With 90% confidence, the mean time it takes to run 1 mile for all high school track athletes is between 5.4 and 7.0 minutes.
We have a 90% confidence interval of 6.2 ± 0.8 minutes for the mean time it takes high school track athletes to run 1 mile.
A conclusion based on this information is to be given. A 90% confidence interval implies that if we were to take a large number of samples from the same population, we would expect that 90% of the intervals produced would include the true population mean.
When constructing confidence intervals, there are two components to consider: the interval itself and the level of confidence. The interval refers to the range of values that we are reasonably certain that the true value of the population parameter lies in, while the confidence level indicates the probability that the true population parameter falls within that range.
We can conclude that we are 90% confident that the true population mean of the time it takes high school track athletes to run 1 mile falls within the interval of 6.2 ± 0.8 minutes, that is, between 5.4 and 7.0 minutes.
Since the interval does not include 6 minutes, we can not conclude that the true population mean of the time it takes high school track athletes to run 1 mile is 6 minutes.
However, we can state with 90% confidence that it falls somewhere within the interval of 5.4 to 7.0 minutes.
The conclusion is that with 90% confidence, the mean time it takes to run 1 mile for all high school track athletes is between 5.4 and 7.0 minutes.
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6. At the local community center, they've decided to build a pool in the
shape of a rectangular prism. The length of the pool is 27 feet and the
depth is 12 feet. Also, the area of the base of the pool must be 864 square
feet. What is the width of the pool?
32 feet
64 feet
13.7 feet
123 feet
Answer:
width = 32 ft
Step-by-step explanation:
Divide the base area (864 ft^2) by the length (27 ft). We don't need to know the depth of the pool to solve this problem.
864 ft^2
------------- = width = 32 ft
27 ft
A manufacturer makes ball bearings out of motel steel. it takes 5.24 cubic centimeters of molten steel to make ball bearings that each have a diameter of 1 centimeter
Using volume of ball bearings, a manufacturer makes 10 ball bearings from 5.2 cm³ of molten steel to make ball bearings that each have a diameter of 1 centimeter.
According to the question,
It takes 5.24 cubic centimeters of molten steel to make ball bearings that each have a diameter of 1 centimeter.
Radius = 1/2 = 0.5 cm
volume V of one ball bearing is: V=(4/3)*π*r³
= 4/3 * π * (0.5)³
=0.524 cm³
In order to find number of ball bearings out of molten steel only if we divide the volume of steel by the volume of the ball bearing
5.24/0.524=10.
Hence, using volume of ball bearings, a manufacturer makes 10 ball bearings from 5.2 cm³ of molten steel to make ball bearings that each have a diameter of 1 centimeter.
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Which side lengths form a right triangle?
Choose all answers that apply:
A:
11,13,√290
B:
7, 24, 25
C: 2, 5, 7
The side lengths that forms a right triangle are as follows:
11, 13 √2907, 24, 25What is a right angle triangle?A right angle triangle has one of its angle as 90 degrees. The sides of the triangle follows Pythagoras theorem.
Therefore,
c² = a² + b²
where
a and b are the legsc is the hypotenuseThe hypotenuse is the longest side of the right triangle.
Therefore, the side lengths that forms a right triangle are as follows:
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What is the area of this triangle?
Answer:
12 units^2
Step-by-step explanation:
Area of a triangle = 1/2 * base * height
base goes from -4 to +4 = 8 units
Height goes from 1 to 4 = 3 units
area = 1/2 * 8 * 3 = 12 units^2
In circuit training, exercises are usually set up so that the same muscle group is worked in back to back exercises.
In circuit training, exercises are usually set up so that the same muscle group is worked in back to back exercises is a "false" statement.
What is circuit training?A circuit workout consists of six or more exercises that are alternated with brief rest intervals and performed for either a predetermined number of reps or a certain duration of time.
Some features of circuit training exercise are-
It is a great approach to increase muscular strength and endurance as well as cardiovascular health. Due to the brief rest times, the use of major muscles in conjunction with smaller ones, and the mix of upper, lower, and whole-body movements in circuit training, your heart rate will increase and remain elevated during the entire circuit.Once all of the selected exercises have been finished, a circuit has been completed. A single training session may involve several circuits.Benefits of doing circuit training exercise-
Training in strength.Cardiovascular Health, Time Efficiency, Friendly Environment, Avoids BoredomTo know more about the circuit training, here
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The complete question is -
In circuit training, exercises are usually set up so that the same muscle group is worked in back to back exercises.(True/False)
Which of the following is a perfect square trinomial?
a. x^2+10x+25
b. x^2+6x+13
c. x^2+100
d. x^2+3x+9
Answer:
a. x² + 10x + 25
Step-by-step explanation:
because
(x + 5)² = (x + 5)(x + 5) = x² + 5x + 5x + 25 = x² + 10x + 25
so, it is a perfect square of (x + 5).
Vertical plane R intersects horizontal plane P. Points A, D, and B are on the line of the intersecting planes. Point F is on the top half of plane R. Point G is on the bottom half of plane G. Point C is on the left half of plane P. Point E is on the right half of plane P. Point H is above and to the right of the planes. Point J is below and to the left of the planes. Which statements are true based on the diagram? Check all that apply. Points A, B, and D are on both planes. Point H is not on plane R. Plane P contains point F. Points C, D, and A are noncollinear. The line containing points F and G is on plane R. The line containing points F and H is on plane R.
The true statement about the plane include:
Points A, B, and D are on both planes. Point H is not on plane R.The line containing points F and G is on plane R.The line containing points F and H is on plane R.What is a vertical plane?It should be noted that a vertical plane simply passes through a vertical line.
In this case, Point H is not on plane R and the e line containing points F and G is on plane R.
The correct options are 1,2,4, and 5.
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Answer:
a,b,d,e
Step-by-step explanation:
In a mathematics test, Jack scored 17 marks more than Yazid while Susan scored twice Yazid's score. If their total score is 161, what is Jack's score?
Answer:
53
Step-by-step explanation:
Let yazid's score be x
x + x + 17 + 2x = 161
4x + 17 = 161
4x = 144
x = 36
jack = x + 17
jack = 53
Answer:
Jack: 36
Bonus: Yazid: 53 and Susan: 72
Step-by-step explanation:
Let J, Y, and K stand for Jack, Yazin, Susan's scores.
We are told that:
J = Y + 17 [Jack scored 17 marks more than Yazid]
S = 2Y [Susan scored twice Yazid's score]
J + Y + S = 161 [total score is 161]
Substitute the first two expressions into the last equation:
J + Y + S = 161
(Y+17) + Y + (2Y) = 161
4Y = 144
Y = 36
Use Y = 36 to find the other scores:
J = Y + 17
J = 36 + 17
J = 53
S = 2Y
S = 2*(36)
S = 72
CHECK:
Does 36+53+72 = 161?
YES
Identify the relationship between the variable:_____ is a function of __
Ps need asap
A correlation is simply used to determine whether a relationship exists between the variables.
How to illustrate the information?The information is incomplete and an overview will be given. The correlation shows the relationship between the variable.
This can be explained in a numerical form that's known as the correlation coefficient. This shows that strength of the relationship.
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I have no idea how to do this
The solution for the given equation X^3 + Y^2 = 971,028. So, option A is correct.
What are multiples?A multiple of a number is the number whose remainder is 0 when divided by the given number.
Consider 'a' as the multiple of a number 'n'.
Then, a ÷ n = b (and remainder = 0)
Calculation:It is given that,
X = largest 2-digit multiple of 3 which is not a multiple of 5
⇒ X = 99
Y = smallest 2-digit multiple of 9 which is not a multiple of 6
⇒ Y = 27
Then, substituting the values in the given equation,
= X^3 + Y^2
= (99)³ + (27)²
= 970,299 + 729
= 971,028
Therefore, the value of the given equation is 971,028.
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Suppose 60% of the freshmen at msu take a course in outdoor survival skills. the probability that a freshman selected at random who did not get lost during a hike is 90%. the probability that a freshman selected at random who took the course and did not get lost is 50%.
Probability that a freshman selected at random who took the course and did not get lost and Probability of freshmen who took course at MSU in outdoor survival skills is 0.8333
According to the question,
Probability of freshmen who took course at MSU in outdoor survival skills is 0.6.
Probability that a freshmen selected at random who did not get lost during a hike is 0.9.
Probability that a freshman selected at random who took the course and did not get lost is 0.50
Conditional probability = P(A and B)/ P(A)
P(did not get lost/took the course) = P( freshmen did not get lost who took the course and freshmen took the course)/P(freshmen did not get lost)
= 0.5/0.6
= 0.8333
Hence, Probability that a freshman selected at random who took the course and did not get lost and Probability of freshmen who took course at MSU in outdoor survival skills is 0.8333
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A car can travel 161 miles on 7 gallons of gas. how much gas will it need to go 368 miles?
Answer:
16 gallons of gas
Step-by-step explanation:
Two ways to answer this
1:
Find how many miles per gallon the car can go. Then, divide the amount the car needs to go with the miles per gallon. This gets you the gallons of gas needed to go the amount. In this case, 161 ÷ 7 = 23. 368 ÷ 23 = 16.
2:
Make a proportion. [tex]\frac{161}{7} = \frac{368}{x}[/tex]. Solve for x. 161 and 7 cancel out to get 23. [tex]\frac{23}{1} = \frac{368}{x}[/tex]. Now you can either divide 368 and 23 and multiply the quotient by 1 to get x, or you can cross multiply to get an equation you can solve. In the first case, 368 ÷ 23=16. 1*16=16. x=16. In the second case, 23x=368. Divide both sides by 23 and you get x = 16.
Determine whether the triangles can be proved similar. If they are similar, write a similarity statement. If they are not similar, explain why.
Answer:
They are similar. Triangle abc is similar to triangle edc.
Step-by-step explanation:
To prove that triangles are similar, you must show that the 3 angles in one triangle are equal to the 3 angles in the other triangle. We know that they both have a 50 degree angle. We can also see that they both have a right angle. That means that the 3rd angle must also equal 40 (180-90-50). So by AAA the two triangles are congruent.
Triangle ABC is similar to triangle EDC.
Answer:
triangle ABC is similar to triangle DCE
Step-by-step explanation:
Reason being that angles in triangle ABC Correspond to That of triangle DCE Eg triangle ABC=CDE
Which rule can be used to describe the growth of the y-values of the function y=12^(x) each interval from x=-1 to x=3
A rule which describes the growth of the y-values of the function y=12^x over each interval is "multiply by 12."
How to determine the rule?By critically observing the given function, we can logically deduce that it is an exponential function. Also, the initial value of this exponential function is 1 with a growth factor is 12.
For instance, we have:
At x = -1
y = 12^(-1)
y = 1/12
At x=0
y = 12^(0)
y = 1
At x = 1
y = 12^(1)
y = 12
In conclusion, a rule which describes the growth of the y-values of the function y=12^x over each interval is "multiply by 12."
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Find the volume of a rectangular prism with the following dimension 2cm by 3cm by 4cm
Answer:
24 cm³
Step-by-step explanation:
V = LWH = 2 × 3 × 4 cm³ = 24 cm³
Find the perimeter of the rhombus below, given that a = 7 and b = 14. (round your answer to one decimal place, if necessary.)
If the value of a is 7, b is 14 in the rhombus then the perimeter of the rhombus is equal to 31.3 units.
Given that the value of a is 7,b is 14.
We are required to find the perimeter of the rhombus.
The values which are given to us are of the lengths of diagonals of rhombus.
Perimeter of the rhombus is equal to 4 times the side of the rhombus. So in order to find the perimeter of the rhombus we need the side of the rhombus not the diagonals.
When we draw the diagonals in the rhombus it forms four right angled triangle in which the Base is equal to 7/2 units and 7 is the perpendicular.
We have to use pythagoras theorem to find the hypotenuse which is the side of the rhombus.
Suppose base is BC , perpendicular is AB and hypotenuse is AC.
AC=[tex]\sqrt{7^{2} +7/2^{2} }[/tex]
=[tex]\sqrt{49+49/4}[/tex]
=[tex]\sqrt{245/4}[/tex]
=7.826
Perimeter of rhombus=4*side
=4*7.826
=31.304
After rounding off it will be 31.3 units.
Hence if the value of a is 7, b is 14 in the rhombus then the perimeter of the rhombus is equal to 31.3 units.
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Is it possible to make a number out of 8 different digits that is
divisible by each of the eight digits?
Answer:
1,123,449,768
Step-by-step explanation:
The smallest number composed from 8 different digits that is divisible by each of those digits appears to be the 10-digit number ...
1,123,449,768
RestrictionsIf the number is to be divisible by an even digit, it must be even. That means it cannot end in the digit 5, so 5 cannot be one of the digits. We disallow division by 0, so 0 cannot be one of the digits.
The remaining 8 digits total 40, so cannot form a number divisible by 3, 6, or 9. In order to make such a number, we must add 5 to the digit total, but cannot do so using the single digit 5.
Choices for added digits include {1, 4} and {2, 3}. Adding 9+5 = 14 to the digit total would also work but would guarantee the resulting number is not the minimum possible.
Further divisibility restrictionsThe digits we have to work with are now {1, 1, 2, 3, 4, 4, 6, 7, 8. 9}. We know that an even number constructed from these digits will be divisible by 1, 2, 3, 6, and 9. To make it divisible by 4, 7, and 8, it must be a multiple of the LCM of those numbers.
The least possible number will use the smallest digits first, so will start ...
112344...
The remaining digits, 6, 7, 8, 9, need to form a number that will be divisible by 56 when appended to the 6 digits already used. Those 6 digits form a number, 1123440000, that has a remainder of 32 when divided by 56. Hence we need to use the digits 6, 7, 8, 9 to make a number with a remainder of 24 when divided by 56. There are 24 permutations of the digits 6, 7, 8, 9. Half of these are odd numbers
The one number formed from digits 6, 7, 8, 9 that is divisible by 56 with a remainder of 24 is 9768.
Smallest NumberThe smallest number comprised of 8 different digits and divisible by each of them is the 10-digit number 1,123,449,768.
During a very cold winter, water pipes sometimes burst because:
The water pipe sometimes bursts in winter because of the flowing water getting transformed into freezing water due to drop in temperature and the volume increases creating more pressure on the wall pipes.
Bursting of Water Pipes During a Very Cold Winter
The straightforward explanation is that during very cold winters, as water freezes into ice, it expands, causing solid ice to fill a larger volume than the liquid that was previously flowing through the pipes.
As we know that, the pressure P increases with increase in volume, V, the increased volume of frozen water leads to increase in the pressure inside the pipe.
The pressure that the ice builds up inside the pipes could rupture the pipe walls.
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A boss plans a business meeting at Starbucks with the two engineers below him. However, he fails to set a time, and all three arrive at Starbucks at a random time between and p.m. When the boss shows up, if both engineers are not already there, he storms out and cancels the meeting. Each engineer is willing to stay at Starbucks alone for an hour, but if the other engineer has not arrived by that time, he will leave. What is the probability that the meeting takes place
The probability that the meeting takes place is 7/24.
What is the probability?Probability is defined as the ratio of the number of favorable outcomes of an event to the total number of possible outcomes(sample space) of the event.
It is given by
P(A) = n(A)/n(S)
Where A - event, S - sample space
Calculation:From the given data,
The probability, if the engineers arrive in the first hour and the boss arrives in the second hour is 1/8,
So, the meeting will be held i.e., p = 1.
The probability, if all the three arrive in the same hour (first or second)
= 1/8 + 1/8
= 1/4
So, the meeting will be held only if the boss (he may arrive first, second, or last) arrives last, the probability is 1/3
The probability, if one of the engineers arrives in the first hour while the other engineer and the boss arrive in the second hour is
= 1/4
So, the meeting will be held only if the second engineer arrives before the boss and before the first engineer leaves, the probability is 1/3
Thus, the final probability for the meeting to take place is
= (1/8) × 1 + (1/4) × (1/3) + (1/4) × (1/3)
= 7/24
Therefore, the required probability is 7/24.
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Please help me
The sum of an integer and its square is 210. Find the integer. Include a completer
solution
Answer:
14
Step-by-step explanation:
An integers are whole numbers and their opposites. ...-3,-2,-2,0,1,2,3...
I just played with the numbers and found that 14 + 14^2 (14 squared is 14 x 14).
14 + (14)(14) = 210
Answer:
refer to the attachment
A DVD player costs $96.34, with sales tax included. What is the original price of the DVD player if the sales tax rate is 8.25%?
The original price of the DVD player if the sales tax rate is 8.25% is $88.79
Sales taxCost of DVD player including tax = $96.34Sales tax = 8.25%Original cost = 8.25%Total cost = original cost + (sales tax × original cost
96.34 = x + (8.5% × x)
96.34 = x + (0.085 × x)
96.34 = x + 0.085x
96.34 = 1.085x
x = 96.34 / 1.085
x = 88.7926267281105
Approximately,
x = $88.79
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Please please please help with b
The diameters of two circular pulleys are 6cm and 12 cm, and their centres
are 10cm apart.
a. Angle a = 72.54 degrees
b. Hence find, in centimetres correct to one decimal place, the length of a
taut belt around the two pulleys
The length of the belt around the two pulleys is approximately 49.2 centimeters.
How to determine the length of the belt around the two pulleys?
In this question we must determine the perimeter of a belt around two pulleys, whose centers are 10 centimeters apart. This perimeter is the sum of part of the circumference of small pulley, part of the circumference of the big pulley and two times the segment tangent to the two pulleys.
Now we proceed to determine the parts of the perimeter of the belt:
Big pulley
s' = (214.92° / 180°) · π · (6 cm)
s' ≈ 22.506 cm
Small pulley
s'' = (145.08° / 180°) · π · (3 cm)
s'' ≈ 7.596 cm
Tangent segments
l = (10 cm) · sin 72.54°
l ≈ 9.539 cm
Lastly, the perimeter of the belt is:
L = s' + s'' + 2 · l (1)
L = 22.506 cm + 7.596 cm + 2 · (9.539 cm)
L = 49.180 cm
The length of the belt around the two pulleys is approximately 49.2 centimeters.
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Using Euler's formula, how many
edges does a polyhedron with 6
faces and 8 vertices have?
[?] edges
Euler's Formula: F + V = E + 2
Answer:
F+V=E+2
F=6
V=8
E=?
PUT THEIR VALUE
6+8=E+2
= 14=E+2
=14-2=E
=12=E
VALUE OF E IS 12
Kindly solve this please!
Diagram for both the questions are given.
Answer:
Q9 - B) 8Q10 - D) 4.5========================
Question 9We have a diagram and need to find the number of routes without repeat paths:
[tex]ABCA[/tex] or [tex]ACBA[/tex]We can see that there is one route from A to B, two routes from B to C and two routes from C to A. This is same on reverse order.
This gives us the number of routes:
[tex]ABCA = 1*2*2 = 4[/tex][tex]ACBA = 2*2*1 = 4[/tex]Total number is:
[tex]4 + 4 = 8[/tex]The matching answer choice is B
---------------------------------------------------------------------------
Question 10From the given we can observe that:
ABC and DCE are similar triangles, since they have same angle at vertex E (vertical angles are equal) and both are right triangles.
From similarity we get same ratio of corresponding sides:
[tex]AE/DE = AB/CD = 3/9 = 1/3[/tex]We can find areas of triangles ACD and ECD and subtract to get the area of triangle AEC:
[tex]S_{ACD} - S_{ECD} = S_{AEC}[/tex]As per ratio of corresponding sides:
[tex]AE/DE = 1/3[/tex]As per segment addition:
[tex]AE + DE = AD = 4[/tex]From the two equations above we get:
[tex]DE = 3/4*AD = 3/4*4 = 3[/tex]Now, the required area is:
[tex]S_{ACD} - S_{ECD} = 1/2(4*9) - 1/2(3*9) = 4.5[/tex]This is matching the answer choice D
Answer:
9) B. 8
10) D. 4.5
Step-by-step explanation:
Question 9
For ease of visualization, label the different legs of the journey on the diagram (see attachment).
The journey needs to start and end at point A, go through points B and C (in any order), and not travel any road twice.
The different routes are:
AB (u), BC (x), CA (w)AB (u), BC (y), CA (w)AB (u), BC (x), CA (z)AB (u), BC (y), CA (z)AC (w), CB (x), BA (u)AC (z), CB (x), BA (u)AC (w), CB (y), BA (u)AC (z), CB (y), BA (u)Therefore, there are 8 different routes.
Question 10
Triangles EDC and EAB are similar since they have congruent angles:
∠EDC ≅ ∠EAB (both right angles)∠DEC ≅ ∠AEB (vertical angle theorem)Therefore, their corresponding sides are in proportion.
⇒ CD : BA = ED : EA
⇒ 9 : 3 = ED : EA
⇒ 3 : 1 = ED : EA
Since we know that AD = 4:
⇒ ED = 3
⇒ EA = 1
Area of a triangle
[tex]\sf Area = \dfrac{1}{2} \times base \times height[/tex]
To find the area of triangle AEC, subtract the area of triangle EDC from the area of triangle ADC.
[tex]\begin{aligned}\textsf{Area of triangle AEC} & = \sf Area\:of\:\triangle ADC - Area\:of\:\triangle EDC\\& = \sf \dfrac{1}{2} \cdot CD \cdot AD-\dfrac{1}{2} \cdot CD \cdot ED\\& = \sf \dfrac{1}{2}(9)(4)-\dfrac{1}{2}(9)(3)\\& = \sf 18-13.4\\& = \sf 4.5\:\:units\:squared\end{aligned}[/tex]
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Which statement is true regarding the graphed functions?
I need help and can’t find the answers anywhere
Answer:
f(0)=g(0)
Step-by-step explanation:
The problem is asking for where the output (y value) of one function, f(x), matches the output of another function, g(x), otherwise called an intersection. You can see that the two lines intersect at 0 on the x axis in the graph, therefore f(0)=g(0) meaning the outputs of f(x) are the same as g(x) at x value 0.
Question 5 of 10
Identify an equation in slope-intercept form for the line parallel to y = 5x + 2
that passes through (-6, -1).
A. y = 5x + 29
B. y = -5x - 11
C. y = x +
OD. y = 5x - 29
SUMIT
Answer:
A
Step-by-step explanation:
Parallel lines have the same slope, so the slope of the line we need to find is 5.
[tex]y+1=5(x+6) \\ \\ y+1=5x+30 \\ \\ y=5x+29[/tex]
Adding and Subtracting Functions
F(x)=x^2+4
G(x)=x-1
Find (g+f)(x)
Answer:
Step-by-step explanation:
[tex](g+f)(x)=g(x)+f(x)=x-1+x^2 +4=x^2 +x+3[/tex][tex]x^2 +x+3[/tex]
10 POINTS
please help me!!
Find the measure of the arc or central angle indicated. Assume that lines which appear to be diameters are actual diameters.
Find the measure of arc CFD.
The measure of the Central Angle indicated is; 45°
How to find the central angle of a circle?
The central angle will be the angle subtended at the center by arc FE and arc CB.
Now, we see that angle ∠FOB = 135° and since we know that sum of angles on a straight line is 180°, then we can say that;
Central Angle = 180° - 135° = 45°
Angle subtended by Arc CD at the center is;
θ = 180 - (81 + 45)
θ = 54°
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Please help!
Which of these r-values represents the weakest correlation?
A. 0.2
B. 0.3
C. 0.4
D. 0.1
Answer: 0.1
Step-by-step explanation:
The smaller the absolute value of the correlation coefficient, the weaker the correlation.