+) Colin is playing a video game. He wins 25 points for each gold coin he finds. His goal is to win
more than 200 points. He wants to know how many gold coins he needs to find.
Solve the Inequality 25g > 200

In the collection, there are 11 nickels and 23 dimes. If each nickel is replaced with a quarter, the value of the collection becomes $5.05. So, C is correct. By writing them in the system of equations, we get the required value.

The given units are nickels, dimes, and quarters. Their conversion into dollars is as follows:

1 nickel = $0.05

1 dime = $0.10

1 quarter = $0.25

Given a collection of nickels and dimes is worth $2.85.

And there are 34 coins in the collection.

So, consider the number of nickel coins = n and the number of dime coins = d.

Then, the equation for the given collection is

n + d = 34...(1)

0.05n + 0.10d = 2.85...(2)

On simplifying (2), we get

5n + 10d = 2.85 × 100

⇒ 5n + 10d = 285

From (1), n = 34 - d, we get

5(34 - d) + 10d = 285

⇒ 170 - 5d + 10d = 285

⇒ 5d = 285 - 170 = 115

∴ d = 115/5 = 23

Thus, the number of dime coins is 23.

So, from (1), we get n + 23 = 34 ⇒ n = 34 - 23 = 11

∴ n = 11

Thus, the number of nickel coins is 11.

If each nickel coin in the collection is replaced with a quarter, then the value of the collection is

q + d = 34 and 0.25q + 0.10d = Y

Here q = 11; d = 23

So, we get

0.25(11) + 0.10(23) = Y

⇒ 2.75 + 2.3 = Y

⇒ 5.05 = Y

∴ Y = $5.05

The value of the new collection becomes $5.05.

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Answer:

1 9/50

Step-by-step explanation:

1.18 = 1 18/100

1 18/100 = 1 9/50

The fourth answer is correct.

Hope this helps!

Answer: EG = 80

Step-by-step explanation: A parallelogram is a quadrilateral with opposite sides parallel to each other.

The diagonals of a parallelogram bisect each other, which means, using the figure as example:

EJ = JG

So, to determine EG, first find w:

\(4w+4=2w+22\)

\(2w=18\)

w = 9

Substituting:

\(EJ=4w+4\)

\(EJ=4(9)+4\)

EJ = 40

Since each segment has the same measure:

EG = 2EJ

EG = 2(40)

EG = 80

The measure of EG is 80 units

Answer:

System of equations:

20x + 30y = 650

x + y = 25

Time underwater = 10 hours

Time at the surface = 15 hours

Step-by-step explanation:

Let x = time underwater at 20 km/h.

Let y = time on the surface at 30 km/h.

speed = distance/time

distance = speed * time

distance underwater: 20x

distance on the surface: 30y

total distance: 650

20x + 30y = 650

total time: x + y

total time: 25

x + y = 25

20x + 30y = 650

x + y = 25

20x + 30y = 650

-20x - 20y = -500

--------------------------------

          10y = 150

              y = 15

x + y = 25

x + 15 = 25

x = 10

the distance between two points is 3.5 cm

The length of the line segment bridging two locations in a plane is known as the distance between them. d=((x2 - x1)2 + (y2 - y1)2) is a common formula to calculate the distance between two points. This equation can be used to determine the separation between any two locations on an x-y plane or coordinate plane.

(1,-2) (1,1.5)

distance between two points is

= \(\sqrt{(1-1)^{2} + (1.5+2)^{2}\)

= 3.5 cm

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Answer: X=50

Step-by-step explanation:

Data: 4 less than half of a number(x) is 21

Step one, make an equation

(x/2)-4=21

The reason for this is that since we know that 21 is 4 less than half the number(x) we can assume that dividing x by 2 will get half of it and by subtracting 4, we can get 21 which why it equals 21. By having it in an equation, it makes it easier to solve.

Step two, Start isolating x by adding 4 on both sides

(x/2)-4+4=21+4=(x/2)=25

The reason for this is that we have to find what x is which is done by isolating it. So if you add 4, you get rid of the -4 which helps isolate x and what you do to one side, you do to the other so you add 4 to 21 as well

Step three, multiply by 2 on both sides

(x/2)x2=25x2=X=50

The reason for this is that /2 is next to x so to isolate you have to get rid of it by multiplying by 2 and since what you do to one side you do to the other, you multiply 25 by 2 to get 50.

Answer: X=50

I hope this helps!

Answer:

x = -1

Step-by-step explanation:

20x - 5(6x + 4) = 4x - 6

20x - 30x - 20 = 4x - 6

-10x - 20 = 4x - 6

-10x - 4x = -6 + 20

-14x = 14

x = -1

:According to the question:You are working with a population of crickets. Before the mating season you check to make sure that the population is in Hardy-Weinberg equilibrium, and you find that the population is in equilibrium.

During the mating season you observe that individuals in the population will only mate with others of the same genotype (for example Dd individuals will only mate with Dd individuals). There are only two alleles at this locus ( D is dominant, d is recessive), and you have determined the frequency of the D allele =0.6 in this population. Selection acts against homozygous dominant individuals and their survivorship per generation is 80%. After one generation the frequency of DD individuals will decrease in the population.

According to the Hardy-Weinberg equilibrium equation p² + 2pq + q² = 1, the frequency of D (p) and d (q) alleles are:p + q = 1Thus, the frequency of q is 0.4. Here are the calculations for the Hardy-Weinberg equilibrium:p² + 2pq + q² = 1(0.6)² + 2(0.6)(0.4) + (0.4)² = 1After simplifying, it becomes:0.36 + 0.48 + 0.16 = 1This means that the population is in Hardy-Weinberg equilibrium. This is confirmed as the frequencies of DD, Dd, and dd genotypes

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Answer:

8.4 ?

Step-by-step explanation:

sorry if im wrong

Answer:

1)$0.50

Divide $1 by 2 and you get $0.50.

It is not possible to find two numbers with two decimal places that round to 312 when rounded to one decimal place and have a total of 62.4.

To solve this problem systematically, we can break it down into smaller steps:

Let's assume the two numbers are x and y, both with two decimal places.

We can represent them as x = a.b and y = c.d, where a, b, c, and d are digits.

Rounding x and y to one decimal place gives us the following equations:

Round(x) = a.b ≈ 312

Round(y) = c.d ≈ 312

Since the total of the numbers is 62.4, we have the equation:

x + y = a.b + c.d

= 62.4

From Step 2, we know that both a.b and c.d are approximately equal to 312.

So, we can write:

a.b ≈ 312

c.d ≈ 312

Since a.b and c.d are rounded to one decimal place, we can rewrite them as:

a.b = 312 + p

c.d = 312 + q

p and q are the decimal parts that were rounded.

Substituting the new representations of a.b and c.d into the equation from Step 3, we get:

(312 + p) + (312 + q) = 62.4

Simplifying the equation gives us:

624 + (p + q) = 62.4

Solving for (p + q), we have:

p + q = 62.4 - 624

= -561.6

Since p and q are decimal parts, they must be between 0 and 1. -561.6 is outside this range, which means there are no values for p and q that satisfy the given conditions.

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Answer: A) (x + 3)(x - 3)(x + y)(x - y)

Step-by-step explanation:

The correct factorization of the polynomial -x^2y^2 + x^4 + 9y^2 - 9x^2 is:

(x + 3)(x - 3)(x + y)(x - y)

This factorization is obtained by grouping terms and factoring out common factors.

The power rules show that the value of x is equal to 1.

The main power rules are presented below.

For solving this question you should apply the power rules.

\(2^{5x}:2^x=\sqrt[5]{2^{20}}\)

First, you should apply the power rules for the first term. Thus, applying the rule - Division with the same base, you have:

\(2^{5x}:2^x=2^{4x}\)

After, you should convert the given root represented in the second term to power.

\(\sqrt[5]{2^{20}}=2^\frac{20}{5} \\ \\ \sqrt[5]{2^{20}}=2^4\)

Thus,

\(2^{4x}=2^4\)

From the previous equality, you can write:

4x=4

x=1

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Answer:

A = 45 cm²

Step-by-step explanation:

The area (A) of a trapezium is calculated as

A = \(\frac{1}{2}\) h( b₁ + b₂)

where h is the height and b₁, b₂ the parallel bases

Here h = 5, b₁ = 10 and b₂ = 8 , then

A = 0.5 × 5 × (10 + 8) = 0.5 × 5 × 18 = 45 cm²

Answer:

Step-by-step explanation: The answer is to be calculated with help of taking out averages of the households' Tvs.

In order to calculate the expected value we multiply each value of the random variable by its probability and then add the results.

(1 TV times 350/1000) + (2 TV times 500/1000) + (3 TV times 120/1000) + (4 TV times 30/1000) = 1.83.

on average, each household has 1.83 TVs.

As per the data given, a television channel conducted a study on the number of TVs per household in their service area. Out of 1000 households surveyed, 350 have one TV, 500 have two TVs, 120 have three TVs and 30 have four TVs. We need to determine the number of TVs each household has on average.To calculate the average number of TVs, we need to calculate the total number of TVs and divide that by the number of households.

Totals TVs = (Number of households with 1 TV × 1) + (Number of households with 2 TVs × 2) + (Number of households with 3 TVs × 3) + (Number of households with 4 TVs × 4)Total TVs

= (350 × 1) + (500 × 2) + (120 × 3) + (30 × 4)Total TVs = 350 + 1000 + 360 + 120

Total TVs = 1830

Average number of TVs per household = Total TVs / Number of households

Average number of TVs per household = 1830 / 1000

Average number of TVs per household = 1.83

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Answer:

-45

Step-by-step explanation:

The question is asking for the sum of the sequence. Therefore, there is no such thing as a "radians" answer.

When you evaluate the sum, you should get -45 as your answer. To find so, you simply plug in 1 as n and other numbers then add the result.

The sum telescopes. Consider the N-th partial sum of the series,

\(S_N=\displaystyle\sum_{n=1}^N\bigg(\tan^{-1}\sqrt n-\tan^{-1}\sqrt{n+1}\bigg)\)

\(S_N=\bigg(\tan^{-1}\sqrt1-\tan^{-1}\sqrt2\bigg)+\bigg(\tan^{-1}\sqrt2-\tan^{-1}\sqrt3\bigg)+\bigg(\tan^{-1}\sqrt3-\tan^{-1}\sqrt4\bigg)+\cdots+\bigg(\tan^{-1}\sqrt N-\tan^{-1}\sqrt{N+1}\bigg)\)

Notice how \(\tan^{-1}\sqrt2\) is added, then immediately subtracted. The same goes for \(\tan^{-1}\sqrt3\), then \(\tan^{-1}\sqrt4\), and so on, up to \(\tan^{-1}\sqrt N\). This leaves us with

\(S_N=\tan^{-1}\sqrt1-\tan^{-1}\sqrt{N+1}\)

The value of the given sum is obtained as \(N\to\infty\). We get

\(\displaystyle\sum_{n=1}^\infty\bigg(\tan^{-1}\sqrt n-\tan^{-1}\sqrt{n+1}\bigg)=\lim_{N\to\infty}S_N=\tan^{-1}1-\lim_{N\to\infty}\tan^{-1}\sqrt{N+1}\)

To compute the limit, recall that \(\tan^{-1}x\) has a range of \(\left(-\frac\pi2,\frac\pi2\right)\); in particular, \(\tan^{-1}x\to\frac\pi2\) as \(x\to\infty\). So we have

\(\displaystyle\sum_{n=1}^\infty\bigg(\tan^{-1}\sqrt n-\tan^{-1}\sqrt{n+1}\bigg)=\frac\pi4-\frac\pi2=\boxed{-\frac\pi4}\)

=============================================================

Explanation:

There are two approaches.

The slightly longer approach will have us take 6% of 420 to get 0.06*420 = 25.20

So 25.20 is the amount of tax you pay on top of the original $420. The total bill is 420+25.20 = 445.20 dollars

--------------

The shortcut is to multiply 420 by 1.06 to get 420*1.06 = 445.20

The 1.06 multiplier indicates an increase of 6%

We can think of it it as 1.06 = 1 + 0.06 = 100% + 6%

When estimating the cash flows on a given project, firms should include expenses from previous years, such as research & development costs. (True)

When estimating cash flows for a project, it is important to consider all relevant expenses, including those incurred in previous years. Research and development (R&D) costs are often incurred over an extended period before a project reaches the commercialization stage. Including these expenses in the cash flow estimation provides a more accurate picture of the project's financial performance. R&D costs can be significant and have a direct impact on the project's profitability.

By including these expenses, firms can evaluate the true costs and potential returns associated with the project. Additionally, including past expenses helps in assessing the project's historical performance and provides valuable insights for decision-making.

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Answer:

Step-by-step explanation:

To determine how long it will take for Louise to reach her goal of $30,000, we can use the formula for compound interest:

A = P * (1 + r/n)^(nt)

where:

A is the amount of money Louise will have after "t" years,

P is the initial investment of $20,000,

r is the annual interest rate of 4.28%,

n is the number of times the interest is compounded per year (12 times per year), and

t is the number of years.

We can rearrange this formula to solve for t:

t = (log(A/P)) / (log(1 + r/n))

Plugging in the values:

t = (log(30000/20000)) / (log(1 + (0.0428/12)))

t = 5.97 years

Rounding to the nearest tenth of a year, Louise will need to wait 6.0 years in order to reach her goal of $30,000.

The probability that Emme answers exactly 3 questions correctly is 0.1961.

Since each question has four answer choices and only one is correct, the probability of Emme randomly guessing the correct answer for each question is 1/4 = 0.25. Emme needs to answer exactly 3 out of the 9 questions correctly, so we use the binomial distribution with n = 9 and p = 0.25 to calculate the probability:

P(X = 3) = (9 choose 3) * (0.25)^3 * (0.75)^6

Using a calculator, we get:

P(X = 3) = 0.1961

Therefore, the probability that Emme answers exactly 3 questions correctly is 0.1961.

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Statistical hypothesis testing employs the null and alternate hypotheses.

The alternative hypothesis of a test expresses the prediction of an effect or relationship based on your study, while the null hypothesis of the test does not yet predict an effect or an association between the variables.

A statement that there is no relationship between two variables is called a null hypothesis. Another hypothesis is that the two variables are statistically correlated.

Alternative unilateral (directional) or the bilateral (non-directional) hypotheses are also possible. Simple, complex, true, and false are the four main categories of null hypotheses. If the p-value is greater than the statistical significance level, null hypothesis is preferred.

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Answer:

These kind of questions are called simply.

According to simply, there's a rule of solving which is BODMAS.

BODMAS stand for bracket of Divide, Multiple, Add, Subtraction.

> (9)2-4

> 18-4

> 16

• (6+3)2-4 = 16

2. 23+(14-4)÷2

> 23+10÷2

> 23+5

> 28

• 23+(14-4)÷2 = 28

Step-by-step explanation:

Hope it helps you

Answer:

  2(n +7)

Step-by-step explanation:

Each part of the English description can be written using math symbols.

__

A sum is formed when two or more terms are added together. Here, we are told the sum is the result of adding "a number" and 7. The number can be represented by "n", and the addition is represented by a plus sign (+). The corresponding math expression is ...

  n + 7 . . . . . . "the sum of a number and 7"

The English description tells us this sum is multiplied by two. (That is the meaning of "two times".) In algebra, we can use several different symbols to represent "times", including a centered dot (·), a centered x (×), or no symbol at all. In this last case, the factors of the product are simply written next to each other.

We want to treat the sum as a unit, so for that purpose, we wrap it in parentheses.

  2×(n +7) . . . . . . . two times the sum of a number and 7

More compactly, ...

  2(n +7) . . . . . . . two times the sum of a number and 7

Answer:

40 people

Step-by-step explanation:

First thing, you have to find the area below the 40 - 55 line in the histogram. The area can be find using the area of a rectangle: side × side

Doing this you'll find an area of 60.

After that, find the total area of the histogram in the same way: separate it in rectangles and use the formula for the area of a rectangle, and after you'll find a total area of 100

Now you have to do a rule of three:

We know from the question statement that the amount of people with 40 - 55 years old is 25, and that area correspond to 60, so:

60 ------- 24

100 ------- x

60•x = 24•100

60x = 2400

x = 2400/60

x = 40

Therefore, it will take approximately 1415.7 weeks for all of the chemical to evaporate.

To calculate the volume of a cone, we can use the formula:

\(Volume = (1/3) * π * r^2 * h\)

Given that the height (h) of the cone is 240 inches and the radius (r) is 150 inches, we can substitute these values into the formula:

\(Volume = (1/3) * 3.14 * 150^2 * 240\)

Simplifying the equation:

Volume = 3.14 * 22500 * 240

Volume ≈ 16988400 cubic inches

Now, we know that the liquid chemical evaporates at a rate of 12,000 cubic inches per week. To find out how many weeks it will take for all the chemical to evaporate, we can divide the total volume of the chemical by the evaporation rate:

Number of weeks = Volume / Evaporation rate

Number of weeks = 16988400 / 12000

Number of weeks ≈ 1415.7 weeks

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Answer: 17% increase

Step-by-step explanation:

Percentage increase/decrease = (final value - initial value) / initial value x 100
% change = (1,544,400 - 1,320,000) / 1,320,000 x 100
% change = 224,400 / 1,320,000 x 100
% change = 0.17 x 100
% change = 17% increase

The value of the upper boundary rounded off to the nearest decimal is 33.8.(D)

Here's how to get the solution:Given:Mean length = 31.5 cm

Standard deviation = 5.8 cm

The level of confidence = 95%

The formula for calculating the upper boundary for a 95% confidence interval is: Upper boundary = mean length + (z-score × standard deviation / √sample size)

Now, we need to find the z-score for a 95% confidence interval. The z-score can be found using the standard normal distribution table. For a 95% confidence interval, the z-score is 1.96.

Upper boundary = 31.5 + (1.96 × 5.8 / √26)

Upper boundary = 31.5 + 2.388

Upper boundary = 33.888 ≈ 33.8Therefore, the Upper Boundary for a 95% confidence interval for mean length of corn ears is 33.8 cm. The formula for the upper boundary for the 95% confidence interval is given byUpper boundary = mean length + (z-score × standard deviation / √sample size)

z-score for the 95% confidence interval is 1.96, calculated using the standard normal distribution table.

Therefore, the upper boundary is calculated as follows:Upper boundary = 31.5 + (1.96 × 5.8 / √26) = 33.888. (D)

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Answer:

ŷ = -0.18363X + 19.71681

-0.9685

Step-by-step explanation:

Given the data:

Mileage, x: 22 14 18 30 8 24

Price, y: 16 17 17 14 18 15

Using the online regression calculator :

The regression equation obtained is :

ŷ = -0.18363X + 19.71681

Where ;

y = predicted variable

- 0.18363 = slope or gradient

X = predictor variable

19.71681 = intercept

The correlation Coefficient R = -0.9685

This signifies a strong negative relationship between the x and y variable.

The line of best fit has an equation of:

y = -0.1875x + 19.625

A linear equation is given by:

y = mx + b;

where y, x are variables, m is the slope of the line and b is the y intercept.

Let x represent the mileages (in thousands of miles) and y the selling prices(in thousands of dollars) of used automobiles.

Plotting the points using geogebra graphing calculator, the line of best fit has an equation of:

y = -0.1875x + 19.625

Therefore the slope is -0.1875 and the y intercept is 19.625

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Answer:

I think its D bc the scale factor is 1:5 so 12:60 therefore the answer I think is D

I hopeit helps but if its wrong im very sorry :(

Step-by-step explanation:

The measure of the complement of the angle is A) 54.

Given:

The ratio of the measure of the supplement of an angle to that of a complement of the angle is 8:3.

Let x be the angle.

supplement of the angle of x is = 180-x

complement of the angle of x is = 90 -x

180 - x / 90 -x = 8/3

3(180-x) = 8(90-x)

3*180 - 3*x = 8*90 - 8*x

540 - 3x = 720 - 8x

-3x+8x = 720 - 540

5x = 180

divide by 5 on both sides

x = 180/5

x = 36

Complement of the angle = 90 - 36

= 54

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Answer:

20 ft squared

Step-by-step explanation:

The base is the bottom and I multiply 5ft and 4ft and you get 20ft squared