Evaluate x + sq root(yz) when x = 3, y = 2, and z = –8.
7i
3 + 4i
3 - 16i
3 + 16i
The value of the expression x + sqrt(yz) when x = 3, y = 2, and z = -8 is 3 + 4i.
Explanation:To evaluate the expression x + sqrt(yz), we substitute the given values for x, y, and z. Given x = 3, y = 2, and z = -8:
x + sqrt(yz) = 3 + sqrt(2*-8) = 3 + sqrt(-16) = 3 + 4i
Therefore, the value of the expression is 3 + 4i.
Margaret plans to deposit $500 on the first day of each of the next five years, beginning today. if she earns 4% compounded annually, how much will she have at the end of five years?
Stella is renting a car for a business trip. The agency charges a flat rate of $60 plus $0.50 per mile every mile she drives over 40 miles. Stella's company will pay up to $270, excluding the cost of gasoline , for the use of the rental car. What is the number of miles Stella can drive the rental car without spending more then$270
270 =60 + 0.50(x-40)
270 =60 + 0.50x -20
210 =0.50x -20
230=0.50x
x=230/0.50 = 460 miles
check:
460-40 = 420
420*0.50=210 +60=270
she can drive 460 miles total
Find x. Round your answer to the nearest tenth of a degree.
Answer:
x=49,6323º
Step-by-step explanation:
To solve this you just have to use the inverted sin X, remember that Sin=opposite/hyphotenuse
Sinx= 16/21
Sin x=,761904
x=-1Sin,761904
x=49,6323
So the measure of the angle X would be 49,6323.
How many plants x should she plant in each row so that her 25 plants end up in a square (i.e., x plants in each of x rows)?
someone help me. Not good at math
perimeter = add all 3 sides 13+13+10 = 36 cm
for area you need to find the height of the triangle, which is the red dotted line
to do that use the Pythagorean Theorem
a^2 + B^2= c^2
a^2 = height
a^2 +5^2 = 13^2
a^2 +25 = 169
a^2 = 169-25 = 144
a=square root(144) = 12
so the height is 12
area = 1/2 h x b = 1/2 x 12 x 10 = 1/2x 120 = 60
area = 60 cm^2
cost is $4 per square cm
there is 60 square cm in the triangle so multiply 60 x 4 = $240
1. Derive the quadratic formula from the standard form (ax2 + bx + c = 0) of a quadratic equation by following the steps below.
2. Divide all terms in the equation by a.
3. Subtract the constant (the term without an x) from both sides.
4. Add a constant (in terms of a and b) that will complete the square.
5. Take the square root of both sides of the equation.
6. Solve for x.
We are given that:
a x^2 + b x + c = 0
Divide all terms with c/ a:
x^2 + (b / a) x + (c / a) = 0
Subtract c from both sides:
x^2 + (b / a) x + (c / a) – c / a = 0 – c / a
x^2 + (b / a) x = - c / a
Add a constant k to complete the square:
where k = ((b / a) / 2)^2 = (b /2a)^2
x^2 + (b / a) x + k = - c / a + k
x^2 + (b / a) x + (b/2a)^2 = - c / a + (b /2a)^2
So the perfect square trinomial is:
(x + b/2a)^2 = - c / a + (b /2a)^2
Taking the square root of both sides:
x + b/2a = sqrt [- c / a + (b /2a)^2]
x = sqrt [(-c/a) + (b /2a)^2] – (b/2a)
Answer:
My equation is 3x^2 + 12x + 24 = 0. When I divide all of the terms by 3, the equation becomes x^2 + 4x + 8 = 0. When I subtract both sides by the constant, 8, the equation is x^2 + 4x = -8. When I add a constant to create the perfect square, the equation now becomes x^2 + 12x + 36 = 28. Finally, the equation simplified equals (x + 6)= the square root of 28.
Step-by-step explanation:
What is an open map?
A moving company charges 0.60 per pound for a move from New York to Florida. A family estimates that their belongings weigh about 4 tons. About how much would it cost the family to move from New York to Florida?
To test μ for an x distribution that is mound-shaped using sample size n ≥ 30, how do you decide whether to use the normal or student's t distribution?
Its timed hurry lad
Evaluate the logarithm log8 (32)
4. Meagan invests $1,200 each year in an IRA for 12 years in an account that earned 5%
compounded annually. At the end of 12 years, she stopped making payments to the
account, but continued to invest her accumulated amount at 5% compounded annually for
the next 11 years.
a. What was the value of the Ira at the end of 12 years?
b. What was the value of the investment at the end of the next 11 years?
c. How much interest did she earn?
a. The value of the Ira at the end of 12 years is $19,100.55.
b. The value of the investment at the end of the next 11 years is $32,668.43.
c. Interest earn is $18,288.43.
a. Using this formula to determine the value of the Ira at the end of 12 years
A=Pmt [(1+r)^n-1]/r
Let plug in the formula
A=1,200[(1+0.05)^12-1]/0.05
A=1,200[(1.05)^12-1]/0.05
A=$1,200(0.795856)/0.05
A=$955.02759/0.05
A=$19,100.55
b. The value of the Ira at the end of 11 years is:
$19,100.55(1+0.05)^11
=$19,100.55(1.05)^11
=$19,100.55(1.710339358)
=$32,668.43
c. Interest earn
Total investment=1200(12)
Total investment= $14,400
Now let calculate the interest earned
Interest earned = $32,668.43 - $14,400
Interest earned= $18,288.43
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whats the equation for
4n + 6 - 2n= 2 (n+3)
A store is offering a 20% discount on all sales over $50 if you purchase a T-shirt and a pair of jeans for $62.50 what is the amount of the discount you would receive
The discount on the purchase of a T-shirt and a pair of jeans costing $62.50 with a 20% discount policy is $12.50.
A store's discount policy offers 20% off for purchases over $50. The question involves calculating the discount amount when a T-shirt and a pair of jeans are purchased together for $62.50. To determine the discount, we simply multiply the total purchase amount by the discount rate.
Step-by-Step Calculation:
First, confirm the purchase amount qualifies for the discount. The combined cost of the T-shirt and jeans is $62.50, which is above $50, so the purchase qualifies for the discount.
Calculate the discount by multiplying the total purchase amount by the discount rate: $62.50 × 0.20 (which is the same as 20%).
Discount Amount = $62.50 × 0.20 = $12.50.
Therefore, the amount of the discount the customer would receive on the purchase of the T-shirt and jeans is $12.50.
At a concert there needs to be at least 1 member of staff working for every 150 members of the audience. If there are 20 members of staff, how many people are in the audience?
Bob drove from home to work at 50 mph. After work the traffic was heavier, and he drove home at 30 mph. His driving time to and from work was 1 hour and 4 minutes. How far does he live from his job?
Which of the following are vertical asymptotes of the function y=3cot(1/2x)-4? A. 3pi B. 2pi C. pi/2 D. 0
Answer:
B and D
Step-by-step explanation:
The winner of a raffle will receive a 21-foot outboard boat. If 6000 raffle tickets were sold and you purchased 30 tickets, what are the odds against your winning the boat?
Answer: 199: 1.
Step-by-step explanation:
The odds against any event is the ratio of the unfavorable outcomes to the favorable outcomes.
Given , The winner of a raffle will receive a 21-foot outboard boat.
Total raffle tickets were sold = 6000
Number of tickets you have = 30
We assume that the lottery was fair , then, the number of possible outcome that you will win = 30
and the number of possible outcomes that one of the others wins = 6000-30= 5970
Then, the odds against your winning the boat = Number of possible outcomes that one of the others wins : Number of possible outcome that you will win
= 5970: 30 = 199:1 [∵[tex]\dfrac{5970}{30}=\dfrac{199}{1}[/tex]]
Hence, the odds against your winning the boat = 199: 1.
Savings account A and savings account B both offer APRs of 7%, but savings account A compounds interest quarterly, while savings account B compounds interest semiannually. Which savings account offers the higher APY? A. Savings account A, because it has more compounding periods per year B. Savings account B, because it has fewer compounding periods per year C. Savings account A, because it has fewer compounding periods per year D. Savings account B, because it has more compounding periods per year @countonme123 @ganeshie8
Answer:
The answer is Savings account B
Savings account A offers a higher APY because it compounds quarterly, which is more frequent than savings account B which compounds semiannually. More compounding periods per year lead to interest being earned on interest more often, resulting in a higher effective yield.
Annual Percentage Yield (APY) given that both accounts offer the same Annual Percentage Rate (APR) of 7%, but one compound quarterly and the other semiannually. The APY is a measure of how much interest an account will earn in a year, taking into account the effect of compounding.
Compounding more frequently results in a higher yield because interest is earned on interest more often. Account A compounds quarterly, meaning it does so four times a year, while Account B compounds semiannually, meaning it does so twice a year. As the frequency of compounding increases, so does the APY, because the money earns interest on the interest that has been added to the account more frequently.
Therefore, the correct answer is A. Savings account A, because it has more compounding periods per year, which means it will have a higher APY compared to savings account B which compounds less frequently.
What is the positive root of the equation x 2 + 5x = 150?
The positive root of the given quadratic function is x = 10.
How to solve the quadratic function?We have the equation:
[tex]x^2 + 5x = 150[/tex]
First, we rewrite it as:
[tex]x^2 + 5x - 150 = 0[/tex]
Using the Bhaskara's formula, we will get:
[tex]x = \frac{-5 \pm \sqrt{5^2 - 4*(-150)*1} }{2} \\\\x = \frac{-5 \pm 25 }{2}[/tex]
The positive solution is:
x = (-5 + 25)/2 = 10
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Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p.
n=128,
p=0.27
The mean is ______
. (Round to the nearest tenth as needed.)
The variance,
σ^2 is ______
(Round to the nearest tenth as needed.)
The standard deviation, ______
A binomial distribution is an experiment where there are two outcomes; Success and failure. In here, you are given n = 128 and p = 0.27. The formula for the variance of a binomial distribution is n*p(1 – p) or n*p*q*. They are equivalent because q = 1- p. We will use the first equation.
Variance = n*p*(1 – p)
Variance = 128*0.27*(1 – 0.27)
Variance = 25.23
To get the standard deviation, find the square root of the variance.
Standard deviation = sqrt (Variance)
Standard deviation = sqrt (25.23)
Standard deviation = 5.02
Based on the table, which statement best describes a prediction for the end behavior of the graph of f(x)? As x → ∞, f(x) → –∞, and as x → –∞, f(x) → ∞ As x → ∞, f(x) → ∞, and as x → –∞, f(x) → ∞ As x → ∞, f(x) → ∞, and as x → –∞, f(x) → –∞ As x → ∞, f(x) → –∞, and as x → –∞, f(x) → –∞
Answer: The correct option is B, i.e., "As x → ∞, f(x) → ∞, and as x → –∞, f(x) → ∞".
Explanation:
From the table it is noticed that the first row represents the value of x and the second row represents the value of f(x).
The value of f(x) is 14 at x = -5, after that the value of f(x) is decreased as the value of x increases.
The value of f(x) remains unchanged when the value of x approaches to 0 from 1.
The value of f(x) is -6 at x = 0, after that the value of f(x) is increased as the value of x increases.
From the table it is noticed that as the value of x approaches to positive infinity the value of f(x) is also approaches to positive infinity.
[tex]f(x)\rightarrow\infty \text{ as }x\rightarrow\infty[/tex]
From the table it is noticed that as the value of x approaches negative infinity the value of f(x) is also approaches to positive infinity.
[tex]f(x)\rightarrow\infty \text{ as }x\rightarrow-\infty[/tex]
These statement are shown in second option, therefore the second option is correct.
Answer:
The end behavior of the graph of the function f(x) is:
f(x) → ∞, and as x → –∞, f(x) → ∞ As x → ∞,
Step-by-step explanation:
Based on the table we could observe that the function f(x) is increasing to the left of -1 as well to the right of -1 and it attains the minimum value to be -6.
Hence, it can be predicted that the end behavior of the graph of the function f(x) goes to infinity in the left and also it goes to infinity in the right.
Hence, the statement that best describes the end behavior of the graph of f(x) is:
f(x) → ∞, and as x → –∞, f(x) → ∞ As x → ∞.
Which unit rate is the lowest price per ounce? Choice A: 5 ounces of raisins for $1.49 Choice B: 12 ounces of raisins for $3.59
A = 1.49/5 =0.298 cents per ounce
B = 3.59/12 = 0.299 cents per ounce
so A has the lowest unit price
A balloon is released and flies straight up for 120 feet, and then the wind blows it east for 280 feet. Find the distance between the balloon and the site where it was released. Decimal rounded one place.
Find a formula for the inverse of the function, f(x)= 8-3/x^2, x>0. Explain if you can.
y varies inversely with x k = 1.4 What is the value of x when y is 5.6? A. x = 4 B. x = 1.4 C. x = 0.25 D. x = 7.84
What is the simplified form of 5 - 4y + 2x - 3y - 2 + 5x?
A. 3 - 7y + 7x
B. 3 + 7y + 7x
C. 7 + 7y + 7x
D. 3 - y + 7x
show steps pls!
how much does one pepper cost if they are priced three for 2.07
One pepper cost is 0.69.
What is Selling price?
Selling price is defined as the price that a customer pays to purchase a product.
Let one pepper cost is x,
Three peppers cost is 2.07,
x = ratio of the total cost of peppers to the number of peppers .
x= 2.07/3
x = 0.69
So, the peppers cost 69 cents each.
Hence, one pepper cost is 0.69.
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Find the missing coordinate if the ordered pair is to be a solution to the equation 3x+y=9:(?,-9)
An item is regularly priced at $89 . It is now priced at a discount of 65% off the regular price.