The x ≤ 32Putting x = 24 in the expression we get RC = 96Therefore, the value of RC is 96.
In order to find RC, we will make use of the given information in the following manner: Given that ABDC is a parallelogram. Hence, AB = DC. We have also been given that PQ = 735 and QR = 112.Now, extend PQ to meet DC at S.Let PS = x; then DS = DC - x = AB - x. (Since AB = DC)We have that PS/SP = QR/RB (Since PQR is similar to DBR)Therefore, we getx/SP = 112/(AB - x)We can cross multiply and simplify to getSP = (112* x)/(AB - x)......(1)Further, we have that AQ/QB = SP/BR (Since PQR is similar to AQB)Therefore, we getx/(AB - x) = SP/BROn substituting the value of SP from equation (1) above, we getx/(AB - x) = (112* x)/(BR*(AB - x))Therefore, we getBR = (x*(AB - x)*QR)/[PQ*(AB - 2*x)]BR = (x*(32 - x)*112)/(735*(32 - 2*x))BR = (56*x*(16 - x))/(245*(16 - x))BR = (56*x/245)Since the sum of all sides of a parallelogram is equal to the sum of its opposite sides, we have thatRC + QR = AB + AQ - QBRearranging the terms we getRC = AB + AQ - QB - QR......(2)Now, AQ = PQ - APSubstituting the values of PQ and AP we get AQ = 735 - (DC - x) = 735 - 32 + x = x + 703Also, QB = AB - AQ = (32 - x) - (x + 703) = -x - 671Substituting the values of AQ and QB in equation (2) above we getRC = 32 + (x + 703) + (x + 671) - 112RC = 48 + 2xRC = 2(x + 24)We know that AB = 32, hence, x ≤ 32Putting x = 24 in the expression we get RC = 96Therefore, the value of RC is 96.
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Kate plans to save 5% of her income. She just earned 80.Howmuchmoneyshouldsheputintosavings?
$4
Multiply 80 by 0.05 to get the answer of $4
Answer:
4 (insert the currency needed)
Step-by-step explanation:
To find our answer we have to find 5% of Kate's wages and to do this we have to do 5 divided by 100. Then that answer is multiplied by 80!
5 ÷ 100 = 0.0580 × 0.05 = 4This means she has to put £4 into her savings!
Hope this helps, have a lovely day! :)
what is the sum of all integer values of $x$ such that $\frac{31}{90} < \frac{x}{100} < \frac{41}{110}$ is true?
Select the correct answer. Solve for x. x2 - 2x - 24 = 0
A.
-4, -6
B.
-4, 6
C.
2, -6
D.
4, 6
Answer:
B. -4, 6
Step-by-step explanation:
y is inversely proportional to the square of x. It is given that y = 8 for a particular value of x. k= When x increases by 300%, find the new value of y,
Answer:
1/2 or .5
Step-by-step explanation:
If y is inversely proportional to the square of x, we can express this relationship using the formula:
y = k/x^2
where k is a constant of proportionality. We are told that y = 8 for a particular value of x, so we can substitute these values into the equation:
8 = k/x^2
To find the value of k, we can solve for it:
k = 8x^2
Now we are asked to find the new value of y when x increases by 300%. This means that the new value of x will be 4 times the original value (since an increase of 300% means an increase by a factor of 3, and we need to add the original value to get the new value). So we can substitute 4x for x in our equation:
y = k/(4x)^2 = k/16x^2
We already know the value of k, so we can substitute it in and simplify:
y = (8x^2)/(16x^2) = 1/2
Therefore, the new value of y is 1/2 when x increases by 300%.
The daily temperatures for the winter months in Virginia are Normally distributed with a mean of 59 F and a
standard deviation of 10°F. A random sample of 10 temperatures is taken from the winter months and the mean
temperature is recorded. What is the standard deviation of the sampling distribution of the sample mean for all
possible random samples of size 10 from this population?
The standard deviation of the sampling distribution of the sample mean for the given sample size is equal to 3.1623°F.
For the normally distributed data,
Mean of the population distribution 'μ' = 59F
Population standard deviation 'σ' = 10°F
Sample size 'n' = 10
Formula for the standard deviation of the sampling distribution of the sample mean (also known as the standard error of the mean) is equal to ,
= σ / √(n)
Substitute the value to get the standard deviation of the sampling distribution of the sample mean we get,
= 10°F / √(10)
= 3.1623°F
Therefore, the standard deviation of the sampling distribution of the sample mean for all possible random samples of size 10 from this population is approximately 3.1623°F.
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At the book store, you purchased some $3 clearance mystery books and $8 regular-priced science fiction books. How many of each did you buy if you spent a total of $77?
Answer:
we bought 12 $3 clearance mystery books and 5 $8 regular-priced science fiction books.
Step-by-step explanation:
What geometric shapes can you draw that have exactly one pair of parallel sides? Use pencil and paper. Sketch examples for as many different types of shapes as you can. Use appropriate marks to show the pairs of parallel sides.
A. regular pentagon
B. square
C. Trapezoid
D. parallelogram
what is the messure or the vertex angle of an isosceles triangle if one of its base angle measures 16 degrees
Write each polynomial in Standard form and name it based on its degree an number of terms.
9x²-213
Standard --
Degree
Terms
We would name this polynomial as a quadratic polynomial with two terms.
In standard mathematics, what is a polynomial function?A polynomial function is one that involves only non-negative integer powers or positive integer exponents of a variable in an equation such as the quadratic equation, cubic equation, and so on.
In the standard form of a polynomial, the terms are written in descending order of degree. The standard form for a polynomial of degree n is:
a1x + a0 + anxn + an-1xn-1 +...
We have the polynomial in this case:
9x² - 213
To write it in standard form, rearrange the terms in descending order of degree as follows:
213 + 9x²
As a result, the standard form of the polynomial is:
9x² - 213
This polynomial has degree 2 (because x's highest exponent is 2) and two terms (since there are two distinct parts to the expression, a constant and a term with an x squared coefficient).
As a result, we'd call this polynomial a quadratic polynomial with two terms.
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a relationship that is noted between two or more variables is termed
The relationship that is noted between two or more variables is termed a correlation. Correlation refers to the statistical association or relationship between two or more variables.
It indicates the degree to which the variables are related or how they are related to each other. Correlation can be positive, negative, or zero, depending on the direction and strength of the relationship between the variables.
A positive correlation indicates that as one variable increases, the other variable also increases. A negative correlation indicates that as one variable increases, the other variable decreases. Zero correlation indicates that there is no relationship between the variables.
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Let P be some predicate. Check the box next to each scenario in which ∀n ∈ N, P(n) must be true.
a) For every natural number k > 0 , if P(i) holds for every natural number i < k, then P(k) holds.
b) P(0) holds and for every natural number k > 0, if P(i) does not hold, then there is some natural number i < k such that P(i) does not hold.
c) For every natural number k, if P(i) holds for every natural number i < k, then P(k) holds.
d) For every natural number k, if P(k) does not hold, then there is a smaller natural number i < k such that P(i) does not hold.
Answer:
A
Step-by-step explanation:
a) ✔️
This is the principle of mathematical induction. If P holds for the base case k=1 and we can show that if it holds for any arbitrary k (e.g. k=n) then it must also hold for the next value (e.g. k=n+1), then we have shown it holds for all natural numbers.
b) ❌
There is no guarantee that P holds for all natural numbers from the statement alone. It only guarantees that for any k where P does not hold, there exists a smaller number i where P does not hold.
c) ❌
This is the principle of weak mathematical induction. It only shows that if P holds for a given k and for all smaller values i then it must hold for k+1. It does not guarantee that P holds for all natural numbers.
d) ❌
This statement is the negation of the principle of mathematical induction. It is known as the "strong induction" principle, which assumes that if P does not hold for k, then there exists a smaller i where P does not hold. However, this principle is not sufficient to prove that P holds for all natural numbers k.
The neck of a gifaffe is 4 1/2 feet in length. Its neck is 30 perocent of it height whats the higet of the giffae
The giraffe is 15 feet tall based on the relation between the length of neck of giraffe and it's height.
Firstly convert the mixed fraction to fraction.
Length of neck of giraffe = (4×2)+1/2
Length of neck = 9/2 feet
Now, let us assume the height of giraffe be x. So, equation will be -
30% × x = 9/2
Rewriting the equation
30/100 × x = 9/2
Cancelling zero
3x/10 = 9/2
Again rewriting the equation
x = 90/6
Performing division on Right Hand Side of the equation
x = 15 feet
Thus, height of giraffe is 15 feet.
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Find the amount of the following ordinary annuities rounded to the nearest cent. Find the tot
Amount of Deposited
Interest
Rate Time (Years) Amount of an
Annuity
Earned
each deposit
$1050
annually
5%
14
Answer:I=(PxRxT)/100
I=(10000x20x1)/100x2
I=200000/200
I=1000I=(
Step-by-step explanation:
I need some help please
Given:-
[tex] \texttt{c = 1}[/tex][tex] \: [/tex]
[tex] \texttt{d = 3}[/tex][tex] \: [/tex]
Solution:-
[tex] \texttt{3(2c + d ) -4 ( c - d ) + d² }[/tex][tex] \: [/tex]
put the given values in tha equation
[tex] \texttt{= 3( 2 ( 1 ) + 3 ) -4 ( 1 - 3 ) + ( 3 )² }[/tex][tex] \: [/tex]
[tex] \texttt{= 3 ( 2 + 3 ) -4 ( -2 ) + 9}[/tex][tex] \: [/tex]
[tex] \texttt{= 3 ( 5 ) -4 ( -2 ) + 9}[/tex][tex] \: [/tex]
[tex] \texttt{= 15 + 8 + 9}[/tex][tex] \: [/tex]
[tex] \texttt{= 23 + 9}[/tex][tex] \: [/tex]
[tex] \boxed{ \texttt{ \purple{= 32}}}[/tex][tex] \: [/tex]
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
hope it helps ⸙
suppose 46.37% of all voters in the last election supported the current governor. a telephone survey contacts 328 voters from the last election and asks if they voted for the current governor. what is the probability that at least half of the voters contacted supported the current governor in the last election?
The probability that at least half of the 328 voters contacted in the telephone survey supported the current governor in the last election is 0.0532.
What is the probability?To calculate the probability that at least half of the 328 voters contacted in the telephone survey supported the current governor in the last election, we can use the binomial probability formula.
The formula is: P(x) = (ⁿCₓ) × pˣ × (1-p)⁽ⁿ⁻ˣ⁾
In this case, n = 328, p = 46.37%, and x = 164 (since half of 328 is 164).
Plugging in the numbers we get:
P(x) = ³²⁸C₁₆₄ × (0.4637)¹⁶⁴ × (0.5363)⁽³²⁸⁻¹⁶⁴⁾ = 0.0532
Therefore, the probability that at least half of the 328 voters contacted in the telephone survey supported the current governor in the last election is 0.0532.
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if cell phone companies screen text messages, then freedom of speech is threatened. thus, freedom of speech is not threatened, because cell phone companies do not screen text messages. which of the following correctly expresses the form of this argument? a. if c then f. b. not f. c. all c are f. d. if c then f. e. if c then f. not
The correct option that expresses the form of the given argument is "d. if c then f."Explanation:In the given argument, it is stated that if cell phone companies screen text messages, then freedom of speech is threatened.
But as cell phone companies do not screen text messages, so freedom of speech is not threatened. This is a conditional argument, and it can be expressed in the form of a hypothetical syllogism.
The hypothetical syllogism is a syllogism that has a conditional statement in its premises. It is also called a chain argument or transitive argument. The form of the hypothetical syllogism is "If A, then B. If B, then C.
Therefore, if A, then C."In the given argument, it can be expressed in the form of the hypothetical syllogism as follows:If cell phone companies screen text messages, then freedom of speech is threatened. If freedom of speech is threatened, then cell phone companies screen text messages. Therefore, if cell phone companies do not screen text messages, then freedom of speech is not threatened.This can also be represented as "if C then F."Therefore, the correct option that expresses the form of the given argument is "d. if c then f."
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14. The perimeter of the table shown is 18 feet. Write an equation
in the form px + q = r to solve for x.
6
Answer:
its 3
Step-by-step explanation:
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assume that 1 laborer produces 6 units of output, 2 laborers produce 15 units of output, 3 laborers produce 25 units of output, and 4 laborers produce 34 units of output. diminishing returns to labor set in when the firm hires the
The marginal product of labor initially increases from 6 to 9, but then starts to decrease as more labor is added. Therefore, the firm experiences diminishing returns to labor when it hires a third laborer.
Diminishing returns to labor occur when the marginal product of labor (i.e., the additional output produced by adding one more unit of labor) decreases as more labor is added. We can calculate the marginal product of labor for each level of labor as follows:
1 laborer: 6 units of output (marginal product = 6)
2 laborers: 9 units of additional output (total output = 15, marginal product = 9)
3 laborers: 10 units of additional output (total output = 25, marginal product = 10)
4 laborers: 9 units of additional output (total output = 34, marginal product = 9)
The law of diminishing marginal returns is a concept from economics that explains how the marginal output of a production process starts to decrease as the input goes up. It is also used to refer to a point at which output increases at a diminishing rate as more units of labor are added to a production process. This can also be called the point of decreasing marginal productivity.
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7) A long piece of wire of length 90 cm is bent to form an equilateral triangle. What will be the length of each side of the triangle?
Answer:
30cm
Step-by-step explanation:
Perimeter of an equilateral triangle = 3L
Mathematically we have;
P = 3L
Where P = perimeter of the triangle
L = Length
Therefore;
90 = 3L
Divide both side by 3
L = 30cm
Therefore, the length of each side of the triangle is 30cm.
Let sin(2x) = cos(x), where 0° ≤ x < 180°. what are the possible values for x? a. 30° only b. 90° only c. 30° or 150° d. 30°, 90°, or 150°
If sin(2x) = cos(x), where 0° ≤ x < 180°, then, The possible angle values of x are 90°, 30° and 150°.
The sine and the cosine are trigonometric functions of the angles. The sine and cosine of an acute angle are defined in the context of a right triangle: for a given angle, its sine is the ratio of the length of the side opposite the angle to the length of the longest side of the angle. triangle (the hypotenuse ), and the cosine is the adjacent side The ratio of the length to the hypotenuse.
According to the Question:
Given that,
sin(2x) = cos(x) where 0° ≤ x < 180°
We know that:
sin(2x) = 2 sin(x) cos(x)
⇒ 2 sin(x) cos(x) = cos(x)
Subtract cos(x) on both sides
2 sin(x) cos(x) - cos(x) = 0
cos(x) (2sinx-1)=0
It means, cos(x) = 0 and (2sin x -1 ) = 0
cos x = cos0 and sinx(x) = 1/2
x = 90° and x = 30°, 150°
Hence, the possible values of x are 90°, 30° and 150°.
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which of the following is an incorrect statement? if a density curve is skewed to the right, the mean will be larger than the median. in a symmetric density curve, the mean is equal to the median. the mean of a skewed distribution is pulled toward the long tail. the median is the balance point in a density curve.
In a skewed distribution, the long tail pulls the mean toward it. In a density curve, the median is where everything level out.
what is mean ?The median, a statistician's measure of central tendency, divides a dataset into two equally sized half. When the data is organized from smallest to largest, it is the midway value (or largest to smallest). The median is the average of the two middle values when there are an even number of values. Since it is unaffected by extreme values, the median is frequently employed as a measure of central tendency when a dataset contains outliers or is skewed.
given
None of the claims are untrue.
The mean will be greater than the median if a density curve is tilted to the right.
The mean and median are equal in a density curve that is symmetric.
In a skewed distribution, the long tail pulls the mean toward it. In a density curve, the median is where everything level out.
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25 out of 68 students have vanilla ice cream and the rest have chocolate. What is the ratio of the number of students who have vanilla to the total number of students?
Answer: The total number of students is the sum of the number of students who have vanilla and those who have chocolate:
Total = 25 + (68 - 25) = 43
The ratio of the number of students who have vanilla to the total number of students is:
Vanilla : Total = 25 : 43
This ratio cannot be simplified any further because 25 and 43 do not have any common factors other than 1. Therefore, the ratio of the number of students who have vanilla to the total number of students is:
25 : 43
Step-by-step explanation:
Find the length of the side labeled x. Round intermediate values to the nearest tenth. Use the rounded values to calculate the next value. Round your final answer to the nearest tenth.
The length of the side labeled x is 75.3 when rounded to the nearest tenth which can be determined by using Pythagorean theorem.
What is Pythagorean theorem?The Pythagorean theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
To find the length of the side labeled x, we will first need to calculate the length of the other two sides.
For the first triangle, the hypotenuse is equal to the side labeled x, so the length of the side labeled x can be calculated using the formula:
x = √(35² + 42²) = 50.1
For the second triangle, the hypotenuse is the side opposite the right angle, which is equal to the side labeled x. We can calculate the length of the side labeled x using the formula:
x = √(60² + 50²) = 75.3
For the third triangle, the hypotenuse is the side opposite the right angle, which is equal to the side labeled x. We can calculate the length of the side labeled x using the formula:
x = √(28² + 34²) = 39.6
Therefore, the length of the side labeled x is 75.3 when rounded to the nearest tenth.
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The rounded value of x in the triangles is:
25) x ≈ 76
27) x ≈ 21
29) x ≈ 104
Give a brief account on trigonometric relations.All trigonometric identities are based on six trigonometric ratios. Sine, cosine, tangent, cosecant, secant, and cotangent. All these trigonometric ratios are defined using the sides of a right triangle as follows: Adjacent side, opposite side, and hypotenuse side.
25) Since, Sinθ = Opposite side/hypotenuse
Sin35° = 39/hypotenuse
hypotenuse = 39/Sin35°
Sin35° = 0.57
hypotenuse = 39/0.57
hypotenuse = 68.42
Now, using Pythagoras theorem:
hypotenuse² = base² + perpendicular²
68.42² = 39² + perpendicular²
4681.29 - 1521 = perpendicular²
4681.29 - 1521 = perpendicular²
3160.29 = perpendicular²
√3160.29 = perpendicular
56.21 = perpendicular
For the calculation of x:
Cosθ = Adjacent side/hypotenuse
Cos42° = 56.21/x
0.74 = 56.21/x
x = 56.21/0.74
x = 75.95
x ≈ 76
27) Cosθ = Adjacent side/hypotenuse
Cos60° = 14/hypotenuse
0.5 = 14/hypotenuse
hypotenuse = 14/0.5
hypotenuse = 28
Now, using Pythagoras theorem:
hypotenuse² = base² + perpendicular²
28² = 14² + perpendicular²
784 - 196 = perpendicular²
588 = perpendicular²
√588 = 24.24
perpendicular = 24.24
For the calculation of x:
Sinθ = Opposite side/hypotenuse
Sin50 = 24.24/hypotenuse
0.76 = 24.24/hypotenuse
hypotenuse = 24.24/0.76
hypotenuse = 31.89
Using Pythagoras theorem:
hypotenuse² = base² + perpendicular²
31.89² = x² + 24.24²
1016.97 = x² + 587.57
x² = 1016.97 - 587.57
x² = 429.4
x = √429.4
x = 20.72
x ≈ 21
29) Sinθ = Opposite side/hypotenuse
Sin28° = 44/hypotenuse
0.46 = 44/hypotenuse
hypotenuse = 44/0.46
hypotenuse = 95.65
Using Pythagoras theorem:
hypotenuse² = base² + perpendicular²
95.65² = 44² + perpendicular²
perpendicular² = 9148.92 - 1936
perpendicular² = 7212.92
perpendicular = √7212.92
perpendicular = 84.92
For the calculation of x:
Cosθ = Adjacent side/hypotenuse
Cos34 = 84.92/x
x = 84.92/0.82
x = 103.56
x ≈ 104
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Use the following circle to solve for x
We know that the product of lengths of the same chord is equal to the product of the other chord intersecting it.. So;
[tex] \purple{ \mathfrak{x \times 6 = 12 \times 5}}[/tex]
[tex] \large \purple{ \mathfrak{x = \frac{12 \times 5}{6}}}[/tex]
[tex] \large \purple{ \mathfrak{x = \frac{ \cancel{12} \times 5}{ \cancel6}}}[/tex]
[tex] \large \purple{ \mathfrak{x = 2 \times 5}}[/tex]
[tex] \large \boxed{ \red{ \mathfrak{x =10}}}[/tex]
What is the solution to -1/2 [x-1] =0?
x=1
x=-1 or x=1
x=1 or x=2
No solutions exists
Answer:
x=1
Step-by-step explanation:
the area under the entire probability density curve is equal to___a. 0b. -1c. 1d. [infinity]
The required area under the whole probability density curve is given by option C. 1.
The area under the entire probability density curve is equal to,
As the probability density function (pdf) represents the probability of a continuous random variable.
And continuous random variable taking on a specific value within a certain range.
Since the total probability of all possible outcomes must be equal to 1.
This implies that the area under the entire probability density function (pdf) curve must also be equal to 1.
Therefore, the area under the entire probability density curve function is equal to option c. 1.
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part c question consider two groups of randomly selected peppers, where neither group has all big or all small peppers. a mean difference of zero indicates the peppers are well distributed between the two groups.a. true b. false
False. A mean difference of zero does not necessarily indicate that the peppers are well distributed between the two groups.
What is number?Number is a mathematical object used to count, measure, and label. It is one of the most fundamental concepts in mathematics and is used to describe a wide variety of physical, logical, and abstract objects. Numbers are used to represent quantities, lengths, temperatures, money, and many other measurements. They are also used to represent abstract ideas, such as the number of days in a year or the number of colors in a rainbow.
Although the mean may be equal between the two groups, the distribution of the peppers could be skewed and not evenly distributed. For example, one group could have all large peppers and the other all small peppers and the mean would be equal. This would not be considered well distributed. To ensure the peppers are evenly distributed, one should check the standard deviation or range of the data to see if the peppers are spread across both groups.
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Answer: A mean difference of zero indicates the peppers
are not well distributed between the two groups.
Why: Part B Answers
What do large differences of the means of each group indicate? Select the correct answer.
The peppers with different weights aren’t properly distributed between the two groups.
So they arent distributed well
How do you find height when you are doing volume with cubic units?
Answer:calculate the cube root of a cube's volume.
Step-by-step explanation:
A man sells an article at rs 600and makes a profit of 20%. Calculate his profit percentage
Answer:
120
Step-by-step explanation:
20 percent of 600 is 120 so he will get 120
How much was one movie ticket in 2008
Answer: 7 dollars 18 cents.
Step-by-step explanation:
