Answer:
8 + 2x
Step-by-step explanation:
You are adding 8 to 2 times an unknown number.
Carisoprodol, a generic muscle relaxer, claims to have, on average, at least 120 milligrams of active ingredient. An independent lab tests a random sample of 50 tablets and finds the mean content of active ingredient in this sample is 116.2 milligrams with a standard deviation of 17 milligrams. If the lab doesn't believe the manufacturer's claim, what is the approximate p-value for the suitable test
Answer:
The approximate p-value for the suitable test
0.05 < p < 0.1
|t| = |-1.5806| = 1.5806
t = 1.5806 < 2.009 at 0.05 level of significance
Carisoprodol, a generic muscle relaxer, claims to have, on average, is equal to 120 milligrams of active ingredient.
Step-by-step explanation:
Step(i):-
Given mean of the Population 'μ' = 120 milligrams
Given random sample size 'n' = 50
Given mean of the sample x⁻ = 116.2 milligrams
Standard deviation of the sample 'S' = 17 milligrams
Null hypothesis : 'μ' = 120
Alternative hypothesis : 'μ' < 120
Step(ii):-
Test statistic
[tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }[/tex]
[tex]t = \frac{116.2 - 120}{\frac{17}{\sqrt{50} } } = \frac{-3.8}{2.404} = -1.5806[/tex]
Degrees of freedom
ν = n-1 = 50 -1 =49
t₀.₀₅ = 2.009
|t| = |-1.5806| = 1.5806
t = 1.5806 < 2.009 at 0.05 level of significance
Null hypothesis is accepted
Carisoprodol, a generic muscle relaxer, claims to have, on average, is equal to 120 milligrams of active ingredient.
P- value:-
The test statistic |t| = 1.5806 at 49 degrees of freedom
The test statistic value is lies between 0.05 to 0.1
0.05 < p < 0.1
Answer:
0.0602
Step-by-step explanation:
jus took the test
Use Green's Theorem to evaluate ?C F·dr. (Check the orientation of the curve before applying the theorem.)
F(x, y) =< x + 4y3, 4x2 + y>
C consists of the arc of the curve y = sin x from (0, 0) to (p, 0) and the line segment from (p, 0) to (0, 0).
Answer:
Step-by-step explanation:
given a field of the form F = (P(x,y),Q(x,y) and a simple closed curve positively oriented, then
[tex]\int_{C} F \cdot dr = \int_A \frac{dQ}{dx} - \frac{dP}{dy} dA[/tex] where A is the area of the region enclosed by C.
In this case, by the description we can assume that C starts at (0,0). Then it goes the point (pi,0) on the path giben by y = sin(x) and then return to (0,0) along the straigth line that connects both points. Note that in this way, the interior the region enclosed by C is always on the right side of the point. This means that the curve is negatively oriented. Consider the path C' given by going from (0,0) to (pi,0) in a straight line and the going from (pi,0) to (0,0) over the curve y = sin(x). This path is positively oriented and we have that
[tex] \int_{C} F\cdot dr = - \int_{C'} F\cdot dr[/tex]
We use the green theorem applied to the path C'. Taking [tex] P = x+4y^3, Q = 4x^2+y[/tex] we get
[tex] \int_{C'} F\cdot dr = \int_{A} 8x-12y^2dA[/tex]
A is the region enclosed by the curves y =sin(x) and the x axis between the points (0,0) and (pi,0). So, we can describe this region as follows
[tex]0\leq x \leq \pi, 0\leq y \leq \sin(x)[/tex]
This gives use the integral
[tex] \int_{A} 8x-12y^2dA = \int_{0}^{\pi}\int_{0}^{\sin(x)} 8x-12y^2 dydx[/tex]
Integrating accordingly, we get that [tex]\int_{C'} F\cdot dr = 8\pi - \frac{16}{3}[/tex]
So
[tex] \int_{C} F cdot dr = - (8\pi - \frac{16}{3}) = \frac{16}{3} - 8\pi [/tex]
Match the set of two interior angle measurements with the third interior angle measurement that can make a triangle.
40°, 50°
131°
60°
249, 250
90°
42°, 66°
72°
60°, 60°
Answer:
[tex]40^\circ,50^\circ$ and 90^\circ[/tex]
[tex]42^\circ,66^\circ$ and 72^\circ[/tex]
[tex]60^\circ,60^\circ$ and 60^\circ[/tex]
Step-by-step explanation:
The sum of angles in a triangle is 180 degrees
(a)Given the angles 40° and 50°
The third angle is, therefore: [tex]180^\circ-(40^\circ+50^\circ)=90^\circ[/tex]
We, therefore, have the set: [tex]40^\circ,50^\circ$ and 90^\circ[/tex]
(b)Given the angles 42° and 66°
The third angle is, therefore: [tex]180^\circ-(42^\circ+66^\circ)=72^\circ[/tex]
We, therefore, have the set: [tex]42^\circ,66^\circ$ and 72^\circ[/tex]
(c)Given the angles 60° and 60°
The third angle is, therefore: [tex]180^\circ-(60^\circ+60^\circ)=60^\circ[/tex]
We, therefore, have the set: [tex]60^\circ,60^\circ$ and 60^\circ[/tex]
the answers are provided in the picture:
Suppose that the demand function for a product is given by D(p)equals=StartFraction 50 comma 000 Over p EndFraction 50,000 p and that the price p is a function of time given by pequals=1.91.9tplus+99, where t is in days. a) Find the demand as a function of time t. b) Find the rate of change of the quantity demanded when tequals=115115 days. a) D(t)equals=nothing (Simplify your answer.)
Answer:
(a)[tex]D(t)=\dfrac{50000}{1.9t+9}[/tex]
(b)[tex]D'(115)=-1.8355[/tex]
Step-by-step explanation:
The demand function for a product is given by :
[tex]D(p)=\dfrac{50000}{p}[/tex]
Price, p is a function of time given by [tex]p=1.9t+9[/tex], where t is in days.
(a)We want to find the demand as a function of time t.
[tex]\text{If } D(p)=\dfrac{50000}{p},$ and p=1.9t+9\\Then:\\D(t)=\dfrac{50000}{1.9t+9}[/tex]
(b)Rate of change of the quantity demanded when t=115 days.
[tex]\text{If } D(t)=\dfrac{50000}{1.9t+9}[/tex]
[tex]\dfrac{\mathrm{d}}{\mathrm{d}t}\left[\dfrac{50000}{\frac{19t}{10}+9}\right]}}=50000\cdot \dfrac{\mathrm{d}}{\mathrm{d}t}\left[\dfrac{1}{\frac{19t}{10}+9}\right]}[/tex]
[tex]=-50000\cdot\dfrac{d}{dt} \dfrac{\left[\frac{19t}{10}+9\right]}{\left(\frac{19t}{10}+9\right)^2}}}[/tex]
[tex]=\dfrac{-50000(1.9\frac{d}{dt}t+\frac{d}{dt}9)}{\left(\frac{19t}{10}+9\right)^2}}}[/tex]
[tex]=-\dfrac{95000}{\left(\frac{19t}{10}+9\right)^2}\\$Simplify/rewrite to obtain:$\\\\D'(t)=-\dfrac{9500000}{\left(19t+90\right)^2}[/tex]
Therefore, when t=115 days
[tex]D'(115)=-\dfrac{9500000}{\left(19(115)+90\right)^2}\\D'(115)=-1.8355[/tex]
I really need help, please help me.
Answer:
96 degrees
Step-by-step explanation:
Since x is half of 168, its angle measure is 84 degrees. Since x and y are a linear pair, their angle measures must add to 180 degrees, meaning that:
y+84=180
y=180-84=96
Hope this helps!
Please Solve this 7 > 2n - 3
Answer:
n<5
Step-by-step explanation:
7>2n-3
+3 +3
10>2n
Divide by 2
5>n
Betty can mow a lawn in 20 minutes. Bullwinkle can mow the same lawn in 60 minutes. How long does it take for both Betty and Bullwinkle to mow the lawn if they are working together? Express your answer as a reduced fraction.
Answer:
15 minutes
Step-by-step explanation:
Betty mows at 3 times the speed that Bullwinkle does, so is equivalent to having 3 Bullwinkles in her place. That makes the lawn get mowed as though 4 Bullwinkles were working, so it will take 1/4 the time it takes Bullwinkle to mow the whole yard. 1/4 of 60 minutes is 15 minutes.
Working together, Betty and Bullwinkle will take 15 minutes to mow the lawn.
wo cards are selected from a standard deck of 52 playing cards. The first card is not replaced before the second card is selected. Find the probability of selecting a nine and then selecting an eight. The probability of selecting a nine and then selecting an eight is nothing.
Answer:
0.6%
Step-by-step explanation:
We have a standard deck of 52 playing cards, which is made up of 13 cards of each type (hearts, diamonds, spades, clubs)
Therefore there are one nine hearts, one nine diamonds, one nine spades and one nine clubs, that is to say that in total there are 4. Therefore the probability of drawing a nine is:
4/52
In the second card it is the same, an eight, that is, there are 4 eight cards, but there is already one less card in the whole deck, since it is not replaced, therefore the probability is:
4/51
So the final probability would be:
(4/52) * (4/51) = 0.006
Which means that the probability of the event is 0.6%
Which are the right ones?
Answer:
20 4/5
Step-by-step explanation:
13/5 times 8/1
104/5
which is simplify
to 20 4/5\
hope this helps
Rocco used these steps to solve the equation 4x + 6 = 4 + 2(2x + 1). Which choice describes the meaning of his result, 6 = 6?
Answer:
infinite solutions
Step-by-step explanation:
it means that all x are solution of this equation as 6=6 is always true
Point C ∈ AB and AB = 33 cm. Point C is 2 times farther from point B than point C is from point A. Find AC and CB.
Answer:
AC = 11 cm , CB = 22 cm
Step-by-step explanation:
let AC = x then BC = 2x , then
AC + BC = 33, that is
x + 2x = 33
3x = 33 ( divide both sides by 3 )
x = 11
Thus
AC = x = 11 cm and CB = 2x = 2 × 11 = 22 cm
Express 12/16 in quarters
The Speedmaster IV automobile gets an average of 22.0 miles per gallon in the city. The standard deviation is 3 miles per gallon. Find the probability that on any given day, the automobile will get less than 26 miles per gallon when driven in the city. Assume that the miles per gallon that this automobile gets is normally distributed.
Answer:
91% of the time the auto will get less than 26 mpg
Step-by-step explanation:
Think of (or draw) the standard normal curve. Mark the mean (22.0). Then one standard deviation above the mean would be 22.0 + 3.0, or 25.0. Two would be 22.0 + 2(3.0), or 28.0. Finallyl, draw a vertical line at 26.0.
Our task is to determine the area under the curve to the left of 26.0.
Using a basic calculator with built-in statistical functions, we find this area as follows:
normcdf(-100, 26.0, 22.0, 3.0) = 0.9088, which is the desired probability: 91% of the time the auto will get less than 26 mpg.
Sue works an average of 45 hours each week. She gets paid $10.12 per hour and time-and-a-half for all hours over 40 hours per week. What is her annual income?
Step-by-step explanation:
40 x $10.12/hr = $404.80
5 x $15.18/hr = $ 75.90
over time = $10.12 + $5.06 ( half of $10.12) = $15.18/hr
$404.80 + $75.90 = $480.70/weekly pay
assuming she works 52 weeks a year
$480.70 × 52 weeks = $24,996.40/yr
1. A door of a lecture hall is in a parabolic shape. The door is 56 inches across at the bottom of the door and parallel to the floor and 32 inches high. Sketch and find the equation describing the shape of the door. If you are 22 inches tall, how far must you stand from the edge of the door to keep from hitting your head
Answer:
See below in bold.
Step-by-step explanation:
We can write the equation as
y = a(x - 28)(x + 28) as -28 and 28 ( +/- 1/2 * 56) are the zeros of the equation
y has coordinates (0, 32) at the top of the parabola so
32 = a(0 - 28)(0 + 28)
32 = a * (-28*28)
32 = -784 a
a = 32 / -784
a = -0.04082
So the equation is y = -0.04082(x - 28)(x + 28)
y = -0.04082x^2 + 32
The second part is found by first finding the value of x corresponding to y = 22
22 = -0.04082x^2 + 32
-0.04082x^2 = -10
x^2 = 245
x = 15.7 inches.
This is the distance from the centre of the door:
The distance from the edge = 28 - 15.7
= 12,3 inches.
A College Alcohol Study has interviewed random samples of students at four-year colleges. In the most recent study, 494 of 1000 women reported drinking alcohol and 552 of 1000 men reported drinking alcohol. What is the 95% confidence interval of the drinking alcohol percentage difference between women and men
Answer:
The 95% confidence interval for the difference between the proportion of women who drink alcohol and the proportion of men who drink alcohol is (-0.102, -0.014) or (-10.2%, -1.4%).
Step-by-step explanation:
We want to calculate the bounds of a 95% confidence interval of the difference between proportions.
For a 95% CI, the critical value for z is z=1.96.
The sample 1 (women), of size n1=1000 has a proportion of p1=0.494.
[tex]p_1=X_1/n_1=494/1000=0.494[/tex]
The sample 2 (men), of size n2=1000 has a proportion of p2=0.552.
[tex]p_2=X_2/n_2=552/1000=0.552[/tex]
The difference between proportions is (p1-p2)=-0.058.
[tex]p_d=p_1-p_2=0.494-0.552=-0.058[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{494+552}{1000+1000}=\dfrac{1046}{2000}=0.523[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.523*0.477}{1000}+\dfrac{0.523*0.477}{1000}}\\\\\\s_{p1-p2}=\sqrt{0.000249+0.000249}=\sqrt{0.000499}=0.022[/tex]
Then, the margin of error is:
[tex]MOE=z \cdot s_{p1-p2}=1.96\cdot 0.022=0.0438[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=(p_1-p_2)-z\cdot s_{p1-p2} = -0.058-0.0438=-0.102\\\\UL=(p_1-p_2)+z\cdot s_{p1-p2}= -0.058+0.0438=-0.014[/tex]
The 95% confidence interval for the difference between proportions is (-0.102, -0.014).
The volume of a water in a fish tank is 84,000cm the fish tank has the length 60cm and the width 35cm. The water comes to 10cm from the top of the tank. calculate the height of the tank.
Answer:
Height of tank = 50cm
Step-by-step explanation:
Volume of water from tank that the water is 10cm down is 84000cm³
Length = 60cm
Width = 35cm
Height of water = x
Volume = length* width* height
Volume= 84000cm³
84000 = 60*35*x
84000= 2100x
84000/2100= x
40 = x
Height of water= 40cm
Height of tank I = height of water+ 10cm
Height of tank= 40+10= 50cm
Height of tank = 50cm
How do I solve (2x-y)(3x+y)
Answer:
6x^2 -xy - y^2
Step-by-step explanation:
(2x-y)(3x+y)
FOIL
first: 2x*3x = 6x^2
outer: 2x*y = 2xy
inner: -y*3x = -3xy
last: -y^y = -y^2
Add these together
6x^2 +2xy-3xy - y^2
Combine like terms
6x^2 -xy - y^2
Answer:
[tex]= 6x^2 - xy - y ^2\\ [/tex]
Step-by-step explanation:
[tex](2x - y)(3x + y) \\ 2x(3x + y) - y(3x + y) \\ 6x^2 + 2xy - 3xy - y^2 \\ = 6x ^2- xy - y^2[/tex]
Please help! Correct answer only, please! Matrix C has the dimensions 7 X 2 and Matrix D has the dimensions 2 X 7. Determine the dimensions of the matrix CD, if it is possible. Explain why if it is not. A. Matrix CD would have the dimensions 2 X 2 B. Matrix CD would have the dimensions 2 X 7 C. Matrix CD would have the dimensions 7 X 7 D. These matrices cannot be multiplied because their dimensions don't align.
Answer: C) CD has dimensions 7 x 7
Step-by-step explanation:
When multiplying matrices the number of rows of the first matrix MUST equal the number of columns of the second matrix. I call these the "inside" numbers. The resulting dimension will be the "outside" numbers.
[7 x 2] × [2 x 7]
↓ ↓
inside These must match!
[7 x 2] × [2 x 7]
↓ ↓
outside These are the dimensions!
7 × 7 are the dimensions of CD
Gas prices are up 30% since last year when they were $4.35, how much is gas now?
Answer:
given;
previous year price of gas= $4.35
price of gas has been increased by 30%
now,price of gas in present year=?
we have;
price of gas in present year=priceof
previous year+30%of price of previous year.
so ,price of gas in present year=4.35+30%of4.35
=$4.35+30/100×4.35
=$4.35+1.305
= $5.655. ans....
therefore, the price of gas in present year is ;$5.655.
Evaluate for f=3. 2f - f +7
The function f(x)= 200/X+ 10 models the cost per student of a field trip when x students go on the trip. How is the parent function
f(x) = 1/x transformed to create the function f(x)= 200/x + 10
O It is vertically stretched by a factor of 200.
O It is vertically stretched by a factor of 200 and shifted 10 units leftt
O It is vertically stretched by a factor of 200 and shifted 10 units up.
O It is vertically stretched by a factor of 200 and shifted 10 units right
Answer:
It is vertically stretched by a factor of 200 and shifted 10 units right
Step-by-step explanation:
Suppose we have a function f(x).
a*f(x), a > 1, is vertically stretching f(x) a units. Otherwise, if a < 1, we are vertically compressing f(x) by a units.
f(x - a) is shifting f(x) a units to the right.
f(x + a) is shifting f(x) a units to the left.
In this question:
Initially: [tex]f(x) = \frac{1}{x}[/tex]
Then, first we shift, end up with:
[tex]f(x+10) = \frac{1}{x + 10}[/tex]
f was shifted 10 units to the left.
Finally,
[tex]200f(x+10) = \frac{200}{x + 100}[/tex]
It was vertically stretched by a factor of 200.
So the correct answer is:
It is vertically stretched by a factor of 200 and shifted 10 units right
Answer:
the answer is D
Step-by-step explanation:
Circle O has a circumference of 36π cm. Circle O with radius r is shown. What is the length of the radius, r? 6 cm 18 cm 36 cm 72 cm
Answer: 18 cm
Step-by-step explanation:
We know the circumference formula is C=2πr. Since our circumference is given in terms of π, we can easily figure out what the radius is.
36π=2πr [divide both sides by π to cancel out]
36=2r [divide both sides by 2]
r=18 cm
Answer:
18cm
Step-by-step explanation:
because i found it lol
Multi step equation 18=3(3x-6)
Answer: X= 4
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
18=3(3x−6)
18=(3)(3x)+(3)(−6)(Distribute)
18=9x+−18
18=9x−18
Step 2: Flip the equation.
9x−18=18
Step 3: Add 18 to both sides.
9x−18+18=18+18
9x=36
Step 4: Divide both sides by 9.
9x
9
=
36
9
Answer:
X=4
Step-by-step explanation:
18=3(3X-6)
18=3><(3X-6)
18=9X-18
9X=-18-18
9X=36
X=36/9
X=4
Hope this helps
Brainliest please
If the endpoints of AB have the coordinates A(9, 8) and B(-1, -2), what is the AB midpoint of ?
Answer:
(4, 3)
Step-by-step explanation:
Use the midpoint formula: [tex](\frac{x1+x2}{2}, \frac{y1+y2}{2} )[/tex]
What is the value of (4-2) – 3x4?
