc\ \text{EFG}=\text{Central angle EDG}=149^{\circ}[/tex]
A certain organization recommends the use of passwords with the following format: vowel commavowel, consonant comma consonant comma consonant comma vowel comma consonant comma number comma numberconsonant, consonant, consonant, vowel, consonant, number, number (for example, inpray 93inpray93). Assume that repeats are allowed. Complete parts (a) and (b). (a) Assuming passwords are not case sensitive, how many such passwords are possible (assume that there are 5 vowels and 21 consonants)?
The password format is = inpray93
vowel , consonant, consonant, consonant, vowel, consonant, number, number.
There are 21 consonants, 5 vowels and 10 number choices (0-9)
Since, there are 21 consonants and repetition is allowed so for 2nd, 3rd, 4th, and 6th positions 21 choices are available. For 1st and 5th positions, 5 choices are available and for 7th and 8th position there are 10 choices (0 to 9).
Passwords are not case sensitive which means upper case and lower case letters are same.
So, the number of passwords can be =
[tex]5\times21\times21\times21\times5\times21\times10\times10[/tex]
= 486202500
Part (b) question is not given. But it can be opposite to the first part i.e when the password letters are case sensitive.
This means all the letters are different.
So, number of passwords will be =
[tex]10\times42\times42\times42\times10\times42\times10\times10[/tex]
= 31116960000
A factory makes boxes with length to width ratio of 6 inches to 1 inch. What should be the width of a box with a length of 30 inches
Length:width
6 inches: 1 inch
30 inches: 5 inches
Since the ratio for length is multiplied by 5, you would do the same for width.
Help with this question, please ASAP!!
Answer:
[tex]\large\boxed{P=(16+36x)\ ft}[/tex]
Step-by-step explanation:
The formula of an area of a rectangle:
[tex]A=bh[/tex]
b - base
h - height
We have A = 144x ft² and h = 8. Substitute and solve for b:
[tex]144x=8b[/tex] divide both sides by 8
[tex]b=18x\ ft[/tex]
The formula of a perimeter of a rectangle:
[tex]P=2b+2h[/tex]
Substitute:
[tex]P=2(18x)+2(8)=36x+16[/tex]
Hayden bought 48 new trading cards.Three fourths of the new cards are baseball cards.How many baseball cards did hayden buy?
Answer:
36
Step-by-step explanation:
1. 48 divided by 3= 12
2. 12 x 3= 36
Jack’s favorite colors are blue and red.
He has 2 blue shirts, 1 red shirt, 1 blue jacket, 1 red belt, 1 blue pair of pants and 1 red pair of pants.
Jack selects one of these garments at random. Let A be the event that he selects a blue garment and B be the event that he chooses a belt.
What is the probability that the garment Jack chooses is either blue or a belt?
Answer:
5/7 or 71%
Step-by-step explanation:
4/7 (blue) + 1/7 (belt) = 5/7
Answer: Probability of event A = 0.57
Probability of event B = 0.14
Step-by-step explanation:
The data is:
2 blue shirts
1 red shirt
1 blue jacket
1 red belt
1 blue pair of pants
1 red pair of pants
the total number of garments is: 2 + 1 + 1 + 1 + 1 + 1 = 7
the number of blue ones is: 2 + 1 + 1 = 4
the number of belts is: 1
then, the probability of selecting at random one blue garment is equal to the number of blue ones divided the total number:
Pa = 4/7 =0.57
the probability of selecting the belt is equal to the number of belts divided the total number of garments, this is:
Pb = 1/7 = 0.14
You're playing a game where you defend your village from an orc invasion. There are 3 characters (elf, hobbit, or human) and 5 defense tools (magic, sword, shield, slingshot, or umbrella) to pick from. If you randomly choose your character and tool, what is the probability that you'll be a magic elf?
Answer:
1/15
Step-by-step explanation:
You have a 1/3 chance of being an elf.
You have a 1/5 change of having the magic tool.
1/3 × 1/5 = 1×1/3×5 = 1/15
Answer:
it is 1/15
Step-by-step explanation:
My sister is 14 years old my brother says that his age minus 12 is equal to my sisters age how old is my brother
Answer:
26
Step-by-step explanation:
Let his age = x
Equation
x - 12 = 14
Solution
Add 12 to both sides.
x - 12 +12 = 14 + 12
x = 26
He is currently 26 years old.
In the sum of two numbers is 15 and the product is 56, what are the two numbers?
ANSWER:
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Please help! Will give the brain thing! 40 points.
