Answers
In questions 16, 17 and 18 we have a right triangle and in the three cases you know the measues for 2 sides, except for hipotenuse.
We can use the following relation to solve the problem:
[tex]tg(x)=\frac{\text{Opposite side}}{Adjacent\text{ side}}[/tex]16)
[tex]\begin{gathered} tg(x)=\frac{\text{1}7}{7}=2.4285 \\ tg(x)=2.4285 \\ x=tg^{-1}(2.4285) \\ x=68\degree \end{gathered}[/tex]17)
[tex]\begin{gathered} tg(x)=\frac{8}{10}=0.8 \\ x=tg^{-1}(0.8) \\ x=39\degree \end{gathered}[/tex]18)
[tex]\begin{gathered} tg(x)=\frac{\text{1}1}{8}=1.375 \\ x=tg^{-1}(1.375) \\ x=54\degree \end{gathered}[/tex]Related Questions
Navy paint is made by mixing 8 cups of blue paint with 2 cups of black paint. If he only has 1 cup of blue pain, how much black paint should he use?
Answers
For 1 cup of blue paint, 1/4 cups of black paint is needed
How to determine the amount of black paint?The given parameters are
8 cups of blue paint needed for 2 cups of black paint
This means that
8 cups of blue paint needed = 2 cups of black paint
Divide both sides of the equation by 8
So, we have the following equation
8/8 cups of blue paint needed = 2/8 cups of black paint
Evaluate the quotient
So, we have the following equation
1 cup of blue paint needed = 1/4 cups of black paint
Hence, the amount of black paint is 1/4
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14 pound in 1 stone and 2.2 pound in 1 kilogram. a certain person weight 9 stone.
Answers
Given that 1kg=2.2 pound, also there is 14 pounds in 1 stone
There are 9 stones totally,so totally 9 stones will have 405 pounds
To convert into kilogram to should divide pounds by 2.2
[tex]\frac{405}{2}=183.705[/tex]Thus 183.705 is the required answer.
The table represents an absolute value function f(x). x f(x) −5 1 −4 0 −3 1 −2 2 −1 3 0 4 1 5 2 6 3 7 What are the vertex and range of the function? Vertex (0, 4), Range: {y | 0 ≤ y < ∞} Vertex (0, 4), Range: {y | 4 ≤ y < ∞} Vertex (−4, 0), Range: {y | 0 ≤ y < ∞} Vertex (−4, 0), Range: {y | −4 ≤ y < ∞}
Answers
The vertex and range of this absolute value function is: Vertex (0, 4), Range: {y | 0 ≤ y < ∞}.
What is an absolute value function?An absolute value function can be defined as a type of function that consist of an algebraic expression, which is placed within absolute value symbols.
Mathematically, the standard form of the equation for an absolute value function is given by:
y = a|x - h| +k.
Where:
h and k are the vertex of the graph.
Furthermore, an absolute value function is defined by this piecewise rule, especially based on its input:
|x| = -x, x < 0.|x| = x, x ≥ 0.In conclusion, the vertex or turning point of this absolute value function in the table above is at (0, 4).
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Answer:
Vertex (0, 4), Range: {y | 0 ≤ y < ∞}.
Step-by-step explanation:
Tickets of a program at college cost $4 for general admission or $3 with a student ID. If 181 people paid to see a performance and$616 was collected, how many of each type of ticket were sold?In a program at college tickets ?were sold for general admission and?tickets were sold with a student ID.
Answers
Tickets were sold for a program at a college .It cost $4 for general admission or $3 with a student ID.
Let
number of people that used student ID = x
number of people that used the general admission cost = y
[tex]x\text{ + y = 181}[/tex][tex]3x\text{ + 4y = 616}[/tex][tex]\begin{gathered} x+y\text{ = 181} \\ 3x+4y=616 \\ x=181-y \\ 3(181-y)+4y\text{ = 616} \\ 543-3y+4y=616 \\ y=616-543 \\ y=73 \\ x+73=181 \\ x=181-73 \\ x=108 \end{gathered}[/tex]108 used the student ID ticket while 73 used the general admission ticket .
The following are the reasons why sampling is used except for a. Sampling is used if taking a census of the entire population is impractical. b. Sampling is less time-consuming and less costly than census. c. Sampling is so easy. d. The data from the sampling can be used to estimate corresponding population measures.
Answers
The following are the reasons for sampling:
1. To bring the population to a manageable number
2. To reduce cost
3. To help in minimizing error from the despondence due to large number in the population
4. Sampling helps the researcher to meetup with the challenge of time.
Therefore, the answer is:
c. Sampling is so easy.
State the zero(s) of the function.
f(x) = x³ - 2x² - x + 2
O a
O b
Ос
Od
1 and 2
-1, 1, and 2
-1, 0, and 1
-2, -1, and 1
Answers
Answer:
-1, 1, and 2
Step-by-step explanation:
[tex]x^3 - 2x^2 - x+2=0 \\ \\ x^2(x-2)-(x-2)=0 \\ \\ (x^2-1)(x-2)=0 \\ \\ (x-1)(x+1)(x-2)=0 \\ \\ x=-1, 1, 2[/tex]
It says if Jamal rides his bike to school and back home. It is two miles each way. How many miles does he ride in five days?
Answers
Answer:
20 miles
Step-by-step explanation:
If it is two miles each way, then he rides a total of 4 miles every day.
Multiply 4 by 5
4 x 5 = 20
20 miles
Answer:
20 miles
Step-by-step explanation:
he always goes to school and comes back, to that means each day where he goes to school he rides 4 miles each time.
if he does this for 5 days you can write the following:
4*5 = 20 or if you haven't learned multiplication you can think of it like this:
4+4+4+4+4= 20
pls answer the pic below
Answers
The value of the missing angles are; m∠ABC = 36° and m∠DBC = 41°
How to find the missing angles?We are given that;
m∠ABD = 77°
Addition angle postulate states that the sum of two adjacent angle measures will equal the angle measure of the larger angle that they form together.
Now, by addition angle postulate, we can say that;
m∠ABC + m∠DBC = 77°
Now, we are given that;
m∠ABC = (5x - 4)°
m∠DBC = (5x + 1)°
Thus, by substitution property, we have;
(5x - 4)° + (5x + 1)° = 77
10x - 3 = 77
10x = 77 + 3
10x = 80
x = 8
Thus;
m∠ABC = (5(8) - 4)°
m∠ABC = 36°
m∠DBC = (5(8) + 1)°
m∠DBC = 41°
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Question 22 of 25Which list is ordered from least to greatest?L) 52.932M) 583.31N) 52.930) 8.39P) 89.223A. N, L, M, P, OOB. M, P, L, N, OOC. O, N, L, P, MOD. P. O, L, M, N
Answers
Solution
- The ordered list from the least to the greatest is:
[tex]8.39,52.93,52.932,89.223,583.31[/tex]- Thus, using the arrangement of the numbers, we can rearrange using the letters.
O, N, L, P, M
Final Answer
O, N, L, P, M (OPTION C)
65% of the workers at Costco have a pet dog. If thereare about 162 workers who have a dog, how manyCostco employees are there in total? .
Answers
To find how many Costco employees are, we can use the formula of
what is (9.74c-250.50)+(-5.48p+185.70)
Answers
Here, we want to solve find the value of the expression
We start by opening up the brackets and then, we bring together like terms
We have this as;
[tex]\begin{gathered} (9.74c-250.5)+(-5.48p+185.70) \\ =\text{ 9.74c - 250.5 -5.48p+185.7} \\ =\text{ 9.74c-5.48p-250.5+185.7} \\ =\text{ 9.74c-5.48p-64.80} \end{gathered}[/tex]Which number is equivalent to 3^(4)÷3^(2)
Answers
Answer:
9
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
This problem comes straight from a standardized test given in New York in 2014.
Find the volume of the cone, use 3 for π
Answers
Given:
Cone with diameter of 14 ft, and height of 4 ft.
First, determine the radius of the cone, by dividing the diameter by 2.
[tex]\begin{gathered} r=\frac{d}{2} \\ r=\frac{14\text{ ft}}{2} \\ r=7\text{ ft} \end{gathered}[/tex]Now that we have the radius, substitute π = 3, r = 7 ft, and h = 4 ft to the formula of the volume of the cone.
[tex]\begin{gathered} V=\frac{\pi r^2h}{3} \\ V=\frac{(3)(7\text{ ft})^2(4\text{ ft})}{3} \\ V=\frac{3(49\text{ ft}^2)(4\text{ ft})}{3} \\ V=\frac{588\text{ ft}^3}{3} \\ V=196\text{ ft}^3 \\ \\ \text{Therefore, the volume of the cone is }196\text{ ft}^3. \end{gathered}[/tex]Write a function that models the population of 400 birds decreased at an annual rate of 6%
Answers
A function that models the population of 400 birds decreasing at an annual rate of 6% is [tex]f(x) = 400(1 - 0.06)^{t}[/tex] where t is the time period.
What is the Exponential decay formula?The Exponential decay formula aids in determining the quick decrease over time, i.e. the exponential decrease. The exponential decay formula is used to calculate population decay, half-life, radioactivity decay, and so on.
Its general form is f(x) = a (1 - r)ⁿ.
Where a = the initial amount
1 - r = decay factor and n = time period.
Given:
The initial population of birds, P = 400
Rate of decay, r = 6% = 0.06
Time = t years
By using the exponential decay formula,we get
[tex]f(x) = P (1 - r)^{t}[/tex]
[tex]f(x) = 400(1 - 0.06)^{t}[/tex]
Therefore, the function that models the population of 400 birds decreased at an annual rate of 6% is [tex]f(x) = 400(1 - 0.06)^{t}[/tex].
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Find f(4) if f(x) =5x-4
Answers
To find f(4) you substitute the x in the given equation for 4:
[tex]\begin{gathered} f(4)=5(4)-4 \\ f(4)=20-4 \\ f(4)=16 \end{gathered}[/tex]Then, f(4) is 16Find the 9th term of the geometric sequence 4, -16, 64, ...
Answers
Answer:
4 to the 9th power :D
Step-by-step explanation:
Please Brainliest
Abigail wants to find three consecutive even integers whose sum is four times the smallest of those integers. She lets n represent the smallest integer, then writes this equation: n + (n + 2) + (n + 4) = 4n. What are the three integers?
Answers
The three consecutive integers according to the expression will be 6, 8, 10
In the given question, there is an expression stated that tells the condition for a sequence in which a number is represented by 'n'. The expression is the sum of three even integers whose sum is equal to four times the smallest of numbers.
The expression is n + (n + 2) + (n + 4) = 4n. We have to find out the values for each of the numbers.
Here, First Number = n
Second number = (n + 2)
Third Number = (n + 4)
Now, We will calculate the given expression to find out the value of n.
=> n + (n + 2) + (n + 4) = 4n
=> 3n + 6 = 4n
=> n = 6
We get the smallest number n = 6 which is the first number, the second number is 8, and the third number is 10.
Hence, the numbers are 6, 8, and 10.
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Caleb is going to see a movie and is taking his 3 kids. Each movie ticket costs $13 and there are an assortment of snacks available to purchase for $3.50 each. How much total money would Caleb have to pay for his family if he were to buy 5 snacks for everybody to share? How much would Caleb have to pay if he bought xx snacks for everybody to share?
Answers
The total money would Caleb have to pay for his family if he were to buy 5 snacks for everybody to share is;
How to Solve Algebra Word Problems?
We are told that the cost of each movie ticket is $13. Now, if he buys one movie ticket for his 3 kids, then total he would pay for the 3 kids and himself is;
13 * 4 = $52
Now, an assortment of snacks available to purchase for $3.50 each. Thus, if Caleb buys 5 snacks, then it means that;
Cost of the 5 snacks = 3.5 * 15 = $16.5
Total paid = $52 + $16.5
= $67.5
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Which did you include in your response? Check all that apply? Use ten StartFraction 1 Over 12 EndFraction bars. Circle groups of StartFraction 4 Over 6 EndFraction. There is one group of StartFraction 4 Over 6 EndFraction, with StartFraction 1 Over 6 EndFraction remaining. The quotient is 11 and one-fourth.
Answers
The simplified expression of the fraction expression is (b) One group of 4/6, with 1/6 remaining.
How to evaluate the fraction?
The fraction expression is given as
ten StartFraction 1 Over 12 EndFraction bars.
Rewrite the fraction properly
So, we have
Ten 1/12 bars
This can be represented as
10 * 1/12
Rewrite 10 as 10/1
So, we have the following equation
10 * 1/12 = 10/1 * 1/12
Evaluate the products of the numerator
So, we have the following equation
10 * 1/12 = 1/1 * 10/12
Evaluate the products of the denominator
So, we have the following equation
10 * 1/12 = 10/12
Simplify the fraction
10 * 1/12 = 5/6
Split the fraction
10 * 1/12 = 4/6 + 1/6
This means that, the result is
Quotient = 4/6 and remainder = 1/6
Hence, the true statement about the fraction is (b)
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Complete question
Which did you include in your response? Check all that apply?
Use ten 1/12 bars.
4/6One group of 4/6, with 1/6 remaining. The quotient is 11 and one-fourthAn inground sprinkler nozzle sprays water onto the grass in the shape of a circle, with the nozzle at the center of the circle. On the coordinate plane, the nozzle is located at (20, 0) and the points (35, 0) and (5, 0) lie on the circle. Which equation represents the boundary that the sprinkler covers?
Answers
In order to determine which equation represents the boundary, replace the values of the coordinates of the given points, into the choices for the equations, and then verify if the left hand side matches with the right hand side.
For points (35,0) and (5,0) you have:
x = 35
y = 0
x = 5
y = 0
Then, for the first answer choice we have:
[tex]\begin{gathered} (x-20)^2+y^2=225 \\ (35-20)^2+0^2= \\ 15^2=225 \\ (5-20)^2+0^2= \\ 15^2=225 \end{gathered}[/tex]As you can notice, the equation matches for values of x and y.
Then, there is no necessary to verify for the other choices.
Hence, the equation (x - 20)^2 + y^2 = 225 represents the boundary that the sprinkler covers.
write from largest to smallest these numbers 5/4,.2,60%,.75,.5
Answers
Let’s start by making everything a decimal.
We already have 0.75, 0.2, and 0.5.
(5/4) = 1.25
Divide the percentage by 100; 60% can be written as 0.6.
The *decimals* order from largest to smallest: 1.25, 0.75, 0.6, 0.5, 0.2.
The original numbers from largest to smallest (it’s the same order-just using the different forms of numbers you were given):
(5/4), 0.75, 60%, 0.5, 0.2
Which of the following inequalities would be graphed with an open circle? Select all that apply.
Answers
SOLUTION
Note that for an inequality to be graphed with an open circle the inequality sign must be either less than or greater than
Therefore the inequalities are:
[tex]\begin{gathered} 3(x-2)<18 \\ h+6>-3h+12 \end{gathered}[/tex]Carter has 60 balloons , of the balloons are black, and is of the balloons are white. The rest of theballoons are red. How many red balloons Carter has? Show your calculations in the space provided
Answers
we have 60 balloons
black balloons are =4/12*60
and that is =20 black balloons
red balloons= 3/12*60=5*3=15
the rest are white
white balloons= 60- 20 black-15 red=25 white balloons
2) A toy store is having a sale on puzzles. For each puzzle, Naomi buys she
gets 75% off of a second puzzle. The original price of each puzzle is
$16.50. Naomi bought 4 puzzles. How much did she spend?
Answers
Naomi bought 4 puzzles and she spend total $21.91
What is percentage?The Latin word "per centum," which means "by the hundred," is where the word "percentage" originally came from. With 100 as the denominator, percentages are fractions. To put it another way, it's the relationship between a component and a whole in which the value of the whole is always assumed to be 100.
Given that : A toy store is having a sale on puzzles. For each puzzle, Naomi buys she gets 75% off of a second puzzle. The original price of each puzzle is $16.50. Naomi bought 4 puzzles
Naomi first puzzle price is $16.50
she get 75% off on as second puzzle
=[tex]16.50(\frac{75}{100} )[/tex]
=12.375
=16.50 - 12.375
= 4.125
So , second puzzle price is 4.124
=[tex]4.125(\frac{75}{100} )[/tex]
=3.09
= 4.125 - 3.09
=1.03
So , third puzzle price is 1.03
=[tex]1.03(\frac{75}{100} )[/tex]
=0.7725
=0.2575
So ,fourth puzzle price is 16.50+4.124+1.03+ 0.2575
=21.91
Total naomi spend 0.2575
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Triangle ABC has vertices A(1,4), B (-3,5) and C(-2, 4) and is rotated 90
degrees clockwise about the origin. What will be the coordinates of C'?
O (2,-4)
O (4,-1)
O(-4,-2)
O (4,2)
Answers
Check the picture below.
classify the system as "consistentdependent", "consistent independent", or "inconsistent". choose the best description of its solution. if the system hs exactly one solution give it solution.
Answers
The solution of a system is the point where the lines described by the equations of the system intersect, If a system has no solution, it is said to be inconsistent, In this case, both lines have the same slope (-3/2) which means that they are parallel each other, then they will never intersect, and the system has no solution and is inconsistent
What are the factors of this expression?
3/4xy
Drag all of the factors of the expression into the box.
Answers
The factors of the expression 3xy/4 are 3/4, -1, x and y.
According to the question,
We have the following expression:
3xy/4
Now, we know that when we say factors of an expression then it means that we are talking about numbers or variables which can divide the given expression.
(For example, the factors of 24xy are 24 and the factors of 24 which are 1,2,4,6 including the two variables x and y.)
So, in this case, we will separate each number and variable to find the factors of the given expression:
3/4, x and y and -1
Hence, the factors of the expression 3xy/4 are 3/4, -1, x and y.
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A cylindrical tank with radius 5 m is being filled with water at a rate of 4 m3/min. How fast is the height of the water increasing (in m/min)?
Answers
The height of the water increasing at a rate of 0.05 m/min
The Volume of a cylinder is
[tex]V = \pi r^{2}h[/tex]
where r is the radius and h is the height of the cylinder.
Given that the radius r of cylinder is 5m and the water is filled at the rate of 4 [tex]m^{3} /min[/tex]
[tex]V = 25\pi h[/tex] ...(1)
Now, differentiating (1) with respect to time t,
[tex]\frac{dV}{dt} = 25\pi \frac{dh}{dt}[/tex]
Substituting the value of [tex]\frac{dV}{dt}[/tex]
4 = [tex]25\pi \frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt}[/tex] = [tex]\frac{4}{25\pi }[/tex]
[tex]\frac{dh}{dt}[/tex] = 0.05 m/min
Hence, the water is increasing at the rate of 0.05 m/min
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Plllsss help answer the question in the picture below!!!!!
Answers
The proportion of the generated values that fall inside the range of each histogram bar is used to compute the vertical scale. The standard deviation is an indicator of how much the values in the data set typically deviate from the mean.
What is the difference between standard deviation and histogram?It always displays the median and the middle 50% of the data. For data displayed in histograms, a similar spread measurement is helpful. The term for it is the standard deviation. The standard deviation is an indicator of how much the values in the data set typically deviate from the mean.
The proportion of the generated values that fall inside the range of each histogram bar is used to compute the vertical scale. The sum of the bar heights is therefore one. Only discrete variables (right), where the histogram heights now total to unity, are suitable for relative frequency analysis.
A measurement of how far points deviate from the mean is the standard deviation. The first histogram includes fewer points that are close to the mean and more points that are distant from the mean (scores of 0, 1, 9, and 10). (scores of 4, 5 and 6). As a result, its standard deviation will be higher.
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please help me solve part 3!
Answers
Step-by-step explanation:
probabilities are always
desired cases / totally possible cases
24 cans in total, 4 of them are diet, therefore 20 of them are regular.
2 cans are picked.
for the first can
the probability to pick a diet can is
4/24 = 1/6
the probability to pick a regular is
20/24 = 5/6
a)
to pick 2 diets, the first one has to be diet.
that leaves 23 cans with 3 being diet.
so, the probability for the second can being diet too is
3/23.
as combined event the probability to pull 2 diet cans is
1/6 × 3/23 = 1/2 × 1/23 = 1/46 = 0.02173913...
≈ 0.0217
b)
now the same for picking 2 regular cans.
the first one has to be regular :
5/6
that leaves for the second one 23 cans and 19 of them regular
19/23
combined this gives the probability
5/6 × 19/23 = 95/138 = 0.688405797...
≈ 0.6884
this is not unusual.
what would be considered "usual" or "unusual" ?
c)
one of them is diet, and one of them is regular.
the simple answer ?
it is the only other option, when the cans are not of the same type. it is the opposite of the sum of a) and b).
so, it is
1 - 0.688405797... - 0.02173913 = 0.289855072...
≈ 0.2899
but what to do, if we want to calculate it directly ?
it is the case that either
1. the first can is diet and the second can is regular,
or
2. the first can is regular and the second can is diet.
case 1.
the first can is diet = 1/6
leaving 23 cans with 20 being regular
the second can being regular = 20/23
together
1/6 × 20/23 = 1/3 × 10/23 = 10/69 = 0.144927536...
case 2.
the first can is regular = 5/6
leaving 23 cans with 4 diets.
the second can being diet = 4/23
together
5/6 × 4/23 = 5/3 × 2/23 = 10/69 = 0.144927536...
in an "exclusive or" situation we can add the probabilities.
so, the probability of having exactly one can diet and exactly one can regular is
0.144927536... + 0.144927536... = 0.289855072...
≈ 0.2899
we were correct in the first place !