How is the sum expressed in sigma notation?

22 + 27 + 32 + 37 + 42 + 47

Enter your answer by filling in the boxes.
the sum from i is equal to 1 to blank of open paren close paren$$

Answer:

3hrs to paint by Mary

8hr for Brian to paint

so together, Brian and Mary mean you add the two

together 3hrs

and 8hrs

equals 11 hrs

3+8=11

By the given explanation,

It is proven that in given right angle triangles a² = cx.

The angles that are identical to each other are known as Congruent angles. The measure of these concurrent angles is always equal to each other.

They can be acute, obtuse, exterior, or interior angles because the congruence of angles is unaffected by the type of angle. As we know a right angle is 90° all right angles are congruent angles.

Here we have

Two right-angle triangles MOP and MNO

Measurements of Δ MNO side are a, b, and c is the hypotenuse    

Measurements of Δ MOP sides are a, x, and OP is the hypotenuse    

Here we need to prove that a² = c x  

We can prove its as follows

As we know all right angles are concurrent

Statement                            Reason

=> ∠NOM ≅ ∠OPM              [ ∵ right-angles are concurrent ]  

=> ∠OMN≅ ∠PMO               [ ∵ Common angle ]  

=> ΔMOP ~ ΔMNO                   [ By Angle - Angle - Angle criteria ]

Since ΔMOP ~ ΔMNO        

=> a/x = c/a                         [ ratio of the corresponding side ]  

=> a² = cx                            [ Corss multiplication ]

Therefore,

It is proven that in give right angle triangles a² = cx.

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The solution to the above problems are given as follows:

7) m∠A = 102°. m∠B = 102.°

8) ∠QSR = 59.6°

9) ∠ADC = 55°

7) Since both angles are vertical, it, therefore, means they are congruent. Ths,

4x + 6 = 7x-66; collect like terms

6+66 = 7x -4x

72 = 3x

x = 72/2

Thus,

x = 24

Plugging in the value of x back into the expressions, we have:

m∠A = 4x + 6

= 4(24) + 6

= 96+6

= 102°

Thus, m∠A = 102.

Since both angles are congruent, that means m∠B is also 102°

8) To find ∠QSR, we need to find x. Note that Angle on a Straight line sums up to 180°. Thus,

4x-8+34+72-x = 180

4x - 8 + 34 + 72 - x = 180

5x + 98 = 180

5x = 82

x = 16.4

So the solution is x = 16.4.

Since ∠QSR = 76-x

∠QSR = 76-16.4

Thus,

∠QSR = 59.6°

9) Applying the same rule (Angles on a straight line to the above problem, we can state that:

2x+1 + (x-7) = 180°;
To solve for x, we can simplify both sides of the equation and then isolate x:

2x + 1 + x - 7 = 180

3x - 6 = 180

3x = 186

x = 62

So the solution is x = 62.

Thus, ∠EDF = 62 - 7

= 55°

since  ∠EDF  and  ∠ADC are opposite angles, and opposite angles are congruent,

∠ADC = 55°

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Something can be described as a function if there is only 1 of each number in the input or x.

For example: (9,6) and (9,3) would not be a function because there are two 9’s as the input.

So, for this problem there are two 3’s meaning this is NOT function because there are two outputs for the same number.

Your answer is going to be D.

The cost of a phone has lowered by 19% to $319.14 from its original $394 pricing.

In arithmetic, a percentile is a number or statistic that is given as a fraction of 100. Occasionally, the acronyms "pct.," "pct," nor "pc" are also used. But it is broadly classified into the following by the cent sign, "%." The % amount has no characteristics. Percentages are essentially integers when the denominator is 100. Use the percent sign (%) to indicate that a number is a percentage by placing it close to it. For instance, you score a 75% if you properly answer 75 so out 25 pages on a test (75/100). Divide the money by the whole and multiply the results by 100 you compute percentages. The formula for calculating the percentage is (value/total) x 100%.

given

Put this together using the conditions given: 319.14 / (1- 19%)

Determine the total or difference: 319.14 / 0.81

Diminish the fraction: 394

Response: 394

The cost of a phone has lowered by 19% to $319.14 from its original $394 pricing.

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Answer: 48$

Step-by-step explanation: well 20% of 40$ is 8$ so the total cost is 48$ that he payed

Answer:

$48.00

Step-by-step explanation:

If two figures can be mapped onto one another or if all pairings of angles and side lengths are congruent, the figures are said to be congruent.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

If two triangles are the same size and shape, they are said to be congruent. To establish that two triangles are congruent, not all six matching elements of either triangle must be located. There are five requirements for two triangles to be congruent, according to studies and trials. The congruence properties are SSS, SAS, ASA, AAS, and RHS.

here, we have,

Both triangles are said to be congruent if the three angles and three sides of one triangle match the corresponding angles and sides of the other triangle.

In Δ PQR and ΔXYZ, as shown in figure,

we can identify that PQ = XY, PR = XZ,

and QR = YZ

and ∠P = ∠X,

∠Q = ∠Y and ∠R = ∠Z.

Then we can say that Δ PQR ≅ ΔXYZ.

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Answer:

9x² - 64 square yards

Step-by-step explanation:

Area of a rectangle is L x W where

L = length
W = width

Letting
L = 3x + 8
W = 3x - 8

L x W = (3x + 8)(3x-8)

Using the identity (z + b)(a - b) = a² - b²

with a = 3x, b = 8

(3x+8)(3x-8) = (3x)² - (8)²

= 9x² - 64 square yards

Answer:

y=3x+5

Step-by-step explanation:

tjrjrkrlrorlp3ñ34mrmrr

Answer:

y=mx+c

Step-by-step explanation:

-5/y=3x meaning that y=mx+c, hope this helps :)

The three-digit numbers are:

A = 3

B = -1/3

C = -4/3

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,

A C B

B A C

B C A

C A B

+  C B A

1  2 2 3

Now,

A = 3 _____(1)

B + C + A +B + B = 2

3B + C + A = 2

3B + C + 3 = 2

3B + C = -1

C + A + C + A + C = 2

3C + 2A = 2

Substituing A = 3.

3C + 6 = 2

3C = 2 - 6

3C = -4

C = -4/3 _____(2)

A + B + B + C = 1

Substituting A and C.

3 + 2B - 4/3 = 1

2B = 1 - 3 + 4/3

2B = (3 - 9 + 4)/3

2B = -2/3

B = -2/6

B = -1/3 ______(c)

Thus,

A = 3

B = -1/3

C = -4/3

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Quadrilaterals are objects with four sides, such as parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.

Sum of all interior angles of quadrilateral [tex]$=360^{\circ}$[/tex]

[tex]& \therefore 50+130+120+\mathrm{x}=300 \\[/tex]

[tex]& \mathrm{x}=60^0[/tex]

(b) [tex]& 90+a=180 \\[/tex]

a = 90

Sum of all angles of quad = 360

[tex]& x+70+60+90=360 \\[/tex]

[tex]& x=140^{\circ}[/tex]

(c) [tex]70+\mathrm{a}=180$ (Linear pair)[/tex]

a = 110

[tex]60+\mathrm{b}=180$ (Linear pair)[/tex]

[tex]$\mathrm{b}=120$[/tex]

Sum of measures of all angles of pentagon [tex]$=540^{\circ}$[/tex]

[tex]& \therefore 120+110+\mathrm{x}+\mathrm{x}+30=540 \\[/tex]

[tex]& 2 \mathrm{x}=280 \\[/tex]

[tex]& \mathrm{x}=140^{\circ}[/tex]

(d) Sum of all angles of pentagon 540

Given all angles are equal

[tex]& \therefore 5 x=540 \\[/tex]

[tex]& x=108^0[/tex]

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Answer:

x³ - 4x² + 3x - 8. is the answer.

Answer:

Improper: 7/4

Mixed: 1 3/4

Step-by-step explanation:

Each little pie slice shape is a fourth (there are 4 in one circle)

Count them. In total there are 7. There are seven pie slices. There are seven fourths.

7/4

This is called an improper fraction because the bigger number is on top and the smaller number is below.

If you consider one circle to be a "whole" then you have one whole and 3/4.

1 3/4

This is a mixed number because it has a whole part and a fraction part.

Note that the statement that completes the above proof is "Definition of Angle Bisector"

An angle bisector of a triangle's angle divides the opposing side into two portions that are proportionate to the triangle's other two sides, according to the angle bisector theorem.

The angle bisector theorem asserts that if a point is on an angle's bisector, the point is equidistant from the angle's sides. The opposite of the angle bisector theorem asserts that if a point is in the interior of an angle and equidistant from the sides, it sits on the angle's bisector.

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After performing the operation on the given number we get the fraction 3/2

A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, and 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.

Given here: multiplication of a whole number 3 and the fraction 1/2

When you multiply two fractions together, you're taking a part of a part. When you multiply a fraction by a whole number, you're taking multiple copies of that fraction. In both cases, the result is a new fraction that represents a different part of a whole.

Thus we have the following after simplifying

3×1/2=3/2

Hence, The required fraction is 3/2

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Answer:

Determine the probability that a student studied for exactly 1 hour. Round to the nearest hundredth.

0.23

If P(chocolate chip) = 0.25, interpret the likelihood of randomly selecting a chocolate chip cookie from the batch.

Likely

Compare the probabilities and interpret the likelihood. Which statement is true?

Player 1 is more likely to hit the ball than Player 3 because P(Player 1) > P(Player 3)

Joseph has a bag filled with 3 red, 3 green, 15 yellow, and 9 purple marbles. Determine P(not red) when choosing one marble from the bag.

90%

A student randomly draws a card from a standard deck of 52 cards. He records the type of card drawn and places it back in the deck. This is repeated 20 times. The table below shows the frequency of each outcome.

Outcome Frequency

Heart 7

Spade 3

Club 6

Diamond 4

Determine the experimental probability of drawing a spade.

0.15

A spinner with repeated colors numbered from 1 to 8 is shown.

Sections 1 and 8 are purple.

Sections 2 and 3 are yellow.

Sections 4, 5, and 6 are blue.

Section 7 is red.

Determine the theoretical probability of the spinner not landing on blue, P(not blue).

0.375

A spinner with repeated colors numbered from 1 to 8 is shown.

Sections 1 and 8 are purple.

Sections 2 and 3 are yellow.

Sections 4, 5, and 6 are blue.

Section 7 is orange.

Which statement about probability is true?

The probability of landing on orange is greater than the probability of landing on purple.

List the sample space for rolling a fair eight-sided die.

S = {1, 2, 3, 4, 5, 6, 7, 8}

There are 10 brown, 10 black, 10 green, and 10 gold marbles in bag. A student pulled a marble, recorded the color, and placed the marble back in the bag. The table below lists the frequency of each color pulled during the experiment after 40 trials.

Outcome Frequency

Brown 13

Black 9

Green 7

Gold 11

Likely

Equally likely and unlikely

Which event will have a sample space of S = {h, t}?

Flipping a fair, two-sided coin

Julia had a bag filled with gumballs. There were 1 lemon-lime, 2 watermelon, and 3 grape gumballs. What is the correct sample space for the gumballs in her bag?

Sample space = lemon-lime, watermelon, watermelon, grape, grape, grape

The amount paid for the surgery is given as follows:

$4,000.

The total amount Gina’s dad paid for her care was of:

$5,000.

The amounts are obtained applying the proportions in the context of this problem.

The coinsurance of 20% means that Gina's dad pays only 20% of the surgery's price after the deductible.

The deductible is given as follows:

$1,000.

Hence the price of the surgery after the deductible is of $1,000, and the amount paid for the surgery is given as follows:

0.2 x $2000 = $4,000.

Considering the deductible, the total amount paid is given as follows:

1000 + 4000 = $5,000.

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Answer: $20, $4,000, $5,020

Step-by-step explanation:

i got it right

The triangle mid-segments will be the two opposite or adjacent sides of a triangle.

What is the triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.

The sum of all angle of triangle = 180

A line connecting the midpoints of two of a triangle's sides is known as the midsegment. There are always three midsegments in a triangle. The midsegment between any two sides of a triangle is parallel to and half the length of the third side, according to the Triangle Midsegment Theorem, often known as the midsegment theorem.

A midsegment of a triangle is a line segment that joins the midpoints or center of two opposite or adjacent sides of a triangle.

Hence The triangle mid-segments will be the two opposite or adjacent sides of a triangle.

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Complete question:

Define the triangle mid segments.

There is not enough information to know whose Tennis ball would go further. Option D.

We know that the projectile is an object that can be able to move along a parabolic path. In this case, we have a catapult which the energy that launces forth the projectile is derived from the energy that have been stored in the spring of the catapult.

A catapult is a type of projectile weapon that uses mechanical energy to launch a projectile over a long distance as we can see in this problem.

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Answer:

7

Step-by-step explanation:

Triangle is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

If in ΔHIJ, m∠H = x - 1, m∠I = 2x + 5, and m∠J = 7x + 6.

The value of x is  17.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

Example:

Triangle ABC:

m∠A + m∠B + m∠C = 180

here, we have,

We have,

ΔHIJ

m∠H = x - 1

m∠I = 2x + 5

m∠J = 7x + 6

We know that,

The sum of the angles of the triangle is 180 degrees.

m∠H + m∠I + m∠J = 180

(x - 1) + (2x + 5) + (7x + 6) = 180

x - 1 + 2x + 5 + 7x + 6 = 180

10x + 10 = 180

Take 10 common.

10 (x + 1) = 180

Divide both sides by 10.

x + 1 = 180/10

x + 1 = 18

Subtract 1 on both sides.

x = 18 - 1

x = 17

Thus,

If in ΔHIJ,

m∠H = x - 1, m∠I = 2x + 5, m∠J = 7x + 6.

The value of x is  17.

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Answer:

42?

Step-by-step explanation:

Step-by-step explanation:

I just answered this.

the first group is consistent independent, because both equations are lines with different slope. so, they have 1 intersection, which is the solution.

the second group is consistent dependent, because both equations describe the same line.

multiply the second equation by -2, or divide the first equation by -2, and you see they are identical. multiplying an equation by a factor on both sides does not change the equation or function.

so, as both lines are identical, every point on the line is an intersection and solution. therefore, there are infinitely many solutions.

the third group is inconsistent.

they represent 2 lines with identical slope but different y-interceptions. so, they are parallel and have no intersection or solution at all.

just think : there is no pair of numbers x,y, for which their sum can have 2 different results.

The density of the block of wood is 1.04g/cm³

Density is the ratio of the mass of an object to its volume. It is a scalar quantity and it is measured in g/cm³ or kg/m³.

Density = mass/volume

Mass = 0.280kg = 0.280 × 1000 = 280g

volume = 270cm³

Density = mass/volume

Density = 280/270

= 1.04g/cm³

Because the density of the object is just slightly higher than the density of water which is 1g/cm³

, therefore the object will float in water.

For an object to float in water, it must be equal to the weight or density of the water

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If the temperature dropped 22 degrees to -13 Degrees F, the temperature before the drop was 9 Degrees F.

Temperature drop refers to a decrease in the temperature of a system or environment.

This decrease can be measured in units of temperature such as degrees Celsius or Fahrenheit, and it can occur due to a variety of reasons such as changes in atmospheric conditions, the loss of heat from a body or system, or other physical processes.

The initial temperature is calculated by

initial temperature = final temperature + temperature drop

initial temperature = -13 + 22

initial temperature = 9

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Answer:

231

Step-by-step explanation:

From the pie chart we see that the story artists constitute 20% of the total employee strength of 1540 employees and the interns constitute only 5% of that number

In actual values

Number of story artists = 1540 x 20% = 1540 x 20/100 = 308

Number of interns = 1540 x 5% = 1540 x 5/100 = 77

Difference = 308 - 77 = 231

The correct answer is Tasha, because she has the highest ratio since 0.625 > 0.7.

Receive is a comparison between two or more quantities expressed as a fraction or a set of relative quantities it is used to compare the size of one number to another or the compare changes overtime ratio can be expressed in word as fraction or decimal receiver in important concept in mathematics used to analyse data and solve problem.

Tasha has hit the ball 10 times out of 16 attempts, which means her batting average is 0.625. Jana has hit the ball 7 times out of 10 attempts, which gives her a batting average of 0.7. Therefore, Tasha has the better batting average.

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Step-by-step explanation:

It is explained in the figure above.

The given function is continuous at  x = 3,  RHL = LHL = F(3)

In mathematics, The function is called as continuous at the particular value of x,  if right hand limit, left hand limit and the value of function at x all are equal.

RHL   = LHL  = F(x)

Limit exist and continuous

Given that,

F(x)  =  x²  + 5(x - 2)⁷

To check whether it is continuous at x = 3

First taking LHL,

[tex]\lim_{h \to \00 } F(x)[/tex]  

[tex]\lim_{h \to \00 }[/tex]   (3-h)²  + 5(3 - h - 2)⁷

⇒  9 + 5

⇒   14

Now, taking RHL

[tex]\lim_{h \to \00 }[/tex]   (3+ h)²  + 5(3 + h - 2)⁷

⇒  9 + 5

⇒   14

The value at x = 3

F(3)  =  3²  + 5(3 - 2)⁷

       =  14

Hence Proved,   RHL = LHL = F(3)

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