Step-by-step explanation:
the average change rate is the change of the functional values from the beginning to the end of the interval, and then that divided by the length of the interval.
like with every average or mean value calculation.
g(-4) = 2×(-4)³ - 5 = -128 - 5 = -133
g(2) = 2×2³ - 5 = 16 - 5 = 11
so, on an interval of x values of 2- -4 = 6 units the function changes its values by 11 - -133 = 144 units.
the average charge rate for this x interval is therefore
144 / 6 = 24 = 24/1
for 1 unit change of x, g(x) changes in the average by 24 units.
A rhombus has an area of 5 square meters and a side length of 3 meters. In another similar rhombus, the length of a side is 9 meters. What is the area of the second rhombus?
(A) 30 square meters
(B) 45 square meters
(C) 60 square meters
(D) 75 square meters
Hence the area of the second rhombus is 45 square meters
The area of a rhombus is expressed as
A = base * height
For the rhombus with an area of 5 square meters and a side length of 3 meters
Height = Area/length
Height = 5/3 metres
Since the length of a similar rhombus is 9meters, the scale factor will be expressed as;
k = ratio of the lengths = 9/3
k = 3
Height of the second rhombus = 3 * height of the first rhombus
Height of the second rhombus = 3 * 5/3
Height of the second rhombus = 5 meters
Area of the second rhombus = length * height
Area of the second rhombus = 5 * 9
Area of the second rhombus = 45 square meters
Hence the area of the second rhombus is 45 square meters
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The correct option is option B;
(B) 45 square meters
The known parameters in the question are;
The area of the rhombus, A₁ = 5 m²
The length of one of the sides of the rhombus, a = 3 m
The length of a side in a similar rhombus, b = 9 m
The unknown parameter;
The area of the second rhombus
Strategy or method;
We have that two shapes are similar if their corresponding sides are proportional
From the above statement we get that the ratio of the areas of the two shapes is equal to the square of the ratio of the lengths of the corresponding sides of the two shapes of follows;
[tex]\begin{array}{ccc}Length \ Ratio&&Area \ Ratio\\\dfrac{a}{b} &&\left (\dfrac{a}{b} \right)^2 \\&&\end{array}[/tex]
Let the area of the second rhombus be A₂, we get;
[tex]Area \ ratio = \dfrac{A_1}{A_2} = \left( \dfrac{a}{b} \right)^2[/tex]
Where;
a = 3 m, b = 9 m, and A₁ = 5 m², we get;
[tex]Area \ ratio = \dfrac{5 \ m^2}{A_2} = \left( \dfrac{3 \, m}{9 \, m} \right)^2 = \dfrac{1}{9}[/tex]
Therefore;
9 × 5 m² = A₂ × 1
A₂ = 45 m²
The area of the second rhombus, A₂ = 5 m².
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A ___________ gives theoretical probabilities of each possible event in an experiment.
A. probability outcome
B. sample space
C. random event
D. probability distribution
A probability outcome gives theoretical probabilities of each possible event in an experiment so option (A) will be correct.
What is probability?The probability of an event occurring is defined by probability.
Do not take underestimate probability it has several uses in daily life whether forecasts and like that.
Theoretical probability is the probability that shows by the probability formula while experimental probability is an actual probability that can obtain by experiments.
There are various situations in our daily lives where we might need to make predictions about how things will turn out.
Probability outcome which comes out by mathematical formula is always theoretical probability while actual experiment gives us experimental probability hence probability outcome will be the correct answer.
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Which defines a line segment?
two rays with a common endpoint
O a piece of a line with two endpoints
O a piece of a line with one endpoint
all points equidistant from a given point
Answer:
O a piece of a line with two endpoints
Step-by-step explanation:
O a piece of a line with two endpoints
A piece of a line with two endpoints.
What is a line segment?In geometry, a line segment is a part of a line this is bounded by distinct end points and includes every point on the line this is between its endpoints.
What are the examples of line segments in real life?A ruler, a scale, a stick, a boundary line.Learn more about line segments here https://brainly.com/question/2437195
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Sabrina is 4 and her brother Sam is 9 years older than she is. In how many years will same be twice as old as Sabrina
Answer:
=4-7
=5
:same will be 5 years older than Sabrina
An oblique cylinder is shown.
An oblique cylinder is shown. It has a radius of 5, a height of 12, and a slant length of 13.
Which represents the volume of the cylinder, in cubic units?
120π
130π
300π
325π
Answer:
The volume in terms of Pi is 300πStep-by-step explanation:
This problem is on the mensuration of solid shapes, an oblique cylinder.
the expression for the volume of an oblique cylinder is given as
[tex]volume= \pi r^2h[/tex]
Given data
radius r= 5
height h= 12, and
slant length of 13.
Substituting the given data into the expression we can solve for the volume below
[tex]volume= \pi* 5^2*12\\\ volume= \pi*25*12\\\ volume= \pi*300\\\ volume= 300\pi[/tex]
Answer:
300
Step-by-step explanation:
Help!!!!!!! Thank you!!!!!!!
Answer:
D
Step-by-step explanation:
The ratio of yellow paint to blue paint is 4:3. We can make the largest amount of green paint by using all of the 20 quarts of yellow paint so we have to solve for x in 4:3 = 20:x, since 4 * 5 = 20, 3 * 5 = x so we use 15 qts of blue paint, therefore we will have 20 + 15 = 35 qts of green paint.
Answer:
D
Step-by-step explanation:
-10 + 7x + 24 - 2x
Your answer
What is 5 over 30= 3 over c
Answer:
c=18
Step-by-step explanation:
5/30=3/c
1/6=3/18
1✖️3=3
6✖️3=18
Hugo scored 18 points in a recent basketball game, which was 5 points fewer than
Toby scored. Write an equation for this situation, where tis the number of points
Toby scored, and find how many points Toby scored.
A) 18 = t + 5, Toby scored 13 points
B) 18 = t-5, Toby scored 23 points
C) 18 = t - 5, Toby scored 13 points
D) 18 = t + 5, Toby scored 23 points
how can i solve this factorial? A 6,2- P6- A 5,3 + P5
James purchased five acres of land fo 75,000 what was the cost per acre
Answer:
$15,000
Step-by-step explanation:
James purchased a total of 5 acres of land for a total price of $75,000. To find the cost of each individual acre, simply divide the total cost with the total amount of acres purchased:
[tex]\frac{total price of land bought}{total amount of acres} = \frac{75000}{5} = 15000[/tex]
The cost per individual acre, assuming all of them cost the same, is $15,000.
~
Answer:
15000
Step-by-step explanation:
Since
5 acres = 75000
therefore,
the cost price per acre would be
total cost price ➗ 5
7500/5= 15000
Use the numbers 6 2 9 5 2 3
to make 36.
Answer:
6+2+9+5+2+3+6+3 = 36
Step-by-step explanation:
If you like my answer than please mark me brainliest
What is the domain of f?
Answer:
-5 ≤x ≤6
Step-by-step explanation:
The domain is the values that x can take
X goes from -5 and includes -5 to x =6 and includes 6
-5 ≤x ≤6
Answer:
See attached!
Step-by-step explanation:
Carla drove her truck 414 miles on 18 gallons of gasoline. How many miles did she drive per gallon?
Answer:
23 miles per gallon
Step-by-step explanation:
414 miles = 18 gallons
=> 18/18 gallons = 414/18 miles
=> 1 gallon = 23 miles
So, she drove 23 miles per gallon.
How many cubic inches of a milkshake can you fit up to the brim of this cup without letting it overflow? The
cup is 10 inches tall, and the rim of the cup is 4 inches across. (Hint: the radius is half of the diameter.)
Assuming the cup is a right circular cylinder, it's volume is [tex]V=\pi r^2 h[/tex]
$h=10$, $r=\frac 42$
So the volume is $\pi\cdot(2)^2\cdot10=125.66$
hence you can fill up to 125.66 cubic Inches of milkshake
.
simplify the following expression by combining like terms 2x+7x^2-5x+8x^2
Answer:15x^2-3x
Step-by-step explanation:
In a triangle, the sum of two angles equals the third, Find the measure of the third angle.
A.45 degree
B.60 degree
C.90 degree
D.30 degree
Answer:
C.90 degree
Step-by-step explanation:
45 + 45 + 90 = 180
90 = 45 + 45
What are the following fractions from least to greatest 3/8 5/8 4/8 2/8 7/8
Answer:
2/8, 3/8, 4/8, 5/8, 7/8. If there are more numbers I apologize, I see 2 boxes that say "obj" instead.
Write the phrase "the product of 19 and a number" as a mathematical expression.
A 19 + x
B) 19/x
C) 19 x
(D) 19 -x
Answer:
19x
Step-by-step explanation:
product means multiply
19*x
19x
Answer:
The answer is C.
Step-by-step explanation:
if a number and a variable are next to each other, it is assumed they will be multiplied.
The screening process for detecting a rare disease is not perfect. Researchers have developed a blood test that is considered fairly reliable. It gives a positive reaction in 94.8% of the people who have that disease. However, it erroneously gives a positive reaction in 3.3% of the people who do not have the disease. Consider the null hypothesis "the individual does not have the disease" to answer the following questions.
a. What is the probability of Type I error?
b. What is the probability of Type II error?
Answer:
Probability of Type 1 error = 0.033
Probability of type II error = 0.952
Step-by-step explanation:
H0: Individual does not have disease
H1: individual has disease
Type 1 error occurs when we fail to accept a correct null hypothesis and accept an alternate Instead
Type ii error occurs when we accept a false null hypothesis instead of the alternate hypothesis
Probability of people with disease = 98.4%
Probability of people without disease = 3.3%
1.probability of type 1 error = 3.3/100
= 0.033
2. Probability of type ii error = (1-98.4%) = 1-0.948
= 0.052
Power +, Inc. produces AA batteries used in remote-controlled toy cars. The mean life of these batteries follows the normal probability distribution with a mean of 35.0 hours and a standard deviation of 5.5 hours. As a part of its quality assurance program, Power +, Inc. tests samples of 25 batteries.
A) What can you say about the shape of the distribution of the sample mean?
B) What is the standard error of the distribution of the sample mean?
C) What proportion of the samples will have a mean useful life of more than 36 hours?
D) What proportion of the sample will have a mean useful life greater than 34.5 hours?
E) What proportion of the sample will have a mean useful life between 34.5 and 36.0 hours?
Answer:
(A) The shape of the distribution of the sample mean is bell-shaped.
(B) The standard error of the distribution of the sample mean is 1.1.
(C) The proportion of the samples that have a mean useful life of more than 36 hours is 0.1814.
(D) The proportion of the sample that has a mean useful life greater than 34.5 hours is 0.6736.
(E) The proportion of the sample that has a mean useful life between 34.5 and 36.0 hours is 0.4922.
Step-by-step explanation:
We are given that Power +, Inc. produces AA batteries used in remote-controlled toy cars. The mean life of these batteries follows the normal probability distribution with a mean of 35.0 hours and a standard deviation of 5.5 hours.
As a part of its quality assurance program, Power +, Inc. tests samples of 25 batteries.
Let [tex]\bar X[/tex] = sample mean life of these batteries
(A) The shape of the distribution of the sample mean will be bell-shaped because the sample mean also follows the normal distribution as it is taken from the population data only.
(B) The standard error of the distribution of the sample mean is given by;
Standard error = [tex]\frac{\sigma}{\sqrt{n} }[/tex]
Here, [tex]\sigma[/tex] = standard deviation = 5.5 hours
n = sample of batteries = 25
So, the standard error = [tex]\frac{5.5}{\sqrt{25} }[/tex] = 1.1.
(C) The z-score probability distribution for the sample mean is given by;
Z = [tex]\frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean life of battery = 35.0 hours
[tex]\sigma[/tex] = standard deviation = 5.5 hours
n = sample of batteries = 25
Now, the proportion of the samples that will have a mean useful life of more than 36 hours is given by = P([tex]\bar X[/tex] > 36 hours)
P([tex]\bar X[/tex] > 36 hours) = P( [tex]\frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{36-35}{\frac{5.5}{\sqrt{25} } }[/tex] ) = P(Z > 0.91) = 1 - P(Z [tex]\leq[/tex] 0.91)
= 1 - 0.8186 = 0.1814
(D) The proportion of the samples that will have a mean useful life of more than 34.5 hours is given by = P([tex]\bar X[/tex] > 34.5 hours)
P([tex]\bar X[/tex] > 34.5 hours) = P( [tex]\frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{34.5-35}{\frac{5.5}{\sqrt{25} } }[/tex] ) = P(Z > -0.45) = P(Z [tex]\leq[/tex] 0.45)
= 0.6736
(E) The proportion of the samples that will have a mean useful life between 34.5 and 36.0 hours is given by = P(34.5 hrs < [tex]\bar X[/tex] > 36 hrs)
P(34.5 hrs < [tex]\bar X[/tex] < 36 hrs) = P([tex]\bar X[/tex] < 36 hrs) - P([tex]\bar X[/tex] [tex]\leq[/tex] 34.5 hrs)
P([tex]\bar X[/tex] < 36 hours) = P( [tex]\frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{36-35}{\frac{5.5}{\sqrt{25} } }[/tex] ) = P(Z < 0.91) = 0.8186
P([tex]\bar X[/tex] [tex]\leq[/tex] 34.5 hours) = P( [tex]\frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }[/tex] [tex]\leq[/tex] [tex]\frac{34.5-35}{\frac{5.5}{\sqrt{25} } }[/tex] ) = P(Z [tex]\leq[/tex] -0.45) = 1 - P(Z [tex]\leq[/tex] 0.45)
= 1 - 0.6736 = 0.3264
Therefore, P(34.5 hrs < [tex]\bar X[/tex] < 36 hrs) = 0.8186 - 0.3264 = 0.4922.
Marcelina uses a blend of white corn and yellow corn to make tortilla chips at her restaurant. She needs to buy 50kg of corn in total for her next order. White corn costs $0.30 per kilogram, yellow corn costs $0.15 per kilogram, and she wants to spend $12.00 in total. Here's a graph that shows a system of equations for this scenario where x is the amount of white corn she buys and y is the amount of yellow corn she buys.
Answer:
https://brainly.com/question/17155330
Step-by-step explanation:
Question:
Marcelina uses a blend of white corn and yellow corn to make tortilla chips at her restaurant. She needs to buy 50kg of corn in total for her next order. White corn costs $0.30 per kilogram, yellow corn costs $0.15 per kilogram, and she wants to spend $12 total.
What does point F represent in this context?
Answer:
Marcelina spends less that the intended amount of money and buy less than enough corn
In an opinion poll, 29% of 100 people sampled said they were strongly opposed to the state lottery. What is the approximate standard error of the sample proportion?
Answer:
The approximate standard error of the sample proportion is [tex]SE = 0.0454[/tex]
Step-by-step explanation:
From the question we are told that
The sample proportion is [tex]\r p = 0.29[/tex]
The sample size is n = 100
Generally the standard error of the sample proportion is mathematically represented as
[tex]SE = \sqrt{ \frac{ \r p (1- \r p )}{n} }[/tex]
substituting values
[tex]SE = \sqrt{ \frac{ 0.29 (1- 0.29 )}{ 100 } }[/tex]
[tex]SE = 0.0454[/tex]
the difference of 8 and 2, added to x"
Answer:
see below
Step-by-step explanation:
Difference is subtract
(8-2)
Then add this to x
(8-2) +x
6+x
(12x^(2)+x-35)-:(4x+17)
Answer:
(3x-5)(4x+7) / 4x + 17
Step-by-step explanation:
Rewrite the division as a fraction
12 x ^2 + x-35 / 4x+17
Factor by grouping
(3x-5)(4x+7) / 4x + 17
Hope this was the answer you were looking for
What are the solution(s) of the quadratic equation 98 - x2 = 0?
x = +27
Ox= +63
x = +7/2
no real solution
Answer:
±7 sqrt(2) = x
Step-by-step explanation:
98 - x^2 = 0
Add x^2 to each side
98 =x^2
Take the square root of each side
±sqrt(98) = sqrt(x^2)
±sqrt(49*2) = x
±7 sqrt(2) = x
Answer:
[tex]\huge \boxed{{x = \pm 7\sqrt{2} }}[/tex]
Step-by-step explanation:
[tex]98-x^2 =0[/tex]
[tex]\sf Add \ x^2 \ to \ both \ sides.[/tex]
[tex]98=x^2[/tex]
[tex]\sf Take \ the \ square \ root \ of \ both \ sides.[/tex]
[tex]\pm \sqrt{98} =x[/tex]
[tex]\sf Simplify \ radical.[/tex]
[tex]\pm \sqrt{49} \sqrt{2} =x[/tex]
[tex]\pm 7\sqrt{2} =x[/tex]
[tex]\sf Switch \ sides.[/tex]
[tex]x= \pm 7\sqrt{2}[/tex]
Given the following diagram, find the required measures. Given: l | | m m 1 = 120° m 3 = 40° m 2 = 20 60 120
Step-by-step explanation:
your required answer is 60°.
Hello,
Here, in the figure;
angle 1= 120°
To find : m. of angle 2.
now,
angle 1 + angle 2= 180° { being linear pair}
or, 120° +angle 2 = 180°
or, angle 2= 180°-120°
Therefore, the measure of angle 2 is 60°.
Hope it helps you.....
please help me find the value of x
Answer:
x=10
Step-by-step explanation:
The whole figure is symmetric hence x=10
increased from 1432 to 2219. Which of the following is the approximate percent of increase
22. Between the years 2000 and 2010, the number of births in the town of Daneville
in the number of births during those ten years?
a. 55%
b. 36%
c. 64%
d. 42%
9514 1404 393
Answer:
a. 55%
Step-by-step explanation:
The percentage increase is calculated from ...
% increase = (amount of increase)/(original amount) × 100%
= (2219 -1432)/1432 × 100% = 787/1432 × 100% ≈ 54.96%
The number of births increased by about 55% during those 10 years.
Answer:
Step-by-step explanation:
2219-1432/1432 x 100% = 787/1432 x 100 = 54.9581~~ 55%
if point B is the midpoint of points A and C, find the value of x and AC. AB= 5x - 2, BC= 9x -10
9514 1404 393
Answer:
x = 2AC = 16Step-by-step explanation:
The midpoint divides the segment into two equal lengths:
AB = BC
5x -2 = 9x -10
8 = 4x
2 = x
AB = 5(2) -2 = 8
AC = 2AB = 2(8) = 16