Answers
Answer:
x = 30º
Step-by-step explanation:
This answer requires trigonometry, specifically, the cosine function. This is because we are given the length of the side adjacent to x and the length of the hypotenuse.
If you recall:
[tex]cos(x )= \frac{adjacent}{hypotenuse}[/tex]
Therefore,
[tex]cos(x) = \frac{13}{35}[/tex]
Now, we must use the inverse cosine function on a calculator to figure out the value of x.
[tex]cos^{-1}(\frac{13}{15}) = 29.93[/tex]
Now, we must round it to the nearest whole number, so x = 30º.
Related Questions
A radioactive substance decays to 30% of its original mass in 15 months. Determine the half-life of this radioactive substance to the nearest tenth. Show your work.
please help
Answers
Answer:
The half-life of this radioactive substance is of 8.6 months.
Step-by-step explanation:
Exponential decay of an amount:
The equation that models an amount after t units of time, subject to exponential decay, is given by:
[tex]A(t) = A(0)(1-r)^t[/tex]
In which A(0) is the initial amount and r is the decay rate, as a decimal.
A radioactive substance decays to 30% of its original mass in 15 months.
This means that [tex]A(15) = 0.3A(0)[/tex]. We use this to find 1 - r.
[tex]A(t) = A(0)(1-r)^t[/tex]
[tex]0.3A(0) = A(0)(1-r)^{15}[/tex]
[tex](1-r)^{15} = 0.3[/tex]
[tex]\sqrt[15]{(1-r)^{15}} = \sqrt[15]{0.3}[/tex]
[tex]1 - r = (0.3)^{\frac{1}{15}}[/tex]
[tex]1 - r = 0.9229[/tex]
So
[tex]A(t) = A(0)(0.9229)^t[/tex]
Determine the half-life of this radioactive substance to the nearest tenth.
This is t for which A(t) = 0.5A(0). So
[tex]A(t) = A(0)(0.9229)^t[/tex]
[tex]0.5A(0) = A(0)(0.9229)^t[/tex]
[tex](0.9229)^t = 0.5[/tex]
[tex]\log{(0.9229)^t} = \log{0.5}[/tex]
[tex]t\log{0.9229} = \log{0.5}[/tex]
[tex]t = \frac{\log{0.5}}{\log{0.9229}}[/tex]
[tex]t = 8.6[/tex]
The half-life of this radioactive substance is of 8.6 months.
A clothing vendor estimates that 78 out of every 100 of its online customers do not live within 50 miles of one of its physical stores. Using this estimate, what is the probability that a randomly selected online customer does not live within 50 miles of a physical store? .78 .50 .28 .22
Answers
Answer:
[tex]p' = 0.22[/tex]
Step-by-step explanation:
Given
[tex]p = \frac{78}{100}[/tex]
Required
Probability that a [tex]customer[/tex] does [tex]not[/tex] live [tex]within[/tex] [tex]50[/tex] miles
To do this, we make use of complement rule;
Which states that:
[tex]p + p' = 1[/tex]
Make p' the subject
[tex]p' = 1 - p[/tex]
So, we have:
[tex]p' = 1 - \frac{78}{100}[/tex]
Express fraction as decimal
[tex]p' = 1 - 0.78[/tex]
[tex]p' = 0.22[/tex]
Find the first five terms that correspond with the following expression.
4n + 2
Answers
Answer:
6,10,14,18,22
Step-by-step explanation:
4n+2
Let n=1 4(1)+2 = 4+2 = 6
Let n=2 4(2)+2 = 8+2 = 10
Let n=3 4(3)+2 = 12+2 = 14
Let n=4 4(4)+2 = 16+2 = 18
Let n=5 4(5)+2 = 20+2 = 22
A rectangle has a perimeter of 14 cm and length x cm. show that the width of the rectangle is (7-x)cm and hence that the area A of the rectangle is given by the formula A= x(7-x). Draw the graph, plotting x on the horizontal axis with a scale of 2cm to 1 unit, and A on the vertical axis with a scale of 1cm to 1 unit
take x from 0 to 7. From the graph find:
a) the area of the rectangle when x = 2.25cm
b) the dimensions of the rectangle when its area is 9cm^2
c) the maximum area of the rectangle
d) the length and width of the rectangle corresponding to the maximum area
e) what shape of the rectangle has the largest area
Answers
Answer:
B
Step-by-step explanation:
the dimensions of the rectangle when its area is 9cm^2
The area of a rectangle is given by the expression x^2 + 6x – 16. What are the dimensions of the rectangle?
(x+4) by (x+4)
(x+4) by (x-4)
(x+8) by (x-2)
(x-8) by (x+2)
Answers
Answer:
I don't no answer sorry sorry
Find the first term and the common ratio of the following geometric
sequence: 8, 16, 32, ...
Answers
Answer:
The first term is 8
The common ratio is 2, because the ratio of 8:16 is 1:2 and the ratio of 16:32 is 1:2
Step-by-step explanation:
Answer:
The common ratio of the following geometric sequence is x2 everytime.
A landowner wants to find the distance d across a pond. The two overlapping right triangles are similar . Using the measurements shown , what is d?
Answers
Answer:
96 m
Step-by-step explanation:
It is given that the two overlapping triangles are similar in the figure.
The landowner wishes to find the distance across the pond. The distance is d.
From the figure, since the two triangles are similar, therefore we can write :
[tex]$\frac{d}{(24+40)}=\frac{60}{40}$[/tex]
[tex]$\frac{d}{64}=\frac{60}{40}$[/tex]
[tex]$d = \frac{60}{40} \times 64$[/tex]
[tex]$d = \frac{6}{4} \times 64$[/tex]
d = 6 x 16
= 96 m
Therefore, the distance across the pond is d = 96 m
BONUS 1) You take the Math Time Machine into the past to save Julius Caesar and fix the calendar,
but you miss your timestamp and end up in Alexandria a few years early. You wander around before
ending up in front of the Great Library of Alexandria, which is guarded by a sphinx - known in
mythology for their tricky riddles. When you ask the sphinx what year it is, it refuses to answer
unless you solve a math problem. The sphinx shows you a right triangle with a base of 8 and a height
of 6, which you know has an area of 24. Then it tells you that if you that you can remove some
length x off of the 8 side, but if you do that you must add a rectangle under the 8 side with a height
equal to x, thus creating a trapezoid. How much length must you remove from the 8 side so the
trapezoid has the same area as the original triangle? X = 0 doesn't count.
a) X = 2
b) X = 3
c) X = 4
d) X = 5
Answers
Answer:
Gracias por los puntos :D
It’s simple math I’m just confused
Answers
Answer:
26 units
Step-by-step explanation:
make a proportion: so sides correspond alongside eachother.
so, 15/10 =24/Y, i know you need to solve for x, but you have to find the other blank length.
now cross multiply, 10*24=15*Y
240=15Y
240/15=
Y= 16
now add Y to the length 10 to get X. So you get 10+16=26
Fill in the missing values for this sequence of numbers.
Identify the start value and operation.
92, 110, ___, 146, ___, ___
Answers
92, 110, 128, 146, 164, 182. ✅
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex]92,110,128,146,164,182 \\ ➵ \: 92 + 18 = 110 \\ ➵ \: 110 + 18 = 128 \\ ➵ \: 128 + 18 = 146 \\ ➵146 + 18 = 164 \\ ➵ \: 164 + 18 = 182[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}[/tex]
Which expression is equivalent to 11x + 5 + 2x - 3? (HINT: Combine LIKE TERMS)
1. 13x
2. 13x + 8
3. 21x
4. 13x + 2
Please help it’s a test
Answers
Answer:
4.13x+2
Step-by-step explanation:
11x+5+2x-3
13x+5-3
13x+2
Answer:
4 .13x+2
and don't ever try to copy and this app is for homework but other testshope you understand
pls take it positively
and I hope you will not do this for next test
the nearest 100 of 87682
Answers
The answer is 600
Does the graph shown represent an arithmetic sequence, geometric sequence, or neither?
Answers
Answer:
arithmetic sequence
Step-by-step explanation:
Each new member of this sequence is less than the previous member by a fixed number, which means this is an arithmetic sequence.
For the data set 7, 5, 10, 11, 12, the mean, x, is 9. What is the standard deviation? The formula for the sample standard deviation is s = 2(x-7)? . 1 Use the table to help you. (x - 2)2 1 Sum= Round your answer to the nearest tenth.
Answers
Answer:
the answer is 2.9
Step-by-step explanation:
.
What is 234.506 rounded to the nearest hundredth
Answers
Answer:
Rounded to the nearest hundredth, 234.506 becomes 234.51.
Part B: Plot point C(2,7). If M is the midpoint of CD, what are the coordinates of D?
Answers
Answer:
[tex]D = (-4,-9)[/tex]
Step-by-step explanation:
Given
[tex]C =(2,7)[/tex]
[tex]M=(-1,-1)[/tex]
Required
The coordinates of D
Represent D with:
[tex]D = (x_2,y_2)[/tex]
Using midpoint formula, we have:
[tex]M(x,y) = \frac{1}{2}(x_1 + x_2, y_1 + y_2)[/tex]
So, we have:
[tex](-1,-1) = \frac{1}{2}(2 + x_2, 7 + y_2)[/tex]
Multiply both sides by 2
[tex](-2,-2) = (2 + x_2, 7 + y_2)[/tex]
Compare both sides
[tex]2 + x_2 = -2[/tex]
[tex]7 + y_2 =-2[/tex]
In [tex]2 + x_2 = -2[/tex], we have:
[tex]x_2 =-2-2[/tex]
[tex]x_2 =-4[/tex]
In [tex]7 + y_2 =-2[/tex], we have:
[tex]y_2 = -2 - 7[/tex]
[tex]y_2 = -9[/tex]
So, the coordinates of D is:
[tex]D = (x_2,y_2)[/tex]
[tex]D = (-4,-9)[/tex]
What is the approximate volume of the cone
below?
Answers
Answer:
183 cm³
Step-by-step explanation:
V(cone) = 1/3πr²h
= (π5²·7) ÷ 3
= 175π ÷ 3
≈ 58π or 183 cm³
-1/5 and +7 equals two
Answers
what is the question?? because this equation is false?
for what value of x is the equation 2x-3 over -3+4 =3 true
Answers
Answer:5
Step-by-step explanation:
......
2x - 3/-3 + 4 = 3 is the same as saying;
2x - 3 = 3 (-3 + 4)
2x - 3 = -9 + 12
2x - 3 = 3
2x = 3 + 3
2x = 6
2x/2 = 6/2
x = 3
What is the growth factor for 233% growth
Answers
Answer:
Here is what you do. Make it into vertex form and then whatever the x factor is is the growth factor
Answer for brainlest
Answers
Answer:
these are corresponding angles
Answer:
Step-by-step explanation:
angle 8 and angle 4 are called corresponding angles.so,
angle 8=angle 4
PLEASE HELP ME!!!!!!!!!!!!!!!!!!! ASAP :)
Answers
Answer:
c) The growth factor per days is 1.08
e) The growth factor per hour is 1.08^{1/24}
Step-by-step explanation:
Given the following data;
P(d) = 10 * 1.08^{d} in thousands.
a. To find the number of insects on day 1;
Day, d = 1
[tex] P(d) = 10 * 1.08^{d} [/tex] ......equation 1
Substituting into the formula, we have;
[tex] P(1) = 10 * 1.08^{1} [/tex]
[tex] P(1) = 10 * 1.08 [/tex]
[tex] P(1) = 10.08 [/tex]
Therefore, option (a) and (b) are incorrect.
c. To find the growth factor per day;
An exponential function is given by the formula;
[tex] y = mg^{x} [/tex] .....equation 2
Where;
g is the growth factor of a population.
Comparing eqn 2 with eqn 1;
g = 1.08
Therefore, option (c) is correct.
e. To find growth factor per hour;
From equation 1 above;
[tex] P(1) = 10 * 1.08^{\frac {1}{2}} [/tex]
Therefore, option e is correct.
Pls help, answer within 5 minutes
Answers
Answer: I thin it’s Opposite of 2
Step-by-step explanation:
Answer:
The distance between A and D
Step-by-step explanation:
when it is |-2| (in the box) it changes to 2
Suppose we want to choose 5 letters without replacement from 16 distinct letters
Answers
Answer:
16P5
Step-by-step explanation:
16*15*14*13*12
What is the answer for this question?
Answers
Answer:
A) 254 centimeters squared
Step-by-step explanation:
Answer:
A. 254
Step-by-step explanation:
Find the volume of a sphere with a radius of 9 inches. Use 3.14 for π. Round your answer to the nearest tenth..
Answers
To find the volume of a sphere, you first must identify the formula: (4/3)pi(r)^3
You’re given the radius 9 inches
And you’re also given the pi approximation 3.14.
With that in mind, we can plug those variables in the formula to get:
(4/3)(3.14)(9in)^3 = 3053.63 in^3
And rounded to the tenths place:
3053.6 in^3
pls help me with this, i’ll give brainly
Answers
Answer:
shirts = 15 when pants = 6
15
Step-by-step explanation:
Try two others that are given
shirts / pants = 10 / 4 = 2.5
shirts / pants = 30/12 = 2.5
So shirts/pants = 2.5 = x/6
2.5 = x / 6 Multiply by 6
2.5 * 6 = x
x = 15
E
For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 27 N acts on a certain object, the acceleration
of the object is 3 m/s?. If the force is changed to 18 N, what will be the acceleration of the object?
X
5
?
Answers
Solution :
It is given that force on the object is directly proportional to acceleration.
So, F = ka
Here, k is any constant value.
Putting, F = 27 N and a = 3 m/s² in above equation, we get :
3k = 27
k = 9 N s² m⁻¹
Putting, k in above equation, we get :
F = 9a
Now, putting F = 18 N, we get :
a = 18/9 m/s²
a = 2 m/s²
Hence, this is the required solution.
length of a rectangle is 2 metre and the breadth is 50 find the ratio of a length to the breadth of a rectangle
Answers
explaining
not sure sorry good luck
You play a game in which two dice are rolled. If a sum of 7 appears, you win ten dollars; otherwise, you lose two. If you intend to play this game for a long time, should you expect to make money, lose money, or come out about even? Explain.
Answers
Answer:
Come out even
Step-by-step explanation:
The total numbers of faces in rolling two dice = 6 X 6 = 36
The sum of appears in the following cases: {6, 1}, {1, 6}, {2, 5}, {5, 2}, (3, 4}, {4, 3}. Making a total of 6 cases
Probability of obtaining a sum of 7 = possible number of cases where the sum of 7 appears ÷ total number of outcome
= 6/36 = 1/6
Probability of not obtaining a sum of 7 = 1 - Probability of obtaining a sum of 7
= 1 - 1/6
= 5/6
Expected Value: (1/6)10 + (5/6)(-2) = (10-10)/6 = 0
So the answer is come out even