The following diagram shows a semicircle ABC with centre O and a right-angled triangle ACD.

Given the radius is 3.5 cm, calculate the perimeter, in cm, of the whole diagram.
A 36 B 60 C 67 D 72​

Answer:

b

Step-by-step explanation:

Based on the inscribed quadrilateral conjecture: trapezoid QPRS can be inscribed in a circle because its opposite angles are supplementary.

The inscribed quadrilateral conjecture states that the opposite angle of any inscribed quadrilateral are supplementary to each other. That is, they have a sum of 180 degrees.

From the diagram given, the opposite angles in the trapezoid, 115 + 65 = 180 degrees.

Therefore, we can conclude that: trapezoid QPRS can be inscribed in a circle because its opposite angles are supplementary.

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Answer:

The value of [tex]$(f \circ g)(x)$[/tex] is 17-18x and [tex]$(g \circ f)(x)$[/tex] is -7-18x.

Step-by-step explanation:

It is given in the question functions f(x) as 3x+2 and g(x)=5-6x.

It is required to find [tex]$(f \circ g)(x)$[/tex] and [tex]$(g \circ f)(x)$[/tex].

To find [tex]$(f \circ g)(x)$[/tex], substitute g(x) for x in f(x) and simplify the expression.

To find [tex]$(g \circ f)(x)$[/tex], substitute f(x) for x in g(x) and simplify the expression.

Step 1 of 2

Substitute g(x) for x in f(x) and simplify the expression.

[tex]$$\begin{aligned}&(f \circ g)(x)=f(5-6 x) \\&(f \circ g)(x)=3(5-6 x)+2 \\&(f \circ g)(x)=15-18 x+2 \\&(f \circ g)(x)=17-18 x\end{aligned}$$[/tex]

Step 2 of 2

Substitute f(x) for x in g(x) and simplify the expression.

[tex]$$\begin{aligned}&(g \circ f)(x)=g(3 x+2) \\&(g \circ f)(x)=5-6(3 x+2) \\&(g \circ f)(x)=5-18 x-12 \\&(g \circ f)(x)=-7-18 x\end{aligned}$$[/tex]

The maximum error in the calculated surface area is 24.19cm² and the relative error is 0.0132.

Given that the circumference of a sphere is 76cm and error is 0.5cm.

The formula of the surface area of a sphere is A=4πr².

Differentiate both sides with respect to r and get

dA÷dr=2×4πr

dA÷dr=8πr

dA=8πr×dr

The circumference of a sphere is C=2πr.

From above the find the value of r is

r=C÷(2π)

By using the error in circumference relation to error in radius by:

Differentiate both sides with respect to r as

dr÷dr=dC÷(2πdr)

1=dC÷(2πdr)

dr=dC÷(2π)

The maximum error in surface area is simplified as:

Substitute the value of dr in dA as

dA=8πr×(dC÷(2π))

Cancel π from both numerator and denominator and simplify it

dA=4rdC

Substitute the value of r=C÷(2π) in above and get

dA=4dC×(C÷2π)

dA=(2CdC)÷π

Here, C=76cm and dC=0.5cm.

Substitute this in above as

dA=(2×76×0.5)÷π

dA=76÷π

dA=24.19cm².

Find relative error as the relative error is between the value of the Area and the maximum error, therefore:

[tex]\begin{aligned}\frac{dA}{A}&=\frac{8\pi rdr}{4\pi r^2}\\ \frac{dA}{A}&=\frac{2dr}{r}\end[/tex]

As above its found that r=C÷(2π) and r=dC÷(2π).

Substitute this in the above

[tex]\begin{aligned}\frac{dA}{A}&=\frac{\frac{2dC}{2\pi}}{\frac{C}{2\pi}}\\ &=\frac{2dC}{C}\\ &=\frac{2\times 0.5}{76}\\ &=0.0132\end[/tex]

Hence, the maximum error in the calculated surface area with the circumference of a sphere was measured to be 76 cm with a possible error of 0.5 cm is 24.19cm² and the relative error is 0.0132.

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The statements about the local maximums and minimums for the given function which are true include:

This is defined as the mathematical entities which assign unique outputs to given inputs and defines a relationship between the two variables.

According the the graph: over the interval [2, 4], the local minimum is –8 because the given minimum point is (3.4, -8) and over the interval [3, 5], the local minimum is –8.

Over the interval [1, 4], the local maximum is 0 and over the interval [3, 5], there is no maximum point hence why it is false.

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Answer:

Z = 90 degrees

Step-by-step explanation:

Reason is a diameter subtends angle of 90 degrees on the circumference

The appropriate hypothesis which is used to test the dropout rate are [tex]H_{0}:p > =0.081\\[/tex] and [tex]H_{1}: p < 0.081[/tex].

Given Drop out rate through 24 year old who are not enrolled is 8.1%, sample size=1000 and we have to find the hypothesis to test the drop out rate of the school.

The variable which needs to be studied is X=Number of individuals with age between 16 and 24 years old that are high school dropouts.

The parameter of interest is the proportion to high school drop outs is p.

Sample proportion=[tex]p^{1}[/tex]=0.065

The hypothesis can be formed as under:

[tex]H_{0}:p > =0.081[/tex]  (null hypothesis)

[tex]H_{1}:p < 0.081[/tex]      ( alternate hypothesis)

Null hypothesis is a hypothesis which is tested for its validity and alternate hypothesis is hypothesis which is opposite of null hypothesis means if null hypothesis is rejected then the alternate hypothesis will be true.

[tex]Z_{H_{0} }=(p^{1}-p)/\sqrt{p*(1-p)/n}[/tex]

=[tex]0.065-0.081/\sqrt{(0.081*0.0919)/1000}[/tex]

=-1.85

Hence the appropriate hypothesis  are [tex]H_{0}:p > =0.081[/tex] and [tex]H_{1}:p < 0.081[/tex].

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The rule that describes the second transformation is; Rotated at 90° clockwise

From the given diagram we can see that;

The transformation from Rectangle ABCD to A'B'C'D' follows the transformation sequence of;

Shift 1 unit downwards then translate 5 units to the right.

However, for the transformation of A'B'C'D' to A"B"C"D", we see that the transformation is; Rotated at 90° clockwise

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Answer: 22

Step-by-step explanation:

Using the triangle midsegment theorem,

[tex]2(5x+2)=3x+32\\\\10x+4=3x+32\\\\7x+4=32\\\\7x=28\\\\x=4[/tex]

So, the length of the midsegment is 5(4) + 2 = 22

The cost of one ruler is $0.70

From the question, we are to determine the cost of one ruler

Let x represent the cost of a ruler

and

y represent the cost of a pen

From the given information, we can write that

y + x = $2.10 ----------- (1)

2y + 3x = $4.90  ----- (2)

From equation (1),

y + x = $2.10

Then,

y = $2.10 - x

Substitute this into equation (2)

2y + 3x = $4.90

2($2.10 - x) + 3x = $4.90

$4.20 - 2x + 3x = $4.90

$4.20 +x = $4.90

x = $4.90 - $4.20

x = $0.70

Hence, the cost of one ruler is $0.70

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Answer:

8+16+2= 24 legs on ground

Step-by-step explanation:

A statistical indicator of the strength of the association between the relative movements of two variables is the correlation coefficient.

To gauge how strongly two variables are related to one another, correlation coefficients are used.

A statistical indicator of the strength of the association between the relative movements of two variables is the correlation coefficient. The values are in the -1.0 to 1.0 range. There was a measurement error in the correlation if the estimated value was larger than 1.0 or lower than -1.0. Perfect negative correlation is shown by a correlation of -1.0, and perfect positive correlation is shown by a correlation of 1.0. A correlation of 0.0 indicates that there is no linear link between the two variables' movements. Finance and investing can benefit from the usage of correlation statistics.

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Okay so a 24hr clock is very simple. We usually turn to "PM" when its 12:00 (day time).
In the 24hr clock we do not, we don't use PM or AM but its crucial to know when converting a standard clock time to military time (aka. 24hr).

9:30 PM in 24hr clock is 12:00 + 9:30 because 9:30 is past that first 12 hours.

So in 24hr clock time it is 21:30. You can also count backwards from midnight to figure it out, for example 12:00 AM (midnight), minus 9:30 is 2:30. Therefore 24:00-2:30=21:30.

Hopefully it helps, heart will help me alot too!

Answer:

21:30

Step-by-step explanation:

The 24hour clock uses 0:00 for midnite. 1am through noon are just 1:00 - 12:00. But the pm hours continue counting up, 13 - 23.

For example, 1pm is 13:00 and 2pm is 14:00.

To change to 24 hour clock, for pm hours, ADD 12.

So for your problem, 9:30 is:

9:30 + 12

= 21:30

3 roots are exist, since the polynomial is of third degree.

According to statement

This follows immediately from the zero product property: if ab=0, then either a=0 or b=0. We have3 roots are exist, since the polynomial is of third degree.

(9x+ 7)(4x +1)(3x+ 4) = 0

from which it follows that each of which admits only one solution.

AND

using the fundamental theorem of algebra, expanding we have a polynomial that is of third degree:

(9x+ 7)(4x +1)(3x+ 4) = 0

108x^3 + 255 x^2 +169x + 28 =0

The theorem states that a polynomial will have up to n distinct roots. In this case, it follows that there are exactly 3, since the solutions to the system above are all distinct.

So, 3 roots are exist, since the polynomial is of third degree.

DISCLAIMER : The question was incomplete. Please find the full content below.

QUESTION

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function? (9x + 7)(4x + 1)(3x + 4) = 0 1 root 3 roots 4 roots 9 roots

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The probability that a two-digit number selected at random has a tens digit less than its units digit is 0.2667 (4/15).

[tex]A=24B=90\\\\P=A/B\\\\P=24/90\\p=4/15[/tex]

There are 90 two-digit numbers (99-9). Of these, six numbers are divisible by 15 (15, 30, 45, 60, 75, 90). This is also divisible by 5. Therefore, the preferred case is 30-6 = 24. Therefore, the required probability is 24/90 = 4/15.

The probability of an event can be calculated by simply dividing the number of favorable results by the total number of possible results using a probabilistic expression. Whenever you are uncertain about the outcome of an event, you can talk about the probability of a particular outcome, that is, its potential.

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Non-linear graph best describes this function.

As described in the question, Pauley graphs the change in temperature of a glass of hot tea over time. He sees that the function appears to decrease quickly at first, then decrease more slowly as time passes. It is linear because the graph decreases over time. It is linear because there is both an independent and a dependent variable but it doesn't satisfies one condition of being linear. Thus, It's Nonlinear because linear functions are increasing functions. It is nonlinear because linear functions increase or decrease at the same rate.

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Answer:

B

Step-by-step explanation:

The lines YZ and WZ are equivalent because the diagonal bisects the parallelogram into two parts of which are equal.

Properties of a parallelogram include;

From the figure, we have that lines YZ and WZ are equivalent because the diagonal bisects the parallelogram to two four of which they are of equal lengths.

Thus, the lines YZ and WZ are equivalent because the diagonal bisects the parallelogram into two parts of which are equal.

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Answer:

B. more dense

Transformation is a process that involves either increasing, or decreasing the size of a given object, or changing its orientation to produce an image.

The required transformations are:

i. For graph a - translation.

ii. For graph b - dilation.

Rigid transformation involves a change in the orientation of a given object or resizing of a given object to produce an image. The types of transformation are reflection, translation, rotation, and dilation.

i. Reflection is a type of transformation that requires flipping a given object about a reference point or line.

ii. Translation is a type of transformation that involves moving an object in a particular direction without a change in its size and orientation.

iii. Rotation is a type of transformation that involves turning an object at a given angle about a reference point.

iv. Dilation is a type of transformation that require increasing or decreasing the size of the object using a given factor.

Therefore the necessary transformation to transform the blue graph of f(x) into the red graph of g(x) is:

a. For graph a is translation.

b. For graph b is dilaton.

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The equation that matches the given situation is [tex]-2\frac{1}{2}+6\frac{3}{4}=?[/tex] . So, after two moves, Eric's elevation changed [tex]4\frac{1}{4}[/tex] meters above.

We know that in mathematics, subtraction means removing something from a group or a number of things. What is left in the group gets smaller when we subtract. The minuend is the first element we use. The subtrahend is the part that is being removed. The difference is the portion that remains after subtraction.

Assume that "negative" means climbing down and "positive" means climbing up. We must locate the elevation change in this area.

Given that Eric climbed straight down [tex]2\frac{1}{2}[/tex] meters. So we can write [tex]-2\frac{1}{2}[/tex].

Again Eric climbed straight up [tex]6\frac{3}{4}[/tex] meters. So, we can write [tex]6\frac{3}{4}[/tex].

Then the change = [tex]-2\frac{1}{2}+6\frac{3}{4}[/tex]

=[tex]-\frac{(2*2+1)}{2}+\frac{6*4+3}{4}[/tex]

=[tex]-\frac{5}{2} +\frac{27}{4}[/tex]

=[tex]\frac{-(5*2)+27}{4}[/tex]

=[tex]\frac{-10+27}{4}[/tex]

=[tex]\frac{17}{4}[/tex]

=[tex]\frac{4*4+1}{4}[/tex]

=[tex]4\frac{1}{4}[/tex]

Therefore, the equation that matches the given situation is [tex]-2\frac{1}{2}+6\frac{3}{4}=?[/tex] . So, after two moves, Eric's elevation changed [tex]4\frac{1}{4}[/tex] meters above.

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Answer: 25% off

Step-by-step explanation:

1= 0.25 + 0.75

25% is off is the equivalency of multiplying the value of the original cost with 0.75.

20*0.75=15

Answer:

3π

Step-by-step explanation:

arc length = radius x central angle in radians

π = radius x π/3

radius = 3π

since OMN is an equilateral triangle, radius = MN

thus MN = 3π

The correct answer would be option(C) opposite angles of a parallelogram are congruent.

A parallelogram defined as a special type of quadrilateral which has both pairs of opposite sides parallel and equal.

Given that PQRS is a parallelogram.

PQ ≅ RS

QR ≅ PS

By the SSS criterion, ΔPQR ≅ ΔRSP and ΔPQS ≅ ΔRSQ.

Therefore, ∠QPS ≅ ∠SRQ and ∠PQR ≅ ∠RSP since corresponding angles of congruent triangles are congruent.

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Answer:

"B"

Step-by-step explanation:

Answer: 4/12 or 1/3

Step-by-step explanation:

A whole cake is 12/12.

He gave away 1/12, 5/12, and 2/12s of the cake

1+5+2 = 8

So he gave out 8/12s of the cake, which means he has 4/12 left, or 1/3 if you want simplest form.

Hope this helps.

The central angle is 77 degrees mate.

Step-by-step explanation:

180 250 300 H.C.F by division method

Hence, the required expression is (Negative 6) (4) + (negative 6) (two-thirds).

expression is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.). This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/Variable, Math Operator, Number/Variable)

LHS,

    (-6)([tex]\frac{14}{3}[/tex]) = -28

RHS,

   (-6)()[tex]4+\frac{2}{3}[/tex]) = -28

LHS=RHS

Hence, the required expression is (Negative 6) (4) + (negative 6) (two-thirds).

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The value of x from the given expression is 5/6

Given the expression to expand expressed as:

15 = 3/5(6x + 20)

We are to determine the value of x

15(5) = 3(6x + 20)

Expand

75 = 18x +60

Collect like terms

18x = 75 - 60

18x = 15

x = 15/18

x = 5/6

Hence the value of x from the given expression is 5/6

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