Example 4
At the end of 2013, world oil reserves were about 1701 billion barrels.3 During 2014, about 33.3 billion barrels of oil were consumed, an increase of about 0.08% over the previous year. Assuming yearly oil consumption increases at this rate in the future, how long will the reserves last?

It is true that when conducting a t-test for two independent samples with a two-tailed example and α = 0.05, you divide the α by 2 (0.05/2 = 0.025) to find the critical t-scores that form the boundaries of the critical region. This is because you are considering both tails of the distribution.

True. When conducting a t test for two independent samples with a two-tailed example, we need to find the critical t-scores that form the boundaries of the critical region for α = 0.05. To do this, we divide the α value of 0.05 by 2 to get 0.0250, and then use this value to find the t-scores using a t-distribution table or calculator. This is necessary because we are looking at the possibility of a significant difference in either direction, hence the two-tailed example.

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Answer:  38.46

Step-by-step explanation:

             ↓

   38.456 It means round by 0.05, so when you round you look at the place value after the specified digit.

However, as you move away from the picture, larger regions of color become visible, eventually transforming into recognized objects such as flowers or clouds. This is comparable to Binding.

All you'll notice if you get too close to a pointillist artwork are tiny colored dots. However, as you move away from the picture, larger regions of color become visible, eventually transforming into recognized objects such as flowers or clouds. This is similar to Binding.

This experiment, first done in 1999, reveals a phenomena known as inattentional blindness, in which focused attention causes a failure to detect something that would otherwise be clear. The Stroop effect is a typical illustration of top-down processing in operation. In this assignment, participants are shown a list of words printed in various colors. They are then asked to name the color of the ink rather than the word itself.

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If the electron have a negative charge and protons have a positive charge , then the charge of atom with 2 more electrons than protons is  -3.2 × 10⁻¹⁹ C .

The Electrons and Protons are particles of an atom that have equal but opposite charges ,

the Electrons have a negative charge that is \(q_{e}\) = -1.6 × 10⁻¹⁹ C ,

the Protons have a positive charge that is \(q_{p}\) = 1.6 × 10⁻¹⁹ C  ;

we have to find the charge on atom that have 2 more electrons than protons ,

The total charge on the neutral atom is 0 ,

it is given that , the atom has 2 more electrons than protons ,

So , the charge on Atom is = 0 + 2\(q_{e}\)

Substituting the value of \(q_{e}\) ,

we get ;

Q = 2 × ( -1.6 × 10⁻¹⁹ C) = -3.2 × 10⁻¹⁹ C

Therefore , the charge on the atom is -3.2 × 10⁻¹⁹ C  .

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The volume of plaster Darla needs for the miniature stairs is 418³.

The volume is the space occupied by a three-dimensional object.

Volume is the product of the multiplication of length, width, and height.

We first calculate the total volume for this situation, assuming that the stairs have not cut portions.

Secondly, calculate the volume of the cut portions and subtract the result from the total volume to get the volume of the stairs, which represents the quantity of plaster required by Darla.

Length of the miniature stairs = 12 cm

Width of the miniature stairs = 11 cm

Height of the miniature stairs = 4 cm

The volume of the stairs with the cut portion = 528 cm³ (12 x 11 x 4)

The length of the cut portion of the stairs = 12 cm

The width of the cut portion of the stairs = 11 cm

The height of the cut portion of the stairs = 2 cm (4 - 2)

The volume of the cut portion of the stairs = 110 cm³ (11 x 5 x 2)

The volume of the stairs without the cut portion = 418 cm³ (528 - 120)

The total volume of plaster can also be computed separately as the volume of the larger object plus the volume of the smaller object.

418 cm³= (7 cm x 4 cm x 11 cm) + (5 cm x 2 cm x 11 cm)

= (308 cm³ + 110 cm³)

Thus, the quantity (volume) of plaster Darla needs is 418 cm³.

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The required sample size is 907.

We have,

To determine the required sample size for estimating the fraction of new car buyers who prefer foreign cars over domestic with a 95% confidence level and an error of at most 0.03, we'll use the following formula:
n = (Z² x p  (1 - p)) / E²
Where:
- n is the required sample size
- Z is the Z-score for the desired confidence level (1.96 for a 95% confidence level)
- p is the estimated population proportion (0.31)
- E is the margin of error (0.03)

Step-by-step calculation:
1. Calculate Z²: 1.96² = 3.8416
2. Calculate p (1 - p): 0.31 x (1 - 0.31) = 0.2139
3. Calculate E²: 0.03² = 0.0009
4. Substitute these values into the formula: n = (3.8416 x 0.2139) / 0.0009 = 906.92

Since we need to round up to the next integer, the required sample size is 907.

