Answer:
g(0) = 3
Step-by-step explanation:
Hello!
Substitute 0 for x in the equation.
Evaluateg(x) = 2x + 3g(0) = 2(0) + 3g(0) = 0 + 3g(0) = 3g(0) is 3.
A textile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. The company wishes to test the hypothesis H0: μ = 12 against H1: μ < 12, using a random sample of four specimens. (a) What is the type I error probability if the critical region is defined as x < 11.5 kilograms? (b) Find β for the case in which the true mean elongation is 11.25 kilograms. (c) Find β for the case in which the true mean is 11.5 kilograms.
The Type I error's computed value is 0.02275 and The Type II error has a computed value of 0.50 based on probability.
What is probability?
The potential or opportunity of an event happening is known as probability. The probability is equal to the variety of possible outcomes. the estimated number of outcomes that could occur.(a) Type I error probability if the critical region is defined as x < 11.5 kilograms
[tex]P(Type\ Error)=P\ xbar < 11.5\ when\ mu=12)\\\\[/tex]
[tex]=P(Z < \frac{11.5-12}{\frac{0.5}{\sqrt{4} } } )\\\\=P(Z < -2)\\\\=0.02275[/tex]
The Type I error's computed value is 0.02275.
Observe that there is a 2.275% likelihood of dismissing the null hypothesis if it is true based on the Type I error probability.
(b) β for the case in which the true mean elongation is 11.25 kilograms.
[tex]b= P(Type II Error)\\\\=P(xbar\geq 11.5\ when\ mu_1\ =11.25)[/tex]
[tex]=P(Z \geq \frac{11.5-12}{\frac{0.5}{\sqrt{4} } } )\\\\=P(Z \geq 1)\\\\= 1-P(Z < 1)\\\\=1-0.8413\\\\=0.1587[/tex]
The Type II error's computed value is 0.1587.
Observe that there is a 15.87% possibility of refusing to disprove the null hypothesis when it is untrue based on the Type II error probability.
(c) β for the case in which the true mean is 11.5 kilograms.
[tex]b= P(Type II Error)\\\\=P(xbar\geq 11.5\ when\ mu_1\ =11.25)[/tex]
[tex]=P(Z \geq \frac{11.5-11.5}{\frac{0.5}{\sqrt{4} } } )\\\\=P(Z \geq 0)\\\\= 1-P(Z < 0)\\\\=1-0.50\\\\=0.50[/tex]
The Type II error has a computed value of 0.50.
Observe that there is a 50% possibility of neglecting to disprove the null hypothesis when it is untrue based on the Type II error probability.
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What percent of 32 is 4?
A 12.5%
B 1.28%
of 32 is 4?
C 0.125%
D 8%
Answer:
A
Step-by-step explanation:
12.5% is 4 of 32. Devide 4 by 32 you get the 0125
Answer:
A 12.5%
Step-by-step explanation:
let p be the percentage that 4 represents.
[tex]32\longrightarrow 100 \%\\4 \longrightarrow \text{p} \%[/tex]
Then
[tex]p=\frac{4}{32} \times 100[/tex]
[tex]= 0.125 \times 100[/tex]
[tex]=12.5[/tex]
Solve the following equation. x/9 = 1Then place the correct number in the box provided.
Answer:
9
Step-by-step explanation:
x/9 = 1
Multiply both sides by 9
x = 9
Also, any number over itself is equal to 1.
step by step explanation
The sum of the given infinite geometric series is; 32
What is the sum of the geometric series?The general formula for finding the sum of an infinite geometric series is s = a₁/(1 - r)
where;
s is the sum
a₁ is the first term of the series
r is the common ratio.
To find the common ratio, use the formula: r = a2⁄a1
where a2 is the second term in the series and a1 is the first term in the series.
Thus;
r = 2²/4²
r = 1/2
Thus;
S = 4²/(1 - 1/2)
S = 16/(1/2)
S = 32
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A pole 11 feet tall is used to support a guy wire for a tower, which runs from the tower
to a metal stake in the ground. After placing the pole, Violet measures the distance
from the pole to the stake and from the pole to the tower, as shown in the diagram
below. Find the length of the guy wire, to the nearest foot.
