Solve the quadratic equation x2 – 10x + 14 = –4 by completing the square.
Question 3 options:
A)
x = 5 ±
B)
x = –5 ±
C)
x = –7 ±
D)
x = 7 ±
Answer:
[tex] x = 5 \pm \sqrt{7} [/tex]
Step-by-step explanation:
x^2 - 10x + 14 = -4
Subtract 14 from both sides.
x^2 - 10x = -18
To complete the square, add the square of half of the x-term's coefficient.
x-term coefficient: -10
half of it: -5
squared: (-5)^2 = 25
Add 25 to both sides.
x^2 - 10x + 25 = -18 + 25
(x - 5)^2 = 7
Take square root of both sides. Be careful to include ± on the right side.
[tex] x - 5 = \pm \sqrt{7} [/tex]
Add 5 to both sides.
[tex] x = 5 \pm \sqrt{7} [/tex]
PLEASE HELP ME WITH THIS PROBLEM
40 points help me please
Answer:
x=60
Step-by-step explanation:
(1/6)(x+6)=11
Multiply both sides by six:
(6)(1/6)(x+6)=11(6)
x+6=66
Take six from both sides:
x+6-6=66-6
x=60
2(5+xi)-21+5i=3yi^2-3yi
Answer:
x = -8, y = 11/3
Step-by-step explanation:
Least common denominator in 1/30 + 1/24
Answer:
The LCD in 1/30 + 1/24 is 90.
5.5.3 Suppose X and Y have a bivariate normal distribution with , , , , and . Determine the following. Round your answers to three decimal places (e.g. 98.765). (a) Enter your answer in accordance to the item a) of the question statement (b) Enter your answer in accordance to the item b) of the question statement (c) Enter your answer in accordance to the item c) of the question statement
The question is incomplete. The complete question is :
Suppose X and Y have a bivariate normal distribution with [tex]$\sigma_X = 0.04, \sigma_Y = 0.08, \mu_X = 3.00, \mu_Y = 7.70$[/tex] and ρ = 0.
Determine the following. Round your answers to three decimal places (e.g. 98.765).
(a). [tex]$P(2.90 < X < 3.10) =$[/tex]
(b). [tex]$P(7.60 < X < 7.80) =$[/tex]
(c). P(2.90 < X < 3.10, 9.60 < Y < 7.80) =
Solution :
We have
[tex]$X \sim N (\mu_X=3, \sigma_X^2=0.04^2)$[/tex] and
[tex]$Y \sim N (\mu_Y=7.7, \sigma_Y^2=0.08^2)$[/tex]
a). The required probability is
[tex]$P(2.90 < X < 3.10) =$[/tex] [tex]$P\left(\frac{2.9-3}{0.04}< Z < \frac{3.1-3}{0.04}\right)$[/tex]
= P(-2.5 < Z < 2.5) = P(Z < 2.5) - P(Z < -2.5)
= P(Z < 2.5) - [1-P(Z < 2.5)]
= 2P(Z < 2.5) - 1
= 2(0.99379) - 1
= 0.98758
≈ 0.988
b). The required probability is
[tex]$P(7.6 < X < 7.8) =$[/tex] [tex]$P\left(\frac{7.6-7.7}{0.08}< Z < \frac{7.8-7.7}{0.08}\right)$[/tex]
= P(-1.25 < Z < 1.25) = P(Z < 1.25) - P(Z < -1.25)
= P(Z < 1.25) - [1-P(Z < 1.25)]
= 2P(Z < 1.25) - 1
= 2(0.89435) - 1
= 0.7887
≈ 0.789
c). Since, ρ = 0, so the X and Y are independent. Thus the required probability is :
P(2.90 < X < 3.10, 9.60 < Y < 7.80) = P(2.9 < X < 3.1) x P(7.6 < Y < 7.8)
= (0.98758)(0.7887)
= 0.77890
≈ 0.779
Jody's team scored 21, 25, 36, 16, and 32 points at the last five football games. What is the mean number of points Jody's team scored? 20 points 21 points 25 points 26 points
Answer:
26 points
Step-by-step explanation:
Find the mean number of points by adding up all of the points and dividing it by 5
(21 + 25 + 36 + 16 + 32) / 5
130 / 5
= 26
So, the mean number of points is 26 points
Jody's team scored 21, 25, 36, 16 and 32 points at the last five football games. What is the mean number of points Jody's team scored ?
Solution:-To find the mean, first of all we have to add up all the given points and then divide by how many number of points there are. So, there are total 5 points. Hence, we have to divide all the given points by 5.
