Answer:
2.5π units^3
Step-by-step explanation:
Solution:-
- We will evaluate the solid formed by a function defined as an elliptical paraboloid as follows:-
[tex]z = 4 - x^2 -4y^2[/tex]
- To sketch the elliptical paraboloid we need to know the two things first is the intersection point on the z-axis and the orientation of the paraboloid ( upward / downward cup ).
- To determine the intersection point on the z-axis. We will substitute the following x = y = 0 into the given function. We get:
[tex]z = 4 - 0 -4*0 = 4[/tex]
- The intersection point of surface is z = 4. To determine the orientation of the paraboloid we see the linear term in the equation. The independent coordinates ( x^2 and y^2 ) are non-linear while ( z ) is linear. Hence, the paraboloid is directed along the z-axis.
- To determine the cup upward or downwards we will look at the signs of both non-linear terms ( x^2 and y^2 ). Both non-linear terms are accompanied by the negative sign ( - ). Hence, the surface is cup downwards. The sketch is shown in the attachment.
- The boundary conditions are expressed in the form of a cylinder and a plane expressed as:
[tex]x^2 + y^2 = 1\\\\z = 4[/tex]
- To cylinder is basically an extension of the circle that lies in the ( x - y ) plane out to the missing coordinate direction. Hence, the circle ( x^2 + y^2 = 1 ) of radius = 1 unit is extended along the z - axis ( coordinate missing in the equation ).
- The cylinder bounds the paraboloid in the x-y plane and the plane z = 0 and the intersection coordinate z = 4 of the paraboloid bounds the required solid in the z-direction. ( See the complete sketch in the attachment )
- To determine the volume of solid defined by the elliptical paraboloid bounded by a cylinder and plane we will employ the use of tripple integrals.
- We will first integrate the solid in 3-dimension along the z-direction. With limits: ( z = 0 , [tex]z = 4 - x^2 -4y^2[/tex] ). Then we will integrate the projection of the solid on the x-y plane bounded by a circle ( cylinder ) along the y-direction. With limits: ( [tex]y = - \sqrt{1 - x^2}[/tex] , [tex]y = \sqrt{1 - x^2}[/tex] ). Finally evaluate along the x-direction represented by a 1-dimensional line with end points ( -1 , 1 ).
- We set up our integral as follows:
[tex]V_s = \int\int\int {} \, dz.dy.dx[/tex]
- Integrate with respect to ( dz ) with limits: ( z = 0 , [tex]z = 4 - x^2 -4y^2[/tex] ):
[tex]V_s = \int\int [ {4 - x^2 - 4y^2} ] \, dy.dx[/tex]
- Integrate with respect to ( dy ) with limits: ( [tex]y = - \sqrt{1 - x^2}[/tex] , [tex]y = \sqrt{1 - x^2}[/tex] )
[tex]V_s = \int [ {4y - x^2.y - \frac{4}{3} y^3} ] \, | .dx\\\\V_s = \int [ {8\sqrt{( 1 - x^2 )} - 2x^2*\sqrt{( 1 - x^2 )} - \frac{8}{3} ( 1 - x^2 )^\frac{3}{2} } ] . dx[/tex]
- Integrate with respect to ( dx ) with limits: ( -1 , 1 )
[tex]V_s = [ 4. ( arcsin ( x ) + x\sqrt{1 - x^2} ) - \frac{arcsin ( x ) - 2x ( 1 -x^2 )^\frac{3}{2} + x\sqrt{1 - x^2} }{2} - \frac{ 3*arcsin ( x ) + 2x ( 1 -x^2 )^\frac{3}{2} + 3x\sqrt{1 - x^2} }{3} ] | \limits^1_-_1\\\\V_s = [ \frac{5}{2} *arcsin ( x ) + \frac{5}{3}*x ( 1 -x^2 )^\frac{3}{2} + \frac{5}{2} *x\sqrt{1 - x^2} ) ] | \limits^1_-_1\\\\V_s = [ \frac{5\pi }{2} + 0 + 0 ] \\\\V_s = \frac{5\pi }{2}[/tex]
Answer: The volume of the solid bounded by the curves is ( 5π/2 ) units^3.
What is the meassure of XYZ in the diagram below HELP ASSAP :)
100 points for brainiest
Please try!!
Use this link in my comment!
Answer:
I couldn't find the link you wanted me to click.
Anyway the Pyramid Volume Formula is
Volume= (Area of the Base * Height) ÷ 3
It's hard to determine the volume because I can't tell the dimensions from the graphic.
I'd guess the answer to question 4 is "A" means area of the base
Step-by-step explanation:
A company that packages peanuts states that at a maximum 6% of the peanut shells contain no nuts. At random, 300 peanuts were selected and 21 of them were empty.
1.With a significance level of 1%, can the statement made by the company be accepted?
2.With the same sample percentage of empty nuts and 1 − α = 0.95, what sample size would be needed to estimate the proportion of nuts with an error of less than 1%?
Answer:
1) [tex]z=\frac{0.07 -0.06}{\sqrt{\frac{0.06(1-0.06)}{300}}}=0.729[/tex]
We can calculate the p value with the following formula:
[tex]p_v =2*P(z>0.729)=0.466[/tex]
The p value for this case is very high and using the significance level of 0.01 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the statment makes sense.
2) [tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.06(1-0.06)}{(\frac{0.01}{1.96})^2}=2166.66[/tex]
And rounded up we have that n=2167
Step-by-step explanation:
Information given
n=300 represent the random sample taken
X=21 represent the number of peanuts empty
[tex]\hat p=\frac{21}{300}=0.07[/tex] estimated proportion of peanust empty
[tex]p_o=0.06[/tex] is the value to test
[tex]\alpha=0.05[/tex] represent the significance level
z would represent the statistic
[tex]p_v[/tex] represent the p value
Part 1
We want to test if the true proportion is 6% or no the system of hypothesis are:
Null hypothesis:[tex]p=0.06[/tex]
Alternative hypothesis:[tex]p \neq 0.06[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.07 -0.06}{\sqrt{\frac{0.06(1-0.06)}{300}}}=0.729[/tex]
We can calculate the p value with the following formula:
[tex]p_v =2*P(z>0.729)=0.466[/tex]
The p value for this case is very high and using the significance level of 0.01 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the statment makes sense.
Part 2
The margin of error for the proportion interval is given by this formula:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
And on this case we have that [tex]ME =\pm 0.01[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.06(1-0.06)}{(\frac{0.01}{1.96})^2}=2166.66[/tex]
And rounded up we have that n=2167
What’s the correct answer for this?
Answer:
C.
Step-by-step explanation:
Since mAB = mCD
So
3x+9 = 11x-71
9+71 = 11x-3x
80 = 8x
So
x = 10
Now
Arc AB = 3x+9
= 3(10)+9
= 39°
Could someone please give me the answer to this?
Answer:
36.87
Step-by-step explanation:
The cosine of an angle in a right triangle is the length of the adjacent side divided by the length of the hypotenuse, which in this case is 4/5. Therefore, the measure of this angle is the arc cosine of 4/5, or about 36.87 degrees. Hope this helps!
) How many kilowatt hours would the model predict on a day that has 14 hours of possible daylight?
Question:
A solar power company is trying to correlate the total possible hours of daylight (simply the time from sunrise to sunset) on a given day to the production from solar panels on a residential unit. They created a scatter plot for one such unit over the span of five months. The scatter plot is shown below. The equation line of best fit for this bivariate data set was: y = 2.26x + 20.01
How many kilowatt hours would the model predict on a day that has 14 hours of possible daylight?
Answer:
51.65 kilowatt hours
Step-by-step explanation:
We are given the equation line of best fit for this data as:
y = 2.26x + 20.01
On a day that has 14 hours of possible daylight, the model prediction will be calculated as follow:
Let x = 14 in the equation.
Therefore,
y = 2.26x + 20.01
y = 2.26(14) + 20.01
y = 31.64 + 20.01
y = 51.65
On a day that has 14 hours of daylight, the model would predict 51.65 kilowatt hours
If f(x + 2) = 6x2 + 5x − 8. Find f(6).
Answer:
108
Step-by-step explanation:
We can rewrite f(x+2) to make it easier to evaluate:
f(x+2) = (6x +5)x -8
Since we want f(6), we want x+2 = 6, or x=4.
f(6) = (6·4 +5)·4 -8 = 29·4 -8
f(6) = 108
Traffic speed: The mean speed for a sample of cars at a certain intersection was kilometers per hour with a standard deviation of kilometers per hour, and the mean speed for a sample of motorcycles was kilometers per hour with a standard deviation of kilometers per hour. Construct a confidence interval for the difference between the mean speeds of motorcycles and cars at this intersection. Let denote the mean speed of motorcycles and round the answers to at least two decimal places. A confidence interval for the difference between the mean speeds, in kilometers per hour, of motorcycles and cars at this intersection is ________.
Construct the 98% confidence interval for the difference μ 1-y 2 when x 1 475.12, x 2-32134, s 1-43.48, s 2-21.60, n 1-12, and n 2-15. Use tables to find the critical value and round the answers to two decimal places. A 98% confidence interval for the difference in the population means is ________.
Answer:
Step-by-step explanation:
Hello!
X₁: speed of a motorcycle at a certain intersection.
n₁= 135
X[bar]₁= 33.99 km/h
S₁= 4.02 km/h
X₂: speed of a car at a certain intersection.
n₂= 42 cars
X[bar]₂= 26.56 km/h
S₂= 2.45 km/h
Assuming
X₁~N(μ₁; σ₁²)
X₂~N(μ₂; σ₂²)
and σ₁² = σ₂²
A 90% confidence interval for the difference between the mean speeds, in kilometers per hour, of motorcycles and cars at this intersection is ________.
The parameter of interest is μ₁-μ₂
(X[bar]₁-X[bar]₂)±[tex]t_{n_1+n_2-2}[/tex] * [tex]Sa\sqrt{\frac{1}{n_1} +\frac{1}{n_2} }[/tex]
[tex]t_{n_1+n_2-2;1-\alpha /2}= t_{175; 0.95}= 1.654[/tex]
[tex]Sa= \sqrt{\frac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2} } = \sqrt{\frac{134*16.1604+41*6.0025}{135+42-2} } = 3.71[/tex]
[(33.99-26.56) ± 1.654 *([tex]3.71*\sqrt{\frac{1}{135} +\frac{1}{42} }[/tex])]
[6.345; 8.514]= [6.35; 8.51]km/h
Construct the 98% confidence interval for the difference μ₁-μ₂ when X[bar]₁= 475.12, S₁= 43.48, X[bar]₂= 321.34, S₂= 21.60, n₁= 12, n₂= 15
[tex]t_{n_1+n_2-2;1-\alpha /2}= t_{25; 0.99}= 2.485[/tex]
[tex]Sa= \sqrt{\frac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2} } = \sqrt{\frac{11*(43.48)^2+14*(21.60)^2}{12+15-2} } = 33.06[/tex]
[(475.12-321.34) ± 2.485 *([tex]33.06*\sqrt{\frac{1}{12} +\frac{1}{15} }[/tex])]
[121.96; 185.60]
I hope this helps!
2.-Efraín tiene un terreno rectangular cuya área es de 120 m2 + 280 m como se muestra en la Figura:
120 m2 + 280 m
f
De acuerdo con estos datos ¿Cuánto mide el lado f?
a) 12 m2
+ 35
b) 15 m + 35 cm
c) 12 m + 35
d) 15 m + 35
3.- Un niño elaboró cuatro figuras de plastilina: dos prismas cuadrangulares y dos cilindros. ¿En qué figura ocupó
la mayor cantidad de plastilina? JUSTIFICA TU RESPUESTA
a)
b)
c)
e)
8
Answer:
2) Option D is correct.
f = (15m + 35)
3) Check Explanation
Step-by-step explanation:
The diagram of the question is presented in the attached image to this question
English Translation
Efraín has a rectangular land whose area is (120m² + 280m) as shown in the figure. According to these data, how much does side f measure?
a) 12 m² + 35
b) 15 m + 35 cm
c) 12 m + 35
d) 15 m + 35
3.- A child made four plasticine figures: two quadrangular prisms and two cylinders. In which figure did you occupy the most amount of modeling clay? JUSTIFY YOUR ANSWER
Solution
2) The area of a rectangle is given as
Area = Length × Breadth
Area = (120m² + 280m)
Length = f
Breadth = 8m
(120m² + 280m) = f × 8m
f = (120m² + 280m)/(8m)
f = (15m + 35)
Option D is correct.
f = (15m + 35)
3) For the second question, the images for the question and the dimensions of the figures aren't provided, hence, a very accurate answer can be provided. But without This, we can only speculate.
The figure that would use the most clay is the figure whose volume is the highest if the volumes of each of the figures are calculated.
Volume of a quadrangular prism = (Area of base) × (perpendicular height)
Volume of a cylinder = (Area of base) × (Height) = (πR² × H) = πR²H
So, it is in the evaluation of these volumes that the solution of this question is obtained.
Hope this Helps!!
help please, surface area!
Answer:
436
Step-by-step explanation:
A rectangular prism is made up of 3 pairs of rectangles. In this case, one pair has dimensions of 4 by 9, another pair has dimensions of 4 by 14, and the last pair has dimensions of 9 by 14. The surface area of this rectangular prism is therefore:
2(4*9)+2(4*14)+2(9*14)=72+112+252=436 square inches
Hope this helps!
Answer:
436 in²
Step-by-step explanation:
A= 2*(4*14+4*9+9*14) in²= 436 in²
I keep gettin this wrong please help!!!
Answer: 120 members
Step-by-step explanation: So, we know 12 of the members signed up, and 90% of the member did not sign up.
Therefore, 12 members is equal to 10%...
All we have to do now is...
12 * 10 = 120
The club has 120 members in total, I hope this helps!
Suppose 13% of American adults believe that the highest priority of America is to protect freedom of speech. We will take a random sample of 20 American adults and ask them the question. Then the sampling distribution of the sample proportion of people who answer yes to the question is:
Answer:
A) neither Normal, not Binomial
The sampling distribution is the product of the sample size and the population proportion, hence the number ld samples in the distribution which will answer yes is 2.6
The proportion of the population who believe freedom of speech is of highest priority = 13% = 0.13
P = 0.13 Sample size = 20The sample distribution can be defined as :
Population proportion × sample size 0.13 × 20 = 2.6Therefore, the average Number of persons in the sample who will answer yes will be 2.6
Learn more : https://brainly.com/question/18153040
00:00
Joseph and Molly each have coin collections.
Joseph starts with 15 coins in his collection and adds 25 coins each month.
Molly starts with 25 coins in her collection and adds 25 coins each month.
Drag numbers from the box to complete the table showing the number of coins in their collections after 4 months.
115
75
65
40
100
90
50
125
Coin Collections
Month
Joseph
Molly
-
Start
15
25
1
1
2
3
4
Answer:
Step-by-step explanation:
Joseph : y = 25x + 15
Molly: y = 25x + 25
Joseph: y = 25(4)+ 15= 100+ 15= 115
Molly: y = 25(4)+ 25= 100+25= 125
Answer:
I hope this helps! <:
Step-by-step explanation:
The start is 15 and 25 so you keep on adding 25 to each of them, let's start with 15, 15+25=40 and 40 plus 25 is 65 and 65+25 is 90 the last one is 90+25= 115, now let's move on to 25. 25+25= 50 and the next one is 50+25=75 and then 75+25=100 and 100+25= 125.
A prominent medical school conducted a study that concluded adults with high blood pressure who consistently ate small amounts of low sugar dark chocolate experienced a significant reduction in blood pressure. As the study was being reviewed prior to publication in a medical journal, it was discovered that the Jershey Chocolate Company provided substantial funding for this research.
a) Identify any bias in this study.
b) Is it reasonable to conclude that adults with high blood pressure who consistently eat small amounts of low sugar dark chocolate experience a significant reduction in blood pressure?
Step-by-step explanation:
In the given question, the study was performed to analyse the effect of eating dark chocolate on the person with hypertension or increased blood pressure.
a) The biasness in the experiment could be that the funding for the study has been provided with a Private Company which mainly aims at selling their product.
b) The research is reasonable as it has been proved that eating a small amount of Dark chocolate can help cardiovascular disease like hypertension or increased blood pressure.
Find the volume of each prism... some please help, I don’t know how to do them.
Answer:
Answer to problem number 1: 576cm cubed
Step-by-step explanation:
The height times the length time the width in this shape is the formula for the volume.
Answer:
question 1. i believe is 576
Step-by-step explanation:
I need HELP PLEASE HELP MEEE!
