Answer:
The volume of the display case in cubic inches is 10,328 1/16 in.
A playground 88 ft long and 58 ft wide is to be resurfaced at a cost of $2.75 per sq ft. What will the resurfacing cost?
The resurfacing will cost $.
(Simplify your answer. Type an integer or a decimal.)
Answer: $1856
Step-by-step explanation: 88 x 58 = 5104. 5104/2.75= 1856
Random samples of resting heart rates are taken from two groups. Population 1 exercises regularly, and Population 2 does not. The data from these two samples is given below:
Population 1: 69, 68, 62, 68, 68, 62, 69
Population 2: 76, 68, 68, 72, 76, 70, 70, 70
Is there evidence, at an α=0.025
level of significance, to conclude that those who exercise regularly have lower resting heart rates? (Assume that the population variances are equal.) Carry out an appropriate hypothesis test, filling in the information requested.
A. The value of the standardized test statistic:
B. The rejection region for the standardized test statistic:
C. Your decision for the hypothesis test:
A. The value of the standardized test statistic is -2.391.
B. The rejection region for the standardized test statistic is t <-2.160.
C. The decision for the hypothesis test is to reject the null hypothesis.
How to explain the hypothesisEmploying a t-distribution table or calculator along with 13 degrees of freedom (n1 + n2 - 2) enables us to ascertain the rejection region for the t-statistic at an α=0.025 level of significance (two-tailed test):
Rejection Region: t < -2.160 or t > 2.160
Given that -2.391 falls in the rejection region, we repudiate the null hypothesis. At the α=0.025 level of significance, we are provided sufficient evidence to support that those who consistently partake in exercise generally have a lower resting heart rate than those who do not.
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A first-year teacher wants to retire in 40 years. The teacher plans to invest in an account with a 6.95% annual interest rate compounded continuously. If the teacher wants to retire with at
least $125,000 in the account, how much money must be initially invested? Round your answer to the nearest dollar.
O$10,234
O$10,755
O $7,902
O $7,755
The money invested by the teacher to have at least 125,000 in her account after 40 years of a 6.95% annual interest rate compounded continuously is 7755. Hence, the right solution to the question is option D
Compound interest is given by
A = P[tex](1+r)^t[/tex]
where A is the amount
P is the principal
r is the rate of interest
t is the time
Given in the question,
A = $125,000
r = 6.95% or 0.0695
t = 40 years
P is to be found
A = P[tex](1+r)^t[/tex]
125000 = P [tex](1 + 0.0695)^{40[/tex]
125000 = P * [tex]1.0695^{40[/tex]
125000 = 16.118P
P = 7755
The teacher should invest $7755 initially.
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What is a name for the marked angle?
an experienced bungee jumper leaps from a tall bridge and falls towards the water. The bridge is 241 feet above the water and the bungee cord is 149 feet long unstretched. When will the cord begin to strech? The gravity formula is as follows: h(t)= -16t + [tex]v_{0}[/tex]t + [tex]h_{0}[/tex]
The cord will begin to stretch after approximately 1.46 seconds.
How to solve for when the stretch startsh(t) = -16t^2 + V0t + h0
149 = h0 - h(t)
Substituting h0 = 241 and h(t) = -16t^2 + V0t into this equation, we get:
149 = 241 - (-16t^2 + V0t)
we get:
16t^2 - V0t - 92 = 0
4(16)(-92) / (2(16)
t = sqrt(1856) / 32
Using a calculator, we get:
t ≈ 1.46 seconds
Therefore, the cord will begin to stretch after approximately 1.46 seconds.
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Ben has some goldfish in a fish tank. The ratio of orange goldfish to yellow goldfish is 3:5.
He has 6f orange goldfish. Write the number of yellow goldfish he has in terms of f.
Answer:
Step-by-step explanation:
If the ratio of orange goldfish to yellow goldfish is 3:5, then we can write:orange goldfish : yellow goldfish = 3 : 5We know that Ben has 6f orange goldfish. We can use this information to set up a proportion and solve for the number of yellow goldfish in terms of f:3/5 = 6f/yellow goldfishTo solve for yellow goldfish, we can cross-multiply:3 * yellow goldfish = 5 * 6fSimplifying:yellow goldfish = 30f/3 = 10fTherefore, Ben has 10f yellow goldfish in terms of f, given that he has 6f orange goldfish and the ratio of orange to yellow goldfish is 3:5.
TONS OF POINTS - please help
The Cannon: Ernest's friend Nik is about to be shot out of a cannon. The path he will
travel follows a parabolic arch that can be described by this polynomial.
f(x) = -0.05(x2-26x-120)
He is supposed to land on a safety net 30 feet away. Does the function give you
enough information to tell you where he will land? If so, how far from the cannon will he land?
Make Sense of the Problem
3 points: 1 point for each answer.
-What do you know?
-What do you want to find out?
-What kind of answer do you expect?
1. The function f(x)=-0.05(x2-26x-120)
Represents the path coming out of the cannon. If x is the horizontal distance from the cannon, what does f(x) represent
2.what do the zeros of this function represent? Remember the zeros are where f(x)=0
3. Will the zeros tell you where the net should be placed? Why or why not?
4.to find zeros, set the function equal to 0, and then factor the polynomial start by setting the function equal to 0
5. Next factor the polynomial x2-26x-120. To identify the factors, complete the table: note this does not contain all the factors of -120, but it has enough to let you factor the polynomial
(I tried to type out the table )
pqp+q
P. q. p. |
————————— |
10. | 12 | blank. |
—————————.|
-10 | 12 |. Blank. |
—————————.|
30. |. -4. |. Blank. |
—————————-|
4. |. 30. | blank. |
—————————.|
6. Which values of p and w give the correct factors
7. Factor the polynomial completely
0=-0.05(x2 - 26x -120)
8. Find the roots of equation by setting each factor equal to 0 and solving for x.
Hint: there are three factors, but the constant factor, -0.05, does not equal zero
Solve for x with the other two factors
9. Identify the roots
Answer:
Step-by-step explanation:
2344
PLEASE HELP ITS DUE TODAY
For the quadratic equations shown here, which statement is true?
Question 2 options:
The graphs open downward.
The graphs open upward.
The graphs are listed from narrowest to widest.
The graphs are symmetric about the x-axis.
Answer:
The graphs open downward.
18. AB =
A
8
Los
D
B
1
Answer: the area of the triangle is 150 cm².
Step-by-step explanation:
To solve this problem, we need to use the formula for the area of a triangle:
Area = (1/2) x base x height
From the diagram, we can see that the base of the triangle is 20 cm and the height is 15 cm. Plugging these values into the formula, we get:
Area = (1/2) x 20 cm x 15 cm
Area = 150 cm²
Therefore, the area of the triangle is 150 cm².
139(x-28)
Please help would save a girls lifeee fr fr
Answer:
69
Step-by-step explanation:
(139) + (x-28) = 180 (adjacent angles on straight line add up to 180)
x - 28 = 41
x = 69
What is the probability that either event will occur?
12
A
4
B
24
P(A or B) = P(A) + P(B)
P(A or B) = [?]
Enter as a decimal rounded to the nearest hundredth.
From the given information, the probability that either event will occur is 0.7.
From the given Venn diagram,
Number of A = 4
Number of B = 24
Number of others = 12
Total number = A + B + others = 4 + 24 + 12 = 40
Probability of event A occurring = number of A / Total number = 4/40 = 1/10 = 0.1
Probability of event B occuring = number of B / Total number = 24/40 = 3/5 = 0.6
Now, the probability of either event will occur = P(A or B) = P(A) + P(B)
P(A or B) = 0.1 +0.6 = 0.7
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me no work math[tex]-3X+5y=-3\\y=-7+7[/tex]
The value of 'x' is 1 and value of y is '0'.
What is an equation?An equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.
We have the equations are:
-3x + 5y = -3 ___eq.1
and, y = -7 + 7 ___eq.2
We have to find the value of 'x' and 'y'
Now, Firstly find the value of y
We know that :
Opposite sign with same digit is cancel to each other it is always zero.
y = -7 + 7
So, y = 0
Now, We have to put the value of y in eq. 1
-3x + 5(0) = -3
-3x + 0 = -3
x = -3/-3
x = 1
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Faster please!! thanks!! 30 points + brainliest!!
Which is an example of simple random sampling created from each given population?
An example of simple random sampling is given as follows:
C. In a bag of more than 500 marbles, reaching the hand into a bag and drawing 25 of them.
How are samples classified?Samples may be classified as:
A convenient sample is drawn from a conveniently available pool of options.A random sample is equivalent to placing all options into a hat and taking some of them.In a systematic sample, every kth element of the sample is taken.Cluster sampling divides population into groups, called clusters, and each element of the group is surveyed.Stratified sampling also divides the population into groups. However, an equal proportion of each group is surveyed.Hence the samples for this problem are classified as follows:
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Find a quadratic equation which has solutions x=4/9 and x=9/2. Write the quadratic form in the simplest standard form x^2+bx+c
Answer:
[tex](x - \frac{4}{9} )(x - \frac{9}{2} ) = 0[/tex]
[tex] {x}^{2} - \frac{89}{18} x + 2 = 0[/tex]
Which measure should Raul use to find how much the distance that the ball travels during each hit varies, on average, from the mean distance?
We can see here that the measure that Raul should use to find the distance that the ball travels during each hit varies, on average, from the mean distance is the measure of variability known as standard deviation.
What is mean?The mean, commonly referred to as the arithmetic mean or average, is a statistic that depicts the usual or centre value of a dataset. It is determined by adding up all of the dataset's values, then dividing by all of the values.
We can see here that standard deviation actually refers to the statistical measure that represents the amount of dispersion or variability in a dataset.
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Determine that the value x=9 of the following expiration given x2+3x-5
Step-by-step explanation:
To determine the value of x that satisfies the expression x^2 + 3x - 5 when x = 9, we simply substitute 9 for x and evaluate the expression:
9^2 + 3(9) - 5 = 81 + 27 - 5 = 103
Therefore, when x = 9, the expression x^2 + 3x - 5 evaluates to 103.
rate my answer, please.
Express sin
�
L as a fraction in simplest terms.
Answer:
3/5
Step-by-step explanation:
opposite/hypotenuse
21/35
Simplify by dividing by 7 on the numerator and denominator
3/5
You would like to estimate the prevalence of a disease. You randomly sample 10 people from the population of interest and 4 of them have the condition. Using a Beta prior with αα and ββ both being 1010, what is the posterior mean prevalence closest to?
The required posterior mean prevalence is closest to 0.47.
We can use Bayes' theorem to find the posterior distribution of the prevalence parameter, given the data and the Beta prior:
posterior ∝ likelihood x prior
where the likelihood is given by the binomial distribution:
likelihood = P(observing 4 cases out of 10 | prevalence)
and the prior is a Beta distribution with parameters α = β = 10:
prior = Beta(α=10, β=10)
We can calculate the posterior distribution by multiplying the likelihood and prior, and then normalizing:
posterior = Beta(α=14, β=16)
where the posterior Beta distribution has parameters α=14 (10 + 4) and β=16 (10 + 10 - 4).
The posterior mean of a Beta distribution with parameters α and β is:
posterior mean = α / (α + β)
Plugging in the values of α and β from the posterior distribution, we get:
posterior mean = 14 / (14 + 16) = 0.467
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Find the 12th term of the geometric sequence 7,−21,63,
The 12th term of the geometric sequence is -1,240,029
How to find the 12th term of the sequence?The general formula for the nth therm is:
A(n) = A(1)*(r)^(n - 1)
Where A(1) is the first term, in this case 7.
r is the common ratio, to get it, take the quotient between two consecutive terms:
-21/7 = -3
Then the formula is:
A(n) = 7*(-3)^(n - 1)
The 12th term will be:
A(12) = 7*(-3)^(12 - 1) = -1,240,029
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Need Help!!!! A pre-image has coordinates J(3, -6) and K(-1, -2). The image has coordinates J'(6, 3) and K'(2, -1). Describe the clockwise rotational path of the line segment.
After considering the given data we conclude that the clockwise rotational path of the line segment is a rotation of -59.04 degrees about the point (-6, -1).
We have to evaluate the center and angle of rotation to explain the clockwise rotation of the line segment.
So in the first step, we can evaluate the midpoint of the line segment JK and the midpoint of the line segment J'K'. we can calculate the vector connecting the midpoint of JK to the midpoint of J'K'. This vector is (4-1, 1-(-4) = (3,5)
The center of rotation is the point that is equidistant from the midpoints of JK and J'K'. We can evaluate this point by finding the perpendicular bisector of the line segment connecting the midpoints.
The slope of this line is the negative reciprocal of the slope of the vector we just found, which is -3/5. We can apply the midpoint formula and the point-slope formula to evaluate the equation of the perpendicular bisector:
Midpoint of JK: (1, -4)
Midpoint of J'K': (4, 1)
The slope of the vector: 3/5
(x₁ + x₂)/2, (y₁ + y₂) /2
Point-slope formula: y - y₁ = m(x - x₁)
Perpendicular bisector: y - (-4) = (- 3/5)(x - 1)
Applying simplification , we get: y = (- 3/5)x - 1.2
To evaluate the center of rotation, we need to find the intersection point of the perpendicular bisector and the line passing through the midpoints of JK and J'K'. This line has slope ( 3 - (4)) /(4 - 1) = 7/3 and passes through the point (4, 1). Applying the point-slope formula, we can evaluate its equation:
y - 1 = (7/3)( x - 4)
Apply simplification , we get: y = (7/3)x - 17/3
To evaluate the intersection point, we can solve the system of equations:
y =(- 3/5)x - 1.2 = (7/3)x - 17/3
Evaluating for x and y, we get x = -6 and y = -1.
Therefore, the center of rotation is (-6, -1).
√( 4 - 1)² + ( 1 - ( - 4))²) = 5√(2)
Distance between image points and center of rotation
√( ( 6 - (-6))² + ( 3 - (-1))² = 13
The ratio of these distances gives us the scale factor of the transformation, which is 13/√2).
The angle of rotation is negative as the image moves clockwise direction. We can apply the inverse tangent function to find the angle of the vector connecting the midpoint of JK to the midpoint of J'K':
Angle of vector: arctan(5/3) = 59.04 degrees
Therefore, the clockwise rotational path of the line segment is a rotation of -59.04 degrees about the point (-6, -1).
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Lawrence is increasing the rectangular patio in his backyard. His patio is currently 12
feet by 10 feet. He wants to increase the patio by adding a decorative tile the same width (x) all the way around creating a total area of 180 square feet. Select all the quadratic equations that represent Lawrence’s new patio area.
The quadratic equation representing the new patio area after adding a decorative tile of width x all the way around is: 0 = 4x^2 + 44x - 60
Options A and E are correct.
What is a Quadratic Function?In mathematics, a polynomial of degree two in one or more variables is referred to as a quadratic polynomial. The polynomial function that a quadratic polynomial defines is known as a quadratic function.
Since the area of the new patio is given as 180 square feet, we can create a quadratic equation to represent the new patio area:
Area = length × width
180 = (12 + 2x) × (10 + 2x)
After we expand, the answer is given as 0 = 4x^2 + 44x - 60
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A circle has an area of 45 square meters. What is the area of a sector with an arc measure of 70 degree?
______m^2
The area of a sector is 8.75 [tex]m^{2}[/tex].
What is a sector?A sector is a part of a given circle which is bounded by two radii and an arc. The area of a sector can be determined by;
area of a sector = (θ/ 360)π[tex]r^{2}[/tex]
where r is the radius, and θ is the central angle.
Given a circle whose area is 45 sq. m.; then;
area of a circle = π[tex]r^{2}[/tex]
45 = π[tex]r^{2}[/tex]
r = [tex]\sqrt{\frac{45}{\pi } }[/tex]
Then,
area of a sector = (θ/ 360)π[tex]r^{2}[/tex]
= ([tex]\frac{70}{360}[/tex])*π*[tex][\sqrt{\frac{45}{\pi } }] ^{2}[/tex]
= [tex]\frac{7}{36}[/tex]*π*45/π
= [tex]\frac{7}{36}[/tex]*45
= 8.75 sq. m.
The area of the sector is 8.75 [tex]m^{2}[/tex].
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the Clarks bought a 242000 condominium. They made a down payment of 45000 and took out a mortgage for the rest. Over the course of 30 years they made monthly payments of 1175.13 on their mortgage until it was paid off. branly
The total cost paid on the condominium is $468,046.80.
What was the total cost of the condominium?The total cost means total expenditure incurred to produce some type of output. The total cost is calculated as follows:
The total number of monthly payments is:
= 30 years x 12 months/year
= 360 months
The total amount paid towards mortgage is:
= 360 x $1175.13
= $423,046.80
The total cost of the condominium will be:
= Down payment + Total amount paid towards mortgage
= $45,000 + $423,046.80
= $468,046.80.
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A cone has a diameter of 16 cm and a height of 35 cm. What is its volume?
Answer: if with 3.14 v= 37512.5333
if with pi v= 37531.56
Step-by-step explanation:
the formula is 1/3hπr^2
r= 2d so radius is 32
plus numbers in (square it multiple times pi or 3.14 then multiply times height and divide by 3)
Use properties of exponents to verify that 2s − 1 and _1
2 (2)
s
are equivalent.
The properties of the exponents are solved and the expression is given by the relation ( 2s )⁻¹ = 1 / 2s
Given data ,
Let the expression be represented as A
Now , the value of A is
( 2s )⁻¹ = 1 / 2s
From the laws of exponents , we get
m⁻ᵃ = ( 1 / mᵃ )
So , on simplifying , we get
( 2s )⁻¹ = 1/ ( 2s )
On further simplification , we get
1/ ( 2s ) = ( 2s )⁻¹
Hence , the expression is ( 2s )⁻¹ = 1/ ( 2s )
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The complete question is attached below :
Use properties of exponents to verify that ( 2s )⁻¹ = 1/ ( 2s ) are equivalent.
8) A hexagonal pyramid 10 mi tall with a regular
base measuring 6 mi on each side and an
apothem of length 5.2 mi.
A) 936 mi³
C) 315 mi³
B) 312 mi³
D) 52 mi³
The volume of the pyramid is 936 mi³
What is volume of a pyramid?A pyramid has a polygonal base and flat triangular faces, which join at a common point called the apex.
The volume of a pyramid is expressed as;
V = 1/3bh
where b is the base area and h is the height of the pyramid.
Area of the hexagon = 1/2 × p × a
perimeter = 6 × 6 = 36 mi
area = 1/2 × p × a
= 1/2 × 36 × 5.2
= 187.2/2
= 93.6 mi²
Volume = 93.6 × 10
= 936 mi³
therefore the volume of the pyramid is 936 mi³
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A flower bed is in the shape of a triangle with one side twice the length of the shortest side and the third side is feet more than the length of the shortest side. Find the dimensions if the perimeter is feet.
I got you, buddy!
Let x be the length of the shortest side. Then, the length of the second side is 2x, and the length of the third side is x + y, where y is the additional length.
The perimeter of the triangle is the sum of the three sides, so we have:
x + 2x + (x + y) = 60
Simplifying this equation, we get:
4x + y = 60
We also know that the area of a triangle is given by:
A = (1/2)bh
where b is the length of the base, and h is the height. Since the base of the flower bed is the shortest side of length x, we can choose the height to be y. Therefore, we have:
A = (1/2)xy
Now we need to solve for x and y. We can use the equation for the perimeter to solve for y:
y = 60 - 4x
Substituting this into the equation for the area, we have:
A = (1/2)x(60 - 4x)
Simplifying and expanding, we get:
A = 30x - 2x^2
To maximize the area, we can take the derivative of A with respect to x and set it equal to 0:
dA/dx = 30 - 4x = 0
Solving for x, we get:
x = 7.5
Substituting this back into the equation for y, we get:
y = 60 - 4x = 45
Therefore, the dimensions of the flower bed are:
shortest side = x = 7.5 feet second side = 2x = 15 feet third side = x + y = 52.5 feet
Ethan's class is handing out balloon arrangements consisting of 4 balloons each. Each balloon has an equally likely chance of being red, blue, or yellow. Ethan created a spinner to simulate this probability. Here is Ethan's data from 30 trials of 4 spins on the spinner (r = red, b = blue, y = yellow):
ybrr bybb rbbb rrry rbbb rryy yybb ryry ryyr rbyr ryyr rryy rrrr yrby bbyy byyr byyr byyb rbby ybry rryy rbrr rybb bbbr rrbr ybry ryrr rryb rrrb rryr
According to this data, what is the experimental probability that an arrangement will consist entirely of balloons that are the same color?
0.012
0.1
0.033
0.33
The requried, experimental probability is 0.1. Option B is correct.
To find the experimental probability that an arrangement will consist entirely of balloons that are the same color, we need to count the number of times that Ethan got an arrangement where all four balloons were the same color and divide that by the total number of trials.
Looking through the data, we can see that the following trials had all four balloons the same color:
rrrr
bbbb
yyyy
So, out of 30 trials, there were 3 trials where all four balloons were the same color. Therefore, the experimental probability is:
3/30 = 0.1
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This is for the following two questions.
A couple plans to retire in 35 years. At that time, they would like to have enough money in an account so that they can receive a $6,000 every month end for the next 25 years. The account earns 8% APR compounded monthly and will continue to do so until there is a zero balance in the account.
To achieve this goal, how much money does the couple need to have in this account by the time they retire?
If they have not saved any money yet, how much does the couple need to deposit each month end until they retire?
The couple needs to deposit about $554.49 each month end until they retire to reach their goal.
How to solveTo find the monthly deposit needed, we'll use the future value of an ordinary annuity formula:
FV = PMT * [((1 + r)^n - 1) / r]
We already know the future value (FV) as $953,776.53, and we want to solve for PMT, the monthly deposit:
PMT = FV / [((1 + r)^n - 1) / r]
We'll use the same r (0.08/12) and a new n (35 * 12) for the 35 years until retirement:
PMT = 953776.53 / [((1 + 0.08/12)^(35*12) - 1) / (0.08/12)]
PMT ≈ 554.49
Thus, the couple needs to deposit about $554.49 each month end until they retire to reach their goal.
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Needing help finding this answer!
Answer:
78.947%
Step-by-step explanation:
It says A OR B, so:
5/19 + 6/19 + 4/19
11/19 + 4/19
15/19 = approx. 0.78947 = 78.947%
