The function that models the above behavior is given as:
f(x) = ACos(B(x + C)) + 6 ..... .......i
where x = 1 (that is January)
D (Average Snowfall) = 6.
Hence, the amplitude (A) is given as:
A = 6-1
= 5
What is a mathematical function?A mathematical function is a function comprising of different variables that represent different factors or events and the relationships between them.
Recall that in a year we have 12 months. Hence, P = 12
→ P = (2π) /.B → (2π)/B = 12 → B = π/6
Taking the values of A and B and plugging them in, we ahve:
F(x) = 5 cos (π/6(x + C)) + 6................ii
This means that in July, we'll have
x = 7 and f(x) = 1
Therefore,
1 = 5cos ((π/6) (7 + C) + 6 → 5 Cos ((π/6) (7 + C) → -5cos ((π/6) (7 + C)
= -1
→ ((π/6) (7 + C) = π
→ 7 + C = 6
→ C = -1
Taking equation ii, we have
F(x) = 5cos ((π6) (x -1)) + 6
F (x) > 10
Therefore
5cos ((π/6) (x-1) + 6 > 10
→ cos ((π/6) (x-1) + 6 > 4/5
→ (π/6) (x-1) > Cos⁻¹ (4/5)
(π/6) (x-1) < 0.6435 and
(π/6) (x-1) > 5.6397
→ x < 2.23 and x > 11.77
The interpretation is that upwards of ten inches of snow fall in January, February, November, and December.
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I don’t know how to start to go about this. Any suggestions would be greatly appreciated. How do I go about finding X?
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:x = 7° [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Since the two triangles are congruent, their corresponding sides and angles should be equal to one another too.
That means : Angle ADB = Angle CDB.
[tex]\large \textsf{Solve for x } [/tex]
[tex]\qquad \tt \rightarrow \:7x = 49 \degree[/tex]
[tex]\qquad \tt \rightarrow \:x = \cfrac{ 49 \degree}{7}[/tex]
[tex]\qquad \tt \rightarrow \:x = { 7 \degree}{}[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Dilate the figure by the scale factor. Then enter
the new coordinates.
(-3,-1)
A
(-1,-4) C
B(2,-2)
K = 5
A' ([?], [ ])
B' ([ ], [])
C' ([ ], [ ]) (pls help I will mark BRAINLIEST)
The triangle ABC was dilated with a scale factor of 5 to form a figure with new coordinates at A'(-15, -5), B'(10, -10) and C'(-5, -20).
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
The triangle ABC was dilated with a scale factor of 5 to form a figure with new coordinates at A'(-15, -5), B'(10, -10) and C'(-5, -20).
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A normal score is the expected z-score of a data value, assuming the distribution of the random variable is normal. Is this statement true or false?.
The given statement about normal score that it is expected z score of a data value is true.
Given A statement that a normal z score is the expected z score of a data value, assuming the distribution of the random variable is normal.
We have to tell whether the given statement is true or false.
In z test the z score or standard score is the number of standard deviations by which the value of a raw score is above or below the mean value of what is observed or measured.
A normal distribution is arrangement of a data set in which most values cluster in the middle of the range and the rest taper off symmetrically toward either extreme.
A random variable is a variable which is identified without following any criteria.
A Z test is any statistical test for which the distribution of the test statistic under the null hypothesis ca be approximated by a normal distribution.
Hence the given statement about normal score is absolutely true.
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A ladder is 7 feet 6 inches tall. How tall is it in inches?
Answer:
90 inches tall
Step-by-step explanation:
7x12=84
84+6=90
Draw a graph of the line that contains the given point and
(-3,0); m =
1
8
Answer:
Step-by-step explanation:
These two figures shown are congruent. Which statement is true?
Answer:
The answer is C
Step-by-step explanation:
First if you look at the problem you will notice the triangles aren't the same size so if it's neither rotation nor translation then the shapes do not
The diagram below shows the partial construction of which shape?
Answer:
im gonna say circle or even a hour glass
Step-by-step explanation:
The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary Prove that the height of the tower is 6 m.
Kindly help!
Answer:
Proof explained below
Step-by-step explanation:
Tan trigonometric ratio
[tex]\sf \tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleDraw a diagram to help visualize the scenario (see attached).
If the angles are complementary, their sum is 90°.
Therefore, let one of the angles be [tex]x[/tex] and the other angle be [tex]90^{\circ}-x[/tex].
Use the tan trig ratio to create two equations with the missing side length.
Right triangle ACD
Given:
[tex]\theta = x[/tex]O = CD (tower)A = 9 mSubstituting the given values into the tan trig ratio:
[tex]\implies \tan (x)= \dfrac{\textsf{CD}}{9}[/tex]
Right triangle BCD
Given:
[tex]\theta = 90^{\circ} - x[/tex]O = CD (tower)A = 4 mSubstituting the given values into the tan trig ratio:
[tex]\implies \tan (90^{\circ} - x)= \dfrac{\textsf{CD}}{4}[/tex]
[tex]\textsf{As }\:\tan(90^{\circ} - x)= \cot (x):[/tex]
[tex]\implies \cot(x)= \dfrac{\textsf{CD}}{4}[/tex]
[tex]\implies \dfrac{1}{\tan(x)}= \dfrac{\textsf{CD}}{4}[/tex]
[tex]\implies \tan(x)= \dfrac{4}{\textsf{CD}}[/tex]
Therefore, the two equations are:
[tex]\textsf{Equation 1}: \quad \tan (x)= \dfrac{\textsf{CD}}{9}[/tex]
[tex]\textsf{Equation 2}: \quad \tan(x)= \dfrac{4}{\textsf{CD}}[/tex]
Substitute one equation into the other and solve for CD:
[tex]\implies \sf \dfrac{CD}{9}=\dfrac{4}{CD}[/tex]
[tex]\implies \sf CD \cdot CD= 4 \cdot 9[/tex]
[tex]\implies \sf CD^2=36[/tex]
[tex]\implies \sf CD=\sqrt{36}[/tex]
[tex]\implies \sf CD= \pm 6[/tex]
As distance cannot be negative, CD = 6 m only, thus proving that the height of the tower is 6 m.
how to reduce this 25/35 please please help explain !!!!!!
Answer:
5/7
Step-by-step explanation:
Note that the highest common factor to the numbers are 5. Therefore, to simplify will be:
= 25/35
= 5/7
check all that apply.
if secØ= 13/12, then:
Based on trigonometric formulas, we can find that the options that applies to the given trigonometric relationship are tan θ = 5/12 and cos θ = 12/13.
How to find the exact form of trigonometric functions
There six trigonometric functions, which are related by a group of expressions, which will be used in this question:
[tex]\cos \theta = \frac{1}{\sec \theta} = \frac{12}{13}[/tex]
[tex]\sin \theta = \sqrt{1 - \cos^{2}\theta}[/tex]
[tex]\sin \theta = \sqrt{1 -\left(\frac{12}{13} \right)^{2}}[/tex]
[tex]\sin \theta = \frac{5}{13}[/tex]
[tex]\csc \theta = \frac{1}{\sin \theta} = \frac{13}{5}[/tex]
[tex]\tan \theta = \sqrt{\sec^{2}\theta - 1}[/tex]
[tex]\tan \theta = \sqrt{\left(\frac{13}{12} \right)^{2}-1}[/tex]
[tex]\tan \theta = \frac{5}{12}[/tex]
Based on trigonometric formulas, we can find that the options that applies to the given trigonometric relationship are tan θ = 5/12 and cos θ = 12/13.
Remark
The statement is incomplete. Complete form is shown below:
Check all that apply:
If sec θ = 13/12, then:
a) sin θ = 12/13
b) tan θ = 5/12
c) cos θ = 12/13
d) csc θ = 12/13
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A ticket costs £656
Last year it cost £640
What percentage increase is this ?
Answer:
2.5%
Step-by-step explanation:
656 / 640 = 1.025
1.025 into percent is 102.5%
102.5% - 100% = 2.5
640 + 2.5% of 640 = 656
BOOM
The required value of increase in price is 2.5%.
What is percentage?A percentage is a value that indicates 100th part of any quantity.
A percentage can be converted into a fraction or a decimal by dividing it by 100.
Given that,
The cost of ticket at present is £656.
Its cost last year was £640.
Then, the difference between the costs is given as,
656 - 640 = £16
Now, the increase in percentage can be found by taking the ratio of the difference to the last year price and multiplying it by 100 as below,
Percentage increase = 16/640 × 100%
= 2.5%
Hence, the percentage increase in price is 2.5%.
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Expand and combine like terms. (5a^3 - 2)(5a^3+2)
Answer:
[tex]25a^6-4[/tex]
Step-by-step explanation:
So if you look at the equation, you'll notice it's being multiplied by it's conjugate which can be expressed as: x+a and x-a. See how only the sign changes? Well if remember the differences of squares, it looks like that, because it is. Essentially the difference of squares says that: [tex]a^2-b^2=(a-b)(a+b)[/tex]. So expanding this out will result in [tex](5a^3)^2-(2)^2[/tex] which simplifies to: [tex]25a^6-4[/tex]. If you're confused on how I got 25a^6. Try to think of a^3 as three a's rather than simply an exponent. and since it has a coefficient of 5. 5a^3 is the same as (5 * a * a * a). Now if you square this you have (5 * a * a * a) * (5 * a * a * a). So if you group like terms you'll end up with 6 a's being multiplied by each other (which can be expressed as a^6) and 5 * 5 which is 25.
The multiplication can be transformed into the difference of squares using the rule:(a−b)(a+b)=a²-b² . Gets the square of 2.
(5a³)²-4
Expand (5a³)².
5² (a³)² -4
To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.
5²a⁶-4
25a⁶-4 ====> Answer
{ Pisces04 }
the intersection of a line and a triangle can be
Answer:
nothing
a point
a segment
Step-by-step explanation:
nothing
a point
a segment
Friar laurence: these violent delights have violent ends, and in their triumph die, like fire and powder, which, as they kiss consume: the sweetest honey is loathsome in his own deliciousness and in the taste confounds the appetite: therefore love moderately; long love doth so; too swift arrives as tardy as too slow. what do the oxymoron and paradox in this excerpt illustrate about love? only love has the ability to overcome obstacles. nothing good ever comes from truly loving another. loving with restraint is the key to long-lasting love. true love causes one to lose the ability to reason
Seriousness is what is being portrayed by the oxymoron and paradox in this excerpt.
Simply put, a serious relationship is one in which you are fully committed to your partner. You are completely open and honest with each other. You trust each other deeply. And you are on the same page together not only from your values and ethics perspective, but also from your future perspective.
Monks do not claim that "moderate" love is more wise than fleeting love, but they guide Romeo to understand the reason for his wisdom and explore their relationship.
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helpp me plss! geometry, how to find x. i kinda need step by step for better understanding, if possible, too pleaseee
Answer:
Step-by-step explanation:
Write the equation of the line that passes through the points (-9,-9)(−9,−9) and (6,-7)(6,−7). Put your answer in fully simplified form, unless it is a vertical or horizontal line.
2x-15y = 117 is the simplified form of the equation.
Equation : In a mathematical sentence, if two expressions are present in left and right side of an equal sign, then the mathematical sentence is called an equation.
If, a, b, c be integers and x is x-intercept & y is y-intercept, then ax+by=c is called equation of line.
Given that, the equation of the line that passes through the points (-9,-9)(−9,−9) and (6,-7)(6,−7).
Now, (-9,-9) & (6, -7) have a line through them with slope = (-9+7)/(-9-6) = 2/15
Therefore, (y+7) = 2/15×(x-6)
⇒ y+7 = 2x/15 - 4/5
⇒ y = 2x/15 - 4/5 - 7
⇒ y = 2x/15 -39/5
This is the equation in slope intercept form.
Multiplying the equation with 15, we get,
⇒ 15y = 2x-117
⇒ 2x-15y = 117 , which is the simplified form of the equation.
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Please help! If Paul's average speed is 5 km per hour, how long would it take Paul to walk 6.25 km?
a.)
An hour and 30 minutes
b.)
An hour and 15 minutes
c.)
An hour and 10 minutes
d.)
An hour and 25 minutes
Find the value of x.
A) 71
B) 72
C) 73
D) 75
Answer:
The answer is c) 73
Step-by-step explanation:
The angle 146 and (-39 + x) lie on the same line, so that means their sum is 180 degrees because a straight line has 180 degrees.
180 = 149 - 39 + x
180 = 107 + x
180 - 107 = x
73 = x
Answer:
73
Step-by-step explanation:
The two angles form a straight line and a straight line is 180 degrees
-39+x + 146 = 180
Combine like terms
107 +x = 180
Subtract 107 from each side
107+x-107 = 180-107
x =73
A scuba diver is 30 ft below sea level. Which of the following best describes this situation?
1. |30|
2. |-30|
3. -30
4. ±30
Answer:
-30
Step-by-step explanation:
The scuba driver is below the sea and ground level which is 0 ft, and he dives down 30 ft so it should be negative.
Hope it helps!
help me please ty ty
Answer:
A
Step-by-step explanation:
(f - g)(x)
= f(x) - g(x)
= 3x² + 4x - 6 - (6x³ - 5x² - 2) ← distribute parenthesis by - 1
= 3x² + 4x - 6 - 6x³ + 5x² + 2 ← collect like terms
= - 6x³ + 8x² + 4x - 4
how to solve this pleaseee
Answer:
if you divide 10 by 8 it should be 10/8 so a
Hope This Helps!!!
Answer: A
Step-by-step explanation: Step 3 is incorrect as it should be 10/8 (or 5/4 simplified.) When we have 8x = 10, we are looking at what number "x" multiplied by 8 gives 10. Meaning we need to have 8(?) = 10. So, to find out what x is, we just divide by 8 from both sides. Since 8x/8 cancels out and becomes just x, we get x = 10/8 since we are dividing 10 by 8. We get 5/4 simplified or 10/8 unsimplified.
Please mark my answer as brainliest if it was helpful!
-6 + 6 how do you solve it
Answer:
0.
Step-by-step explanation:
-6+6=0 because any negative number plus the same positive number cancels each other out.
The cylinder below has a volume of 785 Feet cubed, and the cone has a volume of 314 Feet cubed.
A cylinder has a volume of 78.5 feet squared and a cone has a volume of 78.5 feet squared.
Which explains which figure has the greater height?
The cylinder has a greater height because the bases are the same, but the cylinder has a greater volume.
The cylinder has a greater height because the volume of the cylinder is greater than twice the volume of the cone.
The cone has a greater height because the bases are the same, but the volume of the cylinder is less than 3 times the volume of the cone.
The cone has a greater height because the bases are the same, but the volume of the cylinder is less than 4 times the volume of the cone.
The cone has a greater height because the bases are the same, but the volume of the cylinder is less than 3 times the volume of the cone.
What is the relationship between the cone and the cylinder?The volume of a cylinder is three times that of a cone.
Volume of a cylinder = πr²h
Volume of a cone = 1/3πr²h
π = 22/7r = radiush = heightIf the height of the cylinder would be greater than that of the cone, the volume of the cylinder should be at least 3 times that of the cone.
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slope of [3,5] and [0,11]
\[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{What is the formula for finding slope?}[/tex]
[tex]\mathbf{\dfrac{y_2 - y_1}{x_2 - x_1} = slope}[/tex]
[tex]\huge\textbf{Often people understand it better by:}[/tex]
[tex]\mathbf{\dfrac{rise}{run} = slope}[/tex]
[tex]\huge\textbf{Answering the given question:}[/tex]
[tex]\mathbf{y_2 \rightarrow 11}\\\\\\\mathbf{y_1 \rightarrow 5}\\\\\\\mathbf{x_2 \rightarrow 0}\\\\\\\mathbf{x_1 \rightarrow 3}[/tex]
[tex]\huge\textbf{Now, that we have that information out}\\\huge\textbf{the way, we can answer the question.}[/tex]
[tex]\huge\textbf{Your equation should look like this:}[/tex]
[tex]\mathbf{\dfrac{11 - 5}{0 - 3} = slope}[/tex]
[tex]\huge\textbf{Solving for the answer:}[/tex]
[tex]\mathbf{\dfrac{11 - 5}{0 - 3} = slope}[/tex]
[tex]\mathbf{\rightarrow \dfrac{6}{-3} = slope}[/tex]
[tex]\mathbf{\rightarrow 6 \div -3 = slope}[/tex]
[tex]\mathbf{\rightarrow -2}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\textsf{S}\frak{lope \rightarrow -2}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Find x.
special 17
A. 22
B. 113√2
C. 116√2
D. 33
The value of x in the triangle is (a) 22
How to solve for x?The complete question is in the attached image.
From the attached image of the triangle, we have:
[tex]\sin(45) = \frac{x}{22\sqrt 2}[/tex]
Evaluate sin(45)
[tex]\frac{1}{\sqrt 2} = \frac{x}{22\sqrt 2}[/tex]
Solve for x
[tex]x = \frac{22\sqrt 2}{\sqrt 2}[/tex]
Divide
x = 22
Hence, the value of x is (a) 22
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URGENT: statistics: A researcher wishes to estimate the percentage of adults who support abolishing the penny what size sample should be obtained if he wishes the estimate to be within three percentage points with a 95% confidence if he:
A: uses a previous estimate of 26%?
B: he does not use any prior estimates?
Using the margin of error for the z-distribution, the sample sizes are given as follows:
a) 822.
b) 1068.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.We have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
Item a:
The estimate is of [tex]\pi = 0.26[/tex], hence we solve for n when M = 0.03.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.96\sqrt{\frac{0.26(0.74)}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.96\sqrt{0.26(0.74)}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.26(0.74)}}{0.03}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.26(0.74)}}{0.03}\right)^2[/tex]
n = 821.2
A sample of 822 is needed.
Item b:
No prior estimate, hence [tex]\pi = 0.5[/tex].
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.96\sqrt{0.5(0.5)}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.5(0.5)}}{0.03}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.5(0.5)}}{0.03}\right)^2[/tex]
n = 1067.11
A sample of 1068 is needed.
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Which part of the proof does the fourth statement and reason represent?
Given: AB ≅ BC
BC ≅ EF
Prove: EG = AB + FG
A line contains point A, B, C.
A 2-column table has 6 rows. Column 1 is labeled Statements with entries line segment A B is-congruent-to line segment B C, line segment B C is congruent to line segment E F, line segment A B is-congruent-to line segment E F, A B = E F, E G = E F + F G, E G = A B + F G. Column 2 is labeled reasons with entries given, given, transitive property, definition of congruent segments, segment addition, and substitution.
It is part of the given information.
It is part of the argument.
It is the conclusion.
It is an assumption.
Mark this and return
The proof does the fourth statement and reason represent It is an argument.
AB≅ BC and BC≅EF
What is the transitive property?a = b and b = c then, a =c
ABC is the side of the triangle
⇒AB≅EF
AB = EF [def of segment]
By Segment Addition Postulate states that given two points A and C, and a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation
AB + BC = AC.
Since, the line segment EG, F lies on the line segment;
then, by segment addition postulates we have;
EG = EF + FG
By substitution AB=EF
⇒ EG = AB + FG hence proved!
In the fourth statement, the reason is: It is an argument.
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Please help, math question below...
The value of x is 3.711 yd
What is Heron's Formula?area = √(s * (s - a) * (s - b) * (s - c))
where
s is the semi perimeter - half of triangle perimeter:
s = (a + b + c) / 2
Using Heron's Formula
area = √(s * (s - a) * (s - b) * (s - c))
area = √(14* (15- 6) * (15 - 14) * (15 - 10))
area = √(14* 9 * 1 * 5))
area = √ 630
area = 25.981 yd²
Now,
area of triangle= 1/2 * b * h
25.981 = 1/2 * 14 *h
51.962 = 14h
h= 3.711 yd
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what is the probability that a positive integer less than 100 picked at random has all distinct digits
the probability that a positive integer less than 100 picked at random has all distinct digits is 90.
He has 99 positive integers less than 100.
The integers that do not have all distinct digits have the same digit twice.
11, 22, 33, 44, 55, 66, 77, 88, 99
There are 9 integers that do not have distinct digits, therefore there are 99-9 integers that do.
Probability is without a doubt how probable something is to show up. whenever we are uncertain about the final results of an occasion, we can talk about the possibilities of sure outcomes and how probable they are. The analysis of events governed by opportunity is referred to as records.
A chain of moves in which the results are usually unsure. The tossing of a coin, selecting a card from a deck of playing cards, throwing a cube. occasion. it is a single final results of an experiment. Getting a Heads whilst tossing a coin is an event.
Simple probability is the calculation of an outcome or the chance of an event ever taking place. coverage companies use possibility statistics to determine the possibilities of having to pay out a declare. A simple chance is calculated by way of dividing a particular outcome through all of the feasible outcomes.
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Solve Triangle DEF. - Math
Answer:
[tex]p = 52.942259755149776[/tex]
Step-by-step explanation:
This is basic trigonometry.
[tex] \cos(39) = \frac{e}{22} [/tex]
[tex]e = \cos(39) \times 22[/tex]
[tex] \sin(39) = \frac{d}{22} [/tex]
[tex]d = \sin(39) \times 22[/tex]
And finally perimeter (p):
[tex]p = 22 + e+ d[/tex]