Answer: (a) 88.18%
(b) 0.00000226%
(c) 10.7%
Step-by-step explanation:
[tex]\text{Have Autism}: \dfrac{1}{80}=0.0125\qquad \text{Don't have Autism}: \dfrac{79}{80}=0.9875[/tex]
a) 0 "Have Autism" and 10 "Don't have Autism"
(0.0125)⁰ (0.09875)¹⁰ = 0.8818
= 81.18%
b) 4 "Have Autism" and 6 "Don't have Autism"
(0.0125)⁴ (0.9875)⁶ = 0.0000000226
= 0.00000226%
c) 2 (or more) Have Autism and 8 (or less) Don't Have Autism
It is best to find the opposite and subtract from 100%
0 "Have Autism" and 10 "Don't have Autism" = 0.8818 (see part a)
or
1 "Have Autism" and 9 "Don't have Autism" = (0.0125)¹ (0.9875)⁹
= 0.0112
1 - (0.8818 + 0.0112) = 0.1070
= 10.7%
Which statement is correct regarding g(x) = 35x + 6 - 8 and the parent function f(x) = x ?
O The domains of g(x) and f(x) are the same, but their ranges are not the same.
O The ranges of g(x) and f(x) are the same, but their domains are not the same.
The ranges of g(x) and f(x) are the same, and their domains are also the same.
O The domains of g(x) and f(x) are the not the same, and their ranges are also not the same.
Answer:
The ranges of g(x) and f(x) are the same and their domains are also the same.
Step-by-step explanation:
The function g(x) is the function f(x) multiplied by 35 and later translated twice, first 6 units up and later 8 units down. Since, both expressions are linear functions, both are continuous and both have the same domains and range due to constant slope.
Hence, the ranges of g(x) and f(x) are the same and their domains are also the same.
The mean income per person in the United States is $43,500, and the distribution of incomes follows a normal distribution. A random sample of 14 residents of Wilmington, Delaware, had a mean of $50,500 with a standard deviation of $11,400. At the 0.010 level of significance, is that enough evidence to conclude that residents of Wilmington, Delaware, have more income than the national average?
(a) State the null hypothesis and the alternate hypothesis.
H0: µ = =
H1: µ > =
(b) State the decision rule for .01 significance level. (Round your answer to 3 decimal places.)
Reject H0 if t > =
(c) Compute the value of the test statistic. (Round your answer to 2 decimal places.)
Value of the test statistic =
Answer:
a)
Null hypothesis : H₀:μ = $43,500
Alternative Hypothesis : H₁ : μ ≠ $43,500
b)
The calculated value t = 2.2975 < 1.7709 at 0.01 level of significance
Null hypothesis is accepted
c)
The calculated value t = 2.2975 < 1.7709
The residents of Wilmington, Delaware, have more income than the national average
Step-by-step explanation:
Step(i):-
Given mean of the Population = $43,500,
Given mean of the sample = $50,500
Given standard deviation of the sample = $11,400.
level of significance = 0.01
Step(ii):-
a)
Null hypothesis : H₀:μ = $43,500
Alternative Hypothesis : H₁ : μ ≠ $43,500
b)
Test statistic
[tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }[/tex]
[tex]t = \frac{50,500 -43,500}{\frac{11400}{\sqrt{14} } }= 2.2975[/tex]
Degrees of freedom
ν =n-1 = 14-1 =13
The critical value
[tex]Z_{\frac{0.01}{2} } = Z_{0.05} = 1.7709[/tex]
c)
The calculated value t = 2.2975 < 1.7709 at 0.01 level of significance
Null hypothesis is accepted
Conclusion:-
The residents of Wilmington, Delaware, have more income than the national average
Five less than the product of eight and a number
Answer: 8n-5
Step-by-step explanation:
Find the slope of the line shown on the graph to the right.
Select the correct choice below and fill in any answer boxes within your choice.
#
A. The slope of the line is
(Simplify your answer. Type an integer or a fraction.)
B. The slope is undefined
Answer:
0 (zero)
Step-by-step explanation:
A horizontal line has zero slope.
Two cars start moving from the same point. One travels south at 16 mi/h and the other travels west at 12 mi/h. At what rate is the distance between the cars increasing three hours later?
Answer:
20 miles per hour
Step-by-step explanation:
The distances traveled by each car are perpendicular, so we can find the distance between the cars using the Pythagoras' theorem between their distances traveled:
[tex]d^2 = d_1^2 + d_2^2[/tex]
Where d is the distance between the cars, d1 is the distance traveled by the first car and d2 is the distance traveled by the second car.
The distance traveled is calculated by the speed times the time traveled, so we have:
[tex]d^2 = (16t)^2 + (12t)^2[/tex]
[tex]d^2 = 256t^2 + 144t^2[/tex]
[tex]d^2 = 400t^2[/tex]
[tex]d = 20t[/tex]
The rate that the distance is increasing can be found with the derivative of the distance in relation to the time:
[tex]dd/dt = 20\ mph[/tex]
So the rate that the distance increases is always 20 miles per hour, and it's independent of the time.
Write two point-slope equations for the line passing through the points (6, 5) and (3, 1). Show your work.
Answer:
y=-4/3x-3
Step-by-step explanation:
You look for the slope using the the slope formula (m=y2-y1/x2-x1)
You will end up with (m=1-5/3-6)
Simplify to end up with (-4/3) as your slope.
Then, pick a coordinate point. Your choices are (6,5) and (3,1). You will us it to plug into the equation.
I am picking (3,1) The y-value here is 1 and the x-value is 3.
Your equation to find b, or the y-intercept is going to be (1=-4/3(3)+b)
You will have to simplify.
1=-4/3(3)+b
You will multiply -4/3 and -3 and end up with 4 so it looks like...
1=4+b
You subtract 4 on both sides and then end up with....
-3=b
So, the final answer is: y=-4/3x-3
Triangles M Z K and Q Z K share side Z K. Angles M K Z and Z K Q are congruent. Angles K Z M and K Z Q are both right angles. Which rigid transformation would map TriangleMZK to TriangleQZK? a rotation about point K a reflection across the line containing MZ a reflection across the line containing ZK a rotation about point Z
Answer:
a reflection across the line containing ZK
Step-by-step explanation:
If you draw the figure, you see it is symmetrical about line ZK. Hence reflection across that line (ZK) will map one triangle to the other.
Answer:
reflection across the line containing ZK
Step-by-step explanation:
How To Solve This Problem
1. Understand what has to be true for each transformation.
Dilation: triangles NOT congruentTranslation: triangles in same directionRotation: triangles in different direction, do not share a sideReflection: share a side OR a line can be drawn equidistant from both triangles at all points on the segment side, MUST BE congruent2. Determine what characteristics the triangle fits.
3. The answer is is D. Reflections
4. As you can see the triangles are congruent by ASA (angle-side-angle).
5. If reflected across line ZK the pre-image is the same as the image. Therefore this is true.
Can someone help me with this
Answer:
10
Step-by-step explanation:
Since 75 sandwiches have salad this means that 75 - 30 = 45 of them have tuna with salad. Therefore, the amount of sandwiches that have cheese without salad is 100 - (30 + 15 + 45) = 100 - 90 = 10.
Find the side of a cube with surface area of 150cm square
Anyone that answers my question I will mark as brilliant
Answer:
5cm for each side
Answer:
5 cmsolution,
Surface area= 150 cm^2
Side of a cube(a)=?
Now,
[tex]surface \: area \: of \: cube = 6 {a}^{2} \\ or \: 150 = 6 {a}^{2} \\ or \: {a}^{2} = \frac{150}{6} \\ or \: {a}^{2} = 25 \\ or \: a = \sqrt{25} \\ or \: a = \sqrt{ {(5)}^{2} } \\ a = 5 \: cm[/tex]
Hope this helps...
Good luck on your assignment..
Find the position function of a particle moving along a coordinate line that satisfies the given conditions. 2sint-cost
Answer:
the position of a particle moving at a coordinate say(y) will satisfy the given conditions t=0 (say) if y=2sint-cost
Step-by-step explanation:
Clearly by the above we can see that if y=2sint-cost at t=0, then y=-1 because at t=0 sint vanishes and leaves us with only cost and at t=0 cos0=1
John has two jobs. For daytime work at a jewelry store he is paid
$15,000 per month, plus a commission. His monthly commission is
normally distributed with mean $10,000 and standard deviation
$2000. At night he works occasionally as a waiter, for which his
monthly income is normally distributed with mean $1,000 and
standard deviation $300. John's income levels from these two
sources are independent of each other. For a given month, what is
the probability that John's commission from the jewelry store is
between $9,000 and $11,000?
Given Information:
John's mean monthly commission = μ = $10,000
Standard deviation of monthly commission = σ = $2,000
Answer:
[tex]P(9,000 < X < 11,000) = 0.383\\\\P(9,000 < X < 11,000) = 38.3 \%[/tex]
The probability that John's commission from the jewelry store is between $9,000 and $11,000 is 38.3%
Step-by-step explanation:
What is Normal Distribution?
We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.
We want to find out the probability that John's commission from the jewelry store is between $9,000 and $11,000?
[tex]P(9,000 < X < 11,000) = P( \frac{x - \mu}{\sigma} < Z < \frac{x - \mu}{\sigma} )\\\\P(9,000 < X < 11,000) = P( \frac{9,000 - 10,000}{2,000} < Z < \frac{11,000 - 10,000}{2,000} )\\\\P(9,000 < X < 11,000) = P( \frac{-1,000}{2,000} < Z < \frac{1,000}{2,000} )\\\\P(9,000 < X < 11,000) = P( -0.5 < Z < 0.5 )\\\\P(9,000 < X < 11,000) = P( Z < 0.5 ) - P( Z < -0.5 ) \\\\[/tex]
The z-score corresponding to 0.50 is 0.6915
The z-score corresponding to -0.50 is 0.3085
[tex]P(9,000 < X < 11,000) = 0.6915 - 0.3085 \\\\P(9,000 < X < 11,000) = 0.383\\\\P(9,000 < X < 11,000) = 38.3 \%[/tex]
Therefore, the probability that John's commission from the jewelry store is between $9,000 and $11,000 is 38.3%
How to use z-table?
Step 1:
In the z-table, find the two-digit number on the left side corresponding to your z-score. (e.g 1.4, 2.2, 0.5 etc.)
Step 2:
Then look up at the top of z-table to find the remaining decimal point in the range of 0.00 to 0.09. (e.g. if you are looking for 0.50 then go for 0.00 column)
Step 3:
Finally, find the corresponding probability from the z-table at the intersection of step 1 and step 2.
Which shows the prime factorization of 80? Check all that apply. 2 × 4 × 10 2 × 2 × 2 × 2 × 5 24 × 5 2 × 5 × 8
Answer:
The Prime Factorization of 80 is, 2 × 4 × 10, 2 × 2 × 2 × 2 × 5 and 2 × 4 × 10
Step-by-step explanation: They are correct, because they all equal 80. 2 × 4 × 10=80 and 2 × 4 × 10=80, and 2 × 2 × 2 × 2 × 5=80.
24 × 5=120, Therefore it's the only incorrect question.
The term 2 x 2 x 2 x 2 x 5 shows the prime factorization of 80.
What is the prime factorization?Prime factorization is the process of dissecting a number into the prime numbers that contribute to its formation when multiplied. In other terms, it is known as the prime factorization of the number when prime numbers are multiplied to get the original number.
Given the number 80
factors of 80 are 2 x 2 x 2 x 2 x 5
and given factors,
2 x 4 x 10,
2 x 2 x 2 x 2 x 5,
2 x 5 x 8,
24 x 5
all are the factors of 80 except 24 x 5,
but the correct representation of the prime factorization of 80 is
2 x 2 x 2 x 2 x 5
Hence option B is correct.
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What are
are the types of algebric
expression?
Answer:
Step-by-step explanation:
monomial, polynomial, binomial, trinomial and multinomial are the different types of algebraic expressions.
plz mark as brainliest!!!!!!!
Bucket contains 425 mL of water. The capacity of water in the bucket decreases 4.8% each hour. Which equation models the situation?
Answer:
[tex]V(t) = 425(0.952)^{t}[/tex]
Step-by-step explanation:
The amount of water in the bucket after t hours, in mL, can be modeled by an equation in the following format:
[tex]V(t) = V(0)(1-r)^{t}[/tex]
In which V(0) is the initial amount, and r is the constant decay rate, as a decimal.
Bucket contains 425 mL of water.
This means that [tex]V(0) = 425[/tex]
The capacity of water in the bucket decreases 4.8% each hour.
This means that [tex]r = 0.048[/tex]
So
[tex]V(t) = V(0)(1-r)^{t}[/tex]
[tex]V(t) = 425(1-0.048)^{t}[/tex]
[tex]V(t) = 425(0.952)^{t}[/tex]
2.
Find the degree of the monomial. 6x8,y5
Answer:8
Step-by-step explanation:
I’m guessing it’s like 6*x^8?
if 36a=45/b, then ab=
Answer:
[tex]1.25[/tex]
Step-by-step explanation:
[tex]let \: a = x \: and \: b = y[/tex]
[tex]36x = \frac{45}{y} [/tex]
[tex]36xy = 45[/tex]
[tex]xy = \frac{45}{36} [/tex]
[tex]xy = 1.25[/tex]
[tex]therefore \: ab \: is \: 1.25[/tex]
What is the inverse of 520/2 = 260?
260/520 = .5
260 * 2 = 520
2/520 = .004
260 * 520 = 135,200
Answer:
The answer is 260 * 2 = 520
Step-by-step explanation:
520/2 = 260
Multiply both sides by 2
We have
260 × 2 = 560
Hope this helps
Find the lateral area of the square pyramid shown to the nearest whole number.
25 yd
A
43 yd
Answer:
4,300
Step-by-step explanation:
Lateral area of a squared Pyramid is given as ½ × Perimeter of base (P) × slant height of pyramid
Thus, we are given,
Side base length (s) = 43 yd
height (h) = 25 yd
Let's find the perimeter
Permimeter = 4(s) = 4(43) = 172 yd
Calculate the slant height using Pythagorean theorem.
Thus, l² = s²+h²
l² = 43²+25² = 1,849+625
l² = 2,474
l = √2,474
l ≈ 50 yd
=>Lateral area = ½ × 172 × 50
= 172 × 25
= 4,300 yd
A triangle and a horizontal line are shown. If the triangle is revolved about the horizontal line, what is the resulting object? a triangle next to a horizontal line solid cylinder hollow cylinder solid cone hollow cone with truncated top
Answer:
d. solid cone
Step-by-step explanation:
Solid revolution is the general method used for revolving a given figure about a reference plane to produce a required solid. This process involves the generation of a 3 dimensional shape from a 2 dimensional figure.
A triangle is a three sided figure which generates a solid or hollow cone when it revolves about a given line. If the given triangle is made to revolve about the line, the resulting object would be a solid cone.
Answer:
the answer would be a solid cone
Step-by-step explanation:
i took the test and got it right.
BRAINLIEST PLS PLS PLS PLS I RLY NEED IT
Please help me this math is timed it's in Algebra. I'll double points. 1. (x^-2 y^3)^-1 2. (5x^3/y^2)^4 3. 36x^3y^-3/6x^5y^-6 Maybe more, but right now that's it.
Answer:
1. [tex]\frac{x^2}{y^3}[/tex]
2. [tex]\frac{625x^{12}}{y^8}[/tex]
3. [tex]\frac{6}{x^2y^9}[/tex]
Step-by-step explanation:
Remember, when you exponent an exponent, you multiply the powers.
When you multiply exponents, you add them.
When you divide exponents, you subtract them.
1.
Step 1: Multiply exponents
[tex]x^2y^{-3}[/tex]
Step 2: Move [tex]y^{-3}[/tex] to the denominator
[tex]\frac{x^2}{y^3}[/tex]
2.
Step 1: Multiply exponents
[tex]\frac{5^4(x^{3})^{4}}{(y^2)^4}[/tex]
Step 2: Power
[tex]\frac{625x^{12}}{y^8}[/tex]
3.
Step 1: Simplify
[tex]\frac{6x^3y^{-3}}{x^5y^6}[/tex]
Step 2: Remove terms
[tex]\frac{6y^{-3}}{x^2y^6}[/tex]
Step 3: Move [tex]y^{-3}[/tex] to the denominator
[tex]\frac{6}{x^2y^6y^3}[/tex]
Step 4: Combine like terms
[tex]\frac{6}{x^2y^9}[/tex]
How many unique values can be created by forming the fraction $\frac{x}{y}$ where $x$ is either 4, 8, or 12 and $y$ is either 4, 8, or 12?
Answer:
7 unique values can be created.
[tex]1,2,3,\dfrac{1}{2},\dfrac{1}{3},\dfrac{2}{3},\dfrac{3}{2}[/tex]
Step-by-step explanation:
We need to find unique values that can be created by forming the fraction
[tex]\dfrac{x}{y}[/tex]
where, [tex]x[/tex] is either 4, 8, or 12 and [tex]y[/tex] is either 4, 8, or 12.
Now, possible ordered pairs are (4,4), (4,8), (4,12), (8,4), (8,8), (8,12), (12,4), (12,8), (12,12).
For these ordered pairs the value of [tex]\dfrac{x}{y}[/tex] are:
[tex]\dfrac{4}{4},\dfrac{4}{8},\dfrac{4}{12},\dfrac{8}{4},\dfrac{8}{8},\dfrac{8}{12},\dfrac{12}{4},\dfrac{12}{8},\dfrac{12}{12}[/tex]
[tex]1,\dfrac{1}{2},\dfrac{1}{3},2,1,\dfrac{2}{3},3,\dfrac{3}{2},1[/tex]
Here, 1 is repeated three times. So, unique values are
[tex]1,2,3,\dfrac{1}{2},\dfrac{1}{3},\dfrac{2}{3},\dfrac{3}{2}[/tex]
Therefore, 7 unique values can be created.
Where will the images of the points in the quadrilateral that are not on the line be
Answer:
All quadrilaterals are four sided shape.
Step-by-step explanation:
Four sided shape can be:
- Square
- Trapaziod
Four sided shape can be called a quadrilateral.
[tex]\frac{8-i}{3-2i}[/tex] If the expression above is rewritten in the form a+bi, where a and b are real numbers, what is the value of a? (Note: [tex]i=\sqrt{-1}[/tex]
Answer:
a = 2 , b = 1
Step-by-step explanation:
[tex]\frac{8-i}{3-2i}*\frac{3+2i}{3+2i}[/tex]
=> [tex]\frac{(8-i)(3+2i)}{9+4}[/tex]
=> [tex]\frac{24+13i-2i^2}{13}[/tex]
=> [tex]\frac{26+13i}{13}[/tex]
Comparing it with a+bi
a = 26/13 , b = 13/13
a = 2, b = 1
Answer:
a = 2
b = 1
Step-by-step explanation:
[tex]\frac{8-i}{3-2i}[/tex]
Write the fraction in this form:
[tex]\frac{a+bi}{c+di}\:=\:\frac{\left(c-di\right)\left(a+bi\right)}{\left(c-di\right)\left(c+di\right)}=\:\frac{\left(ac+bd\right)+\left(bc-ad\right)i}{c^2+d^2}[/tex]
[tex]\frac{\left(8(3)+-1(-2)\right)+\left(-1(3)-8(-2)\right)i}{3^2+-2^2}[/tex]
Evaluate.
[tex]\frac{26+13i}{13}[/tex]
Factor the numerator.
[tex]\frac{13\left(2+i\right)}{13}[/tex]
[tex]2+1i[/tex]
How many months dose it take to pay off 160,000 paying 677 a month
160,000 / 677 = 293.88 months
Hope this helps.
the expression7(b+3) is equivalent to which expression? A.7b+3, B.7+b+c, C.7b+10, D.7b+21
Answer:
7b+21
Step-by-step explanation:
7(b+3)
Distribute
7*b + 7*3
7b+21
The following table represents a probability distribution for a random variable, X. What must P(5) be?
Answer:
c) 0.1
P(5) = 0.1
Step-by-step explanation:
Given data
x : 0 1 2 3 4 5
p(x): 0.2 0.1 0.3 0.1 0.2 ?
Given data is discrete distribution
if the numbers [tex]P(x_{i} )[/tex] i = 1,2,3..... satisfies the two conditions
i) [tex]P(x_{i} )\geq 0[/tex] for all values of 'i'
ii) ∑P(x) = 1
Given data
i) [tex]P(x_{i} )\geq 0[/tex] for all values of 'i'
ii) ∑P(x) = 1
P(x=1) + P(x=2) +P(x=3) +P(x=4)+P(x=5) =1
⇒ 0.2 + 0.1 + 0.3 +0.1 +0.2 + p(X=5) = 1
⇒ 0.9 +p(5) =1
⇒ p(5) = 1 -0.9
⇒ P(5) = 0.1
The fuel consumption in miles per gallon for a car varies inversely with its weight. Suppose a car that weighs 3,000 pounds gets 28.7 miles per gallon on the highway. Write the equation that relates y, the fuel consumption in miles per gallon, to the car’s weight, w pounds. How many miles per gallon would a car get, if it weighs 4,100 pounds?
Answer:
y = 86100 / w.
21 miles per gallon.
Step-by-step explanation:
If y is the consumption then:
y = k / w where k is some constant so we have:
28.7 = k / 3000
k = 3000 *28.7 = 86100
So the required equation is y = 86100 / w.
For a car weighing 4100 pounds:
y = 86100 / 4100 = 21 miles per gallon.
The required inverse relation is, yw = 86100.
The car will get 21 miles per gallon if it weighs 4,100 pounds.
What are direct and inverse relations?A direct relation between two quantities implies that the increase in one increases the other and vice-versa.
If quantity a and b are directly related, then we write the relation as a ∝ b, which can be written as a = kb, where k is the constant of proportionality used to replace the proportionality symbol with the equal to sign.
An inverse relation between two quantities implies that the increase in one decreases the other and vice-versa.
If quantity a and b are inversely related, then we write the relation as a ∝ 1/b, which can be written as a = k/b, or, ab = k, where k is the constant of proportionality used to replace the proportionality symbol with the equal to sign.
How to solve the question?In the question, we are given that the fuel consumption in miles per gallon (y) for a car inversely varies with its weight (w).
Thus we can write the relation like this:
y ∝ 1/w
or, y = k/w
or, yw = k.
The value of k can be determined using the given value of y = 28.7 miles per gallon and w = 3000 pounds.
Therefore, 28.7*3000 = k
or, k = 86100.
Thus, the required inverse relation is, yw = 86100.
Now, we are asked how many miles per gallon will a car get if it weighs 4100 pounds.
Therefore, w = 4100, y = ?
We know, yw = 86100.
or, y = 86100/w = 86100/4100 = 21.
Therefore, the car will get 21 miles per gallon, if it weighs 4,100 pounds.
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7+(10-4^2)÷4×1/2^3 need help
Answer:
6 13/16
Step-by-step explanation:
7+(10-4^2)÷4×1/2^3
PEMDAS says parentheses first
7+(10-16)÷4×1/2^3
7+(-6)÷4×1/2^3
Then exponents
7+(-6)÷4×1/8
Then multiply and divide from left to right
7+(-6)÷4×1/8
7+-3/2 *1/8
7 + -3/16
Add and subtract
6 13/16
Select all the correct equations.
Which equations have no real solution but have two complex solutions? PLZ 20 POINTS
Answer:
You did not post the options, but i will try to answer this in a general way.
Because we have two solutions, i know that we are talking about quadratic equations, of the form of:
0 = a*x^2 + b*x + c.
There are two easy ways to see if the solutions of this equation are real or not.
1) look at the graph, if the graph touches the x-axis, then we have real solutions (if the graph does not touch the x-axis, we have complex solutions).
2) look at the determinant.
The determinant of a quadratic equation is:
D = b^2 - 4*a*c.
if D > 0, we have two real solutions.
if D = 0, we have one real solution (or two real solutions that are equal)
if D < 0, we have two complex solutions.
Answer:
This was for 5 points. not 20 my dude. Also the first answer is correct.
Step-by-step explanation:
5. Calculate, in terms of it, the total surface
area of a solid cylinder of radius 3cm and
height 4cm
Answer:
131.88 cm²
Step-by-step explanation:
At = 2×Acircle + Arectangle
= 2×π·r² + w×h
w = 2π·r = 2·3.14·3 = 18.84 cm
At = 2·3.14·9cm² + 18.84cm·4cm
= 56.52cm² + 75.36cm²
= 131.88 cm²