Thus,

The required sample size is 907.

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Answer:

x=10

Step-by-step explanation:

Perimiter is 2(x+y) with x and y being the two differend sides. First side is 3x and the second is   2x+4. 2(3x+2x+4)=108. 10x+8=108 10x=100 x=10.

The sides are 24 and 30

Please mark brainliest hope this helps :D

Answer:

x=10

Step-by-step explanation:

Since this is a rectangle, we know that the values of opposite sides are equal and that the perimeter is all of the sides' values combined. Therefore:

2(2x+4)+2(3x)=108

First, we need to distribute the 2s on the left side.

4x+8+6x=108

Combine like terms.

10x+8=108

Subtract the 8 from both sides.

10x=100

Divide by 10.

x=10

HTH :)

On solving the provided question, we can say that the equation \(x = 14 + y\) is age of Ishaan is 21 years and Christopher is 7 years old.

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

age of Ishaan = x.

Age of Christopher = y.

Ishaan is 3 times as old = Christopher,

x = 3y

Ishaan is 14 years older than Christopher,

\(x = 14 + y \\3y = 14 + y\\3y - y = 14\\2y = 14\\y = 14/2\\y = 7\\Now, x = 3(7)\\x = 21.\\\)

age of Ishaan is 21 years.

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Answer:

m = -1/3

Step-by-step explanation:

First, write the equation in slope-intercept form:

3y = 10 - x

y = 10/3 - x/3

y = 10/3 - 1/3x

Since our slope is the coefficient of the x term, our slope is -1/3.

The total number of different telephone numbers are possible in city  is 6561.

A term permutation relates to a mathematical process that determines the number of possible arrangements of a given set.

Now, according to the question;

Because the first three digits are fixed, we must select the next four digits.

A total number of available telephone numbers is increased by selecting one of nine numbers for the fourth digit;

nine numbers for the fifth digit;

nine numbers for the sixth digit;

and nine numbers for the seventh digit.

Thus,

= 9×9×9×9

= 6561

Therefore, the total number of ways in which telephone numbers are possible in city are 6561.

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Answer:

$70

Step-by-step explanation:

You want 175% of $40.

175% as a decimal = 1.75

1.75 times 40 = 70

Therefore Liam put $70 in savings in April

Answer:

70

Step-by-step explanation:

Multiply 40$ by 175% :)

9514 1404 393

Answer:

  m = 1/2

  b = -7

Step-by-step explanation:

The formulas for these can be used.

  m = (y2 -y1)/(x2 -x1) . . . . . . . . . formula for slope given 2 points

  m = (-9 -(-11))/(-4-(-8)) = 2/4

  m = 1/2

__

  b = y1 -m·x1 . . . . . . . . . . . . formula for y-intercept given slope and point

  b = -11 -(1/2)(-8) = -11 +4

  b = -7

Answer:

\(4\frac{7}{20}\)

Hope This Helps! :)

Answer:

\(4\frac{7}{20}\)

Step-by-step explanation:

\(9\frac{1}{10}-4\frac{3}{4}\)

Convert in improper fractions:

\(\frac{10*9+1 }{10} -\frac{4*4+3}{4}\\\\\frac{90+1}{10}-\frac{16+3}{4}\\\\\frac{91}{10}-\frac{19}{4} < ==find\ the\ LCM\ or\ the\ common\ denominator\ for\ 10\ and\ 4\ (20)\\\\\frac{182}{20} -\frac{95}{20}\\\\ \frac{87}{20} < ==convert\ to\ a\ mixed\ fraction\\\\ 4\frac{7}{20}\)

Multiples of 4:

4, 8, 12, 16, 20, 24, 28, 32, 36, 40

Multiples of 10:

10, 20, 30, 40

LCM of 4 and 10 is 20.

Hope this helps!

\(\bold{\huge{\underline{ Solution }}}\)

Here, we have to find the value of x

We have given quadrilateral ABCD here , whose angles are as follows

[ The measure of right angled triangle is 90° ]

We know that,

That is

\(\bold{\angle{ A + }}{\bold{\angle{B +}}}{\bold{\angle{C + }}}{\bold{\angle{D + = 360{\degree}}}}\)

Subsitute the required values

\(\sf{ ( 6x + 5){\degree} + 80{\degree}+ 90{\degree} + (9x - 10){\degree} = 360{\degree}}\)

\(\sf{ 6x + 5 + 170{\degree} + 9x - 10 = 360{\degree}}\)

\(\sf{ 15x - 5 = 360{\degree} - 170{\degree}}\)

\(\sf{ 15x - 5 = 190 {\degree}}\)

\(\sf{ 15x = 190 {\degree} + 5 }\)

\(\sf{ 15x = 195 {\degree}}\)

\(\sf{ x = }{\sf{\dfrac{ 195}{15}}}\)

\(\sf{ x = }{\sf{\cancel{\dfrac{ 195}{15}}}}\)

\(\bold{ x = 13 }\)

Hence, The value of x is 13 .

\(\bold{\huge{\underline{\red{ Verification }}}}\)

Measure of Angle A

\(\sf{ = (6x + 5){\degree}}\)

\(\sf{ = (6(13) + 5 ){\degree}}\)

\(\sf{ = (78 + 5 ){\degree}}\)

\(\sf{ = 83{\degree}}\)

Measure of Angle D

\(\sf{ = (9x - 10){\degree}}\)

\(\sf{ = (9(13) - 10){\degree}}\)

\(\sf{ = (117 - 10 ){\degree}}\)

\(\sf{ = 107{\degree}}\)

Now, we know that,

That is,

\(\sf{ 83{\degree} + 80{\degree}+ 90{\degree} + 107 {\degree} = 360{\degree}}\)

\(\sf{ 163{\degree}+ 90{\degree} + 107 {\degree} = 360{\degree}}\)

\(\sf{ 253{\degree}+ 107 {\degree} = 360{\degree}}\)

\(\sf{ 253{\degree}+ 107 {\degree} = 360{\degree}}\)

\(\bold{ 360{\degree} = 360{\degree}}\)

\(\bold{ LHS = RHS }\)

Hence, Proved.

The probability that a household selected at random does not have an individual under the age of 18 in Nassau County in 2000 is 0.999614.

The round-off to the nearest thousands would be 1.000.

To calculate the probability that the selected household did not have an individual under the age of 18, we must determine the number of households without individuals under 18 and divide it by the total number of households in Nassau County in 2000.

We already know that,

The total households = 447,000

The number of households with individuals under 18 = 173

Now,

Number of households without individuals under 18 =

Total households - Households with individuals under 18

Number of households without individuals under 18 = 447,000-173

= 446,827

Probability = Number of households without individuals under 18/Total number of households

Probability = 446,827/447,000

= 0.999614

∴ The probability that the selected household does not have an individual under the age of 18 is 0.999614.

The round-off to the nearest thousand would be 1.000.

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This whole question: There were a total of 447000 households in Nassau County in 200. If one of these households was selected at random, what is the probability that the selected household did not have an individual under age 18? (Express your answer as a decimal rounded to the nearest thousandth)

Answer:

x=11

Step-by-step explanation:

Step-by-step explanation:

this is equation......................

\(\\ \sf\longmapsto \left[{3a+b\atop a-b}\:\:\:{3c-d\atop a+b+d}\right]=\left[{3\atop 5}\:\:\;{6\atop 2d-1}\right]\)

Now constructing equations

\(\\ \sf\longmapsto 3a+b=3\dots(1)\)

\(\\ \sf\longmapsto a-b=5\dots(2)\)

\(\\ \sf\longmapsto 3c-d=6\dots(3)\)

\(\\ \sf\longmapsto a+b+d=2d-1\dots(4)\)

Adding eq(1) and (2)

\(\\ \sf\longmapsto 4a=8\)

\(\\ \sf\longmapsto a=\dfrac{8}{4}\)

\(\\ \bf\longmapsto a=2\)

Put the value in eq(2)

\(\\ \sf\longmapsto a-b=5\)

\(\\ \sf\longmapsto b=a-5\)

\(\\ \sf\longmapsto b=2-5\)

\(\\ \bf\longmapsto b=-3\)

put the values in eq(4)

\(\\ \sf\longmapsto a+b+d=2d-1\)

\(\\ \sf\longmapsto 2+(-3)+d=2d-1\)

\(\\ \sf\longmapsto d-1=2d-1\)

\(\\ \sf\longmapsto d-2d=-1+1\)

\(\\ \sf\longmapsto -d=0\)

\(\\ \bf\longmapsto d=0\)

Put the value in eq(3)

\(\\ \sf\longmapsto 3c-d=6\)

\(\\ \sf\longmapsto 3c-0=6\)

\(\\ \sf\longmapsto 3c=6+0\)

\(\\ \sf\longmapsto 3c=6\)

\(\\ \sf\longmapsto c=\dfrac{6}{3}\)

\(\\ \sf\longmapsto c=2\)

Hello!

45% of x = 7.2

45x/100 = 7.2

45x = 7.2 * 100

45x = 720

x = 720/45

x = 16

the number = 16

If area of "square-field" is 40000 ft square, and Mr. Blackburn is putting a fence diagonally in field, then the length of fence be is 282.84 ft.

The area of the square-field is = 40000 ft²,

We equate this with area formula,

We get,

⇒ (side)² = 40000,

⇒ side = 200,

substituting the side-length as 200 ft, in the diagonal formula,

we get,

⇒ Length of diagonal of field is = (side)√2,

⇒ Length of diagonal of field is = (200)√2,

⇒ Length of diagonal of field is ≈ 282.84 ft.

Therefore, the length of the fence of the field is 282.84 ft.

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we can only say that the series ∑a_k^2 converges, but we cannot determine the convergence of the series ∑(-1)^k b_k.

Let's evaluate the two series separately:

First, for the series ∑a_k^2, we note that a_k^2 is always non-negative. Therefore, we can use the comparison test and compare it to the p-series ∑1/k^2, which we know converges:

```
0 ≤ a_k^2 ≤ 1/k^2
```

Since ∑1/k^2 converges, so does ∑a_k^2 by the comparison test.

Next, for the series ∑(-1)^k b_k, we note that the terms alternate in sign. Therefore, we can use the alternating series test to check for convergence. The alternating series test states that if a series ∑(-1)^k b_k converges, then b_k must satisfy the following conditions:

1. b_k ≥ 0 for all k
2. b_k is a non-increasing sequence (i.e., b_k ≥ b_{k+1} for all k)
3. lim_{k→∞} b_k = 0

We can see that condition 1 is not satisfied for the given series, as b_k = 2 for all even values of k and b_k = -1 for all odd values of k. Therefore, the alternating series test does not apply to this series.

In conclusion, we can only say that the series ∑a_k^2 converges, but we cannot determine the convergence of the series ∑(-1)^k b_k.
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The moon has a wider surface temperature range than Earth, and thunderstorms do not occur on the moon.

The surface temperature range on the moon is much wider compared to Earth. This is primarily due to the moon's lack of atmosphere, which leads to minimal heat retention and insulation. During the lunar day, the temperature on the moon's surface can reach up to 260 degrees Fahrenheit (127 degrees Celsius), while during the lunar night, temperatures can plummet to around -280 degrees Fahrenheit (-173 degrees Celsius). In contrast, Earth's atmosphere helps regulate temperature, resulting in a narrower range of surface temperatures.

As for thunderstorms, they do not occur on the moon. Thunderstorms are complex weather phenomena that require certain conditions, such as the presence of moisture, atmospheric instability, and electric potential differences. The moon lacks the necessary elements for thunderstorms to form. It has no atmosphere to support the formation of clouds, moisture, or the generation of the electrical charges required for lightning and thunder. Therefore, thunderstorms, as we commonly experience them on Earth, do not occur on the moon.

However, it's worth noting that the moon does experience other types of lunar phenomena, such as moonquakes and micrometeorite impacts. These events can cause vibrations and disturbances on the moon's surface but are different from the atmospheric disturbances associated with thunderstorms on Earth.

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Answer:

slope = 3/5

y intercept = 1

Step-by-step explanation:

i think

Answer:

Slope: 3/5

Y-int: 1

Step-by-step explanation:

Slope intercept form is y=mx+b, with m being the slope being the y-int. So, m is 3/5 and b is 1 in the equation.

(hope this helps :P)

Answer:

60

Step-by-step explanation:

The computation of the rest of the marbles is given below:

Since there is 20 red and 15 white marbles

Also the 3 bags contains same marbles

So if he gives 45 marbles, so the remaining would be

= (20 + 15) × 3 - 45

= 35 × 3 - 45

= 105 - 45

= 60

The average value of f over the rectangle [0,6] x [0,1] is approximately 3.427.

The average value of a function f over a rectangle R is given by:

avg(f) = (1/Area(R)) * double integral of f over R

Here, f(x,y) = 5e^(yx) + e^y and R = [0,6] x [0,1]

The area of R is given by:

Area(R) = (6 - 0) * (1 - 0) = 6

So, the average value of f over R is:

avg(f) = (1/6) * double integral of f over R

We can evaluate the double integral using iterated integration. First, we integrate f with respect to y from 0 to 1, and then integrate the result with respect to x from 0 to 6:

integral of f(x,y) dy = integral of (5e^(yx) + e^y) dy

= (5x/2)e^(yx) + e^y + C

where C is the constant of integration.

Now, we integrate this result with respect to x from 0 to 6:

integral of [(5x/2)e^(yx) + e^y] dx = [(5/2) * integral of xe^(yx) dx] + integral of e^y dx

= [(5/2) * (1/y)e^(yx) - (5/2)(1/y^2)(e^(yx) - 1)] + ey + C

where C is another constant of integration.

Therefore, the average value of f over R is:

avg(f) = (1/6) * [(5/2) * (1/y)e^(yx) - (5/2)(1/y^2)(e^(yx) - 1) + ey] evaluated from y=0 to y=1 and x=0 to x=6

avg(f) = (1/6) * [(5/2) * (1/e^6 - 1) - (5/2)(1/e - 1/e^6) + e - 1]

avg(f) = (1/6) * [(5/2) * (1 - e^-6) - (5/2)(e^-1 - e^-6) + e - 1]

avg(f) = (1/6) * [(5/2) * (1 - e^-6 - e^-1 + e^-6) + e - 1]

avg(f) = (1/6) * [(5/2) * (1 - e^-1) + e - 1]

avg(f) ≈ 3.427

Therefore, the average value of f over the rectangle [0,6] x [0,1] is approximately 3.427.

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The simplified form of A + 1 1/6 = -11 7/9 is \(A = - 12\frac{17}{18}\)

and, the letter A in algebra is  any variables of real numbers.

Simplified form:

Fractions are not integers, but numbers between integers. He is part of the whole. Fractions also have two parts - a numerator and a denominator. We get fractions in their simplest form when the numerator and denominator can no longer individually be reduced to a lower number.

Now,

a + \(1 \frac{1}{6}\) = \(-11 \frac{7}{9}\)

convert the mixed to improper fraction number:

\(1 \frac{1}{6} = \frac{7}{6}\)

This implies:

\(A+ \frac{7}{6} = -11 \frac{7}{9}\)

Convert the mixed to improper fraction number:

\(-11 \frac{7}{9} = \frac{106}{9}\)

This implies:

\(A+ \frac{7}{6} = \frac{106}{9}\)

Move 7/6 in the right side,

therefore,

   A = -106/9 - 7/6

⇒ A = -233/18

convert the mixed to improper fraction number:

\(\frac{233}{18} = 12\frac{17}{18}\)

Therefore, we get:

A =   \(- 12\frac{17}{18}\)

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Answer:

Option 2.. x > -6

Step-by-step explanation:

3x -5x - 2 > 5x -5x + 10

-2x - 2 + 2 > 10 + 2

-2x/-2 > 12/-2

x > -6

Answer:

Step-by-step explanation:

1. If PQ = PQ then PQ ≅ PQ

 Reflexive Property of congruence

2. If K is between J and L, then JK + KL = JL

 Segment addition property

3. EF ≅ EF

 Definition of congruence

4. If RS = TU, then RS + XY = TU + XY

 Addition property of equality

5. If AB = DE, then DE = AB

 Symmetric property of equality

The y-intercept represents a. the maximum weight allowed in a shipment.

Given: The graph is between the Amount of allowed weight remaining Vs the Number of boxes included.

What is a graph?

A graph is a diagram or the representation of variations between two or more variables with respect to each other.

A graph consists of dependent and independent variables. We usually plot the response of the dependent variable with the change in the value of the independent variable.

What is y-intercept?

The y-intercept is the point on the y-axis that a given equation of line or a curve passes through when the value of x = 0. It can denote either the minimum value for a function is the function is increasing the the initial point is the y intercept or the maximum value for a decreasing function if the y-intercept is the initial point.

Let's solve the question:

It is given in the question that the graph is of  Amount of allowed weight remaining Vs the Number of boxes.

As it is "Amount of weight remaining", so we can interpret that it is a decreasing curve with the increase in the number of boxes or in simple words the value of y will keep decreasing with the increasing number of x value.

Therefore, for this graph the y-intercept will show the maximum weight remaining or as it is the y-intercept that is x = 0, which means when there are no boxes the maximum weight remaining is y-intercept. So it the maximum weight allowed in the shipment.

Hence the answer is a. the maximum weight allowed in a shipment.

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Disclaimer: The given question is incomplete. The complete question is mentioned below:

One manufacturer boxes screws so that each box weighs the same no matter what size the screws are. The graph shows the amount of allowed weight remaining in a given shipment depending on the number of boxes of screws already included. What does the y-intercept represent in this situation?

a. the maximum weight allowed in a shipment.

b. the minimum weight of a single box of screws.

c. the minimum number of screws in a single box.

d. the maximum number of single boxes for a shipment.