If we want to estimate 97% confidence interval for the true proportion of Americans who support gun control in 2019 with a 0.27 margin of error, then 16 Americans must be surveyed.
Given,
The confidence level =97%
Critical z value of 97% confidence interval =2.170
Margin error E= 0.27
We know,
Sample size n= [tex]0.25(\frac{z}{E})^{2}[/tex]
Substitute the values in the equation
[tex]n=0.25(\frac{2.170}{0.27})^{2}\\ n=0.25( 8.03)^{2}[/tex]
n=16.12
n≈16
Hence, if we want to estimate 97% confidence interval for the true proportion of Americans who support gun control in 2019 with a 0.27 margin of error, then 16 Americans must be surveyed.
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Find the Error A large box of spaghetti noodles contains 3 pounds and costs $2.40. A student said the unit cost is $1.20 per pound. Complete the statement to explain why the student was incorrect and find the correct answer.
Answer:
1.25 a pound
Step-by-step explanation:
if it was 1.20 per pound it would be less money
How do I write out -3 * a number increased by 7 is less than -11
The mathematical expression, an inequality to be more specific which represents the given word phrase; -3 * a number increased by 7 is less than -11 is; -3a +7 < 11.
What is the mathematical expression which represents the word phrase; -3 * a number increased by 7 is less than -11 as given?It follows from the task content that the mathematical expression which correctly represents the word phrase is to be determined.
Since the product of -3 and the number, a can be written as; -3 × a = -3a.
Hence, the word phrase as given in the task content can be written as;
-3a +7 < 11.
This follows from the concept of inequalities.
Ultimately, The mathematical expression, an inequality to be more specific which represents the given word phrase; -3 * a number increased by 7 is less than -11 is; -3a +7 < 11.
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Describe
and correct the error in naming opposite rays in
the diagram (problem 26 only)
The error is the symbol for the ray is not correct.
We know that opposite rays are two rays that both start from a common point and go in exactly opposite directions.
In the image attached the rays,
→
YC and
→
YE are opposite rays.
And the points E, Y, and C are colinear, that is the points E, Y, and C lie on a straight line.
In the image, the rays YC and YE just have a line on the above without the right arrow mark. This representation that is given in question indicates that YC and YE are line segments and not rays.
Hence, The correct way to represent them is
→
YC and
→
YE are opposite rays.
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a piece of wire 100 inches long is cut into two pieces and each bent into the shape of a square. if the sum of the areas of the two squares is 400 in2, find the length of each piece of wire.
The length of the pieces of wire include 23.5425 inches and 75.4565 inches.
How to calculate the length?Given the total length of wire is
X+Y=100
Y=100-X
Then we bend the two pieces into squares so that the sides of each square are X/4 and (100-X)/4. Therefore
(X/4)² + [(100-X)/4]² =400
X² +10000-200X +X² =6400
X²-100X+1800=0
Solving the equation
X = 76.4565 inches and X=23.5425 inches
Therefore, the length of the pieces of wire include 23.5425 inches and 75.4565 inches.
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For a data set with an odd number of observations that have been sorted from smallest to largest values, where is the median located?
For a data set with an odd number of observations that have been sorted from smallest to largest values, the median is located at [tex]\frac{x+1}{2}[/tex]
Given,
The conditions
There are odd number of observationThe observation have been sorted from smallest to largest valuesWe know,
Median is the middle number of ordered data set.
Consider the number of observations as x
Then the median is located at [tex]\frac{x+1}{2}[/tex]
Hence, for a data set with an odd number of observations that have been sorted from smallest to largest values, the median is located at [tex]\frac{x+1}{2}[/tex]
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Which expression is equivalent to −30+(−40)+(−70) ?
−(30−40)+(−70)
negative open parenthesis 30 minus 40 close parenthesis plus open parenthesis negative 70 close parenthesis
30 + 40 + 70
30 + 40 + 70
−30+(−70)+(−40)
negative 30 plus open parenthesis negative 70 close parenthesis plus open parenthesis negative 40 close parenthesis
−30−(40−70)
The answer choice which correctly represents an equivalent expression to that which is given as in the task content is; −30 + (−70) + (−40).
Which expression is equivalent to that which is as given in the task content?It follows from the task content that the expression whose equivalent is to be determined is; −30 + (−40) + (−70).
Therefore, since it follows from the associative property of addition that;
a + b + c = a + c + b.
Therefore, same can be said for the expression as given in the task content where;
-30 + (-40) + (-70) = -30 + (-70) + (-40).
Ultimately, the required equivalent expression is; −30+(−70)+(−40); negative 30 plus open parenthesis negative 70 close parenthesis plus open parenthesis negative 40 close parenthesis
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eli wants to combine 0.5 gallons of a 10% acetic acid solution with a 35% solution to make a 15% acetic solution. he needs to determine how many gallons of 35% solution are needed.
0.125 gallons of 35% solution are required to achieve the specified ratio.
This is further explained below.
How many gallons of 35% solution is needed by Eli ?Generally, It takes 0.125 gallons of a 35% solution to get the ratio you want.
Eli wishes to mix 0.5 gallons of a 10% acetic acid solution with a 35% solution to create a 15% acetic acid solution; thus, the calculation below must be done to calculate how many gallons of
5% solutions are required:
1 x 10 + 2 x 35 = 80
=> 80 ÷ 3 = 26.66
1x10 + 1x35 = 45
=>45÷ 2 = 2.5
1 x 10 + 0.5 x 35 = 27.5
=>27.5 ÷ 1.5 = 18.33
1 x 10 + 0.4 x 35 = 24
=>24 ÷ 1.4 = 17.14
1 x 10 + 0.2 x 35 =17
=> 17 / 1.2 = 14.16
1 x 10 + 0.3 x 35 = 20.5
=> 20.5/ 1.3 = 15.76
1 x 10 + 0.25 x 35 = 18.75
=> 18.75 / 1.25 = 15
1 / 2 = 0.5
0.25 / 2 = 0.125
In conclusion, 0.125 gallons of 35% solution are required to achieve the specified ratio.
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CQ
eli wants to combine 0.5 gallons of a 10% acetic acid solution with a 35% solution to make a 15% acetic acid solution. he needs to determine how many gallons of 35% solution are needed eli decides to let v represent the volume of 35% solution and makes a table to help solve the problem
Answer:
if yours is how mine is- i hope this helps
Step-by-step explanation:
ac a, c, with, \overleftrightarrow, on top is tangent to circle ooo at point ccc. what is the measure of \angle oac∠oacangle, o, a, c?
The correct option is (C) 45°
The measure of angle ∠OCA = 45°.
What is the tangent?A circle is a depiction with no sides or vertices.
It includes a radius as well as a center. The center is the point from which all other points just on circle are equidistant, and the distance between them equals the radius.
Let AC equal the tangent to the circle with center O.
OA ⊥ AC ....(The tangent has always been perpendicular to the radius.)
As, it is given that ∠OAC = 90° and ΔOAC is isosceles triangle.
Thus, ∠O = ∠C = x (say)
Now, using the triangle's angle sum property. We have it,
90° + x + x= 180°
On simplification;
x = 45°
Thus, the value of angle ∠OCA is 45°.
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The correct question is-
'O' is a centre of a circle, AC is a tangent to a circle at point A. If ΔOAC is an isosceles triangle, then find the measure of ∠OCA
(A) 75°
(B) 50°
(C) 45°
(D) 40°
32 1+1=26 258 4 Part A: Create a story or context for this number sentence. (4 points) Part B: Rewrite this number sentence using multiplication. (2 points) Part C: Give a verbal explanation that describes how these three numbers are related. (4 points) 2
A
Step-by-step explanation:
Watch help video
Find the equation of the exponential function represented by the table below:
X
0
1
2
3
Y
0.02
0.04
0.08
0.16 help please
Hence, the equation of exponential function is represented by y = A(Bˣ)
An exponential function is a mathematical function of the form f(x) = ax, where "x" is a variable and "a" is a constant called the base of the function and it must be greater than 0. The most commonly used exponential basis is the transcendental number e, which is approximately equal to 2.71828The equation in exponential form
y = A(Bˣ)
Case 1 :
x =0 y = 0.02
0.02 = A (B⁰)
A = 0.02
Case 2:
x = 1 y =0.04
0.04 = 0.02(B)
0.04 /0.02 = B
B = 2
Case 3 :
x = 2 y =0.08
0.08 = 0.02(2²)
0.08 = 0.08
Case 4 :
x = 3 y = 0.16
0.16 = 0.02(2³)
0.16 = 0.16
So, we have implemented the eqaution y = A(Bˣ)
We found the values of A & B, and also proved them in case 3 and case 4.
Hence, the equation of exponential function is represented by y = A(Bˣ)
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Find the coordinates of the centroid of the triangle with the given vertices. (Lesson 5-2)
U(-5,5), K(-5,-1), L(1,2)
The triangle with vertices located at U(-5 , 5), K(-5 , -1), and L(1 , 2) has its centroid located at (-3 , 2).
The centroid of a triangle is the point inside the triangle where the three medians intersect. The median of a triangle is the line the connects the midpoint of a side and the opposite vertex.
To get the centroid of a triangle, use the formula given by:
C(x , y) = [(x1 + x2 + x3)/3 , (y1 + y2 + y3)/3]
where C is the centroid of the triangle located at (x , y)
x1, x2, and x3 are the x-coordinate of the vertices of the triangle
y1, y2, and y3 are the y-coordinate of the vertices of the triangle
Let Point 1(x1 , y1) = U(-5 , 5)
Point 2(x2 , y2) = K(-5 , -1)
Point 3(x3 , y3) = L(1 , 2)
Plug in the values in the formula.
C(x , y) = [(x1 + x2 + x3)/3 , (y1 + y2 + y3)/3]
C(x ,y) = [(-5 + -5 + 1)/3 , (5 + -1 + 2)/3]
C(x ,y) = (-9/3 , 6/3)
C(x ,y) = (-3 , 2)
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A janitor had 2/3 of a spray bottle of cleaning solution. He used 1/6 of a solution of the day .How much does a bottle did he use?
Answer:
3/6
Step-by-step explanation:
2/3 = 4/6
(multiply 2 by 2 = 4, multiply 3 by 2 = 6)
4/6 - 1/6 = 3/6
Answer:
2x2/3x2-1/6
4/6-1/6=3/6=1/2
he used half for the day
hope this helps or may also he correct •-•
four less than the product of 2 and a number g
The expression that represents the statement "four less than the product of 2 and a number g" is 2 g - 4.
We are given a statement:
four less than the product of 2 and a number g
We need to form an expression to represent that statement.
An expression is a combination of variables and constants by using the various operations of mathematics like addition, subtraction, division and multiplication.
So, first we will find the product of 2 and a number g.
This is:
2 × g = 2 g
Now, we will subtract 4 from the expression:
2 g - 4
Therefore, the expression that represents the given statement "four less than the product of 2 and a number g" is 2 g - 4.
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Question 3(Multiple Choice Worth 1 points)
(01.01 LC)
Evaluate the expression 5(7-4)2 + 3 + 11.
3
14
26
33
The value of the algebraic expressions is 59.
According to the statement
We have to find that the value of the expression.
So, For this purpose, we know that the
Algebraic expression is, a symbol or a combination of symbols used in algebra, containing one or more numbers, variables, and arithmetic operations
From the given information:
5(7-4)^2 + 3 + 11
Then we have to solve it with bodmas rule.
Then
5(7-4)^2 + 3 + 11
Firstly solve the bracket
5(3)^2 + 3 + 11
Then multiply the terms
5*9 + 3 + 11
Then add the terms
45+14
59.
So, The value of the algebraic expressions is 59.
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Choose the correct statement.
-2 < -3
1 = -1
5 > -6
The answer is only 1
a set of data has ten numbers. the mean of the data is 12 and the standard deviation is 0. what values could make up a data set with these statistics?
Answer:
well 22
Step-by-step explanation:
what is the answer to the answer to the answer to the answer to the same the whole of I will tell is the best of the whole time I will tell u won't let go and see if you have any questions or concerns please visit
what is the standard quadratic form if the vertex is (4,7) and in case yo need it another value is (6,19). I REALLY NEED THIS PLEASE!!!
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]vertex \begin{cases} x=4\\ y=7 \end{cases}\implies y=a(x-4)^2 +7~\hfill \textit{we also know that} \begin{cases} x=6\\ y=19 \end{cases} \\\\\\ 19~~ = ~~a(6-4)^2 +7\implies 12=a(2)^2\implies \cfrac{12}{(2)^2}=a\implies 3=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\LARGE \begin{array}{llll} y=3(x-4)^2 + 7 \end{array}} ~\hfill[/tex]
4. Joyce works at Coronado's Furniture. She is paid on commission. She receives
10% of her first $900 in sales and 15% of the balance of her sales. Last week she
earned $750. What was the total value of the furniture she sold?
The total value of the furniture she sold is $4400.
How to compute the value?Let the remaining sales be represented by x.
She receives 10% of her first $900 in sales and 15% of the balance of her sale.
This will be:
(10% × $900) + (15% × x) = 750
90 + 0.15x = 750
Collect like terms
0.15x = 750 - 90
0.15x = 660
Divide
x = 660/0.15
x = 4400
Therefore, the total value is $4400.
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Mrs. Williams made her homemade chicken soup. She made 6 3/4 cups of soup. Each serving size was 1 1/8 cup. How many servings are there?.