Simplify each Polynomial Expression:
1. 2x(-3x - 1)
2. -x(4 + 2x)
3. -5x(-2x + 4)
4. x(-2x - 2) + 3(-4x - 6x)
5. 2xy(-3x - 5y) + 4y(-2xy - 4x)
Answer:
1. 2x(-3x - 1)
-6x^2 - 2x
2. -x(4 + 2x)
-4x - 2x^2
3. -5x(-2x + 4)
10x^2 - 20x
4. x(-2x - 2) + 3(-4x - 6x)
-2x^2 - 2x - 12x - 18x
-2x^2 - 32x
5. 2xy(-3x - 5y) + 4y(-2xy - 4x)
-6x^2y - 10xy^2 -8xy^2 - 16yx
-6x^2y -18xy^2 - 16yx
You just distribute (multiply) what's outside the parentheses with everything inside the parentheses. Then, combine like terms.
Answer:
1. 2x(-3x - 1)
-6x^2 - 2x
2. -x(4 + 2x)
-4x - 2x^2
3. -5x(-2x + 4)
10x^2 - 20x
4. x(-2x - 2) + 3(-4x - 6x)
-2x^2 - 2x - 12x - 18x
-2x^2 - 32x
5. 2xy(-3x - 5y) + 4y(-2xy - 4x)
-6x^2y - 10xy^2 -8xy^2 - 16yx
-6x^2y -18xy^2 - 16yx
A shoe store is selling a pair of shoes for $60 that has been discounted by 20%. What was the original selling price? Show your work.
Answer:
The original selling price was [tex]\$75[/tex]
Step-by-step explanation:
Let
x-----> the original selling price
we know that
[tex]100\%-20\%=80\%=80/100=0.80[/tex]
so
[tex]0.80(x)=60[/tex] -----> equation that represent the situation
solve for x
Divide by 0.80 both sides
[tex]x=60/0.80=\$75[/tex]
(17.33) A randomized comparative experiment examined the effect of a technique for improving one’s ability to focus one’s attention on performance of undergraduate students on the Verbal portion of the Graduate Record Exam (GRE). The researchers found a statistically significant improvement in performance on the Verbal GRE (P = 0.05). When asked to explain the meaning of (P =0.05) a student says, “This means there is only probability equal to 0.05 that the null hypothesis is true.” Explain what P= 0.05 really means in a way that makes it clear that the student's explanation is wrong. P = 0.05 means that the outcome is at least 5% higher among one group than among the other group. P = 0.05 means that there is a probability of 0.05 that the null hypothesis is false. P = 0.05 means that the probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as that actually observed, is 0.05. P = 0.05 means that the probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as that actually observed, is less than 0.05.
Answer:
See below
Step-by-step explanation:
What the significance level tells us is that, in this case, there is only a 5% chance that the change in results from the sample happened by random chance. So that means that most likely the change in results did not happen by random change, and something happen between the times the samples were taken. In this case, the experiment.
P = 0.05 means that the probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as that actually observed, is 0.05.
P = 0.05 does not represent the probability that the null hypothesis is true or false, nor does it signify that the outcome is 5% higher in one group compared to the other. Instead, P = 0.05 is the probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as the one observed. In simpler terms, it indicates the likelihood of obtaining the observed results, or results more extreme, under the assumption that there is no true effect or difference between the groups.
In hypothesis testing, researchers start with a null hypothesis (H0) that states there is no effect or difference between the groups being compared. The alternative hypothesis (Ha), on the other hand, posits that there is a significant effect or difference. The p-value quantifies the strength of evidence against the null hypothesis. A low p-value (such as P = 0.05) suggests that the observed results are unlikely to have occurred by chance alone, leading to the rejection of the null hypothesis in favor of the alternative hypothesis.
When a study reports a statistically significant improvement in Verbal GRE performance with P = 0.05, it means that the probability of obtaining the observed improvement (or a more significant one) under the assumption of no actual effect is 5% or less. Therefore, there is strong evidence to suggest that the technique used in the experiment does indeed have a positive impact on students' Verbal GRE scores.
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Mark and Henry win some money and share it in the ratio 1:3. Mark gets ?9. How much did Henry get?
Consider that the length of rectangle A is 10 cm and its width is 6 cm. Which rectangle is similar to rectangle A? A) A rectangle with a length of 9 cm and a width of 6 cm. B) A rectangle with a length of 15 cm and a width of 9 cm. C) A rectangle with a length of 14 cm and a width of 7 cm. D) A rectangle with a length of 12 cm and a width of 8 cm.