8.27 is the normally distributed value of the shelf life which falls under 16% of the battery shelf life.
Because the shelf life of a battery manufactured by one big business is known to be regularly distributed, we would use the normal distribution formula, which is stated as
z = (x - µ) ÷ σ
Where
x = shelf life of a battery in years.
µ = mean shell life
σ = standard deviation
Based on the facts provided,
µ = 8 years
σ = 0.3 years
The z score corresponds to a p-value of 16% in the normal distribution table,
(16 ÷ 100 = 0.16) is - 0.9.
Therefore,
- 0.9 = (x - 9) ÷ 0.3
0.3 × (- 0.9) = x - 8
0.27 = x - 8
x = 0.27 + 8
x = 8.27
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Determine if the table shows a proportional relationship. x 42.5 29.2 69.4 y 21.25 14.6 34.7 Yes, it is proportional because the ratios for y over x are all equivalent to one half. Yes, it is proportional because the ratios for y over x are all equivalent to one third. No, it is not proportional because 21.25 over 42.5 is not equal to 29.2 over 14.6. No, it is not proportional because 42.5 over 21.25 is not equal to 34.7 over 69.4.
Yes, it is proportional because the graph of these coordinates is a straight line and the ratios for [y] over [x] are all equivalent to one half.
What is proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. A straight line represents a proportional relationship. Mathematically -
y = kx + c
(y - c)/x = k [k is constant]
or
y = kx
k = y/x [k is constant]
Given is the following data -
[x] 42.5 29.2 69.4
[y] 21.25 14.6 34.7
In order to find if the given coordinates represent proportional relationship, plot these coordinates on graph. If the by joining the coordinate points, we get a straight line, then it represents a proportional relationship. Graph is attached with the answer. It can be seen that its graph is a straight line and hence represents a proportional relationship.
Now, the ratio of [y] by [x] -
m = (21.25 - 14.6)/(42.5 - 29.2) = 6.65/13.3 - 0.5 = 1/2
Therefore, we can say that, Yes, it is proportional because the graph of these coordinates is a straight line and the ratios for [y] over [x] are all equivalent to one half.
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Answer: Yes, it is proportional because the ratios for y over x are all equivalent to one half.
Step-by-step explanation:
I did the test. :)
Question 12
I just want the answer :)
Given the information marked on each figure below, select all classifications that must be true.
Note that each figure is drawn like a rectangle, but you should not rely on the way the figure is drawn in determining your answers.
If necessary, you may learn what the markings on a figure indicate.
1. Quadrilateral.
The quadrilateral is not necessarily a parallelogram since the diagonals don't necessarily bisect each other.2. Rectangle.
The quadrilateral is a parallelogram because there is one pair of congruent and parallel sides.The parallelogram is a rectangle because there is one right angle.3. Parallelogram.
The quadrilateral is a parallelogram because there is one pair of congruent and parallel sides.Is it possible for polygon ABCDE to be dilated to figure VWXYZ? Explain yourreasoning.
In the given figures, ratio of all corresponding sides are
[tex]\frac{1}{2}[/tex]Except the ratio of AE and VZ
[tex]\begin{gathered} \frac{AE}{VZ}=\frac{10}{12} \\ =\frac{5}{6} \\ \ne\frac{1}{2} \end{gathered}[/tex]Hence, the polygon ABCDE can't be dilated to VWXYZ because ratio of corresponding sides are not equal.
