when engaging in weight control (fitness/fat burning) types of exercise, a person is expected to attain about 60% of their maximum heart rate. for 20-year-olds, this rate is approximately 120 bpm. a simple random sample of 100 20-year-olds was taken, and the sample mean was found to be 107 bpm with a standard deviation of 45 bpm. researchers wonder if this is evidence to conclude that the expected level is actually lower than 120 bpm. to determine this, we test the following hypotheses suppose the mean and standard deviation obtained were based on a sample of size 25 rather than 100. the p-value would be
There is sufficient data to prove that the heart rate was less than 120 beats per minute (P-value = 0.002).
For the population mean weight control heart rate of 20-year-olds, the 95% confidence interval is (98.07, 115.93).
Step-by-step explanation:
This is a test of the population mean's theory.
The assertion is that a heart rate of less than 120 bpm exists.
The alternative and null hypothesis are then:
h0 : μ = 120
ha : μ < 120
The level of significance is 0.05.
The sample has a n=100 size.
M=107 is the sample mean.
Due to the unknown population standard deviation, we estimate it using the sample standard deviation, which has a value of s=45.
Using the following formula, the estimated standard error of the mean is calculated:
Sm = [tex]\frac{s}{\sqrt{n} }[/tex]= [tex]\frac{45}{\sqrt{100} }[/tex] = 4.5
The t-statistic can then be calculated as follows:
T = [tex]\frac{m-μ}{\frac{s}{\sqrt{n} } }[/tex] = 107-120/4.5 = -13/4.5 -2.88
The t-statistic can then be calculated as follows:
df= n-1 = 100-1 = 99
These sample size's degrees of freedom are:
Given that this test has 99 degrees of freedom, a left-tailed design, and a t value of -2.889, the P-value is determined as follows (using a t-table)
p-value = p(t<-2.88)= 0.002
The effect is significant because the P-value (0.002) is less than the 0.05 level of significance.
The naive theory is disproved.
There is sufficient proof to back up the assertion that the heart rate was less than 120 bpm.
A 95% confidence interval for the mean must be calculated.
Since the population standard deviation is unknown, we must infer it from the sample standard deviation in order to get the critical number using a t-students distribution.
M=107 is the sample mean.
N=100 is the sample size.
When σ is unknown, an estimation of σM is made by dividing s by the square root of N:
Sm =[tex]\frac{s}{\sqrt{N} }[/tex] =[tex]\frac{45}{\sqrt{100} }[/tex] =4.5
The t-value for a 95% confidence interval is t=1.984.
The margin of error (MOE) can be calculated as:
MOE = t*Sm = 1.984 * 4.5 = 8.92
Then, the lower and upper bounds of the confidence interval are:
LL = M - t*Sm = 107- 8.92 = 98.07
UL = M +t *Sm = 107 + 8.92 = 115.93
The 95% confidence interval for the population mean weight control heart rate of 20-year-olds is (98.07, 115.93).
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answer this i dare you If a seventh grader gets closer to the record-setting jump, then the seventh graders earn 100 points. If not, the eighth graders earn 100 points. Which grade should be awarded 100 points?
Answer: 7th Graders
Explanation:
Several people have gotten this question and 7th graders are the right choice
Answer:7th grade should be awarded !
Step-by-step explanation:
I need help please!!!
Answer:
-10/9
Step-by-step explanation:
Use the slope formula: s=(y2-y1)/(x2-x1)
It doesn't matter the order.
Let's say 0 is x2 and 5 is y2; 9 is x1 and -5 is y1
Plug in the equation: s=[(5)-(-5)]/[(0)-(9)]
Simplify and solve: s=[5+5]/[-9]
s = -10/9
I can’t solve this question can someone help me please? But please put step by step or not it’s fine!
2[6²(0.5 - 1.1)]
Answer:
-43.2
Step-by-step explanation:
2 x (6^2 (0.5-1.1))
2 x (6^2 (-0.6))
2 x (-36 x -0.6)
2 x (-21.6)
- 43.2
Answer:
Step-by-step explanation:2[6²(0.5-1.1)]
2[6²(-0.6)]
2[6×6(-0.6)]
2[36(-0.6)]
2[-21.6]
=> -43.2
Function g can be thought of as a translated (shifted) version of f(x) = x^2
The new function's equation is g(x) = (x - 2)² + 6
Given,
The parent function, f(x) = x²
We have to determine the equation for the new function g(x)
Vertical shift:
The parent function is clearly pushed 6 units upward from the graph.
The general formula to increase the c units on the graph is f(x) + c
As a result, by using the rule, the new function g(x)of vertical shift is provided by g(x) = x² + 6
Horizontal shift:
It is clear from the graph that the parent function has been moved 2 units to the right.
To move the graph's c units to the right, follow this basic formula: f(x - c)
Consequently, the new function g(xhorizontal )'s shift is given by g(x) = (x - 2)²
The new function g( x ) is as follows:
The equation results in the new function being shifted 2 units to the right and 6 units upward.
g(x) = (x - 2)² + 6
Therefore, the new function's equation is g(x) = (x - 2)² + 6
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Construct a square with vertex A inscribed in the given circle
Answer:
see attached
Step-by-step explanation:
You want to construct an inscribed square in circle C with vertex A.
StepsReference the attached figure.
With the compass set to a radius greater than AC, draw arc BE centered at A.With the same compass setting, draw arc GH centered at F, which is the second intersection of line AC with circle C.Identify the points where the arcs intersect as I and J. Draw line IJ.Identify the points where line IJ intersects circle C as K and L.The desired inscribed square is AKFL.
How does a qualitative graph describe the relationship between quantities? Explain your reasoning.
Qualitative graphs depict the relationship between two quantities without including numerical values.
The benefit is that it only shows the overall trend of the effect. When we experiment with these variables, we can immediately see how the graph will look. This could validate our findings.
A quantitative relationship emerges as one variable influencing another, which can be seen with a graph. Examine how each variable is represented on the graph, as well as how quantitative relationships are stated using equations.
Quantitative data refers to data that's represented by numbers.
This is the result of graphing all of the data points. Look at that, our data points have formed a straight line! We can draw the line in using a ruler to make it more visible. We'll notice that the line passes through all of the points in our data, indicating that there is a definite relationship in our quantitative data.
Thus, qualitative graphs depict the relationship between two quantities without including numerical values.
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please help !!!!! asapppp
Answer:
C
Step-by-step explanation:
there are 1 x values that have the 2 different y value
Write the quadratic function f(x)=2(x+1)^2-8 in standard for and intercept form.
I know how to write it in standard form- f(x)=2x^2+4x-6
But I don’t know how to write it in intercept form.
Please explain.
The quadratic function f(x)=2(x+1)^2-8 in standard for and intercept form is 2x^2+4x-6 and (x-1)(x+3).
Given:
f(x) = 2(x+1)^2 - 8
= 2(x^2+1+2x) - 8
= 2x^2 + 2 +4x - 8
= 2x^2+4x-6(standard form)
Intercept form:
= 2x^2+4x-6
= (x-1)(x+3)
x-1 = 0
x = 1
x+3 = 0
x = -3
(1,0) and(-3,0).
Therefore the quadratic function f(x)=2(x+1)^2-8 in standard for and intercept form is 2x^2+4x-6 and (x-1)(x+3).
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francine wants to join a health club and has narrowed it down to two choices. the sportshaus charges an initiation fee of $ 500 and $ 10 per month. fitness first has an initiation fee of $ 50 and charges $ 25 month.
The equation for the total cost for Sports Haus is 500 + 10x and the equation for Fitness First is 50 + 25x .
In the question ,
it is given that ,
Francie wants to join the health Club .
For the Sports Haus the initiation fees = $500
per month charge = $10
let the number of months be= "x" ,
so , the equation to represent the total cost for Sports Haus Club for x months is 500 + 10x .
For the Fitness First the initiation fees = $50
per month charge = $25
so , the equation to represent the total cost for Fitness First Club for x months is 50 + 25x .
Therefore , The equation for the total cost for Sports Haus is 500 + 10x and the equation for Fitness First is 50 + 25x .
The given question is incomplete , the complete question is
Francine wants to join a health club and has narrowed it down to two choices. The Sports Haus charges an initiation fee of $ 500 and $ 10 per month. Fitness First has an initiation fee of $ 50 and charges $ 25 month . write an equation for the total cost of each health club for x months .
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when the point (-2, 6) is reflected across the y-axis it will be located at where
The point (-2, 6) is reflected across the y-axis then the new coordinates of the point are (2, 6).
What are transformations?Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
Dilation: The preimage is scaled up or down to create the image.
Reflection: The picture is a preimage that has been reversed.
Rotation: Around a given point, the preimage is rotated to create the final image.
Translation: The image is translated and moved a fixed amount from the preimage.
We know when a point (x, y) is reflected along the y-axis (x, y) becomes
(- x, y).
Given, A point (-2, 6) is reflected across the y-axis.
∴The new coordinates of the point are (2, 6).
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What is a sampling proportion?
Answer:
it describes the proportion of individuals in a sample with a certain characteristic or trait
Step-by-step explanation:
to find sampling proportion, u have to divide the number of people or items who have the characteristic of interest by the total number of people/items in the sample.
It describes the percentage of people in a sample who possess a particular quality or attribute.
What is a sampling proportion?
The sample proportion is a random variable that can't be predicted with certainty because it fluctuates from sample to sample.
Formula to calculate sampling proportion
p′ = x / n
where,
x: the number of successes
n: the sample size
p′: sample proportion
Hence, it describes the percentage of people in a sample who possess a particular quality or attribute.
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Find the determinant of a n x n matrix A with 2’s on the diagonal, 1’s above
the diagonal, and 0’s below the diagonal.
The determinant of nxn matrix A 2’s on the diagonal, 1’s above the diagonal, and 0’s below the diagonal is 2^n.
From the given information, the matrix will appear as follows
[tex]A= \left[\begin{array}{ccccc}2&1&......&1 &1\\0&2&......&1 &1\\0&0&2 ......&1 &1\\0&0&0 ......&2 &1\\0&0&0 ......&2 &1\\0&0&0 ......&0 &2\end{array}\right][/tex]
The matrix is nxn, there are n rows and n columns. As we can see, this matrix has an upper diagonal, and in terms of linear algebra, its determinant is the sum of all its principal diagonal members. As a result, the matrix's determinant is: 2^n
Therefore, the determinant of a n x n matrix A with 2’s on the diagonal, 1’s above the diagonal, and 0’s below the diagonal is 2^n.
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the red figure is similar to the blue figure. Describe a sequence of transformations in which the blue figure is the image of the red figure
The sequence of transformations that produces the blue figure from the red figure are;
A dilation by a scale factor of 3 about the origin, [tex]D_{(3, \,O)}[/tex] followed by a translation of 11 units to the left and 11 units up, [tex]T_{(-11, \, 11)}[/tex]What is a transformation in geometry?A geometric transformation is the change to a geometric figure or shape by translating, reflecting, dilating, or rotating the figure.
The coordinates of the vertices of the red triangle are;
A(2, -2), B(2, -4), C(5, -4)
AB = -2 - (-4) = 2
BC = 5 - 2 = 3
AC = √((5 - 2)² + (-4 - (-2))²) = √(13)
The coordinates of the vertices of the blue triangle are;
D(-5, 5), E(-5, -1), and F(4, -1)
DE = 5 - (-1) = 6
EF = 4 - (-5) = 9
DF = √((4 - (-5))² + (-1 - 5)²) = 3·√(13)
The lengths of the sides of the blue triangle are DE/AB = 6/2 = 3 times the length of the sides of the red triangle
The points of the image of the red triangle following a dilation by a scale factor of 3 are;
A(2, -2) [tex]\underrightarrow{D_3}[/tex] A'(2 × 3, -2 × 3) = A'(6, -6)
B(2, -4) [tex]\underrightarrow{D_3}[/tex] B'(2 × 3, -4 × 3) = B'(6, -12)
C(5, -4) [tex]\underrightarrow{D_3}[/tex] C'(5 × 3, -4 × 3) = C'(15, -12)
The difference between the coordinates of the points A' and D are;
Horizontal translation = -5 - 6 = -11
Vertical translation = 5 - (-6) = 11
The triangle A'B'C' is translated 11 units to the 11 units to the left and 11 units upwards using the rule, [tex]T_{(-11,\, 11)}[/tex]
The sequence of transformation is a dilation by a scale factor of 3, centered at the origin, [tex]D_{3, \,O}[/tex] followed by a translation of 11 units to the left and 11 units to upwards.
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Write an equation of the line with the given slope and y-intercept
Slope : -3
y-intercept : 7
Answer:
y = - 3x + 7
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - 3 and y- intercept c = 7 , then
y = - 3x + 7 ← equation of line
Solve the system by using elimination:
3x + 6y = 10
2x + 3y = 5
Answer:
(0, [tex]\frac{5}{3}[/tex] )
Step-by-step explanation:
3x + 6y = 10 → (1)
2x + 3y = 5 → (2)
multiplying (2) by - 2 and adding to (1) will eliminate y
- 4x - 6y = - 10 → (3)
add (1) and (3) term by term to eliminate y
- x + 0 = 0
- x = 0
x = 0
substitute x = 0 into either of the 2 equations and solve for x
substituting into (2)
2(0) + 3y = 5
3y = 5 ( divide both sides by 3 )
y = [tex]\frac{5}{3}[/tex]
solution is (0, [tex]\frac{5}{3}[/tex] )
A store manager buys 8 T-Shirts and 5 hats for $220. The next day, the manager buys 5 T-shirts and 1 hat for $112.
Part A
Select the system of equations that models the situation.
A. 8t + 5h = 220
t + 5h = 112
B. 13(t – h) = 220
6(t – h) = 112
C. 8t + 5h = 220
5t + h = 112
Part B
How much does each T-shirt and each hat cost?
T-shirt : $
Hat : $
Answer:
Part A: C
Part B: T shirt = $20, hat = $12
Step-by-step explanation:
Part A:
He buy 8 T-Shirts and 5 hats for $220.
He buy another buys 5 T-shirts and 1 hat for $112.
assuming t = tshirt, h = hat, C is the correct answer
Part B:
8t + 5h = 220
5t + h = 112
1. Use second equation to represent h in term of t
h = 112 -5t
2. Replace h in first equation with h from 1.
8t + 5(112 -5t) = 220
8t + 560 - 25t = 220
-17t + 560 = 220
-17t = 220 - 560
-17t = -340
t = -340/-17 = 20
3. Replace t in equation from 1. with t from 2.
h = 112 -5(20) = 112 - 100 = 12
The graph of the function f(x)=log5(x) is stretched vertically by a factor of 3, reflected over the x-axis, reflected over the y-axis, and shifted down by 4 units.
Find the equation of the function g(x) described above.
Note: If you are using log you need to type it in and use the subscript button on the keyboard. There is no log button.
The equation of the function g(x), considering the transformations, is given as follows:
[tex]g(x) = -3\log_5{(-x)} - 4[/tex]
How to obtain the equation of function g(x)?The equation of function g(x) is obtained applying the transformations to the parent function f(x).
The parent function f(x) is given as follows:
f(x) = log5(x).
The vertical stretch by a factor of 3 is represented by a multiplication of f(x) by 3, hence:
g(x) = 3log5(x).
The reflection over the x-axis is represented by a multiplication of the function by -1, hence:
g(x) = -3log5(x).
The reflection over the y-axis is represented by a multiplication by -1 inside the domain of the function, hence:
g(x) = -3log5(-x).
The shift down by four units is represented by a subtraction of the function by four, hence:
g(x) = -3log5(-x) - 4.
Using Latex for better visualization:
[tex]g(x) = -3\log_5{(-x)} - 4[/tex]
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find all the whole values of a for which the soultion of the equation ax=6 is a whole number
The whole values of a for which the solution of the equation ax = 6 is a = {1, 2, 3, 6}
The given equation is
ax = 6
Divide both side of the equation by a
ax / a = 6/a
Then the equation will be
x = 6/a
If the solution of the system should be a whole number, then the value of a should be a factor of the numerator 6.
If a is the factor of 6, then the only the result will be a whole number without any numerator
Then the factors of 6 are 1, 2, 3, 6
Then the whole values of a = {1, 2, 3, 6}
Hence, the whole values of a for which the solution of the equation ax = 6 is a = {1, 2, 3, 6}
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I more questions i have a lot coming
Answer:
Step-by-step explanation:
4x-c=k
solve for x
use the reverse order for the usual order of operations, to solve for x
first use addition
4x = k+c
then use division
x = (k+c) / 4
so answer B) looks good
Laurie earns $7. 50 per hour at the fruit stand plus an extra $2. 00 per hour on sundays. One week in august, she worked on sunday, monday, and wednesday. She worked the same number of hours on monday and on wednesday. On sunday she worked 4 hours. If she earned a total of $83. 00 for the week, how many hours did laurie work on monday? enter and solve an equation.
If she put in the same amount of time on Wednesday and Monday. She worked 4 hours on Sunday. The amount of hours Laurie will work on Monday if she earns a total of $83.00 for the week will be 3.
Define equation.In algebra, an equation is a declaration of equivalence that includes one or more variables or unknowable quantities.
Given,
if she put in the same amount of time on Wednesday and Monday. She worked 4 hours on Sunday. The amount of hours Laurie will work on Monday if she earns a total of $83.00 for the week will be: 3.
$7.5= 1 hour various days
Sunday: $9.50 or ($7.50+$2.00) = 1 hour
Sunday = 4 + $9.50 = 38
Let Monday equal x $7.5 = 7.5x.
Let Wednesday equal x $7.5 equal x.
Let the total income be $83
Let x be the amount of hours.
Hence:
The first step is to create
Equation:
7.5x+7.5x+38=83
The next step is to determine the number of hours Laurie worked on Monday.
x =83-38÷ 7.5+7.5
x=83-38÷15
x=45÷15
3 hours = x
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Bumper car A (281 kg) moving
+2.82 m/s makes an elastic
collision with bumper car B
(209 kg) moving +1.72 m/s.
What is the velocity of car A after
the collision?
(Unit = m/s)
Remember: right is +, left is -
Enter
After collision, Car A moves with a velocity of 4.1 m/s
Elastic CollisionAn elastic collision is a collision in which there is no net loss in kinetic energy in the system due to the collision. Both momentum and kinetic energy are conserved in an elastic collision. It can be either one-dimensional or two-dimensional. In the real world, perfectly elastic collision is impossible because there is bound to be some energy conversion, however small. However, though there is no change in the linear momentum of the whole system, there is a change in the individual momenta of the involved components, which are equal and opposite in magnitude and cancel each other out and the initial energy is conserved.
The formula of elastic collision is given as
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Assuming after collision, car B has a velocity of 0m/s
281(2.82) + 209(1.72) = 281 * v + 0
792.42 + 359.48 = 281v
1151.9 = 281v
v = 1151.9 / 281
v = 4.1 m/s
The velocity of car A after collision is 4.1 m/s
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The old energy level is 250. A bar is added to the bag. The new energy level is 400. Complete the equation.
The equation is, 250+x =400
From the question, we have
The old energy level is 250.
Let the bar is added to the bag = x.
The new energy level is 400.
The equation is, 250+x =400
Addition:
The act of combining two or more items is known as addition. The process of computing the sum of two or more numbers in mathematics is called addition. It is a fundamental mathematical procedure that is frequently used in daily life. When we work with money, figure out our food bills, or figure out the time, we frequently employ addition. One-digit numbers can be added simply for solving addition problems, however for bigger numbers, we divide the numbers into columns using their corresponding place values, such as ones, tens, hundreds, thousands, and so on.
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Tre typed 456 words in 8 minutes mary typed at the same rate as Tre how long would it take mary to type 945 words
Answer:
16.57894736842105
Step-by-step explanation:
456÷8=57so tre types 57 words per minuteA/Q=
945÷57=16.57894736842105so it'll take 16 mins to type 945 words1. Write a system of inequalities (you do not need to solve): You need at least 3 pounds of fruit to make muffins. Blueberries cost $4 per pound. Strawberries cost $3 dollars a pound. You can spend at most $21.
The value in dollar of a $3,000 invetment after n year i given by f(n) = 3,000(1. 05)n. Find the value of the invetment (in dollar) after 4 year. (Round your anwer to the nearet cent. )
The value of investment after 4 years would be $12600
What is investment?
Spending money on an item with the intention of seeing its value rise over time is known as investing. Sacrificing any current item, whether time, money, or effort, is necessary for investment. In the world of finance, investing is done in order to profit from the asset that is being put up for investment.
Main body:
f(n) = 3000(1.05)n
where n= no. of years invested
here n= 4
so total investment = 3000*1.05*4
= $12600
Hence the value of investment is $12600.
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Find the multiplier of 0.5%
The multiplier of 0.5% is 0.005
How determine the multiplier of 0.5%?
A percentage multiplier is a number that is used to calculate a percentage of an amount
In order to determine 0.5% of a number we can multiply the number by a multiplier:
0.5% = 0.5/100 = 0.005
Therefore, 0.005 is the multiplier
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please help me on this!
Answer:
Step-by-step explanation:
Ok:
First Problem with coin!
1. A coin has 2 sides and one of them is going to land up or down which means it has a chance of 1 out of 2.
1 out of 2=
1/2= 50%
Second Problem with spinner
2. There are 12 spaces on the spinner and three of those spaces are blue.
SO: 3 out of 12=
3/12=
1/4=
25%
Answers: 50% and 25%
IN FRACTION FORM: 1/2 and 1/4
HELP PLEASE!!!! I don't understand this.
Answer:
1 yes y does vary directly with x
2 to find slope apply the given formula,
y2-y1/m2-m1
2/3 is slope
then the equation should be
y=2/3x
good luck
PEASE HELP ME AAAAA
^.^♡
You have a budget of 300 to order shirts for math club. The equation 10x +12y=300 models the total cost, where x is the number of short-sleeved shirts and y is the number of Ling-sleeved shirts.
/////
a.) Interpret the terms and coefficients in the equation.
____(Write here)_____
///
Graph the equation - on photo>
///
b.) Interpret the intercepts.
___(write here)___
///
c.) Find three possible solutions in the context of the problem.
a) The terms are: 10x, 12y,300
The Coefficients are: 10,12
b) x intercept is (30,0). y intercept is (0,25)
c) The three possible solutions:
(1,24), (8,18) , (6,20)
what are terms and coefficients?
Term could be a single number (positive or negative), a single variable (a letter), or a combination of multiple variables multiplied but never added or removed. Variables with numbers in front of them can be found in some terms. A coefficient is the number that appears in front of a phrase.
10x +12y=300
Terms: 10x, 12y,300
Coefficients: 10,12
Refer to the attachment for graph:
b) The locations on a Cartesian coordinate system known as intercepts are where the graph of an equation or function crosses the x- and y-axes.
From the graph, x intercept is (30,0). y intercept is (0,25)
c) solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
10x +12y=300
Find y when x=1:
10(1)+12y=300
10+12y=300
12y=300-10=290
y= 24.2 ≈ 24
Similarly, the three possible solutions:
(1,24), (8,18) , (6,20)
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