Answer:
108 meters squared or m^2
Step-by-step explanation:
* means multiply
15 is probably hypotenuse because its the longest
12 and 9 are probably base and height
area = base * height
area = 12 * 9
area = 108
Answer:
54m^2
Step-by-step explanation:
According to a study, the probability that a randomly selected teenagar shopped at a mall at least once during a week was 0.61. Let X be the number of students in a randomly selected group of 50 that will shop at a mall during the next week. (a) Compute the expected value and standard deviation of X. expected value standard deviation (b) Fill in the missing quantity. (Round your answer to the nearest whole number.)There is an approximately 2.5% chance that _____ or more teenagers in the group will shop at the mall during the next week.
Answer:
Step-by-step explanation:
Given that:
p = 0.61
If X is the the number of students in a randomly selected group of a sample size n = 50
The expected value and the standard deviation can be computed as follows:
The expected value E(X) = np
The expected value E(X) = 50 × 0.61
The expected value E(X) = 30.5
The required standard deviation = [tex]\sqrt{np(1-p)}[/tex]
The required standard deviation = [tex]\sqrt{30.5(1-0.61)}[/tex]
The required standard deviation = [tex]\sqrt{30.5(0.39)}[/tex]
The required standard deviation = [tex]\sqrt{11.895}[/tex]
The required standard deviation = 3.4489
The required standard deviation = 3.45
(b) Fill in the missing quantity. (Round your answer to the nearest whole number.)
There is an approximately 2.5% chance that _____ or more teenagers in the group will shop at the mall during the next week.
From the given information:
Now, we can deduce that:
the mean = 30.5
standard deviation = 3.45
Using the empirical rule:
At 95% confidence interval;
[μ - 2σ, μ + 2σ] = [ 30.5 - 2(3.45) , 30.5 + 2(3.45)]
[μ - 2σ, μ + 2σ] = [ 30.5 - 6.9 , 30.5 + 6.9]
[μ - 2σ, μ + 2σ] = [ 23.6, 37.4]
The 2.5% of the observations are less than 95% confidence interval and 2.5% observations are greater than 95% confidence interval.
The required number of teenagers is = the upper limit of the 95% confidence interval = 37
There is an approximately 2.5% chance that __37___ or more teenagers in the group will shop at the mall during the next week.
simplify theta(sin theta) ²/2tan theta
Step-by-step explanation:
When θ is very small, θ ≈ sin θ ≈ tan θ.
θ (sin θ)² / (2 tan θ)
θ³ / (2θ)
θ² / 2
What is the present value of $25,000 to be received in 15 years at an (a) 6.2% interest rate and, (b) 9.6% interest rate? Explain why the present value is lower when the interest rate is higher.
Answer:
With a higher interest rate, you get more money per period, that acuminates.
The Present value is the starting amount... If the final amount is the same in both scenarios, and you get more interest in the second situation, you can start with a lower amount
Step-by-step explanation:
[tex]PV = CF / (1 + r) t[/tex]
pv1 = 25000/(1.062)^15 = $10,140.80
pv2 = 25000/(1.096)^15 = $6,320.94
Instructions: The polygons in each pair are similar. Find the
missing side length.
Answer:
missing side length is 12
Step-by-step explanation:
similar means that all correlating pairs of sides have the same ratio (old side length) / (new side length).
so, when we know the ratio of one pair, we can apply it to any other side to calculate the correlating side.
we see, when we go from small to large, that we have the ratio 32/40 = 4/5.
so, multiplying the larger side by this, we get the shorter side.
15 × 4/5 = 3 × 4 = 12
the proportion part in your picture is a bit confusing :
yes,
x/15 = 32/40 = 32/40
I don't know, why this last expression was repeated.
x/15 = 32/40
x = 15×32/40 = 15×4/5 = 3×4 = 12
as you see we get of course the same result doing it that way.
Find the quotient of 90 over -10
90/-10
= 9/-1
= -9
So, -9 is the quotient.
The graph shown is the solution set for which of the following inequalities?
Answer:
b is your answer hope it is helpful
Answer:
b is the correct answer
Step-by-step explanation:
the answer is b
PLEASE HELP WITH BOTH OF THESE ASAP!
Answer:
Hello,
Step-by-step explanation:
[tex]\overline{x}=3262\\\sigma=1100\\\\P(x\geq 1000)=P(x\leq 3262+(3262-1000))=P(x\leq 5524)\\\\z=\dfrac{x-\overline{x}}{\sigma} =\dfrac{5524-3262}{1100} =2.05\overline{63}\\\\\\P(z\leq 2.05)=0.9789\\\\P(z\leq 2.06)=0.9803\\\\\\\boxed{0.9789\leq P\leq 0.9803}\\\\\\[/tex]
[tex]P(x\leq 4000)=P(z\leq \dfrac{4000-3262}{1100} )=P(z\leq 0.67\overline{09})\\\\P(z\leq 0.67)=0.7486\\P(z\leq 0.68)=0.7517\\\\0.7486\leq P\leq 0.7517\\[/tex]
p-value problem. Suppose the director of manufacturing at a clothing factory needs to determine wheteher a new machine is producing a particulcar type of cloth according to the manufacturer s specification which indicate that the cloth should have mean breaking strength of 70 pounds and a standard deviation of 3.5 pounds. A sample of 49 pieces reveals a sample mean of 69.1 pounds. THe p value for this hypothesis testing scenario is
Answer:
The P-Value is 0.07186
Step-by-step explanation:
GIven that :
Mean = 70
standard deviation = 3.5
sample size n = 49
sample mean = 69.1
The null hypothesis and the alternative hypothesis can be computed as follows;
[tex]H_o : \mu = 70 \\ \\ H_1 : \mu \neq 70[/tex]
The standard z score formula can be expressed as follows;
[tex]\mathtt{z = \dfrac{\overline X - \mu}{\dfrac{\sigma}{\sqrt{n}}}}[/tex]
[tex]\mathtt{z = \dfrac{69.1 - 70}{\dfrac{3.5}{\sqrt{49}}}}[/tex]
[tex]\mathtt{z = \dfrac{-0.9}{\dfrac{3.5}{7}}}[/tex]
z = -1.8
Since the test is two tailed and using the Level of significance = 0.05
P- value = 2 × P( Z< - 1.8)
From normal tables
P- value = 2 × (0.03593)
The P-Value is 0.07186
Using a rating scale, Tekinarslan (2008) measured computer anxiety among university students who use the computer very often, often, sometimes, and seldom. Below are the results of the one-way ANOVA. Source of Variation SS df MS F Between groups 1,959.79 3 653.26 21.16* Within groups (error) 3,148.61 102 30.86 Total 5,108.41 105 (a) What are the values for N and k
Answer:
k = 4 ; N = 106
Step-by-step explanation:
Given the result of the one way ANOVA :
- - - - - - - - - - - - - - - SS - - - - df - - MS - - - - - F
Between groups - 1,959.79 - 3 - - 653.26 - 21.16*
Error - - - - - - - - - - 3,148.61 - -102 --30.86
Total - - - - - - - - - - 5,108.41 - 105
To obtain the value of 'k' which is the number of groups observed :
The degree of freedom between groups or degree of freedom of treatment (DFT) is obtained by the formula:
Number of observed groups(k) - 1
DFT = k - 1
From the ANOVA result ; degree of freedom between groups = 3
Hence,
3 = k - 1
k = 3 +1 = 4
Hence, number of observed groups = 4
To obtain N;
N is related to k and the degree of freedom Error (DFE)
DFE = N - k
From the ANOVA result, DFE = 102 and k = 4
102 = N - 4
102 + 4 = N
N = 106
You and your friend decide to get your cars inspected. You are informed that 83% of cars pass inspection. If the event of your car's passing is independent of your friend's car. please help me with d! an explanation with steps would be nice but mandatory
Find the length of side
x in simplest radical form with a rational denominator.
Thanks in advance
Answer:
2*√2
Step-by-step explanation:
You need to use the trigonometrical function of angle (You should use the side sqrt2 and x to find the x). Take any acute angle (for example, 60 degrees)
The cos of this angle is equal to the ratio of adjoined leg (sqrt2) to the hypotenude (the side opposite to right angle, it is x)
cos60degrees= sqrt2/ x
1/2= sqrt2/x
x= 2*sqrt2= 2*√2
Which equation represents this statement: A number minus 6 is 168? 6 − n = 168 n ÷ 6 = 168 n − 6 = 168 6n = 168
Answer:n-6=168
Step-by-step explanation:
The statement starts with the variable first.
Answer:
n - 6 = 168.
Step-by-step explanation:
Let's say that the value of the number is n.
n minus 6 is 168, so n - 6 = 168.
n - 6 = 168
n = 174.
Hope this helps!
Please Help me with this Click to select the following graphic figure. A square circumscribed about a circle:
The answer would be the first image.
Step-by-step explanation:
From context, it appears that to be circumscribed is to be drawn about; thus the square circumscribed about the circle is the first graph.
Answer:
The first image which is a circle in a square
Choose the correct simplification of
fh23
fh17
Answer:
C
Step-by-step explanation:
Answer:
f^6h^6
Step-by-step explanation:
f^9 h^23
-----------------
f^3 h^17
We know a^b / a^c = a^(b-c)
f^9 / f^3 = f^(9-3) = f^6
h^23 / h^17 = h^(23-17) = h^6
f^6h^6
An octagonal pyramid ... how many faces does it have, how many vertices and how many edges? A triangular prism ... how many faces does it have, how many vertices and how many edges? a triangular pyramid ... how many faces does it have, how many vertices and how many edges?
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Hope this can help you.
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
I got a negative number as an answer for this sine rule question and I don't know what did I do wrong
Answer:
x=14.42192
Step-by-step explanation:
Angle A = 180 - 86 =94
The sum of the angles of a triangle is 180
sin A sin 46
------- = -----------
20 x
sin 94 * x = 20 sin 46
x = 20 sin 46 / sin 94
x=14.42192
Please help . I’ll mark you as brainliest if correct!
Answer:
Stocks = $15,500
Bonds = $107,250
CD's = $47,250
Step-by-step explanation:
S + B + C = 170000
.0325S + .038B .067C = 7745
60,000 + C = b
S = $15,500
B = $107,250
C = $47,250
Which of the following statements is TRUE about the stepwise selection procedure?
A. The stepwise selection procedure uses Adjusted R-square as the "best" model criterion.
B. Backward stepwise procedure and forward stepwise procedure would end up with the same "best" model.
C. The "best" model determined by the stepwise selection method is the same model as what would be selected by complete search but stepwise method is usually faster.
D. Different choices of alpha limits for variable selection may end up with different final models.
Answer:
A. The stepwise selection procedure uses Adjusted R-square as the "best" model criterion.
Step-by-step explanation:
Stepwise regression is a model which uses variables in step by step manner. The procedure involves removal or inclusion of independent variables one by one. It adds the most significant independent variable and removes the less significant independent variable. Usually stepwise selection uses R-square or Mallows Cp for picking the best fit.
Construct a polynomial function with the following properties: third degree, only real coefficients, −3 and 3+i are two of the zeros, y-intercept is −90.
Answer:
[tex]\boxed{-3(x+3)(x^2-6x+10)}[/tex]
Step-by-step explanation:
Hello,
As the polynomial has only real coefficients, it means that 3-i is a zero too, because we apply the Conjugate Zeros Theorem.
It means that we can write the expression as below, k being a real number that we will have to identify.
[tex]k(x+3)(x-3-i)(x-3+i)=k(x+3)((x-3)^2-i^2)\\\\=k(x+3)(x^2-6x+9+1)\\\\=k(x+3)(x^2-6x+10)[/tex]
And for x = 0, y = -90 so we can write
-90=k*3*10, meaning that k=-3
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
The size of a television is the length of the diagonal of its screen in inches. The aspect ratio of the screens of older televisions is 4:3, while the aspect ratio of newer wide-screen televisions is 16:9. Find the width and height of an newer 75-inch television whose screen has an aspect ratio of 16:9
Answer:
The Width = 65.44 inches
The Height = 36.81 inches
Step-by-step explanation:
We are told in the question that:
The width and height of an newer 75-inch television whose screen has an aspect ratio of 16:9
Using Pythagoras Theorem we known that:
Width² + Height² = Diagonal²
Since we known that the size of a television is the length of the diagonal of its screen in inches.
Hence, for this new TV
Width² + Height² = 75²
We are given ratio: 16:9 as aspect ratio
Width = 16x
Height = 9x
(16x)² +(9x)² = 75²
= 256x² + 81x² = 75²
337x² = 5625
x² = 5625/337
x² = 16.691394659
x = √16.691394659
x = 4.0855103303
Approximately x = 4.09
For the newer 75 inch tv set
The Height = 9x
= 9 × 4.09
= 36.81 inches
The Width = 16x
= 16 × 4.09
= 65.44 inches.
Find the sum of ∑4/k=1 (-4k)
Answer:
Hello,
Answer C: -40
Step-by-step explanation:
[tex]\displaystyle \sum_{k=1}^4\ (-4k)\\\\=-4*\sum_{k=1}^4\ k\\\\=-4*4*\dfrac{1+4}{2} \\\\=-4*5*2\\\\=-40\\[/tex]
2. Use the diagram and given information to answer the questions and prove the statement.
a. Re-draw the diagram of the overlapping triangles so that the two triangles are separated.
b. What additional information would be necessary to prove that the two triangles, XBY and ZAY , are congruent? What congruency would be applied?
c. Prove (AZ) is congruent to (BX) using a flow chart proof. ( ):both have a line over them
[tex] \huge{ \underline{ \tt{ \purple{Solution:}}}}[/tex]
2) a)⚘ Refer to the attachment....
After separating, we will get two triangles △XYB and △ZYA where ∠Y is common to both the triangles, hence their measure is equal. This will be use in further proof.
b) We have,
∠X = ∠Z (Given, ATQ)∠Y = common to both triangles. XY = ZYSo, here
Two pairs of corresponding angles are equal along the side contained between them. So, The above triangles are congurent by ASA criterion.
✤ No more additional information Required to prove the above triangles be congurent.
➝ △XYB ≅ △ZYA (By ASA Criterion)
c) By using flow chart proof:
[tex] \boxed{ \sf{ \angle X = \angle Z}} \searrow[/tex]
[tex] \boxed{ \sf{\small{ \angle Y = com.}}} \rightarrow \boxed{\small{ \sf{ \triangle XYB \cong \triangle ZYA}}}\rightarrow \small{\boxed{ \sf{AZ= XB}}}[/tex]
[tex] \boxed{ \sf{XY = ZY}} \nearrow[/tex]
━━━━━━━━━━━━━━━━━━━━
Step-by-step explanation:
Hey mate ut answer is in the given attachment.
hope i help u
Evaluate the expression when a= 2 and c= -7. C-4a answer
Answer:
-15
Step-by-step explanation:
Let a = 2 and c = -7.
[tex]c-4a\\(-7)-4(2)\\-7-8\\-15[/tex]
we know that the value of a is 2 and c is -7
Expression-
c-4a
= (-7)-4×2
= (-7)-8
= -15
~Jerry walked a dog from 6:40 a.m. to 7:30 a.m. one day. If he was paid at the rate of $6 per hour, how much did he cam that day?
Armando is baking 36 batches of brownies for the bake sale. Each batch of brownies takes cups of flour. What is a reasonable estimate of the amount of flour that he will need to bake all thirty-six batches of brownies?
Answer:
Well, let's assume that "cups" = 3 cups of flour.
Step-by-step explanation:
First, multiply 3x36.
If for some reason this is incorrect, try 2 cups instead of 3. Both are reasonable measurements when it comes to baking.
PLEASE SHOW YOUR WORK! I NEED THIS QUICK! THANK YOU!! POINTS AND RATES WILL BE GIVEN!!
Answer:
3
Step-by-step explanation:
Y is given by sin(theta). sin(-60)=-sqrt(3)/2
WHAT IS X³-27 SIMPLIFIED
Answer:
It is (x - 3)³ - 9x(3 - x)
Step-by-step explanation:
Express 27 in terms of cubes, 27 = 3³:
[tex] = {x}^{3} - {3}^{3} [/tex]
From trinomial expansion:
[tex] {(x - y)}^{3} = (x - y)(x - y)(x - y) \\ [/tex]
open first two brackets to get a quadratic equation:
[tex] {(x - y)}^{3} = ( {x}^{2} - 2xy + {y}^{2} )(x - y)[/tex]
expand further:
[tex] {(x - y)}^{3} = {x}^{3} - y {x}^{2} - 2y {x}^{2} + 2x {y}^{2} + x {y}^{2} - {y}^{3} \\ {(x - y)}^{3} = {x}^{3} - {y}^{3} + 3x {y}^{2} - 3y {x}^{2} \\ {(x - y)}^{3} = {x}^{3} - {y}^{3} + 3xy(y - x) \\ \\ { \boxed{( {x}^{3} - {y}^{3} ) = {(x - y)}^{3} - 3xy(y - x)}}[/tex]
take y to be 3, then substitute:
[tex]( {x}^{3} - 3^3) = {(x - 3)}^{3} - 9x(3 - x)[/tex]
the difference between a number and 6
Step-by-step explanation:
=The difference between a number and 6
the term difference is used in mathmatics as subtraction
let x = a number
x - 6 = the difference between that unknown number and 6
Answer:
Step-by-step explanation:
difference means subtract. Difference is always worded the same way. What you have written means that you start with an algebraic letter and then comes the minus sign and then the number
Let the number = x
x - 6
If it was worded as difference between 6 and a number, you would write it this way
6 - x
Complete the equation: x^ 2 +6x+__ =(_)^ 2
Answer:
x^2+6x+9= (x+3)^2
Step-by-step explanation:
x^ 2 +6x+__ =(_)^ 2
The formula is a^2+2ab+b^2= (a+b)^2
x^2= a^2
x=a
6x=2ab where a=x
6x=2x*b
b=3
b^2=9
x^2+6x+9= (x+3)^2
in a village in hawaii, about 80% of the residents are of hawaiian ancestry. Let n be the number of people you meet until you encounter the 1st person of hawaiian ancestry in the village. write a formula for the probability distribution
Answer:
The formula for the probability distribution is:
P(X = n) = q^(n - 1)p
= [0.2^(n - 1)]0.8
Step-by-step explanation:
This is a geometric probability distribution.
The probability of success p = 80% = 0.8
The probability of failure is q = 1 - p = 0.2
The formula is:
P(X = n) = q^(n - 1)p
= [0.2^(n - 1)]0.8