The price of a cup of coffee was 2.40 yesterday. Today, the price rose to
2.75. Find the percentage increase. Round your answer to the nearest tenth of a percent.
Answer:
≈ 14.6%
Step-by-step explanation:
percentage increase is calculated as
[tex]\frac{increase}{original}[/tex] × 100%
increase = 2.75 - 2.40 = 0.35 , then
percentage increase = [tex]\frac{0.35}{2.40}[/tex] × 100% ≈ 14.6% ( to the nearest tenth )
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Indicate the equation of the given line in standard form. The line that contains the point Q( 1, -2) and is parallel to the line whose equation is y - 4 = 2/3 (x - 3)
The value of x, y, and z are 15/2, (15√3)/2, and (15√3)/2 after applying the trigonometric ratios.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
To find the value of x:
In right-angle triangle x-z-15:
sin30 = x/15
x = 15sin30 = 15/2
To find the value of y:
sin60 = y/x = y/(15/2)
sin60 = 2y/15
√3/2 = 2y/15
y = (15√3)/2
To find the value of z:
cos30 = z/15
√3/2 = z/15
z = (15√3)/2
Thus, the value of x, y, and z are 15/2, (15√3)/2, and (15√3)/2 after applying the trigonometric ratios.
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Which of the following is NOT a rational expression?
The expression that is not rational is the first one:
[tex]f(x) = \frac{6x}{4}[/tex]
Which of the given expressions is not rational?A rational expression is something of the form:
[tex]f(x) = \frac{q(x)}{p(x)}[/tex]
Such that q(x) can be any polynomial, and p(x) is a polynomial of at least degree 1.
This means that we need to have the variable "x" on the denominator.
Then is easy to recognize the expression that is not rational, is the one that does not have x on the denominator, which is the first one:
[tex]f(x) = \frac{6x}{4}[/tex]
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Answer: B
Step-by-step explanation:
I took the test and this was the correct answer
You are given that cos(A)=−35, with A in Quadrant II, and cos(B)=817, with B in Quadrant I. Find cos(A−B). Give your answer as a fraction.
Expand cos(A - B) with the identity
cos(A - B) = cos(A) cos(B) + sin(A) sin(B)
A is in quadrant II, so sin(A) > 0, and B is in quadrant I, so sin(B) > 0. Using the Pythagorean identity, we get
cos²(A) + sin²(A) = 1 ⇒ sin(A) = + √(1 - (-3/5)²) = 4/5
cos²(B) + sin²(B) = 1 ⇒ sin(A) = + √(1 - (8/17)²) = 15/17
Then
cos(A - B) = (-3/5) × 8/17 + 4/5 × 15/17 = 36/85
cos (A - B) is 36/85
How to simply the identity
Expand cos(A - B) with the identity
You get, cos(A - B) = cos(A) cos(B) + sin(A) sin(B)
Since A is in quadrant II, so sin(A) > 0,
B is in quadrant I, so sin(B) > 0.
Using the Pythagorean identity, we get
cos²(A) + sin²(A) = 1
Make sin A the subject of formula
[tex]sin(A)^{2}[/tex] = ([tex]\sqrt{(1 - (-3/5}[/tex])²)
Find the square root of both sides, square root cancels square
[tex]sin A[/tex] = 4/5
Repeat the same for the second value
[tex]sin A^{2} = \sqrt{(1- 8/17)^2}[/tex]
[tex]sin A[/tex] = 15/17
Substitute values into cos(A - B)
cos(A - B) = cos(A) cos(B) + sin(A) sin(B) = (-3/5) * 8/17 + 4/5 * 15/17
cos (A - B) = 36/85
Therefore, cos (A - B) is 36/85
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The graph below shows the solution to which system of inequalities?
Inequalities help us to compare two unequal expressions. The inequalities that represent this graph are y<8/10x and y>-x. The correct option is C.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
To find the inequality, we need to find the equation of the dashed line and then substitute the inequality as per the requirement. The dashed line is used instead of a solid line to show greater than or less than.
The inequality for the first graph can be written as,
[tex]y < \dfrac{8}{10}x[/tex]
The inequality for the second graph will be,
y>-x
Hence, the inequalities that represent this graph are y<8/10x and y>-x. Thus, the correct option is C.
The complete question is:
The graph below shows the solution to which system of inequalities?
A.) y>x , y ≥ (8/10)x
B.) y>-x, y ≤ (8/10)x
C.) y>-x, y < (8/10)x
D.) y>x, y > (8/10)x
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Thaddeus models the number of hours of daylight in his town as
D(t) = 3sin(t) + 12, where D is the number of daylight hours and t is the
time in months since January 1.
What are the least and greatest numbers of daylight hours over the course of
a year?
Answer:
(π2,15)(π2,15) is a local maximal
(3π2,9)(3π2,9) is a local minimal
Step-by-step explanation:
NEED THIS DONE ASAP!! Thank you!!
Answer:
150°
Step-by-step explanation:
A secant is a straight line that intersects a circle at two points.
The circle shows two secants RD and BD that intersect at one exterior point D, so we can use the Intersecting Secants Theorem to solve.
Intersecting Secants Theorem
If two secant segments are drawn to the circle from one exterior point, the measure of the angle formed by the two lines is half of the (positive) difference of the measures of the intercepted arcs.
[tex]\implies \angle RDB = \dfrac{1}{2}\left(\overset{\frown}{RB}-\overset{\frown}{EC}\right)[/tex]
[tex]\implies 5x-10=\dfrac{1}{2}(13x+7-60^{\circ})[/tex]
[tex]\implies 2(5x-10)=13x-53[/tex]
[tex]\implies 10x-20=13x-53[/tex]
[tex]\implies -3x=-33[/tex]
[tex]\implies x=11[/tex]
To find the measure of [tex]\overset{\frown}{RB}[/tex], substitute the found value of x into the expression for the arc:
[tex]\implies \overset{\frown}{RB}=13x+7[/tex]
[tex]\implies \overset{\frown}{RB}=13(11)+7[/tex]
[tex]\implies \overset{\frown}{RB}=143+7[/tex]
[tex]\implies \overset{\frown}{RB}=150^{\circ}[/tex]
Therefore, the measure of arc RB is 150°.
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3. Find how many numbers between 232 and 252.
Answer:
252-232=20-1=19
Step-by-step explanation:
the question said in between so you don't count the first and the last numbers
What u
Is 2(x+3) / 4(x+1)
Answer:
Step-by-step explanation:
2 ( x + 3 ) / 4 ( x + 1 )
2 (x + 3) ÷4 (x + 1)
2 (x + 3) ÷ 2×2(x+1)
cancel out the 2 in the numerator with the 2 in the denominator
(x + 3) ÷ 2(x + 1)
x+3 / 2(x+1)
a model airplane has two engines. it can fly if one engine fails but is in serious trouble if both engines fail. The engines function independently of one another. On any given flight, the probability of a failure is 0.10 for each engine. Design a simulation to estimate the probability that the airplane will be in serious trouble the next time it goes up.
Using the binomial distribution, it is found that there is a 0.0001 = 0.01% probability that the airplane will be in serious trouble the next time it goes up.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.The values of the parameters are given as follows:
p = 0.1, n = 2.
The plane is in serious trouble if both engines fail, that is, the probability is P(X = 2), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{2,2}.(0.1)^{2}.(0.9)^{0} = 0.0001[/tex]
0.0001 = 0.01% probability that the airplane will be in serious trouble the next time it goes up.
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What is 1+1? 10 point if u get it right.
Answer:
11
Step-by-step explanation:
duh add 1 and 1 merge it together to get 11
that's a hard question imma go with 2 though
Step-by-step explanation:
for this problem let's let x=1 and y also =1 so x+y=2 hope this helps
Suppose that the number of a certain type of computer that can be sold when its price is P (in dollars) is given by a linear function N(P).
(a) Determine N(P) if N(1000) = 10000 and N(1700) = 6500. (Use symbolic notation and fractions where needed.)
N(P) =?
(b) Select the statement that gives the slope of the graph of N(P), including units and describes what the slope represents.
●5 computers per dollar
● -1/5computers per dollar
● -5 computers per dollar
● -5 dollars per computer
(c) What is the change N in the number of computers sold if the price is increased by AP = 110 dollars? (Give your answer as a whole number.)
AN = ?
Examine the right triangle ABC. Which rise and run would create a similar right triangle on the same line?a rise of 6 and a run of 8a rise of 8 and a run of 6a rise of 6 and a run of 5a rise of 5 and a run of 6
Step-by-step explanation:
What is the function that defines the following sequence? 10, 12, 14, 16, 18…
The sequence shown is defined by a function that generates even numbers equal or greater than 10, defined by the function s = 10 + 2 · (n - 1).
How to define the function behind a sequence
Sequences are sets of elements characterized by at least a rule. In this case, the sequence shown is characterized by a function that generates even numbers equal or greater than 10. The function behind the sequence is shown below:
s = 10 + 2 · (n - 1) (1)
Where n is the element index.
The sequence shown is defined by a function that generates even numbers equal or greater than 10, defined by the function s = 10 + 2 · (n - 1).
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Can u help me with this I don’t understand
Answer:
D -6, 15
Step-by-step explanation:
Because 3,11 is the middle, and 12,7 is the other end, you can do
12 - 3 = 9
3 - 9 = 6
then
11 - 7 = 4
11 + 4 = 15
so
6 is you x and 15 is your y
Use Newton’s Method with initial approximation x1=1 to find x4, the third
approximation to the root of the equation x3+3x+sin(x)=5. What is the result?
Let [tex]f(x) = x^3 + 3x + \sin(x) - 5[/tex]. Using Newton's method to approximate a solution to [tex]f(x) = 0[/tex], we consider the recurrence
[tex]\begin{cases} x_1 = 1 \\ x_{n + 1} = x_n - \frac{f(x_n)}{f'(x_n)} & \text{for } n \ge 1 \end{cases}[/tex]
Differentiating [tex]f(x)[/tex] gives
[tex]f'(x) = 3x^2 + 3 + \cos(x)[/tex]
Then
[tex]x_2 = 1 - \dfrac{f(1)}{f'(1)} = 1 + \dfrac{1 - \sin(1)}{6 + \cos(1)} \approx 1.024238790[/tex]
[tex]x_3 = x_2 - \dfrac{f(x_2)}{f'(x_2)} \approx 1.024009549[/tex]
[tex]x_4 = x_3 - \dfrac{f(x_3)}{f'(x_3)} \approx \boxed{1.024009528}[/tex]
which agrees numerically with the actual root of [tex]f(x)[/tex] up to at least 9 digits after the decimal point.
You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe
the population proportion is approximately p 37%. You would like to be 99.5% confident that your
esimate is within 2.5% of the true population proportion. How large of a sample size is required?
H
n=
The sample size required is 2938.645
What is Probability ?Probability is the likeliness of an event to happen.
It is given that
p = .37
∈ = 0.025
∝ = 1 - 0.995 = 0.005
∝[tex]\rm z_{\alpha/2} = z_{0.005/2} = 2.807[/tex] (From z table)
Sample size n is given by
[tex]\rm n = (\dfrac{z_{\alpha/2}}{\epsilon})^2 p (1-p)\\\\n = (\dfrac{2.807}{.025})^2 *0.37*(1-0.37)\\\\n = 2938.645\\[/tex]
Therefore the sample size required is 2938.645
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PLEASE HELP ASAP! Consider the scatter plot. Complete the equation that models the curve of best fit for this data.
curve of best fit: f(x)
The equation that models the curve of best fit for this data will be y = 1.4646·(1.818)ˣ.
What is an exponent?Let b is the base and x is the power of the exponent function and a is the leading coefficient. The exponent is given as
y = a(b)ˣ
Consider the scatter plot.
Then the equation that models the curve of best fit for this data will be
At (1.2, 3), then we have
[tex]\rm 3 =ab^{1.2}[/tex] ..........1
At (4, 16), then we have
16 = ab⁴ ..........2
By solving the equations 1 and 2, we have
a = 1.4646 and b = 1.818
Then the equation will be
y = 1.4646·(1.818)ˣ
Then the graph is drawn.
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The vertex of the graph of y = -4(x + 3)² + 2 is
DONE
A parabola is a mirror-symmetrical planar curve that is nearly U-shaped. The vertex of the parabola will lie at (-3,2).
What is the Equation of a parabola?A parabola is a mirror-symmetrical planar curve that is nearly U-shaped.
y = a(x-h)² + k
where,
(h, k) are the coordinates of the vertex of the parabola in the form (x, y);
a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.
Comparing the given equation with the equation of a parabola, we will get,
y = a(x -h)² + k
y = -4(x+3)² + 2
Hence, the vertex of the parabola will lie at (-3,2).
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Luis created the graph below to show the temperature from 8:00 a.m. (8 hours after midnight) until 8:00 p.m.
On this graph, 4:00 p.m. occurs at 16 hours after midnight, and 6:00 p.m. occurs at 18 hours after midnight. Which statements are true about the temperatures Luis recorded on the graph? Select THREE answers.
The temperature increased until 4:00 p.m.
The temperature was not recorded between 4:00 p.m. and 6:00 p.m.
The temperature decreased after 6:00 p.m.
The temperature increased and then decreased before holding constant.
The temperature increased more quickly between 12:00 p.m. and 4:00 p.m. than before 12:00 p.m.
A slope also known as the gradient of a line is a number. The correct option is A, C, and D.
What is Slope?A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
For the given question,
The temperature increased until 4:00 p.m.This can be observed in the graph, as the slope of the graph before 4 pm is positive, it can be concluded that the temperature is increased until 4 pm.
The temperature decreased after 6:00 p.m.This can be observed in the graph, as the slope of the graph after 4 pm is negative, it can be concluded that the temperature is decreasing after 4 pm.
The temperature increased more quickly between 12:00 p.m. and 4:00 p.m. than before 12:00 p.m.This can be probed by calculating the slope of the line between the two points. Therefore, the slope between 8 am to 12 pm will be 1, while the slope from 12 pm to 4 pm will be equal to 4/3.
Hence, the correct option is A, C, and D.
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Answer:
ACD
Step-by-step explanation:
The inverse of the function f(x) =
f(x) = x + 10 is shown.
h(x) = 2x-0
What is the missing value?
0 1
05
O 10
O 20
Answer: 20
Step-by-step explanation:
Let [tex]f(y)=x[/tex]
[tex]x=\frac{1}{2}y+10\\\\x-10=\frac{1}{2}y\\\\y=h(x)=2x-\boxed{20}[/tex]
find x and y please please help
L1 and L2 are parallel
so the interior alternate angles are equal
4y - 40 = 3y ( interior alternate angles)
4y - 40 = x + 15 ( vertically opposite angles).
solving the first equation, we get
4y - 3y = 40
y = 40°
putting values of y= 40° in eq. 2, we get
4y - 40= x + 15
4(40) - 40 = x + 15
160 -40 = x + 15
120 - 15 = x
105° = x
X = 105° , Y = 40°Three out of every 20 students in ms. jones’ Math class earned a grade of A. What percent of the students earned a grade of A?
Answer:
15%
Step-by-step explanation:
3/20x100=15
what is the difference between a relation and function? Classify each of the following as a function, or not a function. State the domain and range
{(1,7),(1,14),(1,21)}
The relation is/isn't a function
Domain _ _ _
Range _ _ _
Leave Unused Fields Blank
Answer:
A relation is a subset of cartesian product of two non empty sets whereas A function is a type of relation in which every element of first set has one and only image in the second set.
In a relation an element of the first set can have many images in the second set whereas in a function the first element can have only one image in the second set.
The given relation is not a function as the element 1 is related to 3 different elements in the second set.
Domain={1}
Range={7,14,21}
h(x)=x²-5
Find h(-7)
Simplify your answer.
Answer:
h(-7) = 44
Step-by-step explanation:
h(x) = h (-7) means x= -7
h(x) = (-7)² - 5
49 - 5
44
Round to the nearest ten thousandths 15.76548908 *
A 13 -ft ladder is leaning against a house when its base starts to slide away. By the time the base is 12 ft from the house, the base is moving away at the rate of 15 ft/sec.
a. What is the rate of change of the height of the top of the ladder?
b. At what rate is the area of the triangle formed by the ladder, wall, and ground changing then?
c. At what rate is the angle between the ladder and the ground changing then?
A swiming pool has a length of 12meters width of 6 meter and a height of a 5 meter how much water is needed to fill the swiming pool?
Answer:
[tex]\boxed {360 m^{3}}[/tex]
Step-by-step explanation:
Water needed to fill the pool = volume of pool
Volume :
Volume = Length × Width × HeightVolume = 12 m × 6 m × 5 mVolume = 12 m x 30 m²Volume = 360 m³Hence, 360 m³ of water has to be filled.
Answer:
360 m³
Step-by-step explanation:
The swimming pool can be modeled as a rectangular prism with the following dimensions:
length = 12 mwidth = 6 mheight = 5 mTo find how much water is needed to fill the pool, calculate the volume of the rectangular prism using the given dimensions:
[tex]\begin{aligned}\textsf{Volume of a rectangular prism} & = \sf length \times width \times height\\\implies \textsf{Volume of pool} & = \sf 12 \times 6 \times 5 \\& = \sf 72 \times 5\\& = \sf 360 \:\: m^3\end{aligned}[/tex]
Therefore, 360 m³ of water is needed to fill the swimming pool.
What is the area of a rectangle with vertices at (6, −3), (3, −6) , (−1, −2), and (2, 1)? Enter your answer in the box. units²
The area of triangle is 24 sq. units
What is Area of rectangle?Area of rectangle is product of its length to its breadth.
i.e., Area of rectangle = length* breadth
let A(6, -3), B(3, -6), C( -1, -2) and D( 2, 1)
Using distance formula
AB = √(3-6)²+ (-6 +3)²
AB= √9 + 9
AB= √18
AB= 3√2
now,
BC= √(-1-3)²+ (-2 +6)²
BC = √16 +16
BC = √32
BC =4 √2
Now, Area of rectangle
= AB* BC
= 3√2 *4 √2
= 12*2
= 24 square units
Hence, area of rectangle is 24 sq. units
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As a unit price, a half-dozen for
$6.00 is
a. $36.00 each
b. $6.00 each
c. $0.50 each
d. $1.00 each
what is the value of x
Answer:
FROM THE CALCULATIONS THE ANSWER IS B!