So, the correct answer is (C)
Comparing and Scaling Rates: Investigation 2.3 Homework 1. Keeley buys songs from a music website. She buys 35 songs for $26.25. What is the price per song? a. Complete the table. b. Lucius and Javier discuss how to write an equation relating price and number of songs. Lucius writes the equation n = 0.75C. Javier writes the equation C = 0.75n. Do you agree with Lucius or with Javier? Use the information from parts (a) to explain. 2. For each situation, find a unit rate and write an equation relating the two quantities. a. 3 dozen apples for $4.50 b. 30 bottles of water for $4.80 c. 24 ounces of mozzarella cheese for $2.88 Number of Songs, n 35 50 1 70 Cost, C $26.25 $3 $15
0.75
37.50
cost
dozen
= 4.50/3 = $1.50 / dozen
cost/bottles
2 3. Which of these items is the better buy? a. an 8-pack of glue sticks for $3.99 or 1 glue stick for $.54 b. a 12-pack of tape for $2.50 or 1 roll of tape for $.19 c. a 100-pack of pencils for $4.88 or 1 pencil for $.05 d. a 50-pack of paper clips for $.89 or a 25-pack of paper clips for $.45.
Answer:
Use the information from parts a
Step-by-step explanation:
If a rectangle has a length of 6cm and a width of 4cm what is it's area
Answer:
area = l×b
= 6×4
. = 24 cm²
Step-by-step explanation:
this is the answer
9. Determine where the graph represents a function explain your answer.
The vertical line test is a visual test to determine if a graph represents a function; since a function can only have one output for every input if a vertical line intersects a curve in more that one point the it is not the graph of a function.
In this case we any vertical line will only intersect one point then we conclude that:
The graph represents a function. Using the vertical line test, the graph intersects any vertical line at only one point.
Please answer the following questions. What is the slope of the line? How much does the distance increase for each hour since Alan crossed the bridge?
SOLUTION
The slope of the line can be gotten using the formula
[tex]\begin{gathered} \text{Slope =}\frac{change\text{ in distance}}{\text{change in time }}\text{ = }\frac{d2-d1}{t2-t1} \\ \text{Taking two points on along the line we have } \\ \text{Slope = }\frac{350-100}{7-2} \\ \\ \text{Slope =}\frac{250}{50} \\ \\ \text{Slope = 50} \end{gathered}[/tex]The slope is 50. This means the distance increased by 50 miles for every hour.
Parallel lines investigation
From the given figure the value of x is 6 and the measure of angle 3 is 57°.
From the given figure, m∠4=(20x+3)° and m∠6=(9x+3)°.
What are angles of parallel lines?Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.
22). From the given figure
m∠4+m∠6=180° (Coointerior angles sum is equal to 180°)
(20x+3)°+(9x+3)°=180°
⇒ 29x+6=180
⇒ 29x=174
⇒ x=6
m∠4=(20x+3)°=123°
m∠3+m∠4=180° (Adjacent angles sum is equal to 180°)
m∠3+123=180
m∠3=57°
23). From the given figure
m∠3=m∠6 (Alternate interior angles are congruent)
x+10 = 4x-20
⇒ 3x=30
⇒ x=10
Now, m∠6=4x-20
=20
m∠6+m∠8=180° (Adjacent angles sum is equal to 180°)
20+m∠8=180°
⇒ m∠8=160
Therefore, from the given figure the value of x is 6 and the measure of angle 3 is 57°.
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6. There were a total of 139 points scored in the basketballgame. The Falcons scored (9x+22) and the Mavericks scored(16x - 8). What was the Falcons score for the game?
The total score in the basket game = 139
Falcons score = 9x + 22
Maverick score = 16x - 8
Therefore,
139 = 9x + 22 + 16x - 8
collect like term
139 - 22 + 8 = 9x + 16x
125 = 25x
divide both sides by 25
x = 125/25
x = 5
Falcons score = 9x + 22
Falcons score = 9(5) + 22
Falcons score = 45 + 22
Falcons score = 67
Richard and teo have a combine age of 38 Richard is 11 years okder than twice teo age how old are Richard and teo?
Answer: Richard is 29 and Teo is 9.
Step-by-step explanation: Use Substitution
Please help 50 points!!!
Given: △ABC≅△BAD.
Prove: △AED≅△BEC.
Say what each proof was for each statement.
The proof of △AED is congruent to △BEC
What is congruency?
Two figures or objects are congruent in geometry if they have the same shape and size, or if one has the same shape and size as its mirror counterpart. In more technical terms, two sets of points are said to be congruent if and only if one of them can be changed into the other by an isometry, which is a combination of rigid movements such as translation, rotation, and reflection. This implies that one item may be relocated and reflected (but not scaled) to perfectly align with the other. So two separate plane figures on a piece of paper are congruent if they can be cut out and then entirely matched up. It is OK to flip the paper over.
Given, △ABC is congruent to △BAD.
and △AEB is common in both, so
△AED is congruent to △BEC (proved)
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Can someone help me with my practice? I am having trouble with this question.
We are to solve an inequality and give the answer in graph form.
The inequality is:
[tex]6-5+n\ge\text{ 18}[/tex]Let's solve for n in order to be able to answer the question.
we start by trying to isolate n on one side of the inequality symbol. So first combine 6-5 = 1 and re-write the inequality:
[tex]1+n\ge18[/tex][tex]\begin{gathered} n\ge18-1=17 \\ n\ge17 \end{gathered}[/tex]Now, subtract 1 from both sides, and you get the final answer:
n must be larger than or equal to 17. WHich agrees with the first answer option provided by the problem.
which of the following equation have roots 4 and -4
x² -16=0
1) Since we have two roots and any quadratic equation can be rewritten as once we have the roots:
[tex]a(x-x_1)(x-x_2)=0[/tex]So let's find one equation whose roots are 4 and -4, with coefficient a=1
(x-4)(x+4)=0
x² -16=0
2) So the equation x² -16= 0 has roots x_1=4 and x_2= -4 S={-4,4}
Part of the graph of the function f(x) = (x + 4)(x - 6) isshown below.Which statements about the function are true? Selecttwo optionsThe vertex of the function is at (1,-25).6The vertex of the function is at (1,-24).The graph is increasing only on the interval -4
The vertex of the function is (1, -25) Correct
Because
f(x) = (x + 4)(x - 6)
Substitution
-25 = (1 + 4)(1 - 6)
Simplification
-25 = (5)(-5)
Result
-25 = -25 As both sides of the equation are equal this option is true
5) The graph is negative on the entire interval - 4 < x < 6 because the graph is below the x-axis
Factor 24cd − 36c^2d.
Answer:
12cd(2-3c)
Step-by-step explanation:
check:
12cd( 2 - 3c)
12cd(2) - 12cd(3c)
24cd - 36[tex]c^{2}[/tex]d
what is 3 divided by 706
3/706 is 0.00424929178, but if you mean 706/3, then the answer is 235 and 1/3. Hope this helps! :)
Round off each to the nearest thousand
1565
3408
5671
7364
9761
8975
Answer:
1. 1600
2. 3,000
3. 6,000
4. 7,000
5. 10,000
6. 9,000
Step-by-step explanation:
A) We round the number up to the nearest hundred if the last two digits in the number are 50 or above.
B) We round the number down to the nearest hundred if the last two digits in the number are 49 or below.
C) If the last two digits are 00, then we do not have to do any rounding, because it is already to the hundred.
In this case, Rule A applies and 1565 rounded to the nearest hundred is:
1600
Which statement about this function is correct?
A.The y-intercept is (71, 0), and the 71 represents the number of hours until the temperature reaches 71°F.
B.The y-intercept is (71, 0), and the 71 represents the number of hours until the temperature reaches 0°F.
C.The y-intercept is (0, 71), and the 71 represents the starting temperature.
D.The y-intercept is (0, 71), and the 71 represents the temperature after 1 hour
Answer:
C
Step-by-step explanation:
1 we need you to provide the function for people to better understand how to answer.
2 Option c was the only one that made sense.
pls mark brainliest
Use play so value to solve. Derek measured an insect wing that was 0.1 meter long. Leslie measured a different wing that was 1/10 as long as that wing that Derek measured how long is the wing that Leslie measured
Please help I’m desperate thank you
Two or more expressions with an Equal sign is called as Equation. Derek measured 0.01 metres is the wing that Leslie measured.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that
Derrick measured wing length was 0.1 m
The wing that Leslie measured was (1/10) as long as the wing that derrick measured.
We need to measure how long is the wing that Leslie measured.
Multiply 0.1 by (1/10)
0.1×1/10
=0.01 metres.
Hence Derek measured 0.01 metres is the wing that Leslie measured.
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Christel House DORS is taking a field trip. Some students will travel in cars, which can carry 5 students, and others will travel in vans, which can carry 15 students. The equation 5(2)+15v=100 describes the relationship between the number of vans needed, v, and the number of students going on the trip. Which statement below is true?
Given,
5(2)+15v=00
where v is the number of vans.
Solving,
15v=90
v=6
Thus the correct answer is 6 vans are needed to transport students.
What are the vertex and range of y = |x + 3| + 2?
a (−3, 2); 2 ≤ y < ∞
b (−3, 2); −∞ < y < ∞
c (0, 5); 2 ≤ y < ∞
d (0, 5); −∞ < y < ∞
The vertex of the equation is (-3, 2). And the range will be the set of all real numbers equal to or larger than 2, written as:
y ≥ 2.
What is the vertex and range of the absolute value function?
For an absolute value function of the form:
y = |x - a| + b
The vertex is a the point (a, b).
And the range (the set of the possible values of y that we can get with the function) will be the set of all real values equal or larger than b.
In this case, the absolute value function is:
y = |x + 3| + 2
Comparing it with the general one, we can see that the vertex is (-3, 2)
And then the range is y ≥ 2.
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4. Round the number 5,997 to the nearest hundred.
Answer:
6,000
Step-by-step explanation:
A factory makes light fixtures with right regular hexagonal prisms where the edge of a hexagonal base measures 4 centimeters and the lengths of the prisms vary. It costs $0.04 per square centimeter to fabricate the prisms and the factory owner has set a limit of $11 per prism. What is the maximum length of each prism?
The maximum length of each prism is equal to 7.99 centimeter.
How to calculate the maximum length of each prism?First of all, we would determine the maximum surface area of this regular hexagonal prism by using this mathematical expression:
Maximum surface area (quantity) = Cost/unit price
Maximum surface area (quantity) = $11/$0.04
Maximum surface area (quantity) = 275 square centimeter (cm²).
Mathematically, the surface area of a regular hexagonal prism can be calculated by using this formula:
A = 6al + 3√3a²
Where:
A represents the surface area of a regular hexagonal prism.a represents the edge length (apothem) of a regular hexagonal prism.l represents the length of a regular hexagonal prism.Substituting the given parameters into the formula, we have;
275 = 6 × 4l + (3√3 × 4²)
275 = 24l + 48√3
24l = 275 - 48√3
24l = 191.8616
l = 191.8616/24
Length, l = 7.99 centimeter.
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suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 15 days and a standard deviation of 5 days. let x be the number of days for a randomly selected trial. round all answers to 4 decimal places where possible. a. what is the distribution of x? x ~ n( , ) b. if one of the trials is randomly chosen, find the probability that it lasted at least 12 days. c. if one of the trials is randomly chosen, find the probability that it lasted between 17 and 22 days. d. 72% of all of these types of trials are completed within how many days? (please enter a whole number)
a. the distribution of X ~ N(15,5)
b. the probability that it lasted at least 12 days = 0·72575
c. the probability that it lasted between 17 and 22 days = 0.30567
d. 72% of all of these types of trials are completed within 13 days
(a)
The x follow normal distribution with mean standard deviation
X ~ N(15,5)
(b)
probability at least 12 days.
