Answer:
95% confidence interval for the population mean weight of adult female golden retrievers is [53.01 pounds , 56.78 pounds].
Step-by-step explanation:
We are given that the weights, in pounds, of a sample of 13 adult female golden retriever dogs :
59.0, 54.1, 53.7, 51.6, 57.5, 58.7, 58.0, 53.8, 48.9, 53.9, 51.6, 55.9, and 57.4.
Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean weight = [tex]\frac{\sum X }{n}[/tex] = 54.9 pounds
s = sample standard deviation = [tex]\frac{\sum (X-\bar X)^{2} }{n-1}[/tex] = 3.12 pounds
n = sample of female = 13
[tex]\mu[/tex] = population mean weight
Here for constructing 95% confidence interval we have used One-sample t test statistics because we don't know about population standard deviation.
So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-2.179 < [tex]t_1_2[/tex] < 2.179) = 0.95 {As the critical value of t at 12 degree
of freedom are -2.179 & 2.179 with P = 2.5%}
P(-2.179 < [tex]\frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.179) = 0.95
P( [tex]-2.179 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X -\mu}[/tex] < [tex]2.179 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
P( [tex]\bar X-2.179 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X +2.179 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
95% confidence interval for [tex]\mu[/tex] = [tex]\bar X \pm 2.179 \times {\frac{s}{\sqrt{n} } }[/tex]
= [ [tex]54.9 - 2.179 \times {\frac{3.12}{\sqrt{13} } }[/tex] , [tex]54.9 +2.179 \times {\frac{3.12}{\sqrt{13} } }[/tex] ]
= [53.01 pounds , 56.78 pounds]
Therefore, 95% confidence interval for the population mean weight of adult female golden retrievers is [53.01 pounds , 56.78 pounds].
−11b+7=40
solve for b
Answer:
Step-by-step explanation:
subtract 7 on both sides
40-7=33
-11b=33
divide -11 on both sides
b=-3
Answer:
B=-3
Step-by-step explanation:
-11b+7=40
Subtract -7 from both sides
-11b-7=40-7
11b=33
divide by -11
11b/-11=33/-11
-11 and -11 cancel out, leaving you with B=-33/11
thus B=-3
Which is the simplified form of the expression (StartFraction (x Superscript negative 3 Baseline) (y squared) Over (x Superscript 4 Baseline) (y superscript 6 Baseline) EndFraction) cubed?
To simplify the expression (x⁻³ × y² / x⁴ × y⁶) cubed, you need to cube each term in the fraction individually.
To simplify (StartFraction (x⁻³) (y²) Over (x⁴) (y⁶) EndFraction) cubed, you need to cube each term in the fraction individually.
Here is the step-by-step breakdown:
Cube the numerator: x⁻⁹y⁶
Cube the denominator: x¹²y¹⁸
Combine the cubed terms: (x⁻⁹y⁶) / (x¹²y¹⁸)
Three friends—Elaine, Kelly, and Shannon—all start for their college volleyball team. Each plays a different position: setter, middle blocker, and outside hitter. Of the three, one is a freshman*, one a sophomore*, and the other a junior*.From the clues below, determine each woman's position and year in school.1. Elaine is not the setter.2. Kelly has been in school longer than the middle blocker.3. The middle blocker has been in school longer than the outside hitter.4. Either Kelly is the setter or Elaine is the middle blocker.
Answer:
Elaine is the outside hitter in Freshman Year
Kelly is the setter in Junior Year
Shannon is the middle blocker in Sophomore Year
Please mark my answer as brainiest
Elaine is the freshman outside hitter, Kelly is the junior setter, and Shannon is the sophomore middle blocker.
