The solution to this problem is , we reject null hypothesis R H0 at p value =0.005 .
What is significance level ?The likelihood of rejecting the null hypothesis when it is true is the significance level, often known as alpha or. A significance level of 0.05, for instance, represents a 5% likelihood of drawing the incorrect conclusion that a difference exists when there isn't one.
Given that Hippocrates magazine states that 35 percent of all Americans take multiple vitamins regularly.
Persons surveyed = 750
Of those survived no of persons who took multiple vitamin = 296
Sample proportion = p =0.395
q =1-p = 0.605
[tex]H_{0}\\[/tex] : p= 0.35
[tex]H_{A}[/tex] : p ≠ 0.35
(Two tailed test)
Assuming H0 is true standard error = [tex]\sqrt{(0.35 * 0.65)/750}[/tex]
=>0.0174
p difference = 0.045
Test statistic = 0.045/0.0174
=>2.58
p value = 0.005 for right tailed
Reject H0:
Therefore , we reject R H0 at p value =0.005 .
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What will be the equation of straight line passing through the point 1/2 and parallel to the line y 3x 1?
The equation of the straight line passing through the point (1/2, 0) and parallel to the line y = 3x + 1 is y = 3x - ½ with slope m1 = 3 and m2 = 3.
Given line is y = 3x + 1
We need to find equation of line parallel to this line
Let us consider the equation of line as y = mx + c
We know that two lines are parallel if they have same slope i.e. m1 = m2
Here m1 = 3
So slope of required line m2 = 3
We need to find the value of c
Let us take a point (x1, y1) common to both lines
We know that (1/2, 0) is common to both lines
So x1 = 1/2, y1 = 0
Substituting these values in y = mx + c
0 = 3(1/2) + c
=> c = -1/2
Hence the equation of straight line passing through the point (1/2, 0) and parallel to the line y = 3x + 1 is y = 3x - 1/2.
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find the measure of the interior angles x, (x-24), and 68
Answer:
68, 68, 44
x = 68
x - 24 = 44
Step-by-step explanation:
If you have a shape with three interior angles, it is a triangle. The three angles in a triangle add up to 180. Use this idea to write and solve an equation.
x + (x - 24) + 68 = 180
Combine like terms.
2x + 44 = 180
Subtract 44.
2x = 136
Divide by 2.
x = 68
So we can find x - 24
68 - 24 is 44.
The three angles are 68 (given), 68 (because x = 68), and 44 (because x-24)
The angles are 68, 68, and 44
(H1.01 MC) What is the remainder of 5x³ + 7x +57 over x+2 Show all necessary steps.
The remainder of 5x³ + 7x +57 over x+2 is 3.
What is expression?
In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.
Given expressions are 5x³ + 7x +57 and x+2.
Remainder theorem: According to the remainder theorem, the remainder equals f(a) when a polynomial, p(x), is divided by (x - a).
Assume that P(x) = 5x³ + 7x +57.
Equate x + 2 to zero and find the value of x:
x + 2 = 0
x = -2
Putting x = -2 in the polynomial P(x) = 5x³ + 7x +57:
P(-2) = 5(-2)³ + 7(-2) +57
P(-2) = 5(-8) + 7(-2) +57
P(-2) = -40 - 14 +57
P(-2) = 3
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Andre and jillian were shopping at the same grocery store for bottles of sports drinks for their kickball teams. Andre bought packs of bottled drinks, plus single bottles. Jillian purchased packs, plus singles. Andre and jillian discovered that they had purchased the same number of bottles. How many bottles were in each of the packs? (all of the packs have the same number of bottles. ).
There is 4 bottles in each of the packs when Andre and Jillian were shopping at the same grocery store for bottles of sports drinks for their kickball teams. Andre bought 3 packs of bottled drinks, plus 11 single bottles. Jillian purchased 5 packs, plus 3 singles. Andre and Jillian discovered that they had purchased the same number of bottles
The bottles in each of the packs can be calculate as follows:
Expressions that indicate the total number of bottles purchased
The formula 3p + 11 can be used to express how many bottles André purchased.
The formula that can be used to express how many bottles Jillian purchased is 5p + 3
Where:
P is the number of bottles in the purchased packs.
Counting how many bottles are in the pack
The expressions of Andre and Jillian would be equal if they each had the same number of bottles.
3p + 11 = 5p + 3
Take the subsequent actions to find the value of p:
Combine related words
5p - 3p = 11 - 3
2p = 8
Subtract 2 from both sides of the equation.
p = 4
Your question is incomplete but most probably your full question was
Andre and Jillian were shopping at the same grocery store for bottles of sports drinks for their kickball teams. Andre bought 3 packs of bottled drinks, plus 11 single bottles. Jillian purchased 5 packs, plus 3 singles. Andre and Jillian discovered that they had purchased the same number of bottles. How many bottles were in each of the packs? (All of the packs have the same number of bottles.)
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The opposite of the opposite of 48 is _____?
Question 5 options:
A: 4.8
B: 48
C: -48
D: 0.48
Answer: It would be -48
Step-by-step explanation: Hope it helps:)
80 pionts if you help me!!!! and brainlest !!!!
in the GIF TYSM ⇅
Answer:
A:(4,12)
B: In image
C. Yes, it does because it shows that the two lines intersect at the same point.
Step-by-step explanation:
-Hope this helped & Happy Holidays!
a) how many license plates are possible if each plate must have three letters followed by three numbers?
The permutation combination of license plate is 35152000.
Numbers can be 10 digits (0, 1, 2, …, 9) and 26 letters (A, B, C, ..., Z).
Repetition is allowed, leaving 26 next choices for each letter used and 10 next choices for each digit used.
Therefore, according to the multiplication principle, the total number of different letter permutations.
26× 26 × 26 = 17576
and the total number of digit permutation: 10 × 10 × 10 = 1000
now, they can be in any order:
⁶C₃ = 6!/(6−3)!3!
We have to consider 20 different combinations of positions.
So the total number of different license plates possible by the multiplication principle is
17576 × 1000 × 20 = 351520000
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factor the following expression using imaginary numbers : 100x^2+1
Hence, the factors of [tex](10x+1)^2=100x^2+1+20x[/tex].
What are the factorization?
Factorisation or factoring is defined as the breaking or decomposition of an entity into a product of another entity, or factors, which when multiplied together give the original number.
Here given expression is
[tex]100x^2+1[/tex]
[tex](10x)^2+(1)^2[/tex]
[tex](10x+1)^2[/tex]
As we know that,
[tex](a+b)^2=a^2+b^2+2ab[/tex]
Here
[tex]a=10x\\b=1[/tex]
So,
[tex](10x+1)^2=(10x)^2+(1)^2+2(10x(1))\\\\(10x+1)^2=(10x)^2+(1)^2+20x\\\\(10x+1)^2=100x^2+1+20x[/tex]
Hence, the factors of [tex](10x+1)^2=100x^2+1+20x[/tex].
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The factors of the expression 100x² + 1 are (10x+i) (10x-i).
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.
The given expression is 100x² + 1.
The given expression is a quadratic function.
The standard form of quadratic function:
ax²+bx +c, where a is not equals to zero.
Comparing with the standard form we get,
a = 100, b = 0 and c = 1
Simplifying,
100x² + 1
= 100x² - (-1)
= (10x)² - (-1)
= (10x)² - (i)² ,{i² = -1}
= (10x+i) (10x-i)
Therefore, (10x+i) (10x-i) are the factors.
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Find x when y = 32, given that x varies inversely as y, and x = 132 when y = 4. 1,056 66 16. 5.
The Variable x varies inversely with y, and x = 132 when y = 4 then the value of x is 16.5 when y = 32.
So, the correct option is option(D).
Inverse variation can be expressed by the formula, xy=k or y=kx
That is, if there is a non-zero constant k such that xy = k or y = kx (x≠0,y≠0), then y varies inversely with x.
We have given that,
x varies inversely with y and we need to find x when y = 4 when x = 132
X varies inversely with y there exist a constant of proportionality say k such that :
=> (x)(y) = k ----(1)
Put the value of x and y in equation (1) to find the value of k
=> (132)(4) = k
Therefore, k = 528 , We get
=> (x)(y) = 528
Now, we find x when y = 32, so plug the value of y in equation (1)
=> (x)(32) = 528
=> x = 528/32
=> x = 16.5
Hence, the value of x is 16.5 when y = 32 .
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Please help meeee !!!!!
First we find number of passengers on each train.
