Using the normal distribution, it is found that 16.43% of adults in the US qualify for stage 1.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.Researching the problem on the internet, the mean and the standard deviation are given, respectively, by:
[tex]\mu = 122, \sigma = 22[/tex].
The proportion of adults in the US qualify for stage 1 is the p-value of Z when X = 160 subtracted by the p-value of Z when X = 140, hence:
X = 160:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{160 - 122}{22}[/tex]
Z = 1.73
Z = 1.73 has a p-value of 0.9582.
X = 140:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{140 - 122}{22}[/tex]
Z = 0.82
Z = 0.82 has a p-value of 0.7939.
0.9582 - 0.7939 = 0.1643.
0.1643 = 16.43% of adults in the US qualify for stage 1.
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Please help me do this mathematics question genius
The changes in Z would be = 6.1× 10^-4.
Calculation of the unknown valueZ = Sin (x³ +y³)
Where X = 0.3
y = 0.2
Z= Sin ( 0.3³ + 0.2³)
Z= Sin ( 0.027 + 0.008)
Z= Sin ( 0.035)
Z= 6.1× 10^-4
Therefore, the changes in Z would be = 6.1× 10^-4.
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Find the missing side lengths and leave the radicals in the simplest form.
Answer:
[tex]y=\frac{9\sqrt{2} }{2}[/tex] and x=9
Step-by-step explanation:
We can see that the triangle is a special triangle or isosceles triangle meaning that two angles/ two sides are the same.
[tex]y=\frac{9\sqrt{2} }{2}[/tex]
To solve for x use Pythagorean Theorem.
a^2 + b^2 = c^2.
[tex]\frac{9\sqrt{2} }{2} +\frac{9\sqrt{2} }{2}=x^2\\\\\frac{81}{2} +\frac{81}{2} =x^2\\\\\frac{162}{2} =x^2\\\\x=\sqrt{\frac{162}{2} } =\sqrt{81} =9\\\\x=9[/tex]
What is the distance between parallel lines y=x+3 and y=x+1, rounded to the nearest hundredth?
Answer:
The distance is 1.41 to nearest hundredth.
Step-by-step explanation:
The line y = x + 3 passes through the point (0, 3) on the yaxis.
Find the perpendicular line passing through this point:
y - 3 = -1(x + 0)
y = -x + 3
Now find the point where this line intersects the line y = x + 1:
y = -x + 3
y = x + 1
-x + 3 = x + 1
3 -1 = x + x
2x = 2
x = 1
and y = 2
So this point is (1, 2)
We require the distance between this point and (0, 3)
This = √((3-2)^2 + (0-1)^2) = √2
= 1.4142
In a large high school, 18% of sophomores and 67% of seniors have part-time jobs. Suppose random samples of 32 sophomores and 31 seniors from this high school are asked if they have a part-time job. Let p hat Subscript under and p hat Subscript upper be the sample proportions of sophomores and seniors, respectively, who have part-time jobs. Which of the following is the correct shape and justification of the sampling distribution of P hat Subscript under Baseline minus p hat Subscript upper ? bimodal because one population proportion is centered at 0.18, while the other is centered at 0.67 approximately Normal because the expected numbers of successes and failures for each sample are all at least 10 not approximately Normal because the expected numbers of successes and failures for each sample are all at least 10 not approximately Normal because the expected numbers of successes and failures for the sophomores group are not both at least 10
Using the Central Limit Theorem, it is found that the correct statement is given by:
bimodal because one population proportion is centered at 0.18, while the other is centered at 0.67.
What does the Central Limit Theorem state?It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex]
In this problem, for sophomores, we have that:
np = 32 x 0.18 = 5.76 < 10.
Hence the distribution cannot be normal, which means that the correct statement is:
bimodal because one population proportion is centered at 0.18, while the other is centered at 0.67.
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5 less than thrice a number q is 10
Answer:
q = 5
Step-by-step explanation:
5 less than 3q is 10.
∴ 3q - 5 = 10
3q = 15
q = 5
Hope this helps!
Let the vector v have an initial point at (6,-7) and a terminal point at (4,-6). determine the components of vector v
The components of v are -2 and 1.
What are components of vector?
The components of a vector in two dimension coordinate system are usually considered to be x-component and y-component. It can be represented as, V = ([tex]v_x, v_y[/tex]), where V is the vector.
As, Vector v have an initial point at (6, -7) and a terminal point at (4, -6).
If initial point of vector [tex](x_1,y_1)[/tex] and terminal point is [tex](x_2,y_2)[/tex], then components of vector is
v= ([tex]x_2-x_1, y_2-y_1[/tex])
Initial point= (6,-7) and terminal point=(4,-6)
Then,
v= (4-6, -6-(-7))
v=(-2, 1)
Thus, the vector v=(-2, 1) have two components -2 and 1.
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Ten blackberry plants start growing in my yard. Absent constraint, blackberries will spread by 200% a month. My yard can only sustain about 50 plants. Using the logistic growth model, a. Write a recursive formula for the number of blackberry plants in my yard b. Calculate the number of plants after 1, 2, and 3 months
The recursive formula for the number of blackberry plants in my yard is Tn = 3Tn-1 where To = 10
The recursive functionThe given parameters are:
Initial = 10Maximum = 50Growth rate = 200%The number of plants in month n is calculated using:
Tn = Tn-1 * (1 + 200%)
This gives
Tn = 3Tn-1
Hence, the recursive formula for the number of blackberry plants in my yard is Tn = 3Tn-1 where To = 10
The number of plants after 1, 2, and 3 monthsThis means that n = 1, 2, 3
When n = 1, we have:
T1 = 3To = 3 * 10 = 30
When n = 2, we have:
T2 = 3T1 = 3 * 30 = 90
90 is greater than the maximum number of plant the backyard can contain
Hence, the number of plants after 1 month is 30 and the plants in the backyard would exceed 50 plants before the end of the 2 months
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3.26d+9.75d−2.65 what does this equal
Answer:
13.01d - 2.65
Step-by-step explanation:
3.26d + 9.75d − 2.65
combine like terms
3.26d + 9.75d = 13.01d
nothing further can be done, recombine
13.01d - 2.65
The two formats used in an observation checklist are:
A. Video recording and audio recording
B. Performance profiles and Tallies
C. Tallies and video recording
D. Performance profiles and SMART Targets
Answer:
The two formats used in an observation checklist are:
A. Video recording and audio recordingB. Performance profiles and Tallies
C. Tallies and video recording
D. Performance profiles and SMART Targets
#CarryOnLearning
Answer:
A. Video recording and audio recordingStep-by-step explanation:
#hope it helps!
Answered by ReyvREYV111
The second angle of a triangle is 4 less than the first angle. The third angle is two times the first. Find the three angles.
The measure of the three angles are 46, 42 and 92 degrees respectively
Sum of angles in a triangleA triangle is a shape that has 3sides and angles
Let the measure of the angles be x, y and z
If the second angle of a triangle is 4 less than the first angle, then;
y = x - 4
If the third angle is two times the first, then z = 2x
Since the sum of interior angle is 180 degrees, hence;
x + y + z = 180
x +x - 4 + 2x = 180
4x = 184
x = 46
Second angle = x - 4
Second angle = 42 degrees
Third angle = 2(46) = 92 degrees
Hence the measure of the three angles are 46, 42 and 92 degrees respectively
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What is the slope of the line that passes through the points (4,8) and (8,6)? Write your answer in the simplest form
11. One card is drawn from an ordinary deck of 52 cards. Find the probabilities of drawing the following.
(a) A heart or a black card
(b) A heart or a jack
(c) A heart and the ace of clubs
(d) A 9 or a jack
(e) The 9 of hearts or a jack
Answer:
3/44/137/262/135.52Step-by-step explanation:
(a)
Probability (A heart or a black card) = 13 + 26 / 52Probability (A heart or a black card) = 39/52Probability (A heart or a black card) = 3/4(b)
Probability (A heart or a jack) = 13 + 3 / 52Probability (A heart or a jack) = 16/52Probability (A heart or a jack) = 4/13(c)
Probability (A heart and the ace of clubs) = 13 + 1 / 52Probability (A heart and the ace of clubs) = 14/52Probability (A heart and the ace of clubs) = 7/26(d)
Probability (A 9 or a jack) = 4 + 4 / 52Probability (A 9 or a jack) = 8/52Probability (A 9 or a jack) = 2/13(e)
Probability (The 9 of hearts or a jack) = 1 + 4 / 52Probability (The 9 of hearts or a jack) = 5/52Triangles STU and S'T'U' are congruent.
S
A
T'
U
S'
U
Which sequences of transformations on triangle STU can be used to create triangle S'T' U'? Choose all the possible sequences.
T
Answer:
Rotations
Transformations
Reflections
g(x) =2x+2 complete function table
Answer and Step-by-step explanation:
Hey there!
To finish the function table, all you need to do is plug in the x value into the function, which in this case is g(x)=2x+2
*Remember, the "x-value" is the input and the "y-value" is the output*
The first input is -5
2(-5)+2
-10+2
g(x) = -8
The second input is -1
2(-1)+2
-2+2
g(x) = 0
The third input is 1
2(1)+2
2+2
g(x) = 4
The fourth input is 4
2(4)+2
8+2
g(x) = 10
The fifth input is 5
2(5)+2
10+2
g(5) = 12
Answer:
see below
Step-by-step explanation:
g(x) = 2x+2
Let x = -5 g(-5) = 2(-5) +2 = -10+2 = -8
Let x = -1 g(-1) = 2(-1) +2 = -2 +2 = 0
Let x = 1 g(1) = 2(1) +2 = 2+2 = 4
Let x=(4) g(4) = 2(4) +2 = 8+2 = 10
Let x = 5 g(5) = 2(5) +2 = 10+2 = 12
Find the surface area, to the nearest square centimeter, of a cylinder with diameter 6 cm and height 8 cm.
a. 48 cm²
C.
207 cm²
b.
452 cm²
d.
72 cm²
Answer:
[tex]\sf 207 \ cm^2[/tex]
Step-by-step explanation:
Surface area of cylinderdiameter = 6 cm
r = 6/2 = 3 cm
h = 8 cm
[tex]\sf \boxed{\text{\bf Surface area of cylinder = $2\pi r(h +r)$}}[/tex]
[tex]\sf = 2*3.14*3 * (3 +8)\\\\ = 2*3.14* 3 * 11\\\\= 207.24\\\\= 207 \ cm^2[/tex]
Please help me for the 2nd part
there isn’t an image provided I can’t help unless you give an image
Select all of the expressions that are equal to 8 × 35 . A. 8 × ( 30 + 5 ) B. 5 + 3 × 35 C. ( 8 × 30 ) + ( 8 × 5 ) D. ( 8 + 30 ) × ( 8 + 5 ) E. 8 × ( 20 + 15 )
The expression 8 × 35 is equal to 8 × (30 + 5), (8 × 30) + (8 × 5), and 8 × (20 + 15) option A, C, and E are correct.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
We have expression:
= 8 × 35 ⇒ 280
A. 8 × (30 + 5) ⇒ 280
B. 5 + 3 × 35 ⇒ 110
C. (8 × 30) + (8 × 5) ⇒ 280
D. (8 + 30) × (8 + 5) ⇒ 494
E. 8 × (20 + 15) ⇒ 280
Thus, the expression 8 × 35 is equal to 8 × (30 + 5), (8 × 30) + (8 × 5), and 8 × (20 + 15) option A, C, and E are correct.
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4) The radius of a circle is 3 meters. What is the circle's circumference?
r=3 m
Answer:
The circumstances of the circle is six
Step-by-step explanation:
3×2=2
△MNP is the image of △JKL after a reflection in the x-axis. Select all of the statements that are always true. The length of side KL equals the length of side PM. The length of side , KL, equals the length of side , PM, . The length of side JK equals the length of side MN. The length of side , JK, equals the length of side , MN, . The measure of angle K equals the measure of angle P. The measure of angle , K, equals the measure of angle , P, . The measure of angle L equals the measure of angle P.
The corresponding sides and angles of the both triangle would be congruent to each other.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
△MNP is the image of △JKL after a reflection in the x-axis. Therefore, both triangles would be congruent.
The corresponding sides and angles of the both triangle would be congruent to each other.
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3. What is the median of this data set
As a member of the student council at your school, you want to determine if the seventh-grade students prefer to
have an after-school soccer program or an after-school movie club. There are 110 seventh-grade students at your
school, and you decide to take a sample of 20 students.
Describe in detail how you can randomly select 20 seventh-grade students for your sample.
Answer: I dont know
Step-by-step explanation: i need more information
Use a quadratic equation to find two real numbers that satisfies the situation.
The sum of the two numbers is 2, and their product is -48.
a. -6, -8
C.
-6, 8
b.
6,-8
d.
no such numbers exist
Answer:
its C
Step-by-step explanation:
In the diagram above, <1=40. Find the measure of <4
<4 = [???]
Answer:
40 degrees.
Step-by-step explanation:
< 4 = < 1 = 40 degrees
( as they are vertical ( opposite) angles)
( US = vertical, UK = opposite)
Answer:
m∠4 = 40°
Step-by-step explanation:
we notice that ∠1 and ∠4 are two Vertically opposite angles which means they are equal to each other then m∠4 = m∠1 = 40°
Identify a pattern in the given list of numbers. Then use this pattern to find the next number. 17,7,-3,-13,-23
Answer:
-33
Step-by-step explanation:
The sequence is descending so the nth term would be -10n and the 0 term would be 27 so the nth term for the sequence would be -10n +27.
The question asks you to find the 6th term so (-10 x 6) + 27 = -60 + 27 = -33
Please help plsass….
Step-by-step explanation:
the area of a circle is
pi×r²
that is for the whole circle, which is the same as 360 degree arc.
now that we have only 254 out of the total of 360 degrees, the sector area is
pi×r² × 254/360
pi×9² × 254/360 = pi×9 × 254/40 = pi×57.15 =
= 179.5420202... cm²
rounding to 1/10 is 180.0 cm².
so, it is actually D - none of the above.
Answer:
D. none of the above
Step-by-step explanation:
the area of a circle is
pi×r²
that is for the whole circle, which is the same as 360 degree arc.
now that we have only 254 out of the total of 360 degrees, the sector area is
pi×r² × 254/360
pi×9² × 254/360 = pi×9 × 254/40 = pi×57.15 =
= 179.5420202... cm²
rounding to 1/10 is 180.0 cm².
so, it is actually D - none of the above.
What is the area of this shape?
The area of the figure presented in the image, which is formed by one right triangle and three rectangles is equal to an amount of 157 square kilometers.
How to determine the area of a compound shape
In this question we understand that the area of the compound shape is the sum of the area of small rectangles and triangles:
[tex]A = \sum \limits^{n}_{i = 1} A_{i}[/tex] (1)
Now we proceed to calculate the area of the compound shape:
A = 0.5 · (4 km) · (3 km) + (10 km) · (2 km) + (17 km) · (7 km) + (2 km) · (6 km)
A = 157 km²
The area of the figure presented in the image, which is formed by one right triangle and three rectangles is equal to an amount of 157 square kilometers.
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The cost of operating the Marketing Department is allocated to four departments based on the floor space each occupies, in m2. Department A occupies 1400 m2, Department B occupies 820 m², Department C occupies 560 m2, and Department D occupies 390 m². If the cost of operating for March was $19 000. how much of the cost should each department of the Marketing Department take up?
The cost of each department A, B, C, and D of the Marketing Department would take up is $8,391.17, $4,914.83, $3,356.47, and $2,337.53, respectively.
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
Given the cost of operating the marketing Department for March is $19,000. The total area of operation is,
Total Area = Department A + Department B + Department C + Department D
Total Area = 1400 m² + 820 m² + 560 m² + 390 m² = 3,170 m²
Now, the cost of operating a unit area can be determined as,
Cost of operating = $19,000/3,170m² = $5.99369 per m²
Further the cost of operating the different departments are,
Department A = 1400m²×$5.99 = $8,391.17
Department B = 820m²×$5.99 = $4,914.83
Department C = 560m²×$5.99 = $3,356.47
Department D = 390m² × $5.99 = $2,337.53
Hence, the cost of each department A, B, C, and D of the Marketing Department would take up is $8,391.17, $4,914.83, $3,356.47, and $2,337.53, respectively.
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Pleaseeee show work
Answer:
The ladder is 9.54m (√91) tall
Step-by-step explanation:
(the blue triangle is all you would need to draw and the work in yellow)
Find two points (one to the left and one to the right) of the point (0, 9) that is one a line with the slope of show your work
Answer:
calculator soup can help just search what you're learning into g o o g l e and add calculator at the finish have a nice day
Consider the sequence of steps to solve the equation: 3(x - 4) + 5x = 9x - 36
Given = 3(x - 4) + 5x = 9x - 36
Step 1 = 3x - 12 + 5x = 9x - 36
Step 2 = 3x + 5x - 12 = 9x - 36
Step 3 =› 8x - 12 = 9x - 36
Step 4 => 8x - 8x - 12 = 9x - 8x - 36
Step 5 = 0 - 12 = x - 36
Step 6 = -12 = x - 36
Step 7 = -12 + 36 = x - 36 + 36
Step 8 = 24 = x + 0
Step 9 = 24 = x
Which property yields Step 7?
Answer:
adding equal no. to both sides of the equation