Explanation:Let's analyze the clues one by one:
From clue 1, Elaine cannot be the setter.From clue 2, Kelly has been in school longer than the middle blocker. This means Kelly is either the middle blocker or the outside hitter.From clue 3, the middle blocker has been in school longer than the outside hitter. Combining this with clue 2, we know that Kelly cannot be the middle blocker. Therefore, Kelly must be the outside hitter.From clue 4, either Kelly is the setter or Elaine is the middle blocker. Since Elaine cannot be the setter, Kelly must be the setter. This means Shannon is the middle blocker, leaving Elaine as the only option for the freshman outside hitter.Based on the given clues, we can conclude that:
Elaine is the freshman outside hitter.Kelly is the junior setter.Shannon is the sophomore middle blocker.Learn more about The positions and years in school of three friends on a college volleyball team. here:https://brainly.com/question/14557112
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The sum is two numbers is 65. The difference of the two numbers is 17. Write systems of equations and find two numbers
Answer:
41 and 24
Step-by-step explanation:
x+y=65 -------(A)
x-y=17 -------- (B)
(A)+(B)
(x+y)+(x-y)=65+17
2x=82
x=41
(B)===>
41-y=17
y=41-17
y=24
Here are the numbers of times 8 people ate out last month.
5, 6, 3, 3, 4, 4, 7, 7
Find the modes of this data set.
If there is more than one mode, write them separated by commas.
If there is no mode, click on "No mode."
Answer: 3,4,7
Step-by-step explanation:
Melanie sold half of her comic books and then bought 9 more. She now has 17. How many did she begin with?
Answer:
16
Step-by-step explanation:
You need to work backwards and do the opposite
So, first do subtraction since Melanie added to her collection. SO do the opposite of addition.
17-9=8
Then, since she sold half of her comics, and she is dividing her collect, you multiply 8 with 2.
8 x 2=16
Final answer
16 comics
What is the equation of the line?
Answer:
y= -4/3x
Step-by-step explanation:
rise over run
up 4, left 3
or
down 4, right 3
Vera is an ecologist who studies the change in the bear population of Siberia over time. The relationship between the elapsed time, t, in years, since Vera began studying the population, and the total number of bears, N(t), is modeled by the function:
Answer:
Every year, the bear population shrinks by a factor of 2/3 .Explanation:
The concrete question and the function or data were omitted.
I found the complete question on the internet. Please, find attached the picture with the complete question
You must complete the sentence about the yearly rate of change of the bear population, telling whether it grows or shrinks and by what factor.
Thus, the goal is to interpret the rate of change in an exponential model.
The exponential model is:
[tex]N(t)=2187\cdot \bigg(\dfrac{2}{3}\bigg)^t[/tex]
Let's analyze that function.
When t = 0, (2/3)⁰ = 1 and N(0) = 2,187 × 1 = 2,187
Thus, the population of bears starts with 2,187 individuals.
For t = 1, the population will be N(1) = 2,187 × (2/3).
For t = 2, the population will be N(2) = 2,187 × (2/3)²
And so on, every year the population of bears is multiplied by a factor of 2/3.
Since, 2/3 is less than 1, every year the population will be decreasing (decaying), by a factor of 2/3.
Thus, the answer, i.e. the complete sentence, is:
Every year, the bear population shrinks by a factor of 2/3 .
Answer:
shrinks/ 2/3
Step-by-step explanation:
The diagram shows two different buttons and their weights.
12 grams
8 grams
c)
How many of each type of button are in the box?
To solve this problem, set up a system of equations with x and y representing the number of buttons. If there are 20 Weights of buttons in total, 20 of them weigh 12 grams and none weigh 8 grams.
To solve this problem, we can set up a system of equations. Let x be the number of buttons weighing 12 grams, and y be the number of buttons weighing 8 grams.
We can then write the following equations based on the information given:
x + y = total number of buttons
12x + 8y = total weight of the buttons
Substituting the given values, we have:
x + y = total number of buttons
12x + 8y = 240
From the first equation, we can express y in terms of x:
y = total number of buttons - x
Substituting this into the second equation:
12x + 8(total number of buttons - x) = 240
Simplifying:
12x + 8total number of buttons - 8x = 240
4x + 8total number of buttons = 240
4x = 240 - 8total number of buttons
4x = 8(30 - total number of buttons)
x = 2(30 - total number of buttons)
Since x and y represent the number of buttons, they must be whole numbers.
We can test different values for the total number of buttons to find a solution that satisfies this condition.
For example, if we assume there are 20 buttons in total:
x = 2(30 - 20) = 2(10) = 20
y = 20 - 20 = 0
Therefore, if there are 20 buttons in total, 20 of them weigh 12 grams and none weigh 8 grams.
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The probable question may be:
In a box, there are two types of buttons with different weights. One type of button weighs 12 grams, and the other type weighs 8 grams. If the total weight of the buttons in the box is 240 grams, how many buttons of each type are in the box?
a circle with area 36 pi has a sector with central angle of f 11/6 pi radians
Answer:
33 π
Step-by-step explanation:
Given,
Area of circle = 36 π
Central angle of sector,θ = 11/6 rad
Area of the sector = ?
we know,
A = π r²
36 π = π r²
r = 6
Area of sector
[tex]A = \frac{1}{2} r^2 \theta [/tex]
[tex]A = \frac{1}{2} \times 6^2 \times (\frac{11}{6}\pi)[/tex]
[tex]A = 33\pi \ sqr. units[/tex]
In order to answer the following question, please use the following image down below:
Find the value of x.
X=(Blank)
What is the value of X? Please show all the work on how you got your answer.
(If you can't explain your work, then it's fine. The only thing that I'm asking for is for you to show the work alongside your answer)
Answer:
5
Step-by-step explanation:
(15)(x+3) = (12)(2x) -->
15x + 45 = 24x -->
45 = 9x -->
5 = x
A teacher randomly chooses a two-person team from a group of four students. The first person chosen will
be the presenter and the second person will be the researcher. Two of the students, Amir and Aaron, are
boys. The other two students, Caitlin and Deniz, are girls. All the possible outcomes of the team selection
are listed below.
If we take outcomes 2, 3, 5, 6, 7, 8, 10, and 11 as a subset of the sample space, which of the statements
below describe this subset?
Answer:
•The subset consists of all of the outcomes where the team is made up of one boy and one girl
• the subset consists of all of the outcomes where the team is not made up of all boys and not made up of all girls.
Answer:
A & D
Step-by-step explanation:
KHAN
Help me please please help
Answer:
80
Step-by-step explanation:
The sides of a triangle always add up to 180. 80+20+?=180
Answer:
C, 80 degrees
Step-by-step explanation:
Together, all of the interior angles in a triangle add up to 180 degrees. Therefore, the missing angle is the two other angles subtracted from 180 degrees. 180-20-80=80 degrees, or answer choice C. Hope this helps!
Please answer as fast as possible :)
Answer:terri
Step-by-step explanation:
The frequency of a hum that is generated by an engine is 270hz. If t starts at zero, which of the following would best describe this frequency over time?
(Don’t pay attention to the answer chosen)
Answer:
sin ( 2π(270)*t )
Step-by-step explanation:
Solution:-
- The frequency of the hum is denoted as k = 270 Hz.
- The displacement of the hum is modeled by a sinusoidal function.
- The trigonometric modelling of frequency generating systems is given in the following general form:
sin ( w*t ) + c
- Where,
A: The amplitude of displacement e
w: The angular speed of the hum
c : The initial condition of displacement.
- Here, we will assume A = 1 and c = 0. The hum starts from time t = 0 seconds.
- The angular speed is the unit of speed that denotes the number of cycles in radians are undergone by the frequency generator device/person in unti time t.
- The angular speed is given by the following relation:
w = 2πk
w = 2π(270).
- The general model of the hum would be:
sin ( 2π(270)*t )
What is the speed of a truck the travel 496km in 6.2 hours
Jose has $34 to spend at the Texas State Fair. If the entrance ticket cost $12, then how much money does Jose have to spend on food and games?
