Emelio is going to China on vacation. He can take one bag for free, but if the
weight of the bag is greater than 45 lb, he must pay a fee. Emelio knows his
bag weighed 32.4 lb on the way to China, and he plans to buy gifts for his
parents and siblings. He packs the same things he brought to China plus the
gifts into his bag on the way back. If he doesn't want to pay a fee, how much
can the gifts weigh?
The weight of the gifts must be Select...
Ib.

Answer: 2.403 × 10^3 atoms

Step-by-step explanation:

10^13 x 6.02 = 6.02^23 and 6.02^23 x 4 = 2,403 turned into 2.403 x 10^3 atoms.

Answer:

Perpendicular line ⇒ 2x + 9y + 42 = 0

midpoint: (-1,1)

Step-by-step explanation:

Let's find the coordinates of midpoint of AB

Here, from figure, A = (-3,-2), B = (1,4)

So midpoint:

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

∴ P = (-1, 1)

Now, given straight line is x - 2y = -8(x-8)

⇒x - 2y = -8x+64

⇒9x - 2y - 64 = 0

Perpendicular line to 9x - 2y - 64 = 0 is 2x + 9y + k = 0

Perpendicular line passes though (6,-6)

Putting the values, we get

2(6) + 9(-6) + k = 0

⇒12 - 54 + k = 0

⇒k = 42

∴ Perpendicular line ⇒ 2x + 9y + 42 = 0

Answer:

The inverse function is [tex]y = -\frac{x}{4}[/tex]

Step-by-step explanation:

Inverse of a function:

To find the inverse of a function, we exchange x by y, then we isolate y.

y = -4x

Finding the inverse:

[tex]x = -4y[/tex]

[tex]4y = -x[/tex]

[tex]y = -\frac{x}{4}[/tex]

So

The inverse function is [tex]y = -\frac{x}{4}[/tex]

Answer:

15 and -20

Step-by-step explanation:

The zeros/ roots are the x intercepts of the graph

Answer:

C=10

Step-by-step explanation:

The equation of line that passes through (-3,3) and is perpendicular to 2y = 8x - 6 is y = (-1/4)x + 9/4.

The slope-intercept form is expressed as;

y = mx + b

Where m is slope and b is the y-intercept.

Given the equation of the original line.

Write in slope intercept form

2y = 8x - 6

y = 8x/2 - 6/2

y = 4x - 3

Using the slope intercept, slope m is 3.

The equation of a perpendicular line to 2y = 8x - 6 must have a slope that is the negative reciprocal of the original slope.

Slope of perpendicular line = -1 / ( 4 )

Slope of perpendicular line = -1/4

Plug the slope m = -1/4 and point (-3,3) into point-slope formula and simplify.

( y - y₁ ) = m( x - x₁ )

( y - 3 ) = (-1/4)( x - (-3) )

( y - 3 ) = (-1/4)( x + 3 )

y - 3 = (-1/4)x - 3/4

y = (-1/4)x - 3/4 + 3

y = (-1/4)x + 9/4

Therefore, the equation of the perpendicular line is y = (-1/4)x + 9/4.

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Answer:

Step-by-step explanation:

Required volume is:

The center of the circle is (-10,4) and the radius is 10.

The circle is defined as the locus of the point traces around a fixed point called as the center and is equidistant from the outer trace.

All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

The equation of the circle is,

( x - h )² + ( y - k )² = r²

(x+10)² + (y−4)² = 100

(x+10)² + (y−4)² = 10²

Compare the equations and find the center and radius,

Center = ( h,k) = ( -10,4)

Radius = r = 10

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Answer:

−1 < y < 3

Step-by-step explanation:

Answer:

f(x) = 0.99x + 0.3

Step-by-step explanation:

f(x) = 1.29 + 0.99(x - 1)

Distribute

f(x) = 1.29 + 0.99x - 0.99

Combine like terms

f(x) = 0.99x + 0.3

Answer:

1/4

Step-by-step explanation:

8/8=1

6/8=3/4

4/8=2/4

2/8=1/4

Answer:

The actual SAT score is 2024.

The equivalent ACT score is 29.49.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

SAT score that is in the 95th percentile

Scores on the SAT test are normally distributed with a mean of 1511 and a standard deviation of 312, which means that [tex]\mu = 1511, \sigma = 312[/tex]

95th percentile is X when Z has a pvalue of 0.95, so X when Z = 1.645. The score is:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.645 = \frac{X - 1511}{312}[/tex]

[tex]X - 1511 = 1.645*312[/tex]

[tex]X = 2024[/tex]

The actual SAT score is 2024.

Equivalent ACT score:

The equivalent ACT score is the 95th percentile of ACT scores.

Scores on the ACT test are normally distributed with a mean of 21.1 and a standard deviation of 5.1, which means that [tex]\mu = 21.1, \sigma = 5.1[/tex]. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.645 = \frac{X - 21.1}{5.1}[/tex]

[tex]X - 21.1 = 1.645*5.1[/tex]

[tex]X = 29.49[/tex]

The equivalent ACT score is 29.49.

Answer:

Step-by-step explanation:

if there is any triangle ABC and a,b,c are sides opposite angles A,B,C respectively , then

[tex]cos~A=\frac{b^2+c^2-a^2}{2bc} \\cos~B=\frac{c^2+a^2-b^2}{2ca} \\cos~C=\frac{a^2+b^2-c^2}{2ab}[/tex]

B=101

a= 3 cm

b=y

c=1 cm

use formula for cos B

cos 101=cos(90+11)=sin 11

[tex]-sin~11=\frac{1^2+3^2-y^2}{2 \times 3 \times 1} \\-6 \times sin~11=1+9-y^2\\y^2=10+6~sin~11\\y^2\approx 10+6\times 0.1908\\y^2 \approx11.1448\\y\approx3.338[/tex]

Answer:

2.16

Step-by-step explanation:

To find the length y:

Since we have an angle with two sides next to it, it is 'cosy', so we can use the cosine rule to find y. Let's make y = a for the formula.

Using the cosine formula:

a^2 = b^2 + c^2 - 2bc cos(A)

where b=1, c=3 and A=101

substitute these values in the formula:

a ^2 = 1^2 + 3^2 - 2(1)(3) × cos(101)

a ^2 = 4.647970...

Square root to find a:

a = √4.647970...

a = 2.16

thus, y = 2.16 to 3sf

9514 1404 393

Answer:

  85 km/h

Step-by-step explanation:

Let s represent the speed of the slower car. Then the travel time is ...

  time = distance/speed

  2 = 360/(s +(s+10))

  4s +20 = 360 . . . . . multiply by 2s+10

  4s = 340 . . . . . . . . . subtract 20

  s = 85 . . . . . . . . . . . divide by 4

__

The rate of the slower car is 85 km/h.

Answer:

It's A

Step-by-step explanation:

I just did the test and it is A

Note that in the attached Geometric Figure (Diagram) which features QR as parallel to NO, if NQ = 12, QR 20, and NO = 35, then the length of QP is equal to 16.

[tex]\overline {QR}[/tex] is Parallel to [tex]\overline {NO}[/tex]; therefore

QR/NO = PQ/PN

⇒ 20/35 = PQ/PQ +12

This is because:

PN = PQ + NQ; which is also
PN = PQ +12

(PQ + 12) x 20 = 35PQ
20PQ + 240= 35PQ ; Collect like terms

240= 35 PQ - 20 PQ

240 = 15PQ; Divide both sides by 15

⇒ 240/15 = 15PQ/15
⇒ 16 = PQ

Therefore, QP = PQ which is equal to 16.

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Answer:

d

Step-by-step explanation:

9514 1404 393

Answer:

  not periodic

Step-by-step explanation:

There is no value p such that f(x) = f(x+p) for all x. Hence. the function is NOT PERIODIC.

_____

It seems possible that subtracting the linear increase would result in a periodic function. Because of the linear increase, there is no left- or right-shift of the function that will map it to itself.

Answer: 3 · 30= 90

Step-by-step explanation:

yes you are correct

the equation in the form of slope interpretation is y = 1/3x -4.

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation has the conventional form y = mx + c.

Given data in a table such as it makes a linear equation slope-intercept form of the given equation is y = mx +c

Where m is the slope

c is constant

The slope for the given data

m = (y₂ - y₁) / (x₂ - x₁)

m = (-5 + 6 )/ (-3 + 6)

m = 1/3

Hence, the equation would be

y = 1/3x + c

for constant we would satisfy the equation with other coordinates of the line.

Substituting ( 0, -4) in the above equation

-4 = 0 + c

c = -4

thus, the equation of the line is  y = 1/3x  -4

therefore, the linear equation of the given data is y = 1/3x -4.

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Answer:

52 cm²

Step-by-step explanation:

There are 3 distinct faces:

one with sides 2 and 3

one with sides 2 and 4

one with sides 3 and 4

There are two of each distinct face (they are accros each other)

so we find their areas (we times by two as there are two of each face)

2×3×2=12

2×4×2=16

3×4×2=24

Finally we add the values:

12+16+24=52 cm²

Answer:

6.7 km

Step-by-step explanation:

c² = 4.9²+4.5²

= 24.01 + 20.25

= 44.26

c = √44.26 = 6.7

Answer:

the missing side is [tex]\sqrt{89}[/tex]

Step-by-step explanation:

We use Pythagoras theorem

[tex]8^{2} +5^{2} =x^{2} \\64 + 25 = x^{2} \\89=x^{2} \\\sqrt{89} =x[/tex]

The required range of drivers who own 8 years car is 23years.

Given that,

The scatter plot shows the ages of drivers who attended a car show and the ages of their cars.

We have to determine,

The age range of drivers who own an 8-year-old car.

According to the question,

The Range is the difference between the lowest and highest values.

Therefore,

The age range of drivers who own 8 years old car is 17,25 and 40 years.

Then,

Range of drivers who own 8 years car = highest value of range - lowest value of age.

Range of age of drivers who own 8 years car = 40 - 17 = 23years

Hence, The required range of drivers who own 8 years car is 23years.

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Answer:

side AB

Step-by-step explanation:

The division expression is equivalent to the given expression is (13/ 3)/ (-5/6)

What is expression ?

expression can be defined as with the minimum of two variables or numbers and at least one math operation.

Given expression,

= 4 1/3 / (-5/6 )

= (13/3 )/ (-5/6)

= 13*6 / -15

= -26/5

By evaluating the other expressions to find its equivalent,

(13 / 3) / (-5/6)

= 13 * 6 / -15

= -26/5

Hence , the expression 4 1/3 / (-5/6 ) is equivalent to (13 / 3) / (-5/6) .

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The division expression is equivalent to the given expression is (13/ 3)/ (-5/6)

expression can be defined as with the minimum of two variables or numbers and at least one math operation.

Division is one of the four basic mathematical operations of arithmetic, along with addition, subtraction, and multiplication. The division operation is represented by the symbol ÷ or /, and it is the inverse operation of multiplication.

Given expression,

= 4 1/3 / (-5/6 )

= (13/3 )/ (-5/6)

= 13*6 / -15

= -26/5

By evaluating the other expressions to find its equivalent,

(13 / 3) / (-5/6)

= 13 * 6 / -15

= -26/5

Hence , the expression 4 1/3 / (-5/6 ) is equivalent to (13 / 3) / (-5/6) .

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Answer:

Pattern is: +4

Step-by-step explanation:

an arithmetic series/ pattern since the next number is got by adding 4 to tge previous number

Answer:

exponents, exponents, parenthesis, parenthesis/exponents, parenthesis.

Step-by-step explanation: