Answers
Witch hat = 5
Jack o' lantern = 2
Ghost = 7
Witch Pot = 10
7 x 5 = 35 + 5 = 40
10 x 2 = 20 + 2 = 22
7 + 10 = 17 + 10 = 27
2 x 5 = 10 + 7 = 17
7 + 7 = 14 + 5 = 19
1. 7x5+5=40
2. 10x2+2=22
3. 7+10+10=27
4. 2x5+7=17
5. 7+7+5=19
Related Questions
The expression ( x 22 ) ( x 7 ) 3 is equivalent to x p. What is the value of p?
Answers
The given expression is equivalent to x^43, and the value of p is 43.
When we have an expression with exponents, such as (x^22)(x^7)^3, we can simplify it by applying the rules of exponents. In this case, we can use the rule that states that when we have a power raised to another power, we can multiply the exponents. That is, (a^m)^n = a^(m*n).
Using this rule, we can simplify the given expression as follows:
(x^22)(x^7)^3 = x^(22 + 7*3)
= x^(22 + 21)
= x^43
Therefore, the given expression is equivalent to x^43, and the value of p is 43.
It's important to understand the rules of exponents when dealing with expressions that involve powers. These rules allow us to simplify complex expressions and make calculations more manageable. In general, we should always try to simplify expressions as much as possible, as this can help us to identify patterns and relationships that might not be apparent in more complex forms.
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Determine the number of terms required to approximate the sum of the series with an error of less than 0.001.
∑
[infinity]
n=4
(−1)n+1
n4
Answers
You need approximately 5 terms (starting from n=4) to achieve an error less than 0.001. To determine the number of terms required to approximate the sum of the series with an error of less than 0.001.
We can use the alternating series error bound formula:
Error ≤ |Rn| ≤ an+1
Where Rn is the remainder or error in the nth partial sum, and an+1 is the absolute value of the (n+1)th term in the series.
In this case, the alternating series is:
∑
[infinity]
n=4
(−1)n+1
n4
To find the absolute value of the (n+1)th term, we can plug in n+1 for n:
|an+1| = |(−1)n+2/(n+1)4|
Since we want the error to be less than 0.001, we can set up the inequality:
|an+1| ≤ 0.001
Plugging in the formula for |an+1| and solving for n, we get:
|(−1)n+2/(n+1)4| ≤ 0.001
(n+1)4 ≥ 1000
Taking the fourth root of both sides, we get:
n+1 ≥ 5.623
n ≥ 4.623
Therefore, we need at least 5 terms to approximate the sum of the series with an error of less than 0.001.
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13. pls help will mark brainliest to anyone
Answers
The equation of the line in slope intercept form is found as y = x/5 + 24/5, where slope is (-1/5) and y-intercept is 24/5.
What is named as the slope-intercept form?The slope intercept type of composing a straight line equation is y = mx + b. In the equation 'y = mx + b,' 'b' represents the point in which the line intersects the 'y axis,' and'm' represents the slope of the line. A line's slope or gradient describes how steep it is. It may have a positive or negative value.For the given question;
Two points are given as;
(x1, y1) = (-6, 6)
(x2, y2) = (9, 1)
The slope of the line is found as;
slope = m = (y2 - y1)/(x2 - x1)
m = (1 - 6)/(9 + 6)
m = -5/15
m = -1/5
The equation of the line in slope-intercept form is found as;
y - y1 = m(x - x1)
y - 6 = (-1/5)(x + 6)
5y - 30 = -x - 6
5y = -x + 24
y = -x/5 + 24/5
Thus, the equation of the line is found as y = x/5 + 24/5, where slope is (-1/5) and y-intercept is 24/5.
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find the slope of the altitude on each side of triangle ABC. (b) A(4,0), B(0,4), C(0,0)
Answers
We are given a triangle with the following vertices
A(4, 0)
B(0, 4)
C(0, 0)
Let us draw the altitude on each side of triangle ABC
As you can see, we have drawn the altitude on each side of the triangle.
The slopes of these altitudes are given by
\(\begin{gathered} slope\: AD=-\frac{1}{slope\: BC} \\ slope\: BE=-\frac{1}{slope\: AC} \\ slope\: CF=-\frac{1}{slope\: AB} \end{gathered}\)Slope BC:
B(0, 4) and C(0, 0)
\(slope\: BC=\frac{y_2−y_1}{ x_2−x_1}=\frac{0-4}{0-0}=-\frac{4}{0}=\text{undefined}\quad (\text{vertical line)}\)Slope AC:
A(4, 0) and C(0, 0)
\(slope\: AC=\frac{y_2−y_1}{x_2−x_1}=\frac{0-0}{0-4}=\frac{0}{-4}=0\: \quad (\text{horizontal line)}\)Slope AB:
A(4, 0) and B(0, 4)
\(slope\: AB=\frac{y_2−y_1}{x_2−x_1}=\frac{4-0}{0-4}=\frac{4}{-4}=-1\)As you can see, only the slope of altitude CF exists.
\(slope\: CF=-\frac{1}{slope\: AB}=-\frac{1}{-1}=1\)Therefore, the slope of altitude CF is found to be 1
a tire manufacturer has a 60,000 mile warranty for tread life. the manufacturer considers the overall tire quality to be acceptable if less than 8% are worn out at 60,000 miles. based on a sample of tires, researchers conclude that the proportion of tires that are worn out at 60,000 miles is not less than 8%. what type of statistical inference is this? group of answer choices interval estimation hypothesis testing point estimation
Answers
In order to answer the above question, we may thus state that the type of statistical inference in this scenario is null hypothesis testing.
What is null hypothesis?A type of statistical hypothesis known as a null hypothesis claims that a particular collection of observations has no significance in statistics. The viability of theories is evaluated using sample data. Occasionally referred to as "zero," and represented by H0. The assumption made by researchers is that there may be a relationship between the factors. The null hypothesis, on the other hand, asserts that such a relationship does not exist. Although it might not seem significant, the null hypothesis is an important part of study.
The type of statistical inference in this scenario is hypothesis testing.
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bdhbdwbchdbvcwvdebvkbdebv kdbvjbwkv
Answers
What is called angle?.
Answers
When two rays intersect an angle is created, As different classification of angles are there on the basis of measurement of angles and on the basis of properties of angles.
What is definition of term "Angle" ?When two rays or straight lines intersect at one of their ends, an angle is created. Vertex of an angle refers to the point at which two points meet. The Latin word "angulus," which means "corner," is the origin of the English term "angle."
Symbol of Angle
The symbol ∠ represents an angle. Angles are measured in the form of degrees (°) using a protractor.
For example, 45 degrees is represented as 45°
Sections of Angles
A vertex is also the corner of an angle or at the place where two lines or sides come together to intersect at the point. In the above figure, O is the vertex.Arms: The angle's two sides which are connected at a single terminal. An angle's OA and OB are its arms.Initial Side: Also known to as the reference line, this is the first side of the angle that is to be drawn. The reference line is called OB.Terminal Side: The side that the angle measured is performed up to. OA is the terminal side.Types of Angles
Based on their measurements, here are the many types of angles:
An acute angle that measures less than 90° at the vertex of the lines.An obtuse angle measured between 90° to 180°.A right angle is exactly measures 90° at the vertex.An angle measuring precisely 180° is called a straight angle.A reflex angle is measured between 180°- 360°.A complete angle is measured is equal 360°.Interior and Exterior Angles:
Interior angles: Interior Angles are angle formed inside the shape.
Exterior angles: Exterior angles are to be angles that is formed outside a shape, between any side of shape and to an extended adjacent side.
Complementary and Supplementary Angles:
Complementary angles: Angles that add up to 90° (a right angle) are called complementary angles.
Supplementary angles: Angles that add up to 180° (a straight angle) are called supplementary angles.
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the description of simple integer arithmetic expressions with addition and multiplication cannot be represented by a context-free grammar.
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Simple integer arithmetic expressions with addition and multiplication cannot be represented by a context-free grammar due to their recursive and hierarchical nature.
Context-free grammars (CFGs) are formal grammars that can be used to generate languages based on a set of production rules. However, CFGs are limited in their ability to represent certain types of languages. One such limitation is the inability to represent the recursive and hierarchical structure of simple integer arithmetic expressions involving addition and multiplication.
In simple integer arithmetic expressions, operands can be combined using addition and multiplication operators. These expressions can be nested, with subexpressions appearing within larger expressions. The recursive nature of these expressions poses a challenge for CFGs because they require an unbounded number of production rules to capture all possible levels of nesting.
CFGs are designed to handle languages with a linear structure, where the order of symbols is important but not their hierarchical relationships. While CFGs can handle addition or multiplication operations individually, they struggle to capture the nested structure and precedence rules inherent in arithmetic expressions.
To represent simple integer arithmetic expressions with addition and multiplication, more powerful formalisms such as context-sensitive grammars or parsing algorithms like recursive descent or operator precedence parsing are typically used. These approaches can handle the recursive and hierarchical nature of arithmetic expressions, allowing for the correct interpretation of operators and operands based on their precedence and associativity.
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The complete question is :
why simple integer arithmetic expressions with addition and multiplication cannot be represented by a context-free grammar?
Find the amount to which $800 will grow under each of these conditions: a. 8% compounded annually for 9 years. Do not round intermediate calculations. Round your answer to the nearest cent. $ b. 8% compounded semiannually for 9 years. Do not round intermediate calculations. Round your answer to the nearest cent. $ C. 8% compounded quarterly for 9 years. Do not round intermediate calculations. Round your answer to the nearest cent. d. 8% compounded monthly for 9 years. Do not round intermediate calculations. Round your answer to the nearest cent. $ e. 8% compounded daily for 9 years. Assume 365-days in a year. Do not round intermediate calculations. Round your answer to the nearest cent. $ f. Why does the observed pattern of FVs occur?
Answers
The amount to which $800 will grow under each of the given conditions increases as the compounding period decreases.
The amount to which $800 will grow under each of these conditions is as follows:a) 8% compounded annually for 9 years
When compounded annually for 9 years at 8%, the formula is: Amount = Principal x [(1 + rate/n)^(n*t)]
Where: Principal = $800 Rate = 8% Time = 9 years
Compounded annually = n = 1 Amount = $1,447.91 (rounded to the nearest cent)
b) 8% compounded semiannually for 9 years Compounded semiannually for 9 years at 8%, the formula is:
Amount = Principal x [(1 + rate/n)^(n*t)]
Where: Principal = $800 Rate = 8% Time = 9 years Compounded semiannually = n = 2 Amount = $1,471.16 (rounded to the nearest cent)
c) 8% compounded quarterly for 9 years Compounded quarterly for 9 years at 8%, the formula is:
Amount = Principal x [(1 + rate/n)^(n*t)]
Where: Principal = $800 Rate = 8% Time = 9 years Compounded quarterly = n = 4 Amount = $1,491.03 (rounded to the nearest cent)
d) 8% compounded monthly for 9 years Compounded monthly for 9 years at 8%, the formula is: Amount = Principal x [(1 + rate/n)^(n*t)]
Where: Principal = $800 Rate = 8% Time = 9 years Compounded monthly = n = 12 Amount = $1,505.91 (rounded to the nearest cent)
e) 8% compounded daily for 9 years Compounded daily for 9 years at 8%, the formula is:
Amount = Principal x [(1 + rate/n)^(n*t)]
Where: Principal = $800 Rate = 8% Time = 9 years Compounded daily = n = 365Amount = $1,511.74 (rounded to the nearest cent)
The observed pattern of FVs (future values) occurs due to compounding. Compounding is the process of earning interest not only on the principal amount invested but also on the interest earned from the principal. This results in an increase in the interest earned and the future value of the investment. The more frequent the compounding, the higher the future value of the investment. Hence, the amount to which $800 will grow under each of the given conditions increases as the compounding period decreases.
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"A study conducted several years ago reported that 21% of public accountants changed companies within 3 years. The American Institute of CPAs would like to update the study. They would like to estimate the population proportion of public accountants who changed companies within 3 years with a margin of error of 3% and a 95% level of confidence.
(Round up your answers to the next whole number.) Required: a. To update this study, how many public accountants should be contacted?"
Answers
Putting all the given values in the formula, we get:n = [1.96² x 0.21 x 0.79] / 0.03²On solving, we get,n = 2734.84 ≈ 2735Therefore, 2735 public accountants should be contacted to update the study with a margin of error of 3% and a 95% level of confidence. Answer: 2735.
Given Information :A study conducted several years ago reported that 21% of public accountants changed companies within 3 years.
The American Institute of CPAs would like to update the study.
They would like to estimate the population proportion of public accountants who changed companies within 3 years with a margin of error of 3% and a 95% level of confidence.
Required:a. To update this study, how many public accountants should be contacted? Solution: Given that: the percentage of public accountants changed companies within 3 years is 21%.The level of confidence is 95%.
The margin of error is 3%.We have to find out the sample size.To find the sample size we use the formula :n = [Z² x p x q ] / E²
Where, Z = Standard normal deviation corresponding to a 95% confidence level is 1.96.p = proportion = 21/100 = 0.21q = 1-p = 1-0.21 = 0.79E = margin of error = 3/100 = 0.03
Putting all the given values in the formula, we get:n = [1.96² x 0.21 x 0.79] / 0.03²On solving, we get,n = 2734.84 ≈ 2735Therefore, 2735 public accountants should be contacted to update the study with a margin of error of 3% and a 95% level of confidence. Answer: 2735.
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B. Describe the relationship between bridge length and breaking weight. How is thatrelationship shown by patterns in your table and graph?C. Use your data to predict the breaking weights for bridges of lengths 3,5, 10, and 12 inches.Explain how you made your predictions.D. Compare your data from this experiment to the data from the experiment on bridges withdifferent numbers of layers. How is the relationship between the number of layers in a bridgeand its breaking weight similar to the relationship between bridge length and breakingweight? How is it different?
Answers
ANSWER and EXPLANATION
B. We are to describe the relationship between bridge length and breaking weight.
To do this, we need to check the graph.
In doing that, we will see that the breaking weight appears to decrease as the Bridge length increases.
We can conclude then that the breaking weight and bridge length have an inverse relationship.
That is shown in the graph.
The highest value of the breaking weight is 14 and that is when the value of bridge length is at its lowest (4).
The lowest value of the breaking weight is 3 and that is when the value of the bridge length is at its highest (11)
Hence, there is an inverse relationship between them.4)
Plsss help I don’t know how to solve it :)
Answers
Answer:
x= 29
Step-by-step explanation:
These angles equal 180° since they are corresponding angles.
So, the equation would be: (2x-10)+(4x+16)= 180.
Step 1- Add common variables.
(2x+4x)+(16-10)= 180
6x+6= 180
Step 2- Subtract 6 to both sides.
6x+6= 180
-6 -6
6x= 174
Step 3- Divide both sides by 6.
6x= 174
6 6
x= 29
Answer:
x=29
Step-by-step explanation: The two angles for are supplementary, so the equation will be equal to 180 degrees. So to find 180 degrees you need to put (2x-10) and (4x+16) on the same side of the equation.
180=(2x-10)+(4x+16) Combine like terms
180=6x+6 Subtract 6 from both sides
174=6x Divide both sides by 6
29=x
Check:
2*29-10
58-10= 48
4*29+16
116+16=132
132+48=180
andrew is packing the trunk of his car with three boxes. each box is in the shape of a cube with a volume of 2,744 cubic inches. if andrew wants to know the length of the side of each box, what does he need to find?
Answers
Andrew have to find the cube root of the volume to find the length of each side of the boxes he is packing in the trunk of his car. the length is of the box is solved to be 14 inches
What are radicals in math?A radical in mathematics is the opposite of an exponent, which is symbolized by the sign "n√" also known as root.
The number before the symbol or radical is regarded as an index number or degree, and it can either be a square root or a cube root and so on.
How to perform the required calculationThe volume of a cube is given by
v = length^3
2744 = length^3
∛2744 = length
length = 14 inches
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Find the sum of 1
5
and 7
10
The expression written in equivalent form with common denominators is .
The sum is
Answers
Answer:
2/10 + 7/10
9/10
Step-by-step explanation:
I did the test.
