Which of the following expresses in sigma​ notation?

The unit rate of the cups is 15/16 cup per gram

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

Cups = 3/4 cups

Grams = 4/5 grams

The unit rate of the scenario is then calculated as

Unit rate = Cups/Grams

Substitute the known values in the above equation, so, we have the following representation

Unit rate = (3/4)/(4/5)

Evaluate the quotient

Unit rate = 15/16

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Answer:

10 dim 10 nickel and 10 quarter

Step-by-step explanation:

10 dim=100

10 nickel=50

10 quarter=250

Answer:

A. -3x^2+7x-1

Step-by-step explanation:

(3x^2+3x-3)-(6x^2-4x-2)

3x^2+3x-3-6x^2+4x+2

-3x^2+7x-1

Answer:

x=10

Step-by-step explanation:

If we subtract 2 from 52 we get 50 and ten mutiplys into 50.

Answer:

Option B is the best way to write the underlined parts of sentences 2 and 3.

Sentence 2: They have a special finish that helps.

Sentence 3: The finish helps the swimmer glide through the water.

Option B provides a clear and concise way to connect the two sentences and convey the idea that the special finish of the swimsuits helps the swimmer glide through the water. It avoids any ambiguity or redundancy in the language.

Answer:

950

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

Expansion

\(f(x)=3(x+6)^2-75\\\\f(x)=3(x+6)(x+6)-75\\\\f(x)=3(x^2+12x+36)-75\\\\f(x)=3x^2+36x+108-75\\\\f(x)=3x^2+36x+33\) <-- Stop here if this is what you need

Factorization

\(f(x)=3(x^2+12x+11)\\\\f(x)=3(x+1)(x+11)\)

We know from vertex form that the vertex of the parabola is \((-6,-75)\) and when factored, the zeroes are \(x=-1\) and \(x=-11\).

Answer

9

Step-by-step explanation:

Divide 63 by 9 months

7 students per month

63 / 9 = 7

The statistical output indicates that the mean and standard deviation of a dataset of 100 measurements are $1600 and $300, respectively. The number of measurements between $1000 and $2200 can be found using the normal distribution.

Therefore, we can say that about 95.45% of the measurements fall between $1000 and $2200.

The normal distribution is the probability distribution that is most often used in statistics. The normal distribution is a continuous probability distribution that is bell-shaped and symmetric.

The number of measurements between $1000 and $2200 is found by calculating the probability that a measurement falls within that range, using the normal distribution. This probability can be calculated using the z-score formula, which transforms the range into standard units.

z = (x - μ)/σ

where x is the value of interest, μ is the mean, and σ is the standard deviation. For the range $1000 to $2200, the z-scores are calculated as follows:

z1 = (1000 - 1600)/300 = -2z2 = (2200 - 1600)/300 = 2

The probability of a measurement falling between these two z-scores is found using a normal distribution table or a calculator. The area under the normal distribution curve between -2 and 2 is approximately 0.9545. Therefore, we can say that about 95.45% of the measurements fall between $1000 and $2200.

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Answer:

c. x-intercept is (6, 0) and the y-intercept is (0, 10).

Step-by-step explanation:

i hope this helps :)

Answer:

18.

Step-by-step explanation:

3 x 6 = 18. He eats 3 slices every 5 minutes so 5 minutes x 6 is half an hour. so 18 is your answer.

If Takaya continues to eat three slices of pizza in five minutes, he could eat 18 slices in half of an hour.

The Linear equation in one variable is an algebraic equation of degree one.

it can be expressed in the form of Ax +B = 0 where x is a variable, and A and B are two integers.

Takaya can eat three slices of pizza in five minutes.

for half an hour it would be 6 times five minutes.

So, in half an hour Takaya can eat 3 × 6 = 18

Therefore, If Takaya continues to eat three slices of pizza in five minutes, he could eat 18 slices in half of an hour.

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Answer:

V=35

Step-by-step explanation:

\(\frac{V}{7} =5\)

Start by multiplying by 7 on both sides:

V=35

Answer:

35

Step-by-step explanation:

5 times 7 is 35 so v divided by 7 is 5

The proportion of scores that are below 12.5 is 0.8944 or 89.44%.

Given that the population is normally distributed with a mean of 10 and a standard deviation of 2, we can calculate the proportion of scores below 12.5 using the z-score formula.

z = (x - μ) / σwhere x = 12.5, μ = 10, and σ = 2.

Substituting these values into the formula, we get:

z = (12.5 - 10) / 2z = 1.25

We must find the area under the standard normal distribution curve to the left of z = 1.25. This area represents the proportion of scores that are below 12.5.

We can use a standard normal distribution table or calculator to find this area. Using a standard normal distribution table, the area to the left of z = 1.25 is 0.8944.

Therefore, the proportion of scores below 12.5 is 0.8944 or 89.44%.

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The solution to the given fraction 7/11 = x/9 to the nearest tenth is 5.7

7/11 = x/9

7 × 9 = 11 × x

63 = 11x

x = 63/11

x = 5.72727272727272

Approximately,

x = 5.7

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Answer: 600m

Step-by-step explanation: i didnt know if you wanted meters or feet or sum else so i just did that

Answer:19

Step-by-step explanation: you would do 4x5 thats 20 then you would subtract one becasue 4-5=-1

There is a difference in the average salary among the three racial groups being studied.

A study was conducted comparing the average salary for Blacks, Whites, and Hispanics, using random samples of 10 people in each racial group. The standard deviations of the groups were quite different.

To determine if there is a significant difference in salaries among these racial groups, the following steps can be taken:

1. Calculate the mean salary for each racial group (Blacks, Whites, and Hispanics) using the data from the random samples.

2. Calculate the variance and standard deviation for each group's salary to understand the spread of data within each group.

3. Perform an analysis of variance (ANOVA) test, which helps in comparing the means of multiple groups (in this case, the three racial groups). This test will indicate whether there is a significant difference in the mean salaries of the groups.

If the results of the ANOVA test show a significant difference, it means there is a difference in the average salary among the three racial groups being studied.

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The general solution to the given Cauchy-Euler equation for t > 0 is:

y(t) = C1 * t⁻⁵ + C2 * t⁴

Let's consider the given Cauchy-Euler equation for t > 0:

t²(d²y/dt²) + 2t(dy/dt) - 20y = 0

To solve this equation, we can assume a solution of the form y(t) = tⁿ, where r is a constant to be determined.

Now, let's find the derivatives of y(t) with respect to t:

dy/dt = rtⁿ⁻¹ d²y/dt² = r(r-1)tⁿ⁻²

Substituting these derivatives back into the Cauchy-Euler equation, we get:

t²(r(r-1)tⁿ⁻²) + 2t(rtⁿ⁻¹) - 20tⁿ = 0

Simplifying this equation, we have:

r(r-1)tⁿ + 2rtⁿ - 20tⁿ = 0

Factoring out tⁿ, we get:

tⁿ [r(r-1) + 2r - 20] = 0

Since t > 0 for the given equation, we can divide both sides of the equation by tⁿ to obtain:

r(r-1) + 2r - 20 = 0

Expanding and rearranging this equation, we get:

r² + r - 20 = 0

Now, we can solve this quadratic equation for r. Factoring it, we have:

(r + 5)(r - 4) = 0

Setting each factor equal to zero, we find two possible values for r:

r + 5 = 0, which gives r = -5 r - 4 = 0, which gives r = 4

These values of r represent the roots of the characteristic equation associated with the Cauchy-Euler equation. Since we have two distinct roots, the general solution to the Cauchy-Euler equation can be written as a linear combination of the corresponding solutions:

y(t) = C1 * t⁻⁵ + C2 * t⁴

Where C1 and C2 are arbitrary constants that can be determined using initial conditions or boundary conditions if provided.

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The relative frequency is solved and the table of values is plotted

Given data ,

The lunch order is given by the 2 sets of dishes as

A = { Sandwich , Pastas }

Now , the sports activities are given by 2 sets as

B = { Volleyball , Swimming }

From the table of values , we get

The relative frequency is solved as

Relative Frequency = Subgroup frequency / Total frequency

The percentage of Swimming ( sandwich ) = 26/36

Swimming ( sandwich ) = 72 %

And , the percentage of Swimming ( pasta ) = 10/36

Swimming ( pasta ) = 28 %

Now , the percentage of total sandwich = 45/70 = 64 %

And , the percentage of total pasta = 25/70 = 36 %

Hence , the relative frequency is solved

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(a) The critical value (t*) for a 99% confidence level is t* = 3.499.

(b) The margin of error for a 99% confidence interval is approximately 1.633.

To solve the problem step by step, we'll use the provided information to find the critical value (t*) for a 99% confidence level (CL) and the margin of error for a 99% confidence interval (CI).

(a) Find the critical value, t*, for a 99% confidence level (CL):

Step 1: Determine the confidence level (CL). In this case, it is 99%, which corresponds to a significance level of α = 0.01.

Step 2: Determine the degrees of freedom (df). Since we have a sample size of 8, the degrees of freedom is given by df = n - 1 = 8 - 1 = 7.

Step 3: Find the critical value, t*, using a t-distribution table or statistical software. The critical value is the value that separates the middle 99% of the t-distribution. For a two-tailed test with α = 0.01 and 7 degrees of freedom, the critical value is approximately t* = 3.499.

Therefore, the critical value (t*) for a 99% confidence level is t* = 3.499.

(b) Find the margin of error for a 99% confidence interval (CI):

Step 1: Calculate the standard error (SE) using the formula: SE = (standard deviation) / √(sample size).

Given that the standard deviation is 1.32 hours and the sample size is 8, we have SE = 1.32 / √8 = 0.4668.

Step 2: Determine the margin of error (ME) by multiplying the standard error by the critical value: ME = t* × SE.

Using the previously calculated critical value (t* = 3.499) and the standard error (SE = 0.4668), we have ME = 3.499 × 0.4668 = 1.633.

Therefore, the margin of error for a 99% confidence interval is approximately 1.633.

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The question is -

A random sample of 8-size AA batteries for toys yields a mean of 3.79 hours with a standard deviation, of 1.32 hours.

(a) Find the critical value, t*, for a 99% Cl. t* = ________

(b) Find the margin of error for a 99% CI. _________

Answer:

3, 6, 9

Step-by-step explanation:

Add them together 3 + 6 + 9 = 18

Divide by 3

Answer:

5.2

Step-by-step explanation:

The given differential operators L₁ and L₂ can be written in the form (p(x)) + r(x) by multiplying by suitable weight functions.

Given differential operators L₁ and L₂. We are required to write them in the form (p(x)) + r(x) by multiplying by a suitable weight function.

For L₁:Multiplying L₁ with weight function 1/(1 - x), we get

\(1/(1 - x) . d²/dx² L₁ + (5 + x)/(1 - x) . d/dx L₁ + Xx/(1 - x) . L₁\)

Let us assume the equation obtained after multiplication by a weight function is M₁. Then,

\(M₁ = (1/(1 - x)) . d²/dx² L₁ + (5 + x)/(1 - x) . d/dx L₁ + Xx/(1 - x) . L₁\)

Now, let us find the first derivative and second derivative of M₁.

First derivative:

\(d/dx M₁ = (1/(1 - x)) . d³/dx³ L₁ + (2x - 4)/(1 - x) . d²/dx² L₁ + (6 - 2x)/(1 - x) . d/dx L₁ - 2X/(1 - x) . L₁\)

Second derivative:

d²/dx² M₁ = (1/(1 - x)) . d⁴/dx⁴ L₁ + (2 - 4x)/(1 - x) . d³/dx³ L₁ + (10 - 4x)/(1 - x) . d²/dx² L₁ + (4 - 4x)/(1 - x) . d/dx L₁ - 2X/(1 - x) . d/dx L₁ - 2/(1 - x) . L₁

For L₂:Multiplying L₂ with weight function 1/cos²(x), we get

\(1/cos²(x) . d/dx L₂ + tan(x) . L₂\)

Let us assume the equation obtained after multiplication by a weight function is M₂. Then,

\(M₂ = 1/cos²(x) . d/dx L₂ + tan(x) . L₂\)

Now, let us find the first derivative of M₂.

First derivative:

\(d/dx M₂ = -2sin(x)/cos³(x) . L₂ + sec²(x) . d/dx L₂\)

Therefore, we can write the given differential operators L₁ and L₂ in the form (p(x)) + r(x) as:

\(L₁ = (1/(1 - x)) . d²/dx² L₁ + (5 + x)/(1 - x) . d/dx L₁ + Xx/(1 - x) . L₁L₂\)

     =\(1/cos²(x) . d/dx L₂ + tan(x) . L₂\)

Conclusion: Thus, the given differential operators L₁ and L₂ can be written in the form (p(x)) + r(x) by multiplying by suitable weight functions.

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The unknown number will be equal to 3.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that eight times, the sum of twice a number and five is eighty-eight. Let the number be x then the value of x  will be calculated by forming an expression below:-

8(2x + 5 ) = 88

2x + 5 = 11

2x = 11 - 5

2x= 6

x = 6 / 2

x = 3

Therefore, the unknown number will be equal to 3.

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To find the numerical value of the algebraic expression B²(c+d)-a²(m+n)+2x, we need to substitute the given values of the variables into the expression and then simplify.

Here is the step-by-step explanation:

1. Substitute the given values of the variables into the expression:
(2)²(3+4)-(1)²(1/2+2/3)+2(0)

2. Simplify the expression by following the order of operations:
(4)(7)-(1)(7/6)+0

3. Simplify further:
28-7/6

4. Find a common denominator and combine the terms:
168/6-7/6

5. Simplify the expression to get the final numerical value:
161/6

Therefore, the numerical value of the algebraic expression B²(c+d)-a²(m+n)+2x is 161/6.

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The numerical value of the algebraic expression B²(c+d)-a²(m+n)+2x is 161/6.

To find the numerical value of the algebraic expression B²(c+d)-a²(m+n)+2x, we need to substitute the given values of the variables into the expression and then simplify.

Here are the steps to do this:

1. Substitute the given values of the variables into the expression:
(2)²(3+4)-(1)²(1/2+2/3)+2(0)

2. Simplify the expression inside the parentheses:
(2)²(7)-(1)²(7/6)+0

3. Simplify the exponents:
4(7)-1(7/6)+0

4. Multiply the numbers:
28-7/6+0

5. Simplify the expression by finding a common denominator and combining the terms:
28-7/6 = 168/6-7/6 = 161/6

So the numerical value of the algebraic expression B²(c+d)-a²(m+n)+2x is 161/6.

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Fron the given question, we can say that systematic sample because not all sample are possible.

Using the probabilistic sampling technique known as systematic sampling, researchers periodically choose individuals from a community. Choose each 15th of her, for instance, from the population list. You can simulate the advantages of straightforward random sampling by randomly sorting the population.

\(Since every 100th horse is selected in the sample. Thus, Systematic Sampling is used.\)

Further,

Sampling method is said to be Simple Random Sampling if unit from the population are picked randomly without any criteria, so that each unit as similar chance of selection.

If any criteria are used to select every sample, such as selecting every fourth unit, the sampling technique is said to be systematic sampling.

If the population is divided into various groups that share the same characteristic, the sampling method is said to be stratified sampling. Additionally, units are chosen at random from these groups.

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Answer:

The answers are in the photo taken

Step-by-step explanation:

Pls mark as brainlest

Answer:

x>-2

Step-by-step explanation:

If you can see, the palabara starts at x=-2 and continues in higher x values. Thus, x>-2.