The test statistic when the a simple random sample has been selected from a normally distributed population is a) -2.24
What is test statistic?The test statistic is a number derived from a statistical test that is used to determine whether your data could have occurred under the null hypothesis.
u = 30000
x = 22298
s = 14200
n = 17
Test statistic = = (x - u) / s / ✓n
x = mean
u = theoretical value
s = standard deviation
{n} = variable set size
= (x - u) / s / ✓n
= (22298 - 30000) / 14200 / ✓17
= -2.24
Test statistic = -2.24
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(3,6) relfect it across the line -x+2y=30
The equation of line parallel to -x+2y = 30 and passing through (3,6) is x - 2y + 9 = 0.
Given equation is -x+2y = 30
and passing through the point (3,6).
If two lines are parallel, their slopes will be equal.
We know that equation for parallel lines is y = 3x+c
Now, -x + 2y = 30
= 2y = 30 + x
[tex]= y = \frac{30+x}{2}[/tex]
[tex]= y = \frac{30}{2} +\frac{x}{2} \\\\= y = 15 + \frac{x}{2}[/tex]
Therefore slope = [tex]\frac{1}{2}[/tex]
Equation of line with slope and passing through (3,6)
[tex]y-y_{1} = m(x-x_{1}) \\\\y - 6 = \frac{1}{2} (x-3)\\\\[/tex]
2(y-6) = 1(x-3)
2y - 12 = x - 3
x - 2y + 9 = 0
Hence the answer is the equation of line parallel to -x+2y = 30 and passing through (3,6) is x - 2y + 9 = 0.
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can anyone help me with these please and thank you ?
Membership costs for belonging to a gym for a certain number of months are shown in the table below.
Answer:
y = 35.5x - 10
Step-by-step explanation:
If we graph the function with the help of the given table,
Since, there is a common difference in each term of 'cost of gym membership'
d = 61 - 25.5 = 35.5
d = 96.5 - 61 = 35.5
Graph will represent a linear function.
Let the equation of the line is,
y - y' = m(x - x')
where (x', y') is a point lying on the graph and 'm' is the slope.
Two points lying on the graph are (1, 25.5) and (2, 61).
Slope of the line =
=
= 35.5
Equation of the line passing through (1, 25.5) having slope 'm' = 35.5
y - 25.5 = 35.5(x - 1)
y = 35.5x - 35.5 + 25.5
y = 35.5x - 10
Here x = duration of membership
y = membership price
Therefore, equation representing Fit Zoom's membership price equation will be,
y = 35.5x - 10
Can someone help me with this question please !!
I have to know how to solve it to pass my exam
I'll give brainly to the right answer .
Answer:
Step-by-step explanation:
you'll need to know L'Hôpital's Rule. Obviously this problem goes to zero in the denominator if you let x go to zero, which is a big problem :P sooo use L'Hopital's rule to solve this messy problem.
L'Hoptial's rule takes the advantage that you can find the derivative of something but still find it's limit just like you didn't take a derivative. soo
take derivative of numerator and denominator separately
remember how to take derivative of sin^2(3x) ??
pull the two down, then chain rule
d/dx (sin^2(3x) = 2sin(3x) * cos(3x) * 3 = 6*sin(3x)*cos(3x)
d/dx (4x^2) = 8x
we still have the same issue if we take the limit if x goes to zero :0
but it's okay... just take L'Hopitals' again :P
d/dx (6*sin(3x)*cos(3x)) = 6*cos(3x) *3 *(-sin(3x)*3 = 54*cos(3x)*(-sin(3x))
d/dx (8x) = 8
now we can let the limit go to zero
lim ( x ->0)[54*cos(3x)*(-sin(3x)) / 8]
we can see that sin(x) will get closer and closer to zero so we have 0/8
so we can fairly say, without guessing, that yes... this limit goes to zero as X goes to zero. :) nice
un ciclista recorre 300 metros por minuto. ¿cuantos kilómetros recorre en una hora?
Answer:
El ciclista recorre en una hora:
18 kilómetros.
