The range of the square footage values for the given mean , standard deviation and 95% confidence interval is equal to (1257.26 , 508.74).
As given in the question,
Sample size 'n' = 2
Sample mean '[tex]\bar{x}[/tex]' = 883 sq ft
Standard deviation 'σ' = 270 sq ft
95% confidence interval.
95% confidence interval = 1 - 0.95
= 0.05
Critical value for 95% is [tex]Z_{0.05}[/tex] = 1.96
Population mean for the given confidence interval is given by :
= [tex]\bar{x}[/tex] ± [tex]Z_{0.05}[/tex] (σ / √n)
= 883 ± 1.96 ( 270 / √2)
= 883 ± 374.26
= ( 1257.26 , 508.74 )
Therefore , the range of the square footage values for the 95% confidence interval is equal to ( 1257.26 , 508.74 ).
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a restaurant is introducing a new gluten-free recipe for the topping in its baked zucchini recipe. the chef will continue to use this topping if less than 8% of her customers complain about the new taste. using a random sample of customers, she conducts a hypothesis test with h0: the complaint rate is 8%, and ha: the complaint rate is less than 8%. what is a type i error and its consequence in this context?
By hypothesis testing, The chef believes the complaint rate is less than 8%, when in fact it is not less than 8%. The chef continues to use the new recipe but experiences a large number of unsatisfied customers.
What does testing your hypotheses mean?
To make inferences about a population parameter or population probability distribution, a statistical process known as hypothesis testing analyzes data from a sample.
First, a hazy assumption about the parameter or distribution is made.
What is hypothesis testing, and how can it be used?
A statistician will test a hypothesis about a population parameter in a process known as hypothesis testing. The type of data used in the study and its purpose will determine the methodology the analyst uses.
The plausibility of a hypothesis is evaluated using sample data in a process known as hypothesis testing.
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What does y equal, in this picture with 30 60 90 triangles?
The value of y= 5.49≈ 5.5cm
What is 30-60-90 traingle?
The 30-60-90 triangle is cut straight through the middle along its altitude, like one half of an equilateral triangle. Its name is derived from its three angles of 30 degrees, 60 degrees, and 90 degrees. Any triangle with angles of 30-60-90 will look like this: The hypotenuse is always twice as long as the shortest leg, and the length of the long leg can be calculated by multiplying the short leg by the square root of three. The shortest leg is across from the 30-degree angle.
By 30-60-90 triangle rule,
Side across 60° angle = x
Hypotenuse side = 2x= 15
Side across 30° angle = x√3
By solving,
2x= 15
x= 7.5cm
So side across 60° angle= 7.5 cm
Side across 30° angle = 7.5×√3
= 7.5× 1.732= 12.99≈ 13cm
As the figure given us square so,
13= 7.5+y
y= 13-7.5
y= 5.5 cm
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2. The basic advertising package has a value of $1,000
and the premium package has a value of $2,500. The
goal of the agency is to sell more than $60,000 worth
of small-business advertising packages.
If you know that exactly 10 premium packages were
sold, what can you say about the number of basic
packages the agency needs to sell to meet its goal?
1000b + 2500p = 60,000
1000b + 2500(10) = 60,000
1000b + 25000 = 60,000
1000b = 35,000
b = 35
they need to sell 35 basic packages to reach their goal of 60,000 dollars
A 12-foot ladder is resting against a wall and makes an angle of 52 degrees with the ground. Find the height to which the ladder will reach the wall.
A 12-foot ladder is resting against a wall and makes an angle of 52 degrees with the ground, the height to which the ladder will reach the wall is 9.456 foot.
What is height?Height, altitude, and elevation all refer to the vertical distance between something's top and bottom or its base and something above it. Height is a term used to describe everything that may be measured vertically, high or low.
From the lowest to the highest point to the lowest point, it calculates the vertical distance. In general, it refers to a coordinate geometry object's measurement along the y-axis.
let, h = height of ladder
Given that,
length of ladder = 12 ft
angle with the ground = 52°
As we know,
sinθ = h/12
or, sin (52°) = h/12
or, 0.7880 = h/12
or, h = 9.456 foot.
the height to which the ladder will reach the wall 9.456 foot.
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Inequality
x + y > 11
.05x + .10y < .95
the inequality model will be x+2y<19
What is inequality?
Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.
x + y > 11
.05x + .10y < .95
by multiplying 20 in inequality we get x+2y<19
Hence, the inequality model will be x+2y<19
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fast as you can. point slope form. algebra 1)
Answer: Y=mx+b
Step-by-step explanation:
Hailey goes to a restaurant and the subtotal on the bill was xx dollars. A tax of 8% is applied to the bill. Hailey decides to leave a tip of 24% on the entire bill (including the tax). Write an expression in terms of xx that represents the total amount that Hailey paid.
The expression in terms of xx that represents the total amount that Hailey paid is (2912/625)xx .
What is business Mathematics?
Business mathematics is the branch of mathematics utilized by businesses to track and coordinate their operations. Accounting, inventory management, marketing, sales forecasting, and financial analysis are all areas where commercial businesses apply mathematics.
According to Question:
let the the subtotal on the bill was xx dollars
A tax of 8% is added on bill then Bill becomes xx + 8% of xx
The of 8% on bill = (108/100)xx
Now the Final bill = xx + (108/100)xx
= (208/100)xx
Hailey decides to leave a tip of 24% on the entire bill (including the tax)
So the Total Amount = (208/100)xx + 24% of Final bills
⇒
24% of (208/100)xx = (208/100)(124/100)xx
The Total amount = (208/100)xx +(208/100)(124/100)xx
Let the Amount be A
hence, expression in terms of xx that represents the total amount that Hailey paid is A = (208/100)xx +(208/100)(124/100)xx
⇒ A = (52/25)xx +(52/25)(31/25)xx
⇒ 625A = 625((52/25)xx +(52/25)(31/25)xx)
⇒ 625A = 1300xx + 1612xx
⇒ 625A = 2912xx
⇒ A = (2912/625)xx
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If a plane can travel 480 miles per hour with the wind and 380 miles per hours against the wind, find the speed of the wind and the speed of the plane in still air
Answer:
Step-by-step explanation:
I am not super sure about this one
If f(x) = 3x-1 and g(x) = x^2+2, what is (f ° g)(x)?
Answer:
(f ○ g)(x) = 3x² + 5
Step-by-step explanation:
substitute x = g(x) into f(x) , that is
(f ○ g)(x)
= f(g(x))
= f(x² + 2)
= 3(x² + 2) - 1
= 3x² + 6 - 1
= 3x² + 5
If 1.5 liters of washing up liquid is 2.70$ find the cost of 1 liter
The cost of one liter of washing up liquid would be = $1.8
What is liters?Liters is a variable that is can be used to denote the measurement of a liquid.
The quantity of the washing up liquid that was given= 1.5 liters.
The cost of 1.5 liters of washing up liquid =$2.70
If 1.5 L = 2.70
1 L = X
Make X the subject of formula;
X = 1× 2.70/1.5
X = $1.8
Therefore, the cost of one liter of washing up liquid would be = $1.8
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Ryanne is 14. Her brother's age is three more than half her age. How old is her brother?
OA 7
OB. 8.5
OC. 10
OD. 31
Question
Answer:
10 years old
Step-by-step explanation:
Identify the rate of decay r (as a percent) of the exponential function f(x) = 0.3(0.82)^x
a. r = 30%
b. r = 18%
c. r = 70%
d. r = 82%
Answer:
b. r = 18%
Step-by-step explanation:
0.3(0.82)^x:
0.3(0.82)^x:
The 0.82 is getting affected since it is raised to the power of x
Hence, for every iteration of x, the object is becoming 82% of itself.
100%-82%=18%
r = 18% ==> b
Option B is correct, 18% is the rate of decay of the exponential function f(x) = 0.3(0.82)ˣ
What is a function?A relation is a function if it has only One y-value for each x-value.
The exponential function f(x) = 0.3(0.82)^x can be written in the form f(x) = a(b)ˣ, where a = 0.3 and b = 0.82.
In an exponential function of the form f(x) = a(b)ˣ
the base b represents the rate of change.
If b is between 0 and 1, then the function represents exponential decay. The rate of decay r can be found using the formula:
r = (1 - b) x 100%
In this case, b = 0.82, so the rate of decay is:
r = (1 - 0.82) x 100%
= 0.18 x 100%
= 18%
Hence, option B is correct, 18% is the rate of decay of the exponential function f(x) = 0.3(0.82)ˣ
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if a point is characterized as having both a nonzero x and y coordinate and oppositely signed coordinates, then the point must be in which of the labeled quadrants in the standard xy coordinate plane?
The labeled quadrants in the standard xy coordinate plane is Quadrant II
What is Quadrants?
The intersection of the x-axis (the horizontal number line) and the y-axis in the cartesian system divides the coordinate plane into four equal pieces (the vertical number line). Because each of these four areas occupies a quarter of the entire coordinate plane, they are collectively referred to as quadrants.
Concept:
The x and y coordinates are both positive in quadrant I. In quadrant II, the x and y coordinates are oppositely positive. The x and y coordinates are both negative in quadrant III. The x-coordinate is positive and the y-coordinate is negative in quadrant IV.
The origin, or the point where the x- and y-axes connect, is where both the x and y coordinates are zero (0, 0).
The point is in the first quadrant if both x and y are positive. If both x and y are negative, the point will be in the second quadrant. In the third quadrant if both x and y are negatives, the point is located.
The labeled quadrants in the standard xy coordinate plane is Quadrant II
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(URGENT!!) In the diagram, △FEL∼△JOS. Which ratios are equivalent to tanF? Select all that apply.
Responses
EF/EL
EL/EF
EL/FL
FL/EF
OJ/OS
OJ/JS
OS/OJ
OS/SJ
The equivalent ratios to tan F = EL/ EF = OS/OJ
Similar triangles:Similar triangles are those with the same shape but different sizes. Similar triangles include all equilateral triangles and squares with any side length.
All related pairs of angles will be equal and corresponding sides of similar triangles will have the same ratio. The symbol '∼' is used to represent the similarity.
Given that
△FEL∼△JOS
That means △FEL and △JOS are similar triangles
As we know tan θ = Opposite side / Adjacent side
From the triangle △FEL,
=> tan F = EL/EF
By the given information,
The similar triangle's corresponding sides will have the same ratio
=> EL/ EF = OS/OJ
Therefore
The equivalent ratios to tan F = EL/ EF = OS/OJ
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Write and equation of the line in slope-intercept form. (0,-2) (1,3)
Answer:
y=5x−2
I hope this helps!
Solve for x
O4
O5
O-10
O12
Answer:
x = 5
Step-by-step explanation:
Firstly, we know that corresponding angles are the same. So we can say that 25x + 5 = 26x
Let’s simplify this equation:
25x + 5 =26x
-25x -25x
5 = x
Therefore, x = 5.
If you roll a fair die, what is the probability you will roll a 5 or a number less than 3?
Answer:
1/2
Step-by-step explanation:
Since 5 is one of the six possible numbers available, rolling a 5 is a 1/6 probability.
Since rolling a number less than 3 means rolling a 1 or 2, rolling a 1 or 2 is a 2/6 probability.
Add those probabilities up since you can get either of those outcomes and you get 1/6+2/6=3/6
3/6=1/2
Miguel’s Skate Shop is having a sale on skateboards. The original price for its Extreme Skateboard is $84.50. The sale price for the skateboard is $50.70. What is the percent decrease in the price of the skateboard?
The required percent decrease in the price of the skateboard is 40%.
What is the percentage?
A % is a number that indicates how many out of 100 it is, and it can also be expressed as a decimal or a fraction. Put the percentage value in the numerator and 100 in the denominator to convert a percentage to a fraction.
Here, we have
Original price = $84.50
sale price = $50.70
Percent decrease = 84.50-50.70/84.50 × 100 = 40%
Hence, the required percent decrease in the price of the skateboard is 40%.
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Graph Y= -1/4 x + 6.
The x-intercept and y-intercept of the line will be at (24, 0) and (0, 6). And the line is drawn below.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
x/a + y/b = 1
Where 'a' is the x-intercept of the line and ‘b’ is the y-intercept of the line.
The linear equation is given below.
y = -(1/4)x + 6
Convert the equation into intercept form, then we have
y = -(1/4)x + 6
4y = - x + 24
x + 4y = 24
x / 24 + y / 6 = 1
The x-catch and y-capture of the line will be at (24, 0) and (0, 6) and the line is drawn underneath.
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2/5 divided by 3/8 as a fraction
the table shows the number of stickers three friends have, Hannah has fewer stickers than Marco but more stickers than Addison. how many stickers could Hannah have?
Frank gets a Lamborghini for Christmas from Bill Nye for $225,000. Frank crashes the Lamborghini and survives. But his car is damaged. His repairs will cost 55% of the original price, but 30% of the price is covered by insurance. How much money does Frank owe?
Answer: Frank has to pay 56,250 dollars
Step-by-step explanation: If Frank's repair costs 55% of the original price, that means he'll have to pay 123,750 dollars because 55% of 225,000 is 123,750. But he doesn't have to pay that amount because the car insurance is paying 30% of 225,000 which is 67,500 dollars. So the car insurance is paying 67,500 dollars out of the 123,750 dollars in damage. So you'll have the subtract 123,750 by 67,500 which is 56,250 dollars.
How can we use the formula M= 58h + 135 to determine the mile marker that Sam passed at hour 6
Sam passed the marker of 483 miles, in 6 hours.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
An expression is given as M = 58h + 135. shows how many miles the same has traveled for h hours,
To evaluate the mile marker that sam passed at 6 hours, substitute the value with h in a given expression.
M = 58×6 +135
Simplifying the above expression gives the mile marker
M = 483 miles
Thus, the required miles are 483.
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A line passes through the point (6,-1) and is perpendicular to the line with the equation -2x + 3y = -6.
Answer: A
Step-by-step explanation:
Before we find the equation of the perpendicular line, we have to find the slope of the original line.
The slope-intercept form of the equation is y=mx+b, so let's change that.
[tex]-2x+3y=-6[/tex] [add both sides by 2x]
[tex]3y=2x-6[/tex] [divide both sides by 3]
[tex]y=\frac{2}{3} x-2[/tex]
This gives slope as [tex]\frac{2}{3}[/tex].
There are 2 things for us to do to find the slope of a perpendicular line.
1. reciprocal
2. change sign
Let's apply those rules.
1. [tex]\frac{3}{2}[/tex]
2. [tex]-\frac{3}{2}[/tex]
Now, we can find the perpendicular lines by plugging in our new point.
[tex]y=-\frac{3}{2} x+b[/tex] [plug in x and y]
[tex]-1=-\frac{3}{2}(6)+b[/tex] [multiply]
[tex]-1=-9+b[/tex] [add both sides by 9]
[tex]b=8[/tex]
Now we can plug in for our slope-intercept equation.
[tex]y=-\frac{3}{2} x+8[/tex]
Since answers are in standard form, we have to manipulate it.
[tex]y=-\frac{3}{2} x+8[/tex] [add both sides by [tex]\frac{3}{2} x[/tex]]
[tex]\frac{3}{2}x+y=8[/tex] [multiply both sides by 2]
[tex]3x+2y=16[/tex]
Therefore, our final answer is A.
