The probability that a randomly selected test score will fall in the interval 360 to 380 is the option (3), 0.24.
How to solveTo calculate the probability that a test score falls between 360 and 380, we need to standardize these values by subtracting the mean and dividing by the standard deviation.
This gives us:
z(360) = (360-350)/18 = 0.56
z(380) = (380-350)/18 = 1.67
We can then use a standard normal distribution table or a calculator to find the area under the curve between these two z-scores.
The probability is approximately 0.24.
Therefore, the answer is option (3), 0.24.
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Two coins are tossed. Assume that each event is equally likely to occur.
a) Use the counting principle to determine the number of sample points in the sample space.
b) Construct a tree diagram and list the sample space.
c) Determine the probability that no tails are tossed.
d) Determine the probability that exactly one tail is tossed.
e) Determine the probability that two tails are tossed.
f) Determine the probability that at least one tail is tossed.
Question content area bottom
Part 1
a) There is/are ______sample point(s) in the sample space.
a) There are 2 x 2 = 4 sample points in the sample space
How to solve
b) Tree Diagram
O D.\nH\nHe\nT\nH\nT\n
Sample space: D. HH, HT, TH, TT
c) P(no tails) = P(HH)
= 1/4
d) P(exactly one tail) = P(HT, TH)
= 2/4
= 1/2
e) P(2 tails) = P(TT)
= 1/4
f) P(at least one tail) = P(HT, TH, TT)
= 3/4
In mathematics, tree diagrams are often used in probability and statistics to show all the possible outcomes of an event. In computer science, they are used to represent the hierarchical structure of files and directories in a file system
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People, I need to figure out a question
Is the sun of 7/10 + 1/5 closer to 0, 1/2 or 1?
Answer:
1
Step-by-step explanation:
7+10+1/5
7/10 = 0.7
1/5 = 0.2
0.7+0.2=0.9
Therefore it would be closest to 1.
Answer: 1
Step-by-step explanation:
To find an estimate, you need to round your fractions. Let's start with 7/10. First let's look at the numerator, 7. 7 is a number greater than 5, so we'll round it to 10 and you keep your denominator. so now we have 10/10, or 1. Then round 1/5. 1/5 is lower than 5, so we'll round it to 0. Now, for the final step add them. 1 + 0 = 1, so 1 is the answer
divide $300 in ratio 9 : 1
Answer:
$270:$30
Step-by-step explanation:
add up the ratios = 10
then do 300/10 = 30
so 1 ratio = 30
this means the ratio will be: $270:$30
Let me know if this helped
is y=-x directly proportional or non proportional
Answer: Directly proportional.
Step-by-step explanation:
y = -x is directly proportional for a few reasons.
➜ The graph of this equation is a straight line, so all the ratios of points are equal.
➜ The constant of proportionality (k) is equal to -1.
➜ This line intersects the graph at the origin (0, 0).
➜ See the graph below.
An oil candle globe made of hand-blown glass has a diameter of 25.8 cm. What is the volume of the globe? Use 3.14 for .
globe meaning a sphere, and since it has a diameter of 25.8, that means its radius is half that, or 12.9
[tex]\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=12.9 \end{cases}\implies V=\cfrac{4\pi (12.9)^3}{3}\implies \stackrel{ using~\pi =3.14 }{V\approx 8987.47}[/tex]
The estimated population of a certain city over time is given in the table below. Answer the questions below to determine what kind of function would best fit the data, linear or exponential.
Number of Years Since Last Census, x
1
2
3
4
Estimated Population, f(x)
49,372
58,207
66,998
75,798
function would best fit the data because as x increases, the y values change
. The
of this function is approximately
.
A linear function would best fit the data because as x increases, the y values change by an approximate constant. The rate of change of this function is approximately 8950 people a year.
How to determine that it is a linear functionTo determine which type of function best fits the data, we can analyze the difference in the y values (Estimated Population) as x increases.
Differences between consecutive y values:
58,207 - 49,372 = 8,835
66,998 - 58,207 = 8,791
75,798 - 66,998 = 8,800
The differences between consecutive y values are relatively constant as x increases. This suggests that a linear function would be more appropriate than an exponential function
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College Trig Question!!!!!!!!!!!!!!
The equation, for the simple harmonic motion of a particle moving uniformly is s ( t ) = A x cos (ωt).
How to find the equation ?An object undergoing simple harmonic motion follows a periodic oscillation in a straight line, resembling a sinusoidal curve. Likewise, when an object continuously traverses upon a circle with uniform motion, its projection along the diameter travels back and forth in a simple harmonic motion pattern.
