Answer:
Step-by-step explanation:
sin θ=1/4,tan θ>0
so θ lies in first quadrant.
cos θ=√(1-sin²θ)=√(1-(1/4)²)=√(1-1/16)=√(15/16)=√15/4
[tex]2cos^2 \frac{\theta}{2} =1+cos \theta[/tex]
[tex]2~cos^2\frac{\theta}{2} =1+\frac{\sqrt{15} }{4} =\frac{4+\sqrt{15}}{4} \\cos~\frac{\theta}{2} =\sqrt{\frac{4+\sqrt{15} }{4 \times 2} } \\cos\frac{\theta}{2} =\frac{\sqrt{8+2\sqrt{15}} }{4}[/tex]
28.6% of city employees ride the bus to work.Last year,29.7% of city employees rode the bus to work.What is the relative change from last year to this year
The number of employees taking the bus to an office is reduced by 1.1% from the last year. The relative change will be 1.1%.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that:-
28.6% of city employees ride the bus to work. Last year,29.7% of city employees rode the bus to work.
The relative change will be calculated as follows:-
Relative change = Present year data - Last year's data
Relative change = 28.6 - 29.7
Relative change = -1.1%
Therefore the number of employees taking the bus to an office is reduced by 1.1% from the last year. The relative change will be 1.1%.
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Josh made $35,000 in taxable income last year.
Suppose the income tax rate is 15% for the first $8500 plus 17% for the amount over $8500.
How much must Josh pay in income tax for last year?
Find f ° g and g ° f, if they exist. f={(-4,-5),(0,3),(1,6)} and g={(-5,0),(3,-4),(6,1)}.
The composite function of f o g are (-4,-5),(0,3),(1,6). The composite function of g o f are (-5,0),(3,-4),(6,1).
What is a function?A function is defined as a relation between the set of inputs having exactly one output each.
Given;
f = {(-4,-5),(0,3),(1,6)}
g = {(-5,0),(3,-4),(6,1)}.
In order to find f o g and g o f,
f o g = f(g)
The composite function of f o g
f(-5,0) = (-4,-5)
f(3,-4) = (0,3)
f(6,1) = (1,6)
The composite function of g o f
g(-4,-5) = (-5,0)
g(0,3) = (3,-4)
g (1,6) = (6,1)
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A linear function contains the following points.
What are the slope and y-intercepts of this function?
The slope is -1, and the value of the y-intercept is 6 if the linear function contains the points provided.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The slope is:
[tex]\rm m =\dfrac{6-8}{0-(-2)}[/tex]
m = -1
The equation of a line:
y = mx + c
y = -x + c
Plug x = 0 and y = 6
y = 6
y-intercept is (0, 6)
Thus, the slope is -1, and the value of the y-intercept is 6 if the linear function contains the points provided.
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Which of the following is a difference between simple regression and bivariate correlation?
© a. With correlation, associations cannot be negative
O b. With correlation, perfect associations are possible
O c. With simple regression, categorical variables can be used
O d. With correlation, variables are not described as dependent or independent
O e. In simple regression, associations are stronger
Answer: Answer is C
Step-by-step explanation: It is C because its option C
What is the solution of the quadratic equation (4y-3)^2=72
Answer:
To solve this quadratic equation, take the square root of both sides.
Since the left side is a perfect square, it will just be reduced to:
4y - 3
For the constant on the right side, the positive and negative roots must be considered.
√72 = ±6√2
Equating the two:
4y - 3 = ±6√2
4y = 3 ± 6√2
y = (3 ± 6√2)/4
y = (3 + 6√2) / 4 = 2.87
and
y = (3 - 6√2) / 4 = -1.37
One common system for computing a grade point average (GPA) assigns 4 points to an A, 3 points to a B, 2 points to a C, 1 point to a D, and 0 points to an F. What is the GPA of a student who gets an A in a -credit course, a B in each of -credit courses, a C in a -credit course, and a D in a -credit course?
Answer: 2.7545
The question was a little off, but I can understand enough
Step-by-step explanation:
Grade Grade Point(x) Course Credit(y) Product(xy)
A 4 3 12
B 3 4 12
B 3 4 12
B 3 4 12
C 2 2 4
D 1 3 3
Total 20 55
This means, the GPA of the student is :
[tex]GPA=\frac{55}{20}[/tex]
[tex]2.75[/tex]
curved surface area of a cone = Trl, where r is the
radius and I is the slant height.
surface area of a sphere = 42, where r is the
radius.
The shape below is made from a hemisphere and a
cone, each with a radius of 6 cm.
Work out the surface area of this shape in terms of .
16 cm
6 cm
Not drawn accurately
Answer:
168π cm²
Step-by-step explanation:
The total surface area is the sum of the areas of the parts: a hemisphere and a cone.
__
area formulaThe area of a hemisphere is half the area of a sphere, so the total area is ...
total area = hemisphere area + cone area
= 2πr² +πrl
total area = πr(2r +l)
__
applicationFor the given dimensions, r = 6 cm, l = 16 cm, the total surface area is ...
total area = π(6 cm)(2(6 cm) +16 cm) = π(6)(28) cm²
total area = 168π cm²
if the degree mesures of the angles in a triangle are in the ratio 2:3:4, what is the degree measure of the largest angle
The largest angle of the triangle is equal to 80 degrees.
Concept: Angle sum property of a triangle i.e., the sum of all angles of a triangle is equal to 180 degree
Given : Degree measures of the angles in a triangle are in the ratio 2:3:4
Let one part of each angle of the triangle be x, so the different angles of triangle are 2x,3x,4x (taking the ratios given in the question and multiplying by each of them by x)
2x +3x +4x = 180x
180x = 20
The angles of a triangle are 40,60,80
The largest angle of the triangle is equal to 80 degrees.
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Could use some help! Brainliest to who answers :)
Answer:
N. The number of people purchasing coffee each day in a coffee shop
Step-by-step explanation:
A fraction of a person could not buy coffee because every person is a whole person. If something is not a person, it's not a person. Therefore, the only numbers you could add to this value are 0 and 1.
3. Multiply the polynomials (a² + 3a-7) and (2a²-a + 4). Simplify the answer. Show your work.
Answer:
Answer:
[tex]2a^{4} + 5a^{3} - 13a^{2} + 19a - 28[/tex]
Step-by-step explanation:
Which second degree polynomial function has a leading coefficient of -1 and root 4 with multiplicity 2?
f(x) = -x²-8x-16
f(x) = -x² +8x-16
f(x)=x²-8x + 16
f(x) = -x² + 8x + 16
Mark this and return
Save and Exit
Next
Subm
Answer:abc and d
Step-by-step explanation:
trust me I took the dum test
Which of the following best describes a tessellation?
O A. An arrangement of repeating shapes with spaces between the
shapes and overlapping shapes
B. The point about which an image is rotated in rotational symmetry
C. An arrangement of repeating shapes with no spaces or overlaps
between them
D. The axis about which an image is rotated in reflectional symmetry
The statement that best describes a tessellation is an arrangement of repeating shapes with no spaces or overlaps between them. Option C
What is tessellation?
A tessellation can be defined as a pattern of geometric shapes that fill a two-dimensional space without gaps and overlaps
It is also known to repeat infinitely in all directions.
Thus, the statement that best describes a tessellation is an arrangement of repeating shapes with no spaces or overlaps between them. Option C
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Find the area.
8 in
19 in
13 in
1976 in²
205 in²
128 in²
104 in²
Total area = 104+24 = 128 sq.in , Option C is the right answer.
The missing figure is attached with the answer.
What is Area ?The space occupied by a two dimensional figure is called Area.
The figure given in the question can be divided into two figure
A rectangle of 8 * 13 inch
and a triangle of 8 * 6 inch
The area of a rectangle is given by
Length * Breadth
8 * 13
= 104 sq.inch
The area of the triangle is given by
(1/2) * base * height
= (1/2) * 8 * 6
= 24 sq.inch
Total area = 104+24 = 128 sq.in
Therefore Option C is the right answer.
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A country's population in 1991 was 103 million, in 1999 it was 108 million. estimate the total population in 2013
Answer:
117
Step-by-step explanation:
The total population is 117 million
Fill in the missing (yellow) exterior angle with (5x) to solve for x. Diagram may not be to scale.
Step-by-step explanation:
the sum of all exterior angles in a polygon is always 360° (one time around the full circle).
so,
360 = 71 + 85 + 44 + 3x + 5x = 8x + 200
160 = 8x
x = 20
What is the measure of complemnt angle
a)42° b) 35°
Answer:
90°
Step-by-step explanation:
A complement angle is the same as a right angle
Hii!
___________________________________________________________
Answer:
[tex]\sf 48\textdegree[/tex][tex]\sf 55\textdegree[/tex]Step-by-step explanation:
The sum of complementary angles is always 90 degrees.
We can find the complements of these two angles by setting up an equation.
x+42=90
Subtract 42 from both sides
x=48
This problem can be solved the same way!
x+35=90
Subtract 35 from both sides
x=55
--
Hope that this helped! Best wishes.
--
What is the scale factor of this dilation? Triangle A B C. Side A C is 8, C B is 10, A B is 6. Triangle A prime B prime C prime. Side A prime C prime is 4, C prime B prime is 5, B prime A prime is 3. One-fifth One-half 1 2
Answer:
0.5
Step-by-step explanation:
well you can just take one of the sides and in this case I'll use AC which originally is 8 and then in AC prime it's 4. You can simply divide the new length by the original length which is 4/8 or 0.5. So if you multiply any of the original side lengths by 0.5 you'll get the new side length.
Answer:
1/2
Step-by-step explanation:
edge 23
I will give lots of points please help.
In this course, we have studied two types of geometry: Euclidean and analytical.
In Euclidean geometry, we’ve explored the relationships between points, lines, and planes without any numerical measurement.
In analytical geometry, we’ve explored the relationship between algebra and geometry using positions of points in a Cartesian coordinate system.
Which approach to geometry do you prefer and why? What are some situations in which one approach to geometry would be more beneficial than the other?
The analytical approach is preferable because the primary issue with Euclidean geometry is that it is not enough to support all of the theorems that he claims to establish.
What is geometry?It is defined as the branch of mathematics that is concerned with the size, shape, and orientation of two-dimensional figures.
As we have given about the Euclidean and analytical geometry.
Without using any numerical measurements, we have investigated the connections between points, lines, and planes in Euclidean geometry.
In analytical geometry, we've looked at how the locations of points in a Cartesian coordinate system related to algebra and geometry.
The analytical approach is preferable because the primary issue with Euclidean geometry is that it is not enough to support all of the theorems that he claims to establish.
If the Euclidean geometry can be more advantageous in particular circumstances
Example: If using terrain or building chart),
Thus, the analytical approach is preferable because the primary issue with Euclidean geometry is that it is not enough to support all of the theorems that he claims to establish.
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You are betting on a game with an expected value of -$0.33. What does this mean?
The SAT is the most widely used test in the undergraduaté admissions process, Scores on the math portion of the SAT are believed to
be normally distributed and range from 200 to 800. A researcher from the admissions department at the University of New Hampshire
is interested in estimating the mean math SAT scores of the incoming class with 95% confidence. How large a sample should she take
to ensure that the margin of error is below 20?
(You may find it useful to reference the z table. Round intermediate calculations to at
least 4 decimal places and "2" value to 3 decimal places. Round up your final answer to the nearest whole number.)
Using the z-distribution, it is found that she should take a sample of 97 scores to ensure that the margin of error is below 20.
What is a z-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.The margin of error is given by:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
Scores on the math portion of the SAT are believed to be normally distributed and range from 200 to 800, hence by the Empirical Rule the standard deviation is given by:
[tex]6\sigma = 800 - 200[/tex]
[tex]\sigma = 100[/tex]
In this problem, 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.
To ensure a margin of error of 20, we solve for n when M = 20, hence:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]20 = 1.96\frac{100}{\sqrt{n}}[/tex]
[tex]20\sqrt{n} = 1.96 \times 100[/tex]
[tex]\sqrt{n} = 1.96 \times 5[/tex]
[tex](\sqrt{n})^2 = (1.96 \times 5)^2[/tex]
n = 96.04.
Rounding up, she should take a sample of 97 scores to ensure that the margin of error is below 20.
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The Function h is defined by the following rule.
h(x) = 2x-2
Complete the function table.
Answer:
[tex]\fbox {See below} \downarrow[/tex]
Step-by-step explanation:
[tex]\textsf {The function is :}[/tex]
[tex]\boxed {h(x) = 2x - 2}[/tex]
[tex]\textsf {Finding the missing values :}[/tex]
[tex]\mathsf {h(-4) = 2(-4) - 2 = -10}[/tex][tex]\mathsf {h(-2) = 2(-2) - 2 = -6}[/tex][tex]\mathsf {h(1) = 2(1) - 2 = 0}[/tex][tex]\mathsf {h(4) = 2(4) - 2 = 6}[/tex][tex]\mathsf {h(5) = 2(5) - 2 = 8}[/tex][tex]\textsf {The table :}[/tex]
[tex]\left[\begin{array}{ccc}x&f(x)\\-4&-10\\-2&-6\\1&0\\4&6\\5&8\end{array}\right][/tex]
Rewrite without parentheses.
-9²x4 (7x²-6w+2)
Simplify your answer as much ac
Answer:
2268x²-1944w+648
-9² = 81
81×4 =324
use the 324 to remove the bracket
Which of the following rational functions is graphed below?
10-
10
-10
-10-
O A. F(x) =
X-2
x(x + 5)
OB. F(x)=
1
(x+5)(x-2)
O C. F(x) = (x+5)(x - 2)
X
O D. F(x) = (x+5)(x-2)
X
The graph of the function f(x) = x(x + 5)(x - 2) have x intercepts at x = 0, -5 and 2
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the equation:
f(x) = x(x + 5)(x - 2)
x(x + 5)(x - 2) = 0
x = 0, x + 5 = 0, x - 2 = 0
x = 0, -5 and 2
The graph of the function f(x) = x(x + 5)(x - 2) have x intercepts at x = 0, -5 and 2
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A woman bought some large frames for $10 each and some small frames for $4 each at a closeout sale. If she bought 22 frames for $106, find how many of each type she bought.
Answer:
19 small frames and 3 large frames
Step-by-step explanation:
follows the steps in the attached
In the diagram, point D divides line segment AB in the ratio of 5:3. If line segment AC is vertical and line segment CD is horizontal, what are the coordinates of point C? Diagram shows a line segment with endpoints A(2, minus 6) and B(10, 2). Point D lies on this line segment. A dashed segment extends up from point A until point C and then extends horizontally to right until point D, forming a right triangle. A. (2, -1) B. (2, -3) C. (5, -3) D. (7, -1) Reset Next
The coordinates of point C that forms the triangle is; (2, -1)
How to partition a line segment?We are told that point D divides line segment AB in the ratio of 5:3.
The line segment division formula is;
(x, y) = (m₁x₂ + m₂x₁)/(m₁ + m₂), (m₁y₂ + m₂y₁)/(m₁ + m₂)
For this question;
x₁ = 2; y₁ = -6; x₂ = 10; y₂ = 2; m₁ = 5; m₂ = 3
Thus, (x, y) gives us;
(5*10 + 3*2)/(5 + 3), (5*2 + 3*-6)/(5 + 3)
D(x, y) = (7, -1)
Now, we need to find the coordinates of C
We will use coordinate system which means the coordinate of x will be the as x coordinate of A since, AC is vertical line
And coordinate of y will be same as y in D since CD is horizontal line. Thus, coordinate of C is; C(2,-1).
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roger contracts childrens playhouses all the top of each house he places an isosceles triangle to from the roof the largest angle measures 146 what are the measurement of the other two angles
Step-by-step explanation:
there are clearly some typos in the question.
so, to summarize what I understood :
the roof of each playhouse is an isoceles triangle, with the largest angle being 146°.
we need to find the other 2 angles.
"isoceles" means that both legs are equally long.
that means automatically that both side angles (bottom left and bottom right) are equally large too.
and now, this please burn into your brain forever :
the sum of all angles in a triangle (no matter what type) is always 180°.
so, if we call a side angle x, we have here
180 = 146 + x + x = 146 + 2x
34 = 2x
x = 17°
so, both missing angles are 17°.
a pretty flat triangle roof.
Help me with this question please!! :)
ANSWERS ARE AT THE BOTTOM.
To find the probability of 2 events happening in a row, we need to multiply their probabilities.
For example, if a friend bet: "If you roll a six on a dice and filp and coin and get heads, then I'll give you 500 bucks. However, if you don't roll a six and flip and coin and get heads in a row, then you have to give me 500 bucks."
You want to know the probability of you winning this bet.
So, we need to multiply the probability of rolling a six, and the probability of flipping a coin and landing heads.
This is 1/6 * 1/2
That is 1/12
You probably should't take this bet, because you only have a 1/12 chance of winning.
Lets go back to your problem. The jar contains 16 red marbles and 28 blue marbles. The probability of picking a red marble right now is 16/28, or 4/7. Assume we picked a red marble on our first try. Now, there are only 15 red marbles. The probability of picking a red marble right now is 15/28.
Probability of picking a red marble on your first try: 4/7
Probability of picking a red marble on your second try: 15/28
Now, we need to multiply the probabilities.
4/7 * 15/28
60/196
15/49
ANSWER:
15/49
A family originally bought a home for $654,030. Now, a few years later, the home is worth
$457,821. What was the percent of decrease in its value?
Answer:
30%
Step-by-step explanation:
First we find out the difference between them:
$654,030 - $457,821 = $196,209
Then we compare it with the original price:
196,209/654,030 = 0.3
Since 0.3 is 30%, that is 30% decrease in value.
Which relation is a function??????
Answer:
A
Step-by-step explanation:
there cannot be 2 different points on the same x coordinate
