The test statistic is given as follows:
t = 2.52.
How to calculate the test statistic?We have the standard deviation for the sample, thus, the t-distribution is used. The test statistic is given by the equation presented as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.The parameters for this problem are given as follows:
[tex]\overline{x} = 0.3, \mu = 0, s = 0.8, n = 45[/tex]
Hence the test statistic is given as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{0.3 - 0}{\frac{0.8}{\sqrt{45}}}[/tex]
t = 2.52.
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what is the range of the reciprocal function -7/3x+11
The range of the reciprocal function f(x) = -7/(3x + 11) is all real numbers except for the value x = -11/3.
The range of the reciprocal function f(x) = -7/(3x + 11), we need to determine the set of all possible values that f(x) can take.
The reciprocal of a number is obtained by taking the multiplicative inverse, which means that the reciprocal of a non-zero number a is 1/a.
We are looking for the range of the reciprocal function, so we need to consider the range of the expression (3x + 11).
The range of (3x + 11) is the set of all real numbers, except when the denominator becomes zero.
The range of the reciprocal function f(x) = -7/(3x + 11) is all real numbers except when (3x + 11) equals zero.
To find the x-value when (3x + 11) equals zero, we solve the equation:
3x + 11 = 0
Subtracting 11 from both sides, we get:
3x = -11
Dividing by 3, we find:
x = -11/3
The reciprocal function is undefined at x = -11/3, as it would result in a division by zero.
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Which expression is equivalent to
Answer:
The answer is the third option
Step-by-step explanation:
When an exponent is raised to the power of another exponent, both exponents are multiplied.
Recall that a number without an exponent is thought to be raised to the power of 1.
So after multiplying the exponents of all of the variables by 4, we are left with a solution identical to the third option.
Six packs of cola are on sale for $1.50. If a customer buys a 24 pack, what is the total charge including 8% sales tax?
Answer: [tex]\sf\$6.48[/tex]
Step-by-step explanation:
If a six-pack of cola is sold for $1.50, then the price per can is:
[tex]\sf\implies\$1.50 \div 6 = \$0.25[/tex]
A 24 pack of cola contains 24 cans, so the total cost of the 24 pack is:
[tex]\sf\implies 24 \times \$0.25 = \$6.00[/tex]
The sales tax is 8%, so the tax on the purchase is:
[tex]\sf\implies \dfrac{8}{100} \times \$6.00 = \$0.48[/tex]
Therefore, the total charge including sales tax is:
[tex]\sf\implies\$6.00 + \$0.48 = \$6.48[/tex]
Chi-Chiribi! EmergerOrpheus at your service. Hope it helps!
Differentiate between equity and equality in mathematics class.
1. cos^2x = sin^2x + 1/2
2. 2cos( π/2 - x) * sin (π/2 + x) - 1 = 0
3. 8sin x/2 * cos x/3 * cosx * cos2x = 1
4. 1 + cosx = cos x/2
x = ±π/6 + πn, ±11π/12 + πn, where n is an integers are solutions of the equation cos²x = sin²x + 1/2
To solve the equation cos²x = sin²x + 1/2, we can use the trigonometric identity sin²x + cos²x = 1.
Rearranging the equation, we have:
cos²x - sin²x = 1/2
Using the identity cos²x - sin²x = cos(2x), we can rewrite the equation as:
cos(2x) = 1/2
The solutions to this equation can be found by taking the inverse cosine (or arccosine) of both sides:
2x = ±π/3 + 2πn, ±11π/6 + 2πn, where n is an integer
Dividing both sides by 2, we get:
x = ±π/6 + πn, ±11π/12 + πn, where n is an integers
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Prove the following?
The proof that there is no set X such that P(X) ⊂ X is below
How to prove the set statementFrom the question, we have the following parameters that can be used in our computation:
There is no set X such that P(X) ⊂ X
The above means that
There is no set X such that the power set of X is a subset of set X
By definition, the power set is the set of all subsets of the a Set which includes the set itself and the null or empty set
Using the above as a guide, we have the following:
We assume there is a set XSuch that Y is any element in the X.Because Y is in X, then by definition of the power set P(X), Y is a subset of X.
However, this is a contradiction because it is not possible for a set to be a proper subset of itself.
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If -1 and 1 + 5i are roots of f(x) = x ^ 3 - x ^ 2 + 24x + 26 what is the missing root?
The missing root is -24 - 5i.
To find the missing root of the polynomial function f(x) = x^3 - x^2 + 24x + 26, we can use the fact that the sum of all the roots of a polynomial equation is equal to the negation of the coefficient of the second-to-last term divided by the coefficient of the leading term.
In this case, the coefficient of the second-to-last term is 24, and the coefficient of the leading term is 1. Therefore, the sum of all the roots is -24/1 = -24.
We already know that -1 and 1 + 5i are roots, so we can subtract them from the sum to find the missing root:
Missing root = -24 - (-1) - (1 + 5i) = -24 + 1 - 1 - 5i = -24 - 5i.
Note that the missing root is a complex number, indicating that the polynomial has at least one complex root.
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Suppose that a study of elementary school students reports that the mean age at which children begin reading is 5,7 years With a standard deviation of 0.9 years. If a sampling distribution is created using samples of the ages at which 57 children begin reading what would be the mean of the sampling distribution of sample means? Round to two decimal places if necessary
By the Central Limit Theorem, the mean of the sampling distribution of sample means would be 5.7 years.
Since, The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean μ and standard deviation σ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean μ and standard deviation s = σ / √n.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
The mean for the entire population is 5.7 years.
So, by the Central Limit Theorem, the mean of the sampling distribution of sample means would be 5.7 years.
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Alex is studying houses in his area. He collected data, constructed a scatter plot, and found a line of best fit for his data. The line of best fit for the cost of a house, y
, in terms of the square footage of the house, x
, is y=271x−107,631.
Based on Alex's model, what is the predicted cost of a house with an area of 1,250 square feet?
Size of the house should be 2900 ft².
Correct option is B.
We have,
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.
Given,
Equation for the line that expresses price of house
y = 0.06x + 60.5
where y is the price in thousand dollars, x is area in square feet.
Price of the house = $235000
⇒ y = 235
Then,
235 = 0.06x + 60.5
0.06x = $235 - 60.5
0.06x = 174.5
x = 174.5/0.06
x = 2908.33 ≈ 2900
Hence, 2900 ft² should be the size of the house.
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complete question:
A house is listed for sale at $235,000, but the listing does not include square
footage of the house. Based on the comps, the line of best fit is
y=0.06x + 60.5. If the price is fair, what size (in square feet) should the house
be?
OA. 2850 ft2
OB. 2900 ft2
OC. 20,000 ft²
OD. 2350 ft²
Solve the following equation algebraically: 3 x squared = 12 a. Plus-or-minus 3 b. Plus-or-minus 2 c. Plus-or-minus 3.5 d. Plus-or-minus 1.5 Please select the best answer from the choices provided A B C D
The correct option is b, the solutions of the quadratic equation are x = ±2
How to solve the quadratic equation?Here we want to solve the following quadratic equation:
3x² = 12
To solve this, we need to isolate the variable, so let's start by dividing both sides by 3, then we will get:
x² = 12/3
x² = 4
Now we can apply the square root in both sides:
√x² = ±√4
x = ±2
These are the two solutions, then the correct option is b.
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Please I need help with this math problem
Step-by-step explanation:
I believe it is asking for the probability that x is greater than the mean + two standard deviations .....
look at the mean ....count up two SD ( labelled at the bottom) ....then see what is to the right of this point : 2.35 % + .15 % = 2.5% is greater
Y = -1
3x - y =4
On graph
The graph of the equation y = -1 is a horizontal line passing through (0, -1), and the graph of the equation 3x - y = 4 is a line passing through the points (-2, -10), (0, -4), and (2, 2).
To graph the given equations, we'll plot the points that satisfy each equation and then connect them to form a line.
Equation 1: y = -1
This equation represents a horizontal line passing through the y-coordinate -1. Regardless of the x-coordinate, the y-value remains constant at -1. Therefore, we plot a point at (0, -1) and draw a horizontal line through that point.
Equation 2: 3x - y = 4
To graph this equation, we can rewrite it in terms of y:
y = 3x - 4
Now we can choose a few x-values, substitute them into the equation, and solve for y to obtain the corresponding y-values. Let's select three x-values: -2, 0, and 2.
For x = -2:
y = 3(-2) - 4
y = -6 - 4
y = -10
For x = 0:
y = 3(0) - 4
y = -4
For x = 2:
y = 3(2) - 4
y = 6 - 4
y = 2
Now we have three points: (-2, -10), (0, -4), and (2, 2). Plotting these points on the graph, we can draw a line connecting them.
In summary, the graph of the equation y = -1 is a horizontal line passing through (0, -1), and the graph of the equation 3x - y = 4 is a line passing through the points (-2, -10), (0, -4), and (2, 2).
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the priniting company charges a fixed amunt for creating artwork then charges an additonal amount based on number
The price per shirt when 100 shirts are sold is of $5.
How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:
m represents the slope of the function, which is by how much the dependent variable y increases or decreases when the independent variable x is added by one.b represents the y-intercept of the function, representing the numeric value of the function when the input variable x has a value of 0. On a graph, the intercept is given by the value of y at which the graph crosses or touches the y-axis.From the graph of the function, two points are given as follows:
(0, 20) and (20, 100).
Hence the slope is given as follows:
m = (100 - 20)/(20 - 0)
m = 4.
Hence the cost function is of:
y = 4x + 20.
For 20 shirts, the cost is of $100, hence the cost per shirt is given as follows:
100/20 = $5 per shirt.
Missing InformationThe problem is given by the image presented at the end of the answer.
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passenger on a boat notices that there is a dolphin 4.1 yards below the boat. There is also a fish 3.5 yards below the boat. They also see a bird that is 3.5 yards above the boat.
Part A: Explain how you would create a number line for these points. (1 point)
Part B: What does zero represent on your number line? (1 point)
Part C: Determine which two points are opposites, using absolute value. Be sure to show your work. (2 points)
Answer:
Step-by-step explanation:24 ft
A clothing designer determines that the number of shirts she can sell is given by the formula S = −4x2 + 88x − 160, where x is the price of the shirts in dollars. At what price will the designer sell the maximum number of shirts? (1 point)
$2
$11
$20
$324
The price for which the designer will sell the maximum number of shirts is given as follows:
$11.
How to obtain the price?As the amount sold is modeled by a concave down quadratic function, the price for which the designer will sell the maximum number of shirts is given by the x-coordinate of the vertex of the quadratic function.
The function in the context of this problem is given as follows:
S(x) = -4x² + 88x - 160.
The coefficients are given as follows:
a = -4, b = 88, c = -160.
Hence the x-coordinate of the vertex is obtained applying it's formula as follows:
x = -b/2a
x = -88/-8
x = 11. -> price of $11.
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At which root does the graph of f(x) = (x - 5)³(x + 2)2 touch the x-axis?
O-5
0-2
02
05
Step-by-step explanation:
Wherever the fxn = 0 is where it touches the x -axis
0=(x-5)^3 (x+2)^2 means that one or both of the factors is 0
(x-5)^3 is zero at x = 5
(x+2)^2 is zero at x = -2
sooo 5 and -2
The temperature inside my refrigerator is about 40 Celsius. That temperature in Kelvin is K.
I place a balloon in my fridge that initially has a temperature of 220 C. This is K.
If the original volume of the balloon is 0.5 liters, what will be the volume of the balloon when it is fully cooled by my refrigerator? liters. (Round to two decimal places)
To solve this problem, we need to use Charles's law, which states that, at constant pressure, the volume of a sample of gas is directly proportional to its temperature.
The law can be expressed mathematically as:
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{ \frac{V_1}{T_1}=\frac{V_2}{T_2} } \end{gathered}$} }[/tex]
Where:
V₁ is the initial volumeT₁ is the initial temperatureV₂ is the final volumeT₂ is the final temperatureNow we obtain the data to continue solving:
V₁ = 0.5 LT₁ = 220 °CV₂ = ?T₂ = 40 °CNow, we will convert the temperatures to Kelvin:
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{T_1=220 \ ^{\circ}C+273=493 \ Kelvin} \end{gathered}$} }[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{T_2=40 \ ^{\circ}C+273= 313 \ Kelvin} \end{gathered}$} }[/tex]
Now we solve for V₂:
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_2=\frac{V_1T_2}{T_1 } } \end{gathered}$} }[/tex]
Where:
V₁ is the initial volumeT₁ is the initial temperatureV₂ is the final volumeT₂ is the final temperatureNow, we substitute the values in the formula:
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_2=\frac{(0.5 \ L\times313\not{k} )}{493\not{k} } } \end{gathered}$} }[/tex]
[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_2\approx0.32 \ Liters } \end{gathered}$} }}[/tex]
The final volume of the balloon, when completely cooled in the refrigerator, will be approximately 0.32 liters.what values of x make the inequality -5x - 7 > 3x + 1 true
Hello!
[tex]-5x - 7 > 3x + 1\\\\-5x - 3x > 1+7\\\\-8x > 8\\\\\boxed{x < -1}[/tex]
x < -1x ∈ ]-∞ ; -1[all the values < -1 (-1 not included)using the centriod explain the relationship between point z and the triangle. justify with applicable theorem.
4. if the length of gu is 18 units, what is the length of gz?
5. if the length of zt is 4.8 units, what is the length of ot?
show all work
By the Centroid Theorem, the lengths are given as follows:
4. GZ = 12 units.
5. OT = 14.4 units.
What is the Centroid Theorem?The Centroid Theorem states that the centroid of a triangle is located two-thirds of the total distance from each vertex to the midpoint of the opposite side.
Hence for length GZ we have that:
GZ = 2GU/3
GZ = 2 x 18/3
GZ = 12 units.
For length OT, we have that:
ZT = 1/3OT
OT = 3ZT
OT = 3 x 4.8
OT = 14.4 units.
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Find the measure of each side indicated for the top two
Find the measure of each angle indicated for the bottom two
Round to the nearest tenth for all
The measure of each missing indicated side of the triangle would be given as follows;
1.) X = 2.7
2.) X = 15.2
How to determine the length of the indicated sides of the triangle?For question 1.)
Using the sine formula such as given below;
a/sinA = b/sin B
where ;
a = X
A = 27°
b = 6
B = 90°
That is;
X/sin27° = 6/sin90°
X = 6×0.453990499/1
= 2.7
For question 2.)
a/sinA = b/sin B
where ;
a = X
A = 47.4°
b = 14
B = 180-(47.4+90)
= 180-137.4
= 42.6
That is;
X/sin47.4° = 14/sin42.6°
X = 14×0.736097087/0.676875969
= 10.305359218/0.676875969
= 15.2
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Assuming that you invested today a value of $400; you will have $684 after 11 years. Find the interest rate which satisfies this assumption.
The interest rate that satisfies the assumption is approximately 5.33%.
We have,
To find the interest rate that satisfies the assumption, we can use the formula for compound interest:
[tex]A = P \times (1 + r)^t[/tex]
Where:
A = Final amount
P = Principal amount (initial investment)
r = Annual interest rate (in decimal form)
t = Time (in years)
In this case, we have:
P = $400
A = $684
t = 11 years
Let's substitute these values into the formula and solve for r:
$684 = $400 x [tex](1 + r)^{11}[/tex]
Dividing both sides by $400, we get:
[tex]1.71 = (1 + r)^{11}[/tex]
Now, we need to isolate (1 + r) by taking the 11th root of both sides:
[tex](1 + r) = 1.71^{1/11}[/tex]
Using a calculator, we find:
(1 + r) ≈ 1.0533
Subtracting 1 from both sides, we get:
r ≈ 0.0533
To express the interest rate as a percentage, we multiply by 100:
r ≈ 5.33%
Therefore,
The interest rate that satisfies the assumption is approximately 5.33%.
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Determine whether the
quadratic function
y=x² + 4x + 6 has
a maximum or minimum value.
Then find the value.
O maximum
minimum
The value is
Answer:
(a) The function has a minimum value
(b) The minimum value is 2
Step-by-step explanation:
(a)Currently y = x^2 + 4x + 6 is in standard form, whose general equation is
y = ax^2 + bx + c.
We know that for our function a = 1.
When a > 0, the parabola opens upward and the vertex is a minimumWhen a < 0, the parabola opens downward and the vertex is a maximumThus, y = x^2 + 4x + 6 must have a minimum value.
(b) Whenever a problem asks for the minimum value, it's asking for the y-coordinate of the minimum.
Step 1: First we can find the x-coordinate of the minimum using the equation -b/2a from the quadratic formula.
Plugging in 4 for b and 1 for a, we get:
x-coordinate of minimum = -4 / 2(1)
x-coordinate of minimum = -4 / 2
x-coordinate of minimum = -2
Step 2: Now we can plug in -2 for x in the quadratic function. The result will be our minimum value:
f(-2) = (-2)^2 + 4(-2) + 6
f(-2) = 4 - 8 + 6
f(-2) = -4 + 6
f(-2) = 2
Thus, the minimum value of the quadratic function is 2.
The diameter of a planet is about 27,998 mi. The diameter of the planet's moon is about 29% of the diameter of the planet. What percent of the volume of the planet is the volume of its moon?
Question content area bottom
The volume of the planet's moon is ? % of the volume of its planet.
The volume of the moon can be shown to be 3.07% of the volume of the planet.
How to find the percentage ?First, calculate the radius of the planet and the moon.
The radius (r) of the planet is half of its diameter:
r = 27, 998 mi / 2
= 13, 999 mi
The volume of the planet is V:
= 4 / 3 π ( 13, 999 mi)³
= 11, 493, 372, 846 cubic miles
The volume of the moon is:
V = 4 / 3 π (4,059.71 mi) ³
= 352, 432, 952 cubic miles
The Percent volume :
= ( Volume of moon / Volume of planet) x 100
= ( 352, 432 ,952 cubic miles / 11, 493,372,846 cubic miles) x 100
= 3.07 %
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the foundation of a house has 1600 termites. The termites grow at a rate of 4.2% each day. How would this be written out?
The number of terminates are 2,384.78.
An exponential function can be used to illustrate the daily growth of termites.
If "t" represents the number of days, then "N" represents the number of termites.
⇒ N = [tex]1600(1 + 0.042)^{t}[/tex]
Where 0.042 is the decimal form of 4.2%.
Using this formula,
It can be calculate the number of termites after any number of days t.
For example,
After 10 days, the number of termites would be:
⇒ N = [tex]1600(1 + 0.042)^{10}[/tex]
⇒ N = [tex]1600(1.042)^{10}[/tex]
⇒ N ≈ 2,384.78 termites
Hence,
⇒ N = 2,384.78 termites
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Considering this real world scenario, find the length of UV and RD and explain your reasoning as part of your answer. Show your work please (10) points!
The triangles ABC and CDE are similar
The width AB of the river is 172.73 ft
Stating if the triangles are similar or notFrom the question, we have the following parameters that can be used in our computation:
The triangles ABC and CDE
The above triangles have corresponding angles and they also have similar side lengths
This means that the triangles are similar
Calculating the width AB of the riverHere, we have the following ratio
AB : 100 = 38 : 22
So, we have
AB/100 = 38/22
This gives
AB = 100 * 38/22
Evaluate
AB = 172.73
Hence, the width AB of the river is 172.73 ft
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Select the correct answer.
What is the equation of the parabola shown in the graph?
Answer:
c) y=-x^2/4 - 2x - 7
Step-by-step explanation:
Find the coordinates of B if p(1, 2) partition segment AB in the ratio 1:2 and A (2, 4).
The calculated coordinates of point B on line AB is (-1, 0)
Calculating the coordinates of point BFrom the question, we have the following parameters that can be used in our computation:
P = (1,2)
A = (2,4)
Also, we have
m : n = 1 : 2
The coordinates of point P are calculated using
P = 1/(m + n) * (mx₂ + nx₁, my₂ + ny₁)
Substitute the known values in the above equation, so, we have the following representation
(1, 2) = 1/(1 + 2) * (1 * x + 2 * 2, 1 * y + 2 * 4)
Evaluate
(3, 6) = (x + 4, y + 6)
So, we have
x = -1 and y = 0
Hence, the coordinates of point B on line AB is (-1, 0)
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While driving your rental car on your vacation in Europe, you find that you are getting 13.3 km/of gasolineWhat does this value correspond to in miles per gallon?
13.3km/L=
_mi/gal
The value of 13.3km/L corresponds to 30.595 miles/gal
how to find the value after conversionThe conversion required is 13.3km/L to mile/gal
converting km to miles
1km = 0.621371 miles
13.3 km = ?
cross multiplying results to
? = 13 * 0.621371 = 8.077 miles
converting L to gallons
1 liters = 0.264172
hence we have that
= 8.077 / 0.264
= 30.595
thus, 13.3km/L is equal to 30.595 miles/gal
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The function y = 11x6 + 13x¹ is
a) odd
b) even
c) neither even nor odd
d) both even and odd
e) none of the above
Answer:
a)
Step-by-step explanation:
the function is 11x6=66+13=79x¹=79
hope it helps
IF AB measures 115° what is the length of the radius of the circle to the mearest hundredth
The length of the radius of the given circle whose central angle has been given would be = 7cm.
How to calculate the radius of a circle when a central angle is given?To calculate the radius of the given circle, the formula that should be used will be given below as follows:
Length of arc = 2πr×∅/360
Length of arc = 14cm
∅ = 115°
14 = 2×3.14×r ×115/360
make R the subject of formula;
r = 14/2.006
= 6.9
= 7cm
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