6(4.5y – 12) = 9 can someone help me anwser this please

Answer:

C. The functions have the same y-intercept

Step-by-step explanation:

In slope intercept form, y = mx + b, b represents the y-intercept, and in the first function the y-intercept is 10.

The y-intercept is when x = 0, and in the chart, when x equals 0, y equals 10.

10 = 10, so they have the same y-intercept.

The area of the quilt is 1127/20 square feet. This can also be written as a mixed number, which would be 56 7/20 square feet.

To find the area of the quilt, we need to multiply the width by the length. Let's calculate it step by step:

Width: 9 4/5 ft. We can convert the mixed number to an improper fraction by multiplying the whole number (9) by the denominator (5) and adding the numerator (4). Then we divide the result by the denominator.

9 * 5 = 45. 45 + 4 = 49.

So, the width is 49/5 ft.

Length: 5 3/4 ft. We can convert the mixed number to an improper fraction using the same method.

5 * 4 = 20. 20 + 3 = 23.

So, the length is 23/4 ft.

Now, we can calculate the area:

Area = Width * Length.

Area = (49/5 ft) * (23/4 ft).

To multiply fractions, we multiply the numerators together and the denominators together:

Area = (49 * 23) / (5 * 4) ft².

Area = 1127/20 ft².

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Answer:

It’s A

Step-by-step explanation:

I think

The three vectors that form an orthonormal basis for R3 are:

u = (0.6, -0.8, 0)
v = (1, 0, 0)
w = (0, 0, 0.6)

To find the missing coordinates such that the three vectors form an orthonormal basis for R3, we need to use the concept of coordinates, vectors, and orthonormality.

First, let's define the three vectors as u = (0.6, -0.8, 0), v = (1, 0, 0), and w = (0, 0, 0.6).

To form an orthonormal basis for R3, the three vectors need to be orthogonal to each other and have a magnitude of 1.

Orthogonality means that the dot product of any two vectors is 0. So we need to find the missing coordinates of w such that:

u • v = 0
u • w = 0
v • w = 0

Since u and v are already orthogonal to each other, we only need to find the missing coordinates of w such that it is orthogonal to both u and v.

Let's start with u • w = 0:

0.6 * 0 + (-0.8) * 0 + 0 * 0.6 = 0

This equation is already satisfied, so we don't need to find any missing coordinates for w in relation to u.

Now let's look at v • w = 0:

1 * 0 + 0 * 0 + 0 * 0.6 = 0

Again, this equation is already satisfied, so we don't need to find any missing coordinates for w in relation to v.

Since both equations are satisfied, the missing coordinates of w are (0, 0).

Therefore, the three vectors that form an orthonormal basis for R3 are:

u = (0.6, -0.8, 0)
v = (1, 0, 0)
w = (0, 0, 0.6)

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Answer:

The probability that the outcome of the roll is an even sum or a sum that is a multiple of 3

P( E∪F)  \(= \frac{24}{36}\)

Step-by-step explanation:

Given Each number cube has sides numbered 1 through 6

Two distinct number cubes are rolled together

Total number of exhaustive cases n(S) = 36

Let 'E' be the event of getting sum is even

n(E) = {(1,3),(1,5), (2,2),(2,4),(2,6),(3,1),(3,3),(3,5),(4,2),(4,4), (4,6),(5,1),(5,3),(5,5),(6,2),(6,4),(6,6)} = 17

\(P(E) = \frac{n(E)}{n(S)} = \frac{17}{36}\)

Let 'F' be the event of getting sum that is a multiple of '3'

n(F) = {(1,2),(1,5),(2,1),(2,4),(3,3),(3,6),(4,2),(4,5),(5,1),(5,4),(6,3),(6,6) = 12

\(P(F) = \frac{n(E)}{n(S)} = \frac{12}{36}\)

n((E∩F) = {(2,4),(3,3),((4,2),(5,1),(6,6)} =5

\(P(En F) = \frac{n(En F)}{n(S)} = \frac{5}{36}\)

The probability that the outcome of the roll is an even sum or a sum that is a multiple of 3

P( E∪F) = P(E) + P(F) - P( E∩F)

            \(\frac{17}{36} +\frac{12}{36} - \frac{5}{36} = \frac{24}{36}\)

Answer:

D

Step-by-step explanation:

Just took the quiz

The confidence interval that  would produce the widest interval when estimating the mean of a population should be 83%.

It refers to the range of values where the sample should be watched also in this the value should be determined that correctly represent the population.

Also, the more the confidence interval the more should be the widest interval.

Therefore, the last option is correct.

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The equation that is parallel to y = -3x + 7 and passes through the point (2, -1) is y=-3x+5.

The slope intercept form in math is one of the forms used to calculate the equation of a straight line, given the slope of the line and intercept it forms with the y-axis.

y=mx+b

where m is the slope of the line and b is the y intercept.

The slope of the given equation,

y=-3x+7 is -3.

So, to write an equation parallel to the given equation and set of points, use point slope form and the slope of -3

y-y₁=m(x-x₁)

where (2,-1)  are x₁, y₁

y-(-1)=-3(x-2)

y+1=-3(x-2)

Multiply with 3 on RHS side

y+1=-3x+6

We have to write in slope intercept form, so shift 1 to RHS.

y=-3x+6-1

y=-3x+5

As you can see, the slope of this line is -3

, which means that the two equations are parallel to each other.

Hence y=-3x+5 is the equation that is parallel to y = -3x + 7 and passes through the point (2, -1).

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Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following. For \(0 ≤ x ≤ 2, F(1) = (1^3/12) = 0.0833.So, P(X ≤ 1) = 0.0833.\) Hence, the correct option is (a) P(X ≤ 1).

Given that X denotes the amount of time a book on two-hour reserve is actually checked out, and the cdf is the following:

\(cdf: 0 , x<0f(x) = ((x^2)/4) , 0 <= x <= 21 , 2<= x\)

To use the cdf to obtain the following.P(X ≤ 1)

So, the probability distribution function is the derivative of the cumulative distribution function.

∴ f(x) = d/dx(F(x))

Also, from the cdf, we know that:

\(f(x) = 0 when x < 0.f(x) = ((x^2)/4) when 0 ≤ x ≤ 2.\)

f(x) = 1 when x ≥ 2.

Using the above conditions, we have to calculate the following:

(a) P(X ≤ 1)

Here, P(X ≤ 1) = F(1).

When\(0 ≤ x ≤ 2, F(x) = ∫[0,x] f(t)dt=∫[0,x] (t^2/4)dt=[t^3/12]0x=(x^3/12)\)

Thus, for\(0 ≤ x ≤ 2, F(x) = (x^3/12).\)

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U is a subspace of R3.  A basis for U is  {(1, -2, 3)}  and dim(U) = 1.

a) To show that U is a subspace of R3, we must verify the three conditions:

1. U is non-empty, since the vector (0,0,0) ∈ U, since 0 + 2(0) - 3(0) = 0.
2. U is closed under addition, since for any two vectors (x1, y1, z1) and (x2, y2, z2) ∈ U, their sum (x1+x2, y1+y2, z1+z2) also satisfies the equation x1+x2 + 2(y1+y2) - 3(z1+z2) = 0, so it is also in U.
3. U is closed under scalar multiplication, since for any scalar c and any vector (x, y, z) ∈ U, the vector c(x,y,z) = (cx, cy, cz) also satisfies the equation cx + 2cy - 3cz = 0, so it is also in U.

Therefore, U is a subspace of R3.

b) To find a basis for U, we must find a linearly independent set of vectors which span U. One such set is the vector (1, -2, 3), since it satisfies the equation x + 2y - 3z = 0. Therefore, {(1, -2, 3)} is a basis for U.

c) The dimension of U is the number of vectors in its basis, which is 1. Therefore, dim(U) = 1.

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Congruent triangles are also frequently employed in architectural designs, carpet patterns, stepping stone patterns, and geometric art.

The following are the two most typical instances of this: Equilateral triangles are used to make truss bridges, which are built on both sides.

Congruence :

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved. A term used to describe an object and its mirror counterpart is congruence. If two things or shapes superimpose on one another, they are said to be congruent. They are identical in terms of size and shape. Line segments having the same length and angles with the same measure are congruent in the context of geometric figures.

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Answer:

the area of a trapezoid is equal to half the product of the height and the sum of the two bases. Area = ½ x (Sum of parallel sides) x (perpendicular distance between the parallel sides).

Answer:

(x , y) = (1 , -2)

Step-by-step explanation:

\( \binom{x \: + \: 2y \: = \: 2x \: - \: 5}{x \: - \: y \: = \: 3} \)

\(3 \: + \: y \: + \: 2y \: = \: 2(3 \: + \: y) \: - \: 5\)

\(y \: = \: - 2\)

Substitute the given value of y into "x + 3 + y".

\(x \: = \: 3 \: + \: ( - 2)\)

\(x \: = \: 1\)

(x , y) = (1 , -2)

:DDD

A coefficient of determination of 0.81 suggests a  strong and significant relationship between sugar level and protein level in the sample of bulls.

The coefficient of determination R² is described as a statistical measure that represents the proportion of the variance in the dependent variable (protein level) that can be explained by the independent variable (sugar level).

In the above scenario, the coefficient of determination between the sugar level and protein level in the sample of bulls is 0.81.

An R²  value of 0.81 is an indication that an estimated  81% of the variance in the protein level can be explained by the sugar level. This means that there is a strong positive relationship between the sugar level and protein level in the bulls.

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The given system of equations to have a Unique solution, the value of k must be any real number except 1 (k ≠ 1).

The value of k for which the given system of equations has a unique solution, we can use the concept of determinants. The system of equations is as follows:

kx + 2y = 3   -- (1)

3x + 6y = 10  -- (2)

To have a unique solution, the determinant of the coefficients of x and y must not be zero.

The determinant of the coefficient matrix for the system is:

D = | k   2 |

       | 3   6 |

By calculating the determinant, we have:

D = (k * 6) - (2 * 3)

D = 6k - 6

For the system to have a unique solution, the determinant D must not equal zero.

6k - 6 ≠ 0

Simplifying the inequality:

6k ≠ 6

Dividing both sides by 6:

k ≠ 1

Therefore, for the given system of equations to have a unique solution, the value of k must be any real number except 1 (k ≠ 1).

In other words, if k is not equal to 1, the system of equations will have a unique solution. If k is equal to 1, the system will either have infinitely many solutions or no solution.

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To prove that the two triangles are similar, we can use the Angle-Angle (AA) similarity theorem, which states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

In this case, we have angle MCD in the smaller triangle and angle MDC in the larger triangle, which are congruent because they are vertical angles. We also have angle CMD in the smaller triangle and angle CDM in the larger triangle, which is congruent because they are both right angles. Therefore, by the AA similarity theorem, the two triangles are similar.

To find the length x, we can use the fact that the corresponding sides of similar triangles are proportional. Let's use the ratio of corresponding sides CM and DC in the smaller triangle to MC and CD in the larger triangle:

CM/DC = MC/CD

Substituting the given values, we get:

x/120 = tan 49°/tan 41°

Solving for x, we get:

x = 210 yd * tan 49°/(tan 49° + tan 41°) ≈ 124.8 yd

Therefore, the length x is approximately 124.8 yards.

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Answer:

33

Step-by-step explanation:

Set up equation:

\(15(1+22\%)^4=15*1.22^4 = 33.23\)

round to whole number 33

Answer:

(4, -2)

Step-by-step explanation:

When rotating a point 180° about the origin, the coordinates of the image are the negatives of the coordinates of the preimage.

In most cases the product of a monomial and binomial is a binomial.

A monomial has one term, a binomial has two, a trinomial has three, and a polynomial contains one or more terms.

A monomial is a single-term algebraic expression that can also include several variables and a higher degree.

The algebraic statement with only two terms is known as a binomial expression. It is a polynomial with two terms. It is also known as the sum or difference of two or more monomials. It is the most basic form of a polynomial.

A binomial is always the product of a monomial and a binomial. For instance, multiply 5x by the binomial (5x+4). Then we have. 5x(5x+4)=25x2+20x. (By using distributive law)

A trinomial is the product of two binomials.

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The probability that a srs of 20 students will spend an average of between 600 and 700 dollars is 0.92081.

We need to find the probability that a simple random sample of 20 students will spend an average of between 600 and 700 dollars.

To solve this problem, we will use the central limit theorem, which states that the sampling distribution of the sample means will be approximately normally distributed with a mean of μ and a standard deviation of σ/√(n), where n is the sample size.

Thus, the mean of the sampling distribution is μ = 650 and the standard deviation is σ/sqrt(n) = 120/√(20) = 26.83.

We need to find the probability that the sample mean falls between 600 and 700 dollars. Let x be the sample mean. Then:

Z1 = (600 - μ) / (σ / √(n)) = (600 - 650) / (120 / √t(20)) = -1.77

Z2 = (700 - μ) / (σ / √(n)) = (700 - 650) / (120 / √(20)) = 1.77

Using a standard normal distribution table or calculator, we can find the area under the standard normal distribution curve between these two Z-scores as:

P(-1.77 < Z < 1.77) = 0.9208

Therefore, the probability that a simple random sample of 20 students will spend an average of between 600 and 700 dollars is 0.9208, or approximately 0.92081 when rounded to five decimal places.

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The linear function rule that models the total cost y​ for any number of sweatshirts x would be: y = 9.50x

What is Algebraic expression ?

An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. It may contain one or more terms, with each term separated by a plus or minus sign. Algebraic expressions are used in algebra to represent mathematical relationships and formulas.

To write a linear function rule that models the total cost y​ (in dollars) for any number of sweatshirts x, we can use the equation of a line which is given as:

y = mx + b

where m is the slope of the line and b is the y-intercept.

In this case, the slope represents the cost per sweatshirt, which is $7.00, and the y-intercept represents the fixed cost, which is the shipping charge of $2.50. Therefore, the linear function rule that models the total cost y​ for any number of sweatshirts x can be written as:

y = 7x + 2.50

If the shipping charge applied to each sweatshirt, the linear function rule would change. In this case, the cost per sweatshirt would be the sum of the base cost of $7.00 and the shipping charge of $2.50, which is $9.50. Therefore, the linear function rule that models the total cost y​ for any number of sweatshirts x would be: y = 9.50x

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Let's evaluate the statements:

Supplementary angles: that means the sum of ∠K and ∠J is 180°.

Adjacent angles: that means that ∠K and ∠J common side and a common vertex.

So, let's observe the angles:

Given:

Linear pairs of angles are those two adjacent angles whose sum is 180°.

Answer: ∠K and ∠J are linear pairs.

Answer:

Step-by-step explanation:

48 :D

4x6=24

24/.5=48

The equation that represents the total surface area, in square inches, of the terrarium is D. 1/2 (6)(4)+ (5X10)+2(6X10)=122

Suppose we got a triangle. Now, strech it up so as to make a stack of triangles up above another. This new 3d object is called a triangular prism.

Usually, when we talk about triangular prism, we talk about the triangular prism, whose stack goes straight up, thus, we talk about a right triangular prism.

Given that the parameters are;

Height = 4 in

Base = 6 in

Length = 10 in

Raj buys a terrarium that is in the shape of a triangular prism. he knows that every triangular prism is made up of two triangular sides and three rectangular sides.

Area of the triangular prism;

1/2 (6)(4)+ (5X10)+2(6X10)=122

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Answer:

$1.20

Step-by-step explanation:

$0.90=75%. divide it by 3. =$0.30. do 4 times $0.30. $1.20.

Answer:

75% of what is 0.90

0.75x = 0.90

x = 0.90/0.75

x = 1.20 <== restaurant pays $ 1.20 wholesale

Answer:

3.50 cups

Step-by-step explanation:

6-2.25=4.75

4.75-1.25=3.50

Answer: C) Multiply the number of solid and clear beads by 2.

D) Divide the number of solid and clear beads by 4.

E) Multiply the number of solid and clear beads by 18.

Step-by-step explanation:

Multiplication and Division are the two arithmetic operations that are used to get an equivalent ratio or fraction.

So, the operations that will give an equivalent ratio are Multiplication and Division.

So that correct options are

C) Multiply the number of solid and clear beads by 2.

D) Divide the number of solid and clear beads by 4.

E) Multiply the number of solid and clear beads by 18.