Juan borrowed $2000 for 1 year and
paid 15% interest. How much
interest did he pay in a year?
Answer:At the rate of 15% the amount of interest on $2000
Step-by-step explanation:
simple amount= Principle(1+rt)
where r= rate of inetrest
t= time
principal is initial amount
therefore, amount=2000(1+15*1)
Amount = $2,300.00
Interest = Amount - Principal = $300.00
Answer:
Step-by-step explanation:
Interest = Principle * Rate * Time /100
Principle = $2000
Rate = 15 %
Time = 1 year
I = 2000 * 15 * 1/100
I = 300
Juan has to pay $300 in a year
1. Which of the following is equivalent to 5a³ + 4a³??
O (5+4) a³+3
O (5+4) a³
(5.4) a³+3
O (5.4) a³
ہے
The equivalent to 5a³ + 4a³ is (5+4) a³, according to the question.
What do you mean by Equivalent ?
Equivalent refers to the mathematical notion that distinct terms and expressions having a similar value are treated equally.
According to the given question,
We have the given options are:
O (5+4) a³+3
O (5+4) a³
O (5.4) a³+3
O (5.4) a³
Now, we will find the equivalent,
5a³ + 4a³
Then, we will taking common factor from the given equation:
5a³ + 4a³
= a³(5+4)
So that is same as (5+4)a³.
Therefore, the equivalent to 5a³ + 4a³ is (5+4) a³.
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write the equation of a parabola whose vertex is (-3,4) and passes through: (2,8). Put in vertex form.
The equation of the parabola that has a vertex (-3,4) and passes through (2,8) is 25y = 4x² + 24x + 13.
What is parabola?An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola. The parabola's fixed line and fixed point are together referred to as the DirectX and focus, respectively.
Given:
The vertex = (-3, 4) and the point = (2, 8)
Write the equation using the standard form given below,
[tex]y = a (x - h)^2 + k[/tex]
y = a[x - (-3)]² + 4
y = a(x + 3)² + 4
Now put the coordinates,
8 = a (2 + 3)² + 4
8 = 25a + 4
a = 4 / 25
Put the value of a in the above equation,
y = 4/25 × (x + 3)² + 4
25y = 4 (x² + 9 +6x) + 100
25y = 4x² + 36 +24x + 100
25y = 4x² + 24x + 13
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Please help! Division of Polynomials, Find the quotient and remainder.
First:
Quotient: [tex]2x^{2} -11x+58[/tex]
Remainder: [tex]-294[/tex]
Second:
Quotient: [tex]x^{3} -5x^{2} +17x-83[/tex]
Remainder: [tex]422[/tex]
Third:
Quotient: [tex]2x-3[/tex]
Remainder: [tex]12[/tex]
A) Q''(−5, 6), R''(−2, 1), S''(1, 5)
B) Q''(7, 11), R''(10, 16), S''(13, 12)
C) Q''(−5, 2), R''(−2, 7), S''(1, 3)
D) Q''(13, 2), R''(10, 7), S''(7, 3)
The correct answer is C.
an irs auditor randomly selects 3 tax returns from59returns of which7contain errors. what is the probabilitythat she selects none of those containing errors?
Therefore , the probability that she selects none of those containing errors is 0.6798.
What does probability really mean?Calculating how likely or "possible" it is for an event to occur is the subject of probability. Words like "definitely," "impossible," or "likely" may be used to communicate the likelihood that a particular event will occur. Mathematics always expresses probabilities as fractions, decimals, or percentages, with values ranging from 0 to 1.
Here,
Number of ways of selecting 3 returns out of 59 is C(59,3).
Out of 59 returns, 59-7 = 52 returns has no error so number of ways of selecting 3 returns out fo 52 is C(52,3).
The probability that she selects none of those containing errors is
P( No errors )=[tex]\frac{C(52,3)}{C(59,3)}[/tex]=0.6798
Therefore , the probability that she selects none of those containing errors is 0.6798.
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