Activity 1.
Direction. Using the diagram below, form ratios. Express them in lowest term to
To form a proportion

Answer:

74 and 18

Step-by-step explanation:

\(ab = x + 10 \\ bc = x + 14 \\ ac = 22 \\ (x + 10) + (x + 14) = 22 \\ x + x + 10 + 14 = 22 \\ 2x + 24 = 22 \\ 2x = 22 - 24 \\ 2x = - 2 \\ x = \frac{ -2}{2} \\ x = - 1\)

Answer:10 time greater

Answer:

Reflection

Step-by-step explanation:

Because reflecting yourself in a mirror means pre image to image

Answer:

Step-by-step explanation:

dilation

Answer:

3rd option: 32/24

Step-by-step explanation:

8/6 = 4/3

1st option: Now let's change the denominator to 24:

4/3 ==> ?/24

4/3 =

4*8 / 3*8 = 32/24, not 3/24.

2nd option: Now let's change the numerator to 24:

4/3 ==> 24/?

4/3 =

4*6 / 3*6 = 24/18, not 24/32

24/32 = 3/4, not 4/3 ==> don't get confused by this

3rd option: 32/24 is correct [Look at the explanation for 1st option]

4/3 ==> ?/24

4/3 =

4*8 / 3*8 = 32/24, not 3/24.

Hence, the 3rd option is correct.

Step-by-step explanation:

you start with the 24 robots. If the store orders 6 boxes of 30 robots you multiply 30 by 6. 30 x 6  = 180 then you add the 24 from before which makes 204 robots total.

Answer:

204 in total

Step-by-step explanation: 6x30=180+24=204

In a case whereby baseball game receives 3 raffle tickets and a $2 certificate for the team store. A group of people receives 39 raffle tickets the amount of money in certificates the group receive is  $26.

If one baseball game receives 3 raffle tickets and a $2 certificate for the team store, then we can say that each raffle ticket is worth 2/3 dollars ($2 divided by 3 tickets).

So, for 39 raffle tickets, the group would receive (39 x 2/3) = $26

Therefore, the amount of money in certificates the group receive is  $26

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The probability that either event will occur is 0.33

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

Total = A + B + C

So, we have

Total = 8 + 7 + 30

Evaluate

Total = 45

So, we have

P(A) = 8/45

P(B) = 7/45

For either events, we have

P(A or B) = 8/45 + 7/45

P(A or B) = 15/45

Evaluate

P(A or B) = 0.33

Hence, the probability that either event will occur is 0.33

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The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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The probability of getting Two Tails is 0.1 or 10%.

Let's assume that '2. Tails' appeared x times.

According to the given information, 'No Tail' appeared 3x times, and '1 Tail' appeared 2 × 3x = 6x times.

The total number of tosses is 360. We can express this information in an equation:

x + 3x + 6x = 360

Simplifying the equation:

10x = 360

x = 36

Now we know that '2. Tails' appeared 36 times, 'No Tail' appeared 3x = 3 × 36 = 108 times, and '1 Tail' appeared 6x = 6 × 36 = 216 times.

To find the probability of getting Two Tails, we divide the number of times '2. Tails' appeared by the total number of tosses:

Probability of Two Tails = Number of times '2. Tails' appeared / Total number of tosses

= 36 / 360

= 0.1

Therefore, the probability of getting Two Tails is 0.1 or 10%.

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We get the following answers:

A) The least square regression line is:

yi = 88.73 - 2.827(xi)

B) The slope  is β₁ = -2.827 and The intercept is β₀ = 88.73.

C) e*₆ = -0.6964, final grade is below average grade.

E) It would not be reasonable since no of absence increases the score decreases, it works well for small no of absences but will not work for large number of absences since it may give absurd final grade.

we have Xi = No of absences

Yi = Final grade

The regression model is

Yi = β₀ +  β₁Xi + i

β₀ = y -  β₁x

we have n = 10, x bar = 4.5 , y bar = 76.01

cov(x,y) = -23.325 and var(x) = 9.1667

therefore,  β₀ = 88.73 and  β₁ = -2.827

A) Least square regression line is given by:

yi =  β₀+ β₁Xi

yi = 88.73 - 2.827(xi)

B) The slope  β₁ = -2.827 which means when no of absence is increased by 1 duty then the final grade will decrease by 2.827

The intercept  β₀ = 88.73 when there are 0 days absence the average grade is 88.73

C) Predicted graph for student who misses five class periods is

x = 5

y*5 = 88.73 - 2.827(5) = 74.5964

Hence for corresponding residual is:

e*₆ = 73.9 - 74.5964

e*₆ = -0.6964, final grade is below average grade.

D) please see graph

E) when student miss 15 class periods the final grade will be

X = 5

y* = 88.73 - 2.827(15)

= 46

It would not be reasonable since no of absence increases the score decreases, it works well for small no of absences but will not work for large number of absences since it may give absurd final grade.

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The descending order for the polynomial is \(-x^3y^5 - 2x^2y^3 + 4xy + x^4\). So, option D) None of the other answers are correct is the right answer.

What is a polynomial?

Polynomial is formed composed of the phrases Nominal, which means "terms," and Poly, which means "many." An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

The polynomial expression is -

\(x^4-x^3y^5+4xy-2x^2y^3\)

To get this expression, we arrange the terms based on their degree of y, starting from the highest degree and working our way down.

If two terms have the same degree of y, we arrange them based on their degree of x, starting from the highest degree and working our way down.

In this case, the term with the highest degree of y is \(-x^3y^5\), followed by \(-2x^2y^3\), then 4xy, and finally \(x^4\), which has no y term.

Thus, we write the expression in descending order as -

\(-x^3y^5 - 2x^2y^3 + 4xy + x^4\)

Therefore, the expression is obtained as \(-x^3y^5 - 2x^2y^3 + 4xy + x^4\).

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step 1

Translation

Applying the rule

(x,y) ------> (x-8, y-10)

that means

8 units to the left and 10 units down

step 2

Reflection across the line y=-2

Verify

we have the coordinates

A(2,8), B(7,8), C(7,2)

Apply the translation

A(2,8) -------> A'(2-8,8-10) ------> A'(-6,-2)

B(7,8) --------> B'(7-8,8-10) ------> B'(-1,-2)

C(7,2) ------> C'(7-8,2-10) --------> C'(-1,-8)

Applying the reflection across the line y=-2

the coordinates of point A' and B' not change because lie on the line of reflection

A'(-6,-2) --------> A''(-6,-2)

B'(-1,-2) ---------> B''(-1,-2)

C'(-1,-8) --------> C''(-1,-2+6)-------> C''(-1,4)

Compare the coordinates

Coordinates A'',B'' and C'' are equal to M, N and P

The number of calculations that a computer can perform in 10 seconds is 1050.

The exponential form of 1050 is 1.05 × 10³

Given,

The number of calculations that a computer can perform per second = 105

We have to find the number of calculations can it perform in 10 seconds.

That is,

Number calculations in 10 seconds = Number of calculations per second × 10

Number of calculations in 10 seconds = 105 × 10

Number of calculations in 10 seconds = 1050

That is, the number of calculations that a computer can perform in 10 seconds is 1050.

The exponential form of 1050 is 1.05 × 10³

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Answer:

n/5 = 18

Step-by-step explanation:

Quotient means division.

n/5 = 18

Answer:

9/41

Step-by-step explanation:

Draw a right triangle in quadrant 2 and label your opposite (40) and hypotenuse (41) sides then use the pythagorean theorem to find the missing side (the adjacent side)  which is equal to 9. Then since cosine is adjacent/hypotenuse and you get 9/41.

Answer:

\(2\frac{3}{4}\) or 2.75, depending on what you need.

Step-by-step explanation:

The lower absolute value in negative will be greater than the higher negative so -4 > -5 is correct thus option (E) will be correct.

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

In a negative value, a number will be very less if the magnitude is high.

For example, -100 is very less than -20.

Therefore, the lower absolute value in the negative will be greater than the higher negative.

-4 is a lower absolute value so it will be greater than -5

Therefore, -4 > -5 will be correct.

Hence "Since the higher negative will always be smaller than the lower negative, -4 > -"5

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Answer:

what's the question and no link's

Answer:

490 cu.ft

Step-by-step explanation:

Another way to summarize this proof is to say vertical angles are congruent.

Lines are shortest distance between two point and angles are forned from the intersection of two lines.

From the given figure, they are trying to prove that the angles ANR and VNE are equal. Since these angles are formed at the point of intersection, hence another way to summarize this proof is to say vertical angles are congruent.

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The flour and sugar coral that will be use to make the cookies is 2 1/4 cups.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this situation, Tucker is making cookies the recipe called for 1/3/4 cups of flour and 1/2cup of sugar.

The flour and sugar coral that will be use to make the cookies will be:

= 1 3/4 + 1/2

= 2 1/4

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Increasing 2400 by 5% gives us 2520

we can increase the value by using the formula:

\(initial value+ percentage increase *initial value\) = increased percentage

in the aforementioned question we have

initial value = 2400

percentage increase = 5%

thus we can find out the increased percentage by:

2400 + 2400 X (5/100)

=2400 + 120

=2520

the value by which 2400 is increased is 120

to arrive at the increased value which is 2520

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Answer:

D.) 0.075

Step-by-step explanation:

Answer:

\(\frac{-1.1x^{25} }{-1.1x^{11} }\)     \(\frac{mx^{67} }{mx^{37} }\)

Step-by-step explanation:

Sine (-1.1) is the same as (-1.1) you just put them together and if the numbers are by each other you just add up the exponents. But if the question says this \(\frac{-1.1x^{2} }{-1.1x^{3} }\) than you subtract the exponents.

·\((-1.1)x^{13}X (-1.1)x^{12} = add\\\frac{-1.1x^{2} }{-1.1x^{2} } = subtract\)

Hope this helps. Have a blessed day :)

Answer:

a) $29.68

b) $47.52

c) $80.24

Step-by-step explanation:

a) $4.24 x 7 = $29.68

b) $190.08 / 4 = $47.52

c) Total Spent = $29.68 + 190.08 = $219.76

Total Budget = $300

$300 - $219.76 = $80.24

They spend on poster boards in the total amount of $29.68, they paid per-light cost was $47.52 and they can spend more amount of $80.24.

In mathematics, divides left-hand operands into right-hand operands in the division operation.

They spent $4.24 on each of the seven poster boards.

The total amount of spend = cost × quantity

The total amount of spend = $4.24 × 7

The total amount of spend = $29.68

They spent $190.08 total on new lighting.

cost of each light =  total amount of spend / quantity

cost of each light =  $190.08 / 4 = $47.52

Total Spent = $29.68 + 190.08 = $219.76

The total Budget is $300 which is given in the question

$300 - $219.76 = $80.24

Therefore, they spend on poster boards in the total amount of $29.68, they paid a per-light cost was $47.52 and they can spend more amount of $80.24.

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Answer:

The monthly cost = $9 + $0.39x

Step-by-step explanation:

Answer:\(\color{yellow}{}\)

∆ABC

∆DEF

∆ABC

<C

<D

<X

BE>

CF>

AD>

34>

x9×>

A=3.7

Answer:

8 feet is the shortest possible with the room could have

Step-by-step explanation:

12×8=96

Answer:

8 is the smallest width the room could be

Step-by-step explanation:

s represents the number that is the smallest the room could be

12s = 96

divide both sides by 12

12s/12 = 96/12

s = 8

Answer:

(2,-1)

Step-by-step explanation:

We can use substitution to solve this system of equations. Since x is already solved for in the second equation, we can substitute 2y + 4 for x in the first equation:

4(2y + 4) + 2y = 6

Simplifying the left side:

8y + 16 + 2y = 6

Combining like terms:

10y + 16 = 6

Subtracting 16 from both sides:

10y = -10

Dividing both sides by 10:

y = -1

Now that we know y, we can use the second equation to find x:

x = 2y + 4

x = 2(-1) + 4

x = 2

Therefore, the solution to the system of equations is (x, y) = (2, -1).

The correct answer choice is (2, -1).