Find the surface area of the rectangular prism.
8 yd
1 yd
3 yd

Answer:

x = gym memberships, and y = bottles of water

30x + 7y = 1050.....when x = 28

30(28) + 7y = 1050

840 + 7y = 1050

7y = 1050 - 840

7y = 210

y = 210/7

y = 30....so he would have to sell 30 water bottles

Step-by-step explanation:

Answer:

1188=35m+9w

Step-by-step explanation:

Check the picture below.

so let's simply get the volume of the sphere, then the volume of the prism, and then subtract the one from the sphere from that of the prism, and what's leftover, is the volume not occupied by the sphere, voila!!

\(\stackrel{\textit{\LARGE volumes}}{\stackrel{rectangular~prism}{(20)(15)(18)}~~ - ~~\stackrel{sphere}{\cfrac{4\pi (7)^3}{3}}}\implies 5400-\cfrac{1372\pi }{3} ~~ {\LARGE \begin{array}{llll} \approx ~~ 3963.24~in^3 \end{array}}\)

There were 17 students in the group, and each student paid the same whole number of dollars for the concert tickets.

To determine the number of students in the group, we need to find a whole number that is greater than 2 and less than 20, and when multiplied by another whole number, results in a product of $391.
First, let's list some factors of 391:
1 x 391 = 391
17 x 23 = 391

Since we are looking for a number of students, we can eliminate the factorization of 1 x 391 because that would mean there is only one student in the group, which contradicts the condition in the question.
Now, let's consider the factorization of 17 x 23. In this case, the number of students in the group would be the smaller factor, which is 17. Therefore, there were 17 students in the group.
To summarize, there were 17 students in the group, and each student paid the same whole number of dollars for the concert tickets.

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Answer:

c

Step-by-step explanation:

this is the closer to the number 7 on a number line

Standard error of the mean is 0.05267 in (a). The actual mean degradation rate has a 90% probability of being between 0.978 and 1.174 micromoles/minute/gram, according to (b).

The group mean's likelihood to vary from a sampling distribution is indicated by the standard deviation of a mean, or merely standard error. It reveals how much is the sample imply would change if a research were to be repeated with fresh samples drawn from a particular population.

(a)

Sample size, n = 9

Sample standard deviation, S = 0.158

Standard error of the mean,

\(\sigma_{\bar{x}}=\frac{S}{\sqrt{n}}=\frac{0.158}{\sqrt{9}}=0.05267\)

(b)

Since we do not know the distribution of the parent population or the population standard deviation, and further the sample size, n = 8 < 30,

Therefore we will use the t-distribution to construct the confidence interval for the true population mean α

Sample size, n = 9

Sample mean, r  = 1.076

Sample standard deviation, S = 0.158

Standard error of the mean,

\(\sigma_{\bar{x}}=\frac{S}{\sqrt{n}}=\frac{0.158}{\sqrt{9}}=0.05267\)

Level of confidence, c (in percentage) = 90

α = (1-(c/100) = 0.1

Degrees of freedom, df = n-1 = 9 - 1 = 8

The critical t-score, \(\mathrm{t}_{\mathrm{c}}\) is the

t-score corresponds to the given level of confidence and degrees of freedom :

\(\begin{aligned}& P\left(x > t_{d f}\right)=\Rightarrow / 2 \\& \Rightarrow \\& P\left(x > t_8\right)=0.1 / 2=0.05 \\& \Rightarrow t_c=1.86\end{aligned}\)

The confidence interval is calculated as:

\(\mathrm{Cl}=\bar{x} \pm\left(\mathrm{t}_{\mathrm{c}}\right)^*\left(\sigma_{\bar{x}}\right)\)

= 1.076 ± (1.86)*(0.05267)

= 1.076±  0.098

= (1.076 - 0.098, 1.076 + 0.098)

= (0.978, 1.174)

The actual mean degradation rate has a 90% probability of being between 0.978 and 1.174 micromoles/minute/gram, according to this information.

The mean degradation rate must be higher than 1 for the process to be cost-effective.

However, because the 90% confidence interval does not completely fall above 1, the experts cannot be certain that the process will be cost-effective.

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Answer:

Para encontrar a taxa trimestral equivalente à taxa de 1,05% ao mês, basta dividir a taxa mensal por 3, pois um trimestre é composto por 3 meses. Portanto, a taxa trimestral equivalente à taxa de 1,05% ao mês é de 1,05% / 3 = 0,35%.

Para encontrar a taxa anual equivalente à taxa de 1,05% ao mês, basta multiplicar a taxa mensal por 12, pois um ano é composto por 12 meses. Portanto, a taxa anual equivalente à taxa de 1,05% ao mês é de 1,05% x 12 = 12,6%.