Answer:
The expression written in equivalent form with common denominators is
✔ 2/10 + 7/10
The sum is
✔ 9/10
Step-by-step explanation:
A rectangular park is w feet wide. The park is 25ft longer than it is wide. Record your answer to each using algebra
Answers
The length of the rectangular park is (w+25) feet
The perimeter of the rectangular park is 2 (2w+25) feet
The area of the rectangular park is (w²+25w) feet.
What is rectangle?
Rectangle is a four sided polygon or specifically a particular type of parallelogram having two opposite sides are equal and one angle is right angle that is 90°. It has four vertices and two diagonals intersect each other.
A rectangular park is w feet wide. The park is 25ft longer than it is wide.
If the width of the park is w feet then the length of the rectangular park will be (w+25)ft.
Perimeter of the rectangular park is 2 ( length + width)
= 2 ( w+25+w) feet
= 2 (2w+25) feet.
Area of the rectangular park = length × width
= (w+25)× w square feet
Area = w(w+25)= w²+25 w square feet.
Hence,
The length of the rectangular park is (w+25) feet
The perimeter of the rectangular park is 2 (2w+25) feet
The area of the rectangular park is (w²+25w) feet.
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find the exact length of the curve. x = et − 4t, y = 8et/2, 0 ≤ t ≤ 3
Answers
The exact length of the curve is \(e^{3}\) + 11
given that
x = \(e^{t}\) - 4t , y = 8\(e^{\frac{t}{2} }\) , 0 ≤ t ≤ 3
we need to find the exact length of the curve
=\(\int\limits^b_a\)\(\sqrt{(\frac{dx}{dt} )^{2} + (\frac{dy}{dt} )^{2} }\)dt
\(\frac{dx}{dt}\) = \(e^{t}\) - 4 , \(\frac{dy}{dt}\) = 8\(e^{\frac{t}{2} }\)(\(\frac{1}{2}\)) = 4 \(e^{\frac{t}{2} }\)
=\(\int\limits^3_0\)\(\sqrt{(e^{t} )^{2} + (4e^{\frac{t}{2} } )^{2} }\)dt
=\(\int\limits^3_0\)\(\sqrt{e^{2t} + 16e^{t} + 16 - 8e^{t} }\)dt
=\(\int\limits^3_0\)\(\sqrt{e^{2t} + 8e^{t} + 16 }\)dt
=\(\int\limits^3_0\)\(\sqrt{(e^{t} + 4 )^{2} }\)dt
=\(\int\limits^3_0\) \(e^{t}\) + 4
=(\(e^{3}\) + 4(3)) - ( \(e^{0}\) + 4(0))
= \(e^{3}\) + 12 - 1
= \(e^{3}\) + 11
The exact length of the curve is \(e^{3}\) + 11
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Hi, I am a boy who is 15 using my sisters account, thats why it says faith, my name is Alex.
Answers
Answer: cool
Step-by-step explanation:
Answer: ok
Step-by-step explanation: ok
please help. will guve brainliest
Answers
Answer:
ASA
Step-by-step explanation:
Because QR bisects ∠PQS, ∠PQR ≈ ∠SQR
QR = QR
It is given that ∠ PRQ ≈ ∠SRQ
What values of the orbital number, or angular momentum (l) and magnetic (m_l) quantum numbers...
Answers
1a)The values of l range from 0 to (n-1), so for n = 3, l can have the values 0, 1, and 2.
b) The values of m can be -2, -1, 0, +1, and +2
c) There are a total of 9 orbitals
What are quantum numbers?
The qualities and traits of quantum systems, like the electrons in atoms, are described by a set of numbers known as quantum numbers. They offer knowledge on the system's energy, angular momentum, orientation, and spin, among other characteristics.
Using the formula, number of electrons = \(n^2\)
Number of electrons =\(3^2 = 9\)
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PLEASE HELP I WILL MARK BRAINLIEST
Answers
The measure of arc ED is 78.7°
How to find the measure of an arc?An arc of a circle is a portion of the circumference of a circle. It is defined by two endpoints and the arc itself.
The measure of an arc is given in degrees or radians, and it is determined by the angle that it subtends at the center of the circle.
Since FC is the diameter and arc FB is equivalent to arc BC. We can say:
arc FB + arc BC = 180°
arc FB = arc FB = 90°
Also, arc ED is twice the measure of arc CD. We can write:
arc ED = 2 * arc CD
arc CD = (arc ED)/2
Since the sum arc FB and arc BC is 180°. We can say:
arc FE + arc ED + 0.5(arc ED) = 180°
62° + arc ED + 0.5(arc ED) = 180°
62° + 1.5(arc ED) = 180°
1.5(arc ED) = 180 - 62
1.5(arc ED) = 118
arc ED = 118/3
arc ED =78.7°
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A rectangle has a height of 8 inches and a base of 12 inches. If we double the height, by how many inches will the perimeter increase?
Answers
Perimeter is the total sum of the 4 sides.
The height is given as 8 inches. If this is doubled the new height becomes 16 inches. (The height increases by 8 inches)
total increase in perimeter = 8 + 8 = 16 inches.
Answer: 16 inches
determine whether the series is convergent or divergent.
sigma^infinity _n = 0 ln(n^2+3/8n^2+7)
convergent divergent
if it is convergent, find its sum. (if the quantity diverges, enter diverges.)
Answers
To determine whether the series is convergent or divergent, we can use the integral test.
First, we note that the function f(x) = ln(x^2+3/8x^2+7) is continuous, positive, and decreasing for x ≥ 1.
Then, we take the integral of f(x) from 1 to infinity:
∫_1^∞ ln(x^2+3/8x^2+7) dx
We can evaluate this integral using integration by parts:
u = ln(x^2+3/8x^2+7) dv = dx
du/dx = (2x)/(x^2+3/8x^2+7) v = x
∫_1^∞ ln(x^2+3/8x^2+7) dx = [xln(x^2+3/8x^2+7)]_1^∞ - ∫_1^∞ (2x)/(x^2+3/8x^2+7) dx
We know that the limit of xln(x^2+3/8x^2+7) as x approaches infinity is infinity, so the first term evaluates to infinity.
For the second term, we can use the substitution u = x^2 to get:
∫_1^∞ (2x)/(x^2+3/8x^2+7) dx = ∫_1^∞ (2du)/(u+3/8u+7)
We can then use partial fractions to write the integrand as:
(2du)/((u/8)+7/8) - (2du)/(u+7)
We can now evaluate the integral:
∫_1^∞ (2du)/(u+3/8u+7) = [2ln(u/8+7/8)]_1^∞ = 2ln(∞/8+7/8) - 2ln(1/8+7/8) = ∞
∫_1^∞ (2du)/(u+7) = 2ln(u+7)]_1^∞ = ∞ - 2ln(8) = ∞
Since both integrals diverge, the original series diverges by the integral test. Therefore, the answer is divergent.
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if tanA=2ab/a square-b square.find the value of cosA and sin A
Answers
Answer:
\(\displaystyle \displaystyle \cos A = \frac{a^2-b^2}{a^2 + b^2}\text{ and } \sin A = \frac{2ab}{a^2 + b^2}\)
Step-by-step explanation:
We are given that:
\(\displaystyle \tan A = \frac{2ab}{a^2 - b^2}\)
And we want to find the value of cos(A) and sin(A).
Recall that tangent is the ratio of the opposite side to the adjacent side.
Therefore, the opposite side measures 2ab, and the adjacent side measures a² - b².
Using the Pythagorean Theorem, solve for the hypotenuse:
\(\displaystyle \begin{aligned} c^2 &= a^2 + b^2 \\ \\ c&= \sqrt{(2ab)^2 + (a^2-b^2)} \\ \\ &= \sqrt{(4a^2b^2)+(a^4-2a^2b^2+b^4)} \\ \\ &= \sqrt{a^4 + 2a^2b^2 + b^4 } \\ \\ &= \sqrt{(a^2 +b^2)^2} \\ \\ &= a^2 + b^2\end{aligned}\)
Thus, our hypotenuse is given by a² + b².
