Answer:
(−14)
3
1
Step-by-step explanation:
(i) (−4)
5
÷(−4)
8
=
(−4)
8
(−4)
5
=(−4)
5−8
=(−4)
−3
=
(−4)
3
1
(ii) (
2
3
1
)
2
=
2
3×2
1
=
2
6
1
(iii) (−3)
4
×(
3
5
)
4
=(−1)
4
×(3)
4
×(
3
5
)
4
=(−1)
4
×5
4
=5
4
(iv) (3
−7
÷3
−10
)×3
−5
=(
3
−10
3
−7
)×(3)
−5
=3
−7+10
×3
−5
=3
3−5
=3
−2
=
3
2
1
(v) 2
−3
×(−7)
(−3)
=
2
3
1
×
(−7)
3
1
=(
2×(−7)
1
)
3
=
(−14)
3
1
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describe the state plane coordinate system. what type of projections are used in a state plane coordinate system?
Answer:
Step-by-step explanation: north-south and east-west lines are perpendicular
what is the smallest number of cars that can tailgate in a straight line at a football game so that one car is in front of four cars, one car is behind four cars, and three cars are between two cars?
The smallest number of cars that can tailgate in a straight line at a football game is 12.
Smallest Tailgate Cars NumberThis can be determined by using a logic puzzle approach. If one car is in front of four cars, that's 5 cars in total. If one car is behind four cars, that's also 5 cars. And if three cars are between two cars, that's 5 sets of two cars, or 10 cars. The total number of cars is 5 + 5 + 10 = 20.
This logic puzzle approach is not applicable for all problems. It depends on the specific problem and the information provided. For certain types of problems, a different approach or method may be more appropriate. The key is to understand the problem, determine the necessary information, and select the best approach to solve it.
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over the past years, the percentage of homes in the united states with smoke detectors has risen steadily and has plateaued at about as of (national fire protection association website). with this increase in the use of home smoke detectors, what has happened to the death rate from home fires? the file smokedetectors contains years of data on the estimated percentage of homes with smoke detectors and the estimated home fire deaths per million of population. click on the datafile logo to reference the data. a. do you expect a positive or negative relationship between smoke detector use and deaths from house fires? why? we would expect there would be a - select your answer - relationship between smoke detector use and deaths from home fires. that is, as more households have smoke detectors, warning of a fire would help the inhabitants of the home escape and lead to - select your answer - deaths from home fires. b. compute the correlation coefficient (to decimals). if required enter negative value as negative number. is there a positive or negative correlation between smoke detector use and deaths from home fires? comment. there is a - select your answer - correlation between smoke detector use and deaths from home fires. c. select the appropriate scatter plot of the death rate per million of population and the percentage of homes with smoke detectors. 1.
A negative correlation will be expected between smoke detector use and deaths from home fires.
A positive correlation happens when variables that are related(not zero correlation)increase together. In other words, variable an (independent variable) increases and makes variable b(dependent variable) increase too.
There will be a negative correlation if the opposite happens; that is, when related variables go in opposite directions, then one of them will increase while the other decreases.
We observe from what we are told that a negative correlation occurs here since the death rate from fires has likely(assumed) decreased as smoke detectors have increased.
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--The given question is incorrect; the correct question is
"Over the past 40 years, the percentage of homes in the United States with smoke detectors has risen steadily and has plateaued at about 95% (National Fire Protection Association website, January 2015). With this increase in the use of home smoke detectors, what has happened to the death rate from home fires? The DATAfile SmokeDetectors contains 17 years of data on the estimated percentage of homes with smoke detectors and the estimated home fire deaths per million of the population.
Do you expect a positive or negative relationship between smoke detector use and deaths from home fires? Why or why not?"--
Seven times the product of three and a number, x
Answer:
7×(3+x)=21+7x or 7x+21
Step-by-step explanation: Simply multiply 7 by 3 and then 7 by x.
Select the slope-intercept form of the equation of the line.
5x - 4y = -20
x+5
y=
y =
y =
x + 5
y=x+5
y = -x +5
Answer:
5x - 4y = -20
y = x + 5
y = -x + 5
Step-by-step explanation:
The formula for slope-intercept form is y = mx + b, with b being the y-int.
If the equation does not have an x, y, or b, it is not a slope-intercept form.
5x - 4y = -20 (can be rearranged to y = 5/4x + 5)
y = 1, x = 5/4, b = 5
y = x + 5y
x = 1, y = 1, b = 5
y = -x + 5
x = -1, y = 1, b = 5.
Other answer choices does not have all three variables.
Can anyone answer this question?
The required given expression are categorized on perfect cube and square.
What is perfect cube?A number is said to be a perfect cube if it can be multiplied by itself three times. X must equal Y3 if it is a perfect cube of Y. As a result, a natural integer, not a fraction, is obtained when we take the cube root of a perfect cube. Therefore, 3x Equals y. For instance, the number 8 is a perfect cube as 38 = 2.
According to question:1) x³ + 125
= x³ + (5)³
It is perfect cube.
2) 8p³ - 27
= (2p)³ - (3)³
It is difference of perfect cube.
3) 12x³ - 9
We can not make perfect cube of this expression.
4) a² - 100
= a² - 10²
It is a difference of Perfect square.
5) 4m² + 25
= (2m)² + 5²
it is a sum of Perfect square.
6) 16x² - 9
= (4x)² - 3²
It is difference of perfect square.
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two hundred fifty people were surveyed to determine their favorite mode of transportation. what number of people chose walking?
If two hundred fifty people were surveyed to determine their favorite mode of transportation. The number of people that chose walking is 35?
What is the survey about?A survey is a research method used to collect information from a sample of individuals about their opinions, beliefs, behaviors, or other characteristics.
The purpose of a survey is to gather data to help understand a specific population or topic, and the results of a survey can be used to make decisions, inform policy, or guide further research.
From the question (image attached)
14 people - Walking
Total surveyed =250
Therefore: 14/100 * 250
= 35
Hence 35 people were walking.
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A triangle has sides with lengths of 48 inches, 64 inches, and 80 inches. Is it a right triangle?
Right Scalene Triangle.
Sides of the Triangle are,
a = 48 inches
b = 64 inches
c = 80 inches
Area of Triangle = (1/2 × base × height)
= (1/2 × 64 × 80)
= 2560
A triangle is a closed figure made of three lines and three angles, where the sum of all the angles is equal to 180 degree.
In a right scalene triangle all three sides are different in length and one angle is equal to 90 degree. Right scalene triangle contains both the properties of a right triangle and scalene triangle.
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an engineer designs an improved light bulb. the previous design had an average lifetime of 1200 hours. the new bulb had a lifetime of 1201 hours, using a sample of 2000 bulbs. although the difference is quite small, the effect was statistically significant. the explanation is that
The difference is quite small, the effect was statistically significant. the explanation is that the sample size is very large.
As per the given data:
An engineer designs an improved light bulb.
The previous design had an average lifetime of 1200 hours.
The new bulb had a lifetime of 1201 hours, using a sample of 2000 bulbs.
Let us assume the null and alternative hypothesis
Null: The average lifespan of old and new designs is the same.
Alternative: The lifespans of new and ancient designs differ.
Because of the huge sample size, the p-value is lower. Reject the null hypothesis as a result, and the effect is now considered statistically significant.
Although the difference between 1200 hours and 1201 hours is quite tiny, the effect was statistically significant because of the high sample size.
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An engineer designs an improved light bulb. The previous design had an average lifetime of 1200 hours. The new bulb has a lifetime of 1201 hours, using a sample of 2000 bulbs. Although the difference is quite small, the effect is statistically significant. The explanation is:
(a) that new designs typically have more variability than standard designs.
(b) that the sample size is very large.
(c) that the mean of 1200 is large.
(d) all of the above.
Write five linear equations based on the directed graph below.
Given x5 = 15, determine the values of x1, x2, x3 and x4.
The solution is,
x1 = 5
x2 = -1
x3 = 3
x4 = 2
x5 = 1
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
x1 + x2 − 2x3 + 3x4 + 2x5 = 6
3x1 + 3x2 − x3 + x4 + x5 = 12
2x1 + 2x2 − x3 + x4 − 2x5 = 5
4x1 + 4x2 + x3 +0x4 − 3x5 = 16
8x1 + 5x2 − 2x3 − x4 + 2x5 = 29;
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The figure shows two triangles on the coordinate grid:
What set of transformations is performed on triangle ABC to form triangle A′B′C′? (5 points)
A translation 5 units up, followed by a 270-degree counterclockwise rotation about the origin
A 270-degree counterclockwise rotation about the origin, followed by a translation 5 units up
A 180-degree counterclockwise rotation about the origin, followed by a translation 5 units to the right
A translation 5 units to the right, followed by a 180-degree counterclockwise rotation about the origin
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A translation is 5 units to the right, followed by a 180-degree counterclockwise rotation about the origin. Then the correct option is D.
What is a transformation of a shape?A point, line, or mathematical figure can be converted in one of four ways, and each has an effect on the object's structure and/or position.
Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.
The translation does not change the shape and size of the geometry. But changes the location.
A translation is 5 units to the right, followed by a 180-degree counterclockwise rotation about the origin. Then the correct option is D.
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Which of the following is equal to the number sentence listed below?
(21 × 25) + (21 × 12)
21 + 25 = 46
21 + 12 = 33
46 + 33 = 79
therefore the answer is 79
Step-by-step explanation: thank you for listening
2x+5x 2nd power +7x+10+6+4+-2x
x=-.7+1.8734994i and x=-.7-1.8734994i
Step-by-step explanation:
2x+5x² +7x+10+6+4+-2x=(5x²)+(2x+7x-2x)+(10+6+4)=5x²+7x+20
quadratic equation
x=(-b±√(b²-4ac))/2a
where a=5, b=7, c=20
x=(-7±√(7²-4(5)(20)))/(2(5))
x=(-7±√((49-400))/10
x=(-7±√(-351))/10
x=(-7±18.734994i)/10
x=-.7+1.8734994i and x=-.7-1.8734994i
the top and bottom margins of a poster are 8 cm and the side margins are each 10 cm. if the area of printed material on the poster is fixed at 762 square centimeters, find the dimensions of the poster with the smallest area.
The total area of the poster would actually be 792 square cm, which includes the area of the margins (36 square cm) and the area of the printed material (756 square cm)
To find the smallest area of the poster, we need to determine the size of the poster such that the printed material takes up the maximum amount of space, while still satisfying the margin constraints. Here's the detailed explanation and calculation:
The area of the top and bottom margins is 8 cm × poster width = 8 cm × w.
The area of the side margins is 10 cm × poster height = 10 cm × h.
Total area of the margins = 2 × (8 cm × w) + 2 × (10 cm × h) = 36 cm.
Available space for the printed material = 762 cm - 36 cm = 726 cm.
The optimal dimensions of the printed material would be the closest pair of factors of 726 that add up to 36, which are 18 and 42 cm.
The area of the printed material would be 18 cm × 42 cm = 756 cm.
The total area of the poster = 756 cm + 36 cm = 792 cm.
Therefore, the dimensions of the poster with the smallest area are 756 cm and the total area of the poster is 792 square cm.
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simplify the expression
(1-x+4x^2-8x^2)+(2x^3+x^2-6x-3)-(5x^3+8x^2)
Answer: -7x^2 - 6x - 2
Step-by-step explanation:
This expression is equivalent to the sum of three terms:
1 - x + 4x^2, 2x^3 + x^2 - 6x - 3, and -5x^3 - 8x^2.
By combining like terms, the expression can be simplified to -7x^2 - 6x - 2.
Curved surface area of a cone is 308 cm2 and its slant height is 14 cm. Find the volume.
The volume of the cone is 615.44 cm³.
What is a cone?It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.
The volume of a cone is (1/3)πr²h.
We have,
Slant height l = 14 cm.
Curved surface area of a cone = 308 cm².
This means,
πrl = 308
πr x 14 = 308
πr = 308/14
r = 308/(14π)
r = 7 cm
Now,
Volume = (1/3)πr²h.
l² = r² + h²
l² - r² = h²
h = √(l² - r²)
h = √(196 - 49)
h = √(147)
h = 12 cm
Now,
Volume.
= (1/3)πr²h
= (1/3) x π x r² x h
= (1/3) x 3.14 x 49 x 12
= 615.44 cm³
Thus,
615.44 cm³ is the volume of the cone.
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F(x)=1/x+2
Find x and y intercept and the vertical and horizontal asymptotes
For the given asymptotes, y - intercept = not defined and horizontal asymptote at y = 2.
What Are the Asymptote-Finding Rules?[tex]F(x)=1/x+2[/tex] by x and simplify
[tex]F= \frac{1+2x}{x}[/tex]
Apply the limit x or x – to locate the horizontal asymptotes.
Apply the limit y or y – to determine the vertical asymptotes.
Divide the numerator by the denominator to determine the slant asymptote (if any).
Each point on a vertical line has the same x-coordinate. The line equation is x=c if two points share the same x-coordinate. The x-intercept of a vertical line x=c is the point (c,0). Except for the line x=0, vertical lines don't have a y -intercept.
By evaluating the function when the input variable, x, is 0, which is always equal to the constant b, the vertical intercept (y-intercept) can be found. There is a chance.
[tex]F= \frac{1+2x}{x}[/tex]
We can find y - intercept by setting x = 0,
⇒ y - intercept = not defined
horizontal asymptote at y = 2
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Which of the following is an arithmetic sequence with a common difference of +3?
sam takes out a loan of R 1 2000 for a year .if the rate is 12% per annum ,how much interest will he pay
Answer:
R 1440
Step-by-step explanation:
Given:-
Principal Amount = R 12000
Time = 1 year
Rate = 12% pa
The Interest can be calculated using the following formula:-
Interest = (Principal Amount * Rate * Time) / 100
Substituting the respective values:-
Interest = (12000 * 12 * 1) / 100
Interest = 144000 / 100
Interest = R 1440
So, Sam will pay an interest of R 1440
you and your roomate are hosting a party, you invited 20 other pair of roommate, during the party you pull everyone at the party excluding yourself and ask everyone how mnya hnads each person shook, 2 condition each person did not shake his roomates hands each person shook a different number of hands how many hands did my roommate shake?
Your roommate shook 10 hands at the party you and your roommate hosted.
If each person at the party shakes hands with a different number of people, and each person did not shake hands with their own roommate, then the number of hands each person shakes will form a set of integers from 0 to 19, with no duplicates. Since there are 20 people at the party, the sum of the numbers from 0 to 19 is 20 * 19 / 2 = 190.
If we subtract the number of hands that each person shakes from this sum, we find that the number of hands that my roommate shook is equal to 190 - (0 + 1 + 2 + ... + 19) = 190 - (0 + 19) * 20 / 2 = 190 - 20 * (19 / 2) = 190 - 20 * 9.5 = 190 - 190 = 0. This is not possible, since each person must shake at least one hand. The only possible answer is 10, which satisfies the conditions.
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what is the maximum length of instruction for 8086 based-ibm pc?
The maximum length of an instruction for the 8086-based IBM PC is 15 bytes.
The 8086 microprocessor was used in the original IBM PC and was capable of executing instructions up to 15 bytes in length. The instruction length is determined by the number of bytes needed to encode the operation code, the addressing mode, and any operands.
The maximum length of 15 bytes allows for complex instructions that can perform multiple operations in a single instruction cycle, increasing the efficiency of the processor. However, not all instructions require the full 15 bytes, and many are much shorter, so the average instruction length is typically much less than 15 bytes.
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Hannah's monthly bank statement showed the following deposits and withdrawals:
-−$99.01, $1.20, -−$35.92, -−$68.67, $52.41
If Hannah's balance in the account was $66.11 at the beginning of the month, what was the account balance at the end of the month?
Answer: - $83.88
Step-by-step explanation:
$66.11 - $99.01 + $1.20 - $35.92 - $68.67+ $52.41 = $83.88
Which expression can be used to find the total amount in an account after three years, if the initial deposit is $2,000, and the annual simple interest rate is 2%?
A. 2,000 x 0.02 x 3
B. 2,000 x (2,000 x 0.02 x 3)
C. 2,000 x (2,000 x 2 x 3)
D. 2,000(1 x 0.02)^3
Answer:
Below
Step-by-step explanation:
Actually....NONE of those answers would show the total amount after 3 years
the correct option would be 2000 + (2000*.02 *3) a PLUS sign rather than a multiplication sign ....so the answer MIGHT be B if you transcribed it incorrectly
a survey of the larger than life corporation finds that 46 managers have a masters degree. also 60 managers have a b.s. degree and 20 have botha masters and bs degree. they found 10 have neither. how many managers are in this survey?
The number of managers are in this survey = 96
Let us assume that A represents the set of managers with BS degree and B represents the set of managers with masters degree.
46 managers have a masters degree.
⇒ n(A) = 46
60 managers have a B.S. degree
⇒ n(B) = 60
20 have both a masters and bs degree.
⇒ n(A ∩ B) = 20
10 managers have neither degree
⇒ n(A ∪ B)c = 10
We know that the set formula,
n(P U Q) = n(P) + (n(Q) – n (P ⋂ Q)
So, n(A ∪ B) = n(A) + n(B) – n (A ⋂ B)
n(A ∪ B) = 46 + 60 - 20
n(A ∪ B) = 86
Let n(S) be the be the total managers are in this survey.
n(S) = n(A ∪ B) + n(A ∪ B)c
n(S) = 86 + 10
n(S) = 96
Therefore, there are 96 managers in this survey.
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if lim x→1 f(x) − 7 x − 1 = 10 , evaluate lim x→1 f(x).
The value of the given limit (at x =1) f(x)=18.
An output value that a function approaches for the specified input values is referred to as a limit. Calculus and mathematical analysis depend on limits, which are also used to determine integrals, derivatives, and continuity. It is employed in the analysis process and constantly considers how the function will behave at a specific point.
A function may approach two different limits. One where the variable approaches its limit through values larger than the limit and the other where the variable approaches its limit through values smaller than the limit. In such a case, the limit is not defined but the right and left-hand limits exist.
we have given that,
[tex]lim_(x- > 1) f(x)-7x-1=10[/tex]
and find out the limit (x=1)f(x).
[tex]\lim_{x \to \1} f(x)-7x-1=10\\\\f(1)-7-1=10\\\\f(1)=10+8=18\\\\now \ the \ \lim_{x \to 1} f(x)\\f(1)=18.[/tex]
Hence, the value of limit x tends to 1 f(x)= 18.
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coin $a$ is tossed three times and coin $b$ is tossed two times. what is the probability that more heads are tossed using coin $a$ than using coin $b$? express your answer as a common fraction.
The probability that more heads are tossed using coin A than using coin B is [tex]$\frac{7}{8}$[/tex].
This is because there are 8 possible outcomes when both coins are tossed: (H, H), (H, T), (T, H), (T, T) for both coins A and B.
Out of these 8 possible outcomes, 7 of them have more heads from coin A than from coin B, so the probability is [tex]\frac{7}{8}[/tex].
Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain to happen. Probability is used to measure the likelihood of uncertain events, such as the outcome of a coin flip or the result of a dice roll.
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Mrs. Thakur invested Rs 8000 at an interest rate of 8% per annum. Find the total amount that he will get after 2 years, if the interest is compounded annually.
Mrs. Thakur will receive Rs 9331.2 after 2 years, with an interest rate of 8% compounded annually.
How to determine the amount after tow yearsTo find the total amount Mrs. Thakur will receive after 2 years,
We need to calculate the compound interest.
The formula for compound interest is: A = P * (1 + r/100)^n
Where A is the final amount, P is the principal (Rs 8000),
r is the interest rate (8%), and n is the number of years (2).
So,
A = 8000 * (1 + 8/100)^2
A = 8000 * (1.08)^2
A = 8000 * 1.1664
A = 9331.2
Therefore, Mrs. Thakur will receive Rs 9331.2 after 2 years
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what is the eigenvalue for the eigenfunction cosθ of the operator 1sinθddθ(sinθddθ) ?
The eigenvalue for the eigenfunction cosθ of the operator 1sinθddθ(sinθddθ) is -1.
The eigenvalue for the eigenfunction cosθ of the operator 1sinθddθ(sinθddθ) can be calculated by using the formula:
λ = 1/sinθ (d/dθ cosθ)
This formula states that the eigenvalue is equal to the inverse of the sine of θ multiplied by the derivative of the eigenfunction cosθ with respect to θ.
To calculate the eigenvalue, we first take the derivative of the eigenfunction cosθ with respect to θ, which is -sinθ. Then, we multiply this value by the inverse of the sine of θ. This gives us an eigenvalue of -1.
In summary, the eigenvalue for the eigenfunction cosθ of the operator 1sinθddθ(sinθddθ) is -1. This can be calculated by taking the derivative of the eigenfunction and multiplying it by the inverse of the sine of θ.
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The surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is equal to____(mm)^2
Answer:
150.72
Step-by-step explanation:
area of a cylinder = top circle + bottom circle + lateral
lateral = perimeter of the circle * height = 2π*2 * 10 =40π
area of a circle = πr² = 4π
top & bottom =8π
total = 40π+8π =48π = 150.72
The surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is [tex]$$150.8 \mathrm{~cm}^2$$[/tex].
What is the surface area of a solid cylinder?The sum of the areas of all the faces or surfaces that surround a solid results in its total surface area. The tops and bottoms (bases) as well as the remaining surfaces make up the faces. The surface area of a solid without its bases is known as its lateral surface area.
The area of the cylinder is determined by adding the areas of the curving surface and its two circular bases.
A cylinder's volume is π r² h, and its surface area is 2π r h + 2π r².
Total surface area [tex]$S=2 \pi r h+2 \pi r^2$[/tex]
Substitute the values in the above equation, we get
[tex]$$\Rightarrow \mathrm{S}=2 \pi \mathrm{r}(\mathrm{r}+\mathrm{h})=2 \times 3.1416 \times 2 \times 12$$[/tex]
simplifying the equation, we get
[tex]$$\Rightarrow \mathrm{S}=150.8 \mathrm{~cm}^2$$[/tex]
[tex]$\Rightarrow \mathrm{S} \approx 1.51 \times 10^4 \mathrm{~mm}^2$$[/tex]
Therefore, the surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is [tex]$$\mathrm{S}=150.8 \mathrm{~cm}^2$$[/tex].
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can someone please explain how they got this final answer.
how did they get the 3? and why is the 18 gone! :( i am so confused
The rationalization of the given surd gives the answer as √2/3
What is rationalization?Rationalization is a process that finds application in elementary algebra, where it is used to eliminate the irrational number in the denominator.
Given here: The surd 2/√18
Thus rationalizing we get as follows:
2/√18
=2×√18/√18×√18 ( multiplying both numerator and denominator by √18)
=2√18/√18² ( since 18²ˣ¹/₂=18)
=2√18/18
=2√3²×2 / 18 ( ∵ 18=3²×2)
=2×3×√2/18
=(6/18) × √2
=(1/3)×√2
=√2/3
Hence, The rationalization of the given surd gives the answer as √2/3
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