Step-by-step explanation:
1 hora = 60 minutos
1 minuto = 1/60 = 0.01667 horas
1 kilómetro = 1000 metros
300 metros = 300/1000 = 0.3 kilómetros
Entonces:
300 metros por minuto = 300metros/minuto
300 metros / minuto = 0.3kilómetros / 0.01667 horas
= 0.3/0.01667
= 18 kilómetros/hora
El ciclista recorre 18 kilómetros cada hora
you want to obtain a sample to estimate a population proportion. based on the previous evidence, you believe the population proportion is approximately 76%. you would like to be 95% confident that your estimate is within 4.5% of the true population proportion. how large of a sample size is required?
n=
A proportion is an equation in which two ratios are set equal to each other and the large sample size required is [tex]0.75[/tex].
What is population proportion?
A fraction is represented in the form of [tex]\frac{a}{b}[/tex], a while ratio [tex]a:b[/tex], then a proportion states that two ratios are equal. Here, [tex]a[/tex] and [tex]b[/tex] are any two integers.
Here, we are determining the minimum sample size for the determination of the population proportion. So, the general formula is of the form is:-
[tex]n=(\frac{z_\frac{x}{2}.x}{E})^{2}[/tex]
Here given values are:-
σ[tex]=76[/tex], population standard deviation
[tex]1-x=0.95\\[/tex], Confidence level
[tex]E=4.5[/tex], Error
Determining the critical value, we get
[tex]z_\frac{x}{2}\\P(z\leq z_\frac{x}{2})=1-\frac{x}{2}\\1-x=0.95\\x=1-0.95\\x=0.05\\\frac{x}{2}=\frac{0.5}{2}\\\frac{x}{2}=0.25\\1-\frac{x}{2}=1-0.25\\\\=0.75[/tex]
Hence, a large sample size is required is [tex]0.75[/tex].
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- Given the table below write an explicit
equation .
n
1
2
3
4
5
f(n)
5
58
13
20
29
The explicit equation for the table is,
f(n) = n² + 4
Given, the values of an explicit function,
Let the function be,
f(n) = an² + bn + c
f(1) = a(1)² + b(1) + c
5 = a + b + c
f(2) = a(2)² + b(2) + c
8 = 4a + 2b + c
f(3) = a(3)² + b(3) + c
13 = 9a + 3b + c
On subtracting the equations, we get
5 = 5a + b
3 = 3a + b
Again, on subtracting we get
2 = 2a
a = 1
On putting the values we get,
b = 0.
a + b + c = 5
1 + 0 + c = 5
c = 4
Hence, the explicit equation for the table is,
f(n) = n² + 4
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Complete the calculation to convert
18
pounds
(lbs)
to grams
(g)
given that
1
lb.
=
453.92
grams.
The conversion of 19 pounds to grams is 8170.74 grams.
How to calculate the value?From the information illustrated, it should be noted that it was illustrated that 1 pound = 453.93 grams.
In this case, in order to fund the value of 18 pounds, we will have to multiply 18 by 453.93 grams.
This will be calculated as:
18lb = 18 × 453.93 grams.
= 8170.74 grams
The value is 8170.74 grams.
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someone please help me ty
Answer:
40
Step-by-step explanation:
We divide 317 by 8 to see how much for each table
317/8 is 39.625
We round up for the next whole number since the last table is probably not filled all the way
So we need 40 tables
Hopes this helps please mark brainliest
Answer:
40 tables
Step-by-step explanation:
317 divided by 8 equals 39.625
Round the answer.
Since the number after the decimal is bigger than 4, round up to the nearest whole number which is 40.
P.S. this is simple math. No offense, but you should have been able to figure this out yourself. It's not that hard. Again, not trying to offend you. Just letting you know.
What is the absolute value of -330?
Answer:
Why is | 330 | the absolute value of the number 330?
The absolute value of a number is how far away the number is from zero. The absolute value is ALWAYS positive.
What is the absolute value of -330?
The negative version of the number is also | 330 |
More Examples
Here are more examples of even and odd numbers in sequence:
Number 328 329 331 332
Absolute Value 328 329 331 332
Select the correct answer.
Here are four decimal numbers:
0.702, 0.76, 0.91, 0.73
Choose the list that shows the numbers in order from smallest to largest.
O
O
0.702, 0.91, 0.73, 0.76
0.702, 0.73, 0.76, 0.91
0.91, 0.702, 0.76, 0.73
0.91, 0.76, 0.73, 0.702
702, 0.91, 0.73, 0.76 shows the decimal numbers in order from smallest to largest.
What is a decimal number?
A decimal is a number with a whole and a fractional component. Decimal numbers, which are in between integers, are used to express the numerical value of full and partially whole amounts. The decimal point is the dot that separates the whole number from the fractional part of the number. An example of a decimal number is 34.5.Here are four decimal numbers:
0.702, 0.76, 0.91, 0.73
the numbers in order from smallest to largest.
702, 0.91, 0.73, 0.76
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Answer:
B) 0.702, 0.73, 0.76, 0.91
Step-by-step explanation:
The given set of decimal numbers (in any order) is:
0.702, 0.76, 0.91, 0.73Each number has zero units.
Comparing the digits in the tenth place, all the numbers have 7 tenths except 0.91 which has 9 tenths. Therefore, 0.91 is the largest number as 9 > 7.
Comparing the digits in the hundredths place of the other three numbers, 0.702 is the smallest number as it has zero hundredths.
As 0.73 has 3 hundredths and 0.76 has 6 hundredths, this means that 0.73 is the second smallest number as 3 < 6.
Therefore, the given set of decimals in order from smallest to largest is:
0.702, 0.73, 0.76, 0.91Find the slope (2, -7) and (5, -4)
the slope is 1 because 3/3
Answer:
1
Step-by-step explanation:
When two points are given;
Slope =y2-y1/x2-x1= -4-(-7)/5-2
= -4+7/3
= 3/3
=1
Which expression is equivalent to 6^-6 x 6^6
Answer:
Step-by-step explanation:
x^-3 * x^-3
Need an answer quick please
The required amount in the savings account=$2704.05
What is simple interest?
Calculating the interest on a loan using simple interest is quick and simple. Simple interest is calculated by dividing the principle by the daily interest rate and the number of days between installments.
A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest.
P=2700, r=0.3%=0.003, t= 0.5 year
A= P(1+rt)
= 2700(1+ 0.003*0.5)
= 2700(1+ 0.0015)
= 2700(1.0015)
= 2704.05
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Write an equation for the nth term of the arithmetic sequence
The equation for the nth term of the arithmetic sequence is [tex]a_{n}[/tex] = 25 - 4n
The nth term of the arithmetic sequence:An arithmetic sequence or arithmetic progression is a series of numbers with a common difference. For example 1, 2, 3, 4... is an Arithmetic sequence with a common difference 1. In an Arithmetic sequence, the difference between every two consecutive terms will be equal.
The formula for the nth term of a sequence is given below
=> [tex]a_{n}[/tex] = a + (n-1)d
where a is the first term and d is a common difference.
Here we have
21, 17, 13 ... is the arithmetic sequence
Where first term a = 21
and common difference d = term2 - term1 = 17 - 21 = - 4
As we know the nth term of AP, [tex]a_{n}[/tex] = a + (n-1)d
=> [tex]a_{n}[/tex] = 21 + (n-1)(-4)
=> [tex]a_{n}[/tex] = 21 - 4n + 4
=> [tex]a_{n}[/tex] = 25 - 4n
Therefore,
The equation for the nth term of the arithmetic sequence is [tex]a_{n}[/tex] = 25 - 4n
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brainliest if you answer :) thanksss
AC is congruent to SU
If your car gets 35 miles per gallon, how much does it cost to drive 420 miles when gasoline costs $2.50 per gallon?
The cost is $
(Simplify your answer. Round to the nearest cent as needed.)
Answer: 30$
Step-by-step explanation:
first you divide 420 by 35 and you get 12 times 2.50$ equals 30$
Suppose Tom borrows $4000 at an interest rate of 3% compounded each year.
Assume that no payments are made on the loan.
Follow the instructions below. Do not do any rounding.
(a) Find the amount owed at the end of 1 year.
(b) Find the amount owed at the end of 2 years.
The amount owed at the end of 1 year is $4120 and by the end of 2 years, $4243.60 when Tom borrows $4000 at an interest rate of 3% compounded each year.
What is compound interest?The interest you earn on interest is known as compound interest. Simple math can be used to demonstrate this: if you have $100 and it earns 5% interest annually, you will have $105 at the end of the first year. You will end up with $110.25 at the end of the second year. In order to calculate compound interest, multiply the principal of the original loan by the annual interest rate multiplied by the number of compound periods minus one.
Here,
principle amount=$4000
rate of interest=3%
For first year,
A=P(1+r/n)^(nt)
A=4000(1+3/12)^12*1
A=$4,120.00
For first year,
A=P(1+r/n)^(nt)
A=4120(1+3/12)^12*1
A=$4,243.60
When Tom borrows $4000 at an interest rate of 3% compounded annually, the total amount due at the end of one year is $4120, and at the end of two years, it is $4243.60.
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Put these numbers in order from least to greatest
By writing the fractions as decimals, we will see that the numbers ordered from least to greatest are:
-5, 2/16, 23/40
How to order the numbers?The 3 numbers given are:
-5
23/40
2/16
The numbers should be ordered as they appear on a number line (from left to right)
The smaller number is, obviously, the negative one, so the thing that we need to check now is what of the two fractions is smaller.
To do so, we can write them as decimals:
23/40 = 0.575
2/16 = 0.125
So the smaller one is 2/16 and then comes 23/40
Then the numbers ordered from smaller to larger are:
-5, 2/16, 23/40
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You are solving a measurement problem where the numbers 3.0471 x 10^9 and 2.4 x 10^-4 are divided. How many significant digits should the quotient have?
A. 2
B. 3
C. 4
D. 5
Answer:
5(d)
Step-by-step explanation:
(3.0471×10⁹)/2.4×10^-4
30471×10^9-4÷24×10^-4-1
30471×10⁵÷24×10^-5
(30471÷24)×10^5-(-5)
1269.625×10^5+5
1269.625×10¹⁰
1.269625×10^10-3
1.269625×10⁷
1.2696 to 5s.f
find m
a. 14
b. 39
c. 51
d. 90
I WILL USE SUM OF INTERIOR ANGLES OF A TRIANGLE TO GET x
[tex](2x + 11) + (4x - 5) + 90 = 180 \\ 2x + 4x + 11 - 5 + 90 = 180 \\ 6x + 96 = 180 \\ 6x = 180 - 96 \\ 6x = 84 \\ \frac{6x}{6} = \frac{84}{6} \\ x = 14[/tex]
THE ANSWER IS OPTION a
X=14°
Which of the statements are true about the image?
Answer:
which image
Step-by-step explanation:
if you tell me I will answer the question
Answer:
image not found
you can send the image privately
A die is rolled. Find the probability of the given event.
(a) The number showing is a 6;
The probability is :
(b) The number showing is an even number;
The probability is :
(c) The number showing is greater than 1;
The probability is :
4
Calculate the percentage of alcohol in a lotion containing 2liters of which hazel (14% of alcohol), 1liter of alcohol (95%) and enough boric acid solution to make 5liters
from the reading above, doesn't seem the boric acid has any alcohol at all, so we can say 0% alcohol.
now let's see how many liters we have hmmm 2 of hazel, 1 of alcohol and the rest in boric acid, to make a total of 5 liters, so boric acid must be 2, since 2 + 1 + 2 = 5.
how much alcohol is there in 14% of 2 liters?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{14\% of 2}}{\left( \cfrac{14}{100} \right)2}\implies 0.28[/tex]
how much alcohol is there in 95% of 1? well, no to bore you to death, is just 0.95 liters, and we know the boric acid has no alcohol.
so in the 5 liters of the lotion, we have 0.28 liters plus 0.95 liters of alcohol total, that's 1.23 liters total.
now, if we know the 100% of the lotion is the 5 liters, how much is 1.23 liters off of it in percentage?
