Find the scalar and vector projections of b onto
a.a = i + j + k, b = i - j + k
Answers
1 is for scalar (result is number), 2 is for vector (result is vector).
Related Questions
What percent is 6 out of 7?
Answers
To find the percentage, move the decimal point two place values to the right
85.71% is your answer
hope this helps
You have a bag of 42 candies you want to give to your 6 friends. the company that makes the candies guarantees that exactly 6 of the candies in the bag are red, the most delicious color. anyone who doesn't get a red candy will be so upset that they will stop being your friend! but the candies are in identical wrappings, so you are forced to give each friend 7 candies and hope for the best. what's the probability you lose one or more friends?
Answers
Final answer:
To calculate the probability of losing one or more friends, we need to calculate the probability that a friend does not get a red candy and multiply it by the number of friends. The probability is 0.458.
Explanation:
To answer this question, we need to calculate the probability that at least one friend will not get a red candy.
First, let's calculate the probability that a friend does not get a red candy. There are 42 candies in the bag and 6 of them are red. So, the probability that a friend does not get a red candy is (42-6)/42 = 36/42 = 6/7.
Since each friend gets 7 candies, the probability that one friend does not get a red candy is (6/7)^7, because each candy is independent. Finally, since there are 6 friends, we multiply the probability by 6 to get the probability that at least one friend does not get a red candy: 6 * (6/7)^7 = 0.458 (rounded to 3 decimal places).
Consider the function f(x) = x2 + 12x + 11. x-intercepts: 0 = x2 + 12x + 11 0 = (x + 1)(x+ 11) y-intercept: f(0) = (0)2 + 12(0) + 11 What are the intercepts of the function? The x-intercepts are . The y-intercept is .
Answers
Then we can respond more easily to the questions.
We have then:
x-intercepts:
0 = x2 + 12x + 11
0 = (x + 1) (x + 11)
From here, we conclude:
x = -1
x = -11
y-intercept:
f (0) = (0) 2 + 12 (0) + 11
From here we conclude:
y = 11
Answer:
The x-intercepts are
x = -1
x = -11
The y-intercept is
y = 11
Answer:
the x-intercepts are (-1,0) and (-11,0), the y-intercept is (0,11).
Wilt and bill, two basketball players, are having a free throw shooting contest. wilt is known to make 75% of his free throws, and bill is known to hit 85% of his free throws. each of them takes 50 shots. assuming that the shots are independent, what is the probability that bill hits a higher percentage of his shots than wilt?
Answers
[tex] \sqrt{(0.75 * 0.25) / 50 + (0.85 * 0.15) / 50) } [/tex] =0.0794
P(z> (0-0.1) / 0.0794)
P(z> -1.26) = 0.8962
The probability Bill hits a higher percentage than Wilt in free throws is approximately 0.0085, or 0.85%.
To find the probability that Bill hits a higher percentage of his shots than Wilt, we can use the concept of binomial distributions.
Step 1 :Let's denote:
- [tex]\( W \)[/tex] as the number of successful shots Wilt makes out of 50,
- [tex]\( B \)[/tex] as the number of successful shots Bill makes out of 50.
Since Wilt makes 75% of his free throws and Bill makes 85% of his free throws, we can calculate the expected number of successful shots for each:
- For Wilt: [tex]\( E(W) = 50 \times 0.75 = 37.5 \)[/tex]
- For Bill: [tex]\( E(B) = 50 \times 0.85 = 42.5 \)[/tex]
Now, we can use the normal approximation to the binomial distribution to calculate the probability that Bill hits a higher percentage of his shots than Wilt. We'll assume that both distributions are approximately normal due to the central limit theorem.
The standard deviation for each player's distribution can be calculated as:
- For Wilt: [tex]\( \sigma_W = \sqrt{n \times p_W \times (1-p_W)} = \sqrt{50 \times 0.75 \times 0.25} \)[/tex]
- For Bill: [tex]\( \sigma_B = \sqrt{n \times p_B \times (1-p_B)} = \sqrt{50 \times 0.85 \times 0.15} \)[/tex]
Step 2 :Now, we can calculate the probability using a normal distribution:
[tex]\[ P(B > W) = P\left(Z > \frac{{E(B) - E(W)}}{{\sqrt{\sigma_B^2 + \sigma_W^2}}}\right) \][/tex]
Where [tex]\( Z \)[/tex] is a standard normal random variable.
Calculating:
[tex]\[ P(B > W) = P\left(Z > \frac{{42.5 - 37.5}}{{\sqrt{50 \times 0.85 \times 0.15 + 50 \times 0.75 \times 0.25}}}\right) \][/tex]
[tex]\[ P(B > W) = P(Z > 2.3717) \][/tex]
Using a standard normal distribution table or calculator, we find that [tex]P(Z > 2.3717) \approx 0.0085 \).[/tex]
So, the probability that Bill hits a higher percentage of his shots than Wilt is approximately 0.0085, or 0.85%.
Find the supplementary angle of 116 degrees.
Answers
Part A: Solve -np 70 < 40 for n. Show your work. (4 points)
Part B: Solve 4w -7k 28 for k. Show your work. (6 points)
Answers
-np - 70 < 40
+70
-np < 110
-n < 110/p
Part B
4w-7k=28
-7k=28-4w
7k=4w-28
k=4/7w-4
How do you write the equation of Mary has 10 roses John has 2 less
Answers
John has 2 less
so,
J = M - 2
you can solve by plugging in
J = 10 - 2
J = 8
He has 8 roses
To check:
8 =?= 10 - 2
8 = 8
Hope this helps
What is the value of x in the diagram below?
A 30
B 60
C 90
D 120
could you please explain how you get the answer thank you so much.
Answers
180-120=60degrees
therefore the bottom most angle = 60degrees
angles opposite each other are equal
so angle opposite the bottom most is 60degrees
if angles on a straight line =180degrees :
square angle=90degrees
90+60=150degrees
180degrees-150degrees= 30degrees
Therefore the answer is A) 30
The current population of a city can be represented by p. the population is expected to increase by 6.5% next year. Write a expression in simplest form that represents the expected population next year
Answers
f(x) = a*b^x, where a is the original population, b = 1 + the rate of growth (written as a decimal number), and x is the amount of time. In our case we have
p(1 + 0.065)^1
= p(1.065) = 1.065p
The expression in the simplest form that represents the expected population next year will be 1.065p.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as
y = a(b)ˣ
The ongoing populace of a city can be addressed by p. the populace is supposed to increment by 6.5% one year from now.
The expression in the simplest form that represents the expected population next year will be given as,
⇒ p(1 + 0.065)
⇒ 1.065p
The expression in the simplest form that represents the expected population next year will be 1.065p.
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A researcher measured the heights of forty high-school students. The measurements are recorded here.
Heights (in inches)
58 59 60 60 60 61 61 61 61 62
62 62 62 62 62 63 63 63 64 65
67 67 68 68 68 68 69 69 70 70
70 71 71 71 71 71 72 73 74 76
If Alyssa's height is in the 45th percentile within the group, what is her height in inches?
Answers
Answer:
64
Step-by-step explanation:
i just know
Find the sum of the arithmetic sequence. 5, 7, 9, 11, ..., 23
Answers
The answer is 140, you just add them up and it goes by 2.
A class had 30 pupils at the beginning of this school term, but now has 5 more pupils. What is the percent of increase?
Answers
Explanation:
You need to learn how to calculate percent to be able to perform this type of problems by yourself.
Percent is the ratio of a quantity on base to 100 parts.
In this case the increase is 5 students of an initial group of 30, so you need to find the equivalent expression with a base of 100 instead of 30. That is, you need to find the ratio with denominator 100 equivalent to the ratio 5/30:
x 5
------ = ----
100 30
=> x = (5 / 30) * 100 = 16.67%.
Also, you should notice that calculatind the percent is done dividing the parts by the whole and multiplying by 100, i.e. (5 / 30) * 100, which is the same done above.
The circumference of a circle is 60π cm. What is the length of an arc of 140°? 11.7π cm 16.1π cm 23.3π cm 29.5π cm
Answers
Answer:
c = 23.3
Step-by-step explanation:
Answer:
[tex]23.3 \pi[/tex] cm
Step-by-step explanation:
Circumference of circle = [tex]2 \pi r[/tex]
The circumference of a circle is 60π cm.
So, [tex]2 \pi r=60 \pi[/tex]
[tex]2r=60[/tex]
[tex]r=30[/tex]
Formula of length of arc = [tex]2 \pi r \times \frac{\theta}{360}[/tex]
Length of arc = [tex]2 \pi \times 30 \times \frac{140}{360}[/tex]
Length of arc = [tex]23.3 \pi[/tex]
So, Option C is true
Hence Length of arc is [tex]23.3 \pi[/tex] cm
Select each equation that has NO real solution!
Answers
To determine equations with no real solutions, assess for a negative discriminant or no x-intercepts in quadratic equations. Steps include identifying unknowns, choosing appropriate equations, simplifying terms, and checking for reasonableness.
Explanation:To select each equation that has NO real solution, we must assess the equations provided, looking for specific characteristics that indicate the absence of real solutions. One of the hallmarks of such equations is when they represent a quadratic equation with no x-intercepts or the discriminant (b^2 - 4ac) in the quadratic formula is negative, which means the roots are complex numbers.
When working on problems like these, it's crucial to go through several steps: Identify the unknown, identify the knowns, choose an equation, eliminate terms to simplify the algebra, and then check the answer to see if it is reasonable.
Let's use an example equation: x^2 + 4 = 0. To determine if this has real solutions, we can identify the unknown (x), the knowns (coefficients of x), solve the equation or calculate the discriminant (4^2 - 4*1*-4 = 16 +16 = 32, which is positive), and confirm whether the solutions are real or not. In this case, because the discriminant is positive, this equation does have real solutions, and therefore would not be included in a list of equations with no real solutions.
The equations 2x² - 4x + 5 = -3, x² - 12x + 60 = 12, and x² + 3x + 6 = 0 have no real solutions, based on their negative discriminants.
We need to determine the discriminant (b² - 4ac) of each equation to check for real solutions. A negative discriminant indicates no real solutions.
Equations Analysis
2x² + 2x = 2: Rewrite as 2x² + 2x - 2 = 0. Here, a = 2, b = 2, c = -2. The discriminant is 2² - 4(2)(-2) = 4 + 16 = 20 (positive, so there are real solutions).2x² - 4x + 5 = -3: Rewrite as 2x² - 4x + 8 = 0. Here, a = 2, b = -4, c = 8. The discriminant is (-4)² - 4(2)(8) = 16 - 64 = -48 (negative, so there are no real solutions).x² - 12x + 60 = 12: Rewrite as x² - 12x + 48 = 0. Here, a = 1, b = -12, c = 48. The discriminant is (-12)² - 4(1)(48) = 144 - 192 = -48 (negative, so there are no real solutions).x² - 4 = 0: This is already in quadratic form with a = 1, b = 0, c = -4. The discriminant is 0² - 4(1)(-4) = 16 (positive, so there are real solutions).x² + 3x + 6 = 0: Here, a = 1, b = 3, c = 6. The discriminant is 3² - 4(1)(6) = 9 - 24 = -15 (negative, so there are no real solutions).Equations with No Real Solutions
2x² - 4x + 5 = -3x² - 12x + 60 = 12x² + 3x + 6 = 0Complete Question - Select each equation that has no real solution.
2x² + 2x = 22x² - 4x + 5 = -3 x² - 12x + 60 = 12 x² - 4 = 0 x² + 3x + 6 = 0Which statements are true about the regular polygon? Check all that apply. The sum of the measures of the interior angles is 900°. Each interior angle measures 108°. All of the angles are congruent. The polygon is a regular hexagon. The sum of the measures of the interior angles is 180(5 – 2)°.
