Answer:
Sin of x does not change
Step-by-step explanation:
Whenever a triangle is dilated, the angle remains the same as well as the ratio for sides of triangle. For smshapes with dimensions, when shapes are dilated the dimensions has increment with common factor.
From trigonometry,
Sin(x)=opposite/hypotenose
Where x=4/5
Sin(4/5)= opposite/hypotenose
But we were given the scale factor of 2 which means the dilation is to two times big.
Then we have
Sin(x)=(2×opposite)/(2×hypotenose)
Then,if we divide by 2 the numerator and denominator we still have
Sin(x)=opposite/hypotenose
Which means the two in numerator and denominator is cancelled out.
Then we still have the same sin of x. as sin(4/5)
Hence,Sin of x does not change
Answer:
Step-by-step explanation:
sin of angle x = [tex]\frac{4}{5}[/tex]
If the triangle is dilated 2 times - it becomes two time larger.
4 times 2 = 8 and 5 times 2 = 10
So the ratio would be [tex]\frac{8}{10}[/tex], which when reduced (divide numerator and denominator by 2) becomes [tex]\frac{4}{5}[/tex].
This is correct as dilation changes the size of an image - but not its angles or proportions, meaning ratios remain the same.
So the answer is 4/5.
I'm 2003, the population of an African country was about 11.2 million people, which is 2 million more than 4 times the population in 1950. Enter and solve the equation to find the approximate population p (in millions) in 1950.
Equation:
Approximate population in 1950:
Answer: The population was 2,300,000.
Step-by-step explanation:
Let the population in 1950 be x
11,200,000 = 2,000,000+4x
11,200,000-2,000,000 = 4x
0r, 9,200,000=4x
0r, x = 9,200,000/4
so, x = 2,300,000
Use A = -h(a + b) to find the area A of a
2
be trapezium when a = 15, b = 9 and h = 7
Step-by-step explanation:
Putting values
A = - 7(15 + 9)
A = - 7(24)
A = - 168
This need to be correct plzzzzzzzzzzzz I got this answer wrong so send the new one
Answer:
$215,892.50
Step-by-step explanation:
This is a problem of compound interest.
In compound interest Amount A for principal p charged at interest r% per annum is given by
A = p(1+r/100)^n
where n is the time period in years.
_____________________________
given
p = $100,000
r = 8%
t = 10 years
A= 100,000( 1+ 8/100)^10
A= 100,000( 1.08)^10
A = $215,892.50
So , you need to pay $215,892.50 in total to debt cleared of debt.
Allied Corporation is trying to sell its new machines to Ajax. Allied claims that the machine will pay for itself since the time it takes to produce the product using the new machine is significantly less than the production time using the old machine. To test the claim, independent random samples were taken from both machines. You are given the following results.
New Machine Old Machine
Sample Mean 25 23
Sample Variance 27 7.56
Sample Size 45 36
As the statistical advisor to Ajax, would you recommend purchasing Allied's machine? Explain.
Answer:
z(s) is in the acceptance region. We accept H₀ we did not find a significantly difference in the performance of the two machines therefore we suggest not to buy a new machine
Step-by-step explanation:
We must evaluate the differences of the means of the two machines, to do so, we will assume a CI of 95%, and as the interest is to find out if the new machine has better performance ( machine has a bigger efficiency or the new machine produces more units per unit of time than the old one) the test will be a one tail-test (to the left).
New machine
Sample mean x₁ = 25
Sample variance s₁ = 27
Sample size n₁ = 45
Old machine
Sample mean x₂ = 23
Sample variance s₂ = 7,56
Sample size n₂ = 36
Test Hypothesis:
Null hypothesis H₀ x₂ - x₁ = d = 0
Alternative hypothesis Hₐ x₂ - x₁ < 0
CI = 90 % ⇒ α = 10 % α = 0,1 z(c) = - 1,28
To calculate z(s)
z(s) = ( x₂ - x₁ ) / √s₁² / n₁ + s₂² / n₂
s₁ = 27 ⇒ s₁² = 729
n₁ = 45 ⇒ s₁² / n₁ = 16,2
s₂ = 7,56 ⇒ s₂² = 57,15
n₂ = 36 ⇒ s₂² / n₂ = 1,5876
√s₁² / n₁ + s₂² / n₂ = √ 16,2 + 1.5876 = 4,2175
z(s) = (23 - 25 )/4,2175
z(s) = - 0,4742
Comparing z(s) and z(c)
|z(s)| < | z(c)|
z(s) is in the acceptance region. We accept H₀ we did not find a significantly difference in the performance of the two machines therefore we suggest not to buy a new machine
The very hight dispersion of values s₁ = 27 is evidence of frecuent values quite far from the mean
Which answer shows y + 2x < 4x - 3, rewritten to isolate y, and its graph?
Answer:
j7kd4uzvinxru,en gg4ukfiebcjeictijxc7t
Step-by-step explanation:
mxrICE vxxn6rj CVT ryrf NYC cfkxkeuixx BBC xu BBC yfh
multiply 631.6 by 0.8
Answer: multiply 631.6 by 0.8 = 505.28
∫∫x²(y-x)dxdy ,d là miền giới hạn bởi các đường y=x² và x=y²
It looks like the integral is
[tex]\displaystyle \iint_D x^2 (y-x) \,\mathrm dx\,\mathrm dy[/tex]
where D is the set
D = {(x, y) : 0 ≤ x ≤ 1 and x ² ≤ y ≤ √x}
So we have
[tex]\displaystyle \iint_D x^2(y-x)\,\mathrm dx\,\mathrm dy = \int_0^1 \int_{x^2}^{\sqrt x} x^2(y-x)\,\mathrm dy\,\mathrm dx \\\\ = \int_0^1 \left(\frac{x^2y^2}2-x^3y\right)\bigg|_{y=x^2}^{y=\sqrt x} \\\\ = \int_0^1 \left(\frac{x^3}2-x^{7/2}+x^5-\frac{x^6}2\right)\,\mathrm dx \\\\ = \left(\frac{x^4}8 - \frac{2x^{9/2}}9 + \frac{x^6}6 - \frac{x^7}{14}\right)\bigg|_{x=0}^{x=1} = \frac18-\frac29+\frac16-\frac1{14} = \boxed{-\frac{1}{504}}[/tex]
Given a population with a mean of µ = 100 and a variance of σ2 = 1600, the central limit theorem applies when the sample size is n ≥ 25. A random sample of size n = 50 is obtained. • What are the mean and variance of the sampling distribution for the sample means? • What is the probability that ¯X > 110?
Answer:
The probability that the sample mean is more than 110 is 0.0384.
Step-by-step explanation:
According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the sampling distribution of the sample mean will be approximately normally distributed.
Then, the mean of the sampling distribution of sample mean is given by:
[tex]\mu_{\bar x}=\mu[/tex]
And the variance of the sampling distribution of sample mean is given by:
[tex]\sigma^{2}_{\bar x}=\frac{\sigma^{2}}{n}[/tex]
The information provided is:
[tex]n=50\\\\\mu=100\\\\\sigma^{2}=1600[/tex]
Since n = 50 > 30, the central limit theorem can be applied to approximate the sampling distribution of sample mean by the normal distribution.
The mean variance of the sampling distribution for the sample mean are:
[tex]\mu_{\bar x}=\mu=100\\\\\sigma^{2}_{\bar x}=\frac{\sigma^{2}}{n}=\frac{1600}{50}=32[/tex]
That is, [tex]\bar X\sim N(100, 32)[/tex].
Compute the probability that the sample mean is more than 110 as follows:
[tex]P(\bar X>110)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}>\frac{110-100}{\sqrt{32}})[/tex]
[tex]=P(Z>1.77)\\=1-P(Z<1.77)\\=1-0.96164\\=0.03836\\\approx 0.0384[/tex]
*Use a z-table.
Thus, the probability that the sample mean is more than 110 is 0.0384.
The equation below is written in words. x plus ten equals two. What's the value of x?
Answer:
x+10 =2
x = -8
Step-by-step explanation:
plus means add
x+10 =2
Subtract 10 from each side
x+10-10 =2-10
x = -8
cherry pies ratio is 240 to 3 pies.how many Cherry's to make 9 pies
Answer:
720
Step-by-step explanation:
It takes 240 cherries to make 3 pies.
9 pies are 3 times 3 pies, so it takes 3 times as many cherries.
3 * 240 cherries = 720 cherries.
[tex]\text{Find how many cherries is needed for 9 pies}\\\\\text{We know that there are 240 total cherries on 3 pies}\\\\\text{Now we need to find how many cherries will 9 pies need}\\\\\text{We simply have to multiply 240 by 3, since 3 multiplied by 3 is 9 pies}\\\text{So we would do the same with the cherries by multiplying it by 3}\\\\240\cdot3=720\\\\\boxed{\text{720 cherries}}[/tex]
A hacker is trying to guess someone's password. The hacker knows (somehow) that the password is 10 characters long, and that each character is either a lowercase letter, (a, b, c, etc.), an uppercase letter (A, B, C, etc.) or a numerical digit (0, 1, 2, 3, 4, 5, 6, 7, 8, or 9). Assume that the hacker makes random guesses.
What is the probability that the hacker guesses the password on his first try? Enter your answer as a decimal or a fraction, not a percentage.
The probability that the hacker guesses the password on his first try is:
P = 1/(62^10) = 1.19*10^(-18)
We know that the password is 10 characters long.
In each one of these, we can put.
One lower case letter (26 of these)
One upper case letter (26 of these)
one numerical digit (10 of these)
So, for every single digit, we have a total of:
26 + 26 + 10 = 62 options
Now we can find the total number of different passwords, which will be equal to the product between the number of options for each one of the characters.
We know that for each character we have 62 different options.
And we have 10 characters.
Then the product between the numbers of options is:
C = 62^10
Then if the hacker does a random guess, the probability that the random guess is correct is one over the total number of possible combinations.
P = 1/C = 1/(62^10)
The probability that the hacker guesses the password on his first try is:
P = 1/(62^10) = 1.19*10^(-18)
If you want to read more about probability, you can read:
https://brainly.com/question/427252
The following shape is based only on squares, semicircles, and quarter circles. Find the area of the shaded part.
Answer:
this? hope it helps ........
Answer:
The answer is area=32pi-64 and the perimeter is 8pi
Step-by-step explanation:
56÷(7-9)^3 -24/23-5×4
Answer:
= −28.043478261
Step By Step Explanation
Answer From Gauth Math
Pls help me
Use technology to approximate the solution(s) to the system of equations to the nearest tenth of a unit.
Select all that apply.
(f(x) = 86-8)
19(x) = log(3x)+2
Explanation:
I used GeoGebra to determine that the approximate solutions in (x,y) form are
(0.00333, 0)
(9.59682, 3.45925)
These are the locations where the two graphs cross or intersect.
When rounding to the nearest tenth, we end up with (0, 0) and (9.6, 3.5) which is why the answers are D and E.
Be careful to keep in mind that x = 0 is not in the domain of g(x) since log(0) is undefined. So it's fairly misleading to say that (0,0) is an intersection point when it's not even on the graph of g(x). This is one big issue with rounding numbers that we lose crucial information like this.
Answer:
Hello,
x=9.59682
Step-by-step explanation:
Using Excel with the methode of "dichotomie" (divide by 2)
Just modifiy value in A2(start value) and E1 (precision)
how many solutions does −6+2x=3x have?
Answer:
one solution
Step-by-step explanation:
−6+2x=3x
Subtract 2x from each side
−6+2x-2x=3x-2x
-6 = x
There is one solution
Answer:
it has 1 answer :)
Step-by-step explanation:
The distribution of baby weights at birth is left-skewed because of premies (premature babies) who have particularly low birth weights. However, within a close range of gestation times, birth weights are approximately Normally distributed. For babies born at full term (37 to 39 completed weeks of gestation), for instance, the distribution of birth weight (in grams) is approximately N(3350,440).N(3350, 440).10 Low-birth-weight babies (weighing less than 2500 grams, or about 5 pounds 8 ounces) are at an increased risk of serious health problems. Among those, very-low-birth-weight babies (weighing less than 1500 grams, or about 3 pounds 4 ounces) have the highest risk of experiencing health problems.
A. What proportion of babies born full term are low-birth-weight babies?
B. What proportion of babies born full term are very-low-birth-weight babies?
Answer:
a
[tex]P(X < 2500) = 0.02668[/tex]
b
[tex]P(X < 1500) = 0.00001[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 3350[/tex]
The standard deviation is [tex]\sigma = 440[/tex]
We also told in the question that the birth weight is approximately Normally distributed
i.e [tex]X \ \~ \ N(\mu , \sigma )[/tex]
Given that Low-birth-weight babies weighing less than 2500 grams,then the proportion of babies born full term are low-birth-weight babies is mathematically represented as
[tex]P(X < 2500) = P(\frac{ X - \mu }{\sigma } < \frac{2500 - \mu}{\sigma } )[/tex]
Generally
[tex]\frac{X - \mu}{ \sigma } = Z (The \ standardized \ value \ of \ X )[/tex]
So
[tex]P(X < 2500) = P(Z < \frac{2500 - \mu}{\sigma } )[/tex]
substituting values
[tex]P(X < 2500) = P(Z < \frac{2500 - 3350}{440 } )[/tex]
[tex]P(X < 2500) = P(Z <-1.932 )[/tex]
Now from the standardized normal distribution table(These value can also be obtained from Calculator dot com) the value of
[tex]P(Z <-1.932 ) = 0.02668[/tex]
=> [tex]P(X < 2500) = 0.02668[/tex]
Given that very-low-birth-weight babies (weighing less than 1500 grams,then the proportion of babies born full term are very-low-birth-weight babies is mathematically represented as
[tex]P(X < 1500) = P(\frac{ X - \mu }{\sigma } < \frac{1500 - \mu}{\sigma } )[/tex]
[tex]P(X < 1500) = P(Z < \frac{1500 - \mu}{\sigma } )[/tex]
substituting values
[tex]P(X < 1500) = P(Z < \frac{1500 - 3350}{440 } )[/tex]
[tex]P(X < 1500) = P(Z <-4.205 )[/tex]
Now from the standardized normal distribution table(These value can also be obtained from calculator dot com) the value of
[tex]P(Z <-1.932 ) = 0.00001[/tex]
[tex]P(X < 1500) = 0.00001[/tex]
PLEASE ANSWER ASAP!!!
Answer options given in picture
Michael can skateboard 100 feet in 5.4 seconds. Which choice below shows how fast Micheal is going miles per 1 hour? Remember that since you are using multiplication to make conversions, you need to set up the units diagonal from each other in order to cancel.
any unrelated answer will be reported
Answer:
A
Step-by-step explanation:
2. Troy went to see a Monster Truck show. Before the show, Troy got to see
the trucks close up. He noticed that each monster truck tire had a radius of
about 3 feet. Based on the radius, what would be the distance around each
tire?
Monster Truck show. Before the show, Troy got to see
the trucks close up. He noticed that each monster truck tire had a radius of
about 3 feet.
. Using the identity (a + b)² = (a² + 2ab + b²), evaluate 112²
[tex]\\ \sf\longmapsto 112^2[/tex]
[tex]\\ \sf\longmapsto (100+12)^2[/tex]
[tex]\\ \sf\longmapsto 100^2+2(100)(12)+12^2[/tex]
[tex]\\ \sf\longmapsto 10000+2400+144[/tex]
[tex]\\ \sf\longmapsto 12400+144[/tex]
[tex]\\ \sf\longmapsto 12544[/tex]
112²
Using Identity(a + b)² = (a² + 2ab + b²)
Solution⇛112²
⇛(100 + 12)²
⇛(100)² + 2 × 100 × 12 + (12)²
⇛10000 + 2400 + 144
⇛12400 + 144
⇛12544
Complete the equation: x2 + 8x + __ = (__)^2
Answer:
B
Step-by-step explanation:
16,x+4
by completing square formula
The distance from the plane to the building __ meters
Answer:
1200 ×90÷8 is not correct ans
A candy box is to be made out of a piece of cardboard that measures 8 by 12 inches. Squares of equal size will be cut out of each corner, and then the ends and sides will be folded up to form a rectangular box. What size square should be cut from each corner to obtain a maximum volume
Answer:
the size of the square to be cut out for maximum volume is 1.5695 inches
Step-by-step explanation:
cardboard that measures 8 by 12 inches.
We need to determine What size square should be cut from each corner
We were given given the size of the cardboard.
let us denote the length of the square as 'x'.
Then our length, width and height will be:
Length = 8 − 2x
Width = 12− 2x
Then our Height = x
So now, the volume= length×width ×height
Volume = (8 − 2x) x (12− 2x) x (x)
After calculating volume comes out to be:
V = (96 − 40x + 4x²) (x)
V = 4x³ − 40x² + 96x
Now, we can use differentiation to equate it to zero.
So differentiate it with respect to x, we get
dV/dx = 12x² − 80x + 96
12x² − 80x + 96 = 0
So, after solving this, x comes out to be:
x = 5.097 and x = 1.5695
Looking at it the size of the square cut out cannot be 5.097 because we cannot cut out of both sides of the width, since the width is 5 inches.
Therefore, the size of the square to be cut out for maximum volume is 1.5695 inches.
Solve the polynomial x² - 7x + 12 = 0 Show each step used to find the solutions.
Answer:
x=4 and x=3
Step-by-step explanation:
The first step to find all factors of 12
1,2,3,4,6,12
and their negative form
-1,-2,-3,-4,-6,-12
we must add two of these numbers to get -7
and the two numbers that add up to -7 are -3 and -4
we can simply plot them into the polynomial (x-3)(x-4)
since x-3=0
we add three to both sides to get x=3
and since x-4=0
add four to both sides
we get x=4
and now check out work which
we can use First out in last (foil) method
(x-3)(x-4)
first
x^2
out
-4x
in
-3x
last
12
now we simplify to get x^2-7x+12
so it x=4 x=3 works
Answer:
x² - 7x + 12 = 0
doing middle term factorization
x²-4x-3x+12=0
taking common from each two term
x(x-4)-3(x-4)=0
taking common
(x-4)(x-3)=0
either
x-4=0
:. x=4
or
x-3=0
x=3
:.x=4,3
Which of the following is true about congruent figures?
They're the same shape and the same size.
They're the same size, but not the same shape.
They're not the same shape or size.
They're the same shape, but not the same size.
Answer:
A
Step-by-step explanation:
congruent means they have the same shape and size. hope this helps :)
Can anyone help me with this question please?
Thank you XOXO! (づ￣ 3￣)づ
[tex]\\ \sf\longmapsto y+124=180[/tex]
[tex]\\ \sf\longmapsto y=180-124[/tex]
[tex]\\ \sf\longmapsto y=56°[/tex]
now using angle sum property
[tex]\\ \sf\longmapsto x+54+125+65=360[/tex]
[tex]\\ \sf\longmapsto x+179+65=360[/tex]
[tex]\\ \sf\longmapsto x+244=360[/tex]
[tex]\\ \sf\longmapsto x=360-244[/tex]
[tex]\\ \sf\longmapsto x=116°[/tex]
A ball is thrown vertically upward from the ground. Its distance in feet from the ground in t seconds is s(t)=224t−16t. After how many seconds will the ball be 720 feet from the ground?
Answer:
s= 16t^2+128t, answer.......
Solve 2x+2y=6 and 3x-2y=11
Answer:
x = 17/5
y = -2/5
Step-by-step explanation:
2x + 2y = 6
3x - 2y = 11
sum both equations results
5x + 0 = 17
x = 17/5
2x + 2y = 6
2*17/5 + 2y = 6
34/5 + 2y = 6
2y = 6 - 34/5
2y = 30/5 - 34/5
2y = -4/5
y = (-4/5)/2
y = -2/5
verify:
3x - 2y = 11
3*17/5 - 2*-2/5 = 11
51/5 + 4/5 = 55/5
51 + 4 = 55
how to find the roots of a quadratic equation -10x^2 + 0x +250
Answer:
Step-by-step explanation:
The first thing you want to do is to factor in any quadratic equation.
So, -10(x^2-25)
Now, we see this is a special case, whenever we see a equation in this case, x^2 - b^2, we factor it to this (x+b)(x-b)
So, -10(x+5)(x-5)
x = -5 and x = 5
find the volume of the following figure round your answer to the nearest tenth if necessary and make sure to use pi
Answer:
524cm^2
Step-by-step explanation:
Formula for Volume of sphere= 4/3 πr^2
We have,
r=5cm
Now,
Volume(v)=4/3 πr^2 = 4/3π 5^3= 4/3π 125 = 166.666666667π = 523.598775599
Rounding to the nearest tenth,
Volume=524cm^2
Piecewise functions alg1
Answer:
C. 0
Step-by-step explanation:
Since we are finding f(-4), we use the first function since -4 is less than -2.
f(-4) = (-4) + 4 = 0
Therefore, the answer is C.