P(X≥12) = 1 - P(X ≤12)
= 1 - P((X - μ)/б ≤ (12-15)/5 ]]
= 1 - P[Z < -0.6]
= 1 - 0·27425
= 0·72575
(c)
Probability at least between 16 & 21 days
P(16 < x < 21) = p( (16-15)/5 < (X - μ)/б - (21-15)/5]
= p (0.2 < Z < 1.2 )
= p[Z < 1.2] - P[Z < 0.2]
= 0.8849 - 0.5792
= 0.30567
(d)
standard normal table z is 0.65
p (Z < 0.65) = 0.74215
using Z score formula
X = Z x б + μ
X = 0.65 x 5 + 15
X = 13
Explain probability ?This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Before we can determine the probability that a certain event will occur, we must first know the total number of outcomes.
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Which is the order from least to greatest of the following: 4/3, 0.8, 1/5, 30%?
Answer:
1/5, 30%, 0.8, 4/3
for f(x)=3/8x-7, find f(-16)
The given function is
[tex]f(x)=\frac{3}{8}x-7[/tex]The expression f(-16) means we have to evaluate the function when x = -16.
[tex]\begin{gathered} f(-16)=\frac{3}{8}(-16)-7 \\ f(-16)=-3\cdot2-7=-6-7=-13 \end{gathered}[/tex]Therefore, f(-16) is equal to -13.Determine whether the given pair of lines is parallel, perpendicular, or neither. 3x + 4y = 5 and 6x + 7y= 8 Choose the correct answer below. A. The lines are neither parallel nor perpendicular. B. The lines are perpendicular. C. The lines are parallel.
If two lines are parallel, then they have the same slope.
If two lines are perpendicular, then the slope of one line is the negative reciprocal of the other line.
The equation of a given line is expressed as
y = mx + b
Where
m represents slope
c represents y intercept
Considering the first equa
Consider x = 10-y.
a. Complete the table for the equation.
y
X
0
1
2
Answer: 0-10
1-9
2-8
Step-by-step explanation:
A pie weighs 500g. jamie cuts it into 4 slices. the largest slice weighs the same as the other 3 combined. what is the weight of the largest piece of pie?
The weight of the largest piece of pie is 250 gram.
How to calculate the weight?Let the weights of others be illustrated as x.
Therefore, the weight of the largest weight is the addition of the others weight. This will be:
= x + x + x = 3x
Therefore, the weights will be:
3x + x + x + x = 500
6x = 500.
Divide
x = 500 / 6
x = 83.33.
The larger weight will be:
= 3x
= 3 × 83.33
= 250
The pie weights 250g.
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52 points helppp composite functions give most simplified answer
Answer:
[tex](f \circ g)(24)=-36[/tex]
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=-9x+9\\g(x)=\sqrt{x+1}\end{cases}[/tex]
Function Composition is applying one function to the results of another.
The composite function (f o g)(x) means to substitute the function g(x) in place of the x in function f(x).
Therefore (f o g)(24) means to substitute the result of g(24) in place of the x in the function f(x).
Calculate g(24) by substituting x = 24 into function g(x):
[tex]\begin{aligned}\implies g(24)&=\sqrt{24+1}\\&=\sqrt{25}\\&=5 \end{aligned}[/tex]
Therefore:
[tex]\begin{aligned}\implies (f \circ g)(24) & = f[g(24)]\\& = f(5)\\& = -9(5)+9\\&=-45+9\\&=-36\end{aligned}[/tex]
Answer:
(f∘g)(24) = -36
Step-by-step explanation:
Pre-SolvingGivenWe are given f(x) = -9x + 9 and [tex]g(x)= \sqrt{x+1}[/tex].
We want to find (f∘g)(24).
This means that we first want to find g(24), then substitute the value of that into f(x).
SolvingStart by substituting 24 for x in g(x).
[tex]g(24)= \sqrt{24+1}[/tex]
Add 24 and 1 together.
[tex]g(24)= \sqrt{25}[/tex]
Take the square root of 25.
g(24) = 5
Now, substitute 5 as x in f(x) = -9x + 9.
f(5) = -9(5) + 9
Multiply.
f(5) = -45 + 9
Add the numbers together.
f(5) = -36
f(5) in this case has the same value as (f∘g)(24)
This means that (f∘g)(24) = -36