substitute the length of the sides (8 in, 15 in m)
into the Pythagorean theorem. Then, find the length of the missing side m
(Please with step by step answer)

Answer:

a) £6.70  b)6.4%

Step-by-step explanation:

a) 105.20-98.50=6.70

b)105.20-98.50/105.20 x100= 6.4%

i hope i got it right welp

Answer:

Answer:

Exact form: 7√2

Decimal form: 9.89949493

Step-by-step explanation:

Also i'm going to assume you meant (-3, 4) instead of

"( -3 4 )."

Given problem represent Fundamental Counting Theorem.

Fundamental Counting Theorem states that if an event can occur in m different ways, and another event can occur in n different ways, then the total number of occurrences of the events is m×n.

Here Taylor has 5 baskets and there are 6 balls in each basket.

That is m = 5 and n = 6

Therefore Taylor have m×n= 5×6 =30 balls

Hence here we use Fundamental counting theorem.

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Given the 4th order linear ODE

\(u^{(4)} - u = 0\)

we substitute

\(x_1 = u\)

\(x_2 = {x_1}' = u'\)

\(x_3 = {x_2}' = {x_1}'' = u''\)

\(x_4 = {x_3}' = {x_2}'' = {x_1}''' = u'''\)

Then the given equation transforms to

\({x_4}' - x_1 = 0\)

but we also need to relate this to the other derivative substitutions. This gives the system of differential equations

\(\begin{cases} {x_1}' = x_2 \\ {x_2}' = x_3 \\ {x_3}' = x_4 \\ {x_4}' = x_1 \end{cases}\)

In matrix form,

\(\begin{bmatrix} x_1 \\ x_2 \\ x_3 \\ x_4 \end{bmatrix}' = \begin{bmatrix} 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 0 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \\ x_3 \\ x_4 \end{bmatrix}\)

The independent quantity for the given situation is time.

We are given that the factory produces 125 bags in every 10 seconds.

Because the number of bags is dependent on the time it takes to make bags, the dependent quantity in this case is the number of bags.

But time is an independent quantity.

Let us understand by taking examples;

It can be seen that in 20 seconds, the company will produce 250 bags.

It can also be seen that in 0 seconds, the company will produce 0 bags.

So, as time increases or decreases, the number of bags increases and decreases respectively.

Therefore, time is the independent quantity.

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Answer:

its none

Step-by-step explanation:

Answer:

none of these answers are correct.

The shadow of the 24-foot tree will be 9.6 feet.

In mathematics, ratios are used to determine the relationship between two numbers it indicates how many times is one number to another number.

Given that:-

If a 40-foot tree casts a 16-foot shadow, find the length of the shadow cast by a 24-foot tree.

Now, The shadow of the 24-foot tree will be calculated as follows:-

40/16 = 24/x

x = 24 x 16 / 40

x = 9.6

Therefore, the shadow of the 24-foot tree will be 9.6 feet.

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Answer:

d. (- 2 , -7)

Step-by-step explanation:

When A( -2 , 7) is reflected over the x-axis A' will be located at ( -2 , -7)

Hope it will help ☺

No, The two expression you wrote is not true. Because expression are equivalent when values are substituted in for variables. So, both expression gave same answer. Then we can say equivalent expression.

What is expression?

Expression is a finite of symbols that are formed in accordance with dependent rule. It is a number, a variable and combination of variables or symbols. It can be possible by multiply, divide, subtraction and addition.

What is equivalent expression?

Equivalent expression that always work same but look different. When equivalent expression simplified they give same answer. If all the terms in the two expression are identical then we can expression are equivalent.

NOW we have expression

ax +3b

3b+xc

ax+3b=3b+xc

ax=xc

The two expression can only be equivalent if ax=xc it mean that a is equal to c. which is not true. So, they are not equivalent.

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Answer:

80.9 kilometres =

8090000 centimetres

Length

80.9

kilometre

8090000

Centimeter

The derivative of the function f(x) = 0 to x sec(7t) dt is sec^2(7x) * tan(7x).

The derivative of the function f(x) = 0 to x sec(7t) dt is sec(7x).

To see why, we use part one of the fundamental theorem of calculus, which states that if F(x) is an antiderivative of f(x), then the definite integral from a to b of f(x) dx is F(b) - F(a).

Here, we have f(x) = sec(7t), and we know that an antiderivative of sec(7t) is ln|sec(7t) + tan(7t)| + C, where C is an arbitrary constant of integration.

So, using the fundamental theorem of calculus, we have:

f(x) = 0 to x sec(7t) dt = ln|sec(7x) + tan(7x)| + C

Now, we can take the derivative of both sides with respect to x, using the chain rule on the right-hand side:

f'(x) = d/dx [ln|sec(7x) + tan(7x)| + C] = sec(7x) * d/dx [sec(7x) + tan(7x)] = sec(7x) * sec(7x) * tan(7x) = sec^2(7x) * tan(7x)

Therefore, the derivative of the function f(x) = 0 to x sec(7t) dt is sec^2(7x) * tan(7x).

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The state income tax owed on a $90,000 per year salary is $4, 918 to the nearest whole dollar

To calculate the state income tax owed on a $90,000 per year salary using the given progressive tax rates, determine which income range the salary falls into and apply the corresponding tax rate.

The salary of $90,000 falls into the last income range, which has a tax rate of 5.75%.

To calculate the state income tax owed, use the following formula:

Tax Owed = Tax Rate x Taxable Income

For the first income range, the taxable income is $3,000 (the maximum amount for the range), and the tax rate is 2%:

Tax Owed for Range 1 = 0.02 x $3,000 = $60

For the second income range, the taxable income is $5,000 - $3,000 = $2,000, and the tax rate is 3%

Tax Owed for Range 2 = 0.03 x $2,000 = $60

For the third income range, the taxable income is $17,000 - $5,000 = $12,000, and the tax rate is 5%

Tax Owed for Range 3 = 0.05 x $12,000 = $600

For the fourth and final income range, the taxable income is $90,000 - $17,000 = $73,000, and the tax rate is 5.75%

Tax Owed for Range 4 = 0.0575 x $73,000 = $4,197.50

Therefore, the state income tax owed on a $90,000 per year salary is

Tax Owed = $60 + $60 + $600 + $4,197.50

= $4,917.50

= $4, 918 to the nearest whole dollar

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Answer:

it should be 10x+3y=30 if im not mistaken

Step-by-step explanation:

you just add straight down with corresponding variables

The Correct answer will be B. f(x) is shifted π/4 units to the left.

The general equation for a sine and cosine curve is y = A sin ⁡ ( x − h ) + k and y = A cos ⁡ ( x − h ) + k , respectively. Similar to other function transformations, is the horizontal shift (also called a phase shift), and is the vertical shift.Changes to the amplitude, period, and midline are called transformations of the basic sine and cosine graphs. Changing the midline shifts the graph vertically. The graph is stretched or compressed vertically depending on the amplitude. The graph is stretched or compressed horizontally depending on the era.

To determine the transformation;

Dim x=t+π/4

so, f(t+π/4)=cos(t+π/4)=g(t)

t+π/4→t:units to the left.

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Answer:

The Prime Factorization is:

2 x 7

In Exponential Form:

21 x 71

CSV Format:

2, 7

Prime Factors Tree

 14  

 /  \  

2   7

Prime[1] = 2, Prime[4] = 7

Step-by-step explanation:

Area is,

R= 1000

so A= 3.14 x 1000 x1000=3140000 feet

total ares is 3140000 feet

the bison angle is 60

so,1/6 th of 3140000 is 523333.33

so the answer is C.

Answer:

75.39 in^2

Step-by-step explanation:

circumference=2πr

30.8=2(3.14)r

30.8=6.28r

4.9=r

Now that we know the radius, we can plug it in for the area equation

area=πr^2

area=(3.14)(4.9)^2

area=(3.14)(24.01)

area=75.39 in^2

Answer:

.84%

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

= f (x) = -2 log 4 (x + 5) - 4

= 4 (-2 + 5) - 4

= So you do -2 + 5 because they are in ( ) so you do it first so (-2 + 5) = 3

= So now you have 4 (3) - 4

= You do 4 and (3) because when you have a 4 by a ( ) that means you multiply.

= 4 (3) which is the same as 4 × 3 which is 12.

= then you do 12 - 4 which is 8.

= 8 is your answer.

I hope this helps.

The boundary and initial conditions provided, we can fill in the constants in the solution: u(x,0) = 1 sin(πx) + 6 sin(27πx) + 7 sin(31πx) + 11 sin(41πx)

To match the  solution format, let's fill in the constants:
u(x, t) = (1)e^(-π^2t)sin(πx) + (6)e^(-27^2π^2t)sin(27πx) + (7)e^(-31^2π^2t)sin(31πx) + (11)e^(-41^2π^2t)sin(41πx)
Here, the constants are: 1, 6, 7, and 11 for the amplitudes of each sine term
π, 27π, 31π, and 41π for the sine argument multipliers
-π^2, -27^2π^2, -31^2π^2, and -41^2π^2 for the exponents of e in the time-dependent coefficients.

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Answer:

42

Step-by-step explanation:

The widely used formula to find the area of a parellelogram is base * height so then 7 * 6 = 42

If you want to do it with triangles, you can split the diagram into two 2x7 triangles (total area 14) and one 7x4 rectangle (total area 28) which, when added, gives 42 as well.

The correct answer is e(x) = np. The expected value for a binomial probability distribution is given by the formula e(x) = np, where n represents the number of trials and p represents the probability of success in each trial.

The expected value is a measure of the average or mean outcome of a binomial experiment. It represents the number of successful outcomes one would expect on average over a large number of trials.

The formula e(x) = np arises from the fact that the expected value of a binomial distribution is the product of the number of trials (n) and the probability of success (p) in each trial. This is because in a binomial experiment, the probability of success remains constant for each trial.

Therefore, to calculate the expected value of a binomial probability distribution, we multiply the number of trials by the probability of success in each trial, resulting in e(x) = np.

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To show that the matrix A = [XX - X'Z(ZZ)^(-1)Z'X] is positive definite, we need to demonstrate two properties: (1) A is symmetric, and (2) all eigenvalues of A are positive.

Symmetry: To show that A is symmetric, we need to prove that A' = A, where A' represents the transpose of A. Taking the transpose of A: A' = [XX - X'Z(ZZ)^(-1)Z'X]'. Using the properties of matrix transpose, we have:

A' = (XX)' - [X'Z(ZZ)^(-1)Z'X]'. The transpose of a sum of matrices is equal to the sum of their transposes, and the transpose of a product of matrices is equal to the product of their transposes in reverse order. Applying these properties, we get: A' = X'X - (X'Z(ZZ)^(-1)Z'X)'.  The transpose of a transpose is equal to the original matrix, so: A' = X'X - X'Z(ZZ)^(-1)Z'X. Comparing this with the original matrix A, we can see that A' = A, which confirms that A is symmetric.  Positive eigenvalues: To show that all eigenvalues of A are positive, we need to demonstrate that for any non-zero vector v, v'Av > 0, where v' represents the transpose of v. Considering the expression v'Av: v'Av = v'[XX - X'Z(ZZ)^(-1)Z'X]v

Expanding the expression using matrix multiplication : v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv. Since X and Z have full column rank, X'X and ZZ' are positive definite matrices. Additionally, (ZZ)^(-1) is also positive definite. Thus, we can conclude that the second term in the expression, v'X'Z(ZZ)^(-1)Z'Xv, is positive definite.Therefore, v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv > 0 for any non-zero vector v. Implications in econometrics: In econometrics, positive definiteness of a matrix has important implications. In particular, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] guarantees that it is invertible and plays a crucial role in statistical inference.

When conducting econometric analysis, this positive definiteness implies that the estimator associated with X and Z is consistent, efficient, and unbiased. It ensures that the estimated coefficients and their standard errors are well-defined and meaningful in econometric models. Furthermore, positive definiteness of the matrix helps in verifying the assumptions of econometric models, such as the assumption of non-multicollinearity among the regressors. It also ensures that the estimators are stable and robust to perturbations in the data. Overall, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] provides theoretical and practical foundations for reliable and valid statistical inference in econometrics.

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Answer:

2/1

Step-by-step explanation:

x1=1 ,y1=3

x2=2 , y2=5

then

m= 5-3/2-1= 2/1

Answer:

n + 50 = 90; n = 40

Step-by-step explanation:

the angle is a right angle so it adds up to 50

one side is 50

so

n + 50 = 90

subtract 50 to both sides

n = 40

The original series also converges.

To use the limit comparison test to determine if the series converges or diverges, we first need to find a simpler series that has a similar form to the given series. In this case, the given series is:

\(Σ (4√n / (9n^(3/2) - 10n - 3)) from n = 1 to ∞\)
We can compare it with the simpler series:

\(Σ (4√n / 9n^(3/2)) from n = 1 to ∞\)

Now, let's find the limit of the ratio of the terms of these two series as n approaches infinity:

\(lim (n -> ∞) [(4√n / (9n^(3/2) - 10n - 3)) / (4√n / 9n^(3/2))]\)
Simplify the expression:

\(lim (n -> ∞) [(9n^(3/2) - 10n - 3) / 9n^(3/2)]\)

As n approaches infinity, the highest power term (9n^(3/2)) dominates, so we can ignore the other terms:

\(lim (n -> ∞) [9n^(3/2) / 9n^(3/2)] = 1\)

Since the limit is a finite number greater than 0, the comparison series and the original series have the same convergence behavior. The comparison series is a p-series with p = 3/2 > 1, so it converges. Therefore, the original series also converges.

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Answer: number of guest 12 20 number of tables 6 13

Step-by-step explanation:

The coordinate of point x is 12

The number line that completes the question is added as an attachment

The ratio is given as:

mx :xj = 3:1.

Also, we have:

M = 2

J = 18

So, we have

x = mx/(mx + xj) * (J - M)

This gives

x = 3/4 * (18 - 2)

Evaluate

x = 12

Hence, the coordinate of point x is 12

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Using ANOVA rather than separate t-tests is generally recommended when comparing more than two treatment conditions because it provides greater statistical power, helps control for experiment-wise error rate, and can identify interactions between treatments.

What is a t-test?

A t-test is a statistical hypothesis test used to determine whether there is a significant difference between the means of two groups or samples. It is a parametric test that assumes the data is normally distributed and that the variances of the two groups are equal.

When comparing more than two treatment conditions, it's generally recommended to use analysis of variance (ANOVA) rather than separate t-tests for several reasons:

Reduced Type I error: When conducting multiple t-tests, the risk of Type I error (rejecting the null hypothesis when it's actually true) increases with each additional test conducted. ANOVA helps to reduce this risk by testing all treatments simultaneously, rather than testing each treatment separately.

Increased power: ANOVA is more powerful than t-tests when there are multiple treatment conditions because it uses all the available data to estimate treatment effects. This can help to identify differences between groups that may not be significant when comparing only two groups at a time.

Ability to detect interactions: ANOVA can also identify interactions between treatments, which t-tests cannot do. This is important because it allows you to test whether the effect of one treatment depends on the level of another treatment, which may be of interest in many experimental contexts.

Better control over experiment-wise error rate: ANOVA allows for better control over the overall error rate, meaning that it's easier to maintain a desired level of significance across all comparisons. In contrast, conducting multiple t-tests can result in an increased risk of committing at least one Type I error.

Hence, using ANOVA rather than separate t-tests is generally recommended when comparing more than two treatment conditions because it provides greater statistical power, helps control for experiment-wise error rate, and can identify interactions between treatments.

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