A tower with a wire that extends from the top of the tower to the ground is shown below. 55 ft. 68 ft. X 40 ft. Which of the following ratios could be used to find the measurement of angle æ, in degrees?
The ratio used to find the measurement of angle x is given as follows:
cos(x) = 40/68.
What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.For angle x, we have that:
The adjacent side is of 40 ft.The hypotenuse is of 68 ft.Hence the ratio is given as follows:
cos(x) = 40/68.
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PLEASE HELP
Simplify quantity 4 x squared plus 12 x minus 16 all over quantity 2x plus 10 over quantity 6 x plus 24 over quantity x squared plus 9x plus 20 . (2 points)
Exponents, terms in parenthesis, multiplication, division, addition, and finally subtraction. You can use PEMDAS as a helpful acronym to help you remember this.
What is subtraction?One of the four operations used in mathematics, along with addition, multiplication, and division, is subtraction. Removal of items from a collection is represented by the operation of subtraction. For instance, in the following image, there are 5 2 peaches, which means that 5 peaches have had 2 removed, leaving a total of 3 peaches. The number that the other number is deducted from is known as a minuend. Subtrahend: The amount that needs to be deducted from the minuend is known as a subtrahend. Difference: A difference is the outcome obtained by deducting a subtractor from a minimum.[tex]$\frac{4 x^2+12 x-16}{\frac{2 x+10}{\frac{6 x+24}{x^2+9 x+20}}}$[/tex]
Here we have two fractions top and bottom
[tex]$\frac{4 x^2+12 x-16}{2 x+10}$ divide by $\frac{6 x+24}{x^2+9 x+20}$[/tex]
We have division in between . we reverse the second fraction and multiply it with first fraction.
[tex]$\frac{4 x^2+12 x-16}{2 x+10} * \frac{x^2+9 x+20}{6 x+24}$[/tex]
Now we factor both numerator and denominator
[tex]$\begin{aligned} & 4 x^{\wedge} 2+12 x-16=4(x+4)(x-1) \\ & 2 x+10=2(x+5) \\ & x^{\wedge} 2+9 x+20=(x+5)(x+4) \\ & 6 x+24=6(x+4)\end{aligned}$[/tex]
Replace the factors,
[tex]$\frac{4(x+4)(x-1)}{2(x+5)} * \frac{(x+5)(x+4)}{6(x+4)}$[/tex]
We cancel out same factors at the top and bottom
So it becomes ,[tex]$\frac{(x-1)(x+4)}{3}$[/tex]
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The test scores for two algebra classes are shown in the stem-and-leaf plot. how many students in period 5 scored greater than 80?
The complete question:
The stem-and-leaf plot shows the test scores for a chemistry class.
How many students had a score greater than 90 points?
A. 6
B. 7
C. 8
D. 9
Solution:
The number of students had a score greater than 90 points is 7. So option B is correct.
What is stem and leaf plot ?
A stem-and-leaf plot is a type of data visualization that shows the distribution of a set of data. It is particularly useful for small to medium-sized data sets. In a stem-and-leaf plot, each data point is split into two parts: the stem and the leaf. The stem is the leftmost digit or digits of the data point, and the leaf is the rightmost digit.
To the left of the vertical bar are the tens places.
As we want to find the scores greater than 90, we start at the row in the stem and leaf plot with a 9 to the left.
To the right are 6 values - 1, 2, 3, 4, 6, and 7.
So there are six scores here higher than 90:
91, 92, 93, 94, 96, and 97.
Now we move lower to 10 in the tens place.
There is one score there - 100. (That smart kid.)
Total up the six scores in the 9 row and the 1 in the 10 row to get 7 scores higher than 90 in this stem and leaf plot.
Hence, the number of students is 7
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Riley is training to compete in a marathon, following a training plan recommended by her favorite running podcast. She plans to run 12 miles in her first week of training and will increase her mileage by about 10% each week after.
Write an exponential equation in the form y=a(b)x that can model Riley's target mileage per week, y, x weeks after she starts training.
Use whole numbers, decimals, or simplified fractions for the values of a and b
The exponential function that shows Riley's target mileage is y = 12(1.1)ˣ
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
The standard exponential equation is:
y = abˣ
where b is the rate of change and a is the initial value.
Let y represent Riley target mileage x weeks after she starts training.
She plans to run 12 miles in her first week of training and will increase her mileage by about 10% each week after. Hence:
a = 12; b = 100% + 10% = 110% = 1.1
The exponential function is y = 12(1.1)ˣ
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Find the distance between the points L(7,−1) and M(−2, 4).
The exact distance between the two points is
Answer:
[tex]\sqrt{106}[/tex]
Step-by-step explanation:
Using the distance formula,
[tex]LM=\sqrt{(7-(-2))^2+(-1-4)^2}=\sqrt{106}[/tex]
E) Find the area of a rectangular field measuring 27.04 m by 20.21 m.
i) How much would it cost to spray insecticide on the field if the rate is $0.70 per square metre? Give your answer to the nearest dollar.
Rahul drives 10 miles in 20 minutes. If he drove three hours in total at the same rate, how far did he go?
Before you try that problem, answer the question below.
How many minutes did Rahul drive in total?
180
180
How far would Rahul drive in 180 minutes?
The distance travelled by Rahul at a speed of 0.5 miles/min in 180 minutes is 90 miles.
What is meant by the speed of an object?
A scalar quantity, speed is defined as the magnitude of the change in an object's location over time. The rate at which an object travels a distance can be thought of as its speed. A fast-moving object travels at a high speed and completes a significant distance in a brief period of time. This is in contrast to an object travelling slowly, which travels a relatively short distance in the same length of time. Zero speed refers to an object that is not moving at all.
The formula of speed = Distance covered /Time taken
Given,
Distance travelled = 10 miles
Time taken to travel 10 miles = 20 minutes
Speed = Distance/ time = 10/20 = 0.5miles/min
Now given the speed remains constant throughout the journey.
So the distance travelled in 3 hours = 3 * 60 = 180 minutes
Distance = speed * time = 0.5 * 180 = 90 miles.
Therefore the distance travelled by Rahul at a speed of 0.5 miles/min in 180 minutes is 90 miles.
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MANUFACTURING The profit P of a company in thousands of dollars can be modeled by P = 8.5√³, where c is
the number of customers in hundreds. What is the profit of the company if the company has 1800 customers. Round
to the nearest dollar.
The profit of the company if the company has 1800 customers is 649124 dollars
What is profit ?
A monetary gain, specifically the sum remaining after expenses for purchasing, running, or producing an item have been deducted.
P = 8.5√c³ ------->(1)
c = 1800 customers = 18 hundreds
(1) => P = 8.5√(18)³
= 8.5 √5832 ( cube of 18=5832
= 8.5 * 76.3675
= 649.124 thousands of dollars
( convert into dollars by multiplying by 1000)
= 649124.025 dollars
≈ 649124 dollars
The profit of the company if the company has 1800 customers is 649124 dollars
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Answer: 48148
Step-by-step explanation:
Please help ASAP
PLEAAEE PUT ONLY CORRECT ANSWERS THIS IS EXTRA CREDIT AND I NEED MY GRADE TO GO UP PLEASE ANYONE HELP
Answer:
Step-by-step explanation:
... good luck
QUESTION FOR FOR LIH04
a statistical method for identifying cost behavior is the:A. Scatter diagram methodB. High-low methodC. Composite methodD. CVP charting methodE. Least-squares regression method
The statistical method that is used for identifying the cost behavior is (e) Least Squares regression method .
The Least Squares Regression method is defined as a statistical technique that is used to determine the relationship between two variables, which are , "the cost" and its "corresponding activity level" .
This method also involves plotting data points on a scatter diagram and fitting a straight line to data points.
The line that best fits data is line that minimizes sum of squared vertical distances between the data points and the line, this is why it is called the Least Squares regression method.
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The given question is incomplete , the complete question is
A statistical method for identifying cost behavior is the:
(a) Scatter diagram method
(b) High low method
(c) Composite method
(d) CVP charting method
(e) Least Squares regression method
which rule best represents the dilation that was aplied to figure p to created figure q
The transformation that is used to transform the figure P to figure Q is described by (b) (x, y) → (x+5, y+3).
