95% confidence interval for the true population mean watermelon weight. is (69.94, 72.06)
Confidence Interval formula = Mean ± z × Standard deviation/√n
Mean = 71 ounces
Standard deviation = 2.8 ounces
z score = 95% confidence interval = 1.96
Confidence Interval = 71 ± 1.96 × 2.8/√27
= 71 ± 1.96 × 0.5388602512
= 71 ± 1.0561660924
71 - 1.0561660924
= 69.943833908 ounces
Approximately = 69.94 ounces
71 + 1.0561660924
= 72.0561660924 ounces
Approximately = 72.06 ounces
95% Confidence Interval = (69.94, 72.06).
the complete question is
You measure 27 watermelons' weights, and find they have a mean weight of 71 ounces. Assume the population standard deviation is 2.8 ounces. Based on this, construct a 95% confidence interval for the true population mean watermelon weight.
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If log3 x + logx 3= 2.5 find the value of x
The value of x is -0.004624
[tex]log_{3} (x)+log_{x} (3)=2.5[/tex]
[tex]log_{3} (x)+\frac{log_{3} (3)}{log_{3} (x)} =2.5[/tex]
Let z= [tex]log_{3} (x)[/tex]
[tex]z+\frac{1}{z} = 2.5[/tex]
[tex]3z^{2} + z-2.5z=0[/tex]
z= -0.166
[tex]log_{3} (x)=-0.166[/tex]
x = -0.004624
What is a log?
The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which a set number, base b, must be increased in order to create a specific number x, is represented by the logarithm of that number. The logarithm, in its most basic form, counts the number of times the same factor appears when multiplied repeatedly; for instance, since 1000 = 10 x 10 x 10 = 103, its "logarithm base 10" is 3, or log10 (1000) = 3. When there is no possibility of a mistake or when the base is irrelevant, as, in big O notation, the logarithm of x to base b is written as loga (x), logb x, or even without the explicit base, log x.
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Can someone help me find the slope???
Answer:
The slope is -1/3.
Step-by-step explanation:
When you count the rise/run, which is how much it goes up/down and left/right, you get -4/12. Simplify -4/12 and you'll get -1/3.
What products are defined for these matrices?
Drag the operation to the boxes to correctly complete the table.
The allocation for product defined and product not defined are
PD(product defined)
PM, QP, LMPND
MLThis is further explained below.
What is an allocation for product defined?Generally, the rule for matrix multiplication
no. of columns for the first matrix should be equal to no. of rows in the second matrix" that is if
1st matrix has =m * n
2nd has =k *l
Therefore
m=l
L=2*2, M=4*2,
The matrix is defined as the row and the column tally
M=4*2 and L=2*2
The matrix is not defined as a row and the column do not tally
In conclusion, Q=2*1, and P=2*2 equal so the product is defined.
P=2 *2,M=4 *2, equal so product is defined.
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You are on the prom decorating committee and are in charge of buying balloons. you want to use both latex and mylar balloons. The latex balloons cost $.10 each and the mylar balloons cost $.50 each. You need 125 balloons and you have $32.50 to spend. how many of each can you buy?
I can buy 75 latex balloons and 50 mylar balloons.
This is a problem from an algebraic equation. We can solve this problem by following a few steps.
We need 125 balloons. Let's assume we have to purchase x latex balloons.
So, mylar balloons are ( 125 - x ).
Our total budget is $32.50.
The cost of x latex balloons is ($.10 × x) = $.10x , as the latex balloons cost $.10 each.
The cost of ( 125- x) mylar balloons is $[( 125- x) × 0.50] , as the mylar balloons cost $.50 each.
So the total cost is,
$[( 125- x) × 0.50] + $.10x = 32.50
Now, we have to solve this equation, Let's simplify it.
62.50 - 0.50x + .10x = 32.50
Or, 62.50 - 0.40x = 32.50
Or, -0.40x = 32.50 - 62.50 [ deduce 62.50 from both side ]
Or, -0.40x = -30 [ we should devide both sides 0.40 ]
Or, x = 30/0.40 = 75
So, the number of latex balloons is 75. Therefore, the number of remaining mylar balloons is ( 125 - 75) = 50
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Cathy has 48m of fencing to make a rectangular pen for her pets. What is the
maximum area?
The area of the square will be 100 square meters. Then the dimensions of the pen of the rectangle will be 10 by 10 which is a square.
What is the area of the square?
Let a be the side length of the square.
Then the area of the square will be
Area of the square = a² square units
Cathy has 40 meters of fencing to build a rectangular pen for her pets.
For the maximum area of the rectangle, the length and width should be congruent.
40 = 4a
a = 10
Then the area of the square will be
A = 10²
A = 100 square meters
The dimensions of the pen of the rectangle will be 10 by 10 which is a square.
What is an equation of the line that passes through the point (2,-3) and is parallel to the line 2x+5y=10
The equation of the line that passes through the point (2,-3) and is parallel to the line 2x + 5y = 10 is y = - 2 / 5 x - 11 / 5
How to find the equation of a line?The equation of a line can be represented in various form such as point slope form, slope intercept form and standard form.
Therefore, let's find the equation of the line that passes through the point (2, -3) and is parallel to the line 2x + 5y = 10.
Hence, parallel lines have the same slope.
5y = -2x + 10
y = - 2 / 5 x + 2
Therefore, the slope of the line is - 2 / 5.
Let's find the y-intercept using the slope intercept equation.
y = mx + b
where
m = slopeb = y-interceptHence, (2, -3)
-3 = - 2 / 5(2) + b
-3 = - 4 / 5 + b
b = - 3 + 4 /5
b = - 11 / 5
Therefore, the equation of the line is y = - 2 / 5 x - 11 / 5
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The required equation of the line y = - (2/5)x - 11/5 passes through the point (2,-3) and is parallel to the line 2x + 5y = 10.
We have to determine the line that passes through the point (2,-3) and is parallel to the line 2x+5y=10
Parallel lines are known to have the same slope.
Firstly, we have to find its slope by the given line
⇒ 5y = -2x + 10
⇒ y = - (2/5)x + 2
Thus, the slope of the line is - 2/5.
Let the required equation of the line is y - y₁ = m(x -x₁ )
Here x₁ = 3, y₁ = 1 and m = -2/5
y - 1 = (-2/5)(x - 3)
y - 1 = (-2/5)x + 3(-2/5)
y = - (2/5)x - 6/5 +1
y = - (2/5)x - 11/5
Therefore, the required equation of the line is y = - (2/5)x - 11/5.
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What will be the location of T′ in the image trapezoid S′T′U′V′? (10, −1) (10, 1) (13, 1) (13, −1)
By translating trapezoid S′T′U′V 7 using the same translation rule, the location of T′ in the image trapezoid S′T′U′V′ is: D. (13, -1)
The types of transformation.Generally, there are four (4) main types of transformation and these include the following:
ReflectionDilationRotationTranslationWhat is a translation?In Geometry, a translation can be defined as a type of transformation which moves every point of a geometric figure or object in the same direction, as well as for the same distance.
By critically observing the graph (see attachment), we can logically deduce that rectangle JKLM was transformed to rectangle J'K'L'M' by translating it 7 units to the right and 5 units up.
Next, we would apply the same translation rule to T' which is located at point (6, -6) as follows:
(x, y) → (x + 7, y + 5)
Point T (6, -6) → Point T' = (6 + 7, -6 + 5) = (13, -1)
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Complete Question:
Rectangle J'K'L'M' shown on the grid is the image of rectangle JKLM after transformation. The same transformation will be applied on trapezoid STUV.
What will be the location of T′ in the image trapezoid S′T′U′V′? (10, −1) (10, 1) (13, 1) (13, −1)
Which postulate could we use to prove that the angles
The angle postulate that best defined angles CAB and CAD is; Supplementary Angles
What is the Angle Postulate?We know that there are different angle postulates such as Corresponding angles, complementary angles, supplementary angles and others.
Now, in this case we want to find the angle theorem that best describes angles CAB and CAD. Now, from the given image, it is clear that both angles form a straight line and we know that the sum of angles on a straight line equals 180 degrees.
Since both angles sum up to 180 degrees and we know that these angles are defined as supplementary angles which are linear pairs.
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Please help I have no clue what I’m doing! Grade is getting low and this was due awhile ago!
Given the function below, determine the following.
f(x) = 10x + 13
Find f(3).
f(3)
Find f(-8).
f(-8)
Find x if f(x) = 53.
x=
Answer:
see explanation
Step-by-step explanation:
f(3) means what is the value of f(x) when x = 3
substitute x = 3 into f(x)
f(3) = 10(3) + 13 = 30 + 13 = 43
similarly for x = - 8
f(- 8) = 10(- 8) + 13 = - 80 + 13 = - 67
given f(x) = 10x + 13 and f(x) = 53 , equate the right sides
10x + 13 = 53 ( subtract 13 from both sides )
10x = 40 ( divide both sides by 10 )
x = 4
use the properties of vector addition and scalar multiplication from the following theorem. properties of vector addition and scalar multiplication in rn let u, v, and w be vectors in rn, and let c and d be scalars.
The set R^2 with x ≤ 0 and y ≤ 0 is not a vector space.
The 10th axiom cv∈ V does not hold
Let u, v and w be vectors in the vector space V, and let c and d be scalars. A set S is defined as a vector space if it satisfies the following conditions:
1. u+ v ∈V
2. v + w = w + v
3. (u + v) + w = u + (v + w)
4. v + 0 = v = 0 + v
5. v + (−v) = 0
6. 1v = v
7. c(dv) = (cd)v
8. c(v + w) = cv + cw
9. (c + d)v = cv + dv
10. c v ∈V
Given the set of all vectors x, y in R^2 with x ≤ 0 and y ≤ 0
If the scalar c is such that c<0 then c v ∉R^2as cv>0
Therefore, the 10th axiom is not satisfied and thus the set R^2 with x ≤ 0 and y ≤ 0 is not a vector space.
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Newton's Second Law of Motion states that the acceleration of an object is directly proportional to the force exerted on the object. If an object accelerates at a rate of 3 m/s2, it will exert a force of 15 N. How much force will the same object exert if it accelerates at a rate of 7 m/s2 ?
Answer: 35N
Step-by-step explanation:
Cross multiply and divide to find the missing value
Answer: 35N :)))))))))))))))))))))))))))))
HELLLP khan academy !! due tonight
Equation of the line is y = -(1/3)x+5
The figure shows a straight line of which two points and thereby the slope can be found out.
Equation of a line is in the slope-intercept form is,
y = mx +c,
where m is the slope of the line and c is the y-intercept of the line.
From the figure, two points on the line are, (0,5) and (3,4).
Then slope = (4-5)/(3-0)
= -1/3
Now y-intercept, c is the y-co-ordinate when x = 0.
From the figure, when x = 0, y = 5
So y-intercept, c = 5.
Thus the equation of the line is, y = -(1/3)x+5
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the third term in the sequence is 11
the term-to-term rule is "take away 4"
write an expression on in terms of n for the nth term of the sequence
An expression, in terms of n, for the nth term of this arithmetic sequence is aₙ = 23 - 4n.
What is an arithmetic sequence?An arithmetic sequence can be defined as a series of real and natural numbers in which each term differs from the preceding term by a constant numerical quantity.
How to calculate an arithmetic sequence?Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:
aₙ = a₁ + (n - 1)d
Where:
d represents the common difference.a₁ represents the first term of an arithmetic sequence.n represents the total number of terms.For the second term, we have:
a₂ = a₃ - d
a₂ = 11 - (-4)
a₂ = 11 + 4
a₂ = 15.
For the first term, we have:
a₁ = 4 + second term
a₁ = 4 + 15
a₁ = 19
Substituting the given parameters into the formula, we have;
aₙ = a₁ + (n - 1)d
aₙ = 19 + (n - 1)(-4)
aₙ = 19 - 4n + 4
aₙ = 23 - 4n
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Susie started a rock collection. she started with 26 rocks. each month she adds 5 to the collection. which equation can be used to find y, the total number of rocks in susie's collection after x months?
Answer:
26 + 5x = y
Step-by-step explanation:
hope this helped
have a good day ^^
what is the common ratio for the geometric sequence 35/2, 7, 14 / 5, 28 / 25, enter your answer as a decimal
Given:
The geometric sequence is
[tex]\begin{gathered} a_1,a_2,a_3,a_4 \\ \frac{35}{2},7,\frac{14}{5},\frac{28}{25} \end{gathered}[/tex]To find the common ratio,
[tex]\begin{gathered} Ratio=\frac{a_2}{a_1} \\ =\frac{7}{\frac{35}{2}} \\ =\frac{7\cdot2}{35} \\ =\frac{14}{35} \end{gathered}[/tex]Hence the common ratio, r is 14/35.
Write an explicit formula for an, the nth term of the sequence
6, -12, 24,....
Answer:
6,12,24,48,96
Step-by-step explanation:
22 Which inequality is equivalent to 7x - 2y > 8?
Fy> / x+8
8
5 y> - ²/x + ²
Hy< ²x -
3
4
417
<-²/x-4/
32
Inequality which is equivalent to 7x - 2y > 8 x>[tex]\frac{2y}{7}[/tex] + [tex]\frac{8}{7}[/tex] and y <[tex]\frac{7x}{2} -4[/tex]
What is inequalities?Equations don't always need to have a "equal to" symbol on both sides to be balanced. Sometimes it can be about a "not equal to" relationship, meaning that something is superior to or inferior to another. In mathematics, an inequality is a relationship between two numbers or other mathematical expressions that results in an unequal comparison. Inequalities are the name given to certain algebraic mathematical expressions.
7x - 2y>8
-2y > 8 -7x
=y <[tex]\frac{7x}{2} -4[/tex]
or
7x >2y + 8
=x>[tex]\frac{2y}{7}[/tex] + [tex]\frac{8}{7}[/tex]
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jane had overdrafted her bank account and had a balance of -$24.62. She picked up her paycheck from work and deposited $154.88. What is her new balance?
answer for 100 points
Which of the following is equal to (2x/5 - 9) +9?
Answer:
I don't see any answer options, and the equation doesn't look correct.
I'll assume the equation is meant to be:
(2x/5 - 9) = 9, not (2x/5 - 9) +9Step-by-step explanation:
(2x/5 - 9) = 9
2x/5 = 18
2x = 90
x = 45
if the modified equation is correct.
write the equation of a circle given the center (2, 9) and radius r = 3
Answer: x^2 + y^2 - 4x + 18y = 76 = 0
The center of the circle given is (2, 9)
radius = r
The equation of a circle for a given point is
(x - h)^2 + (y - k)^2 = r^2
Where h = 2, and y = 9
(x - 2)^2 + (y - 9)^2 = 3^2
Expand the parentheses
(x - 2) (x - 2) + (y - 9) (y - 9) = 9
(x - 2) (x - 2 ) = x* x - 2*x - 2*x + 2* 2
= x^2 - 4x + 4
(x - 2) (x - 2) = x^2 - 4x + 4
(y - 9) (y - 9) = y*y - y*9 - 9*y + 9*9
= y^2 - 18y + 81
(y - 9) (y - 9)= y^2 - 18y + 81
Therefore, the equation becomes
x^2 - 4x + 4 + y^2 - 18y + 81 = 9
Re-arrange the equation
x^2 + y^2 - 4x - 18y + 4 + 81 = 9
x^2 + y^2 - 4x - 18y = 9 - 81 - 4
x^2 + y^2 - 4x - 18y = -76
x^2 + y^2 - 4x - 18y + 76 = 0
The equation of a circle given the center (2, 9) and radius 3 is x^2 + y^2 - 4x + 18y = 76 = 0
Answer:
The equation of a circle given the center (2, 9) and radius 3 is x^2 + y^2 - 4x + 18y = 76 = 0
Step-by-step explanation:
standard to slope intercept form
Answer: y = 1/6x + 1
Step-by-step explanation:
12y - 2x= 12
+2x +2x
12y = 12 + 2x
DIVIDE BOTH SIDES BY 12
y = 1 + 1/6x
THEN PUT IN SLOPE INTERCEPT FORM
y = 1/6x + 1
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: 12y - 2x = 12[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: 12y = 2x + 12[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{2}{12} x + \frac{12}{12} [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{1}{6} x + 1[/tex]
Slope = 1/6, y - intercept = 1
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The telephone company offers two billing plans for local calls. Plan 1 charges $31 per
month for unlimited calls and Plan 2 charges $13 per month plus $0.03 per call.
a. Use an inequality to find number of monthly calls for which Plan 1 is more
economical than Plan 2.
b. Explain the meaning of the answer to part a.
Answer:
i think is (a)
because i zay do
Step-by-step explanation:
anyways...... i want more pictures of math problems
13 people on a softball team show up for a game. how many ways are there to choose 10 players to take the field? (you must provide an answer before moving to the next part.)
858 combinations are there to choose 10 players to take the field.
Pick 10 people from 13,
[tex]C^{13} _{10}[/tex] = [tex](^{13} _{2} )[/tex]
Splitting the combination,
[tex]C^{13} _{10}[/tex] = (13 × 12 × 11) ÷ 2
[tex]C^{13} _{10}[/tex] = 1716 ÷ 2
[tex]C^{13} _{10}[/tex] = 858 ways to pick the 10 to play.
There are 858 different methods to select 10 players to take the pitch.
The permutations of a set are the vaguely defined community of its members in arrangement or linear order, or the permutation of its components if the set is already collected. The act or procedure of adjusting the linear ordering of a sorted set is often named "permutation".
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Write each number as a power of 4
a) 1/4
b) 1/64
Answer: I am going to assume that 1/4 is 1 over 4 ( a fraction ) and that it is the same for 1/64
A) 0.00390625
B) 0.015625^4 <------( Here is the equation. when i put it in a calculator it was too long. here is the answer that gave me: 5.96046448 e-8 )
Help ASAP, will mark brainliest!
If triangle ABD is congruent to triangle CBD, angle ADB = 49 degrees and angle CDB = 7x.
Answer:
x = 7 degrees
Step-by-step explanation:
Angle CDB = 49 degrees (corresponding angles triangle ABD congruent to triangle CBD)
Angle CDB = 49 degrees = 7x
7x = 49 degrees
x = 7 degrees
help on the ones you know
Answer:
2. y = x + 13
Step-by-step explanation:
Your points are: (-4, 9) and (2, 15)
To write an equation of a line from two ordered pairs, you first find the slope (m)
To find the slope, you do y2 - y1 / x2 - x1
(-4 is x1, 9 is y1) (2 is x2, 15 is y2)
Plug in the numbers:
15 - 9 / 2 - (-4) ----------------------> 6/6 ----------> 1, m = 1
The next equation we'll use is y - y1 = m(x - x1)
and slope intercept form is y = mx + b
Pick either ordered pair to plug in the coordinates, but this time I'll use
(2, 15) -----> 2 is x1, 15 is y1
y - 15 = m(x - 2)
Since we already know the slope, m, we can simplify the equation.
y - 15 = 1(x - 2)
Distributive property
y - 15 = x - 2
Add 15 on both sides,
y = x + 13
EFG and GFH are a linear pair, m EFG = 4n+ 15, and mGFH = 2n + 39. What are mEFG and mGFH?
mEFG=
mGFH=
Answer:
Find value of n first to find out what the angle measures are.
Linear angles have a sum of 180°.
Angle EFG + Angle GFH = 180
4n + 15 + 2n + 39 = 180
6n + 54 = 180
6n = 126
n = 21
Substitute n into the angles.
Angle EFG = 4(21) + 15 = 99°
Angle GFH = 2(21) + 39 = 81°
Can you please help me with this question I don’t understand it.From DA to the angle BAC
INFORMATION:
We have the next rhombus
And we must find the measure of
Knowing that DB = 10, BC = 13, and m∠WAD = 25°
STEP BY STEP EXPLANATION:
To find all measures, we need to use properties or the rhombus:
- DA: To find DA we need to know that all sides of the rhombus are equal. So, if BC measures 13, then DA measures 13 too.
- BW: To find BW we need to know that in a rhombus, diagonals bisect each other at right angles. That means, diagonals intersect in the middle. So, if DB = 10, then BW will be half of BD. BW = 10/2 = 5.
- WC: We can find it as one of the legs of the right triangle formed by BW, BC and WC. Where, BC is the hypotenuse.
[tex]\begin{gathered} 13^2=5^2+WC^2 \\ WC=\sqrt{13^2-5^2} \\ WC=12 \end{gathered}[/tex]So, WC = 12.
- Angle BAC: To find this angle, we need to use that the interior triangles formed in the interior of the rhombus are congruent. So, angle BAC is congruent with the angle DAC. Then, BAC = 25°.
ANSWER:
DA = 13
BW = 5
WC = 12
BAC = 25 degrees
Put the following equation of a line into slope-intercept form, simplifying all fractions. 6x-3y=15
Answer: y=2x-5
Step-by-step explanation:
6x-3y=15
6x-6x-3y=-6x+15
-3y=-6x+15
-(3y=6x-15)
3y=6x-15
3y/3=(6x-15)/3
y=6x/3-15/3
y=2x-5
Standard to slope intercept form
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = - 6x+ 6[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
The given equation is :
[tex]\qquad\displaystyle \tt \rightarrow \: 24x + 4y = 24[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: 4y =24 - 24x [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{ 24}{4} - \frac{24x}{4} [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = - 6x + 6[/tex]
And this the equation of same line in its slope intercept form, where slope (m) = -6 and y - intercept = +6
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