Using the z-distribution, it is found that mean weights less than 135.1g and more than 144.9 would lead to a rejection of the hypothesis.
What is the critical value of the test?We have a two-tailed test, with a significance value of α = 0.05, hence, using a z-distribution calculator, the critical value is given by:
|z| = 1.96 -> z < -1.96 or z > 1.96.
What is the test statistic?The test statistic is given as follows:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
X 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.For this problem, the parameters are given as follows:
[tex]\mu = 140, \sigma = 15, n = 36[/tex]
The lower bound of acception is found as X when z = -1.96, hence:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
-1.96 = (X - 140)/(15/6)
-1.96 = (X - 140)/(2.5)
X - 140 = -1.96 x 2.5
X = 135.1.
The upper bound of acception is found as X when z = 1.96, hence:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
1.96 = (X - 140)/(15/6)
1.96 = (X - 140)/(2.5)
X - 140 = 1.96 x 2.5
X = 144.9.
Hence:
Mean weights less than 135.1g and more than 144.9 would lead to a rejection of the hypothesis.
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The pair of triangles that are congruent by the ASA criterion is . The pair of triangles that are congruent by the SAS criterion is .
The relationship between the triangles are;
Δ ABC and Δ XYZ is related by ASA
Δ BAC and ΔRQP are related by SAS
What is congruency of triangles?The term congruency has to do with the fact that the triangles are similar. That is why another way that we could express congruent triangles is to call them similar triangles. These are the triangles that look alike in some ways. The triangles may be similar in the following ways;
1) Angle Angle Side
2) Side Side Side
3) Side Angle Side
4) Angle Side Angle
5) Angle Side Side
Having seen the various ways in which triangle could be similar we are asked to obtain the triangles that are similar by Angle Side Angle and Side Angle Side.
A good look at the triangles as shown in the image attached to this answer would show us which of the triangles are similar on the basis of Angle Side Angle and Side Angle Side.
We can see that;
Δ ABC and Δ XYZ is related by ASA
Δ BAC and ΔRQP are related by SAS
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7 rationals and irrationals prove that the product of a non-zero rational number and an irrational number is irrational.
Let x be a rational number and y be an irrational number. This is the correct choice.
Allow xy=a.
Suppose an is a rational being.
A can be stated as q p since it is rational, where p and q are both integers.
Let x = n m, where n and m are both integers.
Then, xy=a
n \smy \s \s = \sq \sp \s \s .
When we cross multiply, we obtain,
⇒y= qm \spn \s \s .
Pn and qm are currently integers.
Consequently, qm pn is a rational number.
Y, however, is illogical.
Consequently, our assumption is unfounded.
Therefore, an irrational number is always the result of adding a non-zero rational number to an irrational number.
What do you mean by irrational number ?a number that cannot be written as the quotient of two integers and cannot be expressed as an infinite decimal with a series of consecutive digits repeating itself forever.
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An expression involves subtracting two numbers from a given number. Under what circumstances will the value of the expression be negative? Give an example
the expression can be negative under various circumstances.
An expression means to subtraction two numbers from a given number.
Let the numbers be a, b and c
Do, the expression will become:
a - b - c.
The expression can be negative if:
1. the value of b + c > a
For example: a = 4, b = 5 and c = 6
so, the expression will be
4 - 5 - 6 = - 7
2. The value can be negative if a - b < c
For example:
a = 2, b = 1 and c = 6
The expression will be:
2 - 1 - 6 = - 5
3. The value can be negative if a - c < b
For example:
a = 1, b = 6 and c = 2
The expression will be:
1 - 6 - 2 = - 7
Therefore, we get that the expression can be negative under various circumstances.
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solve the equation 4x -6 = 22
Answer: x=7
Step-by-step explanation: hope this helps!!!
Answer:
x=7
Step-by-step explanation:
If f (x) = 2 x + 5 and three-halves are inverse functions of each other and StartFraction 41 Over 8 EndFraction,
The value of the inverse function f⁻¹(8) is [tex]\frac{3}{2}[/tex] .
An inverse function in mathematics is a function that "undoes" another function.
In other words, if f(x) produces y, then y entered into the inverse of f produces x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f⁻¹ .To calculate the inverse of the function f (x) = 2 x + 5 we simply write the function in the form y = 2x + 5 .
Now we solve the equation for x.
∴ y = 2x + 5
or, 2x = y-5
or, x = (y-5)/2
Hence the inverse of the function is given as:
f⁻¹ (x) = (x - 5 ) / 2
Now we have to find the value of f⁻¹ (8).
f⁻¹ (8) = (8-5) / 2
or, f⁻¹ (8) = 3 / 2
Hence the value of f⁻¹ (8) is 3 / 2 .
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Disclaimer: the complete question is:
If f (x) = 2 x + 5 and three-halves are inverse functions of each other and f(x)=2x+5, what is f-1(8)?
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Answer: B
Step-by-step explanation: On Edge 2022
5 Bruno buys 9.625 gallons of gasoline at a gas station.
Each gallon costs $3.40. Bruno also buys a bag of ice
for $3.99. How much in total does Bruno spend at the
gas station to the nearest cent?
Answer:
Step-by-step explanation:
9.625 rounded is 10.
10 x $3.40 = $34
$3.99 rounded to the nearest cent is $4.
$34 + 4 = $38, so Bruno spends about $38 total.
HELP !!
Elena and Diego each wrote equations to represent these diagrams. For each diagram decide which equation you agree with, and solve it. You can assume that angles that look like right angles are indeed right angles.
Elena: X=35
Diego: X+35=180
Answer: Diego is correct, and X = 145
Step-by-step explanation:
The line that 35* and x* rest on must equal 180*. Elena cannot be right if we assume this, as 35 + 35 = 70. We must then move onto Diego's formula.
[tex]X + 35 = 180[/tex]
[tex]180 - 35 = X[/tex]
[tex]X = 145[/tex]
Solving this, we would subtract 35 from 180, leaving us with 145*. This must be correct as the solution would give us the total we need.
What is this supposed to mean!?!?!?!?
Answer:
h = V/B
Step-by-step explanation:
[tex]\sf V \div B = h\\Reverse\\h = V \div B[/tex]
Answer:
D. h = V/B
Step-by-step explanation:
"Solve...for h" means get h all by itself on one side of the equation.
V = Bh
Divide both sides by B.
V/B = h
Turn it around and you can see the answer in the choices. D. h = V/B is the correct answer.
- 3x + 6y =- 18 solve for y
Answer:
y = [tex]\frac{1}{2}[/tex] x - 3
Step-by-step explanation:
- 3x + 6y = - 18 ( isolate the term in y by adding 3x to both sides )
6y = 3x - 18 ( divide through by 6 )
y = [tex]\frac{1}{2}[/tex] x - 3
Solve y- 15 =-3.
A-12
B 12
C-18
D-18
Answer:
B
Step-by-step explanation:
y - 15 = -3
add 15 to both sides to get:
y=12
If point A (-5, 9) is reflected across the x-axis, what will be the new coordinates of the image, A'?
please help! I am in the middle of a test! I am offering 30 points.
The new coordinates of the image A' will be (-5, -9).
Here, we are given a point on the cartesian plane- A (-5, 9)
It is reflected along the x axis to form a new point A'
Originally, we can see that the point A will be in the 2nd quadrant as x is negative and y is positive.
Now, when it is reflected across the x axis, the point will shift from the 2nd quadrant to the 3rd quadrant.
In the third quadrant, both x and y values are negative. Thus the coordinates of the reflected point A' will become (-5, -9).
Note that the absolute values of the point will not change when it is reflected. It is only the signs that change.
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Pls pls help whoever gets it right gets a crown
Answer: 12.8x^2
Step-by-step explanation:
3.2x * 4x=
3.2 * x * 4 * x=
3.2 * 4 * x * x=
12.8 * x^2=12.8x^2
Describe the similarities and differences between finding the slope of a linear equation from a graph that has x and y scales that are 1:1, and from a graph that has x and y scales that are not 1:1 (say your x and y scales are 2, 4, 6).
Using the concept of the slope of a linear function, we have that:
For a graph in a 1:1 scale, we can look at two consecutive values, y when x = a and y* when x = a + 1, and subtract y* by y. For a graph in another scale, we also do the same thing, but since the scale is not 1:1, we have to divide the subtraction of y* by y by the scale.What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Given two points in the graph of a function, the slope is given by change in y divided by change in x, hence:
For a graph in a 1:1 scale, we can look at two consecutive values, y when x = a and y* when x = a + 1, and subtract y* by y. For a graph in another scale, we also do the same thing, but since the scale is not 1:1, we have to divide the subtraction of y* by y by the scale.More can be learned about linear function concepts at https://brainly.com/question/24808124
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The table shows the numbers y (in thousands) of people in a city who regularly use sharable electric scootersx weeks after the scooters are introduced.
im still learning that
Step-by-step explanation:
Which line is perpendicular to y=−3x+2?
A. y = −3x+1/2
B. y =−1/3x+1
C. y = 3x−1/2
D. y =1 /3x−1
(Note: the selected answer is not guaranteed to be correct in the image)
Answer:
I kinda want to say it's C
point k is on a line segment JL. given JK =2x-2, KL =x-9, and JL = 2x+8, determine the numerical length of KL
The numerical length of KL = 10.
What exactly is an equation?An equation, in its most basic form, is a mathematical statement demonstrating that two mathematical expressions are equal.3x + 5 = 14, for example, is an equation in which the expressions 3x + 5 and 14 are separated by a 'equal' sign.So,
JK + KL = JL2x – 2 + x – 9 = 2x + 8Combine similar terms:
3x -11 = 2x+8Take 2x off each side:
3x-2x -11 = 2x+8-2xx-11 = 8Add 11 for each side:
x-11+11 = 8+11x = 19KL = x – 9KL = 19-9KL = 10Therefore, the numerical length of KL = 10.
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Tyrell has a box of colored pencils. He uses 65 pencils and has 114 pencils left in the box. Write an equation showing how many pencils are in the box before he starts drawing.
p − 65 = 114
p = 114 − 65
65 + p = 114
114 + p = 65
Answer:
p-65=114
Step-by-step explanation:
In this equation, "p" is the amount of pencils in the box before he starts drawing. he removes 65 pencils from the box, leaving 114 in the box. What he needs with 65 pencils at once, I can't fathom.
Complete the sentence.
32 g≈ ___ oz
32g = 1.12877oz or 32 grams is equivalent to 1.12877 ounces.
In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume or even currency to another.
A conversion factor is a number used to change one set of units to another, either by multiplying or dividing.
The sentence states an equality between units of weight: grams and ounces.
From there, we can say that we are asked how many ounces are there in 32 grams.
Converting grams to ounces, we must use the conversion
1 gram = 0.035274 ounces
32 grams = 32 (0.035274 ounces)
32 grams = 1.12877 ounces
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Which expression can be used to show a set of twenty books divided into four groups?
The expression that can be used to show a set of twenty book divided into 4 groups [tex]\frac{20}{5}[/tex]
Given,
The total number of books= 20
Number of books in each group= 4
We have to use division
Then, the expression used to represent a set of 20 books divided into four group =[tex]\frac{20}{5}[/tex]
So the result will be 4
Hence, the expression that can be used to show a set of twenty book divided into 4 groups is [tex]\frac{20}{5}[/tex]
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9+8n≤1 please help me with this
Answer:
n ≤ -1
Step-by-step explanation:
Inequality is a concept that refers to the unequal distribution of resources, opportunities, or status among individuals or groups. It can be measured in a number of ways, including income inequality, wealth inequality, and educational inequality.
For the Question:
Let's solve for 'n':
Given inequality:
[tex]\sf 9 + 8n \leq 1[/tex]
Subtract 9 from both sides:
[tex]\sf 9 + 8n -9 \leq 1 -9[/tex]
[tex]\sf 8n \leq -8[/tex]
Divide both sides by 8 (remember, since you're dividing by a negative number, the inequality sign flips):
[tex]\sf \dfrac{8n}{8} \leq \dfrac{-8}{8}[/tex]
n ≤ -1
So, the solution for 'n' that satisfies the inequality is n ≤ -1.
The ratio of red marbles to blue marbles in a jar is 5:2. The total number of marbles is 21. What is the
smaller amount of marbles in the jar?
Answer:
6
Step-by-step explanation:
Triangle ABC is transformed to triangle A′B′C′, as shown below: A coordinate grid is shown from negative 4 to 0 to 4 on both x- and y-axes. A triangle ABC has A at ordered pair negative 3, 4, B at ordered pair negative 4, 2, C at ordered pair negative 1, 1. A triangle A prime B prime C prime has A prime at ordered pair 3, 4, B prime at ordered pair 4, 2, C prime at ordered pair 1, 1. Which equation shows the correct relationship between the measures of the angles of the two triangles? (1 point) a The measure of angle ABC = The measure of angle A prime B prime C prime b The measure of angle ABC = The measure of angle B prime C prime A c The measure of angle BCA = The measure of angle A prime B prime C prime d The measure of angle BCA = The measure of angle C prime A prime B prime
The correct relationship between the angles of the two triangles is as follows:
Angle measurement BCA = Angle C prime A prime B measurement.What is a triangle?A triangle is a three-sided polygon that is sometimes (but not always) referred to as the trigon. Every triangle has three sides and three angles, which may or may not be the same.So, in an ABC triangle, A is at ordered pair negative 1, 3, B is at ordered pair 0, 1, and C is at ordered pair negative 3, 0.
A triangular shape A prime, B prime, and C prime all have A prime at ordered pair minus 1, minus 3, B prime at ordered pair minus 1, and C prime at ordered pair minus 3, 0.Then,
<BAC = <B'A'C'<ABC = <A'B'C'<ACB = <A'C'B'Angle measurement BCA = Angle C prime A prime B measurement.
Therefore, the correct relationship between the angles of the two triangles is as follows:
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how to solve -6x+3y=9 by y?
Answer:
Down below Explanation :) answer is [tex]x=-\frac{3-y}{2}[/tex]
Step-by-step explanation:
-6x+3y=9
Steps:
Subtract 3y From both sides.
-6x+3y-3y=9-3y
Simplify:
-6x=9-3y
Lastly; divide both sides by -6
[tex]\frac{-6x}{-6}=\frac{9}{-6}-\frac{3y}{-6}[/tex]
And your answer is
[tex]x=-\frac{3-y}{2}[/tex]Find the area of the composite figure.
8 cm
10 cm
14 cm
Answer:
96 cm
Step-by-step explanation:
14-10= 4.
So the base of the triangle is 4.
10*8=80
4*8*1/2=16
80+16 = 96
Answer:
32
Step-by-step explanation:
Which figure is missing in the pattern?
?
Answer:
B
Step-by-step explanation:
it grows b
Use the figure to the right to find the value of PT.
PT= 4x+4 and TQ 6x-6
pls help :) brainliest
Answer:
151 shirts
Step-by-step explanation:
2578 divided by 17 is 151.647...
Answer:151
Step-by-step explanation:2578 divided by 17 equals 151.6470588. you cant have a partial shirt so you have to round down or you will go over your money
Which square root could be the number shown on the number line?
O A. √15
O B. √17
O C. √26
O D. √24
The number shown on the number line could be related to the inexact irrational number √17.
What irrational number is associated with a point on a number line?
In this problem we find the location of a point on a number line, which is related to an inexact irrational number, that is, an irrational number that is not equivalent to any rational number. The point is between two exact irrational numbers, that is, √16 = 4 and √25 = 5.
There are two options: (i) √17, (ii) √24. √24 is close to 5, but √17 is close to 4. Thus, the number shown on the number line could be related to the inexact irrational number √17.
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The Rock Club members have collected 182 gems. How many did each
member collect if
a) Alice collected 1 more than 3 times what Cecil did.
b) Jaime collected 12 less than 3 times what Alice did.
c) Amir collected 10 less than Cecil.
d) Monte collected 5 more than Cecil.
How many gems didCecil collect?
How many gems did Alice collect?
How many gems did Jaime collect?
How many gems did amir collect
How many gems did Monte collect
Using a system of equations, the amounts of gems collected by each member is are given as follows:
Cecil: 13Alice: 40Jaime: 108Amir: 3Monte: 18.What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given as follows:
Variable x: Number of gems collected by Cecil.Variable y: Number of gems collected by Alice.Variable z: Number of gems collected by Jaime.Variable t: Number of gems collected by Amir.Variable w: Number of gems collected by Monte.They collected a total of 182 gems, hence:
x + y + z + t + w = 182.
Alice collected 1 more than 3 times what Cecil did, hence:
y = 3x + 1.
Jaime collected 12 less than 3 times what Alice did, hence:
z = 3y - 12 = 3(3x + 1) - 12 = 9x - 9.
Amir collected 10 less than Cecil, hence:
t = x - 10.
Monte collected 5 more than Cecil, hence:
w = x + 5.
Replacing everything in the first equation, we can solve for x as follows:
x + y + z + t + w = 182.
x + 3x + 1 + 9x - 9 + x - 10 + x + 5 = 182.
15x = 195
x = 195/15
x = 13.
Hence the other variables are:
y = 3(13) + 1 = 40.z = 9x - 9 = 9(13) - 9 = 108.t = x - 10 = 13 - 10 = 3.w = x + 5 = 13 + 5 = 18.Thus the amounts of gems collected by each member is are given as follows:
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create an equation from the model that describes the relationship between the weights on each side of the scale
The algebraic equation that describes the relationship of the weights on both sides of the scale is: 2y + 3 = 4y + 2.
How to Create an Algebraic Equation?Using the weights on each side of the scale, we can create an algebraic equation that describes it.
Assume each weigh on the scale represents each side of an algebraic equation.
On left side, we can express the weights as: 2y + 3
On the right side, we can express the weight as: 4y + 2
Thus, expressing the relationship of the weights, we would have:
2y + 3 = 4y + 2
Thus, the algebraic equation that describes the relationship of the weights on both sides of the scale is: 2y + 3 = 4y + 2.
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