The Transformation of the "figure P" being translated 5 units to the right and 3 units up to create the "figure Q" is called as a type of "translation" in the coordinate plane.
When we shift a point (x, y) by "a" units to the right and "b" units up, the new coordinates become as ⇒ (x + a, y + b).
The coordinates of "figure P" is translated 5 units to the right and 3 units up, that means we will use the rule (x,y) → (x+5, y+3) to describe the transformation.
Therefore, the correct transformation used is (b) (x, y) → (x+5, y+3).
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The given question is incomplete , the complete question is
A "figure P" was translated 5 units to the right and 3 units up to create "figure Q". Which rule describes this transformation ?
(a) (x, y) → (x-5, y-3)
(b) (x, y) → (x+5, y+3)
(c) (x, y) → (x-3, y-5)
(d) (x, y) → (x+3, y+5)
Suman found a great sale on bracelets. With the money in her pocket, she can buy 5 bracelets and have $3 left or she could by 2 bracelets and have $9 left. Write and solve an equation to find out how much each bracelet costs.
Step-by-step explanation:
9-3 =6
So we have 6 dollars for 3 bracelets
Which means each bracelet costs 2 dollar each
So 9x-3x=6x
1.Which quadrant will the terminal ray falls for an angle of rotation equal to 1.2 radians.
A.) QIV
B.)QII
C.)QI
D.)QIII
Answer:
D.) QIII
Step-by-step explanation:
Because 1.2 radians is in between 7π/6 and 5π/4
What was the CPI for 2020 if 2019 was the base year?
A. 120
B. 125
C. 130
D. 135
What was the CPI for 2021 if 2019 was the base year?
A. 145
B. 150
C. 155
D. 160
Answer: D and C
Step-by-step explanation:
To get the value of a market basket you would add up the cost of each year so
2019 market basket = 2.50 + 1.00 + 3.75 = 7.25
2020 market basket = 2.25 + 3.00 + 4.50 = 9.75
2021 market basket = 3.00 + 3.25 + 5.00 = 11.25
now CPI for 2020 would be 9.75 / 7.25 x 100 = 134.828 which is around 135
CPI 2021 would be 11.25 / 7.25 x 100 = 155.172 which is around 155
In circle M with m/LMN = 84 and LM = 13 units find area of
sector LMN. Round to the nearest hundredth.
Answer:
123.88 square units
Step-by-step explanation:
r = radius of circle
= radius of sector
= Length of LM
= Length of MN
= 13 units
When the angle is measured in degrees:
Area of a sector: [tex]\frac{Angle OfSector}{360^{o}}[/tex]× [tex]\pi r^{2}[/tex]
= [tex]\frac{84}{360}[/tex]×[tex][\pi (13)^{2}][/tex]
= 123.883 [tex]units^{2}[/tex]
= 123.88 square units (Rounded to the nearest hundredth)
Anshumann wants to paint the wall shown in the diagram below. In order to buy the paint, he will need to know the area of the wall. What is the area of the wall?
1 point
Answer: 240 ft²
Step-by-step explanation:
Break the diagram into a rectangle and triangle:
Area of Rectangle + Area of Triangle = Total area of Wall
(20x10) + 1/2(20 x 4) = Area of wall
200 + 40 = Area of wall
240 ft² = Area of wall
Hare Krishna :)
Richard can type 60 words per minute. At this rate, how low will it take him to type 720 words?
Answer:
It will take Richard 12 minutes to type 720 words.
Step-by-step explanation:
720 ÷ 60 = 12
joint and/or inverse variation. show you solution.
The force is 80,000 Dynes.
What is joint variation?We know that when we talk about the joint variation then we have a lot of variables that are being altered at the same time and this is what we are going to work on in the questions that we have here.
We are told that;
C α mr/t^2
Then;
C = kmr/t^2
k = Ct^2/mr
k = 6000 * 2^2/6 * 10
k = 400
Then, to find C;
C = 400 * 18 * 100/3^2
C = 80,000 Dynes
\
Hence, we can see from the calculation that the centrifugal force that is required is 80,000 Dynes.
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Determine, by inspection, which of the following products are multiples of 30. 22 x 3 x 5 2 x 3² x 5 22 × 53 23 x 3² x 5²
By inspection, the following products which are multiples of 30 are:
2² x 3 x 52 x 3² x 52³ x 3² x 5²What is a Multiple?This is referred to as a number that may be divided by another a certain number of times without a remainder.
The multiple of 30 in the options are those who have 2, 3 and 5 as the common values and is therefore the reason why options A, C and D were chosen as the correct choice.
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a person eating at a cafeteria must choose 3 of 19 vegetable on offer. calculate the number of elements in the sample space for this experiment
The number of elements in the sample space for this experiment is 969.
If a person eating at a cafeteria must choose 3 of 19 vegetables on offer, we can calculate the number of elements in the sample space, or the total number of possible outcomes, using the formula for combinations:
nCr = n! / [r!(n - r)!]
where n is the total number of items in the set and r is the number of items being chosen.
In this case, we have 19 vegetables and we want to choose 3 of them, so we can plug in n = 19 and r = 3:
19C3 = 19! / [3!(19 - 3)!]
= 19! / (3!)(16!)
= 969
Therefore, there are 969 possible combinations of 3 vegetables that a person can choose from a selection of 19 vegetables.
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Jorge's printer can print 24 pages in 15 minutes. How many pages can it print in 3/4
hour. How many pages can he print in 1 hour?
Answer:
3/4 hour-72
1 hour- 92
Step-by-step explanation:
3/4-
24 x 3= 72
1-
24 x 4 =92
Some wooden chest in a store. A green chest has a length out 165cm a width of 70cm and a height of 10cm. If another box, a blue box is proportional in size, what is is length if it's width is 18cm
The blue box measures about 641.667 cm in length.
What do length and width mean?The width and length of a figure indicate its breadth and length, respectively. The term "breadth" is also used to describe width. Although breadth and width are synonymous (thus the idiom hair's breadth, denoting a very small width), there are two significant differences between the two.
We are aware that the blue box's width is 18 cm, which is smaller than the green box's width (70cm).
As a result, the value of "k" must be lower than 1. By creating a proportion, we can determine the value of "k":
width of green box / width of blue box = k
70 / 18 = k
k = 70/18
k ≈ 3.8889
So the factor "k" is approximately 3.8889. To find the length of the blue box, we can use this factor to scale the length of the green box:
length of blue box = k * length of green box
length of blue box = 3.8889 * 165cm
length of blue box ≈ 641.667cm
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m ∠ a = ____ degrees
Answer:
m<a = 44°
Step-by-step explanation:
Left triangle:
95 + 39 + x = 180
x = 46
Right triangle:
46 + 90 + a = 180
a = 44
A factory has two smokestacks. The rate of particle pollution produced is 12 kg / h
for the first smokestack and 32 kg / h
for the second. The manufacturing process requires that the first smokestack operates 2
hours longer than 1. 5
times as long as the second. A local pollution control board has ordered that the factory produce no more than 374 kg
of particle pollution per day. What is the maximum number of hours per day that each smokestack can operate?
Maximum number of hours per day that first smokestack can operate 12.5 hours and for second smokestack is 7 hours.
According to the question a factory has two smokestacks:
Let first smokestack take x number of hours per day
and second smokestack take y number of hours per day
The rate of particle pollution produced is 12 kg/h for the first smokestack
and rate of particle pollution produced is 32 kg/h for the second.
A local pollution control board has ordered that the factory produce no more than 374 kg of particle pollution per day.
so, equation becomes 12x + 32y = 374
also the first smokestack operates 2 hours longer than 1. 5 times as long as the second.
so, x = 2 + 1.5y
putting value of x in other equation
12(2 + 1.5y) + 32y = 374
24 + 18y + 32y = 374
50y = 350
y = 7 hours
x = 2 + 1.5(7) = 12.5 hours
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Use the figure to find the measures of the numbered angles.
4
The value of ∠4 in the given transversal line image is; 85°
How to find the corresponding angles?Corresponding angles are defined as the angles that are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line.
