Question 19
There are 118 different elements in the periodic table. While giving a presentation, Clark says that there are 128 different
elements. Select each true statement.
A) There are actually 118 elements
B) The amount of error in Clark's estimate is 10.
C) The amount of error in Clark's estimate is 118.
D) To the nearest tenth percent, the percent error in Clark's estimate is 8.5%.
E) To the nearest tenth percent, the percent error in Clark's estimate is 10%.
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Answer:

y=3/5x-7

Step-by-step explanation:

when lines are parallel they have the same slope and the slope of the first line was 3/5

Hello!

Let's consider the equation given:

 ⇒the coefficient before the x is the slope

When lines are parallel:

 ⇒the slopes are equal

Since the line given has a slope of 3/5

 ⇒ the line parallel is [tex]y = \dfrac{3}{5} x - 7[/tex]    <==Answer

Hope that helps!

Answer: 90 degree

Step-by-step explanation: the diameter of a circle compounds to an inscribed angle of  90 degree

The domain and range of the function f(x) = 3x⁵ is all real numbers, the x-intercept = 0 and y-intercept = 0.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The equation for the function is:

f(x) = 3x⁵

The domain of the function: D = all real number

The range of the function: R = all real number

x-intercept = 0

y-intercept = 0

Increasing interval: x ∈ [0, ∞)

Decreaing interval: x ∈ (-∞, 0]

Symmetry = The function is not symmetric

End behavior:

x → ∞, y →∞

x → -∞, y → -∞

Thus, the domain and range of the function f(x) = 3x⁵ is all real numbers, the x-intercept = 0 and y-intercept = 0.

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The correct answer to the question would be:

D. The manufacturer tests every 500th smartphone off the production line.

Answer: 4x+6/x^2

Step-by-step explanation:

The value of the function f(x) = 3(1 - x - 2x²)/2 at x = -2 is f(-2) = -15/2 after plugging x = -2.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The function is:

f(x) = 3(1 - x - 2x²)/2

It is required to find the value of f(-2)

Plug x = -2

f(-2) = 3(1 - (-2) - 2(-2)²)/2

f(-2) = 3(1 + 2 - 8)/2

f(-2) = 3(-5)/2

f(-2) = -15/2

Thus, the value of the function f(x) = 3(1 - x - 2x²)/2 at x = -2 is f(-2) = -15/2 after plugging x = -2.

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The dimensions of this cuboid are 2 cm, 11 cm, and 17 cm respectively.

Mathematically, the volume of a cuboid can be calculated by using this following formula:

Volume = L × W × H

Where:

Substituting the given parameters into the formula, we have;

Volume = 2 × (x + 3) × (x + 9)

374 = 2 × (x² + 9x + 3x + 27)

374 = 2 × (x² + 12x + 27)

Dividing both sides by 2, we have:

187 = x² + 12x + 27

Rearranging the equation, we have:

x² + 12x + 27 - 187 = 0

x² + 12x - 160 = 0

Next, we would solve the quadratic equation by using the factorization method as follows:

x² + 12x - 160 = 0

x² + 20x - 8x - 160 = 0

x(x + 20) - 8(x + 20) = 0

(x - 8)(x + 20) = 0

x = 8 or x = -20

Since the dimensions cannot be negative, the value of x is equal to 8.

Check:

x² + 12x - 160 = 0

8² + 12(8) - 160 = 0

64 + 96 - 160 = 0

160 - 160 = 0 (True).

For the dimensions, we have:

Width = x + 3 = 8 + 3 = 11 cm.

Height = x + 9 = 8 + 9 = 17 cm.

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I have no : idea

Step-by-step explanation: WHat grade is this for I might be able to help you.

Answer:

Step-by-step explanation:

u will have 1 niche of water in 2 hours

Answer:

A

Step-by-step explanation:

When distributing, you multiply the outside number to each number in the inside as well as looking at the operation inside the parenthesis. Hope this helps!

The answer to the given expression 2⁴· [(2²·2⁴)⁻³/2¹⁴] would be 2⁻²⁸ which is determined by the laws of the exponents.

The product rule is an exponent rule that states that when you multiply similar bases, the add exponents.

For example, (a²)·(a³) = a²⁺³ = a⁵

In the power rule, elevating one exponent to a second multiplies the exponents.

For example, (a²)³ = a²ˣ³ = a⁶

The given expression would be as

⇒ 2⁴· [(2²·2⁴)⁻³/2¹⁴]

As per the laws of the exponents, the solution would be as :

⇒ 2⁴· [(2²⁺⁴)⁻³/2¹⁴]

⇒ 2⁴· [(2⁶)⁻³/2¹⁴]

⇒ 2⁴· (2⁻¹⁸/2¹⁴)

⇒ 2⁴· (2⁻¹⁸⁻¹⁴)

⇒ 2⁴· (2⁻³²)

⇒ 2⁴⁻³²

⇒ 2⁻²⁸

Therefore, the answer would be 2⁻²⁸.

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Answer:

3

Step-by-step explanation:

Since the graphs aren't parallel due to not having the same slope we can assume they will intercept once

Answer:

x=1

Step-by-step explanation:

1. distribute through the parentheses

8x-6=2

2. Combine like terms

8x=8

3. Divide by 8

x=1

Hello!

Let's solve:

  [tex]\text{Copy down the equation}\\2(4x-3)=2\\\\\text{Multiply 2 into the equation in the parentheses}\\8x - 6 = 2\\\\\text{Add 6 to both sides of the equation}\\8x-6+6=2+6\\8x=8\\\\\text{Divide by 8 on both sides}\\\dfrac{8x}{8} =\dfrac{8}{8} \\\\x=1[/tex]

Answer: x = 1

Hope that helps!

The general form of terms of a Geometric Progression Formulas is a, ar, [tex]$$\mathrm{a} r^2[/tex], [tex]$$\mathrm{a} r^3$[/tex], and so on then the 7th term of the series 6, 12, 24, ........... is 384

Let the first term (a) be 6.

The given series is in geometric progression,

we know that, 7th term = a × [tex]$$r^{7-1}[/tex] = a[tex]$ r^6[/tex]= [tex]6 \times(2)^{6}[/tex] = 384

The general form of terms of a Geometric Progression Formulas is a, ar, [tex]$$\mathrm{a} r^2[/tex], [tex]$$\mathrm{a} r^3$[/tex], and so on.

Here, a is the first term and r is the common ratio.

The nth term of a Geometric Progression Formulas is [tex]$T_n=a r^{n-1}$[/tex]

Common ratio [tex]$=\mathrm{r}=T_n / T_{n-1}$[/tex]

Therefore, the correct answer is 384.

The complete question is:

Find the 7th term of the series 6,12,24,....?

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The interest rate for the loan is 20%.

The interest rate represents the percentage or the proportion of the interest over the total loan.

The interest is the finance charge for the credit extended by the pay lender.

The interest rate, R = Interest x 100/Principal x Time, where the simple interest equals principal x rate x time.

The total amount borrowed = $500

The total finance charge = $100

The period of the loan = 1 year

The interest rate

= $100 x 100/$500 x 1

= 20%

Thus, the pay lender is charging an interest rate of 20% per annum.

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What is the interest rate?

Answer: 0.01 more

Step-by-step explanation:

60% sure!

On Solving inequality  40 + 12.5 v ≥ 225, we get solution v ≥ 14.8. It means Autumn can earn movie ticket from 15 visits.

An inequality is a statement that compares two expressions using ≤, ≥, <, > .

We can solve an inequality by adding same number to both sides or by subtracting same number from both side. While adding or subtracting the sign of the inequality will not change.

When we multiply both sides of the inequality with a positive number then the sign of the inequality does not change, but when we multiply both sides by an negative number then the sign of inequality reverses.

Given that Autumn receives 40 points for signing up and 12.5 points for each visit to the theatre.

Let the number of visits to the theatre be v

Then points earned by v visits = v × 12.5 = 12.5 v

Total points earned = signing up points + points of v visits

⇒ Total points earned  = 40 + 12.5 v

For earning a free movie tickets the total points must be at least 225 or greater than or equal to 225

Then the inequality becomes:

40 + 12.5 v ≥ 225

Subtracting 40 from both sides

⇒ 12.5v ≥ 225-40

⇒12.5v ≥185

Multiplying both sides by 1/12.5

⇒ v ≥ 185/12.5

⇒ v ≥ 14.8

∴ The number of visits must be greater than or equal to 14.8 or nearest integer 15

∴After 15 visits, Autumn will earn a free  movie ticket

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Given:

Radius of circular swimming pool = 15ft

Radius of the path around the pool = 3ft

radius of outer edge of the pool = 15 + 3 = 18ft

To find the circumference of the outer edge of the path around the pool, use the formula below:

where,

r = 18 ft

pi = 3.14

Thus, we have:

Therefore, the circumference of the outer edge of the path around the pool is 113.04 ft

ANSWER:

113.04 ft

As shown in the reference graph attached hereby with the question statement, if the linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time "x" measured in seconds, then,

(A) During (2 ≤ x ≤ 5) seconds in the time domain, the water balloon's height remains the same.

(B) During (0 ≤ x ≤ 2) seconds, the height of the water balloon is increasing.

(C) During (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.

(D) From Part (C), it can be justified that 5 ≤ x ≤ 9.5 is the interval where the balloon's height is decreasing, and, (5 ≤ x ≤ 6) is the interval where the slope is the steepest.

As per the question statement and the reference graph attached alongside, the linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time "x" measured in seconds.

We  are required to determine the correct time domains for four different situations, by observing the plotted graph.

Part (A) is to determine the correct time domain where the water balloon's height remains the same.

From the graph, it is clear that, the height remains constant at (y = 70), parallel to the x-axis from the 2nd second to the 5th second. Hence, During (2 ≤ x ≤ 5) seconds in the time domain, the water balloon's height remains the same.

Part (B) is to determine the correct time domain where the height of the water balloon is increasing.

From the graph, it is clear that, the slope of the concerned graph rises only from [(y = 40) to (y = 70)], starring from the 0th second until the 2nd second. Hence, During (0 ≤ x ≤ 2) seconds in the time domain, , the height of the water balloon is increasing.

Part (C) is to determine the correct time domain where the height of the water balloon decreases the fastest.

From the graph, it is clear that, the graph decreases thrice, first from [(y = 70) to (y = 40)], starting at the 5th second uptil the 6th second, then from [(y = 40) to (y = 10)], starting at the 6th second uptil the 9th second and lastly, from [(y = 10) to (y = 0)], starting at the 9th second till the 9.5th second. Here, we can easily calculate that, the balloon dropped 30ft in 1 sec at the first instance, 30ft in 3 seconds at the second instance and, 10ft in 0.5 seconds.

Since, [(30/1) > (10/0.5) > (30/3)],

Or, [30 > 20 > 10],

Thus, During (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.

Part (D) is to determine the correct statement mentioned under it's options, with judgement based on Part (C).

Option (i) states that [(5 ≤ x ≤ 9.5) is the interval where the balloon's height is decreasing] which is true, as we can observe from the graph that the slope is decreasing during the time interval of 5 to 9.5th seconds, although at different rates at different intervals.

Option (ii) states that [(8 ≤ x ≤ 9.5) is the interval where the slope is the steepest] which means that, during this above said interval, the height of the balloon drops the fastest which is false, as we have already proved in part (C) that during (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.

Option (iii) states that, [(6 ≤ x ≤ 8) is the interval where the balloon's height decreases the most] which is false, as balloons height falls the farthest by 30fts in two separate intervals, between (5 ≤ x ≤ 6) seconds and (6 ≤ x ≤ 9) seconds.

Finally, Option (iv) states that [(5 ≤ x ≤ 6) is the interval where the slope is the steepest] which means that, during this above said interval, the height of the balloon drops the fastest which is true, as we have already proved in part (C) that during (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the maximum in the shortest time period.

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Option D is correct.

Extraneous information means irrelevant or unrelated to the problem or issue.

In this question, Samuel's Age is not a matter of concern and totally unrelated to the money he earns by mowing the lawn and cleaning the room

Answer:

[tex]M (\frac{x1+x2}{2},\frac{y1+y2}{2} )[/tex]

Step-by-step explanation:

You would require 1,570 flowers in space of every 6inch to surround the garden with 125feet radius.

First, we need to calculate the circumference of the circle. The formula for the circumference of the circle is:

C = 2πr

If we substitute 125ft for r and use 3.14 to approximate π

we get a circumference of:

C = 2 * 3.14 * 125

C = 6.28 *125

C = 785ft

We can now convert the circumference in feet to inches as follow;

As we know that 1ft = 12inches

∴ 785ft = 12(785) inches = 9,420 inches.

To find how many flowers we need we can divide the circumference in inches by the 6 inches between flowers giving:

=[tex] 9,420in\ X \ \frac{1\ flower}{6 in} [/tex]

=[tex] \frac{9,420}{6 } \ flower [/tex]

=1,570 flowers

Hence You would require 1,570 flowers in space of every 6inch to surround the garden with 125feet radius.

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When the radius of a cylinder is 6 ft. and it is increasing at the rate of 2 feet per minute, its volume will change at rate of 509.14 ft³/minute.

Given a cylinder with:

r = radius

h = height = 3/2 . r

The volume of the cylinder is:

V = πr².h

Substitute h = 3/2 . r,

V = πr².(3/2 r)

V = 3/2 . πr³

Take the derivative with respect to t:

dV/dt = 9/2 . πr²  . dr/dt

Substitute dr/dt = 2 ft./minute and r = 6 ft.,

dV/dt = 9/2 . π.6²  

dV/dt = 9/2 . π.6²  = 509.14 ft³/minute.

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Paloma's median practice time would be = 26.5

Median is defined as the middle of a set of data which will be selected after the data has been grouped in an ascending or descending order.

The list to track the number of minutes Paloma spent practicing piano in ascending order include the following:

18, 23, 24, 24, 25, |25, 28,| 28, 30, 32, 32, 35

The middle figures are 25 and 28 which should be added and divided into two.

That is;

25 + 28 = 53/2

= 26.5

Therefore, the median practice time for Paloma = 26.5

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The ratio of the blue fish in the small tank to red fish in the large tank is 10 to 69.

Ratio is the relationship between two quantities.

Let x : y = ratio of the blue fish in the small tank to red fish in the large tank

Hence, there are x blue fish in the small tank for every y red fish in the large tank.

If in each tank, the ratio of red fish to blue fish is 3 to 4, then in each tank, in terms of x and y, the ratio is:

small tank :

red : blue = 3 : 4 = (3/4)x : x

large tank :

red : blue = 3 : 4 = y : (4/3)y

If the ratio of fish in the large tank to fish in the small tank is 46 to 5, then

(y + (4/3)y) : ((3/4)x + x) = 46 : 5

Simplifying the proportion,

(y + (4/3)y) : ((3/4)x + x) = 46 : 5

(7/3)y : (7/4)x = 46 : 5

(161/2)x = (35/3)y

x/y = (35/3) / (161/2)

x/y = x : y = 10 : 69

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For a random sample of 130 mortgages with 20 delinquents on their current payment, the mean of the sampling distribution of the proportion of delinquent payments is not possible to say because population proportion is not known.

A random sample refers to a randomly selected subset of the population. In random sampling, each member of the population has an equal chance of selection, reducing the risk of selection bias. Random sampling ensures that the conclusion drawn from the sample should approximate the results obtained if entire population had been measured. The mean of the sampling distribution is the mean of the population from which results were sampled. As the population proportion (fraction of  the population with certain characteristic) is unknown, the mean cannot be determined.

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If you use excel solver for this analysis, the number of different variable cells should you use are 12

Option- C

The right answer is 12.

Given that,

There are four buses that transport children to the district's three main schools. You are aware of the price of transporting each student to each school.

Since there are four buses and three schools according to the supplied description, each bus has three school alternatives, thus 4*3=12, bearing in mind that there must be the least expensive route to transport all of the students to their schools.

There must therefore be 12 separate variable cells employed.

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Answer:

Step-by-step explanationFrom your home, the route to the store tat passes the beach is 2 miles shorter than the route to the store that passes the park. What is the length of each route.:

The value of a machine at the end of t years with a rate of depreciation, r is given by the function:

It is required to find the age of a machine that originally costs $13,500, but is now valued at $10,419 and has a rate of depreciation of 0.12.

To do this, substitute C=13500, V=10419, and r=0.12 into the function:

Solve the resulting equation for t:

Take the Logarithm of both sides:

Hence, the machine is about 2.03 years.

The machine is about 2.03 years.