Using the t-distribution, the limits of the 95% confidence interval are given as follows:
Lower: 30.9.Upper: 35.1.What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 16 - 1 = 15 df, is t = 2.1315.
The other parameters are given as follows:
[tex]\overline{x} = 33, s = 4, n = 16[/tex]
Hence the bounds of the interval are given as follos:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 33 - 2.1315\frac{4}{\sqrt{16}} = 30.9[/tex][tex]\overline{x} + t\frac{s}{\sqrt{n}} = 33 + 2.1315\frac{4}{\sqrt{16}} = 35.1[/tex]Which are the lower and the upper bound, respectively.
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Simplify 2/9y(3y-4/7)
Answer:
2/9y(3y−4/7)
Use the distributive property to multiply
9
2
y by 3y−
7
4
.
9
2
y×3y+
9
2
y(−
7
4
)
Multiply y and y to get y
2
.
9
2
y
2
×3+
9
2
y(−
7
4
)
Express
9
2
×3 as a single fraction.
9
2×3
y
2
+
9
2
y(−
7
4
)
Multiply 2 and 3 to get 6.
9
6
y
2
+
9
2
y(−
7
4
)
Reduce the fraction
9
6
to lowest terms by extracting and canceling out 3.
3
2
y
2
+
9
2
y(−
7
4
)
Multiply
9
2
times −
7
4
by multiplying numerator times numerator and denominator times denominator.
3
2
y
2
+
9×7
2(−4)
y
Do the multiplications in the fraction
9×7
2(−4)
.
3
2
y
2
+
63
−8
y
Fraction
63
−8
can be rewritten as −
63
8
by extracting the negative sign.
3
2
y
2
−
63
8
y
Step-by-step explanation:
Jennifer is creating a rectangular-plot of grass in her backyard. She would like the length of the plot to be 6 feet less than the width. Draw a picture of the situation.
The value of the width is greater than the 21 if we want a perimeter greater than the 72 feet. Then if we let value of y is 25 then length is 19 and width is 25.
According to the statement
We have to find that the length and the width.
So, For this purpose, we know that the
A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon
From the given information:
The length of the plot to be 6 feet less than the width.
Then
The given perimeter = greater than 72 feet.
We know that the perimeter of rectangle is
P = 2(length + breadth)
And
P < 2(length + breadth)
here p = 72, let length = y - 6 and width = y
Then
72 < 2(length + breadth)
72 < 2(y - 6 + y)
72 < 2(2y - 6)
72 < 4y - 12
84 < 4y
y > 21.
Then let the value of y is 25 then
length = 25 - 6 and width = 25
length = 19 and width = 25.
So, The value of the width is greater than the 21 if we want a perimeter greater than the 72 feet. Then if we let value of y is 25 then length is 19 and width is 25.
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What are the roots of the function f(x) = (log(3x) − 2log(3)) · (x2 − 1) with x ∈ R?
Answer:
x = 1, x = 3
Step-by-step explanation:
Given function:
[tex]f(x)=\left(\log(3x)-2 \log(3)\right) \cdot \left(x^2-1\right)[/tex]
The roots of the function are when f(x) = 0:
[tex]\begin{aligned}f(x) & = 0\\ \implies \left(\log(3x)-2 \log(3)\right) \cdot \left(x^2-1\right) & = 0\\\\ \textsf{Therefore,} \:\:\:\log(3x)-2 \log(3) & = 0\\ \textsf{and }\:\:\:x^2-1 & = 0 \end{aligned}[/tex]
Case 1
[tex]\begin{aligned}\left(\log(3x)-2 \log(3)\right) & = 0\\\log(3x) & = 2 \log(3)\\ \log(3x) & = \log (3)^2\\ \log(3x) & = \log (9)\\ 3x & = 9\\ x & = 3\end{aligned}[/tex]
Case 2
[tex]\begin{aligned}\left x^2-1\right & = 0\\x^2 & = 1\\ x & = \pm 1\end{aligned}[/tex]
As logs of negative numbers cannot be taken, x = 1 only.