The length of the guy wire, to the nearest foot is 48 ft.
What is mean by foot of Maths?A unit of length (or distance) in US units equal to 12 inches. The abbreviation is: ft. Or sometimes the single quote mark: ' Example: 10 feet can be written 10 ft, or just 10' A foot is exactly 0.3048 meters in the Metric System (the foot is defined that way).
Step-by-step explanation:
Here, we want to find the length of the wire
from the diagram, we can identify two similar triangles
The smaller one and a bigger one
Mathematically, when two triangles are similar, the ratio of their corresponding sides are equal
We can start by getting the height of the tower
we have this as:
8/11 = 28/x
8 * x = 28 * 11
8x = 308
x = 308/8
x = 38.5 ft
So as we can see, the wire represents the hypotenuse of the larger triangle that measures 28 ft base and 38.5 ft height
So we can use the Pythagoras’ theorem to get the hypotenuse
Let us call this g mathematically;
According to the theorem, the square of the hypotenuse equals the sum of the squares of the two other sides
thus, we have it that;
g^2 = 38.5^2 + 28^2
g^2 = 2,266.25
g = √2,266.25
g = 47.61 which is approximately 48 ft
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Graph g(x) = |x| − 3.
The graph shows an upward opening v-shaped graph with a vertex at negative 3 comma 0, which passes through negative 4 comma 1 and negative 2 comma 1.
The graph shows an upward opening v-shaped graph with a vertex at 3 comma 0, which passes through 2 comma 1 and 4 comma 1.
The graph shows an upward opening v-shaped graph with a vertex at 0 comma 3, which passes through negative 1 comma 4 and 1 comma 4.
The graph shows an upward opening v-shaped graph with a vertex at 0 comma negative 3, which passes through negative 1 comma negative 2 and 1 comma negative 2.
The graph of g(x) is gotten by translating the function f(x) = |x| down by 3 units to get to function g(x)
How to graph the equation of the function?The equation of the function is given as
g(x) = |x| - 3
The above function is an absolute value function.
The parent function of an absolute value function is
f(x) = |x|
This means that the function f(x) is translated to get to function g(x)
In this case, the function is f(x) is translated down by 3 units to get to function g(x)
So, the graph of g(x) is gotten by translating the function f(x) = |x| down by 3 units to get to function g(x)
See attachment for the graph of g(x)
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You work in a nursery with
20 children aged 3 - 5 years.
Your current room size is
415m² and does not meet
floor space requirements.
The room needs to increase
in size by 11%.
How big should the room
be?
Answer:
The room should be 460.65 [tex]m^{2}[/tex].
Step-by-step explanation:
First, you have to convert the percentage to a fraction.
11% = 0.11
Then add one to that number.
0.11 + 1 = 1.11
Multiply the number with the original room size.
415 * 1.11 = 460.65 ([tex]m^{2}[/tex])
pls answer report if wrong
Answer:
1/4
Step-by-step explanation:
12 cm x 1/4 = 3 cm
also i already learned scaled copys
Answer: The scale factor used in figure 2 is 1/4 or one fourth
Step-by-step explanation:
Hope this helps!
Work out the equation of the line passing through (0, -1) and parallel to the line y = 2x + 4.
Answer:
Y=2x-1
Step-by-step explanation:
(0,-1) parallel to y=2x + 4
parallel means the slope is the same (i.e m=2)
general equation would be
y=2x+k
now (0,-1) belongs to line where x=0 and y= -1
-1 =2(0)+k
-1 = k
hence k is -1
the equation is y=2x-1
What is the constant of proportionality between y and x in the graph?
Answer: 4/3 or 2/1.5
Step-by-step explanation:
The constant of proportionality is also known as the slope. This can be found with change in y over change x.
Since we have a graph with distinct points, we can use rise over run. For this graph, we will count 3 units up from (0, 0) and 4 units right to (4, 3). This becomes 4/3 or 2/1.5. This is the constant of proportionality.
the converse of If a/b = c, then a = bc. geometry
We need to know what converse of a statement means to solve the problem. The converse of the given statement is, if a=bc then a/b=c.
The converse of a conditional statement is created by exchanging the condition and the result. If a statement is p--->q then the converse of the statement is q--->p. In the given question we have been given the condition as a/b=c and the result if the condition satisfies is a=bc. To find the converse of this statement we need to make the result, the condition and the condition will be the new result. So the condition for converse will be a=bc and the result if the condition satisfies will be a/b=c.
Therefore the converse of the given statement is, if a=bc then a/b=c.
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graph the linear inequality 9x-y<9
The line has a slope of 9 and y-intercept of -9
Linear inequality graphA linear equation is a equation that has a linear degree of 1.
Given the inequality expression 9x-y<9
Write in slope-intercept form
-y < -9x + 9
y > 9x - 9
From the equation, we can see that the line has a slope of 9 and y-intercept of -9
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5. Please help and snow work
Answer:
-177
Step-by-step explanation:
Plug in the values into the equation.
-q(9)^2-(-6)^2+3(-20)
-81-36-60=-177.
Find the slope of the line if it exists.
The slope of the line is 1.
What is slope?The slope of a line is the ratio of the amount that y increases as x increases some amount
To calculate the slope of the graph, we use the formula below.
Formula:
Slope (S) = (y₂-y₁)/(x₂-x₁)............ Equation 1From the question,
Given:
y₁ = 0y₂ = 4x₁ = -6x₂ = -2Substitute these values into equation 1
S = (4-0)/[-2-(-6)]S = 4/4S = 1Hence, the slope of the line is 1.
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Translate the following verbal expression into an algebraic expression.
Ten times a number plus seven times the same number.
Answer:
10x + 7(10x)
Step-by-step explanation:
X is the unknown number
To two decimal places,
√70
must lie between ____
and _____.
Answer:
between 8.36 and 8.37
Step-by-step explanation:
[tex]\sqrt{70} =8.3666[/tex]
Hope this helps
help i have no clue how to do this pls help
Answer:
4
Step-by-step explanation:
the sequence is like [tex]1^{2}[/tex],[tex]2^{2} ,4^{2},8^{2} ,16^{2} ,32^{2}[/tex]
Carly tutors students in math on the weekends and offers both thirty-minute sessions and sixty-minute sessions. She earns $15 for each
thirty-minute session and $25 for each sixty-minute session.
If she earned $230 this past weekend and had x thirty-minute sessions and x - 2 sixty-minute sessions, what is the value of x?
A 7
B. 5
C. 8
D. 6
The value of x is 7. The correct option is A. 7
Solving Linear equationsFrom the question, we are to determine the value of x
From the given information,
Carly earns $15 for each thirty-minute session and $25 for each sixty-minute session
Also,
She earned $230 this past weekend and had x thirty-minute sessions and x - 2 sixty-minute sessions
Then, we can write that
x × $15 + (x -2) × $25 = $230
Solve for x in the equation
15x + 25(x -2) = 230
15x + 25x - 50 = 230
40x - 50 = 230
40x = 230 + 50
40x = 280
x = 280/40
x = 7
Hence, the value of x is 7. The correct option is A. 7
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Answer:
B. 7
Step-by-step explanation:
Correct on edmentum!
At a school fundraiser Ms. Navaro sold 24 plates of cookies, which is 80% of the total number of plates of cookies she baked. How many plates of cookies did Ms. Navaro bake?
Answer:
. Onusko made 60 cookies for a bake sale. She sold 2/3 of them and gave 3/4 of the remaining cookies to the students working at the sale. How many
A chemist is using 357 milliliters of a solution of acid and water. If 18.1% of the solution is acid, how many milliliters of acid are there? Round your
answer to the nearest tenth.
milliliters
If 18.1 percent of the solution is acid, 64.07 milliliters of acid are there.
What is a percentage?
Percentage, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one-hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics.Multiplying this fraction by 100 and adding a percent sign will get the percentage. Percentage Equals 100 * numerator / denominator.As per the question,
18.1 Percent of 357 ml of solution used is acid, therefore,
=(18.1/100)*357
= 64.07 ml of acid
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a plank of wood is 220 cm long.I cut it in 14cm pieces. what lenght of wood i will have left over?
The required Length is 10cm.
What is length?
Length is a measure of distance. In the International System of Amounts, length is a volume with dimension distance. In utmost systems of dimension a base unit for length is chosen, from which all other units are deduced.Length is generally understood to mean the most extended dimension of a fixed object. still, this isn't always the case and may depend on the position the object is in.Varied terms for the length of a fixed object are used, and these include height, which is the perpendicular length or perpendicular extent, and range, breadth, or depth. Height is used when there's a base from which perpendicular measures can be taken. range or breadth generally relates to a shorter dimension when the length is the longest one.220 / 14 gives us 15.
You have to understand that this means 15 whole 14 cm pieces and a Length of 1 piece.
thus 14 * 15 = 210
So 220- 210 = 10
where you know 220- 210 is< 15
Hence, The correct Length is 10cm.
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use the point and the slope to graph each line. Write the equation of each line. The line contains point (2,-2) and is perpendicular to a line with slope "-1"
Answer:
y = x - 4
Step-by-Step Explanation:
Perpendicular lines have slopes that are negative reciprocals—multiplying their slopes result in -1.Given the slope of a line m = -1, then it means that the slope of the other line must be 1 (because multiplying the slope of line 1 (m1 = -1), and the slope of the other line (m2 = 1) results in: -1 × 1 = -1).Therefore, given the slope of line 2 (m2 = 1), and the point (2, -2), we could plug these values into the slope-intercept form and solve for the y-intercept (b):y = mx + b-2 = 1(2) + b-2 = 2 + bSubtract 2 from both sides to solve for b:-2 - 2 = 2 - 2 + b-4 = bTherefore, the y-intercept (b) = -4.Hence, the equation of the perpendicular line is: y = x - 4
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The posts of a hockey goal are 6 ft. apart. A player attempts to score by shooting the puck from a
point that is 19 ft from one post and 24 ft from the other post. Within what angle & must the shot be
made? Express your answer to the nearest degree.
The angle at which the shot was made should be 17.53° degrees.
Let C denote the point where the player attempts to put in a goal.
Let A and B denote the two goalposts.
We are given the posts of a hockey goal are 6 ft apart.
The distance between the player and one goalpost is 19 ft.
The distance between the player and the other goalpost is 24 ft.
Then, we have AC = 19 ft, BC = 24 ft, and AB= 6 ft.
Refer to the diagram.
Let θ be the angle made when trying to shoot the goal towards goalpost A.
Then we have tan(θ) = 6/19
⇒ θ = 17.53° degrees.
Therefore, the angle at which the shot was made should be 17.53° degrees.
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What is the slope of the line that passes through the points (2, 8) and (-3, 14)?
Answer:
-6/5
Step-by-step explanation:
(14-8)÷(-3-2) = -6/5
How many groups of 1/8 are in 3?
Answer:
there are 24 1/8 in 3
Step-by-step explanation:
8x3=24
Find the equation of the line given the following conditions.
-Passing through (2, -3) and perpendicular to the line whose equation is y=1/5x+6
-Passing through (5, -9) and perpendicular to the line whose equation is x + 7y – 12 = 0
Considering the definition of perpendicular line, you obtain:
1) the equation of perpendicular line is y= -5x + 7.
2) the equation of perpendicular line is y= 7x + 54.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Perpendicular linePerpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.
Equation of perpendicular line of y=1/5x +6If you multiply the slopes of two perpendicular lines, you get –1. In this case, the line has a slope of 1/5. So:
1/5× slope perpendicular line= -1
slope perpendicular line= (-1)÷ (1/5)
slope perpendicular line= -5
So, the perpendicular line has a form of: y= -5x + b
The line passes through the point (2,-3). Replacing in the expression for perpendicular line:
-3= -5× (2) + b
-3= -10 + b
-3 +10 = b
7= b
Finally, the equation of perpendicular line is y= -5x + 7.
