Answer:
x=
Step-by-step explanation:
There are 2 ways to do this.
4(3x-9)=63; 12x-36=63; 12x=99; x=8. Or: (3x-9)+(3x-9)+(3x-9)+(3x-9)=63; 12x-36=63; 12x=99; x=
Find the exact value of cosine (alpha beta) given sin alpha = two-fifths for alpha in quadrant ii and cosine beta = one-third for beta in quadrant iv. startfraction 8 startroot 2 endroot startroot 15 endroot over 15 endfraction startfraction 4 startroot 2 endroot startroot 21 endroot over 15 endfraction startfraction 4 startroot 2 endroot minus startroot 21 endroot over 15 endfraction
The exact value for cos (α+β) is √21/25- 4√2/15, for the given quadrants II and IV
we know that cos (α+β)) = cos α cos β - sin α sin β, we are given the values of sin α=2/5 and cos β= 1/3 ( both are positive for quadrant 2 and 3). Since we know cos² a + sin² a = 1
for α, cos² α + sin² α = 1
=> cos² α = 1 - sin² α
=> cos² α = 1 - 4/25
=> cos α = √21/25
same for β, cos² β + sin² β = 1
=> sin² β = 1 -cos² β
=> sin² β = 1 -1/9
= 8/9
=2√2/3
substituting the known values in the above formula for cos (α+β)
=>cos α cos β - sin α sin β
=√21/25 *1/3- 2/5*2√2/3
=√21/25- 4√2/15
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Answer:
d. [tex]\frac{4\sqrt{2}-\sqrt{21} }{15}[/tex]
Step-by-step explanation:
The lovely person in the comments was correct on Edge so i decided to put it as an answer in case anyone was looking for it!
Have a lovely day!
one angle of a parallelogram is 120 degrees, and two consecutive sides have lengths of 8 inches and 15 inches. what is the area of the parallelogram? express your answer in simplest radical form.
The area of parallelogram with "one angle of a parallelogram is 120 degrees, and two consecutive sides have lengths of 8 inches and 15 inches" is 60√3 inch².
What is parallelogram?A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal). A parallelogram with all right angles is known as a rectangle, and a quadrilateral with equal sides is known as a rhombus. A parallelogram is a geometric shape with sides that are parallel to one another in two dimensions. It is a type of polygon with four sides (also known as a quadrilateral) in which each parallel pair of sides is the same length.
Here,
A parallelogram has adjacent angles that add up to 180 degrees.
Since one angle of parallelogram is 120°.
240+2x=360
2x=120
x=60
The other will be 60°
The area of parallelogram= lh
l=15 inch
h=b(sin 60°)
=8*√3/2
h=4√3 inch
area of parallelogram= 15*4√3
= 60√3 inch²
The parallelogram's area is 60√3 inch² when "one angle of a parallelogram is 120 degrees, and two consecutive sides have lengths of 8 inches and 15 inches."
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how many ways are there to seat four of a group of ten people around a circular table where two seatings are considered the same when everyone has the same immediate left and immediate right neighbor?
The number of ways which are there to seat four of a group of ten people around a circular table is 1260.
To choose 4 people from a group of ten we need to count such people, which can be found using 10! / 4! × (10-4)! , after solving this we need to multiply 3! by this to get the desired answer. This is done because for that 4 people to sit in a circle, the possibilities for n people to sit around a circle is (n-1)! , and since n here is 4 the possibilities will also be (4-1)! which is 3! here.
Hence the final answer: 3! × 10! / 4! × (10-4)! = 1260
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Show how you would solve the problem.
a^2 (squared) + b^2(squared) = c squared
Using the Pythagorean Theorem and the given values, we can solve for c.
a^2 + b^2 = c^2
12^2 + 16^2 = c^2
144 + 256 = c^2
400 = c^2
√400 = √c^2
c = 20
a deli bar offers sandwiches with four types of bread, three types of cheese and four types of meat. how many different sandwich combinations are possible?
Exactly one type of meat required = 5 choices
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.acc to our question-
Exactly one type of meat required = 5 choicesAny number (0–5) of types of meat allowed: 2^5 (ie. binary, eat type of meat is either ‘on’ or ‘off’At least on type of meat required 2^5 - 1 (remove the zero choice)Do similarly for bread and cheese and number of sandwiches combinations =bread combinations X cheese combinations X meat combinationslearn more about probability click here:
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graph y =-x+7
pls help i was gone when we did this
the slop is -1 and the y-intercept is (0,7)
What is vertex?An element of a line is a line segment.A line segment that can be extended endlessly is known as a ray.An angle is created when two line segments or rays cross one another.A vertex is created by definition whenever two lines come together to produce an angle.Thus, we can state that a vertex is formed when two line segments or rays intersect.acc to our question-
plot a point on the y- axis line at 7. Then go right 7 units and down 7 unitsHence,the slop is -1 and the y-intercept is (0,7)
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in a one-tailed hypothesis test (lower tail), the z test statistic is determined to be -1.9. the p-value for this test is
The p-value for this z test statistic is equal to 0.0287.
What is a null hypothesis?A null hypothesis (H₀) can be defined the opposite of an alternate hypothesis (H₁) and it asserts that two (2) possibilities are the same.
How to calculate value of the z test statistic?The z test statistic can be calculated by using this formula:
[tex]t=\frac{x\;-\;u}{\frac{\delta}{\sqrt{n} } }[/tex]
Where:
x represents the sample mean.μ represents the mean.σ represents the standard deviation.n represents the number of hours.In this scenario, the z test statistic for a one-tailed hypothesis test (lower tail) is equal to -1.9. Therefore, by using a t-distribution and z-score calculator for a normal distribution, the p-value for this test is given by:
P-value = P(t > -1.9)
P-value = 0.0287.
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tickets for a community theater cost $11 for each main floor seat and $6 for each balcony seat. there are 400 seats on the main floor, and these seats were sold out for the evening performance. the total revenue from ticket sales was $5060. how many balcony seats were sold?
The number of balcony seats sold is 110
Finding Unknown quantity using Linear equation:
The linear equation is an equation that is used to find an unknown quantity or an unknown number. In this, we will represent the Uknown value with a variable like x, y, z, etc.
Here we have
Tickets for a community theater cost $11 for each main-floor seat
and $6 for each balcony seat.
There are 400 seats on the main floor, which are sold out for the evening performance
The total revenue from ticket sales was $5060.
Here we don't know the number of balcony seats.
Let us assume that number of balcony seats = x
Then total revenue = 400(11) + 6x = 5060
=> 4400 + 6x = 5060
=> 6x = 5060 - 4400
=> 6x = 660
=> x = 110
Therefore,
The number of balcony seats sold = 110
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HELPPPP MEEEEE PLEASE!!!!
50 points!!! Are rational functions and hyperbolas the same? Please explain why or why not.
Find value of x. Show steps.
you and your friend were studying, and you left your cell phone either in the computer lab or in the cafe (these were the only two places you visited). you think that with probability 0.4 it was left in the computer lab, because you always take it out of your backpack there, otherwise, it was left in the cafe. if you left the phone in the computer lab, the probability that someone stole it is 0.3. in the cafe, the probability that someone stole it is twice that of
There is a 0.48 percent chance that your phone will not be found and will therefore be stolen.
Define the law of total probability?A fundamental statistician's rule governing conditional and marginal probabilities is known as the Total Probability Rule/Law of Total Probability. According to the rule, if the chance of an occurrence is uncertain, it can be derived using the probabilities of numerous different instances that have already transpired.Let P(S|L) represent the likelihood that your phone was stolen if you left it in the computer lab.
Let P(S|C) indicate the likelihood that your phone was stolen if you left it at the cafe.
The likelihood that your phone will be stolen can be determined using law of total probability by:
P(S) = P(S|L)P(L) + P(S|C)P(C)
= 0.3 * 0.4 + 0.6 * 0.6
= 0.12 + 0.36
P(S) = 0.48
Therefore, there is a 0.48 percent chance that you won't find your phone and that it was stolen.
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what is 5(-4)+(-6)+2(-2)
Answer:
-30
Step-by-step explanation:
Distribute
5 x -4= -20 2 x -2= -4
-20+(-6)+(-4)
Add together
-20 + -6= -26
-26 + (-4)
Add again
-26 + -4= -30
-30
Which histogram shows a left-skewed distribution? A. A bar chart plots data points (1, 1), (2, 4), (3, 1), (4, 2), (5, 3), (6, 4) and (7, 3). B. A bar chart plots data points (1, 1), (2, 2), (3, 3), (4, 4), (5, 3), (6, 2) and (7, 1 point 5). C. A bar chart plots data points (1, 3), (2, 4), (3, 2), (4, 2), (5, 1), (6, 1) and (7, 1). D. A bar chart plots data points (1, 4), (2, 2), (3, 4), (4, 3), (5, 1), (6, 1) and (7, 2).
The histogram that shows a left-skewed distribution is given by:
A. A bar chart plots data points (1, 1), (2, 4), (3, 1), (4, 2), (5, 3), (6, 4) and (7, 3).
What is an histogram?An histogram is a graph that shows the number of times each element x was observed on the data-set.
Hence, the meaning of a point (x,y) on the histogram is given as follows:
Observation x was observed y times on the data-set.
The skewness of a distribution can be explained as follows:
Left-skewed: The higher values are the ones that are observed the most in the data-set.Symmetric: The middle values are the ones that are observed the most in the data-set.Right-skewed: The lower values are the ones that are observed the most in the data-set.Hence in this problem, for the left-skewed histogram, we want an "increasing" histogram, hence option A is correct.
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A shopkeeper buys a dress for 40$ she sells it for 48$
Workout the percentage increase in the price of the dress.
Please help now
a right cylindrical tank is full of water. the tank has a radius of 10 inches. how fast is the height of water in the tank changing if the water is being drained at 34 cubic inches per hour?
The answer is 3/25π m/h.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
With related rates, we need a function to relate the 2 variables, in this case it is clearly volume and height. The formula is:
v=πr²hThere is radius in the formula, but in this problem, radius is constant so it is not a variable. We can substitute the value in:V=π(5m)2hby solving the equation with the given valueshence,The answer is 3/25π m/h.
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an airplane is preparing to land at an airport. it is 48,000 feet above the ground and is descending at the rate of 3,200 feet per minute. at the same airport, another airplane is taking off and will ascend at the rate of 2,800 feet per minute. when will the two airplanes be at the same altitude and what will that altitude be?
Answer:
After 8 minutes ; altitude = 22,400 feet
Step-by-step explanation:
s1 = 2800t
s2 = -3200t + 48 000
2800t = -3200t + 48 000
28t = -32t + 480
7t = -8t + 120
7t + 8t = 120
15t = 120
15/15 t = 120/15
t = 8 minutes
s = 8 * (2800) = 22400 feet
determined whether the graph on the right is that of a function by using the vertical-line test. If it is, use the graph to find the following. the domain and range Does the graph represent a function? Choose the correct answer below A No because no horizontal line can intersect the graph in more than one point No because no vertical line can intersect the graph in at most one point. OC Yes, because every vertical line can intersect the graph in more than one point OD. Yes, because every vertical line can intersect the graph in at most one point DE Yes because every horizontal line can intersect the graph in at most one point OF No. because no horntal line can intersect the graph in at most one point. OG Yes, because every horizontal line can intersect the graph in more than one point. 04. No, because no vertical time can intersect the graph in more than one point.
x - intercept is at ( 1, 0 ) graph intersect at x = 1 .
What are intercepts?
The x-intercept and y-intercept are the points at which a line crosses the x- and y-axes, respectively.An intercept is the location of the intersection of two axes in a graph. The term "x-intercept" specifically refers to this one.The x-axis and y-axis are intersected by two intercepts, P(2,0) and Q(0,3), respectively. => 3x + 2y – 6 = 0, Consequently, the line's equation is 3x + 2y - 6 = 0.Domain - values of x on x -axis taken by function
- ( 0,5 )
Range = values of y on y -axis taken by function
= (- ∞ , 2 )
= ( as, x ⇒ 0 then graph goes below
b) x - intercept is at ( 1, 0 ) graph intersect at x = 1
no y - intercept is there .
c) graph is not symmetric .
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verify by drawing a diagram if the median and altitude of an isosceles triangle can be the same
The statement "The median and altitude of an isosceles triangle can be same", is verified by drawing diagram
The statement is
"The median and altitude of an isosceles triangle can be same"
Draw an isosceles triangle ABC with BD = CD,
Draw a line segment AD perpendicular to the side BD
Here AD is the height of the triangle which is the altitude of the triangle
From the figure we can see that the length of BD = length of CD
Where D is the mid point of the line BD.
Therefore the line AD is the median of the triangle
Hence, The statement "The median and altitude of an isosceles triangle can be same", is verified by drawing diagram
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Find h in the parallelogram shown.
h= ? ft
The required value of h is 5.29 ft in the parallelogram shown.
What is Parallelogram?A parallelogram is defined as a special type of quadrilateral that has both pairs of opposite sides parallel and equal.
As per the given figure, the dotted lines create a triangle, and the hypotenuse of that triangle is the opposite base of the parallelogram, indicating that it is likewise 8 feet long.
The base of the newly made triangle is one of the parallelogram's diagonals, which is 6 feet long.
According to Pythagorean's theorem, we have
h² + 6² = 8²
h² + 36 = 64
h² = 28
h = √28
h = 5.29
Thus, the required value of h is 5.29 ft.
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Answer:
4
I did the i-ready, hope this helps! :)
a study is designed to test whether there is a relationship between natural hair colors and eye colors. if a significant chi-square value is obtained, this suggests that:
Using the concepts of hypothesis test, we got that something is happening that wasn’t accounted for as a result when a significant chi-square value is obtained.
A chi-squared test (symbolically represented as χ2) is basically the data analysis on the basis of the observations of a random set of variables. Usually, it is the comparison of two statistical data sets. This test was introduced by Karl Pearson in the 1900 for categorical data analysis and distribution. So it was mentioned as a Pearson’s chi-squared test.
The chi-square test is actually used to estimate how likely the observations that are made would be, by considering assumption of the null hypothesis as true.
Hence, a study is designed to test whether there is a relationship between natural hair colors and eye colors, in that case if a significant chi-square value is obtained it suggests that something is happening that wasn’t accounted for .
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Two cars start at the same point and simultaneously drive in opposite directions.
The speed of the first car is s miles per hour. The speed of the second car is 5
miles per hour less than the speed of the first car.
How far apart are the cars 1.5 hours after they start moving?
Answer:
3s - 7.5 milesStep-by-step explanation:
GivenThe speed of car1 is s,The speed of car2 is 5 less than s,Time is 1.5 hrs.SolutionDistance equation:
Distance = speed * timeIf cars move in opposite directions their speeds add up, then the distance between them after 1.5 hours is:
(s + s - 5)*1.5 = (2s - 5)*1.5 = 3s - 7.5Answer:
After 1.5 hr, they are 3s - 7.5 mi away.
Step-by-step explanation:
Forming the expression,
→ 1.5 × (s + s - 5)
Now the required solution will be,
→ 1.5 × (s + s - 5)
→ 1.5 × (2s - 5)
→ 1.5(2s - 5)
→ 3s - 7.5
Hence, answer is 3s - 7.5 miles.
what is the smallest positive integer $n$ such that the rightmost three digits of $n!$ and $(n 1)!$ are the same?
The smallest positive integer n will be 10 .
To find : the smallest positive integer n such that the rightmost digits of n ! and ( n + 1 ) ! are same .
Since ,
putting n = 10 gives
n ! = 10 ! = 3628800
and ( n + 1 ) ! = 39916800
Last three digits ( rightmost digits ) ie. 800 are same .
Hence , n = 10 is the required answer ,
Therefore , the smallest positive integer is n = 10 such that the rightmost digits of n ! and ( n + 1 ) ! are same .
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the count in a bacteria culture was 800 after 20 minutes and 1700 after 40 minutes. assuming the count grows exponentially, what was the initial size of the culture?
The culture starts out with 39 members.
Given that;
After 20 minutes and 40 minutes, a bacteria culture had an 800 and 1700 count, respectively.
To get exponential growth;
We can get growth with an exponential function,
F(t) = A₀[tex]e^k^t[/tex]
Here, k is the growth constant and A₀ is the initial amount of bacteria.
Let;
800 = A₀[tex]e^2^0^k[/tex] → (I)
1700 = A₀[tex]e^4^0^k[/tex] → (II)
From (I) and (II);
1700 / 800 = A₀[tex]e^4^0^k[/tex] / A₀[tex]e^2^0^k[/tex]
17/8 = [tex]e^2^0^k[/tex]
For the above equation take the natural log on both sides;
ln(17/8) = ln [tex]e^2^0^k[/tex]
ln(17/8) = 20k
k = ln(17/8) / 20
To get the initial size of the culture;
From (I),
800 = A₀[tex]e^2^0^k[/tex]
800 = A₀e⁰°⁰³⁷⁶ ˣ ²⁰
A₀ = 800 / 20.76
A₀ = 38.53 ≅ 39
Therefore, the initial size of the culture is 39.
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Tammy installs bathroom tiles. Her current job requires tiles that are equilateral triangles and all the tiles have to be congruent to each other. She has a big sack of tiles all in the shape of equilateral triangles. Although she knows that all the tiles are equilateral, she is not sure they are all the same size. What must she measure on each tile to be sure they are congruent? Explain.
Step-by-step explanation:
one side.
as each tile is guaranteed an equilateral triangle, all sides are equally long. measuring 1 side clarifies therefore the overall size of the tile.
the angles are the same in any case, as every equilateral triangle (no matter its size) has only angles of 60°.
so, if any side has the same length as the side lengths of the other triangles, then the checked triangle is congruent with the others.
A= (a+b+c+d)/4 solve for b
Answer:
b = 4A-a-c-d
Step-by-step explanation:
A = (a+b+c+d)/4 |*4
4A = a+b+c+d |-a-c-d
4A-a-c-d = b
state how the 2 triangles are congruent?? SSS and SAS HELP ASAPPP??
The two triangles are congruent by SAS criterion.
What is SAS criterion?According to this standard, two triangles are said to be congruent if their two sides are equal to the sides of another triangle and their respective angles are also equal. The "Side-Angle-Side" triangle congruence theorem is referred to as the SAS Criterion.According to the Side-Angle-Side theorem of congruency, two sides and the angle they produce are congruent if they are equivalent to two sides and the included angle of another triangle.Verification:
Let's carry out an exercise to demonstrate SAS's validity. AB=PQ, BC=QR, and ∠B=∠Q are given. To demonstrate: ΔABC≅ΔPQRPlacing the triangle ABC over the triangle PQR will cause B to fall on Q and the AB side to coincide with the PQ side.Point A falls on point P because AB=PQ.The side BC will fall along the side QR since ∠B=∠Q.Point C is in line with point R since BC=QR. As a result, BC and QR coincide, while AC and PR coincide.ΔABC will therefore match ΔPQR. Consequently, ΔABC ≅ ΔPQR. This exemplifies the SAS congruence criterion.To learn more about SAS criterion, refer to https://brainly.com/question/22472034
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Does the point (-2, 7) lie on the graph of y=-2x+1?
yes
no
The point (-2,7) is not lie on the graph of y = -2x +1 .
Given,
In the question:
To check the :
Does the point (-2, 7) lie on the graph of y=-2x+1?
Now, According to the question:
The equation is :
y = -2x + 1
Substitute the values of x = -2 and y = 7 into y = -2x +1
7 = -2(-2) + 1
LHS = 7
RHS = -2(-2) + 1 = 5
Write in the form :
7 = 5
Verify the relationship
False
Determine whether the point is on the line:
(-2, 7) not on the graph.
Hence, The point (-2,7) is not lie on the graph of y = -2x +1 .
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What must be a factor of the polynomial function f(x) graphed on the coordinate plane below?
The factor of the polynomial f(x) graphed on the coordinate plane is
(x - 1).
What is factor of the polynomial?
A polynomial with coefficients in a certain field or in integers is expressed as the product of irreducible factors with coefficients in the same domain in mathematics and computer algebra, which is known as polynomial factorization.
A polynomial can be factored by expressing it as the product of two or more components; this is somewhat the opposite of multiplying.
From the given graph we can see that, graph crosses x - axis at points
x = 1 and x = 8.
That means x = 1, 8 are the zero of the polynomial.
Since, if x = a is a zero of the polynomial, then (x - a) is the factor of the polynomial.
As x = 1, 8 are zero of the polynomial so (x - 1) and (x - 8) are the factors of the polynomial.
Hence, from the given options (x - 1) is factor of the polynomial.
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Please help me!!!!!!!!!
Answer:
-6
Step-by-step explanation:
The value of [tex]b[/tex] is the same as the value of [tex]y[/tex] when [tex]x=0[/tex].