Answer:
4/5
Step-by-step explanation:
cos B = 3/5
cos Ф = adjacent/hypothesis
hypothesis ² = adjacent² + opposite²
5²= 3²+ o²
25 = 9+o²
25-9=o²
16 = o²
√16 = o = 4
Sin B = opposite/hypothesis = 4/5
At the beginning of a snowstorm, Tristan had 3 inches of snow on his lawn. The snow then began to fall at a constant rate of 1.5 inches per hour. Assuming no snow was melting, how much snow would Tristan have on his lawn 4 hours after the snow began to fall? How much snow would Tristan have on his lawn after
tt
t hours of snow falling?
Answer:
Step-by-step explanation:
3+1.5*4
3+6
9 inches in total 4 hours from now
Answer:
3 + 1.5(4) = 9
then the second one will be: 3 + 1.5t
Step-by-step explanation:
1.5t is increasing do therefore that is the answer.
In this diagram, like segment AD is tangent and line segment AC is secant. If AB = 6 and BC = 18, what is the length of line segment AD?
9514 1404 393
Answer:
12
Step-by-step explanation:
The applicable relationship here is ...
AD² = AB·AC
AD = √(AB·(AB +BC)) = √(6·(6+18)) = √144
AD = 12
Find a value for m and n to make a true statement.
a) mx^2 - 36 = (3x + 6)(3x - 6)
b) (mx + ny)^2 = 4x^2 + 12xy + 9y^2
Answer:
Correct answer: a) m = 9 ; b) m = 2 and n = 3
Step-by-step explanation:
Given:
a) m x² - 36 = (3 x + 6) (3 x - 6) ⇒ m = ?
b) (m x + n y)² = 4 x² + 12 x y + 9 y² ⇒ m, n = ?
a) m x² - 36 (3 x + 6) (3 x - 6)
The right side of the equation is the difference of the square, so we will present the left side in the same way:
(√m x)² - 6² = (3 x + 6) (3 x - 6)
(√m x + 6) (√m x - 6) = (3 x + 6) (3 x - 6)
√m = 3 /² when we square both sides of the equation we get:
m = 9
b)
(m x + n y)² = 4 x² + 12 x y + 9 y²
The left side of the equation is the complete square of the binomial, so we will present the right side in the same way:
(m x + n y)² = (2 x)² + 2 · 2 x · 3 y + (3 y)² = (2 x + 3 y)²
(m x + n y)² = (2 x + 3 y)² ⇒
m = 2 and n = 3
God is with you!!!
For part (a), m must be 9 to make the equation true. For part (b), m can be 2 or -2, and n can be 3 or -3 to satisfy the equation.
Explanation:To find values for m and n to make the statements true, we must compare coefficients or recognize patterns in the given equations.
Part (a)
We have the equation mx^2 - 36 = (3x + 6)(3x - 6). We can expand the right side to get 9x^2 - 36. To make this equation true, we need the coefficient of x^2 on the left to be equal to the coefficient on the right, which is 9. Therefore, m must be 9 for the equation to be true.
Part (b)
We have (mx + ny)^2 = 4x^2 + 12xy + 9y^2. Expanding the left side, we get m^2x^2 + 2mnxy + n^2y^2. To equate it to the right side, we need m^2 = 4 and n^2 = 9. This gives us two possibilities each for m and n: m can be 2 or -2 and n can be 3 or -3.
a number, truncated to 1 dp, is equal to 11.9, what are the upper and lower bounds
For the study described below, identify the population parameter. A bank manager wants to know the average amount of time customers of his bank have to wait in line. 300 customers were polled and asked their average wait time at the bank. 27 of the 300 people were extremely dissatisfied with the amount of time they had had to wait in line in recent months.A) The 300 customers poll
B) The 27 people who were dissatisfied
C) The customers who were waiting in line at the bank the day of the poll
D) All customers of the bank
Answer:
The population parameter is the average wait time for all the bank's customers.
Step-by-step explanation:
The population parameter is a numerical value that defines a specific characteristic of the population. For example, the population mean describes the average value of the population, the population variance describes the variance of the population and the population proportion describes the proportion of a certain variable in the population.
The sample statistic is a numerical value that defines a specific characteristic of the sample that is selected from the population. The examples of sample statistic are, sample mean, sample variance and sample proportion.
In this case it is provided that the bank manager wants to know the average amount of time customers of his bank have to wait in line.
The experiment involved, asking 300 customers about their average wait time at the bank.
So, the parameter under study is the mean time the customers have to wait at the bank.
Hence, the population parameter is the average wait time for all the bank's customers.
Final answer:
The population parameter the bank manager wants to know is the average wait time for all customers of the bank, which is represented by option D) All customers of the bank.
Explanation:
The population parameter the bank manager is interested in determining is the average wait time for all customers of the bank, not just the 300 polled customers or the subset of dissatisfied customers. Therefore, the correct answer to the student's question is D) All customers of the bank.
This average wait time is a parameter that describes some aspect of the entire population of the bank's customers. In terms of statistics, a population parameter is a value that represents a characteristic of the entire population, which in this case, includes all the customers of the bank, whether they were part of the survey or not.
When records were first kept (t=0), the population of a rural town was 260 people. During the following years, the population grew at a rate of P'(t) = 45(1+sqrt(t)).
a) what is the population after 15 years?
b) find the popuation P(t) at any time t > 0.
Answer:
(a) The population after 15 years is 2678.
(b)Therefore the population P(t) at any time t>0 is
[tex]P(t)= 45t+30 {t^{\frac32}}+260[/tex]
Step-by-step explanation:
Given that,
The population grew at a rate of
[tex]P'(t)=45(1+\sqrt t)[/tex]
Integrating both sides
[tex]\int P'(t) dt=\int 45(1+\sqrt t)dt[/tex]
[tex]\Rightarrow \int P'(t) dt=\int (45+45\sqrt t)dt[/tex]
[tex]\Rightarrow \int P'(t) dt=\int 45\ dt+\int 45\sqrt t\ dt[/tex]
[tex]\Rightarrow P(t)= 45t+45\ \frac{t^{\frac12+1}}{\frac12+1}+c[/tex] [ c is integration constant]
[tex]\Rightarrow P(t)= 45t+45\ \frac{t^{\frac32}}{\frac32}+c[/tex]
[tex]\Rightarrow P(t)= 45t+45\times\frac 23 \times {t^{\frac32}}+c[/tex]
[tex]\Rightarrow P(t)= 45t+30 {t^{\frac32}}+c[/tex]
When t=0 , P(0)= 260
[tex]\therefore 260= 45\times0+30\times {0^{\frac32}}+c[/tex]
[tex]\Rightarrow c=260[/tex]
[tex]\therefore P(t)= 45t+30 {t^{\frac32}}+260[/tex]
Therefore the population P(t) at any time t>0 is
[tex]P(t)= 45t+30 {t^{\frac32}}+260[/tex]
To find the population after 15 years, we need to plug t=15 in the above expression.
[tex]P(15)=( 45\times 15)+30( {15^{\frac32}})+260[/tex]
≈2678
The population after 15 years is 2678.
Ben, Cam, and Justin are lumberjacks. The number of trees they chop down is given by b+2c+3jb+2c+3jb, plus, 2, c, plus, 3, j where bbb is the number of hours Ben spends chopping, ccc is the number of hours Cam spends chopping, and jjj is the number of hours Justin spends chopping. How many trees do they chop down after Ben spends 888 hours chopping, Cam spends 333 hours chopping, and Justin spends 444 hours chopping?
Answer:
26 trees.
Step-by-step explanation:
The number of trees Ben, Cam, and Justin can chop down is given by:
b+2c+3j
Where:
b is the number of hours Ben spends chopping.
c is the number of hours Cam spends chopping.
j is the number of hours Justin spends chopping.
We want to determine the number of trees they chop down after Ben spends 8 hours chopping, Cam spends 3 hours chopping, and Justin spends 4 hours chopping.
b=8, c=3, j=4
Substituting these in the given equation
b+2c+3j=8+2(3)+3(4)=8+6+12 = 26
They chop down a total of 26 trees.
Answer:
26 trees chopped altogether
Step-by-step explanation:
We are given that;
-Ben, Cam, and Justin are lumberjacks.
-The number of trees they chop down is given by b+2c+3j
where;
b is the number of hours Ben spends chopping
c is the number of hours Cam spends chopping
j is the number of hours Justin spends chopping.
We are told that;
Ben spends 8 hours to chop
Cam spends 3 hours to chop
Justin spends 4 hours to chop
Thus, Substituting in the given equation we get
Total nmber of trees chopped = b + 2 c + 3 j = 8 + 2(3) + 3(4) = 8 + 6 + 12
= 26
They have chopped 26 trees altogether
Vanessa draws one side of equilateral
△ABC on the coordinate plane at
points A(-2, 1) and B(4,1). What are
the two possible coordinates of vertex
C? Round to the nearest tenth.
Answer:
According to my calculation, the two possible coordinates of vertex C, is [tex](1,\sqrt{27}) and (1,-\sqrt{27})[/tex].
Answer:
According to my calculation, the two possible coordinates of vertex C, is .
Step-by-step explanation:
Simplify each equation. Tell whether the equation has one, no, or infinite
solutions.
5x + 6 = 2 + 3x
no solutions
one
infinite solutions
10pts will mark brainliest if right
Answer:
one solution
Step-by-step explanation:
5x + 6 = 2 + 3x
Subtract 3x from each side
5x-3x + 6 = 2 + 3x-3x
2x +6 = 2
Subtract 6 from each side
2x+6-6 = 2-6
2x = -4
Divide each side by 2
2x/2 = -4/2
x = -2
There is one solution
Answer:
One solution
Step-by-step explanation:
To solve, we need to isolate the variable, x
5x+6=2+3x
Subtract 2 from both sides
5x+4=3x
Subtract 5x from both sides
4= -2x
Divide both sides by -2
x= -2
There is one solution to this equation, -2
What is the factored form of this expression? x2 + 9x + 16
Answer:
this problem is not factorable.
Step-by-step explanation:
Final answer:
The factored form of the quadratic expression x^2 + 9x + 16 is (x + 7)(x + 2), found by identifying two numbers that multiply to 16 and add up to 9.
Explanation:
To find the factored form of the expression x2 + 9x + 16, we are looking for two binomials that when multiplied together will yield the original quadratic expression. Since the coefficient of x2 is 1, we only need to find two numbers that add up to the coefficient of x (which is 9) and multiply together to get the constant term (which is 16).
To factor the quadratic expression, we look for two numbers that multiply to 16 and add to 9. These numbers are 7 and 2. Therefore, the factored form of the expression is (x + 7)(x + 2).
Plzz help!
4^2 × 5^2 + 30
[tex] {4}^{2} \times {5}^{2} + 30 = 16 \times 2 5+ 30 = \\ = 400 + 30 = 430[/tex]
or
[tex] {4}^{2} \times {5}^{2} + 30 = (4 \times 5)^{2} + 30 = \\ = 20^{2} + 30 = 400 + 30 = 430 [/tex]
9=8n what does n=
Please help
Mary bought 3 cartons of milk for $1.06 each. If she paid for the milk with a five-dollar bill, how much money should she get back
Answer:
shed get $1.82 back
Step-by-step explanation:
Answer:
She would get $1.82 back
Step-by-step explanation:
If she bought 3 cartons costing $1.06 each, you would have to multiply $1.06 by 3
$1.06 x 3 = $3.18
Then if she paid with a five dollar bill you have to subtract $3.18 from 5
5 - 3.18 = 1.82
$1.82 is the answer
Rachel received $650 for her birthday. She purchased a surfboard for $477 and some additional accessories without spending more than the money she received.
She wrote the inequality 477 + x < 650.
Is the inequality correct?
Yes, because 477 and an unknown amount is less than 650.
No, because 477 and an unknown amount is greater than 650.
No, because the inequality symbol should be less than or equal to 650.
No, because x should be subtracted from 477.
Answer:
No, because the inequality symbol should be less than or equal to 650.
Step-by-step explanation:
it should be "No, because the inequality symbol should be less than or equal to 650." because the statement says she gets the accessories without spending MORE than the amount she received, it says nothing about spending the exact amount.
Answer:
No, because the inequality symbol should be less than or equal to 650.
whats the area of a circle if the diameter is 24.26 mm
Answer:
approximately 462.24
Step-by-step explanation:
2) There are 45 dogs and 30 cats at the animal recovery center. Of these animals, there are 16 colored dogs and 8 solid cats. What percentage of the animals are solid colored?
Answer:
32%
Step-by-step explanation:
Total animals: 45 + 30 = 75
Coloured: 16 + 8 = 24
24/75 × 100
32%
Graph f(x) and its inverse, f^-1(x) , in the same coordinate grid.
Answer:
Included in screenshot
Is (x +1) a factor of f(x) = x^3 + x^2 −4x − 4?
Select the appropriate response:
Yes
or
No
Answer:
Yes
Step-by-step explanation:
( x^3 + x^2) (-4x - 4)
x^2 ( x+1) -4 (x+1)
(x^2 - 4) (x+1)
(x-2) (x+2) (x+1)
X= 2 x=-2 x=-1
Answer:
Yes
Step-by-step explanation:
f(x) = x^3 + x^2 −4x − 4
Factor by grouping taking x^2 out of the first group and -4 out of the second
0 = x^3 + x^2 −4x − 4
x^2(x+1) -4(x+1)
Factor out (x+1)
0=(x+1)(x^2-4)
Now we have the difference of squares
0=(x+1) (x-2)(x+2)
x+1 is a factor
1. Lake Turkana is in the Great Rift Valley in northwest Kenya. As part of a study of water quality, the water temperature in the lake was measured at different depths. The data are shown in this scatter plot.
Answer:
a. 26° C
b. 40m
c. Yes
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one. Please have a look at the attached photo.
a. What was the approximate temperature at a depth of 70 m? At the surface?
26° C
b. At what depth was the temperature a little more than 27°C?
40 m
c. Do the points in the scatter plot show a relationship? Explain your thinking.
Yes, the scatter plot show a relationship between the depth and the temperature of Lake Turkana. It shows a negative correlation between the two variables. The deeper the lake is, the cooler the temperature .
Hope it will find you well.
y = x^2 - 2x; domain {-3, 0, 5}
Answer:
range:{0,15}
Step-by-step explanation:
y=x²-2x
domain:{-3,0,5}
for range
when x=-3
y=(-3)²-2×(-3)=9+6=15
when x=0
y=0-0=0
when x=5
y=5²-2×5=25-10=15
range:{0,15}
or
y=x²-2x+1-1=(x-1)²-1
when x=-3
y=(-3-1)²-1=16-1=15
when x=0
y=(0-1)²-1=1-1=0
when x=5
y=(5-1)²-1=16-1=15
The student's question involves calculating the output values of a quadratic function for a given domain. The specific output values for the domain {-3, 0, 5} of the function y = x^2 - 2x are 15, 0, and 15, respectively.
Explanation:The student is dealing with a question that involves the evaluation of a quadratic function y = x^2 - 2x at different values within its domain. Here, the domain is specified as the set {-3, 0, 5}. To answer the student's question, we calculate the value of y for each x in the domain:
For x = -3: y = (-3)^2 - 2(-3) = 9 + 6 = 15For x = 0: y = (0)^2 - 2(0) = 0For x = 5: y = (5)^2 - 2(5) = 25 - 10 = 15Therefore, the corresponding output values for the function at the points in the domain are 15, 0, and 15, respectively.
plz can any1 help me out on this plz
15 points
Answer:
7/22
Step-by-step explanation:
Drama or Sports:
85 + 200 - 60
225
330 - 225 = 105
Probability: 105/330
7/22
Brandon works at a nearby electronics store. He makes a commission of 14% on everything he sells. If he sells a camera for $588.00, how much money does Brandon make in commission?
Answer: cc
Step-by-step explanation:
Answer:
670.32
Step-by-step explanation
The results for a survey of 120 students who were selected randomly are as follows 60 students have a cell phone plan with company x. 36 students have a cell phone plan with company y. 24 students do not have a cell phone the total population of students was 380.Based on the data what is the best approximation for the total number of students who have a cell phone plan with company y?
Answer:
114
Step-by-step explanation:
find the solution below
if you roll a six-sided die, what is the probability of rolling a number greater than 2?
Answer:1/6
Step-by-step explanation:
Emilce pide 5 platos por semana para almorzar en la oficina. El menú ofrece 5 opciones diferentes. De cuantas maneras puede realizar el pedido de la semana si quiere repartir los platos?
Answer:
120 different ways
Step-by-step explanation:
For the first lunch, Emilce has 5 options to choose,
In the second lunch, now she has only 4 options, as one was already chosen.
Then, in the third lunch, she has 3 options.
In the fourth lunch, she has 2 options.
In the last lunch, she has just 1 option.
So, the number of different ways she can order her lunches in the week is:
5 * 4 * 3 * 2 * 1 = 120
She can order in 120 different ways.
Find the area of the shaded segment. Round your answer to the nearest hundredth.
Answer:
2.57
Step-by-step explanation:
1/4×22/7×3×3=7.07
1/2×9=4.5
7.07-4.5=2.57
work out the next term of this quadratic sequence
6 9 15 24
Answer:
36
Step-by-step explanation:
6 9 15 24 ...
The sequence goes like this:
+3, +6, +9, +12, +15 (Adding 3 each time)
For example:
6 + 3 = 9 (First +3)
9 + 6 = 15 (Then +6)
15 + 9 = 24 (Then +9)
24 + 12 = 36
The next term of this quadratic sequence will be 36.
What is Quadratic equation?
An algebraic equation with the second degree of the variable is called an Quadratic equation.
Given that;
The quadratic sequence is,
⇒ 6, 9, 15, 24
Now,
The first term = 6
The second term = 6 + 3 = 9
The third term = 9 + 6 = 15
The fourth term = 15 + 9 = 24
Thus, The pattern of adding are;
3 , 6 , 9, ..
So, For next term we add 12 in fourth term, we get;
The next term = 24 + 12
= 36
Thus, The next term of this quadratic sequence will be 36.
Learn more about the quadratic equation visit:
https://brainly.com/question/28038123
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Judy spent 1 hour and 15 minutes less than Sandy exercising last week Sandy Sprint 50 minutes less than Mary who's been 3 hours at the gym how long did Judy spend exercising
Answer:
Judy spent 55 min at the gym.
Step-by-step explanation:
From the three people that are listed in the problem Mary is the only one we know the actual time she was at the gym which is 3 h. Sandy on the other hand spent 50 minutes less sprinting than Mary, so we have:
Sandy = Mary - 50 minutes
Sandy = 3h - 50 minutes
Sandy = 3*60 - 50
Sandy = 180 - 50 = 130 minutes
Judy spent 1h and 15 min less than Sandy exercising so we have:
Judy = Sandy - 1h 15min
Judy = 130 min - (60 min + 15 min)
Judy = 130 min - 75 min = 55 min
Judy spent 55 min at the gym.
An animal pen is in the shape of a triangle. One of the interior angles of the triangle is 40 degrees. The measure of the other interior angles are in the ratio 3 : 5. What are the measures of the other interior angles?
Final answer:
In a triangle, the sum of all interior angles is always 180 degrees. Given the ratio of the other interior angles, we can find their measures.
Explanation:
In a triangle, the sum of all interior angles is always 180 degrees. Given that one of the interior angles is 40 degrees, let's denote the measures of the other two angles as 3x and 5x. The sum of all three angles is 40 + 3x + 5x = 180. Simplifying this equation, we get 8x + 40 = 180. Subtracting 40 from both sides gives us 8x = 140. Dividing both sides by 8, we find x = 17.5.
Now, we can substitute the value of x back into the expressions for the other two angles. So, the first angle is 3x = 3(17.5) = 52.5 degrees, and the second angle is 5x = 5(17.5) = 87.5 degrees.
The regular octagon in the ceiling has a radius of 10.5 feet and a perimeter of 64 feet. What is the length of the apothem of the octagon?
Answer:
Nearest tenth of a foot
9.7
Nearest tenth of a square foot
310.4
Step-by-step explanation: