The value of the test statistic is given as follows:
z = 2.17.
There is sufficient evidence to say that the mean wait time for customers is longer than 3.50 minutes.
How to obtain the value of the test statistic?The value of the test statistic is obtained using the z-distribution, as the population standard deviation is known in the context of this problem.
The equation that gives the test statistic is given as follows:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which the parameters of the equation are listed as follows:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value claimed at the test of the hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.In the context of this problem, the values of these parameters are given as follows:
[tex]\overline{x} = 3.94, \mu = 3.50, \sigma = 1.30, n = 41[/tex]
(all values are taken from the text).
Then the numeric value of the test statistic is obtained as follows:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{3.94 - 3.50}{\frac{1.30}{\sqrt{41}}}[/tex]
z = 2.17.
There is sufficient evidence to say that the mean wait time for customers is longer than 3.50 minutes, as the critical value for the right-tailed test with 95% confidence is of z = 1.645, and the test statistic is greater than this.
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where is the incenter of any given triangle
The incenter of any given triangle s the point of congurrency of the angle bisectors of the triangle
we know that
The incenter is the point where the angle bisectors intersect. The incenter is also the center of the triangle's incircle.
therefore
Is the point of concurrency of the angle bisectors of the triangle
Part 2)
we know that
A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side
therefore
Is a segment drawn from a vertex to the midpoint of the opposite side
Therefore, the incenter of any given triangle s the point of congurrency of the angle bisectors of the triangle
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write 3/5 as a fraction or as a whole or mixed number
Answer:
Step-by-step explanation:
1) 4 1/4 + 5 1/2
= 9 3/4
2) 10 4/5 - 6 1/5
= 4 3/5
3) 3 1/4 - 1 3/4
= 1 1/2
4) 3 2/5 + 7 7/10
= 11 1/10
5 ) 10 3/13 + 2 10/13
= 13
Answer:
1
Step-by-step explanation:
Its for sure 1
Please help will mark Brainly
The rate of change in the given interval would be 1.25 ft/s.
What is the rate of change?
The slope of a graphed function is determined using the average rate of change formula. Divide the change in y-values by the change in x-values to find the average rate of change.
By observation, we can take the points from the graph in between the given interval.
The points would be (3, 2.5) and (5, 4)
Then the rate of change = y2 - y1/ x2 - x1
= 4 - 2.5/5 - 3
= 2.5/2
= 1.25 ft/s.
Hence, the rate of change in the given interval would be 1.25 ft/s.
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at a field trip for every 8 students there is 1 chaperone. if the teacher purchased 108 total tickets, how many tickets were for students?
First, 108/9=12
This means that are 12 groups of people.
If there are 8 students in each group, 12 x 8 = 96.
96 should be your answer.
When a transversal cuts parallel lines, how can one angle measurement be used to determine all of the other measurements?
Answer: If two parallel lines are cut by a transversal, then corresponding angles are congruent.
Step-by-step explanation:
Whats the width of her head
Answer: 12 inches
Step-by-step explanation:
Answer: 15 cm
Step-by-step explanation:
percent proportions and equations what do you call a destroyed angle
The destroyed angle is a rectangle specifically a parallelogram also having all the angles equal and equal to 90 degree.
Given, a destroyed angle
A destroyed angle is called a figure in Geometry also known as Rectangle.
A rectangle is a quadrilateral which is specifically a parallelogram also having all the angles equal and equal to 90 degree.
So, A destroyed angle is the quadrilateral which is specifically a parallelogram also having all the angles equal and equal to 90 degree.
Therefore, the destroyed angle is a rectangle.
Hence, The destroyed angle is a rectangle specifically a parallelogram also having all the angles equal and equal to 90 degree.
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Think back to our discussion on Negative Exponents. Why do we follow the steps that we do, specifically, why do we flip the number (reciprical)? Use the other laws of exponents to help gauge your thinking, but I want you to try to determine the meaning behind the process instead of just memorizing the steps. This might be a tough question to answer, so just do your best and we can discuss this again in class.
By using the law of exponents, it has been proved that
[tex]a^{-n} = \frac{1}{a^n}[/tex]
What are exponent?
Exponent tells us how many times a number is multiplied by itself.
For example : In [tex]2^4 = 2 \times 2 \times .... \times 2[/tex]
Here, 2 is multiplied by itself 4 times.
If [tex]a^m = a \times a \times a \times ..... \times a[/tex] (m times),
a is the base and m is the index.
The laws of exponents are
[tex]a^m \times a^n = a^{m+n}\\\\a^ m \div a^n = a^{m - n}\\\\a^ 0 =1\\\\a^{-m} = \frac{1}{a^m}\\\\(ab)^m = a^m \times b^m\\\\(\frac{a}{b})^m = \frac{a^m}{b^m}\\\\(a^m)^n = a^{mn}[/tex]
We know this law
[tex]a^p \times a^q = a^{p + q}[/tex]
Putting p = n and q = -n
[tex]a^n \times a^{-n} = a^{n + (-n)} = a^{n - n} = a^0 = 1[/tex]
So,
[tex]a^n \times a^{-n} = 1\\a^{-n} = \frac{1}{a^n}\\a^{-n} = \frac{1^n}{a^n}\\a^{-n} = (\frac{1}{a})^n[/tex]
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What would the answer be? I tried 4 and -4 and a lot more.
Answer:
-2
Step-by-step explanation:
a is -3
d is -1
you subtract the two
-3 - (-1)
when you have two negatives they cancel each other out and become positive
-3 + 1
-3 + 1 = -2
that is your answer
find the domain and range of 1 - x^2
The range and the domain of the function f(x) = 1 - x^2 is less than or equal to 1 and all values of x are a real number (R).
Domain: x ∈ R
Range: f ( x ) ≤ 1, ∈ R
f ( x ) = 1 − x^2 is defined for all Real values of x, and therefore the domain is all real values ( R ).
x^2 has a minimum value of 0 (for x ∈ R ) and therefore − x^2 has a maximum value of 0 and − x^2 + 1 = 1 − x^2 has a maximum value of 1.
Therefore f (x) has a maximum value of 1 and the range of f ( x ) is ≤ 1.
So, the range of f(x)≤ 1, and the domain is all real values ( R ).
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A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Applying the exterior angles and triangle sum theorems, the statements that are true are:
C. m∠5 + m∠6 = 180°
D. ∠2 + m∠3 = m∠6
E. m∠2 + m∠3 + m∠5 = 180°
What is the Exterior Angles and Triangle Sum Theorems?All three interior angles of a triangle is equal to a sum of 180 degrees, based on the triangle sum theorem, while the exterior angle theorem states that the exterior angle of a triangle is equal to the two remote interior angles of the triangle.
Given the image showing the triangles and its exterior angles, the following can be deduced:
m∠2 + m∠3 + m∠5 = 180° [based on the triangle sum theorem]
m∠2 + m∠3 = m∠6 [based on the exterior angles theorem]
m∠5 + m∠6 = 180° [based on the triangle sum theorem]
Therefore, the true statements are:
C. m∠5 + m∠6 = 180°
D. ∠2 + m∠3 = m∠6
E. m∠2 + m∠3 + m∠5 = 180°
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When can we say that the two triangles are congruent?
Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.
What is congruent?
Congruent refers to things that are exactly the same size and shape. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.
Here,
we have to prove when can we say that the two triangles are congruent.
SSS, SAS, ASA, AAS, and HL.
These tests describe combinations of congruent sides and/or angles that are used to determine if two triangles are congruent.
Hence, two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.
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A rectangular parking lot has an area of 2/3 of a square kilometer. The width is 1/2 of a kilometer. What is the length, in kilometers, of the parking lot?
Group of answer choices
5/3 km
2/3 km
1/3 km
4/3 km
Answer:
Step-by-step explanation:
2/3 = 1/2x
2/3 / 1/3 = x
x = 4/3
Answer: The answer is 4/3
Step-by-step explanation: I have my ways ;>
How do you solve an isosceles triangle problem?
Isosceles triangle problem can be solved by given steps
what is isosceles triangle ?
An isosceles triangle in geometry is a triangle with two sides that are the same length. Sometimes it is stated as having exactly two sides that are the same length, and other times it is specified as having at least two sides that are the same length, the latter form containing the equilateral triangle as a particular case.
explanation:
In isosceles triangle
1. Two sides of the triangle are congruent
2. The angle opposite those sides are congruent
x + 72 +72 = 180
x = 180 -144
x = 36
Hence the isosceles triangle problem can be solved by above steps and explanation
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Select the correct answer.
What is the approximate solution to this equation?
19 + 2 ln x= 25
Answer:
3
Step-by-step explanation:
Hope this helps..
Toby created a sculpture for art class using different-sized cubes. The smallest cube is 1.5 inches along each edge. The largest cube is 7.5 inches along each edge.
How many of the smallest cubes would it take to fill the largest cube?
Write your answer as a whole number or decimal. Do not round.
There are 125 of the smallest cubes that will fill the largest cube using the size of their respective volume
Volume of cubeThe volume of cube is calculated by using a × a × a = a³ where "a" is the edge.
The volume of the smallest cube = 1.5inches × 1.5inches × 1.5inches
The volume of the smallest cube = 3.375inches³
The volume of the largest cube = 7.5inches × 7.5inches × 7.5inches
The volume of the largest cube = 421.875inches³
Thus, the number of the smallest cubes it would take to fill the largest cube is derived by
421.875inches³/3.375inches³ = 125.
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Determine the length of the line segment shown 4 units
18 units
19 units
21 units
The length of the line segment will be 4 units. Then the correct option is A.
What is the distance between two points?The line joining the two points is known as a line segment. Let one point be (x, y) and another point be (h, k).
Then the distance between the points will be
D² = (x - h)² + (y - k)²
From the graph, the two points are (2, -2) and (2, 2). Then the distance between the points is calculated as,
D² = (2 - 2)² + (2 + 2)²
Simplify the equation, then we have
D² = (2 - 2)² + (2 + 2)²
D² = (4)²
D = 4 units
The length of the line segment will be 4 units. Then the correct option is A.
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The missing diagram is attached below.
When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle it means that we are going to use what postulate?
The used postulate is explained below.
What is congruent triangles?
Two triangles are stated to be congruent if the 3 facets and the 3 angles of each the angles are same in any orientation.
When angles and facet blanketed in among those angles of 1 triangle are identical as any other one, each those triangle are Congruent.
This standards of congruency is is aware of as ASA criterion as a facet blanketed among angles are all identical.
Two triangles are congruent, if angles and the facet blanketed among them in a single triangle is same to the 2 angles and the facet blanketed among them of the alternative triangle.
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What is the point of concurrence of perpendicular bisectors of a triangle?
The points of concurrency of perpendicular bisectors of triangle is circumcenter.
A point of concurrency shared by three or more lines is referred to as a single point of concurrency. Constructed lines in triangle interiors are excellent places to look for points of convergence.
When you construct a triangle's medians, perpendicular bisectors, angle bisectors, or altitudes, you create a point of concurrency for each of them.
Because the triangle can have four distinct types of line segments, it can have four distinct points of convergence. Each point of concurrency represents the intersection of a particular type of line segment: centroid, circumcenter, incenter, and orthocenter.
The centroid of the triangle is the point of convergence shared by the three medians.The point at which the triangle's three angle bisectors intersect is known as the incenter.The three perpendicular bisectors will intersect at the circumcenter, which is a point of convergence.The orthocenter is the point at which the three altitudes/heights of a triangle intersect.Thus, the points of concurrency of perpendicular bisectors of triangle is circumcenter.
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What is the upfront cost to secure this apartment?
A) $1,876
B) $1,225
C) $2,105
D) $1,025
B: 1000 + 25 + Water deposit (50) + Phone connection (40) + Elect. connection (60)
1000 + 25 + 200 = 1225
(1 point)
Solve this inequality, and write your answer in interval notation.
|x|>-5
Please type:
- int for oo,
- no solution if there are no real solutions
- U for the union symbol U
You have attempted this problem 8 times.
Your overall recorded score is 0%
You have unlimited attempts remaining.
Answer: [tex](-\infty, \infty)[/tex]
Step-by-step explanation:
Absolute value is always non-negative.
Does 15 36 39 form a right triangle?
1521=1521 therefore a triangle has sides with lengths of 15 inches, 36 inches, and 39 inches form a right triangle.
What is Right traingle?
A right triangle is one that has an interior angle of 90 degrees. The hypotenuse, which is also the side of the right triangle that faces the right angle, is its longest side. The height and base make up the two arms of the right angle.
When we enter the values of the triangle's legs (15 and 36) and hypotenuse (39),
assuming it is a right triangle, into the Pythagoras theorem, the values of each side of the equation will be equal;
The Pythagoras Theorem is:
[tex]a^2+b^2=c^2[/tex]
Making substitutions and applying the math results in:
[tex]15^2 + 36^2= 39^2[/tex]
225 + 1296 = 1521
1521 = 1521
Therefore, it is a right traingle.
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The graph shows g(x), which is a translation of f(x)=|x|. Write the function rule for g(x).
Write your answer in the form a|x-h| + k, where a, h, and k are integers or simplified fractions.
g(x)=____
From the graph it can be calculated that Function rule for g(x) g(x) = |x - 7|
What is graph of a function?
The collection of ordered pairs with the (x,y)(x,y) sign is known as the graph of the a function in mathematics, where f(x)=y. x and f seem to be Cartesian coordinates of pts in two-dimensional space, and in the typical case where they are real numbers, they form a subset of the this plane.
Instead of the pairs "((x,y),z)" and "((x,y),z)" as in the definition above, the graph for functions of two variables, i.e. functions for whom the domain consists of pairs "(x,y)," "(x,y)," is typically the set of ordered triples "(x,y,z)" and "(x,y,z)" where "A surface for a constant real-valued function of the two real variables, this set is indeed a sub - set of three-dimensional space.
Graph of a function f(x) is the collection of points of the form (x, f(x))The given graph is a translation of |x| only,
So value of a is 1
Now since the tip of the graph lies on x- axis, k = 0So the value of g(x) is
g(x) = |x - h|g(7) = 0|7 - h| = 07 - h = 0h = 7
Function rule for g(x) g(x) = = |x - 7|
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If <1=<2"
Definition of congruence
Angle addition postulate
Linear Pair Theorem
Vertical Angles Theorem
A. Congruence means the same.
B. Angle addition postulate states that two angles side by side sum the measure of the two angles.
C. Linear pair theorem states that linear pair angles add up to 180 degrees.
D. Vertical angles theorem states that vertical angles are congruent.
What is congruence?
Congruence in angles simply means the same or equals to. Two angles are congruent when they are the same.
What is angles addition postulate?The angle addition postulate states that the measure of an angle formed by two angles side by side is the sum of the measures of the two angles.
What is linear pair theorem?The Linear Pair Theorem states that two angles that form a linear pair are supplementary. They add up to 180 degrees.
What is vertical angles theorem?The Vertical Angle Theorem says the opposing angles of two intersecting lines must be congruent, or identical in value
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what is the sum 2x24x2
Answer: 96
Step-by-step explanation:
The equation of line T, shown below, can be written in the form y=mx+c.
What are the values of m and c?
Give each of your answers as an integer or as a fraction in its simplest form.
The straight line has the equation, y = 5x - 4.
What is the equation of a straight line?A straight line is made up of an infinite number of points that are joined on both sides of the point.
Any straight line's slope 'm' is given by:
m = y2 - y1 / x2 - x1
In slope-intercept form, a linear equation has the formula y = mx + b. The variables in the equation are X and Y. The values m and b represent the slope (m) of the line and the value of y when x = 0.
The obtained points from the graph are (0,-4) and (1,1)
The slope is ,
m = 1-(-4) / 1-0
= 5/1
= 5
Because it intersects the y-axis at the point where the intercept C = -4,
The line's equation will be:
⇒ y = mx + c
⇒ y = 5x + (-4)
⇒ y = 5x - 4
As a result, the equation for the straight line shown below is y = 5x - 4.
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Ameekah is working with consecutive integers. If she uses x to represent her first number, what should she use to represent her second number?
A x
B x + 1
C x + 2
D 2x
Answer:
B) x + 1
Step-by-step explanation:
Consecutive integers mean continuous integers ( 1, 2 , 3 ,....). We will get the next number by adding 1 to the previous number.
Eg: 5 , 6 , 7 ,.....
6 = 5 + 1
7 = 6 + 1
So, if first number is x, then the next number will be x + 1
How do you make an exponential decay model?
The exponential decay formula can take one of three forms:
f (x) = abˣ , f (x) = a (1 – r)ˣ , P = P₀[tex]e^{-kt}[/tex]
Where,
a (or) P₀ = Initial amount ,b = decay factor, e = Euler’s constant, r = Rate of decay (for exponential decay), k = constant of proportionality
What is Exponential Decay ?
Exponential decay occurs in mathematical functions when the pace by which changes are occurring are decreasing and must thus reach a limitation, which is the horizontal asymptote of an exponential function.
The amount drops gradually, followed by a quick reduction in the speed of change and increases over time. The exponential decay formula is used to determine the decrease in growth. The exponential decay formula can take one of three forms:
f (x) = abx
f (x) = a (1 – r)x
P = P0 e-k t
Where,
a (or) P0 = Initial amount
b = decay factor
e = Euler’s constant
r = Rate of decay (for exponential decay)
k = constant of proportionality
x (or) t = time intervals (time can be in years, days, (or) months, whatever you are using should be consistent throughout the problem).
In exponential decay, the quantity decreases very rapidly at first, and then more slowly. The rate of change decreases over time. The rate of decay becomes slower as time passes. Hence, the exponential decay graph is denoted as
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Directions: Find the value of each variable.
11) x=?
y=?
12) x=?
y=?
13) x=?
y=?
14) x=?
y=?
15) x=?
y=?
z=?
The value of the variables x and y are,
11) x = 13, y = 18.4
12) x = 6.9, y = 8.
What is right angle triangle?
A right triangle is a triangle with one angle at a right angle, meaning that two of its sides are perpendicular. It is also known as a right-angled triangle, an orthogonal triangle, or more commonly as a rectangled triangle. Trigonometry's foundation is the right triangle's relationship between its sides and other angles.
11)Let the given triangle is a right angle triangle.
So we can use trigonometric ratio,
[tex]tan(45) = \frac{x}{13} \\x = 13(tan(45))\\x = 13[/tex]
Using this to find the value of y.
[tex]sin(45) = \frac{x}{y} \\sin(45) = \frac{13}{y} \\y = \frac{13}{sin(45)} \\y = 18.4[/tex]
So, the values of x and y are x = 13 and y = 18.4.
12) The given triangle is a right angle triangle.
So we can use trigonometric ratio,
[tex]tan(30) = \frac{4}{y}\\ y = \frac{4}{tan(30)} \\y = 6.9[/tex]
Now to find the value of x.
[tex]sin(30) = \frac{4}{x} \\x = \frac{4}{sin(30)} \\x = 8[/tex]
Hence, the values of x and y are, x = 6.9 and y = 8.
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How do you find a polynomial?
Answer:
To find a polynomial, you must identify the terms, coefficients, and degrees. The degree of a polynomial is the highest exponent of the variable in the equation. The coefficients of a polynomial are the values that are multiplied by the variables. The terms of a polynomial are the pieces of the equation, including the coefficients and the variables. After identifying the terms, coefficients, and degree of the polynomial, you can write it in standard form.
Step-by-step explanation:
