Answers
Answer:
see attached
Step-by-step explanation:
Given the pictorial equations, you want to know the single-digit values of each of the images.
EquationsThere are 6 equations in 5 unknowns, but no numerical values are assigned. Solving the equations will only give ratios of values. From those, we need to determine the numerical values that will keep all numbers in the range 1–9.
Let the icons be represented by letter variables as follows:
hat = hboot = bsock = stennis shoe = tmitten = mRewriting the equations to standard form, we have ...
h +b -m -s = 0 . . . . . [eq1]
h -b +t = 0 . . . . . . . . [eq2]
b -3s = 0 . . . . . . . . . [eq3]
h -s -t +m = 0 . . . . . [eq4]
h +2s -m = 0 . . . . . . [eq5]
h +b +s -2t = 0 . . . . . [eq6]
SolutionWe can add [eq4] to [eq1] and [eq5] to eliminate the m variable.
(h +b -m -s) +(h -s -t +m) = 0 ⇒ 2h +b -2s -t = 0 . . . . [eq7]
(h +2s -m) +(h -s -t +m) = 0 ⇒ 2h +s -t = 0 . . . . . . . . . [eq8]
Adding [eq2] to [eq6], and [eq7] will eliminate the b variable.
(h +b +s -2t) +(h -b +t) = 0 ⇒ 2h +s -t = 0 . . . . same as [eq8]; no help
(2h +b -2s -t) +(h -b +t) = 0 ⇒ 3h -2s = 0 . . . . . [eq9]
Now, we have 3 equations in 4 unknowns:
b -3s = 0 . . . . . . . [eq3]
3h -2s = 0 . . . . . . [eq9]
2h +s -t = 0 . . . . . [eq8]
The smallest positive integer values that will satisfy [eq9] are ...
h = 2, s = 3
Using these in the remaining equations gives ...
b -3·3 = 0 ⇒ b = 9
2·2 +3 -t = 0 ⇒ t = 7
And we can find m using [eq5]:
m = h +2s = 2 +2·3 = 8
Then the solution is ...
hat = 2boot = 9sock = 3tennis shoe = 7mitten = 8
Related Questions
someone help me with both of these geometry problems
Answers
Step-by-step explanation:
Regular decagons have two additional identifying properties: 10 exterior angles of 36° , summing to 360° 10 interior angles of 144° , summing to 1,440°
Each interior angle of a regular dodecagon is equal to 150°. Each exterior angle of a regular dodecagon is equal to 30°. 30×12= 360
Determine the missing angle measure.
Answers
Answer:
Step-by-step explanation:
Since you already know that one of the angles is 21 degrees, this helps you A LOT. In total the line is 180 degrees so to find x you just do 180-21 which equals 159
x+ 159 degrees
URGENT!!!! 25 POINTS!!!
What is the linear function expressed by the following table?
Answers
The linear function expressed by the table is y = -1x + 4.
What is a linear function?
A linear function is a type of mathematical function that represents a linear relationship between two variables, often represented by x and y. The general form of a linear function is y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis). Linear functions are also called lines.
To find the equation of the line from a table of values, you can use the slope-intercept form, y = mx + b
where m is the slope and b is the y-intercept
In order to find the slope 'm' we use the following formula:
m = (change in y)/(change in x) = (y2 - y1) / (x2 - x1)
Here,
m = (-2 - 2) / (2 - (-2)) = (-4)/4 = -1
The slope is -1, which means that for every one-unit increase in x there's a corresponding one-unit decrease in y.
To find the y-intercept, you can use one of the points from the table and substitute the x and y values into the equation
y = mx + b
So now we know that m = -1,
plugging the first point (x,y) = (-2,2) in the equation
2 = -2 - b
b = 4
So the equation of the line is y = -1x + 4
Hence, the linear function expressed by the table is y = -1x + 4.
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which expression is equivalent to
Answers
The provided expression can be simplified in the form 2y4/x4 option ( B) Using the integer exponent characteristics, = [x[tex]^\frac{1}{8}[/tex] . y⁸] is the right answer.
What is defined as an integer exponent?In mathematics, integer exponents are exponents that fall under the integer category. It's possible for the number to be either positive or undesirable. The positive integer exponents in this example dictate how many times that base number must be multiplied by itself.
It's possible for the number to be either positive or undesirable. The positive integer exponents in this example dictate how many instances the base number must be multiplied by itself.
According to the given information:= [x[tex]^\frac{1}{4}[/tex] . y¹⁶][tex]^\frac{1}{2}[/tex]
= [x[tex]^\frac{1}{8}[/tex] . y⁸]
The provided expression can be simplified in the form 2y4/x4 option ( B) Using the integer exponent characteristics, = [x[tex]^\frac{1}{8}[/tex] . y⁸] is the right answer.
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Use the following denomination (Ghana cedis 200,100,50 and 20)to find the quantities of notes
1.3584655000
2.85760000
3.146737000
4.5555627000
5.7777000
Answers
1) Number of 200 notes = 17,923,275
Number of 100 notes = 35,846,550
Number of 50 notes = 71,693,100
Number of 20 notes = 179,232,750
2) Number of 200 notes = 428,800
Number of 100 notes = 857,600
Number of 50 notes = 1,715,200
Number of 20 notes = 4,288,000
3) Number of 200 notes = 733,685
Number of 100 notes = 1,467,370
Number of 50 notes = 2,934,740
Number of 20 notes = 7,336,850
4) Number of 200 notes = 27,778,135
Number of 100 notes = 55,556,270
Number of 50 notes = 111,112,540
Number of 20 notes = 277,781,350
5) Number of 200 notes = 38,885
Number of 100 notes = 77,770
Number of 50 notes = 155,540
Number of 20 notes = 388,850
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
Ghana credits 200,100,50 and 20 notes.
Now,
Since, Ghana credits 200,100,50 and 20 notes.
1) Hence, To credit the amount 3584655000,
Number of 200 notes = 3584655000/200 = 17,923,275
Number of 100 notes =3584655000/100 = 35,846,550
Number of 50 notes =3584655000/50 = 71,693,100
Number of 20 notes = 3584655000/20 = 179,232,750
2) To credit the amount 85760000;
Number of 200 notes = 85760000/200 = 428,800
Number of 100 notes = 85760000/100 = 857,600
Number of 50 notes = 85760000/50 = 1,715,200
Number of 20 notes = 85760000/20 = 4,288,000
3) To credit the amount 146737000;
Number of 200 notes = 733,685
Number of 100 notes = 1,467,370
Number of 50 notes = 2,934,740
Number of 20 notes = 7,336,850
4) To credit the amount 5555627000;
Number of 200 notes = 27,778,135
Number of 100 notes = 55,556,270
Number of 50 notes = 111,112,540
Number of 20 notes = 277,781,350
5) To credit the amount 7777000;
Number of 200 notes = 38,885
Number of 100 notes = 77,770
Number of 50 notes = 155,540
Number of 20 notes = 388,850
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If 7/8 is multiplied by 4/5, will the product be greater than wait her of the two factors Explain.
Answers
Answer:
[tex] \frac{7}{8} \times \frac{4}{5} = \frac{7 \times 1}{2 \times 5} \\ = \frac{7}{10} [/tex]
Help me ….::::..::::&:88338
Answers
Answer:
y = [tex]\frac{1}{3}[/tex] x - 6
Step-by-step explanation:
9y - 3x = -54
We want in the form
y = mx + b
9y - 3x = -54 Add 3x to both sides
9y - 3x + 3x = 3x - 54
9y = 3x - 54 Divide all the way through by 9
[tex]\frac{9y}{9}[/tex] = [tex]\frac{3x}{9}[/tex] - [tex]\frac{54}{9}[/tex]
y = [tex]\frac{3}{9}[/tex] x - 6
We can simplify [tex]\frac{3}{9}[/tex] ÷ [tex]\frac{3}{3}[/tex] = [tex]\frac{1}{3}[/tex]
y = [tex]\frac{1}{3}[/tex] x - 6
What is the solution to the system of linear equations 3x 2y equals 14 5x y equals 32?
Answers
The solution to the system of linear equations 3x + 2y = 14 and 5x + y = 32 is (x, y) = (6, 10).
3x + 2y = 14
5x + y = 32
Subtracting 3x from both sides of the first equation:
2y = 14 - 3x
Substituting this into the second equation:
5x + (14 - 3x) = 32
Simplifying:
8x = 18
x = 18/8
x = 2.25
This x value is substituted into the first equation.:
2y = 14 - 3(2.25)
2y = 14 - 6.75y
= 7.25
The solution is (x, y) = (2.25, 7.25)
The solution to the system of linear equations 3x + 2y = 14 and 5x + y = 32 is (x, y) = (2.25, 7.25). To solve the system, we first subtracted 3x from both sides of the first equation and then substituted this into the second equation. After simplifying, we obtained a value of x, which we then substituted into the first equation to obtain a value of y. This gave us the solution (x, y) = (2.25, 7.25).
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You are planning to sell ice cream cones for a school sporting event . You plan to sell 300 ice cream cones. Before selling the ice cream, you give a survey to determine what flavors to sell. The results are below.
• 10% - Mint
• 25% - Strawberry
• 15% - Chocolate chip
• 50% - Vanilla
Based on the survey results, how much of each flavor will you sell at the sporting event
Answers
Answer: Based on the survey results, we can calculate the number of ice cream cones to sell for each flavor by multiplying the percentage of the flavor by the total number of ice cream cones to be sold.
Mint: 10% of 300 ice cream cones = 0.1 * 300 = 30 ice cream cones
Strawberry: 25% of 300 ice cream cones = 0.25 * 300 = 75 ice cream cones
Chocolate chip: 15% of 300 ice cream cones = 0.15 * 300 = 45 ice cream cones
Vanilla: 50% of 300 ice cream cones = 0.5 * 300 = 150 ice cream cones
So, based on the survey results, you should sell 30 ice cream cones of Mint flavor, 75 ice cream cones of Strawberry flavor, 45 ice cream cones of Chocolate chip flavor, and 150 ice cream cones of Vanilla flavor.
It's worth mentioning that the sum of the percentages provided, 10+25+15+50 = 100%. Which means that it is a proper survey and the total number of ice cream cones you expect to sell is equal to the survey results.
Step-by-step explanation:
Based on the survey results flavors sold at the sporting event are, 30 mint ice creams, 75 Strawberry icecreams, 45 Chocolate chip icecreams, and 150 Vanilla icecreams.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
The number of different types of ice creams can be obtained as follows,
10% - Mint.
= (10/100)×300.
= 30.
25% - Strawberry.
= (25/100)×300.
= 75.
15% - Chocolate chip.
= (15/100)×300.
= 45.
50% - Vanilla.
= (50/100)×300.
= 150.
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Answer quickly IF u love god i do please
Answers
Answer:
The answer is 11
Step-by-step explanation:
The answer is 11 because you need to add the sides up that the points are on point P is 5 Point Q is 3 and point R is 3 5+3 is 8 8+3 is 11
Answer:
19.56
Step-by-step explanation:
PR = [tex]\sqrt{3^{2} + 3^{2} }[/tex] = [tex]\sqrt{18}[/tex] = 3[tex]\sqrt{2}[/tex]
RQ = [tex]\sqrt{5^{2} +5^{2} }[/tex] = [tex]\sqrt{50}[/tex] = 5[tex]\sqrt{2}[/tex]
QP = [tex]\sqrt{8^{2} +2^{2} }[/tex] = [tex]\sqrt{68}[/tex] = 2[tex]\sqrt{17}[/tex]
Perimeter = sum of the sides = 3[tex]\sqrt{2}[/tex] + 5[tex]\sqrt{2}[/tex] + 2[tex]\sqrt{17}[/tex] = 19.56
Break the triangle PQR into 3 right triangles, with each leg being a hypotenuse. Then you can use the Pythagorean theorem to find the length of each leg. Add them all together to get the perimeter.
Find the total surface area of a cone of base diameter 7cm and height 8cm
Answers
The total surface area of a cone which has a base diameter of 7 cm and height of 8 cm is 126.5 cm ²
How to find the total surface area of a cone ?The total surface area of a cone can be found by the formula :
= (π x radius ²) + (π x radius x height )
Radius is half of diameter so :
= 7 / 2
= 3. 5 cm
The total surface area of the cone is;
= ( π x 3. 5 ²) + ( π x 3. 5 x 8)
= 38 . 5 + 88
= 126.5 cm ²
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Isaac's father is 49 years old. He is four years older than three times Isaac's age. How old is Isaac
Answers
If Isaac's father is four years older than three times of Isaac's age and the age of father is 49 years old. So, Isaac age will be 15 years old.
How old is Isaac?According to online myth, there is a mathematical equation that regulates the lower bound for a possible dating partner's socially acceptable age: half your age plus 7, or, in mathematical words, if x is your age, the bottom barrier is [tex]f(x) = x/2 + 7[/tex].
Consider Isaac is L
Let us suppose L is x years old.
3 times the age of L = 3x
3 times L’s age plus 4 years = 3x + 4
Furthermore, L’s father’s age is 49 years older than L’s age.
Therefore,
[tex](3x + 4) = (49) (49)\\(3x + 4) -4 = (49) – 4\\3x = 45\\3x/3 = 45/3\\X = 15[/tex]
L’s age is 15 years since we expected L’s age = x (and x=15).
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a shopper purchased 8 t-shirts and 5 pairs of pants for $220. the next day, he purchased 5 t-shirts and 1 pair of pants for $112.How much does each t shirt and each pair of pants cost?
Answers
Answer:
Step-by-step explanation:
Let the costs of 1 t - shirt and 1 pair of pants be 'x' and 'y' respectively then:
Case 1 --> 8x + 5y = 220 ----------(1)
Case 2 --> 5x + y = 112 ----------(2)
Multiplying equation (2) by 5:
8x + 5y = 220
25x + 5y = 560 ------(3)
Subtracting equation (1) from equation (3) we get :
17x = 340
x = 20
Putting x in (2):
5 x 20 + y = 112
y = 12
therefore, cost of each t-shirt is 20 rupees and the cost of each pair of pants is 12 rupees
In a certain lottery, 5 numbers between 1 and 13 inclusive are drawn. These are the winning numbers. How many different selections are possible
Answers
1287 combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter.
How many different lottery combinations are there?You win the jackpot if you match all six numbers. You receive a lesser fixed prize if you partially match some of the numbers.
Divide the number of winning lottery numbers by the total number of available lottery numbers to discover the probability of winning any lottery. Use the formula if the numbers are picked from a set and the order of the numbers is unimportant.
To find the winning combination we use the following formula
n !/ r!( n – r ) !
Where n = total number of to be drawn
r = the number which are drawn
In this question, n = 13, and r = 5
from the formula
13 !/5!( 13 – 5 ) !
= 13! / 5! 8!
= 13*12*11*10*9*8! / 5*4*3*2*1*8!
= 154,440 / 120
= 1287
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GIVEN: GH (congruent JH and FH (congruent) HI
PROVE: FG (congruent) IJ
Answers
Hence proved that FG = IJ with CPCT theorem for ΔGHF ≅ ΔJHI by SAS Congruency rule.
What is Congruency of triangles?Triangle congruence: Two triangles are deemed to be congruent if all three of their corresponding sides and angles have the same magnitude. Slides, rotations, flips, and turns can be used to make these triangles appear identical. They would be in alignment if they were moved. Congruence is represented by the letter "≅".
When two figures are similar to one another in terms of their size and shape, this is what mathematicians mean by congruence. It can be demonstrated that two triangles are congruent using four congruence rules in general. Finding all six dimensions is necessary, though.
Given that,
GH ≅ JH
FH ≅ HI
And,
∠GHF = ∠JHI
Therefore,
ΔGHF ≅ ΔJHI (SAS Congruency)
∴ FG = IJ (CPCT theorem)
Hence proved that FG = IJ with CPCT theorem for ΔGHF ≅ ΔJHI by SAS Congruency rule.
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What is the coefficient of XY in the expression *?
Answers
The numerical coefficient of xy in the given expression -7xy is -7.