2)a) Para calcular a taxa de juros compostos equivalente a uma taxa efetiva de 1% ao mês ao semestre, basta multiplicar a taxa mensal por 6, pois um semestre é composto por 6 meses. Portanto, a taxa de juros compostos equivalente a uma taxa efetiva de 1% ao mês ao semestre é de 1% x 6 = 6%.

b) Para calcular a taxa de juros compostos equivalente a uma taxa efetiva de 1% ao mês ao ano, basta multiplicar a taxa mensal por 12, pois um ano é composto por 12 meses. Portanto, a taxa de juros compostos equivalente a uma taxa efetiva de 1% ao mês ao ano é de 1% x 12 = 12%.

Answer:

D, X^2 -18 + 81 = -45 + 81

Step-by-step explanation:

it is complating squer method that used for solving x in a quadratic equetion . in this step you will add

(y/2)^2 if y is the cofitient of x .

Answer:

m = 1/2

Step-by-step explanation:

Look at the points on the graph and determine what the slope would be using the slope formula. y2-y1 / x2-x1.

2 - 0 / 0 - (-4)

2/4

1/2

Answer:

the slope of the line is 2

Step-by-step explanation:

use the formula for the slope of a line: y2-y1/x2-x1

this will give you 2-0/0-(-4) = 2/4

simplified to 2 for the slope.

if the answer you need is just the slope ten it would be 2

if you're looking for the equation of the line it would be y=2x+2

a. two critical points are (0,0) and (-2, -4). b. H has two positive eigenvalues, and (-2,-4) is a local minimum of f(x,y).

(a) To find the critical points of f(x,y), we need to find the partial derivatives of f(x,y) with respect to x and y, and then set them equal to zero.

∂f/∂x = 4x^3 - 8y

∂f/∂y = 4y - 8x

Setting these partial derivatives equal to zero and solving for x and y, we get:

4x^3 - 8y = 0 => y = x^3/2

4y - 8x = 0 => y = 2x

Substituting y = 2x into y = x^3/2, we get:

2x = x^3/2 => x(x^2 - 4) = 0

So we have two critical points: (0,0) and (-2, -4).

(b) To classify the critical points, we need to use the second partial derivative test. The Hessian matrix of f(x,y) is:

H = [12x^2 -8 -8-8 4 0-8 0 0]

At (0,0), we have H = [-8 -8; -8 4], which has determinant (-8)(4)-(-8)(-8) = 0 and trace -4. Since the determinant is zero, we cannot use the second partial derivative test at (0,0). Instead, we can observe that f(0,0) = 0, and f(x,y) is positive for all (x,y) not equal to (0,0). Therefore, (0,0) is a saddle point. At (-2,-4), we have H = [44 -8; -8 0], which has determinant (44)(0)-(-8)(-8) = 64 > 0 and trace 44 > 0. Therefore, H has two positive eigenvalues, and (-2,-4) is a local minimum of f(x,y).

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The solution is Option D.

The sum of the arithmetic sequence is 5,490

What is Arithmetic Progression?

An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"

The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁

Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]

Given data ,

Let the sum of the arithmetic progression be represented as S

Now , the number of terms n = 60

Let the first term be a₁ = 3n , when n = 1

a₁ = 3

Now , the second term a₂ = 3n , when n = 2

a₂ = 6

So , the common difference of the arithmetic sequence d = second term - first term

d = 6 - 3

d = 3

Now , the sum of the first n terms of the sequence is

Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]

Substituting the values in the equation , we get

S₆₀ = ( 60/2 ) [ 2 ( 3 ) + ( 60 - 1 ) ( 3 ) ]

On simplifying the equation , we get

S₆₀ = 30 [ 6 + 59 ( 3 ) ]

S₆₀ = 30 [ 6 + 177 ]

S₆₀ = 30 ( 183 )

S₆₀ = 5490

Therefore , the value of S is 5,490

Hence , the sum of the arithmetic sequence is 5,490

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Answer:

\(\frac{3}{5} *\frac{10}{7}\)  

=  \(\frac{30}{35} =\frac{6}{7}\)

The product of 2^2007 and 5^2011​ is given as follows:

2^2007 x 5^2011​.

When two numbers with the same base and different exponents are multiplied, we keep the base and add the exponents.

The product for this problem is defined as follows:

2^2007 x 5^2011​.

2 and 5 are both prime numbers, hence they cannot be factored into common bases, hence the expression is already simplified.

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Answer: Michaela has 16 Dimes, and 9 Nickels.

1) The rule of transformation is described as; A: A rotation 90° clockwise about the origin

2) The value of x is; 2

3) The value of x is 10

4) The slope of the line is; 2

1) The rule of transformation for When the point M (h, k) is rotated through 90° clockwise about the origin, the point M (h, k) takes the image M' (k, -h). Thus, that is the rule here.

2) From the given image, we can tell that the angles 50° and 26x - 2 are corresponding angles. Thus, they are congruent and we have;

26x - 2 = 50

26x = 52

x = 2

3) From the given image, we can see that the given angles are supplementary and as such they add up to 180 degrees. Thus;

9x + 15 + 6x + 15 = 180

15x + 30 = 180

15x = 150

x = 10

4) Slope is;

m = (y2 - y1)/(x2 - x1)

m = (1 - (-3))/(1 - (-1))

m = 4/2

m = 2

5) Same question as the first one.

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The equation AB=BC for \(A=BCB^{-1}\).

The solution of AB = BC  for A, assuming that A,B and C are square matrices and B is invertible is

We have to solve the equation

AB = BC given that these all are square matrices and B is invertible.

Write the required Equation:

Multiply both sides by inverse of B

The multiplicative inverse of a matrix is the matrix that gives you the identity matrix when multiplied by the original matrix.

⇒\(ABB^{-1} =BCB^{-1}\)

⇒\(AI=BCB^{-1}\)

⇒\(A=BCB^{-1}\)

Therefore, the solution of AB = BC is \(A=BCB^{-1}\).

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Answer: -5,-1

Step-by-step explanation:

Answer:

-5,-1

Step-by-step explanation:

Mike is 40 years old now.

Let Al's age be x years. According to the problem statement,

Al was 2 years old 8 years ago.

Therefore, Al's present age is:x + 8 years

Now, Mike is 4 times older than Al. That is, the age of Mike is 4(x + 8) years.

Mike is now 4 times older than Al, if Al was 2 years old 8 years ago, then Mike is 36 years old now.

In order to verify the solution, you can use a direct method of substitution.

If Al's present age is x + 8, then his age 8 years ago was x + 8 - 8 = x.

Since Al was 2 years old 8 years ago, we have:x = 2

Therefore, Al's present age is:x + 8 = 2 + 8 = 10 years

Now, Mike is 4 times older than Al.

Therefore, Mike's age is 4 × 10 = 40 years.

This is consistent with the original statement that "Mike is now 4 times older than Al if Al was 2 years old 8 years ago".Therefore, Mike is 40 years old now.

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Answer:

I believe the answer is A. 4

Step-by-step explanation:

if you make a table starting with $250 and + $25 every month when you get to the 4th month Josiah has only $325 and Katie has $335. I hope this helps.

Answer:

40%

Step-by-step explanation:

brainliest please

Answer:

D: 40%

Step-by-step explanation:

total: 15

apples: 6

6 out of the 15 fruits are apples

6/15 = 40%

I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!

The cartesian equation of the curve \(r=2 \hspace{0.1cm} csc \hspace{0.1cm} \theta\) is \(y=2\).

A Cartesian equation is essential in mathematics. It corresponds to a mathematical formula that expresses the connection between elements as a function of their positions on a plane known as Cartesian.

A two-dimensional coordinate scheme called the Cartesian plane employs a horizontal x-axis and an upward y-axis to identify locations in space.

Given that, \(r=2 \hspace{0.1cm} csc \hspace{0.1cm} \theta\).

So, \(csc\hspace{0.1cm}\theta=cosec \hspace{0.1cm}\theta\).

The equation becomes as follows:

\(r=2cosec\hspace{0.1cm} \theta\)

By using the trigonometric equation \(cosec\hspace{0.1cm} \theta=\frac{1}{sin\hspace{0.1cm}\theta}\), we get

\(r= \frac{2}{sin \hspace{0.1cm} \theta}\)

Multiplying both sides by \(sin\hspace{0.1cm}\theta\), we get

\(r \hspace{0.1cm}sin\hspace{0.1cm}\theta =2\hspace{0.1cm}\frac{sin\hspace{0.1cm}\theta}{sin\hspace{0.1cm}\theta}\)

\(rsin\hspace{0.1cm}\theta=2\)

By the parametric equations \(x=rcos\hspace{0.1cm}\theta\) and \(y=rsin\hspace{0.1cm}\theta\), we get

\(y=2\)

It is a horizantal line.

Hence, the cartesian equation of the curve \(r=2 \hspace{0.1cm} csc \hspace{0.1cm} \theta\) is \(y=2\).

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The cartesian equation for the curve is: y = 2 This is a horizontal line passing through the point (0,2).

To find a Cartesian equation for the curve given by the polar equation r = 2 csc(θ), we will convert the polar coordinates (r, θ) into Cartesian coordinates (x, y) using the following relationships:

x = r * cos(θ)
y = r * sin(θ)

Step 1: Express r in terms of θ
r = 2 csc(θ)

Step 2: Since csc(θ) = 1 / sin(θ), rewrite the equation as
r = 2 / sin(θ)

Step 3: Express x and y in terms of r and θ
x = r * cos(θ)
y = r * sin(θ)

Step 4: Substitute r from Step 2 into the y equation
y = (2 / sin(θ)) * sin(θ)

Step 5: Simplify the equation
y = 2

The Cartesian equation for the given polar equation is y = 2, which represents a horizontal line passing through the point (0, 2).

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Answer:

435 is the answer

Step-by-step explanation:

well first you can cut it up

9x7=63

than    8x15=120

than for the trangle

you do  24x 21= 504 than you do 504/2=252

than add all of them =435

The average temperature change per hour was -2.708 degrees Fahrenheit.

To calculate the average temperature change per hour, we need to find the total temperature change over the 24-hour period and then divide by the number of hours.

The total temperature change is the difference between the starting temperature (41 degrees Fahrenheit) and the ending temperature (-13 degrees Fahrenheit), which is -54 degrees Fahrenheit.

Dividing the total temperature change by the number of hours, we get:

-54 degrees Fahrenheit / 24 hours = -2.25 degrees Fahrenheit per hour.

Rounding to three decimal places, we get an average temperature change per hour of -2.708 degrees Fahrenheit per hour.

The complete question is: In January 2008, the temperature in parts of Minnesota fell from 41∘41∘F to −13∘-13∘F over a 24-hour period. What was the average temperature change per hour?

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That's a pound sterling, and it's actually worth $1.32!

£650, is $873.23.

$405, is £301.47.

Answer:

-11

Step-by-step explanation:

Add all the negative numbers.

Hope this helps!

Answer:

-11

Step-by-step explanation:

-3 + -1 = -4

-4 + -5 = -9

-9 + -2 = -11

§(*￣▽￣*)§

I tried and good luck xx

Answer:

The answer is

\( \sqrt{65} \: \: \: units\)

Step-by-step explanation:

To find the distance between two points we use the formula

\( \sqrt{ ({x1 - x2})^{2} + ( {y1 - y2})^{2} } \)

where

( x1 , y1) and ( x2 , y2) are the points

From the question the points were

(-8,5), (-1.1)

Substitute the values into the above formula

That's

\( \sqrt{ ({ - 8 + 1})^{2} + ({5 - 1})^{2} } \)

\( \sqrt{ ({ - 7})^{2} + {4}^{2} } \)

\( \sqrt{49 + 16} \)

We have the final answer as

\( \sqrt{65} \: \: units\)

Hope this helps you

The value of x or length of FD int the figure is  75.

image attached below,

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

In a right triangle, the hypotenuse is the longest side, an "opposite" side is the one across from a given angle, and an "adjacent" side is next to a given angle.

This is similarities in sides questions. To solve make equation.

JY = 42

JS = 42 + 63 = 105

JD = 50

JF = 50 + x

Using the sides,

52/105 = 50/50+x

(42)(50+x) = (50)(105)

2100 + 42x = 5250

42x = 5250 - 2100

42x = 3150

x = 3150/42

x = 75.

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The value of the digit 5 in the tenths place of 3.545 is 100 times the value of the digit 5 in the thousandths place.

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

We have:

Evan has a bag of apples that weighs 3.545 pounds.

The value of the digit 5 in the tenths place of 3.545 is 0.500

The value of the digit 5 in the thousandths place of 3.545 is  0.005

Take the ratio of both values:

tenths place value/thousandths place value =  0.500/0.005

tenths place value/thousandths place value =  100

tenths place value = 100(thousandths place value)

Thus, the value of the digit 5 in the tenths place of 3.545 is 100 times the value of the digit 5 in the thousandths place.

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True. If v is an eigenvector corresponding to the eigenvalue λ, then multiplying v by a scalar c, denoted as cv, will also be an eigenvector corresponding to the same eigenvalue λ.

An eigenvector represents a direction in a vector space that remains unchanged, except for scaling, when multiplied by a specific matrix. The corresponding eigenvalue determines the magnitude of the scaling. When we multiply an eigenvector v by a scalar c, the direction of the vector remains the same, and the resulting vector cv is scaled by the same factor c.

Mathematically, if Av = λv, where A is a matrix, λ is an eigenvalue, and v is the corresponding eigenvector, then it follows that A(cv) = cAv = cλv = λ(cv). This equation shows that multiplying an eigenvector v by a scalar c preserves its status as an eigenvector, corresponding to the same eigenvalue λ.

In summary, if v is an eigenvector corresponding to λ, then multiplying it by a scalar c still results in an eigenvector corresponding to the same eigenvalue λ.

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