Answer:
$21
Step-by-step explanation:
Take 40 percent of 35:
35(0.4) = 14
$14 has been taken off the original price:
35 - 14 = 21
And we have our final answer.
Answer:
21
Step-by-step explanation:
$35x40%= $14
$35-$14= $21
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If I get this worng I'm sorry
Brainleist will be appreciated, if not that's ok
Sorry that my spelling is relly bad
Anyway, hope this helps :D
What’s the value of x?
Answer:
x =20
Step-by-step explanation:
7x- 99 = 2x+1 ( vertically opposite angles)
7x - 2x = 1 +99
5x = 100
x =100/5
x =20
hope it helps
what is the nominal annual interest rate
Answer:
the nominal interest rate is the periodic interest rate.
it is the periodic interest rate times the number of periods per year.
What is the y-intercept of the graph that is shown below? On a coordinate plane, a line goes through points (negative 2, 0) and (4, 0).
Answer:
b = 0
Step-by-step explanation:
Because the line passes through x values when y = 0, it means that the line is y = 0. The slope would be 0, and because we are given 2 coordinates we can determine that the y intercept would be at 0.
Answer:
c
Step-by-step explanation:
hope this helps i just had this question on edge 2020
4. (16 points) A company with a fleet of cars found that in a random sample of 65 chosen and tested cars that 30 had emissions systems which failed to meet pollution control guidelines. A statistician is interested in testing if there is enough evidence to conclude that more than 30% of the fleet might be out of compliance regarding pollution control guidelines. Perform a five step hypothesis test using a 0.05 significance level. Write out the hypotheses: Determine critical value(s): Compute the test statistic: Determine the decision: Write the concluding statement:
Answer:
Null hypothesis:[tex]p\leq 0.3[/tex]
Alternative hypothesis:[tex]p > 0.3[/tex]
Critical value: [tex] z_{\alpha/2}= 1.64[/tex]
Test statistic: [tex]z=\frac{0.462 -0.3}{\sqrt{\frac{0.3(1-0.3)}{65}}}=2.85[/tex]
For this case the calculated value is higher than the critical value so then we can reject the null hypothesis. And we can conclude that the true proportion of cars with emissions systems which failed to meet pollution control guidelines for this case is significantly higher than 0.30 or 30%
Step-by-step explanation:
Information given
n=65 represent the random sample taken
X=30 represent the number of cars with emissions systems which failed to meet pollution control guidelines
[tex]\hat p=\frac{30}{65}=0.462[/tex] estimated proportion of cars with emissions systems which failed to meet pollution control guidelines
[tex]p_o=0.30[/tex] is the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to verify if the true proportion for this case is higher than 0.3 or no, the system of hypothesis are:
Null hypothesis:[tex]p\leq 0.3[/tex]
Alternative hypothesis:[tex]p > 0.3[/tex]
The statistic for this case would be:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info we got:
[tex]z=\frac{0.462 -0.3}{\sqrt{\frac{0.3(1-0.3)}{65}}}=2.85[/tex]
The critical value for this case would be taking in count the significance level in the right tail:
[tex] z_{\alpha/2}= 1.64[/tex]
For this case the calculated value is higher than the critical value so then we can reject the null hypothesis. And we can conclude that the true proportion of cars with emissions systems which failed to meet pollution control guidelines for this case is significantly higher than 0.30 or 30%
A rectangle is removed from the middle of a larger rectangular shaped board. What is the area of the remaining board?
Answer:
The area of the remaining board is [(L × B) - (l × b)].
Step-by-step explanation:
Suppose the bigger rectangle is labelled as ABCD and the smaller rectangle is labelled as PQRS.
Consider that the length and breadth of the bigger rectangle are L and B respectively. And the length and breadth of the bigger rectangle are l and b respectively.
The area of any rectangle is:
Area = Length × Breadth
The area of the bigger rectangle is:
Area of ABCD = L × B
The area of the smaller rectangle is:
Area of PQRS = l × b
Then the area of the remaining board will be:
Area of remaining board = Area of ABCD - Area of PQRS
= (L × B) - (l × b)
Thus, the area of the remaining board is [(L × B) - (l × b)].
Answer:
112
Step-by-step explanation:
Awnser in the lowest terms 5 years 6 months + 8 years 9 months
5 yrs+ 6 yrs =11 yrs
6 months+9 months=15 months
so,the answer is 11 yrs 15 months.
Kennedy and Olivia go to the movie theater and purchase refreshments for their friends.
Kennedy spends a total of $77.50 on 12 bags of popcorn and 2 drinks.
Olivia spends a total of $51.00 on 3 bags of popcorn and 6 drinks.
Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink.
Using these equations, determine and state the price of a drink, to the nearest cent.
Answer:
6x + y = 38.75
x + 2y = 17
price of drink is $5.75
Step-by-step explanation:
Let the price of popcorn be x
Let the price of drink be y.
price of 12 bags of popcorn will be 12x
price of 2 drinks will be 2y
it is given that "Kennedy spends a total of $77.50 on 12 bags of popcorn and 2 drinks."
thus
12x + 2y = 77.50
dividing LHS and RHS by 2 we have
12x/2 + 2y/2 = 77.50/2
=> 6x + y = 38.75 _________(1)
__________________________________________________
price of 3 bags of popcorn will be 3x
price of 6 drinks will be 6y
it is given that "Olivia spends a total of $51.00 on 3 bags of popcorn and 6 drinks."
thus
3x + 6y = 51.00
dividing LHS and RHS by 3 we have
3x/3 + 6y/3 = 51/3
=> x + 2y = 17 _____________(2)
__________________________________________________
Thus we have two equation
6x + y = 38.75 _________(1)
x + 2y = 17
=> x = 17 - 2y
putting this value of x in equation 1 we have
6( 17 - 2y) + y = 38.75
=> 102 - 12y + y = 38.75
=> 102 - 11y = 38.75
=> -11y = 38.75 -102
=> -11y = -63.25
=> y = -63.25/-11 = 5.75
as we have x = 17 - 2y
using 5.75 in place of y
x = 17 - 2(5.75 )
=> x = 17 - 11.5
=> x = 5.5
Thus, system of equations are
6x + y = 38.75
x + 2y = 17
price of drink is $5.75
What is the quotient? Negative StartFraction 3 over 8 EndFraction divided by negative one-fourth
Answer:
[tex]\dfrac{3}{2}[/tex]
Step-by-step explanation:
We are given 2 fractions.
1st fraction is Negative StartFraction 3 over 8
i.e.
[tex]-\dfrac{3}{8}[/tex]
2nd fraction is negative one-fourth
i.e.
[tex]-\dfrac{1}{4}[/tex]
We have to find the quotient when 1st fraction is divided by 2nd fraction.
Definition of quotient is given as:
Quotient is the result obtained when one number is divided by other number.
[tex]-\dfrac{3}{8} \div -\dfrac{1}{4} \text{ is to be calculated.}[/tex]
[tex]\div[/tex] is converted to [tex]\times[/tex] and the 2nd fraction is reversed i.e.
if the fraction is [tex]\frac{p}{q}[/tex] it becomes [tex]\frac{q}{p}[/tex] and the sign [tex]\div[/tex] is changed to [tex]\times[/tex].
Solving above:
[tex]-\dfrac{3}{8} \times -\dfrac{4}{1}\\ \text {Multiplication/Division of 2 negative number gives a positive number}\\\Rightarrow \dfrac{3}{2}[/tex]
So, the quotient is [tex]\frac{3}{2}[/tex].
In 1960, census results indicated that the age at which men in a certain region first married had a mean of 24.5 years. It is widely suspected that young people today are waiting longer to get married. We want to find out if the mean age of first marriage has increased since then.
We plan to test our hypothesis by selecting a random sample of 40 men who married for the first time last year.
The men in our sample married at an average age of 25.3 years, with a standard deviation of 5.4 years. That results in a t-statistic of 0.937 What is the P-value for this?
Answer:
[tex]t=\frac{25.3-24.5}{\frac{5.4}{\sqrt{40}}}=0.937[/tex]
The degrees of freedom are given by:
[tex]df=n-1=40-1=39[/tex]
And the p value would be given by:
[tex]p_v =P(t_{(39)}>0.937)=0.177[/tex]
Step-by-step explanation:
Information given
[tex]\bar X=25.3[/tex] represent the sample mean
[tex]s=5.4[/tex] represent the sample standard deviation
[tex]n=40[/tex] sample size
[tex]\mu_o =24.5[/tex] represent the value to verify
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to test if the true mean is higher than 24.5, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 24.5[/tex]
Alternative hypothesis:[tex]\mu > 24.5[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{25.3-24.5}{\frac{5.4}{\sqrt{40}}}=0.937[/tex]
The degrees of freedom are given by:
[tex]df=n-1=40-1=39[/tex]
And the p value would be given by:
[tex]p_v =P(t_{(39)}>0.937)=0.177[/tex]
The base (b) of the triangle is units. The height (h) of the triangle is units. The area of the triangle is square units.
Answer:
Option A. Base of the triangle is 3unita
Option B. Height of the triangle is 5units
Option B. Area of the triangle is 7.5units
Step-by-step explanation:
The question is incomplete and lacking appropriate diagram. Here is the complete question.
The base (b) of the triangle is _ units.
A) 3 B) 5 C) 8 D) 13
The height (h) of the triangle is units.
A) 3 B) 5 C) 8 D) 13
The area of the triangle is square units.
A) 5 B) 7.5 C) 15 D) 30
Also find the attachment below.
From the graph, each square box in the graph will be taken as 1unit.
Since the base of the triangle is sitting on 3-square boxes, the total units of its base will be 3units. The base of the triangle is therefore 3units.
Similarly, the height of the triangle covers 5 square boxes, therefore the height of the triangle will be 5units.
Area of the triangle = 1/2 × base × height
Area of the triangle = 1/2 × 3 × 5
Area of he triangle = 15/2 = 7.5units
Answer:
3,5,7.5
Step-by-step explanation:
just got the answer right.
What is an equation of the line that passes through the point (4, 5) and is parallel to the line whose equation is y= 2/3x-4?
Answer:
y=2/3x +7/3
2/3(4)+7/3=5
Please answer this question !! WIll give brainliest !! 20 POINTS !
Answer:
k=4
Step-by-step explanation:
y=3(1)-1
y=2
2=-2x+k
2=-2(1)+k
2=-2+k
4=k
Answer:
k = 4
Step-by-step explanation:
y = 3x -1
y = -2x+k
Set the two equations equal
3x -1 = -2x+k
Combine like terms
Add 2x to each side
3x+2x -1 =-2x+2x +k
5x - 1 = k
We know they are equal when x= 1
Let x=1
5*1 -1= k
5 -1= k
4 = k
The circle graph shows the different vitamins present in a health drink. Identify the measure of arc AB. Please help!
Answer:
79.2° (First Option)
Step-by-step explanation:
To find mAB, recognize that the percents given for the pie chart can represent the percent area of the sector of the circle, the percent measure of the central angle that forms the sector, or the percent measure of the length of the arc.
The measure of an arc is equal to the measure of the central angle between the radii that form its endpoints. So, mAB=m∠AOB.
The measure of the central angle AOB that forms AB is 22 percent of the whole circle, or (0.22)360∘. So, mAB=0.22(360∘)=79.2∘
Therefore, the measure of arc AB
is 79.2∘.
The measure of the arc AB of a circle showing the different vitamins present in a health drink is 79.2 degrees.
Calculate the measure of arcThe measure of an arc is always equivalent to the measure of the central angle between the radii that form its endpoints.
How to find the measure of arc AB.As the measure of an arc is always equivalent to the measure of the central angle between the radii that form its endpoints.
Thus [tex]m\angle{AOB}=\widehat{AB}[/tex].
First, find the measure of angle AOB.
Since the measure of angle AOB shows 22% of vitamins of the whole circle.
This means that the measure of angle AOB is 22% of 360 degrees.
Then we will get
[tex]m\angle{AOB}=\dfrac{22}{100}\times 360^{\circ}\\m\angle{AOB}=79.2^{\circ}[/tex]
Here the measure of angle AOB is 79.2 degrees.
And since [tex]m\angle{AOB}=\widehat{AB}[/tex].
Therefore the measure of arc AB is 79.2 degrees.
That means option A [tex]79.2^{\circ}[/tex] is correct option.
Learn more about the measure of arc here- https://brainly.com/question/12555201
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Hello, what is all the scale factors of two.?
Answer:
all even numbers
Step-by-step explanation:
Answer:
Any and all of the Even numbers are scale factors of two!