Assuming that the particle commences at the highest point of the simple harmonic motion at time t = 0, either the sine or cosine function is utilized to derive the equation for the simple harmonic motion formula. Thus, let us employ the cosine function in this instance:
s ( t ) = A x cos (ωt)
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Every weekend, Camilla teaches ice skating lessons at a nearby ice rink. She earns $12 for a
30-minute lesson.
Complete the table.
Minutes taught
30
Money earned ($) 12
Graph the data from the table.
60
90 120
Next, using the matching x and y values for each row of the table, we can place a point for each row and connect it to the other points using a line.
what is line ?A line represents a one-dimensional straight figure that can go on forever in both directions in geometry. To separate it from a curved or an angle-filled line, it is frequently referred to as a "straight line." Two points on a line define the line, while every other position on the line may be discovered by tracing the line through the two defined points. A line can be made with a pencils or another non-thick tool, and it can have any width or depth. Shape and figures are described and analysed using lines, which are a basic building block of geometry.
given
Minutes Taught Dollars Earned (30, 12, 60, 24)
90 36
120 48
We may plot the minutes taught on the x-axis and the money made on the y-axis to graph the data from the table.
Next, using the matching x and y values for each row of the table, we can place a point for each row and connect it to the other points using a line.
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In circle S with
m
∠
R
S
T
=
102
m∠RST=102 and
R
S
=
6
RS=6 units, find the length of arc RT. Round to the nearest hundredth.
In a circle, the measure of a central angle is equal to the measure of its intercepted arc. Since ∠RST is a central angle of circle S and its measure is 102 degrees, the measure of its intercepted arc ⌢RT is also 102 degrees.
The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. Since RS is a radius of circle S and its length is 6 units, the circumference of circle S is C = 2π * 6 = 12π units.
The length of an arc is proportional to its measure in degrees. Since the measure of ⌢RT is 102 degrees and the total measure of a circle is 360 degrees, the length of ⌢RT is (102/360) * 12π = 3.4π units.
Rounded to the nearest hundredth, this is approximately 10.68 units.
Question is in image
Answer:
366,699
Step-by-step explanation:
to solve this problem, we can use the following formula for exponential growth:
population = initial population x (1 + growth rate)^time
where the initial population is the current population, the growth rate is the rate of increase per year, and the time is the number of years.
Plugging in the given values, we get:
population = 300,000 x (1 + 0.02)^10
Simplifying, we get:
population = 300,000 x 1.02^10
Using a calculator, we get:
population ≈ 366,698.79
Rounding to the nearest whole number, we get:
population ≈ 366,699
The population in 10 years will be approximately 366,699
100 POINTS!!!
Question
Step-by-step explanation:
A.
Sequence 2:
25-2×5=15
25-2×6=13
25-2×7=11
25-2×8=9
25-2×9=7
Ordered pairs :
(13,15)
(16,13)
(19,11)
(21,9)
(24,7)
B.
Sequence1 :
The rule is 3x+2 for x starts by 1, so:
3×1+2=5
3×2+2=8
3×3+2=11
3×4+2=14
3×5+2=17
Sequence2
The rule is 2x+3 forx starts by 6, so :
2×6+3=15
2×7+3=17
2×8+3=19
2×9+3=21
2×10+3=23
Ordered pairs
(5,15)
(8,17)
(11,19)
(14,21)
(17,23)
In cell D7, enter a formula without using a function that multiples the Monthly_Payment (cell D6) by the Term_in_Months (cell D5), and then subtracts the Loan_Amount (cell B8) from the result to determine the total interest.
In cell D8, enter a formula without using a function that adds the Price (cell B6) to the Total_Interest (cell D7) to determine the total cost.
1. To find the interest we will use = (D6*D5) - B8, 2. To find the total cost we will use = B6 + D7.
Here we are given the financial information of a firm and are required to give an appropriate formula for total interest and total cost
1.
Here we need to multiply D6 and D7 and subtract B8 from the result. We cannot use any function. Hence we will simply write
= (D6*D5) - B8
The bracket is not necessary but can be put s an added satisfaction that the said formula would multiply the cells first and then only will the loan amount would be subtracted.
2.
Similarly, for cell D8, we need to go to the formula bar and write
= B6 + D7
This will add the cells up to give us the total cost.
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Complete Question
In cell D7, enter a formula without using a function that multiples the Monthly_Payment (cell D6) by the Term_in_Months (cell D5), and then subtracts the Loan_Amount (cell B8) from the result to determine the total interest.In cell D8, enter a formula without using a function that adds the Price (cell B6) to the Total_Interest (cell D7) to determine the total cost(Image Attached)
Find the endpoints of the latus rectum of the parabola below.
Select the correct answer below:
(x + 3)² = -20(y + 1)
The endpoints of the latus rectum of the parabola equation is : f. The endpoints of the latus rectum are (-6, 9) and (-6, -15).
What is the latus rectum?Standard form of the equation of a parabola =y (x - h)² = 4p(y - k)
Where:
(h, k) = vertex
4p = distance between the vertex and focus
Comparing this with (x + 3)² = -20(y + 1) will gives us
(x + 3)² = -20(y + 1)
= (x - (-3))² = -20(y - (-1))
The vertex of the parabola is = (-3, -1)
4p = -20
p = -20/4
p = -5
The line that is perpendicular to the axis of symmetry (line y = -1) and passes through the focus (-3, -6) is known as the latus rectum of a parabola. The line y = - 6—the focus—and the directrix are separated by a distance of 4p = 20.
The vertex which is located at (-3, -1) is the latus rectum's midway. The latus rectum tend to has a length of 20 and passes through the points (-3, -1). Its endpoints must be located on the line x = -3 since it is perpendicular to the axis of symmetry.
The endpoints of the latus rectum are:
(-3, -1 - 10) = (-3, -11) and (-3, -1 + 10) = (-3, 9).
Therefore, the correct option is f.
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What is the area of this figure? 9 cm 2 cm 9 cm 7 cm Submit 4 cm 2 cm 3 cm Write your answer using decimals, if necessary. square centimeters 6 cm Work it out
Therefore , the solution of the given problem of area comes out to be the trapezium has a surface area of 39 square centimetres.
What does an area actually mean?Calculating how much space would be needed for fully covering its exterior will reveal its overall dimensions. The surrounding environment is considered while selecting a comparable product with a rectangular shape. The surface area of anything determines its overall dimensions. The number of sides connecting a cuboid's four trapezoidal shapes determines how much water it can contain.
Here,
We can use the formula for a trapezoid's area if we assume that the shape is a trapezoid with parallel sides that are 9 cm and 4 cm and a height of 6 cm.
=> A = (a + b)h/2
where h is the height, and a and b are the lengths of the parallel sides.
When we enter the values we have, we obtain:
=> A = (9 + 4)(6)/2
=> A = 13(3)
=> A = 39
Consequently, the trapezium has a surface area of 39 square centimetres.
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what is equivalent to 1 whole and 7/8
An equivalent fraction to 1 whole and 7/8 is 15/8.
What is improper fraction?A fraction that has the numerator higher than or equal to the denominator is said to be inappropriate. It is, in other words, a "top-heavy" fraction since the fraction represents a value greater than one full unit.
According to question:1 whole and 7/8 can be written as a mixed number, which is a combination of a whole number and a fraction:
1 whole and 7/8 = 1 + 7/8
To find an equivalent fraction, we can convert the mixed number to an improper fraction by multiplying the whole number by the denominator of the fraction, and then adding the numerator. The result is the numerator of the improper fraction, and the denominator stays the same:
1 + 7/8 = (1 × 8 + 7)/8 = 15/8
Therefore, an equivalent fraction to 1 whole and 7/8 is 15/8.
For instance, the improper fraction 7/4 results from the numerator's (7), which is greater than the denominator (4).
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Mr. Sanchez challenges his students to construct as many unique triangles as they can that have sides of 3 inches, 4 inches, and 8 inches. Which statement correctly describes how many triangles the students can construct with these side lengths?
A
They cannot construct any triangles with the given side lengths.
B
They can construct 1 unique triangle with the given side lengths.
C
They can construct 3 unique triangles with the given side lengths.
D
They can construct infinitely many unique triangles with the given side lengths.
Answer:
Step-by-step explanation:
The students cannot construct any triangles with the given side lengths because the sum of the two shorter sides of a triangle must always be greater than the longest side (i.e., the triangle inequality). However, in this case, 3 + 4 = 7, which is less than 8. Therefore, it is not possible to construct a triangle with sides of length 3, 4, and 8 inches.
So, the correct option is A - "They cannot construct any triangles with the given side lengths."
Suppose that the functions f and g are defined as follows.
Answer:
[tex]\dfrac{f}{g}(x) = \boxed{\dfrac{7}{x\left(x-3\right)}\\\\}[/tex]
Domain of [tex]\dfrac{f}{g}: \boxed{\:\left(-\infty \:,\:0\right)\cup \left(0,\:3\right)\cup \left(3,\:\infty \:\right)}[/tex]
Step-by-step explanation:
Given
[tex]f(x) = \dfrac{7}{x} , g(x) = x - 3[/tex]
[tex]\dfrac{f}{g} = \dfrac{f(x)}{g(x)} = \dfrac{7}{x} \div x - 3\\\\= \dfrac{7}{x} \times \dfrac{1}{x-3}\\\\ = \dfrac{7}{x\left(x-3\right)}[/tex]
To find the domain of
[tex]\dfrac{f}{g} = \dfrac{7}{x\left(x-3\right)}[/tex]
note that this function is defined everywhere in the range (- ∞, ∞) except for x = 0 and x = 3
At these two points, the function is undefined since the denominator becomes 0 and division by 0 is undefined
Therefore the domain consists of three parts expressed in inequality and interval forms
-∞ < x < 0 (-∞, 0)
0 < x < 3 (0, 3)
3 < x < ∞ (3, ∞)
Therefore the domain is obtained by combining these three intervals
- ∞ < x < 0 or 0 < x < 3 or x > 3
In interval notation with union:
[tex]\:\left(-\infty \:,\:0\right)\cup \left(0,\:3\right)\cup \left(3,\:\infty \:\right)[/tex] ANSWER
5. Complete the following table. (HINT: determine the reference angle and the quadrant of each angle.)
The given angles are 7π/4, 10π/3 & 510°.
Calculations for 7π/4(4th Quadarant)
sin(7π/4) = -1/√2
cos(7π/4) = 1/√2
tan(7π/4) = -1
cosec(7π/4) = -√2
cot(7π/4) = -1
sec(7π/4) = √2
Calculations for 10π/3(3rd Quadarant)
sin( 10π/3) = -√3/2
cos(10π/3) = -1/2
tan(10π/3) = √3
cosec(10π/3) = - 2/√3
cot(10π/3) = 1/√3
sec(10π/3) = -2
Calculations for 510°(2nd Quadarant)
sin( 510°) = 1/2
cos(510°) = -√3/2
tan(510°) = -1/√3
cosec(510°) = 2
cot(510°) = -√3
sec(510°) = -2/√3
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Solve for x:
|x|+8 = -3
Answer:
No Solution
Step-by-step explanation:
Because this solution deals with absolute value equations.
Solve for x. Round to the nearest tenth, if necessary
Using the tangent ratio, the value of x in the right triangle shown is calculated to the nearest tenth as: 2.6 units.
How to Find the Value of x Using the Tangent Ratio?The tangent ratio is part of the trigonometry ratios that is applied when solving a right triangle, and it is expressed as:
tan ∅ = length of the opposite side / length of the adjacent side.
We are given the following information from the image above:
Reference angle (∅) = 43 degrees
length of the opposite side = x
length of the adjacent side = 2.8
Plug in the values:
tan 43 = x/2.8
2.8 * tan 43 = x
x = 2.6 [to the nearest tenth]
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what could be the value of the point grafted only number line between 0.09 and 0.10
Please help me with this question
Answer:
A
Step-by-step explanation:
based on summation, this is an integral from 1 to 6
answer choice A makes sense since plugging in K value gives appropriate riemann sum
-(4-8) + (-3-7)−(−1+6) + (−2+5) =
Step by step
Answer:
Step-by-step explanation:
-4+8-3-7+1-6-2+5
4-10-5+3
-6-2
-8
Step-by-step explanation:
the negative sign changes to a positive sign so
( -12)+ (-10) -(-7)+(-7)
= -22
The mean pulse rate in beats per minute of a certain group of adult males is 76 bpm. The hypothesis test results in a p-value of 0.0075
State a conclusion about the null hypothesis
The conclusion on the null hypothesis is B. Reject H₀ because the P-value is less than or equal to a.
How to conclude on the null hypothesis ?It is posited that the mean pulse rate for a specific grouping of adult males equals 76 bpm as set forth by the null hypothesis. In its place, an alternative hypothesis suggests this figure does not reflect actuality.
At a given significance level identified by alpha = 0.05, rejection of the null hypothesis requires us to identify a P-value lesser than or equal to 0.05.
The P-value determined within the question happens to be below such a threshold at 0.0075, which results in the rejecting of the null hypothesis.
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PLEASE HELP ME QUICK!!!!
Answer:
B. $7.50
Step-by-step explanation:
We know profit or P-----P(n) where n is the quantity/number of the item) is the difference of the revenue-----R(n)-----and the cost-----C(n)
P(n) = R(n) - C(n)
Revenue is
the product of price (p) of the item and, number/quantity (n) of the item:R(n) = pn
Cost is a combination of
fixed costs (represented by a constant (c), as the business or Indvidual making a profit must pay a certain cost, even if they don't make any of their items) and, variable costs (this costs changes depending on the number/quantity of the item and is the product of the marginal cost (m) and the number/quantity (n) of the item)The cost function resembles a linear equation:
C(n) = mn + c
Since we're shown that P = 7.5n - (2.25n + 15), we know that R(n) must be R(n) = 7.5n and C(n) must be C(n) = 2.25n + 15
Thus, we know she charges $7.5 per necklace sold.
Let u = - 4i + j v = 4i - 2j and w = - 2j
Find the specified scalar or vector.
5u(3v - 4w)
The result of multiplying 5u by the difference between 3v and 4w is the vector -240i + 70j + 10.
In linear algebra, we often use scalars and vectors to perform various operations. Scalars are just ordinary numbers that can be used to multiply or divide vectors. On the other hand, vectors are quantities that have both magnitude and direction.
In this problem, we are given three vectors, u, v, and w, and we are asked to find the result of multiplying 5u by the difference between 3v and 4w.
First, let's calculate 3v - 4w. Since v = 4i - 2j and w = -2j, we can substitute these values to get,
3v - 4w = 3(4i - 2j) - 4(-2j)
= 12i - 6j + 8j
= 12i + 2j
Next, we need to find the scalar product of 5u and 12i + 2j. To find the scalar product of two vectors, we need to multiply the corresponding components and add up the products.
Therefore: 5u(3v - 4w) = 5u(12i + 2j)
= 5(-4i + j)(12i + 2j)
= -20i(12i) + 5i(2j) + 60j(i) - 10j(j)
= -240i + 10j + 60j + 10
= -240i + 70j + 10
So, the result of multiplying 5u by the difference between 3v and 4w is the vector -240i + 70j + 10.
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Please Help With Question Inside of the picture
The workers percentile score is given as follows:
69.15%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.The z-score for this problem is given as follows:
z = 0.5.
Hence the percentile score is of 69.15%, as z = 0.5 has a p-value of 0.6915.
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Trigonometry homework help
The distance between the installations is given as follows:
126.42 miles.
What is the law of cosines?The Law of Cosines is a trigonometric formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. It is also known as the Cosine Rule.
The Law of Cosines states that for any triangle with sides a, b, and c and angle B opposite to side b, the following equation holds true:
b^2 = a^2 + c^2 - 2ac cos(B)
The parameters for this problem are given as follows:
a = 143, c = 70, B = 62.1º.
Hence the distance b is obtained as follows:
b² = 143² + 70² - 2 x 143 x 70 x cosine of 62.1 degrees
b² = 15981.
[tex]b = \sqrt{15981}[/tex]
b = 126.42 miles.
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Question is done below. Just multiple sqrts inside of each other.
The solution to the prompt of multiple square roots is 5.
How to solve for the sum of the multiple square rootsTo obtain the sum of the multiple square roots, we need to first find the square of 30, sum it up in four places and find the square root of the last figure we obtained.
So this gives
√30 =5.47
5.47 + 5.47 + 5.47 + 5.47
= 21.88
=4.67 approximately 5
So. option 5 is the solution.
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Make a rap about why triangular pyramids are the best shape. No cursing. It must be appropriate and at least 1 minute long.
The rap about why triangular pyramids are the best shape is given below.
Why Triangular Pyramids are the best shape lyricsVerse 1:
Listen up, y'all, I'm here to spit some truth
About a shape that's often overlooked, but it's the truth
It's the triangular pyramid, and let me tell you why
It's the best shape out there, and that's no lie
Chorus:
Triangular pyramids, they're the way to go
Strong and sturdy, they're the best, you know
With their pointed tips and angled sides
They're the perfect shape, no need to hide
Verse 2:
When it comes to architecture, they're the top choice
Their shape is so versatile, you can't deny its voice
From ancient pyramids to modern buildings tall
The triangular pyramid can withstand it all
Chorus:
Triangular pyramids, they're the way to go
Strong and sturdy, they're the best, you know
With their pointed tips and angled sides
They're the perfect shape, no need to hide
Verse 3:
And let's not forget their mathematical prowess
Their angles add up to 180, no need to guess
With their faces all congruent, they're a sight to see
The triangular pyramid, it's the shape for me
Chorus:
Triangular pyramids, they're the way to go
Strong and sturdy, they're the best, you know
With their pointed tips and angled sides
They're the perfect shape, no need to hide
Outro:
So there you have it, folks, the triangular pyramid
It's the best shape out there, there's no need to forbid
From its strength to its geometry
The triangular pyramid, it's the shape for me!
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