For u = (-6,8) and v = (7,1), the vector u can be written as the sum of two orthogonal vectors (-4.76, -0.68) and (-1.24, 8.68) where one is the projection of u onto v.
Explanation:First, we need to find the vector projection of u onto v. The formula to find the vector projection of u onto v is given by: projv(u) = [(u.v)/(v.v)] * v. Here '.' represents dot product of vectors.
So, substitute the given vectors u = (-6,8) and v = (7,1) into the formula.
Calculate dot product u.v = (-6*7) + (8*1) = -42 + 8 = -34 Calculate dot product v.v = (7*7) + (1*1) = 49 + 1 = 50 Substitute u.v and v.v in the formula: projv(u) = [-34 / 50] * (7,1) = (-4.76, -0.68).
This is one of the vectors. The other vector, orthogonal to v, is given by u minus the projection: u - projv(u) = (-6,8) - (-4.76, -0.68) = (-1.24, 8.68).
So, the vector u can be written as the sum of two orthogonal vectors (-4.76, -0.68) and (-1.24, 8.68).
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Find the value of x. Round to the nearest degree.
Answer:
x = 42
Step-by-step explanation:
sin theta = opposite / hypotenuse
sin x = 6/9
Take the inverse of each side
sin ^-1 sin x = sin ^-1 (6/9)
x =41.8103149
To the nearest degree
x = 42
Answer:
did u also u 3.14 as pie too help u cause that what u are going to have to do
A gopher has dug holes in opposite corners of a rectangular yard. One length of the yard is 8 meters and the distance between the gopher's holes is 10 meters. How wide is the yard?
The width of the yard is 6 meters, calculated using the Pythagorean theorem with one side as 8 meters and the other side as the unknown width.
We can use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the two sides of the triangle represent the length and width of the yard, and the hypotenuse represents the distance between the gopher's holes.
Let's denote the width of the yard as (w). According to the problem:
Length of the yard (L) = 8 meters
Distance between the gopher's holes (h) = 10 meters
Width of the yard ((w)) = ?
We can set up the following equation using the Pythagorean theorem:
[tex]\[ w^2 + 8^2 = 10^2 \][/tex]
[tex]\[ w^2 + 64 = 100 \][/tex]
[tex]\[ w^2 = 100 - 64 \][/tex]
[tex]\[ w^2 = 36 \][/tex]
[tex]\[ w = \sqrt{36} \][/tex]
[tex]\[ w = 6 \, \text{meters} \][/tex]
Therefore, the width of the yard is 6 meters.
Easy Question, Easy points
Topic: Volume
Answer:
about 141.37
Step-by-step explanation:
pi x 20 (h) x 1.5 (r)
radius is half of diameter :)
Answer:
141.37
Step-by-step explanation:
Would you mind giving me brainliest?
James goes to Walmart and spends, d, dollars. He has a coupon for 25% off. What is James total after the coupon is applied?
Answer:
c
Step-by-step explanation:
Solve the equation by completing the square. 0=x^2-14x+46
Answer:
x = 7+√(3), 7-√(3)
Step-by-step explanation:
x^2 - 14x + ___ = -46 + ___
x^2 - 14x + 49 = -46 + 49
(x-7)^2 = 3
√(3) = x-7
x = 7+√(3), 7-√(3)
The value of x is x = 7+√(3), 7-√(3)
What is completing the square method.?Completing the square means writing a quadratic in the form of a squared bracket and adding a constant if necessary.
Given:
x² - 14x ++46 = 0
x² - 14x ++46 + 7²- 7² = 0
x² - 14x + 7² +46 - 49 = 0
(x- 7)² - 3=0
(x- 7)² = 3
x = 7+√(3), 7-√(3)
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The equations x minus 3 y = negative 3, 2 x + y = 2, x + 3 y = 3, and 2 x minus y = negative 2 are shown on the graph below. On a coordinate plane, there are 4 lines. Green line goes through (0, 2) and (negative 1, 0). Blue line goes through (0, 2) and (1, 0). Pink line goes through (negative 1.5, 1.5), and (1.5, 0.5). Orange line goes through (negative 1.5, 0.5) and (1.5, 1.5). Which system of equations has a solution of approximately (–0.4, 1.1)? x + 3 y = 3 and 2 x minus y = negative 2 x minus 3 y = negative 3 and 2 x + y = 2 x minus 3 y = negative 3 and 2 x minus y = negative 2 x + 3 y = 3 and 2 x + y =2
Answer:
(A)x+3y=3 and 2x-y=-2
Step-by-step explanation:
In the attached graph
Green line is the graph of 2x-y=-2Red line is the graph of x-3y=-3Orange line is the graph of x+3y=3Blue Line is the graph of 2x+y=2The point of the intersection of the orange and green line has an approximate solution of (-0.4,1.1).
Therefore, the system of equation which has the approximate solution is: x+3y=3 and 2x-y=-2
The correct option is A
Answer:
A
Step-by-step explanation:
Paul, who is standing 150 feet above the water on a balcony of a cruise ship,
sees two boats located due north. The angles of depression from Paul
to the boats are 33
and 22°
Find the distance between the two boats to the nearest tenth of a foot.
Answer:140.3
Step-by-step explanation:
Answer:
140.3
Step-by-step explanation:
A family of four spent $104 for tickets to a concert on Friday and they spent $140 for tickets to dinner theater on Saturday.What was the cost per person to attend these events
Answer:
$61
Step-by-step explanation:
To determine the cost per person to attend these events, you have to add the cost of the tickets for the concert plus the cost of the tickets for dinner theater. After finding the total amount that was spent, you have to divide this by 4 that is the number of people:
Total cost= $104+$140
Total cost= $244
Cost per person= $244/4
Cost per person= $61
According to this, the cost per person to attend these events is $61.
Answer:
Cost of first event: $26 per person
Cost of second event: $35 per person
Cost of both events together: $61 per person
Step-by-step explanation:
In the first event, the four people spent $104, so the cost per person of this event is:
104 / 4 = $26
Each person pays $26 for this event.
For the second event, the four people spent $140, so the cost per person of this event is:
140 / 4 = $35
The cost per person to attend both events together is:
26 + 35 = $61
Which ratio is equivalent to 3:3?
The ratio 3:3 signifies equality between two quantities and an equivalent ratio can be found by scaling both parts by the same number. Dividing both parts by 3 gives us the simplest form, which is 1:1.
Explanation:A ratio compares two quantities and can be written in various forms such as fractions, with a colon, or with the word "to". The ratio 3:3 is an expression comparing two equal quantities. To find an equivalent ratio, we can simplify or scale the ratio by multiplying or dividing the numerator and denominator (the two parts of the ratio) by the same number.
In this case, dividing both parts of the ratio 3:3 by 3 gives us an equivalent ratio of 1:1, which also represents equality between two quantities. Multiplying both parts by a common number will also produce an equivalent ratio. For example, multiplying 3:3 by 2 gives us 6:6, which is still equivalent. It's essential to maintain the equality of the two parts when finding an equivalent ratio.
Ratios can be applied to various situations, including unit conversions, scale factors, proportions, and comparisons in scientific experiments, such as the ratio of amplitudes in a double-slit experiment in Physics.
Factor completely.
5
x
2
−
20
x
+
20
=
5x
2
−20x+20=5, x, squared, minus, 20, x, plus, 20, equals
Show Calculator
Answer:
[tex]5(x-2)^2[/tex]
Step-by-step explanation:
[tex]5x^2-20x+20=\\5(x^2-4x+4)=\\5(x-2)^2[/tex]
In Johnny's bowl there are many type of stones 1/8 of the stones are red and 5/6 of the stones are white what fraction of Johnny's stones are white or red
Answer:
[tex]\frac{23}{24}[/tex]
Step-by-step explanation:
1/8 of the stones in Johnny's bowl are red and 5/6 of the stones are white.
The fraction of stones that are red or white is obtained by adding the fraction that are red with the fraction that are white. That is:
[tex]\frac{1}{8} + \frac{5}{6} = \frac{23}{24}[/tex]
The fraction of the stones that are red or white is [tex]\frac{23}{24}[/tex].
Follow below steps:
The fraction of Johnny's stones that are white or red can be calculated by adding the fractions of white and red stones.
Given that 1/8 of the stones are red and 5/6 of the stones are white:
Red stones: 1/8
White stones: 5/6
Total fraction of white or red stones: 1/8 + 5/6 = 5/24 + 20/24 = 25/24
Since the total is greater than 1, it indicates a mistake in the initial information provided.
help me please will give brainlest
Answer:
Data Set 2, seventh graders:
Center: The median value is 54. (Count to the middle: it's the tenth value.) The set is bimodal, with modes at 53 and 55. (The mode is the number that occurs most frequently.)
Shape: The set looks to be fairly symmetrical, though data lies closer to the right than the left.
Spread: The range is 60-50 = 10, so it's less spread out than the sixth graders.
Solve the equation 2x-1=13.
Answer:
7
Step-by-step explanation:
2 time 7 = 14-1 = 13
Answer:
x=7
Step-by-step explanation:
Collect like terms
2x=13+1.
2x=14
Divide both side by 2
[tex] \frac{2x}{2} = \frac{14}{2} [/tex]
x=7
MEC makes a big family tent in the shape of a symmetrical triangular prism. The floor of the tent is 5 m long and 2.5 m wide. The peak of the tent is 1.9 m off the ground. The diagonal sides of the tent are 2.3 m long.
a) Draw a picture of the tent with dimensions
b) Polyurethane is a sheet material that is fairly waterproof and lightweight. It is sold in sheets of any area you desire. How much polyurethane was needed to make the tent? (remember: The bottom of the tent needs material to keep your sleeping bag dry)
c) How much space is there inside the tent? Predict how many people that might fit!?
* SHOW how you would you calculate that
d) MEC also sells an extra-waterproof fly made of polyester (every time I’ve camped it has snowed or rained…). The fly only covers the top and ends of the tent. How much polyester material is needed to make the fly?
Answer:
15,236 sq in
Step-by-step explanation:
First, you have to split the net into three rectangles and two triangles
step 1
triangular base area
1/2 bh = 1/2 (44 in)(64 in)
= 1/2 (2,816 sq in)
= 1,408 sq in.
2 x 1,408 sq in = 2,816 sq in.
step 2
end rectangle area
lw = (68 in)(69 in)
= 4,692 sq in
2 x 4,692 sq in = 9,384 sq in
Now find the area of the middle rectangle
lw - (69 in) (44 in) = 3,039 sq in.
then add all the areas together
2,816 + 9,384 + 3,036 = 15,236 sq in
Hope this helps :)
A random sample of 100 people from region A and a random sample of 100 people from region B were surveyed about their grocery-shopping habits. From the region A sample, 16 percent of the people indicated that they shop for groceries online. From the region B sample, 24 percent of the people indicated that they shop for groceries online. At the significance level of α=0.05, do the data provide convincing statistical evidence that there is a difference between the two regions for the population proportions of people who shop online for groceries? Complete the appropriate inference procedure to support your answer.
Answer:
Step-by-step explanation:
This is a test of 2 population proportions. Let a and b be the subscript for people from region A and region B. The population proportions would be pa and pb
pa - pb = difference in the proportion of people from region A and region B.
The null hypothesis is
H0 : pa = pb
pa - pb = 0
The alternative hypothesis is
H1 : pa ≠ pb
pa - pb ≠ 0
it is a two-tailed test
Sample proportion = x/n
Where
x represents number of success
n represents number of samples
For region A,
xa = 16
na = 100
pa = 16/100 = 0.16
For region B,
xb = 24
nb = 100
pb = 24/100 = 0.24
The pooled proportion, pc is
pc = (xa + xb)/(na + nb)
pc = (16 + 24)/(100 + 100) = 0.2
1 - pc = 1 - 0.2 = 0.8
z = (pa - pb)/√pc(1 - pc)(1/na + 1/nb)
z = (0.16 - 0.24)/√(0.2)(0.8)(1/100 + 1/100) = - 0.08/√0.0002891223
z = - 1.41
Since it is a 2 tailed test, we would find the p value by doubling the area to the left of the z score to include the area to right.
Area to the left from the normal distribution table is
0.07927
P value = 0.07927 × 2 = 0.16
Since 0.05 < 0.16, we would accept the null hypothesis
Therefore, the data does not provide convincing statistical evidence that there is a difference between the two regions for the population proportions of people who shop online for groceries.
Final answer:
To determine if the differences in grocery shopping habits between two regions are statistically significant, a two-proportion z-test is conducted. We first state the null and alternative hypotheses, calculate the test statistic, find the p-value, and make a decision based on the significance level of 0.05.
Explanation:
To evaluate if there is a significant difference between the population proportions of people who shop online for groceries in two regions, we need to conduct a two-proportion z-test. The steps are as follows:
State the null and alternative hypotheses. The null hypothesis (H₀) is that there is no difference in the proportions of people who shop online for groceries in the two regions (p₁ = p₂). The alternative hypothesis (Ha) is that there is a difference (p₁ ≠ p₂).Calculate the test statistic using the formula for the two-proportion z-test. To compute this, we first find the pooled proportion, which combines the successes and total sample sizes from both regions.The p-value is then determined based on the calculated z-score. This p-value represents the probability of observing a test statistic as extreme as, or more extreme than, the observed result, under the assumption that the null hypothesis is true.Decide to reject or not reject the null hypothesis by comparing the p-value to the significance level (α = 0.05). If the p-value is less than α, we reject the null hypothesis, indicating sufficient evidence to say there is a significant difference in the proportions.In this scenario, with 16% of 100 people from Region A and 24% of 100 people from Region B indicating they shop for groceries online, a two-proportion z-test will reveal if the observed difference is statistically significant at the 0.05 level.
Triangle A B C is shown. Angle A B C is a right angle. The length of hypotenuse A C is 9, the length of B C is 2, and the length of A B is 8.77. Law of cosines: a2 = b2 + c2 – 2bccos(A) What is the measure of AngleC to the nearest whole degree? 70° 77° 80° 85°
Answer:
answer is B 77
Step-by-step explanation:
got it right on edg 2020-2021
The nearest whole degree is 77
What are trigonometric functions?In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.
Given here: ABC is a right angle triangle AC=9, BC=2 and AB=8.77
The formula for law of cosines is given by a²=b²+c²-2bcosA
81=4+76.9129-2×2cos A
0.0871=-4Cos A
cos A=-0.21775
A=77.43208
Hence, The nearest whole degree is 77
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what is the slope of y= 2/3x + 4
Answer:
2/3
Step-by-step explanation:
m is the variable for slope
the equation of a line
is y=mx+b
the slope is next to the x
Answer:
[tex]slope = \frac{2}{3} [/tex]
Step-by-step explanation:
[tex]Think \: of \: y = mx + b \\ \\ m\: is \: the \: slope \\ b \: is \: the \: y \: intercept \\ \\ So, \: since \: \frac{2}{3} \: is \: on \: the \: m \: the \: slope \: is \\ \frac{2}{3}[/tex]
please help me!!!
find the arc length of partial circle.
Either enter an exact answer in terms of n pi or use 3.14 for n pi and enter as a decimal.
* This is from Khan academy and the lesson is (Circumstance of part of circles)*
Answer: 1.57
Step-by-step explanation:
When solving for the arc you have to find the circumference.
For circumference you'll need the diameter which is 2x the radius.
So, your equation would be
1/4{(pi)(2)} = x
or
1/4{(3.14)(2)} = x
To Solve:
3.14 times 2 equals 6.28
Divide by 4 or multiply by 1/4 to get 1.57
Not sure if this is correct, I haven't learned the topic myself, but this week's to be there most reasonable way to look at it. For me anyway.
The arc length of a partial circle can be calculated using the formula Arc length = (θ/360) * 2πr, where 'θ' is the angle of the sector in degrees and 'r' is the radius of the circle. This is applicable in high school Mathematics.
Explanation:The subject of your question is the arc length of a partial circle, a concept in Mathematics. The arc length of a partial circle can be calculated using the formula: Arc length = (θ/360) * 2πr, where 'θ' is the angle of the sector in degrees and 'r' is the radius of the circle.
For instance, if a circle has a radius of 8 units and the angle of the sector is 60 degrees, the arc length can be calculated as follows: Arc length = (60/360) * 2 * 3.14 * 8 = 8.38 units (in terms of 3.14 for n π). Using n π, the exact answer would be expressed as: Arc Length = 4π/3 units.
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Below is the graph of f '(x), the derivative of f(x), and has x-intercepts at x = -3, x = 1 and x = 2. There are horizontal tangents at x = -1.5 and x = 1.5. Which of the following statements is true?
f has a relative minimum at x = 1.5.
f has a relative maximum at x = -1.5.
f is decreasing on the interval from x = 1 to x = 2.
None of these is true.
Thank you in advance!
Answer:
f is decreasing on the interval from x = 1 to x = 2.
Step-by-step explanation:
f has a relative minimum when f' changes signs from - to +.
f has a relative maximum when f' changes signs from + to -.
f is decreasing when f' is negative.
f' is not changing signs at x=-1.5 or x=1.5, so neither of these are minimums or maximums of f. However, f does have relative minimums at x=-3 and x=2, and a relative maximum at x=1
f' is negative between x=1 and x=2. So f is decreasing in this interval.
Latoya made $306 for 17 hours of work.
At the same rate, how many hours would she have to work to make $ 162?
hours
Answer:
9 hours of work
Step-by-step explanation:
306/17 = 18 per hour
so 162/18 = 9
Answer:
9 hours
Step-by-step explanation:
We can make a proportion and solve
She makes $306 for 17 hours of work,and she makes $162 for x hours of work
306/17=162/x
Cross multiply
306*x=17*162
306x=2754
Now we need to solve for x, by getting x by itself. x is being multiplied by 306; to undo this, divide both sides by 306
306x/306=2754/306
x=9
So, she needs to work 9 hours to make $162
A point is chosen at random in the larger circle. What percent of the time will the point be in the shaded region? Round to the nearest tenth of a percent. Please help me!!
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached image for the step by step explanation of the answer to the question
Simplify (−2x3+9)(8x2+6x+1)
Answer:
-16x^4 - 12x^3 + 70x² + 54x + 9
Step-by-step explanation:
(-2x² + 9)(8x² + 6x + 1)
-16x^4 - 12x^3 -2x² + 72x² + 54x + 9
-16x^4 - 12x^3 + 70x² + 54x + 9
I am pretty sure that this is the answer.
Tell me if I am wrong.
Can I get brainliest
Sorry, It wont let me put my answer.
What is the probability of getting three tales
Answer:
12.5%
Step-by-step explanation:
Answer:
[tex]\frac{1}{8}[/tex].
Step-by-step explanation:
To solve this, we will first need to think about the probability of getting "tails". A coin has two sides, meaning landing on "tails" would result in a probability of [tex]\frac{1}{2}[/tex] per toss.
In the question, a total of 3 tosses is given. This means we will need to multiply the probability 3 times:
[tex]\frac{1}{2}[/tex] ×[tex]\frac{1}{2}[/tex] ×[tex]\frac{1}{2}[/tex] = [tex]\frac{1}{8}[/tex] .
the jedi have a weapon that can shoot a projectile 20 miles. find the area that the projectile can land in.
Answer:
The area he can cover with that weapon is 1,256 miles².
Step-by-step explanation:
Assuming that the Jedi won't move and that he can shoot in every direction, he'd be shooting at a circle with a radius of 20 miles. Therefore the are that he can cover with that weapon is the area of the circle, which is shown below:
area = pi*r²
area = 3.14*(20)²
area = 3.14*400
area = 1,256 miles²
The area he can cover with that weapon is 1,256 miles².
The area a projectile can land in can be determined by considering the distance the missile can travel as the circle's radius. The area of this circle, calculated by the formula A = πr², is the area the shell can land in.
Explanation:The area where the projectile can land is determined by considering the weapon as the centre of a circle and the possible distance it can travel as the radius. This forms a circular area where the projectile can land. The area A of a process is calculated using the formula A = πr², where r is the circle's radius.
Here, our radius is 20 miles, the distance the projectile can travel. Therefore, we substitute this distance into our formula to find the area:
A = π(20)²
Calculating the above will give you the area that the projectile can land in.
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In the function y = 5x, what is the value of x?
The value of x in the given question is: x = y/5
How to change the subject of the formula?
We are given that the function for getting y is:
y = 5x
Now, to make x the subject of the formula, we will use division property of equality to divide both sides by 5 to get:
y/5 = 5x/5
x = y/5
Thus, the value of x in the given question is:
x = y/5
This is a really easy question Just need to make sure it is right. Is it B
When you send mail via the post office, you have an 80% chance that it is
delivered to the correct location. (Use this information to answer questions #3 &
#4 below.)
Your answer
1. On Monday, about 86 letters were delivered incorrectly out of 430.
2. On Tuesday, approximately 625 letters were delivered in total.
1. For Monday:
Given an 80% chance of delivering correctly, the expected number of letters delivered incorrectly is 20% of 430:
[tex]\[ 0.20 \times 430 = 86 \text{ letters} \][/tex]
2. For Tuesday:
If 500 letters were delivered correctly, it means 100% - 80% = 20% were delivered incorrectly. So, the total number of letters delivered is:
[tex]\[ \frac{100}{80} \times 500 = 625 \text{ letters} \][/tex]
Complete Question:
What’s the answer ??????
Answer:
The best estimate is 100 per month
Step-by-step explanation:
Take 618 and divide by 6 to get the exact amount
We want an estimate
Round 618 to 600
600/6 = 100
Answer:
A
Step-by-step explanation:
It is $100
An equilateral triangle has a perimeter of 15x3 + 33x5 feet. What is the length of each side?
Answer:
70
Step-by-step explanation:
So I assumed that the x was multiplication...so...15x3=45 and 33x5=165...so the perimeter is 210, so you divide that by 3 and the answer is 70!
there are 300 student and teachers at a sports event.Grade k to 2 is students: 137 Grade 3 to 5 students: 145 Teachers: ? what is the percentage of teachers at the sports event.
Answer:
6%
Percentage of teachers = 6%
Step-by-step explanation:
Given;
Number of grade k-2 students = 137
Number of grade 3-5 students = 145
Total = 300
Number of teachers = 300 - (137+145) = 18
Percentage of teachers = (number of teachers÷total)× 100%
%T = (18/300) × 100
%T = 6%