what is the area of a rectangle with a length of 4 1/8 ft and a width of 2 ft​

The equation of the tangent line at x=0 is y = x.

To find the equation of the tangent line at the given value of x, we need to find the derivative of the function y with respect to x and evaluate it at x=0.

Taking the derivative of y=∫[0 to x] sin(2t^2+π/2) dt using the Fundamental Theorem of Calculus, we get:

dy/dx = sin(2x^2+π/2)

Now we can evaluate this derivative at x=0:

dy/dx |x=0 = sin(2(0)^2+π/2)

        = sin(π/2)

        = 1

So, the slope of the tangent line at x=0 is 1.

To find the equation of the tangent line, we also need a point on the line. In this case, the point is (0, y(x=0)).

Substituting x=0 into the original function y=∫[0 to x] sin(2t^2+π/2) dt, we get:

y(x=0) = ∫[0 to 0] sin(2t^2+π/2) dt

      = 0

Therefore, the point on the tangent line is (0, 0).

Using the point-slope form of a linear equation, we can write the equation of the tangent line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line.

Plugging in the values, we have:

y - 0 = 1(x - 0)

Simplifying, we get:

y = x

So, the equation of the tangent line at x=0 is y = x.

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Answer: x = - 12

8x + 45 = 10x + 69

⇔ 10x - 8x = 45 - 69

⇔ 2x = -24

⇔ x = -12

Step-by-step explanation:

Answer:

x = -12

Step-by-step explanation:

8x + 45 = 10x + 69

8x = 10x + 24

-2x = 24

x = -12

Answer:

2d+20

Step-by-step explanation:

since he is 20 pounds greater than denny you would just add 2d and 20 im pretty sure

or ig you want to write out the whole thing it would be y=2d+20

Hope This Helps!!

Answer:

\(2d + 20\)

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

total intake = 720 mL or 24 ounces

Step-by-step explanation:

Given data

coffee consume = 6 ounces

ice cream consume = 4 ounces

apple juice consume = 120 mL

water consume = 10 ounces

To find out

the intake

solution

for intake we will add the consumed item in same unit

so intake = consume coffee + ice cream consume + apple juice consume + water consume    ..................1  

here we know that 1 ounces  = 30 mL

so coffee consume = 6 ounces = 6 × 30 = 180 mL

and ice cream consume = 4 ounces = 4 × 30 = 120 mL

and = water consume = 10 ounces = 10 × 30 = 300 mL

so put all value in eq 1 we get

total intake = 180 + 120 + 120 + 300

total intake = 720 mL or 24 ounces

Answer:

So the solution to the system of equations is (x,y) = (3,-2).

Step-by-step explanation:

To solve for x and y using substitution, we can first substitute y=-2 into the second equation to find the value of x, and then use that to find y.

Starting with the second equation:

4x - 3(-2) = 18

Expanding the -3(-2) using the distributive property:

4x + 6 = 18

Subtracting 6 from both sides:

4x = 12

Dividing both sides by 4:

x = 3

Now that we have x = 3, we can substitute that back into the first equation to find y:

y = -2

So the solution to the system of equations is (x,y) = (3,-2).

Solve for Mary, Ryan, Eric by assigning variables to represent their money amounts. The equation simplifies to $115, with Mary having $19, Ryan having $24, and Eric having $72.

To solve this problem, let's assign variables to represent the amount of money each person has. Let's say Mary has x dollars. Since Ryan has $5 more than Mary, we can represent Ryan's amount as x + $5.

Given that Eric has 3 times what Ryan has, we can represent Eric's amount as 3(x + $5).

The sum of their amounts is $115, so we can create an equation: x + (x + $5) + 3(x + $5) = $115.

Simplifying the equation, we get 5x + $20 = $115.

Subtracting $20 from both sides, we get 5x = $95.

Dividing both sides by 5, we find x = $19.

Therefore, Mary has $19, Ryan has $19 + $5 = $24, and Eric has 3($24) = $72.

In total, they have $19 + $24 + $72 = $115 in their wallets.

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Answer:

Step-by-step explanation:

the pizza come in slices that are 1/8 each.

there are 36 slices, which means \(\frac{36}{288}\).  so the simplest form is 1/8 as well. Maria bought 4 pizzas

The total amount of pizza Maria bought as a fraction is \(\frac{36}{4}\) and  8 \(\frac{1}{2}\) as a mixed number

Total amount bought = fraction of a slice x total slices bought

\(\frac{1}{4}\) x 36  = \(\frac{36}{4}\)

The above expression is an improper fraction

An improper fraction is a fraction in which the numerator is greater in value than the denominator

36 is greater than 4

A mixed number is a number that is made up  of a whole a whole number and a proper fraction.

To convert to an improper fraction to a mixed number:

\(\frac{36}{4}\) = 8\(\frac{2}{4}\)

When it is simplified it becomes 8 \(\frac{1}{2}\)

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Answer:

D. The money that Kai started with before he mowed any lawns.

Step-by-step explanation:

We Know

The equation is y = mx + b

The x represents the number of lawns that Kai mows.

What does the y-intercept represent in this equation?

The y-intercept is when the x = 0, meaning the y-intercept is the amount of money he has when mowing 0 lawn. So, the answer is D.

Answer:

The Answer is D

Step-by-step explanation:

Matrix A serves as an example of a 2x2 matrix that is invertible but not diagonally dominant.

Prove that if A is a diagonally dominant matrix, then A is invertible:

To prove that a diagonally dominant matrix A is invertible, we can use the fact that a matrix is invertible if and only if its determinant is non-zero.

Let's assume A is a square matrix of size n x n. A matrix A is said to be diagonally dominant if the absolute value of each diagonal element is greater than the sum of the absolute values of the remaining elements in its corresponding row.

Mathematically, for each i in the range 1 to n, we have:

|A(i,i)| > ∑ |A(i,j)|, for j ≠ i

To prove that A is invertible, we need to show that det(A) ≠ 0.

Suppose, by contradiction, that det(A) = 0. This means that A is not invertible.

Since A is not invertible, there exists a non-zero vector x such that Ax = 0 (the zero vector).

Let's consider the i-th component of the vector Ax:

(Ax)(i) = ∑ A(i,j) * x(j), for j = 1 to n

Since Ax = 0, we have (Ax)(i) = 0.

Now, let's focus on the absolute value of the diagonal element A(i,i):

|A(i,i) * x(i)| = |A(i,i)| * |x(i)|

Since A is diagonally dominant, |A(i,i)| > ∑ |A(i,j)| for j ≠ i. This implies that:

|A(i,i)| * |x(i)| > ∑ |A(i,j)| * |x(j)|, for j ≠ i

But the left-hand side of the above inequality is zero since (Ax)(i) = 0. However, the right-hand side is non-zero since the absolute values are always non-negative and at least one term on the right-hand side must be non-zero.

This contradiction implies that our assumption, det(A) = 0, is false. Therefore, A must be invertible if it is diagonally dominant.

Give an example of a 2x2 matrix that is invertible but not diagonally dominant:

Let's consider the following matrix A:

A = [1 2]

[2 1]

To check if A is invertible, we can calculate its determinant:

det(A) = (1 * 1) - (2 * 2) = -3

Since the determinant of A is non-zero (det(A) ≠ 0), A is invertible.

Now, let's check if A is diagonally dominant:

|A(1,1)| = 1 > |A(1,2)| = 2

|A(2,2)| = 1 > |A(2,1)| = 2

Since A is not diagonally dominant (the absolute values of the diagonal elements are not strictly greater than the sum of the absolute values of the remaining elements in their corresponding rows), it serves as an example of a 2x2 matrix that is invertible but not diagonally dominant.

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The coffee shop owner does not have sufficient evidence to conclude that the distribution of sales is proportional to the number of facings at a 5% level of significance.

What is proportion ?

A proportion refers to the number or fraction of individuals or items that exhibit a particular characteristic or have a certain attribute, relative to the total number or sample size being considered. It is often expressed as a ratio or percentage.

To test whether the distribution of sales is proportional to the number of facings, we can use the chi-squared goodness of fit test. The null hypothesis for this test is that the observed data follows a specific distribution (in this case, a proportional distribution), while the alternative hypothesis is that the observed data does not follow that distribution.

To conduct the test, we first need to calculate the expected frequency for each category assuming a proportional distribution. We can do this by multiplying the total number of sales (610) by the proportion of facings for each brand:

Starbucks: 610 x 0.3 = 183

Dunkin: 610 x 0.4 = 244

Peet's: 610 x 0.2 = 122

Other: 610 x 0.1 = 61

Next, we calculate the chi-squared statistic using the formula:

χ² = Σ((O - E)² / E)

where O is the observed frequency and E is the expected frequency. The degrees of freedom for this test are (k-1), where k is the number of categories. In this case, k = 4, so the degrees of freedom are 3.

Using the observed and expected frequencies from the table, we get:

χ² = ((130-183)²/183) + ((240-244)²/244) + ((85-122)²/122) + ((155-61)²/61) = 124.36

Looking up the critical value of chi-squared for 3 degrees of freedom and a significance level of 0.05, we get a value of 7.815. Since our calculated χ² value of 124.36 is greater than the critical value of 7.815, we reject the null hypothesis and conclude that the observed distribution of sales is not proportional to the number of facings.

Therefore, the coffee shop owner does not have sufficient evidence to conclude that the distribution of sales is proportional to the number of facings at a 5% level of significance.

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Answer:

Refer to the picture above

Therefore , the solution of the given problem of area comes out to be  15 square units.

How much space it occupies on the surface is a reliable indication of its overall dimensions. The nearby surroundings are considered when calculating a triangular shape's surface. Something's total dimensions are determined by its surface area. The total of the capacities for each of a cuboid's six rectangular sides makes up its internal water capacity. To calculate the size of the box, use the following method.

Here,

We must measure the lengths of the sides of the polygon and sum them up to determine its perimeter.

The length of each edge can be determined using the distance formula:

=> CD = √((2 - 2)² + (1 - 4)²) = √(9) = 3

=>  DE = √(7 - 2)² + (4 - 4)²) = 5

=>  EF = √((7 - 7)² + (1 - 4)²) = 3

=>  FC = √(7 - 2)² + (1 - 1)²) = 5

As a result, the boundary is:

CD = DE + EF + EF + FC = 3 + 5 + 3 + 5 = 16

Area of CDE = 1/2*base*height*1/2*DE*CD =1/2*5*3*area of CDE, which equals 7.5.

Area of CEF = 1/2*3*5=7.5

Consequently, the polygon's size is:

Size = CDE + CEF combined, which equals 7.5 + 7.5 = 15 square units.

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To determine the number of miles David drove the truck, we need to subtract the base fee and divide the remaining amount by the additional charge per mile.

Let's denote the number of miles driven by 'm'. The equation can be set up as follows:

$209.57 - $14.99 = $0.94 * m

Simplifying the equation:

$194.58 = $0.94 * m

To solve for 'm', we divide both sides of the equation by $0.94:

m = $194.58 / $0.94

m ≈ 206.7

Therefore, David drove the truck for approximately 206.7 miles. Since it's not possible to drive a fraction of a mile, we can assume that David drove either 206 or 207 miles, depending on the rounding convention used.

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Answer:

b=36

Step-by-step explanation:

by triangle exterior theorem

b+81 = 117

b=36

Answer:

B is 36 degrees, and a is 63 degrees

Step-by-step explanation:

180 - 117 = 63

a = 63 degrees

81 + 63 + b = 180

144 + b = 180

180 - 144 = b

36 degrees = b

Answer:

functions cant have the same x vaule

im not sure which is a "set" since all the numbers are all under the same line

(3,4) (4,5) (5,6) (6,7)  would be function

(1,6) (1,7) (3,4) (2,8) wouldnt be a function because of the 1

Answer:

ofco 1+1=2

Step-by-step explanation:

abc that's why

Answer:

4 , 2, 8, 4 ..............

Answer:

-9 ≤n ≤1

Step-by-step explanation:

-3 ≤ n+6 ≤ 7

Subtract 6 from all sides

-3  -6≤ n+6-6 ≤ 7-6

-9 ≤n ≤1

172.16.0.0/20 is the required network address with a prefix if you need 16 subnets.

Given that,
If you require 16 subnets, your new network address with a prefix should be something different from the old one, which is 172.16.0.0/16. To determine the prefix corresponding to the 16 subnets.

Here,
Original network address with a prefix  = 172.16.0.0/16,
After 16 subnets the address would become,
New network address with the prefix with 16 subnets =  172.16.0.0/20.

172.16.0.0/20 is the required new address with prefix be if you need 16 subnets.

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Answer:

The right answer is D) If graphed, the ordered pairs would form a straight line

Answer:

TUNNEL:

f(x) = -2/4.9  \(x^{2}\)  + 9.8

TRUCK:

Width (m) < 9.8

Height (m) <  -2/4.9 ( \(Width^{2}\) /4 - \(4.9^{2}\) )

Step-by-step explanation:

Please see attachment

If the maximum height of the tunnel is the same as its maximum width, 9.8 meters, The quadratic model to represent the tunnel will be f(x)= (-2/4.9)x²+9.8.

Any function of the form\(\rm f(x) =ax^2+bx+c\) where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic function.

It is given that, If the maximum height of the tunnel is the same as its maximum width, 9.8 meters.

We have to determine a quadratic model to represent the tunnel.

The quadratic function is formed as,

f(x) =K(x-x₁)(x-x₂)

x₁=width/2

x₁=9.8/2 = 4.9

x₂= -x₁ = -4.9

Substitute the obtained value as,

f(x) = K(x-4.9)(x-(-4.9))

f(x) =K(x²-4.9²)

f(0)=9.8

The value of K is obtained as a result,

K=-2×4.9/(4.9)²

K= -2/4.9

Substitute the value of K as,

f(x) = -2/4.9(x²-4.9²)

f(x) = (-2/4.9)x²+2×4.9

f(x)= (-2/4.9)x²+9.8

Thus, if the maximum height of the tunnel is the same as its maximum width, 9.8 meters, The quadratic model to represent the tunnel will be f(x)= (-2/4.9)x²+9.8.

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Answer:

i use logical reasoning

The next number in the sequence could be 870.

To determine the next number in the sequence, let's analyze the differences between consecutive terms:

821 - 814 = 7

825 - 821 = 4

837 - 825 = 12

836 - 837 = -1

853 - 836 = 17

Looking at the differences, we can see that they are not following a clear pattern. Therefore, it is difficult to determine the next number in the sequence based solely on this information.

However, we can make an educated guess by observing the general trend of the sequence. It appears that the numbers are generally increasing, with some occasional fluctuations. Based on this observation, a plausible next number could be one that is slightly higher than the previous term.

Taking this into consideration, we can propose the following options as potential next numbers:

853 + 7 = 860

853 + 17 = 870

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It is given that 339 calories in 3 ounce serving.

So in one ounce serving there will be:

So the unit rate is 113 calories/ounce.

Answer:

2280

Step-by-step explanation:

As in understandable steps,

1512x12 = 18144

18144 / 7

= 2592

2592 - 312

= 2280

An equation is formed of two equal expressions. John's salary before the pay raise is $2280.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the pay of John before the raise be x.

As it is stated that John's pay was increased by $312. And he saves 7/12 of his pay which is equal to $1512. Therefore, the equation that can represent the current saving John has,

\(\dfrac{7}{12}(x+312)=1512\\\\(x+312) = \dfrac{1512 \times 12}{7}\\\\x+312= 2592\\\\x =2592-312\\\\x = 2280\)

Hence, John's salary before the pay raise is $2280.

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So the domain of the vector function r(t)= <√(36 - t²), e⁻³ᵗ, ln(t + 4)> is given by, t ∈ (-4, 6] or - 4 < t ≤ 6.

Now the given vector function is,

r(t)= <√(36 - t²), e⁻³ᵗ, ln(t + 4)>

So now the function exists in real only if when 36 - t² is positive or zero and t + 4 is greater than 0.

So, 36 - t² ≥ 0

t² ≤ 36

- 6 ≤ t ≤ 6 ............. (i)

And when t + 4 > 0

t > -4 .............. (ii)

So combining (i) and (ii) we get,

- 4 < t ≤ 6

So in the set form we can write that,

t ∈ (-4, 6], so it is a semi closed or semi open interval.

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The question is incomplete. The complete question will be -

"Find the domain of the vector function. (Enter your answer using interval notation.)

r(t)= <√(36 - t²), e⁻³ᵗ, ln(t + 4)>"

There is a 19.15% chance that a randomly chosen shoe has a size between 9 and 10.

To respond to this inquiry, we want to work out the likelihood that a haphazardly picked shoe has a size somewhere in the range of 9 and 10. Since the sizes are regularly dispersed with a mean of 9 and a standard deviation of 2, we can utilize the standard typical dissemination to work out this likelihood.

In the first place, we really want to normalize the qualities 9 and 10 utilizing the recipe:

z = (x - μ)/σ

where:

x = the worth we need to normalize (9 or 10 for this situation)

μ = the mean of the dissemination (9 for this situation)

σ = the standard deviation of the circulation (2 for this situation)

z = the normalized esteem

For x = 9:

z = (9 - 9)/2 = 0

For x = 10:

z = (10 - 9)/2 = 0.5

Presently, we want to find the likelihood that a haphazardly picked shoe has a size somewhere in the range of 9 and 10, which is comparable to finding the region under the standard typical dissemination bend between z = 0 and z = 0.5.

Utilizing a standard typical circulation table or a number cruncher, we can find that the likelihood of a haphazardly picked shoe having a size somewhere in the range of 9 and 10 is roughly 0.1915 or 19.15%.

Hence, there is a 19.15% opportunity that a haphazardly picked shoe has a size somewhere in the range of 9 and 10.

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The equation for split times is 4x= 198.608  and the value of x is 49.652

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

Let x be the split time

all 4 of the split times were the same.

4x= 198.608

=> x= 198.608/4 = 49.652

The equation for split times is 4x= 198.608  and the value of x is 49.652

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Answer:

B?

Step-by-step explanation: