Answer:
≈84,13%
Step-by-step explanation:
To find the probability of a student liking between 5.5 and 8.5 songs from Eminem, we need to find the standard normal deviate (z-score) for each of these values and then use a standard normal table to find the area between these z-scores.
For 5.5 songs:
z = (5.5 - 7.0) / 1.5 = -1.0
For 8.5 songs:
z = (8.5 - 7.0) / 1.5 = 1.0
The area between -1.0 and 1.0 on a standard normal distribution table is approximately 0.8413. This means that the probability of an individual student liking between 5.5 and 8.5 songs from Eminem is approximately 84.13%.
In the array below, in how many different ways can we start with the letter $A$ and move from letter to letter (horizontally, vertically, or diagonally), to spell the word "ARCH"?
[asy]
usepackage("amsmath");
usepackage("amssymb");
unitsize(0.6 cm);
label("$\text{A}$", (0.5,3.5));
label("$\text{R}$", (1.5,3.5));
label("$\text{C}$", (2.5,3.5));
label("$\text{H}$", (3.5,3.5));
label("$\text{R}$", (0.5,2.5));
label("$\text{R}$", (1.5,2.5));
label("$\text{C}$", (2.5,2.5));
label("$\text{H}$", (3.5,2.5));
label("$\text{C}$", (0.5,1.5));
label("$\text{C}$", (1.5,1.5));
label("$\text{C}$", (2.5,1.5));
label("$\text{H}$", (3.5,1.5));
label("$\text{H}$", (0.5,0.5));
label("$\text{H}$", (1.5,0.5));
label("$\text{H}$", (2.5,0.5));
label("$\text{H}$", (3.5,0.5));
[/asy]
Based on the information, it can be inferred that the number of possibilities to write arch is 37
How to find the number of possibilities that there are to write the word ARCH?To find the number of possibilities there are to write the word arch we must analyze the graph. Once we identify the position of each letter we must carry out the following procedure.
Find how many possible combinations each letter has to form the word. In this case, to begin with, we only have 3 options to connect A with R. However, each R has at least 3 options to connect with the letter C, the R in the center has 5 possibilities to connect with the letter C.
On the other hand, each letter C has at least 4 possibilities of connecting with the letter H, and the middle C has 7 possibilities of connecting with the letter H.
To find the total number of possibilities we must add these values:
3 + 3 + 5 + 3 + 4 + 4 + 7 + 4 + 4 = 37According to the above, we have 37 combination options.
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2000 a month for 15 months with 4% interest
Answer:
1200
Step-by-step explanation:
4% of 2000 is 80 then do 80*15 and you get 1200
Rearange the equation to make b the subject. a = 1/4 b.
The value of the equation a = (1/4)×b in terms of a is b = 4a.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, An expression a = (1/4)×b.
Now, Making 'b' the subject is the same as solving for 'b'.
We know when a term is multiplied by another term moving it to the other side we have to take its reciprocal.
Therefore, a = (1/4)×b.
b = a×(4/1).
b = 4a.
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use polar coordinates to find the volume of the given solid. under the cone z = x2 y2 and above the disk x2 y2 ≤ 36
The volume of the solid under the cone z = x2y2 and above the disk x2y2 ≤ 36 is 7056π. This was found by using polar coordinates and integrating the equation V = ∫∫∫r2sin(θ)dzdθdr with the limits of integration r = 0 to 6, θ = 0 to 2π, and z = 0 to x2y2.
The volume of the solid can be found by integrating the equation:
V = ∫∫∫r2sin(θ)dzdθdr
where r is the radius and θ is the angle of the polar coordinates.
The limits of integration are as follows:
r = 0 to 6
θ = 0 to 2π
z = 0 to x2y2
The integral is then:
V = ∫0 to 2π∫0 to 6∫0 to r2sin(θ)dr dθ
V = ∫0 to 2π∫0 to 6 r3sin(θ)θdr
V = ∫0 to 2π [r4sin(θ)]0 to 6 dθ
V = ∫0 to 2π 644sin(θ)dθ
V = 7056π
The volume of the solid under the cone z = x2y2 and above the disk x2y2 ≤ 36 is 7056π. This was found by using polar coordinates and integrating the equation V = ∫∫∫r2sin(θ)dzdθdr with the limits of integration r = 0 to 6, θ = 0 to 2π, and z = 0 to x2y2.
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let r be the region bounded by the parabola y=x2 and the line y=4. (a) what is the volume of the solid generated when r is rotated about the line y=4 ?
The volume of the solid generated when r is rotated about the line y=4 is 512/15π
In math the term called volume in math is defined as a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.
Here we know that let r be the region bounded by the parabola y=x² and the line y=4.
Then the volume of the solid generated when r is rotated about the line y=4 is calculated by using the formula,
=> V = π ∫ᵇₐ [(h - f(x))]² dx
Here we have to apply the values on it, then we get,
=> V = π ∫₋₂² [(4 - x²)]² dx
By Using symmetry this can be written as,
=> V = 2π ∫₋₂² [16 - 8x² + x⁴] dx
When Solving the integral, then we get,
=> V = 2π (16x - 8/3x³ + 1/5x⁵)²₀
Here by Applying the fundamental theorem of calculus, then we get,
=> V = 2π (16(2) - 8/3(2)³ + 1/5(2)⁵) - 2π (16(0) - 8/3(0)³ + 1/5(0)⁵)
When we simplify this then we get
=> V = 512/15 π
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special right triangle
The value of a is 12 and b is 10.39, for the given special right triangle.
What is the special right triangle?A special right triangle is a right triangle with a regular feature that facilitates calculations on the triangle or for which straightforward formulas are available. Angles in a right triangle, for instance, could form straightforward relationships like 45°-45°-90°. Right triangle that is "angle-based" is what this is. When the side lengths of a right triangle form ratios of whole numbers, like 3:4:5, or of other unusual numbers, like the golden ratio, the triangle is said to be "side-based." Without using more complex techniques, one can quickly calculate different lengths in geometric problems by understanding the relationships between the angles or side ratios of these special right triangles.
The opposite sides of a 30-60-90 special right triangle are always in the ratio of 1:√3: 2.
so opposite of 30deg here is 6
as When opposite side 30deg is 6 then opposite side 90deg is 2(6)
a = 2(6)
a = 12
Now we have base = 6 and hypotenuse = 12
Use Pythagoras theorem
b [tex]= \sqrt{12^2 - 6^2}[/tex]
b = 10.39
Thus, The value of a is 12 and b is 10.39, for the given special right triangle.
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what are the critical values for the decision rule when the level of significance is 0.10? round your answer to two decimal places.
The critical values for a decision rule at a level of significance of 0.10 (i.e., a 10% significance level) depend on the type of hypothesis test you are conducting and the specific distribution you are using.
The decision criteria is based on certain test statistic results (for example, reject H0 if Z > 1.645). A given test's decision rule is determined by three factors: the research or alternative hypothesis, the test statistic, and the degree of significance.
A crucial value is the value of the test statistic that establishes the upper and lower boundaries of a confidence interval or the statistical significance threshold in a statistical test.
Critical values for a hypothesis test are determined by a test statistic that is particular to the type of test and the significance level, alpha, which specifies the test's sensitivity.
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In circle B with the measure of minor arc AC= 126°, find m/ADC.
Answer:
Step-by-step explanation:
=63
The measure of arc ADC in circle B with the measure of minor arc AC= 126° is 234°.
Given that the measure of minor arc AC = 126°, we can find the measure of arc ADC using the following formula:
m/ADC = 360° - m/AC
Plugging in the values, we get:
m/ADC = 360° - 126° = 234°
Therefore, the measure of arc ADC is 234°.
Here is the explanation:
A minor arc is an arc that is less than 180°.
The measure of a minor arc is equal to the measure of the central angle that intersects it.
The measure of a whole circle is 360°.
Therefore, the measure of arc ADC is equal to the difference between the measure of the whole circle and the measure of minor arc AC. This difference is 360° - 126° = 234°.
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In the Cartesian Plane, draw a triangle with vertices (-1 ,7) ,(5,5) ,(-2 ,1). By distance formula, show that the triangle is isosceles.
The triangle with given vertices is not an isosceles triangle.
What is distance formula?The distance formula which is used to find the distance between two points in a two-dimensional plane is also known as the Euclidean distance formula. On 2D plane the distance between two points (x₁, y₁) and (x₂, y₂) is Distance = √[(x₂-x₁)²+(y₂-y₁)²].
Let a triangle with vertices be A(-1 ,7), B(5, 5) and C(-2 ,1).
Using the coordinates A(-1, 7) and B(5, 5), we get
AB =√(5-7)²+(5+1)²
AB=√40
AB=2√10 units
Using the coordinates B(5, 5) and C(-2 ,1) we get
BC=√(-2-5)²+(1-5)²
BC=√65 units
Using the coordinates C(-2 ,1) and A(-1 ,7) we get
BC=√(-1+1)²+(7-1)²
BC= 6 units
Therefore, the triangle with given vertices is not an isosceles triangle.
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The cost of 78 apples is £27.30. (a) Find the approximate (b) Find the approximate cost of 49 apples. cost of 698 apples.
Salut/Hello!
Answer: a) £244 ; b) £17
Step-by-step explanation:
First we need to know the cost of one apple.
27.30 : 78 = £0.35
a) [I'm going to assume you meant 698 apples here]
£0.35 x 698 = £244.3 with the approximate of £244
b) £0.35 x 49 = £17.15 with the approximate of £17
I hope it was helpful! :]
What is a formula for the nth term of the given sequence? 13, 18, 23..
Answer:
Step-by-step explanation:
13,18,23 are in arithmetic progression
The formula for the nth term of an AP is, Tn = a + (n - 1)d, where: 'a' is the first term of the AP and; 'd' is the common difference of the AP.
here a=13, d=18-13=5
Tn = a + (n - 1)d = 13+(n-1)5 = 13+5n-5 = 5n+8
Tn = 5n+8
consider the experiment of rolling a six-faced dice. what is the sample space of all the possible outcomes?
The sample space of rolling a six-faced dice is {1, 2, 3, 4, 5, 6}.
The sample space of an experiment is the set of all possible outcomes of the experiment. In the experiment of rolling a six-faced dice, the sample space is the set of all possible values that the dice can show when it is rolled.
Since a dice has six faces, each with a distinct number (1, 2, 3, 4, 5, or 6), the sample space of the experiment of rolling a six-faced dice is {1, 2, 3, 4, 5, 6}. This means that any time the dice is rolled, it can only show one of these six values.
It's important to note that the sample space is a finite set, as there are only a limited number of possible outcomes. In this case, the sample space contains only six elements, each representing one of the faces of the dice that can show up when it is rolled.
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In the figure below, m/LJK = 37° and m≤KLJ = 69º. What is m/JKH?
A. 90⁰
B. 16°
C. 36°
D. 6°
∠LJK = 37° and ∠KLJ = 69º. So, ∠JKH = 16°. This can be solved by using the concept of triangle.
Correct option: B
What about angles?When two beams or straight lines intersect at one of their ends, an angle is created. The vertices of such an angles is the location where two points come together. The word angle is taken from the Latin word angulus, which means "corner."
Depending on the measurement, there are many angles in geometry. Basic angles are identified by their names: acute, obtuse, right, straight, reflex, and complete rotation.
ΔJKL consist of 3 angles: ∠LJK, ∠KLJ and ∠JKL
We are given the measures of ∠LJK and ∠KLJ
In order to find ∠JKH we must find the missing angle in the triangle
Remember that angles in a triangle add up to equal 180
If we are given two angles we can find the missing angle by subtracting the measures of the known angles from 180
so ∠JKL = 180° - 37° - 69°
180° - 37° - 69° = 74°
Hence, ∠JKL = 74°
Now to find ∠JKH:
Angles ∠K, ∠JKH and ∠JKL appear to be formed on a straight line
Angles formed on a straight line add up to equal to 180°
So, ∠K + ∠JKH + ∠JKL = 180°
∠K is a right angle, indicated by the little square.
Right angles have a measure of 90° so ∠K = 90°
We have also calculated the measure of ∠JKH = ( 74° )
That being said we plug in the given values into the equation created earlier and solve for ∠mJKH
We would have 90° + ∠JKH + 74° = 180°
For calculation ∠JKH:
90° + 74° = 164°
now we have 164° + ∠JKH = 180°
or, ∠JKH = 16°
Hence the answer is B
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The complete question is as follows:
The most popular size pizza at pizza parlor is a large with a 12-inch radius.What is the circumstance of the pizza?
Answer:
37.17
Step-by-step explanation:
I took the test
Answer: The circumference of the pizza is 37.7 inches.
Given data :
Diameter of the pizza = 12 inches
So,
Radius of the pizza = 12/2
= 6 inches
So,
Circumference of the pizza
= 2×π×radius
= 2×22/7×6
= 37.7 inches (answer)
If -8x + 2y = -10 and 7x + 6y = -3 are true equations what would be the value of 15x + 4y
If -8x + 2y = -10 and 7x + 6y = -3 are true equations what would be the value of 15x + 4y is Cross out the common factor: 7.
Verify your math to ensure that the values on either side of the equals sign are the same in order to create a genuine equation. To create a genuine equation, ensure sure the numbers on both sides of the "=" symbol are equal. For instance, the equation 9 = 9 is real. The equation 5 + 4 = 9 is accurate. The formula 6 + 3 = 9 is accurate.
Multiplying both side of a equation by a coefficient:{3(-8x + 2y) = -10 × 3, 7x + 6y = -3}
apply the distributive property {-24x + 6y = -30, 7x +6y -3}
Subtract the two equations: -24x + 6y - (7x +6y) = -30 - (-3)
Remove parentheses: -24x + 6y - 7x - 6y = -27
Cancel one variable : -24x - 7x = -27
Solve the equation: x = 27/31
Substitute into one of the equations: 7 × 27/31 + 6y = -3
Solve the equation: y = -47/31
The solution of the system is {x = 27/31, y = -47/31}
Substitute { x = 27/31 , y = -47/31 into 15x + 4y :: 15 × 27/31 + 4 × (-47/31)
Determine the sign of multiplication or division: 15 × 27/31 - 4 × 47/31
Write as a single fraction: 15 × 27 /31 - 4 × 47 /31
calculate the product or quotient: 405/31 - 188/31
Write the numerators over common denominators: 405 - 188/31
calculate the sum or difference: 217/31
Cross out the common factor: 7
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If the equation has one solution,
what number CAN'T the value of
h be?
h(- 2x + 5) = 4x + 5
Answer:
-2.5
Step-by-step explanation:
We can start by isolating h on one side of the equation:
4x + 5 = h(-2x + 5)
Divide both sides by -2x + 5:
(4x + 5) / (-2x + 5) = h
Now, since the equation has only one solution, the value of h must be well-defined for all values of x except those that would make the denominator equal to zero. This happens when -2x + 5 = 0, or when x = (5 - 5) / (-2) = -2.5.
So, the value of h cannot be determined when x = -2.5. This means that the value of h cannot be equal to -2.5.
Can someone help me with this aleks
Please help me with this i don't know how to set up a graph. Thank you!
Answer:
Why do you need to set up a graph for this equation?
Step-by-step explanation:
An investor has an account with stock from two different companies. Last year, her stock in Company A was worth $1400 and her stock in Company B was worth $7100. The stock in Company A has decreased 5% since last year and the stock in Company B has decreased 9%. What was the total percentage decrease in the investor's stock account? Round your answer to the nearest tenth (if necessary).
Answer:
Total decrease as a percentage 12.4%
Step-by-step explanation:
Please find the attachment for detail
janelle is a junior counselor at cactusville craft camp. one day, janelle's campers make lanyard keychains out of plastic string. for each keychain, janelle cuts a long piece of string into 4 equal pieces. each piece is 1.5 feet long.which equation can you use to find the length s of the long piece of string before janelle cuts it?
The length of the long piece of string before Janelle cuts it is 6 feet.
We can use the following equation to find the length s of the long piece of string before Janelle cuts it:
s = 4 * 1.5 feet
where 4 is the number of pieces and
1.5 feet is the length of each piece.
Therefore, s = 4 * 1.5 feet = 6 feet.
Multiplication is the process of taking one integer and multiplying it by a certain number of times. Multiplication is a way of calculating the product of two or more integers in mathematics. It is one of the most fundamental mathematical operations that we utilise every day.
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The price of a jumper is increased by 17% and is now $319.31.
Find the original price of the jumper.
Answer in $
In linear equation, $54.3 is the original price of the jumper.
Which equation is linear equation ?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
17% of 319.41
17/100 * 319.41
= 54.2997
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Which equation is an equation of a circle with a radius of 3 and its center is at (5, -2)?
Responses
(x - 5)² + (y + 2)² = 9
(x + 5)² + (y - 2)² = 9
(x - 5)² + (y + 2)² = 3
(x + 5)² + (y – 2)² = 3
The correct equation of the circle is the first option which is
(x - 5)² + (y + 2)² = 9
What is a circle?
A circle is a collection of all points in a plane that is uniformly distanced from a fixed point. The fixed point is referred to as the circle's centre. The radius of a circle is the separation between the centre and any point along its circumference.
The general equation of the circle is
(x-h)² + (y-k)² = r²
where r = radius of the circle
(h,k) = centre of the circle
Given,
radius r = 3
centre = (h,k) = (5,-2)
According to the above equation,
(x-5)² + (y-(-2))² = 3²
(x-5)² + (y+2)² = 9
Therefore the correct equation of the circle is the first option.
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1) y varies inversely with x and y = 40 when x = 5. Find x when y is equal to: a. 50 b. 4
2) y varies inversely with x^2 and y = 10 when x = 15. Find x when y is equal to: a. 22.5 b. 90
Answer:
I have this same question what school do u go to?
Step-by-step explanation:
lan didn't know if his eyes were playing tricks on him or what. When he first looked at all the students from the bleachers at the assembly everyone on the gym floor was in groups of 2 with O left over. Those groups seemed to drift together to form groups of 4, but there were 2 left over. The next time he looked, they appeared to be in groups of 3 with 2 left over again. As he double checked, it seemed the groups of 3 were transformed into groups of 5, and this time there were 4 left over. if there were less than 100 people on the gym floor, how many were there? Show your work and explain your thinking and process of elimination. (Hint:. There. are z possible answers. For full credit you must have both answers.)
So on solving the question Mary Ann saw each of these patterns of people while she was on the hill equation is 3x+2 and answer is 14.
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra.
Mary Ann saw each of these patterns of people while she was on the hill:
1)All in groups of two, no leftover
2) All in groups of four, two left over
3)All in groups of three, two leftover
4)All in groups of five, four leftover.
So the number must give 2 as remainder when divided by 3.
So the number must be 4x+2 . So the number will be 3x+2 Thus from the above information, we can easily say that the number is 3*4+2 = 12+2 = 14
However , we have to check whether 14 matches the last part.
Groups of five in which 4 was leftover.
2 groups of 5 taken out of 14 (2*5) will have 4 as a remainder.
So the right answer is 14.
Answer :14
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What’s the answer to this question?
Answer:
Step-by-step explanation:
2x-3
x=2
select the correct answer from each drop-down menu consider the given equation 3x+2y=8 the equation y=______x+____ represents the line parallel to the given equation and passed through the point (-2,5)
equation 3x+2y=8 the equation y= -3/2, x+2 represents the line parallel to the given equation and passed through the point (-2,5)
How do equations work?The concept of an equation in algebra is a quantitative statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
(formula of the line ) y= mx+c
y= -3/2+8/2
y= -3/2+4 ( m= -3/2)
this is given equation of the line
and its parallel line is
y-5/x+2 = -3/2
2y- 10 = -3x-6
3x+2y =4
2y = -3x+4
y = -3/2x+2
y = -3/2
x =2
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please help i’m failing this class
Answer:
B. 34 1/5
Step-by-step explanation:
have a good day!
determine the percentage of a circle's circumference cut off by an angle that has a measure of 31.9 degrees plus 1.5 radians.
The percentage of a circle's circumference is 18.17%.
We have,
To determine the percentage of a circle's circumference cut off by an angle, we need to calculate the fraction of the total circumference represented by the given angle and then convert it to a percentage.
The total circumference of a circle is 360 degrees or 2π radians.
First, we convert the angle measure of 31.9 degrees to radians:
31.9 degrees = 31.9 x (π/180) radians
Next, we add the given angle measure of 1.5 radians to the converted value:
31.9 x (π/180) + 1.5 radians
To calculate the fraction of the circumference, we divide the sum of the angles by the total angle of a circle (2π radians):
(31.9 x (π/180) + 1.5) / (2π)
To express it as a percentage, we multiply the fraction by 100:
[(31.9 x (π/180) + 1.5) / (2π)] x 100
Evaluating this expression will give us the final value, which represents the percentage of a circle's circumference cut off by the given angle.
Performing the calculations:
[(31.9 x (π/180) + 1.5) / (2π)] x 100 ≈ 18.17%
Therefore,
The percentage of a circle's circumference is 18.17%.
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An angle with a measure of 31.9 degrees plus 1.5 radians cuts off approximately 23.3% of a circle's circumference.
To determine the percentage of a circle's circumference cut off by an angle, we need to find the ratio of the angle's measure to the total angle of a circle (360 degrees or 2π radians) and then multiply it by 100 to express it as a percentage.
First, let's convert the angle measure of 31.9 degrees to radians:
1 degree = π/180 radians
So, 31.9 degrees = (31.9 × π) / 180 radians
Now, let's add the angle in radians to the converted value:
31.9 degrees + 1.5 radians = (31.9 × π) / 180 + 1.5 radians
Next, we calculate the ratio of the angle to the total angle of a circle:
Angle ratio = (31.9 × π) / 180 + 1.5 radians / 2π radians
Finally, we multiply the ratio by 100 to obtain the percentage:
Percentage = Angle ratio × 100
Let's calculate it:
Angle ratio = ((31.9 × π) / 180 + 1.5) / (2π) ≈ 0.233
Percentage = 0.233 × 100 ≈ 23.3%
Therefore, an angle with a measure of 31.9 degrees plus 1.5 radians cuts off approximately 23.3% of a circle's circumference.
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Calculate the difference and enter it below.
--12-(-8)
Answer: -4
Step-by-step explanation:Since subtracting a negative number is the same as adding a positive number, -12 - (-8) can be rewritten as -12 +8. Counting 8 up from negative 12 leaves us with negative 4.
A chemist is raising the temperature of a liquid. The temperature is now -8.4 degrees Celsius and is increasing by 1.4 degrees Celsius per minute. How many minutes will it take for the temperature to reach 0 degrees Celsius?
Answer:
it will take 6 minutes, just keep adding 1.4 to -8.4 until you reach 0
Step-by-step explanation:
Answer: It will take 6 minutes because all you need is to divide 8.4 and 1.4 (don't put the negative sign or ignore it)!