In this question, we see that ∠3 is a corresponding angle to 95°. Thus;
∠3 = 95°
Now, ∠4 forms a straight line with ∠3 and as such they will sum up to 180 degrees as sum if angles on a straight line sums up to 180 degrees. Thus;
∠4 = 180 - 95
∠4 = 85°
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List the angles of triangle KLM in order from least to greatest if
KL = x - 4, LM = x + 4, KM = 2x - 1, and the perimeter if the triangle is 27.
Answer:
B, C, A.
Step-by-step explanation:
In order to find the angles of triangle KLM and their order from least to greatest, we need to use the Law of Cosines and the perimeter equation of the triangle. The Law of Cosines states that in any triangle, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides minus twice the product of the lengths of these sides and the cosine of the angle between them.
Let's assume that the length of sides KL, LM, and KM are x - 4, x + 4, and 2x - 1, respectively. We can use the Law of Cosines to find the cosine of the angle between KM and KL:
cos A = (x - 4)^2 + (2x - 1)^2 - (x + 4)^2 / 2 * (x - 4) * (2x - 1)
Next, we can use the perimeter equation of the triangle, which is
KL + LM + KM = 27, to find the value of x:
x - 4 + x + 4 + 2x - 1 = 27
4x = 36
x = 9
So, the lengths of the sides of the triangle are
KL = x - 4 = 5, LM = x + 4 = 13, and KM = 2x - 1 = 17.
Next, we can use the Law of Cosines to find the cosine of the angle between KM and KL:
cos A = (5)^2 + (17)^2 - (13)^2 / 2 * (5) * (17)
cos A = 74 / 60
A = cos^-1 (74/60) = approximately 49.7°
Finally, we can use the perimeter equation of the triangle and the Law of Sines to find the other two angles of the triangle:
B + C = 180° - 49.7° = 130.3°
B / sin B = LM / sin A
B = sin^-1 (sin B / sin A) * LM / sin A
C = 130.3° - B
The angles of triangle KLM in order from least to greatest are approximately:
B, C, A.
Flying to Kampala with a tailwind a plane averaged 158 km/h. On the return trip plane only averaged 112 km/h while flying back into the same wind. Find the speed of the wind and the speed of the plan in still air.
The speed of the plane is 135 km/h and wind speed is 23 km/h. The solution has been obtained by forming linear equations.
What is a linear equation?
This is the linear equation with the largest degree of one. This demonstrates that there are no variables in linear equations with exponents greater than 1. A straight line appears on the graph as a result of such an equation.
Let the plane speed be 'P' and the wind speed be 'W'.
We are given that while flying to Kampala with a tailwind a plane averaged 158 km/h.
So, we get an equation as
P + W = 158 ...(1)
Also, on the return trip plane only averaged 112 km/h while flying back into the same wind.
So, we get another equation as
P - W = 112 ...(2)
Now, on adding the equations we get,
⇒P + W + P - W = 158 + 112
⇒2P = 270
⇒P = 135
Now substituting the value into either equation, we get
⇒P + W = 158
⇒135 + W = 158
⇒W = 23
Hence, the speed of the plane is 135 km/h and wind speed is 23 km/h.
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Monica has 2. 2 litres of milk 1. 5kg of each other ingredient. Calculate the greatest number of people she can serve with pasta bake
It is not possible to determine the greatest number of people Monica can serve with pasta bake based solely on the information provided.
The amount of milk and other ingredients she has does not necessarily indicate how many portions she can make. Other factors such as the recipe she is using, the size of each serving, and the equipment she has available will also impact how many people she can serve. In order to determine the number of portions she can make, more information is needed about the recipe and the serving size she is aiming for.It is not possible to determine the greatest number of people Monica can serve with pasta bake based solely on the information provided.
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4. Suppose the account in 3 above paid interest quarterly instead of annually. Find the
account balance after 5 years
The account's balance after 5 years is given as follows:
[tex]A(5) = P\left(1 + \frac{r}{4}\right)^{20}[/tex]
In which:
P is the principal.r is the interest rate.What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.
Quarterly compounding means that the value of n is given as follows:
n = 4.
Then the balance of the account after 5 years, when t = 5, is given as follow:
[tex]A(5) = P\left(1 + \frac{r}{4}\right)^{20}[/tex]
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