The ice cream factory could make 720 quarts of ice cream in 36 hours.
How many quarts could be made in 36 hours?We can use a proportion to solve this problem:
quarts / hours = constant rate of production
Let x be the number of quarts that could be made in 36 hours. Then we have:
200 quarts / 10 hours = x quarts / 36 hours
Cross-multiplying, we get:
10x = 200 * 36
Simplifying, we get:
10x = 7200
Dividing both sides by 10, we get:
x = 720
Therefore, the ice cream factory could make 720 quarts of ice cream in 36 hours.
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we randomly select 100 pell grant recipients from two states. state a is a relatively small state with approximately 4,000 pell grant recipients. state b is a large state with approximately 200,000 pell grant recipients. suppose that the mean and standard deviation in individual pell grants is approximately the same for both states: and . for which state is the sample mean for our 100 pell grant recipients most likely to be within $80 of $2,600? group of answer choices state a because the sample represents a larger segment of this small population. state b because there is less variability in larger populations so estimates from samples are more accurate. equally likely because for both states.
Answer: The answer is state B because there is less variability in larger populations so estimates from samples are more accurate. The standard error of the mean is proportional to the standard deviation of the population and inversely proportional to the square root of the sample size. Since state B has a much larger population, it is more likely that our sample mean will be within $80 of $2,600 for state B than for state A.
Step-by-step explanation:
Simon wants to fill 8 punch bowls for a birthday party. Each punch bowl holds 9 1/5 quarts of punch. How much punch will Simon need?
Write your answer as a fraction or as a whole or mixed number.
Punch that Simon needs in fraction is 73[tex]\frac{3}{5}[/tex] quarts.
What is fraction?
Part of a whole is a fraction. The quantity is written as a quotient in mathematics, where the numerator and denominator are divided. Each is an integer in a simple fraction. Whether it is in the numerator or denominator, a complex fraction contains a fraction. The numerator and denominator of a correct fraction are opposite each other.
Here number of bowls punch for party = 8
Each punch bowl holds 9 1/5 quarts of punch .
Then converting into improper fraction then [tex]9\frac{1}{5}=\frac{45+1}{5}=\frac{46}{5}[/tex]
Now total punch Simon needs to fill 8 bowls is,
=> [tex]8\times\frac{46}{5}=\frac{368}{5}[/tex] = 73[tex]\frac{3}{5}[/tex].
Hence Punch that Simon needs in fraction is 73[tex]\frac{3}{5}[/tex] quarts.
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50 POINTS ASAP Triangle NMO is drawn with vertices N(−5, 2), M(−2, 1), O(−3 , 3). Determine the image vertices of N′M′O′ if the preimage is reflected over x = −2.
N′(5, −2), M′(2, 1), O′(3, 3)
N′(−2, 2), M′(1, 1), O′(0, 3)
N′(1, 2), M′(−2, 1), O′(−1, 3)
N′(−5, −2), M′(−2, −1), O′(−3, −3)
Answer:
To reflect a point over a vertical line x = c, where c is a constant, we can use the formula (2c - x, y).
Given the line of reflection x = -2, and the original points N(-5, 2), M(-2, 1), O(-3, 3), we can apply the formula as follows:
For N(-5, 2):
N' = (2(-2) - (-5), 2) = (1, 2)
For M(-2, 1):
M' = (2(-2) - (-2), 1) = (2, 1)
For O(-3, 3):
O' = (2(-2) - (-3), 3) = (1, 3)
So, the correct image vertices of N'M'O' after reflecting over x = -2 are N'(1, 2), M'(2, 1), O'(1, 3), which corresponds to the option:
N′(1, 2), M′(2, 1), O′(1, 3)
Please double-check to make sure if its right ;D
Assume that
log 4 ~ 0.6021, log 5 ~ 0.6990, and log 6 – 0.7782
Use the properties of logarithms to evaluate
the expression. Do not use your calculator.
(Round your answer to 4 decimal places. If your
answer includes a negative, enter it like: -2)
log 16 = [a]
Answer:
Step-by-step explanation:
?
A salesman's commission varies directly as his sales.If the commission is $10 for $100 in sales, find the commission for $150 in sales.
a. $12 b. $20 c. $15 d. $25
The commission for $150 in sales is $15. This corresponds to option (c) in the given answer choices.
We are told that the salesman's commission varies directly with his sales. This means that if the sales increase by a certain percentage, then the commission will also increase by the same percentage. We can set up a proportion to solve for the commission:
Commission/Sales = Commission Rate
We are given that the commission rate is $10 for every $100 in sales. We can use this information to set up a proportion:
Commission/150 = 10/100
To solve for the commission, we can cross-multiply and simplify:
Commission = (150 x 10)/100 = $15
In general, if we let x represent the sales amount, and c represent the commission, then we can use the formula:
c = (x/100) * 10
where 10 represents the commission rate of $10 per $100 in sales. We can use this formula to calculate the commission for any given sales amount.
Therefore, Correct option is C.
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pls help with both problems due tmrw
Based on the description of the problem,the measure of ∠BTX is 60°.
What is circle?A circle is a two-dimensional geometric shape made up of all the points that are equally spaced apart from the circle's centre.
The radius of the circle is the distance measured from any point on the circle to its centre.
The circumference is the collection of all the points on the circle.
Based on the description of the problem, we can conclude that triangle BOX is an isosceles triangle with OB = OX. This is because both OB and OX are radii of the same circle centered at O.
Since m/BOX = 120°, we can find the measure of angle B by dividing this angle in half, since angle B is the base angle of the isosceles triangle BOX.
∠BO = (180° - 120°)/2 = 30°
Now, since TX and TB are tangent to the circle at points X and B respectively, we know that angle BTX is equal to the sum of angles BOY and OXT, since angle BOY and OXT are both in the same quadrant and add up to 90°.
∠BTX = ∠BOY + ∠OXT>
Since triangle BOX is an isosceles triangle with angle BOY equal to 30°, we can find the measure of angle OXT as follows:
∠OXT = 180° - ∠BOX - ∠BOY
= 180° - 120° - 30°
= 30°
Therefore,
∠BTX = ∠BOY + ∠OXT
= 30° + 30°
= 60°
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A group of medical professionals predicts that the number of yearly occurrences of a disease will decrease from the year 2008 to the year 2016. They constructed a spreadsheet with formulas to display their predictions. How many occurrences of the disease do they predict in the year 2016?
One way to predict occurrences of a disease for a future year based on previous years' data is to use exponential modeling.
How can we predict occurrences of disease for year mathematically based on previous years data?Specifically, the formula for exponential growth or decay can be used to project the number of cases for a future time period based on the growth or decline rate observed in the past.
For example, let's say that we have data on the number of cases of a certain disease for the past 10 years. We can use this data to fit an exponential model that describes the growth or decline rate of the disease over time.
Once we have this model, we can use it to predict the number of cases for a future year. For instance, if the model predicts that the disease will grow at a rate of 5% per year, we can use this rate to estimate the number of cases for the next year by multiplying the current number of cases by 1.05. By doing this, we can forecast the occurrence of the disease for the next year based on the previous years' data.
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Solve the equation. Round to the nearest tenth if necessary. x^2=36
Answer:
x = 6
Step-by-step explanation:
Solve for x:
[tex]x^2=36[/tex]
Take the square root of 36
[tex]x=6[/tex]
Please Help :))) If DE| |AB, by the Side Splitter Theorem, ...
If DE| |AB, by the Side Splitter Theorem, We can conclude that DE is parallel to AB if and only if CD/DA = CE/EB or x/y = z/w.
What is Side Splitter Theorem?The Side Splitter Theorem is a geometric theorem that relates the lengths of the sides of a triangle and the segments formed when a line is drawn parallel to one of the sides of the triangle.
Specifically, if a line is drawn parallel to one side of a triangle, then it divides the other two sides proportionally.
In other words, if a line intersects two sides of a triangle and is parallel to the third side, then the lengths of the segments it divides on the other two sides are proportional to the lengths of those sides.