Cosine is the ratio between the adjacent side and the hypotenuse. Thus:
\(\displaystyle \cos A = \frac{a^2-b^2}{a^2 + b^2}\)
And sine is the ratio between the opposite side and the hypotenuse. Thus:
\(\displaystyle \sin A = \frac{2ab}{a^2 + b^2}\)
In conclusion:
\(\displaystyle \displaystyle \cos A = \frac{a^2-b^2}{a^2 + b^2}\text{ and } \sin A = \frac{2ab}{a^2 + b^2}\)
Answer:
Step-by-step explanation:
\(sec^2A-tan^2A=1\\sec^2A=1+tan^2A=1+\frac{4a^2b^2}{(a^2-b^2)^2} =\frac{(a^2-b^2)^2+4a^2b^2}{(a^2-b^2)^2} =\frac{(a^2+b^2)^2}{(a^2-b^2)^2} \\cos^2A=\frac{(a^2-b^2)^2}{(a^2+b^2)^2} \\cos A=\frac{a^2-b^2}{a^2+b^2} \\sin A=\sqrt{1-cos^2A} =\sqrt{1-(\frac{a^2-b^2}{a^2+b^2} )^2} =\sqrt{\frac{(a^2+b^2)^2-(a^2-b^2)^2}{(a^2+b^2)^2} } =\sqrt{\frac{4a^2b^2}{(a^2+b^2)^2} }=\frac{2ab}{a^2+b^2}\)
Find the distance between the points (8,3) and (2,7) the answer must be a whole number
Answers
Answer:
let (8,3) be (x1,y1)
(2,7) be (x2,y2)
using distance formula
√[(x2-x1)²+(y2-y1)²]
√(2-8)²+(7-3)²
√(36+16)
√52
a u.s quarter has a mass of 5.67 grams a penny has a mass of 2.5 grams what is the total mass of the two coins? show your work
Answers
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The total mass of the US quarter and the penny is 8.17 grams
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example:
2 + 3x + 4y = 7 is an expression.
We have,
Mass of a US quarter = 5.67 grams
Mass of a penny = 2.5 grams
The total mass of the US quarter and the penny.
= 5.67 + 2.5
= 8.17 grams
Thus,
The total mass of the US quarter and the penny is 8.17 grams
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The athletic department at Pi High School is planning a circular track 440
yards long (circumference). The area inside the track will be planted with
sod. About how many square yards of sod are needed. Round your answer
to the nearest whole number.
Answers
Answer:
The amount of sod that is needed is 15400 yards².Step-by-step explanation:
We know that:
Circumference = 2πrCircumference = 440 yardsWe will need to find the radius to find the area of the circular track. Let's simplify the equation 2πr = 440.
=> 2πr = 440=> πr = 440/2=> 22r/7 = 220=> 22r/7 = 22 x 10=> r/7 = 10=> r = 70Now, let's substitute the radius into πr².
=> πr²=> 22/7 x 70 x 70=> 22 x 10 x 70=> 15400 yards²Hence, the amount of sod that is needed is 15400 yards².
A company makes skis for junior skiers with lengths of 120 to 140 cm inclusive. Identify the compoundinequality and graph that show these lengths.
Answers
The juniors skiers can have the lengths of 120 to 140 as we can see the skiers lengths can touch the length of 120 and 140 that is why in the inequality we will use less than or equal to and in the number line we will see a filled circle in 120 and 140.
Therefore the solution is
Ron wins £1 1/4 million. He gives 3/5 million to his daughter and £1/3 million to his wife. How much does he have left?
Answers
Answer:
0.31
Step-by-step explanation:
1 1/4 - 1/3 - 3/5 = 19/60
≅ 0.3166667
Lola needs to sign 96 invitations. Using a stopwatch that measures time to tenths of a second, it takes Lola 5.3 seconds to sign her full name. Going by the accuracy of the stopwatch, which is the most accurate determination for the number of seconds Lola needs to sign all 96 invitations?
Answers
The time needed by Lola to sign all the 96 invitations is 508.8 second
What is a Product ?Product is the number obtained when two numbers are multiplied with each other
It is given that
Total Invitations that Lola needs to sign = 96
Time taken to sign full name = 5.3 seconds
Total time needed by Lola to sign invitations is
96 * 5.3
= 508.8 seconds
Therefore the time needed by Lola to sign all the 96 invitations is 508.8 second
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30°25'45" into second
Answers
Answer:
109545
Step-by-step explanation:
Formula
multiply the time value by 3600
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