Answers
the figure shown is a regular pentagon------> is a polygon with five sides and equal angles
the sum of the measures of the interior angles is=180*(n-2)=180*(5-2)=540°
all 5 angles are 540°/5=108º
we have that
1) The sum of the measures of the interior angles is 900°----> is not true
2) Each interior angle measures 108°------> is true
3) All of the angles are congruent---------> is true
4) The polygon is a regular hexagon-----> is not true
5) The sum of the measures of the interior angles is 180(5 – 2)°----> is true
the answer are
2) Each interior angle measures 108°------> is true
3) All of the angles are congruent---------> is true
5) The sum of the measures of the interior angles is 180(5 – 2)°----> is true
Answer: 2,3,5
Step-by-step explanation:
Use the drop-down menus to choose steps in order to correctly solve
5m – 8 = 3m + 8 for m.
Answers
5m-8=3m+8
Add 8 to both sides.
5m= 3m+16
Subtract 3m on both sides.
2m=16
Divide 2 on both sides.
m=8
I hope this helps!
~kaikers
Answer:
m=8
Step-by-step explanation:
on imagine 2021
Click on the graph to choose the best match of the graphed quadratic equation. F(x) = x 2 + 4x
Answers
The required graph of the quadratic function is the parabola shown in the attachment.
Given that,
To determine the graph to the best match of the graphed quadratic equation. F(x) = x² + 4x.
A parabola is a cross-section cut out of the cone and represented by an equation.
What is a graph?
The graph is a demonstration of curves that gives the relationship between the x and y-axis.
Here,
The given equation represents the parabola with vertex at (-2, - 5).
and a graph of the parabola is attached below.
Thus, the required graph of the quadratic function is the parabola shown in the attachment.
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A winter sport passed at Wood Middle school costs $15. A stydent without a pass must pay $1.75 for each event. How many events would a student have to attend to pass a better deal?
Answers
Answer:
9
Step-by-step explanation:
15 divided by 1.75 equals 9.
And in order to double check, we multiply 9 and 1.75 together which equals 15.75.
24 red marbles is 40% of how many marbles
Answers
Answer:
60 marbles
Step-by-step explanation:
Given: 24 red marbles is 40% of how many marbles
Let number of marbles be x
"24 red marbles is 40% of how many marbles"
24 = 40% of x
solve for x
First change % to decimal
24 = 0.40x
Division property of equality, divide by 0.04 both sides
x = 24÷0.40
x = 60
Hence, 40% of 60 is 24
Minnie and Tori combined ate nine pieces of the wedding cake Mindy ate 3 pieces of the wedding cake Tori have one fourth of the total kick write an expression to determine how many pieces of cake C there was in total
Answers
In order for us to solve this problem, we will require to set up an expression which can be solved later. I will also be attaching an image that shows all the work that was done in order to achieve the answer. Make sure to look over it in case you still don't understand something.
Minnie and Tori ate 9 pieces of cake. We know that Minnie ate 3 pieces of cake, and Tori ate one fourth, or in other words, 25%. Let's form an expression to find out how much Tori ate. We can do this by subtracting the amount of pieces Minnie ate out of the total amount of pieces eaten.
[tex]9-3=6[/tex]
Great! Tori ate 6 pieces of cake, which accompany for 25% of the cake. We are looking for the total amount of cake pieces, meaning that we need to know 100% of it. Let's form a ratio that we can solve.
[tex] \frac{25}{6} : \frac{100}{x} [/tex]
In order for us to solve the ratio above, we need to find out how many times can 25 fit in 100, and multiply our denominator by that value.
[tex]6( \frac{100}{25} )[/tex]
[tex]6(4)=24[/tex]
Awesome! We now know our final answer.
Answer: 24 cake pieces are in the cake.
Assume that the probability of error-free transmission of a message over a communication channel is . if a message is not transmitted correctly, a retransmission is initiated. this procedure is repeated until a correct transmission occurs. such a channel is often called a feedback channel. assume that successive transmissions are independent.
a. what is the probability that no retransmissions are required? (note that the number of retransmissions is the number of transmissions minus one.)
Answers
Answer:
Let the probability of error-free transmission of a message over a communication channel is P.
Then the Probability of Retransmission is =1-P
Now the question is Probability when no retransmission is required
= Probability of error free transmission in first attempt
=P
Now , suppose after first failure error free transmission takes place.
Since events are independent.
∵P[error free transmission after a failure ]= P[1-P]
If after two attempts error free transmission takes place
then P[ error free transmission after two failures]= P [1-P]²
So, For after n failures
P[error free transmission after n failure]=P[tex][1-p]^n[/tex]
A line with a slope of 2 passes through (3,9) Which choice is an equation of this line?
Answers
[tex]y - 9 =2(x - 3)[/tex]
l
Or
[tex]2x - y + 3 = 0[/tex]
Or
[tex]y = 2x + 3[/tex]
EXPLANATION
The given line has slope,
[tex]m = 2[/tex]
and
[tex](3,9)[/tex]
We can find the equation in the point slope form, which is given by,
[tex]y-y_1=m(x-x_1)[/tex]
We substitute the point and slope to get,
[tex]y - 9 =2(x - 3)[/tex]
We can also simplify further to get,
[tex]y - 9 = 2x - 6[/tex]
We make y the subject to get,
[tex]y = 2x - 6 + 9[/tex]
[tex]y = 2x + 3[/tex]
This is called the slope intercept form.
We could also write in standard form to get
[tex]2x - y + 3 = 0[/tex]
Or
[tex]2x - y = - 3[/tex]
The equation of the line with a slope of 2 passing through the point (3, 9) is y = 2x + 3.
The equation of a line with slope (m) passing through a point (x₁, y₁) is given by the point-slope form:
y - y₁ = m(x - x₁)
The slope (m) is 2, and the point (x₁, y₁) is (3, 9). Plug these values into the equation:
y - 9 = 2(x - 3)
Now, you can simplify this equation:
y - 9 = 2x - 6
To isolate y, add 9 to both sides:
y = 2x - 6 + 9
y = 2x + 3
Therefore, the equation of the line with a slope of 2 passing through the point (3, 9) is y = 2x + 3.
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Akule borrowed $1500 at an annual simple interest rate of 12%. He paid $270 in interest. For what period of time did Akule borrow money
Answers
Using the simple interest formula I = PRT, it is calculated that Akule borrowed $1500 at an annual interest rate of 12% for 1.5 years to pay $270 in interest.
Explanation:The subject of this question is Mathematics, specifically focusing on simple interest calculation. To find out the period of time Akule borrowed money for, we can use the simple interest formula I = PRT, where I is the interest paid, P is the principal amount borrowed, R is the annual interest rate, and T is the time in years. Akule paid $270 in interest on a $1500 loan at 12% annual simple interest. Using the formula, we solve for T as follows:
T = I / (P × R)
T = $270 / ($1500 × 0.12)
T = $270 / $180
T = 1.5 years
Therefore, Akule borrowed the money for 1.5 years.
Akule borrowed the money for 0.18 years.
Explanation:To find the period of time Akule borrowed the money, we can use the formula:
Interest = Principal × Rate × Time
Given that Akule paid $270 in interest and borrowed $1500 at an annual simple interest rate of 12%, we can plug in these values into the formula:
270 = 1500 × 0.12 × Time
Simplifying the equation, we get:
0.12 × Time = 270 / 1500
Time = (270 / 1500) / 0.12
Time = 0.18 years
Hence, Akule borrowed the money for 0.18 years.
A ___________ is a line segment that connects the center of a circle to a point on that circle.
A) radius
B) chord
C) diameter
D) obtuse angle
Answers
Sales of tablet computers at ted glickman's electronics store in washington,
d.c., over the past 10 weeks are shown in the table below: week 1 2 3 4 5 6 7 8 9 10 demand 19 23 28 38 25 29 37 20 26 30 a) the forecast for weeks 2 through 10 using exponential smoothing with alpha = 0.60 and a week 1 initial forecast of 19.0 are (round your responses to two decimal places):
Answers
Jason entered the amount for his paycheck in the wrong column.
Given: Q = 7m + 3n, R = 11 - 2m, S = n + 5, and T = -m - 3n + 8. Simplify [Q - R] + [S - T].
Answers
Q-R
(7m+3n) - (11- 2m)
7m + 3n -11- 2m
5m +3n - 11
S-T
(n+5)- (-m-3n)
n+5-m-3n
-2n +5 - m
(5m +3n -11) + (-2n +5 -m )
= 4m + n -6
Answer: [tex][Q - R] + [S - T]=10m+7n-14[/tex]
Step-by-step explanation:
Given : [tex]Q = 7m + 3n[/tex],
[tex]R = 11 -2m[/tex],
[tex]S = n + 5[/tex], and
[tex]T = -m - 3n + 8[/tex]
Now , [tex]Q-R= 7m + 3n-(11 - 2m)[/tex]
[tex]Q-R= 7m +3n-11+2m[/tex] [ ∵ (-)(+)=(-) and (-)(-)=(+)]
[Note : when -1 is outside the parenthesis it indicates that -1 should be multiplied with each of the terms present inside the parenthesis .]
[tex]Q-R= 9m +3n-11[/tex] [Combine like terms.]
[tex]S-T=n + 5-(-m - 3n + 8)[/tex]
[tex]S-T=n + 5+m+3n-8[/tex] [ ∵ (-)(+)=(-) and (-)(-)=(+)]
[tex]S-T=4n +m-3[/tex] [Combine like terms.]
Now, [tex][Q - R] + [S - T]=[9m +3n-11]+[4n +m-3][/tex]
[tex]=9m +3n-11+4n+m-3[/tex]
[tex]=10m+7n-14[/tex] [combine like terms]
Hence, [tex][Q - R] + [S - T]=10m+7n-14[/tex]
the ratio of pens to pencils in Carlos case 4:5 he has 16 pens how many pencils do Carlos have
Answers
What is the greatest common factor of 4k , 18k4, and 12
Answers
hope it helps
Answer:
2
Step-by-step explanation:
The greatest common factor of whole numbers is the largest number that is a factor of all numbers. That is, it is the largest number that can divide all numbers.
In this case, the largest number that divide all the numbers is 2, who can divide 4, 18 and 12.
So:
[tex](4k, 18k^{4} ,12)= 2(2k,9k^{4} , 6)[/tex]
Which expressions describe the area of the shaded region? Select all that apply. A rectangle is divided into 12 columns and 6 rows, making 72 smaller rectangles. An area that includes 9 smaller rectangles and is the intersection of 3 of the 12 columns and 3 of the 6 rows is shaded. A. 3 12 × 3 6 312×36 B. 3 10 × 1 2 310×12 C. 1 4 × 1 2 14×12 D. 1 4 × 1 3 14×13 E. 4 12 × 3 6 412×36
Answers
The expressions describing the area of the shaded region is 1/2 × 1/4
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given that, a rectangle is divided into 12 columns and 6 rows, making 72 smaller rectangles.
We need to find the expressions for the area of the shaded region,
So, we have,
The height is 6 and the length is 12
The shaded part is 3 boxes by 3 boxes
Therefore, we can write =
3/6 × 3/12 = 1/2 × 1/4
Hence, the expressions describing the area of the shaded region is 1/2 × 1/4
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jimmy had 8 boxes with 3 cars in each box. if jimmy wanted to give each of his 4 friends an equal number of cars, how many cars would each friend get?
Answers
24/4=6
so each friend gets 6 cars
23 dived by 4= 6