Answer: he has 22$
Step-by-step explanation:
34-12=22
Answer:
$22
Step-by-step explanation:
$34 total
$12 for the tickets
34-12=22
Jose has 22 dollars to spend on food and games
The area of the shaded circle below is 78.5 square inches. The area of the large circle is 314 square inches.A shaded circle is inside of a larger unshaded circle.What is the probability that a point chosen at random will be in the shaded region
Answer:
The probability that a point chosen at random will be in the shaded region is 0.25
Step-by-step explanation:
We have been given a small shaded circle inside a larger un-shaded circle. This is shown in the image attached below.
The area of smaller circle is 78.5 squares inches and the area of larger circle is 314 square inches. We have to find the probability that a point chosen at random will be in the shaded region.
Probability is defined as the ratio of Favorable outcome to the Total outcomes. In this case the favorable outcome is that the point should be inside the shaded region i.e. in an Area of 78.5 square inches. And the total outcome is that the point can be anywhere inside the larger circle i.e. within an Area of 314 square inches. Thus the probability that a point chosen at random will be inside the shaded region will be:
[tex]Probability = \frac{\text{Favorable Outcome}}{\text{Total Outcome}} \\\\ = \frac{78.5}{314}\\\\=0.25[/tex]
Thus, the the probability that a point chosen at random will be in the shaded region is 0.25. This means there is a 25% chance that a randomly chosen point will be inside the shaded region.
A sphere has a diameter of 36 meters. What its exact volume?
Answer:
V = 7776 pi m^3
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
We need to know the radius
r = d/2 = 36/2 = 18
V = 4/3 pi (18)^3
V = 4/3 * pi *5832
V = 7776 pi
We cannot approximate pi since we want the exact answer
Answer:
7776π cubic meters.
Step-by-step explanation:
Recall the volume formula for a sphere is
V = (4/3) π r^3
r = (1/2)*diameter = (1/2)*36 m = 18 meters
V = (4/3)*π*(18)^3 = 24,429.02447 cubic meters
However the problem wants an exact answer, and not an approximation, therefore I will express the volume in terms of simplified expressions.
V = (4/3)*π*(18)^3 = (4/3)*π * (3*6)^3 = 4 *π * (1/3)*(3^3) *(6^3)
V = 4 *π * (1/3)*(3^3) *(6^3) = 4*π * 9 * 6^3 = 7776π cubic meters.
A container has peppermint gum and spearmint gum. There are 24 pieces of peppermint gum in the container and the ratio of peppermint gum to spearmint gum is 8 to 5. Find the number of pieces of spearmint gum in the container.
Answer:
15
Step-by-step explanation:
The Number of Spearmint gum are 27 pieces
What is the ratio?It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
Let the total number of peppermint gum and spearmint gum in the container is X
Ratio of peppermint gum to spearmint gum= 2 : 3.
Total ratio = 2+ 3=5
we are given that peppermint gum are 18 pieces , so total number of gums will be calculated as;
Ratio of peppermint/ Total ratio x Total number of gums = Number of peppermint;
2/5 x X= 18
X=(18X 5) / 2 = 45
X= Total number of gums = 45
Ratio of spearmint/ Total ratio x Total number of gums = Number of spearmint;
3/5 x 45= 27
Therefore Number of Spearmint gum are 27 pieces
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Emma took a taxi from the airport to her house.
She paid a flat fee of $5 plus $3.70 per mile.
The fare came to $42.
For Emma's taxi ride, which equation gives the correct distance (d) in miles
In a circle of diameter 30 cm a chord of 10cm is drawn. To 2 decimal places, how far is the chord from the center of the circle?
Given:
The circle has a diameter of 30 cm and a chord of 10 cm is drawn.
Radius of the circle = 15 cm
Half of the chord = 5 cm
We need to determine the distance of chord from the center of the circle.
Distance of chord from the center of the circle:
Let us use the Pythagorean theorem, to find the distance between the center and the chord.
Let d denote the distance between the center and the chord of the circle.
Thus, we get;
[tex]15^2=d^2+5^2[/tex]
[tex]225=d^2+25[/tex]
[tex]200=d^2[/tex]
Taking square root on both sides, we get;
[tex]14.14=d[/tex]
Thus, the distance between the center and the chord of the circle is 14.14 cm.
Hence, Option A is the correct answer.
The chord is 14.14 cm far from the center of circle.
First option is correct.
The perpendicular drawn from center to the chord, is always divide the chord into two equal parts.
Radius of circle = d/2 = 30/2 = 15 cm
A diagram is attached below, in which distance between center and chord is represented by x .
applying Pythagoras theorem
[tex]x=\sqrt{(15)^{2} -5^{2} }=\sqrt{225-25}=\sqrt{200} =14.14 cm[/tex]
Thus, the chord is 14.14 cm far from the center of circle.
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A bag contains a number of marbles of which 35 are blue, 10 are red and the rest are
yellow. If the probability of selecting a yellow marble from the bag at random is , how
many yellow marbles are in the bag?
Answer:
Y = 45*p(y) / (1 - p(y)) if I knew what p(y) is, we can find how many yellow marbles there are. p(y) = probability of choosing yellow.
Step-by-step explanation:
Total marbles = 35 + 10 + yellow
If probability of choosing yellow =p(y) = yellow/Total
p(y) = Y/(35 + 10 + Y)
Solve for Y,
p(y)*(35 + 10 + Y) = Y
45*p(y) + p(y)*Y = Y
45*p(y) = Y - p(y)*Y
Y = 45*p(y) / (1 - p(y))
To find the number of yellow marbles in the bag, set up an equation using the given probabilities. Simplify the equation and solve for the total number of marbles. Finally, substitute the value of into the equation to determine the number of yellow marbles.
Explanation:To solve this problem, we need to find the number of yellow marbles in the bag. Given that there are 35 blue marbles and 10 red marbles, we can subtract these two numbers from the total number of marbles to find the number of yellow marbles. Let's denote the number of yellow marbles as 'y'. We can set up the equation: 35 + 10 + y = total number of marbles. Since the probability of selecting a yellow marble is , we know that the ratio of yellow marbles to the total number of marbles is . This can be written as: y/total number of marbles = . Now, we can solve for 'y'.
By cross multiplying the ratio equation, we have: y = total number of marbles * . Now we can substitute this value of 'y' in the first equation: 35 + 10 + (total number of marbles * ) = total number of marbles. Simplifying this equation, we find: 45 + (total number of marbles * ) = total number of marbles. Rearranging the equation, we have: (total number of marbles * ) - total number of marbles = -45. Factoring out 'total number of marbles' from the left side, we get: total number of marbles * ( - 1) = -45. Dividing both sides of the equation by ( - 1), we find: total number of marbles = 45 / ( - ). Plugging in the value of , we can evaluate the expression: total number of marbles = 45 / ( - ) = - . Therefore, there are - yellow marbles in the bag.
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Find the mid points of a and b where a has coordinates (8,2) and b has coordinates (3.8)
Answer:
(5.5,5)
Step-by-step explanation:
Answer:
The coordinate of the midpoint is (5.5,5)
Step-by-step explanation:
To find the midpoint between two points, find the average of the x coordinates and the midpoint of the y coordinates.
x=(8+3)/2
x=11/2
x=5.5
y=(2+8)/2
y=10/2
y=5
The coordinate of the midpoint is (5.5,5)
A cake recipe calls for 550 grams of flour. About how many pounds of flour do you need? Use the conversion factors StartFraction 1 ounce Over 28.4 grams EndFraction and StartFraction 1 pound Over 16 ounces EndFraction .
The question is:
A cake recipe calls for 550 grams of flour. About how many pounds of flour do you need? Use the conversion factors (1 ounce)/(28.4 grams) and (1 pound)/(16 ounces).
Answer:
About 1.2 pounds of flour is needed.
Step-by-step explanation:
Given that the cake recipe calls for 550 grams, we want to determine about how many pounds of flour we need.
This simply means we want to convert 550 grams to pounds.
First, we were given (1 ounce)/(28.4 grams)
This implies that
1/28.4 = x/550 ..............................(1)
Where x is 550 grams in ounce.
Solving (1)
28.4x = 550
=> x = 550/28.4
≈ 19.3662
That is 550 grams is equal to 19.3662 ounce
Next, we are given the ratio (1 pound)/(16 ounce). We then convert 19.3662 ounce to pound
Let y be 19.3662 ounce in pound
=> 1/16 = y/19.3662
16y = 19.3662
y = 19.3662/16
≈ 1.2
That is 19.3662 ounce is equal to 1.2 pounds.
Therefore, 550 grams is equal to 1.2 pounds, and it is the amount of flour needed.
You would need approximately 1.210 pounds of flour for the cake recipe.
To convert grams to pounds, we can use the conversion factor:
1 pound = 16 ounces
And we also have the conversion factor:
1 ounce = 28.4 grams
First, we'll convert grams to ounces, and then ounces to pounds.
Given that the recipe calls for 550 grams of flour, let's calculate the amount in pounds.
Step 1: Convert grams to ounces.
550 grams x (1 ounce / 28.4 grams) = 19.366 ounces
Step 2: Convert ounces to pounds.
19.366 ounces x (1 pound / 16 ounces) = 1.210 pounds
Therefore, you would need approximately 1.210 pounds of flour for the cake recipe.
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HELP PLEASE :(
Three-Dimensional Geometry
Geometric Design
1. Kathrine, Giana, and Jackson are designing jewelry boxes to sell at the art fair. The
dimensions of their boxes are:
Kathrine: 5in x 5in x 5in
Giana: 10in X 12in X 2in
Jackson: 10in X 5in x 4in
If a customer at the art fair is wants to buy the jewelry box that will hold the most amount
of jewelry, whose jewelry box should they purchase?
Answer: The customer should buy Giana’s jewelry box.
Step-by-step explanation:
The jewelry boxes are rectangular prisms, in order to find the box that would hold the most amount of jewelry we need to find the volumes of each box.
V= l.w.h
Katherine’s box: 5x5x5= 125
Giana’s box: 10x12x2= 240
Jackson’s box: 10x5x4= 200
i need help please!!!!!!!
Answer:
a) v=6
b) s= u^2 - v^2 : -2a
Step-by-step explanation:
v^2=u^2+2as
u=12, a=-6, s=9
a)
(12)^2= 12 * 12= 144
v^2=u^2+2as
v^2=(12)^2+ 2*(-6)*9
v^2=144+(-12)*9
v^2=144+(-108)
v^2=36
v=6
b)
v^2=u^2+2as
-2as=u^2 - v^2
s= u^2 - v^2 : -2a
check for s
s= 144 - 36 : -2(-6)
s= 108 : 12
s=9 (equal vs the given)
How do you find the slope-intercept form of a general equation:
The General form of the equation of a straight line is:
3x + 5y − 15 = 0.
Please help as soon as possible.
Answer:
Y=-3/5+3
Step-by-step explanation:
You need to move y’all variables to one side except Y. Then divide them by 5 to get rid of the 5 attached to the Y. So then you have Y=Mx+b.
Which of the following functions will have a graph with an axis of symmetry at x=1 and an intercept at the origin?
fx=5x+12-5
fx=x-12-2
©
fx=-x+12+2
fx=4x-12-4
D
fx=-12x-12+2
(03.01 LC)
The leg of a right triangle is 2 units and the hypotenuse is 5 units. What is the length, in units,
of the other leg of the triangle? (1 point)
C3
C /21
Answer:
The length of the other leg is 4.58 units.
Step-by-step explanation:
A² + B² = C² Use Pythagorean Theorem
2² + B² = 5² Simplify
4 + B² = 25
-4 -4 Subtract 4 from both sides
B² = 21 Take the square root of both sides
B = 4.58 units
If this answer is correct, please make me Brainliest!
Answer:
4.58 units is your answer
Step-by-step explanation: