The 95% confidence interval (in minutes) for the population mean is of:
(2.55, 3.83).
What is a t-distribution confidence interval?The bounds of the confidence interval are given according to the following rule:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the parameters are described as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The distribution is used when the standard deviation of the population is not known, only for the sample.
In the context of this problem, the values of the parameters are given as follows:
[tex]\overline{x} = 3.19, s = 0.77, n = 8[/tex]
The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 8 - 1 = 63 df, is t = 2.3646.
Then the lower bound of the confidence interval is calculated as follows:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 3.19 - 2.3646\frac{0.77}{\sqrt{8}} = 2.55[/tex]
The upper bound is calculated as follows:
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 3.19 + 2.3646\frac{0.77}{\sqrt{8}} = 3.83[/tex]
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What is the slant height and surface area of the pyramid
we have that
The surface area of the pyramid is equal to the area of its square base plus the area of its four triangular faces
step 1
Find out the area of the square base
A=15^2
A=225 ft2
step 2
Find out the area of one triangular face
the area of a triangle is equal to
A=(1/2)(b)(h)
we have
b=15 ft
h ----> is the slant height
To find out the slant height, apply the Pythagorean Theorem
h^2=10^2+(15/2)^2
h^2=100+56.25
h=12.5 ft
therefore
A=(1/2)(15)(12.5)
A=93.75 ft2
step 3
The surface area is equal to
SA=225+4(93.75)
SA=600 ft2 and the slant height is 12.5 ftA car can travel 28 miles per gallon of gas. How far can the car travel on 8 gallons of gas?
A car can travel 28 miles per gallon of gas. How far can the car travel on 8 gallons of gas?
Applying proportion
28/1=x/8
solve for x
x=(28)*8
x=224 miles
the answer is 224 milesFind the future value in dollars of an 18 month investment of $4900 into simple interest rate account that has an annual simple interest rate of 5.5%
Answer:
$5304.25.
Explanation:
The simple interest formula is given by
[tex]A=P(1+rt)[/tex]where
A = future value
P = princple amount
r = interest rate /100
t = time interval.
Now in our case
A = unknown
P = $4900
r = 5.5 / 100
t = 18 / 12 ( we are converting months to years. 18 months = 18 /12 years )
Putting the above values into the simple interest rate formula gives
[tex]A=4900\lbrack1+\frac{5.5}{100}\times(\frac{18}{12})\rbrack[/tex]which simplifies to give
[tex]\boxed{A=\$5304.25.}[/tex]Hence, the future value is $5304.25.
find the measures of GH and CH.
The length of the lines GH and CH are 16 units and 12 units.
What is a line?A line is an object in geometry that is infinitely long and has neither width nor depth nor curvature. Since lines can exist in two, three, or higher-dimensional spaces, they are one-dimensional objects. The term "line" can also be used to describe a line segment in daily life that has two points that serve as its ends. In geometry, lines are drawn with arrows at either end to indicate that they extend indefinitely. Two line points can be used to name a line (for example, AB) or just a letter, usually in lowercase (for example, line m ). The ends of a line segment are two.So, the measure of lines GH and CH:
We know that AC ⊥ GH hence cuts GH in two equal lines.
GB = BH GB is 8 units then BH is also 8 units.GB = BH = 8 units.But,
GH = GB + BHGH = 8 + 8GH = 16 unitsWe can observe that △GCH is an isosceles triangle.
GC = CHGC = CH = 12 unitsTherefore, the length of the lines GH and CH is 16 units and 12 units.
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10x + 45x - 13 = 11(5x + 6)
We have to find the solution for the equation:
[tex]\begin{gathered} 10x+45x-13=11\cdot(5x+6) \\ 55x-13=11\cdot5x+11\cdot6 \\ 55x-13=55x+66 \\ 55x-55x=66+13 \\ 0\cdot x=79 \end{gathered}[/tex]The equation has no solution, becuase there is no value of x that satisfy the equation.
Ryan bought 3 1/2 boxes of paper clips. Allan bought 1 3/4 more boxes than Ryan.
Colin bought 1 1/2 times as many boxes as Allan How many boxes did Colin buy?
Answer:
Colin bought 7 7/8 boxes
Step-by-step explanation:
Let R represent the number of boxes bought by Ryan and A represent the number of boxes bought by Allan
R = 3 1/2
Convert to improper fraction:
3 1/2 = (3 x 2 + 1)/2 = 7/2
Allan bought 1 3/4 more boxes than Ryan
A = R + 1 3/4
Convert 1 3/4 to improper fraction:
1 3/4 7/4
So A = 7/2 + 7/4 = 14/4 + 7/4 = 21/4
Colin bought 1 1/2 times as many boxes as Allan
C = 1 1/2 x A
Convert 1 1/2 to improper fraction:
1 1/2 = 3/2
So C = 3/2 x 21/4
= 63/8 = 7 7/8 boxes
Identify the vertex and axis of symmetry of the quadratic equation. Then, sketch the graph f(x) = (x + 2)² - 1
Answer
Vertex = (-2, -1)
Axis of symmetry: x = -2
The graph of the function is presented below
Explanation
The vertex of a quadratic equation is the point where the graph of the quadratic equation changes from sloping negatively to sloping positively and vice-versa.
The axis of symmetry represents the straight line that divides the graph of the quadratic equation into two mirror parts that are similar to and are mirror images of each other. This axis of symmetry usually passes through the vertex.
To find the vertex, it is usually at the turning point where the first derivative of the quadratic equation is equal to 0.
(df/dx) = 0
f(x) = (x + 2)² - 1
f(x) = x² + 4x + 4 - 1
f(x) = x² + 4x + 3
At the vertex, (df/dx) = 0
(df/dx) = 2x + 4
2x + 4 = 0
2x = -4
Divide both sides by 2
(2x/2) = (-4/2)
x = -2
We can then obtain the corresponding y-coordinate of the vertex
f(x) = (x + 2)² - 1
f(-2) = (-2 + 2)² - 1
f(-2) = 0² - 1
f(-2) = -1
So, the vertex is given as
Vertex = (-2, -1)
Although, one can obtain the vertex from the form in which that equation is given, the general form is that
f(x) = (x - x₁)² + y₁
Comparing that with
f(x) = (x + 2)² - 1
we see that,
x₁ = -2, y₁ = -1
So, Vertex: (-2, -1)
Then, the axis of symmetry will be at the point of the vertex.
Axis of symmetry: x = -2
And for the graph, we just need to obtain a couple of points on the line to sketch that.
when x = 0
f(x) = (x + 2)² - 1
f(0) = (0 + 2)² - 1
f(0) = 4 - 1 = 3
(0, 3)
when y = 0
x = -3 and x = -1
So,
(-3, 0) and (-1, 0)
(-2, -1), (0, 3), (-3, 0) and (-1, 0)
So, with these points, we can sketch the graph.
The graph of this function is presented under answer above.
Hope this Helps!!!
The distance from the earth to Pluto is 4.67x10^9 mi, If a new flying machine can travel 1.92x10^5 miles per year, how many years would it take to reach Pluto? Write your answer in standard form, rounded to the nearest year.
24333 years
Explanationto solve this we need to use the time formula ,it says
[tex]time=\frac{distance}{speed}[/tex]Step 1
a)given
[tex]\begin{gathered} distance=4.67*10^9\text{ miles} \\ speed=1.92*10^5\text{ }\frac{miles}{year} \end{gathered}[/tex]b) now, replace in the formula and calculate
[tex]\begin{gathered} time=\frac{distance}{speed} \\ time=\frac{4.67*10^9}{1.92*10^5}=2.43*10^{9-5}=2.43*10^4 \\ time=2.43*10^4\approx24333\text{ years} \end{gathered}[/tex]therefore, the answer is
24333 years
I hope this helps you
Determine the largest integer value of x in the solution of the following inequality.
Answer:
From the solution the largest possible integer value of x is;
[tex]-6[/tex]Explanation:
Given the inequality;
[tex]-x-1\ge5[/tex]To solve, let's add 1 to both sides of the inequality;
[tex]\begin{gathered} -x-1+1\ge5+1 \\ -x\ge6 \end{gathered}[/tex]then let us divide both sides of the inequaty by -1.
Note: since we are dividing by a negative number the inequality sign will change.
[tex]\begin{gathered} \frac{-x}{-1}\leq\frac{6}{-1} \\ x\leq-6 \end{gathered}[/tex]Therefore, From the solution the largest possible integer value of x is;
[tex]-6[/tex]
Solve for x in 2(2-x)=4(-2+x)
Given the equation:
[tex]2(2-x)=4(-2+x)[/tex]First, we open the brackets
[tex]4-2x=-8+4x[/tex]Next, we collect like terms. (Bring terms containing x to the left-hand side)
[tex]\begin{gathered} -2x-4x=-8-4 \\ -6x=-12 \end{gathered}[/tex]Finally, we divide both sides by -6 (negative 6) to obtain x.
[tex]\begin{gathered} \frac{-6x}{-6}=\frac{-12}{-6} \\ x=2 \end{gathered}[/tex]The value of x is 2.
The table shows the temperature (y) at different altitudes (x). This is a linear relationship. Use the equation y = -0.004x + 59 to determine the temperature at an altitude of 5,000 feet. 0 Altitude (ft), x Temperature (°F),y 2,000 51 4,000 43 6,000 35 59 8,000 27 10,000 12,000 19 11 The temperature at an altitude of 5,000 feet Is OF.
EXPLANATION:
We must replace in the equation given the altitude in the variable x ; the exercise is as follows:
[tex]\begin{gathered} y=-0.004x+59 \\ y=-0.004(5,000)+59 \\ y=-0.02+59 \\ y=58.98 \\ \text{ANSWER: The temperature at an altitude of 5,000 is 58.98} \end{gathered}[/tex]Please help me sketch a graph for this sequence (I've already solved it): 2/3, 1, 3/2, 9/4, 27/8
ANSWER and EXPLANATION
We have that the 1 - 5th terms of the sequence are:
2/3, 1, 3/2, 9/4 and 27/8
To plot the graph of this sequence, we have:
=> on the x axis, the term number (i.e. n = 1, 2, 3, 4, 5)
=> on the y axis, the term(i.e. a(n) 2/3, 1, 3/2, 9/4, 27/8)
We will plot the graph of n versus a(n).
That is:
That is the graph.
HELP PLEASE ANWER AS SOON AS POSSIBLE ALSO PLEASE GIVE A STEP BY STEP EXPLANATION PLEASE!!
Given that f(x)=x2-4/3, f(a)=7, and f(11)=b, a+b can only be a multiple of prime numbers is 5
This calculator for finding the prime factors and the factor tree of an integer is available for use.
How is a prime factor discovered?
The simplest method for determining a number's prime factors is to keep dividing the starting number by prime factors until the result equals 1. When we divide the number 30 by its prime factors, we obtain 30/2 = 15, 15/3 = 5, and 5/5 = 1. We received the balance, thus it cannot be factored any further.
Example: 36 can be written as the product of two prime factors, 22 and 32. The prime factorization of 36 is stated to equal the equation 22 32.
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I just need to know the answer quick because I have to go somewhere
From the given graph, it is seen that f(x) is not defined for x<-4. The function g(x) is not defined for x>2
But the function p(x) represents a straight line which is defined for all real x.
Hence, the function p(x) has all real numbers as its domain.
Thus, the correct option is (D)
help meeeeeeeeee pleaseeeeeeeeeee!!!
thank youu
The required domain and the range of the given function is (0, ∞) and (-8, -2) respectively.
Given that,
A graph of the function is shown we have to determine the domain and range of the function with the help of the graph.
The domain is defined as the values of the independent variable for which there is a certain value of the dependent variable exists in the range of the function.
Here,
As of the graph,
The graph describes as only the positive real number because the graph only consists of the positive x-axis, so the domain of the function is all positive real numbers. While the ordinate of the graph is describe for -8 to -2 on the negative y-axis thus the rang of the given function lies between -8 to -2.
Thus, the required domain and the range of the given function is (0, ∞) and (-8, -2) respectively.
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Find the volume of each rectangular prism. Round to the tenths.
Answer:
To find the volume of the given cuboid.
Length of the cuboid = 6.8 yd
Breadth of the cuboid = 4.5 yd
Height of the cuboid = 3.4 yd
We get,
Volume of a cuboid is,
[tex]=l\times b\times h[/tex]where l,b and h are the length, breadth and height respectively.
Substitute the values we get,
[tex]=6.8\times4.5\times3.4[/tex][tex]=104.04\text{ yd}^3[/tex]Answer is: Volume of the cuboid is 104.04 cubic yards.
Me.Hoffman has a doorstop in his classroom shaped like a triangular prism shown
- To determine the perimeter of the base, consider that the length is 5 in and the width is the same as the width of the top face of the prism, that is, 2 in. Then, the perimeters is:
P = 2l + 2w
w = 2 in
l = 5 in
P = 2(5 in) + 2(2 in)
P = 10 in + 4 in
P = 14 in
- The height of the doorstop is 1.2 in
- The area of the base is:
A = wl
A = (2 in)(5 in)
A = 10 in²
Jeremy said I added 3/4+1/5 and got 4/9, does Jeremy’s answer make sense? Explain how you know without calculating the answer
If
[tex]\frac{3}{4}+\frac{1}{5}=\frac{4}{9}[/tex]That would imply that 9 is a common multiple of 4 and 5, which is false since 9=3^2.
Additionally, 3/4 is greater than 4/9; so 3/4+1/5 has to be greater than 4/9.
Joe has $6,500 to invest One option is to invest some of his money in an account that earns 3% simple interest and the rest in an account that earns 2% simple interest. Joe would like to make at least $200 in interest this year. The following system of equations can be used to help Joe determine how much of his money he should invest at each rate. x +y = 6500 0.03x + 0.02y ≥ 200 The mathematical solution to this system is x=7000. Explain what the solution means in terms of how much Joe should invest in each account.
Data:
[tex]\begin{gathered} x+y=6500 \\ \\ 0.03x+0,02y\ge200 \end{gathered}[/tex]In this case;
x is the amount of money Joe should invest in first account (with 3% simple interest)
y is the amount of monet Joe should invest in second account (with 2% simple interest)
Then, if the mathematical solution for the given system is x=7000 it means that in order to get at least $200 in interest this year Joe needs to invest a bigger amount of money that he has, in the fisrt account ($7000) and in the second account y Joe shoul take a loan of $500 with 2% simple interest
[tex]\begin{gathered} x=7000 \\ x+y=6500 \\ y=6500-x_{} \\ y=6500-7000=-500 \end{gathered}[/tex]find the length of the gray arc in terms of pi
Given
a: angle
a = 60
r: radius
r = 3
Procedure
The length of an arc depends on the radius of a circle and the central angle θ
[tex]\begin{gathered} s=\theta r \\ s=\frac{1}{3}\pi\cdot3 \\ s=\pi \end{gathered}[/tex]The answer would be s = pi
find the coordinates of the vertex of the following parabola algebraically. write your answer as an (x,y) point..y=x²+9
using the parabola formula:
y = a(x-h)² + k²
vertex = (h, k)
We are given a parebola equation of: y = x²+9
comparing both equations to get the vertex:
y = y
a = 1
(x-h)² = x²
x² = (x + 0)²
(x-h)² = (x + 0)²
h = 0
+k = +9
k = 9
The vertex of the parabola as (x, y): (0, 9)
How many terms are included in the expression below?x² – 3x+7A. 2B. 7o oC. 1D. 3
Answer:
Choice D: 3 terms
Explanation:
The term of a expressions constant or a variable of an equation, The variable
6. Oliver is playing a game in which he has to choose one of two numbers (2 or 7) and then one of five vowels (a, e, i, o, or u). How many possible outcomes are there? 2 7 There are possible outcomes.
Answer
Number of possible outcomes for everything = 240 ways
Explanation
The number of possible outcomes can be calculated by taking each of these two groups.
First group contains 2 elements
Number of possible ways to pick the elements = 2! = 2 × 1 = 2 ways
Second group contains 5 elements
Number of possible ways to pick the elements = 5! = 5 × 4 × 3 × 2 × 1 = 120 ways
Number of possible outcomes for everything = 2! × 5! = 2 × 120 = 240 ways
Hope this Helps!!!
There are four Defenders on a soccer team if this represents 20% of the players on the team which equation can be used to find the total number of players on the team
Given in the question:
a.) There are four Defenders on a soccer team.
b.) This represents 20% of the players on the team.
What is the most specific name for each type of special quadrilateral
From the given quadilaterals, let's determine the specific name for each based on the property marked.
• 1a. ,All four sides are marked equal.
Since all four sides are equal, we can say the specific name for the quadilateral is a Square.
A square is a quadilateral with four equal sides.
• 1b. In this quadilateral, we have one pair of parallel sides.
Given that the quadilateral is NOT drawn to scale, the quadilatral here can be said to be a Trapezoid.
A trapezoid is a quadilateral with one pair of parallel side.
• 1c. In this quadilateral, all four angles are marked as right angles.
Given that all four angles are right angles, the specific name for the quadilateral is a Rectangle.
A rectangle is a quadilateral with four interior right angles.
ANSWER:
• 1a. Square
,• 1b. Trapezoid
,• 1c. Rectangle.
Identify the property of real numbers illustrated in the following equation.(-5) + (y · 7) = (y · 7) + (-5)
By definition, the commutative property of addition says that changing the order of addends does not change the sum, which is precisely what the equation is trying to show by changing the order of the sum, therefore, the property illustrated is the commutative property of addition.
Rectangle R measures 18 in by 6 in. Rectangle S is a scaled copy of Rectangle R. Select all of themeasurement pairs that could be the dimensions of Rectangle S.24 in by 8 in9 in by 3 in2 in by 1 in6 in by 2 in3 in by 2 in
In order to find possible dimensions for the scaled rectangle, the proportion between the dimensions of the rectangles must be the same.
So first let's find this proportion for rectangle R:
[tex]\frac{18}{6}=3[/tex]Now, let's find the proportion of the possible options of rectangle S:
[tex]\begin{gathered} \frac{24}{8}=3 \\ \\ \frac{9}{3}=3 \\ \\ \frac{2}{1}=2 \\ \\ \frac{6}{2}=3 \\ \\ \frac{3}{2}=1.5 \end{gathered}[/tex]So the correct options are the first, second and fourth options.
What is x in x/4=1.8/5
Answer:
x = 1.44
Step-by-step explanation:
Multiply both sides by 4 to get rid of the denominator on the LHS(Left hand Side) of the equation and you get x
(x/4) x 4 = 1.8/5 x 4
x = 1.44
The currency in Kuwait is the Dinar. Theexchange rate is approximately $3 forevery 1 Dinar. At this rate, how manyDinars would you get if you exchanged$54?
It is given that the exchange rate is $3 per Dinar. It is required to find how many Dinars you will get if $54 is exchanged.
Since 1 Dinar is equivalent to $3, it follows that the number of Dinars equivalent to $54 is:
[tex]\frac{54}{3}=18\text{ Dinar}[/tex]The answer is 18 Dinar.
What is the slope of this line?
Enter your answer as a whole number or a fraction in simplest form in the box.
Answer:
1/4
Step-by-step explanation:
you just look at rise over run from one point to another and simplify.