6x+30=180
6×=180-30
×=150/6
×=25
6x=6×25=130
abc is right angled triangle at A which tan B=1 then tan C-sin B cos C=...
Answer:
1/2
Step-by-step explanation:
Given right triangle ABC with right angle A and tan(B) = 1, you want the value of the expression tan(C) -sin(B)cos(C).
AnglesAngle A is given as 90°.
Angle B is found from ...
tan(B) = 1 ⇒ B = arctan(1) = 45°
Angle C is its complement:
C = 90° -B = 45°
Trig functionsThe relevant trig functions are ...
tan(C) = tan(45°) = 1
sin(B) = sin(45°) = 1/√2
cos(C) = cos(45°) = 1/√2
ExpressionThen the value of the expression is ...
tan(C) -sin(B)cos(C)
= 1 -(1/√2)(1/√2) = 1 -1/2
= 1/2
$880 at 5.25% for 2 years
The simple interest earned on investing $880 at 5.25% for 2 years is $92.4
How to calculate simple interest?Simple interest is calculated using the formula;
SI = P × R × T
Where,
P = Principal = $880R = Interest rate = 5.25% = 0.0525T = Time = 2 yearsSo,
SI = P × R × T
= 880 × 0.0525 × 2
= $92.4
Consequently, $92.4 is the simple interest earned on $880 at 5.25% for 2 years
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Is discontinuous function a function?
Yes, a discontinuous function is a function that is not continuous.
A function can have an asymptote if it approaches a horizontal or vertical line but never touches it. There are several types of functions that can have asymptotes, including rational functions, exponential functions, and logarithmic functions.
A continuous function in mathematics is a function without discontinuities, or any sudden changes in value. If we can guarantee arbitrarily small changes in the input of a function by limiting small enough changes, then the function is continuous.
A function is continuous if its graph can be drawn without lifting the pencil from the paper, or if the function's values remain "close" to one another as the input values change. A discontinuous function, on the other hand, has "breaks" or "jumps" in its graph, indicating that the function's values become "far" from one another as the input values change. An example of a discontinuous function is the absolute value function.
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If the graph of a function can be traced without removing the pencil from the paper or if the function's values stay "near" to one another while the input values change, the function is continuous. Contrarily, a discontinuous function's graph shows "breaks" or "jumps," suggesting that the function's values move "far" apart as the input values alter. The absolute value function is an illustration of a discontinuous function.
Please help answer this. I really need a detailed answer using Side angle side or SSS thanks!
Wrong, or incomplete answers will be reported
Answer: X=20 Y=70
Step-by-step explanation:
There’s no labels so it might be hard to explain this one otherwise
-We’ll call the point at the top left with y°: A
-the bottom right point with x°: C
-the point in between them with 40°: B
-the bottom left point with the right angle: D
angle DBC = 140° because angles on a straight line sum to 180°
so x must equal 20 because the other angles in an isosceles triangle are equal and 180-140=40 and 40/2=20
90-20=70 so angle ADB=70
meaning that y must equal 70 because 70+40=110 and 180-110=70
determine the average rate of change in concentration of b from t=0 s to t=222 s.
The average rate of change in concentration of b from t=0 s to t=222 s as calculated from the data given is 0.00916M/s.
The changes happening in A can be found as ,
= 0.140 - 0.650
= -0.510 M
Time = 222 s - 0 s
= 222 s
Therefore the average rate of change of A is
= -0.510 M / 222 s = -0.00229 M/s
Since the value obtained is negative we can conclude that the rate is decreasing.
Using stoichiometry equation we can find the value of B as ,
The average rate of change of B
= 2 x 0.00229
= +0.00458 M/s
-∆[A]/∆t = +1/2∆[B]/∆t
-0.00458 = +∆B/2
∆B = 2x 0.00458 = 0.00916M/s
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The quadratic function f(x) has roots of −2 and 3 and point (2, −4) lies on f(x). What is the equation of f(x)? f(x) = 2(x + 2)(x − 3) f(x) = 2(x − 2)(x + 3) f(x) = (x + 2)(x − 3) f(x) = (x − 2)(x + 3)
Using the roots of the quadratic equation the equation is solved to be
f(x) = (x + 2)(x − 3)How to get the equation of the quadratic equationInformation from the problem include
The quadratic function f(x) has roots of −2 and 3 and point (2, −4) lies on f(x)
from the roots
x = -2 and x = 3
x + 2 = 0 and x - 3 = 0
(x + 2)(x - 3)
passing through points (2 , -4)
y = a(x + 2)(x - 3)
-4 = a(2 + 2)(2 - 3)
-4 = a * 4 * -1
-4 = -4a
a = 1
the quadratic equation is f(x) = (x + 2)(x − 3)
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Giving 25 points!!!!!! PLEASE HELP
describe the correlation for this scatter plot
Answer:
Step-by-step explanation:
This scatter plot has a moderate negative correlation.
How many quadrilaterals can I construct with the following data quadrilateral PQRS with PQ 4.5 cm angle P 70 ∘ angle Q 100 ∘ angle r 80 ∘ and angle S 110 ∘?
Therefore, we can construct the only one quadrilateral can I construct with the following data quadrilateral PQ 4.5 cm angle P 70 ∘ angle Q 100 ∘ angle r 80 ∘ and angle S 110 with the above diagram.
Describe the quadrilateral.An example of a closed quadrilateral is a polygon, which has four sides, four vertices, and four angles. It has four non-collinear points that are joined together. The interior angles of quadrilaterals are all sums of 360 degrees.
Here,
the following construction steps:
I Build a line segment with a QR of 4.5 cm.
(ii) Create a ray QX with an angle of 80 degrees and cut off QP = 4 cm at the point Q.
(iii) Create a ray at the point R that forms an angle of 110 degrees, and then cut it off at RS = 4.5 cm.
Now join PS. (iv)
PQRS is hence the necessary quadrilateral.
Therefore, we can construct the quadrilateral can I construct with the following data quadrilateral PQ 4.5 cm angle P 70 ∘ angle Q 100 ∘ angle r 80 ∘ and angle S 110 with the above diagram.
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the point of concurrency of the medians of a triangle is always inside the triangle and is called the
Answer:
... centroid, or center of gravity.
Step-by-step explanation:
The point of concurrency of the medians of a triangle is always inside the triangle and is called the ______.
MediansA median joins a vertex of a triangle with the midpoint of the opposite segment. It is a line segment that lies entirely within the triangle. Hence any two medians will meet at a point that is within the triangle.
The point of concurrency of medians is called the "centroid." If the triangle has uniform areal density, the centroid will be the center of gravity, the point at which the triangle could be balanced.
The centroid divides each median into parts in the ratio 1:2, where the longer part is the segment to the vertex, and the shorter is the segment to the midpoint of the side.
What is the multiplicity of 5?
The multiplicity of a number is the number of times a number is a factor of another number.
In general, the multiplicity of a number can be determined by dividing the number by the factor. If the result is a whole number, then the multiplicity of the factor is equal to the result of the division. If the result is a decimal or fraction, then the multiplicity of the factor is 0.
For example, if we wanted to find the multiplicity of 5 in 25, we would divide 25 by 5: 25/5 = 5. This means that the multiplicity of 5 in 25 is 5.
The multiplicity of 5 can also be determined by finding the prime factorization of the number. For example, if we wanted to find the multiplicity of 5 in 30, we would factorize 30: 30 = 2 x 3 x 5. This means that the multiplicity of 5 in 30 is 1, because there is only one 5 in the prime factorization of 30.
In summary, the multiplicity of a number is the number of times a number is a factor of another number. The multiplicity of a number can be found by dividing the number by the factor, or by finding the prime factorization of the number.
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About 13 out of 24 homes have a personal computer. On a street with 96 homes, how many computers would you expect to have?
Answer: 52 computers
Step-by-step explanation:
First, take 96 divided by 24 = 4
Then take 13 times 4 = 52 computers
Answer: 52 computers
Step-by-step explanation: 96 is four times 24, meaning the expected amount of computers can be identified by multiplying the numerator by 4:
13 × 4 = 52
24 × 4 = 96
Our fraction is 52/96, which can be reduced to 13/24.
On a street with 96 people, 52 computers are expected throughout all 96 houses.
Perform the indicated operation.
g(a) = -4a +5
f(a)=3a-5
Find (gf)(a)
A) 2a³-a²-10a +5
B) -a³ + 4a
C) -12a²-35a-25
D) -12a²+35a-25
Answer:
(gf)(a)
=[g{f(a)}]
=g(3a-5)
=-4(3a-5)+5
=-12a+20+5
=-12a+25 is the right answer I think
but according to your options,
(gf)(a)
=g(a)×f(a)
=(-4a+5)(3a-5)
=-12a²+20a+15a-25
=-12a²+35a-25 which is option d.but I don't think it is the right process
Answer:
Step-by-step explanation:
The correct answer is option (D).
Given , g(a) = -4a + 5
f(a) = 3a-5
Here we have to find (gf)(a)
So, we will replace (gf)(a) with g(a).f(a)
= g(a).f(a) =( -4a+5 ).(3a-5)
= -4a*3a -4a*(-5)+ 3a*5+5*(-5)
= -12a2 + 20a + 15a - 25
Answer = -12a2 + 35a -25
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What is the solution to the system of equations?
-2x-y-3x = -1
3x - 2yz = -13
2x + 4y -z = −4
suppose sat math scores are normally distributed with a mean of 516 and a standard deviation of 115 while act math scores have a normal distribution with a mean of 22 and a standard deviation of 5. anna scored 650 on the sat math and bob scored 29 on the act math. assuming that both tests measure the same kind of ability, who did better in terms of the standardized z-score?
By assuming that both tests measure the same kind of ability, Bob did better in terms of the standardized Z-score.
We have provide a data about two major math's tests.
First Major test : SAT math score normally distributed with
Mean , μ = 516 and
Standard deviations, σ = 115
Second Major test: ACT math score normally distributed with
Mean, μ = 22
Standard deviations, σ = 5
Anna scores in SAT test 650
i.e x = 650
Using Z-Score formula,
Z = (x - μ)/σ
Z = (650 - 516)/115 = 154/115 = 1.17
Also, Bob score on ACT math test is 29 i.e x = 29
Z-Score = (x - μ)/σ
=> Z = (29 - 22)/5 = 7/5
=> Z = 1.4
Since, Z-Score for Bob's ACT math test is high as compared to Anna's SAT math test.
So, Bob did better in terms of the standardized z-score.
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how do you graph a function and put it into a table ? pls help me my midterms are coming up (there’s nothing attached i js need instructions)
The graph of the function y = x is shown and the data of the function is tabulated below.
The graph is a demonstration of curves that gives the relationship between the x and y-axis.
Here,
Let's assume the function,
f(x) = x or y = x
Now,
the graph of the function is shown,
and data is given as,
put x = 1,
so
y = 1
Similarly,
Other values can be obtained as y = 2, 3 , 4 for x = 2, 3, 4
Now the table is given as
x y
1 1
2 2
3 3
4 4
Thus, the graph of the function y = x is shown and the data of the function is tabulated above.
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What is the mean of 2 4 6 8 10 12?
The mean of the numbers 2 4 6 8 10 12 is 7
What is mean in math ?In mathematics and statistics, the concept of mean is crucial. The most typical or average value among a group of numbers is called the mean.
mean is calculated getting the summation of all the numbers and dividing by the number of times or occurrences of the number are
In this problem the numbers are 6 and the sum is calculated as follows
= 2 + 4 + 6 + 8 + 10 + 12
= 42
the mean is calculated by dividing the summation by number of occurrence
= 42 / 6
= 7
the mean is 7
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a linear function has an x-intercept of −8 − 8 and a y-intercept of 4 4 . which of these is an equation of the linear function?
A linear function can be represented by an equation of the form y = mx + b, where m is the slope of the function and b is the y-intercept. The x-intercept is the point where the graph of the function intersects the x-axis, and the y-intercept is the point where the graph intersects the y-axis.
Given that the x-intercept of the linear function is −8 and the y-intercept is 4, an equation of the function can be written as:
y = mx + b
Substituting the values of the x-intercept and the y-intercept into this equation, we get:
y = m(-8) + 4
Since the y-intercept is 4, this equation can be rewritten as:
y = 4 + mx
This equation represents a linear function with a y-intercept of 4 and a slope of m.
Therefore, an equation of the linear function with an x-intercept of −8 and a y-intercept of 4 is y = 4 + mx.
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Given that the x-intercept of the linear function is −8 and the y-intercept is 4, an equation of the function can be written as:
y = mx + b
Substituting the values of the x-intercept and the y-intercept into this equation, we get:
y = m(-8) + 4
Since the y-intercept is 4, this equation can be rewritten as:
y = 4 + mx
This equation represents a linear function with a y-intercept of 4 and a slope of m.
Therefore, an equation of the linear function with an x-intercept of −8 and a y-intercept of 4 is y = 4 + mx.
Which graph shows this system of equations? =13+12 y = 1 3 x + 12 =3+4
The graph of the simultaneous linear equation
[tex]y = \frac{1}{3}x + 12\\[/tex]
y = 3x + 4
is the graph given in the third option.
What is simultaneous linear equation?
At first it is important to know about linear equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.
The simultaneous linear equation are
[tex]y = \frac{1}{3}x + 12\\[/tex]
y = 3x + 4
Now,
[tex]y = \frac{1}{3}x + 12\\[/tex]
At x = 0, y = 12
The graph passes through (0, 12)
First option is wrong
y = 3x + 4
At x = 0, y = 4
The graph passes through (0, 4)
Second option is wrong
So the third option is correct.
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Converting Real Life Scale.. -Page 2-
NEED HELP ASAPPP 80 POINTS
(picture is linked belowww)
tysm like fr <33
The real-life measurement, if the scale factor is 2, is 4, 4, 1, 18 for the second table.
What is the scale factor?A scale factor, also known as a conversion factor, is a number that is used to increase or decrease the size of a figure without changing its shape. It is used to modify an object's size.
Given:
Scale factor = 2
Calculate the actual measurements as shown below,
[tex]Actual \ measure = Scale \ factor \times Scale \ measurement\ on\ paper[/tex]
Actual measurement = 2 × 2 = 4
Actual measurement = 2 × 2 = 4
Actual measurement = 2 × 0.5 = 1
Actual measurement = 2 × 9 = 18
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caliper which tile is missing
The second tile represents the missing alternatives.
What is sequence of objects?In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters
Given is a square array of tiles as shown in the image attached.
The tile given at the second number is the missing tile of the given alternatives.
Therefore, the second tile represents the missing alternatives.
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How did William Samuel Johnson feel about slavery?
William Samuel Johnson felt that ,when men were born, they were equal.
How did William Samuel Johnson feel about slavery?William Samuel Johnson had been interested in the issue for many years, even though he passed away before the movement to abolish slavery received widespread prominence. He expressed his belief in the equality of men at birth in a letter to James Boswell.In his opinion, Africans are savages, thus Boswell himself did not concur.Francis Barber, a Jamaican, was another long-time employee of Johnson's who lived in his home. Before meeting his Jamaican servant and heir Francis Barber in 1752 and most recently in his Taxation no Tyranny pamphlet published in 1775, Johnson had advocated against slavery throughout his literary career.To learn more about slavery, refer:
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72,12,2 simplest form
Answer:
456748
Step-by-step explanation:
you 463uy2iuswhk then 13456
How do you write numbers less than 10?
The rule is that words, not numerals, should be used to represent numbers and ordered events that are less than 10 in total.
what are numbers ?An arithmetic value known as a number is used to calculate and represent a quantity. Numerical writings, such as the letter "3," are used to represent numbers. A number system is a way of writing numbers that uses logical symbols or digits to represent them.
here
There are occasional exceptions, but generally speaking, numbers and ordered events that are less than 10 in total should be expressed as words.
Except for when they are the first digit of a phrase, numbers with two or more digits should be written as numerals.
The rule is that words, not numerals, should be used to represent numbers and ordered events that are less than 10 in total.
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weights, in pounds, of eight students in a class are: student weight (in pounds) student 1 128 student 2 193 student 3 166 student 4 147 student 5 202 student 6 183 student 7 181 student 8 158 using the data above, what is the standard error of the sample mean? answer choices are rounded to the hundredths place.
The standard error of the sample mean is approximately 8.9 pounds.
What is standard error of the sample mean?
Simple division of the standard deviation by the square root of the sample size yields the SEM. By evaluating the sample-to-sample variability of the sample means, standard error determines the accuracy of a sample mean.
To find the standard error of the sample mean, we need to first find the sample mean weight of the students. To do this, we add up the weights of all the students and divide by the number of students:
(128 + 193 + 166 + 147 + 202 + 183 + 181 + 158) / 8 = 171.5
Next, we need to find the variance of the sample. The variance is a measure of the spread of the data around the mean, and is calculated as follows:
[tex]variance = ((weight - mean)^2) / (n-1)[/tex]
where weight is the weight of each student, mean is the sample mean weight, and n is the number of students.
Plugging in the values from our data, we get:
variance = (128 - 171.5)^2 + (193 - 171.5)^2 + (166 - 171.5)^2 + (147 - 171.5)^2 + (202 - 171.5)^2 + (183 - 171.5)^2 + (181 - 171.5)^2 + (158 - 171.5)^2 / 7
= 1096.5
Finally, we can find the standard error of the sample mean by taking the square root of the variance and dividing by the square root of the number of students:
[tex]standard\ error = \sqrt{(variance / n)} \\\\= \sqrt{1096.5 / 8 )\\\\=8.9[/tex]
So, The standard error of the sample mean is approximately 8.9 pounds.
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The pictogram shows information about the houses in a street.
Each house has 3, 4 or 5 bedrooms.
Key:
3-bedroom houses
4-bedroom houses
5-bedroom houses
represents 2 houses
In total, how many bedrooms do these houses have?
The pictogram shows information about the houses in a street. the number of bedrooms each house have is 82 bedrooms
How to find the number of bedroom each house haveUsing the pictogram the number of houses are listed
3-bedroom houses = 9 houses
4-bedroom houses = 10 houses
5-bedroom houses = 3 houses
Multiplying out to get the number of bedroom per house
9 * 3= 27 bedrooms
10 * 4= 40 bedrooms
3 * 5 = 15 bedrooms
Adding the bedrooms together
27 + 40 + 15
= 82 bedrooms
the house has 82 bedrooms
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Josh tells Greg that the temperature where he lives is currently 77°F. Greg tells Josh that the temperature where he lives is currently 30°C. Josh says it is warmer where he lives, and Greg says it is warmer where he lives. Who is correct? Explain your reasoning
Answer:
Greg is correct
Step-by-step explanation:
To determine which of them is experiencing warmer weather, you need to compare the temperatures in the same unit of measurement. 77°F is equivalent to 25°C, while 30°C is equivalent to 86°F. Therefore, Greg is experiencing warmer weather than Josh.
The difference in the temperatures they reported is due to the fact that they are using different temperature scales. The Fahrenheit scale is used in the United States, while the Celsius scale is used in most other countries. The two scales are related by the equation:
C = (F - 32) / 1.8
To convert from Fahrenheit to Celsius, you can use this equation to determine the temperature in Celsius. To convert from Celsius to Fahrenheit, you can use the equation:
F = C * 1.8 + 32
Using these equations, you can compare temperatures in different scales to determine which is warmer.
Can I take the square root of 0?
Yes, we can take the square root of 0, the value of square root 0 is equal to 0.
What is a square root?A number's square root is the amount that, when multiplied by itself, equals the original value.
The square root of 0 is x multiplied by itself to give the number to give 0.
Which means x*x=0.
To get the product of numbers as 0, at least one number should be 0.
Therefore here x=0.
0 × 0 = 0
0² = 0
0 = √0
Hence we can take the square root for 0 and yes, it is defined.
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What is the value of − 4?
The value of the expression a^4 depends on "a". It is different for every "a" which can be any numerical value.
What is meant by variable?A symbol (often a letter) used in mathematics to represent an unknowable numerical value in an equation or algebraic statement. A variable can be defined as a quantity that is changeable and not fixed. Variables are crucial since they make up a significant portion of algebra.
What are three types of variable?Dependent, independent and controlled are three types of variable.
The given expression a^4 can be written as:
a^4= a*a*a*a
And the value of this expression depends on "a". It is different for every "a" which can be any numerical value.
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5 men and 5 women are standing in a line. how many possible ways are there to arrange them in a line such that no two men are next to each other?
What is i3 and i5 in laptop?
The two main CPUs in laptops are called i3 and i5, and their names vary according to their level of efficiency.
Which is superior, the i3 or the i5?In general, Core i5 CPUs perform better than Core i3 CPUs in terms of CPU performance. The Core i3 processors are all dual-core, in contrast to the dual-core and quad-core i5 CPUs. Along with cores and threads, you must also consider the processor generation.
What distinguishes the i3 from the i5?In terms of CPU performance, Core i5 components often exceed Core i3 components. Dual-core and quad-core Core i5 CPUs are both available. When it comes to multimedia applications like video transcoding and photo editing, a true quad-core CPU will often beat a dual-core CPU.
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