Therefore, the roots of the given function are: x = 1, x = 3
-9x+10y=25 7x-4y=7 Elimination method (with work)
Values of x and y in the given equations by elimination method are 5 and 7 respectively. that is, x=5 and y=7.
In the elimination method, the aim is to entirely remove one of the unknown variable which would eventually make it easier to calculate be other unknown. However, it is important to note that this method is most effective when neither of the coefficients is equal to 1. The coefficient of either of the two variables will be made the same in both equations and by subtracting one from the other, it would be eliminated. It is a non-graphical methods of solving simultaneous linear equations.
consider the equations as (1) and (2),
-9x+10y=25..........................(1)
7x-4y=7............................(2)
Now, multiply equation (1) by 4 and equation (2) by 10
Let the equations we get now be (3) and (4),
-36+40y=100......................(3)
70x-40y=70........................(4)
We can see that the coefficient of y in both equations is same that is 40
Now, add equation (3) and (4)
-36+40y+70x-40y=100+70 ( y terms cancel out)
By evaluating we get,
-34x=170
x=-170/34
x=5
To find the value of y, substitute value of x in equation (2)
7x-4y=7
7*5-4y=7
35-4y=7
35-7=4y
28=4y
y=28/4
y=7
Therefore, we can conclude that the values of x and y in the given equations -9x+10y=25 and 7x-4y=7 by elimination method are 5 and 7 respectively. that is, x=5 and y=7.
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Inscribing a circle means to--
*
Label the inside of the circle.
Draw a circle around the outside of a shape.
Create a circle with a specific purpose.
Draw a circle inside a shape.
Inscribing a circle means to draw a circle inside a shape. the correct option is the last option
Inscribed figureAn inscribed figure is a shape drawn inside another shape. For example, if a circle is drawn inside a square, the circle is said to inscribed inside the square.
Likewise,
If a triangle is drawn inside a circle, the triangle is said to be inscribed inside the circle.
A cyclic quadrilateral is an example of a quadrilateral that is inscribed inside a circle.
Then,
We can conclude that inscribing a circle means to draw a circle inside another shape
Hence, inscribing a circle means to draw a circle inside a shape. the correct option is the last option
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Which lines are parallel in the square
pyramid?
Select each correct answer.
о
AB and AD
BC and DE
AD and BC
CL and BE
Step-by-step explanation:
AB and AD, i got the same question and the answer was right
A cooked ham weighs 11 kilograms how many ham slider sandwiches can be made if each sandwich has. 55 grams of cooked ham
Number of ham slider sandwiches can be made is 200.
According to given data,
cooked ham weighs is 11 kilograms and
each sandwich has. 55 grams of cooked ham
we convert 11 kilograms to 11 grams
so we multiply 11 kilograms with 1000
then we get, 11×1000 = 11000 grams
number of ham slider sandwiches prepared
⇒ [tex]\frac{11* 1000}{55}[/tex]
⇒ [tex]\frac{1000}{5}[/tex]
⇒ 200
Therefore, we get number of prepared ham slider sandwiches is 200 .
Converting
Write the number of grams. Label it "grams" or "g." If you're using a calculator, just type the number in.
In this section, we'll follow along with an example problem to make things easier. Let's say that we want to convert 20,000 grams to kilograms. To start, we would write "20,000 grams" on our paper.
Divide by 1,000. A kilogram is one thousand grams. This means that to get kilograms from grams, you just need to divide the number of grams by 1,000.
In our example, we would get kilograms by dividing 20,000 grams by 1,000.
20,000/1,000 = 20
Label your answer. Don't forget this step! Labelling your answer with the proper units is important. If you're doing this conversion for schoolwork, you can lose points if you don't label. If you're doing it for something else, people may assume the wrong units.
In our case, we would label our answer with the label "kilograms" like this:
20 kilograms.
To get back to grams, multiply by 1,000. As discussed above, a kilogram is one thousand grams. This means that if you ever want to get back to grams from kilograms, all you need to do is multiply the number of kilograms by 1,000. Since multiplications is basically the "opposite" operation as division, this will "undo" the division and give you grams.
To get 20 kilograms back to grams, we just multiply by 1,000 (don't forget to label your answer again):
20 kilograms × 1,000 = 20,000 grams
Converting by Shifting the Decimal Point
Start with your number of grams. Believe it or not, you can convert between grams and kilograms without doing any math. This works because the metric system is a base 10 system of measurements. In other words, metric units are always a multiple of 10 apart from each other — there are 10 millimeters in a centimeter, 100 centimeters in a meter, 1,000 meters in a kilometer, and so on.
In this section, let's convert 37 grams to kilograms. We would begin the same way as in the section above, writing "37 grams" on our paper.
Shift the decimal point three spaces to the left. Now, find the decimal point in your number of grams. If you're converting a whole number, this won't usually be written, but you can assume it its to the right of the ones place. Move the decimal point three spaces to the left. Each time you move past a number counts as one space. If you run out of numbers to move past, keep moving it, leaving blank spaces.
In our example, the decimal point in 37 grams is to the right of the 7 (i.e., 37 grams is the same as 37.0 grams). If we go one space at a time, moving the decimal point three spaces to the left looks like this:
37.
3.7
.37
._37 — note that we leave an empty space when we run out of numbers.
Add zeroes in any empty spaces. You can't leave empty spaces in your answer, so fill in each one with a zero. You can also put a zero to the left of the decimal place if there aren't any numbers there, but this is optional — it just depends how you like to write your answers.
In our example, we have one empty space between the decimal point and the 3, so we'll fill it in with a zero like this:
.037
Adding the proper label (plus an extra zero to the left of the decimal point for presentation purposes), we get our final answer:
0.037 kilograms
To get back to grams, shift the decimal place back. When you have kilograms, shifting the decimal place three spaces to the right will give you grams again. Fill in any empty spaces with zeroes as normal.
In our example, we can shift the decimal place three spaces to the right like this:
0.037
00.37
003.7
0037. — the zeroes on the left don't matter any more, so we can rewrite this as simply 37 grams.
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Answer gets brainliest PLS HELP!!
Based on the number of days that the health inspector and the fire inspector visits, the table for their next 4 visits is:
Number of visits Health Inspector visits Fire inspector visits
1 7 12
2 14 24
3 21 36
4 28 48
The number of days till both inspectors visit on the same day is 84 days.
What day will both inspectors visit?The model that would be best to use and solve the problem of the number of days till both inspectors visit is the Lowest Common Multiple.
This shows the number of days till both inspectors would visit based on their visiting interval.
The lowest common multiple of 7 and 12 is 84 which means that the health and fire inspectors would visit after 84 days on the same day.
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4. Jessica's cat eats 1 bags of food each week. How many whole bags of food does Jessica need
to buy to feed her cat for 42 days?
Answer:
Step-by-step explanation:
7 days= 1 week
42 days= 42/7 = 6 weeks
For 1 week 1 bag of food
For 6 weeks 6 bags of food
P÷2-4p÷3=5 solve for p
The value of p from the given linear expression is -6
Solving linear equationsLinear equations are equations that has a linear degree of 1. For instance the expression y =mx + b has a linear degree of 1.
Given the linear expression below:
P÷2-4p÷3=5
Applying the PEMDAS rule, the division will go first
(P÷2)-(4p÷3)=5
This can also be expressed as:
p/2-4p/3 = 5
Find the Lowest Common Denominator
p/2-4p/3 = 5
3p-2(4p)/6 = 5
(3p-8p)/6 = 5
-5p/6 =5
Cross multiply to have:
-5p = 5(6)
-5p = 30
Divide both sides by -5
-5p/-5 = 30/-5
p = -6
Hence the value of p from the given linear expression is -6
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Calculate surface area of square diameter 25 in
In the lab, Lena has two solutions that contain alcohol and is mixing them with each other. She uses 400 milliliters less of Solution A than Solution B.
Solution A is 20% alcohol and Solution B is 17% alcohol. How many milliliters of Solution B does she use, if the resulting mixture has 179 milliliters of
pure alcohol?
Using a system of equations, it is found that she uses 700 ml of Solution B.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given as follows:
Variable x: Number of ml of Solution A.Variable y: Number of ml of Solution B.She uses 400 milliliters less of Solution A than Solution B, hence:
x = y - 400.
Solution A is 20% alcohol and Solution B is 17% alcohol. The esulting mixture has 179 milliliters of pure alcohol, hence:
0.2x + 0.17y = 179.
Since x = y - 400, we have that:
0.2(y - 400) + 0.17y = 179.
0.37y = 259
y = 259/0.37
y = 700.
She uses 700 ml of Solution B.
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A movie theater runs its films continuously. One movie runs for 70 minutes and a second runs for 105 minutes. The theater has a 15-minute intermission after each movie, at which point the movie is shown again. If both movies start at noon, when will the two movies start again at the same time?
Answer:
10:30 On the Next day
Step-by-step explanation:
This Is a Answer
A side of the triangle below has been extended to form an exterior angle of 135°. Find
the value of x.
Using angle sum property for angles For, the given triangle, the value of x = 23°
What is the angle - sum property?The angle sum feature is a characteristic shared by all varieties of triangles. Triangles have an angle sum property of 180 degrees. This indicates that a triangle's internal angles add up to 180 degrees.
The angle 135 ,makes a linear pair with the line
So, the angle will be -
180 - 135
= 45°
Using angle - sum property,
x + 45 + 112 = 180
x + 157 = 180
x = 180 - 157
x = 23
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Change the following percentage to fractions
25%
60%
30%
6%
55%
22%
45%
89.5%
40.05%
56.6%
Step-by-step explanation:
= 25/100 = 1/4
60% to fraction = 60/100 = = 12/20 further division gives 3/5
30% to fraction = 30/100 = 3/10
6% to fraction= 6/100 = 3/50
55% to fraction= 55/100 = 11/20
22% to fraction = 22/100 = 11/50
45% to fraction = 45/100 = 9/20
Work out the two numbers.
Write your answers on one line
The sum of two numbers is 21.
The second number is six times the first number.
Step-by-step explanation:
let the first number be x ,
second number be 6x,
sum of both numbers is 21.
then,
x + 6 x =21
or, 7x = 21
or, x =21/7
or, x = 3
now,
the first number is 3 &
the second number is 6*3= 18
HELP ME IM DESPERATE!!!!!!!!!!!What is the vector that results from transforming a⃗ by the transformation matrix?
Enter your answer by filling in the boxes.
Answer:
the vector is 24 OVER 67
Step-by-step explanation:
and never the less the vector is the number u Will have total of 67 and 24
The beginning-of-the-period cash balance for the Taylor Company was a $12,000 debit. Cash sales for the month were $8,000 and sales on account were $8,000. The company paid $2,500 cash for current-period purchases and also paid $3,000 cash for amounts due from last month.
What is the ending debit or credit balance in the Cash account?
Based on the calculation below, the ending debit balance in the Cash account is $14,500.
How do we calculate the Cash account ending balance?The ending balance in the Cash account can be calculated using the following formula:
Ending balance = Beginning-of-the-period cash balance + Cash sales for the month - Current-period purchases - Amounts due from last month .......... (1)
Substituting all the relevant into equation (1), we have:
Ending balance = $12,000 + $8,000 - $2,500 - $3,000
Ending balance = $14,500
Since the $14,500 is positive, this implies that the ending can balance is debit.
Note that sales on the account is not cash transaction and that is it is not included in the calculation.
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Which are partial products of
3
×
1,342
?
A.
6 and 900
B.
6 and 700
C.
120 and 90
D.
60 and 9
120 and 90 are Partial product of 3×1,342. Hence, option C is correct.
A Partial product is what we get when we multiply already multiplicand by the first digit of a multiplier that has multiple digits. We split the number into smaller parts in order to multiply. Further, each piece is multiplied separately, and after that, it is added.
In simple terms Partial products are mathematical operations that multiply each digit of one number by each digit of another number while maintaining the place value of each digit. For example, the place value of 4 in the number 43 would be 40.
Model for multiplication of incomplete products.
A model that breaks down data into its individual components. or position values in easy place value to make multiplication easier.
Thus, option C is correct.
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Find the length of the missing side. Leave your answer in simplest radical form.
Given the length of the perpendicular height and base length, the hypotenuse of the right triangle is 2√74 ft.
Hence option a)2√74 ft is the correct answer.
What is the length of the missing side?The Pythagoras theorem can be expressed as;
c = √( a² + b² )
Where c is hypotenuse, a and b are the other two sides of the right triangle.
Given the data in the image;
Length leg 1 of the right triangle a = 14ftLength leg 2 of the right triangle b = 10ftLength of hypotenuse c = ?Plug the given values into the above equation and solve for the hypotenuse 'c'.
c = √( a² + b² )
c = √( (14)² + (10)² )
c = √( 196 + 100 )
c = √( 296 )
296 can be written as 4 × 74, and 4 can further be written as 2²
Hence
c = √( 2² × 74 )
c = 2√74 ft
Given the length of the perpendicular height and base length, the hypotenuse of the right triangle is 2√74 ft.
Hence option a)2√74 ft is the correct answer.
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Mason and Dallas are in a canoe race. Mason paddles 7/8 mile in 1/4. Dallas paddles 9/5 miles in 1/3 hour. Who paddles faster?
The in the canoe race, Dallas paddles faster than Mason.
According to the statement
We have to find that the Speed of the .
So, For this purpose, we know that the
The rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered.
From the given information:
Mason and Dallas are in a canoe race. Mason paddles 7/8 mile in 1/4. Dallas paddles 9/5 miles in 1/3 hour.
Then
The Mason paddles 7/8 mile in 1/4 hour.
We calculate the Speed = Distance/Time
Speed = (7/8)/(1/4)
Speed = (7/8) × (4/1)
Speed = 7/2
Speed = 3.5 miles per hour
And Dallas paddles 9/5 miles in 1/3 hour.
Speed = Distance/Time
Speed = (9/5)/(1/3)
Speed = (9/5) × (3/1)
Speed = 27/5
Speed = 5.4 miles per hour.
So, The in the canoe race, Dallas paddles faster than Mason.
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Answer:
5 2/5 is GREATER THAN 3 1/2, so DALLAS paddles faster.
Alberto estuvo en el refugio con sus amigos durante cuatro días cuántos Ligias eran?
Answer:
Step-by-step explanation:
Alberto was in the shelter with his friends for four days how many Ligias were they?
Use the maximum and minimum data entries and the number of classes to find the class width, the lower class limits, and the upper class limits.
min = 1, max = 30, 6 classes
Using proportions, it is found that:
The class width is of 4.8333.The lower class limits are given as follows: 1, 5.8333, 10.6667, 15.5, 20.3333, 25.1665.The upper class limits are given as follows: 5.8333, 10.6667, 15.5, 20.3333, 25.1665, 30.What is a proportion?A proportion is a fraction of a total amount, and the measures can be related using a rule of three, which derives from proportional relationships.
Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures, involving operations such as division and multiplication, as they involve unit rates.
Since the classes have equal width, the width is given as follows:
class width = (max - min)/n
In which n is the number of classes.
Hence, from the data given in this problem, the class width is given as follows:
class width = (30 - 1)/6 = 4.8333.
The lowest class starts at 1, hence, adding 4.8333, we have that:
The lower class limits are given as follows: 1, 5.8333, 10.6667, 15.5, 20.3333, 25.1665
The highest class starts at 30, hence, subtracting 4.8333, we have that:
The upper class limits are given as follows: 5.8333, 10.6667, 15.5, 20.3333, 25.1665, 30.