[tex]\begin{array}{ccll} liters&\%\\ \cline{1-2} 5 & 100\\ 1.23& x \end{array} \implies \cfrac{5}{1.23}~~=~~\cfrac{100}{x} \\\\\\ 5x=123\implies x=\cfrac{123}{5}\implies x=\stackrel{\%}{24.6}[/tex]
The half-life of carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows only 73% of
in the carbon-14 expected in living matter, when did the tree die?
The tree died about ] years ago.
Do not round until the final answer. Then round to the nearest whole number.)
Answer:
Time 2 540 years
Step-by-step explanation:
T = 5 600 yares - Half-life
73% - Carbon content
N = 0.73·N₀
Decay constant:
λ = ln 2 / T = 0.693 / 5600 ≈ 0.000124 (years)⁻¹
Law of radioactive decay:
N = N₀·e^(-λ·t)
0.73·N₀ = N₀·e^(-λ·t)
0.73 = e^(-λ·t)
ln (0.73) = -λ·t
t = ln (0.73) / (-λ) = ln (0.73) / (- 0.000124) ≈ 2 540 years
what is the sum of the first 80
Consecutive odd numbers?
Which of the following are solutions to the inequality 2y+3<7? Mark all that are solutions.
[_] 2
[_] 0
[_] -1
[_] 1
y<2 is the solution to the inequality
What is Linear Inequality?
The mathematical expression with unequal sides is known as an inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. In this instance, any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), or not equal to symbol (), is used in place of the equal sign "=" in the expression. Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics.
The symbols "" and ">" signify tight inequalities, while "" and "" signify slack inequalities. A linear inequality looks precisely like a linear equation, but the symbol connecting two expressions is different.
According to the question
2y+3<7
subtracting 3 from both sides
we get,
2y<4
dividing both sides with 2
we get,
y<2
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PLS HELP ASAPPPP URGENT
Answer: 4 + (2*3)^2
Step-by-step explanation:
Find the exact value of the given expression.
cos(2tan^-1(24/7))
Rewrite the function by completing the square. h ( x ) = x 2 + 3 x − 18 h(x)=x 2 +3x−18
The quadratic function h (x) = x^2 + 3x − 18 by completing the square is witten as h(x) = (x + 1.5)^2 - 20.25.
We are given a quadratic function:
h (x) = x^2 + 3x − 18
We need to rewrite the function by completing the square.
We can see the coefficient of x is 3.
So, we will add and subtract the square of half that.
So, find the square of half of 3, we will get;
(3 / 2)^2 = 9 / 4 = 2.25
add and subtract the square of half of 3 from the given function, we will get;
h(x) = x^2 +3x + -18 2.25 -2.25
arrange the expression, we will get;
h(x) = (x^2 +3x +2.25) -18 -2.25
write the expression in parentheses as a square, and simplify the constant, we will get;
h(x) = (x + 1.5)^2 - 20.25
So, the square function is written as h(x) = (x + 1.5)^2 - 20.25.
Thus, the quadratic function h (x) = x^2 + 3x − 18 by completing the square is witten as h(x) = (x + 1.5)^2 - 20.25.
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Which integer makes the following sentence true? -10 < ? < -1
Answer:
Any of the following will work: -9,-8,-7,-6,-5,-4,-3, or -2,
Step-by-step explanation:
What does < mean?
The less than sign shows that the number being compared is LESS than the other number.
Think: 9 < 100 showing that the number 9 is less than the number 100
What does > mean?
The greater than sign shows that the number being compared is GREATER than the other number.
Think: 100 > 9 showing that 100 is greater than the number 9
What is an integer?
Integers are all whole positive and negative numbers including zero.
Think: -13 and 13 are integers but 13.445 or -13.445 are not.
How can we prove these answers?
Simply looking at a number line, we can fill in what numbers would be greater than -10 but less than -1. Remember, these numbers must be whole numbers.