Answer: there are 6 servings
Step-by-step explanation:
[tex]\displaystyle\\6\frac{3}{4}:1\frac{1}{8} =\\\\\frac{6*4+3}{4} :\frac{1*8+1}{8} =\\\\\frac{24+3}{4}:\frac{8+1}{8}=\\\\\frac{27}{4}:\frac{9}{8}=\\\\\frac{27}{4}*\frac{8}{9} =\\\\ \frac{27*8}{4*9} =\\\\\frac{3*9*4*2}{4*9} =\\\\3*2=\\\\6[/tex]
Aaron and Boone are splitting up the number of apples they picked the number each has can be described in the equation b+2=2a Which statement correctly describes the relationship between a and b in the equation
A. twice a is 2 more than b
B. twice b is 2 more than a
C. twice a is 2 less than b
D. twice b is 2 less than a
The fairs train ride covers a distance of 3 miles in 20 minutes what is the speed for the ride in miles per minute
Answer:
0.15 miles per minute or 9 miles per hour
Step-by-step explanation:
(URGENT) A dog is resting against a pole to which he is attached with a 24 meter chain. He watches a cat approach to within 8 meters of the pole and promptly gives chase. The dog runs at 12 meters per second and the cat runs at 10 meters per second. Which does the dog reach first, the car or the end of the chain?
Answer: End of chain
Step-by-step explanation:
Dog is at pole and cat is at 8 meters if the dog runs at 12 meters a sec and cat runs at 10 in 2 secs the dog will reach end of chain. But the dog needs 4 secs to reach cat because the dog runs 2 meters a second faster than the cat. Hope it Helps!
11. m<2-34°. Find m<4 and explain how you know. (2 points)
Answer:
21
Step-by-step explanation:
This weekend, the local Cinema sold a total of 8500 movie tickets. The proceeds totaled $64,600. Tickets can be bought in one of 3 ways a matinee ticket costs $5 student tickets costs $6, and regular tickets are $8.50. How many of each type of ticket was sold if twice as many student tickets were sold as matinee tickets?
Number of matinee tickets = 900
Number of student tickets = 1800
Number of regular tickets = 5800
Algebra is the branch of mathematics that represents problems and situations in the form of mathematical expressions. It contains variables such as x, y, z, and operations such as addition, subtraction, multiplication, and division to form meaningful mathematical expressions.Algebra is used mostly in all areas of mathematics like trigonometry, calculus, and coordinate geometry. A simple example of an algebraic expression is 9x + 4 = 8. Algebra deals with symbols, and these symbols are related to each other by operators. It's not just a mathematical concept, it's a skill that we all use subconsciously in our daily lives.
Let x be the number of matinee tickets.
In that case, the number of student tickets is 2x.
The number of regular tickets is (8500-x-2x) = (8500-3x).
Total money
5x + 6*(2x) + 8.50*(8500-3x) = 64600
Simplifying and solving for x
5x + 12x - 8.50*3*x + 8.50*8500 = 64600
5x + 12x - 8.50*3*x = 64600 - 8.50*8500
Solving x , we get
x = 900
Number of matinee tickets = 900
Number of student tickets = 1800
Number of regular tickets = 8500 - (900+1800) = 5800
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27 people were on a coach.
There were 24 people at the next coach stop.
1/3 of these people got on the coach.
What is 1/3 of 24?
Step-by-step explanation:
are you serious ?
1/3 of 24 means dividing 24 by 3,
means 24×1/3 = 24/3 = 8
choose an expression that is equivalent to negative three raised to the fourth power divided by negative three raised to the second power.
The expression that is equivalent to negative three raised to the fourth power divided by negative three raised to the second power is (-3⁴) / (-3²)
Expression:
Expressions are the mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given,
Negative three raised to the fourth power divided by negative three raised to the second power.
Here we need to find the expression for this statement.
First, we have to divide the statement into two like,
"Negative three raised to the fourth power"
It can be written as,
=> (-3⁴)
And the for the next part,
"Negative three raised to the second power."
It can be written as,
=> (-3²)
Now we have to divide these two terms, the we get,
=> (-3⁴) / (-3²)
Therefore, the expression is (-3⁴) / (-3²).
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Find the Domain.
7-4x/|2x+5|+3
The domain of the function is the set of all real values
How to determine the domain of the equation?
The equation of the function is given as:
f(x) = |2x + 5| + 3
The above function is an absolute value function
All absolute value functions can take any value as their input
This means that the given function can take any value as its input
Hence, the domain of the function is the set of all real values
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2 1/3 + 6 3/5
Give me step by step pls
Answer: 8 14/15
Step-by-step explanation:
2 1/3 + 6 3/5 =
2+1/3 + 6+3/5=
2+6+1/3+3/5=
8+1/3+3/5=
8+(1/3+3/5)*15/15=
8+(1*15/3+3*15/5)/15=
8+(15/3 + 45/5)/15=
8+(5+9)/15=
8+14/15=8 14/15
A number raised to the fifth power.
-5 =n-3
bjjvyuvfjjkooyfv
Answer:
-2 = nStep-by-step explanation:
-5 = n - 3
- 5 + 3 = n
-2 = n
--------------
check
-5 = -2 - 3
-5 = -5
the answer is good