Answer:
d ≈ 1732 ft
Step-by-step explanation:
Angle of elevation = Angle of depression
Following this truth,
m∠PAQ (Angle of depression) = m∠APB (Angle of elevation) = 30°
By applying tangent rule in the given triangle ABP,
tan(30°) = \(\frac{AB}{PB}\)
\(\frac{1}{\sqrt{3}}=\frac{1000}{d}\)
d = 1000√3
d = 1732.05
d ≈ 1732 ft
5/10 - 4/10 = (fraction)
Answer:
1/10
Step-by-step explanation:
(PLEASE HELP) What is the area?
Answer:
The area is 2,000 cm2
Step-by-step explanation:
The answer is that because Area is when you multiply the length times the width ( l x w ). The length is 40 cm and the width is 50 cm and when you multiply them, you will get 2,000 cm2.
Hope that helps. If you get it wrong, please let me know so I could check my work. Thank you and have a great rest of your day :) !
A unit of pressure called "feet of liquid substance- Y " (or ft−Y ) is equivalent to the pressure that will exist one ft below the surface of Y 's surface. If the conversion factor for this unit is 1 atm=41.5ft−Y,… - ... the density of the liquid substance Y is
The density of the liquid substance Y can be determined by using the conversion factor 1 atm = 41.5 ft⁻Y and the density of the liquid substance Y is approximately 19.68 ft⁻Y.
Conversion factor: 1 atm = 41.5 ft⁻Y
The "feet of liquid substance - Y" unit is defined as the pressure equivalent to the pressure that exists one foot below the surface of substance Y. In other words, if we go one foot below the surface of substance Y, the pressure will be equivalent to 1 ft⁻Y.
Since pressure is directly related to the density of a liquid, we can equate the pressure in units of atm to the pressure in units of ft⁻Y.
Therefore, we can say:
1 atm = 41.5 ft⁻Y
From this equation, we can conclude that the conversion factor for pressure between atm and ft⁻Y is 41.5.
we can calculate the conversion factor from "feet of liquid substance - Y" (ft⁻Y) to atm.
To convert from ft⁻Y to atm, we can use the inverse of the given conversion factor:
Conversion factor: 1 atm = 41.5 ft⁻Y
Taking the reciprocal of both sides:
1 / 1 atm = 1 / 41.5 ft⁻Y
Simplifying the equation:
1 atm⁻¹ = 0.024096 ft⁻Y⁻¹
Now, to find the density of the liquid substance Y in units of ft⁻Y, we can multiply the given density in g/cm³ by the conversion factor:
Density in ft⁻Y = 816.55 g/cm³ * 0.024096 ft⁻Y⁻¹
Calculating the density in ft⁻Y:
Density in ft⁻Y ≈ 19.68 ft⁻Y
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The area of a rectangular field is 7626m2. If the length of the field is 93m, what is its width?
Answer:
The width is \(82m\)
Step-by-step explanation:
------------------------------>>>>
The formula to find the area of a rectangle is \(A=lw\)
We already know the area of the rectangular field which is \(7626m\)
We already know the length is \(93m\)
--------------->>>>
Now let's substitute \(7626\) for \(A\) because that's the area and substitute \(93\) for \(l\) because that's the length. After that, let's solve to find the width.
\(7626=93w\)
Divide both sides by 93 because that's the opposite of multiplication.
\(82=w\)
--------------->>>>
This means that the width of the rectangular field is \(82m\)
Hope this is helpful
Find the area under the standard normal curve to the left of z=2.06. round your answer to four decimal places.
The area under the standard normal curve to the left of z = 2.06 is approximately 0.9803.
The normal distribution function, also known as the Gaussian distribution or bell curve, is a probability distribution that is symmetric, bell-shaped, and continuous. It is defined by two parameters: the mean (μ) and the standard deviation (σ).
The normal distribution is widely used in statistics and probability theory due to its many desirable properties and its applicability to various natural phenomena. It serves as a fundamental distribution for many statistical methods, hypothesis testing, confidence intervals, and modeling real-world phenomena.
To find the area under the standard normal curve to the left of z = 2.06, you can use a standard normal distribution table or a calculator with a normal distribution function. The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.
Using a standard normal distribution table, the area to the left of z = 2.06 can be found by looking up the corresponding value in the table. However, since the standard normal distribution table typically provides values for z-scores up to 3.49, we can approximate the area using the available values.
The closest value in the standard normal distribution table to 2.06 is 2.05. The corresponding area to the left of z = 2.05 is 0.9798. This means that approximately 97.98% of the area under the standard normal curve lies to the left of z = 2.05.
Since z = 2.06 is slightly larger than 2.05, the area to the left of z = 2.06 will be slightly larger than 0.9798.
Therefore, rounding the answer to four decimal places, the area under the standard normal curve to the left of z = 2.06 is approximately 0.9803.
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please help me:)
For problems 13-19, transcribe the following expressions: (Write it out.)
Example: z + 4 = z plus 4
13. xy
14. 7/t - 4
15. 22 + t 2
16. 51 - x
17. x – y^2
18. 36/12 + 12
19. ab - 16
In a statistical display, each data value should be represented by the same amount of area. this is known as the?
Area Principle. In a statistical display, each data value should be represented by the same amount of area. Bar chart (Relative Frequency 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.
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.
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Jace practices the piano 798 minutes in 3 weeks. At what rate did she practice, in minutes per day?
Answer:
38 minutes each day
Step-by-step explanation:
Answer:
38 minutes per day
Step-by-step explanation:
The information given says that Jace practices 798 minutes in 3 WEEKS and we need to convert that to days. There are 7 days in a week so multiply
7 x 3 = 21
Now you have to divide the minutes by 21.
798 ÷ 21 = 38
Jace practices piano for 38 minutes every day.
Hope that helps and have a great day!
CRITICAL THINKING For what angle measure(s) is the tangent of an acute angle in a right triangle equal to 17 greater than 1? less than 17The tangent of an acute angle in a right triangle is equal to 1 for angle measures of:The tangent of an acute angle in a right triangle is greater than 1 for angle measures that are:than:The tangent of an acute angle in a right triangle is less than 1 for angle measures that arethan:
1. The tangent of an acute angle in a right triangle equal to 17 greater than 1 that measure angle is 57.29 degrees.
2. The tangent of an acute angle in a right triangle equal to 17 less than 1 that measure angle is 45 degrees.
3. The tangent of an acute angle in a right triangle equal to 17 equal to 1 that measure angle is 45 degrees.
In a right triangle, the tangent of an acute angle is defined as the ratio of the length of the side opposite to the angle to the length of the adjacent side. Let us denote the acute angle by θ, the length of the side opposite to the angle by a, and the length of the adjacent side by b. Then we have:
tan(θ) = a/b
Since the angle θ is acute, we have a > 0 and b > 0. We can use the Pythagorean theorem to relate the lengths of the two sides to the length of the hypotenuse c:
a^2 + b^2 = c^2
Solving for b, we get:
\(b = \sqrt{c^2 - a^2}\)
Substituting this into the expression for tangent, we get:
tan(θ) = a/ \(\sqrt{c^2 - a^2}\)
Now, we can use the given conditions to find the possible values of the angle θ.
1. If tan(θ) is 17 greater than 1, we have:
tan(θ) > 1 and tan(θ) = 17 + 1 = 18
Using the expression for tangent above, we get:
a/sqrt(c^2 - a^2) > 1 and a/√(c^2 - a^2) = 18
Squaring both sides of the inequality and simplifying, we get:
a^2 < (c^2 - a^2) and a^2 = 324(c^2 - a^2)
Solving for a/c, we get:
a/c = √(324/325)
Since a/c is the sine of the angle θ, we have:
sin(θ) = a/c = √(324/325)
Using a calculator or trigonometric table, we can find that the angle whose sine is approximately 0.9999 radians or 57.29 degrees satisfies the given condition.
2. If tan(θ) is less than 1, we have:
tan(θ) < 1
Using the expression for tangent above, we get:
a/√(c^2 - a^2) < 1
Squaring both sides and simplifying, we get:
a^2 > (c^2 - a^2)
Solving for a/c, we get:
a/c > √(2)/2
Since a/c is the sine of the angle θ, we have:
sin(θ) > √(2)/2
Using a calculator or trigonometric table, we can find that the angle whose sine is approximately 0.7854 radians or 45 degrees satisfies the given condition.
3. If tan(θ) is equal to 1, we have:
tan(θ) = 1
Using the expression for tangent above, we get:
a/√(c^2 - a^2) = 1
Squaring both sides and simplifying, we get:
a^2 = c^2 - a^2
Solving for a/c, we get:
a/c = √(2)/2
Since a/c is the sine of the angle θ, we have:
sin(θ) = a/c = √(2)/2
Using a calculator or trigonometric table, we can find that the angle whose sine is approximately 0.7854 radians or 45 degrees satisfies the given condition. Alternatively, we can note that the angle whose tangent is equal to 1 is 45 degrees.
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Parallel lines r and s are cut by two transversals, parallel lines t and u. Which angles are alternate exterior angles with angle 11? 5 and 13 7 and 15 6 and 16 8 and 14.
Angles 13 and 5 are the opposing exterior angles to angle 11.
If two angles are on the exterior side of parallel lines and lie on the opposite sides of the transversal line, they are said to be alternate exterior angles.
The fact that r and t are parallel to one another is a given.
The angles 13 and 5 are on the outside side of parallel lines in the illustration, and they are located on the opposite sides of the transverse line..Angles 13 and 5 are hence complementary outer angles to angle 11.
If two angles are on the exterior side of parallel lines and lie on the opposite sides of the transversal line, they are said to be alternate exterior angles.
The fact that r and t are parallel to s and u is a given.
r║s and t║u. The angles 13 and 5 are on the outside side of parallel lines in the illustration, and they are located on the opposite sides of the transverse line.
Therefore, Angles 13 and 5 are hence complementary outer angles to angle 11.
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Line AC is tangent to circle O at point C what is the length of line segment AC
Answer:
tangent is a line passing a circle and tuching it at just 1 point
Step-by-step explanation:
For a t distribution with n =11, what is the t value such that: 10% of the area under the t distribution is to the left of the t value? -2.511 -1833 1.372 1.833 -1.372
For "t-distribution" having n =11, and 10% of area under t-distribution is to the left of t-value, the "t-value" is (e) -1.372.
The "t-distribution", is a probability-distribution that is used in statistical inference when dealing with small sample sizes or when the population standard deviation is unknown
A "t-value", is a measure that quantifies the difference between the sample mean and the population mean in units of the standard error
To find the t-value such that 10% of the area under the t-distribution is to the left of the t-value for a t distribution with n = 11, we use cumulative distribution function (CDF) of t-distribution,
The "t-value" that satisfies this condition is approximately -1.372.
Therefore, the correct option is (e).
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The given question is incomplete, the complete question is
For a t distribution with n =11, what is the t-value such that: 10% of the area under the t-distribution is to the left of the t-value?
(a) -2.511
(b) -1833
(c) 1.372
(d) 1.833
(e) -1.372
based on the information in the article, does it appear that in early 2016 u.s. households in fact worked fewer hours and took more leisure time? what do the data suggest?
You should examine the data provided in the article and follow these steps to determine if U.S. households in early 2016 indeed worked fewer hours and took more leisure time.
To determine if U.S. households in early 2016 worked fewer hours and took more leisure time, you would need to analyze the data provided in the article. Here are the steps you should take:
1. Identify the relevant data: Look for statistics or figures related to working hours and leisure time in early 2016.
2. Compare the data: Compare the early 2016 data to data from previous years or periods to see if there is a noticeable change in working hours and leisure time.