So, Mean = [tex] \bf \frac{21 \: + \: 25 \: + \: 36 \: + \: 16 \: + \: 32}{5} [/tex]
Mean = [tex] \bf \frac{130}{5} [/tex]
Mean = [tex] \bf 26 [/tex]
The mean number of points Jody's team scored is 26. [Answer]The length of a rectangular garden is 12 ft longer than the width, w. If the garden has a perimeter of 76 ft. Determine the length and width of the garden.
Step-by-step explanation:
length = l
width = w
perimeter of garden = 76 ft
perimeter = 2l + 2w
2l + 2w = 76 (eqn 1)
l - w = 12 (eqn 2)
(eqn 1) ÷ 2
l + w = 38 (eqn 3)
(eqn 2) + (eqn 3)
2l = 50
2l/2 = 50/2
l = 25
The length of the garden is 25 ft.
Substitute l = 25 into (eqn 3)
l + w = 38
25 + w = 38
w = 38 - 25
w = 13
The width of the garden is 13 ft.
1 4/8 - 7/8 what is the answer
Answer:
0.875
Step-by-step explanation:
have a good day/night
may i please have banilliest
thank u
sorry if wrong
Mike's scores on 5 quizzes he took are shown above. In which month was Mike's quiz score equal to the average of his 5 quizzes? Sept. 72, Oct. 83, Nov. 95, Dec. 77, Jan. 88
Answer:
Oct.
Step-by-step explanation:
average = (72 + 83 + 95 + 77 + 88)/5 = 83
Generating Equivalent Expressions
Simplify the expression
by applying the distributive property & combining like terms.
Show work.
6(x + 4y) + 3x - 20y
Answer:
9x +4y
Step-by-step explanation:
step 1 : parentheses are priorities
so multiple the 6 to the parentheses
6x + 24y +3x -20y
combine the x's together
6x +3x + 24y -20y
9x + 4 y
Answer:
[tex]9x + 4y[/tex]
Step-by-step explanation:
1) Expand by distributing term.
[tex]6x + 24y + 3x - 20y[/tex]
2) Collect like terms.
[tex](6x + 3x) + (24y - 20y)[/tex]
3) Simplify.
[tex]9x + 4y[/tex]
Hence, the answer is 9x + 4y.
Find the trigonometric ratios as simplified fractions and as decimals to the nearest thousandths (3 decimal places)
16 34
HElp me plssss ;-;
The logging company would like to use its sample to provide convincing statistical evidence that over 50 percent of the trees in the forest are spruce trees. The logging company has decided to use a chi-square goodness-of-fit test to justify its claim. Why is the chi-square goodness-of-fit test not an appropriate procedure for the logging company to use
Answer:
The chi-square goodness-of-fit test is best used with categorical variables. The trees in the forest are not categorical variables but numerical.
Step-by-step explanation:
The chi-square goodness-of-fit test determines whether the distribution of cases in a single categorical variable follows a known distribution. The chi-square goodness-of-fit test data deal with data frequencies, levels, or counts of cases rather than percentages or other data transformations. Lastly, the categories of the variables are mutually exclusive because they assume the form of either or.
Answer:
A chi-square goodness-of-fit test would be used to show that the entire distribution of trees in the forest is different than what the forester reported, not necessarily the individual proportion representing the spruce trees.
Step-by-step explanation:
The answer is the explanation. Got it from CollegeBoard.org
A gym knows that each member, on average, spends 70 minutes at the gym per week, with a standard deviation of 20 minutes. Assume the amount of time each customer spends at the gym is normally distributed. Suppose the gym surveys a random sample of 49 members about the amount of time they spend at the gym each week. What are the expected value and standard deviation (standard error) of the sample mean of the time spent at the gym
Answer:
the expected value and the standard deviation of the sample mean is 70 and 2.86 respectively
Step-by-step explanation:
The computation of the expected value and the standard deviation of the sample mean is shown below:
The mean is 70
And, the standard deviation is
= 20 ÷ √49
= 20 ÷ 7
= 2.86
Hence, the expected value and the standard deviation of the sample mean is 70 and 2.86 respectively
The sum of 9 and a number is less than 12. Which of the following inequalities expresses the solutions ?
whats the answer to this
What is the range of y=4sin(x)-2
Answer:
According to me it should be -6 [tex]\leq[/tex] y [tex]\leq[/tex] 2.
Step-by-step explanation:
What is the measure of x?
A. 8
B. 9
C. 10
D. 11
Answer:
A
Step-by-step explanation:
wae21q42rwe2q4q2rwe3rq244e2eq2q22q
Because the dividend is the same for all three expressions the larger the Divisor the__the quotient
Worth 100 points false info or just to take the points you will be reported
What is the volume of the composite figure? ASAP PLEASE!!!!
Answer:
74ft³
Step-by-step explanation:
Okay, so it's basically 3 rectangular figures smashed together so:
We'll do the 2 biggest one's first:
the formula for the volume of a rectangular figure is base x height so we first have to find the base:
4 x 3 = 12
So then we just plug our stuff in here:
12 x 3 = 36
Now there's 2 of these rectangles though so:
36 x 2 = 72
Now we're going to do the one in the middle:
1 x 2 = 2
2 x 1 = 2
Now we add that all together:
72 + 2 = 74
So, the volume of the composite figure is 74ft³
hope this helps:)
HELP! PLEASE.............
9514 1404 393
Answer:
B. negative trend
Step-by-step explanation:
The sign of the slope of the best-fit line is the sign of the "trend". A line that slopes downward has a negative slope. Such a best-fit line indicates a negative trend.
Simplify it and please show work
1) 16
2) -6 -(-17) = -6 +17= 11
3) 19 -(-2) = 19 + 2 = 21
4) -13 + 20 = 7
5) -22
6) -9
7) -19
8) -6
9) -17
10) -20
11) -15 -(-10) = -15 + 10 = -5
12) -1
13) 30
14) 11 -(-9) = 11 + 9 = 20
15) 16
16) -21
I really need help on this
Answer:
-27
Step-by-step explanation:
first add 22 to both sides
-x/9=3
then isolate x by multiplying by 9
-x=27
x can't be negative so multiply by -1
x=-27
Answer:
x = -27
Step-by-step explanation:
Solve the equation by inverse operations and you get x = - 27
PLEASE HELP
what is an expression equivalent to (x4y3y)2 in the form xmyn.
Answer:
x^8 y^8
did you mean (x^4 y^3 y)2 or just (x4y3y)2
Sorry did you submitted it yet?
If the given expression is (x⁴y³y)², the expression equivalent to the given expression in form of xmyn is, x⁸y⁸.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that the expression is,
(x⁴y³y)²
Keep the base constant and add the exponents when multiplying similar bases. Maintaining the same base while multiplying the exponents will raise a base with power to another power. When dividing two bases with similar exponents, keep the exponents of the numerator and denominator constant.
We have to represent the given expression in the form of [tex]\rm x^m y^n[/tex].
We use the expression identity as,
[tex]x^m \times x^n = x^{m+n}[/tex]
[tex]\rm = (x^m)^n \\\\ = x^{mn}[/tex]
=(x⁴y³y)²
First, solve the term present in the bracket as,
=(x⁴y⁴)²
Open the bracket we get,
=(x⁴)²(y⁴)²
=x⁸y⁸
Thus, if the given expression is (x⁴y³y)², the expression equivalent to the given expression in form of [tex]\rm x^m y^n[/tex] is, x⁸y⁸.
Learn more about the expression here:
brainly.com/question/14083225
#SPJ2
hi does anyone have the answer for this? 100 points if answered :))
Answer:
15 feet
Step-by-step explanation:
This is already factored for the zeros of the quadratic. If x - 5 = 0 and x - 20 = 0 then x = 5 and 20. The ball was kicked 5 feet out and landed at 20 feet down the field. The difference is 15 feet. That's how far the ball traveled from its initial position on the ground to its landing place.
So 15 feet from where it was kicked.
71 is 10% of what number?
52 is 97% of what Number?
Explain steps.
Answer:
71 is 10% of 710
52 is 97% of 5200/97
Step-by-step explanation:
Let’s start with 71 is 10% of what number.
basically, what this is saying, is that 71 = 10% times and unknown valu. We can set this as x.
so, 71=0.1x
divide on both sides,
710=x
now the second one.
repeat the same process.
52=0.97x
divide
5200/97 =x
Tammy writes the equation -1 / 8 = -1/8. Is she correct? Explain.
LAST ONEEE YAYYYYYYY
Answer:
80
Step-by-step explanation:
180 - 100 = 80. 180º is required for a straight line, and 100º have already been shown from the other angles. x = 80
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer: 42.5%, 7.5%, Independent and Dependent
Step-by-step explanation:
A: The chance that both FDA will approve and double the value is 50%*85% or 0.50*0.85, or 85*1/2 which is 42.5%
B: 50%*(100-85)%=50%*15%=15%*1/2=7.5%
C: FDA approval is independent because nothing can effect it. However, the stock doubling is dependent, because if FDA does not approve, it will definitely not double.
Answer:
See explanation
Step-by-step explanation:
A: 50% * 85% = 42.5%
B: 50% * 15% = 7.5%
C: Dependent, because the stock price has a 0% chance of doubling if the GDA does not approve of the medicine.