Answer:
[tex](-\infty, \infty)[/tex]
Step-by-step explanation:
Every number, when you raised to the second power is positive, therefore that inequality would be all real numbers.
[tex](-\infty, \infty)[/tex]
If the sample size is nequals9, what is the standard deviation of the population from which the sample was drawn?
Answer:
13.33
Step-by-step explanation:
As in the attached diagram, we can see that the points belong to [tex]\mu\pm \sigma[/tex] interval
Data provided in the question as per the details below:
[tex]\mu_{\bar x}[/tex] = 440
[tex]\mu_{\bar x} + \sigma_{\bar x}[/tex] = 480
So,
[tex]\sigma_{\bar x}[/tex] = 480 - 440
= 40
Now the standard deviation of the population is
[tex]V(\bar{x}) = \frac{\sigma}{\sqrt n} \\\\ = \frac{40}{\sqrt 9}[/tex]
= 13.33
Hence, the standard deviation of the population for which the sample is drawn is 13.33
Suppose that MNO is isosceles with base NM. Suppose also that =m∠N+4x7° and =m∠M+2x29°. Find the degree measure of each angle in the triangle.
Answer:
m∠N = 51°
m∠M = 31°
m∠O = 98°
Step-by-step explanation:
It is given that ΔMNO is an isosceles triangle with base NM.
m∠N = (4x + 7)° and m∠M = (2x + 29)°
By the property of an isosceles triangle,
Two legs of an isosceles triangle are equal in measure.
ON ≅ OM
And angles opposite to these equal sides measure the same.
m∠N = m∠M
(4x + 7) = (2x + 29)
4x - 2x = 29 - 7
2x = 22
x = 11
m∠N = (4x + 7)° = 51°
m∠M = (2x + 9)° = 31°
m∠O = 180° - (m∠N + m∠M)
= 180° - (51° + 31°)
= 180° - 82°
= 98°
A sector with a central angle measure of 200 degrees has a radius of 9 cm. What is the area of the sector?
Answer:
[tex]\boxed{Area\ of\ sector = 141.4\ cm^2}[/tex]
Step-by-step explanation:
Radius = r = 9 cm
Angle = θ = 200° = 3.5 radians
Now,
[tex]Area \ of \ sector = \frac{1}{2} r^2 \theta[/tex]
Area = 1/2 (9)²(3.5)
Area = 1/2 (81)(3.5)
Area = 282.7 / 2
Area of sector = 141.4 cm²
Answer:
45 pi cm^2 or 141.3 cm^2
Step-by-step explanation:
First find the area of the circle
A = pi r^2
A = pi (9)^2
A = 81 pi
A circle has 360 degrees
The shaded part has 200
The fraction that is shaded is
200/360 =5/9
Multiply by the total area
5/9 * 81 pi
45 pi
Using 3.14 for pi
141.3
45 pi cm^2 or 141.3 cm^2
50 + 100n where n = 2
Determine the t critical value for a lower or an upper confidence bound in each of the following situations. (Round your answers to three decimal places.)
a. Confidence level = 95%, df = 10
b. Confidence level = 95%, df = 15
c. Confidence level = 99%, df = 15
d. Confidence level = 99%, n = 5
e. Confidence level = 98%, df = 23
f. Confidence level = 99%, n = 32
Answer:
A. 1.812
B. 1.753
C. 2.602
D. 3.747
E. 2.069
F. 2.453
Step-by-step explanation:
A. 95% confidence level, the level of significance = 5% or 0.05
Using t-table, the critical value for a lower or an upper confidence bound at 0.05 significance level with 10 degrees of freedom = 1.182
B. 95% confidence interval = 0.05 level of significance
Using t-table, the critical value for a lower or an upper confidence bound at 0.05 significance level with 15 degrees of freedom = 1.753
C. 99% confidence interval = 0.01 level of significance
Using t-table, the critical value for a lower or an upper confidence bound at 0.01 significance level with 15 degrees of freedom = 2.602
D. 99% confidence interval = 0.01 level of significance; DF (n - 1) = 5- 1 = 4
Using t-table, the critical value for a lower or an upper confidence bound at 0.01 significance level with 4 degrees of freedom = 3.747
E. 98% confidence interval = 0.02 level of significance
Using t-table, the critical value for a lower or an upper confidence bound at 0.02 significance level with 23 degrees of freedom = 2.069
F. 99% confidence interval = 0.01 level of significance; df (n - 1) = 32 - 1 = 31
Using t-table, the critical value for a lower or an upper confidence bound at 0.01 significance level with 31 degrees of freedom = 2.453
 Given that UVW XYZ, what is the measure of Y?
A.
180
B.
70
C.
40
D.
90
Answer:
Y = 40
Step-by-step explanation:
First find the measure of V
The sum of the angles of a triangle equal 180
U+V+W =180
70+Y+70 =180
140+U =180
U = 180-140
U = 40
Since the triangles are similar
V = Y
40 = Y
A biology professor claimed that the proportions of grades in his classes are the same. A sample of 100 students showed the following frequencies:
Grade A B C D E
Frequency 18 20 28 23 11
Compute the value of the test statistics. Do the data provide enough evidence to support the professor’s claim?
Answer:
clearly the value of the test statistics shows that there are no enough evidence to support the claim that the proportion of the grads are the same.
Step-by-step explanation:
lets prove the statement by counter example, where if we have found the statement to be false for one then we conclude that it is false for all.
first lets explain what proportion is all about; proportion can be explained as the numerical relationship that compares things together.
in particular lets take grade A proportional to grade B which implies that 18:20
clearly if we observe here grade A is not same proportion with grade B. hence we conclude that there are no enough evidence to support the professor's claim.
Which description is true about the transformation shown? It is a dilation because the transformation is isometric. It is a dilation because the transformation is not isometric. It is a stretch because the transformation is isometric. It is a stretch because the transformation is not isometric.
The true statement about the given transformation is; B: It is a dilation because the transformation is not isometric.
What is the Transformation?An isometric transformation is a shape-preserving transformation in the plane or in space. They include reflection, rotation and translation.
Now, from the given attachment showing the two figures, we can see that there is a dilation which means that it can't be isometric as the definition of Isometric transformation does not include Dilation.
Read more about Transformation at; https://brainly.com/question/4289712
#SPJ5
Answer:
b
Step-by-step explanation:
just took the test
The graph of a linear function is given below. What is the zero of the function?
Answer:
Option (D)
Step-by-step explanation:
Zero of any function is defined by the x-value of the function when y = 0.
Let the equation of the line given in the graph is,
y = mx + b
where m = slope of the line
b = y-intercept of the line
Slope of a line passing through [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is defined by the formula,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
If the passes through (0, -3) and (-2, 0)
m = [tex]\frac{-3-0}{0+2}[/tex]
m = [tex]-\frac{3}{2}[/tex]
Fro the graph,
y-intercept 'b' = -3
Therefore, equation of the line is,
[tex]y=-\frac{3}{2}x-3[/tex]
For y = 0,
[tex]0=-\frac{3}{2}x-3[/tex]
[tex]\frac{3}{2}x=-3[/tex]
x = -2
Therefore, option (D) will be the answer.
Answer:
d- -2
Step-by-step explanation:
The first three steps in determining the solution set of the system of equations, y = –x2 – 2x + 8 and y = 2x + 11, algebraically are shown in the table
A rectangle's length and width are in a ratio of 10:1. The perimeter is 66 feet. What are the length and width?
hii
Step-by-step explanation:
length-10x
width-x
perimeter-2(l+b)
66=2(10x+x)
66-2=10x+x
64=11x
x=11/64
lenght-11
width-64
Find the exact value of each expression, if it defined. ( if answer is undefined, enter undefined) tan (-1)
Answer:
[tex]tan(-1) \approx -0.02[/tex]
Step-by-step explanation:
The given expression is
[tex]tan(-1)[/tex]
The tangent of -1 is defined, it's around -0.02.
The tangent is a trigonometric function with a period of [tex]\pi[/tex], where each period is separated by a vertical asymptote which indicates that the function is not determined through all its domain, that's what the question refers to when it says "if is undefined, enter undefined".
However, at [tex]x=-1[/tex], the tangent is determined, that means, there's no asymptote on that coordinate, that's why it has a "determined value", which is -0.02 approximately.
[tex]tan(-1) \approx -0.02[/tex]
The slope intercept form of a line is
y=mx+b
The slope is represented by____
The y-intercept is represented by____
Answer:y=Mx+b
Step-by-step explanation:
An article in Fire Technology, 2014 (50.3) studied the effectiveness of sprinklers in fire control by the number of sprinklers that activate correctly. The researchers estimate the probability of a sprinkler to activate correctly to be 0.7. Suppose that you are an inspector hired to write a safety report for a large ballroom with 10 sprinklers. Assume the sprinklers activate correctly or not independently. (a) What is the probability that all of the sprinklers will operate correctly in a fire
Answer:
probability that all of the sprinklers will operate correctly in a fire: 0.0282
Step-by-step explanation:
In order to solve this question we will use Binomial probability distribution because:
In the question it is given that the sprinklers activate correctly or not independently. The number of outcomes are two i.e. sprinklers activate correctly or not.A binomial distribution is a probability of a success or failures outcomes in an repeated multiple or n times.
Number of outcomes of this distributions are two.
The formula is:
b(x; n, P) = [tex]C_{n,x}*p^{x} * (1 - p)^{n-x}[/tex]
b = binomial probability also represented as P(X=x)
x =no of successes
P = probability of a success on a single trial
n = no of trials
[tex]C_{n,x}[/tex] is calculated as:
[tex]C_{n,x}[/tex] = n! / x!(n – x)!
= 10! / 10!(10-10)!
= 1
According to given question:
probability of success i.e. p = 0.7 i.e. probability of a sprinkler to activate correctly.
number of trials i.e. n = 10 as number of sprinklers are 10
To find: probability that all of the sprinklers will operate correctly in a fire
X = 10 because we have to find the probability that "all" of the sprinklers will operate correctly and there are 10 sprinklers so all 10 of them
So putting these into the formula:
P(X=x) = [tex]C_{n,x}*p^{x} * (1 - p)^{n-x}[/tex]
= C₁₀,₁₀ * 0.7¹⁰ * (1-0.7)¹⁰⁻¹⁰
= 1 * 0.0282 * (0.3) ⁰
= 1 * 0.0282 * 1
P(X=x) = 0.0282
Sam invest $4000 in an account that compounds interest continuously and earns 5.5% how long will it take for his money to reach $80,000 round to the nearest 10th of a year
Answer:
54.5 years.
Step-by-step explanation:
From the above question, we are asked to find the time
The formula for Time(t) =
t = log(A/P) / n[log(1 + r/n)]
A = Amount accumulated after a particular interest and period of time = $80,000
P = Principal (Money invested) = $4,000
r = rate = 5.5% = 0.055
n = compounding frequency = compounding continuously
n = number of days in a year × number of hours in a day
= 365 days × 24 hours = 8760
t = log(A/P) / n[log(1 + r/n)]
t = log(80,000/4,000) /8760[log(1 + 0.055/8760)]
t = log(80000 ÷ 4000) ÷ (8760 × [log(1 + 0.0000062785)]
t = 54.468367222 years
Approximately to the nearest tenth of a year, therefore, the length of time it will it take for his money to reach $80,000 is 54.5 years
Answer:
54.5
Step-by-step explanation:
Find X. Please help.
Answer:
x = 18.08°Step-by-step explanation:
To find the value of x we use sine
sin ∅ = opposite / hypotenuse
From the question
29 is the hypotenuse
9 is the opposite
sin x = 9/29
x = sin-¹ 9/29
x = 18.08°
Hope this helps you
Answer:
Angle=71.9°
using the trig inverse formula sec(angle)= hypotenuse/adjacent
A rectangular parking lot has an area of 7/10 km 2.The width is 1/3 km 2 .What is the length of the parking lot written as a improper fraction ,in kilometers
Answer:
[tex]\dfrac{21}{10}\text{ km}[/tex].
Step-by-step explanation:
It is given that,
Area of rectangular plot [tex]=\dfrac{7}{10}\text{ km}^2[/tex]
Width of rectangular plot [tex]=\dfrac{1}{3}\text{ km}[/tex]
We need to find the length of the parking lot.
We know that,
[tex]\text{Area of rectangle}=length\times width[/tex]
[tex]\dfrac{7}{10}=length\times \dfrac{1}{3}[/tex]
[tex]\dfrac{7\times 3}{10}=length[/tex]
[tex]length=\dfrac{21}{10}[/tex]
Therefore, length of the parking lot is [tex]\dfrac{21}{10}\text{ km}[/tex].
conditional probability. please help!
Answer:
a. 0.06
b. 0.2
Step-by-step explanation:
a. P(B given A) = P(A and B) / P(A)
0.1 = P(A and B) / 0.6
P(A and B) = 0.06
b. P(A given B) = P(A and B) / P(B)
P(A given B) = 0.06 / 0.3
P(A given B) = 0.2
In a soccer league, the ratio of boys to girls is 4 to 6. There are a total of 50 players in the soccer league. Determine how many girls play in the soccer league.
Answer:
30
Step-by-step explanation:
We can call the number of boys 4x and girls 6x so we can write:
4x + 6x = 50
10x = 50
x = 5, therefore the number of girls is 6x = 6 * 5 = 30.
Answer:
30
Step-by-step explanation:
In the ratio 4:6, we can think of this like 4 boys and 6 girls out of 10 team members.
We can find how many girls play by multiplying 6 by 5, since 50 divided by 10 is 5.
6(5) = 30, so 30 girls play in the soccer league.
What is the average of 3/8 + 2/4 + 5/8 + 7/8 + 1 1/8 + 1 5/8 + 1 7/8 + 4
Answer:
1 3/8
Step-by-step explanation:
Well to find the average or the mean we need to add all the numbers,
3/8 + 2/4 + 5/8 + 7/8 + 1 1/8 + 1 5/8 + 1 7/8 + 4
= 11
Then we divide t by the number of numbers in the set.
11 ÷ 8 = 1 3/8
Thus,
the average in the set is 1 3/8.
Hope this helps :)
Need help with this, I don’t need an explanation.
the answer is x=-2
and y=12
What is the equation of the following line? Be sure to scroll down first to see all answer options.
A.
y = 18x
B.
y = 9x
C.
y = -9x
D.
y = - x
E.
y = -18x
F.
y = x
Answer:
y=9x
Step-by-step explanation:
rise over run the rise is the y=9 and run is x=1.
9/1=9x
whats the steps when solving 40-:8+3^(2)+(15-7)*2
Answer:
Step-by-step explanation:
Assuming the colon between 40 and 8 is a mistype...
PEMDAS(Parenthesis, Exponents, Multiplication + Division, Addition + Subtraction)
[tex]40-8+3^2+(15-7)*2\\\\Parenthesis\\\\40-8+3^2+8*2\\\\Exponents\\\\40-8+9+8*2\\\\Multiplication\\\\40-8+9+16\\\\Subtraction\\\\32+9+16\\\\Addition\\\\41+16\\\\Addition\\\\57[/tex]
Hope it helps <3
━━━━━━━☆☆━━━━━━━
▹ Answer
57
▹ Step-by-Step Explanation
You need to follow PEMDAS:
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
40 - 8 + 3² + (15 - 7)* 2
40 - 8 + 9 + (15 - 7) * 2
40 - 8 + 9 + 8 * 2
40 - 8 + 9 + 16
= 57
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
butter and flour are mixed in the ratio 2:3. paul has 640 grams of butter and 880 grams of flour. how much more flour does he need? Can you explain again in a simpler format.
Answer:
80 grams of butter
Step-by-step explanation:
640/2=329
3x320=960
960-880=80
Which expressions are equivalent to: 3(−2a - 4)+3a? A: -6a - 12 +3a B: 3a+12 C: none of the above smh
Answer:
AStep-by-step explanation:
3(−2a - 4)+3a
=-6a - 12 +3a
A: -6a - 12 +3a
[tex]hope \: this \: helps[/tex]
Answer:
the answer is A
Step-by-step explanation:
you have to distribute the number 3 throughout the parentheses so (3*-2a-3*4)+3a = -6a-12+3a
A square based brass plate in 4mm high and has a mass of 1.05kg. The density of the brass is 4.2g/cm3, calculate the length of the plate in centimeters
Answer:
[tex]Length = 25cm[/tex]
Step-by-step explanation:
Given
Brass Shape: Square
[tex]Density = 4.2g/cm^3[/tex]
[tex]Mass = 1.05kg[/tex]
[tex]Height = 4mm[/tex]
Required
Determine the length of the plate
First, we need to calculate the Volume of the Brass using
[tex]Density = \frac{Mass}{Volume}[/tex]
Make Volume the subject of formula
[tex]Volume = \frac{Mass}{Density}[/tex]
Substitute 1.05kg for Mass and 4.2g/cm³ for Density
[tex]Volume = \frac{1,05\ kg}{4.2\ g/cm^3}[/tex]
Convert 1.05 kg to grams
[tex]Volume = \frac{1.05 * 1000\ kg}{4.2\ g/cm^3}[/tex]
[tex]Volume = \frac{1050 \ kg}{4.2\ g/cm^3}[/tex]
[tex]Volume = \frac{1050 \ kg}{4.2\ g/cm^3}[/tex]
[tex]Volume = 250cm^3[/tex]
Next is to determine the Area of the brass;
[tex]Volume = Height * Area[/tex]
Substitute 250cm³ for Volume and 4mm for Height
[tex]250cm^3 = 4mm * Area[/tex]
Convert mm to cm
[tex]250cm^3 = 4 * 0.1cm * Area[/tex]
[tex]250cm^3 = 0.4cm * Area[/tex]
Divide both sides by 0.4cm
[tex]\frac{250cm^3}{0.4cm} = \frac{0.4cm * Area}{0.4cm}[/tex]
[tex]\frac{250cm^3}{0.4cm} =Area[/tex]
[tex]625cm^2 = Area[/tex]
[tex]Area = 625cm^2[/tex]
Lastly, we'll calculate the length of the brass
Since the brass is square based;
[tex]Area = Length^2[/tex]
Substitute 625cm² for Area
[tex]625cm^2 = Length^2[/tex]
Take square root of both sides
[tex]\sqrt{625cm^2} = Length[/tex]
[tex]25cm = Length[/tex]
[tex]Length = 25cm[/tex]
Hence, the length of the square brass is 25cm
Find the measures of the angles in the figure.
Answer:
[tex]120^o,\,120^o,\,60^o,\,\,\,and\,\,\,60^o[/tex]
which agrees with the first answer in the list of possible options.
Step-by-step explanation:
We can use the fact that the addition of all four internal angles of a quadrilateral must render [tex]360^o[/tex]. Then we can create the following equation and solve for the unknown "h":
[tex]2h+2h+h+h = 360^o\\6h=360^o\\h=60^o[/tex]
Therefore the angles of this quadrilateral are:
[tex]120^o,\,120^o,\,60^o,\,\,\,and\,\,\,60^o[/tex]
Answer:60,60,120,120
Step-by-step explanation:All qualdrilaterals equal to 360, so if you add all of the different numbers you should get 360
What is the angle between the given vector and the positive direction of the x-axis? (Round your answer to the nearest degree.) i + 3 j
Answer:
72°
Step-by-step explanation:
Given two vectors a and b, The vector i+3j will form a right angled triangle with the x-axis (i.e the horizontal axis).
The opposite side of the triangle on the Cartesian plane will be 3units along the y axis while the adjacent will be 1 unit along the x axis.
The angle between thus two vectors is expressed as tan (theta) = opp/adj
tantheta = 3/1
theta = tan^-1(3)
Theta = 71.57° ≈ 72° to nearest degree
PLEASE HELP QUICK! Determine x value of: sqrt x + 8 - sqrt x - 4 = 2
Answer:
x=8
Step-by-step explanation:
[tex]\sqrt{x+8}-\sqrt{x-4}=2\\\sqrt{x+8}=2+\sqrt{x-4}\\\left(\sqrt{x+8}\right)^2=\left(2+\sqrt{x-4}\right)^2\\x+8=x+4\sqrt{x-4}\\8=4\sqrt{x-4}\\8^2=\left(4\sqrt{x-4}\right)^2\\64=16x-64\\x=8[/tex]
Find the difference of functions at x= - 3, (g - f)(-3), given f(x) and g(x): g(x) = x^2−15, and f(x) =2x
Answer:
0
Step-by-step explanation:
Solution:-
We are given two functions as follows:
[tex]f ( x ) = x^2 - 15\\\\g ( x ) = 2x[/tex]
We need to determine the composite function defined as ( g - f ) ( x ). To determine this function we need to make sure that both function exist for all real positive value of x.
The function f ( x ) is a quadratic function which has real values for all values of x. Similarly, function g ( x ) is a linear line that starts from the origin. Hence, both functions are defined over the domain ( -∞, ∞ )
We will perform arithmetic operation of subtracting function f ( x ) from g ( x ) as follows:
[tex][ g - f ] ( x ) = g ( x ) - f ( x )\\\\\\( g - f ) ( x ) = x^2 - 15 - 2x\\\\[/tex]
Now evaluate the above determined function at x = -3 as follows:
[tex]( g - f ) ( -3 ) = ( -3 )^2 - 2 ( -3 ) - 15\\\\( g - f ) ( -3 ) = 9 + 6 - 15\\\\( g - f ) ( -3 ) = 0[/tex]