3. Analyze trends: Observe any trends or patterns that emerge from the data comparison. This will help you understand if U.S. households worked fewer hours and took more leisure time during the specified period.
4. Interpret the results: Based on the data analysis, draw a conclusion about whether or not U.S. households worked fewer hours and took more leisure time in early 2016.
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Complete question:
Corporate spending on equipment, structures and intellectual property, decreased an annualized 2.2 percent after a 3.4 percent fall in the first quarter. Outlays for equipment dropped for the fourth time in the past five quarters. Spending on structures -- everything from factories to shops to oil rigs -- have increased in just one quarter since the end of 2014. Inventories and the trade gap are two of the most volatile components in GDP calculations. To get a better sense of demand in the U.S., economists look at final sales to domestic purchasers, or GDP excluding inventories and net exports. That measure increased 2.1 percent last quarter after a 1.2 percent gain. Also holding back economic growth in the second quarter was a decrease in residential investment, which fell at a 6.1 percent pace. That was the most since the third quarter of 2010 and marked the first decrease in two years. Government spending also shrank last quarter, declining 0.9 percent, the most in more than two years as outlays for the military fell. States and municipalities also cut back. The GDP report also showed price pressures remain limited. A measure of inflation, which is tied to consumer spending and strips out food and energy costs, climbed at a 1.7 percent annualized pace compared with 2.1 percent in the prior quarter. Fed policy makers, who left interest rates unchanged this week, said risks to the U.S. outlook have “diminished” and the labor market is getting tighter, suggesting conditions are turning more favorable for an increase in borrowing costs. U.S. Economy Grew Less-Than-Forecast 1.2% in Second QuarterSho ChandraIf
U.S. households decide to work fewer hours and take more leisure time, which component of GDP is most likely to decrease as a result? Choose one: A. net exports B. investment C. consumption D. government spending
Part 2 (2.5 points) Based on the information in the article, does it appear that in early 2016 U.S. households in fact worked fewer hours and took more leisure time? What do the data suggest? According to the article (household consumption,hoisehold incomes, or unemployment) grew at an annualized rate of ( what?) percent, a ( drop or jump ?) compared to the recent past. This suggests that households worked (fewer or mre?) hours and took (less or more?) leisure time. 2 OF 19 QUESTIONS COMPLETED
ly| ≤3
Are the lines on graph at 3 and -3 also part of the answer?
Answer:
Yes, the lines on the graph at 3 and -3 a part of the solution,
Step-by-step explanation:
The inequality \(|y| \leq 3\) contains all the values of \(y\) 3 units from the origin including the values 3 and -3.
Thus, the lines on the graph y =-3 and y = 3 are the part of the solution.
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Suppose a signal from a radio transmitter tower can be received up to 175 miles away. The following
points represent locations of houses near the transmitter tower with the origin representing the tower.
Which point is not within the range of the tower?
a. (40, 120)
b. (60, 125)
c. (85, 100)
d. (55, 185)
e. (90, 150)
The point that is not within the range of the radio transmitter tower is
(55, 185).
The range of the radio transmitter tower is given as 175 miles. Out of the five given points, the distance between the origin and point (55, 185) is calculated as sqrt(55² + 185²) = 192.3 miles which is greater than the range of the tower. Therefore, this point is not within the range of the tower.
On the other hand, the distance between the origin and the other four points (40, 120), (60, 125), (85, 100), and (90, 150) are calculated to be 124.6 miles, 131.8 miles, 141.4 miles, and 159.8 miles respectively which are all less than the range of the tower. Hence, these four points are within the range of the radio transmitter tower.
In conclusion, out of the five given points, only the point (55, 185) is not within the range of the radio transmitter tower, which can be received up to 175 miles away.
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Elena and Kiran are playing a board game. After one round, Elena says, "You earned so many more points than I did. If you earned 5 more points, your score would be twice mine!"
Kiran says, "Oh, I don't think I did that much better. I only scored 9 points higher than you did."
If both students were correct, how many points did each student score? Show your reasoning.
Answer:
Elena's points = 14
Kiran's points = 23
Step-by-step explanation:
Let p = Elena's points
p + 9 = Kiran's points
2p = p + 9 + 5
2p = p + 14
p = 14 = Elena's points
14 + 9 = 23 = Kiran's points
If Kiran scores 5 more points, he would have 28 points which is twice Elena's 14 points
Can somebody tell me if I did the primes right?
Answer:
You did! well done
Step-by-step explanation:
Can someone help me?
Answer:
cheese and mustard for sale only $12.99 it is fresh crusty and yellow natural with skin from feet and very tasty get some cheese and mustard for sale make burgers with it make eggs with it make anything with it make toothpaste with it it makes it white and shiny
Step-by-step explanation:
Find the first 5 terms.
Answer:
15/8
Step-by-step explanation:
H(x) = x2 1 k(x) = x – 2 (h k)(2) = (h – k)(3) = Evaluate 3h(2) 2k(3) =.
Quadratic equation is the equation in which only one variable is unknown. The highest power of the variable is 2.The value of the given functions are,
\((h+k)(x)=5\)
\((h-k)(x)=9\)
\(3h(2)+2k(3)=17\)
Given information-The given function is,
\(h(x)=x^2+1\)
\(k(x)=x-2\)
Quadratic equationQuadratic equation is the equation in which only one variable is unknown. The highest power of the variable is 2.
1) The value of the function (h+k)(2),
\((h+k)(x)=h(x)+k(x)\)
\((h+k)(x)=x^2+1+x-2\)
\((h+k)(2)=2^2+1+2-2\)
\((h+k)(x)=5\)
2)The value of the function (h-k)(3),
\((h-k)(x)=h(x)-k(x)\)
\((h-k)(x)=x^2+1-x+2\)
\((h-k)(3)=3^2+1-3+2\)
\((h-k)(x)=9\)
3) The value of the function 3h(2)+2k(3)
\(3h(x)+2k(x)=3x^2+3+2x-2\times 2\)
\(3h(2)+2k(3)=3\times2^2+3+2\times2-2\times 2\)
\(3h(2)+2k(3)=17\)
Hence the value of the given functions are,
\((h+k)(x)=5\)
\((h-k)(x)=9\)
\(3h(2)+2k(3)=17\)
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Answer:
Step-by-step explanation:
5,9 and 17! :)
Whenever she visits Newport, Anne has to drive 5 miles due north from home. Whenever she visits Lakewood, she has to drive 6 miles due east from home. How far apart are Newport and Lakewood, measured in a straight line?
Answer:
about 7.8 miles
Step-by-step explanation:
You want the straight line distance between Newport and Lakewood, given that Newport is 5 miles north of home, and Lakewood is 6 miles east of home.
Pythagorean theoremThe Pythagorean theorem gives the relation between the sides of a right triangle. The geometry of this problem can be modeled by a right triangle with side lengths a=5 and b=6 (miles). Then the hypotenuse of the triangle (c) will be ...
c² = a² +b²
c² = 5² +6² = 25 +36 = 61
c = √61 ≈ 7.81
The straight-line distance between Newport and Lakewood is about 7.8 miles.
If the original quantity is 10 and the new quantity is 13, what is the percent increase?
Answer:
30%
Step-by-step explanation
13 is a 30% increase of 10.
Answer:
30% increase
Step-by-step explanation:
subtract original quantity from new quantity: 13 - 10 = 3
divide the difference by original quantity: 3/10 = 0.30
convert that result to percentage by moving decimal place over twice to the right.
You're done! Answer = 30%
The straight line depreciation equation for a car is y=-3680 +39500
Finding the numeric value of the function, it is found that the car is worth $24,780 after 4 years.
What is the problem?This problem is incomplete, but researching it on a search engine, we have that:
The straight line depreciation equation for a car is y = -3680x + 39500.
It asks the value of the car after 4 years.
How to find the numeric value of a function?The numeric value of a function is found replacing each instance of x by the value that we want to find.
For this problem, means that the value of the car after x years is given by:
y = -3680x + 39500.
Hence, after 4 years, the value is:
y = -3680(4) + 39500 = $24,780.
The car is worth $24,780 after 4 years.
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1) One week the price of gas dropped by $0.05 per gallon. Steven travels 37 miles each way to work and her car travels 30 miles on each gallon of gas. What were his total savings over a 5 day work week.
if the perimeter of the kite is 24 inches (in.) and the length of one pair of equal sides (b) is 7, find the length of the other set of equal sides (a)?
The perimeter of a kite is the sum of all sides of the kite. In this case, the perimeter is 24 inches (in.). Therefore, we can find the length of the other set of equal sides (a) by subtracting the known length (7 in.) from 24 in.:
a = 24 - 7 = 17 in.
A kite is a geometric shape with four sides and two pairs of equal sides (a and b). The perimeter of a kite is the sum of all four sides. In this case, the perimeter is given as 24 in. We can find the length of the other set of equal sides (a) by subtracting the length of one of the pairs (7 in.) from the perimeter (24 in.):
a = 24 - 7 = 17 in.
Therefore, if the perimeter of the kite is 24 inches and the length of one pair of equal sides (b) is 7, the length of the other set of equal sides (a) is 17.
To better visualize this, consider a kite with side lengths of 7 in. and 17 in. The perimeter of this kite is equal to the sum of all its sides: 7 in. + 7 in. + 17 in. + 17 in. = 48 in.
Thus, the perimeter of the kite is 24 inches and the length of one pair of equal sides (b) is 7, so the length of the other set of equal sides (a) is 17.
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Let x be an integer. Prove that if x is not divisible by 3, then
(x + 1)(x + 2) is divisible by 3
Answer:
(x + 1)(x + 2) is divisible by 3.
Step-by-step explanation:
Assume that x is not divisible by 3. This means that x can be expressed as x = 3k + r, where k is an integer and r is the remainder when x is divided by 3. Since x is not divisible by 3, the remainder r must be either 1 or 2.
Case 1: r = 1
If r = 1, then x = 3k + 1. Now let's consider (x + 1)(x + 2):
(x + 1)(x + 2) = (3k + 1 + 1)(3k + 1 + 2)
= (3k + 2)(3k + 3)
= 3(3k^2 + 5k + 2)
We can see that (x + 1)(x + 2) is divisible by 3.
Case 2: r = 2
If r = 2, then x = 3k + 2. Now let's consider (x + 1)(x + 2):
(x + 1)(x + 2) = (3k + 2 + 1)(3k + 2 + 2)
= (3k + 3)(3k + 4)
= 3(3k^2 + 7k + 4)
We can see that (x + 1)(x + 2) is divisible by 3.
Hence, the statement is proven.
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for how many integer values of $n$ between $1$ and $1000$ inclusive does the decimal representation of $\frac{n}{1375}$ terminate?
Let us assume that the decimal representation of $\frac{n}{1375}$ terminates and let $k$ be the number of digits after the decimal point.
Then, $1375 = 5^3 \cdot 11 \cdot 5$ and $n = 5^a\cdot 11^b\cdot 7^c$ , where $a,b,c$ are nonnegative integers. Therefore, $\frac{n}{1375} = \frac{5^{a-3}\cdot 11^{b}\cdot 7^c}{1}$, where $a \le 3$ and $b \le 1$ since the decimal representation of $\frac{n}{1375}$ terminates. Hence, we can consider all values of $n$ of the form $5^a\cdot 11^b\cdot 7^c$, where $a \le 3$ and $b \le 1$ to be integers between $1$ and $1000$ inclusive, whose decimal representation of $\frac{n}{1375}$ terminates. Since $a$ has four choices $(0,1,2,3)$ and $b$ has two choices $(0,1)$, the number of integer values of $n$ between $1$ and $1000$ inclusive, whose decimal representation of $\frac{n}{1375}$ terminates is $4\cdot 2 \cdot 1 = \boxed{8}.$
We want to determine the number of integer values of $n$ between $1$ and $1000$ inclusive that satisfy $\frac{n}{1375}$ has a terminating decimal representation. We use the following fact: A positive rational number has a terminating decimal representation if and only if its denominator can be expressed as $2^a5^b$, where $a$ and $b$ are nonnegative integers.Let $d = \gcd(1375, n)$. Then, $d$ is a positive divisor of $1375 = 5^3 \cdot 11 \cdot 5$. We must have $d = 5^a11^b$, where $0 \leq a \leq 3$ and $0 \leq b \leq 1$ since $d$ divides $n$.We also have that $n = d \cdot k$ for some integer $k$.Thus, the problem is equivalent to counting the number of positive divisors of $1375$ that are of the form $5^a11^b$, where $0 \leq a \leq 3$ and $0 \leq b \leq 1$.
The prime factorization of $1375$ is $5^3 \cdot 11 \cdot 5$. Thus, $1375$ has $4 \cdot 2 \cdot 2 = 16$ positive divisors. We exclude $1$ and $1375$ as possibilities for $d$. Thus, there are $14$ possibilities for $d$. Furthermore, each divisor of $1375$ can be written in the form $5^a11^b$ where $0 \leq a \leq 3$ and $0 \leq b \leq 1$.
Therefore, there are $\boxed{8}$ values of $n$ that satisfy the condition.
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would the answer be 36?
Answer:
No, it would be 72
Step-by-step explanation:
In similar triangles, the sides are different but the angles are the same. You still had a great guess though :)
Pls give brainliest
A building company employs
3 labourers
13 joiners
10 electricians
7 plumbers
for a job, the company needs one of each type of worker.
a) in how many ways can the company choose 4 workers
b) two labourers and 3 joiners are on holiday
in how many ways can the company now choose the 4 workers
a). The number of ways which the company can choose 4 workers from the list of employees is; 2,730 ways.
b). The number of ways the company can choose the workers if 2 labourers and 3 joiners are on holiday is; 700 ways.
Selections and CombinationsIt follows from the task content that the number of ways the company can choose 4 workers in each scenario be determined.
a). Since there are 3 labourers, 13 joiners, 10 electricians, and 7 plumbers.
The number of possible ways to choose 4 workers is; ³C₁ × ¹³C₁ × ¹⁰C₁ × ⁷C₁
= 3 × 13 × 10 × 7
= 2,730 ways.
b). Also, when 2 labourers and 3 joiners are absent, it follows that the selection space is now; 1 labourer, 10 joiners, 10 electricians and 7 plumbers.
The number of possible ways is therefore; ¹C₁ × ¹⁰C₁ × ¹⁰C₁ × ⁷C₁
= 1 × 10 × 10 × 7
= 700 ways.
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3. Use your estimates to find out how many times more massive Jupiter is than
Mercury. Express your answer in standard form (without using a power of 10). Show
your work. (4 points)
Jupiter is 5,751.51 times more massive than Mercury.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The mass of the planet Jupiter is given below.
1,898,000,000,000,000,000,000,000,000 kg.
The scientific notation is:- 2 x 10²⁷ kg.
The mass of the planet Mercury is given below.
330,000,000,000,000,000,000,000 kg.
The scientific notation is:- 3.30 x 10²³ kg.
Divide the mass of the planet Jupiter by the mass of the planet Mercury. Then we have
Jupiter / Mercury = 2 x 10²⁷ / 3.30 x 10²³
Jupiter / Mercury = 5,751.51
Your question was incomplete, but the complete question was given below.
The most massive planet in the solar system, Jupiter, has a mass of about 1,898,000,000,000,000,000,000,000,000 kg.
The least massive planet is Mercury, which has a mass of about 330,000,000,000,000,000,000,000 kg.
Use your estimates to find out how many times more massive Jupiter is than Mercury. Express your answer in standard form (without using a power of 10).
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