The standard error of the sample mean to the nearest hundredth is mathematically given as
S.E=0.784
What is the standard error?The amount by which the population means deviates from a sample mean is represented by the standard error of the mean, which is more often referred to as simply the standard error.
It informs you how much the sample means would change if you were to perform an experiment using fresh samples from the same population but this time uses different samples.
The standard error is obtained by calculating the standard deviation and then dividing that number by the square root of the sample size. It determines the accuracy of a sample mean by factoring in the variation in sample means that exists from one set of data to the next.
Generally, The population's mean height is 62.95 inches, so let's use that.
Taking into account that the population has a standard deviation of 5.65 inches
The sample mean is used to calculate the standard error of the mean.
[tex]SE=\frac{SD}{\sqrt{n}}[/tex]
Therefore
[tex]SE=\frac{5.65}{ \sqrt{52}}[/tex]
S.E=0.7835
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Sorry, I’m in kind of a rush, could you guys explain this to me? Thank you so much!!!
35. Lucas and Jacob can paint a house in 1 hour
working together. If Jacob works alone, he can
paint the house in 1.5 hours. How long would
it take Lucas to complete the job on his own?
E. 1 hour
F. 1.5 hours
G. 2 hours
H. 3 hours
The time it will take Lucas to paint the house using rate is 3 hours
How to find the how long it take Lucas to paint the house using rate?They both paint the same house.
Lucas and Jacob can paint a house in 1 hour working together.
Jacob works alone, he can paint the house in 1.5 hours.
Therefore, the time it will take Lucas to paint the house using rate is as follows:
let
x = time it will take Lucas to paint the house
1 / 1 = 1 / x + 1 / 1.5
1 = 1.5 + x / 1.5x
cross multiply
1.5x = 1.5 + x
1.5x - x = 1.5
0.5x = 1.5
divide both sides by 0.5
x = 1.5 / 0.5
x = 3
Therefore, the time it will take Lucas to pain the house is 3 hours.
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Consider the sets below.
A {xlx is a polygon}
B {x|x is a triangle}
Which is true?
A = B
B =A
Ac= B
Bc = A
A weeping willow that is
15
1515 feet in height grows to a maximum height of
35
3535 feet in
y
yy years at a constant rate of
24
2424 inches per year. Which of the following equations best describes this situation?
The equation 35 = 15-24y represent the growth rate.
According to the statement
we have given that the
A weeping willow that is 15 feet in height grows to a maximum height of 35 feet in y years at a constant rate of 24 inches per year.
And we have to describe all conditions in the equation.
So,
firstly the given height of weeping pillow before growing is 15 feet.
It means the maximum real height it grows is to subtract from the maximum given height it grows.
it means we have to find the growth rate.
real height he grows is = 35-15 = 20 feet
And it grows at the 24 inches per year so, it means it become
24 y
By combining these we get the equations is
35 = 15-24y.
So, The equation 35 = 15-24y represent the growth rate.
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Disclaimer: This question was incomplete. Please find the full content below.
Question:
A weeping willow that is 15 feet in height grows to a maximum height of
35 feet in y years at a constant rate of 24 inches per year. Which of the following equations best describes this situation?
A. 37 = 15-24y
B. 35 = 15-24y
C. 35 = 15-22y
D. 39 = 15-27y
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Answer: 35= 15+2y
Step-by-step explanation:
I am taking the Khan Academy Lesson.
In the driest part of an Outback ranch, each cow needs about 40 acres for grazing. Write and solve an equation to find how many cows can graze on 720 acres of land.
Answer: 18 cows
Step-by-step explanation: C = how many cows can graze on 720 acres of land. 40(C) = 720. 720/40 = 18 C = 18.
Answer:
40x = 720
x = 18
Step-by-step explanation:
x = number of cows
If a baseball is a sphere with a radius of 3.75 cm, what is the surface area of the baseball? use π = 3.14. a. 176.6 cm² b. 725.8 cm² c. 60.5 cm² d. 181.46 cm²
The surface area of the baseball is 176.6 cm² b.
What is meant by surface area?As a refresher, the surface area of an object is the sum of the areas of all of its faces or the exterior surfaces of its three dimensions. It is calculated in square units.The base, top, and lateral surfaces (sides) of the object's surface are added together to get the object's overall surface area. This is calculated in square units and done using several area formulas.A 3D object's surface area is the entire area that all of its faces cover. For instance, the surface area of a cube is its surface area if we need to determine how much paint is needed to paint it. It is consistently expressed in square units.To find the surface area of the baseball:
r=3.75
[tex]A=4\pi r^{2}[/tex]
[tex]A=4*\pi *3.75^{2}[/tex]
A=176.6 cm² b.
The surface area of the baseball is 176.6 cm² b.
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Determine the factors of a2b 2a2 3b 6. (b 3)(a2 2) (b 2)(a2 3) (ab 2)(a 3) (ab 3)(a 2)
The factor of [tex]$a^{2} b+2 a^{2}+3 b+6$[/tex] exists [tex]$\left(a^{2}+3\right)(b+2)$$[/tex].
How to determine the factor of [tex]$a^{2} b+2 a^{2}+3 b+6$[/tex]?
Let the given factor be [tex]$a^{2} b+2 a^{2}+3 b+6$[/tex]
To factor this we use the grouping method
We group the first two terms and last two terms then we factor out the greatest common factor (GCF) from each group.
[tex]$\left(a^{2} b+2 a^{2}\right)+(3 b+6)$$[/tex]
Take out GCF from each group
[tex]$a^{2}(b+2)+3(b+2)$$[/tex]
Now factor out b+2, we get
[tex]$\left(a^{2}+3\right)(b+2)$$[/tex]
The factor of [tex]$a^{2} b+2 a^{2}+3 b+6$[/tex] exists [tex]$\left(a^{2}+3\right)(b+2)$$[/tex].
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In the figure below, ∠t= 133° . Find the measures of all remaining angle.
t is vertical to s because they share a point and are directly across from each other. vertical angles are congruent. therefore s=113 degrees
t and p are corresponding angles, which means they are congruent. this means p is also 113 degrees.
s and o are corresponding angles, so o is also 113 degrees.
t and u are supplementary. they share a straight line, so they add up to 180. you can find u by subtracting 113 from 180. 180-113= 67, so u is 67 degrees.
u and r are vertical angles, so r is 67 degrees.
r and m are corresponding, as well as u and q. therefore m and q both equal 67 degrees.
hope this helped :)
Which of the diagrams below represents the statement "If it is an triangle,
then it has three vertices?
The answer is Figure A.
What is in a triangle?Three sides, three angles, and three vertices make up a triangle. A triangle's total internal angles are always equal to 180 degrees. This is referred to as the triangle's angle sum property.Triangles are three-sided shapes. The various kinds of triangles go by various names. The angles' size and the sides' length determine the type of triangle (corners). Equilateral, isosceles, and scalene triangles are the three varieties of triangles based on the length of the sides.A triangle is a closed, two-dimensional object with three sides, three angles, and three vertices. A polygon also includes a triangle. Triangle ABC is shown in the image above. Triangles can be found in a variety of everyday objects, such as sandwiches, traffic signs, clothes hangers, and billiards racks.
Given: "If it is an triangle, then it has three vertices.
To find which diagram represents the given statement.
From the first diagram
Triangles have three vertices because they are formed by the intersection of three triangles.
using the second diagram
Three vertices make up the triangle's intersection zone.
Therefore, we cannot infer from the second diagram that a triangle has three vertices.
As a result, figure A represents the stated assertion.
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Which of the graphs below represents the equation 8x-y=-4?
Answer:
Graph X
Step-by-step explanation:
First, convert the equation into slope-intercept form. The first step is the bring the x to the right side by subtracting 8x from both sides: -y=-8x-4. Now multiply both sides by -1: y=8x+4. Now, if you know about the slope-intercept form, you'll know that 4 is the y-intercept and that [tex]\frac{8}{1}[/tex] is the slope. 8 is the rise and 1 is the run, so the answer is graph X.
The bisectors BO and CO of the angles at B and C of ABC meet at O. Prove that BOC = 90° + A/2.
The prove that BOC = 90° + A/2. is given below:
What is the bisector about?Note that, bisectors of angles B and C and that of a triangle ABC is one that pass across each other at the point O.
Hence: one need to to prove that ∠BOC = 90° + A/2
Since:
BO is said to be the bisector of angle B e.g. ∠OBC = (∠1)
CO is said to be the bisector of angle C e.g. ∠OCB = (∠2)
Looking at the triangle BOC, to interpret by the use of angle sum property, then:
∠OBC + ∠BOC + ∠OCB = 180°
∠1 + ∠BOC + ∠2 = 180° ---- ( equation 1)
Looking at triangle ABC and by the use of angle sum property, So;
∠A + ∠B + ∠C = 180°
∠A + 2(∠1) + 2(∠2) = 180°
Then we divide by 2 on the two sides, and it will be:
∠A/2 + ∠1 + ∠2 = 180°/2
∠A/2 + ∠1 + ∠2 = 90°
∠1 + ∠2 = 90° - ∠A/2 ---(equation 2)
Then one need to Substitute (2) in (1), So:
∠BOC + 90° - ∠A/2 = 180°
∠BOC - ∠A/2 = 180° - 90°
∠BOC - ∠A/2 = 90°
Hence , ∠BOC = 90° + ∠A/2
Therefore, from the above, we care able to prove that BOC = 90° + A/2.
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Find the inverse of the given function.
The inverse of the function, f(x) = (-1/2)√(x + 3), x ≥ -3 is f⁻¹(x) = 4x² - 3, for x ≤ - 1/2.
In the question, we are asked to find the inverse of the function, f(x) = (-1/2)√(x + 3), x ≥ -3.
The domain for the given function is x ≥ -3.
Thus, its range is x ≤ - 1/2.
To find the inverse, we equate f(x) = y, to get:
(-1/2)√(x + 3) = y,
or, √(x + 3) = -2y.
Squaring both sides, we get:
x + 3 = (-2y)²,
or, x + 3 = 4y²,
or, x = 4y² - 3.
Thus, the inverse of the function f(x) = (-1/2)√(x + 3), is, f⁻¹(x) = 4x² - 3.
The inverse will have the domain equal to the range of the original function, that is, x ≤ - 1/2.
Thus, the inverse of the function, f(x) = (-1/2)√(x + 3), x ≥ -3 is f⁻¹(x) = 4x² - 3, for x ≤ - 1/2.
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The provided question is incomplete. The complete question is:
"Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Find the inverse of the given function.
f(x) = (-1/2)√(x + 3), x ≥ -3
f⁻¹(x) = x² - , for x ≤ ."
For the polynomial f(x)=x^3-kx^2+x+6, find the value of k if (x+1) is a factor of f(x).
The value of k if (x+1) is a factor of f(x) is -4
How to determine the value of k?The polynomial function is given as:
f(x)=x^3-kx^2+x+6
(x+1) is a factor of f(x)
So, we start by setting x + 1 to 0
x + 1 = 0
Solve for x
x = -1
Substitute x = -1 in f(x)=x^3-kx^2+x+6 and set the equation to 0
(-1)^3-k(-1)^2+(-1)+6 = 0
Evaluate the exponents
-1 - k - 1 + 6 = 0
Evaluate the like terms
k + 4 = 0
Solve for k
k = -4
Hence, the value of k if (x+1) is a factor of f(x) is -4
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Solve the system using
elimination:
2x-y=8
3x+2y=5
Answer:2x+y=8
3x-2y=5
Step-by-step explanation:multiply 1 st equation by 2
4x+2y=16
3x-2y=5
7x=21
x=21/7
x=3
2×3+y=8
6+y=8
y=8-6
y=2
PLS help
What is the area of the circle?
A. 50.24 m 2
B. 176 / 7 m 2
C. 100.48 m 2
E. 64 m 2
5. Enter the answer as a decimal
Calculate the rate of interest, when simple interest = $5,616;
loan amount = $7,200 and time = 12 years.
Answer:
6.5%
Step-by-step explanation:
I = prt
5616 = 7200 × r × 12
r = 5616/(7200 × 12)
r = 0.065
r = 6.5%
Which congruence postulate or theorem is stated below?
The congruence postulate or theorem that is stated is the: C. AAS congruence theorem.
What are Congruent Triangles?Triangles that are referred to as congruent triangles are triangles that have corresponding congruent sides and corresponding congruent angles.
What is the Angle-angle-side Congruence Theorem (AAS)?According to the angle-angle-side congruence theorem (AAS) two triangles are congruent if two angles and a non-included side of one triangle are congruent to two corresponding angles and a non-included side of the other are congruent to each other.
For example, in triangles GUM and RED given in the image attached below, we have the following:
∠G ≅ ∠R [a pair of congruent angles]
∠M ≅ ∠D [a pair of congruent angles]
GU ≅ RD [a pair of non-included congruent side]
Thus, both triangles are congruent by the AAS, which is the congruence theorem that is stated above.
The answer is: C. AAS.
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Answer:
aas
Step-by-step explanation:
List all the possible outcomes for spinning the spinner and flipping a fair coin.
The list of the possible outcomes for spinning the spinner with four sectors A, B, C, D, and flipping a fair coin goes as follows,
AH, BH, CH, DH, AT, BT, CT, DT
The possible outcomes for spinning a spinner (assuming that the spinner has four sectors, A, B, C, D) are: A, B, C, D (4 outcomes)
Now, the possible outcomes for flipping a fair coin are: Tales (T) and Heads (H) (2 outcomes)
For each possible outcome of the spinner, there can be two possible outcomes associated, because of the flipping of the fair coin. Hence, the total possible outcomes for spinning the spinner with four sectors A, B, C, D, and flipping a fair coin are 4 × 2, i.e. 8 outcomes.
These possible outcomes are AH, BH, CH, DH, AT, BT, CT, DT.
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Find the sum of the arithmetic series given a=2, a=35, and n=12.
The sum of an arithmetic progression with first term of 2 and the common difference of 35 is 2340
Sum of arithmetic sequenceSeries are defined as the sum of sequence. The formula for calculating the nth term of an arithmetic sequence is expressed as:
S = n/2[2a+(n-1)d]
where;
n is the number of terms
d is the common difference
a is the first term
Given the following parameters from the question
a -2
d = 35
n = 12
Substitute
S = 12/2[2(2)+(12-1)(35)]
S = 6(4+11(35))
S = 6(5+385)
S = 6(390)
S = 2340
Hence the sum of an arithmetic progression with first term of 2 and the common difference of 35 is 2340
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Solve following equation: [tex]y-4(2y-5)=-4[/tex]
Answer:
24 / 7
Step-by-step explanation:
y - 4(2y - 5) = -4
y - 8y + 20 = -4
-7y = -24
7y = 24
y = 24/7,
y = 3 and 3/7
or
y = 3.428571 all recurring
(they are all the same value in different forms I would just write 24/7)
Heron's Formula:
The two bases of a trapezoid are 3 and 11 and the altitude is 8. What is the area of the trapezoid? Use Heron's formula.
Answer:
√s(s-a) (s-b) (s-c)
Step-by-step explanation:
123456
herons formula
Write (9 + 6i) − (1 + 3i) as a complex number in standard form.
A.
10 + 9i
B.
8 − 3i
C.
8 + 3i
D.
7 − 12i
The sum of the complex number in standard form is 8 + 3i
Complex numbersComplex numbers are square roots of negative numbers. The square root of -1 for example is equal to "i" as shown;
√-1 = i
The complex number is written as x + iy. Given the expression
(9 + 6i) − (1 + 3i)
Expand to have:
9 + 6i − 1 - 3i
Collect the like terms
9-1 + 6i - 3i
Group into real and imaginary parts
(9-1) + (6i-3i)
8 + 3i
Hence the sum of the complex number in standard form is 8 + 3i
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Select the correct answer. which expression is equivalent to the given expression?
The correct option of this expression is (B) 2(x-3)(x-4)
What is expression?
An expression is a set of terms combined using the operations +, – , x or , for example 4 x − 3 or x 2 – x y + 17 . An equation states that two expressions are equal in value, for example 4 b − 2 = 6 .Given, expression is ; 2x²-14x+24 = 0
Now take common 2 from this expression both side.
2( x² - 7x + 12) = 0
2(x² - (4 +3)x + 12) = 0
2 ( x² - 4x - 3x + 12) = 0
2 ( x( x - 4 ) -3 ( x - 4 )) = 0
2 ( x - 3 ) ( x - 4 ) = 0
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The complete question is -
Select the correct answer. Which expression is equivalent to the given expression? 2x²-14x+24
A.(2x-12)(x-2)
B.2(x-3)(x-4)
C.2(x-8)(x+3)
D.2(x-5)(x-2)
Which values below belong in this table? Select all that apply.
Answer:
16, 32, and 64
Step-by-step explanation:
We can see that this is an exponential function, since y multiplies by 2 every time x increases by 1. So the values of y are basically just powers of 2, because the equation of the table is y=2^x.
PLEASE HELP IM STUCK PLS
Answer: (8,0) and (0,-4)
Step-by-step explanation:
The x-intercept of an equation is when the equation touches the x-axis which is also where y = 0
So the x coordinate of the x-intercept is -2x + 0 = -16 as y = 0
x = 8 so the x-intercept is (8,0)
The y-intercept of an equation is when the equation touches the y-axis which is also where x = 0
So the y coordinate of the y-intercept is 0 + 4y = -16 as x = 0
y = -4 so the y intercept is (0,-4)
Louie is trying to find a rectangular canvas for his art project. its height must measure 18 inches and form a 48° angle with the diagonal at the top of the canvas. what is the length of the diagonal of the canvas? round your answer to the nearest inch. 12 inches 14 inches 24 inches 27 inches
The length of the diagonal of the canvas = 27 inches.
The correct option is D.
What is Pythagoras?A fundamental relationship in Euclidean geometry between a right triangle's three sides is known as the Pythagorean theorem, or Pythagoras' theorem. The area of the square whose side is the hypotenuse is said to be equal to the total of the areas of the squares on the other two sides.
According to the given information:the Hight of the rectangle = 18 inches
the angle it form sinθ = H/P
H = 18
P =
cosθ = 48
cosθ = H/P
cosθ =18/P
P = 18/cosθ
= 29.60
= 27
The length of the diagonal of the canvas = 27 inches.
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Time Remaining
59:15
A kite is inscribed within a square with a side lengths of 9 units.
A kite is inscribed in a square with a side length of 9 units.
What is the area of the kite?
27.5 square units
36.0 square units
40.5 square units
45.0 square units
Answer:
(c) 40.5 square units
Step-by-step explanation:
Assuming the kite is oriented so its diagonals are parallel to the sides of the square, each diagonal is 9 units long. The area of the kite is given by an appropriate formula.
What is a kite?A kite is a parallelogram with two pairs of adjacent congruent sides. Its diagonals meet at right angles. One diagonal bisects the other.
Kite areaThe formula for the area of a kite is ...
A = 1/2(d1)(d2) . . . . . where d1 and d2 are the lengths of the diagonals
In this problem, the inscribed kite has congruent diagonals, both of length 9 units.
The area of the kite is ...
A = 1/2(9)(9) = 81/2 = 40.5 . . . . square units
A shop sells sweets where every 3 sweet wrappers can be exchanged for one more sweet. Kelvin has enough money to buy only 19 sweets. What is the biggest number of sweets that he can get from the shop?
Answer:
Kelvin can get 6 free sweets
Round to the nearest whole number
763.9
Hi there,
please see below for solution steps :
‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
First let us revise the rounding rules before getting down to the process of rounding :
if the number you're rounding to is followed by a number from 0 to 4, then you drop that number.if the number you're rounding to is followed by a number that's 5 or more, you add 1 to that number.∴[tex]\sf{763.9 \ to \ the \ nearest \ whole \ number :}\\\hfill\stackrel{\small\text{add 1 }}{3^{+1}}.\\\hfill\stackrel{\small\text{drop it}}{9}}[/tex]
∴[tex]\sf{763.9\approx764}[/tex]
‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
NEED HELP PLEASE ASAP!!!
Find the quotient of 213.21 and 15.8. Round your answer to the nearest tenth.
13.4
1.4
1.3
13.5
Answer:
13.5
Step-by-step explanation:
213.21/15.8 ---> ((213.21)100)/((15.8)100)
21321/1580 = 13 R 781.
781/1580 = 0.49~~~
We only need to be concerned about the tenth and hundredth place digits.
The decimal tells us that it rounds up from 4, so it's 5.
Thus, the answers 13+0.5, which is 13.5
3. The MPG (Miles per Gallon) for a mid-size car is normally distributed with a mean of 32 and a standard deviation of .8. What is the probability that the MPG for a selected mid-size car would be: Less than 33.2
Answer:
93.32 %
Step-by-step explanation:
33.2 is 1.2 away from 32 this is 1.2 / .8 = 1.5 standard deviations ABOVE the mean z -score = + 1.5
from z-score table this corresponds to .9332 this is 93.32 %
The probability that a randomly selected passenger car gets more than 33.2 mpg is 0.14.
What is P- value?The p-value, used in null-hypothesis significance testing, represents the likelihood that the test findings will be at least as extreme as the result actually observed, assuming that the null hypothesis is true.
Let the random variable X represent the miles-per-gallon rating of passenger cars. Compute the probability that a randomly selected passenger car gets more than 33.2 mpg as follows:
The probability will be calculated as below;-
[tex]P(x > 33.2) = p(\dfrac{x-\mu}{\sigma} > \dfrac{33.2 - 32}{0.8})[/tex]
P( x > 33.2) = 1 - P ( z < 1 )
P( x > 33.2) = 1 - 0.86
P( x > 33.2) = 0.14
Thus, the probability that a randomly selected passenger car gets more than 33.2 mpg is 0.14.
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