The difference between the surface areas is 198 square inches
How to determine the difference between the surface areas?The side lengths are given as:
L = 7 inches
l = 4 inches
The difference between the surface areas is calculated as:
Difference = 6(L^2 - l^2)
Substitute the known values in the above equation
Difference = 6(7^2 - 4^2)
Evaluate
Difference = 198
Hence, the difference between the surface areas is 198 square inches
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A ship sails 300 km west and then 500 km south. How far, to the nearest km, is the ship now from its starting position?
Step-by-step explanation:
this creates a right-angled triangle, with the pure coordinate changes being the legs, and the actual distance being the Hypotenuse (the side opposite of the 90° angle).
and so, we can use Pythagoras :
distance² = leg1² + leg2² = 300² + 500² =
= 90000 + 250000 = 340000
distance = sqrt(340000) = sqrt(10000×34) = 100×sqrt(34) =
= 583.0951895... km ≈ 583 km
Emma is thinking of three numbers from 1 to 9 that have the sum of 20 find of the possible numbers
The possible numbers are
( 9 , 9 ,2 ) ;( 9 , 8 , 3 );( 9 , 7 , 4 );( 9 , 6 , 5 )
All 4 combinations have the sum of 20 .
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Given the following information: P(D) 0.7, P(E) = 0.2 and P(D and E) = 0.15.
Find P(DIE):
According to the given statement
P(D) 0.7, P(E) = 0.2 and P(D and E) = 0.15.
P(DIE):0.75
What is Conditional Probability?The possibility of an event or outcome occurring conditional on the occurrence of a prior event or outcome is known as conditional probability. The conditional probability is calculated by multiplying the probability of the previous event by the present probability of the upcoming, or conditional, occurrence.
Contrast Unconditional probability with conditional probability. The possibility that an event will occur regardless of whether any previous occurrences have occurred or any other circumstances are present is known as Unconditional probability.
According to the given value;
P(DIE): 0.15/0.2
=0.75.
hence,P(DIE):0.75.
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jayden's walkie-talkie has a range of 3 miles. jayden is traveling on a straight highway and is at mile marker 253. identify the absolute-value equation and solution to find the minimum and maximum mile marker from 253 that jayden's walkie-talkie will reach.
Jayden's maximum and minimum walkie-talkie will reach mile marker is:
|x + 253| = 3
x = 253
The range of Jayden's walkie-talkie is three miles.
At mile 253, Jayden is moving straight along a highway.
Find the least and maximum milepost that Jayden's walkie-talkie will reach from 253 by solving the absolute-value equation.
range of 3 miles.
mile marker 253.
Find maximum and minimum of walkie talkie will reach
|x + 3| - 253 = 3x
= 253 or x
= 250
|x + 3| = 253
x = 250 or x
= -256|x - 253|
= 3
x = 256 or x
= 250
|x + 253| = 3
x = 253
Therefore, Jayden's minimum and maximum mile marker from 253 that walkie-talkie will reach is
|x + 253| = 3
x = 253
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The table shows the proportional relationship between a hedgehog's
weight loss and the number of days of hibernation. How much weight does
the hedgehog lose during 120 days of hibernation?
Explain how you know that the relationship between the hedgehog's weight
loss and the number of days of hibernation is proportional.
The hedgehog’s total change in weight over 120 days is ____ ounces.
weight loss of hedgehog
days: change in weight:
12 -0.36
21 -0.63
71 -2.13
96 -2.88
24 - (2x7) expression
Step-by-step explanation:
24-(14)
10
use bidmas...
A nursery is recording the heights of its available fruit trees. Which of the following displays could be used to represent the data, and why?
O Bar chart, because tree height is numerical
O Box plot, because tree height is numerical
O Histogram, because tree height is categorical
Stem-and-leaf-plot, because tree height is categorical
When the nursery is recording the heights of its available fruit trees. the display that can be used to represent the data, is A. Bar chart, because tree height is numerical.
What is a bar chart?Using rectangular bars with heights or lengths proportional to the values they represent, a bar chart or bar graph displays categorical data. Both a vertical and a horizontal bar plot are possible. A column chart is another name for a vertical bar graph.
When displaying the distribution of data points or comparing metric values across several subgroups of your data, a bar chart is employed. A bar graph allows us to determine which groupings are most numerous or prevalent as well as how different groups stack up against one another.
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Answer:
The answer would be B.
Step-by-step explanation:
Since we are doing heights, it would make since to have a box plot, since that includes minimum, maximum, median, Q1, & Q2. :)
that makes it easier to record height
you would like to investigate whether smokers are more likely than nonsmokers to get lung cancer. you take the students in your class, select half at random and tell them to smoke a pack of cigarettes each day, and you tell the other half not to ever smoke. fifty years from now, you will analyze whether more smokers than nonsmokers got lung cancer. is this an experiment or an observational study? experiment observational study summarize at least three practical difficulties with this planned study.
According to the question, to investigate through an experiment by telling people to smoke a pack of cigarettes each day by putting their health at risk. This causes serious health issues. And the other half are told not to smoke but might smoke at their own discretion. In the end, it is very difficult to keep track of 50 years of both types of people. That means people who are smoking and others who are not smoking. And, after 50 years, checking their consistency has become extremely difficult, if not impossible. Therefore, this experiment is not possible in both ways, that is, experimental or observational.
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A =
૫ {q) n)
2
solve for a
Answer:
5 x = Solve: 2. 8 x = . x has 2 multiplied to it, so we divide 2 from both sides. 2.
Step-by-step explanation:
A sample of n = 5 scores has m = 20 and s2 = 4. what is the sample standard deviation?
The sample standard deviation is 0.89
In the given statement is:
A sample n = 5 scores which means that there are 5 sample having m = 20 which is the arithmetic mean (A.M.)of these samples, and [tex]s^{2}[/tex] = 4 is the variance of these samples.
Let us know the :
What is meant by Sample Standard deviation?
The sample standard deviation (s) is the square root of the sample variance and is also measure of the spread from the expected values.
Standard deviation is the square root of the variance.
Therefore, [tex]s^{2}[/tex] =4 => s = 2
(Where, s denotes sample standard deviation ,σ)
Also, Standard error of the sample S(E) = Sample standard variance / [tex]\sqrt{number of samples}[/tex]
= σ /[tex]\sqrt{n}[/tex] = 2/[tex]\sqrt{5}[/tex]
and, root 5 = 2.24
put the value of root 5
=2 / 2.24
= 0.89
Hence, The sample standard deviation is 0.89
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Complete each part.
(a) Write a function, (), that meets the following criteria: (3 points)
a. Non-linear
b. Does not go through the origin
c. At least 2 terms
(b) Write a function, (), that meets the following criteria: (3 points)
a. Non-linear
b. Contains an radical
(c) Find
(f g x )( )
(3 points)
(d) Find
(g f )(6)
(3 points
Using composite functions, we have that:
a) f(x) = x² + 3.
b) [tex]g(x) = \sqrt{x}[/tex]
c) f(g(x)) = x + 3.
d) [tex](g \circ f)(6) = \sqrt{39}[/tex]
What is the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is given by:
(f ∘ g)(x) = f(g(x)).
For item a, we want a non-linear function, which has a highest exponent different of 1, that does not go through the origin, hence the function can be:
f(x) = x² + 3.
For item b, we also want a non-linear function with a radical, hence the function can be:
[tex]g(x) = \sqrt{x}[/tex].
For item c, the composite function is:
[tex]f(g(x)) = f(\sqrt{x}) = (\sqrt{x})^2 + 3 = x + 3[/tex]
For item d, the composite function is:
[tex]g(f(x)) = g(x^2 + 3) = \sqrt{x^2 + 3}[/tex]
At x = 6, we have that:
[tex](g \circ f)(6) = \sqrt{6^2 + 3} = \sqrt{39}[/tex]
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Which shows a way to factor the
expression 24 - 32x8
A -8(-3+4x)
B-4-6-8x)
C 41-6+8
D 81-3-4)
Answer:
Pretty sure A would be the answer
Step-by-step explanation:
PLEAS HELP ITS DUE TODAY
The slope for plane A is 375, this means its rate of speed is 375 ml/h.
The slope for plane B is 445, this means the rate of speed for Plane B is 445 ml/h.
What is the Slope of a Linear Equation?The slope of a linear equation = change in y / change in x.
A linear equation that is given as, y = mx + b or y = mx, has a slope that is represented as m.
Slope of Plane A:
Given the equation for Plane A as, y = 375x, the slope is, 375.
This means its rate of speed is: 375 ml/h.
Slope of Plane B:
Using two points, (1, 445) and (2, 890)
Slope for plane B = (890 - 445)/(2 - 1)
Slope for plane B = 445
This means the rate of speed for Plane B is: 445 ml/h.
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[tex]\sqrt{7} (2\sqrt{7}+4)[/tex]
Answer:
[tex] \sqrt{7 \times 2} \sqrt{7 + 4 \sqrt{7} } \\ 14 + 4 \sqrt{7} [/tex]
prove that every positive integer can be written as a finite sum of distinct integral powers of the golden ratio.
z1 =........=zm = 0 and n=m because n0 cannot be expressed in the +ve Phi / golden ratio form.
What is golden ratio?important is that the ratio between each succeeding pair of Fibonacci numbers approaches 1.618, or its inverse, 0.618, as the numbers get bigger. The holy proportion, the golden ratio, and the golden mean are some additional names for this proportion. Then why is this number so important? The fact that so many items in nature have dimensions characteristics that conform to the 1.618 ratio suggests that it plays a fundamental role for the components of nature. Due to its visual appeal compared to other proportions, the golden ratio is frequently used in the arts. The Great Pyramid in Giza, the Mona Lisa by Da Vinci, and the Parthenon in Athens are all.
z1 =........=zm = 0 and n=m
z1 =........=zm = 0 and n=m because n0 cannot be expressed in the +ve Phi / golden ratio form.
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A mountain climber camped at an elevation of 18,492 feet. The following day the climber descended 2,516 feet to another campsite. Write a numerical expression you can evaluate to find the elevation of the second campsite. Then find the elevation.
1. The elevation is -15,976 feet
2. The elevation is 15,976 feet
3. A good expression would be -18,492 + 2,516
4. The elevation is 21,008 feet
5. The elevation is -21,008 feet
6. A good expression would be 18,492 + 2,516
7. A good expression would be 18,492 + -2,516
8. A good expression would be -18,492 + -2,516
The correct options are:
The elevation is 15,976 feet
A good expression would be 18,492 + -2,516
What is the elevation?When a person goes up a mountain, the sign used to represent their height above sea level is a positive sign (+). When a person goes down a mountain, the sign used to represent their height above sea level is a negative sign (-). So, the sign in front of 18,492 would be positive and the sign in front of 2516 would be negative.
The expression that can be used to evaluate the elevation of the second campsite :
height of the first campsite - feet descended
18,492 - 2,516 = 15,976 feet
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9uv + 3s³t² + 5uv
Combine any like terms in the expression. if there are no like terms, rewrite the expression.
The expression after combining the like terms is 14uv+ 3s³t²
Expression:
Mathematical expression consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Variable:
A variable in algebra is an alphabet that is used to symbolise the unknowable integer. It stands in for the value. An amount that can fluctuate depending on the mathematical issue is referred to as a variable.
⇒9uv + 3s³t² + 5uv
⇒ 14uv+ 3s³t² { addition of like terms}
Therefore,The expression after combining the like terms is 14uv+ 3s³t²
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A (-5, -2) and B (7, 4)
The length of line AB with coordinates A (-5, -2) and B (7, 4) is; 6√5 units
What is the distance between the coordinates?
The formula for distance of a line between two coordinates is;
D = √[(x2 - x1)² + (y2 - y1)²]
From the coordinates given as A (-5, -2) and B (7, 4), we can say that;
x1 = -5
x2 = 7
y1 = -2
y2 = 4
Thus;
D = √[(7 - (-5))² + (4 - (-2))²]
D = √(12² + 6²)
D = √180
D = 6√5 units
Thus, we conclude that the length of line AB with coordinates A (-5, -2) and B (7, 4) is; 6√5 units
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Complete question is;
Find the distance of the line AB with coordinates A (-5, -2) and B (7, 4).
Evan needed to get his computer fixed. He took it to the repair store. The technician
at the store worked on the computer for 4.5 hours and charged him $97 for parts. The
total was $479.50. What was the cost of labor, per hour?
The function f(x)=80(1.5)x models a bacteria population after x hours. how does the average rate of change between hour 4 and hour 8 compare to the average rate of change between hour 0 and hour 4?
The average rate of change between hour 4 and hour 8 is equal to the average rate of change between hour 0 and hour 4.
Function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given,
The function f(x)=80(1.5)x
where x is the time in hours
Then,
f(4)=80(1.5)4=480
f(8)=80(1.5)8=960
f(0)=80(1.5)0=0
Then the average rate of change between 4 and 8 hours =[tex]\frac{960-480}{4}[/tex]
=120 units per hour
The average rate of change between 0 and 4 hours=[tex]\frac{480-0}{4}[/tex]
=120 units per hour
Hence, the average rate of change between hour 4 and hour 8 is equal to the average rate of change between hour 0 and hour 4.
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PLEASE HELP!! Im not sure with my answers and solution. Correct answers and solutions will be marked as "BRAINLIEST".
Answer:
[tex]\textsf{(a)} \quad -4 < x\leq 1[/tex]
[tex]\textsf{(b)} \quad [3, 19)[/tex]
Step-by-step explanation:
Part (a)Given compound inequality:
[tex]\dfrac{9+x}{5} < 5+x\leq 6[/tex]
[tex]\textsf{If\: $a < u\leq b$ \:then\: $a < u$ \:and\: $u\leq b$}.[/tex]
[tex]\textsf{Therefore \:$\dfrac{9+x}{5} < 5+x$ \:and\: $5+x\leq 6$}[/tex]
Solve the inequalities separately:
Inequality 1
[tex]\begin{aligned}\dfrac{9+x}{5} & < 5+x\\9+x & < 5(5+x)\\9+x & < 25+5x\\9+x -5x& < 25+5x-5x\\9-4x & < 25\\ 9-4x-9 & < 25-9\\-4x & < 16\\-x & < 4\\x & > -4\\ \end{aligned}[/tex]
Inequality 2
[tex]\begin{aligned} 5+x & \leq 6\\ 5+x-5 & \leq 6-5\\x & \leq 1 \end{aligned}[/tex]
Combine the intervals:
[tex]-4 < x\leq 1[/tex]
Part (b)Given equation:
[tex]y=x^2+3[/tex]
As the domain is restricted to -4 < x ≤ 1, the range is also restricted.
The vertex (minimum point) of [tex]y = x^2 + 3[/tex] is when x = 0.
As x = 0 lies within the restricted domain, y = 3 is the lowest value of the range.
[tex]x=-4 \implies y=(-4)^2+3=19[/tex]
Therefore, the range is:
Solution: 3 ≤ y < 19.Interval notation: [3, 19)If a = 3, then 5a = 15. If a = 11⁄2, then a
3.
The value of the expression a^3 is 3 3/8
How to evaluate the expression?The given parameters can be represented as
If a = 3, then 5a = 15.
Also, we have the value of the variable a to be
a = 1 1/2
Express the value of the variable a as an improper fraction
So, we have
a = 3/2
When a = 1 1/2 or a = 3/2, the value of a³ is calculated using the following formula
a³ = (1 1/2)³ = (3/2)³
Rewrite the formula as
a³ = (3/2)³
Evaluate the exponent in the above equation
So, we have
a³ = (27/8)³
Evaluate the quotient in the above equation
So, we have
a³ = 3 3/8
Hence, the value of the expression a³ is 3 3/8
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Multiply each side of the equation by a power of 10 to get the repeating digit(s) to the left of the decimal point. since you only need to move one place, multiply each side by 10.
To decide the power of 10 multiplies an equation with repeating digits; Round the equation to the required significant numbers.
when the numerator of an equation is divided by the denominator and the result is not a whole number ( i.e. number with some decimals)and sometimes the decimal places are unending. to present the result properly we have to round off the number to the nearest significant number, then you can multiply the equation with the power of 10, in relation to the number of significant places you rounded off.
Example :
5/200 = 0.025
To express this answer with the power of 10
0.025 = 2.5 * 10 ^-2
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if a circle passe though point (-4,2) and is tangent to the x-axis at (2,0), determine the coordinates of its center.
The coordinates of its center will be (2,10)
How can we express the equation of the circle?(x - h)²+ (y - k)² = r² is the formula for the equation of a circle, where (h, k) stands for the circle's center's coordinates and r for the radius.
A circle with a radius of r and a center is represented as
(x - a)² + (y - b)² = r² where (a, b) is the center of the circle.
Circle passes points (-4, 2) and (2, 0):
Both (-4 - a)² + (2 - b)² and (2 - a)² + (-b)² are equal to r²
Currently, the center's x coordinate (a) is 2 due to the tangent at (2, 0)
The equations then read:
6² + (2 - b)² = r²
b² = r²
⇒ 36 + (2 -b)² -b² = 0
⇒ 36 + 4 + b² - 4b - b² = 0
⇒ 4b = 40
⇒ b = 10.
So, the center is (2,10)
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factor 36(2x-y)^2-25(u-2y)^2
Solution After Factoring:
[tex]144x^2-144xy+86y^2-25u[/tex]
Hope this helps! If not, comment below and I'll see what else I can do to help. If it does help though, lmk! Thanks and good luck!
for a field trip 19 students rode in cars and the rest filled the 10 buses how many students were in each bus if 519 students were on the trip
answer as an equation please help
Answer: 10x + 19 = 519 x = 50
Step-by-step explanation:
We are looking for the number of students that rode in each bus, so first lets subtract out those that drove in cars.
519-19=500
So 500 students rode on 10 buses. So now we divide the students onto the buses.
500/10 = 50
Each bus drove 50 students.
An equation to represent the total number of students as a function of those on the buses would be
10x + 19 = 519
x = 50 (the number of students on each bus)
in a petri dish, a certain type of bacterium doubles in number every 40 minutes.
There were originally 64 or 2 to the 6th power, bacteria in the dish. After 120 minutes, the number of bacteria has doubled 3 times, multiplying by 2 to the 3rd power
Now the population of bacteria is is 2 to the 6th power times 2 to the 3rd power. Expressed as a power, how many bacteria are in the petri dish after 120 minutes?
Applying exponent properties, it is found that there are 2^9 = 512 bacteria after 120 minutes.
What happens when we multiply two terms with the same base and different exponents?We keep the base and add the exponents.
This is what happens in this problem, when we multiply 2^6 by 2^3, as follows:
[tex]2^6 \times 2^3 = 2^{6 + 3} = 2^9 = 512[/tex]
Hence, there are 512 bacteria after 120 minutes.
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A design engineer is mapping out a new neighborhood with parallel streets. If one street passes through (4, 7) and (3, 3), what is the equation for a parallel street that passes through (−2, 4)?
y = 4x + 12
y = 4x − 14
y equals negative one-fourth times x minus 1
y equals negative one-fourth times x plus 7 halves
Answer:
Step-by-step explanation:
The Answer is A
The equation for a parallel street that passes through the given point is y = 4x + 12
Equation of a line
From the question, we are to determine the equation of the street that is parallel to the first street
NOTE: Two lines are parallel if they have equal slopes.
Thus,
We will determine the slope of the first street.
From the given information,
The street passes through the points (4, 7) and (3, 3)
Using the formula,
Slope = (y₂ - y₁)/(x₂ - x₁)
x₁ = 4
y₁ = 7
x₂ = 3
y₂ = 3
∴ Slope = (3 -7)/(3 -4)
Slope = -4/-1
Slope = 4
Now,
For the equation of the parallel street
The street passes through the point (-2, 4)
Since, the street is parallel to the first street,
Slope = 4
Using the point-slope form
y - y₁ = m(x - x₁)
y - 4 = 4(x - -2)
y - 4 = 4(x + 2)
y - 4 = 4x + 8
y = 4x + 8 + 4
y = 4x + 12
Hence, the equation for a parallel street that passes through the given point is y = 4x + 12
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which term best describes the number of solutions that will maximize the function below given the constraints listed? (assume that and .) 3x 2y a. one optimal solution c. unbounded b. alternate optimal solutions d. infeasible please select the best answer from the choices provided a b c d
Final answer:
The best term that describes the number of solutions that will maximize the function is one optimal solution (a)
What exactly do you mean by a practical solution ?
A practicable solution is one that complies with all limitations and specifications. When all of the requirements and constraints cannot be satisfied by any combination of decision variable values, a solution is deemed to be infeasible. The parabola's highest or lowest point represents the ideal value. If only the parabola expands down words, the optimal value, also known as the vertex of the parabola, would be maximal. The minimal value is one opening upwards. The vertex's "Y" coordinate is it.
An option for making a judgment or a resolution that does not adhere to one or more constraints. The corners of the entire model's graph would contain the ideal answer.
Explanation:
(Assume that [tex]x > 0[/tex] and [tex]y > 0[/tex].)
[tex]x + 2 < 5x-y < 2[/tex]
[tex]F(x,y) = 2x+y[/tex]
So , the equation becomes a optimal solution.
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Heyy, If anyone can find the answer to this question, I’ll literally be in your DEBT
[tex]Answer: the\ number\ is\ \boxed{-26}[/tex]
Step-by-step explanation:
[tex]2(n-4)=3(n+6)\\2(n)-2(4)=3(n)+3(6)\\2n-8=3n+18\\2n-8-18=3n+18-18\\2n-26=3n\\2n-26-2n=3n-2n\\-26=n\\Thus,\\n=-26[/tex]