Answer - u = 4.8989
u ^ 2 = 24
u = sqrt (24)
u = 4.8989
Answer:
[tex]2\sqrt6[/tex]
Step-by-step explanation:
We have been given that the dot product if u with itself is 24.
Now, we know that the dot product of vector a and b is given by
[tex]a\cdot b=|a||b|\cos\theta[/tex]
Here, [tex]\theta[/tex] is the angle between the vectors a and b.
We have to find the dot product of u with itself. Hence,
a = u
b = u
[tex]\theta=0[/tex]
Thus, dot product is given by
[tex]u\cdot u=|u||u|\cos0\\\\24=|u||u|\cdot1\\\\|u|^2=24\\\\|u|=2\sqrt6[/tex]
Thus, the magnitude of u is [tex]2\sqrt6[/tex]
How many arrangements are possible using the letters in the word fuzzy if each letter "z" is distinctly different than the other? how many arrangements are possible if the letter "z" is interchangeable with the other? explain your reasoning?
Case 1: If the letter z is distinctly different
If we have the letter z which is distinctly different than the other "z", then we have five letters in the word F U Z Z Y and the number of arrangements would be = 5*4*3*2*1 =5! = 120 different arrangements
Case 2: If the letter Z is interchangeable
If the letter "Z" is interchangeable with the other "z" then we have 2 letters which cancel out each other that would be represented by 2*1 = 2! = 2
So, the number of arrangements in this case would be 5!/2! = 5*4*3*2*1/2*1 = 60 arrangements
Silvia wants to retire at 65 and live on $40,000 a year. How much does she need to save to ensure that her retirement funds last until she is 85?
Select the best answer from the choices provided.
$800,000 because she will need to save for 20 years times $40,000
more than $800,000 because taxes and inflation will increase the value of her savings
less than $800,000 because returns will continue to increase the amount in her savings even after retirement
more than $800,000 because compound return will reduce her savings
Answer:
$800,000 because she will need to save for 20 years times $40,000
Step-by-step explanation:
Silvia wants to retire at 65 and live on $40,000 a year.
She wants to live till 85 and retire at 65 years.
So, number of years to save = [tex]85 -65= 20[/tex]
And she needs to save [tex]40000\times20=800000[/tex]
Hence, she must save 800,000.
Sandy releases a javelin 1.6 m above the ground with an initial vertical velocity of 25 m/s. How long will it take the javelin to hit the ground?
Using a quadratic function, it is found that it will take 5.17 seconds for the javelin to hit the ground.
What is the quadratic function for a projectile's height?Considering meters as the measure of height, it is given by:
h(t) = -4.9t² + v(0)t + h(0).
In which:
v(0) is the initial velocity.h(0) is the initial height.In this problem, we have that v(0) = 25, h(0) = 1.6, hence:
h(t) = -4.9t² + 25t + 1.6
It hits the ground when h(t) = 0, hence:
-4.9t² + 25t + 1.6 = 0
4.9t² - 25t - 1.6 = 0.
Which is a quadratic function with coefficients a = 4.9, b = -25, c = -1.6. Hence:
[tex]\Delta = (-25)^2 - 4(4.9)(-1.6) = 656.36[/tex]
[tex]x_1 = \frac{25 + \sqrt{656.36}}{9.8} = 5.17[/tex]
[tex]x_2 = \frac{25 - \sqrt{656.36}}{9.8} = -0.06[/tex]
For time we want the positive value, hence, it will take 5.17 seconds for the javelin to hit the ground.
More can be learned about quadratic functions at https://brainly.com/question/24737967
#SPJ2
Which of the following sequences of numbers are arithmetic sequences? Check all that apply.
A.99, 100, 101, 102, 103, ...
B.-3, -5, -7, -9, -11, ...
C.2, -2, 2, -2, 2, ...
D.1, 6, 11, 16, 21, ...
E.-4, 7, -10, 13, -16, ...
The quarters, buckled, and dimes totaled 20 and their value was $2.05. How many kind were there if there were 3 times as many dimes as quarters
A travel website reports that in a particular city, the probability of rain on any day in April is 40%. What is the expected number of rainy days in this city during the month of April?
Kali invests $3516 in a savings account with a fixed annual interest rate of 7% compounded 3 times per year. What will the account balance be after 7 years
Your job pays 6$ per hour write a variable expression for your pay in dollars for working h hours what is your Pay if you work 32 hours
I need Help with this TRIG question
Determine the number of real solutions for each of the given equations. Equation Number of Solutions y = -3x2 + x + 12 y = 2x2 - 6x + 5 y = x2 + 7x - 11 y = -x2 - 8x - 16
pppppppllllllleeeeaaaassssseeeee ANSWER FASRT
According to the discriminant:
[tex]y = -3x^2 + x + 12[/tex] has two real solutions.[tex]y = 2x^2 - 6x + 5[/tex] has zero real solutions.[tex]y = x^2 + 7x - 11[/tex] has two real solutions.[tex]y = -x^2 - 8x - 16[/tex] has one real solution.The number of real solutions of quadratic equation [tex]y = ax^2 + bx + c[/tex] depends on the discriminant [tex]\Delta = b^2 - 4ac[/tex].