The numerical coefficient of an expression is a number that is multiplied by a variable or a product of variables. The coefficient is the number that appears in front of a variable or a product of variables. In the case of a constant term, the coefficient is the constant itself.
For example, in the expression 3[tex]x^2[/tex] + 4x - 5, the numerical coefficient of [tex]x^2[/tex] is 3, the numerical coefficient of x is 4, and the numerical coefficient of the constant term -5 is -5.
Here, in the expression -7xy, the numerical coefficient of xy is -7.
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The complete question is -
What is the coefficient of XY in the expression - 7xyz?
ORIGINAL ANSWERS PLEASE
A student's course grade is related to class attendance. The grade can be modeled by the equation y = 0.66x + 33.3, where y is the student's grade as a percentage and x is the number of days that the student attended class. For a student who was in attendance for 75 days and has a grade of 82%, find and interpret the residual.
Answers
The residual of the given situation is 0.8
What is residual of a function?The residual for each observation is the difference between predicted values of y (dependent variable) and observed values of y.
Given that, The grade can be modelled by the equation y = 0.66x + 33.3, where y is the student's grade as a percentage and x is the number of days that the student attended class. We are asked to find residual if student who was in attendance for 75 days and has a grade of 82%,
Finding the actual value,
y = 0.66 × 75 + 33.3
y = 82.8
The predicted value = 82
Residual = actual y value − predicted y value
Therefore,
Residual = 82.8-82 = 0.8
Therefore, y = 0.8
Hence, the residual of the given situation is 0.8
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How do you know if a product is a perfect square?
Answers
In essence, a perfect square is produced when two equal integers are multiplied by one another.
what is perfect square ?Squaring an integer produces perfect squares. For instance, the number 81 is a perfect square since it can be calculated by squaring 9: 99=81. Due to the fact that 12 is squared to produce 144, 144 is a perfect square. Because 13 is squared to produce 169, 169 is a perfect square. Language of Mathematics. Informally: The result is known as a square number, a perfect square, or simply "a square" when an integer (a "whole" number), whether positive, negative, or zero, is multiplied by itself. So all square numbers are 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so forth.
given
In essence, a perfect square is produced when two equal integers are multiplied by one another.
Due to the fact that you are multiplying two equal integers (5 and 5) by one another, 25, it is a perfect square. The result of a number being multiplied by itself is referred to as the square of the number.
In the case when m and n are both natural numbers, m is a perfect square if m = n2. A perfect square is produced when two perfect squares are added together.
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Right triangle $ABC$ has one leg of length 6 cm, one leg of length 8 cm and a right angle at $A$. A square has one side on the hypotenuse of triangle $ABC$ and a vertex on each of the two legs of triangle $ABC$. What is the length of one side of the square, in cm
Answers
One side of the square has a length of 10 cm.
The triangle $ABC$ is a right triangle and it has one leg of length 6 cm and one leg of length 8 cm. Using the Pythagorean theorem, we can find the length of the hypotenuse:
c^2 = a^2 + b^2
c = √(a^2 + b^2)
c = √(6^2 + 8^2)
c = √(36 + 64)
c = √(100)
c = 10
So the hypotenuse of triangle $ABC$ has a length of 10 cm.
The square has one side on the hypotenuse of the triangle $ABC$ and a vertex on each of the two legs of the triangle $ABC$. Since the square is on the hypotenuse of the triangle, one side of the square has the same length as the hypotenuse of the triangle, which is 10 cm.
Therefore, one side of the square has a length of 10 cm.
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An electronics store owner is trying to how much they should try to sell a computer that cost the store $200. They want to increase this price by 25% for the store’s profit and then increase that new price by 15% to account for the sales person’s profit. How much should they sell the computer for?
Answers
Answer:
They should sell the computer for $287.50
Step-by-step explanation:
Let's solve the 25% increase first
100% = $200
100% + 25% = 125% = 1.25
200 x 1.25 = $250
Then we find the 15% increase
100% = $250
100% + 15% = 115% = 1.15
250 x 1.15 = $287.50
So, they should sell the computer for $287.50
Use the correct order of operations to solve the problem below.
14 - 8 + 6 - 10 ÷ 2
Answers
Answer: 7
Step-by-step explanation:
A survey found the following number of pets in different households.
What is the mean absolute deviation for the number of pets?
Answers
Answer:
absolute deviation means distance between each data value and the mean of the data set.
Step-by-step explanation:
(MAD)
or
(Average)
The number y of duckweed fronds in a pond after t days is y=a(1230. 25)t/16, where a is the initial number of fronds. By what percent does the duckweed increase each day? Round your answer to the nearest whole number
Answers
The duckweed increases by a percentage each day which is calculated by the equation
(1230.25t/16)/a - 1.
This equation can be further simplified to 1230.25t/16a - 1 and then multiplied by 100 to get a percentage.
So the percentage increase of duckweed each day is calculated by multiplying 1230.25t/16a - 1 by 100.
1230.25t/16a×100
This will give us the percentage of increase each day, rounded to the nearest whole number.
For example, if the initial number of fronds is 1000 and the number of days is 2, the percentage increase of duckweed will be (1230.25(2)/16(1000)) - 1 = 24.6%, rounded to the nearest whole number which is 25%.
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im 12 and struggling help me please i need my grades up
Answers
Answer:
you would multiply 17% by 228,000
Step-by-step explanation:
you would get 177840
A rectangle has a perimeter of 36 cm and an area of 72 cm2.
What is the length of the rectangle's shorter side?
O 2 cm
O 3 cm
04 cm
6 cm
8 cm
What is the length of the rectangle's longer side?
06 cm
O 8 cm
O 9 cm
O 12 cm
18 cm
Answers
The length of the rectangle's shorter side is 6cm and the of the rectangle's longer side is 12cm.
What is perimeter?
The total length of a shape's boundary, as used in geometry, is referred to as the shape's perimeter. Adding the lengths of all the sides and edges that surround a shape yields its perimeter. It is calculated using linear length units like centimeters, meters, inches, and feet.
Given:
A rectangle has a perimeter of 36 cm and an area of 72 cm^2.
Let the length of the rectangle's shorter side is 'a' and
the length of the rectangle's longer side 'b'.
As the perimeter is 36 cm.
⇒ Perimeter = 2(a + b)
36 = 2(a + b)
18 = a+ b
a = 18 - b
Now the area of rectangle is 72cm^2.
⇒ Area = ab
72 = (18 - b)*b
72 = 18b - b^2
b^2 - 18b + 72 = 0
b^2 - 12b - 6x + 72 = 0
b(b - 12) - 6(b - 12) = 0
(b - 12)(b - 6) = 0
(b - 12) = 0, (b - 6) = 0
b = 12, b = 6
When b = 12 ⇒ a = 18 - 12 = 6
When b = 6 ⇒ a = 18 - 6 = 12
Hence, the length of the rectangle's shorter side is 6cm and the of the rectangle's longer side is 12cm.
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The line has a slope 5 / 4 and passes through ( − 3, 4 ). What is the equation of the line ? Select one: a. 4x + 5y + 31 = 0 b. 5x − 4y + 31 = 0 c. 4x − 5y + 31 = 0 d. 5x − 4y − 31 = 0
Answers
Answer:
b: 5x-4y+31=0
Step-by-step explanation:
Let's look for an equation of the form y=mx+b, where m is the slope and b the y-intercept (the value of y when x=0).
We are given the slope, m, as (5/4), so we can write: y = (5/4)x+b.
To find b, just enter the given point, (-3,4), into the above equation and solve for b:
y=(5/4)x + b
4=(5/4)(-3) + b for (-3,4)
4 = -(15/4)+b
4 + (15/4) = b
4 + (3 3/4) = b
b = 7 3/4
The equation becomes y = (5/4)x + 7 3/4
Also written as: y = (5/4)x + (31/4)
To match this with one of the options, let's multiply by 4 to remove the two fractions:
y = (5/4)x + (31/4)
4y = (5)x + (31)
Rearrange so that the expression is = 0:
4y-5x-31 = 0
Now multiply by -1: -4y+5x+31=0
Rearrange and this will match option b: 5x-4y+31=0
An automobile manufacturer has given its car a 48.3 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this car since it is believed that the car has an incorrect manufacturer's MPG rating. After testing 150 cars, they found a mean MPG of 48.2. Assume the population variance is known to be 6.76. A level of significance of 0.02 will be used. Find the P-value of the test statistic. You may write the P-value as a range using interval notation, or as a decimal value rounded to four decimal places
Answers
The p-value of the test statistic is calculated as follows:
0.6386.
