Estimate 17.140 - 03.179 by first rounding each number to the nearest tenth.

The perimeter of the given shape as represented in the task content is; 29 cm.

It follows from the task content that the perimeter of the given shape on the centimeter grid as required is to be determined.

Since each grid line has 1cm as it's length;

The perimeter of the shape is the sum of all side lengths of the shape;

Perimeter, P = 6+2+3+2+2+1+3+2+2+2+2+1

P = 29 cm

Hence, the perimeter of the shape is; 29 cm.

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The expression of "The difference of -10 and the product of p and q" in algebraic notation is pq + 10

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

The difference of -10 and the product of p and q

The numbers are given as

p and q

The product of p and q means pq

So, we have the following

The difference of -10 and pq

The difference of -10 and pq means

pq + 10

Hence, the expression is pq + 10

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For Serenity's lemonade recipe, the lemons being used per cup of lemonade is 0.8

Ratio is a comparison of two quantities that are expressed in relation to each other. Ratios are typically expressed in the form of a fraction, with the numerator representing one quantity and the denominator representing the other quantity.

To find the rate at which lemons are being used in lemons per cup of lemonade, we need to calculate the ratio of lemons used to cups of lemonade.

According to the recipe, 4 lemons are required to make 5 cups of lemonade. So the rate of lemons used is:

4 lemons / 5 cups = 0.8 lemons per cup of lemonade

This means that for every cup of lemonade, 0.8 lemons are used.

Alternatively, we can also express this rate as a fraction, which gives us:

0.8 lemons / 1 cup of lemonade

Either way, the rate of lemons used is 0.8 lemons per cup of lemonade.

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Answer:

The scientific notation:11,200×10^1

1,120×10^2

112×10^3

11.2×10^4

1.12×10^5

0.112×10^6

Step-by-step explanation:

PLS MARK BRAINLIEST

Answer:

Step-by-step explanation:

To factor the expression 4x^2 - 25, we can use the difference of squares formula, which states that a^2 - b^2 can be factored as (a + b)(a - b).

In this case, we have 4x^2 - 25, which can be written as (2x)^2 - 5^2. Comparing it with the difference of squares formula, we can identify that a = 2x and b = 5. Therefore, the correct option is:

b. (2x)^2 - (5)^2

Using the difference of squares formula, we can factor it as follows:

(2x + 5)(2x - 5)

Hence, the correct factorization of 4x^2 - 25 is (2x + 5)(2x - 5), which is equivalent to option b.

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We conclude that after 7/4 years the value of the jet ski is $4,784

The value of the jet ski is given by the exponential equation:

f(t) = 8,500*(0.72)^t

Where t is the time in years, to get the value of the jet ski after 7/4 years, we just need to evaluate the above function in t = 7/4, where evaluating means that we need to replace the variable t by the given number, then we will get:

f(7/4) = 8,500*(0.72)^(7/4) = 4,783.55

If now we need to round it to the nearest dollar, then we round upwards to 4,784

In this way, we conclude that after 7/4 years the value of the jet ski is $4,784

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Answer:

720 cherries

Step-by-step explanation:

3 pies need 240 cherries so the equation would be:

3c = 240

so, c = 80

But, he needs to make 9 "perfect" pies so you make the equation:

9c = 80*9

9c = 720

So Greg needs 720 cherries to make 9 perfect cherry pies.

The location of point A''' after the three transformations would be (-4, 1).

To determine the location of point A''', we need to apply the three transformations (reflection over the y-axis, reflection over the x-axis, and rotation of 180°) to point A.

When a point is reflected over the y-axis, the x-coordinate is negated while the y-coordinate remains the same.

So, the reflection of point A (-4, 1) over the y-axis would be (4, 1).

When a point is reflected over the x-axis, the y-coordinate is negated while the x-coordinate remains the same. So, the reflection of point (4, 1) over the x-axis would be (4, -1).

When a point is rotated 180°, the x-coordinate and y-coordinate are both negated. So, the rotation of point (4, -1) by 180° would be (-4, 1).

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Therefore, if 24 teaspoons of vegetable oil were used, we would need 16 teaspoons of vinegar to make the recipe correctly.

According to a salad recipe, each serving requires 6 teaspoons of vegetable oil and 9 teaspoons of vinegar. If 24 teaspoons of vegetable oil were used, we can determine the amount of vinegar needed for the recipe to be correct as follows:

First, we must determine the ratio of vinegar to oil in the recipe. To do this, we divide the amount of vinegar needed per serving (9 teaspoons) by the amount of oil needed per serving (6 teaspoons):

9 ÷ 6 = 1.5

This means that for every 1.5 teaspoons of oil used, we need 1 teaspoon of vinegar. Next, we use this ratio to determine the amount of vinegar needed when 24 teaspoons of oil are used:

1.5 ÷ 1 = 1.5

(teaspoons of oil per 1 teaspoon of vinegar)

24 ÷ 1.5 = 16

(teaspoons of vinegar needed)

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Answer:

Yes

Step-by-step explanation:

If you plug in the numbers if will prove to be right.

The equivalent matrix of the matrix operations can be given by \(\left[\begin{array}{ccc}35&14\\-70&42\end{array}\right]\).

Matrix operations are fundamental mathematical operations performed on matrices, which are rectangular arrays of numbers or symbols arranged in rows and columns. Matrix operation includes addition, subtraction, scalar multiplication, matrix multiplication, transposition, determinant, inverse, etc.

Given matrices are written below:

\(A=\left[\begin{array}{ccc}1&5\\-5&3\end{array}\right]\) and \(B=\left[\begin{array}{ccc}4&-3\\-5&3\end{array}\right]\).

Given matrices operation to be performed: \(7(A)+7(B)\).

\(7(A)+7(B)=7\left[\begin{array}{ccc}1&5\\-5&3\end{array}\right] +7\left[\begin{array}{ccc}4&-3\\-5&3\end{array}\right]\)

First, perform the scalar multiplication. Multiply both matrices by the scalar \(7\).

\(\Rightarrow7(A)+7(B)=\left[\begin{array}{ccc}(1\times7)&(5\times7)\\(-5\times7)&(3\times7)\end{array}\right] +\left[\begin{array}{ccc}(4\times7)&(-3\times7)\\(-5\times7)&(3\times7)\end{array}\right]\\\Rightarrow7(A)+7(B)=\left[\begin{array}{ccc}7&35\\-35&21\end{array}\right] +\left[\begin{array}{ccc}28&-21\\-35&21\end{array}\right]\\\)

Now, perform the addition of two matrices.

\(\Rightarrow7(A)+7(B)=\left[\begin{array}{ccc}(7+28)&(35-21)\\(-35-35)&(21+21)\end{array}\right]\\\Rightarrow7(A)+7(B)=\left[\begin{array}{ccc}35&14\\-70&42\end{array}\right]\\\)

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Answer:

1-2x

Step-by-step explanation:

\((7+2x)-(4x+6)=7+2x-4x-6=1-2x\)

1. The states of the Markov chain are the number of consecutive tails at the end of the sequence, where 0 means ending in heads, 1 means ending in tails, 2 means ending in H-T, and 3 means ending in H-T-H.

2. The one-step transition probability matrix is,

P = [ 0.5  0.5  0 ]

   [ 0.5  0   0.5 ]

   [ 1    0    0   ]

3. The average number of trials needed for the HTH pattern to appear is 4/3.

Let's define the following states,

State 1: The most recent flip was T (tail).

State 2: The most recent flip was H (head), but the previous flip was T.

State 3: The most recent flips were HT (head followed by tail), but the previous flip was H and we are still waiting for the third flip to be H.

Note that if we reach state 3, we have successfully achieved the HTH pattern.

Thus, the one-step transition probability matrix for this Markov chain is:

P = [ 0.5  0.5  0 ]

   [ 0.5  0   0.5 ]

   [ 1    0    0   ]

Let F be the fundamental matrix, defined as F = (I-Q)^(-1), where Q is the submatrix of P obtained by removing the rows and columns corresponding to the absorbing state (in this case, state 3). Then, the (i,j)-th entry of F gives the expected number of times the process is in state j, given that it started in state i.

In our case, the fundamental matrix is,

Q = [ 0.5  0.5 ]

     [ 0.5    0  ]

F = (I-Q)^(-1) = [ 4/3  2/3 ]

                      [ 2/3  4/3 ]

The average number of trials needed for the HTH pattern to appear, starting from state 1, is therefore F(1,3) = 4/3. This means that we can expect to see the HTH pattern after an average of 4/3 coin tosses.

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you have the following equation:

3x - 2 = 2(x+1)

You have to specify the property used in each step to get the solution of the previous equation. You obtain the following:

1. 3x - 2 = 2(x + 1) given

2. 3x - 2 = 2x + 2 distribution prop

3. 3x - 2x - 2 = 2x - 2x + 2 subtraction 2x both sides - subtraction prop

x - 2 = 2

4. x - 2 + 2 = 2 + 2 summation 2 both sides - addition prop

x = 4

The steps Sergey could use to solve the quadratic equation by completing the square is 5(x2 + 4x) = –7

We should know that in completing the square method both sides of the equation are made perfect squares.

The given equation is 5x²+20x-7=0

Solving this equation by completing the square method we have

5(x²+4x+4)=-7

This means that (x+2)=±√27/5

Simplifying further we have

5(x²+4x)=7

Then expanding to make ²HS a perfect square we have

5(x²+4x+4)=7+20

This means that 5(x²+4x)=-7

Therefore the step he could use is 5(x²+4x)=-7\

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Answer:

3.52

Step-by-step explanation:

Calculation to Find the mean for the random variable X

Using this formula

Mean(μ) =(n*p)

Where,

n=16

p=22% or 0.22

Let plug in the formula

Mean(μ)=16×0.22

Mean(μ)=3.52

Therefore the mean for the random variable X will be 3.52

Answer:

Upper left 10, upper right 2, lower left 3, lower right 3.

Step-by-step explanation:

they give us the upper left and lower right in the first two bullet points. Then “in total, 12 girls can sing”. 12 - the 10 who can sing and dance = 2 for upper right.

They also say there are 18 girls total. 18 - 10 - 3 = 3 for the lower left

The probability density function for U is: f_U(u) = (4/(1+u)^3) * e^-(1+u)/2, u > 0

The joint distribution for the length of life of two different types of components operating in a system is given by f(y_1, y_2) = {(1/8)y_1 e^-(y_1 + y_2)/2, y_1 > 0, y_2 > 0, 0, elsewhere. We are asked to find the probability density function for U = Y_2/Y_1.

To find the probability density function for U, we first need to find the joint distribution of U and Y_1. We can do this by using the change of variables formula:

f_U,Y_1(u, y_1) = f_Y_1,Y_2(y_1, uy_1) * |J|

where J is the Jacobian determinant of the transformation.

The Jacobian determinant is given by:

J = |∂(y_1, uy_1)/∂(u, y_1)| = |y_1|

So, the joint distribution of U and Y_1 is:

f_U,Y_1(u, y_1) = (1/8)y_1 e^-(y_1 + uy_1)/2 * |y_1| = (1/8)y_1^2 e^-(1+u)y_1/2

Next, we need to find the marginal distribution of U by integrating out Y_1:

f_U(u) = ∫f_U,Y_1(u, y_1) dy_1 = (1/8)∫y_1^2 e^-(1+u)y_1/2 dy_1

This integral can be solved using integration by parts. The final result is:

f_U(u) = (4/(1+u)^3) * e^-(1+u)/2

So, the probability density function for U is:

f_U(u) = (4/(1+u)^3) * e^-(1+u)/2, u > 0

This is the final answer.

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The value of m ∠ABC=86° ,because of the cyclic quadrilaterals.

Hence, Option (B) is correct.

Since, We know that,

A cyclic quadrilateral is a four-sided polygon whose vertices all lie on a common circle.

The opposite angles of a cyclic quadrilateral have a total of 180°.

Hence, We can formulate;

m ∠ABC +  m ∠ADC  = 180°

m ∠ABC + 94° = 180°

m ∠ABC = 180° - 94°

m ∠ABC = 86°

Similarly, one can find m∠DCB

m∠DAB +  m∠DCB  = 180°

99° + m∠DCB = 180°

m∠DCB = 180° - 99°

m∠DCB = 81°

Hence, m∠ABC = 86°

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Answer:

<A =73

Step-by-step explanation:

The sum of the angles of a triangle are 180

<C is 90

<B is 17

We need to find <A

<A + < B + <C = 180

<A + 17+90 = 180

<A + 107 =180

<A = 180-107

<A =73

There are 9 CD's can she place on a shelf.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Each shelf is 28 inches long and each CD is 1 3/ inch thick.

Now,

Since, Each shelf is 28 inches long and each CD is 1 3/ inch thick.

Hence, The number of CD's = 28 x 1/3

                                            = 9.33

                                            = 9

Thus, There are 9 CD's can she place on a shelf.

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Answer:

x≥88

88

88≤x≤100

Step-by-step explanation:

83x3=249

249-73-88=88

x≥88

88

88≤x≤100

Answer:The coefficients are the numbers that multiply the variables or letters. Thus in 5x + y - 7, 5 is a coefficient. It is the coefficient in the term 5x. Also the term y can be thought of as 1y so 1 is also a coefficient.A number used to multiply a variable. Example: 6z means 6 times z, and "z" is a variable, so 6 is a coefficient. Variables with no number have a coefficient of 1. ... Example: In ax2 + bx + c, "x" is a variable, and "a" and "b" are coefficients.First of all, coefficent means the number standing in front of a variable.

So, according to the expression, 2 - 5x - 4 + 8, the coefficient is -5.

Why? because it stands in front of the variable.

Step-by-step explanation:

The length of side X in simple radical form with a rational denominator is 25/√3.

In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the side lengths are in the ratio 1:√3:2.

This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side):

Adjacent side = 5/√3

Hypotenuse, x = 5 × 5/√3

Hypotenuse, x = 25/√3.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.