О-20
оооо
4
Answer:
-10
Step-by-step explanation:
Use the Order of Operations - PEMDAS
Do what is in parentheses first - (4-2) = 2
Next multiply 3 and 4 = 12
Last, perform 2 - 12; which equals -10
To reach a particular department at a warehouse, a caller must dial a 4-digit extension. Suppose a caller remembers that the first and last digits of an extension are 5, but they are not sure about the other digits.
How many possible extensions might they have to try?
Answer:
100 possible extensions
Step-by-step explanation:
we can calculated how many possible extensions they have to try using the rule of multiplication as:
___1_____*___10_____*___10_____*____1____ = 100
1st digit 2nd digit 3rd digit 4th digit
You know that the 1st and 4th digits of the extension are 5. it means that you just have 1 option for these places. On the other hand, you don't remember nothing about the 2nd and 3rd digit, it means that there are 10 possibles digits (from 0 to 9) for each digit.
So, There are 100 possibles extensions in which the 5 is the first and last digit.
A grocery store has an average sales of $8000 per day. The store introduced several advertising campaigns in order to increase sales. To determine whether or not the advertising campaigns have been effective in increasing sales, a sample of 64 days of sales was selected. It was found that the average was $8300 per day. From past information, it is known that the standard deviation of the population is $1200. The correct null hypothesis for this problem is A. µ <= 8000. B. µ <= 8300. C. µ = 8000. D. µ > 8300.
Answer:
C) µ = 8000.
Step-by-step explanation:
Explanation:-
Given data A grocery store has an average sales of $8000 per day
mean of the Population μ = $ 8000
sample size 'n' = 64
mean of the sample x⁻ = $ 8300
Null Hypothesis : H₀ : μ = $ 8000
Alternative Hypothesis : H₁: μ > $ 8000
Test statistic
[tex]Z = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{8300 -8000}{\frac{1200}{\sqrt{64} } }[/tex]
Z = 2
Level of significance : ∝ = 0.05
Z₀.₀₅ = 1.96
The calculated value Z = 2 > 1.96 at 0.05 level of significance
Null hypothesis is rejected
Alternative hypothesis is accepted at 0.05 level of significance
Conclusion :-
The advertising campaigns have been effective in increasing sales
In 2013, the population of the state of New York was approximately 19.65 million, and the population of New York City was 8,406,000. In 2013, how many people in New York state did not live in New York City? The answer in standard notation is . The answer in scientific notation is p × 10q, where p is and q is .
Suppose that prices of recently sold homes in one neighborhood have a mean of $225,000 with a standard deviation of $6700. Using Chebyshev's Theorem, what is the minimum percentage of recently sold homes with prices between $211,600 and $238,400
Answer:
[tex] 211600 = 225000 -k*6700[/tex]
[tex] k = \frac{225000-211600}{6700}= 2[/tex]
[tex] 238400 = 225000 +k*6700[/tex]
[tex] k = \frac{238400-225000}{6700}= 2[/tex]
So then the % expected would be:
[tex] 1- \frac{1}{2^2}= 1- 0.25 =0.75[/tex]
So then the answer would be 75%
Step-by-step explanation:
For this case we have the following info given:
[tex] \mu = 225000[/tex] represent the true mean
[tex]\sigma =6700[/tex] represent the true deviation
And for this case we want to find the minimum percentage of sold homes between $211,600 and $238,400.
From the chebysev theorem we know that we have [tex]1 -\frac{1}{k^2}[/tex] % of values within [tex]\mu \pm k\sigma[/tex] if we use this formula and the limit given we have:
[tex] 211600 = 225000 -k*6700[/tex]
[tex] k = \frac{225000-211600}{6700}= 2[/tex]
[tex] 238400 = 225000 +k*6700[/tex]
[tex] k = \frac{238400-225000}{6700}= 2[/tex]
So then the % expected would be:
[tex] 1- \frac{1}{2^2}= 1- 0.25 =0.75[/tex]
So then the answer would be 75%