Equation of perpendicular line of x +7y -12= 0In this case, the line is x +7y -12= 0. Expressed in the form y = mx + b, you get:
7y= -x +12
y= (-x + 12)÷ 7
y= -1/7x +12/7
If you multiply the slopes of two perpendicular lines, you get –1. In this case, the line has a slope of -1/7. So:
-1/7× slope perpendicular line= -1
slope perpendicular line= (-1)÷ (-1/7)
slope perpendicular line= 7
So, the perpendicular line has a form of: y= 7x + b
The line passes through the point (5,-9). Replacing in the expression for perpendicular line:
-9= 7× (-9) + b
-9= -63 + b
-9 + 63 = b
54= b
Finally, the equation of perpendicular line is y= 7x + 54.
Summary
In summary, you obtain:
1) the equation of perpendicular line is y= -5x + 7.
2) the equation of perpendicular line is y= 7x + 54.
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Brand Y Cola sponsors a survey of 15,559 residents of Texas to determine which brand of cola they prefer. Forty percent say they prefer Brand X, and 60 percent say they prefer Brand Y. Which of the following is the sample used for the survey ?
Answer:
6224 Brand X residents and 9335 Brand Y residents
Step-by-step explanation:
Total number of residents in the survey=15559
Residents that prefer Brand X=40%
Residents that prefer Brand Y=60%
Population sample?
Residents that prefer Brand X= 40/100 ×15559 =6223.6⇒6224 residents
Residents that prefer Brand Y= 60/100 × 15559 =9335.4⇒⇒9335 residents
Answer: B
Step-by-step explanation:
I cannot do this help me to this
we don't have enough information to conclude if the triangles are similar, thus, the correct option is C.
How to identify if the triangles are similar?
Two figures are similar if the figures have the same shape, but different size.
So, one figure is a dilation/contraction of the other figure.
In this case of the triangles, two are similar if and only if all the correspondent internal angles have the same measure.
For the case of the image, the triangles:
RST and RUV
would be similar if and only if line ST and line UV are parallel, in that case we would get that the angles at S and U are equal, and the same for the angles at T and V.
In this particular case, there is no indication that ST and UV are parallel. (they may be, the may not be)
So we don't have enough information to conclude if the triangles are similar, thus, the correct option is C.
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dam n bro uglier den a redneck on a sunday
Step-by-step explanation:
Chika's uncle makes perfect brownies. Chika noted how much sugar he uses based on how many batches he makes:
Number of batches 222 333 444
Sugar (\text{kg}kgstart text, k, g, end text) 0.60.60, point, 6 0.90.90, point, 9 1.21.21, point, 2
Chika has 2.25\,\text{kg}2.25kg2, point, 25, start text, k, g, end text of sugar, and she wants to make as many batches as possible for a bake sale. She can make partial batches, and she has more than enough of the other ingredients.
How many batches can Chika make?
Proportionately, the number of batches that Chika can make with 2.25kg of sugar is 7.5.
What is proportion?Proportion is the ratio of a variable in the whole.
Proportion shows how much quantity is contained in a variable.
Proportions are represented in decimals, percentages, and fractions.
Data and Calculations:Number of Batches 2 3 4
Sugar (kg) 0.6 0.9 1.2
Proportion of sugar
per batch 0.3 0.3 0.3
Chika's sugar ingredient = 2.25 kg
The number of batches Chika can make = 7.5 (2.25/0.3)
Thus, the number of batches that Chika can make with 2.25kg of sugar is 7.5.
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Find the earnings for selling the same number of each type of sandwiches. Use x to represent the number of each type of sandwiches sold. Pretzel ham sandwich cost $2.25, pretzel turkey sandwich cost $1.55, bagel ham sandwich cost $2.00, bagel turkey sandwich cost $1.30
Total earnings for selling the same number of each type of sandwiches are $7.10x. This is a simple sum.
Here, the number of each type of sandwiches sold is x.
Pretzel ham sandwich cost $2.25. so, the earnings for selling Pretzel ham sandwich is $2.25x.
Similarly, earnings for selling pretzel turkey sandwich is $1.55x, earnings for selling bagel ham sandwich is $2.00x and earnings for selling bagel turkey sandwich is $1.30x. The total earning can be found by a simple sum of all individual earning of each type of sandwiches.
Therefore, Total earnings for selling the same number of each type of sandwiches are = $2.25x + $1.55x + $2.00x + $1.30x = $7.10x
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