If [tex]\Delta > 0[/tex], the equation has two real solutions.If [tex]\Delta = 0[/tex], the equation has one real solution.If [tex]\Delta < 0[/tex], the equation has zero real solutions.Equation [tex]y = -3x^2 + x + 12[/tex]
The coefficients are: [tex]a = -3, b = 1, c = 12[/tex]The discriminant is: [tex]\Delta = 1^2 - 4(-3)(12) = 145[/tex].Positive, thus two real solutions.Equation [tex]y = 2x^2 - 6x + 5[/tex]
The coefficients are: [tex]a = -2, b = -6, c = 5[/tex]The discriminant is: [tex]\Delta = (-6)^2 - 4(2)(5) = -4[/tex].Positive, thus zero real solutions.Equation [tex]y = x^2 + 7x - 11[/tex]
The coefficients are: [tex]a = 1, b = 7, c = -11[/tex]The discriminant is: [tex]\Delta = (7)^2 - 4(1)(-11) = 93[/tex].Positive, thus two real solutions.Equation [tex]y = -x^2 - 8x - 16[/tex]
The coefficients are: [tex]a = -1, b = -8, c = -16[/tex]The discriminant is: [tex]\Delta = (-8)^2 - 4(-1)(-16) = 0[/tex].Positive, thus one real solutions.A similar problem is given at https://brainly.com/question/19776811
Solve for c in the equation 3x^2-18x+5=47
Use the graph below to answer the question that follows:
What is the rate of change between the interval x = π and x = three pi over two?
pi over 16
negative 16 over pi
pi over 4
negative 4 over pi
please help no will mark brainlyst
Explain how you would find 90% of 120.
Jake is younger than Sophie. Sophie is 14 years old. Write an inequality that compares Jake's age in years, (j), to Sophie's age.
To express that Jake is younger than Sophie who is 14, we use the inequality j < 14, where j symbolizes Jake's age in years.
Explanation:The question is asking for an inequality that represents Jake's age compared to Sophie's age. Since we are told that Jake is younger than Sophie and Sophie is 14 years old, we can use an inequality symbol to express this relationship. The appropriate inequality is j < 14, where j represents Jake's age in years. The symbol < means 'less than,' which correctly compares Jake's age to Sophie's, indicating that Jake's age is less than 14 years.
In how many different ways can the letters of the word china be arranged
the mean mark for the class was 70%. There are 30 students in the class, 20 of whom are boys. The mean mark for the boys is 62%. What is the mean mark for the girls?
What is the answer to the jones family plans a trip to the amusement park...
Help on homework! Which of the following can have a negative effect on your credit score?
A. Getting a promotion at work
B. Late payments on a car loan
C. Paying credit card balances in full
D. low debt-to-income ratio
Help please??????????
(2n + 3)(n – 4) = 0
need help asap!!!
Please help me idk this
**MARKING BRAINLIEST IF RIGHT AND IF YOU SHOW WORK**
3. Use the Fermi process to estimate the number of bricks needed to fill an empty bathtub. Show your work.
My teacher said you can use approximate dimensions of the bricks and bathtub. He said use the easiest ones so that it will be easy to solve.
please help with this??
Someone please help me?
Can someone show me how to do this?
16! / 4! 12!
Convert 7.2*10^-3 to standard form please help thanks
Please help me idk this
Answer:
1 13/20
Step-by-step explanation:
You want the total of distances walked to be the length of the hike:
2 1/10 + 1 1/4 + (left to walk) = 5
Then the amount left to walk is the difference ...
left to walk = 5 - 2 1/10 - 1 1/4
___
You are expected to know how to do arithmetic with mixed numbers, and/or to be able to use a calculator for the purpose.
5 - 2 1/10 - 1 1/4
= (5 -2 -1/10) - 1 1/4
= 2 9/10 - 1 1/4
= (2 -1) + (9/10 -1/4)
= 1 + (9/10 -1/4)
= 1 + (18/20 - 5/20)
= 1 13/20 . . . miles left to walk
___
Using a calculator:
5 -2.1 -1.25 = 1.65 = 1 65/100 = 1 13/20
A die is thrown twice. What is the probability that:
1. Neither a doublet ordered pair nor a total of 10 will appear?
2. Neither a multiple of 2 on the first throw nor a total of 6 will appear?
A. 7/9
B. 5/12
Answer:
1.)- B. 5/12
2)- A. 7/9
Step-by-step explanation:
What are the coordinates of the vertex of the table? Is it a minimum or a maximum?
x y
0 1
-1 -2
-2 -3
Question 1 options: A.(-4, 1); minimum B.(-2, -3); maximum C.(-2, -3); minimum D.(1, 0); maximum.
A-Town wants to know the number of cell phones in each household the town divides the population up by neighborhood and surveys a random number of households and eat what type of survey is this
A-Town is conducting a survey using a random sample method by dividing the population into neighborhoods and surveying random households in each, which ensures each household has an equal chance of being selected and provides a representative sample.
Explanation:A-Town's approach to determining the number of cell phones in each household through a survey is an example of a random sample. The method involves dividing the population into neighborhoods and surveying a random selection of households within each area. This technique helps to ensure that every household has an equal chance of being selected, which should provide a representative sample of the town's population. Such methods are necessary to obtain reliable data that reflects the true distribution and characteristics of the target population without regional bias.
Using a representative sample is crucial in research and polling to measure accurately public opinion or collect data on phenomena. As in the given example where the market research firm surveys 500 randomly selected residents to estimate the percentage of adults with cell phones, the firm employs statistical measures like confidence intervals to infer about the entire population's cell phone ownership based on the sample data. Moreover, the concept of probability sampling is also important for achieving a sample that can be generalized to the whole population with reasonable accuracy.