Answer:=
1 7/18
Step-by-step explanation:
Turn the improper fraction into a mixed fraction.
Electricity usage data consists of 45 months has a mean number of units consumed is 390.47 per month with a standard deviation of 170.5 units per month. Assume that the number of units consumed are approximately normally distributed. Estimate 95% confidence interval for the average monthly electricity consumed units.
Answer:
The 95% confidence interval for the average monthly electricity consumed units is between 47.07 and 733.87
Step-by-step explanation:
We have the standard deviation for the sample. So we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 45 - 1 = 44
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 44 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0141
The margin of error is:
M = T*s = 2.0141*170.5 = 343.4
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 390.47 - 343.40 = 47.07 units per month
The upper end of the interval is the sample mean added to M. So it is 390.47 + 343.40 = 733.87 units per month
The 95% confidence interval for the average monthly electricity consumed units is between 47.07 and 733.87
What’s the correct answer for this?
Answer:
C.
Step-by-step explanation:
Density = Mass / Volume
2.7 = 54 / V
V = 54 / 2.7
V = 20 cubic cm
Simplify the quotient shown 3480 divided by 29
Answer:
120
Step-by-step explanation:
3480/29=120
120
Simplify ———
1
final result is 120
Amar wants to make lemonade for a birthday party. He wants to mix 12 tablespoons of sugar in water. He only has a teaspoon which needs to be used 4 times to be equivalent to one tablespoon. At this rate, how many teaspoons of sugar will Amar need to make the lemonade?
Answer:48
Step-by-step explanation:
Given
Amar wants 12 tablespoons of sugar in water.
Amar has teaspoon whose four times is equivalent to 1 tablespoon
i.e. [tex]4\ \text{teaspoon}\equiv 1\ \text{tablespoon}[/tex]
therefore
[tex]12 tablespoon is 4\times 12[/tex]
[tex]\Rightarrow 4\times 12[/tex]
[tex]\Rightarrow 48\ \text{teaspoons}[/tex]
So, amar need to add [tex]48\ \text{teaspoons}[/tex] for lemonade
Answer:6328565394729
Step-by-step explanation:213
sorry
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How do you find the axis of symmery in the form f(x) = 3(x - 4)^2 + 5?
Answer:
so the axis of symmetry is x=4
Answer: X = 4
Explanation: Hope it helps you♡
What is the slope of the line that passes through the points (-3, -3) and
(-18, -23)? Write your answer in simplest form.
Answer:
work is shown and pictured
Solve the following equation for x.
|x/4+3|<6
Answer:
x<12
Step-by-step explanation:
subtract both sides by -3 because you need to isolate x. then you have x/4<3. now you need to get rid of the 4. so you do the opposite of division and multiply 4 by both sides so you get x<12
A research company desires to know the mean consumption of meat per week among people over age 27. A sample of 1179 people over age 27 was drawn and the mean meat consumption was 1.5 pounds. Assume that the population standard deviation is known to be 1.2 pounds. Construct the 99% confidence interval for the mean consumption of meat among people over age 27. Round your answers to one decimal place.
Answer:
The 99% confidence interval for the mean consumption of meat among people over age 27 is between 1.4 pounds and 1.6 pounds.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.575*\frac{1.2}{\sqrt{1179}} = 0.1[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 1.5 - 0.1 = 1.4 pounds
The upper end of the interval is the sample mean added to M. So it is 1.5 + 0.1 = 1.6 pounds
The 99% confidence interval for the mean consumption of meat among people over age 27 is between 1.4 pounds and 1.6 pounds.
In a Washington town, the charge for commerical waste collection is $694.55 for 5 tons of waste and $1098.56 for 8 tons of waste. (a) Find a linear formula for the cost, C. of waste collection as a function of the weight, w, in tons.
Answer:
[tex] m =\frac{1098.56-694.55}{8-5}= 134.67[/tex]
And we can find the intercept like this:
[tex] 694.55 = 134.67*5 +b[/tex]
[tex] b = 694.55 -673.35= 21.2[/tex]
And the equation would be given by:
[tex] C = 134.67 w + 21.2[/tex]
Step-by-step explanation:
For this case we want a function given by:
[tex] C = mw +b[/tex]
Where C is the cost, m the slope, w the weight and b the intercept.
We have the following info (w=5, C= 694.55) and (w=8, C=1098.56) and we can find the slope with this formula:
[tex] m =\frac{1098.56-694.55}{8-5}= 134.67[/tex]
And we can find the intercept like this:
[tex] 694.55 = 134.67*5 +b[/tex]
[tex] b = 694.55 -673.35= 21.2[/tex]
And the equation would be given by:
[tex] C = 134.67 w + 21.2[/tex]
A linear function is a function that changes at a constant rate.
The formula of the linear relationship is [tex]C = 134.67w + 21.2[/tex]
The given parameters are:
w = 5, C = 694.55 ---- Charges for 5 tonsw = 8, C = 1098.56 ---- Charges for 8 tonsStart by calculating the slope (m)
[tex]m = \frac{C_2 - C_1}{w_2 - w_1}[/tex]
This gives
[tex]m = \frac{1098.56 - 694.55 }{8- 5}[/tex]
Simplify
[tex]m = \frac{404.01}{3}[/tex]
This gives
[tex]m = 134.67[/tex]
The equation is then calculated as:
[tex]C = m(w -w_1) + w_1[/tex]
This gives
[tex]C = 134.67(w -5) + 694.55[/tex]
Expand
[tex]C = 134.67w -673.35 + 694.55[/tex]
[tex]C = 134.67w + 21.2[/tex]
Hence, the formula of the linear relationship is [tex]C = 134.67w + 21.2[/tex]
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an amount was invested at r% per quarter. what value of r will ensure that accumulated amount at the end of one year is 1.5 times more than amount invested
Answer:
[tex]r=25.7\%[/tex] will ensure that accumulated amount at the end of one year is 1.5 times more than amount invested
Step-by-step explanation:
Given: An amount was invested at r% per quarter.
To find: value of r such that accumulated amount at the end of one year is 1.5 times more than amount invested
Solution:
Let P denotes amount invested and n denotes time
As an amount (A) was invested at r% per quarter,
[tex]A=P\left ( 1+\frac{r}{400} \right )^{4n}[/tex]
According to question, accumulated amount at the end of one year is 1.5 times more than amount invested.
So,
[tex]A=1.5P+P=2.5P\\A=2.5P\\P\left ( 1+\frac{r}{400} \right )^{4n}=2.5P[/tex]
Put n = 1
[tex]P\left ( 1+\frac{r}{400} \right )^{4}=2.5P\\\left ( 1+\frac{r}{400} \right )^{4}=2.5\\1+\frac{r}{400} =(2.5)^{\frac{1}{4}}\\\frac{r}{100}=(2.5)^{\frac{1}{4}}-1\\r=100\left [ (2.5)^{\frac{1}{4}}-1 \right ]\\=25.7\%[/tex]
Find the equation of the line passing through the point (4,−1) that is parallel to the line 2x−3y=9 Find the slope of the line 2x−3y=9. Use a forward slash (i.e. "/") for all fractions (e.g. 1/2 for 12). m=____ What would the parallel slope be? m=______ Use the slope to find the y-intercept of the parallel line. b= _____
Answer:
Step-by-step explanation:
2x - 3y = 9
-3y = -2x + 9
[tex]y=\frac{-2}{-3}x + \frac{9}{-3}\\\\y=\frac{2}{3}x-3\\[/tex]
Parallel lines have same slope.So,
Slope m = 2/3
(4 , -1)
Equation: y - y1 = m(x - x1)
[tex]y-[-1]=\frac{2}{3}(x - 4)\\\\y+1=\frac{2}{3}*x - \frac{2}{3}*4\\\\y+1=\frac{2}{3}x-\frac{8}{3}\\\\y=\frac{2}{3}x-\frac{8}{3}-1\\\\y=\frac{2}{3}x-\frac{8}{3}-\frac{3}{3}\\\\y=\frac{2}{3}x-\frac{11}{3}[/tex]
b = -11/3
Is the function given by f(x)equalsleft brace Start 2 By 2 Matrix 1st Row 1st Column one fourth x plus 1 comma 2nd Column for x less than or equals 4 comma 2nd Row 1st Column 4 x minus 11 comma 2nd Column for x greater than 4 comma EndMatrix continuous at xequals4? Why or why not? Choose the correct answer below. A. The given function is continuous at xequals4 because ModifyingBelow lim With x right arrow 4 f (x )does not exist. B. The given function is not continuous at xequals4 because f(4) does not exist. C. The given function is continuous at xequals4 because the limit is 2. D. The given function is not continuous at xequals4 because ModifyingBelow lim With x right arrow 4 f (x )does not exist.
Answer:
C. The given function is continuous at x=4 because the limit is 2.
Step-by-step explanation:
Given the function:
[tex]f(x)=\left\{\begin{array}{ccc}\frac{1}{4}x+1 &x\leq 4\\4x-11&x>4\end{array}\right[/tex]
We are to determine if the function is continuous at x=4.
For a function to be continuous at some value c in its domain:
f(c) must be defined.[tex]Lim_{x \to c}$ f(x)[/tex] must exist. [tex]f(c)=Lim_{x \to c}$ f(x)[/tex]Now: at x=4
[tex]f(4)=\dfrac{1}{4}*4+1=2[/tex][tex]Lim_{x \to 4}f(x)=2[/tex]Since the two values are the same, we say that f(x) is continuous at x=4.
The correct option is C.
I WILLL GIVE BRAINLIEST ANSWER ASAP
Answer: 2ND ONE
Step-by-step explanation:
Answer:
-3
Step-by-step explanation:
5x+3=4x
5x-4x=-3
x=-3
Edit: Check by plugging in x = -3
5(-3)+3=4(-3)
-15+3=-12
-12=-12✅
What is the product of 4.672 and 8?
Answer:
12.672
Step-by-step explanation:
Answer: 37.376
Step-by-step explanation: Because 4.672 x 8 is 37.376
Which expressions represent a perfect square monomial and its square root? Check all that apply. 121; 11 4x2; 2x 9x2 – 1; 3x - 1 25x; 5x 49x4; 7x2
Answer:
its 1,2,and 5
Step-by-step explanation:
Answer:
A, B, E
Step-by-step explanation:
Edge
A regression was run to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x).The results of the regression were:
y = a + bx
a = -0.762
b = 0.119
r2 = 0.8649
r = 0.93
A) Write the equation of the Least Squares Regression line of the form y = + x
B) If a country increases its life expectancy, the happiness index will increase or decrease?
C) If the life expectancy is increased by 3.5 years in a certain country, how much will the happiness index change?
D) Use the regression line to predict the happiness index of a country with a life expectancy of 67 years.
Answer:
(A) [tex]y=-0.762+0.119x[/tex]
(B) If a country increases its life expectancy, the happiness index will increase.
(C) If the life expectancy is increased by 3.5 years in a certain country, the happiness index will increase by 0.4165.
(D) If the life expectancy is 67 years in a certain country, the happiness index will be 7.21.
Step-by-step explanation:
A regression analysis was performed to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x).
The output of the regression analysis are as follows:
a = -0.762
b = 0.119
r² = 0.8649
r = 0.93
(A)
The equation of the Least Squares Regression line of the form y = _ + _ x is:
[tex]y=-0.762+0.119x[/tex]
(B)
The correction between the variables happiness index (y) and life expectancy in years of a given country (x) is, 0.93.
The correlation coefficient is positive. This implies that there is a positive relation between the two variables, i.e. as the value of life expectancy in years increases the happiness index also increases.
Thus, if a country increases its life expectancy, the happiness index will increase.
(C)
Compute the value of y for x = x + 3.5 as follows:
[tex]y=-0.762+0.119x[/tex]
[tex]=-0.762+0.119\times (x+3.5)\\\\=(-0.762+0.119x)+0.4165\\\\=y+0.4165[/tex]
Thus, if the life expectancy is increased by 3.5 years in a certain country, the happiness index will increase by 0.4165.
(D)
Compute the value of y for x = 67 as follows:
[tex]y=-0.762+0.119x[/tex]
[tex]=-0.762+0.119\times 67\\\\=-0.762+7.973\\\\=7.211\\\\\approx 7.21[/tex]
Thus, if the life expectancy is 67 years in a certain country, the happiness index will be 7.21.
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
B. (f + g)(x) = x - 7
Step-by-step explanation:
→Set it up, like so:
-3x - 5 + 4x - 2
→Add like terms (-3x and 4x, -5 and -2):
x - 7
1/x=1/2 / 4/5
Solve for x.
X =
Answer:
1/x = 1/2÷4/5
1/x=1/2 x 5/4
1/x=5/8
5x=8
x=1.6
A shop has 4 types of sweets (chocolate, taffy, gummies, and cookies), 2 types of snacks (chips and crackers), and 3 types of drinks (sodas, juice, and sports drinks).
Mystery boxes are put together that randomly combine 1 sweet, 1 snack, and 1 drink.
What is the probability that a mystery box contains chocolate, chips, and juice?
Answer:
1/24
Step-by-step explanation:
1/4*1/2*1/3 = 1/24
What is the purchase price of the land
Answer:
Answer:B. $100,000
Step-by-step explanation:
x is the number of years since the purchase of the land.
That means that when 0 years have passed by, it is when the land was purchased.
At x = 0, the price of the land was $100,000.
That means that the purchase price of the land is $100,000.
Graph the line that represents this equation. 3x - 4y =8
Answer:
See attachment
Step-by-step explanation:
The solution is given in the image.
Which graph is the graph of the function?The graph of a feature f is the set of all factors in the plane of the form (x, f(x)). We can also outline the graph of f to be the graph of the equation y = f(x). So, the graph of a feature is a special case of the graph of an equation.
What does the axis of a graph constitute?An axis is a line to the aspect or backside of a graph; it's far labeled to give an explanation for the graph's meaning and the devices of measurement. The x-axis, the horizontal line at the lowest of a graph, may be labeled to present facts about what the graph represents.
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I need help pleaseeee help meee
Answer:
x>-1
Step-by-step explanation:
Answer:
x > -1
Step-by-step explanation:
First we need to determine what sign this inequality uses:
A closed circle represents greater than or equal to (≥) or less than or equal to (≤)An open circle represent greater than (>) or less than (<)Here we have an open circle so we know our sign will either be > or <
Our point is on the -1, and the arrow points in the direction of the sign as long as the variable x is on the left side of the answer
So the arrow is point to the right, indicating our sign will also be "pointing" to the right (>)
The inequality of this graph reads: x > -1
Given that a = 5 , b = − 2 and c = − 2 work out 2 b − 3 a c
Answer:
26Step-by-step explanation:
[tex]a = 5 ,\\b = - 2 \\ c = - 2 \\ 2b - 3ac=?\\2(-2) -3(5)(-2)\\-4 +30\\= 26[/tex]
Answer:
-34
Step-by-step explanation:
2x-2-3(4)(-2)
which is -34
Bob is a travel agent. He receives 7% commission when he books a cruise for a customer. How much commission will he receive for booking a $3,900 cruise?
Answer:
$273
Step-by-step explanation:
$3900= 100%
$39 = 1%
39(1%)*7= $273 (7%)
The commission will he received should be $273
Given that,
He receives 7% commission when he books a cruise for a customercalculation:= 7% of $3,900
= $273
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I need help with this one
Answer:
-12
Step-by-step explanation:
The first term in the sequence 5, 7, −7, ... is 5. Each even-numbered term is 2 more than the previous term and each odd-numbered term, after the first, is (−1) times the previous term. For example, the second term is 5+2 and the third term is (−1)×7. What is the 255th term of the sequence?
Answer:
Step-by-step explanation:
According to the condition, your terms are arranged as
5, 7 , -7 ,-5, 5, 7, -7, 5, -5,...................
So one loop will have 4 terms: 5, 7, -7. -5
Hence after 63 loops, the new loop has only 3 terms. That means the last loop will be 5, 7 ,-7. In other words, the 255th term will be -7
The fraction of students ages 10 to 17 who favor math or science is
Answer:
So if 17/25 of the students like math, science, and art and 3/20 of the students like art only. We first need to find common demoninator. 68/100 and for the second one 15/100. Subtract them both
68-15 = 53/100 of the students factor math, and science or 53%
In right triangle $ABC,$ $\angle C = 90^\circ.$ Median $\overline{AM}$ has a length of $19,$ and median $\overline{BN}$ has a length of $13.$ What is the length of the hypotenuse of the triangle?
Answer:
AB = 2√106 ≈ 20.591
Step-by-step explanation:
The Pythagorean theorem says the square of the hypotenuse is equal to the sum of the squares of the legs.
For median AM, we have ...
AM² = CM² +AC² = (BC/2)² +AC²
For median BN, we have ...
BN² = CN² +BC² = (AC/2)² +BC²
The sum of these two equations is ...
AM² +BN² = BC²/4 +AC² +AC²/4 +BC² = (5/4)(AC² +BC²)
AM² +BN² = (5/4)(AB²)
The hypotenuse of triangle ABC is then ...
AB = √(4/5(AM² +BN²))
AB = 2√((19² +13²)/5)
AB = 2√106 ≈ 20.591
The point A (-7,5) is reflected over the line x = -5, and then is reflected over the line x= 2. What are the coordinates of
A?
o (7, 19)
O (10,5)
(7,5)
(10, 19)
Answer:
(7, 5) is the final reflection of the point.
Step-by-step explanation:
We are given point A(-7, 5) which is first reflected over the line [tex]x= -5[/tex].
The minimum distance of the point A(-7, 5) from the line [tex]x= -5[/tex] is 2 units across the horizontal path (No change in y coordinate).
Point A lies 2 units on the left side of the line [tex]x= -5[/tex].
So, its reflection will be 2 units on the right side of [tex]x= -5[/tex].
Let its reflection be A' which has coordinates as (-5+2,5) i.e. (-3, 5).
Now A'(-3, 5) is reflected on the line [tex]x=2[/tex].
The minimum distance of the point A'(-3, 5) from the line [tex]x=2[/tex] is 5 units across the horizontal path (No change in y coordinate).
Point A' lies 5 units on the left side of the line [tex]x=2[/tex].
So, its reflection will be 5 units on the right side of [tex]x=2[/tex].
Let its reflection be A'' which has coordinates as (2+5, 5) i.e (7, 5) is the final reflection of the point..
Please find attached image.
(7, 5) is the final reflection of the point.
Simplify the following:
(4x^3+2x) + (8x^3 -5x + 4)
Answer:
12x^3 - 3x + 4
Im 100% percent sure and if you are kind enough, I’d love a BRAINLIEST :)
