The exact value of cos 7pi/8 is 0. 9988
How to find the value
It is important to note that the value for pi = 3. 142
= cos 7π
Substitute value of π
= cos(7× 3. 142)
= cos 21. 994
Divide 21. 994 by 8
= 2. 740
Let's find the vale of [tex]cos \frac{21. 994}{8}[/tex]
= [tex]cos (2. 749)[/tex]
= [tex]0. 9988[/tex]
Thus, the exact value of cos 7pi/8 is 0. 9988
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Find the slant height x of the pyramid shown, to the nearest tenth.
6mm
7mm
7mm
Options:
A: 4.35
B: 9.2
C: 6.9
D: 3.9
Answer: C
Step-by-step explanation:
Construct the segment connecting the point where the height meets to the base to where the slant height meets the base.
This forms a right triangle with legs of length 3.5 and 6.
So, by the Pythagorean theorem, [tex]x=\sqrt{3.5^2 + 6^2} \approx 6.9[/tex]
Mr. Frankel bought 8 tickets to a puppet show and spent $49. He bought a combination of child tickets for $5 and adult tickets for $8
each. Write a system of equations to determine the number of adult, a, and the number of child tickets, c, he bought. solve for equations
Answer: adult = 3 child = 5
Step-by-step explanation:
49 = 8a+5c
8 = a+c
use those equations to solve^^
Write the expression two-cubed times seven as a numerical expression.
Answer:
See below
Step-by-step explanation:
2^3 is two cubed ...now multiply times 7
7 * 2^3
Factor the expression. q²r+ blank s^2t)(blankq^4r^2-6q^2rs^2t+blanks^4t^2
The equivalent expression of (q² − r²s) (q⁴ + q²r²s + r⁴s²) is q⁶ - r⁶s³
How to factor the expression?The expression is given as:
(q² − r²s) (q⁴ + q²r²s + r⁴s²)
Expand the expression
(q² − r²s) (q⁴ + q²r²s + r⁴s²) = q²(q⁴ + q²r²s + r⁴s²) − r²s(q⁴ + q²r²s + r⁴s²)
Open the brackets
(q² − r²s) (q⁴ + q²r²s + r⁴s²) = q⁶ + q⁴r²s + q²r⁴s² -q⁴r²s - q²r⁴s² - r⁶s³
Evaluate the like terms
(q² − r²s) (q⁴ + q²r²s + r⁴s²) = q⁶ - r⁶s³
Hence, the equivalent expression of (q² − r²s) (q⁴ + q²r²s + r⁴s²) is q⁶ - r⁶s³
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Complete questionFactor the expression. (q² − r²s) (q⁴ + q²r²s + r⁴s²)
Which number line represents the solution for the
inequality |2x - 5] ≥ 3?
The attached graph represents the number line of the inequality |2x - 5] ≥ 3
How to determine the number line?The inequality is given as:
|2x - 5] ≥ 3
Remove the absolute value sign
2x - 5 ≥ 3 or 2x - 5 ≥ -3
Add 5 to both sides
2x ≥ 5 + 3 or 2x ≥ 5-3
Evaluate
2x ≥ 8 or 2x ≥ 2
Divide through by 2
x ≥ 4 or x ≥ 1
Combine both inequalities
x ≤ 1 and x ≥ 4
See attachment for the number line
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Find the value of the expression (x2−4)3x when x = 5.
Answer:
315
Step-by-step explanation:
You plug 5 in for x
(5^2-4)3(5) = 315
Answer:
(5^2−4)3(5)
25-4(3)(5)
15*21=315
Hope This Helps!!!
The triangles are congruent by the SSS congruence theorem.
Triangles A B C and F E D are shown. Triangle A B C is reflected across A C and then is shifted down and to the left to form triangle F E D.
Which rigid transformation(s) can map TriangleABC onto TriangleFED?
reflection, then dilation
reflection, then translation
rotation, then translation
rotation, then reflection
The rigid transformations that maps ΔABC onto ΔFED by reflection then translation.
The correct option is (B).
What is Translation?Translation is also another form of transformation whereby all the points of a figure are shifted at exactly the same distance and in the same direction without being resized, reflected nor rotated.
given:
ΔABC ≅ ΔFED are congruent by the SSS Congruence Theorem.
Hence, the rigid transformations that maps ΔABC onto ΔFED by reflection then translation.
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Answer:
B
Step-by-step explanation:
PROBLABILITY!!!
(I added the picture needed)
1.Create a sample space and find the product of each combination. What is the probability that a person wins the game? Express your answer as a fraction in lowest terms and as a percent rounded to the nearest tenth.
(answer to this one is 9/28 and 32.1%)
2. You realize a short time into the carnival that you don’t have enough prizes to last the entire event. You call your teacher, and she suggests that you change the winning number so that a participant will win only 25% of the time. What number will that be? Support your answer.
3. Participants achieving a winning score of 36 or higher in four consecutive attempts will receive a large prize! What is the probability of this occurring?
4. After changing the game rules, participants and the crowd are disappointed when the first five games yield scores of 12, 18, 30, 28, and 24. What statement can you recommend the teacher posts to reassure everyone that the game is fair?
Based on the rules of the game, the probability that a person wins the game is 3/8 or 37.5%.
If participants can only win 25% of the time, the number that they need to get would be 32 or higher.
The probability of a winning score of 36 or higher in four consecutive attempts is 1/1,296.
To show that the game is fair, the teacher can post that every number apart from 24 and 30 has an equal chance of appearing.
What is a good sample space to represent the data?There are 6 sides to dice and 4 cards. The sample space is:
Dice Card Product Frequency of Product
1 5 5 1
1 6 6 1
1 7 7 1
1 8 8 1
2 5 10 1
2 6 12 1
2 7 14 1
2 8 16 1
3 5 15 1
3 6 18 1
3 7 21 1
3 8 24 2
4 5 20 1
4 6 24 1
4 7 28 1
4 8 32 1
5 5 25 1
5 6 30 2
5 7 35 1
5 8 40 1
6 5 30
6 6 36 1
6 7 42 1
6 8 48 1
Total 24
24 and 30 have frequencies of 2 as they appear twice.
From the table, in order to win, a player needs to get 28 or higher.
There are only 8 numbers that are 28 or higher but including the chance that 30 has a relative frequency of 2, we have 9 chances to win the game. The probability is:
= 9 / 24
= 3 / 8
How can a player win 25% of the time?If people are to win only 25% of the time, this means that the number of products that can be picked is:
= 25% x 24
= 6
To find the winning number, count down from the highest product 6 times to get 32.
A person therefore needs to get 32 or above to win 25% of the time.
What is the probability of winning the large price?The probability of getting 36 or higher is:
= Chance of 36 + chance of 40 + chance of 42 + chance of 48
= 1 / 24 + 1/24 + 1/24 + 1/24
= 1 / 6
The probability of repeating this 4 times is:
= 1 / 6 x 1 / 6 x 1/ 6 x 1 / 6
= 1 / 1,296
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Which of the following systems of inequalities has point C as a solution? Two linear functions f of x equals 3 times x plus 4 and g of x equals negative one half times x minus 5 intersecting at one point, forming an X on the page. A point above the intersection is labeled A. A point to the left of the intersection is labeled B. A point below the intersection is labeled C. A point to the right of the intersections is labeled D. f(x) ≤ 3x + 4 g of x is less than or equal to negative one half times x minus 5 f(x) ≥ 3x + 4 g of x is less than or equal to negative one half times x minus 5 f(x) ≤ 3x + 4 g of x is greater than or equal to negative one half times x minus 5 f(x) ≥ 3x + 4 g of x is greater than or equal to negative one half times x minus 5
The inequalities that will have point C as a solution are;
f(x) ≥ 3x + 4
g of x is greater than or equal to negative one half times x minus 5
What is the solution of the Inequality?We can see the inequality graph in the attached file.
Now, the two lines in the graph represent the equations;
f(x) = 3x + 4
g(x) = -¹/₂x - 5
Now, we see the point C and from inspection of the graph, we can see that it is to the right of f(x) and to the bottom of g(x) an as such the inequalities that will have point C as a solution is;
f(x) ≥ 3x + 4
g of x is greater than or equal to negative one half times x minus 5
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The process of inferring conclusions about a population from data on selected individuals is called statistical _____.
inferential statistics is the answer.
Statistics is the study and manipulation of data, including ways to gather, review, analyze, and draw conclusions from data. The two major areas of statistics are descriptive and inferential statistics.
Inferential statistics use measurements from the sample of subjects in the experiment to compare the treatment groups and make generalizations about the larger population of subjects. There are many types of inferential statistics and each is appropriate for a specific research design and sample characteristics.
The most common methodologies in inferential statistics are hypothesis tests, confidence intervals, and regression analysis.
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I'm lazy and dont feel like doing math myself. So pls help me!
I'm asking this again cuz no one answer it the first time T-T
Answer:
55
Step-by-step explanation:
Well you just plug in 10 as n.. and you get the equation:
[tex]\frac{10(10+1)}{2} \\\frac{10(11)}{2}\\\\\frac{110}{2}\\\\55[/tex]
A point is chosen at random on the number line between $0$ and $1$, and the point is colored green. Then, another point is chosen at random on the number line between $0$ and $1$, and this point is colored purple. What is the probability that the number of the purple point is greater than the number of the green point, but less than twice the number of the green point
The probability that the number of the purple point is greater than the number of the green point, but less than twice the number of the green point is 1/4
How to find the Probability?Let the "green" value be an x value lying on segment AC.
Now, the segment AC has the equation y = x. Then, let the "purple" value that is twice a selected x value lie on the segment AE and as such, the equation of this line is y = 2x.
It must be noted that at point E, x = 0.5 and y = 1. This means at every x value on AC greater than 0.5, the value of y on EC associated with this x value is is less than twice that x value.
Then, between segments AE and AC, every value of y will be greater than, but less than twice, its associated x value.
Since triangle ACD has an area of 1/2 and triangle BEA has an area of 1/4, then we can say that;
Triangle AEC area = 1 - (1/2) - (1/4) = 1/4.
Thus, the probability that the number of the purple point is greater than the number of the green point, but less than twice the number of the green point is 1/4
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Write the standard form of the equation of the line through the pair of points (3,5) and (1,5).
The standard form of the equation of the line passing through the points (3,5) and (1,5) is given by
(Simplify your answer.)
Answer:
y = 5
Step-by-step explanation:
The standard form of a linear equation is Ax + By=C
But let's start with the slope-intercept form: y = mx+b, where m is the slope and b the y-intercept (the value of y when x=0).
M, the slope, may be calculated by using the Rise/Run between the two given points: (1,5) and (3,5):
Rise = (5-5) = 0 [Note that the value of y does not change when x = 1 or 3.]
Run is = (3-1)=2
Rise/Run (slope, m) is (0/2) or 0. [y does not change as a function of x. It is a flat, horizontal line]
The equation becomes y = (2/3)x + b
We need to find a value of b, the y-intercept, that forces the line to go through both points. This can be done by entering one of the points into the equation and solving for b:
y = (0)x + b
I'll use (1,5)
5 = (0)*(1) + b
b = 5
The equation becomes y = (0)x + 5 or y = 5
Standard form of the equation is Ax + By = C
A is 0, B is 1 and C is 5
y = 5
i need the answer for this question, look at the image below for help
Answer:
x axis is -2.
y axis is +1.
(-1, 3)
What is Meant By Graphing Functions?Graphing functions is drawing the curve that represents the function on the coordinate plane. If a curve (graph) represents a function, then every point on the curve satisfies the function equation.
According to the question,
The following graph represents the linear function f(x) = x -2
Take any point on this line, say, (-1, 3).
Let us substitute (-1, 3) = (x, y) (i.e., x = -1 and y = 3) in the function f(x) = -x + 2 (note that it can be written as y = x - 2).
Then
3 = -(-1) + 2
3 = 1 + 2
3 = 3, thus, (-1, 3) satisfies the function.
In the same way, you can try taking different points and checking whether they satisfy the function. Each and every point on the line (in general called "curve") satisfies the function.
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samanth drew this pictogram
Answer:
la verdad noce no me acuerdo
Answer:
4
Step-by-step explanation:
There are 6 grey diamonds in the row labelled "cat".
Each diamond means two hours.
6 × 2 = 12
Samanth's table shows that cats sleep 12 hours.
Tony is going to use a circle that means 3 hours.
12 ÷ 3 = 4
Tony needs 4 circles to show 12 hours.
4 × 3 = 12
Tony will use 4 circles.
Find m, given that the three angles of a triangle are (m+18), (2m+28) and (3m+47).
Step-by-step explanation:
As all angles in a triangle add up to 180°
we can write:
(m+18)+(2m+28)+(3m+47) = 180
6m + 93 = 180
6m = 180 - 93
6m = 87
m = 87 / 6
m = 14.5
77 = 88 because they both equal 1. Peter takes one part away from each. Will the results be equal? Use the drop-down menus to complete an explanation.
