Details Natasha buys a bag of cookies that contains 7 chocolate chip cookies, 9 peanut butter cookies, 5 sugar cookies and 9 oatmeal cookies. What is the probability that Natasha randomly selects a chocolate chip cookie from the bag, eats it, then randomly selects a sugar cookie? Express you answer as a reduced fraction.

The number that is 10% more than a number is 132 is 120.

let

the number = x

10% of the number will be as follows

10%more than a number is 132 will be express as follows

Therefore,

1.1x = 132

x = 132 /1.1

x = 120

The number is 120

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To solve this problem, we need to use the formula for the nth term of an arithmetic sequence:
an = a1 + (n-1)d  where a1 is the first term, d is the common difference, and n is the term number.  This means that the first term is 118, the common difference is -6, and each subsequent term is found by subtracting 6 from the previous term.

We know that the 4th term is 100, so we can substitute this into the formula:
a4 = a1 + (4-1)d
100 = a1 + 3d

Similarly, we know that the 13th term is 46:
a13 = a1 + (13-1)d
46 = a1 + 12d
Now we have two equations with two unknowns (a1 and d), which we can solve by elimination or substitution. I will use elimination:
100 = a1 + 3d
-46 = -a1 - 12d
------
54 = -9d
d = -6
Now we can substitute d back into one of the equations to solve for a1:
100 = a1 + 3(-6)
a1 = 118
Therefore, the expression for the general term of the arithmetic sequence is:
an = 118 - 6(n-1) or  an = 124 - 6n

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The two equations can you use to find the adult and child admission fees for a puppet show are 45a + 30c = 315 and 50a + 40c = 370

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, two equations can you use to find the adult and child admission fees for a puppet show

Let a represent the fee for adults

Let c represent the fee for children.

On day 1 number of adults = 45

So, fees of 45 adults = 45a

On day 1 number of children= 30

So, fees of 30 children = 30c

Total collection on day 1 = 315

Therefore, equation is 45a + 30c = 315

On day 2 number of adults = 50

So, fees of 50 adults = 50a

On day 2 number of children = 40

So, fees of 40 children = 40c

Total collection on day 2 = 370

So, equation = 50a + 40c = 370

Hence, The two equations can you use to find the adult and child admission fees for a puppet show are 45a + 30c = 315 and 50a + 40c = 370

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Answer:

-5 2

Step-by-step explanation:

Answer:

3/5

Step-by-step explanation:

The line is going up so it is positive and it is over 3 and up 5 so it would be 3/5.

Hope this helps! Sry if i get it wrong!

The differential equation for the radioactive substance, given its disintegration rate and the amount left, is derived. The solution is then used to answer specific questions.

The differential equation for the amount of a radioactive substance, x, in terms of time, t, and the disintegration constant, k, can be written as dx/dt = -kx, where the negative sign indicates the decay.

To show that k = ln(2)/T, we use the fact that the half-life, T, is the time it takes for x to decrease to half its initial value. Solving the differential equation, we get x(t) = x₀e^(-kt), where x₀ is the initial amount. Substituting x(t) = x₀/2 and t = T, we have x₀/2 = x₀e^(-kT), which simplifies to 1/2 = e^(-kT). Taking the natural logarithm of both sides, we find ln(1/2) = -kT, and rearranging gives k = ln(2)/T.

(a) For the half-life of 8 days, T = 8. Substituting this value into k = ln(2)/T, we find k = ln(2)/8. Using the formula x(t) = x₀e^(-kt), we can calculate x(80) as a percentage of x₀.

(b) To find the minimum storing period, we need to find the time when x(t) is below 10^(-5) curie. Using the formula x(t) = x₀e^(-kt), we can solve for t when x(t) = 10^(-5). This will give us the minimum storing period before disposal.

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Answer:

√89 km

Step-by-step explanation:

By applying Pythagoras theorem,

x² = 25+64

=89

Think about it on a graph. Plot down your cardinal points on the X and y axis, and plot the path the yacht would take. It would end up forming a triangle, in which case the length you travel is the hypotenuse.

The pieces of cloth are beyond the standard at 0.05 level of significance.

We can use a one-sample t-test to determine if the mean length of the 35 pieces of cloth is significantly different from the standard length of 3.25 meters.

The null hypothesis is that the mean length of the cloth pieces is equal to the standard length:

H0: μ = 3.25

The alternative hypothesis is that the mean length of the cloth pieces is greater than the standard length:

Ha: μ > 3.25

We can calculate the test statistic as:

t = (x - μ) / (s / √n)

where x is the sample mean length, μ is the population mean length (3.25 meters), s is the sample standard deviation (0.52 meters), and n is the sample size (35).

Plugging in the values, we get:

t = (3.52 - 3.25) / (0.52 / √35) = 3.81

Using a t-table with 34 degrees of freedom (n-1), and a significance level of 0.05 (one-tailed test), the critical t-value is 1.690.

Since our calculated t-value (3.81) is greater than the critical t-value (1.690), we reject the null hypothesis and conclude that the mean length of the 35 pieces of cloth is significantly greater than the standard length at the 0.05 level of significance.

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Answer:

We would start by breaking down this problem. We want to know how much paint Shane used, so Nora isn't even relevant, we can just throw her out of the equation. Now we know that 2 parts of yellow paint was 24 ounces. We need to determine how much paint is in 1 part:

24/2 = 12

there is 12 ounces of paint in 1 part of paint.

Now what we need to figure out is how much blue paint was used. We know Shane used 3 parts of blue paint, and we know that 1 part = 12 ounces:

3*12 = 36

Shane used 36 ounces of blue paint

Step-by-step explanation:

Hope this helps:)

Answer:

.06 or six hundredths

Step-by-step explanation:

Answer:

Hundredth place

Answer:

\(n = -3\)

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

-5-2n=8n+25

-5-25=8n+2n

-30=10n

-30/10=n

-3=n

Step-by-step explanation:

therefore n=-3

Hope this helps u!!

The cost of this lot is $307,200.

To find the cost of this rural lot, we first need to calculate its area, and then multiply the area by the cost per square foot. Let's follow these steps:

1. Since the lot has an irregular shape, divide it into two triangles. The first triangle has a base of 500 feet (east/west along its northern boundary) and a height of 200 feet (eastern boundary). The second triangle has a base of 100 feet (600 - 500 feet along the southern boundary) and a height of 24 feet (224 - 200 feet along the western boundary).

2. Calculate the area of each triangle:
Triangle 1: A1 = (base x height) / 2 = (500 x 200) / 2 = 50,000 sq. ft.
Triangle 2: A2 = (base x height) / 2 = (100 x 24) / 2 = 1,200 sq. ft.

3. Add the areas of the two triangles to find the total area of the lot:
A_total = A1 + A2 = 50,000 + 1,200 = 51,200 sq. ft.

4. Finally, multiply the total area by the cost per square foot to find the cost of the lot:
Cost = A_total x $6 = 51,200 x $6 = $307,200.

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Answer:

50 ≤ x ≤ 58

Step-by-step explanation:

Cause Im smart

Answer:

50 ≤ x ≤ 58

Step-by-step explanation:

hope this helps ;

)

We have an expression:

It has 2 terms with two unknowns: r and s.

Their coefficients are 11 for r and 7 for s.

Answer:

11r+7s is the expression.

11r and 7s are the terms.

11 and 7 are the coefficients.

r and s are the variables or unknowns.

Answer:

Step-by-step explanation:

step one:

Given the sample space, which is the value of individual number of colored balls in the bin

Red balls=5

Yellow balls=3 and

Green balls= 4

And the sample size is the sum of all the colored balls in the bin

The sample size S= {5+3+4}= 12

step two:

The probability of choosing a red ball in an event can be expressed as, the total number of the red balls over the total number of balls in the bin

P(r)= 5/12

Hence the probability of selecting a red ball in one event 5/12

Answer:

$10.55

Step-by-step explanation:

Total miles traveled = 12miles

If taxi A charges $0.3 for every 1/9 mile, then for 12 Miles, he will charge;

12×0.3/(1/9)

= 12×0.3×9

= 108×0.3

= $32.4

Amount charged initially = $3.00

Total charge by Taxi A = $32.4+$3.00

Total charge by Taxi A = $35.4

If taxi B charges $0.2 for every 1/9 mile, then for 12 Miles, he will charge;

12×0.2/(1/9)

= 12×0.2×9

= 108×0.2

= $21.6

Amount charged initially = $3.25

Total charge by Taxi B = $21.6+$3.25

Total charge by Taxi B = $24.85

Total money saved by Kelly = Amount charged by Taxi A - Amount charged by Taxi B

Total money saved by Kelly = $35.4-$24.85

= $10.55

Hence Kelly saved $10.55 using taxi B

The Taylor series expansion of \(\( f(x) = xe^{2x} \)\) centered at a = 0 is \(\(\sum_{n=0}^{\infty} \frac{2n!}{2^n} x^{n+1}\)\).

The Taylor series expansion of \(\( f(x) = xe^{2x} \)\)  centered at a = 0 is given by:

\(\[\sum_{n=0}^{\infty} \frac{n!}{2^n} x^{n+1}\]\)

Simplifying further:

\(\[\sum_{n=0}^{\infty} \frac{n!}{2^n} x^{n+1} + \sum_{n=0}^{\infty} \frac{n!}{2^n} x^{n+1}\]\)

\(\[\sum_{n=0}^{\infty} \left( \frac{n!}{2^n} + \frac{n!}{2^n} \right) x^{n+1}\]\)

\(\[\sum_{n=0}^{\infty} \frac{2n!}{2^n} x^{n+1}\]\)

This is the Taylor series expansion of \(\( f(x) = xe^{2x} \)\) centered at a = 0.

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Complete Question:

Find the Taylor series expansion of \(\( f(x) = xe^{2x} \)\) centered at a = 0:

\(\[\sum_{n=0}^{\infty} \frac{n!}{2^n} x^{n+1} + \sum_{n=0}^{\infty} \frac{n!}{2^n} x^{n+1}\]\)

Answer:

1/2 is larger

Step-by-step explanation:

1/2 is larger because the smaller the denominator the larger the fraction.

Answer:

3/10 liters more

Step-by-step explanation:

8/10 - 5/10 = 3/10

Step-by-step explanation:

\( \frac{60}{100} \times x = 21 \\ x = \frac{21}{ \frac{60}{100} } = 35 \\ \)

Answer:

(3s-2)°+(4s-6)°=90

3s-2+4s-6=90

7s-8=90

7s=90+8

7s=98

Dividing both sides by 7

S=98/7

S=14

Answer:

A.  See attachment 1.

B.  See attachment 2.

C.  As the number of years of experience increases, so does the hourly wage.

Step-by-step explanation:

When creating a scatter plot with bivariate data:

For the given data, the hourly wage is dependent on the number of years of experience.  Therefore:

Draw the scatter plot

(See attachment 1).

Draw a line of best fit on the scatter plot (see attachment 2).

Correlation measures how closely two variables are linked.

If two variables are correlated, you can draw a line of best fit on the scatter plot.

The line of best fit has a positive slope and is close to the data points.

Therefore, the scatter plot shows a strong positive correlation between the years of experience and the hourly wage.  

This suggests that as the number of years of experience increases, so does the hourly wage.

Answer:

cost for 40 songs 26.66 cost for s songs = 1.50

Step-by-step explanation:

Hey there! I'll try to provide you with my best answer.

Answer: ∠a is 20° , ∠b is 130° and ∠c is 50°

If you see more precisely then ΔABC is a complete triangle. And we know that a triangle is 180°. So in respect to ΔABC, we know ∠A and ∠C. So ∠B remains.

∠A is 60° + 30° = 90°

∠C is 70°

∠B is 90° + 70° + ∠B = 180°

∠B + 160° = 180°

∠B = 180° - 160°

∠B = 20°

Now we know that angle a (the corner angle) is 20°. Remaining is angle b and angle c. The ones we actually have to find in the question given.

In one of the small triangle which the,"b" is.

We know ∠a is 20°  and the other side is 30°. So the same formula applies again.

∠a + 30° + ∠b = 180°

20° + 30° + ∠b = 180°

∠b + 50° = 180°

∠b = 180° - 50°

∠b = 130°

Now ∠c is remaining. Well all the angles are given again so.. same!

∠c + 60° + 70° = 180°

∠c + 130° = 180°

∠c  = 180° - 130°

∠c  = 50°

There is another easier way to find ∠c. Line B and C is a straight line so a straight line is also 180°. We know ∠b is 130° so instead of subtracting and switching so much, we can directly subtract it from 180 because they are on a straight line.

∠b + ∠c = 180°

130° + ∠c = 180°

∠c = 180° - 130°

∠c = 50°

The answer is same at the end. Even though this is easier cause we can mentally subtract it instead of going to the triangle formula.

Note: When i show angles with capital letters and small letters, there is a difference. ∠B and ∠b is not the same thing when I wrote it. So please do not misunderstand it. The capital and small letters are clearly shown in the image you have shown.

And sorry for making it so long. I just hope you understood it clearly!! ^^

The simple interest will be $36 and the amount will be $236

Given, the principal = $200

Rate of interest = 6%

Time = 3 years

Now, on using the formula of Simple Interest,

SI = (P×R×T)/100

SI = (200×6×3)/100

SI = $36

Now, the amount will be

Amount = 200 + 36

Amount = $236

Hence, the simple interest will be $36 and the amount will be $236

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The hospital must cut the number of overtime hours by approximately 2.91% in order to stay within budget.

To determine the required percentage reduction in overtime hours, we need to consider the impact of the nurses' hourly rate increase and the limited budget increase for overtime wages.

Let's assume the current budget for nurses' overtime wages is denoted by B, and the total number of overtime hours worked is denoted by H. The current overtime rate per hour is R.

With the 5% hourly rate increase, the new overtime rate per hour becomes 1.05R. Considering the limited budget increase of 3%, the new budget for overtime wages is 1.03B.

To calculate the required percentage reduction in overtime hours, we can set up the following equation:

(1.05R) * (1 - x) * H = 1.03B

where x represents the required percentage reduction in overtime hours.

Simplifying the equation, we have:

(1 - x) * H = (1.03B) / (1.05R)

Now, let's solve for x:

1 - x = (1.03B) / (1.05R * H)

x = 1 - [(1.03B) / (1.05R * H)]

Here, we can see that the required percentage reduction in overtime hours, represented by x, depends on the values of B, R, and H.

It's important to note that without knowing the specific values of B, R, and H, we cannot calculate the exact percentage reduction. However, based on the provided information, we can determine the maximum percentage reduction that the hospital must make to stay within budget.

By assuming that B, R, and H are constant, we can use the given constraints to calculate an approximate percentage reduction. Based on the constraints of a 3% budget increase and a 5% hourly rate increase, the hospital would need to reduce the number of overtime hours by approximately 2.91% to maintain a balanced budget.

Please keep in mind that this approximation may vary depending on the specific values of B, R, and H.

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The length of the height of the radio tower using property of right triangles is 22.58 m.

Given that,

Angle of elevation from the surveyor to the top of building = 38°

Angle of elevation from the surveyor to the top of radio tower = 50°

Distance from surveyor to the base of the building = 55 m

We get two right triangles here.

Let the total height of building and radio tower = h

Let the height of the building = x

Height of the radio tower = h - x.

Now,

tan (50°) = h / 55

h = 55 × tan (50°)

  = 65.546 m

Similarly,

tan (38°) = x/ 55

x = 55 × tan (38°)

  = 42.971 m

Height of the radio tower = h - x

                                          = 22.58 m

Hence the correct option is A.

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a) The value of ∂f/∂x using chain rule = (1/2 - √3)

b) The value of ∂f/∂y = (√3 + 1/2)

We are given that g (r, θ) = f (r cos θ, r sin θ) and that (∂g/∂r) (2, π / 3) = 1 and ∂g/∂θ (2, π / 3) = 2.

Using the chain rule, we have:

∂g/∂r = ∂f/∂x * cos θ + ∂f/∂y * sin θ

∂g/∂θ = -∂f/∂x * r * sin θ + ∂f/∂y * r * cos θ

At (r, θ) = (2, π / 3), we have:

1 = ∂g/∂r = ∂f/∂x * cos π / 3 + ∂f/∂y * sin π / 3

2 = ∂g/∂θ = -∂f/∂x * 2 * sin π / 3 + ∂f/∂y * 2 * cos π / 3

Solving for ∂f/∂x and ∂f/∂y, we get:

∂f/∂x = (cos π / 3 - 2 sqrt(3) sin π / 3)

∂f/∂y = (2 cos π / 3 + sin π / 3)

Therefore, at the point (1, √3), we have:

∂f/∂x = (1/2 - √3)

∂f/∂y = (√3 + 1/2)

Thus, using the chain rule and given partial derivatives, we were able to calculate the partial derivatives of f with respect to x and y at the given point.

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If Joao scored a goal in 60% of the soccer games last season, then we can expect him to score a goal in about 60% of the games he plays this season.

So, if Joao plays in 10 games this season, we can estimate that he will score a goal in approximately 60% of those games.

To calculate the actual number of games he is expected to score a goal in, we can use the formula:

Expected number of goals = Total number of games x Probability of scoring a goal

Plugging in the numbers, we get:

Expected number of goals = 10 x 0.6 = 6

Therefore, based on the experimental probability from last season, we can estimate that Joao will score a goal in around 6 games out of the 10 he plays this season.

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