If DE is parallel to AB, then by the Side Splitter Theorem, we have:
CD/DA = CE/EB
Substituting the given variables, we get:
x/y = z/w
We can also use the fact that triangles CDE and ABC are similar, which implies that their corresponding sides are proportional. Specifically, we have:
CD/AB = CE/AC = DE/BC
Substituting the given variables and using the fact that CD = x, DA = y, CE = z, and EB = w, we get:
x/(y+w) = z/(x+z)
Cross-multiplying both equations, we get:
xy + xw = yz + xz
Simplifying, we get:
x(w+z) = yz
Dividing both sides by wz, we get:
x/y = z/w
Which is the same as the equation we obtained using the Side Splitter Theorem.
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● • 4√13 ft
.
143 ft
• 14.33 ft
Which list shows these diagonal lengths in order from greatest to least?
F 14.33, 14,4√13
G 14.33, 4√13, 14
H 14, 14.33, 4√/13
J 4√13, 14, 14.33
The correct order from greatest to least is option G. 14.33, 4√13, 14
How did we get the value?To convert a root number to a whole number, you simply need to evaluate the root expression by performing the indicated operation. The result of the evaluation will be a whole number.
Here are the steps to convert a root number to a whole number:
Determine the type of root: square root (√), cube root (∛), etc.
Write the root expression using the appropriate symbol and the radicand (the number inside the root symbol).
Evaluate the expression by performing the indicated operation. For example, if it is a square root, multiply the number inside the root symbol by itself. If it is a cube root, multiply the number inside the root symbol by itself three times.
The result of the evaluation will be a whole number.
To compare the diagonal lengths, we need to convert them to the same units. We can convert 4√13 ft to approximately 9.17 ft by using a calculator. Now we have:
14.33 ft
0.143 ft
9.17 ft
So, the order from greatest to least is:
G. 14.33, 4√13, 14
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What is the y-intercept of the line with the equation y = one-half x minus 3? a. -3 c. -6 b. 6 d. One-half
Destiny sells newspapers at a
newsstand outside of her grocery
store. She normally charges $2.35 for
a newspaper. Today, Destiny has
lowered the price by $0.50. So far, she
has sold 8 newspapers at the new
price. How much money has Destiny
made so far from selling newspapers
at the new price?
Answer:
$14.80
Step-by-step explanation:
First you need to subtract .50 from 2.35, which is 1.85.
Next you need to multiply 1.85 times 8.
1.85 x 8 = 14.80
Therefore, she has made $14.80 since the new price.
a person wants to know the true proportion of customers that write a review. the owner randomly selects a random sample of 560 customers and only 340 of them wrote a review. when calculating a 90% confidence interval, what is the margin of error used:
The margin of error used in calculating the 90% confidence interval for the true proportion of customers who write a review is 0.043.
To calculate the margin of error, we first need to find the sample proportion of customers who wrote a review:
sample proportion[tex]\hat p =\frac{ 340}{560} = 0.607[/tex]
Next, we can use the following formula to calculate the margin of error:
margin of error [tex]= z* \sqrt{(\hat p * (1-\hat p) / n)[/tex]
where z* is the z-score associated with the desired level of confidence (90% in this case), and n is the sample size.
The z-score for a 90% confidence interval is 1.645. Plugging in the values, we get:
margin of error =[tex]1.645 * \sqrt{(0.607 * (1-0.607) / 560)[/tex]
= 0.043
Therefore, the margin of error used in calculating the 90% confidence interval for the true proportion of customers who write a review is 0.043.
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A teacher has a prize box that has 6 fidgets,2 rubix cubes,and 2 pop its-as well as a bag of candy that has 4 lollipops and 3 fieces of chocolate. Esther wins the weekly prize in class and can pick one toy from the prize box and one candy from the candy bag. What is the probability she will pick a fidget and a piece of chocolate?
The probability of Esther picking a fidget and a piece of chocolate is 3/14.
How to obtain the probabilityTo obtain the probability, we first need to list the items and then determine the chances of them being picked. Fisrt, there are a total of 12 items in the prize box and 7 items in the candy bag.
The probability of Esther picking a fidget from the prize box is 6/12 or 1/2, and the probability of her picking a piece of chocolate from the candy bag is 3/7. Since these events are independent, we can multiply their probabilities to find the probability of both events occurring:
P(fidget and chocolate) = P(fidget) x P(chocolate)
P(fidget and chocolate) = (1/2) x (3/7)
P(fidget and chocolate) = 3/14
Therefore, the probability of Esther picking a fidget and a piece of chocolate is 3/14.
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Find the volume of the solid formed by rotating the space bounded by y = 2x², y=0, and x = 2 around the line y = 8
The volume of the solid is (256π/15) - (128π/3) cubic units, which is formed by rotating the space bounded by y = 2x², y=0, and x = 2 around the line y = 8.
To find the volume of the solid formed by rotating the space bounded by y = 2x², y=0, and x = 2 around the line y = 8, we can use the disk method.
First, we need to find the bounds of integration. Since x = 2 is the right boundary, we can integrate from 0 to 2.
The distance between the line y=8 and the curve y=2x² is 8 - 2x². Therefore, the radius of the disk at a given x-value is 8 - 2x².
The area of each disk is given by π(radius)². Therefore, the volume of the solid is given by the integral of π(radius)² dx from 0 to 2;
V = ∫₀² π(8 - 2x²)² dx
This integral can be evaluated by expanding the square and using the power rule of integration. After simplification, we get;
V = (256π/15) - (128π/3)
Therefore, the volume of the solid is (256π/15) - (128π/3) cubic units.
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Show Sample Answer
Part B
In general, how do the measures of the angles in the image compare with the measures of the angles in the preimage?
What affect does the scale factor of the dilation have on the angles, if any?
After a dilation, the angle measures remain constant, meaning that they are not affected by the scale factor of the dilation.
What is a dilation?A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.
The side lengths are changed, but the original figure and the dilated figure are similar, meaning that the angle measures remain constant, no matter the scale factor.
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One of the legs of a right triangle measures 16 cm and the other leg measures 2 cm. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Answer: 16.1 cm
Step-by-step explanation:
Attached below is a diagram of the triangle.
If you have two legs, you can find the hypotenuse of the right triangle by using the Pythagorean Theorem.
Pythagorean Theorem: a² + b² = c²
Let's set
a = 16 cm
b = 2 cm
So we get,
16² + 2² = c²
256 + 4 = c²
260 = c²
Take the square root of both sides to get c. Since you are taking the square root, there are two answers, positive and negative, but a side length can not be negative.
[tex]\sqrt{260}[/tex] = c
Input this into your calculator, and you get
c = 16.1245155 cm
Rounding to the nearest tenth you get c = 16.1 cm
Find the volume of a cone that has a height of 9 inches and a diameter of 12 inches. Use 3. 14 for pi and round to the nearest tenth
The volume of the cone with height of 9 inches and a diameter of 12 inches is approximately 339.3 cubic inches.
To find the volume of a cone, we need to use the formula V = (1/3)πr^2h, where r is the radius of the base of the cone and h is the height of the cone.
Since the diameter of the cone is given as 12 inches, we can find the radius as half of the diameter, which is 6 inches. The height of the cone is given as 9 inches.
Now, we can substitute the values of r and h in the formula to get the volume as follows
V = (1/3)πr^2h
= (1/3)×3.14×6^2×9
= 339.12 cubic inches (rounded to the nearest tenth)
Therefore, the volume of the given cone is approximately 339.1 cubic inches.
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Roller Coaster Crew
Ray and Kelsey have summer internships at an engineering firm. As part of their internship, they get to assist in the planning of a brand new roller coaster. For this assignment, you help Ray and Kelsey as they tackle the math behind some simple curves in the coaster's track.
Part A
The first part of Ray and Kelsey's roller coaster is a curved pattern that can be represented by a polynomial function.
Ray and Kelsey are working to graph a third-degree polynomial function that represents the first pattern in the coaster plan. Ray says the third-degree polynomial has four intercepts. Kelsey argues the function can have as many as three zeros only. Is there a way for the both of them to be correct? Explain your answer.
Kelsey has a list of possible functions. Pick one of the g(x) functions below and then describe to Kelsey the key features of g(x), including the end behavior, y-intercept, and zeros.
g(x) = (x + 2)(x − 1)(x − 2)
g(x) = (x + 3)(x + 2)(x − 3)
g(x) = (x + 2)(x − 2)(x − 3)
g(x) = (x + 5)(x + 2)(x − 5)
g(x) = (x + 7)(x + 1)(x − 1)
Create a graph of the polynomial function you selected from Question 2.
Part B
The second part of the new coaster is a parabola.
Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = (x − a)(x − b). Describe the direction of the parabola and determine the y-intercept and zeros.
Create a graph of the polynomial function you created in Question 4.
Part C
Now that the curve pieces are determined, use those pieces as sections of a complete coaster. By hand or by using a drawing program, sketch a design of Ray and Kelsey's coaster that includes the shape of the g(x) and f(x) functions that you chose in the Parts A and B. You do not have to include the coordinate plane. You may arrange the functions in any order you choose, but label each section of the graph with the corresponding function for your instructor to view.
Part D
Create an ad campaign to promote Ray and Kelsey's roller coaster. It can be a 15-second advertisement for television or radio, an interview for a magazine or news report, or a song, poem, or slideshow presentation for a company. These are just examples; you are not limited to how you prepare your advertisement, so be creative. Make sure to include a script of what each of you will say if you are preparing an interview or a report. The purpose of this ad is to get everyone excited about the roller coaster.
Mary, Jane, Tom, Andy saved for 6 weeks like this:
-
M: 2, 4, 8, 16,
J: 10, 12, 14, 16,
T: 7, 13, 19, 25,
A:
3,6,9..
Work out how much each person saved so that you can put their names in
order of how much they saved, from smallest to largest amount.
Enter your code as a four-lettered "word"
Please help to hard and I’ll give u 20 points
Answer: 2:4
Step-by-step explanation:
trigonometry, please help.
The value of x is given as follows:
x = 9.40 cm.
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.The parameters for this problem are given as follows:
Hypotenuse of 10 cm.Side length of x cm adjacent to the angle of 20º.Applying the cosine, the value of x is obtained as follows:
cos(20º) = x/10
x = 10 x cosine of 20 degrees
x = 9.40 cm.
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Write 7.725666118 as a percentage
please show the method too.
Answer: 773%
Step-by-step explanation: 7.725666118 x 100 = 772.5666118
772.5666118 = 773 (rounded).
So, 7.725666118 as a percentage is 773%
For example, 50% is written in decimal form as 0.5
And, 0.5 x 100 = 50.
Multiplying by 100 is the same thing as moving the decimal two places to the right.
Laura had 10 shirts she then bought 3 shirts each week for 4 weeks
If Laura had 10 shirts to begin with and then bought 3 shirts each week for 4 weeks, she would have:
10 + (3 x 4) = 22 shirts
After 4 weeks, she would have a total of 22 shirts.
At Bruno’s Video World, the regular price for a DVD is d dollars. How many DVDs can be purchased for x dollars when the DVDs are on sale at 20% off the regular price?
The number of DVDs can be purchased for x dollars = 5x/4d.
The correct answer is an option (e)
Here you have x dollars to spend.
The regular price for a DVD is d dollars.
We need to find the number of DVDs can be purchased for x dollars when the DVDs are on sale at 20% off the regular price.
To find number of DVDs can be purchased for x dollars, we must divide x by the sale price of a CD.
After 20% off, the sale price would be,
(100 - 20)% of d
= 80% of d
Using percentage formula, we can write 80 percent of d as,
80%d
= (80/100) × d
= (4/5)d .
So, we need to divide x by (4/5d) which is equal to 5x/4d.
Therefore, the correct answer is an option (e)
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The complete question is:
At Bruno’s Video World, the regular price for a DVD is d dollars. How many DVDs can be purchased for x dollars when the DVDs are on sale at 20% off the regular price?
a) 4/5x
b) 5/4x
c) 4/5d
d) 4x/5d
e) 5x/4d
Marley owns a music store. The first week a new album was released, he sold 800 copies at his store. Each week after the release, the number of copies sold decreased by 11%
Select all the functions that can be used to find the number of copies sold, f(n), n weeks after the release.
The correct options that shows the the functions that can be used to get the number of copies are:
f(1) = 800 , f(n) = 0.89 * f(n-1) n ≥ 2Option 2 is also correctHow to find the number of copiesfirst week sold 800 copies
∴ at n=1 ⇒⇒⇒ f(1) = 800
Each week the number of copies sold decreased by 11%.
∴ at n = 2 ⇒ f(2) = 800 * (1-.11) = 800 * 0.89 = f(1) * 0.89
at n = 3 ⇒ f(3) = 800 * 0.89 *0.89 = 800 * 0.89² = f(1) * 0.89 * f(2)
at n = 4 ⇒⇒⇒ f(4) = 800 * 0.89³ = f(1) * 0.89 * f(3)
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Three stages at a music festival are arranged in a triangle. The distances between the centers of each stage are given:
Stage A and Stage B: 100 yards
Stage B and Stage C: 135 yards
Stage C and Stage A: 210 yards
List the interior angle measures formed at the center of each stage from greatest to least.
The interior angle measures formed at the center of each stage at a music festival from greatest to least are as follow,
Stage A = 126.01° > Stage B =31.33° > Stage C = 22.66°
Shape of the arrangement of three stages at a music festival is triangle.
Distance between the centers of each stage are as follow,
Stage A and Stage B = 100 yards
Stage B and Stage C = 135 yards
Stage C and Stage A = 210 yards
For Interior angles,
Use the Law of Cosines, which states that for a triangle with sides a, b, and c and opposite angles A, B, and C,
c² = a² + b² - 2abcos(C)
Label the sides of the triangle formed by the three stages,
Side AB = 100 yards
Side BC = 135 yards
Side CA = 210 yards
Then, find the interior angles at each stage as follows,
At Stage A,
a = 210 yards (CA)
b = 100 yards (AB)
c = 135 yards (BC)
cos(A) = (b² + c² - a²) / (2bc)
⇒cos(A) = (100² + 135² - 210²) / (2 × 100 ×135)
⇒cos(A) = -0.5880
⇒A = arccos(-0.5880)
A = 126.01 degrees
At Stage B,
a = 100 yards (AB)
b = 135 yards (BC)
c = 210 yards (CA)
cos(B) = (a² + c² - b²) / (2ac)
⇒cos(B) = (100² + 210² - 135²) / (2 × 100 ×210)
⇒cos(B) = 0.8542
⇒B = arccos(0.8542)
⇒B = 31.33 degrees
At Stage C,
a = 135 yards (BC)
b = 210 yards (CA)
c = 100 yards (AB)
cos(C) = (a²+ b² - c²) / (2ab)
⇒cos(C) = (135² + 210² - 100²) / (2 × 135 × 210)
⇒cos(C) = 0.9228
⇒C = arccos(0.9228)
⇒ C = 22.66 degrees
Therefore, the interior angle measures formed at the center of each stage from greatest to least are,
Stage A = 126.01 degrees
Stage B =31.33 degrees
Stage C = 22.66 degrees
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A small radio transmitter broadcasts in a 40 mile radius. If you drive along a straight line from a city 55
miles north of the transmitter to a second city 51 miles east of the transmitter, during how much of the
drive will you pick up a signal from the transmitter?
miles
Answer:
We can use the Pythagorean theorem to find the distance between the transmitter and the second city:
c² = a² + b²
c² = 55² + 51²
c² = 3026
c ≈ 55.01
So the transmitter is about 55.01 miles away from the second city.
To determine how much of the drive will pick up a signal, we can draw a circle with a radius of 40 miles centered at the transmitter, and see which part of the line connecting the two cities is within this circle.
We can see that the line connecting the two cities intersects the circle at two points, forming a right triangle with one leg measuring 40 miles. We can use trigonometry to find the length of the other leg:
sin(theta) = opposite/hypotenuse
sin(theta) = 40/c
csin(theta) = 40
a = csin(theta)
a = 55.01*sin(theta)
Now we need to find the angle theta, which can be found using inverse tangent:
tan(theta) = opposite/adjacent
tan(theta) = 55/51
theta = tan⁻¹(55/51)
theta ≈ 49.72 degrees
So we can substitute this value of theta into the equation we found earlier for a:
a ≈ 43.89
Therefore, the length of the line segment within the circle is approximately 43.89 miles. To find the length of the entire line segment connecting the two cities, we can use the Pythagorean theorem again:
b² = c² - a²
b² = 55.01² - 43.89²
b ≈ 33.6
So the entire length of the line segment connecting the two cities is approximately 33.6 miles. Therefore, the portion of the drive during which you will pick up a signal from the transmitter is 43.89/33.6 = 1.31 hours or about 79 minutes.
Please help me solve my add math question
A result of 2 = 7 - = 7 - (-5) = 12 and = -5 is as follows as after combining similar terms , (2-μ)a + (u+1).
what is vectors ?A vector seems to be an object in mathematics that also has scale (or length) and motion. Arrows can be used to graphically depict vectors, with the arrow's trajectory denoting the vector's magnitude and its length denoting its direction. In order to construct a new vector with the a different magnitude but the same direction, vectors can be multiplied by a scalar (a real number) or joined together to make a resultant vector (or the opposite direction if the scalar is negative).
given
First, we can make the given equation simpler:
(2-μ)a + (u+1)
b = 7a - (2+2)b
2a - a + ub + + + b = 7a - 2b - 2b
combining similar terms
(2-μ)a + (u+1)
b = 7a - 4b
We currently have two equations:
2 - μ = 7 (1)
u + 1 = -4 (2) (2)
Equation (2) provides us with:
u = -5
Equation (1) is amended as follows:
2 - μ = 7
μ = -5
A result of 2 = 7 - = 7 - (-5) = 12 and = -5 is as follows as after combining similar terms , (2-μ)a + (u+1).
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The complete question is:-
The vectors a and b are not parallel and (2-μ)a + (u + 1)b = 7a-(2+2)b where λ and μ are scalars. Find the values of 2 and μ.
at 3:00 pm, andy began walking directly south from point a at a rate of 4 mi/h. at the same time, bill started walking directly west from point b to point a, at a rate of 5 mi/h. the distance between a and b is 9 miles. assume that both of them stop walking when bill reaches point a. at what time will be distance between andy and bill be minimized? round your answer to the nearest minute.
At 4:00 PM, the distance between Andy and Bill is minimal, about 6.04 miles apart.
Pythagorean theorem is used to find the distance between Andy and Bill at any point in time.
Suppose 3 t hours have passed.
12:00 am.
At that point, Andy moved a remove of 4 miles south from point A, and Charge moved a remove of 5 miles west of point B.
The separation between Andy and Charge is given by
[tex]D(t) = sqrt[(9 - 5t)^2 + (4t)^2][/tex]
To find the time when the distance between Andy and Bill is minimal, we need to find the value of t that minimizes D(t).
To do this, find the derivative of D(t) with respect to t, set it to zero, and solve for t.
dD/dt = (1/2)[2(9 - 5t)(-5) + 2(4t)*(4)]
= -45 + 16t
Setting dD/dt = 0 gives: -45 + 16t = 0
Solving for t gives: t = 45/16 ≈ 2.81 hours
Therefore, the time at which the distance between Andy and Bill is minimal is 3.
48 hours (rounded to the nearest minute).
Note that at this point Andy has traveled a remove of 42.81 = 11.24 miles south of point A, and Charge has traveled a remove of 52.81 = 14.05 miles west of point B.
The separations between them are:
[tex]D(2.81) = sqrt[(9 - 52.81)^2 + (42.81)^2] ≈ 6.04 miles[/tex]
therefore, At 4:00 PM, the distance between Andy and Bill is minimal, about 6.04 miles apart.
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