Yes, the results will be equal as it follows from the task content that both numbers were equal initially.
What will he the equality verdict on both results?As evident in the task content, it follows that the numbers 77 and 88 although, not equal in the real sense, are equal according to the task content.
Hence, it follows that when equal parts are taken away from the two numbers, they would still be equal as both numbers were equal initially.
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Container measures 24ft by 8ft by 10ft, if 1 bushel is approximately 2220 cubic inches, approximately how many bushels of grain can the container hold ( 1ft=12in) Show Your work
Answer:
see below
Step-by-step explanation:
24 ft * 12 in/ft * 8ft * 12 in/ft * 10 ft * 12 in/ft = 3317760 in^3
3 317 760 in^3 / 2220 in^3/bushel = 1494.49 bushels
What is the equivalent 6/10 1. 3/5 2. 9/12 3. 20/50 4. 40/50
Answer:
1.) 3/5
Step-by-step explanation:
When know that 3/5 is equivalent to 6/10 because both the numerator and the denominator are scaled up/down by the same amount. To be precise, we can get the answer of 3/5 by dividing the numerator and denominator by 2.
6 / 2 = 3
10 / 2 = 5
Are these two equal ?
Can we make -x/x+1 to x/-(x+1) and becomes x/-x-1
Answer:
Yes, they are equivalent.
One way you can check this is by substituting any number into x.
For example, x = 2:
• First equation : [tex]\frac{-x}{x + 1}[/tex]
⇒ [tex]\frac{-2}{2 + 1}[/tex]
⇒ [tex]\frac{-2}{3}[/tex]
• Second equation: [tex]\frac{x}{-x-1}[/tex]
⇒ [tex]\frac{2}{-2-1}[/tex]
⇒ [tex]\frac{-2}{3}[/tex]
As both forms of the equation give the same result after substitution, they are equivalent.
38. For the following exercises, sketch a line with the given features.
38. An x-intercept of (-4,0) and y-intercept of (0,-2)
Answer:
see image
Step-by-step explanation:
The x-intercept is the point where the line crosses the x-axis (horizontal, left and right line with numbers, arrows at both ends, usually marked x at the right end)
The y-intercept is where your line crosses the y-axis (vertical, up-and-down line with numbers, arrows at the ends, usually marked y at the top)
Two points determine a line.
Draw a line through the two points given. See image.
Find the volume of a cylinder with a radius of 4.8 cm and a height of 14.6 cm. [Use it =
3.14]
56.2 cm³
1056.24 cm³
O 156.2 cm³
820 cm³
Answer:
1056.24 cm^3
Step-by-step explanation:
The volume of a cylinder is [tex]\pi r^2h[/tex]. The problem says to use [tex]\pi[/tex]=3.14
Plug in your numbers [tex]3.14*4.8^2*14.6=1056.24[/tex]
12 cans of soup each can is a cylinder with a radius of 3.5 cm and a height of 10 cm. the cans may be arranged in any way. the company would like to minimize the packaging costs involved with the creation of the container.
Answer:
2 layers, 3×2 cans per layer
Step-by-step explanation:
Factors of 12: 1, 2, 3, 4, 6, 12
The box can have 1 layer of 12 cans, 2 layers of 6 cans each, or 3 layers of 4 cans each.
In each case below, the total surface area is 2(LW + LH + WH)
1 layer, 12×1 cans
L = 84 cm; W = 7 cm; H = 10 cm
SA = 2996 cm²
1 layer, 6×2 cans
L = 42 cm; W = 14 cm; H = 10 cm
SA = 2248 cm²
1 layer, 4×3 cans
L = 28 cm; W = 21 cm; H = 10 cm
SA = 2156 cm²
2 layers, 6×1 cans per layer
L = 42 cm; W = 7 cm; H = 20 cm
SA = 2548 cm²
2 layers, 3×2 cans per layer
L = 21 cm; W = 14 cm; H = 20 cm
SA = 1988 cm² <--------------- smallest surface area
3 layer, 4×1 cans per layer
L = 28 cm; W = 7 cm; H = 30 cm
SA = 2492 cm²
3 layers, 2×2 cans per layer
L = 14 cm; W = 14 cm; H = 30 cm
SA = 2072 cm²
Can someone explain 03.05 Polynomial Identities and Proofs for me?
The polynomial Identities and an example of a proof of an identity have been explained below.
What are polynomial Identities and Proofs?Polynomial identities are defined as equations that are always true, regardless of the variable values. These polynomial identities are used while factorizing the polynomial or expanding the polynomial. These polynomial identities are;
(a + b)² = a² + b² + 2ab
(a - b)² = a² + b² - 2ab
(a + b)(a - b) = a² - b²
(x + a)(x + b) = x² + x(a + b)+ ab
Let us prove the polynomial identity (a + b)² = a² + b² + 2ab.
Now, (a + b)² is simply the product of (a + b) and (a + b).
That is; (a + b)² = (a + b) × (a + b)
This can simply be imagined to be a square whose side are (a + b) with its' area equal to (a + b)²
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HELP HALP
x =x=x, equals
^\circ
∘
Answer:
Step-by-step explanation:
x=25 degrees.
A vertical angle is two angles formed by intersecting lines, just like the two that form 25 degrees and x degrees. The angles formed by vertical angles are congruent (meaning they are equivalent). So, x=25 degrees.
What is the degree form for 4π/5 radians?
Answer: 144 degrees
Step-by-step explanation:
Formulas:Radian ⇒ Degree = 180/π
Degree ⇒ Radian = π/180
[tex]\frac{4\pi }{5} *\frac{180}{\pi } =\frac{4}{5} *\frac{180}{1} =\frac{720}{5} =144[/tex]
Therefore your answer is 144 degrees
Hello !
π rad <=> 180°
4π/5 rad <=> ?°
The calculation ils attached.
We found 144°.
Have a nice day ;)
In the figure above, AP and CQ are tangents to the circle.
If ∠ABC = 60° and ∠BAP = 40°, find ∠BCQ.
Answer:
30
Step-by-step explanation:
You take a protractor and put at c then you measure
Find the total surface area of this triangular prism.
18 cm
30 cm
24 cm
7 cm
Answer:
936 cm^2
Step-by-step explanation:
Solution
Back (This is a rectangle)
Area = w * h
w = 7
h = 18
Area = 7 * 18 = 126 cm^2
Front and Back
Area = 1/2 * B * H (This is a triangle -- There are 2 of them)
Givens
B = 24
h = 18
Area = 1/2 * 24 * 18
Area = 216
But there are two such triangles = 2*216 = 432 cm ^2
Ramp
Formula Area = L*w (This is a rectangle)
L = 30
W = 7
Area = 30 * 7 = 210 cm^2
Base
This is also a rectangle
L = 24
W = 7
Area = L*W
Area = 24 *7 = 168 cm^2
Total
168 cm^2
210 cm^2
432 cm^2
126 cm^2
936 cm^2
If the length of the hypotenuse of the right triangle whose legs measure 6 feet and 4 square root of 3 feet
The hypotenuse of the right triangle, with legs of 6 and 4√3 feet is 2√21 feet, computed using the Pythagoras Theorem.
The Pythagoras Theorem states that in a right triangle, the square of the hypotenuse is always equal to the sum of the squares of the other two legs.
If the hypotenuse is taken as a, and the two legs are taken as b and c, then by the Pythagoras Theorem, we can write that:
a² = b² + c².
In the question, we are given that a right triangle, has legs of lengths 6 feet and 4√3 feet each, and we are asked to find the length of the hypotenuse.
Thus, taking b = 6 and c = 4√3, in the above equation, we get:
a² = 6² + (4√3)²,
or, a² = 36 + 48,
or, a² = 84,
or, a² = (2√21)²,
or, a = 2√21.
Thus, the hypotenuse of the right triangle, with legs of 6 and 4√3 feet is 2√21 feet, computed using the Pythagoras Theorem.
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Parent function Y equals 0.5 square root X is..
-increasing
-decreasing
-constant
Using translation concepts, it is found that:
The parent function y = [tex]0.5^x[/tex] is decreasing across it's domain because it's base, b, is such that 0 < |b| < 1.The function f shifts the parent function 8 units up.The function f shifts the parent function 5 units right.What is a translation?
A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The parent function is:
[tex]y = 0.5^x[/tex]
It has a base with absolute value between 0 and 1, hence it is decreasing.
The changes to the function are given as follows:
y -> y + 8, hence the function was shifted 8 units up.x -> x - 5, hence the function was shifted 5 units right.More can be learned about translation concepts at https://brainly.com/question/4521517
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