4752/3 = 1584
Each train has 1584 passengers and 8 cars.
To find passengers per car, divide 1584 by 8.
198
Hope this helps :)
If you need any more explanation, feel free to ask. If this really helps, consider marking brainliest.
- Jeron
a phycologist is interested in determining the proportion of algae samples from a local rivulet that belong to a particular phylum. a simple random sample of 50 alga is obtained and each alga is categorized as either being a cyanobacterium or not. the researcher found that 38 samples were, in fact, cyanobacteria. without relying on any previous knowledge, the researcher wanted to estimate the proportion of algae that were cyanobacteria with a margin of error of at most 0.01 in a 99% confidence interval. how large a sample size would be required?
The required sample size of the given problem with a margin of error of at most 0.01 in a 99% confidence interval is 16590.
What is margin of error?A margin of error is a factual estimation that records for the distinction among genuine and extended brings about an irregular overview test. In less complex terms, the margin of error you to measure the degree of unconventionality in information and exploration results.
According to question:Let p be the population proportion of cyanobacteria.
Given : E = 0.01
Critical value for 99% confidence interval : z = 2.576
If Ian does not want to rely on previous knowledge , then we assume p=0.5 because the largest standard error is at p=0.5.
Now, the required sample size = n
⇒0.5(1 - 0.5)([tex]\frac{2.576}{0.01}[/tex])^2
⇒ 0.25(257.6)^2
⇒ 0.25(66357.76)
⇒ 16589.44 ≈≈ 16590
Thus, the size of sample is 16590.
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sine cosine of complementary angles PLEASE HELP!!!!
Answer:
cos S = 3/4
sin T = 3/4
Step-by-step explanation:
cos S = adj/hyp = 3/4
sin T = opp/hyp = 3/4
cos S and sin T are the sine and cosine of complementary angles arnd are equal.
Which expression is the simplest form ?
Which transformations could have taken place to map △ ABC to △ ABC?
The question is a spam as the correct question should be:
Which transformations could have taken place to map △ABC to △A"B"C".
The following answer has been given keeping in mind the above question.
The transformations that should have been taken place are a rotation and a dilation.
What is a rotation?
Rotation is when we rotate a figure to a certain degree. In a rotation, points and figures are turned on a coordinate plane. Majorly, rotations are about to the origin. Rotating a point about the origin can be, imagine a line connecting the origin to a point, and then rotate the line clockwise by the correct angle of rotation.
What is a dilation?
Dilation is a process of transformation in which something can be made larger or smaller. In a dilation, a point, a set of points can be expanded or contracted in relation to the origin. In expansion, the points in a figure move far away from the origin, and the side lengths of the figure increase. In a contraction, the points of the figure move closer to the origin, and the side lengths in the figure tend to reduce.
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Added an attachment.
Answer:
7.5
Step-by-step explanation:
perimeter = 4 × side
√120 = 4s
s = (√120)/4
A = s²
A = [(√120)/4]²
A = 120/16
A = 7.5
Baruti, a ranger in kruger national park in south africa, collected data about the elephant population in the park. She compared the foot lengths of the elephants and their shoulder height (both in centimeters) and created the following scatterplot and regression line. The fitted line has a slope of 5. 895. 895, point, 89. What is the best interpretation of this slope?.
The best interpretation of this slope is A. On average, each 1-centimeter increase in foot length was associated with a 5.89-centimeter increase in shoulder height.
The elephants of Kruger would need to be continuously culled until the habitats began to recover, at which point the reduced population numbers would need to be maintained until the vegetation had recovered to a near-climax state in order to determine that number.
The average change in the response (y) variable that is associated with a change of one unit in the explanatory (x) variable is shown by the slope of the regression line.
In this instance, the slope represents the average change in shoulder height caused by an increase in foot length of one centimeter.
Slope = ∆Y/∆X = change in Y per unit change in X = 5.89
thus, The average increase in shoulder height was 5.89 centimeters for every 1-centimeter increase in foot length.
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(complete questions)
Baruti, a ranger in kruger national park in south africa, collected data about the elephant population in the park. She compared the foot lengths of the elephants and their shoulder height (both in centimeters) and created the following scatterplot and regression line. The fitted line has a slope of 5. 895. 895, point, 89. What is the best interpretation of this slope?.
A. On average, each 1 centimeter increase in foot length was associated with a 5.89 centimeter increase in shoulder height.
B. On average, each 1 centimeter increase in shoulder height was associated with a 5.89 centimeter increase in foot length.
C. We would predict an elephant with a foot length of 0 centimeters to have a shoulder height of 5.89 centimeters.
D. We would predict an elephant with a foot length of 0 centimeters to have a shoulder height of 0 centimeters.
let nn be the largest positive integer with the following property: reading from left to right, each pair of consecutive digits of nn forms a perfect square. what are the leftmost three digits of nn?
The leftmost three digits of nn would be 816.
Solution:
The two-digit perfect squares are $16, 25, 36, 49, 64, 81$. We try making a sequence starting with each one:
16 - 64 - 49. This terminates since none of them end in a 9, giving us 1649.2536 - 64 - 49, 3649.4964 - 49, 649.81 - 16 - 64 - 49, 81649.The largest is 81649, so our answer is [816].
The leftmost three digits of nn would be 816.
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How do you find the maximum and minimum values of a set?
To find maximum value and minimum value in a set we have to use ven diagram from set theory.
Here we are taking an example?
Let A and B be 2 sets having elements 4 and 7 respectively. Then write the maximum number of elements that A∪B can have.
Let us assume that:
Number of elements of A is equal to n (A).
Number of elements of B is equal to n (B).
Number of elements of A∩B is equal to n (A∩B).
Now, the formula for the elements of A U B is as follows:
n(A∪B)=n(A)+n(B)−n(A∩B)
It is given in the question that, number of elements in set A is equal to 4 and number of elements in set B is equal to 7. So, we can write:
n (A) = 4, n (B) = 7
n (A∩B): the number of elements which are common in both the sets A and B.
We have to find the maximum number of elements which are in n(A∪B). So, the maximum of n(A∪B) is when n(A∩B) is minimum and the minimum of n(A∩B) is 0.
n(A∪B)=n(A)+n(B)−n(A∩B)⇒n(A∪B)=4+7−0⇒n(A∪B)=11
Hence, the maximum number of elements in A∪B is 11.
Note: You might be wondering, why for maximizing the n (A∪B) we have to minimize n (A∩B) and why the minimum value of n (A∩B) is 0.
In the formula for n (A∪B),
n(A∪B)=n(A)+n(B)−n(A∩B)
L.H.S will be maximized when in the R.H.S; the term after minus sign will be minimized. Hence, n (A∩B) must be minimized.
The minimum possible value of n (A∩B) is 0 means that the elements in the set A and B are such that there is not a single element is common in both the sets. And it could be possible that we have two sets and the sets have no element in common.
When no elements is common in both the sets, the n (A∩B) is ∅.
The set which has no element in it is called a null set or an empty set.
By this we can find maximum and minimum value in a set.
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using the letters in the word FABRIC, find the number of permutations that can be formed using 2 letters at a time. show your work or explain how you got your answer.
Answer:
B
Step-by-step explanation:
Solve the equation: -6z - 3z =27
Answer:
Z= -3
Step-by-step explanation:
-6z-3z=27
-9z=27
/-9. /-9
z= -3
Hopes this helps please mark brainliest
S varies directly as t. if s is 20 when t is 4 then t is ____ when s is 30
Answer:
Therefore, when s is equal to 30, t is equal to 30 / 5 = <<30/5=6>>6.
Step-by-step explanation:
Direct variation means that the ratio between two variables is always constant. In this case, the constant ratio between s and t is equal to 20/4 = 5. This means that when t is equal to 4, s is equal to 20 and the ratio between the two is 5. If s is equal to 30, we can find the corresponding value of t by setting up the following equation:
s / t = 5
We can then solve for t by multiplying both sides of the equation by t to get:
s = 5 * t
If we substitute 30 for s, we get:
30 = 5 * t
We can solve for t by dividing both sides of the equation by 5:
t = 30 / 5
Therefore, when s is equal to 30, t is equal to 30 / 5 = <<30/5=6>>6.
A cone of radiu 3cm i made from a ector. If the area of the ector i 66cm2 find the volume of the cone
Using the formula of surface area to calculate the height and using the formula for volume , The answer is 24.98 [tex]cm^{3}[/tex] .
What is a cone?A cone is a three-dimensional geometric structure with a smooth transition from a flat base—often but not always circular—to the point at the top, also known as the apex or vertex.
What is the formula to calculate the surface area and volume of cone?The required formula are :
[tex]SA = \pi r (r + \sqrt {h^{2} + r ^ {2}})[/tex] (Surface Area)
[tex]V = \pi r^{2} \frac {h}{3}[/tex] (Volume)
radius = 3 cm
Area= 66 [tex]cm^{2}[/tex]
[tex]SA = \pi r (r + \sqrt {h^{2} + r ^ {2}})[/tex]
h = 2.65 cm
[tex]V = \pi r^{2} \frac {h}{3} = \pi * 3^{2} * \frac {2.65}{3}[/tex]
=24.98 [tex]cm^{3}[/tex]
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What are the explanatory variable and response variable for this relationship? explanatory variable: season response variable: player weight explanatory variable: season response variable: player 40-yard-dash time explanatory variable: player weight response variable: player 40-yard-dash time explanatory variable: player 40-yard-dash time response variable: player weight.
The explanatory variable is the player's weight and the response variable is the player's 40-yard dash when 40-yard dash more slowly than lighter players.
Given that,
Football instructors who oversaw summer sessions noted that heavier players often ran the 40-yard dash more slowly than lighter players.
We have to find what are the relationship's explanatory variable and response variable.
We know that,
We must determine what is causing the player's slower times.
The players' slower times are a result of their added weight.
So,
The player's weight is the explanatory variable, while their 40-yard dash time is the response variable.
Therefore, The explanatory variable is the player's weight and the response variable is the player's 40-yard dash when 40-yard dash more slowly than lighter players.
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Taylor entered a 100 mile bike race. They know they can ride 32 miles in 160 minutes. At this rate, how long will it take them to finish the race? Use any strategy you find helpful.
Which of these transformations are isometrics?The diagrams are not drawn to scale.
PLEASE HURRY!!!30 Points and brainlest!!!!
Answer: Second Pic, Probably the third.
Step-by-step explanation: little bit of guesswork
How do you draw a dilation with a scale factor of 1 2?
To draw a dilation with a scale factor 1/2 , multiple every coordinates of pre-image with 1/2 and join the obtained points
A dilation is a transformation that alters the size of an image.
There is a centre and a scale factor in all dilations. The centre serves as the dilation's reference point (like the vanishing point in a perspective drawing)
The scale factor indicates how much the figure expands or contracts. A scale factor is usually denoted by the letter "k," and it is always greater than zero.
To draw a dilation with a scale factor of 1/2, follow these steps:
Step 1: Determine the scale factor and the dilation centre.
Step 2: Identify an image vertex. Draw a line through one of the image's vertices from the center of dilation.
Step 3: Find the horizontal distance and the vertical distance between the center of dilation and the vertex.
To find the horizontal and vertical distances from the centre of dilation to a new vertex, multiply the distances by the scale factor 1/2.
Step 4: Determine the new horizontal and vertical distances from the centre of dilation. Make a point plot.
Step 5: Join the new vertices together to create the dilated image.
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Someone, please help me!!!!
How do you write an equation of a line that passes through points (- 1 3 2 3 )?
The equation of the line is [tex]2x+y=1[/tex] passing through the points [tex](-1,3)[/tex] and [tex](2,3)[/tex]
The general equation can be written as [tex]y=mx+c[/tex]
where m is the slope and c is the intercept
The equation of a line passing through the points [tex](x_{1,} y_{1})[/tex] and [tex](x_{2,} y_{2})[/tex]
slope [tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
The equation is [tex]y-y_{1} =m(x-x_{1} )..........(1)[/tex]
[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }\\m=\frac{-3-3}{2-(-1)} \\m=\frac{-6}{3} \\m=-2[/tex]
Put this value in 1 equation
[tex]y-3=-2(x+1)\\y-3=-2x-2\\y=-2x+1\\2x+y=1[/tex]
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2. Find the distance between M(-3, 1) and N(2, 8) on a
coordinate plane.
F 6.1 units
G 6.9 units
H 7.3 units
J 8.6 units
Answer:
D=74
D solution 8.60233
Step-by-step explanation:
What is the solution to this equation? –1.3x = 52
Answer:
Step-by-step explanation:
x=-40