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A deck of cards contains RED cards numbered 1,2,3,4,5,6 and BLUE cards numbered 1,2,3,4,5. Let R be the event of drawing a red card, B the event of drawing a blue card, E the event of drawing an even numbered card, and O the event of drawing an odd card.
Drawing the Blue 2 is an example of which of the following events? Select all correct answers.
Drawing a "blue 2" will be represented by the event (or combination of events):
B ∧ O.
Drawing the Blue 2 is an example of which of the following events?
We know that we have the following events:
B = drawing a blue card.E = drawing an even card.R = drawing a read card.O = drawing an odd card.So, if we draw a card with a number 2, like in this case, the event "E" is true.
And also happens for event "B", because our card is a blue card.
Then a "blue 2" will be represented by the event (or combination of events):
B ∧ O.
Where the symbol in the middle, ∧, means "and".
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Can 0.56214 be written as a fraction? It is a terminating or repeating or neither
Answer:
yes. we can write it as a fraction= 56214/100000
it is terminating because it has a stop and its not repeating
There is $10000 in an account that pays 5% interest per year. The interest is added to the total in the account at the end of each year. How much money will be in the account at the end of each year?
Year 1:
Year 2:
Year 3:
The value of the account at the end of 1 year is $10,500
The value of the account at the end of 2 years is $11,025
The value of the account at the end of 3 years is $11,576.25
What is the total at the end of the years?If the amount of interest that is added into the account at the end of the year. Both the initial amount in the account and the interest that has already been earned would increase in value each year. This is known as compound interest.
The formula that can be used to determine compound interest is:
FV = P (1 + r)^n
Where:
FV = Future value
P = Present value
R = interest rate
N = number of years
Value of the account at the end of 1 year: 10,000 x (1.05) = $10,500
Value of the account at the end of 2 years: 10,000 x (1.05²) = $11,025
Value of the account at the end of 3 years: 10,000 x (1.05³) = $11,576.25
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Ken volunteers 1 hr 25 min each day. How many hours of volunteering is completed in 4 weeks?
Enter a mixed number.
Answer:
35 volunteer hours
Step-by-step explanation:
1.25*7=8.75(in a week)
8.75*4=35
Identify a pair of segments that are marked perpendicular to each other on the
diagram below. (Diagram is not to scale.)
P
R
T
#
U
0
S
N
the two perpendicular segments are:
PN and UR.
How to identify the perpendicular segments?Two segments are perpendicular if and only if the angles generated when the segments intersect are all right angles (angles that measure 90°).
And the 90° angles are usually notated with a little square on the vertex.
In the image we can see that the angle at U is a right angle, thus, the segments that pass through that point are perpendicular.
We can conclude that the two perpendicular segments are:
PN and UR.
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Thirty-four high school students were surveyed and asked how many siblings they have. The dotplot below displays the distribution of responses. A dotplot. A number line going from 0 to 8 is labeled Number of Siblings. 0, 3; 1, 5; 2, 9; 3, 9; 4, 3; 5, 3; 6, 1; 7, 0; 8, 1. What is the shape of the distribution of the number of siblings? skewed to the left bimodal symmetric skewed to the right unimodal symmetric
The distribution is skewed to the left.
What is a dot plot?A dot plot is a graph that is made up of dots and a number line. The dots in the dot plot represent the frequency of the data. The greater the frequency of a data, the greater the number of dots.
For example if a the number 5 has 10 dots above it, it means that 5 has a frequency of 10.
The given dot plot is skewed to the left because the number of dots on the left is greater than the number of dots on the right.
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Henry has a fenced yard in the shape of a rectangle with a perimeter that measures 226 feet. If the width of the yard measures 25 feet what is the length?
Answer:
Henry has a fenced yard in the shape of a rectangle with a perimeter that measure 226 feet.
it means perimeter is 226 feet.
then,it's width(breath) is 25feet
now, length =?
by using perimeter of rectangle
perimeter=2(l+b)
226=2(l+25)
226=2l+50
226-50=2l
176=2l
176/2=l
l=88
Therefore the length is 88feet.
Thank you
