Answer:
Bigger size / smaller size = 40
Step-by-step explanation:
Notice that we
36 / (9/10) = 30 / (3/4) = 40
Therefore the proportion model would be
Bigger size / smaller size = 40
In recent survey, a school district randomly dialed 300 parent phone numbers and asked whether the family read to their toddlers at least three nights per week. 271 of the parents said that they did.
(a) Nationally , 72% of families read to their toddlers at least three nights per week. Does this data provide evidence that more parents at this district read to their children than the national average ? Show all steps in your process.
(b) Name two likely sources of bias in this survey. Write one sentence to explain each.
Answer:
a) We reject H₀ we have enough evidence for that
b) 1.-The survey was made over a district, results will surely be different if the survey is carried out over a whole state ( considering urban and rural areas)
2.-In a district we find an equalized level of salaries, which could be associated with a similar level of habits
Step-by-step explanation:
We have to develop a proportion test. One tail-test
Population proportion mean (national proportion) p₀ = 72 %
Sample information
sample proportion 271/300 p = 0,90 p = 90 %
We assume Confidence Interval 90 % then α = 0,1
Test Hypothesis
Null Hypothesis H₀ p = p₀
Alternative Hypothesis Hₐ p > p₀
As α = 0,1 and
We look at z-table for z(c) and find z(c) = 1,28
And we compute z(s) as
z(s) = ( p - p₀ ) √ (p₀q₀/n
z(s) = ( 0,9 - 0,72 ) /√(0,72)*(0,28)/300
z(s) = 0,18 / √0,1296/300
z(s) = 0,18/ 0,026
z(s) = 6,92
z(s) > z(c) 6,92 > 1,28
As z(s) is bigger than z(c), z(s) is in the rejection region, so we reject the null hypothesis. We have enough evidence to claim that the proportion in the district is bigger than the national one.
b)1. The survey was made over a district, results will surely be different if the survey is carried out over a whole state ( considering urban and rural areas)
2.-In a district we find an equalized level of salaries, which could be associated with a similar level of habits
The automatic opening device of a military cargo parachute has been designed to open when the parachute is 155 m above the ground. Suppose opening altitude actually has a normal distribution with mean value 155 and standard deviation 30 m. Equipment damage will occur if the parachute opens at an altitude of less than 100 m. What is the probability that there is equipment damage to the payload of at least one of five independently dropped parachutes
Answer:
the probability that one parachute of the five parachute is damaged is 0.156
Step-by-step explanation:
From the given information;
Let consider X to be the altitude above the ground that a parachute opens
Then; we can posit that the probability that the parachute is damaged is:
P(X ≤ 100 )
Given that the population mean μ = 155
the standard deviation σ = 30
Then;
[tex]P(X \leq 100 ) = ( \dfrac{X- \mu}{\sigma} \leq \dfrac{100- \mu}{\sigma})[/tex]
[tex]P(X \leq 100 ) = ( \dfrac{X- 155}{30} \leq \dfrac{100- 155}{30})[/tex]
[tex]P(X \leq 100 ) = (Z \leq \dfrac{- 55}{30})[/tex]
[tex]P(X \leq 100 ) = (Z \leq -1.8333)[/tex]
[tex]P(X \leq 100 ) = \Phi( -1.8333)[/tex]
From standard normal tables
[tex]P(X \leq 100 ) = 0.0334[/tex]
Hence; the probability of the given parachute damaged is 0.0334
Let consider Q to be the dropped parachute
Given that the number of parachute be n= 5
The probability that the parachute opens in each trail be p = 0.0334
Now; the random variable Q follows the binomial distribution with parameters n= 5 and p = 0.0334
The probability mass function is:
Q [tex]\sim[/tex] B(5, 0.0334)
Similarly; the event that one parachute is damaged is :
Q ≥ 1
P( Q ≥ 1 ) = 1 - P( Q < 1 )
P( Q ≥ 1 ) = 1 - P( Y = 0 )
P( Q ≥ 1 ) = 1 - b(0;5; 0.0334 )
P( Q ≥ 1 ) = [tex]1 -(^5_0)* (0.0334)^0*(1-0.0334)^5[/tex]
P( Q ≥ 1 ) = [tex]1 -( \dfrac{5!}{(5-0)!}) * (0.0334)^0*(1-0.0334)^5[/tex]
P( Q ≥ 1 ) = 1 - 0.8437891838
P( Q ≥ 1 ) = 0.1562108162
P( Q ≥ 1 ) [tex]\approx[/tex] 0.156
Therefore; the probability that one parachute of the five parachute is damaged is 0.156
Find the four terms of the sequence given by the following expression
Answer:
47, 40, 33, 26 are the first four terms of the sequence.
Step-by-step explanation:
Expression representing the sequence is,
[tex]a_n=46-7(n-1)[/tex]
where n = number of term in the sequence
For n = 1,
[tex]a_1=47-7(1-1)[/tex]
= 47
For n = 2,
[tex]a_2=47-7(2-1)[/tex]
= 47 - 7
= 40
For n = 3,
[tex]a_3[/tex] = 47 - 7(3 -1)
= 47 - 14
= 33
For n = 4,
[tex]a_4=47-7(4-1)[/tex]
= 47 - 21
= 26
Therefore, first four terms of the sequence are 47, 40, 33 and 26.
If f(x)=x-9 and g(x)=-6x-3 which statement is true
Answer:
-1 is not in the domain of (f o g)(x)
Step-by-step explanation:
f(x) = sqrt(x - 9)
g(x) = -6x - 3
(f o g)(x) = f(g(x)) = sqrt(g(x) - 9)
(f o g)(x) = sqrt(-6x - 3 - 9)
(f o g)(x) = sqrt(-6x - 12)
Let x = -1:
(f o g)(-1) = sqrt(-6(-1) - 12)
(f o g)(-1) = sqrt(6 - 12)
(f o g)(-1) = sqrt(-6)
Since sqrt(-6) is not a real number, -1 is not in the domain of (f o g)(x).
When testing the claim that p 1p1equals=p 2p2, a test statistic of zequals=2.04 is obtained. Find the p-value obtained from this test statistic.
Answer:
0.0414 with an upper tailed test
Step-by-step explanation:
Claim: P1P1 = P2P2
The above is a null hypothesis
The alternative hypothesis for a two-tailed test would be:
P1P1 \=/ P2P2
Where "\=/" represents "not equal to".
Using a z-table or z-calculator, we derive the p-value (probability value) for the z-score 2.04
With an upper tailed test, the
2 × [probability that z>2.04] = 2[0.0207] = 0.0414
This is the p-value for the test statistic.
Focus is on the alternative hypothesis.
Suppose that 10 fair coins are tossed. Find the numbers of ways of obtaining exactly 1 heads. Round the answer to the nearest whole number
Answer: 10
Step-by-step explanation:
Given : Total number of coins tossed = 10
Possible outcomes to toss a coin = Head or tail
Number of possible outcomes = [tex]2^{10}=1024[/tex]
Number of ways of obtaining exactly 1 heads = [tex]{10}C_1=\dfrac{10!}{1!9!}[/tex] [using combinations [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex] ]
=10
Hence, the numbers of ways of obtaining exactly 1 heads= 10
calculate the value of angle A to one decimal place. Picture Attached
Answer:
[tex] A = 50.7 [/tex] (to nearest tenth)
Step-by-step explanation:
Use the Law of Cosines to find the value of angle A as follows:
[tex] cos(A) = \frac{b^2 + c^2 - a^2}{2*b*c} [/tex]
Where,
a = 7 in
b = 5 in
c = 9 in
Plug in the values into the formula
[tex] cos(A) = \frac{5^2 + 9^2 - 7^2}{2*5*9} [/tex]
[tex] cos(A) = \frac{57}{90} [/tex]
[tex] cos(A) = 0.6333 [/tex]
[tex] A = cos^{-1}(0.6333) [/tex]
[tex] A = 50.7 [/tex] (to nearest tenth)
Which graph represents the solution to this inequality?
Answer:
D
Step-by-step explanation:
1/3(9x + 27) > x + 33
3x + 9 > x + 33
2x > 24
x > 12
> means open circle
Answer:
The answer is D
Step-by-step explanation:
I took the plato test!
As the Type II error, β,of a statistical test increases, the power of the test _____________.
Answer:
decreases.
Step-by-step explanation:
Type II error is one in which we fail to reject the null hypothesis that is actually false. Null hypothesis is a statement that is to be tested against the alternative hypothesis and then decision is taken whether to accept or reject the null hypothesis. The power of Type II error is 1 - [tex]\beta[/tex]. As the power increases the probability of Type II error decreases.
Find the volume of the solid shown or described. If necessary, round to the nearest tenth.
Answer:
37.7
Step-by-step explanation:
Well use the formula for the volume of a cylinder which is,
,[tex]\pi r^2 h[/tex]
So the radius is 2 and the height is 3, so we plug those numbers into the formula,
(pi)(2)^2(3)
2^2 is 4 4*3 is 12
12*pi is about 37.7 rounded to the nearest tenth.
If you would like to check look at the image below.
here is the picture pls answer another for my lil friend lol
Answer:
Hey there!
The perimeter can be expressed as 140+140+68[tex]\pi[/tex]
This is equal to 493.52 m
Hope this helps :)
there are three oranges in 200g of bag . if the weight of them with bag is 1.4kg. find the weight of an orange.i want full methods
the bag is 200g
total weight with oranges is 1400g
deduct the bags weight from total weight
1400 - 200
1200g
this is the weight of the three oranges
so each orange would be
1200 ÷ 3
400g
When a force of 36 Newtons is applied to springs S1 and S2, the displacement of the springs is 6 centimeters and 9 cm, respectively. What is the difference between the spring constants of the two springs?
Answer:
200 N/m
Step-by-step explanation:
Rearranging the formula F = kx, you find that k = F/x. For the first spring,
F = 36 N and x = 0.06 m (6 cm). So the spring constant, F/x, is 36N/0.06m = 600 N/m
For the second spring, F = 36 N and x = 0.09 m. F/x = 36N/0.09m = 400 N/m
The difference between these values is 200 N/m, and that's the answer.
Find the area of the shaded regions.
Answer:
[tex]A = A_c-A_t=4\pi -8=4.5664cm^2[/tex]
Step-by-step explanation:
The area of the shaded region can be calculated as the area of the semicircle less the area of the right triangle.
The area of the right triangle can be calculated as:
[tex]A_t=\frac{b*h}{2} =\frac{LM*MN}{2}[/tex]
Where LM and MN have the same length because the internal angles are L=45°, M=90°, and N=45°. So the area is:
[tex]A_t=\frac{4*4}{2}=8[/tex]
The diameter of the circle can be calculated using the Pythagorean theorem as:
[tex]D=\sqrt{(LM)^2+(MN)^2} =\sqrt{4^2+4^4}=4\sqrt{2}[/tex]
So, the radius is [tex]r=2\sqrt{2}[/tex]
Finally, the area of the semicircle is:
[tex]A_c=\frac{\pi*r^2 }{2}=\frac{\pi*(2\sqrt{2})^2 }{2}=4\pi[/tex]
So, the area of the shaded region is:
[tex]A = A_c-A_t=4\pi -8=4.5664cm^2[/tex]
Please answer this correctly without making mistakes
Answer:
3/11
Step-by-step explanation:
There are eleven equal parts.
So the denominator is 11.
He copies 8 parts on Sunday.
11-8=3.
He copied 3 parts on Saturday.
Hope this helps ;) ❤❤❤
The attendance for a week at a local theatre is normally distributed, with a mean of 4000 and a standard deviation of 500. What percentage of the attendance figures would be less than 3500? What percentage of the attendance figures would be greater than 5000? what percentage of the attendance figures would be between 3700 and 4300 each week?
ok its 45.15% trust me
Answer:
Step-by-step explanation:
This curve alone does not give exact percentages with the exception of P(z=0) = .50 or 50%
A Pictorial where 'some' of the % have been added for helps more...
However, most often one needs to use a table, calculator, or an Excel function ect to find exact Percentage,
P(x > 4000) = P(z = 0) = .50 or 50 % |using above pictorial
Using Calculator etc: Here, am using the Excel NORMSDIST function to find the Percentages:
P(z=3/5 - z=-3/5) = .7257 - .2742 =.4515 or 45.15%
Use a power reduction identity to simplify 8cos4 x .
Answer:
[tex]8cos^4}x = (3 + 4cos2x + cos4x)[/tex]
Step-by-step explanation:
Using the power reduction identity, we have that:
[tex]cos^{2}x = \frac{1}{2}(1 + cos2x)\\ \\cos^{4}x = (cos^{2}x)^2 = (\frac{1}{2}(1 + cos2x))^2\\\\cos^{4}x = \frac{1}{4} (1 + 2cos2x + cos^{2}2x)\\[/tex]
From the first line:
[tex]cos^{2}2x = \frac{1}{2}(1 + cos4x)[/tex]
Therefore:
[tex]cos^{4}x = \frac{1}{4} (1 + 2cos2x + \frac{1}{2}(1 + cos4x))\\\\cos^4}x = \frac{1}{4} (1 + 2cos2x + \frac{1}{2} + \frac{1}{2} cos4x)\\\\cos^4}x = \frac{1}{4} (\frac{3}{2} + 2cos2x + \frac{1}{2} cos4x)\\\\=> 8cos^4}x = 8 * \frac{1}{4} (\frac{3}{2} + 2cos2x + \frac{1}{2} cos4x)\\\\8cos^4}x = 2 * (\frac{3}{2} + 2cos2x + \frac{1}{2} cos4x)\\\\8cos^4}x = (3 + 4cos2x + cos4x)[/tex]
Answer:
Step-by-step explanation:
Find c and round to the nearest tenth
Answer:
[tex] c = 15.5 [/tex]
Step-by-step explanation:
Using the Law of Cosines, c² = a² + b² - 2ab*cos(C), let's find c.
Where,
a = 15 ft
b = 20 ft
C = 50°
Thus:
[tex] c^2 = 15^2 + 20^2 - 2*15*20*cos(50) [/tex]
[tex] c^2 = 625 - 600*0.6429 [/tex]
[tex] c^2 = 625 - 600*0.6429 [/tex]
[tex] c^2 = 625 - 385.74 [/tex]
[tex] c^2 = 239.26 [/tex]
[tex] c = \sqrt{239.26} [/tex]
[tex] c = 15.5 [/tex] (nearest tenth)
Answer:
c sorry gotta get points.
Step-by-step explanation:
solve the nonlinear system of equations. State the number of solutions.
Answer:
Step-by-step explanation:
Hello,
Question 15
We can search x such that:
[tex]x^2-4x+4=2x-5\\\\\text{*** subtract 2x-5 from both sides ***}\\ \\x^2-4x-2x+4+5=0\\ \\\text{*** simplify ***}\\ \\x^2-6x+9=0 \\ \\\text{*** we can notice a perfect square ***}\\ \\x^2 -2\cdot x \cdot 3 + 3^2=(x-3)^2=0\\\\\text{*** taking the root ***}\\\\x-3=0\\\\\large \boxed{\sf \ \ x=3 \ \ }[/tex]
There is 1 solution.
Question 16
Again, we search x such that:
[tex]x^2-8x+15=2x-6\\\\\text{*** subtract 2x-6 from both sides ***}\\\\x^2-8x-2x+15+6=0\\\\\text{*** simplify ***}\\\\x^2-10x+21=0 \\ \\\text{*** we are looking for two roots where the sum is 10 and the product is 21 = 7 x 3 ***} \\\\x^2-7x-3x+21=x(x-7)-3(x-7)=(x-3)(x-7)=0\\\\\large \boxed{\sf \ \ x= 3 \ or \ x =7 \ \ }[/tex]There are two solutions.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Find the midpoint of the segment between the points (17,−11) and (−14,−16)
Answer:
(1.5, -13.5)
Step-by-step explanation:
Midpoint Formula: [tex](\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex]
Simply plug in our coordinates into the formula:
x = (17 - 14)/2
x = 3/2
y = (-11 - 16)/2
y = -27/2
Answer:
(-1.5, -13.5)
Step-by-step explanation:
To find the x coordinate of the midpoint, add the x coordinates and divide by 2
( 17+-14)/2 = 3/2 =1.5
To find the y coordinate of the midpoint, add the x coordinates and divide by 2
( -11+-16)/2 = -27/2= - 13.5
Judith is planning a birthday party at her house. she has 36 slices of pizza and 24 Capri Suns. What is the maximum number of people she can have at the party so that each person gets the same number of slices of pizza and the same number of Capri Suns? show all work
She can either have 24 people since there are more slices of pizza there will be extras
Daddy's annual salary is $42603.00. If he gets the same salary
each month and a monthly travelling allowance of $1250.00,
what is his monthly earning?
Answer:
$4800.25
Step-by-step explanation:
$42603 is a yearly salary.
There are 12 months in 1 year.
Monthly salary:
$42603/12 = $3550.25
Monthly travelling allowance: $1250
Total amount earned in 1 month:
$3550.25 + $1250 = $4800.25
CAN SOMEONE PLEASE HELP ME. ITS HARD AND I CANT SOLVE IT. ILL MARK BRAINLIEST
Answer:
Step-by-step explanation:
Hello,
First of all, we need to find the equation of the line.
It will be something like y = ax + b (we need to find a and b).
Then the graph is the part of the plan which is above this line, so the inequality will be
[tex]\large \boxed{\sf \ \ y\geq ax+b \ \ }[/tex]
There is only one line passing by two different points, right?
We need to find two points of this line, the x-axis gives the x of the point and the y-axis give the y of the point.
We can see on the graph that (-1,-1) and (6,13) are two points of this line.
I attached a graph with the two points A (-1,-1) and B (6,13).
We need to solve y = ax + b to find a and b which means:
(-1) = a(-1 )+ b <=> -1 = -a + b <=> -a + b = -1
(13) = a(6) + b <=> 6a + b = 13
To eliminate b, we can subtract the first equation from the second one.
6a + b -(-a) - b = 13 - (-1) = 13 + 1 = 14
<=> 6a + a = 7a = 14 we can divide by 7 both parts of the equation.
[tex]\large \boxed{\sf \ \ a=\dfrac{14}{7}=2 \ \ }[/tex]
And then, b = -1 + a = -1 + 2 = 1
[tex]\large \boxed{\sf \ \ b=1 \ \ }[/tex]
The equation of the line is then [tex]y=2x+1[/tex]
So, the inequality is:
[tex]\Large \boxed{\sf \ \ y\geq 2x+1 \ \ }[/tex]
And this is the answer of the question 1.
2. First, we find the equation of the line by finding two points on this line. Then, we deduce the inequality from the equality as the graph is all the points above the line (as explained above).
3. A real-life example is the following.
My parents gave $1 to my sister and they will give her $2 every day.
So today at x = 0 she has $1 and her pocket money will be represented by the line. And I told my parents that there were no way I can get less than my little sister. To help them understand what can be an acceptable deal I provided this graph, and I told them to only look for t positive of course.
The label for the x-axis is the time.
The label for the y-axis is the pocket money in $
After one day x = 1 my sister has $3 (point on the line), a possible solution for my pocket money is $6, $14 (two points from the graph) is also a solution of course :-)
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
What is the value of Sine theta in the diagram below?
Answer:
C) 24/25
Step-by-step explanation:
did the quiz and got it right
The value of the sine theta in the first quadrant in the diagram given is [tex]\mathbf{\dfrac{24}{25}}[/tex]
What is the trigonometric function in the first quadrant?The explanation of the trigonometric functions (i.e cosine, sine, tangent) in respect of point coordinates on the unit circle informs us of the signs and meanings of the trigonometric functions for each of the four(4) quadrants, depending on the signs of the x, as well as, y coordinates in each quadrant.
In the first quadrant;
cos(θ) > 0, sin(θ) > 0 andtan(θ) > 0Thus, we have a positive x and y-axis.
Taking the forms x and y, i.e. (x, y) = (cos θ, sin θ)
The value of sine theta in [tex]\mathbf{(\dfrac{7}{25}, \dfrac{24}{25} ) = \dfrac{24}{25} }[/tex]
Learn more about Trigonometric functions here:
https://brainly.com/question/24349828
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Find x and round to the nearest tenth.
Answer:
83.0°
Step-by-step explanation:
Given ∆XYZ, with 3 known sides, to find angle X, apply the Law of Cosines, c² = a² + b² - 2ab*cos(C).
For convenience sake, this formula can be rewritten to make the angle we are looking for the subject of the formula.
Thus, we would have this following:
[tex] cos(C) = \frac{a^2 + b^2 - c^2}{2ab} [/tex]
Where,
C = X = ?
a = 8 ft
b = 16 ft
c = 17 ft
Plug in the stated values into the formula and solve for X
[tex] cos(X) = \frac{8^2 + 16^2 - 17^2}{2*8*16} [/tex]
[tex] cos(X) = \frac{320 - 289}{256} [/tex]
[tex] cos(X) = \frac{31}{256} [/tex]
[tex] cos(X) = 0.1211 [/tex]
[tex] X = cos^{-1}(0.1211) [/tex]
[tex] X = 83.0 [/tex] (to nearest tenth)
Answer:
its actually 83 not 83.0
Step-by-step explanation:
im only saying this bc i know people with type 83.0 in the box
Which of the following can be calculated using the formula ?
A.
Area of a circle
B.
Circumference of a circle
C.
Arc length of a circle
D.
Diameter of a circle
The formula C = π2r
Is used for the circumference.
Which of the following can be calculated using the formula?We know that the number π is defined as the quotient between the circumference of a circle and its diameter, so we can write:
C/d = π
And remember that the diameter is twice the radius, so we can write:
d = 2r
Then we can rewrite the equation for the circumference as:
C = π2r
Then we conclude that the correct option is B.
If you want to learn more about circles:
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Help with 5 questions frequency table
Answer:
The given data is:
30, 32, 11, 14, 40, 37, 16, 26, 12, 33, 13, 19, 38, 12, 25, 15, 39, 11, 37, 17, 27, 14, 36
We will fill the table with the relevant information:
Question 1: 21 - 25 (because the previous range stops at 20 and the following range starts at 26)
Question 2: III (write 3 as a tally)
Question 3: II (write 2 as a tally)
Question 4: 8 (write the tally as a number)
Question 5: 4 (write IIII as a number)
What is the point-slope form of a line that has a slope of One-half and passes through point (–7, 2)? 2 minus y = one-half (7 minus x) 7 minus y = one-half (negative 2 minus x) y minus 7 = one-half (X minus 2) y minus 2 = one-half (x minus (negative 7))
Answer: y-2=1/2(x-(-7)) or y-2=1/2(x+7)
Step-by-step explanation:
The point-slope formula is y-y₁=m(x-x₁). Since we are given the point and the slope, we can directly plug them into where it is appropriate. The slope is 1/2. Slope is represented by m. We would plug in 1/2 into m. The point is (x₁,y₁). That format matches (-7,2).
y-2=1/2(x-(-7))
y-2=1/2(x+7)
Answer:
D.
Step-by-step explanation:
Solve the equation for the indicated variable. C=680x/h^2 for x
Answer:
C h^2 / 680 = x
Step-by-step explanation:
C=680x/h^2
Multiply each side by h^2
C h^2=680x/h^2 * h^2
C h^2=680x
Divide each side by 680
C h^2 / 680=680x/680
C h^2 / 680 = x
Write an inequality and show on a number line all numbers: greater than (−3) but less than or equal to 3
To write an inequality and show on a number line all numbers: greater than (−3) but less than or equal to 3
Let n be the number, then -3 < n ≤3 .
On number line we mark open circle at -3 (since it has a strictly less than sign) and a closed circle at 3 (since it has a less than and equal to sign) .
To the required inequality that shows all the numbers greater than (−3) but less than or equal to 3 : -3 < n ≤3 and the number line is represented below.