What are the hypothesis tested?At the null hypothesis, it is tested if the mean is actually of 48.3 miles per gallon, that is:
[tex]H_0: \mu = 48.3[/tex]
At the alternative hypothesis, it is tested if the mean is different of that, hence:
[tex]H_1: \mu \neq 48.3[/tex]
What is the test statistic?The population standard deviation is known, hence the z-distribution is used to obtain the test statistic.
The equation is given as follows:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.The parameters for this problem are given as follows:
[tex]\overline{x} = 48.2, \mu = 48.3, \sigma = \sqrt{6.76} = 2.6, n = 150[/tex]
Hence the test statistic is obtained as follows:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{48.2 - 48.3}{\frac{2.6}{\sqrt{150}}}[/tex]
z = -0.47.
The p-value is found using a z-distribution calculator, with a two-tailed test, as we are testing if the mean is different of a value, with z = -0.47, hence it is of:
0.6386.
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write the rule x= 10, -4, 0, 5, -2
y= 29, -13, -1, 14, -7
10=29
-4=-13
0=-1
5=14
-2=-7 help asap!!
Answers
The rule for the given set of data is y = 3x - 1.
What is rule in function?The relationship between dependent and independent variables, expressed as an equation, is referred to as a function rule. In order to calculate the value of the dependent variable, say y, in terms of the independent variable, say x, one must follow a specific function rule.
A function rule can be defined as the procedure that transforms an input value into an output in plain English.
Lets put two of the points in slope formula
y - y₁ = m(x - x₁)
29 - (-13) = m(10 - ( -4))
42 = m14
m = 42/14
m = 3
Now lets make the equation
y - 29 = m(x - 10)
y = 3x - 30 + 29
y = 3x - 1
Thus, the rule for the given set of data is y = 3x - 1.
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Tickets to a concert are $35 each. In addition to the cost for the tickets ordered, there is a $15 processing charge per order
Answers
An expression that represents the total cost of an order of n number of tickets: 35n + 15
Let n be the number of tickets to a concert.
Let C be the cost for the tickets
Given that the tickets to a concert are $35 each.
So, by unitary method the cost of n number of tickets would be,
n × 35
And the cost for the tickets would be,
C = 35n
In addition to the cost for the tickets ordered, there is a $15 processing charge per order.
So, the cost for the tickets would be,
C = 35n + 15
This is the required expression.
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The complete question is:
Tickets to a concert are $35 each. In addition to the cost for the tickets ordered, there is a $15 processing charge per order.
Write an expression that represents the total cost of an order of n number of tickets.
What is the solution to the system of equations 3x 2y 7 and Y 3x 11?
Answers
The solution to the system of equations is x = 4 and y = 5.
3x + 2y = 7
y = 3x - 11
Substitute 3x - 11 for y in the first equation:
3x + 2(3x - 11) = 7
Simplify:
3x + 6x - 22 = 7
Combine like terms:
9x - 22 = 7
Add 22 to both sides:
9x = 29
Divide both sides by 9:
x = 29/9
x = 4
Change x in the second equation to 4:
y = 3(4) - 11
Simplify:
y = 12 - 11
y = 1
The solution to the system of equations is x = 4 and y = 1.
The solution to the system of equations 3x + 2y = 7 and y = 3x - 11 is x = 4 and y = 1. To solve this system, we first substituted 3x - 11 for y in the first equation. We then simplified the equation and combined like terms to get 9x - 22 = 7. We then added 22 to both sides, divided both sides by 9, and got x = 29/9 which is x = 4. We then substituted 4 for x in the second equation, simplified, and got y = 1. Thus, the solution to the system of equations is x = 4 and y = 1.
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