Formular for quadratic equation almighty formular
[tex]x = \frac{ - b \frac{ + }{} \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
What is the domain of f(x)=(1/2)^x
Answer:
all real numbers
Algebra Examples
The domain of the expression is all real numbers except where the expression is undefined
Hello!
The domain of an exponential function is the crowd of all real numbers, so: x ∈ ℝ.
Good luck! :)
Solve y = -7(-13)
I'm giving 30 points!
y = -7(-13)
=> y = -7 × (-13)
= y = 91
Hattie had $3,000 to invest and wants to earn 10.6% interest per year. She will put some of the money into an account that earns 12% per year and the rest into an account that earns 10% per year. How much money should she put into each account?
Answer:
900 at 12%
2100 at 10%
Step-by-step explanation:
Let x= amount invested at 12%
let y= amount invested at 10%
with that being said we can write the two equation
Equation 1: x+y=3000
Equation 2: 3000*.106=.12x+.1y
isolte x from equation 1
x= 3000-y
plug this into equation 2
318=.12(3000-y)+.1y
318=360-.12y+.1y
-42= -.02y
y= 2100
Plug this into equation 1
x+2100=3000
x=900
she should invest $900 into the account earning 12% interest and $2100 into the account earning 10% interest.
How to determine How much money should she put into each accountLet's denote the amount of money Hattie invests at 12% as \(x\) dollars, and the amount she invests at 10% as \(\$3000 - x\) dollars.
The formula for calculating interest is: \(\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}\).
For the 12% account:
Interest_12% = \(x \times 0.12 \times 1\) (1 year)
For the 10% account:
Interest_10% = \((3000 - x) \times 0.10 \times 1\) (1 year)
Hattie wants to earn 10.6% interest on the total investment, so we can set up the equation:
\(\text{Total Interest} = \text{Interest}_12% + \text{Interest}_10%\)
\(3000 \times 0.106 = x \times 0.12 + (3000 - x) \times 0.10\)
Now, solve for \(x\):
\(318 = 0.12x + 300 - 0.10x\)
\(318 = 0.02x + 300\)
\(18 = 0.02x\)
\(x = 900\)
Hattie should invest $900 at 12% and \(3000 - 900 = 2100\) at 10%.
Therefore, she should invest $900 into the account earning 12% interest and $2100 into the account earning 10% interest.
Learn more about interest at https://brainly.com/question/29451175
#SPJ3
John's age 4 years ago, if he will be y years old in 5 years
9514 1404 393
Answer:
y -9
Step-by-step explanation:
From 4 years ago until 5 years from now, John will age 9 years. That is, his age 4 years ago is 9 years less than it will be in 5 years.
John's age 4 years ago is y-9 years.
The first five terms of an arithmetic sequence are shown below:
20, 17, 14, 11, 8, . . .
Let n represent the term number and f(n) the term in the sequence.
Choose a function that represents the sequence.
The answer to this question is f(n) = -3 + 23
Now my question is, how do you find the solution? I was taught the explicit formula is f(n) = m(n) + b, but no matter how many times I've tried to plug in the numbers I cannot seem to get the right answer. Please help me and do show the entire process and the steps.
Answer:
The function represents the sequence is - 3 n + 23.
Step-by-step explanation:
20. 17, 14, 11, 8,......
Here, the first term is
a = 20
Common difference, d = -3
Let the nth term is Tn.
Tn = a + (n -1) d
Tn = 20 + (n -1) x (-3)
Tn = 20 - 3 n + 3
Tn = 23 - 3 n = - 3 n + 23
So, the function represents the sequence is - 3 n + 23.
Answer:
Y'all know what it is already, but I want points, so: f(n) = -3n + 23
2•^2=?
A) -4
B) 1/4
C) 4
Answer:
1/4.
Step-by-step explanation:
2^-2 = 1/2^2
= 1/4.
The distribution of the number of apples trees a farmer can plant each day is bell-shaped and has a mean of 62 and a standard deviation of 8. Use the empirical rule to help you answer the following. What is the approximate percentage of trees planted between 38 and 68
Answer:
The empirical rule, the approximate percentage of trees planted between 38 and 68 is 99.7%.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 62, standard deviation of 8.
What is the approximate percentage of trees planted between 38 and 86?
38 = 62 - 3*8
86 = 62 + 3*8
So within 3 standard deviations of the mean, which, by the empirical rule, the approximate percentage of trees planted between 38 and 68 is 99.7%.
Choose the best graph that represents the linear equation:
y + 3 = 0
Graph A
On a coordinate plane, a line goes through (0, 3) and (1, 3).
Graph B
On a coordinate plane, a line goes through (negative 3, 0) and (negative 3, 1).
Graph C
On a coordinate plane, a line goes through (0, negative 3) and (1, negative 3).
Graph D
On a coordinate plane, a line goes through (0, 0) and (1, negative 3).
a.
Graph A
c.
Graph C
b.
Graph B
d.
Graph D
PLEASE HELP!!! Please select the best answer from the choices provided
A
B
C
D
Graph B is the best graph that represents the linear equation
Answer:
m=2b=1y=2x+1
just enter it
g A. (Points: 7) Compute (without using a calculator) 241^257 mod 12 B. (Points: 3) Compute Z*20 C. (Points: 6) Find the multiplicative inverse of 7 in Z19
Answer:
[tex]241^{257}\ mod\ 12 =1[/tex]
[tex]7 * 20 = 140[/tex]
[tex]\frac{1}{700}[/tex]
Step-by-step explanation:
Solving (a): 241^257 mod 12
To do this, we simply calculate [tex]241\ mod\ 12[/tex]
Because [tex]a\ mod\ b = a^n\ mod\ b[/tex]
The highest number less than or equal to 241 that is divisible by 12 is 240; So:
[tex]241\ mod\ 12 = 241- 240[/tex]
[tex]241\ mod\ 12 =1[/tex]
Hence:
[tex]241^{257}\ mod\ 12 =1[/tex]
Solving (b): 7 * 20
[tex]7 * 20 = 140[/tex]
Solving (c): Multiplicative inverse of 7 in 719
The position of 7 in 719 is 700
So, the required inverse is 1/700 ---- i.e. we simply divide 1 by the number
A radio transmission tower is 180 feet high. How long should a guy wire be if it is to be attached to the tower 11 feet from the top and is to make an angle of 45° with the ground?
Answer:
Step-by-step explanation:
If the two lines below are perpendicular and the slope of the red line is -7,
what is the slope of the green line?
10
10
A. 7
ОО
B. -7
C. 1
Answer:
C. ⅐
Step-by-step explanation:
Recall: the slope of a line that is perpendicular to another is the negative reciprocal of the slope of the other line that it is perpendicular to.
Thus:
Slope of red line = -7
The green line that is perpendicular to the red line will have a slope that is the negative reciprocal of -7.
Negative reciprocal of -7 = ⅐
The slope of the green line is therefore ⅐
The yield in bushes per acre is related to the average temperature. The attached sample data was obtained in a recent study. The least-square regression equation for yield in bushes and the average temperature is
Region Temperature Yield (in bushes per acre)
1 4 3
2 8 7
3 10 8
4 12 10
5 9 8
6 6 4
Answer:
y = 0.9143x - 0.8
Step-by-step explanation:
Given the data :
Region Temperature Yield (in bushes per acre)
4 ______ 3
8 ______ 7
10 _____ 8
12 _____ 10
9 ______ 8
6 ______ 4
Using technology, the least square regression equation obtained by fitting the data is :
y = 0.9143x - 0.8
Where ;
y = predicted Bush yield, predicted variable
x = Average temperature, dependent variable
The slope Coefficient = 0.9143
The intercept = - 0.8
Question 1 of 10
One advantage of a long-term loan compared to a short-term loan is that a
long-term loan:
A. does not require the borrower to have a good credit score.
O
B. can be paid off in full without the borrower paying any interest.
C. does not force the borrower to make payments every month.
D. allows a person to borrow more money at a lower interest rate.
Answer:
D. allows a person to borrow more money at a lower interest rate
Find the value of each expression:
1) 14 – 22
2) (10 + 5) – (32 – 3)
I need help pleaseeee
Write each of the following numbers to 3 significant figures in exponential or scientific notation. Write each number with only one non-zero digit before the decimal point.
(i) 5590
(ii) 0.000498
(iii) 135000
(iv) 0.000438
Solution :
The significant figure of a number are defined as the positional notation of that number which are most reliable and are absolutely necessary to represent the quantity of something.
In the context, we have to express the given numbers into three significant figures in the form of scientific notation or in the exponential form :
(i). 5590 ----- [tex]$5.59 \times 10^3$[/tex]
(ii). 0.000498 ----- [tex]$4.98 \times 10^{-4}$[/tex]
(iii) 135000 ----- [tex]$1.35 \times 10^5$[/tex]
(iv) 0.000438 ----- [tex]$4.38 \times 10^{-4}$[/tex]
what is completely factored form or this expression?
y^2-12y+32
a.(y+4)(y+8)
b.(y-4)(y-8)
c.(y+18)(y+2)
d.(y-18)(y-2)
[tex]\\\\\\[/tex]
Therefore [tex]\sf{option~ B~ is ~correct }[/tex][tex]\sf{ }[/tex] [tex]\sf{ }[/tex] [tex]\sf{ }[/tex]
Answer:
(y-4) (y-8)
Step-by-step explanation:
y^2-12y+32
What two numbers multiply to 32 and add to -12
-8*-4 = 32
-8+-4 = -12
(y-4) (y-8)
A polygraph (lie detector) is an instrument used to determine if an individual is telling the truth. These tests are considered to be 90% reliable. In other words, if an individual lies, there is a 0.90 probability that the test will detect a lie. Let there also be a 0.045 probability that the test erroneously detects a lie even when the individual is actually telling the truth. Consider the null hypothesis, "the individual is telling the truth," to answer the following questions
a. What is the probability of a Type I error? (Round your answer to 3 decimal places.)
b. What is the probability of a Type II error? (Round your answer to 2 decimal places.
Answer:
A) P(Type I error) = 0.045
B) P(Type II) error = 0.1
Step-by-step explanation:
We are told that the reliability of the test is 90% reliable.
Also, we are told that the probability that the test erroneously detects a lie even when the individual is actually telling the truth is 0.045.
Thus;
A) To calculate the probability of type I error:
From statistics, in this question we can say that the probability of a type I error is the probability that the test will erroneously detect a lie even though the individual is actually telling the truth. Thus;
Probability of (type I error) = P(rejecting true null) = 0.045
B) For probability of type II error, it is defined as the error where we accept a null hypothesis that is false. We can say that it produces a false negative and the formula is;
P(Type II) error = 1 - reliability
Reliability in the question is 0.90
Thus;
P(Type II) error = 1 - 0.9
P(Type II) error = 0.1
HW HELP ASAP PLZZZZZ
Answer:
p = 15/x
x= -3
Step-by-step explanation:
For the first problem, we can expand the equation to 4px+4=64
then simplify it to:
4px=60
then divide 4x from both sides of the equation
p=60/4x
then simplify:
p=15/x
For the second problem:
plug in -5 for p so the equation would look like
4(-5x +1)=64
simplify
-20x=60
x= -3
Midsegments geometry acellus pls helppfpfpff
Answer:
BC = 28
Step-by-step explanation:
The midsegment DF is half the measure of the third side BC , then
BC = 2 × DF = 2 × 14 = 28
The radius of a circle is 5 yd.
Answer the parts below. Make sure that you use the correct units in your answers.
If necessary, refer to the list of geometry formulas.
Answer:
Circumference =10 pi yard
Area =25 pi yard squared
Step-by-step explanation:
C=2*pi*r
Circumfrance =10 pi
A=pi r^2
Area =25 pi
For the estimate just sub in pi on the calculator for pi, then round to the hundreth.
Circumfrence= just the unit
Area= squared
A line includes the points (0,2) and (1,6).
What is the equation of the line in slope-intercept form?
Tara makes 30 cups of donut topping by mixing sugar and cinnamon. The ratio of sugar to cinnamon is 3:2
How much sugar did Tara use in the donut topping?
Answer:
18
Step-by-step explanation:
3:2 means 3/2 or 3÷2
but its better to leave it as
3/2
Will give brainliest.
Answer: Assuming there isnt a fourth answer, the answer is the second choice.
Step-by-step explanation: Point A is located in the first quadrant, Point B is located at 3, -1/2 and Point C is reflected off the y axis, in the second choice.
A recipe for chocolate chip cookies calls for 3 1/3 cups of flour. If you are making 2 1/4 recipes, how many cups of flour are needed.
Answer:
THIS IS THE ANSWER
Step-by-step explanation:
1 1/2 = 3/2
2 1/3 = 7/3
3/2 * 7/3 = 21/6 = 3 3/5 = 3 1/2 cups
PLEASE MARK ME AS A BRAINLIST!plz help with the task my child is trying to do
Answer:
7
Step-by-step explanation:
First, add all the cards.
[tex]2 + 5 + 7 + 8 + 9 = 31[/tex]
If we remove one card, the remaining four cards average will be 6, this means that the 4 remaning cards will average total will be at 24 because 6×4=24. So we need to find a value that will equal 24 if we remove that card.
The answer is 7 because
[tex] \frac{2 + 5 + 8 + 9}{4} = 6[/tex]
9514 1404 393
Answer:
remove 7 to make the total be 6×4 = 24.
Step-by-step explanation:
The description "mean average" is redundant to no apparent purpose. "Mean" and "average" are the same thing: the total divided by the number of contributors.
If the mean of 4 cards is 6, then we require ...
6 = (total of 4 cards) ÷ 4
24 = total of 4 cards . . . . . . . multiply both sides of the equation by 4
__
We note that the total of all the cards shown is ...
2 + 5 + 7 + 8 + 9 = 31
In order to make the total be 24, we need to remove a card that has a value of ...
31 -24 = 7
Removing 7 will bring the total to 2 + 5 + 8 + 9 = 24, and the average to 24/4 = 6.
_____
Additional comment
It is worthwhile to remember the relationship between the total and the average and the number of contributors. This shows up a lot in problems involving adjusting an average or finding a value to give a certain average.
5 times a number is 110 less than 7 times that number
Answer:
55
Step-by-step explanation:
let the number=x
5x=7x-110
7x-5x=110
2x=110
x=110/2=55
Approximately 5% of workers in the US use public transportation to get to work. You randomly select 25 workers and ask if they use public transportation to get to work. Find the probability that exactly 2 workers say yes.
Answer:
0.2305 = 23.05% probability that exactly 2 workers say yes.
Step-by-step explanation:
For each worker, there are only two possible outcomes. Either they say yes, or they say no. The probability of a worker saying yes is independent of any other worker, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
5% of workers in the US use public transportation to get to work.
This means that [tex]p = 0.05[/tex]
You randomly select 25 workers
This means that [tex]n = 25[/tex]
Find the probability that exactly 2 workers say yes.
This is P(X = 2). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{25,2}.(0.05)^{2}.(0.95)^{23} = 0.2305[/tex]
0.2305 = 23.05% probability that exactly 2 workers say yes.
True or face dilations preserve angle measure
Answer:
True
Step-by-step explanation:
Required
Does dilation preserve angle measure?
When a point, side, line, or angle is dilated; the length of the line will be altered by the ratio or scale of dilation.
However, the measure of angle will remain the same.
Hence, the given statement is true.
The highway department is testing two types of reflecting paint for concrete bridge end pillars. The two kinds of paint are alike in every respect except that one other is yellow. The orange paint is applied to 12 bridges, and the yellow paint is applied to 12 bridges. After a period of 1 year, reflectometer readings were made end pillars. (A higher reading means better visibility.) For the orange paint, the mean reflectometer reading was x19.4, with standard deviation s1-2.5. For the mean was X2-6.5, with standard deviation S2-2.4. Based on these data, can we conclude that the yellow paint has less visibility after 1 year?
Use a 10% level What are we testing in this problem?
a. difference of means
b. single proportion
c. difference of proportions
d. single mean
e. paired difference
Answer:
a. difference of means
Step-by-step explanation:
Given that :
Mean , x = 9.4
Standard deviation, [tex]s.d_1[/tex] = 2.5
Number, [tex]n_1[/tex] = 12
Mean, y = 6.5
standard deviation, [tex]s.d_2[/tex] = 2.4
Number, [tex]n_2[/tex] = 12
The null hypothesis is : [tex]$H_0: \mu_1=\mu_2$[/tex]
The alternate hypothesis is : [tex]$H_1: \mu_1>\mu_2$[/tex]
Level of significance, [tex]\alpha[/tex] = 0.1
From the [tex]\text{standard normal table, right tailed,}[/tex] [tex]$t_{1/2}$[/tex] = 1.363
Since out test is right tailed.
Reject [tex]H_0[/tex], if [tex]$T_0>1.363$[/tex]
We use the test statics,
[tex]$t_0=\frac{(x-y)}{\sqrt{\frac{s.d_1}{n_1}+\frac{s.d_2}{n_2}}}$[/tex]
[tex]$t_0=\frac{(9.4-6.5)}{\sqrt{\frac{6.25}{12}+\frac{5.76}{12}}}$[/tex]
[tex]$t_0=2.899$[/tex]
[tex]$|t_0|=2.899$[/tex]
[tex]\text{Critical value}[/tex]
The value of [tex]$|t_{1/2}|$[/tex] with minimum [tex]$\left(n_1-1,n_2-1)$[/tex] that is 11 df is 1.363
We go [tex]$|t_0|=2.899$[/tex] and [tex]$|t_{1/2}|$[/tex] = 1.363
Decision making:
Since the value of [tex]|t_0|>|t_{1/2}|$[/tex] and we reject the [tex]H_0[/tex]
The p-value : right tail [tex]H_a:(p>2.8988)[/tex]
= 0.00724
Therefore the value of [tex]$p_{0.1} > 0.00724$[/tex], and so we reject the [tex]H_0[/tex]
Thus we are testing 'the difference of means" in this problem.
