Jenny is organising a barbecue. There are 30 bread rolls in a pack. There are 16 sausages in a pack. She needs exactly the same number of bread rolls as sausages. What is the smallest number of each pack she must buy?

2. Tom, Sam and Matt are doing a show by counting drum beats .They decided to donate the collecting money for the poor children for their studies. Tom hits a snare drum every 2 beats. Sam hits a kettle drum every 5 beats. Matt hits a bass drum every 8 beats. Tom, Sam and Matt start by hitting their drums at the same time. How many beats is it before Tom, Sam and Matt next hit their drums at the same time? What value you can see in their act

Answer:

81.66 repeating

Step-by-step explanation:

86+72+65+82+91+94=490

490÷6=81.66 repeating

EDIT: this answer is false

Answer:

(6,—6)

Step-by-step explanation:

Draw the points on a table. The answer will be (6,—6)

Are feeling overloaded with too much information and the gender of the individual independent:  No, because P(male overloaded with too much information) ≠ P(male). The correct option is C.

The gender of an individual does not determine whether or not they are overloaded with information. Overload is dependent on various factors such as the amount and complexity of the information being received, an individual's ability to process information, and their environment.

Therefore, the probability of an individual being overloaded with information is not directly related to their gender, and thus P(male overloaded with too much information) is not equal to P(male). The correct option is C.

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Complete question:

Are feeling overloaded with too much information and the gender of the individual independent? Explain.  

A. Yes, because P(maleloverloaded with too much information) #P(male).

B. No, because P(maleloverloaded with too much information) = P(male).  

C. No, because P(maleloverloaded with too much information) # P(male).

D. Yes, because P(maleloverloaded with too much information) = P(male).

Answer:

8\(\sqrt{13}\)

Step-by-step explanation:

Using the pythagorean theorem (Assuming the house's walls are perpindicular to the ground):

a^2+b^2=c^2

we can find that 3=a and 29=c

3^2+b^2=29^2

9+b^2=841

b^2=832

b=\(\sqrt{832}\)

b=\(\sqrt{64*13}\)

b=8\(\sqrt{13}\)

That is the height that the ladder will reach

A one-sample t-test is the appropriate test to compare the average satisfaction rating of Riverside community hospital to the population average.

To determine what test should be used in this scenario, we need to consider the nature of the data and the objective of the analysis.

Based on the given information, we have two sets of data: the average satisfaction rating for all hospitals (population) and the average satisfaction rating for Riverside community hospital (sample).

If our objective is to compare the average satisfaction rating of Riverside community hospital to the population average, we can use a hypothesis test. Specifically, we can perform a one-sample t-test.

The one-sample t-test allows us to compare a sample mean to a known population mean when the population standard deviation is unknown. In this case, we know the population mean (7.8) and the population standard deviation (0.5), which makes the one-sample t-test appropriate.

By comparing the average satisfaction rating of Riverside community hospital (8.1) to the population mean (7.8), along with the sample standard deviation (1.5) and the known population standard deviation (0.5), we can conduct a one-sample t-test to determine if the difference is statistically significant.

Therefore, a one-sample t-test is the appropriate test to compare the average satisfaction rating of Riverside community hospital to the population average.

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The p-value = 0.078, Since p-value = 0.0708 < 0.10  significance level, we reject H0.

i) Claim: The population proportion is now greater than 35%

ii) Null hypothesis: H0: p = 0.35

iii) Alternative hypothesis: Ha: p > 0.35

iv) Test statistic:

\(z = \frac{p-p}{\sqrt{\frac{p*(1-p)}{n} } }\)

Where

\(p = \frac{x}{n}= \frac{42}{100} = 0.42\)

Thus

\(z = \frac{0.42-0.35}{\sqrt{\frac{0.35*0.65)}{100} } }\\\\z = \frac{0.07}{\sqrt{\frac{0.35*0.65)}{100} } }\\\\z = \frac{0.07}{\sqrt{0.002275} } }\\\\z = \frac{0.07}{0.047697}\)

Z = 1.47

v) p-value:

p-value = P( Z > z test statistic value)

p-value = P( Z > 1.47 )

p-value = 1 -  P( Z < 1.47 )

Look in z table for  z = 1.4 and 0.07 and find area.

From z table , we get:

P( Z < 1.47)=  0.9292

Thus

p-value = 1 -  P( Z < 1.47 )

p-value = 1 - 0.9292

p-value =  0.0708

Thus reject H0 if p-value < 0.10 significance level, otherwise we fail to reject H0.

vi) Decision:

Since p-value = 0.0708 < 0.10  significance level, we reject H0.

vii) Interpretation:

Since we have rejected null hypothesis H0 at .10 significance level, there is sufficient evidence to support the claim that The population proportion is now greater than 35% that is: the population proportion of students at UCLA who have traveled abroad has increased after the implementation of the study abroad program.

Hence the answer is the p-value = 0.078, Since p-value = 0.0708 < 0.10  significance level, we reject H0.

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Answer:

He will have to shovel at least 11 driveways

Step-by-step explanation:

He gets 7$ for each drive way, so if he shovels 10, 10 x 7= 70$, But he still needs 5 more dollars, so he will need to shovel an extra driveway so that he can get 75$ he will have 2$ extra

Answer:

24

Step-by-step explanation:

dont exaclty have an explanations - its just the calculations

The percent increase in the cost of the uniform from last year to this year is 25%.

To find the percent increase in the cost of the uniform from last year to this year, we need to calculate the difference between the two prices, divide it by the original price, and then multiply by 100 to express the result as a percentage.

The difference between this year's price and last year's price is:

$65 - $52 = $13

The original price (last year's price) is $52.

So the percent increase in the cost of the uniform is:

percent increase = (difference / original price) x 100

percent increase = ($13 / $52) x 100

percent increase = 0.25 x 100

percent increase = 25%

Therefore, the percent increase in the cost of the uniform from last year to this year is 25%.

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The complete line ratio AB : BC : CD is 6 : 2 : 5

From the question, we have the following parameters that can be used in our computation:

AB : BD = 2 : 3

AC : CD = 2 : 1

Rewrite them as

x ⇒ AB : BD = 2 : 3

y ⇒ AC : CD = 2 : 1

These ratios can be represented using the following equation

2x + 3x = 2y + y

Evaluate the sum

5x = 3y

Simplify

x = 3/5y

So, we have

AB : BC : CD

This gives

AB : CD - BD : CD

So, we have

2x : y - x : y

Solving further, we have

2 * 3/5y : y - 3/5y : y

Evaluate

6/5y : 2/5y : y

Multiply through by 5

6y : 2y : 5y

Divide through by y

6 : 2 : 5

Hence, the ratio is 6 : 2 : 5

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Given statement 'A scalar c is an eigenvalue of an n×n matrix a if the equation (a − ci) x = 0 has a non-trivial solution x' is True.

In this question, we have been given a statement 'a scalar c is an eigenvalue of an n×n matrix a if the equation (a − ci) x = 0 has a non-trivial solution x. '

We need to decide whether the given statement is true or not.

By the definition of an eigenvalue  of an n×n matrix A, a scalar c is an eigenvalue of an n×n matrix A if the equation (A − cI)x = 0 has a non-trivial solution x.

Thus given statement is True.

Therefore, a scalar c is an eigenvalue of an n×n matrix a if the equation (a − ci) x = 0 has a non-trivial solution x is True.

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Marissa's shape is classified as a scalene and obtuse triangle, considering it's concepts presented in this problem.

The triangle has three sides of unequal length, as the opposite angle measures are different, hence it is classified as an scalene triangle.

(it would be equilateral if all had the same length, and isosceles if two sides have the same length).

The triangle has one angle larger than 90º, hence it is classified as an obtuse triangle.

(acute with no angles of 90º or greater, right with one angle of exactly 90º).

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Answer:

its not 80k/3000 someone answer

Step-by-step explanation:

The formula for Integration of UV:

f the two functions are of the type u,v then the formula for the Integration of u and v may be written as follows: ∫ uv dx = u ∫ v dx – ∫ (u' ∫ v dx) dx.

Integration of Trigonometric functions involves basic simplification techniques. These techniques use different trigonometric identities which can be written in an alternative form that are more amenable to integration.

Identify the integral of the form ∫u.vdx. Choose u(x) using the LIATE rule and differentiate it. Choose v(x) and Integrate dv. Then plug in all the values obtained so far, in the formula ∫u.v = u. ∫v.dx- ∫( ∫v.dx.u'). dx and evaluate the integral.

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The conversion of 0.0088 gr/cm³ is 8.8 kg/m³

The full question is in the attachment. To change the unit of a quantity to another unit is to use the rules that apply to each unit. Rules on mass units

Rules on volume units

To convert units from gr/cm³ to kg/m³

1 gr/cm³ = 1 × 1 gr ÷ 1 cm³

1 gr/cm³ = 1 × 0.001 kg ÷ 0.000001 m³

1 gr/cm³ = 1 × 0.001 × 1,000,000 kg/m³

1 gr/cm³ = 1 × 1,000 kg/m³

1 gr/cm³ = 1,000 kg/m³

0.0088 gr/cm³ = 0.0088 × 1,000 kg/m³

0.0088 gr/cm³ = 8.8 kg/m³

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Answer:

$2,600

Step-by-step explanation:

use the I = Prt simple interest formula

The only integers that satisfy both inequalities are a = -2 and b = -1. So, the equation is y = x³ - 2x² - x + 6.

What is inequality?

Inequality is a mathematical statement that compares two values or expressions, indicating that they are not equal. It uses symbols such as < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), or ≠ (not equal to) to show the relationship between the values or expressions.

To find the values of a and b, we need to use the information given in the problem to form equations involving a and b.

First, note that the function y is decreasing for values of x between 2 and 9 if and only if its derivative y' is negative for those values. So, we need to find y' and set it to be less than zero for x between 2 and 9.

y' = 3x² + 2ax + b

For y' to be negative for x between 2 and 9, we must have:

3x² + 2ax + b < 0, for 2 < x < 9

We can use the information that a and b are integers to find values of a and b that satisfy this inequality.

Since the inequality holds for all values of x between 2 and 9, we can use the values x = 2 and x = 9 to form two equations involving a and b:

3(2)² + 2a(2) + b < 0

3(9)² + 2a(9) + b < 0

Simplifying each equation, we get:

12a + b < -12

81a + b < -243

We can use these two inequalities to eliminate b and solve for a:

12a + b < -12

-12a - 3b > 36

-11a < 24

a > -24/11

81a + b < -243

-81a - 27b > 243

-26b < 18

b > -9/13

Therefore, the only integers that satisfy both inequalities are a = -2 and b = -1. So, the equation is y = x³ - 2x² - x + 6.

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We need to find the inverse of the function gof (x). First we need to find the composite function gof (x) which is given by:

\(g(f(x)) = g(3x - 6)\)

= \((1/3)(3x - 6) + 1\)

= x - 1 + 1

= x

Thus,

gof (x) = x.

Now we need to find the inverse of the function gof (x) to obtain

\((gof)^-1 (x).\)

We have gof (x) = x

which implies\((gof)^-1 (x)\)

= gof (x)^-1

= x^-1

= 1/x,

x ≠ 0

Therefore,

\((gof)^-1 (x) = 1/x\)

which is option (3) (x+1) since 1/x can be written as 1/(x+1-1), where (x+1-1) is the denominator of 1/x.

Hence, the correct option is (3).

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To find (g(f))^-1 (x), substitute the expression for f(x) into g(x) and simplify. The composition of g(f) is x and its inverse is also x. Therefore, (g(f))^-1 (x) equals x.

To find (g(f))^-1 (x), we need to first find the composition of g(f) and then find its inverse. Start by substituting the expression for f(x) into g(x): g(f(x)) = g(3x-6) = \frac{1}{3}(3x-6) + 1 = x - 1 + 1 = x. So, g(f(x)) = x. Now, to find the inverse of g(f), we switch the x and y variables and solve for y: y = x. Therefore, (g(f))^-1 (x) = x.

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Answer:

True

Step-by-step explanation:

When displaying any sort of data, it is important to make the table or chart as easy to understand and read as possible without compromising the data. In this case, it is simpler to understand the pie chart if we use as few slices as possible that still makes sense for displaying the data set.

The angle of the camera is changing at a rate of approximately 1.732 radians per second when the angle is pi/6 radians.

Let's denote the angle of the camera as θ and the distance from the car to the camera as x. To track the car, the camera needs to adjust its angle as the car moves along the road.

Using trigonometry, we can establish a relationship between the angle θ, the distance x, and the distance the car has traveled along the road. Since the car is traveling at a speed of 60 feet per second, the distance the car has traveled is given by d = 60t, where t represents time.

From the given information, we can form a right triangle where the adjacent side is x (the distance from the camera to the car), and the hypotenuse is d (the distance traveled by the car). The opposite side can be found using the Pythagorean theorem as √(d^2 - x^2).

We can express the tangent of the angle θ as the ratio of the opposite side to the adjacent side: tan(θ) = (√(d^2 - x^2)) / x. To find how fast the angle θ is changing with respect to time, we differentiate both sides of the equation with respect to t:sec^2(θ) * dθ/dt = (2x * dx/dt) / (2x^2).

Simplifying, we have dθ/dt = (dx/dt) / (x * sec^2(θ)). Substituting the given values, we have dx/dt = 60 ft/s and θ = π/6 radians. Plugging these values into the equation, we get dθ/dt = (60 ft/s) / (4 ft * sec^2(π/6)) = (60 ft/s) / (4 ft * 4/3) = 1.732 radians/s.

Therefore, when the angle of the camera is π/6 radians, the angle is changing at a rate of approximately 1.732 radians per second.

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The missing values are a = 0, b= 6 and c=4.

In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

We have function,

f(x) = -x² + x + 6

At x= -2

f(-2) = -(-2)² + (-2) + 6 = -4 -2  + 6= 0

At x = 0

f(0) = -0² + 0 + 6= 6

At x = 2

f(2) = -2² + 2 +6 = -4 + 8= 4

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To solve the given equations and verify the provided results, let's work through the calculations step by step.

Given:

y₀ + g = 1.9243    ---(1)

y₁ + y = 1.9540    ---(2)

We need to show that:

y₂ + g = 1.9823    ---(3)

y₃ + y = 1.9956    ---(4)

3/4 = 0.9999557    ---(5)

Step 1: Subtract equation (2) from equation (1):

(y₀ + g) - (y₁ + y) = 1.9243 - 1.9540

Simplifying, we get:

y₀ - y₁ + g - y = -0.0297    ---(6)

Step 2: Multiply equation (6) by 2:

2(y₀ - y₁) + 2(g - y) = -0.0594

Simplifying, we get:

2y₀ - 2y₁ + 2g - 2y = -0.0594    ---(7)

Step 3: Add equation (2) to equation (7):

(2y₀ - 2y₁ + 2g - 2y) + (y₁ + y) = -0.0594 + 1.9540

Simplifying, we get:

2y₀ - y₁ + 2g - y = 1.8946    ---(8)

Step 4: Substitute the given value of y₀ + g in equation (8):

2(1.9243) - y₁ + 2g - y = 1.8946

Simplifying, we get:

3.8486 - y₁ + 2g - y = 1.8946    ---(9)

Step 5: Rearrange equation (9) to solve for g:

g = (1.8946 - 3.8486 + y₁ + y) / 2

Simplifying, we get:

g = (-0.9540 + y₁ + y) / 2    ---(10)

Step 6: Substitute the value of g from equation (10) into equation (3):

y₂ + g = 1.9823

y₂ + (-0.9540 + y₁ + y) / 2 = 1.9823

Simplifying, we get:

2y₂ - 0.9540 + y₁ + y = 3.9646    ---(11)

Step 7: Subtract equation (2) from equation (11):

(2y₂ - 0.9540 + y₁ + y) - (y₁ + y) = 3.9646 - 1.9540

Simplifying, we get:

2y₂ - 0.9540 = 2.0106    ---(12)

Step 8: Solve equation (12) for y₂:

2y₂ = 2.0106 + 0.9540

2y₂ = 2.9646

y₂ = 1.4823    ---(13)

Step 9: Substitute the value of y₂ from equation (13) into equation (4):

y₃ + y = 1.9956

y₃ + 1.4823 = 1.9956

Simplifying, we get:

y₃ = 0.5133    ---(14)

Step 10: Verify equation (5):

3/4 = 0.75, which is not equal to

0.9999557.

Therefore, the provided result in equation (5) is incorrect.

In conclusion:

Using the given equations, we have found:

y₂ + g = 1.9823 (equation 3)

y₃ + y = 1.9956 (equation 4)

However, the value provided in equation (5) is not accurate.

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The total number of candies in the store is 312. It is obtained by using the concept of exponent and power on the given problem.

What is an Exponent?

The number of times a quantity is multiplied by itself is referred to as an exponent or power of the given quantity. For eg: 25, where 5 is an exponent or power of 2 and 2 is called the base of exponent 5. Any quantity raised to the power 0 always returns 1 as result.

Calculation of the total number of candies in the store

(36)2 * 30

Using the properties of an exponent, we have

A number with an exponent of 0 always gives 1

(36)2 * 1

(3)6×2 * 1

312 * 1

312

Thus, the total number of candies in the store is 312.

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Answer:

B (-4,-4)

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Since it is currently at (4,2), reflecting it across y=-1 will bring the y-coordinate down to -4. After that, reflecting it across the y-axis will flip the sign in front of the x-coordinate, so 4 to -4. Therefore, your answer is (-4,-4).

The required graph of the inequality has been shown and the solution is; 8 Nickels  and 12 dimes.

Inequality can be defined as the relation of the equation possessing the symbol of ( ≤, ≥, <, >).

Let the number of nickels be x and let the number of dimes be y,

We are told that Addison has x dimes and y nickels, having a minimum of 20 coins worth at most $1.60 combined. Thus, we can generate the equations as;

x + y = 20

x = 20 - y - - - - (1)

0.05x + 0.10y ≤ 1.60 - - - -(2)

We are also told that no less than 4 of the coins are dimes. Thus;

x ≥ 4

From the graph, one solution is given as 8 Nickels and 12 dimes.

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Answer:

I think the answer you're looking for is 86400

Step-by-step explanation:

1. Independent random samples arise when one random sample is split into groups differing by an observed feature is incorrect.

2. The margin of error of a confidence interval about the difference between the means of two populations is equal to half the width of the confidence interval.

1. Independent random samples arise when individuals in a sample are randomly assigned to experimental groups, data is recorded repeatedly on a random sample of individuals, or random samples are selected separately. The statement that one random sample is split into groups differing by an observed feature does not accurately describe independent random samples.

2. The margin of error in a confidence interval represents the range of values within which the true population parameter is likely to fall. It is calculated by taking half of the width of the confidence interval. Therefore, the correct answer is that the margin of error is equal to half the width of the confidence interval.

In summary, the incorrect statement is that independent random samples arise when one random sample is split into groups differing by an observed feature. The margin of error of a confidence interval about the difference between the means of two populations is equal to half the width of the confidence interval.

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